[{"data":1,"prerenderedAt":100039},["ShallowReactive",2],{"sidebar-courses-with-stats":3,"wiki-zaklady-matematicke-ekonomie":1626,"course-stats-imek":1953,"course-topics-imek":1957,"backlinks-zaklady-matematicke-ekonomie":100025,"related-zaklady-matematicke-ekonomie":100038},{"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":1952},{"id":1628,"title":757,"body":1629,"course":1128,"courses":659,"created":1129,"description":1938,"extension":661,"meta":1939,"navigation":664,"path":1940,"seo":1941,"sources":1942,"stem":1943,"tags":1944,"type":1950,"updated":677,"__hash__":1951},"topics\u002Ftopics\u002Fzaklady-matematicke-ekonomie.md",{"type":9,"value":1630,"toc":1930},[1631,1634,1644,1653,1657,1667,1671,1707,1711,1767,1770,1831,1835,1868,1872,1896,1900],[12,1632,757],{"id":1633},"základy-matematické-ekonomie",[724,1635,1636,1637,1643],{},"Úvodní pojmy a princip modelování v ",[207,1638,1642],{"className":1639,"dataFsResolvedFilePath":1640,"href":1641},[210],"courses\u002Fimek.md","\u002Fwiki\u002Fimek","matematické ekonomii",". Slouží jako vstupní bod pro celý kurz — bez těchto pojmů nedávají další kapitoly smysl.",[724,1645,1646],{},[1647,1648],"img",{"alt":1649,"className":1650,"src":1652},"imek-model-promenne",[210,1651],"wikilink-broken","\u002Fwiki-assets\u002Fimek-model-promenne.jpeg",[115,1654,1656],{"id":1655},"co-je-matematická-ekonomie","Co je matematická ekonomie",[724,1658,1659,1662,1663,1666],{},[38,1660,1661],{},"Vědní disciplína",", která ekonomické vztahy vyjadřuje ",[38,1664,1665],{},"exaktními (matematickými) prostředky"," a provádí jejich analýzu. Cílem není jen popis, ale i predikce a optimalizace.",[115,1668,1670],{"id":1669},"klíčové-pojmy","Klíčové pojmy",[120,1672,1673,1679,1685,1691,1701],{},[123,1674,1675,1678],{},[38,1676,1677],{},"Model"," — zjednodušený obraz reálné situace nebo jevu. Vždy jde o redukci skutečnosti, ne její kopii.",[123,1680,1681,1684],{},[38,1682,1683],{},"Endogenní proměnné"," — zahrnuté do modelu, mohou se měnit (vysvětlované).",[123,1686,1687,1690],{},[38,1688,1689],{},"Exogenní proměnné"," — nejsou v modelu zahrnuté (potenciálně by mohly), berou se jako dané.",[123,1692,1693,1696,1697,1700],{},[38,1694,1695],{},"Ceteris paribus"," — ",[614,1698,1699],{},"za jinak stejných podmínek",". Sledujeme změnu jedné proměnné, ostatní fixní.",[123,1702,1703,1706],{},[38,1704,1705],{},"Komparativní statika"," — odezva endogenních proměnných na změnu některé exogenní.",[115,1708,1710],{"id":1709},"ilustrace-funkce-poptávky","Ilustrace — funkce poptávky",[724,1712,1713,1766],{},[883,1714,1716],{"className":1715},[886],[888,1717,1718],{"xmlns":890},[892,1719,1720,1763],{},[895,1721,1722,1725,1729,1732,1736,1739,1743,1746,1748,1751,1753,1755,1757,1760],{},[898,1723,1724],{},"Q",[1726,1727,1728],"mo",{},"=",[898,1730,1731],{},"D",[1726,1733,1735],{"stretchy":1734},"false","(",[898,1737,1738],{},"P",[1726,1740,1742],{"separator":1741},"true",",",[898,1744,1745],{},"Y",[1726,1747,1742],{"separator":1741},[898,1749,1750],{},"N",[1726,1752,1742],{"separator":1741},[898,1754,900],{},[1726,1756,1742],{"separator":1741},[1726,1758,1759],{},"…",[1726,1761,1762],{"stretchy":1734},")",[902,1764,1765],{"encoding":904},"Q = D(P, Y, N, U, \\ldots)"," — plná (vícefaktorová) funkce poptávky.",[724,1768,1769],{},"Zjednodušení:",[120,1771,1772,1802],{},[123,1773,1774,1777,1778],{},[38,1775,1776],{},"Jednofaktorový model:"," ",[883,1779,1781],{"className":1780},[886],[888,1782,1783],{"xmlns":890},[892,1784,1785,1799],{},[895,1786,1787,1789,1791,1793,1795,1797],{},[898,1788,1724],{},[1726,1790,1728],{},[898,1792,1731],{},[1726,1794,1735],{"stretchy":1734},[898,1796,1738],{},[1726,1798,1762],{"stretchy":1734},[902,1800,1801],{"encoding":904},"Q = D(P)",[123,1803,1804,1777,1807],{},[38,1805,1806],{},"Inverzní zápis:",[883,1808,1810],{"className":1809},[886],[888,1811,1812],{"xmlns":890},[892,1813,1814,1828],{},[895,1815,1816,1818,1820,1822,1824,1826],{},[898,1817,1738],{},[1726,1819,1728],{},[898,1821,1731],{},[1726,1823,1735],{"stretchy":1734},[898,1825,1724],{},[1726,1827,1762],{"stretchy":1734},[902,1829,1830],{"encoding":904},"P = D(Q)",[115,1832,1834],{"id":1833},"principy-řešení-ekonomických-úloh","Principy řešení ekonomických úloh",[152,1836,1837,1848],{},[123,1838,1839,1842,1843,1847],{},[38,1840,1841],{},"Princip rovnováhy"," — hledáme stav, kdy se protichůdné síly vyrovnají (např. tržní rovnováha, viz ",[207,1844,1846],{"className":1845,"dataFsResolvedFilePath":800,"href":801},[210],"poptavka-nabidka",").",[123,1849,1850,1853,1854,1857,1858,1862,1863,1867],{},[38,1851,1852],{},"Princip optimalizace"," — hledáme extrém účelové funkce, případně vázaný omezujícími podmínkami (viz ",[207,1855,1145],{"className":1856,"dataFsResolvedFilePath":764,"href":765},[210]," pro 1D, ",[207,1859,1861],{"className":1860,"dataFsResolvedFilePath":782,"href":783},[210],"funkce-vice-promennych"," pro 2D, ",[207,1864,1866],{"className":1865,"dataFsResolvedFilePath":791,"href":792},[210],"lagrangeova-metoda"," pro vázané extrémy).",[115,1869,1871],{"id":1870},"konvence-z-přednášek","Konvence z přednášek",[120,1873,1874,1882,1889],{},[123,1875,1876,1877,1881],{},"Symbol ",[1878,1879,1880],"code",{},"≈"," pro přibližné rovnosti (typicky linearizace přes diferenciál).",[123,1883,1884,1885,1888],{},"Numerické výsledky ",[38,1886,1887],{},"na 3 desetinná místa",".",[123,1890,1891,1892,1895],{},"Termín ",[614,1893,1894],{},"jednotková změna"," má standardní význam (změna o 1).",[115,1897,1899],{"id":1898},"navigace","Navigace",[120,1901,1902,1908,1917],{},[123,1903,1904,1907],{},[38,1905,1906],{},"Předchozí:"," —",[123,1909,1910,1777,1913],{},[38,1911,1912],{},"Navazující:",[207,1914,1916],{"className":1915,"dataFsResolvedFilePath":764,"href":765},[210],"Derivace a diferenciál",[123,1918,1919,1777,1922,1343,1926],{},[38,1920,1921],{},"Souvislosti:",[207,1923,1925],{"className":1924,"dataFsResolvedFilePath":745,"href":746},[210],"Souhrn KS 1. blok",[207,1927,1929],{"className":1928,"dataFsResolvedFilePath":1640,"href":1641},[210],"kurz ImeK",{"title":641,"searchDepth":642,"depth":642,"links":1931},[1932,1933,1934,1935,1936,1937],{"id":1655,"depth":642,"text":1656},{"id":1669,"depth":642,"text":1670},{"id":1709,"depth":642,"text":1710},{"id":1833,"depth":642,"text":1834},{"id":1870,"depth":642,"text":1871},{"id":1898,"depth":642,"text":1899},"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":1938},[1135],"topics\u002Fzaklady-matematicke-ekonomie",[1128,1945,1946,1947,1948,1949],"model","endogenni","exogenni","ceteris-paribus","komparativni-statika","topic","UZ1xD3l_gK41y8KlCBmpjprMOjIWmHZR8WZt-takTSI","topics",{"zapisku":1625,"topics":1954,"summaries":1955,"outputs":1956},15,5,1,[1958,3850,9553,11109,11981,16261,17867,27746,36740,50806,55098,74442,86554,95513,95740],{"id":1959,"title":1960,"body":1961,"course":1128,"courses":659,"created":1129,"description":3839,"extension":661,"meta":3840,"navigation":664,"path":3841,"seo":3842,"sources":3843,"stem":3844,"tags":3845,"type":1950,"updated":677,"__hash__":3849},"topics\u002Ftopics\u002Fderivace.md","Derivace, diferenciál a extrémy funkcí jedné proměnné",{"type":9,"value":1962,"toc":3822},[1963,1966,1985,1989,2068,2071,2202,2356,2359,2442,2446,2507,2557,2564,2568,2704,2754,2758,2801,2870,2941,2949,2953,2992,3064,3068,3149,3198,3242,3246,3250,3320,3324,3374,3453,3460,3463,3516,3786,3788],[12,1964,1960],{"id":1965},"derivace-diferenciál-a-extrémy-funkcí-jedné-proměnné",[724,1967,1968,1969,1973,1974,1977,1978,1981,1982,1888],{},"Matematický aparát kurzu ",[207,1970,1972],{"className":1971,"dataFsResolvedFilePath":1640,"href":1641},[210],"ImeK",". Bez derivace se neobejdou ",[38,1975,1976],{},"mezní veličiny"," (mezní náklady, mezní příjem, mezní užitečnost), bez extrémů se neobejde ",[38,1979,1980],{},"maximalizace zisku"," ani ",[38,1983,1984],{},"minimalizace nákladů",[115,1986,1988],{"id":1987},"funkce-a-polynomy","Funkce a polynomy",[724,1990,1991,1992,2019,2020,2033,2034,2047,2048,1888],{},"Funkce jedné proměnné ",[883,1993,1995],{"className":1994},[886],[888,1996,1997],{"xmlns":890},[892,1998,1999,2016],{},[895,2000,2001,2004,2006,2009,2011,2014],{},[898,2002,2003],{},"y",[1726,2005,1728],{},[898,2007,2008],{},"f",[1726,2010,1735],{"stretchy":1734},[898,2012,2013],{},"x",[1726,2015,1762],{"stretchy":1734},[902,2017,2018],{"encoding":904},"y = f(x)"," — předpis závislosti ",[883,2021,2023],{"className":2022},[886],[888,2024,2025],{"xmlns":890},[892,2026,2027,2031],{},[895,2028,2029],{},[898,2030,2013],{},[902,2032,2013],{"encoding":904}," (nezávislá) → ",[883,2035,2037],{"className":2036},[886],[888,2038,2039],{"xmlns":890},[892,2040,2041,2045],{},[895,2042,2043],{},[898,2044,2003],{},[902,2046,2003],{"encoding":904}," (závislá). Hodnota v bodě: ",[883,2049,2051],{"className":2050},[886],[888,2052,2053],{"xmlns":890},[892,2054,2055,2065],{},[895,2056,2057,2059,2061,2063],{},[898,2058,2008],{},[1726,2060,1735],{"stretchy":1734},[898,2062,207],{},[1726,2064,1762],{"stretchy":1734},[902,2066,2067],{"encoding":904},"f(a)",[724,2069,2070],{},"Polynomy:",[120,2072,2073,2106,2150],{},[123,2074,2075],{},[152,2076,2077],{},[123,2078,2079,2080],{},"stupně: ",[883,2081,2083],{"className":2082},[886],[888,2084,2085],{"xmlns":890},[892,2086,2087,2103],{},[895,2088,2089,2091,2093,2095,2097,2100],{},[898,2090,2003],{},[1726,2092,1728],{},[898,2094,207],{},[898,2096,2013],{},[1726,2098,2099],{},"+",[898,2101,2102],{},"b",[902,2104,2105],{"encoding":904},"y = ax + b",[123,2107,2108],{},[152,2109,2110],{"start":642},[123,2111,2079,2112],{},[883,2113,2115],{"className":2114},[886],[888,2116,2117],{"xmlns":890},[892,2118,2119,2147],{},[895,2120,2121,2123,2125,2127,2136,2138,2140,2142,2144],{},[898,2122,2003],{},[1726,2124,1728],{},[898,2126,207],{},[2128,2129,2130,2132],"msup",{},[898,2131,2013],{},[2133,2134,2135],"mn",{},"2",[1726,2137,2099],{},[898,2139,2102],{},[898,2141,2013],{},[1726,2143,2099],{},[898,2145,2146],{},"c",[902,2148,2149],{"encoding":904},"y = ax^2 + bx + c",[123,2151,2152],{},[152,2153,2154],{"start":649},[123,2155,2079,2156],{},[883,2157,2159],{"className":2158},[886],[888,2160,2161],{"xmlns":890},[892,2162,2163,2199],{},[895,2164,2165,2167,2169,2171,2178,2180,2182,2188,2190,2192,2194,2196],{},[898,2166,2003],{},[1726,2168,1728],{},[898,2170,207],{},[2128,2172,2173,2175],{},[898,2174,2013],{},[2133,2176,2177],{},"3",[1726,2179,2099],{},[898,2181,2102],{},[2128,2183,2184,2186],{},[898,2185,2013],{},[2133,2187,2135],{},[1726,2189,2099],{},[898,2191,2146],{},[898,2193,2013],{},[1726,2195,2099],{},[898,2197,2198],{},"d",[902,2200,2201],{"encoding":904},"y = ax^3 + bx^2 + cx + d",[724,2203,2204,1777,2207,2264,2265,2305,2306,1888],{},[38,2205,2206],{},"Příklad rozkladu:",[883,2208,2210],{"className":2209},[886],[888,2211,2212],{"xmlns":890},[892,2213,2214,2261],{},[895,2215,2216,2218,2220,2226,2229,2232,2234,2236,2239,2241,2243,2245,2247,2249,2251,2253,2255,2257,2259],{},[898,2217,2003],{},[1726,2219,1728],{},[2128,2221,2222,2224],{},[898,2223,2013],{},[2133,2225,2135],{},[1726,2227,2228],{},"−",[2133,2230,2231],{},"5",[898,2233,2013],{},[1726,2235,2099],{},[2133,2237,2238],{},"6",[1726,2240,1728],{},[1726,2242,1735],{"stretchy":1734},[898,2244,2013],{},[1726,2246,2228],{},[2133,2248,2135],{},[1726,2250,1762],{"stretchy":1734},[1726,2252,1735],{"stretchy":1734},[898,2254,2013],{},[1726,2256,2228],{},[2133,2258,2177],{},[1726,2260,1762],{"stretchy":1734},[902,2262,2263],{"encoding":904},"y = x^2 - 5x + 6 = (x-2)(x-3)",", kořeny ",[883,2266,2268],{"className":2267},[886],[888,2269,2270],{"xmlns":890},[892,2271,2272,2302],{},[895,2273,2274,2282,2284,2286,2288,2292,2298,2300],{},[2275,2276,2277,2279],"msub",{},[898,2278,2013],{},[2133,2280,2281],{},"1",[1726,2283,1728],{},[2133,2285,2135],{},[1726,2287,1742],{"separator":1741},[2289,2290,2291],"mtext",{}," ",[2275,2293,2294,2296],{},[898,2295,2013],{},[2133,2297,2135],{},[1726,2299,1728],{},[2133,2301,2177],{},[902,2303,2304],{"encoding":904},"x_1 = 2,\\ x_2 = 3",". Vrcholový tvar ",[883,2307,2309],{"className":2308},[886],[888,2310,2311],{"xmlns":890},[892,2312,2313,2353],{},[895,2314,2315,2317,2319,2321,2323,2325,2336,2342,2344],{},[898,2316,2003],{},[1726,2318,1728],{},[1726,2320,1735],{"stretchy":1734},[898,2322,2013],{},[1726,2324,2228],{},[2326,2327,2329],"mstyle",{"scriptlevel":2328,"displaystyle":1734},"0",[2330,2331,2332,2334],"mfrac",{},[2133,2333,2231],{},[2133,2335,2135],{},[2128,2337,2338,2340],{},[1726,2339,1762],{"stretchy":1734},[2133,2341,2135],{},[1726,2343,2228],{},[2326,2345,2346],{"scriptlevel":2328,"displaystyle":1734},[2330,2347,2348,2350],{},[2133,2349,2281],{},[2133,2351,2352],{},"4",[902,2354,2355],{"encoding":904},"y = (x - \\tfrac{5}{2})^2 - \\tfrac{1}{4}",[115,2357,2358],{"id":1145},"Derivace",[724,2360,2361,2362,1348,2389,2417,2418,1888],{},"Označení ",[883,2363,2365],{"className":2364},[886],[888,2366,2367],{"xmlns":890},[892,2368,2369,2386],{},[895,2370,2371,2380,2382,2384],{},[2128,2372,2373,2375],{},[898,2374,2008],{},[1726,2376,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},"normal","0em","′",[1726,2381,1735],{"stretchy":1734},[898,2383,2013],{},[1726,2385,1762],{"stretchy":1734},[902,2387,2388],{"encoding":904},"f'(x)",[883,2390,2392],{"className":2391},[886],[888,2393,2394],{"xmlns":890},[892,2395,2396,2414],{},[895,2397,2398],{},[2326,2399,2400],{"scriptlevel":2328,"displaystyle":1741},[2330,2401,2402,2408],{},[895,2403,2404,2406],{},[898,2405,2198],{},[898,2407,2003],{},[895,2409,2410,2412],{},[898,2411,2198],{},[898,2413,2013],{},[902,2415,2416],{"encoding":904},"\\dfrac{dy}{dx}",". Hodnota v bodě: ",[883,2419,2421],{"className":2420},[886],[888,2422,2423],{"xmlns":890},[892,2424,2425,2439],{},[895,2426,2427,2433,2435,2437],{},[2128,2428,2429,2431],{},[898,2430,2008],{},[1726,2432,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,2434,1735],{"stretchy":1734},[898,2436,207],{},[1726,2438,1762],{"stretchy":1734},[902,2440,2441],{"encoding":904},"f'(a)",[198,2443,2445],{"id":2444},"geometrická-interpretace","Geometrická interpretace",[724,2447,2448,2471,2472,2475,2476,2506],{},[883,2449,2451],{"className":2450},[886],[888,2452,2453],{"xmlns":890},[892,2454,2455,2469],{},[895,2456,2457,2463,2465,2467],{},[2128,2458,2459,2461],{},[898,2460,2008],{},[1726,2462,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,2464,1735],{"stretchy":1734},[898,2466,207],{},[1726,2468,1762],{"stretchy":1734},[902,2470,2441],{"encoding":904}," = ",[38,2473,2474],{},"sklon tečny"," ke grafu funkce v bodě ",[883,2477,2479],{"className":2478},[886],[888,2480,2481],{"xmlns":890},[892,2482,2483,2503],{},[895,2484,2485,2488,2490,2492,2494,2496,2498,2500],{},[1726,2486,2487],{"stretchy":1734},"[",[898,2489,207],{},[1726,2491,1742],{"separator":1741},[898,2493,2008],{},[1726,2495,1735],{"stretchy":1734},[898,2497,207],{},[1726,2499,1762],{"stretchy":1734},[1726,2501,2502],{"stretchy":1734},"]",[902,2504,2505],{"encoding":904},"[a, f(a)]",". Rovnice tečny:",[724,2508,2509],{},[883,2510,2512],{"className":2511},[886],[888,2513,2514],{"xmlns":890},[892,2515,2516,2554],{},[895,2517,2518,2520,2522,2524,2526,2528,2530,2532,2538,2540,2542,2544,2546,2548,2550,2552],{},[898,2519,2003],{},[1726,2521,2228],{},[898,2523,2008],{},[1726,2525,1735],{"stretchy":1734},[898,2527,207],{},[1726,2529,1762],{"stretchy":1734},[1726,2531,1728],{},[2128,2533,2534,2536],{},[898,2535,2008],{},[1726,2537,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,2539,1735],{"stretchy":1734},[898,2541,207],{},[1726,2543,1762],{"stretchy":1734},[1726,2545,1735],{"stretchy":1734},[898,2547,2013],{},[1726,2549,2228],{},[898,2551,207],{},[1726,2553,1762],{"stretchy":1734},[902,2555,2556],{"encoding":904},"y - f(a) = f'(a)(x - a)",[724,2558,2559],{},[1647,2560],{"alt":2561,"className":2562,"src":2563},"imek-derivace-tecna",[210,1651],"\u002Fwiki-assets\u002Fimek-derivace-tecna.jpeg",[198,2565,2567],{"id":2566},"inženýrská-interpretace","Inženýrská interpretace",[724,2569,2570,2471,2593,1777,2596,2609,2610,2623,2624,2642,2643,2656,2657,2670,2671,2684,2685,2703],{},[883,2571,2573],{"className":2572},[886],[888,2574,2575],{"xmlns":890},[892,2576,2577,2591],{},[895,2578,2579,2585,2587,2589],{},[2128,2580,2581,2583],{},[898,2582,2008],{},[1726,2584,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,2586,1735],{"stretchy":1734},[898,2588,207],{},[1726,2590,1762],{"stretchy":1734},[902,2592,2441],{"encoding":904},[38,2594,2595],{},"rychlost změny",[883,2597,2599],{"className":2598},[886],[888,2600,2601],{"xmlns":890},[892,2602,2603,2607],{},[895,2604,2605],{},[898,2606,2003],{},[902,2608,2003],{"encoding":904}," vzhledem k ",[883,2611,2613],{"className":2612},[886],[888,2614,2615],{"xmlns":890},[892,2616,2617,2621],{},[895,2618,2619],{},[898,2620,2013],{},[902,2622,2013],{"encoding":904}," v bodě ",[883,2625,2627],{"className":2626},[886],[888,2628,2629],{"xmlns":890},[892,2630,2631,2639],{},[895,2632,2633,2635,2637],{},[898,2634,2013],{},[1726,2636,1728],{},[898,2638,207],{},[902,2640,2641],{"encoding":904},"x = a","; přibližná změna ",[883,2644,2646],{"className":2645},[886],[888,2647,2648],{"xmlns":890},[892,2649,2650,2654],{},[895,2651,2652],{},[898,2653,2003],{},[902,2655,2003],{"encoding":904}," při změně ",[883,2658,2660],{"className":2659},[886],[888,2661,2662],{"xmlns":890},[892,2663,2664,2668],{},[895,2665,2666],{},[898,2667,2013],{},[902,2669,2013],{"encoding":904}," z ",[883,2672,2674],{"className":2673},[886],[888,2675,2676],{"xmlns":890},[892,2677,2678,2682],{},[895,2679,2680],{},[898,2681,207],{},[902,2683,207],{"encoding":904}," na ",[883,2686,2688],{"className":2687},[886],[888,2689,2690],{"xmlns":890},[892,2691,2692,2700],{},[895,2693,2694,2696,2698],{},[898,2695,207],{},[1726,2697,2099],{},[2133,2699,2281],{},[902,2701,2702],{"encoding":904},"a+1",":",[724,2705,2706],{},[883,2707,2709],{"className":2708},[886],[888,2710,2711],{"xmlns":890},[892,2712,2713,2751],{},[895,2714,2715,2717,2719,2721,2723,2725,2727,2729,2731,2733,2735,2737,2739,2745,2747,2749],{},[898,2716,2008],{},[1726,2718,1735],{"stretchy":1734},[898,2720,207],{},[1726,2722,2099],{},[2133,2724,2281],{},[1726,2726,1762],{"stretchy":1734},[1726,2728,1880],{},[898,2730,2008],{},[1726,2732,1735],{"stretchy":1734},[898,2734,207],{},[1726,2736,1762],{"stretchy":1734},[1726,2738,2099],{},[2128,2740,2741,2743],{},[898,2742,2008],{},[1726,2744,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,2746,1735],{"stretchy":1734},[898,2748,207],{},[1726,2750,1762],{"stretchy":1734},[902,2752,2753],{"encoding":904},"f(a+1) \\approx f(a) + f'(a)",[198,2755,2757],{"id":2756},"příklad-mezní-náklady","Příklad — mezní náklady",[724,2759,2760,2761,1888],{},"Celkové náklady ",[883,2762,2764],{"className":2763},[886],[888,2765,2766],{"xmlns":890},[892,2767,2768,2798],{},[895,2769,2770,2773,2776,2778,2781,2783,2785,2787,2789,2792],{},[898,2771,2772],{},"T",[898,2774,2775],{},"C",[1726,2777,1728],{},[2133,2779,2780],{},"1000",[1726,2782,2099],{},[2133,2784,2135],{},[898,2786,1724],{},[1726,2788,2099],{},[2133,2790,2791],{},"0,1",[2128,2793,2794,2796],{},[898,2795,1724],{},[2133,2797,2135],{},[902,2799,2800],{"encoding":904},"TC = 1000 + 2Q + 0{,}1 Q^2",[724,2802,2803,2804,2842,2843,1888],{},"Mezní náklady: ",[883,2805,2807],{"className":2806},[886],[888,2808,2809],{"xmlns":890},[892,2810,2811,2839],{},[895,2812,2813,2816,2818,2820,2822,2828,2830,2832,2834,2837],{},[898,2814,2815],{},"M",[898,2817,2775],{},[1726,2819,1728],{},[898,2821,2772],{},[2128,2823,2824,2826],{},[898,2825,2775],{},[1726,2827,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,2829,1728],{},[2133,2831,2135],{},[1726,2833,2099],{},[2133,2835,2836],{},"0,2",[898,2838,1724],{},[902,2840,2841],{"encoding":904},"MC = TC' = 2 + 0{,}2 Q",", takže ",[883,2844,2846],{"className":2845},[886],[888,2847,2848],{"xmlns":890},[892,2849,2850,2867],{},[895,2851,2852,2854,2856,2858,2861,2863,2865],{},[898,2853,2815],{},[898,2855,2775],{},[1726,2857,1735],{"stretchy":1734},[2133,2859,2860],{},"10",[1726,2862,1762],{"stretchy":1734},[1726,2864,1728],{},[2133,2866,2352],{},[902,2868,2869],{"encoding":904},"MC(10) = 4",[724,2871,2872,1777,2875,2924,2925,1777,2928,1888],{},[38,2873,2874],{},"Skutečný přírůstek:",[883,2876,2878],{"className":2877},[886],[888,2879,2880],{"xmlns":890},[892,2881,2882,2921],{},[895,2883,2884,2887,2889,2891,2893,2895,2897,2899,2902,2904,2906,2908,2910,2912,2914,2916,2918],{},[898,2885,2886],{"mathvariant":2377},"Δ",[898,2888,2772],{},[898,2890,2775],{},[1726,2892,1728],{},[898,2894,2772],{},[898,2896,2775],{},[1726,2898,1735],{"stretchy":1734},[2133,2900,2901],{},"11",[1726,2903,1762],{"stretchy":1734},[1726,2905,2228],{},[898,2907,2772],{},[898,2909,2775],{},[1726,2911,1735],{"stretchy":1734},[2133,2913,2860],{},[1726,2915,1762],{"stretchy":1734},[1726,2917,1728],{},[2133,2919,2920],{},"4,2",[902,2922,2923],{"encoding":904},"\\Delta TC = TC(11) - TC(10) = 4{,}2",". ",[38,2926,2927],{},"Přibližný (lineární):",[883,2929,2931],{"className":2930},[886],[888,2932,2933],{"xmlns":890},[892,2934,2935,2939],{},[895,2936,2937],{},[2133,2938,2352],{},[902,2940,2352],{"encoding":904},[724,2942,2943,2944,2948],{},"(Viz aplikace v ",[207,2945,2947],{"className":2946,"dataFsResolvedFilePath":827,"href":828},[210],"prijem-naklady-zisk",".)",[115,2950,2952],{"id":2951},"diferenciál","Diferenciál",[724,2954,2955],{},[883,2956,2958],{"className":2957},[886],[888,2959,2960],{"xmlns":890},[892,2961,2962,2989],{},[895,2963,2964,2966,2968,2970,2976,2978,2980,2982,2985,2987],{},[898,2965,2198],{},[898,2967,2008],{},[1726,2969,1728],{},[2128,2971,2972,2974],{},[898,2973,2008],{},[1726,2975,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,2977,1735],{"stretchy":1734},[898,2979,2013],{},[1726,2981,1762],{"stretchy":1734},[2289,2983,2984],{}," ",[898,2986,2198],{},[898,2988,2013],{},[902,2990,2991],{"encoding":904},"df = f'(x)\\, dx",[724,2993,2994,2995,3011,3012,3060,3061,1888],{},"Pro malá ",[883,2996,2998],{"className":2997},[886],[888,2999,3000],{"xmlns":890},[892,3001,3002,3008],{},[895,3003,3004,3006],{},[898,3005,2198],{},[898,3007,2013],{},[902,3009,3010],{"encoding":904},"dx"," platí: ",[883,3013,3015],{"className":3014},[886],[888,3016,3017],{"xmlns":890},[892,3018,3019,3057],{},[895,3020,3021,3023,3025,3027,3029,3031,3033,3035,3037,3039,3041,3043,3045,3047,3049,3051,3053,3055],{},[898,3022,2886],{"mathvariant":2377},[898,3024,2008],{},[1726,3026,1728],{},[898,3028,2008],{},[1726,3030,1735],{"stretchy":1734},[898,3032,2013],{},[1726,3034,2099],{},[898,3036,2198],{},[898,3038,2013],{},[1726,3040,1762],{"stretchy":1734},[1726,3042,2228],{},[898,3044,2008],{},[1726,3046,1735],{"stretchy":1734},[898,3048,2013],{},[1726,3050,1762],{"stretchy":1734},[1726,3052,1880],{},[898,3054,2198],{},[898,3056,2008],{},[902,3058,3059],{"encoding":904},"\\Delta f = f(x + dx) - f(x) \\approx df",". Diferenciál je ",[38,3062,3063],{},"lineární odhad přírůstku",[198,3065,3067],{"id":3066},"příklad","Příklad",[724,3069,3070,3101,3102,3127,3128,3148],{},[883,3071,3073],{"className":3072},[886],[888,3074,3075],{"xmlns":890},[892,3076,3077,3098],{},[895,3078,3079,3081,3083,3085,3088,3090,3092],{},[898,3080,2772],{},[898,3082,2775],{},[1726,3084,1728],{},[2133,3086,3087],{},"100",[1726,3089,2099],{},[2133,3091,2791],{},[2128,3093,3094,3096],{},[898,3095,1724],{},[2133,3097,2135],{},[902,3099,3100],{"encoding":904},"TC = 100 + 0{,}1 Q^2",", odhad změny při ",[883,3103,3105],{"className":3104},[886],[888,3106,3107],{"xmlns":890},[892,3108,3109,3124],{},[895,3110,3111,3113,3115,3118,3121],{},[898,3112,1724],{},[1726,3114,2703],{},[2133,3116,3117],{},"50",[1726,3119,3120],{},"→",[2133,3122,3123],{},"60",[902,3125,3126],{"encoding":904},"Q: 50 \\to 60"," (tj. ",[883,3129,3131],{"className":3130},[886],[888,3132,3133],{"xmlns":890},[892,3134,3135,3145],{},[895,3136,3137,3139,3141,3143],{},[898,3138,2198],{},[898,3140,1724],{},[1726,3142,1728],{},[2133,3144,2860],{},[902,3146,3147],{"encoding":904},"dQ = 10","):",[724,3150,3151],{},[883,3152,3154],{"className":3153},[886],[888,3155,3156],{"xmlns":890},[892,3157,3158,3195],{},[895,3159,3160,3162,3164,3166,3168,3170,3172,3175,3177,3179,3181,3183,3185,3187,3189,3191,3193],{},[898,3161,2198],{},[898,3163,2772],{},[898,3165,2775],{},[1726,3167,1728],{},[2133,3169,2836],{},[898,3171,1724],{},[1726,3173,3174],{},"⋅",[898,3176,2198],{},[898,3178,1724],{},[1726,3180,1728],{},[2133,3182,2836],{},[1726,3184,3174],{},[2133,3186,3117],{},[1726,3188,3174],{},[2133,3190,2860],{},[1726,3192,1728],{},[2133,3194,3087],{},[902,3196,3197],{"encoding":904},"dTC = 0{,}2 Q \\cdot dQ = 0{,}2 \\cdot 50 \\cdot 10 = 100",[724,3199,3200,3201,3224,3225,3241],{},"Přesná změna: ",[883,3202,3204],{"className":3203},[886],[888,3205,3206],{"xmlns":890},[892,3207,3208,3221],{},[895,3209,3210,3212,3214,3216,3218],{},[898,3211,2886],{"mathvariant":2377},[898,3213,2772],{},[898,3215,2775],{},[1726,3217,1728],{},[2133,3219,3220],{},"110",[902,3222,3223],{"encoding":904},"\\Delta TC = 110",". Lineární odhad mírně podstřeluje, protože ",[883,3226,3228],{"className":3227},[886],[888,3229,3230],{"xmlns":890},[892,3231,3232,3238],{},[895,3233,3234,3236],{},[898,3235,2772],{},[898,3237,2775],{},[902,3239,3240],{"encoding":904},"TC"," je konvexní.",[115,3243,3245],{"id":3244},"extrémy-funkce-jedné-proměnné","Extrémy funkce jedné proměnné",[198,3247,3249],{"id":3248},"nutná-podmínka","Nutná podmínka",[724,3251,3252,3253,2623,3273,3286,3287,3315,3316,3319],{},"Má-li ",[883,3254,3256],{"className":3255},[886],[888,3257,3258],{"xmlns":890},[892,3259,3260,3270],{},[895,3261,3262,3264,3266,3268],{},[898,3263,2008],{},[1726,3265,1735],{"stretchy":1734},[898,3267,2013],{},[1726,3269,1762],{"stretchy":1734},[902,3271,3272],{"encoding":904},"f(x)",[883,3274,3276],{"className":3275},[886],[888,3277,3278],{"xmlns":890},[892,3279,3280,3284],{},[895,3281,3282],{},[898,3283,207],{},[902,3285,207],{"encoding":904}," extrém, pak ",[883,3288,3290],{"className":3289},[886],[888,3291,3292],{"xmlns":890},[892,3293,3294,3312],{},[895,3295,3296,3302,3304,3306,3308,3310],{},[2128,3297,3298,3300],{},[898,3299,2008],{},[1726,3301,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,3303,1735],{"stretchy":1734},[898,3305,207],{},[1726,3307,1762],{"stretchy":1734},[1726,3309,1728],{},[2133,3311,2328],{},[902,3313,3314],{"encoding":904},"f'(a) = 0",". Body splňující tuto podmínku se nazývají ",[38,3317,3318],{},"stacionární"," (podezřelé) body.",[198,3321,3323],{"id":3322},"postačující-podmínka","Postačující podmínka",[724,3325,3326,3327,3340,3341,2703],{},"Pro stacionární bod ",[883,3328,3330],{"className":3329},[886],[888,3331,3332],{"xmlns":890},[892,3333,3334,3338],{},[895,3335,3336],{},[898,3337,207],{},[902,3339,207],{"encoding":904},", je-li ",[883,3342,3344],{"className":3343},[886],[888,3345,3346],{"xmlns":890},[892,3347,3348,3371],{},[895,3349,3350,3360,3362,3364,3366,3369],{},[2128,3351,3352,3354],{},[898,3353,2008],{},[895,3355,3356,3358],{},[1726,3357,2379],{"mathvariant":2377},[1726,3359,2379],{"mathvariant":2377},[1726,3361,1735],{"stretchy":1734},[898,3363,207],{},[1726,3365,1762],{"stretchy":1734},[1726,3367,3368],{"mathvariant":2377},"≠",[2133,3370,2328],{},[902,3372,3373],{"encoding":904},"f''(a) \\neq 0",[120,3375,3376,3415],{},[123,3377,3378,3411,3412],{},[883,3379,3381],{"className":3380},[886],[888,3382,3383],{"xmlns":890},[892,3384,3385,3408],{},[895,3386,3387,3397,3399,3401,3403,3406],{},[2128,3388,3389,3391],{},[898,3390,2008],{},[895,3392,3393,3395],{},[1726,3394,2379],{"mathvariant":2377},[1726,3396,2379],{"mathvariant":2377},[1726,3398,1735],{"stretchy":1734},[898,3400,207],{},[1726,3402,1762],{"stretchy":1734},[1726,3404,3405],{},">",[2133,3407,2328],{},[902,3409,3410],{"encoding":904},"f''(a) > 0"," ⇒ ",[38,3413,3414],{},"lokální minimum",[123,3416,3417,3411,3450],{},[883,3418,3420],{"className":3419},[886],[888,3421,3422],{"xmlns":890},[892,3423,3424,3447],{},[895,3425,3426,3436,3438,3440,3442,3445],{},[2128,3427,3428,3430],{},[898,3429,2008],{},[895,3431,3432,3434],{},[1726,3433,2379],{"mathvariant":2377},[1726,3435,2379],{"mathvariant":2377},[1726,3437,1735],{"stretchy":1734},[898,3439,207],{},[1726,3441,1762],{"stretchy":1734},[1726,3443,3444],{},"\u003C",[2133,3446,2328],{},[902,3448,3449],{"encoding":904},"f''(a) \u003C 0",[38,3451,3452],{},"lokální maximum",[724,3454,3455],{},[1647,3456],{"alt":3457,"className":3458,"src":3459},"imek-extremy-1d",[210,1651],"\u002Fwiki-assets\u002Fimek-extremy-1d.jpeg",[198,3461,3067],{"id":3462},"příklad-1",[724,3464,3465],{},[883,3466,3468],{"className":3467},[886],[888,3469,3470],{"xmlns":890},[892,3471,3472,3513],{},[895,3473,3474,3476,3478,3480,3482,3484,3486,3492,3494,3496,3502,3504,3507,3509,3511],{},[898,3475,2008],{},[1726,3477,1735],{"stretchy":1734},[898,3479,2013],{},[1726,3481,1762],{"stretchy":1734},[1726,3483,1728],{},[2133,3485,2135],{},[2128,3487,3488,3490],{},[898,3489,2013],{},[2133,3491,2177],{},[1726,3493,2228],{},[2133,3495,2177],{},[2128,3497,3498,3500],{},[898,3499,2013],{},[2133,3501,2135],{},[1726,3503,2228],{},[2133,3505,3506],{},"12",[898,3508,2013],{},[1726,3510,2099],{},[2133,3512,2177],{},[902,3514,3515],{"encoding":904},"f(x) = 2x^3 - 3x^2 - 12x + 3",[120,3517,3518,3629,3669,3732],{},[123,3519,3520,3592,3593],{},[883,3521,3523],{"className":3522},[886],[888,3524,3525],{"xmlns":890},[892,3526,3527,3589],{},[895,3528,3529,3535,3537,3539,3541,3543,3545,3551,3553,3555,3557,3559,3561,3563,3565,3567,3569,3571,3573,3575,3577,3579,3581,3583,3585,3587],{},[2128,3530,3531,3533],{},[898,3532,2008],{},[1726,3534,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,3536,1735],{"stretchy":1734},[898,3538,2013],{},[1726,3540,1762],{"stretchy":1734},[1726,3542,1728],{},[2133,3544,2238],{},[2128,3546,3547,3549],{},[898,3548,2013],{},[2133,3550,2135],{},[1726,3552,2228],{},[2133,3554,2238],{},[898,3556,2013],{},[1726,3558,2228],{},[2133,3560,3506],{},[1726,3562,1728],{},[2133,3564,2238],{},[1726,3566,1735],{"stretchy":1734},[898,3568,2013],{},[1726,3570,2099],{},[2133,3572,2281],{},[1726,3574,1762],{"stretchy":1734},[1726,3576,1735],{"stretchy":1734},[898,3578,2013],{},[1726,3580,2228],{},[2133,3582,2135],{},[1726,3584,1762],{"stretchy":1734},[1726,3586,1728],{},[2133,3588,2328],{},[902,3590,3591],{"encoding":904},"f'(x) = 6x^2 - 6x - 12 = 6(x+1)(x-2) = 0"," ⇒ S.B. ",[883,3594,3596],{"className":3595},[886],[888,3597,3598],{"xmlns":890},[892,3599,3600,3626],{},[895,3601,3602,3608,3610,3612,3614,3616,3622,3624],{},[2275,3603,3604,3606],{},[898,3605,2013],{},[2133,3607,2281],{},[1726,3609,1728],{},[1726,3611,2228],{},[2133,3613,2281],{},[1726,3615,1742],{"separator":1741},[2275,3617,3618,3620],{},[898,3619,2013],{},[2133,3621,2135],{},[1726,3623,1728],{},[2133,3625,2135],{},[902,3627,3628],{"encoding":904},"x_1 = -1, x_2 = 2",[123,3630,3631],{},[883,3632,3634],{"className":3633},[886],[888,3635,3636],{"xmlns":890},[892,3637,3638,3666],{},[895,3639,3640,3650,3652,3654,3656,3658,3660,3662,3664],{},[2128,3641,3642,3644],{},[898,3643,2008],{},[895,3645,3646,3648],{},[1726,3647,2379],{"mathvariant":2377},[1726,3649,2379],{"mathvariant":2377},[1726,3651,1735],{"stretchy":1734},[898,3653,2013],{},[1726,3655,1762],{"stretchy":1734},[1726,3657,1728],{},[2133,3659,3506],{},[898,3661,2013],{},[1726,3663,2228],{},[2133,3665,2238],{},[902,3667,3668],{"encoding":904},"f''(x) = 12x - 6",[123,3670,3671,3411,3712,3715,3716],{},[883,3672,3674],{"className":3673},[886],[888,3675,3676],{"xmlns":890},[892,3677,3678,3709],{},[895,3679,3680,3690,3692,3694,3696,3698,3700,3702,3705,3707],{},[2128,3681,3682,3684],{},[898,3683,2008],{},[895,3685,3686,3688],{},[1726,3687,2379],{"mathvariant":2377},[1726,3689,2379],{"mathvariant":2377},[1726,3691,1735],{"stretchy":1734},[1726,3693,2228],{},[2133,3695,2281],{},[1726,3697,1762],{"stretchy":1734},[1726,3699,1728],{},[1726,3701,2228],{},[2133,3703,3704],{},"18",[1726,3706,3444],{},[2133,3708,2328],{},[902,3710,3711],{"encoding":904},"f''(-1) = -18 \u003C 0",[38,3713,3714],{},"maximum"," v ",[883,3717,3719],{"className":3718},[886],[888,3720,3721],{"xmlns":890},[892,3722,3723,3729],{},[895,3724,3725,3727],{},[1726,3726,2228],{},[2133,3728,2281],{},[902,3730,3731],{"encoding":904},"-1",[123,3733,3734,3411,3770,3715,3773],{},[883,3735,3737],{"className":3736},[886],[888,3738,3739],{"xmlns":890},[892,3740,3741,3767],{},[895,3742,3743,3753,3755,3757,3759,3761,3763,3765],{},[2128,3744,3745,3747],{},[898,3746,2008],{},[895,3748,3749,3751],{},[1726,3750,2379],{"mathvariant":2377},[1726,3752,2379],{"mathvariant":2377},[1726,3754,1735],{"stretchy":1734},[2133,3756,2135],{},[1726,3758,1762],{"stretchy":1734},[1726,3760,1728],{},[2133,3762,3704],{},[1726,3764,3405],{},[2133,3766,2328],{},[902,3768,3769],{"encoding":904},"f''(2) = 18 > 0",[38,3771,3772],{},"minimum",[883,3774,3776],{"className":3775},[886],[888,3777,3778],{"xmlns":890},[892,3779,3780,3784],{},[895,3781,3782],{},[2133,3783,2135],{},[902,3785,2135],{"encoding":904},[115,3787,1899],{"id":1898},[120,3789,3790,3797,3804],{},[123,3791,3792,1777,3794],{},[38,3793,1906],{},[207,3795,757],{"className":3796,"dataFsResolvedFilePath":755,"href":756},[210],[123,3798,3799,1777,3801],{},[38,3800,1912],{},[207,3802,775],{"className":3803,"dataFsResolvedFilePath":773,"href":774},[210],[123,3805,3806,1777,3808,3811,3812,3816,3817,3821],{},[38,3807,1921],{},[207,3809,784],{"className":3810,"dataFsResolvedFilePath":782,"href":783},[210]," (rozšíření na 2D), ",[207,3813,3815],{"className":3814,"dataFsResolvedFilePath":827,"href":828},[210],"Příjem, náklady, zisk"," (aplikace mezních veličin), ",[207,3818,3820],{"className":3819,"dataFsResolvedFilePath":848,"href":849},[210],"Elasticita"," (procentní citlivost přes derivaci)",{"title":641,"searchDepth":642,"depth":642,"links":3823},[3824,3825,3830,3833,3838],{"id":1987,"depth":642,"text":1988},{"id":1145,"depth":642,"text":2358,"children":3826},[3827,3828,3829],{"id":2444,"depth":649,"text":2445},{"id":2566,"depth":649,"text":2567},{"id":2756,"depth":649,"text":2757},{"id":2951,"depth":642,"text":2952,"children":3831},[3832],{"id":3066,"depth":649,"text":3067},{"id":3244,"depth":642,"text":3245,"children":3834},[3835,3836,3837],{"id":3248,"depth":649,"text":3249},{"id":3322,"depth":649,"text":3323},{"id":3462,"depth":649,"text":3067},{"id":1898,"depth":642,"text":1899},"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":1960,"description":3839},[1135],"topics\u002Fderivace",[1128,1145,3846,3847,3848],"diferencial","extremy","mezni-naklady","U4vqwJqO65hVzq9khEr5sxPHpHJLXAz_kTaaHdKCCIw",{"id":3851,"title":3852,"body":3853,"course":1128,"courses":659,"created":9541,"description":641,"extension":661,"meta":9542,"navigation":664,"path":9543,"seo":9544,"sources":9545,"stem":9546,"tags":9547,"type":1950,"updated":677,"__hash__":9552},"topics\u002Ftopics\u002Felasticita.md","Elasticita poptávky a nabídky",{"type":9,"value":3854,"toc":9514},[3855,3858,3881,3885,3910,3914,3955,4046,4090,4094,4118,4125,4129,4139,4151,4155,4182,4191,4248,4254,4257,4263,4290,4296,4394,4554,4844,4848,4928,4934,4938,5036,5102,5270,5274,5352,5383,5410,5416,5448,5526,5613,5617,5680,5686,5689,5695,5809,5894,5938,5942,5988,5995,6312,6317,6341,6370,6437,6534,6538,6545,6552,6623,6743,6827,6830,6836,7162,7166,7329,7337,7473,7481,7719,7727,7730,7735,7991,7995,8169,8303,8340,8384,8387,8517,8607,8625,8629,8636,8642,8703,8706,8730,8733,8739,8742,8748,8751,8755,8793,8851,9040,9044,9116,9122,9129,9133,9139,9281,9285,9291,9327,9332,9509],[12,3856,3852],{"id":3857},"elasticita-poptávky-a-nabídky",[3859,3860,3861],"blockquote",{},[724,3862,3863,3866,3867,3869,3870,3873,3874,3877,3878,1888],{},[883,3864,3865],{},"!abstract"," TL;DR\n",[38,3868,3820],{}," 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: ",[38,3871,3872],{},"cenovou elasticitu poptávky"," (a nabídky), ",[38,3875,3876],{},"křížově-cenovou elasticitu"," a ",[38,3879,3880],{},"důchodovou elasticitu",[115,3882,3884],{"id":3883},"úvod-motivace","Úvod — motivace",[724,3886,1891,3887,3890,3891,3894,3895,3898,3899,3902,3903,3906,3907,1847],{},[614,3888,3889],{},"elasticita"," (alternativně ",[614,3892,3893],{},"pružnost",") patří ke klíčovým pojmům ekonomické teorie. Slouží ke ",[38,3896,3897],{},"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 ",[614,3900,3901],{},"cenové elasticity poptávky"," (resp. ",[614,3904,3905],{},"nabídky","). Matematickým modelem míry citlivosti je elasticita funkce (viz ",[207,3908,2358],{"className":3909,"dataFsResolvedFilePath":764,"href":765},[210],[198,3911,3913],{"id":3912},"srovnání-trh-1-vs-trh-2","Srovnání Trh 1 vs Trh 2",[724,3915,3916,3917,3935,3936,3954],{},"Uvažujme dvě různá tržní prostředí. Zboží má na obou trzích stejnou cenu ",[883,3918,3920],{"className":3919},[886],[888,3921,3922],{"xmlns":890},[892,3923,3924,3932],{},[895,3925,3926,3928,3930],{},[898,3927,1738],{},[1726,3929,1728],{},[2133,3931,2860],{},[902,3933,3934],{"encoding":904},"P=10"," a při této ceně se prodá ",[883,3937,3939],{"className":3938},[886],[888,3940,3941],{"xmlns":890},[892,3942,3943,3951],{},[895,3944,3945,3947,3949],{},[898,3946,1724],{},[1726,3948,1728],{},[2133,3950,3087],{},[902,3952,3953],{"encoding":904},"Q=100"," jednotek. Prodejce sníží cenu z 10 na 9:",[120,3956,3957,4003],{},[123,3958,3959,3962,3963,4002],{},[38,3960,3961],{},"Trh 1"," zareaguje zvýšením množství na 110 ",[883,3964,3966],{"className":3965},[886],[888,3967,3968],{"xmlns":890},[892,3969,3970,3999],{},[895,3971,3972,3975,3978,3980,3982,3985,3987,3990,3992,3994,3996],{},[2289,3973,3974],{},"  ",[1726,3976,3977],{},"⇒",[2289,3979,3974],{},[898,3981,2772],{},[898,3983,3984],{},"R",[1726,3986,1728],{},[2133,3988,3989],{},"9",[1726,3991,3174],{},[2133,3993,3220],{},[1726,3995,1728],{},[2133,3997,3998],{},"990",[902,4000,4001],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 110 = 990"," (pokles z 1000).",[123,4004,4005,4008,4009,4045],{},[38,4006,4007],{},"Trh 2"," zareaguje zvýšením množství na 120 ",[883,4010,4012],{"className":4011},[886],[888,4013,4014],{"xmlns":890},[892,4015,4016,4042],{},[895,4017,4018,4020,4022,4024,4026,4028,4030,4032,4034,4037,4039],{},[2289,4019,3974],{},[1726,4021,3977],{},[2289,4023,3974],{},[898,4025,2772],{},[898,4027,3984],{},[1726,4029,1728],{},[2133,4031,3989],{},[1726,4033,3174],{},[2133,4035,4036],{},"120",[1726,4038,1728],{},[2133,4040,4041],{},"1080",[902,4043,4044],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 120 = 1080"," (růst z 1000).",[724,4047,4048,4049,4052,4053,4056,4057,4060,4061,4064,4065,4068,4069,4085,4086,4089],{},"Závěr: snížení ceny bylo na Trhu 1 ",[38,4050,4051],{},"nerozumné",", na Trhu 2 ",[38,4054,4055],{},"rozumné",". Trh 2 je ",[38,4058,4059],{},"relativně citlivý"," na změnu ceny — říkáme, že poptávka je ",[614,4062,4063],{},"elastická"," a snížení ceny je „překompenzováno\" zvýšením poptávaného množství. Na Trhu 1 je poptávka ",[614,4066,4067],{},"neelastická"," a vyššího ",[883,4070,4072],{"className":4071},[886],[888,4073,4074],{"xmlns":890},[892,4075,4076,4082],{},[895,4077,4078,4080],{},[898,4079,2772],{},[898,4081,3984],{},[902,4083,4084],{"encoding":904},"TR"," lze naopak dosáhnout ",[614,4087,4088],{},"zvýšením"," ceny.",[198,4091,4093],{"id":4092},"hypotéza-41","Hypotéza 4.1",[3859,4095,4096],{},[724,4097,4098,4099],{},"Aby nedošlo k poklesu celkového příjmu, musí být procentní růst poptávaného množství alespoň takový, jaký je procentní pokles jeho ceny. ",[883,4100,4102],{"className":4101},[886],[888,4103,4104],{"xmlns":890},[892,4105,4106,4115],{},[895,4107,4108,4110,4113],{},[1726,4109,1735],{"stretchy":1734},[2133,4111,4112],{},"4.1",[1726,4114,1762],{"stretchy":1734},[902,4116,4117],{"encoding":904},"(4.1)",[724,4119,4120,4121,4124],{},"Rozhodující nejsou nominální změny (jsou měřeny v různých jednotkách), nýbrž ",[38,4122,4123],{},"procentní změny"," obou faktorů.",[115,4126,4128],{"id":4127},"pojem-elasticity","Pojem elasticity",[724,4130,4131,4132,4134,4135,4138],{},"Obecně ",[38,4133,3889],{}," jedné veličiny vzhledem k druhé kvantifikuje, o kolik procent se první veličina přibližně změní, když se druhá veličina změní o 1 %. Jde o ",[38,4136,4137],{},"bezrozměrnou veličinu"," — nezávislou na jednotkách, ve kterých jsou proměnné měřeny (viz čl. 1.5.1).",[3859,4140,4141],{},[724,4142,4143,4146,4147,4150],{},[883,4144,4145],{},"!info"," Intuice\nElasticitu lze číst jako ",[38,4148,4149],{},"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.",[115,4152,4154],{"id":4153},"cenová-elasticita-poptávky-jednofaktorový-model","Cenová elasticita poptávky — jednofaktorový model",[724,4156,4157,4158,4181],{},"Nechť ",[883,4159,4161],{"className":4160},[886],[888,4162,4163],{"xmlns":890},[892,4164,4165,4179],{},[895,4166,4167,4169,4171,4173,4175,4177],{},[898,4168,1724],{},[1726,4170,1728],{},[898,4172,1731],{},[1726,4174,1735],{"stretchy":1734},[898,4176,1738],{},[1726,4178,1762],{"stretchy":1734},[902,4180,1801],{"encoding":904}," je funkce poptávky (ceteris paribus). Zkoumáme podíl procentních změn",[724,4183,4184],{},[883,4185,4190],{"className":4186,"title":4188,"style":4189},[4187],"katex-error","ParseError: KaTeX parse error: \\tag works only in display equations","color:#cc0000","E^A = -\\frac{\\Delta Q\\%}{\\Delta P\\%}. \\tag{4.2}",[724,4192,4193,4194,3877,4210,4226,4227,4247],{},"Znaménko minus je korekce: změny ",[883,4195,4197],{"className":4196},[886],[888,4198,4199],{"xmlns":890},[892,4200,4201,4207],{},[895,4202,4203,4205],{},[898,4204,2886],{"mathvariant":2377},[898,4206,1724],{},[902,4208,4209],{"encoding":904},"\\Delta Q",[883,4211,4213],{"className":4212},[886],[888,4214,4215],{"xmlns":890},[892,4216,4217,4223],{},[895,4218,4219,4221],{},[898,4220,2886],{"mathvariant":2377},[898,4222,1738],{},[902,4224,4225],{"encoding":904},"\\Delta P"," mají vždy opačná znaménka, takže bez korekce by ",[883,4228,4230],{"className":4229},[886],[888,4231,4232],{"xmlns":890},[892,4233,4234,4244],{},[895,4235,4236],{},[2128,4237,4238,4241],{},[898,4239,4240],{},"E",[898,4242,4243],{},"A",[902,4245,4246],{"encoding":904},"E^A"," bylo záporné; pro pohodlí pracujeme s nezápornými hodnotami. Pro procentní změny platí",[724,4249,4250],{},[883,4251,4253],{"className":4252,"title":4188,"style":4189},[4187],"\\Delta Q\\% = \\frac{\\Delta Q}{Q}\\cdot 100, \\qquad \\Delta P\\% = \\frac{\\Delta P}{P}\\cdot 100. \\tag{4.3}",[724,4255,4256],{},"Po dosazení:",[724,4258,4259],{},[883,4260,4262],{"className":4261,"title":4188,"style":4189},[4187],"E^A = -\\frac{\\frac{\\Delta Q}{Q}}{\\frac{\\Delta P}{P}} = -\\frac{P}{Q}\\cdot \\frac{\\Delta Q}{\\Delta P}. \\tag{4.4}",[724,4264,4265,4266,4286,4287,4289],{},"Limitním přechodem ",[883,4267,4269],{"className":4268},[886],[888,4270,4271],{"xmlns":890},[892,4272,4273,4283],{},[895,4274,4275,4277,4279,4281],{},[898,4276,2886],{"mathvariant":2377},[898,4278,1738],{},[1726,4280,3120],{},[2133,4282,2328],{},[902,4284,4285],{"encoding":904},"\\Delta P \\to 0"," získáme definici ",[38,4288,3901],{}," (price elasticity of demand):",[724,4291,4292],{},[883,4293,4295],{"className":4294,"title":4188,"style":4189},[4187],"\\boxed{\\;E = E(P) = -\\frac{P}{Q}\\cdot \\frac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\frac{P}{Q}\\,Q'(P)\\;} \\tag{4.5}",[724,4297,4298,4299,4322,4323,4346,4347,4371,4372,4393],{},"kde ",[883,4300,4302],{"className":4301},[886],[888,4303,4304],{"xmlns":890},[892,4305,4306,4320],{},[895,4307,4308,4310,4312,4314,4316,4318],{},[898,4309,1724],{},[1726,4311,1728],{},[898,4313,1731],{},[1726,4315,1735],{"stretchy":1734},[898,4317,1738],{},[1726,4319,1762],{"stretchy":1734},[902,4321,1801],{"encoding":904},". Pro pevnou cenu ",[883,4324,4326],{"className":4325},[886],[888,4327,4328],{"xmlns":890},[892,4329,4330,4343],{},[895,4331,4332,4334,4336],{},[898,4333,1738],{},[1726,4335,1728],{},[2128,4337,4338,4340],{},[898,4339,1738],{},[1726,4341,4342],{},"∗",[902,4344,4345],{"encoding":904},"P = P^*"," se ",[883,4348,4350],{"className":4349},[886],[888,4351,4352],{"xmlns":890},[892,4353,4354,4368],{},[895,4355,4356,4358,4360,4366],{},[898,4357,4240],{},[1726,4359,1735],{"stretchy":1734},[2128,4361,4362,4364],{},[898,4363,1738],{},[1726,4365,4342],{},[1726,4367,1762],{"stretchy":1734},[902,4369,4370],{"encoding":904},"E(P^*)"," nazývá ",[614,4373,4374,4375],{},"elasticita poptávky při ceně ",[883,4376,4378],{"className":4377},[886],[888,4379,4380],{"xmlns":890},[892,4381,4382,4390],{},[895,4383,4384],{},[2128,4385,4386,4388],{},[898,4387,1738],{},[1726,4389,4342],{},[902,4391,4392],{"encoding":904},"P^*"," a je to vždy nezáporné číslo.",[3859,4395,4396],{},[724,4397,4398,4401,4402,4420,4421,4449,4450,4479,4480,1343,4498,1343,4516,4534,4535,4550,4551,1888],{},[883,4399,4400],{},"!warning"," Pozor na znaménko\nV (4.5) je ",[38,4403,4404,4405],{},"explicitní ",[883,4406,4408],{"className":4407},[886],[888,4409,4410],{"xmlns":890},[892,4411,4412,4418],{},[895,4413,4414,4416],{},[1726,4415,2228],{},[2133,4417,2281],{},[902,4419,3731],{"encoding":904}," právě proto, že ",[883,4422,4424],{"className":4423},[886],[888,4425,4426],{"xmlns":890},[892,4427,4428,4446],{},[895,4429,4430,4436,4438,4440,4442,4444],{},[2128,4431,4432,4434],{},[898,4433,1724],{},[1726,4435,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,4437,1735],{"stretchy":1734},[898,4439,1738],{},[1726,4441,1762],{"stretchy":1734},[1726,4443,3444],{},[2133,4445,2328],{},[902,4447,4448],{"encoding":904},"Q'(P) \u003C 0"," (poptávka klesá s cenou). Díky korekčnímu znaménku je výsledné ",[883,4451,4453],{"className":4452},[886],[888,4454,4455],{"xmlns":890},[892,4456,4457,4476],{},[895,4458,4459,4461,4463,4469,4471,4474],{},[898,4460,4240],{},[1726,4462,1735],{"stretchy":1734},[2128,4464,4465,4467],{},[898,4466,1738],{},[1726,4468,4342],{},[1726,4470,1762],{"stretchy":1734},[1726,4472,4473],{},"≥",[2133,4475,2328],{},[902,4477,4478],{"encoding":904},"E(P^*) \\ge 0"," a s touto nezápornou konvencí pracuje celá klasifikace ",[883,4481,4483],{"className":4482},[886],[888,4484,4485],{"xmlns":890},[892,4486,4487,4495],{},[895,4488,4489,4491,4493],{},[898,4490,4240],{},[1726,4492,3405],{},[2133,4494,2281],{},[902,4496,4497],{"encoding":904},"E > 1",[883,4499,4501],{"className":4500},[886],[888,4502,4503],{"xmlns":890},[892,4504,4505,4513],{},[895,4506,4507,4509,4511],{},[898,4508,4240],{},[1726,4510,3444],{},[2133,4512,2281],{},[902,4514,4515],{"encoding":904},"E \u003C 1",[883,4517,4519],{"className":4518},[886],[888,4520,4521],{"xmlns":890},[892,4522,4523,4531],{},[895,4524,4525,4527,4529],{},[898,4526,4240],{},[1726,4528,1728],{},[2133,4530,2281],{},[902,4532,4533],{"encoding":904},"E = 1",". V některých starších pramenech se ",[883,4536,4538],{"className":4537},[886],[888,4539,4540],{"xmlns":890},[892,4541,4542,4548],{},[895,4543,4544,4546],{},[1726,4545,2228],{},[2133,4547,2281],{},[902,4549,3731],{"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 ",[38,4552,4553],{},"absolutní hodnotou",[3859,4555,4556,4576],{},[724,4557,4558,4561,4562,4575],{},[883,4559,4560],{},"!tip"," Postup: jak spočítat ",[883,4563,4565],{"className":4564},[886],[888,4566,4567],{"xmlns":890},[892,4568,4569,4573],{},[895,4570,4571],{},[898,4572,4240],{},[902,4574,4240],{"encoding":904}," v bodě",[152,4577,4578,4629,4669,4722,4787],{},[123,4579,4580,4581,4604,4605,4628],{},"Zapište ",[883,4582,4584],{"className":4583},[886],[888,4585,4586],{"xmlns":890},[892,4587,4588,4602],{},[895,4589,4590,4592,4594,4596,4598,4600],{},[898,4591,1724],{},[1726,4593,1728],{},[898,4595,1731],{},[1726,4597,1735],{"stretchy":1734},[898,4599,1738],{},[1726,4601,1762],{"stretchy":1734},[902,4603,1801],{"encoding":904},". Pokud je poptávka zadaná jako ",[883,4606,4608],{"className":4607},[886],[888,4609,4610],{"xmlns":890},[892,4611,4612,4626],{},[895,4613,4614,4616,4618,4620,4622,4624],{},[898,4615,1738],{},[1726,4617,1728],{},[898,4619,1731],{},[1726,4621,1735],{"stretchy":1734},[898,4623,1724],{},[1726,4625,1762],{"stretchy":1734},[902,4627,1830],{"encoding":904},", použijte vztah (4.9).",[123,4630,4631,4632,1888],{},"Spočítejte derivaci ",[883,4633,4635],{"className":4634},[886],[888,4636,4637],{"xmlns":890},[892,4638,4639,4666],{},[895,4640,4641,4647,4649,4651,4653,4655,4657,4659,4662,4664],{},[2128,4642,4643,4645],{},[898,4644,1724],{},[1726,4646,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,4648,1735],{"stretchy":1734},[898,4650,1738],{},[1726,4652,1762],{"stretchy":1734},[1726,4654,1728],{},[898,4656,2198],{"mathvariant":2377},[898,4658,1724],{},[898,4660,4661],{"mathvariant":2377},"\u002F",[898,4663,2198],{"mathvariant":2377},[898,4665,1738],{},[902,4667,4668],{"encoding":904},"Q'(P) = \\mathrm{d}Q\u002F\\mathrm{d}P",[123,4670,4671,4672,4689,4690,1888],{},"Dosaďte zadanou cenu ",[883,4673,4675],{"className":4674},[886],[888,4676,4677],{"xmlns":890},[892,4678,4679,4687],{},[895,4680,4681],{},[2128,4682,4683,4685],{},[898,4684,1738],{},[1726,4686,4342],{},[902,4688,4392],{"encoding":904}," a dopočítejte odpovídající ",[883,4691,4693],{"className":4692},[886],[888,4694,4695],{"xmlns":890},[892,4696,4697,4719],{},[895,4698,4699,4705,4707,4709,4711,4717],{},[2128,4700,4701,4703],{},[898,4702,1724],{},[1726,4704,4342],{},[1726,4706,1728],{},[898,4708,1731],{},[1726,4710,1735],{"stretchy":1734},[2128,4712,4713,4715],{},[898,4714,1738],{},[1726,4716,4342],{},[1726,4718,1762],{"stretchy":1734},[902,4720,4721],{"encoding":904},"Q^* = D(P^*)",[123,4723,4724,4725,1888],{},"Dosaďte do (4.5): ",[883,4726,4728],{"className":4727},[886],[888,4729,4730],{"xmlns":890},[892,4731,4732,4784],{},[895,4733,4734,4736,4738,4744,4746,4748,4750,4766,4768,4774,4776,4782],{},[898,4735,4240],{},[1726,4737,1735],{"stretchy":1734},[2128,4739,4740,4742],{},[898,4741,1738],{},[1726,4743,4342],{},[1726,4745,1762],{"stretchy":1734},[1726,4747,1728],{},[1726,4749,2228],{},[2326,4751,4752],{"scriptlevel":2328,"displaystyle":1741},[2330,4753,4754,4760],{},[2128,4755,4756,4758],{},[898,4757,1738],{},[1726,4759,4342],{},[2128,4761,4762,4764],{},[898,4763,1724],{},[1726,4765,4342],{},[2289,4767,2984],{},[2128,4769,4770,4772],{},[898,4771,1724],{},[1726,4773,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,4775,1735],{"stretchy":1734},[2128,4777,4778,4780],{},[898,4779,1738],{},[1726,4781,4342],{},[1726,4783,1762],{"stretchy":1734},[902,4785,4786],{"encoding":904},"E(P^*) = -\\dfrac{P^*}{Q^*}\\,Q'(P^*)",[123,4788,4789,4790,4807,4808,4825,4826,4843],{},"Klasifikujte: ",[883,4791,4793],{"className":4792},[886],[888,4794,4795],{"xmlns":890},[892,4796,4797,4805],{},[895,4798,4799,4801,4803],{},[898,4800,4240],{},[1726,4802,3405],{},[2133,4804,2281],{},[902,4806,4497],{"encoding":904}," elastická, ",[883,4809,4811],{"className":4810},[886],[888,4812,4813],{"xmlns":890},[892,4814,4815,4823],{},[895,4816,4817,4819,4821],{},[898,4818,4240],{},[1726,4820,1728],{},[2133,4822,2281],{},[902,4824,4533],{"encoding":904}," jednotková, ",[883,4827,4829],{"className":4828},[886],[888,4830,4831],{"xmlns":890},[892,4832,4833,4841],{},[895,4834,4835,4837,4839],{},[898,4836,4240],{},[1726,4838,3444],{},[2133,4840,2281],{},[902,4842,4515],{"encoding":904}," neelastická.",[198,4845,4847],{"id":4846},"interpretace-46","Interpretace (4.6)",[3859,4849,4850],{},[724,4851,4852,4853,4876,4877,4890,4891,4908,4909],{},"Číslo ",[883,4854,4856],{"className":4855},[886],[888,4857,4858],{"xmlns":890},[892,4859,4860,4874],{},[895,4861,4862,4864,4866,4872],{},[898,4863,4240],{},[1726,4865,1735],{"stretchy":1734},[2128,4867,4868,4870],{},[898,4869,1738],{},[1726,4871,4342],{},[1726,4873,1762],{"stretchy":1734},[902,4875,4370],{"encoding":904}," udává, o kolik % se přibližně změní poptávané množství ",[883,4878,4880],{"className":4879},[886],[888,4881,4882],{"xmlns":890},[892,4883,4884,4888],{},[895,4885,4886],{},[898,4887,1724],{},[902,4889,1724],{"encoding":904},", jestliže se cena ",[883,4892,4894],{"className":4893},[886],[888,4895,4896],{"xmlns":890},[892,4897,4898,4906],{},[895,4899,4900],{},[2128,4901,4902,4904],{},[898,4903,1738],{},[1726,4905,4342],{},[902,4907,4392],{"encoding":904}," změní o 1 %. ",[883,4910,4912],{"className":4911},[886],[888,4913,4914],{"xmlns":890},[892,4915,4916,4925],{},[895,4917,4918,4920,4923],{},[1726,4919,1735],{"stretchy":1734},[2133,4921,4922],{},"4.6",[1726,4924,1762],{"stretchy":1734},[902,4926,4927],{"encoding":904},"(4.6)",[724,4929,4930,4933],{},[38,4931,4932],{},"Historicky:"," úvahy vedoucí k hypotéze (4.1) formuloval již Cournot (1838), dnešní vymezení se připisuje Marshallovi (1881).",[198,4935,4937],{"id":4936},"příklad-41","Příklad 4.1",[724,4939,4940,4941,4975,4976,1343,5002,2703],{},"Poptávka ",[883,4942,4944],{"className":4943},[886],[888,4945,4946],{"xmlns":890},[892,4947,4948,4972],{},[895,4949,4950,4952,4954,4956,4958,4960,4962,4964,4966,4968,4970],{},[898,4951,1738],{},[1726,4953,1728],{},[898,4955,1731],{},[1726,4957,1735],{"stretchy":1734},[898,4959,1724],{},[1726,4961,1762],{"stretchy":1734},[1726,4963,1728],{},[2133,4965,3117],{},[1726,4967,2228],{},[2133,4969,2135],{},[898,4971,1724],{},[902,4973,4974],{"encoding":904},"P = D(Q) = 50 - 2Q",". Vyjádříme ",[883,4977,4979],{"className":4978},[886],[888,4980,4981],{"xmlns":890},[892,4982,4983,4999],{},[895,4984,4985,4987,4989,4992,4994,4997],{},[898,4986,1724],{},[1726,4988,1728],{},[2133,4990,4991],{},"25",[1726,4993,2228],{},[2133,4995,4996],{},"0,5",[898,4998,1738],{},[902,5000,5001],{"encoding":904},"Q = 25 - 0{,}5P",[883,5003,5005],{"className":5004},[886],[888,5006,5007],{"xmlns":890},[892,5008,5009,5033],{},[895,5010,5011,5027,5029,5031],{},[2326,5012,5013],{"scriptlevel":2328,"displaystyle":1741},[2330,5014,5015,5021],{},[895,5016,5017,5019],{},[898,5018,2198],{"mathvariant":2377},[898,5020,1724],{},[895,5022,5023,5025],{},[898,5024,2198],{"mathvariant":2377},[898,5026,1738],{},[1726,5028,1728],{},[1726,5030,2228],{},[2133,5032,4996],{},[902,5034,5035],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -0{,}5",[724,5037,5038],{},[883,5039,5041],{"className":5040},[886],[888,5042,5043],{"xmlns":890},[892,5044,5045,5099],{},[895,5046,5047,5049,5051,5053,5067,5069,5071,5073,5075,5077,5079,5097],{},[898,5048,4240],{},[1726,5050,1728],{},[1726,5052,2228],{},[2330,5054,5055,5057],{},[898,5056,1738],{},[895,5058,5059,5061,5063,5065],{},[2133,5060,4991],{},[1726,5062,2228],{},[2133,5064,4996],{},[898,5066,1738],{},[1726,5068,3174],{},[1726,5070,1735],{"stretchy":1734},[1726,5072,2228],{},[2133,5074,4996],{},[1726,5076,1762],{"stretchy":1734},[1726,5078,1728],{},[2330,5080,5081,5087],{},[895,5082,5083,5085],{},[2133,5084,4996],{},[898,5086,1738],{},[895,5088,5089,5091,5093,5095],{},[2133,5090,4991],{},[1726,5092,2228],{},[2133,5094,4996],{},[898,5096,1738],{},[898,5098,1888],{"mathvariant":2377},[902,5100,5101],{"encoding":904},"E = -\\frac{P}{25-0{,}5P}\\cdot(-0{,}5) = \\frac{0{,}5P}{25-0{,}5P}.",[724,5103,5104,5105,1343,5129,1343,5159,1343,5183,5208,5209,5232,5233,2684,5251,1847],{},"Potom ",[883,5106,5108],{"className":5107},[886],[888,5109,5110],{"xmlns":890},[892,5111,5112,5126],{},[895,5113,5114,5116,5118,5120,5122,5124],{},[898,5115,4240],{},[1726,5117,1735],{"stretchy":1734},[2133,5119,2328],{},[1726,5121,1762],{"stretchy":1734},[1726,5123,1728],{},[2133,5125,2328],{},[902,5127,5128],{"encoding":904},"E(0)=0",[883,5130,5132],{"className":5131},[886],[888,5133,5134],{"xmlns":890},[892,5135,5136,5156],{},[895,5137,5138,5140,5142,5144,5146,5148],{},[898,5139,4240],{},[1726,5141,1735],{"stretchy":1734},[2133,5143,2860],{},[1726,5145,1762],{"stretchy":1734},[1726,5147,1728],{},[2326,5149,5150],{"scriptlevel":2328,"displaystyle":1734},[2330,5151,5152,5154],{},[2133,5153,2281],{},[2133,5155,2352],{},[902,5157,5158],{"encoding":904},"E(10)=\\tfrac{1}{4}",[883,5160,5162],{"className":5161},[886],[888,5163,5164],{"xmlns":890},[892,5165,5166,5180],{},[895,5167,5168,5170,5172,5174,5176,5178],{},[898,5169,4240],{},[1726,5171,1735],{"stretchy":1734},[2133,5173,4991],{},[1726,5175,1762],{"stretchy":1734},[1726,5177,1728],{},[2133,5179,2281],{},[902,5181,5182],{"encoding":904},"E(25)=1",[883,5184,5186],{"className":5185},[886],[888,5187,5188],{"xmlns":890},[892,5189,5190,5205],{},[895,5191,5192,5194,5196,5199,5201,5203],{},[898,5193,4240],{},[1726,5195,1735],{"stretchy":1734},[2133,5197,5198],{},"40",[1726,5200,1762],{"stretchy":1734},[1726,5202,1728],{},[2133,5204,2352],{},[902,5206,5207],{"encoding":904},"E(40)=4",". Např. ",[883,5210,5212],{"className":5211},[886],[888,5213,5214],{"xmlns":890},[892,5215,5216,5230],{},[895,5217,5218,5220,5222,5224,5226,5228],{},[898,5219,4240],{},[1726,5221,1735],{"stretchy":1734},[2133,5223,5198],{},[1726,5225,1762],{"stretchy":1734},[1726,5227,1728],{},[2133,5229,2352],{},[902,5231,5207],{"encoding":904}," znamená, že zvýšení ceny o 1 % (z 40 na 40,4) způsobí pokles množství o 4 % (z ",[883,5234,5236],{"className":5235},[886],[888,5237,5238],{"xmlns":890},[892,5239,5240,5248],{},[895,5241,5242,5244,5246],{},[898,5243,1724],{},[1726,5245,1728],{},[2133,5247,2231],{},[902,5249,5250],{"encoding":904},"Q=5",[883,5252,5254],{"className":5253},[886],[888,5255,5256],{"xmlns":890},[892,5257,5258,5267],{},[895,5259,5260,5262,5264],{},[898,5261,1724],{},[1726,5263,1728],{},[2133,5265,5266],{},"4,8",[902,5268,5269],{"encoding":904},"Q=4{,}8",[198,5271,5273],{"id":5272},"oblouková-průměrná-vs-bodová-okamžitá-elasticita","Oblouková (průměrná) vs. bodová (okamžitá) elasticita",[120,5275,5276,5332],{},[123,5277,5278,5281,5282,5299,5300,1888],{},[38,5279,5280],{},"Oblouková"," (průměrná) elasticita: výraz ",[883,5283,5285],{"className":5284},[886],[888,5286,5287],{"xmlns":890},[892,5288,5289,5297],{},[895,5290,5291],{},[2128,5292,5293,5295],{},[898,5294,4240],{},[898,5296,4243],{},[902,5298,4246],{"encoding":904}," ze (4.4) vztažený k intervalu ",[883,5301,5303],{"className":5302},[886],[888,5304,5305],{"xmlns":890},[892,5306,5307,5329],{},[895,5308,5309,5312,5314,5316,5318,5320,5322,5324,5326],{},[1726,5310,5311],{"stretchy":1734},"⟨",[898,5313,1738],{},[1726,5315,1742],{"separator":1741},[2289,5317,2984],{},[898,5319,1738],{},[1726,5321,2099],{},[898,5323,2886],{"mathvariant":2377},[898,5325,1738],{},[1726,5327,5328],{"stretchy":1734},"⟩",[902,5330,5331],{"encoding":904},"\\langle P,\\, P+\\Delta P\\rangle",[123,5333,5334,5337,5338,5351],{},[38,5335,5336],{},"Bodová"," (okamžitá) elasticita: ",[883,5339,5341],{"className":5340},[886],[888,5342,5343],{"xmlns":890},[892,5344,5345,5349],{},[895,5346,5347],{},[898,5348,4240],{},[902,5350,4240],{"encoding":904}," dle (4.5) — výchozí pojem dále v textu.",[198,5353,5355,5356,5369,5370],{"id":5354},"výpočet-je-li-dáno-pp-jako-funkce-qq","Výpočet, je-li dáno ",[883,5357,5359],{"className":5358},[886],[888,5360,5361],{"xmlns":890},[892,5362,5363,5367],{},[895,5364,5365],{},[898,5366,1738],{},[902,5368,1738],{"encoding":904}," jako funkce ",[883,5371,5373],{"className":5372},[886],[888,5374,5375],{"xmlns":890},[892,5376,5377,5381],{},[895,5378,5379],{},[898,5380,1724],{},[902,5382,1724],{"encoding":904},[724,5384,5385,5386,5409],{},"Pokud je poptávka zadaná ve tvaru ",[883,5387,5389],{"className":5388},[886],[888,5390,5391],{"xmlns":890},[892,5392,5393,5407],{},[895,5394,5395,5397,5399,5401,5403,5405],{},[898,5396,1738],{},[1726,5398,1728],{},[898,5400,1731],{},[1726,5402,1735],{"stretchy":1734},[898,5404,1724],{},[1726,5406,1762],{"stretchy":1734},[902,5408,1830],{"encoding":904},", využijeme vztah pro derivaci inverzní funkce",[724,5411,5412],{},[883,5413,5415],{"className":5414,"title":4188,"style":4189},[4187],"\\frac{\\mathrm{d}Q}{\\mathrm{d}P} = \\frac{1}{\\frac{\\mathrm{d}P}{\\mathrm{d}Q}}. \\tag{4.9}",[724,5417,5418,1777,5421,5447],{},[38,5419,5420],{},"Příklad 4.3.",[883,5422,5424],{"className":5423},[886],[888,5425,5426],{"xmlns":890},[892,5427,5428,5444],{},[895,5429,5430,5432,5434,5436,5438],{},[898,5431,1738],{},[1726,5433,1728],{},[2133,5435,3087],{},[1726,5437,2228],{},[2128,5439,5440,5442],{},[898,5441,1724],{},[2133,5443,2135],{},[902,5445,5446],{"encoding":904},"P = 100 - Q^2",", ptáme se na elasticitu při ceně 36. Dostáváme",[724,5449,5450],{},[883,5451,5453],{"className":5452},[886],[888,5454,5455],{"xmlns":890},[892,5456,5457,5523],{},[895,5458,5459,5461,5463,5465,5481,5483,5495,5497,5521],{},[898,5460,4240],{},[1726,5462,1728],{},[1726,5464,2228],{},[2330,5466,5467,5479],{},[895,5468,5469,5471,5473],{},[2133,5470,3087],{},[1726,5472,2228],{},[2128,5474,5475,5477],{},[898,5476,1724],{},[2133,5478,2135],{},[898,5480,1724],{},[1726,5482,3174],{},[2330,5484,5485,5487],{},[2133,5486,2281],{},[895,5488,5489,5491,5493],{},[1726,5490,2228],{},[2133,5492,2135],{},[898,5494,1724],{},[1726,5496,1728],{},[2330,5498,5499,5511],{},[895,5500,5501,5503,5505],{},[2133,5502,3087],{},[1726,5504,2228],{},[2128,5506,5507,5509],{},[898,5508,1724],{},[2133,5510,2135],{},[895,5512,5513,5515],{},[2133,5514,2135],{},[2128,5516,5517,5519],{},[898,5518,1724],{},[2133,5520,2135],{},[898,5522,1888],{"mathvariant":2377},[902,5524,5525],{"encoding":904},"E = -\\frac{100-Q^2}{Q}\\cdot \\frac{1}{-2Q} = \\frac{100-Q^2}{2Q^2}.",[724,5527,5528,5529,5556,5557,5576,5577,1888],{},"Z rovnice ",[883,5530,5532],{"className":5531},[886],[888,5533,5534],{"xmlns":890},[892,5535,5536,5553],{},[895,5537,5538,5540,5542,5548,5550],{},[2133,5539,3087],{},[1726,5541,2228],{},[2128,5543,5544,5546],{},[898,5545,1724],{},[2133,5547,2135],{},[1726,5549,1728],{},[2133,5551,5552],{},"36",[902,5554,5555],{"encoding":904},"100 - Q^2 = 36"," plyne ",[883,5558,5560],{"className":5559},[886],[888,5561,5562],{"xmlns":890},[892,5563,5564,5573],{},[895,5565,5566,5568,5570],{},[898,5567,1724],{},[1726,5569,1728],{},[2133,5571,5572],{},"8",[902,5574,5575],{"encoding":904},"Q = 8",", tedy ",[883,5578,5580],{"className":5579},[886],[888,5581,5582],{"xmlns":890},[892,5583,5584,5610],{},[895,5585,5586,5588,5590,5592,5594,5596,5605,5607],{},[898,5587,4240],{},[1726,5589,1735],{"stretchy":1734},[2133,5591,5572],{},[1726,5593,1762],{"stretchy":1734},[1726,5595,1728],{},[2326,5597,5598],{"scriptlevel":2328,"displaystyle":1734},[2330,5599,5600,5602],{},[2133,5601,5552],{},[2133,5603,5604],{},"128",[1726,5606,1728],{},[2133,5608,5609],{},"0,281",[902,5611,5612],{"encoding":904},"E(8) = \\tfrac{36}{128} = 0{,}281",[198,5614,5616],{"id":5615},"přibližné-změny","Přibližné změny",[724,5618,5619,5620,5656,5657,5679],{},"Diferenciál ",[883,5621,5623],{"className":5622},[886],[888,5624,5625],{"xmlns":890},[892,5626,5627,5653],{},[895,5628,5629,5631,5633,5635,5641,5643,5645,5647,5649,5651],{},[898,5630,2198],{"mathvariant":2377},[898,5632,1724],{},[1726,5634,1728],{},[2128,5636,5637,5639],{},[898,5638,1724],{},[1726,5640,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,5642,1735],{"stretchy":1734},[898,5644,1738],{},[1726,5646,1762],{"stretchy":1734},[2289,5648,2984],{},[898,5650,2198],{"mathvariant":2377},[898,5652,1738],{},[902,5654,5655],{"encoding":904},"\\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P"," s ",[883,5658,5660],{"className":5659},[886],[888,5661,5662],{"xmlns":890},[892,5663,5664,5676],{},[895,5665,5666,5668,5670,5672,5674],{},[898,5667,2198],{"mathvariant":2377},[898,5669,1738],{},[1726,5671,1728],{},[898,5673,2886],{"mathvariant":2377},[898,5675,1738],{},[902,5677,5678],{"encoding":904},"\\mathrm{d}P = \\Delta P"," dává nominální odhad",[724,5681,5682],{},[883,5683,5685],{"className":5684,"title":4188,"style":4189},[4187],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P. \\tag{4.10}",[724,5687,5688],{},"Po přechodu na procentní změny (vztah (4.3)):",[724,5690,5691],{},[883,5692,5694],{"className":5693,"title":4188,"style":4189},[4187],"\\boxed{\\;\\Delta Q\\% \\approx -E(P)\\,\\Delta P\\%\\;} \\tag{4.11}",[724,5696,5697,1777,5700,5735,5736,5755,5756,5790,5791,5808],{},[38,5698,5699],{},"Příklad 4.5.",[883,5701,5703],{"className":5702},[886],[888,5704,5705],{"xmlns":890},[892,5706,5707,5732],{},[895,5708,5709,5711,5713,5715,5721,5723,5725,5727,5729],{},[898,5710,1738],{},[1726,5712,1728],{},[1726,5714,2228],{},[2128,5716,5717,5719],{},[898,5718,1724],{},[2133,5720,2135],{},[1726,5722,2228],{},[2133,5724,2352],{},[898,5726,1724],{},[1726,5728,2099],{},[2133,5730,5731],{},"96",[902,5733,5734],{"encoding":904},"P = -Q^2 - 4Q + 96",", cena ",[883,5737,5739],{"className":5738},[886],[888,5740,5741],{"xmlns":890},[892,5742,5743,5752],{},[895,5744,5745,5747,5749],{},[898,5746,1738],{},[1726,5748,1728],{},[2133,5750,5751],{},"51",[902,5753,5754],{"encoding":904},"P=51",". Z rovnice ",[883,5757,5759],{"className":5758},[886],[888,5760,5761],{"xmlns":890},[892,5762,5763,5787],{},[895,5764,5765,5767,5769,5771,5777,5779,5781,5783,5785],{},[2133,5766,5751],{},[1726,5768,1728],{},[1726,5770,2228],{},[2128,5772,5773,5775],{},[898,5774,1724],{},[2133,5776,2135],{},[1726,5778,2228],{},[2133,5780,2352],{},[898,5782,1724],{},[1726,5784,2099],{},[2133,5786,5731],{},[902,5788,5789],{"encoding":904},"51 = -Q^2-4Q+96"," volíme (kladný kořen) ",[883,5792,5794],{"className":5793},[886],[888,5795,5796],{"xmlns":890},[892,5797,5798,5806],{},[895,5799,5800,5802,5804],{},[898,5801,1724],{},[1726,5803,1728],{},[2133,5805,2231],{},[902,5807,5250],{"encoding":904},". Elasticita:",[724,5810,5811],{},[883,5812,5814],{"className":5813},[886],[888,5815,5816],{"xmlns":890},[892,5817,5818,5891],{},[895,5819,5820,5822,5824,5862,5864,5868,5870,5872,5874,5876,5878,5885,5888],{},[898,5821,4240],{},[1726,5823,1728],{},[2330,5825,5826,5846],{},[895,5827,5828,5830,5836,5838,5840,5842,5844],{},[1726,5829,2228],{},[2128,5831,5832,5834],{},[898,5833,1724],{},[2133,5835,2135],{},[1726,5837,2228],{},[2133,5839,2352],{},[898,5841,1724],{},[1726,5843,2099],{},[2133,5845,5731],{},[895,5847,5848,5850,5852,5854,5856,5858,5860],{},[898,5849,1724],{},[1726,5851,1735],{"stretchy":1734},[2133,5853,2135],{},[898,5855,1724],{},[1726,5857,2099],{},[2133,5859,2352],{},[1726,5861,1762],{"stretchy":1734},[1726,5863,1742],{"separator":1741},[5865,5866],"mspace",{"width":5867},"2em",[898,5869,4240],{},[1726,5871,1735],{"stretchy":1734},[2133,5873,2231],{},[1726,5875,1762],{"stretchy":1734},[1726,5877,1728],{},[2330,5879,5880,5882],{},[2133,5881,5751],{},[2133,5883,5884],{},"70",[1726,5886,5887],{},"≐",[2133,5889,5890],{},"0,728.",[902,5892,5893],{"encoding":904},"E = \\frac{-Q^2-4Q+96}{Q(2Q+4)}, \\qquad E(5) = \\frac{51}{70} \\doteq 0{,}728.",[724,5895,5896,5897,1888],{},"Jde o neelastickou poptávku. Zvýší-li se cena o 2 %, pak ",[883,5898,5900],{"className":5899},[886],[888,5901,5902],{"xmlns":890},[892,5903,5904,5935],{},[895,5905,5906,5908,5910,5913,5915,5917,5920,5922,5924,5926,5928,5931,5933],{},[898,5907,2886],{"mathvariant":2377},[898,5909,1724],{},[898,5911,5912],{"mathvariant":2377},"%",[1726,5914,1880],{},[1726,5916,2228],{},[2133,5918,5919],{},"0,728",[1726,5921,3174],{},[2133,5923,2135],{},[1726,5925,1728],{},[1726,5927,2228],{},[2133,5929,5930],{},"1,456",[2289,5932,2984],{},[898,5934,5912],{"mathvariant":2377},[902,5936,5937],{"encoding":904},"\\Delta Q\\% \\approx -0{,}728\\cdot 2 = -1{,}456\\,\\%",[115,5939,5941],{"id":5940},"klasifikace-elasticit-poptávky","Klasifikace elasticit poptávky",[724,5943,5944,5945,5968,5969,2703],{},"V závislosti na hodnotě ",[883,5946,5948],{"className":5947},[886],[888,5949,5950],{"xmlns":890},[892,5951,5952,5966],{},[895,5953,5954,5956,5958,5964],{},[898,5955,4240],{},[1726,5957,1735],{"stretchy":1734},[2128,5959,5960,5962],{},[898,5961,1738],{},[1726,5963,4342],{},[1726,5965,1762],{"stretchy":1734},[902,5967,4370],{"encoding":904}," mluvíme o poptávce podle následující tabulky ",[883,5970,5972],{"className":5971},[886],[888,5973,5974],{"xmlns":890},[892,5975,5976,5985],{},[895,5977,5978,5980,5983],{},[1726,5979,1735],{"stretchy":1734},[2133,5981,5982],{},"4.7",[1726,5984,1762],{"stretchy":1734},[902,5986,5987],{"encoding":904},"(4.7)",[724,5989,5990],{},[1647,5991],{"alt":5992,"className":5993,"src":5994},"imek-typy-elasticity-5panelu",[210,1651],"\u002Fwiki-assets\u002Fimek-typy-elasticity-5panelu.jpeg",[16,5996,5997,6036],{},[19,5998,5999],{},[22,6000,6001,6027,6030,6033],{},[25,6002,6003,6004],{},"Hodnota ",[883,6005,6007],{"className":6006},[886],[888,6008,6009],{"xmlns":890},[892,6010,6011,6025],{},[895,6012,6013,6015,6017,6023],{},[898,6014,4240],{},[1726,6016,1735],{"stretchy":1734},[2128,6018,6019,6021],{},[898,6020,1738],{},[1726,6022,4342],{},[1726,6024,1762],{"stretchy":1734},[902,6026,4370],{"encoding":904},[25,6028,6029],{},"Typ poptávky",[25,6031,6032],{},"Termín",[25,6034,6035],{},"Význam",[30,6037,6038,6071,6133,6208,6265],{},[22,6039,6040,6060,6065,6068],{},[35,6041,6042],{},[883,6043,6045],{"className":6044},[886],[888,6046,6047],{"xmlns":890},[892,6048,6049,6057],{},[895,6050,6051,6053,6055],{},[898,6052,4240],{},[1726,6054,1728],{},[2133,6056,2328],{},[902,6058,6059],{"encoding":904},"E = 0",[35,6061,6062],{},[38,6063,6064],{},"dokonale neelastická",[35,6066,6067],{},"perfectly inelastic",[35,6069,6070],{},"množství se nemění bez ohledu na cenu",[22,6072,6073,6097,6101,6104],{},[35,6074,6075],{},[883,6076,6078],{"className":6077},[886],[888,6079,6080],{"xmlns":890},[892,6081,6082,6094],{},[895,6083,6084,6086,6088,6090,6092],{},[2133,6085,2328],{},[1726,6087,3444],{},[898,6089,4240],{},[1726,6091,3444],{},[2133,6093,2281],{},[902,6095,6096],{"encoding":904},"0 \u003C E \u003C 1",[35,6098,6099],{},[38,6100,4067],{},[35,6102,6103],{},"inelastic",[35,6105,6106,6119,6120],{},[883,6107,6109],{"className":6108},[886],[888,6110,6111],{"xmlns":890},[892,6112,6113,6117],{},[895,6114,6115],{},[898,6116,1724],{},[902,6118,1724],{"encoding":904}," se mění pomaleji než ",[883,6121,6123],{"className":6122},[886],[888,6124,6125],{"xmlns":890},[892,6126,6127,6131],{},[895,6128,6129],{},[898,6130,1738],{},[902,6132,1738],{"encoding":904},[22,6134,6135,6154,6159,6162],{},[35,6136,6137],{},[883,6138,6140],{"className":6139},[886],[888,6141,6142],{"xmlns":890},[892,6143,6144,6152],{},[895,6145,6146,6148,6150],{},[898,6147,4240],{},[1726,6149,1728],{},[2133,6151,2281],{},[902,6153,4533],{"encoding":904},[35,6155,6156],{},[38,6157,6158],{},"jednotkově elastická",[35,6160,6161],{},"unit elastic",[35,6163,6164,6177,6178,6191,6192,6207],{},[883,6165,6167],{"className":6166},[886],[888,6168,6169],{"xmlns":890},[892,6170,6171,6175],{},[895,6172,6173],{},[898,6174,1724],{},[902,6176,1724],{"encoding":904}," i ",[883,6179,6181],{"className":6180},[886],[888,6182,6183],{"xmlns":890},[892,6184,6185,6189],{},[895,6186,6187],{},[898,6188,1738],{},[902,6190,1738],{"encoding":904}," se mění stejně rychle; ",[883,6193,6195],{"className":6194},[886],[888,6196,6197],{"xmlns":890},[892,6198,6199,6205],{},[895,6200,6201,6203],{},[898,6202,2772],{},[898,6204,3984],{},[902,6206,4084],{"encoding":904}," má maximum",[22,6209,6210,6229,6233,6236],{},[35,6211,6212],{},[883,6213,6215],{"className":6214},[886],[888,6216,6217],{"xmlns":890},[892,6218,6219,6227],{},[895,6220,6221,6223,6225],{},[898,6222,4240],{},[1726,6224,3405],{},[2133,6226,2281],{},[902,6228,4497],{"encoding":904},[35,6230,6231],{},[38,6232,4063],{},[35,6234,6235],{},"elastic",[35,6237,6238,6251,6252],{},[883,6239,6241],{"className":6240},[886],[888,6242,6243],{"xmlns":890},[892,6244,6245,6249],{},[895,6246,6247],{},[898,6248,1724],{},[902,6250,1724],{"encoding":904}," se mění rychleji než ",[883,6253,6255],{"className":6254},[886],[888,6256,6257],{"xmlns":890},[892,6258,6259,6263],{},[895,6260,6261],{},[898,6262,1738],{},[902,6264,1738],{"encoding":904},[22,6266,6267,6288,6293,6296],{},[35,6268,6269],{},[883,6270,6272],{"className":6271},[886],[888,6273,6274],{"xmlns":890},[892,6275,6276,6285],{},[895,6277,6278,6280,6282],{},[898,6279,4240],{},[1726,6281,3120],{},[898,6283,6284],{"mathvariant":2377},"∞",[902,6286,6287],{"encoding":904},"E \\to \\infty",[35,6289,6290],{},[38,6291,6292],{},"dokonale elastická",[35,6294,6295],{},"perfectly elastic",[35,6297,6298,6299],{},"sebemenší změna ceny úplně mění ",[883,6300,6302],{"className":6301},[886],[888,6303,6304],{"xmlns":890},[892,6305,6306,6310],{},[895,6307,6308],{},[898,6309,1724],{},[902,6311,1724],{"encoding":904},[724,6313,6314],{},[38,6315,6316],{},"Pravidlo růstu elasticity s cenou:",[3859,6318,6319],{},[724,6320,6321,6322],{},"S rostoucí cenou elasticita poptávky roste. ",[883,6323,6325],{"className":6324},[886],[888,6326,6327],{"xmlns":890},[892,6328,6329,6338],{},[895,6330,6331,6333,6336],{},[1726,6332,1735],{"stretchy":1734},[2133,6334,6335],{},"4.8",[1726,6337,1762],{"stretchy":1734},[902,6339,6340],{"encoding":904},"(4.8)",[724,6342,6343,6344,6347,6348,6351,6352,6369],{},"Z toho plyne, že při ",[614,6345,6346],{},"dostatečně nízkých"," cenách je poptávka neelastická a při ",[614,6349,6350],{},"dostatečně vysokých"," elastická. Existuje tedy cena ",[883,6353,6355],{"className":6354},[886],[888,6356,6357],{"xmlns":890},[892,6358,6359,6367],{},[895,6360,6361],{},[2128,6362,6363,6365],{},[898,6364,1738],{},[1726,6366,4342],{},[902,6368,4392],{"encoding":904},", při které je poptávka jednotkově elastická, a ta rozděluje reálné cenové rozpětí na obě zóny.",[3859,6371,6372,6377],{},[724,6373,6374,6376],{},[883,6375,4560],{}," Postup: jak klasifikovat poptávku",[152,6378,6379,6406,6409],{},[123,6380,6381,6382,6405],{},"Spočítejte ",[883,6383,6385],{"className":6384},[886],[888,6386,6387],{"xmlns":890},[892,6388,6389,6403],{},[895,6390,6391,6393,6395,6401],{},[898,6392,4240],{},[1726,6394,1735],{"stretchy":1734},[2128,6396,6397,6399],{},[898,6398,1738],{},[1726,6400,4342],{},[1726,6402,1762],{"stretchy":1734},[902,6404,4370],{"encoding":904}," dle (4.5).",[123,6407,6408],{},"Porovnejte s jedničkou (viz tabulka výše).",[123,6410,6411,6412,6436],{},"Chcete-li najít hranici mezi elastickou a neelastickou zónou, řešte rovnici ",[883,6413,6415],{"className":6414},[886],[888,6416,6417],{"xmlns":890},[892,6418,6419,6433],{},[895,6420,6421,6423,6425,6427,6429,6431],{},[898,6422,4240],{},[1726,6424,1735],{"stretchy":1734},[898,6426,1738],{},[1726,6428,1762],{"stretchy":1734},[1726,6430,1728],{},[2133,6432,2281],{},[902,6434,6435],{"encoding":904},"E(P) = 1"," a výsledek porovnejte s reálným cenovým rozpětím.",[724,6438,6439,6442,6443,6460,6461,6479,6480,6507,6508,1888],{},[38,6440,6441],{},"Příklad 4.2."," Pro poptávku z Příkladu 4.1: ",[883,6444,6446],{"className":6445},[886],[888,6447,6448],{"xmlns":890},[892,6449,6450,6458],{},[895,6451,6452,6454,6456],{},[898,6453,4240],{},[1726,6455,1728],{},[2133,6457,2281],{},[902,6459,4533],{"encoding":904}," pro ",[883,6462,6464],{"className":6463},[886],[888,6465,6466],{"xmlns":890},[892,6467,6468,6476],{},[895,6469,6470,6472,6474],{},[898,6471,1738],{},[1726,6473,1728],{},[2133,6475,4991],{},[902,6477,6478],{"encoding":904},"P = 25",". Podle (4.8) je poptávka neelastická pro ",[883,6481,6483],{"className":6482},[886],[888,6484,6485],{"xmlns":890},[892,6486,6487,6504],{},[895,6488,6489,6491,6494,6496,6498,6500,6502],{},[898,6490,1738],{},[1726,6492,6493],{},"∈",[1726,6495,5311],{"stretchy":1734},[2133,6497,2328],{},[1726,6499,1742],{"separator":1741},[2133,6501,4991],{},[1726,6503,1762],{"stretchy":1734},[902,6505,6506],{"encoding":904},"P \\in \\langle 0, 25)"," a elastická pro ",[883,6509,6511],{"className":6510},[886],[888,6512,6513],{"xmlns":890},[892,6514,6515,6531],{},[895,6516,6517,6519,6521,6523,6525,6527,6529],{},[898,6518,1738],{},[1726,6520,6493],{},[1726,6522,1735],{"stretchy":1734},[2133,6524,4991],{},[1726,6526,1742],{"separator":1741},[2133,6528,3117],{},[1726,6530,5328],{"stretchy":1734},[902,6532,6533],{"encoding":904},"P \\in (25, 50\\rangle",[115,6535,6537],{"id":6536},"elasticita-a-celkový-příjem","Elasticita a celkový příjem",[724,6539,6540],{},[1647,6541],{"alt":6542,"className":6543,"src":6544},"imek-elasticita-tr",[210,1651],"\u002Fwiki-assets\u002Fimek-elasticita-tr.jpeg",[724,6546,6547],{},[1647,6548],{"alt":6549,"className":6550,"src":6551},"imek-elasticita-podel-linearni-poptavky",[210,1651],"\u002Fwiki-assets\u002Fimek-elasticita-podel-linearni-poptavky.jpeg",[724,6553,6554,6555,6605,6606,6622],{},"Pro celkový příjem platí ",[883,6556,6558],{"className":6557},[886],[888,6559,6560],{"xmlns":890},[892,6561,6562,6602],{},[895,6563,6564,6566,6568,6570,6572,6574,6576,6578,6580,6582,6584,6586,6588,6590,6592,6594,6596,6598,6600],{},[898,6565,2772],{},[898,6567,3984],{},[1726,6569,1728],{},[898,6571,2772],{},[898,6573,3984],{},[1726,6575,1735],{"stretchy":1734},[898,6577,1724],{},[1726,6579,1762],{"stretchy":1734},[1726,6581,1728],{},[898,6583,1738],{},[1726,6585,3174],{},[898,6587,1724],{},[1726,6589,1728],{},[898,6591,1724],{},[1726,6593,3174],{},[898,6595,1731],{},[1726,6597,1735],{"stretchy":1734},[898,6599,1724],{},[1726,6601,1762],{"stretchy":1734},[902,6603,6604],{"encoding":904},"TR = TR(Q) = P\\cdot Q = Q\\cdot D(Q)",". Pro mezní příjem ",[883,6607,6609],{"className":6608},[886],[888,6610,6611],{"xmlns":890},[892,6612,6613,6619],{},[895,6614,6615,6617],{},[898,6616,2815],{},[898,6618,3984],{},[902,6620,6621],{"encoding":904},"MR"," odvodíme:",[724,6624,6625],{},[883,6626,6628],{"className":6627},[886],[888,6629,6630],{"xmlns":890},[892,6631,6632,6740],{},[895,6633,6634,6636,6638,6640,6642,6648,6650,6652,6654,6656,6658,6660,6662,6664,6666,6668,6670,6676,6678,6680,6682,6684,6686,6688,6690,6704,6706,6708],{},[898,6635,2815],{},[898,6637,3984],{},[1726,6639,1728],{},[898,6641,2772],{},[2128,6643,6644,6646],{},[898,6645,3984],{},[1726,6647,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,6649,1735],{"stretchy":1734},[898,6651,1724],{},[1726,6653,1762],{"stretchy":1734},[1726,6655,1728],{},[898,6657,1731],{},[1726,6659,1735],{"stretchy":1734},[898,6661,1724],{},[1726,6663,1762],{"stretchy":1734},[1726,6665,2099],{},[898,6667,1724],{},[2289,6669,2984],{},[2128,6671,6672,6674],{},[898,6673,1731],{},[1726,6675,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,6677,1735],{"stretchy":1734},[898,6679,1724],{},[1726,6681,1762],{"stretchy":1734},[1726,6683,1728],{},[898,6685,1738],{},[1726,6687,2099],{},[898,6689,1724],{},[2330,6691,6692,6698],{},[895,6693,6694,6696],{},[898,6695,2198],{"mathvariant":2377},[898,6697,1738],{},[895,6699,6700,6702],{},[898,6701,2198],{"mathvariant":2377},[898,6703,1724],{},[1726,6705,1728],{},[898,6707,1738],{},[895,6709,6710,6712,6714,6716,6722,6724,6738],{},[1726,6711,1735],{"fence":1741},[2133,6713,2281],{},[1726,6715,2099],{},[2330,6717,6718,6720],{},[898,6719,1724],{},[898,6721,1738],{},[1726,6723,3174],{},[2330,6725,6726,6732],{},[895,6727,6728,6730],{},[898,6729,2198],{"mathvariant":2377},[898,6731,1738],{},[895,6733,6734,6736],{},[898,6735,2198],{"mathvariant":2377},[898,6737,1724],{},[1726,6739,1762],{"fence":1741},[902,6741,6742],{"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)",[724,6744,6745],{},[883,6746,6748],{"className":6747},[886],[888,6749,6750],{"xmlns":890},[892,6751,6752,6824],{},[895,6753,6754,6756,6758,6800,6802,6804],{},[1726,6755,1728],{},[898,6757,1738],{},[895,6759,6760,6762,6764,6766,6798],{},[1726,6761,1735],{"fence":1741},[2133,6763,2281],{},[1726,6765,2099],{},[2330,6767,6768,6770],{},[2133,6769,2281],{},[895,6771,6772,6780,6782],{},[2326,6773,6774],{"scriptlevel":2328,"displaystyle":1734},[2330,6775,6776,6778],{},[898,6777,1738],{},[898,6779,1724],{},[1726,6781,3174],{},[2326,6783,6784],{"scriptlevel":2328,"displaystyle":1734},[2330,6785,6786,6792],{},[895,6787,6788,6790],{},[898,6789,2198],{"mathvariant":2377},[898,6791,1724],{},[895,6793,6794,6796],{},[898,6795,2198],{"mathvariant":2377},[898,6797,1738],{},[1726,6799,1762],{"fence":1741},[1726,6801,1728],{},[898,6803,1738],{},[895,6805,6806,6808,6810,6812,6822],{},[1726,6807,1735],{"fence":1741},[2133,6809,2281],{},[1726,6811,2099],{},[2330,6813,6814,6816],{},[2133,6815,2281],{},[895,6817,6818,6820],{},[1726,6819,2228],{},[898,6821,4240],{},[1726,6823,1762],{"fence":1741},[902,6825,6826],{"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)",[724,6828,6829],{},"a tedy",[724,6831,6832],{},[883,6833,6835],{"className":6834,"title":4188,"style":4189},[4187],"\\boxed{\\;MR = P\\left(1 - \\frac{1}{E}\\right) = D(Q)\\left(1 - \\frac{1}{E}\\right)\\;} \\tag{4.12}",[3859,6837,6838,6907,7156],{},[724,6839,6840,6842,6843,6877,6878,6893,6894,2703],{},[883,6841,4145],{}," Intuice: vztah ",[883,6844,6846],{"className":6845},[886],[888,6847,6848],{"xmlns":890},[892,6849,6850,6874],{},[895,6851,6852,6854,6856,6858,6860,6862,6864,6866,6868,6870,6872],{},[898,6853,2815],{},[898,6855,3984],{},[1726,6857,1728],{},[898,6859,1738],{},[1726,6861,1735],{"stretchy":1734},[2133,6863,2281],{},[1726,6865,2228],{},[2133,6867,2281],{},[898,6869,4661],{"mathvariant":2377},[898,6871,4240],{},[1726,6873,1762],{"stretchy":1734},[902,6875,6876],{"encoding":904},"MR = P(1 - 1\u002FE)","\nVztah (4.12) je „most\" mezi elasticitou a mezním příjmem — znaménko ",[883,6879,6881],{"className":6880},[886],[888,6882,6883],{"xmlns":890},[892,6884,6885,6891],{},[895,6886,6887,6889],{},[898,6888,2815],{},[898,6890,3984],{},[902,6892,6621],{"encoding":904}," jednoznačně určuje hodnota ",[883,6895,6897],{"className":6896},[886],[888,6898,6899],{"xmlns":890},[892,6900,6901,6905],{},[895,6902,6903],{},[898,6904,4240],{},[902,6906,4240],{"encoding":904},[120,6908,6909,7018,7087],{},[123,6910,6911,6928,6929,1777,6943,1777,6969,1777,6982,1696,7002,7017],{},[883,6912,6914],{"className":6913},[886],[888,6915,6916],{"xmlns":890},[892,6917,6918,6926],{},[895,6919,6920,6922,6924],{},[898,6921,4240],{},[1726,6923,3405],{},[2133,6925,2281],{},[902,6927,4497],{"encoding":904}," (elastická) ",[883,6930,6932],{"className":6931},[886],[888,6933,6934],{"xmlns":890},[892,6935,6936,6940],{},[895,6937,6938],{},[1726,6939,3977],{},[902,6941,6942],{"encoding":904},"\\Rightarrow",[883,6944,6946],{"className":6945},[886],[888,6947,6948],{"xmlns":890},[892,6949,6950,6966],{},[895,6951,6952,6954,6956,6958,6960,6962,6964],{},[2133,6953,2281],{},[1726,6955,2228],{},[2133,6957,2281],{},[898,6959,4661],{"mathvariant":2377},[898,6961,4240],{},[1726,6963,3405],{},[2133,6965,2328],{},[902,6967,6968],{"encoding":904},"1 - 1\u002FE > 0",[883,6970,6972],{"className":6971},[886],[888,6973,6974],{"xmlns":890},[892,6975,6976,6980],{},[895,6977,6978],{},[1726,6979,3977],{},[902,6981,6942],{"encoding":904},[883,6983,6985],{"className":6984},[886],[888,6986,6987],{"xmlns":890},[892,6988,6989,6999],{},[895,6990,6991,6993,6995,6997],{},[898,6992,2815],{},[898,6994,3984],{},[1726,6996,3405],{},[2133,6998,2328],{},[902,7000,7001],{"encoding":904},"MR > 0",[883,7003,7005],{"className":7004},[886],[888,7006,7007],{"xmlns":890},[892,7008,7009,7015],{},[895,7010,7011,7013],{},[898,7012,2772],{},[898,7014,3984],{},[902,7016,4084],{"encoding":904}," roste s množstvím, tj. klesá s cenou.",[123,7019,7020,7037,7038,1777,7051,1696,7071,7086],{},[883,7021,7023],{"className":7022},[886],[888,7024,7025],{"xmlns":890},[892,7026,7027,7035],{},[895,7028,7029,7031,7033],{},[898,7030,4240],{},[1726,7032,1728],{},[2133,7034,2281],{},[902,7036,4533],{"encoding":904}," (jednotková) ",[883,7039,7041],{"className":7040},[886],[888,7042,7043],{"xmlns":890},[892,7044,7045,7049],{},[895,7046,7047],{},[1726,7048,3977],{},[902,7050,6942],{"encoding":904},[883,7052,7054],{"className":7053},[886],[888,7055,7056],{"xmlns":890},[892,7057,7058,7068],{},[895,7059,7060,7062,7064,7066],{},[898,7061,2815],{},[898,7063,3984],{},[1726,7065,1728],{},[2133,7067,2328],{},[902,7069,7070],{"encoding":904},"MR = 0",[883,7072,7074],{"className":7073},[886],[888,7075,7076],{"xmlns":890},[892,7077,7078,7084],{},[895,7079,7080,7082],{},[898,7081,2772],{},[898,7083,3984],{},[902,7085,4084],{"encoding":904}," je extrém (maximum).",[123,7088,7089,7106,7107,1777,7120,1696,7140,7155],{},[883,7090,7092],{"className":7091},[886],[888,7093,7094],{"xmlns":890},[892,7095,7096,7104],{},[895,7097,7098,7100,7102],{},[898,7099,4240],{},[1726,7101,3444],{},[2133,7103,2281],{},[902,7105,4515],{"encoding":904}," (neelastická) ",[883,7108,7110],{"className":7109},[886],[888,7111,7112],{"xmlns":890},[892,7113,7114,7118],{},[895,7115,7116],{},[1726,7117,3977],{},[902,7119,6942],{"encoding":904},[883,7121,7123],{"className":7122},[886],[888,7124,7125],{"xmlns":890},[892,7126,7127,7137],{},[895,7128,7129,7131,7133,7135],{},[898,7130,2815],{},[898,7132,3984],{},[1726,7134,3444],{},[2133,7136,2328],{},[902,7138,7139],{"encoding":904},"MR \u003C 0",[883,7141,7143],{"className":7142},[886],[888,7144,7145],{"xmlns":890},[892,7146,7147,7153],{},[895,7148,7149,7151],{},[898,7150,2772],{},[898,7152,3984],{},[902,7154,4084],{"encoding":904}," klesá s množstvím, tj. roste s cenou.",[724,7157,7158,7159,1888],{},"Viz také ",[207,7160,3815],{"className":7161,"dataFsResolvedFilePath":827,"href":828},[210],[198,7163,7165],{"id":7164},"pravidla-13-odvození-z-412","Pravidla 1–3 (odvození z (4.12))",[724,7167,7168,7188,7189,7215,7216,7231,7232,7245,7246,7259,7260,7273,7274,7290,7291,1777,7306,7309,7310,7290,7326,1888],{},[38,7169,7170,7171,1847],{},"(a) Poptávka elastická (",[883,7172,7174],{"className":7173},[886],[888,7175,7176],{"xmlns":890},[892,7177,7178,7186],{},[895,7179,7180,7182,7184],{},[898,7181,4240],{},[1726,7183,3405],{},[2133,7185,2281],{},[902,7187,4497],{"encoding":904}," Z (4.12) plyne ",[883,7190,7192],{"className":7191},[886],[888,7193,7194],{"xmlns":890},[892,7195,7196,7212],{},[895,7197,7198,7200,7202,7204,7206,7208,7210],{},[898,7199,2815],{},[898,7201,3984],{},[1726,7203,1735],{"stretchy":1734},[898,7205,1724],{},[1726,7207,1762],{"stretchy":1734},[1726,7209,3405],{},[2133,7211,2328],{},[902,7213,7214],{"encoding":904},"MR(Q) > 0",", a tedy celkový příjem ",[883,7217,7219],{"className":7218},[886],[888,7220,7221],{"xmlns":890},[892,7222,7223,7229],{},[895,7224,7225,7227],{},[898,7226,2772],{},[898,7228,3984],{},[902,7230,4084],{"encoding":904}," je rostoucí funkcí ",[883,7233,7235],{"className":7234},[886],[888,7236,7237],{"xmlns":890},[892,7238,7239,7243],{},[895,7240,7241],{},[898,7242,1724],{},[902,7244,1724],{"encoding":904},". Avšak růst ",[883,7247,7249],{"className":7248},[886],[888,7250,7251],{"xmlns":890},[892,7252,7253,7257],{},[895,7254,7255],{},[898,7256,1724],{},[902,7258,1724],{"encoding":904}," je odezvou na pokles ceny ",[883,7261,7263],{"className":7262},[886],[888,7264,7265],{"xmlns":890},[892,7266,7267,7271],{},[895,7268,7269],{},[898,7270,1738],{},[902,7272,1738],{"encoding":904},". Tudíž s ",[614,7275,7276,7277],{},"poklesem ceny ",[883,7278,7280],{"className":7279},[886],[888,7281,7282],{"xmlns":890},[892,7283,7284,7288],{},[895,7285,7286],{},[898,7287,1738],{},[902,7289,1738],{"encoding":904}," celkový příjem ",[883,7292,7294],{"className":7293},[886],[888,7295,7296],{"xmlns":890},[892,7297,7298,7304],{},[895,7299,7300,7302],{},[898,7301,2772],{},[898,7303,3984],{},[902,7305,4084],{"encoding":904},[614,7307,7308],{},"roste"," a s ",[614,7311,7312,7313],{},"růstem ceny ",[883,7314,7316],{"className":7315},[886],[888,7317,7318],{"xmlns":890},[892,7319,7320,7324],{},[895,7321,7322],{},[898,7323,1738],{},[902,7325,1738],{"encoding":904},[614,7327,7328],{},"klesá",[3859,7330,7331],{},[724,7332,7333,7336],{},[38,7334,7335],{},"Pravidlo 1."," Je-li poptávka elastická, pak s poklesem ceny celkový příjem roste a s růstem ceny celkový příjem klesá.",[724,7338,7339,7188,7359,1343,7385,7400,7401,7414,7415,7428,7429,7442,7443,7290,7456,1777,7471,1888],{},[38,7340,7341,7342,1847],{},"(b) Poptávka neelastická (",[883,7343,7345],{"className":7344},[886],[888,7346,7347],{"xmlns":890},[892,7348,7349,7357],{},[895,7350,7351,7353,7355],{},[898,7352,4240],{},[1726,7354,3444],{},[2133,7356,2281],{},[902,7358,4515],{"encoding":904},[883,7360,7362],{"className":7361},[886],[888,7363,7364],{"xmlns":890},[892,7365,7366,7382],{},[895,7367,7368,7370,7372,7374,7376,7378,7380],{},[898,7369,2815],{},[898,7371,3984],{},[1726,7373,1735],{"stretchy":1734},[898,7375,1724],{},[1726,7377,1762],{"stretchy":1734},[1726,7379,3444],{},[2133,7381,2328],{},[902,7383,7384],{"encoding":904},"MR(Q) \u003C 0",[883,7386,7388],{"className":7387},[886],[888,7389,7390],{"xmlns":890},[892,7391,7392,7398],{},[895,7393,7394,7396],{},[898,7395,2772],{},[898,7397,3984],{},[902,7399,4084],{"encoding":904}," je klesající funkce ",[883,7402,7404],{"className":7403},[886],[888,7405,7406],{"xmlns":890},[892,7407,7408,7412],{},[895,7409,7410],{},[898,7411,1724],{},[902,7413,1724],{"encoding":904},", tj. s růstem ",[883,7416,7418],{"className":7417},[886],[888,7419,7420],{"xmlns":890},[892,7421,7422,7426],{},[895,7423,7424],{},[898,7425,1724],{},[902,7427,1724],{"encoding":904}," (s poklesem ceny ",[883,7430,7432],{"className":7431},[886],[888,7433,7434],{"xmlns":890},[892,7435,7436,7440],{},[895,7437,7438],{},[898,7439,1738],{},[902,7441,1738],{"encoding":904},") celkový příjem klesá. S růstem ceny ",[883,7444,7446],{"className":7445},[886],[888,7447,7448],{"xmlns":890},[892,7449,7450,7454],{},[895,7451,7452],{},[898,7453,1738],{},[902,7455,1738],{"encoding":904},[883,7457,7459],{"className":7458},[886],[888,7460,7461],{"xmlns":890},[892,7462,7463,7469],{},[895,7464,7465,7467],{},[898,7466,2772],{},[898,7468,3984],{},[902,7470,4084],{"encoding":904},[614,7472,7308],{},[3859,7474,7475],{},[724,7476,7477,7480],{},[38,7478,7479],{},"Pravidlo 2."," Je-li poptávka neelastická, pak s poklesem ceny celkový příjem klesá a s růstem ceny celkový příjem roste.",[724,7482,7483,7188,7503,7522,7523,7538,7539,7609,7610,3877,7638,7671,7672,5576,7700,7715,7716,1888],{},[38,7484,7485,7486,1847],{},"(c) Jednotková elasticita (",[883,7487,7489],{"className":7488},[886],[888,7490,7491],{"xmlns":890},[892,7492,7493,7501],{},[895,7494,7495,7497,7499],{},[898,7496,4240],{},[1726,7498,1728],{},[2133,7500,2281],{},[902,7502,4533],{"encoding":904},[883,7504,7506],{"className":7505},[886],[888,7507,7508],{"xmlns":890},[892,7509,7510,7520],{},[895,7511,7512,7514,7516,7518],{},[898,7513,2815],{},[898,7515,3984],{},[1726,7517,1728],{},[2133,7519,2328],{},[902,7521,7070],{"encoding":904}," — nutná podmínka extrému ",[883,7524,7526],{"className":7525},[886],[888,7527,7528],{"xmlns":890},[892,7529,7530,7536],{},[895,7531,7532,7534],{},[898,7533,2772],{},[898,7535,3984],{},[902,7537,4084],{"encoding":904},". Dále ",[883,7540,7542],{"className":7541},[886],[888,7543,7544],{"xmlns":890},[892,7545,7546,7606],{},[895,7547,7548,7550,7560,7562,7564,7570,7572,7578,7580,7582,7584,7586,7588,7590,7600,7602,7604],{},[898,7549,2772],{},[2128,7551,7552,7554],{},[898,7553,3984],{},[895,7555,7556,7558],{},[1726,7557,2379],{"mathvariant":2377},[1726,7559,2379],{"mathvariant":2377},[1726,7561,1728],{},[898,7563,2815],{},[2128,7565,7566,7568],{},[898,7567,3984],{},[1726,7569,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,7571,1728],{},[2128,7573,7574,7576],{},[898,7575,1731],{},[1726,7577,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,7579,1735],{"stretchy":1734},[898,7581,1724],{},[1726,7583,1762],{"stretchy":1734},[1726,7585,2099],{},[898,7587,1724],{},[2289,7589,2984],{},[2128,7591,7592,7594],{},[898,7593,1731],{},[895,7595,7596,7598],{},[1726,7597,2379],{"mathvariant":2377},[1726,7599,2379],{"mathvariant":2377},[1726,7601,1735],{"stretchy":1734},[898,7603,1724],{},[1726,7605,1762],{"stretchy":1734},[902,7607,7608],{"encoding":904},"TR'' = MR' = D'(Q) + Q\\,D''(Q)","; za normálních podmínek ",[883,7611,7613],{"className":7612},[886],[888,7614,7615],{"xmlns":890},[892,7616,7617,7635],{},[895,7618,7619,7625,7627,7629,7631,7633],{},[2128,7620,7621,7623],{},[898,7622,1731],{},[1726,7624,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,7626,1735],{"stretchy":1734},[898,7628,1724],{},[1726,7630,1762],{"stretchy":1734},[1726,7632,3444],{},[2133,7634,2328],{},[902,7636,7637],{"encoding":904},"D'(Q) \u003C 0",[883,7639,7641],{"className":7640},[886],[888,7642,7643],{"xmlns":890},[892,7644,7645,7668],{},[895,7646,7647,7657,7659,7661,7663,7666],{},[2128,7648,7649,7651],{},[898,7650,1731],{},[895,7652,7653,7655],{},[1726,7654,2379],{"mathvariant":2377},[1726,7656,2379],{"mathvariant":2377},[1726,7658,1735],{"stretchy":1734},[898,7660,1724],{},[1726,7662,1762],{"stretchy":1734},[1726,7664,7665],{},"≤",[2133,7667,2328],{},[902,7669,7670],{"encoding":904},"D''(Q) \\le 0",", odkud ",[883,7673,7675],{"className":7674},[886],[888,7676,7677],{"xmlns":890},[892,7678,7679,7697],{},[895,7680,7681,7683,7693,7695],{},[898,7682,2772],{},[2128,7684,7685,7687],{},[898,7686,3984],{},[895,7688,7689,7691],{},[1726,7690,2379],{"mathvariant":2377},[1726,7692,2379],{"mathvariant":2377},[1726,7694,3444],{},[2133,7696,2328],{},[902,7698,7699],{"encoding":904},"TR'' \u003C 0",[883,7701,7703],{"className":7702},[886],[888,7704,7705],{"xmlns":890},[892,7706,7707,7713],{},[895,7708,7709,7711],{},[898,7710,2772],{},[898,7712,3984],{},[902,7714,4084],{"encoding":904}," nabývá ",[38,7717,7718],{},"maxima",[3859,7720,7721],{},[724,7722,7723,7726],{},[38,7724,7725],{},"Pravidlo 3."," Celkový příjem nabývá maxima při ceně, pro kterou je poptávka jednotkově elastická.",[724,7728,7729],{},"Tato tři pravidla potvrzují hypotézu (4.1) a jsou klíčem k regulaci ceny za účelem zvýšení (maximalizace) celkového příjmu.",[724,7731,7732],{},[38,7733,7734],{},"Souhrnná tabulka Pravidel 1–3:",[16,7736,7737,7841],{},[19,7738,7739],{},[22,7740,7741,7744,7759,7776,7807,7838],{},[25,7742,7743],{},"Charakter poptávky",[25,7745,7746],{},[883,7747,7749],{"className":7748},[886],[888,7750,7751],{"xmlns":890},[892,7752,7753,7757],{},[895,7754,7755],{},[898,7756,4240],{},[902,7758,4240],{"encoding":904},[25,7760,7761],{},[883,7762,7764],{"className":7763},[886],[888,7765,7766],{"xmlns":890},[892,7767,7768,7774],{},[895,7769,7770,7772],{},[898,7771,2815],{},[898,7773,3984],{},[902,7775,6621],{"encoding":904},[25,7777,7778,7779,1777,7792],{},"Pokles ceny ",[883,7780,7782],{"className":7781},[886],[888,7783,7784],{"xmlns":890},[892,7785,7786,7790],{},[895,7787,7788],{},[1726,7789,3977],{},[902,7791,6942],{"encoding":904},[883,7793,7795],{"className":7794},[886],[888,7796,7797],{"xmlns":890},[892,7798,7799,7805],{},[895,7800,7801,7803],{},[898,7802,2772],{},[898,7804,3984],{},[902,7806,4084],{"encoding":904},[25,7808,7809,7810,1777,7823],{},"Růst ceny ",[883,7811,7813],{"className":7812},[886],[888,7814,7815],{"xmlns":890},[892,7816,7817,7821],{},[895,7818,7819],{},[1726,7820,3977],{},[902,7822,6942],{"encoding":904},[883,7824,7826],{"className":7825},[886],[888,7827,7828],{"xmlns":890},[892,7829,7830,7836],{},[895,7831,7832,7834],{},[898,7833,2772],{},[898,7835,3984],{},[902,7837,4084],{"encoding":904},[25,7839,7840],{},"Doporučení",[30,7842,7843,7892,7942],{},[22,7844,7845,7847,7865,7883,7885,7887],{},[35,7846,4063],{},[35,7848,7849],{},[883,7850,7852],{"className":7851},[886],[888,7853,7854],{"xmlns":890},[892,7855,7856,7862],{},[895,7857,7858,7860],{},[1726,7859,3405],{},[2133,7861,2281],{},[902,7863,7864],{"encoding":904},"> 1",[35,7866,7867],{},[883,7868,7870],{"className":7869},[886],[888,7871,7872],{"xmlns":890},[892,7873,7874,7880],{},[895,7875,7876,7878],{},[1726,7877,3405],{},[2133,7879,2328],{},[902,7881,7882],{"encoding":904},"> 0",[35,7884,7308],{},[35,7886,7328],{},[35,7888,7889],{},[38,7890,7891],{},"snížit cenu",[22,7893,7894,7897,7915,7933,7935,7937],{},[35,7895,7896],{},"jednotková",[35,7898,7899],{},[883,7900,7902],{"className":7901},[886],[888,7903,7904],{"xmlns":890},[892,7905,7906,7912],{},[895,7907,7908,7910],{},[1726,7909,1728],{},[2133,7911,2281],{},[902,7913,7914],{"encoding":904},"= 1",[35,7916,7917],{},[883,7918,7920],{"className":7919},[886],[888,7921,7922],{"xmlns":890},[892,7923,7924,7930],{},[895,7925,7926,7928],{},[1726,7927,1728],{},[2133,7929,2328],{},[902,7931,7932],{"encoding":904},"= 0",[35,7934,3714],{},[35,7936,3714],{},[35,7938,7939],{},[38,7940,7941],{},"držet cenu",[22,7943,7944,7946,7964,7982,7984,7986],{},[35,7945,4067],{},[35,7947,7948],{},[883,7949,7951],{"className":7950},[886],[888,7952,7953],{"xmlns":890},[892,7954,7955,7961],{},[895,7956,7957,7959],{},[1726,7958,3444],{},[2133,7960,2281],{},[902,7962,7963],{"encoding":904},"\u003C 1",[35,7965,7966],{},[883,7967,7969],{"className":7968},[886],[888,7970,7971],{"xmlns":890},[892,7972,7973,7979],{},[895,7974,7975,7977],{},[1726,7976,3444],{},[2133,7978,2328],{},[902,7980,7981],{"encoding":904},"\u003C 0",[35,7983,7328],{},[35,7985,7308],{},[35,7987,7988],{},[38,7989,7990],{},"zvýšit cenu",[198,7992,7994],{"id":7993},"příklad-46-aplikace-pravidel-13","Příklad 4.6 — aplikace Pravidel 1–3",[724,7996,7997,7998,8023,8024,8046,8047,8060,8061,8074,8075,8088,8089,5576,8116,8168],{},"Aplikujme pravidla 1–3 pro poptávku ",[883,7999,8001],{"className":8000},[886],[888,8002,8003],{"xmlns":890},[892,8004,8005,8021],{},[895,8006,8007,8009,8011,8013,8015],{},[898,8008,1738],{},[1726,8010,1728],{},[2133,8012,3087],{},[1726,8014,2228],{},[2128,8016,8017,8019],{},[898,8018,1724],{},[2133,8020,2135],{},[902,8022,5446],{"encoding":904},". Reálné cenové rozpětí je ",[883,8025,8027],{"className":8026},[886],[888,8028,8029],{"xmlns":890},[892,8030,8031,8043],{},[895,8032,8033,8035,8037,8039,8041],{},[1726,8034,5311],{"stretchy":1734},[2133,8036,2281],{},[1726,8038,1742],{"separator":1741},[2133,8040,3087],{},[1726,8042,5328],{"stretchy":1734},[902,8044,8045],{"encoding":904},"\\langle 1, 100\\rangle",". Pro výpočet elasticity vyjádříme ",[883,8048,8050],{"className":8049},[886],[888,8051,8052],{"xmlns":890},[892,8053,8054,8058],{},[895,8055,8056],{},[898,8057,1724],{},[902,8059,1724],{"encoding":904}," jako funkci ",[883,8062,8064],{"className":8063},[886],[888,8065,8066],{"xmlns":890},[892,8067,8068,8072],{},[895,8069,8070],{},[898,8071,1738],{},[902,8073,1738],{"encoding":904},"; pro nezáporné ",[883,8076,8078],{"className":8077},[886],[888,8079,8080],{"xmlns":890},[892,8081,8082,8086],{},[895,8083,8084],{},[898,8085,1724],{},[902,8087,1724],{"encoding":904}," je ",[883,8090,8092],{"className":8091},[886],[888,8093,8094],{"xmlns":890},[892,8095,8096,8113],{},[895,8097,8098,8100,8102],{},[898,8099,1724],{},[1726,8101,1728],{},[8103,8104,8105],"msqrt",{},[895,8106,8107,8109,8111],{},[2133,8108,3087],{},[1726,8110,2228],{},[898,8112,1738],{},[902,8114,8115],{"encoding":904},"Q = \\sqrt{100 - P}",[883,8117,8119],{"className":8118},[886],[888,8120,8121],{"xmlns":890},[892,8122,8123,8165],{},[895,8124,8125,8141,8143,8145],{},[2326,8126,8127],{"scriptlevel":2328,"displaystyle":1741},[2330,8128,8129,8135],{},[895,8130,8131,8133],{},[898,8132,2198],{"mathvariant":2377},[898,8134,1724],{},[895,8136,8137,8139],{},[898,8138,2198],{"mathvariant":2377},[898,8140,1738],{},[1726,8142,1728],{},[1726,8144,2228],{},[2326,8146,8147],{"scriptlevel":2328,"displaystyle":1741},[2330,8148,8149,8151],{},[2133,8150,2281],{},[895,8152,8153,8155],{},[2133,8154,2135],{},[8103,8156,8157],{},[895,8158,8159,8161,8163],{},[2133,8160,3087],{},[1726,8162,2228],{},[898,8164,1738],{},[902,8166,8167],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\dfrac{1}{2\\sqrt{100-P}}",". Podle (4.5):",[724,8170,8171],{},[883,8172,8174],{"className":8173},[886],[888,8175,8176],{"xmlns":890},[892,8177,8178,8300],{},[895,8179,8180,8182,8184,8186,8188,8190,8192,8198,8200,8214,8216,8218,8232,8234,8260,8262,8280,8282,8298],{},[898,8181,4240],{},[1726,8183,1735],{"stretchy":1734},[898,8185,1738],{},[1726,8187,1762],{"stretchy":1734},[1726,8189,1728],{},[1726,8191,2228],{},[2330,8193,8194,8196],{},[898,8195,1738],{},[898,8197,1724],{},[1726,8199,3174],{},[2330,8201,8202,8208],{},[895,8203,8204,8206],{},[898,8205,2198],{"mathvariant":2377},[898,8207,1724],{},[895,8209,8210,8212],{},[898,8211,2198],{"mathvariant":2377},[898,8213,1738],{},[1726,8215,1728],{},[1726,8217,2228],{},[2330,8219,8220,8222],{},[898,8221,1738],{},[8103,8223,8224],{},[895,8225,8226,8228,8230],{},[2133,8227,3087],{},[1726,8229,2228],{},[898,8231,1738],{},[1726,8233,3174],{},[895,8235,8236,8238,8240,8258],{},[1726,8237,1735],{"fence":1741},[1726,8239,2228],{},[2330,8241,8242,8244],{},[2133,8243,2281],{},[895,8245,8246,8248],{},[2133,8247,2135],{},[8103,8249,8250],{},[895,8251,8252,8254,8256],{},[2133,8253,3087],{},[1726,8255,2228],{},[898,8257,1738],{},[1726,8259,1762],{"fence":1741},[1726,8261,1728],{},[2330,8263,8264,8266],{},[898,8265,1738],{},[895,8267,8268,8270,8272,8274,8276,8278],{},[2133,8269,2135],{},[1726,8271,1735],{"stretchy":1734},[2133,8273,3087],{},[1726,8275,2228],{},[898,8277,1738],{},[1726,8279,1762],{"stretchy":1734},[1726,8281,1728],{},[2330,8283,8284,8290],{},[895,8285,8286,8288],{},[2133,8287,4996],{},[898,8289,1738],{},[895,8291,8292,8294,8296],{},[2133,8293,3087],{},[1726,8295,2228],{},[898,8297,1738],{},[898,8299,1888],{"mathvariant":2377},[902,8301,8302],{"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}.",[724,8304,8305,8306,2703],{},"Stanovíme cenu, při které je poptávka jednotkově elastická. Řešíme ",[883,8307,8309],{"className":8308},[886],[888,8310,8311],{"xmlns":890},[892,8312,8313,8337],{},[895,8314,8315,8333,8335],{},[2326,8316,8317],{"scriptlevel":2328,"displaystyle":1741},[2330,8318,8319,8325],{},[895,8320,8321,8323],{},[2133,8322,4996],{},[898,8324,1738],{},[895,8326,8327,8329,8331],{},[2133,8328,3087],{},[1726,8330,2228],{},[898,8332,1738],{},[1726,8334,1728],{},[2133,8336,2281],{},[902,8338,8339],{"encoding":904},"\\dfrac{0{,}5P}{100-P} = 1",[724,8341,8342],{},[883,8343,8345],{"className":8344},[886],[888,8346,8347],{"xmlns":890},[892,8348,8349,8381],{},[895,8350,8351,8357,8359,8366,8368,8371,8379],{},[2128,8352,8353,8355],{},[898,8354,1738],{},[1726,8356,4342],{},[1726,8358,1728],{},[2330,8360,8361,8364],{},[2133,8362,8363],{},"200",[2133,8365,2177],{},[1726,8367,5887],{},[2133,8369,8370],{},"66,",[8372,8373,8374,8376],"mover",{"accent":1741},[2133,8375,2238],{},[1726,8377,8378],{"stretchy":1741},"‾",[898,8380,1888],{"mathvariant":2377},[902,8382,8383],{"encoding":904},"P^* = \\frac{200}{3} \\doteq 66{,}\\overline{6}.",[724,8385,8386],{},"S využitím vlastnosti (4.8):",[120,8388,8389,8435,8477],{},[123,8390,8391,8392,8427,8428,8430,8431,8434],{},"Při cenách ",[883,8393,8395],{"className":8394},[886],[888,8396,8397],{"xmlns":890},[892,8398,8399,8424],{},[895,8400,8401,8403,8405,8407,8409,8412,8414,8416,8422],{},[898,8402,1738],{},[1726,8404,6493],{},[1726,8406,5311],{"stretchy":1734},[2133,8408,2281],{},[1726,8410,8411],{"separator":1741},";",[2289,8413,2984],{},[2133,8415,8370],{},[8372,8417,8418,8420],{"accent":1741},[2133,8419,2238],{},[1726,8421,8378],{"stretchy":1741},[1726,8423,1762],{"stretchy":1734},[902,8425,8426],{"encoding":904},"P \\in \\langle 1;\\, 66{,}\\overline{6})"," je poptávka ",[38,8429,4067],{}," — dle ",[614,8432,8433],{},"Pravidla 2"," přiměřené zvýšení ceny zvýší celkový příjem.",[123,8436,8391,8437,8427,8471,8430,8473,8476],{},[883,8438,8440],{"className":8439},[886],[888,8441,8442],{"xmlns":890},[892,8443,8444,8468],{},[895,8445,8446,8448,8450,8452,8454,8460,8462,8464,8466],{},[898,8447,1738],{},[1726,8449,6493],{},[1726,8451,1735],{"stretchy":1734},[2133,8453,8370],{},[8372,8455,8456,8458],{"accent":1741},[2133,8457,2238],{},[1726,8459,8378],{"stretchy":1741},[1726,8461,8411],{"separator":1741},[2289,8463,2984],{},[2133,8465,3087],{},[1726,8467,5328],{"stretchy":1734},[902,8469,8470],{"encoding":904},"P \\in (66{,}\\overline{6};\\, 100\\rangle",[38,8472,4063],{},[614,8474,8475],{},"Pravidla 1"," přiměřené snížení ceny povede ke zvýšení celkového příjmu.",[123,8478,8479,8480,8483,8484,8512,8513,8516],{},"Dle ",[614,8481,8482],{},"Pravidla 3"," je při ceně ",[883,8485,8487],{"className":8486},[886],[888,8488,8489],{"xmlns":890},[892,8490,8491,8509],{},[895,8492,8493,8499,8501,8503],{},[2128,8494,8495,8497],{},[898,8496,1738],{},[1726,8498,4342],{},[1726,8500,1728],{},[2133,8502,8370],{},[8372,8504,8505,8507],{"accent":1741},[2133,8506,2238],{},[1726,8508,8378],{"stretchy":1741},[902,8510,8511],{"encoding":904},"P^* = 66{,}\\overline{6}"," dosaženo ",[38,8514,8515],{},"maxima celkového příjmu"," ve výši",[724,8518,8519],{},[883,8520,8522],{"className":8521},[886],[888,8523,8524],{"xmlns":890},[892,8525,8526,8604],{},[895,8527,8528,8530,8532,8534,8540,8542,8544,8550,8552,8566,8568,8574,8576,8584,8586,8599,8601],{},[898,8529,2772],{},[898,8531,3984],{},[1726,8533,1735],{"stretchy":1734},[2128,8535,8536,8538],{},[898,8537,1738],{},[1726,8539,4342],{},[1726,8541,1762],{"stretchy":1734},[1726,8543,1728],{},[2128,8545,8546,8548],{},[898,8547,1738],{},[1726,8549,4342],{},[1726,8551,3174],{},[8103,8553,8554],{},[895,8555,8556,8558,8560],{},[2133,8557,3087],{},[1726,8559,2228],{},[2128,8561,8562,8564],{},[898,8563,1738],{},[1726,8565,4342],{},[1726,8567,1728],{},[2330,8569,8570,8572],{},[2133,8571,8363],{},[2133,8573,2177],{},[1726,8575,3174],{},[8103,8577,8578],{},[2330,8579,8580,8582],{},[2133,8581,3087],{},[2133,8583,2177],{},[1726,8585,1728],{},[2330,8587,8588,8591],{},[2133,8589,8590],{},"2000",[895,8592,8593,8595],{},[2133,8594,2177],{},[8103,8596,8597],{},[2133,8598,2177],{},[1726,8600,5887],{},[2133,8602,8603],{},"384,9.",[902,8605,8606],{"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.",[724,8608,8609,8610,1888],{},"Ke stejnému výsledku bychom dospěli přímým hledáním maxima funkce ",[883,8611,8613],{"className":8612},[886],[888,8614,8615],{"xmlns":890},[892,8616,8617,8623],{},[895,8618,8619,8621],{},[898,8620,2772],{},[898,8622,3984],{},[902,8624,4084],{"encoding":904},[115,8626,8628],{"id":8627},"cenová-elasticita-nabídky","Cenová elasticita nabídky",[724,8630,8631,8632,8635],{},"Analogicky se definuje ",[38,8633,8634],{},"cenová elasticita nabídky"," (price elasticity of supply):",[724,8637,8638],{},[883,8639,8641],{"className":8640,"title":4188,"style":4189},[4187],"\\boxed{\\;E = E(P) = \\frac{P}{Q}\\cdot\\frac{\\mathrm{d}Q}{\\mathrm{d}P}\\;} \\tag{4.13}",[724,8643,4298,8644,8669,8670,8702],{},[883,8645,8647],{"className":8646},[886],[888,8648,8649],{"xmlns":890},[892,8650,8651,8666],{},[895,8652,8653,8655,8657,8660,8662,8664],{},[898,8654,1724],{},[1726,8656,1728],{},[898,8658,8659],{},"S",[1726,8661,1735],{"stretchy":1734},[898,8663,1738],{},[1726,8665,1762],{"stretchy":1734},[902,8667,8668],{"encoding":904},"Q = S(P)"," je funkce nabídky. Protože nabídka je rostoucí, ",[883,8671,8673],{"className":8672},[886],[888,8674,8675],{"xmlns":890},[892,8676,8677,8699],{},[895,8678,8679,8695,8697],{},[2326,8680,8681],{"scriptlevel":2328,"displaystyle":1741},[2330,8682,8683,8689],{},[895,8684,8685,8687],{},[898,8686,2198],{"mathvariant":2377},[898,8688,1724],{},[895,8690,8691,8693],{},[898,8692,2198],{"mathvariant":2377},[898,8694,1738],{},[1726,8696,3405],{},[2133,8698,2328],{},[902,8700,8701],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} > 0",", a elasticita nabídky je vždy nezáporná — proto zde není znaménková korekce jako u poptávky.",[724,8704,8705],{},"Klasifikace na elastickou \u002F jednotkově elastickou \u002F neelastickou je analogická jako u poptávky (tabulka (4.7)). Platí paralela k (4.8):",[3859,8707,8708],{},[724,8709,8710,8711],{},"S rostoucí cenou elasticita nabídky roste. ",[883,8712,8714],{"className":8713},[886],[888,8715,8716],{"xmlns":890},[892,8717,8718,8727],{},[895,8719,8720,8722,8725],{},[1726,8721,1735],{"stretchy":1734},[2133,8723,8724],{},"4.14",[1726,8726,1762],{"stretchy":1734},[902,8728,8729],{"encoding":904},"(4.14)",[724,8731,8732],{},"Pro nominální změny platí",[724,8734,8735],{},[883,8736,8738],{"className":8737,"title":4188,"style":4189},[4187],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P, \\qquad \\mathrm{d}P = \\Delta P, \\tag{4.15}",[724,8740,8741],{},"a pro procentní změny",[724,8743,8744],{},[883,8745,8747],{"className":8746,"title":4188,"style":4189},[4187],"\\boxed{\\;\\Delta Q\\% \\approx E(P)\\,\\Delta P\\%\\;} \\tag{4.16}",[724,8749,8750],{},"(bez znaménka minus).",[198,8752,8754],{"id":8753},"příklad-47","Příklad 4.7",[724,8756,8757,8758,2703],{},"Nabídka ",[883,8759,8761],{"className":8760},[886],[888,8762,8763],{"xmlns":890},[892,8764,8765,8790],{},[895,8766,8767,8769,8771,8773,8779,8781,8783,8785,8787],{},[898,8768,1724],{},[1726,8770,1728],{},[2133,8772,2791],{},[2128,8774,8775,8777],{},[898,8776,1738],{},[2133,8778,2135],{},[1726,8780,2099],{},[2133,8782,2231],{},[898,8784,1738],{},[1726,8786,2099],{},[2133,8788,8789],{},"150",[902,8791,8792],{"encoding":904},"Q = 0{,}1P^2 + 5P + 150",[724,8794,8795],{},[883,8796,8798],{"className":8797},[886],[888,8799,8800],{"xmlns":890},[892,8801,8802,8848],{},[895,8803,8804,8806,8808,8832,8834,8836,8838,8840,8842,8844,8846],{},[898,8805,4240],{},[1726,8807,1728],{},[2330,8809,8810,8812],{},[898,8811,1738],{},[895,8813,8814,8816,8822,8824,8826,8828,8830],{},[2133,8815,2791],{},[2128,8817,8818,8820],{},[898,8819,1738],{},[2133,8821,2135],{},[1726,8823,2099],{},[2133,8825,2231],{},[898,8827,1738],{},[1726,8829,2099],{},[2133,8831,8789],{},[2289,8833,2984],{},[1726,8835,1735],{"stretchy":1734},[2133,8837,2836],{},[898,8839,1738],{},[1726,8841,2099],{},[2133,8843,2231],{},[1726,8845,1762],{"stretchy":1734},[898,8847,1888],{"mathvariant":2377},[902,8849,8850],{"encoding":904},"E = \\frac{P}{0{,}1P^2 + 5P + 150}\\,(0{,}2P + 5).",[724,8852,5104,8853,1343,8883,1343,8910,8946,8947,8972,8973,8991,8992,1888],{},[883,8854,8856],{"className":8855},[886],[888,8857,8858],{"xmlns":890},[892,8859,8860,8880],{},[895,8861,8862,8864,8866,8868,8870,8872],{},[898,8863,4240],{},[1726,8865,1735],{"stretchy":1734},[2133,8867,2860],{},[1726,8869,1762],{"stretchy":1734},[1726,8871,1728],{},[2326,8873,8874],{"scriptlevel":2328,"displaystyle":1734},[2330,8875,8876,8878],{},[2133,8877,2281],{},[2133,8879,2177],{},[902,8881,8882],{"encoding":904},"E(10) = \\tfrac{1}{3}",[883,8884,8886],{"className":8885},[886],[888,8887,8888],{"xmlns":890},[892,8889,8890,8907],{},[895,8891,8892,8894,8896,8901,8903,8905],{},[898,8893,4240],{},[1726,8895,1735],{"stretchy":1734},[8103,8897,8898],{},[2133,8899,8900],{},"1500",[1726,8902,1762],{"stretchy":1734},[1726,8904,1728],{},[2133,8906,2281],{},[902,8908,8909],{"encoding":904},"E(\\sqrt{1500}) = 1",[883,8911,8913],{"className":8912},[886],[888,8914,8915],{"xmlns":890},[892,8916,8917,8943],{},[895,8918,8919,8921,8923,8925,8927,8929,8938,8940],{},[898,8920,4240],{},[1726,8922,1735],{"stretchy":1734},[2133,8924,3087],{},[1726,8926,1762],{"stretchy":1734},[1726,8928,1728],{},[2326,8930,8931],{"scriptlevel":2328,"displaystyle":1734},[2330,8932,8933,8935],{},[2133,8934,3117],{},[2133,8936,8937],{},"33",[1726,8939,5887],{},[2133,8941,8942],{},"1,515",[902,8944,8945],{"encoding":904},"E(100) = \\tfrac{50}{33} \\doteq 1{,}515",". Dle (4.14): pro ",[883,8948,8950],{"className":8949},[886],[888,8951,8952],{"xmlns":890},[892,8953,8954,8969],{},[895,8955,8956,8958,8960,8964,8966],{},[898,8957,1738],{},[1726,8959,3405],{},[8103,8961,8962],{},[2133,8963,8900],{},[1726,8965,1880],{},[2133,8967,8968],{},"38,7",[902,8970,8971],{"encoding":904},"P > \\sqrt{1500} \\approx 38{,}7"," je nabídka elastická, pro ",[883,8974,8976],{"className":8975},[886],[888,8977,8978],{"xmlns":890},[892,8979,8980,8988],{},[895,8981,8982,8984,8986],{},[898,8983,1738],{},[1726,8985,3444],{},[2133,8987,8968],{},[902,8989,8990],{"encoding":904},"P \u003C 38{,}7"," neelastická. Zvýší-li se cena z 10 o 20 %, pak ",[883,8993,8995],{"className":8994},[886],[888,8996,8997],{"xmlns":890},[892,8998,8999,9037],{},[895,9000,9001,9003,9005,9007,9009,9017,9019,9022,9024,9027,9033,9035],{},[898,9002,2886],{"mathvariant":2377},[898,9004,1724],{},[898,9006,5912],{"mathvariant":2377},[1726,9008,1880],{},[2326,9010,9011],{"scriptlevel":2328,"displaystyle":1734},[2330,9012,9013,9015],{},[2133,9014,2281],{},[2133,9016,2177],{},[1726,9018,3174],{},[2133,9020,9021],{},"20",[1726,9023,1728],{},[2133,9025,9026],{},"6,",[8372,9028,9029,9031],{"accent":1741},[2133,9030,2238],{},[1726,9032,8378],{"stretchy":1741},[2289,9034,2984],{},[898,9036,5912],{"mathvariant":2377},[902,9038,9039],{"encoding":904},"\\Delta Q\\% \\approx \\tfrac{1}{3}\\cdot 20 = 6{,}\\overline{6}\\,\\%",[115,9041,9043],{"id":9042},"vícefaktorový-model","Vícefaktorový model",[724,9045,9046,9047,9060,9061,1777,9064,9077,9078,1777,9081,9099,9100,1777,9103,2703],{},"Předpokládejme, že poptávané množství ",[883,9048,9050],{"className":9049},[886],[888,9051,9052],{"xmlns":890},[892,9053,9054,9058],{},[895,9055,9056],{},[898,9057,1724],{},[902,9059,1724],{"encoding":904}," závisí na ",[38,9062,9063],{},"ceně základního zboží",[883,9065,9067],{"className":9066},[886],[888,9068,9069],{"xmlns":890},[892,9070,9071,9075],{},[895,9072,9073],{},[898,9074,1738],{},[902,9076,1738],{"encoding":904},", na ",[38,9079,9080],{},"ceně alternativního zboží",[883,9082,9084],{"className":9083},[886],[888,9085,9086],{"xmlns":890},[892,9087,9088,9096],{},[895,9089,9090],{},[2275,9091,9092,9094],{},[898,9093,1738],{},[898,9095,4243],{},[902,9097,9098],{"encoding":904},"P_A"," a na ",[38,9101,9102],{},"důchodu",[883,9104,9106],{"className":9105},[886],[888,9107,9108],{"xmlns":890},[892,9109,9110,9114],{},[895,9111,9112],{},[898,9113,1745],{},[902,9115,1745],{"encoding":904},[724,9117,9118],{},[883,9119,9121],{"className":9120,"title":4188,"style":4189},[4187],"Q = D(P, P_A, Y). \\tag{4.17}",[724,9123,9124,9125,9128],{},"V analogii jednofaktorového modelu pracujeme s ",[38,9126,9127],{},"parciálními derivacemi"," funkce poptávky.",[198,9130,9132],{"id":9131},"cenová-elasticita-poptávky-vícefaktorová","Cenová elasticita poptávky (vícefaktorová)",[724,9134,9135],{},[883,9136,9138],{"className":9137,"title":4188,"style":4189},[4187],"\\boxed{\\;E_P = -\\frac{P}{Q}\\,Q'_P\\;} \\tag{4.18}",[724,9140,4298,9141,9162,9163,9176,9177,2924,9199,1777,9202,9248,9249,9262,9263,9280],{},[883,9142,9144],{"className":9143},[886],[888,9145,9146],{"xmlns":890},[892,9147,9148,9159],{},[895,9149,9150],{},[9151,9152,9153,9155,9157],"msubsup",{},[898,9154,1724],{},[898,9156,1738],{},[1726,9158,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[902,9160,9161],{"encoding":904},"Q'_P"," je parciální derivace (4.17) podle ",[883,9164,9166],{"className":9165},[886],[888,9167,9168],{"xmlns":890},[892,9169,9170,9174],{},[895,9171,9172],{},[898,9173,1738],{},[902,9175,1738],{"encoding":904},". Vždy ",[883,9178,9180],{"className":9179},[886],[888,9181,9182],{"xmlns":890},[892,9183,9184,9196],{},[895,9185,9186,9192,9194],{},[2275,9187,9188,9190],{},[898,9189,4240],{},[898,9191,1738],{},[1726,9193,4473],{},[2133,9195,2328],{},[902,9197,9198],{"encoding":904},"E_P \\ge 0",[614,9200,9201],{},"Interpretace:",[883,9203,9205],{"className":9204},[886],[888,9206,9207],{"xmlns":890},[892,9208,9209,9245],{},[895,9210,9211,9217,9219,9225,9227,9235,9237,9243],{},[2275,9212,9213,9215],{},[898,9214,4240],{},[898,9216,1738],{},[1726,9218,1735],{"stretchy":1734},[2128,9220,9221,9223],{},[898,9222,1738],{},[1726,9224,4342],{},[1726,9226,1742],{"separator":1741},[9151,9228,9229,9231,9233],{},[898,9230,1738],{},[898,9232,4243],{},[1726,9234,4342],{},[1726,9236,1742],{"separator":1741},[2128,9238,9239,9241],{},[898,9240,1745],{},[1726,9242,4342],{},[1726,9244,1762],{"stretchy":1734},[902,9246,9247],{"encoding":904},"E_P(P^*, P_A^*, Y^*)"," udává přibližnou procentní změnu ",[883,9250,9252],{"className":9251},[886],[888,9253,9254],{"xmlns":890},[892,9255,9256,9260],{},[895,9257,9258],{},[898,9259,1724],{},[902,9261,1724],{"encoding":904}," při 1% změně ",[883,9264,9266],{"className":9265},[886],[888,9267,9268],{"xmlns":890},[892,9269,9270,9278],{},[895,9271,9272],{},[2128,9273,9274,9276],{},[898,9275,1738],{},[1726,9277,4342],{},[902,9279,4392],{"encoding":904},", ceteris paribus.",[198,9282,9284],{"id":9283},"křížová-křížově-cenová-elasticita-poptávky","Křížová (křížově-cenová) elasticita poptávky",[724,9286,9287],{},[883,9288,9290],{"className":9289,"title":4188,"style":4189},[4187],"\\boxed{\\;E_{P_A} = \\frac{P_A}{Q}\\,Q'_{P_A}\\;} \\tag{4.19}",[724,9292,9293,9248,9295,9308,9309,9326],{},[614,9294,9201],{},[883,9296,9298],{"className":9297},[886],[888,9299,9300],{"xmlns":890},[892,9301,9302,9306],{},[895,9303,9304],{},[898,9305,1724],{},[902,9307,1724],{"encoding":904}," základního zboží při 1% změně ceny ",[883,9310,9312],{"className":9311},[886],[888,9313,9314],{"xmlns":890},[892,9315,9316,9324],{},[895,9317,9318],{},[2275,9319,9320,9322],{},[898,9321,1738],{},[898,9323,4243],{},[902,9325,9098],{"encoding":904}," alternativního zboží (ceteris paribus).",[724,9328,9329],{},[38,9330,9331],{},"Znaménko závisí na povaze alternativního zboží:",[120,9333,9334,9422],{},[123,9335,9336,9337,9340,9341,9358,9359,1777,9372,1888],{},"Je-li alternativní zboží ",[38,9338,9339],{},"komplement",", růst ",[883,9342,9344],{"className":9343},[886],[888,9345,9346],{"xmlns":890},[892,9347,9348,9356],{},[895,9349,9350],{},[2275,9351,9352,9354],{},[898,9353,1738],{},[898,9355,4243],{},[902,9357,9098],{"encoding":904}," způsobí zdražení dvojice, pokles ",[883,9360,9362],{"className":9361},[886],[888,9363,9364],{"xmlns":890},[892,9365,9366,9370],{},[895,9367,9368],{},[898,9369,1724],{},[902,9371,1724],{"encoding":904},[883,9373,9375],{"className":9374},[886],[888,9376,9377],{"xmlns":890},[892,9378,9379,9419],{},[895,9380,9381,9383,9385,9397,9399,9401,9403,9405,9415,9417],{},[1726,9382,3977],{},[2289,9384,3974],{},[9151,9386,9387,9389,9395],{},[898,9388,1724],{},[2275,9390,9391,9393],{},[898,9392,1738],{},[898,9394,4243],{},[1726,9396,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,9398,3444],{},[2133,9400,2328],{},[1726,9402,1742],{"separator":1741},[2289,9404,3974],{},[2275,9406,9407,9409],{},[898,9408,4240],{},[2275,9410,9411,9413],{},[898,9412,1738],{},[898,9414,4243],{},[1726,9416,3444],{},[2133,9418,2328],{},[902,9420,9421],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} \u003C 0,\\; E_{P_A} \u003C 0",[123,9423,9336,9424,9340,9427,9444,9445,9458,9459,1888],{},[38,9425,9426],{},"substitut",[883,9428,9430],{"className":9429},[886],[888,9431,9432],{"xmlns":890},[892,9433,9434,9442],{},[895,9435,9436],{},[2275,9437,9438,9440],{},[898,9439,1738],{},[898,9441,4243],{},[902,9443,9098],{"encoding":904}," učiní základní zboží relativně levnější, zájem se přesune, ",[883,9446,9448],{"className":9447},[886],[888,9449,9450],{"xmlns":890},[892,9451,9452,9456],{},[895,9453,9454],{},[898,9455,1724],{},[902,9457,1724],{"encoding":904}," roste ",[883,9460,9462],{"className":9461},[886],[888,9463,9464],{"xmlns":890},[892,9465,9466,9506],{},[895,9467,9468,9470,9472,9484,9486,9488,9490,9492,9502,9504],{},[1726,9469,3977],{},[2289,9471,3974],{},[9151,9473,9474,9476,9482],{},[898,9475,1724],{},[2275,9477,9478,9480],{},[898,9479,1738],{},[898,9481,4243],{},[1726,9483,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,9485,3405],{},[2133,9487,2328],{},[1726,9489,1742],{"separator":1741},[2289,9491,3974],{},[2275,9493,9494,9496],{},[898,9495,4240],{},[2275,9497,9498,9500],{},[898,9499,1738],{},[898,9501,4243],{},[1726,9503,3405],{},[2133,9505,2328],{},[902,9507,9508],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} > 0,\\; E_{P_A} > 0",[883,9510,9513],{"className":9511,"title":9512,"style":4189},[4187],"ParseError: KaTeX parse error: Expected 'EOF', got '&' at position 9: E_{P_A} &̲> 0 \\;\\;\\Leftri…","undefined",{"title":641,"searchDepth":642,"depth":642,"links":9515},[9516,9520,9521,9529,9530,9534,9537],{"id":3883,"depth":642,"text":3884,"children":9517},[9518,9519],{"id":3912,"depth":649,"text":3913},{"id":4092,"depth":649,"text":4093},{"id":4127,"depth":642,"text":4128},{"id":4153,"depth":642,"text":4154,"children":9522},[9523,9524,9525,9526,9528],{"id":4846,"depth":649,"text":4847},{"id":4936,"depth":649,"text":4937},{"id":5272,"depth":649,"text":5273},{"id":5354,"depth":649,"text":9527},"Výpočet, je-li dáno PP jako funkce QQ",{"id":5615,"depth":649,"text":5616},{"id":5940,"depth":642,"text":5941},{"id":6536,"depth":642,"text":6537,"children":9531},[9532,9533],{"id":7164,"depth":649,"text":7165},{"id":7993,"depth":649,"text":7994},{"id":8627,"depth":642,"text":8628,"children":9535},[9536],{"id":8753,"depth":649,"text":8754},{"id":9042,"depth":642,"text":9043,"children":9538},[9539,9540],{"id":9131,"depth":649,"text":9132},{"id":9283,"depth":649,"text":9284},"2026-04-22",{},"\u002Ftopics\u002Felasticita",{"title":3852,"description":641},[1138,1136],"topics\u002Felasticita",[1128,3889,9548,9549,9550,9551],"cenova-elasticita","krizova-elasticita","duchodova-elasticita","mr-tr","c_Ilj6dK9Ey4kbyp6EKogVl_p8zmryyIur0pCOtxlhM",{"id":9554,"title":9555,"body":9556,"course":1128,"courses":659,"created":1129,"description":11097,"extension":661,"meta":11098,"navigation":664,"path":11099,"seo":11100,"sources":11101,"stem":11102,"tags":11103,"type":1950,"updated":677,"__hash__":11108},"topics\u002Ftopics\u002Ffunkce-vice-promennych.md","Kalkul funkcí více proměnných",{"type":9,"value":9557,"toc":11082},[9558,9561,9634,9641,9645,9709,9798,9802,9829,9896,9951,9955,9982,10075,10077,10109,10280,10284,10354,10402,10406,10467,10573,10588,10592,10594,10622,10687,10689,10696,10784,10809,11007,11011,11047,11049],[12,9559,9555],{"id":9560},"kalkul-funkcí-více-proměnných",[724,9562,9563,9564,9567,9568,1343,9597,1888],{},"Většina ekonomických veličin závisí na ",[38,9565,9566],{},"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 ",[883,9569,9571],{"className":9570},[886],[888,9572,9573],{"xmlns":890},[892,9574,9575,9594],{},[895,9576,9577,9580,9582,9584,9586,9588,9590,9592],{},[898,9578,9579],{},"z",[1726,9581,1728],{},[898,9583,2008],{},[1726,9585,1735],{"stretchy":1734},[898,9587,2013],{},[1726,9589,1742],{"separator":1741},[898,9591,2003],{},[1726,9593,1762],{"stretchy":1734},[902,9595,9596],{"encoding":904},"z = f(x, y)",[883,9598,9600],{"className":9599},[886],[888,9601,9602],{"xmlns":890},[892,9603,9604,9631],{},[895,9605,9606,9609,9611,9613,9615,9617,9619,9621,9623,9625,9627,9629],{},[898,9607,9608],{},"w",[1726,9610,1728],{},[898,9612,2008],{},[1726,9614,1735],{"stretchy":1734},[898,9616,2013],{},[1726,9618,1742],{"separator":1741},[898,9620,2003],{},[1726,9622,1742],{"separator":1741},[898,9624,9579],{},[1726,9626,1762],{"stretchy":1734},[1726,9628,1742],{"separator":1741},[1726,9630,1759],{},[902,9632,9633],{"encoding":904},"w = f(x, y, z), \\ldots",[724,9635,9636],{},[1647,9637],{"alt":9638,"className":9639,"src":9640},"imek-funkce-2d-vrstevnice",[210,1651],"\u002Fwiki-assets\u002Fimek-funkce-2d-vrstevnice.jpeg",[115,9642,9644],{"id":9643},"indiferenční-izokvantové-křivky","Indiferenční \u002F izokvantové křivky",[724,9646,9647,9648,9675,9676,9704,9705,9708],{},"Pro ",[883,9649,9651],{"className":9650},[886],[888,9652,9653],{"xmlns":890},[892,9654,9655,9673],{},[895,9656,9657,9659,9661,9663,9665,9667,9669,9671],{},[898,9658,9579],{},[1726,9660,1728],{},[898,9662,2008],{},[1726,9664,1735],{"stretchy":1734},[898,9666,2013],{},[1726,9668,1742],{"separator":1741},[898,9670,2003],{},[1726,9672,1762],{"stretchy":1734},[902,9674,9596],{"encoding":904}," se křivkou s předpisem ",[883,9677,9679],{"className":9678},[886],[888,9680,9681],{"xmlns":890},[892,9682,9683,9701],{},[895,9684,9685,9687,9689,9691,9693,9695,9697,9699],{},[898,9686,2008],{},[1726,9688,1735],{"stretchy":1734},[898,9690,2013],{},[1726,9692,1742],{"separator":1741},[898,9694,2003],{},[1726,9696,1762],{"stretchy":1734},[1726,9698,1728],{},[898,9700,2146],{},[902,9702,9703],{"encoding":904},"f(x, y) = c"," (konstanta) rozumí ",[38,9706,9707],{},"vrstevnice"," funkce. V ekonomii:",[120,9710,9711,9758],{},[123,9712,9713,9716,9717,9753,9754,1888],{},[38,9714,9715],{},"Indiferenční křivky"," užitečnosti ",[883,9718,9720],{"className":9719},[886],[888,9721,9722],{"xmlns":890},[892,9723,9724,9750],{},[895,9725,9726,9728,9730,9736,9738,9744,9746,9748],{},[898,9727,900],{},[1726,9729,1735],{"stretchy":1734},[2275,9731,9732,9734],{},[898,9733,1724],{},[2133,9735,2281],{},[1726,9737,1742],{"separator":1741},[2275,9739,9740,9742],{},[898,9741,1724],{},[2133,9743,2135],{},[1726,9745,1762],{"stretchy":1734},[1726,9747,1728],{},[898,9749,2146],{},[902,9751,9752],{"encoding":904},"U(Q_1, Q_2) = c"," — viz ",[207,9755,9757],{"className":9756,"dataFsResolvedFilePath":878,"href":879},[210],"uzitecnost",[123,9759,9760,9763,9764,9753,9794,1888],{},[38,9761,9762],{},"Izokvanty"," produkce ",[883,9765,9767],{"className":9766},[886],[888,9768,9769],{"xmlns":890},[892,9770,9771,9791],{},[895,9772,9773,9775,9777,9780,9782,9785,9787,9789],{},[898,9774,1724],{},[1726,9776,1735],{"stretchy":1734},[898,9778,9779],{},"L",[1726,9781,1742],{"separator":1741},[898,9783,9784],{},"K",[1726,9786,1762],{"stretchy":1734},[1726,9788,1728],{},[898,9790,2146],{},[902,9792,9793],{"encoding":904},"Q(L, K) = c",[207,9795,9797],{"className":9796,"dataFsResolvedFilePath":857,"href":858},[210],"produkce",[115,9799,9801],{"id":9800},"parciální-derivace","Parciální derivace",[724,9803,9647,9804,9828],{},[883,9805,9807],{"className":9806},[886],[888,9808,9809],{"xmlns":890},[892,9810,9811,9825],{},[895,9812,9813,9815,9817,9819,9821,9823],{},[898,9814,2008],{},[1726,9816,1735],{"stretchy":1734},[898,9818,2013],{},[1726,9820,1742],{"separator":1741},[898,9822,2003],{},[1726,9824,1762],{"stretchy":1734},[902,9826,9827],{"encoding":904},"f(x, y)"," derivujeme jako kdyby druhá proměnná byla konstanta:",[724,9830,9831],{},[883,9832,9834],{"className":9833},[886],[888,9835,9836],{"xmlns":890},[892,9837,9838,9893],{},[895,9839,9840,9848,9850,9865,9867,9869,9877,9879],{},[9151,9841,9842,9844,9846],{},[898,9843,2008],{},[898,9845,2013],{},[1726,9847,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,9849,1728],{},[2330,9851,9852,9859],{},[895,9853,9854,9857],{},[898,9855,9856],{"mathvariant":2377},"∂",[898,9858,2008],{},[895,9860,9861,9863],{},[898,9862,9856],{"mathvariant":2377},[898,9864,2013],{},[1726,9866,1742],{"separator":1741},[5865,9868],{"width":5867},[9151,9870,9871,9873,9875],{},[898,9872,2008],{},[898,9874,2003],{},[1726,9876,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,9878,1728],{},[2330,9880,9881,9887],{},[895,9882,9883,9885],{},[898,9884,9856],{"mathvariant":2377},[898,9886,2008],{},[895,9888,9889,9891],{},[898,9890,9856],{"mathvariant":2377},[898,9892,2003],{},[902,9894,9895],{"encoding":904},"f'_x = \\frac{\\partial f}{\\partial x}, \\qquad f'_y = \\frac{\\partial f}{\\partial y}",[724,9897,9898,9899,1888],{},"Hodnoty v bodě: ",[883,9900,9902],{"className":9901},[886],[888,9903,9904],{"xmlns":890},[892,9905,9906,9948],{},[895,9907,9908,9916,9918,9920,9922,9924,9926,9928,9930,9938,9940,9942,9944,9946],{},[9151,9909,9910,9912,9914],{},[898,9911,2008],{},[898,9913,2013],{},[1726,9915,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,9917,1735],{"stretchy":1734},[898,9919,207],{},[1726,9921,1742],{"separator":1741},[898,9923,2102],{},[1726,9925,1762],{"stretchy":1734},[1726,9927,1742],{"separator":1741},[2289,9929,2291],{},[9151,9931,9932,9934,9936],{},[898,9933,2008],{},[898,9935,2003],{},[1726,9937,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,9939,1735],{"stretchy":1734},[898,9941,207],{},[1726,9943,1742],{"separator":1741},[898,9945,2102],{},[1726,9947,1762],{"stretchy":1734},[902,9949,9950],{"encoding":904},"f'_x(a, b),\\ f'_y(a, b)",[198,9952,9954],{"id":9953},"ekonomické-značení","Ekonomické značení",[724,9956,9957,9958,2703],{},"Pro produkční funkci ",[883,9959,9961],{"className":9960},[886],[888,9962,9963],{"xmlns":890},[892,9964,9965,9979],{},[895,9966,9967,9969,9971,9973,9975,9977],{},[898,9968,1724],{},[1726,9970,1735],{"stretchy":1734},[898,9972,9779],{},[1726,9974,1742],{"separator":1741},[898,9976,9784],{},[1726,9978,1762],{"stretchy":1734},[902,9980,9981],{"encoding":904},"Q(L, K)",[120,9983,9984,10030],{},[123,9985,9986,2471,10006,10009,10010,1762],{},[883,9987,9989],{"className":9988},[886],[888,9990,9991],{"xmlns":890},[892,9992,9993,10003],{},[895,9994,9995],{},[9151,9996,9997,9999,10001],{},[898,9998,1724],{},[898,10000,9779],{},[1726,10002,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[902,10004,10005],{"encoding":904},"Q'_L",[38,10007,10008],{},"mezní produkt práce"," (",[883,10011,10013],{"className":10012},[886],[888,10014,10015],{"xmlns":890},[892,10016,10017,10027],{},[895,10018,10019,10021],{},[898,10020,2815],{},[2275,10022,10023,10025],{},[898,10024,1738],{},[898,10026,9779],{},[902,10028,10029],{"encoding":904},"MP_L",[123,10031,10032,2471,10052,10009,10055,1762],{},[883,10033,10035],{"className":10034},[886],[888,10036,10037],{"xmlns":890},[892,10038,10039,10049],{},[895,10040,10041],{},[9151,10042,10043,10045,10047],{},[898,10044,1724],{},[898,10046,9784],{},[1726,10048,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[902,10050,10051],{"encoding":904},"Q'_K",[38,10053,10054],{},"mezní produkt kapitálu",[883,10056,10058],{"className":10057},[886],[888,10059,10060],{"xmlns":890},[892,10061,10062,10072],{},[895,10063,10064,10066],{},[898,10065,2815],{},[2275,10067,10068,10070],{},[898,10069,1738],{},[898,10071,9784],{},[902,10073,10074],{"encoding":904},"MP_K",[198,10076,2567],{"id":2566},[724,10078,10079,2703],{},[883,10080,10082],{"className":10081},[886],[888,10083,10084],{"xmlns":890},[892,10085,10086,10106],{},[895,10087,10088,10096,10098,10100,10102,10104],{},[9151,10089,10090,10092,10094],{},[898,10091,2008],{},[898,10093,2013],{},[1726,10095,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,10097,1735],{"stretchy":1734},[898,10099,207],{},[1726,10101,1742],{"separator":1741},[898,10103,2102],{},[1726,10105,1762],{"stretchy":1734},[902,10107,10108],{"encoding":904},"f'_x(a, b)",[120,10110,10111,10169],{},[123,10112,10113,10114,10127,10128,10141,10142,10168],{},"rychlost změny ",[883,10115,10117],{"className":10116},[886],[888,10118,10119],{"xmlns":890},[892,10120,10121,10125],{},[895,10122,10123],{},[898,10124,2008],{},[902,10126,2008],{"encoding":904}," vůči ",[883,10129,10131],{"className":10130},[886],[888,10132,10133],{"xmlns":890},[892,10134,10135,10139],{},[895,10136,10137],{},[898,10138,2013],{},[902,10140,2013],{"encoding":904}," při ",[883,10143,10145],{"className":10144},[886],[888,10146,10147],{"xmlns":890},[892,10148,10149,10165],{},[895,10150,10151,10153,10155,10157,10159,10161,10163],{},[898,10152,2013],{},[1726,10154,1728],{},[898,10156,207],{},[1726,10158,1742],{"separator":1741},[898,10160,2003],{},[1726,10162,1728],{},[898,10164,2102],{},[902,10166,10167],{"encoding":904},"x = a, y = b"," (kapitál fixní),",[123,10170,10171,10172,2656,10185,10198,10199,10217,10218,1888],{},"přibližná změna ",[883,10173,10175],{"className":10174},[886],[888,10176,10177],{"xmlns":890},[892,10178,10179,10183],{},[895,10180,10181],{},[898,10182,2008],{},[902,10184,2008],{"encoding":904},[883,10186,10188],{"className":10187},[886],[888,10189,10190],{"xmlns":890},[892,10191,10192,10196],{},[895,10193,10194],{},[898,10195,2013],{},[902,10197,2013],{"encoding":904}," o 1 (a pevném ",[883,10200,10202],{"className":10201},[886],[888,10203,10204],{"xmlns":890},[892,10205,10206,10214],{},[895,10207,10208,10210,10212],{},[898,10209,2003],{},[1726,10211,1728],{},[898,10213,2102],{},[902,10215,10216],{"encoding":904},"y = b","): ",[883,10219,10221],{"className":10220},[886],[888,10222,10223],{"xmlns":890},[892,10224,10225,10277],{},[895,10226,10227,10229,10231,10233,10235,10237,10239,10241,10243,10245,10247,10249,10251,10253,10255,10257,10259,10267,10269,10271,10273,10275],{},[898,10228,2008],{},[1726,10230,1735],{"stretchy":1734},[898,10232,207],{},[1726,10234,2099],{},[2133,10236,2281],{},[1726,10238,1742],{"separator":1741},[898,10240,2102],{},[1726,10242,1762],{"stretchy":1734},[1726,10244,1880],{},[898,10246,2008],{},[1726,10248,1735],{"stretchy":1734},[898,10250,207],{},[1726,10252,1742],{"separator":1741},[898,10254,2102],{},[1726,10256,1762],{"stretchy":1734},[1726,10258,2099],{},[9151,10260,10261,10263,10265],{},[898,10262,2008],{},[898,10264,2013],{},[1726,10266,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,10268,1735],{"stretchy":1734},[898,10270,207],{},[1726,10272,1742],{"separator":1741},[898,10274,2102],{},[1726,10276,1762],{"stretchy":1734},[902,10278,10279],{"encoding":904},"f(a+1, b) \\approx f(a, b) + f'_x(a, b)",[115,10281,10283],{"id":10282},"diferenciál-funkce-dvou-proměnných","Diferenciál funkce dvou proměnných",[724,10285,10286],{},[883,10287,10289],{"className":10288},[886],[888,10290,10291],{"xmlns":890},[892,10292,10293,10351],{},[895,10294,10295,10297,10299,10301,10309,10311,10313,10315,10317,10319,10321,10323,10325,10327,10335,10337,10339,10341,10343,10345,10347,10349],{},[898,10296,2198],{},[898,10298,2008],{},[1726,10300,1728],{},[9151,10302,10303,10305,10307],{},[898,10304,2008],{},[898,10306,2013],{},[1726,10308,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,10310,1735],{"stretchy":1734},[898,10312,2013],{},[1726,10314,1742],{"separator":1741},[898,10316,2003],{},[1726,10318,1762],{"stretchy":1734},[2289,10320,2984],{},[898,10322,2198],{},[898,10324,2013],{},[1726,10326,2099],{},[9151,10328,10329,10331,10333],{},[898,10330,2008],{},[898,10332,2003],{},[1726,10334,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,10336,1735],{"stretchy":1734},[898,10338,2013],{},[1726,10340,1742],{"separator":1741},[898,10342,2003],{},[1726,10344,1762],{"stretchy":1734},[2289,10346,2984],{},[898,10348,2198],{},[898,10350,2003],{},[902,10352,10353],{"encoding":904},"df = f'_x(x, y)\\, dx + f'_y(x, y)\\, dy",[724,10355,2994,10356,10378,10379,10401],{},[883,10357,10359],{"className":10358},[886],[888,10360,10361],{"xmlns":890},[892,10362,10363,10375],{},[895,10364,10365,10367,10369,10371,10373],{},[898,10366,2198],{},[898,10368,2013],{},[1726,10370,1742],{"separator":1741},[898,10372,2198],{},[898,10374,2003],{},[902,10376,10377],{"encoding":904},"dx, dy"," platí ",[883,10380,10382],{"className":10381},[886],[888,10383,10384],{"xmlns":890},[892,10385,10386,10398],{},[895,10387,10388,10390,10392,10394,10396],{},[898,10389,2886],{"mathvariant":2377},[898,10391,2008],{},[1726,10393,1880],{},[898,10395,2198],{},[898,10397,2008],{},[902,10399,10400],{"encoding":904},"\\Delta f \\approx df",". Linearizace přírůstku ve dvou směrech současně.",[115,10403,10405],{"id":10404},"implicitní-funkce","Implicitní funkce",[724,10407,10408,10409,10438,10439,10452,10453,10466],{},"Je-li vztah dán rovnicí ",[883,10410,10412],{"className":10411},[886],[888,10413,10414],{"xmlns":890},[892,10415,10416,10435],{},[895,10417,10418,10421,10423,10425,10427,10429,10431,10433],{},[898,10419,10420],{},"F",[1726,10422,1735],{"stretchy":1734},[898,10424,2013],{},[1726,10426,1742],{"separator":1741},[898,10428,2003],{},[1726,10430,1762],{"stretchy":1734},[1726,10432,1728],{},[2133,10434,2328],{},[902,10436,10437],{"encoding":904},"F(x, y) = 0"," a chceme derivaci ",[883,10440,10442],{"className":10441},[886],[888,10443,10444],{"xmlns":890},[892,10445,10446,10450],{},[895,10447,10448],{},[898,10449,2003],{},[902,10451,2003],{"encoding":904}," podle ",[883,10454,10456],{"className":10455},[886],[888,10457,10458],{"xmlns":890},[892,10459,10460,10464],{},[895,10461,10462],{},[898,10463,2013],{},[902,10465,2013],{"encoding":904}," (nebo naopak):",[724,10468,10469],{},[883,10470,10472],{"className":10471},[886],[888,10473,10474],{"xmlns":890},[892,10475,10476,10570],{},[895,10477,10478,10484,10486,10500,10502,10504,10522,10524,10526,10532,10534,10548,10550,10552],{},[2128,10479,10480,10482],{},[898,10481,2003],{},[1726,10483,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,10485,1728],{},[2330,10487,10488,10494],{},[895,10489,10490,10492],{},[898,10491,2198],{},[898,10493,2003],{},[895,10495,10496,10498],{},[898,10497,2198],{},[898,10499,2013],{},[1726,10501,1728],{},[1726,10503,2228],{},[2330,10505,10506,10514],{},[9151,10507,10508,10510,10512],{},[898,10509,10420],{},[898,10511,2013],{},[1726,10513,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[9151,10515,10516,10518,10520],{},[898,10517,10420],{},[898,10519,2003],{},[1726,10521,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,10523,1742],{"separator":1741},[5865,10525],{"width":5867},[2128,10527,10528,10530],{},[898,10529,2013],{},[1726,10531,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,10533,1728],{},[2330,10535,10536,10542],{},[895,10537,10538,10540],{},[898,10539,2198],{},[898,10541,2013],{},[895,10543,10544,10546],{},[898,10545,2198],{},[898,10547,2003],{},[1726,10549,1728],{},[1726,10551,2228],{},[2330,10553,10554,10562],{},[9151,10555,10556,10558,10560],{},[898,10557,10420],{},[898,10559,2003],{},[1726,10561,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[9151,10563,10564,10566,10568],{},[898,10565,10420],{},[898,10567,2013],{},[1726,10569,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[902,10571,10572],{"encoding":904},"y' = \\frac{dy}{dx} = -\\frac{F'_x}{F'_y}, \\qquad x' = \\frac{dx}{dy} = -\\frac{F'_y}{F'_x}",[724,10574,10575,10576,10579,10580,3877,10584,1888],{},"Tato vzorec dává ",[38,10577,10578],{},"sklon vrstevnice"," — používá se mj. pro výpočet ",[207,10581,10583],{"className":10582,"dataFsResolvedFilePath":857,"href":858},[210],"MRTS",[207,10585,10587],{"className":10586,"dataFsResolvedFilePath":878,"href":879},[210],"MRCS",[115,10589,10591],{"id":10590},"volné-extrémy-funkce-dvou-proměnných","Volné extrémy funkce dvou proměnných",[198,10593,3249],{"id":3248},[724,10595,10596,10597,10621],{},"V bodě extrému ",[883,10598,10600],{"className":10599},[886],[888,10601,10602],{"xmlns":890},[892,10603,10604,10618],{},[895,10605,10606,10608,10610,10612,10614,10616],{},[898,10607,4243],{},[1726,10609,2487],{"stretchy":1734},[898,10611,207],{},[1726,10613,1742],{"separator":1741},[898,10615,2102],{},[1726,10617,2502],{"stretchy":1734},[902,10619,10620],{"encoding":904},"A[a, b]"," musí platit současně:",[724,10623,10624],{},[883,10625,10627],{"className":10626},[886],[888,10628,10629],{"xmlns":890},[892,10630,10631,10684],{},[895,10632,10633,10641,10643,10645,10647,10649,10651,10653,10655,10657,10660,10662,10670,10672,10674,10676,10678,10680,10682],{},[9151,10634,10635,10637,10639],{},[898,10636,2008],{},[898,10638,2013],{},[1726,10640,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,10642,1735],{"stretchy":1734},[898,10644,207],{},[1726,10646,1742],{"separator":1741},[898,10648,2102],{},[1726,10650,1762],{"stretchy":1734},[1726,10652,1728],{},[2133,10654,2328],{},[2289,10656,3974],{},[1726,10658,10659],{},"∧",[2289,10661,3974],{},[9151,10663,10664,10666,10668],{},[898,10665,2008],{},[898,10667,2003],{},[1726,10669,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,10671,1735],{"stretchy":1734},[898,10673,207],{},[1726,10675,1742],{"separator":1741},[898,10677,2102],{},[1726,10679,1762],{"stretchy":1734},[1726,10681,1728],{},[2133,10683,2328],{},[902,10685,10686],{"encoding":904},"f'_x(a, b) = 0 \\;\\wedge\\; f'_y(a, b) = 0",[198,10688,3323],{"id":3322},[724,10690,10691,10692,10695],{},"Definujeme ",[38,10693,10694],{},"diskriminant"," (Hessián zjednodušeně):",[724,10697,10698],{},[883,10699,10701],{"className":10700},[886],[888,10702,10703],{"xmlns":890},[892,10704,10705,10781],{},[895,10706,10707,10709,10711,10713,10715,10717,10719,10721,10737,10739,10755,10757,10759,10775],{},[898,10708,1731],{},[1726,10710,1735],{"stretchy":1734},[898,10712,2013],{},[1726,10714,1742],{"separator":1741},[898,10716,2003],{},[1726,10718,1762],{"stretchy":1734},[1726,10720,1728],{},[9151,10722,10723,10725,10731],{},[898,10724,2008],{},[895,10726,10727,10729],{},[898,10728,2013],{},[898,10730,2013],{},[895,10732,10733,10735],{},[1726,10734,2379],{"mathvariant":2377},[1726,10736,2379],{"mathvariant":2377},[1726,10738,3174],{},[9151,10740,10741,10743,10749],{},[898,10742,2008],{},[895,10744,10745,10747],{},[898,10746,2003],{},[898,10748,2003],{},[895,10750,10751,10753],{},[1726,10752,2379],{"mathvariant":2377},[1726,10754,2379],{"mathvariant":2377},[1726,10756,2228],{},[1726,10758,1735],{"stretchy":1734},[9151,10760,10761,10763,10769],{},[898,10762,2008],{},[895,10764,10765,10767],{},[898,10766,2013],{},[898,10768,2003],{},[895,10770,10771,10773],{},[1726,10772,2379],{"mathvariant":2377},[1726,10774,2379],{"mathvariant":2377},[2128,10776,10777,10779],{},[1726,10778,1762],{"stretchy":1734},[2133,10780,2135],{},[902,10782,10783],{"encoding":904},"D(x, y) = f''_{xx} \\cdot f''_{yy} - (f''_{xy})^2",[724,10785,10786,10787,2703],{},"V podezřelém bodě ",[883,10788,10790],{"className":10789},[886],[888,10791,10792],{"xmlns":890},[892,10793,10794,10806],{},[895,10795,10796,10798,10800,10802,10804],{},[1726,10797,2487],{"stretchy":1734},[898,10799,207],{},[1726,10801,1742],{"separator":1741},[898,10803,2102],{},[1726,10805,2502],{"stretchy":1734},[902,10807,10808],{"encoding":904},"[a, b]",[152,10810,10811,10938,10974],{},[123,10812,10813,10843,10844],{},[38,10814,10815,2703],{},[883,10816,10818],{"className":10817},[886],[888,10819,10820],{"xmlns":890},[892,10821,10822,10840],{},[895,10823,10824,10826,10828,10830,10832,10834,10836,10838],{},[898,10825,1731],{},[1726,10827,1735],{"stretchy":1734},[898,10829,207],{},[1726,10831,1742],{"separator":1741},[898,10833,2102],{},[1726,10835,1762],{"stretchy":1734},[1726,10837,3405],{},[2133,10839,2328],{},[902,10841,10842],{"encoding":904},"D(a, b) > 0"," je to extrém.\n",[120,10845,10846,10892],{},[123,10847,10848,3411,10890],{},[883,10849,10851],{"className":10850},[886],[888,10852,10853],{"xmlns":890},[892,10854,10855,10887],{},[895,10856,10857,10873,10875,10877,10879,10881,10883,10885],{},[9151,10858,10859,10861,10867],{},[898,10860,2008],{},[895,10862,10863,10865],{},[898,10864,2013],{},[898,10866,2013],{},[895,10868,10869,10871],{},[1726,10870,2379],{"mathvariant":2377},[1726,10872,2379],{"mathvariant":2377},[1726,10874,1735],{"stretchy":1734},[898,10876,207],{},[1726,10878,1742],{"separator":1741},[898,10880,2102],{},[1726,10882,1762],{"stretchy":1734},[1726,10884,3405],{},[2133,10886,2328],{},[902,10888,10889],{"encoding":904},"f''_{xx}(a, b) > 0",[38,10891,3772],{},[123,10893,10894,3411,10936],{},[883,10895,10897],{"className":10896},[886],[888,10898,10899],{"xmlns":890},[892,10900,10901,10933],{},[895,10902,10903,10919,10921,10923,10925,10927,10929,10931],{},[9151,10904,10905,10907,10913],{},[898,10906,2008],{},[895,10908,10909,10911],{},[898,10910,2013],{},[898,10912,2013],{},[895,10914,10915,10917],{},[1726,10916,2379],{"mathvariant":2377},[1726,10918,2379],{"mathvariant":2377},[1726,10920,1735],{"stretchy":1734},[898,10922,207],{},[1726,10924,1742],{"separator":1741},[898,10926,2102],{},[1726,10928,1762],{"stretchy":1734},[1726,10930,3444],{},[2133,10932,2328],{},[902,10934,10935],{"encoding":904},"f''_{xx}(a, b) \u003C 0",[38,10937,3714],{},[123,10939,10940,1777,10970,10973],{},[38,10941,10942,2703],{},[883,10943,10945],{"className":10944},[886],[888,10946,10947],{"xmlns":890},[892,10948,10949,10967],{},[895,10950,10951,10953,10955,10957,10959,10961,10963,10965],{},[898,10952,1731],{},[1726,10954,1735],{"stretchy":1734},[898,10956,207],{},[1726,10958,1742],{"separator":1741},[898,10960,2102],{},[1726,10962,1762],{"stretchy":1734},[1726,10964,3444],{},[2133,10966,2328],{},[902,10968,10969],{"encoding":904},"D(a, b) \u003C 0",[38,10971,10972],{},"sedlo"," (v daném bodě extrém není).",[123,10975,10976,11006],{},[38,10977,10978,2703],{},[883,10979,10981],{"className":10980},[886],[888,10982,10983],{"xmlns":890},[892,10984,10985,11003],{},[895,10986,10987,10989,10991,10993,10995,10997,10999,11001],{},[898,10988,1731],{},[1726,10990,1735],{"stretchy":1734},[898,10992,207],{},[1726,10994,1742],{"separator":1741},[898,10996,2102],{},[1726,10998,1762],{"stretchy":1734},[1726,11000,1728],{},[2133,11002,2328],{},[902,11004,11005],{"encoding":904},"D(a, b) = 0"," podmínka nerozhoduje.",[115,11008,11010],{"id":11009},"vázané-extrémy","Vázané extrémy",[724,11012,11013,11014,11043,11044,1888],{},"Pro extrémy s omezující podmínkou ",[883,11015,11017],{"className":11016},[886],[888,11018,11019],{"xmlns":890},[892,11020,11021,11040],{},[895,11022,11023,11026,11028,11030,11032,11034,11036,11038],{},[898,11024,11025],{},"g",[1726,11027,1735],{"stretchy":1734},[898,11029,2013],{},[1726,11031,1742],{"separator":1741},[898,11033,2003],{},[1726,11035,1762],{"stretchy":1734},[1726,11037,1728],{},[2133,11039,2328],{},[902,11041,11042],{"encoding":904},"g(x, y) = 0"," se používá ",[207,11045,793],{"className":11046,"dataFsResolvedFilePath":791,"href":792},[210],[115,11048,1899],{"id":1898},[120,11050,11051,11058,11065],{},[123,11052,11053,1777,11055],{},[38,11054,1906],{},[207,11056,775],{"className":11057,"dataFsResolvedFilePath":773,"href":774},[210],[123,11059,11060,1777,11062],{},[38,11061,1912],{},[207,11063,793],{"className":11064,"dataFsResolvedFilePath":791,"href":792},[210],[123,11066,11067,1777,11069,11073,11074,11077,11078,11081],{},[38,11068,1921],{},[207,11070,11072],{"className":11071,"dataFsResolvedFilePath":857,"href":858},[210],"Produkce"," (parciální derivace = mezní produkty), ",[207,11075,880],{"className":11076,"dataFsResolvedFilePath":878,"href":879},[210]," (parciální derivace = mezní užitečnost), ",[207,11079,3820],{"className":11080,"dataFsResolvedFilePath":848,"href":849},[210]," (vícefaktorový model)",{"title":641,"searchDepth":642,"depth":642,"links":11083},[11084,11085,11089,11090,11091,11095,11096],{"id":9643,"depth":642,"text":9644},{"id":9800,"depth":642,"text":9801,"children":11086},[11087,11088],{"id":9953,"depth":649,"text":9954},{"id":2566,"depth":649,"text":2567},{"id":10282,"depth":642,"text":10283},{"id":10404,"depth":642,"text":10405},{"id":10590,"depth":642,"text":10591,"children":11092},[11093,11094],{"id":3248,"depth":649,"text":3249},{"id":3322,"depth":649,"text":3323},{"id":11009,"depth":642,"text":11010},{"id":1898,"depth":642,"text":1899},"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":9555,"description":11097},[1135],"topics\u002Ffunkce-vice-promennych",[1128,11104,3846,11105,11106,11107],"parcialni-derivace","implicitni-funkce","volne-extremy","indiferencni-krivky","iuWLbpl-7gHnuMDZKTa3RcRM2uCyFhGx9GhXHIN1R_A",{"id":11110,"title":775,"body":11111,"course":1128,"courses":659,"created":1129,"description":11967,"extension":661,"meta":11968,"navigation":664,"path":11969,"seo":11970,"sources":11971,"stem":11972,"tags":11973,"type":1950,"updated":677,"__hash__":11980},"topics\u002Ftopics\u002Fintegral.md",{"type":9,"value":11112,"toc":11957},[11113,11116,11127,11131,11176,11256,11260,11336,11378,11385,11389,11393,11422,11480,11527,11565,11569,11619,11671,11723,11767,11770,11773,11845,11848,11920,11927,11929],[12,11114,775],{"id":11115},"integrál",[724,11117,11118,11119,11122,11123,11126],{},"Druhá polovina kalkulu jedné proměnné. Slouží k ",[38,11120,11121],{},"rekonstrukci totální veličiny z mezní"," (TR z MR, TC z MC) a k výpočtu ",[38,11124,11125],{},"přebytků"," (consumer\u002Fproducer surplus).",[115,11128,11130],{"id":11129},"neurčitý-integrál","Neurčitý integrál",[724,11132,11133],{},[883,11134,11136],{"className":11135},[886],[888,11137,11138],{"xmlns":890},[892,11139,11140,11173],{},[895,11141,11142,11144,11146,11148,11150,11152,11155,11157,11159,11161,11163,11165,11167,11169,11171],{},[898,11143,10420],{},[1726,11145,1735],{"stretchy":1734},[898,11147,2013],{},[1726,11149,1762],{"stretchy":1734},[1726,11151,1728],{},[1726,11153,11154],{},"∫",[898,11156,2008],{},[1726,11158,1735],{"stretchy":1734},[898,11160,2013],{},[1726,11162,1762],{"stretchy":1734},[2289,11164,2984],{},[898,11166,2198],{},[898,11168,2013],{},[1726,11170,2099],{},[898,11172,2775],{},[902,11174,11175],{"encoding":904},"F(x) = \\int f(x)\\, dx + C",[724,11177,4298,11178,2924,11212,8088,11225,11228,11229,1343,11242,11255],{},[883,11179,11181],{"className":11180},[886],[888,11182,11183],{"xmlns":890},[892,11184,11185,11209],{},[895,11186,11187,11193,11195,11197,11199,11201,11203,11205,11207],{},[2128,11188,11189,11191],{},[898,11190,10420],{},[1726,11192,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,11194,1735],{"stretchy":1734},[898,11196,2013],{},[1726,11198,1762],{"stretchy":1734},[1726,11200,1728],{},[898,11202,2008],{},[1726,11204,1735],{"stretchy":1734},[898,11206,2013],{},[1726,11208,1762],{"stretchy":1734},[902,11210,11211],{"encoding":904},"F'(x) = f(x)",[883,11213,11215],{"className":11214},[886],[888,11216,11217],{"xmlns":890},[892,11218,11219,11223],{},[895,11220,11221],{},[898,11222,10420],{},[902,11224,10420],{"encoding":904},[38,11226,11227],{},"primitivní funkce"," k ",[883,11230,11232],{"className":11231},[886],[888,11233,11234],{"xmlns":890},[892,11235,11236,11240],{},[895,11237,11238],{},[898,11239,2008],{},[902,11241,2008],{"encoding":904},[883,11243,11245],{"className":11244},[886],[888,11246,11247],{"xmlns":890},[892,11248,11249,11253],{},[895,11250,11251],{},[898,11252,2775],{},[902,11254,2775],{"encoding":904}," konstanta.",[115,11257,11259],{"id":11258},"určitý-integrál","Určitý integrál",[724,11261,11262],{},[883,11263,11265],{"className":11264},[886],[888,11266,11267],{"xmlns":890},[892,11268,11269,11333],{},[895,11270,11271,11279,11281,11283,11285,11287,11289,11291,11293,11295,11297,11299,11301,11303,11305,11313,11315,11317,11319,11321,11323,11325,11327,11329,11331],{},[9151,11272,11273,11275,11277],{},[1726,11274,11154],{},[898,11276,207],{},[898,11278,2102],{},[898,11280,2008],{},[1726,11282,1735],{"stretchy":1734},[898,11284,2013],{},[1726,11286,1762],{"stretchy":1734},[2289,11288,2984],{},[898,11290,2198],{},[898,11292,2013],{},[1726,11294,1728],{},[1726,11296,2487],{"stretchy":1734},[898,11298,10420],{},[1726,11300,1735],{"stretchy":1734},[898,11302,2013],{},[1726,11304,1762],{"stretchy":1734},[9151,11306,11307,11309,11311],{},[1726,11308,2502],{"stretchy":1734},[898,11310,207],{},[898,11312,2102],{},[1726,11314,1728],{},[898,11316,10420],{},[1726,11318,1735],{"stretchy":1734},[898,11320,2102],{},[1726,11322,1762],{"stretchy":1734},[1726,11324,2228],{},[898,11326,10420],{},[1726,11328,1735],{"stretchy":1734},[898,11330,207],{},[1726,11332,1762],{"stretchy":1734},[902,11334,11335],{"encoding":904},"\\int_a^b f(x)\\, dx = [F(x)]_a^b = F(b) - F(a)",[724,11337,11338,11339,1777,11342,11355,11356,11377],{},"Geometricky ",[38,11340,11341],{},"plocha pod grafem",[883,11343,11345],{"className":11344},[886],[888,11346,11347],{"xmlns":890},[892,11348,11349,11353],{},[895,11350,11351],{},[898,11352,2008],{},[902,11354,2008],{"encoding":904}," na intervalu ",[883,11357,11359],{"className":11358},[886],[888,11360,11361],{"xmlns":890},[892,11362,11363,11375],{},[895,11364,11365,11367,11369,11371,11373],{},[1726,11366,2487],{"stretchy":1734},[898,11368,207],{},[1726,11370,1742],{"separator":1741},[898,11372,2102],{},[1726,11374,2502],{"stretchy":1734},[902,11376,10808],{"encoding":904}," (orientovaná).",[724,11379,11380],{},[1647,11381],{"alt":11382,"className":11383,"src":11384},"imek-integral-plocha",[210,1651],"\u002Fwiki-assets\u002Fimek-integral-plocha.jpeg",[115,11386,11388],{"id":11387},"aplikace-v-ekonomii","Aplikace v ekonomii",[198,11390,11392],{"id":11391},"příklad-tr-z-mr","Příklad — TR z MR",[724,11394,11395,11396,1888],{},"Mezní příjem ",[883,11397,11399],{"className":11398},[886],[888,11400,11401],{"xmlns":890},[892,11402,11403,11419],{},[895,11404,11405,11407,11409,11411,11413,11415,11417],{},[898,11406,2815],{},[898,11408,3984],{},[1726,11410,1728],{},[2133,11412,3087],{},[1726,11414,2228],{},[2133,11416,2135],{},[898,11418,1724],{},[902,11420,11421],{"encoding":904},"MR = 100 - 2Q",[724,11423,11424],{},[883,11425,11427],{"className":11426},[886],[888,11428,11429],{"xmlns":890},[892,11430,11431,11477],{},[895,11432,11433,11435,11437,11439,11441,11443,11445,11447,11449,11451,11453,11455,11457,11459,11461,11463,11465,11467,11473,11475],{},[898,11434,2772],{},[898,11436,3984],{},[1726,11438,1728],{},[1726,11440,11154],{},[1726,11442,1735],{"stretchy":1734},[2133,11444,3087],{},[1726,11446,2228],{},[2133,11448,2135],{},[898,11450,1724],{},[1726,11452,1762],{"stretchy":1734},[2289,11454,2984],{},[898,11456,2198],{},[898,11458,1724],{},[1726,11460,1728],{},[2133,11462,3087],{},[898,11464,1724],{},[1726,11466,2228],{},[2128,11468,11469,11471],{},[898,11470,1724],{},[2133,11472,2135],{},[1726,11474,2099],{},[898,11476,2146],{},[902,11478,11479],{"encoding":904},"TR = \\int (100 - 2Q)\\, dQ = 100Q - Q^2 + c",[724,11481,11482,11483,3411,11509,2703],{},"Okrajová podmínka ",[883,11484,11486],{"className":11485},[886],[888,11487,11488],{"xmlns":890},[892,11489,11490,11506],{},[895,11491,11492,11494,11496,11498,11500,11502,11504],{},[898,11493,2772],{},[898,11495,3984],{},[1726,11497,1735],{"stretchy":1734},[2133,11499,2328],{},[1726,11501,1762],{"stretchy":1734},[1726,11503,1728],{},[2133,11505,2328],{},[902,11507,11508],{"encoding":904},"TR(0) = 0",[883,11510,11512],{"className":11511},[886],[888,11513,11514],{"xmlns":890},[892,11515,11516,11524],{},[895,11517,11518,11520,11522],{},[898,11519,2146],{},[1726,11521,1728],{},[2133,11523,2328],{},[902,11525,11526],{"encoding":904},"c = 0",[724,11528,11529],{},[883,11530,11532],{"className":11531},[886],[888,11533,11534],{"xmlns":890},[892,11535,11536,11562],{},[895,11537,11538,11540,11542,11544,11546,11548,11550,11552,11554,11556],{},[898,11539,2772],{},[898,11541,3984],{},[1726,11543,1735],{"stretchy":1734},[898,11545,1724],{},[1726,11547,1762],{"stretchy":1734},[1726,11549,1728],{},[2133,11551,3087],{},[898,11553,1724],{},[1726,11555,2228],{},[2128,11557,11558,11560],{},[898,11559,1724],{},[2133,11561,2135],{},[902,11563,11564],{"encoding":904},"TR(Q) = 100Q - Q^2",[198,11566,11568],{"id":11567},"příklad-tc-z-mc","Příklad — TC z MC",[724,11570,11571,11572,11598,11599,1888],{},"Mezní náklady ",[883,11573,11575],{"className":11574},[886],[888,11576,11577],{"xmlns":890},[892,11578,11579,11595],{},[895,11580,11581,11583,11585,11587,11589,11591,11593],{},[898,11582,2815],{},[898,11584,2775],{},[1726,11586,1728],{},[2133,11588,2135],{},[1726,11590,2099],{},[2133,11592,2836],{},[898,11594,1724],{},[902,11596,11597],{"encoding":904},"MC = 2 + 0{,}2 Q",", fixní náklady ",[883,11600,11602],{"className":11601},[886],[888,11603,11604],{"xmlns":890},[892,11605,11606,11616],{},[895,11607,11608,11610,11612,11614],{},[898,11609,10420],{},[898,11611,2775],{},[1726,11613,1728],{},[2133,11615,3087],{},[902,11617,11618],{"encoding":904},"FC = 100",[724,11620,11621],{},[883,11622,11624],{"className":11623},[886],[888,11625,11626],{"xmlns":890},[892,11627,11628,11668],{},[895,11629,11630,11632,11634,11636,11638,11640,11642,11644,11646,11648,11650,11652,11654,11656,11658,11664,11666],{},[898,11631,2772],{},[898,11633,2775],{},[1726,11635,1728],{},[1726,11637,11154],{},[898,11639,2815],{},[898,11641,2775],{},[2289,11643,2984],{},[898,11645,2198],{},[898,11647,1724],{},[1726,11649,1728],{},[2133,11651,2135],{},[898,11653,1724],{},[1726,11655,2099],{},[2133,11657,2791],{},[2128,11659,11660,11662],{},[898,11661,1724],{},[2133,11663,2135],{},[1726,11665,2099],{},[898,11667,2146],{},[902,11669,11670],{"encoding":904},"TC = \\int MC\\, dQ = 2Q + 0{,}1 Q^2 + c",[724,11672,11482,11673,3411,11705,2703],{},[883,11674,11676],{"className":11675},[886],[888,11677,11678],{"xmlns":890},[892,11679,11680,11702],{},[895,11681,11682,11684,11686,11688,11690,11692,11694,11696,11698,11700],{},[898,11683,2772],{},[898,11685,2775],{},[1726,11687,1735],{"stretchy":1734},[2133,11689,2328],{},[1726,11691,1762],{"stretchy":1734},[1726,11693,1728],{},[898,11695,10420],{},[898,11697,2775],{},[1726,11699,1728],{},[2133,11701,3087],{},[902,11703,11704],{"encoding":904},"TC(0) = FC = 100",[883,11706,11708],{"className":11707},[886],[888,11709,11710],{"xmlns":890},[892,11711,11712,11720],{},[895,11713,11714,11716,11718],{},[898,11715,2146],{},[1726,11717,1728],{},[2133,11719,3087],{},[902,11721,11722],{"encoding":904},"c = 100",[724,11724,11725],{},[883,11726,11728],{"className":11727},[886],[888,11729,11730],{"xmlns":890},[892,11731,11732,11764],{},[895,11733,11734,11736,11738,11740,11742,11744,11746,11748,11750,11752,11754,11756,11758],{},[898,11735,2772],{},[898,11737,2775],{},[1726,11739,1735],{"stretchy":1734},[898,11741,1724],{},[1726,11743,1762],{"stretchy":1734},[1726,11745,1728],{},[2133,11747,3087],{},[1726,11749,2099],{},[2133,11751,2135],{},[898,11753,1724],{},[1726,11755,2099],{},[2133,11757,2791],{},[2128,11759,11760,11762],{},[898,11761,1724],{},[2133,11763,2135],{},[902,11765,11766],{"encoding":904},"TC(Q) = 100 + 2Q + 0{,}1 Q^2",[198,11768,820],{"id":11769},"přebytek-spotřebitele-a-výrobce",[724,11771,11772],{},"Přebytek spotřebitele:",[724,11774,11775],{},[883,11776,11778],{"className":11777},[886],[888,11779,11780],{"xmlns":890},[892,11781,11782,11842],{},[895,11783,11784,11786,11788,11790,11796,11798,11800,11812,11814,11816,11818,11820,11822,11824,11826,11828,11834,11836],{},[898,11785,2775],{},[898,11787,8659],{},[1726,11789,1735],{"stretchy":1734},[2275,11791,11792,11794],{},[898,11793,1724],{},[2133,11795,2328],{},[1726,11797,1762],{"stretchy":1734},[1726,11799,1728],{},[9151,11801,11802,11804,11806],{},[1726,11803,11154],{},[2133,11805,2328],{},[2275,11807,11808,11810],{},[898,11809,1724],{},[2133,11811,2328],{},[898,11813,1731],{},[1726,11815,1735],{"stretchy":1734},[898,11817,1724],{},[1726,11819,1762],{"stretchy":1734},[2289,11821,2984],{},[898,11823,2198],{},[898,11825,1724],{},[1726,11827,2228],{},[2275,11829,11830,11832],{},[898,11831,1738],{},[2133,11833,2328],{},[2289,11835,2984],{},[2275,11837,11838,11840],{},[898,11839,1724],{},[2133,11841,2328],{},[902,11843,11844],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\, dQ - P_0\\, Q_0",[724,11846,11847],{},"Přebytek výrobce:",[724,11849,11850],{},[883,11851,11853],{"className":11852},[886],[888,11854,11855],{"xmlns":890},[892,11856,11857,11917],{},[895,11858,11859,11861,11863,11865,11871,11873,11875,11881,11883,11889,11891,11903,11905,11907,11909,11911,11913,11915],{},[898,11860,1738],{},[898,11862,8659],{},[1726,11864,1735],{"stretchy":1734},[2275,11866,11867,11869],{},[898,11868,1724],{},[2133,11870,2328],{},[1726,11872,1762],{"stretchy":1734},[1726,11874,1728],{},[2275,11876,11877,11879],{},[898,11878,1738],{},[2133,11880,2328],{},[2289,11882,2984],{},[2275,11884,11885,11887],{},[898,11886,1724],{},[2133,11888,2328],{},[1726,11890,2228],{},[9151,11892,11893,11895,11897],{},[1726,11894,11154],{},[2133,11896,2328],{},[2275,11898,11899,11901],{},[898,11900,1724],{},[2133,11902,2328],{},[898,11904,8659],{},[1726,11906,1735],{"stretchy":1734},[898,11908,1724],{},[1726,11910,1762],{"stretchy":1734},[2289,11912,2984],{},[898,11914,2198],{},[898,11916,1724],{},[902,11918,11919],{"encoding":904},"PS(Q_0) = P_0\\, Q_0 - \\int_0^{Q_0} S(Q)\\, dQ",[724,11921,11922,11923,1888],{},"Detailně viz ",[207,11924,11926],{"className":11925,"dataFsResolvedFilePath":800,"href":801},[210],"Poptávka a nabídka",[115,11928,1899],{"id":1898},[120,11930,11931,11938,11945],{},[123,11932,11933,1777,11935],{},[38,11934,1906],{},[207,11936,766],{"className":11937,"dataFsResolvedFilePath":764,"href":765},[210],[123,11939,11940,1777,11942],{},[38,11941,1912],{},[207,11943,784],{"className":11944,"dataFsResolvedFilePath":782,"href":783},[210],[123,11946,11947,1777,11949,11952,11953,11956],{},[38,11948,1921],{},[207,11950,3815],{"className":11951,"dataFsResolvedFilePath":827,"href":828},[210]," (TR\u002FTC), ",[207,11954,11926],{"className":11955,"dataFsResolvedFilePath":800,"href":801},[210]," (přebytky CS\u002FPS)",{"title":641,"searchDepth":642,"depth":642,"links":11958},[11959,11960,11961,11966],{"id":11129,"depth":642,"text":11130},{"id":11258,"depth":642,"text":11259},{"id":11387,"depth":642,"text":11388,"children":11962},[11963,11964,11965],{"id":11391,"depth":649,"text":11392},{"id":11567,"depth":649,"text":11568},{"id":11769,"depth":649,"text":820},{"id":1898,"depth":642,"text":1899},"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":11967},[1135],"topics\u002Fintegral",[1128,11974,11975,11976,11977,11978,11979],"integral","neurcity","urcity","primitivni-funkce","tr-z-mr","tc-z-mc","H1oOmn3Z5yZ_KZm1LLzfN_DVUhYSxx7eveFc7CASwZY",{"id":11982,"title":11983,"body":11984,"course":1128,"courses":659,"created":9541,"description":641,"extension":661,"meta":16249,"navigation":664,"path":16250,"seo":16251,"sources":16252,"stem":16253,"tags":16254,"type":1950,"updated":677,"__hash__":16260},"topics\u002Ftopics\u002Fis-lm.md","IS-LM analýza — simultánní rovnováha trhu zboží a peněz",{"type":9,"value":11985,"toc":16237},[11986,11989,11993,12137,12144,12148,12218,12256,12359,12363,12393,12459,12506,12509,12578,12581,12616,12652,12656,12704,12711,12757,12803,12806,12885,12982,13065,13069,13113,13143,13149,13178,13200,13250,13303,13369,13372,13438,13467,13526,13542,13629,13727,13858,13862,14019,14168,14548,14552,14555,14614,14617,14703,14731,14769,14772,14809,14849,14883,14885,14922,14954,15052,15057,15181,15233,15315,15454,15458,15578,15585,15696,15703,15705,16180,16182],[12,11987,11983],{"id":11988},"is-lm-analýza-simultánní-rovnováha-trhu-zboží-a-peněz",[115,11990,11992],{"id":11991},"tldr","TL;DR",[724,11994,11995,11998,11999,10009,12002,12015,12016,12030,12031,12034,12035,1343,12038,12041,12042,1343,12045,12048,12049,1777,12052,12082,12083,12086,12087,1343,12101,12114,12115,12118,12119,1847],{},[38,11996,11997],{},"IS-LM"," je makroekonomický model se ",[38,12000,12001],{},"dvěma neznámými",[883,12003,12005],{"className":12004},[886],[888,12006,12007],{"xmlns":890},[892,12008,12009,12013],{},[895,12010,12011],{},[898,12012,1745],{},[902,12014,1745],{"encoding":904}," — národní důchod a ",[883,12017,12019],{"className":12018},[886],[888,12020,12021],{"xmlns":890},[892,12022,12023,12028],{},[895,12024,12025],{},[898,12026,12027],{},"r",[902,12029,12027],{"encoding":904}," — úroková míra) a ",[38,12032,12033],{},"dvěma trhy",": trhem zboží (křivka ",[38,12036,12037],{},"IS",[614,12039,12040],{},"Investment = Savings",") a trhem peněz (křivka ",[38,12043,12044],{},"LM",[614,12046,12047],{},"Liquidity of Money","). Průsečík obou křivek určuje ",[38,12050,12051],{},"simultánní rovnováhu",[883,12053,12055],{"className":12054},[886],[888,12056,12057],{"xmlns":890},[892,12058,12059,12079],{},[895,12060,12061,12063,12069,12071,12077],{},[1726,12062,1735],{"stretchy":1734},[2128,12064,12065,12067],{},[898,12066,1745],{},[898,12068,4240],{},[1726,12070,1742],{"separator":1741},[2128,12072,12073,12075],{},[898,12074,12027],{},[898,12076,4240],{},[1726,12078,1762],{"stretchy":1734},[902,12080,12081],{"encoding":904},"(Y^E, r^E)",", v níž jsou oba trhy vyvážené zároveň. Model je klíčovým nástrojem pro analýzu ",[38,12084,12085],{},"fiskální politiky"," (posun IS změnou ",[883,12088,12090],{"className":12089},[886],[888,12091,12092],{"xmlns":890},[892,12093,12094,12099],{},[895,12095,12096],{},[898,12097,12098],{},"G",[902,12100,12098],{"encoding":904},[883,12102,12104],{"className":12103},[886],[888,12105,12106],{"xmlns":890},[892,12107,12108,12112],{},[895,12109,12110],{},[898,12111,2772],{},[902,12113,2772],{"encoding":904},") a ",[38,12116,12117],{},"monetární politiky"," (posun LM změnou nabídky peněz ",[883,12120,12122],{"className":12121},[886],[888,12123,12124],{"xmlns":890},[892,12125,12126,12134],{},[895,12127,12128],{},[2128,12129,12130,12132],{},[898,12131,2815],{},[1726,12133,4342],{},[902,12135,12136],{"encoding":904},"M^*",[724,12138,12139],{},[1647,12140],{"alt":12141,"className":12142,"src":12143},"imek-is-lm-model",[210,1651],"\u002Fwiki-assets\u002Fimek-is-lm-model.jpeg",[115,12145,12147],{"id":12146},"motivace-proč-přejít-od-c-i-g-x-k-is-lm","Motivace — proč přejít od C-I-G-X k IS-LM",[724,12149,12150,12151,12155,12156,10009,12159,12182,12183,12186,12187,12203,12204,12217],{},"V modelech ",[207,12152,12154],{"className":12153,"dataFsResolvedFilePath":934,"href":935},[210],"C-I, C-I-G a C-I-G-X"," byly ",[38,12157,12158],{},"investice pokládány za konstantní",[883,12160,12162],{"className":12161},[886],[888,12163,12164],{"xmlns":890},[892,12165,12166,12179],{},[895,12167,12168,12171,12173],{},[898,12169,12170],{},"I",[1726,12172,1728],{},[2128,12174,12175,12177],{},[898,12176,12170],{},[1726,12178,4342],{},[902,12180,12181],{"encoding":904},"I = I^*","). To není realistické — investice firem závisejí na ",[38,12184,12185],{},"ceně peněz",", tedy na ",[38,12188,12189,12190],{},"úrokové míře ",[883,12191,12193],{"className":12192},[886],[888,12194,12195],{"xmlns":890},[892,12196,12197,12201],{},[895,12198,12199],{},[898,12200,12027],{},[902,12202,12027],{"encoding":904},": čím vyšší ",[883,12205,12207],{"className":12206},[886],[888,12208,12209],{"xmlns":890},[892,12210,12211,12215],{},[895,12212,12213],{},[898,12214,12027],{},[902,12216,12027],{"encoding":904},", tím dražší úvěr a tím méně investic. IS-LM analýza proto zavádí:",[120,12219,12220,12250],{},[123,12221,12222,1777,12225,12249],{},[38,12223,12224],{},"funkci investic",[883,12226,12228],{"className":12227},[886],[888,12229,12230],{"xmlns":890},[892,12231,12232,12246],{},[895,12233,12234,12236,12238,12240,12242,12244],{},[898,12235,12170],{},[1726,12237,1728],{},[898,12239,12170],{},[1726,12241,1735],{"stretchy":1734},[898,12243,12027],{},[1726,12245,1762],{"stretchy":1734},[902,12247,12248],{"encoding":904},"I = I(r)"," jako klesající funkci úrokové míry,",[123,12251,12252,12255],{},[38,12253,12254],{},"trh peněz",", jehož rovnováha (poptávka = nabídka peněz) doplňuje druhou rovnici potřebnou pro určení obou neznámých.",[3859,12257,12258],{},[724,12259,12260,12262,12263,12282,12283,12310,12311,12324,12325,12354,12355,12358],{},[883,12261,4400],{}," Pozor — dvě neznámé vyžadují dvě rovnice\nV modelech ",[883,12264,12266],{"className":12265},[886],[888,12267,12268],{"xmlns":890},[892,12269,12270,12279],{},[895,12271,12272,12274,12277],{},[898,12273,2775],{},[2289,12275,12276],{},"-",[898,12278,12170],{},[902,12280,12281],{"encoding":904},"C\\text{-}I"," až ",[883,12284,12286],{"className":12285},[886],[888,12287,12288],{"xmlns":890},[892,12289,12290,12307],{},[895,12291,12292,12294,12296,12298,12300,12302,12304],{},[898,12293,2775],{},[2289,12295,12276],{},[898,12297,12170],{},[2289,12299,12276],{},[898,12301,12098],{},[2289,12303,12276],{},[898,12305,12306],{},"X",[902,12308,12309],{"encoding":904},"C\\text{-}I\\text{-}G\\text{-}X"," byla hlavní neznámou jen ",[883,12312,12314],{"className":12313},[886],[888,12315,12316],{"xmlns":890},[892,12317,12318,12322],{},[895,12319,12320],{},[898,12321,1745],{},[902,12323,1745],{"encoding":904},". V IS-LM jsou ",[38,12326,12327,12328,3877,12341],{},"dvě neznámé ",[883,12329,12331],{"className":12330},[886],[888,12332,12333],{"xmlns":890},[892,12334,12335,12339],{},[895,12336,12337],{},[898,12338,1745],{},[902,12340,1745],{"encoding":904},[883,12342,12344],{"className":12343},[886],[888,12345,12346],{"xmlns":890},[892,12347,12348,12352],{},[895,12349,12350],{},[898,12351,12027],{},[902,12353,12027],{"encoding":904},", a proto potřebujeme ",[38,12356,12357],{},"dvě rovnice",": jednu z trhu zboží (křivka IS) a jednu z trhu peněz (křivka LM).",[115,12360,12362],{"id":12361},"funkce-investic-a-funkce-spotřeby","Funkce investic a funkce spotřeby",[724,12364,12365,12366,12379,12380,2703],{},"Lineární závislost investic ",[883,12367,12369],{"className":12368},[886],[888,12370,12371],{"xmlns":890},[892,12372,12373,12377],{},[895,12374,12375],{},[898,12376,12170],{},[902,12378,12170],{"encoding":904}," na úrokové míře ",[883,12381,12383],{"className":12382},[886],[888,12384,12385],{"xmlns":890},[892,12386,12387,12391],{},[895,12388,12389],{},[898,12390,12027],{},[902,12392,12027],{"encoding":904},[724,12394,12395],{},[883,12396,12398],{"className":12397},[886],[888,12399,12400],{"xmlns":890},[892,12401,12402,12456],{},[895,12403,12404,12406,12408,12410,12412,12414,12416,12418,12420,12422,12424,12426,12428,12430,12432,12434,12436,12438,12440,12442,12444,12447,12449,12451,12454],{},[898,12405,12170],{},[1726,12407,1728],{},[898,12409,12170],{},[1726,12411,1735],{"stretchy":1734},[898,12413,12027],{},[1726,12415,1762],{"stretchy":1734},[1726,12417,1728],{},[898,12419,2146],{},[898,12421,12027],{},[1726,12423,2099],{},[898,12425,2198],{},[1726,12427,1742],{"separator":1741},[5865,12429],{"width":5867},[898,12431,2146],{},[1726,12433,3444],{},[2133,12435,2328],{},[1726,12437,1742],{"separator":1741},[2289,12439,2291],{},[898,12441,2198],{},[1726,12443,3405],{},[2133,12445,12446],{},"0.",[5865,12448],{"width":5867},[1726,12450,1735],{"stretchy":1734},[2133,12452,12453],{},"7.11",[1726,12455,1762],{"stretchy":1734},[902,12457,12458],{"encoding":904},"I = I(r) = cr + d, \\qquad c \u003C 0,\\ d > 0. \\qquad (7.11)",[120,12460,12461,12482],{},[123,12462,12463,12481],{},[883,12464,12466],{"className":12465},[886],[888,12467,12468],{"xmlns":890},[892,12469,12470,12478],{},[895,12471,12472,12474,12476],{},[898,12473,2198],{},[1726,12475,3405],{},[2133,12477,2328],{},[902,12479,12480],{"encoding":904},"d > 0"," zřejmé,",[123,12483,12484,12502,12503,1888],{},[883,12485,12487],{"className":12486},[886],[888,12488,12489],{"xmlns":890},[892,12490,12491,12499],{},[895,12492,12493,12495,12497],{},[898,12494,2146],{},[1726,12496,3444],{},[2133,12498,2328],{},[902,12500,12501],{"encoding":904},"c \u003C 0",", protože růst úrokové míry tlumí investice — funkce investic je ",[38,12504,12505],{},"klesající",[724,12507,12508],{},"Spotřeba zůstává lineární funkcí důchodu:",[724,12510,12511],{},[883,12512,12514],{"className":12513},[886],[888,12515,12516],{"xmlns":890},[892,12517,12518,12575],{},[895,12519,12520,12522,12524,12526,12528,12530,12532,12534,12536,12538,12540,12542,12544,12546,12548,12550,12552,12554,12556,12558,12560,12562,12564,12566,12568,12570,12573],{},[898,12521,2775],{},[1726,12523,1728],{},[898,12525,2775],{},[1726,12527,1735],{"stretchy":1734},[898,12529,1745],{},[1726,12531,1762],{"stretchy":1734},[1726,12533,1728],{},[898,12535,207],{},[898,12537,1745],{},[1726,12539,2099],{},[898,12541,2102],{},[1726,12543,1742],{"separator":1741},[5865,12545],{"width":5867},[2133,12547,2328],{},[1726,12549,3444],{},[898,12551,207],{},[1726,12553,3444],{},[2133,12555,2281],{},[1726,12557,1742],{"separator":1741},[2289,12559,2291],{},[898,12561,2102],{},[1726,12563,3405],{},[2133,12565,12446],{},[5865,12567],{"width":5867},[1726,12569,1735],{"stretchy":1734},[2133,12571,12572],{},"7.12",[1726,12574,1762],{"stretchy":1734},[902,12576,12577],{"encoding":904},"C = C(Y) = aY + b, \\qquad 0 \u003C a \u003C 1,\\ b > 0. \\qquad (7.12)",[724,12579,12580],{},"Podmínka rovnováhy na trhu zboží:",[724,12582,12583],{},[883,12584,12586],{"className":12585},[886],[888,12587,12588],{"xmlns":890},[892,12589,12590,12613],{},[895,12591,12592,12594,12596,12598,12600,12602,12604,12606,12608,12611],{},[898,12593,1745],{},[1726,12595,1728],{},[898,12597,2775],{},[1726,12599,2099],{},[898,12601,12170],{},[898,12603,1888],{"mathvariant":2377},[5865,12605],{"width":5867},[1726,12607,1735],{"stretchy":1734},[2133,12609,12610],{},"7.13",[1726,12612,1762],{"stretchy":1734},[902,12614,12615],{"encoding":904},"Y = C + I. \\qquad (7.13)",[724,12617,12618,12619,1777,12622,12648,12649,1888],{},"To dává ",[38,12620,12621],{},"tři rovnice o čtyřech neznámých",[883,12623,12625],{"className":12624},[886],[888,12626,12627],{"xmlns":890},[892,12628,12629,12645],{},[895,12630,12631,12633,12635,12637,12639,12641,12643],{},[898,12632,1745],{},[1726,12634,1742],{"separator":1741},[898,12636,2775],{},[1726,12638,1742],{"separator":1741},[898,12640,12170],{},[1726,12642,1742],{"separator":1741},[898,12644,12027],{},[902,12646,12647],{"encoding":904},"Y, C, I, r",". Pro jednoznačné určení rovnováhy potřebujeme čtvrtou rovnici — odvodí se z ",[38,12650,12651],{},"rovnováhy na trhu peněz",[115,12653,12655],{"id":12654},"křivka-is-rovnováha-na-trhu-zboží","Křivka IS — rovnováha na trhu zboží",[724,12657,12658,12659,5556,12681,12699,12700,12703],{},"Podmínka (7.13) reprezentuje rovnováhu na trhu zboží, protože s ohledem na ",[883,12660,12662],{"className":12661},[886],[888,12663,12664],{"xmlns":890},[892,12665,12666,12678],{},[895,12667,12668,12670,12672,12674,12676],{},[898,12669,1745],{},[1726,12671,1728],{},[898,12673,2775],{},[1726,12675,2099],{},[898,12677,8659],{},[902,12679,12680],{"encoding":904},"Y = C + S",[883,12682,12684],{"className":12683},[886],[888,12685,12686],{"xmlns":890},[892,12687,12688,12696],{},[895,12689,12690,12692,12694],{},[898,12691,12170],{},[1726,12693,1728],{},[898,12695,8659],{},[902,12697,12698],{"encoding":904},"I = S"," (plánované ",[38,12701,12702],{},"investice = úspory","). Dosazením (7.11) a (7.12) do (7.13):",[724,12705,12706],{},[1647,12707],{"alt":12708,"className":12709,"src":12710},"imek-odvozeni-is-4panelu",[210,1651],"\u002Fwiki-assets\u002Fimek-odvozeni-is-4panelu.jpeg",[724,12712,12713],{},[883,12714,12716],{"className":12715},[886],[888,12717,12718],{"xmlns":890},[892,12719,12720,12754],{},[895,12721,12722,12724,12726,12728,12730,12732,12734,12736,12738,12740,12742,12744,12746,12748,12750,12752],{},[898,12723,1745],{},[1726,12725,1728],{},[1726,12727,1735],{"stretchy":1734},[898,12729,207],{},[898,12731,1745],{},[1726,12733,2099],{},[898,12735,2102],{},[1726,12737,1762],{"stretchy":1734},[1726,12739,2099],{},[1726,12741,1735],{"stretchy":1734},[898,12743,2146],{},[898,12745,12027],{},[1726,12747,2099],{},[898,12749,2198],{},[1726,12751,1762],{"stretchy":1734},[1726,12753,1742],{"separator":1741},[902,12755,12756],{"encoding":904},"Y = (aY + b) + (cr + d),",[724,12758,12759],{},[883,12760,12762],{"className":12761},[886],[888,12763,12764],{"xmlns":890},[892,12765,12766,12800],{},[895,12767,12768,12770,12772,12774,12776,12778,12780,12782,12784,12786,12788,12790,12792,12794,12796,12798],{},[1726,12769,1735],{"stretchy":1734},[2133,12771,2281],{},[1726,12773,2228],{},[898,12775,207],{},[1726,12777,1762],{"stretchy":1734},[898,12779,1745],{},[1726,12781,2228],{},[898,12783,2146],{},[898,12785,12027],{},[1726,12787,2228],{},[898,12789,2102],{},[1726,12791,2228],{},[898,12793,2198],{},[1726,12795,1728],{},[2133,12797,2328],{},[1726,12799,1742],{"separator":1741},[902,12801,12802],{"encoding":904},"(1 - a)Y - cr - b - d = 0,",[724,12804,12805],{},"odkud",[724,12807,12808],{},[883,12809,12811],{"className":12810},[886],[888,12812,12813],{"xmlns":890},[892,12814,12815,12882],{},[895,12816,12817,12873,12875,12877,12880],{},[12818,12819,12821],"menclose",{"notation":12820},"box",[2326,12822,12823],{"scriptlevel":2328,"displaystyle":1734},[2326,12824,12825],{"scriptlevel":2328,"displaystyle":1734},[2326,12826,12827],{"scriptlevel":2328,"displaystyle":1741},[895,12828,12829,12831,12833,12835,12847,12849,12851,12853,12871],{},[2289,12830,2984],{},[898,12832,1745],{},[1726,12834,1728],{},[2330,12836,12837,12839],{},[898,12838,2146],{},[895,12840,12841,12843,12845],{},[2133,12842,2281],{},[1726,12844,2228],{},[898,12846,207],{},[2289,12848,2984],{},[898,12850,12027],{},[1726,12852,2099],{},[2330,12854,12855,12863],{},[895,12856,12857,12859,12861],{},[898,12858,2102],{},[1726,12860,2099],{},[898,12862,2198],{},[895,12864,12865,12867,12869],{},[2133,12866,2281],{},[1726,12868,2228],{},[898,12870,207],{},[2289,12872,2984],{},[5865,12874],{"width":5867},[1726,12876,1735],{"stretchy":1734},[2133,12878,12879],{},"7.14",[1726,12881,1762],{"stretchy":1734},[902,12883,12884],{"encoding":904},"\\boxed{\\,Y = \\frac{c}{1 - a}\\,r + \\frac{b + d}{1 - a}\\,} \\qquad (7.14)",[724,12886,12887,12888,10009,12891,12894,12895,12898,12899,12901,12902,12924,12925,12953,12954,12975,12976,12978,12979,12981],{},"Tento vztah se nazývá ",[38,12889,12890],{},"funkce IS",[614,12892,12893],{},"IS schedule",") a její graf ",[38,12896,12897],{},"křivka IS",". Křivka je ",[38,12900,12505],{}," přímka v rovině ",[883,12903,12905],{"className":12904},[886],[888,12906,12907],{"xmlns":890},[892,12908,12909,12921],{},[895,12910,12911,12913,12915,12917,12919],{},[1726,12912,1735],{"stretchy":1734},[898,12914,12027],{},[1726,12916,1742],{"separator":1741},[898,12918,1745],{},[1726,12920,1762],{"stretchy":1734},[902,12922,12923],{"encoding":904},"(r, Y)",", neboť ",[883,12926,12928],{"className":12927},[886],[888,12929,12930],{"xmlns":890},[892,12931,12932,12950],{},[895,12933,12934,12946,12948],{},[2330,12935,12936,12938],{},[898,12937,2146],{},[895,12939,12940,12942,12944],{},[2133,12941,2281],{},[1726,12943,2228],{},[898,12945,207],{},[1726,12947,3444],{},[2133,12949,2328],{},[902,12951,12952],{"encoding":904},"\\frac{c}{1-a} \u003C 0"," (čitatel záporný, jmenovatel kladný). Název vyjadřuje, že křivka popisuje ty kombinace ",[883,12955,12957],{"className":12956},[886],[888,12958,12959],{"xmlns":890},[892,12960,12961,12973],{},[895,12962,12963,12965,12967,12969,12971],{},[1726,12964,1735],{"stretchy":1734},[898,12966,12027],{},[1726,12968,1742],{"separator":1741},[898,12970,1745],{},[1726,12972,1762],{"stretchy":1734},[902,12974,12923],{"encoding":904},", pro které plánované ",[38,12977,12170],{},"nvestment = ",[38,12980,8659],{},"avings.",[3859,12983,12984],{},[724,12985,12986,12988,12989,13002,13003,1777,13006,13019,13020,13033,13034,3877,13047,13060,13061,13064],{},[883,12987,4145],{}," Intuice — proč IS klesá\nNižší úroková míra ",[883,12990,12992],{"className":12991},[886],[888,12993,12994],{"xmlns":890},[892,12995,12996,13000],{},[895,12997,12998],{},[898,12999,12027],{},[902,13001,12027],{"encoding":904}," → levnější úvěr → ",[38,13004,13005],{},"více investic",[883,13007,13009],{"className":13008},[886],[888,13010,13011],{"xmlns":890},[892,13012,13013,13017],{},[895,13014,13015],{},[898,13016,12170],{},[902,13018,12170],{"encoding":904}," → vyšší agregátní poptávka → vyšší rovnovážný důchod ",[883,13021,13023],{"className":13022},[886],[888,13024,13025],{"xmlns":890},[892,13026,13027,13031],{},[895,13028,13029],{},[898,13030,1745],{},[902,13032,1745],{"encoding":904},". Vztah mezi ",[883,13035,13037],{"className":13036},[886],[888,13038,13039],{"xmlns":890},[892,13040,13041,13045],{},[895,13042,13043],{},[898,13044,12027],{},[902,13046,12027],{"encoding":904},[883,13048,13050],{"className":13049},[886],[888,13051,13052],{"xmlns":890},[892,13053,13054,13058],{},[895,13055,13056],{},[898,13057,1745],{},[902,13059,1745],{"encoding":904}," na trhu zboží je proto ",[38,13062,13063],{},"nepřímý"," (klesající křivka).",[115,13066,13068],{"id":13067},"křivka-lm-rovnováha-na-trhu-peněz","Křivka LM — rovnováha na trhu peněz",[724,13070,13071,13072,13090,13091,2924,13109,13112],{},"Rovnováha na trhu peněz: poptávka po penězích ",[883,13073,13075],{"className":13074},[886],[888,13076,13077],{"xmlns":890},[892,13078,13079,13087],{},[895,13080,13081],{},[2128,13082,13083,13085],{},[898,13084,2815],{},[898,13086,1731],{},[902,13088,13089],{"encoding":904},"M^D"," se rovná nabídce peněz ",[883,13092,13094],{"className":13093},[886],[888,13095,13096],{"xmlns":890},[892,13097,13098,13106],{},[895,13099,13100],{},[2128,13101,13102,13104],{},[898,13103,2815],{},[898,13105,8659],{},[902,13107,13108],{"encoding":904},"M^S",[38,13110,13111],{},"Nabídka"," je pod kontrolou národní banky a je pevně zadána:",[724,13114,13115],{},[883,13116,13118],{"className":13117},[886],[888,13119,13120],{"xmlns":890},[892,13121,13122,13140],{},[895,13123,13124,13130,13132,13138],{},[2128,13125,13126,13128],{},[898,13127,2815],{},[898,13129,8659],{},[1726,13131,1728],{},[2128,13133,13134,13136],{},[898,13135,2815],{},[1726,13137,4342],{},[898,13139,1888],{"mathvariant":2377},[902,13141,13142],{"encoding":904},"M^S = M^*.",[724,13144,13145,13148],{},[38,13146,13147],{},"Poptávka"," po penězích má tři zdroje:",[120,13150,13151,13160,13169],{},[123,13152,13153,10009,13156,13159],{},[38,13154,13155],{},"transakční poptávka",[614,13157,13158],{},"transactions demand",") — peníze pro nákup zboží,",[123,13161,13162,10009,13165,13168],{},[38,13163,13164],{},"opatrnostní poptávka",[614,13166,13167],{},"precautionary demand",") — peníze pro nenadálé výdaje,",[123,13170,13171,10009,13174,13177],{},[38,13172,13173],{},"spekulační poptávka",[614,13175,13176],{},"speculative demand",") — peníze pro zhodnocení (akcie, obligace).",[724,13179,13180,13181,13199],{},"Součet transakční a opatrnostní poptávky ",[883,13182,13184],{"className":13183},[886],[888,13185,13186],{"xmlns":890},[892,13187,13188,13196],{},[895,13189,13190],{},[2275,13191,13192,13194],{},[898,13193,9779],{},[2133,13195,2281],{},[902,13197,13198],{"encoding":904},"L_1"," je úměrný důchodu:",[724,13201,13202],{},[883,13203,13205],{"className":13204},[886],[888,13206,13207],{"xmlns":890},[892,13208,13209,13247],{},[895,13210,13211,13217,13219,13226,13228,13230,13232,13234,13236,13242,13244],{},[2275,13212,13213,13215],{},[898,13214,9779],{},[2133,13216,2281],{},[1726,13218,1728],{},[2275,13220,13221,13224],{},[898,13222,13223],{},"k",[2133,13225,2281],{},[898,13227,1745],{},[1726,13229,1742],{"separator":1741},[5865,13231],{"width":5867},[2133,13233,2328],{},[1726,13235,3444],{},[2275,13237,13238,13240],{},[898,13239,13223],{},[2133,13241,2281],{},[1726,13243,3444],{},[2133,13245,13246],{},"1.",[902,13248,13249],{"encoding":904},"L_1 = k_1 Y, \\qquad 0 \u003C k_1 \u003C 1.",[724,13251,13252,13253,13271,13272,1343,13285,13302],{},"Spekulační poptávka ",[883,13254,13256],{"className":13255},[886],[888,13257,13258],{"xmlns":890},[892,13259,13260,13268],{},[895,13261,13262],{},[2275,13263,13264,13266],{},[898,13265,9779],{},[2133,13267,2135],{},[902,13269,13270],{"encoding":904},"L_2"," závisí na úrokové míře (roste-li ",[883,13273,13275],{"className":13274},[886],[888,13276,13277],{"xmlns":890},[892,13278,13279,13283],{},[895,13280,13281],{},[898,13282,12027],{},[902,13284,12027],{"encoding":904},[883,13286,13288],{"className":13287},[886],[888,13289,13290],{"xmlns":890},[892,13291,13292,13300],{},[895,13293,13294],{},[2275,13295,13296,13298],{},[898,13297,9779],{},[2133,13299,2135],{},[902,13301,13270],{"encoding":904}," klesá, protože vyšší výnos obligací snižuje atraktivitu držby peněz):",[724,13304,13305],{},[883,13306,13308],{"className":13307},[886],[888,13309,13310],{"xmlns":890},[892,13311,13312,13366],{},[895,13313,13314,13320,13322,13328,13330,13332,13338,13340,13342,13348,13350,13352,13354,13356,13362,13364],{},[2275,13315,13316,13318],{},[898,13317,9779],{},[2133,13319,2135],{},[1726,13321,1728],{},[2275,13323,13324,13326],{},[898,13325,13223],{},[2133,13327,2135],{},[898,13329,12027],{},[1726,13331,2099],{},[2275,13333,13334,13336],{},[898,13335,13223],{},[2133,13337,2177],{},[1726,13339,1742],{"separator":1741},[5865,13341],{"width":5867},[2275,13343,13344,13346],{},[898,13345,13223],{},[2133,13347,2135],{},[1726,13349,3444],{},[2133,13351,2328],{},[1726,13353,1742],{"separator":1741},[2289,13355,2291],{},[2275,13357,13358,13360],{},[898,13359,13223],{},[2133,13361,2177],{},[1726,13363,3405],{},[2133,13365,12446],{},[902,13367,13368],{"encoding":904},"L_2 = k_2 r + k_3, \\qquad k_2 \u003C 0,\\ k_3 > 0.",[724,13370,13371],{},"Celková poptávka po penězích:",[724,13373,13374],{},[883,13375,13377],{"className":13376},[886],[888,13378,13379],{"xmlns":890},[892,13380,13381,13435],{},[895,13382,13383,13389,13391,13397,13399,13405,13407,13413,13415,13417,13423,13425,13427,13433],{},[2128,13384,13385,13387],{},[898,13386,2815],{},[898,13388,1731],{},[1726,13390,1728],{},[2275,13392,13393,13395],{},[898,13394,9779],{},[2133,13396,2281],{},[1726,13398,2099],{},[2275,13400,13401,13403],{},[898,13402,9779],{},[2133,13404,2135],{},[1726,13406,1728],{},[2275,13408,13409,13411],{},[898,13410,13223],{},[2133,13412,2281],{},[898,13414,1745],{},[1726,13416,2099],{},[2275,13418,13419,13421],{},[898,13420,13223],{},[2133,13422,2135],{},[898,13424,12027],{},[1726,13426,2099],{},[2275,13428,13429,13431],{},[898,13430,13223],{},[2133,13432,2177],{},[898,13434,1888],{"mathvariant":2377},[902,13436,13437],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3.",[724,13439,13440,13441,2703],{},"Podmínka rovnováhy na trhu peněz ",[883,13442,13444],{"className":13443},[886],[888,13445,13446],{"xmlns":890},[892,13447,13448,13464],{},[895,13449,13450,13456,13458],{},[2128,13451,13452,13454],{},[898,13453,2815],{},[898,13455,1731],{},[1726,13457,1728],{},[2128,13459,13460,13462],{},[898,13461,2815],{},[1726,13463,4342],{},[902,13465,13466],{"encoding":904},"M^D = M^*",[724,13468,13469],{},[883,13470,13472],{"className":13471},[886],[888,13473,13474],{"xmlns":890},[892,13475,13476,13523],{},[895,13477,13478,13484,13486,13492,13494,13496,13502,13504,13506,13512,13514,13516,13518,13521],{},[2128,13479,13480,13482],{},[898,13481,2815],{},[1726,13483,4342],{},[1726,13485,1728],{},[2275,13487,13488,13490],{},[898,13489,13223],{},[2133,13491,2281],{},[898,13493,1745],{},[1726,13495,2099],{},[2275,13497,13498,13500],{},[898,13499,13223],{},[2133,13501,2135],{},[898,13503,12027],{},[1726,13505,2099],{},[2275,13507,13508,13510],{},[898,13509,13223],{},[2133,13511,2177],{},[1726,13513,1742],{"separator":1741},[5865,13515],{"width":5867},[1726,13517,1735],{"stretchy":1734},[2133,13519,13520],{},"7.15",[1726,13522,1762],{"stretchy":1734},[902,13524,13525],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3, \\qquad (7.15)",[724,13527,13528,13529,3148],{},"po úpravě (vyjádření ",[883,13530,13532],{"className":13531},[886],[888,13533,13534],{"xmlns":890},[892,13535,13536,13540],{},[895,13537,13538],{},[898,13539,1745],{},[902,13541,1745],{"encoding":904},[724,13543,13544],{},[883,13545,13547],{"className":13546},[886],[888,13548,13549],{"xmlns":890},[892,13550,13551,13626],{},[895,13552,13553,13617,13619,13621,13624],{},[12818,13554,13555],{"notation":12820},[2326,13556,13557],{"scriptlevel":2328,"displaystyle":1734},[2326,13558,13559],{"scriptlevel":2328,"displaystyle":1734},[2326,13560,13561],{"scriptlevel":2328,"displaystyle":1741},[895,13562,13563,13565,13567,13569,13571,13585,13587,13589,13591,13615],{},[2289,13564,2984],{},[898,13566,1745],{},[1726,13568,1728],{},[1726,13570,2228],{},[2330,13572,13573,13579],{},[2275,13574,13575,13577],{},[898,13576,13223],{},[2133,13578,2135],{},[2275,13580,13581,13583],{},[898,13582,13223],{},[2133,13584,2281],{},[2289,13586,2984],{},[898,13588,12027],{},[1726,13590,2099],{},[2330,13592,13593,13609],{},[895,13594,13595,13601,13603],{},[2128,13596,13597,13599],{},[898,13598,2815],{},[1726,13600,4342],{},[1726,13602,2228],{},[2275,13604,13605,13607],{},[898,13606,13223],{},[2133,13608,2177],{},[2275,13610,13611,13613],{},[898,13612,13223],{},[2133,13614,2281],{},[2289,13616,2984],{},[5865,13618],{"width":5867},[1726,13620,1735],{"stretchy":1734},[2133,13622,13623],{},"7.16",[1726,13625,1762],{"stretchy":1734},[902,13627,13628],{"encoding":904},"\\boxed{\\,Y = -\\frac{k_2}{k_1}\\,r + \\frac{M^* - k_3}{k_1}\\,} \\qquad (7.16)",[724,13630,12887,13631,10009,13634,13637,13638,12898,13641,12901,13644,12924,13665,13697,13698,13720,13721,13723,13724,13726],{},[38,13632,13633],{},"funkce LM",[614,13635,13636],{},"LM schedule","), její graf ",[38,13639,13640],{},"křivka LM",[38,13642,13643],{},"rostoucí",[883,13645,13647],{"className":13646},[886],[888,13648,13649],{"xmlns":890},[892,13650,13651,13663],{},[895,13652,13653,13655,13657,13659,13661],{},[1726,13654,1735],{"stretchy":1734},[898,13656,12027],{},[1726,13658,1742],{"separator":1741},[898,13660,1745],{},[1726,13662,1762],{"stretchy":1734},[902,13664,12923],{"encoding":904},[883,13666,13668],{"className":13667},[886],[888,13669,13670],{"xmlns":890},[892,13671,13672,13694],{},[895,13673,13674,13676,13690,13692],{},[1726,13675,2228],{},[2330,13677,13678,13684],{},[2275,13679,13680,13682],{},[898,13681,13223],{},[2133,13683,2135],{},[2275,13685,13686,13688],{},[898,13687,13223],{},[2133,13689,2281],{},[1726,13691,3405],{},[2133,13693,2328],{},[902,13695,13696],{"encoding":904},"-\\frac{k_2}{k_1} > 0"," (čitatel kladný, protože ",[883,13699,13701],{"className":13700},[886],[888,13702,13703],{"xmlns":890},[892,13704,13705,13717],{},[895,13706,13707,13713,13715],{},[2275,13708,13709,13711],{},[898,13710,13223],{},[2133,13712,2135],{},[1726,13714,3444],{},[2133,13716,2328],{},[902,13718,13719],{"encoding":904},"k_2 \u003C 0",", jmenovatel kladný). Název: ",[38,13722,9779],{},"iquidity of ",[38,13725,2815],{},"oney.",[3859,13728,13729],{},[724,13730,13731,13733,13734,13747,13748,13776,13777,13794,13795,13808,13809,13826,13827,3877,13840,13853,13854,13857],{},[883,13732,4145],{}," Intuice — proč LM roste\nVyšší důchod ",[883,13735,13737],{"className":13736},[886],[888,13738,13739],{"xmlns":890},[892,13740,13741,13745],{},[895,13742,13743],{},[898,13744,1745],{},[902,13746,1745],{"encoding":904}," → větší transakční poptávka po penězích ",[883,13749,13751],{"className":13750},[886],[888,13752,13753],{"xmlns":890},[892,13754,13755,13773],{},[895,13756,13757,13763,13765,13771],{},[2275,13758,13759,13761],{},[898,13760,9779],{},[2133,13762,2281],{},[1726,13764,1728],{},[2275,13766,13767,13769],{},[898,13768,13223],{},[2133,13770,2281],{},[898,13772,1745],{},[902,13774,13775],{"encoding":904},"L_1 = k_1 Y"," → při pevné nabídce ",[883,13778,13780],{"className":13779},[886],[888,13781,13782],{"xmlns":890},[892,13783,13784,13792],{},[895,13785,13786],{},[2128,13787,13788,13790],{},[898,13789,2815],{},[1726,13791,4342],{},[902,13793,12136],{"encoding":904}," vzniká na trhu peněz přebytek poptávky → úroková míra ",[883,13796,13798],{"className":13797},[886],[888,13799,13800],{"xmlns":890},[892,13801,13802,13806],{},[895,13803,13804],{},[898,13805,12027],{},[902,13807,12027],{"encoding":904}," musí vzrůst, aby se spekulační poptávka ",[883,13810,13812],{"className":13811},[886],[888,13813,13814],{"xmlns":890},[892,13815,13816,13824],{},[895,13817,13818],{},[2275,13819,13820,13822],{},[898,13821,9779],{},[2133,13823,2135],{},[902,13825,13270],{"encoding":904}," stlačila a trh se vyrovnal. Vztah mezi ",[883,13828,13830],{"className":13829},[886],[888,13831,13832],{"xmlns":890},[892,13833,13834,13838],{},[895,13835,13836],{},[898,13837,1745],{},[902,13839,1745],{"encoding":904},[883,13841,13843],{"className":13842},[886],[888,13844,13845],{"xmlns":890},[892,13846,13847,13851],{},[895,13848,13849],{},[898,13850,12027],{},[902,13852,12027],{"encoding":904}," na trhu peněz je proto ",[38,13855,13856],{},"přímý"," (rostoucí křivka).",[115,13859,13861],{"id":13860},"simultánní-rovnováha-is-lm","Simultánní rovnováha IS-LM",[724,13863,13864,13865,13868,13869,1777,13872,3877,13890,1777,13893,13911,13912,13930,13931,13949,13950,13966,13967,3877,13982,13997,13998,1888],{},"Řešením ",[38,13866,13867],{},"soustavy dvou lineárních rovnic"," (7.14) a (7.15) určíme ",[38,13870,13871],{},"rovnovážný důchod",[883,13873,13875],{"className":13874},[886],[888,13876,13877],{"xmlns":890},[892,13878,13879,13887],{},[895,13880,13881],{},[2128,13882,13883,13885],{},[898,13884,1745],{},[898,13886,4240],{},[902,13888,13889],{"encoding":904},"Y^E",[38,13891,13892],{},"rovnovážnou úrokovou míru",[883,13894,13896],{"className":13895},[886],[888,13897,13898],{"xmlns":890},[892,13899,13900,13908],{},[895,13901,13902],{},[2128,13903,13904,13906],{},[898,13905,12027],{},[898,13907,4240],{},[902,13909,13910],{"encoding":904},"r^E","; zpětným dosazením do (7.11) a (7.12) pak rovnovážné investice ",[883,13913,13915],{"className":13914},[886],[888,13916,13917],{"xmlns":890},[892,13918,13919,13927],{},[895,13920,13921],{},[2128,13922,13923,13925],{},[898,13924,12170],{},[898,13926,4240],{},[902,13928,13929],{"encoding":904},"I^E"," a rovnovážnou spotřebu ",[883,13932,13934],{"className":13933},[886],[888,13935,13936],{"xmlns":890},[892,13937,13938,13946],{},[895,13939,13940],{},[2128,13941,13942,13944],{},[898,13943,2775],{},[898,13945,4240],{},[902,13947,13948],{"encoding":904},"C^E",". Graficky jde o ",[38,13951,13952,13953],{},"průsečík ",[883,13954,13956],{"className":13955},[886],[888,13957,13958],{"xmlns":890},[892,13959,13960,13964],{},[895,13961,13962],{},[898,13963,4240],{},[902,13965,4240],{"encoding":904}," křivek ",[883,13968,13970],{"className":13969},[886],[888,13971,13972],{"xmlns":890},[892,13973,13974,13980],{},[895,13975,13976,13978],{},[898,13977,12170],{},[898,13979,8659],{},[902,13981,12037],{"encoding":904},[883,13983,13985],{"className":13984},[886],[888,13986,13987],{"xmlns":890},[892,13988,13989,13995],{},[895,13990,13991,13993],{},[898,13992,9779],{},[898,13994,2815],{},[902,13996,12044],{"encoding":904}," v rovině ",[883,13999,14001],{"className":14000},[886],[888,14002,14003],{"xmlns":890},[892,14004,14005,14017],{},[895,14006,14007,14009,14011,14013,14015],{},[1726,14008,1735],{"stretchy":1734},[898,14010,12027],{},[1726,14012,1742],{"separator":1741},[898,14014,1745],{},[1726,14016,1762],{"stretchy":1734},[902,14018,12923],{"encoding":904},[724,14020,14021],{},[614,14022,14023,14024,14045,14046,14061,14062,14077,14078,14091,14092,14109,14110,12114,14123,14109,14140,14153,14154,14167],{},"Obrázek 7.6 — Schematický graf v rovině ",[883,14025,14027],{"className":14026},[886],[888,14028,14029],{"xmlns":890},[892,14030,14031,14043],{},[895,14032,14033,14035,14037,14039,14041],{},[1726,14034,1735],{"stretchy":1734},[898,14036,12027],{},[1726,14038,1742],{"separator":1741},[898,14040,1745],{},[1726,14042,1762],{"stretchy":1734},[902,14044,12923],{"encoding":904},". Rostoucí přímka ",[883,14047,14049],{"className":14048},[886],[888,14050,14051],{"xmlns":890},[892,14052,14053,14059],{},[895,14054,14055,14057],{},[898,14056,9779],{},[898,14058,2815],{},[902,14060,12044],{"encoding":904}," a klesající přímka ",[883,14063,14065],{"className":14064},[886],[888,14066,14067],{"xmlns":890},[892,14068,14069,14075],{},[895,14070,14071,14073],{},[898,14072,12170],{},[898,14074,8659],{},[902,14076,12037],{"encoding":904}," se protínají v bodě ",[883,14079,14081],{"className":14080},[886],[888,14082,14083],{"xmlns":890},[892,14084,14085,14089],{},[895,14086,14087],{},[898,14088,4240],{},[902,14090,4240],{"encoding":904}," se souřadnicemi ",[883,14093,14095],{"className":14094},[886],[888,14096,14097],{"xmlns":890},[892,14098,14099,14107],{},[895,14100,14101],{},[2128,14102,14103,14105],{},[898,14104,12027],{},[898,14106,4240],{},[902,14108,13910],{"encoding":904}," (na ose ",[883,14111,14113],{"className":14112},[886],[888,14114,14115],{"xmlns":890},[892,14116,14117,14121],{},[895,14118,14119],{},[898,14120,12027],{},[902,14122,12027],{"encoding":904},[883,14124,14126],{"className":14125},[886],[888,14127,14128],{"xmlns":890},[892,14129,14130,14138],{},[895,14131,14132],{},[2128,14133,14134,14136],{},[898,14135,1745],{},[898,14137,4240],{},[902,14139,13889],{"encoding":904},[883,14141,14143],{"className":14142},[886],[888,14144,14145],{"xmlns":890},[892,14146,14147,14151],{},[895,14148,14149],{},[898,14150,1745],{},[902,14152,1745],{"encoding":904},"); tečkované čáry z ",[883,14155,14157],{"className":14156},[886],[888,14158,14159],{"xmlns":890},[892,14160,14161,14165],{},[895,14162,14163],{},[898,14164,4240],{},[902,14166,4240],{"encoding":904}," kolmé k osám vyznačují polohu rovnovážné úrokové míry a rovnovážného národního důchodu.",[3859,14169,14170,14175],{},[724,14171,14172,14174],{},[883,14173,4560],{}," Postup — jak najít IS-LM rovnováhu",[152,14176,14177,14253,14321,14379,14452],{},[123,14178,14179,14182,14183,3877,14203,14223,14224,3877,14237,14250,14251,1888],{},[38,14180,14181],{},"Z trhu zboží (7.13)"," dosaď funkce ",[883,14184,14186],{"className":14185},[886],[888,14187,14188],{"xmlns":890},[892,14189,14190,14200],{},[895,14191,14192,14194,14196,14198],{},[898,14193,2775],{},[1726,14195,1735],{"stretchy":1734},[898,14197,1745],{},[1726,14199,1762],{"stretchy":1734},[902,14201,14202],{"encoding":904},"C(Y)",[883,14204,14206],{"className":14205},[886],[888,14207,14208],{"xmlns":890},[892,14209,14210,14220],{},[895,14211,14212,14214,14216,14218],{},[898,14213,12170],{},[1726,14215,1735],{"stretchy":1734},[898,14217,12027],{},[1726,14219,1762],{"stretchy":1734},[902,14221,14222],{"encoding":904},"I(r)"," a vyjádři vztah mezi ",[883,14225,14227],{"className":14226},[886],[888,14228,14229],{"xmlns":890},[892,14230,14231,14235],{},[895,14232,14233],{},[898,14234,1745],{},[902,14236,1745],{"encoding":904},[883,14238,14240],{"className":14239},[886],[888,14241,14242],{"xmlns":890},[892,14243,14244,14248],{},[895,14245,14246],{},[898,14247,12027],{},[902,14249,12027],{"encoding":904}," — dostaneš rovnici ",[38,14252,12037],{},[123,14254,14255,14258,14259,3877,14276,14293,14294,14250,14319,1888],{},[38,14256,14257],{},"Z trhu peněz (7.15)"," dosaď ",[883,14260,14262],{"className":14261},[886],[888,14263,14264],{"xmlns":890},[892,14265,14266,14274],{},[895,14267,14268],{},[2275,14269,14270,14272],{},[898,14271,9779],{},[2133,14273,2281],{},[902,14275,13198],{"encoding":904},[883,14277,14279],{"className":14278},[886],[888,14280,14281],{"xmlns":890},[892,14282,14283,14291],{},[895,14284,14285],{},[2275,14286,14287,14289],{},[898,14288,9779],{},[2133,14290,2135],{},[902,14292,13270],{"encoding":904}," a vztah ",[883,14295,14297],{"className":14296},[886],[888,14298,14299],{"xmlns":890},[892,14300,14301,14317],{},[895,14302,14303,14309,14311],{},[2128,14304,14305,14307],{},[898,14306,2815],{},[898,14308,1731],{},[1726,14310,1728],{},[2128,14312,14313,14315],{},[898,14314,2815],{},[1726,14316,4342],{},[902,14318,13466],{"encoding":904},[38,14320,12044],{},[123,14322,14323,14326,14327,3877,14340,14353,14354,14378],{},[38,14324,14325],{},"Vyřeš soustavu"," dvou lineárních rovnic o dvou neznámých ",[883,14328,14330],{"className":14329},[886],[888,14331,14332],{"xmlns":890},[892,14333,14334,14338],{},[895,14335,14336],{},[898,14337,1745],{},[902,14339,1745],{"encoding":904},[883,14341,14343],{"className":14342},[886],[888,14344,14345],{"xmlns":890},[892,14346,14347,14351],{},[895,14348,14349],{},[898,14350,12027],{},[902,14352,12027],{"encoding":904}," — nejsnáze substituční metodou (vyjádři z IS ",[883,14355,14357],{"className":14356},[886],[888,14358,14359],{"xmlns":890},[892,14360,14361,14375],{},[895,14362,14363,14365,14367,14369,14371,14373],{},[898,14364,1745],{},[1726,14366,1728],{},[898,14368,2008],{},[1726,14370,1735],{"stretchy":1734},[898,14372,12027],{},[1726,14374,1762],{"stretchy":1734},[902,14376,14377],{"encoding":904},"Y = f(r)"," a dosaď do LM).",[123,14380,14381,1777,14384,3877,14418,1888],{},[38,14382,14383],{},"Zpětně dopočítej",[883,14385,14387],{"className":14386},[886],[888,14388,14389],{"xmlns":890},[892,14390,14391,14415],{},[895,14392,14393,14399,14401,14403,14405,14411,14413],{},[2128,14394,14395,14397],{},[898,14396,2775],{},[898,14398,4240],{},[1726,14400,1728],{},[898,14402,207],{},[2289,14404,2984],{},[2128,14406,14407,14409],{},[898,14408,1745],{},[898,14410,4240],{},[1726,14412,2099],{},[898,14414,2102],{},[902,14416,14417],{"encoding":904},"C^E = a\\,Y^E + b",[883,14419,14421],{"className":14420},[886],[888,14422,14423],{"xmlns":890},[892,14424,14425,14449],{},[895,14426,14427,14433,14435,14437,14439,14445,14447],{},[2128,14428,14429,14431],{},[898,14430,12170],{},[898,14432,4240],{},[1726,14434,1728],{},[898,14436,2146],{},[2289,14438,2984],{},[2128,14440,14441,14443],{},[898,14442,12027],{},[898,14444,4240],{},[1726,14446,2099],{},[898,14448,2198],{},[902,14450,14451],{"encoding":904},"I^E = c\\,r^E + d",[123,14453,14454,14457,14458,14492,14493,14547],{},[38,14455,14456],{},"Ověř:"," musí platit ",[883,14459,14461],{"className":14460},[886],[888,14462,14463],{"xmlns":890},[892,14464,14465,14489],{},[895,14466,14467,14473,14475,14481,14483],{},[2128,14468,14469,14471],{},[898,14470,1745],{},[898,14472,4240],{},[1726,14474,1728],{},[2128,14476,14477,14479],{},[898,14478,2775],{},[898,14480,4240],{},[1726,14482,2099],{},[2128,14484,14485,14487],{},[898,14486,12170],{},[898,14488,4240],{},[902,14490,14491],{"encoding":904},"Y^E = C^E + I^E"," (rovnováha trhu zboží) i ",[883,14494,14496],{"className":14495},[886],[888,14497,14498],{"xmlns":890},[892,14499,14500,14544],{},[895,14501,14502,14508,14510,14516,14522,14524,14530,14536,14538],{},[2128,14503,14504,14506],{},[898,14505,2815],{},[1726,14507,4342],{},[1726,14509,1728],{},[2275,14511,14512,14514],{},[898,14513,13223],{},[2133,14515,2281],{},[2128,14517,14518,14520],{},[898,14519,1745],{},[898,14521,4240],{},[1726,14523,2099],{},[2275,14525,14526,14528],{},[898,14527,13223],{},[2133,14529,2135],{},[2128,14531,14532,14534],{},[898,14533,12027],{},[898,14535,4240],{},[1726,14537,2099],{},[2275,14539,14540,14542],{},[898,14541,13223],{},[2133,14543,2177],{},[902,14545,14546],{"encoding":904},"M^* = k_1 Y^E + k_2 r^E + k_3"," (rovnováha trhu peněz).",[115,14549,14551],{"id":14550},"příklad-76-is-lm","Příklad 7.6 (IS-LM)",[724,14553,14554],{},"Pro trh zboží jsou dány:",[120,14556,14557,14585],{},[123,14558,14559,14560,1742],{},"spotřeba ",[883,14561,14563],{"className":14562},[886],[888,14564,14565],{"xmlns":890},[892,14566,14567,14582],{},[895,14568,14569,14571,14573,14576,14578,14580],{},[898,14570,2775],{},[1726,14572,1728],{},[2133,14574,14575],{},"0,8",[898,14577,1745],{},[1726,14579,2099],{},[2133,14581,3087],{},[902,14583,14584],{"encoding":904},"C = 0{,}8Y + 100",[123,14586,14587,14588,1888],{},"investice ",[883,14589,14591],{"className":14590},[886],[888,14592,14593],{"xmlns":890},[892,14594,14595,14611],{},[895,14596,14597,14599,14601,14603,14605,14607,14609],{},[898,14598,12170],{},[1726,14600,1728],{},[1726,14602,2228],{},[2133,14604,9021],{},[898,14606,12027],{},[1726,14608,2099],{},[2133,14610,2780],{},[902,14612,14613],{"encoding":904},"I = -20r + 1000",[724,14615,14616],{},"Pro trh peněz:",[120,14618,14619,14645,14677],{},[123,14620,14621,1742],{},[883,14622,14624],{"className":14623},[886],[888,14625,14626],{"xmlns":890},[892,14627,14628,14642],{},[895,14629,14630,14636,14638,14640],{},[2275,14631,14632,14634],{},[898,14633,9779],{},[2133,14635,2281],{},[1726,14637,1728],{},[2133,14639,2791],{},[898,14641,1745],{},[902,14643,14644],{"encoding":904},"L_1 = 0{,}1Y",[123,14646,14647,1742],{},[883,14648,14650],{"className":14649},[886],[888,14651,14652],{"xmlns":890},[892,14653,14654,14674],{},[895,14655,14656,14662,14664,14666,14668,14670,14672],{},[2275,14657,14658,14660],{},[898,14659,9779],{},[2133,14661,2135],{},[1726,14663,1728],{},[1726,14665,2228],{},[2133,14667,4991],{},[898,14669,12027],{},[1726,14671,2099],{},[2133,14673,8590],{},[902,14675,14676],{"encoding":904},"L_2 = -25r + 2000",[123,14678,14679,14680,1888],{},"nabídka peněz ",[883,14681,14683],{"className":14682},[886],[888,14684,14685],{"xmlns":890},[892,14686,14687,14700],{},[895,14688,14689,14695,14697],{},[2128,14690,14691,14693],{},[898,14692,2815],{},[1726,14694,4342],{},[1726,14696,1728],{},[2133,14698,14699],{},"2375",[902,14701,14702],{"encoding":904},"M^* = 2375",[724,14704,14705,14708,14709,2703],{},[38,14706,14707],{},"Funkce IS"," — dosazením do (7.13) ",[883,14710,14712],{"className":14711},[886],[888,14713,14714],{"xmlns":890},[892,14715,14716,14728],{},[895,14717,14718,14720,14722,14724,14726],{},[898,14719,1745],{},[1726,14721,1728],{},[898,14723,2775],{},[1726,14725,2099],{},[898,14727,12170],{},[902,14729,14730],{"encoding":904},"Y = C + I",[724,14732,14733],{},[883,14734,14736],{"className":14735},[886],[888,14737,14738],{"xmlns":890},[892,14739,14740,14766],{},[895,14741,14742,14744,14746,14748,14750,14752,14754,14756,14758,14760,14762,14764],{},[898,14743,1745],{},[1726,14745,1728],{},[2133,14747,14575],{},[898,14749,1745],{},[1726,14751,2099],{},[2133,14753,3087],{},[1726,14755,2228],{},[2133,14757,9021],{},[898,14759,12027],{},[1726,14761,2099],{},[2133,14763,2780],{},[1726,14765,1742],{"separator":1741},[902,14767,14768],{"encoding":904},"Y = 0{,}8Y + 100 - 20r + 1000,",[724,14770,14771],{},"tj.",[724,14773,14774],{},[883,14775,14777],{"className":14776},[886],[888,14778,14779],{"xmlns":890},[892,14780,14781,14806],{},[895,14782,14783,14785,14787,14789,14791,14793,14795,14798,14800,14802,14804],{},[2133,14784,2836],{},[898,14786,1745],{},[1726,14788,2099],{},[2133,14790,9021],{},[898,14792,12027],{},[1726,14794,1728],{},[2133,14796,14797],{},"1100.",[5865,14799],{"width":5867},[1726,14801,1735],{"stretchy":1734},[2289,14803,12037],{},[1726,14805,1762],{"stretchy":1734},[902,14807,14808],{"encoding":904},"0{,}2Y + 20r = 1100. \\qquad (\\text{IS})",[724,14810,14811,14814,14815,2703],{},[38,14812,14813],{},"Funkce LM"," — dosazením do (7.15) ",[883,14816,14818],{"className":14817},[886],[888,14819,14820],{"xmlns":890},[892,14821,14822,14846],{},[895,14823,14824,14830,14832,14838,14840],{},[2128,14825,14826,14828],{},[898,14827,2815],{},[1726,14829,4342],{},[1726,14831,1728],{},[2275,14833,14834,14836],{},[898,14835,9779],{},[2133,14837,2281],{},[1726,14839,2099],{},[2275,14841,14842,14844],{},[898,14843,9779],{},[2133,14845,2135],{},[902,14847,14848],{"encoding":904},"M^* = L_1 + L_2",[724,14850,14851],{},[883,14852,14854],{"className":14853},[886],[888,14855,14856],{"xmlns":890},[892,14857,14858,14880],{},[895,14859,14860,14862,14864,14866,14868,14870,14872,14874,14876,14878],{},[2133,14861,14699],{},[1726,14863,1728],{},[2133,14865,2791],{},[898,14867,1745],{},[1726,14869,2228],{},[2133,14871,4991],{},[898,14873,12027],{},[1726,14875,2099],{},[2133,14877,8590],{},[1726,14879,1742],{"separator":1741},[902,14881,14882],{"encoding":904},"2375 = 0{,}1Y - 25r + 2000,",[724,14884,14771],{},[724,14886,14887],{},[883,14888,14890],{"className":14889},[886],[888,14891,14892],{"xmlns":890},[892,14893,14894,14919],{},[895,14895,14896,14898,14900,14902,14904,14906,14908,14911,14913,14915,14917],{},[2133,14897,2791],{},[898,14899,1745],{},[1726,14901,2228],{},[2133,14903,4991],{},[898,14905,12027],{},[1726,14907,1728],{},[2133,14909,14910],{},"375.",[5865,14912],{"width":5867},[1726,14914,1735],{"stretchy":1734},[2289,14916,12044],{},[1726,14918,1762],{"stretchy":1734},[902,14920,14921],{"encoding":904},"0{,}1Y - 25r = 375. \\qquad (\\text{LM})",[724,14923,14924,14927,14928,14953],{},[38,14925,14926],{},"Řešení soustavy."," Z (IS) vyjádříme ",[883,14929,14931],{"className":14930},[886],[888,14932,14933],{"xmlns":890},[892,14934,14935,14950],{},[895,14936,14937,14939,14941,14944,14946,14948],{},[898,14938,1745],{},[1726,14940,1728],{},[2133,14942,14943],{},"5500",[1726,14945,2228],{},[2133,14947,3087],{},[898,14949,12027],{},[902,14951,14952],{"encoding":904},"Y = 5500 - 100r"," a dosadíme do (LM):",[724,14955,14956],{},[883,14957,14959],{"className":14958},[886],[888,14960,14961],{"xmlns":890},[892,14962,14963,15049],{},[895,14964,14965,14967,14969,14971,14973,14975,14977,14979,14981,14983,14985,14987,14990,14992,14995,14997,15000,15002,15004,15006,15008,15010,15012,15014,15016,15018,15020,15022,15025,15027,15029,15032,15034,15036,15038,15044,15046],{},[2133,14966,2791],{},[1726,14968,1735],{"stretchy":1734},[2133,14970,14943],{},[1726,14972,2228],{},[2133,14974,3087],{},[898,14976,12027],{},[1726,14978,1762],{"stretchy":1734},[1726,14980,2228],{},[2133,14982,4991],{},[898,14984,12027],{},[1726,14986,1728],{},[2133,14988,14989],{},"375",[2289,14991,3974],{},[1726,14993,14994],{},"⟹",[2289,14996,3974],{},[2133,14998,14999],{},"550",[1726,15001,2228],{},[2133,15003,2860],{},[898,15005,12027],{},[1726,15007,2228],{},[2133,15009,4991],{},[898,15011,12027],{},[1726,15013,1728],{},[2133,15015,14989],{},[2289,15017,3974],{},[1726,15019,14994],{},[2289,15021,3974],{},[2133,15023,15024],{},"35",[898,15026,12027],{},[1726,15028,1728],{},[2133,15030,15031],{},"175",[2289,15033,3974],{},[1726,15035,14994],{},[2289,15037,3974],{},[2128,15039,15040,15042],{},[898,15041,12027],{},[898,15043,4240],{},[1726,15045,1728],{},[2133,15047,15048],{},"5.",[902,15050,15051],{"encoding":904},"0{,}1(5500 - 100r) - 25r = 375 \\;\\Longrightarrow\\; 550 - 10r - 25r = 375 \\;\\Longrightarrow\\; 35r = 175 \\;\\Longrightarrow\\; r^E = 5.",[724,15053,15054],{},[38,15055,15056],{},"Zpětné dosazení:",[120,15058,15059,15105,15142],{},[123,15060,15061,1742],{},[883,15062,15064],{"className":15063},[886],[888,15065,15066],{"xmlns":890},[892,15067,15068,15102],{},[895,15069,15070,15076,15078,15080,15082,15084,15086,15088,15090,15092,15094,15097,15099],{},[2128,15071,15072,15074],{},[898,15073,1745],{},[898,15075,4240],{},[1726,15077,1728],{},[2133,15079,14943],{},[1726,15081,2228],{},[2133,15083,3087],{},[1726,15085,3174],{},[2133,15087,2231],{},[1726,15089,1728],{},[2133,15091,14943],{},[1726,15093,2228],{},[2133,15095,15096],{},"500",[1726,15098,1728],{},[2133,15100,15101],{},"5000",[902,15103,15104],{"encoding":904},"Y^E = 5500 - 100 \\cdot 5 = 5500 - 500 = 5000",[123,15106,15107,1742],{},[883,15108,15110],{"className":15109},[886],[888,15111,15112],{"xmlns":890},[892,15113,15114,15139],{},[895,15115,15116,15122,15124,15126,15128,15130,15132,15134,15136],{},[2128,15117,15118,15120],{},[898,15119,2775],{},[898,15121,4240],{},[1726,15123,1728],{},[2133,15125,14575],{},[1726,15127,3174],{},[2133,15129,15101],{},[1726,15131,2099],{},[2133,15133,3087],{},[1726,15135,1728],{},[2133,15137,15138],{},"4100",[902,15140,15141],{"encoding":904},"C^E = 0{,}8 \\cdot 5000 + 100 = 4100",[123,15143,15144,1888],{},[883,15145,15147],{"className":15146},[886],[888,15148,15149],{"xmlns":890},[892,15150,15151,15178],{},[895,15152,15153,15159,15161,15163,15165,15167,15169,15171,15173,15175],{},[2128,15154,15155,15157],{},[898,15156,12170],{},[898,15158,4240],{},[1726,15160,1728],{},[1726,15162,2228],{},[2133,15164,9021],{},[1726,15166,3174],{},[2133,15168,2231],{},[1726,15170,2099],{},[2133,15172,2780],{},[1726,15174,1728],{},[2133,15176,15177],{},"900",[902,15179,15180],{"encoding":904},"I^E = -20 \\cdot 5 + 1000 = 900",[724,15182,15183,1777,15186,15232],{},[38,15184,15185],{},"Ověření:",[883,15187,15189],{"className":15188},[886],[888,15190,15191],{"xmlns":890},[892,15192,15193,15229],{},[895,15194,15195,15201,15203,15209,15211,15213,15215,15217,15219,15221,15223],{},[2128,15196,15197,15199],{},[898,15198,2775],{},[898,15200,4240],{},[1726,15202,2099],{},[2128,15204,15205,15207],{},[898,15206,12170],{},[898,15208,4240],{},[1726,15210,1728],{},[2133,15212,15138],{},[1726,15214,2099],{},[2133,15216,15177],{},[1726,15218,1728],{},[2133,15220,15101],{},[1726,15222,1728],{},[2128,15224,15225,15227],{},[898,15226,1745],{},[898,15228,4240],{},[902,15230,15231],{"encoding":904},"C^E + I^E = 4100 + 900 = 5000 = Y^E",". ✓",[724,15234,15235],{},[883,15236,15238],{"className":15237},[886],[888,15239,15240],{"xmlns":890},[892,15241,15242,15312],{},[895,15243,15244],{},[12818,15245,15246],{"notation":12820},[2326,15247,15248],{"scriptlevel":2328,"displaystyle":1734},[2326,15249,15250],{"scriptlevel":2328,"displaystyle":1734},[2326,15251,15252],{"scriptlevel":2328,"displaystyle":1741},[895,15253,15254,15256,15262,15264,15266,15268,15271,15277,15279,15281,15283,15285,15291,15293,15295,15297,15299,15305,15307,15310],{},[2289,15255,2984],{},[2128,15257,15258,15260],{},[898,15259,1745],{},[898,15261,4240],{},[1726,15263,1728],{},[2133,15265,15101],{},[1726,15267,1742],{"separator":1741},[5865,15269],{"width":15270},"1em",[2128,15272,15273,15275],{},[898,15274,12027],{},[898,15276,4240],{},[1726,15278,1728],{},[2133,15280,2231],{},[1726,15282,1742],{"separator":1741},[5865,15284],{"width":15270},[2128,15286,15287,15289],{},[898,15288,2775],{},[898,15290,4240],{},[1726,15292,1728],{},[2133,15294,15138],{},[1726,15296,1742],{"separator":1741},[5865,15298],{"width":15270},[2128,15300,15301,15303],{},[898,15302,12170],{},[898,15304,4240],{},[1726,15306,1728],{},[2133,15308,15309],{},"900.",[2289,15311,2984],{},[902,15313,15314],{"encoding":904},"\\boxed{\\,Y^E = 5000, \\quad r^E = 5, \\quad C^E = 4100, \\quad I^E = 900.