[{"data":1,"prerenderedAt":103862},["ShallowReactive",2],{"sidebar-courses-with-stats":3,"wiki-zdaneni-trhu":1626,"course-stats-imek":6053,"course-topics-imek":6057,"backlinks-zdaneni-trhu":103845,"related-zdaneni-trhu":103856},{"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":6052},{"id":1628,"title":1629,"body":1630,"course":1128,"courses":659,"created":6039,"description":641,"extension":661,"meta":6040,"navigation":664,"path":6041,"seo":6042,"sources":6043,"stem":6044,"tags":6045,"type":6050,"updated":677,"__hash__":6051},"topics\u002Ftopics\u002Fzdaneni-trhu.md","Zdanění trhu — dopady daně na rovnováhu",{"type":9,"value":1631,"toc":6022},[1632,1635,1742,1746,1772,1786,1848,1851,1855,1925,1973,1994,2163,2266,2270,2345,2350,2483,2523,2553,2666,2711,2783,2836,2912,2968,2970,2974,3038,3082,3102,3264,3267,3353,3451,3455,3521,3525,3574,3600,3705,3769,3774,3870,3917,3919,3923,3946,3988,3997,4030,4034,4106,4160,4270,4274,4369,4446,4717,4756,4758,4762,4765,4772,5086,5089,5147,5330,5359,5361,5365,5373,5517,5528,5530,5534,5963,5965,5969],[12,1633,1629],{"id":1634},"zdanění-trhu-dopady-daně-na-rovnováhu",[1636,1637,1638],"blockquote",{},[724,1639,1640,1643,1644,1658,1659,1662,1663,1666,1667,1670,1671,1695,1696,1723,1724,1727,1728,1741],{},[883,1641,1642],{},"!info"," TL;DR\nJednotková daň ",[883,1645,1647],{"className":1646},[886],[888,1648,1649],{"xmlns":890},[892,1650,1651,1656],{},[895,1652,1653],{},[898,1654,1655],{},"T",[902,1657,1655],{"encoding":904}," uložená na každou prodanou jednotku zboží posouvá jednu z křivek — ",[38,1660,1661],{},"nabídku"," (je-li daň uložena výrobci) nebo ",[38,1664,1665],{},"poptávku"," (je-li uložena spotřebiteli). Výsledné ",[38,1668,1669],{},"daňové břemeno"," se dělí mezi obě strany trhu na ",[883,1672,1674],{"className":1673},[886],[888,1675,1676],{"xmlns":890},[892,1677,1678,1692],{},[895,1679,1680],{},[1681,1682,1683,1685],"msub",{},[898,1684,1655],{},[895,1686,1687,1690],{},[898,1688,1689],{},"s",[898,1691,724],{},[902,1693,1694],{"encoding":904},"T_{sp}"," (spotřebitel) a ",[883,1697,1699],{"className":1698},[886],[888,1700,1701],{"xmlns":890},[892,1702,1703,1720],{},[895,1704,1705],{},[1681,1706,1707,1709],{},[898,1708,1655],{},[895,1710,1711,1714,1717],{},[898,1712,1713],{},"v",[898,1715,1716],{},"y",[898,1718,1719],{},"r",[902,1721,1722],{"encoding":904},"T_{vyr}"," (výrobce). Klíčovým zjištěním je ",[38,1725,1726],{},"ekvivalence obou přístupů",": rovnovážné množství i čistá cena pro výrobce jsou v obou režimech totožné; liší se pouze nominální cena na trhu o ",[883,1729,1731],{"className":1730},[886],[888,1732,1733],{"xmlns":890},[892,1734,1735,1739],{},[895,1736,1737],{},[898,1738,1655],{},[902,1740,1655],{"encoding":904},".",[115,1743,1745],{"id":1744},"dvě-formy-zdanění","Dvě formy zdanění",[724,1747,1748,1749,1771],{},"Uvažujme jednotkovou daň ",[883,1750,1752],{"className":1751},[886],[888,1753,1754],{"xmlns":890},[892,1755,1756,1768],{},[895,1757,1758,1760,1764],{},[898,1759,1655],{},[1761,1762,1763],"mo",{},">",[1765,1766,1767],"mn",{},"0",[902,1769,1770],{"encoding":904},"T > 0"," (Kč na kus), kterou stát ukládá na každou prodanou jednotku zboží. Daň může být uložena buď:",[120,1773,1774,1780],{},[123,1775,1776,1779],{},[38,1777,1778],{},"(a) výrobci"," — výrobce ji musí odvést státu z každé prodané jednotky,",[123,1781,1782,1785],{},[38,1783,1784],{},"(b) spotřebiteli"," — spotřebitel ji platí navíc k ceně, kterou si účtuje prodejce.",[724,1787,1788,1789,1802,1803,1806,1807,1741],{},"V obou případech dochází k posunu jedné z křivek o ",[883,1790,1792],{"className":1791},[886],[888,1793,1794],{"xmlns":890},[892,1795,1796,1800],{},[895,1797,1798],{},[898,1799,1655],{},[902,1801,1655],{"encoding":904}," svisle (buď nabídky nahoru, nebo poptávky dolů) a k rozdělení ",[38,1804,1805],{},"daňového břemene"," mezi spotřebitele a výrobce. Výchozí rovnovážný bod bez daně označujeme ",[883,1808,1810],{"className":1809},[886],[888,1811,1812],{"xmlns":890},[892,1813,1814,1845],{},[895,1815,1816,1819,1823,1831,1835,1842],{},[898,1817,1818],{},"E",[1761,1820,1822],{"stretchy":1821},"false","[",[1824,1825,1826,1829],"msup",{},[898,1827,1828],{},"Q",[898,1830,1818],{},[1761,1832,1834],{"separator":1833},"true",",",[1824,1836,1837,1840],{},[898,1838,1839],{},"P",[898,1841,1818],{},[1761,1843,1844],{"stretchy":1821},"]",[902,1846,1847],{"encoding":904},"E[Q^E, P^E]",[1849,1850],"hr",{},[115,1852,1854],{"id":1853},"daň-uložená-výrobci","Daň uložená výrobci",[724,1856,1857,1858,1871,1872,1891,1892,1924],{},"Je-li daň ",[883,1859,1861],{"className":1860},[886],[888,1862,1863],{"xmlns":890},[892,1864,1865,1869],{},[895,1866,1867],{},[898,1868,1655],{},[902,1870,1655],{"encoding":904}," uložena výrobci, pak z podmínky, že výrobce za každou prodanou jednotku obdrží ",[883,1873,1875],{"className":1874},[886],[888,1876,1877],{"xmlns":890},[892,1878,1879,1888],{},[895,1880,1881,1883,1886],{},[898,1882,1839],{},[1761,1884,1885],{},"−",[898,1887,1655],{},[902,1889,1890],{"encoding":904},"P - T"," (hrubá cena mínus odvod), plyne z rovnice ",[883,1893,1895],{"className":1894},[886],[888,1896,1897],{"xmlns":890},[892,1898,1899,1921],{},[895,1900,1901,1903,1905,1907,1910,1913,1916,1918],{},[898,1902,1839],{},[1761,1904,1885],{},[898,1906,1655],{},[1761,1908,1909],{},"=",[898,1911,1912],{},"S",[1761,1914,1915],{"stretchy":1821},"(",[898,1917,1828],{},[1761,1919,1920],{"stretchy":1821},")",[902,1922,1923],{"encoding":904},"P - T = S(Q)"," nová funkce nabídky:",[883,1926,1928],{"className":1927},[886],[888,1929,1931],{"xmlns":890,"display":1930},"block",[892,1932,1933,1970],{},[895,1934,1935,1937,1939,1946,1948,1950,1952,1954,1956,1958,1960,1962,1965,1967],{},[898,1936,1839],{},[1761,1938,1909],{},[1681,1940,1941,1943],{},[898,1942,1912],{},[1765,1944,1945],{},"1",[1761,1947,1915],{"stretchy":1821},[898,1949,1828],{},[1761,1951,1920],{"stretchy":1821},[1761,1953,1909],{},[898,1955,1912],{},[1761,1957,1915],{"stretchy":1821},[898,1959,1828],{},[1761,1961,1920],{"stretchy":1821},[1761,1963,1964],{},"+",[898,1966,1655],{},[898,1968,1741],{"mathvariant":1969},"normal",[902,1971,1972],{"encoding":904},"P = S_1(Q) = S(Q) + T.",[724,1974,1975,1976,1989,1990,1993],{},"Nabídka se tedy posouvá o ",[883,1977,1979],{"className":1978},[886],[888,1980,1981],{"xmlns":890},[892,1982,1983,1987],{},[895,1984,1985],{},[898,1986,1655],{},[902,1988,1655],{"encoding":904}," ",[38,1991,1992],{},"svisle nahoru"," (ekvivalentně doleva). Poptávka se nemění.",[724,1995,1996,1997,2038,2039,2068,2069,2097,2098,2118,2119,2143,2144,2162],{},"Nový rovnovážný bod ",[883,1998,2000],{"className":1999},[886],[888,2001,2002],{"xmlns":890},[892,2003,2004,2035],{},[895,2005,2006,2012,2014,2023,2025,2033],{},[1681,2007,2008,2010],{},[898,2009,1818],{},[1765,2011,1945],{},[1761,2013,1822],{"stretchy":1821},[2015,2016,2017,2019,2021],"msubsup",{},[898,2018,1828],{},[1765,2020,1945],{},[898,2022,1818],{},[1761,2024,1834],{"separator":1833},[2015,2026,2027,2029,2031],{},[898,2028,1839],{},[1765,2030,1945],{},[898,2032,1818],{},[1761,2034,1844],{"stretchy":1821},[902,2036,2037],{"encoding":904},"E_1[Q_1^E, P_1^E]"," splňuje ",[883,2040,2042],{"className":2041},[886],[888,2043,2044],{"xmlns":890},[892,2045,2046,2065],{},[895,2047,2048,2056,2059],{},[2015,2049,2050,2052,2054],{},[898,2051,1828],{},[1765,2053,1945],{},[898,2055,1818],{},[1761,2057,2058],{},"\u003C",[1824,2060,2061,2063],{},[898,2062,1828],{},[898,2064,1818],{},[902,2066,2067],{"encoding":904},"Q_1^E \u003C Q^E"," a ",[883,2070,2072],{"className":2071},[886],[888,2073,2074],{"xmlns":890},[892,2075,2076,2094],{},[895,2077,2078,2086,2088],{},[2015,2079,2080,2082,2084],{},[898,2081,1839],{},[1765,2083,1945],{},[898,2085,1818],{},[1761,2087,1763],{},[1824,2089,2090,2092],{},[898,2091,1839],{},[898,2093,1818],{},[902,2095,2096],{"encoding":904},"P_1^E > P^E",". Spotřebitel platí ",[883,2099,2101],{"className":2100},[886],[888,2102,2103],{"xmlns":890},[892,2104,2105,2115],{},[895,2106,2107],{},[2015,2108,2109,2111,2113],{},[898,2110,1839],{},[1765,2112,1945],{},[898,2114,1818],{},[902,2116,2117],{"encoding":904},"P_1^E",", výrobci ale zůstává pouze čistá cena ",[883,2120,2122],{"className":2121},[886],[888,2123,2124],{"xmlns":890},[892,2125,2126,2140],{},[895,2127,2128,2136,2138],{},[2015,2129,2130,2132,2134],{},[898,2131,1839],{},[1765,2133,1945],{},[898,2135,1818],{},[1761,2137,1885],{},[898,2139,1655],{},[902,2141,2142],{"encoding":904},"P_1^E - T"," (ta je nižší než původní rovnovážná ",[883,2145,2147],{"className":2146},[886],[888,2148,2149],{"xmlns":890},[892,2150,2151,2159],{},[895,2152,2153],{},[1824,2154,2155,2157],{},[898,2156,1839],{},[898,2158,1818],{},[902,2160,2161],{"encoding":904},"P^E",").",[724,2164,2165],{},[614,2166,2167,2168,2199,2200,2213,2214,2232,2233,2247,2248,1741],{},"Obrázek 2.17 (resp. 2.18): Posun ",[883,2169,2171],{"className":2170},[886],[888,2172,2173],{"xmlns":890},[892,2174,2175,2196],{},[895,2176,2177,2179,2182,2188,2190,2192,2194],{},[898,2178,1912],{},[1761,2180,2181],{},"→",[1681,2183,2184,2186],{},[898,2185,1912],{},[1765,2187,1945],{},[1761,2189,1909],{},[898,2191,1912],{},[1761,2193,1964],{},[898,2195,1655],{},[902,2197,2198],{"encoding":904},"S \\to S_1 = S + T","; svislá vzdálenost mezi křivkami je přesně ",[883,2201,2203],{"className":2202},[886],[888,2204,2205],{"xmlns":890},[892,2206,2207,2211],{},[895,2208,2209],{},[898,2210,1655],{},[902,2212,1655],{"encoding":904},". Průsečík ",[883,2215,2217],{"className":2216},[886],[888,2218,2219],{"xmlns":890},[892,2220,2221,2229],{},[895,2222,2223],{},[1681,2224,2225,2227],{},[898,2226,1912],{},[1765,2228,1945],{},[902,2230,2231],{"encoding":904},"S_1"," s ",[883,2234,2236],{"className":2235},[886],[888,2237,2238],{"xmlns":890},[892,2239,2240,2245],{},[895,2241,2242],{},[898,2243,2244],{},"D",[902,2246,2244],{"encoding":904}," je nový rovnovážný bod ",[883,2249,2251],{"className":2250},[886],[888,2252,2253],{"xmlns":890},[892,2254,2255,2263],{},[895,2256,2257],{},[1681,2258,2259,2261],{},[898,2260,1818],{},[1765,2262,1945],{},[902,2264,2265],{"encoding":904},"E_1",[198,2267,2269],{"id":2268},"příklad-29","Příklad 2.9",[724,2271,2272,2275,2276,2302,2303,2324,2325,2344],{},[38,2273,2274],{},"Zadání:"," Poptávka ",[883,2277,2279],{"className":2278},[886],[888,2280,2281],{"xmlns":890},[892,2282,2283,2299],{},[895,2284,2285,2287,2289,2292,2294,2297],{},[898,2286,1839],{},[1761,2288,1909],{},[1765,2290,2291],{},"12",[1761,2293,1885],{},[1765,2295,2296],{},"2",[898,2298,1828],{},[902,2300,2301],{"encoding":904},"P = 12 - 2Q",", nabídka ",[883,2304,2306],{"className":2305},[886],[888,2307,2308],{"xmlns":890},[892,2309,2310,2321],{},[895,2311,2312,2314,2316,2319],{},[898,2313,1839],{},[1761,2315,1909],{},[1765,2317,2318],{},"4",[898,2320,1828],{},[902,2322,2323],{"encoding":904},"P = 4Q",". Na výrobce je uložena jednotková daň ",[883,2326,2328],{"className":2327},[886],[888,2329,2330],{"xmlns":890},[892,2331,2332,2341],{},[895,2333,2334,2336,2338],{},[898,2335,1655],{},[1761,2337,1909],{},[1765,2339,2340],{},"6",[902,2342,2343],{"encoding":904},"T = 6"," Kč.",[724,2346,2347],{},[38,2348,2349],{},"Řešení:",[724,2351,2352,2355,2356,2382,2383,2403,2404,1343,2426,2458,2459,1741],{},[614,2353,2354],{},"Bez daně."," Z rovnosti ",[883,2357,2359],{"className":2358},[886],[888,2360,2361],{"xmlns":890},[892,2362,2363,2379],{},[895,2364,2365,2367,2369,2371,2373,2375,2377],{},[1765,2366,2291],{},[1761,2368,1885],{},[1765,2370,2296],{},[898,2372,1828],{},[1761,2374,1909],{},[1765,2376,2318],{},[898,2378,1828],{},[902,2380,2381],{"encoding":904},"12 - 2Q = 4Q"," plyne ",[883,2384,2386],{"className":2385},[886],[888,2387,2388],{"xmlns":890},[892,2389,2390,2400],{},[895,2391,2392,2394,2396,2398],{},[1765,2393,2340],{},[898,2395,1828],{},[1761,2397,1909],{},[1765,2399,2291],{},[902,2401,2402],{"encoding":904},"6Q = 12",", tedy ",[883,2405,2407],{"className":2406},[886],[888,2408,2409],{"xmlns":890},[892,2410,2411,2423],{},[895,2412,2413,2419,2421],{},[1824,2414,2415,2417],{},[898,2416,1828],{},[898,2418,1818],{},[1761,2420,1909],{},[1765,2422,2296],{},[902,2424,2425],{"encoding":904},"Q^E = 2",[883,2427,2429],{"className":2428},[886],[888,2430,2431],{"xmlns":890},[892,2432,2433,2455],{},[895,2434,2435,2441,2443,2445,2448,2450,2452],{},[1824,2436,2437,2439],{},[898,2438,1839],{},[898,2440,1818],{},[1761,2442,1909],{},[1765,2444,2318],{},[1761,2446,2447],{},"⋅",[1765,2449,2296],{},[1761,2451,1909],{},[1765,2453,2454],{},"8",[902,2456,2457],{"encoding":904},"P^E = 4 \\cdot 2 = 8",". Rovnovážný bod ",[883,2460,2462],{"className":2461},[886],[888,2463,2464],{"xmlns":890},[892,2465,2466,2480],{},[895,2467,2468,2470,2472,2474,2476,2478],{},[898,2469,1818],{},[1761,2471,1822],{"stretchy":1821},[1765,2473,2296],{},[1761,2475,1834],{"separator":1833},[1765,2477,2454],{},[1761,2479,1844],{"stretchy":1821},[902,2481,2482],{"encoding":904},"E[2, 8]",[724,2484,2485,2488,2489,2522],{},[614,2486,2487],{},"S daní uloženou výrobci."," Nová nabídka je ",[883,2490,2492],{"className":2491},[886],[888,2493,2494],{"xmlns":890},[892,2495,2496,2519],{},[895,2497,2498,2504,2507,2509,2511,2513,2515,2517],{},[1681,2499,2500,2502],{},[898,2501,1912],{},[1765,2503,1945],{},[1761,2505,2506],{},":",[898,2508,1839],{},[1761,2510,1909],{},[1765,2512,2318],{},[898,2514,1828],{},[1761,2516,1964],{},[1765,2518,2340],{},[902,2520,2521],{"encoding":904},"S_1: P = 4Q + 6",". Z rovnice",[883,2524,2526],{"className":2525},[886],[888,2527,2528],{"xmlns":890,"display":1930},[892,2529,2530,2550],{},[895,2531,2532,2534,2536,2538,2540,2542,2544,2546,2548],{},[1765,2533,2291],{},[1761,2535,1885],{},[1765,2537,2296],{},[898,2539,1828],{},[1761,2541,1909],{},[1765,2543,2318],{},[898,2545,1828],{},[1761,2547,1964],{},[1765,2549,2340],{},[902,2551,2552],{"encoding":904},"12 - 2Q = 4Q + 6",[724,2554,2555,2556,2403,2576,1343,2600,2637,2638,1741],{},"plyne ",[883,2557,2559],{"className":2558},[886],[888,2560,2561],{"xmlns":890},[892,2562,2563,2573],{},[895,2564,2565,2567,2569,2571],{},[1765,2566,2340],{},[898,2568,1828],{},[1761,2570,1909],{},[1765,2572,2340],{},[902,2574,2575],{"encoding":904},"6Q = 6",[883,2577,2579],{"className":2578},[886],[888,2580,2581],{"xmlns":890},[892,2582,2583,2597],{},[895,2584,2585,2593,2595],{},[2015,2586,2587,2589,2591],{},[898,2588,1828],{},[1765,2590,1945],{},[898,2592,1818],{},[1761,2594,1909],{},[1765,2596,1945],{},[902,2598,2599],{"encoding":904},"Q_1^E = 1",[883,2601,2603],{"className":2602},[886],[888,2604,2605],{"xmlns":890},[892,2606,2607,2634],{},[895,2608,2609,2617,2619,2621,2623,2625,2627,2629,2631],{},[2015,2610,2611,2613,2615],{},[898,2612,1839],{},[1765,2614,1945],{},[898,2616,1818],{},[1761,2618,1909],{},[1765,2620,2318],{},[1761,2622,2447],{},[1765,2624,1945],{},[1761,2626,1964],{},[1765,2628,2340],{},[1761,2630,1909],{},[1765,2632,2633],{},"10",[902,2635,2636],{"encoding":904},"P_1^E = 4 \\cdot 1 + 6 = 10",". Nový rovnovážný bod ",[883,2639,2641],{"className":2640},[886],[888,2642,2643],{"xmlns":890},[892,2644,2645,2663],{},[895,2646,2647,2653,2655,2657,2659,2661],{},[1681,2648,2649,2651],{},[898,2650,1818],{},[1765,2652,1945],{},[1761,2654,1822],{"stretchy":1821},[1765,2656,1945],{},[1761,2658,1834],{"separator":1833},[1765,2660,2633],{},[1761,2662,1844],{"stretchy":1821},[902,2664,2665],{"encoding":904},"E_1[1, 10]",[724,2667,2668,2671,2672,2696,2697,2710],{},[614,2669,2670],{},"Rozklad daňového břemene."," Spotřebitel platí ",[883,2673,2675],{"className":2674},[886],[888,2676,2677],{"xmlns":890},[892,2678,2679,2693],{},[895,2680,2681,2689,2691],{},[2015,2682,2683,2685,2687],{},[898,2684,1839],{},[1765,2686,1945],{},[898,2688,1818],{},[1761,2690,1909],{},[1765,2692,2633],{},[902,2694,2695],{"encoding":904},"P_1^E = 10"," Kč namísto původních ",[883,2698,2700],{"className":2699},[886],[888,2701,2702],{"xmlns":890},[892,2703,2704,2708],{},[895,2705,2706],{},[1765,2707,2454],{},[902,2709,2454],{"encoding":904},", navýšení je",[883,2712,2714],{"className":2713},[886],[888,2715,2716],{"xmlns":890,"display":1930},[892,2717,2718,2780],{},[895,2719,2720,2730,2732,2740,2742,2748,2750,2752,2754,2756,2758,2760,2764,2778],{},[1681,2721,2722,2724],{},[898,2723,1655],{},[895,2725,2726,2728],{},[898,2727,1689],{},[898,2729,724],{},[1761,2731,1909],{},[2015,2733,2734,2736,2738],{},[898,2735,1839],{},[1765,2737,1945],{},[898,2739,1818],{},[1761,2741,1885],{},[1824,2743,2744,2746],{},[898,2745,1839],{},[898,2747,1818],{},[1761,2749,1909],{},[1765,2751,2633],{},[1761,2753,1885],{},[1765,2755,2454],{},[1761,2757,1909],{},[1765,2759,2296],{},[2761,2762,2763],"mtext",{}," ",[895,2765,2766,2769],{},[2761,2767,2768],{},"K",[2770,2771,2772,2775],"mover",{"accent":1833},[2761,2773,2774],{},"c",[1761,2776,2777],{},"ˇ",[898,2779,1741],{"mathvariant":1969},[902,2781,2782],{"encoding":904},"T_{sp} = P_1^E - P^E = 10 - 8 = 2\\ \\text{Kč}.",[724,2784,2785,2786,2696,2822,2835],{},"Výrobci zůstává čistá cena ",[883,2787,2789],{"className":2788},[886],[888,2790,2791],{"xmlns":890},[892,2792,2793,2819],{},[895,2794,2795,2803,2805,2807,2809,2811,2813,2815,2817],{},[2015,2796,2797,2799,2801],{},[898,2798,1839],{},[1765,2800,1945],{},[898,2802,1818],{},[1761,2804,1885],{},[898,2806,1655],{},[1761,2808,1909],{},[1765,2810,2633],{},[1761,2812,1885],{},[1765,2814,2340],{},[1761,2816,1909],{},[1765,2818,2318],{},[902,2820,2821],{"encoding":904},"P_1^E - T = 10 - 6 = 4",[883,2823,2825],{"className":2824},[886],[888,2826,2827],{"xmlns":890},[892,2828,2829,2833],{},[895,2830,2831],{},[1765,2832,2454],{},[902,2834,2454],{"encoding":904},", pokles je",[883,2837,2839],{"className":2838},[886],[888,2840,2841],{"xmlns":890,"display":1930},[892,2842,2843,2909],{},[895,2844,2845,2857,2859,2865,2867,2869,2877,2879,2881,2883,2885,2887,2889,2891,2893,2895,2897,2907],{},[1681,2846,2847,2849],{},[898,2848,1655],{},[895,2850,2851,2853,2855],{},[898,2852,1713],{},[898,2854,1716],{},[898,2856,1719],{},[1761,2858,1909],{},[1824,2860,2861,2863],{},[898,2862,1839],{},[898,2864,1818],{},[1761,2866,1885],{},[1761,2868,1915],{"stretchy":1821},[2015,2870,2871,2873,2875],{},[898,2872,1839],{},[1765,2874,1945],{},[898,2876,1818],{},[1761,2878,1885],{},[898,2880,1655],{},[1761,2882,1920],{"stretchy":1821},[1761,2884,1909],{},[1765,2886,2454],{},[1761,2888,1885],{},[1765,2890,2318],{},[1761,2892,1909],{},[1765,2894,2318],{},[2761,2896,2763],{},[895,2898,2899,2901],{},[2761,2900,2768],{},[2770,2902,2903,2905],{"accent":1833},[2761,2904,2774],{},[1761,2906,2777],{},[898,2908,1741],{"mathvariant":1969},[902,2910,2911],{"encoding":904},"T_{vyr} = P^E - (P_1^E - T) = 8 - 4 = 4\\ \\text{Kč}.",[724,2913,2914,2915,2967],{},"Kontrola: ",[883,2916,2918],{"className":2917},[886],[888,2919,2920],{"xmlns":890},[892,2921,2922,2964],{},[895,2923,2924,2934,2936,2948,2950,2952,2954,2956,2958,2960,2962],{},[1681,2925,2926,2928],{},[898,2927,1655],{},[895,2929,2930,2932],{},[898,2931,1689],{},[898,2933,724],{},[1761,2935,1964],{},[1681,2937,2938,2940],{},[898,2939,1655],{},[895,2941,2942,2944,2946],{},[898,2943,1713],{},[898,2945,1716],{},[898,2947,1719],{},[1761,2949,1909],{},[1765,2951,2296],{},[1761,2953,1964],{},[1765,2955,2318],{},[1761,2957,1909],{},[1765,2959,2340],{},[1761,2961,1909],{},[898,2963,1655],{},[902,2965,2966],{"encoding":904},"T_{sp} + T_{vyr} = 2 + 4 = 6 = T",". Spotřebitel nese třetinu daně, výrobce dvě třetiny.",[1849,2969],{},[115,2971,2973],{"id":2972},"daň-uložená-spotřebiteli","Daň uložená spotřebiteli",[724,2975,1857,2976,2989,2990,3008,3009,3037],{},[883,2977,2979],{"className":2978},[886],[888,2980,2981],{"xmlns":890},[892,2982,2983,2987],{},[895,2984,2985],{},[898,2986,1655],{},[902,2988,1655],{"encoding":904}," uložena spotřebiteli, pak spotřebitel platí celkem ",[883,2991,2993],{"className":2992},[886],[888,2994,2995],{"xmlns":890},[892,2996,2997,3005],{},[895,2998,2999,3001,3003],{},[898,3000,1839],{},[1761,3002,1964],{},[898,3004,1655],{},[902,3006,3007],{"encoding":904},"P + T"," (cena prodejce plus daň). Z podmínky ",[883,3010,3012],{"className":3011},[886],[888,3013,3014],{"xmlns":890},[892,3015,3016,3034],{},[895,3017,3018,3020,3022,3024,3026,3028,3030,3032],{},[898,3019,1839],{},[1761,3021,1964],{},[898,3023,1655],{},[1761,3025,1909],{},[898,3027,2244],{},[1761,3029,1915],{"stretchy":1821},[898,3031,1828],{},[1761,3033,1920],{"stretchy":1821},[902,3035,3036],{"encoding":904},"P + T = D(Q)"," plyne nová funkce poptávky:",[883,3039,3041],{"className":3040},[886],[888,3042,3043],{"xmlns":890,"display":1930},[892,3044,3045,3079],{},[895,3046,3047,3049,3051,3057,3059,3061,3063,3065,3067,3069,3071,3073,3075,3077],{},[898,3048,1839],{},[1761,3050,1909],{},[1681,3052,3053,3055],{},[898,3054,2244],{},[1765,3056,2296],{},[1761,3058,1915],{"stretchy":1821},[898,3060,1828],{},[1761,3062,1920],{"stretchy":1821},[1761,3064,1909],{},[898,3066,2244],{},[1761,3068,1915],{"stretchy":1821},[898,3070,1828],{},[1761,3072,1920],{"stretchy":1821},[1761,3074,1885],{},[898,3076,1655],{},[898,3078,1741],{"mathvariant":1969},[902,3080,3081],{"encoding":904},"P = D_2(Q) = D(Q) - T.",[724,3083,3084,3085,1989,3098,3101],{},"Poptávka se tedy posouvá o ",[883,3086,3088],{"className":3087},[886],[888,3089,3090],{"xmlns":890},[892,3091,3092,3096],{},[895,3093,3094],{},[898,3095,1655],{},[902,3097,1655],{"encoding":904},[38,3099,3100],{},"svisle dolů",". Nabídka se