\\,}",[724,15316,15317],{},[614,15318,15319,15320,15333,15334,15347,15348,15363,15364,15377,15378,15393,15394,15407,15408,15421,15422,1888],{},"Obrázek 7.7 — Konkrétní numerický příklad IS-LM rovnováhy. Na ose ",[883,15321,15323],{"className":15322},[886],[888,15324,15325],{"xmlns":890},[892,15326,15327,15331],{},[895,15328,15329],{},[898,15330,1745],{},[902,15332,1745],{"encoding":904}," jsou vyznačeny hodnoty 3750, 5000, 5500; na ose ",[883,15335,15337],{"className":15336},[886],[888,15338,15339],{"xmlns":890},[892,15340,15341,15345],{},[895,15342,15343],{},[898,15344,12027],{},[902,15346,12027],{"encoding":904}," hodnoty 5 a 55. Přímka ",[883,15349,15351],{"className":15350},[886],[888,15352,15353],{"xmlns":890},[892,15354,15355,15361],{},[895,15356,15357,15359],{},[898,15358,9779],{},[898,15360,2815],{},[902,15362,12044],{"encoding":904}," stoupá z oblasti nízkých ",[883,15365,15367],{"className":15366},[886],[888,15368,15369],{"xmlns":890},[892,15370,15371,15375],{},[895,15372,15373],{},[898,15374,12027],{},[902,15376,12027],{"encoding":904},", přímka ",[883,15379,15381],{"className":15380},[886],[888,15382,15383],{"xmlns":890},[892,15384,15385,15391],{},[895,15386,15387,15389],{},[898,15388,12170],{},[898,15390,8659],{},[902,15392,12037],{"encoding":904}," klesá a protíná osu ",[883,15395,15397],{"className":15396},[886],[888,15398,15399],{"xmlns":890},[892,15400,15401,15405],{},[895,15402,15403],{},[898,15404,12027],{},[902,15406,12027],{"encoding":904}," kolem hodnoty 55. Průsečík ",[883,15409,15411],{"className":15410},[886],[888,15412,15413],{"xmlns":890},[892,15414,15415,15419],{},[895,15416,15417],{},[898,15418,4240],{},[902,15420,4240],{"encoding":904}," leží v bodě ",[883,15423,15425],{"className":15424},[886],[888,15426,15427],{"xmlns":890},[892,15428,15429,15451],{},[895,15430,15431,15433,15435,15437,15439,15441,15443,15445,15447,15449],{},[1726,15432,2487],{"stretchy":1734},[898,15434,12027],{},[1726,15436,1728],{},[2133,15438,2231],{},[1726,15440,1742],{"separator":1741},[2289,15442,2291],{},[898,15444,1745],{},[1726,15446,1728],{},[2133,15448,15101],{},[1726,15450,2502],{"stretchy":1734},[902,15452,15453],{"encoding":904},"[r = 5,\\ Y = 5000]",[115,15455,15457],{"id":15456},"ekonomická-interpretace-fiskální-a-monetární-politika","Ekonomická interpretace — fiskální a monetární politika",[724,15459,15460,15463,15464,15477,15478,1696,15491,15494,15495,15513,15514,15531,15532,15549,15550,15563,15564,15577],{},[38,15461,15462],{},"Posun křivky IS (fiskální politika)."," Expanzivní fiskální politika — zvýšení vládních výdajů ",[883,15465,15467],{"className":15466},[886],[888,15468,15469],{"xmlns":890},[892,15470,15471,15475],{},[895,15472,15473],{},[898,15474,12098],{},[902,15476,12098],{"encoding":904}," nebo snížení daní ",[883,15479,15481],{"className":15480},[886],[888,15482,15483],{"xmlns":890},[892,15484,15485,15489],{},[895,15486,15487],{},[898,15488,2772],{},[902,15490,2772],{"encoding":904},[38,15492,15493],{},"posouvá IS doprava",": při dané úrokové míře vzroste rovnovážný důchod trhu zboží. Nová rovnováha ",[883,15496,15498],{"className":15497},[886],[888,15499,15500],{"xmlns":890},[892,15501,15502,15510],{},[895,15503,15504],{},[2128,15505,15506,15508],{},[898,15507,4240],{},[1726,15509,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[902,15511,15512],{"encoding":904},"E'"," má vyšší ",[883,15515,15517],{"className":15516},[886],[888,15518,15519],{"xmlns":890},[892,15520,15521,15529],{},[895,15522,15523],{},[2128,15524,15525,15527],{},[898,15526,1745],{},[898,15528,4240],{},[902,15530,13889],{"encoding":904}," i vyšší ",[883,15533,15535],{"className":15534},[886],[888,15536,15537],{"xmlns":890},[892,15538,15539,15547],{},[895,15540,15541],{},[2128,15542,15543,15545],{},[898,15544,12027],{},[898,15546,4240],{},[902,15548,13910],{"encoding":904}," (vyšší ",[883,15551,15553],{"className":15552},[886],[888,15554,15555],{"xmlns":890},[892,15556,15557,15561],{},[895,15558,15559],{},[898,15560,1745],{},[902,15562,1745],{"encoding":904}," zvedá poptávku po penězích, což tlačí ",[883,15565,15567],{"className":15566},[886],[888,15568,15569],{"xmlns":890},[892,15570,15571,15575],{},[895,15572,15573],{},[898,15574,12027],{},[902,15576,12027],{"encoding":904}," nahoru).",[724,15579,15580],{},[1647,15581],{"alt":15582,"className":15583,"src":15584},"imek-posun-is-lm-politiky",[210,1651],"\u002Fwiki-assets\u002Fimek-posun-is-lm-politiky.jpeg",[724,15586,15587,15590,15591,15608,15609,15612,15613,15630,15631,15648,15649,15662,15663,15682,15683,1847],{},[38,15588,15589],{},"Posun křivky LM (monetární politika)."," Expanzivní monetární politika — zvýšení nabídky peněz ",[883,15592,15594],{"className":15593},[886],[888,15595,15596],{"xmlns":890},[892,15597,15598,15606],{},[895,15599,15600],{},[2128,15601,15602,15604],{},[898,15603,2815],{},[1726,15605,4342],{},[902,15607,12136],{"encoding":904}," národní bankou — ",[38,15610,15611],{},"posouvá LM doprava\u002Fdolů",": při daném důchodu je trh peněz v rovnováze při nižší úrokové míře. Nová rovnováha má nižší ",[883,15614,15616],{"className":15615},[886],[888,15617,15618],{"xmlns":890},[892,15619,15620,15628],{},[895,15621,15622],{},[2128,15623,15624,15626],{},[898,15625,12027],{},[898,15627,4240],{},[902,15629,13910],{"encoding":904}," a vyšší ",[883,15632,15634],{"className":15633},[886],[888,15635,15636],{"xmlns":890},[892,15637,15638,15646],{},[895,15639,15640],{},[2128,15641,15642,15644],{},[898,15643,1745],{},[898,15645,4240],{},[902,15647,13889],{"encoding":904}," (nižší ",[883,15650,15652],{"className":15651},[886],[888,15653,15654],{"xmlns":890},[892,15655,15656,15660],{},[895,15657,15658],{},[898,15659,12027],{},[902,15661,12027],{"encoding":904}," povzbuzuje investice ",[883,15664,15666],{"className":15665},[886],[888,15667,15668],{"xmlns":890},[892,15669,15670,15680],{},[895,15671,15672,15674,15676,15678],{},[898,15673,12170],{},[1726,15675,1735],{"stretchy":1734},[898,15677,12027],{},[1726,15679,1762],{"stretchy":1734},[902,15681,14222],{"encoding":904},", ty zvedají ",[883,15684,15686],{"className":15685},[886],[888,15687,15688],{"xmlns":890},[892,15689,15690,15694],{},[895,15691,15692],{},[898,15693,1745],{},[902,15695,1745],{"encoding":904},[724,15697,15698,15699,15702],{},"IS-LM tak dává jednotný rámec pro diskusi ",[38,15700,15701],{},"dopadu obou typů politik"," na důchod a úrokovou míru současně.",[115,15704,1670],{"id":1669},[120,15706,15707,15780,15826,15908,15958,16025,16082,16123,16156],{},[123,15708,15709,1696,15742,1343,15759,15776,15777,15779],{},[38,15710,15711,15712],{},"Funkce investic ",[883,15713,15715],{"className":15714},[886],[888,15716,15717],{"xmlns":890},[892,15718,15719,15739],{},[895,15720,15721,15723,15725,15727,15729,15731,15733,15735,15737],{},[898,15722,12170],{},[1726,15724,1735],{"stretchy":1734},[898,15726,12027],{},[1726,15728,1762],{"stretchy":1734},[1726,15730,1728],{},[898,15732,2146],{},[898,15734,12027],{},[1726,15736,2099],{},[898,15738,2198],{},[902,15740,15741],{"encoding":904},"I(r) = cr + d",[883,15743,15745],{"className":15744},[886],[888,15746,15747],{"xmlns":890},[892,15748,15749,15757],{},[895,15750,15751,15753,15755],{},[898,15752,2146],{},[1726,15754,3444],{},[2133,15756,2328],{},[902,15758,12501],{"encoding":904},[883,15760,15762],{"className":15761},[886],[888,15763,15764],{"xmlns":890},[892,15765,15766,15774],{},[895,15767,15768,15770,15772],{},[898,15769,2198],{},[1726,15771,3405],{},[2133,15773,2328],{},[902,15775,12480],{"encoding":904},"; ",[38,15778,12505],{}," funkce úrokové míry.",[123,15781,15782,15785,15786,15807,15808,15825],{},[38,15783,15784],{},"Trh zboží"," — rovnováha ",[883,15787,15789],{"className":15788},[886],[888,15790,15791],{"xmlns":890},[892,15792,15793,15805],{},[895,15794,15795,15797,15799,15801,15803],{},[898,15796,1745],{},[1726,15798,1728],{},[898,15800,2775],{},[1726,15802,2099],{},[898,15804,12170],{},[902,15806,14730],{"encoding":904},", ekvivalentně ",[883,15809,15811],{"className":15810},[886],[888,15812,15813],{"xmlns":890},[892,15814,15815,15823],{},[895,15816,15817,15819,15821],{},[898,15818,12170],{},[1726,15820,1728],{},[898,15822,8659],{},[902,15824,12698],{"encoding":904}," (investice = úspory).",[123,15827,15828,10009,15831,15833,15834,15884,15885,12901,15887,1888],{},[38,15829,15830],{},"Křivka IS",[614,15832,12040],{},") — ",[883,15835,15837],{"className":15836},[886],[888,15838,15839],{"xmlns":890},[892,15840,15841,15881],{},[895,15842,15843,15845,15847,15859,15861,15863],{},[898,15844,1745],{},[1726,15846,1728],{},[2330,15848,15849,15851],{},[898,15850,2146],{},[895,15852,15853,15855,15857],{},[2133,15854,2281],{},[1726,15856,2228],{},[898,15858,207],{},[898,15860,12027],{},[1726,15862,2099],{},[2330,15864,15865,15873],{},[895,15866,15867,15869,15871],{},[898,15868,2102],{},[1726,15870,2099],{},[898,15872,2198],{},[895,15874,15875,15877,15879],{},[2133,15876,2281],{},[1726,15878,2228],{},[898,15880,207],{},[902,15882,15883],{"encoding":904},"Y = \\frac{c}{1-a}r + \\frac{b+d}{1-a}"," (7.14); ",[38,15886,12505],{},[883,15888,15890],{"className":15889},[886],[888,15891,15892],{"xmlns":890},[892,15893,15894,15906],{},[895,15895,15896,15898,15900,15902,15904],{},[1726,15897,1735],{"stretchy":1734},[898,15899,12027],{},[1726,15901,1742],{"separator":1741},[898,15903,1745],{},[1726,15905,1762],{"stretchy":1734},[902,15907,12923],{"encoding":904},[123,15909,15910,15785,15913,15939,15940,1888],{},[38,15911,15912],{},"Trh peněz",[883,15914,15916],{"className":15915},[886],[888,15917,15918],{"xmlns":890},[892,15919,15920,15936],{},[895,15921,15922,15928,15930],{},[2128,15923,15924,15926],{},[898,15925,2815],{},[898,15927,1731],{},[1726,15929,1728],{},[2128,15931,15932,15934],{},[898,15933,2815],{},[898,15935,8659],{},[902,15937,15938],{"encoding":904},"M^D = M^S"," při pevné nabídce ",[883,15941,15943],{"className":15942},[886],[888,15944,15945],{"xmlns":890},[892,15946,15947,15955],{},[895,15948,15949],{},[2128,15950,15951,15953],{},[898,15952,2815],{},[1726,15954,4342],{},[902,15956,15957],{"encoding":904},"M^* ",[123,15959,15960,1696,15963,1888],{},[38,15961,15962],{},"Transakční, opatrnostní, spekulační poptávka",[883,15964,15966],{"className":15965},[886],[888,15967,15968],{"xmlns":890},[892,15969,15970,16022],{},[895,15971,15972,15978,15980,15986,15988,15994,15996,16002,16004,16006,16012,16014,16016],{},[2128,15973,15974,15976],{},[898,15975,2815],{},[898,15977,1731],{},[1726,15979,1728],{},[2275,15981,15982,15984],{},[898,15983,9779],{},[2133,15985,2281],{},[1726,15987,2099],{},[2275,15989,15990,15992],{},[898,15991,9779],{},[2133,15993,2135],{},[1726,15995,1728],{},[2275,15997,15998,16000],{},[898,15999,13223],{},[2133,16001,2281],{},[898,16003,1745],{},[1726,16005,2099],{},[2275,16007,16008,16010],{},[898,16009,13223],{},[2133,16011,2135],{},[898,16013,12027],{},[1726,16015,2099],{},[2275,16017,16018,16020],{},[898,16019,13223],{},[2133,16021,2177],{},[902,16023,16024],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3",[123,16026,16027,10009,16030,15833,16032,16078,16079,16081],{},[38,16028,16029],{},"Křivka LM",[614,16031,12047],{},[883,16033,16035],{"className":16034},[886],[888,16036,16037],{"xmlns":890},[892,16038,16039,16075],{},[895,16040,16041,16047,16049,16055,16057,16059,16065,16067,16069],{},[2128,16042,16043,16045],{},[898,16044,2815],{},[1726,16046,4342],{},[1726,16048,1728],{},[2275,16050,16051,16053],{},[898,16052,13223],{},[2133,16054,2281],{},[898,16056,1745],{},[1726,16058,2099],{},[2275,16060,16061,16063],{},[898,16062,13223],{},[2133,16064,2135],{},[898,16066,12027],{},[1726,16068,2099],{},[2275,16070,16071,16073],{},[898,16072,13223],{},[2133,16074,2177],{},[902,16076,16077],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3"," (7.15); ",[38,16080,13643],{}," přímka.",[123,16083,16084,16087,16088,16122],{},[38,16085,16086],{},"Simultánní rovnováha"," — průsečík ",[883,16089,16091],{"className":16090},[886],[888,16092,16093],{"xmlns":890},[892,16094,16095,16119],{},[895,16096,16097,16099,16101,16103,16109,16111,16117],{},[898,16098,4240],{},[1726,16100,1728],{},[1726,16102,1735],{"stretchy":1734},[2128,16104,16105,16107],{},[898,16106,12027],{},[898,16108,4240],{},[1726,16110,1742],{"separator":1741},[2128,16112,16113,16115],{},[898,16114,1745],{},[898,16116,4240],{},[1726,16118,1762],{"stretchy":1734},[902,16120,16121],{"encoding":904},"E = (r^E, Y^E)"," křivek IS a LM.",[123,16124,16125,16128,16129,1343,16142,16155],{},[38,16126,16127],{},"Fiskální politika"," — nástroje ",[883,16130,16132],{"className":16131},[886],[888,16133,16134],{"xmlns":890},[892,16135,16136,16140],{},[895,16137,16138],{},[898,16139,12098],{},[902,16141,12098],{"encoding":904},[883,16143,16145],{"className":16144},[886],[888,16146,16147],{"xmlns":890},[892,16148,16149,16153],{},[895,16150,16151],{},[898,16152,2772],{},[902,16154,2772],{"encoding":904}," posouvající křivku IS.",[123,16157,16158,16161,16162,16179],{},[38,16159,16160],{},"Monetární politika"," — nástroj ",[883,16163,16165],{"className":16164},[886],[888,16166,16167],{"xmlns":890},[892,16168,16169,16177],{},[895,16170,16171],{},[2128,16172,16173,16175],{},[898,16174,2815],{},[1726,16176,4342],{},[902,16178,12136],{"encoding":904}," posouvající křivku LM.",[115,16181,1899],{"id":1898},[120,16183,16184,16193,16202,16212],{},[123,16185,16186,1777,16189],{},[38,16187,16188],{},"Kurz:",[207,16190,16192],{"className":16191,"dataFsResolvedFilePath":1640,"href":1641},[210],"Matematická ekonomie",[123,16194,16195,1777,16198],{},[38,16196,16197],{},"Přednáška:",[207,16199,16201],{"className":16200,"dataFsResolvedFilePath":868,"href":869},[210],"imek-blok-03",[123,16203,16204,1777,16207,16211],{},[38,16205,16206],{},"Nadřazené téma:",[207,16208,16210],{"className":16209,"dataFsResolvedFilePath":934,"href":935},[210],"narodni-duchod"," — makroekonomické modely C-I, C-I-G, C-I-G-X a úvod do IS-LM",[123,16213,16214,16217],{},[38,16215,16216],{},"Související:",[120,16218,16219,16225,16231],{},[123,16220,16221,16224],{},[207,16222,1846],{"className":16223,"dataFsResolvedFilePath":800,"href":801},[210]," — paralela rovnovážného bodu (průsečík dvou křivek) v mikroekonomii",[123,16226,16227,16230],{},[207,16228,1145],{"className":16229,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro směrnice IS a LM",[123,16232,16233,16236],{},[207,16234,1861],{"className":16235,"dataFsResolvedFilePath":782,"href":783},[210]," — dvě neznámé a řešení lineárních soustav",{"title":641,"searchDepth":642,"depth":642,"links":16238},[16239,16240,16241,16242,16243,16244,16245,16246,16247,16248],{"id":11991,"depth":642,"text":11992},{"id":12146,"depth":642,"text":12147},{"id":12361,"depth":642,"text":12362},{"id":12654,"depth":642,"text":12655},{"id":13067,"depth":642,"text":13068},{"id":13860,"depth":642,"text":13861},{"id":14550,"depth":642,"text":14551},{"id":15456,"depth":642,"text":15457},{"id":1669,"depth":642,"text":1670},{"id":1898,"depth":642,"text":1899},{},"\u002Ftopics\u002Fis-lm",{"title":11983,"description":641},[1138,1137],"topics\u002Fis-lm",[1128,16255,1143,16256,16257,16258,16259,16210],"is-lm","trh-zbozi","trh-penez","urokova-mira","investice","OcXqlUxNqiCsj643lVoQEu_ZWU2vH0D_lWZ_-SxoyHk",{"id":16262,"title":16263,"body":16264,"course":659,"courses":17856,"created":1129,"description":17857,"extension":661,"meta":17858,"navigation":664,"path":17859,"seo":17860,"sources":17861,"stem":17862,"tags":17863,"type":1950,"updated":677,"__hash__":17866},"topics\u002Ftopics\u002Flagrangeova-metoda.md","Lagrangeova metoda (vázané extrémy)",{"type":9,"value":16265,"toc":17844},[16266,16269,16364,16371,16391,16395,16400,16463,16482,16484,16487,16623,16625,16835,16869,17006,17010,17074,17090,17118,17122,17220,17224,17228,17281,17387,17601,17605,17648,17754,17806,17808],[12,16267,16263],{"id":16268},"lagrangeova-metoda-vázané-extrémy",[724,16270,16271,16272,3902,16295,16327,16328,16331,16332,16359,16360,16363],{},"Hledáme extrém funkce ",[883,16273,16275],{"className":16274},[886],[888,16276,16277],{"xmlns":890},[892,16278,16279,16293],{},[895,16280,16281,16283,16285,16287,16289,16291],{},[898,16282,2008],{},[1726,16284,1735],{"stretchy":1734},[898,16286,2013],{},[1726,16288,1742],{"separator":1741},[898,16290,2003],{},[1726,16292,1762],{"stretchy":1734},[902,16294,9827],{"encoding":904},[883,16296,16298],{"className":16297},[886],[888,16299,16300],{"xmlns":890},[892,16301,16302,16324],{},[895,16303,16304,16306,16308,16314,16316,16322],{},[898,16305,900],{},[1726,16307,1735],{"stretchy":1734},[2275,16309,16310,16312],{},[898,16311,1724],{},[2133,16313,2281],{},[1726,16315,1742],{"separator":1741},[2275,16317,16318,16320],{},[898,16319,1724],{},[2133,16321,2135],{},[1726,16323,1762],{"stretchy":1734},[902,16325,16326],{"encoding":904},"U(Q_1, Q_2)"," apod.) ",[38,16329,16330],{},"podmíněný"," rovnicí ",[883,16333,16335],{"className":16334},[886],[888,16336,16337],{"xmlns":890},[892,16338,16339,16357],{},[895,16340,16341,16343,16345,16347,16349,16351,16353,16355],{},[898,16342,11025],{},[1726,16344,1735],{"stretchy":1734},[898,16346,2013],{},[1726,16348,1742],{"separator":1741},[898,16350,2003],{},[1726,16352,1762],{"stretchy":1734},[1726,16354,1728],{},[2133,16356,2328],{},[902,16358,11042],{"encoding":904},". V ",[207,16361,1642],{"className":16362,"dataFsResolvedFilePath":1640,"href":1641},[210]," se používá pro:",[724,16365,16366],{},[1647,16367],{"alt":16368,"className":16369,"src":16370},"imek-lagrange-tecnost",[210,1651],"\u002Fwiki-assets\u002Fimek-lagrange-tecnost.jpeg",[120,16372,16373,16382,16388],{},[123,16374,16375,16378,16379,1762],{},[38,16376,16377],{},"Maximalizaci užitečnosti"," při rozpočtovém omezení (viz ",[207,16380,9757],{"className":16381,"dataFsResolvedFilePath":878,"href":879},[210],[123,16383,16384,16387],{},[38,16385,16386],{},"Minimalizaci výdajů"," při dané úrovni užitečnosti (duální úloha)",[123,16389,16390],{},"Optimalizaci produkce \u002F nákladů za omezení",[115,16392,16394],{"id":16393},"princip","Princip",[724,16396,10691,16397,2703],{},[38,16398,16399],{},"Lagrangeovu funkci",[724,16401,16402],{},[883,16403,16405],{"className":16404},[886],[888,16406,16407],{"xmlns":890},[892,16408,16409,16460],{},[895,16410,16411,16413,16415,16417,16419,16421,16423,16426,16428,16430,16432,16434,16436,16438,16440,16442,16444,16446,16448,16450,16452,16454,16456,16458],{},[898,16412,9779],{},[1726,16414,1735],{"stretchy":1734},[898,16416,2013],{},[1726,16418,1742],{"separator":1741},[898,16420,2003],{},[1726,16422,1742],{"separator":1741},[898,16424,16425],{},"λ",[1726,16427,1762],{"stretchy":1734},[1726,16429,1728],{},[898,16431,2008],{},[1726,16433,1735],{"stretchy":1734},[898,16435,2013],{},[1726,16437,1742],{"separator":1741},[898,16439,2003],{},[1726,16441,1762],{"stretchy":1734},[1726,16443,2099],{},[898,16445,16425],{},[2289,16447,2984],{},[898,16449,11025],{},[1726,16451,1735],{"stretchy":1734},[898,16453,2013],{},[1726,16455,1742],{"separator":1741},[898,16457,2003],{},[1726,16459,1762],{"stretchy":1734},[902,16461,16462],{"encoding":904},"L(x, y, \\lambda) = f(x, y) + \\lambda\\, g(x, y)",[724,16464,4298,16465,8088,16479,1888],{},[883,16466,16468],{"className":16467},[886],[888,16469,16470],{"xmlns":890},[892,16471,16472,16476],{},[895,16473,16474],{},[898,16475,16425],{},[902,16477,16478],{"encoding":904},"\\lambda",[38,16480,16481],{},"Lagrangeův multiplikátor",[115,16483,3249],{"id":3248},[724,16485,16486],{},"Řešíme soustavu:",[724,16488,16489,16537,16585],{},[883,16490,16492],{"className":16491},[886],[888,16493,16494],{"xmlns":890},[892,16495,16496,16534],{},[895,16497,16498,16506,16508,16516,16518,16520,16522,16530,16532],{},[9151,16499,16500,16502,16504],{},[898,16501,9779],{},[898,16503,2013],{},[1726,16505,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,16507,1728],{},[9151,16509,16510,16512,16514],{},[898,16511,2008],{},[898,16513,2013],{},[1726,16515,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,16517,2099],{},[898,16519,16425],{},[2289,16521,2984],{},[9151,16523,16524,16526,16528],{},[898,16525,11025],{},[898,16527,2013],{},[1726,16529,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,16531,1728],{},[2133,16533,2328],{},[902,16535,16536],{"encoding":904},"L'_x = f'_x + \\lambda\\, g'_x = 0",[883,16538,16540],{"className":16539},[886],[888,16541,16542],{"xmlns":890},[892,16543,16544,16582],{},[895,16545,16546,16554,16556,16564,16566,16568,16570,16578,16580],{},[9151,16547,16548,16550,16552],{},[898,16549,9779],{},[898,16551,2003],{},[1726,16553,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,16555,1728],{},[9151,16557,16558,16560,16562],{},[898,16559,2008],{},[898,16561,2003],{},[1726,16563,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,16565,2099],{},[898,16567,16425],{},[2289,16569,2984],{},[9151,16571,16572,16574,16576],{},[898,16573,11025],{},[898,16575,2003],{},[1726,16577,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,16579,1728],{},[2133,16581,2328],{},[902,16583,16584],{"encoding":904},"L'_y = f'_y + \\lambda\\, g'_y = 0",[883,16586,16588],{"className":16587},[886],[888,16589,16590],{"xmlns":890},[892,16591,16592,16620],{},[895,16593,16594,16602,16604,16606,16608,16610,16612,16614,16616,16618],{},[9151,16595,16596,16598,16600],{},[898,16597,9779],{},[898,16599,16425],{},[1726,16601,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,16603,1728],{},[898,16605,11025],{},[1726,16607,1735],{"stretchy":1734},[898,16609,2013],{},[1726,16611,1742],{"separator":1741},[898,16613,2003],{},[1726,16615,1762],{"stretchy":1734},[1726,16617,1728],{},[2133,16619,2328],{},[902,16621,16622],{"encoding":904},"L'_\\lambda = g(x, y) = 0",[115,16624,3323],{"id":3322},[724,16626,16627],{},[883,16628,16630],{"className":16629},[886],[888,16631,16632],{"xmlns":890},[892,16633,16634,16832],{},[895,16635,16636,16638,16640,16642,16644,16646,16648,16650,16652,16654,16656,16672,16674,16676,16692,16694,16696,16704,16710,16712,16714,16730,16732,16734,16750,16752,16754,16762,16768,16770,16772,16774,16790,16792,16794,16810,16812,16814,16822,16824],{},[898,16637,1731],{},[1726,16639,1735],{"stretchy":1734},[898,16641,2013],{},[1726,16643,1742],{"separator":1741},[898,16645,2003],{},[1726,16647,1742],{"separator":1741},[898,16649,16425],{},[1726,16651,1762],{"stretchy":1734},[1726,16653,1728],{},[1726,16655,1735],{"stretchy":1734},[9151,16657,16658,16660,16666],{},[898,16659,2008],{},[895,16661,16662,16664],{},[898,16663,2013],{},[898,16665,2013],{},[895,16667,16668,16670],{},[1726,16669,2379],{"mathvariant":2377},[1726,16671,2379],{"mathvariant":2377},[1726,16673,2099],{},[898,16675,16425],{},[9151,16677,16678,16680,16686],{},[898,16679,11025],{},[895,16681,16682,16684],{},[898,16683,2013],{},[898,16685,2013],{},[895,16687,16688,16690],{},[1726,16689,2379],{"mathvariant":2377},[1726,16691,2379],{"mathvariant":2377},[1726,16693,1762],{"stretchy":1734},[1726,16695,1735],{"stretchy":1734},[9151,16697,16698,16700,16702],{},[898,16699,11025],{},[898,16701,2003],{},[1726,16703,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[2128,16705,16706,16708],{},[1726,16707,1762],{"stretchy":1734},[2133,16709,2135],{},[1726,16711,2099],{},[1726,16713,1735],{"stretchy":1734},[9151,16715,16716,16718,16724],{},[898,16717,2008],{},[895,16719,16720,16722],{},[898,16721,2003],{},[898,16723,2003],{},[895,16725,16726,16728],{},[1726,16727,2379],{"mathvariant":2377},[1726,16729,2379],{"mathvariant":2377},[1726,16731,2099],{},[898,16733,16425],{},[9151,16735,16736,16738,16744],{},[898,16737,11025],{},[895,16739,16740,16742],{},[898,16741,2003],{},[898,16743,2003],{},[895,16745,16746,16748],{},[1726,16747,2379],{"mathvariant":2377},[1726,16749,2379],{"mathvariant":2377},[1726,16751,1762],{"stretchy":1734},[1726,16753,1735],{"stretchy":1734},[9151,16755,16756,16758,16760],{},[898,16757,11025],{},[898,16759,2013],{},[1726,16761,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[2128,16763,16764,16766],{},[1726,16765,1762],{"stretchy":1734},[2133,16767,2135],{},[1726,16769,2228],{},[2133,16771,2135],{},[1726,16773,1735],{"stretchy":1734},[9151,16775,16776,16778,16784],{},[898,16777,2008],{},[895,16779,16780,16782],{},[898,16781,2013],{},[898,16783,2003],{},[895,16785,16786,16788],{},[1726,16787,2379],{"mathvariant":2377},[1726,16789,2379],{"mathvariant":2377},[1726,16791,2099],{},[898,16793,16425],{},[9151,16795,16796,16798,16804],{},[898,16797,11025],{},[895,16799,16800,16802],{},[898,16801,2013],{},[898,16803,2003],{},[895,16805,16806,16808],{},[1726,16807,2379],{"mathvariant":2377},[1726,16809,2379],{"mathvariant":2377},[1726,16811,1762],{"stretchy":1734},[2289,16813,2984],{},[9151,16815,16816,16818,16820],{},[898,16817,11025],{},[898,16819,2013],{},[1726,16821,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[2289,16823,2984],{},[9151,16825,16826,16828,16830],{},[898,16827,11025],{},[898,16829,2003],{},[1726,16831,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[902,16833,16834],{"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",[724,16836,16837,16838,16868],{},"Je-li ",[883,16839,16841],{"className":16840},[886],[888,16842,16843],{"xmlns":890},[892,16844,16845,16865],{},[895,16846,16847,16849,16851,16853,16855,16857,16863],{},[1726,16848,2487],{"stretchy":1734},[898,16850,207],{},[1726,16852,1742],{"separator":1741},[898,16854,2102],{},[1726,16856,1742],{"separator":1741},[2275,16858,16859,16861],{},[898,16860,16425],{},[2133,16862,2328],{},[1726,16864,2502],{"stretchy":1734},[902,16866,16867],{"encoding":904},"[a, b, \\lambda_0]"," podezřelý bod:",[120,16870,16871,16939],{},[123,16872,16873,3411,16909,16911,16912],{},[883,16874,16876],{"className":16875},[886],[888,16877,16878],{"xmlns":890},[892,16879,16880,16906],{},[895,16881,16882,16884,16886,16888,16890,16892,16894,16900,16902,16904],{},[898,16883,1731],{},[1726,16885,1735],{"stretchy":1734},[898,16887,207],{},[1726,16889,1742],{"separator":1741},[898,16891,2102],{},[1726,16893,1742],{"separator":1741},[2275,16895,16896,16898],{},[898,16897,16425],{},[2133,16899,2328],{},[1726,16901,1762],{"stretchy":1734},[1726,16903,3444],{},[2133,16905,2328],{},[902,16907,16908],{"encoding":904},"D(a, b, \\lambda_0) \u003C 0",[38,16910,3714],{}," vázané podmínkou ",[883,16913,16915],{"className":16914},[886],[888,16916,16917],{"xmlns":890},[892,16918,16919,16937],{},[895,16920,16921,16923,16925,16927,16929,16931,16933,16935],{},[898,16922,11025],{},[1726,16924,1735],{"stretchy":1734},[898,16926,2013],{},[1726,16928,1742],{"separator":1741},[898,16930,2003],{},[1726,16932,1762],{"stretchy":1734},[1726,16934,1728],{},[2133,16936,2328],{},[902,16938,11042],{"encoding":904},[123,16940,16941,3411,16977,16911,16979],{},[883,16942,16944],{"className":16943},[886],[888,16945,16946],{"xmlns":890},[892,16947,16948,16974],{},[895,16949,16950,16952,16954,16956,16958,16960,16962,16968,16970,16972],{},[898,16951,1731],{},[1726,16953,1735],{"stretchy":1734},[898,16955,207],{},[1726,16957,1742],{"separator":1741},[898,16959,2102],{},[1726,16961,1742],{"separator":1741},[2275,16963,16964,16966],{},[898,16965,16425],{},[2133,16967,2328],{},[1726,16969,1762],{"stretchy":1734},[1726,16971,3405],{},[2133,16973,2328],{},[902,16975,16976],{"encoding":904},"D(a, b, \\lambda_0) > 0",[38,16978,3772],{},[883,16980,16982],{"className":16981},[886],[888,16983,16984],{"xmlns":890},[892,16985,16986,17004],{},[895,16987,16988,16990,16992,16994,16996,16998,17000,17002],{},[898,16989,11025],{},[1726,16991,1735],{"stretchy":1734},[898,16993,2013],{},[1726,16995,1742],{"separator":1741},[898,16997,2003],{},[1726,16999,1762],{"stretchy":1734},[1726,17001,1728],{},[2133,17003,2328],{},[902,17005,11042],{"encoding":904},[115,17007,17009],{"id":17008},"význam-multiplikátoru","Význam multiplikátoru",[724,17011,17012],{},[883,17013,17015],{"className":17014},[886],[888,17016,17017],{"xmlns":890},[892,17018,17019,17071],{},[895,17020,17021,17023,17025,17047,17049],{},[898,17022,16425],{},[1726,17024,1728],{},[2330,17026,17027,17035],{},[9151,17028,17029,17031,17033],{},[898,17030,2008],{},[898,17032,2013],{},[1726,17034,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[895,17036,17037,17039],{},[1726,17038,2228],{},[9151,17040,17041,17043,17045],{},[898,17042,11025],{},[898,17044,2013],{},[1726,17046,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,17048,1728],{},[2330,17050,17051,17059],{},[9151,17052,17053,17055,17057],{},[898,17054,2008],{},[898,17056,2003],{},[1726,17058,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[895,17060,17061,17063],{},[1726,17062,2228],{},[9151,17064,17065,17067,17069],{},[898,17066,11025],{},[898,17068,2003],{},[1726,17070,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[902,17072,17073],{"encoding":904},"\\lambda = \\frac{f'_x}{-g'_x} = \\frac{f'_y}{-g'_y}",[724,17075,17076,17089],{},[883,17077,17079],{"className":17078},[886],[888,17080,17081],{"xmlns":890},[892,17082,17083,17087],{},[895,17084,17085],{},[898,17086,16425],{},[902,17088,16478],{"encoding":904}," udává:",[120,17091,17092,17098],{},[123,17093,17094,17095],{},"konstantní ",[38,17096,17097],{},"poměr mezi mezním prospěchem a mezním nákladem",[123,17099,17100,17103,17104,17117],{},[38,17101,17102],{},"náklady příležitosti"," (opportunity cost) — o kolik vzroste optimální hodnota ",[883,17105,17107],{"className":17106},[886],[888,17108,17109],{"xmlns":890},[892,17110,17111,17115],{},[895,17112,17113],{},[898,17114,2008],{},[902,17116,2008],{"encoding":904},", uvolní-li se omezení o jednotku",[115,17119,17121],{"id":17120},"alternativní-postup","Alternativní postup",[724,17123,17124,17125,17152,17153,17177,17178,17202,17203,17216,17217,1888],{},"Lze-li z ",[883,17126,17128],{"className":17127},[886],[888,17129,17130],{"xmlns":890},[892,17131,17132,17150],{},[895,17133,17134,17136,17138,17140,17142,17144,17146,17148],{},[898,17135,11025],{},[1726,17137,1735],{"stretchy":1734},[898,17139,2013],{},[1726,17141,1742],{"separator":1741},[898,17143,2003],{},[1726,17145,1762],{"stretchy":1734},[1726,17147,1728],{},[2133,17149,2328],{},[902,17151,11042],{"encoding":904}," vyjádřit ",[883,17154,17156],{"className":17155},[886],[888,17157,17158],{"xmlns":890},[892,17159,17160,17174],{},[895,17161,17162,17164,17166,17168,17170,17172],{},[898,17163,2003],{},[1726,17165,1728],{},[898,17167,2003],{},[1726,17169,1735],{"stretchy":1734},[898,17171,2013],{},[1726,17173,1762],{"stretchy":1734},[902,17175,17176],{"encoding":904},"y = y(x)"," (nebo ",[883,17179,17181],{"className":17180},[886],[888,17182,17183],{"xmlns":890},[892,17184,17185,17199],{},[895,17186,17187,17189,17191,17193,17195,17197],{},[898,17188,2013],{},[1726,17190,1728],{},[898,17192,2013],{},[1726,17194,1735],{"stretchy":1734},[898,17196,2003],{},[1726,17198,1762],{"stretchy":1734},[902,17200,17201],{"encoding":904},"x = x(y)","), dosadíme do ",[883,17204,17206],{"className":17205},[886],[888,17207,17208],{"xmlns":890},[892,17209,17210,17214],{},[895,17211,17212],{},[898,17213,2008],{},[902,17215,2008],{"encoding":904}," a převedeme na ",[38,17218,17219],{},"extrém funkce jedné proměnné",[115,17221,17223],{"id":17222},"použití-v-imek","Použití v ImeK",[198,17225,17227],{"id":17226},"maximalizace-užitečnosti","Maximalizace užitečnosti",[724,17229,17230,17231,1888],{},"Rozpočtové omezení: ",[883,17232,17234],{"className":17233},[886],[888,17235,17236],{"xmlns":890},[892,17237,17238,17278],{},[895,17239,17240,17246,17248,17256,17262,17264,17272],{},[2128,17241,17242,17244],{},[898,17243,1745],{},[1726,17245,4342],{},[1726,17247,1728],{},[9151,17249,17250,17252,17254],{},[898,17251,1738],{},[2133,17253,2281],{},[1726,17255,4342],{},[2275,17257,17258,17260],{},[898,17259,1724],{},[2133,17261,2281],{},[1726,17263,2099],{},[9151,17265,17266,17268,17270],{},[898,17267,1738],{},[2133,17269,2135],{},[1726,17271,4342],{},[2275,17273,17274,17276],{},[898,17275,1724],{},[2133,17277,2135],{},[902,17279,17280],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2",[724,17282,17283],{},[883,17284,17286],{"className":17285},[886],[888,17287,17288],{"xmlns":890},[892,17289,17290,17384],{},[895,17291,17292,17294,17296,17302,17304,17310,17312,17314,17316,17318,17320,17322,17328,17330,17336,17338,17340,17342,17344,17350,17352,17360,17366,17368,17376,17382],{},[898,17293,9779],{},[1726,17295,1735],{"stretchy":1734},[2275,17297,17298,17300],{},[898,17299,1724],{},[2133,17301,2281],{},[1726,17303,1742],{"separator":1741},[2275,17305,17306,17308],{},[898,17307,1724],{},[2133,17309,2135],{},[1726,17311,1742],{"separator":1741},[898,17313,16425],{},[1726,17315,1762],{"stretchy":1734},[1726,17317,1728],{},[898,17319,900],{},[1726,17321,1735],{"stretchy":1734},[2275,17323,17324,17326],{},[898,17325,1724],{},[2133,17327,2281],{},[1726,17329,1742],{"separator":1741},[2275,17331,17332,17334],{},[898,17333,1724],{},[2133,17335,2135],{},[1726,17337,1762],{"stretchy":1734},[1726,17339,2099],{},[898,17341,16425],{},[1726,17343,1735],{"stretchy":1734},[2128,17345,17346,17348],{},[898,17347,1745],{},[1726,17349,4342],{},[1726,17351,2228],{},[9151,17353,17354,17356,17358],{},[898,17355,1738],{},[2133,17357,2281],{},[1726,17359,4342],{},[2275,17361,17362,17364],{},[898,17363,1724],{},[2133,17365,2281],{},[1726,17367,2228],{},[9151,17369,17370,17372,17374],{},[898,17371,1738],{},[2133,17373,2135],{},[1726,17375,4342],{},[2275,17377,17378,17380],{},[898,17379,1724],{},[2133,17381,2135],{},[1726,17383,1762],{"stretchy":1734},[902,17385,17386],{"encoding":904},"L(Q_1, Q_2, \\lambda) = U(Q_1, Q_2) + \\lambda (Y^* - P_1^* Q_1 - P_2^* Q_2)",[724,17388,17389,17390,1343,17422,1343,17454,17503,17504,17558,17559,1888],{},"Soustava: ",[883,17391,17393],{"className":17392},[886],[888,17394,17395],{"xmlns":890},[892,17396,17397,17419],{},[895,17398,17399,17407,17409,17411],{},[9151,17400,17401,17403,17405],{},[898,17402,900],{},[2133,17404,2281],{},[1726,17406,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,17408,1728],{},[898,17410,16425],{},[9151,17412,17413,17415,17417],{},[898,17414,1738],{},[2133,17416,2281],{},[1726,17418,4342],{},[902,17420,17421],{"encoding":904},"U'_1 = \\lambda P_1^*",[883,17423,17425],{"className":17424},[886],[888,17426,17427],{"xmlns":890},[892,17428,17429,17451],{},[895,17430,17431,17439,17441,17443],{},[9151,17432,17433,17435,17437],{},[898,17434,900],{},[2133,17436,2135],{},[1726,17438,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,17440,1728],{},[898,17442,16425],{},[9151,17444,17445,17447,17449],{},[898,17446,1738],{},[2133,17448,2135],{},[1726,17450,4342],{},[902,17452,17453],{"encoding":904},"U'_2 = \\lambda P_2^*",[883,17455,17457],{"className":17456},[886],[888,17458,17459],{"xmlns":890},[892,17460,17461,17501],{},[895,17462,17463,17469,17471,17479,17485,17487,17495],{},[2128,17464,17465,17467],{},[898,17466,1745],{},[1726,17468,4342],{},[1726,17470,1728],{},[9151,17472,17473,17475,17477],{},[898,17474,1738],{},[2133,17476,2281],{},[1726,17478,4342],{},[2275,17480,17481,17483],{},[898,17482,1724],{},[2133,17484,2281],{},[1726,17486,2099],{},[9151,17488,17489,17491,17493],{},[898,17490,1738],{},[2133,17492,2135],{},[1726,17494,4342],{},[2275,17496,17497,17499],{},[898,17498,1724],{},[2133,17500,2135],{},[902,17502,17280],{"encoding":904},". Z prvních dvou: ",[883,17505,17507],{"className":17506},[886],[888,17508,17509],{"xmlns":890},[892,17510,17511,17555],{},[895,17512,17513,17533,17535],{},[2326,17514,17515],{"scriptlevel":2328,"displaystyle":1734},[2330,17516,17517,17525],{},[9151,17518,17519,17521,17523],{},[898,17520,900],{},[2133,17522,2281],{},[1726,17524,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[9151,17526,17527,17529,17531],{},[898,17528,900],{},[2133,17530,2135],{},[1726,17532,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,17534,1728],{},[2326,17536,17537],{"scriptlevel":2328,"displaystyle":1734},[2330,17538,17539,17547],{},[9151,17540,17541,17543,17545],{},[898,17542,1738],{},[2133,17544,2281],{},[1726,17546,4342],{},[9151,17548,17549,17551,17553],{},[898,17550,1738],{},[2133,17552,2135],{},[1726,17554,4342],{},[902,17556,17557],{"encoding":904},"\\tfrac{U'_1}{U'_2} = \\tfrac{P_1^*}{P_2^*}",", tj. ",[883,17560,17562],{"className":17561},[886],[888,17563,17564],{"xmlns":890},[892,17565,17566,17598],{},[895,17567,17568,17570,17572,17574,17576,17578],{},[898,17569,2815],{},[898,17571,3984],{},[898,17573,2775],{},[898,17575,8659],{},[1726,17577,1728],{},[2326,17579,17580],{"scriptlevel":2328,"displaystyle":1734},[2330,17581,17582,17590],{},[9151,17583,17584,17586,17588],{},[898,17585,1738],{},[2133,17587,2281],{},[1726,17589,4342],{},[9151,17591,17592,17594,17596],{},[898,17593,1738],{},[2133,17595,2135],{},[1726,17597,4342],{},[902,17599,17600],{"encoding":904},"MRCS = \\tfrac{P_1^*}{P_2^*}",[198,17602,17604],{"id":17603},"minimalizace-výdajů","Minimalizace výdajů",[724,17606,17607,17608,1888],{},"Podmínka dané užitečnosti ",[883,17609,17611],{"className":17610},[886],[888,17612,17613],{"xmlns":890},[892,17614,17615,17645],{},[895,17616,17617,17623,17625,17627,17629,17635,17637,17643],{},[2128,17618,17619,17621],{},[898,17620,900],{},[1726,17622,4342],{},[1726,17624,1728],{},[898,17626,900],{},[1726,17628,1735],{"stretchy":1734},[2275,17630,17631,17633],{},[898,17632,1724],{},[2133,17634,2281],{},[1726,17636,1742],{"separator":1741},[2275,17638,17639,17641],{},[898,17640,1724],{},[2133,17642,2135],{},[1726,17644,1762],{"stretchy":1734},[902,17646,17647],{"encoding":904},"U^* = U(Q_1, Q_2)",[724,17649,17650],{},[883,17651,17653],{"className":17652},[886],[888,17654,17655],{"xmlns":890},[892,17656,17657,17751],{},[895,17658,17659,17661,17663,17669,17671,17677,17679,17681,17683,17685,17693,17699,17701,17709,17715,17717,17719,17721,17727,17729,17731,17733,17739,17741,17747,17749],{},[898,17660,9779],{},[1726,17662,1735],{"stretchy":1734},[2275,17664,17665,17667],{},[898,17666,1724],{},[2133,17668,2281],{},[1726,17670,1742],{"separator":1741},[2275,17672,17673,17675],{},[898,17674,1724],{},[2133,17676,2135],{},[1726,17678,1742],{"separator":1741},[898,17680,16425],{},[1726,17682,1762],{"stretchy":1734},[1726,17684,1728],{},[9151,17686,17687,17689,17691],{},[898,17688,1738],{},[2133,17690,2281],{},[1726,17692,4342],{},[2275,17694,17695,17697],{},[898,17696,1724],{},[2133,17698,2281],{},[1726,17700,2099],{},[9151,17702,17703,17705,17707],{},[898,17704,1738],{},[2133,17706,2135],{},[1726,17708,4342],{},[2275,17710,17711,17713],{},[898,17712,1724],{},[2133,17714,2135],{},[1726,17716,2099],{},[898,17718,16425],{},[1726,17720,1735],{"stretchy":1734},[2128,17722,17723,17725],{},[898,17724,900],{},[1726,17726,4342],{},[1726,17728,2228],{},[898,17730,900],{},[1726,17732,1735],{"stretchy":1734},[2275,17734,17735,17737],{},[898,17736,1724],{},[2133,17738,2281],{},[1726,17740,1742],{"separator":1741},[2275,17742,17743,17745],{},[898,17744,1724],{},[2133,17746,2135],{},[1726,17748,1762],{"stretchy":1734},[1726,17750,1762],{"stretchy":1734},[902,17752,17753],{"encoding":904},"L(Q_1, Q_2, \\lambda) = P_1^* Q_1 + P_2^* Q_2 + \\lambda (U^* - U(Q_1, Q_2))",[724,17755,17756,17757,1888],{},"Duálně dostaneme Hicksovy poptávkové funkce ",[883,17758,17760],{"className":17759},[886],[888,17761,17762],{"xmlns":890},[892,17763,17764,17803],{},[895,17765,17766,17773,17775,17781,17783,17789,17791,17797,17799,17801],{},[2275,17767,17768,17770],{},[898,17769,1724],{},[898,17771,17772],{},"i",[1726,17774,1728],{},[2275,17776,17777,17779],{},[898,17778,1731],{},[898,17780,17772],{},[1726,17782,1735],{"stretchy":1734},[2275,17784,17785,17787],{},[898,17786,1738],{},[2133,17788,2281],{},[1726,17790,1742],{"separator":1741},[2275,17792,17793,17795],{},[898,17794,1738],{},[2133,17796,2135],{},[1726,17798,1742],{"separator":1741},[898,17800,900],{},[1726,17802,1762],{"stretchy":1734},[902,17804,17805],{"encoding":904},"Q_i = D_i(P_1, P_2, U)",[115,17807,1899],{"id":1898},[120,17809,17810,17817,17824,17833],{},[123,17811,17812,1777,17814],{},[38,17813,1906],{},[207,17815,784],{"className":17816,"dataFsResolvedFilePath":782,"href":783},[210],[123,17818,17819,1777,17821],{},[38,17820,1912],{},[207,17822,11926],{"className":17823,"dataFsResolvedFilePath":800,"href":801},[210],[123,17825,17826,1777,17829,17832],{},[38,17827,17828],{},"Aplikace v kurzu:",[207,17830,880],{"className":17831,"dataFsResolvedFilePath":878,"href":879},[210]," (maximalizace užitečnosti při rozpočtovém omezení), minimalizace výdajů (duální úloha), optimalizace produkce",[123,17834,17835,1777,17837,1343,17840,17843],{},[38,17836,1921],{},[207,17838,936],{"className":17839,"dataFsResolvedFilePath":934,"href":935},[210],[207,17841,1400],{"className":17842,"dataFsResolvedFilePath":1398,"href":1399},[210]," (IpmrK)",{"title":641,"searchDepth":642,"depth":642,"links":17845},[17846,17847,17848,17849,17850,17851,17855],{"id":16393,"depth":642,"text":16394},{"id":3248,"depth":642,"text":3249},{"id":3322,"depth":642,"text":3323},{"id":17008,"depth":642,"text":17009},{"id":17120,"depth":642,"text":17121},{"id":17222,"depth":642,"text":17223,"children":17852},[17853,17854],{"id":17226,"depth":649,"text":17227},{"id":17603,"depth":649,"text":17604},{"id":1898,"depth":642,"text":1899},[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":16263,"description":17857},[1135,1137],"topics\u002Flagrangeova-metoda",[1128,1619,17864,17865],"vazane-extremy","multiplikator","PRnK6wpMGySFp-C47ico7wAs4MDBp47Titm-Obyzgow",{"id":17868,"title":936,"body":17869,"course":1128,"courses":659,"created":9541,"description":641,"extension":661,"meta":27736,"navigation":664,"path":27737,"seo":27738,"sources":27739,"stem":27740,"tags":27741,"type":1950,"updated":677,"__hash__":27745},"topics\u002Ftopics\u002Fnarodni-duchod.md",{"type":9,"value":17870,"toc":27698},[17871,17874,17876,17999,18134,18138,18141,18254,18258,18285,18332,18335,18401,18446,18449,18475,18506,18510,18514,18558,18602,18664,18719,18722,18726,18729,18776,18873,18979,18985,19062,19091,19230,19234,19263,19313,19460,19550,19554,19580,19618,19645,19683,19745,19820,19898,19956,20022,20066,20070,20128,20177,20222,20435,20555,20561,20565,20588,20592,20599,20603,20634,20669,20673,20723,20811,20853,20874,20936,20996,21000,21071,21139,21211,21326,21374,21378,21381,21422,21461,21484,21598,21762,21770,21797,21827,21830,21907,22060,22144,22483,22487,22611,22747,22883,22936,22939,23189,23270,23274,23277,23335,23367,23370,23419,23422,23493,23689,23693,23844,24074,24112,24165,24211,24214,24270,24319,24523,24613,24617,24633,24640,24809,24813,24884,24965,25046,25125,25271,25359,25363,25546,25677,25722,25819,25823,26562,26564,27615,27617],[12,17872,936],{"id":17873},"národní-důchod",[115,17875,11992],{"id":11991},[724,17877,17878,17879,1777,17883,17886,17887,1777,17890,17903,17904,17907,17908,17911,17912,17915,17916,17918,17919,1777,17921,17938,17939,17956,17957,17960,17961,1847],{},"Kapitola 7 ",[207,17880,17882],{"className":17881,"dataFsResolvedFilePath":1640,"href":1641},[210],"Matematické ekonomie",[38,17884,17885],{},"přechází z mikroekonomie do makroekonomie",": předmětem zkoumání už není jedna firma, ale celá národní ekonomika popsaná ",[38,17888,17889],{},"národním důchodem",[883,17891,17893],{"className":17892},[886],[888,17894,17895],{"xmlns":890},[892,17896,17897,17901],{},[895,17898,17899],{},[898,17900,1745],{},[902,17902,1745],{"encoding":904},". Budují se postupně bohatší modely — ",[38,17905,17906],{},"C-I"," (jen spotřeba a investice) → ",[38,17909,17910],{},"C-I-G"," (přidá vládu a zdanění) → ",[38,17913,17914],{},"C-I-G-X"," (otevře ekonomiku o čistý export) → ",[38,17917,11997],{}," (propojí trh zboží s trhem peněz přes úrokovou míru). V každém modelu hledáme ",[38,17920,13871],{},[883,17922,17924],{"className":17923},[886],[888,17925,17926],{"xmlns":890},[892,17927,17928,17936],{},[895,17929,17930],{},[2128,17931,17932,17934],{},[898,17933,1745],{},[898,17935,4240],{},[902,17937,13889],{"encoding":904}," jako řešení soustavy lineárních rovnic; citlivost ",[883,17940,17942],{"className":17941},[886],[888,17943,17944],{"xmlns":890},[892,17945,17946,17954],{},[895,17947,17948],{},[2128,17949,17950,17952],{},[898,17951,1745],{},[898,17953,4240],{},[902,17955,13889],{"encoding":904}," na exogenní veličiny popisují ",[38,17958,17959],{},"multiplikátory"," (zejména Keynesův multiplikátor investic ",[883,17962,17964],{"className":17963},[886],[888,17965,17966],{"xmlns":890},[892,17967,17968,17996],{},[895,17969,17970,17972,17974,17976,17978,17980,17982,17984,17986,17988,17990,17992,17994],{},[2133,17971,2281],{},[898,17973,4661],{"mathvariant":2377},[1726,17975,1735],{"stretchy":1734},[2133,17977,2281],{},[1726,17979,2228],{},[898,17981,207],{},[1726,17983,1762],{"stretchy":1734},[1726,17985,1728],{},[2133,17987,2281],{},[898,17989,4661],{"mathvariant":2377},[898,17991,2815],{},[898,17993,1738],{},[898,17995,8659],{},[902,17997,17998],{"encoding":904},"1\u002F(1-a) = 1\u002FMPS",[3859,18000,18001],{},[724,18002,18003,18005,18006,18009,18010,18028,18029,18059,18060,18107,18108,18110,18111,18133],{},[883,18004,4145],{}," Intuice\n",[38,18007,18008],{},"Makroekonomie je zrcadlovým obrazem mikroekonomie"," na úrovni celé ekonomiky. Mezní sklon ke spotřebě ",[883,18011,18013],{"className":18012},[886],[888,18014,18015],{"xmlns":890},[892,18016,18017,18025],{},[895,18018,18019,18021,18023],{},[898,18020,2815],{},[898,18022,1738],{},[898,18024,2775],{},[902,18026,18027],{"encoding":904},"MPC"," je „ta část dodatečné korunky důchodu, kterou domácnost utratí“; zbytek ",[883,18030,18032],{"className":18031},[886],[888,18033,18034],{"xmlns":890},[892,18035,18036,18056],{},[895,18037,18038,18040,18042,18044,18046,18048,18050,18052,18054],{},[898,18039,2815],{},[898,18041,1738],{},[898,18043,8659],{},[1726,18045,1728],{},[2133,18047,2281],{},[1726,18049,2228],{},[898,18051,2815],{},[898,18053,1738],{},[898,18055,2775],{},[902,18057,18058],{"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 ",[883,18061,18063],{"className":18062},[886],[888,18064,18065],{"xmlns":890},[892,18066,18067,18104],{},[895,18068,18069,18071,18073,18075,18077,18083,18085,18088,18090,18092,18094,18096,18098,18100,18102],{},[2133,18070,2281],{},[1726,18072,2099],{},[898,18074,207],{},[1726,18076,2099],{},[2128,18078,18079,18081],{},[898,18080,207],{},[2133,18082,2135],{},[1726,18084,2099],{},[1726,18086,18087],{},"⋯",[1726,18089,1728],{},[2133,18091,2281],{},[898,18093,4661],{"mathvariant":2377},[1726,18095,1735],{"stretchy":1734},[2133,18097,2281],{},[1726,18099,2228],{},[898,18101,207],{},[1726,18103,1762],{"stretchy":1734},[902,18105,18106],{"encoding":904},"1 + a + a^2 + \\dots = 1\u002F(1-a)","). ",[38,18109,11997],{}," 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 ",[883,18112,18114],{"className":18113},[886],[888,18115,18116],{"xmlns":890},[892,18117,18118,18130],{},[895,18119,18120,18122,18124,18126,18128],{},[1726,18121,1735],{"stretchy":1734},[898,18123,1745],{},[1726,18125,1742],{"separator":1741},[898,18127,12027],{},[1726,18129,1762],{"stretchy":1734},[902,18131,18132],{"encoding":904},"(Y, r)"," jsou oba trhy v rovnováze současně.",[115,18135,18137],{"id":18136},"úvod-cílové-znalosti-kapitoly-7","Úvod — cílové znalosti kapitoly 7",[724,18139,18140],{},"Po prostudování kapitoly by čtenář měl umět:",[120,18142,18143,18146,18149,18152,18155,18158,18161,18251],{},[123,18144,18145],{},"popsat zjednodušený model národní ekonomiky,",[123,18147,18148],{},"formulovat pojmy funkcí spotřeby a úspor spolu s jejich základními vlastnostmi,",[123,18150,18151],{},"popsat lineární model spotřeby a úspor,",[123,18153,18154],{},"stanovit mezní sklony ke spotřebě a úsporám,",[123,18156,18157],{},"vymezit pojem makroekonomické rovnováhy ve vztahu k agregátní poptávce a nabídce,",[123,18159,18160],{},"vyložit pojmy křivek agregátní poptávky, agregátní nabídky a rovnovážného bodu,",[123,18162,18163,18164,1343,18181,1343,18203,3877,18228,18250],{},"popsat modely ",[883,18165,18167],{"className":18166},[886],[888,18168,18169],{"xmlns":890},[892,18170,18171,18179],{},[895,18172,18173,18175,18177],{},[898,18174,2775],{},[2289,18176,12276],{},[898,18178,12170],{},[902,18180,12281],{"encoding":904},[883,18182,18184],{"className":18183},[886],[888,18185,18186],{"xmlns":890},[892,18187,18188,18200],{},[895,18189,18190,18192,18194,18196,18198],{},[898,18191,2775],{},[2289,18193,12276],{},[898,18195,12170],{},[2289,18197,12276],{},[898,18199,12098],{},[902,18201,18202],{"encoding":904},"C\\text{-}I\\text{-}G",[883,18204,18206],{"className":18205},[886],[888,18207,18208],{"xmlns":890},[892,18209,18210,18226],{},[895,18211,18212,18214,18216,18218,18220,18222,18224],{},[898,18213,2775],{},[2289,18215,12276],{},[898,18217,12170],{},[2289,18219,12276],{},[898,18221,12098],{},[2289,18223,12276],{},[898,18225,12306],{},[902,18227,12309],{"encoding":904},[883,18229,18231],{"className":18230},[886],[888,18232,18233],{"xmlns":890},[892,18234,18235,18247],{},[895,18236,18237,18239,18241,18243,18245],{},[898,18238,12170],{},[898,18240,8659],{},[2289,18242,12276],{},[898,18244,9779],{},[898,18246,2815],{},[902,18248,18249],{"encoding":904},"IS\\text{-}LM"," národních ekonomik a vypočítat rovnovážné veličiny,",[123,18252,18253],{},"formulovat a stanovit základní makroekonomické multiplikátory.",[115,18255,18257],{"id":18256},"gnp-a-národní-důchod","GNP a národní důchod",[724,18259,18260,1777,18263,10009,18281,18284],{},[38,18261,18262],{},"Hrubý národní produkt",[883,18264,18266],{"className":18265},[886],[888,18267,18268],{"xmlns":890},[892,18269,18270,18278],{},[895,18271,18272,18274,18276],{},[898,18273,12098],{},[898,18275,1750],{},[898,18277,1738],{},[902,18279,18280],{"encoding":904},"GNP",[614,18282,18283],{},"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:",[724,18286,18287],{},[883,18288,18290],{"className":18289},[886],[888,18291,18292],{"xmlns":890},[892,18293,18294,18329],{},[895,18295,18296,18298,18300,18302,18304,18306,18308,18310,18312,18314,18316,18318,18320,18322,18324,18327],{},[898,18297,12098],{},[898,18299,1750],{},[898,18301,1738],{},[1726,18303,1728],{},[898,18305,2775],{},[1726,18307,2099],{},[898,18309,12170],{},[1726,18311,2099],{},[898,18313,12098],{},[1726,18315,2099],{},[898,18317,12306],{},[1726,18319,1742],{"separator":1741},[5865,18321],{"width":5867},[1726,18323,1735],{"stretchy":1734},[2133,18325,18326],{},"7.1",[1726,18328,1762],{"stretchy":1734},[902,18330,18331],{"encoding":904},"GNP = C + I + G + X, \\qquad (7.1)",[724,18333,18334],{},"kde",[120,18336,18337,18353,18369,18385],{},[123,18338,18339,18352],{},[883,18340,18342],{"className":18341},[886],[888,18343,18344],{"xmlns":890},[892,18345,18346,18350],{},[895,18347,18348],{},[898,18349,2775],{},[902,18351,2775],{"encoding":904}," — výdaje domácností na spotřebu,",[123,18354,18355,18368],{},[883,18356,18358],{"className":18357},[886],[888,18359,18360],{"xmlns":890},[892,18361,18362,18366],{},[895,18363,18364],{},[898,18365,12170],{},[902,18367,12170],{"encoding":904}," — hrubé domácí investice,",[123,18370,18371,18384],{},[883,18372,18374],{"className":18373},[886],[888,18375,18376],{"xmlns":890},[892,18377,18378,18382],{},[895,18379,18380],{},[898,18381,12098],{},[902,18383,12098],{"encoding":904}," — vládní výdaje,",[123,18386,18387,18400],{},[883,18388,18390],{"className":18389},[886],[888,18391,18392],{"xmlns":890},[892,18393,18394,18398],{},[895,18395,18396],{},[898,18397,12306],{},[902,18399,12306],{"encoding":904}," — čistý export.",[724,18402,18403,18404,18421,18422,18425,18426,1777,18429,10009,18442,18445],{},"K měření ",[883,18405,18407],{"className":18406},[886],[888,18408,18409],{"xmlns":890},[892,18410,18411,18419],{},[895,18412,18413,18415,18417],{},[898,18414,12098],{},[898,18416,1750],{},[898,18418,1738],{},[902,18420,18280],{"encoding":904}," se užívá ",[38,18423,18424],{},"důchodová metoda",". Jejím hlavním konstrukčním prvkem je ",[38,18427,18428],{},"národní důchod",[883,18430,18432],{"className":18431},[886],[888,18433,18434],{"xmlns":890},[892,18435,18436,18440],{},[895,18437,18438],{},[898,18439,1745],{},[902,18441,1745],{"encoding":904},[614,18443,18444],{},"national income",") — součet důchodů všech vrstev domácností, tj. tok důchodů od firem k domácnostem jako platba za pronájem výrobních faktorů.",[724,18447,18448],{},"Pro tvorbu základních makroekonomických modelů se zjednodušeně ztotožňuje hrubý národní produkt s národním důchodem (rovněž s agregátní poptávkou):",[724,18450,18451],{},[883,18452,18454],{"className":18453},[886],[888,18455,18456],{"xmlns":890},[892,18457,18458,18472],{},[895,18459,18460,18462,18464,18466,18468,18470],{},[898,18461,12098],{},[898,18463,1750],{},[898,18465,1738],{},[1726,18467,1880],{},[898,18469,1745],{},[1726,18471,1742],{"separator":1741},[902,18473,18474],{"encoding":904},"GNP \\approx Y,",[724,18476,18477,18478,10009,18481,18484,18485,18498,18499,18502,18503,1888],{},"a užívá se společného názvu ",[38,18479,18480],{},"důchod",[614,18482,18483],{},"income",") s označením ",[883,18486,18488],{"className":18487},[886],[888,18489,18490],{"xmlns":890},[892,18491,18492,18496],{},[895,18493,18494],{},[898,18495,1745],{},[902,18497,1745],{"encoding":904},". Domácnosti důchod použijí ke ",[38,18500,18501],{},"spotřebě"," zboží a služeb nebo ke tvorbě ",[38,18504,18505],{},"úspor",[115,18507,18509],{"id":18508},"spotřeba-a-úspory","Spotřeba a úspory",[198,18511,18513],{"id":18512},"funkce-spotřeby-a-úspor","Funkce spotřeby a úspor",[724,18515,18516,18517,18530,18531,18544,18545,2703],{},"Jak spotřeba ",[883,18518,18520],{"className":18519},[886],[888,18521,18522],{"xmlns":890},[892,18523,18524,18528],{},[895,18525,18526],{},[898,18527,2775],{},[902,18529,2775],{"encoding":904},", tak úspory ",[883,18532,18534],{"className":18533},[886],[888,18535,18536],{"xmlns":890},[892,18537,18538,18542],{},[895,18539,18540],{},[898,18541,8659],{},[902,18543,8659],{"encoding":904}," závisejí na důchodu ",[883,18546,18548],{"className":18547},[886],[888,18549,18550],{"xmlns":890},[892,18551,18552,18556],{},[895,18553,18554],{},[898,18555,1745],{},[902,18557,1745],{"encoding":904},[724,18559,18560],{},[883,18561,18563],{"className":18562},[886],[888,18564,18565],{"xmlns":890},[892,18566,18567,18599],{},[895,18568,18569,18571,18573,18575,18577,18579,18581,18583,18585,18587,18589,18591,18593,18595,18597],{},[898,18570,2775],{},[1726,18572,1728],{},[898,18574,2775],{},[1726,18576,1735],{"stretchy":1734},[898,18578,1745],{},[1726,18580,1762],{"stretchy":1734},[1726,18582,1742],{"separator":1741},[5865,18584],{"width":5867},[898,18586,8659],{},[1726,18588,1728],{},[898,18590,8659],{},[1726,18592,1735],{"stretchy":1734},[898,18594,1745],{},[1726,18596,1762],{"stretchy":1734},[898,18598,1888],{"mathvariant":2377},[902,18600,18601],{"encoding":904},"C = C(Y), \\qquad S = S(Y).",[724,18603,18604,8088,18623,10009,18626,18629,18630,8088,18650,10009,18653,18656,18657,3877,18660,18663],{},[883,18605,18607],{"className":18606},[886],[888,18608,18609],{"xmlns":890},[892,18610,18611,18621],{},[895,18612,18613,18615,18617,18619],{},[898,18614,2775],{},[1726,18616,1735],{"stretchy":1734},[898,18618,1745],{},[1726,18620,1762],{"stretchy":1734},[902,18622,14202],{"encoding":904},[38,18624,18625],{},"funkce spotřeby",[614,18627,18628],{},"consumption function","), ",[883,18631,18633],{"className":18632},[886],[888,18634,18635],{"xmlns":890},[892,18636,18637,18647],{},[895,18638,18639,18641,18643,18645],{},[898,18640,8659],{},[1726,18642,1735],{"stretchy":1734},[898,18644,1745],{},[1726,18646,1762],{"stretchy":1734},[902,18648,18649],{"encoding":904},"S(Y)",[38,18651,18652],{},"funkce úspor",[614,18654,18655],{},"savings function","); jejich grafy se nazývají ",[38,18658,18659],{},"křivka spotřeby",[38,18661,18662],{},"křivka úspor",". Platí základní identita",[724,18665,18666],{},[883,18667,18669],{"className":18668},[886],[888,18670,18671],{"xmlns":890},[892,18672,18673,18716],{},[895,18674,18675,18677,18679,18681,18683,18685,18687,18689,18691,18693,18695,18697,18699,18701,18703,18705,18707,18709,18711,18714],{},[898,18676,1745],{},[1726,18678,1728],{},[898,18680,2775],{},[1726,18682,2099],{},[898,18684,8659],{},[1726,18686,1728],{},[898,18688,2775],{},[1726,18690,1735],{"stretchy":1734},[898,18692,1745],{},[1726,18694,1762],{"stretchy":1734},[1726,18696,2099],{},[898,18698,8659],{},[1726,18700,1735],{"stretchy":1734},[898,18702,1745],{},[1726,18704,1762],{"stretchy":1734},[898,18706,1888],{"mathvariant":2377},[5865,18708],{"width":5867},[1726,18710,1735],{"stretchy":1734},[2133,18712,18713],{},"7.2",[1726,18715,1762],{"stretchy":1734},[902,18717,18718],{"encoding":904},"Y = C + S = C(Y) + S(Y). \\qquad (7.2)",[724,18720,18721],{},"Známe-li jednu z funkcí, je tím určena i druhá. Obě funkce jsou rostoucí (s růstem důchodu roste spotřeba i úspory).",[198,18723,18725],{"id":18724},"lineární-model-spotřeby-a-úspor","Lineární model spotřeby a úspor",[724,18727,18728],{},"Nejjednodušší model předpokládá lineární tvar",[724,18730,18731],{},[883,18732,18734],{"className":18733},[886],[888,18735,18736],{"xmlns":890},[892,18737,18738,18773],{},[895,18739,18740,18742,18744,18746,18748,18750,18752,18754,18756,18758,18760,18762,18764,18766,18768,18771],{},[898,18741,2775],{},[1726,18743,1728],{},[898,18745,2775],{},[1726,18747,1735],{"stretchy":1734},[898,18749,1745],{},[1726,18751,1762],{"stretchy":1734},[1726,18753,1728],{},[898,18755,207],{},[898,18757,1745],{},[1726,18759,2099],{},[898,18761,2102],{},[1726,18763,1742],{"separator":1741},[5865,18765],{"width":5867},[1726,18767,1735],{"stretchy":1734},[2133,18769,18770],{},"7.3",[1726,18772,1762],{"stretchy":1734},[902,18774,18775],{"encoding":904},"C = C(Y) = aY + b, \\qquad (7.3)",[724,18777,4298,18778,3877,18796,18818,18819,18859,18860,1888],{},[883,18779,18781],{"className":18780},[886],[888,18782,18783],{"xmlns":890},[892,18784,18785,18793],{},[895,18786,18787,18789,18791],{},[898,18788,2102],{},[1726,18790,3405],{},[2133,18792,2328],{},[902,18794,18795],{"encoding":904},"b > 0",[883,18797,18799],{"className":18798},[886],[888,18800,18801],{"xmlns":890},[892,18802,18803,18815],{},[895,18804,18805,18807,18809,18811,18813],{},[2133,18806,2328],{},[1726,18808,3444],{},[898,18810,207],{},[1726,18812,3444],{},[2133,18814,2281],{},[902,18816,18817],{"encoding":904},"0 \u003C a \u003C 1",". Směrnice ",[883,18820,18822],{"className":18821},[886],[888,18823,18824],{"xmlns":890},[892,18825,18826,18856],{},[895,18827,18828,18830,18832,18839,18841,18844,18846,18848,18850,18852,18854],{},[898,18829,207],{},[1726,18831,1728],{},[895,18833,18834,18837],{},[898,18835,18836],{"mathvariant":2377},"t",[898,18838,11025],{"mathvariant":2377},[2289,18840,2984],{},[898,18842,18843],{},"α",[1726,18845,1728],{},[898,18847,2886],{"mathvariant":2377},[898,18849,2775],{},[898,18851,4661],{"mathvariant":2377},[898,18853,2886],{"mathvariant":2377},[898,18855,1745],{},[902,18857,18858],{"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 ",[883,18861,18863],{"className":18862},[886],[888,18864,18865],{"xmlns":890},[892,18866,18867,18871],{},[895,18868,18869],{},[898,18870,1745],{},[902,18872,1745],{"encoding":904},[724,18874,18875],{},[614,18876,18877,18878,18902,18903,18941,18942,18958,18959,1888],{},"Obrázek 7.1 — Přímka spotřeby ",[883,18879,18881],{"className":18880},[886],[888,18882,18883],{"xmlns":890},[892,18884,18885,18899],{},[895,18886,18887,18889,18891,18893,18895,18897],{},[898,18888,2775],{},[1726,18890,1728],{},[898,18892,207],{},[898,18894,1745],{},[1726,18896,2099],{},[898,18898,2102],{},[902,18900,18901],{"encoding":904},"C = aY + b"," se směrnicí ",[883,18904,18906],{"className":18905},[886],[888,18907,18908],{"xmlns":890},[892,18909,18910,18938],{},[895,18911,18912,18914,18916,18922,18924,18926,18928,18930,18932,18934,18936],{},[898,18913,207],{},[1726,18915,1728],{},[895,18917,18918,18920],{},[898,18919,18836],{"mathvariant":2377},[898,18921,11025],{"mathvariant":2377},[2289,18923,2984],{},[898,18925,18843],{},[1726,18927,1728],{},[898,18929,2886],{"mathvariant":2377},[898,18931,2775],{},[898,18933,4661],{"mathvariant":2377},[898,18935,2886],{"mathvariant":2377},[898,18937,1745],{},[902,18939,18940],{"encoding":904},"a = \\mathrm{tg}\\,\\alpha = \\Delta C\u002F\\Delta Y","; znázornění ",[883,18943,18945],{"className":18944},[886],[888,18946,18947],{"xmlns":890},[892,18948,18949,18955],{},[895,18950,18951,18953],{},[898,18952,2886],{"mathvariant":2377},[898,18954,2775],{},[902,18956,18957],{"encoding":904},"\\Delta C"," při jednotkovém přírůstku ",[883,18960,18962],{"className":18961},[886],[888,18963,18964],{"xmlns":890},[892,18965,18966,18976],{},[895,18967,18968,18970,18972,18974],{},[898,18969,2886],{"mathvariant":2377},[898,18971,1745],{},[1726,18973,1728],{},[2133,18975,2281],{},[902,18977,18978],{"encoding":904},"\\Delta Y = 1",[724,18980,18981,18982,2703],{},"Dosazením do (7.2) plyne ",[38,18983,18984],{},"lineární model úspor",[724,18986,18987],{},[883,18988,18990],{"className":18989},[886],[888,18991,18992],{"xmlns":890},[892,18993,18994,19059],{},[895,18995,18996,18998,19000,19002,19004,19006,19008,19010,19012,19014,19016,19018,19020,19022,19024,19026,19028,19030,19032,19034,19036,19038,19040,19042,19044,19046,19048,19050,19052,19054,19057],{},[898,18997,8659],{},[1726,18999,1728],{},[898,19001,1745],{},[1726,19003,2228],{},[898,19005,2775],{},[1726,19007,1735],{"stretchy":1734},[898,19009,1745],{},[1726,19011,1762],{"stretchy":1734},[1726,19013,1728],{},[898,19015,1745],{},[1726,19017,2228],{},[1726,19019,1735],{"stretchy":1734},[898,19021,207],{},[898,19023,1745],{},[1726,19025,2099],{},[898,19027,2102],{},[1726,19029,1762],{"stretchy":1734},[1726,19031,1728],{},[1726,19033,1735],{"stretchy":1734},[2133,19035,2281],{},[1726,19037,2228],{},[898,19039,207],{},[1726,19041,1762],{"stretchy":1734},[898,19043,1745],{},[1726,19045,2228],{},[898,19047,2102],{},[898,19049,1888],{"mathvariant":2377},[5865,19051],{"width":5867},[1726,19053,1735],{"stretchy":1734},[2133,19055,19056],{},"7.4",[1726,19058,1762],{"stretchy":1734},[902,19060,19061],{"encoding":904},"S = Y - C(Y) = Y - (aY + b) = (1 - a)Y - b. \\qquad (7.4)",[724,19063,19064,19065,1847],{},"Úspory jsou také lineární a „pomalu rostoucí“ (protože ",[883,19066,19068],{"className":19067},[886],[888,19069,19070],{"xmlns":890},[892,19071,19072,19088],{},[895,19073,19074,19076,19078,19080,19082,19084,19086],{},[2133,19075,2328],{},[1726,19077,3444],{},[2133,19079,2281],{},[1726,19081,2228],{},[898,19083,207],{},[1726,19085,3444],{},[2133,19087,2281],{},[902,19089,19090],{"encoding":904},"0 \u003C 1 - a \u003C 1",[724,19092,19093],{},[614,19094,19095,19096,3877,19119,19151,19152,2623,19165,19195,19196,2623,19214,1888],{},"Obrázek 7.2 — Přímky ",[883,19097,19099],{"className":19098},[886],[888,19100,19101],{"xmlns":890},[892,19102,19103,19117],{},[895,19104,19105,19107,19109,19111,19113,19115],{},[898,19106,2775],{},[1726,19108,1728],{},[898,19110,207],{},[898,19112,1745],{},[1726,19114,2099],{},[898,19116,2102],{},[902,19118,18901],{"encoding":904},[883,19120,19122],{"className":19121},[886],[888,19123,19124],{"xmlns":890},[892,19125,19126,19148],{},[895,19127,19128,19130,19132,19134,19136,19138,19140,19142,19144,19146],{},[898,19129,8659],{},[1726,19131,1728],{},[1726,19133,1735],{"stretchy":1734},[2133,19135,2281],{},[1726,19137,2228],{},[898,19139,207],{},[1726,19141,1762],{"stretchy":1734},[898,19143,1745],{},[1726,19145,2228],{},[898,19147,2102],{},[902,19149,19150],{"encoding":904},"S = (1-a)Y - b",". Přímka úspor protíná osu ",[883,19153,19155],{"className":19154},[886],[888,19156,19157],{"xmlns":890},[892,19158,19159,19163],{},[895,19160,19161],{},[898,19162,1745],{},[902,19164,1745],{"encoding":904},[883,19166,19168],{"className":19167},[886],[888,19169,19170],{"xmlns":890},[892,19171,19172,19192],{},[895,19173,19174,19176,19178,19180,19182,19184,19186,19188,19190],{},[898,19175,1745],{},[1726,19177,1728],{},[898,19179,2102],{},[898,19181,4661],{"mathvariant":2377},[1726,19183,1735],{"stretchy":1734},[2133,19185,2281],{},[1726,19187,2228],{},[898,19189,207],{},[1726,19191,1762],{"stretchy":1734},[902,19193,19194],{"encoding":904},"Y = b\u002F(1-a)"," a osu ",[883,19197,19199],{"className":19198},[886],[888,19200,19201],{"xmlns":890},[892,19202,19203,19211],{},[895,19204,19205,19207,19209],{},[898,19206,2775],{},[1726,19208,1742],{"separator":1741},[898,19210,8659],{},[902,19212,19213],{"encoding":904},"C, S",[883,19215,19217],{"className":19216},[886],[888,19218,19219],{"xmlns":890},[892,19220,19221,19227],{},[895,19222,19223,19225],{},[1726,19224,2228],{},[898,19226,2102],{},[902,19228,19229],{"encoding":904},"-b",[198,19231,19233],{"id":19232},"příklad-71","Příklad 7.1",[724,19235,19236,19237,19262],{},"Pro spotřebu ",[883,19238,19240],{"className":19239},[886],[888,19241,19242],{"xmlns":890},[892,19243,19244,19259],{},[895,19245,19246,19248,19250,19253,19255,19257],{},[898,19247,2775],{},[1726,19249,1728],{},[2133,19251,19252],{},"0,4",[898,19254,1745],{},[1726,19256,2099],{},[2133,19258,2860],{},[902,19260,19261],{"encoding":904},"C = 0{,}4Y + 10"," jsou úspory",[724,19264,19265],{},[883,19266,19268],{"className":19267},[886],[888,19269,19270],{"xmlns":890},[892,19271,19272,19310],{},[895,19273,19274,19276,19278,19280,19282,19284,19286,19288,19290,19292,19294,19296,19298,19300,19303,19305,19307],{},[898,19275,8659],{},[1726,19277,1728],{},[898,19279,1745],{},[1726,19281,2228],{},[898,19283,2775],{},[1726,19285,1728],{},[898,19287,1745],{},[1726,19289,2228],{},[2133,19291,19252],{},[898,19293,1745],{},[1726,19295,2228],{},[2133,19297,2860],{},[1726,19299,1728],{},[2133,19301,19302],{},"0,6",[898,19304,1745],{},[1726,19306,2228],{},[2133,19308,19309],{},"10.",[902,19311,19312],{"encoding":904},"S = Y - C = Y - 0{,}4Y - 10 = 0{,}6Y - 10.",[724,19314,19315],{},[614,19316,19317,19318,3877,19341,19365,19366,8088,19379,19403,19404,8088,19421,19437,19438,1888],{},"Obrázek 7.3 — Přímky ",[883,19319,19321],{"className":19320},[886],[888,19322,19323],{"xmlns":890},[892,19324,19325,19339],{},[895,19326,19327,19329,19331,19333,19335,19337],{},[898,19328,2775],{},[1726,19330,1728],{},[2133,19332,19252],{},[898,19334,1745],{},[1726,19336,2099],{},[2133,19338,2860],{},[902,19340,19261],{"encoding":904},[883,19342,19344],{"className":19343},[886],[888,19345,19346],{"xmlns":890},[892,19347,19348,19362],{},[895,19349,19350,19352,19354,19356,19358,19360],{},[898,19351,8659],{},[1726,19353,1728],{},[2133,19355,19302],{},[898,19357,1745],{},[1726,19359,2228],{},[2133,19361,2860],{},[902,19363,19364],{"encoding":904},"S = 0{,}6Y - 10","; průsečík přímky úspor s osou ",[883,19367,19369],{"className":19368},[886],[888,19370,19371],{"xmlns":890},[892,19372,19373,19377],{},[895,19374,19375],{},[898,19376,1745],{},[902,19378,1745],{"encoding":904},[883,19380,19382],{"className":19381},[886],[888,19383,19384],{"xmlns":890},[892,19385,19386,19400],{},[895,19387,19388,19390,19393],{},[1726,19389,1880],{},[2133,19391,19392],{},"16,",[8372,19394,19395,19397],{"accent":1741},[2133,19396,2238],{},[1726,19398,19399],{},"ˉ",[902,19401,19402],{"encoding":904},"\\approx 16{,}\\bar{6}",", s osou ",[883,19405,19407],{"className":19406},[886],[888,19408,19409],{"xmlns":890},[892,19410,19411,19419],{},[895,19412,19413,19415,19417],{},[898,19414,2775],{},[1726,19416,1742],{"separator":1741},[898,19418,8659],{},[902,19420,19213],{"encoding":904},[883,19422,19424],{"className":19423},[886],[888,19425,19426],{"xmlns":890},[892,19427,19428,19434],{},[895,19429,19430,19432],{},[1726,19431,2228],{},[2133,19433,2860],{},[902,19435,19436],{"encoding":904},"-10","; přímka spotřeby prochází bodem ",[883,19439,19441],{"className":19440},[886],[888,19442,19443],{"xmlns":890},[892,19444,19445,19457],{},[895,19446,19447,19449,19451,19453,19455],{},[1726,19448,1735],{"stretchy":1734},[2133,19450,2328],{},[1726,19452,1742],{"separator":1741},[2133,19454,2860],{},[1726,19456,1762],{"stretchy":1734},[902,19458,19459],{"encoding":904},"(0, 10)",[724,19461,19462,19463,8088,19481,19511,19512,10009,19515,19518,19519,8088,19543,10009,19546,19549],{},"Funkce úspor může nabývat záporných hodnot — pro ",[883,19464,19466],{"className":19465},[886],[888,19467,19468],{"xmlns":890},[892,19469,19470,19478],{},[895,19471,19472,19474,19476],{},[898,19473,1745],{},[1726,19475,1728],{},[2133,19477,2328],{},[902,19479,19480],{"encoding":904},"Y = 0",[883,19482,19484],{"className":19483},[886],[888,19485,19486],{"xmlns":890},[892,19487,19488,19508],{},[895,19489,19490,19492,19494,19496,19498,19500,19502,19504,19506],{},[898,19491,8659],{},[1726,19493,1735],{"stretchy":1734},[2133,19495,2328],{},[1726,19497,1762],{"stretchy":1734},[1726,19499,1728],{},[1726,19501,2228],{},[898,19503,2102],{},[1726,19505,3444],{},[2133,19507,2328],{},[902,19509,19510],{"encoding":904},"S(0) = -b \u003C 0","; hovoří se o ",[38,19513,19514],{},"autonomních úsporách",[614,19516,19517],{},"autonomous savings","). Analogicky ",[883,19520,19522],{"className":19521},[886],[888,19523,19524],{"xmlns":890},[892,19525,19526,19540],{},[895,19527,19528,19530,19532,19534,19536,19538],{},[898,19529,2775],{},[1726,19531,1735],{"stretchy":1734},[2133,19533,2328],{},[1726,19535,1762],{"stretchy":1734},[1726,19537,1728],{},[898,19539,2102],{},[902,19541,19542],{"encoding":904},"C(0) = b",[38,19544,19545],{},"autonomní spotřeba",[614,19547,19548],{},"autonomous consumption",") — spotřeba při nulovém důchodu krytá dřívějšími úsporami.",[115,19551,19553],{"id":19552},"mezní-sklon-ke-spotřebě-mpc-a-k-úsporám-mps","Mezní sklon ke spotřebě (MPC) a k úsporám (MPS)",[724,19555,19556,1777,19559,10009,19576,19579],{},[38,19557,19558],{},"Mezní sklon ke spotřebě",[883,19560,19562],{"className":19561},[886],[888,19563,19564],{"xmlns":890},[892,19565,19566,19574],{},[895,19567,19568,19570,19572],{},[898,19569,2815],{},[898,19571,1738],{},[898,19573,2775],{},[902,19575,18027],{"encoding":904},[614,19577,19578],{},"marginal propensity to consume",") je derivace spotřeby podle důchodu:",[724,19581,19582],{},[883,19583,19585],{"className":19584},[886],[888,19586,19587],{"xmlns":890},[892,19588,19589,19615],{},[895,19590,19591,19593,19595,19597,19599,19613],{},[898,19592,2815],{},[898,19594,1738],{},[898,19596,2775],{},[1726,19598,1728],{},[2330,19600,19601,19607],{},[895,19602,19603,19605],{},[898,19604,2198],{"mathvariant":2377},[898,19606,2775],{},[895,19608,19609,19611],{},[898,19610,2198],{"mathvariant":2377},[898,19612,1745],{},[898,19614,1888],{"mathvariant":2377},[902,19616,19617],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y}.",[724,19619,19620,1777,19623,10009,19641,19644],{},[38,19621,19622],{},"Mezní sklon k úsporám",[883,19624,19626],{"className":19625},[886],[888,19627,19628],{"xmlns":890},[892,19629,19630,19638],{},[895,19631,19632,19634,19636],{},[898,19633,2815],{},[898,19635,1738],{},[898,19637,8659],{},[902,19639,19640],{"encoding":904},"MPS",[614,19642,19643],{},"marginal propensity to save",") je derivace úspor podle důchodu:",[724,19646,19647],{},[883,19648,19650],{"className":19649},[886],[888,19651,19652],{"xmlns":890},[892,19653,19654,19680],{},[895,19655,19656,19658,19660,19662,19664,19678],{},[898,19657,2815],{},[898,19659,1738],{},[898,19661,8659],{},[1726,19663,1728],{},[2330,19665,19666,19672],{},[895,19667,19668,19670],{},[898,19669,2198],{"mathvariant":2377},[898,19671,8659],{},[895,19673,19674,19676],{},[898,19675,2198],{"mathvariant":2377},[898,19677,1745],{},[898,19679,1888],{"mathvariant":2377},[902,19681,19682],{"encoding":904},"MPS = \\frac{\\mathrm{d}S}{\\mathrm{d}Y}.",[724,19684,19685,19686,19744],{},"Z (7.2) plyne ",[883,19687,19689],{"className":19688},[886],[888,19690,19691],{"xmlns":890},[892,19692,19693,19741],{},[895,19694,19695,19709,19711,19725,19727],{},[2330,19696,19697,19703],{},[895,19698,19699,19701],{},[898,19700,2198],{"mathvariant":2377},[898,19702,1745],{},[895,19704,19705,19707],{},[898,19706,2198],{"mathvariant":2377},[898,19708,1745],{},[1726,19710,1728],{},[2330,19712,19713,19719],{},[895,19714,19715,19717],{},[898,19716,2198],{"mathvariant":2377},[898,19718,2775],{},[895,19720,19721,19723],{},[898,19722,2198],{"mathvariant":2377},[898,19724,1745],{},[1726,19726,2099],{},[2330,19728,19729,19735],{},[895,19730,19731,19733],{},[898,19732,2198],{"mathvariant":2377},[898,19734,8659],{},[895,19736,19737,19739],{},[898,19738,2198],{"mathvariant":2377},[898,19740,1745],{},[902,19742,19743],{"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",[724,19746,19747],{},[883,19748,19750],{"className":19749},[886],[888,19751,19752],{"xmlns":890},[892,19753,19754,19817],{},[895,19755,19756,19808,19810,19812,19815],{},[12818,19757,19758],{"notation":12820},[2326,19759,19760],{"scriptlevel":2328,"displaystyle":1734},[2326,19761,19762],{"scriptlevel":2328,"displaystyle":1734},[2326,19763,19764],{"scriptlevel":2328,"displaystyle":1741},[895,19765,19766,19768,19770,19772,19774,19776,19778,19780,19782,19784,19786,19788,19790,19792,19794,19796,19798,19800,19802,19804,19806],{},[898,19767,2815],{},[898,19769,1738],{},[898,19771,2775],{},[1726,19773,2099],{},[898,19775,2815],{},[898,19777,1738],{},[898,19779,8659],{},[1726,19781,1728],{},[2133,19783,2281],{},[1726,19785,1742],{"separator":1741},[5865,19787],{"width":5867},[898,19789,2815],{},[898,19791,1738],{},[898,19793,8659],{},[1726,19795,1728],{},[2133,19797,2281],{},[1726,19799,2228],{},[898,19801,2815],{},[898,19803,1738],{},[898,19805,2775],{},[898,19807,1888],{"mathvariant":2377},[5865,19809],{"width":5867},[1726,19811,1735],{"stretchy":1734},[2133,19813,19814],{},"7.5",[1726,19816,1762],{"stretchy":1734},[902,19818,19819],{"encoding":904},"\\boxed{MPC + MPS = 1, \\qquad MPS = 1 - MPC.} \\qquad (7.5)",[724,19821,19822,1777,19825,19848,19849,3877,19871,19897],{},[38,19823,19824],{},"Pro lineární model",[883,19826,19828],{"className":19827},[886],[888,19829,19830],{"xmlns":890},[892,19831,19832,19846],{},[895,19833,19834,19836,19838,19840,19842,19844],{},[898,19835,2775],{},[1726,19837,1728],{},[898,19839,207],{},[898,19841,1745],{},[1726,19843,2099],{},[898,19845,2102],{},[902,19847,18901],{"encoding":904}," vychází ",[883,19850,19852],{"className":19851},[886],[888,19853,19854],{"xmlns":890},[892,19855,19856,19868],{},[895,19857,19858,19860,19862,19864,19866],{},[898,19859,2815],{},[898,19861,1738],{},[898,19863,2775],{},[1726,19865,1728],{},[898,19867,207],{},[902,19869,19870],{"encoding":904},"MPC = a",[883,19872,19874],{"className":19873},[886],[888,19875,19876],{"xmlns":890},[892,19877,19878,19894],{},[895,19879,19880,19882,19884,19886,19888,19890,19892],{},[898,19881,2815],{},[898,19883,1738],{},[898,19885,8659],{},[1726,19887,1728],{},[2133,19889,2281],{},[1726,19891,2228],{},[898,19893,207],{},[902,19895,19896],{"encoding":904},"MPS = 1 - a"," — tedy směrnice přímek spotřeby a úspor.",[724,19899,19900,19903,19904,19926,19927,19955],{},[38,19901,19902],{},"Interpretace diferenciálem."," Pro pevné ",[883,19905,19907],{"className":19906},[886],[888,19908,19909],{"xmlns":890},[892,19910,19911,19923],{},[895,19912,19913,19915,19917],{},[898,19914,1745],{},[1726,19916,1728],{},[2128,19918,19919,19921],{},[898,19920,1745],{},[1726,19922,4342],{},[902,19924,19925],{"encoding":904},"Y = Y^*"," udává ",[883,19928,19930],{"className":19929},[886],[888,19931,19932],{"xmlns":890},[892,19933,19934,19952],{},[895,19935,19936,19938,19940,19942,19944,19950],{},[898,19937,2815],{},[898,19939,1738],{},[898,19941,2775],{},[1726,19943,1735],{"stretchy":1734},[2128,19945,19946,19948],{},[898,19947,1745],{},[1726,19949,4342],{},[1726,19951,1762],{"stretchy":1734},[902,19953,19954],{"encoding":904},"MPC(Y^*)"," přibližnou změnu spotřeby při jednotkovém přírůstku důchodu:",[724,19957,19958],{},[883,19959,19961],{"className":19960},[886],[888,19962,19963],{"xmlns":890},[892,19964,19965,20019],{},[895,19966,19967,19969,19971,19973,19975,19977,19979,19985,19987,19989,19991,19993,19995,19997,19999,20001,20003,20005,20007,20009,20011,20013,20015,20017],{},[898,19968,2886],{"mathvariant":2377},[898,19970,2775],{},[1726,19972,1880],{},[898,19974,2198],{"mathvariant":2377},[898,19976,2775],{},[1726,19978,1728],{},[2128,19980,19981,19983],{},[898,19982,2775],{},[1726,19984,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,19986,1735],{"stretchy":1734},[898,19988,1745],{},[1726,19990,1762],{"stretchy":1734},[2289,19992,2984],{},[898,19994,2198],{"mathvariant":2377},[898,19996,1745],{},[1726,19998,1728],{},[898,20000,2815],{},[898,20002,1738],{},[898,20004,2775],{},[1726,20006,1735],{"stretchy":1734},[898,20008,1745],{},[1726,20010,1762],{"stretchy":1734},[2289,20012,2984],{},[898,20014,2198],{"mathvariant":2377},[898,20016,1745],{},[898,20018,1888],{"mathvariant":2377},[902,20020,20021],{"encoding":904},"\\Delta C \\approx \\mathrm{d}C = C'(Y)\\,\\mathrm{d}Y = MPC(Y)\\,\\mathrm{d}Y.",[724,20023,20024,20025,20061,20062,20065],{},"Analogicky ",[883,20026,20028],{"className":20027},[886],[888,20029,20030],{"xmlns":890},[892,20031,20032,20058],{},[895,20033,20034,20036,20038,20040,20042,20044,20046,20048,20050,20052,20054,20056],{},[898,20035,2886],{"mathvariant":2377},[898,20037,8659],{},[1726,20039,1880],{},[898,20041,2815],{},[898,20043,1738],{},[898,20045,8659],{},[1726,20047,1735],{"stretchy":1734},[898,20049,1745],{},[1726,20051,1762],{"stretchy":1734},[2289,20053,2984],{},[898,20055,2198],{"mathvariant":2377},[898,20057,1745],{},[902,20059,20060],{"encoding":904},"\\Delta S \\approx MPS(Y)\\,\\mathrm{d}Y",". Viz ",[207,20063,1145],{"className":20064,"dataFsResolvedFilePath":764,"href":765},[210]," a její ekonomická interpretace.",[198,20067,20069],{"id":20068},"příklad-72","Příklad 7.2",[724,20071,19236,20072,20107,20108,20127],{},[883,20073,20075],{"className":20074},[886],[888,20076,20077],{"xmlns":890},[892,20078,20079,20104],{},[895,20080,20081,20083,20085,20088,20094,20096,20098,20100,20102],{},[898,20082,2775],{},[1726,20084,1728],{},[2133,20086,20087],{},"0,001",[2128,20089,20090,20092],{},[898,20091,1745],{},[2133,20093,2135],{},[1726,20095,2099],{},[2133,20097,2836],{},[898,20099,1745],{},[1726,20101,2099],{},[2133,20103,3117],{},[902,20105,20106],{"encoding":904},"C = 0{,}001Y^2 + 0{,}2Y + 50"," (pro ",[883,20109,20111],{"className":20110},[886],[888,20112,20113],{"xmlns":890},[892,20114,20115,20124],{},[895,20116,20117,20119,20121],{},[898,20118,1745],{},[1726,20120,3444],{},[2133,20122,20123],{},"400",[902,20125,20126],{"encoding":904},"Y \u003C 400",") platí",[724,20129,20130],{},[883,20131,20133],{"className":20132},[886],[888,20134,20135],{"xmlns":890},[892,20136,20137,20174],{},[895,20138,20139,20141,20143,20145,20147,20161,20163,20166,20168,20170,20172],{},[898,20140,2815],{},[898,20142,1738],{},[898,20144,2775],{},[1726,20146,1728],{},[2330,20148,20149,20155],{},[895,20150,20151,20153],{},[898,20152,2198],{"mathvariant":2377},[898,20154,2775],{},[895,20156,20157,20159],{},[898,20158,2198],{"mathvariant":2377},[898,20160,1745],{},[1726,20162,1728],{},[2133,20164,20165],{},"0,002",[898,20167,1745],{},[1726,20169,2099],{},[2133,20171,2836],{},[1726,20173,1742],{"separator":1741},[902,20175,20176],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y} = 0{,}002Y + 0{,}2,",[724,20178,20179],{},[883,20180,20182],{"className":20181},[886],[888,20183,20184],{"xmlns":890},[892,20185,20186,20219],{},[895,20187,20188,20190,20192,20194,20196,20198,20200,20202,20204,20206,20208,20210,20212,20214,20216],{},[898,20189,2815],{},[898,20191,1738],{},[898,20193,8659],{},[1726,20195,1728],{},[2133,20197,2281],{},[1726,20199,2228],{},[898,20201,2815],{},[898,20203,1738],{},[898,20205,2775],{},[1726,20207,1728],{},[1726,20209,2228],{},[2133,20211,20165],{},[898,20213,1745],{},[1726,20215,2099],{},[2133,20217,20218],{},"0,8.",[902,20220,20221],{"encoding":904},"MPS = 1 - MPC = -0{,}002Y + 0{,}8.",[120,20223,20224,20304,20383],{},[123,20225,20226,1343,20254,20282,20283,8088,20301,1888],{},[883,20227,20229],{"className":20228},[886],[888,20230,20231],{"xmlns":890},[892,20232,20233,20251],{},[895,20234,20235,20237,20239,20241,20243,20245,20247,20249],{},[898,20236,2815],{},[898,20238,1738],{},[898,20240,2775],{},[1726,20242,1735],{"stretchy":1734},[2133,20244,3087],{},[1726,20246,1762],{"stretchy":1734},[1726,20248,1728],{},[2133,20250,19252],{},[902,20252,20253],{"encoding":904},"MPC(100) = 0{,}4",[883,20255,20257],{"className":20256},[886],[888,20258,20259],{"xmlns":890},[892,20260,20261,20279],{},[895,20262,20263,20265,20267,20269,20271,20273,20275,20277],{},[898,20264,2815],{},[898,20266,1738],{},[898,20268,8659],{},[1726,20270,1735],{"stretchy":1734},[2133,20272,3087],{},[1726,20274,1762],{"stretchy":1734},[1726,20276,1728],{},[2133,20278,19302],{},[902,20280,20281],{"encoding":904},"MPS(100) = 0{,}6"," — při ",[883,20284,20286],{"className":20285},[886],[888,20287,20288],{"xmlns":890},[892,20289,20290,20298],{},[895,20291,20292,20294,20296],{},[898,20293,1745],{},[1726,20295,1728],{},[2133,20297,3087],{},[902,20299,20300],{"encoding":904},"Y = 100",[38,20302,20303],{},"větší sklon k úsporám",[123,20305,20306,1343,20334,20282,20362,8088,20380,1888],{},[883,20307,20309],{"className":20308},[886],[888,20310,20311],{"xmlns":890},[892,20312,20313,20331],{},[895,20314,20315,20317,20319,20321,20323,20325,20327,20329],{},[898,20316,2815],{},[898,20318,1738],{},[898,20320,2775],{},[1726,20322,1735],{"stretchy":1734},[2133,20324,8363],{},[1726,20326,1762],{"stretchy":1734},[1726,20328,1728],{},[2133,20330,19302],{},[902,20332,20333],{"encoding":904},"MPC(200) = 0{,}6",[883,20335,20337],{"className":20336},[886],[888,20338,20339],{"xmlns":890},[892,20340,20341,20359],{},[895,20342,20343,20345,20347,20349,20351,20353,20355,20357],{},[898,20344,2815],{},[898,20346,1738],{},[898,20348,8659],{},[1726,20350,1735],{"stretchy":1734},[2133,20352,8363],{},[1726,20354,1762],{"stretchy":1734},[1726,20356,1728],{},[2133,20358,19252],{},[902,20360,20361],{"encoding":904},"MPS(200) = 0{,}4",[883,20363,20365],{"className":20364},[886],[888,20366,20367],{"xmlns":890},[892,20368,20369,20377],{},[895,20370,20371,20373,20375],{},[898,20372,1745],{},[1726,20374,1728],{},[2133,20376,8363],{},[902,20378,20379],{"encoding":904},"Y = 200",[38,20381,20382],{},"větší sklon ke spotřebě",[123,20384,20385,20386,20404,20405,1847],{},"Přesně při ",[883,20387,20389],{"className":20388},[886],[888,20390,20391],{"xmlns":890},[892,20392,20393,20401],{},[895,20394,20395,20397,20399],{},[898,20396,1745],{},[1726,20398,1728],{},[2133,20400,8789],{},[902,20402,20403],{"encoding":904},"Y = 150"," se oba sklony rovnají (",[883,20406,20408],{"className":20407},[886],[888,20409,20410],{"xmlns":890},[892,20411,20412,20432],{},[895,20413,20414,20416,20418,20420,20422,20424,20426,20428,20430],{},[898,20415,2815],{},[898,20417,1738],{},[898,20419,2775],{},[1726,20421,1728],{},[898,20423,2815],{},[898,20425,1738],{},[898,20427,8659],{},[1726,20429,1728],{},[2133,20431,4996],{},[902,20433,20434],{"encoding":904},"MPC = MPS = 0{,}5",[724,20436,20437,20438,20455,20456,20470,20471,2684,20484,20498,20499,20512,20513,20554],{},"Interpretace: při ",[883,20439,20441],{"className":20440},[886],[888,20442,20443],{"xmlns":890},[892,20444,20445,20453],{},[895,20446,20447,20449,20451],{},[898,20448,1745],{},[1726,20450,1728],{},[2133,20452,3087],{},[902,20454,20300],{"encoding":904}," se spotřeba mění ",[883,20457,20459],{"className":20458},[886],[888,20460,20461],{"xmlns":890},[892,20462,20463,20467],{},[895,20464,20465],{},[2133,20466,19252],{},[902,20468,20469],{"encoding":904},"0{,}4","-krát rychleji než důchod; změní-li se důchod ze ",[883,20472,20474],{"className":20473},[886],[888,20475,20476],{"xmlns":890},[892,20477,20478,20482],{},[895,20479,20480],{},[2133,20481,3087],{},[902,20483,3087],{"encoding":904},[883,20485,20487],{"className":20486},[886],[888,20488,20489],{"xmlns":890},[892,20490,20491,20496],{},[895,20492,20493],{},[2133,20494,20495],{},"101",[902,20497,20495],{"encoding":904},", změní se spotřeba přibližně o ",[883,20500,20502],{"className":20501},[886],[888,20503,20504],{"xmlns":890},[892,20505,20506,20510],{},[895,20507,20508],{},[2133,20509,19252],{},[902,20511,20469],{"encoding":904},". Skutečná změna ",[883,20514,20516],{"className":20515},[886],[888,20517,20518],{"xmlns":890},[892,20519,20520,20551],{},[895,20521,20522,20524,20526,20528,20530,20532,20534,20536,20538,20540,20542,20544,20546,20548],{},[898,20523,2886],{"mathvariant":2377},[898,20525,2775],{},[1726,20527,1728],{},[898,20529,2775],{},[1726,20531,1735],{"stretchy":1734},[2133,20533,20495],{},[1726,20535,1762],{"stretchy":1734},[1726,20537,2228],{},[898,20539,2775],{},[1726,20541,1735],{"stretchy":1734},[2133,20543,3087],{},[1726,20545,1762],{"stretchy":1734},[1726,20547,1728],{},[2133,20549,20550],{},"0,401",[902,20552,20553],{"encoding":904},"\\Delta C = C(101) - C(100) = 0{,}401"," — aproximace diferenciálem je přesná na setiny.",[724,20556,20557,20558],{},"Obecný trend: ",[38,20559,20560],{},"s růstem důchodu se sklon ke spotřebě zvětšuje.",[115,20562,20564],{"id":20563},"makroekonomická-rovnováha","Makroekonomická rovnováha",[724,20566,20567,20568,10009,20571,20574,20575,10009,20578,12114,20581,10009,20584,20587],{},"Při modelování národní ekonomiky hraje klíčovou roli ",[38,20569,20570],{},"makroekonomická rovnováha",[614,20572,20573],{},"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 ",[38,20576,20577],{},"agregátní poptávky",[614,20579,20580],{},"aggregate demand",[38,20582,20583],{},"agregátní nabídky",[614,20585,20586],{},"aggregate supply",") — obě popisují závislost mezi cenovou hladinou a množstvím, které jsou spotřebitelé ochotni koupit (agregátními výdaji).",[115,20589,20591],{"id":20590},"model-c-i-uzavřená-ekonomika-bez-vlády","Model C-I — uzavřená ekonomika bez vlády",[724,20593,20594],{},[1647,20595],{"alt":20596,"className":20597,"src":20598},"imek-keynesian-kriz",[210,1651],"\u002Fwiki-assets\u002Fimek-keynesian-kriz.jpeg",[198,20600,20602],{"id":20601},"zadání-modelu","Zadání modelu",[724,20604,20605,20606,20619,20620,20633],{},"Nejjednodušší model uzavřené ekonomiky bez vlády obsahuje jen spotřebu ",[883,20607,20609],{"className":20608},[886],[888,20610,20611],{"xmlns":890},[892,20612,20613,20617],{},[895,20614,20615],{},[898,20616,2775],{},[902,20618,2775],{"encoding":904}," a investice ",[883,20621,20623],{"className":20622},[886],[888,20624,20625],{"xmlns":890},[892,20626,20627,20631],{},[895,20628,20629],{},[898,20630,12170],{},[902,20632,12170],{"encoding":904},". Podmínka rovnováhy:",[724,20635,20636],{},[883,20637,20639],{"className":20638},[886],[888,20640,20641],{"xmlns":890},[892,20642,20643,20666],{},[895,20644,20645,20647,20649,20651,20653,20655,20657,20659,20661,20664],{},[898,20646,1745],{},[1726,20648,1728],{},[898,20650,2775],{},[1726,20652,2099],{},[898,20654,12170],{},[898,20656,1888],{"mathvariant":2377},[5865,20658],{"width":5867},[1726,20660,1735],{"stretchy":1734},[2133,20662,20663],{},"7.6",[1726,20665,1762],{"stretchy":1734},[902,20667,20668],{"encoding":904},"Y = C + I. \\qquad (7.6)",[198,20670,20672],{"id":20671},"soustava-rovnic","Soustava rovnic",[724,20674,20675,20676,20697,20698,20722],{},"Pro pevně zadané (plánované) investice ",[883,20677,20679],{"className":20678},[886],[888,20680,20681],{"xmlns":890},[892,20682,20683,20695],{},[895,20684,20685,20687,20689],{},[898,20686,12170],{},[1726,20688,1728],{},[2128,20690,20691,20693],{},[898,20692,12170],{},[1726,20694,4342],{},[902,20696,12181],{"encoding":904}," a funkci spotřeby ",[883,20699,20701],{"className":20700},[886],[888,20702,20703],{"xmlns":890},[892,20704,20705,20719],{},[895,20706,20707,20709,20711,20713,20715,20717],{},[898,20708,2775],{},[1726,20710,1728],{},[898,20712,2775],{},[1726,20714,1735],{"stretchy":1734},[898,20716,1745],{},[1726,20718,1762],{"stretchy":1734},[902,20720,20721],{"encoding":904},"C = C(Y)"," dostáváme soustavu",[724,20724,20725],{},[883,20726,20728],{"className":20727},[886],[888,20729,20730],{"xmlns":890},[892,20731,20732,20808],{},[895,20733,20734,20799,20801,20803,20806],{},[20735,20736,20739,20771],"mtable",{"rowspacing":20737,"columnalign":20738,"columnspacing":2378},"0.25em","right left",[20740,20741,20742,20749],"mtr",{},[20743,20744,20745],"mtd",{},[2326,20746,20747],{"scriptlevel":2328,"displaystyle":1741},[898,20748,1745],{},[20743,20750,20751],{},[2326,20752,20753],{"scriptlevel":2328,"displaystyle":1741},[895,20754,20755,20757,20759,20761,20763,20769],{},[895,20756],{},[1726,20758,1728],{},[898,20760,2775],{},[1726,20762,2099],{},[2128,20764,20765,20767],{},[898,20766,12170],{},[1726,20768,4342],{},[1726,20770,1742],{"separator":1741},[20740,20772,20773,20779],{},[20743,20774,20775],{},[2326,20776,20777],{"scriptlevel":2328,"displaystyle":1741},[898,20778,2775],{},[20743,20780,20781],{},[2326,20782,20783],{"scriptlevel":2328,"displaystyle":1741},[895,20784,20785,20787,20789,20791,20793,20795,20797],{},[895,20786],{},[1726,20788,1728],{},[898,20790,2775],{},[1726,20792,1735],{"stretchy":1734},[898,20794,1745],{},[1726,20796,1762],{"stretchy":1734},[1726,20798,1742],{"separator":1741},[5865,20800],{"width":5867},[1726,20802,1735],{"stretchy":1734},[2133,20804,20805],{},"7.7",[1726,20807,1762],{"stretchy":1734},[902,20809,20810],{"encoding":904},"\\begin{aligned} Y &= C + I^*, \\\\ C &= C(Y), \\end{aligned} \\qquad (7.7)",[724,20812,20813,20814,1777,20816,3877,20833,1777,20836,1888],{},"jejímž řešením jsou ",[38,20815,13871],{},[883,20817,20819],{"className":20818},[886],[888,20820,20821],{"xmlns":890},[892,20822,20823,20831],{},[895,20824,20825],{},[2128,20826,20827,20829],{},[898,20828,1745],{},[898,20830,4240],{},[902,20832,13889],{"encoding":904},[38,20834,20835],{},"rovnovážná spotřeba",[883,20837,20839],{"className":20838},[886],[888,20840,20841],{"xmlns":890},[892,20842,20843,20851],{},[895,20844,20845],{},[2128,20846,20847,20849],{},[898,20848,2775],{},[898,20850,4240],{},[902,20852,13948],{"encoding":904},[198,20854,20856,20857],{"id":20855},"výpočet-yeye","Výpočet ",[883,20858,20860],{"className":20859},[886],[888,20861,20862],{"xmlns":890},[892,20863,20864,20872],{},[895,20865,20866],{},[2128,20867,20868,20870],{},[898,20869,1745],{},[898,20871,4240],{},[902,20873,13889],{"encoding":904},[724,20875,20876,20877,20900,20901,7671,20933],{},"Pro lineární spotřebu ",[883,20878,20880],{"className":20879},[886],[888,20881,20882],{"xmlns":890},[892,20883,20884,20898],{},[895,20885,20886,20888,20890,20892,20894,20896],{},[898,20887,2775],{},[1726,20889,1728],{},[898,20891,207],{},[898,20893,1745],{},[1726,20895,2099],{},[898,20897,2102],{},[902,20899,18901],{"encoding":904}," plyne z (7.7) rovnice ",[883,20902,20904],{"className":20903},[886],[888,20905,20906],{"xmlns":890},[892,20907,20908,20930],{},[895,20909,20910,20912,20914,20916,20918,20920,20922,20924],{},[898,20911,1745],{},[1726,20913,1728],{},[898,20915,207],{},[898,20917,1745],{},[1726,20919,2099],{},[898,20921,2102],{},[1726,20923,2099],{},[2128,20925,20926,20928],{},[898,20927,12170],{},[1726,20929,4342],{},[902,20931,20932],{"encoding":904},"Y = aY + b + I^*",[38,20934,20935],{},"redukovaný tvar",[724,20937,20938],{},[883,20939,20941],{"className":20940},[886],[888,20942,20943],{"xmlns":890},[892,20944,20945,20993],{},[895,20946,20947],{},[12818,20948,20949],{"notation":12820},[2326,20950,20951],{"scriptlevel":2328,"displaystyle":1734},[2326,20952,20953],{"scriptlevel":2328,"displaystyle":1734},[2326,20954,20955],{"scriptlevel":2328,"displaystyle":1741},[895,20956,20957,20959,20965,20967,20989,20991],{},[2289,20958,2984],{},[2128,20960,20961,20963],{},[898,20962,1745],{},[898,20964,4240],{},[1726,20966,1728],{},[2330,20968,20969,20981],{},[895,20970,20971,20973,20975],{},[898,20972,2102],{},[1726,20974,2099],{},[2128,20976,20977,20979],{},[898,20978,12170],{},[1726,20980,4342],{},[895,20982,20983,20985,20987],{},[2133,20984,2281],{},[1726,20986,2228],{},[898,20988,207],{},[898,20990,1888],{"mathvariant":2377},[2289,20992,2984],{},[902,20994,20995],{"encoding":904},"\\boxed{\\,Y^E = \\frac{b + I^*}{1 - a}.\\,}",[198,20997,20999],{"id":20998},"příklad-73","Příklad 7.3",[724,21001,21002,21003,8088,21020,3877,21044,21070],{},"V modelu ",[883,21004,21006],{"className":21005},[886],[888,21007,21008],{"xmlns":890},[892,21009,21010,21018],{},[895,21011,21012,21014,21016],{},[898,21013,2775],{},[2289,21015,12276],{},[898,21017,12170],{},[902,21019,12281],{"encoding":904},[883,21021,21023],{"className":21022},[886],[888,21024,21025],{"xmlns":890},[892,21026,21027,21041],{},[895,21028,21029,21031,21033,21035,21037,21039],{},[898,21030,2775],{},[1726,21032,1728],{},[2133,21034,19302],{},[898,21036,1745],{},[1726,21038,2099],{},[2133,21040,2860],{},[902,21042,21043],{"encoding":904},"C = 0{,}6Y + 10",[883,21045,21047],{"className":21046},[886],[888,21048,21049],{"xmlns":890},[892,21050,21051,21067],{},[895,21052,21053,21055,21057,21059,21061],{},[898,21054,12170],{},[1726,21056,1728],{},[2133,21058,3506],{},[1726,21060,1728],{},[2128,21062,21063,21065],{},[898,21064,12170],{},[1726,21066,4342],{},[902,21068,21069],{"encoding":904},"I = 12 = I^*",". Soustava",[724,21072,21073],{},[883,21074,21076],{"className":21075},[886],[888,21077,21078],{"xmlns":890},[892,21079,21080,21136],{},[20735,21081,21082,21108],{"rowspacing":20737,"columnalign":20738,"columnspacing":2378},[20740,21083,21084,21090],{},[20743,21085,21086],{},[2326,21087,21088],{"scriptlevel":2328,"displaystyle":1741},[898,21089,1745],{},[20743,21091,21092],{},[2326,21093,21094],{"scriptlevel":2328,"displaystyle":1741},[895,21095,21096,21098,21100,21102,21104,21106],{},[895,21097],{},[1726,21099,1728],{},[898,21101,2775],{},[1726,21103,2099],{},[2133,21105,3506],{},[1726,21107,1742],{"separator":1741},[20740,21109,21110,21116],{},[20743,21111,21112],{},[2326,21113,21114],{"scriptlevel":2328,"displaystyle":1741},[898,21115,2775],{},[20743,21117,21118],{},[2326,21119,21120],{"scriptlevel":2328,"displaystyle":1741},[895,21121,21122,21124,21126,21128,21130,21132,21134],{},[895,21123],{},[1726,21125,1728],{},[2133,21127,19302],{},[898,21129,1745],{},[1726,21131,2099],{},[2133,21133,2860],{},[1726,21135,1742],{"separator":1741},[902,21137,21138],{"encoding":904},"\\begin{aligned} Y &= C + 12, \\\\ C &= 0{,}6Y + 10, \\end{aligned}",[724,21140,21141,21142,1343,21165,21188,21189,1847],{},"má řešení ",[883,21143,21145],{"className":21144},[886],[888,21146,21147],{"xmlns":890},[892,21148,21149,21162],{},[895,21150,21151,21157,21159],{},[2128,21152,21153,21155],{},[898,21154,1745],{},[898,21156,4240],{},[1726,21158,1728],{},[2133,21160,21161],{},"55",[902,21163,21164],{"encoding":904},"Y^E = 55",[883,21166,21168],{"className":21167},[886],[888,21169,21170],{"xmlns":890},[892,21171,21172,21185],{},[895,21173,21174,21180,21182],{},[2128,21175,21176,21178],{},[898,21177,2775],{},[898,21179,4240],{},[1726,21181,1728],{},[2133,21183,21184],{},"43",[902,21186,21187],{"encoding":904},"C^E = 43"," (a ",[883,21190,21192],{"className":21191},[886],[888,21193,21194],{"xmlns":890},[892,21195,21196,21208],{},[895,21197,21198,21204,21206],{},[2128,21199,21200,21202],{},[898,21201,8659],{},[898,21203,4240],{},[1726,21205,1728],{},[2133,21207,3506],{},[902,21209,21210],{"encoding":904},"S^E = 12",[724,21212,21213],{},[614,21214,21215,21216,21238,21239,12114,21260,21283,21284,1888],{},"Obrázek 7.5 — Přímky ",[883,21217,21219],{"className":21218},[886],[888,21220,21221],{"xmlns":890},[892,21222,21223,21235],{},[895,21224,21225,21227,21229,21231,21233],{},[898,21226,2775],{},[1726,21228,1728],{},[898,21230,1745],{},[1726,21232,2228],{},[2133,21234,3506],{},[902,21236,21237],{"encoding":904},"C = Y - 12"," (rovnováha ",[883,21240,21242],{"className":21241},[886],[888,21243,21244],{"xmlns":890},[892,21245,21246,21258],{},[895,21247,21248,21250,21252,21254,21256],{},[898,21249,1745],{},[1726,21251,1728],{},[898,21253,2775],{},[1726,21255,2099],{},[898,21257,12170],{},[902,21259,14730],{"encoding":904},[883,21261,21263],{"className":21262},[886],[888,21264,21265],{"xmlns":890},[892,21266,21267,21281],{},[895,21268,21269,21271,21273,21275,21277,21279],{},[898,21270,2775],{},[1726,21272,1728],{},[2133,21274,19302],{},[898,21276,1745],{},[1726,21278,2099],{},[2133,21280,2860],{},[902,21282,21043],{"encoding":904}," (funkce spotřeby) se protínají v bodě ",[883,21285,21287],{"className":21286},[886],[888,21288,21289],{"xmlns":890},[892,21290,21291,21323],{},[895,21292,21293,21295,21301,21303,21309,21311,21313,21315,21317,21319,21321],{},[1726,21294,2487],{"stretchy":1734},[2128,21296,21297,21299],{},[898,21298,1745],{},[898,21300,4240],{},[1726,21302,1742],{"separator":1741},[2128,21304,21305,21307],{},[898,21306,2775],{},[898,21308,4240],{},[1726,21310,2502],{"stretchy":1734},[1726,21312,1728],{},[1726,21314,2487],{"stretchy":1734},[2133,21316,21161],{},[1726,21318,1742],{"separator":1741},[2133,21320,21184],{},[1726,21322,2502],{"stretchy":1734},[902,21324,21325],{"encoding":904},"[Y^E, C^E] = [55, 43]",[724,21327,21328,21331,21332,21349,21350,1888],{},[38,21329,21330],{},"Komentář k přechodu."," Model ",[883,21333,21335],{"className":21334},[886],[888,21336,21337],{"xmlns":890},[892,21338,21339,21347],{},[895,21340,21341,21343,21345],{},[898,21342,2775],{},[2289,21344,12276],{},[898,21346,12170],{},[902,21348,12281],{"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 ",[38,21351,21352,21353],{},"model ",[883,21354,21356],{"className":21355},[886],[888,21357,21358],{"xmlns":890},[892,21359,21360,21372],{},[895,21361,21362,21364,21366,21368,21370],{},[898,21363,2775],{},[2289,21365,12276],{},[898,21367,12170],{},[2289,21369,12276],{},[898,21371,12098],{},[902,21373,18202],{"encoding":904},[115,21375,21377],{"id":21376},"model-c-i-g-s-vládním-sektorem","Model C-I-G — s vládním sektorem",[198,21379,20602],{"id":21380},"zadání-modelu-1",[724,21382,21383,21384,21401,21402,1777,21405,10009,21418,21421],{},"Rozšíření modelu ",[883,21385,21387],{"className":21386},[886],[888,21388,21389],{"xmlns":890},[892,21390,21391,21399],{},[895,21392,21393,21395,21397],{},[898,21394,2775],{},[2289,21396,12276],{},[898,21398,12170],{},[902,21400,12281],{"encoding":904}," o ",[38,21403,21404],{},"vládní výdaje",[883,21406,21408],{"className":21407},[886],[888,21409,21410],{"xmlns":890},[892,21411,21412,21416],{},[895,21413,21414],{},[898,21415,12098],{},[902,21417,12098],{"encoding":904},[614,21419,21420],{},"government expenditure","). Podmínka rovnováhy:",[724,21423,21424],{},[883,21425,21427],{"className":21426},[886],[888,21428,21429],{"xmlns":890},[892,21430,21431,21458],{},[895,21432,21433,21435,21437,21439,21441,21443,21445,21447,21449,21451,21453,21456],{},[898,21434,1745],{},[1726,21436,1728],{},[898,21438,2775],{},[1726,21440,2099],{},[898,21442,12170],{},[1726,21444,2099],{},[898,21446,12098],{},[898,21448,1888],{"mathvariant":2377},[5865,21450],{"width":5867},[1726,21452,1735],{"stretchy":1734},[2133,21454,21455],{},"7.8",[1726,21457,1762],{"stretchy":1734},[902,21459,21460],{"encoding":904},"Y = C + I + G. \\qquad (7.8)",[724,21462,21463,21464,1777,21467,10009,21480,21483],{},"Stát se stává spotřebitelem, jehož „důchod“ získává ",[38,21465,21466],{},"zdaněním domácností",[883,21468,21470],{"className":21469},[886],[888,21471,21472],{"xmlns":890},[892,21473,21474,21478],{},[895,21475,21476],{},[898,21477,2772],{},[902,21479,2772],{"encoding":904},[614,21481,21482],{},"taxation","). Zdanění bývá:",[120,21485,21486,21519,21544],{},[123,21487,21488,21489,1742],{},"úměrné důchodu: ",[883,21490,21492],{"className":21491},[886],[888,21493,21494],{"xmlns":890},[892,21495,21496,21516],{},[895,21497,21498,21500,21502,21504,21506,21508,21510,21512,21514],{},[898,21499,2772],{},[1726,21501,1728],{},[898,21503,2772],{},[1726,21505,1735],{"stretchy":1734},[898,21507,1745],{},[1726,21509,1762],{"stretchy":1734},[1726,21511,1728],{},[898,21513,18836],{},[898,21515,1745],{},[902,21517,21518],{"encoding":904},"T = T(Y) = tY",[123,21520,21521,21522,1742],{},"fixní: ",[883,21523,21525],{"className":21524},[886],[888,21526,21527],{"xmlns":890},[892,21528,21529,21541],{},[895,21530,21531,21533,21535],{},[898,21532,2772],{},[1726,21534,1728],{},[2128,21536,21537,21539],{},[898,21538,2772],{},[1726,21540,4342],{},[902,21542,21543],{"encoding":904},"T = T^*",[123,21545,21546,21547,21575,21576,1888],{},"kombinované: ",[883,21548,21550],{"className":21549},[886],[888,21551,21552],{"xmlns":890},[892,21553,21554,21572],{},[895,21555,21556,21558,21560,21566,21568,21570],{},[898,21557,2772],{},[1726,21559,1728],{},[2128,21561,21562,21564],{},[898,21563,2772],{},[1726,21565,4342],{},[1726,21567,2099],{},[898,21569,18836],{},[898,21571,1745],{},[902,21573,21574],{"encoding":904},"T = T^* + tY",", kde ",[883,21577,21579],{"className":21578},[886],[888,21580,21581],{"xmlns":890},[892,21582,21583,21595],{},[895,21584,21585,21587,21589,21591,21593],{},[2133,21586,2328],{},[1726,21588,7665],{},[898,21590,18836],{},[1726,21592,3444],{},[2133,21594,2281],{},[902,21596,21597],{"encoding":904},"0 \\le t \u003C 1",[3859,21599,21600],{},[724,21601,21602,21604,21605,21626,21627,21630,21631,21644,21645,12114,21671,1777,21674,21700,21701,21729,21730,3877,21743,21761],{},[883,21603,4400],{}," Pozor na disponibilní důchod\nV modelu ",[883,21606,21608],{"className":21607},[886],[888,21609,21610],{"xmlns":890},[892,21611,21612,21624],{},[895,21613,21614,21616,21618,21620,21622],{},[898,21615,2775],{},[2289,21617,12276],{},[898,21619,12170],{},[2289,21621,12276],{},[898,21623,12098],{},[902,21625,18202],{"encoding":904}," je nutné ",[38,21628,21629],{},"důsledně rozlišovat dva důchody",": celkový národní důchod ",[883,21632,21634],{"className":21633},[886],[888,21635,21636],{"xmlns":890},[892,21637,21638,21642],{},[895,21639,21640],{},[898,21641,1745],{},[902,21643,1745],{"encoding":904}," (vstupuje do podmínky rovnováhy ",[883,21646,21648],{"className":21647},[886],[888,21649,21650],{"xmlns":890},[892,21651,21652,21668],{},[895,21653,21654,21656,21658,21660,21662,21664,21666],{},[898,21655,1745],{},[1726,21657,1728],{},[898,21659,2775],{},[1726,21661,2099],{},[898,21663,12170],{},[1726,21665,2099],{},[898,21667,12098],{},[902,21669,21670],{"encoding":904},"Y = C + I + G",[38,21672,21673],{},"disponibilní důchod",[883,21675,21677],{"className":21676},[886],[888,21678,21679],{"xmlns":890},[892,21680,21681,21697],{},[895,21682,21683,21689,21691,21693,21695],{},[2275,21684,21685,21687],{},[898,21686,1745],{},[898,21688,1731],{},[1726,21690,1728],{},[898,21692,1745],{},[1726,21694,2228],{},[898,21696,2772],{},[902,21698,21699],{"encoding":904},"Y_D = Y - T"," (na něm závisí spotřeba domácností, ",[883,21702,21704],{"className":21703},[886],[888,21705,21706],{"xmlns":890},[892,21707,21708,21726],{},[895,21709,21710,21712,21714,21716,21718,21724],{},[898,21711,2775],{},[1726,21713,1728],{},[898,21715,2775],{},[1726,21717,1735],{"stretchy":1734},[2275,21719,21720,21722],{},[898,21721,1745],{},[898,21723,1731],{},[1726,21725,1762],{"stretchy":1734},[902,21727,21728],{"encoding":904},"C = C(Y_D)","). Záměna ",[883,21731,21733],{"className":21732},[886],[888,21734,21735],{"xmlns":890},[892,21736,21737,21741],{},[895,21738,21739],{},[898,21740,1745],{},[902,21742,1745],{"encoding":904},[883,21744,21746],{"className":21745},[886],[888,21747,21748],{"xmlns":890},[892,21749,21750,21758],{},[895,21751,21752],{},[2275,21753,21754,21756],{},[898,21755,1745],{},[898,21757,1731],{},[902,21759,21760],{"encoding":904},"Y_D"," ve funkci spotřeby je nejčastější zdroj chyb.",[724,21763,21764,10009,21767,1762],{},[38,21765,21766],{},"Disponibilní důchod",[614,21768,21769],{},"disposable income",[724,21771,21772],{},[883,21773,21775],{"className":21774},[886],[888,21776,21777],{"xmlns":890},[892,21778,21779,21795],{},[895,21780,21781,21787,21789,21791,21793],{},[2275,21782,21783,21785],{},[898,21784,1745],{},[898,21786,1731],{},[1726,21788,1728],{},[898,21790,1745],{},[1726,21792,2228],{},[898,21794,2772],{},[902,21796,21699],{"encoding":904},[724,21798,21799,21800,1888],{},"je to, co zbývá domácnostem po zdanění. Spotřeba je pak funkcí disponibilního důchodu: ",[883,21801,21803],{"className":21802},[886],[888,21804,21805],{"xmlns":890},[892,21806,21807,21825],{},[895,21808,21809,21811,21813,21815,21817,21823],{},[898,21810,2775],{},[1726,21812,1728],{},[898,21814,2775],{},[1726,21816,1735],{"stretchy":1734},[2275,21818,21819,21821],{},[898,21820,1745],{},[898,21822,1731],{},[1726,21824,1762],{"stretchy":1734},[902,21826,21728],{"encoding":904},[198,21828,20672],{"id":21829},"soustava-rovnic-1",[724,21831,21832,21833,1343,21854,21876,21877,2703],{},"Pro pevně zadané ",[883,21834,21836],{"className":21835},[886],[888,21837,21838],{"xmlns":890},[892,21839,21840,21852],{},[895,21841,21842,21844,21846],{},[898,21843,12170],{},[1726,21845,1728],{},[2128,21847,21848,21850],{},[898,21849,12170],{},[1726,21851,4342],{},[902,21853,12181],{"encoding":904},[883,21855,21857],{"className":21856},[886],[888,21858,21859],{"xmlns":890},[892,21860,21861,21873],{},[895,21862,21863,21865,21867],{},[898,21864,12098],{},[1726,21866,1728],{},[2128,21868,21869,21871],{},[898,21870,12098],{},[1726,21872,4342],{},[902,21874,21875],{"encoding":904},"G = G^*"," dostáváme soustavu 4 rovnic o 4 neznámých ",[883,21878,21880],{"className":21879},[886],[888,21881,21882],{"xmlns":890},[892,21883,21884,21904],{},[895,21885,21886,21888,21890,21892,21894,21900,21902],{},[898,21887,1745],{},[1726,21889,1742],{"separator":1741},[898,21891,2775],{},[1726,21893,1742],{"separator":1741},[2275,21895,21896,21898],{},[898,21897,1745],{},[898,21899,1731],{},[1726,21901,1742],{"separator":1741},[898,21903,2772],{},[902,21905,21906],{"encoding":904},"Y, C, Y_D, T",[724,21908,21909],{},[883,21910,21912],{"className":21911},[886],[888,21913,21914],{"xmlns":890},[892,21915,21916,22057],{},[895,21917,21918,22048,22050,22052,22055],{},[20735,21919,21920,21958,21986,22018],{"rowspacing":20737,"columnalign":20738,"columnspacing":2378},[20740,21921,21922,21928],{},[20743,21923,21924],{},[2326,21925,21926],{"scriptlevel":2328,"displaystyle":1741},[898,21927,1745],{},[20743,21929,21930],{},[2326,21931,21932],{"scriptlevel":2328,"displaystyle":1741},[895,21933,21934,21936,21938,21940,21942,21948,21950,21956],{},[895,21935],{},[1726,21937,1728],{},[898,21939,2775],{},[1726,21941,2099],{},[2128,21943,21944,21946],{},[898,21945,12170],{},[1726,21947,4342],{},[1726,21949,2099],{},[2128,21951,21952,21954],{},[898,21953,12098],{},[1726,21955,4342],{},[1726,21957,1742],{"separator":1741},[20740,21959,21960,21966],{},[20743,21961,21962],{},[2326,21963,21964],{"scriptlevel":2328,"displaystyle":1741},[898,21965,2772],{},[20743,21967,21968],{},[2326,21969,21970],{"scriptlevel":2328,"displaystyle":1741},[895,21971,21972,21974,21976,21978,21980,21982,21984],{},[895,21973],{},[1726,21975,1728],{},[898,21977,2772],{},[1726,21979,1735],{"stretchy":1734},[898,21981,1745],{},[1726,21983,1762],{"stretchy":1734},[1726,21985,1742],{"separator":1741},[20740,21987,21988,21994],{},[20743,21989,21990],{},[2326,21991,21992],{"scriptlevel":2328,"displaystyle":1741},[898,21993,2775],{},[20743,21995,21996],{},[2326,21997,21998],{"scriptlevel":2328,"displaystyle":1741},[895,21999,22000,22002,22004,22006,22008,22014,22016],{},[895,22001],{},[1726,22003,1728],{},[898,22005,2775],{},[1726,22007,1735],{"stretchy":1734},[2275,22009,22010,22012],{},[898,22011,1745],{},[898,22013,1731],{},[1726,22015,1762],{"stretchy":1734},[1726,22017,1742],{"separator":1741},[20740,22019,22020,22030],{},[20743,22021,22022],{},[2326,22023,22024],{"scriptlevel":2328,"displaystyle":1741},[2275,22025,22026,22028],{},[898,22027,1745],{},[898,22029,1731],{},[20743,22031,22032],{},[2326,22033,22034],{"scriptlevel":2328,"displaystyle":1741},[895,22035,22036,22038,22040,22042,22044,22046],{},[895,22037],{},[1726,22039,1728],{},[898,22041,1745],{},[1726,22043,2228],{},[898,22045,2772],{},[1726,22047,1742],{"separator":1741},[5865,22049],{"width":5867},[1726,22051,1735],{"stretchy":1734},[2133,22053,22054],{},"7.9",[1726,22056,1762],{"stretchy":1734},[902,22058,22059],{"encoding":904},"\\begin{aligned} Y &= C + I^* + G^*, \\\\ T &= T(Y), \\\\ C &= C(Y_D), \\\\ Y_D &= Y - T, \\end{aligned} \\qquad (7.9)",[724,22061,22062,22063,22107,22108,1888],{},"s řešeními ",[883,22064,22066],{"className":22065},[886],[888,22067,22068],{"xmlns":890},[892,22069,22070,22104],{},[895,22071,22072,22078,22080,22086,22088,22094,22096],{},[2128,22073,22074,22076],{},[898,22075,1745],{},[898,22077,4240],{},[1726,22079,1742],{"separator":1741},[2128,22081,22082,22084],{},[898,22083,2775],{},[898,22085,4240],{},[1726,22087,1742],{"separator":1741},[2128,22089,22090,22092],{},[898,22091,2772],{},[898,22093,4240],{},[1726,22095,1742],{"separator":1741},[9151,22097,22098,22100,22102],{},[898,22099,1745],{},[898,22101,1731],{},[898,22103,4240],{},[902,22105,22106],{"encoding":904},"Y^E, C^E, T^E, Y_D^E",", případně rovnovážnými úsporami domácností ",[883,22109,22111],{"className":22110},[886],[888,22112,22113],{"xmlns":890},[892,22114,22115,22141],{},[895,22116,22117,22123,22125,22133,22135],{},[2128,22118,22119,22121],{},[898,22120,8659],{},[898,22122,4240],{},[1726,22124,1728],{},[9151,22126,22127,22129,22131],{},[898,22128,1745],{},[898,22130,1731],{},[898,22132,4240],{},[1726,22134,2228],{},[2128,22136,22137,22139],{},[898,22138,2775],{},[898,22140,4240],{},[902,22142,22143],{"encoding":904},"S^E = Y_D^E - C^E",[3859,22145,22146,22151],{},[724,22147,22148,22150],{},[883,22149,4560],{}," Postup — jak sestavit a vyřešit soustavu C-I-G",[152,22152,22153,22176,22259,22314,22404],{},[123,22154,22155,22158,22159,1888],{},[38,22156,22157],{},"Zapiš všechny 4 rovnice"," ze zadání: podmínku rovnováhy, daňovou funkci, funkci spotřeby, definici ",[883,22160,22162],{"className":22161},[886],[888,22163,22164],{"xmlns":890},[892,22165,22166,22174],{},[895,22167,22168],{},[2275,22169,22170,22172],{},[898,22171,1745],{},[898,22173,1731],{},[902,22175,21760],{"encoding":904},[123,22177,22178,22227,22228,22245,22246,1888],{},[38,22179,22180,22181,22201,22202],{},"Dosaď ",[883,22182,22184],{"className":22183},[886],[888,22185,22186],{"xmlns":890},[892,22187,22188,22198],{},[895,22189,22190,22192,22194,22196],{},[898,22191,2772],{},[1726,22193,1735],{"stretchy":1734},[898,22195,1745],{},[1726,22197,1762],{"stretchy":1734},[902,22199,22200],{"encoding":904},"T(Y)"," do ",[883,22203,22205],{"className":22204},[886],[888,22206,22207],{"xmlns":890},[892,22208,22209,22225],{},[895,22210,22211,22217,22219,22221,22223],{},[2275,22212,22213,22215],{},[898,22214,1745],{},[898,22216,1731],{},[1726,22218,1728],{},[898,22220,1745],{},[1726,22222,2228],{},[898,22224,2772],{},[902,22226,21699],{"encoding":904}," — dostaneš ",[883,22229,22231],{"className":22230},[886],[888,22232,22233],{"xmlns":890},[892,22234,22235,22243],{},[895,22236,22237],{},[2275,22238,22239,22241],{},[898,22240,1745],{},[898,22242,1731],{},[902,22244,21760],{"encoding":904}," jako lineární funkci ",[883,22247,22249],{"className":22248},[886],[888,22250,22251],{"xmlns":890},[892,22252,22253,22257],{},[895,22254,22255],{},[898,22256,1745],{},[902,22258,1745],{"encoding":904},[123,22260,22261,22227,22288,22245,22301,1888],{},[38,22262,22180,22263,22287],{},[883,22264,22266],{"className":22265},[886],[888,22267,22268],{"xmlns":890},[892,22269,22270,22284],{},[895,22271,22272,22278,22280,22282],{},[2275,22273,22274,22276],{},[898,22275,1745],{},[898,22277,1731],{},[1726,22279,1735],{"stretchy":1734},[898,22281,1745],{},[1726,22283,1762],{"stretchy":1734},[902,22285,22286],{"encoding":904},"Y_D(Y)"," do funkce spotřeby",[883,22289,22291],{"className":22290},[886],[888,22292,22293],{"xmlns":890},[892,22294,22295,22299],{},[895,22296,22297],{},[898,22298,2775],{},[902,22300,2775],{"encoding":904},[883,22302,22304],{"className":22303},[886],[888,22305,22306],{"xmlns":890},[892,22307,22308,22312],{},[895,22309,22310],{},[898,22311,1745],{},[902,22313,1745],{"encoding":904},[123,22315,22316,1777,22338,22372,22373,22386,22387,1888],{},[38,22317,22180,22318,22337],{},[883,22319,22321],{"className":22320},[886],[888,22322,22323],{"xmlns":890},[892,22324,22325,22335],{},[895,22326,22327,22329,22331,22333],{},[898,22328,2775],{},[1726,22330,1735],{"stretchy":1734},[898,22332,1745],{},[1726,22334,1762],{"stretchy":1734},[902,22336,14202],{"encoding":904}," do podmínky rovnováhy",[883,22339,22341],{"className":22340},[886],[888,22342,22343],{"xmlns":890},[892,22344,22345,22369],{},[895,22346,22347,22349,22351,22353,22355,22361,22363],{},[898,22348,1745],{},[1726,22350,1728],{},[898,22352,2775],{},[1726,22354,2099],{},[2128,22356,22357,22359],{},[898,22358,12170],{},[1726,22360,4342],{},[1726,22362,2099],{},[2128,22364,22365,22367],{},[898,22366,12098],{},[1726,22368,4342],{},[902,22370,22371],{"encoding":904},"Y = C + I^* + G^*"," — zbývá jediná rovnice o jedné neznámé ",[883,22374,22376],{"className":22375},[886],[888,22377,22378],{"xmlns":890},[892,22379,22380,22384],{},[895,22381,22382],{},[898,22383,1745],{},[902,22385,1745],{"encoding":904},", odtud ",[883,22388,22390],{"className":22389},[886],[888,22391,22392],{"xmlns":890},[892,22393,22394,22402],{},[895,22395,22396],{},[2128,22397,22398,22400],{},[898,22399,1745],{},[898,22401,4240],{},[902,22403,13889],{"encoding":904},[123,22405,22406,22409,22410,1343,22428,1343,22448,1343,22465,1888],{},[38,22407,22408],{},"Zpětným dosazením"," dopočítej ",[883,22411,22413],{"className":22412},[886],[888,22414,22415],{"xmlns":890},[892,22416,22417,22425],{},[895,22418,22419],{},[2128,22420,22421,22423],{},[898,22422,2772],{},[898,22424,4240],{},[902,22426,22427],{"encoding":904},"T^E",[883,22429,22431],{"className":22430},[886],[888,22432,22433],{"xmlns":890},[892,22434,22435,22445],{},[895,22436,22437],{},[9151,22438,22439,22441,22443],{},[898,22440,1745],{},[898,22442,1731],{},[898,22444,4240],{},[902,22446,22447],{"encoding":904},"Y_D^E",[883,22449,22451],{"className":22450},[886],[888,22452,22453],{"xmlns":890},[892,22454,22455,22463],{},[895,22456,22457],{},[2128,22458,22459,22461],{},[898,22460,2775],{},[898,22462,4240],{},[902,22464,13948],{"encoding":904},[883,22466,22468],{"className":22467},[886],[888,22469,22470],{"xmlns":890},[892,22471,22472,22480],{},[895,22473,22474],{},[2128,22475,22476,22478],{},[898,22477,8659],{},[898,22479,4240],{},[902,22481,22482],{"encoding":904},"S^E",[198,22484,22486],{"id":22485},"příklad-74","Příklad 7.4",[724,22488,21002,22489,22510,22511,1343,22542,1343,22566,1343,22588,22610],{},[883,22490,22492],{"className":22491},[886],[888,22493,22494],{"xmlns":890},[892,22495,22496,22508],{},[895,22497,22498,22500,22502,22504,22506],{},[898,22499,2775],{},[2289,22501,12276],{},[898,22503,12170],{},[2289,22505,12276],{},[898,22507,12098],{},[902,22509,18202],{"encoding":904}," jsou dány ",[883,22512,22514],{"className":22513},[886],[888,22515,22516],{"xmlns":890},[892,22517,22518,22539],{},[895,22519,22520,22522,22524,22527,22529,22535,22537],{},[898,22521,2775],{},[1726,22523,1728],{},[2133,22525,22526],{},"0,9",[2289,22528,2984],{},[2275,22530,22531,22533],{},[898,22532,1745],{},[898,22534,1731],{},[1726,22536,2099],{},[2133,22538,5884],{},[902,22540,22541],{"encoding":904},"C = 0{,}9\\,Y_D + 70",[883,22543,22545],{"className":22544},[886],[888,22546,22547],{"xmlns":890},[892,22548,22549,22563],{},[895,22550,22551,22553,22555,22557,22559,22561],{},[898,22552,2772],{},[1726,22554,1728],{},[2133,22556,2836],{},[898,22558,1745],{},[1726,22560,2099],{},[2133,22562,4991],{},[902,22564,22565],{"encoding":904},"T = 0{,}2Y + 25",[883,22567,22569],{"className":22568},[886],[888,22570,22571],{"xmlns":890},[892,22572,22573,22585],{},[895,22574,22575,22581,22583],{},[2128,22576,22577,22579],{},[898,22578,12170],{},[1726,22580,4342],{},[1726,22582,1728],{},[2133,22584,15024],{},[902,22586,22587],{"encoding":904},"I^* = 35",[883,22589,22591],{"className":22590},[886],[888,22592,22593],{"xmlns":890},[892,22594,22595,22607],{},[895,22596,22597,22603,22605],{},[2128,22598,22599,22601],{},[898,22600,12098],{},[1726,22602,4342],{},[1726,22604,1728],{},[2133,22606,9021],{},[902,22608,22609],{"encoding":904},"G^* = 20",". Soustava (7.9):",[724,22612,22613],{},[883,22614,22616],{"className":22615},[886],[888,22617,22618],{"xmlns":890},[892,22619,22620,22744],{},[20735,22621,22622,22652,22680,22714],{"rowspacing":20737,"columnalign":20738,"columnspacing":2378},[20740,22623,22624,22630],{},[20743,22625,22626],{},[2326,22627,22628],{"scriptlevel":2328,"displaystyle":1741},[898,22629,1745],{},[20743,22631,22632],{},[2326,22633,22634],{"scriptlevel":2328,"displaystyle":1741},[895,22635,22636,22638,22640,22642,22644,22646,22648,22650],{},[895,22637],{},[1726,22639,1728],{},[898,22641,2775],{},[1726,22643,2099],{},[2133,22645,15024],{},[1726,22647,2099],{},[2133,22649,9021],{},[1726,22651,1742],{"separator":1741},[20740,22653,22654,22660],{},[20743,22655,22656],{},[2326,22657,22658],{"scriptlevel":2328,"displaystyle":1741},[898,22659,2772],{},[20743,22661,22662],{},[2326,22663,22664],{"scriptlevel":2328,"displaystyle":1741},[895,22665,22666,22668,22670,22672,22674,22676,22678],{},[895,22667],{},[1726,22669,1728],{},[2133,22671,2836],{},[898,22673,1745],{},[1726,22675,2099],{},[2133,22677,4991],{},[1726,22679,1742],{"separator":1741},[20740,22681,22682,22688],{},[20743,22683,22684],{},[2326,22685,22686],{"scriptlevel":2328,"displaystyle":1741},[898,22687,2775],{},[20743,22689,22690],{},[2326,22691,22692],{"scriptlevel":2328,"displaystyle":1741},[895,22693,22694,22696,22698,22700,22702,22708,22710,22712],{},[895,22695],{},[1726,22697,1728],{},[2133,22699,22526],{},[2289,22701,2984],{},[2275,22703,22704,22706],{},[898,22705,1745],{},[898,22707,1731],{},[1726,22709,2099],{},[2133,22711,5884],{},[1726,22713,1742],{"separator":1741},[20740,22715,22716,22726],{},[20743,22717,22718],{},[2326,22719,22720],{"scriptlevel":2328,"displaystyle":1741},[2275,22721,22722,22724],{},[898,22723,1745],{},[898,22725,1731],{},[20743,22727,22728],{},[2326,22729,22730],{"scriptlevel":2328,"displaystyle":1741},[895,22731,22732,22734,22736,22738,22740,22742],{},[895,22733],{},[1726,22735,1728],{},[898,22737,1745],{},[1726,22739,2228],{},[898,22741,2772],{},[898,22743,1888],{"mathvariant":2377},[902,22745,22746],{"encoding":904},"\\begin{aligned} Y &= C + 35 + 20, \\\\ T &= 0{,}2Y + 25, \\\\ C &= 0{,}9\\,Y_D + 70, \\\\ Y_D &= Y - T. \\end{aligned}",[724,22748,22749,22752,22753,22807,22808,22854,22855,2703],{},[38,22750,22751],{},"Řešení."," Z definice ",[883,22754,22756],{"className":22755},[886],[888,22757,22758],{"xmlns":890},[892,22759,22760,22804],{},[895,22761,22762,22768,22770,22772,22774,22776,22778,22780,22782,22784,22786,22788,22790,22792,22794,22796,22798,22800,22802],{},[2275,22763,22764,22766],{},[898,22765,1745],{},[898,22767,1731],{},[1726,22769,1728],{},[898,22771,1745],{},[1726,22773,2228],{},[898,22775,2772],{},[1726,22777,1728],{},[898,22779,1745],{},[1726,22781,2228],{},[1726,22783,1735],{"stretchy":1734},[2133,22785,2836],{},[898,22787,1745],{},[1726,22789,2099],{},[2133,22791,4991],{},[1726,22793,1762],{"stretchy":1734},[1726,22795,1728],{},[2133,22797,14575],{},[898,22799,1745],{},[1726,22801,2228],{},[2133,22803,4991],{},[902,22805,22806],{"encoding":904},"Y_D = Y - T = Y - (0{,}2Y + 25) = 0{,}8Y - 25",". Dosazením do spotřeby: ",[883,22809,22811],{"className":22810},[886],[888,22812,22813],{"xmlns":890},[892,22814,22815,22851],{},[895,22816,22817,22819,22821,22823,22825,22827,22829,22831,22833,22835,22837,22839,22841,22844,22846,22848],{},[898,22818,2775],{},[1726,22820,1728],{},[2133,22822,22526],{},[1726,22824,1735],{"stretchy":1734},[2133,22826,14575],{},[898,22828,1745],{},[1726,22830,2228],{},[2133,22832,4991],{},[1726,22834,1762],{"stretchy":1734},[1726,22836,2099],{},[2133,22838,5884],{},[1726,22840,1728],{},[2133,22842,22843],{},"0,72",[898,22845,1745],{},[1726,22847,2099],{},[2133,22849,22850],{},"47,5",[902,22852,22853],{"encoding":904},"C = 0{,}9(0{,}8Y - 25) + 70 = 0{,}72Y + 47{,}5",". Dosazením do rovnovážné rovnice ",[883,22856,22858],{"className":22857},[886],[888,22859,22860],{"xmlns":890},[892,22861,22862,22880],{},[895,22863,22864,22866,22868,22870,22872,22874,22876,22878],{},[898,22865,1745],{},[1726,22867,1728],{},[2133,22869,22843],{},[898,22871,1745],{},[1726,22873,2099],{},[2133,22875,22850],{},[1726,22877,2099],{},[2133,22879,21161],{},[902,22881,22882],{"encoding":904},"Y = 0{,}72Y + 47{,}5 + 55",[724,22884,22885],{},[883,22886,22888],{"className":22887},[886],[888,22889,22890],{"xmlns":890},[892,22891,22892,22933],{},[895,22893,22894,22897,22899,22901,22904,22906,22908,22910,22916,22918,22928,22930],{},[2133,22895,22896],{},"0,28",[898,22898,1745],{},[1726,22900,1728],{},[2133,22902,22903],{},"102,5",[2289,22905,3974],{},[1726,22907,14994],{},[2289,22909,3974],{},[2128,22911,22912,22914],{},[898,22913,1745],{},[898,22915,4240],{},[1726,22917,1728],{},[2326,22919,22920],{"scriptlevel":2328,"displaystyle":1734},[2330,22921,22922,22925],{},[2133,22923,22924],{},"5125",[2133,22926,22927],{},"14",[1726,22929,5887],{},[2133,22931,22932],{},"366,071.",[902,22934,22935],{"encoding":904},"0{,}28Y = 102{,}5 \\;\\Longrightarrow\\; Y^E = \\tfrac{5125}{14} \\doteq 366{,}071.",[724,22937,22938],{},"Rovnovážné veličiny:",[120,22940,22941,22976,23028,23082,23130],{},[123,22942,22943,1742],{},[883,22944,22946],{"className":22945},[886],[888,22947,22948],{"xmlns":890},[892,22949,22950,22973],{},[895,22951,22952,22958,22960,22968,22970],{},[2128,22953,22954,22956],{},[898,22955,1745],{},[898,22957,4240],{},[1726,22959,1728],{},[2326,22961,22962],{"scriptlevel":2328,"displaystyle":1734},[2330,22963,22964,22966],{},[2133,22965,22924],{},[2133,22967,22927],{},[1726,22969,5887],{},[2133,22971,22972],{},"366,071",[902,22974,22975],{"encoding":904},"Y^E = \\tfrac{5125}{14} \\doteq 366{,}071",[123,22977,22978,1742],{},[883,22979,22981],{"className":22980},[886],[888,22982,22983],{"xmlns":890},[892,22984,22985,23025],{},[895,22986,22987,22993,22995,22997,22999,23005,23007,23009,23011,23020,23022],{},[2128,22988,22989,22991],{},[898,22990,2772],{},[898,22992,4240],{},[1726,22994,1728],{},[2133,22996,2836],{},[2289,22998,2984],{},[2128,23000,23001,23003],{},[898,23002,1745],{},[898,23004,4240],{},[1726,23006,2099],{},[2133,23008,4991],{},[1726,23010,1728],{},[2326,23012,23013],{"scriptlevel":2328,"displaystyle":1734},[2330,23014,23015,23018],{},[2133,23016,23017],{},"1375",[2133,23019,22927],{},[1726,23021,5887],{},[2133,23023,23024],{},"98,214",[902,23026,23027],{"encoding":904},"T^E = 0{,}2\\,Y^E + 25 = \\tfrac{1375}{14} \\doteq 98{,}214",[123,23029,23030,1742],{},[883,23031,23033],{"className":23032},[886],[888,23034,23035],{"xmlns":890},[892,23036,23037,23079],{},[895,23038,23039,23047,23049,23055,23057,23063,23065,23074,23076],{},[9151,23040,23041,23043,23045],{},[898,23042,1745],{},[898,23044,1731],{},[898,23046,4240],{},[1726,23048,1728],{},[2128,23050,23051,23053],{},[898,23052,1745],{},[898,23054,4240],{},[1726,23056,2228],{},[2128,23058,23059,23061],{},[898,23060,2772],{},[898,23062,4240],{},[1726,23064,1728],{},[2326,23066,23067],{"scriptlevel":2328,"displaystyle":1734},[2330,23068,23069,23072],{},[2133,23070,23071],{},"3750",[2133,23073,22927],{},[1726,23075,5887],{},[2133,23077,23078],{},"267,857",[902,23080,23081],{"encoding":904},"Y_D^E = Y^E - T^E = \\tfrac{3750}{14} \\doteq 267{,}857",[123,23083,23084,1742],{},[883,23085,23087],{"className":23086},[886],[888,23088,23089],{"xmlns":890},[892,23090,23091,23127],{},[895,23092,23093,23099,23101,23107,23109,23111,23113,23122,23124],{},[2128,23094,23095,23097],{},[898,23096,2775],{},[898,23098,4240],{},[1726,23100,1728],{},[2128,23102,23103,23105],{},[898,23104,1745],{},[898,23106,4240],{},[1726,23108,2228],{},[2133,23110,21161],{},[1726,23112,1728],{},[2326,23114,23115],{"scriptlevel":2328,"displaystyle":1734},[2330,23116,23117,23120],{},[2133,23118,23119],{},"4355",[2133,23121,22927],{},[1726,23123,5887],{},[2133,23125,23126],{},"311,071",[902,23128,23129],{"encoding":904},"C^E = Y^E - 55 = \\tfrac{4355}{14} \\doteq 311{,}071",[123,23131,23132,23188],{},[883,23133,23135],{"className":23134},[886],[888,23136,23137],{"xmlns":890},[892,23138,23139,23185],{},[895,23140,23141,23147,23149,23157,23159,23165,23167,23169,23178,23180,23182],{},[2128,23142,23143,23145],{},[898,23144,8659],{},[898,23146,4240],{},[1726,23148,1728],{},[9151,23150,23151,23153,23155],{},[898,23152,1745],{},[898,23154,1731],{},[898,23156,4240],{},[1726,23158,2228],{},[2128,23160,23161,23163],{},[898,23162,2775],{},[898,23164,4240],{},[1726,23166,1728],{},[1726,23168,2228],{},[2326,23170,23171],{"scriptlevel":2328,"displaystyle":1734},[2330,23172,23173,23176],{},[2133,23174,23175],{},"605",[2133,23177,22927],{},[1726,23179,5887],{},[1726,23181,2228],{},[2133,23183,23184],{},"43,214",[902,23186,23187],{"encoding":904},"S^E = Y_D^E - C^E = -\\tfrac{605}{14} \\doteq -43{,}214"," (záporné — domácnosti při této kalibraci čerpají úspory).",[724,23190,23191,21331,23193,23214,23215,23218,23219,23242,23243,1888],{},[38,23192,21330],{},[883,23194,23196],{"className":23195},[886],[888,23197,23198],{"xmlns":890},[892,23199,23200,23212],{},[895,23201,23202,23204,23206,23208,23210],{},[898,23203,2775],{},[2289,23205,12276],{},[898,23207,12170],{},[2289,23209,12276],{},[898,23211,12098],{},[902,23213,18202],{"encoding":904}," stále uvažuje ",[38,23216,23217],{},"uzavřenou"," ekonomiku. Reálné ekonomiky dovážejí a vyvážejí zboží — otevření ekonomiky o čistý export ",[883,23220,23222],{"className":23221},[886],[888,23223,23224],{"xmlns":890},[892,23225,23226,23239],{},[895,23227,23228,23230,23232,23235,23237],{},[898,23229,12306],{},[1726,23231,1728],{},[898,23233,23234],{},"B",[1726,23236,2228],{},[898,23238,2815],{},[902,23240,23241],{"encoding":904},"X = B - M"," dává ",[38,23244,21352,23245],{},[883,23246,23248],{"className":23247},[886],[888,23249,23250],{"xmlns":890},[892,23251,23252,23268],{},[895,23253,23254,23256,23258,23260,23262,23264,23266],{},[898,23255,2775],{},[2289,23257,12276],{},[898,23259,12170],{},[2289,23261,12276],{},[898,23263,12098],{},[2289,23265,12276],{},[898,23267,12306],{},[902,23269,12309],{"encoding":904},[115,23271,23273],{"id":23272},"model-c-i-g-x-otevřená-ekonomika","Model C-I-G-X — otevřená ekonomika",[198,23275,20602],{"id":23276},"zadání-modelu-2",[724,23278,23279,23280,1777,23283,21575,23304,23317,23318,12114,23321,23334],{},"Rozšíření o ",[38,23281,23282],{},"čistý export",[883,23284,23286],{"className":23285},[886],[888,23287,23288],{"xmlns":890},[892,23289,23290,23302],{},[895,23291,23292,23294,23296,23298,23300],{},[898,23293,12306],{},[1726,23295,1728],{},[898,23297,23234],{},[1726,23299,2228],{},[898,23301,2815],{},[902,23303,23241],{"encoding":904},[883,23305,23307],{"className":23306},[886],[888,23308,23309],{"xmlns":890},[892,23310,23311,23315],{},[895,23312,23313],{},[898,23314,23234],{},[902,23316,23234],{"encoding":904}," je hrubý export (",[614,23319,23320],{},"brutto export",[883,23322,23324],{"className":23323},[886],[888,23325,23326],{"xmlns":890},[892,23327,23328,23332],{},[895,23329,23330],{},[898,23331,2815],{},[902,23333,2815],{"encoding":904}," import. Obvyklá konstrukce: import závisí (nejčastěji je úměrný) disponibilnímu důchodu:",[724,23336,23337],{},[883,23338,23340],{"className":23339},[886],[888,23341,23342],{"xmlns":890},[892,23343,23344,23364],{},[895,23345,23346,23348,23350,23352,23354,23360,23362],{},[898,23347,2815],{},[1726,23349,1728],{},[898,23351,2815],{},[1726,23353,1735],{"stretchy":1734},[2275,23355,23356,23358],{},[898,23357,1745],{},[898,23359,1731],{},[1726,23361,1762],{"stretchy":1734},[898,23363,1888],{"mathvariant":2377},[902,23365,23366],{"encoding":904},"M = M(Y_D).",[724,23368,23369],{},"Podmínka rovnováhy:",[724,23371,23372],{},[883,23373,23375],{"className":23374},[886],[888,23376,23377],{"xmlns":890},[892,23378,23379,23416],{},[895,23380,23381,23383,23385,23387,23389,23391,23393,23395,23397,23399,23401,23403,23405,23407,23409,23412,23414],{},[898,23382,1745],{},[1726,23384,1728],{},[898,23386,2775],{},[1726,23388,2099],{},[898,23390,12170],{},[1726,23392,2099],{},[898,23394,12098],{},[1726,23396,2099],{},[898,23398,23234],{},[1726,23400,2228],{},[898,23402,2815],{},[898,23404,1888],{"mathvariant":2377},[5865,23406],{"width":5867},[1726,23408,1735],{"stretchy":1734},[2133,23410,23411],{},"7.10",[2289,23413,207],{},[1726,23415,1762],{"stretchy":1734},[902,23417,23418],{"encoding":904},"Y = C + I + G + B - M. \\qquad (7.10\\text{a})",[198,23420,20672],{"id":23421},"soustava-rovnic-2",[724,23423,21832,23424,23458,23459,2703],{},[883,23425,23427],{"className":23426},[886],[888,23428,23429],{"xmlns":890},[892,23430,23431,23455],{},[895,23432,23433,23439,23441,23447,23449],{},[2128,23434,23435,23437],{},[898,23436,12170],{},[1726,23438,4342],{},[1726,23440,1742],{"separator":1741},[2128,23442,23443,23445],{},[898,23444,12098],{},[1726,23446,4342],{},[1726,23448,1742],{"separator":1741},[2128,23450,23451,23453],{},[898,23452,23234],{},[1726,23454,4342],{},[902,23456,23457],{"encoding":904},"I^*, G^*, B^*"," dostáváme soustavu 5 rovnic o 5 neznámých ",[883,23460,23462],{"className":23461},[886],[888,23463,23464],{"xmlns":890},[892,23465,23466,23490],{},[895,23467,23468,23470,23472,23474,23476,23478,23480,23486,23488],{},[898,23469,1745],{},[1726,23471,1742],{"separator":1741},[898,23473,2775],{},[1726,23475,1742],{"separator":1741},[898,23477,2772],{},[1726,23479,1742],{"separator":1741},[2275,23481,23482,23484],{},[898,23483,1745],{},[898,23485,1731],{},[1726,23487,1742],{"separator":1741},[898,23489,2815],{},[902,23491,23492],{"encoding":904},"Y, C, T, Y_D, M",[724,23494,23495],{},[883,23496,23498],{"className":23497},[886],[888,23499,23500],{"xmlns":890},[892,23501,23502,23686],{},[895,23503,23504,23678,23680,23682,23684],{},[20735,23505,23506,23538,23568,23596,23628],{"rowspacing":20737,"columnalign":20738,"columnspacing":2378},[20740,23507,23508,23514],{},[20743,23509,23510],{},[2326,23511,23512],{"scriptlevel":2328,"displaystyle":1741},[898,23513,2775],{},[20743,23515,23516],{},[2326,23517,23518],{"scriptlevel":2328,"displaystyle":1741},[895,23519,23520,23522,23524,23526,23528,23534,23536],{},[895,23521],{},[1726,23523,1728],{},[898,23525,2775],{},[1726,23527,1735],{"stretchy":1734},[2275,23529,23530,23532],{},[898,23531,1745],{},[898,23533,1731],{},[1726,23535,1762],{"stretchy":1734},[1726,23537,1742],{"separator":1741},[20740,23539,23540,23550],{},[20743,23541,23542],{},[2326,23543,23544],{"scriptlevel":2328,"displaystyle":1741},[2275,23545,23546,23548],{},[898,23547,1745],{},[898,23549,1731],{},[20743,23551,23552],{},[2326,23553,23554],{"scriptlevel":2328,"displaystyle":1741},[895,23555,23556,23558,23560,23562,23564,23566],{},[895,23557],{},[1726,23559,1728],{},[898,23561,1745],{},[1726,23563,2228],{},[898,23565,2772],{},[1726,23567,1742],{"separator":1741},[20740,23569,23570,23576],{},[20743,23571,23572],{},[2326,23573,23574],{"scriptlevel":2328,"displaystyle":1741},[898,23575,2772],{},[20743,23577,23578],{},[2326,23579,23580],{"scriptlevel":2328,"displaystyle":1741},[895,23581,23582,23584,23586,23588,23590,23592,23594],{},[895,23583],{},[1726,23585,1728],{},[898,23587,2772],{},[1726,23589,1735],{"stretchy":1734},[898,23591,1745],{},[1726,23593,1762],{"stretchy":1734},[1726,23595,1742],{"separator":1741},[20740,23597,23598,23604],{},[20743,23599,23600],{},[2326,23601,23602],{"scriptlevel":2328,"displaystyle":1741},[898,23603,2815],{},[20743,23605,23606],{},[2326,23607,23608],{"scriptlevel":2328,"displaystyle":1741},[895,23609,23610,23612,23614,23616,23618,23624,23626],{},[895,23611],{},[1726,23613,1728],{},[898,23615,2815],{},[1726,23617,1735],{"stretchy":1734},[2275,23619,23620,23622],{},[898,23621,1745],{},[898,23623,1731],{},[1726,23625,1762],{"stretchy":1734},[1726,23627,1742],{"separator":1741},[20740,23629,23630,23636],{},[20743,23631,23632],{},[2326,23633,23634],{"scriptlevel":2328,"displaystyle":1741},[898,23635,1745],{},[20743,23637,23638],{},[2326,23639,23640],{"scriptlevel":2328,"displaystyle":1741},[895,23641,23642,23644,23646,23648,23650,23656,23658,23664,23666,23672,23674,23676],{},[895,23643],{},[1726,23645,1728],{},[898,23647,2775],{},[1726,23649,2099],{},[2128,23651,23652,23654],{},[898,23653,12170],{},[1726,23655,4342],{},[1726,23657,2099],{},[2128,23659,23660,23662],{},[898,23661,12098],{},[1726,23663,4342],{},[1726,23665,2099],{},[2128,23667,23668,23670],{},[898,23669,23234],{},[1726,23671,4342],{},[1726,23673,2228],{},[898,23675,2815],{},[898,23677,1888],{"mathvariant":2377},[5865,23679],{"width":5867},[1726,23681,1735],{"stretchy":1734},[2133,23683,23411],{},[1726,23685,1762],{"stretchy":1734},[902,23687,23688],{"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)",[198,23690,23692],{"id":23691},"příklad-75","Příklad 7.5",[724,23694,23695,23696,1343,23728,1343,23755,1343,23776,1343,23798,1343,23820,23843],{},"Dáno: ",[883,23697,23699],{"className":23698},[886],[888,23700,23701],{"xmlns":890},[892,23702,23703,23725],{},[895,23704,23705,23707,23709,23712,23714,23720,23722],{},[898,23706,2775],{},[1726,23708,1728],{},[2133,23710,23711],{},"0,75",[2289,23713,2984],{},[2275,23715,23716,23718],{},[898,23717,1745],{},[898,23719,1731],{},[1726,23721,2099],{},[2133,23723,23724],{},"750",[902,23726,23727],{"encoding":904},"C = 0{,}75\\,Y_D + 750",[883,23729,23731],{"className":23730},[886],[888,23732,23733],{"xmlns":890},[892,23734,23735,23752],{},[895,23736,23737,23739,23741,23744,23746],{},[898,23738,2815],{},[1726,23740,1728],{},[2133,23742,23743],{},"0,15",[2289,23745,2984],{},[2275,23747,23748,23750],{},[898,23749,1745],{},[898,23751,1731],{},[902,23753,23754],{"encoding":904},"M = 0{,}15\\,Y_D",[883,23756,23758],{"className":23757},[886],[888,23759,23760],{"xmlns":890},[892,23761,23762,23773],{},[895,23763,23764,23766,23768,23771],{},[898,23765,2772],{},[1726,23767,1728],{},[2133,23769,23770],{},"0,25",[898,23772,1745],{},[902,23774,23775],{"encoding":904},"T = 0{,}25Y",[883,23777,23779],{"className":23778},[886],[888,23780,23781],{"xmlns":890},[892,23782,23783,23795],{},[895,23784,23785,23791,23793],{},[2128,23786,23787,23789],{},[898,23788,12170],{},[1726,23790,4342],{},[1726,23792,1728],{},[2133,23794,15096],{},[902,23796,23797],{"encoding":904},"I^* = 500",[883,23799,23801],{"className":23800},[886],[888,23802,23803],{"xmlns":890},[892,23804,23805,23817],{},[895,23806,23807,23813,23815],{},[2128,23808,23809,23811],{},[898,23810,12098],{},[1726,23812,4342],{},[1726,23814,1728],{},[2133,23816,8789],{},[902,23818,23819],{"encoding":904},"G^* = 150",[883,23821,23823],{"className":23822},[886],[888,23824,23825],{"xmlns":890},[892,23826,23827,23840],{},[895,23828,23829,23835,23837],{},[2128,23830,23831,23833],{},[898,23832,23234],{},[1726,23834,4342],{},[1726,23836,1728],{},[2133,23838,23839],{},"800",[902,23841,23842],{"encoding":904},"B^* = 800",". Soustava:",[724,23845,23846],{},[883,23847,23849],{"className":23848},[886],[888,23850,23851],{"xmlns":890},[892,23852,23853,24071],{},[20735,23854,23855,23901,23943,23979,24021],{"rowspacing":20737,"columnalign":20738,"columnspacing":2378},[20740,23856,23857,23873],{},[20743,23858,23859],{},[2326,23860,23861],{"scriptlevel":2328,"displaystyle":1741},[895,23862,23863,23865,23867,23869,23871],{},[1726,23864,1735],{"stretchy":1734},[898,23866,12027],{},[2133,23868,2281],{},[1726,23870,1762],{"stretchy":1734},[2289,23872,2291],{},[20743,23874,23875],{},[2326,23876,23877],{"scriptlevel":2328,"displaystyle":1741},[895,23878,23879,23881,23883,23885,23887,23889,23895,23897,23899],{},[895,23880],{},[898,23882,2775],{},[1726,23884,1728],{},[2133,23886,23711],{},[2289,23888,2984],{},[2275,23890,23891,23893],{},[898,23892,1745],{},[898,23894,1731],{},[1726,23896,2099],{},[2133,23898,23724],{},[1726,23900,1742],{"separator":1741},[20740,23902,23903,23919],{},[20743,23904,23905],{},[2326,23906,23907],{"scriptlevel":2328,"displaystyle":1741},[895,23908,23909,23911,23913,23915,23917],{},[1726,23910,1735],{"stretchy":1734},[898,23912,12027],{},[2133,23914,2135],{},[1726,23916,1762],{"stretchy":1734},[2289,23918,2291],{},[20743,23920,23921],{},[2326,23922,23923],{"scriptlevel":2328,"displaystyle":1741},[895,23924,23925,23927,23933,23935,23937,23939,23941],{},[895,23926],{},[2275,23928,23929,23931],{},[898,23930,1745],{},[898,23932,1731],{},[1726,23934,1728],{},[898,23936,1745],{},[1726,23938,2228],{},[898,23940,2772],{},[1726,23942,1742],{"separator":1741},[20740,23944,23945,23961],{},[20743,23946,23947],{},[2326,23948,23949],{"scriptlevel":2328,"displaystyle":1741},[895,23950,23951,23953,23955,23957,23959],{},[1726,23952,1735],{"stretchy":1734},[898,23954,12027],{},[2133,23956,2177],{},[1726,23958,1762],{"stretchy":1734},[2289,23960,2291],{},[20743,23962,23963],{},[2326,23964,23965],{"scriptlevel":2328,"displaystyle":1741},[895,23966,23967,23969,23971,23973,23975,23977],{},[895,23968],{},[898,23970,2772],{},[1726,23972,1728],{},[2133,23974,23770],{},[898,23976,1745],{},[1726,23978,1742],{"separator":1741},[20740,23980,23981,23997],{},[20743,23982,23983],{},[2326,23984,23985],{"scriptlevel":2328,"displaystyle":1741},[895,23986,23987,23989,23991,23993,23995],{},[1726,23988,1735],{"stretchy":1734},[898,23990,12027],{},[2133,23992,2352],{},[1726,23994,1762],{"stretchy":1734},[2289,23996,2291],{},[20743,23998,23999],{},[2326,24000,24001],{"scriptlevel":2328,"displaystyle":1741},[895,24002,24003,24005,24007,24009,24011,24013,24019],{},[895,24004],{},[898,24006,2815],{},[1726,24008,1728],{},[2133,24010,23743],{},[2289,24012,2984],{},[2275,24014,24015,24017],{},[898,24016,1745],{},[898,24018,1731],{},[1726,24020,1742],{"separator":1741},[20740,24022,24023,24039],{},[20743,24024,24025],{},[2326,24026,24027],{"scriptlevel":2328,"displaystyle":1741},[895,24028,24029,24031,24033,24035,24037],{},[1726,24030,1735],{"stretchy":1734},[898,24032,12027],{},[2133,24034,2231],{},[1726,24036,1762],{"stretchy":1734},[2289,24038,2291],{},[20743,24040,24041],{},[2326,24042,24043],{"scriptlevel":2328,"displaystyle":1741},[895,24044,24045,24047,24049,24051,24053,24055,24057,24059,24061,24063,24065,24067,24069],{},[895,24046],{},[898,24048,1745],{},[1726,24050,1728],{},[898,24052,2775],{},[1726,24054,2099],{},[2133,24056,15096],{},[1726,24058,2099],{},[2133,24060,8789],{},[1726,24062,2099],{},[2133,24064,23839],{},[1726,24066,2228],{},[898,24068,2815],{},[898,24070,1888],{"mathvariant":2377},[902,24072,24073],{"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}",[724,24075,24076,24077,24111],{},"Postupná substituce — z (r3) do (r2): ",[883,24078,24080],{"className":24079},[886],[888,24081,24082],{"xmlns":890},[892,24083,24084,24108],{},[895,24085,24086,24092,24094,24096,24098,24100,24102,24104,24106],{},[2275,24087,24088,24090],{},[898,24089,1745],{},[898,24091,1731],{},[1726,24093,1728],{},[898,24095,1745],{},[1726,24097,2228],{},[2133,24099,23770],{},[898,24101,1745],{},[1726,24103,1728],{},[2133,24105,23711],{},[898,24107,1745],{},[902,24109,24110],{"encoding":904},"Y_D = Y - 0{,}25Y = 0{,}75Y",". Dosazením do (r1) a (r4):",[724,24113,24114],{},[883,24115,24117],{"className":24116},[886],[888,24118,24119],{"xmlns":890},[892,24120,24121,24162],{},[895,24122,24123,24125,24127,24129,24131,24133,24135,24137,24139,24141,24143,24145,24147,24149,24151,24154,24156,24158,24160],{},[1726,24124,1735],{"stretchy":1734},[898,24126,12027],{},[2133,24128,2238],{},[1726,24130,1762],{"stretchy":1734},[2289,24132,2291],{},[898,24134,2775],{},[1726,24136,1728],{},[2133,24138,23711],{},[1726,24140,3174],{},[2133,24142,23711],{},[898,24144,1745],{},[1726,24146,2099],{},[2133,24148,23724],{},[1726,24150,1728],{},[2133,24152,24153],{},"0,5625",[898,24155,1745],{},[1726,24157,2099],{},[2133,24159,23724],{},[1726,24161,1742],{"separator":1741},[902,24163,24164],{"encoding":904},"(r6)\\ C = 0{,}75 \\cdot 0{,}75Y + 750 = 0{,}5625Y + 750,",[724,24166,24167],{},[883,24168,24170],{"className":24169},[886],[888,24171,24172],{"xmlns":890},[892,24173,24174,24208],{},[895,24175,24176,24178,24180,24183,24185,24187,24189,24191,24193,24195,24197,24199,24201,24204,24206],{},[1726,24177,1735],{"stretchy":1734},[898,24179,12027],{},[2133,24181,24182],{},"7",[1726,24184,1762],{"stretchy":1734},[2289,24186,2291],{},[898,24188,2815],{},[1726,24190,1728],{},[2133,24192,23743],{},[1726,24194,3174],{},[2133,24196,23711],{},[898,24198,1745],{},[1726,24200,1728],{},[2133,24202,24203],{},"0,1125",[898,24205,1745],{},[898,24207,1888],{"mathvariant":2377},[902,24209,24210],{"encoding":904},"(r7)\\ M = 0{,}15 \\cdot 0{,}75Y = 0{,}1125Y.",[724,24212,24213],{},"Dosazením do (r5):",[724,24215,24216],{},[883,24217,24219],{"className":24218},[886],[888,24220,24221],{"xmlns":890},[892,24222,24223,24267],{},[895,24224,24225,24227,24229,24231,24233,24235,24237,24239,24241,24243,24245,24247,24249,24251,24253,24255,24257,24260,24262,24264],{},[898,24226,1745],{},[1726,24228,1728],{},[2133,24230,24153],{},[898,24232,1745],{},[1726,24234,2099],{},[2133,24236,23724],{},[1726,24238,2099],{},[2133,24240,15096],{},[1726,24242,2099],{},[2133,24244,8789],{},[1726,24246,2099],{},[2133,24248,23839],{},[1726,24250,2228],{},[2133,24252,24203],{},[898,24254,1745],{},[1726,24256,1728],{},[2133,24258,24259],{},"0,45",[898,24261,1745],{},[1726,24263,2099],{},[2133,24265,24266],{},"2200.",[902,24268,24269],{"encoding":904},"Y = 0{,}5625Y + 750 + 500 + 150 + 800 - 0{,}1125Y = 0{,}45Y + 2200.",[724,24271,24272,24273,5576,24295,24318],{},"Odtud ",[883,24274,24276],{"className":24275},[886],[888,24277,24278],{"xmlns":890},[892,24279,24280,24292],{},[895,24281,24282,24285,24287,24289],{},[2133,24283,24284],{},"0,55",[898,24286,1745],{},[1726,24288,1728],{},[2133,24290,24291],{},"2200",[902,24293,24294],{"encoding":904},"0{,}55Y = 2200",[883,24296,24298],{"className":24297},[886],[888,24299,24300],{"xmlns":890},[892,24301,24302,24315],{},[895,24303,24304,24310,24312],{},[2128,24305,24306,24308],{},[898,24307,1745],{},[898,24309,4240],{},[1726,24311,1728],{},[2133,24313,24314],{},"4000",[902,24316,24317],{"encoding":904},"Y^E = 4000",". Rovnovážné veličiny:",[120,24320,24321,24344,24376,24411,24444,24480],{},[123,24322,24323,1742],{},[883,24324,24326],{"className":24325},[886],[888,24327,24328],{"xmlns":890},[892,24329,24330,24342],{},[895,24331,24332,24338,24340],{},[2128,24333,24334,24336],{},[898,24335,1745],{},[898,24337,4240],{},[1726,24339,1728],{},[2133,24341,24314],{},[902,24343,24317],{"encoding":904},[123,24345,24346,1742],{},[883,24347,24349],{"className":24348},[886],[888,24350,24351],{"xmlns":890},[892,24352,24353,24373],{},[895,24354,24355,24361,24363,24365,24367,24369,24371],{},[2128,24356,24357,24359],{},[898,24358,2772],{},[898,24360,4240],{},[1726,24362,1728],{},[2133,24364,23770],{},[1726,24366,3174],{},[2133,24368,24314],{},[1726,24370,1728],{},[2133,24372,2780],{},[902,24374,24375],{"encoding":904},"T^E = 0{,}25 \\cdot 4000 = 1000",[123,24377,24378,1742],{},[883,24379,24381],{"className":24380},[886],[888,24382,24383],{"xmlns":890},[892,24384,24385,24408],{},[895,24386,24387,24395,24397,24399,24401,24403,24405],{},[9151,24388,24389,24391,24393],{},[898,24390,1745],{},[898,24392,1731],{},[898,24394,4240],{},[1726,24396,1728],{},[2133,24398,23711],{},[1726,24400,3174],{},[2133,24402,24314],{},[1726,24404,1728],{},[2133,24406,24407],{},"3000",[902,24409,24410],{"encoding":904},"Y_D^E = 0{,}75 \\cdot 4000 = 3000",[123,24412,24413,1742],{},[883,24414,24416],{"className":24415},[886],[888,24417,24418],{"xmlns":890},[892,24419,24420,24441],{},[895,24421,24422,24428,24430,24432,24434,24436,24438],{},[2128,24423,24424,24426],{},[898,24425,2815],{},[898,24427,4240],{},[1726,24429,1728],{},[2133,24431,23743],{},[1726,24433,3174],{},[2133,24435,24407],{},[1726,24437,1728],{},[2133,24439,24440],{},"450",[902,24442,24443],{"encoding":904},"M^E = 0{,}15 \\cdot 3000 = 450",[123,24445,24446,1742],{},[883,24447,24449],{"className":24448},[886],[888,24450,24451],{"xmlns":890},[892,24452,24453,24477],{},[895,24454,24455,24461,24463,24465,24467,24469,24471,24473,24475],{},[2128,24456,24457,24459],{},[898,24458,2775],{},[898,24460,4240],{},[1726,24462,1728],{},[2133,24464,23711],{},[1726,24466,3174],{},[2133,24468,24407],{},[1726,24470,2099],{},[2133,24472,23724],{},[1726,24474,1728],{},[2133,24476,24407],{},[902,24478,24479],{"encoding":904},"C^E = 0{,}75 \\cdot 3000 + 750 = 3000",[123,24481,24482,24522],{},[883,24483,24485],{"className":24484},[886],[888,24486,24487],{"xmlns":890},[892,24488,24489,24519],{},[895,24490,24491,24497,24499,24507,24509,24515,24517],{},[2128,24492,24493,24495],{},[898,24494,8659],{},[898,24496,4240],{},[1726,24498,1728],{},[9151,24500,24501,24503,24505],{},[898,24502,1745],{},[898,24504,1731],{},[898,24506,4240],{},[1726,24508,2228],{},[2128,24510,24511,24513],{},[898,24512,2775],{},[898,24514,4240],{},[1726,24516,1728],{},[2133,24518,2328],{},[902,24520,24521],{"encoding":904},"S^E = Y_D^E - C^E = 0"," (při této kalibraci domácnosti celý disponibilní důchod spotřebují).",[724,24524,24525,24527,24528,1343,24545,3877,24566,24591,24592,24595,24596,24609,24610,1888],{},[38,24526,21330],{}," Modely ",[883,24529,24531],{"className":24530},[886],[888,24532,24533],{"xmlns":890},[892,24534,24535,24543],{},[895,24536,24537,24539,24541],{},[898,24538,2775],{},[2289,24540,12276],{},[898,24542,12170],{},[902,24544,12281],{"encoding":904},[883,24546,24548],{"className":24547},[886],[888,24549,24550],{"xmlns":890},[892,24551,24552,24564],{},[895,24553,24554,24556,24558,24560,24562],{},[898,24555,2775],{},[2289,24557,12276],{},[898,24559,12170],{},[2289,24561,12276],{},[898,24563,12098],{},[902,24565,18202],{"encoding":904},[883,24567,24569],{"className":24568},[886],[888,24570,24571],{"xmlns":890},[892,24572,24573,24589],{},[895,24574,24575,24577,24579,24581,24583,24585,24587],{},[898,24576,2775],{},[2289,24578,12276],{},[898,24580,12170],{},[2289,24582,12276],{},[898,24584,12098],{},[2289,24586,12276],{},[898,24588,12306],{},[902,24590,12309],{"encoding":904}," pokládají investice za ",[38,24593,24594],{},"konstantní",". To není realistické — investice závisejí na úrokové míře ",[883,24597,24599],{"className":24598},[886],[888,24600,24601],{"xmlns":890},[892,24602,24603,24607],{},[895,24604,24605],{},[898,24606,12027],{},[902,24608,12027],{"encoding":904},". Přidáním trhu peněz a úrokové míry vzniká ",[38,24611,24612],{},"model IS-LM",[115,24614,24616],{"id":24615},"_74-multiplikátory-pro-makroekonomické-proměnné","7.4 Multiplikátory pro makroekonomické proměnné",[724,24618,24619,24620,24624,24625,24628,24629,24632],{},"V článku ",[207,24621,24623],{"className":24622,"dataFsResolvedFilePath":827,"href":828},[210],"2.4"," (mikroekonomie) byly zavedeny multiplikátory pro mikroekonomické proměnné. ",[38,24626,24627],{},"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 ",[38,24630,24631],{},"výraznější"," než v mikroekonomických modelech.",[724,24634,24635],{},[1647,24636],{"alt":24637,"className":24638,"src":24639},"imek-multiplikatorovy-efekt-chain",[210,1651],"\u002Fwiki-assets\u002Fimek-multiplikatorovy-efekt-chain.jpeg",[724,24641,12150,24642,1343,24659,1343,24680,24705,24706,24709,24710,24728,24729,24747,24748,24766,24767,24770,24771,1343,24788,24805,24806,24808],{},[883,24643,24645],{"className":24644},[886],[888,24646,24647],{"xmlns":890},[892,24648,24649,24657],{},[895,24650,24651,24653,24655],{},[898,24652,2775],{},[2289,24654,12276],{},[898,24656,12170],{},[902,24658,12281],{"encoding":904},[883,24660,24662],{"className":24661},[886],[888,24663,24664],{"xmlns":890},[892,24665,24666,24678],{},[895,24667,24668,24670,24672,24674,24676],{},[898,24669,2775],{},[2289,24671,12276],{},[898,24673,12170],{},[2289,24675,12276],{},[898,24677,12098],{},[902,24679,18202],{"encoding":904},[883,24681,24683],{"className":24682},[886],[888,24684,24685],{"xmlns":890},[892,24686,24687,24703],{},[895,24688,24689,24691,24693,24695,24697,24699,24701],{},[898,24690,2775],{},[2289,24692,12276],{},[898,24694,12170],{},[2289,24696,12276],{},[898,24698,12098],{},[2289,24700,12276],{},[898,24702,12306],{},[902,24704,12309],{"encoding":904}," se vyšetřuje vliv změn ",[38,24707,24708],{},"exogenních"," veličin (plánovaných investic ",[883,24711,24713],{"className":24712},[886],[888,24714,24715],{"xmlns":890},[892,24716,24717,24725],{},[895,24718,24719],{},[2128,24720,24721,24723],{},[898,24722,12170],{},[1726,24724,4342],{},[902,24726,24727],{"encoding":904},"I^*",", vládních výdajů ",[883,24730,24732],{"className":24731},[886],[888,24733,24734],{"xmlns":890},[892,24735,24736,24744],{},[895,24737,24738],{},[2128,24739,24740,24742],{},[898,24741,12098],{},[1726,24743,4342],{},[902,24745,24746],{"encoding":904},"G^*",", exportu ",[883,24749,24751],{"className":24750},[886],[888,24752,24753],{"xmlns":890},[892,24754,24755,24763],{},[895,24756,24757],{},[2128,24758,24759,24761],{},[898,24760,23234],{},[1726,24762,4342],{},[902,24764,24765],{"encoding":904},"B^*",") na změny ",[38,24768,24769],{},"endogenních"," rovnovážných veličin (",[883,24772,24774],{"className":24773},[886],[888,24775,24776],{"xmlns":890},[892,24777,24778,24786],{},[895,24779,24780],{},[2128,24781,24782,24784],{},[898,24783,1745],{},[898,24785,4240],{},[902,24787,13889],{"encoding":904},[883,24789,24791],{"className":24790},[886],[888,24792,24793],{"xmlns":890},[892,24794,24795,24803],{},[895,24796,24797],{},[2128,24798,24799,24801],{},[898,24800,2775],{},[898,24802,4240],{},[902,24804,13948],{"encoding":904}," atd.). Tyto citlivosti se vyjadřují ",[38,24807,17959],{}," — parciálními derivacemi rovnovážných veličin podle exogenních veličin.",[198,24810,24812],{"id":24811},"multiplikátory-v-modelu-c-i","Multiplikátory v modelu C-I",[724,24814,20876,24815,24838,24839,24883],{},[883,24816,24818],{"className":24817},[886],[888,24819,24820],{"xmlns":890},[892,24821,24822,24836],{},[895,24823,24824,24826,24828,24830,24832,24834],{},[898,24825,2775],{},[1726,24827,1728],{},[898,24829,207],{},[898,24831,1745],{},[1726,24833,2099],{},[898,24835,2102],{},[902,24837,18901],{"encoding":904}," dává (7.7) redukovaný tvar ",[883,24840,24842],{"className":24841},[886],[888,24843,24844],{"xmlns":890},[892,24845,24846,24880],{},[895,24847,24848,24854,24856],{},[2128,24849,24850,24852],{},[898,24851,1745],{},[898,24853,4240],{},[1726,24855,1728],{},[2326,24857,24858],{"scriptlevel":2328,"displaystyle":1741},[2330,24859,24860,24872],{},[895,24861,24862,24864,24866],{},[898,24863,2102],{},[1726,24865,2099],{},[2128,24867,24868,24870],{},[898,24869,12170],{},[1726,24871,4342],{},[895,24873,24874,24876,24878],{},[2133,24875,2281],{},[1726,24877,2228],{},[898,24879,207],{},[902,24881,24882],{"encoding":904},"Y^E = \\dfrac{b + I^*}{1 - a}",". Parciální derivace:",[724,24885,24886],{},[883,24887,24889],{"className":24888},[886],[888,24890,24891],{"xmlns":890},[892,24892,24893,24962],{},[895,24894,24895,24913,24915,24945,24947],{},[2330,24896,24897,24907],{},[895,24898,24899,24901],{},[898,24900,9856],{"mathvariant":2377},[2128,24902,24903,24905],{},[898,24904,1745],{},[898,24906,4240],{},[895,24908,24909,24911],{},[898,24910,9856],{"mathvariant":2377},[898,24912,207],{},[1726,24914,1728],{},[2330,24916,24917,24929],{},[895,24918,24919,24921,24923],{},[898,24920,2102],{},[1726,24922,2099],{},[2128,24924,24925,24927],{},[898,24926,12170],{},[1726,24928,4342],{},[895,24930,24931,24933,24935,24937,24939],{},[1726,24932,1735],{"stretchy":1734},[2133,24934,2281],{},[1726,24936,2228],{},[898,24938,207],{},[2128,24940,24941,24943],{},[1726,24942,1762],{"stretchy":1734},[2133,24944,2135],{},[5865,24946],{"width":5867},[895,24948,24949,24952,24959],{},[2289,24950,24951],{},"(multiplik",[8372,24953,24954,24956],{"accent":1741},[2289,24955,207],{},[1726,24957,24958],{},"ˊ",[2289,24960,24961],{},"tor MPC)",[902,24963,24964],{"encoding":904},"\\frac{\\partial Y^E}{\\partial a} = \\frac{b + I^*}{(1 - a)^2} \\qquad \\text{(multiplikátor MPC)}",[724,24966,24967],{},[883,24968,24970],{"className":24969},[886],[888,24971,24972],{"xmlns":890},[892,24973,24974,25043],{},[895,24975,24976,24994,24996,25008,25010],{},[2330,24977,24978,24988],{},[895,24979,24980,24982],{},[898,24981,9856],{"mathvariant":2377},[2128,24983,24984,24986],{},[898,24985,1745],{},[898,24987,4240],{},[895,24989,24990,24992],{},[898,24991,9856],{"mathvariant":2377},[898,24993,2102],{},[1726,24995,1728],{},[2330,24997,24998,25000],{},[2133,24999,2281],{},[895,25001,25002,25004,25006],{},[2133,25003,2281],{},[1726,25005,2228],{},[898,25007,207],{},[5865,25009],{"width":5867},[895,25011,25012,25014,25020,25023,25030,25033,25040],{},[2289,25013,24951],{},[8372,25015,25016,25018],{"accent":1741},[2289,25017,207],{},[1726,25019,24958],{},[2289,25021,25022],{},"tor autonomn",[8372,25024,25025,25028],{"accent":1741},[2289,25026,25027],{},"ı",[1726,25029,24958],{},[2289,25031,25032],{}," spot",[8372,25034,25035,25037],{"accent":1741},[2289,25036,12027],{},[1726,25038,25039],{},"ˇ",[2289,25041,25042],{},"eby)",[902,25044,25045],{"encoding":904},"\\frac{\\partial Y^E}{\\partial b} = \\frac{1}{1 - a} \\qquad \\text{(multiplikátor autonomní spotřeby)}",[724,25047,25048],{},[883,25049,25051],{"className":25050},[886],[888,25052,25053],{"xmlns":890},[892,25054,25055,25122],{},[895,25056,25057,25079,25081,25093,25095,25107,25109],{},[2330,25058,25059,25069],{},[895,25060,25061,25063],{},[898,25062,9856],{"mathvariant":2377},[2128,25064,25065,25067],{},[898,25066,1745],{},[898,25068,4240],{},[895,25070,25071,25073],{},[898,25072,9856],{"mathvariant":2377},[2128,25074,25075,25077],{},[898,25076,12170],{},[1726,25078,4342],{},[1726,25080,1728],{},[2330,25082,25083,25085],{},[2133,25084,2281],{},[895,25086,25087,25089,25091],{},[2133,25088,2281],{},[1726,25090,2228],{},[898,25092,207],{},[1726,25094,1728],{},[2330,25096,25097,25099],{},[2133,25098,2281],{},[895,25100,25101,25103,25105],{},[898,25102,2815],{},[898,25104,1738],{},[898,25106,8659],{},[5865,25108],{"width":5867},[895,25110,25111,25113,25119],{},[2289,25112,24951],{},[8372,25114,25115,25117],{"accent":1741},[2289,25116,207],{},[1726,25118,24958],{},[2289,25120,25121],{},"tor investic)",[902,25123,25124],{"encoding":904},"\\frac{\\partial Y^E}{\\partial I^*} = \\frac{1}{1 - a} = \\frac{1}{MPS} \\qquad \\text{(multiplikátor investic)}",[3859,25126,25127],{},[724,25128,25129,25131,25132,25135,25136,25149,25150,25167,25168,25186,25187,25231,25232,21401,25249,25252,25253,25270],{},[883,25130,4145],{}," Intuice — proč Keynesův multiplikátor funguje\nInvestice o 1 Kč se stanou něčím ",[38,25133,25134],{},"důchodem","; z něj se utratí ",[883,25137,25139],{"className":25138},[886],[888,25140,25141],{"xmlns":890},[892,25142,25143,25147],{},[895,25144,25145],{},[898,25146,207],{},[902,25148,207],{"encoding":904}," Kč (= ",[883,25151,25153],{"className":25152},[886],[888,25154,25155],{"xmlns":890},[892,25156,25157,25165],{},[895,25158,25159,25161,25163],{},[898,25160,2815],{},[898,25162,1738],{},[898,25164,2775],{},[902,25166,18027],{"encoding":904},"), to je zase něčí důchod, z něj ",[883,25169,25171],{"className":25170},[886],[888,25172,25173],{"xmlns":890},[892,25174,25175,25183],{},[895,25176,25177],{},[2128,25178,25179,25181],{},[898,25180,207],{},[2133,25182,2135],{},[902,25184,25185],{"encoding":904},"a^2"," Kč… Součet geometrické řady ",[883,25188,25190],{"className":25189},[886],[888,25191,25192],{"xmlns":890},[892,25193,25194,25228],{},[895,25195,25196,25198,25200,25202,25204,25210,25212,25214,25216],{},[2133,25197,2281],{},[1726,25199,2099],{},[898,25201,207],{},[1726,25203,2099],{},[2128,25205,25206,25208],{},[898,25207,207],{},[2133,25209,2135],{},[1726,25211,2099],{},[1726,25213,18087],{},[1726,25215,1728],{},[2330,25217,25218,25220],{},[2133,25219,2281],{},[895,25221,25222,25224,25226],{},[2133,25223,2281],{},[1726,25225,2228],{},[898,25227,207],{},[902,25229,25230],{"encoding":904},"1 + a + a^2 + \\dots = \\frac{1}{1-a}",". Proto jedna koruna investic navíc zvedne ",[883,25233,25235],{"className":25234},[886],[888,25236,25237],{"xmlns":890},[892,25238,25239,25247],{},[895,25240,25241],{},[2128,25242,25243,25245],{},[898,25244,1745],{},[898,25246,4240],{},[902,25248,13889],{"encoding":904},[38,25250,25251],{},"více"," než korunu — čím vyšší ",[883,25254,25256],{"className":25255},[886],[888,25257,25258],{"xmlns":890},[892,25259,25260,25268],{},[895,25261,25262,25264,25266],{},[898,25263,2815],{},[898,25265,1738],{},[898,25267,2775],{},[902,25269,18027],{"encoding":904},", tím silnější multiplikační efekt.",[724,25272,25273,25276,25277,25303,25304,25307,25308,3877,25329,25354,25355,1888],{},[38,25274,25275],{},"Multiplikátor autonomní spotřeby se rovná multiplikátoru investic"," — oba činí ",[883,25278,25280],{"className":25279},[886],[888,25281,25282],{"xmlns":890},[892,25283,25284,25300],{},[895,25285,25286],{},[2326,25287,25288],{"scriptlevel":2328,"displaystyle":1734},[2330,25289,25290,25292],{},[2133,25291,2281],{},[895,25293,25294,25296,25298],{},[2133,25295,2281],{},[1726,25297,2228],{},[898,25299,207],{},[902,25301,25302],{"encoding":904},"\\tfrac{1}{1-a}",", což je standardní ",[38,25305,25306],{},"Keynesův multiplikátor",". Analogicky se v modelech ",[883,25309,25311],{"className":25310},[886],[888,25312,25313],{"xmlns":890},[892,25314,25315,25327],{},[895,25316,25317,25319,25321,25323,25325],{},[898,25318,2775],{},[2289,25320,12276],{},[898,25322,12170],{},[2289,25324,12276],{},[898,25326,12098],{},[902,25328,18202],{"encoding":904},[883,25330,25332],{"className":25331},[886],[888,25333,25334],{"xmlns":890},[892,25335,25336,25352],{},[895,25337,25338,25340,25342,25344,25346,25348,25350],{},[898,25339,2775],{},[2289,25341,12276],{},[898,25343,12170],{},[2289,25345,12276],{},[898,25347,12098],{},[2289,25349,12276],{},[898,25351,12306],{},[902,25353,12309],{"encoding":904}," zavádějí multiplikátory vládních výdajů, zdanění a exportu. Paralela k mikroekonomickým multiplikátorům viz ",[207,25356,25358],{"className":25357,"dataFsResolvedFilePath":800,"href":801},[210],"poptávka a nabídka",[115,25360,25362],{"id":25361},"is-lm-analýza-stručný-přehled","IS-LM analýza (stručný přehled)",[724,25364,12150,25365,1343,25382,3877,25403,12155,25428,10009,25431,25452,25453,1777,25456,25469,25470,5656,25499,25516,25517,25520,25521,25523,25524,25545],{},[883,25366,25368],{"className":25367},[886],[888,25369,25370],{"xmlns":890},[892,25371,25372,25380],{},[895,25373,25374,25376,25378],{},[898,25375,2775],{},[2289,25377,12276],{},[898,25379,12170],{},[902,25381,12281],{"encoding":904},[883,25383,25385],{"className":25384},[886],[888,25386,25387],{"xmlns":890},[892,25388,25389,25401],{},[895,25390,25391,25393,25395,25397,25399],{},[898,25392,2775],{},[2289,25394,12276],{},[898,25396,12170],{},[2289,25398,12276],{},[898,25400,12098],{},[902,25402,18202],{"encoding":904},[883,25404,25406],{"className":25405},[886],[888,25407,25408],{"xmlns":890},[892,25409,25410,25426],{},[895,25411,25412,25414,25416,25418,25420,25422,25424],{},[898,25413,2775],{},[2289,25415,12276],{},[898,25417,12170],{},[2289,25419,12276],{},[898,25421,12098],{},[2289,25423,12276],{},[898,25425,12306],{},[902,25427,12309],{"encoding":904},[38,25429,25430],{},"investice konstantní",[883,25432,25434],{"className":25433},[886],[888,25435,25436],{"xmlns":890},[892,25437,25438,25450],{},[895,25439,25440,25442,25444],{},[898,25441,12170],{},[1726,25443,1728],{},[2128,25445,25446,25448],{},[898,25447,12170],{},[1726,25449,4342],{},[902,25451,12181],{"encoding":904},"). Reálnější je předpoklad, že ",[38,25454,25455],{},"investice závisejí na úrokové míře",[883,25457,25459],{"className":25458},[886],[888,25460,25461],{"xmlns":890},[892,25462,25463,25467],{},[895,25464,25465],{},[898,25466,12027],{},[902,25468,12027],{"encoding":904}," — klesající funkce ",[883,25471,25473],{"className":25472},[886],[888,25474,25475],{"xmlns":890},[892,25476,25477,25497],{},[895,25478,25479,25481,25483,25485,25487,25489,25491,25493,25495],{},[898,25480,12170],{},[1726,25482,1735],{"stretchy":1734},[898,25484,12027],{},[1726,25486,1762],{"stretchy":1734},[1726,25488,1728],{},[898,25490,2146],{},[898,25492,12027],{},[1726,25494,2099],{},[898,25496,2198],{},[902,25498,15741],{"encoding":904},[883,25500,25502],{"className":25501},[886],[888,25503,25504],{"xmlns":890},[892,25505,25506,25514],{},[895,25507,25508,25510,25512],{},[898,25509,2146],{},[1726,25511,3444],{},[2133,25513,2328],{},[902,25515,12501],{"encoding":904},". Přidáním ",[38,25518,25519],{},"trhu peněz"," k trhu zboží vzniká model ",[38,25522,11997],{}," se dvěma neznámými ",[883,25525,25527],{"className":25526},[886],[888,25528,25529],{"xmlns":890},[892,25530,25531,25543],{},[895,25532,25533,25535,25537,25539,25541],{},[1726,25534,1735],{"stretchy":1734},[898,25536,1745],{},[1726,25538,1742],{"separator":1741},[898,25540,12027],{},[1726,25542,1762],{"stretchy":1734},[902,25544,18132],{"encoding":904}," a dvěma rovnicemi:",[120,25547,25548,25598],{},[123,25549,25550,10009,25552,25554,25555,25576,25577,1888],{},[38,25551,15830],{},[614,25553,12040],{},") — klesající přímka v rovině ",[883,25556,25558],{"className":25557},[886],[888,25559,25560],{"xmlns":890},[892,25561,25562,25574],{},[895,25563,25564,25566,25568,25570,25572],{},[1726,25565,1735],{"stretchy":1734},[898,25567,12027],{},[1726,25569,1742],{"separator":1741},[898,25571,1745],{},[1726,25573,1762],{"stretchy":1734},[902,25575,12923],{"encoding":904},", odvozená z rovnováhy trhu zboží ",[883,25578,25580],{"className":25579},[886],[888,25581,25582],{"xmlns":890},[892,25583,25584,25596],{},[895,25585,25586,25588,25590,25592,25594],{},[898,25587,1745],{},[1726,25589,1728],{},[898,25591,2775],{},[1726,25593,2099],{},[898,25595,12170],{},[902,25597,14730],{"encoding":904},[123,25599,25600,10009,25602,25604,25605,21575,25630,25676],{},[38,25601,16029],{},[614,25603,12047],{},") — rostoucí přímka, odvozená z rovnováhy trhu peněz ",[883,25606,25608],{"className":25607},[886],[888,25609,25610],{"xmlns":890},[892,25611,25612,25628],{},[895,25613,25614,25620,25622],{},[2128,25615,25616,25618],{},[898,25617,2815],{},[898,25619,1731],{},[1726,25621,1728],{},[2128,25623,25624,25626],{},[898,25625,2815],{},[1726,25627,4342],{},[902,25629,13466],{"encoding":904},[883,25631,25633],{"className":25632},[886],[888,25634,25635],{"xmlns":890},[892,25636,25637,25673],{},[895,25638,25639,25645,25647,25653,25655,25657,25663,25665,25667],{},[2128,25640,25641,25643],{},[898,25642,2815],{},[898,25644,1731],{},[1726,25646,1728],{},[2275,25648,25649,25651],{},[898,25650,13223],{},[2133,25652,2281],{},[898,25654,1745],{},[1726,25656,2099],{},[2275,25658,25659,25661],{},[898,25660,13223],{},[2133,25662,2135],{},[898,25664,12027],{},[1726,25666,2099],{},[2275,25668,25669,25671],{},[898,25670,13223],{},[2133,25672,2177],{},[902,25674,25675],{"encoding":904},"M^D = k_1 Y + k_2 r + k_3"," (transakční, opatrnostní a spekulační poptávka).",[724,25678,25679,1777,25682,25715,25716,25718,25719,25721],{},[38,25680,25681],{},"Simultánní rovnovážný bod",[883,25683,25685],{"className":25684},[886],[888,25686,25687],{"xmlns":890},[892,25688,25689,25713],{},[895,25690,25691,25693,25695,25697,25703,25705,25711],{},[898,25692,4240],{},[1726,25694,1728],{},[1726,25696,1735],{"stretchy":1734},[2128,25698,25699,25701],{},[898,25700,12027],{},[898,25702,4240],{},[1726,25704,1742],{"separator":1741},[2128,25706,25707,25709],{},[898,25708,1745],{},[898,25710,4240],{},[1726,25712,1762],{"stretchy":1734},[902,25714,16121],{"encoding":904}," je průsečík křivek IS a LM; určuje současně rovnovážný důchod a rovnovážnou úrokovou míru. Model slouží jako rámec pro analýzu ",[38,25717,12085],{}," (posun IS) a ",[38,25720,12117],{}," (posun LM).",[724,25723,25724],{},[38,25725,25726,25727,1343,25749,1343,25771,1343,25793,25815,25816,1888],{},"Pro detailní odvození obou křivek, řešení Příkladu 7.6 (",[883,25728,25730],{"className":25729},[886],[888,25731,25732],{"xmlns":890},[892,25733,25734,25746],{},[895,25735,25736,25742,25744],{},[2128,25737,25738,25740],{},[898,25739,1745],{},[898,25741,4240],{},[1726,25743,1728],{},[2133,25745,15101],{},[902,25747,25748],{"encoding":904},"Y^E = 5000",[883,25750,25752],{"className":25751},[886],[888,25753,25754],{"xmlns":890},[892,25755,25756,25768],{},[895,25757,25758,25764,25766],{},[2128,25759,25760,25762],{},[898,25761,12027],{},[898,25763,4240],{},[1726,25765,1728],{},[2133,25767,2231],{},[902,25769,25770],{"encoding":904},"r^E = 5",[883,25772,25774],{"className":25773},[886],[888,25775,25776],{"xmlns":890},[892,25777,25778,25790],{},[895,25779,25780,25786,25788],{},[2128,25781,25782,25784],{},[898,25783,2775],{},[898,25785,4240],{},[1726,25787,1728],{},[2133,25789,15138],{},[902,25791,25792],{"encoding":904},"C^E = 4100",[883,25794,25796],{"className":25795},[886],[888,25797,25798],{"xmlns":890},[892,25799,25800,25812],{},[895,25801,25802,25808,25810],{},[2128,25803,25804,25806],{},[898,25805,12170],{},[898,25807,4240],{},[1726,25809,1728],{},[2133,25811,15177],{},[902,25813,25814],{"encoding":904},"I^E = 900",") a ekonomickou interpretaci posunů viz ",[207,25817,945],{"className":25818,"dataFsResolvedFilePath":943,"href":944},[210],[115,25820,25822],{"id":25821},"shrnutí-kapitoly-7","Shrnutí kapitoly 7",[152,25824,25825,25889,26000,26143,26385,26453],{},[123,25826,25827,25830,25831,25853,25854,25888],{},[38,25828,25829],{},"Zjednodušený makroekonomický model"," ztotožňuje ",[883,25832,25834],{"className":25833},[886],[888,25835,25836],{"xmlns":890},[892,25837,25838,25850],{},[895,25839,25840,25842,25844,25846,25848],{},[898,25841,12098],{},[898,25843,1750],{},[898,25845,1738],{},[1726,25847,1880],{},[898,25849,1745],{},[902,25851,25852],{"encoding":904},"GNP \\approx Y"," (národní důchod). Základ: ",[883,25855,25857],{"className":25856},[886],[888,25858,25859],{"xmlns":890},[892,25860,25861,25885],{},[895,25862,25863,25865,25867,25869,25871,25873,25875,25877,25879,25881,25883],{},[898,25864,12098],{},[898,25866,1750],{},[898,25868,1738],{},[1726,25870,1728],{},[898,25872,2775],{},[1726,25874,2099],{},[898,25876,12170],{},[1726,25878,2099],{},[898,25880,12098],{},[1726,25882,2099],{},[898,25884,12306],{},[902,25886,25887],{"encoding":904},"GNP = C + I + G + X"," (7.1).",[123,25890,25891,25893,25894,25915,25916,1343,25939,25970,25971,25984,25985,1888],{},[38,25892,18509],{}," splňují ",[883,25895,25897],{"className":25896},[886],[888,25898,25899],{"xmlns":890},[892,25900,25901,25913],{},[895,25902,25903,25905,25907,25909,25911],{},[898,25904,1745],{},[1726,25906,1728],{},[898,25908,2775],{},[1726,25910,2099],{},[898,25912,8659],{},[902,25914,12680],{"encoding":904}," (7.2); lineární model ",[883,25917,25919],{"className":25918},[886],[888,25920,25921],{"xmlns":890},[892,25922,25923,25937],{},[895,25924,25925,25927,25929,25931,25933,25935],{},[898,25926,2775],{},[1726,25928,1728],{},[898,25930,207],{},[898,25932,1745],{},[1726,25934,2099],{},[898,25936,2102],{},[902,25938,18901],{"encoding":904},[883,25940,25942],{"className":25941},[886],[888,25943,25944],{"xmlns":890},[892,25945,25946,25968],{},[895,25947,25948,25950,25952,25954,25956,25958,25960,25962,25964,25966],{},[898,25949,8659],{},[1726,25951,1728],{},[1726,25953,1735],{"stretchy":1734},[2133,25955,2281],{},[1726,25957,2228],{},[898,25959,207],{},[1726,25961,1762],{"stretchy":1734},[898,25963,1745],{},[1726,25965,2228],{},[898,25967,2102],{},[902,25969,19150],{"encoding":904}," s autonomní spotřebou ",[883,25972,25974],{"className":25973},[886],[888,25975,25976],{"xmlns":890},[892,25977,25978,25982],{},[895,25979,25980],{},[898,25981,2102],{},[902,25983,2102],{"encoding":904}," a autonomními úsporami ",[883,25986,25988],{"className":25987},[886],[888,25989,25990],{"xmlns":890},[892,25991,25992,25998],{},[895,25993,25994,25996],{},[1726,25995,2228],{},[898,25997,2102],{},[902,25999,19229],{"encoding":904},[123,26001,26002,1777,26005,1343,26035,26065,26066,26096,26097,1343,26118,1888],{},[38,26003,26004],{},"Mezní sklony",[883,26006,26008],{"className":26007},[886],[888,26009,26010],{"xmlns":890},[892,26011,26012,26032],{},[895,26013,26014,26016,26018,26020,26022,26024,26026,26028,26030],{},[898,26015,2815],{},[898,26017,1738],{},[898,26019,2775],{},[1726,26021,1728],{},[898,26023,2198],{"mathvariant":2377},[898,26025,2775],{},[898,26027,4661],{"mathvariant":2377},[898,26029,2198],{"mathvariant":2377},[898,26031,1745],{},[902,26033,26034],{"encoding":904},"MPC = \\mathrm{d}C\u002F\\mathrm{d}Y",[883,26036,26038],{"className":26037},[886],[888,26039,26040],{"xmlns":890},[892,26041,26042,26062],{},[895,26043,26044,26046,26048,26050,26052,26054,26056,26058,26060],{},[898,26045,2815],{},[898,26047,1738],{},[898,26049,8659],{},[1726,26051,1728],{},[898,26053,2198],{"mathvariant":2377},[898,26055,8659],{},[898,26057,4661],{"mathvariant":2377},[898,26059,2198],{"mathvariant":2377},[898,26061,1745],{},[902,26063,26064],{"encoding":904},"MPS = \\mathrm{d}S\u002F\\mathrm{d}Y",", vazba ",[883,26067,26069],{"className":26068},[886],[888,26070,26071],{"xmlns":890},[892,26072,26073,26093],{},[895,26074,26075,26077,26079,26081,26083,26085,26087,26089,26091],{},[898,26076,2815],{},[898,26078,1738],{},[898,26080,2775],{},[1726,26082,2099],{},[898,26084,2815],{},[898,26086,1738],{},[898,26088,8659],{},[1726,26090,1728],{},[2133,26092,2281],{},[902,26094,26095],{"encoding":904},"MPC + MPS = 1"," (7.5). V lineárním modelu ",[883,26098,26100],{"className":26099},[886],[888,26101,26102],{"xmlns":890},[892,26103,26104,26116],{},[895,26105,26106,26108,26110,26112,26114],{},[898,26107,2815],{},[898,26109,1738],{},[898,26111,2775],{},[1726,26113,1728],{},[898,26115,207],{},[902,26117,19870],{"encoding":904},[883,26119,26121],{"className":26120},[886],[888,26122,26123],{"xmlns":890},[892,26124,26125,26141],{},[895,26126,26127,26129,26131,26133,26135,26137,26139],{},[898,26128,2815],{},[898,26130,1738],{},[898,26132,8659],{},[1726,26134,1728],{},[2133,26136,2281],{},[1726,26138,2228],{},[898,26140,207],{},[902,26142,19896],{"encoding":904},[123,26144,26145,26148,26149],{},[38,26146,26147],{},"Modely národní ekonomiky"," postupně bohatnou:\n",[120,26150,26151,26239,26308],{},[123,26152,26153,26170,26171,26192,26193,1742],{},[883,26154,26156],{"className":26155},[886],[888,26157,26158],{"xmlns":890},[892,26159,26160,26168],{},[895,26161,26162,26164,26166],{},[898,26163,2775],{},[2289,26165,12276],{},[898,26167,12170],{},[902,26169,12281],{"encoding":904},": ",[883,26172,26174],{"className":26173},[886],[888,26175,26176],{"xmlns":890},[892,26177,26178,26190],{},[895,26179,26180,26182,26184,26186,26188],{},[898,26181,1745],{},[1726,26183,1728],{},[898,26185,2775],{},[1726,26187,2099],{},[898,26189,12170],{},[902,26191,14730],{"encoding":904}," (uzavřená ekonomika bez vlády), ",[883,26194,26196],{"className":26195},[886],[888,26197,26198],{"xmlns":890},[892,26199,26200,26236],{},[895,26201,26202,26208,26210,26212,26214,26216,26222,26224,26226,26228,26230,26232,26234],{},[2128,26203,26204,26206],{},[898,26205,1745],{},[898,26207,4240],{},[1726,26209,1728],{},[1726,26211,1735],{"stretchy":1734},[898,26213,2102],{},[1726,26215,2099],{},[2128,26217,26218,26220],{},[898,26219,12170],{},[1726,26221,4342],{},[1726,26223,1762],{"stretchy":1734},[898,26225,4661],{"mathvariant":2377},[1726,26227,1735],{"stretchy":1734},[2133,26229,2281],{},[1726,26231,2228],{},[898,26233,207],{},[1726,26235,1762],{"stretchy":1734},[902,26237,26238],{"encoding":904},"Y^E = (b + I^*)\u002F(1-a)",[123,26240,26241,26262,26263,26282,26283,1742],{},[883,26242,26244],{"className":26243},[886],[888,26245,26246],{"xmlns":890},[892,26247,26248,26260],{},[895,26249,26250,26252,26254,26256,26258],{},[898,26251,2775],{},[2289,26253,12276],{},[898,26255,12170],{},[2289,26257,12276],{},[898,26259,12098],{},[902,26261,18202],{"encoding":904},": přidává vládu, zdanění ",[883,26264,26266],{"className":26265},[886],[888,26267,26268],{"xmlns":890},[892,26269,26270,26280],{},[895,26271,26272,26274,26276,26278],{},[898,26273,2772],{},[1726,26275,1735],{"stretchy":1734},[898,26277,1745],{},[1726,26279,1762],{"stretchy":1734},[902,26281,22200],{"encoding":904}," a disponibilní důchod ",[883,26284,26286],{"className":26285},[886],[888,26287,26288],{"xmlns":890},[892,26289,26290,26306],{},[895,26291,26292,26298,26300,26302,26304],{},[2275,26293,26294,26296],{},[898,26295,1745],{},[898,26297,1731],{},[1726,26299,1728],{},[898,26301,1745],{},[1726,26303,2228],{},[898,26305,2772],{},[902,26307,21699],{"encoding":904},[123,26309,26310,26335,26336,21575,26357,1888],{},[883,26311,26313],{"className":26312},[886],[888,26314,26315],{"xmlns":890},[892,26316,26317,26333],{},[895,26318,26319,26321,26323,26325,26327,26329,26331],{},[898,26320,2775],{},[2289,26322,12276],{},[898,26324,12170],{},[2289,26326,12276],{},[898,26328,12098],{},[2289,26330,12276],{},[898,26332,12306],{},[902,26334,12309],{"encoding":904},": otevírá ekonomiku čistým exportem ",[883,26337,26339],{"className":26338},[886],[888,26340,26341],{"xmlns":890},[892,26342,26343,26355],{},[895,26344,26345,26347,26349,26351,26353],{},[898,26346,12306],{},[1726,26348,1728],{},[898,26350,23234],{},[1726,26352,2228],{},[898,26354,2815],{},[902,26356,23241],{"encoding":904},[883,26358,26360],{"className":26359},[886],[888,26361,26362],{"xmlns":890},[892,26363,26364,26382],{},[895,26365,26366,26368,26370,26372,26374,26380],{},[898,26367,2815],{},[1726,26369,1728],{},[898,26371,2815],{},[1726,26373,1735],{"stretchy":1734},[2275,26375,26376,26378],{},[898,26377,1745],{},[898,26379,1731],{},[1726,26381,1762],{"stretchy":1734},[902,26383,26384],{"encoding":904},"M = M(Y_D)",[123,26386,26387,26390,26391,1777,26394,26452],{},[38,26388,26389],{},"Multiplikátory"," (parciální derivace rovnovážných veličin podle exogenních) — klíčový ",[38,26392,26393],{},"multiplikátor investic",[883,26395,26397],{"className":26396},[886],[888,26398,26399],{"xmlns":890},[892,26400,26401,26449],{},[895,26402,26403,26405,26411,26413,26415,26421,26423,26425,26427,26429,26431,26433,26435,26437,26439,26441,26443,26445,26447],{},[898,26404,9856],{"mathvariant":2377},[2128,26406,26407,26409],{},[898,26408,1745],{},[898,26410,4240],{},[898,26412,4661],{"mathvariant":2377},[898,26414,9856],{"mathvariant":2377},[2128,26416,26417,26419],{},[898,26418,12170],{},[1726,26420,4342],{},[1726,26422,1728],{},[2133,26424,2281],{},[898,26426,4661],{"mathvariant":2377},[1726,26428,1735],{"stretchy":1734},[2133,26430,2281],{},[1726,26432,2228],{},[898,26434,207],{},[1726,26436,1762],{"stretchy":1734},[1726,26438,1728],{},[2133,26440,2281],{},[898,26442,4661],{"mathvariant":2377},[898,26444,2815],{},[898,26446,1738],{},[898,26448,8659],{},[902,26450,26451],{"encoding":904},"\\partial Y^E\u002F\\partial I^* = 1\u002F(1-a) = 1\u002FMPS"," (Keynesův multiplikátor).",[123,26454,26455,26457,26458,26473,26474,18629,26491,26506,26507,26532,26533,1888],{},[38,26456,945],{}," doplňuje obraz o trh peněz: investice závisejí na úrokové míře, ",[883,26459,26461],{"className":26460},[886],[888,26462,26463],{"xmlns":890},[892,26464,26465,26471],{},[895,26466,26467,26469],{},[898,26468,12170],{},[898,26470,8659],{},[902,26472,12037],{"encoding":904}," popisuje rovnováhu trhu zboží (",[883,26475,26477],{"className":26476},[886],[888,26478,26479],{"xmlns":890},[892,26480,26481,26489],{},[895,26482,26483,26485,26487],{},[898,26484,12170],{},[1726,26486,1728],{},[898,26488,8659],{},[902,26490,12698],{"encoding":904},[883,26492,26494],{"className":26493},[886],[888,26495,26496],{"xmlns":890},[892,26497,26498,26504],{},[895,26499,26500,26502],{},[898,26501,9779],{},[898,26503,2815],{},[902,26505,12044],{"encoding":904}," rovnováhu trhu peněz (",[883,26508,26510],{"className":26509},[886],[888,26511,26512],{"xmlns":890},[892,26513,26514,26530],{},[895,26515,26516,26522,26524],{},[2128,26517,26518,26520],{},[898,26519,2815],{},[898,26521,1731],{},[1726,26523,1728],{},[2128,26525,26526,26528],{},[898,26527,2815],{},[1726,26529,4342],{},[902,26531,13466],{"encoding":904},"); průsečík dává ",[883,26534,26536],{"className":26535},[886],[888,26537,26538],{"xmlns":890},[892,26539,26540,26560],{},[895,26541,26542,26544,26550,26552,26558],{},[1726,26543,1735],{"stretchy":1734},[2128,26545,26546,26548],{},[898,26547,1745],{},[898,26549,4240],{},[1726,26551,1742],{"separator":1741},[2128,26553,26554,26556],{},[898,26555,12027],{},[898,26557,4240],{},[1726,26559,1762],{"stretchy":1734},[902,26561,12081],{"encoding":904},[115,26563,1670],{"id":1669},[120,26565,26566,26604,26644,26734,26816,26870,26926,26985,27020,27025,27097,27172,27258,27320,27388,27446,27499,27538],{},[123,26567,26568,1696,26571,25888],{},[38,26569,26570],{},"Hrubý národní produkt (GNP)",[883,26572,26574],{"className":26573},[886],[888,26575,26576],{"xmlns":890},[892,26577,26578,26602],{},[895,26579,26580,26582,26584,26586,26588,26590,26592,26594,26596,26598,26600],{},[898,26581,12098],{},[898,26583,1750],{},[898,26585,1738],{},[1726,26587,1728],{},[898,26589,2775],{},[1726,26591,2099],{},[898,26593,12170],{},[1726,26595,2099],{},[898,26597,12098],{},[1726,26599,2099],{},[898,26601,12306],{},[902,26603,25887],{"encoding":904},[123,26605,26606,26622,26623,1888],{},[38,26607,26608,26609],{},"Národní důchod ",[883,26610,26612],{"className":26611},[886],[888,26613,26614],{"xmlns":890},[892,26615,26616,26620],{},[895,26617,26618],{},[898,26619,1745],{},[902,26621,1745],{"encoding":904}," — součet důchodů domácností; v modelech ",[883,26624,26626],{"className":26625},[886],[888,26627,26628],{"xmlns":890},[892,26629,26630,26642],{},[895,26631,26632,26634,26636,26638,26640],{},[898,26633,12098],{},[898,26635,1750],{},[898,26637,1738],{},[1726,26639,1880],{},[898,26641,1745],{},[902,26643,25852],{"encoding":904},[123,26645,26646,26672,26673,1343,26696,1343,26717,1888],{},[38,26647,26648,26649],{},"Funkce spotřeby ",[883,26650,26652],{"className":26651},[886],[888,26653,26654],{"xmlns":890},[892,26655,26656,26670],{},[895,26657,26658,26660,26662,26664,26666,26668],{},[898,26659,2775],{},[1726,26661,1728],{},[898,26663,2775],{},[1726,26665,1735],{"stretchy":1734},[898,26667,1745],{},[1726,26669,1762],{"stretchy":1734},[902,26671,20721],{"encoding":904}," — lineární model ",[883,26674,26676],{"className":26675},[886],[888,26677,26678],{"xmlns":890},[892,26679,26680,26694],{},[895,26681,26682,26684,26686,26688,26690,26692],{},[898,26683,2775],{},[1726,26685,1728],{},[898,26687,207],{},[898,26689,1745],{},[1726,26691,2099],{},[898,26693,2102],{},[902,26695,18901],{"encoding":904},[883,26697,26699],{"className":26698},[886],[888,26700,26701],{"xmlns":890},[892,26702,26703,26715],{},[895,26704,26705,26707,26709,26711,26713],{},[2133,26706,2328],{},[1726,26708,3444],{},[898,26710,207],{},[1726,26712,3444],{},[2133,26714,2281],{},[902,26716,18817],{"encoding":904},[883,26718,26720],{"className":26719},[886],[888,26721,26722],{"xmlns":890},[892,26723,26724,26732],{},[895,26725,26726,26728,26730],{},[898,26727,2102],{},[1726,26729,3405],{},[2133,26731,2328],{},[902,26733,18795],{"encoding":904},[123,26735,26736,1696,26763,26784,26785,1888],{},[38,26737,26738,26739],{},"Funkce úspor ",[883,26740,26742],{"className":26741},[886],[888,26743,26744],{"xmlns":890},[892,26745,26746,26760],{},[895,26747,26748,26750,26752,26754,26756,26758],{},[898,26749,8659],{},[1726,26751,1728],{},[898,26753,8659],{},[1726,26755,1735],{"stretchy":1734},[898,26757,1745],{},[1726,26759,1762],{"stretchy":1734},[902,26761,26762],{"encoding":904},"S = S(Y)",[883,26764,26766],{"className":26765},[886],[888,26767,26768],{"xmlns":890},[892,26769,26770,26782],{},[895,26771,26772,26774,26776,26778,26780],{},[898,26773,1745],{},[1726,26775,1728],{},[898,26777,2775],{},[1726,26779,2099],{},[898,26781,8659],{},[902,26783,12680],{"encoding":904},"; lineární ",[883,26786,26788],{"className":26787},[886],[888,26789,26790],{"xmlns":890},[892,26791,26792,26814],{},[895,26793,26794,26796,26798,26800,26802,26804,26806,26808,26810,26812],{},[898,26795,8659],{},[1726,26797,1728],{},[1726,26799,1735],{"stretchy":1734},[2133,26801,2281],{},[1726,26803,2228],{},[898,26805,207],{},[1726,26807,1762],{"stretchy":1734},[898,26809,1745],{},[1726,26811,2228],{},[898,26813,2102],{},[902,26815,19150],{"encoding":904},[123,26817,26818,1696,26821,1343,26844,1888],{},[38,26819,26820],{},"Autonomní spotřeba\u002Fúspory",[883,26822,26824],{"className":26823},[886],[888,26825,26826],{"xmlns":890},[892,26827,26828,26842],{},[895,26829,26830,26832,26834,26836,26838,26840],{},[898,26831,2775],{},[1726,26833,1735],{"stretchy":1734},[2133,26835,2328],{},[1726,26837,1762],{"stretchy":1734},[1726,26839,1728],{},[898,26841,2102],{},[902,26843,19542],{"encoding":904},[883,26845,26847],{"className":26846},[886],[888,26848,26849],{"xmlns":890},[892,26850,26851,26867],{},[895,26852,26853,26855,26857,26859,26861,26863,26865],{},[898,26854,8659],{},[1726,26856,1735],{"stretchy":1734},[2133,26858,2328],{},[1726,26860,1762],{"stretchy":1734},[1726,26862,1728],{},[1726,26864,2228],{},[898,26866,2102],{},[902,26868,26869],{"encoding":904},"S(0) = -b",[123,26871,26872,26904,26905,1847],{},[38,26873,26874,26875],{},"Mezní sklon ke spotřebě ",[883,26876,26878],{"className":26877},[886],[888,26879,26880],{"xmlns":890},[892,26881,26882,26902],{},[895,26883,26884,26886,26888,26890,26892,26894,26896,26898,26900],{},[898,26885,2815],{},[898,26887,1738],{},[898,26889,2775],{},[1726,26891,1728],{},[898,26893,2198],{"mathvariant":2377},[898,26895,2775],{},[898,26897,4661],{"mathvariant":2377},[898,26899,2198],{"mathvariant":2377},[898,26901,1745],{},[902,26903,26034],{"encoding":904}," (v lineárním modelu ",[883,26906,26908],{"className":26907},[886],[888,26909,26910],{"xmlns":890},[892,26911,26912,26924],{},[895,26913,26914,26916,26918,26920,26922],{},[898,26915,2815],{},[898,26917,1738],{},[898,26919,2775],{},[1726,26921,1728],{},[898,26923,207],{},[902,26925,19870],{"encoding":904},[123,26927,26928,26904,26960,1847],{},[38,26929,26930,26931],{},"Mezní sklon k úsporám ",[883,26932,26934],{"className":26933},[886],[888,26935,26936],{"xmlns":890},[892,26937,26938,26958],{},[895,26939,26940,26942,26944,26946,26948,26950,26952,26954,26956],{},[898,26941,2815],{},[898,26943,1738],{},[898,26945,8659],{},[1726,26947,1728],{},[898,26949,2198],{"mathvariant":2377},[898,26951,8659],{},[898,26953,4661],{"mathvariant":2377},[898,26955,2198],{"mathvariant":2377},[898,26957,1745],{},[902,26959,26064],{"encoding":904},[883,26961,26963],{"className":26962},[886],[888,26964,26965],{"xmlns":890},[892,26966,26967,26983],{},[895,26968,26969,26971,26973,26975,26977,26979,26981],{},[898,26970,2815],{},[898,26972,1738],{},[898,26974,8659],{},[1726,26976,1728],{},[2133,26978,2281],{},[1726,26980,2228],{},[898,26982,207],{},[902,26984,19896],{"encoding":904},[123,26986,26987,1777,26990,27019],{},[38,26988,26989],{},"Vztah",[883,26991,26993],{"className":26992},[886],[888,26994,26995],{"xmlns":890},[892,26996,26997,27017],{},[895,26998,26999,27001,27003,27005,27007,27009,27011,27013,27015],{},[898,27000,2815],{},[898,27002,1738],{},[898,27004,2775],{},[1726,27006,2099],{},[898,27008,2815],{},[898,27010,1738],{},[898,27012,8659],{},[1726,27014,1728],{},[2133,27016,2281],{},[902,27018,26095],{"encoding":904}," (7.5).",[123,27021,27022,27024],{},[38,27023,20564],{}," — rovnováha agregátní poptávky a nabídky.",[123,27026,27027,27030,27031,15776,27052,1888],{},[38,27028,27029],{},"Model C-I"," — uzavřená ekonomika bez vlády; ",[883,27032,27034],{"className":27033},[886],[888,27035,27036],{"xmlns":890},[892,27037,27038,27050],{},[895,27039,27040,27042,27044,27046,27048],{},[898,27041,1745],{},[1726,27043,1728],{},[898,27045,2775],{},[1726,27047,2099],{},[898,27049,12170],{},[902,27051,14730],{"encoding":904},[883,27053,27055],{"className":27054},[886],[888,27056,27057],{"xmlns":890},[892,27058,27059,27095],{},[895,27060,27061,27067,27069,27071,27073,27075,27081,27083,27085,27087,27089,27091,27093],{},[2128,27062,27063,27065],{},[898,27064,1745],{},[898,27066,4240],{},[1726,27068,1728],{},[1726,27070,1735],{"stretchy":1734},[898,27072,2102],{},[1726,27074,2099],{},[2128,27076,27077,27079],{},[898,27078,12170],{},[1726,27080,4342],{},[1726,27082,1762],{"stretchy":1734},[898,27084,4661],{"mathvariant":2377},[1726,27086,1735],{"stretchy":1734},[2133,27088,2281],{},[1726,27090,2228],{},[898,27092,207],{},[1726,27094,1762],{"stretchy":1734},[902,27096,26238],{"encoding":904},[123,27098,27099,27102,27103,1343,27122,15776,27147,1888],{},[38,27100,27101],{},"Model C-I-G"," — ekonomika s vládou, zdaněním ",[883,27104,27106],{"className":27105},[886],[888,27107,27108],{"xmlns":890},[892,27109,27110,27120],{},[895,27111,27112,27114,27116,27118],{},[898,27113,2772],{},[1726,27115,1735],{"stretchy":1734},[898,27117,1745],{},[1726,27119,1762],{"stretchy":1734},[902,27121,22200],{"encoding":904},[883,27123,27125],{"className":27124},[886],[888,27126,27127],{"xmlns":890},[892,27128,27129,27145],{},[895,27130,27131,27137,27139,27141,27143],{},[2275,27132,27133,27135],{},[898,27134,1745],{},[898,27136,1731],{},[1726,27138,1728],{},[898,27140,1745],{},[1726,27142,2228],{},[898,27144,2772],{},[902,27146,21699],{"encoding":904},[883,27148,27150],{"className":27149},[886],[888,27151,27152],{"xmlns":890},[892,27153,27154,27170],{},[895,27155,27156,27158,27160,27162,27164,27166,27168],{},[898,27157,1745],{},[1726,27159,1728],{},[898,27161,2775],{},[1726,27163,2099],{},[898,27165,12170],{},[1726,27167,2099],{},[898,27169,12098],{},[902,27171,21670],{"encoding":904},[123,27173,27174,27177,27178,27199,27200,15776,27224,1888],{},[38,27175,27176],{},"Model C-I-G-X"," — otevřená ekonomika s čistým exportem ",[883,27179,27181],{"className":27180},[886],[888,27182,27183],{"xmlns":890},[892,27184,27185,27197],{},[895,27186,27187,27189,27191,27193,27195],{},[898,27188,12306],{},[1726,27190,1728],{},[898,27192,23234],{},[1726,27194,2228],{},[898,27196,2815],{},[902,27198,23241],{"encoding":904},", importem ",[883,27201,27203],{"className":27202},[886],[888,27204,27205],{"xmlns":890},[892,27206,27207,27221],{},[895,27208,27209,27211,27213,27219],{},[898,27210,2815],{},[1726,27212,1735],{"stretchy":1734},[2275,27214,27215,27217],{},[898,27216,1745],{},[898,27218,1731],{},[1726,27220,1762],{"stretchy":1734},[902,27222,27223],{"encoding":904},"M(Y_D)",[883,27225,27227],{"className":27226},[886],[888,27228,27229],{"xmlns":890},[892,27230,27231,27255],{},[895,27232,27233,27235,27237,27239,27241,27243,27245,27247,27249,27251,27253],{},[898,27234,1745],{},[1726,27236,1728],{},[898,27238,2775],{},[1726,27240,2099],{},[898,27242,12170],{},[1726,27244,2099],{},[898,27246,12098],{},[1726,27248,2099],{},[898,27250,23234],{},[1726,27252,2228],{},[898,27254,2815],{},[902,27256,27257],{"encoding":904},"Y = C + I + G + B - M",[123,27259,27260,1696,27263,26452],{},[38,27261,27262],{},"Multiplikátor investic",[883,27264,27266],{"className":27265},[886],[888,27267,27268],{"xmlns":890},[892,27269,27270,27318],{},[895,27271,27272,27274,27280,27282,27284,27290,27292,27294,27296,27298,27300,27302,27304,27306,27308,27310,27312,27314,27316],{},[898,27273,9856],{"mathvariant":2377},[2128,27275,27276,27278],{},[898,27277,1745],{},[898,27279,4240],{},[898,27281,4661],{"mathvariant":2377},[898,27283,9856],{"mathvariant":2377},[2128,27285,27286,27288],{},[898,27287,12170],{},[1726,27289,4342],{},[1726,27291,1728],{},[2133,27293,2281],{},[898,27295,4661],{"mathvariant":2377},[1726,27297,1735],{"stretchy":1734},[2133,27299,2281],{},[1726,27301,2228],{},[898,27303,207],{},[1726,27305,1762],{"stretchy":1734},[1726,27307,1728],{},[2133,27309,2281],{},[898,27311,4661],{"mathvariant":2377},[898,27313,2815],{},[898,27315,1738],{},[898,27317,8659],{},[902,27319,26451],{"encoding":904},[123,27321,27322,1696,27353,1343,27370,27387],{},[38,27323,15711,27324],{},[883,27325,27327],{"className":27326},[886],[888,27328,27329],{"xmlns":890},[892,27330,27331,27351],{},[895,27332,27333,27335,27337,27339,27341,27343,27345,27347,27349],{},[898,27334,12170],{},[1726,27336,1735],{"stretchy":1734},[898,27338,12027],{},[1726,27340,1762],{"stretchy":1734},[1726,27342,1728],{},[898,27344,2146],{},[898,27346,12027],{},[1726,27348,2099],{},[898,27350,2198],{},[902,27352,15741],{"encoding":904},[883,27354,27356],{"className":27355},[886],[888,27357,27358],{"xmlns":890},[892,27359,27360,27368],{},[895,27361,27362,27364,27366],{},[898,27363,2146],{},[1726,27365,3444],{},[2133,27367,2328],{},[902,27369,12501],{"encoding":904},[883,27371,27373],{"className":27372},[886],[888,27374,27375],{"xmlns":890},[892,27376,27377,27385],{},[895,27378,27379,27381,27383],{},[898,27380,2198],{},[1726,27382,3405],{},[2133,27384,2328],{},[902,27386,12480],{"encoding":904},"; klesající.",[123,27389,27390,27392,27393,27395,27396,27445],{},[38,27391,15830],{}," — rovnováha na trhu zboží (",[614,27394,12040],{},"); ",[883,27397,27399],{"className":27398},[886],[888,27400,27401],{"xmlns":890},[892,27402,27403,27443],{},[895,27404,27405,27407,27409,27421,27423,27425],{},[898,27406,1745],{},[1726,27408,1728],{},[2330,27410,27411,27413],{},[898,27412,2146],{},[895,27414,27415,27417,27419],{},[2133,27416,2281],{},[1726,27418,2228],{},[898,27420,207],{},[898,27422,12027],{},[1726,27424,2099],{},[2330,27426,27427,27435],{},[895,27428,27429,27431,27433],{},[898,27430,2102],{},[1726,27432,2099],{},[898,27434,2198],{},[895,27436,27437,27439,27441],{},[2133,27438,2281],{},[1726,27440,2228],{},[898,27442,207],{},[902,27444,15883],{"encoding":904}," (7.14); klesající.",[123,27447,27448,27450,27451,27395,27453,27498],{},[38,27449,16029],{}," — rovnováha na trhu peněz (",[614,27452,12047],{},[883,27454,27456],{"className":27455},[886],[888,27457,27458],{"xmlns":890},[892,27459,27460,27496],{},[895,27461,27462,27468,27470,27476,27478,27480,27486,27488,27490],{},[2128,27463,27464,27466],{},[898,27465,2815],{},[1726,27467,4342],{},[1726,27469,1728],{},[2275,27471,27472,27474],{},[898,27473,13223],{},[2133,27475,2281],{},[898,27477,1745],{},[1726,27479,2099],{},[2275,27481,27482,27484],{},[898,27483,13223],{},[2133,27485,2135],{},[898,27487,12027],{},[1726,27489,2099],{},[2275,27491,27492,27494],{},[898,27493,13223],{},[2133,27495,2177],{},[902,27497,16077],{"encoding":904}," (7.15); rostoucí.",[123,27500,27501,1696,27504,1888],{},[38,27502,27503],{},"Transakční, opatrnostní a spekulační poptávka po penězích",[883,27505,27507],{"className":27506},[886],[888,27508,27509],{"xmlns":890},[892,27510,27511,27535],{},[895,27512,27513,27519,27521,27527,27529],{},[2128,27514,27515,27517],{},[898,27516,2815],{},[898,27518,1731],{},[1726,27520,1728],{},[2275,27522,27523,27525],{},[898,27524,9779],{},[2133,27526,2281],{},[1726,27528,2099],{},[2275,27530,27531,27533],{},[898,27532,9779],{},[2133,27534,2135],{},[902,27536,27537],{"encoding":904},"M^D = L_1 + L_2",[123,27539,27540,16087,27542,13966,27555,3877,27570,27585,27586,1888],{},[38,27541,945],{},[883,27543,27545],{"className":27544},[886],[888,27546,27547],{"xmlns":890},[892,27548,27549,27553],{},[895,27550,27551],{},[898,27552,4240],{},[902,27554,4240],{"encoding":904},[883,27556,27558],{"className":27557},[886],[888,27559,27560],{"xmlns":890},[892,27561,27562,27568],{},[895,27563,27564,27566],{},[898,27565,12170],{},[898,27567,8659],{},[902,27569,12037],{"encoding":904},[883,27571,27573],{"className":27572},[886],[888,27574,27575],{"xmlns":890},[892,27576,27577,27583],{},[895,27578,27579,27581],{},[898,27580,9779],{},[898,27582,2815],{},[902,27584,12044],{"encoding":904}," určuje ",[883,27587,27589],{"className":27588},[886],[888,27590,27591],{"xmlns":890},[892,27592,27593,27613],{},[895,27594,27595,27597,27603,27605,27611],{},[1726,27596,1735],{"stretchy":1734},[2128,27598,27599,27601],{},[898,27600,1745],{},[898,27602,4240],{},[1726,27604,1742],{"separator":1741},[2128,27606,27607,27609],{},[898,27608,12027],{},[898,27610,4240],{},[1726,27612,1762],{"stretchy":1734},[902,27614,12081],{"encoding":904},[115,27616,1899],{"id":1898},[120,27618,27619,27626,27633],{},[123,27620,27621,1777,27623],{},[38,27622,16188],{},[207,27624,16192],{"className":27625,"dataFsResolvedFilePath":1640,"href":1641},[210],[123,27627,27628,1777,27630],{},[38,27629,16197],{},[207,27631,16201],{"className":27632,"dataFsResolvedFilePath":868,"href":869},[210],[123,27634,27635,27637],{},[38,27636,16216],{},[120,27638,27639,27645,27651,27657],{},[123,27640,27641,27644],{},[207,27642,16255],{"className":27643,"dataFsResolvedFilePath":943,"href":944},[210]," — detailní IS-LM analýza (odvození křivek, Příklad 7.6, fiskální vs monetární politika)",[123,27646,27647,27650],{},[207,27648,1846],{"className":27649,"dataFsResolvedFilePath":800,"href":801},[210]," — paralela mikroekonomických multiplikátorů (multiplikátory rovnovážné ceny a množství)",[123,27652,27653,27656],{},[207,27654,2947],{"className":27655,"dataFsResolvedFilePath":827,"href":828},[210]," — mikroekonomické analogie, článek 2.4 o multiplikátorech",[123,27658,27659,27662,27663,1343,27680,27697],{},[207,27660,1145],{"className":27661,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro ",[883,27664,27666],{"className":27665},[886],[888,27667,27668],{"xmlns":890},[892,27669,27670,27678],{},[895,27671,27672,27674,27676],{},[898,27673,2815],{},[898,27675,1738],{},[898,27677,2775],{},[902,27679,18027],{"encoding":904},[883,27681,27683],{"className":27682},[886],[888,27684,27685],{"xmlns":890},[892,27686,27687,27695],{},[895,27688,27689,27691,27693],{},[898,27690,2815],{},[898,27692,1738],{},[898,27694,8659],{},[902,27696,19640],{"encoding":904}," a interpretaci změn diferenciálem",{"title":641,"searchDepth":642,"depth":642,"links":27699},[27700,27701,27702,27703,27708,27711,27712,27719,27724,27729,27732,27733,27734,27735],{"id":11991,"depth":642,"text":11992},{"id":18136,"depth":642,"text":18137},{"id":18256,"depth":642,"text":18257},{"id":18508,"depth":642,"text":18509,"children":27704},[27705,27706,27707],{"id":18512,"depth":649,"text":18513},{"id":18724,"depth":649,"text":18725},{"id":19232,"depth":649,"text":19233},{"id":19552,"depth":642,"text":19553,"children":27709},[27710],{"id":20068,"depth":649,"text":20069},{"id":20563,"depth":642,"text":20564},{"id":20590,"depth":642,"text":20591,"children":27713},[27714,27715,27716,27718],{"id":20601,"depth":649,"text":20602},{"id":20671,"depth":649,"text":20672},{"id":20855,"depth":649,"text":27717},"Výpočet YEY^E",{"id":20998,"depth":649,"text":20999},{"id":21376,"depth":642,"text":21377,"children":27720},[27721,27722,27723],{"id":21380,"depth":649,"text":20602},{"id":21829,"depth":649,"text":20672},{"id":22485,"depth":649,"text":22486},{"id":23272,"depth":642,"text":23273,"children":27725},[27726,27727,27728],{"id":23276,"depth":649,"text":20602},{"id":23421,"depth":649,"text":20672},{"id":23691,"depth":649,"text":23692},{"id":24615,"depth":642,"text":24616,"children":27730},[27731],{"id":24811,"depth":649,"text":24812},{"id":25361,"depth":642,"text":25362},{"id":25821,"depth":642,"text":25822},{"id":1669,"depth":642,"text":1670},{"id":1898,"depth":642,"text":1899},{},"\u002Ftopics\u002Fnarodni-duchod",{"title":936,"description":641},[1138,1137],"topics\u002Fnarodni-duchod",[1128,16210,1143,27742,27743,27744,16255,17865],"gnp","mpc","mps","BMicmr68yKQbb8qpoE9KfzU5NFshq3Inq6w0tL8-GjU",{"id":27747,"title":27748,"body":27749,"course":1128,"courses":659,"created":9541,"description":641,"extension":661,"meta":36729,"navigation":664,"path":36730,"seo":36731,"sources":36732,"stem":36733,"tags":36734,"type":1950,"updated":677,"__hash__":36739},"topics\u002Ftopics\u002Foptimalizace-spotrebitele.md","Optimalizace spotřebitele — Lagrange, poptávka, minimalizace výdajů",{"type":9,"value":27750,"toc":36698},[27751,27754,27756,27985,27989,28042,28112,28224,28383,28387,28503,28507,28510,28632,28635,28828,28852,28920,29084,29102,29168,29546,29550,29557,29801,29857,29861,29926,30044,30176,30208,30328,30410,30413,30535,30728,30949,30953,30993,31098,31155,31255,31432,31562,31615,31618,31705,31709,31885,31889,31892,31977,31980,32037,32142,32146,32267,32270,32453,32456,32564,32773,33093,33141,33214,33288,33290,33514,33749,34017,34021,34024,34129,34186,34220,34267,34300,34384,34386,34618,34751,34828,34950,35105,35109,35250,35257,35481,35492,35496,35500,35605,35747,35857,35956,35960,36119,36229,36231,36624,36626],[12,27752,27748],{"id":27753},"optimalizace-spotřebitele-lagrange-poptávka-minimalizace-výdajů",[115,27755,11992],{"id":11991},[724,27757,27758,27760,27761,27795,27796,27799,27800,27831,27832,27878,27879,27882,27883,27925,27926,27944,27945,27949,27950,27980,27981,27984],{},[38,27759,913],{}," řeší, jaký svazek zboží ",[883,27762,27764],{"className":27763},[886],[888,27765,27766],{"xmlns":890},[892,27767,27768,27792],{},[895,27769,27770,27772,27780,27782,27790],{},[1726,27771,2487],{"stretchy":1734},[9151,27773,27774,27776,27778],{},[898,27775,1724],{},[2133,27777,2281],{},[1726,27779,4342],{},[1726,27781,1742],{"separator":1741},[9151,27783,27784,27786,27788],{},[898,27785,1724],{},[2133,27787,2135],{},[1726,27789,4342],{},[1726,27791,2502],{"stretchy":1734},[902,27793,27794],{"encoding":904},"[Q_1^*, Q_2^*]"," zvolit při známých cenách a důchodu. Existují dvě ekvivalentní formulace: ",[38,27797,27798],{},"primární úloha"," — maximalizace užitečnosti ",[883,27801,27803],{"className":27802},[886],[888,27804,27805],{"xmlns":890},[892,27806,27807,27829],{},[895,27808,27809,27811,27813,27819,27821,27827],{},[898,27810,900],{},[1726,27812,1735],{"stretchy":1734},[2275,27814,27815,27817],{},[898,27816,1724],{},[2133,27818,2281],{},[1726,27820,1742],{"separator":1741},[2275,27822,27823,27825],{},[898,27824,1724],{},[2133,27826,2135],{},[1726,27828,1762],{"stretchy":1734},[902,27830,16326],{"encoding":904}," při rozpočtovém omezení ",[883,27833,27835],{"className":27834},[886],[888,27836,27837],{"xmlns":890},[892,27838,27839,27875],{},[895,27840,27841,27847,27849,27855,27861,27863,27869],{},[2128,27842,27843,27845],{},[898,27844,1745],{},[1726,27846,4342],{},[1726,27848,1728],{},[2275,27850,27851,27853],{},[898,27852,1738],{},[2133,27854,2281],{},[2275,27856,27857,27859],{},[898,27858,1724],{},[2133,27860,2281],{},[1726,27862,2099],{},[2275,27864,27865,27867],{},[898,27866,1738],{},[2133,27868,2135],{},[2275,27870,27871,27873],{},[898,27872,1724],{},[2133,27874,2135],{},[902,27876,27877],{"encoding":904},"Y^* = P_1 Q_1 + P_2 Q_2",", a ",[38,27880,27881],{},"duální úloha"," — minimalizace výdajů ",[883,27884,27886],{"className":27885},[886],[888,27887,27888],{"xmlns":890},[892,27889,27890,27922],{},[895,27891,27892,27894,27896,27902,27908,27910,27916],{},[898,27893,4240],{},[1726,27895,1728],{},[2275,27897,27898,27900],{},[898,27899,1738],{},[2133,27901,2281],{},[2275,27903,27904,27906],{},[898,27905,1724],{},[2133,27907,2281],{},[1726,27909,2099],{},[2275,27911,27912,27914],{},[898,27913,1738],{},[2133,27915,2135],{},[2275,27917,27918,27920],{},[898,27919,1724],{},[2133,27921,2135],{},[902,27923,27924],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2"," při zadané hladině užitečnosti ",[883,27927,27929],{"className":27928},[886],[888,27930,27931],{"xmlns":890},[892,27932,27933,27941],{},[895,27934,27935],{},[2128,27936,27937,27939],{},[898,27938,900],{},[1726,27940,4342],{},[902,27942,27943],{"encoding":904},"U^*",". Obě úlohy se řeší ",[207,27946,27948],{"className":27947,"dataFsResolvedFilePath":791,"href":792},[210],"metodou Lagrangeových multiplikátorů"," a vedou na tentýž bod dotyku indiferenční křivky a rozpočtové přímky, v němž platí ",[883,27951,27953],{"className":27952},[886],[888,27954,27955],{"xmlns":890},[892,27956,27957,27977],{},[895,27958,27959,27961,27963,27969,27971],{},[2289,27960,10587],{},[1726,27962,1728],{},[2275,27964,27965,27967],{},[898,27966,1738],{},[2133,27968,2281],{},[898,27970,4661],{"mathvariant":2377},[2275,27972,27973,27975],{},[898,27974,1738],{},[2133,27976,2135],{},[902,27978,27979],{"encoding":904},"\\text{MRCS} = P_1\u002FP_2",". Výstupem jsou ",[38,27982,27983],{},"funkce poptávky"," — Marshallova (závislá na důchodu) a Hicksova (závislá na hladině užitečnosti).",[115,27986,27988],{"id":27987},"úvod-proč-optimalizovat","Úvod — proč optimalizovat",[724,27990,27991,27992,28010,28011,28041],{},"Racionální spotřebitel má omezený důchod a musí se rozhodnout, jak jej rozdělit mezi spotřebovávané zboží. V modelu pro dvě zboží je k dispozici částka ",[883,27993,27995],{"className":27994},[886],[888,27996,27997],{"xmlns":890},[892,27998,27999,28007],{},[895,28000,28001],{},[2128,28002,28003,28005],{},[898,28004,1745],{},[1726,28006,4342],{},[902,28008,28009],{"encoding":904},"Y^*"," a ceny ",[883,28012,28014],{"className":28013},[886],[888,28015,28016],{"xmlns":890},[892,28017,28018,28038],{},[895,28019,28020,28028,28030],{},[9151,28021,28022,28024,28026],{},[898,28023,1738],{},[2133,28025,2281],{},[1726,28027,4342],{},[1726,28029,1742],{"separator":1741},[9151,28031,28032,28034,28036],{},[898,28033,1738],{},[2133,28035,2135],{},[1726,28037,4342],{},[902,28039,28040],{"encoding":904},"P_1^*, P_2^*",", rozpočtové omezení má tvar",[883,28043,28045],{"className":28044},[886],[888,28046,28048],{"xmlns":890,"display":28047},"block",[892,28049,28050,28109],{},[20735,28051,28053],{"width":28052},"100%",[20740,28054,28055,28058,28102,28104],{},[20743,28056],{"width":28057},"50%",[20743,28059,28060],{},[895,28061,28062,28068,28070,28078,28084,28086,28094,28100],{},[2128,28063,28064,28066],{},[898,28065,1745],{},[1726,28067,4342],{},[1726,28069,1728],{},[9151,28071,28072,28074,28076],{},[898,28073,1738],{},[2133,28075,2281],{},[1726,28077,4342],{},[2275,28079,28080,28082],{},[898,28081,1724],{},[2133,28083,2281],{},[1726,28085,2099],{},[9151,28087,28088,28090,28092],{},[898,28089,1738],{},[2133,28091,2135],{},[1726,28093,4342],{},[2275,28095,28096,28098],{},[898,28097,1724],{},[2133,28099,2135],{},[1726,28101,1742],{"separator":1741},[20743,28103],{"width":28057},[20743,28105,28106],{},[2289,28107,28108],{},"(6.12)",[902,28110,28111],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2, \\tag{6.12}",[724,28113,28114,28115,28118,28119,3877,28155,28191,28192,28205,28206,28220,28221,1888],{},"geometricky ",[38,28116,28117],{},"rozpočtová přímka (budget line)"," procházející body ",[883,28120,28122],{"className":28121},[886],[888,28123,28124],{"xmlns":890},[892,28125,28126,28152],{},[895,28127,28128,28130,28136,28138,28146,28148,28150],{},[1726,28129,2487],{"stretchy":1734},[2128,28131,28132,28134],{},[898,28133,1745],{},[1726,28135,4342],{},[898,28137,4661],{"mathvariant":2377},[9151,28139,28140,28142,28144],{},[898,28141,1738],{},[2133,28143,2281],{},[1726,28145,4342],{},[1726,28147,1742],{"separator":1741},[2133,28149,2328],{},[1726,28151,2502],{"stretchy":1734},[902,28153,28154],{"encoding":904},"[Y^*\u002FP_1^*, 0]",[883,28156,28158],{"className":28157},[886],[888,28159,28160],{"xmlns":890},[892,28161,28162,28188],{},[895,28163,28164,28166,28168,28170,28176,28178,28186],{},[1726,28165,2487],{"stretchy":1734},[2133,28167,2328],{},[1726,28169,1742],{"separator":1741},[2128,28171,28172,28174],{},[898,28173,1745],{},[1726,28175,4342],{},[898,28177,4661],{"mathvariant":2377},[9151,28179,28180,28182,28184],{},[898,28181,1738],{},[2133,28183,2135],{},[1726,28185,4342],{},[1726,28187,2502],{"stretchy":1734},[902,28189,28190],{"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 ",[883,28193,28195],{"className":28194},[886],[888,28196,28197],{"xmlns":890},[892,28198,28199,28203],{},[895,28200,28201],{},[898,28202,900],{},[902,28204,900],{"encoding":904},", indiferenční křivky a ",[883,28207,28209],{"className":28208},[886],[888,28210,28211],{"xmlns":890},[892,28212,28213,28217],{},[895,28214,28215],{},[2289,28216,10587],{},[902,28218,28219],{"encoding":904},"\\text{MRCS}"," — je shrnuta v ",[207,28222,880],{"className":28223,"dataFsResolvedFilePath":878,"href":879},[210],[3859,28225,28226],{},[724,28227,28228,28230,28231,28234,28235,28248,28249,28251,28252,28265,28266,1777,28269,28309,28310,28327,28328,28345,28346,28363,28364,28382],{},[883,28229,4400],{}," Pozor — dvě úlohy, totéž řešení\n",[38,28232,28233],{},"Primární úloha"," (max ",[883,28236,28238],{"className":28237},[886],[888,28239,28240],{"xmlns":890},[892,28241,28242,28246],{},[895,28243,28244],{},[898,28245,900],{},[902,28247,900],{"encoding":904}," při pevném rozpočtu) a ",[38,28250,27881],{}," (min ",[883,28253,28255],{"className":28254},[886],[888,28256,28257],{"xmlns":890},[892,28258,28259,28263],{},[895,28260,28261],{},[898,28262,4240],{},[902,28264,4240],{"encoding":904}," při pevné užitečnosti) vedou na ",[38,28267,28268],{},"tentýž bod",[883,28270,28272],{"className":28271},[886],[888,28273,28274],{"xmlns":890},[892,28275,28276,28306],{},[895,28277,28278,28284,28286,28294,28296,28304],{},[2128,28279,28280,28282],{},[898,28281,1724],{},[1726,28283,4342],{},[1726,28285,2487],{"stretchy":1734},[9151,28287,28288,28290,28292],{},[898,28289,1724],{},[2133,28291,2281],{},[1726,28293,4342],{},[1726,28295,1742],{"separator":1741},[9151,28297,28298,28300,28302],{},[898,28299,1724],{},[2133,28301,2135],{},[1726,28303,4342],{},[1726,28305,2502],{"stretchy":1734},[902,28307,28308],{"encoding":904},"Q^*[Q_1^*, Q_2^*]",". Rozdíl je v tom, co je „vstup\" a co „výstup\": u primární úlohy je zadán důchod ",[883,28311,28313],{"className":28312},[886],[888,28314,28315],{"xmlns":890},[892,28316,28317,28325],{},[895,28318,28319],{},[2128,28320,28321,28323],{},[898,28322,1745],{},[1726,28324,4342],{},[902,28326,28009],{"encoding":904}," a hledáme maximální ",[883,28329,28331],{"className":28330},[886],[888,28332,28333],{"xmlns":890},[892,28334,28335,28343],{},[895,28336,28337],{},[2128,28338,28339,28341],{},[898,28340,900],{},[1726,28342,4342],{},[902,28344,27943],{"encoding":904},"; u duální úlohy je zadána hladina ",[883,28347,28349],{"className":28348},[886],[888,28350,28351],{"xmlns":890},[892,28352,28353,28361],{},[895,28354,28355],{},[2128,28356,28357,28359],{},[898,28358,900],{},[1726,28360,4342],{},[902,28362,27943],{"encoding":904}," a hledáme minimální ",[883,28365,28367],{"className":28366},[886],[888,28368,28369],{"xmlns":890},[892,28370,28371,28379],{},[895,28372,28373],{},[2128,28374,28375,28377],{},[898,28376,4240],{},[1726,28378,4342],{},[902,28380,28381],{"encoding":904},"E^*",". Z pozorování je přirozenější minimalizace výdajů (výdaje lze měřit).",[115,28384,28386],{"id":28385},"maximalizace-užitečnosti-za-rozpočtového-omezení","Maximalizace užitečnosti za rozpočtového omezení",[724,28388,28389,28390,28421,28422,28498,28499,1888],{},"Úlohou je najít maximum ",[883,28391,28393],{"className":28392},[886],[888,28394,28395],{"xmlns":890},[892,28396,28397,28419],{},[895,28398,28399,28401,28403,28409,28411,28417],{},[898,28400,900],{},[1726,28402,1735],{"stretchy":1734},[2275,28404,28405,28407],{},[898,28406,1724],{},[2133,28408,2281],{},[1726,28410,1742],{"separator":1741},[2275,28412,28413,28415],{},[898,28414,1724],{},[2133,28416,2135],{},[1726,28418,1762],{"stretchy":1734},[902,28420,16326],{"encoding":904}," vázané podmínkou (6.12) ve tvaru ",[883,28423,28425],{"className":28424},[886],[888,28426,28427],{"xmlns":890},[892,28428,28429,28495],{},[895,28430,28431,28433,28435,28441,28443,28449,28451,28453,28459,28461,28469,28475,28477,28485,28491,28493],{},[898,28432,11025],{},[1726,28434,1735],{"stretchy":1734},[2275,28436,28437,28439],{},[898,28438,1724],{},[2133,28440,2281],{},[1726,28442,1742],{"separator":1741},[2275,28444,28445,28447],{},[898,28446,1724],{},[2133,28448,2135],{},[1726,28450,1762],{"stretchy":1734},[1726,28452,1728],{},[2128,28454,28455,28457],{},[898,28456,1745],{},[1726,28458,4342],{},[1726,28460,2228],{},[9151,28462,28463,28465,28467],{},[898,28464,1738],{},[2133,28466,2281],{},[1726,28468,4342],{},[2275,28470,28471,28473],{},[898,28472,1724],{},[2133,28474,2281],{},[1726,28476,2228],{},[9151,28478,28479,28481,28483],{},[898,28480,1738],{},[2133,28482,2135],{},[1726,28484,4342],{},[2275,28486,28487,28489],{},[898,28488,1724],{},[2133,28490,2135],{},[1726,28492,1728],{},[2133,28494,2328],{},[902,28496,28497],{"encoding":904},"g(Q_1, Q_2) = Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",". Použijeme ",[207,28500,28502],{"className":28501,"dataFsResolvedFilePath":791,"href":792},[210],"metodu Lagrangeových multiplikátorů",[198,28504,28506],{"id":28505},"lagrangeova-funkce-a-podmínky-optimality","Lagrangeova funkce a podmínky optimality",[724,28508,28509],{},"Sestavíme",[883,28511,28513],{"className":28512},[886],[888,28514,28515],{"xmlns":890,"display":28047},[892,28516,28517,28629],{},[20735,28518,28519],{"width":28052},[20740,28520,28521,28523,28622,28624],{},[20743,28522],{"width":28057},[20743,28524,28525],{},[895,28526,28527,28530,28532,28538,28540,28546,28548,28550,28552,28554,28556,28558,28564,28566,28572,28574,28576,28578,28580,28586,28588,28596,28602,28604,28612,28618,28620],{},[898,28528,9779],{"mathvariant":28529},"script",[1726,28531,1735],{"stretchy":1734},[2275,28533,28534,28536],{},[898,28535,1724],{},[2133,28537,2281],{},[1726,28539,1742],{"separator":1741},[2275,28541,28542,28544],{},[898,28543,1724],{},[2133,28545,2135],{},[1726,28547,1742],{"separator":1741},[898,28549,16425],{},[1726,28551,1762],{"stretchy":1734},[1726,28553,1728],{},[898,28555,900],{},[1726,28557,1735],{"stretchy":1734},[2275,28559,28560,28562],{},[898,28561,1724],{},[2133,28563,2281],{},[1726,28565,1742],{"separator":1741},[2275,28567,28568,28570],{},[898,28569,1724],{},[2133,28571,2135],{},[1726,28573,1762],{"stretchy":1734},[1726,28575,2099],{},[898,28577,16425],{},[1726,28579,1735],{"stretchy":1734},[2128,28581,28582,28584],{},[898,28583,1745],{},[1726,28585,4342],{},[1726,28587,2228],{},[9151,28589,28590,28592,28594],{},[898,28591,1738],{},[2133,28593,2281],{},[1726,28595,4342],{},[2275,28597,28598,28600],{},[898,28599,1724],{},[2133,28601,2281],{},[1726,28603,2228],{},[9151,28605,28606,28608,28610],{},[898,28607,1738],{},[2133,28609,2135],{},[1726,28611,4342],{},[2275,28613,28614,28616],{},[898,28615,1724],{},[2133,28617,2135],{},[1726,28619,1762],{"stretchy":1734},[898,28621,1888],{"mathvariant":2377},[20743,28623],{"width":28057},[20743,28625,28626],{},[2289,28627,28628],{},"(6.13)",[902,28630,28631],{"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}",[724,28633,28634],{},"Soustava prvního řádu:",[883,28636,28638],{"className":28637},[886],[888,28639,28640],{"xmlns":890,"display":28047},[892,28641,28642,28825],{},[20735,28643,28644],{"width":28052},[20740,28645,28646,28648,28818,28820],{},[20743,28647],{"width":28057},[20743,28649,28650],{},[20735,28651,28652,28702,28752],{"rowspacing":20737,"columnalign":20738,"columnspacing":2378},[20740,28653,28654,28666],{},[20743,28655,28656],{},[2326,28657,28658],{"scriptlevel":2328,"displaystyle":1741},[9151,28659,28660,28662,28664],{},[898,28661,9779],{"mathvariant":28529},[2133,28663,2281],{},[1726,28665,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[20743,28667,28668],{},[2326,28669,28670],{"scriptlevel":2328,"displaystyle":1741},[895,28671,28672,28674,28676,28684,28686,28688,28696,28698,28700],{},[895,28673],{},[1726,28675,1728],{},[9151,28677,28678,28680,28682],{},[898,28679,900],{},[2133,28681,2281],{},[1726,28683,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,28685,2228],{},[898,28687,16425],{},[9151,28689,28690,28692,28694],{},[898,28691,1738],{},[2133,28693,2281],{},[1726,28695,4342],{},[1726,28697,1728],{},[2133,28699,2328],{},[1726,28701,1742],{"separator":1741},[20740,28703,28704,28716],{},[20743,28705,28706],{},[2326,28707,28708],{"scriptlevel":2328,"displaystyle":1741},[9151,28709,28710,28712,28714],{},[898,28711,9779],{"mathvariant":28529},[2133,28713,2135],{},[1726,28715,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[20743,28717,28718],{},[2326,28719,28720],{"scriptlevel":2328,"displaystyle":1741},[895,28721,28722,28724,28726,28734,28736,28738,28746,28748,28750],{},[895,28723],{},[1726,28725,1728],{},[9151,28727,28728,28730,28732],{},[898,28729,900],{},[2133,28731,2135],{},[1726,28733,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,28735,2228],{},[898,28737,16425],{},[9151,28739,28740,28742,28744],{},[898,28741,1738],{},[2133,28743,2135],{},[1726,28745,4342],{},[1726,28747,1728],{},[2133,28749,2328],{},[1726,28751,1742],{"separator":1741},[20740,28753,28754,28766],{},[20743,28755,28756],{},[2326,28757,28758],{"scriptlevel":2328,"displaystyle":1741},[9151,28759,28760,28762,28764],{},[898,28761,9779],{"mathvariant":28529},[898,28763,16425],{},[1726,28765,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[20743,28767,28768],{},[2326,28769,28770],{"scriptlevel":2328,"displaystyle":1741},[895,28771,28772,28774,28776,28782,28784,28792,28798,28800,28808,28814,28816],{},[895,28773],{},[1726,28775,1728],{},[2128,28777,28778,28780],{},[898,28779,1745],{},[1726,28781,4342],{},[1726,28783,2228],{},[9151,28785,28786,28788,28790],{},[898,28787,1738],{},[2133,28789,2281],{},[1726,28791,4342],{},[2275,28793,28794,28796],{},[898,28795,1724],{},[2133,28797,2281],{},[1726,28799,2228],{},[9151,28801,28802,28804,28806],{},[898,28803,1738],{},[2133,28805,2135],{},[1726,28807,4342],{},[2275,28809,28810,28812],{},[898,28811,1724],{},[2133,28813,2135],{},[1726,28815,1728],{},[2133,28817,12446],{},[20743,28819],{"width":28057},[20743,28821,28822],{},[2289,28823,28824],{},"(6.14)",[902,28826,28827],{"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}",[724,28829,28830,28831,28834,28835,28848,28849,2703],{},"Díky konvexitě indiferenčních křivek je řešení ",[38,28832,28833],{},"vázaným maximem",". Z prvních dvou rovnic po vyloučení ",[883,28836,28838],{"className":28837},[886],[888,28839,28840],{"xmlns":890},[892,28841,28842,28846],{},[895,28843,28844],{},[898,28845,16425],{},[902,28847,16478],{"encoding":904}," dostáváme ",[38,28850,28851],{},"podmínku optimality",[883,28853,28855],{"className":28854},[886],[888,28856,28857],{"xmlns":890,"display":28047},[892,28858,28859,28917],{},[895,28860,28861],{},[12818,28862,28863],{"notation":12820},[2326,28864,28865],{"scriptlevel":2328,"displaystyle":1734},[2326,28866,28867],{"scriptlevel":2328,"displaystyle":1734},[2326,28868,28869],{"scriptlevel":2328,"displaystyle":1741},[895,28870,28871,28873,28875,28877,28895,28897,28915],{},[2289,28872,3974],{},[2289,28874,10587],{},[1726,28876,1728],{},[2330,28878,28879,28887],{},[9151,28880,28881,28883,28885],{},[898,28882,900],{},[2133,28884,2281],{},[1726,28886,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[9151,28888,28889,28891,28893],{},[898,28890,900],{},[2133,28892,2135],{},[1726,28894,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,28896,1728],{},[2330,28898,28899,28907],{},[9151,28900,28901,28903,28905],{},[898,28902,1738],{},[2133,28904,2281],{},[1726,28906,4342],{},[9151,28908,28909,28911,28913],{},[898,28910,1738],{},[2133,28912,2135],{},[1726,28914,4342],{},[2289,28916,3974],{},[902,28918,28919],{"encoding":904},"\\boxed{\\; \\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*} \\;}",[3859,28921,28922],{},[724,28923,28924,28926,28927,28961,28962,28965,28966,28984,28985,29003,29004,29034,29035,29052,29053,29083],{},[883,28925,4145],{}," Intuice — mezní poměr užitečnosti = mezní poměr cen\nPodmínka ",[883,28928,28930],{"className":28929},[886],[888,28931,28932],{"xmlns":890},[892,28933,28934,28958],{},[895,28935,28936,28938,28940,28948,28950],{},[2289,28937,10587],{},[1726,28939,1728],{},[9151,28941,28942,28944,28946],{},[898,28943,1738],{},[2133,28945,2281],{},[1726,28947,4342],{},[898,28949,4661],{"mathvariant":2377},[9151,28951,28952,28954,28956],{},[898,28953,1738],{},[2133,28955,2135],{},[1726,28957,4342],{},[902,28959,28960],{"encoding":904},"\\text{MRCS} = P_1^*\u002FP_2^*"," říká, že v optimu je ",[38,28963,28964],{},"sklon indiferenční křivky roven sklonu rozpočtové přímky",". Ekonomicky: spotřebitel je ochoten vyměnit ",[883,28967,28969],{"className":28968},[886],[888,28970,28971],{"xmlns":890},[892,28972,28973,28981],{},[895,28974,28975],{},[2275,28976,28977,28979],{},[898,28978,1724],{},[2133,28980,2281],{},[902,28982,28983],{"encoding":904},"Q_1"," za ",[883,28986,28988],{"className":28987},[886],[888,28989,28990],{"xmlns":890},[892,28991,28992,29000],{},[895,28993,28994],{},[2275,28995,28996,28998],{},[898,28997,1724],{},[2133,28999,2135],{},[902,29001,29002],{"encoding":904},"Q_2"," v přesně tom poměru, v jakém je trh (ceny) umožňuje vyměňovat. Kdyby ",[883,29005,29007],{"className":29006},[886],[888,29008,29009],{"xmlns":890},[892,29010,29011,29031],{},[895,29012,29013,29015,29017,29023,29025],{},[2289,29014,10587],{},[1726,29016,3405],{},[2275,29018,29019,29021],{},[898,29020,1738],{},[2133,29022,2281],{},[898,29024,4661],{"mathvariant":2377},[2275,29026,29027,29029],{},[898,29028,1738],{},[2133,29030,2135],{},[902,29032,29033],{"encoding":904},"\\text{MRCS} > P_1\u002FP_2",", vyplatilo by se nakupovat více ",[883,29036,29038],{"className":29037},[886],[888,29039,29040],{"xmlns":890},[892,29041,29042,29050],{},[895,29043,29044],{},[2275,29045,29046,29048],{},[898,29047,1724],{},[2133,29049,2281],{},[902,29051,28983],{"encoding":904}," (subjektivní ocenění převažuje nad tržním); kdyby ",[883,29054,29056],{"className":29055},[886],[888,29057,29058],{"xmlns":890},[892,29059,29060,29080],{},[895,29061,29062,29064,29066,29072,29074],{},[2289,29063,10587],{},[1726,29065,3444],{},[2275,29067,29068,29070],{},[898,29069,1738],{},[2133,29071,2281],{},[898,29073,4661],{"mathvariant":2377},[2275,29075,29076,29078],{},[898,29077,1738],{},[2133,29079,2135],{},[902,29081,29082],{"encoding":904},"\\text{MRCS} \u003C P_1\u002FP_2",", vyplatil by se opak.",[198,29085,29087,29088,29101],{"id":29086},"interpretace-λlambda-mezní-užitečnost-důchodu","Interpretace ",[883,29089,29091],{"className":29090},[886],[888,29092,29093],{"xmlns":890},[892,29094,29095,29099],{},[895,29096,29097],{},[898,29098,16425],{},[902,29100,16478],{"encoding":904}," — mezní užitečnost důchodu",[724,29103,29104,29105,29123,29124,29127,29128,29145,29146,29163,29164,29167],{},"Lagrangeův multiplikátor ",[883,29106,29108],{"className":29107},[886],[888,29109,29110],{"xmlns":890},[892,29111,29112,29120],{},[895,29113,29114],{},[2128,29115,29116,29118],{},[898,29117,16425],{},[1726,29119,4342],{},[902,29121,29122],{"encoding":904},"\\lambda^*"," představuje ",[38,29125,29126],{},"mezní užitečnost důchodu"," — přibližnou změnu maximální užitečnosti ",[883,29129,29131],{"className":29130},[886],[888,29132,29133],{"xmlns":890},[892,29134,29135,29143],{},[895,29136,29137],{},[2128,29138,29139,29141],{},[898,29140,900],{},[1726,29142,4342],{},[902,29144,27943],{"encoding":904}," při jednotkové změně důchodu ",[883,29147,29149],{"className":29148},[886],[888,29150,29151],{"xmlns":890},[892,29152,29153,29161],{},[895,29154,29155],{},[2128,29156,29157,29159],{},[898,29158,1745],{},[1726,29160,4342],{},[902,29162,28009],{"encoding":904},". Je to ",[38,29165,29166],{},"stínová cena"," rozpočtového omezení.",[3859,29169,29170,29175],{},[724,29171,29172,29174],{},[883,29173,4560],{}," Postup — maximalizace užitečnosti Lagrangeovou metodou",[152,29176,29177,29237,29324,29360,29447],{},[123,29178,29179,29182,29183,1888],{},[38,29180,29181],{},"Zapiš rozpočtové omezení"," ve tvaru ",[883,29184,29186],{"className":29185},[886],[888,29187,29188],{"xmlns":890},[892,29189,29190,29234],{},[895,29191,29192,29198,29200,29208,29214,29216,29224,29230,29232],{},[2128,29193,29194,29196],{},[898,29195,1745],{},[1726,29197,4342],{},[1726,29199,2228],{},[9151,29201,29202,29204,29206],{},[898,29203,1738],{},[2133,29205,2281],{},[1726,29207,4342],{},[2275,29209,29210,29212],{},[898,29211,1724],{},[2133,29213,2281],{},[1726,29215,2228],{},[9151,29217,29218,29220,29222],{},[898,29219,1738],{},[2133,29221,2135],{},[1726,29223,4342],{},[2275,29225,29226,29228],{},[898,29227,1724],{},[2133,29229,2135],{},[1726,29231,1728],{},[2133,29233,2328],{},[902,29235,29236],{"encoding":904},"Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",[123,29238,29239,1777,29242,1888],{},[38,29240,29241],{},"Sestav Lagrangeovu funkci",[883,29243,29245],{"className":29244},[886],[888,29246,29247],{"xmlns":890},[892,29248,29249,29321],{},[895,29250,29251,29253,29255,29257,29259,29265,29267,29273,29275,29277,29279,29281,29287,29289,29297,29303,29305,29313,29319],{},[898,29252,9779],{"mathvariant":28529},[1726,29254,1728],{},[898,29256,900],{},[1726,29258,1735],{"stretchy":1734},[2275,29260,29261,29263],{},[898,29262,1724],{},[2133,29264,2281],{},[1726,29266,1742],{"separator":1741},[2275,29268,29269,29271],{},[898,29270,1724],{},[2133,29272,2135],{},[1726,29274,1762],{"stretchy":1734},[1726,29276,2099],{},[898,29278,16425],{},[1726,29280,1735],{"stretchy":1734},[2128,29282,29283,29285],{},[898,29284,1745],{},[1726,29286,4342],{},[1726,29288,2228],{},[9151,29290,29291,29293,29295],{},[898,29292,1738],{},[2133,29294,2281],{},[1726,29296,4342],{},[2275,29298,29299,29301],{},[898,29300,1724],{},[2133,29302,2281],{},[1726,29304,2228],{},[9151,29306,29307,29309,29311],{},[898,29308,1738],{},[2133,29310,2135],{},[1726,29312,4342],{},[2275,29314,29315,29317],{},[898,29316,1724],{},[2133,29318,2135],{},[1726,29320,1762],{"stretchy":1734},[902,29322,29323],{"encoding":904},"\\mathcal{L} = U(Q_1, Q_2) + \\lambda(Y^* - P_1^* Q_1 - P_2^* Q_2)",[123,29325,29326,10452,29329,29359],{},[38,29327,29328],{},"Spočítej parciální derivace",[883,29330,29332],{"className":29331},[886],[888,29333,29334],{"xmlns":890},[892,29335,29336,29356],{},[895,29337,29338,29344,29346,29352,29354],{},[2275,29339,29340,29342],{},[898,29341,1724],{},[2133,29343,2281],{},[1726,29345,1742],{"separator":1741},[2275,29347,29348,29350],{},[898,29349,1724],{},[2133,29351,2135],{},[1726,29353,1742],{"separator":1741},[898,29355,16425],{},[902,29357,29358],{"encoding":904},"Q_1, Q_2, \\lambda"," a polož je rovny nule.",[123,29361,29362,29378,29379,29412,29413,3877,29430,1888],{},[38,29363,29364,29365],{},"Vyluč ",[883,29366,29368],{"className":29367},[886],[888,29369,29370],{"xmlns":890},[892,29371,29372,29376],{},[895,29373,29374],{},[898,29375,16425],{},[902,29377,16478],{"encoding":904}," dělením prvních dvou rovnic — dostaneš podmínku ",[883,29380,29382],{"className":29381},[886],[888,29383,29384],{"xmlns":890},[892,29385,29386,29410],{},[895,29387,29388,29390,29392,29400,29402],{},[2289,29389,10587],{},[1726,29391,1728],{},[9151,29393,29394,29396,29398],{},[898,29395,1738],{},[2133,29397,2281],{},[1726,29399,4342],{},[898,29401,4661],{"mathvariant":2377},[9151,29403,29404,29406,29408],{},[898,29405,1738],{},[2133,29407,2135],{},[1726,29409,4342],{},[902,29411,28960],{"encoding":904},", která dá vztah mezi ",[883,29414,29416],{"className":29415},[886],[888,29417,29418],{"xmlns":890},[892,29419,29420,29428],{},[895,29421,29422],{},[2275,29423,29424,29426],{},[898,29425,1724],{},[2133,29427,2281],{},[902,29429,28983],{"encoding":904},[883,29431,29433],{"className":29432},[886],[888,29434,29435],{"xmlns":890},[892,29436,29437,29445],{},[895,29438,29439],{},[2275,29440,29441,29443],{},[898,29442,1724],{},[2133,29444,2135],{},[902,29446,29002],{"encoding":904},[123,29448,29449,29452,29453,29483,29484,29501,29502,1888],{},[38,29450,29451],{},"Dosaď do rozpočtového omezení"," a vypočítej ",[883,29454,29456],{"className":29455},[886],[888,29457,29458],{"xmlns":890},[892,29459,29460,29480],{},[895,29461,29462,29470,29472],{},[9151,29463,29464,29466,29468],{},[898,29465,1724],{},[2133,29467,2281],{},[1726,29469,4342],{},[1726,29471,1742],{"separator":1741},[9151,29473,29474,29476,29478],{},[898,29475,1724],{},[2133,29477,2135],{},[1726,29479,4342],{},[902,29481,29482],{"encoding":904},"Q_1^*, Q_2^*",", případně ",[883,29485,29487],{"className":29486},[886],[888,29488,29489],{"xmlns":890},[892,29490,29491,29499],{},[895,29492,29493],{},[2128,29494,29495,29497],{},[898,29496,16425],{},[1726,29498,4342],{},[902,29500,29122],{"encoding":904}," a maximální užitečnost ",[883,29503,29505],{"className":29504},[886],[888,29506,29507],{"xmlns":890},[892,29508,29509,29543],{},[895,29510,29511,29517,29519,29521,29523,29531,29533,29541],{},[2128,29512,29513,29515],{},[898,29514,900],{},[1726,29516,4342],{},[1726,29518,1728],{},[898,29520,900],{},[1726,29522,1735],{"stretchy":1734},[9151,29524,29525,29527,29529],{},[898,29526,1724],{},[2133,29528,2281],{},[1726,29530,4342],{},[1726,29532,1742],{"separator":1741},[9151,29534,29535,29537,29539],{},[898,29536,1724],{},[2133,29538,2135],{},[1726,29540,4342],{},[1726,29542,1762],{"stretchy":1734},[902,29544,29545],{"encoding":904},"U^* = U(Q_1^*, Q_2^*)",[115,29547,29549],{"id":29548},"geometrie-optima-tečnost-ic-a-rozpočtové-přímky","Geometrie optima — tečnost IC a rozpočtové přímky",[724,29551,29552],{},[1647,29553],{"alt":29554,"className":29555,"src":29556},"imek-uzitecnost-optimum",[210,1651],"\u002Fwiki-assets\u002Fimek-uzitecnost-optimum.jpeg",[724,29558,29559],{},[614,29560,29561,29562,29611,29612,3877,29640,29668,29669,29703,29704,29743,29744,29762,29763,29781,29782,29800],{},"Obrázek 6.7 — Rozpočtová přímka ",[883,29563,29565],{"className":29564},[886],[888,29566,29567],{"xmlns":890},[892,29568,29569,29609],{},[895,29570,29571,29577,29579,29587,29593,29595,29603],{},[2128,29572,29573,29575],{},[898,29574,1745],{},[1726,29576,4342],{},[1726,29578,1728],{},[9151,29580,29581,29583,29585],{},[898,29582,1738],{},[2133,29584,2281],{},[1726,29586,4342],{},[2275,29588,29589,29591],{},[898,29590,1724],{},[2133,29592,2281],{},[1726,29594,2099],{},[9151,29596,29597,29599,29601],{},[898,29598,1738],{},[2133,29600,2135],{},[1726,29602,4342],{},[2275,29604,29605,29607],{},[898,29606,1724],{},[2133,29608,2135],{},[902,29610,17280],{"encoding":904}," protíná osy v ",[883,29613,29615],{"className":29614},[886],[888,29616,29617],{"xmlns":890},[892,29618,29619,29637],{},[895,29620,29621,29627,29629],{},[2128,29622,29623,29625],{},[898,29624,1745],{},[1726,29626,4342],{},[898,29628,4661],{"mathvariant":2377},[9151,29630,29631,29633,29635],{},[898,29632,1738],{},[2133,29634,2281],{},[1726,29636,4342],{},[902,29638,29639],{"encoding":904},"Y^*\u002FP_1^*",[883,29641,29643],{"className":29642},[886],[888,29644,29645],{"xmlns":890},[892,29646,29647,29665],{},[895,29648,29649,29655,29657],{},[2128,29650,29651,29653],{},[898,29652,1745],{},[1726,29654,4342],{},[898,29656,4661],{"mathvariant":2377},[9151,29658,29659,29661,29663],{},[898,29660,1738],{},[2133,29662,2135],{},[1726,29664,4342],{},[902,29666,29667],{"encoding":904},"Y^*\u002FP_2^*",". Tři indiferenční křivky ",[883,29670,29672],{"className":29671},[886],[888,29673,29674],{"xmlns":890},[892,29675,29676,29700],{},[895,29677,29678,29684,29686,29692,29694],{},[2275,29679,29680,29682],{},[898,29681,2146],{},[2133,29683,2281],{},[1726,29685,3444],{},[2128,29687,29688,29690],{},[898,29689,2146],{},[1726,29691,4342],{},[1726,29693,3444],{},[2275,29695,29696,29698],{},[898,29697,2146],{},[2133,29699,2135],{},[902,29701,29702],{"encoding":904},"c_1 \u003C c^* \u003C c_2",". Optimum ",[883,29705,29707],{"className":29706},[886],[888,29708,29709],{"xmlns":890},[892,29710,29711,29741],{},[895,29712,29713,29719,29721,29729,29731,29739],{},[2128,29714,29715,29717],{},[898,29716,1724],{},[1726,29718,4342],{},[1726,29720,2487],{"stretchy":1734},[9151,29722,29723,29725,29727],{},[898,29724,1724],{},[2133,29726,2281],{},[1726,29728,4342],{},[1726,29730,1742],{"separator":1741},[9151,29732,29733,29735,29737],{},[898,29734,1724],{},[2133,29736,2135],{},[1726,29738,4342],{},[1726,29740,2502],{"stretchy":1734},[902,29742,28308],{"encoding":904}," je bod dotyku rozpočtové přímky s křivkou ",[883,29745,29747],{"className":29746},[886],[888,29748,29749],{"xmlns":890},[892,29750,29751,29759],{},[895,29752,29753],{},[2128,29754,29755,29757],{},[898,29756,2146],{},[1726,29758,4342],{},[902,29760,29761],{"encoding":904},"c^*",". Křivka ",[883,29764,29766],{"className":29765},[886],[888,29767,29768],{"xmlns":890},[892,29769,29770,29778],{},[895,29771,29772],{},[2275,29773,29774,29776],{},[898,29775,2146],{},[2133,29777,2281],{},[902,29779,29780],{"encoding":904},"c_1"," je dosažitelná, ale nemaximalizuje užitečnost; křivka ",[883,29783,29785],{"className":29784},[886],[888,29786,29787],{"xmlns":890},[892,29788,29789,29797],{},[895,29790,29791],{},[2275,29792,29793,29795],{},[898,29794,2146],{},[2133,29796,2135],{},[902,29798,29799],{"encoding":904},"c_2"," není při daném důchodu dosažitelná.",[724,29802,29803,29804,29807,29808,29826,29827,29856],{},"Geometrie je jádrem intuice: přímka (rozpočet) a křivka (užitečnost) se v optimu ",[38,29805,29806],{},"dotýkají",", tj. mají v bodě ",[883,29809,29811],{"className":29810},[886],[888,29812,29813],{"xmlns":890},[892,29814,29815,29823],{},[895,29816,29817],{},[2128,29818,29819,29821],{},[898,29820,1724],{},[1726,29822,4342],{},[902,29824,29825],{"encoding":904},"Q^*"," společnou tečnu. To přímo převádí podmínku ",[883,29828,29830],{"className":29829},[886],[888,29831,29832],{"xmlns":890},[892,29833,29834,29854],{},[895,29835,29836,29838,29840,29846,29848],{},[2289,29837,10587],{},[1726,29839,1728],{},[2275,29841,29842,29844],{},[898,29843,1738],{},[2133,29845,2281],{},[898,29847,4661],{"mathvariant":2377},[2275,29849,29850,29852],{},[898,29851,1738],{},[2133,29853,2135],{},[902,29855,27979],{"encoding":904}," — poměr mezních užitečností (sklon IC) = poměr cen (sklon přímky).",[115,29858,29860],{"id":29859},"příklad-65-mrcs-pro-cobb-douglasovu-užitečnost","Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost",[724,29862,9647,29863,29925],{},[883,29864,29866],{"className":29865},[886],[888,29867,29868],{"xmlns":890},[892,29869,29870,29922],{},[895,29871,29872,29874,29876,29882,29884,29890,29892,29894,29908],{},[898,29873,900],{},[1726,29875,1735],{"stretchy":1734},[2275,29877,29878,29880],{},[898,29879,1724],{},[2133,29881,2281],{},[1726,29883,1742],{"separator":1741},[2275,29885,29886,29888],{},[898,29887,1724],{},[2133,29889,2135],{},[1726,29891,1762],{"stretchy":1734},[1726,29893,1728],{},[9151,29895,29896,29898,29900],{},[898,29897,1724],{},[2133,29899,2281],{},[895,29901,29902,29904,29906],{},[2133,29903,2281],{},[898,29905,4661],{"mathvariant":2377},[2133,29907,2135],{},[9151,29909,29910,29912,29914],{},[898,29911,1724],{},[2133,29913,2135],{},[895,29915,29916,29918,29920],{},[2133,29917,2281],{},[898,29919,4661],{"mathvariant":2377},[2133,29921,2135],{},[902,29923,29924],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F2} Q_2^{1\u002F2}"," platí",[724,29927,29928],{},[883,29929,29931],{"className":29930},[886],[888,29932,29933],{"xmlns":890},[892,29934,29935,30041],{},[895,29936,29937,29939,29941,30023,30025,30039],{},[2289,29938,10587],{},[1726,29940,1728],{},[2330,29942,29943,29983],{},[895,29944,29945,29953,29969],{},[2326,29946,29947],{"scriptlevel":2328,"displaystyle":1734},[2330,29948,29949,29951],{},[2133,29950,2281],{},[2133,29952,2135],{},[9151,29954,29955,29957,29959],{},[898,29956,1724],{},[2133,29958,2281],{},[895,29960,29961,29963,29965,29967],{},[1726,29962,2228],{},[2133,29964,2281],{},[898,29966,4661],{"mathvariant":2377},[2133,29968,2135],{},[9151,29970,29971,29973,29975],{},[898,29972,1724],{},[2133,29974,2135],{},[895,29976,29977,29979,29981],{},[2133,29978,2281],{},[898,29980,4661],{"mathvariant":2377},[2133,29982,2135],{},[895,29984,29985,29993,30007],{},[2326,29986,29987],{"scriptlevel":2328,"displaystyle":1734},[2330,29988,29989,29991],{},[2133,29990,2281],{},[2133,29992,2135],{},[9151,29994,29995,29997,29999],{},[898,29996,1724],{},[2133,29998,2281],{},[895,30000,30001,30003,30005],{},[2133,30002,2281],{},[898,30004,4661],{"mathvariant":2377},[2133,30006,2135],{},[9151,30008,30009,30011,30013],{},[898,30010,1724],{},[2133,30012,2135],{},[895,30014,30015,30017,30019,30021],{},[1726,30016,2228],{},[2133,30018,2281],{},[898,30020,4661],{"mathvariant":2377},[2133,30022,2135],{},[1726,30024,1728],{},[2330,30026,30027,30033],{},[2275,30028,30029,30031],{},[898,30030,1724],{},[2133,30032,2135],{},[2275,30034,30035,30037],{},[898,30036,1724],{},[2133,30038,2281],{},[898,30040,1888],{"mathvariant":2377},[902,30042,30043],{"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}.",[724,30045,30046,30047,2924,30092,30094,30095,30115,30116,30146,30147,1888],{},"Tedy ",[883,30048,30050],{"className":30049},[886],[888,30051,30052],{"xmlns":890},[892,30053,30054,30089],{},[895,30055,30056,30058,30060,30063,30065,30067,30069,30071,30079,30081],{},[2289,30057,10587],{},[1726,30059,1735],{"stretchy":1734},[2133,30061,30062],{},"300",[1726,30064,1742],{"separator":1741},[2133,30066,15096],{},[1726,30068,1762],{"stretchy":1734},[1726,30070,1728],{},[2326,30072,30073],{"scriptlevel":2328,"displaystyle":1734},[2330,30074,30075,30077],{},[2133,30076,15096],{},[2133,30078,30062],{},[1726,30080,1728],{},[2326,30082,30083],{"scriptlevel":2328,"displaystyle":1734},[2330,30084,30085,30087],{},[2133,30086,2231],{},[2133,30088,2177],{},[902,30090,30091],{"encoding":904},"\\text{MRCS}(300, 500) = \\tfrac{500}{300} = \\tfrac{5}{3}",[614,30093,9201],{}," zvýší-li spotřebitel nákup prvního zboží o 1 jednotku, musí snížit nákup druhého zboží přibližně o ",[883,30096,30098],{"className":30097},[886],[888,30099,30100],{"xmlns":890},[892,30101,30102,30112],{},[895,30103,30104],{},[2326,30105,30106],{"scriptlevel":2328,"displaystyle":1734},[2330,30107,30108,30110],{},[2133,30109,2231],{},[2133,30111,2177],{},[902,30113,30114],{"encoding":904},"\\tfrac{5}{3}"," jednotky, aby se užitečnost zachovala. Tato forma ",[883,30117,30119],{"className":30118},[886],[888,30120,30121],{"xmlns":890},[892,30122,30123,30143],{},[895,30124,30125,30127,30129,30135,30137],{},[2289,30126,10587],{},[1726,30128,1728],{},[2275,30130,30131,30133],{},[898,30132,1724],{},[2133,30134,2135],{},[898,30136,4661],{"mathvariant":2377},[2275,30138,30139,30141],{},[898,30140,1724],{},[2133,30142,2281],{},[902,30144,30145],{"encoding":904},"\\text{MRCS} = Q_2\u002FQ_1"," je typická pro symetrické Cobb-Douglasovy preference a vstupuje do optimalizace skrze podmínku ",[883,30148,30150],{"className":30149},[886],[888,30151,30152],{"xmlns":890},[892,30153,30154,30174],{},[895,30155,30156,30158,30160,30166,30168],{},[2289,30157,10587],{},[1726,30159,1728],{},[2275,30161,30162,30164],{},[898,30163,1738],{},[2133,30165,2281],{},[898,30167,4661],{"mathvariant":2377},[2275,30169,30170,30172],{},[898,30171,1738],{},[2133,30173,2135],{},[902,30175,27979],{"encoding":904},[115,30177,30179,30180],{"id":30178},"příklad-66-maximalizace-užitečnosti-pro-uq1q2u-q_1-q_2","Příklad 6.6 — maximalizace užitečnosti pro ",[883,30181,30183],{"className":30182},[886],[888,30184,30185],{"xmlns":890},[892,30186,30187,30205],{},[895,30188,30189,30191,30193,30199],{},[898,30190,900],{},[1726,30192,1728],{},[2275,30194,30195,30197],{},[898,30196,1724],{},[2133,30198,2281],{},[2275,30200,30201,30203],{},[898,30202,1724],{},[2133,30204,2135],{},[902,30206,30207],{"encoding":904},"U = Q_1 Q_2",[724,30209,30210,30211,1343,30257,1343,30281,1343,30305,30327],{},"Je dána ",[883,30212,30214],{"className":30213},[886],[888,30215,30216],{"xmlns":890},[892,30217,30218,30254],{},[895,30219,30220,30222,30224,30230,30232,30238,30240,30242,30248],{},[898,30221,900],{},[1726,30223,1735],{"stretchy":1734},[2275,30225,30226,30228],{},[898,30227,1724],{},[2133,30229,2281],{},[1726,30231,1742],{"separator":1741},[2275,30233,30234,30236],{},[898,30235,1724],{},[2133,30237,2135],{},[1726,30239,1762],{"stretchy":1734},[1726,30241,1728],{},[2275,30243,30244,30246],{},[898,30245,1724],{},[2133,30247,2281],{},[2275,30249,30250,30252],{},[898,30251,1724],{},[2133,30253,2135],{},[902,30255,30256],{"encoding":904},"U(Q_1, Q_2) = Q_1 Q_2",[883,30258,30260],{"className":30259},[886],[888,30261,30262],{"xmlns":890},[892,30263,30264,30278],{},[895,30265,30266,30274,30276],{},[9151,30267,30268,30270,30272],{},[898,30269,1738],{},[2133,30271,2281],{},[1726,30273,4342],{},[1726,30275,1728],{},[2133,30277,2135],{},[902,30279,30280],{"encoding":904},"P_1^* = 2",[883,30282,30284],{"className":30283},[886],[888,30285,30286],{"xmlns":890},[892,30287,30288,30302],{},[895,30289,30290,30298,30300],{},[9151,30291,30292,30294,30296],{},[898,30293,1738],{},[2133,30295,2135],{},[1726,30297,4342],{},[1726,30299,1728],{},[2133,30301,2231],{},[902,30303,30304],{"encoding":904},"P_2^* = 5",[883,30306,30308],{"className":30307},[886],[888,30309,30310],{"xmlns":890},[892,30311,30312,30324],{},[895,30313,30314,30320,30322],{},[2128,30315,30316,30318],{},[898,30317,1745],{},[1726,30319,4342],{},[1726,30321,1728],{},[2133,30323,3087],{},[902,30325,30326],{"encoding":904},"Y^* = 100",". Lagrangeova funkce:",[883,30329,30331],{"className":30330},[886],[888,30332,30333],{"xmlns":890,"display":28047},[892,30334,30335,30407],{},[895,30336,30337,30339,30341,30347,30349,30355,30357,30359,30361,30363,30369,30375,30377,30379,30381,30383,30385,30387,30393,30395,30397,30403,30405],{},[898,30338,9779],{"mathvariant":28529},[1726,30340,1735],{"stretchy":1734},[2275,30342,30343,30345],{},[898,30344,1724],{},[2133,30346,2281],{},[1726,30348,1742],{"separator":1741},[2275,30350,30351,30353],{},[898,30352,1724],{},[2133,30354,2135],{},[1726,30356,1742],{"separator":1741},[898,30358,16425],{},[1726,30360,1762],{"stretchy":1734},[1726,30362,1728],{},[2275,30364,30365,30367],{},[898,30366,1724],{},[2133,30368,2281],{},[2275,30370,30371,30373],{},[898,30372,1724],{},[2133,30374,2135],{},[1726,30376,2099],{},[898,30378,16425],{},[1726,30380,1735],{"stretchy":1734},[2133,30382,3087],{},[1726,30384,2228],{},[2133,30386,2135],{},[2275,30388,30389,30391],{},[898,30390,1724],{},[2133,30392,2281],{},[1726,30394,2228],{},[2133,30396,2231],{},[2275,30398,30399,30401],{},[898,30400,1724],{},[2133,30402,2135],{},[1726,30404,1762],{"stretchy":1734},[898,30406,1888],{"mathvariant":2377},[902,30408,30409],{"encoding":904},"\\mathcal{L}(Q_1, Q_2, \\lambda) = Q_1 Q_2 + \\lambda(100 - 2 Q_1 - 5 Q_2).",[724,30411,30412],{},"Soustava:",[883,30414,30416],{"className":30415},[886],[888,30417,30418],{"xmlns":890,"display":28047},[892,30419,30420,30532],{},[20735,30421,30422,30456,30490],{"rowspacing":20737,"columnalign":20738,"columnspacing":2378},[20740,30423,30424,30442],{},[20743,30425,30426],{},[2326,30427,30428],{"scriptlevel":2328,"displaystyle":1741},[895,30429,30430,30436,30438,30440],{},[2275,30431,30432,30434],{},[898,30433,1724],{},[2133,30435,2135],{},[1726,30437,2228],{},[2133,30439,2135],{},[898,30441,16425],{},[20743,30443,30444],{},[2326,30445,30446],{"scriptlevel":2328,"displaystyle":1741},[895,30447,30448,30450,30452,30454],{},[895,30449],{},[1726,30451,1728],{},[2133,30453,2328],{},[1726,30455,1742],{"separator":1741},[20740,30457,30458,30476],{},[20743,30459,30460],{},[2326,30461,30462],{"scriptlevel":2328,"displaystyle":1741},[895,30463,30464,30470,30472,30474],{},[2275,30465,30466,30468],{},[898,30467,1724],{},[2133,30469,2281],{},[1726,30471,2228],{},[2133,30473,2231],{},[898,30475,16425],{},[20743,30477,30478],{},[2326,30479,30480],{"scriptlevel":2328,"displaystyle":1741},[895,30481,30482,30484,30486,30488],{},[895,30483],{},[1726,30485,1728],{},[2133,30487,2328],{},[1726,30489,1742],{"separator":1741},[20740,30491,30492,30520],{},[20743,30493,30494],{},[2326,30495,30496],{"scriptlevel":2328,"displaystyle":1741},[895,30497,30498,30500,30502,30504,30510,30512,30514],{},[2133,30499,3087],{},[1726,30501,2228],{},[2133,30503,2135],{},[2275,30505,30506,30508],{},[898,30507,1724],{},[2133,30509,2281],{},[1726,30511,2228],{},[2133,30513,2231],{},[2275,30515,30516,30518],{},[898,30517,1724],{},[2133,30519,2135],{},[20743,30521,30522],{},[2326,30523,30524],{"scriptlevel":2328,"displaystyle":1741},[895,30525,30526,30528,30530],{},[895,30527],{},[1726,30529,1728],{},[2133,30531,12446],{},[902,30533,30534],{"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}",[724,30536,30537,30538,1343,30562,30586,30587,5576,30627,30645,30646,30696,30697,1888],{},"Z prvních dvou rovnic ",[883,30539,30541],{"className":30540},[886],[888,30542,30543],{"xmlns":890},[892,30544,30545,30559],{},[895,30546,30547,30553,30555,30557],{},[2275,30548,30549,30551],{},[898,30550,1724],{},[2133,30552,2135],{},[1726,30554,1728],{},[2133,30556,2135],{},[898,30558,16425],{},[902,30560,30561],{"encoding":904},"Q_2 = 2\\lambda",[883,30563,30565],{"className":30564},[886],[888,30566,30567],{"xmlns":890},[892,30568,30569,30583],{},[895,30570,30571,30577,30579,30581],{},[2275,30572,30573,30575],{},[898,30574,1724],{},[2133,30576,2281],{},[1726,30578,1728],{},[2133,30580,2231],{},[898,30582,16425],{},[902,30584,30585],{"encoding":904},"Q_1 = 5\\lambda","; dosazením do třetí ",[883,30588,30590],{"className":30589},[886],[888,30591,30592],{"xmlns":890},[892,30593,30594,30624],{},[895,30595,30596,30598,30600,30602,30604,30606,30608,30610,30612,30614,30616,30618,30620,30622],{},[2133,30597,3087],{},[1726,30599,1728],{},[2133,30601,2135],{},[1726,30603,3174],{},[2133,30605,2231],{},[898,30607,16425],{},[1726,30609,2099],{},[2133,30611,2231],{},[1726,30613,3174],{},[2133,30615,2135],{},[898,30617,16425],{},[1726,30619,1728],{},[2133,30621,9021],{},[898,30623,16425],{},[902,30625,30626],{"encoding":904},"100 = 2 \\cdot 5\\lambda + 5 \\cdot 2\\lambda = 20\\lambda",[883,30628,30630],{"className":30629},[886],[888,30631,30632],{"xmlns":890},[892,30633,30634,30642],{},[895,30635,30636,30638,30640],{},[898,30637,16425],{},[1726,30639,1728],{},[2133,30641,2231],{},[902,30643,30644],{"encoding":904},"\\lambda = 5",". Odtud ",[38,30647,30648,1343,30672],{},[883,30649,30651],{"className":30650},[886],[888,30652,30653],{"xmlns":890},[892,30654,30655,30669],{},[895,30656,30657,30665,30667],{},[9151,30658,30659,30661,30663],{},[898,30660,1724],{},[2133,30662,2281],{},[1726,30664,4342],{},[1726,30666,1728],{},[2133,30668,4991],{},[902,30670,30671],{"encoding":904},"Q_1^* = 25",[883,30673,30675],{"className":30674},[886],[888,30676,30677],{"xmlns":890},[892,30678,30679,30693],{},[895,30680,30681,30689,30691],{},[9151,30682,30683,30685,30687],{},[898,30684,1724],{},[2133,30686,2135],{},[1726,30688,4342],{},[1726,30690,1728],{},[2133,30692,2860],{},[902,30694,30695],{"encoding":904},"Q_2^* = 10",", maximální užitečnost ",[883,30698,30700],{"className":30699},[886],[888,30701,30702],{"xmlns":890},[892,30703,30704,30725],{},[895,30705,30706,30712,30714,30716,30718,30720,30722],{},[2128,30707,30708,30710],{},[898,30709,900],{},[1726,30711,4342],{},[1726,30713,1728],{},[2133,30715,4991],{},[1726,30717,3174],{},[2133,30719,2860],{},[1726,30721,1728],{},[2133,30723,30724],{},"250",[902,30726,30727],{"encoding":904},"U^* = 25 \\cdot 10 = 250",[724,30729,30730],{},[614,30731,30732,30733,28118,30771,3877,30795,30819,30820,30850,30851,30875,30876,30898,30899,1888],{},"Obrázek 6.8 — Rozpočtová přímka ",[883,30734,30736],{"className":30735},[886],[888,30737,30738],{"xmlns":890},[892,30739,30740,30768],{},[895,30741,30742,30744,30746,30748,30754,30756,30758,30764,30766],{},[2133,30743,3087],{},[1726,30745,2228],{},[2133,30747,2135],{},[2275,30749,30750,30752],{},[898,30751,1724],{},[2133,30753,2281],{},[1726,30755,2228],{},[2133,30757,2231],{},[2275,30759,30760,30762],{},[898,30761,1724],{},[2133,30763,2135],{},[1726,30765,1728],{},[2133,30767,2328],{},[902,30769,30770],{"encoding":904},"100 - 2 Q_1 - 5 Q_2 = 0",[883,30772,30774],{"className":30773},[886],[888,30775,30776],{"xmlns":890},[892,30777,30778,30792],{},[895,30779,30780,30782,30784,30786,30788,30790],{},[898,30781,4243],{},[1726,30783,2487],{"stretchy":1734},[2133,30785,2328],{},[1726,30787,1742],{"separator":1741},[2133,30789,9021],{},[1726,30791,2502],{"stretchy":1734},[902,30793,30794],{"encoding":904},"A[0, 20]",[883,30796,30798],{"className":30797},[886],[888,30799,30800],{"xmlns":890},[892,30801,30802,30816],{},[895,30803,30804,30806,30808,30810,30812,30814],{},[898,30805,23234],{},[1726,30807,2487],{"stretchy":1734},[2133,30809,3117],{},[1726,30811,1742],{"separator":1741},[2133,30813,2328],{},[1726,30815,2502],{"stretchy":1734},[902,30817,30818],{"encoding":904},"B[50, 0]","; hyperbolická indiferenční křivka ",[883,30821,30823],{"className":30822},[886],[888,30824,30825],{"xmlns":890},[892,30826,30827,30847],{},[895,30828,30829,30835,30837,30839,30841],{},[2275,30830,30831,30833],{},[898,30832,1724],{},[2133,30834,2135],{},[1726,30836,1728],{},[2133,30838,30724],{},[898,30840,4661],{"mathvariant":2377},[2275,30842,30843,30845],{},[898,30844,1724],{},[2133,30846,2281],{},[902,30848,30849],{"encoding":904},"Q_2 = 250\u002FQ_1"," se dotýká rozpočtové přímky v bodě ",[883,30852,30854],{"className":30853},[886],[888,30855,30856],{"xmlns":890},[892,30857,30858,30872],{},[895,30859,30860,30862,30864,30866,30868,30870],{},[898,30861,4240],{},[1726,30863,2487],{"stretchy":1734},[2133,30865,4991],{},[1726,30867,1742],{"separator":1741},[2133,30869,2860],{},[1726,30871,2502],{"stretchy":1734},[902,30873,30874],{"encoding":904},"E[25, 10]",". Sklon přímky ",[883,30877,30879],{"className":30878},[886],[888,30880,30881],{"xmlns":890},[892,30882,30883,30895],{},[895,30884,30885,30887],{},[1726,30886,2228],{},[2326,30888,30889],{"scriptlevel":2328,"displaystyle":1734},[2330,30890,30891,30893],{},[2133,30892,2135],{},[2133,30894,2231],{},[902,30896,30897],{"encoding":904},"-\\tfrac{2}{5}"," odpovídá ",[883,30900,30902],{"className":30901},[886],[888,30903,30904],{"xmlns":890},[892,30905,30906,30946],{},[895,30907,30908,30910,30912,30914,30916,30918,30920,30922,30924,30926,30934,30936,30938],{},[1726,30909,2228],{},[2289,30911,10587],{},[1726,30913,1735],{"stretchy":1734},[2133,30915,4991],{},[1726,30917,1742],{"separator":1741},[2133,30919,2860],{},[1726,30921,1762],{"stretchy":1734},[1726,30923,1728],{},[1726,30925,2228],{},[2326,30927,30928],{"scriptlevel":2328,"displaystyle":1734},[2330,30929,30930,30932],{},[2133,30931,2860],{},[2133,30933,4991],{},[1726,30935,1728],{},[1726,30937,2228],{},[2326,30939,30940],{"scriptlevel":2328,"displaystyle":1734},[2330,30941,30942,30944],{},[2133,30943,2135],{},[2133,30945,2231],{},[902,30947,30948],{"encoding":904},"-\\text{MRCS}(25, 10) = -\\tfrac{10}{25} = -\\tfrac{2}{5}",[115,30950,30952],{"id":30951},"funkce-poptávky-spotřebitele-marshallova","Funkce poptávky spotřebitele (Marshallova)",[724,30954,30955,30956,28984,30986,30989,30990,2703],{},"Považujeme-li v úloze ",[883,30957,30959],{"className":30958},[886],[888,30960,30961],{"xmlns":890},[892,30962,30963,30983],{},[895,30964,30965,30971,30973,30979,30981],{},[2275,30966,30967,30969],{},[898,30968,1738],{},[2133,30970,2281],{},[1726,30972,1742],{"separator":1741},[2275,30974,30975,30977],{},[898,30976,1738],{},[2133,30978,2135],{},[1726,30980,1742],{"separator":1741},[898,30982,1745],{},[902,30984,30985],{"encoding":904},"P_1, P_2, Y",[38,30987,30988],{},"parametry"," (nikoli čísla), dostáváme z první řádové podmínky ",[38,30991,30992],{},"Marshallovy poptávkové funkce",[883,30994,30996],{"className":30995},[886],[888,30997,30998],{"xmlns":890,"display":28047},[892,30999,31000,31095],{},[20735,31001,31002],{"width":28052},[20740,31003,31004,31006,31088,31090],{},[20743,31005],{"width":28057},[20743,31007,31008],{},[895,31009,31010,31016,31018,31024,31026,31032,31034,31040,31042,31044,31046,31048,31050,31056,31058,31064,31066,31072,31074,31080,31082,31084,31086],{},[2275,31011,31012,31014],{},[898,31013,1724],{},[2133,31015,2281],{},[1726,31017,1728],{},[2275,31019,31020,31022],{},[898,31021,1731],{},[2133,31023,2281],{},[1726,31025,1735],{"stretchy":1734},[2275,31027,31028,31030],{},[898,31029,1738],{},[2133,31031,2281],{},[1726,31033,1742],{"separator":1741},[2275,31035,31036,31038],{},[898,31037,1738],{},[2133,31039,2135],{},[1726,31041,1742],{"separator":1741},[898,31043,1745],{},[1726,31045,1762],{"stretchy":1734},[1726,31047,1742],{"separator":1741},[5865,31049],{"width":15270},[2275,31051,31052,31054],{},[898,31053,1724],{},[2133,31055,2135],{},[1726,31057,1728],{},[2275,31059,31060,31062],{},[898,31061,1731],{},[2133,31063,2135],{},[1726,31065,1735],{"stretchy":1734},[2275,31067,31068,31070],{},[898,31069,1738],{},[2133,31071,2281],{},[1726,31073,1742],{"separator":1741},[2275,31075,31076,31078],{},[898,31077,1738],{},[2133,31079,2135],{},[1726,31081,1742],{"separator":1741},[898,31083,1745],{},[1726,31085,1762],{"stretchy":1734},[1726,31087,1742],{"separator":1741},[20743,31089],{"width":28057},[20743,31091,31092],{},[2289,31093,31094],{},"(6.15)",[902,31096,31097],{"encoding":904},"Q_1 = D_1(P_1, P_2, Y), \\quad Q_2 = D_2(P_1, P_2, Y), \\tag{6.15}",[883,31099,31101],{"className":31100},[886],[888,31102,31103],{"xmlns":890,"display":28047},[892,31104,31105,31152],{},[20735,31106,31107],{"width":28052},[20740,31108,31109,31111,31145,31147],{},[20743,31110],{"width":28057},[20743,31112,31113],{},[895,31114,31115,31117,31119,31121,31123,31129,31131,31137,31139,31141,31143],{},[898,31116,16425],{},[1726,31118,1728],{},[898,31120,16425],{},[1726,31122,1735],{"stretchy":1734},[2275,31124,31125,31127],{},[898,31126,1738],{},[2133,31128,2281],{},[1726,31130,1742],{"separator":1741},[2275,31132,31133,31135],{},[898,31134,1738],{},[2133,31136,2135],{},[1726,31138,1742],{"separator":1741},[898,31140,1745],{},[1726,31142,1762],{"stretchy":1734},[898,31144,1888],{"mathvariant":2377},[20743,31146],{"width":28057},[20743,31148,31149],{},[2289,31150,31151],{},"(6.16)",[902,31153,31154],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, Y). \\tag{6.16}",[724,31156,31157,31187,31188,31254],{},[38,31158,31159,31160,1888],{},"Odvození pro ",[883,31161,31163],{"className":31162},[886],[888,31164,31165],{"xmlns":890},[892,31166,31167,31185],{},[895,31168,31169,31171,31173,31179],{},[898,31170,900],{},[1726,31172,1728],{},[2275,31174,31175,31177],{},[898,31176,1724],{},[2133,31178,2281],{},[2275,31180,31181,31183],{},[898,31182,1724],{},[2133,31184,2135],{},[902,31186,30207],{"encoding":904}," Lagrangeova funkce ",[883,31189,31191],{"className":31190},[886],[888,31192,31193],{"xmlns":890},[892,31194,31195,31251],{},[895,31196,31197,31199,31201,31207,31213,31215,31217,31219,31221,31223,31229,31235,31237,31243,31249],{},[898,31198,9779],{"mathvariant":28529},[1726,31200,1728],{},[2275,31202,31203,31205],{},[898,31204,1724],{},[2133,31206,2281],{},[2275,31208,31209,31211],{},[898,31210,1724],{},[2133,31212,2135],{},[1726,31214,2099],{},[898,31216,16425],{},[1726,31218,1735],{"stretchy":1734},[898,31220,1745],{},[1726,31222,2228],{},[2275,31224,31225,31227],{},[898,31226,1738],{},[2133,31228,2281],{},[2275,31230,31231,31233],{},[898,31232,1724],{},[2133,31234,2281],{},[1726,31236,2228],{},[2275,31238,31239,31241],{},[898,31240,1738],{},[2133,31242,2135],{},[2275,31244,31245,31247],{},[898,31246,1724],{},[2133,31248,2135],{},[1726,31250,1762],{"stretchy":1734},[902,31252,31253],{"encoding":904},"\\mathcal{L} = Q_1 Q_2 + \\lambda(Y - P_1 Q_1 - P_2 Q_2)"," dává soustavu",[883,31256,31258],{"className":31257},[886],[888,31259,31260],{"xmlns":890,"display":28047},[892,31261,31262,31429],{},[20735,31263,31264],{"width":28052},[20740,31265,31266,31268,31422,31424],{},[20743,31267],{"width":28057},[20743,31269,31270],{},[20735,31271,31272,31318,31364],{"rowspacing":20737,"columnalign":20738,"columnspacing":2378},[20740,31273,31274,31286],{},[20743,31275,31276],{},[2326,31277,31278],{"scriptlevel":2328,"displaystyle":1741},[9151,31279,31280,31282,31284],{},[898,31281,9779],{"mathvariant":28529},[2133,31283,2281],{},[1726,31285,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[20743,31287,31288],{},[2326,31289,31290],{"scriptlevel":2328,"displaystyle":1741},[895,31291,31292,31294,31296,31302,31304,31306,31312,31314,31316],{},[895,31293],{},[1726,31295,1728],{},[2275,31297,31298,31300],{},[898,31299,1724],{},[2133,31301,2135],{},[1726,31303,2228],{},[898,31305,16425],{},[2275,31307,31308,31310],{},[898,31309,1738],{},[2133,31311,2281],{},[1726,31313,1728],{},[2133,31315,2328],{},[1726,31317,1742],{"separator":1741},[20740,31319,31320,31332],{},[20743,31321,31322],{},[2326,31323,31324],{"scriptlevel":2328,"displaystyle":1741},[9151,31325,31326,31328,31330],{},[898,31327,9779],{"mathvariant":28529},[2133,31329,2135],{},[1726,31331,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[20743,31333,31334],{},[2326,31335,31336],{"scriptlevel":2328,"displaystyle":1741},[895,31337,31338,31340,31342,31348,31350,31352,31358,31360,31362],{},[895,31339],{},[1726,31341,1728],{},[2275,31343,31344,31346],{},[898,31345,1724],{},[2133,31347,2281],{},[1726,31349,2228],{},[898,31351,16425],{},[2275,31353,31354,31356],{},[898,31355,1738],{},[2133,31357,2135],{},[1726,31359,1728],{},[2133,31361,2328],{},[1726,31363,1742],{"separator":1741},[20740,31365,31366,31378],{},[20743,31367,31368],{},[2326,31369,31370],{"scriptlevel":2328,"displaystyle":1741},[9151,31371,31372,31374,31376],{},[898,31373,9779],{"mathvariant":28529},[898,31375,16425],{},[1726,31377,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[20743,31379,31380],{},[2326,31381,31382],{"scriptlevel":2328,"displaystyle":1741},[895,31383,31384,31386,31388,31390,31392,31398,31404,31406,31412,31418,31420],{},[895,31385],{},[1726,31387,1728],{},[898,31389,1745],{},[1726,31391,2228],{},[2275,31393,31394,31396],{},[898,31395,1738],{},[2133,31397,2281],{},[2275,31399,31400,31402],{},[898,31401,1724],{},[2133,31403,2281],{},[1726,31405,2228],{},[2275,31407,31408,31410],{},[898,31409,1738],{},[2133,31411,2135],{},[2275,31413,31414,31416],{},[898,31415,1724],{},[2133,31417,2135],{},[1726,31419,1728],{},[2133,31421,12446],{},[20743,31423],{"width":28057},[20743,31425,31426],{},[2289,31427,31428],{},"(6.17)",[902,31430,31431],{"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}",[724,31433,31434,31435,31463,31464,31492,31493,31561],{},"Z prvních dvou: ",[883,31436,31438],{"className":31437},[886],[888,31439,31440],{"xmlns":890},[892,31441,31442,31460],{},[895,31443,31444,31450,31452,31458],{},[2275,31445,31446,31448],{},[898,31447,1724],{},[2133,31449,2135],{},[1726,31451,1728],{},[2275,31453,31454,31456],{},[898,31455,1738],{},[2133,31457,2281],{},[898,31459,16425],{},[902,31461,31462],{"encoding":904},"Q_2 = P_1 \\lambda"," (6.18), ",[883,31465,31467],{"className":31466},[886],[888,31468,31469],{"xmlns":890},[892,31470,31471,31489],{},[895,31472,31473,31479,31481,31487],{},[2275,31474,31475,31477],{},[898,31476,1724],{},[2133,31478,2281],{},[1726,31480,1728],{},[2275,31482,31483,31485],{},[898,31484,1738],{},[2133,31486,2135],{},[898,31488,16425],{},[902,31490,31491],{"encoding":904},"Q_1 = P_2 \\lambda"," (6.19). Dosazením do třetí ",[883,31494,31496],{"className":31495},[886],[888,31497,31498],{"xmlns":890},[892,31499,31500,31558],{},[895,31501,31502,31504,31506,31512,31514,31520,31522,31524,31530,31532,31538,31540,31542,31544,31550,31556],{},[898,31503,1745],{},[1726,31505,1728],{},[2275,31507,31508,31510],{},[898,31509,1738],{},[2133,31511,2281],{},[1726,31513,3174],{},[2275,31515,31516,31518],{},[898,31517,1738],{},[2133,31519,2135],{},[898,31521,16425],{},[1726,31523,2099],{},[2275,31525,31526,31528],{},[898,31527,1738],{},[2133,31529,2135],{},[1726,31531,3174],{},[2275,31533,31534,31536],{},[898,31535,1738],{},[2133,31537,2281],{},[898,31539,16425],{},[1726,31541,1728],{},[2133,31543,2135],{},[2275,31545,31546,31548],{},[898,31547,1738],{},[2133,31549,2281],{},[2275,31551,31552,31554],{},[898,31553,1738],{},[2133,31555,2135],{},[898,31557,16425],{},[902,31559,31560],{"encoding":904},"Y = P_1 \\cdot P_2 \\lambda + P_2 \\cdot P_1 \\lambda = 2 P_1 P_2 \\lambda",", odtud",[883,31563,31565],{"className":31564},[886],[888,31566,31567],{"xmlns":890,"display":28047},[892,31568,31569,31612],{},[20735,31570,31571],{"width":28052},[20740,31572,31573,31575,31605,31607],{},[20743,31574],{"width":28057},[20743,31576,31577],{},[895,31578,31579,31581,31583,31603],{},[898,31580,16425],{},[1726,31582,1728],{},[2330,31584,31585,31587],{},[898,31586,1745],{},[895,31588,31589,31591,31597],{},[2133,31590,2135],{},[2275,31592,31593,31595],{},[898,31594,1738],{},[2133,31596,2281],{},[2275,31598,31599,31601],{},[898,31600,1738],{},[2133,31602,2135],{},[898,31604,1888],{"mathvariant":2377},[20743,31606],{"width":28057},[20743,31608,31609],{},[2289,31610,31611],{},"(6.20)",[902,31613,31614],{"encoding":904},"\\lambda = \\frac{Y}{2 P_1 P_2}. \\tag{6.20}",[724,31616,31617],{},"Zpětně:",[883,31619,31621],{"className":31620},[886],[888,31622,31623],{"xmlns":890,"display":28047},[892,31624,31625,31702],{},[20735,31626,31627],{"width":28052},[20740,31628,31629,31631,31695,31697],{},[20743,31630],{"width":28057},[20743,31632,31633],{},[12818,31634,31635],{"notation":12820},[2326,31636,31637],{"scriptlevel":2328,"displaystyle":1734},[2326,31638,31639],{"scriptlevel":2328,"displaystyle":1734},[2326,31640,31641],{"scriptlevel":2328,"displaystyle":1741},[895,31642,31643,31645,31651,31653,31667,31669,31671,31677,31679,31693],{},[2289,31644,3974],{},[2275,31646,31647,31649],{},[898,31648,1724],{},[2133,31650,2281],{},[1726,31652,1728],{},[2330,31654,31655,31657],{},[898,31656,1745],{},[895,31658,31659,31661],{},[2133,31660,2135],{},[2275,31662,31663,31665],{},[898,31664,1738],{},[2133,31666,2281],{},[1726,31668,1742],{"separator":1741},[5865,31670],{"width":15270},[2275,31672,31673,31675],{},[898,31674,1724],{},[2133,31676,2135],{},[1726,31678,1728],{},[2330,31680,31681,31683],{},[898,31682,1745],{},[895,31684,31685,31687],{},[2133,31686,2135],{},[2275,31688,31689,31691],{},[898,31690,1738],{},[2133,31692,2135],{},[2289,31694,3974],{},[20743,31696],{"width":28057},[20743,31698,31699],{},[2289,31700,31701],{},"(6.21)",[902,31703,31704],{"encoding":904},"\\boxed{\\; Q_1 = \\frac{Y}{2 P_1}, \\quad Q_2 = \\frac{Y}{2 P_2} \\;} \\tag{6.21}",[198,31706,31708],{"id":31707},"engelova-funkce","Engelova funkce",[724,31710,9647,31711,31714,31715,31718,31719,19848,31736,1343,31766,31796,31797,31831,31832,1343,31858,31884],{},[38,31712,31713],{},"pevné ceny"," a proměnný důchod se Marshallova poptávka stává ",[38,31716,31717],{},"Engelovou funkcí",": pro ",[883,31720,31722],{"className":31721},[886],[888,31723,31724],{"xmlns":890},[892,31725,31726,31734],{},[895,31727,31728,31730,31732],{},[898,31729,1745],{},[1726,31731,1728],{},[2133,31733,3087],{},[902,31735,20300],{"encoding":904},[883,31737,31739],{"className":31738},[886],[888,31740,31741],{"xmlns":890},[892,31742,31743,31763],{},[895,31744,31745,31751,31753,31755,31757],{},[2275,31746,31747,31749],{},[898,31748,1724],{},[2133,31750,2281],{},[1726,31752,1728],{},[2133,31754,3117],{},[898,31756,4661],{"mathvariant":2377},[2275,31758,31759,31761],{},[898,31760,1738],{},[2133,31762,2281],{},[902,31764,31765],{"encoding":904},"Q_1 = 50\u002FP_1",[883,31767,31769],{"className":31768},[886],[888,31770,31771],{"xmlns":890},[892,31772,31773,31793],{},[895,31774,31775,31781,31783,31785,31787],{},[2275,31776,31777,31779],{},[898,31778,1724],{},[2133,31780,2135],{},[1726,31782,1728],{},[2133,31784,3117],{},[898,31786,4661],{"mathvariant":2377},[2275,31788,31789,31791],{},[898,31790,1738],{},[2133,31792,2135],{},[902,31794,31795],{"encoding":904},"Q_2 = 50\u002FP_2",". Pro pevné ceny ",[883,31798,31800],{"className":31799},[886],[888,31801,31802],{"xmlns":890},[892,31803,31804,31828],{},[895,31805,31806,31812,31814,31816,31818,31824,31826],{},[2275,31807,31808,31810],{},[898,31809,1738],{},[2133,31811,2281],{},[1726,31813,1728],{},[2133,31815,2860],{},[1726,31817,1742],{"separator":1741},[2275,31819,31820,31822],{},[898,31821,1738],{},[2133,31823,2135],{},[1726,31825,1728],{},[2133,31827,9021],{},[902,31829,31830],{"encoding":904},"P_1 = 10, P_2 = 20"," dostáváme Engelovy funkce ",[883,31833,31835],{"className":31834},[886],[888,31836,31837],{"xmlns":890},[892,31838,31839,31855],{},[895,31840,31841,31847,31849,31851,31853],{},[2275,31842,31843,31845],{},[898,31844,1724],{},[2133,31846,2281],{},[1726,31848,1728],{},[898,31850,1745],{},[898,31852,4661],{"mathvariant":2377},[2133,31854,9021],{},[902,31856,31857],{"encoding":904},"Q_1 = Y\u002F20",[883,31859,31861],{"className":31860},[886],[888,31862,31863],{"xmlns":890},[892,31864,31865,31881],{},[895,31866,31867,31873,31875,31877,31879],{},[2275,31868,31869,31871],{},[898,31870,1724],{},[2133,31872,2135],{},[1726,31874,1728],{},[898,31876,1745],{},[898,31878,4661],{"mathvariant":2377},[2133,31880,5198],{},[902,31882,31883],{"encoding":904},"Q_2 = Y\u002F40"," — lineární závislost spotřebovaného množství na důchodu.",[115,31886,31888],{"id":31887},"duální-úloha-minimalizace-výdajů","Duální úloha — minimalizace výdajů",[724,31890,31891],{},"Výdaje spotřebitele jsou",[883,31893,31895],{"className":31894},[886],[888,31896,31897],{"xmlns":890,"display":28047},[892,31898,31899,31974],{},[20735,31900,31901],{"width":28052},[20740,31902,31903,31905,31967,31969],{},[20743,31904],{"width":28057},[20743,31906,31907],{},[895,31908,31909,31911,31913,31915,31917,31923,31925,31931,31933,31935,31943,31949,31951,31959,31965],{},[898,31910,4240],{},[1726,31912,1728],{},[898,31914,4240],{},[1726,31916,1735],{"stretchy":1734},[2275,31918,31919,31921],{},[898,31920,1724],{},[2133,31922,2281],{},[1726,31924,1742],{"separator":1741},[2275,31926,31927,31929],{},[898,31928,1724],{},[2133,31930,2135],{},[1726,31932,1762],{"stretchy":1734},[1726,31934,1728],{},[9151,31936,31937,31939,31941],{},[898,31938,1738],{},[2133,31940,2281],{},[1726,31942,4342],{},[2275,31944,31945,31947],{},[898,31946,1724],{},[2133,31948,2281],{},[1726,31950,2099],{},[9151,31952,31953,31955,31957],{},[898,31954,1738],{},[2133,31956,2135],{},[1726,31958,4342],{},[2275,31960,31961,31963],{},[898,31962,1724],{},[2133,31964,2135],{},[1726,31966,1742],{"separator":1741},[20743,31968],{"width":28057},[20743,31970,31971],{},[2289,31972,31973],{},"(6.22)",[902,31975,31976],{"encoding":904},"E = E(Q_1, Q_2) = P_1^* Q_1 + P_2^* Q_2, \\tag{6.22}",[724,31978,31979],{},"a je pevně zadána hladina užitečnosti",[883,31981,31983],{"className":31982},[886],[888,31984,31985],{"xmlns":890,"display":28047},[892,31986,31987,32034],{},[20735,31988,31989],{"width":28052},[20740,31990,31991,31993,32027,32029],{},[20743,31992],{"width":28057},[20743,31994,31995],{},[895,31996,31997,32003,32005,32007,32009,32015,32017,32023,32025],{},[2128,31998,31999,32001],{},[898,32000,900],{},[1726,32002,4342],{},[1726,32004,1728],{},[898,32006,900],{},[1726,32008,1735],{"stretchy":1734},[2275,32010,32011,32013],{},[898,32012,1724],{},[2133,32014,2281],{},[1726,32016,1742],{"separator":1741},[2275,32018,32019,32021],{},[898,32020,1724],{},[2133,32022,2135],{},[1726,32024,1762],{"stretchy":1734},[898,32026,1888],{"mathvariant":2377},[20743,32028],{"width":28057},[20743,32030,32031],{},[2289,32032,32033],{},"(6.23)",[902,32035,32036],{"encoding":904},"U^* = U(Q_1, Q_2). \\tag{6.23}",[724,32038,32039,32042,32043,32075,32076,1888],{},[38,32040,32041],{},"Úlohou o minimalizaci výdajů"," je najít minimum ",[883,32044,32046],{"className":32045},[886],[888,32047,32048],{"xmlns":890},[892,32049,32050,32072],{},[895,32051,32052,32054,32056,32062,32064,32070],{},[898,32053,4240],{},[1726,32055,1735],{"stretchy":1734},[2275,32057,32058,32060],{},[898,32059,1724],{},[2133,32061,2281],{},[1726,32063,1742],{"separator":1741},[2275,32065,32066,32068],{},[898,32067,1724],{},[2133,32069,2135],{},[1726,32071,1762],{"stretchy":1734},[902,32073,32074],{"encoding":904},"E(Q_1, Q_2)"," vázané podmínkou (6.23) ve tvaru ",[883,32077,32079],{"className":32078},[886],[888,32080,32081],{"xmlns":890},[892,32082,32083,32139],{},[895,32084,32085,32087,32089,32095,32097,32103,32105,32107,32113,32115,32117,32119,32125,32127,32133,32135,32137],{},[898,32086,11025],{},[1726,32088,1735],{"stretchy":1734},[2275,32090,32091,32093],{},[898,32092,1724],{},[2133,32094,2281],{},[1726,32096,1742],{"separator":1741},[2275,32098,32099,32101],{},[898,32100,1724],{},[2133,32102,2135],{},[1726,32104,1762],{"stretchy":1734},[1726,32106,1728],{},[2128,32108,32109,32111],{},[898,32110,900],{},[1726,32112,4342],{},[1726,32114,2228],{},[898,32116,900],{},[1726,32118,1735],{"stretchy":1734},[2275,32120,32121,32123],{},[898,32122,1724],{},[2133,32124,2281],{},[1726,32126,1742],{"separator":1741},[2275,32128,32129,32131],{},[898,32130,1724],{},[2133,32132,2135],{},[1726,32134,1762],{"stretchy":1734},[1726,32136,1728],{},[2133,32138,2328],{},[902,32140,32141],{"encoding":904},"g(Q_1, Q_2) = U^* - U(Q_1, Q_2) = 0",[198,32143,32145],{"id":32144},"lagrangeova-funkce","Lagrangeova funkce",[883,32147,32149],{"className":32148},[886],[888,32150,32151],{"xmlns":890,"display":28047},[892,32152,32153,32264],{},[20735,32154,32155],{"width":28052},[20740,32156,32157,32159,32257,32259],{},[20743,32158],{"width":28057},[20743,32160,32161],{},[895,32162,32163,32165,32167,32173,32175,32181,32183,32185,32187,32189,32197,32203,32205,32213,32219,32221,32223,32225,32231,32233,32235,32237,32243,32245,32251,32253,32255],{},[898,32164,9779],{"mathvariant":28529},[1726,32166,1735],{"stretchy":1734},[2275,32168,32169,32171],{},[898,32170,1724],{},[2133,32172,2281],{},[1726,32174,1742],{"separator":1741},[2275,32176,32177,32179],{},[898,32178,1724],{},[2133,32180,2135],{},[1726,32182,1742],{"separator":1741},[898,32184,16425],{},[1726,32186,1762],{"stretchy":1734},[1726,32188,1728],{},[9151,32190,32191,32193,32195],{},[898,32192,1738],{},[2133,32194,2281],{},[1726,32196,4342],{},[2275,32198,32199,32201],{},[898,32200,1724],{},[2133,32202,2281],{},[1726,32204,2099],{},[9151,32206,32207,32209,32211],{},[898,32208,1738],{},[2133,32210,2135],{},[1726,32212,4342],{},[2275,32214,32215,32217],{},[898,32216,1724],{},[2133,32218,2135],{},[1726,32220,2099],{},[898,32222,16425],{},[1726,32224,1735],{"stretchy":1734},[2128,32226,32227,32229],{},[898,32228,900],{},[1726,32230,4342],{},[1726,32232,2228],{},[898,32234,900],{},[1726,32236,1735],{"stretchy":1734},[2275,32238,32239,32241],{},[898,32240,1724],{},[2133,32242,2281],{},[1726,32244,1742],{"separator":1741},[2275,32246,32247,32249],{},[898,32248,1724],{},[2133,32250,2135],{},[1726,32252,1762],{"stretchy":1734},[1726,32254,1762],{"stretchy":1734},[898,32256,1888],{"mathvariant":2377},[20743,32258],{"width":28057},[20743,32260,32261],{},[2289,32262,32263],{},"(6.24)",[902,32265,32266],{"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}",[724,32268,32269],{},"Soustava podmínek prvního řádu:",[883,32271,32273],{"className":32272},[886],[888,32274,32275],{"xmlns":890,"display":28047},[892,32276,32277,32450],{},[20735,32278,32279],{"width":28052},[20740,32280,32281,32283,32443,32445],{},[20743,32282],{"width":28057},[20743,32284,32285],{},[20735,32286,32287,32337,32387],{"rowspacing":20737,"columnalign":20738,"columnspacing":2378},[20740,32288,32289,32301],{},[20743,32290,32291],{},[2326,32292,32293],{"scriptlevel":2328,"displaystyle":1741},[9151,32294,32295,32297,32299],{},[898,32296,9779],{"mathvariant":28529},[2133,32298,2281],{},[1726,32300,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[20743,32302,32303],{},[2326,32304,32305],{"scriptlevel":2328,"displaystyle":1741},[895,32306,32307,32309,32311,32319,32321,32323,32331,32333,32335],{},[895,32308],{},[1726,32310,1728],{},[9151,32312,32313,32315,32317],{},[898,32314,1738],{},[2133,32316,2281],{},[1726,32318,4342],{},[1726,32320,2228],{},[898,32322,16425],{},[9151,32324,32325,32327,32329],{},[898,32326,900],{},[2133,32328,2281],{},[1726,32330,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,32332,1728],{},[2133,32334,2328],{},[1726,32336,1742],{"separator":1741},[20740,32338,32339,32351],{},[20743,32340,32341],{},[2326,32342,32343],{"scriptlevel":2328,"displaystyle":1741},[9151,32344,32345,32347,32349],{},[898,32346,9779],{"mathvariant":28529},[2133,32348,2135],{},[1726,32350,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[20743,32352,32353],{},[2326,32354,32355],{"scriptlevel":2328,"displaystyle":1741},[895,32356,32357,32359,32361,32369,32371,32373,32381,32383,32385],{},[895,32358],{},[1726,32360,1728],{},[9151,32362,32363,32365,32367],{},[898,32364,1738],{},[2133,32366,2135],{},[1726,32368,4342],{},[1726,32370,2228],{},[898,32372,16425],{},[9151,32374,32375,32377,32379],{},[898,32376,900],{},[2133,32378,2135],{},[1726,32380,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,32382,1728],{},[2133,32384,2328],{},[1726,32386,1742],{"separator":1741},[20740,32388,32389,32401],{},[20743,32390,32391],{},[2326,32392,32393],{"scriptlevel":2328,"displaystyle":1741},[9151,32394,32395,32397,32399],{},[898,32396,9779],{"mathvariant":28529},[898,32398,16425],{},[1726,32400,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[20743,32402,32403],{},[2326,32404,32405],{"scriptlevel":2328,"displaystyle":1741},[895,32406,32407,32409,32411,32417,32419,32421,32423,32429,32431,32437,32439,32441],{},[895,32408],{},[1726,32410,1728],{},[2128,32412,32413,32415],{},[898,32414,900],{},[1726,32416,4342],{},[1726,32418,2228],{},[898,32420,900],{},[1726,32422,1735],{"stretchy":1734},[2275,32424,32425,32427],{},[898,32426,1724],{},[2133,32428,2281],{},[1726,32430,1742],{"separator":1741},[2275,32432,32433,32435],{},[898,32434,1724],{},[2133,32436,2135],{},[1726,32438,1762],{"stretchy":1734},[1726,32440,1728],{},[2133,32442,12446],{},[20743,32444],{"width":28057},[20743,32446,32447],{},[2289,32448,32449],{},"(6.25)",[902,32451,32452],{"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}",[724,32454,32455],{},"Postačující podmínka pro minimum (vzhledem k linearitě funkce výdajů) má tvar",[883,32457,32459],{"className":32458},[886],[888,32460,32461],{"xmlns":890,"display":28047},[892,32462,32463,32561],{},[20735,32464,32465],{"width":28052},[20740,32466,32467,32469,32554,32556],{},[20743,32468],{"width":28057},[20743,32470,32471],{},[895,32472,32473,32475,32477,32483,32485,32491,32493,32495,32497,32499,32501,32503,32552],{},[898,32474,1731],{},[1726,32476,1735],{"stretchy":1734},[2275,32478,32479,32481],{},[898,32480,1724],{},[2133,32482,2281],{},[1726,32484,1742],{"separator":1741},[2275,32486,32487,32489],{},[898,32488,1724],{},[2133,32490,2135],{},[1726,32492,1742],{"separator":1741},[898,32494,16425],{},[1726,32496,1762],{"stretchy":1734},[1726,32498,1728],{},[1726,32500,2228],{},[898,32502,16425],{},[895,32504,32505,32507,32519,32521,32534,32536,32538,32550],{},[1726,32506,1735],{"fence":1741},[9151,32508,32509,32511,32513],{},[898,32510,900],{},[2133,32512,2901],{},[895,32514,32515,32517],{},[1726,32516,2379],{"mathvariant":2377},[1726,32518,2379],{"mathvariant":2377},[1726,32520,2099],{},[9151,32522,32523,32525,32528],{},[898,32524,900],{},[2133,32526,32527],{},"22",[895,32529,32530,32532],{},[1726,32531,2379],{"mathvariant":2377},[1726,32533,2379],{"mathvariant":2377},[1726,32535,2099],{},[2133,32537,2135],{},[9151,32539,32540,32542,32544],{},[898,32541,900],{},[2133,32543,3506],{},[895,32545,32546,32548],{},[1726,32547,2379],{"mathvariant":2377},[1726,32549,2379],{"mathvariant":2377},[1726,32551,1762],{"fence":1741},[898,32553,1888],{"mathvariant":2377},[20743,32555],{"width":28057},[20743,32557,32558],{},[2289,32559,32560],{},"(6.26)",[902,32562,32563],{"encoding":904},"D(Q_1, Q_2, \\lambda) = -\\lambda \\left(U''_{11} + U''_{22} + 2 U''_{12}\\right). \\tag{6.26}",[724,32565,32566,32569,32570,32609,32610,32649,32650,32700,32701,32727,32728,32745,32746,32772],{},[38,32567,32568],{},"Geometrie (obrázek 6.9)."," Řešením je bod ",[883,32571,32573],{"className":32572},[886],[888,32574,32575],{"xmlns":890},[892,32576,32577,32607],{},[895,32578,32579,32585,32587,32595,32597,32605],{},[2128,32580,32581,32583],{},[898,32582,1724],{},[1726,32584,4342],{},[1726,32586,2487],{"stretchy":1734},[9151,32588,32589,32591,32593],{},[898,32590,1724],{},[2133,32592,2281],{},[1726,32594,4342],{},[1726,32596,1742],{"separator":1741},[9151,32598,32599,32601,32603],{},[898,32600,1724],{},[2133,32602,2135],{},[1726,32604,4342],{},[1726,32606,2502],{"stretchy":1734},[902,32608,28308],{"encoding":904}," dotyku křivky užitečnosti ",[883,32611,32613],{"className":32612},[886],[888,32614,32615],{"xmlns":890},[892,32616,32617,32647],{},[895,32618,32619,32625,32627,32629,32631,32637,32639,32645],{},[2128,32620,32621,32623],{},[898,32622,900],{},[1726,32624,4342],{},[1726,32626,1728],{},[898,32628,900],{},[1726,32630,1735],{"stretchy":1734},[2275,32632,32633,32635],{},[898,32634,1724],{},[2133,32636,2281],{},[1726,32638,1742],{"separator":1741},[2275,32640,32641,32643],{},[898,32642,1724],{},[2133,32644,2135],{},[1726,32646,1762],{"stretchy":1734},[902,32648,17647],{"encoding":904}," s přímkou výdajů ",[883,32651,32653],{"className":32652},[886],[888,32654,32655],{"xmlns":890},[892,32656,32657,32697],{},[895,32658,32659,32665,32667,32675,32681,32683,32691],{},[2128,32660,32661,32663],{},[898,32662,4240],{},[1726,32664,4342],{},[1726,32666,1728],{},[9151,32668,32669,32671,32673],{},[898,32670,1738],{},[2133,32672,2281],{},[1726,32674,4342],{},[2275,32676,32677,32679],{},[898,32678,1724],{},[2133,32680,2281],{},[1726,32682,2099],{},[9151,32684,32685,32687,32689],{},[898,32686,1738],{},[2133,32688,2135],{},[1726,32690,4342],{},[2275,32692,32693,32695],{},[898,32694,1724],{},[2133,32696,2135],{},[902,32698,32699],{"encoding":904},"E^* = P_1^* Q_1 + P_2^* Q_2",". Hladina ",[883,32702,32704],{"className":32703},[886],[888,32705,32706],{"xmlns":890},[892,32707,32708,32724],{},[895,32709,32710,32716,32718],{},[2275,32711,32712,32714],{},[898,32713,4240],{},[2133,32715,2328],{},[1726,32717,3444],{},[2128,32719,32720,32722],{},[898,32721,4240],{},[1726,32723,4342],{},[902,32725,32726],{"encoding":904},"E_0 \u003C E^*"," nestačí k dosažení ",[883,32729,32731],{"className":32730},[886],[888,32732,32733],{"xmlns":890},[892,32734,32735,32743],{},[895,32736,32737],{},[2128,32738,32739,32741],{},[898,32740,900],{},[1726,32742,4342],{},[902,32744,27943],{"encoding":904},", hladina ",[883,32747,32749],{"className":32748},[886],[888,32750,32751],{"xmlns":890},[892,32752,32753,32769],{},[895,32754,32755,32761,32763],{},[2275,32756,32757,32759],{},[898,32758,4240],{},[2133,32760,2281],{},[1726,32762,3405],{},[2128,32764,32765,32767],{},[898,32766,4240],{},[1726,32768,4342],{},[902,32770,32771],{"encoding":904},"E_1 > E^*"," je nadbytečná.",[3859,32774,32775,32780],{},[724,32776,32777,32779],{},[883,32778,4560],{}," Postup — duální úloha (minimalizace výdajů)",[152,32781,32782,32832,32918,32958,33033],{},[123,32783,32784,1777,32787,32831],{},[38,32785,32786],{},"Zapiš vazbu",[883,32788,32790],{"className":32789},[886],[888,32791,32792],{"xmlns":890},[892,32793,32794,32828],{},[895,32795,32796,32802,32804,32806,32808,32814,32816,32822,32824,32826],{},[2128,32797,32798,32800],{},[898,32799,900],{},[1726,32801,4342],{},[1726,32803,2228],{},[898,32805,900],{},[1726,32807,1735],{"stretchy":1734},[2275,32809,32810,32812],{},[898,32811,1724],{},[2133,32813,2281],{},[1726,32815,1742],{"separator":1741},[2275,32817,32818,32820],{},[898,32819,1724],{},[2133,32821,2135],{},[1726,32823,1762],{"stretchy":1734},[1726,32825,1728],{},[2133,32827,2328],{},[902,32829,32830],{"encoding":904},"U^* - U(Q_1, Q_2) = 0"," (zadaná hladina užitečnosti).",[123,32833,32834,1777,32836,1888],{},[38,32835,29241],{},[883,32837,32839],{"className":32838},[886],[888,32840,32841],{"xmlns":890},[892,32842,32843,32915],{},[895,32844,32845,32847,32849,32857,32863,32865,32873,32879,32881,32883,32885,32891,32893,32895,32897,32903,32905,32911,32913],{},[898,32846,9779],{"mathvariant":28529},[1726,32848,1728],{},[9151,32850,32851,32853,32855],{},[898,32852,1738],{},[2133,32854,2281],{},[1726,32856,4342],{},[2275,32858,32859,32861],{},[898,32860,1724],{},[2133,32862,2281],{},[1726,32864,2099],{},[9151,32866,32867,32869,32871],{},[898,32868,1738],{},[2133,32870,2135],{},[1726,32872,4342],{},[2275,32874,32875,32877],{},[898,32876,1724],{},[2133,32878,2135],{},[1726,32880,2099],{},[898,32882,16425],{},[1726,32884,1735],{"stretchy":1734},[2128,32886,32887,32889],{},[898,32888,900],{},[1726,32890,4342],{},[1726,32892,2228],{},[898,32894,900],{},[1726,32896,1735],{"stretchy":1734},[2275,32898,32899,32901],{},[898,32900,1724],{},[2133,32902,2281],{},[1726,32904,1742],{"separator":1741},[2275,32906,32907,32909],{},[898,32908,1724],{},[2133,32910,2135],{},[1726,32912,1762],{"stretchy":1734},[1726,32914,1762],{"stretchy":1734},[902,32916,32917],{"encoding":904},"\\mathcal{L} = P_1^* Q_1 + P_2^* Q_2 + \\lambda(U^* - U(Q_1, Q_2))",[123,32919,32920,32923,32924,32957],{},[38,32921,32922],{},"Derivace rovny nule",", z prvních dvou rovnic podílem dostaneš podmínku ",[883,32925,32927],{"className":32926},[886],[888,32928,32929],{"xmlns":890},[892,32930,32931,32955],{},[895,32932,32933,32935,32937,32945,32947],{},[2289,32934,10587],{},[1726,32936,1728],{},[9151,32938,32939,32941,32943],{},[898,32940,1738],{},[2133,32942,2281],{},[1726,32944,4342],{},[898,32946,4661],{"mathvariant":2377},[9151,32948,32949,32951,32953],{},[898,32950,1738],{},[2133,32952,2135],{},[1726,32954,4342],{},[902,32956,28960],{"encoding":904}," (stejná jako u maximalizace!).",[123,32959,32960,1777,32963,33003,33004,1888],{},[38,32961,32962],{},"Dosaď do vazby",[883,32964,32966],{"className":32965},[886],[888,32967,32968],{"xmlns":890},[892,32969,32970,33000],{},[895,32971,32972,32974,32976,32982,32984,32990,32992,32994],{},[898,32973,900],{},[1726,32975,1735],{"stretchy":1734},[2275,32977,32978,32980],{},[898,32979,1724],{},[2133,32981,2281],{},[1726,32983,1742],{"separator":1741},[2275,32985,32986,32988],{},[898,32987,1724],{},[2133,32989,2135],{},[1726,32991,1762],{"stretchy":1734},[1726,32993,1728],{},[2128,32995,32996,32998],{},[898,32997,900],{},[1726,32999,4342],{},[902,33001,33002],{"encoding":904},"U(Q_1, Q_2) = U^*"," a vyřeš pro ",[883,33005,33007],{"className":33006},[886],[888,33008,33009],{"xmlns":890},[892,33010,33011,33031],{},[895,33012,33013,33021,33023],{},[9151,33014,33015,33017,33019],{},[898,33016,1724],{},[2133,33018,2281],{},[1726,33020,4342],{},[1726,33022,1742],{"separator":1741},[9151,33024,33025,33027,33029],{},[898,33026,1724],{},[2133,33028,2135],{},[1726,33030,4342],{},[902,33032,29482],{"encoding":904},[123,33034,33035,1777,33038,33092],{},[38,33036,33037],{},"Vypočítej minimální výdaje",[883,33039,33041],{"className":33040},[886],[888,33042,33043],{"xmlns":890},[892,33044,33045,33089],{},[895,33046,33047,33053,33055,33063,33071,33073,33081],{},[2128,33048,33049,33051],{},[898,33050,4240],{},[1726,33052,4342],{},[1726,33054,1728],{},[9151,33056,33057,33059,33061],{},[898,33058,1738],{},[2133,33060,2281],{},[1726,33062,4342],{},[9151,33064,33065,33067,33069],{},[898,33066,1724],{},[2133,33068,2281],{},[1726,33070,4342],{},[1726,33072,2099],{},[9151,33074,33075,33077,33079],{},[898,33076,1738],{},[2133,33078,2135],{},[1726,33080,4342],{},[9151,33082,33083,33085,33087],{},[898,33084,1724],{},[2133,33086,2135],{},[1726,33088,4342],{},[902,33090,33091],{"encoding":904},"E^* = P_1^* Q_1^* + P_2^* Q_2^*"," a případně ověř druhou podmínku (6.26).",[115,33094,33096,33097],{"id":33095},"příklad-67-minimalizace-výdajů-pro-uq112q212u-q_112-q_212","Příklad 6.7 — minimalizace výdajů pro ",[883,33098,33100],{"className":33099},[886],[888,33101,33102],{"xmlns":890},[892,33103,33104,33138],{},[895,33105,33106,33108,33110,33124],{},[898,33107,900],{},[1726,33109,1728],{},[9151,33111,33112,33114,33116],{},[898,33113,1724],{},[2133,33115,2281],{},[895,33117,33118,33120,33122],{},[2133,33119,2281],{},[898,33121,4661],{"mathvariant":2377},[2133,33123,2135],{},[9151,33125,33126,33128,33130],{},[898,33127,1724],{},[2133,33129,2135],{},[895,33131,33132,33134,33136],{},[2133,33133,2281],{},[898,33135,4661],{"mathvariant":2377},[2133,33137,2135],{},[902,33139,33140],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F2}",[724,33142,33143,33144,1343,33166,1343,33190,30327],{},"Dáno ",[883,33145,33147],{"className":33146},[886],[888,33148,33149],{"xmlns":890},[892,33150,33151,33163],{},[895,33152,33153,33159,33161],{},[2128,33154,33155,33157],{},[898,33156,900],{},[1726,33158,4342],{},[1726,33160,1728],{},[2133,33162,2135],{},[902,33164,33165],{"encoding":904},"U^* = 2",[883,33167,33169],{"className":33168},[886],[888,33170,33171],{"xmlns":890},[892,33172,33173,33187],{},[895,33174,33175,33183,33185],{},[9151,33176,33177,33179,33181],{},[898,33178,1738],{},[2133,33180,2281],{},[1726,33182,4342],{},[1726,33184,1728],{},[2133,33186,23770],{},[902,33188,33189],{"encoding":904},"P_1^* = 0{,}25",[883,33191,33193],{"className":33192},[886],[888,33194,33195],{"xmlns":890},[892,33196,33197,33211],{},[895,33198,33199,33207,33209],{},[9151,33200,33201,33203,33205],{},[898,33202,1738],{},[2133,33204,2135],{},[1726,33206,4342],{},[1726,33208,1728],{},[2133,33210,2281],{},[902,33212,33213],{"encoding":904},"P_2^* = 1",[883,33215,33217],{"className":33216},[886],[888,33218,33219],{"xmlns":890,"display":28047},[892,33220,33221,33285],{},[895,33222,33223,33225,33227,33229,33235,33237,33243,33245,33247,33249,33251,33253,33267,33281,33283],{},[898,33224,9779],{"mathvariant":28529},[1726,33226,1728],{},[2133,33228,23770],{},[2275,33230,33231,33233],{},[898,33232,1724],{},[2133,33234,2281],{},[1726,33236,2099],{},[2275,33238,33239,33241],{},[898,33240,1724],{},[2133,33242,2135],{},[1726,33244,2099],{},[898,33246,16425],{},[1726,33248,1735],{"stretchy":1734},[2133,33250,2135],{},[1726,33252,2228],{},[9151,33254,33255,33257,33259],{},[898,33256,1724],{},[2133,33258,2281],{},[895,33260,33261,33263,33265],{},[2133,33262,2281],{},[898,33264,4661],{"mathvariant":2377},[2133,33266,2135],{},[9151,33268,33269,33271,33273],{},[898,33270,1724],{},[2133,33272,2135],{},[895,33274,33275,33277,33279],{},[2133,33276,2281],{},[898,33278,4661],{"mathvariant":2377},[2133,33280,2135],{},[1726,33282,1762],{"stretchy":1734},[898,33284,1888],{"mathvariant":2377},[902,33286,33287],{"encoding":904},"\\mathcal{L} = 0{,}25 Q_1 + Q_2 + \\lambda(2 - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,33289,30412],{},[883,33291,33293],{"className":33292},[886],[888,33294,33295],{"xmlns":890,"display":28047},[892,33296,33297,33511],{},[20735,33298,33299,33375,33451],{"rowspacing":20737,"columnalign":20738,"columnspacing":2378},[20740,33300,33301,33313],{},[20743,33302,33303],{},[2326,33304,33305],{"scriptlevel":2328,"displaystyle":1741},[9151,33306,33307,33309,33311],{},[898,33308,9779],{"mathvariant":28529},[2133,33310,2281],{},[1726,33312,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[20743,33314,33315],{},[2326,33316,33317],{"scriptlevel":2328,"displaystyle":1741},[895,33318,33319,33321,33323,33325,33327,33329,33331,33339,33355,33369,33371,33373],{},[895,33320],{},[1726,33322,1728],{},[2133,33324,23770],{},[1726,33326,2228],{},[898,33328,16425],{},[1726,33330,3174],{},[2326,33332,33333],{"scriptlevel":2328,"displaystyle":1734},[2330,33334,33335,33337],{},[2133,33336,2281],{},[2133,33338,2135],{},[9151,33340,33341,33343,33345],{},[898,33342,1724],{},[2133,33344,2281],{},[895,33346,33347,33349,33351,33353],{},[1726,33348,2228],{},[2133,33350,2281],{},[898,33352,4661],{"mathvariant":2377},[2133,33354,2135],{},[9151,33356,33357,33359,33361],{},[898,33358,1724],{},[2133,33360,2135],{},[895,33362,33363,33365,33367],{},[2133,33364,2281],{},[898,33366,4661],{"mathvariant":2377},[2133,33368,2135],{},[1726,33370,1728],{},[2133,33372,2328],{},[1726,33374,1742],{"separator":1741},[20740,33376,33377,33389],{},[20743,33378,33379],{},[2326,33380,33381],{"scriptlevel":2328,"displaystyle":1741},[9151,33382,33383,33385,33387],{},[898,33384,9779],{"mathvariant":28529},[2133,33386,2135],{},[1726,33388,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[20743,33390,33391],{},[2326,33392,33393],{"scriptlevel":2328,"displaystyle":1741},[895,33394,33395,33397,33399,33401,33403,33405,33407,33415,33429,33445,33447,33449],{},[895,33396],{},[1726,33398,1728],{},[2133,33400,2281],{},[1726,33402,2228],{},[898,33404,16425],{},[1726,33406,3174],{},[2326,33408,33409],{"scriptlevel":2328,"displaystyle":1734},[2330,33410,33411,33413],{},[2133,33412,2281],{},[2133,33414,2135],{},[9151,33416,33417,33419,33421],{},[898,33418,1724],{},[2133,33420,2281],{},[895,33422,33423,33425,33427],{},[2133,33424,2281],{},[898,33426,4661],{"mathvariant":2377},[2133,33428,2135],{},[9151,33430,33431,33433,33435],{},[898,33432,1724],{},[2133,33434,2135],{},[895,33436,33437,33439,33441,33443],{},[1726,33438,2228],{},[2133,33440,2281],{},[898,33442,4661],{"mathvariant":2377},[2133,33444,2135],{},[1726,33446,1728],{},[2133,33448,2328],{},[1726,33450,1742],{"separator":1741},[20740,33452,33453,33465],{},[20743,33454,33455],{},[2326,33456,33457],{"scriptlevel":2328,"displaystyle":1741},[9151,33458,33459,33461,33463],{},[898,33460,9779],{"mathvariant":28529},[898,33462,16425],{},[1726,33464,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[20743,33466,33467],{},[2326,33468,33469],{"scriptlevel":2328,"displaystyle":1741},[895,33470,33471,33473,33475,33477,33479,33493,33507,33509],{},[895,33472],{},[1726,33474,1728],{},[2133,33476,2135],{},[1726,33478,2228],{},[9151,33480,33481,33483,33485],{},[898,33482,1724],{},[2133,33484,2281],{},[895,33486,33487,33489,33491],{},[2133,33488,2281],{},[898,33490,4661],{"mathvariant":2377},[2133,33492,2135],{},[9151,33494,33495,33497,33499],{},[898,33496,1724],{},[2133,33498,2135],{},[895,33500,33501,33503,33505],{},[2133,33502,2281],{},[898,33504,4661],{"mathvariant":2377},[2133,33506,2135],{},[1726,33508,1728],{},[2133,33510,12446],{},[902,33512,33513],{"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}",[724,33515,33516,33517,17558,33547,33575,33576,5576,33638,1343,33688,33710,33711,1888],{},"Podílem prvních dvou rovnic: ",[883,33518,33520],{"className":33519},[886],[888,33521,33522],{"xmlns":890},[892,33523,33524,33544],{},[895,33525,33526,33528,33530,33536,33538],{},[2133,33527,23770],{},[1726,33529,1728],{},[2275,33531,33532,33534],{},[898,33533,1724],{},[2133,33535,2135],{},[898,33537,4661],{"mathvariant":2377},[2275,33539,33540,33542],{},[898,33541,1724],{},[2133,33543,2281],{},[902,33545,33546],{"encoding":904},"0{,}25 = Q_2 \u002F Q_1",[883,33548,33550],{"className":33549},[886],[888,33551,33552],{"xmlns":890},[892,33553,33554,33572],{},[895,33555,33556,33562,33564,33566],{},[2275,33557,33558,33560],{},[898,33559,1724],{},[2133,33561,2135],{},[1726,33563,1728],{},[2133,33565,23770],{},[2275,33567,33568,33570],{},[898,33569,1724],{},[2133,33571,2281],{},[902,33573,33574],{"encoding":904},"Q_2 = 0{,}25 Q_1",". Dosazením do třetí: ",[883,33577,33579],{"className":33578},[886],[888,33580,33581],{"xmlns":890},[892,33582,33583,33635],{},[895,33584,33585,33599,33601,33603,33609,33621,33623,33625,33631,33633],{},[9151,33586,33587,33589,33591],{},[898,33588,1724],{},[2133,33590,2281],{},[895,33592,33593,33595,33597],{},[2133,33594,2281],{},[898,33596,4661],{"mathvariant":2377},[2133,33598,2135],{},[1726,33600,1735],{"stretchy":1734},[2133,33602,23770],{},[2275,33604,33605,33607],{},[898,33606,1724],{},[2133,33608,2281],{},[2128,33610,33611,33613],{},[1726,33612,1762],{"stretchy":1734},[895,33614,33615,33617,33619],{},[2133,33616,2281],{},[898,33618,4661],{"mathvariant":2377},[2133,33620,2135],{},[1726,33622,1728],{},[2133,33624,4996],{},[2275,33626,33627,33629],{},[898,33628,1724],{},[2133,33630,2281],{},[1726,33632,1728],{},[2133,33634,2135],{},[902,33636,33637],{"encoding":904},"Q_1^{1\u002F2} (0{,}25 Q_1)^{1\u002F2} = 0{,}5 Q_1 = 2",[38,33639,33640,1343,33664],{},[883,33641,33643],{"className":33642},[886],[888,33644,33645],{"xmlns":890},[892,33646,33647,33661],{},[895,33648,33649,33657,33659],{},[9151,33650,33651,33653,33655],{},[898,33652,1724],{},[2133,33654,2281],{},[1726,33656,4342],{},[1726,33658,1728],{},[2133,33660,2352],{},[902,33662,33663],{"encoding":904},"Q_1^* = 4",[883,33665,33667],{"className":33666},[886],[888,33668,33669],{"xmlns":890},[892,33670,33671,33685],{},[895,33672,33673,33681,33683],{},[9151,33674,33675,33677,33679],{},[898,33676,1724],{},[2133,33678,2135],{},[1726,33680,4342],{},[1726,33682,1728],{},[2133,33684,2281],{},[902,33686,33687],{"encoding":904},"Q_2^* = 1",[883,33689,33691],{"className":33690},[886],[888,33692,33693],{"xmlns":890},[892,33694,33695,33707],{},[895,33696,33697,33703,33705],{},[2128,33698,33699,33701],{},[898,33700,16425],{},[1726,33702,4342],{},[1726,33704,1728],{},[2133,33706,2281],{},[902,33708,33709],{"encoding":904},"\\lambda^* = 1",". Minimální výdaje: ",[883,33712,33714],{"className":33713},[886],[888,33715,33716],{"xmlns":890},[892,33717,33718,33746],{},[895,33719,33720,33726,33728,33730,33732,33734,33736,33738,33740,33742,33744],{},[2128,33721,33722,33724],{},[898,33723,4240],{},[1726,33725,4342],{},[1726,33727,1728],{},[2133,33729,23770],{},[1726,33731,3174],{},[2133,33733,2352],{},[1726,33735,2099],{},[2133,33737,2281],{},[1726,33739,3174],{},[2133,33741,2281],{},[1726,33743,1728],{},[2133,33745,2135],{},[902,33747,33748],{"encoding":904},"E^* = 0{,}25 \\cdot 4 + 1 \\cdot 1 = 2",[724,33750,33751,33754,33755,1343,33821,1343,33887,33953,33954,33991,33992,34014,34015,1888],{},[614,33752,33753],{},"Ověření postačující podmínky"," (6.26): ",[883,33756,33758],{"className":33757},[886],[888,33759,33760],{"xmlns":890},[892,33761,33762,33818],{},[895,33763,33764,33776,33778,33780,33788,33804],{},[9151,33765,33766,33768,33770],{},[898,33767,900],{},[2133,33769,2901],{},[895,33771,33772,33774],{},[1726,33773,2379],{"mathvariant":2377},[1726,33775,2379],{"mathvariant":2377},[1726,33777,1728],{},[1726,33779,2228],{},[2326,33781,33782],{"scriptlevel":2328,"displaystyle":1734},[2330,33783,33784,33786],{},[2133,33785,2281],{},[2133,33787,2352],{},[9151,33789,33790,33792,33794],{},[898,33791,1724],{},[2133,33793,2281],{},[895,33795,33796,33798,33800,33802],{},[1726,33797,2228],{},[2133,33799,2177],{},[898,33801,4661],{"mathvariant":2377},[2133,33803,2135],{},[9151,33805,33806,33808,33810],{},[898,33807,1724],{},[2133,33809,2135],{},[895,33811,33812,33814,33816],{},[2133,33813,2281],{},[898,33815,4661],{"mathvariant":2377},[2133,33817,2135],{},[902,33819,33820],{"encoding":904},"U''_{11} = -\\tfrac{1}{4} Q_1^{-3\u002F2} Q_2^{1\u002F2}",[883,33822,33824],{"className":33823},[886],[888,33825,33826],{"xmlns":890},[892,33827,33828,33884],{},[895,33829,33830,33842,33844,33846,33854,33868],{},[9151,33831,33832,33834,33836],{},[898,33833,900],{},[2133,33835,32527],{},[895,33837,33838,33840],{},[1726,33839,2379],{"mathvariant":2377},[1726,33841,2379],{"mathvariant":2377},[1726,33843,1728],{},[1726,33845,2228],{},[2326,33847,33848],{"scriptlevel":2328,"displaystyle":1734},[2330,33849,33850,33852],{},[2133,33851,2281],{},[2133,33853,2352],{},[9151,33855,33856,33858,33860],{},[898,33857,1724],{},[2133,33859,2281],{},[895,33861,33862,33864,33866],{},[2133,33863,2281],{},[898,33865,4661],{"mathvariant":2377},[2133,33867,2135],{},[9151,33869,33870,33872,33874],{},[898,33871,1724],{},[2133,33873,2135],{},[895,33875,33876,33878,33880,33882],{},[1726,33877,2228],{},[2133,33879,2177],{},[898,33881,4661],{"mathvariant":2377},[2133,33883,2135],{},[902,33885,33886],{"encoding":904},"U''_{22} = -\\tfrac{1}{4} Q_1^{1\u002F2} Q_2^{-3\u002F2}",[883,33888,33890],{"className":33889},[886],[888,33891,33892],{"xmlns":890},[892,33893,33894,33950],{},[895,33895,33896,33908,33910,33918,33934],{},[9151,33897,33898,33900,33902],{},[898,33899,900],{},[2133,33901,3506],{},[895,33903,33904,33906],{},[1726,33905,2379],{"mathvariant":2377},[1726,33907,2379],{"mathvariant":2377},[1726,33909,1728],{},[2326,33911,33912],{"scriptlevel":2328,"displaystyle":1734},[2330,33913,33914,33916],{},[2133,33915,2281],{},[2133,33917,2352],{},[9151,33919,33920,33922,33924],{},[898,33921,1724],{},[2133,33923,2281],{},[895,33925,33926,33928,33930,33932],{},[1726,33927,2228],{},[2133,33929,2281],{},[898,33931,4661],{"mathvariant":2377},[2133,33933,2135],{},[9151,33935,33936,33938,33940],{},[898,33937,1724],{},[2133,33939,2135],{},[895,33941,33942,33944,33946,33948],{},[1726,33943,2228],{},[2133,33945,2281],{},[898,33947,4661],{"mathvariant":2377},[2133,33949,2135],{},[902,33951,33952],{"encoding":904},"U''_{12} = \\tfrac{1}{4} Q_1^{-1\u002F2} Q_2^{-1\u002F2}",". Po dosazení ",[883,33955,33957],{"className":33956},[886],[888,33958,33959],{"xmlns":890},[892,33960,33961,33988],{},[895,33962,33963,33965,33967,33969,33971,33973,33975,33977,33979,33981,33984,33986],{},[898,33964,1731],{},[1726,33966,1735],{"stretchy":1734},[2133,33968,2352],{},[1726,33970,1742],{"separator":1741},[2133,33972,2281],{},[1726,33974,1742],{"separator":1741},[2133,33976,2281],{},[1726,33978,1762],{"stretchy":1734},[1726,33980,1728],{},[2133,33982,33983],{},"0,28125",[1726,33985,3405],{},[2133,33987,2328],{},[902,33989,33990],{"encoding":904},"D(4, 1, 1) = 0{,}28125 > 0"," — v bodě ",[883,33993,33995],{"className":33994},[886],[888,33996,33997],{"xmlns":890},[892,33998,33999,34011],{},[895,34000,34001,34003,34005,34007,34009],{},[1726,34002,2487],{"stretchy":1734},[2133,34004,2352],{},[1726,34006,1742],{"separator":1741},[2133,34008,2281],{},[1726,34010,2502],{"stretchy":1734},[902,34012,34013],{"encoding":904},"[4, 1]"," je vázané ",[38,34016,3772],{},[115,34018,34020],{"id":34019},"poptávka-minimalizující-výdaje-hicksova","Poptávka minimalizující výdaje (Hicksova)",[724,34022,34023],{},"Obecně:",[883,34025,34027],{"className":34026},[886],[888,34028,34029],{"xmlns":890,"display":28047},[892,34030,34031,34126],{},[20735,34032,34033],{"width":28052},[20740,34034,34035,34037,34119,34121],{},[20743,34036],{"width":28057},[20743,34038,34039],{},[895,34040,34041,34047,34049,34055,34057,34063,34065,34071,34073,34075,34077,34079,34081,34087,34089,34095,34097,34103,34105,34111,34113,34115,34117],{},[2275,34042,34043,34045],{},[898,34044,1724],{},[2133,34046,2281],{},[1726,34048,1728],{},[2275,34050,34051,34053],{},[898,34052,1731],{},[2133,34054,2281],{},[1726,34056,1735],{"stretchy":1734},[2275,34058,34059,34061],{},[898,34060,1738],{},[2133,34062,2281],{},[1726,34064,1742],{"separator":1741},[2275,34066,34067,34069],{},[898,34068,1738],{},[2133,34070,2135],{},[1726,34072,1742],{"separator":1741},[898,34074,900],{},[1726,34076,1762],{"stretchy":1734},[1726,34078,1742],{"separator":1741},[5865,34080],{"width":15270},[2275,34082,34083,34085],{},[898,34084,1724],{},[2133,34086,2135],{},[1726,34088,1728],{},[2275,34090,34091,34093],{},[898,34092,1731],{},[2133,34094,2135],{},[1726,34096,1735],{"stretchy":1734},[2275,34098,34099,34101],{},[898,34100,1738],{},[2133,34102,2281],{},[1726,34104,1742],{"separator":1741},[2275,34106,34107,34109],{},[898,34108,1738],{},[2133,34110,2135],{},[1726,34112,1742],{"separator":1741},[898,34114,900],{},[1726,34116,1762],{"stretchy":1734},[1726,34118,1742],{"separator":1741},[20743,34120],{"width":28057},[20743,34122,34123],{},[2289,34124,34125],{},"(6.27)",[902,34127,34128],{"encoding":904},"Q_1 = D_1(P_1, P_2, U), \\quad Q_2 = D_2(P_1, P_2, U), \\tag{6.27}",[883,34130,34132],{"className":34131},[886],[888,34133,34134],{"xmlns":890,"display":28047},[892,34135,34136,34183],{},[20735,34137,34138],{"width":28052},[20740,34139,34140,34142,34176,34178],{},[20743,34141],{"width":28057},[20743,34143,34144],{},[895,34145,34146,34148,34150,34152,34154,34160,34162,34168,34170,34172,34174],{},[898,34147,16425],{},[1726,34149,1728],{},[898,34151,16425],{},[1726,34153,1735],{"stretchy":1734},[2275,34155,34156,34158],{},[898,34157,1738],{},[2133,34159,2281],{},[1726,34161,1742],{"separator":1741},[2275,34163,34164,34166],{},[898,34165,1738],{},[2133,34167,2135],{},[1726,34169,1742],{"separator":1741},[898,34171,900],{},[1726,34173,1762],{"stretchy":1734},[898,34175,1888],{"mathvariant":2377},[20743,34177],{"width":28057},[20743,34179,34180],{},[2289,34181,34182],{},"(6.28)",[902,34184,34185],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, U). \\tag{6.28}",[724,34187,34188,34189,1777,34192,34205,34206,34219],{},"Hicksova poptávka závisí na ",[38,34190,34191],{},"hladině užitečnosti",[883,34193,34195],{"className":34194},[886],[888,34196,34197],{"xmlns":890},[892,34198,34199,34203],{},[895,34200,34201],{},[898,34202,900],{},[902,34204,900],{"encoding":904}," (nikoli na důchodu ",[883,34207,34209],{"className":34208},[886],[888,34210,34211],{"xmlns":890},[892,34212,34213,34217],{},[895,34214,34215],{},[898,34216,1745],{},[902,34218,1745],{"encoding":904}," jako u Marshallovy). Fyzická interpretace: jaké množství zboží koupit při daných cenách, abych dosáhl předem stanovené úrovně uspokojení s minimálními výdaji.",[115,34221,34223,34224],{"id":34222},"příklad-68-obecné-odvození-pro-uq112q212u-q_112-q_212","Příklad 6.8 — obecné odvození pro ",[883,34225,34227],{"className":34226},[886],[888,34228,34229],{"xmlns":890},[892,34230,34231,34265],{},[895,34232,34233,34235,34237,34251],{},[898,34234,900],{},[1726,34236,1728],{},[9151,34238,34239,34241,34243],{},[898,34240,1724],{},[2133,34242,2281],{},[895,34244,34245,34247,34249],{},[2133,34246,2281],{},[898,34248,4661],{"mathvariant":2377},[2133,34250,2135],{},[9151,34252,34253,34255,34257],{},[898,34254,1724],{},[2133,34256,2135],{},[895,34258,34259,34261,34263],{},[2133,34260,2281],{},[898,34262,4661],{"mathvariant":2377},[2133,34264,2135],{},[902,34266,33140],{"encoding":904},[724,34268,34269,34299],{},[883,34270,34272],{"className":34271},[886],[888,34273,34274],{"xmlns":890},[892,34275,34276,34296],{},[895,34277,34278,34284,34286,34292,34294],{},[2275,34279,34280,34282],{},[898,34281,1738],{},[2133,34283,2281],{},[1726,34285,1742],{"separator":1741},[2275,34287,34288,34290],{},[898,34289,1738],{},[2133,34291,2135],{},[1726,34293,1742],{"separator":1741},[898,34295,900],{},[902,34297,34298],{"encoding":904},"P_1, P_2, U"," jsou parametry. Lagrangeova funkce:",[883,34301,34303],{"className":34302},[886],[888,34304,34305],{"xmlns":890,"display":28047},[892,34306,34307,34381],{},[895,34308,34309,34311,34313,34319,34325,34327,34333,34339,34341,34343,34345,34347,34349,34363,34377,34379],{},[898,34310,9779],{"mathvariant":28529},[1726,34312,1728],{},[2275,34314,34315,34317],{},[898,34316,1738],{},[2133,34318,2281],{},[2275,34320,34321,34323],{},[898,34322,1724],{},[2133,34324,2281],{},[1726,34326,2099],{},[2275,34328,34329,34331],{},[898,34330,1738],{},[2133,34332,2135],{},[2275,34334,34335,34337],{},[898,34336,1724],{},[2133,34338,2135],{},[1726,34340,2099],{},[898,34342,16425],{},[1726,34344,1735],{"stretchy":1734},[898,34346,900],{},[1726,34348,2228],{},[9151,34350,34351,34353,34355],{},[898,34352,1724],{},[2133,34354,2281],{},[895,34356,34357,34359,34361],{},[2133,34358,2281],{},[898,34360,4661],{"mathvariant":2377},[2133,34362,2135],{},[9151,34364,34365,34367,34369],{},[898,34366,1724],{},[2133,34368,2135],{},[895,34370,34371,34373,34375],{},[2133,34372,2281],{},[898,34374,4661],{"mathvariant":2377},[2133,34376,2135],{},[1726,34378,1762],{"stretchy":1734},[898,34380,1888],{"mathvariant":2377},[902,34382,34383],{"encoding":904},"\\mathcal{L} = P_1 Q_1 + P_2 Q_2 + \\lambda(U - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,34385,30412],{},[883,34387,34389],{"className":34388},[886],[888,34390,34391],{"xmlns":890,"display":28047},[892,34392,34393,34615],{},[20735,34394,34395,34475,34555],{"rowspacing":20737,"columnalign":20738,"columnspacing":2378},[20740,34396,34397,34409],{},[20743,34398,34399],{},[2326,34400,34401],{"scriptlevel":2328,"displaystyle":1741},[9151,34402,34403,34405,34407],{},[898,34404,9779],{"mathvariant":28529},[2133,34406,2281],{},[1726,34408,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[20743,34410,34411],{},[2326,34412,34413],{"scriptlevel":2328,"displaystyle":1741},[895,34414,34415,34417,34419,34425,34427,34429,34431,34439,34455,34469,34471,34473],{},[895,34416],{},[1726,34418,1728],{},[2275,34420,34421,34423],{},[898,34422,1738],{},[2133,34424,2281],{},[1726,34426,2228],{},[898,34428,16425],{},[1726,34430,3174],{},[2326,34432,34433],{"scriptlevel":2328,"displaystyle":1734},[2330,34434,34435,34437],{},[2133,34436,2281],{},[2133,34438,2135],{},[9151,34440,34441,34443,34445],{},[898,34442,1724],{},[2133,34444,2281],{},[895,34446,34447,34449,34451,34453],{},[1726,34448,2228],{},[2133,34450,2281],{},[898,34452,4661],{"mathvariant":2377},[2133,34454,2135],{},[9151,34456,34457,34459,34461],{},[898,34458,1724],{},[2133,34460,2135],{},[895,34462,34463,34465,34467],{},[2133,34464,2281],{},[898,34466,4661],{"mathvariant":2377},[2133,34468,2135],{},[1726,34470,1728],{},[2133,34472,2328],{},[1726,34474,1742],{"separator":1741},[20740,34476,34477,34489],{},[20743,34478,34479],{},[2326,34480,34481],{"scriptlevel":2328,"displaystyle":1741},[9151,34482,34483,34485,34487],{},[898,34484,9779],{"mathvariant":28529},[2133,34486,2135],{},[1726,34488,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[20743,34490,34491],{},[2326,34492,34493],{"scriptlevel":2328,"displaystyle":1741},[895,34494,34495,34497,34499,34505,34507,34509,34511,34519,34533,34549,34551,34553],{},[895,34496],{},[1726,34498,1728],{},[2275,34500,34501,34503],{},[898,34502,1738],{},[2133,34504,2135],{},[1726,34506,2228],{},[898,34508,16425],{},[1726,34510,3174],{},[2326,34512,34513],{"scriptlevel":2328,"displaystyle":1734},[2330,34514,34515,34517],{},[2133,34516,2281],{},[2133,34518,2135],{},[9151,34520,34521,34523,34525],{},[898,34522,1724],{},[2133,34524,2281],{},[895,34526,34527,34529,34531],{},[2133,34528,2281],{},[898,34530,4661],{"mathvariant":2377},[2133,34532,2135],{},[9151,34534,34535,34537,34539],{},[898,34536,1724],{},[2133,34538,2135],{},[895,34540,34541,34543,34545,34547],{},[1726,34542,2228],{},[2133,34544,2281],{},[898,34546,4661],{"mathvariant":2377},[2133,34548,2135],{},[1726,34550,1728],{},[2133,34552,2328],{},[1726,34554,1742],{"separator":1741},[20740,34556,34557,34569],{},[20743,34558,34559],{},[2326,34560,34561],{"scriptlevel":2328,"displaystyle":1741},[9151,34562,34563,34565,34567],{},[898,34564,9779],{"mathvariant":28529},[898,34566,16425],{},[1726,34568,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[20743,34570,34571],{},[2326,34572,34573],{"scriptlevel":2328,"displaystyle":1741},[895,34574,34575,34577,34579,34581,34583,34597,34611,34613],{},[895,34576],{},[1726,34578,1728],{},[898,34580,900],{},[1726,34582,2228],{},[9151,34584,34585,34587,34589],{},[898,34586,1724],{},[2133,34588,2281],{},[895,34590,34591,34593,34595],{},[2133,34592,2281],{},[898,34594,4661],{"mathvariant":2377},[2133,34596,2135],{},[9151,34598,34599,34601,34603],{},[898,34600,1724],{},[2133,34602,2135],{},[895,34604,34605,34607,34609],{},[2133,34606,2281],{},[898,34608,4661],{"mathvariant":2377},[2133,34610,2135],{},[1726,34612,1728],{},[2133,34614,12446],{},[902,34616,34617],{"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}",[724,34619,34620,34621,34691,34692,34750],{},"Podílem rovnic: ",[883,34622,34624],{"className":34623},[886],[888,34625,34626],{"xmlns":890},[892,34627,34628,34688],{},[895,34629,34630,34636,34638,34644,34646,34652,34654,34660,34662,34668,34674,34676,34682],{},[2275,34631,34632,34634],{},[898,34633,1738],{},[2133,34635,2281],{},[898,34637,4661],{"mathvariant":2377},[2275,34639,34640,34642],{},[898,34641,1738],{},[2133,34643,2135],{},[1726,34645,1728],{},[2275,34647,34648,34650],{},[898,34649,1724],{},[2133,34651,2135],{},[898,34653,4661],{"mathvariant":2377},[2275,34655,34656,34658],{},[898,34657,1724],{},[2133,34659,2281],{},[1726,34661,3977],{},[2275,34663,34664,34666],{},[898,34665,1738],{},[2133,34667,2281],{},[2275,34669,34670,34672],{},[898,34671,1724],{},[2133,34673,2281],{},[1726,34675,1728],{},[2275,34677,34678,34680],{},[898,34679,1738],{},[2133,34681,2135],{},[2275,34683,34684,34686],{},[898,34685,1724],{},[2133,34687,2135],{},[902,34689,34690],{"encoding":904},"P_1\u002FP_2 = Q_2\u002FQ_1 \\Rightarrow P_1 Q_1 = P_2 Q_2",", tedy celkové výdaje ",[883,34693,34695],{"className":34694},[886],[888,34696,34697],{"xmlns":890},[892,34698,34699,34747],{},[895,34700,34701,34703,34705,34711,34717,34719,34725,34731,34733,34735,34741],{},[898,34702,4240],{},[1726,34704,1728],{},[2275,34706,34707,34709],{},[898,34708,1738],{},[2133,34710,2281],{},[2275,34712,34713,34715],{},[898,34714,1724],{},[2133,34716,2281],{},[1726,34718,2099],{},[2275,34720,34721,34723],{},[898,34722,1738],{},[2133,34724,2135],{},[2275,34726,34727,34729],{},[898,34728,1724],{},[2133,34730,2135],{},[1726,34732,1728],{},[2133,34734,2135],{},[2275,34736,34737,34739],{},[898,34738,1738],{},[2133,34740,2281],{},[2275,34742,34743,34745],{},[898,34744,1724],{},[2133,34746,2281],{},[902,34748,34749],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2 = 2 P_1 Q_1",". Odtud",[883,34752,34754],{"className":34753},[886],[888,34755,34756],{"xmlns":890,"display":28047},[892,34757,34758,34825],{},[20735,34759,34760],{"width":28052},[20740,34761,34762,34764,34818,34820],{},[20743,34763],{"width":28057},[20743,34765,34766],{},[895,34767,34768,34774,34776,34790,34792,34794,34800,34802,34816],{},[2275,34769,34770,34772],{},[898,34771,1724],{},[2133,34773,2281],{},[1726,34775,1728],{},[2330,34777,34778,34780],{},[898,34779,4240],{},[895,34781,34782,34784],{},[2133,34783,2135],{},[2275,34785,34786,34788],{},[898,34787,1738],{},[2133,34789,2281],{},[1726,34791,1742],{"separator":1741},[5865,34793],{"width":15270},[2275,34795,34796,34798],{},[898,34797,1724],{},[2133,34799,2135],{},[1726,34801,1728],{},[2330,34803,34804,34806],{},[898,34805,4240],{},[895,34807,34808,34810],{},[2133,34809,2135],{},[2275,34811,34812,34814],{},[898,34813,1738],{},[2133,34815,2135],{},[898,34817,1888],{"mathvariant":2377},[20743,34819],{"width":28057},[20743,34821,34822],{},[2289,34823,34824],{},"(6.29)",[902,34826,34827],{"encoding":904},"Q_1 = \\frac{E}{2 P_1}, \\quad Q_2 = \\frac{E}{2 P_2}. \\tag{6.29}",[724,34829,34830,34831,17558,34913,34949],{},"Ze třetí rovnice ",[883,34832,34834],{"className":34833},[886],[888,34835,34836],{"xmlns":890},[892,34837,34838,34910],{},[895,34839,34840,34842,34844,34882,34884],{},[898,34841,900],{},[1726,34843,1728],{},[8103,34845,34846],{},[895,34847,34848,34864,34866],{},[2326,34849,34850],{"scriptlevel":2328,"displaystyle":1734},[2330,34851,34852,34854],{},[898,34853,4240],{},[895,34855,34856,34858],{},[2133,34857,2135],{},[2275,34859,34860,34862],{},[898,34861,1738],{},[2133,34863,2281],{},[1726,34865,3174],{},[2326,34867,34868],{"scriptlevel":2328,"displaystyle":1734},[2330,34869,34870,34872],{},[898,34871,4240],{},[895,34873,34874,34876],{},[2133,34875,2135],{},[2275,34877,34878,34880],{},[898,34879,1738],{},[2133,34881,2135],{},[1726,34883,1728],{},[2326,34885,34886],{"scriptlevel":2328,"displaystyle":1734},[2330,34887,34888,34890],{},[898,34889,4240],{},[895,34891,34892,34894],{},[2133,34893,2135],{},[8103,34895,34896],{},[895,34897,34898,34904],{},[2275,34899,34900,34902],{},[898,34901,1738],{},[2133,34903,2281],{},[2275,34905,34906,34908],{},[898,34907,1738],{},[2133,34909,2135],{},[902,34911,34912],{"encoding":904},"U = \\sqrt{\\tfrac{E}{2 P_1} \\cdot \\tfrac{E}{2 P_2}} = \\tfrac{E}{2\\sqrt{P_1 P_2}}",[883,34914,34916],{"className":34915},[886],[888,34917,34918],{"xmlns":890},[892,34919,34920,34946],{},[895,34921,34922,34924,34926,34928,34930],{},[898,34923,4240],{},[1726,34925,1728],{},[2133,34927,2135],{},[898,34929,900],{},[8103,34931,34932],{},[895,34933,34934,34940],{},[2275,34935,34936,34938],{},[898,34937,1738],{},[2133,34939,2281],{},[2275,34941,34942,34944],{},[898,34943,1738],{},[2133,34945,2135],{},[902,34947,34948],{"encoding":904},"E = 2 U \\sqrt{P_1 P_2}",". Dosazením:",[883,34951,34953],{"className":34952},[886],[888,34954,34955],{"xmlns":890,"display":28047},[892,34956,34957,35102],{},[20735,34958,34959],{"width":28052},[20740,34960,34961,34963,35095,35097],{},[20743,34962],{"width":28057},[20743,34964,34965],{},[12818,34966,34967],{"notation":12820},[2326,34968,34969],{"scriptlevel":2328,"displaystyle":1734},[2326,34970,34971],{"scriptlevel":2328,"displaystyle":1734},[2326,34972,34973],{"scriptlevel":2328,"displaystyle":1741},[895,34974,34975,34977,34983,34985,34987,35003,35005,35011,35013,35019,35021,35027,35029,35031,35033,35035,35037,35043,35045,35047,35063,35065,35071,35073,35079,35081,35087,35089,35091,35093],{},[2289,34976,3974],{},[2275,34978,34979,34981],{},[898,34980,1724],{},[2133,34982,2281],{},[1726,34984,1728],{},[898,34986,900],{},[8103,34988,34989],{},[2330,34990,34991,34997],{},[2275,34992,34993,34995],{},[898,34994,1738],{},[2133,34996,2135],{},[2275,34998,34999,35001],{},[898,35000,1738],{},[2133,35002,2281],{},[1726,35004,1728],{},[2275,35006,35007,35009],{},[898,35008,1731],{},[2133,35010,2281],{},[1726,35012,1735],{"stretchy":1734},[2275,35014,35015,35017],{},[898,35016,1738],{},[2133,35018,2281],{},[1726,35020,1742],{"separator":1741},[2275,35022,35023,35025],{},[898,35024,1738],{},[2133,35026,2135],{},[1726,35028,1742],{"separator":1741},[898,35030,900],{},[1726,35032,1762],{"stretchy":1734},[1726,35034,1742],{"separator":1741},[5865,35036],{"width":15270},[2275,35038,35039,35041],{},[898,35040,1724],{},[2133,35042,2135],{},[1726,35044,1728],{},[898,35046,900],{},[8103,35048,35049],{},[2330,35050,35051,35057],{},[2275,35052,35053,35055],{},[898,35054,1738],{},[2133,35056,2281],{},[2275,35058,35059,35061],{},[898,35060,1738],{},[2133,35062,2135],{},[1726,35064,1728],{},[2275,35066,35067,35069],{},[898,35068,1731],{},[2133,35070,2135],{},[1726,35072,1735],{"stretchy":1734},[2275,35074,35075,35077],{},[898,35076,1738],{},[2133,35078,2281],{},[1726,35080,1742],{"separator":1741},[2275,35082,35083,35085],{},[898,35084,1738],{},[2133,35086,2135],{},[1726,35088,1742],{"separator":1741},[898,35090,900],{},[1726,35092,1762],{"stretchy":1734},[2289,35094,3974],{},[20743,35096],{"width":28057},[20743,35098,35099],{},[2289,35100,35101],{},"(6.30)",[902,35103,35104],{"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}",[115,35106,35108],{"id":35107},"vztah-primární-a-duální-úlohy","Vztah primární a duální úlohy",[724,35110,35111,35112,35125,35126,35143,35144,35157,35158,35175,35176,35179,35180,35219,35220,35249],{},"Primární (max ",[883,35113,35115],{"className":35114},[886],[888,35116,35117],{"xmlns":890},[892,35118,35119,35123],{},[895,35120,35121],{},[898,35122,900],{},[902,35124,900],{"encoding":904}," při rozpočtu ",[883,35127,35129],{"className":35128},[886],[888,35130,35131],{"xmlns":890},[892,35132,35133,35141],{},[895,35134,35135],{},[2128,35136,35137,35139],{},[898,35138,1745],{},[1726,35140,4342],{},[902,35142,28009],{"encoding":904},") a duální (min ",[883,35145,35147],{"className":35146},[886],[888,35148,35149],{"xmlns":890},[892,35150,35151,35155],{},[895,35152,35153],{},[898,35154,4240],{},[902,35156,4240],{"encoding":904}," při užitečnosti ",[883,35159,35161],{"className":35160},[886],[888,35162,35163],{"xmlns":890},[892,35164,35165,35173],{},[895,35166,35167],{},[2128,35168,35169,35171],{},[898,35170,900],{},[1726,35172,4342],{},[902,35174,27943],{"encoding":904},") úloha jsou ",[38,35177,35178],{},"ekvivalentní",": mají tentýž bod optima ",[883,35181,35183],{"className":35182},[886],[888,35184,35185],{"xmlns":890},[892,35186,35187,35217],{},[895,35188,35189,35195,35197,35205,35207,35215],{},[2128,35190,35191,35193],{},[898,35192,1724],{},[1726,35194,4342],{},[1726,35196,2487],{"stretchy":1734},[9151,35198,35199,35201,35203],{},[898,35200,1724],{},[2133,35202,2281],{},[1726,35204,4342],{},[1726,35206,1742],{"separator":1741},[9151,35208,35209,35211,35213],{},[898,35210,1724],{},[2133,35212,2135],{},[1726,35214,4342],{},[1726,35216,2502],{"stretchy":1734},[902,35218,28308],{"encoding":904}," a v obou platí ",[883,35221,35223],{"className":35222},[886],[888,35224,35225],{"xmlns":890},[892,35226,35227,35247],{},[895,35228,35229,35231,35233,35239,35241],{},[2289,35230,10587],{},[1726,35232,1728],{},[2275,35234,35235,35237],{},[898,35236,1738],{},[2133,35238,2281],{},[898,35240,4661],{"mathvariant":2377},[2275,35242,35243,35245],{},[898,35244,1738],{},[2133,35246,2135],{},[902,35248,27979],{"encoding":904},". Rozdíl je v tom, která veličina je zadána a která se optimalizuje:",[724,35251,35252],{},[1647,35253],{"alt":35254,"className":35255,"src":35256},"imek-primarni-vs-dualni",[210,1651],"\u002Fwiki-assets\u002Fimek-primarni-vs-dualni.jpeg",[120,35258,35259,35370],{},[123,35260,35261,35264,35265,35278,35279,35319,35320,1888],{},[38,35262,35263],{},"Primární"," (Marshall): zadáno ",[883,35266,35268],{"className":35267},[886],[888,35269,35270],{"xmlns":890},[892,35271,35272,35276],{},[895,35273,35274],{},[898,35275,1745],{},[902,35277,1745],{"encoding":904},", hledáme maximální ",[883,35280,35282],{"className":35281},[886],[888,35283,35284],{"xmlns":890},[892,35285,35286,35316],{},[895,35287,35288,35294,35296,35302,35304,35310,35312,35314],{},[2128,35289,35290,35292],{},[898,35291,900],{},[1726,35293,4342],{},[1726,35295,1735],{"stretchy":1734},[2275,35297,35298,35300],{},[898,35299,1738],{},[2133,35301,2281],{},[1726,35303,1742],{"separator":1741},[2275,35305,35306,35308],{},[898,35307,1738],{},[2133,35309,2135],{},[1726,35311,1742],{"separator":1741},[898,35313,1745],{},[1726,35315,1762],{"stretchy":1734},[902,35317,35318],{"encoding":904},"U^*(P_1, P_2, Y)"," a poptávku ",[883,35321,35323],{"className":35322},[886],[888,35324,35325],{"xmlns":890},[892,35326,35327,35367],{},[895,35328,35329,35335,35337,35345,35347,35353,35355,35361,35363,35365],{},[2275,35330,35331,35333],{},[898,35332,1724],{},[898,35334,17772],{},[1726,35336,1728],{},[9151,35338,35339,35341,35343],{},[898,35340,1731],{},[898,35342,17772],{},[898,35344,2815],{},[1726,35346,1735],{"stretchy":1734},[2275,35348,35349,35351],{},[898,35350,1738],{},[2133,35352,2281],{},[1726,35354,1742],{"separator":1741},[2275,35356,35357,35359],{},[898,35358,1738],{},[2133,35360,2135],{},[1726,35362,1742],{"separator":1741},[898,35364,1745],{},[1726,35366,1762],{"stretchy":1734},[902,35368,35369],{"encoding":904},"Q_i = D_i^M(P_1, P_2, Y)",[123,35371,35372,35375,35376,35389,35390,35319,35430,1888],{},[38,35373,35374],{},"Duální"," (Hicks): zadáno ",[883,35377,35379],{"className":35378},[886],[888,35380,35381],{"xmlns":890},[892,35382,35383,35387],{},[895,35384,35385],{},[898,35386,900],{},[902,35388,900],{"encoding":904},", hledáme minimální ",[883,35391,35393],{"className":35392},[886],[888,35394,35395],{"xmlns":890},[892,35396,35397,35427],{},[895,35398,35399,35405,35407,35413,35415,35421,35423,35425],{},[2128,35400,35401,35403],{},[898,35402,4240],{},[1726,35404,4342],{},[1726,35406,1735],{"stretchy":1734},[2275,35408,35409,35411],{},[898,35410,1738],{},[2133,35412,2281],{},[1726,35414,1742],{"separator":1741},[2275,35416,35417,35419],{},[898,35418,1738],{},[2133,35420,2135],{},[1726,35422,1742],{"separator":1741},[898,35424,900],{},[1726,35426,1762],{"stretchy":1734},[902,35428,35429],{"encoding":904},"E^*(P_1, P_2, U)",[883,35431,35433],{"className":35432},[886],[888,35434,35435],{"xmlns":890},[892,35436,35437,35478],{},[895,35438,35439,35445,35447,35456,35458,35464,35466,35472,35474,35476],{},[2275,35440,35441,35443],{},[898,35442,1724],{},[898,35444,17772],{},[1726,35446,1728],{},[9151,35448,35449,35451,35453],{},[898,35450,1731],{},[898,35452,17772],{},[898,35454,35455],{},"H",[1726,35457,1735],{"stretchy":1734},[2275,35459,35460,35462],{},[898,35461,1738],{},[2133,35463,2281],{},[1726,35465,1742],{"separator":1741},[2275,35467,35468,35470],{},[898,35469,1738],{},[2133,35471,2135],{},[1726,35473,1742],{"separator":1741},[898,35475,900],{},[1726,35477,1762],{"stretchy":1734},[902,35479,35480],{"encoding":904},"Q_i = D_i^H(P_1, P_2, U)",[724,35482,35483,35484,35487,35488,35491],{},"Proč se studují obě? Marshallova poptávka je ",[38,35485,35486],{},"pozorovatelná"," (lze odhadnout z dat o spotřebě a důchodech), zatímco Hicksova umožňuje čistě oddělit ",[38,35489,35490],{},"substituční efekt"," změny ceny od efektu důchodového — je klíčová pro teorii blahobytu a cenové indexy.",[115,35493,35495],{"id":35494},"úlohy-k-optimalizaci","Úlohy k optimalizaci",[198,35497,35499],{"id":35498},"maximalizace-užitečnosti-a-marshallova-poptávka","Maximalizace užitečnosti a Marshallova poptávka",[724,35501,35502,35505,35506,35538,35539,35577,35578,35604],{},[38,35503,35504],{},"6.8"," Jsou dány užitečnost ",[883,35507,35509],{"className":35508},[886],[888,35510,35511],{"xmlns":890},[892,35512,35513,35535],{},[895,35514,35515,35517,35519,35527],{},[898,35516,900],{},[1726,35518,1728],{},[9151,35520,35521,35523,35525],{},[898,35522,1724],{},[2133,35524,2281],{},[2133,35526,4996],{},[9151,35528,35529,35531,35533],{},[898,35530,1724],{},[2133,35532,2135],{},[2133,35534,4996],{},[902,35536,35537],{"encoding":904},"U = Q_1^{0{,}5} Q_2^{0{,}5}",", ceny ",[883,35540,35542],{"className":35541},[886],[888,35543,35544],{"xmlns":890},[892,35545,35546,35574],{},[895,35547,35548,35556,35558,35560,35562,35570,35572],{},[9151,35549,35550,35552,35554],{},[898,35551,1738],{},[2133,35553,2281],{},[1726,35555,4342],{},[1726,35557,1728],{},[2133,35559,2352],{},[1726,35561,1742],{"separator":1741},[9151,35563,35564,35566,35568],{},[898,35565,1738],{},[2133,35567,2135],{},[1726,35569,4342],{},[1726,35571,1728],{},[2133,35573,2860],{},[902,35575,35576],{"encoding":904},"P_1^* = 4, P_2^* = 10"," za jednotku zboží a důchod spotřebitele 200. Určete množství ",[883,35579,35581],{"className":35580},[886],[888,35582,35583],{"xmlns":890},[892,35584,35585,35601],{},[895,35586,35587,35593,35595],{},[2275,35588,35589,35591],{},[898,35590,1724],{},[2133,35592,2281],{},[1726,35594,1742],{"separator":1741},[2275,35596,35597,35599],{},[898,35598,1724],{},[2133,35600,2135],{},[902,35602,35603],{"encoding":904},"Q_1, Q_2"," maximalizující užitečnost.",[724,35606,35607,35610,35611,35653,35654,35685,35686,35708,35709,1888],{},[38,35608,35609],{},"6.9"," Jsou dány rozpočtové omezení ",[883,35612,35614],{"className":35613},[886],[888,35615,35616],{"xmlns":890},[892,35617,35618,35650],{},[895,35619,35620,35622,35624,35630,35636,35638,35644],{},[898,35621,1745],{},[1726,35623,1728],{},[2275,35625,35626,35628],{},[898,35627,1738],{},[2133,35629,2281],{},[2275,35631,35632,35634],{},[898,35633,1724],{},[2133,35635,2281],{},[1726,35637,2099],{},[2275,35639,35640,35642],{},[898,35641,1738],{},[2133,35643,2135],{},[2275,35645,35646,35648],{},[898,35647,1724],{},[2133,35649,2135],{},[902,35651,35652],{"encoding":904},"Y = P_1 Q_1 + P_2 Q_2"," a užitečnost ",[883,35655,35657],{"className":35656},[886],[888,35658,35659],{"xmlns":890},[892,35660,35661,35683],{},[895,35662,35663,35665,35667,35675],{},[898,35664,900],{},[1726,35666,1728],{},[9151,35668,35669,35671,35673],{},[898,35670,1724],{},[2133,35672,2281],{},[2133,35674,4996],{},[9151,35676,35677,35679,35681],{},[898,35678,1724],{},[2133,35680,2135],{},[2133,35682,4996],{},[902,35684,35537],{"encoding":904},". (a) Odvoďte funkce poptávky maximalizující užitečnost. (b) Najděte funkce poptávky pro důchod ",[883,35687,35689],{"className":35688},[886],[888,35690,35691],{"xmlns":890},[892,35692,35693,35705],{},[895,35694,35695,35701,35703],{},[2128,35696,35697,35699],{},[898,35698,1745],{},[1726,35700,4342],{},[1726,35702,1728],{},[2133,35704,15096],{},[902,35706,35707],{"encoding":904},"Y^* = 500",". (c) Najděte Engelovy funkce pro ceny ",[883,35710,35712],{"className":35711},[886],[888,35713,35714],{"xmlns":890},[892,35715,35716,35744],{},[895,35717,35718,35726,35728,35730,35732,35740,35742],{},[9151,35719,35720,35722,35724],{},[898,35721,1738],{},[2133,35723,2281],{},[1726,35725,4342],{},[1726,35727,1728],{},[2133,35729,2231],{},[1726,35731,1742],{"separator":1741},[9151,35733,35734,35736,35738],{},[898,35735,1738],{},[2133,35737,2135],{},[1726,35739,4342],{},[1726,35741,1728],{},[2133,35743,2860],{},[902,35745,35746],{"encoding":904},"P_1^* = 5, P_2^* = 10",[724,35748,35749,35752,35753,21575,35785,35815,35816,1888],{},[38,35750,35751],{},"6.10"," Odvoďte funkce poptávky pro Cobb-Douglasovy funkce užitečnosti ",[883,35754,35756],{"className":35755},[886],[888,35757,35758],{"xmlns":890},[892,35759,35760,35782],{},[895,35761,35762,35764,35766,35774],{},[898,35763,900],{},[1726,35765,1728],{},[9151,35767,35768,35770,35772],{},[898,35769,1724],{},[2133,35771,2281],{},[898,35773,207],{},[9151,35775,35776,35778,35780],{},[898,35777,1724],{},[2133,35779,2135],{},[898,35781,2102],{},[902,35783,35784],{"encoding":904},"U = Q_1^a Q_2^b",[883,35786,35788],{"className":35787},[886],[888,35789,35790],{"xmlns":890},[892,35791,35792,35812],{},[895,35793,35794,35796,35798,35800,35802,35804,35806,35808,35810],{},[898,35795,207],{},[1726,35797,1742],{"separator":1741},[898,35799,2102],{},[1726,35801,6493],{},[1726,35803,5311],{"stretchy":1734},[2133,35805,2328],{},[1726,35807,1742],{"separator":1741},[2133,35809,2281],{},[1726,35811,5328],{"stretchy":1734},[902,35813,35814],{"encoding":904},"a, b \\in \\langle 0, 1 \\rangle"," a rozpočtové omezení ",[883,35817,35819],{"className":35818},[886],[888,35820,35821],{"xmlns":890},[892,35822,35823,35855],{},[895,35824,35825,35827,35829,35835,35841,35843,35849],{},[898,35826,1745],{},[1726,35828,1728],{},[2275,35830,35831,35833],{},[898,35832,1738],{},[2133,35834,2281],{},[2275,35836,35837,35839],{},[898,35838,1724],{},[2133,35840,2281],{},[1726,35842,2099],{},[2275,35844,35845,35847],{},[898,35846,1738],{},[2133,35848,2135],{},[2275,35850,35851,35853],{},[898,35852,1724],{},[2133,35854,2135],{},[902,35856,35652],{"encoding":904},[724,35858,35859,35862,35863,21575,35897,35815,35915,1888],{},[38,35860,35861],{},"6.11"," Odvoďte funkce poptávky pro funkce užitečnosti CES typu ",[883,35864,35866],{"className":35865},[886],[888,35867,35868],{"xmlns":890},[892,35869,35870,35894],{},[895,35871,35872,35874,35876,35884,35886],{},[898,35873,900],{},[1726,35875,1728],{},[9151,35877,35878,35880,35882],{},[898,35879,1724],{},[2133,35881,2281],{},[898,35883,207],{},[1726,35885,2099],{},[9151,35887,35888,35890,35892],{},[898,35889,1724],{},[2133,35891,2135],{},[898,35893,207],{},[902,35895,35896],{"encoding":904},"U = Q_1^a + Q_2^a",[883,35898,35900],{"className":35899},[886],[888,35901,35902],{"xmlns":890},[892,35903,35904,35912],{},[895,35905,35906,35908,35910],{},[898,35907,207],{},[1726,35909,3368],{"mathvariant":2377},[2133,35911,2328],{},[902,35913,35914],{"encoding":904},"a \\neq 0",[883,35916,35918],{"className":35917},[886],[888,35919,35920],{"xmlns":890},[892,35921,35922,35954],{},[895,35923,35924,35926,35928,35934,35940,35942,35948],{},[898,35925,1745],{},[1726,35927,1728],{},[2275,35929,35930,35932],{},[898,35931,1738],{},[2133,35933,2281],{},[2275,35935,35936,35938],{},[898,35937,1724],{},[2133,35939,2281],{},[1726,35941,2099],{},[2275,35943,35944,35946],{},[898,35945,1738],{},[2133,35947,2135],{},[2275,35949,35950,35952],{},[898,35951,1724],{},[2133,35953,2135],{},[902,35955,35652],{"encoding":904},[198,35957,35959],{"id":35958},"minimalizace-výdajů-a-hicksova-poptávka","Minimalizace výdajů a Hicksova poptávka",[724,35961,35962,35505,35965,1343,35992,36014,36015,1343,36038,36062,36063,36088,36089,1888],{},[38,35963,35964],{},"6.12",[883,35966,35968],{"className":35967},[886],[888,35969,35970],{"xmlns":890},[892,35971,35972,35990],{},[895,35973,35974,35976,35978,35984],{},[898,35975,900],{},[1726,35977,1728],{},[2275,35979,35980,35982],{},[898,35981,1724],{},[2133,35983,2281],{},[2275,35985,35986,35988],{},[898,35987,1724],{},[2133,35989,2135],{},[902,35991,30207],{"encoding":904},[883,35993,35995],{"className":35994},[886],[888,35996,35997],{"xmlns":890},[892,35998,35999,36011],{},[895,36000,36001,36007,36009],{},[2128,36002,36003,36005],{},[898,36004,900],{},[1726,36006,4342],{},[1726,36008,1728],{},[2133,36010,2860],{},[902,36012,36013],{"encoding":904},"U^* = 10"," hladina užitečnosti a ceny ",[883,36016,36018],{"className":36017},[886],[888,36019,36020],{"xmlns":890},[892,36021,36022,36036],{},[895,36023,36024,36032,36034],{},[9151,36025,36026,36028,36030],{},[898,36027,1738],{},[2133,36029,2281],{},[1726,36031,4342],{},[1726,36033,1728],{},[2133,36035,2135],{},[902,36037,30280],{"encoding":904},[883,36039,36041],{"className":36040},[886],[888,36042,36043],{"xmlns":890},[892,36044,36045,36059],{},[895,36046,36047,36055,36057],{},[9151,36048,36049,36051,36053],{},[898,36050,1738],{},[2133,36052,2135],{},[1726,36054,4342],{},[1726,36056,1728],{},[2133,36058,2352],{},[902,36060,36061],{"encoding":904},"P_2^* = 4",". Určete množství ",[883,36064,36066],{"className":36065},[886],[888,36067,36068],{"xmlns":890},[892,36069,36070,36086],{},[895,36071,36072,36078,36080],{},[2275,36073,36074,36076],{},[898,36075,1724],{},[2133,36077,2281],{},[1726,36079,1742],{"separator":1741},[2275,36081,36082,36084],{},[898,36083,1724],{},[2133,36085,2135],{},[902,36087,35603],{"encoding":904}," minimalizující výdaje spotřebitele ",[883,36090,36092],{"className":36091},[886],[888,36093,36094],{"xmlns":890},[892,36095,36096,36116],{},[895,36097,36098,36100,36102,36108,36110],{},[898,36099,900],{},[1726,36101,1728],{},[2275,36103,36104,36106],{},[898,36105,1724],{},[2133,36107,2281],{},[1726,36109,3174],{},[2275,36111,36112,36114],{},[898,36113,1724],{},[2133,36115,2135],{},[902,36117,36118],{"encoding":904},"U = Q_1 \\cdot Q_2",[724,36120,36121,36124,36125,36166,36167,36189,36190,1888],{},[38,36122,36123],{},"6.13"," Jsou dány výdaje spotřebitele ",[883,36126,36128],{"className":36127},[886],[888,36129,36130],{"xmlns":890},[892,36131,36132,36164],{},[895,36133,36134,36136,36138,36144,36150,36152,36158],{},[898,36135,4240],{},[1726,36137,1728],{},[2275,36139,36140,36142],{},[898,36141,1738],{},[2133,36143,2281],{},[2275,36145,36146,36148],{},[898,36147,1724],{},[2133,36149,2281],{},[1726,36151,2099],{},[2275,36153,36154,36156],{},[898,36155,1738],{},[2133,36157,2135],{},[2275,36159,36160,36162],{},[898,36161,1724],{},[2133,36163,2135],{},[902,36165,27924],{"encoding":904}," a užitečnost. (a) Najděte funkce poptávky minimalizující výdaje spotřebitele. (b) Určete funkce poptávky pro užitečnost ",[883,36168,36170],{"className":36169},[886],[888,36171,36172],{"xmlns":890},[892,36173,36174,36186],{},[895,36175,36176,36182,36184],{},[2128,36177,36178,36180],{},[898,36179,900],{},[1726,36181,4342],{},[1726,36183,1728],{},[2133,36185,4991],{},[902,36187,36188],{"encoding":904},"U^* = 25"," a stanovte příslušné výdaje spotřebitele při cenách ",[883,36191,36193],{"className":36192},[886],[888,36194,36195],{"xmlns":890},[892,36196,36197,36226],{},[895,36198,36199,36207,36209,36211,36213,36221,36223],{},[9151,36200,36201,36203,36205],{},[898,36202,1738],{},[2133,36204,2281],{},[1726,36206,4342],{},[1726,36208,1728],{},[2133,36210,9021],{},[1726,36212,1742],{"separator":1741},[9151,36214,36215,36217,36219],{},[898,36216,1738],{},[2133,36218,2135],{},[1726,36220,4342],{},[1726,36222,1728],{},[2133,36224,36225],{},"15",[902,36227,36228],{"encoding":904},"P_1^* = 20, P_2^* = 15",[115,36230,1670],{"id":1669},[120,36232,36233,36290,36329,36349,36384,36438,36443,36449,36545,36590],{},[123,36234,36235,1777,36238,36287,36288,1888],{},[38,36236,36237],{},"Rozpočtové omezení (budget constraint)",[883,36239,36241],{"className":36240},[886],[888,36242,36243],{"xmlns":890},[892,36244,36245,36285],{},[895,36246,36247,36253,36255,36263,36269,36271,36279],{},[2128,36248,36249,36251],{},[898,36250,1745],{},[1726,36252,4342],{},[1726,36254,1728],{},[9151,36256,36257,36259,36261],{},[898,36258,1738],{},[2133,36260,2281],{},[1726,36262,4342],{},[2275,36264,36265,36267],{},[898,36266,1724],{},[2133,36268,2281],{},[1726,36270,2099],{},[9151,36272,36273,36275,36277],{},[898,36274,1738],{},[2133,36276,2135],{},[1726,36278,4342],{},[2275,36280,36281,36283],{},[898,36282,1724],{},[2133,36284,2135],{},[902,36286,17280],{"encoding":904}," — (6.12); ",[38,36289,28117],{},[123,36291,36292,36295,36296,1888],{},[38,36293,36294],{},"Úloha o maximalizaci užitečnosti"," (primární) — Lagrangeova funkce (6.13), soustava (6.14), podmínka optimality ",[883,36297,36299],{"className":36298},[886],[888,36300,36301],{"xmlns":890},[892,36302,36303,36327],{},[895,36304,36305,36307,36309,36317,36319],{},[2289,36306,10587],{},[1726,36308,1728],{},[9151,36310,36311,36313,36315],{},[898,36312,1738],{},[2133,36314,2281],{},[1726,36316,4342],{},[898,36318,4661],{"mathvariant":2377},[9151,36320,36321,36323,36325],{},[898,36322,1738],{},[2133,36324,2135],{},[1726,36326,4342],{},[902,36328,28960],{"encoding":904},[123,36330,36331,36346,36347,1888],{},[38,36332,29104,36333],{},[883,36334,36336],{"className":36335},[886],[888,36337,36338],{"xmlns":890},[892,36339,36340,36344],{},[895,36341,36342],{},[898,36343,16425],{},[902,36345,16478],{"encoding":904}," — stínová cena uvolnění omezení; u maximalizace ",[38,36348,29126],{},[123,36350,36351,36354,36355,1888],{},[38,36352,36353],{},"Podmínka tečnosti"," — sklon indiferenční křivky = sklon rozpočtové přímky; ",[883,36356,36358],{"className":36357},[886],[888,36359,36360],{"xmlns":890},[892,36361,36362,36382],{},[895,36363,36364,36366,36368,36374,36376],{},[2289,36365,10587],{},[1726,36367,1728],{},[2275,36369,36370,36372],{},[898,36371,1738],{},[2133,36373,2281],{},[898,36375,4661],{"mathvariant":2377},[2275,36377,36378,36380],{},[898,36379,1738],{},[2133,36381,2135],{},[902,36383,27979],{"encoding":904},[123,36385,36386,1696,36389,36437],{},[38,36387,36388],{},"Poptávka maximalizující užitečnost (Marshallova)",[883,36390,36392],{"className":36391},[886],[888,36393,36394],{"xmlns":890},[892,36395,36396,36434],{},[895,36397,36398,36404,36406,36412,36414,36420,36422,36428,36430,36432],{},[2275,36399,36400,36402],{},[898,36401,1724],{},[898,36403,17772],{},[1726,36405,1728],{},[2275,36407,36408,36410],{},[898,36409,1731],{},[898,36411,17772],{},[1726,36413,1735],{"stretchy":1734},[2275,36415,36416,36418],{},[898,36417,1738],{},[2133,36419,2281],{},[1726,36421,1742],{"separator":1741},[2275,36423,36424,36426],{},[898,36425,1738],{},[2133,36427,2135],{},[1726,36429,1742],{"separator":1741},[898,36431,1745],{},[1726,36433,1762],{"stretchy":1734},[902,36435,36436],{"encoding":904},"Q_i = D_i(P_1, P_2, Y)"," — (6.15).",[123,36439,36440,36442],{},[38,36441,31708],{}," — poptávka jako funkce důchodu při pevných cenách.",[123,36444,36445,36448],{},[38,36446,36447],{},"Úloha o minimalizaci výdajů"," (duální) — Lagrangeova funkce (6.24), soustava (6.25), postačující podmínka (6.26).",[123,36450,36451,1696,36453,36500,36501,36544],{},[38,36452,34020],{},[883,36454,36456],{"className":36455},[886],[888,36457,36458],{"xmlns":890},[892,36459,36460,36498],{},[895,36461,36462,36468,36470,36476,36478,36484,36486,36492,36494,36496],{},[2275,36463,36464,36466],{},[898,36465,1724],{},[898,36467,17772],{},[1726,36469,1728],{},[2275,36471,36472,36474],{},[898,36473,1731],{},[898,36475,17772],{},[1726,36477,1735],{"stretchy":1734},[2275,36479,36480,36482],{},[898,36481,1738],{},[2133,36483,2281],{},[1726,36485,1742],{"separator":1741},[2275,36487,36488,36490],{},[898,36489,1738],{},[2133,36491,2135],{},[1726,36493,1742],{"separator":1741},[898,36495,900],{},[1726,36497,1762],{"stretchy":1734},[902,36499,17805],{"encoding":904}," — (6.27); obecný výsledek pro ",[883,36502,36504],{"className":36503},[886],[888,36505,36506],{"xmlns":890},[892,36507,36508,36542],{},[895,36509,36510,36512,36514,36528],{},[898,36511,900],{},[1726,36513,1728],{},[9151,36515,36516,36518,36520],{},[898,36517,1724],{},[2133,36519,2281],{},[895,36521,36522,36524,36526],{},[2133,36523,2281],{},[898,36525,4661],{"mathvariant":2377},[2133,36527,2135],{},[9151,36529,36530,36532,36534],{},[898,36531,1724],{},[2133,36533,2135],{},[895,36535,36536,36538,36540],{},[2133,36537,2281],{},[898,36539,4661],{"mathvariant":2377},[2133,36541,2135],{},[902,36543,33140],{"encoding":904},": (6.30).",[123,36546,36547,36589],{},[38,36548,36549,36550],{},"Bod dotyku ",[883,36551,36553],{"className":36552},[886],[888,36554,36555],{"xmlns":890},[892,36556,36557,36587],{},[895,36558,36559,36565,36567,36575,36577,36585],{},[2128,36560,36561,36563],{},[898,36562,1724],{},[1726,36564,4342],{},[1726,36566,2487],{"stretchy":1734},[9151,36568,36569,36571,36573],{},[898,36570,1724],{},[2133,36572,2281],{},[1726,36574,4342],{},[1726,36576,1742],{"separator":1741},[9151,36578,36579,36581,36583],{},[898,36580,1724],{},[2133,36582,2135],{},[1726,36584,4342],{},[1726,36586,2502],{"stretchy":1734},[902,36588,28308],{"encoding":904}," — řešení obou úloh; totožný pro primární i duální formulaci.",[123,36591,36592,36595,36596,36609,36610,36623],{},[38,36593,36594],{},"Dualita"," — ekvivalence max ",[883,36597,36599],{"className":36598},[886],[888,36600,36601],{"xmlns":890},[892,36602,36603,36607],{},[895,36604,36605],{},[898,36606,900],{},[902,36608,900],{"encoding":904}," a min ",[883,36611,36613],{"className":36612},[886],[888,36614,36615],{"xmlns":890},[892,36616,36617,36621],{},[895,36618,36619],{},[898,36620,4240],{},[902,36622,4240],{"encoding":904},"; Marshallova a Hicksova poptávka.",[115,36625,1899],{"id":1898},[120,36627,36628,36651,36667,36680,36691],{},[123,36629,36630,1777,36633,36636,36637,36650],{},[38,36631,36632],{},"Teorie před optimalizací:",[207,36634,880],{"className":36635,"dataFsResolvedFilePath":878,"href":879},[210]," (funkce ",[883,36638,36640],{"className":36639},[886],[888,36641,36642],{"xmlns":890},[892,36643,36644,36648],{},[895,36645,36646],{},[898,36647,900],{},[902,36649,900],{"encoding":904},", indiferenční křivky, MRCS).",[123,36652,36653,1777,36656,36659,36660,36663,36664,1888],{},[38,36654,36655],{},"Matematický aparát:",[207,36657,793],{"className":36658,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace), ",[207,36661,784],{"className":36662,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace), ",[207,36665,2358],{"className":36666,"dataFsResolvedFilePath":764,"href":765},[210],[123,36668,36669,1777,36672,36675,36676,36679],{},[38,36670,36671],{},"Paralely:",[207,36673,11072],{"className":36674,"dataFsResolvedFilePath":857,"href":858},[210]," (MRTS ↔ MRCS, izokvanty ↔ IC, Eulerova věta pro CD), ",[207,36677,11926],{"className":36678,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallova poptávka jako vstup tržního modelu).",[123,36681,36682,1777,36685,1343,36688],{},[38,36683,36684],{},"Přednášky:",[207,36686,1094],{"className":36687,"dataFsResolvedFilePath":838,"href":839},[210],[207,36689,1101],{"className":36690,"dataFsResolvedFilePath":868,"href":869},[210],[123,36692,36693,1777,36695],{},[38,36694,16188],{},[207,36696,16192],{"className":36697,"dataFsResolvedFilePath":1640,"href":1641},[210],{"title":641,"searchDepth":642,"depth":642,"links":36699},[36700,36701,36702,36707,36708,36709,36711,36714,36717,36719,36720,36722,36723,36727,36728],{"id":11991,"depth":642,"text":11992},{"id":27987,"depth":642,"text":27988},{"id":28385,"depth":642,"text":28386,"children":36703},[36704,36705],{"id":28505,"depth":649,"text":28506},{"id":29086,"depth":649,"text":36706},"Interpretace λ\\lambda — mezní užitečnost důchodu",{"id":29548,"depth":642,"text":29549},{"id":29859,"depth":642,"text":29860},{"id":30178,"depth":642,"text":36710},"Příklad 6.6 — maximalizace užitečnosti pro U=Q1Q2U = Q_1 Q_2",{"id":30951,"depth":642,"text":30952,"children":36712},[36713],{"id":31707,"depth":649,"text":31708},{"id":31887,"depth":642,"text":31888,"children":36715},[36716],{"id":32144,"depth":649,"text":32145},{"id":33095,"depth":642,"text":36718},"Příklad 6.7 — minimalizace výdajů pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":34019,"depth":642,"text":34020},{"id":34222,"depth":642,"text":36721},"Příklad 6.8 — obecné odvození pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":35107,"depth":642,"text":35108},{"id":35494,"depth":642,"text":35495,"children":36724},[36725,36726],{"id":35498,"depth":649,"text":35499},{"id":35958,"depth":649,"text":35959},{"id":1669,"depth":642,"text":1670},{"id":1898,"depth":642,"text":1899},{},"\u002Ftopics\u002Foptimalizace-spotrebitele",{"title":27748,"description":641},[1138,1137],"topics\u002Foptimalizace-spotrebitele",[1128,36735,1144,9757,36736,36737,36738],"optimalizace-spotrebitele","poptavka-spotrebitele","minimalizace-vydaju","dualita","jxXhWsWsCIcDvEqLkcWTWs-jk9CvI-eFUi2Afo7U40o",{"id":36741,"title":802,"body":36742,"course":1128,"courses":659,"created":9541,"description":641,"extension":661,"meta":50794,"navigation":664,"path":50795,"seo":50796,"sources":50797,"stem":50798,"tags":50799,"type":1950,"updated":677,"__hash__":50805},"topics\u002Ftopics\u002Fpoptavka-nabidka.md",{"type":9,"value":36743,"toc":50750},[36744,36747,36773,36777,36784,36936,36950,36953,36955,37042,37046,37082,37155,37176,37301,37311,37324,37328,37333,37363,37425,37434,37438,37500,37507,37528,37646,37724,37728,37731,37790,37905,37910,37942,38004,38052,38107,38111,38132,38156,38204,38208,38220,38224,38334,38338,38354,38395,38406,38565,38575,38580,38584,38706,38716,38723,38727,38805,38816,38896,38902,38909,39048,39055,39058,39115,39119,39197,39243,39287,39293,39406,39410,39413,39608,39612,39849,39852,40006,40159,40161,40163,40243,40246,40351,40420,40429,40433,40436,40497,40506,40510,40543,40621,40660,40664,40713,40767,40771,40800,40829,40881,40888,40942,41020,41024,41067,41134,41178,41282,41301,41303,41307,41415,41419,41487,41536,41543,41628,41632,41704,41709,41757,41946,41950,41955,42131,42136,42195,42300,42304,42331,42335,42342,42506,42593,42598,42600,42603,42703,42853,42925,42999,43001,43005,43019,43023,43156,43211,43323,43400,43404,43461,43564,43623,43784,43788,43863,43935,44033,44091,44185,44238,44259,44313,44318,44396,44444,44531,44569,44657,44810,44846,44900,44903,44905,44907,44956,44963,44971,45058,45067,45154,45161,45163,45167,45392,45394,45398,45402,45471,45522,45725,45731,45742,45810,45816,46238,46242,46306,46330,46526,46532,46546,46614,46617,46657,46881,46949,47251,47660,47737,47903,47909,47912,47987,48440,48491,48897,49002,49665,49668,49745,49753,49827,49858,49860,49864,49908,49910,49912,49916,50146,50150,50241,50246,50340,50345,50518,50522,50639,50644,50693,50695,50697],[12,36745,802],{"id":36746},"poptávka-nabídka-a-tržní-rovnováha",[3859,36748,36749],{},[724,36750,36751,36753,36754,36757,36758,36761,36762,36765,36766,36768,36769,36772],{},[883,36752,4145],{}," TL;DR\nKapitola buduje základní mikroekonomický model trhu: chování spotřebitele (",[38,36755,36756],{},"poptávka",") a výrobce (",[38,36759,36760],{},"nabídka","), jejich interakci v ",[38,36763,36764],{},"tržní rovnováze"," a kvantitativní analýzu reakce modelu na změnu exogenních proměnných (posuny, zdanění, ",[38,36767,17959],{},"). Uzavírá ji pojem ",[38,36770,36771],{},"přebytku spotřebitele a výrobce"," jako míry čistého prospěchu obou stran trhu.",[115,36774,36776],{"id":36775},"úvod-model-a-proměnné","Úvod — model a proměnné",[724,36778,36779,36780,36783],{},"Cílem je popsat chování spotřebitele a výrobce za předpokladu racionality jedince (",[614,36781,36782],{},"homo economicus","). Mezi hlavní proměnné patří:",[120,36785,36786,36803,36845,36861],{},[123,36787,36788,36789,36802],{},"cena ",[883,36790,36792],{"className":36791},[886],[888,36793,36794],{"xmlns":890},[892,36795,36796,36800],{},[895,36797,36798],{},[898,36799,1738],{},[902,36801,1738],{"encoding":904}," zkoumaného zboží,",[123,36804,36805,36806,1742],{},"ceny alternativních zboží ",[883,36807,36809],{"className":36808},[886],[888,36810,36811],{"xmlns":890},[892,36812,36813,36842],{},[895,36814,36815,36821,36823,36829,36831,36833,36835],{},[2275,36816,36817,36819],{},[898,36818,1738],{},[2133,36820,2281],{},[1726,36822,1742],{"separator":1741},[2275,36824,36825,36827],{},[898,36826,1738],{},[2133,36828,2135],{},[1726,36830,1742],{"separator":1741},[1726,36832,1759],{},[1726,36834,1742],{"separator":1741},[2275,36836,36837,36839],{},[898,36838,1738],{},[898,36840,36841],{},"n",[902,36843,36844],{"encoding":904},"P_1, P_2, \\dots, P_n",[123,36846,36847,36848,1742],{},"důchod ",[883,36849,36851],{"className":36850},[886],[888,36852,36853],{"xmlns":890},[892,36854,36855,36859],{},[895,36856,36857],{},[898,36858,1745],{},[902,36860,1745],{"encoding":904},[123,36862,36863,36864,36877,36878,36891,36892,36905,36906,36920,36921,36935],{},"preference, očekávání, populace, výrobní faktory (práce ",[883,36865,36867],{"className":36866},[886],[888,36868,36869],{"xmlns":890},[892,36870,36871,36875],{},[895,36872,36873],{},[898,36874,9779],{},[902,36876,9779],{"encoding":904},", kapitál ",[883,36879,36881],{"className":36880},[886],[888,36882,36883],{"xmlns":890},[892,36884,36885,36889],{},[895,36886,36887],{},[898,36888,9784],{},[902,36890,9784],{"encoding":904},", půda ",[883,36893,36895],{"className":36894},[886],[888,36896,36897],{"xmlns":890},[892,36898,36899,36903],{},[895,36900,36901],{},[898,36902,4240],{},[902,36904,4240],{"encoding":904},"), technologie, počet výrobců ",[883,36907,36909],{"className":36908},[886],[888,36910,36911],{"xmlns":890},[892,36912,36913,36918],{},[895,36914,36915],{},[898,36916,36917],{},"O",[902,36919,36917],{"encoding":904},", počasí ",[883,36922,36924],{"className":36923},[886],[888,36925,36926],{"xmlns":890},[892,36927,36928,36933],{},[895,36929,36930],{},[898,36931,36932],{},"W",[902,36934,36932],{"encoding":904}," atd.",[724,36937,36938,36939,36942,36943,36946,36947,1888],{},"Vybereme-li právě jeden z faktorů jako endogenní (",[614,36940,36941],{},"ceteris paribus","), hovoříme o ",[38,36944,36945],{},"jednofaktorovém modelu","; jinak jde o model ",[38,36948,36949],{},"vícefaktorový",[36951,36952],"hr",{},[115,36954,13147],{"id":36756},[3859,36956,36957],{},[724,36958,36959,36961,36962,36975,36976,36989,36990,36993,36994,37017,37018,1888],{},[883,36960,4145],{}," TL;DR\nPoptávka vyjadřuje závislost nakupovaného množství ",[883,36963,36965],{"className":36964},[886],[888,36966,36967],{"xmlns":890},[892,36968,36969,36973],{},[895,36970,36971],{},[898,36972,1724],{},[902,36974,1724],{"encoding":904}," na ceně ",[883,36977,36979],{"className":36978},[886],[888,36980,36981],{"xmlns":890},[892,36982,36983,36987],{},[895,36984,36985],{},[898,36986,1738],{},[902,36988,1738],{"encoding":904}," (případně dalších proměnných). Základní vlastností je ",[38,36991,36992],{},"zákon klesající poptávky",": při růstu ceny množství klesá. Z důvodu přehlednosti se pracuje s jednofaktorovým modelem ",[883,36995,36997],{"className":36996},[886],[888,36998,36999],{"xmlns":890},[892,37000,37001,37015],{},[895,37002,37003,37005,37007,37009,37011,37013],{},[898,37004,1724],{},[1726,37006,1728],{},[898,37008,1731],{},[1726,37010,1735],{"stretchy":1734},[898,37012,1738],{},[1726,37014,1762],{"stretchy":1734},[902,37016,1801],{"encoding":904}," a jeho lineární verzí ",[883,37019,37021],{"className":37020},[886],[888,37022,37023],{"xmlns":890},[892,37024,37025,37039],{},[895,37026,37027,37029,37031,37033,37035,37037],{},[898,37028,1738],{},[1726,37030,1728],{},[898,37032,207],{},[898,37034,1724],{},[1726,37036,2099],{},[898,37038,2102],{},[902,37040,37041],{"encoding":904},"P = aQ + b",[198,37043,37045],{"id":37044},"obecný-vícefaktorový-model","Obecný vícefaktorový model",[724,37047,37048,37049,37062,37063,37076,37077,10009,37079,3148],{},"Ve vícefaktorovém modelu uvažujeme, že poptávané množství ",[883,37050,37052],{"className":37051},[886],[888,37053,37054],{"xmlns":890},[892,37055,37056,37060],{},[895,37057,37058],{},[898,37059,1724],{},[902,37061,1724],{"encoding":904}," závisí na ceně ",[883,37064,37066],{"className":37065},[886],[888,37067,37068],{"xmlns":890},[892,37069,37070,37074],{},[895,37071,37072],{},[898,37073,1738],{},[902,37075,1738],{"encoding":904},", na cenách alternativních zboží a důchodu. Závislost vyjadřuje ",[38,37078,27983],{},[614,37080,37081],{},"demand function",[883,37083,37085],{"className":37084},[886],[888,37086,37087],{"xmlns":890,"display":28047},[892,37088,37089,37152],{},[20735,37090,37091],{"width":28052},[20740,37092,37093,37095,37145,37147],{},[20743,37094],{"width":28057},[20743,37096,37097],{},[895,37098,37099,37101,37103,37105,37107,37109,37111,37117,37119,37125,37127,37129,37131,37137,37139,37141,37143],{},[898,37100,1724],{},[1726,37102,1728],{},[898,37104,1731],{},[1726,37106,1735],{"stretchy":1734},[898,37108,1738],{},[1726,37110,1742],{"separator":1741},[2275,37112,37113,37115],{},[898,37114,1738],{},[2133,37116,2281],{},[1726,37118,1742],{"separator":1741},[2275,37120,37121,37123],{},[898,37122,1738],{},[2133,37124,2135],{},[1726,37126,1742],{"separator":1741},[1726,37128,1759],{},[1726,37130,1742],{"separator":1741},[2275,37132,37133,37135],{},[898,37134,1738],{},[898,37136,36841],{},[1726,37138,1742],{"separator":1741},[898,37140,1745],{},[1726,37142,1762],{"stretchy":1734},[898,37144,1888],{"mathvariant":2377},[20743,37146],{"width":28057},[20743,37148,37149],{},[2289,37150,37151],{},"(2.1)",[902,37153,37154],{"encoding":904},"Q = D(P, P_1, P_2, \\dots, P_n, Y). \\tag{2.1}",[724,37156,37157,37158,37161,37162,37175],{},"Důležitou vlastností je ",[38,37159,37160],{},"homogenita",": změní-li se všechny nezávisle proměnné ",[883,37163,37165],{"className":37164},[886],[888,37166,37167],{"xmlns":890},[892,37168,37169,37173],{},[895,37170,37171],{},[898,37172,12027],{},[902,37174,12027],{"encoding":904},"-krát, poptávané množství se nezmění,",[883,37177,37179],{"className":37178},[886],[888,37180,37181],{"xmlns":890,"display":28047},[892,37182,37183,37298],{},[20735,37184,37185],{"width":28052},[20740,37186,37187,37189,37291,37293],{},[20743,37188],{"width":28057},[20743,37190,37191],{},[895,37192,37193,37195,37197,37199,37201,37203,37205,37207,37209,37215,37217,37219,37225,37227,37229,37231,37233,37239,37241,37243,37245,37247,37249,37251,37253,37255,37257,37263,37265,37271,37273,37275,37277,37283,37285,37287,37289],{},[898,37194,1724],{},[1726,37196,1728],{},[898,37198,1731],{},[1726,37200,1735],{"stretchy":1734},[898,37202,12027],{},[898,37204,1738],{},[1726,37206,1742],{"separator":1741},[898,37208,12027],{},[2275,37210,37211,37213],{},[898,37212,1738],{},[2133,37214,2281],{},[1726,37216,1742],{"separator":1741},[898,37218,12027],{},[2275,37220,37221,37223],{},[898,37222,1738],{},[2133,37224,2135],{},[1726,37226,1742],{"separator":1741},[1726,37228,1759],{},[1726,37230,1742],{"separator":1741},[898,37232,12027],{},[2275,37234,37235,37237],{},[898,37236,1738],{},[898,37238,36841],{},[1726,37240,1742],{"separator":1741},[898,37242,12027],{},[898,37244,1745],{},[1726,37246,1762],{"stretchy":1734},[1726,37248,1728],{},[898,37250,1731],{},[1726,37252,1735],{"stretchy":1734},[898,37254,1738],{},[1726,37256,1742],{"separator":1741},[2275,37258,37259,37261],{},[898,37260,1738],{},[2133,37262,2281],{},[1726,37264,1742],{"separator":1741},[2275,37266,37267,37269],{},[898,37268,1738],{},[2133,37270,2135],{},[1726,37272,1742],{"separator":1741},[1726,37274,1759],{},[1726,37276,1742],{"separator":1741},[2275,37278,37279,37281],{},[898,37280,1738],{},[898,37282,36841],{},[1726,37284,1742],{"separator":1741},[898,37286,1745],{},[1726,37288,1762],{"stretchy":1734},[898,37290,1888],{"mathvariant":2377},[20743,37292],{"width":28057},[20743,37294,37295],{},[2289,37296,37297],{},"(2.2)",[902,37299,37300],{"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}",[3859,37302,37303],{},[724,37304,37305,37307,37308,1888],{},[883,37306,4400],{}," Pozor\nHomogenita platí pouze v zidealizovaném vícefaktorovém modelu; ",[38,37309,37310],{},"v jednofaktorových modelech neplatí",[724,37312,37313,37314,1343,37317,3877,37320,37323],{},"Rozlišuje se poptávka ",[38,37315,37316],{},"individuální",[38,37318,37319],{},"tržní",[38,37321,37322],{},"agregátní"," (není-li specifikováno, rozumí se tržní).",[198,37325,37327],{"id":37326},"jednofaktorové-modely","Jednofaktorové modely",[37329,37330,37332],"h4",{"id":37331},"funkce-poptávky-v-užším-slova-smyslu","Funkce poptávky v užším slova smyslu",[724,37334,37335,37336,37349,37350,2703],{},"Poptávané množství ",[883,37337,37339],{"className":37338},[886],[888,37340,37341],{"xmlns":890},[892,37342,37343,37347],{},[895,37344,37345],{},[898,37346,1724],{},[902,37348,1724],{"encoding":904}," závisí pouze na ceně ",[883,37351,37353],{"className":37352},[886],[888,37354,37355],{"xmlns":890},[892,37356,37357,37361],{},[895,37358,37359],{},[898,37360,1738],{},[902,37362,1738],{"encoding":904},[883,37364,37366],{"className":37365},[886],[888,37367,37368],{"xmlns":890,"display":28047},[892,37369,37370,37422],{},[20735,37371,37372],{"width":28052},[20740,37373,37374,37376,37415,37417],{},[20743,37375],{"width":28057},[20743,37377,37378],{},[895,37379,37380,37382,37384,37386,37388,37390,37392,37394,37396,37399,37401,37403,37405,37407,37409,37411,37413],{},[898,37381,1724],{},[1726,37383,1728],{},[898,37385,1731],{},[1726,37387,1735],{"stretchy":1734},[898,37389,1738],{},[1726,37391,1762],{"stretchy":1734},[1726,37393,1742],{"separator":1741},[5865,37395],{"width":5867},[2289,37397,37398],{},"resp.",[5865,37400],{"width":5867},[898,37402,1738],{},[1726,37404,1728],{},[898,37406,1731],{},[1726,37408,1735],{"stretchy":1734},[898,37410,1724],{},[1726,37412,1762],{"stretchy":1734},[898,37414,1888],{"mathvariant":2377},[20743,37416],{"width":28057},[20743,37418,37419],{},[2289,37420,37421],{},"(2.3)",[902,37423,37424],{"encoding":904},"Q = D(P), \\qquad \\text{resp.