nemění.",[724,3103,1996,3104,2038,3144,2068,3172,3200,3201,3221,3222,3246,3247,2162],{},[883,3105,3107],{"className":3106},[886],[888,3108,3109],{"xmlns":890},[892,3110,3111,3141],{},[895,3112,3113,3119,3121,3129,3131,3139],{},[1681,3114,3115,3117],{},[898,3116,1818],{},[1765,3118,2296],{},[1761,3120,1822],{"stretchy":1821},[2015,3122,3123,3125,3127],{},[898,3124,1828],{},[1765,3126,2296],{},[898,3128,1818],{},[1761,3130,1834],{"separator":1833},[2015,3132,3133,3135,3137],{},[898,3134,1839],{},[1765,3136,2296],{},[898,3138,1818],{},[1761,3140,1844],{"stretchy":1821},[902,3142,3143],{"encoding":904},"E_2[Q_2^E, P_2^E]",[883,3145,3147],{"className":3146},[886],[888,3148,3149],{"xmlns":890},[892,3150,3151,3169],{},[895,3152,3153,3161,3163],{},[2015,3154,3155,3157,3159],{},[898,3156,1828],{},[1765,3158,2296],{},[898,3160,1818],{},[1761,3162,2058],{},[1824,3164,3165,3167],{},[898,3166,1828],{},[898,3168,1818],{},[902,3170,3171],{"encoding":904},"Q_2^E \u003C Q^E",[883,3173,3175],{"className":3174},[886],[888,3176,3177],{"xmlns":890},[892,3178,3179,3197],{},[895,3180,3181,3189,3191],{},[2015,3182,3183,3185,3187],{},[898,3184,1839],{},[1765,3186,2296],{},[898,3188,1818],{},[1761,3190,2058],{},[1824,3192,3193,3195],{},[898,3194,1839],{},[898,3196,1818],{},[902,3198,3199],{"encoding":904},"P_2^E \u003C P^E",". Výrobce obdrží ",[883,3202,3204],{"className":3203},[886],[888,3205,3206],{"xmlns":890},[892,3207,3208,3218],{},[895,3209,3210],{},[2015,3211,3212,3214,3216],{},[898,3213,1839],{},[1765,3215,2296],{},[898,3217,1818],{},[902,3219,3220],{"encoding":904},"P_2^E",", spotřebitel platí celkem ",[883,3223,3225],{"className":3224},[886],[888,3226,3227],{"xmlns":890},[892,3228,3229,3243],{},[895,3230,3231,3239,3241],{},[2015,3232,3233,3235,3237],{},[898,3234,1839],{},[1765,3236,2296],{},[898,3238,1818],{},[1761,3240,1964],{},[898,3242,1655],{},[902,3244,3245],{"encoding":904},"P_2^E + T"," (tato částka je vyšší než původní ",[883,3248,3250],{"className":3249},[886],[888,3251,3252],{"xmlns":890},[892,3253,3254,3262],{},[895,3255,3256],{},[1824,3257,3258,3260],{},[898,3259,1839],{},[898,3261,1818],{},[902,3263,2161],{"encoding":904},[724,3265,3266],{},"Daňové břemeno:",[883,3268,3270],{"className":3269},[886],[888,3271,3272],{"xmlns":890,"display":1930},[892,3273,3274,3350],{},[895,3275,3276,3286,3288,3290,3298,3300,3302,3304,3306,3312,3314,3318,3330,3332,3338,3340,3348],{},[1681,3277,3278,3280],{},[898,3279,1655],{},[895,3281,3282,3284],{},[898,3283,1689],{},[898,3285,724],{},[1761,3287,1909],{},[1761,3289,1915],{"stretchy":1821},[2015,3291,3292,3294,3296],{},[898,3293,1839],{},[1765,3295,2296],{},[898,3297,1818],{},[1761,3299,1964],{},[898,3301,1655],{},[1761,3303,1920],{"stretchy":1821},[1761,3305,1885],{},[1824,3307,3308,3310],{},[898,3309,1839],{},[898,3311,1818],{},[1761,3313,1834],{"separator":1833},[3315,3316],"mspace",{"width":3317},"2em",[1681,3319,3320,3322],{},[898,3321,1655],{},[895,3323,3324,3326,3328],{},[898,3325,1713],{},[898,3327,1716],{},[898,3329,1719],{},[1761,3331,1909],{},[1824,3333,3334,3336],{},[898,3335,1839],{},[898,3337,1818],{},[1761,3339,1885],{},[2015,3341,3342,3344,3346],{},[898,3343,1839],{},[1765,3345,2296],{},[898,3347,1818],{},[898,3349,1741],{"mathvariant":1969},[902,3351,3352],{"encoding":904},"T_{sp} = (P_2^E + T) - P^E, \\qquad T_{vyr} = P^E - P_2^E.",[724,3354,3355],{},[614,3356,3357,3358,3388,3389,2213,3402,2232,3420,2247,3433,1741],{},"Obrázek 2.19: Posun ",[883,3359,3361],{"className":3360},[886],[888,3362,3363],{"xmlns":890},[892,3364,3365,3385],{},[895,3366,3367,3369,3371,3377,3379,3381,3383],{},[898,3368,2244],{},[1761,3370,2181],{},[1681,3372,3373,3375],{},[898,3374,2244],{},[1765,3376,2296],{},[1761,3378,1909],{},[898,3380,2244],{},[1761,3382,1885],{},[898,3384,1655],{},[902,3386,3387],{"encoding":904},"D \\to D_2 = D - T","; svislá vzdálenost mezi poptávkovými křivkami je ",[883,3390,3392],{"className":3391},[886],[888,3393,3394],{"xmlns":890},[892,3395,3396,3400],{},[895,3397,3398],{},[898,3399,1655],{},[902,3401,1655],{"encoding":904},[883,3403,3405],{"className":3404},[886],[888,3406,3407],{"xmlns":890},[892,3408,3409,3417],{},[895,3410,3411],{},[1681,3412,3413,3415],{},[898,3414,2244],{},[1765,3416,2296],{},[902,3418,3419],{"encoding":904},"D_2",[883,3421,3423],{"className":3422},[886],[888,3424,3425],{"xmlns":890},[892,3426,3427,3431],{},[895,3428,3429],{},[898,3430,1912],{},[902,3432,1912],{"encoding":904},[883,3434,3436],{"className":3435},[886],[888,3437,3438],{"xmlns":890},[892,3439,3440,3448],{},[895,3441,3442],{},[1681,3443,3444,3446],{},[898,3445,1818],{},[1765,3447,2296],{},[902,3449,3450],{"encoding":904},"E_2",[198,3452,3454],{"id":3453},"příklad-210","Příklad 2.10",[724,3456,3457,3459,3460,2302,3483,3502,3503,3520],{},[38,3458,2274],{}," Pokračuje z Příkladu 2.9 — stejný trh, poptávka ",[883,3461,3463],{"className":3462},[886],[888,3464,3465],{"xmlns":890},[892,3466,3467,3481],{},[895,3468,3469,3471,3473,3475,3477,3479],{},[898,3470,1839],{},[1761,3472,1909],{},[1765,3474,2291],{},[1761,3476,1885],{},[1765,3478,2296],{},[898,3480,1828],{},[902,3482,2301],{"encoding":904},[883,3484,3486],{"className":3485},[886],[888,3487,3488],{"xmlns":890},[892,3489,3490,3500],{},[895,3491,3492,3494,3496,3498],{},[898,3493,1839],{},[1761,3495,1909],{},[1765,3497,2318],{},[898,3499,1828],{},[902,3501,2323],{"encoding":904},". Daň ",[883,3504,3506],{"className":3505},[886],[888,3507,3508],{"xmlns":890},[892,3509,3510,3518],{},[895,3511,3512,3514,3516],{},[898,3513,1655],{},[1761,3515,1909],{},[1765,3517,2340],{},[902,3519,2343],{"encoding":904}," Kč je tentokrát uložena na spotřebitele.",[724,3522,3523],{},[38,3524,2349],{},[724,3526,3527,3528,2522],{},"Nová poptávka je ",[883,3529,3531],{"className":3530},[886],[888,3532,3533],{"xmlns":890},[892,3534,3535,3571],{},[895,3536,3537,3543,3545,3547,3549,3551,3553,3555,3557,3559,3561,3563,3565,3567,3569],{},[1681,3538,3539,3541],{},[898,3540,2244],{},[1765,3542,2296],{},[1761,3544,2506],{},[898,3546,1839],{},[1761,3548,1909],{},[1765,3550,2291],{},[1761,3552,1885],{},[1765,3554,2296],{},[898,3556,1828],{},[1761,3558,1885],{},[1765,3560,2340],{},[1761,3562,1909],{},[1765,3564,2340],{},[1761,3566,1885],{},[1765,3568,2296],{},[898,3570,1828],{},[902,3572,3573],{"encoding":904},"D_2: P = 12 - 2Q - 6 = 6 - 2Q",[883,3575,3577],{"className":3576},[886],[888,3578,3579],{"xmlns":890,"display":1930},[892,3580,3581,3597],{},[895,3582,3583,3585,3587,3589,3591,3593,3595],{},[1765,3584,2340],{},[1761,3586,1885],{},[1765,3588,2296],{},[898,3590,1828],{},[1761,3592,1909],{},[1765,3594,2318],{},[898,3596,1828],{},[902,3598,3599],{"encoding":904},"6 - 2Q = 4Q",[724,3601,2555,3602,2403,3621,1343,3645,2637,3677,1741],{},[883,3603,3605],{"className":3604},[886],[888,3606,3607],{"xmlns":890},[892,3608,3609,3619],{},[895,3610,3611,3613,3615,3617],{},[1765,3612,2340],{},[898,3614,1828],{},[1761,3616,1909],{},[1765,3618,2340],{},[902,3620,2575],{"encoding":904},[883,3622,3624],{"className":3623},[886],[888,3625,3626],{"xmlns":890},[892,3627,3628,3642],{},[895,3629,3630,3638,3640],{},[2015,3631,3632,3634,3636],{},[898,3633,1828],{},[1765,3635,2296],{},[898,3637,1818],{},[1761,3639,1909],{},[1765,3641,1945],{},[902,3643,3644],{"encoding":904},"Q_2^E = 1",[883,3646,3648],{"className":3647},[886],[888,3649,3650],{"xmlns":890},[892,3651,3652,3674],{},[895,3653,3654,3662,3664,3666,3668,3670,3672],{},[2015,3655,3656,3658,3660],{},[898,3657,1839],{},[1765,3659,2296],{},[898,3661,1818],{},[1761,3663,1909],{},[1765,3665,2318],{},[1761,3667,2447],{},[1765,3669,1945],{},[1761,3671,1909],{},[1765,3673,2318],{},[902,3675,3676],{"encoding":904},"P_2^E = 4 \\cdot 1 = 