} \\qquad P = D(Q). \\tag{2.3}",[724,37426,37427,37428,10009,37431,1847],{},"Graf této funkce se nazývá ",[38,37429,37430],{},"křivka poptávky",[614,37432,37433],{},"demand curve",[37329,37435,37437],{"id":37436},"zákon-klesající-poptávky","Zákon klesající poptávky",[3859,37439,37440],{},[724,37441,37442],{},[38,37443,37444,37445,37458,37459,37472,37473,37458,37486,37499],{},"Roste-li cena ",[883,37446,37448],{"className":37447},[886],[888,37449,37450],{"xmlns":890},[892,37451,37452,37456],{},[895,37453,37454],{},[898,37455,1738],{},[902,37457,1738],{"encoding":904},", pak množství ",[883,37460,37462],{"className":37461},[886],[888,37463,37464],{"xmlns":890},[892,37465,37466,37470],{},[895,37467,37468],{},[898,37469,1724],{},[902,37471,1724],{"encoding":904}," klesá; klesá-li cena ",[883,37474,37476],{"className":37475},[886],[888,37477,37478],{"xmlns":890},[892,37479,37480,37484],{},[895,37481,37482],{},[898,37483,1738],{},[902,37485,1738],{"encoding":904},[883,37487,37489],{"className":37488},[886],[888,37490,37491],{"xmlns":890},[892,37492,37493,37497],{},[895,37494,37495],{},[898,37496,1724],{},[902,37498,1724],{"encoding":904}," roste.",[724,37501,37502,37503,37506],{},"Spotřebitelé jsou ochotni nakoupit větší množství za nižší cenu (mezní užitečnost — viz kap. 6). Zákon platí za ",[38,37504,37505],{},"normálních podmínek","; první kvantitativní formulaci podal Marshall (1890).",[3859,37508,37509,37514],{},[724,37510,37511,37513],{},[883,37512,4145],{}," Intuice — proč zákon platí",[120,37515,37516,37522],{},[123,37517,37518,37521],{},[38,37519,37520],{},"Substituční efekt"," — růst ceny vede ke snaze nahradit zboží jiným.",[123,37523,37524,37527],{},[38,37525,37526],{},"Důchodový efekt"," — růst ceny způsobí nevítaný úbytek reálného důchodu.",[724,37529,37530,37531,37544,37545,37558,37559,37585,37586,37612,37613,8088,37639,37642,37643,1888],{},"Každá funkce poptávky je tedy klesající. Cena ",[883,37532,37534],{"className":37533},[886],[888,37535,37536],{"xmlns":890},[892,37537,37538,37542],{},[895,37539,37540],{},[898,37541,1738],{},[902,37543,1738],{"encoding":904}," se vynáší na svislou osu, množství ",[883,37546,37548],{"className":37547},[886],[888,37549,37550],{"xmlns":890},[892,37551,37552,37556],{},[895,37553,37554],{},[898,37555,1724],{},[902,37557,1724],{"encoding":904}," na vodorovnou. Hypotetická křivka prochází body ",[883,37560,37562],{"className":37561},[886],[888,37563,37564],{"xmlns":890},[892,37565,37566,37582],{},[895,37567,37568,37570,37572,37574,37580],{},[1726,37569,2487],{"stretchy":1734},[2133,37571,2328],{},[1726,37573,1742],{"separator":1741},[2275,37575,37576,37578],{},[898,37577,1738],{},[2133,37579,2328],{},[1726,37581,2502],{"stretchy":1734},[902,37583,37584],{"encoding":904},"[0, P_0]"," (cena, při níž je zboží neprodejné) a ",[883,37587,37589],{"className":37588},[886],[888,37590,37591],{"xmlns":890},[892,37592,37593,37609],{},[895,37594,37595,37597,37603,37605,37607],{},[1726,37596,2487],{"stretchy":1734},[2275,37598,37599,37601],{},[898,37600,1724],{},[2133,37602,2328],{},[1726,37604,1742],{"separator":1741},[2133,37606,2328],{},[1726,37608,2502],{"stretchy":1734},[902,37610,37611],{"encoding":904},"[Q_0, 0]"," (teoretický objem při nulové ceně). Interval ",[883,37614,37616],{"className":37615},[886],[888,37617,37618],{"xmlns":890},[892,37619,37620,37636],{},[895,37621,37622,37624,37626,37628,37634],{},[1726,37623,1735],{"stretchy":1734},[2133,37625,2328],{},[1726,37627,1742],{"separator":1741},[2275,37629,37630,37632],{},[898,37631,1738],{},[2133,37633,2328],{},[1726,37635,1762],{"stretchy":1734},[902,37637,37638],{"encoding":904},"(0, P_0)",[38,37640,37641],{},"reálné cenové rozpětí",". Za teoretických předpokladů je křivka ",[38,37644,37645],{},"konvexní",[724,37647,37648],{},[614,37649,37650,37651,37673,37674,3877,37699,1888],{},"Obrázek 2.1: Hypotetická křivka poptávky v rovině ",[883,37652,37654],{"className":37653},[886],[888,37655,37656],{"xmlns":890},[892,37657,37658,37670],{},[895,37659,37660,37662,37664,37666,37668],{},[1726,37661,1735],{"stretchy":1734},[898,37663,1724],{},[1726,37665,1742],{"separator":1741},[898,37667,1738],{},[1726,37669,1762],{"stretchy":1734},[902,37671,37672],{"encoding":904},"(Q, P)"," — klesající, konvexní, procházející body ",[883,37675,37677],{"className":37676},[886],[888,37678,37679],{"xmlns":890},[892,37680,37681,37697],{},[895,37682,37683,37685,37687,37689,37695],{},[1726,37684,2487],{"stretchy":1734},[2133,37686,2328],{},[1726,37688,1742],{"separator":1741},[2275,37690,37691,37693],{},[898,37692,1738],{},[2133,37694,2328],{},[1726,37696,2502],{"stretchy":1734},[902,37698,37584],{"encoding":904},[883,37700,37702],{"className":37701},[886],[888,37703,37704],{"xmlns":890},[892,37705,37706,37722],{},[895,37707,37708,37710,37716,37718,37720],{},[1726,37709,2487],{"stretchy":1734},[2275,37711,37712,37714],{},[898,37713,1724],{},[2133,37715,2328],{},[1726,37717,1742],{"separator":1741},[2133,37719,2328],{},[1726,37721,2502],{"stretchy":1734},[902,37723,37611],{"encoding":904},[37329,37725,37727],{"id":37726},"lineární-model-poptávky","Lineární model poptávky",[724,37729,37730],{},"Nejjednodušší závislostí je",[883,37732,37734],{"className":37733},[886],[888,37735,37736],{"xmlns":890,"display":28047},[892,37737,37738,37787],{},[20735,37739,37740],{"width":28052},[20740,37741,37742,37744,37780,37782],{},[20743,37743],{"width":28057},[20743,37745,37746],{},[895,37747,37748,37750,37752,37754,37756,37758,37760,37762,37764,37766,37768,37770,37772,37774,37776,37778],{},[898,37749,1738],{},[1726,37751,1728],{},[898,37753,207],{},[898,37755,1724],{},[1726,37757,2099],{},[898,37759,2102],{},[1726,37761,1742],{"separator":1741},[5865,37763],{"width":5867},[898,37765,207],{},[1726,37767,3444],{},[2133,37769,2328],{},[1726,37771,1742],{"separator":1741},[2289,37773,2291],{},[898,37775,2102],{},[1726,37777,3405],{},[2133,37779,12446],{},[20743,37781],{"width":28057},[20743,37783,37784],{},[2289,37785,37786],{},"(2.4)",[902,37788,37789],{"encoding":904},"P = aQ + b, \\qquad a \u003C 0,\\ b > 0. \\tag{2.4}",[724,37791,37792,37793,21575,37829,3877,37853,8023,37879,37901,37902,1888],{},"Křivka poptávky je přímka se záporným sklonem. Alternativně ",[883,37794,37796],{"className":37795},[886],[888,37797,37798],{"xmlns":890},[892,37799,37800,37826],{},[895,37801,37802,37804,37806,37814,37816,37818],{},[898,37803,1724],{},[1726,37805,1728],{},[2326,37807,37808],{"scriptlevel":2328,"displaystyle":1734},[2330,37809,37810,37812],{},[2133,37811,2281],{},[898,37813,207],{},[898,37815,1738],{},[1726,37817,2228],{},[2326,37819,37820],{"scriptlevel":2328,"displaystyle":1734},[2330,37821,37822,37824],{},[898,37823,2102],{},[898,37825,207],{},[902,37827,37828],{"encoding":904},"Q = \\tfrac{1}{a}P - \\tfrac{b}{a}",[883,37830,37832],{"className":37831},[886],[888,37833,37834],{"xmlns":890},[892,37835,37836,37850],{},[895,37837,37838,37846,37848],{},[2326,37839,37840],{"scriptlevel":2328,"displaystyle":1734},[2330,37841,37842,37844],{},[2133,37843,2281],{},[898,37845,207],{},[1726,37847,3444],{},[2133,37849,2328],{},[902,37851,37852],{"encoding":904},"\\tfrac{1}{a} \u003C 0",[883,37854,37856],{"className":37855},[886],[888,37857,37858],{"xmlns":890},[892,37859,37860,37876],{},[895,37861,37862,37864,37872,37874],{},[1726,37863,2228],{},[2326,37865,37866],{"scriptlevel":2328,"displaystyle":1734},[2330,37867,37868,37870],{},[898,37869,2102],{},[898,37871,207],{},[1726,37873,3405],{},[2133,37875,2328],{},[902,37877,37878],{"encoding":904},"-\\tfrac{b}{a} > 0",[883,37880,37882],{"className":37881},[886],[888,37883,37884],{"xmlns":890},[892,37885,37886,37898],{},[895,37887,37888,37890,37892,37894,37896],{},[1726,37889,1735],{"stretchy":1734},[2133,37891,2328],{},[1726,37893,1742],{"separator":1741},[898,37895,2102],{},[1726,37897,1762],{"stretchy":1734},[902,37899,37900],{"encoding":904},"(0, b)",". Tento model odpovídá ",[38,37903,37904],{},"nedokonalé konkurenci",[37906,37907,37909],"h5",{"id":37908},"příklad-21","Příklad 2.1",[724,37911,37912,37915,37916,1888],{},[38,37913,37914],{},"Zadání:"," Lineární poptávka ",[883,37917,37919],{"className":37918},[886],[888,37920,37921],{"xmlns":890},[892,37922,37923,37939],{},[895,37924,37925,37927,37929,37931,37933,37935,37937],{},[898,37926,1738],{},[1726,37928,1728],{},[1726,37930,2228],{},[2133,37932,2135],{},[898,37934,1724],{},[1726,37936,2099],{},[2133,37938,3123],{},[902,37940,37941],{"encoding":904},"P = -2Q + 60",[724,37943,37944,37947,37948,37970,37971,1888],{},[38,37945,37946],{},"Řešení:"," Reálné cenové rozpětí je ",[883,37949,37951],{"className":37950},[886],[888,37952,37953],{"xmlns":890},[892,37954,37955,37967],{},[895,37956,37957,37959,37961,37963,37965],{},[1726,37958,1735],{"stretchy":1734},[2133,37960,2328],{},[1726,37962,1742],{"separator":1741},[2133,37964,3123],{},[1726,37966,1762],{"stretchy":1734},[902,37968,37969],{"encoding":904},"(0, 60)","; alternativní tvar je ",[883,37972,37974],{"className":37973},[886],[888,37975,37976],{"xmlns":890},[892,37977,37978,38001],{},[895,37979,37980,37982,37984,37986,37994,37996,37998],{},[898,37981,1724],{},[1726,37983,1728],{},[1726,37985,2228],{},[2326,37987,37988],{"scriptlevel":2328,"displaystyle":1734},[2330,37989,37990,37992],{},[2133,37991,2281],{},[2133,37993,2135],{},[898,37995,1738],{},[1726,37997,2099],{},[2133,37999,38000],{},"30",[902,38002,38003],{"encoding":904},"Q = -\\tfrac{1}{2}P + 30",[16,38005,38006,38029],{},[19,38007,38008],{},[22,38009,38010,38025,38027],{},[25,38011,38012],{},[883,38013,38015],{"className":38014},[886],[888,38016,38017],{"xmlns":890},[892,38018,38019,38023],{},[895,38020,38021],{},[898,38022,1738],{},[902,38024,1738],{"encoding":904},[25,38026,5198],{},[25,38028,9021],{},[30,38030,38031],{},[22,38032,38033,38048,38050],{},[35,38034,38035],{},[883,38036,38038],{"className":38037},[886],[888,38039,38040],{"xmlns":890},[892,38041,38042,38046],{},[895,38043,38044],{},[898,38045,1724],{},[902,38047,1724],{"encoding":904},[35,38049,2860],{},[35,38051,9021],{},[724,38053,38054],{},[614,38055,38056,38057,3877,38079,1888],{},"Obrázek 2.2 \u002F 2.3: Lineární poptávka — přímka s průsečíky ",[883,38058,38060],{"className":38059},[886],[888,38061,38062],{"xmlns":890},[892,38063,38064,38076],{},[895,38065,38066,38068,38070,38072,38074],{},[1726,38067,2487],{"stretchy":1734},[2133,38069,2328],{},[1726,38071,1742],{"separator":1741},[898,38073,2102],{},[1726,38075,2502],{"stretchy":1734},[902,38077,38078],{"encoding":904},"[0, b]",[883,38080,38082],{"className":38081},[886],[888,38083,38084],{"xmlns":890},[892,38085,38086,38104],{},[895,38087,38088,38090,38092,38094,38096,38098,38100,38102],{},[1726,38089,2487],{"stretchy":1734},[1726,38091,2228],{},[898,38093,2102],{},[898,38095,4661],{"mathvariant":2377},[898,38097,207],{},[1726,38099,1742],{"separator":1741},[2133,38101,2328],{},[1726,38103,2502],{"stretchy":1734},[902,38105,38106],{"encoding":904},"[-b\u002Fa, 0]",[37329,38108,38110],{"id":38109},"poptávka-při-dokonalé-konkurenci","Poptávka při dokonalé konkurenci",[724,38112,38113,38114,38131],{},"Přebírá-li každý účastník trhu pevnou tržní cenu ",[883,38115,38117],{"className":38116},[886],[888,38118,38119],{"xmlns":890},[892,38120,38121,38129],{},[895,38122,38123],{},[2128,38124,38125,38127],{},[898,38126,1738],{},[1726,38128,4342],{},[902,38130,4392],{"encoding":904},", je funkce poptávky konstantní:",[883,38133,38135],{"className":38134},[886],[888,38136,38137],{"xmlns":890,"display":28047},[892,38138,38139,38153],{},[895,38140,38141,38143,38145,38151],{},[898,38142,1738],{},[1726,38144,1728],{},[2128,38146,38147,38149],{},[898,38148,1738],{},[1726,38150,4342],{},[898,38152,1888],{"mathvariant":2377},[902,38154,38155],{"encoding":904},"P = P^*.",[724,38157,38158],{},[614,38159,38160,38161,38182,38183,1888],{},"Obrázek 2.4: Vodorovná přímka v rovině ",[883,38162,38164],{"className":38163},[886],[888,38165,38166],{"xmlns":890},[892,38167,38168,38180],{},[895,38169,38170,38172,38174,38176,38178],{},[1726,38171,1735],{"stretchy":1734},[898,38173,1724],{},[1726,38175,1742],{"separator":1741},[898,38177,1738],{},[1726,38179,1762],{"stretchy":1734},[902,38181,37672],{"encoding":904}," na úrovni ",[883,38184,38186],{"className":38185},[886],[888,38187,38188],{"xmlns":890},[892,38189,38190,38202],{},[895,38191,38192,38194,38196],{},[898,38193,1738],{},[1726,38195,1728],{},[2128,38197,38198,38200],{},[898,38199,1738],{},[1726,38201,4342],{},[902,38203,4345],{"encoding":904},[37329,38205,38207],{"id":38206},"giffenův-statek","Giffenův statek",[724,38209,38210,38211,38213,38214,38216,38217,1888],{},"Existují zboží, u nichž je křivka poptávky ",[38,38212,13643],{}," — tzv. ",[38,38215,38207],{},". Jde o případy, kdy důchodový efekt převáží substituční (klasický příklad: rýže u chudých asijských spotřebitelů). Giffenův statek patří k ",[38,38218,38219],{},"podřadnému zboží",[37906,38221,38223],{"id":38222},"příklad-22","Příklad 2.2",[724,38225,38226,38229,38230,38248,38249,38271,38272,38290,38291,38309,38310,38333],{},[38,38227,38228],{},"Zadání a popis:"," Křivka ",[883,38231,38233],{"className":38232},[886],[888,38234,38235],{"xmlns":890},[892,38236,38237,38245],{},[895,38238,38239],{},[2275,38240,38241,38243],{},[898,38242,1731],{},[2133,38244,2281],{},[902,38246,38247],{"encoding":904},"D_1"," reprezentuje poptávku rodiny po cukru s reálným cenovým rozpětím ",[883,38250,38252],{"className":38251},[886],[888,38253,38254],{"xmlns":890},[892,38255,38256,38268],{},[895,38257,38258,38260,38262,38264,38266],{},[1726,38259,1735],{"stretchy":1734},[2133,38261,2328],{},[1726,38263,1742],{"separator":1741},[2133,38265,36225],{},[1726,38267,1762],{"stretchy":1734},[902,38269,38270],{"encoding":904},"(0, 15)"," pencí za libru; je nejprve konvexní, od inflexního bodu ",[883,38273,38275],{"className":38274},[886],[888,38276,38277],{"xmlns":890},[892,38278,38279,38287],{},[895,38280,38281],{},[2275,38282,38283,38285],{},[898,38284,1724],{},[2133,38286,2328],{},[902,38288,38289],{"encoding":904},"Q_0"," konkávní, se saturací kolem 17 liber. Křivka ",[883,38292,38294],{"className":38293},[886],[888,38295,38296],{"xmlns":890},[892,38297,38298,38306],{},[895,38299,38300],{},[2275,38301,38302,38304],{},[898,38303,1731],{},[2133,38305,2135],{},[902,38307,38308],{"encoding":904},"D_2"," na širším trhu je konvexní klesající z bodu ",[883,38311,38313],{"className":38312},[886],[888,38314,38315],{"xmlns":890},[892,38316,38317,38330],{},[895,38318,38319,38321,38323,38325,38328],{},[1726,38320,2487],{"stretchy":1734},[2133,38322,2328],{},[1726,38324,1742],{"separator":1741},[2133,38326,38327],{},"21",[1726,38329,2502],{"stretchy":1734},[902,38331,38332],{"encoding":904},"[0, 21]"," centů.",[198,38335,38337],{"id":38336},"engelova-funkce-závislost-na-důchodu","Engelova funkce (závislost na důchodu)",[724,38339,38340,38341,2703],{},"Druhý jednofaktorový model předpokládá závislost množství pouze na důchodu ",[883,38342,38344],{"className":38343},[886],[888,38345,38346],{"xmlns":890},[892,38347,38348,38352],{},[895,38349,38350],{},[898,38351,1745],{},[902,38353,1745],{"encoding":904},[883,38355,38357],{"className":38356},[886],[888,38358,38359],{"xmlns":890,"display":28047},[892,38360,38361,38392],{},[20735,38362,38363],{"width":28052},[20740,38364,38365,38367,38385,38387],{},[20743,38366],{"width":28057},[20743,38368,38369],{},[895,38370,38371,38373,38375,38377,38379,38381,38383],{},[898,38372,1724],{},[1726,38374,1728],{},[898,38376,4240],{},[1726,38378,1735],{"stretchy":1734},[898,38380,1745],{},[1726,38382,1762],{"stretchy":1734},[898,38384,1888],{"mathvariant":2377},[20743,38386],{"width":28057},[20743,38388,38389],{},[2289,38390,38391],{},"(2.5)",[902,38393,38394],{"encoding":904},"Q = E(Y). \\tag{2.5}",[724,38396,38397,38398,38401,38402,38405],{},"Funkce se nazývá ",[38,38399,38400],{},"Engelova",", její graf ",[38,38403,38404],{},"Engelova křivka",". Tvar závisí na typu zboží:",[120,38407,38408,38540],{},[123,38409,38410,1696,38413,38426,38427,38440,38441,38458,38459],{},[38,38411,38412],{},"Normální (superior) zboží",[883,38414,38416],{"className":38415},[886],[888,38417,38418],{"xmlns":890},[892,38419,38420,38424],{},[895,38421,38422],{},[898,38423,1724],{},[902,38425,1724],{"encoding":904}," roste s ",[883,38428,38430],{"className":38429},[886],[888,38431,38432],{"xmlns":890},[892,38433,38434,38438],{},[895,38435,38436],{},[898,38437,1745],{},[902,38439,1745],{"encoding":904},", nepřesáhne hodnotu ",[883,38442,38444],{"className":38443},[886],[888,38445,38446],{"xmlns":890},[892,38447,38448,38456],{},[895,38449,38450],{},[2275,38451,38452,38454],{},[898,38453,1724],{},[2133,38455,2328],{},[902,38457,38289],{"encoding":904},":\n",[120,38460,38461,38493],{},[123,38462,38463,38466,38467,38470,38471,1888],{},[38,38464,38465],{},"Nezbytné zboží"," (potraviny, léky) — malá citlivost, ",[38,38468,38469],{},"konkávní"," křivka, autonomní spotřeba ",[883,38472,38474],{"className":38473},[886],[888,38475,38476],{"xmlns":890},[892,38477,38478,38490],{},[895,38479,38480,38486,38488],{},[2275,38481,38482,38484],{},[898,38483,1724],{},[2133,38485,2281],{},[1726,38487,3405],{},[2133,38489,2328],{},[902,38491,38492],{"encoding":904},"Q_1 > 0",[123,38494,38495,38498,38499,38517,38518,38520,38521,1777,38538,1888],{},[38,38496,38497],{},"Luxusní zboží"," — velká citlivost až od hladiny ",[883,38500,38502],{"className":38501},[886],[888,38503,38504],{"xmlns":890},[892,38505,38506,38514],{},[895,38507,38508],{},[2275,38509,38510,38512],{},[898,38511,1745],{},[2133,38513,2281],{},[902,38515,38516],{"encoding":904},"Y_1",", křivka je nejprve ",[38,38519,37645],{}," a od ",[883,38522,38524],{"className":38523},[886],[888,38525,38526],{"xmlns":890},[892,38527,38528,38536],{},[895,38529,38530],{},[2275,38531,38532,38534],{},[898,38533,1745],{},[2133,38535,2281],{},[902,38537,38516],{"encoding":904},[38,38539,38469],{},[123,38541,38542,38545,38546,38564],{},[38,38543,38544],{},"Podřadné (inferior) zboží"," — od hladiny ",[883,38547,38549],{"className":38548},[886],[888,38550,38551],{"xmlns":890},[892,38552,38553,38561],{},[895,38554,38555],{},[2275,38556,38557,38559],{},[898,38558,1745],{},[2133,38560,2328],{},[902,38562,38563],{"encoding":904},"Y_0"," množství s růstem důchodu klesá.",[724,38566,38567,38568,38571,38572,1847],{},"Mírou citlivosti je ",[614,38569,38570],{},"důchodová elasticita"," (viz ",[207,38573,3889],{"className":38574,"dataFsResolvedFilePath":848,"href":849},[210],[724,38576,38577],{},[614,38578,38579],{},"Obrázek 2.6: Tři panely Engelových křivek — (a) nezbytné, (b) luxusní, (c) podřadné zboží.",[37329,38581,38583],{"id":38582},"intuice-co-vlastně-znamená-podřadné","Intuice — co vlastně znamená „podřadné\"?",[3859,38585,38586,38657,38700],{},[724,38587,38588,38590,38591,1777,38594,1777,38607,5656,38609,38622,38623,38626,38627,1888],{},[883,38589,4400],{}," Pozor — nezbytné ≠ podřadné\n",[38,38592,38593],{},"Nezbytné zboží:",[883,38595,38597],{"className":38596},[886],[888,38598,38599],{"xmlns":890},[892,38600,38601,38605],{},[895,38602,38603],{},[898,38604,1724],{},[902,38606,1724],{"encoding":904},[38,38608,7308],{},[883,38610,38612],{"className":38611},[886],[888,38613,38614],{"xmlns":890},[892,38615,38616,38620],{},[895,38617,38618],{},[898,38619,1745],{},[902,38621,1745],{"encoding":904},", ale ",[38,38624,38625],{},"pomaleji"," než důchod (2× plat → třeba 1,3× spotřeba). ",[883,38628,38630],{"className":38629},[886],[888,38631,38632],{"xmlns":890},[892,38633,38634,38654],{},[895,38635,38636,38642,38644,38646,38648,38650,38652],{},[2275,38637,38638,38640],{},[898,38639,4240],{},[898,38641,1745],{},[1726,38643,6493],{},[1726,38645,1735],{"stretchy":1734},[2133,38647,2328],{},[1726,38649,1742],{"separator":1741},[2133,38651,2281],{},[1726,38653,1762],{"stretchy":1734},[902,38655,38656],{"encoding":904},"E_Y \\in (0, 1)",[724,38658,38659,1777,38662,1777,38675,38677,38678,1888],{},[38,38660,38661],{},"Podřadné zboží:",[883,38663,38665],{"className":38664},[886],[888,38666,38667],{"xmlns":890},[892,38668,38669,38673],{},[895,38670,38671],{},[898,38672,1724],{},[902,38674,1724],{"encoding":904},[38,38676,7328],{}," v absolutních číslech (2× plat → třeba 0,7× spotřeba). ",[883,38679,38681],{"className":38680},[886],[888,38682,38683],{"xmlns":890},[892,38684,38685,38697],{},[895,38686,38687,38693,38695],{},[2275,38688,38689,38691],{},[898,38690,4240],{},[898,38692,1745],{},[1726,38694,3444],{},[2133,38696,2328],{},[902,38698,38699],{"encoding":904},"E_Y \u003C 0",[724,38701,38702,38703,1888],{},"Klíčový rozdíl: u podřadného zboží si při vyšším důchodu kupuješ ",[38,38704,38705],{},"méně kusů, ne jen proporčně méně",[724,38707,38708,38711,38712,38715],{},[38,38709,38710],{},"Mechanismus — substituce „nahoru\"."," Samotné zboží se nezhoršilo, jen si teď můžeš dovolit ",[38,38713,38714],{},"kvalitnější alternativu",". Růst důchodu → přesun k prémiovému substitutu → absolutní pokles nákupu „levnější verze\".",[724,38717,38718],{},[1647,38719],{"alt":38720,"className":38721,"src":38722},"imek-engelovy-krivky-3typy",[210,1651],"\u002Fwiki-assets\u002Fimek-engelovy-krivky-3typy.jpeg",[37906,38724,38726],{"id":38725},"české-příklady","České příklady",[16,38728,38729,38739],{},[19,38730,38731],{},[22,38732,38733,38736],{},[25,38734,38735],{},"Podřadné",[25,38737,38738],{},"Nahradí se za",[30,38740,38741,38749,38757,38765,38773,38781,38789,38797],{},[22,38742,38743,38746],{},[35,38744,38745],{},"Instantní polévky, ramen",[35,38747,38748],{},"Čerstvé jídlo, restaurace",[22,38750,38751,38754],{},[35,38752,38753],{},"MHD (autobus, tramvaj)",[35,38755,38756],{},"Vlastní auto, Uber, taxi",[22,38758,38759,38762],{},[35,38760,38761],{},"Mražené polotovary, pizza z mrazáku",[35,38763,38764],{},"Čerstvé suroviny, hotovky",[22,38766,38767,38770],{},[35,38768,38769],{},"Privátní značky supermarketů (K-Classic, Clever)",[35,38771,38772],{},"Značkové produkty",[22,38774,38775,38778],{},[35,38776,38777],{},"Paštika Májka, obyčejný měkký salám",[35,38779,38780],{},"Kvalitní uzeniny, šunka od kosti",[22,38782,38783,38786],{},[35,38784,38785],{},"Second hand oblečení",[35,38787,38788],{},"Nové oblečení, značky",[22,38790,38791,38794],{},[35,38792,38793],{},"Krabicové víno, nejlevnější pivo",[35,38795,38796],{},"Lahvové víno, řemeslná piva",[22,38798,38799,38802],{},[35,38800,38801],{},"Ojetá auta nižších tříd",[35,38803,38804],{},"Nová auta, prémiové značky",[3859,38806,38807],{},[724,38808,38809,38811,38812,38815],{},[883,38810,4560],{}," Test 50 milionů\nPředstav si, že vyhraješ 50 milionů. ",[38,38813,38814],{},"Čeho si najednou koupíš méně"," (nebo vůbec)? To je tvoje podřadné zboží.",[724,38817,38818,38821,38822,10009,38825,38847,38848,10009,38851,38872,38873,38891,38892,38895],{},[38,38819,38820],{},"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 ",[38,38823,38824],{},"luxus",[883,38826,38828],{"className":38827},[886],[888,38829,38830],{"xmlns":890},[892,38831,38832,38844],{},[895,38833,38834,38840,38842],{},[2275,38835,38836,38838],{},[898,38837,4240],{},[898,38839,1745],{},[1726,38841,3405],{},[2133,38843,2281],{},[902,38845,38846],{"encoding":904},"E_Y > 1","), pro manažera s 200k platem ",[38,38849,38850],{},"podřadné",[883,38852,38854],{"className":38853},[886],[888,38855,38856],{"xmlns":890},[892,38857,38858,38870],{},[895,38859,38860,38866,38868],{},[2275,38861,38862,38864],{},[898,38863,4240],{},[898,38865,1745],{},[1726,38867,3444],{},[2133,38869,2328],{},[902,38871,38699],{"encoding":904},"). Proto je ",[883,38874,38876],{"className":38875},[886],[888,38877,38878],{"xmlns":890},[892,38879,38880,38888],{},[895,38881,38882],{},[2275,38883,38884,38886],{},[898,38885,4240],{},[898,38887,1745],{},[902,38889,38890],{"encoding":904},"E_Y"," vždy ",[38,38893,38894],{},"lokální veličina"," — platí pro danou úroveň důchodu, ne absolutně.",[724,38897,38898,38899,38901],{},"Extrémním případem podřadného zboží, kde substituční efekt převáží už na straně ceny, je ",[38,38900,38207],{}," (viz níže) — tam poptávková křivka dokonce roste.",[198,38903,38905,38906,1762],{"id":38904},"posun-poptávky-shift-of-demand","Posun poptávky (",[614,38907,38908],{},"shift of demand",[724,38910,38911,38912,38930,38931,38948,38949,38962,38963,2684,38976,38998,38999,39016,39017,39043,39044,39047],{},"Při změně exogenní proměnné (např. důchodu) se celá křivka poptávky posouvá. Uvažujme normální zboží. Ceně ",[883,38913,38915],{"className":38914},[886],[888,38916,38917],{"xmlns":890},[892,38918,38919,38927],{},[895,38920,38921],{},[2275,38922,38923,38925],{},[898,38924,1738],{},[2133,38926,2328],{},[902,38928,38929],{"encoding":904},"P_0"," odpovídá množství ",[883,38932,38934],{"className":38933},[886],[888,38935,38936],{"xmlns":890},[892,38937,38938,38946],{},[895,38939,38940],{},[2275,38941,38942,38944],{},[898,38943,1724],{},[2133,38945,2328],{},[902,38947,38289],{"encoding":904}," na křivce ",[883,38950,38952],{"className":38951},[886],[888,38953,38954],{"xmlns":890},[892,38955,38956,38960],{},[895,38957,38958],{},[898,38959,1731],{},[902,38961,1731],{"encoding":904},"; vzroste-li důchod z ",[883,38964,38966],{"className":38965},[886],[888,38967,38968],{"xmlns":890},[892,38969,38970,38974],{},[895,38971,38972],{},[898,38973,1745],{},[902,38975,1745],{"encoding":904},[883,38977,38979],{"className":38978},[886],[888,38980,38981],{"xmlns":890},[892,38982,38983,38995],{},[895,38984,38985,38991,38993],{},[2275,38986,38987,38989],{},[898,38988,1745],{},[2133,38990,2281],{},[1726,38992,3405],{},[898,38994,1745],{},[902,38996,38997],{"encoding":904},"Y_1 > Y",", pak stejné ceně ",[883,39000,39002],{"className":39001},[886],[888,39003,39004],{"xmlns":890},[892,39005,39006,39014],{},[895,39007,39008],{},[2275,39009,39010,39012],{},[898,39011,1738],{},[2133,39013,2328],{},[902,39015,38929],{"encoding":904}," odpovídá vyšší ",[883,39018,39020],{"className":39019},[886],[888,39021,39022],{"xmlns":890},[892,39023,39024,39040],{},[895,39025,39026,39032,39034],{},[2275,39027,39028,39030],{},[898,39029,1724],{},[2133,39031,2281],{},[1726,39033,3405],{},[2275,39035,39036,39038],{},[898,39037,1724],{},[2133,39039,2328],{},[902,39041,39042],{"encoding":904},"Q_1 > Q_0"," — křivka se ",[38,39045,39046],{},"posouvá doprava",". Pokles důchodu vede k posunu doleva.",[724,39049,39050],{},[1647,39051],{"alt":39052,"className":39053,"src":39054},"imek-posun-vs-pohyb-po-krivce",[210,1651],"\u002Fwiki-assets\u002Fimek-posun-vs-pohyb-po-krivce.jpeg",[724,39056,39057],{},"Posun může být způsoben i jinými faktory (např. zdaněním spotřebitele — viz dále).",[724,39059,39060],{},[614,39061,39062,39063,13997,39093,39114],{},"Obrázek 2.7: Posun poptávky — tři křivky ",[883,39064,39066],{"className":39065},[886],[888,39067,39068],{"xmlns":890},[892,39069,39070,39090],{},[895,39071,39072,39078,39080,39082,39084],{},[2275,39073,39074,39076],{},[898,39075,1731],{},[2133,39077,2135],{},[1726,39079,1742],{"separator":1741},[898,39081,1731],{},[1726,39083,1742],{"separator":1741},[2275,39085,39086,39088],{},[898,39087,1731],{},[2133,39089,2281],{},[902,39091,39092],{"encoding":904},"D_2, D, D_1",[883,39094,39096],{"className":39095},[886],[888,39097,39098],{"xmlns":890},[892,39099,39100,39112],{},[895,39101,39102,39104,39106,39108,39110],{},[1726,39103,1735],{"stretchy":1734},[898,39105,1724],{},[1726,39107,1742],{"separator":1741},[898,39109,1738],{},[1726,39111,1762],{"stretchy":1734},[902,39113,37672],{"encoding":904},", šipky naznačují posuny.",[37906,39116,39118],{"id":39117},"příklad-23-zdanění-kupujícího","Příklad 2.3 — zdanění kupujícího",[724,39120,39121,39123,39124,39147,39148,39165,39166,39183,39184,1888],{},[38,39122,37914],{}," Poptávce ",[883,39125,39127],{"className":39126},[886],[888,39128,39129],{"xmlns":890},[892,39130,39131,39145],{},[895,39132,39133,39135,39137,39139,39141,39143],{},[898,39134,1738],{},[1726,39136,1728],{},[898,39138,1731],{},[1726,39140,1735],{"stretchy":1734},[898,39142,1724],{},[1726,39144,1762],{"stretchy":1734},[902,39146,1830],{"encoding":904}," odpovídá ceně ",[883,39149,39151],{"className":39150},[886],[888,39152,39153],{"xmlns":890},[892,39154,39155,39163],{},[895,39156,39157],{},[2275,39158,39159,39161],{},[898,39160,1738],{},[2133,39162,2328],{},[902,39164,38929],{"encoding":904}," množství ",[883,39167,39169],{"className":39168},[886],[888,39170,39171],{"xmlns":890},[892,39172,39173,39181],{},[895,39174,39175],{},[2275,39176,39177,39179],{},[898,39178,1724],{},[2133,39180,2328],{},[902,39182,38289],{"encoding":904},". Na kupujícího je uložena jednotková daň ",[883,39185,39187],{"className":39186},[886],[888,39188,39189],{"xmlns":890},[892,39190,39191,39195],{},[895,39192,39193],{},[898,39194,2772],{},[902,39196,2772],{"encoding":904},[724,39198,39199,39201,39202,39219,39220,39242],{},[38,39200,37946],{}," Kupující nakupuje množství ",[883,39203,39205],{"className":39204},[886],[888,39206,39207],{"xmlns":890},[892,39208,39209,39217],{},[895,39210,39211],{},[2275,39212,39213,39215],{},[898,39214,1724],{},[2133,39216,2281],{},[902,39218,28983],{"encoding":904},", které odpovídá ceně ",[883,39221,39223],{"className":39222},[886],[888,39224,39225],{"xmlns":890},[892,39226,39227,39239],{},[895,39228,39229,39235,39237],{},[2275,39230,39231,39233],{},[898,39232,1738],{},[2133,39234,2328],{},[1726,39236,2099],{},[898,39238,2772],{},[902,39240,39241],{"encoding":904},"P_0 + T"," na původní křivce. Nová poptávka je",[883,39244,39246],{"className":39245},[886],[888,39247,39248],{"xmlns":890,"display":28047},[892,39249,39250,39284],{},[895,39251,39252,39254,39256,39262,39264,39266,39268,39270,39272,39274,39276,39278,39280,39282],{},[898,39253,1738],{},[1726,39255,1728],{},[2275,39257,39258,39260],{},[898,39259,1731],{},[2133,39261,2281],{},[1726,39263,1735],{"stretchy":1734},[898,39265,1724],{},[1726,39267,1762],{"stretchy":1734},[1726,39269,1728],{},[898,39271,1731],{},[1726,39273,1735],{"stretchy":1734},[898,39275,1724],{},[1726,39277,1762],{"stretchy":1734},[1726,39279,2228],{},[898,39281,2772],{},[1726,39283,1742],{"separator":1741},[902,39285,39286],{"encoding":904},"P = D_1(Q) = D(Q) - T,",[724,39288,39289,39290,1888],{},"tj. dojde k ",[38,39291,39292],{},"posunu poptávky doleva",[724,39294,39295],{},[614,39296,39297,39298,39319,39320,1343,39337,1343,39350,39371,39372,3877,39389,1888],{},"Obrázek 2.8: Dvě klesající poptávkové přímky v ",[883,39299,39301],{"className":39300},[886],[888,39302,39303],{"xmlns":890},[892,39304,39305,39317],{},[895,39306,39307,39309,39311,39313,39315],{},[1726,39308,1735],{"stretchy":1734},[898,39310,1724],{},[1726,39312,1742],{"separator":1741},[898,39314,1738],{},[1726,39316,1762],{"stretchy":1734},[902,39318,37672],{"encoding":904},"; na svislé ose jsou vyznačeny ",[883,39321,39323],{"className":39322},[886],[888,39324,39325],{"xmlns":890},[892,39326,39327,39335],{},[895,39328,39329],{},[2275,39330,39331,39333],{},[898,39332,1738],{},[2133,39334,2328],{},[902,39336,38929],{"encoding":904},[883,39338,39340],{"className":39339},[886],[888,39341,39342],{"xmlns":890},[892,39343,39344,39348],{},[895,39345,39346],{},[898,39347,2772],{},[902,39349,2772],{"encoding":904},[883,39351,39353],{"className":39352},[886],[888,39354,39355],{"xmlns":890},[892,39356,39357,39369],{},[895,39358,39359,39365,39367],{},[2275,39360,39361,39363],{},[898,39362,1738],{},[2133,39364,2328],{},[1726,39366,2099],{},[898,39368,2772],{},[902,39370,39241],{"encoding":904},"; na vodorovné ",[883,39373,39375],{"className":39374},[886],[888,39376,39377],{"xmlns":890},[892,39378,39379,39387],{},[895,39380,39381],{},[2275,39382,39383,39385],{},[898,39384,1724],{},[2133,39386,2281],{},[902,39388,28983],{"encoding":904},[883,39390,39392],{"className":39391},[886],[888,39393,39394],{"xmlns":890},[892,39395,39396,39404],{},[895,39397,39398],{},[2275,39399,39400,39402],{},[898,39401,1724],{},[2133,39403,2328],{},[902,39405,38289],{"encoding":904},[198,39407,39409],{"id":39408},"vícekomoditní-dvoukomoditní-trh","Vícekomoditní (dvoukomoditní) trh",[724,39411,39412],{},"Uvažujme dvě tržně závislá zboží s lineárními funkcemi poptávky:",[883,39414,39416],{"className":39415},[886],[888,39417,39418],{"xmlns":890,"display":28047},[892,39419,39420,39605],{},[20735,39421,39422],{"width":28052},[20740,39423,39424,39426,39598,39600],{},[20743,39425],{"width":28057},[20743,39427,39428],{},[20735,39429,39430,39514],{"rowspacing":20737,"columnalign":20738,"columnspacing":2378},[20740,39431,39432,39442],{},[20743,39433,39434],{},[2326,39435,39436],{"scriptlevel":2328,"displaystyle":1741},[2275,39437,39438,39440],{},[898,39439,1724],{},[2133,39441,2281],{},[20743,39443,39444],{},[2326,39445,39446],{"scriptlevel":2328,"displaystyle":1741},[895,39447,39448,39450,39452,39458,39460,39466,39468,39474,39476,39478,39484,39486,39492,39498,39500,39506,39512],{},[895,39449],{},[1726,39451,1728],{},[2275,39453,39454,39456],{},[898,39455,1731],{},[2133,39457,2281],{},[1726,39459,1735],{"stretchy":1734},[2275,39461,39462,39464],{},[898,39463,1738],{},[2133,39465,2281],{},[1726,39467,1742],{"separator":1741},[2275,39469,39470,39472],{},[898,39471,1738],{},[2133,39473,2135],{},[1726,39475,1762],{"stretchy":1734},[1726,39477,1728],{},[2275,39479,39480,39482],{},[898,39481,207],{},[2133,39483,2281],{},[1726,39485,2099],{},[2275,39487,39488,39490],{},[898,39489,2102],{},[2133,39491,2281],{},[2275,39493,39494,39496],{},[898,39495,1738],{},[2133,39497,2281],{},[1726,39499,2099],{},[2275,39501,39502,39504],{},[898,39503,2146],{},[2133,39505,2281],{},[2275,39507,39508,39510],{},[898,39509,1738],{},[2133,39511,2135],{},[1726,39513,1742],{"separator":1741},[20740,39515,39516,39526],{},[20743,39517,39518],{},[2326,39519,39520],{"scriptlevel":2328,"displaystyle":1741},[2275,39521,39522,39524],{},[898,39523,1724],{},[2133,39525,2135],{},[20743,39527,39528],{},[2326,39529,39530],{"scriptlevel":2328,"displaystyle":1741},[895,39531,39532,39534,39536,39542,39544,39550,39552,39558,39560,39562,39568,39570,39576,39582,39584,39590,39596],{},[895,39533],{},[1726,39535,1728],{},[2275,39537,39538,39540],{},[898,39539,1731],{},[2133,39541,2135],{},[1726,39543,1735],{"stretchy":1734},[2275,39545,39546,39548],{},[898,39547,1738],{},[2133,39549,2281],{},[1726,39551,1742],{"separator":1741},[2275,39553,39554,39556],{},[898,39555,1738],{},[2133,39557,2135],{},[1726,39559,1762],{"stretchy":1734},[1726,39561,1728],{},[2275,39563,39564,39566],{},[898,39565,207],{},[2133,39567,2135],{},[1726,39569,2099],{},[2275,39571,39572,39574],{},[898,39573,2102],{},[2133,39575,2135],{},[2275,39577,39578,39580],{},[898,39579,1738],{},[2133,39581,2281],{},[1726,39583,2099],{},[2275,39585,39586,39588],{},[898,39587,2146],{},[2133,39589,2135],{},[2275,39591,39592,39594],{},[898,39593,1738],{},[2133,39595,2135],{},[898,39597,1888],{"mathvariant":2377},[20743,39599],{"width":28057},[20743,39601,39602],{},[2289,39603,39604],{},"(2.6)",[902,39606,39607],{"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}",[37329,39609,39611],{"id":39610},"znaménková-analýza-parametrů","Znaménková analýza parametrů",[120,39613,39614,39661,39708],{},[123,39615,39616,1343,39638,39660],{},[883,39617,39619],{"className":39618},[886],[888,39620,39621],{"xmlns":890},[892,39622,39623,39635],{},[895,39624,39625,39631,39633],{},[2275,39626,39627,39629],{},[898,39628,207],{},[2133,39630,2281],{},[1726,39632,3405],{},[2133,39634,2328],{},[902,39636,39637],{"encoding":904},"a_1 > 0",[883,39639,39641],{"className":39640},[886],[888,39642,39643],{"xmlns":890},[892,39644,39645,39657],{},[895,39646,39647,39653,39655],{},[2275,39648,39649,39651],{},[898,39650,207],{},[2133,39652,2135],{},[1726,39654,3405],{},[2133,39656,2328],{},[902,39658,39659],{"encoding":904},"a_2 > 0"," (při nulových cenách je poptávané množství kladné),",[123,39662,39663,1343,39685,39707],{},[883,39664,39666],{"className":39665},[886],[888,39667,39668],{"xmlns":890},[892,39669,39670,39682],{},[895,39671,39672,39678,39680],{},[2275,39673,39674,39676],{},[898,39675,2102],{},[2133,39677,2281],{},[1726,39679,3444],{},[2133,39681,2328],{},[902,39683,39684],{"encoding":904},"b_1 \u003C 0",[883,39686,39688],{"className":39687},[886],[888,39689,39690],{"xmlns":890},[892,39691,39692,39704],{},[895,39693,39694,39700,39702],{},[2275,39695,39696,39698],{},[898,39697,2146],{},[2133,39699,2135],{},[1726,39701,3444],{},[2133,39703,2328],{},[902,39705,39706],{"encoding":904},"c_2 \u003C 0"," (vlastní koeficienty — zákon klesající poptávky),",[123,39709,39710,39711,1343,39728,39746,39747],{},"zkřížené koeficienty ",[883,39712,39714],{"className":39713},[886],[888,39715,39716],{"xmlns":890},[892,39717,39718,39726],{},[895,39719,39720],{},[2275,39721,39722,39724],{},[898,39723,2146],{},[2133,39725,2281],{},[902,39727,29780],{"encoding":904},[883,39729,39731],{"className":39730},[886],[888,39732,39733],{"xmlns":890},[892,39734,39735,39743],{},[895,39736,39737],{},[2275,39738,39739,39741],{},[898,39740,2102],{},[2133,39742,2135],{},[902,39744,39745],{"encoding":904},"b_2"," určují povahu vztahu:\n",[120,39748,39749,39799],{},[123,39750,39751,39754,39755,1343,39777,1742],{},[38,39752,39753],{},"substituty"," (máslo vs. margarín): ",[883,39756,39758],{"className":39757},[886],[888,39759,39760],{"xmlns":890},[892,39761,39762,39774],{},[895,39763,39764,39770,39772],{},[2275,39765,39766,39768],{},[898,39767,2146],{},[2133,39769,2281],{},[1726,39771,3405],{},[2133,39773,2328],{},[902,39775,39776],{"encoding":904},"c_1 > 0",[883,39778,39780],{"className":39779},[886],[888,39781,39782],{"xmlns":890},[892,39783,39784,39796],{},[895,39785,39786,39792,39794],{},[2275,39787,39788,39790],{},[898,39789,2102],{},[2133,39791,2135],{},[1726,39793,3405],{},[2133,39795,2328],{},[902,39797,39798],{"encoding":904},"b_2 > 0",[123,39800,39801,39804,39805,1343,39827,1888],{},[38,39802,39803],{},"komplementy"," (auto vs. benzín): ",[883,39806,39808],{"className":39807},[886],[888,39809,39810],{"xmlns":890},[892,39811,39812,39824],{},[895,39813,39814,39820,39822],{},[2275,39815,39816,39818],{},[898,39817,2146],{},[2133,39819,2281],{},[1726,39821,3444],{},[2133,39823,2328],{},[902,39825,39826],{"encoding":904},"c_1 \u003C 0",[883,39828,39830],{"className":39829},[886],[888,39831,39832],{"xmlns":890},[892,39833,39834,39846],{},[895,39835,39836,39842,39844],{},[2275,39837,39838,39840],{},[898,39839,2102],{},[2133,39841,2135],{},[1726,39843,3444],{},[2133,39845,2328],{},[902,39847,39848],{"encoding":904},"b_2 \u003C 0",[724,39850,39851],{},"Schematicky:",[724,39853,39854,39857],{},[38,39855,39856],{},"Substituty",[883,39858,39860],{"className":39859},[886],[888,39861,39862],{"xmlns":890},[892,39863,39864,40003],{},[895,39865,39866,39872,39874,39889,39891,39911,39913,39933,39935,39937,39943,39945,39959,39961,39981,39983],{},[2275,39867,39868,39870],{},[898,39869,1724],{},[2133,39871,2281],{},[1726,39873,1728],{},[898,39875,39876],{},[39877,39878,39879,39887],"munder",{},[1726,39880,39881],{},[2275,39882,39883,39885],{},[898,39884,207],{},[2133,39886,2281],{},[1726,39888,2099],{"lspace":2378,"rspace":2378},[1726,39890,2099],{},[898,39892,39893],{},[39877,39894,39895,39909],{},[1726,39896,39897,39903],{},[2275,39898,39899,39901],{},[898,39900,2102],{},[2133,39902,2281],{},[2275,39904,39905,39907],{},[898,39906,1738],{},[2133,39908,2281],{},[1726,39910,2228],{"lspace":2378,"rspace":2378},[1726,39912,2099],{},[898,39914,39915],{},[39877,39916,39917,39931],{},[1726,39918,39919,39925],{},[2275,39920,39921,39923],{},[898,39922,2146],{},[2133,39924,2281],{},[2275,39926,39927,39929],{},[898,39928,1738],{},[2133,39930,2135],{},[1726,39932,2099],{"lspace":2378,"rspace":2378},[1726,39934,1742],{"separator":1741},[5865,39936],{"width":5867},[2275,39938,39939,39941],{},[898,39940,1724],{},[2133,39942,2135],{},[1726,39944,1728],{},[898,39946,39947],{},[39877,39948,39949,39957],{},[1726,39950,39951],{},[2275,39952,39953,39955],{},[898,39954,207],{},[2133,39956,2135],{},[1726,39958,2099],{"lspace":2378,"rspace":2378},[1726,39960,2099],{},[898,39962,39963],{},[39877,39964,39965,39979],{},[1726,39966,39967,39973],{},[2275,39968,39969,39971],{},[898,39970,2102],{},[2133,39972,2135],{},[2275,39974,39975,39977],{},[898,39976,1738],{},[2133,39978,2281],{},[1726,39980,2099],{"lspace":2378,"rspace":2378},[1726,39982,2099],{},[898,39984,39985],{},[39877,39986,39987,40001],{},[1726,39988,39989,39995],{},[2275,39990,39991,39993],{},[898,39992,2146],{},[2133,39994,2135],{},[2275,39996,39997,39999],{},[898,39998,1738],{},[2133,40000,2135],{},[1726,40002,2228],{"lspace":2378,"rspace":2378},[902,40004,40005],{"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}",[724,40007,40008,40011],{},[38,40009,40010],{},"Komplementy",[883,40012,40014],{"className":40013},[886],[888,40015,40016],{"xmlns":890},[892,40017,40018,40156],{},[895,40019,40020,40026,40028,40042,40044,40064,40066,40086,40088,40090,40096,40098,40112,40114,40134,40136],{},[2275,40021,40022,40024],{},[898,40023,1724],{},[2133,40025,2281],{},[1726,40027,1728],{},[898,40029,40030],{},[39877,40031,40032,40040],{},[1726,40033,40034],{},[2275,40035,40036,40038],{},[898,40037,207],{},[2133,40039,2281],{},[1726,40041,2099],{"lspace":2378,"rspace":2378},[1726,40043,2099],{},[898,40045,40046],{},[39877,40047,40048,40062],{},[1726,40049,40050,40056],{},[2275,40051,40052,40054],{},[898,40053,2102],{},[2133,40055,2281],{},[2275,40057,40058,40060],{},[898,40059,1738],{},[2133,40061,2281],{},[1726,40063,2228],{"lspace":2378,"rspace":2378},[1726,40065,2099],{},[898,40067,40068],{},[39877,40069,40070,40084],{},[1726,40071,40072,40078],{},[2275,40073,40074,40076],{},[898,40075,2146],{},[2133,40077,2281],{},[2275,40079,40080,40082],{},[898,40081,1738],{},[2133,40083,2135],{},[1726,40085,2228],{"lspace":2378,"rspace":2378},[1726,40087,1742],{"separator":1741},[5865,40089],{"width":5867},[2275,40091,40092,40094],{},[898,40093,1724],{},[2133,40095,2135],{},[1726,40097,1728],{},[898,40099,40100],{},[39877,40101,40102,40110],{},[1726,40103,40104],{},[2275,40105,40106,40108],{},[898,40107,207],{},[2133,40109,2135],{},[1726,40111,2099],{"lspace":2378,"rspace":2378},[1726,40113,2099],{},[898,40115,40116],{},[39877,40117,40118,40132],{},[1726,40119,40120,40126],{},[2275,40121,40122,40124],{},[898,40123,2102],{},[2133,40125,2135],{},[2275,40127,40128,40130],{},[898,40129,1738],{},[2133,40131,2281],{},[1726,40133,2228],{"lspace":2378,"rspace":2378},[1726,40135,2099],{},[898,40137,40138],{},[39877,40139,40140,40154],{},[1726,40141,40142,40148],{},[2275,40143,40144,40146],{},[898,40145,2146],{},[2133,40147,2135],{},[2275,40149,40150,40152],{},[898,40151,1738],{},[2133,40153,2135],{},[1726,40155,2228],{"lspace":2378,"rspace":2378},[902,40157,40158],{"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}",[36951,40160],{},[115,40162,13111],{"id":36760},[3859,40164,40165],{},[724,40166,40167,40169,40170,36975,40183,36989,40196,40199,40200,5656,40224,40242],{},[883,40168,4145],{}," TL;DR\nNabídka vyjadřuje závislost nabízeného množství ",[883,40171,40173],{"className":40172},[886],[888,40174,40175],{"xmlns":890},[892,40176,40177,40181],{},[895,40178,40179],{},[898,40180,1724],{},[902,40182,1724],{"encoding":904},[883,40184,40186],{"className":40185},[886],[888,40187,40188],{"xmlns":890},[892,40189,40190,40194],{},[895,40191,40192],{},[898,40193,1738],{},[902,40195,1738],{"encoding":904},[38,40197,40198],{},"zákon rostoucí nabídky",": při vyšší ceně je výrobce ochoten nabídnout více. Lineární model ",[883,40201,40203],{"className":40202},[886],[888,40204,40205],{"xmlns":890},[892,40206,40207,40221],{},[895,40208,40209,40211,40213,40215,40217,40219],{},[898,40210,1738],{},[1726,40212,1728],{},[898,40214,2146],{},[898,40216,1724],{},[1726,40218,2099],{},[898,40220,2198],{},[902,40222,40223],{"encoding":904},"P = cQ + d",[883,40225,40227],{"className":40226},[886],[888,40228,40229],{"xmlns":890},[892,40230,40231,40239],{},[895,40232,40233,40235,40237],{},[898,40234,2146],{},[1726,40236,3405],{},[2133,40238,2328],{},[902,40240,40241],{"encoding":904},"c > 0"," je standardní aproximací.",[198,40244,37045],{"id":40245},"obecný-vícefaktorový-model-1",[724,40247,40248,10009,40251,40254,40255,40268,40269,36877,40282,36891,40295,40308,40309,40323,40324,36920,40337,40350],{},[38,40249,40250],{},"Nabízené množství",[614,40252,40253],{},"quantity supplied",") závisí na ceně ",[883,40256,40258],{"className":40257},[886],[888,40259,40260],{"xmlns":890},[892,40261,40262,40266],{},[895,40263,40264],{},[898,40265,1738],{},[902,40267,1738],{"encoding":904},", cenách výrobních faktorů (práce ",[883,40270,40272],{"className":40271},[886],[888,40273,40274],{"xmlns":890},[892,40275,40276,40280],{},[895,40277,40278],{},[898,40279,9779],{},[902,40281,9779],{"encoding":904},[883,40283,40285],{"className":40284},[886],[888,40286,40287],{"xmlns":890},[892,40288,40289,40293],{},[895,40290,40291],{},[898,40292,9784],{},[902,40294,9784],{"encoding":904},[883,40296,40298],{"className":40297},[886],[888,40299,40300],{"xmlns":890},[892,40301,40302,40306],{},[895,40303,40304],{},[898,40305,4240],{},[902,40307,4240],{"encoding":904},"), očekávání ",[883,40310,40312],{"className":40311},[886],[888,40313,40314],{"xmlns":890},[892,40315,40316,40321],{},[895,40317,40318],{},[898,40319,40320],{},"V",[902,40322,40320],{"encoding":904},", počtu výrobců ",[883,40325,40327],{"className":40326},[886],[888,40328,40329],{"xmlns":890},[892,40330,40331,40335],{},[895,40332,40333],{},[898,40334,36917],{},[902,40336,36917],{"encoding":904},[883,40338,40340],{"className":40339},[886],[888,40341,40342],{"xmlns":890},[892,40343,40344,40348],{},[895,40345,40346],{},[898,40347,36932],{},[902,40349,36932],{"encoding":904}," a dalších:",[883,40352,40354],{"className":40353},[886],[888,40355,40356],{"xmlns":890,"display":28047},[892,40357,40358,40417],{},[20735,40359,40360],{"width":28052},[20740,40361,40362,40364,40410,40412],{},[20743,40363],{"width":28057},[20743,40365,40366],{},[895,40367,40368,40370,40372,40374,40376,40378,40380,40382,40384,40386,40388,40390,40392,40394,40396,40398,40400,40402,40404,40406,40408],{},[898,40369,1724],{},[1726,40371,1728],{},[898,40373,8659],{},[1726,40375,1735],{"stretchy":1734},[898,40377,1738],{},[1726,40379,1742],{"separator":1741},[898,40381,9779],{},[1726,40383,1742],{"separator":1741},[898,40385,9784],{},[1726,40387,1742],{"separator":1741},[898,40389,4240],{},[1726,40391,1742],{"separator":1741},[898,40393,40320],{},[1726,40395,1742],{"separator":1741},[898,40397,36917],{},[1726,40399,1742],{"separator":1741},[898,40401,36932],{},[1726,40403,1742],{"separator":1741},[1726,40405,1759],{},[1726,40407,1762],{"stretchy":1734},[898,40409,1888],{"mathvariant":2377},[20743,40411],{"width":28057},[20743,40413,40414],{},[2289,40415,40416],{},"(2.7)",[902,40418,40419],{"encoding":904},"Q = S(P, L, K, E, V, O, W, \\ldots). \\tag{2.7}",[724,40421,38397,40422,10009,40425,40428],{},[38,40423,40424],{},"funkce nabídky",[614,40426,40427],{},"supply function",") v širším slova smyslu.",[198,40430,40432],{"id":40431},"jednofaktorový-model","Jednofaktorový model",[724,40434,40435],{},"V nejpřirozenějším jednofaktorovém modelu",[883,40437,40439],{"className":40438},[886],[888,40440,40441],{"xmlns":890,"display":28047},[892,40442,40443,40494],{},[20735,40444,40445],{"width":28052},[20740,40446,40447,40449,40487,40489],{},[20743,40448],{"width":28057},[20743,40450,40451],{},[895,40452,40453,40455,40457,40459,40461,40463,40465,40467,40469,40471,40473,40475,40477,40479,40481,40483,40485],{},[898,40454,1724],{},[1726,40456,1728],{},[898,40458,8659],{},[1726,40460,1735],{"stretchy":1734},[898,40462,1738],{},[1726,40464,1762],{"stretchy":1734},[1726,40466,1742],{"separator":1741},[5865,40468],{"width":5867},[2289,40470,37398],{},[5865,40472],{"width":5867},[898,40474,1738],{},[1726,40476,1728],{},[898,40478,8659],{},[1726,40480,1735],{"stretchy":1734},[898,40482,1724],{},[1726,40484,1762],{"stretchy":1734},[898,40486,1888],{"mathvariant":2377},[20743,40488],{"width":28057},[20743,40490,40491],{},[2289,40492,40493],{},"(2.8)",[902,40495,40496],{"encoding":904},"Q = S(P), \\qquad \\text{resp.} \\qquad P = S(Q). \\tag{2.8}",[724,40498,40499,40500,10009,40503,1847],{},"Graf je ",[38,40501,40502],{},"křivka nabídky",[614,40504,40505],{},"supply curve",[37329,40507,40509],{"id":40508},"zákon-rostoucí-nabídky","Zákon rostoucí nabídky",[3859,40511,40512],{},[724,40513,40514],{},[38,40515,37444,40516,40529,40530,37499],{},[883,40517,40519],{"className":40518},[886],[888,40520,40521],{"xmlns":890},[892,40522,40523,40527],{},[895,40524,40525],{},[898,40526,1738],{},[902,40528,1738],{"encoding":904},", pak nabízené množství ",[883,40531,40533],{"className":40532},[886],[888,40534,40535],{"xmlns":890},[892,40536,40537,40541],{},[895,40538,40539],{},[898,40540,1724],{},[902,40542,1724],{"encoding":904},[724,40544,40545,40546,40571,40572,40602,40603,40620],{},"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 ",[883,40547,40549],{"className":40548},[886],[888,40550,40551],{"xmlns":890},[892,40552,40553,40569],{},[895,40554,40555,40557,40559,40561,40567],{},[1726,40556,2487],{"stretchy":1734},[2133,40558,2328],{},[1726,40560,1742],{"separator":1741},[2275,40562,40563,40565],{},[898,40564,1738],{},[2133,40566,2328],{},[1726,40568,2502],{"stretchy":1734},[902,40570,37584],{"encoding":904}," na svislé ose (případně z ",[883,40573,40575],{"className":40574},[886],[888,40576,40577],{"xmlns":890},[892,40578,40579,40599],{},[895,40580,40581,40583,40589,40591,40597],{},[1726,40582,2487],{"stretchy":1734},[2275,40584,40585,40587],{},[898,40586,1724],{},[2133,40588,2281],{},[1726,40590,1742],{"separator":1741},[2275,40592,40593,40595],{},[898,40594,1738],{},[2133,40596,2281],{},[1726,40598,2502],{"stretchy":1734},[902,40600,40601],{"encoding":904},"[Q_1, P_1]","), kde ",[883,40604,40606],{"className":40605},[886],[888,40607,40608],{"xmlns":890},[892,40609,40610,40618],{},[895,40611,40612],{},[2275,40613,40614,40616],{},[898,40615,1738],{},[2133,40617,2328],{},[902,40619,38929],{"encoding":904}," je minimální cena, při které je výrobce ochoten vyrábět.",[724,40622,40623],{},[614,40624,40625,40626,3715,40639,1888],{},"Obrázek 2.9: Typická rostoucí křivka nabídky ",[883,40627,40629],{"className":40628},[886],[888,40630,40631],{"xmlns":890},[892,40632,40633,40637],{},[895,40634,40635],{},[898,40636,8659],{},[902,40638,8659],{"encoding":904},[883,40640,40642],{"className":40641},[886],[888,40643,40644],{"xmlns":890},[892,40645,40646,40658],{},[895,40647,40648,40650,40652,40654,40656],{},[1726,40649,1735],{"stretchy":1734},[898,40651,1724],{},[1726,40653,1742],{"separator":1741},[898,40655,1738],{},[1726,40657,1762],{"stretchy":1734},[902,40659,37672],{"encoding":904},[37329,40661,40663],{"id":40662},"lineární-model-nabídky","Lineární model nabídky",[883,40665,40667],{"className":40666},[886],[888,40668,40669],{"xmlns":890,"display":28047},[892,40670,40671,40710],{},[20735,40672,40673],{"width":28052},[20740,40674,40675,40677,40703,40705],{},[20743,40676],{"width":28057},[20743,40678,40679],{},[895,40680,40681,40683,40685,40687,40689,40691,40693,40695,40697,40699,40701],{},[898,40682,1738],{},[1726,40684,1728],{},[898,40686,2146],{},[898,40688,1724],{},[1726,40690,2099],{},[898,40692,2198],{},[1726,40694,1742],{"separator":1741},[5865,40696],{"width":5867},[898,40698,2146],{},[1726,40700,3405],{},[2133,40702,12446],{},[20743,40704],{"width":28057},[20743,40706,40707],{},[2289,40708,40709],{},"(2.9)",[902,40711,40712],{"encoding":904},"P = cQ + d, \\qquad c > 0. \\tag{2.9}",[724,40714,40715,40716,40752,40753,40766],{},"Alternativně ",[883,40717,40719],{"className":40718},[886],[888,40720,40721],{"xmlns":890},[892,40722,40723,40749],{},[895,40724,40725,40727,40729,40737,40739,40741],{},[898,40726,1724],{},[1726,40728,1728],{},[2326,40730,40731],{"scriptlevel":2328,"displaystyle":1734},[2330,40732,40733,40735],{},[2133,40734,2281],{},[898,40736,2146],{},[898,40738,1738],{},[1726,40740,2228],{},[2326,40742,40743],{"scriptlevel":2328,"displaystyle":1734},[2330,40744,40745,40747],{},[898,40746,2198],{},[898,40748,2146],{},[902,40750,40751],{"encoding":904},"Q = \\tfrac{1}{c}P - \\tfrac{d}{c}","; znaménko koeficientu u ",[883,40754,40756],{"className":40755},[886],[888,40757,40758],{"xmlns":890},[892,40759,40760,40764],{},[895,40761,40762],{},[898,40763,1738],{},[902,40765,1738],{"encoding":904}," zůstává, znaménko absolutního členu se mění.",[37906,40768,40770],{"id":40769},"příklad-25","Příklad 2.5",[724,40772,40773,40775,40776,1888],{},[38,40774,37914],{}," Lineární nabídka ",[883,40777,40779],{"className":40778},[886],[888,40780,40781],{"xmlns":890},[892,40782,40783,40797],{},[895,40784,40785,40787,40789,40791,40793,40795],{},[898,40786,1738],{},[1726,40788,1728],{},[2133,40790,4996],{},[898,40792,1724],{},[1726,40794,2099],{},[2133,40796,4991],{},[902,40798,40799],{"encoding":904},"P = 0{,}5Q + 25",[724,40801,40802,40804,40805,1888],{},[38,40803,37946],{}," Alternativní tvar ",[883,40806,40808],{"className":40807},[886],[888,40809,40810],{"xmlns":890},[892,40811,40812,40826],{},[895,40813,40814,40816,40818,40820,40822,40824],{},[898,40815,1724],{},[1726,40817,1728],{},[2133,40819,2135],{},[898,40821,1738],{},[1726,40823,2228],{},[2133,40825,3117],{},[902,40827,40828],{"encoding":904},"Q = 2P - 50",[16,40830,40831,40856],{},[19,40832,40833],{},[22,40834,40835,40850,40852,40854],{},[25,40836,40837],{},[883,40838,40840],{"className":40839},[886],[888,40841,40842],{"xmlns":890},[892,40843,40844,40848],{},[895,40845,40846],{},[898,40847,1738],{},[902,40849,1738],{"encoding":904},[25,40851,38000],{},[25,40853,15024],{},[25,40855,5198],{},[30,40857,40858],{},[22,40859,40860,40875,40877,40879],{},[35,40861,40862],{},[883,40863,40865],{"className":40864},[886],[888,40866,40867],{"xmlns":890},[892,40868,40869,40873],{},[895,40870,40871],{},[898,40872,1724],{},[902,40874,1724],{"encoding":904},[35,40876,2860],{},[35,40878,9021],{},[35,40880,38000],{},[198,40882,40884,40885,1762],{"id":40883},"posun-nabídky-shift-of-supply","Posun nabídky (",[614,40886,40887],{},"shift of supply",[724,40889,40890,40891,40894,40895,40912,40913,40938,40939,1888],{},"Posun nastává při změně exogenních proměnných — nová technologie snižuje náklady (posun ",[38,40892,40893],{},"doprava",": při stejné ceně ",[883,40896,40898],{"className":40897},[886],[888,40899,40900],{"xmlns":890},[892,40901,40902,40910],{},[895,40903,40904],{},[2275,40905,40906,40908],{},[898,40907,1738],{},[2133,40909,2328],{},[902,40911,38929],{"encoding":904}," vyrobí výrobce větší ",[883,40914,40916],{"className":40915},[886],[888,40917,40918],{"xmlns":890},[892,40919,40920,40936],{},[895,40921,40922,40928,40930],{},[2275,40923,40924,40926],{},[898,40925,1724],{},[2133,40927,2281],{},[1726,40929,3405],{},[2275,40931,40932,40934],{},[898,40933,1724],{},[2133,40935,2328],{},[902,40937,39042],{"encoding":904},"); zdražení vstupů posune křivku ",[38,40940,40941],{},"doleva",[724,40943,40944],{},[614,40945,40946,40947,40960,40961,40979,40980,40998,40999,1888],{},"Obrázek 2.11: Původní ",[883,40948,40950],{"className":40949},[886],[888,40951,40952],{"xmlns":890},[892,40953,40954,40958],{},[895,40955,40956],{},[898,40957,8659],{},[902,40959,8659],{"encoding":904},", posunuté ",[883,40962,40964],{"className":40963},[886],[888,40965,40966],{"xmlns":890},[892,40967,40968,40976],{},[895,40969,40970],{},[2275,40971,40972,40974],{},[898,40973,8659],{},[2133,40975,2281],{},[902,40977,40978],{"encoding":904},"S_1"," (doprava) a ",[883,40981,40983],{"className":40982},[886],[888,40984,40985],{"xmlns":890},[892,40986,40987,40995],{},[895,40988,40989],{},[2275,40990,40991,40993],{},[898,40992,8659],{},[2133,40994,2135],{},[902,40996,40997],{"encoding":904},"S_2"," (doleva) v ",[883,41000,41002],{"className":41001},[886],[888,41003,41004],{"xmlns":890},[892,41005,41006,41018],{},[895,41007,41008,41010,41012,41014,41016],{},[1726,41009,1735],{"stretchy":1734},[898,41011,1724],{},[1726,41013,1742],{"separator":1741},[898,41015,1738],{},[1726,41017,1762],{"stretchy":1734},[902,41019,37672],{"encoding":904},[37906,41021,41023],{"id":41022},"příklad-26-zdanění-výrobce","Příklad 2.6 — zdanění výrobce",[724,41025,41026,41028,41029,41053,41054,1888],{},[38,41027,37914],{}," Nabídka ",[883,41030,41032],{"className":41031},[886],[888,41033,41034],{"xmlns":890},[892,41035,41036,41050],{},[895,41037,41038,41040,41042,41044,41046,41048],{},[898,41039,1738],{},[1726,41041,1728],{},[898,41043,8659],{},[1726,41045,1735],{"stretchy":1734},[898,41047,1724],{},[1726,41049,1762],{"stretchy":1734},[902,41051,41052],{"encoding":904},"P = S(Q)","; na výrobce je uložena jednotková daň ",[883,41055,41057],{"className":41056},[886],[888,41058,41059],{"xmlns":890},[892,41060,41061,41065],{},[895,41062,41063],{},[898,41064,2772],{},[902,41066,2772],{"encoding":904},[724,41068,41069,41071,41072,41085,41086,41104,41105,41133],{},[38,41070,37946],{}," Spotřebitel zaplatí ",[883,41073,41075],{"className":41074},[886],[888,41076,41077],{"xmlns":890},[892,41078,41079,41083],{},[895,41080,41081],{},[898,41082,1738],{},[902,41084,1738],{"encoding":904},", výrobce obdrží ",[883,41087,41089],{"className":41088},[886],[888,41090,41091],{"xmlns":890},[892,41092,41093,41101],{},[895,41094,41095,41097,41099],{},[898,41096,1738],{},[1726,41098,2228],{},[898,41100,2772],{},[902,41102,41103],{"encoding":904},"P - T",". Z podmínky ",[883,41106,41108],{"className":41107},[886],[888,41109,41110],{"xmlns":890},[892,41111,41112,41130],{},[895,41113,41114,41116,41118,41120,41122,41124,41126,41128],{},[898,41115,1738],{},[1726,41117,2228],{},[898,41119,2772],{},[1726,41121,1728],{},[898,41123,8659],{},[1726,41125,1735],{"stretchy":1734},[898,41127,1724],{},[1726,41129,1762],{"stretchy":1734},[902,41131,41132],{"encoding":904},"P - T = S(Q)"," plyne",[883,41135,41137],{"className":41136},[886],[888,41138,41139],{"xmlns":890,"display":28047},[892,41140,41141,41175],{},[895,41142,41143,41145,41147,41153,41155,41157,41159,41161,41163,41165,41167,41169,41171,41173],{},[898,41144,1738],{},[1726,41146,1728],{},[2275,41148,41149,41151],{},[898,41150,8659],{},[2133,41152,2281],{},[1726,41154,1735],{"stretchy":1734},[898,41156,1724],{},[1726,41158,1762],{"stretchy":1734},[1726,41160,1728],{},[898,41162,8659],{},[1726,41164,1735],{"stretchy":1734},[898,41166,1724],{},[1726,41168,1762],{"stretchy":1734},[1726,41170,2099],{},[898,41172,2772],{},[898,41174,1888],{"mathvariant":2377},[902,41176,41177],{"encoding":904},"P = S_1(Q) = S(Q) + T.",[724,41179,41180,41181,41194,41195,1777,41208,41211,41212,3877,41232,8088,41250,1888],{},"Křivka ",[883,41182,41184],{"className":41183},[886],[888,41185,41186],{"xmlns":890},[892,41187,41188,41192],{},[895,41189,41190],{},[898,41191,8659],{},[902,41193,8659],{"encoding":904}," se tedy posune o ",[883,41196,41198],{"className":41197},[886],[888,41199,41200],{"xmlns":890},[892,41201,41202,41206],{},[895,41203,41204],{},[898,41205,2772],{},[902,41207,2772],{"encoding":904},[38,41209,41210],{},"svisle nahoru"," (tj. doleva). Např. pro ",[883,41213,41215],{"className":41214},[886],[888,41216,41217],{"xmlns":890},[892,41218,41219,41229],{},[895,41220,41221,41223,41225,41227],{},[898,41222,1738],{},[1726,41224,1728],{},[2133,41226,2135],{},[898,41228,1724],{},[902,41230,41231],{"encoding":904},"P = 2Q",[883,41233,41235],{"className":41234},[886],[888,41236,41237],{"xmlns":890},[892,41238,41239,41247],{},[895,41240,41241,41243,41245],{},[898,41242,2772],{},[1726,41244,1728],{},[2133,41246,2238],{},[902,41248,41249],{"encoding":904},"T = 6",[883,41251,41253],{"className":41252},[886],[888,41254,41255],{"xmlns":890},[892,41256,41257,41279],{},[895,41258,41259,41265,41267,41269,41271,41273,41275,41277],{},[2275,41260,41261,41263],{},[898,41262,8659],{},[2133,41264,2281],{},[1726,41266,2703],{},[898,41268,1738],{},[1726,41270,1728],{},[2133,41272,2135],{},[898,41274,1724],{},[1726,41276,2099],{},[2133,41278,2238],{},[902,41280,41281],{"encoding":904},"S_1: P = 2Q + 6",[724,41283,41284],{},[614,41285,41286,41287,41300],{},"Obrázek 2.12: Posun nabídky o ",[883,41288,41290],{"className":41289},[886],[888,41291,41292],{"xmlns":890},[892,41293,41294,41298],{},[895,41295,41296],{},[898,41297,2772],{},[902,41299,2772],{"encoding":904}," svisle nahoru.",[36951,41302],{},[115,41304,41306],{"id":41305},"tržní-rovnováha","Tržní rovnováha",[3859,41308,41309],{},[724,41310,41311,41313,41314,1777,41317,41349,41350,1343,41373,41396,41397,41400,41401,41414],{},[883,41312,4145],{}," TL;DR\nV ",[38,41315,41316],{},"rovnovážném bodě",[883,41318,41320],{"className":41319},[886],[888,41321,41322],{"xmlns":890},[892,41323,41324,41346],{},[895,41325,41326,41328,41330,41336,41338,41344],{},[898,41327,4240],{},[1726,41329,2487],{"stretchy":1734},[2128,41331,41332,41334],{},[898,41333,1724],{},[898,41335,4240],{},[1726,41337,1742],{"separator":1741},[2128,41339,41340,41342],{},[898,41341,1738],{},[898,41343,4240],{},[1726,41345,2502],{"stretchy":1734},[902,41347,41348],{"encoding":904},"E[Q^E, P^E]"," se poptávané a nabízené množství rovnají. Najde se jako řešení soustavy ",[883,41351,41353],{"className":41352},[886],[888,41354,41355],{"xmlns":890},[892,41356,41357,41371],{},[895,41358,41359,41361,41363,41365,41367,41369],{},[898,41360,1738],{},[1726,41362,1728],{},[898,41364,1731],{},[1726,41366,1735],{"stretchy":1734},[898,41368,1724],{},[1726,41370,1762],{"stretchy":1734},[902,41372,1830],{"encoding":904},[883,41374,41376],{"className":41375},[886],[888,41377,41378],{"xmlns":890},[892,41379,41380,41394],{},[895,41381,41382,41384,41386,41388,41390,41392],{},[898,41383,1738],{},[1726,41385,1728],{},[898,41387,8659],{},[1726,41389,1735],{"stretchy":1734},[898,41391,1724],{},[1726,41393,1762],{"stretchy":1734},[902,41395,41052],{"encoding":904},". Čtyři ",[38,41398,41399],{},"pravidla komparativní statiky"," popisují, jak se ",[883,41402,41404],{"className":41403},[886],[888,41405,41406],{"xmlns":890},[892,41407,41408,41412],{},[895,41409,41410],{},[898,41411,4240],{},[902,41413,4240],{"encoding":904}," posune při změně poptávky nebo nabídky.",[198,41416,41418],{"id":41417},"definice","Definice",[724,41420,41421,10009,41423,41426,41427,1777,41430,41448,41449,41480,41481,10009,41484,1847],{},[38,41422,41306],{},[614,41424,41425],{},"market equilibrium",") je stav, kdy poptávané množství = nabízené množství. Při ",[38,41428,41429],{},"rovnovážné ceně",[883,41431,41433],{"className":41432},[886],[888,41434,41435],{"xmlns":890},[892,41436,41437,41445],{},[895,41438,41439],{},[2128,41440,41441,41443],{},[898,41442,1738],{},[898,41444,4240],{},[902,41446,41447],{"encoding":904},"P^E"," není přebytek ani nedostatek zboží. Bod ",[883,41450,41452],{"className":41451},[886],[888,41453,41454],{"xmlns":890},[892,41455,41456,41478],{},[895,41457,41458,41460,41462,41468,41470,41476],{},[898,41459,4240],{},[1726,41461,2487],{"stretchy":1734},[2128,41463,41464,41466],{},[898,41465,1724],{},[898,41467,4240],{},[1726,41469,1742],{"separator":1741},[2128,41471,41472,41474],{},[898,41473,1738],{},[898,41475,4240],{},[1726,41477,2502],{"stretchy":1734},[902,41479,41348],{"encoding":904}," se nazývá ",[38,41482,41483],{},"rovnovážný bod",[614,41485,41486],{},"equilibrium point",[724,41488,41489,41490,1343,41513,1888],{},"Rovnovážný bod je průsečíkem křivek poptávky a nabídky; nalézá se jako řešení soustavy ",[883,41491,41493],{"className":41492},[886],[888,41494,41495],{"xmlns":890},[892,41496,41497,41511],{},[895,41498,41499,41501,41503,41505,41507,41509],{},[898,41500,1738],{},[1726,41502,1728],{},[898,41504,1731],{},[1726,41506,1735],{"stretchy":1734},[898,41508,1724],{},[1726,41510,1762],{"stretchy":1734},[902,41512,1830],{"encoding":904},[883,41514,41516],{"className":41515},[886],[888,41517,41518],{"xmlns":890},[892,41519,41520,41534],{},[895,41521,41522,41524,41526,41528,41530,41532],{},[898,41523,1738],{},[1726,41525,1728],{},[898,41527,8659],{},[1726,41529,1735],{"stretchy":1734},[898,41531,1724],{},[1726,41533,1762],{"stretchy":1734},[902,41535,41052],{"encoding":904},[724,41537,41538],{},[1647,41539],{"alt":41540,"className":41541,"src":41542},"imek-poptavka-nabidka-rovnovaha",[210,1651],"\u002Fwiki-assets\u002Fimek-poptavka-nabidka-rovnovaha.jpeg",[724,41544,41545],{},[614,41546,41547,41548,41561,41562,13997,41575,41596,41597,1888],{},"Obrázek 2.13: Klesající ",[883,41549,41551],{"className":41550},[886],[888,41552,41553],{"xmlns":890},[892,41554,41555,41559],{},[895,41556,41557],{},[898,41558,1731],{},[902,41560,1731],{"encoding":904}," a rostoucí ",[883,41563,41565],{"className":41564},[886],[888,41566,41567],{"xmlns":890},[892,41568,41569,41573],{},[895,41570,41571],{},[898,41572,8659],{},[902,41574,8659],{"encoding":904},[883,41576,41578],{"className":41577},[886],[888,41579,41580],{"xmlns":890},[892,41581,41582,41594],{},[895,41583,41584,41586,41588,41590,41592],{},[1726,41585,1735],{"stretchy":1734},[898,41587,1724],{},[1726,41589,1742],{"separator":1741},[898,41591,1738],{},[1726,41593,1762],{"stretchy":1734},[902,41595,37672],{"encoding":904}," protínající se v ",[883,41598,41600],{"className":41599},[886],[888,41601,41602],{"xmlns":890},[892,41603,41604,41626],{},[895,41605,41606,41608,41610,41616,41618,41624],{},[898,41607,4240],{},[1726,41609,2487],{"stretchy":1734},[2128,41611,41612,41614],{},[898,41613,1724],{},[898,41615,4240],{},[1726,41617,1742],{"separator":1741},[2128,41619,41620,41622],{},[898,41621,1738],{},[898,41623,4240],{},[1726,41625,2502],{"stretchy":1734},[902,41627,41348],{"encoding":904},[198,41629,41631],{"id":41630},"příklad-27-kvadratický-model","Příklad 2.7 (kvadratický model)",[724,41633,41634,41636,41637,41671,41672,1888],{},[38,41635,37914],{}," Poptávka ",[883,41638,41640],{"className":41639},[886],[888,41641,41642],{"xmlns":890},[892,41643,41644,41668],{},[895,41645,41646,41648,41650,41652,41658,41660,41662,41664,41666],{},[898,41647,1738],{},[1726,41649,1728],{},[1726,41651,2228],{},[2128,41653,41654,41656],{},[898,41655,1724],{},[2133,41657,2135],{},[1726,41659,2228],{},[2133,41661,2860],{},[898,41663,1724],{},[1726,41665,2099],{},[2133,41667,8789],{},[902,41669,41670],{"encoding":904},"P = -Q^2 - 10Q + 150",", nabídka ",[883,41673,41675],{"className":41674},[886],[888,41676,41677],{"xmlns":890},[892,41678,41679,41701],{},[895,41680,41681,41683,41685,41691,41693,41695,41697,41699],{},[898,41682,1738],{},[1726,41684,1728],{},[2128,41686,41687,41689],{},[898,41688,1724],{},[2133,41690,2135],{},[1726,41692,2099],{},[2133,41694,22927],{},[898,41696,1724],{},[1726,41698,2099],{},[2133,41700,32527],{},[902,41702,41703],{"encoding":904},"P = Q^2 + 14Q + 22",[724,41705,41706,41708],{},[38,41707,37946],{}," Z rovnosti",[883,41710,41712],{"className":41711},[886],[888,41713,41714],{"xmlns":890,"display":28047},[892,41715,41716,41754],{},[895,41717,41718,41720,41726,41728,41730,41732,41734,41736,41738,41744,41746,41748,41750,41752],{},[1726,41719,2228],{},[2128,41721,41722,41724],{},[898,41723,1724],{},[2133,41725,2135],{},[1726,41727,2228],{},[2133,41729,2860],{},[898,41731,1724],{},[1726,41733,2099],{},[2133,41735,8789],{},[1726,41737,1728],{},[2128,41739,41740,41742],{},[898,41741,1724],{},[2133,41743,2135],{},[1726,41745,2099],{},[2133,41747,22927],{},[898,41749,1724],{},[1726,41751,2099],{},[2133,41753,32527],{},[902,41755,41756],{"encoding":904},"-Q^2 - 10Q + 150 = Q^2 + 14Q + 22",[724,41758,41759,41760,41795,41796,41829,41830,41847,41848,41861,41862,1343,41884,41921,41922,1888],{},"dostaneme ",[883,41761,41763],{"className":41762},[886],[888,41764,41765],{"xmlns":890},[892,41766,41767,41792],{},[895,41768,41769,41771,41777,41779,41782,41784,41786,41788,41790],{},[2133,41770,2135],{},[2128,41772,41773,41775],{},[898,41774,1724],{},[2133,41776,2135],{},[1726,41778,2099],{},[2133,41780,41781],{},"24",[898,41783,1724],{},[1726,41785,2228],{},[2133,41787,5604],{},[1726,41789,1728],{},[2133,41791,2328],{},[902,41793,41794],{"encoding":904},"2Q^2 + 24Q - 128 = 0",", resp. ",[883,41797,41799],{"className":41798},[886],[888,41800,41801],{"xmlns":890},[892,41802,41803,41826],{},[895,41804,41805,41811,41813,41815,41817,41819,41822,41824],{},[2128,41806,41807,41809],{},[898,41808,1724],{},[2133,41810,2135],{},[1726,41812,2099],{},[2133,41814,3506],{},[898,41816,1724],{},[1726,41818,2228],{},[2133,41820,41821],{},"64",[1726,41823,1728],{},[2133,41825,2328],{},[902,41827,41828],{"encoding":904},"Q^2 + 12Q - 64 = 0",". Kořeny jsou ",[883,41831,41833],{"className":41832},[886],[888,41834,41835],{"xmlns":890},[892,41836,41837,41844],{},[895,41838,41839,41841],{},[1726,41840,2228],{},[2133,41842,41843],{},"16",[902,41845,41846],{"encoding":904},"-16"," (nevyhovuje) a ",[883,41849,41851],{"className":41850},[886],[888,41852,41853],{"xmlns":890},[892,41854,41855,41859],{},[895,41856,41857],{},[2133,41858,2352],{},[902,41860,2352],{"encoding":904},". Tedy ",[883,41863,41865],{"className":41864},[886],[888,41866,41867],{"xmlns":890},[892,41868,41869,41881],{},[895,41870,41871,41877,41879],{},[2128,41872,41873,41875],{},[898,41874,1724],{},[898,41876,4240],{},[1726,41878,1728],{},[2133,41880,2352],{},[902,41882,41883],{"encoding":904},"Q^E = 4",[883,41885,41887],{"className":41886},[886],[888,41888,41889],{"xmlns":890},[892,41890,41891,41918],{},[895,41892,41893,41899,41901,41903,41905,41907,41909,41911,41913,41915],{},[2128,41894,41895,41897],{},[898,41896,1738],{},[898,41898,4240],{},[1726,41900,1728],{},[1726,41902,2228],{},[2133,41904,41843],{},[1726,41906,2228],{},[2133,41908,5198],{},[1726,41910,2099],{},[2133,41912,8789],{},[1726,41914,1728],{},[2133,41916,41917],{},"94",[902,41919,41920],{"encoding":904},"P^E = -16 - 40 + 150 = 94",", rovnovážný bod ",[883,41923,41925],{"className":41924},[886],[888,41926,41927],{"xmlns":890},[892,41928,41929,41943],{},[895,41930,41931,41933,41935,41937,41939,41941],{},[898,41932,4240],{},[1726,41934,2487],{"stretchy":1734},[2133,41936,2352],{},[1726,41938,1742],{"separator":1741},[2133,41940,41917],{},[1726,41942,2502],{"stretchy":1734},[902,41944,41945],{"encoding":904},"E[4, 94]",[198,41947,41949],{"id":41948},"příklad-28-dvoukomoditní-trh","Příklad 2.8 (dvoukomoditní trh)",[724,41951,41952,41954],{},[38,41953,37914],{}," Poptávky a nabídky dvou zboží",[883,41956,41958],{"className":41957},[886],[888,41959,41960],{"xmlns":890,"display":28047},[892,41961,41962,42128],{},[20735,41963,41966,42054],{"rowspacing":20737,"columnalign":41964,"columnspacing":41965},"right left right left","0em 1em 0em",[20740,41967,41968,41978,42010,42020],{},[20743,41969,41970],{},[2326,41971,41972],{"scriptlevel":2328,"displaystyle":1741},[2275,41973,41974,41976],{},[898,41975,1724],{},[2133,41977,2281],{},[20743,41979,41980],{},[2326,41981,41982],{"scriptlevel":2328,"displaystyle":1741},[895,41983,41984,41986,41988,41990,41992,41994,42000,42002,42008],{},[895,41985],{},[1726,41987,1728],{},[2133,41989,5198],{},[1726,41991,2228],{},[2133,41993,2231],{},[2275,41995,41996,41998],{},[898,41997,1738],{},[2133,41999,2281],{},[1726,42001,2228],{},[2275,42003,42004,42006],{},[898,42005,1738],{},[2133,42007,2135],{},[1726,42009,1742],{"separator":1741},[20743,42011,42012],{},[2326,42013,42014],{"scriptlevel":2328,"displaystyle":1741},[2275,42015,42016,42018],{},[898,42017,1724],{},[2133,42019,2135],{},[20743,42021,42022],{},[2326,42023,42024],{"scriptlevel":2328,"displaystyle":1741},[895,42025,42026,42028,42030,42032,42034,42036,42042,42044,42046,42052],{},[895,42027],{},[1726,42029,1728],{},[2133,42031,3117],{},[1726,42033,2228],{},[2133,42035,2135],{},[2275,42037,42038,42040],{},[898,42039,1738],{},[2133,42041,2281],{},[1726,42043,2228],{},[2133,42045,2352],{},[2275,42047,42048,42050],{},[898,42049,1738],{},[2133,42051,2135],{},[1726,42053,1742],{"separator":1741},[20740,42055,42056,42066,42092,42102],{},[20743,42057,42058],{},[2326,42059,42060],{"scriptlevel":2328,"displaystyle":1741},[2275,42061,42062,42064],{},[898,42063,1724],{},[2133,42065,2281],{},[20743,42067,42068],{},[2326,42069,42070],{"scriptlevel":2328,"displaystyle":1741},[895,42071,42072,42074,42076,42078,42080,42082,42084,42090],{},[895,42073],{},[1726,42075,1728],{},[1726,42077,2228],{},[2133,42079,2177],{},[1726,42081,2099],{},[2133,42083,2352],{},[2275,42085,42086,42088],{},[898,42087,1738],{},[2133,42089,2281],{},[1726,42091,1742],{"separator":1741},[20743,42093,42094],{},[2326,42095,42096],{"scriptlevel":2328,"displaystyle":1741},[2275,42097,42098,42100],{},[898,42099,1724],{},[2133,42101,2135],{},[20743,42103,42104],{},[2326,42105,42106],{"scriptlevel":2328,"displaystyle":1741},[895,42107,42108,42110,42112,42114,42116,42118,42120,42126],{},[895,42109],{},[1726,42111,1728],{},[1726,42113,2228],{},[2133,42115,24182],{},[1726,42117,2099],{},[2133,42119,2177],{},[2275,42121,42122,42124],{},[898,42123,1738],{},[2133,42125,2135],{},[898,42127,1888],{"mathvariant":2377},[902,42129,42130],{"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}",[724,42132,42133,42135],{},[38,42134,37946],{}," Z rovností poptávek a nabídek dostaneme",[883,42137,42139],{"className":42138},[886],[888,42140,42141],{"xmlns":890,"display":28047},[892,42142,42143,42192],{},[895,42144,42145,42147,42153,42155,42161,42163,42165,42167,42169,42171,42177,42179,42181,42187,42189],{},[2133,42146,3989],{},[2275,42148,42149,42151],{},[898,42150,1738],{},[2133,42152,2281],{},[1726,42154,2099],{},[2275,42156,42157,42159],{},[898,42158,1738],{},[2133,42160,2135],{},[1726,42162,1728],{},[2133,42164,21184],{},[1726,42166,1742],{"separator":1741},[5865,42168],{"width":5867},[2133,42170,2135],{},[2275,42172,42173,42175],{},[898,42174,1738],{},[2133,42176,2281],{},[1726,42178,2099],{},[2133,42180,24182],{},[2275,42182,42183,42185],{},[898,42184,1738],{},[2133,42186,2135],{},[1726,42188,1728],{},[2133,42190,42191],{},"57.",[902,42193,42194],{"encoding":904},"9P_1 + P_2 = 43, \\qquad 2P_1 + 7P_2 = 57.",[724,42196,42197,42198,1343,42222,42246,42247,1343,42272,42296,42297,42299],{},"Řešením je ",[883,42199,42201],{"className":42200},[886],[888,42202,42203],{"xmlns":890},[892,42204,42205,42219],{},[895,42206,42207,42215,42217],{},[9151,42208,42209,42211,42213],{},[898,42210,1738],{},[2133,42212,2281],{},[898,42214,4240],{},[1726,42216,1728],{},[2133,42218,2352],{},[902,42220,42221],{"encoding":904},"P_1^E = 4",[883,42223,42225],{"className":42224},[886],[888,42226,42227],{"xmlns":890},[892,42228,42229,42243],{},[895,42230,42231,42239,42241],{},[9151,42232,42233,42235,42237],{},[898,42234,1738],{},[2133,42236,2135],{},[898,42238,4240],{},[1726,42240,1728],{},[2133,42242,24182],{},[902,42244,42245],{"encoding":904},"P_2^E = 7","; zpětným dosazením ",[883,42248,42250],{"className":42249},[886],[888,42251,42252],{"xmlns":890},[892,42253,42254,42269],{},[895,42255,42256,42264,42266],{},[9151,42257,42258,42260,42262],{},[898,42259,1724],{},[2133,42261,2281],{},[898,42263,4240],{},[1726,42265,1728],{},[2133,42267,42268],{},"13",[902,42270,42271],{"encoding":904},"Q_1^E = 13",[883,42273,42275],{"className":42274},[886],[888,42276,42277],{"xmlns":890},[892,42278,42279,42293],{},[895,42280,42281,42289,42291],{},[9151,42282,42283,42285,42287],{},[898,42284,1724],{},[2133,42286,2135],{},[898,42288,4240],{},[1726,42290,1728],{},[2133,42292,22927],{},[902,42294,42295],{"encoding":904},"Q_2^E = 14",". Zboží jsou ",[38,42298,39803],{}," (zkřížené koeficienty v poptávce jsou záporné).",[198,42301,42303],{"id":42302},"dynamický-model-pavučinový-teorém","Dynamický model — pavučinový teorém",[724,42305,42306,42307,42324,42325,10009,42328,1847],{},"Rovnovážná cena se obecně liší od tržní ceny, která vzniká působením tržních sil v čase. Za podmínky stability se tržní cena přibližuje k ",[883,42308,42310],{"className":42309},[886],[888,42311,42312],{"xmlns":890},[892,42313,42314,42322],{},[895,42315,42316],{},[2128,42317,42318,42320],{},[898,42319,1738],{},[898,42321,4240],{},[902,42323,41447],{"encoding":904},"; mechanismus popisuje ",[38,42326,42327],{},"teorém pavučiny",[614,42329,42330],{},"cobweb model",[198,42332,42334],{"id":42333},"pravidla-komparativní-statiky-14","Pravidla komparativní statiky (1–4)",[724,42336,42337],{},[1647,42338],{"alt":42339,"className":42340,"src":42341},"imek-komparativni-statika-4pripady",[210,1651],"\u002Fwiki-assets\u002Fimek-komparativni-statika-4pripady.jpeg",[3859,42343,42344,42385,42425,42465],{},[724,42345,42346,42349,42350,6177,42367,1888],{},[38,42347,42348],{},"Pravidlo 1:"," Růst poptávky ⟹ růst ",[883,42351,42353],{"className":42352},[886],[888,42354,42355],{"xmlns":890},[892,42356,42357,42365],{},[895,42358,42359],{},[2128,42360,42361,42363],{},[898,42362,1738],{},[898,42364,4240],{},[902,42366,41447],{"encoding":904},[883,42368,42370],{"className":42369},[886],[888,42371,42372],{"xmlns":890},[892,42373,42374,42382],{},[895,42375,42376],{},[2128,42377,42378,42380],{},[898,42379,1724],{},[898,42381,4240],{},[902,42383,42384],{"encoding":904},"Q^E",[724,42386,42387,42390,42391,6177,42408,1888],{},[38,42388,42389],{},"Pravidlo 2:"," Pokles poptávky ⟹ pokles ",[883,42392,42394],{"className":42393},[886],[888,42395,42396],{"xmlns":890},[892,42397,42398,42406],{},[895,42399,42400],{},[2128,42401,42402,42404],{},[898,42403,1738],{},[898,42405,4240],{},[902,42407,41447],{"encoding":904},[883,42409,42411],{"className":42410},[886],[888,42412,42413],{"xmlns":890},[892,42414,42415,42423],{},[895,42416,42417],{},[2128,42418,42419,42421],{},[898,42420,1724],{},[898,42422,4240],{},[902,42424,42384],{"encoding":904},[724,42426,42427,42430,42431,9340,42448,1888],{},[38,42428,42429],{},"Pravidlo 3:"," Růst nabídky ⟹ pokles ",[883,42432,42434],{"className":42433},[886],[888,42435,42436],{"xmlns":890},[892,42437,42438,42446],{},[895,42439,42440],{},[2128,42441,42442,42444],{},[898,42443,1738],{},[898,42445,4240],{},[902,42447,41447],{"encoding":904},[883,42449,42451],{"className":42450},[886],[888,42452,42453],{"xmlns":890},[892,42454,42455,42463],{},[895,42456,42457],{},[2128,42458,42459,42461],{},[898,42460,1724],{},[898,42462,4240],{},[902,42464,42384],{"encoding":904},[724,42466,42467,42470,42471,42488,42489,1888],{},[38,42468,42469],{},"Pravidlo 4:"," Pokles nabídky ⟹ růst ",[883,42472,42474],{"className":42473},[886],[888,42475,42476],{"xmlns":890},[892,42477,42478,42486],{},[895,42479,42480],{},[2128,42481,42482,42484],{},[898,42483,1738],{},[898,42485,4240],{},[902,42487,41447],{"encoding":904},", pokles ",[883,42490,42492],{"className":42491},[886],[888,42493,42494],{"xmlns":890},[892,42495,42496,42504],{},[895,42497,42498],{},[2128,42499,42500,42502],{},[898,42501,1724],{},[898,42503,4240],{},[902,42505,42384],{"encoding":904},[16,42507,42508,42553],{},[19,42509,42510],{},[22,42511,42512,42515,42534],{},[25,42513,42514],{},"Změna",[25,42516,42517],{},[883,42518,42520],{"className":42519},[886],[888,42521,42522],{"xmlns":890},[892,42523,42524,42532],{},[895,42525,42526],{},[2128,42527,42528,42530],{},[898,42529,1738],{},[898,42531,4240],{},[902,42533,41447],{"encoding":904},[25,42535,42536],{},[883,42537,42539],{"className":42538},[886],[888,42540,42541],{"xmlns":890},[892,42542,42543,42551],{},[895,42544,42545],{},[2128,42546,42547,42549],{},[898,42548,1724],{},[898,42550,4240],{},[902,42552,42384],{"encoding":904},[30,42554,42555,42565,42575,42584],{},[22,42556,42557,42560,42563],{},[35,42558,42559],{},"Růst poptávky",[35,42561,42562],{},"↑",[35,42564,42562],{},[22,42566,42567,42570,42573],{},[35,42568,42569],{},"Pokles poptávky",[35,42571,42572],{},"↓",[35,42574,42572],{},[22,42576,42577,42580,42582],{},[35,42578,42579],{},"Růst nabídky",[35,42581,42572],{},[35,42583,42562],{},[22,42585,42586,42589,42591],{},[35,42587,42588],{},"Pokles nabídky",[35,42590,42562],{},[35,42592,42572],{},[724,42594,42595],{},[614,42596,42597],{},"Obrázky 2.15–2.18 ilustrují všechny čtyři situace pomocí posunu jedné z křivek.",[36951,42599],{},[115,42601,811],{"id":42602},"zdanění-trhu",[3859,42604,42605,42694],{},[724,42606,42607,42609,42610,42623,42624,2924,42637,42640,42641,36757,42664,42689,42690,42693],{},[883,42608,4145],{}," TL;DR\nJednotková daň ",[883,42611,42613],{"className":42612},[886],[888,42614,42615],{"xmlns":890},[892,42616,42617,42621],{},[895,42618,42619],{},[898,42620,2772],{},[902,42622,2772],{"encoding":904}," uložená na každou prodanou jednotku způsobí posun jedné z křivek o ",[883,42625,42627],{"className":42626},[886],[888,42628,42629],{"xmlns":890},[892,42630,42631,42635],{},[895,42632,42633],{},[898,42634,2772],{},[902,42636,2772],{"encoding":904},[38,42638,42639],{},"Daňové břemeno"," se dělí mezi spotřebitele (",[883,42642,42644],{"className":42643},[886],[888,42645,42646],{"xmlns":890},[892,42647,42648,42661],{},[895,42649,42650],{},[2275,42651,42652,42654],{},[898,42653,2772],{},[895,42655,42656,42659],{},[898,42657,42658],{},"s",[898,42660,724],{},[902,42662,42663],{"encoding":904},"T_{sp}",[883,42665,42667],{"className":42666},[886],[888,42668,42669],{"xmlns":890},[892,42670,42671,42686],{},[895,42672,42673],{},[2275,42674,42675,42677],{},[898,42676,2772],{},[895,42678,42679,42682,42684],{},[898,42680,42681],{},"v",[898,42683,2003],{},[898,42685,12027],{},[902,42687,42688],{"encoding":904},"T_{vyr}","). Klíčová vlastnost — ",[38,42691,42692],{},"ekvivalence zdanění",": výsledné rovnovážné množství i čistá cena pro výrobce jsou stejné bez ohledu na to, zda je daň uložena výrobci, či spotřebiteli.",[724,42695,42696],{},[614,42697,42698,42699,1888],{},"Pro detail, úplné odvození, Příklady 2.9 a 2.10 a geometrickou interpretaci viz ",[207,42700,42702],{"className":42701,"dataFsResolvedFilePath":809,"href":810},[210],"zdaneni-trhu",[724,42704,42705,42706,42709,42710,42736,42737,42740,42741,42767,42768,42785,42786,42826,42827,3877,42840,1888],{},"Existují dvě formy zdanění — daň uložená ",[38,42707,42708],{},"výrobci"," (posun nabídky ",[883,42711,42713],{"className":42712},[886],[888,42714,42715],{"xmlns":890},[892,42716,42717,42733],{},[895,42718,42719,42725,42727,42729,42731],{},[2275,42720,42721,42723],{},[898,42722,8659],{},[2133,42724,2281],{},[1726,42726,1728],{},[898,42728,8659],{},[1726,42730,2099],{},[898,42732,2772],{},[902,42734,42735],{"encoding":904},"S_1 = S + T"," svisle nahoru) a daň uložená ",[38,42738,42739],{},"spotřebiteli"," (posun poptávky ",[883,42742,42744],{"className":42743},[886],[888,42745,42746],{"xmlns":890},[892,42747,42748,42764],{},[895,42749,42750,42756,42758,42760,42762],{},[2275,42751,42752,42754],{},[898,42753,1731],{},[2133,42755,2135],{},[1726,42757,1728],{},[898,42759,1731],{},[1726,42761,2228],{},[898,42763,2772],{},[902,42765,42766],{"encoding":904},"D_2 = D - T"," svisle dolů). V obou případech nové rovnovážné množství ",[883,42769,42771],{"className":42770},[886],[888,42772,42773],{"xmlns":890},[892,42774,42775,42783],{},[895,42776,42777],{},[2128,42778,42779,42781],{},[898,42780,1724],{},[898,42782,4240],{},[902,42784,42384],{"encoding":904}," klesá a vzniká rozklad daně ",[883,42787,42789],{"className":42788},[886],[888,42790,42791],{"xmlns":890},[892,42792,42793,42823],{},[895,42794,42795,42797,42799,42809,42811],{},[898,42796,2772],{},[1726,42798,1728],{},[2275,42800,42801,42803],{},[898,42802,2772],{},[895,42804,42805,42807],{},[898,42806,42658],{},[898,42808,724],{},[1726,42810,2099],{},[2275,42812,42813,42815],{},[898,42814,2772],{},[895,42816,42817,42819,42821],{},[898,42818,42681],{},[898,42820,2003],{},[898,42822,12027],{},[902,42824,42825],{"encoding":904},"T = T_{sp} + T_{vyr}"," mezi obě strany trhu, určený relativními sklony křivek ",[883,42828,42830],{"className":42829},[886],[888,42831,42832],{"xmlns":890},[892,42833,42834,42838],{},[895,42835,42836],{},[898,42837,1731],{},[902,42839,1731],{"encoding":904},[883,42841,42843],{"className":42842},[886],[888,42844,42845],{"xmlns":890},[892,42846,42847,42851],{},[895,42848,42849],{},[898,42850,8659],{},[902,42852,8659],{"encoding":904},[724,42854,42855,42856,42859,42860,3877,42890,42924],{},"Zásadním výsledkem kapitoly je ",[38,42857,42858],{},"věta o ekvivalenci zdanění",": ať je daň uvalena formálně na kohokoli, rovnovážné množství i reálné rozdělení břemene jsou identické — ",[883,42861,42863],{"className":42862},[886],[888,42864,42865],{"xmlns":890},[892,42866,42867,42887],{},[895,42868,42869,42877,42879],{},[9151,42870,42871,42873,42875],{},[898,42872,1724],{},[2133,42874,2281],{},[898,42876,4240],{},[1726,42878,1728],{},[9151,42880,42881,42883,42885],{},[898,42882,1724],{},[2133,42884,2135],{},[898,42886,4240],{},[902,42888,42889],{"encoding":904},"Q_1^E = Q_2^E",[883,42891,42893],{"className":42892},[886],[888,42894,42895],{"xmlns":890},[892,42896,42897,42921],{},[895,42898,42899,42907,42909,42911,42913],{},[9151,42900,42901,42903,42905],{},[898,42902,1738],{},[2133,42904,2281],{},[898,42906,4240],{},[1726,42908,2228],{},[898,42910,2772],{},[1726,42912,1728],{},[9151,42914,42915,42917,42919],{},[898,42916,1738],{},[2133,42918,2135],{},[898,42920,4240],{},[902,42922,42923],{"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.",[724,42926,42927,42928,42931,42932,42958,42959,42987,42988,42991,42992,42995,42996,1888],{},"Podrobný výklad, Příklady ",[38,42929,42930],{},"2.9"," (daň výrobci, ",[883,42933,42935],{"className":42934},[886],[888,42936,42937],{"xmlns":890},[892,42938,42939,42955],{},[895,42940,42941,42951,42953],{},[2275,42942,42943,42945],{},[898,42944,2772],{},[895,42946,42947,42949],{},[898,42948,42658],{},[898,42950,724],{},[1726,42952,1728],{},[2133,42954,2135],{},[902,42956,42957],{"encoding":904},"T_{sp} = 2"," Kč, ",[883,42960,42962],{"className":42961},[886],[888,42963,42964],{"xmlns":890},[892,42965,42966,42984],{},[895,42967,42968,42980,42982],{},[2275,42969,42970,42972],{},[898,42971,2772],{},[895,42973,42974,42976,42978],{},[898,42975,42681],{},[898,42977,2003],{},[898,42979,12027],{},[1726,42981,1728],{},[2133,42983,2352],{},[902,42985,42986],{"encoding":904},"T_{vyr} = 4"," Kč) a ",[38,42989,42990],{},"2.10"," (táž daň, ale na spotřebitele), postup výpočtu rozkladu břemene a ",[38,42993,42994],{},"Obrázky 2.17–2.21"," jsou na samostatné stránce ",[207,42997,42702],{"className":42998,"dataFsResolvedFilePath":809,"href":810},[210],[36951,43000],{},[115,43002,43004],{"id":43003},"multiplikátory-pro-mikroekonomické-proměnné","Multiplikátory pro mikroekonomické proměnné",[3859,43006,43007],{},[724,43008,43009,43011,43012,43015,43016,43018],{},[883,43010,4145],{}," TL;DR\nMultiplikátory jsou ",[38,43013,43014],{},"parciální derivace redukovaného tvaru"," endogenní proměnné podle exogenních parametrů. Udávají přibližnou odezvu rovnovážného bodu na jednotkovou změnu parametru (",[614,43017,36941],{},"). Kvalitativní smysl (znaménko) je invariantní, kvantitativní závisí na konkrétních hodnotách.",[198,43020,43022],{"id":43021},"redukovaný-tvar","Redukovaný tvar",[724,43024,43025,43026,10009,43049,1343,43067,12114,43084,10009,43107,43124,43125,43155],{},"Pro lineární model ",[883,43027,43029],{"className":43028},[886],[888,43030,43031],{"xmlns":890},[892,43032,43033,43047],{},[895,43034,43035,43037,43039,43041,43043,43045],{},[898,43036,1738],{},[1726,43038,1728],{},[898,43040,207],{},[898,43042,1724],{},[1726,43044,2099],{},[898,43046,2102],{},[902,43048,37041],{"encoding":904},[883,43050,43052],{"className":43051},[886],[888,43053,43054],{"xmlns":890},[892,43055,43056,43064],{},[895,43057,43058,43060,43062],{},[898,43059,207],{},[1726,43061,3444],{},[2133,43063,2328],{},[902,43065,43066],{"encoding":904},"a \u003C 0",[883,43068,43070],{"className":43069},[886],[888,43071,43072],{"xmlns":890},[892,43073,43074,43082],{},[895,43075,43076,43078,43080],{},[898,43077,2102],{},[1726,43079,3405],{},[2133,43081,2328],{},[902,43083,18795],{"encoding":904},[883,43085,43087],{"className":43086},[886],[888,43088,43089],{"xmlns":890},[892,43090,43091,43105],{},[895,43092,43093,43095,43097,43099,43101,43103],{},[898,43094,1738],{},[1726,43096,1728],{},[898,43098,2146],{},[898,43100,1724],{},[1726,43102,2099],{},[898,43104,2198],{},[902,43106,40223],{"encoding":904},[883,43108,43110],{"className":43109},[886],[888,43111,43112],{"xmlns":890},[892,43113,43114,43122],{},[895,43115,43116,43118,43120],{},[898,43117,2146],{},[1726,43119,3405],{},[2133,43121,2328],{},[902,43123,40241],{"encoding":904},") dává podmínka rovnováhy ",[883,43126,43128],{"className":43127},[886],[888,43129,43130],{"xmlns":890},[892,43131,43132,43152],{},[895,43133,43134,43136,43138,43140,43142,43144,43146,43148,43150],{},[898,43135,207],{},[898,43137,1724],{},[1726,43139,2099],{},[898,43141,2102],{},[1726,43143,1728],{},[898,43145,2146],{},[898,43147,1724],{},[1726,43149,2099],{},[898,43151,2198],{},[902,43153,43154],{"encoding":904},"aQ + b = cQ + d",", odkud",[883,43157,43159],{"className":43158},[886],[888,43160,43161],{"xmlns":890,"display":28047},[892,43162,43163,43208],{},[20735,43164,43165],{"width":28052},[20740,43166,43167,43169,43201,43203],{},[20743,43168],{"width":28057},[20743,43170,43171],{},[895,43172,43173,43179,43181,43199],{},[2128,43174,43175,43177],{},[898,43176,1724],{},[898,43178,4240],{},[1726,43180,1728],{},[2330,43182,43183,43191],{},[895,43184,43185,43187,43189],{},[898,43186,2102],{},[1726,43188,2228],{},[898,43190,2198],{},[895,43192,43193,43195,43197],{},[898,43194,2146],{},[1726,43196,2228],{},[898,43198,207],{},[898,43200,1888],{"mathvariant":2377},[20743,43202],{"width":28057},[20743,43204,43205],{},[2289,43206,43207],{},"(2.10)",[902,43209,43210],{"encoding":904},"Q^E = \\frac{b - d}{c - a}. \\tag{2.10}",[724,43212,43213,43214,10009,43216,43219,43220,43237,43238,1777,43241,43267,43268,43281,43282,43300,43301,1847],{},"Vztah (2.10) je ",[38,43215,20935],{},[614,43217,43218],{},"reduced form",") pro ",[883,43221,43223],{"className":43222},[886],[888,43224,43225],{"xmlns":890},[892,43226,43227,43235],{},[895,43228,43229],{},[2128,43230,43231,43233],{},[898,43232,1724],{},[898,43234,4240],{},[902,43236,42384],{"encoding":904},": endogenní proměnná je vyjádřena pomocí exogenních ",[38,43239,43240],{},"parametrů",[883,43242,43244],{"className":43243},[886],[888,43245,43246],{"xmlns":890},[892,43247,43248,43264],{},[895,43249,43250,43252,43254,43256,43258,43260,43262],{},[898,43251,207],{},[1726,43253,1742],{"separator":1741},[898,43255,2102],{},[1726,43257,1742],{"separator":1741},[898,43259,2146],{},[1726,43261,1742],{"separator":1741},[898,43263,2198],{},[902,43265,43266],{"encoding":904},"a, b, c, d",". Aby ",[883,43269,43271],{"className":43270},[886],[888,43272,43273],{"xmlns":890},[892,43274,43275,43279],{},[895,43276,43277],{},[898,43278,4240],{},[902,43280,4240],{"encoding":904}," ležel v 1. kvadrantu, musí platit ",[883,43283,43285],{"className":43284},[886],[888,43286,43287],{"xmlns":890},[892,43288,43289,43297],{},[895,43290,43291,43293,43295],{},[898,43292,2102],{},[1726,43294,3405],{},[898,43296,2198],{},[902,43298,43299],{"encoding":904},"b > d"," (neboť ",[883,43302,43304],{"className":43303},[886],[888,43305,43306],{"xmlns":890},[892,43307,43308,43320],{},[895,43309,43310,43312,43314,43316,43318],{},[898,43311,2146],{},[1726,43313,2228],{},[898,43315,207],{},[1726,43317,3405],{},[2133,43319,2328],{},[902,43321,43322],{"encoding":904},"c - a > 0",[724,43324,43325],{},[614,43326,43327,43328,43341,43342,43355,43356,18629,43369,41921,43386,43399],{},"Obrázek 2.22: Lineární poptávka (úsek ",[883,43329,43331],{"className":43330},[886],[888,43332,43333],{"xmlns":890},[892,43334,43335,43339],{},[895,43336,43337],{},[898,43338,2102],{},[902,43340,2102],{"encoding":904}," na ose ",[883,43343,43345],{"className":43344},[886],[888,43346,43347],{"xmlns":890},[892,43348,43349,43353],{},[895,43350,43351],{},[898,43352,1738],{},[902,43354,1738],{"encoding":904},") a nabídka (úsek ",[883,43357,43359],{"className":43358},[886],[888,43360,43361],{"xmlns":890},[892,43362,43363,43367],{},[895,43364,43365],{},[898,43366,2198],{},[902,43368,2198],{"encoding":904},[883,43370,43372],{"className":43371},[886],[888,43373,43374],{"xmlns":890},[892,43375,43376,43384],{},[895,43377,43378,43380,43382],{},[898,43379,2102],{},[1726,43381,3405],{},[898,43383,2198],{},[902,43385,43299],{"encoding":904},[883,43387,43389],{"className":43388},[886],[888,43390,43391],{"xmlns":890},[892,43392,43393,43397],{},[895,43394,43395],{},[898,43396,4240],{},[902,43398,4240],{"encoding":904}," v 1. kvadrantu.",[198,43401,43403],{"id":43402},"definice-multiplikátorů","Definice multiplikátorů",[724,43405,43406,43407,43432,43433,43446,43447,43460],{},"V komparativní statice jsou ",[883,43408,43410],{"className":43409},[886],[888,43411,43412],{"xmlns":890},[892,43413,43414,43430],{},[895,43415,43416,43418,43420,43422,43424,43426,43428],{},[898,43417,207],{},[1726,43419,1742],{"separator":1741},[898,43421,2102],{},[1726,43423,1742],{"separator":1741},[898,43425,2146],{},[1726,43427,1742],{"separator":1741},[898,43429,2198],{},[902,43431,43266],{"encoding":904}," exogenní proměnné a ",[883,43434,43436],{"className":43435},[886],[888,43437,43438],{"xmlns":890},[892,43439,43440,43444],{},[895,43441,43442],{},[898,43443,1724],{},[902,43445,1724],{"encoding":904}," endogenní. Přibližná změna ",[883,43448,43450],{"className":43449},[886],[888,43451,43452],{"xmlns":890},[892,43453,43454,43458],{},[895,43455,43456],{},[898,43457,1724],{},[902,43459,1724],{"encoding":904}," se rovná totálnímu diferenciálu:",[883,43462,43464],{"className":43463},[886],[888,43465,43466],{"xmlns":890,"display":28047},[892,43467,43468,43561],{},[20735,43469,43470],{"width":28052},[20740,43471,43472,43474,43554,43556],{},[20743,43473],{"width":28057},[20743,43475,43476],{},[895,43477,43478,43480,43482,43484,43486,43488,43490,43498,43500,43502,43504,43506,43514,43516,43518,43520,43522,43530,43532,43534,43536,43538,43546,43548,43550,43552],{},[898,43479,2886],{"mathvariant":2377},[898,43481,1724],{},[1726,43483,1880],{},[898,43485,2198],{},[898,43487,1724],{},[1726,43489,1728],{},[9151,43491,43492,43494,43496],{},[898,43493,1724],{},[898,43495,207],{},[1726,43497,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[2289,43499,2984],{},[898,43501,2198],{},[898,43503,207],{},[1726,43505,2099],{},[9151,43507,43508,43510,43512],{},[898,43509,1724],{},[898,43511,2102],{},[1726,43513,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[2289,43515,2984],{},[898,43517,2198],{},[898,43519,2102],{},[1726,43521,2099],{},[9151,43523,43524,43526,43528],{},[898,43525,1724],{},[898,43527,2146],{},[1726,43529,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[2289,43531,2984],{},[898,43533,2198],{},[898,43535,2146],{},[1726,43537,2099],{},[9151,43539,43540,43542,43544],{},[898,43541,1724],{},[898,43543,2198],{},[1726,43545,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[2289,43547,2984],{},[898,43549,2198],{},[898,43551,2198],{},[898,43553,1888],{"mathvariant":2377},[20743,43555],{"width":28057},[20743,43557,43558],{},[2289,43559,43560],{},"(2.11)",[902,43562,43563],{"encoding":904},"\\Delta Q \\approx dQ = Q'_a\\,da + Q'_b\\,db + Q'_c\\,dc + Q'_d\\,dd. \\tag{2.11}",[724,43565,43566,43567,43617,43618,10009,43620,3148],{},"Parciální derivace ",[883,43568,43570],{"className":43569},[886],[888,43571,43572],{"xmlns":890},[892,43573,43574,43614],{},[895,43575,43576,43584,43586,43594,43596,43604,43606],{},[9151,43577,43578,43580,43582],{},[898,43579,1724],{},[898,43581,207],{},[1726,43583,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,43585,1742],{"separator":1741},[9151,43587,43588,43590,43592],{},[898,43589,1724],{},[898,43591,2102],{},[1726,43593,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,43595,1742],{"separator":1741},[9151,43597,43598,43600,43602],{},[898,43599,1724],{},[898,43601,2146],{},[1726,43603,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,43605,1742],{"separator":1741},[9151,43607,43608,43610,43612],{},[898,43609,1724],{},[898,43611,2198],{},[1726,43613,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[902,43615,43616],{"encoding":904},"Q'_a, Q'_b, Q'_c, Q'_d"," se nazývají ",[38,43619,17959],{},[614,43621,43622],{},"multipliers",[883,43624,43626],{"className":43625},[886],[888,43627,43628],{"xmlns":890,"display":28047},[892,43629,43630,43781],{},[20735,43631,43632],{"width":28052},[20740,43633,43634,43636,43774,43776],{},[20743,43635],{"width":28057},[20743,43637,43638],{},[895,43639,43640,43648,43650,43676,43678,43680,43688,43690,43702,43704,43706,43714,43716,43718,43744,43746,43748,43756,43758,43760,43772],{},[9151,43641,43642,43644,43646],{},[898,43643,1724],{},[898,43645,207],{},[1726,43647,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,43649,1728],{},[2330,43651,43652,43660],{},[895,43653,43654,43656,43658],{},[898,43655,2102],{},[1726,43657,2228],{},[898,43659,2198],{},[895,43661,43662,43664,43666,43668,43670],{},[1726,43663,1735],{"stretchy":1734},[898,43665,2146],{},[1726,43667,2228],{},[898,43669,207],{},[2128,43671,43672,43674],{},[1726,43673,1762],{"stretchy":1734},[2133,43675,2135],{},[1726,43677,1742],{"separator":1741},[5865,43679],{"width":15270},[9151,43681,43682,43684,43686],{},[898,43683,1724],{},[898,43685,2102],{},[1726,43687,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,43689,1728],{},[2330,43691,43692,43694],{},[2133,43693,2281],{},[895,43695,43696,43698,43700],{},[898,43697,2146],{},[1726,43699,2228],{},[898,43701,207],{},[1726,43703,1742],{"separator":1741},[5865,43705],{"width":15270},[9151,43707,43708,43710,43712],{},[898,43709,1724],{},[898,43711,2146],{},[1726,43713,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,43715,1728],{},[1726,43717,2228],{},[2330,43719,43720,43728],{},[895,43721,43722,43724,43726],{},[898,43723,2102],{},[1726,43725,2228],{},[898,43727,2198],{},[895,43729,43730,43732,43734,43736,43738],{},[1726,43731,1735],{"stretchy":1734},[898,43733,2146],{},[1726,43735,2228],{},[898,43737,207],{},[2128,43739,43740,43742],{},[1726,43741,1762],{"stretchy":1734},[2133,43743,2135],{},[1726,43745,1742],{"separator":1741},[5865,43747],{"width":15270},[9151,43749,43750,43752,43754],{},[898,43751,1724],{},[898,43753,2198],{},[1726,43755,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,43757,1728],{},[1726,43759,2228],{},[2330,43761,43762,43764],{},[2133,43763,2281],{},[895,43765,43766,43768,43770],{},[898,43767,2146],{},[1726,43769,2228],{},[898,43771,207],{},[898,43773,1888],{"mathvariant":2377},[20743,43775],{"width":28057},[20743,43777,43778],{},[2289,43779,43780],{},"(2.12)",[902,43782,43783],{"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}",[198,43785,43787],{"id":43786},"znaménka-a-interpretace","Znaménka a interpretace",[724,43789,43790,43791,1343,43808,1343,43825,1343,43842,43859,43860,3148],{},"Za podmínek ",[883,43792,43794],{"className":43793},[886],[888,43795,43796],{"xmlns":890},[892,43797,43798,43806],{},[895,43799,43800,43802,43804],{},[898,43801,207],{},[1726,43803,3444],{},[2133,43805,2328],{},[902,43807,43066],{"encoding":904},[883,43809,43811],{"className":43810},[886],[888,43812,43813],{"xmlns":890},[892,43814,43815,43823],{},[895,43816,43817,43819,43821],{},[898,43818,2102],{},[1726,43820,3405],{},[2133,43822,2328],{},[902,43824,18795],{"encoding":904},[883,43826,43828],{"className":43827},[886],[888,43829,43830],{"xmlns":890},[892,43831,43832,43840],{},[895,43833,43834,43836,43838],{},[898,43835,2146],{},[1726,43837,3405],{},[2133,43839,2328],{},[902,43841,40241],{"encoding":904},[883,43843,43845],{"className":43844},[886],[888,43846,43847],{"xmlns":890},[892,43848,43849,43857],{},[895,43850,43851,43853,43855],{},[898,43852,2102],{},[1726,43854,3405],{},[898,43856,2198],{},[902,43858,43299],{"encoding":904}," platí (znaménka se ",[38,43861,43862],{},"nemění",[883,43864,43866],{"className":43865},[886],[888,43867,43868],{"xmlns":890,"display":28047},[892,43869,43870,43932],{},[895,43871,43872,43880,43882,43884,43886,43888,43896,43898,43900,43902,43904,43912,43914,43916,43918,43920,43928,43930],{},[9151,43873,43874,43876,43878],{},[898,43875,1724],{},[898,43877,207],{},[1726,43879,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,43881,3405],{},[2133,43883,2328],{},[1726,43885,1742],{"separator":1741},[5865,43887],{"width":5867},[9151,43889,43890,43892,43894],{},[898,43891,1724],{},[898,43893,2102],{},[1726,43895,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,43897,3405],{},[2133,43899,2328],{},[1726,43901,1742],{"separator":1741},[5865,43903],{"width":5867},[9151,43905,43906,43908,43910],{},[898,43907,1724],{},[898,43909,2146],{},[1726,43911,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,43913,3444],{},[2133,43915,2328],{},[1726,43917,1742],{"separator":1741},[5865,43919],{"width":5867},[9151,43921,43922,43924,43926],{},[898,43923,1724],{},[898,43925,2198],{},[1726,43927,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,43929,3444],{},[2133,43931,12446],{},[902,43933,43934],{"encoding":904},"Q'_a > 0, \\qquad Q'_b > 0, \\qquad Q'_c \u003C 0, \\qquad Q'_d \u003C 0.",[120,43936,43937,43996],{},[123,43938,43939,1777,43942,43962,43963,43980,43981,1343,43994,1888],{},[38,43940,43941],{},"Kvantitativní smysl:",[883,43943,43945],{"className":43944},[886],[888,43946,43947],{"xmlns":890},[892,43948,43949,43959],{},[895,43950,43951],{},[9151,43952,43953,43955,43957],{},[898,43954,1724],{},[898,43956,2013],{},[1726,43958,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[902,43960,43961],{"encoding":904},"Q'_x"," udává, o kolik přibližně vzroste ",[883,43964,43966],{"className":43965},[886],[888,43967,43968],{"xmlns":890},[892,43969,43970,43978],{},[895,43971,43972],{},[2128,43973,43974,43976],{},[898,43975,1724],{},[898,43977,4240],{},[902,43979,42384],{"encoding":904}," při jednotkové změně parametru ",[883,43982,43984],{"className":43983},[886],[888,43985,43986],{"xmlns":890},[892,43987,43988,43992],{},[895,43989,43990],{},[898,43991,2013],{},[902,43993,2013],{"encoding":904},[614,43995,36941],{},[123,43997,43998,44001,44002,44019,44020,1888],{},[38,43999,44000],{},"Kvalitativní smysl:"," znaménko určuje směr reakce ",[883,44003,44005],{"className":44004},[886],[888,44006,44007],{"xmlns":890},[892,44008,44009,44017],{},[895,44010,44011],{},[2128,44012,44013,44015],{},[898,44014,1724],{},[898,44016,4240],{},[902,44018,42384],{"encoding":904}," na růst ",[883,44021,44023],{"className":44022},[886],[888,44024,44025],{"xmlns":890},[892,44026,44027,44031],{},[895,44028,44029],{},[898,44030,2013],{},[902,44032,2013],{"encoding":904},[724,44034,44035,44036,44049,44050,43300,44067,1847],{},"Např. růst ",[883,44037,44039],{"className":44038},[886],[888,44040,44041],{"xmlns":890},[892,44042,44043,44047],{},[895,44044,44045],{},[898,44046,2146],{},[902,44048,2146],{"encoding":904}," (strmější nabídka) ⟹ pokles ",[883,44051,44053],{"className":44052},[886],[888,44054,44055],{"xmlns":890},[892,44056,44057,44065],{},[895,44058,44059],{},[2128,44060,44061,44063],{},[898,44062,1724],{},[898,44064,4240],{},[902,44066,42384],{"encoding":904},[883,44068,44070],{"className":44069},[886],[888,44071,44072],{"xmlns":890},[892,44073,44074,44088],{},[895,44075,44076,44084,44086],{},[9151,44077,44078,44080,44082],{},[898,44079,1724],{},[898,44081,2146],{},[1726,44083,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,44085,3444],{},[2133,44087,2328],{},[902,44089,44090],{"encoding":904},"Q'_c \u003C 0",[724,44092,44093],{},[614,44094,44095,44096,44116,44117,44141,44142,44164,44165,1888],{},"Obrázek 2.23: Pootočení přímky nabídky z ",[883,44097,44099],{"className":44098},[886],[888,44100,44101],{"xmlns":890},[892,44102,44103,44113],{},[895,44104,44105,44107,44109,44111],{},[898,44106,2146],{},[898,44108,1724],{},[1726,44110,2099],{},[898,44112,2198],{},[902,44114,44115],{"encoding":904},"cQ + d"," na strmější ",[883,44118,44120],{"className":44119},[886],[888,44121,44122],{"xmlns":890},[892,44123,44124,44138],{},[895,44125,44126,44132,44134,44136],{},[2275,44127,44128,44130],{},[898,44129,2146],{},[2133,44131,2281],{},[898,44133,1724],{},[1726,44135,2099],{},[898,44137,2198],{},[902,44139,44140],{"encoding":904},"c_1 Q + d"," (při ",[883,44143,44145],{"className":44144},[886],[888,44146,44147],{"xmlns":890},[892,44148,44149,44161],{},[895,44150,44151,44157,44159],{},[2275,44152,44153,44155],{},[898,44154,2146],{},[2133,44156,2281],{},[1726,44158,3405],{},[898,44160,2146],{},[902,44162,44163],{"encoding":904},"c_1 > c",") — rovnovážný bod se posouvá vlevo, ",[883,44166,44168],{"className":44167},[886],[888,44169,44170],{"xmlns":890},[892,44171,44172,44182],{},[895,44173,44174,44180],{},[2128,44175,44176,44178],{},[898,44177,1724],{},[898,44179,4240],{},[1726,44181,42572],{},[902,44183,44184],{"encoding":904},"Q^E \\downarrow",[724,44186,44187,44188,44220,44221,1888],{},"Při změně jediné proměnné se (2.11) redukuje např. na ",[883,44189,44191],{"className":44190},[886],[888,44192,44193],{"xmlns":890},[892,44194,44195,44217],{},[895,44196,44197,44199,44201,44203,44211,44213,44215],{},[898,44198,2886],{"mathvariant":2377},[898,44200,1724],{},[1726,44202,1880],{},[9151,44204,44205,44207,44209],{},[898,44206,1724],{},[898,44208,2102],{},[1726,44210,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[2289,44212,2984],{},[898,44214,2198],{},[898,44216,2102],{},[902,44218,44219],{"encoding":904},"\\Delta Q \\approx Q'_b\\,db",". Analogicky lze odvodit multiplikátory pro ",[883,44222,44224],{"className":44223},[886],[888,44225,44226],{"xmlns":890},[892,44227,44228,44236],{},[895,44229,44230],{},[2128,44231,44232,44234],{},[898,44233,1738],{},[898,44235,4240],{},[902,44237,41447],{"encoding":904},[198,44239,44241,44242],{"id":44240},"příklad-211-komparativní-statika-pro-qeqe","Příklad 2.11 — komparativní statika pro ",[883,44243,44245],{"className":44244},[886],[888,44246,44247],{"xmlns":890},[892,44248,44249,44257],{},[895,44250,44251],{},[2128,44252,44253,44255],{},[898,44254,1724],{},[898,44256,4240],{},[902,44258,42384],{"encoding":904},[724,44260,44261,41636,44263,41671,44289,1888],{},[38,44262,37914],{},[883,44264,44266],{"className":44265},[886],[888,44267,44268],{"xmlns":890},[892,44269,44270,44286],{},[895,44271,44272,44274,44276,44278,44280,44282,44284],{},[898,44273,1738],{},[1726,44275,1728],{},[1726,44277,2228],{},[2133,44279,2177],{},[898,44281,1724],{},[1726,44283,2099],{},[2133,44285,5198],{},[902,44287,44288],{"encoding":904},"P = -3Q + 40",[883,44290,44292],{"className":44291},[886],[888,44293,44294],{"xmlns":890},[892,44295,44296,44310],{},[895,44297,44298,44300,44302,44304,44306,44308],{},[898,44299,1738],{},[1726,44301,1728],{},[2133,44303,4996],{},[898,44305,1724],{},[1726,44307,2099],{},[2133,44309,2860],{},[902,44311,44312],{"encoding":904},"P = 0{,}5Q + 10",[724,44314,44315,44317],{},[38,44316,37946],{}," Rovnovážné množství",[883,44319,44321],{"className":44320},[886],[888,44322,44323],{"xmlns":890,"display":28047},[892,44324,44325,44393],{},[895,44326,44327,44333,44335,44353,44355,44379,44381,44388,44390],{},[2128,44328,44329,44331],{},[898,44330,1724],{},[898,44332,4240],{},[1726,44334,1728],{},[2330,44336,44337,44345],{},[895,44338,44339,44341,44343],{},[898,44340,2102],{},[1726,44342,2228],{},[898,44344,2198],{},[895,44346,44347,44349,44351],{},[898,44348,2146],{},[1726,44350,2228],{},[898,44352,207],{},[1726,44354,1728],{},[2330,44356,44357,44365],{},[895,44358,44359,44361,44363],{},[2133,44360,5198],{},[1726,44362,2228],{},[2133,44364,2860],{},[895,44366,44367,44369,44371,44373,44375,44377],{},[2133,44368,4996],{},[1726,44370,2228],{},[1726,44372,1735],{"stretchy":1734},[1726,44374,2228],{},[2133,44376,2177],{},[1726,44378,1762],{"stretchy":1734},[1726,44380,1728],{},[2330,44382,44383,44385],{},[2133,44384,38000],{},[2133,44386,44387],{},"3,5",[1726,44389,1880],{},[2133,44391,44392],{},"8,571.",[902,44394,44395],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\approx 8{,}571.",[724,44397,44398,44443],{},[38,44399,44400,44401,2670,44414,2684,44428,44442],{},"(a) Změna ",[883,44402,44404],{"className":44403},[886],[888,44405,44406],{"xmlns":890},[892,44407,44408,44412],{},[895,44409,44410],{},[898,44411,2146],{},[902,44413,2146],{"encoding":904},[883,44415,44417],{"className":44416},[886],[888,44418,44419],{"xmlns":890},[892,44420,44421,44425],{},[895,44422,44423],{},[2133,44424,4996],{},[902,44426,44427],{"encoding":904},"0{,}5",[883,44429,44431],{"className":44430},[886],[888,44432,44433],{"xmlns":890},[892,44434,44435,44439],{},[895,44436,44437],{},[2133,44438,19302],{},[902,44440,44441],{"encoding":904},"0{,}6"," (ceteris paribus)."," Dle (2.12):",[883,44445,44447],{"className":44446},[886],[888,44448,44449],{"xmlns":890,"display":28047},[892,44450,44451,44528],{},[895,44452,44453,44461,44463,44465,44467,44469,44471,44497,44499,44501,44503,44505,44507,44517,44519,44521,44523,44525],{},[9151,44454,44455,44457,44459],{},[898,44456,1724],{},[898,44458,2146],{},[1726,44460,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[2289,44462,2984],{},[898,44464,2198],{},[898,44466,2146],{},[1726,44468,1728],{},[1726,44470,2228],{},[2330,44472,44473,44481],{},[895,44474,44475,44477,44479],{},[898,44476,2102],{},[1726,44478,2228],{},[898,44480,2198],{},[895,44482,44483,44485,44487,44489,44491],{},[1726,44484,1735],{"stretchy":1734},[898,44486,2146],{},[1726,44488,2228],{},[898,44490,207],{},[2128,44492,44493,44495],{},[1726,44494,1762],{"stretchy":1734},[2133,44496,2135],{},[2289,44498,2984],{},[898,44500,2198],{},[898,44502,2146],{},[1726,44504,1728],{},[1726,44506,2228],{},[2330,44508,44509,44511],{},[2133,44510,38000],{},[2128,44512,44513,44515],{},[2133,44514,44387],{},[2133,44516,2135],{},[1726,44518,3174],{},[2133,44520,2791],{},[1726,44522,1880],{},[1726,44524,2228],{},[2133,44526,44527],{},"0,245.",[902,44529,44530],{"encoding":904},"Q'_c\\,dc = -\\frac{b - d}{(c - a)^2}\\,dc = -\\frac{30}{3{,}5^2}\\cdot 0{,}1 \\approx -0{,}245.",[724,44532,44533,44534,1888],{},"Nové rovnovážné množství ",[883,44535,44537],{"className":44536},[886],[888,44538,44539],{"xmlns":890},[892,44540,44541,44566],{},[895,44542,44543,44551,44553,44556,44558,44561,44563],{},[9151,44544,44545,44547,44549],{},[898,44546,1724],{},[2133,44548,2281],{},[898,44550,4240],{},[1726,44552,1880],{},[2133,44554,44555],{},"8,571",[1726,44557,2228],{},[2133,44559,44560],{},"0,245",[1726,44562,1728],{},[2133,44564,44565],{},"8,326",[902,44567,44568],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326",[724,44570,44571,44656],{},[38,44572,44573,44574,1343,44594,1343,44616,1343,44636,1888],{},"(b) Současné změny ",[883,44575,44577],{"className":44576},[886],[888,44578,44579],{"xmlns":890},[892,44580,44581,44591],{},[895,44582,44583,44585,44587,44589],{},[898,44584,2198],{},[898,44586,207],{},[1726,44588,1728],{},[2133,44590,4996],{},[902,44592,44593],{"encoding":904},"da = 0{,}5",[883,44595,44597],{"className":44596},[886],[888,44598,44599],{"xmlns":890},[892,44600,44601,44613],{},[895,44602,44603,44605,44607,44609,44611],{},[898,44604,2198],{},[898,44606,2102],{},[1726,44608,1728],{},[1726,44610,2228],{},[2133,44612,2231],{},[902,44614,44615],{"encoding":904},"db = -5",[883,44617,44619],{"className":44618},[886],[888,44620,44621],{"xmlns":890},[892,44622,44623,44633],{},[895,44624,44625,44627,44629,44631],{},[898,44626,2198],{},[898,44628,2146],{},[1726,44630,1728],{},[2133,44632,2791],{},[902,44634,44635],{"encoding":904},"dc = 0{,}1",[883,44637,44639],{"className":44638},[886],[888,44640,44641],{"xmlns":890},[892,44642,44643,44653],{},[895,44644,44645,44647,44649,44651],{},[898,44646,2198],{},[898,44648,2198],{},[1726,44650,1728],{},[2133,44652,2281],{},[902,44654,44655],{"encoding":904},"dd = 1"," Dosazením do (2.11):",[883,44658,44660],{"className":44659},[886],[888,44661,44662],{"xmlns":890,"display":28047},[892,44663,44664,44807],{},[20735,44665,44666,44748,44784],{"rowspacing":20737,"columnalign":20738,"columnspacing":2378},[20740,44667,44668,44678],{},[20743,44669,44670],{},[2326,44671,44672],{"scriptlevel":2328,"displaystyle":1741},[895,44673,44674,44676],{},[898,44675,2886],{"mathvariant":2377},[898,44677,1724],{},[20743,44679,44680],{},[2326,44681,44682],{"scriptlevel":2328,"displaystyle":1741},[895,44683,44684,44686,44688,44698,44700,44702,44704,44710,44712,44714,44716,44718,44720,44722,44732,44734,44736,44738,44744,44746],{},[895,44685],{},[1726,44687,1880],{},[2330,44689,44690,44692],{},[2133,44691,38000],{},[2128,44693,44694,44696],{},[2133,44695,44387],{},[2133,44697,2135],{},[1726,44699,3174],{},[2133,44701,4996],{},[1726,44703,2099],{},[2330,44705,44706,44708],{},[2133,44707,2281],{},[2133,44709,44387],{},[1726,44711,3174],{},[1726,44713,1735],{"stretchy":1734},[1726,44715,2228],{},[2133,44717,2231],{},[1726,44719,1762],{"stretchy":1734},[1726,44721,2228],{},[2330,44723,44724,44726],{},[2133,44725,38000],{},[2128,44727,44728,44730],{},[2133,44729,44387],{},[2133,44731,2135],{},[1726,44733,3174],{},[2133,44735,2791],{},[1726,44737,2228],{},[2330,44739,44740,44742],{},[2133,44741,2281],{},[2133,44743,44387],{},[1726,44745,3174],{},[2133,44747,2281],{},[20740,44749,44750,44756],{},[20743,44751,44752],{},[2326,44753,44754],{"scriptlevel":2328,"displaystyle":1741},[895,44755],{},[20743,44757,44758],{},[2326,44759,44760],{"scriptlevel":2328,"displaystyle":1741},[895,44761,44762,44764,44766,44769,44771,44774,44776,44779,44781],{},[895,44763],{},[1726,44765,1728],{},[2133,44767,44768],{},"1,2245",[1726,44770,2228],{},[2133,44772,44773],{},"1,4286",[1726,44775,2228],{},[2133,44777,44778],{},"0,2449",[1726,44780,2228],{},[2133,44782,44783],{},"0,2857",[20740,44785,44786,44792],{},[20743,44787,44788],{},[2326,44789,44790],{"scriptlevel":2328,"displaystyle":1741},[895,44791],{},[20743,44793,44794],{},[2326,44795,44796],{"scriptlevel":2328,"displaystyle":1741},[895,44797,44798,44800,44802,44804],{},[895,44799],{},[1726,44801,1880],{},[1726,44803,2228],{},[2133,44805,44806],{},"0,735.",[902,44808,44809],{"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}",[724,44811,30046,44812,1888],{},[883,44813,44815],{"className":44814},[886],[888,44816,44817],{"xmlns":890},[892,44818,44819,44843],{},[895,44820,44821,44829,44831,44833,44835,44838,44840],{},[9151,44822,44823,44825,44827],{},[898,44824,1724],{},[2133,44826,2281],{},[898,44828,4240],{},[1726,44830,1880],{},[2133,44832,44555],{},[1726,44834,2228],{},[2133,44836,44837],{},"0,735",[1726,44839,1728],{},[2133,44841,44842],{},"7,836",[902,44844,44845],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 = 7{,}836",[3859,44847,44848],{},[724,44849,44850,44852,44853,44876,44877,44899],{},[883,44851,4400],{}," Pozn. — oprava\nV knize je u této dílčí úlohy uvedena hodnota ",[883,44854,44856],{"className":44855},[886],[888,44857,44858],{"xmlns":890},[892,44859,44860,44873],{},[895,44861,44862,44864,44866,44868,44870],{},[898,44863,2886],{"mathvariant":2377},[898,44865,1724],{},[1726,44867,1880],{},[1726,44869,2228],{},[2133,44871,44872],{},"2,69",[902,44874,44875],{"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 ",[883,44878,44880],{"className":44879},[886],[888,44881,44882],{"xmlns":890},[892,44883,44884,44896],{},[895,44885,44886,44888,44890,44892,44894],{},[898,44887,2886],{"mathvariant":2377},[898,44889,1724],{},[1726,44891,1880],{},[1726,44893,2228],{},[2133,44895,44837],{},[902,44897,44898],{"encoding":904},"\\Delta Q \\approx -0{,}735",". Výsledek byl v této wiki opraven.",[724,44901,44902],{},"Princip multiplikátorů lze uplatnit na libovolné ekonomické proměnné — analogicky v makroekonomii (kap. 7).",[36951,44904],{},[115,44906,820],{"id":11769},[3859,44908,44909],{},[724,44910,44911,3866,44913,10009,44916,12114,44932,10009,44935,44951,44952,1888],{},[883,44912,4145],{},[38,44914,44915],{},"Přebytek spotřebitele",[883,44917,44919],{"className":44918},[886],[888,44920,44921],{"xmlns":890},[892,44922,44923,44929],{},[895,44924,44925,44927],{},[898,44926,2775],{},[898,44928,8659],{},[902,44930,44931],{"encoding":904},"CS",[38,44933,44934],{},"přebytek výrobce",[883,44936,44938],{"className":44937},[886],[888,44939,44940],{"xmlns":890},[892,44941,44942,44948],{},[895,44943,44944,44946],{},[898,44945,1738],{},[898,44947,8659],{},[902,44949,44950],{"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 ",[207,44953,44955],{"className":44954,"dataFsResolvedFilePath":818,"href":819},[210],"prebytek-spotrebitele-vyrobce",[724,44957,44958],{},[1647,44959],{"alt":44960,"className":44961,"src":44962},"imek-prebytky-cs-ps",[210,1651],"\u002Fwiki-assets\u002Fimek-prebytky-cs-ps.jpeg",[724,44964,44965,10009,44967,44970],{},[38,44966,44915],{},[614,44968,44969],{},"consumer surplus",") — rozdíl mezi ochotou platit a skutečnou platbou:",[883,44972,44974],{"className":44973},[886],[888,44975,44976],{"xmlns":890,"display":28047},[892,44977,44978,45055],{},[20735,44979,44980],{"width":28052},[20740,44981,44982,44984,45048,45050],{},[20743,44983],{"width":28057},[20743,44985,44986],{},[895,44987,44988,44990,44992,44994,45000,45002,45004,45016,45018,45020,45022,45024,45026,45028,45030,45032,45038,45040,45046],{},[898,44989,2775],{},[898,44991,8659],{},[1726,44993,1735],{"stretchy":1734},[2275,44995,44996,44998],{},[898,44997,1724],{},[2133,44999,2328],{},[1726,45001,1762],{"stretchy":1734},[1726,45003,1728],{},[9151,45005,45006,45008,45010],{},[1726,45007,11154],{},[2133,45009,2328],{},[2275,45011,45012,45014],{},[898,45013,1724],{},[2133,45015,2328],{},[898,45017,1731],{},[1726,45019,1735],{"stretchy":1734},[898,45021,1724],{},[1726,45023,1762],{"stretchy":1734},[2289,45025,2984],{},[898,45027,2198],{},[898,45029,1724],{},[1726,45031,2228],{},[2275,45033,45034,45036],{},[898,45035,1738],{},[2133,45037,2328],{},[2289,45039,2984],{},[2275,45041,45042,45044],{},[898,45043,1724],{},[2133,45045,2328],{},[898,45047,1888],{"mathvariant":2377},[20743,45049],{"width":28057},[20743,45051,45052],{},[2289,45053,45054],{},"(2.14)",[902,45056,45057],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\,dQ - P_0\\,Q_0. \\tag{2.14}",[724,45059,45060,10009,45063,45066],{},[38,45061,45062],{},"Přebytek výrobce",[614,45064,45065],{},"producer surplus",") — rozdíl mezi tržbou a minimální cenou:",[883,45068,45070],{"className":45069},[886],[888,45071,45072],{"xmlns":890,"display":28047},[892,45073,45074,45151],{},[20735,45075,45076],{"width":28052},[20740,45077,45078,45080,45144,45146],{},[20743,45079],{"width":28057},[20743,45081,45082],{},[895,45083,45084,45086,45088,45090,45096,45098,45100,45106,45108,45114,45116,45128,45130,45132,45134,45136,45138,45140,45142],{},[898,45085,1738],{},[898,45087,8659],{},[1726,45089,1735],{"stretchy":1734},[2275,45091,45092,45094],{},[898,45093,1724],{},[2133,45095,2328],{},[1726,45097,1762],{"stretchy":1734},[1726,45099,1728],{},[2275,45101,45102,45104],{},[898,45103,1738],{},[2133,45105,2328],{},[2289,45107,2984],{},[2275,45109,45110,45112],{},[898,45111,1724],{},[2133,45113,2328],{},[1726,45115,2228],{},[9151,45117,45118,45120,45122],{},[1726,45119,11154],{},[2133,45121,2328],{},[2275,45123,45124,45126],{},[898,45125,1724],{},[2133,45127,2328],{},[898,45129,8659],{},[1726,45131,1735],{"stretchy":1734},[898,45133,1724],{},[1726,45135,1762],{"stretchy":1734},[2289,45137,2984],{},[898,45139,2198],{},[898,45141,1724],{},[898,45143,1888],{"mathvariant":2377},[20743,45145],{"width":28057},[20743,45147,45148],{},[2289,45149,45150],{},"(2.15)",[902,45152,45153],{"encoding":904},"PS(Q_0) = P_0\\,Q_0 - \\int_0^{Q_0} S(Q)\\,dQ. \\tag{2.15}",[724,45155,45156,45157,1888],{},"Geometricky jde o plochy mezi rovnovážnou cenou a příslušnou křivkou; výpočet využívá aparát ",[207,45158,45160],{"className":45159,"dataFsResolvedFilePath":773,"href":774},[210],"určitého integrálu",[36951,45162],{},[115,45164,45166],{"id":45165},"příklady-z-knihy-přehled","Příklady z knihy — přehled",[120,45168,45169,45200,45205,45211,45239,45245,45274,45280,45360,45386],{},[123,45170,45171,45173,45174,45199],{},[38,45172,37909],{}," — lineární poptávka ",[883,45175,45177],{"className":45176},[886],[888,45178,45179],{"xmlns":890},[892,45180,45181,45197],{},[895,45182,45183,45185,45187,45189,45191,45193,45195],{},[898,45184,1738],{},[1726,45186,1728],{},[1726,45188,2228],{},[2133,45190,2135],{},[898,45192,1724],{},[1726,45194,2099],{},[2133,45196,3123],{},[902,45198,37941],{"encoding":904},", alternativní tvar, cenové rozpětí.",[123,45201,45202,45204],{},[38,45203,38223],{}," — empirické křivky poptávky po cukru (rodina vs. trh).",[123,45206,45207,45210],{},[38,45208,45209],{},"Příklad 2.3"," — posun poptávky při zdanění kupujícího.",[123,45212,45213,45215,45216,1888],{},[38,45214,40770],{}," — lineární nabídka ",[883,45217,45219],{"className":45218},[886],[888,45220,45221],{"xmlns":890},[892,45222,45223,45237],{},[895,45224,45225,45227,45229,45231,45233,45235],{},[898,45226,1738],{},[1726,45228,1728],{},[2133,45230,4996],{},[898,45232,1724],{},[1726,45234,2099],{},[2133,45236,4991],{},[902,45238,40799],{"encoding":904},[123,45240,45241,45244],{},[38,45242,45243],{},"Příklad 2.6"," — posun nabídky při zdanění výrobce.",[123,45246,45247,45250,45251,1888],{},[38,45248,45249],{},"Příklad 2.7"," — kvadratická rovnováha, ",[883,45252,45254],{"className":45253},[886],[888,45255,45256],{"xmlns":890},[892,45257,45258,45272],{},[895,45259,45260,45262,45264,45266,45268,45270],{},[898,45261,4240],{},[1726,45263,2487],{"stretchy":1734},[2133,45265,2352],{},[1726,45267,1742],{"separator":1741},[2133,45269,41917],{},[1726,45271,2502],{"stretchy":1734},[902,45273,41945],{"encoding":904},[123,45275,45276,45279],{},[38,45277,45278],{},"Příklad 2.8"," — dvoukomoditní trh, soustava rovnic, komplementy.",[123,45281,45282,45285,45286,45303,45304,1343,45329,45356,45357,2948],{},[38,45283,45284],{},"Příklad 2.9"," — daň ",[883,45287,45289],{"className":45288},[886],[888,45290,45291],{"xmlns":890},[892,45292,45293,45301],{},[895,45294,45295,45297,45299],{},[898,45296,2772],{},[1726,45298,1728],{},[2133,45300,2238],{},[902,45302,41249],{"encoding":904}," na výrobce; rozklad ",[883,45305,45307],{"className":45306},[886],[888,45308,45309],{"xmlns":890},[892,45310,45311,45327],{},[895,45312,45313,45323,45325],{},[2275,45314,45315,45317],{},[898,45316,2772],{},[895,45318,45319,45321],{},[898,45320,42658],{},[898,45322,724],{},[1726,45324,1728],{},[2133,45326,2135],{},[902,45328,42957],{"encoding":904},[883,45330,45332],{"className":45331},[886],[888,45333,45334],{"xmlns":890},[892,45335,45336,45354],{},[895,45337,45338,45350,45352],{},[2275,45339,45340,45342],{},[898,45341,2772],{},[895,45343,45344,45346,45348],{},[898,45345,42681],{},[898,45347,2003],{},[898,45349,12027],{},[1726,45351,1728],{},[2133,45353,2352],{},[902,45355,42986],{"encoding":904},". (Viz ",[207,45358,42702],{"className":45359,"dataFsResolvedFilePath":809,"href":810},[210],[123,45361,45362,45285,45365,45382,45383,2948],{},[38,45363,45364],{},"Příklad 2.10",[883,45366,45368],{"className":45367},[886],[888,45369,45370],{"xmlns":890},[892,45371,45372,45380],{},[895,45373,45374,45376,45378],{},[898,45375,2772],{},[1726,45377,1728],{},[2133,45379,2238],{},[902,45381,41249],{"encoding":904}," na spotřebitele; stejné čisté ceny i množství. (Viz ",[207,45384,42702],{"className":45385,"dataFsResolvedFilePath":809,"href":810},[210],[123,45387,45388,45391],{},[38,45389,45390],{},"Příklad 2.11"," — komparativní statika, multiplikátory, změny parametrů.",[36951,45393],{},[115,45395,45397],{"id":45396},"úlohy-k-samostatnému-řešení","Úlohy k samostatnému řešení",[198,45399,45401],{"id":45400},"základní-analýza-poptávky","Základní analýza poptávky",[724,45403,45404,45407,45408,45443,45444,45470],{},[38,45405,45406],{},"2.1"," Je dána poptávka ",[883,45409,45411],{"className":45410},[886],[888,45412,45413],{"xmlns":890},[892,45414,45415,45440],{},[895,45416,45417,45419,45421,45423,45425,45427,45429,45431,45434,45436,45438],{},[898,45418,1724],{},[1726,45420,1728],{},[898,45422,1731],{},[1726,45424,1735],{"stretchy":1734},[898,45426,1738],{},[1726,45428,1762],{"stretchy":1734},[1726,45430,1728],{},[2133,45432,45433],{},"75",[1726,45435,2228],{},[2133,45437,2231],{},[898,45439,1738],{},[902,45441,45442],{"encoding":904},"Q = D(P) = 75 - 5P",". (a) Načrtněte křivku poptávky. (b) Stanovte reálné cenové rozpětí. (c) Vypočtěte množství při cenách ",[883,45445,45447],{"className":45446},[886],[888,45448,45449],{"xmlns":890},[892,45450,45451,45467],{},[895,45452,45453,45455,45457,45459,45461,45463,45465],{},[2133,45454,2328],{},[1726,45456,1742],{"separator":1741},[2133,45458,2231],{},[1726,45460,1742],{"separator":1741},[2133,45462,2860],{},[1726,45464,1742],{"separator":1741},[2133,45466,36225],{},[902,45468,45469],{"encoding":904},"0, 5, 10, 15"," a výsledky vyznačte na křivku poptávky.",[724,45472,45473,45476,45477,45495,45496,3148],{},[38,45474,45475],{},"2.2"," Ověřte, že uvedené funkce vyjadřují (s případným omezením pro ",[883,45478,45480],{"className":45479},[886],[888,45481,45482],{"xmlns":890},[892,45483,45484,45492],{},[895,45485,45486,45488,45490],{},[898,45487,1738],{},[1726,45489,1742],{"separator":1741},[898,45491,1724],{},[902,45493,45494],{"encoding":904},"P, Q",") poptávku (využijte testu na zápornost derivace), charakterizujte tvar křivky poptávky a vyjádřete ve tvaru poptávky v alternativním tvaru (",[883,45497,45499],{"className":45498},[886],[888,45500,45501],{"xmlns":890},[892,45502,45503,45519],{},[895,45504,45505,45507,45509,45511,45513,45515,45517],{},[898,45506,207],{},[1726,45508,1742],{"separator":1741},[898,45510,2102],{},[1726,45512,1742],{"separator":1741},[898,45514,2146],{},[1726,45516,3405],{},[2133,45518,2328],{},[902,45520,45521],{"encoding":904},"a, b, c > 0",[120,45523,45524,45557,45588,45623,45654,45689],{},[123,45525,45526,45527],{},"(a) ",[883,45528,45530],{"className":45529},[886],[888,45531,45532],{"xmlns":890},[892,45533,45534,45554],{},[895,45535,45536,45538,45540],{},[898,45537,1724],{},[1726,45539,1728],{},[2326,45541,45542],{"scriptlevel":2328,"displaystyle":1741},[2330,45543,45544,45546],{},[898,45545,207],{},[895,45547,45548,45550,45552],{},[898,45549,1738],{},[1726,45551,2099],{},[898,45553,2146],{},[902,45555,45556],{"encoding":904},"Q = \\dfrac{a}{P + c}",[123,45558,45559,45560],{},"(b) ",[883,45561,45563],{"className":45562},[886],[888,45564,45565],{"xmlns":890},[892,45566,45567,45585],{},[895,45568,45569,45571,45573],{},[898,45570,1724],{},[1726,45572,1728],{},[8103,45574,45575],{},[895,45576,45577,45579,45581,45583],{},[898,45578,207],{},[1726,45580,2228],{},[898,45582,2102],{},[898,45584,1724],{},[902,45586,45587],{"encoding":904},"Q = \\sqrt{a - bQ}",[123,45589,45590,45591],{},"(c) ",[883,45592,45594],{"className":45593},[886],[888,45595,45596],{"xmlns":890},[892,45597,45598,45620],{},[895,45599,45600,45602,45604],{},[898,45601,1724],{},[1726,45603,1728],{},[2326,45605,45606],{"scriptlevel":2328,"displaystyle":1741},[2330,45607,45608,45618],{},[895,45609,45610,45612,45614],{},[898,45611,207],{},[1726,45613,2228],{},[8103,45615,45616],{},[898,45617,1738],{},[898,45619,2102],{},[902,45621,45622],{"encoding":904},"Q = \\dfrac{a - \\sqrt{P}}{b}",[123,45624,45625,45626],{},"(d) ",[883,45627,45629],{"className":45628},[886],[888,45630,45631],{"xmlns":890},[892,45632,45633,45651],{},[895,45634,45635,45637,45639,45641,45643,45645],{},[898,45636,1738],{},[1726,45638,1728],{},[898,45640,207],{},[1726,45642,2228],{},[898,45644,2102],{},[2128,45646,45647,45649],{},[898,45648,1724],{},[2133,45650,2135],{},[902,45652,45653],{"encoding":904},"P = a - bQ^2",[123,45655,45656,45657],{},"(e) ",[883,45658,45660],{"className":45659},[886],[888,45661,45662],{"xmlns":890},[892,45663,45664,45686],{},[895,45665,45666,45668,45670,45672,45682,45684],{},[898,45667,1724],{},[1726,45669,1728],{},[898,45671,2102],{},[2128,45673,45674,45676],{},[898,45675,1738],{},[895,45677,45678,45680],{},[1726,45679,2228],{},[898,45681,207],{},[1726,45683,2099],{},[898,45685,2146],{},[902,45687,45688],{"encoding":904},"Q = bP^{-a} + c",[123,45690,45691,45692],{},"(f) ",[883,45693,45695],{"className":45694},[886],[888,45696,45697],{"xmlns":890},[892,45698,45699,45722],{},[895,45700,45701,45703,45705,45707,45709],{},[898,45702,1724],{},[1726,45704,1728],{},[898,45706,207],{},[1726,45708,3174],{},[2128,45710,45711,45714],{},[898,45712,45713],{},"e",[895,45715,45716,45718,45720],{},[1726,45717,2228],{},[898,45719,2102],{},[898,45721,1738],{},[902,45723,45724],{"encoding":904},"Q = a \\cdot e^{-bP}",[724,45726,45727,45730],{},[38,45728,45729],{},"2.3"," Rozhodněte, jak se změní křivka poptávky, jestliže se zvýší (ceteris paribus):",[120,45732,45733,45736,45739],{},[123,45734,45735],{},"(a) Cena substitutu.",[123,45737,45738],{},"(b) Cena komplementu.",[123,45740,45741],{},"(c) Výdaje na reklamu.",[724,45743,45744,45407,45746,45780,45781,45809],{},[38,45745,24623],{},[883,45747,45749],{"className":45748},[886],[888,45750,45751],{"xmlns":890},[892,45752,45753,45777],{},[895,45754,45755,45757,45759,45761,45763,45765,45767,45769,45771,45773,45775],{},[898,45756,1738],{},[1726,45758,1728],{},[898,45760,1731],{},[1726,45762,1735],{"stretchy":1734},[898,45764,1724],{},[1726,45766,1762],{"stretchy":1734},[1726,45768,1728],{},[2133,45770,3506],{},[1726,45772,2228],{},[2133,45774,2135],{},[898,45776,1724],{},[902,45778,45779],{"encoding":904},"P = D(Q) = 12 - 2Q",". Najděte novou poptávku ",[883,45782,45784],{"className":45783},[886],[888,45785,45786],{"xmlns":890},[892,45787,45788,45806],{},[895,45789,45790,45792,45794,45800,45802,45804],{},[898,45791,1738],{},[1726,45793,1728],{},[2128,45795,45796,45798],{},[898,45797,1731],{},[1726,45799,4342],{},[1726,45801,1735],{"stretchy":1734},[898,45803,1724],{},[1726,45805,1762],{"stretchy":1734},[902,45807,45808],{"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.",[724,45811,45812,45815],{},[38,45813,45814],{},"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:",[120,45817,45818,45902,45978,46064,46152],{},[123,45819,45526,45820,1343,45860,1888],{},[883,45821,45823],{"className":45822},[886],[888,45824,45825],{"xmlns":890},[892,45826,45827,45857],{},[895,45828,45829,45835,45837,45839,45841,45843,45849,45851],{},[2275,45830,45831,45833],{},[898,45832,23234],{},[2133,45834,2281],{},[1726,45836,1728],{},[2133,45838,9021],{},[1726,45840,2228],{},[2133,45842,2352],{},[2275,45844,45845,45847],{},[898,45846,4243],{},[2133,45848,2281],{},[1726,45850,2099],{},[2275,45852,45853,45855],{},[898,45854,4243],{},[2133,45856,2135],{},[902,45858,45859],{"encoding":904},"B_1 = 20 - 4A_1 + A_2",[883,45861,45863],{"className":45862},[886],[888,45864,45865],{"xmlns":890},[892,45866,45867,45899],{},[895,45868,45869,45875,45877,45879,45881,45883,45889,45891,45893],{},[2275,45870,45871,45873],{},[898,45872,23234],{},[2133,45874,2135],{},[1726,45876,1728],{},[2133,45878,2860],{},[1726,45880,2099],{},[2133,45882,2135],{},[2275,45884,45885,45887],{},[898,45886,4243],{},[2133,45888,2281],{},[1726,45890,2228],{},[2133,45892,2352],{},[2275,45894,45895,45897],{},[898,45896,4243],{},[2133,45898,2135],{},[902,45900,45901],{"encoding":904},"B_2 = 10 + 2A_1 - 4A_2",[123,45903,45559,45904,1343,45946,1888],{},[883,45905,45907],{"className":45906},[886],[888,45908,45909],{"xmlns":890},[892,45910,45911,45943],{},[895,45912,45913,45919,45921,45923,45925,45927,45933,45935,45937],{},[2275,45914,45915,45917],{},[898,45916,23234],{},[2133,45918,2281],{},[1726,45920,1728],{},[2133,45922,3117],{},[1726,45924,2228],{},[2133,45926,2860],{},[2275,45928,45929,45931],{},[898,45930,4243],{},[2133,45932,2281],{},[1726,45934,2228],{},[2133,45936,2238],{},[2275,45938,45939,45941],{},[898,45940,4243],{},[2133,45942,2135],{},[902,45944,45945],{"encoding":904},"B_1 = 50 - 10A_1 - 6A_2",[883,45947,45949],{"className":45948},[886],[888,45950,45951],{"xmlns":890},[892,45952,45953,45975],{},[895,45954,45955,45961,45963,45965,45967,45969],{},[2275,45956,45957,45959],{},[898,45958,23234],{},[2133,45960,2135],{},[1726,45962,1728],{},[2133,45964,36225],{},[1726,45966,2228],{},[2133,45968,2860],{},[2275,45970,45971,45973],{},[898,45972,4243],{},[2133,45974,2135],{},[902,45976,45977],{"encoding":904},"B_2 = 15 - 10A_2",[123,45979,45590,45980,1343,46022,1888],{},[883,45981,45983],{"className":45982},[886],[888,45984,45985],{"xmlns":890},[892,45986,45987,46019],{},[895,45988,45989,45995,45997,45999,46001,46003,46009,46011,46013],{},[2275,45990,45991,45993],{},[898,45992,23234],{},[2133,45994,2281],{},[1726,45996,1728],{},[2133,45998,38000],{},[1726,46000,2228],{},[2133,46002,2135],{},[2275,46004,46005,46007],{},[898,46006,4243],{},[2133,46008,2281],{},[1726,46010,2228],{},[2133,46012,2352],{},[2275,46014,46015,46017],{},[898,46016,4243],{},[2133,46018,2135],{},[902,46020,46021],{"encoding":904},"B_1 = 30 - 2A_1 - 4A_2",[883,46023,46025],{"className":46024},[886],[888,46026,46027],{"xmlns":890},[892,46028,46029,46061],{},[895,46030,46031,46037,46039,46041,46043,46045,46051,46053,46055],{},[2275,46032,46033,46035],{},[898,46034,23234],{},[2133,46036,2135],{},[1726,46038,1728],{},[2133,46040,36225],{},[1726,46042,2099],{},[2133,46044,2135],{},[2275,46046,46047,46049],{},[898,46048,4243],{},[2133,46050,2281],{},[1726,46052,2228],{},[2133,46054,2135],{},[2275,46056,46057,46059],{},[898,46058,4243],{},[2133,46060,2135],{},[902,46062,46063],{"encoding":904},"B_2 = 15 + 2A_1 - 2A_2",[123,46065,45625,46066,1343,46110,1888],{},[883,46067,46069],{"className":46068},[886],[888,46070,46071],{"xmlns":890},[892,46072,46073,46107],{},[895,46074,46075,46081,46083,46085,46087,46089,46091,46097,46099,46101],{},[2275,46076,46077,46079],{},[898,46078,23234],{},[2133,46080,2281],{},[1726,46082,1728],{},[1726,46084,2228],{},[2133,46086,9021],{},[1726,46088,2228],{},[2133,46090,2135],{},[2275,46092,46093,46095],{},[898,46094,4243],{},[2133,46096,2281],{},[1726,46098,2099],{},[2133,46100,2177],{},[2275,46102,46103,46105],{},[898,46104,4243],{},[2133,46106,2135],{},[902,46108,46109],{"encoding":904},"B_1 = -20 - 2A_1 + 3A_2",[883,46111,46113],{"className":46112},[886],[888,46114,46115],{"xmlns":890},[892,46116,46117,46149],{},[895,46118,46119,46125,46127,46129,46131,46133,46139,46141,46143],{},[2275,46120,46121,46123],{},[898,46122,23234],{},[2133,46124,2135],{},[1726,46126,1728],{},[2133,46128,2860],{},[1726,46130,2099],{},[2133,46132,2135],{},[2275,46134,46135,46137],{},[898,46136,4243],{},[2133,46138,2281],{},[1726,46140,2228],{},[2133,46142,2135],{},[2275,46144,46145,46147],{},[898,46146,4243],{},[2133,46148,2135],{},[902,46150,46151],{"encoding":904},"B_2 = 10 + 2A_1 - 2A_2",[123,46153,45656,46154,1343,46196,1888],{},[883,46155,46157],{"className":46156},[886],[888,46158,46159],{"xmlns":890},[892,46160,46161,46193],{},[895,46162,46163,46169,46171,46173,46175,46177,46183,46185,46187],{},[2275,46164,46165,46167],{},[898,46166,23234],{},[2133,46168,2281],{},[1726,46170,1728],{},[2133,46172,9021],{},[1726,46174,2099],{},[2133,46176,2135],{},[2275,46178,46179,46181],{},[898,46180,4243],{},[2133,46182,2281],{},[1726,46184,2099],{},[2133,46186,2352],{},[2275,46188,46189,46191],{},[898,46190,4243],{},[2133,46192,2135],{},[902,46194,46195],{"encoding":904},"B_1 = 20 + 2A_1 + 4A_2",[883,46197,46199],{"className":46198},[886],[888,46200,46201],{"xmlns":890},[892,46202,46203,46235],{},[895,46204,46205,46211,46213,46215,46217,46219,46225,46227,46229],{},[2275,46206,46207,46209],{},[898,46208,23234],{},[2133,46210,2135],{},[1726,46212,1728],{},[2133,46214,5198],{},[1726,46216,2228],{},[2133,46218,2177],{},[2275,46220,46221,46223],{},[898,46222,4243],{},[2133,46224,2281],{},[1726,46226,2099],{},[2133,46228,2231],{},[2275,46230,46231,46233],{},[898,46232,4243],{},[2133,46234,2135],{},[902,46236,46237],{"encoding":904},"B_2 = 40 - 3A_1 + 5A_2",[198,46239,46241],{"id":46240},"základní-analýza-nabídky","Základní analýza nabídky",[724,46243,46244,46247,46248,46282,46283,46305],{},[38,46245,46246],{},"2.6"," Je dána nabídka ",[883,46249,46251],{"className":46250},[886],[888,46252,46253],{"xmlns":890},[892,46254,46255,46279],{},[895,46256,46257,46259,46261,46263,46265,46267,46269,46271,46273,46275,46277],{},[898,46258,1738],{},[1726,46260,1728],{},[898,46262,8659],{},[1726,46264,1735],{"stretchy":1734},[898,46266,1724],{},[1726,46268,1762],{"stretchy":1734},[1726,46270,1728],{},[2133,46272,9021],{},[1726,46274,2099],{},[2133,46276,2836],{},[898,46278,1724],{},[902,46280,46281],{"encoding":904},"P = S(Q) = 20 + 0{,}2Q",". (a) Načrtněte křivku nabídky. (b) Vypočtěte množství při cenách ",[883,46284,46286],{"className":46285},[886],[888,46287,46288],{"xmlns":890},[892,46289,46290,46302],{},[895,46291,46292,46294,46296,46298,46300],{},[2133,46293,4991],{},[1726,46295,1742],{"separator":1741},[2133,46297,38000],{},[1726,46299,1742],{"separator":1741},[2133,46301,15024],{},[902,46303,46304],{"encoding":904},"25, 30, 35"," a vyznačte výsledky na křivku nabídky.",[724,46307,46308,46311,46312,46329],{},[38,46309,46310],{},"2.7"," Ověřte, že zadané funkce vyjadřují (s případným omezením na ",[883,46313,46315],{"className":46314},[886],[888,46316,46317],{"xmlns":890},[892,46318,46319,46327],{},[895,46320,46321,46323,46325],{},[898,46322,1738],{},[1726,46324,1742],{"separator":1741},[898,46326,1724],{},[902,46328,45494],{"encoding":904},") nabídku (využijte testu na kladnost derivace), charakterizujte tvar křivky nabídky a vyjádřete nabídku v alternativním tvaru:",[120,46331,46332,46358,46386,46419,46453,46489],{},[123,46333,45526,46334],{},[883,46335,46337],{"className":46336},[886],[888,46338,46339],{"xmlns":890},[892,46340,46341,46355],{},[895,46342,46343,46345,46347,46349,46351,46353],{},[898,46344,1738],{},[1726,46346,1728],{},[2133,46348,38000],{},[1726,46350,2099],{},[2133,46352,2135],{},[898,46354,1724],{},[902,46356,46357],{"encoding":904},"P = 30 + 2Q",[123,46359,45559,46360],{},[883,46361,46363],{"className":46362},[886],[888,46364,46365],{"xmlns":890},[892,46366,46367,46383],{},[895,46368,46369,46371,46373,46375,46377,46379,46381],{},[898,46370,1724],{},[1726,46372,1728],{},[1726,46374,2228],{},[2133,46376,2177],{},[1726,46378,2099],{},[2133,46380,3506],{},[898,46382,1738],{},[902,46384,46385],{"encoding":904},"Q = -3 + 12P",[123,46387,45590,46388],{},[883,46389,46391],{"className":46390},[886],[888,46392,46393],{"xmlns":890},[892,46394,46395,46417],{},[895,46396,46397,46399,46401,46407,46409,46411,46413,46415],{},[898,46398,1738],{},[1726,46400,1728],{},[2128,46402,46403,46405],{},[898,46404,1724],{},[2133,46406,2135],{},[1726,46408,2099],{},[2133,46410,22927],{},[898,46412,1724],{},[1726,46414,2099],{},[2133,46416,32527],{},[902,46418,41703],{"encoding":904},[123,46420,45625,46421],{},[883,46422,46424],{"className":46423},[886],[888,46425,46426],{"xmlns":890},[892,46427,46428,46450],{},[895,46429,46430,46432,46434,46440,46442,46444,46446,46448],{},[898,46431,1738],{},[1726,46433,1728],{},[2128,46435,46436,46438],{},[898,46437,1724],{},[2133,46439,2135],{},[1726,46441,2099],{},[2133,46443,2135],{},[898,46445,1724],{},[1726,46447,2099],{},[2133,46449,3506],{},[902,46451,46452],{"encoding":904},"P = Q^2 + 2Q + 12",[123,46454,45656,46455],{},[883,46456,46458],{"className":46457},[886],[888,46459,46460],{"xmlns":890},[892,46461,46462,46486],{},[895,46463,46464,46466,46468,46470,46472,46474,46476,46478,46480],{},[898,46465,1724],{},[1726,46467,1728],{},[2133,46469,8789],{},[1726,46471,2099],{},[2133,46473,2231],{},[898,46475,1738],{},[1726,46477,2099],{},[2133,46479,2791],{},[2128,46481,46482,46484],{},[898,46483,1738],{},[2133,46485,2135],{},[902,46487,46488],{"encoding":904},"Q = 150 + 5P + 0{,}1P^2",[123,46490,45691,46491],{},[883,46492,46494],{"className":46493},[886],[888,46495,46496],{"xmlns":890},[892,46497,46498,46523],{},[895,46499,46500,46502,46504,46506,46508,46510,46512,46514,46517],{},[898,46501,1724],{},[1726,46503,1728],{},[2133,46505,24182],{},[1726,46507,2099],{},[2133,46509,2791],{},[898,46511,1738],{},[1726,46513,2099],{},[2133,46515,46516],{},"0,004",[2128,46518,46519,46521],{},[898,46520,1738],{},[2133,46522,2135],{},[902,46524,46525],{"encoding":904},"Q = 7 + 0{,}1P + 0{,}004P^2",[724,46527,46528,46531],{},[38,46529,46530],{},"2.8"," Rozhodněte, jak se změní křivka nabídky, jestliže se (ceteris paribus):",[120,46533,46534,46537,46540,46543],{},[123,46535,46536],{},"(a) Sníží ceny surovin — vstupů.",[123,46538,46539],{},"(b) Zavede nová ekologičtější technologie zvyšující výrobní náklady.",[123,46541,46542],{},"(c) Zvýší ceny všech energií.",[123,46544,46545],{},"(d) Sníží daňové odvody státu.",[724,46547,46548,46247,46550,46584,46585,46613],{},[38,46549,42930],{},[883,46551,46553],{"className":46552},[886],[888,46554,46555],{"xmlns":890},[892,46556,46557,46581],{},[895,46558,46559,46561,46563,46565,46567,46569,46571,46573,46575,46577,46579],{},[898,46560,1738],{},[1726,46562,1728],{},[898,46564,8659],{},[1726,46566,1735],{"stretchy":1734},[898,46568,1724],{},[1726,46570,1762],{"stretchy":1734},[1726,46572,1728],{},[2133,46574,4996],{},[898,46576,1724],{},[1726,46578,2099],{},[2133,46580,36225],{},[902,46582,46583],{"encoding":904},"P = S(Q) = 0{,}5Q + 15",". Najděte novou nabídku ",[883,46586,46588],{"className":46587},[886],[888,46589,46590],{"xmlns":890},[892,46591,46592,46610],{},[895,46593,46594,46596,46598,46604,46606,46608],{},[898,46595,1738],{},[1726,46597,1728],{},[2128,46599,46600,46602],{},[898,46601,8659],{},[1726,46603,4342],{},[1726,46605,1735],{"stretchy":1734},[898,46607,1724],{},[1726,46609,1762],{"stretchy":1734},[902,46611,46612],{"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.",[198,46615,41306],{"id":46616},"tržní-rovnováha-1",[724,46618,46619,46621,46622,46639,46640,2703],{},[38,46620,42990],{}," Pro zadanou poptávku a nabídku najděte rovnovážné množství ",[883,46623,46625],{"className":46624},[886],[888,46626,46627],{"xmlns":890},[892,46628,46629,46637],{},[895,46630,46631],{},[2128,46632,46633,46635],{},[898,46634,1724],{},[898,46636,4240],{},[902,46638,42384],{"encoding":904}," a rovnovážnou cenu ",[883,46641,46643],{"className":46642},[886],[888,46644,46645],{"xmlns":890},[892,46646,46647,46655],{},[895,46648,46649],{},[2128,46650,46651,46653],{},[898,46652,1738],{},[898,46654,4240],{},[902,46656,41447],{"encoding":904},[120,46658,46659,46712,46763,46822],{},[123,46660,45526,46661,1343,46688,1888],{},[883,46662,46664],{"className":46663},[886],[888,46665,46666],{"xmlns":890},[892,46667,46668,46685],{},[895,46669,46670,46672,46674,46676,46678,46680,46682],{},[898,46671,1738],{},[1726,46673,1728],{},[1726,46675,2228],{},[2133,46677,2231],{},[898,46679,1724],{},[1726,46681,2099],{},[2133,46683,46684],{},"80",[902,46686,46687],{"encoding":904},"P = -5Q + 80",[883,46689,46691],{"className":46690},[886],[888,46692,46693],{"xmlns":890},[892,46694,46695,46709],{},[895,46696,46697,46699,46701,46703,46705,46707],{},[898,46698,1738],{},[1726,46700,1728],{},[2133,46702,2135],{},[898,46704,1724],{},[1726,46706,2099],{},[2133,46708,2860],{},[902,46710,46711],{"encoding":904},"P = 2Q + 10",[123,46713,45559,46714,1343,46740,1888],{},[883,46715,46717],{"className":46716},[886],[888,46718,46719],{"xmlns":890},[892,46720,46721,46737],{},[895,46722,46723,46725,46727,46729,46731,46733,46735],{},[898,46724,1724],{},[1726,46726,1728],{},[1726,46728,2228],{},[2133,46730,4996],{},[898,46732,1738],{},[1726,46734,2099],{},[2133,46736,4991],{},[902,46738,46739],{"encoding":904},"Q = -0{,}5P + 25",[883,46741,46743],{"className":46742},[886],[888,46744,46745],{"xmlns":890},[892,46746,46747,46761],{},[895,46748,46749,46751,46753,46755,46757,46759],{},[898,46750,1724],{},[1726,46752,1728],{},[2133,46754,2135],{},[898,46756,1738],{},[1726,46758,2228],{},[2133,46760,3117],{},[902,46762,40828],{"encoding":904},[123,46764,45590,46765,1343,46791,1888],{},[883,46766,46768],{"className":46767},[886],[888,46769,46770],{"xmlns":890},[892,46771,46772,46788],{},[895,46773,46774,46776,46778,46780,46782,46784,46786],{},[898,46775,1738],{},[1726,46777,1728],{},[1726,46779,2228],{},[2133,46781,2352],{},[898,46783,1724],{},[1726,46785,2099],{},[2133,46787,4036],{},[902,46789,46790],{"encoding":904},"P = -4Q + 120",[883,46792,46794],{"className":46793},[886],[888,46795,46796],{"xmlns":890},[892,46797,46798,46819],{},[895,46799,46800,46802,46804,46812,46814,46816],{},[898,46801,1738],{},[1726,46803,1728],{},[2326,46805,46806],{"scriptlevel":2328,"displaystyle":1734},[2330,46807,46808,46810],{},[2133,46809,2281],{},[2133,46811,2177],{},[898,46813,1724],{},[1726,46815,2099],{},[2133,46817,46818],{},"29",[902,46820,46821],{"encoding":904},"P = \\tfrac{1}{3}Q + 29",[123,46823,45625,46824,1343,46853,1888],{},[883,46825,46827],{"className":46826},[886],[888,46828,46829],{"xmlns":890},[892,46830,46831,46850],{},[895,46832,46833,46835,46837,46839,46845,46847],{},[898,46834,1738],{},[1726,46836,1728],{},[1726,46838,2228],{},[2128,46840,46841,46843],{},[898,46842,1724],{},[2133,46844,2135],{},[1726,46846,2099],{},[2133,46848,46849],{},"52",[902,46851,46852],{"encoding":904},"P = -Q^2 + 52",[883,46854,46856],{"className":46855},[886],[888,46857,46858],{"xmlns":890},[892,46859,46860,46878],{},[895,46861,46862,46864,46866,46868,46874,46876],{},[898,46863,1738],{},[1726,46865,1728],{},[2133,46867,2135],{},[2128,46869,46870,46872],{},[898,46871,1724],{},[2133,46873,2135],{},[1726,46875,2099],{},[2133,46877,2860],{},[902,46879,46880],{"encoding":904},"P = 2Q^2 + 10",[724,46882,46883,46886,46887,46917,46918,46948],{},[38,46884,46885],{},"2.11"," Pro zadanou poptávku a nabídku dvou závislých zboží najděte rovnovážná množství ",[883,46888,46890],{"className":46889},[886],[888,46891,46892],{"xmlns":890},[892,46893,46894,46914],{},[895,46895,46896,46904,46906],{},[9151,46897,46898,46900,46902],{},[898,46899,1724],{},[2133,46901,2281],{},[898,46903,4240],{},[1726,46905,1742],{"separator":1741},[9151,46907,46908,46910,46912],{},[898,46909,1724],{},[2133,46911,2135],{},[898,46913,4240],{},[902,46915,46916],{"encoding":904},"Q_1^E, Q_2^E"," a rovnovážné ceny ",[883,46919,46921],{"className":46920},[886],[888,46922,46923],{"xmlns":890},[892,46924,46925,46945],{},[895,46926,46927,46935,46937],{},[9151,46928,46929,46931,46933],{},[898,46930,1738],{},[2133,46932,2281],{},[898,46934,4240],{},[1726,46936,1742],{"separator":1741},[9151,46938,46939,46941,46943],{},[898,46940,1738],{},[2133,46942,2135],{},[898,46944,4240],{},[902,46946,46947],{"encoding":904},"P_1^E, P_2^E"," (index 1 přísluší prvnímu, index 2 druhému zboží):",[120,46950,46951,47103],{},[123,46952,45526,46953,1343,46993,1343,47035,1343,47069,1888],{},[883,46954,46956],{"className":46955},[886],[888,46957,46958],{"xmlns":890},[892,46959,46960,46990],{},[895,46961,46962,46968,46970,46972,46974,46976,46982,46984],{},[2275,46963,46964,46966],{},[898,46965,1724],{},[2133,46967,2281],{},[1726,46969,1728],{},[2133,46971,2860],{},[1726,46973,2228],{},[2133,46975,2135],{},[2275,46977,46978,46980],{},[898,46979,1738],{},[2133,46981,2281],{},[1726,46983,2099],{},[2275,46985,46986,46988],{},[898,46987,1738],{},[2133,46989,2135],{},[902,46991,46992],{"encoding":904},"Q_1 = 10 - 2P_1 + P_2",[883,46994,46996],{"className":46995},[886],[888,46997,46998],{"xmlns":890},[892,46999,47000,47032],{},[895,47001,47002,47008,47010,47012,47014,47016,47022,47024,47026],{},[2275,47003,47004,47006],{},[898,47005,1724],{},[2133,47007,2135],{},[1726,47009,1728],{},[2133,47011,2231],{},[1726,47013,2099],{},[2133,47015,2135],{},[2275,47017,47018,47020],{},[898,47019,1738],{},[2133,47021,2281],{},[1726,47023,2228],{},[2133,47025,2135],{},[2275,47027,47028,47030],{},[898,47029,1738],{},[2133,47031,2135],{},[902,47033,47034],{"encoding":904},"Q_2 = 5 + 2P_1 - 2P_2",[883,47036,47038],{"className":47037},[886],[888,47039,47040],{"xmlns":890},[892,47041,47042,47066],{},[895,47043,47044,47050,47052,47054,47056,47058,47060],{},[2275,47045,47046,47048],{},[898,47047,1724],{},[2133,47049,2281],{},[1726,47051,1728],{},[1726,47053,2228],{},[2133,47055,2177],{},[1726,47057,2099],{},[2133,47059,2135],{},[2275,47061,47062,47064],{},[898,47063,1738],{},[2133,47065,2281],{},[902,47067,47068],{"encoding":904},"Q_1 = -3 + 2P_1",[883,47070,47072],{"className":47071},[886],[888,47073,47074],{"xmlns":890},[892,47075,47076,47100],{},[895,47077,47078,47084,47086,47088,47090,47092,47094],{},[2275,47079,47080,47082],{},[898,47081,1724],{},[2133,47083,2135],{},[1726,47085,1728],{},[1726,47087,2228],{},[2133,47089,2135],{},[1726,47091,2099],{},[2133,47093,2177],{},[2275,47095,47096,47098],{},[898,47097,1738],{},[2133,47099,2135],{},[902,47101,47102],{"encoding":904},"Q_2 = -2 + 3P_2",[123,47104,45559,47105,1343,47145,1343,47187,1343,47219,1888],{},[883,47106,47108],{"className":47107},[886],[888,47109,47110],{"xmlns":890},[892,47111,47112,47142],{},[895,47113,47114,47120,47122,47124,47126,47128,47134,47136],{},[2275,47115,47116,47118],{},[898,47117,1724],{},[2133,47119,2281],{},[1726,47121,1728],{},[2133,47123,3087],{},[1726,47125,2228],{},[2133,47127,2135],{},[2275,47129,47130,47132],{},[898,47131,1738],{},[2133,47133,2281],{},[1726,47135,2099],{},[2275,47137,47138,47140],{},[898,47139,1738],{},[2133,47141,2135],{},[902,47143,47144],{"encoding":904},"Q_1 = 100 - 2P_1 + P_2",[883,47146,47148],{"className":47147},[886],[888,47149,47150],{"xmlns":890},[892,47151,47152,47184],{},[895,47153,47154,47160,47162,47164,47166,47168,47174,47176,47178],{},[2275,47155,47156,47158],{},[898,47157,1724],{},[2133,47159,2135],{},[1726,47161,1728],{},[2133,47163,2231],{},[1726,47165,2099],{},[2133,47167,2135],{},[2275,47169,47170,47172],{},[898,47171,1738],{},[2133,47173,2281],{},[1726,47175,2228],{},[2133,47177,2177],{},[2275,47179,47180,47182],{},[898,47181,1738],{},[2133,47183,2135],{},[902,47185,47186],{"encoding":904},"Q_2 = 5 + 2P_1 - 3P_2",[883,47188,47190],{"className":47189},[886],[888,47191,47192],{"xmlns":890},[892,47193,47194,47216],{},[895,47195,47196,47202,47204,47206,47208,47210],{},[2275,47197,47198,47200],{},[898,47199,1724],{},[2133,47201,2281],{},[1726,47203,1728],{},[1726,47205,2228],{},[2133,47207,2860],{},[1726,47209,2099],{},[2275,47211,47212,47214],{},[898,47213,1738],{},[2133,47215,2281],{},[902,47217,47218],{"encoding":904},"Q_1 = -10 + P_1",[883,47220,47222],{"className":47221},[886],[888,47223,47224],{"xmlns":890},[892,47225,47226,47248],{},[895,47227,47228,47234,47236,47238,47240,47242],{},[2275,47229,47230,47232],{},[898,47231,1724],{},[2133,47233,2135],{},[1726,47235,1728],{},[2133,47237,2231],{},[1726,47239,2099],{},[2133,47241,2238],{},[2275,47243,47244,47246],{},[898,47245,1738],{},[2133,47247,2135],{},[902,47249,47250],{"encoding":904},"Q_2 = 5 + 6P_2",[724,47252,47253,47256,47257,1343,47305,1343,47351,47401,47402,1343,47434,1343,47468,21575,47502,3877,47520,47538,47539,47552,47553,47579,47580,46917,47620,1888],{},[38,47254,47255],{},"2.12"," Pro tři závislá zboží jsou dány poptávky rovnicemi ",[883,47258,47260],{"className":47259},[886],[888,47261,47262],{"xmlns":890},[892,47263,47264,47302],{},[895,47265,47266,47272,47274,47276,47278,47284,47286,47288,47294,47296],{},[2275,47267,47268,47270],{},[898,47269,1724],{},[2133,47271,2281],{},[1726,47273,1728],{},[2133,47275,36225],{},[1726,47277,2228],{},[2275,47279,47280,47282],{},[898,47281,1738],{},[2133,47283,2281],{},[1726,47285,2099],{},[2133,47287,2135],{},[2275,47289,47290,47292],{},[898,47291,1738],{},[2133,47293,2135],{},[1726,47295,2099],{},[2275,47297,47298,47300],{},[898,47299,1738],{},[2133,47301,2177],{},[902,47303,47304],{"encoding":904},"Q_1 = 15 - P_1 + 2P_2 + P_3",[883,47306,47308],{"className":47307},[886],[888,47309,47310],{"xmlns":890},[892,47311,47312,47348],{},[895,47313,47314,47320,47322,47324,47326,47332,47334,47340,47342],{},[2275,47315,47316,47318],{},[898,47317,1724],{},[2133,47319,2135],{},[1726,47321,1728],{},[2133,47323,3989],{},[1726,47325,2099],{},[2275,47327,47328,47330],{},[898,47329,1738],{},[2133,47331,2281],{},[1726,47333,2228],{},[2275,47335,47336,47338],{},[898,47337,1738],{},[2133,47339,2135],{},[1726,47341,2228],{},[2275,47343,47344,47346],{},[898,47345,1738],{},[2133,47347,2177],{},[902,47349,47350],{"encoding":904},"Q_2 = 9 + P_1 - P_2 - P_3",[883,47352,47354],{"className":47353},[886],[888,47355,47356],{"xmlns":890},[892,47357,47358,47398],{},[895,47359,47360,47366,47368,47370,47372,47374,47380,47382,47388,47390,47392],{},[2275,47361,47362,47364],{},[898,47363,1724],{},[2133,47365,2177],{},[1726,47367,1728],{},[2133,47369,5572],{},[1726,47371,2099],{},[2133,47373,2135],{},[2275,47375,47376,47378],{},[898,47377,1738],{},[2133,47379,2281],{},[1726,47381,2228],{},[2275,47383,47384,47386],{},[898,47385,1738],{},[2133,47387,2135],{},[1726,47389,2228],{},[2133,47391,2352],{},[2275,47393,47394,47396],{},[898,47395,1738],{},[2133,47397,2177],{},[902,47399,47400],{"encoding":904},"Q_3 = 8 + 2P_1 - P_2 - 4P_3"," a nabídky rovnicemi ",[883,47403,47405],{"className":47404},[886],[888,47406,47407],{"xmlns":890},[892,47408,47409,47431],{},[895,47410,47411,47417,47419,47421,47423,47425],{},[2275,47412,47413,47415],{},[898,47414,1724],{},[2133,47416,2281],{},[1726,47418,1728],{},[1726,47420,2228],{},[2133,47422,24182],{},[1726,47424,2099],{},[2275,47426,47427,47429],{},[898,47428,1738],{},[2133,47430,2281],{},[902,47432,47433],{"encoding":904},"Q_1 = -7 + P_1",[883,47435,47437],{"className":47436},[886],[888,47438,47439],{"xmlns":890},[892,47440,47441,47465],{},[895,47442,47443,47449,47451,47453,47455,47457,47459],{},[2275,47444,47445,47447],{},[898,47446,1724],{},[2133,47448,2135],{},[1726,47450,1728],{},[1726,47452,2228],{},[2133,47454,2352],{},[1726,47456,2099],{},[2133,47458,2352],{},[2275,47460,47461,47463],{},[898,47462,1738],{},[2133,47464,2135],{},[902,47466,47467],{"encoding":904},"Q_2 = -4 + 4P_2",[883,47469,47471],{"className":47470},[886],[888,47472,47473],{"xmlns":890},[892,47474,47475,47499],{},[895,47476,47477,47483,47485,47487,47489,47491,47493],{},[2275,47478,47479,47481],{},[898,47480,1724],{},[2133,47482,2177],{},[1726,47484,1728],{},[1726,47486,2228],{},[2133,47488,2231],{},[1726,47490,2099],{},[2133,47492,2135],{},[2275,47494,47495,47497],{},[898,47496,1738],{},[2133,47498,2177],{},[902,47500,47501],{"encoding":904},"Q_3 = -5 + 2P_3",[883,47503,47505],{"className":47504},[886],[888,47506,47507],{"xmlns":890},[892,47508,47509,47517],{},[895,47510,47511],{},[2275,47512,47513,47515],{},[898,47514,1724],{},[898,47516,17772],{},[902,47518,47519],{"encoding":904},"Q_i",[883,47521,47523],{"className":47522},[886],[888,47524,47525],{"xmlns":890},[892,47526,47527,47535],{},[895,47528,47529],{},[2275,47530,47531,47533],{},[898,47532,1738],{},[898,47534,17772],{},[902,47536,47537],{"encoding":904},"P_i"," značí příslušné množství a ceny ",[883,47540,47542],{"className":47541},[886],[888,47543,47544],{"xmlns":890},[892,47545,47546,47550],{},[895,47547,47548],{},[898,47549,17772],{},[902,47551,17772],{"encoding":904},"-tého zboží, ",[883,47554,47556],{"className":47555},[886],[888,47557,47558],{"xmlns":890},[892,47559,47560,47576],{},[895,47561,47562,47564,47566,47568,47570,47572,47574],{},[898,47563,17772],{},[1726,47565,1728],{},[2133,47567,2281],{},[1726,47569,1742],{"separator":1741},[2133,47571,2135],{},[1726,47573,1742],{"separator":1741},[2133,47575,2177],{},[902,47577,47578],{"encoding":904},"i = 1, 2, 3",". Najděte rovnovážná množství ",[883,47581,47583],{"className":47582},[886],[888,47584,47585],{"xmlns":890},[892,47586,47587,47617],{},[895,47588,47589,47597,47599,47607,47609],{},[9151,47590,47591,47593,47595],{},[898,47592,1724],{},[2133,47594,2281],{},[898,47596,4240],{},[1726,47598,1742],{"separator":1741},[9151,47600,47601,47603,47605],{},[898,47602,1724],{},[2133,47604,2135],{},[898,47606,4240],{},[1726,47608,1742],{"separator":1741},[9151,47610,47611,47613,47615],{},[898,47612,1724],{},[2133,47614,2177],{},[898,47616,4240],{},[902,47618,47619],{"encoding":904},"Q_1^E, Q_2^E, Q_3^E",[883,47621,47623],{"className":47622},[886],[888,47624,47625],{"xmlns":890},[892,47626,47627,47657],{},[895,47628,47629,47637,47639,47647,47649],{},[9151,47630,47631,47633,47635],{},[898,47632,1738],{},[2133,47634,2281],{},[898,47636,4240],{},[1726,47638,1742],{"separator":1741},[9151,47640,47641,47643,47645],{},[898,47642,1738],{},[2133,47644,2135],{},[898,47646,4240],{},[1726,47648,1742],{"separator":1741},[9151,47650,47651,47653,47655],{},[898,47652,1738],{},[2133,47654,2177],{},[898,47656,4240],{},[902,47658,47659],{"encoding":904},"P_1^E, P_2^E, P_3^E",[724,47661,47662,47665,47666,47702,47703,1888],{},[38,47663,47664],{},"2.13"," Jsou dány poptávka ",[883,47667,47669],{"className":47668},[886],[888,47670,47671],{"xmlns":890},[892,47672,47673,47699],{},[895,47674,47675,47677,47679,47681,47683,47685,47687,47689,47691,47693,47695,47697],{},[898,47676,1738],{},[1726,47678,1728],{},[898,47680,1731],{},[1726,47682,1735],{"stretchy":1734},[898,47684,1724],{},[1726,47686,1762],{"stretchy":1734},[1726,47688,1728],{},[1726,47690,2228],{},[2133,47692,2352],{},[898,47694,1724],{},[1726,47696,2099],{},[2133,47698,46684],{},[902,47700,47701],{"encoding":904},"P = D(Q) = -4Q + 80"," a nabídka ",[883,47704,47706],{"className":47705},[886],[888,47707,47708],{"xmlns":890},[892,47709,47710,47734],{},[895,47711,47712,47714,47716,47718,47720,47722,47724,47726,47728,47730,47732],{},[898,47713,1738],{},[1726,47715,1728],{},[898,47717,8659],{},[1726,47719,1735],{"stretchy":1734},[898,47721,1724],{},[1726,47723,1762],{"stretchy":1734},[1726,47725,1728],{},[2133,47727,2177],{},[898,47729,1724],{},[1726,47731,2099],{},[2133,47733,2860],{},[902,47735,47736],{"encoding":904},"P = S(Q) = 3Q + 10",[120,47738,47739,47776,47840,47900],{},[123,47740,47741,47742,46639,47759,1888],{},"(a) Určete rovnovážné množství ",[883,47743,47745],{"className":47744},[886],[888,47746,47747],{"xmlns":890},[892,47748,47749,47757],{},[895,47750,47751],{},[2128,47752,47753,47755],{},[898,47754,1724],{},[898,47756,4240],{},[902,47758,42384],{"encoding":904},[883,47760,47762],{"className":47761},[886],[888,47763,47764],{"xmlns":890},[892,47765,47766,47774],{},[895,47767,47768],{},[2128,47769,47770,47772],{},[898,47771,1738],{},[898,47773,4240],{},[902,47775,41447],{"encoding":904},[123,47777,47778,47779,47797,47798,47818,47819,47839],{},"(b) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží výrobci daň ",[883,47780,47782],{"className":47781},[886],[888,47783,47784],{"xmlns":890},[892,47785,47786,47794],{},[895,47787,47788,47790,47792],{},[898,47789,2772],{},[1726,47791,1728],{},[2133,47793,24182],{},[902,47795,47796],{"encoding":904},"T = 7"," Kč na každou jednotku zboží, vypočtěte nové rovnovážné množství ",[883,47799,47801],{"className":47800},[886],[888,47802,47803],{"xmlns":890},[892,47804,47805,47815],{},[895,47806,47807],{},[9151,47808,47809,47811,47813],{},[898,47810,1724],{},[2133,47812,2281],{},[898,47814,4240],{},[902,47816,47817],{"encoding":904},"Q_1^E"," a novou rovnovážnou cenu ",[883,47820,47822],{"className":47821},[886],[888,47823,47824],{"xmlns":890},[892,47825,47826,47836],{},[895,47827,47828],{},[9151,47829,47830,47832,47834],{},[898,47831,1738],{},[2133,47833,2281],{},[898,47835,4240],{},[902,47837,47838],{"encoding":904},"P_1^E"," a určete, kolik z daňového zatížení zaplatí výrobce a kolik spotřebitel.",[123,47841,47842,47843,47797,47860,47818,47880,47839],{},"(c) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží spotřebiteli daň ",[883,47844,47846],{"className":47845},[886],[888,47847,47848],{"xmlns":890},[892,47849,47850,47858],{},[895,47851,47852,47854,47856],{},[898,47853,2772],{},[1726,47855,1728],{},[2133,47857,24182],{},[902,47859,47796],{"encoding":904},[883,47861,47863],{"className":47862},[886],[888,47864,47865],{"xmlns":890},[892,47866,47867,47877],{},[895,47868,47869],{},[9151,47870,47871,47873,47875],{},[898,47872,1724],{},[2133,47874,2135],{},[898,47876,4240],{},[902,47878,47879],{"encoding":904},"Q_2^E",[883,47881,47883],{"className":47882},[886],[888,47884,47885],{"xmlns":890},[892,47886,47887,47897],{},[895,47888,47889],{},[9151,47890,47891,47893,47895],{},[898,47892,1738],{},[2133,47894,2135],{},[898,47896,4240],{},[902,47898,47899],{"encoding":904},"P_2^E",[123,47901,47902],{},"(d) Proveďte analýzu dopadu daňového zatížení na spotřebitele a výrobce vyplývající z výsledků (b) a (c).",[724,47904,47905,47906,1888],{},"Viz též ",[207,47907,42702],{"className":47908,"dataFsResolvedFilePath":809,"href":810},[210],[198,47910,43004],{"id":47911},"multiplikátory-pro-mikroekonomické-proměnné-1",[724,47913,47914,47665,47917,47702,47953,1888],{},[38,47915,47916],{},"2.14",[883,47918,47920],{"className":47919},[886],[888,47921,47922],{"xmlns":890},[892,47923,47924,47950],{},[895,47925,47926,47928,47930,47932,47934,47936,47938,47940,47942,47944,47946,47948],{},[898,47927,1738],{},[1726,47929,1728],{},[898,47931,207],{},[898,47933,1724],{},[1726,47935,2099],{},[898,47937,2102],{},[1726,47939,1728],{},[1726,47941,2228],{},[2133,47943,2135],{},[898,47945,1724],{},[1726,47947,2099],{},[2133,47949,3117],{},[902,47951,47952],{"encoding":904},"P = aQ + b = -2Q + 50",[883,47954,47956],{"className":47955},[886],[888,47957,47958],{"xmlns":890},[892,47959,47960,47984],{},[895,47961,47962,47964,47966,47968,47970,47972,47974,47976,47978,47980,47982],{},[898,47963,1738],{},[1726,47965,1728],{},[898,47967,2146],{},[898,47969,1724],{},[1726,47971,2099],{},[898,47973,2198],{},[1726,47975,1728],{},[2133,47977,19302],{},[898,47979,1724],{},[1726,47981,2099],{},[2133,47983,9021],{},[902,47985,47986],{"encoding":904},"P = cQ + d = 0{,}6Q + 20",[120,47988,47989,48025,48028,48114,48167,48247,48301],{},[123,47990,47741,47991,46639,48008,1888],{},[883,47992,47994],{"className":47993},[886],[888,47995,47996],{"xmlns":890},[892,47997,47998,48006],{},[895,47999,48000],{},[2128,48001,48002,48004],{},[898,48003,1724],{},[898,48005,4240],{},[902,48007,42384],{"encoding":904},[883,48009,48011],{"className":48010},[886],[888,48012,48013],{"xmlns":890},[892,48014,48015,48023],{},[895,48016,48017],{},[2128,48018,48019,48021],{},[898,48020,1738],{},[898,48022,4240],{},[902,48024,41447],{"encoding":904},[123,48026,48027],{},"(b) Určete hodnoty multiplikátorů pro zadané parametry.",[123,48029,48030,48031,48048,48049,2670,48062,2684,48078,48094,48095,1888],{},"(c) Určete přibližnou změnu rovnovážného množství ",[883,48032,48034],{"className":48033},[886],[888,48035,48036],{"xmlns":890},[892,48037,48038,48046],{},[895,48039,48040],{},[2128,48041,48042,48044],{},[898,48043,1724],{},[898,48045,4240],{},[902,48047,42384],{"encoding":904}," odpovídající změně ",[883,48050,48052],{"className":48051},[886],[888,48053,48054],{"xmlns":890},[892,48055,48056,48060],{},[895,48057,48058],{},[898,48059,207],{},[902,48061,207],{"encoding":904},[883,48063,48065],{"className":48064},[886],[888,48066,48067],{"xmlns":890},[892,48068,48069,48075],{},[895,48070,48071,48073],{},[1726,48072,2228],{},[2133,48074,2135],{},[902,48076,48077],{"encoding":904},"-2",[883,48079,48081],{"className":48080},[886],[888,48082,48083],{"xmlns":890},[892,48084,48085,48091],{},[895,48086,48087,48089],{},[1726,48088,2228],{},[2133,48090,2177],{},[902,48092,48093],{"encoding":904},"-3"," (ceteris paribus) a stanovte nové rovnovážné množství ",[883,48096,48098],{"className":48097},[886],[888,48099,48100],{"xmlns":890},[892,48101,48102,48112],{},[895,48103,48104],{},[9151,48105,48106,48108,48110],{},[898,48107,1724],{},[2133,48109,2281],{},[898,48111,4240],{},[902,48113,47817],{"encoding":904},[123,48115,48116,48117,48048,48134,48147,48148,1888],{},"(d) Určete přibližnou změnu rovnovážného množství ",[883,48118,48120],{"className":48119},[886],[888,48121,48122],{"xmlns":890},[892,48123,48124,48132],{},[895,48125,48126],{},[2128,48127,48128,48130],{},[898,48129,1724],{},[898,48131,4240],{},[902,48133,42384],{"encoding":904},[883,48135,48137],{"className":48136},[886],[888,48138,48139],{"xmlns":890},[892,48140,48141,48145],{},[895,48142,48143],{},[898,48144,2102],{},[902,48146,2102],{"encoding":904}," z 50 na 60 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,48149,48151],{"className":48150},[886],[888,48152,48153],{"xmlns":890},[892,48154,48155,48165],{},[895,48156,48157],{},[9151,48158,48159,48161,48163],{},[898,48160,1724],{},[2133,48162,2135],{},[898,48164,4240],{},[902,48166,47879],{"encoding":904},[123,48168,48169,48170,48048,48187,2670,48200,2684,48213,48094,48227,1888],{},"(e) Určete přibližnou změnu rovnovážného množství ",[883,48171,48173],{"className":48172},[886],[888,48174,48175],{"xmlns":890},[892,48176,48177,48185],{},[895,48178,48179],{},[2128,48180,48181,48183],{},[898,48182,1724],{},[898,48184,4240],{},[902,48186,42384],{"encoding":904},[883,48188,48190],{"className":48189},[886],[888,48191,48192],{"xmlns":890},[892,48193,48194,48198],{},[895,48195,48196],{},[898,48197,2146],{},[902,48199,2146],{"encoding":904},[883,48201,48203],{"className":48202},[886],[888,48204,48205],{"xmlns":890},[892,48206,48207,48211],{},[895,48208,48209],{},[2133,48210,19302],{},[902,48212,44441],{"encoding":904},[883,48214,48216],{"className":48215},[886],[888,48217,48218],{"xmlns":890},[892,48219,48220,48224],{},[895,48221,48222],{},[2133,48223,14575],{},[902,48225,48226],{"encoding":904},"0{,}8",[883,48228,48230],{"className":48229},[886],[888,48231,48232],{"xmlns":890},[892,48233,48234,48244],{},[895,48235,48236],{},[9151,48237,48238,48240,48242],{},[898,48239,1724],{},[2133,48241,2177],{},[898,48243,4240],{},[902,48245,48246],{"encoding":904},"Q_3^E",[123,48248,48249,48250,48048,48267,48280,48281,1888],{},"(f) Určete přibližnou změnu rovnovážného množství ",[883,48251,48253],{"className":48252},[886],[888,48254,48255],{"xmlns":890},[892,48256,48257,48265],{},[895,48258,48259],{},[2128,48260,48261,48263],{},[898,48262,1724],{},[898,48264,4240],{},[902,48266,42384],{"encoding":904},[883,48268,48270],{"className":48269},[886],[888,48271,48272],{"xmlns":890},[892,48273,48274,48278],{},[895,48275,48276],{},[898,48277,2198],{},[902,48279,2198],{"encoding":904}," z 20 na 10 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,48282,48284],{"className":48283},[886],[888,48285,48286],{"xmlns":890},[892,48287,48288,48298],{},[895,48289,48290],{},[9151,48291,48292,48294,48296],{},[898,48293,1724],{},[2133,48295,2352],{},[898,48297,4240],{},[902,48299,48300],{"encoding":904},"Q_4^E",[123,48302,48303,48304,48321,48322,48335,48336,21401,48349,1343,48364,21401,48377,3877,48391,21401,48404,48419,48420,1888],{},"(g) Určete přibližnou změnu rovnovážného množství ",[883,48305,48307],{"className":48306},[886],[888,48308,48309],{"xmlns":890},[892,48310,48311,48319],{},[895,48312,48313],{},[2128,48314,48315,48317],{},[898,48316,1724],{},[898,48318,4240],{},[902,48320,42384],{"encoding":904}," odpovídající změnám ",[883,48323,48325],{"className":48324},[886],[888,48326,48327],{"xmlns":890},[892,48328,48329,48333],{},[895,48330,48331],{},[898,48332,207],{},[902,48334,207],{"encoding":904}," o 1, ",[883,48337,48339],{"className":48338},[886],[888,48340,48341],{"xmlns":890},[892,48342,48343,48347],{},[895,48344,48345],{},[898,48346,2102],{},[902,48348,2102],{"encoding":904},[883,48350,48352],{"className":48351},[886],[888,48353,48354],{"xmlns":890},[892,48355,48356,48362],{},[895,48357,48358,48360],{},[1726,48359,2228],{},[2133,48361,2860],{},[902,48363,19436],{"encoding":904},[883,48365,48367],{"className":48366},[886],[888,48368,48369],{"xmlns":890},[892,48370,48371,48375],{},[895,48372,48373],{},[898,48374,2146],{},[902,48376,2146],{"encoding":904},[883,48378,48380],{"className":48379},[886],[888,48381,48382],{"xmlns":890},[892,48383,48384,48388],{},[895,48385,48386],{},[2133,48387,2791],{},[902,48389,48390],{"encoding":904},"0{,}1",[883,48392,48394],{"className":48393},[886],[888,48395,48396],{"xmlns":890},[892,48397,48398,48402],{},[895,48399,48400],{},[898,48401,2198],{},[902,48403,2198],{"encoding":904},[883,48405,48407],{"className":48406},[886],[888,48408,48409],{"xmlns":890},[892,48410,48411,48417],{},[895,48412,48413,48415],{},[1726,48414,2228],{},[2133,48416,2860],{},[902,48418,19436],{"encoding":904}," vzhledem k zadaným hodnotám a stanovte nové rovnovážné množství ",[883,48421,48423],{"className":48422},[886],[888,48424,48425],{"xmlns":890},[892,48426,48427,48437],{},[895,48428,48429],{},[9151,48430,48431,48433,48435],{},[898,48432,1724],{},[2133,48434,2231],{},[898,48436,4240],{},[902,48438,48439],{"encoding":904},"Q_5^E",[724,48441,48442,47665,48445,47702,48468,1888],{},[38,48443,48444],{},"2.15",[883,48446,48448],{"className":48447},[886],[888,48449,48450],{"xmlns":890},[892,48451,48452,48466],{},[895,48453,48454,48456,48458,48460,48462,48464],{},[898,48455,1738],{},[1726,48457,1728],{},[898,48459,207],{},[898,48461,1724],{},[1726,48463,2099],{},[898,48465,2102],{},[902,48467,37041],{"encoding":904},[883,48469,48471],{"className":48470},[886],[888,48472,48473],{"xmlns":890},[892,48474,48475,48489],{},[895,48476,48477,48479,48481,48483,48485,48487],{},[898,48478,1738],{},[1726,48480,1728],{},[898,48482,2146],{},[898,48484,1724],{},[1726,48486,2099],{},[898,48488,2198],{},[902,48490,40223],{"encoding":904},[120,48492,48493,48568,48585,48694,48747,48801],{},[123,48494,48495,48496,48509,48510,48535,48536,48567],{},"(a) Odvoďte redukovaný tvar pro ",[883,48497,48499],{"className":48498},[886],[888,48500,48501],{"xmlns":890},[892,48502,48503,48507],{},[895,48504,48505],{},[898,48506,1738],{},[902,48508,1738],{"encoding":904},". Stanovte podmínky pro ",[883,48511,48513],{"className":48512},[886],[888,48514,48515],{"xmlns":890},[892,48516,48517,48533],{},[895,48518,48519,48521,48523,48525,48527,48529,48531],{},[898,48520,207],{},[1726,48522,1742],{"separator":1741},[898,48524,2102],{},[1726,48526,1742],{"separator":1741},[898,48528,2146],{},[1726,48530,1742],{"separator":1741},[898,48532,2198],{},[902,48534,43266],{"encoding":904}," tak, aby rovnovážný bod ",[883,48537,48539],{"className":48538},[886],[888,48540,48541],{"xmlns":890},[892,48542,48543,48565],{},[895,48544,48545,48547,48549,48555,48557,48563],{},[898,48546,4240],{},[1726,48548,2487],{"stretchy":1734},[2128,48550,48551,48553],{},[898,48552,1724],{},[898,48554,4240],{},[1726,48556,1742],{"separator":1741},[2128,48558,48559,48561],{},[898,48560,1738],{},[898,48562,4240],{},[1726,48564,2502],{"stretchy":1734},[902,48566,41348],{"encoding":904}," patřil do 1. kvadrantu (využijte obrázku 2.22).",[123,48569,48570,48571,48584],{},"(b) Vypočtěte multiplikátory pro ",[883,48572,48574],{"className":48573},[886],[888,48575,48576],{"xmlns":890},[892,48577,48578,48582],{},[895,48579,48580],{},[898,48581,1738],{},[902,48583,1738],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků 2.22, 2.23).",[123,48586,48587,48588,1343,48608,1343,48626,1343,48644,48662,48663,48680,48681,1888],{},"(c) Pro hodnoty parametrů ",[883,48589,48591],{"className":48590},[886],[888,48592,48593],{"xmlns":890},[892,48594,48595,48605],{},[895,48596,48597,48599,48601,48603],{},[898,48598,207],{},[1726,48600,1728],{},[1726,48602,2228],{},[2133,48604,2135],{},[902,48606,48607],{"encoding":904},"a = -2",[883,48609,48611],{"className":48610},[886],[888,48612,48613],{"xmlns":890},[892,48614,48615,48623],{},[895,48616,48617,48619,48621],{},[898,48618,2102],{},[1726,48620,1728],{},[2133,48622,5198],{},[902,48624,48625],{"encoding":904},"b = 40",[883,48627,48629],{"className":48628},[886],[888,48630,48631],{"xmlns":890},[892,48632,48633,48641],{},[895,48634,48635,48637,48639],{},[898,48636,2146],{},[1726,48638,1728],{},[2133,48640,4996],{},[902,48642,48643],{"encoding":904},"c = 0{,}5",[883,48645,48647],{"className":48646},[886],[888,48648,48649],{"xmlns":890},[892,48650,48651,48659],{},[895,48652,48653,48655,48657],{},[898,48654,2198],{},[1726,48656,1728],{},[2133,48658,2860],{},[902,48660,48661],{"encoding":904},"d = 10"," určete rovnovážnou cenu ",[883,48664,48666],{"className":48665},[886],[888,48667,48668],{"xmlns":890},[892,48669,48670,48678],{},[895,48671,48672],{},[2128,48673,48674,48676],{},[898,48675,1738],{},[898,48677,4240],{},[902,48679,41447],{"encoding":904}," a hodnoty multiplikátorů pro ",[883,48682,48684],{"className":48683},[886],[888,48685,48686],{"xmlns":890},[892,48687,48688,48692],{},[895,48689,48690],{},[898,48691,1738],{},[902,48693,1738],{"encoding":904},[123,48695,48696,48697,48048,48714,48727,48728,1888],{},"(d) Určete přibližnou změnu rovnovážné ceny ",[883,48698,48700],{"className":48699},[886],[888,48701,48702],{"xmlns":890},[892,48703,48704,48712],{},[895,48705,48706],{},[2128,48707,48708,48710],{},[898,48709,1738],{},[898,48711,4240],{},[902,48713,41447],{"encoding":904},[883,48715,48717],{"className":48716},[886],[888,48718,48719],{"xmlns":890},[892,48720,48721,48725],{},[895,48722,48723],{},[898,48724,207],{},[902,48726,207],{"encoding":904}," o 5 (ceteris paribus) a stanovte novou rovnovážnou cenu ",[883,48729,48731],{"className":48730},[886],[888,48732,48733],{"xmlns":890},[892,48734,48735,48745],{},[895,48736,48737],{},[9151,48738,48739,48741,48743],{},[898,48740,1738],{},[2133,48742,2281],{},[898,48744,4240],{},[902,48746,47838],{"encoding":904},[123,48748,48749,48750,48767,48768,48781,48782,1888],{},"(e) Určete přibližnou změnu rovnovážné ceny ",[883,48751,48753],{"className":48752},[886],[888,48754,48755],{"xmlns":890},[892,48756,48757,48765],{},[895,48758,48759],{},[2128,48760,48761,48763],{},[898,48762,1738],{},[898,48764,4240],{},[902,48766,41447],{"encoding":904}," odpovídající poklesu ",[883,48769,48771],{"className":48770},[886],[888,48772,48773],{"xmlns":890},[892,48774,48775,48779],{},[895,48776,48777],{},[898,48778,207],{},[902,48780,207],{"encoding":904}," o 1 a stanovte novou rovnovážnou cenu ",[883,48783,48785],{"className":48784},[886],[888,48786,48787],{"xmlns":890},[892,48788,48789,48799],{},[895,48790,48791],{},[9151,48792,48793,48795,48797],{},[898,48794,1738],{},[2133,48796,2135],{},[898,48798,4240],{},[902,48800,47899],{"encoding":904},[123,48802,48803,48804,48321,48821,48834,48835,2684,48848,3877,48863,48876,48877,1888],{},"(f) Určete přibližnou změnu rovnovážné ceny ",[883,48805,48807],{"className":48806},[886],[888,48808,48809],{"xmlns":890},[892,48810,48811,48819],{},[895,48812,48813],{},[2128,48814,48815,48817],{},[898,48816,1738],{},[898,48818,4240],{},[902,48820,41447],{"encoding":904},[883,48822,48824],{"className":48823},[886],[888,48825,48826],{"xmlns":890},[892,48827,48828,48832],{},[895,48829,48830],{},[898,48831,207],{},[902,48833,207],{"encoding":904}," na 35, ",[883,48836,48838],{"className":48837},[886],[888,48839,48840],{"xmlns":890},[892,48841,48842,48846],{},[895,48843,48844],{},[898,48845,2146],{},[902,48847,2146],{"encoding":904},[883,48849,48851],{"className":48850},[886],[888,48852,48853],{"xmlns":890},[892,48854,48855,48860],{},[895,48856,48857],{},[2133,48858,48859],{},"0,7",[902,48861,48862],{"encoding":904},"0{,}7",[883,48864,48866],{"className":48865},[886],[888,48867,48868],{"xmlns":890},[892,48869,48870,48874],{},[895,48871,48872],{},[898,48873,2198],{},[902,48875,2198],{"encoding":904}," na 12 vzhledem k hodnotám dle (d) a stanovte novou rovnovážnou cenu ",[883,48878,48880],{"className":48879},[886],[888,48881,48882],{"xmlns":890},[892,48883,48884,48894],{},[895,48885,48886],{},[9151,48887,48888,48890,48892],{},[898,48889,1738],{},[2133,48891,2177],{},[898,48893,4240],{},[902,48895,48896],{"encoding":904},"P_3^E",[724,48898,48899,47665,48902,47702,48930,21575,48958,3877,48984,1888],{},[38,48900,48901],{},"2.16",[883,48903,48905],{"className":48904},[886],[888,48906,48907],{"xmlns":890},[892,48908,48909,48927],{},[895,48910,48911,48913,48915,48917,48919,48921],{},[898,48912,1738],{},[1726,48914,1728],{},[898,48916,207],{},[1726,48918,2099],{},[898,48920,2102],{},[2128,48922,48923,48925],{},[898,48924,1724],{},[2133,48926,2135],{},[902,48928,48929],{"encoding":904},"P = a + bQ^2",[883,48931,48933],{"className":48932},[886],[888,48934,48935],{"xmlns":890},[892,48936,48937,48955],{},[895,48938,48939,48941,48943,48945,48947,48949],{},[898,48940,1738],{},[1726,48942,1728],{},[898,48944,2146],{},[1726,48946,2099],{},[898,48948,2198],{},[2128,48950,48951,48953],{},[898,48952,1724],{},[2133,48954,2135],{},[902,48956,48957],{"encoding":904},"P = c + dQ^2",[883,48959,48961],{"className":48960},[886],[888,48962,48963],{"xmlns":890},[892,48964,48965,48981],{},[895,48966,48967,48969,48971,48973,48975,48977,48979],{},[898,48968,207],{},[1726,48970,1742],{"separator":1741},[898,48972,2146],{},[1726,48974,1742],{"separator":1741},[898,48976,2198],{},[1726,48978,3405],{},[2133,48980,2328],{},[902,48982,48983],{"encoding":904},"a, c, d > 0",[883,48985,48987],{"className":48986},[886],[888,48988,48989],{"xmlns":890},[892,48990,48991,48999],{},[895,48992,48993,48995,48997],{},[898,48994,2102],{},[1726,48996,3444],{},[2133,48998,2328],{},[902,49000,49001],{"encoding":904},"b \u003C 0",[120,49003,49004,49052,49068,49175,49227,49279,49388,49404,49503,49556],{},[123,49005,48495,49006,49019,49020,49051],{},[883,49007,49009],{"className":49008},[886],[888,49010,49011],{"xmlns":890},[892,49012,49013,49017],{},[895,49014,49015],{},[898,49016,1724],{},[902,49018,1724],{"encoding":904},". Načrtněte křivky poptávky a nabídky a stanovte podmínky, aby rovnovážný bod ",[883,49021,49023],{"className":49022},[886],[888,49024,49025],{"xmlns":890},[892,49026,49027,49049],{},[895,49028,49029,49031,49033,49039,49041,49047],{},[898,49030,4240],{},[1726,49032,2487],{"stretchy":1734},[2128,49034,49035,49037],{},[898,49036,1724],{},[898,49038,4240],{},[1726,49040,1742],{"separator":1741},[2128,49042,49043,49045],{},[898,49044,1738],{},[898,49046,4240],{},[1726,49048,2502],{"stretchy":1734},[902,49050,41348],{"encoding":904}," patřil do 1. kvadrantu.",[123,49053,48570,49054,49067],{},[883,49055,49057],{"className":49056},[886],[888,49058,49059],{"xmlns":890},[892,49060,49061,49065],{},[895,49062,49063],{},[898,49064,1724],{},[902,49066,1724],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků v (b)).",[123,49069,48587,49070,1343,49088,1343,49108,1343,49126,49144,49145,48680,49162,1888],{},[883,49071,49073],{"className":49072},[886],[888,49074,49075],{"xmlns":890},[892,49076,49077,49085],{},[895,49078,49079,49081,49083],{},[898,49080,207],{},[1726,49082,1728],{},[2133,49084,3087],{},[902,49086,49087],{"encoding":904},"a = 100",[883,49089,49091],{"className":49090},[886],[888,49092,49093],{"xmlns":890},[892,49094,49095,49105],{},[895,49096,49097,49099,49101,49103],{},[898,49098,2102],{},[1726,49100,1728],{},[1726,49102,2228],{},[2133,49104,2281],{},[902,49106,49107],{"encoding":904},"b = -1",[883,49109,49111],{"className":49110},[886],[888,49112,49113],{"xmlns":890},[892,49114,49115,49123],{},[895,49116,49117,49119,49121],{},[898,49118,2146],{},[1726,49120,1728],{},[2133,49122,9021],{},[902,49124,49125],{"encoding":904},"c = 20",[883,49127,49129],{"className":49128},[886],[888,49130,49131],{"xmlns":890},[892,49132,49133,49141],{},[895,49134,49135,49137,49139],{},[898,49136,2198],{},[1726,49138,1728],{},[2133,49140,2281],{},[902,49142,49143],{"encoding":904},"d = 1"," určete rovnovážné množství ",[883,49146,49148],{"className":49147},[886],[888,49149,49150],{"xmlns":890},[892,49151,49152,49160],{},[895,49153,49154],{},[2128,49155,49156,49158],{},[898,49157,1724],{},[898,49159,4240],{},[902,49161,42384],{"encoding":904},[883,49163,49165],{"className":49164},[886],[888,49166,49167],{"xmlns":890},[892,49168,49169,49173],{},[895,49170,49171],{},[898,49172,1724],{},[902,49174,1724],{"encoding":904},[123,49176,48116,49177,48048,49194,49207,49208,1888],{},[883,49178,49180],{"className":49179},[886],[888,49181,49182],{"xmlns":890},[892,49183,49184,49192],{},[895,49185,49186],{},[2128,49187,49188,49190],{},[898,49189,1724],{},[898,49191,4240],{},[902,49193,42384],{"encoding":904},[883,49195,49197],{"className":49196},[886],[888,49198,49199],{"xmlns":890},[892,49200,49201,49205],{},[895,49202,49203],{},[898,49204,207],{},[902,49206,207],{"encoding":904}," na 110 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,49209,49211],{"className":49210},[886],[888,49212,49213],{"xmlns":890},[892,49214,49215,49225],{},[895,49216,49217],{},[9151,49218,49219,49221,49223],{},[898,49220,1724],{},[2133,49222,2281],{},[898,49224,4240],{},[902,49226,47817],{"encoding":904},[123,49228,48169,49229,48048,49246,49259,49260,1888],{},[883,49230,49232],{"className":49231},[886],[888,49233,49234],{"xmlns":890},[892,49235,49236,49244],{},[895,49237,49238],{},[2128,49239,49240,49242],{},[898,49241,1724],{},[898,49243,4240],{},[902,49245,42384],{"encoding":904},[883,49247,49249],{"className":49248},[886],[888,49250,49251],{"xmlns":890},[892,49252,49253,49257],{},[895,49254,49255],{},[898,49256,2146],{},[902,49258,2146],{"encoding":904}," na 25 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,49261,49263],{"className":49262},[886],[888,49264,49265],{"xmlns":890},[892,49266,49267,49277],{},[895,49268,49269],{},[9151,49270,49271,49273,49275],{},[898,49272,1724],{},[2133,49274,2135],{},[898,49276,4240],{},[902,49278,47879],{"encoding":904},[123,49280,48249,49281,48321,49298,49311,49312,2684,49325,49340,49341,49354,49355,49368,49369,1888],{},[883,49282,49284],{"className":49283},[886],[888,49285,49286],{"xmlns":890},[892,49287,49288,49296],{},[895,49289,49290],{},[2128,49291,49292,49294],{},[898,49293,1724],{},[898,49295,4240],{},[902,49297,42384],{"encoding":904},[883,49299,49301],{"className":49300},[886],[888,49302,49303],{"xmlns":890},[892,49304,49305,49309],{},[895,49306,49307],{},[898,49308,207],{},[902,49310,207],{"encoding":904}," na 110, poklesu ",[883,49313,49315],{"className":49314},[886],[888,49316,49317],{"xmlns":890},[892,49318,49319,49323],{},[895,49320,49321],{},[898,49322,2102],{},[902,49324,2102],{"encoding":904},[883,49326,49328],{"className":49327},[886],[888,49329,49330],{"xmlns":890},[892,49331,49332,49338],{},[895,49333,49334,49336],{},[1726,49335,2228],{},[2133,49337,2135],{},[902,49339,48077],{"encoding":904},", růstu ",[883,49342,49344],{"className":49343},[886],[888,49345,49346],{"xmlns":890},[892,49347,49348,49352],{},[895,49349,49350],{},[898,49351,2146],{},[902,49353,2146],{"encoding":904}," na 25 a růstu ",[883,49356,49358],{"className":49357},[886],[888,49359,49360],{"xmlns":890},[892,49361,49362,49366],{},[895,49363,49364],{},[898,49365,2198],{},[902,49367,2198],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte nové rovnovážné množství ",[883,49370,49372],{"className":49371},[886],[888,49373,49374],{"xmlns":890},[892,49375,49376,49386],{},[895,49377,49378],{},[9151,49379,49380,49382,49384],{},[898,49381,1724],{},[2133,49383,2177],{},[898,49385,4240],{},[902,49387,48246],{"encoding":904},[123,49389,49390,49391,49067],{},"(i) Vypočtěte multiplikátory pro ",[883,49392,49394],{"className":49393},[886],[888,49395,49396],{"xmlns":890},[892,49397,49398,49402],{},[895,49399,49400],{},[898,49401,1738],{},[902,49403,1738],{"encoding":904},[123,49405,49406,49407,48680,49424,49437,49438,48048,49455,2684,49468,49483,49484,1888],{},"(j) Pro hodnoty parametrů dle (b) určete rovnovážnou cenu ",[883,49408,49410],{"className":49409},[886],[888,49411,49412],{"xmlns":890},[892,49413,49414,49422],{},[895,49415,49416],{},[2128,49417,49418,49420],{},[898,49419,1738],{},[898,49421,4240],{},[902,49423,41447],{"encoding":904},[883,49425,49427],{"className":49426},[886],[888,49428,49429],{"xmlns":890},[892,49430,49431,49435],{},[895,49432,49433],{},[898,49434,1738],{},[902,49436,1738],{"encoding":904},", přibližnou změnu rovnovážné ceny ",[883,49439,49441],{"className":49440},[886],[888,49442,49443],{"xmlns":890},[892,49444,49445,49453],{},[895,49446,49447],{},[2128,49448,49449,49451],{},[898,49450,1738],{},[898,49452,4240],{},[902,49454,41447],{"encoding":904},[883,49456,49458],{"className":49457},[886],[888,49459,49460],{"xmlns":890},[892,49461,49462,49466],{},[895,49463,49464],{},[898,49465,207],{},[902,49467,207],{"encoding":904},[883,49469,49471],{"className":49470},[886],[888,49472,49473],{"xmlns":890},[892,49474,49475,49481],{},[895,49476,49477,49479],{},[1726,49478,2228],{},[2133,49480,2177],{},[902,49482,48093],{"encoding":904}," (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,49485,49487],{"className":49486},[886],[888,49488,49489],{"xmlns":890},[892,49490,49491,49501],{},[895,49492,49493],{},[9151,49494,49495,49497,49499],{},[898,49496,1738],{},[2133,49498,2281],{},[898,49500,4240],{},[902,49502,47838],{"encoding":904},[123,49504,49505,49506,48048,49523,49536,49537,1888],{},"(k) Určete přibližnou změnu rovnovážné ceny ",[883,49507,49509],{"className":49508},[886],[888,49510,49511],{"xmlns":890},[892,49512,49513,49521],{},[895,49514,49515],{},[2128,49516,49517,49519],{},[898,49518,1738],{},[898,49520,4240],{},[902,49522,41447],{"encoding":904},[883,49524,49526],{"className":49525},[886],[888,49527,49528],{"xmlns":890},[892,49529,49530,49534],{},[895,49531,49532],{},[898,49533,207],{},[902,49535,207],{"encoding":904}," na 2 (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,49538,49540],{"className":49539},[886],[888,49541,49542],{"xmlns":890},[892,49543,49544,49554],{},[895,49545,49546],{},[9151,49547,49548,49550,49552],{},[898,49549,1738],{},[2133,49551,2135],{},[898,49553,4240],{},[902,49555,47899],{"encoding":904},[123,49557,49558,49559,48767,49576,49589,49590,2684,49603,49340,49618,49631,49632,49645,49646,1888],{},"(l) Určete přibližnou změnu rovnovážné ceny ",[883,49560,49562],{"className":49561},[886],[888,49563,49564],{"xmlns":890},[892,49565,49566,49574],{},[895,49567,49568],{},[2128,49569,49570,49572],{},[898,49571,1738],{},[898,49573,4240],{},[902,49575,41447],{"encoding":904},[883,49577,49579],{"className":49578},[886],[888,49580,49581],{"xmlns":890},[892,49582,49583,49587],{},[895,49584,49585],{},[898,49586,207],{},[902,49588,207],{"encoding":904}," na 90, poklesu ",[883,49591,49593],{"className":49592},[886],[888,49594,49595],{"xmlns":890},[892,49596,49597,49601],{},[895,49598,49599],{},[898,49600,2102],{},[902,49602,2102],{"encoding":904},[883,49604,49606],{"className":49605},[886],[888,49607,49608],{"xmlns":890},[892,49609,49610,49616],{},[895,49611,49612,49614],{},[1726,49613,2228],{},[2133,49615,2177],{},[902,49617,48093],{"encoding":904},[883,49619,49621],{"className":49620},[886],[888,49622,49623],{"xmlns":890},[892,49624,49625,49629],{},[895,49626,49627],{},[898,49628,2146],{},[902,49630,2146],{"encoding":904}," na 30 a růstu ",[883,49633,49635],{"className":49634},[886],[888,49636,49637],{"xmlns":890},[892,49638,49639,49643],{},[895,49640,49641],{},[898,49642,2198],{},[902,49644,2198],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,49647,49649],{"className":49648},[886],[888,49650,49651],{"xmlns":890},[892,49652,49653,49663],{},[895,49654,49655],{},[9151,49656,49657,49659,49661],{},[898,49658,1738],{},[2133,49660,2177],{},[898,49662,4240],{},[902,49664,48896],{"encoding":904},[198,49666,820],{"id":49667},"přebytek-spotřebitele-a-výrobce-1",[724,49669,49670,47665,49673,47702,49709,1888],{},[38,49671,49672],{},"2.17",[883,49674,49676],{"className":49675},[886],[888,49677,49678],{"xmlns":890},[892,49679,49680,49706],{},[895,49681,49682,49684,49686,49688,49690,49692,49694,49696,49698,49700],{},[898,49683,1738],{},[1726,49685,1728],{},[898,49687,1731],{},[1726,49689,1735],{"stretchy":1734},[898,49691,1724],{},[1726,49693,1762],{"stretchy":1734},[1726,49695,1728],{},[2133,49697,15024],{},[1726,49699,2228],{},[2128,49701,49702,49704],{},[898,49703,1724],{},[2133,49705,2135],{},[902,49707,49708],{"encoding":904},"P = D(Q) = 35 - Q^2",[883,49710,49712],{"className":49711},[886],[888,49713,49714],{"xmlns":890},[892,49715,49716,49742],{},[895,49717,49718,49720,49722,49724,49726,49728,49730,49732,49734,49736],{},[898,49719,1738],{},[1726,49721,1728],{},[898,49723,8659],{},[1726,49725,1735],{"stretchy":1734},[898,49727,1724],{},[1726,49729,1762],{"stretchy":1734},[1726,49731,1728],{},[2133,49733,2177],{},[1726,49735,2099],{},[2128,49737,49738,49740],{},[898,49739,1724],{},[2133,49741,2135],{},[902,49743,49744],{"encoding":904},"P = S(Q) = 3 + Q^2",[120,49746,49747,49750],{},[123,49748,49749],{},"(a) Vypočtěte přebytek spotřebitele při množství 4.",[123,49751,49752],{},"(b) Vypočtěte přebytek výrobce při množství 4.",[724,49754,49755,47665,49758,47702,49792,1888],{},[38,49756,49757],{},"2.18",[883,49759,49761],{"className":49760},[886],[888,49762,49763],{"xmlns":890},[892,49764,49765,49789],{},[895,49766,49767,49769,49771,49773,49775,49777,49779,49781,49783,49785,49787],{},[898,49768,1738],{},[1726,49770,1728],{},[898,49772,1731],{},[1726,49774,1735],{"stretchy":1734},[898,49776,1724],{},[1726,49778,1762],{"stretchy":1734},[1726,49780,1728],{},[2133,49782,3704],{},[1726,49784,2228],{},[2133,49786,2135],{},[898,49788,1724],{},[902,49790,49791],{"encoding":904},"P = D(Q) = 18 - 2Q",[883,49793,49795],{"className":49794},[886],[888,49796,49797],{"xmlns":890},[892,49798,49799,49825],{},[895,49800,49801,49803,49805,49807,49809,49811,49813,49815,49817,49819],{},[898,49802,1738],{},[1726,49804,1728],{},[898,49806,8659],{},[1726,49808,1735],{"stretchy":1734},[898,49810,1724],{},[1726,49812,1762],{"stretchy":1734},[1726,49814,1728],{},[2133,49816,2177],{},[1726,49818,2099],{},[2128,49820,49821,49823],{},[898,49822,1724],{},[2133,49824,2135],{},[902,49826,49744],{"encoding":904},[120,49828,49829,49849,49852,49855],{},[123,49830,49831,49832,1888],{},"(a) Vypočtěte rovnovážné množství ",[883,49833,49835],{"className":49834},[886],[888,49836,49837],{"xmlns":890},[892,49838,49839,49847],{},[895,49840,49841],{},[2128,49842,49843,49845],{},[898,49844,1724],{},[898,49846,4240],{},[902,49848,42384],{"encoding":904},[123,49850,49851],{},"(b) Vypočtěte přebytek spotřebitele při rovnovážném množství.",[123,49853,49854],{},"(b) Vypočtěte přebytek výrobce při rovnovážném množství.",[123,49856,49857],{},"(c) Graficky interpretujte.",[36951,49859],{},[115,49861,49863],{"id":49862},"otázky-k-sebehodnocení","Otázky k sebehodnocení",[152,49865,49866,49869,49872,49875,49878,49881,49884,49887,49890,49893,49896,49899,49902,49905],{},[123,49867,49868],{},"Jaký je rozdíl mezi jednofaktorovým a vícefaktorovým modelem poptávky?",[123,49870,49871],{},"Vyjádřete (vícefaktorovou) funkci poptávky. Jakou má vlastnost?",[123,49873,49874],{},"Definujte funkci poptávky (jednofaktorovou). Jaká je její základní vlastnost? Zdůvodněte.",[123,49876,49877],{},"Definujte Engelovu funkci. Na čem závisí tvar příslušné Engelovy křivky?",[123,49879,49880],{},"Jaký charakter má odezva poptávky na změnu některé z exogenních proměnných?",[123,49882,49883],{},"Definujte funkci nabídky. Jaká je její základní vlastnost? Zdůvodněte.",[123,49885,49886],{},"Co znamená tržní rovnováha? Čím je reprezentována?",[123,49888,49889],{},"Jak se určí rovnovážné množství a rovnovážná cena?",[123,49891,49892],{},"Jaká jsou pravidla pro změnu rovnovážného bodu jako odezvy na posun poptávky, resp. nabídky?",[123,49894,49895],{},"K čemu slouží multiplikátory?",[123,49897,49898],{},"Jak se najde redukovaný tvar pro vybranou rovnovážnou veličinu?",[123,49900,49901],{},"Jak se vypočtou multiplikátory? Mění se jejich znaménka?",[123,49903,49904],{},"Co se rozumí přebytkem spotřebitele? Jak se vypočte?",[123,49906,49907],{},"Co se rozumí přebytkem výrobce? Jak se vypočte?",[36951,49909],{},[115,49911,1670],{"id":1669},[724,49913,49914],{},[38,49915,13147],{},[120,49917,49918,49953,49958,49988,49993,50056,50082,50087,50117,50126,50133,50139],{},[123,49919,49920,10009,49923,18629,49926,1777,49928,1343,49951],{},[38,49921,49922],{},"Poptávané množství",[614,49924,49925],{},"quantity demanded",[38,49927,27983],{},[883,49929,49931],{"className":49930},[886],[888,49932,49933],{"xmlns":890},[892,49934,49935,49949],{},[895,49936,49937,49939,49941,49943,49945,49947],{},[898,49938,1724],{},[1726,49940,1728],{},[898,49942,1731],{},[1726,49944,1735],{"stretchy":1734},[898,49946,1738],{},[1726,49948,1762],{"stretchy":1734},[902,49950,1801],{"encoding":904},[38,49952,37430],{},[123,49954,49955,49957],{},[38,49956,37437],{}," — substituční + důchodový efekt",[123,49959,49960,1777,49963],{},[38,49961,49962],{},"Reálné cenové rozpětí",[883,49964,49966],{"className":49965},[886],[888,49967,49968],{"xmlns":890},[892,49969,49970,49986],{},[895,49971,49972,49974,49976,49978,49984],{},[1726,49973,1735],{"stretchy":1734},[2133,49975,2328],{},[1726,49977,1742],{"separator":1741},[2275,49979,49980,49982],{},[898,49981,1738],{},[2133,49983,2328],{},[1726,49985,1762],{"stretchy":1734},[902,49987,37638],{"encoding":904},[123,49989,49990,11081],{},[38,49991,49992],{},"Homogenita poptávky",[123,49994,49995,1777,49998,1343,50021,1343,50038,50055],{},[38,49996,49997],{},"Lineární poptávka",[883,49999,50001],{"className":50000},[886],[888,50002,50003],{"xmlns":890},[892,50004,50005,50019],{},[895,50006,50007,50009,50011,50013,50015,50017],{},[898,50008,1738],{},[1726,50010,1728],{},[898,50012,207],{},[898,50014,1724],{},[1726,50016,2099],{},[898,50018,2102],{},[902,50020,37041],{"encoding":904},[883,50022,50024],{"className":50023},[886],[888,50025,50026],{"xmlns":890},[892,50027,50028,50036],{},[895,50029,50030,50032,50034],{},[898,50031,207],{},[1726,50033,3444],{},[2133,50035,2328],{},[902,50037,43066],{"encoding":904},[883,50039,50041],{"className":50040},[886],[888,50042,50043],{"xmlns":890},[892,50044,50045,50053],{},[895,50046,50047,50049,50051],{},[898,50048,2102],{},[1726,50050,3405],{},[2133,50052,2328],{},[902,50054,18795],{"encoding":904}," — nedokonalá konkurence",[123,50057,50058,1696,50061],{},[38,50059,50060],{},"Dokonalá konkurence",[883,50062,50064],{"className":50063},[886],[888,50065,50066],{"xmlns":890},[892,50067,50068,50080],{},[895,50069,50070,50072,50074],{},[898,50071,1738],{},[1726,50073,1728],{},[2128,50075,50076,50078],{},[898,50077,1738],{},[1726,50079,4342],{},[902,50081,4345],{"encoding":904},[123,50083,50084,50086],{},[38,50085,38207],{}," — rostoucí křivka poptávky (důchodový efekt > substituční)",[123,50088,50089,1777,50091,1343,50115],{},[38,50090,31708],{},[883,50092,50094],{"className":50093},[886],[888,50095,50096],{"xmlns":890},[892,50097,50098,50112],{},[895,50099,50100,50102,50104,50106,50108,50110],{},[898,50101,1724],{},[1726,50103,1728],{},[898,50105,4240],{},[1726,50107,1735],{"stretchy":1734},[898,50109,1745],{},[1726,50111,1762],{"stretchy":1734},[902,50113,50114],{"encoding":904},"Q = E(Y)",[38,50116,38404],{},[123,50118,50119,50122,50123,50125],{},[38,50120,50121],{},"Normální"," (nezbytné \u002F luxusní) vs. ",[38,50124,38850],{}," zboží",[123,50127,50128,3877,50130,50132],{},[38,50129,39856],{},[38,50131,39803],{}," — znaménka zkřížených koeficientů",[123,50134,50135,50138],{},[38,50136,50137],{},"Dvoukomoditní trh"," (2.6)",[123,50140,50141,10009,50144,1762],{},[38,50142,50143],{},"Posun poptávky",[614,50145,38908],{},[724,50147,50148],{},[38,50149,13111],{},[120,50151,50152,50185,50189,50234],{},[123,50153,50154,10009,50156,18629,50158,1777,50160,1343,50183],{},[38,50155,40250],{},[614,50157,40253],{},[38,50159,40424],{},[883,50161,50163],{"className":50162},[886],[888,50164,50165],{"xmlns":890},[892,50166,50167,50181],{},[895,50168,50169,50171,50173,50175,50177,50179],{},[898,50170,1724],{},[1726,50172,1728],{},[898,50174,8659],{},[1726,50176,1735],{"stretchy":1734},[898,50178,1738],{},[1726,50180,1762],{"stretchy":1734},[902,50182,8668],{"encoding":904},[38,50184,40502],{},[123,50186,50187],{},[38,50188,40509],{},[123,50190,50191,1777,50194,1343,50217],{},[38,50192,50193],{},"Lineární nabídka",[883,50195,50197],{"className":50196},[886],[888,50198,50199],{"xmlns":890},[892,50200,50201,50215],{},[895,50202,50203,50205,50207,50209,50211,50213],{},[898,50204,1738],{},[1726,50206,1728],{},[898,50208,2146],{},[898,50210,1724],{},[1726,50212,2099],{},[898,50214,2198],{},[902,50216,40223],{"encoding":904},[883,50218,50220],{"className":50219},[886],[888,50221,50222],{"xmlns":890},[892,50223,50224,50232],{},[895,50225,50226,50228,50230],{},[898,50227,2146],{},[1726,50229,3405],{},[2133,50231,2328],{},[902,50233,40241],{"encoding":904},[123,50235,50236,10009,50239,1762],{},[38,50237,50238],{},"Posun nabídky",[614,50240,40887],{},[724,50242,50243],{},[38,50244,50245],{},"Rovnováha a komparativní statika",[120,50247,50248,50327,50333],{},[123,50249,50250,10009,50252,18629,50254,1777,50257,1343,50274,1777,50277,1343,50294,1777,50296],{},[38,50251,41306],{},[614,50253,41425],{},[38,50255,50256],{},"rovnovážná cena",[883,50258,50260],{"className":50259},[886],[888,50261,50262],{"xmlns":890},[892,50263,50264,50272],{},[895,50265,50266],{},[2128,50267,50268,50270],{},[898,50269,1738],{},[898,50271,4240],{},[902,50273,41447],{"encoding":904},[38,50275,50276],{},"rovnovážné množství",[883,50278,50280],{"className":50279},[886],[888,50281,50282],{"xmlns":890},[892,50283,50284,50292],{},[895,50285,50286],{},[2128,50287,50288,50290],{},[898,50289,1724],{},[898,50291,4240],{},[902,50293,42384],{"encoding":904},[38,50295,41483],{},[883,50297,50299],{"className":50298},[886],[888,50300,50301],{"xmlns":890},[892,50302,50303,50325],{},[895,50304,50305,50307,50309,50315,50317,50323],{},[898,50306,4240],{},[1726,50308,2487],{"stretchy":1734},[2128,50310,50311,50313],{},[898,50312,1724],{},[898,50314,4240],{},[1726,50316,1742],{"separator":1741},[2128,50318,50319,50321],{},[898,50320,1738],{},[898,50322,4240],{},[1726,50324,2502],{"stretchy":1734},[902,50326,41348],{"encoding":904},[123,50328,50329,50332],{},[38,50330,50331],{},"Pravidla 1–4"," komparativní statiky",[123,50334,50335,10009,50338,1762],{},[38,50336,50337],{},"Teorém pavučiny",[614,50339,42330],{},[724,50341,50342],{},[38,50343,50344],{},"Zdanění",[120,50346,50347,50403,50451],{},[123,50348,50349,50351,50352,50377,50378,1762],{},[38,50350,50344],{}," — daň výrobci (",[883,50353,50355],{"className":50354},[886],[888,50356,50357],{"xmlns":890},[892,50358,50359,50375],{},[895,50360,50361,50367,50369,50371,50373],{},[2275,50362,50363,50365],{},[898,50364,8659],{},[2133,50366,2281],{},[1726,50368,1728],{},[898,50370,8659],{},[1726,50372,2099],{},[898,50374,2772],{},[902,50376,42735],{"encoding":904},") vs. daň spotřebiteli (",[883,50379,50381],{"className":50380},[886],[888,50382,50383],{"xmlns":890},[892,50384,50385,50401],{},[895,50386,50387,50393,50395,50397,50399],{},[2275,50388,50389,50391],{},[898,50390,1731],{},[2133,50392,2135],{},[1726,50394,1728],{},[898,50396,1731],{},[1726,50398,2228],{},[898,50400,2772],{},[902,50402,42766],{"encoding":904},[123,50404,50405,1777,50407,1343,50428],{},[38,50406,42639],{},[883,50408,50410],{"className":50409},[886],[888,50411,50412],{"xmlns":890},[892,50413,50414,50426],{},[895,50415,50416],{},[2275,50417,50418,50420],{},[898,50419,2772],{},[895,50421,50422,50424],{},[898,50423,42658],{},[898,50425,724],{},[902,50427,42663],{"encoding":904},[883,50429,50431],{"className":50430},[886],[888,50432,50433],{"xmlns":890},[892,50434,50435,50449],{},[895,50436,50437],{},[2275,50438,50439,50441],{},[898,50440,2772],{},[895,50442,50443,50445,50447],{},[898,50444,42681],{},[898,50446,2003],{},[898,50448,12027],{},[902,50450,42688],{"encoding":904},[123,50452,50453,1777,50456,1343,50485],{},[38,50454,50455],{},"Ekvivalence zdanění",[883,50457,50459],{"className":50458},[886],[888,50460,50461],{"xmlns":890},[892,50462,50463,50483],{},[895,50464,50465,50473,50475],{},[9151,50466,50467,50469,50471],{},[898,50468,1724],{},[2133,50470,2281],{},[898,50472,4240],{},[1726,50474,1728],{},[9151,50476,50477,50479,50481],{},[898,50478,1724],{},[2133,50480,2135],{},[898,50482,4240],{},[902,50484,42889],{"encoding":904},[883,50486,50488],{"className":50487},[886],[888,50489,50490],{"xmlns":890},[892,50491,50492,50516],{},[895,50493,50494,50502,50504,50506,50508],{},[9151,50495,50496,50498,50500],{},[898,50497,1738],{},[2133,50499,2281],{},[898,50501,4240],{},[1726,50503,2228],{},[898,50505,2772],{},[1726,50507,1728],{},[9151,50509,50510,50512,50514],{},[898,50511,1738],{},[2133,50513,2135],{},[898,50515,4240],{},[902,50517,42923],{"encoding":904},[724,50519,50520],{},[38,50521,26389],{},[120,50523,50524,50570,50601,50606,50612,50618],{},[123,50525,50526,1777,50528],{},[38,50527,43022],{},[883,50529,50531],{"className":50530},[886],[888,50532,50533],{"xmlns":890},[892,50534,50535,50567],{},[895,50536,50537,50543,50545,50547,50549,50551,50553,50555,50557,50559,50561,50563,50565],{},[2128,50538,50539,50541],{},[898,50540,1724],{},[898,50542,4240],{},[1726,50544,1728],{},[1726,50546,1735],{"stretchy":1734},[898,50548,2102],{},[1726,50550,2228],{},[898,50552,2198],{},[1726,50554,1762],{"stretchy":1734},[898,50556,4661],{"mathvariant":2377},[1726,50558,1735],{"stretchy":1734},[898,50560,2146],{},[1726,50562,2228],{},[898,50564,207],{},[1726,50566,1762],{"stretchy":1734},[902,50568,50569],{"encoding":904},"Q^E = (b - d)\u002F(c - a)",[123,50571,50572,1777,50575,50600],{},[38,50573,50574],{},"Parametry",[883,50576,50578],{"className":50577},[886],[888,50579,50580],{"xmlns":890},[892,50581,50582,50598],{},[895,50583,50584,50586,50588,50590,50592,50594,50596],{},[898,50585,207],{},[1726,50587,1742],{"separator":1741},[898,50589,2102],{},[1726,50591,1742],{"separator":1741},[898,50593,2146],{},[1726,50595,1742],{"separator":1741},[898,50597,2198],{},[902,50599,43266],{"encoding":904}," — exogenní proměnné",[123,50602,50603],{},[38,50604,50605],{},"Endogenní \u002F exogenní proměnná",[123,50607,50608,50611],{},[38,50609,50610],{},"Multiplikátor"," — parciální derivace redukovaného tvaru",[123,50613,50614,1343,50616],{},[38,50615,1705],{},[38,50617,36941],{},[123,50619,50620,1777,50622,50638],{},[38,50621,2952],{},[883,50623,50625],{"className":50624},[886],[888,50626,50627],{"xmlns":890},[892,50628,50629,50635],{},[895,50630,50631,50633],{},[898,50632,2198],{},[898,50634,1724],{},[902,50636,50637],{"encoding":904},"dQ"," (2.11)",[724,50640,50641],{},[38,50642,50643],{},"Přebytky a ostatní",[120,50645,50646,50684],{},[123,50647,50648,1777,50650,50665,50666,1777,50668,50683],{},[38,50649,44915],{},[883,50651,50653],{"className":50652},[886],[888,50654,50655],{"xmlns":890},[892,50656,50657,50663],{},[895,50658,50659,50661],{},[898,50660,2775],{},[898,50662,8659],{},[902,50664,44931],{"encoding":904}," (2.14), ",[38,50667,44934],{},[883,50669,50671],{"className":50670},[886],[888,50672,50673],{"xmlns":890},[892,50674,50675,50681],{},[895,50676,50677,50679],{},[898,50678,1738],{},[898,50680,8659],{},[902,50682,44950],{"encoding":904}," (2.15)",[123,50685,50686,1343,50689,50692],{},[38,50687,50688],{},"Homo economicus",[38,50690,50691],{},"Marshallova formulace"," (1890)",[36951,50694],{},[115,50696,1899],{"id":1898},[120,50698,50699,50734,50743],{},[123,50700,50701,1777,50704,50707,50708,1343,50711,50714,50715,50718,50719,50722,50723,50726,50727,50730,50731],{},[38,50702,50703],{},"Související témata:",[207,50705,811],{"className":50706,"dataFsResolvedFilePath":809,"href":810},[210]," (dopady daně, daňové břemeno, ekvivalence), ",[207,50709,820],{"className":50710,"dataFsResolvedFilePath":818,"href":819},[210],[207,50712,2358],{"className":50713,"dataFsResolvedFilePath":764,"href":765},[210]," (zákon klesající\u002Frostoucí, monotonie), ",[207,50716,775],{"className":50717,"dataFsResolvedFilePath":773,"href":774},[210]," (CS a PS), ",[207,50720,784],{"className":50721,"dataFsResolvedFilePath":782,"href":783},[210]," (vícefaktorové modely, multiplikátory), ",[207,50724,793],{"className":50725,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace spotřebitele), ",[207,50728,3820],{"className":50729,"dataFsResolvedFilePath":848,"href":849},[210]," (důchodová a cenová citlivost), ",[207,50732,3815],{"className":50733,"dataFsResolvedFilePath":827,"href":828},[210],[123,50735,50736,1777,50739],{},[38,50737,50738],{},"Shrnutí přednášek:",[207,50740,50742],{"className":50741,"dataFsResolvedFilePath":745,"href":746},[210],"KS — 1. blok",[123,50744,50745,1777,50747],{},[38,50746,16188],{},[207,50748,16192],{"className":50749,"dataFsResolvedFilePath":1640,"href":1641},[210],{"title":641,"searchDepth":642,"depth":642,"links":50751},[50752,50753,50761,50767,50774,50775,50782,50783,50784,50791,50792,50793],{"id":36775,"depth":642,"text":36776},{"id":36756,"depth":642,"text":13147,"children":50754},[50755,50756,50757,50758,50760],{"id":37044,"depth":649,"text":37045},{"id":37326,"depth":649,"text":37327},{"id":38336,"depth":649,"text":38337},{"id":38904,"depth":649,"text":50759},"Posun poptávky (shift of demand)",{"id":39408,"depth":649,"text":39409},{"id":36760,"depth":642,"text":13111,"children":50762},[50763,50764,50765],{"id":40245,"depth":649,"text":37045},{"id":40431,"depth":649,"text":40432},{"id":40883,"depth":649,"text":50766},"Posun nabídky (shift of supply)",{"id":41305,"depth":642,"text":41306,"children":50768},[50769,50770,50771,50772,50773],{"id":41417,"depth":649,"text":41418},{"id":41630,"depth":649,"text":41631},{"id":41948,"depth":649,"text":41949},{"id":42302,"depth":649,"text":42303},{"id":42333,"depth":649,"text":42334},{"id":42602,"depth":642,"text":811},{"id":43003,"depth":642,"text":43004,"children":50776},[50777,50778,50779,50780],{"id":43021,"depth":649,"text":43022},{"id":43402,"depth":649,"text":43403},{"id":43786,"depth":649,"text":43787},{"id":44240,"depth":649,"text":50781},"Příklad 2.11 — komparativní statika pro QEQ^E",{"id":11769,"depth":642,"text":820},{"id":45165,"depth":642,"text":45166},{"id":45396,"depth":642,"text":45397,"children":50785},[50786,50787,50788,50789,50790],{"id":45400,"depth":649,"text":45401},{"id":46240,"depth":649,"text":46241},{"id":46616,"depth":649,"text":41306},{"id":47911,"depth":649,"text":43004},{"id":49667,"depth":649,"text":820},{"id":49862,"depth":642,"text":49863},{"id":1669,"depth":642,"text":1670},{"id":1898,"depth":642,"text":1899},{},"\u002Ftopics\u002Fpoptavka-nabidka",{"title":802,"description":641},[1138,1135],"topics\u002Fpoptavka-nabidka",[1128,50800,50801,50802,17865,50803,50804],"poptavka","nabidka","rovnovaha","zdaneni","prebytek","VHXMOe03Z24g0HTNlL2geCMzNcnJ3vQ8m2Org-s9n8Q",{"id":50807,"title":820,"body":50808,"course":1128,"courses":659,"created":9541,"description":641,"extension":661,"meta":55087,"navigation":664,"path":55088,"seo":55089,"sources":55090,"stem":55091,"tags":55092,"type":1950,"updated":677,"__hash__":55097},"topics\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce.md",{"type":9,"value":50809,"toc":55065},[50810,50812,50880,50930,50932,50935,51193,51269,51274,51276,51295,51299,51375,51460,51462,51776,51869,51871,51890,51894,51968,52053,52056,52232,52237,52239,52659,52661,52665,52669,52905,52949,53049,53115,53118,53151,53327,53389,53519,53597,53708,53742,53940,53959,53978,54043,54047,54050,54095,54098,54216,54262,54264,54268,54616,54618,54620,54898,54900,54904,54939,54946,55019,55021,55023],[12,50811,820],{"id":11769},[3859,50813,50814],{},[724,50815,50816,3866,50818,10009,50820,50835,50836,10009,50838,50853,50854,50876,50877,1888],{},[883,50817,3865],{},[38,50819,44915],{},[883,50821,50823],{"className":50822},[886],[888,50824,50825],{"xmlns":890},[892,50826,50827,50833],{},[895,50828,50829,50831],{},[898,50830,2775],{},[898,50832,8659],{},[902,50834,44931],{"encoding":904},") je rozdíl mezi tím, co byl spotřebitel ochoten zaplatit, a tím, co skutečně zaplatil. ",[38,50837,45062],{},[883,50839,50841],{"className":50840},[886],[888,50842,50843],{"xmlns":890},[892,50844,50845,50851],{},[895,50846,50847,50849],{},[898,50848,1738],{},[898,50850,8659],{},[902,50852,44950],{"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 ",[883,50855,50857],{"className":50856},[886],[888,50858,50859],{"xmlns":890},[892,50860,50861,50873],{},[895,50862,50863,50865,50867,50869,50871],{},[898,50864,2775],{},[898,50866,8659],{},[1726,50868,2099],{},[898,50870,1738],{},[898,50872,8659],{},[902,50874,50875],{"encoding":904},"CS + PS"," měří ",[38,50878,50879],{},"celkový blahobyt trhu",[724,50881,50882,10009,50884,1343,50886,12114,50901,10009,50903,1343,50905,50920,50921,50925,50926,1888],{},[38,50883,44915],{},[614,50885,44969],{},[883,50887,50889],{"className":50888},[886],[888,50890,50891],{"xmlns":890},[892,50892,50893,50899],{},[895,50894,50895,50897],{},[898,50896,2775],{},[898,50898,8659],{},[902,50900,44931],{"encoding":904},[38,50902,44934],{},[614,50904,45065],{},[883,50906,50908],{"className":50907},[886],[888,50909,50910],{"xmlns":890},[892,50911,50912,50918],{},[895,50913,50914,50916],{},[898,50915,1738],{},[898,50917,8659],{},[902,50919,44950],{"encoding":904},") kvantifikují čistý prospěch jednotlivých stran trhu. Navazují na pojmy ",[207,50922,50924],{"className":50923,"dataFsResolvedFilePath":800,"href":801},[210],"tržní rovnováhy"," a využívají aparát ",[207,50927,50929],{"className":50928,"dataFsResolvedFilePath":773,"href":774},[210],"integrálního počtu",[36951,50931],{},[115,50933,1241],{"id":50934},"úvod",[724,50936,50937,50938,50961,50962,50985,50986,51003,51004,3902,51036,51068,51069,51095,51096,51099,51100,51103,51104,13997,51138,21575,51159,1888],{},"Je dána funkce poptávky ",[883,50939,50941],{"className":50940},[886],[888,50942,50943],{"xmlns":890},[892,50944,50945,50959],{},[895,50946,50947,50949,50951,50953,50955,50957],{},[898,50948,1738],{},[1726,50950,1728],{},[898,50952,1731],{},[1726,50954,1735],{"stretchy":1734},[898,50956,1724],{},[1726,50958,1762],{"stretchy":1734},[902,50960,1830],{"encoding":904},", resp. funkce nabídky ",[883,50963,50965],{"className":50964},[886],[888,50966,50967],{"xmlns":890},[892,50968,50969,50983],{},[895,50970,50971,50973,50975,50977,50979,50981],{},[898,50972,1738],{},[1726,50974,1728],{},[898,50976,8659],{},[1726,50978,1735],{"stretchy":1734},[898,50980,1724],{},[1726,50982,1762],{"stretchy":1734},[902,50984,41052],{"encoding":904},". Pro pevně zadané množství ",[883,50987,50989],{"className":50988},[886],[888,50990,50991],{"xmlns":890},[892,50992,50993,51001],{},[895,50994,50995],{},[2275,50996,50997,50999],{},[898,50998,1724],{},[2133,51000,2328],{},[902,51002,38289],{"encoding":904}," je odpovídající cena ",[883,51005,51007],{"className":51006},[886],[888,51008,51009],{"xmlns":890},[892,51010,51011,51033],{},[895,51012,51013,51019,51021,51023,51025,51031],{},[2275,51014,51015,51017],{},[898,51016,1738],{},[2133,51018,2328],{},[1726,51020,1728],{},[898,51022,1731],{},[1726,51024,1735],{"stretchy":1734},[2275,51026,51027,51029],{},[898,51028,1724],{},[2133,51030,2328],{},[1726,51032,1762],{"stretchy":1734},[902,51034,51035],{"encoding":904},"P_0 = D(Q_0)",[883,51037,51039],{"className":51038},[886],[888,51040,51041],{"xmlns":890},[892,51042,51043,51065],{},[895,51044,51045,51051,51053,51055,51057,51063],{},[2275,51046,51047,51049],{},[898,51048,1738],{},[2133,51050,2328],{},[1726,51052,1728],{},[898,51054,8659],{},[1726,51056,1735],{"stretchy":1734},[2275,51058,51059,51061],{},[898,51060,1724],{},[2133,51062,2328],{},[1726,51064,1762],{"stretchy":1734},[902,51066,51067],{"encoding":904},"P_0 = S(Q_0)","). Součin ",[883,51070,51072],{"className":51071},[886],[888,51073,51074],{"xmlns":890},[892,51075,51076,51092],{},[895,51077,51078,51084,51086],{},[2275,51079,51080,51082],{},[898,51081,1738],{},[2133,51083,2328],{},[2289,51085,2984],{},[2275,51087,51088,51090],{},[898,51089,1724],{},[2133,51091,2328],{},[902,51093,51094],{"encoding":904},"P_0 \\, Q_0"," reprezentuje buď ",[38,51097,51098],{},"výdaje spotřebitele",", nebo ",[38,51101,51102],{},"tržby výrobce"," a geometricky odpovídá obsahu obdélníka ",[883,51105,51107],{"className":51106},[886],[888,51108,51109],{"xmlns":890},[892,51110,51111,51135],{},[895,51112,51113,51115,51117,51123,51125,51127,51129],{},[2133,51114,2328],{},[2289,51116,2984],{},[2275,51118,51119,51121],{},[898,51120,1724],{},[2133,51122,2328],{},[2289,51124,2984],{},[898,51126,4243],{},[2289,51128,2984],{},[2275,51130,51131,51133],{},[898,51132,1738],{},[2133,51134,2328],{},[902,51136,51137],{"encoding":904},"0\\,Q_0\\,A\\,P_0",[883,51139,51141],{"className":51140},[886],[888,51142,51143],{"xmlns":890},[892,51144,51145,51157],{},[895,51146,51147,51149,51151,51153,51155],{},[1726,51148,1735],{"stretchy":1734},[898,51150,1724],{},[1726,51152,1742],{"separator":1741},[898,51154,1738],{},[1726,51156,1762],{"stretchy":1734},[902,51158,37672],{"encoding":904},[883,51160,51162],{"className":51161},[886],[888,51163,51164],{"xmlns":890},[892,51165,51166,51190],{},[895,51167,51168,51170,51172,51174,51180,51182,51188],{},[898,51169,4243],{},[1726,51171,1728],{},[1726,51173,2487],{"stretchy":1734},[2275,51175,51176,51178],{},[898,51177,1724],{},[2133,51179,2328],{},[1726,51181,1742],{"separator":1741},[2275,51183,51184,51186],{},[898,51185,1738],{},[2133,51187,2328],{},[1726,51189,2502],{"stretchy":1734},[902,51191,51192],{"encoding":904},"A = [Q_0, P_0]",[3859,51194,51195,51200,51258],{},[724,51196,51197,51199],{},[883,51198,4145],{}," Intuice",[120,51201,51202,51230],{},[123,51203,51204,51205,51208,51209,51211,51212,51229],{},"Za jednotky zboží nakoupené ",[38,51206,51207],{},"před"," posledním kusem je spotřebitel podle funkce poptávky ochoten platit ",[614,51210,25251],{}," než ",[883,51213,51215],{"className":51214},[886],[888,51216,51217],{"xmlns":890},[892,51218,51219,51227],{},[895,51220,51221],{},[2275,51222,51223,51225],{},[898,51224,1738],{},[2133,51226,2328],{},[902,51228,38929],{"encoding":904}," — rozdíl si „šetří do kapsy\" jako přebytek.",[123,51231,51232,51233,51235,51236,51239,51240,51257],{},"Za jednotky zboží prodané ",[38,51234,51207],{}," posledním kusem by výrobce podle funkce nabídky byl ochoten prodávat i za ",[614,51237,51238],{},"nižší"," cenu než ",[883,51241,51243],{"className":51242},[886],[888,51244,51245],{"xmlns":890},[892,51246,51247,51255],{},[895,51248,51249],{},[2275,51250,51251,51253],{},[898,51252,1738],{},[2133,51254,2328],{},[902,51256,38929],{"encoding":904}," — rozdíl je jeho přebytek.",[724,51259,51260,51261,51264,51265,51268],{},"Přebytek je tedy rozdíl mezi ",[614,51262,51263],{},"ochotou"," (platit \u002F prodávat) a ",[614,51266,51267],{},"skutečností"," (zaplaceno \u002F obdrženo).",[724,51270,51271],{},[1647,51272],{"alt":44960,"className":51273,"src":44962},[210,1651],[36951,51275],{},[115,51277,51279,51280,1762],{"id":51278},"přebytek-spotřebitele-cscs","Přebytek spotřebitele (",[883,51281,51283],{"className":51282},[886],[888,51284,51285],{"xmlns":890},[892,51286,51287,51293],{},[895,51288,51289,51291],{},[898,51290,2775],{},[898,51292,8659],{},[902,51294,44931],{"encoding":904},[198,51296,51298],{"id":51297},"definice-vzorec-214","Definice (vzorec 2.14)",[724,51300,51301,51302,51325,51326,51343,51344,2703],{},"Pro poptávku ",[883,51303,51305],{"className":51304},[886],[888,51306,51307],{"xmlns":890},[892,51308,51309,51323],{},[895,51310,51311,51313,51315,51317,51319,51321],{},[898,51312,1738],{},[1726,51314,1728],{},[898,51316,1731],{},[1726,51318,1735],{"stretchy":1734},[898,51320,1724],{},[1726,51322,1762],{"stretchy":1734},[902,51324,1830],{"encoding":904}," a pevně zadané ",[883,51327,51329],{"className":51328},[886],[888,51330,51331],{"xmlns":890},[892,51332,51333,51341],{},[895,51334,51335],{},[2275,51336,51337,51339],{},[898,51338,1724],{},[2133,51340,2328],{},[902,51342,38289],{"encoding":904}," s cenou ",[883,51345,51347],{"className":51346},[886],[888,51348,51349],{"xmlns":890},[892,51350,51351,51373],{},[895,51352,51353,51359,51361,51363,51365,51371],{},[2275,51354,51355,51357],{},[898,51356,1738],{},[2133,51358,2328],{},[1726,51360,1728],{},[898,51362,1731],{},[1726,51364,1735],{"stretchy":1734},[2275,51366,51367,51369],{},[898,51368,1724],{},[2133,51370,2328],{},[1726,51372,1762],{"stretchy":1734},[902,51374,51035],{"encoding":904},[883,51376,51378],{"className":51377},[886],[888,51379,51380],{"xmlns":890,"display":28047},[892,51381,51382,51458],{},[20735,51383,51384],{"width":28052},[20740,51385,51386,51388,51452,51454],{},[20743,51387],{"width":28057},[20743,51389,51390],{},[895,51391,51392,51394,51396,51398,51404,51406,51408,51420,51422,51424,51426,51428,51430,51432,51434,51436,51442,51444,51450],{},[898,51393,2775],{},[898,51395,8659],{},[1726,51397,1735],{"stretchy":1734},[2275,51399,51400,51402],{},[898,51401,1724],{},[2133,51403,2328],{},[1726,51405,1762],{"stretchy":1734},[1726,51407,1728],{},[9151,51409,51410,51412,51414],{},[1726,51411,11154],{},[2133,51413,2328],{},[2275,51415,51416,51418],{},[898,51417,1724],{},[2133,51419,2328],{},[898,51421,1731],{},[1726,51423,1735],{"stretchy":1734},[898,51425,1724],{},[1726,51427,1762],{"stretchy":1734},[2289,51429,2984],{},[898,51431,2198],{},[898,51433,1724],{},[1726,51435,2228],{},[2275,51437,51438,51440],{},[898,51439,1738],{},[2133,51441,2328],{},[2289,51443,2984],{},[2275,51445,51446,51448],{},[898,51447,1724],{},[2133,51449,2328],{},[898,51451,1888],{"mathvariant":2377},[20743,51453],{"width":28057},[20743,51455,51456],{},[2289,51457,45054],{},[902,51459,45057],{"encoding":904},[198,51461,2445],{"id":2444},[120,51463,51464,51556,51618],{},[123,51465,51466,51506,51507,51533,51534,51537,51538,51555],{},[883,51467,51469],{"className":51468},[886],[888,51470,51471],{"xmlns":890},[892,51472,51473,51503],{},[895,51474,51475],{},[2326,51476,51477,51489,51491,51493,51495,51497,51499,51501],{"scriptlevel":2328,"displaystyle":1741},[9151,51478,51479,51481,51483],{},[1726,51480,11154],{},[2133,51482,2328],{},[2275,51484,51485,51487],{},[898,51486,1724],{},[2133,51488,2328],{},[898,51490,1731],{},[1726,51492,1735],{"stretchy":1734},[898,51494,1724],{},[1726,51496,1762],{"stretchy":1734},[2289,51498,2984],{},[898,51500,2198],{},[898,51502,1724],{},[902,51504,51505],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ"," — plocha pod křivkou poptávky v intervalu ",[883,51508,51510],{"className":51509},[886],[888,51511,51512],{"xmlns":890},[892,51513,51514,51530],{},[895,51515,51516,51518,51520,51522,51528],{},[1726,51517,2487],{"stretchy":1734},[2133,51519,2328],{},[1726,51521,1742],{"separator":1741},[2275,51523,51524,51526],{},[898,51525,1724],{},[2133,51527,2328],{},[1726,51529,2502],{"stretchy":1734},[902,51531,51532],{"encoding":904},"[0, Q_0]","; představuje celkovou ",[38,51535,51536],{},"ochotu platit"," (maximální částku, kterou by spotřebitel za ",[883,51539,51541],{"className":51540},[886],[888,51542,51543],{"xmlns":890},[892,51544,51545,51553],{},[895,51546,51547],{},[2275,51548,51549,51551],{},[898,51550,1724],{},[2133,51552,2328],{},[902,51554,38289],{"encoding":904}," jednotek byl ochoten zaplatit).",[123,51557,51558,51584,51585,1847],{},[883,51559,51561],{"className":51560},[886],[888,51562,51563],{"xmlns":890},[892,51564,51565,51581],{},[895,51566,51567,51573,51575],{},[2275,51568,51569,51571],{},[898,51570,1738],{},[2133,51572,2328],{},[2289,51574,2984],{},[2275,51576,51577,51579],{},[898,51578,1724],{},[2133,51580,2328],{},[902,51582,51583],{"encoding":904},"P_0\\,Q_0"," — skutečně zaplacená částka (obdélník ",[883,51586,51588],{"className":51587},[886],[888,51589,51590],{"xmlns":890},[892,51591,51592,51616],{},[895,51593,51594,51596,51598,51604,51606,51608,51610],{},[2133,51595,2328],{},[2289,51597,2984],{},[2275,51599,51600,51602],{},[898,51601,1724],{},[2133,51603,2328],{},[2289,51605,2984],{},[898,51607,4243],{},[2289,51609,2984],{},[2275,51611,51612,51614],{},[898,51613,1738],{},[2133,51615,2328],{},[902,51617,51137],{"encoding":904},[123,51619,51620,51635,51636,51658,51659,51684,51685,21575,51711,3877,51743,1888],{},[883,51621,51623],{"className":51622},[886],[888,51624,51625],{"xmlns":890},[892,51626,51627,51633],{},[895,51628,51629,51631],{},[898,51630,2775],{},[898,51632,8659],{},[902,51634,44931],{"encoding":904}," je plocha mezi křivkou poptávky a vodorovnou přímkou ",[883,51637,51639],{"className":51638},[886],[888,51640,51641],{"xmlns":890},[892,51642,51643,51655],{},[895,51644,51645,51647,51649],{},[898,51646,1738],{},[1726,51648,1728],{},[2275,51650,51651,51653],{},[898,51652,1738],{},[2133,51654,2328],{},[902,51656,51657],{"encoding":904},"P = P_0"," v pásu ",[883,51660,51662],{"className":51661},[886],[888,51663,51664],{"xmlns":890},[892,51665,51666,51682],{},[895,51667,51668,51670,51672,51674,51680],{},[1726,51669,2487],{"stretchy":1734},[2133,51671,2328],{},[1726,51673,1742],{"separator":1741},[2275,51675,51676,51678],{},[898,51677,1724],{},[2133,51679,2328],{},[1726,51681,2502],{"stretchy":1734},[902,51683,51532],{"encoding":904}," — „křivočarý trojúhelník\" ",[883,51686,51688],{"className":51687},[886],[888,51689,51690],{"xmlns":890},[892,51691,51692,51708],{},[895,51693,51694,51700,51702,51704,51706],{},[2275,51695,51696,51698],{},[898,51697,1738],{},[2133,51699,2328],{},[2289,51701,2984],{},[898,51703,23234],{},[2289,51705,2984],{},[898,51707,4243],{},[902,51709,51710],{"encoding":904},"P_0\\,B\\,A",[883,51712,51714],{"className":51713},[886],[888,51715,51716],{"xmlns":890},[892,51717,51718,51740],{},[895,51719,51720,51722,51724,51726,51728,51730,51732,51734,51736,51738],{},[898,51721,23234],{},[1726,51723,1728],{},[1726,51725,2487],{"stretchy":1734},[2133,51727,2328],{},[1726,51729,1742],{"separator":1741},[898,51731,1731],{},[1726,51733,1735],{"stretchy":1734},[2133,51735,2328],{},[1726,51737,1762],{"stretchy":1734},[1726,51739,2502],{"stretchy":1734},[902,51741,51742],{"encoding":904},"B = [0, D(0)]",[883,51744,51746],{"className":51745},[886],[888,51747,51748],{"xmlns":890},[892,51749,51750,51774],{},[895,51751,51752,51754,51756,51758,51764,51766,51772],{},[898,51753,4243],{},[1726,51755,1728],{},[1726,51757,2487],{"stretchy":1734},[2275,51759,51760,51762],{},[898,51761,1724],{},[2133,51763,2328],{},[1726,51765,1742],{"separator":1741},[2275,51767,51768,51770],{},[898,51769,1738],{},[2133,51771,2328],{},[1726,51773,2502],{"stretchy":1734},[902,51775,51192],{"encoding":904},[724,51777,51778],{},[614,51779,51780,51781,51794,51795,51828,51829,29123,51854,1888],{},"Obrázek 2.24: Křivka poptávky ",[883,51782,51784],{"className":51783},[886],[888,51785,51786],{"xmlns":890},[892,51787,51788,51792],{},[895,51789,51790],{},[898,51791,1731],{},[902,51793,1731],{"encoding":904},", bod ",[883,51796,51798],{"className":51797},[886],[888,51799,51800],{"xmlns":890},[892,51801,51802,51826],{},[895,51803,51804,51806,51808,51810,51816,51818,51824],{},[898,51805,4243],{},[1726,51807,1728],{},[1726,51809,2487],{"stretchy":1734},[2275,51811,51812,51814],{},[898,51813,1724],{},[2133,51815,2328],{},[1726,51817,1742],{"separator":1741},[2275,51819,51820,51822],{},[898,51821,1738],{},[2133,51823,2328],{},[1726,51825,2502],{"stretchy":1734},[902,51827,51192],{"encoding":904},", vyšrafovaná plocha trojúhelníku ",[883,51830,51832],{"className":51831},[886],[888,51833,51834],{"xmlns":890},[892,51835,51836,51852],{},[895,51837,51838,51844,51846,51848,51850],{},[2275,51839,51840,51842],{},[898,51841,1738],{},[2133,51843,2328],{},[2289,51845,2984],{},[898,51847,23234],{},[2289,51849,2984],{},[898,51851,4243],{},[902,51853,51710],{"encoding":904},[883,51855,51857],{"className":51856},[886],[888,51858,51859],{"xmlns":890},[892,51860,51861,51867],{},[895,51862,51863,51865],{},[898,51864,2775],{},[898,51866,8659],{},[902,51868,44931],{"encoding":904},[36951,51870],{},[115,51872,51874,51875,1762],{"id":51873},"přebytek-výrobce-psps","Přebytek výrobce (",[883,51876,51878],{"className":51877},[886],[888,51879,51880],{"xmlns":890},[892,51881,51882,51888],{},[895,51883,51884,51886],{},[898,51885,1738],{},[898,51887,8659],{},[902,51889,44950],{"encoding":904},[198,51891,51893],{"id":51892},"definice-vzorec-215","Definice (vzorec 2.15)",[724,51895,51896,51897,51325,51920,51343,51937,2703],{},"Analogicky — pro nabídku ",[883,51898,51900],{"className":51899},[886],[888,51901,51902],{"xmlns":890},[892,51903,51904,51918],{},[895,51905,51906,51908,51910,51912,51914,51916],{},[898,51907,1738],{},[1726,51909,1728],{},[898,51911,8659],{},[1726,51913,1735],{"stretchy":1734},[898,51915,1724],{},[1726,51917,1762],{"stretchy":1734},[902,51919,41052],{"encoding":904},[883,51921,51923],{"className":51922},[886],[888,51924,51925],{"xmlns":890},[892,51926,51927,51935],{},[895,51928,51929],{},[2275,51930,51931,51933],{},[898,51932,1724],{},[2133,51934,2328],{},[902,51936,38289],{"encoding":904},[883,51938,51940],{"className":51939},[886],[888,51941,51942],{"xmlns":890},[892,51943,51944,51966],{},[895,51945,51946,51952,51954,51956,51958,51964],{},[2275,51947,51948,51950],{},[898,51949,1738],{},[2133,51951,2328],{},[1726,51953,1728],{},[898,51955,8659],{},[1726,51957,1735],{"stretchy":1734},[2275,51959,51960,51962],{},[898,51961,1724],{},[2133,51963,2328],{},[1726,51965,1762],{"stretchy":1734},[902,51967,51067],{"encoding":904},[883,51969,51971],{"className":51970},[886],[888,51972,51973],{"xmlns":890,"display":28047},[892,51974,51975,52051],{},[20735,51976,51977],{"width":28052},[20740,51978,51979,51981,52045,52047],{},[20743,51980],{"width":28057},[20743,51982,51983],{},[895,51984,51985,51987,51989,51991,51997,51999,52001,52007,52009,52015,52017,52029,52031,52033,52035,52037,52039,52041,52043],{},[898,51986,1738],{},[898,51988,8659],{},[1726,51990,1735],{"stretchy":1734},[2275,51992,51993,51995],{},[898,51994,1724],{},[2133,51996,2328],{},[1726,51998,1762],{"stretchy":1734},[1726,52000,1728],{},[2275,52002,52003,52005],{},[898,52004,1738],{},[2133,52006,2328],{},[2289,52008,2984],{},[2275,52010,52011,52013],{},[898,52012,1724],{},[2133,52014,2328],{},[1726,52016,2228],{},[9151,52018,52019,52021,52023],{},[1726,52020,11154],{},[2133,52022,2328],{},[2275,52024,52025,52027],{},[898,52026,1724],{},[2133,52028,2328],{},[898,52030,8659],{},[1726,52032,1735],{"stretchy":1734},[898,52034,1724],{},[1726,52036,1762],{"stretchy":1734},[2289,52038,2984],{},[898,52040,2198],{},[898,52042,1724],{},[898,52044,1888],{"mathvariant":2377},[20743,52046],{"width":28057},[20743,52048,52049],{},[2289,52050,45150],{},[902,52052,45153],{"encoding":904},[198,52054,2445],{"id":52055},"geometrická-interpretace-1",[120,52057,52058,52106,52167],{},[123,52059,52060,1696,52085,52088,52089,1888],{},[883,52061,52063],{"className":52062},[886],[888,52064,52065],{"xmlns":890},[892,52066,52067,52083],{},[895,52068,52069,52075,52077],{},[2275,52070,52071,52073],{},[898,52072,1738],{},[2133,52074,2328],{},[2289,52076,2984],{},[2275,52078,52079,52081],{},[898,52080,1724],{},[2133,52082,2328],{},[902,52084,51583],{"encoding":904},[38,52086,52087],{},"tržba"," výrobce za prodané množství ",[883,52090,52092],{"className":52091},[886],[888,52093,52094],{"xmlns":890},[892,52095,52096,52104],{},[895,52097,52098],{},[2275,52099,52100,52102],{},[898,52101,1724],{},[2133,52103,2328],{},[902,52105,38289],{"encoding":904},[123,52107,52108,52148,52149,52166],{},[883,52109,52111],{"className":52110},[886],[888,52112,52113],{"xmlns":890},[892,52114,52115,52145],{},[895,52116,52117],{},[2326,52118,52119,52131,52133,52135,52137,52139,52141,52143],{"scriptlevel":2328,"displaystyle":1741},[9151,52120,52121,52123,52125],{},[1726,52122,11154],{},[2133,52124,2328],{},[2275,52126,52127,52129],{},[898,52128,1724],{},[2133,52130,2328],{},[898,52132,8659],{},[1726,52134,1735],{"stretchy":1734},[898,52136,1724],{},[1726,52138,1762],{"stretchy":1734},[2289,52140,2984],{},[898,52142,2198],{},[898,52144,1724],{},[902,52146,52147],{"encoding":904},"\\displaystyle \\int_0^{Q_0} S(Q)\\,dQ"," — plocha pod křivkou nabídky; minimální částka, za kterou by byl výrobce ochoten ",[883,52150,52152],{"className":52151},[886],[888,52153,52154],{"xmlns":890},[892,52155,52156,52164],{},[895,52157,52158],{},[2275,52159,52160,52162],{},[898,52161,1724],{},[2133,52163,2328],{},[902,52165,38289],{"encoding":904}," jednotek dodat (souvisí s mezními náklady).",[123,52168,52169,52184,52185,52206,52207,1888],{},[883,52170,52172],{"className":52171},[886],[888,52173,52174],{"xmlns":890},[892,52175,52176,52182],{},[895,52177,52178,52180],{},[898,52179,1738],{},[898,52181,8659],{},[902,52183,44950],{"encoding":904}," je plocha mezi vodorovnou přímkou ",[883,52186,52188],{"className":52187},[886],[888,52189,52190],{"xmlns":890},[892,52191,52192,52204],{},[895,52193,52194,52196,52198],{},[898,52195,1738],{},[1726,52197,1728],{},[2275,52199,52200,52202],{},[898,52201,1738],{},[2133,52203,2328],{},[902,52205,51657],{"encoding":904}," a křivkou nabídky v pásu ",[883,52208,52210],{"className":52209},[886],[888,52211,52212],{"xmlns":890},[892,52213,52214,52230],{},[895,52215,52216,52218,52220,52222,52228],{},[1726,52217,2487],{"stretchy":1734},[2133,52219,2328],{},[1726,52221,1742],{"separator":1741},[2275,52223,52224,52226],{},[898,52225,1724],{},[2133,52227,2328],{},[1726,52229,2502],{"stretchy":1734},[902,52231,51532],{"encoding":904},[724,52233,52234],{},[614,52235,52236],{},"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.",[36951,52238],{},[3859,52240,52241,52246],{},[724,52242,52243,52245],{},[883,52244,4560],{}," Postup výpočtu CS a PS",[152,52247,52248,52379,52489,52518,52652],{},[123,52249,52250,52251,52268,52269,52300,52301,52332,52333,1888],{},"Zjisti (nebo si zvol) množství ",[883,52252,52254],{"className":52253},[886],[888,52255,52256],{"xmlns":890},[892,52257,52258,52266],{},[895,52259,52260],{},[2275,52261,52262,52264],{},[898,52263,1724],{},[2133,52265,2328],{},[902,52267,38289],{"encoding":904}," a odpovídající cenu ",[883,52270,52272],{"className":52271},[886],[888,52273,52274],{"xmlns":890},[892,52275,52276,52298],{},[895,52277,52278,52284,52286,52288,52290,52296],{},[2275,52279,52280,52282],{},[898,52281,1738],{},[2133,52283,2328],{},[1726,52285,1728],{},[898,52287,1731],{},[1726,52289,1735],{"stretchy":1734},[2275,52291,52292,52294],{},[898,52293,1724],{},[2133,52295,2328],{},[1726,52297,1762],{"stretchy":1734},[902,52299,51035],{"encoding":904}," resp. ",[883,52302,52304],{"className":52303},[886],[888,52305,52306],{"xmlns":890},[892,52307,52308,52330],{},[895,52309,52310,52316,52318,52320,52322,52328],{},[2275,52311,52312,52314],{},[898,52313,1738],{},[2133,52315,2328],{},[1726,52317,1728],{},[898,52319,8659],{},[1726,52321,1735],{"stretchy":1734},[2275,52323,52324,52326],{},[898,52325,1724],{},[2133,52327,2328],{},[1726,52329,1762],{"stretchy":1734},[902,52331,51067],{"encoding":904},". V rovnováze platí ",[883,52334,52336],{"className":52335},[886],[888,52337,52338],{"xmlns":890},[892,52339,52340,52376],{},[895,52341,52342,52344,52346,52352,52354,52356,52358,52360,52366,52368,52370],{},[898,52343,1731],{},[1726,52345,1735],{"stretchy":1734},[2128,52347,52348,52350],{},[898,52349,1724],{},[898,52351,4240],{},[1726,52353,1762],{"stretchy":1734},[1726,52355,1728],{},[898,52357,8659],{},[1726,52359,1735],{"stretchy":1734},[2128,52361,52362,52364],{},[898,52363,1724],{},[898,52365,4240],{},[1726,52367,1762],{"stretchy":1734},[1726,52369,1728],{},[2128,52371,52372,52374],{},[898,52373,1738],{},[898,52375,4240],{},[902,52377,52378],{"encoding":904},"D(Q^E) = S(Q^E) = P^E",[123,52380,52381,52382,20107,52420,52435,52436,20107,52474,1847],{},"Spočti určitý integrál ",[883,52383,52385],{"className":52384},[886],[888,52386,52387],{"xmlns":890},[892,52388,52389,52417],{},[895,52390,52391,52403,52405,52407,52409,52411,52413,52415],{},[9151,52392,52393,52395,52397],{},[1726,52394,11154],{},[2133,52396,2328],{},[2275,52398,52399,52401],{},[898,52400,1724],{},[2133,52402,2328],{},[898,52404,1731],{},[1726,52406,1735],{"stretchy":1734},[898,52408,1724],{},[1726,52410,1762],{"stretchy":1734},[2289,52412,2984],{},[898,52414,2198],{},[898,52416,1724],{},[902,52418,52419],{"encoding":904},"\\int_0^{Q_0} D(Q)\\,dQ",[883,52421,52423],{"className":52422},[886],[888,52424,52425],{"xmlns":890},[892,52426,52427,52433],{},[895,52428,52429,52431],{},[898,52430,2775],{},[898,52432,8659],{},[902,52434,44931],{"encoding":904},") nebo ",[883,52437,52439],{"className":52438},[886],[888,52440,52441],{"xmlns":890},[892,52442,52443,52471],{},[895,52444,52445,52457,52459,52461,52463,52465,52467,52469],{},[9151,52446,52447,52449,52451],{},[1726,52448,11154],{},[2133,52450,2328],{},[2275,52452,52453,52455],{},[898,52454,1724],{},[2133,52456,2328],{},[898,52458,8659],{},[1726,52460,1735],{"stretchy":1734},[898,52462,1724],{},[1726,52464,1762],{"stretchy":1734},[2289,52466,2984],{},[898,52468,2198],{},[898,52470,1724],{},[902,52472,52473],{"encoding":904},"\\int_0^{Q_0} S(Q)\\,dQ",[883,52475,52477],{"className":52476},[886],[888,52478,52479],{"xmlns":890},[892,52480,52481,52487],{},[895,52482,52483,52485],{},[898,52484,1738],{},[898,52486,8659],{},[902,52488,44950],{"encoding":904},[123,52490,52491,52492,1888],{},"Sestav obdélník ",[883,52493,52495],{"className":52494},[886],[888,52496,52497],{"xmlns":890},[892,52498,52499,52515],{},[895,52500,52501,52507,52509],{},[2275,52502,52503,52505],{},[898,52504,1738],{},[2133,52506,2328],{},[1726,52508,3174],{},[2275,52510,52511,52513],{},[898,52512,1724],{},[2133,52514,2328],{},[902,52516,52517],{"encoding":904},"P_0 \\cdot Q_0",[123,52519,52520,52521],{},"Dosaď:\n",[120,52522,52523,52588],{},[123,52524,52525,52583,52584,52587],{},[883,52526,52528],{"className":52527},[886],[888,52529,52530],{"xmlns":890},[892,52531,52532,52580],{},[895,52533,52534,52536,52538,52540,52552,52554,52556,52558,52560,52562,52564,52566,52568,52574],{},[898,52535,2775],{},[898,52537,8659],{},[1726,52539,1728],{},[9151,52541,52542,52544,52546],{},[1726,52543,11154],{},[2133,52545,2328],{},[2275,52547,52548,52550],{},[898,52549,1724],{},[2133,52551,2328],{},[898,52553,1731],{},[1726,52555,1735],{"stretchy":1734},[898,52557,1724],{},[1726,52559,1762],{"stretchy":1734},[2289,52561,2984],{},[898,52563,2198],{},[898,52565,1724],{},[1726,52567,2228],{},[2275,52569,52570,52572],{},[898,52571,1738],{},[2133,52573,2328],{},[2275,52575,52576,52578],{},[898,52577,1724],{},[2133,52579,2328],{},[902,52581,52582],{"encoding":904},"CS = \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0"," (integrál ",[38,52585,52586],{},"mínus"," obdélník)",[123,52589,52590,52648,52649,52651],{},[883,52591,52593],{"className":52592},[886],[888,52594,52595],{"xmlns":890},[892,52596,52597,52645],{},[895,52598,52599,52601,52603,52605,52611,52617,52619,52631,52633,52635,52637,52639,52641,52643],{},[898,52600,1738],{},[898,52602,8659],{},[1726,52604,1728],{},[2275,52606,52607,52609],{},[898,52608,1738],{},[2133,52610,2328],{},[2275,52612,52613,52615],{},[898,52614,1724],{},[2133,52616,2328],{},[1726,52618,2228],{},[9151,52620,52621,52623,52625],{},[1726,52622,11154],{},[2133,52624,2328],{},[2275,52626,52627,52629],{},[898,52628,1724],{},[2133,52630,2328],{},[898,52632,8659],{},[1726,52634,1735],{"stretchy":1734},[898,52636,1724],{},[1726,52638,1762],{"stretchy":1734},[2289,52640,2984],{},[898,52642,2198],{},[898,52644,1724],{},[902,52646,52647],{"encoding":904},"PS = P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ"," (obdélník ",[38,52650,52586],{}," integrál)",[123,52653,52654,52655,52658],{},"Kontrola znaménka: obě hodnoty musí být ",[38,52656,52657],{},"kladné",". Pokud vyjde záporná, máš prohozené pořadí.",[36951,52660],{},[115,52662,52664],{"id":52663},"příklady","Příklady",[198,52666,52668],{"id":52667},"příklad-211-komparativní-statika-pro-rovnovážné-množství","Příklad 2.11 — komparativní statika pro rovnovážné množství",[3859,52670,52671],{},[724,52672,52673,52676,52677,47702,52700,52723,52724,1343,52744,1343,52761,1343,52778,52795,52796,52872,52873,52890,52891,52904],{},[883,52674,52675],{},"!example"," Zadání\nJsou dány poptávka ",[883,52678,52680],{"className":52679},[886],[888,52681,52682],{"xmlns":890},[892,52683,52684,52698],{},[895,52685,52686,52688,52690,52692,52694,52696],{},[898,52687,1738],{},[1726,52689,1728],{},[898,52691,207],{},[898,52693,1724],{},[1726,52695,2099],{},[898,52697,2102],{},[902,52699,37041],{"encoding":904},[883,52701,52703],{"className":52702},[886],[888,52704,52705],{"xmlns":890},[892,52706,52707,52721],{},[895,52708,52709,52711,52713,52715,52717,52719],{},[898,52710,1738],{},[1726,52712,1728],{},[898,52714,2146],{},[898,52716,1724],{},[1726,52718,2099],{},[898,52720,2198],{},[902,52722,40223],{"encoding":904}," s hodnotami ",[883,52725,52727],{"className":52726},[886],[888,52728,52729],{"xmlns":890},[892,52730,52731,52741],{},[895,52732,52733,52735,52737,52739],{},[898,52734,207],{},[1726,52736,1728],{},[1726,52738,2228],{},[2133,52740,2177],{},[902,52742,52743],{"encoding":904},"a = -3",[883,52745,52747],{"className":52746},[886],[888,52748,52749],{"xmlns":890},[892,52750,52751,52759],{},[895,52752,52753,52755,52757],{},[898,52754,2102],{},[1726,52756,1728],{},[2133,52758,5198],{},[902,52760,48625],{"encoding":904},[883,52762,52764],{"className":52763},[886],[888,52765,52766],{"xmlns":890},[892,52767,52768,52776],{},[895,52769,52770,52772,52774],{},[898,52771,2146],{},[1726,52773,1728],{},[2133,52775,4996],{},[902,52777,48643],{"encoding":904},[883,52779,52781],{"className":52780},[886],[888,52782,52783],{"xmlns":890},[892,52784,52785,52793],{},[895,52786,52787,52789,52791],{},[898,52788,2198],{},[1726,52790,1728],{},[2133,52792,2860],{},[902,52794,48661],{"encoding":904},".\nRovnovážné množství:\n",[883,52797,52799],{"className":52798},[886],[888,52800,52801],{"xmlns":890},[892,52802,52803,52869],{},[895,52804,52805,52811,52813,52831,52833,52857,52859,52865,52867],{},[2128,52806,52807,52809],{},[898,52808,1724],{},[898,52810,4240],{},[1726,52812,1728],{},[2330,52814,52815,52823],{},[895,52816,52817,52819,52821],{},[898,52818,2102],{},[1726,52820,2228],{},[898,52822,2198],{},[895,52824,52825,52827,52829],{},[898,52826,2146],{},[1726,52828,2228],{},[898,52830,207],{},[1726,52832,1728],{},[2330,52834,52835,52843],{},[895,52836,52837,52839,52841],{},[2133,52838,5198],{},[1726,52840,2228],{},[2133,52842,2860],{},[895,52844,52845,52847,52849,52851,52853,52855],{},[2133,52846,4996],{},[1726,52848,2228],{},[1726,52850,1735],{"stretchy":1734},[1726,52852,2228],{},[2133,52854,2177],{},[1726,52856,1762],{"stretchy":1734},[1726,52858,1728],{},[2330,52860,52861,52863],{},[2133,52862,38000],{},[2133,52864,44387],{},[1726,52866,5887],{},[2133,52868,44392],{},[902,52870,52871],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\doteq 8{,}571.","\nZjistěte změnu ",[883,52874,52876],{"className":52875},[886],[888,52877,52878],{"xmlns":890},[892,52879,52880,52888],{},[895,52881,52882],{},[2128,52883,52884,52886],{},[898,52885,1724],{},[898,52887,4240],{},[902,52889,42384],{"encoding":904}," (a) při změně samotného parametru ",[883,52892,52894],{"className":52893},[886],[888,52895,52896],{"xmlns":890},[892,52897,52898,52902],{},[895,52899,52900],{},[898,52901,2146],{},[902,52903,2146],{"encoding":904},", (b) při současné změně všech čtyř parametrů.",[724,52906,52907],{},[38,52908,52909,52910,2670,52923,2684,52936,9280],{},"Řešení (a) — změna ",[883,52911,52913],{"className":52912},[886],[888,52914,52915],{"xmlns":890},[892,52916,52917,52921],{},[895,52918,52919],{},[898,52920,2146],{},[902,52922,2146],{"encoding":904},[883,52924,52926],{"className":52925},[886],[888,52927,52928],{"xmlns":890},[892,52929,52930,52934],{},[895,52931,52932],{},[2133,52933,4996],{},[902,52935,44427],{"encoding":904},[883,52937,52939],{"className":52938},[886],[888,52940,52941],{"xmlns":890},[892,52942,52943,52947],{},[895,52944,52945],{},[2133,52946,19302],{},[902,52948,44441],{"encoding":904},[724,52950,52951,52952,53016,53017,2703],{},"Pomocí vzorce (2.13) pro ",[883,52953,52955],{"className":52954},[886],[888,52956,52957],{"xmlns":890},[892,52958,52959,53013],{},[895,52960,52961,52981,52983,52985],{},[2326,52962,52963],{"scriptlevel":2328,"displaystyle":1741},[2330,52964,52965,52975],{},[895,52966,52967,52969],{},[898,52968,9856],{"mathvariant":2377},[2128,52970,52971,52973],{},[898,52972,1724],{},[898,52974,4240],{},[895,52976,52977,52979],{},[898,52978,9856],{"mathvariant":2377},[898,52980,2146],{},[1726,52982,1728],{},[1726,52984,2228],{},[2326,52986,52987],{"scriptlevel":2328,"displaystyle":1741},[2330,52988,52989,52997],{},[895,52990,52991,52993,52995],{},[898,52992,2102],{},[1726,52994,2228],{},[898,52996,2198],{},[895,52998,52999,53001,53003,53005,53007],{},[1726,53000,1735],{"stretchy":1734},[898,53002,2146],{},[1726,53004,2228],{},[898,53006,207],{},[2128,53008,53009,53011],{},[1726,53010,1762],{"stretchy":1734},[2133,53012,2135],{},[902,53014,53015],{"encoding":904},"\\dfrac{\\partial Q^E}{\\partial c} = -\\dfrac{b-d}{(c-a)^2}",", resp. ekvivalentně ",[883,53018,53020],{"className":53019},[886],[888,53021,53022],{"xmlns":890},[892,53023,53024,53046],{},[895,53025,53026,53028],{},[1726,53027,2228],{},[2326,53029,53030],{"scriptlevel":2328,"displaystyle":1741},[2330,53031,53032,53038],{},[2128,53033,53034,53036],{},[898,53035,1724],{},[898,53037,4240],{},[895,53039,53040,53042,53044],{},[898,53041,2146],{},[1726,53043,2228],{},[898,53045,207],{},[902,53047,53048],{"encoding":904},"-\\dfrac{Q^E}{c-a}",[883,53050,53052],{"className":53051},[886],[888,53053,53054],{"xmlns":890,"display":28047},[892,53055,53056,53112],{},[895,53057,53058,53060,53066,53068,53070,53086,53088,53090,53092,53094,53096,53102,53104,53106,53108,53110],{},[898,53059,2198],{},[2128,53061,53062,53064],{},[898,53063,1724],{},[898,53065,4240],{},[1726,53067,1728],{},[1726,53069,2228],{},[2330,53071,53072,53078],{},[2128,53073,53074,53076],{},[898,53075,1724],{},[898,53077,4240],{},[895,53079,53080,53082,53084],{},[898,53081,2146],{},[1726,53083,2228],{},[898,53085,207],{},[2289,53087,2984],{},[898,53089,2198],{},[898,53091,2146],{},[1726,53093,1728],{},[1726,53095,2228],{},[2330,53097,53098,53100],{},[2133,53099,44555],{},[2133,53101,44387],{},[1726,53103,3174],{},[2133,53105,2791],{},[1726,53107,5887],{},[1726,53109,2228],{},[2133,53111,44527],{},[902,53113,53114],{"encoding":904},"dQ^E = -\\frac{Q^E}{c - a}\\,dc = -\\frac{8{,}571}{3{,}5}\\cdot 0{,}1 \\doteq -0{,}245.",[724,53116,53117],{},"Nové rovnovážné množství:",[883,53119,53121],{"className":53120},[886],[888,53122,53123],{"xmlns":890,"display":28047},[892,53124,53125,53148],{},[895,53126,53127,53135,53137,53139,53141,53143,53145],{},[9151,53128,53129,53131,53133],{},[898,53130,1724],{},[2133,53132,2281],{},[898,53134,4240],{},[1726,53136,1880],{},[2133,53138,44555],{},[1726,53140,2228],{},[2133,53142,44560],{},[1726,53144,1728],{},[2133,53146,53147],{},"8,326.",[902,53149,53150],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326.",[724,53152,53153,1777,53156,1343,53183,1343,53205,1343,53227,5576,53249,1343,53268,1343,53289,1343,53308,1888],{},[38,53154,53155],{},"Řešení (b) — současná změna všech parametrů:",[883,53157,53159],{"className":53158},[886],[888,53160,53161],{"xmlns":890},[892,53162,53163,53180],{},[895,53164,53165,53167,53169,53171,53173,53175,53177],{},[898,53166,207],{},[1726,53168,2703],{},[1726,53170,2228],{},[2133,53172,2177],{},[1726,53174,3120],{},[1726,53176,2228],{},[2133,53178,53179],{},"2,5",[902,53181,53182],{"encoding":904},"a: -3 \\to -2{,}5",[883,53184,53186],{"className":53185},[886],[888,53187,53188],{"xmlns":890},[892,53189,53190,53202],{},[895,53191,53192,53194,53196,53198,53200],{},[898,53193,2102],{},[1726,53195,2703],{},[2133,53197,5198],{},[1726,53199,3120],{},[2133,53201,15024],{},[902,53203,53204],{"encoding":904},"b: 40 \\to 35",[883,53206,53208],{"className":53207},[886],[888,53209,53210],{"xmlns":890},[892,53211,53212,53224],{},[895,53213,53214,53216,53218,53220,53222],{},[898,53215,2146],{},[1726,53217,2703],{},[2133,53219,4996],{},[1726,53221,3120],{},[2133,53223,19302],{},[902,53225,53226],{"encoding":904},"c: 0{,}5 \\to 0{,}6",[883,53228,53230],{"className":53229},[886],[888,53231,53232],{"xmlns":890},[892,53233,53234,53246],{},[895,53235,53236,53238,53240,53242,53244],{},[898,53237,2198],{},[1726,53239,2703],{},[2133,53241,2860],{},[1726,53243,3120],{},[2133,53245,2901],{},[902,53247,53248],{"encoding":904},"d: 10 \\to 11",[883,53250,53252],{"className":53251},[886],[888,53253,53254],{"xmlns":890},[892,53255,53256,53266],{},[895,53257,53258,53260,53262,53264],{},[898,53259,2198],{},[898,53261,207],{},[1726,53263,1728],{},[2133,53265,4996],{},[902,53267,44593],{"encoding":904},[883,53269,53271],{"className":53270},[886],[888,53272,53273],{"xmlns":890},[892,53274,53275,53287],{},[895,53276,53277,53279,53281,53283,53285],{},[898,53278,2198],{},[898,53280,2102],{},[1726,53282,1728],{},[1726,53284,2228],{},[2133,53286,2231],{},[902,53288,44615],{"encoding":904},[883,53290,53292],{"className":53291},[886],[888,53293,53294],{"xmlns":890},[892,53295,53296,53306],{},[895,53297,53298,53300,53302,53304],{},[898,53299,2198],{},[898,53301,2146],{},[1726,53303,1728],{},[2133,53305,2791],{},[902,53307,44635],{"encoding":904},[883,53309,53311],{"className":53310},[886],[888,53312,53313],{"xmlns":890},[892,53314,53315,53325],{},[895,53316,53317,53319,53321,53323],{},[898,53318,2198],{},[898,53320,2198],{},[1726,53322,1728],{},[2133,53324,2281],{},[902,53326,44655],{"encoding":904},[724,53328,53329,53330,53388],{},"Totální diferenciál ",[883,53331,53333],{"className":53332},[886],[888,53334,53335],{"xmlns":890},[892,53336,53337,53385],{},[895,53338,53339,53345,53347,53349,53351,53353,53355,53357,53359,53361,53363,53365],{},[2128,53340,53341,53343],{},[898,53342,1724],{},[898,53344,4240],{},[1726,53346,1735],{"stretchy":1734},[898,53348,207],{},[1726,53350,1742],{"separator":1741},[898,53352,2102],{},[1726,53354,1742],{"separator":1741},[898,53356,2146],{},[1726,53358,1742],{"separator":1741},[898,53360,2198],{},[1726,53362,1762],{"stretchy":1734},[1726,53364,1728],{},[2326,53366,53367],{"scriptlevel":2328,"displaystyle":1741},[2330,53368,53369,53377],{},[895,53370,53371,53373,53375],{},[898,53372,2102],{},[1726,53374,2228],{},[898,53376,2198],{},[895,53378,53379,53381,53383],{},[898,53380,2146],{},[1726,53382,2228],{},[898,53384,207],{},[902,53386,53387],{"encoding":904},"Q^E(a, b, c, d) = \\dfrac{b - d}{c - a}"," podle (2.11) a (2.12):",[883,53390,53392],{"className":53391},[886],[888,53393,53394],{"xmlns":890,"display":28047},[892,53395,53396,53516],{},[895,53397,53398,53400,53406,53408,53434,53436,53438,53440,53442,53454,53456,53458,53460,53462,53488,53490,53492,53494,53496,53508,53510,53512,53514],{},[898,53399,2198],{},[2128,53401,53402,53404],{},[898,53403,1724],{},[898,53405,4240],{},[1726,53407,1728],{},[2330,53409,53410,53418],{},[895,53411,53412,53414,53416],{},[898,53413,2102],{},[1726,53415,2228],{},[898,53417,2198],{},[895,53419,53420,53422,53424,53426,53428],{},[1726,53421,1735],{"stretchy":1734},[898,53423,2146],{},[1726,53425,2228],{},[898,53427,207],{},[2128,53429,53430,53432],{},[1726,53431,1762],{"stretchy":1734},[2133,53433,2135],{},[2289,53435,2984],{},[898,53437,2198],{},[898,53439,207],{},[1726,53441,2099],{},[2330,53443,53444,53446],{},[2133,53445,2281],{},[895,53447,53448,53450,53452],{},[898,53449,2146],{},[1726,53451,2228],{},[898,53453,207],{},[2289,53455,2984],{},[898,53457,2198],{},[898,53459,2102],{},[1726,53461,2228],{},[2330,53463,53464,53472],{},[895,53465,53466,53468,53470],{},[898,53467,2102],{},[1726,53469,2228],{},[898,53471,2198],{},[895,53473,53474,53476,53478,53480,53482],{},[1726,53475,1735],{"stretchy":1734},[898,53477,2146],{},[1726,53479,2228],{},[898,53481,207],{},[2128,53483,53484,53486],{},[1726,53485,1762],{"stretchy":1734},[2133,53487,2135],{},[2289,53489,2984],{},[898,53491,2198],{},[898,53493,2146],{},[1726,53495,2228],{},[2330,53497,53498,53500],{},[2133,53499,2281],{},[895,53501,53502,53504,53506],{},[898,53503,2146],{},[1726,53505,2228],{},[898,53507,207],{},[2289,53509,2984],{},[898,53511,2198],{},[898,53513,2198],{},[898,53515,1888],{"mathvariant":2377},[902,53517,53518],{"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.",[724,53520,53521,53522,1343,53544,1343,53575,3148],{},"Dosazením číselných hodnot (",[883,53523,53525],{"className":53524},[886],[888,53526,53527],{"xmlns":890},[892,53528,53529,53541],{},[895,53530,53531,53533,53535,53537,53539],{},[898,53532,2146],{},[1726,53534,2228],{},[898,53536,207],{},[1726,53538,1728],{},[2133,53540,44387],{},[902,53542,53543],{"encoding":904},"c - a = 3{,}5",[883,53545,53547],{"className":53546},[886],[888,53548,53549],{"xmlns":890},[892,53550,53551,53572],{},[895,53552,53553,53555,53557,53559,53561,53567,53569],{},[1726,53554,1735],{"stretchy":1734},[898,53556,2146],{},[1726,53558,2228],{},[898,53560,207],{},[2128,53562,53563,53565],{},[1726,53564,1762],{"stretchy":1734},[2133,53566,2135],{},[1726,53568,1728],{},[2133,53570,53571],{},"12,25",[902,53573,53574],{"encoding":904},"(c-a)^2 = 12{,}25",[883,53576,53578],{"className":53577},[886],[888,53579,53580],{"xmlns":890},[892,53581,53582,53594],{},[895,53583,53584,53586,53588,53590,53592],{},[898,53585,2102],{},[1726,53587,2228],{},[898,53589,2198],{},[1726,53591,1728],{},[2133,53593,38000],{},[902,53595,53596],{"encoding":904},"b - d = 30",[883,53598,53600],{"className":53599},[886],[888,53601,53602],{"xmlns":890,"display":28047},[892,53603,53604,53705],{},[895,53605,53606,53608,53614,53616,53624,53626,53628,53630,53632,53640,53642,53644,53646,53648,53650,53658,53660,53662,53664,53666,53674,53676,53678,53680,53682,53685,53687,53690,53692,53694,53696,53699,53701,53703],{},[898,53607,2198],{},[2128,53609,53610,53612],{},[898,53611,1724],{},[898,53613,4240],{},[1726,53615,1880],{},[2326,53617,53618],{"scriptlevel":2328,"displaystyle":1734},[2330,53619,53620,53622],{},[2133,53621,38000],{},[2133,53623,53571],{},[1726,53625,1735],{"stretchy":1734},[2133,53627,4996],{},[1726,53629,1762],{"stretchy":1734},[1726,53631,2099],{},[2326,53633,53634],{"scriptlevel":2328,"displaystyle":1734},[2330,53635,53636,53638],{},[2133,53637,2281],{},[2133,53639,44387],{},[1726,53641,1735],{"stretchy":1734},[1726,53643,2228],{},[2133,53645,2231],{},[1726,53647,1762],{"stretchy":1734},[1726,53649,2228],{},[2326,53651,53652],{"scriptlevel":2328,"displaystyle":1734},[2330,53653,53654,53656],{},[2133,53655,38000],{},[2133,53657,53571],{},[1726,53659,1735],{"stretchy":1734},[2133,53661,2791],{},[1726,53663,1762],{"stretchy":1734},[1726,53665,2228],{},[2326,53667,53668],{"scriptlevel":2328,"displaystyle":1734},[2330,53669,53670,53672],{},[2133,53671,2281],{},[2133,53673,44387],{},[1726,53675,1735],{"stretchy":1734},[2133,53677,2281],{},[1726,53679,1762],{"stretchy":1734},[1726,53681,5887],{},[2133,53683,53684],{},"1,224",[1726,53686,2228],{},[2133,53688,53689],{},"1,429",[1726,53691,2228],{},[2133,53693,44560],{},[1726,53695,2228],{},[2133,53697,53698],{},"0,286",[1726,53700,5887],{},[1726,53702,2228],{},[2133,53704,44806],{},[902,53706,53707],{"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.",[724,53709,30046,53710,1888],{},[883,53711,53713],{"className":53712},[886],[888,53714,53715],{"xmlns":890},[892,53716,53717,53739],{},[895,53718,53719,53727,53729,53731,53733,53735,53737],{},[9151,53720,53721,53723,53725],{},[898,53722,1724],{},[2133,53724,2281],{},[898,53726,4240],{},[1726,53728,1880],{},[2133,53730,44555],{},[1726,53732,2228],{},[2133,53734,44837],{},[1726,53736,5887],{},[2133,53738,44842],{},[902,53740,53741],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 \\doteq 7{,}836",[3859,53743,53744],{},[724,53745,53746,53748,53749,53770,53771,53797,53798,53801,53802,53898,53899,53922,53923,53939],{},[883,53747,4400],{}," Pozn. k přepisu učebnice\nV původním skenu přednášky byla u části (b) uvedena hodnota ",[883,53750,53752],{"className":53751},[886],[888,53753,53754],{"xmlns":890},[892,53755,53756,53768],{},[895,53757,53758,53760,53762,53764,53766],{},[898,53759,2886],{"mathvariant":2377},[898,53761,1724],{},[1726,53763,1880],{},[1726,53765,2228],{},[2133,53767,44872],{},[902,53769,44875],{"encoding":904},", což neodpovídá součtu dílčích derivací při daných přírůstcích. Podle vlastního přepočtu vychází ",[883,53772,53774],{"className":53773},[886],[888,53775,53776],{"xmlns":890},[892,53777,53778,53794],{},[895,53779,53780,53782,53788,53790,53792],{},[898,53781,2198],{},[2128,53783,53784,53786],{},[898,53785,1724],{},[898,53787,4240],{},[1726,53789,5887],{},[1726,53791,2228],{},[2133,53793,44837],{},[902,53795,53796],{"encoding":904},"dQ^E \\doteq -0{,}735",". Totální diferenciál je navíc pouze ",[38,53799,53800],{},"lineární aproximací","; přesná změna zjištěná ze změněného vzorce\n",[883,53803,53805],{"className":53804},[886],[888,53806,53807],{"xmlns":890},[892,53808,53809,53895],{},[895,53810,53811,53819,53821,53855,53857,53881,53883,53890,53892],{},[9151,53812,53813,53815,53817],{},[898,53814,1724],{},[2133,53816,2281],{},[898,53818,4240],{},[1726,53820,1728],{},[2330,53822,53823,53839],{},[895,53824,53825,53831,53833],{},[2128,53826,53827,53829],{},[898,53828,2102],{},[1726,53830,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,53832,2228],{},[2128,53834,53835,53837],{},[898,53836,2198],{},[1726,53838,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[895,53840,53841,53847,53849],{},[2128,53842,53843,53845],{},[898,53844,2146],{},[1726,53846,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,53848,2228],{},[2128,53850,53851,53853],{},[898,53852,207],{},[1726,53854,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,53856,1728],{},[2330,53858,53859,53867],{},[895,53860,53861,53863,53865],{},[2133,53862,15024],{},[1726,53864,2228],{},[2133,53866,2901],{},[895,53868,53869,53871,53873,53875,53877,53879],{},[2133,53870,19302],{},[1726,53872,2228],{},[1726,53874,1735],{"stretchy":1734},[1726,53876,2228],{},[2133,53878,53179],{},[1726,53880,1762],{"stretchy":1734},[1726,53882,1728],{},[2330,53884,53885,53887],{},[2133,53886,41781],{},[2133,53888,53889],{},"3,1",[1726,53891,5887],{},[2133,53893,53894],{},"7,742",[902,53896,53897],{"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 ",[883,53900,53902],{"className":53901},[886],[888,53903,53904],{"xmlns":890},[892,53905,53906,53919],{},[895,53907,53908,53910,53912,53914,53916],{},[898,53909,2886],{"mathvariant":2377},[898,53911,1724],{},[1726,53913,5887],{},[1726,53915,2228],{},[2133,53917,53918],{},"0,829",[902,53920,53921],{"encoding":904},"\\Delta Q \\doteq -0{,}829"," — dobře konzistentní s diferenciálem. Hodnota ",[883,53924,53926],{"className":53925},[886],[888,53927,53928],{"xmlns":890},[892,53929,53930,53936],{},[895,53931,53932,53934],{},[1726,53933,2228],{},[2133,53935,44872],{},[902,53937,53938],{"encoding":904},"-2{,}69"," je tedy pravděpodobně chyba v zápisu.",[724,53941,53942],{},[614,53943,53944,53945,53958],{},"Příklad 2.11 je primárně o multiplikátorech pro ",[883,53946,53948],{"className":53947},[886],[888,53949,53950],{"xmlns":890},[892,53951,53952,53956],{},[895,53953,53954],{},[898,53955,1724],{},[902,53957,1724],{"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.",[198,53960,53962,53963],{"id":53961},"příklad-213-numerický-výpočet-psps","Příklad 2.13 — numerický výpočet ",[883,53964,53966],{"className":53965},[886],[888,53967,53968],{"xmlns":890},[892,53969,53970,53976],{},[895,53971,53972,53974],{},[898,53973,1738],{},[898,53975,8659],{},[902,53977,44950],{"encoding":904},[3859,53979,53980],{},[724,53981,53982,53984,53985,54019,54020,54042],{},[883,53983,52675],{}," Zadání\nPro nabídku ",[883,53986,53988],{"className":53987},[886],[888,53989,53990],{"xmlns":890},[892,53991,53992,54016],{},[895,53993,53994,53996,53998,54000,54002,54004,54006,54008,54010,54012,54014],{},[898,53995,1738],{},[1726,53997,1728],{},[898,53999,8659],{},[1726,54001,1735],{"stretchy":1734},[898,54003,1724],{},[1726,54005,1762],{"stretchy":1734},[1726,54007,1728],{},[2133,54009,2860],{},[1726,54011,2099],{},[2133,54013,2135],{},[898,54015,1724],{},[902,54017,54018],{"encoding":904},"P = S(Q) = 10 + 2Q"," a množství ",[883,54021,54023],{"className":54022},[886],[888,54024,54025],{"xmlns":890},[892,54026,54027,54039],{},[895,54028,54029,54035,54037],{},[2275,54030,54031,54033],{},[898,54032,1724],{},[2133,54034,2328],{},[1726,54036,1728],{},[2133,54038,2860],{},[902,54040,54041],{"encoding":904},"Q_0 = 10"," vypočítejte přebytek výrobce.",[724,54044,54045],{},[38,54046,22751],{},[724,54048,54049],{},"Odpovídající cena:",[883,54051,54053],{"className":54052},[886],[888,54054,54055],{"xmlns":890,"display":28047},[892,54056,54057,54092],{},[895,54058,54059,54065,54067,54069,54071,54073,54075,54077,54079,54081,54083,54085,54087,54089],{},[2275,54060,54061,54063],{},[898,54062,1738],{},[2133,54064,2328],{},[1726,54066,1728],{},[898,54068,8659],{},[1726,54070,1735],{"stretchy":1734},[2133,54072,2860],{},[1726,54074,1762],{"stretchy":1734},[1726,54076,1728],{},[2133,54078,2860],{},[1726,54080,2099],{},[2133,54082,2135],{},[1726,54084,3174],{},[2133,54086,2860],{},[1726,54088,1728],{},[2133,54090,54091],{},"30.",[902,54093,54094],{"encoding":904},"P_0 = S(10) = 10 + 2\\cdot 10 = 30.",[724,54096,54097],{},"Dle vzorce (2.15):",[883,54099,54101],{"className":54100},[886],[888,54102,54103],{"xmlns":890,"display":28047},[892,54104,54105,54213],{},[895,54106,54107,54109,54111,54113,54115,54117,54119,54125,54131,54133,54141,54143,54145,54147,54149,54151,54153,54155,54157,54159,54161,54163,54165,54167,54169,54172,54174,54176,54178,54184,54192,54194,54196,54198,54200,54202,54204,54206,54208,54210],{},[898,54108,1738],{},[898,54110,8659],{},[1726,54112,1735],{"stretchy":1734},[2133,54114,2860],{},[1726,54116,1762],{"stretchy":1734},[1726,54118,1728],{},[2275,54120,54121,54123],{},[898,54122,1738],{},[2133,54124,2328],{},[2275,54126,54127,54129],{},[898,54128,1724],{},[2133,54130,2328],{},[1726,54132,2228],{},[9151,54134,54135,54137,54139],{},[1726,54136,11154],{},[2133,54138,2328],{},[2133,54140,2860],{},[1726,54142,1735],{"stretchy":1734},[2133,54144,2860],{},[1726,54146,2099],{},[2133,54148,2135],{},[898,54150,1724],{},[1726,54152,1762],{"stretchy":1734},[2289,54154,2984],{},[898,54156,2198],{},[898,54158,1724],{},[1726,54160,1728],{},[2133,54162,2860],{},[1726,54164,3174],{},[2133,54166,38000],{},[1726,54168,2228],{},[1726,54170,2487],{"fence":1734,"stretchy":1741,"minsize":54171,"maxsize":54171},"1.8em",[2133,54173,2860],{},[898,54175,1724],{},[1726,54177,2099],{},[2128,54179,54180,54182],{},[898,54181,1724],{},[2133,54183,2135],{},[9151,54185,54186,54188,54190],{},[1726,54187,2502],{"fence":1734,"stretchy":1741,"minsize":54171,"maxsize":54171},[2133,54189,2328],{},[2133,54191,2860],{},[1726,54193,1728],{},[2133,54195,30062],{},[1726,54197,2228],{},[1726,54199,1735],{"stretchy":1734},[2133,54201,3087],{},[1726,54203,2099],{},[2133,54205,3087],{},[1726,54207,1762],{"stretchy":1734},[1726,54209,1728],{},[2133,54211,54212],{},"100.",[902,54214,54215],{"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.",[724,54217,54218,54219,54240,54241,54261],{},"Přebytek výrobce při množství ",[883,54220,54222],{"className":54221},[886],[888,54223,54224],{"xmlns":890},[892,54225,54226,54238],{},[895,54227,54228,54234,54236],{},[2275,54229,54230,54232],{},[898,54231,1724],{},[2133,54233,2328],{},[1726,54235,1728],{},[2133,54237,2860],{},[902,54239,54041],{"encoding":904}," je tedy ",[883,54242,54244],{"className":54243},[886],[888,54245,54246],{"xmlns":890},[892,54247,54248,54258],{},[895,54249,54250,54252,54254,54256],{},[898,54251,1738],{},[898,54253,8659],{},[1726,54255,1728],{},[2133,54257,3087],{},[902,54259,54260],{"encoding":904},"PS = 100"," (peněžních jednotek).",[36951,54263],{},[115,54265,54267],{"id":54266},"cheat-sheet","Cheat sheet",[16,54269,54270,54283],{},[19,54271,54272],{},[22,54273,54274,54277,54280],{},[25,54275,54276],{},"Veličina",[25,54278,54279],{},"Vzorec",[25,54281,54282],{},"Geometrie",[30,54284,54285,54403,54517,54585],{},[22,54286,54287,54315,54371],{},[35,54288,54289],{},[883,54290,54292],{"className":54291},[886],[888,54293,54294],{"xmlns":890},[892,54295,54296,54312],{},[895,54297,54298,54300,54302,54304,54310],{},[898,54299,2775],{},[898,54301,8659],{},[1726,54303,1735],{"stretchy":1734},[2275,54305,54306,54308],{},[898,54307,1724],{},[2133,54309,2328],{},[1726,54311,1762],{"stretchy":1734},[902,54313,54314],{"encoding":904},"CS(Q_0)",[35,54316,54317],{},[883,54318,54320],{"className":54319},[886],[888,54321,54322],{"xmlns":890},[892,54323,54324,54368],{},[895,54325,54326],{},[2326,54327,54328,54340,54342,54344,54346,54348,54350,54352,54354,54356,54362],{"scriptlevel":2328,"displaystyle":1741},[9151,54329,54330,54332,54334],{},[1726,54331,11154],{},[2133,54333,2328],{},[2275,54335,54336,54338],{},[898,54337,1724],{},[2133,54339,2328],{},[898,54341,1731],{},[1726,54343,1735],{"stretchy":1734},[898,54345,1724],{},[1726,54347,1762],{"stretchy":1734},[2289,54349,2984],{},[898,54351,2198],{},[898,54353,1724],{},[1726,54355,2228],{},[2275,54357,54358,54360],{},[898,54359,1738],{},[2133,54361,2328],{},[2275,54363,54364,54366],{},[898,54365,1724],{},[2133,54367,2328],{},[902,54369,54370],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0",[35,54372,54373,54374,54377,54378,54381,54382],{},"plocha ",[38,54375,54376],{},"pod"," křivkou poptávky, ",[38,54379,54380],{},"nad"," čárou ",[883,54383,54385],{"className":54384},[886],[888,54386,54387],{"xmlns":890},[892,54388,54389,54401],{},[895,54390,54391,54393,54395],{},[898,54392,1738],{},[1726,54394,1728],{},[2275,54396,54397,54399],{},[898,54398,1738],{},[2133,54400,2328],{},[902,54402,51657],{"encoding":904},[22,54404,54405,54433,54489],{},[35,54406,54407],{},[883,54408,54410],{"className":54409},[886],[888,54411,54412],{"xmlns":890},[892,54413,54414,54430],{},[895,54415,54416,54418,54420,54422,54428],{},[898,54417,1738],{},[898,54419,8659],{},[1726,54421,1735],{"stretchy":1734},[2275,54423,54424,54426],{},[898,54425,1724],{},[2133,54427,2328],{},[1726,54429,1762],{"stretchy":1734},[902,54431,54432],{"encoding":904},"PS(Q_0)",[35,54434,54435],{},[883,54436,54438],{"className":54437},[886],[888,54439,54440],{"xmlns":890},[892,54441,54442,54486],{},[895,54443,54444],{},[2326,54445,54446,54452,54458,54460,54472,54474,54476,54478,54480,54482,54484],{"scriptlevel":2328,"displaystyle":1741},[2275,54447,54448,54450],{},[898,54449,1738],{},[2133,54451,2328],{},[2275,54453,54454,54456],{},[898,54455,1724],{},[2133,54457,2328],{},[1726,54459,2228],{},[9151,54461,54462,54464,54466],{},[1726,54463,11154],{},[2133,54465,2328],{},[2275,54467,54468,54470],{},[898,54469,1724],{},[2133,54471,2328],{},[898,54473,8659],{},[1726,54475,1735],{"stretchy":1734},[898,54477,1724],{},[1726,54479,1762],{"stretchy":1734},[2289,54481,2984],{},[898,54483,2198],{},[898,54485,1724],{},[902,54487,54488],{"encoding":904},"\\displaystyle P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ",[35,54490,54373,54491,54493,54494,54381,54496],{},[38,54492,54380],{}," křivkou nabídky, ",[38,54495,54376],{},[883,54497,54499],{"className":54498},[886],[888,54500,54501],{"xmlns":890},[892,54502,54503,54515],{},[895,54504,54505,54507,54509],{},[898,54506,1738],{},[1726,54508,1728],{},[2275,54510,54511,54513],{},[898,54512,1738],{},[2133,54514,2328],{},[902,54516,51657],{"encoding":904},[22,54518,54519,54522,54549],{},[35,54520,54521],{},"Výdaje \u002F tržby",[35,54523,54524],{},[883,54525,54527],{"className":54526},[886],[888,54528,54529],{"xmlns":890},[892,54530,54531,54547],{},[895,54532,54533,54539,54541],{},[2275,54534,54535,54537],{},[898,54536,1738],{},[2133,54538,2328],{},[1726,54540,3174],{},[2275,54542,54543,54545],{},[898,54544,1724],{},[2133,54546,2328],{},[902,54548,52517],{"encoding":904},[35,54550,54551,54552],{},"obdélník ",[883,54553,54555],{"className":54554},[886],[888,54556,54557],{"xmlns":890},[892,54558,54559,54583],{},[895,54560,54561,54563,54565,54571,54573,54575,54577],{},[2133,54562,2328],{},[2289,54564,2984],{},[2275,54566,54567,54569],{},[898,54568,1724],{},[2133,54570,2328],{},[2289,54572,2984],{},[898,54574,4243],{},[2289,54576,2984],{},[2275,54578,54579,54581],{},[898,54580,1738],{},[2133,54582,2328],{},[902,54584,51137],{"encoding":904},[22,54586,54587,54590,54613],{},[35,54588,54589],{},"Celkový přebytek",[35,54591,54592],{},[883,54593,54595],{"className":54594},[886],[888,54596,54597],{"xmlns":890},[892,54598,54599,54611],{},[895,54600,54601,54603,54605,54607,54609],{},[898,54602,2775],{},[898,54604,8659],{},[1726,54606,2099],{},[898,54608,1738],{},[898,54610,8659],{},[902,54612,50875],{"encoding":904},[35,54614,54615],{},"součet obou ploch v rovnováze",[36951,54617],{},[115,54619,1670],{"id":1669},[120,54621,54622,54644,54666,54710,54754,54817,54845],{},[123,54623,54624,10009,54626,1343,54641,54643],{},[38,54625,44915],{},[883,54627,54629],{"className":54628},[886],[888,54630,54631],{"xmlns":890},[892,54632,54633,54639],{},[895,54634,54635,54637],{},[898,54636,2775],{},[898,54638,8659],{},[902,54640,44931],{"encoding":904},[614,54642,44969],{},") — rozdíl mezi ochotou platit a skutečnou platbou, vzorec (2.14).",[123,54645,54646,10009,54648,1343,54663,54665],{},[38,54647,45062],{},[883,54649,54651],{"className":54650},[886],[888,54652,54653],{"xmlns":890},[892,54654,54655,54661],{},[895,54656,54657,54659],{},[898,54658,1738],{},[898,54660,8659],{},[902,54662,44950],{"encoding":904},[614,54664,45065],{},") — rozdíl mezi tržbou a minimální cenou dle nabídky, vzorec (2.15).",[123,54667,54668,1696,54671,1888],{},[38,54669,54670],{},"Ochota platit",[883,54672,54674],{"className":54673},[886],[888,54675,54676],{"xmlns":890},[892,54677,54678,54708],{},[895,54679,54680],{},[2326,54681,54682,54694,54696,54698,54700,54702,54704,54706],{"scriptlevel":2328,"displaystyle":1741},[9151,54683,54684,54686,54688],{},[1726,54685,11154],{},[2133,54687,2328],{},[2275,54689,54690,54692],{},[898,54691,1724],{},[2133,54693,2328],{},[898,54695,1731],{},[1726,54697,1735],{"stretchy":1734},[898,54699,1724],{},[1726,54701,1762],{"stretchy":1734},[2289,54703,2984],{},[898,54705,2198],{},[898,54707,1724],{},[902,54709,51505],{"encoding":904},[123,54711,54712,1696,54715,1888],{},[38,54713,54714],{},"Minimální cena výrobce",[883,54716,54718],{"className":54717},[886],[888,54719,54720],{"xmlns":890},[892,54721,54722,54752],{},[895,54723,54724],{},[2326,54725,54726,54738,54740,54742,54744,54746,54748,54750],{"scriptlevel":2328,"displaystyle":1741},[9151,54727,54728,54730,54732],{},[1726,54729,11154],{},[2133,54731,2328],{},[2275,54733,54734,54736],{},[898,54735,1724],{},[2133,54737,2328],{},[898,54739,8659],{},[1726,54741,1735],{"stretchy":1734},[898,54743,1724],{},[1726,54745,1762],{"stretchy":1734},[2289,54747,2984],{},[898,54749,2198],{},[898,54751,1724],{},[902,54753,52147],{"encoding":904},[123,54755,54756,1696,54759,52648,54784,1847],{},[38,54757,54758],{},"Výdaje spotřebitele \u002F tržby výrobce",[883,54760,54762],{"className":54761},[886],[888,54763,54764],{"xmlns":890},[892,54765,54766,54782],{},[895,54767,54768,54774,54776],{},[2275,54769,54770,54772],{},[898,54771,1738],{},[2133,54773,2328],{},[2289,54775,2984],{},[2275,54777,54778,54780],{},[898,54779,1724],{},[2133,54781,2328],{},[902,54783,51583],{"encoding":904},[883,54785,54787],{"className":54786},[886],[888,54788,54789],{"xmlns":890},[892,54790,54791,54815],{},[895,54792,54793,54795,54797,54803,54805,54807,54809],{},[2133,54794,2328],{},[2289,54796,2984],{},[2275,54798,54799,54801],{},[898,54800,1724],{},[2133,54802,2328],{},[2289,54804,2984],{},[898,54806,4243],{},[2289,54808,2984],{},[2275,54810,54811,54813],{},[898,54812,1738],{},[2133,54814,2328],{},[902,54816,51137],{"encoding":904},[123,54818,54819,54822,54823,54844],{},[38,54820,54821],{},"Celkový přebytek trhu"," — součet ",[883,54824,54826],{"className":54825},[886],[888,54827,54828],{"xmlns":890},[892,54829,54830,54842],{},[895,54831,54832,54834,54836,54838,54840],{},[898,54833,2775],{},[898,54835,8659],{},[1726,54837,2099],{},[898,54839,1738],{},[898,54841,8659],{},[902,54843,50875],{"encoding":904}," v rovnovážném bodě.",[123,54846,54847,54849,54850,1343,54863,54876,54877,1888],{},[38,54848,2445],{}," — plochy ohraničené křivkami ",[883,54851,54853],{"className":54852},[886],[888,54854,54855],{"xmlns":890},[892,54856,54857,54861],{},[895,54858,54859],{},[898,54860,1731],{},[902,54862,1731],{"encoding":904},[883,54864,54866],{"className":54865},[886],[888,54867,54868],{"xmlns":890},[892,54869,54870,54874],{},[895,54871,54872],{},[898,54873,8659],{},[902,54875,8659],{"encoding":904}," a přímkou ",[883,54878,54880],{"className":54879},[886],[888,54881,54882],{"xmlns":890},[892,54883,54884,54896],{},[895,54885,54886,54888,54890],{},[898,54887,1738],{},[1726,54889,1728],{},[2275,54891,54892,54894],{},[898,54893,1738],{},[2133,54895,2328],{},[902,54897,51657],{"encoding":904},[36951,54899],{},[115,54901,54903],{"id":54902},"dopad-daně-na-přebytky-a-mrtvá-ztráta","Dopad daně na přebytky a mrtvá ztráta",[724,54905,54906,54907,54920,54921,54938],{},"Uvalení jednotkové daně ",[883,54908,54910],{"className":54909},[886],[888,54911,54912],{"xmlns":890},[892,54913,54914,54918],{},[895,54915,54916],{},[898,54917,2772],{},[902,54919,2772],{"encoding":904}," na trh posouvá rovnovážné množství pod ",[883,54922,54924],{"className":54923},[886],[888,54925,54926],{"xmlns":890},[892,54927,54928,54936],{},[895,54929,54930],{},[2128,54931,54932,54934],{},[898,54933,1724],{},[898,54935,4240],{},[902,54937,42384],{"encoding":904}," a rozkládá původní plochu přebytků na nové části.",[724,54940,54941],{},[1647,54942],{"alt":54943,"className":54944,"src":54945},"imek-prebytky-s-dani-deadweight",[210,1651],"\u002Fwiki-assets\u002Fimek-prebytky-s-dani-deadweight.jpeg",[724,54947,54948,54949,54964,54965,54980,54981,52648,54984,55008,55009,10009,55012,55015,55016,1888],{},"Přebytek spotřebitele ",[883,54950,54952],{"className":54951},[886],[888,54953,54954],{"xmlns":890},[892,54955,54956,54962],{},[895,54957,54958,54960],{},[898,54959,2775],{},[898,54961,8659],{},[902,54963,44931],{"encoding":904}," se zmenší (spotřebitelé platí víc a nakupují méně), přebytek výrobce ",[883,54966,54968],{"className":54967},[886],[888,54969,54970],{"xmlns":890},[892,54971,54972,54978],{},[895,54973,54974,54976],{},[898,54975,1738],{},[898,54977,8659],{},[902,54979,44950],{"encoding":904}," se rovněž zmenší (výrobci obdrží po odvodu méně). Stát získává ",[38,54982,54983],{},"daňový příjem",[883,54985,54987],{"className":54986},[886],[888,54988,54989],{"xmlns":890},[892,54990,54991,55005],{},[895,54992,54993,54995,54997],{},[898,54994,2772],{},[1726,54996,3174],{},[9151,54998,54999,55001,55003],{},[898,55000,1724],{},[2133,55002,2281],{},[898,55004,4240],{},[902,55006,55007],{"encoding":904},"T \\cdot Q_1^E","). Zbývající část původních přebytků — ",[38,55010,55011],{},"mrtvá ztráta",[614,55013,55014],{},"deadweight loss",", DWL) — je čistým úbytkem blahobytu, který nikdo neinkasuje, a je důsledkem transakcí, které se kvůli dani vůbec neuskuteční. Detailní rozbor viz ",[207,55017,811],{"className":55018,"dataFsResolvedFilePath":809,"href":810},[210],[36951,55020],{},[115,55022,1899],{"id":1898},[120,55024,55025,55032,55044,55051,55058],{},[123,55026,55027,1777,55029],{},[38,55028,16206],{},[207,55030,802],{"className":55031,"dataFsResolvedFilePath":800,"href":801},[210],[123,55033,55034,1777,55036,55039,55040,55043],{},[38,55035,36655],{},[207,55037,775],{"className":55038,"dataFsResolvedFilePath":773,"href":774},[210]," (určitý integrál, plocha pod křivkou), ",[207,55041,2358],{"className":55042,"dataFsResolvedFilePath":764,"href":765},[210]," (monotonie křivek)",[123,55045,55046,1777,55048],{},[38,55047,16216],{},[207,55049,3815],{"className":55050,"dataFsResolvedFilePath":827,"href":828},[210],[123,55052,55053,1777,55055],{},[38,55054,50738],{},[207,55056,50742],{"className":55057,"dataFsResolvedFilePath":745,"href":746},[210],[123,55059,55060,1777,55062],{},[38,55061,16188],{},[207,55063,16192],{"className":55064,"dataFsResolvedFilePath":1640,"href":1641},[210],{"title":641,"searchDepth":642,"depth":642,"links":55066},[55067,55068,55073,55078,55083,55084,55085,55086],{"id":50934,"depth":642,"text":1241},{"id":51278,"depth":642,"text":55069,"children":55070},"Přebytek spotřebitele (CSCS)",[55071,55072],{"id":51297,"depth":649,"text":51298},{"id":2444,"depth":649,"text":2445},{"id":51873,"depth":642,"text":55074,"children":55075},"Přebytek výrobce (PSPS)",[55076,55077],{"id":51892,"depth":649,"text":51893},{"id":52055,"depth":649,"text":2445},{"id":52663,"depth":642,"text":52664,"children":55079},[55080,55081],{"id":52667,"depth":649,"text":52668},{"id":53961,"depth":649,"text":55082},"Příklad 2.13 — numerický výpočet PSPS",{"id":54266,"depth":642,"text":54267},{"id":1669,"depth":642,"text":1670},{"id":54902,"depth":642,"text":54903},{"id":1898,"depth":642,"text":1899},{},"\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce",{"title":820,"description":641},[1138,1135],"topics\u002Fprebytek-spotrebitele-vyrobce",[1128,50804,55093,55094,11974,1846,55095,55096],"cs","ps","spotrebitel","vyrobce","FhK0gkf2tjMxSgO0-74OuedOn6U35QtJczf-f255pZs",{"id":55099,"title":55100,"body":55101,"course":1128,"courses":659,"created":9541,"description":641,"extension":661,"meta":74430,"navigation":664,"path":74431,"seo":74432,"sources":74433,"stem":74434,"tags":74435,"type":1950,"updated":677,"__hash__":74441},"topics\u002Ftopics\u002Fprijem-naklady-zisk.md","Příjem, náklady, zisk a nabídka firmy",{"type":9,"value":55102,"toc":74394},[55103,55106,55292,55294,55385,55390,55716,55720,55727,55731,55776,55843,55874,55924,55959,55963,56022,56027,56093,56211,56313,56317,56340,56418,56461,56465,56494,56561,56567,56681,56685,56765,56802,56854,57052,57116,57203,57207,57210,57289,57292,57410,57429,57494,57498,57590,57658,57699,57753,57821,57858,57862,57920,57950,58161,58233,58285,58451,58544,58579,58583,58587,58624,58689,58744,58748,58771,58860,58964,59033,59037,59134,59247,59303,59357,59415,59476,59479,59515,59580,59610,59839,59897,59931,59935,59962,60041,60155,60176,60255,60257,60365,60369,60507,60829,60833,60836,60840,60889,60893,61147,61299,61306,61379,61563,61568,61911,61915,61938,61940,61961,62020,62030,62079,62221,62295,62390,62505,62603,62721,62725,62794,62799,62911,63056,63107,63219,63261,63265,63285,63346,63373,63435,63439,63461,63530,63810,63817,63847,63854,64047,64051,64129,64134,64210,64213,64301,64377,64444,64493,64596,64669,64790,65141,65254,65356,65360,65363,65370,65373,65409,65468,65477,65626,65850,65854,65917,66096,66188,66243,66247,66303,66373,66425,66446,66527,66530,66605,66649,66653,66694,66737,66763,66767,66838,66934,66996,67048,67151,67229,67252,67281,67285,67451,67568,67640,67955,68115,68119,68170,68232,68267,68297,68397,68439,68608,68613,68709,68747,68751,68870,69171,69173,69208,69212,69216,69344,69476,69798,69986,70064,70068,70373,70486,70632,70817,70923,71155,71270,71352,71471,71569,71610,71614,71669,71813,71967,72127,72220,72414,72726,72857,72986,72990,73062,73104,73155,73157,74352,74354],[12,55104,55100],{"id":55105},"příjem-náklady-zisk-a-nabídka-firmy",[3859,55107,55108],{},[724,55109,55110,3866,55112,1777,55115,55130,55131,1777,55134,55149,55150,1777,55153,55181,55182,55204,55205,55229,55230,55252,55253,55256,55257,55273,55274,1888],{},[883,55111,3865],{},[38,55113,55114],{},"Příjem",[883,55116,55118],{"className":55117},[886],[888,55119,55120],{"xmlns":890},[892,55121,55122,55128],{},[895,55123,55124,55126],{},[898,55125,2772],{},[898,55127,3984],{},[902,55129,4084],{"encoding":904}," je to, co firma inkasuje (cena krát množství), ",[38,55132,55133],{},"náklady",[883,55135,55137],{"className":55136},[886],[888,55138,55139],{"xmlns":890},[892,55140,55141,55147],{},[895,55142,55143,55145],{},[898,55144,2772],{},[898,55146,2775],{},[902,55148,3240],{"encoding":904}," to, co vynaloží (fixní plus variabilní), a ",[38,55151,55152],{},"zisk",[883,55154,55156],{"className":55155},[886],[888,55157,55158],{"xmlns":890},[892,55159,55160,55178],{},[895,55161,55162,55164,55166,55168,55170,55172,55174,55176],{},[898,55163,1738],{},[898,55165,3984],{},[1726,55167,1728],{},[898,55169,2772],{},[898,55171,3984],{},[1726,55173,2228],{},[898,55175,2772],{},[898,55177,2775],{},[902,55179,55180],{"encoding":904},"PR = TR - TC"," jejich rozdíl. Kapitola pro každou ze tří veličin zavádí celkovou, průměrnou a mezní podobu, ukáže jejich grafický průběh (pro lineární poptávku a kubické náklady) a odvodí tři klíčové optimalizační principy: ",[883,55183,55185],{"className":55184},[886],[888,55186,55187],{"xmlns":890},[892,55188,55189,55201],{},[895,55190,55191,55193,55195,55197,55199],{},[898,55192,4243],{},[898,55194,2775],{},[1726,55196,1728],{},[898,55198,2815],{},[898,55200,2775],{},[902,55202,55203],{"encoding":904},"AC = MC"," v minimu průměrných nákladů, ",[883,55206,55208],{"className":55207},[886],[888,55209,55210],{"xmlns":890},[892,55211,55212,55226],{},[895,55213,55214,55216,55218,55220,55222,55224],{},[898,55215,4243],{},[898,55217,40320],{},[898,55219,2775],{},[1726,55221,1728],{},[898,55223,2815],{},[898,55225,2775],{},[902,55227,55228],{"encoding":904},"AVC = MC"," v minimu průměrných variabilních nákladů a ",[883,55231,55233],{"className":55232},[886],[888,55234,55235],{"xmlns":890},[892,55236,55237,55249],{},[895,55238,55239,55241,55243,55245,55247],{},[898,55240,2815],{},[898,55242,3984],{},[1726,55244,1728],{},[898,55246,2815],{},[898,55248,2775],{},[902,55250,55251],{"encoding":904},"MR = MC"," v maximu zisku. Na závěr se sestaví ",[38,55254,55255],{},"funkce nabídky firmy"," jako rostoucí část křivky ",[883,55258,55260],{"className":55259},[886],[888,55261,55262],{"xmlns":890},[892,55263,55264,55270],{},[895,55265,55266,55268],{},[898,55267,2815],{},[898,55269,2775],{},[902,55271,55272],{"encoding":904},"MC"," nad bodem minima ",[883,55275,55277],{"className":55276},[886],[888,55278,55279],{"xmlns":890},[892,55280,55281,55289],{},[895,55282,55283,55285,55287],{},[898,55284,4243],{},[898,55286,40320],{},[898,55288,2775],{},[902,55290,55291],{"encoding":904},"AVC",[115,55293,1241],{"id":50934},[724,55295,55296,55297,55300,55301,55303,55304,1343,55307,1343,55310,55312,55313,55316,55317,55320,55321,55324,55325,2670,55340,1348,55355,2670,55370,1847],{},"Kapitola 3 se zabývá dvěma základními veličinami popisujícími ekonomickou aktivitu firmy — ",[38,55298,55299],{},"příjmem"," (revenue) a ",[38,55302,55133],{}," (cost) — v jejich třech standardních podobách: celkové, průměrné a mezní. Navazuje analýzou ",[38,55305,55306],{},"zisku",[38,55308,55309],{},"bodů zvratu",[38,55311,1980],{}," a konstrukcí ",[38,55314,55315],{},"nabídkové křivky firmy",". Klíčovými matematickými nástroji jsou ",[207,55318,1145],{"className":55319,"dataFsResolvedFilePath":764,"href":765},[210]," (pro mezní veličiny) a diferenciál (pro odhad přírůstků); v několika úlohách se využívá také ",[207,55322,11115],{"className":55323,"dataFsResolvedFilePath":773,"href":774},[210]," (pro zpětnou rekonstrukci ",[883,55326,55328],{"className":55327},[886],[888,55329,55330],{"xmlns":890},[892,55331,55332,55338],{},[895,55333,55334,55336],{},[898,55335,2772],{},[898,55337,3984],{},[902,55339,4084],{"encoding":904},[883,55341,55343],{"className":55342},[886],[888,55344,55345],{"xmlns":890},[892,55346,55347,55353],{},[895,55348,55349,55351],{},[898,55350,2815],{},[898,55352,3984],{},[902,55354,6621],{"encoding":904},[883,55356,55358],{"className":55357},[886],[888,55359,55360],{"xmlns":890},[892,55361,55362,55368],{},[895,55363,55364,55366],{},[898,55365,2772],{},[898,55367,2775],{},[902,55369,3240],{"encoding":904},[883,55371,55373],{"className":55372},[886],[888,55374,55375],{"xmlns":890},[892,55376,55377,55383],{},[895,55378,55379,55381],{},[898,55380,2815],{},[898,55382,2775],{},[902,55384,55272],{"encoding":904},[724,55386,55387],{},[38,55388,55389],{},"Cílové znalosti:",[120,55391,55392,55556,55559,55562,55655,55702,55709],{},[123,55393,55394,55395,1343,55410,1343,55426,3877,55441,1343,55456,1343,55472,1343,55490,1343,55508,1343,55525,1343,55541,8411],{},"odvodit a interpretovat funkce ",[883,55396,55398],{"className":55397},[886],[888,55399,55400],{"xmlns":890},[892,55401,55402,55408],{},[895,55403,55404,55406],{},[898,55405,2772],{},[898,55407,3984],{},[902,55409,4084],{"encoding":904},[883,55411,55413],{"className":55412},[886],[888,55414,55415],{"xmlns":890},[892,55416,55417,55423],{},[895,55418,55419,55421],{},[898,55420,4243],{},[898,55422,3984],{},[902,55424,55425],{"encoding":904},"AR",[883,55427,55429],{"className":55428},[886],[888,55430,55431],{"xmlns":890},[892,55432,55433,55439],{},[895,55434,55435,55437],{},[898,55436,2815],{},[898,55438,3984],{},[902,55440,6621],{"encoding":904},[883,55442,55444],{"className":55443},[886],[888,55445,55446],{"xmlns":890},[892,55447,55448,55454],{},[895,55449,55450,55452],{},[898,55451,2772],{},[898,55453,2775],{},[902,55455,3240],{"encoding":904},[883,55457,55459],{"className":55458},[886],[888,55460,55461],{"xmlns":890},[892,55462,55463,55469],{},[895,55464,55465,55467],{},[898,55466,10420],{},[898,55468,2775],{},[902,55470,55471],{"encoding":904},"FC",[883,55473,55475],{"className":55474},[886],[888,55476,55477],{"xmlns":890},[892,55478,55479,55487],{},[895,55480,55481,55483,55485],{},[898,55482,2772],{},[898,55484,40320],{},[898,55486,2775],{},[902,55488,55489],{"encoding":904},"TVC",[883,55491,55493],{"className":55492},[886],[888,55494,55495],{"xmlns":890},[892,55496,55497,55505],{},[895,55498,55499,55501,55503],{},[898,55500,4243],{},[898,55502,10420],{},[898,55504,2775],{},[902,55506,55507],{"encoding":904},"AFC",[883,55509,55511],{"className":55510},[886],[888,55512,55513],{"xmlns":890},[892,55514,55515,55523],{},[895,55516,55517,55519,55521],{},[898,55518,4243],{},[898,55520,40320],{},[898,55522,2775],{},[902,55524,55291],{"encoding":904},[883,55526,55528],{"className":55527},[886],[888,55529,55530],{"xmlns":890},[892,55531,55532,55538],{},[895,55533,55534,55536],{},[898,55535,4243],{},[898,55537,2775],{},[902,55539,55540],{"encoding":904},"AC",[883,55542,55544],{"className":55543},[886],[888,55545,55546],{"xmlns":890},[892,55547,55548,55554],{},[895,55549,55550,55552],{},[898,55551,2815],{},[898,55553,2775],{},[902,55555,55272],{"encoding":904},[123,55557,55558],{},"porozumět vzájemným vztahům mezi průměrnou a mezní veličinou, zvláště pro lineární poptávku;",[123,55560,55561],{},"pomocí diferenciálu odhadovat změny celkových veličin;",[123,55563,55564,55565,55568,55569,41795,55611,8411],{},"osvojit si ",[38,55566,55567],{},"princip minimalizace průměrných (variabilních) nákladů"," — podmínku ",[883,55570,55572],{"className":55571},[886],[888,55573,55574],{"xmlns":890},[892,55575,55576,55608],{},[895,55577,55578,55580,55582,55584,55590,55592,55594,55596,55598,55600,55606],{},[898,55579,4243],{},[898,55581,2775],{},[1726,55583,1735],{"stretchy":1734},[2275,55585,55586,55588],{},[898,55587,1724],{},[2133,55589,2328],{},[1726,55591,1762],{"stretchy":1734},[1726,55593,1728],{},[898,55595,2815],{},[898,55597,2775],{},[1726,55599,1735],{"stretchy":1734},[2275,55601,55602,55604],{},[898,55603,1724],{},[2133,55605,2328],{},[1726,55607,1762],{"stretchy":1734},[902,55609,55610],{"encoding":904},"AC(Q_0)=MC(Q_0)",[883,55612,55614],{"className":55613},[886],[888,55615,55616],{"xmlns":890},[892,55617,55618,55652],{},[895,55619,55620,55622,55624,55626,55628,55634,55636,55638,55640,55642,55644,55650],{},[898,55621,4243],{},[898,55623,40320],{},[898,55625,2775],{},[1726,55627,1735],{"stretchy":1734},[2275,55629,55630,55632],{},[898,55631,1724],{},[2133,55633,2328],{},[1726,55635,1762],{"stretchy":1734},[1726,55637,1728],{},[898,55639,2815],{},[898,55641,2775],{},[1726,55643,1735],{"stretchy":1734},[2275,55645,55646,55648],{},[898,55647,1724],{},[2133,55649,2328],{},[1726,55651,1762],{"stretchy":1734},[902,55653,55654],{"encoding":904},"AVC(Q_0)=MC(Q_0)",[123,55656,55564,55657,55568,55660,8411],{},[38,55658,55659],{},"princip maximalizace zisku",[883,55661,55663],{"className":55662},[886],[888,55664,55665],{"xmlns":890},[892,55666,55667,55699],{},[895,55668,55669,55671,55673,55675,55681,55683,55685,55687,55689,55691,55697],{},[898,55670,2815],{},[898,55672,3984],{},[1726,55674,1735],{"stretchy":1734},[2275,55676,55677,55679],{},[898,55678,1724],{},[2133,55680,2328],{},[1726,55682,1762],{"stretchy":1734},[1726,55684,1728],{},[898,55686,2815],{},[898,55688,2775],{},[1726,55690,1735],{"stretchy":1734},[2275,55692,55693,55695],{},[898,55694,1724],{},[2133,55696,2328],{},[1726,55698,1762],{"stretchy":1734},[902,55700,55701],{"encoding":904},"MR(Q_0)=MC(Q_0)",[123,55703,55704,55705,55708],{},"stanovit ",[38,55706,55707],{},"body zvratu"," a interval zisku;",[123,55710,55711,55712,55715],{},"zkonstruovat ",[38,55713,55714],{},"funkci nabídky firmy"," na základě nákladových charakteristik.",[115,55717,55719],{"id":55718},"příjem-firmy","Příjem firmy",[724,55721,55722],{},[1647,55723],{"alt":55724,"className":55725,"src":55726},"imek-ar-mr-dvojnasobny-sklon",[210,1651],"\u002Fwiki-assets\u002Fimek-ar-mr-dvojnasobny-sklon.jpeg",[198,55728,55730],{"id":55729},"celkový-příjem","Celkový příjem",[724,55732,55733,55734,10009,55749,55752,55753,29925],{},"Celkový příjem ",[883,55735,55737],{"className":55736},[886],[888,55738,55739],{"xmlns":890},[892,55740,55741,55747],{},[895,55742,55743,55745],{},[898,55744,2772],{},[898,55746,3984],{},[902,55748,4084],{"encoding":904},[38,55750,55751],{},"total revenue",") je součin ceny a prodaného množství. Při poptávce ",[883,55754,55756],{"className":55755},[886],[888,55757,55758],{"xmlns":890},[892,55759,55760,55774],{},[895,55761,55762,55764,55766,55768,55770,55772],{},[898,55763,1738],{},[1726,55765,1728],{},[898,55767,1731],{},[1726,55769,1735],{"stretchy":1734},[898,55771,1724],{},[1726,55773,1762],{"stretchy":1734},[902,55775,1830],{"encoding":904},[883,55777,55779],{"className":55778},[886],[888,55780,55781],{"xmlns":890,"display":28047},[892,55782,55783,55840],{},[20735,55784,55785],{"width":28052},[20740,55786,55787,55789,55833,55835],{},[20743,55788],{"width":28057},[20743,55790,55791],{},[895,55792,55793,55795,55797,55799,55801,55803,55805,55807,55809,55811,55813,55815,55817,55819,55821,55823,55825,55827,55829,55831],{},[898,55794,2772],{},[898,55796,3984],{},[1726,55798,1728],{},[898,55800,2772],{},[898,55802,3984],{},[1726,55804,1735],{"stretchy":1734},[898,55806,1724],{},[1726,55808,1762],{"stretchy":1734},[1726,55810,1728],{},[898,55812,1738],{},[1726,55814,3174],{},[898,55816,1724],{},[1726,55818,1728],{},[898,55820,1731],{},[1726,55822,1735],{"stretchy":1734},[898,55824,1724],{},[1726,55826,1762],{"stretchy":1734},[1726,55828,3174],{},[898,55830,1724],{},[898,55832,1888],{"mathvariant":2377},[20743,55834],{"width":28057},[20743,55836,55837],{},[2289,55838,55839],{},"(3.1)",[902,55841,55842],{"encoding":904},"TR = TR(Q) = P \\cdot Q = D(Q) \\cdot Q.\n\\tag{3.1}",[724,55844,55845,55846,55849,55850,55873],{},"Graf funkce se nazývá ",[38,55847,55848],{},"křivka celkového příjmu"," (total revenue curve). Za předpokladu linearity poptávky, tj. ",[883,55851,55853],{"className":55852},[886],[888,55854,55855],{"xmlns":890},[892,55856,55857,55871],{},[895,55858,55859,55861,55863,55865,55867,55869],{},[898,55860,1738],{},[1726,55862,1728],{},[898,55864,207],{},[898,55866,1724],{},[1726,55868,2099],{},[898,55870,2102],{},[902,55872,37041],{"encoding":904},", je celkový příjem kvadratickou funkcí, neboť",[883,55875,55877],{"className":55876},[886],[888,55878,55879],{"xmlns":890,"display":28047},[892,55880,55881,55921],{},[895,55882,55883,55885,55887,55889,55891,55893,55895,55897,55899,55901,55903,55905,55907,55913,55915,55917,55919],{},[898,55884,2772],{},[898,55886,3984],{},[1726,55888,1728],{},[898,55890,1724],{},[1726,55892,1735],{"stretchy":1734},[898,55894,207],{},[898,55896,1724],{},[1726,55898,2099],{},[898,55900,2102],{},[1726,55902,1762],{"stretchy":1734},[1726,55904,1728],{},[898,55906,207],{},[2128,55908,55909,55911],{},[898,55910,1724],{},[2133,55912,2135],{},[1726,55914,2099],{},[898,55916,2102],{},[898,55918,1724],{},[1726,55920,1742],{"separator":1741},[902,55922,55923],{"encoding":904},"TR = Q(aQ + b) = aQ^2 + bQ,",[724,55925,55926,55927,55940,55941,55958],{},"a křivka celkového příjmu je parabola tvaru obráceného ",[883,55928,55930],{"className":55929},[886],[888,55931,55932],{"xmlns":890},[892,55933,55934,55938],{},[895,55935,55936],{},[898,55937,900],{},[902,55939,900],{"encoding":904}," (jelikož ",[883,55942,55944],{"className":55943},[886],[888,55945,55946],{"xmlns":890},[892,55947,55948,55956],{},[895,55949,55950,55952,55954],{},[898,55951,207],{},[1726,55953,3444],{},[2133,55955,2328],{},[902,55957,43066],{"encoding":904},") procházející počátkem.",[37329,55960,55962],{"id":55961},"příklad-31","Příklad 3.1",[724,55964,55965,55968,55969,56005,56006,56021],{},[38,55966,55967],{},"Zadání."," Pro poptávku ",[883,55970,55972],{"className":55971},[886],[888,55973,55974],{"xmlns":890},[892,55975,55976,56002],{},[895,55977,55978,55980,55982,55984,55986,55988,55990,55992,55994,55996,55998,56000],{},[898,55979,1738],{},[1726,55981,1728],{},[898,55983,1731],{},[1726,55985,1735],{"stretchy":1734},[898,55987,1724],{},[1726,55989,1762],{"stretchy":1734},[1726,55991,1728],{},[1726,55993,2228],{},[2133,55995,2135],{},[898,55997,1724],{},[1726,55999,2099],{},[2133,56001,3087],{},[902,56003,56004],{"encoding":904},"P = D(Q) = -2Q + 100"," určete ",[883,56007,56009],{"className":56008},[886],[888,56010,56011],{"xmlns":890},[892,56012,56013,56019],{},[895,56014,56015,56017],{},[898,56016,2772],{},[898,56018,3984],{},[902,56020,4084],{"encoding":904}," a charakterizujte jeho křivku.",[724,56023,56024,56026],{},[38,56025,22751],{}," Celkový příjem je",[883,56028,56030],{"className":56029},[886],[888,56031,56032],{"xmlns":890,"display":28047},[892,56033,56034,56090],{},[895,56035,56036,56038,56040,56042,56044,56046,56048,56050,56052,56054,56056,56058,56060,56062,56064,56066,56068,56070,56072,56074,56076,56082,56084,56086,56088],{},[898,56037,2772],{},[898,56039,3984],{},[1726,56041,1728],{},[898,56043,2772],{},[898,56045,3984],{},[1726,56047,1735],{"stretchy":1734},[898,56049,1724],{},[1726,56051,1762],{"stretchy":1734},[1726,56053,1728],{},[898,56055,1724],{},[1726,56057,1735],{"stretchy":1734},[1726,56059,2228],{},[2133,56061,2135],{},[898,56063,1724],{},[1726,56065,2099],{},[2133,56067,3087],{},[1726,56069,1762],{"stretchy":1734},[1726,56071,1728],{},[1726,56073,2228],{},[2133,56075,2135],{},[2128,56077,56078,56080],{},[898,56079,1724],{},[2133,56081,2135],{},[1726,56083,2099],{},[2133,56085,3087],{},[898,56087,1724],{},[898,56089,1888],{"mathvariant":2377},[902,56091,56092],{"encoding":904},"TR = TR(Q) = Q(-2Q + 100) = -2Q^2 + 100Q.",[724,56094,56095,56096,3877,56118,56140,56141,56159,56160,1888],{},"Křivkou je parabola (obrázek 3.1) s nulami v ",[883,56097,56099],{"className":56098},[886],[888,56100,56101],{"xmlns":890},[892,56102,56103,56115],{},[895,56104,56105,56111,56113],{},[2275,56106,56107,56109],{},[898,56108,1724],{},[2133,56110,2281],{},[1726,56112,1728],{},[2133,56114,2328],{},[902,56116,56117],{"encoding":904},"Q_1 = 0",[883,56119,56121],{"className":56120},[886],[888,56122,56123],{"xmlns":890},[892,56124,56125,56137],{},[895,56126,56127,56133,56135],{},[2275,56128,56129,56131],{},[898,56130,1724],{},[2133,56132,2135],{},[1726,56134,1728],{},[2133,56136,3117],{},[902,56138,56139],{"encoding":904},"Q_2 = 50",". Maxima dosahuje při ",[883,56142,56144],{"className":56143},[886],[888,56145,56146],{"xmlns":890},[892,56147,56148,56156],{},[895,56149,56150,56152,56154],{},[898,56151,1724],{},[1726,56153,1728],{},[2133,56155,4991],{},[902,56157,56158],{"encoding":904},"Q = 25"," ve výši ",[883,56161,56163],{"className":56162},[886],[888,56164,56165],{"xmlns":890},[892,56166,56167,56208],{},[895,56168,56169,56171,56181,56183,56185,56187,56189,56192,56194,56196,56198,56200,56202,56204,56206],{},[898,56170,2772],{},[2275,56172,56173,56175,56178],{},[898,56174,3984],{},[898,56176,56177],{},"max",[1726,56179,56180],{},"⁡",[1726,56182,1728],{},[1726,56184,2228],{},[2133,56186,2135],{},[1726,56188,3174],{},[2133,56190,56191],{},"625",[1726,56193,2099],{},[2133,56195,3087],{},[1726,56197,3174],{},[2133,56199,4991],{},[1726,56201,1728],{},[2133,56203,2281],{},[2289,56205,2984],{},[2133,56207,30724],{},[902,56209,56210],{"encoding":904},"TR_{\\max} = -2 \\cdot 625 + 100 \\cdot 25 = 1\\,250",[724,56212,56213],{},[614,56214,56215,56216,56250,56251,3877,56264,56277,56278,2623,56296,1888],{},"Obrázek 3.1: Parabola ",[883,56217,56219],{"className":56218},[886],[888,56220,56221],{"xmlns":890},[892,56222,56223,56247],{},[895,56224,56225,56227,56229,56231,56233,56235,56241,56243,56245],{},[898,56226,2772],{},[898,56228,3984],{},[1726,56230,1728],{},[1726,56232,2228],{},[2133,56234,2135],{},[2128,56236,56237,56239],{},[898,56238,1724],{},[2133,56240,2135],{},[1726,56242,2099],{},[2133,56244,3087],{},[898,56246,1724],{},[902,56248,56249],{"encoding":904},"TR = -2Q^2 + 100Q"," s nulami v ",[883,56252,56254],{"className":56253},[886],[888,56255,56256],{"xmlns":890},[892,56257,56258,56262],{},[895,56259,56260],{},[2133,56261,2328],{},[902,56263,2328],{"encoding":904},[883,56265,56267],{"className":56266},[886],[888,56268,56269],{"xmlns":890},[892,56270,56271,56275],{},[895,56272,56273],{},[2133,56274,3117],{},[902,56276,3117],{"encoding":904}," a maximem ",[883,56279,56281],{"className":56280},[886],[888,56282,56283],{"xmlns":890},[892,56284,56285,56293],{},[895,56286,56287,56289,56291],{},[2133,56288,2281],{},[2289,56290,2984],{},[2133,56292,30724],{},[902,56294,56295],{"encoding":904},"1\\,250",[883,56297,56299],{"className":56298},[886],[888,56300,56301],{"xmlns":890},[892,56302,56303,56311],{},[895,56304,56305,56307,56309],{},[898,56306,1724],{},[1726,56308,1728],{},[2133,56310,4991],{},[902,56312,56158],{"encoding":904},[198,56314,56316],{"id":56315},"průměrný-příjem","Průměrný příjem",[724,56318,56319,1777,56321,10009,56336,56339],{},[38,56320,56316],{},[883,56322,56324],{"className":56323},[886],[888,56325,56326],{"xmlns":890},[892,56327,56328,56334],{},[895,56329,56330,56332],{},[898,56331,4243],{},[898,56333,3984],{},[902,56335,55425],{"encoding":904},[38,56337,56338],{},"average revenue",") je podíl celkového příjmu a množství. Z (3.1) plyne",[883,56341,56343],{"className":56342},[886],[888,56344,56345],{"xmlns":890,"display":28047},[892,56346,56347,56415],{},[895,56348,56349,56351,56353,56355,56357,56359,56361,56363,56365,56367,56383,56385,56403,56405,56407,56409,56411,56413],{},[898,56350,4243],{},[898,56352,3984],{},[1726,56354,1728],{},[898,56356,4243],{},[898,56358,3984],{},[1726,56360,1735],{"stretchy":1734},[898,56362,1724],{},[1726,56364,1762],{"stretchy":1734},[1726,56366,1728],{},[2330,56368,56369,56381],{},[895,56370,56371,56373,56375,56377,56379],{},[898,56372,2772],{},[898,56374,3984],{},[1726,56376,1735],{"stretchy":1734},[898,56378,1724],{},[1726,56380,1762],{"stretchy":1734},[898,56382,1724],{},[1726,56384,1728],{},[2330,56386,56387,56401],{},[895,56388,56389,56391,56393,56395,56397,56399],{},[898,56390,1724],{},[2289,56392,2984],{},[898,56394,1731],{},[1726,56396,1735],{"stretchy":1734},[898,56398,1724],{},[1726,56400,1762],{"stretchy":1734},[898,56402,1724],{},[1726,56404,1728],{},[898,56406,1731],{},[1726,56408,1735],{"stretchy":1734},[898,56410,1724],{},[1726,56412,1762],{"stretchy":1734},[898,56414,1888],{"mathvariant":2377},[902,56416,56417],{"encoding":904},"AR = AR(Q) = \\frac{TR(Q)}{Q} = \\frac{Q \\, D(Q)}{Q} = D(Q).",[3859,56419,56420],{},[724,56421,56422,56425,56426,1343,56429,1888],{},[883,56423,56424],{},"!note"," Klíčové pozorování\n",[38,56427,56428],{},"Průměrný příjem se vždy rovná poptávkové funkci",[883,56430,56432],{"className":56431},[886],[888,56433,56434],{"xmlns":890},[892,56435,56436,56458],{},[895,56437,56438,56440,56442,56444,56446,56448,56450,56452,56454,56456],{},[898,56439,4243],{},[898,56441,3984],{},[1726,56443,1735],{"stretchy":1734},[898,56445,1724],{},[1726,56447,1762],{"stretchy":1734},[1726,56449,1728],{},[898,56451,1731],{},[1726,56453,1735],{"stretchy":1734},[898,56455,1724],{},[1726,56457,1762],{"stretchy":1734},[902,56459,56460],{"encoding":904},"AR(Q) = D(Q)",[198,56462,56464],{"id":56463},"mezní-příjem","Mezní příjem",[724,56466,56467,56468,1777,56471,10009,56486,56489,56490,56493],{},"Pro zkoumání dynamiky změn celkového příjmu zavádíme ",[38,56469,56470],{},"mezní příjem",[883,56472,56474],{"className":56473},[886],[888,56475,56476],{"xmlns":890},[892,56477,56478,56484],{},[895,56479,56480,56482],{},[898,56481,2815],{},[898,56483,3984],{},[902,56485,6621],{"encoding":904},[38,56487,56488],{},"marginal revenue","), definovaný jako ",[207,56491,1145],{"className":56492,"dataFsResolvedFilePath":764,"href":765},[210]," celkového příjmu podle množství:",[883,56495,56497],{"className":56496},[886],[888,56498,56499],{"xmlns":890,"display":28047},[892,56500,56501,56558],{},[20735,56502,56503],{"width":28052},[20740,56504,56505,56507,56551,56553],{},[20743,56506],{"width":28057},[20743,56508,56509],{},[895,56510,56511,56513,56515,56517,56533,56535,56537,56543,56545,56547,56549],{},[898,56512,2815],{},[898,56514,3984],{},[1726,56516,1728],{},[2330,56518,56519,56527],{},[895,56520,56521,56523,56525],{},[898,56522,2198],{"mathvariant":2377},[898,56524,2772],{},[898,56526,3984],{},[895,56528,56529,56531],{},[898,56530,2198],{"mathvariant":2377},[898,56532,1724],{},[1726,56534,1728],{},[898,56536,2772],{},[2128,56538,56539,56541],{},[898,56540,3984],{},[1726,56542,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,56544,1735],{"stretchy":1734},[898,56546,1724],{},[1726,56548,1762],{"stretchy":1734},[898,56550,1888],{"mathvariant":2377},[20743,56552],{"width":28057},[20743,56554,56555],{},[2289,56556,56557],{},"(3.2)",[902,56559,56560],{"encoding":904},"MR = \\frac{\\mathrm{d}TR}{\\mathrm{d}Q} = TR'(Q).\n\\tag{3.2}",[724,56562,56563,56564,56566],{},"Mezní příjem udává ",[38,56565,2595],{}," celkového příjmu vzhledem k množství.",[3859,56568,56569],{},[724,56570,56571,56573,56574,56600,56601,56618,56619,1888],{},[883,56572,4145],{}," Intuice — „kolik vyděláš za další kus\"\nHodnota ",[883,56575,56577],{"className":56576},[886],[888,56578,56579],{"xmlns":890},[892,56580,56581,56597],{},[895,56582,56583,56585,56587,56589,56595],{},[898,56584,2815],{},[898,56586,3984],{},[1726,56588,1735],{"stretchy":1734},[2128,56590,56591,56593],{},[898,56592,1724],{},[1726,56594,4342],{},[1726,56596,1762],{"stretchy":1734},[902,56598,56599],{"encoding":904},"MR(Q^*)"," je přibližně to, o kolik se zvýší celkový příjem, prodá-li firma jednu další jednotku nad aktuální úroveň ",[883,56602,56604],{"className":56603},[886],[888,56605,56606],{"xmlns":890},[892,56607,56608,56616],{},[895,56609,56610],{},[2128,56611,56612,56614],{},[898,56613,1724],{},[1726,56615,4342],{},[902,56617,29825],{"encoding":904},". Jinak řečeno: ",[883,56620,56622],{"className":56621},[886],[888,56623,56624],{"xmlns":890},[892,56625,56626,56678],{},[895,56627,56628,56630,56632,56634,56640,56642,56644,56646,56648,56650,56656,56658,56660,56662,56664,56666,56668,56670,56676],{},[898,56629,2815],{},[898,56631,3984],{},[1726,56633,1735],{"stretchy":1734},[2128,56635,56636,56638],{},[898,56637,1724],{},[1726,56639,4342],{},[1726,56641,1762],{"stretchy":1734},[1726,56643,1880],{},[898,56645,2772],{},[898,56647,3984],{},[1726,56649,1735],{"stretchy":1734},[2128,56651,56652,56654],{},[898,56653,1724],{},[1726,56655,4342],{},[1726,56657,2099],{},[2133,56659,2281],{},[1726,56661,1762],{"stretchy":1734},[1726,56663,2228],{},[898,56665,2772],{},[898,56667,3984],{},[1726,56669,1735],{"stretchy":1734},[2128,56671,56672,56674],{},[898,56673,1724],{},[1726,56675,4342],{},[1726,56677,1762],{"stretchy":1734},[902,56679,56680],{"encoding":904},"MR(Q^*) \\approx TR(Q^* + 1) - TR(Q^*)",[37329,56682,56684],{"id":56683},"příklad-32","Příklad 3.2",[724,56686,56687,55968,56689,56005,56723,56738,56739,1888],{},[38,56688,55967],{},[883,56690,56692],{"className":56691},[886],[888,56693,56694],{"xmlns":890},[892,56695,56696,56720],{},[895,56697,56698,56700,56702,56704,56706,56708,56710,56712,56714,56716,56718],{},[898,56699,1738],{},[1726,56701,1728],{},[898,56703,1731],{},[1726,56705,1735],{"stretchy":1734},[898,56707,1724],{},[1726,56709,1762],{"stretchy":1734},[1726,56711,1728],{},[2133,56713,3087],{},[1726,56715,2228],{},[2133,56717,2135],{},[898,56719,1724],{},[902,56721,56722],{"encoding":904},"P = D(Q) = 100 - 2Q",[883,56724,56726],{"className":56725},[886],[888,56727,56728],{"xmlns":890},[892,56729,56730,56736],{},[895,56731,56732,56734],{},[898,56733,2815],{},[898,56735,3984],{},[902,56737,6621],{"encoding":904}," a interpretujte jeho hodnoty pro ",[883,56740,56742],{"className":56741},[886],[888,56743,56744],{"xmlns":890},[892,56745,56746,56762],{},[895,56747,56748,56750,56752,56754,56756,56758,56760],{},[898,56749,1724],{},[1726,56751,1728],{},[2133,56753,36225],{},[1726,56755,1742],{"separator":1741},[2133,56757,41843],{},[1726,56759,1742],{"separator":1741},[2133,56761,9021],{},[902,56763,56764],{"encoding":904},"Q = 15, 16, 20",[724,56766,56767,1777,56769,56801],{},[38,56768,22751],{},[883,56770,56772],{"className":56771},[886],[888,56773,56774],{"xmlns":890},[892,56775,56776,56798],{},[895,56777,56778,56780,56782,56784,56786,56788,56790,56792],{},[898,56779,2772],{},[898,56781,3984],{},[1726,56783,1728],{},[2133,56785,3087],{},[898,56787,1724],{},[1726,56789,2228],{},[2133,56791,2135],{},[2128,56793,56794,56796],{},[898,56795,1724],{},[2133,56797,2135],{},[902,56799,56800],{"encoding":904},"TR = 100Q - 2Q^2",", tedy",[883,56803,56805],{"className":56804},[886],[888,56806,56807],{"xmlns":890,"display":28047},[892,56808,56809,56851],{},[895,56810,56811,56813,56815,56817,56819,56821,56823,56825,56827,56833,56839,56841,56843,56845,56847,56849],{},[898,56812,2815],{},[898,56814,3984],{},[1726,56816,1728],{},[1726,56818,1735],{"stretchy":1734},[2133,56820,3087],{},[898,56822,1724],{},[1726,56824,2228],{},[2133,56826,2135],{},[2128,56828,56829,56831],{},[898,56830,1724],{},[2133,56832,2135],{},[2128,56834,56835,56837],{},[1726,56836,1762],{"stretchy":1734},[1726,56838,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,56840,1728],{},[2133,56842,3087],{},[1726,56844,2228],{},[2133,56846,2352],{},[898,56848,1724],{},[898,56850,1888],{"mathvariant":2377},[902,56852,56853],{"encoding":904},"MR = (100Q - 2Q^2)' = 100 - 4Q.",[724,56855,9647,56856,8088,56874,56900,56901,4346,56914,56929,56930,56943,56944,21401,56957,4346,56970,56985,56986,56999,57000,57031,57032,57051],{},[883,56857,56859],{"className":56858},[886],[888,56860,56861],{"xmlns":890},[892,56862,56863,56871],{},[895,56864,56865,56867,56869],{},[898,56866,1724],{},[1726,56868,1728],{},[2133,56870,36225],{},[902,56872,56873],{"encoding":904},"Q = 15",[883,56875,56877],{"className":56876},[886],[888,56878,56879],{"xmlns":890},[892,56880,56881,56897],{},[895,56882,56883,56885,56887,56889,56891,56893,56895],{},[898,56884,2815],{},[898,56886,3984],{},[1726,56888,1735],{"stretchy":1734},[2133,56890,36225],{},[1726,56892,1762],{"stretchy":1734},[1726,56894,1728],{},[2133,56896,5198],{},[902,56898,56899],{"encoding":904},"MR(15) = 40",": při množství ",[883,56902,56904],{"className":56903},[886],[888,56905,56906],{"xmlns":890},[892,56907,56908,56912],{},[895,56909,56910],{},[2133,56911,36225],{},[902,56913,36225],{"encoding":904},[883,56915,56917],{"className":56916},[886],[888,56918,56919],{"xmlns":890},[892,56920,56921,56927],{},[895,56922,56923,56925],{},[898,56924,2772],{},[898,56926,3984],{},[902,56928,4084],{"encoding":904}," mění asi ",[883,56931,56933],{"className":56932},[886],[888,56934,56935],{"xmlns":890},[892,56936,56937,56941],{},[895,56938,56939],{},[2133,56940,5198],{},[902,56942,5198],{"encoding":904},"-krát rychleji než množství; s růstem ",[883,56945,56947],{"className":56946},[886],[888,56948,56949],{"xmlns":890},[892,56950,56951,56955],{},[895,56952,56953],{},[898,56954,1724],{},[902,56956,1724],{"encoding":904},[883,56958,56960],{"className":56959},[886],[888,56961,56962],{"xmlns":890},[892,56963,56964,56968],{},[895,56965,56966],{},[2133,56967,2281],{},[902,56969,2281],{"encoding":904},[883,56971,56973],{"className":56972},[886],[888,56974,56975],{"xmlns":890},[892,56976,56977,56983],{},[895,56978,56979,56981],{},[898,56980,2772],{},[898,56982,3984],{},[902,56984,4084],{"encoding":904}," zvýší přibližně o ",[883,56987,56989],{"className":56988},[886],[888,56990,56991],{"xmlns":890},[892,56992,56993,56997],{},[895,56994,56995],{},[2133,56996,5198],{},[902,56998,5198],{"encoding":904},", tj. ze skutečné hodnoty ",[883,57001,57003],{"className":57002},[886],[888,57004,57005],{"xmlns":890},[892,57006,57007,57028],{},[895,57008,57009,57011,57013,57015,57017,57019,57021,57023,57025],{},[898,57010,2772],{},[898,57012,3984],{},[1726,57014,1735],{"stretchy":1734},[2133,57016,36225],{},[1726,57018,1762],{"stretchy":1734},[1726,57020,1728],{},[2133,57022,2281],{},[2289,57024,2984],{},[2133,57026,57027],{},"050",[902,57029,57030],{"encoding":904},"TR(15) = 1\\,050"," na přibližně ",[883,57033,57035],{"className":57034},[886],[888,57036,57037],{"xmlns":890},[892,57038,57039,57048],{},[895,57040,57041,57043,57045],{},[2133,57042,2281],{},[2289,57044,2984],{},[2133,57046,57047],{},"090",[902,57049,57050],{"encoding":904},"1\\,090",". Skutečná změna je",[883,57053,57055],{"className":57054},[886],[888,57056,57057],{"xmlns":890,"display":28047},[892,57058,57059,57113],{},[895,57060,57061,57063,57065,57067,57069,57071,57073,57075,57077,57079,57081,57083,57085,57087,57089,57091,57093,57095,57097,57100,57102,57104,57106,57108,57110],{},[898,57062,2886],{"mathvariant":2377},[898,57064,2772],{},[898,57066,3984],{},[1726,57068,1728],{},[898,57070,2772],{},[898,57072,3984],{},[1726,57074,1735],{"stretchy":1734},[2133,57076,41843],{},[1726,57078,1762],{"stretchy":1734},[1726,57080,2228],{},[898,57082,2772],{},[898,57084,3984],{},[1726,57086,1735],{"stretchy":1734},[2133,57088,36225],{},[1726,57090,1762],{"stretchy":1734},[1726,57092,1728],{},[2133,57094,2281],{},[2289,57096,2984],{},[2133,57098,57099],{},"088",[1726,57101,2228],{},[2133,57103,2281],{},[2289,57105,2984],{},[2133,57107,57027],{},[1726,57109,1728],{},[2133,57111,57112],{},"38.",[902,57114,57115],{"encoding":904},"\\Delta TR = TR(16) - TR(15) = 1\\,088 - 1\\,050 = 38.",[724,57117,57118,57119,1343,57145,2924,57171,57186,57187,57202],{},"Podobně ",[883,57120,57122],{"className":57121},[886],[888,57123,57124],{"xmlns":890},[892,57125,57126,57142],{},[895,57127,57128,57130,57132,57134,57136,57138,57140],{},[898,57129,2815],{},[898,57131,3984],{},[1726,57133,1735],{"stretchy":1734},[2133,57135,41843],{},[1726,57137,1762],{"stretchy":1734},[1726,57139,1728],{},[2133,57141,5552],{},[902,57143,57144],{"encoding":904},"MR(16) = 36",[883,57146,57148],{"className":57147},[886],[888,57149,57150],{"xmlns":890},[892,57151,57152,57168],{},[895,57153,57154,57156,57158,57160,57162,57164,57166],{},[898,57155,2815],{},[898,57157,3984],{},[1726,57159,1735],{"stretchy":1734},[2133,57161,9021],{},[1726,57163,1762],{"stretchy":1734},[1726,57165,1728],{},[2133,57167,9021],{},[902,57169,57170],{"encoding":904},"MR(20) = 20",[883,57172,57174],{"className":57173},[886],[888,57175,57176],{"xmlns":890},[892,57177,57178,57184],{},[895,57179,57180,57182],{},[898,57181,2815],{},[898,57183,3984],{},[902,57185,6621],{"encoding":904}," je klesající funkce — rychlost změny ",[883,57188,57190],{"className":57189},[886],[888,57191,57192],{"xmlns":890},[892,57193,57194,57200],{},[895,57195,57196,57198],{},[898,57197,2772],{},[898,57199,3984],{},[902,57201,4084],{"encoding":904}," s růstem množství klesá.",[198,57204,57206],{"id":57205},"odhad-změny-tr-pomocí-diferenciálu","Odhad změny TR pomocí diferenciálu",[724,57208,57209],{},"Užitím mezního příjmu lze odhadnout změnu celkového příjmu jako odezvu na změnu množství:",[883,57211,57213],{"className":57212},[886],[888,57214,57215],{"xmlns":890,"display":28047},[892,57216,57217,57286],{},[20735,57218,57219],{"width":28052},[20740,57220,57221,57223,57279,57281],{},[20743,57222],{"width":28057},[20743,57224,57225],{},[895,57226,57227,57229,57231,57233,57235,57237,57239,57241,57243,57245,57247,57249,57251,57253,57259,57261,57263,57265,57267,57269,57271,57273,57275,57277],{},[898,57228,2886],{"mathvariant":2377},[898,57230,2772],{},[898,57232,3984],{},[2289,57234,3974],{},[1726,57236,1880],{},[2289,57238,3974],{},[898,57240,2198],{"mathvariant":2377},[898,57242,2772],{},[898,57244,3984],{},[1726,57246,1728],{},[1726,57248,1735],{"stretchy":1734},[898,57250,2772],{},[898,57252,3984],{},[2128,57254,57255,57257],{},[1726,57256,1762],{"stretchy":1734},[1726,57258,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[2289,57260,2984],{},[898,57262,2198],{"mathvariant":2377},[898,57264,1724],{},[1726,57266,1728],{},[898,57268,2815],{},[898,57270,3984],{},[2289,57272,2984],{},[898,57274,2198],{"mathvariant":2377},[898,57276,1724],{},[1726,57278,1742],{"separator":1741},[20743,57280],{"width":28057},[20743,57282,57283],{},[2289,57284,57285],{},"(3.3)",[902,57287,57288],{"encoding":904},"\\Delta TR \\;\\approx\\; \\mathrm{d}TR = (TR)' \\, \\mathrm{d}Q = MR \\, \\mathrm{d}Q,\n\\tag{3.3}",[724,57290,57291],{},"schematicky:",[883,57293,57295],{"className":57294},[886],[888,57296,57297],{"xmlns":890,"display":28047},[892,57298,57299,57407],{},[895,57300,57301,57339,57341,57343,57345,57374,57377,57405],{},[895,57302,57303,57306,57312,57315,57321,57324,57330,57336],{},[2289,57304,57305],{},"zm",[8372,57307,57308,57310],{"accent":1741},[2289,57309,45713],{},[1726,57311,25039],{},[2289,57313,57314],{},"na celkov",[8372,57316,57317,57319],{"accent":1741},[2289,57318,45713],{},[1726,57320,24958],{},[2289,57322,57323],{},"ho p",[8372,57325,57326,57328],{"accent":1741},[2289,57327,12027],{},[1726,57329,25039],{},[8372,57331,57332,57334],{"accent":1741},[2289,57333,25027],{},[1726,57335,24958],{},[2289,57337,57338],{},"jmu",[2289,57340,3974],{},[1726,57342,1880],{},[2289,57344,3974],{},[895,57346,57347,57350,57356,57359,57365,57371],{},[2289,57348,57349],{},"mezn",[8372,57351,57352,57354],{"accent":1741},[2289,57353,25027],{},[1726,57355,24958],{},[2289,57357,57358],{}," p",[8372,57360,57361,57363],{"accent":1741},[2289,57362,12027],{},[1726,57364,25039],{},[8372,57366,57367,57369],{"accent":1741},[2289,57368,25027],{},[1726,57370,24958],{},[2289,57372,57373],{},"jem",[1726,57375,57376],{},"×",[895,57378,57379,57381,57387,57390,57396,57399],{},[2289,57380,57305],{},[8372,57382,57383,57385],{"accent":1741},[2289,57384,45713],{},[1726,57386,25039],{},[2289,57388,57389],{},"na mno",[8372,57391,57392,57394],{"accent":1741},[2289,57393,9579],{},[1726,57395,25039],{},[2289,57397,57398],{},"stv",[8372,57400,57401,57403],{"accent":1741},[2289,57402,25027],{},[1726,57404,24958],{},[898,57406,1888],{"mathvariant":2377},[902,57408,57409],{"encoding":904},"\\text{změna celkového příjmu} \\;\\approx\\; \\text{mezní příjem} \\times \\text{změna množství}.",[724,57411,57412,57413,57428],{},"Pro porovnání skutečná změna ",[883,57414,57416],{"className":57415},[886],[888,57417,57418],{"xmlns":890},[892,57419,57420,57426],{},[895,57421,57422,57424],{},[898,57423,2772],{},[898,57425,3984],{},[902,57427,4084],{"encoding":904}," je",[883,57430,57432],{"className":57431},[886],[888,57433,57434],{"xmlns":890,"display":28047},[892,57435,57436,57491],{},[20735,57437,57438],{"width":28052},[20740,57439,57440,57442,57484,57486],{},[20743,57441],{"width":28057},[20743,57443,57444],{},[895,57445,57446,57448,57450,57452,57454,57456,57458,57460,57462,57464,57466,57468,57470,57472,57474,57476,57478,57480,57482],{},[898,57447,2886],{"mathvariant":2377},[898,57449,2772],{},[898,57451,3984],{},[1726,57453,1728],{},[898,57455,2772],{},[898,57457,3984],{},[1726,57459,1735],{"stretchy":1734},[898,57461,1724],{},[1726,57463,2099],{},[898,57465,2198],{"mathvariant":2377},[898,57467,1724],{},[1726,57469,1762],{"stretchy":1734},[1726,57471,2228],{},[898,57473,2772],{},[898,57475,3984],{},[1726,57477,1735],{"stretchy":1734},[898,57479,1724],{},[1726,57481,1762],{"stretchy":1734},[898,57483,1888],{"mathvariant":2377},[20743,57485],{"width":28057},[20743,57487,57488],{},[2289,57489,57490],{},"(3.4)",[902,57492,57493],{"encoding":904},"\\Delta TR = TR(Q + \\mathrm{d}Q) - TR(Q).\n\\tag{3.4}",[37329,57495,57497],{"id":57496},"příklad-33","Příklad 3.3",[724,57499,57500,57502,57503,57533,57534,2656,57549,2670,57562,2684,57575,57589],{},[38,57501,55967],{}," Pro ",[883,57504,57506],{"className":57505},[886],[888,57507,57508],{"xmlns":890},[892,57509,57510,57530],{},[895,57511,57512,57514,57516,57518,57520,57522,57524],{},[898,57513,2772],{},[898,57515,3984],{},[1726,57517,1728],{},[2133,57519,3087],{},[898,57521,1724],{},[1726,57523,2228],{},[2128,57525,57526,57528],{},[898,57527,1724],{},[2133,57529,2135],{},[902,57531,57532],{"encoding":904},"TR = 100Q - Q^2"," odhadněte změnu ",[883,57535,57537],{"className":57536},[886],[888,57538,57539],{"xmlns":890},[892,57540,57541,57547],{},[895,57542,57543,57545],{},[898,57544,2772],{},[898,57546,3984],{},[902,57548,4084],{"encoding":904},[883,57550,57552],{"className":57551},[886],[888,57553,57554],{"xmlns":890},[892,57555,57556,57560],{},[895,57557,57558],{},[898,57559,1724],{},[902,57561,1724],{"encoding":904},[883,57563,57565],{"className":57564},[886],[888,57566,57567],{"xmlns":890},[892,57568,57569,57573],{},[895,57570,57571],{},[2133,57572,3123],{},[902,57574,3123],{"encoding":904},[883,57576,57578],{"className":57577},[886],[888,57579,57580],{"xmlns":890},[892,57581,57582,57587],{},[895,57583,57584],{},[2133,57585,57586],{},"63",[902,57588,57586],{"encoding":904}," a porovnejte se skutečnou změnou.",[724,57591,57592,1777,57594,57619,57620,1343,57638,2703],{},[38,57593,22751],{},[883,57595,57597],{"className":57596},[886],[888,57598,57599],{"xmlns":890},[892,57600,57601,57617],{},[895,57602,57603,57605,57607,57609,57611,57613,57615],{},[898,57604,2815],{},[898,57606,3984],{},[1726,57608,1728],{},[2133,57610,3087],{},[1726,57612,2228],{},[2133,57614,2135],{},[898,57616,1724],{},[902,57618,11421],{"encoding":904},", tedy při ",[883,57621,57623],{"className":57622},[886],[888,57624,57625],{"xmlns":890},[892,57626,57627,57635],{},[895,57628,57629,57631,57633],{},[898,57630,1724],{},[1726,57632,1728],{},[2133,57634,3123],{},[902,57636,57637],{"encoding":904},"Q = 60",[883,57639,57641],{"className":57640},[886],[888,57642,57643],{"xmlns":890},[892,57644,57645,57655],{},[895,57646,57647,57649,57651,57653],{},[898,57648,2198],{"mathvariant":2377},[898,57650,1724],{},[1726,57652,1728],{},[2133,57654,2177],{},[902,57656,57657],{"encoding":904},"\\mathrm{d}Q = 3",[883,57659,57661],{"className":57660},[886],[888,57662,57663],{"xmlns":890,"display":28047},[892,57664,57665,57696],{},[895,57666,57667,57669,57671,57673,57675,57677,57679,57681,57683,57685,57687,57689,57691,57693],{},[898,57668,2198],{"mathvariant":2377},[898,57670,2772],{},[898,57672,3984],{},[1726,57674,1728],{},[1726,57676,1735],{"stretchy":1734},[2133,57678,3087],{},[1726,57680,2228],{},[2133,57682,4036],{},[1726,57684,1762],{"stretchy":1734},[1726,57686,3174],{},[2133,57688,2177],{},[1726,57690,1728],{},[1726,57692,2228],{},[2133,57694,57695],{},"60.",[902,57697,57698],{"encoding":904},"\\mathrm{d}TR = (100 - 120) \\cdot 3 = -60.",[724,57700,57701,57702,57732,57733,57752],{},"Celkový příjem klesne z ",[883,57703,57705],{"className":57704},[886],[888,57706,57707],{"xmlns":890},[892,57708,57709,57729],{},[895,57710,57711,57713,57715,57717,57719,57721,57723,57725,57727],{},[898,57712,2772],{},[898,57714,3984],{},[1726,57716,1735],{"stretchy":1734},[2133,57718,3123],{},[1726,57720,1762],{"stretchy":1734},[1726,57722,1728],{},[2133,57724,2135],{},[2289,57726,2984],{},[2133,57728,20123],{},[902,57730,57731],{"encoding":904},"TR(60) = 2\\,400"," přibližně na ",[883,57734,57736],{"className":57735},[886],[888,57737,57738],{"xmlns":890},[892,57739,57740,57749],{},[895,57741,57742,57744,57746],{},[2133,57743,2135],{},[2289,57745,2984],{},[2133,57747,57748],{},"340",[902,57750,57751],{"encoding":904},"2\\,340",". Skutečná změna dle (3.4):",[883,57754,57756],{"className":57755},[886],[888,57757,57758],{"xmlns":890,"display":28047},[892,57759,57760,57818],{},[895,57761,57762,57764,57766,57768,57770,57772,57774,57776,57778,57780,57782,57784,57786,57788,57790,57792,57794,57796,57798,57801,57803,57805,57807,57809,57811,57813,57816],{},[898,57763,2886],{"mathvariant":2377},[898,57765,2772],{},[898,57767,3984],{},[1726,57769,1728],{},[898,57771,2772],{},[898,57773,3984],{},[1726,57775,1735],{"stretchy":1734},[2133,57777,57586],{},[1726,57779,1762],{"stretchy":1734},[1726,57781,2228],{},[898,57783,2772],{},[898,57785,3984],{},[1726,57787,1735],{"stretchy":1734},[2133,57789,3123],{},[1726,57791,1762],{"stretchy":1734},[1726,57793,1728],{},[2133,57795,2135],{},[2289,57797,2984],{},[2133,57799,57800],{},"331",[1726,57802,2228],{},[2133,57804,2135],{},[2289,57806,2984],{},[2133,57808,20123],{},[1726,57810,1728],{},[1726,57812,2228],{},[2133,57814,57815],{},"69",[1726,57817,1742],{"separator":1741},[902,57819,57820],{"encoding":904},"\\Delta TR = TR(63) - TR(60) = 2\\,331 - 2\\,400 = -69,",[724,57822,57823,57824,57839,57840,1888],{},"tj. ",[883,57825,57827],{"className":57826},[886],[888,57828,57829],{"xmlns":890},[892,57830,57831,57837],{},[895,57832,57833,57835],{},[898,57834,2772],{},[898,57836,3984],{},[902,57838,4084],{"encoding":904}," klesne na ",[883,57841,57843],{"className":57842},[886],[888,57844,57845],{"xmlns":890},[892,57846,57847,57855],{},[895,57848,57849,57851,57853],{},[2133,57850,2135],{},[2289,57852,2984],{},[2133,57854,57800],{},[902,57856,57857],{"encoding":904},"2\\,331",[198,57859,57861],{"id":57860},"vztah-ar-a-mr-pro-lineární-poptávku","Vztah AR a MR pro lineární poptávku",[724,57863,57864,57865,10378,57888,31561],{},"Obecně pro lineární poptávku ",[883,57866,57868],{"className":57867},[886],[888,57869,57870],{"xmlns":890},[892,57871,57872,57886],{},[895,57873,57874,57876,57878,57880,57882,57884],{},[898,57875,1738],{},[1726,57877,1728],{},[898,57879,207],{},[898,57881,1724],{},[1726,57883,2099],{},[898,57885,2102],{},[902,57887,37041],{"encoding":904},[883,57889,57891],{"className":57890},[886],[888,57892,57893],{"xmlns":890},[892,57894,57895,57917],{},[895,57896,57897,57899,57901,57903,57905,57911,57913,57915],{},[898,57898,2772],{},[898,57900,3984],{},[1726,57902,1728],{},[898,57904,207],{},[2128,57906,57907,57909],{},[898,57908,1724],{},[2133,57910,2135],{},[1726,57912,2099],{},[898,57914,2102],{},[898,57916,1724],{},[902,57918,57919],{"encoding":904},"TR = aQ^2 + bQ",[883,57921,57923],{"className":57922},[886],[888,57924,57925],{"xmlns":890,"display":28047},[892,57926,57927,57947],{},[895,57928,57929,57931,57933,57935,57937,57939,57941,57943,57945],{},[898,57930,2815],{},[898,57932,3984],{},[1726,57934,1728],{},[2133,57936,2135],{},[898,57938,207],{},[898,57940,1724],{},[1726,57942,2099],{},[898,57944,2102],{},[898,57946,1888],{"mathvariant":2377},[902,57948,57949],{"encoding":904},"MR = 2aQ + b.",[724,57951,57952,57953,57968,57969,57984,57985,57998,57999,10009,58002,58018,58019,58032,58033,58048,58049,58064,58065,58080,58081,2623,58094,58124,58125,58144,58145,58160],{},"Křivky ",[883,57954,57956],{"className":57955},[886],[888,57957,57958],{"xmlns":890},[892,57959,57960,57966],{},[895,57961,57962,57964],{},[898,57963,2815],{},[898,57965,3984],{},[902,57967,6621],{"encoding":904}," a poptávky (resp. ",[883,57970,57972],{"className":57971},[886],[888,57973,57974],{"xmlns":890},[892,57975,57976,57982],{},[895,57977,57978,57980],{},[898,57979,4243],{},[898,57981,3984],{},[902,57983,55425],{"encoding":904},") jsou přímky protínající svislou osu v témže bodě ",[883,57986,57988],{"className":57987},[886],[888,57989,57990],{"xmlns":890},[892,57991,57992,57996],{},[895,57993,57994],{},[898,57995,2102],{},[902,57997,2102],{"encoding":904},", přičemž ",[38,58000,58001],{},"přímka mezního příjmu má sklon rovný dvojnásobku sklonu přímky poptávky",[883,58003,58005],{"className":58004},[886],[888,58006,58007],{"xmlns":890},[892,58008,58009,58015],{},[895,58010,58011,58013],{},[2133,58012,2135],{},[898,58014,207],{},[902,58016,58017],{"encoding":904},"2a"," vs. ",[883,58020,58022],{"className":58021},[886],[888,58023,58024],{"xmlns":890},[892,58025,58026,58030],{},[895,58027,58028],{},[898,58029,207],{},[902,58031,207],{"encoding":904},", obrázek 3.2). ",[883,58034,58036],{"className":58035},[886],[888,58037,58038],{"xmlns":890},[892,58039,58040,58046],{},[895,58041,58042,58044],{},[898,58043,2815],{},[898,58045,3984],{},[902,58047,6621],{"encoding":904}," nabývá jak kladných, tak záporných hodnot; křivka ",[883,58050,58052],{"className":58051},[886],[888,58053,58054],{"xmlns":890},[892,58055,58056,58062],{},[895,58057,58058,58060],{},[898,58059,2772],{},[898,58061,3984],{},[902,58063,4084],{"encoding":904}," nejprve roste, v bodě maxima protíná ",[883,58066,58068],{"className":58067},[886],[888,58069,58070],{"xmlns":890},[892,58071,58072,58078],{},[895,58073,58074,58076],{},[898,58075,2815],{},[898,58077,3984],{},[902,58079,6621],{"encoding":904}," osu ",[883,58082,58084],{"className":58083},[886],[888,58085,58086],{"xmlns":890},[892,58087,58088,58092],{},[895,58089,58090],{},[898,58091,1724],{},[902,58093,1724],{"encoding":904},[883,58095,58097],{"className":58096},[886],[888,58098,58099],{"xmlns":890},[892,58100,58101,58121],{},[895,58102,58103,58105,58107,58109],{},[898,58104,1724],{},[1726,58106,1728],{},[1726,58108,2228],{},[2326,58110,58111],{"scriptlevel":2328,"displaystyle":1734},[2330,58112,58113,58115],{},[898,58114,2102],{},[895,58116,58117,58119],{},[2133,58118,2135],{},[898,58120,207],{},[902,58122,58123],{"encoding":904},"Q = -\\tfrac{b}{2a}"," hodnotou ",[883,58126,58128],{"className":58127},[886],[888,58129,58130],{"xmlns":890},[892,58131,58132,58142],{},[895,58133,58134,58136,58138,58140],{},[898,58135,2815],{},[898,58137,3984],{},[1726,58139,1728],{},[2133,58141,2328],{},[902,58143,7070],{"encoding":904},", a dále ",[883,58146,58148],{"className":58147},[886],[888,58149,58150],{"xmlns":890},[892,58151,58152,58158],{},[895,58153,58154,58156],{},[898,58155,2772],{},[898,58157,3984],{},[902,58159,4084],{"encoding":904}," klesá.",[724,58162,58163,58164,58170,58171,58203,58204,58232],{},"V případě ",[38,58165,58166],{},[207,58167,58169],{"className":58168,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurence",", kdy poptávka ",[883,58172,58174],{"className":58173},[886],[888,58175,58176],{"xmlns":890},[892,58177,58178,58200],{},[895,58179,58180,58182,58184,58186,58188,58190,58192,58194],{},[898,58181,1738],{},[1726,58183,1728],{},[898,58185,1731],{},[1726,58187,1735],{"stretchy":1734},[898,58189,1724],{},[1726,58191,1762],{"stretchy":1734},[1726,58193,1728],{},[2128,58195,58196,58198],{},[898,58197,1738],{},[1726,58199,4342],{},[902,58201,58202],{"encoding":904},"P = D(Q) = P^*"," je pevná tržní cena, platí ",[883,58205,58207],{"className":58206},[886],[888,58208,58209],{"xmlns":890},[892,58210,58211,58229],{},[895,58212,58213,58215,58217,58219,58221,58223],{},[898,58214,2772],{},[898,58216,3984],{},[1726,58218,1728],{},[898,58220,1724],{},[1726,58222,3174],{},[2128,58224,58225,58227],{},[898,58226,1738],{},[1726,58228,4342],{},[902,58230,58231],{"encoding":904},"TR = Q \\cdot P^*"," a tedy",[883,58234,58236],{"className":58235},[886],[888,58237,58238],{"xmlns":890,"display":28047},[892,58239,58240,58282],{},[895,58241,58242,58244,58246,58248,58250,58252,58254,58260,58262,58264,58278,58280],{},[898,58243,2815],{},[898,58245,3984],{},[1726,58247,1728],{},[898,58249,4243],{},[898,58251,3984],{},[1726,58253,1728],{},[2128,58255,58256,58258],{},[898,58257,1738],{},[1726,58259,4342],{},[5865,58261],{"width":15270},[1726,58263,1735],{"stretchy":1734},[895,58265,58266,58269,58275],{},[2289,58267,58268],{},"obr",[8372,58270,58271,58273],{"accent":1741},[2289,58272,207],{},[1726,58274,24958],{},[2289,58276,58277],{},"zek 3.4",[1726,58279,1762],{"stretchy":1734},[898,58281,1888],{"mathvariant":2377},[902,58283,58284],{"encoding":904},"MR = AR = P^* \\quad (\\text{obrázek 3.4}).",[724,58286,58287],{},[614,58288,58289,58290,3877,58316,58344,58345,58358,58359,58374,58375,3715,58388,1343,58414,3715,58429,1888],{},"Obrázek 3.2: Přímky ",[883,58291,58293],{"className":58292},[886],[888,58294,58295],{"xmlns":890},[892,58296,58297,58313],{},[895,58298,58299,58301,58303,58305,58307,58309,58311],{},[898,58300,4243],{},[898,58302,3984],{},[1726,58304,1728],{},[898,58306,207],{},[898,58308,1724],{},[1726,58310,2099],{},[898,58312,2102],{},[902,58314,58315],{"encoding":904},"AR = aQ + b",[883,58317,58319],{"className":58318},[886],[888,58320,58321],{"xmlns":890},[892,58322,58323,58341],{},[895,58324,58325,58327,58329,58331,58333,58335,58337,58339],{},[898,58326,2815],{},[898,58328,3984],{},[1726,58330,1728],{},[2133,58332,2135],{},[898,58334,207],{},[898,58336,1724],{},[1726,58338,2099],{},[898,58340,2102],{},[902,58342,58343],{"encoding":904},"MR = 2aQ + b"," v jednom grafu; společný průsečík ",[883,58346,58348],{"className":58347},[886],[888,58349,58350],{"xmlns":890},[892,58351,58352,58356],{},[895,58353,58354],{},[898,58355,2102],{},[902,58357,2102],{"encoding":904}," se svislou osou, ",[883,58360,58362],{"className":58361},[886],[888,58363,58364],{"xmlns":890},[892,58365,58366,58372],{},[895,58367,58368,58370],{},[898,58369,2815],{},[898,58371,3984],{},[902,58373,6621],{"encoding":904}," protíná osu ",[883,58376,58378],{"className":58377},[886],[888,58379,58380],{"xmlns":890},[892,58381,58382,58386],{},[895,58383,58384],{},[898,58385,1724],{},[902,58387,1724],{"encoding":904},[883,58389,58391],{"className":58390},[886],[888,58392,58393],{"xmlns":890},[892,58394,58395,58411],{},[895,58396,58397,58399],{},[1726,58398,2228],{},[2326,58400,58401],{"scriptlevel":2328,"displaystyle":1734},[2330,58402,58403,58405],{},[898,58404,2102],{},[895,58406,58407,58409],{},[2133,58408,2135],{},[898,58410,207],{},[902,58412,58413],{"encoding":904},"-\\tfrac{b}{2a}",[883,58415,58417],{"className":58416},[886],[888,58418,58419],{"xmlns":890},[892,58420,58421,58427],{},[895,58422,58423,58425],{},[898,58424,4243],{},[898,58426,3984],{},[902,58428,55425],{"encoding":904},[883,58430,58432],{"className":58431},[886],[888,58433,58434],{"xmlns":890},[892,58435,58436,58448],{},[895,58437,58438,58440],{},[1726,58439,2228],{},[2326,58441,58442],{"scriptlevel":2328,"displaystyle":1734},[2330,58443,58444,58446],{},[898,58445,2102],{},[898,58447,207],{},[902,58449,58450],{"encoding":904},"-\\tfrac{b}{a}",[724,58452,58453],{},[614,58454,58455,58456,58487,58488,58517,58518,1888],{},"Obrázek 3.3: Parabola ",[883,58457,58459],{"className":58458},[886],[888,58460,58461],{"xmlns":890},[892,58462,58463,58485],{},[895,58464,58465,58467,58469,58471,58473,58479,58481,58483],{},[898,58466,2772],{},[898,58468,3984],{},[1726,58470,1728],{},[898,58472,207],{},[2128,58474,58475,58477],{},[898,58476,1724],{},[2133,58478,2135],{},[1726,58480,2099],{},[898,58482,2102],{},[898,58484,1724],{},[902,58486,57919],{"encoding":904}," s maximem v ",[883,58489,58491],{"className":58490},[886],[888,58492,58493],{"xmlns":890},[892,58494,58495,58515],{},[895,58496,58497,58499,58501,58503],{},[898,58498,1724],{},[1726,58500,1728],{},[1726,58502,2228],{},[2326,58504,58505],{"scriptlevel":2328,"displaystyle":1734},[2330,58506,58507,58509],{},[898,58508,2102],{},[895,58510,58511,58513],{},[2133,58512,2135],{},[898,58514,207],{},[902,58516,58123],{"encoding":904}," a nulou v ",[883,58519,58521],{"className":58520},[886],[888,58522,58523],{"xmlns":890},[892,58524,58525,58541],{},[895,58526,58527,58529,58531,58533],{},[898,58528,1724],{},[1726,58530,1728],{},[1726,58532,2228],{},[2326,58534,58535],{"scriptlevel":2328,"displaystyle":1734},[2330,58536,58537,58539],{},[898,58538,2102],{},[898,58540,207],{},[902,58542,58543],{"encoding":904},"Q = -\\tfrac{b}{a}",[724,58545,58546],{},[614,58547,58548,58549,1888],{},"Obrázek 3.4: Dokonalá konkurence — vodorovná přímka ",[883,58550,58552],{"className":58551},[886],[888,58553,58554],{"xmlns":890},[892,58555,58556,58576],{},[895,58557,58558,58560,58562,58564,58566,58568,58570],{},[898,58559,4243],{},[898,58561,3984],{},[1726,58563,1728],{},[898,58565,2815],{},[898,58567,3984],{},[1726,58569,1728],{},[2128,58571,58572,58574],{},[898,58573,1738],{},[1726,58575,4342],{},[902,58577,58578],{"encoding":904},"AR = MR = P^*",[115,58580,58582],{"id":58581},"náklady-firmy","Náklady firmy",[198,58584,58586],{"id":58585},"celkové-náklady","Celkové náklady",[724,58588,58589,1777,58591,10009,58606,58609,58610,58623],{},[38,58590,58586],{},[883,58592,58594],{"className":58593},[886],[888,58595,58596],{"xmlns":890},[892,58597,58598,58604],{},[895,58599,58600,58602],{},[898,58601,2772],{},[898,58603,2775],{},[902,58605,3240],{"encoding":904},[38,58607,58608],{},"total cost",") jsou veškeré náklady na realizaci ",[883,58611,58613],{"className":58612},[886],[888,58614,58615],{"xmlns":890},[892,58616,58617,58621],{},[895,58618,58619],{},[898,58620,1724],{},[902,58622,1724],{"encoding":904}," jednotek produkce:",[883,58625,58627],{"className":58626},[886],[888,58628,58629],{"xmlns":890,"display":28047},[892,58630,58631,58686],{},[20735,58632,58633],{"width":28052},[20740,58634,58635,58637,58679,58681],{},[20743,58636],{"width":28057},[20743,58638,58639],{},[895,58640,58641,58643,58645,58647,58649,58651,58653,58655,58657,58659,58661,58663,58665,58667,58669,58671,58673,58675,58677],{},[898,58642,2772],{},[898,58644,2775],{},[1726,58646,1728],{},[898,58648,2772],{},[898,58650,2775],{},[1726,58652,1735],{"stretchy":1734},[898,58654,1724],{},[1726,58656,1762],{"stretchy":1734},[1726,58658,1728],{},[898,58660,10420],{},[898,58662,2775],{},[1726,58664,2099],{},[898,58666,2772],{},[898,58668,40320],{},[898,58670,2775],{},[1726,58672,1735],{"stretchy":1734},[898,58674,1724],{},[1726,58676,1762],{"stretchy":1734},[1726,58678,1742],{"separator":1741},[20743,58680],{"width":28057},[20743,58682,58683],{},[2289,58684,58685],{},"(3.5)",[902,58687,58688],{"encoding":904},"TC = TC(Q) = FC + TVC(Q),\n\\tag{3.5}",[724,58690,4298,58691,58706,58707,10009,58710,12114,58713,58706,58737,10009,58740,58743],{},[883,58692,58694],{"className":58693},[886],[888,58695,58696],{"xmlns":890},[892,58697,58698,58704],{},[895,58699,58700,58702],{},[898,58701,10420],{},[898,58703,2775],{},[902,58705,55471],{"encoding":904}," jsou ",[38,58708,58709],{},"fixní náklady",[38,58711,58712],{},"fixed cost",[883,58714,58716],{"className":58715},[886],[888,58717,58718],{"xmlns":890},[892,58719,58720,58734],{},[895,58721,58722,58724,58726,58728,58730,58732],{},[898,58723,2772],{},[898,58725,40320],{},[898,58727,2775],{},[1726,58729,1735],{"stretchy":1734},[898,58731,1724],{},[1726,58733,1762],{"stretchy":1734},[902,58735,58736],{"encoding":904},"TVC(Q)",[38,58738,58739],{},"celkové variabilní náklady",[38,58741,58742],{},"total variable cost","). Celkové náklady jsou rostoucí, neboť růst množství objektivně vynutí jejich růst.",[198,58745,58747],{"id":58746},"průměrné-náklady","Průměrné náklady",[724,58749,58750,1777,58752,10009,58767,58770],{},[38,58751,58747],{},[883,58753,58755],{"className":58754},[886],[888,58756,58757],{"xmlns":890},[892,58758,58759,58765],{},[895,58760,58761,58763],{},[898,58762,4243],{},[898,58764,2775],{},[902,58766,55540],{"encoding":904},[38,58768,58769],{},"average cost",") jsou podíl celkových nákladů a množství. Z (3.5):",[883,58772,58774],{"className":58773},[886],[888,58775,58776],{"xmlns":890,"display":28047},[892,58777,58778,58857],{},[20735,58779,58780],{"width":28052},[20740,58781,58782,58784,58850,58852],{},[20743,58783],{"width":28057},[20743,58785,58786],{},[895,58787,58788,58790,58792,58794,58796,58798,58800,58802,58804,58806,58816,58818,58828,58830,58848],{},[898,58789,4243],{},[898,58791,2775],{},[1726,58793,1728],{},[898,58795,4243],{},[898,58797,2775],{},[1726,58799,1735],{"stretchy":1734},[898,58801,1724],{},[1726,58803,1762],{"stretchy":1734},[1726,58805,1728],{},[2330,58807,58808,58814],{},[895,58809,58810,58812],{},[898,58811,2772],{},[898,58813,2775],{},[898,58815,1724],{},[1726,58817,1728],{},[2330,58819,58820,58826],{},[895,58821,58822,58824],{},[898,58823,10420],{},[898,58825,2775],{},[898,58827,1724],{},[1726,58829,2099],{},[2330,58831,58832,58846],{},[895,58833,58834,58836,58838,58840,58842,58844],{},[898,58835,2772],{},[898,58837,40320],{},[898,58839,2775],{},[1726,58841,1735],{"stretchy":1734},[898,58843,1724],{},[1726,58845,1762],{"stretchy":1734},[898,58847,1724],{},[1726,58849,1742],{"separator":1741},[20743,58851],{"width":28057},[20743,58853,58854],{},[2289,58855,58856],{},"(3.6)",[902,58858,58859],{"encoding":904},"AC = AC(Q) = \\frac{TC}{Q} = \\frac{FC}{Q} + \\frac{TVC(Q)}{Q},\n\\tag{3.6}",[724,58861,4298,58862,58706,58886,1777,58889,10009,58906,12114,58909,58706,58941,1777,58944,10009,58961,3148],{},[883,58863,58865],{"className":58864},[886],[888,58866,58867],{"xmlns":890},[892,58868,58869,58883],{},[895,58870,58871],{},[2326,58872,58873],{"scriptlevel":2328,"displaystyle":1734},[2330,58874,58875,58881],{},[895,58876,58877,58879],{},[898,58878,10420],{},[898,58880,2775],{},[898,58882,1724],{},[902,58884,58885],{"encoding":904},"\\tfrac{FC}{Q}",[38,58887,58888],{},"průměrné fixní náklady",[883,58890,58892],{"className":58891},[886],[888,58893,58894],{"xmlns":890},[892,58895,58896,58904],{},[895,58897,58898,58900,58902],{},[898,58899,4243],{},[898,58901,10420],{},[898,58903,2775],{},[902,58905,55507],{"encoding":904},[38,58907,58908],{},"average fixed cost",[883,58910,58912],{"className":58911},[886],[888,58913,58914],{"xmlns":890},[892,58915,58916,58938],{},[895,58917,58918],{},[2326,58919,58920],{"scriptlevel":2328,"displaystyle":1734},[2330,58921,58922,58936],{},[895,58923,58924,58926,58928,58930,58932,58934],{},[898,58925,2772],{},[898,58927,40320],{},[898,58929,2775],{},[1726,58931,1735],{"stretchy":1734},[898,58933,1724],{},[1726,58935,1762],{"stretchy":1734},[898,58937,1724],{},[902,58939,58940],{"encoding":904},"\\tfrac{TVC(Q)}{Q}",[38,58942,58943],{},"průměrné variabilní náklady",[883,58945,58947],{"className":58946},[886],[888,58948,58949],{"xmlns":890},[892,58950,58951,58959],{},[895,58952,58953,58955,58957],{},[898,58954,4243],{},[898,58956,40320],{},[898,58958,2775],{},[902,58960,55291],{"encoding":904},[38,58962,58963],{},"average variable cost",[883,58965,58967],{"className":58966},[886],[888,58968,58969],{"xmlns":890,"display":28047},[892,58970,58971,59030],{},[20735,58972,58973],{"width":28052},[20740,58974,58975,58977,59023,59025],{},[20743,58976],{"width":28057},[20743,58978,58979],{},[895,58980,58981,58983,58985,58987,58989,58991,58993,58995,58997,58999,59001,59003,59021],{},[898,58982,4243],{},[898,58984,40320],{},[898,58986,2775],{},[1726,58988,1728],{},[898,58990,4243],{},[898,58992,40320],{},[898,58994,2775],{},[1726,58996,1735],{"stretchy":1734},[898,58998,1724],{},[1726,59000,1762],{"stretchy":1734},[1726,59002,1728],{},[2330,59004,59005,59019],{},[895,59006,59007,59009,59011,59013,59015,59017],{},[898,59008,2772],{},[898,59010,40320],{},[898,59012,2775],{},[1726,59014,1735],{"stretchy":1734},[898,59016,1724],{},[1726,59018,1762],{"stretchy":1734},[898,59020,1724],{},[898,59022,1888],{"mathvariant":2377},[20743,59024],{"width":28057},[20743,59026,59027],{},[2289,59028,59029],{},"(3.7)",[902,59031,59032],{"encoding":904},"AVC = AVC(Q) = \\frac{TVC(Q)}{Q}.\n\\tag{3.7}",[37329,59034,59036],{"id":59035},"příklad-34","Příklad 3.4",[724,59038,59039,57502,59041,3877,59066,56005,59090,3877,59105,59120,59121,1888],{},[38,59040,55967],{},[883,59042,59044],{"className":59043},[886],[888,59045,59046],{"xmlns":890},[892,59047,59048,59063],{},[895,59049,59050,59052,59054,59056,59058,59060],{},[898,59051,10420],{},[898,59053,2775],{},[1726,59055,1728],{},[2133,59057,2281],{},[2289,59059,2984],{},[2133,59061,59062],{},"000",[902,59064,59065],{"encoding":904},"FC = 1\\,000",[883,59067,59069],{"className":59068},[886],[888,59070,59071],{"xmlns":890},[892,59072,59073,59087],{},[895,59074,59075,59077,59079,59081,59083,59085],{},[898,59076,2772],{},[898,59078,40320],{},[898,59080,2775],{},[1726,59082,1728],{},[2133,59084,2352],{},[898,59086,1724],{},[902,59088,59089],{"encoding":904},"TVC = 4Q",[883,59091,59093],{"className":59092},[886],[888,59094,59095],{"xmlns":890},[892,59096,59097,59103],{},[895,59098,59099,59101],{},[898,59100,2772],{},[898,59102,2775],{},[902,59104,3240],{"encoding":904},[883,59106,59108],{"className":59107},[886],[888,59109,59110],{"xmlns":890},[892,59111,59112,59118],{},[895,59113,59114,59116],{},[898,59115,4243],{},[898,59117,2775],{},[902,59119,55540],{"encoding":904}," a jejich chování s rostoucím ",[883,59122,59124],{"className":59123},[886],[888,59125,59126],{"xmlns":890},[892,59127,59128,59132],{},[895,59129,59130],{},[898,59131,1724],{},[902,59133,1724],{"encoding":904},[724,59135,59136,1777,59138,3877,59168,59204,59205,4346,59218,59233,59234,2703],{},[38,59137,22751],{},[883,59139,59141],{"className":59140},[886],[888,59142,59143],{"xmlns":890},[892,59144,59145,59165],{},[895,59146,59147,59149,59151,59153,59155,59157,59159,59161,59163],{},[898,59148,2772],{},[898,59150,2775],{},[1726,59152,1728],{},[2133,59154,2281],{},[2289,59156,2984],{},[2133,59158,59062],{},[1726,59160,2099],{},[2133,59162,2352],{},[898,59164,1724],{},[902,59166,59167],{"encoding":904},"TC = 1\\,000 + 4Q",[883,59169,59171],{"className":59170},[886],[888,59172,59173],{"xmlns":890},[892,59174,59175,59201],{},[895,59176,59177,59179,59181,59183,59197,59199],{},[898,59178,4243],{},[898,59180,2775],{},[1726,59182,1728],{},[2326,59184,59185],{"scriptlevel":2328,"displaystyle":1734},[2330,59186,59187,59195],{},[895,59188,59189,59191,59193],{},[2133,59190,2281],{},[2289,59192,2984],{},[2133,59194,59062],{},[898,59196,1724],{},[1726,59198,2099],{},[2133,59200,2352],{},[902,59202,59203],{"encoding":904},"AC = \\tfrac{1\\,000}{Q} + 4",". S rostoucím ",[883,59206,59208],{"className":59207},[886],[888,59209,59210],{"xmlns":890},[892,59211,59212,59216],{},[895,59213,59214],{},[898,59215,1724],{},[902,59217,1724],{"encoding":904},[883,59219,59221],{"className":59220},[886],[888,59222,59223],{"xmlns":890},[892,59224,59225,59231],{},[895,59226,59227,59229],{},[898,59228,4243],{},[898,59230,2775],{},[902,59232,55540],{"encoding":904}," blíží ",[883,59235,59237],{"className":59236},[886],[888,59238,59239],{"xmlns":890},[892,59240,59241,59245],{},[895,59242,59243],{},[2133,59244,2352],{},[902,59246,2352],{"encoding":904},[883,59248,59250],{"className":59249},[886],[888,59251,59252],{"xmlns":890,"display":28047},[892,59253,59254,59300],{},[895,59255,59256,59273,59295,59297],{},[39877,59257,59258,59265],{},[895,59259,59260,59263],{},[898,59261,59262],{},"lim",[1726,59264,56180],{},[895,59266,59267,59269,59271],{},[898,59268,1724],{},[1726,59270,3120],{},[898,59272,6284],{"mathvariant":2377},[895,59274,59275,59277,59289,59291,59293],{},[1726,59276,1735],{"fence":1741},[2330,59278,59279,59287],{},[895,59280,59281,59283,59285],{},[2133,59282,2281],{},[2289,59284,2984],{},[2133,59286,59062],{},[898,59288,1724],{},[1726,59290,2099],{},[2133,59292,2352],{},[1726,59294,1762],{"fence":1741},[1726,59296,1728],{},[2133,59298,59299],{},"4.",[902,59301,59302],{"encoding":904},"\\lim_{Q \\to \\infty} \\left( \\frac{1\\,000}{Q} + 4 \\right) = 4.",[724,59304,59305,59343,59344,1888],{},[883,59306,59308],{"className":59307},[886],[888,59309,59310],{"xmlns":890},[892,59311,59312,59340],{},[895,59313,59314,59316,59318,59320,59322,59336,59338],{},[898,59315,4243],{},[898,59317,10420],{},[898,59319,2775],{},[1726,59321,1728],{},[2326,59323,59324],{"scriptlevel":2328,"displaystyle":1734},[2330,59325,59326,59334],{},[895,59327,59328,59330,59332],{},[2133,59329,2281],{},[2289,59331,2984],{},[2133,59333,59062],{},[898,59335,1724],{},[1726,59337,3120],{},[2133,59339,2328],{},[902,59341,59342],{"encoding":904},"AFC = \\tfrac{1\\,000}{Q} \\to 0"," s rostoucím ",[883,59345,59347],{"className":59346},[886],[888,59348,59349],{"xmlns":890},[892,59350,59351,59355],{},[895,59352,59353],{},[898,59354,1724],{},[902,59356,1724],{"encoding":904},[724,59358,59359],{},[614,59360,59361,59362,59391,59392,1888],{},"Obrázek 3.5: Přímka ",[883,59363,59365],{"className":59364},[886],[888,59366,59367],{"xmlns":890},[892,59368,59369,59389],{},[895,59370,59371,59373,59375,59377,59379,59381,59383,59385,59387],{},[898,59372,2772],{},[898,59374,2775],{},[1726,59376,1728],{},[2133,59378,2281],{},[2289,59380,2984],{},[2133,59382,59062],{},[1726,59384,2099],{},[2133,59386,2352],{},[898,59388,1724],{},[902,59390,59167],{"encoding":904}," protínající svislou osu ve výši ",[883,59393,59395],{"className":59394},[886],[888,59396,59397],{"xmlns":890},[892,59398,59399,59413],{},[895,59400,59401,59403,59405,59407,59409,59411],{},[898,59402,10420],{},[898,59404,2775],{},[1726,59406,1728],{},[2133,59408,2281],{},[2289,59410,2984],{},[2133,59412,59062],{},[902,59414,59065],{"encoding":904},[724,59416,59417],{},[614,59418,59419,59420,59455,59456,1888],{},"Obrázek 3.6: Hyperbola ",[883,59421,59423],{"className":59422},[886],[888,59424,59425],{"xmlns":890},[892,59426,59427,59453],{},[895,59428,59429,59431,59433,59435,59449,59451],{},[898,59430,4243],{},[898,59432,2775],{},[1726,59434,1728],{},[2326,59436,59437],{"scriptlevel":2328,"displaystyle":1734},[2330,59438,59439,59447],{},[895,59440,59441,59443,59445],{},[2133,59442,2281],{},[2289,59444,2984],{},[2133,59446,59062],{},[898,59448,1724],{},[1726,59450,2099],{},[2133,59452,2352],{},[902,59454,59203],{"encoding":904}," s vodorovnou asymptotou ",[883,59457,59459],{"className":59458},[886],[888,59460,59461],{"xmlns":890},[892,59462,59463,59473],{},[895,59464,59465,59467,59469,59471],{},[898,59466,4243],{},[898,59468,2775],{},[1726,59470,1728],{},[2133,59472,2352],{},[902,59474,59475],{"encoding":904},"AC = 4",[724,59477,59478],{},"Celkové variabilní náklady lze často vyjádřit ve tvaru",[883,59480,59482],{"className":59481},[886],[888,59483,59484],{"xmlns":890,"display":28047},[892,59485,59486,59512],{},[895,59487,59488,59490,59492,59494,59496,59498,59500,59502,59504,59506,59508,59510],{},[898,59489,2772],{},[898,59491,40320],{},[898,59493,2775],{},[1726,59495,1728],{},[898,59497,1724],{},[1726,59499,3174],{},[898,59501,40320],{},[898,59503,2775],{},[1726,59505,1735],{"stretchy":1734},[898,59507,1724],{},[1726,59509,1762],{"stretchy":1734},[1726,59511,1742],{"separator":1741},[902,59513,59514],{"encoding":904},"TVC = Q \\cdot VC(Q),",[724,59516,4298,59517,58706,59545,59548,59549,59579],{},[883,59518,59520],{"className":59519},[886],[888,59521,59522],{"xmlns":890},[892,59523,59524,59542],{},[895,59525,59526,59528,59530,59532,59534,59536,59538,59540],{},[898,59527,40320],{},[898,59529,2775],{},[1726,59531,1728],{},[898,59533,40320],{},[898,59535,2775],{},[1726,59537,1735],{"stretchy":1734},[898,59539,1724],{},[1726,59541,1762],{"stretchy":1734},[902,59543,59544],{"encoding":904},"VC = VC(Q)",[38,59546,59547],{},"variabilní náklady na jednotku množství",". Jsou-li konstantní, ",[883,59550,59552],{"className":59551},[886],[888,59553,59554],{"xmlns":890},[892,59555,59556,59576],{},[895,59557,59558,59560,59562,59564,59566,59568,59570,59572,59574],{},[898,59559,2772],{},[898,59561,40320],{},[898,59563,2775],{},[1726,59565,1735],{"stretchy":1734},[898,59567,1724],{},[1726,59569,1762],{"stretchy":1734},[1726,59571,1728],{},[898,59573,207],{},[898,59575,1724],{},[902,59577,59578],{"encoding":904},"TVC(Q) = aQ"," a nejjednodušší model nákladů má tvar",[883,59581,59583],{"className":59582},[886],[888,59584,59585],{"xmlns":890,"display":28047},[892,59586,59587,59607],{},[895,59588,59589,59591,59593,59595,59597,59599,59601,59603,59605],{},[898,59590,2772],{},[898,59592,2775],{},[1726,59594,1728],{},[898,59596,10420],{},[898,59598,2775],{},[1726,59600,2099],{},[898,59602,207],{},[898,59604,1724],{},[898,59606,1888],{"mathvariant":2377},[902,59608,59609],{"encoding":904},"TC = FC + aQ.",[724,59611,59612,59613,59628,59629,59644,59645,59668,59669,59703,59704,59455,59717,59730,59731,3877,59779,59823,59824,1888],{},"Křivkou ",[883,59614,59616],{"className":59615},[886],[888,59617,59618],{"xmlns":890},[892,59619,59620,59626],{},[895,59621,59622,59624],{},[898,59623,2772],{},[898,59625,2775],{},[902,59627,3240],{"encoding":904}," je přímka se svislým průsečíkem ",[883,59630,59632],{"className":59631},[886],[888,59633,59634],{"xmlns":890},[892,59635,59636,59642],{},[895,59637,59638,59640],{},[898,59639,10420],{},[898,59641,2775],{},[902,59643,55471],{"encoding":904}," a sklonem ",[883,59646,59648],{"className":59647},[886],[888,59649,59650],{"xmlns":890},[892,59651,59652,59665],{},[895,59653,59654,59657,59659,59661,59663],{},[898,59655,59656],{},"tan",[1726,59658,56180],{},[898,59660,18843],{},[1726,59662,1728],{},[898,59664,207],{},[902,59666,59667],{"encoding":904},"\\tan\\alpha = a"," (obrázek 3.7). Průměrné náklady tvoří hyperbolu ",[883,59670,59672],{"className":59671},[886],[888,59673,59674],{"xmlns":890},[892,59675,59676,59700],{},[895,59677,59678,59680,59682,59684,59696,59698],{},[898,59679,4243],{},[898,59681,2775],{},[1726,59683,1728],{},[2326,59685,59686],{"scriptlevel":2328,"displaystyle":1734},[2330,59687,59688,59694],{},[895,59689,59690,59692],{},[898,59691,10420],{},[898,59693,2775],{},[898,59695,1724],{},[1726,59697,2099],{},[898,59699,207],{},[902,59701,59702],{"encoding":904},"AC = \\tfrac{FC}{Q} + a"," tvaru ",[883,59705,59707],{"className":59706},[886],[888,59708,59709],{"xmlns":890},[892,59710,59711,59715],{},[895,59712,59713],{},[898,59714,9779],{},[902,59716,9779],{"encoding":904},[883,59718,59720],{"className":59719},[886],[888,59721,59722],{"xmlns":890},[892,59723,59724,59728],{},[895,59725,59726],{},[898,59727,207],{},[902,59729,207],{"encoding":904}," (obrázek 3.8). Limity ",[883,59732,59734],{"className":59733},[886],[888,59735,59736],{"xmlns":890},[892,59737,59738,59776],{},[895,59739,59740,59760,59772,59774],{},[2275,59741,59742,59748],{},[895,59743,59744,59746],{},[898,59745,59262],{},[1726,59747,56180],{},[895,59749,59750,59752,59754],{},[898,59751,1724],{},[1726,59753,3120],{},[2128,59755,59756,59758],{},[2133,59757,2328],{},[1726,59759,2099],{},[2326,59761,59762],{"scriptlevel":2328,"displaystyle":1734},[2330,59763,59764,59770],{},[895,59765,59766,59768],{},[898,59767,10420],{},[898,59769,2775],{},[898,59771,1724],{},[1726,59773,1728],{},[898,59775,6284],{"mathvariant":2377},[902,59777,59778],{"encoding":904},"\\lim_{Q \\to 0^+} \\tfrac{FC}{Q} = \\infty",[883,59780,59782],{"className":59781},[886],[888,59783,59784],{"xmlns":890},[892,59785,59786,59820],{},[895,59787,59788,59804,59816,59818],{},[2275,59789,59790,59796],{},[895,59791,59792,59794],{},[898,59793,59262],{},[1726,59795,56180],{},[895,59797,59798,59800,59802],{},[898,59799,1724],{},[1726,59801,3120],{},[898,59803,6284],{"mathvariant":2377},[2326,59805,59806],{"scriptlevel":2328,"displaystyle":1734},[2330,59807,59808,59814],{},[895,59809,59810,59812],{},[898,59811,10420],{},[898,59813,2775],{},[898,59815,1724],{},[1726,59817,1728],{},[2133,59819,2328],{},[902,59821,59822],{"encoding":904},"\\lim_{Q \\to \\infty} \\tfrac{FC}{Q} = 0"," vysvětlují, proč s rostoucí produkcí fixní náklady stále méně ovlivňují ",[883,59825,59827],{"className":59826},[886],[888,59828,59829],{"xmlns":890},[892,59830,59831,59837],{},[895,59832,59833,59835],{},[898,59834,4243],{},[898,59836,2775],{},[902,59838,55540],{"encoding":904},[724,59840,59841],{},[614,59842,59843,59844,59859,59860,59875,59876,1888],{},"Obrázek 3.7: Přímka ",[883,59845,59847],{"className":59846},[886],[888,59848,59849],{"xmlns":890},[892,59850,59851,59857],{},[895,59852,59853,59855],{},[898,59854,2772],{},[898,59856,2775],{},[902,59858,3240],{"encoding":904}," s osovým průsečíkem ve výši ",[883,59861,59863],{"className":59862},[886],[888,59864,59865],{"xmlns":890},[892,59866,59867,59873],{},[895,59868,59869,59871],{},[898,59870,10420],{},[898,59872,2775],{},[902,59874,55471],{"encoding":904}," a se sklonem ",[883,59877,59879],{"className":59878},[886],[888,59880,59881],{"xmlns":890},[892,59882,59883,59895],{},[895,59884,59885,59887,59889,59891,59893],{},[898,59886,59656],{},[1726,59888,56180],{},[898,59890,18843],{},[1726,59892,1728],{},[898,59894,207],{},[902,59896,59667],{"encoding":904},[724,59898,59899],{},[614,59900,59901,59902,59917,59918,1888],{},"Obrázek 3.8: Klesající hyperbola ",[883,59903,59905],{"className":59904},[886],[888,59906,59907],{"xmlns":890},[892,59908,59909,59915],{},[895,59910,59911,59913],{},[898,59912,4243],{},[898,59914,2775],{},[902,59916,55540],{"encoding":904}," s vodorovnou asymptotou ve výši ",[883,59919,59921],{"className":59920},[886],[888,59922,59923],{"xmlns":890},[892,59924,59925,59929],{},[895,59926,59927],{},[898,59928,207],{},[902,59930,207],{"encoding":904},[198,59932,59934],{"id":59933},"mezní-náklady","Mezní náklady",[724,59936,59937,1777,59939,10009,59954,59957,59958,59961],{},[38,59938,59934],{},[883,59940,59942],{"className":59941},[886],[888,59943,59944],{"xmlns":890},[892,59945,59946,59952],{},[895,59947,59948,59950],{},[898,59949,2815],{},[898,59951,2775],{},[902,59953,55272],{"encoding":904},[38,59955,59956],{},"marginal cost",") jsou ",[207,59959,1145],{"className":59960,"dataFsResolvedFilePath":764,"href":765},[210]," celkových nákladů podle množství:",[883,59963,59965],{"className":59964},[886],[888,59966,59967],{"xmlns":890,"display":28047},[892,59968,59969,60038],{},[20735,59970,59971],{"width":28052},[20740,59972,59973,59975,60031,60033],{},[20743,59974],{"width":28057},[20743,59976,59977],{},[895,59978,59979,59981,59983,59985,59987,59989,59991,59993,59995,59997,60013,60015,60017,60023,60025,60027,60029],{},[898,59980,2815],{},[898,59982,2775],{},[1726,59984,1728],{},[898,59986,2815],{},[898,59988,2775],{},[1726,59990,1735],{"stretchy":1734},[898,59992,1724],{},[1726,59994,1762],{"stretchy":1734},[1726,59996,1728],{},[2330,59998,59999,60007],{},[895,60000,60001,60003,60005],{},[898,60002,2198],{"mathvariant":2377},[898,60004,2772],{},[898,60006,2775],{},[895,60008,60009,60011],{},[898,60010,2198],{"mathvariant":2377},[898,60012,1724],{},[1726,60014,1728],{},[898,60016,2772],{},[2128,60018,60019,60021],{},[898,60020,2775],{},[1726,60022,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,60024,1735],{"stretchy":1734},[898,60026,1724],{},[1726,60028,1762],{"stretchy":1734},[898,60030,1888],{"mathvariant":2377},[20743,60032],{"width":28057},[20743,60034,60035],{},[2289,60036,60037],{},"(3.8)",[902,60039,60040],{"encoding":904},"MC = MC(Q) = \\frac{\\mathrm{d}TC}{\\mathrm{d}Q} = TC'(Q).\n\\tag{3.8}",[3859,60042,60043],{},[724,60044,60045,60047,60048,60074,60075,60092,60093,1888],{},[883,60046,4145],{}," Intuice — „kolik stojí další kus\"\n",[883,60049,60051],{"className":60050},[886],[888,60052,60053],{"xmlns":890},[892,60054,60055,60071],{},[895,60056,60057,60059,60061,60063,60069],{},[898,60058,2815],{},[898,60060,2775],{},[1726,60062,1735],{"stretchy":1734},[2128,60064,60065,60067],{},[898,60066,1724],{},[1726,60068,4342],{},[1726,60070,1762],{"stretchy":1734},[902,60072,60073],{"encoding":904},"MC(Q^*)"," udává přibližné náklady na výrobu jedné další jednotky, když firma aktuálně produkuje ",[883,60076,60078],{"className":60077},[886],[888,60079,60080],{"xmlns":890},[892,60081,60082,60090],{},[895,60083,60084],{},[2128,60085,60086,60088],{},[898,60087,1724],{},[1726,60089,4342],{},[902,60091,29825],{"encoding":904},". Formálně ",[883,60094,60096],{"className":60095},[886],[888,60097,60098],{"xmlns":890},[892,60099,60100,60152],{},[895,60101,60102,60104,60106,60108,60114,60116,60118,60120,60122,60124,60130,60132,60134,60136,60138,60140,60142,60144,60150],{},[898,60103,2815],{},[898,60105,2775],{},[1726,60107,1735],{"stretchy":1734},[2128,60109,60110,60112],{},[898,60111,1724],{},[1726,60113,4342],{},[1726,60115,1762],{"stretchy":1734},[1726,60117,1880],{},[898,60119,2772],{},[898,60121,2775],{},[1726,60123,1735],{"stretchy":1734},[2128,60125,60126,60128],{},[898,60127,1724],{},[1726,60129,4342],{},[1726,60131,2099],{},[2133,60133,2281],{},[1726,60135,1762],{"stretchy":1734},[1726,60137,2228],{},[898,60139,2772],{},[898,60141,2775],{},[1726,60143,1735],{"stretchy":1734},[2128,60145,60146,60148],{},[898,60147,1724],{},[1726,60149,4342],{},[1726,60151,1762],{"stretchy":1734},[902,60153,60154],{"encoding":904},"MC(Q^*) \\approx TC(Q^* + 1) - TC(Q^*)",[724,60156,60157,60158,2703],{},"Analogicky ke vztahu (3.3) platí pro odhad změny ",[883,60159,60161],{"className":60160},[886],[888,60162,60163],{"xmlns":890},[892,60164,60165,60173],{},[895,60166,60167,60169,60171],{},[898,60168,2886],{"mathvariant":2377},[898,60170,2772],{},[898,60172,2775],{},[902,60174,60175],{"encoding":904},"\\Delta TC",[883,60177,60179],{"className":60178},[886],[888,60180,60181],{"xmlns":890,"display":28047},[892,60182,60183,60252],{},[20735,60184,60185],{"width":28052},[20740,60186,60187,60189,60245,60247],{},[20743,60188],{"width":28057},[20743,60190,60191],{},[895,60192,60193,60195,60197,60199,60201,60203,60205,60207,60209,60211,60213,60215,60217,60219,60225,60227,60229,60231,60233,60235,60237,60239,60241,60243],{},[898,60194,2886],{"mathvariant":2377},[898,60196,2772],{},[898,60198,2775],{},[2289,60200,3974],{},[1726,60202,1880],{},[2289,60204,3974],{},[898,60206,2198],{"mathvariant":2377},[898,60208,2772],{},[898,60210,2775],{},[1726,60212,1728],{},[1726,60214,1735],{"stretchy":1734},[898,60216,2772],{},[898,60218,2775],{},[2128,60220,60221,60223],{},[1726,60222,1762],{"stretchy":1734},[1726,60224,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[2289,60226,2984],{},[898,60228,2198],{"mathvariant":2377},[898,60230,1724],{},[1726,60232,1728],{},[898,60234,2815],{},[898,60236,2775],{},[2289,60238,2984],{},[898,60240,2198],{"mathvariant":2377},[898,60242,1724],{},[1726,60244,1742],{"separator":1741},[20743,60246],{"width":28057},[20743,60248,60249],{},[2289,60250,60251],{},"(3.9)",[902,60253,60254],{"encoding":904},"\\Delta TC \\;\\approx\\; \\mathrm{d}TC = (TC)' \\, \\mathrm{d}Q = MC \\, \\mathrm{d}Q,\n\\tag{3.9}",[724,60256,57291],{},[883,60258,60260],{"className":60259},[886],[888,60261,60262],{"xmlns":890,"display":28047},[892,60263,60264,60362],{},[895,60265,60266,60304,60306,60308,60310,60332,60334,60360],{},[895,60267,60268,60270,60276,60278,60284,60287,60293,60296],{},[2289,60269,57305],{},[8372,60271,60272,60274],{"accent":1741},[2289,60273,45713],{},[1726,60275,25039],{},[2289,60277,57314],{},[8372,60279,60280,60282],{"accent":1741},[2289,60281,2003],{},[1726,60283,24958],{},[2289,60285,60286],{},"ch n",[8372,60288,60289,60291],{"accent":1741},[2289,60290,207],{},[1726,60292,24958],{},[2289,60294,60295],{},"klad",[8372,60297,60298,60301],{"accent":1741},[2289,60299,60300],{},"u",[1726,60302,60303],{},"˚",[2289,60305,3974],{},[1726,60307,1880],{},[2289,60309,3974],{},[895,60311,60312,60314,60320,60323,60329],{},[2289,60313,57349],{},[8372,60315,60316,60318],{"accent":1741},[2289,60317,25027],{},[1726,60319,24958],{},[2289,60321,60322],{}," n",[8372,60324,60325,60327],{"accent":1741},[2289,60326,207],{},[1726,60328,24958],{},[2289,60330,60331],{},"klady",[1726,60333,57376],{},[895,60335,60336,60338,60344,60346,60352,60354],{},[2289,60337,57305],{},[8372,60339,60340,60342],{"accent":1741},[2289,60341,45713],{},[1726,60343,25039],{},[2289,60345,57389],{},[8372,60347,60348,60350],{"accent":1741},[2289,60349,9579],{},[1726,60351,25039],{},[2289,60353,57398],{},[8372,60355,60356,60358],{"accent":1741},[2289,60357,25027],{},[1726,60359,24958],{},[898,60361,1888],{"mathvariant":2377},[902,60363,60364],{"encoding":904},"\\text{změna celkových nákladů} \\;\\approx\\; \\text{mezní náklady} \\times \\text{změna množství}.",[37329,60366,60368],{"id":60367},"příklad-35","Příklad 3.5",[724,60370,60371,57502,60373,56005,60409,60424,60425,60440,60441,2670,60454,2684,60467,60480,60481,2684,60494,1888],{},[38,60372,55967],{},[883,60374,60376],{"className":60375},[886],[888,60377,60378],{"xmlns":890},[892,60379,60380,60406],{},[895,60381,60382,60384,60386,60388,60390,60392,60394,60396,60398,60400],{},[898,60383,2772],{},[898,60385,2775],{},[1726,60387,1728],{},[2133,60389,8363],{},[1726,60391,2099],{},[2133,60393,2238],{},[898,60395,1724],{},[1726,60397,2099],{},[2133,60399,2135],{},[2128,60401,60402,60404],{},[898,60403,1724],{},[2133,60405,2135],{},[902,60407,60408],{"encoding":904},"TC = 200 + 6Q + 2Q^2",[883,60410,60412],{"className":60411},[886],[888,60413,60414],{"xmlns":890},[892,60415,60416,60422],{},[895,60417,60418,60420],{},[898,60419,2815],{},[898,60421,2775],{},[902,60423,55272],{"encoding":904}," a odhadněte změny ",[883,60426,60428],{"className":60427},[886],[888,60429,60430],{"xmlns":890},[892,60431,60432,60438],{},[895,60433,60434,60436],{},[898,60435,2772],{},[898,60437,2775],{},[902,60439,3240],{"encoding":904}," při změnách ",[883,60442,60444],{"className":60443},[886],[888,60445,60446],{"xmlns":890},[892,60447,60448,60452],{},[895,60449,60450],{},[898,60451,1724],{},[902,60453,1724],{"encoding":904},[883,60455,60457],{"className":60456},[886],[888,60458,60459],{"xmlns":890},[892,60460,60461,60465],{},[895,60462,60463],{},[2133,60464,36225],{},[902,60466,36225],{"encoding":904},[883,60468,60470],{"className":60469},[886],[888,60471,60472],{"xmlns":890},[892,60473,60474,60478],{},[895,60475,60476],{},[2133,60477,41843],{},[902,60479,41843],{"encoding":904}," a z ",[883,60482,60484],{"className":60483},[886],[888,60485,60486],{"xmlns":890},[892,60487,60488,60492],{},[895,60489,60490],{},[2133,60491,36225],{},[902,60493,36225],{"encoding":904},[883,60495,60497],{"className":60496},[886],[888,60498,60499],{"xmlns":890},[892,60500,60501,60505],{},[895,60502,60503],{},[2133,60504,3506],{},[902,60506,3506],{"encoding":904},[724,60508,60509,1777,60511,2924,60537,1343,60564,60591,60592,60607,60608,60623,60624,60651,60652,60672,60673,20512,60694,60750,60751,2670,60764,2684,60777,8088,60790,1888],{},[38,60510,22751],{},[883,60512,60514],{"className":60513},[886],[888,60515,60516],{"xmlns":890},[892,60517,60518,60534],{},[895,60519,60520,60522,60524,60526,60528,60530,60532],{},[898,60521,2815],{},[898,60523,2775],{},[1726,60525,1728],{},[2133,60527,2238],{},[1726,60529,2099],{},[2133,60531,2352],{},[898,60533,1724],{},[902,60535,60536],{"encoding":904},"MC = 6 + 4Q",[883,60538,60540],{"className":60539},[886],[888,60541,60542],{"xmlns":890},[892,60543,60544,60561],{},[895,60545,60546,60548,60550,60552,60554,60556,60558],{},[898,60547,2815],{},[898,60549,2775],{},[1726,60551,1735],{"stretchy":1734},[2133,60553,36225],{},[1726,60555,1762],{"stretchy":1734},[1726,60557,1728],{},[2133,60559,60560],{},"66",[902,60562,60563],{"encoding":904},"MC(15) = 66",[883,60565,60567],{"className":60566},[886],[888,60568,60569],{"xmlns":890},[892,60570,60571,60588],{},[895,60572,60573,60575,60577,60579,60581,60583,60585],{},[898,60574,2815],{},[898,60576,2775],{},[1726,60578,1735],{"stretchy":1734},[2133,60580,9021],{},[1726,60582,1762],{"stretchy":1734},[1726,60584,1728],{},[2133,60586,60587],{},"86",[902,60589,60590],{"encoding":904},"MC(20) = 86",": s růstem množství se rychlost změny ",[883,60593,60595],{"className":60594},[886],[888,60596,60597],{"xmlns":890},[892,60598,60599,60605],{},[895,60600,60601,60603],{},[898,60602,2772],{},[898,60604,2775],{},[902,60606,3240],{"encoding":904}," zvyšuje (",[883,60609,60611],{"className":60610},[886],[888,60612,60613],{"xmlns":890},[892,60614,60615,60621],{},[895,60616,60617,60619],{},[898,60618,2815],{},[898,60620,2775],{},[902,60622,55272],{"encoding":904}," je rostoucí). Z ",[883,60625,60627],{"className":60626},[886],[888,60628,60629],{"xmlns":890},[892,60630,60631,60648],{},[895,60632,60633,60635,60637,60639,60641,60643,60645],{},[898,60634,2772],{},[898,60636,2775],{},[1726,60638,1735],{"stretchy":1734},[2133,60640,36225],{},[1726,60642,1762],{"stretchy":1734},[1726,60644,1728],{},[2133,60646,60647],{},"740",[902,60649,60650],{"encoding":904},"TC(15) = 740"," se po přírůstku ",[883,60653,60655],{"className":60654},[886],[888,60656,60657],{"xmlns":890},[892,60658,60659,60669],{},[895,60660,60661,60663,60665,60667],{},[898,60662,2198],{"mathvariant":2377},[898,60664,1724],{},[1726,60666,1728],{},[2133,60668,2281],{},[902,60670,60671],{"encoding":904},"\\mathrm{d}Q = 1"," předpokládá ",[883,60674,60676],{"className":60675},[886],[888,60677,60678],{"xmlns":890},[892,60679,60680,60691],{},[895,60681,60682,60684,60686,60688],{},[898,60683,2772],{},[898,60685,2775],{},[1726,60687,1880],{},[2133,60689,60690],{},"806",[902,60692,60693],{"encoding":904},"TC \\approx 806",[883,60695,60697],{"className":60696},[886],[888,60698,60699],{"xmlns":890},[892,60700,60701,60747],{},[895,60702,60703,60705,60707,60709,60711,60713,60715,60717,60719,60721,60723,60725,60727,60729,60731,60733,60735,60738,60740,60742,60744],{},[898,60704,2886],{"mathvariant":2377},[898,60706,2772],{},[898,60708,2775],{},[1726,60710,1728],{},[898,60712,2772],{},[898,60714,2775],{},[1726,60716,1735],{"stretchy":1734},[2133,60718,41843],{},[1726,60720,1762],{"stretchy":1734},[1726,60722,2228],{},[898,60724,2772],{},[898,60726,2775],{},[1726,60728,1735],{"stretchy":1734},[2133,60730,36225],{},[1726,60732,1762],{"stretchy":1734},[1726,60734,1728],{},[2133,60736,60737],{},"808",[1726,60739,2228],{},[2133,60741,60647],{},[1726,60743,1728],{},[2133,60745,60746],{},"68",[902,60748,60749],{"encoding":904},"\\Delta TC = TC(16) - TC(15) = 808 - 740 = 68",". Při poklesu ",[883,60752,60754],{"className":60753},[886],[888,60755,60756],{"xmlns":890},[892,60757,60758,60762],{},[895,60759,60760],{},[898,60761,1724],{},[902,60763,1724],{"encoding":904},[883,60765,60767],{"className":60766},[886],[888,60768,60769],{"xmlns":890},[892,60770,60771,60775],{},[895,60772,60773],{},[2133,60774,36225],{},[902,60776,36225],{"encoding":904},[883,60778,60780],{"className":60779},[886],[888,60781,60782],{"xmlns":890},[892,60783,60784,60788],{},[895,60785,60786],{},[2133,60787,3506],{},[902,60789,3506],{"encoding":904},[883,60791,60793],{"className":60792},[886],[888,60794,60795],{"xmlns":890},[892,60796,60797,60826],{},[895,60798,60799,60801,60803,60805,60807,60809,60811,60813,60815,60817,60819,60821,60823],{},[898,60800,2886],{"mathvariant":2377},[898,60802,2772],{},[898,60804,2775],{},[1726,60806,1880],{},[2133,60808,60560],{},[1726,60810,3174],{},[1726,60812,1735],{"stretchy":1734},[1726,60814,2228],{},[2133,60816,2177],{},[1726,60818,1762],{"stretchy":1734},[1726,60820,1728],{},[1726,60822,2228],{},[2133,60824,60825],{},"198",[902,60827,60828],{"encoding":904},"\\Delta TC \\approx 66 \\cdot (-3) = -198",[198,60830,60832],{"id":60831},"kubická-nákladová-funkce","Kubická nákladová funkce",[724,60834,60835],{},"V ekonomicky reálných situacích mají křivky nákladů charakteristické vazby a tvary.",[37329,60837,60839],{"id":60838},"příklad-36","Příklad 3.6",[724,60841,60842,57502,60844,60888],{},[38,60843,55967],{},[883,60845,60847],{"className":60846},[886],[888,60848,60849],{"xmlns":890},[892,60850,60851,60885],{},[895,60852,60853,60855,60857,60859,60861,60863,60865,60867,60869,60871,60877,60879],{},[898,60854,2772],{},[898,60856,2775],{},[1726,60858,1728],{},[2133,60860,3087],{},[1726,60862,2099],{},[2133,60864,4991],{},[898,60866,1724],{},[1726,60868,2228],{},[2133,60870,2231],{},[2128,60872,60873,60875],{},[898,60874,1724],{},[2133,60876,2135],{},[1726,60878,2099],{},[2128,60880,60881,60883],{},[898,60882,1724],{},[2133,60884,2177],{},[902,60886,60887],{"encoding":904},"TC = 100 + 25Q - 5Q^2 + Q^3"," odvoďte všechny nákladové charakteristiky.",[724,60890,60891],{},[38,60892,22751],{},[883,60894,60896],{"className":60895},[886],[888,60897,60898],{"xmlns":890,"display":28047},[892,60899,60900,61144],{},[20735,60901,60902,60928,60976,61010,61052,61102],{"rowspacing":20737,"columnalign":20738,"columnspacing":2378},[20740,60903,60904,60914],{},[20743,60905,60906],{},[2326,60907,60908],{"scriptlevel":2328,"displaystyle":1741},[895,60909,60910,60912],{},[898,60911,10420],{},[898,60913,2775],{},[20743,60915,60916],{},[2326,60917,60918],{"scriptlevel":2328,"displaystyle":1741},[895,60919,60920,60922,60924,60926],{},[895,60921],{},[1726,60923,1728],{},[2133,60925,3087],{},[1726,60927,1742],{"separator":1741},[20740,60929,60930,60942],{},[20743,60931,60932],{},[2326,60933,60934],{"scriptlevel":2328,"displaystyle":1741},[895,60935,60936,60938,60940],{},[898,60937,2772],{},[898,60939,40320],{},[898,60941,2775],{},[20743,60943,60944],{},[2326,60945,60946],{"scriptlevel":2328,"displaystyle":1741},[895,60947,60948,60950,60952,60954,60956,60958,60960,60966,60968,60974],{},[895,60949],{},[1726,60951,1728],{},[2133,60953,4991],{},[898,60955,1724],{},[1726,60957,2228],{},[2133,60959,2231],{},[2128,60961,60962,60964],{},[898,60963,1724],{},[2133,60965,2135],{},[1726,60967,2099],{},[2128,60969,60970,60972],{},[898,60971,1724],{},[2133,60973,2177],{},[1726,60975,1742],{"separator":1741},[20740,60977,60978,60990],{},[20743,60979,60980],{},[2326,60981,60982],{"scriptlevel":2328,"displaystyle":1741},[895,60983,60984,60986,60988],{},[898,60985,4243],{},[898,60987,10420],{},[898,60989,2775],{},[20743,60991,60992],{},[2326,60993,60994],{"scriptlevel":2328,"displaystyle":1741},[895,60995,60996,60998,61000,61008],{},[895,60997],{},[1726,60999,1728],{},[2326,61001,61002],{"scriptlevel":2328,"displaystyle":1734},[2330,61003,61004,61006],{},[2133,61005,3087],{},[898,61007,1724],{},[1726,61009,1742],{"separator":1741},[20740,61011,61012,61024],{},[20743,61013,61014],{},[2326,61015,61016],{"scriptlevel":2328,"displaystyle":1741},[895,61017,61018,61020,61022],{},[898,61019,4243],{},[898,61021,40320],{},[898,61023,2775],{},[20743,61025,61026],{},[2326,61027,61028],{"scriptlevel":2328,"displaystyle":1741},[895,61029,61030,61032,61034,61036,61038,61040,61042,61044,61050],{},[895,61031],{},[1726,61033,1728],{},[2133,61035,4991],{},[1726,61037,2228],{},[2133,61039,2231],{},[898,61041,1724],{},[1726,61043,2099],{},[2128,61045,61046,61048],{},[898,61047,1724],{},[2133,61049,2135],{},[1726,61051,1742],{"separator":1741},[20740,61053,61054,61064],{},[20743,61055,61056],{},[2326,61057,61058],{"scriptlevel":2328,"displaystyle":1741},[895,61059,61060,61062],{},[898,61061,4243],{},[898,61063,2775],{},[20743,61065,61066],{},[2326,61067,61068],{"scriptlevel":2328,"displaystyle":1741},[895,61069,61070,61072,61074,61082,61084,61086,61088,61090,61092,61094,61100],{},[895,61071],{},[1726,61073,1728],{},[2326,61075,61076],{"scriptlevel":2328,"displaystyle":1734},[2330,61077,61078,61080],{},[2133,61079,3087],{},[898,61081,1724],{},[1726,61083,2099],{},[2133,61085,4991],{},[1726,61087,2228],{},[2133,61089,2231],{},[898,61091,1724],{},[1726,61093,2099],{},[2128,61095,61096,61098],{},[898,61097,1724],{},[2133,61099,2135],{},[1726,61101,1742],{"separator":1741},[20740,61103,61104,61114],{},[20743,61105,61106],{},[2326,61107,61108],{"scriptlevel":2328,"displaystyle":1741},[895,61109,61110,61112],{},[898,61111,2815],{},[898,61113,2775],{},[20743,61115,61116],{},[2326,61117,61118],{"scriptlevel":2328,"displaystyle":1741},[895,61119,61120,61122,61124,61126,61128,61130,61132,61134,61136,61142],{},[895,61121],{},[1726,61123,1728],{},[2133,61125,4991],{},[1726,61127,2228],{},[2133,61129,2860],{},[898,61131,1724],{},[1726,61133,2099],{},[2133,61135,2177],{},[2128,61137,61138,61140],{},[898,61139,1724],{},[2133,61141,2135],{},[898,61143,1888],{"mathvariant":2377},[902,61145,61146],{"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}",[724,61148,61149,61150,15776,61165,15776,61180,61195,61196,61211,61212,1343,61230,61211,61247,1343,61265,61211,61280,61298],{},"Význačné body ",[883,61151,61153],{"className":61152},[886],[888,61154,61155],{"xmlns":890},[892,61156,61157,61162],{},[895,61158,61159],{},[2133,61160,61161],{},"1,67",[902,61163,61164],{"encoding":904},"1{,}67",[883,61166,61168],{"className":61167},[886],[888,61169,61170],{"xmlns":890},[892,61171,61172,61177],{},[895,61173,61174],{},[2133,61175,61176],{},"2,50",[902,61178,61179],{"encoding":904},"2{,}50",[883,61181,61183],{"className":61182},[886],[888,61184,61185],{"xmlns":890},[892,61186,61187,61192],{},[895,61188,61189],{},[2133,61190,61191],{},"4,73",[902,61193,61194],{"encoding":904},"4{,}73"," odpovídají: ",[883,61197,61199],{"className":61198},[886],[888,61200,61201],{"xmlns":890},[892,61202,61203,61209],{},[895,61204,61205,61207],{},[898,61206,2815],{},[898,61208,2775],{},[902,61210,55272],{"encoding":904}," minimum v ",[883,61213,61215],{"className":61214},[886],[888,61216,61217],{"xmlns":890},[892,61218,61219,61227],{},[895,61220,61221,61223,61225],{},[898,61222,1724],{},[1726,61224,5887],{},[2133,61226,61161],{},[902,61228,61229],{"encoding":904},"Q \\doteq 1{,}67",[883,61231,61233],{"className":61232},[886],[888,61234,61235],{"xmlns":890},[892,61236,61237,61245],{},[895,61238,61239,61241,61243],{},[898,61240,4243],{},[898,61242,40320],{},[898,61244,2775],{},[902,61246,55291],{"encoding":904},[883,61248,61250],{"className":61249},[886],[888,61251,61252],{"xmlns":890},[892,61253,61254,61262],{},[895,61255,61256,61258,61260],{},[898,61257,1724],{},[1726,61259,1728],{},[2133,61261,61176],{},[902,61263,61264],{"encoding":904},"Q = 2{,}50",[883,61266,61268],{"className":61267},[886],[888,61269,61270],{"xmlns":890},[892,61271,61272,61278],{},[895,61273,61274,61276],{},[898,61275,4243],{},[898,61277,2775],{},[902,61279,55540],{"encoding":904},[883,61281,61283],{"className":61282},[886],[888,61284,61285],{"xmlns":890},[892,61286,61287,61295],{},[895,61288,61289,61291,61293],{},[898,61290,1724],{},[1726,61292,5887],{},[2133,61294,61191],{},[902,61296,61297],{"encoding":904},"Q \\doteq 4{,}73"," (téma úlohy 3.11).",[724,61300,61301],{},[1647,61302],{"alt":61303,"className":61304,"src":61305},"imek-ac-avc-mc",[210,1651],"\u002Fwiki-assets\u002Fimek-ac-avc-mc.jpeg",[724,61307,61308],{},[614,61309,61310,61311,3877,61326,61343,61344,15776,61363,61378],{},"Obrázek 3.9: Kubické křivky ",[883,61312,61314],{"className":61313},[886],[888,61315,61316],{"xmlns":890},[892,61317,61318,61324],{},[895,61319,61320,61322],{},[898,61321,2772],{},[898,61323,2775],{},[902,61325,3240],{"encoding":904},[883,61327,61329],{"className":61328},[886],[888,61330,61331],{"xmlns":890},[892,61332,61333,61341],{},[895,61334,61335,61337,61339],{},[898,61336,2772],{},[898,61338,40320],{},[898,61340,2775],{},[902,61342,55489],{"encoding":904}," rostoucí od bodu ",[883,61345,61347],{"className":61346},[886],[888,61348,61349],{"xmlns":890},[892,61350,61351,61361],{},[895,61352,61353,61355,61357,61359],{},[898,61354,10420],{},[898,61356,2775],{},[1726,61358,1728],{},[2133,61360,3087],{},[902,61362,11618],{"encoding":904},[883,61364,61366],{"className":61365},[886],[888,61367,61368],{"xmlns":890},[892,61369,61370,61376],{},[895,61371,61372,61374],{},[898,61373,10420],{},[898,61375,2775],{},[902,61377,55471],{"encoding":904}," je vodorovná přímka.",[724,61380,61381],{},[614,61382,61383,61384,1343,61399,1343,61416,29182,61431,61444,61445,2924,61462,61477,61478,6177,61495,61510,61511,26170,61524,1343,61537,1343,61550,1888],{},"Obrázek 3.10: Křivky ",[883,61385,61387],{"className":61386},[886],[888,61388,61389],{"xmlns":890},[892,61390,61391,61397],{},[895,61392,61393,61395],{},[898,61394,4243],{},[898,61396,2775],{},[902,61398,55540],{"encoding":904},[883,61400,61402],{"className":61401},[886],[888,61403,61404],{"xmlns":890},[892,61405,61406,61414],{},[895,61407,61408,61410,61412],{},[898,61409,4243],{},[898,61411,40320],{},[898,61413,2775],{},[902,61415,55291],{"encoding":904},[883,61417,61419],{"className":61418},[886],[888,61420,61421],{"xmlns":890},[892,61422,61423,61429],{},[895,61424,61425,61427],{},[898,61426,2815],{},[898,61428,2775],{},[902,61430,55272],{"encoding":904},[883,61432,61434],{"className":61433},[886],[888,61435,61436],{"xmlns":890},[892,61437,61438,61442],{},[895,61439,61440],{},[898,61441,900],{},[902,61443,900],{"encoding":904}," a klesající hyperbola ",[883,61446,61448],{"className":61447},[886],[888,61449,61450],{"xmlns":890},[892,61451,61452,61460],{},[895,61453,61454,61456,61458],{},[898,61455,4243],{},[898,61457,10420],{},[898,61459,2775],{},[902,61461,55507],{"encoding":904},[883,61463,61465],{"className":61464},[886],[888,61466,61467],{"xmlns":890},[892,61468,61469,61475],{},[895,61470,61471,61473],{},[898,61472,2815],{},[898,61474,2775],{},[902,61476,55272],{"encoding":904}," protíná ",[883,61479,61481],{"className":61480},[886],[888,61482,61483],{"xmlns":890},[892,61484,61485,61493],{},[895,61486,61487,61489,61491],{},[898,61488,4243],{},[898,61490,40320],{},[898,61492,2775],{},[902,61494,55291],{"encoding":904},[883,61496,61498],{"className":61497},[886],[888,61499,61500],{"xmlns":890},[892,61501,61502,61508],{},[895,61503,61504,61506],{},[898,61505,4243],{},[898,61507,2775],{},[902,61509,55540],{"encoding":904}," zdola v jejich minimech; význačné hodnoty na ose ",[883,61512,61514],{"className":61513},[886],[888,61515,61516],{"xmlns":890},[892,61517,61518,61522],{},[895,61519,61520],{},[898,61521,1724],{},[902,61523,1724],{"encoding":904},[883,61525,61527],{"className":61526},[886],[888,61528,61529],{"xmlns":890},[892,61530,61531,61535],{},[895,61532,61533],{},[2133,61534,61161],{},[902,61536,61164],{"encoding":904},[883,61538,61540],{"className":61539},[886],[888,61541,61542],{"xmlns":890},[892,61543,61544,61548],{},[895,61545,61546],{},[2133,61547,61176],{},[902,61549,61179],{"encoding":904},[883,61551,61553],{"className":61552},[886],[888,61554,61555],{"xmlns":890},[892,61556,61557,61561],{},[895,61558,61559],{},[2133,61560,61191],{},[902,61562,61194],{"encoding":904},[724,61564,61565],{},[38,61566,61567],{},"Standardní vlastnosti:",[120,61569,61570,61605,61669,61737,61787,61807],{},[123,61571,61572,3877,61587,61604],{},[883,61573,61575],{"className":61574},[886],[888,61576,61577],{"xmlns":890},[892,61578,61579,61585],{},[895,61580,61581,61583],{},[898,61582,2772],{},[898,61584,2775],{},[902,61586,3240],{"encoding":904},[883,61588,61590],{"className":61589},[886],[888,61591,61592],{"xmlns":890},[892,61593,61594,61602],{},[895,61595,61596,61598,61600],{},[898,61597,2772],{},[898,61599,40320],{},[898,61601,2775],{},[902,61603,55489],{"encoding":904}," jsou kubické funkce;",[123,61606,61607,1343,61622,1343,61639,61654,61655,61668],{},[883,61608,61610],{"className":61609},[886],[888,61611,61612],{"xmlns":890},[892,61613,61614,61620],{},[895,61615,61616,61618],{},[898,61617,4243],{},[898,61619,2775],{},[902,61621,55540],{"encoding":904},[883,61623,61625],{"className":61624},[886],[888,61626,61627],{"xmlns":890},[892,61628,61629,61637],{},[895,61630,61631,61633,61635],{},[898,61632,4243],{},[898,61634,40320],{},[898,61636,2775],{},[902,61638,55291],{"encoding":904},[883,61640,61642],{"className":61641},[886],[888,61643,61644],{"xmlns":890},[892,61645,61646,61652],{},[895,61647,61648,61650],{},[898,61649,2815],{},[898,61651,2775],{},[902,61653,55272],{"encoding":904}," jsou křivky tvaru ",[883,61656,61658],{"className":61657},[886],[888,61659,61660],{"xmlns":890},[892,61661,61662,61666],{},[895,61663,61664],{},[898,61665,900],{},[902,61667,900],{"encoding":904}," (nejprve klesají, po minimu rostou);",[123,61670,61671,61686,61687,1343,61704,61721,61722,8411],{},[883,61672,61674],{"className":61673},[886],[888,61675,61676],{"xmlns":890},[892,61677,61678,61684],{},[895,61679,61680,61682],{},[898,61681,2815],{},[898,61683,2775],{},[902,61685,55272],{"encoding":904}," nabývá minima před ",[883,61688,61690],{"className":61689},[886],[888,61691,61692],{"xmlns":890},[892,61693,61694,61702],{},[895,61695,61696,61698,61700],{},[898,61697,4243],{},[898,61699,40320],{},[898,61701,2775],{},[902,61703,55291],{"encoding":904},[883,61705,61707],{"className":61706},[886],[888,61708,61709],{"xmlns":890},[892,61710,61711,61719],{},[895,61712,61713,61715,61717],{},[898,61714,4243],{},[898,61716,40320],{},[898,61718,2775],{},[902,61720,55291],{"encoding":904}," před ",[883,61723,61725],{"className":61724},[886],[888,61726,61727],{"xmlns":890},[892,61728,61729,61735],{},[895,61730,61731,61733],{},[898,61732,4243],{},[898,61734,2775],{},[902,61736,55540],{"encoding":904},[123,61738,61739,61477,61754,3877,61769,61786],{},[883,61740,61742],{"className":61741},[886],[888,61743,61744],{"xmlns":890},[892,61745,61746,61752],{},[895,61747,61748,61750],{},[898,61749,2815],{},[898,61751,2775],{},[902,61753,55272],{"encoding":904},[883,61755,61757],{"className":61756},[886],[888,61758,61759],{"xmlns":890},[892,61760,61761,61767],{},[895,61762,61763,61765],{},[898,61764,4243],{},[898,61766,2775],{},[902,61768,55540],{"encoding":904},[883,61770,61772],{"className":61771},[886],[888,61773,61774],{"xmlns":890},[892,61775,61776,61784],{},[895,61777,61778,61780,61782],{},[898,61779,4243],{},[898,61781,40320],{},[898,61783,2775],{},[902,61785,55291],{"encoding":904}," zdola právě v jejich minimech;",[123,61788,61789,61806],{},[883,61790,61792],{"className":61791},[886],[888,61793,61794],{"xmlns":890},[892,61795,61796,61804],{},[895,61797,61798,61800,61802],{},[898,61799,4243],{},[898,61801,10420],{},[898,61803,2775],{},[902,61805,55507],{"encoding":904}," je hyperbola, stále klesající;",[123,61808,61809,61841,61842,3877,61857,61874,61875,61888,61889,1847],{},[883,61810,61812],{"className":61811},[886],[888,61813,61814],{"xmlns":890},[892,61815,61816,61838],{},[895,61817,61818,61820,61822,61824,61826,61828,61830,61832,61834,61836],{},[898,61819,4243],{},[898,61821,2775],{},[1726,61823,1728],{},[898,61825,4243],{},[898,61827,10420],{},[898,61829,2775],{},[1726,61831,2099],{},[898,61833,4243],{},[898,61835,40320],{},[898,61837,2775],{},[902,61839,61840],{"encoding":904},"AC = AFC + AVC","; vzdálenost mezi ",[883,61843,61845],{"className":61844},[886],[888,61846,61847],{"xmlns":890},[892,61848,61849,61855],{},[895,61850,61851,61853],{},[898,61852,4243],{},[898,61854,2775],{},[902,61856,55540],{"encoding":904},[883,61858,61860],{"className":61859},[886],[888,61861,61862],{"xmlns":890},[892,61863,61864,61872],{},[895,61865,61866,61868,61870],{},[898,61867,4243],{},[898,61869,40320],{},[898,61871,2775],{},[902,61873,55291],{"encoding":904}," klesá s rostoucím ",[883,61876,61878],{"className":61877},[886],[888,61879,61880],{"xmlns":890},[892,61881,61882,61886],{},[895,61883,61884],{},[898,61885,1724],{},[902,61887,1724],{"encoding":904}," (protože ",[883,61890,61892],{"className":61891},[886],[888,61893,61894],{"xmlns":890},[892,61895,61896,61908],{},[895,61897,61898,61900,61902,61904,61906],{},[898,61899,4243],{},[898,61901,10420],{},[898,61903,2775],{},[1726,61905,3120],{},[2133,61907,2328],{},[902,61909,61910],{"encoding":904},"AFC \\to 0",[115,61912,61914],{"id":61913},"princip-minimalizace-průměrných-nákladů","Princip minimalizace průměrných nákladů",[724,61916,61917,61918,61921,61922,61937],{},"Častou optimalizační úlohou je ",[38,61919,61920],{},"minimalizace průměrných nákladů"," — stanovení produkce, pro niž je ",[883,61923,61925],{"className":61924},[886],[888,61926,61927],{"xmlns":890},[892,61928,61929,61935],{},[895,61930,61931,61933],{},[898,61932,4243],{},[898,61934,2775],{},[902,61936,55540],{"encoding":904}," minimální.",[198,61939,16394],{"id":16393},[724,61941,61942,61943,61960],{},"Mají-li průměrné náklady minimum v bodě ",[883,61944,61946],{"className":61945},[886],[888,61947,61948],{"xmlns":890},[892,61949,61950,61958],{},[895,61951,61952],{},[2275,61953,61954,61956],{},[898,61955,1724],{},[2133,61957,2328],{},[902,61959,38289],{"encoding":904},", pak platí",[883,61962,61964],{"className":61963},[886],[888,61965,61966],{"xmlns":890,"display":28047},[892,61967,61968,62017],{},[20735,61969,61970],{"width":28052},[20740,61971,61972,61974,62010,62012],{},[20743,61973],{"width":28057},[20743,61975,61976],{},[895,61977,61978,61980,61982,61984,61990,61992,61994,61996,61998,62000,62006,62008],{},[898,61979,4243],{},[898,61981,2775],{},[1726,61983,1735],{"stretchy":1734},[2275,61985,61986,61988],{},[898,61987,1724],{},[2133,61989,2328],{},[1726,61991,1762],{"stretchy":1734},[1726,61993,1728],{},[898,61995,2815],{},[898,61997,2775],{},[1726,61999,1735],{"stretchy":1734},[2275,62001,62002,62004],{},[898,62003,1724],{},[2133,62005,2328],{},[1726,62007,1762],{"stretchy":1734},[898,62009,1888],{"mathvariant":2377},[20743,62011],{"width":28057},[20743,62013,62014],{},[2289,62015,62016],{},"(3.10)",[902,62018,62019],{"encoding":904},"AC(Q_0) = MC(Q_0).\n\\tag{3.10}",[3859,62021,62022],{},[724,62023,62024,62026,62027],{},[883,62025,56424],{}," Princip\n",[38,62028,62029],{},"V bodě minima průměrných nákladů se průměrné náklady rovnají mezním nákladům.",[724,62031,62032,62035,62036,62078],{},[38,62033,62034],{},"Odvození."," Z ",[883,62037,62039],{"className":62038},[886],[888,62040,62041],{"xmlns":890},[892,62042,62043,62075],{},[895,62044,62045,62047,62049,62051,62053,62055,62057],{},[898,62046,4243],{},[898,62048,2775],{},[1726,62050,1735],{"stretchy":1734},[898,62052,1724],{},[1726,62054,1762],{"stretchy":1734},[1726,62056,1728],{},[2326,62058,62059],{"scriptlevel":2328,"displaystyle":1734},[2330,62060,62061,62073],{},[895,62062,62063,62065,62067,62069,62071],{},[898,62064,2772],{},[898,62066,2775],{},[1726,62068,1735],{"stretchy":1734},[898,62070,1724],{},[1726,62072,1762],{"stretchy":1734},[898,62074,1724],{},[902,62076,62077],{"encoding":904},"AC(Q) = \\tfrac{TC(Q)}{Q}"," derivací podílu plyne",[883,62080,62082],{"className":62081},[886],[888,62083,62084],{"xmlns":890,"display":28047},[892,62085,62086,62218],{},[895,62087,62088,62090,62096,62098,62100,62102,62104,62144,62146,62186,62188,62216],{},[898,62089,4243],{},[2128,62091,62092,62094],{},[898,62093,2775],{},[1726,62095,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,62097,1735],{"stretchy":1734},[898,62099,1724],{},[1726,62101,1762],{"stretchy":1734},[1726,62103,1728],{},[2330,62105,62106,62138],{},[895,62107,62108,62110,62116,62118,62120,62122,62124,62126,62128,62130,62132,62134,62136],{},[898,62109,2772],{},[2128,62111,62112,62114],{},[898,62113,2775],{},[1726,62115,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,62117,1735],{"stretchy":1734},[898,62119,1724],{},[1726,62121,1762],{"stretchy":1734},[1726,62123,3174],{},[898,62125,1724],{},[1726,62127,2228],{},[898,62129,2772],{},[898,62131,2775],{},[1726,62133,1735],{"stretchy":1734},[898,62135,1724],{},[1726,62137,1762],{"stretchy":1734},[2128,62139,62140,62142],{},[898,62141,1724],{},[2133,62143,2135],{},[1726,62145,1728],{},[2330,62147,62148,62180],{},[895,62149,62150,62152,62154,62156,62158,62160,62162,62164,62166,62168,62170,62172,62174,62176,62178],{},[898,62151,2815],{},[898,62153,2775],{},[1726,62155,1735],{"stretchy":1734},[898,62157,1724],{},[1726,62159,1762],{"stretchy":1734},[1726,62161,3174],{},[898,62163,1724],{},[1726,62165,2228],{},[898,62167,4243],{},[898,62169,2775],{},[1726,62171,1735],{"stretchy":1734},[898,62173,1724],{},[1726,62175,1762],{"stretchy":1734},[1726,62177,3174],{},[898,62179,1724],{},[2128,62181,62182,62184],{},[898,62183,1724],{},[2133,62185,2135],{},[1726,62187,1728],{},[2330,62189,62190,62214],{},[895,62191,62192,62194,62196,62198,62200,62202,62204,62206,62208,62210,62212],{},[898,62193,2815],{},[898,62195,2775],{},[1726,62197,1735],{"stretchy":1734},[898,62199,1724],{},[1726,62201,1762],{"stretchy":1734},[1726,62203,2228],{},[898,62205,4243],{},[898,62207,2775],{},[1726,62209,1735],{"stretchy":1734},[898,62211,1724],{},[1726,62213,1762],{"stretchy":1734},[898,62215,1724],{},[898,62217,1888],{"mathvariant":2377},[902,62219,62220],{"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}.",[724,62222,62223,62224,2623,62239,8088,62261,56801],{},"Nutnou podmínkou minima ",[883,62225,62227],{"className":62226},[886],[888,62228,62229],{"xmlns":890},[892,62230,62231,62237],{},[895,62232,62233,62235],{},[898,62234,4243],{},[898,62236,2775],{},[902,62238,55540],{"encoding":904},[883,62240,62242],{"className":62241},[886],[888,62243,62244],{"xmlns":890},[892,62245,62246,62258],{},[895,62247,62248,62254,62256],{},[2275,62249,62250,62252],{},[898,62251,1724],{},[2133,62253,2328],{},[1726,62255,3405],{},[2133,62257,2328],{},[902,62259,62260],{"encoding":904},"Q_0 > 0",[883,62262,62264],{"className":62263},[886],[888,62265,62266],{"xmlns":890},[892,62267,62268,62292],{},[895,62269,62270,62272,62278,62280,62286,62288,62290],{},[898,62271,4243],{},[2128,62273,62274,62276],{},[898,62275,2775],{},[1726,62277,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,62279,1735],{"stretchy":1734},[2275,62281,62282,62284],{},[898,62283,1724],{},[2133,62285,2328],{},[1726,62287,1762],{"stretchy":1734},[1726,62289,1728],{},[2133,62291,2328],{},[902,62293,62294],{"encoding":904},"AC'(Q_0) = 0",[883,62296,62298],{"className":62297},[886],[888,62299,62300],{"xmlns":890,"display":28047},[892,62301,62302,62387],{},[895,62303,62304,62344,62346,62348,62350,62353,62355,62357,62359,62361,62367,62369,62371,62373,62375,62377,62383,62385],{},[2330,62305,62306,62338],{},[895,62307,62308,62310,62312,62314,62320,62322,62324,62326,62328,62330,62336],{},[898,62309,2815],{},[898,62311,2775],{},[1726,62313,1735],{"stretchy":1734},[2275,62315,62316,62318],{},[898,62317,1724],{},[2133,62319,2328],{},[1726,62321,1762],{"stretchy":1734},[1726,62323,2228],{},[898,62325,4243],{},[898,62327,2775],{},[1726,62329,1735],{"stretchy":1734},[2275,62331,62332,62334],{},[898,62333,1724],{},[2133,62335,2328],{},[1726,62337,1762],{"stretchy":1734},[2275,62339,62340,62342],{},[898,62341,1724],{},[2133,62343,2328],{},[1726,62345,1728],{},[2133,62347,2328],{},[5865,62349],{"width":15270},[1726,62351,62352],{},"⟺",[5865,62354],{"width":15270},[898,62356,2815],{},[898,62358,2775],{},[1726,62360,1735],{"stretchy":1734},[2275,62362,62363,62365],{},[898,62364,1724],{},[2133,62366,2328],{},[1726,62368,1762],{"stretchy":1734},[1726,62370,1728],{},[898,62372,4243],{},[898,62374,2775],{},[1726,62376,1735],{"stretchy":1734},[2275,62378,62379,62381],{},[898,62380,1724],{},[2133,62382,2328],{},[1726,62384,1762],{"stretchy":1734},[898,62386,1888],{"mathvariant":2377},[902,62388,62389],{"encoding":904},"\\frac{MC(Q_0) - AC(Q_0)}{Q_0} = 0 \\quad\\Longleftrightarrow\\quad MC(Q_0) = AC(Q_0).",[724,62391,62392,1777,62395,61477,62410,62425,62426,62441,62442,8088,62459,62481,62482,62504],{},[38,62393,62394],{},"Geometrická interpretace.",[883,62396,62398],{"className":62397},[886],[888,62399,62400],{"xmlns":890},[892,62401,62402,62408],{},[895,62403,62404,62406],{},[898,62405,2815],{},[898,62407,2775],{},[902,62409,55272],{"encoding":904},[883,62411,62413],{"className":62412},[886],[888,62414,62415],{"xmlns":890},[892,62416,62417,62423],{},[895,62418,62419,62421],{},[898,62420,4243],{},[898,62422,2775],{},[902,62424,55540],{"encoding":904}," právě v bodě minima ",[883,62427,62429],{"className":62428},[886],[888,62430,62431],{"xmlns":890},[892,62432,62433,62439],{},[895,62434,62435,62437],{},[898,62436,4243],{},[898,62438,2775],{},[902,62440,55540],{"encoding":904}," (obrázek 3.10); nalevo od ",[883,62443,62445],{"className":62444},[886],[888,62446,62447],{"xmlns":890},[892,62448,62449,62457],{},[895,62450,62451],{},[2275,62452,62453,62455],{},[898,62454,1724],{},[2133,62456,2328],{},[902,62458,38289],{"encoding":904},[883,62460,62462],{"className":62461},[886],[888,62463,62464],{"xmlns":890},[892,62465,62466,62478],{},[895,62467,62468,62470,62472,62474,62476],{},[898,62469,2815],{},[898,62471,2775],{},[1726,62473,3444],{},[898,62475,4243],{},[898,62477,2775],{},[902,62479,62480],{"encoding":904},"MC \u003C AC"," (průměrné náklady klesají), napravo ",[883,62483,62485],{"className":62484},[886],[888,62486,62487],{"xmlns":890},[892,62488,62489,62501],{},[895,62490,62491,62493,62495,62497,62499],{},[898,62492,2815],{},[898,62494,2775],{},[1726,62496,3405],{},[898,62498,4243],{},[898,62500,2775],{},[902,62502,62503],{"encoding":904},"MC > AC"," (průměrné náklady rostou).",[724,62506,62507,62508,62550,62551,62568,62569,1888],{},"Za obvyklých ekonomických podmínek platí i obrácené tvrzení — jestliže ",[883,62509,62511],{"className":62510},[886],[888,62512,62513],{"xmlns":890},[892,62514,62515,62547],{},[895,62516,62517,62519,62521,62523,62529,62531,62533,62535,62537,62539,62545],{},[898,62518,4243],{},[898,62520,2775],{},[1726,62522,1735],{"stretchy":1734},[2275,62524,62525,62527],{},[898,62526,1724],{},[2133,62528,2328],{},[1726,62530,1762],{"stretchy":1734},[1726,62532,1728],{},[898,62534,2815],{},[898,62536,2775],{},[1726,62538,1735],{"stretchy":1734},[2275,62540,62541,62543],{},[898,62542,1724],{},[2133,62544,2328],{},[1726,62546,1762],{"stretchy":1734},[902,62548,62549],{"encoding":904},"AC(Q_0) = MC(Q_0)",", pak ",[883,62552,62554],{"className":62553},[886],[888,62555,62556],{"xmlns":890},[892,62557,62558,62566],{},[895,62559,62560],{},[2275,62561,62562,62564],{},[898,62563,1724],{},[2133,62565,2328],{},[902,62567,38289],{"encoding":904}," je bod minima. V praktických úlohách tedy postačí řešit rovnici ",[883,62570,62572],{"className":62571},[886],[888,62573,62574],{"xmlns":890},[892,62575,62576,62600],{},[895,62577,62578,62580,62582,62584,62586,62588,62590,62592,62594,62596,62598],{},[898,62579,4243],{},[898,62581,2775],{},[1726,62583,1735],{"stretchy":1734},[898,62585,1724],{},[1726,62587,1762],{"stretchy":1734},[1726,62589,1728],{},[898,62591,2815],{},[898,62593,2775],{},[1726,62595,1735],{"stretchy":1734},[898,62597,1724],{},[1726,62599,1762],{"stretchy":1734},[902,62601,62602],{"encoding":904},"AC(Q) = MC(Q)",[3859,62604,62605],{},[724,62606,62607,62609,62610,10378,62628,62649,62650,10378,62653,62674,62675,62690,62691,58018,62706,1847],{},[883,62608,4400],{}," Pozor — neplést s principem maxima zisku\nPro ",[38,62611,62612,62613],{},"minimum ",[883,62614,62616],{"className":62615},[886],[888,62617,62618],{"xmlns":890},[892,62619,62620,62626],{},[895,62621,62622,62624],{},[898,62623,4243],{},[898,62625,2775],{},[902,62627,55540],{"encoding":904},[883,62629,62631],{"className":62630},[886],[888,62632,62633],{"xmlns":890},[892,62634,62635,62647],{},[895,62636,62637,62639,62641,62643,62645],{},[898,62638,4243],{},[898,62640,2775],{},[1726,62642,1728],{},[898,62644,2815],{},[898,62646,2775],{},[902,62648,55203],{"encoding":904},", pro ",[38,62651,62652],{},"maximum zisku",[883,62654,62656],{"className":62655},[886],[888,62657,62658],{"xmlns":890},[892,62659,62660,62672],{},[895,62661,62662,62664,62666,62668,62670],{},[898,62663,2815],{},[898,62665,3984],{},[1726,62667,1728],{},[898,62669,2815],{},[898,62671,2775],{},[902,62673,55251],{"encoding":904},". Obě podmínky využívají ",[883,62676,62678],{"className":62677},[886],[888,62679,62680],{"xmlns":890},[892,62681,62682,62688],{},[895,62683,62684,62686],{},[898,62685,2815],{},[898,62687,2775],{},[902,62689,55272],{"encoding":904},", ale rovnají ho rozdílným veličinám (",[883,62692,62694],{"className":62693},[886],[888,62695,62696],{"xmlns":890},[892,62697,62698,62704],{},[895,62699,62700,62702],{},[898,62701,4243],{},[898,62703,2775],{},[902,62705,55540],{"encoding":904},[883,62707,62709],{"className":62708},[886],[888,62710,62711],{"xmlns":890},[892,62712,62713,62719],{},[895,62714,62715,62717],{},[898,62716,2815],{},[898,62718,3984],{},[902,62720,6621],{"encoding":904},[37329,62722,62724],{"id":62723},"příklad-37","Příklad 3.7",[724,62726,62727,57502,62729,62763,62764,62777,62778,62793],{},[38,62728,55967],{},[883,62730,62732],{"className":62731},[886],[888,62733,62734],{"xmlns":890},[892,62735,62736,62760],{},[895,62737,62738,62740,62742,62744,62750,62752,62754,62756,62758],{},[898,62739,2772],{},[898,62741,2775],{},[1726,62743,1728],{},[2128,62745,62746,62748],{},[898,62747,1724],{},[2133,62749,2135],{},[1726,62751,2099],{},[2133,62753,2177],{},[898,62755,1724],{},[1726,62757,2099],{},[2133,62759,5552],{},[902,62761,62762],{"encoding":904},"TC = Q^2 + 3Q + 36"," najděte ",[883,62765,62767],{"className":62766},[886],[888,62768,62769],{"xmlns":890},[892,62770,62771,62775],{},[895,62772,62773],{},[898,62774,1724],{},[902,62776,1724],{"encoding":904}," minimalizující ",[883,62779,62781],{"className":62780},[886],[888,62782,62783],{"xmlns":890},[892,62784,62785,62791],{},[895,62786,62787,62789],{},[898,62788,4243],{},[898,62790,2775],{},[902,62792,55540],{"encoding":904}," a ověřte princip (3.10).",[724,62795,62796,62798],{},[38,62797,22751],{}," Přímý výpočet:",[883,62800,62802],{"className":62801},[886],[888,62803,62804],{"xmlns":890,"display":28047},[892,62805,62806,62908],{},[895,62807,62808,62810,62812,62814,62836,62838,62840,62842,62844,62846,62852,62854,62856,62858,62860,62862,62868,62870,62872,62874,62884,62886,62906],{},[898,62809,4243],{},[898,62811,2775],{},[1726,62813,1728],{},[2330,62815,62816,62834],{},[895,62817,62818,62824,62826,62828,62830,62832],{},[2128,62819,62820,62822],{},[898,62821,1724],{},[2133,62823,2135],{},[1726,62825,2099],{},[2133,62827,2177],{},[898,62829,1724],{},[1726,62831,2099],{},[2133,62833,5552],{},[898,62835,1724],{},[1726,62837,1728],{},[898,62839,1724],{},[1726,62841,2099],{},[2133,62843,2177],{},[1726,62845,2099],{},[2330,62847,62848,62850],{},[2133,62849,5552],{},[898,62851,1724],{},[1726,62853,1742],{"separator":1741},[5865,62855],{"width":5867},[1726,62857,1735],{"stretchy":1734},[898,62859,4243],{},[898,62861,2775],{},[2128,62863,62864,62866],{},[1726,62865,1762],{"stretchy":1734},[1726,62867,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,62869,1728],{},[2133,62871,2281],{},[1726,62873,2228],{},[2330,62875,62876,62878],{},[2133,62877,5552],{},[2128,62879,62880,62882],{},[898,62881,1724],{},[2133,62883,2135],{},[1726,62885,1728],{},[2330,62887,62888,62900],{},[895,62889,62890,62896,62898],{},[2128,62891,62892,62894],{},[898,62893,1724],{},[2133,62895,2135],{},[1726,62897,2228],{},[2133,62899,5552],{},[2128,62901,62902,62904],{},[898,62903,1724],{},[2133,62905,2135],{},[898,62907,1888],{"mathvariant":2377},[902,62909,62910],{"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}.",[724,62912,62913,62953,62954,62978,62979,63029,63030,1888],{},[883,62914,62916],{"className":62915},[886],[888,62917,62918],{"xmlns":890},[892,62919,62920,62950],{},[895,62921,62922,62924,62926,62928,62934,62936,62938,62940,62946,62948],{},[1726,62923,1735],{"stretchy":1734},[898,62925,4243],{},[898,62927,2775],{},[2128,62929,62930,62932],{},[1726,62931,1762],{"stretchy":1734},[1726,62933,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,62935,1728],{},[2133,62937,2328],{},[1726,62939,3977],{},[2275,62941,62942,62944],{},[898,62943,1724],{},[2133,62945,2281],{},[1726,62947,1728],{},[2133,62949,2238],{},[902,62951,62952],{"encoding":904},"(AC)' = 0 \\Rightarrow Q_1 = 6"," (smysluplné), ",[883,62955,62957],{"className":62956},[886],[888,62958,62959],{"xmlns":890},[892,62960,62961,62975],{},[895,62962,62963,62969,62971,62973],{},[2275,62964,62965,62967],{},[898,62966,1724],{},[2133,62968,2135],{},[1726,62970,1728],{},[1726,62972,2228],{},[2133,62974,2238],{},[902,62976,62977],{"encoding":904},"Q_2 = -6"," (vyloučeno). ",[883,62980,62982],{"className":62981},[886],[888,62983,62984],{"xmlns":890},[892,62985,62986,63026],{},[895,62987,62988,62990,62992,62994,63004,63006,63008,63010,63012,63020,63022,63024],{},[1726,62989,1735],{"stretchy":1734},[898,62991,4243],{},[898,62993,2775],{},[2128,62995,62996,62998],{},[1726,62997,1762],{"stretchy":1734},[895,62999,63000,63002],{},[1726,63001,2379],{"mathvariant":2377},[1726,63003,2379],{"mathvariant":2377},[1726,63005,1735],{"stretchy":1734},[2133,63007,2238],{},[1726,63009,1762],{"stretchy":1734},[1726,63011,1728],{},[2326,63013,63014],{"scriptlevel":2328,"displaystyle":1734},[2330,63015,63016,63018],{},[2133,63017,2281],{},[2133,63019,2177],{},[1726,63021,3405],{},[2133,63023,2328],{},[1726,63025,3977],{},[902,63027,63028],{"encoding":904},"(AC)''(6) = \\tfrac{1}{3} > 0 \\Rightarrow"," minimum. ",[883,63031,63033],{"className":63032},[886],[888,63034,63035],{"xmlns":890},[892,63036,63037,63053],{},[895,63038,63039,63041,63043,63045,63047,63049,63051],{},[898,63040,4243],{},[898,63042,2775],{},[1726,63044,1735],{"stretchy":1734},[2133,63046,2238],{},[1726,63048,1762],{"stretchy":1734},[1726,63050,1728],{},[2133,63052,36225],{},[902,63054,63055],{"encoding":904},"AC(6) = 15",[724,63057,63058,63059,63085,63086,2703],{},"Pomocí principu: ",[883,63060,63062],{"className":63061},[886],[888,63063,63064],{"xmlns":890},[892,63065,63066,63082],{},[895,63067,63068,63070,63072,63074,63076,63078,63080],{},[898,63069,2815],{},[898,63071,2775],{},[1726,63073,1728],{},[2133,63075,2135],{},[898,63077,1724],{},[1726,63079,2099],{},[2133,63081,2177],{},[902,63083,63084],{"encoding":904},"MC = 2Q + 3",", rovnice ",[883,63087,63089],{"className":63088},[886],[888,63090,63091],{"xmlns":890},[892,63092,63093,63105],{},[895,63094,63095,63097,63099,63101,63103],{},[898,63096,4243],{},[898,63098,2775],{},[1726,63100,1728],{},[898,63102,2815],{},[898,63104,2775],{},[902,63106,55203],{"encoding":904},[883,63108,63110],{"className":63109},[886],[888,63111,63112],{"xmlns":890,"display":28047},[892,63113,63114,63216],{},[895,63115,63116,63138,63140,63142,63144,63146,63148,63150,63152,63154,63160,63162,63164,63166,63168,63170,63172,63174,63180,63182,63184,63186,63188,63190,63192,63198,63200,63202,63204,63206,63208,63210,63212,63214],{},[2330,63117,63118,63136],{},[895,63119,63120,63126,63128,63130,63132,63134],{},[2128,63121,63122,63124],{},[898,63123,1724],{},[2133,63125,2135],{},[1726,63127,2099],{},[2133,63129,2177],{},[898,63131,1724],{},[1726,63133,2099],{},[2133,63135,5552],{},[898,63137,1724],{},[1726,63139,1728],{},[2133,63141,2135],{},[898,63143,1724],{},[1726,63145,2099],{},[2133,63147,2177],{},[2289,63149,3974],{},[1726,63151,3977],{},[2289,63153,3974],{},[2128,63155,63156,63158],{},[898,63157,1724],{},[2133,63159,2135],{},[1726,63161,2099],{},[2133,63163,2177],{},[898,63165,1724],{},[1726,63167,2099],{},[2133,63169,5552],{},[1726,63171,1728],{},[2133,63173,2135],{},[2128,63175,63176,63178],{},[898,63177,1724],{},[2133,63179,2135],{},[1726,63181,2099],{},[2133,63183,2177],{},[898,63185,1724],{},[2289,63187,3974],{},[1726,63189,3977],{},[2289,63191,3974],{},[2128,63193,63194,63196],{},[898,63195,1724],{},[2133,63197,2135],{},[1726,63199,1728],{},[2133,63201,5552],{},[2289,63203,3974],{},[1726,63205,3977],{},[2289,63207,3974],{},[898,63209,1724],{},[1726,63211,1728],{},[2133,63213,2238],{},[1726,63215,1742],{"separator":1741},[902,63217,63218],{"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,",[724,63220,63221,63222,63260],{},"a ",[883,63223,63225],{"className":63224},[886],[888,63226,63227],{"xmlns":890},[892,63228,63229,63257],{},[895,63230,63231,63233,63235,63237,63239,63241,63243,63245,63247,63249,63251,63253,63255],{},[898,63232,4243],{},[898,63234,2775],{},[1726,63236,1735],{"stretchy":1734},[2133,63238,2238],{},[1726,63240,1762],{"stretchy":1734},[1726,63242,1728],{},[898,63244,2815],{},[898,63246,2775],{},[1726,63248,1735],{"stretchy":1734},[2133,63250,2238],{},[1726,63252,1762],{"stretchy":1734},[1726,63254,1728],{},[2133,63256,36225],{},[902,63258,63259],{"encoding":904},"AC(6) = MC(6) = 15",". Oba postupy dávají stejný výsledek.",[198,63262,63264],{"id":63263},"princip-minimalizace-průměrných-variabilních-nákladů","Princip minimalizace průměrných variabilních nákladů",[724,63266,63267,63268,2703],{},"Analogicky pro ",[883,63269,63271],{"className":63270},[886],[888,63272,63273],{"xmlns":890},[892,63274,63275,63283],{},[895,63276,63277,63279,63281],{},[898,63278,4243],{},[898,63280,40320],{},[898,63282,2775],{},[902,63284,55291],{"encoding":904},[883,63286,63288],{"className":63287},[886],[888,63289,63290],{"xmlns":890,"display":28047},[892,63291,63292,63343],{},[20735,63293,63294],{"width":28052},[20740,63295,63296,63298,63336,63338],{},[20743,63297],{"width":28057},[20743,63299,63300],{},[895,63301,63302,63304,63306,63308,63310,63316,63318,63320,63322,63324,63326,63332,63334],{},[898,63303,4243],{},[898,63305,40320],{},[898,63307,2775],{},[1726,63309,1735],{"stretchy":1734},[2275,63311,63312,63314],{},[898,63313,1724],{},[2133,63315,2328],{},[1726,63317,1762],{"stretchy":1734},[1726,63319,1728],{},[898,63321,2815],{},[898,63323,2775],{},[1726,63325,1735],{"stretchy":1734},[2275,63327,63328,63330],{},[898,63329,1724],{},[2133,63331,2328],{},[1726,63333,1762],{"stretchy":1734},[898,63335,1888],{"mathvariant":2377},[20743,63337],{"width":28057},[20743,63339,63340],{},[2289,63341,63342],{},"(3.11)",[902,63344,63345],{"encoding":904},"AVC(Q_0) = MC(Q_0).