4",[883,3678,3680],{"className":3679},[886],[888,3681,3682],{"xmlns":890},[892,3683,3684,3702],{},[895,3685,3686,3692,3694,3696,3698,3700],{},[1681,3687,3688,3690],{},[898,3689,1818],{},[1765,3691,2296],{},[1761,3693,1822],{"stretchy":1821},[1765,3695,1945],{},[1761,3697,1834],{"separator":1833},[1765,3699,2318],{},[1761,3701,1844],{"stretchy":1821},[902,3703,3704],{"encoding":904},"E_2[1, 4]",[724,3706,3707,3708,3744,3745,2344],{},"Spotřebitel platí celkem ",[883,3709,3711],{"className":3710},[886],[888,3712,3713],{"xmlns":890},[892,3714,3715,3741],{},[895,3716,3717,3725,3727,3729,3731,3733,3735,3737,3739],{},[2015,3718,3719,3721,3723],{},[898,3720,1839],{},[1765,3722,2296],{},[898,3724,1818],{},[1761,3726,1964],{},[898,3728,1655],{},[1761,3730,1909],{},[1765,3732,2318],{},[1761,3734,1964],{},[1765,3736,2340],{},[1761,3738,1909],{},[1765,3740,2633],{},[902,3742,3743],{"encoding":904},"P_2^E + T = 4 + 6 = 10"," Kč; výrobce obdrží ",[883,3746,3748],{"className":3747},[886],[888,3749,3750],{"xmlns":890},[892,3751,3752,3766],{},[895,3753,3754,3762,3764],{},[2015,3755,3756,3758,3760],{},[898,3757,1839],{},[1765,3759,2296],{},[898,3761,1818],{},[1761,3763,1909],{},[1765,3765,2318],{},[902,3767,3768],{"encoding":904},"P_2^E = 4",[724,3770,3771],{},[614,3772,3773],{},"Rozklad daňového břemene:",[883,3775,3777],{"className":3776},[886],[888,3778,3779],{"xmlns":890,"display":1930},[892,3780,3781,3867],{},[895,3782,3783,3793,3795,3797,3799,3801,3803,3805,3807,3809,3811,3813,3815,3825,3827,3829,3841,3843,3845,3847,3849,3851,3853,3855,3865],{},[1681,3784,3785,3787],{},[898,3786,1655],{},[895,3788,3789,3791],{},[898,3790,1689],{},[898,3792,724],{},[1761,3794,1909],{},[1761,3796,1915],{"stretchy":1821},[1765,3798,2318],{},[1761,3800,1964],{},[1765,3802,2340],{},[1761,3804,1920],{"stretchy":1821},[1761,3806,1885],{},[1765,3808,2454],{},[1761,3810,1909],{},[1765,3812,2296],{},[2761,3814,2763],{},[895,3816,3817,3819],{},[2761,3818,2768],{},[2770,3820,3821,3823],{"accent":1833},[2761,3822,2774],{},[1761,3824,2777],{},[1761,3826,1834],{"separator":1833},[3315,3828],{"width":3317},[1681,3830,3831,3833],{},[898,3832,1655],{},[895,3834,3835,3837,3839],{},[898,3836,1713],{},[898,3838,1716],{},[898,3840,1719],{},[1761,3842,1909],{},[1765,3844,2454],{},[1761,3846,1885],{},[1765,3848,2318],{},[1761,3850,1909],{},[1765,3852,2318],{},[2761,3854,2763],{},[895,3856,3857,3859],{},[2761,3858,2768],{},[2770,3860,3861,3863],{"accent":1833},[2761,3862,2774],{},[1761,3864,2777],{},[898,3866,1741],{"mathvariant":1969},[902,3868,3869],{"encoding":904},"T_{sp} = (4 + 6) - 8 = 2\\ \\text{Kč}, \\qquad T_{vyr} = 8 - 4 = 4\\ \\text{Kč}.",[724,3871,3872,3873,1741],{},"Opět ",[883,3874,3876],{"className":3875},[886],[888,3877,3878],{"xmlns":890},[892,3879,3880,3914],{},[895,3881,3882,3892,3894,3906,3908,3910,3912],{},[1681,3883,3884,3886],{},[898,3885,1655],{},[895,3887,3888,3890],{},[898,3889,1689],{},[898,3891,724],{},[1761,3893,1964],{},[1681,3895,3896,3898],{},[898,3897,1655],{},[895,3899,3900,3902,3904],{},[898,3901,1713],{},[898,3903,1716],{},[898,3905,1719],{},[1761,3907,1909],{},[1765,3909,2340],{},[1761,3911,1909],{},[898,3913,1655],{},[902,3915,3916],{"encoding":904},"T_{sp} + T_{vyr} = 6 = T",[1849,3918],{},[115,3920,3922],{"id":3921},"daňové-břemeno","Daňové břemeno",[724,3924,3925,3927,3928,3931,3932,3945],{},[38,3926,3922],{}," (",[614,3929,3930],{},"tax burden",") je rozdělení zaplacené daně ",[883,3933,3935],{"className":3934},[886],[888,3936,3937],{"xmlns":890},[892,3938,3939,3943],{},[895,3940,3941],{},[898,3942,1655],{},[902,3944,1655],{"encoding":904}," mezi spotřebitele a výrobce:",[883,3947,3949],{"className":3948},[886],[888,3950,3951],{"xmlns":890,"display":1930},[892,3952,3953,3985],{},[895,3954,3955,3957,3959,3969,3971,3983],{},[898,3956,1655],{},[1761,3958,1909],{},[1681,3960,3961,3963],{},[898,3962,1655],{},[895,3964,3965,3967],{},[898,3966,1689],{},[898,3968,724],{},[1761,3970,1964],{},[1681,3972,3973,3975],{},[898,3974,1655],{},[895,3976,3977,3979,3981],{},[898,3978,1713],{},[898,3980,1716],{},[898,3982,1719],{},[898,3984,1741],{"mathvariant":1969},[902,3986,3987],{"encoding":904},"T = T_{sp} + T_{vyr}.",[724,3989,3990],{},[3991,3992],"img",{"alt":3993,"className":3994,"src":3996},"imek-dan-rozklad-bremene-sklony",[210,3995],"wikilink-broken","\u002Fwiki-assets\u002Fimek-dan-rozklad-bremene-sklony.jpeg",[1636,3998,3999],{},[724,4000,4001,4003,4004,2068,4017,1741],{},[883,4002,1642],{}," 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 ",[883,4005,4007],{"className":4006},[886],[888,4008,4009],{"xmlns":890},[892,4010,4011,4015],{},[895,4012,4013],{},[898,4014,2244],{},[902,4016,2244],{"encoding":904},[883,4018,4020],{"className":4019},[886],[888,4021,4022],{"xmlns":890},[892,4023,4024,4028],{},[895,4025,4026],{},[898,4027,1912],{},[902,4029,1912],{"encoding":904},[198,4031,4033],{"id":4032},"geometrická-interpretace","Geometrická interpretace",[724,4035,4036,4037,4059,4060,4073,4074,4091,4092,4105],{},"V grafu ",[883,4038,4040],{"className":4039},[886],[888,4041,4042],{"xmlns":890},[892,4043,4044,4056],{},[895,4045,4046,4048,4050,4052,4054],{},[1761,4047,1915],{"stretchy":1821},[898,4049,1828],{},[1761,4051,1834],{"separator":1833},[898,4053,1839],{},[1761,4055,1920],{"stretchy":1821},[902,4057,4058],{"encoding":904},"(Q, P)"," je svislá vzdálenost mezi původní a posunutou křivkou právě ",[883,4061,4063],{"className":4062},[886],[888,4064,4065],{"xmlns":890},[892,4066,4067,4071],{},[895,4068,4069],{},[898,4070,1655],{},[902,4072,1655],{"encoding":904},". Vedeme-li v novém rovnovážném bodě vodorovnou přímku na úrovni původní rovnovážné ceny ",[883,4075,4077],{"className":4076},[886],[888,4078,4079],{"xmlns":890},[892,4080,4081,4089],{},[895,4082,4083],{},[1824,4084,4085,4087],{},[898,4086,1839],{},[898,4088,1818],{},[902,4090,2161],{"encoding":904},", rozdělí se úsečka ",[883,4093,4095],{"className":4094},[886],[888,4096,4097],{"xmlns":890},[892,4098,4099,4103],{},[895,4100,4101],{},[898,4102,1655],{},[902,4104,1655],{"encoding":904}," na dvě části:",[120,4107,4108,4133],{},[123,4109,4110,4111,4132],{},"horní část odpovídá ",[883,4112,4114],{"className":4113},[886],[888,4115,4116],{"xmlns":890},[892,4117,4118,4130],{},[895,4119,4120],{},[1681,4121,4122,4124],{},[898,4123,1655],{},[895,4125,4126,4128],{},[898,4127,1689],{},[898,4129,724],{},[902,4131,1694],{"encoding":904}," (o kolik vzrostla cena placená spotřebitelem),",[123,4134,4135,4136,4159],{},"dolní část odpovídá ",[883,4137,4139],{"className":4138},[886],[888,4140,4141],{"xmlns":890},[892,4142,4143,4157],{},[895,4144,4145],{},[1681,4146,4147,4149],{},[898,4148,1655],{},[895,4150,4151,4153,4155],{},[898,4152,1713],{},[898,4154,1716],{},[898,4156,1719],{},[902,4158,1722],{"encoding":904}," (o kolik klesla cena přijímaná výrobcem).",[724,4161,4162],{},[614,4163,4164,4165,4178,4179,4200,4201,4224,4225,2068,4246,4269],{},"Obrázky 2.20 a 2.21: Ilustrace rozkladu svislé vzdálenosti ",[883,4166,4168],{"className":4167},[886],[888,4169,4170],{"xmlns":890},[892,4171,4172,4176],{},[895,4173,4174],{},[898,4175,1655],{},[902,4177,1655],{"encoding":904}," na ",[883,4180,4182],{"className":4181},[886],[888,4183,4184],{"xmlns":890},[892,4185,4186,4198],{},[895,4187,4188],{},[1681,4189,4190,4192],{},[898,4191,1655],{},[895,4193,4194,4196],{},[898,4195,1689],{},[898,4197,724],{},[902,4199,1694],{"encoding":904}," (nahoře) a ",[883,4202,4204],{"className":4203},[886],[888,4205,4206],{"xmlns":890},[892,4207,4208,4222],{},[895,4209,4210],{},[1681,4211,4212,4214],{},[898,4213,1655],{},[895,4215,4216,4218,4220],{},[898,4217,1713],{},[898,4219,1716],{},[898,4221,1719],{},[902,4223,1722],{"encoding":904}," (dole). Obrázek 2.21 porovnává obě varianty — daň výrobci vs. daň spotřebiteli — a ukazuje, že velikost ",[883,4226,4228],{"className":4227},[886],[888,4229,4230],{"xmlns":890},[892,4231,4232,4244],{},[895,4233,4234],{},[1681,4235,4236,4238],{},[898,4237,1655],{},[895,4239,4240,4242],{},[898,4241,1689],{},[898,4243,724],{},[902,4245,1694],{"encoding":904},[883,4247,4249],{"className":4248},[886],[888,4250,4251],{"xmlns":890},[892,4252,4253,4267],{},[895,4254,4255],{},[1681,4256,4257,4259],{},[898,4258,1655],{},[895,4260,4261,4263,4265],{},[898,4262,1713],{},[898,4264,1716],{},[898,4266,1719],{},[902,4268,1722],{"encoding":904}," je v obou případech stejná.",[198,4271,4273],{"id":4272},"sklony-křivek-a-rozklad","Sklony křivek a rozklad",[724,4275,4276,4277,4280,4281,3927,4306,4324,4325,3927,4350,4368],{},"Platí obecně: ",[38,4278,4279],{},"čím strmější křivka (menší elasticita), tím větší část daně nese daná strana trhu."," Pro lineární poptávku ",[883,4282,4284],{"className":4283},[886],[888,4285,4286],{"xmlns":890},[892,4287,4288,4303],{},[895,4289,4290,4292,4294,4296,4298,4300],{},[898,4291,1839],{},[1761,4293,1909],{},[898,4295,207],{},[898,4297,1828],{},[1761,4299,1964],{},[898,4301,4302],{},"b",[902,4304,4305],{"encoding":904},"P = aQ + b",[883,4307,4309],{"className":4308},[886],[888,4310,4311],{"xmlns":890},[892,4312,4313,4321],{},[895,4314,4315,4317,4319],{},[898,4316,207],{},[1761,4318,2058],{},[1765,4320,1767],{},[902,4322,4323],{"encoding":904},"a \u003C 0",") a lineární nabídku ",[883,4326,4328],{"className":4327},[886],[888,4329,4330],{"xmlns":890},[892,4331,4332,4347],{},[895,4333,4334,4336,4338,4340,4342,4344],{},[898,4335,1839],{},[1761,4337,1909],{},[898,4339,2774],{},[898,4341,1828],{},[1761,4343,1964],{},[898,4345,4346],{},"d",[902,4348,4349],{"encoding":904},"P = cQ + d",[883,4351,4353],{"className":4352},[886],[888,4354,4355],{"xmlns":890},[892,4356,4357,4365],{},[895,4358,4359,4361,4363],{},[898,4360,2774],{},[1761,4362,1763],{},[1765,4364,1767],{},[902,4366,4367],{"encoding":904},"c > 0",") lze rozklad odvodit pomocí multiplikátorů a platí",[883,4370,4372],{"className":4371},[886],[888,4373,4374],{"xmlns":890,"display":1930},[892,4375,4376,4443],{},[895,4377,4378,4403,4405,4415,4417,4441],{},[4379,4380,4381,4391],"mfrac",{},[1681,4382,4383,4385],{},[898,4384,1655],{},[895,4386,4387,4389],{},[898,4388,1689],{},[898,4390,724],{},[1681,4392,4393,4395],{},[898,4394,1655],{},[895,4396,4397,4399,4401],{},[898,4398,1713],{},[898,4400,1716],{},[898,4402,1719],{},[1761,4404,1909],{},[4379,4406,4407,4409],{},[898,4408,2774],{},[895,4410,4411,4413],{},[1761,4412,1885],{},[898,4414,207],{},[1761,4416,1909],{},[4379,4418,4419,4431],{},[895,4420,4421,4424,4427,4429],{},[898,4422,4423],{"mathvariant":1969},"∣",[2761,4425,4426],{},"sklon ",[898,4428,1912],{},[898,4430,4423],{"mathvariant":1969},[895,4432,4433,4435,4437,4439],{},[898,4434,4423],{"mathvariant":1969},[2761,4436,4426],{},[898,4438,2244],{},[898,4440,4423],{"mathvariant":1969},[898,4442,1741],{"mathvariant":1969},[902,4444,4445],{"encoding":904},"\\frac{T_{sp}}{T_{vyr}} = \\frac{c}{-a} = \\frac{|\\text{sklon } S|}{|\\text{sklon } D|}.",[1636,4447,4448,4454],{},[724,4449,4450,4453],{},[883,4451,4452],{},"!tip"," Postup výpočtu rozkladu",[152,4455,4456,4491,4546,4629],{},[123,4457,4458,4459,4490],{},"Spočti rovnovážný bod ",[883,4460,4462],{"className":4461},[886],[888,4463,4464],{"xmlns":890},[892,4465,4466,4488],{},[895,4467,4468,4470,4472,4478,4480,4486],{},[898,4469,1818],{},[1761,4471,1822],{"stretchy":1821},[1824,4473,4474,4476],{},[898,4475,1828],{},[898,4477,1818],{},[1761,4479,1834],{"separator":1833},[1824,4481,4482,4484],{},[898,4483,1839],{},[898,4485,1818],{},[1761,4487,1844],{"stretchy":1821},[902,4489,1847],{"encoding":904}," bez daně.",[123,4492,4493,4494,1348,4520,2162],{},"Urči posunutou křivku (",[883,4495,4497],{"className":4496},[886],[888,4498,4499],{"xmlns":890},[892,4500,4501,4517],{},[895,4502,4503,4509,4511,4513,4515],{},[1681,4504,4505,4507],{},[898,4506,1912],{},[1765,4508,1945],{},[1761,4510,1909],{},[898,4512,1912],{},[1761,4514,1964],{},[898,4516,1655],{},[902,4518,4519],{"encoding":904},"S_1 = S + T",[883,4521,4523],{"className":4522},[886],[888,4524,4525],{"xmlns":890},[892,4526,4527,4543],{},[895,4528,4529,4535,4537,4539,4541],{},[1681,4530,4531,4533],{},[898,4532,2244],{},[1765,4534,2296],{},[1761,4536,1909],{},[898,4538,2244],{},[1761,4540,1885],{},[898,4542,1655],{},[902,4544,4545],{"encoding":904},"D_2 = D - T",[123,4547,4548,4549,4569,4570,4590,4591,4569,4610,2162],{},"Vyřeš novou rovnovážnou rovnici — získáš ",[883,4550,4552],{"className":4551},[886],[888,4553,4554],{"xmlns":890},[892,4555,4556,4566],{},[895,4557,4558],{},[2015,4559,4560,4562,4564],{},[898,4561,1828],{},[1765,4563,1945],{},[898,4565,1818],{},[902,4567,4568],{"encoding":904},"Q_1^E"," (resp. ",[883,4571,4573],{"className":4572},[886],[888,4574,4575],{"xmlns":890},[892,4576,4577,4587],{},[895,4578,4579],{},[2015,4580,4581,4583,4585],{},[898,4582,1828],{},[1765,4584,2296],{},[898,4586,1818],{},[902,4588,4589],{"encoding":904},"Q_2^E",") a ",[883,4592,4594],{"className":4593},[886],[888,4595,4596],{"xmlns":890},[892,4597,4598,4608],{},[895,4599,4600],{},[2015,4601,4602,4604,4606],{},[898,4603,1839],{},[1765,4605,1945],{},[898,4607,1818],{},[902,4609,2117],{"encoding":904},[883,4611,4613],{"className":4612},[886],[888,4614,4615],{"xmlns":890},[892,4616,4617,4627],{},[895,4618,4619],{},[2015,4620,4621,4623,4625],{},[898,4622,1839],{},[1765,4624,2296],{},[898,4626,1818],{},[902,4628,3220],{"encoding":904},[123,4630,4631,4632,2068,4653,4676,4677,1741],{},"Dopočítej ",[883,4633,4635],{"className":4634},[886],[888,4636,4637],{"xmlns":890},[892,4638,4639,4651],{},[895,4640,4641],{},[1681,4642,4643,4645],{},[898,4644,1655],{},[895,4646,4647,4649],{},[898,4648,1689],{},[898,4650,724],{},[902,4652,1694],{"encoding":904},[883,4654,4656],{"className":4655},[886],[888,4657,4658],{"xmlns":890},[892,4659,4660,4674],{},[895,4661,4662],{},[1681,4663,4664,4666],{},[898,4665,1655],{},[895,4667,4668,4670,4672],{},[898,4669,1713],{},[898,4671,1716],{},[898,4673,1719],{},[902,4675,1722],{"encoding":904}," z definice, vždy ověř ",[883,4678,4680],{"className":4679},[886],[888,4681,4682],{"xmlns":890},[892,4683,4684,4714],{},[895,4685,4686,4696,4698,4710,4712],{},[1681,4687,4688,4690],{},[898,4689,1655],{},[895,4691,4692,4694],{},[898,4693,1689],{},[898,4695,724],{},[1761,4697,1964],{},[1681,4699,4700,4702],{},[898,4701,1655],{},[895,4703,4704,4706,4708],{},[898,4705,1713],{},[898,4707,1716],{},[898,4709,1719],{},[1761,4711,1909],{},[898,4713,1655],{},[902,4715,4716],{"encoding":904},"T_{sp} + T_{vyr} = T",[1636,4718,4719],{},[724,4720,4721,4724,4725,4728,4729,2068,4742,4755],{},[883,4722,4723],{},"!warning"," Pozor — zákonný vs. ekonomický nositel daně\nI když zákon ukládá daň formálně pouze jedné straně (výrobci