\n\\tag{3.11}",[3859,63347,63348],{},[724,63349,63350,62026,63352],{},[883,63351,56424],{},[38,63353,63354,63355,63372],{},"V bodě minima průměrných variabilních nákladů se ",[883,63356,63358],{"className":63357},[886],[888,63359,63360],{"xmlns":890},[892,63361,63362,63370],{},[895,63363,63364,63366,63368],{},[898,63365,4243],{},[898,63367,40320],{},[898,63369,2775],{},[902,63371,55291],{"encoding":904}," rovnají mezním nákladům.",[724,63374,63375,63376,63398,63399,1888],{},"Odvození je analogické (úloha 3.14). V obrázku 3.10 odpovídá ",[883,63377,63379],{"className":63378},[886],[888,63380,63381],{"xmlns":890},[892,63382,63383,63395],{},[895,63384,63385,63391,63393],{},[2275,63386,63387,63389],{},[898,63388,1724],{},[2133,63390,2328],{},[1726,63392,1728],{},[2133,63394,53179],{},[902,63396,63397],{"encoding":904},"Q_0 = 2{,}5",". Za obvyklých podmínek platí i obrácené tvrzení — postačí řešit rovnici ",[883,63400,63402],{"className":63401},[886],[888,63403,63404],{"xmlns":890},[892,63405,63406,63432],{},[895,63407,63408,63410,63412,63414,63416,63418,63420,63422,63424,63426,63428,63430],{},[898,63409,4243],{},[898,63411,40320],{},[898,63413,2775],{},[1726,63415,1735],{"stretchy":1734},[898,63417,1724],{},[1726,63419,1762],{"stretchy":1734},[1726,63421,1728],{},[898,63423,2815],{},[898,63425,2775],{},[1726,63427,1735],{"stretchy":1734},[898,63429,1724],{},[1726,63431,1762],{"stretchy":1734},[902,63433,63434],{"encoding":904},"AVC(Q) = MC(Q)",[115,63436,63438],{"id":63437},"zisk-a-body-zvratu","Zisk a body zvratu",[724,63440,63441,1777,63444,63460],{},[38,63442,63443],{},"Zisk",[883,63445,63447],{"className":63446},[886],[888,63448,63449],{"xmlns":890},[892,63450,63451,63457],{},[895,63452,63453,63455],{},[898,63454,1738],{},[898,63456,3984],{},[902,63458,63459],{"encoding":904},"PR"," (profit) je rozdíl celkového příjmu a celkových nákladů:",[883,63462,63464],{"className":63463},[886],[888,63465,63466],{"xmlns":890,"display":28047},[892,63467,63468,63527],{},[20735,63469,63470],{"width":28052},[20740,63471,63472,63474,63520,63522],{},[20743,63473],{"width":28057},[20743,63475,63476],{},[895,63477,63478,63480,63482,63484,63486,63488,63490,63492,63494,63496,63498,63500,63502,63504,63506,63508,63510,63512,63514,63516,63518],{},[898,63479,1738],{},[898,63481,3984],{},[1726,63483,1728],{},[898,63485,1738],{},[898,63487,3984],{},[1726,63489,1735],{"stretchy":1734},[898,63491,1724],{},[1726,63493,1762],{"stretchy":1734},[1726,63495,1728],{},[898,63497,2772],{},[898,63499,3984],{},[1726,63501,1735],{"stretchy":1734},[898,63503,1724],{},[1726,63505,1762],{"stretchy":1734},[1726,63507,2228],{},[898,63509,2772],{},[898,63511,2775],{},[1726,63513,1735],{"stretchy":1734},[898,63515,1724],{},[1726,63517,1762],{"stretchy":1734},[898,63519,1888],{"mathvariant":2377},[20743,63521],{"width":28057},[20743,63523,63524],{},[2289,63525,63526],{},"(3.12)",[902,63528,63529],{"encoding":904},"PR = PR(Q) = TR(Q) - TC(Q).\n\\tag{3.12}",[724,63531,63532,63533,3877,63548,43617,63563,63565,63566,63569,63570,63586,63587,63602,63603,63618,63619,1343,63632,63645,63646,1343,63664,63682,63683,10009,63686,63689,63690,1348,63712,8088,63734,63756,63757,8088,63787,63809],{},"Body rovnosti ",[883,63534,63536],{"className":63535},[886],[888,63537,63538],{"xmlns":890},[892,63539,63540,63546],{},[895,63541,63542,63544],{},[898,63543,2772],{},[898,63545,3984],{},[902,63547,4084],{"encoding":904},[883,63549,63551],{"className":63550},[886],[888,63552,63553],{"xmlns":890},[892,63554,63555,63561],{},[895,63556,63557,63559],{},[898,63558,2772],{},[898,63560,2775],{},[902,63562,3240],{"encoding":904},[38,63564,55707],{}," (též vyrovnání, ",[614,63567,63568],{},"break-even points","). V nejjednodušším modelu (lineární poptávka, konstantní ",[883,63571,63573],{"className":63572},[886],[888,63574,63575],{"xmlns":890},[892,63576,63577,63583],{},[895,63578,63579,63581],{},[898,63580,40320],{},[898,63582,2775],{},[902,63584,63585],{"encoding":904},"VC",") je ",[883,63588,63590],{"className":63589},[886],[888,63591,63592],{"xmlns":890},[892,63593,63594,63600],{},[895,63595,63596,63598],{},[898,63597,2772],{},[898,63599,3984],{},[902,63601,4084],{"encoding":904}," kvadratická a ",[883,63604,63606],{"className":63605},[886],[888,63607,63608],{"xmlns":890},[892,63609,63610,63616],{},[895,63611,63612,63614],{},[898,63613,2772],{},[898,63615,2775],{},[902,63617,3240],{"encoding":904}," lineární (obrázek 3.11). Křivky se protínají v bodech ",[883,63620,63622],{"className":63621},[886],[888,63623,63624],{"xmlns":890},[892,63625,63626,63630],{},[895,63627,63628],{},[898,63629,4243],{},[902,63631,4243],{"encoding":904},[883,63633,63635],{"className":63634},[886],[888,63636,63637],{"xmlns":890},[892,63638,63639,63643],{},[895,63640,63641],{},[898,63642,23234],{},[902,63644,23234],{"encoding":904}," odpovídajících množstvím ",[883,63647,63649],{"className":63648},[886],[888,63650,63651],{"xmlns":890},[892,63652,63653,63661],{},[895,63654,63655],{},[2275,63656,63657,63659],{},[898,63658,1724],{},[898,63660,4243],{},[902,63662,63663],{"encoding":904},"Q_A",[883,63665,63667],{"className":63666},[886],[888,63668,63669],{"xmlns":890},[892,63670,63671,63679],{},[895,63672,63673],{},[2275,63674,63675,63677],{},[898,63676,1724],{},[898,63678,23234],{},[902,63680,63681],{"encoding":904},"Q_B"," — firma je na ",[38,63684,63685],{},"prahu rentability",[614,63687,63688],{},"break even","). Pro ",[883,63691,63693],{"className":63692},[886],[888,63694,63695],{"xmlns":890},[892,63696,63697,63709],{},[895,63698,63699,63701,63703],{},[898,63700,1724],{},[1726,63702,3444],{},[2275,63704,63705,63707],{},[898,63706,1724],{},[898,63708,4243],{},[902,63710,63711],{"encoding":904},"Q \u003C Q_A",[883,63713,63715],{"className":63714},[886],[888,63716,63717],{"xmlns":890},[892,63718,63719,63731],{},[895,63720,63721,63723,63725],{},[898,63722,1724],{},[1726,63724,3405],{},[2275,63726,63727,63729],{},[898,63728,1724],{},[898,63730,23234],{},[902,63732,63733],{"encoding":904},"Q > Q_B",[883,63735,63737],{"className":63736},[886],[888,63738,63739],{"xmlns":890},[892,63740,63741,63753],{},[895,63742,63743,63745,63747,63749,63751],{},[898,63744,2772],{},[898,63746,2775],{},[1726,63748,3405],{},[898,63750,2772],{},[898,63752,3984],{},[902,63754,63755],{"encoding":904},"TC > TR"," (ztráta); pro ",[883,63758,63760],{"className":63759},[886],[888,63761,63762],{"xmlns":890},[892,63763,63764,63784],{},[895,63765,63766,63772,63774,63776,63778],{},[2275,63767,63768,63770],{},[898,63769,1724],{},[898,63771,4243],{},[1726,63773,3444],{},[898,63775,1724],{},[1726,63777,3444],{},[2275,63779,63780,63782],{},[898,63781,1724],{},[898,63783,23234],{},[902,63785,63786],{"encoding":904},"Q_A \u003C Q \u003C Q_B",[883,63788,63790],{"className":63789},[886],[888,63791,63792],{"xmlns":890},[892,63793,63794,63806],{},[895,63795,63796,63798,63800,63802,63804],{},[898,63797,2772],{},[898,63799,3984],{},[1726,63801,3405],{},[898,63803,2772],{},[898,63805,2775],{},[902,63807,63808],{"encoding":904},"TR > TC"," (zisk).",[3859,63811,63812],{},[724,63813,63814,63816],{},[883,63815,4145],{}," 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.",[724,63818,63819,63820,63846],{},"Body zvratu jsou řešení rovnice ",[883,63821,63823],{"className":63822},[886],[888,63824,63825],{"xmlns":890},[892,63826,63827,63843],{},[895,63828,63829,63831,63833,63835,63837,63839,63841],{},[898,63830,1738],{},[898,63832,3984],{},[1726,63834,1735],{"stretchy":1734},[898,63836,1724],{},[1726,63838,1762],{"stretchy":1734},[1726,63840,1728],{},[2133,63842,2328],{},[902,63844,63845],{"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.",[724,63848,63849],{},[1647,63850],{"alt":63851,"className":63852,"src":63853},"imek-tr-tc-body-zvratu",[210,1651],"\u002Fwiki-assets\u002Fimek-tr-tc-body-zvratu.jpeg",[724,63855,63856],{},[614,63857,63858,63859,63874,63875,63890,63891,3877,63904,43341,63917,63930,63931,3877,63948,63965,63966,63986,63987,3877,64002,6460,64017,64046],{},"Obrázek 3.11: Body zvratu — křivky ",[883,63860,63862],{"className":63861},[886],[888,63863,63864],{"xmlns":890},[892,63865,63866,63872],{},[895,63867,63868,63870],{},[898,63869,2772],{},[898,63871,3984],{},[902,63873,4084],{"encoding":904}," (obrácená parabola) a ",[883,63876,63878],{"className":63877},[886],[888,63879,63880],{"xmlns":890},[892,63881,63882,63888],{},[895,63883,63884,63886],{},[898,63885,2772],{},[898,63887,2775],{},[902,63889,3240],{"encoding":904}," (přímka) se protínají v bodech ",[883,63892,63894],{"className":63893},[886],[888,63895,63896],{"xmlns":890},[892,63897,63898,63902],{},[895,63899,63900],{},[898,63901,4243],{},[902,63903,4243],{"encoding":904},[883,63905,63907],{"className":63906},[886],[888,63908,63909],{"xmlns":890},[892,63910,63911,63915],{},[895,63912,63913],{},[898,63914,23234],{},[902,63916,23234],{"encoding":904},[883,63918,63920],{"className":63919},[886],[888,63921,63922],{"xmlns":890},[892,63923,63924,63928],{},[895,63925,63926],{},[898,63927,1724],{},[902,63929,1724],{"encoding":904}," v hodnotách ",[883,63932,63934],{"className":63933},[886],[888,63935,63936],{"xmlns":890},[892,63937,63938,63946],{},[895,63939,63940],{},[2275,63941,63942,63944],{},[898,63943,1724],{},[898,63945,4243],{},[902,63947,63663],{"encoding":904},[883,63949,63951],{"className":63950},[886],[888,63952,63953],{"xmlns":890},[892,63954,63955,63963],{},[895,63956,63957],{},[2275,63958,63959,63961],{},[898,63960,1724],{},[898,63962,23234],{},[902,63964,63681],{"encoding":904},"; maximum zisku leží mezi nimi v bodě ",[883,63967,63969],{"className":63968},[886],[888,63970,63971],{"xmlns":890},[892,63972,63973,63983],{},[895,63974,63975],{},[2275,63976,63977,63979,63981],{},[898,63978,1724],{},[898,63980,56177],{},[1726,63982,56180],{},[902,63984,63985],{"encoding":904},"Q_{\\max}","; svislá vzdálenost mezi ",[883,63988,63990],{"className":63989},[886],[888,63991,63992],{"xmlns":890},[892,63993,63994,64000],{},[895,63995,63996,63998],{},[898,63997,2772],{},[898,63999,3984],{},[902,64001,4084],{"encoding":904},[883,64003,64005],{"className":64004},[886],[888,64006,64007],{"xmlns":890},[892,64008,64009,64015],{},[895,64010,64011,64013],{},[898,64012,2772],{},[898,64014,2775],{},[902,64016,3240],{"encoding":904},[883,64018,64020],{"className":64019},[886],[888,64021,64022],{"xmlns":890},[892,64023,64024,64044],{},[895,64025,64026,64032,64034,64036,64038],{},[2275,64027,64028,64030],{},[898,64029,1724],{},[898,64031,4243],{},[1726,64033,3444],{},[898,64035,1724],{},[1726,64037,3444],{},[2275,64039,64040,64042],{},[898,64041,1724],{},[898,64043,23234],{},[902,64045,63786],{"encoding":904}," vyznačuje zisk.",[37329,64048,64050],{"id":64049},"příklad-38","Příklad 3.8",[724,64052,64053,64055,64056,1343,64076,1343,64102,64128],{},[38,64054,55967],{}," Dáno ",[883,64057,64059],{"className":64058},[886],[888,64060,64061],{"xmlns":890},[892,64062,64063,64073],{},[895,64064,64065,64067,64069,64071],{},[898,64066,10420],{},[898,64068,2775],{},[1726,64070,1728],{},[2133,64072,2352],{},[902,64074,64075],{"encoding":904},"FC = 4",[883,64077,64079],{"className":64078},[886],[888,64080,64081],{"xmlns":890},[892,64082,64083,64099],{},[895,64084,64085,64087,64089,64091,64093],{},[898,64086,2772],{},[898,64088,40320],{},[898,64090,2775],{},[1726,64092,1728],{},[2128,64094,64095,64097],{},[898,64096,1724],{},[2133,64098,2135],{},[902,64100,64101],{"encoding":904},"TVC = Q^2",[883,64103,64105],{"className":64104},[886],[888,64106,64107],{"xmlns":890},[892,64108,64109,64125],{},[895,64110,64111,64113,64115,64117,64119,64121,64123],{},[898,64112,1738],{},[1726,64114,1728],{},[1726,64116,2228],{},[2133,64118,2135],{},[898,64120,1724],{},[1726,64122,2099],{},[2133,64124,3989],{},[902,64126,64127],{"encoding":904},"P = -2Q + 9",". Určete zisk, body zvratu a bod maxima zisku.",[724,64130,64131,64133],{},[38,64132,22751],{}," Celkové náklady a příjem:",[883,64135,64137],{"className":64136},[886],[888,64138,64139],{"xmlns":890,"display":28047},[892,64140,64141,64207],{},[895,64142,64143,64145,64147,64149,64151,64153,64159,64161,64163,64165,64167,64169,64171,64173,64175,64177,64179,64181,64183,64185,64187,64189,64191,64193,64199,64201,64203,64205],{},[898,64144,2772],{},[898,64146,2775],{},[1726,64148,1728],{},[2133,64150,2352],{},[1726,64152,2099],{},[2128,64154,64155,64157],{},[898,64156,1724],{},[2133,64158,2135],{},[1726,64160,1742],{"separator":1741},[5865,64162],{"width":5867},[898,64164,2772],{},[898,64166,3984],{},[1726,64168,1728],{},[898,64170,1724],{},[1726,64172,3174],{},[1726,64174,1735],{"stretchy":1734},[1726,64176,2228],{},[2133,64178,2135],{},[898,64180,1724],{},[1726,64182,2099],{},[2133,64184,3989],{},[1726,64186,1762],{"stretchy":1734},[1726,64188,1728],{},[1726,64190,2228],{},[2133,64192,2135],{},[2128,64194,64195,64197],{},[898,64196,1724],{},[2133,64198,2135],{},[1726,64200,2099],{},[2133,64202,3989],{},[898,64204,1724],{},[898,64206,1888],{"mathvariant":2377},[902,64208,64209],{"encoding":904},"TC = 4 + Q^2, \\qquad TR = Q \\cdot (-2Q + 9) = -2Q^2 + 9Q.",[724,64211,64212],{},"Zisk dle (3.12):",[883,64214,64216],{"className":64215},[886],[888,64217,64218],{"xmlns":890,"display":28047},[892,64219,64220,64298],{},[895,64221,64222,64224,64226,64228,64230,64232,64234,64236,64238,64240,64242,64244,64246,64252,64254,64256,64258,64260,64262,64264,64266,64268,64274,64276,64278,64280,64282,64288,64290,64292,64294,64296],{},[898,64223,1738],{},[898,64225,3984],{},[1726,64227,1728],{},[898,64229,2772],{},[898,64231,3984],{},[1726,64233,2228],{},[898,64235,2772],{},[898,64237,2775],{},[1726,64239,1728],{},[1726,64241,1735],{"stretchy":1734},[1726,64243,2228],{},[2133,64245,2135],{},[2128,64247,64248,64250],{},[898,64249,1724],{},[2133,64251,2135],{},[1726,64253,2099],{},[2133,64255,3989],{},[898,64257,1724],{},[1726,64259,1762],{"stretchy":1734},[1726,64261,2228],{},[1726,64263,1735],{"stretchy":1734},[2133,64265,2352],{},[1726,64267,2099],{},[2128,64269,64270,64272],{},[898,64271,1724],{},[2133,64273,2135],{},[1726,64275,1762],{"stretchy":1734},[1726,64277,1728],{},[1726,64279,2228],{},[2133,64281,2177],{},[2128,64283,64284,64286],{},[898,64285,1724],{},[2133,64287,2135],{},[1726,64289,2099],{},[2133,64291,3989],{},[898,64293,1724],{},[1726,64295,2228],{},[2133,64297,59299],{},[902,64299,64300],{"encoding":904},"PR = TR - TC = (-2Q^2 + 9Q) - (4 + Q^2) = -3Q^2 + 9Q - 4.",[724,64302,64303,64306,64307,17558,64343,2703],{},[38,64304,64305],{},"Body zvratu"," jsou kořeny rovnice ",[883,64308,64310],{"className":64309},[886],[888,64311,64312],{"xmlns":890},[892,64313,64314,64340],{},[895,64315,64316,64318,64320,64326,64328,64330,64332,64334,64336,64338],{},[1726,64317,2228],{},[2133,64319,2177],{},[2128,64321,64322,64324],{},[898,64323,1724],{},[2133,64325,2135],{},[1726,64327,2099],{},[2133,64329,3989],{},[898,64331,1724],{},[1726,64333,2228],{},[2133,64335,2352],{},[1726,64337,1728],{},[2133,64339,2328],{},[902,64341,64342],{"encoding":904},"-3Q^2 + 9Q - 4 = 0",[883,64344,64346],{"className":64345},[886],[888,64347,64348],{"xmlns":890},[892,64349,64350,64374],{},[895,64351,64352,64354,64360,64362,64364,64366,64368,64370,64372],{},[2133,64353,2177],{},[2128,64355,64356,64358],{},[898,64357,1724],{},[2133,64359,2135],{},[1726,64361,2228],{},[2133,64363,3989],{},[898,64365,1724],{},[1726,64367,2099],{},[2133,64369,2352],{},[1726,64371,1728],{},[2133,64373,2328],{},[902,64375,64376],{"encoding":904},"3Q^2 - 9Q + 4 = 0",[883,64378,64380],{"className":64379},[886],[888,64381,64382],{"xmlns":890,"display":28047},[892,64383,64384,64441],{},[895,64385,64386,64398,64400,64423,64425,64439],{},[2275,64387,64388,64390],{},[898,64389,1724],{},[895,64391,64392,64394,64396],{},[2133,64393,2281],{},[1726,64395,1742],{"separator":1741},[2133,64397,2135],{},[1726,64399,1728],{},[2330,64401,64402,64421],{},[895,64403,64404,64406,64409],{},[2133,64405,3989],{},[1726,64407,64408],{},"±",[8103,64410,64411],{},[895,64412,64413,64416,64418],{},[2133,64414,64415],{},"81",[1726,64417,2228],{},[2133,64419,64420],{},"48",[2133,64422,2238],{},[1726,64424,1728],{},[2330,64426,64427,64437],{},[895,64428,64429,64431,64433],{},[2133,64430,3989],{},[1726,64432,64408],{},[8103,64434,64435],{},[2133,64436,8937],{},[2133,64438,2238],{},[1726,64440,1742],{"separator":1741},[902,64442,64443],{"encoding":904},"Q_{1,2} = \\frac{9 \\pm \\sqrt{81 - 48}}{6} = \\frac{9 \\pm \\sqrt{33}}{6},",[724,64445,64446,64447,3877,64470,1888],{},"numericky ",[883,64448,64450],{"className":64449},[886],[888,64451,64452],{"xmlns":890},[892,64453,64454,64467],{},[895,64455,64456,64462,64464],{},[2275,64457,64458,64460],{},[898,64459,1724],{},[2133,64461,2281],{},[1726,64463,5887],{},[2133,64465,64466],{},"0,543",[902,64468,64469],{"encoding":904},"Q_1 \\doteq 0{,}543",[883,64471,64473],{"className":64472},[886],[888,64474,64475],{"xmlns":890},[892,64476,64477,64490],{},[895,64478,64479,64485,64487],{},[2275,64480,64481,64483],{},[898,64482,1724],{},[2133,64484,2135],{},[1726,64486,5887],{},[2133,64488,64489],{},"2,457",[902,64491,64492],{"encoding":904},"Q_2 \\doteq 2{,}457",[724,64494,64495,1777,64498,7538,64543,17558,64577,64595],{},[38,64496,64497],{},"Maximum zisku.",[883,64499,64501],{"className":64500},[886],[888,64502,64503],{"xmlns":890},[892,64504,64505,64540],{},[895,64506,64507,64509,64515,64517,64519,64521,64523,64525,64527,64529,64531,64533,64535,64537],{},[898,64508,1738],{},[2128,64510,64511,64513],{},[898,64512,3984],{},[1726,64514,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,64516,1728],{},[1726,64518,2228],{},[2133,64520,2238],{},[898,64522,1724],{},[1726,64524,2099],{},[2133,64526,3989],{},[1726,64528,1728],{},[2133,64530,2328],{},[1726,64532,3977],{},[898,64534,1724],{},[1726,64536,1728],{},[2133,64538,64539],{},"1,5",[902,64541,64542],{"encoding":904},"PR' = -6Q + 9 = 0 \\Rightarrow Q = 1{,}5",[883,64544,64546],{"className":64545},[886],[888,64547,64548],{"xmlns":890},[892,64549,64550,64574],{},[895,64551,64552,64554,64564,64566,64568,64570,64572],{},[898,64553,1738],{},[2128,64555,64556,64558],{},[898,64557,3984],{},[895,64559,64560,64562],{},[1726,64561,2379],{"mathvariant":2377},[1726,64563,2379],{"mathvariant":2377},[1726,64565,1728],{},[1726,64567,2228],{},[2133,64569,2238],{},[1726,64571,3444],{},[2133,64573,2328],{},[902,64575,64576],{"encoding":904},"PR'' = -6 \u003C 0",[883,64578,64580],{"className":64579},[886],[888,64581,64582],{"xmlns":890},[892,64583,64584,64592],{},[895,64585,64586,64588,64590],{},[898,64587,1724],{},[1726,64589,1728],{},[2133,64591,64539],{},[902,64593,64594],{"encoding":904},"Q = 1{,}5"," je bod maxima s hodnotou",[883,64597,64599],{"className":64598},[886],[888,64600,64601],{"xmlns":890,"display":28047},[892,64602,64603,64666],{},[895,64604,64605,64607,64609,64611,64613,64615,64617,64619,64621,64623,64625,64627,64633,64635,64637,64639,64641,64643,64645,64647,64649,64652,64654,64657,64659,64661,64663],{},[898,64606,1738],{},[898,64608,3984],{},[1726,64610,1735],{"stretchy":1734},[2133,64612,64539],{},[1726,64614,1762],{"stretchy":1734},[1726,64616,1728],{},[1726,64618,2228],{},[2133,64620,2177],{},[1726,64622,3174],{},[1726,64624,1735],{"stretchy":1734},[2133,64626,64539],{},[2128,64628,64629,64631],{},[1726,64630,1762],{"stretchy":1734},[2133,64632,2135],{},[1726,64634,2099],{},[2133,64636,3989],{},[1726,64638,3174],{},[2133,64640,64539],{},[1726,64642,2228],{},[2133,64644,2352],{},[1726,64646,1728],{},[1726,64648,2228],{},[2133,64650,64651],{},"6,75",[1726,64653,2099],{},[2133,64655,64656],{},"13,5",[1726,64658,2228],{},[2133,64660,2352],{},[1726,64662,1728],{},[2133,64664,64665],{},"2,75.",[902,64667,64668],{"encoding":904},"PR(1{,}5) = -3 \\cdot (1{,}5)^2 + 9 \\cdot 1{,}5 - 4 = -6{,}75 + 13{,}5 - 4 = 2{,}75.",[724,64670,64671,64672,1343,64717,64770,64771,64789],{},"Pro srovnání maximum celkového příjmu (bez ohledu na náklady): ",[883,64673,64675],{"className":64674},[886],[888,64676,64677],{"xmlns":890},[892,64678,64679,64714],{},[895,64680,64681,64683,64689,64691,64693,64695,64697,64699,64701,64703,64705,64707,64709,64711],{},[898,64682,2772],{},[2128,64684,64685,64687],{},[898,64686,3984],{},[1726,64688,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,64690,1728],{},[1726,64692,2228],{},[2133,64694,2352],{},[898,64696,1724],{},[1726,64698,2099],{},[2133,64700,3989],{},[1726,64702,1728],{},[2133,64704,2328],{},[1726,64706,3977],{},[898,64708,1724],{},[1726,64710,1728],{},[2133,64712,64713],{},"2,25",[902,64715,64716],{"encoding":904},"TR' = -4Q + 9 = 0 \\Rightarrow Q = 2{,}25",[883,64718,64720],{"className":64719},[886],[888,64721,64722],{"xmlns":890},[892,64723,64724,64767],{},[895,64725,64726,64728,64736,64738,64740,64742,64744,64746,64748,64754,64756,64758,64760,64762,64764],{},[898,64727,2772],{},[2275,64729,64730,64732,64734],{},[898,64731,3984],{},[898,64733,56177],{},[1726,64735,56180],{},[1726,64737,1728],{},[1726,64739,2228],{},[2133,64741,2135],{},[1726,64743,3174],{},[1726,64745,1735],{"stretchy":1734},[2133,64747,64713],{},[2128,64749,64750,64752],{},[1726,64751,1762],{"stretchy":1734},[2133,64753,2135],{},[1726,64755,2099],{},[2133,64757,3989],{},[1726,64759,3174],{},[2133,64761,64713],{},[1726,64763,1728],{},[2133,64765,64766],{},"10,125",[902,64768,64769],{"encoding":904},"TR_{\\max} = -2 \\cdot (2{,}25)^2 + 9 \\cdot 2{,}25 = 10{,}125",". Leží vpravo od bodu maxima zisku, protože při ",[883,64772,64774],{"className":64773},[886],[888,64775,64776],{"xmlns":890},[892,64777,64778,64786],{},[895,64779,64780,64782,64784],{},[898,64781,1724],{},[1726,64783,1728],{},[2133,64785,64713],{},[902,64787,64788],{"encoding":904},"Q = 2{,}25"," rostou už náklady rychleji než příjem.",[3859,64791,64792],{},[724,64793,64794,64796,64797,1343,64819,64841,64842,1343,64859,64880,64881,64913,64914,64952,64953,2670,64971,64988,64989,3877,65017,65051,65052,7671,65090,3877,65114,1888],{},[883,64795,4400],{}," Nekonzistence v původním zdroji\nSkenovaný knižní text obsahoval v tomto příkladu dvě nesourodé hodnoty: uváděl body zvratu ",[883,64798,64800],{"className":64799},[886],[888,64801,64802],{"xmlns":890},[892,64803,64804,64816],{},[895,64805,64806,64812,64814],{},[2275,64807,64808,64810],{},[898,64809,1724],{},[2133,64811,2281],{},[1726,64813,1728],{},[2133,64815,4996],{},[902,64817,64818],{"encoding":904},"Q_1 = 0{,}5",[883,64820,64822],{"className":64821},[886],[888,64823,64824],{"xmlns":890},[892,64825,64826,64838],{},[895,64827,64828,64834,64836],{},[2275,64829,64830,64832],{},[898,64831,1724],{},[2133,64833,2135],{},[1726,64835,1728],{},[2133,64837,2352],{},[902,64839,64840],{"encoding":904},"Q_2 = 4"," (odpovídající starší verzi zadání) a zároveň maximum v ",[883,64843,64845],{"className":64844},[886],[888,64846,64847],{"xmlns":890},[892,64848,64849,64857],{},[895,64850,64851,64853,64855],{},[898,64852,1724],{},[1726,64854,1728],{},[2133,64856,64713],{},[902,64858,64788],{"encoding":904},[883,64860,64862],{"className":64861},[886],[888,64863,64864],{"xmlns":890},[892,64865,64866,64877],{},[895,64867,64868,64870,64872,64874],{},[898,64869,1738],{},[898,64871,3984],{},[1726,64873,1728],{},[2133,64875,64876],{},"6,125",[902,64878,64879],{"encoding":904},"PR = 6{,}125"," (odpovídající derivaci ",[883,64882,64884],{"className":64883},[886],[888,64885,64886],{"xmlns":890},[892,64887,64888,64910],{},[895,64889,64890,64892,64898,64900,64902,64904,64906,64908],{},[898,64891,1738],{},[2128,64893,64894,64896],{},[898,64895,3984],{},[1726,64897,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,64899,1728],{},[1726,64901,2228],{},[2133,64903,2352],{},[898,64905,1724],{},[1726,64907,2099],{},[2133,64909,3989],{},[902,64911,64912],{"encoding":904},"PR' = -4Q + 9",", tj. zisku ",[883,64915,64917],{"className":64916},[886],[888,64918,64919],{"xmlns":890},[892,64920,64921,64949],{},[895,64922,64923,64925,64927,64929,64931,64933,64939,64941,64943,64945,64947],{},[898,64924,1738],{},[898,64926,3984],{},[1726,64928,1728],{},[1726,64930,2228],{},[2133,64932,2135],{},[2128,64934,64935,64937],{},[898,64936,1724],{},[2133,64938,2135],{},[1726,64940,2099],{},[2133,64942,3989],{},[898,64944,1724],{},[1726,64946,2228],{},[2133,64948,2352],{},[902,64950,64951],{"encoding":904},"PR = -2Q^2 + 9Q - 4"," bez odčtení kvadratického členu ",[883,64954,64956],{"className":64955},[886],[888,64957,64958],{"xmlns":890},[892,64959,64960,64968],{},[895,64961,64962],{},[2128,64963,64964,64966],{},[898,64965,1724],{},[2133,64967,2135],{},[902,64969,64970],{"encoding":904},"Q^2",[883,64972,64974],{"className":64973},[886],[888,64975,64976],{"xmlns":890},[892,64977,64978,64986],{},[895,64979,64980,64982,64984],{},[898,64981,2772],{},[898,64983,40320],{},[898,64985,2775],{},[902,64987,55489],{"encoding":904},"). Zde je uvedena matematicky konzistentní verze: zadané ",[883,64990,64992],{"className":64991},[886],[888,64993,64994],{"xmlns":890},[892,64995,64996,65014],{},[895,64997,64998,65000,65002,65004,65006,65008],{},[898,64999,2772],{},[898,65001,2775],{},[1726,65003,1728],{},[2133,65005,2352],{},[1726,65007,2099],{},[2128,65009,65010,65012],{},[898,65011,1724],{},[2133,65013,2135],{},[902,65015,65016],{"encoding":904},"TC = 4 + Q^2",[883,65018,65020],{"className":65019},[886],[888,65021,65022],{"xmlns":890},[892,65023,65024,65048],{},[895,65025,65026,65028,65030,65032,65034,65036,65042,65044,65046],{},[898,65027,2772],{},[898,65029,3984],{},[1726,65031,1728],{},[1726,65033,2228],{},[2133,65035,2135],{},[2128,65037,65038,65040],{},[898,65039,1724],{},[2133,65041,2135],{},[1726,65043,2099],{},[2133,65045,3989],{},[898,65047,1724],{},[902,65049,65050],{"encoding":904},"TR = -2Q^2 + 9Q"," vedou na ",[883,65053,65055],{"className":65054},[886],[888,65056,65057],{"xmlns":890},[892,65058,65059,65087],{},[895,65060,65061,65063,65065,65067,65069,65071,65077,65079,65081,65083,65085],{},[898,65062,1738],{},[898,65064,3984],{},[1726,65066,1728],{},[1726,65068,2228],{},[2133,65070,2177],{},[2128,65072,65073,65075],{},[898,65074,1724],{},[2133,65076,2135],{},[1726,65078,2099],{},[2133,65080,3989],{},[898,65082,1724],{},[1726,65084,2228],{},[2133,65086,2352],{},[902,65088,65089],{"encoding":904},"PR = -3Q^2 + 9Q - 4",[883,65091,65093],{"className":65092},[886],[888,65094,65095],{"xmlns":890},[892,65096,65097,65111],{},[895,65098,65099,65107,65109],{},[2275,65100,65101,65103,65105],{},[898,65102,1724],{},[898,65104,56177],{},[1726,65106,56180],{},[1726,65108,1728],{},[2133,65110,64539],{},[902,65112,65113],{"encoding":904},"Q_{\\max} = 1{,}5",[883,65115,65117],{"className":65116},[886],[888,65118,65119],{"xmlns":890},[892,65120,65121,65138],{},[895,65122,65123,65125,65133,65135],{},[898,65124,1738],{},[2275,65126,65127,65129,65131],{},[898,65128,3984],{},[898,65130,56177],{},[1726,65132,56180],{},[1726,65134,1728],{},[2133,65136,65137],{},"2,75",[902,65139,65140],{"encoding":904},"PR_{\\max} = 2{,}75",[724,65142,65143],{},[614,65144,65145,65146,65173,65174,65207,65208,1343,65231,1888],{},"Obrázek 3.12: Graf ",[883,65147,65149],{"className":65148},[886],[888,65150,65151],{"xmlns":890},[892,65152,65153,65171],{},[895,65154,65155,65157,65159,65161,65163,65165],{},[898,65156,2772],{},[898,65158,2775],{},[1726,65160,1728],{},[2133,65162,2352],{},[1726,65164,2099],{},[2128,65166,65167,65169],{},[898,65168,1724],{},[2133,65170,2135],{},[902,65172,65016],{"encoding":904}," (parabola) a ",[883,65175,65177],{"className":65176},[886],[888,65178,65179],{"xmlns":890},[892,65180,65181,65205],{},[895,65182,65183,65185,65187,65189,65191,65193,65199,65201,65203],{},[898,65184,2772],{},[898,65186,3984],{},[1726,65188,1728],{},[1726,65190,2228],{},[2133,65192,2135],{},[2128,65194,65195,65197],{},[898,65196,1724],{},[2133,65198,2135],{},[1726,65200,2099],{},[2133,65202,3989],{},[898,65204,1724],{},[902,65206,65050],{"encoding":904}," (parabola); průsečíky vyznačují body zvratu ",[883,65209,65211],{"className":65210},[886],[888,65212,65213],{"xmlns":890},[892,65214,65215,65228],{},[895,65216,65217,65223,65225],{},[2275,65218,65219,65221],{},[898,65220,1724],{},[2133,65222,2281],{},[1726,65224,5887],{},[2133,65226,65227],{},"0,54",[902,65229,65230],{"encoding":904},"Q_1 \\doteq 0{,}54",[883,65232,65234],{"className":65233},[886],[888,65235,65236],{"xmlns":890},[892,65237,65238,65251],{},[895,65239,65240,65246,65248],{},[2275,65241,65242,65244],{},[898,65243,1724],{},[2133,65245,2135],{},[1726,65247,5887],{},[2133,65249,65250],{},"2,46",[902,65252,65253],{"encoding":904},"Q_2 \\doteq 2{,}46",[724,65255,65256],{},[614,65257,65258,65259,58487,65296,65313,65314,1343,65335,1888],{},"Obrázek 3.13: Graf zisku ",[883,65260,65262],{"className":65261},[886],[888,65263,65264],{"xmlns":890},[892,65265,65266,65294],{},[895,65267,65268,65270,65272,65274,65276,65278,65284,65286,65288,65290,65292],{},[898,65269,1738],{},[898,65271,3984],{},[1726,65273,1728],{},[1726,65275,2228],{},[2133,65277,2177],{},[2128,65279,65280,65282],{},[898,65281,1724],{},[2133,65283,2135],{},[1726,65285,2099],{},[2133,65287,3989],{},[898,65289,1724],{},[1726,65291,2228],{},[2133,65293,2352],{},[902,65295,65089],{"encoding":904},[883,65297,65299],{"className":65298},[886],[888,65300,65301],{"xmlns":890},[892,65302,65303,65311],{},[895,65304,65305,65307,65309],{},[898,65306,1724],{},[1726,65308,1728],{},[2133,65310,64539],{},[902,65312,64594],{"encoding":904}," a nulami ",[883,65315,65317],{"className":65316},[886],[888,65318,65319],{"xmlns":890},[892,65320,65321,65333],{},[895,65322,65323,65329,65331],{},[2275,65324,65325,65327],{},[898,65326,1724],{},[2133,65328,2281],{},[1726,65330,5887],{},[2133,65332,65227],{},[902,65334,65230],{"encoding":904},[883,65336,65338],{"className":65337},[886],[888,65339,65340],{"xmlns":890},[892,65341,65342,65354],{},[895,65343,65344,65350,65352],{},[2275,65345,65346,65348],{},[898,65347,1724],{},[2133,65349,2135],{},[1726,65351,5887],{},[2133,65353,65250],{},[902,65355,65253],{"encoding":904},[115,65357,65359],{"id":65358},"princip-maximalizace-zisku","Princip maximalizace zisku",[724,65361,65362],{},"Kromě standardního hledání extrému lze využít následující princip.",[724,65364,65365],{},[1647,65366],{"alt":65367,"className":65368,"src":65369},"imek-max-zisku-dva-pohledy",[210,1651],"\u002Fwiki-assets\u002Fimek-max-zisku-dva-pohledy.jpeg",[198,65371,16394],{"id":65372},"princip-1",[724,65374,65375,65376,2623,65391,65408],{},"Má-li zisk ",[883,65377,65379],{"className":65378},[886],[888,65380,65381],{"xmlns":890},[892,65382,65383,65389],{},[895,65384,65385,65387],{},[898,65386,1738],{},[898,65388,3984],{},[902,65390,63459],{"encoding":904},[883,65392,65394],{"className":65393},[886],[888,65395,65396],{"xmlns":890},[892,65397,65398,65406],{},[895,65399,65400],{},[2275,65401,65402,65404],{},[898,65403,1724],{},[2133,65405,2328],{},[902,65407,38289],{"encoding":904}," maximum, pak platí",[883,65410,65412],{"className":65411},[886],[888,65413,65414],{"xmlns":890,"display":28047},[892,65415,65416,65465],{},[20735,65417,65418],{"width":28052},[20740,65419,65420,65422,65458,65460],{},[20743,65421],{"width":28057},[20743,65423,65424],{},[895,65425,65426,65428,65430,65432,65438,65440,65442,65444,65446,65448,65454,65456],{},[898,65427,2815],{},[898,65429,3984],{},[1726,65431,1735],{"stretchy":1734},[2275,65433,65434,65436],{},[898,65435,1724],{},[2133,65437,2328],{},[1726,65439,1762],{"stretchy":1734},[1726,65441,1728],{},[898,65443,2815],{},[898,65445,2775],{},[1726,65447,1735],{"stretchy":1734},[2275,65449,65450,65452],{},[898,65451,1724],{},[2133,65453,2328],{},[1726,65455,1762],{"stretchy":1734},[898,65457,1888],{"mathvariant":2377},[20743,65459],{"width":28057},[20743,65461,65462],{},[2289,65463,65464],{},"(3.13)",[902,65466,65467],{"encoding":904},"MR(Q_0) = MC(Q_0).\n\\tag{3.13}",[3859,65469,65470],{},[724,65471,65472,62026,65474],{},[883,65473,56424],{},[38,65475,65476],{},"V bodě maxima zisku se mezní příjem rovná mezním nákladům.",[724,65478,65479,65482,65483,8088,65510,17558,65584,1888],{},[38,65480,65481],{},"Odvození"," (úloha 3.21): nutnou podmínkou maxima ",[883,65484,65486],{"className":65485},[886],[888,65487,65488],{"xmlns":890},[892,65489,65490,65508],{},[895,65491,65492,65494,65496,65498,65500,65502,65504,65506],{},[898,65493,1738],{},[898,65495,3984],{},[1726,65497,1728],{},[898,65499,2772],{},[898,65501,3984],{},[1726,65503,2228],{},[898,65505,2772],{},[898,65507,2775],{},[902,65509,55180],{"encoding":904},[883,65511,65513],{"className":65512},[886],[888,65514,65515],{"xmlns":890},[892,65516,65517,65581],{},[895,65518,65519,65521,65527,65529,65535,65537,65539,65541,65547,65549,65555,65557,65559,65561,65567,65569,65575,65577,65579],{},[898,65520,1738],{},[2128,65522,65523,65525],{},[898,65524,3984],{},[1726,65526,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,65528,1735],{"stretchy":1734},[2275,65530,65531,65533],{},[898,65532,1724],{},[2133,65534,2328],{},[1726,65536,1762],{"stretchy":1734},[1726,65538,1728],{},[898,65540,2772],{},[2128,65542,65543,65545],{},[898,65544,3984],{},[1726,65546,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,65548,1735],{"stretchy":1734},[2275,65550,65551,65553],{},[898,65552,1724],{},[2133,65554,2328],{},[1726,65556,1762],{"stretchy":1734},[1726,65558,2228],{},[898,65560,2772],{},[2128,65562,65563,65565],{},[898,65564,2775],{},[1726,65566,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,65568,1735],{"stretchy":1734},[2275,65570,65571,65573],{},[898,65572,1724],{},[2133,65574,2328],{},[1726,65576,1762],{"stretchy":1734},[1726,65578,1728],{},[2133,65580,2328],{},[902,65582,65583],{"encoding":904},"PR'(Q_0) = TR'(Q_0) - TC'(Q_0) = 0",[883,65585,65587],{"className":65586},[886],[888,65588,65589],{"xmlns":890},[892,65590,65591,65623],{},[895,65592,65593,65595,65597,65599,65605,65607,65609,65611,65613,65615,65621],{},[898,65594,2815],{},[898,65596,3984],{},[1726,65598,1735],{"stretchy":1734},[2275,65600,65601,65603],{},[898,65602,1724],{},[2133,65604,2328],{},[1726,65606,1762],{"stretchy":1734},[1726,65608,1728],{},[898,65610,2815],{},[898,65612,2775],{},[1726,65614,1735],{"stretchy":1734},[2275,65616,65617,65619],{},[898,65618,1724],{},[2133,65620,2328],{},[1726,65622,1762],{"stretchy":1734},[902,65624,65625],{"encoding":904},"MR(Q_0) = MC(Q_0)",[3859,65627,65628,65633],{},[724,65629,65630,65632],{},[883,65631,4560],{}," Postup — jak najít maximum zisku",[152,65634,65635,65699,65754,65791,65819],{},[123,65636,65637,65638,3877,65653,65668,65669,1847],{},"Sestavte ",[883,65639,65641],{"className":65640},[886],[888,65642,65643],{"xmlns":890},[892,65644,65645,65651],{},[895,65646,65647,65649],{},[898,65648,2772],{},[898,65650,3984],{},[902,65652,4084],{"encoding":904},[883,65654,65656],{"className":65655},[886],[888,65657,65658],{"xmlns":890},[892,65659,65660,65666],{},[895,65661,65662,65664],{},[898,65663,2772],{},[898,65665,2775],{},[902,65667,3240],{"encoding":904}," ze zadání (typicky ",[883,65670,65672],{"className":65671},[886],[888,65673,65674],{"xmlns":890},[892,65675,65676,65696],{},[895,65677,65678,65680,65682,65684,65686,65688,65690,65692,65694],{},[898,65679,2772],{},[898,65681,3984],{},[1726,65683,1728],{},[898,65685,1738],{},[1726,65687,1735],{"stretchy":1734},[898,65689,1724],{},[1726,65691,1762],{"stretchy":1734},[1726,65693,3174],{},[898,65695,1724],{},[902,65697,65698],{"encoding":904},"TR = P(Q) \\cdot Q",[123,65700,65701,65702,3877,65728,1888],{},"Vypočtěte ",[883,65703,65705],{"className":65704},[886],[888,65706,65707],{"xmlns":890},[892,65708,65709,65725],{},[895,65710,65711,65713,65715,65717,65719],{},[898,65712,2815],{},[898,65714,3984],{},[1726,65716,1728],{},[898,65718,2772],{},[2128,65720,65721,65723],{},[898,65722,3984],{},[1726,65724,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[902,65726,65727],{"encoding":904},"MR = TR'",[883,65729,65731],{"className":65730},[886],[888,65732,65733],{"xmlns":890},[892,65734,65735,65751],{},[895,65736,65737,65739,65741,65743,65745],{},[898,65738,2815],{},[898,65740,2775],{},[1726,65742,1728],{},[898,65744,2772],{},[2128,65746,65747,65749],{},[898,65748,2775],{},[1726,65750,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[902,65752,65753],{"encoding":904},"MC = TC'",[123,65755,65756,65757,1888],{},"Řešte rovnici ",[883,65758,65760],{"className":65759},[886],[888,65761,65762],{"xmlns":890},[892,65763,65764,65788],{},[895,65765,65766,65768,65770,65772,65774,65776,65778,65780,65782,65784,65786],{},[898,65767,2815],{},[898,65769,3984],{},[1726,65771,1735],{"stretchy":1734},[898,65773,1724],{},[1726,65775,1762],{"stretchy":1734},[1726,65777,1728],{},[898,65779,2815],{},[898,65781,2775],{},[1726,65783,1735],{"stretchy":1734},[898,65785,1724],{},[1726,65787,1762],{"stretchy":1734},[902,65789,65790],{"encoding":904},"MR(Q) = MC(Q)",[123,65792,65793,65794,65818],{},"Ověřte druhou derivaci ",[883,65795,65797],{"className":65796},[886],[888,65798,65799],{"xmlns":890},[892,65800,65801,65815],{},[895,65802,65803,65805],{},[898,65804,1738],{},[2128,65806,65807,65809],{},[898,65808,3984],{},[895,65810,65811,65813],{},[1726,65812,2379],{"mathvariant":2377},[1726,65814,2379],{"mathvariant":2377},[902,65816,65817],{"encoding":904},"PR''"," (nebo že má rovnice jediný ekonomicky smysluplný kořen).",[123,65820,65821,65822,65849],{},"Dosaďte do ",[883,65823,65825],{"className":65824},[886],[888,65826,65827],{"xmlns":890},[892,65828,65829,65847],{},[895,65830,65831,65833,65835,65837,65839,65841,65843,65845],{},[898,65832,1738],{},[898,65834,3984],{},[1726,65836,1728],{},[898,65838,2772],{},[898,65840,3984],{},[1726,65842,2228],{},[898,65844,2772],{},[898,65846,2775],{},[902,65848,55180],{"encoding":904}," pro hodnotu maxima.",[37329,65851,65853],{"id":65852},"příklad-39","Příklad 3.9",[724,65855,65856,55968,65858,3877,65880,65916],{},[38,65857,55967],{},[883,65859,65861],{"className":65860},[886],[888,65862,65863],{"xmlns":890},[892,65864,65865,65877],{},[895,65866,65867,65869,65871,65873,65875],{},[898,65868,1738],{},[1726,65870,1728],{},[2133,65872,38000],{},[1726,65874,2228],{},[898,65876,1724],{},[902,65878,65879],{"encoding":904},"P = 30 - Q",[883,65881,65883],{"className":65882},[886],[888,65884,65885],{"xmlns":890},[892,65886,65887,65913],{},[895,65888,65889,65891,65893,65895,65897,65903,65905,65907,65909,65911],{},[898,65890,2772],{},[898,65892,2775],{},[1726,65894,1728],{},[2133,65896,4996],{},[2128,65898,65899,65901],{},[898,65900,1724],{},[2133,65902,2135],{},[1726,65904,2099],{},[2133,65906,2238],{},[898,65908,1724],{},[1726,65910,2099],{},[2133,65912,24182],{},[902,65914,65915],{"encoding":904},"TC = 0{,}5Q^2 + 6Q + 7"," stanovte produkci maximalizující zisk.",[724,65918,65919,1777,65921,1343,65951,65989,65990,15776,66034,66068,66069,1888],{},[38,65920,22751],{},[883,65922,65924],{"className":65923},[886],[888,65925,65926],{"xmlns":890},[892,65927,65928,65948],{},[895,65929,65930,65932,65934,65936,65938,65940,65942],{},[898,65931,2772],{},[898,65933,3984],{},[1726,65935,1728],{},[2133,65937,38000],{},[898,65939,1724],{},[1726,65941,2228],{},[2128,65943,65944,65946],{},[898,65945,1724],{},[2133,65947,2135],{},[902,65949,65950],{"encoding":904},"TR = 30Q - Q^2",[883,65952,65954],{"className":65953},[886],[888,65955,65956],{"xmlns":890},[892,65957,65958,65986],{},[895,65959,65960,65962,65964,65966,65968,65970,65976,65978,65980,65982,65984],{},[898,65961,1738],{},[898,65963,3984],{},[1726,65965,1728],{},[1726,65967,2228],{},[2133,65969,64539],{},[2128,65971,65972,65974],{},[898,65973,1724],{},[2133,65975,2135],{},[1726,65977,2099],{},[2133,65979,41781],{},[898,65981,1724],{},[1726,65983,2228],{},[2133,65985,24182],{},[902,65987,65988],{"encoding":904},"PR = -1{,}5Q^2 + 24Q - 7",". Extrém: ",[883,65991,65993],{"className":65992},[886],[888,65994,65995],{"xmlns":890},[892,65996,65997,66031],{},[895,65998,65999,66001,66007,66009,66011,66013,66015,66017,66019,66021,66023,66025,66027,66029],{},[898,66000,1738],{},[2128,66002,66003,66005],{},[898,66004,3984],{},[1726,66006,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,66008,1728],{},[1726,66010,2228],{},[2133,66012,2177],{},[898,66014,1724],{},[1726,66016,2099],{},[2133,66018,41781],{},[1726,66020,1728],{},[2133,66022,2328],{},[1726,66024,3977],{},[898,66026,1724],{},[1726,66028,1728],{},[2133,66030,5572],{},[902,66032,66033],{"encoding":904},"PR' = -3Q + 24 = 0 \\Rightarrow Q = 8",[883,66035,66037],{"className":66036},[886],[888,66038,66039],{"xmlns":890},[892,66040,66041,66065],{},[895,66042,66043,66045,66055,66057,66059,66061,66063],{},[898,66044,1738],{},[2128,66046,66047,66049],{},[898,66048,3984],{},[895,66050,66051,66053],{},[1726,66052,2379],{"mathvariant":2377},[1726,66054,2379],{"mathvariant":2377},[1726,66056,1728],{},[1726,66058,2228],{},[2133,66060,2177],{},[1726,66062,3444],{},[2133,66064,2328],{},[902,66066,66067],{"encoding":904},"PR'' = -3 \u003C 0"," (maximum); ",[883,66070,66072],{"className":66071},[886],[888,66073,66074],{"xmlns":890},[892,66075,66076,66093],{},[895,66077,66078,66080,66082,66084,66086,66088,66090],{},[898,66079,1738],{},[898,66081,3984],{},[1726,66083,1735],{"stretchy":1734},[2133,66085,5572],{},[1726,66087,1762],{"stretchy":1734},[1726,66089,1728],{},[2133,66091,66092],{},"89",[902,66094,66095],{"encoding":904},"PR(8) = 89",[724,66097,66098,66099,1343,66125,15776,66149,66187],{},"Ověření principu: ",[883,66100,66102],{"className":66101},[886],[888,66103,66104],{"xmlns":890},[892,66105,66106,66122],{},[895,66107,66108,66110,66112,66114,66116,66118,66120],{},[898,66109,2815],{},[898,66111,3984],{},[1726,66113,1728],{},[2133,66115,38000],{},[1726,66117,2228],{},[2133,66119,2135],{},[898,66121,1724],{},[902,66123,66124],{"encoding":904},"MR = 30 - 2Q",[883,66126,66128],{"className":66127},[886],[888,66129,66130],{"xmlns":890},[892,66131,66132,66146],{},[895,66133,66134,66136,66138,66140,66142,66144],{},[898,66135,2815],{},[898,66137,2775],{},[1726,66139,1728],{},[898,66141,1724],{},[1726,66143,2099],{},[2133,66145,2238],{},[902,66147,66148],{"encoding":904},"MC = Q + 6",[883,66150,66152],{"className":66151},[886],[888,66153,66154],{"xmlns":890},[892,66155,66156,66184],{},[895,66157,66158,66160,66162,66164,66166,66168,66170,66172,66174,66176,66178,66180,66182],{},[898,66159,2815],{},[898,66161,3984],{},[1726,66163,1735],{"stretchy":1734},[2133,66165,5572],{},[1726,66167,1762],{"stretchy":1734},[1726,66169,1728],{},[2133,66171,22927],{},[1726,66173,1728],{},[898,66175,2815],{},[898,66177,2775],{},[1726,66179,1735],{"stretchy":1734},[2133,66181,5572],{},[1726,66183,1762],{"stretchy":1734},[902,66185,66186],{"encoding":904},"MR(8) = 14 = MC(8)",", tj. platí (3.13).",[724,66189,66190,66191,66224,66225,66242],{},"V řadě případů — má-li rovnice ",[883,66192,66194],{"className":66193},[886],[888,66195,66196],{"xmlns":890},[892,66197,66198,66222],{},[895,66199,66200,66202,66204,66206,66208,66210,66212,66214,66216,66218,66220],{},[898,66201,2815],{},[898,66203,3984],{},[1726,66205,1735],{"stretchy":1734},[898,66207,1724],{},[1726,66209,1762],{"stretchy":1734},[1726,66211,1728],{},[898,66213,2815],{},[898,66215,2775],{},[1726,66217,1735],{"stretchy":1734},[898,66219,1724],{},[1726,66221,1762],{"stretchy":1734},[902,66223,65790],{"encoding":904}," jediné ekonomicky smysluplné řešení ",[883,66226,66228],{"className":66227},[886],[888,66229,66230],{"xmlns":890},[892,66231,66232,66240],{},[895,66233,66234],{},[2275,66235,66236,66238],{},[898,66237,1724],{},[2133,66239,2328],{},[902,66241,38289],{"encoding":904}," — není třeba provádět test druhé derivace.",[37329,66244,66246],{"id":66245},"příklad-310","Příklad 3.10",[724,66248,66249,66251,66252,66256,66257,66270,66271,66302],{},[38,66250,55967],{}," Firma vyrábí minipočítače v ",[207,66253,66255],{"className":66254,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurenci",", produkuje 30 výrobků denně za ",[883,66258,66260],{"className":66259},[886],[888,66261,66262],{"xmlns":890},[892,66263,66264,66268],{},[895,66265,66266],{},[2133,66267,15177],{},[902,66269,15177],{"encoding":904}," EUR\u002Fks. ",[883,66272,66274],{"className":66273},[886],[888,66275,66276],{"xmlns":890},[892,66277,66278,66299],{},[895,66279,66280,66282,66284,66286,66288,66290,66293],{},[898,66281,2772],{},[898,66283,2775],{},[1726,66285,1728],{},[2133,66287,3117],{},[1726,66289,2099],{},[2133,66291,66292],{},"28",[2128,66294,66295,66297],{},[898,66296,1724],{},[2133,66298,2135],{},[902,66300,66301],{"encoding":904},"TC = 50 + 28Q^2",". Určete optimální denní produkci a zisk.",[724,66304,66305,1777,66307,1343,66329,1343,66349,66372],{},[38,66306,22751],{},[883,66308,66310],{"className":66309},[886],[888,66311,66312],{"xmlns":890},[892,66313,66314,66326],{},[895,66315,66316,66318,66320,66322,66324],{},[898,66317,2772],{},[898,66319,3984],{},[1726,66321,1728],{},[2133,66323,15177],{},[898,66325,1724],{},[902,66327,66328],{"encoding":904},"TR = 900Q",[883,66330,66332],{"className":66331},[886],[888,66333,66334],{"xmlns":890},[892,66335,66336,66346],{},[895,66337,66338,66340,66342,66344],{},[898,66339,2815],{},[898,66341,3984],{},[1726,66343,1728],{},[2133,66345,15177],{},[902,66347,66348],{"encoding":904},"MR = 900",[883,66350,66352],{"className":66351},[886],[888,66353,66354],{"xmlns":890},[892,66355,66356,66369],{},[895,66357,66358,66360,66362,66364,66367],{},[898,66359,2815],{},[898,66361,2775],{},[1726,66363,1728],{},[2133,66365,66366],{},"56",[898,66368,1724],{},[902,66370,66371],{"encoding":904},"MC = 56Q",". Z principu:",[883,66374,66376],{"className":66375},[886],[888,66377,66378],{"xmlns":890,"display":28047},[892,66379,66380,66422],{},[895,66381,66382,66384,66386,66388,66390,66392,66394,66396,66398,66400,66408,66410,66413,66415,66417,66419],{},[2133,66383,15177],{},[1726,66385,1728],{},[2133,66387,66366],{},[898,66389,1724],{},[2289,66391,3974],{},[1726,66393,3977],{},[2289,66395,3974],{},[898,66397,1724],{},[1726,66399,1728],{},[2326,66401,66402],{"scriptlevel":2328,"displaystyle":1734},[2330,66403,66404,66406],{},[2133,66405,15177],{},[2133,66407,66366],{},[1726,66409,5887],{},[2133,66411,66412],{},"16,07",[2289,66414,3974],{},[1726,66416,1880],{},[2289,66418,3974],{},[2133,66420,66421],{},"16.",[902,66423,66424],{"encoding":904},"900 = 56Q \\;\\Rightarrow\\; Q = \\tfrac{900}{56} \\doteq 16{,}07 \\;\\approx\\; 16.",[724,66426,66427,66428,2703],{},"Zisk při ",[883,66429,66431],{"className":66430},[886],[888,66432,66433],{"xmlns":890},[892,66434,66435,66443],{},[895,66436,66437,66439,66441],{},[898,66438,1724],{},[1726,66440,1728],{},[2133,66442,41843],{},[902,66444,66445],{"encoding":904},"Q = 16",[883,66447,66449],{"className":66448},[886],[888,66450,66451],{"xmlns":890,"display":28047},[892,66452,66453,66524],{},[895,66454,66455,66457,66459,66461,66463,66465,66467,66469,66471,66473,66475,66477,66479,66481,66483,66485,66491,66493,66495,66497,66499,66501,66503,66505,66507,66510,66512,66514,66516,66519,66522],{},[898,66456,1738],{},[898,66458,3984],{},[1726,66460,1735],{"stretchy":1734},[2133,66462,41843],{},[1726,66464,1762],{"stretchy":1734},[1726,66466,1728],{},[2133,66468,15177],{},[1726,66470,3174],{},[2133,66472,41843],{},[1726,66474,2228],{},[1726,66476,1735],{"stretchy":1734},[2133,66478,3117],{},[1726,66480,2099],{},[2133,66482,66292],{},[1726,66484,3174],{},[2128,66486,66487,66489],{},[2133,66488,41843],{},[2133,66490,2135],{},[1726,66492,1762],{"stretchy":1734},[1726,66494,1728],{},[2133,66496,22927],{},[2289,66498,2984],{},[2133,66500,20123],{},[1726,66502,2228],{},[2133,66504,24182],{},[2289,66506,2984],{},[2133,66508,66509],{},"218",[1726,66511,1728],{},[2133,66513,24182],{},[2289,66515,2984],{},[2133,66517,66518],{},"182",[2289,66520,66521],{}," EUR",[898,66523,1888],{"mathvariant":2377},[902,66525,66526],{"encoding":904},"PR(16) = 900 \\cdot 16 - (50 + 28 \\cdot 16^2) = 14\\,400 - 7\\,218 = 7\\,182 \\text{ EUR}.",[724,66528,66529],{},"Pro srovnání při původních 30 ks:",[883,66531,66533],{"className":66532},[886],[888,66534,66535],{"xmlns":890,"display":28047},[892,66536,66537,66602],{},[895,66538,66539,66541,66543,66545,66547,66549,66551,66553,66555,66557,66559,66561,66563,66565,66567,66569,66571,66573,66575,66578,66580,66582,66584,66586,66588,66590,66592,66594,66596,66598,66600],{},[898,66540,1738],{},[898,66542,3984],{},[1726,66544,1735],{"stretchy":1734},[2133,66546,38000],{},[1726,66548,1762],{"stretchy":1734},[1726,66550,1728],{},[2133,66552,15177],{},[1726,66554,3174],{},[2133,66556,38000],{},[1726,66558,2228],{},[1726,66560,1735],{"stretchy":1734},[2133,66562,3117],{},[1726,66564,2099],{},[2133,66566,66292],{},[1726,66568,3174],{},[2133,66570,15177],{},[1726,66572,1762],{"stretchy":1734},[1726,66574,1728],{},[2133,66576,66577],{},"27",[2289,66579,2984],{},[2133,66581,59062],{},[1726,66583,2228],{},[2133,66585,4991],{},[2289,66587,2984],{},[2133,66589,30724],{},[1726,66591,1728],{},[2133,66593,2281],{},[2289,66595,2984],{},[2133,66597,23724],{},[2289,66599,66521],{},[898,66601,1888],{"mathvariant":2377},[902,66603,66604],{"encoding":904},"PR(30) = 900 \\cdot 30 - (50 + 28 \\cdot 900) = 27\\,000 - 25\\,250 = 1\\,750 \\text{ EUR}.",[724,66606,66607,66610,66611,66629,66630,66648],{},[38,66608,66609],{},"Doporučení:"," vyrábět 16 ks\u002Fden se ziskem ",[883,66612,66614],{"className":66613},[886],[888,66615,66616],{"xmlns":890},[892,66617,66618,66626],{},[895,66619,66620,66622,66624],{},[2133,66621,24182],{},[2289,66623,2984],{},[2133,66625,66518],{},[902,66627,66628],{"encoding":904},"7\\,182"," EUR namísto původních ",[883,66631,66633],{"className":66632},[886],[888,66634,66635],{"xmlns":890},[892,66636,66637,66645],{},[895,66638,66639,66641,66643],{},[2133,66640,2281],{},[2289,66642,2984],{},[2133,66644,23724],{},[902,66646,66647],{"encoding":904},"1\\,750"," EUR.",[198,66650,66652],{"id":66651},"speciální-tvar-pro-pevnou-cenu","Speciální tvar pro pevnou cenu",[724,66654,66655,66656,62550,66669,66693],{},"Předpokládáme-li, že výrobce prodává za pevnou cenu ",[883,66657,66659],{"className":66658},[886],[888,66660,66661],{"xmlns":890},[892,66662,66663,66667],{},[895,66664,66665],{},[898,66666,1738],{},[902,66668,1738],{"encoding":904},[883,66670,66672],{"className":66671},[886],[888,66673,66674],{"xmlns":890},[892,66675,66676,66690],{},[895,66677,66678,66680,66682,66684,66686,66688],{},[898,66679,2772],{},[898,66681,3984],{},[1726,66683,1728],{},[898,66685,1738],{},[1726,66687,3174],{},[898,66689,1724],{},[902,66691,66692],{"encoding":904},"TR = P \\cdot Q"," a z (3.13) speciálně:",[883,66695,66697],{"className":66696},[886],[888,66698,66699],{"xmlns":890,"display":28047},[892,66700,66701,66734],{},[20735,66702,66703],{"width":28052},[20740,66704,66705,66707,66727,66729],{},[20743,66706],{"width":28057},[20743,66708,66709],{},[895,66710,66711,66713,66715,66717,66719,66721,66723,66725],{},[898,66712,1738],{},[1726,66714,1728],{},[898,66716,2815],{},[898,66718,2775],{},[1726,66720,1735],{"stretchy":1734},[898,66722,1724],{},[1726,66724,1762],{"stretchy":1734},[898,66726,1888],{"mathvariant":2377},[20743,66728],{"width":28057},[20743,66730,66731],{},[2289,66732,66733],{},"(3.14)",[902,66735,66736],{"encoding":904},"P = MC(Q).\n\\tag{3.14}",[724,66738,66739,66740,1888],{},"Výrobce musí nastavit nabízené množství tak, aby se mezní náklady rovnaly ceně. Má-li rovnice (3.14) více řešení, rozhoduje znaménko ",[883,66741,66743],{"className":66742},[886],[888,66744,66745],{"xmlns":890},[892,66746,66747,66761],{},[895,66748,66749,66751],{},[898,66750,1738],{},[2128,66752,66753,66755],{},[898,66754,3984],{},[895,66756,66757,66759],{},[1726,66758,2379],{"mathvariant":2377},[1726,66760,2379],{"mathvariant":2377},[902,66762,65817],{"encoding":904},[37329,66764,66766],{"id":66765},"příklad-311","Příklad 3.11",[724,66768,66769,57502,66771,66818,66819,66837],{},[38,66770,55967],{},[883,66772,66774],{"className":66773},[886],[888,66775,66776],{"xmlns":890},[892,66777,66778,66815],{},[895,66779,66780,66782,66784,66786,66789,66795,66797,66799,66805,66807,66809,66811,66813],{},[898,66781,2772],{},[898,66783,2775],{},[1726,66785,1728],{},[2133,66787,66788],{},"0,04",[2128,66790,66791,66793],{},[898,66792,1724],{},[2133,66794,2177],{},[1726,66796,2228],{},[2133,66798,22526],{},[2128,66800,66801,66803],{},[898,66802,1724],{},[2133,66804,2135],{},[1726,66806,2099],{},[2133,66808,2860],{},[898,66810,1724],{},[1726,66812,2099],{},[2133,66814,2231],{},[902,66816,66817],{"encoding":904},"TC = 0{,}04Q^3 - 0{,}9Q^2 + 10Q + 5"," a pevnou cenu ",[883,66820,66822],{"className":66821},[886],[888,66823,66824],{"xmlns":890},[892,66825,66826,66834],{},[895,66827,66828,66830,66832],{},[898,66829,1738],{},[1726,66831,1728],{},[2133,66833,2352],{},[902,66835,66836],{"encoding":904},"P = 4"," stanovte optimální produkci.",[724,66839,66840,66842,66843,17558,66885,66919,66920,2703],{},[38,66841,22751],{}," Z (3.14): ",[883,66844,66846],{"className":66845},[886],[888,66847,66848],{"xmlns":890},[892,66849,66850,66882],{},[895,66851,66852,66854,66856,66858,66861,66867,66869,66872,66874,66876,66878,66880],{},[898,66853,2815],{},[898,66855,2775],{},[1726,66857,1728],{},[2133,66859,66860],{},"0,12",[2128,66862,66863,66865],{},[898,66864,1724],{},[2133,66866,2135],{},[1726,66868,2228],{},[2133,66870,66871],{},"1,8",[898,66873,1724],{},[1726,66875,2099],{},[2133,66877,2860],{},[1726,66879,1728],{},[2133,66881,2352],{},[902,66883,66884],{"encoding":904},"MC = 0{,}12Q^2 - 1{,}8Q + 10 = 4",[883,66886,66888],{"className":66887},[886],[888,66889,66890],{"xmlns":890},[892,66891,66892,66916],{},[895,66893,66894,66896,66902,66904,66906,66908,66910,66912,66914],{},[2133,66895,66860],{},[2128,66897,66898,66900],{},[898,66899,1724],{},[2133,66901,2135],{},[1726,66903,2228],{},[2133,66905,66871],{},[898,66907,1724],{},[1726,66909,2099],{},[2133,66911,2238],{},[1726,66913,1728],{},[2133,66915,2328],{},[902,66917,66918],{"encoding":904},"0{,}12Q^2 - 1{,}8Q + 6 = 0",", po vydělení ",[883,66921,66923],{"className":66922},[886],[888,66924,66925],{"xmlns":890},[892,66926,66927,66931],{},[895,66928,66929],{},[2133,66930,66860],{},[902,66932,66933],{"encoding":904},"0{,}12",[883,66935,66937],{"className":66936},[886],[888,66938,66939],{"xmlns":890,"display":28047},[892,66940,66941,66993],{},[895,66942,66943,66949,66951,66953,66955,66957,66959,66961,66963,66965,66967,66969,66975,66977,66979,66981,66983,66989,66991],{},[2128,66944,66945,66947],{},[898,66946,1724],{},[2133,66948,2135],{},[1726,66950,2228],{},[2133,66952,36225],{},[898,66954,1724],{},[1726,66956,2099],{},[2133,66958,3117],{},[1726,66960,1728],{},[2133,66962,2328],{},[2289,66964,3974],{},[1726,66966,3977],{},[2289,66968,3974],{},[2275,66970,66971,66973],{},[898,66972,1724],{},[2133,66974,2281],{},[1726,66976,1728],{},[2133,66978,2231],{},[1726,66980,1742],{"separator":1741},[2289,66982,3974],{},[2275,66984,66985,66987],{},[898,66986,1724],{},[2133,66988,2135],{},[1726,66990,1728],{},[2133,66992,19309],{},[902,66994,66995],{"encoding":904},"Q^2 - 15Q + 50 = 0 \\;\\Rightarrow\\; Q_1 = 5, \\; Q_2 = 10.",[724,66997,66998,66999,2703],{},"Dále ",[883,67000,67002],{"className":67001},[886],[888,67003,67004],{"xmlns":890},[892,67005,67006,67045],{},[895,67007,67008,67010,67020,67022,67024,67026,67032,67034,67036,67039,67041,67043],{},[898,67009,1738],{},[2128,67011,67012,67014],{},[898,67013,3984],{},[895,67015,67016,67018],{},[1726,67017,2379],{"mathvariant":2377},[1726,67019,2379],{"mathvariant":2377},[1726,67021,1728],{},[1726,67023,2228],{},[898,67025,2815],{},[2128,67027,67028,67030],{},[898,67029,2775],{},[1726,67031,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,67033,1728],{},[1726,67035,2228],{},[2133,67037,67038],{},"0,24",[898,67040,1724],{},[1726,67042,2099],{},[2133,67044,66871],{},[902,67046,67047],{"encoding":904},"PR'' = -MC' = -0{,}24Q + 1{,}8",[120,67049,67050,67100],{},[123,67051,67052,67096,67097,67099],{},[883,67053,67055],{"className":67054},[886],[888,67056,67057],{"xmlns":890},[892,67058,67059,67093],{},[895,67060,67061,67063,67073,67075,67077,67079,67081,67083,67085,67087,67089,67091],{},[898,67062,1738],{},[2128,67064,67065,67067],{},[898,67066,3984],{},[895,67068,67069,67071],{},[1726,67070,2379],{"mathvariant":2377},[1726,67072,2379],{"mathvariant":2377},[1726,67074,1735],{"stretchy":1734},[2133,67076,2231],{},[1726,67078,1762],{"stretchy":1734},[1726,67080,1728],{},[2133,67082,19302],{},[1726,67084,3405],{},[2133,67086,2328],{},[2289,67088,3974],{},[1726,67090,3977],{},[2289,67092,3974],{},[902,67094,67095],{"encoding":904},"PR''(5) = 0{,}6 > 0 \\;\\Rightarrow\\;"," lokální ",[38,67098,3772],{}," zisku (minimalizace ztráty);",[123,67101,67102,67096,67148,67150],{},[883,67103,67105],{"className":67104},[886],[888,67106,67107],{"xmlns":890},[892,67108,67109,67145],{},[895,67110,67111,67113,67123,67125,67127,67129,67131,67133,67135,67137,67139,67141,67143],{},[898,67112,1738],{},[2128,67114,67115,67117],{},[898,67116,3984],{},[895,67118,67119,67121],{},[1726,67120,2379],{"mathvariant":2377},[1726,67122,2379],{"mathvariant":2377},[1726,67124,1735],{"stretchy":1734},[2133,67126,2860],{},[1726,67128,1762],{"stretchy":1734},[1726,67130,1728],{},[1726,67132,2228],{},[2133,67134,19302],{},[1726,67136,3444],{},[2133,67138,2328],{},[2289,67140,3974],{},[1726,67142,3977],{},[2289,67144,3974],{},[902,67146,67147],{"encoding":904},"PR''(10) = -0{,}6 \u003C 0 \\;\\Rightarrow\\;",[38,67149,3714],{}," zisku, avšak",[883,67152,67154],{"className":67153},[886],[888,67155,67156],{"xmlns":890,"display":28047},[892,67157,67158,67226],{},[895,67159,67160,67162,67164,67166,67168,67170,67172,67174,67176,67178,67180,67182,67184,67186,67188,67190,67192,67194,67196,67198,67200,67202,67204,67206,67208,67210,67212,67214,67216,67218,67220,67222,67224],{},[898,67161,1738],{},[898,67163,3984],{},[1726,67165,1735],{"stretchy":1734},[2133,67167,2860],{},[1726,67169,1762],{"stretchy":1734},[1726,67171,1728],{},[2133,67173,2352],{},[1726,67175,3174],{},[2133,67177,2860],{},[1726,67179,2228],{},[1726,67181,1735],{"stretchy":1734},[2133,67183,66788],{},[1726,67185,3174],{},[2133,67187,2281],{},[2289,67189,2984],{},[2133,67191,59062],{},[1726,67193,2228],{},[2133,67195,22526],{},[1726,67197,3174],{},[2133,67199,3087],{},[1726,67201,2099],{},[2133,67203,3087],{},[1726,67205,2099],{},[2133,67207,2231],{},[1726,67209,1762],{"stretchy":1734},[1726,67211,1728],{},[2133,67213,5198],{},[1726,67215,2228],{},[2133,67217,21161],{},[1726,67219,1728],{},[1726,67221,2228],{},[2133,67223,36225],{},[1726,67225,1742],{"separator":1741},[902,67227,67228],{"encoding":904},"PR(10) = 4 \\cdot 10 - (0{,}04 \\cdot 1\\,000 - 0{,}9 \\cdot 100 + 100 + 5) = 40 - 55 = -15,",[724,67230,67231,67232,1888],{},"tj. ztráta větší než ",[883,67233,67235],{"className":67234},[886],[888,67236,67237],{"xmlns":890},[892,67238,67239,67249],{},[895,67240,67241,67243,67245,67247],{},[898,67242,10420],{},[898,67244,2775],{},[1726,67246,1728],{},[2133,67248,2231],{},[902,67250,67251],{"encoding":904},"FC = 5",[724,67253,67254,67257,67258,67261,67262,1888],{},[38,67255,67256],{},"Závěr:"," firma by měla ",[38,67259,67260],{},"zastavit výrobu"," — i vypnutí provozu způsobí menší ztrátu, a to pouze ve výši ",[883,67263,67265],{"className":67264},[886],[888,67266,67267],{"xmlns":890},[892,67268,67269,67279],{},[895,67270,67271,67273,67275,67277],{},[898,67272,10420],{},[898,67274,2775],{},[1726,67276,1728],{},[2133,67278,2231],{},[902,67280,67251],{"encoding":904},[115,67282,67284],{"id":67283},"konstrukce-křivky-nabídky-firmy","Konstrukce křivky nabídky firmy",[724,67286,67287,67288,67290,67291,67306,67307,67320,67321,67347,67348,67361,67362,67379,67380,2623,67397,67400,67401,67421,67422,67437,67438,2703],{},"Důležitým završením analýzy je konstrukce ",[38,67289,55255],{},". S nabízeným množstvím rostou mezní náklady ",[883,67292,67294],{"className":67293},[886],[888,67295,67296],{"xmlns":890},[892,67297,67298,67304],{},[895,67299,67300,67302],{},[898,67301,2815],{},[898,67303,2775],{},[902,67305,55272],{"encoding":904}," a tyto určují cenu ",[883,67308,67310],{"className":67309},[886],[888,67311,67312],{"xmlns":890},[892,67313,67314,67318],{},[895,67315,67316],{},[898,67317,1738],{},[902,67319,1738],{"encoding":904},", za kterou je firma ochotna toto množství realizovat. Proto platí ",[883,67322,67324],{"className":67323},[886],[888,67325,67326],{"xmlns":890},[892,67327,67328,67344],{},[895,67329,67330,67332,67334,67336,67338,67340,67342],{},[898,67331,1738],{},[1726,67333,1728],{},[898,67335,2815],{},[898,67337,2775],{},[1726,67339,1735],{"stretchy":1734},[898,67341,1724],{},[1726,67343,1762],{"stretchy":1734},[902,67345,67346],{"encoding":904},"P = MC(Q)"," (obrázek 3.14). Cena ",[883,67349,67351],{"className":67350},[886],[888,67352,67353],{"xmlns":890},[892,67354,67355,67359],{},[895,67356,67357],{},[898,67358,1738],{},[902,67360,1738],{"encoding":904}," však nemůže být nižší než ",[883,67363,67365],{"className":67364},[886],[888,67366,67367],{"xmlns":890},[892,67368,67369,67377],{},[895,67370,67371],{},[2128,67372,67373,67375],{},[898,67374,1738],{},[1726,67376,4342],{},[902,67378,4392],{"encoding":904}," odpovídající množství ",[883,67381,67383],{"className":67382},[886],[888,67384,67385],{"xmlns":890},[892,67386,67387,67395],{},[895,67388,67389],{},[2128,67390,67391,67393],{},[898,67392,1724],{},[1726,67394,4342],{},[902,67396,29825],{"encoding":904},[38,67398,67399],{},"minima průměrných variabilních nákladů"," (fixní náklady nelze při optimalizaci zahrnout — jsou konstantní součástí nákladů i zisku). Křivka nabídky se tedy skládá z úsečky ",[883,67402,67404],{"className":67403},[886],[888,67405,67406],{"xmlns":890},[892,67407,67408,67418],{},[895,67409,67410,67412],{},[2133,67411,2328],{},[2128,67413,67414,67416],{},[898,67415,1724],{},[1726,67417,4342],{},[902,67419,67420],{"encoding":904},"0Q^*"," (kde firma nenabízí nic) a rostoucí části ",[883,67423,67425],{"className":67424},[886],[888,67426,67427],{"xmlns":890},[892,67428,67429,67435],{},[895,67430,67431,67433],{},[898,67432,2815],{},[898,67434,2775],{},[902,67436,55272],{"encoding":904}," nad bodem ",[883,67439,67441],{"className":67440},[886],[888,67442,67443],{"xmlns":890},[892,67444,67445,67449],{},[895,67446,67447],{},[898,67448,4243],{},[902,67450,4243],{"encoding":904},[883,67452,67454],{"className":67453},[886],[888,67455,67456],{"xmlns":890,"display":28047},[892,67457,67458,67565],{},[20735,67459,67460],{"width":28052},[20740,67461,67462,67464,67558,67560],{},[20743,67463],{"width":28057},[20743,67465,67466],{},[895,67467,67468,67470,67472,67474,67476,67478,67480,67482],{},[898,67469,1738],{},[1726,67471,1728],{},[898,67473,8659],{},[1726,67475,1735],{"stretchy":1734},[898,67477,1724],{},[1726,67479,1762],{"stretchy":1734},[1726,67481,1728],{},[895,67483,67484,67487],{},[1726,67485,67486],{"fence":1741},"{",[20735,67488,67491,67530],{"rowspacing":67489,"columnalign":67490,"columnspacing":15270},"0.36em","left left",[20740,67492,67493,67509],{},[20743,67494,67495],{},[2326,67496,67497],{"scriptlevel":2328,"displaystyle":1734},[895,67498,67499,67501,67503,67505,67507],{},[898,67500,2815],{},[898,67502,2775],{},[1726,67504,1735],{"stretchy":1734},[898,67506,1724],{},[1726,67508,1762],{"stretchy":1734},[20743,67510,67511],{},[2326,67512,67513],{"scriptlevel":2328,"displaystyle":1734},[895,67514,67515,67518,67520,67522,67528],{},[2289,67516,67517],{},"pro ",[898,67519,1724],{},[1726,67521,4473],{},[2128,67523,67524,67526],{},[898,67525,1724],{},[1726,67527,4342],{},[1726,67529,1742],{"separator":1741},[20740,67531,67532,67538],{},[20743,67533,67534],{},[2326,67535,67536],{"scriptlevel":2328,"displaystyle":1734},[2133,67537,2328],{},[20743,67539,67540],{},[2326,67541,67542],{"scriptlevel":2328,"displaystyle":1734},[895,67543,67544,67546,67548,67550,67556],{},[2289,67545,67517],{},[898,67547,1724],{},[1726,67549,3444],{},[2128,67551,67552,67554],{},[898,67553,1724],{},[1726,67555,4342],{},[1726,67557,1742],{"separator":1741},[20743,67559],{"width":28057},[20743,67561,67562],{},[2289,67563,67564],{},"(3.15)",[902,67566,67567],{"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}",[724,67569,4298,67570,67587,67588,67605,67606,41480,67636,67639],{},[883,67571,67573],{"className":67572},[886],[888,67574,67575],{"xmlns":890},[892,67576,67577,67585],{},[895,67578,67579],{},[2128,67580,67581,67583],{},[898,67582,1724],{},[1726,67584,4342],{},[902,67586,29825],{"encoding":904}," je bod minima ",[883,67589,67591],{"className":67590},[886],[888,67592,67593],{"xmlns":890},[892,67594,67595,67603],{},[895,67596,67597,67599,67601],{},[898,67598,4243],{},[898,67600,40320],{},[898,67602,2775],{},[902,67604,55291],{"encoding":904},". Bod ",[883,67607,67609],{"className":67608},[886],[888,67610,67611],{"xmlns":890},[892,67612,67613,67633],{},[895,67614,67615,67617,67623,67625,67631],{},[1726,67616,1735],{"stretchy":1734},[2128,67618,67619,67621],{},[898,67620,1724],{},[1726,67622,4342],{},[1726,67624,1742],{"separator":1741},[2128,67626,67627,67629],{},[898,67628,1738],{},[1726,67630,4342],{},[1726,67632,1762],{"stretchy":1734},[902,67634,67635],{"encoding":904},"(Q^*, P^*)",[38,67637,67638],{},"shutdown point"," — pod ním se firmě nevyplatí produkovat.",[3859,67641,67642,67647],{},[724,67643,67644,67646],{},[883,67645,4560],{}," Postup — jak odvodit nabídku firmy",[152,67648,67649,67698,67793,67848,67919],{},[123,67650,67651,67652,3877,67674,1888],{},"Ze zadaných nákladů určete ",[883,67653,67655],{"className":67654},[886],[888,67656,67657],{"xmlns":890},[892,67658,67659,67671],{},[895,67660,67661,67663,67665,67667,67669],{},[898,67662,2815],{},[898,67664,2775],{},[1726,67666,1735],{"stretchy":1734},[898,67668,1724],{},[1726,67670,1762],{"stretchy":1734},[902,67672,67673],{"encoding":904},"MC(Q)",[883,67675,67677],{"className":67676},[886],[888,67678,67679],{"xmlns":890},[892,67680,67681,67695],{},[895,67682,67683,67685,67687,67689,67691,67693],{},[898,67684,4243],{},[898,67686,40320],{},[898,67688,2775],{},[1726,67690,1735],{"stretchy":1734},[898,67692,1724],{},[1726,67694,1762],{"stretchy":1734},[902,67696,67697],{"encoding":904},"AVC(Q)",[123,67699,67700,67701,67718,67719,67736,67737,67769,67770,1847],{},"Najděte ",[883,67702,67704],{"className":67703},[886],[888,67705,67706],{"xmlns":890},[892,67707,67708,67716],{},[895,67709,67710],{},[2128,67711,67712,67714],{},[898,67713,1724],{},[1726,67715,4342],{},[902,67717,29825],{"encoding":904}," jako bod minima ",[883,67720,67722],{"className":67721},[886],[888,67723,67724],{"xmlns":890},[892,67725,67726,67734],{},[895,67727,67728,67730,67732],{},[898,67729,4243],{},[898,67731,40320],{},[898,67733,2775],{},[902,67735,55291],{"encoding":904}," (řešením ",[883,67738,67740],{"className":67739},[886],[888,67741,67742],{"xmlns":890},[892,67743,67744,67766],{},[895,67745,67746,67748,67750,67756,67758,67760,67762,67764],{},[898,67747,4243],{},[898,67749,40320],{},[2128,67751,67752,67754],{},[898,67753,2775],{},[1726,67755,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,67757,1735],{"stretchy":1734},[898,67759,1724],{},[1726,67761,1762],{"stretchy":1734},[1726,67763,1728],{},[2133,67765,2328],{},[902,67767,67768],{"encoding":904},"AVC'(Q) = 0",", případně rovnice ",[883,67771,67773],{"className":67772},[886],[888,67774,67775],{"xmlns":890},[892,67776,67777,67791],{},[895,67778,67779,67781,67783,67785,67787,67789],{},[898,67780,4243],{},[898,67782,40320],{},[898,67784,2775],{},[1726,67786,1728],{},[898,67788,2815],{},[898,67790,2775],{},[902,67792,55228],{"encoding":904},[123,67794,65701,67795,67847],{},[883,67796,67798],{"className":67797},[886],[888,67799,67800],{"xmlns":890},[892,67801,67802,67844],{},[895,67803,67804,67810,67812,67814,67816,67818,67824,67826,67828,67830,67832,67834,67836,67842],{},[2128,67805,67806,67808],{},[898,67807,1738],{},[1726,67809,4342],{},[1726,67811,1728],{},[898,67813,2815],{},[898,67815,2775],{},[1726,67817,1735],{"stretchy":1734},[2128,67819,67820,67822],{},[898,67821,1724],{},[1726,67823,4342],{},[1726,67825,1762],{"stretchy":1734},[1726,67827,1728],{},[898,67829,4243],{},[898,67831,40320],{},[898,67833,2775],{},[1726,67835,1735],{"stretchy":1734},[2128,67837,67838,67840],{},[898,67839,1724],{},[1726,67841,4342],{},[1726,67843,1762],{"stretchy":1734},[902,67845,67846],{"encoding":904},"P^* = MC(Q^*) = AVC(Q^*)"," — minimální cenu nabídky.",[123,67849,67850,67851,6460,67883,67905,67906,1888],{},"Zapište nabídku: ",[883,67852,67854],{"className":67853},[886],[888,67855,67856],{"xmlns":890},[892,67857,67858,67880],{},[895,67859,67860,67862,67864,67866,67868,67870,67872,67874,67876,67878],{},[898,67861,8659],{},[1726,67863,1735],{"stretchy":1734},[898,67865,1724],{},[1726,67867,1762],{"stretchy":1734},[1726,67869,1728],{},[898,67871,2815],{},[898,67873,2775],{},[1726,67875,1735],{"stretchy":1734},[898,67877,1724],{},[1726,67879,1762],{"stretchy":1734},[902,67881,67882],{"encoding":904},"S(Q) = MC(Q)",[883,67884,67886],{"className":67885},[886],[888,67887,67888],{"xmlns":890},[892,67889,67890,67902],{},[895,67891,67892,67894,67896],{},[898,67893,1724],{},[1726,67895,4473],{},[2128,67897,67898,67900],{},[898,67899,1724],{},[1726,67901,4342],{},[902,67903,67904],{"encoding":904},"Q \\geq Q^*",", jinak ",[883,67907,67909],{"className":67908},[886],[888,67910,67911],{"xmlns":890},[892,67912,67913,67917],{},[895,67914,67915],{},[2133,67916,2328],{},[902,67918,2328],{"encoding":904},[123,67920,67921,67922,67954],{},"V případě potřeby vyjádřete inverzi ",[883,67923,67925],{"className":67924},[886],[888,67926,67927],{"xmlns":890},[892,67928,67929,67951],{},[895,67930,67931,67933,67935,67945,67947,67949],{},[898,67932,1724],{},[1726,67934,1728],{},[2128,67936,67937,67939],{},[898,67938,8659],{},[895,67940,67941,67943],{},[1726,67942,2228],{},[2133,67944,2281],{},[1726,67946,1735],{"stretchy":1734},[898,67948,1738],{},[1726,67950,1762],{"stretchy":1734},[902,67952,67953],{"encoding":904},"Q = S^{-1}(P)"," doplněním na čtverec.",[724,67956,67957],{},[614,67958,67959,67960,1343,67975,3877,67992,29182,68007,68020,68021,68046,68047,68060,68061,68078,68079,68096,68097,68114],{},"Obrázek 3.14: Křivky ",[883,67961,67963],{"className":67962},[886],[888,67964,67965],{"xmlns":890},[892,67966,67967,67973],{},[895,67968,67969,67971],{},[898,67970,4243],{},[898,67972,2775],{},[902,67974,55540],{"encoding":904},[883,67976,67978],{"className":67977},[886],[888,67979,67980],{"xmlns":890},[892,67981,67982,67990],{},[895,67983,67984,67986,67988],{},[898,67985,4243],{},[898,67987,40320],{},[898,67989,2775],{},[902,67991,55291],{"encoding":904},[883,67993,67995],{"className":67994},[886],[888,67996,67997],{"xmlns":890},[892,67998,67999,68005],{},[895,68000,68001,68003],{},[898,68002,2815],{},[898,68004,2775],{},[902,68006,55272],{"encoding":904},[883,68008,68010],{"className":68009},[886],[888,68011,68012],{"xmlns":890},[892,68013,68014,68018],{},[895,68015,68016],{},[898,68017,900],{},[902,68019,900],{"encoding":904},"; křivka nabídky ",[883,68022,68024],{"className":68023},[886],[888,68025,68026],{"xmlns":890},[892,68027,68028,68044],{},[895,68029,68030,68032,68034,68036,68038,68040,68042],{},[898,68031,1738],{},[1726,68033,1728],{},[898,68035,2815],{},[898,68037,2775],{},[1726,68039,1735],{"stretchy":1734},[898,68041,1724],{},[1726,68043,1762],{"stretchy":1734},[902,68045,67346],{"encoding":904}," začíná v bodě ",[883,68048,68050],{"className":68049},[886],[888,68051,68052],{"xmlns":890},[892,68053,68054,68058],{},[895,68055,68056],{},[898,68057,4243],{},[902,68059,4243],{"encoding":904}," odpovídajícím minimu ",[883,68062,68064],{"className":68063},[886],[888,68065,68066],{"xmlns":890},[892,68067,68068,68076],{},[895,68069,68070,68072,68074],{},[898,68071,4243],{},[898,68073,40320],{},[898,68075,2775],{},[902,68077,55291],{"encoding":904}," při ceně ",[883,68080,68082],{"className":68081},[886],[888,68083,68084],{"xmlns":890},[892,68085,68086,68094],{},[895,68087,68088],{},[2128,68089,68090,68092],{},[898,68091,1738],{},[1726,68093,4342],{},[902,68095,4392],{"encoding":904}," (minimální cena nabídky); pod ",[883,68098,68100],{"className":68099},[886],[888,68101,68102],{"xmlns":890},[892,68103,68104,68112],{},[895,68105,68106],{},[2128,68107,68108,68110],{},[898,68109,1724],{},[1726,68111,4342],{},[902,68113,29825],{"encoding":904}," je nabídka nulová.",[37329,68116,68118],{"id":68117},"příklad-312","Příklad 3.12",[724,68120,68121,57502,68123,68169],{},[38,68122,55967],{},[883,68124,68126],{"className":68125},[886],[888,68127,68128],{"xmlns":890},[892,68129,68130,68166],{},[895,68131,68132,68134,68136,68138,68140,68146,68148,68150,68156,68158,68160,68162,68164],{},[898,68133,2772],{},[898,68135,2775],{},[1726,68137,1728],{},[2133,68139,2791],{},[2128,68141,68142,68144],{},[898,68143,1724],{},[2133,68145,2177],{},[1726,68147,2228],{},[2133,68149,2135],{},[2128,68151,68152,68154],{},[898,68153,1724],{},[2133,68155,2135],{},[1726,68157,2099],{},[2133,68159,36225],{},[898,68161,1724],{},[1726,68163,2099],{},[2133,68165,2860],{},[902,68167,68168],{"encoding":904},"TC = 0{,}1Q^3 - 2Q^2 + 15Q + 10"," odvoďte funkci nabídky firmy.",[724,68171,68172,1777,68174,68211,68212,2703],{},[38,68173,22751],{},[883,68175,68177],{"className":68176},[886],[888,68178,68179],{"xmlns":890},[892,68180,68181,68208],{},[895,68182,68183,68185,68187,68189,68192,68198,68200,68202,68204,68206],{},[898,68184,2815],{},[898,68186,2775],{},[1726,68188,1728],{},[2133,68190,68191],{},"0,3",[2128,68193,68194,68196],{},[898,68195,1724],{},[2133,68197,2135],{},[1726,68199,2228],{},[2133,68201,2352],{},[898,68203,1724],{},[1726,68205,2099],{},[2133,68207,36225],{},[902,68209,68210],{"encoding":904},"MC = 0{,}3Q^2 - 4Q + 15",", takže z ",[883,68213,68215],{"className":68214},[886],[888,68216,68217],{"xmlns":890},[892,68218,68219,68229],{},[895,68220,68221,68223,68225,68227],{},[898,68222,1738],{},[1726,68224,1728],{},[898,68226,2815],{},[898,68228,2775],{},[902,68230,68231],{"encoding":904},"P = MC",[883,68233,68235],{"className":68234},[886],[888,68236,68237],{"xmlns":890,"display":28047},[892,68238,68239,68264],{},[895,68240,68241,68243,68245,68247,68253,68255,68257,68259,68261],{},[898,68242,1738],{},[1726,68244,1728],{},[2133,68246,68191],{},[2128,68248,68249,68251],{},[898,68250,1724],{},[2133,68252,2135],{},[1726,68254,2228],{},[2133,68256,2352],{},[898,68258,1724],{},[1726,68260,2099],{},[2133,68262,68263],{},"15.",[902,68265,68266],{"encoding":904},"P = 0{,}3Q^2 - 4Q + 15.",[724,68268,68269,68270,5369,68283,68296],{},"Vyjádření ",[883,68271,68273],{"className":68272},[886],[888,68274,68275],{"xmlns":890},[892,68276,68277,68281],{},[895,68278,68279],{},[898,68280,1724],{},[902,68282,1724],{"encoding":904},[883,68284,68286],{"className":68285},[886],[888,68287,68288],{"xmlns":890},[892,68289,68290,68294],{},[895,68291,68292],{},[898,68293,1738],{},[902,68295,1738],{"encoding":904}," doplněním na čtverec:",[883,68298,68300],{"className":68299},[886],[888,68301,68302],{"xmlns":890,"display":28047},[892,68303,68304,68394],{},[895,68305,68306,68308,68310,68312,68350,68352,68354,68376,68378,68392],{},[898,68307,1738],{},[1726,68309,1728],{},[2133,68311,68191],{},[895,68313,68314,68316,68338,68340,68348],{},[1726,68315,1735],{"fence":1741},[2128,68317,68318,68336],{},[895,68319,68320,68322,68324,68326,68334],{},[1726,68321,1735],{"fence":1741},[898,68323,1724],{},[1726,68325,2228],{},[2326,68327,68328],{"scriptlevel":2328,"displaystyle":1734},[2330,68329,68330,68332],{},[2133,68331,9021],{},[2133,68333,2177],{},[1726,68335,1762],{"fence":1741},[2133,68337,2135],{},[1726,68339,2099],{},[2326,68341,68342],{"scriptlevel":2328,"displaystyle":1734},[2330,68343,68344,68346],{},[2133,68345,3117],{},[2133,68347,3989],{},[1726,68349,1762],{"fence":1741},[1726,68351,1742],{"separator":1741},[5865,68353],{"width":5867},[2128,68355,68356,68374],{},[895,68357,68358,68360,68362,68364,68372],{},[1726,68359,1735],{"fence":1741},[898,68361,1724],{},[1726,68363,2228],{},[2326,68365,68366],{"scriptlevel":2328,"displaystyle":1734},[2330,68367,68368,68370],{},[2133,68369,9021],{},[2133,68371,2177],{},[1726,68373,1762],{"fence":1741},[2133,68375,2135],{},[1726,68377,1728],{},[2330,68379,68380,68390],{},[895,68381,68382,68384,68386,68388],{},[2133,68383,38000],{},[898,68385,1738],{},[1726,68387,2228],{},[2133,68389,3117],{},[2133,68391,3989],{},[1726,68393,1742],{"separator":1741},[902,68395,68396],{"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},",[883,68398,68400],{"className":68399},[886],[888,68401,68402],{"xmlns":890,"display":28047},[892,68403,68404,68436],{},[895,68405,68406,68408,68410,68416,68418,68434],{},[898,68407,1724],{},[1726,68409,1728],{},[2330,68411,68412,68414],{},[2133,68413,9021],{},[2133,68415,2177],{},[1726,68417,2099],{},[2330,68419,68420,68432],{},[8103,68421,68422],{},[895,68423,68424,68426,68428,68430],{},[2133,68425,38000],{},[898,68427,1738],{},[1726,68429,2228],{},[2133,68431,3117],{},[2133,68433,2177],{},[898,68435,1888],{"mathvariant":2377},[902,68437,68438],{"encoding":904},"Q = \\frac{20}{3} + \\frac{\\sqrt{30P - 50}}{3}.",[724,68440,66998,68441,1343,68479,1343,68527,68561,68562,1888],{},[883,68442,68444],{"className":68443},[886],[888,68445,68446],{"xmlns":890},[892,68447,68448,68476],{},[895,68449,68450,68452,68454,68456,68458,68460,68466,68468,68470,68472,68474],{},[898,68451,4243],{},[898,68453,40320],{},[898,68455,2775],{},[1726,68457,1728],{},[2133,68459,2791],{},[2128,68461,68462,68464],{},[898,68463,1724],{},[2133,68465,2135],{},[1726,68467,2228],{},[2133,68469,2135],{},[898,68471,1724],{},[1726,68473,2099],{},[2133,68475,36225],{},[902,68477,68478],{"encoding":904},"AVC = 0{,}1Q^2 - 2Q + 15",[883,68480,68482],{"className":68481},[886],[888,68483,68484],{"xmlns":890},[892,68485,68486,68524],{},[895,68487,68488,68490,68492,68498,68500,68502,68504,68506,68508,68510,68512,68514,68520,68522],{},[898,68489,4243],{},[898,68491,40320],{},[2128,68493,68494,68496],{},[898,68495,2775],{},[1726,68497,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,68499,1728],{},[2133,68501,2836],{},[898,68503,1724],{},[1726,68505,2228],{},[2133,68507,2135],{},[1726,68509,1728],{},[2133,68511,2328],{},[1726,68513,3977],{},[2128,68515,68516,68518],{},[898,68517,1724],{},[1726,68519,4342],{},[1726,68521,1728],{},[2133,68523,2860],{},[902,68525,68526],{"encoding":904},"AVC' = 0{,}2Q - 2 = 0 \\Rightarrow Q^* = 10",[883,68528,68530],{"className":68529},[886],[888,68531,68532],{"xmlns":890},[892,68533,68534,68558],{},[895,68535,68536,68538,68540,68550,68552,68554,68556],{},[898,68537,4243],{},[898,68539,40320],{},[2128,68541,68542,68544],{},[898,68543,2775],{},[895,68545,68546,68548],{},[1726,68547,2379],{"mathvariant":2377},[1726,68549,2379],{"mathvariant":2377},[1726,68551,1728],{},[2133,68553,2836],{},[1726,68555,3405],{},[2133,68557,2328],{},[902,68559,68560],{"encoding":904},"AVC'' = 0{,}2 > 0"," (minimum). Minimální cena nabídky ",[883,68563,68565],{"className":68564},[886],[888,68566,68567],{"xmlns":890},[892,68568,68569,68605],{},[895,68570,68571,68577,68579,68581,68583,68585,68587,68589,68591,68593,68595,68597,68599,68601,68603],{},[2128,68572,68573,68575],{},[898,68574,1738],{},[1726,68576,4342],{},[1726,68578,1728],{},[898,68580,2815],{},[898,68582,2775],{},[1726,68584,1735],{"stretchy":1734},[2133,68586,2860],{},[1726,68588,1762],{"stretchy":1734},[1726,68590,1728],{},[2133,68592,38000],{},[1726,68594,2228],{},[2133,68596,5198],{},[1726,68598,2099],{},[2133,68600,36225],{},[1726,68602,1728],{},[2133,68604,2231],{},[902,68606,68607],{"encoding":904},"P^* = MC(10) = 30 - 40 + 15 = 5",[724,68609,68610],{},[38,68611,68612],{},"Závěr.",[883,68614,68616],{"className":68615},[886],[888,68617,68618],{"xmlns":890,"display":28047},[892,68619,68620,68706],{},[895,68621,68622,68624,68626,68628,68630,68632,68634,68636],{},[898,68623,1738],{},[1726,68625,1728],{},[898,68627,8659],{},[1726,68629,1735],{"stretchy":1734},[898,68631,1724],{},[1726,68633,1762],{"stretchy":1734},[1726,68635,1728],{},[895,68637,68638,68640],{},[1726,68639,67486],{"fence":1741},[20735,68641,68642,68684],{"rowspacing":67489,"columnalign":67490,"columnspacing":15270},[20740,68643,68644,68668],{},[20743,68645,68646],{},[2326,68647,68648],{"scriptlevel":2328,"displaystyle":1734},[895,68649,68650,68652,68658,68660,68662,68664,68666],{},[2133,68651,68191],{},[2128,68653,68654,68656],{},[898,68655,1724],{},[2133,68657,2135],{},[1726,68659,2228],{},[2133,68661,2352],{},[898,68663,1724],{},[1726,68665,2099],{},[2133,68667,36225],{},[20743,68669,68670],{},[2326,68671,68672],{"scriptlevel":2328,"displaystyle":1734},[895,68673,68674,68676,68678,68680,68682],{},[2289,68675,67517],{},[898,68677,1724],{},[1726,68679,4473],{},[2133,68681,2860],{},[1726,68683,1742],{"separator":1741},[20740,68685,68686,68692],{},[20743,68687,68688],{},[2326,68689,68690],{"scriptlevel":2328,"displaystyle":1734},[2133,68691,2328],{},[20743,68693,68694],{},[2326,68695,68696],{"scriptlevel":2328,"displaystyle":1734},[895,68697,68698,68700,68702,68704],{},[2289,68699,67517],{},[898,68701,1724],{},[1726,68703,3444],{},[2133,68705,19309],{},[902,68707,68708],{"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}",[724,68710,68711],{},[614,68712,68713,68714,68729,68730,1888],{},"Obrázek 3.15: Grafická ilustrace nabídky firmy odvozené z části křivky ",[883,68715,68717],{"className":68716},[886],[888,68718,68719],{"xmlns":890},[892,68720,68721,68727],{},[895,68722,68723,68725],{},[898,68724,2815],{},[898,68726,2775],{},[902,68728,55272],{"encoding":904}," ležící nad minimem ",[883,68731,68733],{"className":68732},[886],[888,68734,68735],{"xmlns":890},[892,68736,68737,68745],{},[895,68738,68739,68741,68743],{},[898,68740,4243],{},[898,68742,40320],{},[898,68744,2775],{},[902,68746,55291],{"encoding":904},[115,68748,68750],{"id":68749},"shrnutí-kapitoly-3","Shrnutí kapitoly 3",[724,68752,68753,68754,68758,68759,68774,68775,68795,68796,3877,68799,68802,68803,68805,68806,19926,68828,68830,68831,3877,68833,58706,68836,1777,68839,41795,68854,68869],{},"Celkový příjem je součin ceny a množství, kde cena je dána funkcí ",[207,68755,68757],{"className":68756,"dataFsResolvedFilePath":800,"href":801},[210],"poptávky",". Pro lineární poptávku je ",[883,68760,68762],{"className":68761},[886],[888,68763,68764],{"xmlns":890},[892,68765,68766,68772],{},[895,68767,68768,68770],{},[898,68769,2772],{},[898,68771,3984],{},[902,68773,4084],{"encoding":904}," kvadratická. Průměrný příjem je podíl ",[883,68776,68778],{"className":68777},[886],[888,68779,68780],{"xmlns":890},[892,68781,68782,68792],{},[895,68783,68784,68786,68788,68790],{},[898,68785,2772],{},[898,68787,3984],{},[898,68789,4661],{"mathvariant":2377},[898,68791,1724],{},[902,68793,68794],{"encoding":904},"TR\u002FQ"," a rovná se poptávkové funkci. Celkové náklady se skládají z ",[38,68797,68798],{},"fixních",[38,68800,68801],{},"celkových variabilních"," nákladů. Průměrné veličiny jsou jejich podíly s množstvím. ",[38,68804,64305],{}," identifikují, kdy se firma nachází na prahu rentability. Rozdíl ",[883,68807,68809],{"className":68808},[886],[888,68810,68811],{"xmlns":890},[892,68812,68813,68825],{},[895,68814,68815,68817,68819,68821,68823],{},[898,68816,2772],{},[898,68818,3984],{},[1726,68820,2228],{},[898,68822,2772],{},[898,68824,2775],{},[902,68826,68827],{"encoding":904},"TR - TC",[38,68829,55152],{},"; klíčový je výpočet produkce, která zisk maximalizuje. ",[38,68832,56464],{},[38,68834,68835],{},"mezní náklady",[207,68837,1145],{"className":68838,"dataFsResolvedFilePath":764,"href":765},[210],[883,68840,68842],{"className":68841},[886],[888,68843,68844],{"xmlns":890},[892,68845,68846,68852],{},[895,68847,68848,68850],{},[898,68849,2772],{},[898,68851,3984],{},[902,68853,4084],{"encoding":904},[883,68855,68857],{"className":68856},[886],[888,68858,68859],{"xmlns":890},[892,68860,68861,68867],{},[895,68862,68863,68865],{},[898,68864,2772],{},[898,68866,2775],{},[902,68868,3240],{"encoding":904}," podle produkce; udávají rychlosti změn, resp. přibližné změny odpovídající jednotkové změně produkce.",[120,68871,68872,68934,69000,69062],{},[123,68873,68874,68877,68878,10378,68893,1888],{},[38,68875,68876],{},"Princip minimalizace průměrných nákladů:"," v bodě minima ",[883,68879,68881],{"className":68880},[886],[888,68882,68883],{"xmlns":890},[892,68884,68885,68891],{},[895,68886,68887,68889],{},[898,68888,4243],{},[898,68890,2775],{},[902,68892,55540],{"encoding":904},[883,68894,68896],{"className":68895},[886],[888,68897,68898],{"xmlns":890},[892,68899,68900,68932],{},[895,68901,68902,68904,68906,68908,68914,68916,68918,68920,68922,68924,68930],{},[898,68903,4243],{},[898,68905,2775],{},[1726,68907,1735],{"stretchy":1734},[2275,68909,68910,68912],{},[898,68911,1724],{},[2133,68913,2328],{},[1726,68915,1762],{"stretchy":1734},[1726,68917,1728],{},[898,68919,2815],{},[898,68921,2775],{},[1726,68923,1735],{"stretchy":1734},[2275,68925,68926,68928],{},[898,68927,1724],{},[2133,68929,2328],{},[1726,68931,1762],{"stretchy":1734},[902,68933,62549],{"encoding":904},[123,68935,68936,68877,68939,10378,68956,1888],{},[38,68937,68938],{},"Princip minimalizace průměrných variabilních nákladů:",[883,68940,68942],{"className":68941},[886],[888,68943,68944],{"xmlns":890},[892,68945,68946,68954],{},[895,68947,68948,68950,68952],{},[898,68949,4243],{},[898,68951,40320],{},[898,68953,2775],{},[902,68955,55291],{"encoding":904},[883,68957,68959],{"className":68958},[886],[888,68960,68961],{"xmlns":890},[892,68962,68963,68997],{},[895,68964,68965,68967,68969,68971,68973,68979,68981,68983,68985,68987,68989,68995],{},[898,68966,4243],{},[898,68968,40320],{},[898,68970,2775],{},[1726,68972,1735],{"stretchy":1734},[2275,68974,68975,68977],{},[898,68976,1724],{},[2133,68978,2328],{},[1726,68980,1762],{"stretchy":1734},[1726,68982,1728],{},[898,68984,2815],{},[898,68986,2775],{},[1726,68988,1735],{"stretchy":1734},[2275,68990,68991,68993],{},[898,68992,1724],{},[2133,68994,2328],{},[1726,68996,1762],{"stretchy":1734},[902,68998,68999],{"encoding":904},"AVC(Q_0) = MC(Q_0)",[123,69001,69002,69005,69006,10378,69021,1888],{},[38,69003,69004],{},"Princip maximalizace zisku:"," v bodě maxima ",[883,69007,69009],{"className":69008},[886],[888,69010,69011],{"xmlns":890},[892,69012,69013,69019],{},[895,69014,69015,69017],{},[898,69016,1738],{},[898,69018,3984],{},[902,69020,63459],{"encoding":904},[883,69022,69024],{"className":69023},[886],[888,69025,69026],{"xmlns":890},[892,69027,69028,69060],{},[895,69029,69030,69032,69034,69036,69042,69044,69046,69048,69050,69052,69058],{},[898,69031,2815],{},[898,69033,3984],{},[1726,69035,1735],{"stretchy":1734},[2275,69037,69038,69040],{},[898,69039,1724],{},[2133,69041,2328],{},[1726,69043,1762],{"stretchy":1734},[1726,69045,1728],{},[898,69047,2815],{},[898,69049,2775],{},[1726,69051,1735],{"stretchy":1734},[2275,69053,69054,69056],{},[898,69055,1724],{},[2133,69057,2328],{},[1726,69059,1762],{"stretchy":1734},[902,69061,65625],{"encoding":904},[123,69063,69064,1777,69067,6460,69103,67905,69124,21575,69137,67587,69154,1888],{},[38,69065,69066],{},"Funkce nabídky firmy:",[883,69068,69070],{"className":69069},[886],[888,69071,69072],{"xmlns":890},[892,69073,69074,69100],{},[895,69075,69076,69078,69080,69082,69084,69086,69088,69090,69092,69094,69096,69098],{},[898,69077,1738],{},[1726,69079,1728],{},[898,69081,8659],{},[1726,69083,1735],{"stretchy":1734},[898,69085,1724],{},[1726,69087,1762],{"stretchy":1734},[1726,69089,1728],{},[898,69091,2815],{},[898,69093,2775],{},[1726,69095,1735],{"stretchy":1734},[898,69097,1724],{},[1726,69099,1762],{"stretchy":1734},[902,69101,69102],{"encoding":904},"P = S(Q) = MC(Q)",[883,69104,69106],{"className":69105},[886],[888,69107,69108],{"xmlns":890},[892,69109,69110,69122],{},[895,69111,69112,69114,69116],{},[898,69113,1724],{},[1726,69115,4473],{},[2128,69117,69118,69120],{},[898,69119,1724],{},[1726,69121,4342],{},[902,69123,67904],{"encoding":904},[883,69125,69127],{"className":69126},[886],[888,69128,69129],{"xmlns":890},[892,69130,69131,69135],{},[895,69132,69133],{},[2133,69134,2328],{},[902,69136,2328],{"encoding":904},[883,69138,69140],{"className":69139},[886],[888,69141,69142],{"xmlns":890},[892,69143,69144,69152],{},[895,69145,69146],{},[2128,69147,69148,69150],{},[898,69149,1724],{},[1726,69151,4342],{},[902,69153,29825],{"encoding":904},[883,69155,69157],{"className":69156},[886],[888,69158,69159],{"xmlns":890},[892,69160,69161,69169],{},[895,69162,69163,69165,69167],{},[898,69164,4243],{},[898,69166,40320],{},[898,69168,2775],{},[902,69170,55291],{"encoding":904},[115,69172,49863],{"id":49862},[152,69174,69175,69178,69181,69184,69187,69190,69193,69196,69199,69202,69205],{},[123,69176,69177],{},"Jaký je vztah pro celkový příjem v podmínkách dokonalé konkurence?",[123,69179,69180],{},"Jaký tvar má křivka celkového příjmu pro lineární poptávku?",[123,69182,69183],{},"Jak se vypočte mezní příjem a co udává?",[123,69185,69186],{},"Z jakých složek se skládají celkové náklady?",[123,69188,69189],{},"Jak se stanoví celkové náklady, známe-li náklady mezní?",[123,69191,69192],{},"Jaký je trend průměrných fixních nákladů a průměrných nákladů, roste-li produkce?",[123,69194,69195],{},"Jak se stanoví přibližně změna celkových nákladů?",[123,69197,69198],{},"Jak se vypočte zisk?",[123,69200,69201],{},"Jaká vlastnost platí v bodě maxima zisku?",[123,69203,69204],{},"Co jsou body zvratu? Jak se najdou?",[123,69206,69207],{},"Z jakých nákladových charakteristik se vychází při konstrukci nabídky?",[115,69209,69211],{"id":69210},"úlohy-31328","Úlohy 3.1–3.28",[198,69213,69215],{"id":69214},"příjem-3135","Příjem (3.1–3.5)",[724,69217,69218,45407,69221,69249,69250,69265,69266,69281,69282,69297,69298,1343,69313,1343,69328,69343],{},[38,69219,69220],{},"3.1",[883,69222,69224],{"className":69223},[886],[888,69225,69226],{"xmlns":890},[892,69227,69228,69246],{},[895,69229,69230,69232,69234,69236,69238,69240,69242,69244],{},[898,69231,1738],{},[1726,69233,1728],{},[898,69235,1731],{},[1726,69237,1735],{"stretchy":1734},[898,69239,1724],{},[1726,69241,1762],{"stretchy":1734},[1726,69243,1728],{},[2133,69245,3087],{},[902,69247,69248],{"encoding":904},"P = D(Q) = 100",". (a) Rozhodněte, v jakých podmínkách konkurence zadaná poptávka platí. (b) Najděte celkový příjem ",[883,69251,69253],{"className":69252},[886],[888,69254,69255],{"xmlns":890},[892,69256,69257,69263],{},[895,69258,69259,69261],{},[898,69260,2772],{},[898,69262,3984],{},[902,69264,4084],{"encoding":904},", průměrný příjem ",[883,69267,69269],{"className":69268},[886],[888,69270,69271],{"xmlns":890},[892,69272,69273,69279],{},[895,69274,69275,69277],{},[898,69276,4243],{},[898,69278,3984],{},[902,69280,55425],{"encoding":904}," a mezní příjem ",[883,69283,69285],{"className":69284},[886],[888,69286,69287],{"xmlns":890},[892,69288,69289,69295],{},[895,69290,69291,69293],{},[898,69292,2815],{},[898,69294,3984],{},[902,69296,6621],{"encoding":904},". (c) Vypočtěte ",[883,69299,69301],{"className":69300},[886],[888,69302,69303],{"xmlns":890},[892,69304,69305,69311],{},[895,69306,69307,69309],{},[898,69308,2772],{},[898,69310,3984],{},[902,69312,4084],{"encoding":904},[883,69314,69316],{"className":69315},[886],[888,69317,69318],{"xmlns":890},[892,69319,69320,69326],{},[895,69321,69322,69324],{},[898,69323,4243],{},[898,69325,3984],{},[902,69327,55425],{"encoding":904},[883,69329,69331],{"className":69330},[886],[888,69332,69333],{"xmlns":890},[892,69334,69335,69341],{},[895,69336,69337,69339],{},[898,69338,2815],{},[898,69340,3984],{},[902,69342,6621],{"encoding":904}," při množství 20. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,69345,69346,45407,69349,69249,69385,69265,69400,69281,69415,69297,69430,1343,69445,1343,69460,69475],{},[38,69347,69348],{},"3.2",[883,69350,69352],{"className":69351},[886],[888,69353,69354],{"xmlns":890},[892,69355,69356,69382],{},[895,69357,69358,69360,69362,69364,69366,69368,69370,69372,69374,69376,69378,69380],{},[898,69359,1738],{},[1726,69361,1728],{},[898,69363,1731],{},[1726,69365,1735],{"stretchy":1734},[898,69367,1724],{},[1726,69369,1762],{"stretchy":1734},[1726,69371,1728],{},[1726,69373,2228],{},[2133,69375,4996],{},[898,69377,1724],{},[1726,69379,2099],{},[2133,69381,9021],{},[902,69383,69384],{"encoding":904},"P = D(Q) = -0{,}5Q + 20",[883,69386,69388],{"className":69387},[886],[888,69389,69390],{"xmlns":890},[892,69391,69392,69398],{},[895,69393,69394,69396],{},[898,69395,2772],{},[898,69397,3984],{},[902,69399,4084],{"encoding":904},[883,69401,69403],{"className":69402},[886],[888,69404,69405],{"xmlns":890},[892,69406,69407,69413],{},[895,69408,69409,69411],{},[898,69410,4243],{},[898,69412,3984],{},[902,69414,55425],{"encoding":904},[883,69416,69418],{"className":69417},[886],[888,69419,69420],{"xmlns":890},[892,69421,69422,69428],{},[895,69423,69424,69426],{},[898,69425,2815],{},[898,69427,3984],{},[902,69429,6621],{"encoding":904},[883,69431,69433],{"className":69432},[886],[888,69434,69435],{"xmlns":890},[892,69436,69437,69443],{},[895,69438,69439,69441],{},[898,69440,2772],{},[898,69442,3984],{},[902,69444,4084],{"encoding":904},[883,69446,69448],{"className":69447},[886],[888,69449,69450],{"xmlns":890},[892,69451,69452,69458],{},[895,69453,69454,69456],{},[898,69455,4243],{},[898,69457,3984],{},[902,69459,55425],{"encoding":904},[883,69461,69463],{"className":69462},[886],[888,69464,69465],{"xmlns":890},[892,69466,69467,69473],{},[895,69468,69469,69471],{},[898,69470,2815],{},[898,69472,3984],{},[902,69474,6621],{"encoding":904}," při množství 10. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,69477,69478,45407,69481,69518,69519,69265,69534,69281,69549,69564,69565,6460,69580,69606,69607,69622,69623,1343,69638,6460,69653,69606,69678,69693,69694,69707,69708,69723,69724,69739,69740,1343,69753,1343,69768,1343,69783,1888],{},[38,69479,69480],{},"3.3",[883,69482,69484],{"className":69483},[886],[888,69485,69486],{"xmlns":890},[892,69487,69488,69515],{},[895,69489,69490,69492,69494,69496,69498,69500,69502,69504,69507,69509],{},[898,69491,1738],{},[1726,69493,1728],{},[898,69495,1731],{},[1726,69497,1735],{"stretchy":1734},[898,69499,1724],{},[1726,69501,1762],{"stretchy":1734},[1726,69503,1728],{},[2133,69505,69506],{},"1200",[1726,69508,2228],{},[2128,69510,69511,69513],{},[898,69512,1724],{},[2133,69514,2135],{},[902,69516,69517],{"encoding":904},"P = D(Q) = 1200 - Q^2",". (a) Najděte celkový příjem ",[883,69520,69522],{"className":69521},[886],[888,69523,69524],{"xmlns":890},[892,69525,69526,69532],{},[895,69527,69528,69530],{},[898,69529,2772],{},[898,69531,3984],{},[902,69533,4084],{"encoding":904},[883,69535,69537],{"className":69536},[886],[888,69538,69539],{"xmlns":890},[892,69540,69541,69547],{},[895,69542,69543,69545],{},[898,69544,4243],{},[898,69546,3984],{},[902,69548,55425],{"encoding":904},[883,69550,69552],{"className":69551},[886],[888,69553,69554],{"xmlns":890},[892,69555,69556,69562],{},[895,69557,69558,69560],{},[898,69559,2815],{},[898,69561,3984],{},[902,69563,6621],{"encoding":904},". (b) Vypočtěte ",[883,69566,69568],{"className":69567},[886],[888,69569,69570],{"xmlns":890},[892,69571,69572,69578],{},[895,69573,69574,69576],{},[898,69575,2772],{},[898,69577,3984],{},[902,69579,4084],{"encoding":904},[883,69581,69583],{"className":69582},[886],[888,69584,69585],{"xmlns":890},[892,69586,69587,69603],{},[895,69588,69589,69591,69593,69595,69597,69599,69601],{},[898,69590,1724],{},[1726,69592,1728],{},[2133,69594,2860],{},[1726,69596,1742],{"separator":1741},[2133,69598,9021],{},[1726,69600,1742],{"separator":1741},[2133,69602,38000],{},[902,69604,69605],{"encoding":904},"Q = 10, 20, 30"," a rozhodněte, kdy ",[883,69608,69610],{"className":69609},[886],[888,69611,69612],{"xmlns":890},[892,69613,69614,69620],{},[895,69615,69616,69618],{},[898,69617,2772],{},[898,69619,3984],{},[902,69621,4084],{"encoding":904}," roste, resp. klesá. (c) Vypočtěte ",[883,69624,69626],{"className":69625},[886],[888,69627,69628],{"xmlns":890},[892,69629,69630,69636],{},[895,69631,69632,69634],{},[898,69633,4243],{},[898,69635,3984],{},[902,69637,55425],{"encoding":904},[883,69639,69641],{"className":69640},[886],[888,69642,69643],{"xmlns":890},[892,69644,69645,69651],{},[895,69646,69647,69649],{},[898,69648,2815],{},[898,69650,3984],{},[902,69652,6621],{"encoding":904},[883,69654,69656],{"className":69655},[886],[888,69657,69658],{"xmlns":890},[892,69659,69660,69676],{},[895,69661,69662,69664,69666,69668,69670,69672,69674],{},[898,69663,1724],{},[1726,69665,1728],{},[2133,69667,2860],{},[1726,69669,1742],{"separator":1741},[2133,69671,9021],{},[1726,69673,1742],{"separator":1741},[2133,69675,38000],{},[902,69677,69605],{"encoding":904},[883,69679,69681],{"className":69680},[886],[888,69682,69683],{"xmlns":890},[892,69684,69685,69691],{},[895,69686,69687,69689],{},[898,69688,2815],{},[898,69690,3984],{},[902,69692,6621],{"encoding":904}," roste, resp. klesá. (d) Vypočtěte ",[883,69695,69697],{"className":69696},[886],[888,69698,69699],{"xmlns":890},[892,69700,69701,69705],{},[895,69702,69703],{},[898,69704,1724],{},[902,69706,1724],{"encoding":904},", které maximalizuje ",[883,69709,69711],{"className":69710},[886],[888,69712,69713],{"xmlns":890},[892,69714,69715,69721],{},[895,69716,69717,69719],{},[898,69718,2772],{},[898,69720,3984],{},[902,69722,4084],{"encoding":904}," a stanovte příslušnou hodnotu maxima ",[883,69725,69727],{"className":69726},[886],[888,69728,69729],{"xmlns":890},[892,69730,69731,69737],{},[895,69732,69733,69735],{},[898,69734,2772],{},[898,69736,3984],{},[902,69738,4084],{"encoding":904},". (e) Určete (je užitečné vyšetřit i jejich průběhy). (f) Charakterizujte geometricky křivky ",[883,69741,69743],{"className":69742},[886],[888,69744,69745],{"xmlns":890},[892,69746,69747,69751],{},[895,69748,69749],{},[898,69750,1731],{},[902,69752,1731],{"encoding":904},[883,69754,69756],{"className":69755},[886],[888,69757,69758],{"xmlns":890},[892,69759,69760,69766],{},[895,69761,69762,69764],{},[898,69763,2772],{},[898,69765,3984],{},[902,69767,4084],{"encoding":904},[883,69769,69771],{"className":69770},[886],[888,69772,69773],{"xmlns":890},[892,69774,69775,69781],{},[895,69776,69777,69779],{},[898,69778,4243],{},[898,69780,3984],{},[902,69782,55425],{"encoding":904},[883,69784,69786],{"className":69785},[886],[888,69787,69788],{"xmlns":890},[892,69789,69790,69796],{},[895,69791,69792,69794],{},[898,69793,2815],{},[898,69795,3984],{},[902,69797,6621],{"encoding":904},[724,69799,69800,69803,69804,69834,69835,69850,69851,10141,69864,1343,69882,1343,69899,69917,69918,69940,69941,69956,69957,69970,69971,1888],{},[38,69801,69802],{},"3.4"," Je dán celkový příjem ",[883,69805,69807],{"className":69806},[886],[888,69808,69809],{"xmlns":890},[892,69810,69811,69831],{},[895,69812,69813,69815,69817,69819,69821,69823,69825],{},[898,69814,2772],{},[898,69816,3984],{},[1726,69818,1728],{},[2133,69820,69506],{},[898,69822,1724],{},[1726,69824,2228],{},[2128,69826,69827,69829],{},[898,69828,1724],{},[2133,69830,2177],{},[902,69832,69833],{"encoding":904},"TR = 1200Q - Q^3",". (a) Určete, jak rychle se (přibližně) mění ",[883,69836,69838],{"className":69837},[886],[888,69839,69840],{"xmlns":890},[892,69841,69842,69848],{},[895,69843,69844,69846],{},[898,69845,2772],{},[898,69847,3984],{},[902,69849,4084],{"encoding":904}," vzhledem ke ",[883,69852,69854],{"className":69853},[886],[888,69855,69856],{"xmlns":890},[892,69857,69858,69862],{},[895,69859,69860],{},[898,69861,1724],{},[902,69863,1724],{"encoding":904},[883,69865,69867],{"className":69866},[886],[888,69868,69869],{"xmlns":890},[892,69870,69871,69879],{},[895,69872,69873,69875,69877],{},[898,69874,1724],{},[1726,69876,1728],{},[2133,69878,2231],{},[902,69880,69881],{"encoding":904},"Q = 5",[883,69883,69885],{"className":69884},[886],[888,69886,69887],{"xmlns":890},[892,69888,69889,69897],{},[895,69890,69891,69893,69895],{},[898,69892,1724],{},[1726,69894,1728],{},[2133,69896,5572],{},[902,69898,5575],{"encoding":904},[883,69900,69902],{"className":69901},[886],[888,69903,69904],{"xmlns":890},[892,69905,69906,69914],{},[895,69907,69908,69910,69912],{},[898,69909,1724],{},[1726,69911,1728],{},[2133,69913,3506],{},[902,69915,69916],{"encoding":904},"Q = 12"," a charakterizujte dynamiku změn. (b) Vypočtěte a ekonomicky interpretujte ",[883,69919,69921],{"className":69920},[886],[888,69922,69923],{"xmlns":890},[892,69924,69925,69937],{},[895,69926,69927,69929,69931,69933,69935],{},[898,69928,2815],{},[898,69930,3984],{},[1726,69932,1735],{"stretchy":1734},[2133,69934,2860],{},[1726,69936,1762],{"stretchy":1734},[902,69938,69939],{"encoding":904},"MR(10)",". (c) Odhadněte, o kolik se přibližně změní ",[883,69942,69944],{"className":69943},[886],[888,69945,69946],{"xmlns":890},[892,69947,69948,69954],{},[895,69949,69950,69952],{},[898,69951,2772],{},[898,69953,3984],{},[902,69955,4084],{"encoding":904},", jestliže se ",[883,69958,69960],{"className":69959},[886],[888,69961,69962],{"xmlns":890},[892,69963,69964,69968],{},[895,69965,69966],{},[898,69967,1724],{},[902,69969,1724],{"encoding":904}," změní z 10 na 12 a porovnejte se skutečnou změnou ",[883,69972,69974],{"className":69973},[886],[888,69975,69976],{"xmlns":890},[892,69977,69978,69984],{},[895,69979,69980,69982],{},[898,69981,2772],{},[898,69983,3984],{},[902,69985,4084],{"encoding":904},[724,69987,69988,69991,69992,70018,70019,70034,70035,69956,70050,70063],{},[38,69989,69990],{},"3.5"," Je dán mezní příjem ",[883,69993,69995],{"className":69994},[886],[888,69996,69997],{"xmlns":890},[892,69998,69999,70015],{},[895,70000,70001,70003,70005,70007,70009,70011,70013],{},[898,70002,2815],{},[898,70004,3984],{},[1726,70006,1728],{},[1726,70008,2228],{},[898,70010,1724],{},[1726,70012,2099],{},[2133,70014,9021],{},[902,70016,70017],{"encoding":904},"MR = -Q + 20",". (a) Určete celkový příjem ",[883,70020,70022],{"className":70021},[886],[888,70023,70024],{"xmlns":890},[892,70025,70026,70032],{},[895,70027,70028,70030],{},[898,70029,2772],{},[898,70031,3984],{},[902,70033,4084],{"encoding":904},". (b) Vypočtěte změnu ",[883,70036,70038],{"className":70037},[886],[888,70039,70040],{"xmlns":890},[892,70041,70042,70048],{},[895,70043,70044,70046],{},[898,70045,2772],{},[898,70047,3984],{},[902,70049,4084],{"encoding":904},[883,70051,70053],{"className":70052},[886],[888,70054,70055],{"xmlns":890},[892,70056,70057,70061],{},[895,70058,70059],{},[898,70060,1724],{},[902,70062,1724],{"encoding":904}," změní z 8 na 12.",[198,70065,70067],{"id":70066},"náklady-36316","Náklady (3.6–3.16)",[724,70069,70070,70073,70074,70114,70115,70130,70131,70148,70149,70166,70167,70182,70183,70198,70199,69564,70214,1343,70229,1343,70246,1343,70263,1343,70278,1343,70293,6460,70308,70326,70327,1343,70342,1343,70357,70372],{},[38,70071,70072],{},"3.6"," Jsou dány celkové náklady ",[883,70075,70077],{"className":70076},[886],[888,70078,70079],{"xmlns":890},[892,70080,70081,70111],{},[895,70082,70083,70085,70087,70089,70091,70093,70095,70097,70099],{},[898,70084,2772],{},[898,70086,2775],{},[1726,70088,1728],{},[2133,70090,3087],{},[1726,70092,2099],{},[2133,70094,2135],{},[898,70096,1724],{},[1726,70098,2099],{},[2326,70100,70101],{"scriptlevel":2328,"displaystyle":1734},[2330,70102,70103,70109],{},[2128,70104,70105,70107],{},[898,70106,1724],{},[2133,70108,2135],{},[2133,70110,2860],{},[902,70112,70113],{"encoding":904},"TC = 100 + 2Q + \\tfrac{Q^2}{10}",". (a) Určete fixní náklady ",[883,70116,70118],{"className":70117},[886],[888,70119,70120],{"xmlns":890},[892,70121,70122,70128],{},[895,70123,70124,70126],{},[898,70125,10420],{},[898,70127,2775],{},[902,70129,55471],{"encoding":904},", celkové variabilní náklady ",[883,70132,70134],{"className":70133},[886],[888,70135,70136],{"xmlns":890},[892,70137,70138,70146],{},[895,70139,70140,70142,70144],{},[898,70141,2772],{},[898,70143,40320],{},[898,70145,2775],{},[902,70147,55489],{"encoding":904},", průměrné variabilní náklady ",[883,70150,70152],{"className":70151},[886],[888,70153,70154],{"xmlns":890},[892,70155,70156,70164],{},[895,70157,70158,70160,70162],{},[898,70159,4243],{},[898,70161,40320],{},[898,70163,2775],{},[902,70165,55291],{"encoding":904},", variabilní náklady na jednotku ",[883,70168,70170],{"className":70169},[886],[888,70171,70172],{"xmlns":890},[892,70173,70174,70180],{},[895,70175,70176,70178],{},[898,70177,40320],{},[898,70179,2775],{},[902,70181,63585],{"encoding":904},", průměrné náklady ",[883,70184,70186],{"className":70185},[886],[888,70187,70188],{"xmlns":890},[892,70189,70190,70196],{},[895,70191,70192,70194],{},[898,70193,4243],{},[898,70195,2775],{},[902,70197,55540],{"encoding":904}," a mezní náklady ",[883,70200,70202],{"className":70201},[886],[888,70203,70204],{"xmlns":890},[892,70205,70206,70212],{},[895,70207,70208,70210],{},[898,70209,2815],{},[898,70211,2775],{},[902,70213,55272],{"encoding":904},[883,70215,70217],{"className":70216},[886],[888,70218,70219],{"xmlns":890},[892,70220,70221,70227],{},[895,70222,70223,70225],{},[898,70224,2772],{},[898,70226,2775],{},[902,70228,3240],{"encoding":904},[883,70230,70232],{"className":70231},[886],[888,70233,70234],{"xmlns":890},[892,70235,70236,70244],{},[895,70237,70238,70240,70242],{},[898,70239,2772],{},[898,70241,40320],{},[898,70243,2775],{},[902,70245,55489],{"encoding":904},[883,70247,70249],{"className":70248},[886],[888,70250,70251],{"xmlns":890},[892,70252,70253,70261],{},[895,70254,70255,70257,70259],{},[898,70256,4243],{},[898,70258,40320],{},[898,70260,2775],{},[902,70262,55291],{"encoding":904},[883,70264,70266],{"className":70265},[886],[888,70267,70268],{"xmlns":890},[892,70269,70270,70276],{},[895,70271,70272,70274],{},[898,70273,40320],{},[898,70275,2775],{},[902,70277,63585],{"encoding":904},[883,70279,70281],{"className":70280},[886],[888,70282,70283],{"xmlns":890},[892,70284,70285,70291],{},[895,70286,70287,70289],{},[898,70288,4243],{},[898,70290,2775],{},[902,70292,55540],{"encoding":904},[883,70294,70296],{"className":70295},[886],[888,70297,70298],{"xmlns":890},[892,70299,70300,70306],{},[895,70301,70302,70304],{},[898,70303,2815],{},[898,70305,2775],{},[902,70307,55272],{"encoding":904},[883,70309,70311],{"className":70310},[886],[888,70312,70313],{"xmlns":890},[892,70314,70315,70323],{},[895,70316,70317,70319,70321],{},[898,70318,1724],{},[1726,70320,1728],{},[2133,70322,3117],{},[902,70324,70325],{"encoding":904},"Q = 50",". (c) Rozhodněte, kdy ",[883,70328,70330],{"className":70329},[886],[888,70331,70332],{"xmlns":890},[892,70333,70334,70340],{},[895,70335,70336,70338],{},[898,70337,2772],{},[898,70339,2775],{},[902,70341,3240],{"encoding":904},[883,70343,70345],{"className":70344},[886],[888,70346,70347],{"xmlns":890},[892,70348,70349,70355],{},[895,70350,70351,70353],{},[898,70352,4243],{},[898,70354,2775],{},[902,70356,55540],{"encoding":904},[883,70358,70360],{"className":70359},[886],[888,70361,70362],{"xmlns":890},[892,70363,70364,70370],{},[895,70365,70366,70368],{},[898,70367,2815],{},[898,70369,2775],{},[902,70371,55272],{"encoding":904}," rostou, resp. klesají.",[724,70374,70375,70378,70379,70198,70409,70424,70425,70440,70441,1343,70456,1343,70471,1888],{},[38,70376,70377],{},"3.7"," Jsou dány průměrné náklady ",[883,70380,70382],{"className":70381},[886],[888,70383,70384],{"xmlns":890},[892,70385,70386,70406],{},[895,70387,70388,70390,70392,70394,70402,70404],{},[898,70389,4243],{},[898,70391,2775],{},[1726,70393,1728],{},[2326,70395,70396],{"scriptlevel":2328,"displaystyle":1734},[2330,70397,70398,70400],{},[2133,70399,3087],{},[898,70401,1724],{},[1726,70403,2099],{},[2133,70405,9021],{},[902,70407,70408],{"encoding":904},"AC = \\tfrac{100}{Q} + 20",[883,70410,70412],{"className":70411},[886],[888,70413,70414],{"xmlns":890},[892,70415,70416,70422],{},[895,70417,70418,70420],{},[898,70419,2815],{},[898,70421,2775],{},[902,70423,55272],{"encoding":904},". (a) Určete celkové náklady ",[883,70426,70428],{"className":70427},[886],[888,70429,70430],{"xmlns":890},[892,70431,70432,70438],{},[895,70433,70434,70436],{},[898,70435,2772],{},[898,70437,2775],{},[902,70439,3240],{"encoding":904},". (b) Načrtněte a geometricky charakterizujte křivky ",[883,70442,70444],{"className":70443},[886],[888,70445,70446],{"xmlns":890},[892,70447,70448,70454],{},[895,70449,70450,70452],{},[898,70451,4243],{},[898,70453,2775],{},[902,70455,55540],{"encoding":904},[883,70457,70459],{"className":70458},[886],[888,70460,70461],{"xmlns":890},[892,70462,70463,70469],{},[895,70464,70465,70467],{},[898,70466,2772],{},[898,70468,2775],{},[902,70470,3240],{"encoding":904},[883,70472,70474],{"className":70473},[886],[888,70475,70476],{"xmlns":890},[892,70477,70478,70484],{},[895,70479,70480,70482],{},[898,70481,2815],{},[898,70483,2775],{},[902,70485,55272],{"encoding":904},[724,70487,70488,70073,70491,70535,70536,1343,70553,1343,70568,1343,70585,1343,70600,1343,70617,1888],{},[38,70489,70490],{},"3.8",[883,70492,70494],{"className":70493},[886],[888,70495,70496],{"xmlns":890},[892,70497,70498,70532],{},[895,70499,70500,70502,70504,70506,70508,70510,70512,70514,70516,70518,70524,70526],{},[898,70501,2772],{},[898,70503,2775],{},[1726,70505,1728],{},[2133,70507,46684],{},[1726,70509,2099],{},[2133,70511,38000],{},[898,70513,1724],{},[1726,70515,2228],{},[2133,70517,2238],{},[2128,70519,70520,70522],{},[898,70521,1724],{},[2133,70523,2135],{},[1726,70525,2099],{},[2128,70527,70528,70530],{},[898,70529,1724],{},[2133,70531,2177],{},[902,70533,70534],{"encoding":904},"TC = 80 + 30Q - 6Q^2 + Q^3",". Určete ",[883,70537,70539],{"className":70538},[886],[888,70540,70541],{"xmlns":890},[892,70542,70543,70551],{},[895,70544,70545,70547,70549],{},[898,70546,2772],{},[898,70548,40320],{},[898,70550,2775],{},[902,70552,55489],{"encoding":904},[883,70554,70556],{"className":70555},[886],[888,70557,70558],{"xmlns":890},[892,70559,70560,70566],{},[895,70561,70562,70564],{},[898,70563,10420],{},[898,70565,2775],{},[902,70567,55471],{"encoding":904},[883,70569,70571],{"className":70570},[886],[888,70572,70573],{"xmlns":890},[892,70574,70575,70583],{},[895,70576,70577,70579,70581],{},[898,70578,4243],{},[898,70580,40320],{},[898,70582,2775],{},[902,70584,55291],{"encoding":904},[883,70586,70588],{"className":70587},[886],[888,70589,70590],{"xmlns":890},[892,70591,70592,70598],{},[895,70593,70594,70596],{},[898,70595,4243],{},[898,70597,2775],{},[902,70599,55540],{"encoding":904},[883,70601,70603],{"className":70602},[886],[888,70604,70605],{"xmlns":890},[892,70606,70607,70615],{},[895,70608,70609,70611,70613],{},[898,70610,4243],{},[898,70612,10420],{},[898,70614,2775],{},[902,70616,55507],{"encoding":904},[883,70618,70620],{"className":70619},[886],[888,70621,70622],{"xmlns":890},[892,70623,70624,70630],{},[895,70625,70626,70628],{},[898,70627,2815],{},[898,70629,2775],{},[902,70631,55272],{"encoding":904},[724,70633,70634,70073,70637,70667,70668,69850,70683,6460,70696,1343,70714,1343,70732,69917,70750,69940,70772,70787,70788,70801,70802,1888],{},[38,70635,70636],{},"3.9",[883,70638,70640],{"className":70639},[886],[888,70641,70642],{"xmlns":890},[892,70643,70644,70664],{},[895,70645,70646,70648,70650,70652,70654,70656,70658],{},[898,70647,2772],{},[898,70649,2775],{},[1726,70651,1728],{},[2133,70653,15096],{},[1726,70655,2099],{},[2133,70657,19302],{},[2128,70659,70660,70662],{},[898,70661,1724],{},[2133,70663,2135],{},[902,70665,70666],{"encoding":904},"TC = 500 + 0{,}6Q^2",". (a) Určete, jak rychle se přibližně mění ",[883,70669,70671],{"className":70670},[886],[888,70672,70673],{"xmlns":890},[892,70674,70675,70681],{},[895,70676,70677,70679],{},[898,70678,2772],{},[898,70680,2775],{},[902,70682,3240],{"encoding":904},[883,70684,70686],{"className":70685},[886],[888,70687,70688],{"xmlns":890},[892,70689,70690,70694],{},[895,70691,70692],{},[898,70693,1724],{},[902,70695,1724],{"encoding":904},[883,70697,70699],{"className":70698},[886],[888,70700,70701],{"xmlns":890},[892,70702,70703,70711],{},[895,70704,70705,70707,70709],{},[898,70706,1724],{},[1726,70708,1728],{},[2133,70710,2860],{},[902,70712,70713],{"encoding":904},"Q = 10",[883,70715,70717],{"className":70716},[886],[888,70718,70719],{"xmlns":890},[892,70720,70721,70729],{},[895,70722,70723,70725,70727],{},[898,70724,1724],{},[1726,70726,1728],{},[2133,70728,9021],{},[902,70730,70731],{"encoding":904},"Q = 20",[883,70733,70735],{"className":70734},[886],[888,70736,70737],{"xmlns":890},[892,70738,70739,70747],{},[895,70740,70741,70743,70745],{},[898,70742,1724],{},[1726,70744,1728],{},[2133,70746,38000],{},[902,70748,70749],{"encoding":904},"Q = 30",[883,70751,70753],{"className":70752},[886],[888,70754,70755],{"xmlns":890},[892,70756,70757,70769],{},[895,70758,70759,70761,70763,70765,70767],{},[898,70760,2815],{},[898,70762,2775],{},[1726,70764,1735],{"stretchy":1734},[2133,70766,36225],{},[1726,70768,1762],{"stretchy":1734},[902,70770,70771],{"encoding":904},"MC(15)",[883,70773,70775],{"className":70774},[886],[888,70776,70777],{"xmlns":890},[892,70778,70779,70785],{},[895,70780,70781,70783],{},[898,70782,2772],{},[898,70784,2775],{},[902,70786,3240],{"encoding":904}," v důsledku změny ",[883,70789,70791],{"className":70790},[886],[888,70792,70793],{"xmlns":890},[892,70794,70795,70799],{},[895,70796,70797],{},[898,70798,1724],{},[902,70800,1724],{"encoding":904}," z 15 na 20 a porovnejte se skutečnou změnou ",[883,70803,70805],{"className":70804},[886],[888,70806,70807],{"xmlns":890},[892,70808,70809,70815],{},[895,70810,70811,70813],{},[898,70812,2772],{},[898,70814,2775],{},[902,70816,3240],{"encoding":904},[724,70818,70819,70822,70823,70424,70859,70874,70875,70034,70894,70787,70909,70922],{},[38,70820,70821],{},"3.10"," Jsou dány mezní náklady ",[883,70824,70826],{"className":70825},[886],[888,70827,70828],{"xmlns":890},[892,70829,70830,70856],{},[895,70831,70832,70834,70836,70838,70840,70842,70844,70846,70848,70850],{},[898,70833,2815],{},[898,70835,2775],{},[1726,70837,1728],{},[2133,70839,3123],{},[1726,70841,2228],{},[2133,70843,41843],{},[898,70845,1724],{},[1726,70847,2099],{},[2133,70849,64539],{},[2128,70851,70852,70854],{},[898,70853,1724],{},[2133,70855,2135],{},[902,70857,70858],{"encoding":904},"MC = 60 - 16Q + 1{,}5Q^2",[883,70860,70862],{"className":70861},[886],[888,70863,70864],{"xmlns":890},[892,70865,70866,70872],{},[895,70867,70868,70870],{},[898,70869,2772],{},[898,70871,2775],{},[902,70873,3240],{"encoding":904},", jestliže fixní náklady ",[883,70876,70878],{"className":70877},[886],[888,70879,70880],{"xmlns":890},[892,70881,70882,70892],{},[895,70883,70884,70886,70888,70890],{},[898,70885,10420],{},[898,70887,2775],{},[1726,70889,1728],{},[2133,70891,3087],{},[902,70893,11618],{"encoding":904},[883,70895,70897],{"className":70896},[886],[888,70898,70899],{"xmlns":890},[892,70900,70901,70907],{},[895,70902,70903,70905],{},[898,70904,2772],{},[898,70906,2775],{},[902,70908,3240],{"encoding":904},[883,70910,70912],{"className":70911},[886],[888,70913,70914],{"xmlns":890},[892,70915,70916,70920],{},[895,70917,70918],{},[898,70919,1724],{},[902,70921,1724],{"encoding":904}," z 15 na 20.",[724,70924,70925,70073,70928,70971,70972,70985,70986,71001,71002,71017,71018,70985,71031,71001,71048,71065,71066,70985,71079,71001,71094,71109,71110,71130,71131,71154],{},[38,70926,70927],{},"3.11",[883,70929,70931],{"className":70930},[886],[888,70932,70933],{"xmlns":890},[892,70934,70935,70969],{},[895,70936,70937,70939,70941,70943,70945,70947,70949,70951,70953,70955,70961,70963],{},[898,70938,2772],{},[898,70940,2775],{},[1726,70942,1728],{},[2133,70944,3087],{},[1726,70946,2099],{},[2133,70948,4991],{},[898,70950,1724],{},[1726,70952,2228],{},[2133,70954,2231],{},[2128,70956,70957,70959],{},[898,70958,1724],{},[2133,70960,2135],{},[1726,70962,2099],{},[2128,70964,70965,70967],{},[898,70966,1724],{},[2133,70968,2177],{},[902,70970,60887],{"encoding":904},". (a) Určete ",[883,70973,70975],{"className":70974},[886],[888,70976,70977],{"xmlns":890},[892,70978,70979,70983],{},[895,70980,70981],{},[898,70982,1724],{},[902,70984,1724],{"encoding":904},", které minimalizuje ",[883,70987,70989],{"className":70988},[886],[888,70990,70991],{"xmlns":890},[892,70992,70993,70999],{},[895,70994,70995,70997],{},[898,70996,2815],{},[898,70998,2775],{},[902,71000,55272],{"encoding":904}," a stanovte příslušnou hodnotu minima ",[883,71003,71005],{"className":71004},[886],[888,71006,71007],{"xmlns":890},[892,71008,71009,71015],{},[895,71010,71011,71013],{},[898,71012,2815],{},[898,71014,2775],{},[902,71016,55272],{"encoding":904},". (b) Určete ",[883,71019,71021],{"className":71020},[886],[888,71022,71023],{"xmlns":890},[892,71024,71025,71029],{},[895,71026,71027],{},[898,71028,1724],{},[902,71030,1724],{"encoding":904},[883,71032,71034],{"className":71033},[886],[888,71035,71036],{"xmlns":890},[892,71037,71038,71046],{},[895,71039,71040,71042,71044],{},[898,71041,4243],{},[898,71043,40320],{},[898,71045,2775],{},[902,71047,55291],{"encoding":904},[883,71049,71051],{"className":71050},[886],[888,71052,71053],{"xmlns":890},[892,71054,71055,71063],{},[895,71056,71057,71059,71061],{},[898,71058,4243],{},[898,71060,40320],{},[898,71062,2775],{},[902,71064,55291],{"encoding":904},". (c) Určete ",[883,71067,71069],{"className":71068},[886],[888,71070,71071],{"xmlns":890},[892,71072,71073,71077],{},[895,71074,71075],{},[898,71076,1724],{},[902,71078,1724],{"encoding":904},[883,71080,71082],{"className":71081},[886],[888,71083,71084],{"xmlns":890},[892,71085,71086,71092],{},[895,71087,71088,71090],{},[898,71089,4243],{},[898,71091,2775],{},[902,71093,55540],{"encoding":904},[883,71095,71097],{"className":71096},[886],[888,71098,71099],{"xmlns":890},[892,71100,71101,71107],{},[895,71102,71103,71105],{},[898,71104,4243],{},[898,71106,2775],{},[902,71108,55540],{"encoding":904}," (rada: hledaný kořen ",[883,71111,71113],{"className":71112},[886],[888,71114,71115],{"xmlns":890},[892,71116,71117,71127],{},[895,71118,71119,71121],{},[898,71120,4243],{},[2128,71122,71123,71125],{},[898,71124,2775],{},[1726,71126,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[902,71128,71129],{"encoding":904},"AC'"," určete přibližně, patří do ",[883,71132,71134],{"className":71133},[886],[888,71135,71136],{"xmlns":890},[892,71137,71138,71151],{},[895,71139,71140,71142,71145,71147,71149],{},[1726,71141,1735],{"stretchy":1734},[2133,71143,71144],{},"4,7",[1726,71146,8411],{"separator":1741},[2133,71148,5266],{},[1726,71150,1762],{"stretchy":1734},[902,71152,71153],{"encoding":904},"(4{,}7; 4{,}8)",", zpřesněte).",[724,71156,71157,71160,71161,2623,71189,71206,71207,21575,71248,71269],{},[38,71158,71159],{},"3.12"," Dokažte, že mají-li průměrné náklady ",[883,71162,71164],{"className":71163},[886],[888,71165,71166],{"xmlns":890},[892,71167,71168,71186],{},[895,71169,71170,71172,71174,71176,71178,71180,71182,71184],{},[898,71171,4243],{},[898,71173,2775],{},[1726,71175,1728],{},[898,71177,4243],{},[898,71179,2775],{},[1726,71181,1735],{"stretchy":1734},[898,71183,1724],{},[1726,71185,1762],{"stretchy":1734},[902,71187,71188],{"encoding":904},"AC = AC(Q)",[883,71190,71192],{"className":71191},[886],[888,71193,71194],{"xmlns":890},[892,71195,71196,71204],{},[895,71197,71198],{},[2275,71199,71200,71202],{},[898,71201,1724],{},[2133,71203,2328],{},[902,71205,38289],{"encoding":904}," minimum, pak platí ",[883,71208,71210],{"className":71209},[886],[888,71211,71212],{"xmlns":890},[892,71213,71214,71246],{},[895,71215,71216,71218,71220,71222,71228,71230,71232,71234,71236,71238,71244],{},[898,71217,4243],{},[898,71219,2775],{},[1726,71221,1735],{"stretchy":1734},[2275,71223,71224,71226],{},[898,71225,1724],{},[2133,71227,2328],{},[1726,71229,1762],{"stretchy":1734},[1726,71231,1728],{},[898,71233,2815],{},[898,71235,2775],{},[1726,71237,1735],{"stretchy":1734},[2275,71239,71240,71242],{},[898,71241,1724],{},[2133,71243,2328],{},[1726,71245,1762],{"stretchy":1734},[902,71247,62549],{"encoding":904},[883,71249,71251],{"className":71250},[886],[888,71252,71253],{"xmlns":890},[892,71254,71255,71267],{},[895,71256,71257,71259,71261,71263,71265],{},[898,71258,2815],{},[898,71260,2775],{},[1726,71262,1735],{"stretchy":1734},[898,71264,1724],{},[1726,71266,1762],{"stretchy":1734},[902,71268,67673],{"encoding":904}," jsou mezní náklady.",[724,71271,71272,70073,71275,70535,71309,70985,71322,71001,71337,1888],{},[38,71273,71274],{},"3.13",[883,71276,71278],{"className":71277},[886],[888,71279,71280],{"xmlns":890},[892,71281,71282,71306],{},[895,71283,71284,71286,71288,71290,71296,71298,71300,71302,71304],{},[898,71285,2772],{},[898,71287,2775],{},[1726,71289,1728],{},[2128,71291,71292,71294],{},[898,71293,1724],{},[2133,71295,2135],{},[1726,71297,2099],{},[2133,71299,2135],{},[898,71301,1724],{},[1726,71303,2099],{},[2133,71305,4991],{},[902,71307,71308],{"encoding":904},"TC = Q^2 + 2Q + 25",[883,71310,71312],{"className":71311},[886],[888,71313,71314],{"xmlns":890},[892,71315,71316,71320],{},[895,71317,71318],{},[898,71319,1724],{},[902,71321,1724],{"encoding":904},[883,71323,71325],{"className":71324},[886],[888,71326,71327],{"xmlns":890},[892,71328,71329,71335],{},[895,71330,71331,71333],{},[898,71332,4243],{},[898,71334,2775],{},[902,71336,55540],{"encoding":904},[883,71338,71340],{"className":71339},[886],[888,71341,71342],{"xmlns":890},[892,71343,71344,71350],{},[895,71345,71346,71348],{},[898,71347,4243],{},[898,71349,2775],{},[902,71351,55540],{"encoding":904},[724,71353,71354,71357,71358,2623,71390,71206,71407,21575,71450,71269],{},[38,71355,71356],{},"3.14"," Dokažte, že mají-li průměrné variabilní náklady ",[883,71359,71361],{"className":71360},[886],[888,71362,71363],{"xmlns":890},[892,71364,71365,71387],{},[895,71366,71367,71369,71371,71373,71375,71377,71379,71381,71383,71385],{},[898,71368,4243],{},[898,71370,40320],{},[898,71372,2775],{},[1726,71374,1728],{},[898,71376,4243],{},[898,71378,40320],{},[898,71380,2775],{},[1726,71382,1735],{"stretchy":1734},[898,71384,1724],{},[1726,71386,1762],{"stretchy":1734},[902,71388,71389],{"encoding":904},"AVC = AVC(Q)",[883,71391,71393],{"className":71392},[886],[888,71394,71395],{"xmlns":890},[892,71396,71397,71405],{},[895,71398,71399],{},[2275,71400,71401,71403],{},[898,71402,1724],{},[2133,71404,2328],{},[902,71406,38289],{"encoding":904},[883,71408,71410],{"className":71409},[886],[888,71411,71412],{"xmlns":890},[892,71413,71414,71448],{},[895,71415,71416,71418,71420,71422,71424,71430,71432,71434,71436,71438,71440,71446],{},[898,71417,4243],{},[898,71419,40320],{},[898,71421,2775],{},[1726,71423,1735],{"stretchy":1734},[2275,71425,71426,71428],{},[898,71427,1724],{},[2133,71429,2328],{},[1726,71431,1762],{"stretchy":1734},[1726,71433,1728],{},[898,71435,2815],{},[898,71437,2775],{},[1726,71439,1735],{"stretchy":1734},[2275,71441,71442,71444],{},[898,71443,1724],{},[2133,71445,2328],{},[1726,71447,1762],{"stretchy":1734},[902,71449,68999],{"encoding":904},[883,71451,71453],{"className":71452},[886],[888,71454,71455],{"xmlns":890},[892,71456,71457,71469],{},[895,71458,71459,71461,71463,71465,71467],{},[898,71460,2815],{},[898,71462,2775],{},[1726,71464,1735],{"stretchy":1734},[898,71466,1724],{},[1726,71468,1762],{"stretchy":1734},[902,71470,67673],{"encoding":904},[724,71472,71473,70073,71476,70535,71522,70985,71535,71001,71552,1888],{},[38,71474,71475],{},"3.15",[883,71477,71479],{"className":71478},[886],[888,71480,71481],{"xmlns":890},[892,71482,71483,71519],{},[895,71484,71485,71487,71489,71491,71493,71495,71497,71499,71501,71503,71509,71511,71513],{},[898,71486,2772],{},[898,71488,2775],{},[1726,71490,1728],{},[2133,71492,3117],{},[1726,71494,2099],{},[2133,71496,36225],{},[898,71498,1724],{},[1726,71500,2228],{},[2133,71502,2135],{},[2128,71504,71505,71507],{},[898,71506,1724],{},[2133,71508,2135],{},[1726,71510,2099],{},[2133,71512,2836],{},[2128,71514,71515,71517],{},[898,71516,1724],{},[2133,71518,2177],{},[902,71520,71521],{"encoding":904},"TC = 50 + 15Q - 2Q^2 + 0{,}2Q^3",[883,71523,71525],{"className":71524},[886],[888,71526,71527],{"xmlns":890},[892,71528,71529,71533],{},[895,71530,71531],{},[898,71532,1724],{},[902,71534,1724],{"encoding":904},[883,71536,71538],{"className":71537},[886],[888,71539,71540],{"xmlns":890},[892,71541,71542,71550],{},[895,71543,71544,71546,71548],{},[898,71545,4243],{},[898,71547,40320],{},[898,71549,2775],{},[902,71551,55291],{"encoding":904},[883,71553,71555],{"className":71554},[886],[888,71556,71557],{"xmlns":890},[892,71558,71559,71567],{},[895,71560,71561,71563,71565],{},[898,71562,4243],{},[898,71564,40320],{},[898,71566,2775],{},[902,71568,55291],{"encoding":904},[724,71570,71571,71574,71575,71588,71589,71609],{},[38,71572,71573],{},"3.16"," Celkové náklady na výstavbu domu o ",[883,71576,71578],{"className":71577},[886],[888,71579,71580],{"xmlns":890},[892,71581,71582,71586],{},[895,71583,71584],{},[898,71585,2013],{},[902,71587,2013],{"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 ",[883,71590,71592],{"className":71591},[886],[888,71593,71594],{"xmlns":890},[892,71595,71596,71606],{},[895,71597,71598,71600,71602,71604],{},[2133,71599,2860],{},[2289,71601,2984],{},[2133,71603,59062],{},[898,71605,2013],{},[902,71607,71608],{"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.",[198,71611,71613],{"id":71612},"zisk-body-zvratu-317325","Zisk, body zvratu (3.17–3.25)",[724,71615,71616,71619,71620,3877,71642,71668],{},[38,71617,71618],{},"3.17"," Jsou dány ",[883,71621,71623],{"className":71622},[886],[888,71624,71625],{"xmlns":890},[892,71626,71627,71639],{},[895,71628,71629,71631,71633,71635,71637],{},[898,71630,2772],{},[898,71632,3984],{},[1726,71634,1728],{},[2133,71636,2860],{},[898,71638,1724],{},[902,71640,71641],{"encoding":904},"TR = 10Q",[883,71643,71645],{"className":71644},[886],[888,71646,71647],{"xmlns":890},[892,71648,71649,71665],{},[895,71650,71651,71653,71655,71657,71659,71661,71663],{},[898,71652,2772],{},[898,71654,2775],{},[1726,71656,1728],{},[2133,71658,3087],{},[1726,71660,2099],{},[2133,71662,2231],{},[898,71664,1724],{},[902,71666,71667],{"encoding":904},"TC = 100 + 5Q",". Určete body zvratu a geometricky výsledek interpretujte.",[724,71670,71671,71674,71675,6177,71690,71705,71706,1343,71728,21575,71755,71777,71778,71812],{},[38,71672,71673],{},"3.18"," Odvoďte, že jestliže ",[883,71676,71678],{"className":71677},[886],[888,71679,71680],{"xmlns":890},[892,71681,71682,71688],{},[895,71683,71684,71686],{},[898,71685,2772],{},[898,71687,3984],{},[902,71689,4084],{"encoding":904},[883,71691,71693],{"className":71692},[886],[888,71694,71695],{"xmlns":890},[892,71696,71697,71703],{},[895,71698,71699,71701],{},[898,71700,2772],{},[898,71702,2775],{},[902,71704,3240],{"encoding":904}," jsou lineární tvaru ",[883,71707,71709],{"className":71708},[886],[888,71710,71711],{"xmlns":890},[892,71712,71713,71725],{},[895,71714,71715,71717,71719,71721,71723],{},[898,71716,2772],{},[898,71718,3984],{},[1726,71720,1728],{},[898,71722,724],{},[898,71724,1724],{},[902,71726,71727],{"encoding":904},"TR = pQ",[883,71729,71731],{"className":71730},[886],[888,71732,71733],{"xmlns":890},[892,71734,71735,71752],{},[895,71736,71737,71739,71741,71743,71746,71748,71750],{},[898,71738,2772],{},[898,71740,2775],{},[1726,71742,1728],{},[898,71744,71745],{},"m",[1726,71747,2099],{},[898,71749,36841],{},[898,71751,1724],{},[902,71753,71754],{"encoding":904},"TC = m + nQ",[883,71756,71758],{"className":71757},[886],[888,71759,71760],{"xmlns":890},[892,71761,71762,71774],{},[895,71763,71764,71766,71768,71770,71772],{},[898,71765,71745],{},[1726,71767,1742],{"separator":1741},[898,71769,36841],{},[1726,71771,1742],{"separator":1741},[898,71773,724],{},[902,71775,71776],{"encoding":904},"m, n, p"," jsou pevně zadány, pak existuje jediný bod zvratu ",[883,71779,71781],{"className":71780},[886],[888,71782,71783],{"xmlns":890},[892,71784,71785,71809],{},[895,71786,71787,71793,71795],{},[2128,71788,71789,71791],{},[898,71790,1724],{},[1726,71792,4342],{},[1726,71794,1728],{},[2326,71796,71797],{"scriptlevel":2328,"displaystyle":1734},[2330,71798,71799,71801],{},[898,71800,71745],{},[895,71802,71803,71805,71807],{},[898,71804,724],{},[1726,71806,2228],{},[898,71808,36841],{},[902,71810,71811],{"encoding":904},"Q^* = \\tfrac{m}{p - n}"," a proveďte diskusi podmínek. Načrtněte obrázek.",[724,71814,71815,71619,71818,3877,71852,70971,71878,71891,71892,69723,71907,71922,71923,69707,71936,69723,71951,71966],{},[38,71816,71817],{},"3.19",[883,71819,71821],{"className":71820},[886],[888,71822,71823],{"xmlns":890},[892,71824,71825,71849],{},[895,71826,71827,71829,71831,71833,71835,71837,71843,71845,71847],{},[898,71828,2772],{},[898,71830,3984],{},[1726,71832,1728],{},[1726,71834,2228],{},[2133,71836,2135],{},[2128,71838,71839,71841],{},[898,71840,1724],{},[2133,71842,2135],{},[1726,71844,2099],{},[2133,71846,22927],{},[898,71848,1724],{},[902,71850,71851],{"encoding":904},"TR = -2Q^2 + 14Q",[883,71853,71855],{"className":71854},[886],[888,71856,71857],{"xmlns":890},[892,71858,71859,71875],{},[895,71860,71861,71863,71865,71867,71869,71871,71873],{},[898,71862,2772],{},[898,71864,2775],{},[1726,71866,1728],{},[2133,71868,2135],{},[898,71870,1724],{},[1726,71872,2099],{},[2133,71874,2860],{},[902,71876,71877],{"encoding":904},"TC = 2Q + 10",[883,71879,71881],{"className":71880},[886],[888,71882,71883],{"xmlns":890},[892,71884,71885,71889],{},[895,71886,71887],{},[898,71888,1724],{},[902,71890,1724],{"encoding":904},", které maximalizuje zisk ",[883,71893,71895],{"className":71894},[886],[888,71896,71897],{"xmlns":890},[892,71898,71899,71905],{},[895,71900,71901,71903],{},[898,71902,1738],{},[898,71904,3984],{},[902,71906,63459],{"encoding":904},[883,71908,71910],{"className":71909},[886],[888,71911,71912],{"xmlns":890},[892,71913,71914,71920],{},[895,71915,71916,71918],{},[898,71917,1738],{},[898,71919,3984],{},[902,71921,63459],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku. (c) Určete ",[883,71924,71926],{"className":71925},[886],[888,71927,71928],{"xmlns":890},[892,71929,71930,71934],{},[895,71931,71932],{},[898,71933,1724],{},[902,71935,1724],{"encoding":904},[883,71937,71939],{"className":71938},[886],[888,71940,71941],{"xmlns":890},[892,71942,71943,71949],{},[895,71944,71945,71947],{},[898,71946,2772],{},[898,71948,3984],{},[902,71950,4084],{"encoding":904},[883,71952,71954],{"className":71953},[886],[888,71955,71956],{"xmlns":890},[892,71957,71958,71964],{},[895,71959,71960,71962],{},[898,71961,2772],{},[898,71963,3984],{},[902,71965,4084],{"encoding":904},". (d) Graficky interpretujte.",[724,71968,71969,47665,71972,1343,71998,1343,72017,70971,72037,71891,72050,69723,72065,72080,72081,72103,72104,71154],{},[38,71970,71971],{},"3.20",[883,71973,71975],{"className":71974},[886],[888,71976,71977],{"xmlns":890},[892,71978,71979,71995],{},[895,71980,71981,71983,71985,71987,71989],{},[898,71982,1738],{},[1726,71984,1728],{},[2133,71986,20123],{},[1726,71988,2228],{},[2128,71990,71991,71993],{},[898,71992,1724],{},[2133,71994,2135],{},[902,71996,71997],{"encoding":904},"P = 400 - Q^2",[883,71999,72001],{"className":72000},[886],[888,72002,72003],{"xmlns":890},[892,72004,72005,72015],{},[895,72006,72007,72009,72011,72013],{},[898,72008,10420],{},[898,72010,2775],{},[1726,72012,1728],{},[2133,72014,3087],{},[902,72016,11618],{"encoding":904},[883,72018,72020],{"className":72019},[886],[888,72021,72022],{"xmlns":890},[892,72023,72024,72034],{},[895,72025,72026,72028,72030,72032],{},[898,72027,2815],{},[898,72029,2775],{},[1726,72031,1728],{},[2133,72033,9021],{},[902,72035,72036],{"encoding":904},"MC = 20",[883,72038,72040],{"className":72039},[886],[888,72041,72042],{"xmlns":890},[892,72043,72044,72048],{},[895,72045,72046],{},[898,72047,1724],{},[902,72049,1724],{"encoding":904},[883,72051,72053],{"className":72052},[886],[888,72054,72055],{"xmlns":890},[892,72056,72057,72063],{},[895,72058,72059,72061],{},[898,72060,1738],{},[898,72062,3984],{},[902,72064,63459],{"encoding":904},[883,72066,72068],{"className":72067},[886],[888,72069,72070],{"xmlns":890},[892,72071,72072,72078],{},[895,72073,72074,72076],{},[898,72075,1738],{},[898,72077,3984],{},[902,72079,63459],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku (rada: jeden z bodů zvratu patří do ",[883,72082,72084],{"className":72083},[886],[888,72085,72086],{"xmlns":890},[892,72087,72088,72100],{},[895,72089,72090,72092,72094,72096,72098],{},[1726,72091,1735],{"stretchy":1734},[2133,72093,2328],{},[1726,72095,1742],{"separator":1741},[2133,72097,2281],{},[1726,72099,1762],{"stretchy":1734},[902,72101,72102],{"encoding":904},"(0, 1)",", druhý do ",[883,72105,72107],{"className":72106},[886],[888,72108,72109],{"xmlns":890},[892,72110,72111,72124],{},[895,72112,72113,72115,72118,72120,72122],{},[1726,72114,1735],{"stretchy":1734},[2133,72116,72117],{},"19",[1726,72119,1742],{"separator":1741},[2133,72121,9021],{},[1726,72123,1762],{"stretchy":1734},[902,72125,72126],{"encoding":904},"(19, 20)",[724,72128,72129,72132,72133,2623,72161,72178,72179,1888],{},[38,72130,72131],{},"3.21"," Dokažte, že má-li zisk ",[883,72134,72136],{"className":72135},[886],[888,72137,72138],{"xmlns":890},[892,72139,72140,72158],{},[895,72141,72142,72144,72146,72148,72150,72152,72154,72156],{},[898,72143,1738],{},[898,72145,3984],{},[1726,72147,1728],{},[898,72149,1738],{},[898,72151,3984],{},[1726,72153,1735],{"stretchy":1734},[898,72155,1724],{},[1726,72157,1762],{"stretchy":1734},[902,72159,72160],{"encoding":904},"PR = PR(Q)",[883,72162,72164],{"className":72163},[886],[888,72165,72166],{"xmlns":890},[892,72167,72168,72176],{},[895,72169,72170],{},[2275,72171,72172,72174],{},[898,72173,1724],{},[2133,72175,2328],{},[902,72177,38289],{"encoding":904}," maximum, pak platí ",[883,72180,72182],{"className":72181},[886],[888,72183,72184],{"xmlns":890},[892,72185,72186,72218],{},[895,72187,72188,72190,72192,72194,72200,72202,72204,72206,72208,72210,72216],{},[898,72189,2815],{},[898,72191,3984],{},[1726,72193,1735],{"stretchy":1734},[2275,72195,72196,72198],{},[898,72197,1724],{},[2133,72199,2328],{},[1726,72201,1762],{"stretchy":1734},[1726,72203,1728],{},[898,72205,2815],{},[898,72207,2775],{},[1726,72209,1735],{"stretchy":1734},[2275,72211,72212,72214],{},[898,72213,1724],{},[2133,72215,2328],{},[1726,72217,1762],{"stretchy":1734},[902,72219,65625],{"encoding":904},[724,72221,72222,72225,72226,3877,72241,56005,72256,71891,72269,72284,72285,1343,72312,72349,72350,1343,72377,1888],{},[38,72223,72224],{},"3.22"," Pro zadané ",[883,72227,72229],{"className":72228},[886],[888,72230,72231],{"xmlns":890},[892,72232,72233,72239],{},[895,72234,72235,72237],{},[898,72236,2815],{},[898,72238,3984],{},[902,72240,6621],{"encoding":904},[883,72242,72244],{"className":72243},[886],[888,72245,72246],{"xmlns":890},[892,72247,72248,72254],{},[895,72249,72250,72252],{},[898,72251,2815],{},[898,72253,2775],{},[902,72255,55272],{"encoding":904},[883,72257,72259],{"className":72258},[886],[888,72260,72261],{"xmlns":890},[892,72262,72263,72267],{},[895,72264,72265],{},[898,72266,1724],{},[902,72268,1724],{"encoding":904},[883,72270,72272],{"className":72271},[886],[888,72273,72274],{"xmlns":890},[892,72275,72276,72282],{},[895,72277,72278,72280],{},[898,72279,1738],{},[898,72281,3984],{},[902,72283,63459],{"encoding":904},". (a) ",[883,72286,72288],{"className":72287},[886],[888,72289,72290],{"xmlns":890},[892,72291,72292,72309],{},[895,72293,72294,72296,72298,72300,72303,72305,72307],{},[898,72295,2815],{},[898,72297,3984],{},[1726,72299,1728],{},[2133,72301,72302],{},"236",[1726,72304,2228],{},[2133,72306,41843],{},[898,72308,1724],{},[902,72310,72311],{"encoding":904},"MR = 236 - 16Q",[883,72313,72315],{"className":72314},[886],[888,72316,72317],{"xmlns":890},[892,72318,72319,72346],{},[895,72320,72321,72323,72325,72327,72329,72335,72337,72340,72342,72344],{},[898,72322,2815],{},[898,72324,2775],{},[1726,72326,1728],{},[2133,72328,2177],{},[2128,72330,72331,72333],{},[898,72332,1724],{},[2133,72334,2135],{},[1726,72336,2228],{},[2133,72338,72339],{},"32",[898,72341,1724],{},[1726,72343,2099],{},[2133,72345,5731],{},[902,72347,72348],{"encoding":904},"MC = 3Q^2 - 32Q + 96",". (b) ",[883,72351,72353],{"className":72352},[886],[888,72354,72355],{"xmlns":890},[892,72356,72357,72374],{},[895,72358,72359,72361,72363,72365,72368,72370,72372],{},[898,72360,2815],{},[898,72362,3984],{},[1726,72364,1728],{},[2133,72366,72367],{},"280",[1726,72369,2228],{},[2133,72371,9021],{},[898,72373,1724],{},[902,72375,72376],{"encoding":904},"MR = 280 - 20Q",[883,72378,72380],{"className":72379},[886],[888,72381,72382],{"xmlns":890},[892,72383,72384,72411],{},[895,72385,72386,72388,72390,72392,72395,72401,72403,72405,72407,72409],{},[898,72387,2815],{},[898,72389,2775],{},[1726,72391,1728],{},[2133,72393,72394],{},"1,6",[2128,72396,72397,72399],{},[898,72398,1724],{},[2133,72400,2135],{},[1726,72402,2228],{},[2133,72404,36225],{},[898,72406,1724],{},[1726,72408,2099],{},[2133,72410,3123],{},[902,72412,72413],{"encoding":904},"MC = 1{,}6Q^2 - 15Q + 60",[724,72415,72416,72225,72419,3877,72434,56005,72449,69707,72462,69723,72477,72284,72492,1343,72523,72349,72559,1343,72591,72635,72636,1343,72668,1888],{},[38,72417,72418],{},"3.23",[883,72420,72422],{"className":72421},[886],[888,72423,72424],{"xmlns":890},[892,72425,72426,72432],{},[895,72427,72428,72430],{},[898,72429,2772],{},[898,72431,3984],{},[902,72433,4084],{"encoding":904},[883,72435,72437],{"className":72436},[886],[888,72438,72439],{"xmlns":890},[892,72440,72441,72447],{},[895,72442,72443,72445],{},[898,72444,2772],{},[898,72446,2775],{},[902,72448,3240],{"encoding":904},[883,72450,72452],{"className":72451},[886],[888,72453,72454],{"xmlns":890},[892,72455,72456,72460],{},[895,72457,72458],{},[898,72459,1724],{},[902,72461,1724],{"encoding":904},[883,72463,72465],{"className":72464},[886],[888,72466,72467],{"xmlns":890},[892,72468,72469,72475],{},[895,72470,72471,72473],{},[898,72472,1738],{},[898,72474,3984],{},[902,72476,63459],{"encoding":904},[883,72478,72480],{"className":72479},[886],[888,72481,72482],{"xmlns":890},[892,72483,72484,72490],{},[895,72485,72486,72488],{},[898,72487,1738],{},[898,72489,3984],{},[902,72491,63459],{"encoding":904},[883,72493,72495],{"className":72494},[886],[888,72496,72497],{"xmlns":890},[892,72498,72499,72520],{},[895,72500,72501,72503,72505,72507,72510,72512,72514],{},[898,72502,2772],{},[898,72504,3984],{},[1726,72506,1728],{},[2133,72508,72509],{},"125",[898,72511,1724],{},[1726,72513,2228],{},[2128,72515,72516,72518],{},[898,72517,1724],{},[2133,72519,2135],{},[902,72521,72522],{"encoding":904},"TR = 125Q - Q^2",[883,72524,72526],{"className":72525},[886],[888,72527,72528],{"xmlns":890},[892,72529,72530,72556],{},[895,72531,72532,72534,72536,72538,72540,72542,72544,72546,72548,72550],{},[898,72533,2772],{},[898,72535,2775],{},[1726,72537,1728],{},[2133,72539,15096],{},[1726,72541,2099],{},[2133,72543,2231],{},[898,72545,1724],{},[1726,72547,2099],{},[2133,72549,4996],{},[2128,72551,72552,72554],{},[898,72553,1724],{},[2133,72555,2135],{},[902,72557,72558],{"encoding":904},"TC = 500 + 5Q + 0{,}5Q^2",[883,72560,72562],{"className":72561},[886],[888,72563,72564],{"xmlns":890},[892,72565,72566,72588],{},[895,72567,72568,72570,72572,72574,72576,72578,72580,72582],{},[898,72569,2772],{},[898,72571,3984],{},[1726,72573,1728],{},[2133,72575,9021],{},[898,72577,1724],{},[1726,72579,2228],{},[2133,72581,2135],{},[2128,72583,72584,72586],{},[898,72585,1724],{},[2133,72587,2135],{},[902,72589,72590],{"encoding":904},"TR = 20Q - 2Q^2",[883,72592,72594],{"className":72593},[886],[888,72595,72596],{"xmlns":890},[892,72597,72598,72632],{},[895,72599,72600,72602,72604,72606,72608,72610,72612,72614,72616,72618,72624,72626],{},[898,72601,2772],{},[898,72603,2775],{},[1726,72605,1728],{},[2133,72607,2135],{},[1726,72609,2099],{},[2133,72611,9021],{},[898,72613,1724],{},[1726,72615,2228],{},[2133,72617,5572],{},[2128,72619,72620,72622],{},[898,72621,1724],{},[2133,72623,2135],{},[1726,72625,2099],{},[2128,72627,72628,72630],{},[898,72629,1724],{},[2133,72631,2177],{},[902,72633,72634],{"encoding":904},"TC = 2 + 20Q - 8Q^2 + Q^3",". (c) ",[883,72637,72639],{"className":72638},[886],[888,72640,72641],{"xmlns":890},[892,72642,72643,72665],{},[895,72644,72645,72647,72649,72651,72653,72655,72657,72659],{},[898,72646,2772],{},[898,72648,3984],{},[1726,72650,1728],{},[2133,72652,2352],{},[898,72654,1724],{},[1726,72656,2228],{},[2133,72658,23770],{},[2128,72660,72661,72663],{},[898,72662,1724],{},[2133,72664,2135],{},[902,72666,72667],{"encoding":904},"TR = 4Q - 0{,}25Q^2",[883,72669,72671],{"className":72670},[886],[888,72672,72673],{"xmlns":890},[892,72674,72675,72723],{},[895,72676,72677,72679,72681,72683,72685,72687,72689,72691,72693,72709,72711],{},[898,72678,2772],{},[898,72680,2775],{},[1726,72682,1728],{},[2133,72684,2352],{},[1726,72686,2099],{},[2133,72688,2135],{},[898,72690,1724],{},[1726,72692,2228],{},[2326,72694,72695],{"scriptlevel":2328,"displaystyle":1734},[2330,72696,72697,72707],{},[895,72698,72699,72701],{},[2133,72700,2177],{},[2128,72702,72703,72705],{},[898,72704,1724],{},[2133,72706,2135],{},[2133,72708,2860],{},[1726,72710,2099],{},[2326,72712,72713],{"scriptlevel":2328,"displaystyle":1734},[2330,72714,72715,72721],{},[2128,72716,72717,72719],{},[898,72718,1724],{},[2133,72720,2177],{},[2133,72722,9021],{},[902,72724,72725],{"encoding":904},"TC = 4 + 2Q - \\tfrac{3Q^2}{10} + \\tfrac{Q^3}{20}",[724,72727,72728,72731,72732,72762,72763,72795,72796,21575,72826,72856],{},[38,72729,72730],{},"3.24"," Firma řeší problém stanovení cen pro malé a velké odběratele za účelem maximalizace zisku. Poptávka pro maloodběratele je ",[883,72733,72735],{"className":72734},[886],[888,72736,72737],{"xmlns":890},[892,72738,72739,72759],{},[895,72740,72741,72747,72749,72751,72753],{},[2275,72742,72743,72745],{},[898,72744,1738],{},[2133,72746,2281],{},[1726,72748,1728],{},[2133,72750,15096],{},[1726,72752,2228],{},[2275,72754,72755,72757],{},[898,72756,1724],{},[2133,72758,2281],{},[902,72760,72761],{"encoding":904},"P_1 = 500 - Q_1",", pro velkoodběratele ",[883,72764,72766],{"className":72765},[886],[888,72767,72768],{"xmlns":890},[892,72769,72770,72792],{},[895,72771,72772,72778,72780,72782,72784,72786],{},[2275,72773,72774,72776],{},[898,72775,1738],{},[2133,72777,2135],{},[1726,72779,1728],{},[2133,72781,30062],{},[1726,72783,2228],{},[2133,72785,64539],{},[2275,72787,72788,72790],{},[898,72789,1724],{},[2133,72791,2135],{},[902,72793,72794],{"encoding":904},"P_2 = 300 - 1{,}5Q_2",". Celkové náklady firmy jsou ",[883,72797,72799],{"className":72798},[886],[888,72800,72801],{"xmlns":890},[892,72802,72803,72823],{},[895,72804,72805,72807,72809,72811,72813,72815,72817,72819,72821],{},[898,72806,2772],{},[898,72808,2775],{},[1726,72810,1728],{},[2133,72812,3117],{},[2289,72814,2984],{},[2133,72816,59062],{},[1726,72818,2099],{},[2133,72820,9021],{},[898,72822,1724],{},[902,72824,72825],{"encoding":904},"TC = 50\\,000 + 20Q",[883,72827,72829],{"className":72828},[886],[888,72830,72831],{"xmlns":890},[892,72832,72833,72853],{},[895,72834,72835,72837,72839,72845,72847],{},[898,72836,1724],{},[1726,72838,1728],{},[2275,72840,72841,72843],{},[898,72842,1724],{},[2133,72844,2281],{},[1726,72846,2099],{},[2275,72848,72849,72851],{},[898,72850,1724],{},[2133,72852,2135],{},[902,72854,72855],{"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.",[724,72858,72859,72862,72863,72893,72894,72795,72926,21575,72956,72985],{},[38,72860,72861],{},"3.25"," Firma řeší problém stanovení cen pro domácí a zahraniční trh za účelem maximalizace zisku. Poptávka pro domácí trh je ",[883,72864,72866],{"className":72865},[886],[888,72867,72868],{"xmlns":890},[892,72869,72870,72890],{},[895,72871,72872,72878,72880,72882,72884],{},[2275,72873,72874,72876],{},[898,72875,1738],{},[2133,72877,2281],{},[1726,72879,1728],{},[2133,72881,30062],{},[1726,72883,2228],{},[2275,72885,72886,72888],{},[898,72887,1724],{},[2133,72889,2281],{},[902,72891,72892],{"encoding":904},"P_1 = 300 - Q_1",", pro zahraniční trh ",[883,72895,72897],{"className":72896},[886],[888,72898,72899],{"xmlns":890},[892,72900,72901,72923],{},[895,72902,72903,72909,72911,72913,72915,72917],{},[2275,72904,72905,72907],{},[898,72906,1738],{},[2133,72908,2135],{},[1726,72910,1728],{},[2133,72912,8363],{},[1726,72914,2228],{},[2133,72916,4996],{},[2275,72918,72919,72921],{},[898,72920,1724],{},[2133,72922,2135],{},[902,72924,72925],{"encoding":904},"P_2 = 200 - 0{,}5Q_2",[883,72927,72929],{"className":72928},[886],[888,72930,72931],{"xmlns":890},[892,72932,72933,72953],{},[895,72934,72935,72937,72939,72941,72943,72945,72947,72949,72951],{},[898,72936,2772],{},[898,72938,2775],{},[1726,72940,1728],{},[2133,72942,2231],{},[2289,72944,2984],{},[2133,72946,59062],{},[1726,72948,2099],{},[2133,72950,3087],{},[898,72952,1724],{},[902,72954,72955],{"encoding":904},"TC = 5\\,000 + 100Q",[883,72957,72959],{"className":72958},[886],[888,72960,72961],{"xmlns":890},[892,72962,72963,72983],{},[895,72964,72965,72967,72969,72975,72977],{},[898,72966,1724],{},[1726,72968,1728],{},[2275,72970,72971,72973],{},[898,72972,1724],{},[2133,72974,2281],{},[1726,72976,2099],{},[2275,72978,72979,72981],{},[898,72980,1724],{},[2133,72982,2135],{},[902,72984,72855],{"encoding":904},". Stanovte ceny, při kterých firma maximalizuje zisk: (a) s cenovou diskriminací, (b) bez cenové diskriminace. Porovnejte zisk firmy v obou případech.",[198,72987,72989],{"id":72988},"konstrukce-nabídky-326328","Konstrukce nabídky (3.26–3.28)",[724,72991,72992,72995,72996,73043,73044,73061],{},[38,72993,72994],{},"3.26"," Jsou dány celkové variabilní náklady ",[883,72997,72999],{"className":72998},[886],[888,73000,73001],{"xmlns":890},[892,73002,73003,73040],{},[895,73004,73005,73007,73009,73011,73013,73016,73022,73024,73027,73033,73035,73038],{},[898,73006,2772],{},[898,73008,40320],{},[898,73010,2775],{},[1726,73012,1728],{},[2133,73014,73015],{},"0,85",[2128,73017,73018,73020],{},[898,73019,1724],{},[2133,73021,2177],{},[1726,73023,2228],{},[2133,73025,73026],{},"11,9",[2128,73028,73029,73031],{},[898,73030,1724],{},[2133,73032,2135],{},[1726,73034,2099],{},[2133,73036,73037],{},"102",[898,73039,1724],{},[902,73041,73042],{"encoding":904},"TVC = 0{,}85Q^3 - 11{,}9Q^2 + 102Q",". Určete minimální cenu ",[883,73045,73047],{"className":73046},[886],[888,73048,73049],{"xmlns":890},[892,73050,73051,73059],{},[895,73052,73053],{},[2128,73054,73055,73057],{},[898,73056,1738],{},[1726,73058,4342],{},[902,73060,4392],{"encoding":904}," nabídky a konstruujte nabídku. Graficky interpretujte.",[724,73063,73064,70822,73067,73103],{},[38,73065,73066],{},"3.27",[883,73068,73070],{"className":73069},[886],[888,73071,73072],{"xmlns":890},[892,73073,73074,73100],{},[895,73075,73076,73078,73080,73082,73084,73090,73092,73094,73096,73098],{},[898,73077,2815],{},[898,73079,2775],{},[1726,73081,1728],{},[2133,73083,2920],{},[2128,73085,73086,73088],{},[898,73087,1724],{},[2133,73089,2135],{},[1726,73091,2228],{},[2133,73093,64420],{},[898,73095,1724],{},[1726,73097,2099],{},[2133,73099,30724],{},[902,73101,73102],{"encoding":904},"MC = 4{,}2Q^2 - 48Q + 250",". Konstruujte nabídku.",[724,73105,73106,70073,73109,73103],{},[38,73107,73108],{},"3.28",[883,73110,73112],{"className":73111},[886],[888,73113,73114],{"xmlns":890},[892,73115,73116,73152],{},[895,73117,73118,73120,73122,73124,73126,73132,73134,73136,73142,73144,73146,73148,73150],{},[898,73119,2772],{},[898,73121,2775],{},[1726,73123,1728],{},[2133,73125,4996],{},[2128,73127,73128,73130],{},[898,73129,1724],{},[2133,73131,2177],{},[1726,73133,2228],{},[2133,73135,24182],{},[2128,73137,73138,73140],{},[898,73139,1724],{},[2133,73141,2135],{},[1726,73143,2099],{},[2133,73145,3123],{},[898,73147,1724],{},[1726,73149,2099],{},[2133,73151,15096],{},[902,73153,73154],{"encoding":904},"TC = 0{,}5Q^3 - 7Q^2 + 60Q + 500",[115,73156,1670],{"id":1669},[120,73158,73159,73187,73232,73304,73369,73409,73501,73607,73647,73761,73854,73918,73950,74010,74016,74080,74129,74183,74291,74346],{},[123,73160,73161,1777,73163,73186],{},[38,73162,55730],{},[883,73164,73166],{"className":73165},[886],[888,73167,73168],{"xmlns":890},[892,73169,73170,73184],{},[895,73171,73172,73174,73176,73178,73180,73182],{},[898,73173,2772],{},[898,73175,3984],{},[1726,73177,1728],{},[898,73179,1738],{},[1726,73181,3174],{},[898,73183,1724],{},[902,73185,66692],{"encoding":904}," — křivka celkového příjmu (total revenue curve).",[123,73188,73189,1777,73191,73231],{},[38,73190,56316],{},[883,73192,73194],{"className":73193},[886],[888,73195,73196],{"xmlns":890},[892,73197,73198,73228],{},[895,73199,73200,73202,73204,73206,73218,73220,73222,73224,73226],{},[898,73201,4243],{},[898,73203,3984],{},[1726,73205,1728],{},[2326,73207,73208],{"scriptlevel":2328,"displaystyle":1734},[2330,73209,73210,73216],{},[895,73211,73212,73214],{},[898,73213,2772],{},[898,73215,3984],{},[898,73217,1724],{},[1726,73219,1728],{},[898,73221,1731],{},[1726,73223,1735],{"stretchy":1734},[898,73225,1724],{},[1726,73227,1762],{"stretchy":1734},[902,73229,73230],{"encoding":904},"AR = \\tfrac{TR}{Q} = D(Q)"," — shoduje se s poptávkovou funkcí.",[123,73233,73234,1777,73236,73272,73273,73288,73289,1888],{},[38,73235,56464],{},[883,73237,73239],{"className":73238},[886],[888,73240,73241],{"xmlns":890},[892,73242,73243,73269],{},[895,73244,73245,73247,73249,73251],{},[898,73246,2815],{},[898,73248,3984],{},[1726,73250,1728],{},[2326,73252,73253],{"scriptlevel":2328,"displaystyle":1734},[2330,73254,73255,73263],{},[895,73256,73257,73259,73261],{},[898,73258,2198],{"mathvariant":2377},[898,73260,2772],{},[898,73262,3984],{},[895,73264,73265,73267],{},[898,73266,2198],{"mathvariant":2377},[898,73268,1724],{},[902,73270,73271],{"encoding":904},"MR = \\tfrac{\\mathrm{d}TR}{\\mathrm{d}Q}"," — rychlost změny ",[883,73274,73276],{"className":73275},[886],[888,73277,73278],{"xmlns":890},[892,73279,73280,73286],{},[895,73281,73282,73284],{},[898,73283,2772],{},[898,73285,3984],{},[902,73287,4084],{"encoding":904},"; pro lineární poptávku má sklon dvojnásobný vůči ",[883,73290,73292],{"className":73291},[886],[888,73293,73294],{"xmlns":890},[892,73295,73296,73302],{},[895,73297,73298,73300],{},[898,73299,4243],{},[898,73301,3984],{},[902,73303,55425],{"encoding":904},[123,73305,73306,1777,73309,1343,73339,1888],{},[38,73307,73308],{},"Diferenciál příjmu\u002Fnákladů",[883,73310,73312],{"className":73311},[886],[888,73313,73314],{"xmlns":890},[892,73315,73316,73336],{},[895,73317,73318,73320,73322,73324,73326,73328,73330,73332,73334],{},[898,73319,2886],{"mathvariant":2377},[898,73321,2772],{},[898,73323,3984],{},[1726,73325,1880],{},[898,73327,2815],{},[898,73329,3984],{},[2289,73331,2984],{},[898,73333,2198],{"mathvariant":2377},[898,73335,1724],{},[902,73337,73338],{"encoding":904},"\\Delta TR \\approx MR \\, \\mathrm{d}Q",[883,73340,73342],{"className":73341},[886],[888,73343,73344],{"xmlns":890},[892,73345,73346,73366],{},[895,73347,73348,73350,73352,73354,73356,73358,73360,73362,73364],{},[898,73349,2886],{"mathvariant":2377},[898,73351,2772],{},[898,73353,2775],{},[1726,73355,1880],{},[898,73357,2815],{},[898,73359,2775],{},[2289,73361,2984],{},[898,73363,2198],{"mathvariant":2377},[898,73365,1724],{},[902,73367,73368],{"encoding":904},"\\Delta TC \\approx MC \\, \\mathrm{d}Q",[123,73370,73371,1777,73373,1888],{},[38,73372,58586],{},[883,73374,73376],{"className":73375},[886],[888,73377,73378],{"xmlns":890},[892,73379,73380,73406],{},[895,73381,73382,73384,73386,73388,73390,73392,73394,73396,73398,73400,73402,73404],{},[898,73383,2772],{},[898,73385,2775],{},[1726,73387,1728],{},[898,73389,10420],{},[898,73391,2775],{},[1726,73393,2099],{},[898,73395,2772],{},[898,73397,40320],{},[898,73399,2775],{},[1726,73401,1735],{"stretchy":1734},[898,73403,1724],{},[1726,73405,1762],{"stretchy":1734},[902,73407,73408],{"encoding":904},"TC = FC + TVC(Q)",[123,73410,73411,1777,73414,1343,73429,1777,73431,1343,73454,1777,73457,1888],{},[38,73412,73413],{},"Fixní náklady",[883,73415,73417],{"className":73416},[886],[888,73418,73419],{"xmlns":890},[892,73420,73421,73427],{},[895,73422,73423,73425],{},[898,73424,10420],{},[898,73426,2775],{},[902,73428,55471],{"encoding":904},[38,73430,58739],{},[883,73432,73434],{"className":73433},[886],[888,73435,73436],{"xmlns":890},[892,73437,73438,73452],{},[895,73439,73440,73442,73444,73446,73448,73450],{},[898,73441,2772],{},[898,73443,40320],{},[898,73445,2775],{},[1726,73447,1735],{"stretchy":1734},[898,73449,1724],{},[1726,73451,1762],{"stretchy":1734},[902,73453,58736],{"encoding":904},[38,73455,73456],{},"variabilní náklady na jednotku",[883,73458,73460],{"className":73459},[886],[888,73461,73462],{"xmlns":890},[892,73463,73464,73498],{},[895,73465,73466,73468,73470,73472,73474,73476,73478],{},[898,73467,40320],{},[898,73469,2775],{},[1726,73471,1735],{"stretchy":1734},[898,73473,1724],{},[1726,73475,1762],{"stretchy":1734},[1726,73477,1728],{},[2326,73479,73480],{"scriptlevel":2328,"displaystyle":1734},[2330,73481,73482,73496],{},[895,73483,73484,73486,73488,73490,73492,73494],{},[898,73485,2772],{},[898,73487,40320],{},[898,73489,2775],{},[1726,73491,1735],{"stretchy":1734},[898,73493,1724],{},[1726,73495,1762],{"stretchy":1734},[898,73497,1724],{},[902,73499,73500],{"encoding":904},"VC(Q) = \\tfrac{TVC(Q)}{Q}",[123,73502,73503,1777,73505,1343,73535,1777,73538,1343,73570,1777,73573,1888],{},[38,73504,58747],{},[883,73506,73508],{"className":73507},[886],[888,73509,73510],{"xmlns":890},[892,73511,73512,73532],{},[895,73513,73514,73516,73518,73520],{},[898,73515,4243],{},[898,73517,2775],{},[1726,73519,1728],{},[2326,73521,73522],{"scriptlevel":2328,"displaystyle":1734},[2330,73523,73524,73530],{},[895,73525,73526,73528],{},[898,73527,2772],{},[898,73529,2775],{},[898,73531,1724],{},[902,73533,73534],{"encoding":904},"AC = \\tfrac{TC}{Q}",[38,73536,73537],{},"průměrné fixní",[883,73539,73541],{"className":73540},[886],[888,73542,73543],{"xmlns":890},[892,73544,73545,73567],{},[895,73546,73547,73549,73551,73553,73555],{},[898,73548,4243],{},[898,73550,10420],{},[898,73552,2775],{},[1726,73554,1728],{},[2326,73556,73557],{"scriptlevel":2328,"displaystyle":1734},[2330,73558,73559,73565],{},[895,73560,73561,73563],{},[898,73562,10420],{},[898,73564,2775],{},[898,73566,1724],{},[902,73568,73569],{"encoding":904},"AFC = \\tfrac{FC}{Q}",[38,73571,73572],{},"průměrné variabilní",[883,73574,73576],{"className":73575},[886],[888,73577,73578],{"xmlns":890},[892,73579,73580,73604],{},[895,73581,73582,73584,73586,73588,73590],{},[898,73583,4243],{},[898,73585,40320],{},[898,73587,2775],{},[1726,73589,1728],{},[2326,73591,73592],{"scriptlevel":2328,"displaystyle":1734},[2330,73593,73594,73602],{},[895,73595,73596,73598,73600],{},[898,73597,2772],{},[898,73599,40320],{},[898,73601,2775],{},[898,73603,1724],{},[902,73605,73606],{"encoding":904},"AVC = \\tfrac{TVC}{Q}",[123,73608,73609,1777,73611,1888],{},[38,73610,59934],{},[883,73612,73614],{"className":73613},[886],[888,73615,73616],{"xmlns":890},[892,73617,73618,73644],{},[895,73619,73620,73622,73624,73626],{},[898,73621,2815],{},[898,73623,2775],{},[1726,73625,1728],{},[2326,73627,73628],{"scriptlevel":2328,"displaystyle":1734},[2330,73629,73630,73638],{},[895,73631,73632,73634,73636],{},[898,73633,2198],{"mathvariant":2377},[898,73635,2772],{},[898,73637,2775],{},[895,73639,73640,73642],{},[898,73641,2198],{"mathvariant":2377},[898,73643,1724],{},[902,73645,73646],{"encoding":904},"MC = \\tfrac{\\mathrm{d}TC}{\\mathrm{d}Q}",[123,73648,73649,1777,73651,73699,73700,73713,73714,1343,73729,1343,73746,1888],{},[38,73650,60832],{},[883,73652,73654],{"className":73653},[886],[888,73655,73656],{"xmlns":890},[892,73657,73658,73696],{},[895,73659,73660,73662,73664,73666,73668,73670,73672,73674,73676,73678,73680,73686,73688,73690],{},[898,73661,2772],{},[898,73663,2775],{},[1726,73665,1728],{},[898,73667,10420],{},[898,73669,2775],{},[1726,73671,2099],{},[898,73673,207],{},[898,73675,1724],{},[1726,73677,2099],{},[898,73679,2102],{},[2128,73681,73682,73684],{},[898,73683,1724],{},[2133,73685,2135],{},[1726,73687,2099],{},[898,73689,2146],{},[2128,73691,73692,73694],{},[898,73693,1724],{},[2133,73695,2177],{},[902,73697,73698],{"encoding":904},"TC = FC + aQ + bQ^2 + cQ^3"," — „standardní\" tvar s ",[883,73701,73703],{"className":73702},[886],[888,73704,73705],{"xmlns":890},[892,73706,73707,73711],{},[895,73708,73709],{},[898,73710,900],{},[902,73712,900],{"encoding":904},"-průběhem ",[883,73715,73717],{"className":73716},[886],[888,73718,73719],{"xmlns":890},[892,73720,73721,73727],{},[895,73722,73723,73725],{},[898,73724,4243],{},[898,73726,2775],{},[902,73728,55540],{"encoding":904},[883,73730,73732],{"className":73731},[886],[888,73733,73734],{"xmlns":890},[892,73735,73736,73744],{},[895,73737,73738,73740,73742],{},[898,73739,4243],{},[898,73741,40320],{},[898,73743,2775],{},[902,73745,55291],{"encoding":904},[883,73747,73749],{"className":73748},[886],[888,73750,73751],{"xmlns":890},[892,73752,73753,73759],{},[895,73754,73755,73757],{},[898,73756,2815],{},[898,73758,2775],{},[902,73760,55272],{"encoding":904},[123,73762,73763,73765,73766,10378,73781,73822,73823,61477,73838,73853],{},[38,73764,61914],{},": v bodě minima ",[883,73767,73769],{"className":73768},[886],[888,73770,73771],{"xmlns":890},[892,73772,73773,73779],{},[895,73774,73775,73777],{},[898,73776,4243],{},[898,73778,2775],{},[902,73780,55540],{"encoding":904},[883,73782,73784],{"className":73783},[886],[888,73785,73786],{"xmlns":890},[892,73787,73788,73820],{},[895,73789,73790,73792,73794,73796,73802,73804,73806,73808,73810,73812,73818],{},[898,73791,4243],{},[898,73793,2775],{},[1726,73795,1735],{"stretchy":1734},[2275,73797,73798,73800],{},[898,73799,1724],{},[2133,73801,2328],{},[1726,73803,1762],{"stretchy":1734},[1726,73805,1728],{},[898,73807,2815],{},[898,73809,2775],{},[1726,73811,1735],{"stretchy":1734},[2275,73813,73814,73816],{},[898,73815,1724],{},[2133,73817,2328],{},[1726,73819,1762],{"stretchy":1734},[902,73821,62549],{"encoding":904},"; geometricky ",[883,73824,73826],{"className":73825},[886],[888,73827,73828],{"xmlns":890},[892,73829,73830,73836],{},[895,73831,73832,73834],{},[898,73833,2815],{},[898,73835,2775],{},[902,73837,55272],{"encoding":904},[883,73839,73841],{"className":73840},[886],[888,73842,73843],{"xmlns":890},[892,73844,73845,73851],{},[895,73846,73847,73849],{},[898,73848,4243],{},[898,73850,2775],{},[902,73852,55540],{"encoding":904}," v jejím minimu.",[123,73855,73856,73765,73858,10378,73875,1888],{},[38,73857,63264],{},[883,73859,73861],{"className":73860},[886],[888,73862,73863],{"xmlns":890},[892,73864,73865,73873],{},[895,73866,73867,73869,73871],{},[898,73868,4243],{},[898,73870,40320],{},[898,73872,2775],{},[902,73874,55291],{"encoding":904},[883,73876,73878],{"className":73877},[886],[888,73879,73880],{"xmlns":890},[892,73881,73882,73916],{},[895,73883,73884,73886,73888,73890,73892,73898,73900,73902,73904,73906,73908,73914],{},[898,73885,4243],{},[898,73887,40320],{},[898,73889,2775],{},[1726,73891,1735],{"stretchy":1734},[2275,73893,73894,73896],{},[898,73895,1724],{},[2133,73897,2328],{},[1726,73899,1762],{"stretchy":1734},[1726,73901,1728],{},[898,73903,2815],{},[898,73905,2775],{},[1726,73907,1735],{"stretchy":1734},[2275,73909,73910,73912],{},[898,73911,1724],{},[2133,73913,2328],{},[1726,73915,1762],{"stretchy":1734},[902,73917,68999],{"encoding":904},[123,73919,73920,1777,73922,73949],{},[38,73921,63443],{},[883,73923,73925],{"className":73924},[886],[888,73926,73927],{"xmlns":890},[892,73928,73929,73947],{},[895,73930,73931,73933,73935,73937,73939,73941,73943,73945],{},[898,73932,1738],{},[898,73934,3984],{},[1726,73936,1728],{},[898,73938,2772],{},[898,73940,3984],{},[1726,73942,2228],{},[898,73944,2772],{},[898,73946,2775],{},[902,73948,55180],{"encoding":904}," — rozdíl mezi celkovým příjmem a celkovými náklady.",[123,73951,73952,10009,73954,73956,73957,73983,73984,74009],{},[38,73953,64305],{},[614,73955,63568],{},") — hodnoty ",[883,73958,73960],{"className":73959},[886],[888,73961,73962],{"xmlns":890},[892,73963,73964,73980],{},[895,73965,73966,73972,73974],{},[2275,73967,73968,73970],{},[898,73969,1724],{},[898,73971,4243],{},[1726,73973,1742],{"separator":1741},[2275,73975,73976,73978],{},[898,73977,1724],{},[898,73979,23234],{},[902,73981,73982],{"encoding":904},"Q_A, Q_B"," splňující ",[883,73985,73987],{"className":73986},[886],[888,73988,73989],{"xmlns":890},[892,73990,73991,74007],{},[895,73992,73993,73995,73997,73999,74001,74003,74005],{},[898,73994,1738],{},[898,73996,3984],{},[1726,73998,1735],{"stretchy":1734},[898,74000,1724],{},[1726,74002,1762],{"stretchy":1734},[1726,74004,1728],{},[2133,74006,2328],{},[902,74008,63845],{"encoding":904},"; oddělují pásma ztráty a zisku.",[123,74011,74012,74015],{},[38,74013,74014],{},"Práh rentability"," — stav firmy v bodě zvratu.",[123,74017,74018,74020,74021,10378,74038,74079],{},[38,74019,65359],{}," — v bodě maxima zisku ",[883,74022,74024],{"className":74023},[886],[888,74025,74026],{"xmlns":890},[892,74027,74028,74036],{},[895,74029,74030],{},[2275,74031,74032,74034],{},[898,74033,1724],{},[2133,74035,2328],{},[902,74037,38289],{"encoding":904},[883,74039,74041],{"className":74040},[886],[888,74042,74043],{"xmlns":890},[892,74044,74045,74077],{},[895,74046,74047,74049,74051,74053,74059,74061,74063,74065,74067,74069,74075],{},[898,74048,2815],{},[898,74050,3984],{},[1726,74052,1735],{"stretchy":1734},[2275,74054,74055,74057],{},[898,74056,1724],{},[2133,74058,2328],{},[1726,74060,1762],{"stretchy":1734},[1726,74062,1728],{},[898,74064,2815],{},[898,74066,2775],{},[1726,74068,1735],{"stretchy":1734},[2275,74070,74071,74073],{},[898,74072,1724],{},[2133,74074,2328],{},[1726,74076,1762],{"stretchy":1734},[902,74078,65625],{"encoding":904}," (3.13).",[123,74081,74082,20282,74084,10378,74103,74128],{},[38,74083,66652],{},[883,74085,74087],{"className":74086},[886],[888,74088,74089],{"xmlns":890},[892,74090,74091,74100],{},[895,74092,74093,74095,74097],{},[898,74094,1738],{},[1726,74096,1728],{},[2289,74098,74099],{},"konst",[902,74101,74102],{"encoding":904},"P = \\text{konst}",[883,74104,74106],{"className":74105},[886],[888,74107,74108],{"xmlns":890},[892,74109,74110,74126],{},[895,74111,74112,74114,74116,74118,74120,74122,74124],{},[898,74113,1738],{},[1726,74115,1728],{},[898,74117,2815],{},[898,74119,2775],{},[1726,74121,1735],{"stretchy":1734},[898,74123,1724],{},[1726,74125,1762],{"stretchy":1734},[902,74127,67346],{"encoding":904}," (3.14).",[123,74130,74131,74134,74135,74164,74165,74182],{},[38,74132,74133],{},"Shutdown point"," — bod ",[883,74136,74138],{"className":74137},[886],[888,74139,74140],{"xmlns":890},[892,74141,74142,74162],{},[895,74143,74144,74146,74152,74154,74160],{},[1726,74145,1735],{"stretchy":1734},[2128,74147,74148,74150],{},[898,74149,1724],{},[1726,74151,4342],{},[1726,74153,1742],{"separator":1741},[2128,74155,74156,74158],{},[898,74157,1738],{},[1726,74159,4342],{},[1726,74161,1762],{"stretchy":1734},[902,74163,67635],{"encoding":904}," v minimu ",[883,74166,74168],{"className":74167},[886],[888,74169,74170],{"xmlns":890},[892,74171,74172,74180],{},[895,74173,74174,74176,74178],{},[898,74175,4243],{},[898,74177,40320],{},[898,74179,2775],{},[902,74181,55291],{"encoding":904},"; pod ním se firmě nevyplatí produkovat.",[123,74184,74185,1777,74188,6460,74223,67905,74244,74257,74258,74273,74274,1888],{},[38,74186,74187],{},"Funkce nabídky firmy",[883,74189,74191],{"className":74190},[886],[888,74192,74193],{"xmlns":890},[892,74194,74195,74221],{},[895,74196,74197,74199,74201,74203,74205,74207,74209,74211,74213,74215,74217,74219],{},[898,74198,1738],{},[1726,74200,1728],{},[898,74202,8659],{},[1726,74204,1735],{"stretchy":1734},[898,74206,1724],{},[1726,74208,1762],{"stretchy":1734},[1726,74210,1728],{},[898,74212,2815],{},[898,74214,2775],{},[1726,74216,1735],{"stretchy":1734},[898,74218,1724],{},[1726,74220,1762],{"stretchy":1734},[902,74222,69102],{"encoding":904},[883,74224,74226],{"className":74225},[886],[888,74227,74228],{"xmlns":890},[892,74229,74230,74242],{},[895,74231,74232,74234,74236],{},[898,74233,1724],{},[1726,74235,4473],{},[2128,74237,74238,74240],{},[898,74239,1724],{},[1726,74241,4342],{},[902,74243,67904],{"encoding":904},[883,74245,74247],{"className":74246},[886],[888,74248,74249],{"xmlns":890},[892,74250,74251,74255],{},[895,74252,74253],{},[2133,74254,2328],{},[902,74256,2328],{"encoding":904}," (3.15); vychází z rostoucí části ",[883,74259,74261],{"className":74260},[886],[888,74262,74263],{"xmlns":890},[892,74264,74265,74271],{},[895,74266,74267,74269],{},[898,74268,2815],{},[898,74270,2775],{},[902,74272,55272],{"encoding":904}," nad minimem ",[883,74275,74277],{"className":74276},[886],[888,74278,74279],{"xmlns":890},[892,74280,74281,74289],{},[895,74282,74283,74285,74287],{},[898,74284,4243],{},[898,74286,40320],{},[898,74288,2775],{},[902,74290,55291],{"encoding":904},[123,74292,74293,1696,74295,74316,74317,1888],{},[38,74294,50060],{},[883,74296,74298],{"className":74297},[886],[888,74299,74300],{"xmlns":890},[892,74301,74302,74314],{},[895,74303,74304,74306,74308],{},[898,74305,1738],{},[1726,74307,1728],{},[2128,74309,74310,74312],{},[898,74311,1738],{},[1726,74313,4342],{},[902,74315,4345],{"encoding":904}," konstantní ⇒ ",[883,74318,74320],{"className":74319},[886],[888,74321,74322],{"xmlns":890},[892,74323,74324,74344],{},[895,74325,74326,74328,74330,74332,74334,74336,74338],{},[898,74327,4243],{},[898,74329,3984],{},[1726,74331,1728],{},[898,74333,2815],{},[898,74335,3984],{},[1726,74337,1728],{},[2128,74339,74340,74342],{},[898,74341,1738],{},[1726,74343,4342],{},[902,74345,58578],{"encoding":904},[123,74347,74348,74351],{},[38,74349,74350],{},"Cenová diskriminace"," — stanovení odlišných cen pro různé segmenty trhu za účelem maximalizace zisku (úlohy 3.24–3.25).",[115,74353,1899],{"id":1898},[120,74355,74356,74375,74387],{},[123,74357,74358,1777,74360,1343,74363,1343,74366,1343,74369,1343,74372],{},[38,74359,50703],{},[207,74361,11926],{"className":74362,"dataFsResolvedFilePath":800,"href":801},[210],[207,74364,3820],{"className":74365,"dataFsResolvedFilePath":848,"href":849},[210],[207,74367,2358],{"className":74368,"dataFsResolvedFilePath":764,"href":765},[210],[207,74370,775],{"className":74371,"dataFsResolvedFilePath":773,"href":774},[210],[207,74373,859],{"className":74374,"dataFsResolvedFilePath":857,"href":858},[210],[123,74376,74377,1777,74379,1343,74383],{},[38,74378,36684],{},[207,74380,74382],{"className":74381,"dataFsResolvedFilePath":745,"href":746},[210],"KS 1. blok — souhrn",[207,74384,74386],{"className":74385,"dataFsResolvedFilePath":838,"href":839},[210],"KS 2. blok — souhrn",[123,74388,74389,1777,74391],{},[38,74390,16188],{},[207,74392,16192],{"className":74393,"dataFsResolvedFilePath":1640,"href":1641},[210],{"title":641,"searchDepth":642,"depth":642,"links":74395},[74396,74397,74404,74410,74414,74415,74419,74420,74421,74422,74428,74429],{"id":50934,"depth":642,"text":1241},{"id":55718,"depth":642,"text":55719,"children":74398},[74399,74400,74401,74402,74403],{"id":55729,"depth":649,"text":55730},{"id":56315,"depth":649,"text":56316},{"id":56463,"depth":649,"text":56464},{"id":57205,"depth":649,"text":57206},{"id":57860,"depth":649,"text":57861},{"id":58581,"depth":642,"text":58582,"children":74405},[74406,74407,74408,74409],{"id":58585,"depth":649,"text":58586},{"id":58746,"depth":649,"text":58747},{"id":59933,"depth":649,"text":59934},{"id":60831,"depth":649,"text":60832},{"id":61913,"depth":642,"text":61914,"children":74411},[74412,74413],{"id":16393,"depth":649,"text":16394},{"id":63263,"depth":649,"text":63264},{"id":63437,"depth":642,"text":63438},{"id":65358,"depth":642,"text":65359,"children":74416},[74417,74418],{"id":65372,"depth":649,"text":16394},{"id":66651,"depth":649,"text":66652},{"id":67283,"depth":642,"text":67284},{"id":68749,"depth":642,"text":68750},{"id":49862,"depth":642,"text":49863},{"id":69210,"depth":642,"text":69211,"children":74423},[74424,74425,74426,74427],{"id":69214,"depth":649,"text":69215},{"id":70066,"depth":649,"text":70067},{"id":71612,"depth":649,"text":71613},{"id":72988,"depth":649,"text":72989},{"id":1669,"depth":642,"text":1670},{"id":1898,"depth":642,"text":1899},{},"\u002Ftopics\u002Fprijem-naklady-zisk",{"title":55100,"description":641},[1138,1135],"topics\u002Fprijem-naklady-zisk",[1128,74436,74437,55152,74438,74439,74440],"prijem","naklady","body-zvratu","maximalizace-zisku","nabidka-firmy","0d2CjMGyTT-GeTvSE65iXk5mUJ-650ilVskfuGcRAwI",{"id":74443,"title":74444,"body":74445,"course":1128,"courses":659,"created":9541,"description":641,"extension":661,"meta":86542,"navigation":664,"path":86543,"seo":86544,"sources":86545,"stem":86546,"tags":86547,"type":1950,"updated":677,"__hash__":86553},"topics\u002Ftopics\u002Fprodukce.md","Produkce — produkční funkce, Cobb-Douglas, MRTS",{"type":9,"value":74446,"toc":86499},[74447,74450,74806,74810,74813,74881,74933,74943,74947,74981,75022,75046,75069,75098,75165,75272,75315,75372,75447,75492,75496,75504,75512,75515,75780,75831,75911,75981,76004,76032,76077,76099,76103,76110,76159,76185,76336,76339,76376,76539,76647,76651,76688,76763,76832,76951,77073,77154,77160,77201,77274,77367,77371,77407,77495,77609,77714,77799,77939,77943,77991,78036,78042,78046,78049,78100,78150,78157,78223,78356,78401,78405,78426,78805,78900,78917,78971,78975,79057,79141,79311,79314,79357,79424,79498,79502,79507,79576,79584,79593,79671,79737,79742,79837,79880,79885,79933,79938,79986,80104,80187,80225,80328,80387,80528,80532,80575,80648,80672,80726,80733,80735,80780,80825,80836,80841,80877,80939,80962,80971,81072,81139,81212,81219,81310,81372,81408,81465,81524,81709,81805,81809,81813,81892,81897,82021,82107,82113,82223,82260,82351,82449,82452,82456,82522,82559,82681,82733,82737,82765,82817,82891,82996,83020,83079,83083,83101,83244,83392,83394,83429,83433,83435,83525,83655,83781,83873,83948,83952,84068,84172,84362,84398,84492,84498,84611,84914,84920,85038,85137,85213,85215,86377,86379],[12,74448,74444],{"id":74449},"produkce-produkční-funkce-cobb-douglas-mrts",[3859,74451,74452],{},[724,74453,74454,3866,74456,74458,74459,36877,74472,74485,74486,16359,74499,10009,74501,74525,74526,1777,74528,3877,74562,1777,74565,74593,74594,10378,74614,74644,74645,10009,74648,74676,74677,74680,74681,74711,74712,74742,74743,1777,74746,74786,74787,74805],{},[883,74455,3865],{},[38,74457,859],{}," popisuje vztah mezi vstupy (práce ",[883,74460,74462],{"className":74461},[886],[888,74463,74464],{"xmlns":890},[892,74465,74466,74470],{},[895,74467,74468],{},[898,74469,9779],{},[902,74471,9779],{"encoding":904},[883,74473,74475],{"className":74474},[886],[888,74476,74477],{"xmlns":890},[892,74478,74479,74483],{},[895,74480,74481],{},[898,74482,9784],{},[902,74484,9784],{"encoding":904},") a výstupem ",[883,74487,74489],{"className":74488},[886],[888,74490,74491],{"xmlns":890},[892,74492,74493,74497],{},[895,74494,74495],{},[898,74496,1724],{},[902,74498,1724],{"encoding":904},[38,74500,36945],{},[883,74502,74504],{"className":74503},[886],[888,74505,74506],{"xmlns":890},[892,74507,74508,74522],{},[895,74509,74510,74512,74514,74516,74518,74520],{},[898,74511,1724],{},[1726,74513,1728],{},[898,74515,1724],{},[1726,74517,1735],{"stretchy":1734},[898,74519,9779],{},[1726,74521,1762],{"stretchy":1734},[902,74523,74524],{"encoding":904},"Q = Q(L)",") studujeme ",[614,74527,10008],{},[883,74529,74531],{"className":74530},[886],[888,74532,74533],{"xmlns":890},[892,74534,74535,74559],{},[895,74536,74537,74539,74545,74547,74553,74555,74557],{},[898,74538,2815],{},[2275,74540,74541,74543],{},[898,74542,1738],{},[898,74544,9779],{},[1726,74546,1728],{},[2128,74548,74549,74551],{},[898,74550,1724],{},[1726,74552,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,74554,1735],{"stretchy":1734},[898,74556,9779],{},[1726,74558,1762],{"stretchy":1734},[902,74560,74561],{"encoding":904},"MP_L = Q'(L)",[614,74563,74564],{},"průměrný produkt",[883,74566,74568],{"className":74567},[886],[888,74569,74570],{"xmlns":890},[892,74571,74572,74590],{},[895,74573,74574,74576,74582,74584,74586,74588],{},[898,74575,4243],{},[2275,74577,74578,74580],{},[898,74579,1738],{},[898,74581,9779],{},[1726,74583,1728],{},[898,74585,1724],{},[898,74587,4661],{"mathvariant":2377},[898,74589,9779],{},[902,74591,74592],{"encoding":904},"AP_L = Q\u002FL","; v maximu ",[883,74595,74597],{"className":74596},[886],[888,74598,74599],{"xmlns":890},[892,74600,74601,74611],{},[895,74602,74603,74605],{},[898,74604,4243],{},[2275,74606,74607,74609],{},[898,74608,1738],{},[898,74610,9779],{},[902,74612,74613],{"encoding":904},"AP_L",[883,74615,74617],{"className":74616},[886],[888,74618,74619],{"xmlns":890},[892,74620,74621,74641],{},[895,74622,74623,74625,74631,74633,74635],{},[898,74624,2815],{},[2275,74626,74627,74629],{},[898,74628,1738],{},[898,74630,9779],{},[1726,74632,1728],{},[898,74634,4243],{},[2275,74636,74637,74639],{},[898,74638,1738],{},[898,74640,9779],{},[902,74642,74643],{"encoding":904},"MP_L = AP_L",". Ve ",[38,74646,74647],{},"dvoufaktorovém modelu",[883,74649,74651],{"className":74650},[886],[888,74652,74653],{"xmlns":890},[892,74654,74655,74673],{},[895,74656,74657,74659,74661,74663,74665,74667,74669,74671],{},[898,74658,1724],{},[1726,74660,1728],{},[898,74662,1724],{},[1726,74664,1735],{"stretchy":1734},[898,74666,9779],{},[1726,74668,1742],{"separator":1741},[898,74670,9784],{},[1726,74672,1762],{"stretchy":1734},[902,74674,74675],{"encoding":904},"Q = Q(L,K)",") dominují ",[38,74678,74679],{},"Cobb-Douglasovy"," funkce ",[883,74682,74684],{"className":74683},[886],[888,74685,74686],{"xmlns":890},[892,74687,74688,74708],{},[895,74689,74690,74692,74694,74696,74702],{},[898,74691,1724],{},[1726,74693,1728],{},[898,74695,4243],{},[2128,74697,74698,74700],{},[898,74699,9779],{},[898,74701,207],{},[2128,74703,74704,74706],{},[898,74705,9784],{},[898,74707,2102],{},[902,74709,74710],{"encoding":904},"Q = AL^a K^b","; mezní produkty ",[883,74713,74715],{"className":74714},[886],[888,74716,74717],{"xmlns":890},[892,74718,74719,74739],{},[895,74720,74721,74723,74729,74731,74733],{},[898,74722,2815],{},[2275,74724,74725,74727],{},[898,74726,1738],{},[898,74728,9779],{},[1726,74730,1742],{"separator":1741},[898,74732,2815],{},[2275,74734,74735,74737],{},[898,74736,1738],{},[898,74738,9784],{},[902,74740,74741],{"encoding":904},"MP_L, MP_K"," jsou parciální derivace a jejich podíl dává ",[38,74744,74745],{},"mezní míru technické substituce",[883,74747,74749],{"className":74748},[886],[888,74750,74751],{"xmlns":890},[892,74752,74753,74783],{},[895,74754,74755,74757,74759,74761,74763,74765,74767,74773,74775,74777],{},[898,74756,2815],{},[898,74758,3984],{},[898,74760,2772],{},[898,74762,8659],{},[1726,74764,1728],{},[898,74766,2815],{},[2275,74768,74769,74771],{},[898,74770,1738],{},[898,74772,9779],{},[898,74774,4661],{"mathvariant":2377},[898,74776,2815],{},[2275,74778,74779,74781],{},[898,74780,1738],{},[898,74782,9784],{},[902,74784,74785],{"encoding":904},"MRTS = MP_L\u002FMP_K"," — sklon izokvanty. Součet exponentů ",[883,74788,74790],{"className":74789},[886],[888,74791,74792],{"xmlns":890},[892,74793,74794,74802],{},[895,74795,74796,74798,74800],{},[898,74797,207],{},[1726,74799,2099],{},[898,74801,2102],{},[902,74803,74804],{"encoding":904},"a+b"," určuje typ výnosů z rozsahu.",[115,74807,74809],{"id":74808},"úvod-cílové-znalosti-kapitoly-5","Úvod — cílové znalosti kapitoly 5",[724,74811,74812],{},"Po prostudování kapitoly 5 student umí:",[120,74814,74815,74821,74831,74837,74843,74848,74854,74864,74869,74875],{},[123,74816,74817,74818,1742],{},"popsat ",[38,74819,74820],{},"jednofaktorový model produkce",[123,74822,74823,74824,3877,74827,74830],{},"vypočítat ",[38,74825,74826],{},"mezní",[38,74828,74829],{},"průměrný produkt práce"," a ekonomicky je interpretovat,",[123,74832,74833,74834,1742],{},"charakterizovat průběh ",[38,74835,74836],{},"křivky produkce",[123,74838,74839,74840,1742],{},"formulovat ",[38,74841,74842],{},"princip maximalizace průměrného produktu práce",[123,74844,74817,74845,1742],{},[38,74846,74847],{},"dvoufaktorový model produkce",[123,74849,74850,74851,1742],{},"uvést tvar ",[38,74852,74853],{},"Cobb–Douglasových produkčních funkcí",[123,74855,74856,74857,1343,74859,1343,74861,1742],{},"vyložit, co jsou ",[38,74858,24594],{},[38,74860,13643],{},[38,74862,74863],{},"klesající výnosy z rozsahu",[123,74865,74823,74866,74830],{},[38,74867,74868],{},"mezní produkty práce a kapitálu",[123,74870,74871,74872,1742],{},"najít ",[38,74873,74874],{},"izokvanty",[123,74876,74823,74877,74880],{},[38,74878,74879],{},"mezní míru technické substituce (MRTS)"," a ekonomicky ji interpretovat.",[724,74882,74883,74884,74887,74888,74891,74892,1777,74895,1343,74908,1777,74911,3877,74924,74927,74928,74930,74931,1888],{},"Každý proces produkce je určován ",[38,74885,74886],{},"faktory"," (též ",[38,74889,74890],{},"vstupy",") produkce. K hlavním patří ",[38,74893,74894],{},"práce",[883,74896,74898],{"className":74897},[886],[888,74899,74900],{"xmlns":890},[892,74901,74902,74906],{},[895,74903,74904],{},[898,74905,9779],{},[902,74907,9779],{"encoding":904},[38,74909,74910],{},"kapitál",[883,74912,74914],{"className":74913},[886],[888,74915,74916],{"xmlns":890},[892,74917,74918,74922],{},[895,74919,74920],{},[898,74921,9784],{},[902,74923,9784],{"encoding":904},[38,74925,74926],{},"půda",". Při modelování se půda obvykle považuje za dlouhodobě konstantní, takže endogenními faktory zůstávají práce a kapitál. Je-li kapitál neměnný, hovoříme o ",[38,74929,36945],{}," (produkce závisí jen na práci); v opačném případě o ",[38,74932,74647],{},[724,74934,74935,74936,1343,74939,74942],{},"Související matematický aparát: ",[207,74937,2358],{"className":74938,"dataFsResolvedFilePath":764,"href":765},[210],[207,74940,784],{"className":74941,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace a totální diferenciál).",[115,74944,74946],{"id":74945},"jednofaktorový-model-produkce","Jednofaktorový model produkce",[724,74948,74949,74950,74963,74964,74977,74978],{},"Uvažujeme proces v krátkém období, kdy kapitál lze považovat za konstantní. Závislost produkce ",[883,74951,74953],{"className":74952},[886],[888,74954,74955],{"xmlns":890},[892,74956,74957,74961],{},[895,74958,74959],{},[898,74960,1724],{},[902,74962,1724],{"encoding":904}," na práci ",[883,74965,74967],{"className":74966},[886],[888,74968,74969],{"xmlns":890},[892,74970,74971,74975],{},[895,74972,74973],{},[898,74974,9779],{},[902,74976,9779],{"encoding":904}," vyjadřuje ",[38,74979,74980],{},"produkční funkce",[883,74982,74984],{"className":74983},[886],[888,74985,74986],{"xmlns":890,"display":28047},[892,74987,74988,75019],{},[20735,74989,74990],{"width":28052},[20740,74991,74992,74994,75012,75014],{},[20743,74993],{"width":28057},[20743,74995,74996],{},[895,74997,74998,75000,75002,75004,75006,75008,75010],{},[898,74999,1724],{},[1726,75001,1728],{},[898,75003,1724],{},[1726,75005,1735],{"stretchy":1734},[898,75007,9779],{},[1726,75009,1762],{"stretchy":1734},[1726,75011,1742],{"separator":1741},[20743,75013],{"width":28057},[20743,75015,75016],{},[2289,75017,75018],{},"(5.1)",[902,75020,75021],{"encoding":904},"Q = Q(L), \\tag{5.1}",[724,75023,75024,75025,10009,75028,75031,75032,75045],{},"jejíž graf se nazývá ",[38,75026,75027],{},"křivka produkce",[614,75029,75030],{},"production curve","). Práce ",[883,75033,75035],{"className":75034},[886],[888,75036,75037],{"xmlns":890},[892,75038,75039,75043],{},[895,75040,75041],{},[898,75042,9779],{},[902,75044,9779],{"encoding":904}," se měří počtem pracovníků, případně počtem pracovních hodin.",[115,75047,75049,75050,1762],{"id":75048},"mezní-produkt-práce-mplmp_l","Mezní produkt práce (",[883,75051,75053],{"className":75052},[886],[888,75054,75055],{"xmlns":890},[892,75056,75057,75067],{},[895,75058,75059,75061],{},[898,75060,2815],{},[2275,75062,75063,75065],{},[898,75064,1738],{},[898,75066,9779],{},[902,75068,10029],{"encoding":904},[724,75070,75071,10009,75074,75077,75078,75097],{},[38,75072,75073],{},"Mezní produkt práce",[614,75075,75076],{},"marginal product of labour",") ",[883,75079,75081],{"className":75080},[886],[888,75082,75083],{"xmlns":890},[892,75084,75085,75095],{},[895,75086,75087,75089],{},[898,75088,2815],{},[2275,75090,75091,75093],{},[898,75092,1738],{},[898,75094,9779],{},[902,75096,10029],{"encoding":904}," je derivace produkce podle práce:",[883,75099,75101],{"className":75100},[886],[888,75102,75103],{"xmlns":890,"display":28047},[892,75104,75105,75162],{},[20735,75106,75107],{"width":28052},[20740,75108,75109,75111,75155,75157],{},[20743,75110],{"width":28057},[20743,75112,75113],{},[895,75114,75115,75117,75123,75125,75139,75141,75147,75149,75151,75153],{},[898,75116,2815],{},[2275,75118,75119,75121],{},[898,75120,1738],{},[898,75122,9779],{},[1726,75124,1728],{},[2330,75126,75127,75133],{},[895,75128,75129,75131],{},[898,75130,2198],{},[898,75132,1724],{},[895,75134,75135,75137],{},[898,75136,2198],{},[898,75138,9779],{},[1726,75140,1728],{},[2128,75142,75143,75145],{},[898,75144,1724],{},[1726,75146,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,75148,1735],{"stretchy":1734},[898,75150,9779],{},[1726,75152,1762],{"stretchy":1734},[898,75154,1888],{"mathvariant":2377},[20743,75156],{"width":28057},[20743,75158,75159],{},[2289,75160,75161],{},"(5.2)",[902,75163,75164],{"encoding":904},"MP_L = \\frac{dQ}{dL} = Q'(L). \\tag{5.2}",[724,75166,75167,75168,19926,75186,75214,75215,75232,75233,2684,75250,1847],{},"Pro pevnou hodnotu ",[883,75169,75171],{"className":75170},[886],[888,75172,75173],{"xmlns":890},[892,75174,75175,75183],{},[895,75176,75177],{},[2128,75178,75179,75181],{},[898,75180,9779],{},[1726,75182,4342],{},[902,75184,75185],{"encoding":904},"L^*",[883,75187,75189],{"className":75188},[886],[888,75190,75191],{"xmlns":890},[892,75192,75193,75211],{},[895,75194,75195,75201,75203,75209],{},[2128,75196,75197,75199],{},[898,75198,1724],{},[1726,75200,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,75202,1735],{"stretchy":1734},[2128,75204,75205,75207],{},[898,75206,9779],{},[1726,75208,4342],{},[1726,75210,1762],{"stretchy":1734},[902,75212,75213],{"encoding":904},"Q'(L^*)"," rychlost změny produkce vzhledem k práci v bodě ",[883,75216,75218],{"className":75217},[886],[888,75219,75220],{"xmlns":890},[892,75221,75222,75230],{},[895,75223,75224],{},[2128,75225,75226,75228],{},[898,75227,9779],{},[1726,75229,4342],{},[902,75231,75185],{"encoding":904},", resp. přibližnou změnu produkce odpovídající jednotkové změně práce (z ",[883,75234,75236],{"className":75235},[886],[888,75237,75238],{"xmlns":890},[892,75239,75240,75248],{},[895,75241,75242],{},[2128,75243,75244,75246],{},[898,75245,9779],{},[1726,75247,4342],{},[902,75249,75185],{"encoding":904},[883,75251,75253],{"className":75252},[886],[888,75254,75255],{"xmlns":890},[892,75256,75257,75269],{},[895,75258,75259,75265,75267],{},[2128,75260,75261,75263],{},[898,75262,9779],{},[1726,75264,4342],{},[1726,75266,2099],{},[2133,75268,2281],{},[902,75270,75271],{"encoding":904},"L^*+1",[3859,75273,75274],{},[724,75275,75276,18005,75278,75297,75298,75301,75302,1888],{},[883,75277,4145],{},[883,75279,75281],{"className":75280},[886],[888,75282,75283],{"xmlns":890},[892,75284,75285,75295],{},[895,75286,75287,75289],{},[898,75288,2815],{},[2275,75290,75291,75293],{},[898,75292,1738],{},[898,75294,9779],{},[902,75296,10029],{"encoding":904}," odpovídá na otázku „",[38,75299,75300],{},"kolik produkce přibude, když přidám jednoho dalšího pracovníka"," (při neměnném kapitálu)?\". Je to sklon křivky produkce v bodě ",[883,75303,75305],{"className":75304},[886],[888,75306,75307],{"xmlns":890},[892,75308,75309,75313],{},[895,75310,75311],{},[898,75312,9779],{},[902,75314,9779],{"encoding":904},[724,75316,75317,75320,75321,75337,75338,2684,75351,75371],{},[38,75318,75319],{},"Přibližná změna produkce"," pro změnu práce o ",[883,75322,75324],{"className":75323},[886],[888,75325,75326],{"xmlns":890},[892,75327,75328,75334],{},[895,75329,75330,75332],{},[898,75331,2198],{},[898,75333,9779],{},[902,75335,75336],{"encoding":904},"dL"," (z ",[883,75339,75341],{"className":75340},[886],[888,75342,75343],{"xmlns":890},[892,75344,75345,75349],{},[895,75346,75347],{},[898,75348,9779],{},[902,75350,9779],{"encoding":904},[883,75352,75354],{"className":75353},[886],[888,75355,75356],{"xmlns":890},[892,75357,75358,75368],{},[895,75359,75360,75362,75364,75366],{},[898,75361,9779],{},[1726,75363,2099],{},[898,75365,2198],{},[898,75367,9779],{},[902,75369,75370],{"encoding":904},"L+dL",") pomocí diferenciálu:",[883,75373,75375],{"className":75374},[886],[888,75376,75377],{"xmlns":890,"display":28047},[892,75378,75379,75444],{},[20735,75380,75381],{"width":28052},[20740,75382,75383,75385,75437,75439],{},[20743,75384],{"width":28057},[20743,75386,75387],{},[895,75388,75389,75391,75393,75395,75397,75399,75401,75407,75409,75411,75413,75415,75417,75419,75421,75423,75429,75431,75433,75435],{},[898,75390,2886],{"mathvariant":2377},[898,75392,1724],{},[1726,75394,1880],{},[898,75396,2198],{},[898,75398,1724],{},[1726,75400,1728],{},[2128,75402,75403,75405],{},[898,75404,1724],{},[1726,75406,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,75408,1735],{"stretchy":1734},[898,75410,9779],{},[1726,75412,1762],{"stretchy":1734},[2289,75414,2984],{},[898,75416,2198],{},[898,75418,9779],{},[1726,75420,1728],{},[898,75422,2815],{},[2275,75424,75425,75427],{},[898,75426,1738],{},[898,75428,9779],{},[2289,75430,2984],{},[898,75432,2198],{},[898,75434,9779],{},[898,75436,1888],{"mathvariant":2377},[20743,75438],{"width":28057},[20743,75440,75441],{},[2289,75442,75443],{},"(5.3)",[902,75445,75446],{"encoding":904},"\\Delta Q \\approx dQ = Q'(L)\\,dL = MP_L\\,dL. \\tag{5.3}",[724,75448,75449,75450,1888],{},"Skutečná změna je ",[883,75451,75453],{"className":75452},[886],[888,75454,75455],{"xmlns":890},[892,75456,75457,75489],{},[895,75458,75459,75461,75463,75465,75467,75469,75471,75473,75475,75477,75479,75481,75483,75485,75487],{},[898,75460,2886],{"mathvariant":2377},[898,75462,1724],{},[1726,75464,1728],{},[898,75466,1724],{},[1726,75468,1735],{"stretchy":1734},[898,75470,9779],{},[1726,75472,2099],{},[898,75474,2198],{},[898,75476,9779],{},[1726,75478,1762],{"stretchy":1734},[1726,75480,2228],{},[898,75482,1724],{},[1726,75484,1735],{"stretchy":1734},[898,75486,9779],{},[1726,75488,1762],{"stretchy":1734},[902,75490,75491],{"encoding":904},"\\Delta Q = Q(L+dL) - Q(L)",[198,75493,75495],{"id":75494},"zákon-klesajících-mezních-výnosů","Zákon klesajících mezních výnosů",[724,75497,75498,10009,75501,3148],{},[38,75499,75500],{},"Zákon klesajících výnosů",[614,75502,75503],{},"law of diminishing marginal productivity",[3859,75505,75506],{},[724,75507,75508,75509,75511],{},"Roste-li postupně některý ze vstupů (",[614,75510,36941],{},"), budou přírůstky výstupu od jistého bodu klesat.",[724,75513,75514],{},"Typická křivka produkce (Obrázek 5.2) má dvě fáze:",[724,75516,75517,75518,1777,75539,75558,75559,75609,75610,75612,75613,1777,75633,75652,75653,75609,75685,2924,75687,75706,75707,21575,75724,75758,75759,8088,75776,75779],{},"1° ",[38,75519,75520,75521,2703],{},"Do bodu ",[883,75522,75524],{"className":75523},[886],[888,75525,75526],{"xmlns":890},[892,75527,75528,75536],{},[895,75529,75530],{},[2275,75531,75532,75534],{},[898,75533,9779],{},[2133,75535,2328],{},[902,75537,75538],{"encoding":904},"L_0",[883,75540,75542],{"className":75541},[886],[888,75543,75544],{"xmlns":890},[892,75545,75546,75556],{},[895,75547,75548,75550],{},[898,75549,2815],{},[2275,75551,75552,75554],{},[898,75553,1738],{},[898,75555,9779],{},[902,75557,10029],{"encoding":904}," roste, tj. ",[883,75560,75562],{"className":75561},[886],[888,75563,75564],{"xmlns":890},[892,75565,75566,75606],{},[895,75567,75568,75570,75572,75578,75584,75586,75596,75598,75600,75602,75604],{},[1726,75569,1735],{"stretchy":1734},[898,75571,2815],{},[2275,75573,75574,75576],{},[898,75575,1738],{},[898,75577,9779],{},[2128,75579,75580,75582],{},[1726,75581,1762],{"stretchy":1734},[1726,75583,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,75585,1728],{},[2128,75587,75588,75590],{},[898,75589,1724],{},[895,75591,75592,75594],{},[1726,75593,2379],{"mathvariant":2377},[1726,75595,2379],{"mathvariant":2377},[1726,75597,1735],{"stretchy":1734},[898,75599,9779],{},[1726,75601,1762],{"stretchy":1734},[1726,75603,3405],{},[2133,75605,2328],{},[902,75607,75608],{"encoding":904},"(MP_L)' = Q''(L) > 0"," — křivka produkce je ",[38,75611,37645],{},".\n2° ",[38,75614,75615,75616,2703],{},"Od bodu ",[883,75617,75619],{"className":75618},[886],[888,75620,75621],{"xmlns":890},[892,75622,75623,75631],{},[895,75624,75625],{},[2275,75626,75627,75629],{},[898,75628,9779],{},[2133,75630,2328],{},[902,75632,75538],{"encoding":904},[883,75634,75636],{"className":75635},[886],[888,75637,75638],{"xmlns":890},[892,75639,75640,75650],{},[895,75641,75642,75644],{},[898,75643,2815],{},[2275,75645,75646,75648],{},[898,75647,1738],{},[898,75649,9779],{},[902,75651,10029],{"encoding":904}," klesá, ",[883,75654,75656],{"className":75655},[886],[888,75657,75658],{"xmlns":890},[892,75659,75660,75682],{},[895,75661,75662,75672,75674,75676,75678,75680],{},[2128,75663,75664,75666],{},[898,75665,1724],{},[895,75667,75668,75670],{},[1726,75669,2379],{"mathvariant":2377},[1726,75671,2379],{"mathvariant":2377},[1726,75673,1735],{"stretchy":1734},[898,75675,9779],{},[1726,75677,1762],{"stretchy":1734},[1726,75679,3444],{},[2133,75681,2328],{},[902,75683,75684],{"encoding":904},"Q''(L) \u003C 0",[38,75686,38469],{},[883,75688,75690],{"className":75689},[886],[888,75691,75692],{"xmlns":890},[892,75693,75694,75704],{},[895,75695,75696,75698],{},[898,75697,2815],{},[2275,75699,75700,75702],{},[898,75701,1738],{},[898,75703,9779],{},[902,75705,10029],{"encoding":904}," v kladných hodnotách klesá do bodu ",[883,75708,75710],{"className":75709},[886],[888,75711,75712],{"xmlns":890},[892,75713,75714,75722],{},[895,75715,75716],{},[2275,75717,75718,75720],{},[898,75719,9779],{},[2133,75721,2281],{},[902,75723,13198],{"encoding":904},[883,75725,75727],{"className":75726},[886],[888,75728,75729],{"xmlns":890},[892,75730,75731,75755],{},[895,75732,75733,75735,75741,75743,75749,75751,75753],{},[898,75734,2815],{},[2275,75736,75737,75739],{},[898,75738,1738],{},[898,75740,9779],{},[1726,75742,1735],{"stretchy":1734},[2275,75744,75745,75747],{},[898,75746,9779],{},[2133,75748,2281],{},[1726,75750,1762],{"stretchy":1734},[1726,75752,1728],{},[2133,75754,2328],{},[902,75756,75757],{"encoding":904},"MP_L(L_1) = 0"," (maximum produkce), a dále pokračuje v záporných hodnotách. Bod ",[883,75760,75762],{"className":75761},[886],[888,75763,75764],{"xmlns":890},[892,75765,75766,75774],{},[895,75767,75768],{},[2275,75769,75770,75772],{},[898,75771,9779],{},[2133,75773,2328],{},[902,75775,75538],{"encoding":904},[38,75777,75778],{},"inflexním bodem"," produkční funkce.",[724,75781,75782,75783,10378,75800,1888],{},"Matematicky: zákon klesajících výnosů znamená, že od určitého ",[883,75784,75786],{"className":75785},[886],[888,75787,75788],{"xmlns":890},[892,75789,75790,75798],{},[895,75791,75792],{},[2275,75793,75794,75796],{},[898,75795,9779],{},[2133,75797,2328],{},[902,75799,75538],{"encoding":904},[883,75801,75803],{"className":75802},[886],[888,75804,75805],{"xmlns":890},[892,75806,75807,75829],{},[895,75808,75809,75819,75821,75823,75825,75827],{},[2128,75810,75811,75813],{},[898,75812,1724],{},[895,75814,75815,75817],{},[1726,75816,2379],{"mathvariant":2377},[1726,75818,2379],{"mathvariant":2377},[1726,75820,1735],{"stretchy":1734},[898,75822,9779],{},[1726,75824,1762],{"stretchy":1734},[1726,75826,3444],{},[2133,75828,2328],{},[902,75830,75684],{"encoding":904},[724,75832,75833,1777,75836,5656,75876,1343,75893,75910],{},[38,75834,75835],{},"Typický polynom třetího stupně:",[883,75837,75839],{"className":75838},[886],[888,75840,75841],{"xmlns":890},[892,75842,75843,75873],{},[895,75844,75845,75847,75849,75851,75853,75855,75857,75863,75865,75867],{},[898,75846,1724],{},[1726,75848,1735],{"stretchy":1734},[898,75850,9779],{},[1726,75852,1762],{"stretchy":1734},[1726,75854,1728],{},[898,75856,207],{},[2128,75858,75859,75861],{},[898,75860,9779],{},[2133,75862,2177],{},[1726,75864,2099],{},[898,75866,2102],{},[2128,75868,75869,75871],{},[898,75870,9779],{},[2133,75872,2135],{},[902,75874,75875],{"encoding":904},"Q(L) = aL^3 + bL^2",[883,75877,75879],{"className":75878},[886],[888,75880,75881],{"xmlns":890},[892,75882,75883,75891],{},[895,75884,75885,75887,75889],{},[898,75886,207],{},[1726,75888,3444],{},[2133,75890,2328],{},[902,75892,43066],{"encoding":904},[883,75894,75896],{"className":75895},[886],[888,75897,75898],{"xmlns":890},[892,75899,75900,75908],{},[895,75901,75902,75904,75906],{},[898,75903,2102],{},[1726,75905,3405],{},[2133,75907,2328],{},[902,75909,18795],{"encoding":904},". Pak",[883,75912,75914],{"className":75913},[886],[888,75915,75916],{"xmlns":890,"display":28047},[892,75917,75918,75978],{},[895,75919,75920,75926,75928,75930,75938,75946,75948,75950,75956,75958,75960,75968,75976],{},[2275,75921,75922,75924],{},[898,75923,9779],{},[2133,75925,2328],{},[1726,75927,1728],{},[1726,75929,2228],{},[2326,75931,75932],{"scriptlevel":2328,"displaystyle":1734},[2330,75933,75934,75936],{},[2133,75935,2281],{},[2133,75937,2177],{},[2326,75939,75940],{"scriptlevel":2328,"displaystyle":1734},[2330,75941,75942,75944],{},[898,75943,2102],{},[898,75945,207],{},[1726,75947,1742],{"separator":1741},[5865,75949],{"width":5867},[2275,75951,75952,75954],{},[898,75953,9779],{},[2133,75955,2281],{},[1726,75957,1728],{},[1726,75959,2228],{},[2326,75961,75962],{"scriptlevel":2328,"displaystyle":1734},[2330,75963,75964,75966],{},[2133,75965,2135],{},[2133,75967,2177],{},[2326,75969,75970],{"scriptlevel":2328,"displaystyle":1734},[2330,75971,75972,75974],{},[898,75973,2102],{},[898,75975,207],{},[898,75977,1888],{"mathvariant":2377},[902,75979,75980],{"encoding":904},"L_0 = -\\tfrac{1}{3}\\tfrac{b}{a}, \\qquad L_1 = -\\tfrac{2}{3}\\tfrac{b}{a}.",[115,75982,75984,75985,1762],{"id":75983},"průměrný-produkt-práce-aplap_l","Průměrný produkt práce (",[883,75986,75988],{"className":75987},[886],[888,75989,75990],{"xmlns":890},[892,75991,75992,76002],{},[895,75993,75994,75996],{},[898,75995,4243],{},[2275,75997,75998,76000],{},[898,75999,1738],{},[898,76001,9779],{},[902,76003,74613],{"encoding":904},[724,76005,76006,10009,76009,75077,76012,76031],{},[38,76007,76008],{},"Průměrný produkt práce",[614,76010,76011],{},"average product of labour",[883,76013,76015],{"className":76014},[886],[888,76016,76017],{"xmlns":890},[892,76018,76019,76029],{},[895,76020,76021,76023],{},[898,76022,4243],{},[2275,76024,76025,76027],{},[898,76026,1738],{},[898,76028,9779],{},[902,76030,74613],{"encoding":904}," je podíl produkce a práce:",[883,76033,76035],{"className":76034},[886],[888,76036,76037],{"xmlns":890,"display":28047},[892,76038,76039,76074],{},[20735,76040,76041],{"width":28052},[20740,76042,76043,76045,76067,76069],{},[20743,76044],{"width":28057},[20743,76046,76047],{},[895,76048,76049,76051,76057,76059,76065],{},[898,76050,4243],{},[2275,76052,76053,76055],{},[898,76054,1738],{},[898,76056,9779],{},[1726,76058,1728],{},[2330,76060,76061,76063],{},[898,76062,1724],{},[898,76064,9779],{},[898,76066,1888],{"mathvariant":2377},[20743,76068],{"width":28057},[20743,76070,76071],{},[2289,76072,76073],{},"(5.4)",[902,76075,76076],{"encoding":904},"AP_L = \\frac{Q}{L}. \\tag{5.4}",[724,76078,76079,76080,1888],{},"Je to nejjednodušší míra produktivity práce. Cílem optimalizace je maximalizace ",[883,76081,76083],{"className":76082},[886],[888,76084,76085],{"xmlns":890},[892,76086,76087,76097],{},[895,76088,76089,76091],{},[898,76090,4243],{},[2275,76092,76093,76095],{},[898,76094,1738],{},[898,76096,9779],{},[902,76098,74613],{"encoding":904},[115,76100,76102],{"id":76101},"princip-maximalizace-průměrného-produktu-práce","Princip maximalizace průměrného produktu práce",[724,76104,76105],{},[1647,76106],{"alt":76107,"className":76108,"src":76109},"imek-q-mpl-apl-tripanel",[210,1651],"\u002Fwiki-assets\u002Fimek-q-mpl-apl-tripanel.jpeg",[3859,76111,76112],{},[724,76113,76114,76117,76118,2623,76137,76154,76155],{},[38,76115,76116],{},"Princip:"," Má-li ",[883,76119,76121],{"className":76120},[886],[888,76122,76123],{"xmlns":890},[892,76124,76125,76135],{},[895,76126,76127,76129],{},[898,76128,4243],{},[2275,76130,76131,76133],{},[898,76132,1738],{},[898,76134,9779],{},[902,76136,74613],{"encoding":904},[883,76138,76140],{"className":76139},[886],[888,76141,76142],{"xmlns":890},[892,76143,76144,76152],{},[895,76145,76146],{},[2275,76147,76148,76150],{},[898,76149,9779],{},[2133,76151,2328],{},[902,76153,75538],{"encoding":904}," maximum, pak platí\n",[883,76156,76158],{"className":76157,"title":4188,"style":4189},[4187],"MP_L(L_0) = AP_L(L_0). \\tag{5.5}",[724,76160,76161,76162,76165,76166,1777,76170,1888],{},"Slovně: ",[38,76163,76164],{},"v bodě maxima průměrného produktu práce se mezní produkt práce rovná průměrnému produktu práce."," Jde o analogii ",[207,76167,76169],{"className":76168,"dataFsResolvedFilePath":827,"href":828},[210],"principu minimalizace průměrných nákladů",[883,76171,76173],{"className":76172},[886],[888,76174,76175],{"xmlns":890},[892,76176,76177,76183],{},[895,76178,76179,76181],{},[898,76180,4243],{},[898,76182,2775],{},[902,76184,55540],{"encoding":904},[3859,76186,76187,76211],{},[724,76188,76189,76191,76192],{},[883,76190,4560],{}," Postup — jak najít max ",[883,76193,76195],{"className":76194},[886],[888,76196,76197],{"xmlns":890},[892,76198,76199,76209],{},[895,76200,76201,76203],{},[898,76202,4243],{},[2275,76204,76205,76207],{},[898,76206,1738],{},[898,76208,9779],{},[902,76210,74613],{"encoding":904},[152,76212,76213,76251,76333],{},[123,76214,76215,76216,76250],{},"Napište ",[883,76217,76219],{"className":76218},[886],[888,76220,76221],{"xmlns":890},[892,76222,76223,76247],{},[895,76224,76225,76227,76233,76235,76237,76239,76241,76243,76245],{},[898,76226,4243],{},[2275,76228,76229,76231],{},[898,76230,1738],{},[898,76232,9779],{},[1726,76234,1728],{},[898,76236,1724],{},[1726,76238,1735],{"stretchy":1734},[898,76240,9779],{},[1726,76242,1762],{"stretchy":1734},[898,76244,4661],{"mathvariant":2377},[898,76246,9779],{},[902,76248,76249],{"encoding":904},"AP_L = Q(L)\u002FL"," a zderivujte.",[123,76252,76253,76254,76286,76287,76290,76291,1888],{},"Položte ",[883,76255,76257],{"className":76256},[886],[888,76258,76259],{"xmlns":890},[892,76260,76261,76283],{},[895,76262,76263,76265,76267,76273,76279,76281],{},[1726,76264,1735],{"stretchy":1734},[898,76266,4243],{},[2275,76268,76269,76271],{},[898,76270,1738],{},[898,76272,9779],{},[2128,76274,76275,76277],{},[1726,76276,1762],{"stretchy":1734},[1726,76278,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,76280,1728],{},[2133,76282,2328],{},[902,76284,76285],{"encoding":904},"(AP_L)' = 0"," a vyřešte. ",[614,76288,76289],{},"Zkratka:"," můžete rovnou řešit ",[883,76292,76294],{"className":76293},[886],[888,76295,76296],{"xmlns":890},[892,76297,76298,76330],{},[895,76299,76300,76302,76308,76310,76312,76314,76316,76318,76324,76326,76328],{},[898,76301,2815],{},[2275,76303,76304,76306],{},[898,76305,1738],{},[898,76307,9779],{},[1726,76309,1735],{"stretchy":1734},[898,76311,9779],{},[1726,76313,1762],{"stretchy":1734},[1726,76315,1728],{},[898,76317,4243],{},[2275,76319,76320,76322],{},[898,76321,1738],{},[898,76323,9779],{},[1726,76325,1735],{"stretchy":1734},[898,76327,9779],{},[1726,76329,1762],{"stretchy":1734},[902,76331,76332],{"encoding":904},"MP_L(L) = AP_L(L)",[123,76334,76335],{},"Ověřte 2. derivací (či grafem), že jde o maximum.",[198,76337,65481],{"id":76338},"odvození",[724,76340,76341,76342,76375],{},"Z ",[883,76343,76345],{"className":76344},[886],[888,76346,76347],{"xmlns":890},[892,76348,76349,76373],{},[895,76350,76351,76353,76359,76361,76363,76365,76367,76369,76371],{},[898,76352,4243],{},[2275,76354,76355,76357],{},[898,76356,1738],{},[898,76358,9779],{},[1726,76360,1728],{},[898,76362,1724],{},[1726,76364,1735],{"stretchy":1734},[898,76366,9779],{},[1726,76368,1762],{"stretchy":1734},[898,76370,4661],{"mathvariant":2377},[898,76372,9779],{},[902,76374,76249],{"encoding":904}," a derivace podílu:",[883,76377,76379],{"className":76378},[886],[888,76380,76381],{"xmlns":890,"display":28047},[892,76382,76383,76536],{},[895,76384,76385,76387,76389,76395,76401,76403,76405,76407,76409,76449,76451,76457,76491,76493,76499,76502,76504,76510,76512,76514,76516,76518,76520,76526,76528,76530,76532,76534],{},[1726,76386,1735],{"stretchy":1734},[898,76388,4243],{},[2275,76390,76391,76393],{},[898,76392,1738],{},[898,76394,9779],{},[2128,76396,76397,76399],{},[1726,76398,1762],{"stretchy":1734},[1726,76400,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,76402,1735],{"stretchy":1734},[898,76404,9779],{},[1726,76406,1762],{"stretchy":1734},[1726,76408,1728],{},[2330,76410,76411,76443],{},[895,76412,76413,76419,76421,76423,76425,76427,76429,76431,76433,76435,76437,76439,76441],{},[2128,76414,76415,76417],{},[898,76416,1724],{},[1726,76418,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,76420,1735],{"stretchy":1734},[898,76422,9779],{},[1726,76424,1762],{"stretchy":1734},[1726,76426,3174],{},[898,76428,9779],{},[1726,76430,2228],{},[898,76432,1724],{},[1726,76434,1735],{"stretchy":1734},[898,76436,9779],{},[1726,76438,1762],{"stretchy":1734},[1726,76440,3174],{},[2133,76442,2281],{},[2128,76444,76445,76447],{},[898,76446,9779],{},[2133,76448,2135],{},[1726,76450,1728],{},[2330,76452,76453,76455],{},[2133,76454,2281],{},[898,76456,9779],{},[895,76458,76459,76461,76467,76469,76471,76473,76475,76489],{},[1726,76460,1735],{"fence":1741},[2128,76462,76463,76465],{},[898,76464,1724],{},[1726,76466,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,76468,1735],{"stretchy":1734},[898,76470,9779],{},[1726,76472,1762],{"stretchy":1734},[1726,76474,2228],{},[2330,76476,76477,76487],{},[895,76478,76479,76481,76483,76485],{},[898,76480,1724],{},[1726,76482,1735],{"stretchy":1734},[898,76484,9779],{},[1726,76486,1762],{"stretchy":1734},[898,76488,9779],{},[1726,76490,1762],{"fence":1741},[1726,76492,1728],{},[2330,76494,76495,76497],{},[2133,76496,2281],{},[898,76498,9779],{},[1726,76500,1735],{"fence":1741,"stretchy":1741,"minsize":76501,"maxsize":76501},"1.2em",[898,76503,2815],{},[2275,76505,76506,76508],{},[898,76507,1738],{},[898,76509,9779],{},[1726,76511,1735],{"stretchy":1734},[898,76513,9779],{},[1726,76515,1762],{"stretchy":1734},[1726,76517,2228],{},[898,76519,4243],{},[2275,76521,76522,76524],{},[898,76523,1738],{},[898,76525,9779],{},[1726,76527,1735],{"stretchy":1734},[898,76529,9779],{},[1726,76531,1762],{"stretchy":1734},[1726,76533,1762],{"fence":1741,"stretchy":1741,"minsize":76501,"maxsize":76501},[898,76535,1888],{"mathvariant":2377},[902,76537,76538],{"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).",[724,76540,9647,76541,8088,76563,76646],{},[883,76542,76544],{"className":76543},[886],[888,76545,76546],{"xmlns":890},[892,76547,76548,76560],{},[895,76549,76550,76556,76558],{},[2275,76551,76552,76554],{},[898,76553,9779],{},[2133,76555,2328],{},[1726,76557,3405],{},[2133,76559,2328],{},[902,76561,76562],{"encoding":904},"L_0 > 0",[883,76564,76566],{"className":76565},[886],[888,76567,76568],{"xmlns":890},[892,76569,76570,76643],{},[895,76571,76572,76574,76576,76582,76588,76590,76596,76598,76600,76602,76605,76607,76613,76615,76621,76623,76625,76627,76633,76635,76641],{},[1726,76573,1735],{"stretchy":1734},[898,76575,4243],{},[2275,76577,76578,76580],{},[898,76579,1738],{},[898,76581,9779],{},[2128,76583,76584,76586],{},[1726,76585,1762],{"stretchy":1734},[1726,76587,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,76589,1735],{"stretchy":1734},[2275,76591,76592,76594],{},[898,76593,9779],{},[2133,76595,2328],{},[1726,76597,1762],{"stretchy":1734},[1726,76599,1728],{},[2133,76601,2328],{},[1726,76603,76604],{},"⇔",[898,76606,2815],{},[2275,76608,76609,76611],{},[898,76610,1738],{},[898,76612,9779],{},[1726,76614,1735],{"stretchy":1734},[2275,76616,76617,76619],{},[898,76618,9779],{},[2133,76620,2328],{},[1726,76622,1762],{"stretchy":1734},[1726,76624,1728],{},[898,76626,4243],{},[2275,76628,76629,76631],{},[898,76630,1738],{},[898,76632,9779],{},[1726,76634,1735],{"stretchy":1734},[2275,76636,76637,76639],{},[898,76638,9779],{},[2133,76640,2328],{},[1726,76642,1762],{"stretchy":1734},[902,76644,76645],{"encoding":904},"(AP_L)'(L_0) = 0 \\Leftrightarrow MP_L(L_0) = AP_L(L_0)",", čímž je (5.5) dokázáno.",[198,76648,76650],{"id":76649},"příklad-51","Příklad 5.1",[724,76652,76653,76654,1888],{},"Je dána produkce ",[883,76655,76657],{"className":76656},[886],[888,76658,76659],{"xmlns":890},[892,76660,76661,76685],{},[895,76662,76663,76665,76667,76669,76675,76677,76679],{},[898,76664,1724],{},[1726,76666,1728],{},[2133,76668,2238],{},[2128,76670,76671,76673],{},[898,76672,9779],{},[2133,76674,2135],{},[1726,76676,2228],{},[2133,76678,2836],{},[2128,76680,76681,76683],{},[898,76682,9779],{},[2133,76684,2177],{},[902,76686,76687],{"encoding":904},"Q = 6L^2 - 0{,}2L^3",[724,76689,76690,57502,76693,76743,76744,1888],{},[38,76691,76692],{},"(a)",[883,76694,76696],{"className":76695},[886],[888,76697,76698],{"xmlns":890},[892,76699,76700,76740],{},[895,76701,76702,76704,76706,76708,76710,76712,76714,76716,76718,76720,76722,76724,76726,76728,76730,76732,76734,76736,76738],{},[898,76703,9779],{},[1726,76705,1728],{},[2133,76707,2135],{},[1726,76709,1742],{"separator":1741},[2133,76711,2231],{},[1726,76713,1742],{"separator":1741},[2133,76715,5572],{},[1726,76717,1742],{"separator":1741},[2133,76719,2860],{},[1726,76721,1742],{"separator":1741},[2133,76723,22927],{},[1726,76725,1742],{"separator":1741},[2133,76727,3704],{},[1726,76729,1742],{"separator":1741},[2133,76731,9021],{},[1726,76733,1742],{"separator":1741},[2133,76735,38327],{},[1726,76737,1742],{"separator":1741},[2133,76739,4991],{},[902,76741,76742],{"encoding":904},"L = 2, 5, 8, 10, 14, 18, 20, 21, 25"," určíme ",[883,76745,76747],{"className":76746},[886],[888,76748,76749],{"xmlns":890},[892,76750,76751,76761],{},[895,76752,76753,76755],{},[898,76754,2815],{},[2275,76756,76757,76759],{},[898,76758,1738],{},[898,76760,9779],{},[902,76762,10029],{"encoding":904},[724,76764,76765,76766,34949],{},"Podle (5.2): ",[883,76767,76769],{"className":76768},[886],[888,76770,76771],{"xmlns":890},[892,76772,76773,76829],{},[895,76774,76775,76777,76783,76785,76791,76793,76795,76797,76799,76801,76803,76805,76807,76813,76815,76817,76819,76821,76823,76825,76827],{},[898,76776,2815],{},[2275,76778,76779,76781],{},[898,76780,1738],{},[898,76782,9779],{},[1726,76784,1728],{},[2128,76786,76787,76789],{},[898,76788,1724],{},[1726,76790,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,76792,1735],{"stretchy":1734},[898,76794,9779],{},[1726,76796,1762],{"stretchy":1734},[1726,76798,1728],{},[2133,76800,3506],{},[898,76802,9779],{},[1726,76804,2228],{},[2133,76806,19302],{},[2128,76808,76809,76811],{},[898,76810,9779],{},[2133,76812,2135],{},[1726,76814,1728],{},[898,76816,9779],{},[1726,76818,1735],{"stretchy":1734},[2133,76820,3506],{},[1726,76822,2228],{},[2133,76824,19302],{},[898,76826,9779],{},[1726,76828,1762],{"stretchy":1734},[902,76830,76831],{"encoding":904},"MP_L = Q'(L) = 12L - 0{,}6L^2 = L(12 - 0{,}6L)",[16,76833,76834,76871],{},[19,76835,76836],{},[22,76837,76838,76853,76855,76857,76859,76861,76863,76865,76867,76869],{},[25,76839,76840],{},[883,76841,76843],{"className":76842},[886],[888,76844,76845],{"xmlns":890},[892,76846,76847,76851],{},[895,76848,76849],{},[898,76850,9779],{},[902,76852,9779],{"encoding":904},[25,76854,2135],{},[25,76856,2231],{},[25,76858,5572],{},[25,76860,2860],{},[25,76862,22927],{},[25,76864,3704],{},[25,76866,9021],{},[25,76868,38327],{},[25,76870,4991],{},[30,76872,76873],{},[22,76874,76875,76896,76899,76902,76905,76907,76910,76912,76914,76933],{},[35,76876,76877],{},[883,76878,76880],{"className":76879},[886],[888,76881,76882],{"xmlns":890},[892,76883,76884,76894],{},[895,76885,76886,76888],{},[898,76887,2815],{},[2275,76889,76890,76892],{},[898,76891,1738],{},[898,76893,9779],{},[902,76895,10029],{"encoding":904},[35,76897,76898],{},"21,6",[35,76900,76901],{},"45",[35,76903,76904],{},"57,6",[35,76906,3123],{},[35,76908,76909],{},"50,4",[35,76911,76898],{},[35,76913,2328],{},[35,76915,76916],{},[883,76917,76919],{"className":76918},[886],[888,76920,76921],{"xmlns":890},[892,76922,76923,76930],{},[895,76924,76925,76927],{},[1726,76926,2228],{},[2133,76928,76929],{},"12,6",[902,76931,76932],{"encoding":904},"-12{,}6",[35,76934,76935],{},[883,76936,76938],{"className":76937},[886],[888,76939,76940],{"xmlns":890},[892,76941,76942,76948],{},[895,76943,76944,76946],{},[1726,76945,2228],{},[2133,76947,45433],{},[902,76949,76950],{"encoding":904},"-75",[724,76952,76953,76972,76973,76991,76992,77009,77010,77028,77029,77053,77054,77072],{},[883,76954,76956],{"className":76955},[886],[888,76957,76958],{"xmlns":890},[892,76959,76960,76970],{},[895,76961,76962,76964],{},[898,76963,2815],{},[2275,76965,76966,76968],{},[898,76967,1738],{},[898,76969,9779],{},[902,76971,10029],{"encoding":904}," nabývá maxima pro ",[883,76974,76976],{"className":76975},[886],[888,76977,76978],{"xmlns":890},[892,76979,76980,76988],{},[895,76981,76982,76984,76986],{},[898,76983,9779],{},[1726,76985,1728],{},[2133,76987,2860],{},[902,76989,76990],{"encoding":904},"L = 10"," (60 jednotek\u002Fprac.). Od ",[883,76993,76995],{"className":76994},[886],[888,76996,76997],{"xmlns":890},[892,76998,76999,77007],{},[895,77000,77001,77003,77005],{},[898,77002,9779],{},[1726,77004,1728],{},[2133,77006,2860],{},[902,77008,76990],{"encoding":904}," přírůstky klesají, v ",[883,77011,77013],{"className":77012},[886],[888,77014,77015],{"xmlns":890},[892,77016,77017,77025],{},[895,77018,77019,77021,77023],{},[898,77020,9779],{},[1726,77022,1728],{},[2133,77024,9021],{},[902,77026,77027],{"encoding":904},"L = 20"," produkce přestává růst (maximum ",[883,77030,77032],{"className":77031},[886],[888,77033,77034],{"xmlns":890},[892,77035,77036,77050],{},[895,77037,77038,77040,77042,77044,77046,77048],{},[898,77039,1724],{},[1726,77041,1735],{"stretchy":1734},[2133,77043,9021],{},[1726,77045,1762],{"stretchy":1734},[1726,77047,1728],{},[2133,77049,23839],{},[902,77051,77052],{"encoding":904},"Q(20) = 800","), od ",[883,77055,77057],{"className":77056},[886],[888,77058,77059],{"xmlns":890},[892,77060,77061,77069],{},[895,77062,77063,77065,77067],{},[898,77064,9779],{},[1726,77066,3405],{},[2133,77068,9021],{},[902,77070,77071],{"encoding":904},"L > 20"," produkce klesá (fyzické přeplnění pracoviště při neměnném kapitálu).",[724,77074,77075],{},[614,77076,77077,77078,77118,77119,2623,77137,1888],{},"Obrázek 5.1 — graf produkce ",[883,77079,77081],{"className":77080},[886],[888,77082,77083],{"xmlns":890},[892,77084,77085,77115],{},[895,77086,77087,77089,77091,77093,77095,77097,77099,77105,77107,77109],{},[898,77088,1724],{},[1726,77090,1735],{"stretchy":1734},[898,77092,9779],{},[1726,77094,1762],{"stretchy":1734},[1726,77096,1728],{},[2133,77098,2238],{},[2128,77100,77101,77103],{},[898,77102,9779],{},[2133,77104,2135],{},[1726,77106,2228],{},[2133,77108,2836],{},[2128,77110,77111,77113],{},[898,77112,9779],{},[2133,77114,2177],{},[902,77116,77117],{"encoding":904},"Q(L) = 6L^2 - 0{,}2L^3"," s maximem ",[883,77120,77122],{"className":77121},[886],[888,77123,77124],{"xmlns":890},[892,77125,77126,77134],{},[895,77127,77128,77130,77132],{},[898,77129,1724],{},[1726,77131,1728],{},[2133,77133,23839],{},[902,77135,77136],{"encoding":904},"Q = 800",[883,77138,77140],{"className":77139},[886],[888,77141,77142],{"xmlns":890},[892,77143,77144,77152],{},[895,77145,77146,77148,77150],{},[898,77147,9779],{},[1726,77149,1728],{},[2133,77151,9021],{},[902,77153,77027],{"encoding":904},[724,77155,77156,77159],{},[38,77157,77158],{},"(b)"," Přibližná změna produkce při růstu pracovníků z 6 na 9.",[724,77161,77162,77163,1343,77181,2703],{},"Podle (5.3) s ",[883,77164,77166],{"className":77165},[886],[888,77167,77168],{"xmlns":890},[892,77169,77170,77178],{},[895,77171,77172,77174,77176],{},[898,77173,9779],{},[1726,77175,1728],{},[2133,77177,2238],{},[902,77179,77180],{"encoding":904},"L = 6",[883,77182,77184],{"className":77183},[886],[888,77185,77186],{"xmlns":890},[892,77187,77188,77198],{},[895,77189,77190,77192,77194,77196],{},[898,77191,2198],{},[898,77193,9779],{},[1726,77195,1728],{},[2133,77197,2177],{},[902,77199,77200],{"encoding":904},"dL = 3",[883,77202,77204],{"className":77203},[886],[888,77205,77206],{"xmlns":890,"display":28047},[892,77207,77208,77271],{},[895,77209,77210,77212,77214,77216,77218,77224,77226,77228,77230,77232,77234,77236,77238,77240,77242,77244,77246,77248,77250,77252,77254,77256,77258,77260,77262,77264,77266,77268],{},[898,77211,2198],{},[898,77213,1724],{},[1726,77215,1728],{},[898,77217,2815],{},[2275,77219,77220,77222],{},[898,77221,1738],{},[898,77223,9779],{},[1726,77225,1735],{"stretchy":1734},[2133,77227,2238],{},[1726,77229,1762],{"stretchy":1734},[1726,77231,3174],{},[2133,77233,2177],{},[1726,77235,1728],{},[1726,77237,1735],{"stretchy":1734},[2133,77239,3506],{},[1726,77241,3174],{},[2133,77243,2238],{},[1726,77245,2228],{},[2133,77247,19302],{},[1726,77249,3174],{},[2133,77251,5552],{},[1726,77253,1762],{"stretchy":1734},[1726,77255,3174],{},[2133,77257,2177],{},[1726,77259,1728],{},[2133,77261,76909],{},[1726,77263,3174],{},[2133,77265,2177],{},[1726,77267,1728],{},[2133,77269,77270],{},"151,2.",[902,77272,77273],{"encoding":904},"dQ = MP_L(6)\\cdot 3 = (12\\cdot 6 - 0{,}6\\cdot 36)\\cdot 3 = 50{,}4 \\cdot 3 = 151{,}2.",[724,77275,77276,77277,57732,77302,77316,77317,1888],{},"Produkce vzroste z ",[883,77278,77280],{"className":77279},[886],[888,77281,77282],{"xmlns":890},[892,77283,77284,77299],{},[895,77285,77286,77288,77290,77292,77294,77296],{},[898,77287,1724],{},[1726,77289,1735],{"stretchy":1734},[2133,77291,2238],{},[1726,77293,1762],{"stretchy":1734},[1726,77295,1728],{},[2133,77297,77298],{},"172,8",[902,77300,77301],{"encoding":904},"Q(6) = 172{,}8",[883,77303,77305],{"className":77304},[886],[888,77306,77307],{"xmlns":890},[892,77308,77309,77314],{},[895,77310,77311],{},[2133,77312,77313],{},"324",[902,77315,77313],{"encoding":904},". Skutečná hodnota: ",[883,77318,77320],{"className":77319},[886],[888,77321,77322],{"xmlns":890},[892,77323,77324,77364],{},[895,77325,77326,77328,77330,77332,77334,77336,77338,77340,77342,77344,77346,77348,77350,77352,77355,77357,77359,77361],{},[898,77327,2886],{"mathvariant":2377},[898,77329,1724],{},[1726,77331,1728],{},[898,77333,1724],{},[1726,77335,1735],{"stretchy":1734},[2133,77337,3989],{},[1726,77339,1762],{"stretchy":1734},[1726,77341,2228],{},[898,77343,1724],{},[1726,77345,1735],{"stretchy":1734},[2133,77347,2238],{},[1726,77349,1762],{"stretchy":1734},[1726,77351,1728],{},[2133,77353,77354],{},"340,2",[1726,77356,2228],{},[2133,77358,77298],{},[1726,77360,1728],{},[2133,77362,77363],{},"167,4",[902,77365,77366],{"encoding":904},"\\Delta Q = Q(9) - Q(6) = 340{,}2 - 172{,}8 = 167{,}4",[198,77368,77370],{"id":77369},"příklad-52","Příklad 5.2",[724,77372,77373,77374,1888],{},"Ověříme princip (5.5) pro ",[883,77375,77377],{"className":77376},[886],[888,77378,77379],{"xmlns":890},[892,77380,77381,77405],{},[895,77382,77383,77385,77387,77389,77395,77397,77399],{},[898,77384,1724],{},[1726,77386,1728],{},[2133,77388,2238],{},[2128,77390,77391,77393],{},[898,77392,9779],{},[2133,77394,2135],{},[1726,77396,2228],{},[2133,77398,2836],{},[2128,77400,77401,77403],{},[898,77402,9779],{},[2133,77404,2177],{},[902,77406,76687],{"encoding":904},[883,77408,77410],{"className":77409},[886],[888,77411,77412],{"xmlns":890,"display":28047},[892,77413,77414,77492],{},[895,77415,77416,77418,77424,77426,77432,77434,77436,77438,77440,77442,77448,77450,77452,77454,77462,77464,77466,77468,77470,77472,77474,77476,77478,77480,77482,77488,77490],{},[898,77417,4243],{},[2275,77419,77420,77422],{},[898,77421,1738],{},[898,77423,9779],{},[1726,77425,1728],{},[2330,77427,77428,77430],{},[898,77429,1724],{},[898,77431,9779],{},[1726,77433,1728],{},[2133,77435,2238],{},[898,77437,9779],{},[1726,77439,2228],{},[2133,77441,2836],{},[2128,77443,77444,77446],{},[898,77445,9779],{},[2133,77447,2135],{},[1726,77449,1742],{"separator":1741},[5865,77451],{"width":15270},[898,77453,4243],{},[9151,77455,77456,77458,77460],{},[898,77457,1738],{},[898,77459,9779],{},[1726,77461,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,77463,1728],{},[2133,77465,2238],{},[1726,77467,2228],{},[2133,77469,19252],{},[898,77471,9779],{},[1726,77473,1728],{},[2133,77475,2328],{},[2289,77477,3974],{},[1726,77479,3977],{},[2289,77481,3974],{},[2275,77483,77484,77486],{},[898,77485,9779],{},[2133,77487,2328],{},[1726,77489,1728],{},[2133,77491,68263],{},[902,77493,77494],{"encoding":904},"AP_L = \\frac{Q}{L} = 6L - 0{,}2L^2, \\quad AP_L' = 6 - 0{,}4L = 0 \\;\\Rightarrow\\; L_0 = 15.",[724,77496,77497,77533,77534,77552,77553,1888],{},[883,77498,77500],{"className":77499},[886],[888,77501,77502],{"xmlns":890},[892,77503,77504,77530],{},[895,77505,77506,77508,77520,77522,77524,77526,77528],{},[898,77507,4243],{},[9151,77509,77510,77512,77514],{},[898,77511,1738],{},[898,77513,9779],{},[895,77515,77516,77518],{},[1726,77517,2379],{"mathvariant":2377},[1726,77519,2379],{"mathvariant":2377},[1726,77521,1728],{},[1726,77523,2228],{},[2133,77525,19252],{},[1726,77527,3444],{},[2133,77529,2328],{},[902,77531,77532],{"encoding":904},"AP_L'' = -0{,}4 \u003C 0",", takže v ",[883,77535,77537],{"className":77536},[886],[888,77538,77539],{"xmlns":890},[892,77540,77541,77549],{},[895,77542,77543,77545,77547],{},[898,77544,9779],{},[1726,77546,1728],{},[2133,77548,36225],{},[902,77550,77551],{"encoding":904},"L = 15"," je maximum, ",[883,77554,77556],{"className":77555},[886],[888,77557,77558],{"xmlns":890},[892,77559,77560,77606],{},[895,77561,77562,77564,77570,77572,77574,77576,77578,77580,77582,77584,77586,77588,77590,77593,77595,77598,77600,77602,77604],{},[898,77563,4243],{},[2275,77565,77566,77568],{},[898,77567,1738],{},[898,77569,9779],{},[1726,77571,1735],{"stretchy":1734},[2133,77573,36225],{},[1726,77575,1762],{"stretchy":1734},[1726,77577,1728],{},[2133,77579,2238],{},[1726,77581,3174],{},[2133,77583,36225],{},[1726,77585,2228],{},[2133,77587,2836],{},[1726,77589,3174],{},[2133,77591,77592],{},"225",[1726,77594,1728],{},[2133,77596,77597],{},"90",[1726,77599,2228],{},[2133,77601,76901],{},[1726,77603,1728],{},[2133,77605,76901],{},[902,77607,77608],{"encoding":904},"AP_L(15) = 6\\cdot 15 - 0{,}2\\cdot 225 = 90 - 45 = 45",[724,77610,77611,41861,77667,77713],{},[883,77612,77614],{"className":77613},[886],[888,77615,77616],{"xmlns":890},[892,77617,77618,77664],{},[895,77619,77620,77622,77628,77630,77632,77634,77636,77638,77640,77642,77644,77646,77648,77650,77652,77655,77657,77660,77662],{},[898,77621,2815],{},[2275,77623,77624,77626],{},[898,77625,1738],{},[898,77627,9779],{},[1726,77629,1735],{"stretchy":1734},[2133,77631,36225],{},[1726,77633,1762],{"stretchy":1734},[1726,77635,1728],{},[2133,77637,3506],{},[1726,77639,3174],{},[2133,77641,36225],{},[1726,77643,2228],{},[2133,77645,19302],{},[1726,77647,3174],{},[2133,77649,77592],{},[1726,77651,1728],{},[2133,77653,77654],{},"180",[1726,77656,2228],{},[2133,77658,77659],{},"135",[1726,77661,1728],{},[2133,77663,76901],{},[902,77665,77666],{"encoding":904},"MP_L(15) = 12\\cdot 15 - 0{,}6\\cdot 225 = 180 - 135 = 45",[883,77668,77670],{"className":77669},[886],[888,77671,77672],{"xmlns":890},[892,77673,77674,77710],{},[895,77675,77676,77678,77684,77686,77688,77690,77692,77694,77700,77702,77704,77706,77708],{},[898,77677,2815],{},[2275,77679,77680,77682],{},[898,77681,1738],{},[898,77683,9779],{},[1726,77685,1735],{"stretchy":1734},[2133,77687,36225],{},[1726,77689,1762],{"stretchy":1734},[1726,77691,1728],{},[898,77693,4243],{},[2275,77695,77696,77698],{},[898,77697,1738],{},[898,77699,9779],{},[1726,77701,1735],{"stretchy":1734},[2133,77703,36225],{},[1726,77705,1762],{"stretchy":1734},[1726,77707,1728],{},[2133,77709,76901],{},[902,77711,77712],{"encoding":904},"MP_L(15) = AP_L(15) = 45",", jak požaduje (5.5).",[724,77715,77716,77719,77720,17558,77749,1888],{},[38,77717,77718],{},"Zkratka bez hledání extrému:"," stačí řešit ",[883,77721,77723],{"className":77722},[886],[888,77724,77725],{"xmlns":890},[892,77726,77727,77747],{},[895,77728,77729,77731,77737,77739,77741],{},[898,77730,2815],{},[2275,77732,77733,77735],{},[898,77734,1738],{},[898,77736,9779],{},[1726,77738,1728],{},[898,77740,4243],{},[2275,77742,77743,77745],{},[898,77744,1738],{},[898,77746,9779],{},[902,77748,74643],{"encoding":904},[883,77750,77752],{"className":77751},[886],[888,77753,77754],{"xmlns":890},[892,77755,77756,77796],{},[895,77757,77758,77760,77762,77764,77766,77772,77774,77776,77778,77780,77782,77788,77790,77792,77794],{},[2133,77759,3506],{},[898,77761,9779],{},[1726,77763,2228],{},[2133,77765,19302],{},[2128,77767,77768,77770],{},[898,77769,9779],{},[2133,77771,2135],{},[1726,77773,1728],{},[2133,77775,2238],{},[898,77777,9779],{},[1726,77779,2228],{},[2133,77781,2836],{},[2128,77783,77784,77786],{},[898,77785,9779],{},[2133,77787,2135],{},[1726,77789,3977],{},[898,77791,9779],{},[1726,77793,1728],{},[2133,77795,36225],{},[902,77797,77798],{"encoding":904},"12L - 0{,}6L^2 = 6L - 0{,}2L^2 \\Rightarrow L = 15",[724,77800,77801],{},[614,77802,77803,77804,77823,77824,12114,77842,77861,77862,77880,77881,77898,77899,77918,77919,77938],{},"Obrázek 5.3 — křivky ",[883,77805,77807],{"className":77806},[886],[888,77808,77809],{"xmlns":890},[892,77810,77811,77821],{},[895,77812,77813,77815],{},[898,77814,2815],{},[2275,77816,77817,77819],{},[898,77818,1738],{},[898,77820,9779],{},[902,77822,10029],{"encoding":904}," (max 60 při ",[883,77825,77827],{"className":77826},[886],[888,77828,77829],{"xmlns":890},[892,77830,77831,77839],{},[895,77832,77833,77835,77837],{},[898,77834,9779],{},[1726,77836,1728],{},[2133,77838,2860],{},[902,77840,77841],{"encoding":904},"L=10",[883,77843,77845],{"className":77844},[886],[888,77846,77847],{"xmlns":890},[892,77848,77849,77859],{},[895,77850,77851,77853],{},[898,77852,4243],{},[2275,77854,77855,77857],{},[898,77856,1738],{},[898,77858,9779],{},[902,77860,74613],{"encoding":904}," (max 45 při ",[883,77863,77865],{"className":77864},[886],[888,77866,77867],{"xmlns":890},[892,77868,77869,77877],{},[895,77870,77871,77873,77875],{},[898,77872,9779],{},[1726,77874,1728],{},[2133,77876,36225],{},[902,77878,77879],{"encoding":904},"L=15","), průsečík v ",[883,77882,77884],{"className":77883},[886],[888,77885,77886],{"xmlns":890},[892,77887,77888,77896],{},[895,77889,77890,77892,77894],{},[898,77891,9779],{},[1726,77893,1728],{},[2133,77895,36225],{},[902,77897,77551],{"encoding":904},". Nalevo od 15 leží ",[883,77900,77902],{"className":77901},[886],[888,77903,77904],{"xmlns":890},[892,77905,77906,77916],{},[895,77907,77908,77910],{},[898,77909,2815],{},[2275,77911,77912,77914],{},[898,77913,1738],{},[898,77915,9779],{},[902,77917,10029],{"encoding":904}," nad ",[883,77920,77922],{"className":77921},[886],[888,77923,77924],{"xmlns":890},[892,77925,77926,77936],{},[895,77927,77928,77930],{},[898,77929,4243],{},[2275,77931,77932,77934],{},[898,77933,1738],{},[898,77935,9779],{},[902,77937,74613],{"encoding":904},", napravo pod ní.",[115,77940,77942],{"id":77941},"dvoufaktorový-model-produkce","Dvoufaktorový model produkce",[724,77944,77945,77946,2684,77959,1777,77962,6177,77975,1777,77978,2703],{},"V dvoufaktorovém modelu závisí produkce ",[883,77947,77949],{"className":77948},[886],[888,77950,77951],{"xmlns":890},[892,77952,77953,77957],{},[895,77954,77955],{},[898,77956,1724],{},[902,77958,1724],{"encoding":904},[38,77960,77961],{},"práci",[883,77963,77965],{"className":77964},[886],[888,77966,77967],{"xmlns":890},[892,77968,77969,77973],{},[895,77970,77971],{},[898,77972,9779],{},[902,77974,9779],{"encoding":904},[38,77976,77977],{},"kapitálu",[883,77979,77981],{"className":77980},[886],[888,77982,77983],{"xmlns":890},[892,77984,77985,77989],{},[895,77986,77987],{},[898,77988,9784],{},[902,77990,9784],{"encoding":904},[883,77992,77994],{"className":77993},[886],[888,77995,77996],{"xmlns":890,"display":28047},[892,77997,77998,78033],{},[20735,77999,78000],{"width":28052},[20740,78001,78002,78004,78026,78028],{},[20743,78003],{"width":28057},[20743,78005,78006],{},[895,78007,78008,78010,78012,78014,78016,78018,78020,78022,78024],{},[898,78009,1724],{},[1726,78011,1728],{},[898,78013,1724],{},[1726,78015,1735],{"stretchy":1734},[898,78017,9779],{},[1726,78019,1742],{"separator":1741},[898,78021,9784],{},[1726,78023,1762],{"stretchy":1734},[898,78025,1888],{"mathvariant":2377},[20743,78027],{"width":28057},[20743,78029,78030],{},[2289,78031,78032],{},"(5.6)",[902,78034,78035],{"encoding":904},"Q = Q(L, K). \\tag{5.6}",[724,78037,78038,78039,78041],{},"Půda je nadále standardní exogenní proměnnou. Vztah (5.6) se nazývá ",[38,78040,74980],{}," (v širším smyslu oproti jednofaktorovému modelu).",[115,78043,78045],{"id":78044},"cobb-douglasova-produkční-funkce","Cobb-Douglasova produkční funkce",[724,78047,78048],{},"Široce používané produkční funkce mají tvar",[883,78050,78052],{"className":78051},[886],[888,78053,78054],{"xmlns":890,"display":28047},[892,78055,78056,78097],{},[20735,78057,78058],{"width":28052},[20740,78059,78060,78062,78090,78092],{},[20743,78061],{"width":28057},[20743,78063,78064],{},[895,78065,78066,78068,78070,78072,78074,78080,78082,78088],{},[898,78067,1724],{},[1726,78069,1728],{},[898,78071,4243],{},[2289,78073,2984],{},[2128,78075,78076,78078],{},[898,78077,9779],{},[898,78079,207],{},[2289,78081,2984],{},[2128,78083,78084,78086],{},[898,78085,9784],{},[898,78087,2102],{},[1726,78089,1742],{"separator":1741},[20743,78091],{"width":28057},[20743,78093,78094],{},[2289,78095,78096],{},"(5.7)",[902,78098,78099],{"encoding":904},"Q = A\\,L^a\\,K^b, \\tag{5.7}",[724,78101,4298,78102,78124,78125,78127,78128,1888],{},[883,78103,78105],{"className":78104},[886],[888,78106,78107],{"xmlns":890},[892,78108,78109,78121],{},[895,78110,78111,78113,78115,78117,78119],{},[898,78112,4243],{},[1726,78114,1742],{"separator":1741},[898,78116,207],{},[1726,78118,1742],{"separator":1741},[898,78120,2102],{},[902,78122,78123],{"encoding":904},"A, a, b"," jsou kladné konstanty. Nazývají se ",[38,78126,74679],{}," (poprvé publikovány v roce 1939). V ekonomických analýzách zpravidla ",[883,78129,78131],{"className":78130},[886],[888,78132,78133],{"xmlns":890},[892,78134,78135,78147],{},[895,78136,78137,78139,78141,78143,78145],{},[898,78138,207],{},[1726,78140,1742],{"separator":1741},[898,78142,2102],{},[1726,78144,3444],{},[2133,78146,2281],{},[902,78148,78149],{"encoding":904},"a, b \u003C 1",[724,78151,78152],{},[1647,78153],{"alt":78154,"className":78155,"src":78156},"imek-vynosy-z-rozsahu-3typy",[210,1651],"\u002Fwiki-assets\u002Fimek-vynosy-z-rozsahu-3typy.jpeg",[724,78158,78159,78160,78163,78164,2684,78177,78193,78194,2684,78207,2703],{},"Reflektují ekonomickou zákonitost, že ",[38,78161,78162],{},"proporcionální změny vstupů mají odezvu v proporcionální změně výstupu",". Změní-li se práce z ",[883,78165,78167],{"className":78166},[886],[888,78168,78169],{"xmlns":890},[892,78170,78171,78175],{},[895,78172,78173],{},[898,78174,9779],{},[902,78176,9779],{"encoding":904},[883,78178,78180],{"className":78179},[886],[888,78181,78182],{"xmlns":890},[892,78183,78184,78190],{},[895,78185,78186,78188],{},[898,78187,12027],{},[898,78189,9779],{},[902,78191,78192],{"encoding":904},"rL"," a kapitál z ",[883,78195,78197],{"className":78196},[886],[888,78198,78199],{"xmlns":890},[892,78200,78201,78205],{},[895,78202,78203],{},[898,78204,9784],{},[902,78206,9784],{"encoding":904},[883,78208,78210],{"className":78209},[886],[888,78211,78212],{"xmlns":890},[892,78213,78214,78220],{},[895,78215,78216,78218],{},[898,78217,12027],{},[898,78219,9784],{},[902,78221,78222],{"encoding":904},"rK",[883,78224,78226],{"className":78225},[886],[888,78227,78228],{"xmlns":890,"display":28047},[892,78229,78230,78353],{},[20735,78231,78232],{"width":28052},[20740,78233,78234,78236,78346,78348],{},[20743,78235],{"width":28057},[20743,78237,78238],{},[895,78239,78240,78242,78244,78246,78248,78250,78252,78254,78256,78258,78260,78262,78264,78266,78272,78274,78276,78278,78284,78286,78288,78290,78302,78304,78310,78316,78318,78330,78332,78334,78336,78338,78340,78342,78344],{},[898,78241,1724],{},[1726,78243,1735],{"stretchy":1734},[898,78245,12027],{},[898,78247,9779],{},[1726,78249,1742],{"separator":1741},[898,78251,12027],{},[898,78253,9784],{},[1726,78255,1762],{"stretchy":1734},[1726,78257,1728],{},[898,78259,4243],{},[1726,78261,1735],{"stretchy":1734},[898,78263,12027],{},[898,78265,9779],{},[2128,78267,78268,78270],{},[1726,78269,1762],{"stretchy":1734},[898,78271,207],{},[1726,78273,1735],{"stretchy":1734},[898,78275,12027],{},[898,78277,9784],{},[2128,78279,78280,78282],{},[1726,78281,1762],{"stretchy":1734},[898,78283,2102],{},[1726,78285,1728],{},[898,78287,4243],{},[2289,78289,2984],{},[2128,78291,78292,78294],{},[898,78293,12027],{},[895,78295,78296,78298,78300],{},[898,78297,207],{},[1726,78299,2099],{},[898,78301,2102],{},[2289,78303,2984],{},[2128,78305,78306,78308],{},[898,78307,9779],{},[898,78309,207],{},[2128,78311,78312,78314],{},[898,78313,9784],{},[898,78315,2102],{},[1726,78317,1728],{},[2128,78319,78320,78322],{},[898,78321,12027],{},[895,78323,78324,78326,78328],{},[898,78325,207],{},[1726,78327,2099],{},[898,78329,2102],{},[2289,78331,2984],{},[898,78333,1724],{},[1726,78335,1735],{"stretchy":1734},[898,78337,9779],{},[1726,78339,1742],{"separator":1741},[898,78341,9784],{},[1726,78343,1762],{"stretchy":1734},[898,78345,1888],{"mathvariant":2377},[20743,78347],{"width":28057},[20743,78349,78350],{},[2289,78351,78352],{},"(5.8)",[902,78354,78355],{"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}",[724,78357,78358,78359],{},"Volně: ",[38,78360,78361,78362,78375,78376,78400],{},"změní-li se vstupy ",[883,78363,78365],{"className":78364},[886],[888,78366,78367],{"xmlns":890},[892,78368,78369,78373],{},[895,78370,78371],{},[898,78372,12027],{},[902,78374,12027],{"encoding":904},"-krát, změní se výstup ",[883,78377,78379],{"className":78378},[886],[888,78380,78381],{"xmlns":890},[892,78382,78383,78397],{},[895,78384,78385],{},[2128,78386,78387,78389],{},[898,78388,12027],{},[895,78390,78391,78393,78395],{},[898,78392,207],{},[1726,78394,2099],{},[898,78396,2102],{},[902,78398,78399],{"encoding":904},"r^{a+b}","-krát.",[198,78402,78404],{"id":78403},"výnosy-z-rozsahu","Výnosy z rozsahu",[724,78406,78407,78408,78425],{},"Součet exponentů ",[883,78409,78411],{"className":78410},[886],[888,78412,78413],{"xmlns":890},[892,78414,78415,78423],{},[895,78416,78417,78419,78421],{},[898,78418,207],{},[1726,78420,2099],{},[898,78422,2102],{},[902,78424,74804],{"encoding":904}," určuje typ výnosů z rozsahu:",[16,78427,78428,78457],{},[19,78429,78430],{},[22,78431,78432,78435,78438,78455],{},[25,78433,78434],{},"Typ",[25,78436,78437],{},"Podmínka",[25,78439,78440,78441,78454],{},"Chování produkce při ",[883,78442,78444],{"className":78443},[886],[888,78445,78446],{"xmlns":890},[892,78447,78448,78452],{},[895,78449,78450],{},[898,78451,12027],{},[902,78453,12027],{"encoding":904},"-násobném zvýšení vstupů",[25,78456,3067],{},[30,78458,78459,78570,78685],{},[22,78460,78461,78469,78493,78526],{},[35,78462,75517,78463,10009,78466,1762],{},[38,78464,78465],{},"Konstantní",[614,78467,78468],{},"constant returns",[35,78470,78471],{},[883,78472,78474],{"className":78473},[886],[888,78475,78476],{"xmlns":890},[892,78477,78478,78490],{},[895,78479,78480,78482,78484,78486,78488],{},[898,78481,207],{},[1726,78483,2099],{},[898,78485,2102],{},[1726,78487,1728],{},[2133,78489,2281],{},[902,78491,78492],{"encoding":904},"a+b = 1",[35,78494,78495,78508,78509,1777,78512,78525],{},[883,78496,78498],{"className":78497},[886],[888,78499,78500],{"xmlns":890},[892,78501,78502,78506],{},[895,78503,78504],{},[898,78505,1724],{},[902,78507,1724],{"encoding":904}," vzroste ",[38,78510,78511],{},"přesně",[883,78513,78515],{"className":78514},[886],[888,78516,78517],{"xmlns":890},[892,78518,78519,78523],{},[895,78520,78521],{},[898,78522,12027],{},[902,78524,12027],{"encoding":904},"-krát",[35,78527,78528],{},[883,78529,78531],{"className":78530},[886],[888,78532,78533],{"xmlns":890},[892,78534,78535,78567],{},[895,78536,78537,78539,78541,78543,78555],{},[898,78538,1724],{},[1726,78540,1728],{},[2133,78542,2135],{},[2128,78544,78545,78547],{},[898,78546,9779],{},[895,78548,78549,78551,78553],{},[2133,78550,2281],{},[898,78552,4661],{"mathvariant":2377},[2133,78554,2352],{},[2128,78556,78557,78559],{},[898,78558,9784],{},[895,78560,78561,78563,78565],{},[2133,78562,2177],{},[898,78564,4661],{"mathvariant":2377},[2133,78566,2352],{},[902,78568,78569],{"encoding":904},"Q = 2L^{1\u002F4}K^{3\u002F4}",[22,78571,78572,78581,78605,78635],{},[35,78573,78574,78575,10009,78578,1762],{},"2° ",[38,78576,78577],{},"Rostoucí",[614,78579,78580],{},"increasing returns",[35,78582,78583],{},[883,78584,78586],{"className":78585},[886],[888,78587,78588],{"xmlns":890},[892,78589,78590,78602],{},[895,78591,78592,78594,78596,78598,78600],{},[898,78593,207],{},[1726,78595,2099],{},[898,78597,2102],{},[1726,78599,3405],{},[2133,78601,2281],{},[902,78603,78604],{"encoding":904},"a+b > 1",[35,78606,78607,78508,78620,51211,78622,78525],{},[883,78608,78610],{"className":78609},[886],[888,78611,78612],{"xmlns":890},[892,78613,78614,78618],{},[895,78615,78616],{},[898,78617,1724],{},[902,78619,1724],{"encoding":904},[38,78621,25251],{},[883,78623,78625],{"className":78624},[886],[888,78626,78627],{"xmlns":890},[892,78628,78629,78633],{},[895,78630,78631],{},[898,78632,12027],{},[902,78634,12027],{"encoding":904},[35,78636,78637,10009,78663,1762],{},[883,78638,78640],{"className":78639},[886],[888,78641,78642],{"xmlns":890},[892,78643,78644,78660],{},[895,78645,78646,78648,78650,78652,78654],{},[898,78647,1724],{},[1726,78649,1728],{},[2133,78651,24182],{},[898,78653,9779],{},[2128,78655,78656,78658],{},[898,78657,9784],{},[2133,78659,2135],{},[902,78661,78662],{"encoding":904},"Q = 7LK^2",[883,78664,78666],{"className":78665},[886],[888,78667,78668],{"xmlns":890},[892,78669,78670,78682],{},[895,78671,78672,78674,78676,78678,78680],{},[898,78673,207],{},[1726,78675,2099],{},[898,78677,2102],{},[1726,78679,1728],{},[2133,78681,2177],{},[902,78683,78684],{"encoding":904},"a+b = 3",[22,78686,78687,78696,78720,78751],{},[35,78688,78689,78690,10009,78693,1762],{},"3° ",[38,78691,78692],{},"Klesající",[614,78694,78695],{},"decreasing returns",[35,78697,78698],{},[883,78699,78701],{"className":78700},[886],[888,78702,78703],{"xmlns":890},[892,78704,78705,78717],{},[895,78706,78707,78709,78711,78713,78715],{},[898,78708,207],{},[1726,78710,2099],{},[898,78712,2102],{},[1726,78714,3444],{},[2133,78716,2281],{},[902,78718,78719],{"encoding":904},"a+b \u003C 1",[35,78721,78722,78508,78735,51211,78738,78525],{},[883,78723,78725],{"className":78724},[886],[888,78726,78727],{"xmlns":890},[892,78728,78729,78733],{},[895,78730,78731],{},[898,78732,1724],{},[902,78734,1724],{"encoding":904},[38,78736,78737],{},"méně",[883,78739,78741],{"className":78740},[886],[888,78742,78743],{"xmlns":890},[892,78744,78745,78749],{},[895,78746,78747],{},[898,78748,12027],{},[902,78750,12027],{"encoding":904},[35,78752,78753,10009,78783,1762],{},[883,78754,78756],{"className":78755},[886],[888,78757,78758],{"xmlns":890},[892,78759,78760,78780],{},[895,78761,78762,78764,78766,78768,78774],{},[898,78763,1724],{},[1726,78765,1728],{},[2133,78767,2860],{},[2128,78769,78770,78772],{},[898,78771,9779],{},[2133,78773,68191],{},[2128,78775,78776,78778],{},[898,78777,9784],{},[2133,78779,4996],{},[902,78781,78782],{"encoding":904},"Q = 10L^{0{,}3}K^{0{,}5}",[883,78784,78786],{"className":78785},[886],[888,78787,78788],{"xmlns":890},[892,78789,78790,78802],{},[895,78791,78792,78794,78796,78798,78800],{},[898,78793,207],{},[1726,78795,2099],{},[898,78797,2102],{},[1726,78799,1728],{},[2133,78801,14575],{},[902,78803,78804],{"encoding":904},"a+b = 0{,}8",[3859,78806,78807],{},[724,78808,78809,78811,78812,78829,78830,78833,78834,1777,78837,78873,78874,78896,78897,1888],{},[883,78810,4400],{}," Pozor\nSoučet ",[883,78813,78815],{"className":78814},[886],[888,78816,78817],{"xmlns":890},[892,78818,78819,78827],{},[895,78820,78821,78823,78825],{},[898,78822,207],{},[1726,78824,2099],{},[898,78826,2102],{},[902,78828,74804],{"encoding":904}," neudává velikost produkce, ale ",[38,78831,78832],{},"elasticitu vůči škálování vstupů",". Speciálně ",[38,78835,78836],{},"ryzí Cobb-Douglas",[883,78838,78840],{"className":78839},[886],[888,78841,78842],{"xmlns":890},[892,78843,78844,78870],{},[895,78845,78846,78848,78850,78852,78858],{},[898,78847,1724],{},[1726,78849,1728],{},[898,78851,4243],{},[2128,78853,78854,78856],{},[898,78855,9779],{},[898,78857,207],{},[2128,78859,78860,78862],{},[898,78861,9784],{},[895,78863,78864,78866,78868],{},[2133,78865,2281],{},[1726,78867,2228],{},[898,78869,207],{},[902,78871,78872],{"encoding":904},"Q = AL^a K^{1-a}"," má ",[883,78875,78877],{"className":78876},[886],[888,78878,78879],{"xmlns":890},[892,78880,78881,78893],{},[895,78882,78883,78885,78887,78889,78891],{},[898,78884,2102],{},[1726,78886,1728],{},[2133,78888,2281],{},[1726,78890,2228],{},[898,78892,207],{},[902,78894,78895],{"encoding":904},"b = 1-a",", tedy vždy ",[38,78898,78899],{},"konstantní výnosy z rozsahu",[198,78901,78903,78904],{"id":78902},"parametr-efektivity-aa","Parametr efektivity ",[883,78905,78907],{"className":78906},[886],[888,78908,78909],{"xmlns":890},[892,78910,78911,78915],{},[895,78912,78913],{},[898,78914,4243],{},[902,78916,4243],{"encoding":904},[724,78918,78919,78920,78933,78934,78947,78948,78966,78967,78970],{},"Konstanta ",[883,78921,78923],{"className":78922},[886],[888,78924,78925],{"xmlns":890},[892,78926,78927,78931],{},[895,78928,78929],{},[898,78930,4243],{},[902,78932,4243],{"encoding":904}," v (5.7) proporcionálně ovlivňuje úroveň produkce ",[883,78935,78937],{"className":78936},[886],[888,78938,78939],{"xmlns":890},[892,78940,78941,78945],{},[895,78942,78943],{},[898,78944,1724],{},[902,78946,1724],{"encoding":904}," při pevně zadaných ",[883,78949,78951],{"className":78950},[886],[888,78952,78953],{"xmlns":890},[892,78954,78955,78963],{},[895,78956,78957,78959,78961],{},[898,78958,9779],{},[1726,78960,1742],{"separator":1741},[898,78962,9784],{},[902,78964,78965],{"encoding":904},"L, K",", a lze ji proto chápat jako ",[38,78968,78969],{},"parametr efektivity"," — indikátor stavu technologie.",[198,78972,78974],{"id":78973},"příklad-53","Příklad 5.3",[724,78976,78977,78978,78873,79020,79022,79023,1888],{},"Produkční funkce ",[883,78979,78981],{"className":78980},[886],[888,78982,78983],{"xmlns":890},[892,78984,78985,79017],{},[895,78986,78987,78989,78991,78993,79005],{},[898,78988,1724],{},[1726,78990,1728],{},[2133,78992,2135],{},[2128,78994,78995,78997],{},[898,78996,9779],{},[895,78998,78999,79001,79003],{},[2133,79000,2281],{},[898,79002,4661],{"mathvariant":2377},[2133,79004,2352],{},[2128,79006,79007,79009],{},[898,79008,9784],{},[895,79010,79011,79013,79015],{},[2133,79012,2177],{},[898,79014,4661],{"mathvariant":2377},[2133,79016,2352],{},[902,79018,79019],{"encoding":904},"Q = 2L^{1\u002F4} K^{3\u002F4}",[38,79021,24594],{}," výnosy z rozsahu, neboť ",[883,79024,79026],{"className":79025},[886],[888,79027,79028],{"xmlns":890},[892,79029,79030,79054],{},[895,79031,79032,79040,79042,79050,79052],{},[2326,79033,79034],{"scriptlevel":2328,"displaystyle":1734},[2330,79035,79036,79038],{},[2133,79037,2281],{},[2133,79039,2352],{},[1726,79041,2099],{},[2326,79043,79044],{"scriptlevel":2328,"displaystyle":1734},[2330,79045,79046,79048],{},[2133,79047,2177],{},[2133,79049,2352],{},[1726,79051,1728],{},[2133,79053,2281],{},[902,79055,79056],{"encoding":904},"\\tfrac{1}{4} + \\tfrac{3}{4} = 1",[724,79058,79059,79060,6177,79073,79086,79087,1777,79100,79140],{},"Změní-li se ",[883,79061,79063],{"className":79062},[886],[888,79064,79065],{"xmlns":890},[892,79066,79067,79071],{},[895,79068,79069],{},[898,79070,9779],{},[902,79072,9779],{"encoding":904},[883,79074,79076],{"className":79075},[886],[888,79077,79078],{"xmlns":890},[892,79079,79080,79084],{},[895,79081,79082],{},[898,79083,9784],{},[902,79085,9784],{"encoding":904}," čtyřnásobně, změní se ",[883,79088,79090],{"className":79089},[886],[888,79091,79092],{"xmlns":890},[892,79093,79094,79098],{},[895,79095,79096],{},[898,79097,1724],{},[902,79099,1724],{"encoding":904},[883,79101,79103],{"className":79102},[886],[888,79104,79105],{"xmlns":890},[892,79106,79107,79137],{},[895,79108,79109,79129,79131],{},[2128,79110,79111,79113],{},[2133,79112,2352],{},[895,79114,79115,79117,79119,79121,79123,79125,79127],{},[2133,79116,2281],{},[898,79118,4661],{"mathvariant":2377},[2133,79120,2352],{},[1726,79122,2099],{},[2133,79124,2177],{},[898,79126,4661],{"mathvariant":2377},[2133,79128,2352],{},[1726,79130,1728],{},[2128,79132,79133,79135],{},[2133,79134,2352],{},[2133,79136,2281],{},[902,79138,79139],{"encoding":904},"4^{1\u002F4 + 3\u002F4} = 4^1","-krát:",[883,79142,79144],{"className":79143},[886],[888,79145,79146],{"xmlns":890,"display":28047},[892,79147,79148,79308],{},[895,79149,79150,79152,79154,79156,79158,79160,79162,79164,79166,79168,79170,79172,79174,79176,79188,79190,79192,79194,79206,79208,79210,79212,79232,79244,79256,79258,79260,79262,79264,79276,79288,79290,79292,79294,79296,79298,79300,79302,79304,79306],{},[898,79151,1724],{},[1726,79153,1735],{"stretchy":1734},[2133,79155,2352],{},[898,79157,9779],{},[1726,79159,1742],{"separator":1741},[2133,79161,2352],{},[898,79163,9784],{},[1726,79165,1762],{"stretchy":1734},[1726,79167,1728],{},[2133,79169,2135],{},[1726,79171,1735],{"stretchy":1734},[2133,79173,2352],{},[898,79175,9779],{},[2128,79177,79178,79180],{},[1726,79179,1762],{"stretchy":1734},[895,79181,79182,79184,79186],{},[2133,79183,2281],{},[898,79185,4661],{"mathvariant":2377},[2133,79187,2352],{},[1726,79189,1735],{"stretchy":1734},[2133,79191,2352],{},[898,79193,9784],{},[2128,79195,79196,79198],{},[1726,79197,1762],{"stretchy":1734},[895,79199,79200,79202,79204],{},[2133,79201,2177],{},[898,79203,4661],{"mathvariant":2377},[2133,79205,2352],{},[1726,79207,1728],{},[2133,79209,2135],{},[1726,79211,3174],{},[2128,79213,79214,79216],{},[2133,79215,2352],{},[895,79217,79218,79220,79222,79224,79226,79228,79230],{},[2133,79219,2281],{},[898,79221,4661],{"mathvariant":2377},[2133,79223,2352],{},[1726,79225,2099],{},[2133,79227,2177],{},[898,79229,4661],{"mathvariant":2377},[2133,79231,2352],{},[2128,79233,79234,79236],{},[898,79235,9779],{},[895,79237,79238,79240,79242],{},[2133,79239,2281],{},[898,79241,4661],{"mathvariant":2377},[2133,79243,2352],{},[2128,79245,79246,79248],{},[898,79247,9784],{},[895,79249,79250,79252,79254],{},[2133,79251,2177],{},[898,79253,4661],{"mathvariant":2377},[2133,79255,2352],{},[1726,79257,1728],{},[2133,79259,2352],{},[1726,79261,3174],{},[2133,79263,2135],{},[2128,79265,79266,79268],{},[898,79267,9779],{},[895,79269,79270,79272,79274],{},[2133,79271,2281],{},[898,79273,4661],{"mathvariant":2377},[2133,79275,2352],{},[2128,79277,79278,79280],{},[898,79279,9784],{},[895,79281,79282,79284,79286],{},[2133,79283,2177],{},[898,79285,4661],{"mathvariant":2377},[2133,79287,2352],{},[1726,79289,1728],{},[2133,79291,2352],{},[2289,79293,2984],{},[898,79295,1724],{},[1726,79297,1735],{"stretchy":1734},[898,79299,9779],{},[1726,79301,1742],{"separator":1741},[898,79303,9784],{},[1726,79305,1762],{"stretchy":1734},[898,79307,1888],{"mathvariant":2377},[902,79309,79310],{"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).",[198,79312,79313],{"id":37160},"Homogenita",[724,79315,79316,79317,8088,79340,79356],{},"Funkce ",[883,79318,79320],{"className":79319},[886],[888,79321,79322],{"xmlns":890},[892,79323,79324,79338],{},[895,79325,79326,79328,79330,79332,79334,79336],{},[898,79327,1724],{},[1726,79329,1735],{"stretchy":1734},[898,79331,9779],{},[1726,79333,1742],{"separator":1741},[898,79335,9784],{},[1726,79337,1762],{"stretchy":1734},[902,79339,9981],{"encoding":904},[38,79341,79342,79343],{},"homogenní stupně ",[883,79344,79346],{"className":79345},[886],[888,79347,79348],{"xmlns":890},[892,79349,79350,79354],{},[895,79351,79352],{},[898,79353,36841],{},[902,79355,36841],{"encoding":904},", jestliže",[883,79358,79360],{"className":79359},[886],[888,79361,79362],{"xmlns":890,"display":28047},[892,79363,79364,79421],{},[20735,79365,79366],{"width":28052},[20740,79367,79368,79370,79414,79416],{},[20743,79369],{"width":28057},[20743,79371,79372],{},[895,79373,79374,79376,79378,79380,79382,79384,79386,79388,79390,79392,79398,79400,79402,79404,79406,79408,79410,79412],{},[898,79375,1724],{},[1726,79377,1735],{"stretchy":1734},[898,79379,12027],{},[898,79381,9779],{},[1726,79383,1742],{"separator":1741},[898,79385,12027],{},[898,79387,9784],{},[1726,79389,1762],{"stretchy":1734},[1726,79391,1728],{},[2128,79393,79394,79396],{},[898,79395,12027],{},[898,79397,36841],{},[2289,79399,2984],{},[898,79401,1724],{},[1726,79403,1735],{"stretchy":1734},[898,79405,9779],{},[1726,79407,1742],{"separator":1741},[898,79409,9784],{},[1726,79411,1762],{"stretchy":1734},[1726,79413,1742],{"separator":1741},[20743,79415],{"width":28057},[20743,79417,79418],{},[2289,79419,79420],{},"(5.10)",[902,79422,79423],{"encoding":904},"Q(rL, rK) = r^n\\,Q(L, K), \\tag{5.10}",[724,79425,4298,79426,79444,79445,79463,79464,43617,79477,79480,79481,1888],{},[883,79427,79429],{"className":79428},[886],[888,79430,79431],{"xmlns":890},[892,79432,79433,79441],{},[895,79434,79435,79437,79439],{},[898,79436,36841],{},[1726,79438,4473],{},[2133,79440,2328],{},[902,79442,79443],{"encoding":904},"n \\geq 0"," je celé číslo a ",[883,79446,79448],{"className":79447},[886],[888,79449,79450],{"xmlns":890},[892,79451,79452,79460],{},[895,79453,79454,79456,79458],{},[898,79455,12027],{},[1726,79457,3405],{},[2133,79459,2328],{},[902,79461,79462],{"encoding":904},"r > 0",". Homogenní funkce stupně ",[883,79465,79467],{"className":79466},[886],[888,79468,79469],{"xmlns":890},[892,79470,79471,79475],{},[895,79472,79473],{},[2133,79474,2281],{},[902,79476,2281],{"encoding":904},[38,79478,79479],{},"lineárně homogenní",". Cobb-Douglasovy funkce jsou homogenní stupně ",[883,79482,79484],{"className":79483},[886],[888,79485,79486],{"xmlns":890},[892,79487,79488,79496],{},[895,79489,79490,79492,79494],{},[898,79491,207],{},[1726,79493,2099],{},[898,79495,2102],{},[902,79497,74804],{"encoding":904},[115,79499,79501],{"id":79500},"ryzí-cobb-douglas-a-ces","Ryzí Cobb-Douglas a CES",[724,79503,79504],{},[38,79505,79506],{},"Ryzí Cobb-Douglasovy funkce:",[883,79508,79510],{"className":79509},[886],[888,79511,79512],{"xmlns":890,"display":28047},[892,79513,79514,79573],{},[20735,79515,79516],{"width":28052},[20740,79517,79518,79520,79566,79568],{},[20743,79519],{"width":28057},[20743,79521,79522],{},[895,79523,79524,79526,79528,79530,79532,79538,79540,79552,79554,79556,79558,79560,79562,79564],{},[898,79525,1724],{},[1726,79527,1728],{},[898,79529,4243],{},[2289,79531,2984],{},[2128,79533,79534,79536],{},[898,79535,9779],{},[898,79537,207],{},[2289,79539,2984],{},[2128,79541,79542,79544],{},[898,79543,9784],{},[895,79545,79546,79548,79550],{},[2133,79547,2281],{},[1726,79549,2228],{},[898,79551,207],{},[1726,79553,1742],{"separator":1741},[5865,79555],{"width":15270},[2133,79557,2328],{},[1726,79559,3444],{},[898,79561,207],{},[1726,79563,3444],{},[2133,79565,13246],{},[20743,79567],{"width":28057},[20743,79569,79570],{},[2289,79571,79572],{},"(5.9)",[902,79574,79575],{"encoding":904},"Q = A\\,L^a\\,K^{1-a}, \\quad 0 \u003C a \u003C 1. \\tag{5.9}",[724,79577,79578,79579,79581,79582,1888],{},"Mají vždy ",[38,79580,78899],{}," a jsou ",[38,79583,79479],{},[724,79585,79586,10009,79589,79592],{},[38,79587,79588],{},"CES produkční funkce",[614,79590,79591],{},"Constant Elasticity of Substitution",", 1961):",[883,79594,79596],{"className":79595},[886],[888,79597,79598],{"xmlns":890,"display":28047},[892,79599,79600,79668],{},[895,79601,79602,79604,79606,79608,79666],{},[898,79603,1724],{},[1726,79605,1728],{},[898,79607,4243],{},[2128,79609,79610,79654],{},[895,79611,79612,79614,79616,79618,79620,79622,79624,79626,79636,79638,79640,79642,79652],{},[1726,79613,2487],{"fence":1741},[1726,79615,1735],{"stretchy":1734},[2133,79617,2281],{},[1726,79619,2228],{},[898,79621,207],{},[1726,79623,1762],{"stretchy":1734},[2289,79625,2984],{},[2128,79627,79628,79630],{},[898,79629,9779],{},[895,79631,79632,79634],{},[1726,79633,2228],{},[898,79635,2102],{},[1726,79637,2099],{},[898,79639,207],{},[2289,79641,2984],{},[2128,79643,79644,79646],{},[898,79645,9784],{},[895,79647,79648,79650],{},[1726,79649,2228],{},[898,79651,2102],{},[1726,79653,2502],{"fence":1741},[895,79655,79656,79658],{},[1726,79657,2228],{},[2326,79659,79660],{"scriptlevel":2328,"displaystyle":1734},[2330,79661,79662,79664],{},[2133,79663,2281],{},[898,79665,2102],{},[1726,79667,1742],{"separator":1741},[902,79669,79670],{"encoding":904},"Q = A\\left[(1-a)\\,L^{-b} + a\\,K^{-b}\\right]^{-\\tfrac{1}{b}},",[724,79672,4298,79673,1343,79691,1343,79712,79736],{},[883,79674,79676],{"className":79675},[886],[888,79677,79678],{"xmlns":890},[892,79679,79680,79688],{},[895,79681,79682,79684,79686],{},[898,79683,4243],{},[1726,79685,3405],{},[2133,79687,2328],{},[902,79689,79690],{"encoding":904},"A > 0",[883,79692,79694],{"className":79693},[886],[888,79695,79696],{"xmlns":890},[892,79697,79698,79710],{},[895,79699,79700,79702,79704,79706,79708],{},[2133,79701,2328],{},[1726,79703,3444],{},[898,79705,207],{},[1726,79707,3444],{},[2133,79709,2281],{},[902,79711,18817],{"encoding":904},[883,79713,79715],{"className":79714},[886],[888,79716,79717],{"xmlns":890},[892,79718,79719,79733],{},[895,79720,79721,79723,79725,79727,79729,79731],{},[1726,79722,2228],{},[2133,79724,2281],{},[1726,79726,3444],{},[898,79728,2102],{},[1726,79730,3368],{"mathvariant":2377},[2133,79732,2328],{},[902,79734,79735],{"encoding":904},"-1 \u003C b \\neq 0",". Cobb-Douglasovy funkce jsou jejich zvláštním případem.",[724,79738,79739],{},[38,79740,79741],{},"Další typy:",[120,79743,79744,79786],{},[123,79745,79746,1777,79749,79785],{},[38,79747,79748],{},"Lineární:",[883,79750,79752],{"className":79751},[886],[888,79753,79754],{"xmlns":890},[892,79755,79756,79782],{},[895,79757,79758,79760,79762,79764,79766,79768,79770,79772,79774,79776,79778,79780],{},[898,79759,1724],{},[1726,79761,1735],{"stretchy":1734},[898,79763,9779],{},[1726,79765,1742],{"separator":1741},[898,79767,9784],{},[1726,79769,1762],{"stretchy":1734},[1726,79771,1728],{},[898,79773,207],{},[898,79775,9779],{},[1726,79777,2099],{},[898,79779,2102],{},[898,79781,9784],{},[902,79783,79784],{"encoding":904},"Q(L, K) = aL + bK"," — dokonalé substituty.",[123,79787,79788,1777,79791,79836],{},[38,79789,79790],{},"Leontiefova:",[883,79792,79794],{"className":79793},[886],[888,79795,79796],{"xmlns":890},[892,79797,79798,79833],{},[895,79799,79800,79802,79804,79806,79808,79810,79812,79814,79817,79819,79821,79823,79825,79827,79829,79831],{},[898,79801,1724],{},[1726,79803,1735],{"stretchy":1734},[898,79805,9779],{},[1726,79807,1742],{"separator":1741},[898,79809,9784],{},[1726,79811,1762],{"stretchy":1734},[1726,79813,1728],{},[898,79815,79816],{},"min",[1726,79818,56180],{},[1726,79820,1735],{"stretchy":1734},[898,79822,207],{},[898,79824,9779],{},[1726,79826,1742],{"separator":1741},[898,79828,2102],{},[898,79830,9784],{},[1726,79832,1762],{"stretchy":1734},[902,79834,79835],{"encoding":904},"Q(L, K) = \\min(aL, bK)"," — dokonalé komplementy (fixní proporce).",[115,79838,79840,79841,1343,79860,79879],{"id":79839},"mezní-produkty-mplmp_l-mpkmp_k-a-totální-diferenciál","Mezní produkty ",[883,79842,79844],{"className":79843},[886],[888,79845,79846],{"xmlns":890},[892,79847,79848,79858],{},[895,79849,79850,79852],{},[898,79851,2815],{},[2275,79853,79854,79856],{},[898,79855,1738],{},[898,79857,9779],{},[902,79859,10029],{"encoding":904},[883,79861,79863],{"className":79862},[886],[888,79864,79865],{"xmlns":890},[892,79866,79867,79877],{},[895,79868,79869,79871],{},[898,79870,2815],{},[2275,79872,79873,79875],{},[898,79874,1738],{},[898,79876,9784],{},[902,79878,10074],{"encoding":904}," a totální diferenciál",[724,79881,79882],{},[38,79883,79884],{},"Mezní produkt práce:",[883,79886,79888],{"className":79887},[886],[888,79889,79890],{"xmlns":890,"display":28047},[892,79891,79892,79930],{},[895,79893,79894,79896,79902,79904,79912,79914,79928],{},[898,79895,2815],{},[2275,79897,79898,79900],{},[898,79899,1738],{},[898,79901,9779],{},[1726,79903,1728],{},[9151,79905,79906,79908,79910],{},[898,79907,1724],{},[898,79909,9779],{},[1726,79911,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,79913,1728],{},[2330,79915,79916,79922],{},[895,79917,79918,79920],{},[898,79919,9856],{"mathvariant":2377},[898,79921,1724],{},[895,79923,79924,79926],{},[898,79925,9856],{"mathvariant":2377},[898,79927,9779],{},[898,79929,1888],{"mathvariant":2377},[902,79931,79932],{"encoding":904},"MP_L = Q'_L = \\frac{\\partial Q}{\\partial L}.",[724,79934,79935],{},[38,79936,79937],{},"Mezní produkt kapitálu:",[883,79939,79941],{"className":79940},[886],[888,79942,79943],{"xmlns":890,"display":28047},[892,79944,79945,79983],{},[895,79946,79947,79949,79955,79957,79965,79967,79981],{},[898,79948,2815],{},[2275,79950,79951,79953],{},[898,79952,1738],{},[898,79954,9784],{},[1726,79956,1728],{},[9151,79958,79959,79961,79963],{},[898,79960,1724],{},[898,79962,9784],{},[1726,79964,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,79966,1728],{},[2330,79968,79969,79975],{},[895,79970,79971,79973],{},[898,79972,9856],{"mathvariant":2377},[898,79974,1724],{},[895,79976,79977,79979],{},[898,79978,9856],{"mathvariant":2377},[898,79980,9784],{},[898,79982,1888],{"mathvariant":2377},[902,79984,79985],{"encoding":904},"MP_K = Q'_K = \\frac{\\partial Q}{\\partial K}.",[724,79987,79988,80018,80019,80040,80041,80059,80060,80073,80074,1888],{},[883,79989,79991],{"className":79990},[886],[888,79992,79993],{"xmlns":890},[892,79994,79995,80015],{},[895,79996,79997,79999,80005,80007,80009,80011,80013],{},[898,79998,2815],{},[2275,80000,80001,80003],{},[898,80002,1738],{},[898,80004,9779],{},[1726,80006,1735],{"stretchy":1734},[898,80008,207],{},[1726,80010,1742],{"separator":1741},[898,80012,2102],{},[1726,80014,1762],{"stretchy":1734},[902,80016,80017],{"encoding":904},"MP_L(a, b)"," udává rychlost změny produkce vzhledem k práci v bodě ",[883,80020,80022],{"className":80021},[886],[888,80023,80024],{"xmlns":890},[892,80025,80026,80038],{},[895,80027,80028,80030,80032,80034,80036],{},[1726,80029,2487],{"stretchy":1734},[898,80031,207],{},[1726,80033,1742],{"separator":1741},[898,80035,2102],{},[1726,80037,2502],{"stretchy":1734},[902,80039,10808],{"encoding":904}," (na hladině ",[883,80042,80044],{"className":80043},[886],[888,80045,80046],{"xmlns":890},[892,80047,80048,80056],{},[895,80049,80050,80052,80054],{},[898,80051,9784],{},[1726,80053,1728],{},[898,80055,2102],{},[902,80057,80058],{"encoding":904},"K = b","), resp. přibližnou změnu produkce při jednotkové změně ",[883,80061,80063],{"className":80062},[886],[888,80064,80065],{"xmlns":890},[892,80066,80067,80071],{},[895,80068,80069],{},[898,80070,9779],{},[902,80072,9779],{"encoding":904},". Analogicky ",[883,80075,80077],{"className":80076},[886],[888,80078,80079],{"xmlns":890},[892,80080,80081,80101],{},[895,80082,80083,80085,80091,80093,80095,80097,80099],{},[898,80084,2815],{},[2275,80086,80087,80089],{},[898,80088,1738],{},[898,80090,9784],{},[1726,80092,1735],{"stretchy":1734},[898,80094,207],{},[1726,80096,1742],{"separator":1741},[898,80098,2102],{},[1726,80100,1762],{"stretchy":1734},[902,80102,80103],{"encoding":904},"MP_K(a, b)",[3859,80105,80106,80110],{},[724,80107,80108,51199],{},[883,80109,4145],{},[120,80111,80112,80150],{},[123,80113,80114,26170,80133],{},[883,80115,80117],{"className":80116},[886],[888,80118,80119],{"xmlns":890},[892,80120,80121,80131],{},[895,80122,80123,80125],{},[898,80124,2815],{},[2275,80126,80127,80129],{},[898,80128,1738],{},[898,80130,9779],{},[902,80132,10029],{"encoding":904},[614,80134,80135,80136,80149],{},"„o kolik vzroste ",[883,80137,80139],{"className":80138},[886],[888,80140,80141],{"xmlns":890},[892,80142,80143,80147],{},[895,80144,80145],{},[898,80146,1724],{},[902,80148,1724],{"encoding":904},", když přidám jednu jednotku práce (a kapitál držím pevně)?\"",[123,80151,80152,26170,80171],{},[883,80153,80155],{"className":80154},[886],[888,80156,80157],{"xmlns":890},[892,80158,80159,80169],{},[895,80160,80161,80163],{},[898,80162,2815],{},[2275,80164,80165,80167],{},[898,80166,1738],{},[898,80168,9784],{},[902,80170,10074],{"encoding":904},[614,80172,80135,80173,80186],{},[883,80174,80176],{"className":80175},[886],[888,80177,80178],{"xmlns":890},[892,80179,80180,80184],{},[895,80181,80182],{},[898,80183,1724],{},[902,80185,1724],{"encoding":904},", když přidám jednu jednotku kapitálu (a práci držím pevně)?\"",[724,80188,80189,80192,80193,80208,80209,2703],{},[38,80190,80191],{},"Totální diferenciál"," — přibližná změna produkce při změně práce o ",[883,80194,80196],{"className":80195},[886],[888,80197,80198],{"xmlns":890},[892,80199,80200,80206],{},[895,80201,80202,80204],{},[898,80203,2198],{},[898,80205,9779],{},[902,80207,75336],{"encoding":904}," a kapitálu o ",[883,80210,80212],{"className":80211},[886],[888,80213,80214],{"xmlns":890},[892,80215,80216,80222],{},[895,80217,80218,80220],{},[898,80219,2198],{},[898,80221,9784],{},[902,80223,80224],{"encoding":904},"dK",[883,80226,80228],{"className":80227},[886],[888,80229,80230],{"xmlns":890,"display":28047},[892,80231,80232,80325],{},[20735,80233,80234],{"width":28052},[20740,80235,80236,80238,80318,80320],{},[20743,80237],{"width":28057},[20743,80239,80240],{},[895,80241,80242,80244,80246,80248,80250,80252,80254,80262,80264,80266,80268,80270,80278,80280,80282,80284,80286,80288,80294,80296,80298,80300,80302,80304,80310,80312,80314,80316],{},[898,80243,2886],{"mathvariant":2377},[898,80245,1724],{},[1726,80247,1880],{},[898,80249,2198],{},[898,80251,1724],{},[1726,80253,1728],{},[9151,80255,80256,80258,80260],{},[898,80257,1724],{},[898,80259,9779],{},[1726,80261,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[2289,80263,2984],{},[898,80265,2198],{},[898,80267,9779],{},[1726,80269,2099],{},[9151,80271,80272,80274,80276],{},[898,80273,1724],{},[898,80275,9784],{},[1726,80277,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[2289,80279,2984],{},[898,80281,2198],{},[898,80283,9784],{},[1726,80285,1728],{},[898,80287,2815],{},[2275,80289,80290,80292],{},[898,80291,1738],{},[898,80293,9779],{},[2289,80295,2984],{},[898,80297,2198],{},[898,80299,9779],{},[1726,80301,2099],{},[898,80303,2815],{},[2275,80305,80306,80308],{},[898,80307,1738],{},[898,80309,9784],{},[2289,80311,2984],{},[898,80313,2198],{},[898,80315,9784],{},[898,80317,1888],{"mathvariant":2377},[20743,80319],{"width":28057},[20743,80321,80322],{},[2289,80323,80324],{},"(5.11)",[902,80326,80327],{"encoding":904},"\\Delta Q \\approx dQ = Q'_L\\,dL + Q'_K\\,dK = MP_L\\,dL + MP_K\\,dK. \\tag{5.11}",[724,80329,80330,80331,1888],{},"Skutečná změna: ",[883,80332,80334],{"className":80333},[886],[888,80335,80336],{"xmlns":890},[892,80337,80338,80384],{},[895,80339,80340,80342,80344,80346,80348,80350,80352,80354,80356,80358,80360,80362,80364,80366,80368,80370,80372,80374,80376,80378,80380,80382],{},[898,80341,2886],{"mathvariant":2377},[898,80343,1724],{},[1726,80345,1728],{},[898,80347,1724],{},[1726,80349,1735],{"stretchy":1734},[898,80351,9779],{},[1726,80353,2099],{},[898,80355,2198],{},[898,80357,9779],{},[1726,80359,1742],{"separator":1741},[898,80361,9784],{},[1726,80363,2099],{},[898,80365,2198],{},[898,80367,9784],{},[1726,80369,1762],{"stretchy":1734},[1726,80371,2228],{},[898,80373,1724],{},[1726,80375,1735],{"stretchy":1734},[898,80377,9779],{},[1726,80379,1742],{"separator":1741},[898,80381,9784],{},[1726,80383,1762],{"stretchy":1734},[902,80385,80386],{"encoding":904},"\\Delta Q = Q(L+dL, K+dK) - Q(L, K)",[724,80388,80389,80391,80392,80410,80411,80424,80425,80444,80445,80477,80478,80510,80511,1888],{},[38,80390,75500],{}," platí ve 2F modelu pro oba vstupy: pro pevné ",[883,80393,80395],{"className":80394},[886],[888,80396,80397],{"xmlns":890},[892,80398,80399,80407],{},[895,80400,80401],{},[2275,80402,80403,80405],{},[898,80404,9784],{},[2133,80406,2328],{},[902,80408,80409],{"encoding":904},"K_0"," se od jistého ",[883,80412,80414],{"className":80413},[886],[888,80415,80416],{"xmlns":890},[892,80417,80418,80422],{},[895,80419,80420],{},[898,80421,9779],{},[902,80423,9779],{"encoding":904}," stane ",[883,80426,80428],{"className":80427},[886],[888,80429,80430],{"xmlns":890},[892,80431,80432,80442],{},[895,80433,80434,80436],{},[898,80435,2815],{},[2275,80437,80438,80440],{},[898,80439,1738],{},[898,80441,9779],{},[902,80443,10029],{"encoding":904}," klesající (",[883,80446,80448],{"className":80447},[886],[888,80449,80450],{"xmlns":890},[892,80451,80452,80474],{},[895,80453,80454,80470,80472],{},[9151,80455,80456,80458,80464],{},[898,80457,1724],{},[895,80459,80460,80462],{},[898,80461,9779],{},[898,80463,9779],{},[895,80465,80466,80468],{},[1726,80467,2379],{"mathvariant":2377},[1726,80469,2379],{"mathvariant":2377},[1726,80471,3444],{},[2133,80473,2328],{},[902,80475,80476],{"encoding":904},"Q''_{LL} \u003C 0","); analogicky ",[883,80479,80481],{"className":80480},[886],[888,80482,80483],{"xmlns":890},[892,80484,80485,80507],{},[895,80486,80487,80503,80505],{},[9151,80488,80489,80491,80497],{},[898,80490,1724],{},[895,80492,80493,80495],{},[898,80494,9784],{},[898,80496,9784],{},[895,80498,80499,80501],{},[1726,80500,2379],{"mathvariant":2377},[1726,80502,2379],{"mathvariant":2377},[1726,80504,3444],{},[2133,80506,2328],{},[902,80508,80509],{"encoding":904},"Q''_{KK} \u003C 0"," pro pevné ",[883,80512,80514],{"className":80513},[886],[888,80515,80516],{"xmlns":890},[892,80517,80518,80526],{},[895,80519,80520],{},[2275,80521,80522,80524],{},[898,80523,9779],{},[2133,80525,2328],{},[902,80527,75538],{"encoding":904},[115,80529,80531],{"id":80530},"eulerova-věta-pro-homogenní-funkce","Eulerova věta pro homogenní funkce",[724,80533,80534,80537,80538,80561,80562,29925],{},[38,80535,80536],{},"Eulerova věta"," (úloha 5.10): pro homogenní funkci ",[883,80539,80541],{"className":80540},[886],[888,80542,80543],{"xmlns":890},[892,80544,80545,80559],{},[895,80546,80547,80549,80551,80553,80555,80557],{},[898,80548,1724],{},[1726,80550,1735],{"stretchy":1734},[898,80552,9779],{},[1726,80554,1742],{"separator":1741},[898,80556,9784],{},[1726,80558,1762],{"stretchy":1734},[902,80560,9981],{"encoding":904}," stupně ",[883,80563,80565],{"className":80564},[886],[888,80566,80567],{"xmlns":890},[892,80568,80569,80573],{},[895,80570,80571],{},[898,80572,36841],{},[902,80574,36841],{"encoding":904},[883,80576,80578],{"className":80577},[886],[888,80579,80580],{"xmlns":890,"display":28047},[892,80581,80582,80645],{},[20735,80583,80584],{"width":28052},[20740,80585,80586,80588,80638,80640],{},[20743,80587],{"width":28057},[20743,80589,80590],{},[895,80591,80592,80594,80596,80604,80606,80608,80610,80618,80620,80622,80624,80626,80628,80630,80632,80634,80636],{},[898,80593,9779],{},[2289,80595,2984],{},[9151,80597,80598,80600,80602],{},[898,80599,1724],{},[898,80601,9779],{},[1726,80603,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,80605,2099],{},[898,80607,9784],{},[2289,80609,2984],{},[9151,80611,80612,80614,80616],{},[898,80613,1724],{},[898,80615,9784],{},[1726,80617,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,80619,1728],{},[898,80621,36841],{},[2289,80623,2984],{},[898,80625,1724],{},[1726,80627,1735],{"stretchy":1734},[898,80629,9779],{},[1726,80631,1742],{"separator":1741},[898,80633,9784],{},[1726,80635,1762],{"stretchy":1734},[898,80637,1888],{"mathvariant":2377},[20743,80639],{"width":28057},[20743,80641,80642],{},[2289,80643,80644],{},"(5.12)",[902,80646,80647],{"encoding":904},"L\\,Q'_L + K\\,Q'_K = n\\,Q(L, K). \\tag{5.12}",[724,80649,80650,80671],{},[38,80651,80652,80653],{},"Speciální případ ",[883,80654,80656],{"className":80655},[886],[888,80657,80658],{"xmlns":890},[892,80659,80660,80668],{},[895,80661,80662,80664,80666],{},[898,80663,36841],{},[1726,80665,1728],{},[2133,80667,2281],{},[902,80669,80670],{"encoding":904},"n = 1"," (konstantní výnosy z rozsahu):",[883,80673,80675],{"className":80674},[886],[888,80676,80677],{"xmlns":890,"display":28047},[892,80678,80679,80723],{},[895,80680,80681,80683,80685,80687,80693,80695,80697,80699,80701,80707,80709,80711,80713,80715,80717,80719,80721],{},[898,80682,9779],{},[1726,80684,3174],{},[898,80686,2815],{},[2275,80688,80689,80691],{},[898,80690,1738],{},[898,80692,9779],{},[1726,80694,2099],{},[898,80696,9784],{},[1726,80698,3174],{},[898,80700,2815],{},[2275,80702,80703,80705],{},[898,80704,1738],{},[898,80706,9784],{},[1726,80708,1728],{},[898,80710,1724],{},[1726,80712,1735],{"stretchy":1734},[898,80714,9779],{},[1726,80716,1742],{"separator":1741},[898,80718,9784],{},[1726,80720,1762],{"stretchy":1734},[898,80722,1888],{"mathvariant":2377},[902,80724,80725],{"encoding":904},"L\\cdot MP_L + K\\cdot MP_K = Q(L, K).",[724,80727,80728,80729,80732],{},"Slovně — ",[38,80730,80731],{},"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).",[115,80734,9762],{"id":74874},[724,80736,80737,10009,80739,80742,80743,80765,80766,2703],{},[38,80738,9762],{},[614,80740,80741],{},"isoquants",") jsou křivky stejné produkce — množina dvojic ",[883,80744,80746],{"className":80745},[886],[888,80747,80748],{"xmlns":890},[892,80749,80750,80762],{},[895,80751,80752,80754,80756,80758,80760],{},[1726,80753,2487],{"stretchy":1734},[898,80755,9779],{},[1726,80757,1742],{"separator":1741},[898,80759,9784],{},[1726,80761,2502],{"stretchy":1734},[902,80763,80764],{"encoding":904},"[L, K]",", pro něž produkční funkce nabývá pevně zvolené hodnoty ",[883,80767,80769],{"className":80768},[886],[888,80770,80771],{"xmlns":890},[892,80772,80773,80778],{},[895,80774,80775],{},[898,80776,80777],{},"q",[902,80779,80777],{"encoding":904},[883,80781,80783],{"className":80782},[886],[888,80784,80785],{"xmlns":890,"display":28047},[892,80786,80787,80822],{},[20735,80788,80789],{"width":28052},[20740,80790,80791,80793,80815,80817],{},[20743,80792],{"width":28057},[20743,80794,80795],{},[895,80796,80797,80799,80801,80803,80805,80807,80809,80811,80813],{},[898,80798,1724],{},[1726,80800,1735],{"stretchy":1734},[898,80802,9779],{},[1726,80804,1742],{"separator":1741},[898,80806,9784],{},[1726,80808,1762],{"stretchy":1734},[1726,80810,1728],{},[898,80812,80777],{},[898,80814,1888],{"mathvariant":2377},[20743,80816],{"width":28057},[20743,80818,80819],{},[2289,80820,80821],{},"(5.13)",[902,80823,80824],{"encoding":904},"Q(L, K) = q. \\tag{5.13}",[724,80826,80827,80828,80831,80832,1847],{},"Jsou to ",[38,80829,80830],{},"indiferenční křivky"," produkční funkce (analogie s indiferenčními křivkami u ",[207,80833,80835],{"className":80834,"dataFsResolvedFilePath":878,"href":879},[210],"užitečnosti",[724,80837,80838],{},[38,80839,80840],{},"Vlastnosti izokvant Cobb-Douglasových funkcí:",[120,80842,80843,80848,80853,80858],{},[123,80844,80845,80847],{},[38,80846,12505],{}," — pokles kapitálu vyžaduje kompenzující růst práce k udržení produkce;",[123,80849,80850,80852],{},[38,80851,37645],{}," (úloha 5.14);",[123,80854,80855,8411],{},[38,80856,80857],{},"neprotínají se",[123,80859,80860,80861,4346,80874,1888],{},"s rostoucím ",[883,80862,80864],{"className":80863},[886],[888,80865,80866],{"xmlns":890},[892,80867,80868,80872],{},[895,80869,80870],{},[898,80871,80777],{},[902,80873,80777],{"encoding":904},[38,80875,80876],{},"vzdalují od počátku",[724,80878,80879],{},[614,80880,80881,80882,80904,80905,1888],{},"Obrázek 5.4 — izokvanty Cobb-Douglasovy funkce v rovině ",[883,80883,80885],{"className":80884},[886],[888,80886,80887],{"xmlns":890},[892,80888,80889,80901],{},[895,80890,80891,80893,80895,80897,80899],{},[1726,80892,1735],{"stretchy":1734},[898,80894,9779],{},[1726,80896,1742],{"separator":1741},[898,80898,9784],{},[1726,80900,1762],{"stretchy":1734},[902,80902,80903],{"encoding":904},"(L, K)",": tři klesající konvexní křivky pro ",[883,80906,80908],{"className":80907},[886],[888,80909,80910],{"xmlns":890},[892,80911,80912,80936],{},[895,80913,80914,80920,80922,80928,80930],{},[2275,80915,80916,80918],{},[898,80917,80777],{},[2133,80919,2281],{},[1726,80921,3444],{},[2275,80923,80924,80926],{},[898,80925,80777],{},[2133,80927,2328],{},[1726,80929,3444],{},[2275,80931,80932,80934],{},[898,80933,80777],{},[2133,80935,2135],{},[902,80937,80938],{"encoding":904},"q_1 \u003C q_0 \u003C q_2",[115,80940,80942,80943,1762],{"id":80941},"mezní-míra-technické-substituce-mrtsmrts","Mezní míra technické substituce (",[883,80944,80946],{"className":80945},[886],[888,80947,80948],{"xmlns":890},[892,80949,80950,80960],{},[895,80951,80952,80954,80956,80958],{},[898,80953,2815],{},[898,80955,3984],{},[898,80957,2772],{},[898,80959,8659],{},[902,80961,10583],{"encoding":904},[724,80963,80964,10009,80967,80970],{},[38,80965,80966],{},"Mezní míra technické substituce",[614,80968,80969],{},"marginal rate of technical substitution",") je podíl mezních produktů:",[883,80972,80974],{"className":80973},[886],[888,80975,80976],{"xmlns":890,"display":28047},[892,80977,80978,81069],{},[20735,80979,80980],{"width":28052},[20740,80981,80982,80984,81062,81064],{},[20743,80983],{"width":28057},[20743,80985,80986],{},[895,80987,80988,80990,80992,80994,80996,80998,81000,81002,81004,81006,81008,81010,81012,81014,81016,81018,81040,81042,81060],{},[898,80989,2815],{},[898,80991,3984],{},[898,80993,2772],{},[898,80995,8659],{},[1726,80997,1728],{},[898,80999,2815],{},[898,81001,3984],{},[898,81003,2772],{},[898,81005,8659],{},[1726,81007,1735],{"stretchy":1734},[898,81009,9779],{},[1726,81011,1742],{"separator":1741},[898,81013,9784],{},[1726,81015,1762],{"stretchy":1734},[1726,81017,1728],{},[2330,81019,81020,81030],{},[895,81021,81022,81024],{},[898,81023,2815],{},[2275,81025,81026,81028],{},[898,81027,1738],{},[898,81029,9779],{},[895,81031,81032,81034],{},[898,81033,2815],{},[2275,81035,81036,81038],{},[898,81037,1738],{},[898,81039,9784],{},[1726,81041,1728],{},[2330,81043,81044,81052],{},[9151,81045,81046,81048,81050],{},[898,81047,1724],{},[898,81049,9779],{},[1726,81051,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[9151,81053,81054,81056,81058],{},[898,81055,1724],{},[898,81057,9784],{},[1726,81059,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[898,81061,1888],{"mathvariant":2377},[20743,81063],{"width":28057},[20743,81065,81066],{},[2289,81067,81068],{},"(5.14)",[902,81070,81071],{"encoding":904},"MRTS = MRTS(L, K) = \\frac{MP_L}{MP_K} = \\frac{Q'_L}{Q'_K}. \\tag{5.14}",[724,81073,81074,1777,81076,81106,81107,81138],{},[38,81075,9201],{},[883,81077,81079],{"className":81078},[886],[888,81080,81081],{"xmlns":890},[892,81082,81083,81103],{},[895,81084,81085,81087,81089,81091,81093,81095,81097,81099,81101],{},[898,81086,2815],{},[898,81088,3984],{},[898,81090,2772],{},[898,81092,8659],{},[1726,81094,1735],{"stretchy":1734},[898,81096,9779],{},[1726,81098,1742],{"separator":1741},[898,81100,9784],{},[1726,81102,1762],{"stretchy":1734},[902,81104,81105],{"encoding":904},"MRTS(L, K)"," udává, ",[38,81108,81109,81110,81123,81124,81137],{},"o kolik se musí přibližně změnit kapitál ",[883,81111,81113],{"className":81112},[886],[888,81114,81115],{"xmlns":890},[892,81116,81117,81121],{},[895,81118,81119],{},[898,81120,9784],{},[902,81122,9784],{"encoding":904},", jestliže se práce ",[883,81125,81127],{"className":81126},[886],[888,81128,81129],{"xmlns":890},[892,81130,81131,81135],{},[895,81132,81133],{},[898,81134,9779],{},[902,81136,9779],{"encoding":904}," změní o jednotku, aby byla zachována produkce"," (pohyb po izokvantě).",[3859,81140,81141],{},[724,81142,81143,18005,81145,81164,81165,81202,81203,81206,81207,81211],{},[883,81144,4145],{},[883,81146,81148],{"className":81147},[886],[888,81149,81150],{"xmlns":890},[892,81151,81152,81162],{},[895,81153,81154,81156,81158,81160],{},[898,81155,2815],{},[898,81157,3984],{},[898,81159,2772],{},[898,81161,8659],{},[902,81163,10583],{"encoding":904}," říká: ",[614,81166,81167,81168,81187,81188,81201],{},"„jednu jednotku práce musím nahradit přibližně ",[883,81169,81171],{"className":81170},[886],[888,81172,81173],{"xmlns":890},[892,81174,81175,81185],{},[895,81176,81177,81179,81181,81183],{},[898,81178,2815],{},[898,81180,3984],{},[898,81182,2772],{},[898,81184,8659],{},[902,81186,10583],{"encoding":904}," jednotkami kapitálu, aby produkce ",[883,81189,81191],{"className":81190},[886],[888,81192,81193],{"xmlns":890},[892,81194,81195,81199],{},[895,81196,81197],{},[898,81198,1724],{},[902,81200,1724],{"encoding":904}," zůstala stejná.\""," Je to ",[38,81204,81205],{},"směnný kurz mezi vstupy"," při zachování produkce — přesná analogie ",[207,81208,81210],{"className":81209,"dataFsResolvedFilePath":878,"href":879},[210],"MRCS z teorie užitečnosti",", kde nahrazujeme spotřební statky při zachování užitku.",[724,81213,81214],{},[1647,81215],{"alt":81216,"className":81217,"src":81218},"imek-izokvanty-mrts",[210,1651],"\u002Fwiki-assets\u002Fimek-izokvanty-mrts.jpeg",[724,81220,81221,81224,81225,8088,81255,81277,81278,3148],{},[38,81222,81223],{},"Geometrická interpretace:"," sklon tečny k izokvantě v bodě ",[883,81226,81228],{"className":81227},[886],[888,81229,81230],{"xmlns":890},[892,81231,81232,81252],{},[895,81233,81234,81236,81242,81244,81250],{},[1726,81235,2487],{"stretchy":1734},[2275,81237,81238,81240],{},[898,81239,9779],{},[2133,81241,2328],{},[1726,81243,1742],{"separator":1741},[2275,81245,81246,81248],{},[898,81247,9784],{},[2133,81249,2328],{},[1726,81251,2502],{"stretchy":1734},[902,81253,81254],{"encoding":904},"[L_0, K_0]",[883,81256,81258],{"className":81257},[886],[888,81259,81260],{"xmlns":890},[892,81261,81262,81274],{},[895,81263,81264,81266,81268,81270,81272],{},[1726,81265,2228],{},[898,81267,2815],{},[898,81269,3984],{},[898,81271,2772],{},[898,81273,8659],{},[902,81275,81276],{"encoding":904},"-MRTS",". Z derivace implicitní funkce (při ",[883,81279,81281],{"className":81280},[886],[888,81282,81283],{"xmlns":890},[892,81284,81285,81307],{},[895,81286,81287,81289,81291,81293,81295,81297,81299,81301],{},[898,81288,1724],{},[1726,81290,1735],{"stretchy":1734},[898,81292,9779],{},[1726,81294,1742],{"separator":1741},[898,81296,9784],{},[1726,81298,1762],{"stretchy":1734},[1726,81300,1728],{},[2275,81302,81303,81305],{},[898,81304,80777],{},[2133,81306,2328],{},[902,81308,81309],{"encoding":904},"Q(L,K) = q_0",[883,81311,81313],{"className":81312},[886],[888,81314,81315],{"xmlns":890,"display":28047},[892,81316,81317,81369],{},[895,81318,81319,81333,81335,81337,81355,81357,81359,81361,81363,81365,81367],{},[2330,81320,81321,81327],{},[895,81322,81323,81325],{},[898,81324,2198],{},[898,81326,9784],{},[895,81328,81329,81331],{},[898,81330,2198],{},[898,81332,9779],{},[1726,81334,1728],{},[1726,81336,2228],{},[2330,81338,81339,81347],{},[9151,81340,81341,81343,81345],{},[898,81342,1724],{},[898,81344,9779],{},[1726,81346,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[9151,81348,81349,81351,81353],{},[898,81350,1724],{},[898,81352,9784],{},[1726,81354,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,81356,1728],{},[1726,81358,2228],{},[898,81360,2815],{},[898,81362,3984],{},[898,81364,2772],{},[898,81366,8659],{},[898,81368,1888],{"mathvariant":2377},[902,81370,81371],{"encoding":904},"\\frac{dK}{dL} = -\\frac{Q'_L}{Q'_K} = -MRTS.",[724,81373,81374,81375,81390,81391,81407],{},"Změní-li se práce o ",[883,81376,81378],{"className":81377},[886],[888,81379,81380],{"xmlns":890},[892,81381,81382,81388],{},[895,81383,81384,81386],{},[898,81385,2198],{},[898,81387,9779],{},[902,81389,75336],{"encoding":904},", lze pro odhad změny kapitálu ",[883,81392,81394],{"className":81393},[886],[888,81395,81396],{"xmlns":890},[892,81397,81398,81404],{},[895,81399,81400,81402],{},[898,81401,2886],{"mathvariant":2377},[898,81403,9784],{},[902,81405,81406],{"encoding":904},"\\Delta K"," k udržení produkce použít diferenciál:",[883,81409,81411],{"className":81410},[886],[888,81412,81413],{"xmlns":890,"display":28047},[892,81414,81415,81462],{},[20735,81416,81417],{"width":28052},[20740,81418,81419,81421,81455,81457],{},[20743,81420],{"width":28057},[20743,81422,81423],{},[895,81424,81425,81427,81429,81431,81433,81435,81437,81439,81441,81443,81445,81447,81449,81451,81453],{},[898,81426,2886],{"mathvariant":2377},[898,81428,9784],{},[1726,81430,1880],{},[898,81432,2198],{},[898,81434,9784],{},[1726,81436,1728],{},[1726,81438,2228],{},[898,81440,2815],{},[898,81442,3984],{},[898,81444,2772],{},[898,81446,8659],{},[2289,81448,2984],{},[898,81450,2198],{},[898,81452,9779],{},[1726,81454,1742],{"separator":1741},[20743,81456],{"width":28057},[20743,81458,81459],{},[2289,81460,81461],{},"(5.15)",[902,81463,81464],{"encoding":904},"\\Delta K \\approx dK = -MRTS\\,dL, \\tag{5.15}",[883,81466,81468],{"className":81467},[886],[888,81469,81470],{"xmlns":890,"display":28047},[892,81471,81472,81521],{},[20735,81473,81474],{"width":28052},[20740,81475,81476,81478,81514,81516],{},[20743,81477],{"width":28057},[20743,81479,81480],{},[895,81481,81482,81484,81486,81488,81506,81508,81510,81512],{},[898,81483,2198],{},[898,81485,9779],{},[1726,81487,1728],{},[2330,81489,81490,81496],{},[895,81491,81492,81494],{},[1726,81493,2228],{},[2133,81495,2281],{},[895,81497,81498,81500,81502,81504],{},[898,81499,2815],{},[898,81501,3984],{},[898,81503,2772],{},[898,81505,8659],{},[2289,81507,2984],{},[898,81509,2198],{},[898,81511,9784],{},[898,81513,1888],{"mathvariant":2377},[20743,81515],{"width":28057},[20743,81517,81518],{},[2289,81519,81520],{},"(5.16)",[902,81522,81523],{"encoding":904},"dL = \\frac{-1}{MRTS}\\,dK. \\tag{5.16}",[3859,81525,81526,81550],{},[724,81527,81528,81530,81531],{},[883,81529,4560],{}," Postup — jak spočítat ",[883,81532,81534],{"className":81533},[886],[888,81535,81536],{"xmlns":890},[892,81537,81538,81548],{},[895,81539,81540,81542,81544,81546],{},[898,81541,2815],{},[898,81543,3984],{},[898,81545,2772],{},[898,81547,8659],{},[902,81549,10583],{"encoding":904},[152,81551,81552,81593,81636,81668],{},[123,81553,81554,81555,3877,81574,1888],{},"Vypočtěte parciální derivace ",[883,81556,81558],{"className":81557},[886],[888,81559,81560],{"xmlns":890},[892,81561,81562,81572],{},[895,81563,81564],{},[9151,81565,81566,81568,81570],{},[898,81567,1724],{},[898,81569,9779],{},[1726,81571,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[902,81573,10005],{"encoding":904},[883,81575,81577],{"className":81576},[886],[888,81578,81579],{"xmlns":890},[892,81580,81581,81591],{},[895,81582,81583],{},[9151,81584,81585,81587,81589],{},[898,81586,1724],{},[898,81588,9784],{},[1726,81590,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[902,81592,10051],{"encoding":904},[123,81594,65821,81595,81635],{},[883,81596,81598],{"className":81597},[886],[888,81599,81600],{"xmlns":890},[892,81601,81602,81632],{},[895,81603,81604,81606,81608,81610,81612,81614,81622,81624],{},[898,81605,2815],{},[898,81607,3984],{},[898,81609,2772],{},[898,81611,8659],{},[1726,81613,1728],{},[9151,81615,81616,81618,81620],{},[898,81617,1724],{},[898,81619,9779],{},[1726,81621,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[898,81623,4661],{"mathvariant":2377},[9151,81625,81626,81628,81630],{},[898,81627,1724],{},[898,81629,9784],{},[1726,81631,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[902,81633,81634],{"encoding":904},"MRTS = Q'_L \u002F Q'_K"," (zlomek zjednodušte).",[123,81637,81638,81639,1888],{},"Případně dosaďte konkrétní ",[883,81640,81642],{"className":81641},[886],[888,81643,81644],{"xmlns":890},[892,81645,81646,81666],{},[895,81647,81648,81650,81656,81658,81664],{},[1726,81649,2487],{"stretchy":1734},[2275,81651,81652,81654],{},[898,81653,9779],{},[2133,81655,2328],{},[1726,81657,1742],{"separator":1741},[2275,81659,81660,81662],{},[898,81661,9784],{},[2133,81663,2328],{},[1726,81665,2502],{"stretchy":1734},[902,81667,81254],{"encoding":904},[123,81669,81670,81671,81705,81706,81708],{},"Pro odhad substituce použijte ",[883,81672,81674],{"className":81673},[886],[888,81675,81676],{"xmlns":890},[892,81677,81678,81702],{},[895,81679,81680,81682,81684,81686,81688,81690,81692,81694,81696,81698,81700],{},[898,81681,2886],{"mathvariant":2377},[898,81683,9784],{},[1726,81685,1880],{},[1726,81687,2228],{},[898,81689,2815],{},[898,81691,3984],{},[898,81693,2772],{},[898,81695,8659],{},[1726,81697,3174],{},[898,81699,2886],{"mathvariant":2377},[898,81701,9779],{},[902,81703,81704],{"encoding":904},"\\Delta K \\approx -MRTS \\cdot \\Delta L"," (znaménko ",[38,81707,52586],{}," — substituce, ne doplnění).",[724,81710,81711],{},[614,81712,81713,81714,81746,81747,2623,81760,15776,81789,81804],{},"Obrázek 5.7 — izokvanta ",[883,81715,81717],{"className":81716},[886],[888,81718,81719],{"xmlns":890},[892,81720,81721,81743],{},[895,81722,81723,81729,81731,81733,81735,81737,81739,81741],{},[2275,81724,81725,81727],{},[898,81726,80777],{},[2133,81728,2328],{},[1726,81730,1728],{},[898,81732,1724],{},[1726,81734,1735],{"stretchy":1734},[898,81736,9779],{},[1726,81738,1742],{"separator":1741},[898,81740,9784],{},[1726,81742,1762],{"stretchy":1734},[902,81744,81745],{"encoding":904},"q_0 = Q(L,K)"," s tečnou ",[883,81748,81750],{"className":81749},[886],[888,81751,81752],{"xmlns":890},[892,81753,81754,81758],{},[895,81755,81756],{},[898,81757,18836],{},[902,81759,18836],{"encoding":904},[883,81761,81763],{"className":81762},[886],[888,81764,81765],{"xmlns":890},[892,81766,81767,81787],{},[895,81768,81769,81771,81777,81779,81785],{},[1726,81770,2487],{"stretchy":1734},[2275,81772,81773,81775],{},[898,81774,9779],{},[2133,81776,2328],{},[1726,81778,1742],{"separator":1741},[2275,81780,81781,81783],{},[898,81782,9784],{},[2133,81784,2328],{},[1726,81786,2502],{"stretchy":1734},[902,81788,81254],{"encoding":904},[883,81790,81792],{"className":81791},[886],[888,81793,81794],{"xmlns":890},[892,81795,81796,81802],{},[895,81797,81798,81800],{},[898,81799,2886],{"mathvariant":2377},[898,81801,9784],{},[902,81803,81406],{"encoding":904}," odhadnut diferenciálem (záporně vzatý sklon tečny).",[115,81806,81808],{"id":81807},"příklady-dvoufaktorový-model","Příklady (dvoufaktorový model)",[198,81810,81812],{"id":81811},"příklad-54","Příklad 5.4",[724,81814,76653,81815,1343,81857,1343,81874,1888],{},[883,81816,81818],{"className":81817},[886],[888,81819,81820],{"xmlns":890},[892,81821,81822,81854],{},[895,81823,81824,81826,81828,81830,81842],{},[898,81825,1724],{},[1726,81827,1728],{},[2133,81829,36225],{},[2128,81831,81832,81834],{},[898,81833,9779],{},[895,81835,81836,81838,81840],{},[2133,81837,2281],{},[898,81839,4661],{"mathvariant":2377},[2133,81841,2135],{},[2128,81843,81844,81846],{},[898,81845,9784],{},[895,81847,81848,81850,81852],{},[2133,81849,2281],{},[898,81851,4661],{"mathvariant":2377},[2133,81853,2177],{},[902,81855,81856],{"encoding":904},"Q = 15 L^{1\u002F2} K^{1\u002F3}",[883,81858,81860],{"className":81859},[886],[888,81861,81862],{"xmlns":890},[892,81863,81864,81872],{},[895,81865,81866,81868,81870],{},[898,81867,9779],{},[1726,81869,1728],{},[2133,81871,9021],{},[902,81873,77027],{"encoding":904},[883,81875,81877],{"className":81876},[886],[888,81878,81879],{"xmlns":890},[892,81880,81881,81889],{},[895,81882,81883,81885,81887],{},[898,81884,9784],{},[1726,81886,1728],{},[2133,81888,3087],{},[902,81890,81891],{"encoding":904},"K = 100",[724,81893,81894],{},[38,81895,81896],{},"(a) Rychlost změny produkce vzhledem k práci.",[883,81898,81900],{"className":81899},[886],[888,81901,81902],{"xmlns":890,"display":28047},[892,81903,81904,82018],{},[895,81905,81906,81908,81914,81916,81924,81926,81934,81948,81960,81962,81964,81966,81972,81974,81976,81978,81980,81982,81984,81992,81994,82004,82006,82013,82015],{},[898,81907,2815],{},[2275,81909,81910,81912],{},[898,81911,1738],{},[898,81913,9779],{},[1726,81915,1728],{},[9151,81917,81918,81920,81922],{},[898,81919,1724],{},[898,81921,9779],{},[1726,81923,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,81925,1728],{},[2326,81927,81928],{"scriptlevel":2328,"displaystyle":1734},[2330,81929,81930,81932],{},[2133,81931,36225],{},[2133,81933,2135],{},[2128,81935,81936,81938],{},[898,81937,9779],{},[895,81939,81940,81942,81944,81946],{},[1726,81941,2228],{},[2133,81943,2281],{},[898,81945,4661],{"mathvariant":2377},[2133,81947,2135],{},[2128,81949,81950,81952],{},[898,81951,9784],{},[895,81953,81954,81956,81958],{},[2133,81955,2281],{},[898,81957,4661],{"mathvariant":2377},[2133,81959,2177],{},[1726,81961,1742],{"separator":1741},[5865,81963],{"width":15270},[898,81965,2815],{},[2275,81967,81968,81970],{},[898,81969,1738],{},[898,81971,9779],{},[1726,81973,1735],{"stretchy":1734},[2133,81975,9021],{},[1726,81977,1742],{"separator":1741},[2133,81979,3087],{},[1726,81981,1762],{"stretchy":1734},[1726,81983,1728],{},[2326,81985,81986],{"scriptlevel":2328,"displaystyle":1734},[2330,81987,81988,81990],{},[2133,81989,36225],{},[2133,81991,2135],{},[1726,81993,3174],{},[2326,81995,81996],{"scriptlevel":2328,"displaystyle":1734},[2330,81997,81998,82000],{},[2133,81999,2281],{},[8103,82001,82002],{},[2133,82003,9021],{},[1726,82005,3174],{},[82007,82008,82009,82011],"mroot",{},[2133,82010,3087],{},[2133,82012,2177],{},[1726,82014,1880],{},[2133,82016,82017],{},"7,153.",[902,82019,82020],{"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.",[724,82022,82023,82024,44141,82046,10217,82063,82084,82085,82106],{},"Přibližná změna při ",[883,82025,82027],{"className":82026},[886],[888,82028,82029],{"xmlns":890},[892,82030,82031,82043],{},[895,82032,82033,82035,82037,82039,82041],{},[898,82034,9779],{},[1726,82036,2703],{},[2133,82038,9021],{},[1726,82040,3120],{},[2133,82042,38327],{},[902,82044,82045],{"encoding":904},"L: 20 \\to 21",[883,82047,82049],{"className":82048},[886],[888,82050,82051],{"xmlns":890},[892,82052,82053,82061],{},[895,82054,82055,82057,82059],{},[898,82056,9784],{},[1726,82058,1728],{},[2133,82060,3087],{},[902,82062,81891],{"encoding":904},[883,82064,82066],{"className":82065},[886],[888,82067,82068],{"xmlns":890},[892,82069,82070,82081],{},[895,82071,82072,82074,82076,82078],{},[898,82073,2886],{"mathvariant":2377},[898,82075,1724],{},[1726,82077,1880],{},[2133,82079,82080],{},"7,153",[902,82082,82083],{"encoding":904},"\\Delta Q \\approx 7{,}153",". Skutečně ",[883,82086,82088],{"className":82087},[886],[888,82089,82090],{"xmlns":890},[892,82091,82092,82103],{},[895,82093,82094,82096,82098,82100],{},[898,82095,2886],{"mathvariant":2377},[898,82097,1724],{},[1726,82099,1880],{},[2133,82101,82102],{},"26,888",[902,82104,82105],{"encoding":904},"\\Delta Q \\approx 26{,}888"," (dle knihy; zaokrouhlení v konkrétním výpočtu).",[724,82108,82109,82112],{},[38,82110,82111],{},"(b) Pokles kapitálu o 1"," (z 100 na 99).",[883,82114,82116],{"className":82115},[886],[888,82117,82118],{"xmlns":890,"display":28047},[892,82119,82120,82220],{},[895,82121,82122,82124,82130,82132,82140,82142,82144,82156,82170,82172,82174,82176,82182,82184,82186,82188,82190,82192,82194,82196,82200,82202,82215,82217],{},[898,82123,2815],{},[2275,82125,82126,82128],{},[898,82127,1738],{},[898,82129,9784],{},[1726,82131,1728],{},[9151,82133,82134,82136,82138],{},[898,82135,1724],{},[898,82137,9784],{},[1726,82139,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,82141,1728],{},[2133,82143,2231],{},[2128,82145,82146,82148],{},[898,82147,9779],{},[895,82149,82150,82152,82154],{},[2133,82151,2281],{},[898,82153,4661],{"mathvariant":2377},[2133,82155,2135],{},[2128,82157,82158,82160],{},[898,82159,9784],{},[895,82161,82162,82164,82166,82168],{},[1726,82163,2228],{},[2133,82165,2135],{},[898,82167,4661],{"mathvariant":2377},[2133,82169,2177],{},[1726,82171,1742],{"separator":1741},[5865,82173],{"width":15270},[898,82175,2815],{},[2275,82177,82178,82180],{},[898,82179,1738],{},[898,82181,9784],{},[1726,82183,1735],{"stretchy":1734},[2133,82185,9021],{},[1726,82187,1742],{"separator":1741},[2133,82189,3087],{},[1726,82191,1762],{"stretchy":1734},[1726,82193,1728],{},[2133,82195,2231],{},[8103,82197,82198],{},[2133,82199,9021],{},[1726,82201,3174],{},[2326,82203,82204],{"scriptlevel":2328,"displaystyle":1734},[2330,82205,82206,82208],{},[2133,82207,2281],{},[82007,82209,82210,82213],{},[2133,82211,82212],{},"10000",[2133,82214,2177],{},[1726,82216,1880],{},[2133,82218,82219],{},"4,525.",[902,82221,82222],{"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.",[724,82224,82225,82226,2684,82243,1847],{},"Produkce poklesne přibližně o 4,525 (z ",[883,82227,82229],{"className":82228},[886],[888,82230,82231],{"xmlns":890},[892,82232,82233,82240],{},[895,82234,82235,82237],{},[1726,82236,1880],{},[2133,82238,82239],{},"905,126",[902,82241,82242],{"encoding":904},"\\approx 905{,}126",[883,82244,82246],{"className":82245},[886],[888,82247,82248],{"xmlns":890},[892,82249,82250,82257],{},[895,82251,82252,82254],{},[1726,82253,1880],{},[2133,82255,82256],{},"900,601",[902,82258,82259],{"encoding":904},"\\approx 900{,}601",[724,82261,82262,3127,82309,1343,82331,1847],{},[38,82263,82264,82265,3877,82287],{},"(c) Změna ",[883,82266,82268],{"className":82267},[886],[888,82269,82270],{"xmlns":890},[892,82271,82272,82284],{},[895,82273,82274,82276,82278,82280,82282],{},[898,82275,9779],{},[1726,82277,2703],{},[2133,82279,9021],{},[1726,82281,3120],{},[2133,82283,36225],{},[902,82285,82286],{"encoding":904},"L: 20 \\to 15",[883,82288,82290],{"className":82289},[886],[888,82291,82292],{"xmlns":890},[892,82293,82294,82306],{},[895,82295,82296,82298,82300,82302,82304],{},[898,82297,9784],{},[1726,82299,2703],{},[2133,82301,3087],{},[1726,82303,3120],{},[2133,82305,8789],{},[902,82307,82308],{"encoding":904},"K: 100 \\to 150",[883,82310,82312],{"className":82311},[886],[888,82313,82314],{"xmlns":890},[892,82315,82316,82328],{},[895,82317,82318,82320,82322,82324,82326],{},[898,82319,2198],{},[898,82321,9779],{},[1726,82323,1728],{},[1726,82325,2228],{},[2133,82327,2231],{},[902,82329,82330],{"encoding":904},"dL = -5",[883,82332,82334],{"className":82333},[886],[888,82335,82336],{"xmlns":890},[892,82337,82338,82348],{},[895,82339,82340,82342,82344,82346],{},[898,82341,2198],{},[898,82343,9784],{},[1726,82345,1728],{},[2133,82347,3117],{},[902,82349,82350],{"encoding":904},"dK = 50",[883,82352,82354],{"className":82353},[886],[888,82355,82356],{"xmlns":890,"display":28047},[892,82357,82358,82446],{},[895,82359,82360,82362,82364,82366,82368,82374,82376,82378,82380,82382,82384,82386,82388,82390,82392,82394,82396,82398,82404,82406,82408,82410,82412,82414,82416,82418,82420,82422,82424,82426,82428,82430,82432,82434,82437,82439,82441,82443],{},[898,82361,2198],{},[898,82363,1724],{},[1726,82365,1728],{},[898,82367,2815],{},[2275,82369,82370,82372],{},[898,82371,1738],{},[898,82373,9779],{},[1726,82375,1735],{"stretchy":1734},[2133,82377,9021],{},[1726,82379,1742],{"separator":1741},[2133,82381,3087],{},[1726,82383,1762],{"stretchy":1734},[1726,82385,3174],{},[1726,82387,1735],{"stretchy":1734},[1726,82389,2228],{},[2133,82391,2231],{},[1726,82393,1762],{"stretchy":1734},[1726,82395,2099],{},[898,82397,2815],{},[2275,82399,82400,82402],{},[898,82401,1738],{},[898,82403,9784],{},[1726,82405,1735],{"stretchy":1734},[2133,82407,9021],{},[1726,82409,1742],{"separator":1741},[2133,82411,3087],{},[1726,82413,1762],{"stretchy":1734},[1726,82415,3174],{},[2133,82417,3117],{},[1726,82419,1728],{},[2133,82421,82080],{},[1726,82423,3174],{},[1726,82425,1735],{"stretchy":1734},[1726,82427,2228],{},[2133,82429,2231],{},[1726,82431,1762],{"stretchy":1734},[1726,82433,2099],{},[2133,82435,82436],{},"4,525",[1726,82438,3174],{},[2133,82440,3117],{},[1726,82442,1880],{},[2133,82444,82445],{},"190,485.",[902,82447,82448],{"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.",[724,82450,82451],{},"Produkce vzroste přibližně z 905,126 na 995,611.",[198,82453,82455],{"id":82454},"příklad-55","Příklad 5.5",[724,82457,82458,82459,82495,82496,1888],{},"Pro produkci ",[883,82460,82462],{"className":82461},[886],[888,82463,82464],{"xmlns":890},[892,82465,82466,82492],{},[895,82467,82468,82470,82472,82474,82476,82478,82480,82482,82488],{},[898,82469,1724],{},[1726,82471,1735],{"stretchy":1734},[898,82473,9779],{},[1726,82475,1742],{"separator":1741},[898,82477,9784],{},[1726,82479,1762],{"stretchy":1734},[1726,82481,1728],{},[82007,82483,82484,82486],{},[898,82485,9779],{},[2133,82487,2177],{},[8103,82489,82490],{},[898,82491,9784],{},[902,82493,82494],{"encoding":904},"Q(L, K) = \\sqrt[3]{L}\\sqrt{K}"," mají izokvanty rovnici ",[883,82497,82499],{"className":82498},[886],[888,82500,82501],{"xmlns":890},[892,82502,82503,82519],{},[895,82504,82505,82511,82515,82517],{},[82007,82506,82507,82509],{},[898,82508,9779],{},[2133,82510,2177],{},[8103,82512,82513],{},[898,82514,9784],{},[1726,82516,1728],{},[898,82518,80777],{},[902,82520,82521],{"encoding":904},"\\sqrt[3]{L}\\sqrt{K} = q",[724,82523,82524,82525,1888],{},"Umocněním na druhou: ",[883,82526,82528],{"className":82527},[886],[888,82529,82530],{"xmlns":890},[892,82531,82532,82556],{},[895,82533,82534,82536,82538,82544,82546],{},[898,82535,9784],{},[1726,82537,1728],{},[2128,82539,82540,82542],{},[898,82541,80777],{},[2133,82543,2135],{},[898,82545,4661],{"mathvariant":2377},[82007,82547,82548,82554],{},[2128,82549,82550,82552],{},[898,82551,9779],{},[2133,82553,2135],{},[2133,82555,2177],{},[902,82557,82558],{"encoding":904},"K = q^2 \u002F \\sqrt[3]{L^2}",[120,82560,82561,82601,82641],{},[123,82562,82563],{},[883,82564,82566],{"className":82565},[886],[888,82567,82568],{"xmlns":890},[892,82569,82570,82598],{},[895,82571,82572,82574,82576,82578,82580,82582,82584,82586,82588],{},[898,82573,80777],{},[1726,82575,1728],{},[2133,82577,2281],{},[1726,82579,3977],{},[898,82581,9784],{},[1726,82583,1728],{},[2133,82585,2281],{},[898,82587,4661],{"mathvariant":2377},[82007,82589,82590,82596],{},[2128,82591,82592,82594],{},[898,82593,9779],{},[2133,82595,2135],{},[2133,82597,2177],{},[902,82599,82600],{"encoding":904},"q = 1 \\Rightarrow K = 1\u002F\\sqrt[3]{L^2}",[123,82602,82603],{},[883,82604,82606],{"className":82605},[886],[888,82607,82608],{"xmlns":890},[892,82609,82610,82638],{},[895,82611,82612,82614,82616,82618,82620,82622,82624,82626,82628],{},[898,82613,80777],{},[1726,82615,1728],{},[2133,82617,2135],{},[1726,82619,3977],{},[898,82621,9784],{},[1726,82623,1728],{},[2133,82625,2352],{},[898,82627,4661],{"mathvariant":2377},[82007,82629,82630,82636],{},[2128,82631,82632,82634],{},[898,82633,9779],{},[2133,82635,2135],{},[2133,82637,2177],{},[902,82639,82640],{"encoding":904},"q = 2 \\Rightarrow K = 4\u002F\\sqrt[3]{L^2}",[123,82642,82643],{},[883,82644,82646],{"className":82645},[886],[888,82647,82648],{"xmlns":890},[892,82649,82650,82678],{},[895,82651,82652,82654,82656,82658,82660,82662,82664,82666,82668],{},[898,82653,80777],{},[1726,82655,1728],{},[2133,82657,2177],{},[1726,82659,3977],{},[898,82661,9784],{},[1726,82663,1728],{},[2133,82665,3989],{},[898,82667,4661],{"mathvariant":2377},[82007,82669,82670,82676],{},[2128,82671,82672,82674],{},[898,82673,9779],{},[2133,82675,2135],{},[2133,82677,2177],{},[902,82679,82680],{"encoding":904},"q = 3 \\Rightarrow K = 9\u002F\\sqrt[3]{L^2}",[724,82682,82683],{},[614,82684,82685,82686,6460,82707,1888],{},"Obrázek 5.5 — tři klesající konvexní izokvanty v rovině ",[883,82687,82689],{"className":82688},[886],[888,82690,82691],{"xmlns":890},[892,82692,82693,82705],{},[895,82694,82695,82697,82699,82701,82703],{},[1726,82696,1735],{"stretchy":1734},[898,82698,9779],{},[1726,82700,1742],{"separator":1741},[898,82702,9784],{},[1726,82704,1762],{"stretchy":1734},[902,82706,80903],{"encoding":904},[883,82708,82710],{"className":82709},[886],[888,82711,82712],{"xmlns":890},[892,82713,82714,82730],{},[895,82715,82716,82718,82720,82722,82724,82726,82728],{},[898,82717,80777],{},[1726,82719,1728],{},[2133,82721,2281],{},[1726,82723,1742],{"separator":1741},[2133,82725,2135],{},[1726,82727,1742],{"separator":1741},[2133,82729,2177],{},[902,82731,82732],{"encoding":904},"q = 1, 2, 3",[198,82734,82736],{"id":82735},"příklad-56","Příklad 5.6",[724,82738,76653,82739,1888],{},[883,82740,82742],{"className":82741},[886],[888,82743,82744],{"xmlns":890},[892,82745,82746,82762],{},[895,82747,82748,82750,82752,82754,82756,82758],{},[898,82749,1724],{},[1726,82751,1728],{},[2133,82753,2135],{},[898,82755,9779],{},[1726,82757,2099],{},[8103,82759,82760],{},[898,82761,9784],{},[902,82763,82764],{"encoding":904},"Q = 2L + \\sqrt{K}",[883,82766,82768],{"className":82767},[886],[888,82769,82770],{"xmlns":890,"display":28047},[892,82771,82772,82814],{},[895,82773,82774,82776,82782,82784,82786,82788,82790,82792,82798,82800,82812],{},[898,82775,2815],{},[2275,82777,82778,82780],{},[898,82779,1738],{},[898,82781,9779],{},[1726,82783,1728],{},[2133,82785,2135],{},[1726,82787,1742],{"separator":1741},[5865,82789],{"width":5867},[898,82791,2815],{},[2275,82793,82794,82796],{},[898,82795,1738],{},[898,82797,9784],{},[1726,82799,1728],{},[2330,82801,82802,82804],{},[2133,82803,2281],{},[895,82805,82806,82808],{},[2133,82807,2135],{},[8103,82809,82810],{},[898,82811,9784],{},[898,82813,1888],{"mathvariant":2377},[902,82815,82816],{"encoding":904},"MP_L = 2, \\qquad MP_K = \\frac{1}{2\\sqrt{K}}.",[883,82818,82820],{"className":82819},[886],[888,82821,82822],{"xmlns":890,"display":28047},[892,82823,82824,82888],{},[895,82825,82826,82828,82830,82832,82834,82836,82858,82860,82878,82880,82882,82886],{},[898,82827,2815],{},[898,82829,3984],{},[898,82831,2772],{},[898,82833,8659],{},[1726,82835,1728],{},[2330,82837,82838,82848],{},[895,82839,82840,82842],{},[898,82841,2815],{},[2275,82843,82844,82846],{},[898,82845,1738],{},[898,82847,9779],{},[895,82849,82850,82852],{},[898,82851,2815],{},[2275,82853,82854,82856],{},[898,82855,1738],{},[898,82857,9784],{},[1726,82859,1728],{},[2330,82861,82862,82864],{},[2133,82863,2135],{},[2326,82865,82866],{"scriptlevel":2328,"displaystyle":1734},[2330,82867,82868,82870],{},[2133,82869,2281],{},[895,82871,82872,82874],{},[2133,82873,2135],{},[8103,82875,82876],{},[898,82877,9784],{},[1726,82879,1728],{},[2133,82881,2352],{},[8103,82883,82884],{},[898,82885,9784],{},[898,82887,1888],{"mathvariant":2377},[902,82889,82890],{"encoding":904},"MRTS = \\frac{MP_L}{MP_K} = \\frac{2}{\\tfrac{1}{2\\sqrt{K}}} = 4\\sqrt{K}.",[724,82892,82893,82894,82937,82938,82977,82978,1888],{},"Například ",[883,82895,82897],{"className":82896},[886],[888,82898,82899],{"xmlns":890},[892,82900,82901,82934],{},[895,82902,82903,82905,82907,82909,82911,82913,82915,82917,82919,82921,82923,82925,82929,82931],{},[898,82904,2815],{},[898,82906,3984],{},[898,82908,2772],{},[898,82910,8659],{},[1726,82912,1735],{"stretchy":1734},[2133,82914,2352],{},[1726,82916,1742],{"separator":1741},[2133,82918,24182],{},[1726,82920,1762],{"stretchy":1734},[1726,82922,1728],{},[2133,82924,2352],{},[8103,82926,82927],{},[2133,82928,24182],{},[1726,82930,1880],{},[2133,82932,82933],{},"10,58",[902,82935,82936],{"encoding":904},"MRTS(4, 7) = 4\\sqrt{7} \\approx 10{,}58",". Klesne-li práce z 4 na 3, je k udržení produkce ",[883,82939,82941],{"className":82940},[886],[888,82942,82943],{"xmlns":890},[892,82944,82945,82974],{},[895,82946,82947,82949,82951,82953,82955,82957,82959,82961,82963,82965,82969,82971],{},[898,82948,1724],{},[1726,82950,1735],{"stretchy":1734},[2133,82952,2352],{},[1726,82954,1742],{"separator":1741},[2133,82956,24182],{},[1726,82958,1762],{"stretchy":1734},[1726,82960,1728],{},[2133,82962,5572],{},[1726,82964,2099],{},[8103,82966,82967],{},[2133,82968,24182],{},[1726,82970,1880],{},[2133,82972,82973],{},"10,646",[902,82975,82976],{"encoding":904},"Q(4,7) = 8 + \\sqrt{7} \\approx 10{,}646"," třeba zvýšit kapitál přibližně o ",[883,82979,82981],{"className":82980},[886],[888,82982,82983],{"xmlns":890},[892,82984,82985,82993],{},[895,82986,82987,82989],{},[2133,82988,2352],{},[8103,82990,82991],{},[2133,82992,24182],{},[902,82994,82995],{"encoding":904},"4\\sqrt{7}",[724,82997,82998,82999,83019],{},"Pokud se práce naopak zvýší ze 4 na 6 (",[883,83000,83002],{"className":83001},[886],[888,83003,83004],{"xmlns":890},[892,83005,83006,83016],{},[895,83007,83008,83010,83012,83014],{},[898,83009,2198],{},[898,83011,9779],{},[1726,83013,1728],{},[2133,83015,2135],{},[902,83017,83018],{"encoding":904},"dL = 2","), k udržení produkce stačí snížit kapitál o",[883,83021,83023],{"className":83022},[886],[888,83024,83025],{"xmlns":890,"display":28047},[892,83026,83027,83076],{},[895,83028,83029,83031,83033,83035,83037,83039,83041,83043,83045,83047,83049,83051,83053,83055,83057,83059,83061,83063,83065,83069,83071,83073],{},[898,83030,2198],{},[898,83032,9784],{},[1726,83034,1728],{},[1726,83036,2228],{},[898,83038,2815],{},[898,83040,3984],{},[898,83042,2772],{},[898,83044,8659],{},[1726,83046,1735],{"stretchy":1734},[2133,83048,2352],{},[1726,83050,1742],{"separator":1741},[2133,83052,24182],{},[1726,83054,1762],{"stretchy":1734},[1726,83056,3174],{},[2133,83058,2135],{},[1726,83060,1728],{},[1726,83062,2228],{},[2133,83064,5572],{},[8103,83066,83067],{},[2133,83068,24182],{},[1726,83070,1880],{},[1726,83072,2228],{},[2133,83074,83075],{},"21,17.",[902,83077,83078],{"encoding":904},"dK = -MRTS(4,7)\\cdot 2 = -8\\sqrt{7} \\approx -21{,}17.",[115,83080,83082],{"id":83081},"shrnutí-kapitoly-5","Shrnutí kapitoly 5",[724,83084,83085,83086,1343,83088,3877,83090,83092,83093,83096,83097,83100],{},"Hlavními faktory produkce jsou ",[38,83087,74894],{},[38,83089,74910],{},[38,83091,74926],{},"; půda je standardní exogenní proměnná. Přicházejí proto v úvahu ",[38,83094,83095],{},"jednofaktorový"," (pouze práce) a ",[38,83098,83099],{},"dvoufaktorový"," (práce + kapitál) model.",[724,83102,83103,83104,83107,83108,83110,83111,83113,83114,26170,83117,83136,83137,83154,83155,83172,83173,83195,83196,4346,83215,1888],{},"V ",[38,83105,83106],{},"1F modelu"," se definuje ",[38,83109,10008],{}," (derivace produkce podle práce) a ",[38,83112,74829],{}," (podíl produkce a práce). Produkční funkce má typický tvar díky ",[38,83115,83116],{},"zákonu klesajících výnosů",[883,83118,83120],{"className":83119},[886],[888,83121,83122],{"xmlns":890},[892,83123,83124,83134],{},[895,83125,83126,83128],{},[898,83127,2815],{},[2275,83129,83130,83132],{},[898,83131,1738],{},[898,83133,9779],{},[902,83135,10029],{"encoding":904}," nejprve roste, od inflexního bodu ",[883,83138,83140],{"className":83139},[886],[888,83141,83142],{"xmlns":890},[892,83143,83144,83152],{},[895,83145,83146],{},[2275,83147,83148,83150],{},[898,83149,9779],{},[2133,83151,2328],{},[902,83153,75538],{"encoding":904}," klesá a v bodě ",[883,83156,83158],{"className":83157},[886],[888,83159,83160],{"xmlns":890},[892,83161,83162,83170],{},[895,83163,83164],{},[2275,83165,83166,83168],{},[898,83167,9779],{},[2133,83169,2281],{},[902,83171,13198],{"encoding":904}," dosahuje nuly (maximum produkce). Platí ",[38,83174,83175,83176],{},"princip maximalizace ",[883,83177,83179],{"className":83178},[886],[888,83180,83181],{"xmlns":890},[892,83182,83183,83193],{},[895,83184,83185,83187],{},[898,83186,4243],{},[2275,83188,83189,83191],{},[898,83190,1738],{},[898,83192,9779],{},[902,83194,74613],{"encoding":904},": v bodě maxima ",[883,83197,83199],{"className":83198},[886],[888,83200,83201],{"xmlns":890},[892,83202,83203,83213],{},[895,83204,83205,83207],{},[898,83206,4243],{},[2275,83208,83209,83211],{},[898,83210,1738],{},[898,83212,9779],{},[902,83214,74613],{"encoding":904},[883,83216,83218],{"className":83217},[886],[888,83219,83220],{"xmlns":890},[892,83221,83222,83242],{},[895,83223,83224,83226,83232,83234,83236],{},[898,83225,2815],{},[2275,83227,83228,83230],{},[898,83229,1738],{},[898,83231,9779],{},[1726,83233,1728],{},[898,83235,4243],{},[2275,83237,83238,83240],{},[898,83239,1738],{},[898,83241,9779],{},[902,83243,74643],{"encoding":904},[724,83245,83246,83247,83250,83251,1777,83254,83283,83284,83301,83302,83305,83306,83335,83336,83338,83339,8088,83369,83391],{},"Ve ",[38,83248,83249],{},"2F modelu"," se obvykle používají ",[38,83252,83253],{},"Cobb-Douglasovy funkce",[883,83255,83257],{"className":83256},[886],[888,83258,83259],{"xmlns":890},[892,83260,83261,83281],{},[895,83262,83263,83265,83267,83269,83275],{},[898,83264,1724],{},[1726,83266,1728],{},[898,83268,4243],{},[2128,83270,83271,83273],{},[898,83272,9779],{},[898,83274,207],{},[2128,83276,83277,83279],{},[898,83278,9784],{},[898,83280,2102],{},[902,83282,74710],{"encoding":904},", které reflektují proporcionalitu změn vstupů a výstupu. Podle ",[883,83285,83287],{"className":83286},[886],[888,83288,83289],{"xmlns":890},[892,83290,83291,83299],{},[895,83292,83293,83295,83297],{},[898,83294,207],{},[1726,83296,2099],{},[898,83298,2102],{},[902,83300,74804],{"encoding":904}," rozlišujeme ",[38,83303,83304],{},"konstantní, rostoucí, klesající výnosy z rozsahu",". Mezní produkty ",[883,83307,83309],{"className":83308},[886],[888,83310,83311],{"xmlns":890},[892,83312,83313,83333],{},[895,83314,83315,83317,83323,83325,83327],{},[898,83316,2815],{},[2275,83318,83319,83321],{},[898,83320,1738],{},[898,83322,9779],{},[1726,83324,1742],{"separator":1741},[898,83326,2815],{},[2275,83328,83329,83331],{},[898,83330,1738],{},[898,83332,9784],{},[902,83334,74741],{"encoding":904}," jsou parciální derivace, totální diferenciál dává přibližnou změnu produkce. ",[38,83337,9762],{}," jsou indiferenční křivky produkční funkce. Podíl ",[883,83340,83342],{"className":83341},[886],[888,83343,83344],{"xmlns":890},[892,83345,83346,83366],{},[895,83347,83348,83350,83356,83358,83360],{},[898,83349,2815],{},[2275,83351,83352,83354],{},[898,83353,1738],{},[898,83355,9779],{},[898,83357,4661],{"mathvariant":2377},[898,83359,2815],{},[2275,83361,83362,83364],{},[898,83363,1738],{},[898,83365,9784],{},[902,83367,83368],{"encoding":904},"MP_L\u002FMP_K",[38,83370,83371,83372,1762],{},"mezní míra technické substituce (",[883,83373,83375],{"className":83374},[886],[888,83376,83377],{"xmlns":890},[892,83378,83379,83389],{},[895,83380,83381,83383,83385,83387],{},[898,83382,2815],{},[898,83384,3984],{},[898,83386,2772],{},[898,83388,8659],{},[902,83390,10583],{"encoding":904}," — udává, o kolik se musí změnit kapitál při jednotkové změně práce pro zachování produkce.",[115,83393,49863],{"id":49862},[152,83395,83396,83399,83402,83405,83408,83411,83414,83417,83420,83423,83426],{},[123,83397,83398],{},"Jaké jsou faktory produkce?",[123,83400,83401],{},"Jak se dospěje k jednofaktorovému a dvoufaktorovému modelu produkce?",[123,83403,83404],{},"Jak je zadána produkční funkce u jednofaktorového modelu?",[123,83406,83407],{},"Co udává mezní produkt práce?",[123,83409,83410],{},"Co musí respektovat průběh křivky produkce?",[123,83412,83413],{},"Jak lze matematicky vyjádřit zákon klesajících výnosů?",[123,83415,83416],{},"Jaký základní ekonomický požadavek respektují Cobb-Douglasovy funkce?",[123,83418,83419],{},"Jak se vypočtou mezní produkty práce a kapitálu?",[123,83421,83422],{},"Jak se stanoví přibližná změna produkce v závislosti na změnách práce a kapitálu?",[123,83424,83425],{},"Co vyjadřují izokvanty? Jaké jsou jejich typické vlastnosti?",[123,83427,83428],{},"Jak se vypočte mezní míra technické substituce a co vyjadřuje?",[115,83430,83432],{"id":83431},"úlohy-51517","Úlohy 5.1–5.17",[198,83434,40432],{"id":40431},[724,83436,83437,83440,83441,83463,83464,1343,83484,1343,83504,83524],{},[38,83438,83439],{},"5.1"," Je dána produkce ",[883,83442,83444],{"className":83443},[886],[888,83445,83446],{"xmlns":890},[892,83447,83448,83460],{},[895,83449,83450,83452,83454,83456],{},[898,83451,1724],{},[1726,83453,1728],{},[2133,83455,2860],{},[8103,83457,83458],{},[898,83459,9779],{},[902,83461,83462],{"encoding":904},"Q = 10\\sqrt{L}",". (a) Vypočtěte ",[883,83465,83467],{"className":83466},[886],[888,83468,83469],{"xmlns":890},[892,83470,83471,83481],{},[895,83472,83473,83475,83477,83479],{},[898,83474,1724],{},[1726,83476,1735],{"stretchy":1734},[2133,83478,2281],{},[1726,83480,1762],{"stretchy":1734},[902,83482,83483],{"encoding":904},"Q(1)",[883,83485,83487],{"className":83486},[886],[888,83488,83489],{"xmlns":890},[892,83490,83491,83501],{},[895,83492,83493,83495,83497,83499],{},[898,83494,1724],{},[1726,83496,1735],{"stretchy":1734},[2133,83498,2352],{},[1726,83500,1762],{"stretchy":1734},[902,83502,83503],{"encoding":904},"Q(4)",[883,83505,83507],{"className":83506},[886],[888,83508,83509],{"xmlns":890},[892,83510,83511,83521],{},[895,83512,83513,83515,83517,83519],{},[898,83514,1724],{},[1726,83516,1735],{"stretchy":1734},[2133,83518,3989],{},[1726,83520,1762],{"stretchy":1734},[902,83522,83523],{"encoding":904},"Q(9)",". (b) Rozhodněte, kdy produkce roste, resp. klesá. (c) Rozhodněte, kdy je křivka produkce konvexní, resp. konkávní. (d) Načrtněte křivku produkce.",[724,83526,83527,83440,83530,83566,83567,83580,83581,83600,83601,83627,83628,2684,83641,83654],{},[38,83528,83529],{},"5.2",[883,83531,83533],{"className":83532},[886],[888,83534,83535],{"xmlns":890},[892,83536,83537,83563],{},[895,83538,83539,83541,83543,83545,83547,83553,83555,83557],{},[898,83540,1724],{},[1726,83542,1728],{},[1726,83544,2228],{},[2133,83546,2791],{},[2128,83548,83549,83551],{},[898,83550,9779],{},[2133,83552,2177],{},[1726,83554,2099],{},[2133,83556,3989],{},[2128,83558,83559,83561],{},[898,83560,9779],{},[2133,83562,2135],{},[902,83564,83565],{"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 ",[883,83568,83570],{"className":83569},[886],[888,83571,83572],{"xmlns":890},[892,83573,83574,83578],{},[895,83575,83576],{},[898,83577,9779],{},[902,83579,9779],{"encoding":904}," (počet pracovníků), které maximalizuje produkci a stanovte příslušné maximum produkce. (d) Načrtněte křivku produkce. (e) Najděte mezní produkt práce ",[883,83582,83584],{"className":83583},[886],[888,83585,83586],{"xmlns":890},[892,83587,83588,83598],{},[895,83589,83590,83592],{},[898,83591,2815],{},[2275,83593,83594,83596],{},[898,83595,1738],{},[898,83597,9779],{},[902,83599,10029],{"encoding":904},". (f) Vypočtěte ",[883,83602,83604],{"className":83603},[886],[888,83605,83606],{"xmlns":890},[892,83607,83608,83624],{},[895,83609,83610,83612,83618,83620,83622],{},[898,83611,2815],{},[2275,83613,83614,83616],{},[898,83615,1738],{},[898,83617,9779],{},[1726,83619,1735],{"stretchy":1734},[2133,83621,2860],{},[1726,83623,1762],{"stretchy":1734},[902,83625,83626],{"encoding":904},"MP_L(10)"," a ekonomicky interpretujte. (g) Určete přibližnou změnu produkce v důsledku zvýšení počtu pracovníků z ",[883,83629,83631],{"className":83630},[886],[888,83632,83633],{"xmlns":890},[892,83634,83635,83639],{},[895,83636,83637],{},[2133,83638,2860],{},[902,83640,2860],{"encoding":904},[883,83642,83644],{"className":83643},[886],[888,83645,83646],{"xmlns":890},[892,83647,83648,83652],{},[895,83649,83650],{},[2133,83651,42268],{},[902,83653,42268],{"encoding":904}," a porovnejte se skutečnou změnou produkce.",[724,83656,83657,83660,83661,83683,83684,83712,83713,83744,83745,1888],{},[38,83658,83659],{},"5.3"," Pro zadanou produkci ověřte platnost zákona klesajících výnosů a charakterizujte vlastnosti mezního produktu práce:\n(a) ",[883,83662,83664],{"className":83663},[886],[888,83665,83666],{"xmlns":890},[892,83667,83668,83680],{},[895,83669,83670,83672,83674,83676],{},[898,83671,1724],{},[1726,83673,1728],{},[2133,83675,15096],{},[8103,83677,83678],{},[898,83679,9779],{},[902,83681,83682],{"encoding":904},"Q = 500\\sqrt{L}",".\n(b) ",[883,83685,83687],{"className":83686},[886],[888,83688,83689],{"xmlns":890},[892,83690,83691,83709],{},[895,83692,83693,83695,83697,83699,83703,83705,83707],{},[898,83694,1724],{},[1726,83696,1728],{},[2133,83698,30062],{},[8103,83700,83701],{},[898,83702,9779],{},[1726,83704,2228],{},[2133,83706,2352],{},[898,83708,9779],{},[902,83710,83711],{"encoding":904},"Q = 300\\sqrt{L} - 4L",".\n(c) ",[883,83714,83716],{"className":83715},[886],[888,83717,83718],{"xmlns":890},[892,83719,83720,83741],{},[895,83721,83722,83724,83726,83728,83730,83732,83735],{},[898,83723,1724],{},[1726,83725,1728],{},[2133,83727,3117],{},[898,83729,9779],{},[1726,83731,2228],{},[2133,83733,83734],{},"0,01",[2128,83736,83737,83739],{},[898,83738,9779],{},[2133,83740,2135],{},[902,83742,83743],{"encoding":904},"Q = 50L - 0{,}01 L^{2}",".\n(d) ",[883,83746,83748],{"className":83747},[886],[888,83749,83750],{"xmlns":890},[892,83751,83752,83778],{},[895,83753,83754,83756,83758,83760,83762,83768,83770,83772],{},[898,83755,1724],{},[1726,83757,1728],{},[1726,83759,2228],{},[2133,83761,68191],{},[2128,83763,83764,83766],{},[898,83765,9779],{},[2133,83767,2177],{},[1726,83769,2099],{},[2133,83771,3989],{},[2128,83773,83774,83776],{},[898,83775,9779],{},[2133,83777,2135],{},[902,83779,83780],{"encoding":904},"Q = -0{,}3 L^{3} + 9 L^{2}",[724,83782,83783,83786,83787,2623,83806,72178,83823,1888],{},[38,83784,83785],{},"5.4"," Dokažte, že má-li průměrný produkt práce ",[883,83788,83790],{"className":83789},[886],[888,83791,83792],{"xmlns":890},[892,83793,83794,83804],{},[895,83795,83796,83798],{},[898,83797,4243],{},[2275,83799,83800,83802],{},[898,83801,1738],{},[898,83803,9779],{},[902,83805,74613],{"encoding":904},[883,83807,83809],{"className":83808},[886],[888,83810,83811],{"xmlns":890},[892,83812,83813,83821],{},[895,83814,83815],{},[2275,83816,83817,83819],{},[898,83818,9779],{},[2133,83820,2328],{},[902,83822,75538],{"encoding":904},[883,83824,83826],{"className":83825},[886],[888,83827,83828],{"xmlns":890},[892,83829,83830,83870],{},[895,83831,83832,83834,83840,83842,83848,83850,83852,83854,83860,83862,83868],{},[898,83833,4243],{},[2275,83835,83836,83838],{},[898,83837,1738],{},[898,83839,9779],{},[1726,83841,1735],{"stretchy":1734},[2275,83843,83844,83846],{},[898,83845,9779],{},[2133,83847,2328],{},[1726,83849,1762],{"stretchy":1734},[1726,83851,1728],{},[898,83853,2815],{},[2275,83855,83856,83858],{},[898,83857,1738],{},[898,83859,9779],{},[1726,83861,1735],{"stretchy":1734},[2275,83863,83864,83866],{},[898,83865,9779],{},[2133,83867,2328],{},[1726,83869,1762],{"stretchy":1734},[902,83871,83872],{"encoding":904},"AP_L(L_0) = MP_L(L_0)",[724,83874,83875,83440,83878,21575,83914,83927,83928,83947],{},[38,83876,83877],{},"5.5",[883,83879,83881],{"className":83880},[886],[888,83882,83883],{"xmlns":890},[892,83884,83885,83911],{},[895,83886,83887,83889,83891,83893,83895,83901,83903,83905],{},[898,83888,1724],{},[1726,83890,1728],{},[1726,83892,2228],{},[2133,83894,2836],{},[2128,83896,83897,83899],{},[898,83898,9779],{},[2133,83900,2177],{},[1726,83902,2099],{},[2133,83904,3506],{},[2128,83906,83907,83909],{},[898,83908,9779],{},[2133,83910,2135],{},[902,83912,83913],{"encoding":904},"Q = -0{,}2 L^{3} + 12 L^{2}",[883,83915,83917],{"className":83916},[886],[888,83918,83919],{"xmlns":890},[892,83920,83921,83925],{},[895,83922,83923],{},[898,83924,9779],{},[902,83926,9779],{"encoding":904}," je počet pracovníků. (a) Určete počet pracovníků, při kterém je dosaženo nejvyšší produktivity práce (= maximálního průměrného produktu práce ",[883,83929,83931],{"className":83930},[886],[888,83932,83933],{"xmlns":890},[892,83934,83935,83945],{},[895,83936,83937,83939],{},[898,83938,4243],{},[2275,83940,83941,83943],{},[898,83942,1738],{},[898,83944,9779],{},[902,83946,74613],{"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.",[198,83949,83951],{"id":83950},"dvoufaktorový-model","Dvoufaktorový model",[724,83953,83954,83957,83958,83683,83984,83712,84026,1888],{},[38,83955,83956],{},"5.6"," Pro zadanou produkci rozhodněte, jaké výnosy z rozsahu představují:\n(a) ",[883,83959,83961],{"className":83960},[886],[888,83962,83963],{"xmlns":890},[892,83964,83965,83981],{},[895,83966,83967,83969,83971,83973,83975],{},[898,83968,1724],{},[1726,83970,1728],{},[2133,83972,24182],{},[898,83974,9779],{},[2128,83976,83977,83979],{},[898,83978,9784],{},[2133,83980,2135],{},[902,83982,83983],{"encoding":904},"Q = 7 L K^{2}",[883,83985,83987],{"className":83986},[886],[888,83988,83989],{"xmlns":890},[892,83990,83991,84023],{},[895,83992,83993,83995,83997,83999,84011],{},[898,83994,1724],{},[1726,83996,1728],{},[2133,83998,3117],{},[2128,84000,84001,84003],{},[898,84002,9779],{},[895,84004,84005,84007,84009],{},[2133,84006,2135],{},[898,84008,4661],{"mathvariant":2377},[2133,84010,2177],{},[2128,84012,84013,84015],{},[898,84014,9784],{},[895,84016,84017,84019,84021],{},[2133,84018,2281],{},[898,84020,4661],{"mathvariant":2377},[2133,84022,2177],{},[902,84024,84025],{"encoding":904},"Q = 50 L^{2\u002F3} K^{1\u002F3}",[883,84027,84029],{"className":84028},[886],[888,84030,84031],{"xmlns":890},[892,84032,84033,84065],{},[895,84034,84035,84037,84039,84041,84053],{},[898,84036,1724],{},[1726,84038,1728],{},[2133,84040,3704],{},[2128,84042,84043,84045],{},[898,84044,9779],{},[895,84046,84047,84049,84051],{},[2133,84048,2177],{},[898,84050,4661],{"mathvariant":2377},[2133,84052,2231],{},[2128,84054,84055,84057],{},[898,84056,9784],{},[895,84058,84059,84061,84063],{},[2133,84060,2135],{},[898,84062,4661],{"mathvariant":2377},[2133,84064,2231],{},[902,84066,84067],{"encoding":904},"Q = 18 L^{3\u002F5} K^{2\u002F5}",[724,84069,84070,83440,84073,84115,84116,1343,84134,84153,84154,84171],{},[38,84071,84072],{},"5.7",[883,84074,84076],{"className":84075},[886],[888,84077,84078],{"xmlns":890},[892,84079,84080,84112],{},[895,84081,84082,84084,84086,84088,84100],{},[898,84083,1724],{},[1726,84085,1728],{},[2133,84087,2860],{},[2128,84089,84090,84092],{},[898,84091,9779],{},[895,84093,84094,84096,84098],{},[2133,84095,2281],{},[898,84097,4661],{"mathvariant":2377},[2133,84099,2135],{},[2128,84101,84102,84104],{},[898,84103,9784],{},[895,84105,84106,84108,84110],{},[2133,84107,2281],{},[898,84109,4661],{"mathvariant":2377},[2133,84111,2135],{},[902,84113,84114],{"encoding":904},"Q = 10 L^{1\u002F2} K^{1\u002F2}",". (a) Vypočtěte produkci pro ",[883,84117,84119],{"className":84118},[886],[888,84120,84121],{"xmlns":890},[892,84122,84123,84131],{},[895,84124,84125,84127,84129],{},[898,84126,9779],{},[1726,84128,1728],{},[2133,84130,20123],{},[902,84132,84133],{"encoding":904},"L = 400",[883,84135,84137],{"className":84136},[886],[888,84138,84139],{"xmlns":890},[892,84140,84141,84150],{},[895,84142,84143,84145,84147],{},[898,84144,9784],{},[1726,84146,1728],{},[2133,84148,84149],{},"17576",[902,84151,84152],{"encoding":904},"K = 17576",". (b) Rozhodněte o tom, jaké výnosy z rozsahu představuje a vyložte, jak se změní produkce, jestliže se vstupy ",[883,84155,84157],{"className":84156},[886],[888,84158,84159],{"xmlns":890},[892,84160,84161,84169],{},[895,84162,84163,84165,84167],{},[898,84164,9779],{},[1726,84166,1742],{"separator":1741},[898,84168,9784],{},[902,84170,78965],{"encoding":904}," zdvojnásobí.",[724,84173,84174,84177,84178,84115,84209,1343,84227,69564,84245,84275,84276,84306,84307,2684,84320,84334,84335,2684,84348,84361],{},[38,84175,84176],{},"5.8"," V jedné empirické studii (40. léta 20. století) ze sektoru manufaktur odhadli Cobb a Douglas produkci ze zjištěných údajů ve tvaru ",[883,84179,84181],{"className":84180},[886],[888,84182,84183],{"xmlns":890},[892,84184,84185,84206],{},[895,84186,84187,84189,84191,84194,84200],{},[898,84188,1724],{},[1726,84190,1728],{},[2133,84192,84193],{},"1,01",[2128,84195,84196,84198],{},[898,84197,9779],{},[2133,84199,23711],{},[2128,84201,84202,84204],{},[898,84203,9784],{},[2133,84205,23770],{},[902,84207,84208],{"encoding":904},"Q = 1{,}01 L^{0{,}75} K^{0{,}25}",[883,84210,84212],{"className":84211},[886],[888,84213,84214],{"xmlns":890},[892,84215,84216,84224],{},[895,84217,84218,84220,84222],{},[898,84219,9779],{},[1726,84221,1728],{},[2133,84223,30724],{},[902,84225,84226],{"encoding":904},"L = 250",[883,84228,84230],{"className":84229},[886],[888,84231,84232],{"xmlns":890},[892,84233,84234,84242],{},[895,84235,84236,84238,84240],{},[898,84237,9784],{},[1726,84239,1728],{},[2133,84241,2780],{},[902,84243,84244],{"encoding":904},"K = 1000",[883,84246,84248],{"className":84247},[886],[888,84249,84250],{"xmlns":890},[892,84251,84252,84272],{},[895,84253,84254,84256,84262,84264,84266,84268,84270],{},[898,84255,2815],{},[2275,84257,84258,84260],{},[898,84259,1738],{},[898,84261,9779],{},[1726,84263,1735],{"stretchy":1734},[2133,84265,30724],{},[1726,84267,1742],{"separator":1741},[2133,84269,2780],{},[1726,84271,1762],{"stretchy":1734},[902,84273,84274],{"encoding":904},"MP_L(250, 1000)"," a výsledek ekonomicky interpretujte. (c) Vypočtěte ",[883,84277,84279],{"className":84278},[886],[888,84280,84281],{"xmlns":890},[892,84282,84283,84303],{},[895,84284,84285,84287,84293,84295,84297,84299,84301],{},[898,84286,2815],{},[2275,84288,84289,84291],{},[898,84290,1738],{},[898,84292,9784],{},[1726,84294,1735],{"stretchy":1734},[2133,84296,30724],{},[1726,84298,1742],{"separator":1741},[2133,84300,2780],{},[1726,84302,1762],{"stretchy":1734},[902,84304,84305],{"encoding":904},"MP_K(250, 1000)"," a výsledek ekonomicky interpretujte. (d) Odhadněte změnu produkce v důsledku zvýšení ",[883,84308,84310],{"className":84309},[886],[888,84311,84312],{"xmlns":890},[892,84313,84314,84318],{},[895,84315,84316],{},[898,84317,9779],{},[902,84319,9779],{"encoding":904},[883,84321,84323],{"className":84322},[886],[888,84324,84325],{"xmlns":890},[892,84326,84327,84332],{},[895,84328,84329],{},[2133,84330,84331],{},"260",[902,84333,84331],{"encoding":904}," a současném poklesu ",[883,84336,84338],{"className":84337},[886],[888,84339,84340],{"xmlns":890},[892,84341,84342,84346],{},[895,84343,84344],{},[898,84345,9784],{},[902,84347,9784],{"encoding":904},[883,84349,84351],{"className":84350},[886],[888,84352,84353],{"xmlns":890},[892,84354,84355,84359],{},[895,84356,84357],{},[2133,84358,15177],{},[902,84360,15177],{"encoding":904}," vzhledem k hladině dle (a) a porovnejte se skutečnou změnou produkce.",[724,84363,84364,84367,84368,1888],{},[38,84365,84366],{},"5.9"," Ověřte platnost zákona klesajících výnosů pro produkci ",[883,84369,84371],{"className":84370},[886],[888,84372,84373],{"xmlns":890},[892,84374,84375,84395],{},[895,84376,84377,84379,84381,84383,84389],{},[898,84378,1724],{},[1726,84380,1728],{},[2133,84382,2860],{},[2128,84384,84385,84387],{},[898,84386,9779],{},[2133,84388,68191],{},[2128,84390,84391,84393],{},[898,84392,9784],{},[2133,84394,4996],{},[902,84396,84397],{"encoding":904},"Q = 10 L^{0{,}3} K^{0{,}5}",[724,84399,84400,84403,84404,80561,84427,10378,84440,10009,84490,1847],{},[38,84401,84402],{},"5.10"," Dokažte, že pro homogenní funkci ",[883,84405,84407],{"className":84406},[886],[888,84408,84409],{"xmlns":890},[892,84410,84411,84425],{},[895,84412,84413,84415,84417,84419,84421,84423],{},[898,84414,1724],{},[1726,84416,1735],{"stretchy":1734},[898,84418,9779],{},[1726,84420,1742],{"separator":1741},[898,84422,9784],{},[1726,84424,1762],{"stretchy":1734},[902,84426,9981],{"encoding":904},[883,84428,84430],{"className":84429},[886],[888,84431,84432],{"xmlns":890},[892,84433,84434,84438],{},[895,84435,84436],{},[898,84437,36841],{},[902,84439,36841],{"encoding":904},[883,84441,84443],{"className":84442},[886],[888,84444,84445],{"xmlns":890},[892,84446,84447,84487],{},[895,84448,84449,84451,84459,84461,84463,84471,84473,84475,84477,84479,84481,84483,84485],{},[898,84450,9779],{},[9151,84452,84453,84455,84457],{},[898,84454,1724],{},[898,84456,9779],{},[1726,84458,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,84460,2099],{},[898,84462,9784],{},[9151,84464,84465,84467,84469],{},[898,84466,1724],{},[898,84468,9784],{},[1726,84470,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,84472,1728],{},[898,84474,36841],{},[898,84476,1724],{},[1726,84478,1735],{"stretchy":1734},[898,84480,9779],{},[1726,84482,1742],{"separator":1741},[898,84484,9784],{},[1726,84486,1762],{"stretchy":1734},[902,84488,84489],{"encoding":904},"L Q'_L + K Q'_K = n Q(L, K)",[614,84491,80536],{},[724,84493,84494,84497],{},[38,84495,84496],{},"5.11"," Ověřte platnost Eulerovy věty (úloha 5.10) pro Cobb-Douglasovu produkční funkci.",[724,84499,84500,83440,84503,84543,84544,1343,84566,1343,84588,84610],{},[38,84501,84502],{},"5.12",[883,84504,84506],{"className":84505},[886],[888,84507,84508],{"xmlns":890},[892,84509,84510,84540],{},[895,84511,84512,84514,84516,84528],{},[898,84513,1724],{},[1726,84515,1728],{},[2128,84517,84518,84520],{},[898,84519,9779],{},[895,84521,84522,84524,84526],{},[2133,84523,2281],{},[898,84525,4661],{"mathvariant":2377},[2133,84527,2177],{},[2128,84529,84530,84532],{},[898,84531,9784],{},[895,84533,84534,84536,84538],{},[2133,84535,2281],{},[898,84537,4661],{"mathvariant":2377},[2133,84539,2352],{},[902,84541,84542],{"encoding":904},"Q = L^{1\u002F3} K^{1\u002F4}",". (a) Najděte rovnici izokvant. (b) Najděte rovnici izokvant pro produkci ",[883,84545,84547],{"className":84546},[886],[888,84548,84549],{"xmlns":890},[892,84550,84551,84563],{},[895,84552,84553,84559,84561],{},[2275,84554,84555,84557],{},[898,84556,80777],{},[2133,84558,2328],{},[1726,84560,1728],{},[2133,84562,2281],{},[902,84564,84565],{"encoding":904},"q_0 = 1",[883,84567,84569],{"className":84568},[886],[888,84570,84571],{"xmlns":890},[892,84572,84573,84585],{},[895,84574,84575,84581,84583],{},[2275,84576,84577,84579],{},[898,84578,80777],{},[2133,84580,2281],{},[1726,84582,1728],{},[2133,84584,2135],{},[902,84586,84587],{"encoding":904},"q_1 = 2",[883,84589,84591],{"className":84590},[886],[888,84592,84593],{"xmlns":890},[892,84594,84595,84607],{},[895,84596,84597,84603,84605],{},[2275,84598,84599,84601],{},[898,84600,80777],{},[2133,84602,2135],{},[1726,84604,1728],{},[2133,84606,2177],{},[902,84608,84609],{"encoding":904},"q_2 = 3",". (c) Načrtněte izokvanty.",[724,84612,84613,83440,84616,84656,84657,1343,84685,1343,84713,1343,84741,1343,84770,1343,84799,1343,84828,1343,84857,1343,84886,1888],{},[38,84614,84615],{},"5.13",[883,84617,84619],{"className":84618},[886],[888,84620,84621],{"xmlns":890},[892,84622,84623,84653],{},[895,84624,84625,84627,84629,84641],{},[898,84626,1724],{},[1726,84628,1728],{},[2128,84630,84631,84633],{},[898,84632,9779],{},[895,84634,84635,84637,84639],{},[2133,84636,2281],{},[898,84638,4661],{"mathvariant":2377},[2133,84640,2177],{},[2128,84642,84643,84645],{},[898,84644,9784],{},[895,84646,84647,84649,84651],{},[2133,84648,2281],{},[898,84650,4661],{"mathvariant":2377},[2133,84652,2135],{},[902,84654,84655],{"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): ",[883,84658,84660],{"className":84659},[886],[888,84661,84662],{"xmlns":890},[892,84663,84664,84682],{},[895,84665,84666,84672,84674,84676,84678,84680],{},[2275,84667,84668,84670],{},[898,84669,4243],{},[2133,84671,2281],{},[1726,84673,2487],{"stretchy":1734},[2133,84675,2281],{},[1726,84677,8411],{"separator":1741},[2133,84679,2281],{},[1726,84681,2502],{"stretchy":1734},[902,84683,84684],{"encoding":904},"A_1[1; 1]",[883,84686,84688],{"className":84687},[886],[888,84689,84690],{"xmlns":890},[892,84691,84692,84710],{},[895,84693,84694,84700,84702,84704,84706,84708],{},[2275,84695,84696,84698],{},[898,84697,4243],{},[2133,84699,2135],{},[1726,84701,2487],{"stretchy":1734},[2133,84703,2281],{},[1726,84705,8411],{"separator":1741},[2133,84707,5572],{},[1726,84709,2502],{"stretchy":1734},[902,84711,84712],{"encoding":904},"A_2[1; 8]",[883,84714,84716],{"className":84715},[886],[888,84717,84718],{"xmlns":890},[892,84719,84720,84738],{},[895,84721,84722,84728,84730,84732,84734,84736],{},[2275,84723,84724,84726],{},[898,84725,4243],{},[2133,84727,2177],{},[1726,84729,2487],{"stretchy":1734},[2133,84731,2281],{},[1726,84733,8411],{"separator":1741},[2133,84735,66577],{},[1726,84737,2502],{"stretchy":1734},[902,84739,84740],{"encoding":904},"A_3[1; 27]",[883,84742,84744],{"className":84743},[886],[888,84745,84746],{"xmlns":890},[892,84747,84748,84767],{},[895,84749,84750,84756,84758,84760,84762,84765],{},[2275,84751,84752,84754],{},[898,84753,4243],{},[2133,84755,2352],{},[1726,84757,2487],{"stretchy":1734},[2133,84759,2135],{},[1726,84761,8411],{"separator":1741},[2133,84763,84764],{},"0,353",[1726,84766,2502],{"stretchy":1734},[902,84768,84769],{"encoding":904},"A_4[2; 0{,}353]",[883,84771,84773],{"className":84772},[886],[888,84774,84775],{"xmlns":890},[892,84776,84777,84796],{},[895,84778,84779,84785,84787,84789,84791,84794],{},[2275,84780,84781,84783],{},[898,84782,4243],{},[2133,84784,2231],{},[1726,84786,2487],{"stretchy":1734},[2133,84788,2135],{},[1726,84790,8411],{"separator":1741},[2133,84792,84793],{},"2,828",[1726,84795,2502],{"stretchy":1734},[902,84797,84798],{"encoding":904},"A_5[2; 2{,}828]",[883,84800,84802],{"className":84801},[886],[888,84803,84804],{"xmlns":890},[892,84805,84806,84825],{},[895,84807,84808,84814,84816,84818,84820,84823],{},[2275,84809,84810,84812],{},[898,84811,4243],{},[2133,84813,2238],{},[1726,84815,2487],{"stretchy":1734},[2133,84817,2135],{},[1726,84819,8411],{"separator":1741},[2133,84821,84822],{},"9,545",[1726,84824,2502],{"stretchy":1734},[902,84826,84827],{"encoding":904},"A_6[2; 9{,}545]",[883,84829,84831],{"className":84830},[886],[888,84832,84833],{"xmlns":890},[892,84834,84835,84854],{},[895,84836,84837,84843,84845,84847,84849,84852],{},[2275,84838,84839,84841],{},[898,84840,4243],{},[2133,84842,24182],{},[1726,84844,2487],{"stretchy":1734},[2133,84846,64539],{},[1726,84848,8411],{"separator":1741},[2133,84850,84851],{},"0,544",[1726,84853,2502],{"stretchy":1734},[902,84855,84856],{"encoding":904},"A_7[1{,}5; 0{,}544]",[883,84858,84860],{"className":84859},[886],[888,84861,84862],{"xmlns":890},[892,84863,84864,84883],{},[895,84865,84866,84872,84874,84876,84878,84881],{},[2275,84867,84868,84870],{},[898,84869,4243],{},[2133,84871,5572],{},[1726,84873,2487],{"stretchy":1734},[2133,84875,64539],{},[1726,84877,8411],{"separator":1741},[2133,84879,84880],{},"14,696",[1726,84882,2502],{"stretchy":1734},[902,84884,84885],{"encoding":904},"A_8[1{,}5; 14{,}696]",[883,84887,84889],{"className":84888},[886],[888,84890,84891],{"xmlns":890},[892,84892,84893,84911],{},[895,84894,84895,84901,84903,84905,84907,84909],{},[2275,84896,84897,84899],{},[898,84898,4243],{},[2133,84900,3989],{},[1726,84902,2487],{"stretchy":1734},[2133,84904,2135],{},[1726,84906,8411],{"separator":1741},[2133,84908,2231],{},[1726,84910,2502],{"stretchy":1734},[902,84912,84913],{"encoding":904},"A_9[2; 5]",[724,84915,84916,84919],{},[38,84917,84918],{},"5.14"," Dokažte, že izokvanty Cobb-Douglasovy produkční funkce jsou klesající a konvexní.",[724,84921,84922,84925,84926,84956,84957,84970,84971,84984,84985,69297,85004,85023,85024,1888],{},[38,84923,84924],{},"5.15"," Produkce firmy je dána vztahem ",[883,84927,84929],{"className":84928},[886],[888,84930,84931],{"xmlns":890},[892,84932,84933,84953],{},[895,84934,84935,84937,84939,84941,84947],{},[898,84936,1724],{},[1726,84938,1728],{},[2133,84940,2135],{},[2128,84942,84943,84945],{},[898,84944,9779],{},[2133,84946,4996],{},[2128,84948,84949,84951],{},[898,84950,9784],{},[2133,84952,23770],{},[902,84954,84955],{"encoding":904},"Q = 2 L^{0{,}5} K^{0{,}25}",". (a) Vypočtěte produkci, mezní produkt práce a mezní produkt kapitálu, zaměstnává-li firma ",[883,84958,84960],{"className":84959},[886],[888,84961,84962],{"xmlns":890},[892,84963,84964,84968],{},[895,84965,84966],{},[2133,84967,3087],{},[902,84969,3087],{"encoding":904}," pracovníků a disponuje-li ",[883,84972,84974],{"className":84973},[886],[888,84975,84976],{"xmlns":890},[892,84977,84978,84982],{},[895,84979,84980],{},[2133,84981,64415],{},[902,84983,64415],{"encoding":904}," jednotkami kapitálu. (b) Určete mezní míru technické substituce ",[883,84986,84988],{"className":84987},[886],[888,84989,84990],{"xmlns":890},[892,84991,84992,85002],{},[895,84993,84994,84996,84998,85000],{},[898,84995,2815],{},[898,84997,3984],{},[898,84999,2772],{},[898,85001,8659],{},[902,85003,10583],{"encoding":904},[883,85005,85007],{"className":85006},[886],[888,85008,85009],{"xmlns":890},[892,85010,85011,85021],{},[895,85012,85013,85015,85017,85019],{},[898,85014,2815],{},[898,85016,3984],{},[898,85018,2772],{},[898,85020,8659],{},[902,85022,10583],{"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 ",[883,85025,85027],{"className":85026},[886],[888,85028,85029],{"xmlns":890},[892,85030,85031,85036],{},[895,85032,85033],{},[2133,85034,85035],{},"95",[902,85037,85035],{"encoding":904},[724,85039,85040,83440,85043,70971,85075,85094,85095,85108,85109,85122,85123,85136],{},[38,85041,85042],{},"5.16",[883,85044,85046],{"className":85045},[886],[888,85047,85048],{"xmlns":890},[892,85049,85050,85072],{},[895,85051,85052,85054,85056,85062,85064,85066],{},[898,85053,1724],{},[1726,85055,1728],{},[2128,85057,85058,85060],{},[898,85059,9784],{},[2133,85061,2135],{},[1726,85063,2099],{},[2133,85065,2135],{},[2128,85067,85068,85070],{},[898,85069,9779],{},[2133,85071,2135],{},[902,85073,85074],{"encoding":904},"Q = K^{2} + 2 L^{2}",[883,85076,85078],{"className":85077},[886],[888,85079,85080],{"xmlns":890},[892,85081,85082,85092],{},[895,85083,85084,85086,85088,85090],{},[898,85085,2815],{},[898,85087,3984],{},[898,85089,2772],{},[898,85091,8659],{},[902,85093,10583],{"encoding":904},". (b) Odhadněte změnu práce potřebné k udržení produkce, která je realizována ",[883,85096,85098],{"className":85097},[886],[888,85099,85100],{"xmlns":890},[892,85101,85102,85106],{},[895,85103,85104],{},[2133,85105,3117],{},[902,85107,3117],{"encoding":904}," pracovníky a ",[883,85110,85112],{"className":85111},[886],[888,85113,85114],{"xmlns":890},[892,85115,85116,85120],{},[895,85117,85118],{},[2133,85119,77597],{},[902,85121,77597],{"encoding":904}," jednotkami kapitálu, jestliže se kapitál sníží na ",[883,85124,85126],{"className":85125},[886],[888,85127,85128],{"xmlns":890},[892,85129,85130,85134],{},[895,85131,85132],{},[2133,85133,46684],{},[902,85135,46684],{"encoding":904}," jednotek.",[724,85138,85139,85142,85143,10378,85173,1888],{},[38,85140,85141],{},"5.17"," Odvoďte, že pro Cobb-Douglasovu produkční funkci ",[883,85144,85146],{"className":85145},[886],[888,85147,85148],{"xmlns":890},[892,85149,85150,85170],{},[895,85151,85152,85154,85156,85158,85164],{},[898,85153,1724],{},[1726,85155,1728],{},[898,85157,4243],{},[2128,85159,85160,85162],{},[898,85161,9779],{},[898,85163,207],{},[2128,85165,85166,85168],{},[898,85167,9784],{},[898,85169,2102],{},[902,85171,85172],{"encoding":904},"Q = A L^{a} K^{b}",[883,85174,85176],{"className":85175},[886],[888,85177,85178],{"xmlns":890},[892,85179,85180,85210],{},[895,85181,85182,85184,85186,85188,85190,85192,85200,85202],{},[898,85183,2815],{},[898,85185,3984],{},[898,85187,2772],{},[898,85189,8659],{},[1726,85191,1728],{},[2326,85193,85194],{"scriptlevel":2328,"displaystyle":1734},[2330,85195,85196,85198],{},[898,85197,207],{},[898,85199,2102],{},[1726,85201,3174],{},[2326,85203,85204],{"scriptlevel":2328,"displaystyle":1734},[2330,85205,85206,85208],{},[898,85207,9784],{},[898,85209,9779],{},[902,85211,85212],{"encoding":904},"MRTS = \\tfrac{a}{b}\\cdot \\tfrac{K}{L}",[115,85214,1670],{"id":1669},[120,85216,85217,85250,85277,85286,85336,85367,85420,85443,85498,85571,85649,85692,85724,85757,85798,85870,85931,85997,86014,86087,86153,86205,86261,86295,86338],{},[123,85218,85219,85222,85223,36877,85236,85249],{},[38,85220,85221],{},"Faktory (vstupy) produkce:"," práce ",[883,85224,85226],{"className":85225},[886],[888,85227,85228],{"xmlns":890},[892,85229,85230,85234],{},[895,85231,85232],{},[898,85233,9779],{},[902,85235,9779],{"encoding":904},[883,85237,85239],{"className":85238},[886],[888,85240,85241],{"xmlns":890},[892,85242,85243,85247],{},[895,85244,85245],{},[898,85246,9784],{},[902,85248,9784],{"encoding":904},", půda.",[123,85251,85252,1696,85254,1888],{},[38,85253,40432],{},[883,85255,85257],{"className":85256},[886],[888,85258,85259],{"xmlns":890},[892,85260,85261,85275],{},[895,85262,85263,85265,85267,85269,85271,85273],{},[898,85264,1724],{},[1726,85266,1728],{},[898,85268,1724],{},[1726,85270,1735],{"stretchy":1734},[898,85272,9779],{},[1726,85274,1762],{"stretchy":1734},[902,85276,74524],{"encoding":904},[123,85278,85279,10009,85281,12114,85284,1888],{},[38,85280,859],{},[614,85282,85283],{},"production function",[38,85285,75027],{},[123,85287,85288,1777,85290,1888],{},[38,85289,75073],{},[883,85291,85293],{"className":85292},[886],[888,85294,85295],{"xmlns":890},[892,85296,85297,85333],{},[895,85298,85299,85301,85307,85309,85311,85313,85315,85317,85319,85321,85327,85329,85331],{},[898,85300,2815],{},[2275,85302,85303,85305],{},[898,85304,1738],{},[898,85306,9779],{},[1726,85308,1728],{},[898,85310,2198],{},[898,85312,1724],{},[898,85314,4661],{"mathvariant":2377},[898,85316,2198],{},[898,85318,9779],{},[1726,85320,1728],{},[2128,85322,85323,85325],{},[898,85324,1724],{},[1726,85326,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,85328,1735],{"stretchy":1734},[898,85330,9779],{},[1726,85332,1762],{"stretchy":1734},[902,85334,85335],{"encoding":904},"MP_L = dQ\u002FdL = Q'(L)",[123,85337,85338,1777,85340,1888],{},[38,85339,76008],{},[883,85341,85343],{"className":85342},[886],[888,85344,85345],{"xmlns":890},[892,85346,85347,85365],{},[895,85348,85349,85351,85357,85359,85361,85363],{},[898,85350,4243],{},[2275,85352,85353,85355],{},[898,85354,1738],{},[898,85356,9779],{},[1726,85358,1728],{},[898,85360,1724],{},[898,85362,4661],{"mathvariant":2377},[898,85364,9779],{},[902,85366,74592],{"encoding":904},[123,85368,85369,85371,85372,10378,85389,1888],{},[38,85370,75495],{}," — od určitého ",[883,85373,85375],{"className":85374},[886],[888,85376,85377],{"xmlns":890},[892,85378,85379,85387],{},[895,85380,85381],{},[2275,85382,85383,85385],{},[898,85384,9779],{},[2133,85386,2328],{},[902,85388,75538],{"encoding":904},[883,85390,85392],{"className":85391},[886],[888,85393,85394],{"xmlns":890},[892,85395,85396,85418],{},[895,85397,85398,85408,85410,85412,85414,85416],{},[2128,85399,85400,85402],{},[898,85401,1724],{},[895,85403,85404,85406],{},[1726,85405,2379],{"mathvariant":2377},[1726,85407,2379],{"mathvariant":2377},[1726,85409,1735],{"stretchy":1734},[898,85411,9779],{},[1726,85413,1762],{"stretchy":1734},[1726,85415,3444],{},[2133,85417,2328],{},[902,85419,75684],{"encoding":904},[123,85421,85422,1777,85425,85442],{},[38,85423,85424],{},"Inflexní bod",[883,85426,85428],{"className":85427},[886],[888,85429,85430],{"xmlns":890},[892,85431,85432,85440],{},[895,85433,85434],{},[2275,85435,85436,85438],{},[898,85437,9779],{},[2133,85439,2328],{},[902,85441,75538],{"encoding":904}," — přechod z konvexity do konkavity.",[123,85444,85445,1777,85448,1696,85465,1888],{},[38,85446,85447],{},"Bod maxima produkce",[883,85449,85451],{"className":85450},[886],[888,85452,85453],{"xmlns":890},[892,85454,85455,85463],{},[895,85456,85457],{},[2275,85458,85459,85461],{},[898,85460,9779],{},[2133,85462,2281],{},[902,85464,13198],{"encoding":904},[883,85466,85468],{"className":85467},[886],[888,85469,85470],{"xmlns":890},[892,85471,85472,85496],{},[895,85473,85474,85476,85482,85484,85490,85492,85494],{},[898,85475,2815],{},[2275,85477,85478,85480],{},[898,85479,1738],{},[898,85481,9779],{},[1726,85483,1735],{"stretchy":1734},[2275,85485,85486,85488],{},[898,85487,9779],{},[2133,85489,2281],{},[1726,85491,1762],{"stretchy":1734},[1726,85493,1728],{},[2133,85495,2328],{},[902,85497,75757],{"encoding":904},[123,85499,85500,85522,85523,10378,85542,1888],{},[38,85501,85502,85503],{},"Princip maximalizace ",[883,85504,85506],{"className":85505},[886],[888,85507,85508],{"xmlns":890},[892,85509,85510,85520],{},[895,85511,85512,85514],{},[898,85513,4243],{},[2275,85515,85516,85518],{},[898,85517,1738],{},[898,85519,9779],{},[902,85521,74613],{"encoding":904}," — v bodě maxima ",[883,85524,85526],{"className":85525},[886],[888,85527,85528],{"xmlns":890},[892,85529,85530,85540],{},[895,85531,85532,85534],{},[898,85533,4243],{},[2275,85535,85536,85538],{},[898,85537,1738],{},[898,85539,9779],{},[902,85541,74613],{"encoding":904},[883,85543,85545],{"className":85544},[886],[888,85546,85547],{"xmlns":890},[892,85548,85549,85569],{},[895,85550,85551,85553,85559,85561,85563],{},[898,85552,2815],{},[2275,85554,85555,85557],{},[898,85556,1738],{},[898,85558,9779],{},[1726,85560,1728],{},[898,85562,4243],{},[2275,85564,85565,85567],{},[898,85566,1738],{},[898,85568,9779],{},[902,85570,74643],{"encoding":904},[123,85572,85573,1777,85576,1343,85615,1343,85632,1888],{},[38,85574,85575],{},"Polynomiální produkční funkce",[883,85577,85579],{"className":85578},[886],[888,85580,85581],{"xmlns":890},[892,85582,85583,85613],{},[895,85584,85585,85587,85589,85591,85593,85595,85597,85603,85605,85607],{},[898,85586,1724],{},[1726,85588,1735],{"stretchy":1734},[898,85590,9779],{},[1726,85592,1762],{"stretchy":1734},[1726,85594,1728],{},[898,85596,207],{},[2128,85598,85599,85601],{},[898,85600,9779],{},[2133,85602,2177],{},[1726,85604,2099],{},[898,85606,2102],{},[2128,85608,85609,85611],{},[898,85610,9779],{},[2133,85612,2135],{},[902,85614,75875],{"encoding":904},[883,85616,85618],{"className":85617},[886],[888,85619,85620],{"xmlns":890},[892,85621,85622,85630],{},[895,85623,85624,85626,85628],{},[898,85625,207],{},[1726,85627,3444],{},[2133,85629,2328],{},[902,85631,43066],{"encoding":904},[883,85633,85635],{"className":85634},[886],[888,85636,85637],{"xmlns":890},[892,85638,85639,85647],{},[895,85640,85641,85643,85645],{},[898,85642,2102],{},[1726,85644,3405],{},[2133,85646,2328],{},[902,85648,18795],{"encoding":904},[123,85650,85651,1777,85654,1888],{},[38,85652,85653],{},"Diferenciál produkce",[883,85655,85657],{"className":85656},[886],[888,85658,85659],{"xmlns":890},[892,85660,85661,85689],{},[895,85662,85663,85665,85667,85669,85671,85673,85675,85677,85683,85685,85687],{},[898,85664,2886],{"mathvariant":2377},[898,85666,1724],{},[1726,85668,1880],{},[898,85670,2198],{},[898,85672,1724],{},[1726,85674,1728],{},[898,85676,2815],{},[2275,85678,85679,85681],{},[898,85680,1738],{},[898,85682,9779],{},[2289,85684,2984],{},[898,85686,2198],{},[898,85688,9779],{},[902,85690,85691],{"encoding":904},"\\Delta Q \\approx dQ = MP_L\\,dL",[123,85693,85694,1696,85696,1888],{},[38,85695,83951],{},[883,85697,85699],{"className":85698},[886],[888,85700,85701],{"xmlns":890},[892,85702,85703,85721],{},[895,85704,85705,85707,85709,85711,85713,85715,85717,85719],{},[898,85706,1724],{},[1726,85708,1728],{},[898,85710,1724],{},[1726,85712,1735],{"stretchy":1734},[898,85714,9779],{},[1726,85716,1742],{"separator":1741},[898,85718,9784],{},[1726,85720,1762],{"stretchy":1734},[902,85722,85723],{"encoding":904},"Q = Q(L, K)",[123,85725,85726,1696,85728,1888],{},[38,85727,78045],{},[883,85729,85731],{"className":85730},[886],[888,85732,85733],{"xmlns":890},[892,85734,85735,85755],{},[895,85736,85737,85739,85741,85743,85749],{},[898,85738,1724],{},[1726,85740,1728],{},[898,85742,4243],{},[2128,85744,85745,85747],{},[898,85746,9779],{},[898,85748,207],{},[2128,85750,85751,85753],{},[898,85752,9784],{},[898,85754,2102],{},[902,85756,74710],{"encoding":904},[123,85758,85759,1696,85762,85797],{},[38,85760,85761],{},"Ryzí Cobb-Douglas",[883,85763,85765],{"className":85764},[886],[888,85766,85767],{"xmlns":890},[892,85768,85769,85795],{},[895,85770,85771,85773,85775,85777,85783],{},[898,85772,1724],{},[1726,85774,1728],{},[898,85776,4243],{},[2128,85778,85779,85781],{},[898,85780,9779],{},[898,85782,207],{},[2128,85784,85785,85787],{},[898,85786,9784],{},[895,85788,85789,85791,85793],{},[2133,85790,2281],{},[1726,85792,2228],{},[898,85794,207],{},[902,85796,78872],{"encoding":904}," (konstantní výnosy).",[123,85799,85800,1696,85802,1888],{},[38,85801,79588],{},[883,85803,85805],{"className":85804},[886],[888,85806,85807],{"xmlns":890},[892,85808,85809,85867],{},[895,85810,85811,85813,85815,85817,85819,85821,85823,85825,85827,85829,85839,85841,85843,85853],{},[898,85812,1724],{},[1726,85814,1728],{},[898,85816,4243],{},[1726,85818,2487],{"stretchy":1734},[1726,85820,1735],{"stretchy":1734},[2133,85822,2281],{},[1726,85824,2228],{},[898,85826,207],{},[1726,85828,1762],{"stretchy":1734},[2128,85830,85831,85833],{},[898,85832,9779],{},[895,85834,85835,85837],{},[1726,85836,2228],{},[898,85838,2102],{},[1726,85840,2099],{},[898,85842,207],{},[2128,85844,85845,85847],{},[898,85846,9784],{},[895,85848,85849,85851],{},[1726,85850,2228],{},[898,85852,2102],{},[2128,85854,85855,85857],{},[1726,85856,2502],{"stretchy":1734},[895,85858,85859,85861,85863,85865],{},[1726,85860,2228],{},[2133,85862,2281],{},[898,85864,4661],{"mathvariant":2377},[898,85866,2102],{},[902,85868,85869],{"encoding":904},"Q = A[(1-a)L^{-b} + aK^{-b}]^{-1\u002Fb}",[123,85871,85872,10009,85875,12114,85897,10009,85900,85930],{},[38,85873,85874],{},"Lineární",[883,85876,85878],{"className":85877},[886],[888,85879,85880],{"xmlns":890},[892,85881,85882,85894],{},[895,85883,85884,85886,85888,85890,85892],{},[898,85885,207],{},[898,85887,9779],{},[1726,85889,2099],{},[898,85891,2102],{},[898,85893,9784],{},[902,85895,85896],{"encoding":904},"aL + bK",[38,85898,85899],{},"Leontiefova",[883,85901,85903],{"className":85902},[886],[888,85904,85905],{"xmlns":890},[892,85906,85907,85927],{},[895,85908,85909,85911,85913,85915,85917,85919,85921,85923,85925],{},[898,85910,79816],{},[1726,85912,56180],{},[1726,85914,1735],{"stretchy":1734},[898,85916,207],{},[898,85918,9779],{},[1726,85920,1742],{"separator":1741},[898,85922,2102],{},[898,85924,9784],{},[1726,85926,1762],{"stretchy":1734},[902,85928,85929],{"encoding":904},"\\min(aL, bK)",") produkční funkce.",[123,85932,85933,1696,85949,1888],{},[38,85934,85935,85936],{},"Homogenita stupně ",[883,85937,85939],{"className":85938},[886],[888,85940,85941],{"xmlns":890},[892,85942,85943,85947],{},[895,85944,85945],{},[898,85946,36841],{},[902,85948,36841],{"encoding":904},[883,85950,85952],{"className":85951},[886],[888,85953,85954],{"xmlns":890},[892,85955,85956,85994],{},[895,85957,85958,85960,85962,85964,85966,85968,85970,85972,85974,85976,85982,85984,85986,85988,85990,85992],{},[898,85959,1724],{},[1726,85961,1735],{"stretchy":1734},[898,85963,12027],{},[898,85965,9779],{},[1726,85967,1742],{"separator":1741},[898,85969,12027],{},[898,85971,9784],{},[1726,85973,1762],{"stretchy":1734},[1726,85975,1728],{},[2128,85977,85978,85980],{},[898,85979,12027],{},[898,85981,36841],{},[898,85983,1724],{},[1726,85985,1735],{"stretchy":1734},[898,85987,9779],{},[1726,85989,1742],{"separator":1741},[898,85991,9784],{},[1726,85993,1762],{"stretchy":1734},[902,85995,85996],{"encoding":904},"Q(rL, rK) = r^n Q(L, K)",[123,85998,85999,78970],{},[38,86000,78903,86001],{},[883,86002,86004],{"className":86003},[886],[888,86005,86006],{"xmlns":890},[892,86007,86008,86012],{},[895,86009,86010],{},[898,86011,4243],{},[902,86013,4243],{"encoding":904},[123,86015,86016,86018,86019,86041,86042,86064,86065,1847],{},[38,86017,78404],{}," — konstantní (",[883,86020,86022],{"className":86021},[886],[888,86023,86024],{"xmlns":890},[892,86025,86026,86038],{},[895,86027,86028,86030,86032,86034,86036],{},[898,86029,207],{},[1726,86031,2099],{},[898,86033,2102],{},[1726,86035,1728],{},[2133,86037,2281],{},[902,86039,86040],{"encoding":904},"a+b=1","), rostoucí (",[883,86043,86045],{"className":86044},[886],[888,86046,86047],{"xmlns":890},[892,86048,86049,86061],{},[895,86050,86051,86053,86055,86057,86059],{},[898,86052,207],{},[1726,86054,2099],{},[898,86056,2102],{},[1726,86058,3405],{},[2133,86060,2281],{},[902,86062,86063],{"encoding":904},"a+b>1","), klesající (",[883,86066,86068],{"className":86067},[886],[888,86069,86070],{"xmlns":890},[892,86071,86072,86084],{},[895,86073,86074,86076,86078,86080,86082],{},[898,86075,207],{},[1726,86077,2099],{},[898,86079,2102],{},[1726,86081,3444],{},[2133,86083,2281],{},[902,86085,86086],{"encoding":904},"a+b\u003C1",[123,86088,86089,1777,86091,1343,86121,1777,86123,1888],{},[38,86090,75073],{},[883,86092,86094],{"className":86093},[886],[888,86095,86096],{"xmlns":890},[892,86097,86098,86118],{},[895,86099,86100,86102,86108,86110],{},[898,86101,2815],{},[2275,86103,86104,86106],{},[898,86105,1738],{},[898,86107,9779],{},[1726,86109,1728],{},[9151,86111,86112,86114,86116],{},[898,86113,1724],{},[898,86115,9779],{},[1726,86117,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[902,86119,86120],{"encoding":904},"MP_L = Q'_L",[38,86122,77977],{},[883,86124,86126],{"className":86125},[886],[888,86127,86128],{"xmlns":890},[892,86129,86130,86150],{},[895,86131,86132,86134,86140,86142],{},[898,86133,2815],{},[2275,86135,86136,86138],{},[898,86137,1738],{},[898,86139,9784],{},[1726,86141,1728],{},[9151,86143,86144,86146,86148],{},[898,86145,1724],{},[898,86147,9784],{},[1726,86149,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[902,86151,86152],{"encoding":904},"MP_K = Q'_K",[123,86154,86155,1777,86157,1888],{},[38,86156,80191],{},[883,86158,86160],{"className":86159},[886],[888,86161,86162],{"xmlns":890},[892,86163,86164,86202],{},[895,86165,86166,86168,86170,86172,86174,86180,86182,86184,86186,86188,86190,86196,86198,86200],{},[898,86167,2198],{},[898,86169,1724],{},[1726,86171,1728],{},[898,86173,2815],{},[2275,86175,86176,86178],{},[898,86177,1738],{},[898,86179,9779],{},[2289,86181,2984],{},[898,86183,2198],{},[898,86185,9779],{},[1726,86187,2099],{},[898,86189,2815],{},[2275,86191,86192,86194],{},[898,86193,1738],{},[898,86195,9784],{},[2289,86197,2984],{},[898,86199,2198],{},[898,86201,9784],{},[902,86203,86204],{"encoding":904},"dQ = MP_L\\,dL + MP_K\\,dK",[123,86206,86207,1696,86209,1888],{},[38,86208,80536],{},[883,86210,86212],{"className":86211},[886],[888,86213,86214],{"xmlns":890},[892,86215,86216,86258],{},[895,86217,86218,86220,86228,86230,86232,86240,86242,86244,86246,86248,86250,86252,86254,86256],{},[898,86219,9779],{},[9151,86221,86222,86224,86226],{},[898,86223,1724],{},[898,86225,9779],{},[1726,86227,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,86229,2099],{},[898,86231,9784],{},[9151,86233,86234,86236,86238],{},[898,86235,1724],{},[898,86237,9784],{},[1726,86239,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,86241,1728],{},[898,86243,36841],{},[2289,86245,2984],{},[898,86247,1724],{},[1726,86249,1735],{"stretchy":1734},[898,86251,9779],{},[1726,86253,1742],{"separator":1741},[898,86255,9784],{},[1726,86257,1762],{"stretchy":1734},[902,86259,86260],{"encoding":904},"L Q'_L + K Q'_K = n\\,Q(L,K)",[123,86262,86263,86266,86267,1888],{},[38,86264,86265],{},"Izokvanta"," — křivka ",[883,86268,86270],{"className":86269},[886],[888,86271,86272],{"xmlns":890},[892,86273,86274,86292],{},[895,86275,86276,86278,86280,86282,86284,86286,86288,86290],{},[898,86277,1724],{},[1726,86279,1735],{"stretchy":1734},[898,86281,9779],{},[1726,86283,1742],{"separator":1741},[898,86285,9784],{},[1726,86287,1762],{"stretchy":1734},[1726,86289,1728],{},[898,86291,80777],{},[902,86293,86294],{"encoding":904},"Q(L, K) = q",[123,86296,86297,1777,86299,1888],{},[38,86298,80966],{},[883,86300,86302],{"className":86301},[886],[888,86303,86304],{"xmlns":890},[892,86305,86306,86336],{},[895,86307,86308,86310,86312,86314,86316,86318,86320,86326,86328,86330],{},[898,86309,2815],{},[898,86311,3984],{},[898,86313,2772],{},[898,86315,8659],{},[1726,86317,1728],{},[898,86319,2815],{},[2275,86321,86322,86324],{},[898,86323,1738],{},[898,86325,9779],{},[898,86327,4661],{"mathvariant":2377},[898,86329,2815],{},[2275,86331,86332,86334],{},[898,86333,1738],{},[898,86335,9784],{},[902,86337,74785],{"encoding":904},[123,86339,86340,1777,86343,1888],{},[38,86341,86342],{},"Substituční vztah",[883,86344,86346],{"className":86345},[886],[888,86347,86348],{"xmlns":890},[892,86349,86350,86374],{},[895,86351,86352,86354,86356,86358,86360,86362,86364,86366,86368,86370,86372],{},[898,86353,2886],{"mathvariant":2377},[898,86355,9784],{},[1726,86357,1880],{},[1726,86359,2228],{},[898,86361,2815],{},[898,86363,3984],{},[898,86365,2772],{},[898,86367,8659],{},[2289,86369,2984],{},[898,86371,2198],{},[898,86373,9779],{},[902,86375,86376],{"encoding":904},"\\Delta K \\approx -MRTS\\,dL",[115,86378,1899],{"id":1898},[120,86380,86381,86478,86485,86492],{},[123,86382,86383,1777,86385,86388,86389,1343,86392,86395,86396,86399,86400,86419,86420,18629,86439,86442,86443,86462,86463,1847],{},[38,86384,50703],{},[207,86386,784],{"className":86387,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace, totální diferenciál), ",[207,86390,2358],{"className":86391,"dataFsResolvedFilePath":764,"href":765},[210],[207,86393,793],{"className":86394,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace produkce s rozpočtovým omezením), ",[207,86397,880],{"className":86398,"dataFsResolvedFilePath":878,"href":879},[210]," (paralela: izokvanty ↔ indiferenční křivky, ",[883,86401,86403],{"className":86402},[886],[888,86404,86405],{"xmlns":890},[892,86406,86407,86417],{},[895,86408,86409,86411,86413,86415],{},[898,86410,2815],{},[898,86412,3984],{},[898,86414,2772],{},[898,86416,8659],{},[902,86418,10583],{"encoding":904}," ↔ ",[883,86421,86423],{"className":86422},[886],[888,86424,86425],{"xmlns":890},[892,86426,86427,86437],{},[895,86428,86429,86431,86433,86435],{},[898,86430,2815],{},[898,86432,3984],{},[898,86434,2775],{},[898,86436,8659],{},[902,86438,10587],{"encoding":904},[207,86440,3815],{"className":86441,"dataFsResolvedFilePath":827,"href":828},[210]," (analogie principu max ",[883,86444,86446],{"className":86445},[886],[888,86447,86448],{"xmlns":890},[892,86449,86450,86460],{},[895,86451,86452,86454],{},[898,86453,4243],{},[2275,86455,86456,86458],{},[898,86457,1738],{},[898,86459,9779],{},[902,86461,74613],{"encoding":904}," ↔ min ",[883,86464,86466],{"className":86465},[886],[888,86467,86468],{"xmlns":890},[892,86469,86470,86476],{},[895,86471,86472,86474],{},[898,86473,4243],{},[898,86475,2775],{},[902,86477,55540],{"encoding":904},[123,86479,86480,1777,86482,1888],{},[38,86481,1906],{},[207,86483,3820],{"className":86484,"dataFsResolvedFilePath":848,"href":849},[210],[123,86486,86487,1777,86489,1888],{},[38,86488,16197],{},[207,86490,1094],{"className":86491,"dataFsResolvedFilePath":838,"href":839},[210],[123,86493,86494,1777,86496,1888],{},[38,86495,16188],{},[207,86497,16192],{"className":86498,"dataFsResolvedFilePath":1640,"href":1641},[210],{"title":641,"searchDepth":642,"depth":642,"links":86500},[86501,86502,86503,86507,86509,86514,86515,86522,86523,86525,86526,86527,86529,86534,86535,86536,86540,86541],{"id":74808,"depth":642,"text":74809},{"id":74945,"depth":642,"text":74946},{"id":75048,"depth":642,"text":86504,"children":86505},"Mezní produkt práce (MPLMP_L)",[86506],{"id":75494,"depth":649,"text":75495},{"id":75983,"depth":642,"text":86508},"Průměrný produkt práce (APLAP_L)",{"id":76101,"depth":642,"text":76102,"children":86510},[86511,86512,86513],{"id":76338,"depth":649,"text":65481},{"id":76649,"depth":649,"text":76650},{"id":77369,"depth":649,"text":77370},{"id":77941,"depth":642,"text":77942},{"id":78044,"depth":642,"text":78045,"children":86516},[86517,86518,86520,86521],{"id":78403,"depth":649,"text":78404},{"id":78902,"depth":649,"text":86519},"Parametr efektivity AA",{"id":78973,"depth":649,"text":78974},{"id":37160,"depth":649,"text":79313},{"id":79500,"depth":642,"text":79501},{"id":79839,"depth":642,"text":86524},"Mezní produkty MPLMP_L, MPKMP_K a totální diferenciál",{"id":80530,"depth":642,"text":80531},{"id":74874,"depth":642,"text":9762},{"id":80941,"depth":642,"text":86528},"Mezní míra technické substituce (MRTSMRTS)",{"id":81807,"depth":642,"text":81808,"children":86530},[86531,86532,86533],{"id":81811,"depth":649,"text":81812},{"id":82454,"depth":649,"text":82455},{"id":82735,"depth":649,"text":82736},{"id":83081,"depth":642,"text":83082},{"id":49862,"depth":642,"text":49863},{"id":83431,"depth":642,"text":83432,"children":86537},[86538,86539],{"id":40431,"depth":649,"text":40432},{"id":83950,"depth":649,"text":83951},{"id":1669,"depth":642,"text":1670},{"id":1898,"depth":642,"text":1899},{},"\u002Ftopics\u002Fprodukce",{"title":74444,"description":641},[1138,1136],"topics\u002Fprodukce",[1128,9797,86548,86549,86550,74874,86551,86552],"produkcni-funkce","mpl-apl","cobb-douglas","mrts","euler","ZO2oG_qVOhQee90SJRry02Lau2bGvK2gaOFbwchTg1Y",{"id":86555,"title":86556,"body":86557,"course":1128,"courses":659,"created":9541,"description":641,"extension":661,"meta":95504,"navigation":664,"path":95505,"seo":95506,"sources":95507,"stem":95508,"tags":95509,"type":1950,"updated":677,"__hash__":95512},"topics\u002Ftopics\u002Fuzitecnost.md","Užitečnost, Cobb-Douglasova funkce užitečnosti a optimalizace spotřebitele",{"type":9,"value":86558,"toc":95478},[86559,86562,86564,86761,86770,86774,86777,86830,86834,86846,86850,86853,86870,86993,86999,87143,87153,87157,87192,87230,87278,87335,87395,87437,88013,88017,88100,88209,88302,88560,88563,88616,88727,88809,88813,88824,89057,89112,89118,89158,89221,89232,89423,89529,89682,89730,89735,89849,89887,90013,90059,90086,90163,90238,90318,90448,90509,90597,90601,90604,90673,90756,90763,90823,91133,91137,91143,91196,91212,91263,91401,91477,91590,91907,91911,91918,92078,92137,92141,92163,92260,92381,92495,92518,92581,92638,92890,92898,92902,92909,93163,93213,93269,93272,93436,93440,93538,93540,93572,93576,93709,93951,94135,94303,94610,94743,94930,94942,94944,95379,95381],[12,86560,86556],{"id":86561},"užitečnost-cobb-douglasova-funkce-užitečnosti-a-optimalizace-spotřebitele",[115,86563,11992],{"id":11991},[724,86565,86566,1777,86568,86599,86600,86603,86604,86634,86635,86653,86654,86694,86695,86698,86699,86712,86713,28234,86716,86729,86730,86743,86744,86757,86758,1888],{},[38,86567,880],{},[883,86569,86571],{"className":86570},[886],[888,86572,86573],{"xmlns":890},[892,86574,86575,86597],{},[895,86576,86577,86579,86581,86587,86589,86595],{},[898,86578,900],{},[1726,86580,1735],{"stretchy":1734},[2275,86582,86583,86585],{},[898,86584,1724],{},[2133,86586,2281],{},[1726,86588,1742],{"separator":1741},[2275,86590,86591,86593],{},[898,86592,1724],{},[2133,86594,2135],{},[1726,86596,1762],{"stretchy":1734},[902,86598,16326],{"encoding":904}," je číselné vyjádření uspokojení spotřebitele ze svazku zboží — v ordinalistickém přístupu slouží jen k ",[38,86601,86602],{},"uspořádání"," svazků (nikoli k měření v jednotkách). Klíčové nástroje jsou mezní užitečnosti ",[883,86605,86607],{"className":86606},[886],[888,86608,86609],{"xmlns":890},[892,86610,86611,86631],{},[895,86612,86613,86615,86621,86623],{},[898,86614,2815],{},[2275,86616,86617,86619],{},[898,86618,900],{},[898,86620,17772],{},[1726,86622,1728],{},[9151,86624,86625,86627,86629],{},[898,86626,900],{},[898,86628,17772],{},[1726,86630,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[902,86632,86633],{"encoding":904},"MU_i = U'_i",", indiferenční křivky ",[883,86636,86638],{"className":86637},[886],[888,86639,86640],{"xmlns":890},[892,86641,86642,86650],{},[895,86643,86644,86646,86648],{},[898,86645,900],{},[1726,86647,1728],{},[898,86649,2146],{},[902,86651,86652],{"encoding":904},"U = c"," a mezní míra komoditní substituce ",[883,86655,86657],{"className":86656},[886],[888,86658,86659],{"xmlns":890},[892,86660,86661,86691],{},[895,86662,86663,86665,86667,86669,86671,86673,86675,86681,86683,86685],{},[898,86664,2815],{},[898,86666,3984],{},[898,86668,2775],{},[898,86670,8659],{},[1726,86672,1728],{},[898,86674,2815],{},[2275,86676,86677,86679],{},[898,86678,900],{},[2133,86680,2281],{},[898,86682,4661],{"mathvariant":2377},[898,86684,2815],{},[2275,86686,86687,86689],{},[898,86688,900],{},[2133,86690,2135],{},[902,86692,86693],{"encoding":904},"MRCS = MU_1\u002FMU_2",". Tato stránka pokrývá ",[38,86696,86697],{},"teorii užitečnosti"," — funkce ",[883,86700,86702],{"className":86701},[886],[888,86703,86704],{"xmlns":890},[892,86705,86706,86710],{},[895,86707,86708],{},[898,86709,900],{},[902,86711,900],{"encoding":904},", její vlastnosti, Cobb-Douglasův tvar, indiferenční křivky a MRCS. ",[38,86714,86715],{},"Optimalizaci spotřebitele",[883,86717,86719],{"className":86718},[886],[888,86720,86721],{"xmlns":890},[892,86722,86723,86727],{},[895,86724,86725],{},[898,86726,900],{},[902,86728,900],{"encoding":904}," při rozpočtu, min ",[883,86731,86733],{"className":86732},[886],[888,86734,86735],{"xmlns":890},[892,86736,86737,86741],{},[895,86738,86739],{},[898,86740,4240],{},[902,86742,4240],{"encoding":904}," při dané ",[883,86745,86747],{"className":86746},[886],[888,86748,86749],{"xmlns":890},[892,86750,86751,86755],{},[895,86752,86753],{},[898,86754,900],{},[902,86756,900],{"encoding":904},", Lagrange, funkce poptávky) viz ",[207,86759,913],{"className":86760,"dataFsResolvedFilePath":911,"href":912},[210],[724,86762,86763,86764,86766,86767,1888],{},"Kapitola 6 knihy ",[614,86765,16192],{}," — model rozhodování spotřebitele. Zde: funkce užitečnosti, indiferenční křivky, mezní míra komoditní substituce. Navazující optimalizace je v ",[207,86768,36735],{"className":86769,"dataFsResolvedFilePath":911,"href":912},[210],[115,86771,86773],{"id":86772},"úvod-cílové-znalosti-kapitoly-6","Úvod — cílové znalosti kapitoly 6",[724,86775,86776],{},"Po prostudování této kapitoly byste měli umět:",[120,86778,86779,86785,86794,86799,86802,86808,86814,86817,86823],{},[123,86780,86781,86782,1742],{},"vyložit, co se rozumí termínem ",[38,86783,86784],{},"užitečnost",[123,86786,86787,86788,3877,86791,1742],{},"definovat pojmy ",[38,86789,86790],{},"svazek zboží",[38,86792,86793],{},"funkce užitečnosti",[123,86795,74823,86796,74830],{},[38,86797,86798],{},"mezní užitečnosti",[123,86800,86801],{},"vyjmenovat základní vlastnosti funkcí užitečnosti,",[123,86803,74850,86804,86807],{},[38,86805,86806],{},"Cobb-Douglasových"," funkcí užitečnosti,",[123,86809,74871,86810,86813],{},[38,86811,86812],{},"křivky užitečnosti"," (indiferenční křivky),",[123,86815,86816],{},"vyjmenovat jejich základní vlastnosti,",[123,86818,74823,86819,86822],{},[38,86820,86821],{},"mezní míru komoditní substituce"," a ekonomicky ji interpretovat,",[123,86824,86825,86826,86829],{},"řešit ",[38,86827,86828],{},"optimalizační úlohy"," s ohledem na užitečnost.",[115,86831,86833],{"id":86832},"_61-pojetí-užitečnosti","6.1 Pojetí užitečnosti",[724,86835,86836,86837,86841,86842,86845],{},"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 ",[207,86838,86840],{"className":86839,"dataFsResolvedFilePath":800,"href":801},[210],"poptávku",". Centrálním pojmem je ",[38,86843,86844],{},"užitečnost (utility)"," — vše, co vede spotřebitele k nákupu zboží (uspokojení, potěšení, splnění přání, pohodlí).",[198,86847,86849],{"id":86848},"kardinalistický-vs-ordinalistický-přístup","Kardinalistický vs. ordinalistický přístup",[724,86851,86852],{},"Historicky se vyvíjela dvě pojetí „měření\" užitečnosti:",[120,86854,86855,86861],{},[123,86856,86857,86860],{},[38,86858,86859],{},"Kardinalistický přístup"," (19. století — Gossen, Jevons, Walras): užitečnost měřena kvantitativně (např. peněžními jednotkami). Tento přístup se ukázal být nevýhodný.",[123,86862,86863,86866,86867,86869],{},[38,86864,86865],{},"Ordinalistický přístup"," (v současnosti preferovaný): postačuje ",[38,86868,86602],{}," svazků zboží podle preferencí; kvantitativní číselné hodnocení užitečnosti se nepožaduje.",[3859,86871,86872],{},[724,86873,86874,86876,86877,86880,86881,1777,86894,86897,86898,3877,86911,86930,86931,1343,86957,86984,86985,86988,86989,86992],{},[883,86875,4400],{}," Pozor — ordinalisté užitečnost ",[38,86878,86879],{},"neměří","\nV ordinalistickém přístupu hodnoty funkce ",[883,86882,86884],{"className":86883},[886],[888,86885,86886],{"xmlns":890},[892,86887,86888,86892],{},[895,86889,86890],{},[898,86891,900],{},[902,86893,900],{"encoding":904},[38,86895,86896],{},"nemají samostatný ekonomický význam"," — slouží pouze k uspořádání svazků. Dvě funkce ",[883,86899,86901],{"className":86900},[886],[888,86902,86903],{"xmlns":890},[892,86904,86905,86909],{},[895,86906,86907],{},[898,86908,900],{},[902,86910,900],{"encoding":904},[883,86912,86914],{"className":86913},[886],[888,86915,86916],{"xmlns":890},[892,86917,86918,86927],{},[895,86919,86920],{},[8372,86921,86922,86924],{"accent":1741},[898,86923,900],{},[1726,86925,86926],{},"~",[902,86928,86929],{"encoding":904},"\\tilde U"," reprezentují tytéž preference, jsou-li navzájem monotónní transformací (např. ",[883,86932,86934],{"className":86933},[886],[888,86935,86936],{"xmlns":890},[892,86937,86938,86954],{},[895,86939,86940,86946,86948],{},[8372,86941,86942,86944],{"accent":1741},[898,86943,900],{},[1726,86945,86926],{},[1726,86947,1728],{},[2128,86949,86950,86952],{},[898,86951,900],{},[2133,86953,2135],{},[902,86955,86956],{"encoding":904},"\\tilde U = U^2",[883,86958,86960],{"className":86959},[886],[888,86961,86962],{"xmlns":890},[892,86963,86964,86981],{},[895,86965,86966,86972,86974,86977,86979],{},[8372,86967,86968,86970],{"accent":1741},[898,86969,900],{},[1726,86971,86926],{},[1726,86973,1728],{},[898,86975,86976],{},"ln",[1726,86978,56180],{},[898,86980,900],{},[902,86982,86983],{"encoding":904},"\\tilde U = \\ln U","). Výroky typu „užitečnost je 250 jednotek\" proto samy o sobě nic neříkají — smysl mají jen ",[38,86986,86987],{},"porovnání"," mezi svazky a ",[38,86990,86991],{},"poměry"," mezních veličin.",[724,86994,86995,86996,2703],{},"Ordinalistický přístup vychází z ",[38,86997,86998],{},"pěti hlavních předpokladů",[152,87000,87001,87007,87013,87131,87137],{},[123,87002,87003,87006],{},[38,87004,87005],{},"Racionalita."," Spotřebitel jedná racionálně — snaží se maximalizovat své uspokojení (užitečnost) s ohledem na daný důchod a tržní ceny; disponuje všemi potřebnými informacemi.",[123,87008,87009,87012],{},[38,87010,87011],{},"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.",[123,87014,87015,87018,87019,61721,87032,87045,87046,61721,87059,2924,87072,87075,87076,3877,87095,62550,87113,1888],{},[38,87016,87017],{},"Konzistence a tranzitivita."," Preferuje-li v jisté době svazek ",[883,87020,87022],{"className":87021},[886],[888,87023,87024],{"xmlns":890},[892,87025,87026,87030],{},[895,87027,87028],{},[898,87029,4243],{},[902,87031,4243],{"encoding":904},[883,87033,87035],{"className":87034},[886],[888,87036,87037],{"xmlns":890},[892,87038,87039,87043],{},[895,87040,87041],{},[898,87042,23234],{},[902,87044,23234],{"encoding":904},", nebude jindy preferovat ",[883,87047,87049],{"className":87048},[886],[888,87050,87051],{"xmlns":890},[892,87052,87053,87057],{},[895,87054,87055],{},[898,87056,23234],{},[902,87058,23234],{"encoding":904},[883,87060,87062],{"className":87061},[886],[888,87063,87064],{"xmlns":890},[892,87065,87066,87070],{},[895,87067,87068],{},[898,87069,4243],{},[902,87071,4243],{"encoding":904},[38,87073,87074],{},"Tranzitivita",": pokud ",[883,87077,87079],{"className":87078},[886],[888,87080,87081],{"xmlns":890},[892,87082,87083,87092],{},[895,87084,87085,87087,87090],{},[898,87086,4243],{},[1726,87088,87089],{},"≻",[898,87091,23234],{},[902,87093,87094],{"encoding":904},"A \\succ B",[883,87096,87098],{"className":87097},[886],[888,87099,87100],{"xmlns":890},[892,87101,87102,87110],{},[895,87103,87104,87106,87108],{},[898,87105,23234],{},[1726,87107,87089],{},[898,87109,2775],{},[902,87111,87112],{"encoding":904},"B \\succ C",[883,87114,87116],{"className":87115},[886],[888,87117,87118],{"xmlns":890},[892,87119,87120,87128],{},[895,87121,87122,87124,87126],{},[898,87123,4243],{},[1726,87125,87089],{},[898,87127,2775],{},[902,87129,87130],{"encoding":904},"A \\succ C",[123,87132,87133,87136],{},[38,87134,87135],{},"Rostoucí užitečnost."," Uspokojení roste s množstvím zboží.",[123,87138,87139,87142],{},[38,87140,87141],{},"Klesající mezní užitečnost."," „Přírůstky\" uspokojení klesají s růstem množství zboží.",[724,87144,87145,87146,87149,87150,1888],{},"K naplnění předpokladů je ordinalistický přístup založen na pojmech ",[614,87147,87148],{},"preference"," a na příbuzné ",[614,87151,87152],{},"funkci užitečnosti",[115,87154,87156],{"id":87155},"_62-model-užitečnosti-svazek-zboží-a-funkce-užitečnosti","6.2 Model užitečnosti — svazek zboží a funkce užitečnosti",[724,87158,87159,87160,87173,87174,87177,87178,87191],{},"Uvažujme ",[883,87161,87163],{"className":87162},[886],[888,87164,87165],{"xmlns":890},[892,87166,87167,87171],{},[895,87168,87169],{},[898,87170,36841],{},[902,87172,36841],{"encoding":904}," různých zboží. ",[38,87175,87176],{},"Svazek zboží (bundle of goods)"," je uspořádaná ",[883,87179,87181],{"className":87180},[886],[888,87182,87183],{"xmlns":890},[892,87184,87185,87189],{},[895,87186,87187],{},[898,87188,36841],{},[902,87190,36841],{"encoding":904},"-tice",[724,87193,87194],{},[883,87195,87197],{"className":87196},[886],[888,87198,87199],{"xmlns":890},[892,87200,87201,87227],{},[895,87202,87203,87205,87211,87213,87215,87217,87223,87225],{},[1726,87204,1735],{"stretchy":1734},[2275,87206,87207,87209],{},[898,87208,1724],{},[2133,87210,2281],{},[1726,87212,1742],{"separator":1741},[1726,87214,1759],{},[1726,87216,1742],{"separator":1741},[2275,87218,87219,87221],{},[898,87220,1724],{},[898,87222,36841],{},[1726,87224,1762],{"stretchy":1734},[1726,87226,1742],{"separator":1741},[902,87228,87229],{"encoding":904},"(Q_1, \\dots, Q_n),",[724,87231,4298,87232,87249,87250,87263,87264,87267,87268,87271,87272,87275,87276,2703],{},[883,87233,87235],{"className":87234},[886],[888,87236,87237],{"xmlns":890},[892,87238,87239,87247],{},[895,87240,87241],{},[2275,87242,87243,87245],{},[898,87244,1724],{},[898,87246,17772],{},[902,87248,47519],{"encoding":904}," značí množství ",[883,87251,87253],{"className":87252},[886],[888,87254,87255],{"xmlns":890},[892,87256,87257,87261],{},[895,87258,87259],{},[898,87260,17772],{},[902,87262,17772],{"encoding":904},"-tého zboží. Spotřebitel je schopen svazky ",[38,87265,87266],{},"uspořádat"," s rostoucí užitečností, případně je prohlásit za ",[38,87269,87270],{},"indiferentní"," (tj. stejně užitečné). Tím je definována ",[38,87273,87274],{},"relace preference",". Preferenci vyjadřujeme číselně: svazku preferovanému přiřadíme větší číslo, indiferentním svazkům stejné číslo. Dostáváme ",[38,87277,87152],{},[883,87279,87281],{"className":87280},[886],[888,87282,87283],{"xmlns":890,"display":28047},[892,87284,87285,87332],{},[20735,87286,87287],{"width":28052},[20740,87288,87289,87291,87325,87327],{},[20743,87290],{"width":28057},[20743,87292,87293],{},[895,87294,87295,87297,87299,87301,87303,87309,87311,87313,87315,87321,87323],{},[898,87296,900],{},[1726,87298,1728],{},[898,87300,900],{},[1726,87302,1735],{"stretchy":1734},[2275,87304,87305,87307],{},[898,87306,1724],{},[2133,87308,2281],{},[1726,87310,1742],{"separator":1741},[1726,87312,1759],{},[1726,87314,1742],{"separator":1741},[2275,87316,87317,87319],{},[898,87318,1724],{},[898,87320,36841],{},[1726,87322,1762],{"stretchy":1734},[1726,87324,1742],{"separator":1741},[20743,87326],{"width":28057},[20743,87328,87329],{},[2289,87330,87331],{},"(6.1)",[902,87333,87334],{"encoding":904},"U = U(Q_1, \\dots, Q_n), \\tag{6.1}",[724,87336,4298,87337,87367,87368,87390,87391,87394],{},[883,87338,87340],{"className":87339},[886],[888,87341,87342],{"xmlns":890},[892,87343,87344,87364],{},[895,87345,87346,87352,87354,87356,87358],{},[2275,87347,87348,87350],{},[898,87349,1724],{},[2133,87351,2281],{},[1726,87353,1742],{"separator":1741},[1726,87355,1759],{},[1726,87357,1742],{"separator":1741},[2275,87359,87360,87362],{},[898,87361,1724],{},[898,87363,36841],{},[902,87365,87366],{"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 ",[883,87369,87371],{"className":87370},[886],[888,87372,87373],{"xmlns":890},[892,87374,87375,87387],{},[895,87376,87377,87379,87381],{},[898,87378,900],{},[1726,87380,1742],{"separator":1741},[8372,87382,87383,87385],{"accent":1741},[898,87384,900],{},[1726,87386,86926],{},[902,87388,87389],{"encoding":904},"U, \\tilde U"," reprezentují stejné preference, pokud mezi nimi existuje ",[38,87392,87393],{},"monotónní transformace"," zachovávající pořadí.",[724,87396,87397,87398,1696,87401,1888],{},"Dále se omezíme na funkce pro ",[38,87399,87400],{},"dvě zboží",[883,87402,87404],{"className":87403},[886],[888,87405,87406],{"xmlns":890},[892,87407,87408,87434],{},[895,87409,87410,87412,87414,87416,87418,87424,87426,87432],{},[898,87411,900],{},[1726,87413,1728],{},[898,87415,900],{},[1726,87417,1735],{"stretchy":1734},[2275,87419,87420,87422],{},[898,87421,1724],{},[2133,87423,2281],{},[1726,87425,1742],{"separator":1741},[2275,87427,87428,87430],{},[898,87429,1724],{},[2133,87431,2135],{},[1726,87433,1762],{"stretchy":1734},[902,87435,87436],{"encoding":904},"U = U(Q_1, Q_2)",[3859,87438,87439,87514],{},[724,87440,87441,87443,87444,2703],{},[883,87442,52675],{}," Příklad 6.1 — uspořádání a indiference\nPro ",[883,87445,87447],{"className":87446},[886],[888,87448,87449],{"xmlns":890},[892,87450,87451,87511],{},[895,87452,87453,87455,87457,87459,87461,87467,87469,87475,87477,87483,87485,87487,87489],{},[898,87454,900],{},[1726,87456,1728],{},[898,87458,900],{},[1726,87460,1735],{"stretchy":1734},[2275,87462,87463,87465],{},[898,87464,1724],{},[2133,87466,2281],{},[1726,87468,1742],{"separator":1741},[2275,87470,87471,87473],{},[898,87472,1724],{},[2133,87474,2135],{},[1726,87476,1742],{"separator":1741},[2275,87478,87479,87481],{},[898,87480,1724],{},[2133,87482,2177],{},[1726,87484,1762],{"stretchy":1734},[1726,87486,1728],{},[2133,87488,2135],{},[8103,87490,87491],{},[895,87492,87493,87499,87505],{},[2275,87494,87495,87497],{},[898,87496,1724],{},[2133,87498,2281],{},[2275,87500,87501,87503],{},[898,87502,1724],{},[2133,87504,2135],{},[2275,87506,87507,87509],{},[898,87508,1724],{},[2133,87510,2177],{},[902,87512,87513],{"encoding":904},"U = U(Q_1, Q_2, Q_3) = 2\\sqrt{Q_1 Q_2 Q_3}",[120,87515,87516,87709],{},[123,87517,87518,87519,87545,87546,12924,87572,3877,87631,5576,87691,8411],{},"svazek ",[883,87520,87522],{"className":87521},[886],[888,87523,87524],{"xmlns":890},[892,87525,87526,87542],{},[895,87527,87528,87530,87532,87534,87536,87538,87540],{},[1726,87529,1735],{"stretchy":1734},[2133,87531,41843],{},[1726,87533,1742],{"separator":1741},[2133,87535,2352],{},[1726,87537,1742],{"separator":1741},[2133,87539,41821],{},[1726,87541,1762],{"stretchy":1734},[902,87543,87544],{"encoding":904},"(16, 4, 64)"," je preferován před ",[883,87547,87549],{"className":87548},[886],[888,87550,87551],{"xmlns":890},[892,87552,87553,87569],{},[895,87554,87555,87557,87559,87561,87563,87565,87567],{},[1726,87556,1735],{"stretchy":1734},[2133,87558,3989],{},[1726,87560,1742],{"separator":1741},[2133,87562,3989],{},[1726,87564,1742],{"separator":1741},[2133,87566,66577],{},[1726,87568,1762],{"stretchy":1734},[902,87570,87571],{"encoding":904},"(9, 9, 27)",[883,87573,87575],{"className":87574},[886],[888,87576,87577],{"xmlns":890},[892,87578,87579,87628],{},[895,87580,87581,87583,87585,87587,87589,87591,87593,87595,87597,87599,87601,87615,87617,87619,87624,87626],{},[898,87582,900],{},[1726,87584,1735],{"stretchy":1734},[2133,87586,41843],{},[1726,87588,1742],{"separator":1741},[2133,87590,2352],{},[1726,87592,1742],{"separator":1741},[2133,87594,41821],{},[1726,87596,1762],{"stretchy":1734},[1726,87598,1728],{},[2133,87600,2135],{},[8103,87602,87603],{},[895,87604,87605,87607,87609,87611,87613],{},[2133,87606,41843],{},[1726,87608,3174],{},[2133,87610,2352],{},[1726,87612,3174],{},[2133,87614,41821],{},[1726,87616,1728],{},[2133,87618,2135],{},[8103,87620,87621],{},[2133,87622,87623],{},"4096",[1726,87625,1728],{},[2133,87627,5604],{},[902,87629,87630],{"encoding":904},"U(16,4,64) = 2\\sqrt{16 \\cdot 4 \\cdot 64} = 2\\sqrt{4096} = 128",[883,87632,87634],{"className":87633},[886],[888,87635,87636],{"xmlns":890},[892,87637,87638,87688],{},[895,87639,87640,87642,87644,87646,87648,87650,87652,87654,87656,87658,87660,87674,87676,87678,87683,87685],{},[898,87641,900],{},[1726,87643,1735],{"stretchy":1734},[2133,87645,3989],{},[1726,87647,1742],{"separator":1741},[2133,87649,3989],{},[1726,87651,1742],{"separator":1741},[2133,87653,66577],{},[1726,87655,1762],{"stretchy":1734},[1726,87657,1728],{},[2133,87659,2135],{},[8103,87661,87662],{},[895,87663,87664,87666,87668,87670,87672],{},[2133,87665,3989],{},[1726,87667,3174],{},[2133,87669,3989],{},[1726,87671,3174],{},[2133,87673,66577],{},[1726,87675,1728],{},[2133,87677,2135],{},[8103,87679,87680],{},[2133,87681,87682],{},"2187",[1726,87684,5887],{},[2133,87686,87687],{},"93,53",[902,87689,87690],{"encoding":904},"U(9,9,27) = 2\\sqrt{9 \\cdot 9 \\cdot 27} = 2\\sqrt{2187} \\doteq 93{,}53",[883,87692,87694],{"className":87693},[886],[888,87695,87696],{"xmlns":890},[892,87697,87698,87706],{},[895,87699,87700,87702,87704],{},[2133,87701,5604],{},[1726,87703,3405],{},[2133,87705,87687],{},[902,87707,87708],{"encoding":904},"128 > 93{,}53",[123,87710,87711,87712,3877,87738,87764,87765,3877,87805,87846,87847,87893,87894,3877,87920,2842,87946,3877,87964,87982,87983,1888],{},"svazky ",[883,87713,87715],{"className":87714},[886],[888,87716,87717],{"xmlns":890},[892,87718,87719,87735],{},[895,87720,87721,87723,87725,87727,87729,87731,87733],{},[1726,87722,1735],{"stretchy":1734},[2133,87724,2352],{},[1726,87726,1742],{"separator":1741},[2133,87728,5572],{},[1726,87730,1742],{"separator":1741},[2133,87732,2135],{},[1726,87734,1762],{"stretchy":1734},[902,87736,87737],{"encoding":904},"(4, 8, 2)",[883,87739,87741],{"className":87740},[886],[888,87742,87743],{"xmlns":890},[892,87744,87745,87761],{},[895,87746,87747,87749,87751,87753,87755,87757,87759],{},[1726,87748,1735],{"stretchy":1734},[2133,87750,41821],{},[1726,87752,1742],{"separator":1741},[2133,87754,2281],{},[1726,87756,1742],{"separator":1741},[2133,87758,2352],{},[1726,87760,1762],{"stretchy":1734},[902,87762,87763],{"encoding":904},"(64, 1, 4)"," jsou indiferentní, protože ",[883,87766,87768],{"className":87767},[886],[888,87769,87770],{"xmlns":890},[892,87771,87772,87802],{},[895,87773,87774,87776,87778,87780,87782,87784,87786,87788,87790,87792,87794,87798,87800],{},[898,87775,900],{},[1726,87777,1735],{"stretchy":1734},[2133,87779,2352],{},[1726,87781,1742],{"separator":1741},[2133,87783,5572],{},[1726,87785,1742],{"separator":1741},[2133,87787,2135],{},[1726,87789,1762],{"stretchy":1734},[1726,87791,1728],{},[2133,87793,2135],{},[8103,87795,87796],{},[2133,87797,41821],{},[1726,87799,1728],{},[2133,87801,41843],{},[902,87803,87804],{"encoding":904},"U(4,8,2) = 2\\sqrt{64} = 16",[883,87806,87808],{"className":87807},[886],[888,87809,87810],{"xmlns":890},[892,87811,87812,87843],{},[895,87813,87814,87816,87818,87820,87822,87824,87826,87828,87830,87832,87834,87839,87841],{},[898,87815,900],{},[1726,87817,1735],{"stretchy":1734},[2133,87819,41821],{},[1726,87821,1742],{"separator":1741},[2133,87823,2281],{},[1726,87825,1742],{"separator":1741},[2133,87827,2352],{},[1726,87829,1762],{"stretchy":1734},[1726,87831,1728],{},[2133,87833,2135],{},[8103,87835,87836],{},[2133,87837,87838],{},"256",[1726,87840,1728],{},[2133,87842,72339],{},[902,87844,87845],{"encoding":904},"U(64,1,4) = 2\\sqrt{256} = 32"," — jsou stejně užitečné mezi sebou, pokud ",[883,87848,87850],{"className":87849},[886],[888,87851,87852],{"xmlns":890},[892,87853,87854,87890],{},[895,87855,87856,87858,87860,87862,87864,87866,87868,87870,87872,87874,87876,87878,87880,87882,87884,87886,87888],{},[898,87857,900],{},[1726,87859,1735],{"stretchy":1734},[2133,87861,2352],{},[1726,87863,1742],{"separator":1741},[2133,87865,5572],{},[1726,87867,1742],{"separator":1741},[2133,87869,2135],{},[1726,87871,1762],{"stretchy":1734},[1726,87873,1728],{},[898,87875,900],{},[1726,87877,1735],{"stretchy":1734},[2133,87879,41821],{},[1726,87881,1742],{"separator":1741},[2133,87883,2281],{},[1726,87885,1742],{"separator":1741},[2133,87887,2352],{},[1726,87889,1762],{"stretchy":1734},[902,87891,87892],{"encoding":904},"U(4,8,2) = U(64,1,4)","; ověření: ",[883,87895,87897],{"className":87896},[886],[888,87898,87899],{"xmlns":890},[892,87900,87901,87917],{},[895,87902,87903,87905,87907,87909,87911,87913,87915],{},[2133,87904,2352],{},[1726,87906,3174],{},[2133,87908,5572],{},[1726,87910,3174],{},[2133,87912,2135],{},[1726,87914,1728],{},[2133,87916,41821],{},[902,87918,87919],{"encoding":904},"4 \\cdot 8 \\cdot 2 = 64",[883,87921,87923],{"className":87922},[886],[888,87924,87925],{"xmlns":890},[892,87926,87927,87943],{},[895,87928,87929,87931,87933,87935,87937,87939,87941],{},[2133,87930,41821],{},[1726,87932,3174],{},[2133,87934,2281],{},[1726,87936,3174],{},[2133,87938,2352],{},[1726,87940,1728],{},[2133,87942,87838],{},[902,87944,87945],{"encoding":904},"64 \\cdot 1 \\cdot 4 = 256",[883,87947,87949],{"className":87948},[886],[888,87950,87951],{"xmlns":890},[892,87952,87953,87961],{},[895,87954,87955,87957,87959],{},[898,87956,900],{},[1726,87958,1728],{},[2133,87960,41843],{},[902,87962,87963],{"encoding":904},"U = 16",[883,87965,87967],{"className":87966},[886],[888,87968,87969],{"xmlns":890},[892,87970,87971,87979],{},[895,87972,87973,87975,87977],{},[898,87974,900],{},[1726,87976,1728],{},[2133,87978,72339],{},[902,87980,87981],{"encoding":904},"U = 32"," — nejsou indiferentní. Správně indiferentní jsou svazky s týmž součinem ",[883,87984,87986],{"className":87985},[886],[888,87987,87988],{"xmlns":890},[892,87989,87990,88010],{},[895,87991,87992,87998,88004],{},[2275,87993,87994,87996],{},[898,87995,1724],{},[2133,87997,2281],{},[2275,87999,88000,88002],{},[898,88001,1724],{},[2133,88003,2135],{},[2275,88005,88006,88008],{},[898,88007,1724],{},[2133,88009,2177],{},[902,88011,88012],{"encoding":904},"Q_1 Q_2 Q_3",[115,88014,88016],{"id":88015},"mezní-užitečnost-mu","Mezní užitečnost (MU)",[724,88018,88019,88020,8088,88055,1777,88058,41795,88075,10009,88092,88095,88096,88099],{},"Pro funkci užitečnosti ",[883,88021,88023],{"className":88022},[886],[888,88024,88025],{"xmlns":890},[892,88026,88027,88053],{},[895,88028,88029,88031,88033,88035,88037,88043,88045,88051],{},[898,88030,900],{},[1726,88032,1728],{},[898,88034,900],{},[1726,88036,1735],{"stretchy":1734},[2275,88038,88039,88041],{},[898,88040,1724],{},[2133,88042,2281],{},[1726,88044,1742],{"separator":1741},[2275,88046,88047,88049],{},[898,88048,1724],{},[2133,88050,2135],{},[1726,88052,1762],{"stretchy":1734},[902,88054,87436],{"encoding":904},[38,88056,88057],{},"mezní