nebo spotřebiteli), ",[38,4726,4727],{},"ekonomicky ji vždy nesou obě strany",". Skutečné rozdělení určují sklony ",[883,4730,4732],{"className":4731},[886],[888,4733,4734],{"xmlns":890},[892,4735,4736,4740],{},[895,4737,4738],{},[898,4739,2244],{},[902,4741,2244],{"encoding":904},[883,4743,4745],{"className":4744},[886],[888,4746,4747],{"xmlns":890},[892,4748,4749,4753],{},[895,4750,4751],{},[898,4752,1912],{},[902,4754,1912],{"encoding":904},", nikoli paragrafové znění zákona. Kupující a prodávající tak fakticky platí daň bez ohledu na to, na koho je uvalena.",[1849,4757],{},[115,4759,4761],{"id":4760},"ekvivalence-obou-přístupů","Ekvivalence obou přístupů",[724,4763,4764],{},"Porovnáním Příkladu 2.9 (daň výrobci) a Příkladu 2.10 (daň spotřebiteli) zjistíme:",[724,4766,4767],{},[3991,4768],{"alt":4769,"className":4770,"src":4771},"imek-dan-ekvivalence-vyrobce-spotrebitel",[210,3995],"\u002Fwiki-assets\u002Fimek-dan-ekvivalence-vyrobce-spotrebitel.jpeg",[16,4773,4774,4787],{},[19,4775,4776],{},[22,4777,4778,4781,4784],{},[25,4779,4780],{},"Veličina",[25,4782,4783],{},"(a) daň výrobci",[25,4785,4786],{},"(b) daň spotřebiteli",[30,4788,4789,4844,4911,4971],{},[22,4790,4791,4794,4819],{},[35,4792,4793],{},"Rovnovážné množství",[35,4795,4796],{},[883,4797,4799],{"className":4798},[886],[888,4800,4801],{"xmlns":890},[892,4802,4803,4817],{},[895,4804,4805,4813,4815],{},[2015,4806,4807,4809,4811],{},[898,4808,1828],{},[1765,4810,1945],{},[898,4812,1818],{},[1761,4814,1909],{},[1765,4816,1945],{},[902,4818,2599],{"encoding":904},[35,4820,4821],{},[883,4822,4824],{"className":4823},[886],[888,4825,4826],{"xmlns":890},[892,4827,4828,4842],{},[895,4829,4830,4838,4840],{},[2015,4831,4832,4834,4836],{},[898,4833,1828],{},[1765,4835,2296],{},[898,4837,1818],{},[1761,4839,1909],{},[1765,4841,1945],{},[902,4843,3644],{"encoding":904},[22,4845,4846,4849,4874],{},[35,4847,4848],{},"Cena placená spotřebitelem",[35,4850,4851],{},[883,4852,4854],{"className":4853},[886],[888,4855,4856],{"xmlns":890},[892,4857,4858,4872],{},[895,4859,4860,4868,4870],{},[2015,4861,4862,4864,4866],{},[898,4863,1839],{},[1765,4865,1945],{},[898,4867,1818],{},[1761,4869,1909],{},[1765,4871,2633],{},[902,4873,2695],{"encoding":904},[35,4875,4876],{},[883,4877,4879],{"className":4878},[886],[888,4880,4881],{"xmlns":890},[892,4882,4883,4909],{},[895,4884,4885,4893,4895,4897,4899,4901,4903,4905,4907],{},[2015,4886,4887,4889,4891],{},[898,4888,1839],{},[1765,4890,2296],{},[898,4892,1818],{},[1761,4894,1964],{},[898,4896,1655],{},[1761,4898,1909],{},[1765,4900,2318],{},[1761,4902,1964],{},[1765,4904,2340],{},[1761,4906,1909],{},[1765,4908,2633],{},[902,4910,3743],{"encoding":904},[22,4912,4913,4916,4946],{},[35,4914,4915],{},"Cena přijímaná výrobcem",[35,4917,4918],{},[883,4919,4921],{"className":4920},[886],[888,4922,4923],{"xmlns":890},[892,4924,4925,4943],{},[895,4926,4927,4935,4937,4939,4941],{},[2015,4928,4929,4931,4933],{},[898,4930,1839],{},[1765,4932,1945],{},[898,4934,1818],{},[1761,4936,1885],{},[898,4938,1655],{},[1761,4940,1909],{},[1765,4942,2318],{},[902,4944,4945],{"encoding":904},"P_1^E - T = 4",[35,4947,4948],{},[883,4949,4951],{"className":4950},[886],[888,4952,4953],{"xmlns":890},[892,4954,4955,4969],{},[895,4956,4957,4965,4967],{},[2015,4958,4959,4961,4963],{},[898,4960,1839],{},[1765,4962,2296],{},[898,4964,1818],{},[1761,4966,1909],{},[1765,4968,2318],{},[902,4970,3768],{"encoding":904},[22,4972,4973,4976,5032],{},[35,4974,4975],{},"Rozklad břemene",[35,4977,4978,1343,5004],{},[883,4979,4981],{"className":4980},[886],[888,4982,4983],{"xmlns":890},[892,4984,4985,5001],{},[895,4986,4987,4997,4999],{},[1681,4988,4989,4991],{},[898,4990,1655],{},[895,4992,4993,4995],{},[898,4994,1689],{},[898,4996,724],{},[1761,4998,1909],{},[1765,5000,2296],{},[902,5002,5003],{"encoding":904},"T_{sp} = 2",[883,5005,5007],{"className":5006},[886],[888,5008,5009],{"xmlns":890},[892,5010,5011,5029],{},[895,5012,5013,5025,5027],{},[1681,5014,5015,5017],{},[898,5016,1655],{},[895,5018,5019,5021,5023],{},[898,5020,1713],{},[898,5022,1716],{},[898,5024,1719],{},[1761,5026,1909],{},[1765,5028,2318],{},[902,5030,5031],{"encoding":904},"T_{vyr} = 4",[35,5033,5034,1343,5059],{},[883,5035,5037],{"className":5036},[886],[888,5038,5039],{"xmlns":890},[892,5040,5041,5057],{},[895,5042,5043,5053,5055],{},[1681,5044,5045,5047],{},[898,5046,1655],{},[895,5048,5049,5051],{},[898,5050,1689],{},[898,5052,724],{},[1761,5054,1909],{},[1765,5056,2296],{},[902,5058,5003],{"encoding":904},[883,5060,5062],{"className":5061},[886],[888,5063,5064],{"xmlns":890},[892,5065,5066,5084],{},[895,5067,5068,5080,5082],{},[1681,5069,5070,5072],{},[898,5071,1655],{},[895,5073,5074,5076,5078],{},[898,5075,1713],{},[898,5077,1716],{},[898,5079,1719],{},[1761,5081,1909],{},[1765,5083,2318],{},[902,5085,5031],{"encoding":904},[724,5087,5088],{},"Výsledek je v obou režimech reálně totožný — liší se pouze to, kterou cenu nazveme \"tržní\":",[883,5090,5092],{"className":5091},[886],[888,5093,5094],{"xmlns":890,"display":1930},[892,5095,5096,5144],{},[895,5097,5098,5106,5108,5116,5118,5120,5128,5130,5132,5134,5142],{},[2015,5099,5100,5102,5104],{},[898,5101,1828],{},[1765,5103,1945],{},[898,5105,1818],{},[1761,5107,1909],{},[2015,5109,5110,5112,5114],{},[898,5111,1828],{},[1765,5113,2296],{},[898,5115,1818],{},[1761,5117,1834],{"separator":1833},[3315,5119],{"width":3317},[2015,5121,5122,5124,5126],{},[898,5123,1839],{},[1765,5125,1945],{},[898,5127,1818],{},[1761,5129,1885],{},[898,5131,1655],{},[1761,5133,1909],{},[2015,5135,5136,5138,5140],{},[898,5137,1839],{},[1765,5139,2296],{},[898,5141,1818],{},[898,5143,1741],{"mathvariant":1969},[902,5145,5146],{"encoding":904},"Q_1^E = Q_2^E, \\qquad P_1^E - T = P_2^E.",[1636,5148,5149,5168,5324],{},[724,5150,5151,5153,5154,5167],{},[883,5152,4452],{}," Věta o ekvivalenci zdanění\nNezávisle na tom, zda je jednotková daň ",[883,5155,5157],{"className":5156},[886],[888,5158,5159],{"xmlns":890},[892,5160,5161,5165],{},[895,5162,5163],{},[898,5164,1655],{},[902,5166,1655],{"encoding":904}," uložena výrobci, nebo spotřebiteli, se po jejím uložení rovnají:",[120,5169,5170,5203,5240,5277],{},[123,5171,5172,5173,1834],{},"rovnovážná množství obou režimů, ",[883,5174,5176],{"className":5175},[886],[888,5177,5178],{"xmlns":890},[892,5179,5180,5200],{},[895,5181,5182,5190,5192],{},[2015,5183,5184,5186,5188],{},[898,5185,1828],{},[1765,5187,1945],{},[898,5189,1818],{},[1761,5191,1909],{},[2015,5193,5194,5196,5198],{},[898,5195,1828],{},[1765,5197,2296],{},[898,5199,1818],{},[902,5201,5202],{"encoding":904},"Q_1^E = Q_2^E",[123,5204,5205,5206,1834],{},"čistá cena přijímaná výrobcem, ",[883,5207,5209],{"className":5208},[886],[888,5210,5211],{"xmlns":890},[892,5212,5213,5237],{},[895,5214,5215,5223,5225,5227,5229],{},[2015,5216,5217,5219,5221],{},[898,5218,1839],{},[1765,5220,1945],{},[898,5222,1818],{},[1761,5224,1885],{},[898,5226,1655],{},[1761,5228,1909],{},[2015,5230,5231,5233,5235],{},[898,5232,1839],{},[1765,5234,2296],{},[898,5236,1818],{},[902,5238,5239],{"encoding":904},"P_1^E - T = P_2^E",[123,5241,5242,5243,1834],{},"celková cena placená