užitečnost",[883,88059,88061],{"className":88060},[886],[888,88062,88063],{"xmlns":890},[892,88064,88065,88073],{},[895,88066,88067],{},[2275,88068,88069,88071],{},[898,88070,1724],{},[2133,88072,2281],{},[902,88074,28983],{"encoding":904},[883,88076,88078],{"className":88077},[886],[888,88079,88080],{"xmlns":890},[892,88081,88082,88090],{},[895,88083,88084],{},[2275,88085,88086,88088],{},[898,88087,1724],{},[2133,88089,2135],{},[902,88091,29002],{"encoding":904},[38,88093,88094],{},"marginal utility",") parciální ",[207,88097,1145],{"className":88098,"dataFsResolvedFilePath":764,"href":765},[210]," užitečnosti podle příslušné proměnné:",[883,88101,88103],{"className":88102},[886],[888,88104,88105],{"xmlns":890,"display":28047},[892,88106,88107,88206],{},[20735,88108,88109],{"width":28052},[20740,88110,88111,88113,88199,88201],{},[20743,88112],{"width":28057},[20743,88114,88115],{},[895,88116,88117,88119,88125,88127,88135,88137,88155,88157,88159,88161,88167,88169,88177,88179,88197],{},[898,88118,2815],{},[2275,88120,88121,88123],{},[898,88122,900],{},[2133,88124,2281],{},[1726,88126,1728],{},[9151,88128,88129,88131,88133],{},[898,88130,900],{},[2133,88132,2281],{},[1726,88134,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,88136,1728],{},[2330,88138,88139,88145],{},[895,88140,88141,88143],{},[898,88142,9856],{"mathvariant":2377},[898,88144,900],{},[895,88146,88147,88149],{},[898,88148,9856],{"mathvariant":2377},[2275,88150,88151,88153],{},[898,88152,1724],{},[2133,88154,2281],{},[1726,88156,1742],{"separator":1741},[5865,88158],{"width":15270},[898,88160,2815],{},[2275,88162,88163,88165],{},[898,88164,900],{},[2133,88166,2135],{},[1726,88168,1728],{},[9151,88170,88171,88173,88175],{},[898,88172,900],{},[2133,88174,2135],{},[1726,88176,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,88178,1728],{},[2330,88180,88181,88187],{},[895,88182,88183,88185],{},[898,88184,9856],{"mathvariant":2377},[898,88186,900],{},[895,88188,88189,88191],{},[898,88190,9856],{"mathvariant":2377},[2275,88192,88193,88195],{},[898,88194,1724],{},[2133,88196,2135],{},[898,88198,1888],{"mathvariant":2377},[20743,88200],{"width":28057},[20743,88202,88203],{},[2289,88204,88205],{},"(6.2)",[902,88207,88208],{"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}",[724,88210,88211,88212,88246,88247,88277,88278,1777,88281,1888],{},"Pro pevné ",[883,88213,88215],{"className":88214},[886],[888,88216,88217],{"xmlns":890},[892,88218,88219,88243],{},[895,88220,88221,88227,88229,88231,88233,88239,88241],{},[2275,88222,88223,88225],{},[898,88224,1724],{},[2133,88226,2281],{},[1726,88228,1728],{},[898,88230,207],{},[1726,88232,1742],{"separator":1741},[2275,88234,88235,88237],{},[898,88236,1724],{},[2133,88238,2135],{},[1726,88240,1728],{},[898,88242,2102],{},[902,88244,88245],{"encoding":904},"Q_1 = a, Q_2 = b"," se hodnota ",[883,88248,88250],{"className":88249},[886],[888,88251,88252],{"xmlns":890},[892,88253,88254,88274],{},[895,88255,88256,88258,88264,88266,88268,88270,88272],{},[898,88257,2815],{},[2275,88259,88260,88262],{},[898,88261,900],{},[2133,88263,2281],{},[1726,88265,1735],{"stretchy":1734},[898,88267,207],{},[1726,88269,1742],{"separator":1741},[898,88271,2102],{},[1726,88273,1762],{"stretchy":1734},[902,88275,88276],{"encoding":904},"MU_1(a, b)"," nazývá mezní užitečnost ",[38,88279,88280],{},"v bodě (na hladině)",[883,88282,88284],{"className":88283},[886],[888,88285,88286],{"xmlns":890},[892,88287,88288,88300],{},[895,88289,88290,88292,88294,88296,88298],{},[1726,88291,2487],{"stretchy":1734},[898,88293,207],{},[1726,88295,1742],{"separator":1741},[898,88297,2102],{},[1726,88299,2502],{"stretchy":1734},[902,88301,10808],{"encoding":904},[3859,88303,88304],{},[724,88305,88306,88308,88309,88339,88368,88369,2609,88382,2623,88399,88420,88421,2670,88438,2684,88451,88468,88469,88491,88492,88521,88522,6460,88542,88559],{},[883,88307,4145],{}," Intuice — co říká ",[883,88310,88312],{"className":88311},[886],[888,88313,88314],{"xmlns":890},[892,88315,88316,88336],{},[895,88317,88318,88320,88326,88328,88330,88332,88334],{},[898,88319,2815],{},[2275,88321,88322,88324],{},[898,88323,900],{},[2133,88325,2281],{},[1726,88327,1735],{"stretchy":1734},[898,88329,207],{},[1726,88331,1742],{"separator":1741},[898,88333,2102],{},[1726,88335,1762],{"stretchy":1734},[902,88337,88338],{"encoding":904},"MU_1(a,b)",[883,88340,88342],{"className":88341},[886],[888,88343,88344],{"xmlns":890},[892,88345,88346,88366],{},[895,88347,88348,88350,88356,88358,88360,88362,88364],{},[898,88349,2815],{},[2275,88351,88352,88354],{},[898,88353,900],{},[2133,88355,2281],{},[1726,88357,1735],{"stretchy":1734},[898,88359,207],{},[1726,88361,1742],{"separator":1741},[898,88363,2102],{},[1726,88365,1762],{"stretchy":1734},[902,88367,88276],{"encoding":904}," je rychlost změny ",[883,88370,88372],{"className":88371},[886],[888,88373,88374],{"xmlns":890},[892,88375,88376,88380],{},[895,88377,88378],{},[898,88379,900],{},[902,88381,900],{"encoding":904},[883,88383,88385],{"className":88384},[886],[888,88386,88387],{"xmlns":890},[892,88388,88389,88397],{},[895,88390,88391],{},[2275,88392,88393,88395],{},[898,88394,1724],{},[2133,88396,2281],{},[902,88398,28983],{"encoding":904},[883,88400,88402],{"className":88401},[886],[888,88403,88404],{"xmlns":890},[892,88405,88406,88418],{},[895,88407,88408,88410,88412,88414,88416],{},[1726,88409,2487],{"stretchy":1734},[898,88411,207],{},[1726,88413,1742],{"separator":1741},[898,88415,2102],{},[1726,88417,2502],{"stretchy":1734},[902,88419,10808],{"encoding":904},". Přibližně: změní-li se ",[883,88422,88424],{"className":88423},[886],[888,88425,88426],{"xmlns":890},[892,88427,88428,88436],{},[895,88429,88430],{},[2275,88431,88432,88434],{},[898,88433,1724],{},[2133,88435,2281],{},[902,88437,28983],{"encoding":904},[883,88439,88441],{"className":88440},[886],[888,88442,88443],{"xmlns":890},[892,88444,88445,88449],{},[895,88446,88447],{},[898,88448,207],{},[902,88450,207],{"encoding":904},[883,88452,88454],{"className":88453},[886],[888,88455,88456],{"xmlns":890},[892,88457,88458,88466],{},[895,88459,88460,88462,88464],{},[898,88461,207],{},[1726,88463,2099],{},[2133,88465,2281],{},[902,88467,2702],{"encoding":904}," při pevném ",[883,88470,88472],{"className":88471},[886],[888,88473,88474],{"xmlns":890},[892,88475,88476,88488],{},[895,88477,88478,88484,88486],{},[2275,88479,88480,88482],{},[898,88481,1724],{},[2133,88483,2135],{},[1726,88485,1728],{},[898,88487,2102],{},[902,88489,88490],{"encoding":904},"Q_2 = b",", změní se užitečnost zhruba o ",[883,88493,88495],{"className":88494},[886],[888,88496,88497],{"xmlns":890},[892,88498,88499,88519],{},[895,88500,88501,88503,88509,88511,88513,88515,88517],{},[898,88502,2815],{},[2275,88504,88505,88507],{},[898,88506,900],{},[2133,88508,2281],{},[1726,88510,1735],{"stretchy":1734},[898,88512,207],{},[1726,88514,1742],{"separator":1741},[898,88516,2102],{},[1726,88518,1762],{"stretchy":1734},[902,88520,88276],{"encoding":904},". Stejně tak ",[883,88523,88525],{"className":88524},[886],[888,88526,88527],{"xmlns":890},[892,88528,88529,88539],{},[895,88530,88531,88533],{},[898,88532,2815],{},[2275,88534,88535,88537],{},[898,88536,900],{},[2133,88538,2135],{},[902,88540,88541],{"encoding":904},"MU_2",[883,88543,88545],{"className":88544},[886],[888,88546,88547],{"xmlns":890},[892,88548,88549,88557],{},[895,88550,88551],{},[2275,88552,88553,88555],{},[898,88554,1724],{},[2133,88556,2135],{},[902,88558,29002],{"encoding":904},". Mezní užitečnost tedy odpovídá „užitku z další jednotky\" a podle předpokladu 5 s množstvím klesá.",[198,88561,80191],{"id":88562},"totální-diferenciál",[724,88564,88565,88566,48321,88582,88612,88613,2703],{},"Přibližnou změnu užitečnosti ",[883,88567,88569],{"className":88568},[886],[888,88570,88571],{"xmlns":890},[892,88572,88573,88579],{},[895,88574,88575,88577],{},[898,88576,2886],{"mathvariant":2377},[898,88578,900],{},[902,88580,88581],{"encoding":904},"\\Delta U",[883,88583,88585],{"className":88584},[886],[888,88586,88587],{"xmlns":890},[892,88588,88589,88609],{},[895,88590,88591,88593,88599,88601,88603],{},[898,88592,2198],{"mathvariant":2377},[2275,88594,88595,88597],{},[898,88596,1724],{},[2133,88598,2281],{},[1726,88600,1742],{"separator":1741},[898,88602,2198],{"mathvariant":2377},[2275,88604,88605,88607],{},[898,88606,1724],{},[2133,88608,2135],{},[902,88610,88611],{"encoding":904},"\\mathrm{d} Q_1, \\mathrm{d} Q_2"," stanovíme pomocí ",[38,88614,88615],{},"totálního diferenciálu",[883,88617,88619],{"className":88618},[886],[888,88620,88621],{"xmlns":890,"display":28047},[892,88622,88623,88724],{},[20735,88624,88625],{"width":28052},[20740,88626,88627,88629,88717,88719],{},[20743,88628],{"width":28057},[20743,88630,88631],{},[895,88632,88633,88635,88637,88639,88641,88643,88645,88653,88655,88661,88663,88671,88673,88679,88681,88683,88689,88691,88697,88699,88701,88707,88709,88715],{},[898,88634,2886],{"mathvariant":2377},[898,88636,900],{},[1726,88638,1880],{},[898,88640,2198],{"mathvariant":2377},[898,88642,900],{},[1726,88644,1728],{},[9151,88646,88647,88649,88651],{},[898,88648,900],{},[2133,88650,2281],{},[1726,88652,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[898,88654,2198],{"mathvariant":2377},[2275,88656,88657,88659],{},[898,88658,1724],{},[2133,88660,2281],{},[1726,88662,2099],{},[9151,88664,88665,88667,88669],{},[898,88666,900],{},[2133,88668,2135],{},[1726,88670,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[898,88672,2198],{"mathvariant":2377},[2275,88674,88675,88677],{},[898,88676,1724],{},[2133,88678,2135],{},[1726,88680,1728],{},[898,88682,2815],{},[2275,88684,88685,88687],{},[898,88686,900],{},[2133,88688,2281],{},[898,88690,2198],{"mathvariant":2377},[2275,88692,88693,88695],{},[898,88694,1724],{},[2133,88696,2281],{},[1726,88698,2099],{},[898,88700,2815],{},[2275,88702,88703,88705],{},[898,88704,900],{},[2133,88706,2135],{},[898,88708,2198],{"mathvariant":2377},[2275,88710,88711,88713],{},[898,88712,1724],{},[2133,88714,2135],{},[898,88716,1888],{"mathvariant":2377},[20743,88718],{"width":28057},[20743,88720,88721],{},[2289,88722,88723],{},"(6.3)",[902,88725,88726],{"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}",[724,88728,75449,88729,1888],{},[883,88730,88732],{"className":88731},[886],[888,88733,88734],{"xmlns":890},[892,88735,88736,88806],{},[895,88737,88738,88740,88742,88744,88746,88748,88754,88756,88758,88764,88766,88772,88774,88776,88782,88784,88786,88788,88790,88796,88798,88804],{},[898,88739,2886],{"mathvariant":2377},[898,88741,900],{},[1726,88743,1728],{},[898,88745,900],{},[1726,88747,1735],{"stretchy":1734},[2275,88749,88750,88752],{},[898,88751,1724],{},[2133,88753,2281],{},[1726,88755,2099],{},[898,88757,2198],{"mathvariant":2377},[2275,88759,88760,88762],{},[898,88761,1724],{},[2133,88763,2281],{},[1726,88765,1742],{"separator":1741},[2275,88767,88768,88770],{},[898,88769,1724],{},[2133,88771,2135],{},[1726,88773,2099],{},[898,88775,2198],{"mathvariant":2377},[2275,88777,88778,88780],{},[898,88779,1724],{},[2133,88781,2135],{},[1726,88783,1762],{"stretchy":1734},[1726,88785,2228],{},[898,88787,900],{},[1726,88789,1735],{"stretchy":1734},[2275,88791,88792,88794],{},[898,88793,1724],{},[2133,88795,2281],{},[1726,88797,1742],{"separator":1741},[2275,88799,88800,88802],{},[898,88801,1724],{},[2133,88803,2135],{},[1726,88805,1762],{"stretchy":1734},[902,88807,88808],{"encoding":904},"\\Delta U = U(Q_1 + \\mathrm{d} Q_1, Q_2 + \\mathrm{d} Q_2) - U(Q_1, Q_2)",[115,88810,88812],{"id":88811},"vlastnosti-funkce-užitečnosti","Vlastnosti funkce užitečnosti",[724,88814,88815,88816,88819,88820,88823],{},"Funkce užitečnosti musí vyjadřovat dva ekonomicky zásadní předpoklady — ",[38,88817,88818],{},"rostoucí užitečnost"," (předpoklad 4) a ",[38,88821,88822],{},"klesající mezní užitečnost"," (předpoklad 5).",[724,88825,88826,88829,88830,41795,88856,88882,88883,1343,88915,88947,88948,3877,89002,89056],{},[38,88827,88828],{},"Předpoklad 4"," (rostoucí užitečnost) znamená, že při pevně zadaných ",[883,88831,88833],{"className":88832},[886],[888,88834,88835],{"xmlns":890},[892,88836,88837,88853],{},[895,88838,88839,88845,88847],{},[2275,88840,88841,88843],{},[898,88842,1724],{},[2133,88844,2135],{},[1726,88846,1728],{},[2275,88848,88849,88851],{},[898,88850,207],{},[2133,88852,2328],{},[902,88854,88855],{"encoding":904},"Q_2 = a_0",[883,88857,88859],{"className":88858},[886],[888,88860,88861],{"xmlns":890},[892,88862,88863,88879],{},[895,88864,88865,88871,88873],{},[2275,88866,88867,88869],{},[898,88868,1724],{},[2133,88870,2281],{},[1726,88872,1728],{},[2275,88874,88875,88877],{},[898,88876,2102],{},[2133,88878,2328],{},[902,88880,88881],{"encoding":904},"Q_1 = b_0"," jsou funkce jedné proměnné ",[883,88884,88886],{"className":88885},[886],[888,88887,88888],{"xmlns":890},[892,88889,88890,88912],{},[895,88891,88892,88894,88896,88902,88904,88910],{},[898,88893,900],{},[1726,88895,1735],{"stretchy":1734},[2275,88897,88898,88900],{},[898,88899,1724],{},[2133,88901,2281],{},[1726,88903,1742],{"separator":1741},[2275,88905,88906,88908],{},[898,88907,207],{},[2133,88909,2328],{},[1726,88911,1762],{"stretchy":1734},[902,88913,88914],{"encoding":904},"U(Q_1, a_0)",[883,88916,88918],{"className":88917},[886],[888,88919,88920],{"xmlns":890},[892,88921,88922,88944],{},[895,88923,88924,88926,88928,88934,88936,88942],{},[898,88925,900],{},[1726,88927,1735],{"stretchy":1734},[2275,88929,88930,88932],{},[898,88931,2102],{},[2133,88933,2328],{},[1726,88935,1742],{"separator":1741},[2275,88937,88938,88940],{},[898,88939,1724],{},[2133,88941,2135],{},[1726,88943,1762],{"stretchy":1734},[902,88945,88946],{"encoding":904},"U(b_0, Q_2)"," rostoucí. To platí, jestliže ",[883,88949,88951],{"className":88950},[886],[888,88952,88953],{"xmlns":890},[892,88954,88955,88999],{},[895,88956,88957,88995,88997],{},[2326,88958,88959],{"scriptlevel":2328,"displaystyle":1741},[2330,88960,88961,88985],{},[895,88962,88963,88965,88967,88969,88975,88977,88983],{},[898,88964,2198],{"mathvariant":2377},[898,88966,900],{},[1726,88968,1735],{"stretchy":1734},[2275,88970,88971,88973],{},[898,88972,1724],{},[2133,88974,2281],{},[1726,88976,1742],{"separator":1741},[2275,88978,88979,88981],{},[898,88980,207],{},[2133,88982,2328],{},[1726,88984,1762],{"stretchy":1734},[895,88986,88987,88989],{},[898,88988,2198],{"mathvariant":2377},[2275,88990,88991,88993],{},[898,88992,1724],{},[2133,88994,2281],{},[1726,88996,3405],{},[2133,88998,2328],{},[902,89000,89001],{"encoding":904},"\\dfrac{\\mathrm{d} U(Q_1, a_0)}{\\mathrm{d} Q_1} > 0",[883,89003,89005],{"className":89004},[886],[888,89006,89007],{"xmlns":890},[892,89008,89009,89053],{},[895,89010,89011,89049,89051],{},[2326,89012,89013],{"scriptlevel":2328,"displaystyle":1741},[2330,89014,89015,89039],{},[895,89016,89017,89019,89021,89023,89029,89031,89037],{},[898,89018,2198],{"mathvariant":2377},[898,89020,900],{},[1726,89022,1735],{"stretchy":1734},[2275,89024,89025,89027],{},[898,89026,2102],{},[2133,89028,2328],{},[1726,89030,1742],{"separator":1741},[2275,89032,89033,89035],{},[898,89034,1724],{},[2133,89036,2135],{},[1726,89038,1762],{"stretchy":1734},[895,89040,89041,89043],{},[898,89042,2198],{"mathvariant":2377},[2275,89044,89045,89047],{},[898,89046,1724],{},[2133,89048,2135],{},[1726,89050,3405],{},[2133,89052,2328],{},[902,89054,89055],{"encoding":904},"\\dfrac{\\mathrm{d} U(b_0, Q_2)}{\\mathrm{d} Q_2} > 0",", tj.",[883,89058,89060],{"className":89059},[886],[888,89061,89062],{"xmlns":890,"display":28047},[892,89063,89064,89109],{},[20735,89065,89066],{"width":28052},[20740,89067,89068,89070,89102,89104],{},[20743,89069],{"width":28057},[20743,89071,89072],{},[895,89073,89074,89082,89084,89086,89088,89090,89098,89100],{},[9151,89075,89076,89078,89080],{},[898,89077,900],{},[2133,89079,2281],{},[1726,89081,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,89083,3405],{},[2133,89085,2328],{},[1726,89087,1742],{"separator":1741},[5865,89089],{"width":15270},[9151,89091,89092,89094,89096],{},[898,89093,900],{},[2133,89095,2135],{},[1726,89097,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,89099,3405],{},[2133,89101,12446],{},[20743,89103],{"width":28057},[20743,89105,89106],{},[2289,89107,89108],{},"(6.4)",[902,89110,89111],{"encoding":904},"U'_1 > 0, \\quad U'_2 > 0. \\tag{6.4}",[724,89113,89114,89115,89117],{},"Tedy mezní užitečnosti obou zboží jsou ",[38,89116,52657],{}," — užitečnost roste s množstvím každého zboží.",[724,89119,89120,89123,89124,89154,89155,2703],{},[38,89121,89122],{},"Předpoklad 5"," (klesající mezní užitečnost) požaduje, aby ",[883,89125,89127],{"className":89126},[886],[888,89128,89129],{"xmlns":890},[892,89130,89131,89151],{},[895,89132,89133,89141,89143],{},[9151,89134,89135,89137,89139],{},[898,89136,900],{},[2133,89138,2281],{},[1726,89140,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,89142,1742],{"separator":1741},[9151,89144,89145,89147,89149],{},[898,89146,900],{},[2133,89148,2135],{},[1726,89150,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[902,89152,89153],{"encoding":904},"U'_1, U'_2"," byly klesající funkce. To znamená, že jejich parciální derivace podle příslušné proměnné jsou ",[38,89156,89157],{},"záporné",[883,89159,89161],{"className":89160},[886],[888,89162,89163],{"xmlns":890,"display":28047},[892,89164,89165,89218],{},[20735,89166,89167],{"width":28052},[20740,89168,89169,89171,89211,89213],{},[20743,89170],{"width":28057},[20743,89172,89173],{},[895,89174,89175,89187,89189,89191,89193,89195,89207,89209],{},[9151,89176,89177,89179,89181],{},[898,89178,900],{},[2133,89180,2901],{},[895,89182,89183,89185],{},[1726,89184,2379],{"mathvariant":2377},[1726,89186,2379],{"mathvariant":2377},[1726,89188,3444],{},[2133,89190,2328],{},[1726,89192,1742],{"separator":1741},[5865,89194],{"width":15270},[9151,89196,89197,89199,89201],{},[898,89198,900],{},[2133,89200,32527],{},[895,89202,89203,89205],{},[1726,89204,2379],{"mathvariant":2377},[1726,89206,2379],{"mathvariant":2377},[1726,89208,3444],{},[2133,89210,12446],{},[20743,89212],{"width":28057},[20743,89214,89215],{},[2289,89216,89217],{},"(6.5)",[902,89219,89220],{"encoding":904},"U''_{11} \u003C 0, \\quad U''_{22} \u003C 0. \\tag{6.5}",[724,89222,89223,89224,89227,89228,1888],{},"Podmínka (6.5) je známa jako ",[38,89225,89226],{},"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 ",[207,89229,89231],{"className":89230,"dataFsResolvedFilePath":857,"href":858},[210],"produkční teorie",[724,89233,89234,89235,3877,89267,89299,89300,3877,89326,89352,89353,89381,89382,3877,89384,89386,89387,89422],{},"Podmínky (6.4), (6.5) určují tvary křivek ",[883,89236,89238],{"className":89237},[886],[888,89239,89240],{"xmlns":890},[892,89241,89242,89264],{},[895,89243,89244,89246,89248,89254,89256,89262],{},[898,89245,900],{},[1726,89247,1735],{"stretchy":1734},[2275,89249,89250,89252],{},[898,89251,1724],{},[2133,89253,2281],{},[1726,89255,1742],{"separator":1741},[2275,89257,89258,89260],{},[898,89259,2102],{},[2133,89261,2328],{},[1726,89263,1762],{"stretchy":1734},[902,89265,89266],{"encoding":904},"U(Q_1, b_0)",[883,89268,89270],{"className":89269},[886],[888,89271,89272],{"xmlns":890},[892,89273,89274,89296],{},[895,89275,89276,89278,89280,89286,89288,89294],{},[898,89277,900],{},[1726,89279,1735],{"stretchy":1734},[2275,89281,89282,89284],{},[898,89283,207],{},[2133,89285,2328],{},[1726,89287,1742],{"separator":1741},[2275,89289,89290,89292],{},[898,89291,1724],{},[2133,89293,2135],{},[1726,89295,1762],{"stretchy":1734},[902,89297,89298],{"encoding":904},"U(a_0, Q_2)"," v souřadnicových rovinách ",[883,89301,89303],{"className":89302},[886],[888,89304,89305],{"xmlns":890},[892,89306,89307,89323],{},[895,89308,89309,89311,89313,89315,89321],{},[1726,89310,1735],{"stretchy":1734},[898,89312,900],{},[1726,89314,1742],{"separator":1741},[2275,89316,89317,89319],{},[898,89318,1724],{},[2133,89320,2281],{},[1726,89322,1762],{"stretchy":1734},[902,89324,89325],{"encoding":904},"(U, Q_1)",[883,89327,89329],{"className":89328},[886],[888,89330,89331],{"xmlns":890},[892,89332,89333,89349],{},[895,89334,89335,89337,89339,89341,89347],{},[1726,89336,1735],{"stretchy":1734},[898,89338,900],{},[1726,89340,1742],{"separator":1741},[2275,89342,89343,89345],{},[898,89344,1724],{},[2133,89346,2135],{},[1726,89348,1762],{"stretchy":1734},[902,89350,89351],{"encoding":904},"(U, Q_2)"," (obrázek 6.1). Tyto křivky procházejí počátkem (neboť obvykle ",[883,89354,89356],{"className":89355},[886],[888,89357,89358],{"xmlns":890},[892,89359,89360,89378],{},[895,89361,89362,89364,89366,89368,89370,89372,89374,89376],{},[898,89363,900],{},[1726,89365,1735],{"stretchy":1734},[2133,89367,2328],{},[1726,89369,1742],{"separator":1741},[2133,89371,2328],{},[1726,89373,1762],{"stretchy":1734},[1726,89375,1728],{},[2133,89377,2328],{},[902,89379,89380],{"encoding":904},"U(0, 0) = 0","), jsou ",[38,89383,13643],{},[38,89385,38469],{},". Typický tvar grafu ",[883,89388,89390],{"className":89389},[886],[888,89391,89392],{"xmlns":890},[892,89393,89394,89420],{},[895,89395,89396,89398,89400,89402,89404,89410,89412,89418],{},[898,89397,900],{},[1726,89399,1728],{},[898,89401,900],{},[1726,89403,1735],{"stretchy":1734},[2275,89405,89406,89408],{},[898,89407,1724],{},[2133,89409,2281],{},[1726,89411,1742],{"separator":1741},[2275,89413,89414,89416],{},[898,89415,1724],{},[2133,89417,2135],{},[1726,89419,1762],{"stretchy":1734},[902,89421,87436],{"encoding":904}," — plocha v prostoru — je na obrázku 6.2.",[724,89424,89425],{},[614,89426,89427,89428,88468,89456,89477,89478,88468,89506,89528],{},"Obrázek 6.1 — typické průběhy funkce užitečnosti ",[883,89429,89431],{"className":89430},[886],[888,89432,89433],{"xmlns":890},[892,89434,89435,89453],{},[895,89436,89437,89439,89441,89447,89449,89451],{},[898,89438,900],{},[1726,89440,1735],{"stretchy":1734},[2275,89442,89443,89445],{},[898,89444,1724],{},[2133,89446,2281],{},[1726,89448,1742],{"separator":1741},[898,89450,2102],{},[1726,89452,1762],{"stretchy":1734},[902,89454,89455],{"encoding":904},"U(Q_1, b)",[883,89457,89459],{"className":89458},[886],[888,89460,89461],{"xmlns":890},[892,89462,89463,89475],{},[895,89464,89465,89471,89473],{},[2275,89466,89467,89469],{},[898,89468,1724],{},[2133,89470,2135],{},[1726,89472,1728],{},[898,89474,2102],{},[902,89476,88490],{"encoding":904}," (vlevo) a ",[883,89479,89481],{"className":89480},[886],[888,89482,89483],{"xmlns":890},[892,89484,89485,89503],{},[895,89486,89487,89489,89491,89493,89495,89501],{},[898,89488,900],{},[1726,89490,1735],{"stretchy":1734},[898,89492,207],{},[1726,89494,1742],{"separator":1741},[2275,89496,89497,89499],{},[898,89498,1724],{},[2133,89500,2135],{},[1726,89502,1762],{"stretchy":1734},[902,89504,89505],{"encoding":904},"U(a, Q_2)",[883,89507,89509],{"className":89508},[886],[888,89510,89511],{"xmlns":890},[892,89512,89513,89525],{},[895,89514,89515,89521,89523],{},[2275,89516,89517,89519],{},[898,89518,1724],{},[2133,89520,2281],{},[1726,89522,1728],{},[898,89524,207],{},[902,89526,89527],{"encoding":904},"Q_1 = a"," (vpravo) pro různé hladiny druhé proměnné.",[724,89530,89531],{},[614,89532,89533,89534,89569,89570,89600,89601,3877,89624,89646,89647,1888],{},"Obrázek 6.2 — plocha funkce užitečnosti ",[883,89535,89537],{"className":89536},[886],[888,89538,89539],{"xmlns":890},[892,89540,89541,89567],{},[895,89542,89543,89545,89547,89549,89551,89557,89559,89565],{},[898,89544,900],{},[1726,89546,1728],{},[898,89548,900],{},[1726,89550,1735],{"stretchy":1734},[2275,89552,89553,89555],{},[898,89554,1724],{},[2133,89556,2281],{},[1726,89558,1742],{"separator":1741},[2275,89560,89561,89563],{},[898,89562,1724],{},[2133,89564,2135],{},[1726,89566,1762],{"stretchy":1734},[902,89568,87436],{"encoding":904}," nad rovinou ",[883,89571,89573],{"className":89572},[886],[888,89574,89575],{"xmlns":890},[892,89576,89577,89597],{},[895,89578,89579,89581,89587,89589,89595],{},[1726,89580,1735],{"stretchy":1734},[2275,89582,89583,89585],{},[898,89584,1724],{},[2133,89586,2281],{},[1726,89588,1742],{"separator":1741},[2275,89590,89591,89593],{},[898,89592,1724],{},[2133,89594,2135],{},[1726,89596,1762],{"stretchy":1734},[902,89598,89599],{"encoding":904},"(Q_1, Q_2)"," s řezy rovinami ",[883,89602,89604],{"className":89603},[886],[888,89605,89606],{"xmlns":890},[892,89607,89608,89621],{},[895,89609,89610,89616,89618],{},[2275,89611,89612,89614],{},[898,89613,1724],{},[2133,89615,2281],{},[1726,89617,1728],{},[2289,89619,89620],{},"const",[902,89622,89623],{"encoding":904},"Q_1 = \\text{const}",[883,89625,89627],{"className":89626},[886],[888,89628,89629],{"xmlns":890},[892,89630,89631,89643],{},[895,89632,89633,89639,89641],{},[2275,89634,89635,89637],{},[898,89636,1724],{},[2133,89638,2135],{},[1726,89640,1728],{},[2289,89642,89620],{},[902,89644,89645],{"encoding":904},"Q_2 = \\text{const}"," a s křivkou ",[883,89648,89650],{"className":89649},[886],[888,89651,89652],{"xmlns":890},[892,89653,89654,89680],{},[895,89655,89656,89658,89660,89666,89668,89674,89676,89678],{},[898,89657,900],{},[1726,89659,1735],{"stretchy":1734},[2275,89661,89662,89664],{},[898,89663,1724],{},[2133,89665,2281],{},[1726,89667,1742],{"separator":1741},[2275,89669,89670,89672],{},[898,89671,1724],{},[2133,89673,2135],{},[1726,89675,1762],{"stretchy":1734},[1726,89677,1728],{},[898,89679,2146],{},[902,89681,9752],{"encoding":904},[198,89683,89685,89686],{"id":89684},"příklad-62-ověření-vlastností-a-dopočet-pro-uq112q213u-q_112-q_213","Příklad 6.2 — ověření vlastností a dopočet pro ",[883,89687,89689],{"className":89688},[886],[888,89690,89691],{"xmlns":890},[892,89692,89693,89727],{},[895,89694,89695,89697,89699,89713],{},[898,89696,900],{},[1726,89698,1728],{},[9151,89700,89701,89703,89705],{},[898,89702,1724],{},[2133,89704,2281],{},[895,89706,89707,89709,89711],{},[2133,89708,2281],{},[898,89710,4661],{"mathvariant":2377},[2133,89712,2135],{},[9151,89714,89715,89717,89719],{},[898,89716,1724],{},[2133,89718,2135],{},[895,89720,89721,89723,89725],{},[2133,89722,2281],{},[898,89724,4661],{"mathvariant":2377},[2133,89726,2177],{},[902,89728,89729],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F3}",[724,89731,89732],{},[38,89733,89734],{},"Ověření (6.4) a (6.5).",[883,89736,89738],{"className":89737},[886],[888,89739,89740],{"xmlns":890,"display":28047},[892,89741,89742,89846],{},[895,89743,89744,89752,89754,89762,89778,89792,89794,89796,89804,89806,89814,89828,89844],{},[9151,89745,89746,89748,89750],{},[898,89747,900],{},[2133,89749,2281],{},[1726,89751,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,89753,1728],{},[2326,89755,89756],{"scriptlevel":2328,"displaystyle":1734},[2330,89757,89758,89760],{},[2133,89759,2281],{},[2133,89761,2135],{},[9151,89763,89764,89766,89768],{},[898,89765,1724],{},[2133,89767,2281],{},[895,89769,89770,89772,89774,89776],{},[1726,89771,2228],{},[2133,89773,2281],{},[898,89775,4661],{"mathvariant":2377},[2133,89777,2135],{},[9151,89779,89780,89782,89784],{},[898,89781,1724],{},[2133,89783,2135],{},[895,89785,89786,89788,89790],{},[2133,89787,2281],{},[898,89789,4661],{"mathvariant":2377},[2133,89791,2177],{},[1726,89793,1742],{"separator":1741},[5865,89795],{"width":15270},[9151,89797,89798,89800,89802],{},[898,89799,900],{},[2133,89801,2135],{},[1726,89803,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,89805,1728],{},[2326,89807,89808],{"scriptlevel":2328,"displaystyle":1734},[2330,89809,89810,89812],{},[2133,89811,2281],{},[2133,89813,2177],{},[9151,89815,89816,89818,89820],{},[898,89817,1724],{},[2133,89819,2281],{},[895,89821,89822,89824,89826],{},[2133,89823,2281],{},[898,89825,4661],{"mathvariant":2377},[2133,89827,2135],{},[9151,89829,89830,89832,89834],{},[898,89831,1724],{},[2133,89833,2135],{},[895,89835,89836,89838,89840,89842],{},[1726,89837,2228],{},[2133,89839,2135],{},[898,89841,4661],{"mathvariant":2377},[2133,89843,2177],{},[1726,89845,1742],{"separator":1741},[902,89847,89848],{"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},",[724,89850,89851,89852,89886],{},"zřejmě ",[883,89853,89855],{"className":89854},[886],[888,89856,89857],{"xmlns":890},[892,89858,89859,89883],{},[895,89860,89861,89869,89871,89879,89881],{},[9151,89862,89863,89865,89867],{},[898,89864,900],{},[2133,89866,2281],{},[1726,89868,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,89870,1742],{"separator":1741},[9151,89872,89873,89875,89877],{},[898,89874,900],{},[2133,89876,2135],{},[1726,89878,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,89880,3405],{},[2133,89882,2328],{},[902,89884,89885],{"encoding":904},"U'_1, U'_2 > 0"," a platí (6.4). Dále:",[883,89888,89890],{"className":89889},[886],[888,89891,89892],{"xmlns":890,"display":28047},[892,89893,89894,90010],{},[895,89895,89896,89908,89910,89912,89920,89936,89950,89952,89954,89966,89968,89970,89978,89992,90008],{},[9151,89897,89898,89900,89902],{},[898,89899,900],{},[2133,89901,2901],{},[895,89903,89904,89906],{},[1726,89905,2379],{"mathvariant":2377},[1726,89907,2379],{"mathvariant":2377},[1726,89909,1728],{},[1726,89911,2228],{},[2326,89913,89914],{"scriptlevel":2328,"displaystyle":1734},[2330,89915,89916,89918],{},[2133,89917,2281],{},[2133,89919,2352],{},[9151,89921,89922,89924,89926],{},[898,89923,1724],{},[2133,89925,2281],{},[895,89927,89928,89930,89932,89934],{},[1726,89929,2228],{},[2133,89931,2177],{},[898,89933,4661],{"mathvariant":2377},[2133,89935,2135],{},[9151,89937,89938,89940,89942],{},[898,89939,1724],{},[2133,89941,2135],{},[895,89943,89944,89946,89948],{},[2133,89945,2281],{},[898,89947,4661],{"mathvariant":2377},[2133,89949,2177],{},[1726,89951,1742],{"separator":1741},[5865,89953],{"width":15270},[9151,89955,89956,89958,89960],{},[898,89957,900],{},[2133,89959,32527],{},[895,89961,89962,89964],{},[1726,89963,2379],{"mathvariant":2377},[1726,89965,2379],{"mathvariant":2377},[1726,89967,1728],{},[1726,89969,2228],{},[2326,89971,89972],{"scriptlevel":2328,"displaystyle":1734},[2330,89973,89974,89976],{},[2133,89975,2135],{},[2133,89977,3989],{},[9151,89979,89980,89982,89984],{},[898,89981,1724],{},[2133,89983,2281],{},[895,89985,89986,89988,89990],{},[2133,89987,2281],{},[898,89989,4661],{"mathvariant":2377},[2133,89991,2135],{},[9151,89993,89994,89996,89998],{},[898,89995,1724],{},[2133,89997,2135],{},[895,89999,90000,90002,90004,90006],{},[1726,90001,2228],{},[2133,90003,2231],{},[898,90005,4661],{"mathvariant":2377},[2133,90007,2177],{},[1726,90009,1742],{"separator":1741},[902,90011,90012],{"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},",[724,90014,90015,90016,90058],{},"opět ",[883,90017,90019],{"className":90018},[886],[888,90020,90021],{"xmlns":890},[892,90022,90023,90055],{},[895,90024,90025,90037,90039,90051,90053],{},[9151,90026,90027,90029,90031],{},[898,90028,900],{},[2133,90030,2901],{},[895,90032,90033,90035],{},[1726,90034,2379],{"mathvariant":2377},[1726,90036,2379],{"mathvariant":2377},[1726,90038,1742],{"separator":1741},[9151,90040,90041,90043,90045],{},[898,90042,900],{},[2133,90044,32527],{},[895,90046,90047,90049],{},[1726,90048,2379],{"mathvariant":2377},[1726,90050,2379],{"mathvariant":2377},[1726,90052,3444],{},[2133,90054,2328],{},[902,90056,90057],{"encoding":904},"U''_{11}, U''_{22} \u003C 0",", platí (6.5).",[724,90060,90061],{},[38,90062,90063,90064,1888],{},"(a) Mezní užitečnosti v bodě ",[883,90065,90067],{"className":90066},[886],[888,90068,90069],{"xmlns":890},[892,90070,90071,90083],{},[895,90072,90073,90075,90077,90079,90081],{},[1726,90074,2487],{"stretchy":1734},[2133,90076,3087],{},[1726,90078,1742],{"separator":1741},[2133,90080,8363],{},[1726,90082,2502],{"stretchy":1734},[902,90084,90085],{"encoding":904},"[100, 200]",[883,90087,90089],{"className":90088},[886],[888,90090,90091],{"xmlns":890,"display":28047},[892,90092,90093,90160],{},[895,90094,90095,90097,90103,90105,90107,90109,90111,90113,90115,90123,90125,90139,90141,90153,90155,90158],{},[898,90096,2815],{},[2275,90098,90099,90101],{},[898,90100,900],{},[2133,90102,2281],{},[1726,90104,1735],{"stretchy":1734},[2133,90106,3087],{},[1726,90108,1742],{"separator":1741},[2133,90110,8363],{},[1726,90112,1762],{"stretchy":1734},[1726,90114,1728],{},[2326,90116,90117],{"scriptlevel":2328,"displaystyle":1734},[2330,90118,90119,90121],{},[2133,90120,2281],{},[2133,90122,2135],{},[1726,90124,3174],{},[2128,90126,90127,90129],{},[2133,90128,3087],{},[895,90130,90131,90133,90135,90137],{},[1726,90132,2228],{},[2133,90134,2281],{},[898,90136,4661],{"mathvariant":2377},[2133,90138,2135],{},[1726,90140,3174],{},[2128,90142,90143,90145],{},[2133,90144,8363],{},[895,90146,90147,90149,90151],{},[2133,90148,2281],{},[898,90150,4661],{"mathvariant":2377},[2133,90152,2177],{},[1726,90154,5887],{},[2133,90156,90157],{},"0,4204",[1726,90159,1742],{"separator":1741},[902,90161,90162],{"encoding":904},"MU_1(100, 200) = \\tfrac{1}{2} \\cdot 100^{-1\u002F2} \\cdot 200^{1\u002F3} \\doteq 0{,}4204,",[883,90164,90166],{"className":90165},[886],[888,90167,90168],{"xmlns":890,"display":28047},[892,90169,90170,90235],{},[895,90171,90172,90174,90180,90182,90184,90186,90188,90190,90192,90200,90202,90214,90216,90230,90232],{},[898,90173,2815],{},[2275,90175,90176,90178],{},[898,90177,900],{},[2133,90179,2135],{},[1726,90181,1735],{"stretchy":1734},[2133,90183,3087],{},[1726,90185,1742],{"separator":1741},[2133,90187,8363],{},[1726,90189,1762],{"stretchy":1734},[1726,90191,1728],{},[2326,90193,90194],{"scriptlevel":2328,"displaystyle":1734},[2330,90195,90196,90198],{},[2133,90197,2281],{},[2133,90199,2177],{},[1726,90201,3174],{},[2128,90203,90204,90206],{},[2133,90205,3087],{},[895,90207,90208,90210,90212],{},[2133,90209,2281],{},[898,90211,4661],{"mathvariant":2377},[2133,90213,2135],{},[1726,90215,3174],{},[2128,90217,90218,90220],{},[2133,90219,8363],{},[895,90221,90222,90224,90226,90228],{},[1726,90223,2228],{},[2133,90225,2135],{},[898,90227,4661],{"mathvariant":2377},[2133,90229,2177],{},[1726,90231,5887],{},[2133,90233,90234],{},"0,63067.",[902,90236,90237],{"encoding":904},"MU_2(100, 200) = \\tfrac{1}{3} \\cdot 100^{1\u002F2} \\cdot 200^{-2\u002F3} \\doteq 0{,}63067.",[724,90239,90240,1777,90242,90277,90278,90299,90300,90317],{},[614,90241,9201],{},[883,90243,90245],{"className":90244},[886],[888,90246,90247],{"xmlns":890},[892,90248,90249,90274],{},[895,90250,90251,90253,90259,90261,90263,90265,90267,90269,90271],{},[898,90252,2815],{},[2275,90254,90255,90257],{},[898,90256,900],{},[2133,90258,2135],{},[1726,90260,1735],{"stretchy":1734},[2133,90262,3087],{},[1726,90264,1742],{"separator":1741},[2133,90266,8363],{},[1726,90268,1762],{"stretchy":1734},[1726,90270,5887],{},[2133,90272,90273],{},"0,63067",[902,90275,90276],{"encoding":904},"MU_2(100, 200) \\doteq 0{,}63067"," znamená, že na hladině ",[883,90279,90281],{"className":90280},[886],[888,90282,90283],{"xmlns":890},[892,90284,90285,90297],{},[895,90286,90287,90289,90291,90293,90295],{},[1726,90288,2487],{"stretchy":1734},[2133,90290,3087],{},[1726,90292,1742],{"separator":1741},[2133,90294,8363],{},[1726,90296,2502],{"stretchy":1734},[902,90298,90085],{"encoding":904}," roste užitečnost při jednotkové změně ",[883,90301,90303],{"className":90302},[886],[888,90304,90305],{"xmlns":890},[892,90306,90307,90315],{},[895,90308,90309],{},[2275,90310,90311,90313],{},[898,90312,1724],{},[2133,90314,2135],{},[902,90316,29002],{"encoding":904}," přibližně o 0,63067.",[724,90319,90320,90339,90340,39165,90361,90378,90379,90405,90406,90423,90424,3148],{},[38,90321,90322,90323,90338],{},"(b) Odhad změny ",[883,90324,90326],{"className":90325},[886],[888,90327,90328],{"xmlns":890},[892,90329,90330,90336],{},[895,90331,90332,90334],{},[898,90333,2886],{"mathvariant":2377},[898,90335,900],{},[902,90337,88581],{"encoding":904}," pomocí totálního diferenciálu (6.3)."," Klesne-li vzhledem k hladině ",[883,90341,90343],{"className":90342},[886],[888,90344,90345],{"xmlns":890},[892,90346,90347,90359],{},[895,90348,90349,90351,90353,90355,90357],{},[1726,90350,2487],{"stretchy":1734},[2133,90352,3087],{},[1726,90354,1742],{"separator":1741},[2133,90356,8363],{},[1726,90358,2502],{"stretchy":1734},[902,90360,90085],{"encoding":904},[883,90362,90364],{"className":90363},[886],[888,90365,90366],{"xmlns":890},[892,90367,90368,90376],{},[895,90369,90370],{},[2275,90371,90372,90374],{},[898,90373,1724],{},[2133,90375,2281],{},[902,90377,28983],{"encoding":904}," na 98 (tj. ",[883,90380,90382],{"className":90381},[886],[888,90383,90384],{"xmlns":890},[892,90385,90386,90402],{},[895,90387,90388,90390,90396,90398,90400],{},[898,90389,2198],{"mathvariant":2377},[2275,90391,90392,90394],{},[898,90393,1724],{},[2133,90395,2281],{},[1726,90397,1728],{},[1726,90399,2228],{},[2133,90401,2135],{},[902,90403,90404],{"encoding":904},"\\mathrm{d} Q_1 = -2",") a vzroste-li ",[883,90407,90409],{"className":90408},[886],[888,90410,90411],{"xmlns":890},[892,90412,90413,90421],{},[895,90414,90415],{},[2275,90416,90417,90419],{},[898,90418,1724],{},[2133,90420,2135],{},[902,90422,29002],{"encoding":904}," o 3 (tj. ",[883,90425,90427],{"className":90426},[886],[888,90428,90429],{"xmlns":890},[892,90430,90431,90445],{},[895,90432,90433,90435,90441,90443],{},[898,90434,2198],{"mathvariant":2377},[2275,90436,90437,90439],{},[898,90438,1724],{},[2133,90440,2135],{},[1726,90442,1728],{},[2133,90444,2177],{},[902,90446,90447],{"encoding":904},"\\mathrm{d} Q_2 = 3",[883,90449,90451],{"className":90450},[886],[888,90452,90453],{"xmlns":890,"display":28047},[892,90454,90455,90506],{},[895,90456,90457,90459,90461,90463,90465,90467,90469,90471,90473,90475,90477,90479,90481,90483,90485,90487,90489,90491,90493,90496,90498,90501,90503],{},[898,90458,2886],{"mathvariant":2377},[898,90460,900],{},[1726,90462,1880],{},[898,90464,2198],{"mathvariant":2377},[898,90466,900],{},[1726,90468,1728],{},[2133,90470,90157],{},[1726,90472,3174],{},[1726,90474,1735],{"stretchy":1734},[1726,90476,2228],{},[2133,90478,2135],{},[1726,90480,1762],{"stretchy":1734},[1726,90482,2099],{},[2133,90484,90273],{},[1726,90486,3174],{},[2133,90488,2177],{},[1726,90490,1728],{},[1726,90492,2228],{},[2133,90494,90495],{},"0,8408",[1726,90497,2099],{},[2133,90499,90500],{},"1,89201",[1726,90502,5887],{},[2133,90504,90505],{},"1,05.",[902,90507,90508],{"encoding":904},"\\Delta U \\approx \\mathrm{d} U = 0{,}4204 \\cdot (-2) + 0{,}63067 \\cdot 3 = -0{,}8408 + 1{,}89201 \\doteq 1{,}05.",[724,90510,90511,90512,90515,90516,90567,90568,1888],{},"Užitečnost se tedy zvýší přibližně o ",[38,90513,90514],{},"1,05",". Skutečná změna je ",[883,90517,90519],{"className":90518},[886],[888,90520,90521],{"xmlns":890},[892,90522,90523,90564],{},[895,90524,90525,90527,90529,90531,90533,90535,90538,90540,90543,90545,90547,90549,90551,90553,90555,90557,90559,90561],{},[898,90526,2886],{"mathvariant":2377},[898,90528,900],{},[1726,90530,1728],{},[898,90532,900],{},[1726,90534,1735],{"stretchy":1734},[2133,90536,90537],{},"98",[1726,90539,1742],{"separator":1741},[2133,90541,90542],{},"203",[1726,90544,1762],{"stretchy":1734},[1726,90546,2228],{},[898,90548,900],{},[1726,90550,1735],{"stretchy":1734},[2133,90552,3087],{},[1726,90554,1742],{"separator":1741},[2133,90556,8363],{},[1726,90558,1762],{"stretchy":1734},[1726,90560,5887],{},[2133,90562,90563],{},"1,031",[902,90565,90566],{"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 ",[883,90569,90571],{"className":90570},[886],[888,90572,90573],{"xmlns":890},[892,90574,90575,90595],{},[895,90576,90577,90579,90585,90587,90589],{},[898,90578,2198],{"mathvariant":2377},[2275,90580,90581,90583],{},[898,90582,1724],{},[2133,90584,2281],{},[1726,90586,1742],{"separator":1741},[898,90588,2198],{"mathvariant":2377},[2275,90590,90591,90593],{},[898,90592,1724],{},[2133,90594,2135],{},[902,90596,88611],{"encoding":904},[115,90598,90600],{"id":90599},"cobb-douglasova-funkce-užitečnosti","Cobb-Douglasova funkce užitečnosti",[724,90602,90603],{},"Nejčastěji používané funkce užitečnosti mají tvar",[883,90605,90607],{"className":90606},[886],[888,90608,90609],{"xmlns":890,"display":28047},[892,90610,90611,90670],{},[20735,90612,90613],{"width":28052},[20740,90614,90615,90617,90663,90665],{},[20743,90616],{"width":28057},[20743,90618,90619],{},[895,90620,90621,90623,90625,90631,90633,90639,90641,90643,90651,90653,90661],{},[898,90622,900],{},[1726,90624,1735],{"stretchy":1734},[2275,90626,90627,90629],{},[898,90628,1724],{},[2133,90630,2281],{},[1726,90632,1742],{"separator":1741},[2275,90634,90635,90637],{},[898,90636,1724],{},[2133,90638,2135],{},[1726,90640,1762],{"stretchy":1734},[1726,90642,1728],{},[9151,90644,90645,90647,90649],{},[898,90646,1724],{},[2133,90648,2281],{},[898,90650,207],{},[1726,90652,3174],{},[9151,90654,90655,90657,90659],{},[898,90656,1724],{},[2133,90658,2135],{},[898,90660,2102],{},[1726,90662,1742],{"separator":1741},[20743,90664],{"width":28057},[20743,90666,90667],{},[2289,90668,90669],{},"(6.6)",[902,90671,90672],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^b, \\tag{6.6}",[724,90674,4298,90675,90693,90694,90696,90697,90701,90702,90732,90733,90755],{},[883,90676,90678],{"className":90677},[886],[888,90679,90680],{"xmlns":890},[892,90681,90682,90690],{},[895,90683,90684,90686,90688],{},[898,90685,207],{},[1726,90687,1742],{"separator":1741},[898,90689,2102],{},[902,90691,90692],{"encoding":904},"a, b"," jsou kladná čísla; nazývají se ",[38,90695,74679],{}," (v příbuznosti s produkčními funkcemi — viz ",[207,90698,90700],{"className":90699,"dataFsResolvedFilePath":857,"href":858},[210],"kapitola 5","). Obvykle se volí ",[883,90703,90705],{"className":90704},[886],[888,90706,90707],{"xmlns":890},[892,90708,90709,90729],{},[895,90710,90711,90713,90715,90717,90719,90721,90723,90725,90727],{},[898,90712,207],{},[1726,90714,1742],{"separator":1741},[898,90716,2102],{},[1726,90718,6493],{},[1726,90720,1735],{"stretchy":1734},[2133,90722,2328],{},[1726,90724,1742],{"separator":1741},[2133,90726,2281],{},[1726,90728,1762],{"stretchy":1734},[902,90730,90731],{"encoding":904},"a, b \\in (0, 1)",", často se klade ",[883,90734,90736],{"className":90735},[886],[888,90737,90738],{"xmlns":890},[892,90739,90740,90752],{},[895,90741,90742,90744,90746,90748,90750],{},[898,90743,2102],{},[1726,90745,1728],{},[2133,90747,2281],{},[1726,90749,2228],{},[898,90751,207],{},[902,90753,90754],{"encoding":904},"b = 1 - a",", čímž (6.6) přejde na tvar",[724,90757,90758],{},[1647,90759],{"alt":90760,"className":90761,"src":90762},"imek-cobb-douglas-3d-plus-ic",[210,1651],"\u002Fwiki-assets\u002Fimek-cobb-douglas-3d-plus-ic.jpeg",[883,90764,90766],{"className":90765},[886],[888,90767,90768],{"xmlns":890,"display":28047},[892,90769,90770,90820],{},[895,90771,90772,90774,90776,90782,90784,90790,90792,90794,90802,90804,90818],{},[898,90773,900],{},[1726,90775,1735],{"stretchy":1734},[2275,90777,90778,90780],{},[898,90779,1724],{},[2133,90781,2281],{},[1726,90783,1742],{"separator":1741},[2275,90785,90786,90788],{},[898,90787,1724],{},[2133,90789,2135],{},[1726,90791,1762],{"stretchy":1734},[1726,90793,1728],{},[9151,90795,90796,90798,90800],{},[898,90797,1724],{},[2133,90799,2281],{},[898,90801,207],{},[1726,90803,3174],{},[9151,90805,90806,90808,90810],{},[898,90807,1724],{},[2133,90809,2135],{},[895,90811,90812,90814,90816],{},[2133,90813,2281],{},[1726,90815,2228],{},[898,90817,207],{},[898,90819,1888],{"mathvariant":2377},[902,90821,90822],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^{1-a}.",[3859,90824,90825,90874,90996,91130],{},[724,90826,90827,90829,90830],{},[883,90828,52675],{}," Příklad 6.3 — ověření vlastností pro ",[883,90831,90833],{"className":90832},[886],[888,90834,90835],{"xmlns":890},[892,90836,90837,90871],{},[895,90838,90839,90841,90843,90857],{},[898,90840,900],{},[1726,90842,1728],{},[9151,90844,90845,90847,90849],{},[898,90846,1724],{},[2133,90848,2281],{},[895,90850,90851,90853,90855],{},[2133,90852,2281],{},[898,90854,4661],{"mathvariant":2377},[2133,90856,2352],{},[9151,90858,90859,90861,90863],{},[898,90860,1724],{},[2133,90862,2135],{},[895,90864,90865,90867,90869],{},[2133,90866,2177],{},[898,90868,4661],{"mathvariant":2377},[2133,90870,2352],{},[902,90872,90873],{"encoding":904},"U = Q_1^{1\u002F4} Q_2^{3\u002F4}",[883,90875,90877],{"className":90876},[886],[888,90878,90879],{"xmlns":890,"display":28047},[892,90880,90881,90993],{},[895,90882,90883,90891,90893,90901,90917,90931,90933,90935,90937,90939,90947,90949,90957,90971,90987,90989,90991],{},[9151,90884,90885,90887,90889],{},[898,90886,900],{},[2133,90888,2281],{},[1726,90890,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,90892,1728],{},[2326,90894,90895],{"scriptlevel":2328,"displaystyle":1734},[2330,90896,90897,90899],{},[2133,90898,2281],{},[2133,90900,2352],{},[9151,90902,90903,90905,90907],{},[898,90904,1724],{},[2133,90906,2281],{},[895,90908,90909,90911,90913,90915],{},[1726,90910,2228],{},[2133,90912,2177],{},[898,90914,4661],{"mathvariant":2377},[2133,90916,2352],{},[9151,90918,90919,90921,90923],{},[898,90920,1724],{},[2133,90922,2135],{},[895,90924,90925,90927,90929],{},[2133,90926,2177],{},[898,90928,4661],{"mathvariant":2377},[2133,90930,2352],{},[1726,90932,3405],{},[2133,90934,2328],{},[1726,90936,1742],{"separator":1741},[5865,90938],{"width":15270},[9151,90940,90941,90943,90945],{},[898,90942,900],{},[2133,90944,2135],{},[1726,90946,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,90948,1728],{},[2326,90950,90951],{"scriptlevel":2328,"displaystyle":1734},[2330,90952,90953,90955],{},[2133,90954,2177],{},[2133,90956,2352],{},[9151,90958,90959,90961,90963],{},[898,90960,1724],{},[2133,90962,2281],{},[895,90964,90965,90967,90969],{},[2133,90966,2281],{},[898,90968,4661],{"mathvariant":2377},[2133,90970,2352],{},[9151,90972,90973,90975,90977],{},[898,90974,1724],{},[2133,90976,2135],{},[895,90978,90979,90981,90983,90985],{},[1726,90980,2228],{},[2133,90982,2281],{},[898,90984,4661],{"mathvariant":2377},[2133,90986,2352],{},[1726,90988,3405],{},[2133,90990,2328],{},[1726,90992,1742],{"separator":1741},[902,90994,90995],{"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,",[883,90997,90999],{"className":90998},[886],[888,91000,91001],{"xmlns":890,"display":28047},[892,91002,91003,91127],{},[895,91004,91005,91017,91019,91021,91029,91045,91059,91061,91063,91065,91067,91079,91081,91083,91091,91105,91121,91123,91125],{},[9151,91006,91007,91009,91011],{},[898,91008,900],{},[2133,91010,2901],{},[895,91012,91013,91015],{},[1726,91014,2379],{"mathvariant":2377},[1726,91016,2379],{"mathvariant":2377},[1726,91018,1728],{},[1726,91020,2228],{},[2326,91022,91023],{"scriptlevel":2328,"displaystyle":1734},[2330,91024,91025,91027],{},[2133,91026,2177],{},[2133,91028,41843],{},[9151,91030,91031,91033,91035],{},[898,91032,1724],{},[2133,91034,2281],{},[895,91036,91037,91039,91041,91043],{},[1726,91038,2228],{},[2133,91040,24182],{},[898,91042,4661],{"mathvariant":2377},[2133,91044,2352],{},[9151,91046,91047,91049,91051],{},[898,91048,1724],{},[2133,91050,2135],{},[895,91052,91053,91055,91057],{},[2133,91054,2177],{},[898,91056,4661],{"mathvariant":2377},[2133,91058,2352],{},[1726,91060,3444],{},[2133,91062,2328],{},[1726,91064,1742],{"separator":1741},[5865,91066],{"width":15270},[9151,91068,91069,91071,91073],{},[898,91070,900],{},[2133,91072,32527],{},[895,91074,91075,91077],{},[1726,91076,2379],{"mathvariant":2377},[1726,91078,2379],{"mathvariant":2377},[1726,91080,1728],{},[1726,91082,2228],{},[2326,91084,91085],{"scriptlevel":2328,"displaystyle":1734},[2330,91086,91087,91089],{},[2133,91088,2177],{},[2133,91090,41843],{},[9151,91092,91093,91095,91097],{},[898,91094,1724],{},[2133,91096,2281],{},[895,91098,91099,91101,91103],{},[2133,91100,2281],{},[898,91102,4661],{"mathvariant":2377},[2133,91104,2352],{},[9151,91106,91107,91109,91111],{},[898,91108,1724],{},[2133,91110,2135],{},[895,91112,91113,91115,91117,91119],{},[1726,91114,2228],{},[2133,91116,2231],{},[898,91118,4661],{"mathvariant":2377},[2133,91120,2352],{},[1726,91122,3444],{},[2133,91124,2328],{},[1726,91126,1742],{"separator":1741},[902,91128,91129],{"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,",[724,91131,91132],{},"tedy podmínky (6.4) i (6.5) jsou splněny.",[115,91134,91136],{"id":91135},"indiferenční-křivky-křivky-užitečnosti-a-jejich-vlastnosti","Indiferenční křivky (křivky užitečnosti) a jejich vlastnosti",[724,91138,91139,91142],{},[38,91140,91141],{},"Křivky užitečnosti"," (utility curves) jsou indiferenční křivky funkce užitečnosti. Jsou dány rovnicí",[883,91144,91146],{"className":91145},[886],[888,91147,91148],{"xmlns":890,"display":28047},[892,91149,91150,91193],{},[20735,91151,91152],{"width":28052},[20740,91153,91154,91156,91186,91188],{},[20743,91155],{"width":28057},[20743,91157,91158],{},[895,91159,91160,91162,91164,91170,91172,91178,91180,91182,91184],{},[898,91161,900],{},[1726,91163,1735],{"stretchy":1734},[2275,91165,91166,91168],{},[898,91167,1724],{},[2133,91169,2281],{},[1726,91171,1742],{"separator":1741},[2275,91173,91174,91176],{},[898,91175,1724],{},[2133,91177,2135],{},[1726,91179,1762],{"stretchy":1734},[1726,91181,1728],{},[898,91183,2146],{},[1726,91185,1742],{"separator":1741},[20743,91187],{"width":28057},[20743,91189,91190],{},[2289,91191,91192],{},"(6.7)",[902,91194,91195],{"encoding":904},"U(Q_1, Q_2) = c, \\tag{6.7}",[724,91197,4298,91198,91211],{},[883,91199,91201],{"className":91200},[886],[888,91202,91203],{"xmlns":890},[892,91204,91205,91209],{},[895,91206,91207],{},[898,91208,2146],{},[902,91210,2146],{"encoding":904}," je kladná konstanta. Pro Cobb-Douglasovu funkci:",[883,91213,91215],{"className":91214},[886],[888,91216,91217],{"xmlns":890,"display":28047},[892,91218,91219,91260],{},[20735,91220,91221],{"width":28052},[20740,91222,91223,91225,91253,91255],{},[20743,91224],{"width":28057},[20743,91226,91227],{},[895,91228,91229,91237,91239,91247,91249,91251],{},[9151,91230,91231,91233,91235],{},[898,91232,1724],{},[2133,91234,2281],{},[898,91236,207],{},[1726,91238,3174],{},[9151,91240,91241,91243,91245],{},[898,91242,1724],{},[2133,91244,2135],{},[898,91246,2102],{},[1726,91248,1728],{},[898,91250,2146],{},[898,91252,1888],{"mathvariant":2377},[20743,91254],{"width":28057},[20743,91256,91257],{},[2289,91258,91259],{},"(6.8)",[902,91261,91262],{"encoding":904},"Q_1^a \\cdot Q_2^b = c. \\tag{6.8}",[724,91264,91265,91266,4346,91296,1777,91299,91312,91313,91348,91349,91366,91367,91396,91397,91400],{},"Body na téže křivce užitečnosti reprezentují kombinace ",[883,91267,91269],{"className":91268},[886],[888,91270,91271],{"xmlns":890},[892,91272,91273,91293],{},[895,91274,91275,91277,91283,91285,91291],{},[1726,91276,2487],{"stretchy":1734},[2275,91278,91279,91281],{},[898,91280,1724],{},[2133,91282,2281],{},[1726,91284,1742],{"separator":1741},[2275,91286,91287,91289],{},[898,91288,1724],{},[2133,91290,2135],{},[1726,91292,2502],{"stretchy":1734},[902,91294,91295],{"encoding":904},"[Q_1, Q_2]",[38,91297,91298],{},"stejnou úrovní uspokojení",[883,91300,91302],{"className":91301},[886],[888,91303,91304],{"xmlns":890},[892,91305,91306,91310],{},[895,91307,91308],{},[898,91309,2146],{},[902,91311,2146],{"encoding":904},". Křivky užitečnosti vznikají jako průsečnice plochy ",[883,91314,91316],{"className":91315},[886],[888,91317,91318],{"xmlns":890},[892,91319,91320,91346],{},[895,91321,91322,91324,91326,91328,91330,91336,91338,91344],{},[898,91323,900],{},[1726,91325,1728],{},[898,91327,900],{},[1726,91329,1735],{"stretchy":1734},[2275,91331,91332,91334],{},[898,91333,1724],{},[2133,91335,2281],{},[1726,91337,1742],{"separator":1741},[2275,91339,91340,91342],{},[898,91341,1724],{},[2133,91343,2135],{},[1726,91345,1762],{"stretchy":1734},[902,91347,87436],{"encoding":904}," s rovinami ",[883,91350,91352],{"className":91351},[886],[888,91353,91354],{"xmlns":890},[892,91355,91356,91364],{},[895,91357,91358,91360,91362],{},[898,91359,900],{},[1726,91361,1728],{},[898,91363,2146],{},[902,91365,86652],{"encoding":904}," rovnoběžnými s rovinou ",[883,91368,91370],{"className":91369},[886],[888,91371,91372],{"xmlns":890},[892,91373,91374,91394],{},[895,91375,91376,91378,91384,91386,91392],{},[1726,91377,1735],{"stretchy":1734},[2275,91379,91380,91382],{},[898,91381,1724],{},[2133,91383,2281],{},[1726,91385,1742],{"separator":1741},[2275,91387,91388,91390],{},[898,91389,1724],{},[2133,91391,2135],{},[1726,91393,1762],{"stretchy":1734},[902,91395,89599],{"encoding":904}," (obrázek 6.2). Jsou v příbuznosti s ",[38,91398,91399],{},"izokvantami"," produkčních funkcí.",[724,91402,91403],{},[614,91404,91405,91406,89477,91424,91442,91443,1888],{},"Obrázek 6.3 — typický tvar křivek užitečnosti pro Cobb-Douglasovu funkci pro ",[883,91407,91409],{"className":91408},[886],[888,91410,91411],{"xmlns":890},[892,91412,91413,91421],{},[895,91414,91415,91417,91419],{},[898,91416,207],{},[1726,91418,3444],{},[898,91420,2102],{},[902,91422,91423],{"encoding":904},"a \u003C b",[883,91425,91427],{"className":91426},[886],[888,91428,91429],{"xmlns":890},[892,91430,91431,91439],{},[895,91432,91433,91435,91437],{},[898,91434,207],{},[1726,91436,3405],{},[898,91438,2102],{},[902,91440,91441],{"encoding":904},"a > b"," (vpravo); různé hladiny ",[883,91444,91446],{"className":91445},[886],[888,91447,91448],{"xmlns":890},[892,91449,91450,91474],{},[895,91451,91452,91458,91460,91466,91468],{},[2275,91453,91454,91456],{},[898,91455,2146],{},[2133,91457,2328],{},[1726,91459,3444],{},[2275,91461,91462,91464],{},[898,91463,2146],{},[2133,91465,2281],{},[1726,91467,3444],{},[2275,91469,91470,91472],{},[898,91471,2146],{},[2133,91473,2135],{},[902,91475,91476],{"encoding":904},"c_0 \u003C c_1 \u003C c_2",[724,91478,91479],{},[614,91480,91481,91482,91511,91512,91570,91571,91589],{},"Obrázek 6.4 — soustava křivek užitečnosti pro tři hladiny (10, 20, 30) v rovině ",[883,91483,91485],{"className":91484},[886],[888,91486,91487],{"xmlns":890},[892,91488,91489,91509],{},[895,91490,91491,91493,91499,91501,91507],{},[1726,91492,1735],{"stretchy":1734},[2275,91494,91495,91497],{},[898,91496,1724],{},[2133,91498,2281],{},[1726,91500,1742],{"separator":1741},[2275,91502,91503,91505],{},[898,91504,1724],{},[2133,91506,2135],{},[1726,91508,1762],{"stretchy":1734},[902,91510,89599],{"encoding":904},"; body ",[883,91513,91515],{"className":91514},[886],[888,91516,91517],{"xmlns":890},[892,91518,91519,91567],{},[895,91520,91521,91523,91525,91527,91533,91535,91541,91543,91545,91547,91549,91551,91557,91559,91565],{},[898,91522,4243],{},[1726,91524,1728],{},[1726,91526,2487],{"stretchy":1734},[2275,91528,91529,91531],{},[898,91530,207],{},[2133,91532,2281],{},[1726,91534,1742],{"separator":1741},[2275,91536,91537,91539],{},[898,91538,207],{},[2133,91540,2135],{},[1726,91542,2502],{"stretchy":1734},[1726,91544,1742],{"separator":1741},[898,91546,23234],{},[1726,91548,1728],{},[1726,91550,2487],{"stretchy":1734},[2275,91552,91553,91555],{},[898,91554,2102],{},[2133,91556,2281],{},[1726,91558,1742],{"separator":1741},[2275,91560,91561,91563],{},[898,91562,2102],{},[2133,91564,2135],{},[1726,91566,2502],{"stretchy":1734},[902,91568,91569],{"encoding":904},"A = [a_1, a_2], B = [b_1, b_2]"," leží na téže křivce (hladina 10), body ",[883,91572,91574],{"className":91573},[886],[888,91575,91576],{"xmlns":890},[892,91577,91578,91586],{},[895,91579,91580,91582,91584],{},[898,91581,2775],{},[1726,91583,1742],{"separator":1741},[898,91585,1731],{},[902,91587,91588],{"encoding":904},"C, D"," na vyšší hladině.",[3859,91591,91592],{},[724,91593,91594,91596,91597,91659,91660,91704,91705,91739,91740,26170,91758,91739,91812,26170,91830,91906],{},[883,91595,52675],{}," Příklad 6.4 — rovnice křivek užitečnosti\nPro ",[883,91598,91600],{"className":91599},[886],[888,91601,91602],{"xmlns":890},[892,91603,91604,91656],{},[895,91605,91606,91608,91610,91616,91618,91624,91626,91628,91642],{},[898,91607,900],{},[1726,91609,1735],{"stretchy":1734},[2275,91611,91612,91614],{},[898,91613,1724],{},[2133,91615,2281],{},[1726,91617,1742],{"separator":1741},[2275,91619,91620,91622],{},[898,91621,1724],{},[2133,91623,2135],{},[1726,91625,1762],{"stretchy":1734},[1726,91627,1728],{},[9151,91629,91630,91632,91634],{},[898,91631,1724],{},[2133,91633,2281],{},[895,91635,91636,91638,91640],{},[2133,91637,2281],{},[898,91639,4661],{"mathvariant":2377},[2133,91641,2352],{},[9151,91643,91644,91646,91648],{},[898,91645,1724],{},[2133,91647,2135],{},[895,91649,91650,91652,91654],{},[2133,91651,2177],{},[898,91653,4661],{"mathvariant":2377},[2133,91655,2352],{},[902,91657,91658],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F4} Q_2^{3\u002F4}"," mají křivky užitečnosti rovnici ",[883,91661,91663],{"className":91662},[886],[888,91664,91665],{"xmlns":890},[892,91666,91667,91701],{},[895,91668,91669,91683,91697,91699],{},[9151,91670,91671,91673,91675],{},[898,91672,1724],{},[2133,91674,2281],{},[895,91676,91677,91679,91681],{},[2133,91678,2281],{},[898,91680,4661],{"mathvariant":2377},[2133,91682,2352],{},[9151,91684,91685,91687,91689],{},[898,91686,1724],{},[2133,91688,2135],{},[895,91690,91691,91693,91695],{},[2133,91692,2177],{},[898,91694,4661],{"mathvariant":2377},[2133,91696,2352],{},[1726,91698,1728],{},[898,91700,2146],{},[902,91702,91703],{"encoding":904},"Q_1^{1\u002F4} Q_2^{3\u002F4} = c",". Umocněním na čtvrtou mocninu dostáváme ",[883,91706,91708],{"className":91707},[886],[888,91709,91710],{"xmlns":890},[892,91711,91712,91736],{},[895,91713,91714,91720,91728,91730],{},[2275,91715,91716,91718],{},[898,91717,1724],{},[2133,91719,2281],{},[9151,91721,91722,91724,91726],{},[898,91723,1724],{},[2133,91725,2135],{},[2133,91727,2177],{},[1726,91729,1728],{},[2128,91731,91732,91734],{},[898,91733,2146],{},[2133,91735,2352],{},[902,91737,91738],{"encoding":904},"Q_1 Q_2^{3} = c^{4}",". Pro ",[883,91741,91743],{"className":91742},[886],[888,91744,91745],{"xmlns":890},[892,91746,91747,91755],{},[895,91748,91749,91751,91753],{},[898,91750,2146],{},[1726,91752,1728],{},[2133,91754,2281],{},[902,91756,91757],{"encoding":904},"c = 1",[883,91759,91761],{"className":91760},[886],[888,91762,91763],{"xmlns":890},[892,91764,91765,91809],{},[895,91766,91767,91773,91775,91791,91793],{},[2275,91768,91769,91771],{},[898,91770,1724],{},[2133,91772,2135],{},[1726,91774,1728],{},[9151,91776,91777,91779,91781],{},[898,91778,1724],{},[2133,91780,2281],{},[895,91782,91783,91785,91787,91789],{},[1726,91784,2228],{},[2133,91786,2281],{},[898,91788,4661],{"mathvariant":2377},[2133,91790,2177],{},[1726,91792,1728],{},[2326,91794,91795],{"scriptlevel":2328,"displaystyle":1741},[2330,91796,91797,91799],{},[2133,91798,2281],{},[82007,91800,91801,91807],{},[2275,91802,91803,91805],{},[898,91804,1724],{},[2133,91806,2281],{},[2133,91808,2177],{},[902,91810,91811],{"encoding":904},"Q_2 = Q_1^{-1\u002F3} = \\dfrac{1}{\\sqrt[3]{Q_1}}",[883,91813,91815],{"className":91814},[886],[888,91816,91817],{"xmlns":890},[892,91818,91819,91827],{},[895,91820,91821,91823,91825],{},[898,91822,2146],{},[1726,91824,1728],{},[2133,91826,2135],{},[902,91828,91829],{"encoding":904},"c = 2",[883,91831,91833],{"className":91832},[886],[888,91834,91835],{"xmlns":890},[892,91836,91837,91903],{},[895,91838,91839,91845,91847,91859,91861,91877,91879],{},[2275,91840,91841,91843],{},[898,91842,1724],{},[2133,91844,2135],{},[1726,91846,1728],{},[2128,91848,91849,91851],{},[2133,91850,2135],{},[895,91852,91853,91855,91857],{},[2133,91854,2352],{},[898,91856,4661],{"mathvariant":2377},[2133,91858,2177],{},[1726,91860,3174],{},[9151,91862,91863,91865,91867],{},[898,91864,1724],{},[2133,91866,2281],{},[895,91868,91869,91871,91873,91875],{},[1726,91870,2228],{},[2133,91872,2281],{},[898,91874,4661],{"mathvariant":2377},[2133,91876,2177],{},[1726,91878,1728],{},[2326,91880,91881],{"scriptlevel":2328,"displaystyle":1741},[2330,91882,91883,91893],{},[895,91884,91885,91887],{},[2133,91886,2135],{},[82007,91888,91889,91891],{},[2133,91890,2135],{},[2133,91892,2177],{},[82007,91894,91895,91901],{},[2275,91896,91897,91899],{},[898,91898,1724],{},[2133,91900,2281],{},[2133,91902,2177],{},[902,91904,91905],{"encoding":904},"Q_2 = 2^{4\u002F3} \\cdot Q_1^{-1\u002F3} = \\dfrac{2 \\sqrt[3]{2}}{\\sqrt[3]{Q_1}}"," (obrázek 6.5).",[198,91908,91910],{"id":91909},"čtyři-vlastnosti-křivek-užitečnosti","Čtyři vlastnosti křivek užitečnosti",[724,91912,91913],{},[1647,91914],{"alt":91915,"className":91916,"src":91917},"imek-ic-4vlastnosti-anotovane",[210,1651],"\u002Fwiki-assets\u002Fimek-ic-4vlastnosti-anotovane.jpeg",[3859,91919,91920,91929,91976,92020,92026,92032],{},[724,91921,91922,91924,91925,91928],{},[883,91923,4400],{}," Čtyři základní vlastnosti indiferenčních křivek\n",[38,91926,91927],{},"1° Klesající."," Je-li nakoupeno méně jednoho zboží, je k dosažení stejného uspokojení třeba kompenzovat větším množstvím druhého zboží. Sklon tečny je",[724,91930,91931],{},[883,91932,91934],{"className":91933},[886],[888,91935,91936],{"xmlns":890},[892,91937,91938,91973],{},[895,91939,91940,91943,91945,91947,91949,91951,91969,91971],{},[898,91941,91942],{"mathvariant":2377},"tg",[1726,91944,56180],{},[898,91946,18843],{},[1726,91948,1728],{},[1726,91950,2228],{},[2330,91952,91953,91961],{},[9151,91954,91955,91957,91959],{},[898,91956,900],{},[2133,91958,2281],{},[1726,91960,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[9151,91962,91963,91965,91967],{},[898,91964,900],{},[2133,91966,2135],{},[1726,91968,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,91970,3444],{},[2133,91972,2328],{},[902,91974,91975],{"encoding":904},"\\operatorname{tg} \\alpha = -\\frac{U'_1}{U'_2} \u003C 0",[724,91977,91978,91979,92019],{},"(derivace implicitně zadané funkce ",[883,91980,91982],{"className":91981},[886],[888,91983,91984],{"xmlns":890},[892,91985,91986,92016],{},[895,91987,91988,91990,91992,91998,92000,92006,92008,92010,92012,92014],{},[898,91989,900],{},[1726,91991,1735],{"stretchy":1734},[2275,91993,91994,91996],{},[898,91995,1724],{},[2133,91997,2281],{},[1726,91999,1742],{"separator":1741},[2275,92001,92002,92004],{},[898,92003,1724],{},[2133,92005,2135],{},[1726,92007,1762],{"stretchy":1734},[1726,92009,2228],{},[898,92011,2146],{},[1726,92013,1728],{},[2133,92015,2328],{},[902,92017,92018],{"encoding":904},"U(Q_1, Q_2) - c = 0","). Ze záporné derivace plyne klesající průběh.",[724,92021,92022,92025],{},[38,92023,92024],{},"2° Neprotínají se."," V průsečíku by týž svazek ležel na dvou různých hladinách užitečnosti, což je spor.",[724,92027,92028,92031],{},[38,92029,92030],{},"3° Čím vzdálenější od počátku, tím vyšší užitečnost"," (obrázek 6.4).",[724,92033,92034,92037,92038,92056,92057,92073,92074,92077],{},[38,92035,92036],{},"4° Konvexní."," Pro každé dva body ",[883,92039,92041],{"className":92040},[886],[888,92042,92043],{"xmlns":890},[892,92044,92045,92053],{},[895,92046,92047,92049,92051],{},[898,92048,4243],{},[1726,92050,1742],{"separator":1741},[898,92052,23234],{},[902,92054,92055],{"encoding":904},"A, B"," na téže křivce leží vnitřní body úsečky ",[883,92058,92060],{"className":92059},[886],[888,92061,92062],{"xmlns":890},[892,92063,92064,92070],{},[895,92065,92066,92068],{},[898,92067,4243],{},[898,92069,23234],{},[902,92071,92072],{"encoding":904},"AB"," ve ",[38,92075,92076],{},"vyšší"," hladině užitečnosti (tj. „nad\" křivkou) — vyjadřuje to preferenci smíšených svazků před krajními.",[724,92079,92080],{},[614,92081,92082,92083,92118,92119,1888],{},"Obrázek 6.6 — klesající a konvexní průběh ",[883,92084,92086],{"className":92085},[886],[888,92087,92088],{"xmlns":890},[892,92089,92090,92116],{},[895,92091,92092,92094,92096,92102,92104,92110,92112,92114],{},[898,92093,900],{},[1726,92095,1735],{"stretchy":1734},[2275,92097,92098,92100],{},[898,92099,1724],{},[2133,92101,2281],{},[1726,92103,1742],{"separator":1741},[2275,92105,92106,92108],{},[898,92107,1724],{},[2133,92109,2135],{},[1726,92111,1762],{"stretchy":1734},[1726,92113,1728],{},[898,92115,2146],{},[902,92117,9752],{"encoding":904}," s tečnou se sklonem ",[883,92120,92122],{"className":92121},[886],[888,92123,92124],{"xmlns":890},[892,92125,92126,92134],{},[895,92127,92128,92130,92132],{},[898,92129,91942],{"mathvariant":2377},[1726,92131,56180],{},[898,92133,18843],{},[902,92135,92136],{"encoding":904},"\\operatorname{tg}\\alpha",[115,92138,92140],{"id":92139},"mezní-míra-komoditní-substituce-mrcs","Mezní míra komoditní substituce (MRCS)",[724,92142,92143,1777,92146,10009,92159,92162],{},[38,92144,92145],{},"Mezní míra komoditní substituce",[883,92147,92149],{"className":92148},[886],[888,92150,92151],{"xmlns":890},[892,92152,92153,92157],{},[895,92154,92155],{},[2289,92156,10587],{},[902,92158,28219],{"encoding":904},[38,92160,92161],{},"marginal rate of commodity substitution",") je podíl mezních užitečností:",[883,92164,92166],{"className":92165},[886],[888,92167,92168],{"xmlns":890,"display":28047},[892,92169,92170,92257],{},[20735,92171,92172],{"width":28052},[20740,92173,92174,92176,92250,92252],{},[20743,92175],{"width":28057},[20743,92177,92178],{},[895,92179,92180,92182,92184,92186,92188,92194,92196,92202,92204,92206,92228,92230,92248],{},[2289,92181,10587],{},[1726,92183,1728],{},[2289,92185,10587],{},[1726,92187,1735],{"stretchy":1734},[2275,92189,92190,92192],{},[898,92191,1724],{},[2133,92193,2281],{},[1726,92195,1742],{"separator":1741},[2275,92197,92198,92200],{},[898,92199,1724],{},[2133,92201,2135],{},[1726,92203,1762],{"stretchy":1734},[1726,92205,1728],{},[2330,92207,92208,92218],{},[895,92209,92210,92212],{},[898,92211,2815],{},[2275,92213,92214,92216],{},[898,92215,900],{},[2133,92217,2281],{},[895,92219,92220,92222],{},[898,92221,2815],{},[2275,92223,92224,92226],{},[898,92225,900],{},[2133,92227,2135],{},[1726,92229,1728],{},[2330,92231,92232,92240],{},[9151,92233,92234,92236,92238],{},[898,92235,900],{},[2133,92237,2281],{},[1726,92239,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[9151,92241,92242,92244,92246],{},[898,92243,900],{},[2133,92245,2135],{},[1726,92247,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[898,92249,1888],{"mathvariant":2377},[20743,92251],{"width":28057},[20743,92253,92254],{},[2289,92255,92256],{},"(6.9)",[902,92258,92259],{"encoding":904},"\\text{MRCS} = \\text{MRCS}(Q_1, Q_2) = \\frac{MU_1}{MU_2} = \\frac{U'_1}{U'_2}. \\tag{6.9}",[724,92261,92262,92263,92297,92298,92330,92331,92366,92367,92380],{},"Geometricky: ",[883,92264,92266],{"className":92265},[886],[888,92267,92268],{"xmlns":890},[892,92269,92270,92294],{},[895,92271,92272,92274],{},[1726,92273,2228],{},[2326,92275,92276],{"scriptlevel":2328,"displaystyle":1734},[2330,92277,92278,92286],{},[9151,92279,92280,92282,92284],{},[898,92281,900],{},[2133,92283,2281],{},[1726,92285,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[9151,92287,92288,92290,92292],{},[898,92289,900],{},[2133,92291,2135],{},[1726,92293,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[902,92295,92296],{"encoding":904},"-\\tfrac{U'_1}{U'_2}"," je derivace funkce ",[883,92299,92301],{"className":92300},[886],[888,92302,92303],{"xmlns":890},[892,92304,92305,92327],{},[895,92306,92307,92313,92315,92317,92319,92325],{},[2275,92308,92309,92311],{},[898,92310,1724],{},[2133,92312,2135],{},[1726,92314,1728],{},[898,92316,2008],{},[1726,92318,1735],{"stretchy":1734},[2275,92320,92321,92323],{},[898,92322,1724],{},[2133,92324,2281],{},[1726,92326,1762],{"stretchy":1734},[902,92328,92329],{"encoding":904},"Q_2 = f(Q_1)"," zadané implicitně rovnicí ",[883,92332,92334],{"className":92333},[886],[888,92335,92336],{"xmlns":890},[892,92337,92338,92364],{},[895,92339,92340,92342,92344,92350,92352,92358,92360,92362],{},[898,92341,900],{},[1726,92343,1735],{"stretchy":1734},[2275,92345,92346,92348],{},[898,92347,1724],{},[2133,92349,2281],{},[1726,92351,1742],{"separator":1741},[2275,92353,92354,92356],{},[898,92355,1724],{},[2133,92357,2135],{},[1726,92359,1762],{"stretchy":1734},[1726,92361,1728],{},[898,92363,2146],{},[902,92365,9752],{"encoding":904},". Protože je vždy záporná (křivka je klesající), bereme absolutní hodnotu a kladný ",[883,92368,92370],{"className":92369},[886],[888,92371,92372],{"xmlns":890},[892,92373,92374,92378],{},[895,92375,92376],{},[2289,92377,10587],{},[902,92379,28219],{"encoding":904}," chápeme jako velikost kompenzace.",[3859,92382,92383],{},[724,92384,92385,92387,92388,8088,92420,92458,92459,92476,92477,92494],{},[883,92386,4145],{}," Intuice — MRCS jako sklon indiferenční křivky\n",[883,92389,92391],{"className":92390},[886],[888,92392,92393],{"xmlns":890},[892,92394,92395,92417],{},[895,92396,92397,92399,92401,92407,92409,92415],{},[2289,92398,10587],{},[1726,92400,1735],{"stretchy":1734},[2275,92402,92403,92405],{},[898,92404,1724],{},[2133,92406,2281],{},[1726,92408,1742],{"separator":1741},[2275,92410,92411,92413],{},[898,92412,1724],{},[2133,92414,2135],{},[1726,92416,1762],{"stretchy":1734},[902,92418,92419],{"encoding":904},"\\text{MRCS}(Q_1, Q_2)",[38,92421,92422,92423,28984,92440,92457],{},"míra, jakou je spotřebitel ochoten zaměnit ",[883,92424,92426],{"className":92425},[886],[888,92427,92428],{"xmlns":890},[892,92429,92430,92438],{},[895,92431,92432],{},[2275,92433,92434,92436],{},[898,92435,1724],{},[2133,92437,2281],{},[902,92439,28983],{"encoding":904},[883,92441,92443],{"className":92442},[886],[888,92444,92445],{"xmlns":890},[892,92446,92447,92455],{},[895,92448,92449],{},[2275,92450,92451,92453],{},[898,92452,1724],{},[2133,92454,2135],{},[902,92456,29002],{"encoding":904}," při zachování užitečnosti"," — tedy kolik jednotek ",[883,92460,92462],{"className":92461},[886],[888,92463,92464],{"xmlns":890},[892,92465,92466,92474],{},[895,92467,92468],{},[2275,92469,92470,92472],{},[898,92471,1724],{},[2133,92473,2135],{},[902,92475,29002],{"encoding":904}," „obětuje\" za jednu jednotku ",[883,92478,92480],{"className":92479},[886],[888,92481,92482],{"xmlns":890},[892,92483,92484,92492],{},[895,92485,92486],{},[2275,92487,92488,92490],{},[898,92489,1724],{},[2133,92491,2281],{},[902,92493,28983],{"encoding":904}," navíc, aby zůstal na téže indiferenční křivce. Geometricky jde o absolutní hodnotu sklonu tečny k indiferenční křivce v daném bodě.",[724,92496,92497,92498,29925],{},"Pro obecnou změnu ",[883,92499,92501],{"className":92500},[886],[888,92502,92503],{"xmlns":890},[892,92504,92505,92515],{},[895,92506,92507,92509],{},[898,92508,2198],{"mathvariant":2377},[2275,92510,92511,92513],{},[898,92512,1724],{},[2133,92514,2281],{},[902,92516,92517],{"encoding":904},"\\mathrm{d} Q_1",[883,92519,92521],{"className":92520},[886],[888,92522,92523],{"xmlns":890,"display":28047},[892,92524,92525,92578],{},[20735,92526,92527],{"width":28052},[20740,92528,92529,92531,92571,92573],{},[20743,92530],{"width":28057},[20743,92532,92533],{},[895,92534,92535,92537,92543,92545,92547,92553,92555,92557,92559,92561,92563,92569],{},[898,92536,2886],{"mathvariant":2377},[2275,92538,92539,92541],{},[898,92540,1724],{},[2133,92542,2135],{},[1726,92544,1880],{},[898,92546,2198],{"mathvariant":2377},[2275,92548,92549,92551],{},[898,92550,1724],{},[2133,92552,2135],{},[1726,92554,1728],{},[1726,92556,2228],{},[2289,92558,10587],{},[1726,92560,3174],{},[898,92562,2198],{"mathvariant":2377},[2275,92564,92565,92567],{},[898,92566,1724],{},[2133,92568,2281],{},[1726,92570,1742],{"separator":1741},[20743,92572],{"width":28057},[20743,92574,92575],{},[2289,92576,92577],{},"(6.10)",[902,92579,92580],{"encoding":904},"\\Delta Q_2 \\approx \\mathrm{d} Q_2 = -\\text{MRCS} \\cdot \\mathrm{d} Q_1, \\tag{6.10}",[883,92582,92584],{"className":92583},[886],[888,92585,92586],{"xmlns":890,"display":28047},[892,92587,92588,92635],{},[20735,92589,92590],{"width":28052},[20740,92591,92592,92594,92628,92630],{},[20743,92593],{"width":28057},[20743,92595,92596],{},[895,92597,92598,92600,92606,92608,92610,92616,92618,92620,92626],{},[898,92599,2198],{"mathvariant":2377},[2275,92601,92602,92604],{},[898,92603,1724],{},[2133,92605,2281],{},[1726,92607,1728],{},[1726,92609,2228],{},[2330,92611,92612,92614],{},[2133,92613,2281],{},[2289,92615,10587],{},[2289,92617,2984],{},[898,92619,2198],{"mathvariant":2377},[2275,92621,92622,92624],{},[898,92623,1724],{},[2133,92625,2135],{},[898,92627,1888],{"mathvariant":2377},[20743,92629],{"width":28057},[20743,92631,92632],{},[2289,92633,92634],{},"(6.11)",[902,92636,92637],{"encoding":904},"\\mathrm{d} Q_1 = -\\frac{1}{\\text{MRCS}}\\, \\mathrm{d} Q_2. \\tag{6.11}",[3859,92639,92640,92706,92823],{},[724,92641,92642,92644,92645,29925],{},[883,92643,52675],{}," Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost\nPro ",[883,92646,92648],{"className":92647},[886],[888,92649,92650],{"xmlns":890},[892,92651,92652,92704],{},[895,92653,92654,92656,92658,92664,92666,92672,92674,92676,92690],{},[898,92655,900],{},[1726,92657,1735],{"stretchy":1734},[2275,92659,92660,92662],{},[898,92661,1724],{},[2133,92663,2281],{},[1726,92665,1742],{"separator":1741},[2275,92667,92668,92670],{},[898,92669,1724],{},[2133,92671,2135],{},[1726,92673,1762],{"stretchy":1734},[1726,92675,1728],{},[9151,92677,92678,92680,92682],{},[898,92679,1724],{},[2133,92681,2281],{},[895,92683,92684,92686,92688],{},[2133,92685,2281],{},[898,92687,4661],{"mathvariant":2377},[2133,92689,2135],{},[9151,92691,92692,92694,92696],{},[898,92693,1724],{},[2133,92695,2135],{},[895,92697,92698,92700,92702],{},[2133,92699,2281],{},[898,92701,4661],{"mathvariant":2377},[2133,92703,2135],{},[902,92705,29924],{"encoding":904},[724,92707,92708],{},[883,92709,92711],{"className":92710},[886],[888,92712,92713],{"xmlns":890},[892,92714,92715,92821],{},[895,92716,92717,92719,92721,92803,92805,92819],{},[2289,92718,10587],{},[1726,92720,1728],{},[2330,92722,92723,92763],{},[895,92724,92725,92733,92749],{},[2326,92726,92727],{"scriptlevel":2328,"displaystyle":1734},[2330,92728,92729,92731],{},[2133,92730,2281],{},[2133,92732,2135],{},[9151,92734,92735,92737,92739],{},[898,92736,1724],{},[2133,92738,2281],{},[895,92740,92741,92743,92745,92747],{},[1726,92742,2228],{},[2133,92744,2281],{},[898,92746,4661],{"mathvariant":2377},[2133,92748,2135],{},[9151,92750,92751,92753,92755],{},[898,92752,1724],{},[2133,92754,2135],{},[895,92756,92757,92759,92761],{},[2133,92758,2281],{},[898,92760,4661],{"mathvariant":2377},[2133,92762,2135],{},[895,92764,92765,92773,92787],{},[2326,92766,92767],{"scriptlevel":2328,"displaystyle":1734},[2330,92768,92769,92771],{},[2133,92770,2281],{},[2133,92772,2135],{},[9151,92774,92775,92777,92779],{},[898,92776,1724],{},[2133,92778,2281],{},[895,92780,92781,92783,92785],{},[2133,92782,2281],{},[898,92784,4661],{"mathvariant":2377},[2133,92786,2135],{},[9151,92788,92789,92791,92793],{},[898,92790,1724],{},[2133,92792,2135],{},[895,92794,92795,92797,92799,92801],{},[1726,92796,2228],{},[2133,92798,2281],{},[898,92800,4661],{"mathvariant":2377},[2133,92802,2135],{},[1726,92804,1728],{},[2330,92806,92807,92813],{},[2275,92808,92809,92811],{},[898,92810,1724],{},[2133,92812,2135],{},[2275,92814,92815,92817],{},[898,92816,1724],{},[2133,92818,2281],{},[898,92820,1888],{"mathvariant":2377},[902,92822,30043],{"encoding":904},[724,92824,30046,92825,2924,92868,30094,92870,92889],{},[883,92826,92828],{"className":92827},[886],[888,92829,92830],{"xmlns":890},[892,92831,92832,92866],{},[895,92833,92834,92836,92838,92840,92842,92844,92846,92848,92856,92858],{},[2289,92835,10587],{},[1726,92837,1735],{"stretchy":1734},[2133,92839,30062],{},[1726,92841,1742],{"separator":1741},[2133,92843,15096],{},[1726,92845,1762],{"stretchy":1734},[1726,92847,1728],{},[2326,92849,92850],{"scriptlevel":2328,"displaystyle":1734},[2330,92851,92852,92854],{},[2133,92853,15096],{},[2133,92855,30062],{},[1726,92857,1728],{},[2326,92859,92860],{"scriptlevel":2328,"displaystyle":1734},[2330,92861,92862,92864],{},[2133,92863,2231],{},[2133,92865,2177],{},[902,92867,30091],{"encoding":904},[614,92869,9201],{},[883,92871,92873],{"className":92872},[886],[888,92874,92875],{"xmlns":890},[892,92876,92877,92887],{},[895,92878,92879],{},[2326,92880,92881],{"scriptlevel":2328,"displaystyle":1734},[2330,92882,92883,92885],{},[2133,92884,2231],{},[2133,92886,2177],{},[902,92888,30114],{"encoding":904}," jednotky, aby se užitečnost zachovala.",[724,92891,92892,92893,92897],{},"(Paralelou je ",[207,92894,92896],{"className":92895,"dataFsResolvedFilePath":857,"href":858},[210],"mezní míra technické substituce MRTS"," z produkční teorie.)",[115,92899,92901],{"id":92900},"_63-64-optimalizace-spotřebitele-přehled","6.3 – 6.4 Optimalizace spotřebitele — přehled",[724,92903,92904,92905,92908],{},"Rámcově se v kapitole 6 studují ",[38,92906,92907],{},"dvě vázané optimalizační úlohy"," s užitečností:",[120,92910,92911,93047],{},[123,92912,92913,92915,92916,10141,92947,1777,92950,92999,93000,1888],{},[38,92914,28233],{}," — maximalizace ",[883,92917,92919],{"className":92918},[886],[888,92920,92921],{"xmlns":890},[892,92922,92923,92945],{},[895,92924,92925,92927,92929,92935,92937,92943],{},[898,92926,900],{},[1726,92928,1735],{"stretchy":1734},[2275,92930,92931,92933],{},[898,92932,1724],{},[2133,92934,2281],{},[1726,92936,1742],{"separator":1741},[2275,92938,92939,92941],{},[898,92940,1724],{},[2133,92942,2135],{},[1726,92944,1762],{"stretchy":1734},[902,92946,16326],{"encoding":904},[38,92948,92949],{},"rozpočtovém omezení",[883,92951,92953],{"className":92952},[886],[888,92954,92955],{"xmlns":890},[892,92956,92957,92997],{},[895,92958,92959,92965,92967,92975,92981,92983,92991],{},[2128,92960,92961,92963],{},[898,92962,1745],{},[1726,92964,4342],{},[1726,92966,1728],{},[9151,92968,92969,92971,92973],{},[898,92970,1738],{},[2133,92972,2281],{},[1726,92974,4342],{},[2275,92976,92977,92979],{},[898,92978,1724],{},[2133,92980,2281],{},[1726,92982,2099],{},[9151,92984,92985,92987,92989],{},[898,92986,1738],{},[2133,92988,2135],{},[1726,92990,4342],{},[2275,92992,92993,92995],{},[898,92994,1724],{},[2133,92996,2135],{},[902,92998,17280],{"encoding":904},". Výstupem je Marshallova poptávka ",[883,93001,93003],{"className":93002},[886],[888,93004,93005],{"xmlns":890},[892,93006,93007,93045],{},[895,93008,93009,93015,93017,93023,93025,93031,93033,93039,93041,93043],{},[2275,93010,93011,93013],{},[898,93012,1724],{},[898,93014,17772],{},[1726,93016,1728],{},[2275,93018,93019,93021],{},[898,93020,1731],{},[898,93022,17772],{},[1726,93024,1735],{"stretchy":1734},[2275,93026,93027,93029],{},[898,93028,1738],{},[2133,93030,2281],{},[1726,93032,1742],{"separator":1741},[2275,93034,93035,93037],{},[898,93036,1738],{},[2133,93038,2135],{},[1726,93040,1742],{"separator":1741},[898,93042,1745],{},[1726,93044,1762],{"stretchy":1734},[902,93046,36436],{"encoding":904},[123,93048,93049,27882,93052,27925,93098,93115,93116,1888],{},[38,93050,93051],{},"Duální úloha",[883,93053,93055],{"className":93054},[886],[888,93056,93057],{"xmlns":890},[892,93058,93059,93095],{},[895,93060,93061,93063,93065,93073,93079,93081,93089],{},[898,93062,4240],{},[1726,93064,1728],{},[9151,93066,93067,93069,93071],{},[898,93068,1738],{},[2133,93070,2281],{},[1726,93072,4342],{},[2275,93074,93075,93077],{},[898,93076,1724],{},[2133,93078,2281],{},[1726,93080,2099],{},[9151,93082,93083,93085,93087],{},[898,93084,1738],{},[2133,93086,2135],{},[1726,93088,4342],{},[2275,93090,93091,93093],{},[898,93092,1724],{},[2133,93094,2135],{},[902,93096,93097],{"encoding":904},"E = P_1^* Q_1 + P_2^* Q_2",[883,93099,93101],{"className":93100},[886],[888,93102,93103],{"xmlns":890},[892,93104,93105,93113],{},[895,93106,93107],{},[2128,93108,93109,93111],{},[898,93110,900],{},[1726,93112,4342],{},[902,93114,27943],{"encoding":904},". Výstupem je Hicksova poptávka ",[883,93117,93119],{"className":93118},[886],[888,93120,93121],{"xmlns":890},[892,93122,93123,93161],{},[895,93124,93125,93131,93133,93139,93141,93147,93149,93155,93157,93159],{},[2275,93126,93127,93129],{},[898,93128,1724],{},[898,93130,17772],{},[1726,93132,1728],{},[2275,93134,93135,93137],{},[898,93136,1731],{},[898,93138,17772],{},[1726,93140,1735],{"stretchy":1734},[2275,93142,93143,93145],{},[898,93144,1738],{},[2133,93146,2281],{},[1726,93148,1742],{"separator":1741},[2275,93150,93151,93153],{},[898,93152,1738],{},[2133,93154,2135],{},[1726,93156,1742],{"separator":1741},[898,93158,900],{},[1726,93160,1762],{"stretchy":1734},[902,93162,17805],{"encoding":904},[724,93164,93165,93166,93169,93170,1777,93173,93212],{},"Obě úlohy se řeší ",[207,93167,27948],{"className":93168,"dataFsResolvedFilePath":791,"href":792},[210]," a vedou na ",[38,93171,93172],{},"tentýž bod dotyku",[883,93174,93176],{"className":93175},[886],[888,93177,93178],{"xmlns":890},[892,93179,93180,93210],{},[895,93181,93182,93188,93190,93198,93200,93208],{},[2128,93183,93184,93186],{},[898,93185,1724],{},[1726,93187,4342],{},[1726,93189,2487],{"stretchy":1734},[9151,93191,93192,93194,93196],{},[898,93193,1724],{},[2133,93195,2281],{},[1726,93197,4342],{},[1726,93199,1742],{"separator":1741},[9151,93201,93202,93204,93206],{},[898,93203,1724],{},[2133,93205,2135],{},[1726,93207,4342],{},[1726,93209,2502],{"stretchy":1734},[902,93211,28308],{"encoding":904}," indiferenční křivky a rozpočtové přímky (resp. přímky výdajů), v němž platí podmínka optimality",[883,93214,93216],{"className":93215},[886],[888,93217,93218],{"xmlns":890,"display":28047},[892,93219,93220,93266],{},[895,93221,93222,93224,93226,93244,93246,93264],{},[2289,93223,10587],{},[1726,93225,1728],{},[2330,93227,93228,93236],{},[9151,93229,93230,93232,93234],{},[898,93231,900],{},[2133,93233,2281],{},[1726,93235,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[9151,93237,93238,93240,93242],{},[898,93239,900],{},[2133,93241,2135],{},[1726,93243,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,93245,1728],{},[2330,93247,93248,93256],{},[9151,93249,93250,93252,93254],{},[898,93251,1738],{},[2133,93253,2281],{},[1726,93255,4342],{},[9151,93257,93258,93260,93262],{},[898,93259,1738],{},[2133,93261,2135],{},[1726,93263,4342],{},[898,93265,1888],{"mathvariant":2377},[902,93267,93268],{"encoding":904},"\\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*}.",[724,93270,93271],{},"Poměr mezních užitečností se rovná poměru cen — sklon indiferenční křivky v optimu se rovná sklonu rozpočtové přímky.",[3859,93273,93274],{},[724,93275,93276,93278,93279,93282,93283,93286,93287,93314,93315,93349,93350,93384,93385,93428,93429,93432,93433,1888],{},[883,93277,4145],{}," Pro detailní postup viz ",[207,93280,36735],{"className":93281,"dataFsResolvedFilePath":911,"href":912},[210],"\nKompletní odvození obou úloh Lagrangeovou metodou, geometrická interpretace, řešené ",[38,93284,93285],{},"Příklady 6.5–6.8"," (MRCS pro Cobb-Douglase, maximalizace ",[883,93288,93290],{"className":93289},[886],[888,93291,93292],{"xmlns":890},[892,93293,93294,93312],{},[895,93295,93296,93298,93300,93306],{},[898,93297,900],{},[1726,93299,1728],{},[2275,93301,93302,93304],{},[898,93303,1724],{},[2133,93305,2281],{},[2275,93307,93308,93310],{},[898,93309,1724],{},[2133,93311,2135],{},[902,93313,30207],{"encoding":904}," s výsledkem ",[883,93316,93318],{"className":93317},[886],[888,93319,93320],{"xmlns":890},[892,93321,93322,93346],{},[895,93323,93324,93330,93332,93334,93336,93342,93344],{},[2275,93325,93326,93328],{},[898,93327,1724],{},[2133,93329,2281],{},[1726,93331,1728],{},[2133,93333,4991],{},[1726,93335,1742],{"separator":1741},[2275,93337,93338,93340],{},[898,93339,1724],{},[2133,93341,2135],{},[1726,93343,1728],{},[2133,93345,2860],{},[902,93347,93348],{"encoding":904},"Q_1 = 25, Q_2 = 10","; minimalizace výdajů s ",[883,93351,93353],{"className":93352},[886],[888,93354,93355],{"xmlns":890},[892,93356,93357,93381],{},[895,93358,93359,93365,93367,93369,93371,93377,93379],{},[2275,93360,93361,93363],{},[898,93362,1724],{},[2133,93364,2281],{},[1726,93366,1728],{},[2133,93368,2352],{},[1726,93370,1742],{"separator":1741},[2275,93372,93373,93375],{},[898,93374,1724],{},[2133,93376,2135],{},[1726,93378,1728],{},[2133,93380,2281],{},[902,93382,93383],{"encoding":904},"Q_1 = 4, Q_2 = 1","; obecná Hicksova poptávka pro ",[883,93386,93388],{"className":93387},[886],[888,93389,93390],{"xmlns":890},[892,93391,93392,93426],{},[895,93393,93394,93396,93398,93412],{},[898,93395,900],{},[1726,93397,1728],{},[9151,93399,93400,93402,93404],{},[898,93401,1724],{},[2133,93403,2281],{},[895,93405,93406,93408,93410],{},[2133,93407,2281],{},[898,93409,4661],{"mathvariant":2377},[2133,93411,2135],{},[9151,93413,93414,93416,93418],{},[898,93415,1724],{},[2133,93417,2135],{},[895,93419,93420,93422,93424],{},[2133,93421,2281],{},[898,93423,4661],{"mathvariant":2377},[2133,93425,2135],{},[902,93427,33140],{"encoding":904},"), odvození Marshallovy i Hicksovy funkce poptávky a Engelových funkcí, vztah dualita primární ↔ duální úlohy a úlohy ",[38,93430,93431],{},"6.8–6.13"," jsou na stránce ",[207,93434,27748],{"className":93435,"dataFsResolvedFilePath":911,"href":912},[210],[115,93437,93439],{"id":93438},"shrnutí-kapitoly-6","Shrnutí kapitoly 6",[724,93441,93442,93443,93456,93457,93459,93460,93462,93463,93465,93466,93468,93469,93471,93472,93474,93475,1777,93477,93512,93513,93526,93527,93530,93531,93534,93535,1888],{},"Každá ",[883,93444,93446],{"className":93445},[886],[888,93447,93448],{"xmlns":890},[892,93449,93450,93454],{},[895,93451,93452],{},[898,93453,36841],{},[902,93455,36841],{"encoding":904},"-tice množství jednotlivých zboží je ",[38,93458,86790],{},". Přiřadíme-li každému svazku kladné číslo (jeho užitečnost), můžeme svazky uspořádat podle rostoucí užitečnosti; svazky se stejnou užitečností jsou indiferentní. Tím je definována ",[38,93461,87274],{}," a současně ",[38,93464,86793],{},". Její parciální derivace (podle jednotlivých množství) jsou ",[38,93467,86798],{}," — přibližná změna užitečnosti při jednotkové změně příslušného zboží. Aby funkce mohla být funkcí užitečnosti, musejí být její první parciální derivace ",[38,93470,52657],{}," (6.4) a druhé parciální derivace ",[38,93473,89157],{}," (6.5 — zákon klesající mezní užitečnosti). ",[38,93476,9715],{},[883,93478,93480],{"className":93479},[886],[888,93481,93482],{"xmlns":890},[892,93483,93484,93510],{},[895,93485,93486,93488,93490,93496,93498,93504,93506,93508],{},[898,93487,900],{},[1726,93489,1735],{"stretchy":1734},[2275,93491,93492,93494],{},[898,93493,1724],{},[2133,93495,2281],{},[1726,93497,1742],{"separator":1741},[2275,93499,93500,93502],{},[898,93501,1724],{},[2133,93503,2135],{},[1726,93505,1762],{"stretchy":1734},[1726,93507,1728],{},[898,93509,2146],{},[902,93511,9752],{"encoding":904}," jsou klesající, neprotínající se, vzdálenější od počátku mají vyšší užitečnost a jsou konvexní. ",[883,93514,93516],{"className":93515},[886],[888,93517,93518],{"xmlns":890},[892,93519,93520,93524],{},[895,93521,93522],{},[2289,93523,10587],{},[902,93525,28219],{"encoding":904}," = podíl mezních užitečností udává náhradu jednoho zboží druhým při zachování užitečnosti. Na tento teoretický základ navazují optimalizační úlohy (",[38,93528,93529],{},"maximalizace užitečnosti"," a duální ",[38,93532,93533],{},"minimalizace výdajů",") řešené Lagrangeovou metodou — viz ",[207,93536,36735],{"className":93537,"dataFsResolvedFilePath":911,"href":912},[210],[115,93539,49863],{"id":49862},[152,93541,93542,93545,93548,93551,93554,93557,93560,93563,93566,93569],{},[123,93543,93544],{},"Co se zahrnuje pod termín užitečnost?",[123,93546,93547],{},"Co se rozumí svazkem zboží? Které svazky zboží jsou indiferentní?",[123,93549,93550],{},"Jak souvisejí hodnoty funkce užitečnosti s preferencí svazků?",[123,93552,93553],{},"Jak se vypočítá mezní užitečnost?",[123,93555,93556],{},"Jak lze ekonomicky interpretovat fakt, že mezní užitečnost určitého zboží se rovná 2,5?",[123,93558,93559],{},"Jaké vlastnosti musí mít funkce více proměnných, aby mohla být funkcí užitečnosti?",[123,93561,93562],{},"Které jsou nejčastěji používané funkce užitečnosti?",[123,93564,93565],{},"Jakou rovnici mají křivky užitečnosti? Co platí v bodech ležících na téže křivce užitečnosti?",[123,93567,93568],{},"Proč mají křivky užitečnosti záporný sklon?",[123,93570,93571],{},"Jak se vypočte mezní míra komoditní substituce? Vysvětlete, co vypočtená hodnota vyjadřuje.",[115,93573,93575],{"id":93574},"úlohy-teorie-užitečnosti-61-67","Úlohy — teorie užitečnosti (6.1 – 6.7)",[724,93577,93578,93581,93582,83463,93624,1343,93652,1343,93680,93708],{},[38,93579,93580],{},"6.1"," Užitečnost pro tři zboží — hudbu, čokoládu a sýr je dána vztahem ",[883,93583,93585],{"className":93584},[886],[888,93586,93587],{"xmlns":890},[892,93588,93589,93621],{},[895,93590,93591,93593,93595,93601,93603,93605,93611,93613,93615],{},[898,93592,900],{},[1726,93594,1728],{},[2275,93596,93597,93599],{},[898,93598,1724],{},[2133,93600,2281],{},[1726,93602,2099],{},[2133,93604,64539],{},[2275,93606,93607,93609],{},[898,93608,1724],{},[2133,93610,2135],{},[1726,93612,2099],{},[2133,93614,2135],{},[2275,93616,93617,93619],{},[898,93618,1724],{},[2133,93620,2177],{},[902,93622,93623],{"encoding":904},"U = Q_1 + 1{,}5 Q_2 + 2 Q_3",[883,93625,93627],{"className":93626},[886],[888,93628,93629],{"xmlns":890},[892,93630,93631,93649],{},[895,93632,93633,93635,93637,93639,93641,93643,93645,93647],{},[898,93634,900],{},[1726,93636,1735],{"stretchy":1734},[2133,93638,2352],{},[1726,93640,1742],{"separator":1741},[2133,93642,2135],{},[1726,93644,1742],{"separator":1741},[2133,93646,2135],{},[1726,93648,1762],{"stretchy":1734},[902,93650,93651],{"encoding":904},"U(4, 2, 2)",[883,93653,93655],{"className":93654},[886],[888,93656,93657],{"xmlns":890},[892,93658,93659,93677],{},[895,93660,93661,93663,93665,93667,93669,93671,93673,93675],{},[898,93662,900],{},[1726,93664,1735],{"stretchy":1734},[2133,93666,2281],{},[1726,93668,1742],{"separator":1741},[2133,93670,2352],{},[1726,93672,1742],{"separator":1741},[2133,93674,2135],{},[1726,93676,1762],{"stretchy":1734},[902,93678,93679],{"encoding":904},"U(1, 4, 2)",[883,93681,93683],{"className":93682},[886],[888,93684,93685],{"xmlns":890},[892,93686,93687,93705],{},[895,93688,93689,93691,93693,93695,93697,93699,93701,93703],{},[898,93690,900],{},[1726,93692,1735],{"stretchy":1734},[2133,93694,2135],{},[1726,93696,1742],{"separator":1741},[2133,93698,2177],{},[1726,93700,1742],{"separator":1741},[2133,93702,2281],{},[1726,93704,1762],{"stretchy":1734},[902,93706,93707],{"encoding":904},"U(2, 3, 1)",". (b) Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků v (a).",[724,93710,93711,93714,93715,93767,93768,1343,93794,1343,93820,1343,93846,1343,93872,1343,93898,1343,93924,93950],{},[38,93712,93713],{},"6.2"," Je dána užitečnost ",[883,93716,93718],{"className":93717},[886],[888,93719,93720],{"xmlns":890},[892,93721,93722,93764],{},[895,93723,93724,93726,93728,93730,93744,93758],{},[898,93725,900],{},[1726,93727,1728],{},[2133,93729,2135],{},[9151,93731,93732,93734,93736],{},[898,93733,1724],{},[2133,93735,2281],{},[895,93737,93738,93740,93742],{},[2133,93739,2281],{},[898,93741,4661],{"mathvariant":2377},[2133,93743,2177],{},[9151,93745,93746,93748,93750],{},[898,93747,1724],{},[2133,93749,2135],{},[895,93751,93752,93754,93756],{},[2133,93753,2281],{},[898,93755,4661],{"mathvariant":2377},[2133,93757,2135],{},[2275,93759,93760,93762],{},[898,93761,1724],{},[2133,93763,2177],{},[902,93765,93766],{"encoding":904},"U = 2 Q_1^{1\u002F3} Q_2^{1\u002F2} Q_3"," pro tři zboží. Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků ",[883,93769,93771],{"className":93770},[886],[888,93772,93773],{"xmlns":890},[892,93774,93775,93791],{},[895,93776,93777,93779,93781,93783,93785,93787,93789],{},[1726,93778,1735],{"stretchy":1734},[2133,93780,5552],{},[1726,93782,1742],{"separator":1741},[2133,93784,66577],{},[1726,93786,1742],{"separator":1741},[2133,93788,2860],{},[1726,93790,1762],{"stretchy":1734},[902,93792,93793],{"encoding":904},"(36, 27, 10)",[883,93795,93797],{"className":93796},[886],[888,93798,93799],{"xmlns":890},[892,93800,93801,93817],{},[895,93802,93803,93805,93807,93809,93811,93813,93815],{},[1726,93804,1735],{"stretchy":1734},[2133,93806,41821],{},[1726,93808,1742],{"separator":1741},[2133,93810,5572],{},[1726,93812,1742],{"separator":1741},[2133,93814,9021],{},[1726,93816,1762],{"stretchy":1734},[902,93818,93819],{"encoding":904},"(64, 8, 20)",[883,93821,93823],{"className":93822},[886],[888,93824,93825],{"xmlns":890},[892,93826,93827,93843],{},[895,93828,93829,93831,93833,93835,93837,93839,93841],{},[1726,93830,1735],{"stretchy":1734},[2133,93832,4991],{},[1726,93834,1742],{"separator":1741},[2133,93836,41821],{},[1726,93838,1742],{"separator":1741},[2133,93840,5572],{},[1726,93842,1762],{"stretchy":1734},[902,93844,93845],{"encoding":904},"(25, 64, 8)",[883,93847,93849],{"className":93848},[886],[888,93850,93851],{"xmlns":890},[892,93852,93853,93869],{},[895,93854,93855,93857,93859,93861,93863,93865,93867],{},[1726,93856,1735],{"stretchy":1734},[2133,93858,2352],{},[1726,93860,1742],{"separator":1741},[2133,93862,72509],{},[1726,93864,1742],{"separator":1741},[2133,93866,2238],{},[1726,93868,1762],{"stretchy":1734},[902,93870,93871],{"encoding":904},"(4, 125, 6)",[883,93873,93875],{"className":93874},[886],[888,93876,93877],{"xmlns":890},[892,93878,93879,93895],{},[895,93880,93881,93883,93885,93887,93889,93891,93893],{},[1726,93882,1735],{"stretchy":1734},[2133,93884,3989],{},[1726,93886,1742],{"separator":1741},[2133,93888,5198],{},[1726,93890,1742],{"separator":1741},[2133,93892,3506],{},[1726,93894,1762],{"stretchy":1734},[902,93896,93897],{"encoding":904},"(9, 40, 12)",[883,93899,93901],{"className":93900},[886],[888,93902,93903],{"xmlns":890},[892,93904,93905,93921],{},[895,93906,93907,93909,93911,93913,93915,93917,93919],{},[1726,93908,1735],{"stretchy":1734},[2133,93910,3989],{},[1726,93912,1742],{"separator":1741},[2133,93914,41821],{},[1726,93916,1742],{"separator":1741},[2133,93918,2231],{},[1726,93920,1762],{"stretchy":1734},[902,93922,93923],{"encoding":904},"(9, 64, 5)",[883,93925,93927],{"className":93926},[886],[888,93928,93929],{"xmlns":890},[892,93930,93931,93947],{},[895,93932,93933,93935,93937,93939,93941,93943,93945],{},[1726,93934,1735],{"stretchy":1734},[2133,93936,41821],{},[1726,93938,1742],{"separator":1741},[2133,93940,5572],{},[1726,93942,1742],{"separator":1741},[2133,93944,2860],{},[1726,93946,1762],{"stretchy":1734},[902,93948,93949],{"encoding":904},"(64, 8, 10)"," a uspořádejte je s neklesající užitečností.",[724,93952,93953,93714,93956,93999,94000,94034,94035,6460,94065,94098,94099,94116,94117,94134],{},[38,93954,93955],{},"6.3",[883,93957,93959],{"className":93958},[886],[888,93960,93961],{"xmlns":890},[892,93962,93963,93997],{},[895,93964,93965,93967,93969,93983],{},[898,93966,900],{},[1726,93968,1728],{},[9151,93970,93971,93973,93975],{},[898,93972,1724],{},[2133,93974,2281],{},[895,93976,93977,93979,93981],{},[2133,93978,2281],{},[898,93980,4661],{"mathvariant":2377},[2133,93982,2135],{},[9151,93984,93985,93987,93989],{},[898,93986,1724],{},[2133,93988,2135],{},[895,93990,93991,93993,93995],{},[2133,93992,2281],{},[898,93994,4661],{"mathvariant":2377},[2133,93996,2135],{},[902,93998,33140],{"encoding":904},". (a) Vypočtěte užitečnost pro ",[883,94001,94003],{"className":94002},[886],[888,94004,94005],{"xmlns":890},[892,94006,94007,94031],{},[895,94008,94009,94015,94017,94019,94021,94027,94029],{},[2275,94010,94011,94013],{},[898,94012,1724],{},[2133,94014,2281],{},[1726,94016,1728],{},[2133,94018,3117],{},[1726,94020,1742],{"separator":1741},[2275,94022,94023,94025],{},[898,94024,1724],{},[2133,94026,2135],{},[1726,94028,1728],{},[2133,94030,46684],{},[902,94032,94033],{"encoding":904},"Q_1 = 50, Q_2 = 80",". (b) Určete mezní užitečnosti ",[883,94036,94038],{"className":94037},[886],[888,94039,94040],{"xmlns":890},[892,94041,94042,94062],{},[895,94043,94044,94046,94052,94054,94056],{},[898,94045,2815],{},[2275,94047,94048,94050],{},[898,94049,900],{},[2133,94051,2281],{},[1726,94053,1742],{"separator":1741},[898,94055,2815],{},[2275,94057,94058,94060],{},[898,94059,900],{},[2133,94061,2135],{},[902,94063,94064],{"encoding":904},"MU_1, MU_2",[883,94066,94068],{"className":94067},[886],[888,94069,94070],{"xmlns":890},[892,94071,94072,94096],{},[895,94073,94074,94080,94082,94084,94086,94092,94094],{},[2275,94075,94076,94078],{},[898,94077,1724],{},[2133,94079,2281],{},[1726,94081,1728],{},[2133,94083,3117],{},[1726,94085,1742],{"separator":1741},[2275,94087,94088,94090],{},[898,94089,1724],{},[2133,94091,2135],{},[1726,94093,1728],{},[2133,94095,46684],{},[902,94097,94033],{"encoding":904}," a výsledky ekonomicky interpretujte. (d) Odhadněte změnu užitečnosti v důsledku změny ",[883,94100,94102],{"className":94101},[886],[888,94103,94104],{"xmlns":890},[892,94105,94106,94114],{},[895,94107,94108],{},[2275,94109,94110,94112],{},[898,94111,1724],{},[2133,94113,2281],{},[902,94115,28983],{"encoding":904}," na 60 a poklesu ",[883,94118,94120],{"className":94119},[886],[888,94121,94122],{"xmlns":890},[892,94123,94124,94132],{},[895,94125,94126],{},[2275,94127,94128,94130],{},[898,94129,1724],{},[2133,94131,2135],{},[902,94133,29002],{"encoding":904}," o 5 vzhledem k hladině dle (a) a porovnejte se skutečnou změnou užitečnosti.",[724,94136,94137,94140,94141,94202,94203,1888],{},[38,94138,94139],{},"6.4"," Je dána funkce ",[883,94142,94144],{"className":94143},[886],[888,94145,94146],{"xmlns":890},[892,94147,94148,94200],{},[895,94149,94150,94152,94154,94160,94162,94168,94170,94172,94186],{},[898,94151,900],{},[1726,94153,1735],{"stretchy":1734},[2275,94155,94156,94158],{},[898,94157,1724],{},[2133,94159,2281],{},[1726,94161,1742],{"separator":1741},[2275,94163,94164,94166],{},[898,94165,1724],{},[2133,94167,2135],{},[1726,94169,1762],{"stretchy":1734},[1726,94171,1728],{},[9151,94173,94174,94176,94178],{},[898,94175,1724],{},[2133,94177,2281],{},[895,94179,94180,94182,94184],{},[2133,94181,2281],{},[898,94183,4661],{"mathvariant":2377},[2133,94185,2135],{},[9151,94187,94188,94190,94192],{},[898,94189,1724],{},[2133,94191,2135],{},[895,94193,94194,94196,94198],{},[2133,94195,2281],{},[898,94197,4661],{"mathvariant":2377},[2133,94199,2135],{},[902,94201,29924],{"encoding":904},". (a) Ověřte, že tato funkce vykazuje vlastnosti funkce užitečnosti. (b) Najděte a načrtněte křivky ",[883,94204,94206],{"className":94205},[886],[888,94207,94208],{"xmlns":890},[892,94209,94210,94300],{},[895,94211,94212,94214,94216,94222,94224,94226,94228,94230,94232,94234,94240,94242,94244,94246,94248,94250,94252,94254,94256,94262,94264,94266,94268,94270,94272,94274,94280,94282,94284,94286,94288,94290,94292,94298],{},[898,94213,900],{},[1726,94215,1735],{"stretchy":1734},[2275,94217,94218,94220],{},[898,94219,1724],{},[2133,94221,2281],{},[1726,94223,1742],{"separator":1741},[2133,94225,2281],{},[1726,94227,1762],{"stretchy":1734},[1726,94229,1742],{"separator":1741},[898,94231,900],{},[1726,94233,1735],{"stretchy":1734},[2275,94235,94236,94238],{},[898,94237,1724],{},[2133,94239,2281],{},[1726,94241,1742],{"separator":1741},[2133,94243,2135],{},[1726,94245,1762],{"stretchy":1734},[1726,94247,1742],{"separator":1741},[898,94249,900],{},[1726,94251,1735],{"stretchy":1734},[2133,94253,2281],{},[1726,94255,1742],{"separator":1741},[2275,94257,94258,94260],{},[898,94259,1724],{},[2133,94261,2135],{},[1726,94263,1762],{"stretchy":1734},[1726,94265,1742],{"separator":1741},[898,94267,900],{},[1726,94269,1735],{"stretchy":1734},[2133,94271,2135],{},[1726,94273,1742],{"separator":1741},[2275,94275,94276,94278],{},[898,94277,1724],{},[2133,94279,2135],{},[1726,94281,1762],{"stretchy":1734},[1726,94283,1742],{"separator":1741},[898,94285,900],{},[1726,94287,1735],{"stretchy":1734},[2133,94289,2177],{},[1726,94291,1742],{"separator":1741},[2275,94293,94294,94296],{},[898,94295,1724],{},[2133,94297,2135],{},[1726,94299,1762],{"stretchy":1734},[902,94301,94302],{"encoding":904},"U(Q_1, 1), U(Q_1, 2), U(1, Q_2), U(2, Q_2), U(3, Q_2)",[724,94304,94305,93714,94308,94352,94353,94461,94462,1343,94487,1343,94512,94554,94555,1343,94584,94609],{},[38,94306,94307],{},"6.5",[883,94309,94311],{"className":94310},[886],[888,94312,94313],{"xmlns":890},[892,94314,94315,94349],{},[895,94316,94317,94319,94321,94335],{},[898,94318,900],{},[1726,94320,1728],{},[9151,94322,94323,94325,94327],{},[898,94324,1724],{},[2133,94326,2281],{},[895,94328,94329,94331,94333],{},[2133,94330,2135],{},[898,94332,4661],{"mathvariant":2377},[2133,94334,2177],{},[9151,94336,94337,94339,94341],{},[898,94338,1724],{},[2133,94340,2135],{},[895,94342,94343,94345,94347],{},[2133,94344,2281],{},[898,94346,4661],{"mathvariant":2377},[2133,94348,2177],{},[902,94350,94351],{"encoding":904},"U = Q_1^{2\u002F3} Q_2^{1\u002F3}",". (a) Najděte rovnici křivek užitečnosti. (b) Určete a načrtněte křivky ",[883,94354,94356],{"className":94355},[886],[888,94357,94358],{"xmlns":890},[892,94359,94360,94458],{},[895,94361,94362,94364,94366,94372,94374,94380,94382,94384,94386,94388,94390,94392,94398,94400,94402,94404,94406,94408,94410,94416,94418,94420,94422,94424,94426,94428,94430,94432,94438,94440,94442,94444,94446,94448,94450,94456],{},[898,94363,900],{},[1726,94365,1735],{"stretchy":1734},[2275,94367,94368,94370],{},[898,94369,1724],{},[2133,94371,2281],{},[1726,94373,1742],{"separator":1741},[2275,94375,94376,94378],{},[898,94377,1724],{},[2133,94379,2135],{},[1726,94381,1762],{"stretchy":1734},[1726,94383,1728],{},[2133,94385,2135],{},[1726,94387,1742],{"separator":1741},[898,94389,900],{},[1726,94391,1735],{"stretchy":1734},[2275,94393,94394,94396],{},[898,94395,1724],{},[2133,94397,2281],{},[1726,94399,1742],{"separator":1741},[2133,94401,2177],{},[1726,94403,1762],{"stretchy":1734},[1726,94405,1742],{"separator":1741},[898,94407,900],{},[1726,94409,1735],{"stretchy":1734},[2275,94411,94412,94414],{},[898,94413,1724],{},[2133,94415,2281],{},[1726,94417,1742],{"separator":1741},[2133,94419,2135],{},[1726,94421,1762],{"stretchy":1734},[1726,94423,1742],{"separator":1741},[898,94425,900],{},[1726,94427,1735],{"stretchy":1734},[2133,94429,2135],{},[1726,94431,1742],{"separator":1741},[2275,94433,94434,94436],{},[898,94435,1724],{},[2133,94437,2135],{},[1726,94439,1762],{"stretchy":1734},[1726,94441,1742],{"separator":1741},[898,94443,900],{},[1726,94445,1735],{"stretchy":1734},[2133,94447,2177],{},[1726,94449,1742],{"separator":1741},[2275,94451,94452,94454],{},[898,94453,1724],{},[2133,94455,2135],{},[1726,94457,1762],{"stretchy":1734},[902,94459,94460],{"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 ",[883,94463,94465],{"className":94464},[886],[888,94466,94467],{"xmlns":890},[892,94468,94469,94484],{},[895,94470,94471,94473,94475,94477,94479,94482],{},[898,94472,4243],{},[1726,94474,2487],{"stretchy":1734},[2133,94476,64539],{},[1726,94478,8411],{"separator":1741},[2133,94480,94481],{},"3,555",[1726,94483,2502],{"stretchy":1734},[902,94485,94486],{"encoding":904},"A[1{,}5; 3{,}555]",[883,94488,94490],{"className":94489},[886],[888,94491,94492],{"xmlns":890},[892,94493,94494,94509],{},[895,94495,94496,94498,94500,94502,94504,94507],{},[898,94497,23234],{},[1726,94499,2487],{"stretchy":1734},[2133,94501,53179],{},[1726,94503,8411],{"separator":1741},[2133,94505,94506],{},"1,28",[1726,94508,2502],{"stretchy":1734},[902,94510,94511],{"encoding":904},"B[2{,}5; 1{,}28]",[883,94513,94515],{"className":94514},[886],[888,94516,94517],{"xmlns":890},[892,94518,94519,94551],{},[895,94520,94521,94523,94525,94527,94529,94531,94533,94539,94541,94543,94545,94547,94549],{},[898,94522,2775],{},[1726,94524,2487],{"stretchy":1734},[2133,94526,2135],{},[1726,94528,8411],{"separator":1741},[898,94530,900],{},[1726,94532,1735],{"stretchy":1734},[2275,94534,94535,94537],{},[898,94536,1724],{},[2133,94538,2281],{},[1726,94540,1742],{"separator":1741},[2133,94542,2177],{},[1726,94544,1762],{"stretchy":1734},[1726,94546,1728],{},[2133,94548,2177],{},[1726,94550,2502],{"stretchy":1734},[902,94552,94553],{"encoding":904},"C[2; U(Q_1, 3) = 3]"," (c) Leží některé z bodů ",[883,94556,94558],{"className":94557},[886],[888,94559,94560],{"xmlns":890},[892,94561,94562,94581],{},[895,94563,94564,94566,94568,94570,94572,94574,94576,94579],{},[898,94565,1731],{},[1726,94567,2487],{"stretchy":1734},[2133,94569,2177],{},[1726,94571,8411],{"separator":1741},[2133,94573,2281],{},[1726,94575,8411],{"separator":1741},[2133,94577,94578],{},"0,832",[1726,94580,2502],{"stretchy":1734},[902,94582,94583],{"encoding":904},"D[3; 1; 0{,}832]",[883,94585,94587],{"className":94586},[886],[888,94588,94589],{"xmlns":890},[892,94590,94591,94606],{},[895,94592,94593,94595,94597,94599,94601,94604],{},[898,94594,4240],{},[1726,94596,2487],{"stretchy":1734},[2133,94598,53179],{},[1726,94600,8411],{"separator":1741},[2133,94602,94603],{},"4,32",[1726,94605,2502],{"stretchy":1734},[902,94607,94608],{"encoding":904},"E[2{,}5; 4{,}32]"," na téže křivce užitečnosti? Když ano, určete ji.",[724,94611,94612,93714,94615,94658,94659,6460,94672,94706,94707,94724,94725,94742],{},[38,94613,94614],{},"6.6",[883,94616,94618],{"className":94617},[886],[888,94619,94620],{"xmlns":890},[892,94621,94622,94656],{},[895,94623,94624,94626,94628,94642],{},[898,94625,900],{},[1726,94627,1728],{},[9151,94629,94630,94632,94634],{},[898,94631,1724],{},[2133,94633,2281],{},[895,94635,94636,94638,94640],{},[2133,94637,2135],{},[898,94639,4661],{"mathvariant":2377},[2133,94641,2177],{},[9151,94643,94644,94646,94648],{},[898,94645,1724],{},[2133,94647,2135],{},[895,94649,94650,94652,94654],{},[2133,94651,2281],{},[898,94653,4661],{"mathvariant":2377},[2133,94655,2177],{},[902,94657,94351],{"encoding":904},". (a) Najděte mezní míru komoditní substituce ",[883,94660,94662],{"className":94661},[886],[888,94663,94664],{"xmlns":890},[892,94665,94666,94670],{},[895,94667,94668],{},[2289,94669,10587],{},[902,94671,28219],{"encoding":904},[883,94673,94675],{"className":94674},[886],[888,94676,94677],{"xmlns":890},[892,94678,94679,94703],{},[895,94680,94681,94687,94689,94691,94693,94699,94701],{},[2275,94682,94683,94685],{},[898,94684,1724],{},[2133,94686,2281],{},[1726,94688,1728],{},[2133,94690,3087],{},[1726,94692,1742],{"separator":1741},[2275,94694,94695,94697],{},[898,94696,1724],{},[2133,94698,2135],{},[1726,94700,1728],{},[2133,94702,8363],{},[902,94704,94705],{"encoding":904},"Q_1 = 100, Q_2 = 200"," a výsledek ekonomicky interpretujte. (c) Odhadněte, o kolik je třeba změnit ",[883,94708,94710],{"className":94709},[886],[888,94711,94712],{"xmlns":890},[892,94713,94714,94722],{},[895,94715,94716],{},[2275,94717,94718,94720],{},[898,94719,1724],{},[2133,94721,2281],{},[902,94723,28983],{"encoding":904},", poklesne-li ",[883,94726,94728],{"className":94727},[886],[888,94729,94730],{"xmlns":890},[892,94731,94732,94740],{},[895,94733,94734],{},[2275,94735,94736,94738],{},[898,94737,1724],{},[2133,94739,2135],{},[902,94741,29002],{"encoding":904}," o 5 vzhledem k hladině dle (b).",[724,94744,94745,94748,94749,94766,94767,94784,94785,94817,94818,94843,94844,94857,94858,1343,94882,1343,94906,1888],{},[38,94746,94747],{},"6.7"," Míra uspokojení z nákupu množství ",[883,94750,94752],{"className":94751},[886],[888,94753,94754],{"xmlns":890},[892,94755,94756,94764],{},[895,94757,94758],{},[2275,94759,94760,94762],{},[898,94761,1724],{},[2133,94763,2281],{},[902,94765,28983],{"encoding":904}," nealko nápojů a množství ",[883,94768,94770],{"className":94769},[886],[888,94771,94772],{"xmlns":890},[892,94773,94774,94782],{},[895,94775,94776],{},[2275,94777,94778,94780],{},[898,94779,1724],{},[2133,94781,2135],{},[902,94783,29002],{"encoding":904}," hamburgerů za týden je dána funkcí užitečnosti ",[883,94786,94788],{"className":94787},[886],[888,94789,94790],{"xmlns":890},[892,94791,94792,94814],{},[895,94793,94794,94796,94798],{},[898,94795,900],{},[1726,94797,1728],{},[8103,94799,94800],{},[895,94801,94802,94808],{},[2275,94803,94804,94806],{},[898,94805,1724],{},[2133,94807,2281],{},[2275,94809,94810,94812],{},[898,94811,1724],{},[2133,94813,2135],{},[902,94815,94816],{"encoding":904},"U = \\sqrt{Q_1 Q_2}",". (a) Najděte vztah pro hodnoty ",[883,94819,94821],{"className":94820},[886],[888,94822,94823],{"xmlns":890},[892,94824,94825,94841],{},[895,94826,94827,94833,94835],{},[2275,94828,94829,94831],{},[898,94830,1724],{},[2133,94832,2281],{},[1726,94834,1742],{"separator":1741},[2275,94836,94837,94839],{},[898,94838,1724],{},[2133,94840,2135],{},[902,94842,35603],{"encoding":904},", pro něž je dosaženo užitečnosti 10 a uveďte několik takových dvojic hodnot. (b) Najděte ",[883,94845,94847],{"className":94846},[886],[888,94848,94849],{"xmlns":890},[892,94850,94851,94855],{},[895,94852,94853],{},[2289,94854,10587],{},[902,94856,28219],{"encoding":904}," na křivce nalezené v (a). (c) Ekonomicky interpretujte smysl ",[883,94859,94861],{"className":94860},[886],[888,94862,94863],{"xmlns":890},[892,94864,94865,94879],{},[895,94866,94867,94869,94871,94873,94875,94877],{},[2289,94868,10587],{},[1726,94870,1735],{"stretchy":1734},[2133,94872,2231],{},[1726,94874,1742],{"separator":1741},[2133,94876,9021],{},[1726,94878,1762],{"stretchy":1734},[902,94880,94881],{"encoding":904},"\\text{MRCS}(5, 20)",[883,94883,94885],{"className":94884},[886],[888,94886,94887],{"xmlns":890},[892,94888,94889,94903],{},[895,94890,94891,94893,94895,94897,94899,94901],{},[2289,94892,10587],{},[1726,94894,1735],{"stretchy":1734},[2133,94896,9021],{},[1726,94898,1742],{"separator":1741},[2133,94900,2231],{},[1726,94902,1762],{"stretchy":1734},[902,94904,94905],{"encoding":904},"\\text{MRCS}(20, 5)",[883,94907,94909],{"className":94908},[886],[888,94910,94911],{"xmlns":890},[892,94912,94913,94927],{},[895,94914,94915,94917,94919,94921,94923,94925],{},[2289,94916,10587],{},[1726,94918,1735],{"stretchy":1734},[2133,94920,2135],{},[1726,94922,1742],{"separator":1741},[2133,94924,3117],{},[1726,94926,1762],{"stretchy":1734},[902,94928,94929],{"encoding":904},"\\text{MRCS}(2, 50)",[3859,94931,94932],{},[724,94933,94934,94936,94937,1888],{},[883,94935,4560],{}," Úlohy 6.8 – 6.13 (optimalizace, Lagrange, poptávka)\nÚlohy navázané na maximalizaci užitečnosti, minimalizaci výdajů a odvození Marshallových\u002FHicksových funkcí poptávky jsou na stránce ",[207,94938,94941],{"className":94939,"dataFsResolvedFilePath":911,"href":94940},[210],"\u002Fwiki\u002Foptimalizace-spotrebitele#Úlohy k optimalizaci","Optimalizace spotřebitele — Úlohy",[115,94943,1670],{"id":1669},[120,94945,94946,94952,94957,94963,95016,95026,95072,95127,95190,95247,95302,95341],{},[123,94947,94948,94951],{},[38,94949,94950],{},"Užitečnost (utility)"," — ordinálně měřený ukazatel uspokojení spotřebitele ze svazku zboží.",[123,94953,94954,94956],{},[38,94955,86849],{}," — historická pojetí užitečnosti; v současnosti se preferuje ordinalistický.",[123,94958,94959,94962],{},[38,94960,94961],{},"Pět předpokladů chování spotřebitele"," — racionalita, ordinalita, konzistence a tranzitivita, rostoucí užitečnost, klesající mezní užitečnost.",[123,94964,94965,94967,94968,94981,94982,1888],{},[38,94966,87176],{}," — uspořádaná ",[883,94969,94971],{"className":94970},[886],[888,94972,94973],{"xmlns":890},[892,94974,94975,94979],{},[895,94976,94977],{},[898,94978,36841],{},[902,94980,36841],{"encoding":904},"-tice ",[883,94983,94985],{"className":94984},[886],[888,94986,94987],{"xmlns":890},[892,94988,94989,95013],{},[895,94990,94991,94993,94999,95001,95003,95005,95011],{},[1726,94992,1735],{"stretchy":1734},[2275,94994,94995,94997],{},[898,94996,1724],{},[2133,94998,2281],{},[1726,95000,1742],{"separator":1741},[1726,95002,1759],{},[1726,95004,1742],{"separator":1741},[2275,95006,95007,95009],{},[898,95008,1724],{},[898,95010,36841],{},[1726,95012,1762],{"stretchy":1734},[902,95014,95015],{"encoding":904},"(Q_1, \\dots, Q_n)",[123,95017,95018,95021,95022,95025],{},[38,95019,95020],{},"Relace preference"," — uspořádání svazků podle užitečnosti; ",[38,95023,95024],{},"indiferentní svazky"," mají stejnou užitečnost.",[123,95027,95028,1777,95031,95071],{},[38,95029,95030],{},"Funkce užitečnosti",[883,95032,95034],{"className":95033},[886],[888,95035,95036],{"xmlns":890},[892,95037,95038,95068],{},[895,95039,95040,95042,95044,95046,95048,95054,95056,95058,95060,95066],{},[898,95041,900],{},[1726,95043,1728],{},[898,95045,900],{},[1726,95047,1735],{"stretchy":1734},[2275,95049,95050,95052],{},[898,95051,1724],{},[2133,95053,2281],{},[1726,95055,1742],{"separator":1741},[1726,95057,1759],{},[1726,95059,1742],{"separator":1741},[2275,95061,95062,95064],{},[898,95063,1724],{},[898,95065,36841],{},[1726,95067,1762],{"stretchy":1734},[902,95069,95070],{"encoding":904},"U = U(Q_1, \\dots, Q_n)"," — vzorec (6.1); ekvivalentní až na monotónní transformaci.",[123,95073,95074,1777,95077,95106,95107,1777,95110,95126],{},[38,95075,95076],{},"Mezní užitečnost",[883,95078,95080],{"className":95079},[886],[888,95081,95082],{"xmlns":890},[892,95083,95084,95104],{},[895,95085,95086,95088,95094,95096],{},[898,95087,2815],{},[2275,95089,95090,95092],{},[898,95091,900],{},[898,95093,17772],{},[1726,95095,1728],{},[9151,95097,95098,95100,95102],{},[898,95099,900],{},[898,95101,17772],{},[1726,95103,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[902,95105,86633],{"encoding":904}," — vzorec (6.2); ",[38,95108,95109],{},"totální diferenciál",[883,95111,95113],{"className":95112},[886],[888,95114,95115],{"xmlns":890},[892,95116,95117,95123],{},[895,95118,95119,95121],{},[898,95120,2198],{"mathvariant":2377},[898,95122,900],{},[902,95124,95125],{"encoding":904},"\\mathrm{d} U"," — (6.3).",[123,95128,95129,95131,95132,95156,95157,95189],{},[38,95130,88812],{}," — (6.4) ",[883,95133,95135],{"className":95134},[886],[888,95136,95137],{"xmlns":890},[892,95138,95139,95153],{},[895,95140,95141,95149,95151],{},[9151,95142,95143,95145,95147],{},[898,95144,900],{},[898,95146,17772],{},[1726,95148,2379],{"mathvariant":2377,"lspace":2378,"rspace":2378},[1726,95150,3405],{},[2133,95152,2328],{},[902,95154,95155],{"encoding":904},"U'_i > 0",", (6.5) ",[883,95158,95160],{"className":95159},[886],[888,95161,95162],{"xmlns":890},[892,95163,95164,95186],{},[895,95165,95166,95182,95184],{},[9151,95167,95168,95170,95176],{},[898,95169,900],{},[895,95171,95172,95174],{},[898,95173,17772],{},[898,95175,17772],{},[895,95177,95178,95180],{},[1726,95179,2379],{"mathvariant":2377},[1726,95181,2379],{"mathvariant":2377},[1726,95183,3444],{},[2133,95185,2328],{},[902,95187,95188],{"encoding":904},"U''_{ii} \u003C 0"," (zákon klesající mezní užitečnosti).",[123,95191,95192,1777,95194,95225,95226,1888],{},[38,95193,90600],{},[883,95195,95197],{"className":95196},[886],[888,95198,95199],{"xmlns":890},[892,95200,95201,95223],{},[895,95202,95203,95205,95207,95215],{},[898,95204,900],{},[1726,95206,1728],{},[9151,95208,95209,95211,95213],{},[898,95210,1724],{},[2133,95212,2281],{},[898,95214,207],{},[9151,95216,95217,95219,95221],{},[898,95218,1724],{},[2133,95220,2135],{},[898,95222,2102],{},[902,95224,35784],{"encoding":904}," — (6.6), speciálně ",[883,95227,95229],{"className":95228},[886],[888,95230,95231],{"xmlns":890},[892,95232,95233,95245],{},[895,95234,95235,95237,95239,95241,95243],{},[898,95236,2102],{},[1726,95238,1728],{},[2133,95240,2281],{},[1726,95242,2228],{},[898,95244,207],{},[902,95246,90754],{"encoding":904},[123,95248,95249,1777,95252,95287,95288,95301],{},[38,95250,95251],{},"Křivky užitečnosti (indiferenční)",[883,95253,95255],{"className":95254},[886],[888,95256,95257],{"xmlns":890},[892,95258,95259,95285],{},[895,95260,95261,95263,95265,95271,95273,95279,95281,95283],{},[898,95262,900],{},[1726,95264,1735],{"stretchy":1734},[2275,95266,95267,95269],{},[898,95268,1724],{},[2133,95270,2281],{},[1726,95272,1742],{"separator":1741},[2275,95274,95275,95277],{},[898,95276,1724],{},[2133,95278,2135],{},[1726,95280,1762],{"stretchy":1734},[1726,95282,1728],{},[898,95284,2146],{},[902,95286,9752],{"encoding":904}," — (6.7), (6.8); čtyři vlastnosti: klesající, neprotínající se, vzdálenější od počátku = vyšší ",[883,95289,95291],{"className":95290},[886],[888,95292,95293],{"xmlns":890},[892,95294,95295,95299],{},[895,95296,95297],{},[898,95298,900],{},[902,95300,900],{"encoding":904},", konvexní.",[123,95303,95304,1777,95306,95340],{},[38,95305,92145],{},[883,95307,95309],{"className":95308},[886],[888,95310,95311],{"xmlns":890},[892,95312,95313,95337],{},[895,95314,95315,95317,95319,95321,95327,95329,95331],{},[2289,95316,10587],{},[1726,95318,1728],{},[898,95320,2815],{},[2275,95322,95323,95325],{},[898,95324,900],{},[2133,95326,2281],{},[898,95328,4661],{"mathvariant":2377},[898,95330,2815],{},[2275,95332,95333,95335],{},[898,95334,900],{},[2133,95336,2135],{},[902,95338,95339],{"encoding":904},"\\text{MRCS} = MU_1 \u002F MU_2"," — (6.9); vztahy (6.10), (6.11).",[123,95342,95343,1777,95346,9753,95375,95378],{},[38,95344,95345],{},"Podmínka optimality",[883,95347,95349],{"className":95348},[886],[888,95350,95351],{"xmlns":890},[892,95352,95353,95373],{},[895,95354,95355,95357,95359,95365,95367],{},[2289,95356,10587],{},[1726,95358,1728],{},[2275,95360,95361,95363],{},[898,95362,1738],{},[2133,95364,2281],{},[898,95366,4661],{"mathvariant":2377},[2275,95368,95369,95371],{},[898,95370,1738],{},[2133,95372,2135],{},[902,95374,27979],{"encoding":904},[207,95376,36735],{"className":95377,"dataFsResolvedFilePath":911,"href":912},[210]," pro plné odvození.",[115,95380,1899],{"id":1898},[120,95382,95383,95420,95461,95471],{},[123,95384,95385,1777,95388,95391,95392,95405,95406,95419],{},[38,95386,95387],{},"Navazující téma:",[207,95389,913],{"className":95390,"dataFsResolvedFilePath":911,"href":912},[210]," (Lagrange, max ",[883,95393,95395],{"className":95394},[886],[888,95396,95397],{"xmlns":890},[892,95398,95399,95403],{},[895,95400,95401],{},[898,95402,900],{},[902,95404,900],{"encoding":904},", min ",[883,95407,95409],{"className":95408},[886],[888,95410,95411],{"xmlns":890},[892,95412,95413,95417],{},[895,95414,95415],{},[898,95416,4240],{},[902,95418,4240],{"encoding":904},", funkce poptávky, Příklady 6.5–6.8, úlohy 6.8–6.13).",[123,95421,95422,1777,95425,11077,95428,86388,95431,95434,95435,95438,95439,18629,95457,95460],{},[38,95423,95424],{},"Související pojmy:",[207,95426,784],{"className":95427,"dataFsResolvedFilePath":782,"href":783},[210],[207,95429,2358],{"className":95430,"dataFsResolvedFilePath":764,"href":765},[210],[207,95432,11072],{"className":95433,"dataFsResolvedFilePath":857,"href":858},[210]," (paralela: MRCS ↔ MRTS, izokvanty ↔ indiferenční křivky, Cobb-Douglas), ",[207,95436,11926],{"className":95437,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallovy poptávkové funkce ",[883,95440,95442],{"className":95441},[886],[888,95443,95444],{"xmlns":890},[892,95445,95446,95454],{},[895,95447,95448],{},[2275,95449,95450,95452],{},[898,95451,1731],{},[898,95453,17772],{},[902,95455,95456],{"encoding":904},"D_i",[207,95458,793],{"className":95459,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace — nástroj pro navazující téma).",[123,95462,95463,1777,95465,1343,95468],{},[38,95464,36684],{},[207,95466,1094],{"className":95467,"dataFsResolvedFilePath":838,"href":839},[210],[207,95469,1101],{"className":95470,"dataFsResolvedFilePath":868,"href":869},[210],[123,95472,95473,1777,95475],{},[38,95474,16188],{},[207,95476,16192],{"className":95477,"dataFsResolvedFilePath":1640,"href":1641},[210],{"title":641,"searchDepth":642,"depth":642,"links":95479},[95480,95481,95482,95485,95486,95489,95493,95494,95497,95498,95499,95500,95501,95502,95503],{"id":11991,"depth":642,"text":11992},{"id":86772,"depth":642,"text":86773},{"id":86832,"depth":642,"text":86833,"children":95483},[95484],{"id":86848,"depth":649,"text":86849},{"id":87155,"depth":642,"text":87156},{"id":88015,"depth":642,"text":88016,"children":95487},[95488],{"id":88562,"depth":649,"text":80191},{"id":88811,"depth":642,"text":88812,"children":95490},[95491],{"id":89684,"depth":649,"text":95492},"Příklad 6.2 — ověření vlastností a dopočet pro U=Q11\u002F2Q21\u002F3U = Q_1^{1\u002F2} Q_2^{1\u002F3}",{"id":90599,"depth":642,"text":90600},{"id":91135,"depth":642,"text":91136,"children":95495},[95496],{"id":91909,"depth":649,"text":91910},{"id":92139,"depth":642,"text":92140},{"id":92900,"depth":642,"text":92901},{"id":93438,"depth":642,"text":93439},{"id":49862,"depth":642,"text":49863},{"id":93574,"depth":642,"text":93575},{"id":1669,"depth":642,"text":1670},{"id":1898,"depth":642,"text":1899},{},"\u002Ftopics\u002Fuzitecnost",{"title":86556,"description":641},[1138,1137],"topics\u002Fuzitecnost",[1128,9757,95510,86550,11107,95511],"mezni-uzitecnost","mrcs","xXggD9rfV5faUAk1b2B3YYbozpQLu-pObiMaZX5f7yI",{"id":1628,"title":757,"body":95514,"course":1128,"courses":659,"created":1129,"description":1938,"extension":661,"meta":95736,"navigation":664,"path":1940,"seo":95737,"sources":95738,"stem":1943,"tags":95739,"type":1950,"updated":677,"__hash__":1951},{"type":9,"value":95515,"toc":95728},[95516,95518,95523,95528,95530,95536,95538,95562,95564,95605,95607,95663,95665,95687,95689,95703,95705],[12,95517,757],{"id":1633},[724,95519,1636,95520,1643],{},[207,95521,1642],{"className":95522,"dataFsResolvedFilePath":1640,"href":1641},[210],[724,95524,95525],{},[1647,95526],{"alt":1649,"className":95527,"src":1652},[210,1651],[115,95529,1656],{"id":1655},[724,95531,95532,1662,95534,1666],{},[38,95533,1661],{},[38,95535,1665],{},[115,95537,1670],{"id":1669},[120,95539,95540,95544,95548,95552,95558],{},[123,95541,95542,1678],{},[38,95543,1677],{},[123,95545,95546,1684],{},[38,95547,1683],{},[123,95549,95550,1690],{},[38,95551,1689],{},[123,95553,95554,1696,95556,1700],{},[38,95555,1695],{},[614,95557,1699],{},[123,95559,95560,1706],{},[38,95561,1705],{},[115,95563,1710],{"id":1709},[724,95565,95566,1766],{},[883,95567,95569],{"className":95568},[886],[888,95570,95571],{"xmlns":890},[892,95572,95573,95603],{},[895,95574,95575,95577,95579,95581,95583,95585,95587,95589,95591,95593,95595,95597,95599,95601],{},[898,95576,1724],{},[1726,95578,1728],{},[898,95580,1731],{},[1726,95582,1735],{"stretchy":1734},[898,95584,1738],{},[1726,95586,1742],{"separator":1741},[898,95588,1745],{},[1726,95590,1742],{"separator":1741},[898,95592,1750],{},[1726,95594,1742],{"separator":1741},[898,95596,900],{},[1726,95598,1742],{"separator":1741},[1726,95600,1759],{},[1726,95602,1762],{"stretchy":1734},[902,95604,1765],{"encoding":904},[724,95606,1769],{},[120,95608,95609,95636],{},[123,95610,95611,1777,95613],{},[38,95612,1776],{},[883,95614,95616],{"className":95615},[886],[888,95617,95618],{"xmlns":890},[892,95619,95620,95634],{},[895,95621,95622,95624,95626,95628,95630,95632],{},[898,95623,1724],{},[1726,95625,1728],{},[898,95627,1731],{},[1726,95629,1735],{"stretchy":1734},[898,95631,1738],{},[1726,95633,1762],{"stretchy":1734},[902,95635,1801],{"encoding":904},[123,95637,95638,1777,95640],{},[38,95639,1806],{},[883,95641,95643],{"className":95642},[886],[888,95644,95645],{"xmlns":890},[892,95646,95647,95661],{},[895,95648,95649,95651,95653,95655,95657,95659],{},[898,95650,1738],{},[1726,95652,1728],{},[898,95654,1731],{},[1726,95656,1735],{"stretchy":1734},[898,95658,1724],{},[1726,95660,1762],{"stretchy":1734},[902,95662,1830],{"encoding":904},[115,95664,1834],{"id":1833},[152,95666,95667,95674],{},[123,95668,95669,1842,95671,1847],{},[38,95670,1841],{},[207,95672,1846],{"className":95673,"dataFsResolvedFilePath":800,"href":801},[210],[123,95675,95676,1853,95678,1857,95681,1862,95684,1867],{},[38,95677,1852],{},[207,95679,1145],{"className":95680,"dataFsResolvedFilePath":764,"href":765},[210],[207,95682,1861],{"className":95683,"dataFsResolvedFilePath":782,"href":783},[210],[207,95685,1866],{"className":95686,"dataFsResolvedFilePath":791,"href":792},[210],[115,95688,1871],{"id":1870},[120,95690,95691,95695,95699],{},[123,95692,1876,95693,1881],{},[1878,95694,1880],{},[123,95696,1884,95697,1888],{},[38,95698,1887],{},[123,95700,1891,95701,1895],{},[614,95702,1894],{},[115,95704,1899],{"id":1898},[120,95706,95707,95711,95718],{},[123,95708,95709,1907],{},[38,95710,1906],{},[123,95712,95713,1777,95715],{},[38,95714,1912],{},[207,95716,1916],{"className":95717,"dataFsResolvedFilePath":764,"href":765},[210],[123,95719,95720,1777,95722,1343,95725],{},[38,95721,1921],{},[207,95723,1925],{"className":95724,"dataFsResolvedFilePath":745,"href":746},[210],[207,95726,1929],{"className":95727,"dataFsResolvedFilePath":1640,"href":1641},[210],{"title":641,"searchDepth":642,"depth":642,"links":95729},[95730,95731,95732,95733,95734,95735],{"id":1655,"depth":642,"text":1656},{"id":1669,"depth":642,"text":1670},{"id":1709,"depth":642,"text":1710},{"id":1833,"depth":642,"text":1834},{"id":1870,"depth":642,"text":1871},{"id":1898,"depth":642,"text":1899},{},{"title":757,"description":1938},[1135],[1128,1945,1946,1947,1948,1949],{"id":95741,"title":95742,"body":95743,"course":1128,"courses":659,"created":9541,"description":641,"extension":661,"meta":100015,"navigation":664,"path":100016,"seo":100017,"sources":100018,"stem":100019,"tags":100020,"type":1950,"updated":677,"__hash__":100024},"topics\u002Ftopics\u002Fzdaneni-trhu.md","Zdanění trhu — dopady daně na rovnováhu",{"type":9,"value":95744,"toc":99998},[95745,95748,95842,95846,95868,95882,95934,95936,95940,96003,96046,96065,96228,96327,96330,96397,96401,96530,96569,96599,96711,96756,96822,96875,96951,97007,97009,97013,97077,97121,97141,97302,97305,97389,97486,97489,97555,97559,97608,97634,97739,97803,97808,97904,97951,97953,97956,97978,98020,98027,98060,98062,98133,98187,98296,98300,98389,98465,98729,98767,98769,98773,98776,98783,99094,99097,99155,99335,99364,99366,99370,99376,99514,99523,99525,99527,99952,99954,99956],[12,95746,95742],{"id":95747},"zdanění-trhu-dopady-daně-na-rovnováhu",[3859,95749,95750],{},[724,95751,95752,42609,95754,95767,95768,95771,95772,95774,95775,95778,95779,95800,95801,95824,95825,95828,95829,1888],{},[883,95753,4145],{},[883,95755,95757],{"className":95756},[886],[888,95758,95759],{"xmlns":890},[892,95760,95761,95765],{},[895,95762,95763],{},[898,95764,2772],{},[902,95766,2772],{"encoding":904}," uložená na každou prodanou jednotku zboží posouvá jednu z křivek — ",[38,95769,95770],{},"nabídku"," (je-li daň uložena výrobci) nebo ",[38,95773,86840],{}," (je-li uložena spotřebiteli). Výsledné ",[38,95776,95777],{},"daňové břemeno"," se dělí mezi obě strany trhu na ",[883,95780,95782],{"className":95781},[886],[888,95783,95784],{"xmlns":890},[892,95785,95786,95798],{},[895,95787,95788],{},[2275,95789,95790,95792],{},[898,95791,2772],{},[895,95793,95794,95796],{},[898,95795,42658],{},[898,95797,724],{},[902,95799,42663],{"encoding":904}," (spotřebitel) a ",[883,95802,95804],{"className":95803},[886],[888,95805,95806],{"xmlns":890},[892,95807,95808,95822],{},[895,95809,95810],{},[2275,95811,95812,95814],{},[898,95813,2772],{},[895,95815,95816,95818,95820],{},[898,95817,42681],{},[898,95819,2003],{},[898,95821,12027],{},[902,95823,42688],{"encoding":904}," (výrobce). Klíčovým zjištěním je ",[38,95826,95827],{},"ekvivalence obou přístupů",": rovnovážné množství i čistá cena pro výrobce jsou v obou režimech totožné; liší se pouze nominální cena na trhu o ",[883,95830,95832],{"className":95831},[886],[888,95833,95834],{"xmlns":890},[892,95835,95836,95840],{},[895,95837,95838],{},[898,95839,2772],{},[902,95841,2772],{"encoding":904},[115,95843,95845],{"id":95844},"dvě-formy-zdanění","Dvě formy zdanění",[724,95847,95848,95849,95867],{},"Uvažujme jednotkovou daň ",[883,95850,95852],{"className":95851},[886],[888,95853,95854],{"xmlns":890},[892,95855,95856,95864],{},[895,95857,95858,95860,95862],{},[898,95859,2772],{},[1726,95861,3405],{},[2133,95863,2328],{},[902,95865,95866],{"encoding":904},"T > 0"," (Kč na kus), kterou stát ukládá na každou prodanou jednotku zboží. Daň může být uložena buď:",[120,95869,95870,95876],{},[123,95871,95872,95875],{},[38,95873,95874],{},"(a) výrobci"," — výrobce ji musí odvést státu z každé prodané jednotky,",[123,95877,95878,95881],{},[38,95879,95880],{},"(b) spotřebiteli"," — spotřebitel ji platí navíc k ceně, kterou si účtuje prodejce.",[724,95883,95884,95885,95898,95899,95902,95903,1888],{},"V obou případech dochází k posunu jedné z křivek o ",[883,95886,95888],{"className":95887},[886],[888,95889,95890],{"xmlns":890},[892,95891,95892,95896],{},[895,95893,95894],{},[898,95895,2772],{},[902,95897,2772],{"encoding":904}," svisle (buď nabídky nahoru, nebo poptávky dolů) a k rozdělení ",[38,95900,95901],{},"daňového břemene"," mezi spotřebitele a výrobce. Výchozí rovnovážný bod bez daně označujeme ",[883,95904,95906],{"className":95905},[886],[888,95907,95908],{"xmlns":890},[892,95909,95910,95932],{},[895,95911,95912,95914,95916,95922,95924,95930],{},[898,95913,4240],{},[1726,95915,2487],{"stretchy":1734},[2128,95917,95918,95920],{},[898,95919,1724],{},[898,95921,4240],{},[1726,95923,1742],{"separator":1741},[2128,95925,95926,95928],{},[898,95927,1738],{},[898,95929,4240],{},[1726,95931,2502],{"stretchy":1734},[902,95933,41348],{"encoding":904},[36951,95935],{},[115,95937,95939],{"id":95938},"daň-uložená-výrobci","Daň uložená výrobci",[724,95941,95942,95943,95956,95957,95974,95975,96002],{},"Je-li daň ",[883,95944,95946],{"className":95945},[886],[888,95947,95948],{"xmlns":890},[892,95949,95950,95954],{},[895,95951,95952],{},[898,95953,2772],{},[902,95955,2772],{"encoding":904}," uložena výrobci, pak z podmínky, že výrobce za každou prodanou jednotku obdrží ",[883,95958,95960],{"className":95959},[886],[888,95961,95962],{"xmlns":890},[892,95963,95964,95972],{},[895,95965,95966,95968,95970],{},[898,95967,1738],{},[1726,95969,2228],{},[898,95971,2772],{},[902,95973,41103],{"encoding":904}," (hrubá cena mínus odvod), plyne z rovnice ",[883,95976,95978],{"className":95977},[886],[888,95979,95980],{"xmlns":890},[892,95981,95982,96000],{},[895,95983,95984,95986,95988,95990,95992,95994,95996,95998],{},[898,95985,1738],{},[1726,95987,2228],{},[898,95989,2772],{},[1726,95991,1728],{},[898,95993,8659],{},[1726,95995,1735],{"stretchy":1734},[898,95997,1724],{},[1726,95999,1762],{"stretchy":1734},[902,96001,41132],{"encoding":904}," nová funkce nabídky:",[883,96004,96006],{"className":96005},[886],[888,96007,96008],{"xmlns":890,"display":28047},[892,96009,96010,96044],{},[895,96011,96012,96014,96016,96022,96024,96026,96028,96030,96032,96034,96036,96038,96040,96042],{},[898,96013,1738],{},[1726,96015,1728],{},[2275,96017,96018,96020],{},[898,96019,8659],{},[2133,96021,2281],{},[1726,96023,1735],{"stretchy":1734},[898,96025,1724],{},[1726,96027,1762],{"stretchy":1734},[1726,96029,1728],{},[898,96031,8659],{},[1726,96033,1735],{"stretchy":1734},[898,96035,1724],{},[1726,96037,1762],{"stretchy":1734},[1726,96039,2099],{},[898,96041,2772],{},[898,96043,1888],{"mathvariant":2377},[902,96045,41177],{"encoding":904},[724,96047,96048,96049,1777,96062,96064],{},"Nabídka se tedy posouvá o ",[883,96050,96052],{"className":96051},[886],[888,96053,96054],{"xmlns":890},[892,96055,96056,96060],{},[895,96057,96058],{},[898,96059,2772],{},[902,96061,2772],{"encoding":904},[38,96063,41210],{}," (ekvivalentně doleva). Poptávka se nemění.",[724,96066,96067,96068,96108,96109,3877,96137,96165,96166,96185,96186,96210,96211,1847],{},"Nový rovnovážný bod ",[883,96069,96071],{"className":96070},[886],[888,96072,96073],{"xmlns":890},[892,96074,96075,96105],{},[895,96076,96077,96083,96085,96093,96095,96103],{},[2275,96078,96079,96081],{},[898,96080,4240],{},[2133,96082,2281],{},[1726,96084,2487],{"stretchy":1734},[9151,96086,96087,96089,96091],{},[898,96088,1724],{},[2133,96090,2281],{},[898,96092,4240],{},[1726,96094,1742],{"separator":1741},[9151,96096,96097,96099,96101],{},[898,96098,1738],{},[2133,96100,2281],{},[898,96102,4240],{},[1726,96104,2502],{"stretchy":1734},[902,96106,96107],{"encoding":904},"E_1[Q_1^E, P_1^E]"," splňuje ",[883,96110,96112],{"className":96111},[886],[888,96113,96114],{"xmlns":890},[892,96115,96116,96134],{},[895,96117,96118,96126,96128],{},[9151,96119,96120,96122,96124],{},[898,96121,1724],{},[2133,96123,2281],{},[898,96125,4240],{},[1726,96127,3444],{},[2128,96129,96130,96132],{},[898,96131,1724],{},[898,96133,4240],{},[902,96135,96136],{"encoding":904},"Q_1^E \u003C Q^E",[883,96138,96140],{"className":96139},[886],[888,96141,96142],{"xmlns":890},[892,96143,96144,96162],{},[895,96145,96146,96154,96156],{},[9151,96147,96148,96150,96152],{},[898,96149,1738],{},[2133,96151,2281],{},[898,96153,4240],{},[1726,96155,3405],{},[2128,96157,96158,96160],{},[898,96159,1738],{},[898,96161,4240],{},[902,96163,96164],{"encoding":904},"P_1^E > P^E",". Spotřebitel platí ",[883,96167,96169],{"className":96168},[886],[888,96170,96171],{"xmlns":890},[892,96172,96173,96183],{},[895,96174,96175],{},[9151,96176,96177,96179,96181],{},[898,96178,1738],{},[2133,96180,2281],{},[898,96182,4240],{},[902,96184,47838],{"encoding":904},", výrobci ale zůstává pouze čistá cena ",[883,96187,96189],{"className":96188},[886],[888,96190,96191],{"xmlns":890},[892,96192,96193,96207],{},[895,96194,96195,96203,96205],{},[9151,96196,96197,96199,96201],{},[898,96198,1738],{},[2133,96200,2281],{},[898,96202,4240],{},[1726,96204,2228],{},[898,96206,2772],{},[902,96208,96209],{"encoding":904},"P_1^E - T"," (ta je nižší než původní rovnovážná ",[883,96212,96214],{"className":96213},[886],[888,96215,96216],{"xmlns":890},[892,96217,96218,96226],{},[895,96219,96220],{},[2128,96221,96222,96224],{},[898,96223,1738],{},[898,96225,4240],{},[902,96227,41447],{"encoding":904},[724,96229,96230],{},[614,96231,96232,96233,96263,96264,96277,96278,5656,96295,96308,96309,1888],{},"Obrázek 2.17 (resp. 2.18): Posun ",[883,96234,96236],{"className":96235},[886],[888,96237,96238],{"xmlns":890},[892,96239,96240,96260],{},[895,96241,96242,96244,96246,96252,96254,96256,96258],{},[898,96243,8659],{},[1726,96245,3120],{},[2275,96247,96248,96250],{},[898,96249,8659],{},[2133,96251,2281],{},[1726,96253,1728],{},[898,96255,8659],{},[1726,96257,2099],{},[898,96259,2772],{},[902,96261,96262],{"encoding":904},"S \\to S_1 = S + T","; svislá vzdálenost mezi křivkami je přesně ",[883,96265,96267],{"className":96266},[886],[888,96268,96269],{"xmlns":890},[892,96270,96271,96275],{},[895,96272,96273],{},[898,96274,2772],{},[902,96276,2772],{"encoding":904},". Průsečík ",[883,96279,96281],{"className":96280},[886],[888,96282,96283],{"xmlns":890},[892,96284,96285,96293],{},[895,96286,96287],{},[2275,96288,96289,96291],{},[898,96290,8659],{},[2133,96292,2281],{},[902,96294,40978],{"encoding":904},[883,96296,96298],{"className":96297},[886],[888,96299,96300],{"xmlns":890},[892,96301,96302,96306],{},[895,96303,96304],{},[898,96305,1731],{},[902,96307,1731],{"encoding":904}," je nový rovnovážný bod ",[883,96310,96312],{"className":96311},[886],[888,96313,96314],{"xmlns":890},[892,96315,96316,96324],{},[895,96317,96318],{},[2275,96319,96320,96322],{},[898,96321,4240],{},[2133,96323,2281],{},[902,96325,96326],{"encoding":904},"E_1",[198,96328,45284],{"id":96329},"příklad-29",[724,96331,96332,41636,96334,41671,96358,96378,96379,96396],{},[38,96333,37914],{},[883,96335,96337],{"className":96336},[886],[888,96338,96339],{"xmlns":890},[892,96340,96341,96355],{},[895,96342,96343,96345,96347,96349,96351,96353],{},[898,96344,1738],{},[1726,96346,1728],{},[2133,96348,3506],{},[1726,96350,2228],{},[2133,96352,2135],{},[898,96354,1724],{},[902,96356,96357],{"encoding":904},"P = 12 - 2Q",[883,96359,96361],{"className":96360},[886],[888,96362,96363],{"xmlns":890},[892,96364,96365,96375],{},[895,96366,96367,96369,96371,96373],{},[898,96368,1738],{},[1726,96370,1728],{},[2133,96372,2352],{},[898,96374,1724],{},[902,96376,96377],{"encoding":904},"P = 4Q",". Na výrobce je uložena jednotková daň ",[883,96380,96382],{"className":96381},[886],[888,96383,96384],{"xmlns":890},[892,96385,96386,96394],{},[895,96387,96388,96390,96392],{},[898,96389,2772],{},[1726,96391,1728],{},[2133,96393,2238],{},[902,96395,41249],{"encoding":904}," Kč.",[724,96398,96399],{},[38,96400,37946],{},[724,96402,96403,96406,96407,5556,96433,5576,96453,1343,96475,96505,96506,1888],{},[614,96404,96405],{},"Bez daně."," Z rovnosti ",[883,96408,96410],{"className":96409},[886],[888,96411,96412],{"xmlns":890},[892,96413,96414,96430],{},[895,96415,96416,96418,96420,96422,96424,96426,96428],{},[2133,96417,3506],{},[1726,96419,2228],{},[2133,96421,2135],{},[898,96423,1724],{},[1726,96425,1728],{},[2133,96427,2352],{},[898,96429,1724],{},[902,96431,96432],{"encoding":904},"12 - 2Q = 4Q",[883,96434,96436],{"className":96435},[886],[888,96437,96438],{"xmlns":890},[892,96439,96440,96450],{},[895,96441,96442,96444,96446,96448],{},[2133,96443,2238],{},[898,96445,1724],{},[1726,96447,1728],{},[2133,96449,3506],{},[902,96451,96452],{"encoding":904},"6Q = 12",[883,96454,96456],{"className":96455},[886],[888,96457,96458],{"xmlns":890},[892,96459,96460,96472],{},[895,96461,96462,96468,96470],{},[2128,96463,96464,96466],{},[898,96465,1724],{},[898,96467,4240],{},[1726,96469,1728],{},[2133,96471,2135],{},[902,96473,96474],{"encoding":904},"Q^E = 2",[883,96476,96478],{"className":96477},[886],[888,96479,96480],{"xmlns":890},[892,96481,96482,96502],{},[895,96483,96484,96490,96492,96494,96496,96498,96500],{},[2128,96485,96486,96488],{},[898,96487,1738],{},[898,96489,4240],{},[1726,96491,1728],{},[2133,96493,2352],{},[1726,96495,3174],{},[2133,96497,2135],{},[1726,96499,1728],{},[2133,96501,5572],{},[902,96503,96504],{"encoding":904},"P^E = 4 \\cdot 2 = 8",". Rovnovážný bod ",[883,96507,96509],{"className":96508},[886],[888,96510,96511],{"xmlns":890},[892,96512,96513,96527],{},[895,96514,96515,96517,96519,96521,96523,96525],{},[898,96516,4240],{},[1726,96518,2487],{"stretchy":1734},[2133,96520,2135],{},[1726,96522,1742],{"separator":1741},[2133,96524,5572],{},[1726,96526,2502],{"stretchy":1734},[902,96528,96529],{"encoding":904},"E[2, 8]",[724,96531,96532,96535,96536,96568],{},[614,96533,96534],{},"S daní uloženou výrobci."," Nová nabídka je ",[883,96537,96539],{"className":96538},[886],[888,96540,96541],{"xmlns":890},[892,96542,96543,96565],{},[895,96544,96545,96551,96553,96555,96557,96559,96561,96563],{},[2275,96546,96547,96549],{},[898,96548,8659],{},[2133,96550,2281],{},[1726,96552,2703],{},[898,96554,1738],{},[1726,96556,1728],{},[2133,96558,2352],{},[898,96560,1724],{},[1726,96562,2099],{},[2133,96564,2238],{},[902,96566,96567],{"encoding":904},"S_1: P = 4Q + 6",". Z rovnice",[883,96570,96572],{"className":96571},[886],[888,96573,96574],{"xmlns":890,"display":28047},[892,96575,96576,96596],{},[895,96577,96578,96580,96582,96584,96586,96588,96590,96592,96594],{},[2133,96579,3506],{},[1726,96581,2228],{},[2133,96583,2135],{},[898,96585,1724],{},[1726,96587,1728],{},[2133,96589,2352],{},[898,96591,1724],{},[1726,96593,2099],{},[2133,96595,2238],{},[902,96597,96598],{"encoding":904},"12 - 2Q = 4Q + 6",[724,96600,96601,96602,5576,96622,1343,96646,96682,96683,1888],{},"plyne ",[883,96603,96605],{"className":96604},[886],[888,96606,96607],{"xmlns":890},[892,96608,96609,96619],{},[895,96610,96611,96613,96615,96617],{},[2133,96612,2238],{},[898,96614,1724],{},[1726,96616,1728],{},[2133,96618,2238],{},[902,96620,96621],{"encoding":904},"6Q = 6",[883,96623,96625],{"className":96624},[886],[888,96626,96627],{"xmlns":890},[892,96628,96629,96643],{},[895,96630,96631,96639,96641],{},[9151,96632,96633,96635,96637],{},[898,96634,1724],{},[2133,96636,2281],{},[898,96638,4240],{},[1726,96640,1728],{},[2133,96642,2281],{},[902,96644,96645],{"encoding":904},"Q_1^E = 1",[883,96647,96649],{"className":96648},[886],[888,96650,96651],{"xmlns":890},[892,96652,96653,96679],{},[895,96654,96655,96663,96665,96667,96669,96671,96673,96675,96677],{},[9151,96656,96657,96659,96661],{},[898,96658,1738],{},[2133,96660,2281],{},[898,96662,4240],{},[1726,96664,1728],{},[2133,96666,2352],{},[1726,96668,3174],{},[2133,96670,2281],{},[1726,96672,2099],{},[2133,96674,2238],{},[1726,96676,1728],{},[2133,96678,2860],{},[902,96680,96681],{"encoding":904},"P_1^E = 4 \\cdot 1 + 6 = 10",". Nový rovnovážný bod ",[883,96684,96686],{"className":96685},[886],[888,96687,96688],{"xmlns":890},[892,96689,96690,96708],{},[895,96691,96692,96698,96700,96702,96704,96706],{},[2275,96693,96694,96696],{},[898,96695,4240],{},[2133,96697,2281],{},[1726,96699,2487],{"stretchy":1734},[2133,96701,2281],{},[1726,96703,1742],{"separator":1741},[2133,96705,2860],{},[1726,96707,2502],{"stretchy":1734},[902,96709,96710],{"encoding":904},"E_1[1, 10]",[724,96712,96713,96716,96717,96741,96742,96755],{},[614,96714,96715],{},"Rozklad daňového břemene."," Spotřebitel platí ",[883,96718,96720],{"className":96719},[886],[888,96721,96722],{"xmlns":890},[892,96723,96724,96738],{},[895,96725,96726,96734,96736],{},[9151,96727,96728,96730,96732],{},[898,96729,1738],{},[2133,96731,2281],{},[898,96733,4240],{},[1726,96735,1728],{},[2133,96737,2860],{},[902,96739,96740],{"encoding":904},"P_1^E = 10"," Kč namísto původních ",[883,96743,96745],{"className":96744},[886],[888,96746,96747],{"xmlns":890},[892,96748,96749,96753],{},[895,96750,96751],{},[2133,96752,5572],{},[902,96754,5572],{"encoding":904},", navýšení je",[883,96757,96759],{"className":96758},[886],[888,96760,96761],{"xmlns":890,"display":28047},[892,96762,96763,96819],{},[895,96764,96765,96775,96777,96785,96787,96793,96795,96797,96799,96801,96803,96805,96807,96817],{},[2275,96766,96767,96769],{},[898,96768,2772],{},[895,96770,96771,96773],{},[898,96772,42658],{},[898,96774,724],{},[1726,96776,1728],{},[9151,96778,96779,96781,96783],{},[898,96780,1738],{},[2133,96782,2281],{},[898,96784,4240],{},[1726,96786,2228],{},[2128,96788,96789,96791],{},[898,96790,1738],{},[898,96792,4240],{},[1726,96794,1728],{},[2133,96796,2860],{},[1726,96798,2228],{},[2133,96800,5572],{},[1726,96802,1728],{},[2133,96804,2135],{},[2289,96806,2291],{},[895,96808,96809,96811],{},[2289,96810,9784],{},[8372,96812,96813,96815],{"accent":1741},[2289,96814,2146],{},[1726,96816,25039],{},[898,96818,1888],{"mathvariant":2377},[902,96820,96821],{"encoding":904},"T_{sp} = P_1^E - P^E = 10 - 8 = 2\\ \\text{Kč}.",[724,96823,96824,96825,96741,96861,96874],{},"Výrobci zůstává čistá cena ",[883,96826,96828],{"className":96827},[886],[888,96829,96830],{"xmlns":890},[892,96831,96832,96858],{},[895,96833,96834,96842,96844,96846,96848,96850,96852,96854,96856],{},[9151,96835,96836,96838,96840],{},[898,96837,1738],{},[2133,96839,2281],{},[898,96841,4240],{},[1726,96843,2228],{},[898,96845,2772],{},[1726,96847,1728],{},[2133,96849,2860],{},[1726,96851,2228],{},[2133,96853,2238],{},[1726,96855,1728],{},[2133,96857,2352],{},[902,96859,96860],{"encoding":904},"P_1^E - T = 10 - 6 = 4",[883,96862,96864],{"className":96863},[886],[888,96865,96866],{"xmlns":890},[892,96867,96868,96872],{},[895,96869,96870],{},[2133,96871,5572],{},[902,96873,5572],{"encoding":904},", pokles je",[883,96876,96878],{"className":96877},[886],[888,96879,96880],{"xmlns":890,"display":28047},[892,96881,96882,96948],{},[895,96883,96884,96896,96898,96904,96906,96908,96916,96918,96920,96922,96924,96926,96928,96930,96932,96934,96936,96946],{},[2275,96885,96886,96888],{},[898,96887,2772],{},[895,96889,96890,96892,96894],{},[898,96891,42681],{},[898,96893,2003],{},[898,96895,12027],{},[1726,96897,1728],{},[2128,96899,96900,96902],{},[898,96901,1738],{},[898,96903,4240],{},[1726,96905,2228],{},[1726,96907,1735],{"stretchy":1734},[9151,96909,96910,96912,96914],{},[898,96911,1738],{},[2133,96913,2281],{},[898,96915,4240],{},[1726,96917,2228],{},[898,96919,2772],{},[1726,96921,1762],{"stretchy":1734},[1726,96923,1728],{},[2133,96925,5572],{},[1726,96927,2228],{},[2133,96929,2352],{},[1726,96931,1728],{},[2133,96933,2352],{},[2289,96935,2291],{},[895,96937,96938,96940],{},[2289,96939,9784],{},[8372,96941,96942,96944],{"accent":1741},[2289,96943,2146],{},[1726,96945,25039],{},[898,96947,1888],{"mathvariant":2377},[902,96949,96950],{"encoding":904},"T_{vyr} = P^E - (P_1^E - T) = 8 - 4 = 4\\ \\text{Kč}.",[724,96952,96953,96954,97006],{},"Kontrola: ",[883,96955,96957],{"className":96956},[886],[888,96958,96959],{"xmlns":890},[892,96960,96961,97003],{},[895,96962,96963,96973,96975,96987,96989,96991,96993,96995,96997,96999,97001],{},[2275,96964,96965,96967],{},[898,96966,2772],{},[895,96968,96969,96971],{},[898,96970,42658],{},[898,96972,724],{},[1726,96974,2099],{},[2275,96976,96977,96979],{},[898,96978,2772],{},[895,96980,96981,96983,96985],{},[898,96982,42681],{},[898,96984,2003],{},[898,96986,12027],{},[1726,96988,1728],{},[2133,96990,2135],{},[1726,96992,2099],{},[2133,96994,2352],{},[1726,96996,1728],{},[2133,96998,2238],{},[1726,97000,1728],{},[898,97002,2772],{},[902,97004,97005],{"encoding":904},"T_{sp} + T_{vyr} = 2 + 4 = 6 = T",". Spotřebitel nese třetinu daně, výrobce dvě třetiny.",[36951,97008],{},[115,97010,97012],{"id":97011},"daň-uložená-spotřebiteli","Daň uložená spotřebiteli",[724,97014,95942,97015,97028,97029,97047,97048,97076],{},[883,97016,97018],{"className":97017},[886],[888,97019,97020],{"xmlns":890},[892,97021,97022,97026],{},[895,97023,97024],{},[898,97025,2772],{},[902,97027,2772],{"encoding":904}," uložena spotřebiteli, pak spotřebitel platí celkem ",[883,97030,97032],{"className":97031},[886],[888,97033,97034],{"xmlns":890},[892,97035,97036,97044],{},[895,97037,97038,97040,97042],{},[898,97039,1738],{},[1726,97041,2099],{},[898,97043,2772],{},[902,97045,97046],{"encoding":904},"P + T"," (cena prodejce plus daň). Z podmínky ",[883,97049,97051],{"className":97050},[886],[888,97052,97053],{"xmlns":890},[892,97054,97055,97073],{},[895,97056,97057,97059,97061,97063,97065,97067,97069,97071],{},[898,97058,1738],{},[1726,97060,2099],{},[898,97062,2772],{},[1726,97064,1728],{},[898,97066,1731],{},[1726,97068,1735],{"stretchy":1734},[898,97070,1724],{},[1726,97072,1762],{"stretchy":1734},[902,97074,97075],{"encoding":904},"P + T = D(Q)"," plyne nová funkce poptávky:",[883,97078,97080],{"className":97079},[886],[888,97081,97082],{"xmlns":890,"display":28047},[892,97083,97084,97118],{},[895,97085,97086,97088,97090,97096,97098,97100,97102,97104,97106,97108,97110,97112,97114,97116],{},[898,97087,1738],{},[1726,97089,1728],{},[2275,97091,97092,97094],{},[898,97093,1731],{},[2133,97095,2135],{},[1726,97097,1735],{"stretchy":1734},[898,97099,1724],{},[1726,97101,1762],{"stretchy":1734},[1726,97103,1728],{},[898,97105,1731],{},[1726,97107,1735],{"stretchy":1734},[898,97109,1724],{},[1726,97111,1762],{"stretchy":1734},[1726,97113,2228],{},[898,97115,2772],{},[898,97117,1888],{"mathvariant":2377},[902,97119,97120],{"encoding":904},"P = D_2(Q) = D(Q) - T.",[724,97122,97123,97124,1777,97137,97140],{},"Poptávka se tedy posouvá o ",[883,97125,97127],{"className":97126},[886],[888,97128,97129],{"xmlns":890},[892,97130,97131,97135],{},[895,97132,97133],{},[898,97134,2772],{},[902,97136,2772],{"encoding":904},[38,97138,97139],{},"svisle dolů",". Nabídka se nemění.",[724,97142,96067,97143,96108,97183,3877,97211,97239,97240,97259,97260,97284,97285,1847],{},[883,97144,97146],{"className":97145},[886],[888,97147,97148],{"xmlns":890},[892,97149,97150,97180],{},[895,97151,97152,97158,97160,97168,97170,97178],{},[2275,97153,97154,97156],{},[898,97155,4240],{},[2133,97157,2135],{},[1726,97159,2487],{"stretchy":1734},[9151,97161,97162,97164,97166],{},[898,97163,1724],{},[2133,97165,2135],{},[898,97167,4240],{},[1726,97169,1742],{"separator":1741},[9151,97171,97172,97174,97176],{},[898,97173,1738],{},[2133,97175,2135],{},[898,97177,4240],{},[1726,97179,2502],{"stretchy":1734},[902,97181,97182],{"encoding":904},"E_2[Q_2^E, P_2^E]",[883,97184,97186],{"className":97185},[886],[888,97187,97188],{"xmlns":890},[892,97189,97190,97208],{},[895,97191,97192,97200,97202],{},[9151,97193,97194,97196,97198],{},[898,97195,1724],{},[2133,97197,2135],{},[898,97199,4240],{},[1726,97201,3444],{},[2128,97203,97204,97206],{},[898,97205,1724],{},[898,97207,4240],{},[902,97209,97210],{"encoding":904},"Q_2^E \u003C Q^E",[883,97212,97214],{"className":97213},[886],[888,97215,97216],{"xmlns":890},[892,97217,97218,97236],{},[895,97219,97220,97228,97230],{},[9151,97221,97222,97224,97226],{},[898,97223,1738],{},[2133,97225,2135],{},[898,97227,4240],{},[1726,97229,3444],{},[2128,97231,97232,97234],{},[898,97233,1738],{},[898,97235,4240],{},[902,97237,97238],{"encoding":904},"P_2^E \u003C P^E",". Výrobce obdrží ",[883,97241,97243],{"className":97242},[886],[888,97244,97245],{"xmlns":890},[892,97246,97247,97257],{},[895,97248,97249],{},[9151,97250,97251,97253,97255],{},[898,97252,1738],{},[2133,97254,2135],{},[898,97256,4240],{},[902,97258,47899],{"encoding":904},", spotřebitel platí celkem ",[883,97261,97263],{"className":97262},[886],[888,97264,97265],{"xmlns":890},[892,97266,97267,97281],{},[895,97268,97269,97277,97279],{},[9151,97270,97271,97273,97275],{},[898,97272,1738],{},[2133,97274,2135],{},[898,97276,4240],{},[1726,97278,2099],{},[898,97280,2772],{},[902,97282,97283],{"encoding":904},"P_2^E + T"," (tato částka je vyšší než původní ",[883,97286,97288],{"className":97287},[886],[888,97289,97290],{"xmlns":890},[892,97291,97292,97300],{},[895,97293,97294],{},[2128,97295,97296,97298],{},[898,97297,1738],{},[898,97299,4240],{},[902,97301,41447],{"encoding":904},[724,97303,97304],{},"Daňové břemeno:",[883,97306,97308],{"className":97307},[886],[888,97309,97310],{"xmlns":890,"display":28047},[892,97311,97312,97386],{},[895,97313,97314,97324,97326,97328,97336,97338,97340,97342,97344,97350,97352,97354,97366,97368,97374,97376,97384],{},[2275,97315,97316,97318],{},[898,97317,2772],{},[895,97319,97320,97322],{},[898,97321,42658],{},[898,97323,724],{},[1726,97325,1728],{},[1726,97327,1735],{"stretchy":1734},[9151,97329,97330,97332,97334],{},[898,97331,1738],{},[2133,97333,2135],{},[898,97335,4240],{},[1726,97337,2099],{},[898,97339,2772],{},[1726,97341,1762],{"stretchy":1734},[1726,97343,2228],{},[2128,97345,97346,97348],{},[898,97347,1738],{},[898,97349,4240],{},[1726,97351,1742],{"separator":1741},[5865,97353],{"width":5867},[2275,97355,97356,97358],{},[898,97357,2772],{},[895,97359,97360,97362,97364],{},[898,97361,42681],{},[898,97363,2003],{},[898,97365,12027],{},[1726,97367,1728],{},[2128,97369,97370,97372],{},[898,97371,1738],{},[898,97373,4240],{},[1726,97375,2228],{},[9151,97377,97378,97380,97382],{},[898,97379,1738],{},[2133,97381,2135],{},[898,97383,4240],{},[898,97385,1888],{"mathvariant":2377},[902,97387,97388],{"encoding":904},"T_{sp} = (P_2^E + T) - P^E, \\qquad T_{vyr} = P^E - P_2^E.",[724,97390,97391],{},[614,97392,97393,97394,97424,97425,96277,97438,5656,97455,96308,97468,1888],{},"Obrázek 2.19: Posun ",[883,97395,97397],{"className":97396},[886],[888,97398,97399],{"xmlns":890},[892,97400,97401,97421],{},[895,97402,97403,97405,97407,97413,97415,97417,97419],{},[898,97404,1731],{},[1726,97406,3120],{},[2275,97408,97409,97411],{},[898,97410,1731],{},[2133,97412,2135],{},[1726,97414,1728],{},[898,97416,1731],{},[1726,97418,2228],{},[898,97420,2772],{},[902,97422,97423],{"encoding":904},"D \\to D_2 = D - T","; svislá vzdálenost mezi poptávkovými křivkami je ",[883,97426,97428],{"className":97427},[886],[888,97429,97430],{"xmlns":890},[892,97431,97432,97436],{},[895,97433,97434],{},[898,97435,2772],{},[902,97437,2772],{"encoding":904},[883,97439,97441],{"className":97440},[886],[888,97442,97443],{"xmlns":890},[892,97444,97445,97453],{},[895,97446,97447],{},[2275,97448,97449,97451],{},[898,97450,1731],{},[2133,97452,2135],{},[902,97454,38308],{"encoding":904},[883,97456,97458],{"className":97457},[886],[888,97459,97460],{"xmlns":890},[892,97461,97462,97466],{},[895,97463,97464],{},[898,97465,8659],{},[902,97467,8659],{"encoding":904},[883,97469,97471],{"className":97470},[886],[888,97472,97473],{"xmlns":890},[892,97474,97475,97483],{},[895,97476,97477],{},[2275,97478,97479,97481],{},[898,97480,4240],{},[2133,97482,2135],{},[902,97484,97485],{"encoding":904},"E_2",[198,97487,45364],{"id":97488},"příklad-210",[724,97490,97491,97493,97494,41671,97517,97536,97537,97554],{},[38,97492,37914],{}," Pokračuje z Příkladu 2.9 — stejný trh, poptávka ",[883,97495,97497],{"className":97496},[886],[888,97498,97499],{"xmlns":890},[892,97500,97501,97515],{},[895,97502,97503,97505,97507,97509,97511,97513],{},[898,97504,1738],{},[1726,97506,1728],{},[2133,97508,3506],{},[1726,97510,2228],{},[2133,97512,2135],{},[898,97514,1724],{},[902,97516,96357],{"encoding":904},[883,97518,97520],{"className":97519},[886],[888,97521,97522],{"xmlns":890},[892,97523,97524,97534],{},[895,97525,97526,97528,97530,97532],{},[898,97527,1738],{},[1726,97529,1728],{},[2133,97531,2352],{},[898,97533,1724],{},[902,97535,96377],{"encoding":904},". Daň ",[883,97538,97540],{"className":97539},[886],[888,97541,97542],{"xmlns":890},[892,97543,97544,97552],{},[895,97545,97546,97548,97550],{},[898,97547,2772],{},[1726,97549,1728],{},[2133,97551,2238],{},[902,97553,41249],{"encoding":904}," Kč je tentokrát uložena na spotřebitele.",[724,97556,97557],{},[38,97558,37946],{},[724,97560,97561,97562,96568],{},"Nová poptávka je ",[883,97563,97565],{"className":97564},[886],[888,97566,97567],{"xmlns":890},[892,97568,97569,97605],{},[895,97570,97571,97577,97579,97581,97583,97585,97587,97589,97591,97593,97595,97597,97599,97601,97603],{},[2275,97572,97573,97575],{},[898,97574,1731],{},[2133,97576,2135],{},[1726,97578,2703],{},[898,97580,1738],{},[1726,97582,1728],{},[2133,97584,3506],{},[1726,97586,2228],{},[2133,97588,2135],{},[898,97590,1724],{},[1726,97592,2228],{},[2133,97594,2238],{},[1726,97596,1728],{},[2133,97598,2238],{},[1726,97600,2228],{},[2133,97602,2135],{},[898,97604,1724],{},[902,97606,97607],{"encoding":904},"D_2: P = 12 - 2Q - 6 = 6 - 2Q",[883,97609,97611],{"className":97610},[886],[888,97612,97613],{"xmlns":890,"display":28047},[892,97614,97615,97631],{},[895,97616,97617,97619,97621,97623,97625,97627,97629],{},[2133,97618,2238],{},[1726,97620,2228],{},[2133,97622,2135],{},[898,97624,1724],{},[1726,97626,1728],{},[2133,97628,2352],{},[898,97630,1724],{},[902,97632,97633],{"encoding":904},"6 - 2Q = 4Q",[724,97635,96601,97636,5576,97655,1343,97679,96682,97711,1888],{},[883,97637,97639],{"className":97638},[886],[888,97640,97641],{"xmlns":890},[892,97642,97643,97653],{},[895,97644,97645,97647,97649,97651],{},[2133,97646,2238],{},[898,97648,1724],{},[1726,97650,1728],{},[2133,97652,2238],{},[902,97654,96621],{"encoding":904},[883,97656,97658],{"className":97657},[886],[888,97659,97660],{"xmlns":890},[892,97661,97662,97676],{},[895,97663,97664,97672,97674],{},[9151,97665,97666,97668,97670],{},[898,97667,1724],{},[2133,97669,2135],{},[898,97671,4240],{},[1726,97673,1728],{},[2133,97675,2281],{},[902,97677,97678],{"encoding":904},"Q_2^E = 1",[883,97680,97682],{"className":97681},[886],[888,97683,97684],{"xmlns":890},[892,97685,97686,97708],{},[895,97687,97688,97696,97698,97700,97702,97704,97706],{},[9151,97689,97690,97692,97694],{},[898,97691,1738],{},[2133,97693,2135],{},[898,97695,4240],{},[1726,97697,1728],{},[2133,97699,2352],{},[1726,97701,3174],{},[2133,97703,2281],{},[1726,97705,1728],{},[2133,97707,2352],{},[902,97709,97710],{"encoding":904},"P_2^E = 4 \\cdot 1 = 4",[883,97712,97714],{"className":97713},[886],[888,97715,97716],{"xmlns":890},[892,97717,97718,97736],{},[895,97719,97720,97726,97728,97730,97732,97734],{},[2275,97721,97722,97724],{},[898,97723,4240],{},[2133,97725,2135],{},[1726,97727,2487],{"stretchy":1734},[2133,97729,2281],{},[1726,97731,1742],{"separator":1741},[2133,97733,2352],{},[1726,97735,2502],{"stretchy":1734},[902,97737,97738],{"encoding":904},"E_2[1, 4]",[724,97740,97741,97742,97778,97779,96396],{},"Spotřebitel platí celkem ",[883,97743,97745],{"className":97744},[886],[888,97746,97747],{"xmlns":890},[892,97748,97749,97775],{},[895,97750,97751,97759,97761,97763,97765,97767,97769,97771,97773],{},[9151,97752,97753,97755,97757],{},[898,97754,1738],{},[2133,97756,2135],{},[898,97758,4240],{},[1726,97760,2099],{},[898,97762,2772],{},[1726,97764,1728],{},[2133,97766,2352],{},[1726,97768,2099],{},[2133,97770,2238],{},[1726,97772,1728],{},[2133,97774,2860],{},[902,97776,97777],{"encoding":904},"P_2^E + T = 4 + 6 = 10"," Kč; výrobce obdrží ",[883,97780,97782],{"className":97781},[886],[888,97783,97784],{"xmlns":890},[892,97785,97786,97800],{},[895,97787,97788,97796,97798],{},[9151,97789,97790,97792,97794],{},[898,97791,1738],{},[2133,97793,2135],{},[898,97795,4240],{},[1726,97797,1728],{},[2133,97799,2352],{},[902,97801,97802],{"encoding":904},"P_2^E = 4",[724,97804,97805],{},[614,97806,97807],{},"Rozklad daňového břemene:",[883,97809,97811],{"className":97810},[886],[888,97812,97813],{"xmlns":890,"display":28047},[892,97814,97815,97901],{},[895,97816,97817,97827,97829,97831,97833,97835,97837,97839,97841,97843,97845,97847,97849,97859,97861,97863,97875,97877,97879,97881,97883,97885,97887,97889,97899],{},[2275,97818,97819,97821],{},[898,97820,2772],{},[895,97822,97823,97825],{},[898,97824,42658],{},[898,97826,724],{},[1726,97828,1728],{},[1726,97830,1735],{"stretchy":1734},[2133,97832,2352],{},[1726,97834,2099],{},[2133,97836,2238],{},[1726,97838,1762],{"stretchy":1734},[1726,97840,2228],{},[2133,97842,5572],{},[1726,97844,1728],{},[2133,97846,2135],{},[2289,97848,2291],{},[895,97850,97851,97853],{},[2289,97852,9784],{},[8372,97854,97855,97857],{"accent":1741},[2289,97856,2146],{},[1726,97858,25039],{},[1726,97860,1742],{"separator":1741},[5865,97862],{"width":5867},[2275,97864,97865,97867],{},[898,97866,2772],{},[895,97868,97869,97871,97873],{},[898,97870,42681],{},[898,97872,2003],{},[898,97874,12027],{},[1726,97876,1728],{},[2133,97878,5572],{},[1726,97880,2228],{},[2133,97882,2352],{},[1726,97884,1728],{},[2133,97886,2352],{},[2289,97888,2291],{},[895,97890,97891,97893],{},[2289,97892,9784],{},[8372,97894,97895,97897],{"accent":1741},[2289,97896,2146],{},[1726,97898,25039],{},[898,97900,1888],{"mathvariant":2377},[902,97902,97903],{"encoding":904},"T_{sp} = (4 + 6) - 8 = 2\\ \\text{Kč}, \\qquad T_{vyr} = 8 - 4 = 4\\ \\text{Kč}.",[724,97905,97906,97907,1888],{},"Opět ",[883,97908,97910],{"className":97909},[886],[888,97911,97912],{"xmlns":890},[892,97913,97914,97948],{},[895,97915,97916,97926,97928,97940,97942,97944,97946],{},[2275,97917,97918,97920],{},[898,97919,2772],{},[895,97921,97922,97924],{},[898,97923,42658],{},[898,97925,724],{},[1726,97927,2099],{},[2275,97929,97930,97932],{},[898,97931,2772],{},[895,97933,97934,97936,97938],{},[898,97935,42681],{},[898,97937,2003],{},[898,97939,12027],{},[1726,97941,1728],{},[2133,97943,2238],{},[1726,97945,1728],{},[898,97947,2772],{},[902,97949,97950],{"encoding":904},"T_{sp} + T_{vyr} = 6 = T",[36951,97952],{},[115,97954,42639],{"id":97955},"daňové-břemeno",[724,97957,97958,10009,97960,97963,97964,97977],{},[38,97959,42639],{},[614,97961,97962],{},"tax burden",") je rozdělení zaplacené daně ",[883,97965,97967],{"className":97966},[886],[888,97968,97969],{"xmlns":890},[892,97970,97971,97975],{},[895,97972,97973],{},[898,97974,2772],{},[902,97976,2772],{"encoding":904}," mezi spotřebitele a výrobce:",[883,97979,97981],{"className":97980},[886],[888,97982,97983],{"xmlns":890,"display":28047},[892,97984,97985,98017],{},[895,97986,97987,97989,97991,98001,98003,98015],{},[898,97988,2772],{},[1726,97990,1728],{},[2275,97992,97993,97995],{},[898,97994,2772],{},[895,97996,97997,97999],{},[898,97998,42658],{},[898,98000,724],{},[1726,98002,2099],{},[2275,98004,98005,98007],{},[898,98006,2772],{},[895,98008,98009,98011,98013],{},[898,98010,42681],{},[898,98012,2003],{},[898,98014,12027],{},[898,98016,1888],{"mathvariant":2377},[902,98018,98019],{"encoding":904},"T = T_{sp} + T_{vyr}.",[724,98021,98022],{},[1647,98023],{"alt":98024,"className":98025,"src":98026},"imek-dan-rozklad-bremene-sklony",[210,1651],"\u002Fwiki-assets\u002Fimek-dan-rozklad-bremene-sklony.jpeg",[3859,98028,98029],{},[724,98030,98031,98033,98034,3877,98047,1888],{},[883,98032,4145],{}," 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 ",[883,98035,98037],{"className":98036},[886],[888,98038,98039],{"xmlns":890},[892,98040,98041,98045],{},[895,98042,98043],{},[898,98044,1731],{},[902,98046,1731],{"encoding":904},[883,98048,98050],{"className":98049},[886],[888,98051,98052],{"xmlns":890},[892,98053,98054,98058],{},[895,98055,98056],{},[898,98057,8659],{},[902,98059,8659],{"encoding":904},[198,98061,2445],{"id":2444},[724,98063,98064,98065,98086,98087,98100,98101,98118,98119,98132],{},"V grafu ",[883,98066,98068],{"className":98067},[886],[888,98069,98070],{"xmlns":890},[892,98071,98072,98084],{},[895,98073,98074,98076,98078,98080,98082],{},[1726,98075,1735],{"stretchy":1734},[898,98077,1724],{},[1726,98079,1742],{"separator":1741},[898,98081,1738],{},[1726,98083,1762],{"stretchy":1734},[902,98085,37672],{"encoding":904}," je svislá vzdálenost mezi původní a posunutou křivkou právě ",[883,98088,98090],{"className":98089},[886],[888,98091,98092],{"xmlns":890},[892,98093,98094,98098],{},[895,98095,98096],{},[898,98097,2772],{},[902,98099,2772],{"encoding":904},". Vedeme-li v novém rovnovážném bodě vodorovnou přímku na úrovni původní rovnovážné ceny ",[883,98102,98104],{"className":98103},[886],[888,98105,98106],{"xmlns":890},[892,98107,98108,98116],{},[895,98109,98110],{},[2128,98111,98112,98114],{},[898,98113,1738],{},[898,98115,4240],{},[902,98117,41447],{"encoding":904},", rozdělí se úsečka ",[883,98120,98122],{"className":98121},[886],[888,98123,98124],{"xmlns":890},[892,98125,98126,98130],{},[895,98127,98128],{},[898,98129,2772],{},[902,98131,2772],{"encoding":904}," na dvě části:",[120,98134,98135,98160],{},[123,98136,98137,98138,98159],{},"horní část odpovídá ",[883,98139,98141],{"className":98140},[886],[888,98142,98143],{"xmlns":890},[892,98144,98145,98157],{},[895,98146,98147],{},[2275,98148,98149,98151],{},[898,98150,2772],{},[895,98152,98153,98155],{},[898,98154,42658],{},[898,98156,724],{},[902,98158,42663],{"encoding":904}," (o kolik vzrostla cena placená spotřebitelem),",[123,98161,98162,98163,98186],{},"dolní část odpovídá ",[883,98164,98166],{"className":98165},[886],[888,98167,98168],{"xmlns":890},[892,98169,98170,98184],{},[895,98171,98172],{},[2275,98173,98174,98176],{},[898,98175,2772],{},[895,98177,98178,98180,98182],{},[898,98179,42681],{},[898,98181,2003],{},[898,98183,12027],{},[902,98185,42688],{"encoding":904}," (o kolik klesla cena přijímaná výrobcem).",[724,98188,98189],{},[614,98190,98191,98192,2684,98205,98226,98227,98250,98251,3877,98272,98295],{},"Obrázky 2.20 a 2.21: Ilustrace rozkladu svislé vzdálenosti ",[883,98193,98195],{"className":98194},[886],[888,98196,98197],{"xmlns":890},[892,98198,98199,98203],{},[895,98200,98201],{},[898,98202,2772],{},[902,98204,2772],{"encoding":904},[883,98206,98208],{"className":98207},[886],[888,98209,98210],{"xmlns":890},[892,98211,98212,98224],{},[895,98213,98214],{},[2275,98215,98216,98218],{},[898,98217,2772],{},[895,98219,98220,98222],{},[898,98221,42658],{},[898,98223,724],{},[902,98225,42663],{"encoding":904}," (nahoře) a ",[883,98228,98230],{"className":98229},[886],[888,98231,98232],{"xmlns":890},[892,98233,98234,98248],{},[895,98235,98236],{},[2275,98237,98238,98240],{},[898,98239,2772],{},[895,98241,98242,98244,98246],{},[898,98243,42681],{},[898,98245,2003],{},[898,98247,12027],{},[902,98249,42688],{"encoding":904}," (dole). Obrázek 2.21 porovnává obě varianty — daň výrobci vs. daň spotřebiteli — a ukazuje, že velikost ",[883,98252,98254],{"className":98253},[886],[888,98255,98256],{"xmlns":890},[892,98257,98258,98270],{},[895,98259,98260],{},[2275,98261,98262,98264],{},[898,98263,2772],{},[895,98265,98266,98268],{},[898,98267,42658],{},[898,98269,724],{},[902,98271,42663],{"encoding":904},[883,98273,98275],{"className":98274},[886],[888,98276,98277],{"xmlns":890},[892,98278,98279,98293],{},[895,98280,98281],{},[2275,98282,98283,98285],{},[898,98284,2772],{},[895,98286,98287,98289,98291],{},[898,98288,42681],{},[898,98290,2003],{},[898,98292,12027],{},[902,98294,42688],{"encoding":904}," je v obou případech stejná.",[198,98297,98299],{"id":98298},"sklony-křivek-a-rozklad","Sklony křivek a rozklad",[724,98301,98302,98303,98306,98307,10009,98330,98347,98348,10009,98371,98388],{},"Platí obecně: ",[38,98304,98305],{},"čím strmější křivka (menší elasticita), tím větší část daně nese daná strana trhu."," Pro lineární poptávku ",[883,98308,98310],{"className":98309},[886],[888,98311,98312],{"xmlns":890},[892,98313,98314,98328],{},[895,98315,98316,98318,98320,98322,98324,98326],{},[898,98317,1738],{},[1726,98319,1728],{},[898,98321,207],{},[898,98323,1724],{},[1726,98325,2099],{},[898,98327,2102],{},[902,98329,37041],{"encoding":904},[883,98331,98333],{"className":98332},[886],[888,98334,98335],{"xmlns":890},[892,98336,98337,98345],{},[895,98338,98339,98341,98343],{},[898,98340,207],{},[1726,98342,3444],{},[2133,98344,2328],{},[902,98346,43066],{"encoding":904},") a lineární nabídku ",[883,98349,98351],{"className":98350},[886],[888,98352,98353],{"xmlns":890},[892,98354,98355,98369],{},[895,98356,98357,98359,98361,98363,98365,98367],{},[898,98358,1738],{},[1726,98360,1728],{},[898,98362,2146],{},[898,98364,1724],{},[1726,98366,2099],{},[898,98368,2198],{},[902,98370,40223],{"encoding":904},[883,98372,98374],{"className":98373},[886],[888,98375,98376],{"xmlns":890},[892,98377,98378,98386],{},[895,98379,98380,98382,98384],{},[898,98381,2146],{},[1726,98383,3405],{},[2133,98385,2328],{},[902,98387,40241],{"encoding":904},") lze rozklad odvodit pomocí multiplikátorů a platí",[883,98390,98392],{"className":98391},[886],[888,98393,98394],{"xmlns":890,"display":28047},[892,98395,98396,98462],{},[895,98397,98398,98422,98424,98434,98436,98460],{},[2330,98399,98400,98410],{},[2275,98401,98402,98404],{},[898,98403,2772],{},[895,98405,98406,98408],{},[898,98407,42658],{},[898,98409,724],{},[2275,98411,98412,98414],{},[898,98413,2772],{},[895,98415,98416,98418,98420],{},[898,98417,42681],{},[898,98419,2003],{},[898,98421,12027],{},[1726,98423,1728],{},[2330,98425,98426,98428],{},[898,98427,2146],{},[895,98429,98430,98432],{},[1726,98431,2228],{},[898,98433,207],{},[1726,98435,1728],{},[2330,98437,98438,98450],{},[895,98439,98440,98443,98446,98448],{},[898,98441,98442],{"mathvariant":2377},"∣",[2289,98444,98445],{},"sklon ",[898,98447,8659],{},[898,98449,98442],{"mathvariant":2377},[895,98451,98452,98454,98456,98458],{},[898,98453,98442],{"mathvariant":2377},[2289,98455,98445],{},[898,98457,1731],{},[898,98459,98442],{"mathvariant":2377},[898,98461,1888],{"mathvariant":2377},[902,98463,98464],{"encoding":904},"\\frac{T_{sp}}{T_{vyr}} = \\frac{c}{-a} = \\frac{|\\text{sklon } S|}{|\\text{sklon } D|}.",[3859,98466,98467,98472],{},[724,98468,98469,98471],{},[883,98470,4560],{}," Postup výpočtu rozkladu",[152,98473,98474,98509,98562,98641],{},[123,98475,98476,98477,98508],{},"Spočti rovnovážný bod ",[883,98478,98480],{"className":98479},[886],[888,98481,98482],{"xmlns":890},[892,98483,98484,98506],{},[895,98485,98486,98488,98490,98496,98498,98504],{},[898,98487,4240],{},[1726,98489,2487],{"stretchy":1734},[2128,98491,98492,98494],{},[898,98493,1724],{},[898,98495,4240],{},[1726,98497,1742],{"separator":1741},[2128,98499,98500,98502],{},[898,98501,1738],{},[898,98503,4240],{},[1726,98505,2502],{"stretchy":1734},[902,98507,41348],{"encoding":904}," bez daně.",[123,98510,98511,98512,1348,98537,1847],{},"Urči posunutou křivku (",[883,98513,98515],{"className":98514},[886],[888,98516,98517],{"xmlns":890},[892,98518,98519,98535],{},[895,98520,98521,98527,98529,98531,98533],{},[2275,98522,98523,98525],{},[898,98524,8659],{},[2133,98526,2281],{},[1726,98528,1728],{},[898,98530,8659],{},[1726,98532,2099],{},[898,98534,2772],{},[902,98536,42735],{"encoding":904},[883,98538,98540],{"className":98539},[886],[888,98541,98542],{"xmlns":890},[892,98543,98544,98560],{},[895,98545,98546,98552,98554,98556,98558],{},[2275,98547,98548,98550],{},[898,98549,1731],{},[2133,98551,2135],{},[1726,98553,1728],{},[898,98555,1731],{},[1726,98557,2228],{},[898,98559,2772],{},[902,98561,42766],{"encoding":904},[123,98563,98564,98565,3902,98584,12114,98603,3902,98622,1847],{},"Vyřeš novou rovnovážnou rovnici — získáš ",[883,98566,98568],{"className":98567},[886],[888,98569,98570],{"xmlns":890},[892,98571,98572,98582],{},[895,98573,98574],{},[9151,98575,98576,98578,98580],{},[898,98577,1724],{},[2133,98579,2281],{},[898,98581,4240],{},[902,98583,47817],{"encoding":904},[883,98585,98587],{"className":98586},[886],[888,98588,98589],{"xmlns":890},[892,98590,98591,98601],{},[895,98592,98593],{},[9151,98594,98595,98597,98599],{},[898,98596,1724],{},[2133,98598,2135],{},[898,98600,4240],{},[902,98602,47879],{"encoding":904},[883,98604,98606],{"className":98605},[886],[888,98607,98608],{"xmlns":890},[892,98609,98610,98620],{},[895,98611,98612],{},[9151,98613,98614,98616,98618],{},[898,98615,1738],{},[2133,98617,2281],{},[898,98619,4240],{},[902,98621,47838],{"encoding":904},[883,98623,98625],{"className":98624},[886],[888,98626,98627],{"xmlns":890},[892,98628,98629,98639],{},[895,98630,98631],{},[9151,98632,98633,98635,98637],{},[898,98634,1738],{},[2133,98636,2135],{},[898,98638,4240],{},[902,98640,47899],{"encoding":904},[123,98642,98643,98644,3877,98665,98688,98689,1888],{},"Dopočítej ",[883,98645,98647],{"className":98646},[886],[888,98648,98649],{"xmlns":890},[892,98650,98651,98663],{},[895,98652,98653],{},[2275,98654,98655,98657],{},[898,98656,2772],{},[895,98658,98659,98661],{},[898,98660,42658],{},[898,98662,724],{},[902,98664,42663],{"encoding":904},[883,98666,98668],{"className":98667},[886],[888,98669,98670],{"xmlns":890},[892,98671,98672,98686],{},[895,98673,98674],{},[2275,98675,98676,98678],{},[898,98677,2772],{},[895,98679,98680,98682,98684],{},[898,98681,42681],{},[898,98683,2003],{},[898,98685,12027],{},[902,98687,42688],{"encoding":904}," z definice, vždy ověř ",[883,98690,98692],{"className":98691},[886],[888,98693,98694],{"xmlns":890},[892,98695,98696,98726],{},[895,98697,98698,98708,98710,98722,98724],{},[2275,98699,98700,98702],{},[898,98701,2772],{},[895,98703,98704,98706],{},[898,98705,42658],{},[898,98707,724],{},[1726,98709,2099],{},[2275,98711,98712,98714],{},[898,98713,2772],{},[895,98715,98716,98718,98720],{},[898,98717,42681],{},[898,98719,2003],{},[898,98721,12027],{},[1726,98723,1728],{},[898,98725,2772],{},[902,98727,98728],{"encoding":904},"T_{sp} + T_{vyr} = T",[3859,98730,98731],{},[724,98732,98733,98735,98736,98739,98740,3877,98753,98766],{},[883,98734,4400],{}," Pozor — zákonný vs. ekonomický nositel daně\nI když zákon ukládá daň formálně pouze jedné straně (výrobci nebo spotřebiteli), ",[38,98737,98738],{},"ekonomicky ji vždy nesou obě strany",". Skutečné rozdělení určují sklony ",[883,98741,98743],{"className":98742},[886],[888,98744,98745],{"xmlns":890},[892,98746,98747,98751],{},[895,98748,98749],{},[898,98750,1731],{},[902,98752,1731],{"encoding":904},[883,98754,98756],{"className":98755},[886],[888,98757,98758],{"xmlns":890},[892,98759,98760,98764],{},[895,98761,98762],{},[898,98763,8659],{},[902,98765,8659],{"encoding":904},", nikoli paragrafové znění zákona. Kupující a prodávající tak fakticky platí daň bez ohledu na to, na koho je uvalena.",[36951,98768],{},[115,98770,98772],{"id":98771},"ekvivalence-obou-přístupů","Ekvivalence obou přístupů",[724,98774,98775],{},"Porovnáním Příkladu 2.9 (daň výrobci) a Příkladu 2.10 (daň spotřebiteli) zjistíme:",[724,98777,98778],{},[1647,98779],{"alt":98780,"className":98781,"src":98782},"imek-dan-ekvivalence-vyrobce-spotrebitel",[210,1651],"\u002Fwiki-assets\u002Fimek-dan-ekvivalence-vyrobce-spotrebitel.jpeg",[16,98784,98785,98797],{},[19,98786,98787],{},[22,98788,98789,98791,98794],{},[25,98790,54276],{},[25,98792,98793],{},"(a) daň výrobci",[25,98795,98796],{},"(b) daň spotřebiteli",[30,98798,98799,98854,98921,98981],{},[22,98800,98801,98804,98829],{},[35,98802,98803],{},"Rovnovážné množství",[35,98805,98806],{},[883,98807,98809],{"className":98808},[886],[888,98810,98811],{"xmlns":890},[892,98812,98813,98827],{},[895,98814,98815,98823,98825],{},[9151,98816,98817,98819,98821],{},[898,98818,1724],{},[2133,98820,2281],{},[898,98822,4240],{},[1726,98824,1728],{},[2133,98826,2281],{},[902,98828,96645],{"encoding":904},[35,98830,98831],{},[883,98832,98834],{"className":98833},[886],[888,98835,98836],{"xmlns":890},[892,98837,98838,98852],{},[895,98839,98840,98848,98850],{},[9151,98841,98842,98844,98846],{},[898,98843,1724],{},[2133,98845,2135],{},[898,98847,4240],{},[1726,98849,1728],{},[2133,98851,2281],{},[902,98853,97678],{"encoding":904},[22,98855,98856,98859,98884],{},[35,98857,98858],{},"Cena placená spotřebitelem",[35,98860,98861],{},[883,98862,98864],{"className":98863},[886],[888,98865,98866],{"xmlns":890},[892,98867,98868,98882],{},[895,98869,98870,98878,98880],{},[9151,98871,98872,98874,98876],{},[898,98873,1738],{},[2133,98875,2281],{},[898,98877,4240],{},[1726,98879,1728],{},[2133,98881,2860],{},[902,98883,96740],{"encoding":904},[35,98885,98886],{},[883,98887,98889],{"className":98888},[886],[888,98890,98891],{"xmlns":890},[892,98892,98893,98919],{},[895,98894,98895,98903,98905,98907,98909,98911,98913,98915,98917],{},[9151,98896,98897,98899,98901],{},[898,98898,1738],{},[2133,98900,2135],{},[898,98902,4240],{},[1726,98904,2099],{},[898,98906,2772],{},[1726,98908,1728],{},[2133,98910,2352],{},[1726,98912,2099],{},[2133,98914,2238],{},[1726,98916,1728],{},[2133,98918,2860],{},[902,98920,97777],{"encoding":904},[22,98922,98923,98926,98956],{},[35,98924,98925],{},"Cena přijímaná výrobcem",[35,98927,98928],{},[883,98929,98931],{"className":98930},[886],[888,98932,98933],{"xmlns":890},[892,98934,98935,98953],{},[895,98936,98937,98945,98947,98949,98951],{},[9151,98938,98939,98941,98943],{},[898,98940,1738],{},[2133,98942,2281],{},[898,98944,4240],{},[1726,98946,2228],{},[898,98948,2772],{},[1726,98950,1728],{},[2133,98952,2352],{},[902,98954,98955],{"encoding":904},"P_1^E - T = 4",[35,98957,98958],{},[883,98959,98961],{"className":98960},[886],[888,98962,98963],{"xmlns":890},[892,98964,98965,98979],{},[895,98966,98967,98975,98977],{},[9151,98968,98969,98971,98973],{},[898,98970,1738],{},[2133,98972,2135],{},[898,98974,4240],{},[1726,98976,1728],{},[2133,98978,2352],{},[902,98980,97802],{"encoding":904},[22,98982,98983,98986,99040],{},[35,98984,98985],{},"Rozklad břemene",[35,98987,98988,1343,99013],{},[883,98989,98991],{"className":98990},[886],[888,98992,98993],{"xmlns":890},[892,98994,98995,99011],{},[895,98996,98997,99007,99009],{},[2275,98998,98999,99001],{},[898,99000,2772],{},[895,99002,99003,99005],{},[898,99004,42658],{},[898,99006,724],{},[1726,99008,1728],{},[2133,99010,2135],{},[902,99012,42957],{"encoding":904},[883,99014,99016],{"className":99015},[886],[888,99017,99018],{"xmlns":890},[892,99019,99020,99038],{},[895,99021,99022,99034,99036],{},[2275,99023,99024,99026],{},[898,99025,2772],{},[895,99027,99028,99030,99032],{},[898,99029,42681],{},[898,99031,2003],{},[898,99033,12027],{},[1726,99035,1728],{},[2133,99037,2352],{},[902,99039,42986],{"encoding":904},[35,99041,99042,1343,99067],{},[883,99043,99045],{"className":99044},[886],[888,99046,99047],{"xmlns":890},[892,99048,99049,99065],{},[895,99050,99051,99061,99063],{},[2275,99052,99053,99055],{},[898,99054,2772],{},[895,99056,99057,99059],{},[898,99058,42658],{},[898,99060,724],{},[1726,99062,1728],{},[2133,99064,2135],{},[902,99066,42957],{"encoding":904},[883,99068,99070],{"className":99069},[886],[888,99071,99072],{"xmlns":890},[892,99073,99074,99092],{},[895,99075,99076,99088,99090],{},[2275,99077,99078,99080],{},[898,99079,2772],{},[895,99081,99082,99084,99086],{},[898,99083,42681],{},[898,99085,2003],{},[898,99087,12027],{},[1726,99089,1728],{},[2133,99091,2352],{},[902,99093,42986],{"encoding":904},[724,99095,99096],{},"Výsledek je v obou režimech reálně totožný — liší se pouze to, kterou cenu nazveme \"tržní\":",[883,99098,99100],{"className":99099},[886],[888,99101,99102],{"xmlns":890,"display":28047},[892,99103,99104,99152],{},[895,99105,99106,99114,99116,99124,99126,99128,99136,99138,99140,99142,99150],{},[9151,99107,99108,99110,99112],{},[898,99109,1724],{},[2133,99111,2281],{},[898,99113,4240],{},[1726,99115,1728],{},[9151,99117,99118,99120,99122],{},[898,99119,1724],{},[2133,99121,2135],{},[898,99123,4240],{},[1726,99125,1742],{"separator":1741},[5865,99127],{"width":5867},[9151,99129,99130,99132,99134],{},[898,99131,1738],{},[2133,99133,2281],{},[898,99135,4240],{},[1726,99137,2228],{},[898,99139,2772],{},[1726,99141,1728],{},[9151,99143,99144,99146,99148],{},[898,99145,1738],{},[2133,99147,2135],{},[898,99149,4240],{},[898,99151,1888],{"mathvariant":2377},[902,99153,99154],{"encoding":904},"Q_1^E = Q_2^E, \\qquad P_1^E - T = P_2^E.",[3859,99156,99157,99176,99330],{},[724,99158,99159,99161,99162,99175],{},[883,99160,4560],{}," Věta o ekvivalenci zdanění\nNezávisle na tom, zda je jednotková daň ",[883,99163,99165],{"className":99164},[886],[888,99166,99167],{"xmlns":890},[892,99168,99169,99173],{},[895,99170,99171],{},[898,99172,2772],{},[902,99174,2772],{"encoding":904}," uložena výrobci, nebo spotřebiteli, se po jejím uložení rovnají:",[120,99177,99178,99210,99246,99283],{},[123,99179,99180,99181,1742],{},"rovnovážná množství obou režimů, ",[883,99182,99184],{"className":99183},[886],[888,99185,99186],{"xmlns":890},[892,99187,99188,99208],{},[895,99189,99190,99198,99200],{},[9151,99191,99192,99194,99196],{},[898,99193,1724],{},[2133,99195,2281],{},[898,99197,4240],{},[1726,99199,1728],{},[9151,99201,99202,99204,99206],{},[898,99203,1724],{},[2133,99205,2135],{},[898,99207,4240],{},[902,99209,42889],{"encoding":904},[123,99211,99212,99213,1742],{},"čistá cena přijímaná výrobcem, ",[883,99214,99216],{"className":99215},[886],[888,99217,99218],{"xmlns":890},[892,99219,99220,99244],{},[895,99221,99222,99230,99232,99234,99236],{},[9151,99223,99224,99226,99228],{},[898,99225,1738],{},[2133,99227,2281],{},[898,99229,4240],{},[1726,99231,2228],{},[898,99233,2772],{},[1726,99235,1728],{},[9151,99237,99238,99240,99242],{},[898,99239,1738],{},[2133,99241,2135],{},[898,99243,4240],{},[902,99245,42923],{"encoding":904},[123,99247,99248,99249,1742],{},"celková cena placená spotřebitelem, ",[883,99250,99252],{"className":99251},[886],[888,99253,99254],{"xmlns":890},[892,99255,99256,99280],{},[895,99257,99258,99266,99268,99276,99278],{},[9151,99259,99260,99262,99264],{},[898,99261,1738],{},[2133,99263,2281],{},[898,99265,4240],{},[1726,99267,1728],{},[9151,99269,99270,99272,99274],{},[898,99271,1738],{},[2133,99273,2135],{},[898,99275,4240],{},[1726,99277,2099],{},[898,99279,2772],{},[902,99281,99282],{"encoding":904},"P_1^E = P_2^E + T",[123,99284,99285,99286,3877,99307,1888],{},"rozklad daňového břemene ",[883,99287,99289],{"className":99288},[886],[888,99290,99291],{"xmlns":890},[892,99292,99293,99305],{},[895,99294,99295],{},[2275,99296,99297,99299],{},[898,99298,2772],{},[895,99300,99301,99303],{},[898,99302,42658],{},[898,99304,724],{},[902,99306,42663],{"encoding":904},[883,99308,99310],{"className":99309},[886],[888,99311,99312],{"xmlns":890},[892,99313,99314,99328],{},[895,99315,99316],{},[2275,99317,99318,99320],{},[898,99319,2772],{},[895,99321,99322,99324,99326],{},[898,99323,42681],{},[898,99325,2003],{},[898,99327,12027],{},[902,99329,42688],{"encoding":904},[724,99331,99332,99333,1888],{},"Z hlediska reálných dopadů na trh (objem transakcí, reálné platby stran) jsou tedy obě formy zdanění ",[38,99334,35178],{},[724,99336,99337,99338,3877,99351,1847],{},"Ekvivalence má zásadní politickou implikaci: otázka, \"kdo má platit daň\", je z hlediska trhu formální — skutečné rozdělení určuje struktura trhu (sklony ",[883,99339,99341],{"className":99340},[886],[888,99342,99343],{"xmlns":890},[892,99344,99345,99349],{},[895,99346,99347],{},[898,99348,1731],{},[902,99350,1731],{"encoding":904},[883,99352,99354],{"className":99353},[886],[888,99355,99356],{"xmlns":890},[892,99357,99358,99362],{},[895,99359,99360],{},[898,99361,8659],{},[902,99363,8659],{"encoding":904},[36951,99365],{},[115,99367,99369],{"id":99368},"úlohy","Úlohy",[724,99371,99372,99373,3148],{},"Z kapitoly 2 se zdanění týkají zejména následující úlohy (zadání v hub-page ",[207,99374,1846],{"className":99375,"dataFsResolvedFilePath":800,"href":801},[210],[120,99377,99378,99408,99439],{},[123,99379,99380,99383,99384,99407],{},[38,99381,99382],{},"Úloha 2.4"," — Poptávka ",[883,99385,99387],{"className":99386},[886],[888,99388,99389],{"xmlns":890},[892,99390,99391,99405],{},[895,99392,99393,99395,99397,99399,99401,99403],{},[898,99394,1738],{},[1726,99396,1728],{},[2133,99398,3506],{},[1726,99400,2228],{},[2133,99402,2135],{},[898,99404,1724],{},[902,99406,96357],{"encoding":904},"; najděte novou poptávku po uložení daně 6 Kč na kupujícího.",[123,99409,99410,99413,99414,99438],{},[38,99411,99412],{},"Úloha 2.9"," — Nabídka ",[883,99415,99417],{"className":99416},[886],[888,99418,99419],{"xmlns":890},[892,99420,99421,99435],{},[895,99422,99423,99425,99427,99429,99431,99433],{},[898,99424,1738],{},[1726,99426,1728],{},[2133,99428,4996],{},[898,99430,1724],{},[1726,99432,2099],{},[2133,99434,36225],{},[902,99436,99437],{"encoding":904},"P = 0{,}5Q + 15","; najděte novou nabídku po uložení daně 5 Kč na výrobce.",[123,99440,99441,99444,99445,3877,99471,99495,99496,99513],{},[38,99442,99443],{},"Úloha 2.13"," — Komplexní úloha se zadáním ",[883,99446,99448],{"className":99447},[886],[888,99449,99450],{"xmlns":890},[892,99451,99452,99468],{},[895,99453,99454,99456,99458,99460,99462,99464,99466],{},[898,99455,1738],{},[1726,99457,1728],{},[1726,99459,2228],{},[2133,99461,2352],{},[898,99463,1724],{},[1726,99465,2099],{},[2133,99467,46684],{},[902,99469,99470],{"encoding":904},"P = -4Q + 80",[883,99472,99474],{"className":99473},[886],[888,99475,99476],{"xmlns":890},[892,99477,99478,99492],{},[895,99479,99480,99482,99484,99486,99488,99490],{},[898,99481,1738],{},[1726,99483,1728],{},[2133,99485,2177],{},[898,99487,1724],{},[1726,99489,2099],{},[2133,99491,2860],{},[902,99493,99494],{"encoding":904},"P = 3Q + 10",": rovnováha, daň ",[883,99497,99499],{"className":99498},[886],[888,99500,99501],{"xmlns":890},[892,99502,99503,99511],{},[895,99504,99505,99507,99509],{},[898,99506,2772],{},[1726,99508,1728],{},[2133,99510,24182],{},[902,99512,47796],{"encoding":904}," Kč uložená postupně výrobci i spotřebiteli, rozklad daňového břemene a analýza ekvivalence.",[724,99515,99516,99517,99519,99520,99522],{},"Související úvodní příklady posunu křivek při zdanění: ",[38,99518,45209],{}," (posun poptávky při zdanění kupujícího) a ",[38,99521,45243],{}," (posun nabídky při zdanění výrobce).",[36951,99524],{},[115,99526,1670],{"id":1669},[120,99528,99529,99548,99606,99663,99746,99792,99835,99880,99946],{},[123,99530,99531,1777,99534,99547],{},[38,99532,99533],{},"Jednotková daň",[883,99535,99537],{"className":99536},[886],[888,99538,99539],{"xmlns":890},[892,99540,99541,99545],{},[895,99542,99543],{},[898,99544,2772],{},[902,99546,2772],{"encoding":904}," — fixní částka na každou prodanou jednotku zboží",[123,99549,99550,99552,99553,99591,99592,99605],{},[38,99551,95939],{}," — posun nabídky ",[883,99554,99556],{"className":99555},[886],[888,99557,99558],{"xmlns":890},[892,99559,99560,99588],{},[895,99561,99562,99568,99570,99572,99574,99576,99578,99580,99582,99584,99586],{},[2275,99563,99564,99566],{},[898,99565,8659],{},[2133,99567,2281],{},[1726,99569,1735],{"stretchy":1734},[898,99571,1724],{},[1726,99573,1762],{"stretchy":1734},[1726,99575,1728],{},[898,99577,8659],{},[1726,99579,1735],{"stretchy":1734},[898,99581,1724],{},[1726,99583,1762],{"stretchy":1734},[1726,99585,2099],{},[898,99587,2772],{},[902,99589,99590],{"encoding":904},"S_1(Q) = S(Q) + T"," (o ",[883,99593,99595],{"className":99594},[886],[888,99596,99597],{"xmlns":890},[892,99598,99599,99603],{},[895,99600,99601],{},[898,99602,2772],{},[902,99604,2772],{"encoding":904}," svisle nahoru)",[123,99607,99608,99610,99611,99591,99649,99662],{},[38,99609,97012],{}," — posun poptávky ",[883,99612,99614],{"className":99613},[886],[888,99615,99616],{"xmlns":890},[892,99617,99618,99646],{},[895,99619,99620,99626,99628,99630,99632,99634,99636,99638,99640,99642,99644],{},[2275,99621,99622,99624],{},[898,99623,1731],{},[2133,99625,2135],{},[1726,99627,1735],{"stretchy":1734},[898,99629,1724],{},[1726,99631,1762],{"stretchy":1734},[1726,99633,1728],{},[898,99635,1731],{},[1726,99637,1735],{"stretchy":1734},[898,99639,1724],{},[1726,99641,1762],{"stretchy":1734},[1726,99643,2228],{},[898,99645,2772],{},[902,99647,99648],{"encoding":904},"D_2(Q) = D(Q) - T",[883,99650,99652],{"className":99651},[886],[888,99653,99654],{"xmlns":890},[892,99655,99656,99660],{},[895,99657,99658],{},[898,99659,2772],{},[902,99661,2772],{"encoding":904}," svisle dolů)",[123,99664,99665,1696,99668,41795,99707],{},[38,99666,99667],{},"Rovnovážný bod s daní",[883,99669,99671],{"className":99670},[886],[888,99672,99673],{"xmlns":890},[892,99674,99675,99705],{},[895,99676,99677,99683,99685,99693,99695,99703],{},[2275,99678,99679,99681],{},[898,99680,4240],{},[2133,99682,2281],{},[1726,99684,2487],{"stretchy":1734},[9151,99686,99687,99689,99691],{},[898,99688,1724],{},[2133,99690,2281],{},[898,99692,4240],{},[1726,99694,1742],{"separator":1741},[9151,99696,99697,99699,99701],{},[898,99698,1738],{},[2133,99700,2281],{},[898,99702,4240],{},[1726,99704,2502],{"stretchy":1734},[902,99706,96107],{"encoding":904},[883,99708,99710],{"className":99709},[886],[888,99711,99712],{"xmlns":890},[892,99713,99714,99744],{},[895,99715,99716,99722,99724,99732,99734,99742],{},[2275,99717,99718,99720],{},[898,99719,4240],{},[2133,99721,2135],{},[1726,99723,2487],{"stretchy":1734},[9151,99725,99726,99728,99730],{},[898,99727,1724],{},[2133,99729,2135],{},[898,99731,4240],{},[1726,99733,1742],{"separator":1741},[9151,99735,99736,99738,99740],{},[898,99737,1738],{},[2133,99739,2135],{},[898,99741,4240],{},[1726,99743,2502],{"stretchy":1734},[902,99745,97182],{"encoding":904},[123,99747,99748,10009,99750,99752,99753],{},[38,99749,42639],{},[614,99751,97962],{},") — rozklad ",[883,99754,99756],{"className":99755},[886],[888,99757,99758],{"xmlns":890},[892,99759,99760,99790],{},[895,99761,99762,99764,99766,99776,99778],{},[898,99763,2772],{},[1726,99765,1728],{},[2275,99767,99768,99770],{},[898,99769,2772],{},[895,99771,99772,99774],{},[898,99773,42658],{},[898,99775,724],{},[1726,99777,2099],{},[2275,99779,99780,99782],{},[898,99781,2772],{},[895,99783,99784,99786,99788],{},[898,99785,42681],{},[898,99787,2003],{},[898,99789,12027],{},[902,99791,42825],{"encoding":904},[123,99793,99794,99817,99818,1762],{},[38,99795,99796],{},[883,99797,99799],{"className":99798},[886],[888,99800,99801],{"xmlns":890},[892,99802,99803,99815],{},[895,99804,99805],{},[2275,99806,99807,99809],{},[898,99808,2772],{},[895,99810,99811,99813],{},[898,99812,42658],{},[898,99814,724],{},[902,99816,42663],{"encoding":904}," — část daně nesená spotřebitelem (navýšení ceny nad ",[883,99819,99821],{"className":99820},[886],[888,99822,99823],{"xmlns":890},[892,99824,99825,99833],{},[895,99826,99827],{},[2128,99828,99829,99831],{},[898,99830,1738],{},[898,99832,4240],{},[902,99834,41447],{"encoding":904},[123,99836,99837,99862,99863,1762],{},[38,99838,99839],{},[883,99840,99842],{"className":99841},[886],[888,99843,99844],{"xmlns":890},[892,99845,99846,99860],{},[895,99847,99848],{},[2275,99849,99850,99852],{},[898,99851,2772],{},[895,99853,99854,99856,99858],{},[898,99855,42681],{},[898,99857,2003],{},[898,99859,12027],{},[902,99861,42688],{"encoding":904}," — část daně nesená výrobcem (pokles čisté přijímané ceny pod ",[883,99864,99866],{"className":99865},[886],[888,99867,99868],{"xmlns":890},[892,99869,99870,99878],{},[895,99871,99872],{},[2128,99873,99874,99876],{},[898,99875,1738],{},[898,99877,4240],{},[902,99879,41447],{"encoding":904},[123,99881,99882,1696,99884,1343,99913],{},[38,99883,50455],{},[883,99885,99887],{"className":99886},[886],[888,99888,99889],{"xmlns":890},[892,99890,99891,99911],{},[895,99892,99893,99901,99903],{},[9151,99894,99895,99897,99899],{},[898,99896,1724],{},[2133,99898,2281],{},[898,99900,4240],{},[1726,99902,1728],{},[9151,99904,99905,99907,99909],{},[898,99906,1724],{},[2133,99908,2135],{},[898,99910,4240],{},[902,99912,42889],{"encoding":904},[883,99914,99916],{"className":99915},[886],[888,99917,99918],{"xmlns":890},[892,99919,99920,99944],{},[895,99921,99922,99930,99932,99934,99936],{},[9151,99923,99924,99926,99928],{},[898,99925,1738],{},[2133,99927,2281],{},[898,99929,4240],{},[1726,99931,2228],{},[898,99933,2772],{},[1726,99935,1728],{},[9151,99937,99938,99940,99942],{},[898,99939,1738],{},[2133,99941,2135],{},[898,99943,4240],{},[902,99945,42923],{"encoding":904},[123,99947,99948,99951],{},[38,99949,99950],{},"Zákonný vs. ekonomický nositel daně"," — rozdíl mezi formálním ustanovením zákona a skutečným rozdělením břemene",[36951,99953],{},[115,99955,1899],{"id":1898},[120,99957,99958,99966,99984,99991],{},[123,99959,99960,1777,99963],{},[38,99961,99962],{},"Kontext (hub):",[207,99964,802],{"className":99965,"dataFsResolvedFilePath":800,"href":801},[210],[123,99967,99968,1777,99970,99973,99974,18629,99976,99979,99980,99983],{},[38,99969,50703],{},[207,99971,820],{"className":99972,"dataFsResolvedFilePath":818,"href":819},[210]," (daň vyvolává ztrátu blahobytu — ",[614,99975,55014],{},[207,99977,2358],{"className":99978,"dataFsResolvedFilePath":764,"href":765},[210]," (sklony křivek, rovnovážný bod jako řešení soustavy), ",[207,99981,3820],{"className":99982,"dataFsResolvedFilePath":848,"href":849},[210]," (kvantifikace, jak se daňové břemeno dělí podle citlivosti stran trhu)",[123,99985,99986,1777,99988],{},[38,99987,50738],{},[207,99989,50742],{"className":99990,"dataFsResolvedFilePath":745,"href":746},[210],[123,99992,99993,1777,99995],{},[38,99994,16188],{},[207,99996,16192],{"className":99997,"dataFsResolvedFilePath":1640,"href":1641},[210],{"title":641,"searchDepth":642,"depth":642,"links":99999},[100000,100001,100004,100007,100011,100012,100013,100014],{"id":95844,"depth":642,"text":95845},{"id":95938,"depth":642,"text":95939,"children":100002},[100003],{"id":96329,"depth":649,"text":45284},{"id":97011,"depth":642,"text":97012,"children":100005},[100006],{"id":97488,"depth":649,"text":45364},{"id":97955,"depth":642,"text":42639,"children":100008},[100009,100010],{"id":2444,"depth":649,"text":2445},{"id":98298,"depth":649,"text":98299},{"id":98771,"depth":642,"text":98772},{"id":99368,"depth":642,"text":99369},{"id":1669,"depth":642,"text":1670},{"id":1898,"depth":642,"text":1899},{},"\u002Ftopics\u002Fzdaneni-trhu",{"title":95742,"description":641},[1138,1135],"topics\u002Fzdaneni-trhu",[1128,50803,100021,100022,100023,1846],"dane","danove-bremeno","posun-krivek","cFuKqHgzIrqvY-l4jNdqjFEM7_ixjw33HOL0So8cPn0",[100026,100028,100030,100034],{"slug":1145,"path":765,"title":1960,"snippet":100027},"… **maximum** v $-1$ - $f''(2) = 18 > 0$ ⇒ **minimum** v $2$ ## Navigace - **Předchozí:** \u003C\u003Czaklady-matematicke-ekonomie>> - **Navazující:** Integrál - **Souvislosti:** [[funkce-vice-promennych|Funkc …",{"slug":1128,"path":1641,"title":681,"snippet":100029},"… ých bloků: ### Blok 1 — Kalkul, poptávka\u002Fnabídka, příjem\u002Fnáklady\u002Fzisk - \u003C\u003Czaklady-matematicke-ekonomie>> — model, endogenní\u002Fexogenní proměnné, ceteris paribus, komparativní statika - [[derivace| …",{"slug":100031,"path":746,"title":100032,"snippet":100033},"imek-blok-01","KS 1. blok — Kalkul a mikroekonomie","… a**, pojem *jednotková změna* znamená změnu o 1. ## Témata bloku — doporučené pořadí 1. \u003C\u003Czaklady-matematicke-ekonomie>> — model, endogenní\u002Fexogenní proměnné, ceteris paribus, komparativní statika, principy řeš …",{"slug":100035,"path":1109,"title":100036,"snippet":100037},"imek-kniha","Kniha — *Úvod do matematické ekonomie pro ekonomy*","… ně úvod \u002F matematický aparát (funkce, derivace, integrály, Lagrange). Teorie je pokryta v \u003C\u003Czaklady-matematicke-ekonomie>>, derivace, integral, funkce-vice-promennych, lagrangeova-metoda ze zdrojů …",[],1777154973837]