spotřebitelem, ",[883,5244,5246],{"className":5245},[886],[888,5247,5248],{"xmlns":890},[892,5249,5250,5274],{},[895,5251,5252,5260,5262,5270,5272],{},[2015,5253,5254,5256,5258],{},[898,5255,1839],{},[1765,5257,1945],{},[898,5259,1818],{},[1761,5261,1909],{},[2015,5263,5264,5266,5268],{},[898,5265,1839],{},[1765,5267,2296],{},[898,5269,1818],{},[1761,5271,1964],{},[898,5273,1655],{},[902,5275,5276],{"encoding":904},"P_1^E = P_2^E + T",[123,5278,5279,5280,2068,5301,1741],{},"rozklad daňového břemene ",[883,5281,5283],{"className":5282},[886],[888,5284,5285],{"xmlns":890},[892,5286,5287,5299],{},[895,5288,5289],{},[1681,5290,5291,5293],{},[898,5292,1655],{},[895,5294,5295,5297],{},[898,5296,1689],{},[898,5298,724],{},[902,5300,1694],{"encoding":904},[883,5302,5304],{"className":5303},[886],[888,5305,5306],{"xmlns":890},[892,5307,5308,5322],{},[895,5309,5310],{},[1681,5311,5312,5314],{},[898,5313,1655],{},[895,5315,5316,5318,5320],{},[898,5317,1713],{},[898,5319,1716],{},[898,5321,1719],{},[902,5323,1722],{"encoding":904},[724,5325,5326,5327,1741],{},"Z hlediska reálných dopadů na trh (objem transakcí, reálné platby stran) jsou tedy obě formy zdanění ",[38,5328,5329],{},"ekvivalentní",[724,5331,5332,5333,2068,5346,2162],{},"Ekvivalence má zásadní politickou implikaci: otázka, \"kdo má platit daň\", je z hlediska trhu formální — skutečné rozdělení určuje struktura trhu (sklony ",[883,5334,5336],{"className":5335},[886],[888,5337,5338],{"xmlns":890},[892,5339,5340,5344],{},[895,5341,5342],{},[898,5343,2244],{},[902,5345,2244],{"encoding":904},[883,5347,5349],{"className":5348},[886],[888,5350,5351],{"xmlns":890},[892,5352,5353,5357],{},[895,5354,5355],{},[898,5356,1912],{},[902,5358,1912],{"encoding":904},[1849,5360],{},[115,5362,5364],{"id":5363},"úlohy","Úlohy",[724,5366,5367,5368,5372],{},"Z kapitoly 2 se zdanění týkají zejména následující úlohy (zadání v hub-page ",[207,5369,5371],{"className":5370,"dataFsResolvedFilePath":800,"href":801},[210],"poptavka-nabidka","):",[120,5374,5375,5405,5438],{},[123,5376,5377,5380,5381,5404],{},[38,5378,5379],{},"Úloha 2.4"," — Poptávka ",[883,5382,5384],{"className":5383},[886],[888,5385,5386],{"xmlns":890},[892,5387,5388,5402],{},[895,5389,5390,5392,5394,5396,5398,5400],{},[898,5391,1839],{},[1761,5393,1909],{},[1765,5395,2291],{},[1761,5397,1885],{},[1765,5399,2296],{},[898,5401,1828],{},[902,5403,2301],{"encoding":904},"; najděte novou poptávku po uložení daně 6 Kč na kupujícího.",[123,5406,5407,5410,5411,5437],{},[38,5408,5409],{},"Úloha 2.9"," — Nabídka ",[883,5412,5414],{"className":5413},[886],[888,5415,5416],{"xmlns":890},[892,5417,5418,5434],{},[895,5419,5420,5422,5424,5427,5429,5431],{},[898,5421,1839],{},[1761,5423,1909],{},[1765,5425,5426],{},"0,5",[898,5428,1828],{},[1761,5430,1964],{},[1765,5432,5433],{},"15",[902,5435,5436],{"encoding":904},"P = 0{,}5Q + 15","; najděte novou nabídku po uložení daně 5 Kč na výrobce.",[123,5439,5440,5443,5444,2068,5471,5496,5497,5516],{},[38,5441,5442],{},"Úloha 2.13"," — Komplexní úloha se zadáním ",[883,5445,5447],{"className":5446},[886],[888,5448,5449],{"xmlns":890},[892,5450,5451,5468],{},[895,5452,5453,5455,5457,5459,5461,5463,5465],{},[898,5454,1839],{},[1761,5456,1909],{},[1761,5458,1885],{},[1765,5460,2318],{},[898,5462,1828],{},[1761,5464,1964],{},[1765,5466,5467],{},"80",[902,5469,5470],{"encoding":904},"P = -4Q + 80",[883,5472,5474],{"className":5473},[886],[888,5475,5476],{"xmlns":890},[892,5477,5478,5493],{},[895,5479,5480,5482,5484,5487,5489,5491],{},[898,5481,1839],{},[1761,5483,1909],{},[1765,5485,5486],{},"3",[898,5488,1828],{},[1761,5490,1964],{},[1765,5492,2633],{},[902,5494,5495],{"encoding":904},"P = 3Q + 10",": rovnováha, daň ",[883,5498,5500],{"className":5499},[886],[888,5501,5502],{"xmlns":890},[892,5503,5504,5513],{},[895,5505,5506,5508,5510],{},[898,5507,1655],{},[1761,5509,1909],{},[1765,5511,5512],{},"7",[902,5514,5515],{"encoding":904},"T = 7"," Kč uložená postupně výrobci i spotřebiteli, rozklad daňového břemene a analýza ekvivalence.",[724,5518,5519,5520,5523,5524,5527],{},"Související úvodní příklady posunu křivek při zdanění: ",[38,5521,5522],{},"Příklad 2.3"," (posun poptávky při zdanění kupujícího) a ",[38,5525,5526],{},"Příklad 2.6"," (posun nabídky při zdanění výrobce).",[1849,5529],{},[115,5531,5533],{"id":5532},"klíčové-pojmy","Klíčové pojmy",[120,5535,5536,5555,5613,5670,5755,5802,5845,5890,5957],{},[123,5537,5538,1989,5541,5554],{},[38,5539,5540],{},"Jednotková daň",[883,5542,5544],{"className":5543},[886],[888,5545,5546],{"xmlns":890},[892,5547,5548,5552],{},[895,5549,5550],{},[898,5551,1655],{},[902,5553,1655],{"encoding":904}," — fixní částka na každou prodanou jednotku zboží",[123,5556,5557,5559,5560,5598,5599,5612],{},[38,5558,1854],{}," — posun nabídky ",[883,5561,5563],{"className":5562},[886],[888,5564,5565],{"xmlns":890},[892,5566,5567,5595],{},[895,5568,5569,5575,5577,5579,5581,5583,5585,5587,5589,5591,5593],{},[1681,5570,5571,5573],{},[898,5572,1912],{},[1765,5574,1945],{},[1761,5576,1915],{"stretchy":1821},[898,5578,1828],{},[1761,5580,1920],{"stretchy":1821},[1761,5582,1909],{},[898,5584,1912],{},[1761,5586,1915],{"stretchy":1821},[898,5588,1828],{},[1761,5590,1920],{"stretchy":1821},[1761,5592,1964],{},[898,5594,1655],{},[902,5596,5597],{"encoding":904},"S_1(Q) = S(Q) + T"," (o ",[883,5600,5602],{"className":5601},[886],[888,5603,5604],{"xmlns":890},[892,5605,5606,5610],{},[895,5607,5608],{},[898,5609,1655],{},[902,5611,1655],{"encoding":904}," svisle nahoru)",[123,5614,5615,5617,5618,5598,5656,5669],{},[38,5616,2973],{}," — posun poptávky ",[883,5619,5621],{"className":5620},[886],[888,5622,5623],{"xmlns":890},[892,5624,5625,5653],{},[895,5626,5627,5633,5635,5637,5639,5641,5643,5645,5647,5649,5651],{},[1681,5628,5629,5631],{},[898,5630,2244],{},[1765,5632,2296],{},[1761,5634,1915],{"stretchy":1821},[898,5636,1828],{},[1761,5638,1920],{"stretchy":1821},[1761,5640,1909],{},[898,5642,2244],{},[1761,5644,1915],{"stretchy":1821},[898,5646,1828],{},[1761,5648,1920],{"stretchy":1821},[1761,5650,1885],{},[898,5652,1655],{},[902,5654,5655],{"encoding":904},"D_2(Q) = D(Q) - T",[883,5657,5659],{"className":5658},[886],[888,5660,5661],{"xmlns":890},[892,5662,5663,5667],{},[895,5664,5665],{},[898,5666,1655],{},[902,5668,1655],{"encoding":904}," svisle dolů)",[123,5671,5672,5675,5676,5715,5716],{},[38,5673,5674],{},"Rovnovážný bod s daní"," — ",[883,5677,5679],{"className":5678},[886],[888,5680,5681],{"xmlns":890},[892,5682,5683,5713],{},[895,5684,5685,5691,5693,5701,5703,5711],{},[1681,5686,5687,5689],{},[898,5688,1818],{},[1765,5690,1945],{},[1761,5692,1822],{"stretchy":1821},[2015,5694,5695,5697,5699],{},[898,5696,1828],{},[1765,5698,1945],{},[898,5700,1818],{},[1761,5702,1834],{"separator":1833},[2015,5704,5705,5707,5709],{},[898,5706,1839],{},[1765,5708,1945],{},[898,5710,1818],{},[1761,5712,1844],{"stretchy":1821},[902,5714,2037],{"encoding":904},", resp. ",[883,5717,5719],{"className":5718},[886],[888,5720,5721],{"xmlns":890},[892,5722,5723,5753],{},[895,5724,5725,5731,5733,5741,5743,5751],{},[1681,5726,5727,5729],{},[898,5728,1818],{},[1765,5730,2296],{},[1761,5732,1822],{"stretchy":1821},[2015,5734,5735,5737,5739],{},[898,5736,1828],{},[1765,5738,2296],{},[898,5740,1818],{},[1761,5742,1834],{"separator":1833},[2015,5744,5745,5747,5749],{},[898,5746,1839],{},[1765,5748,2296],{},[898,5750,1818],{},[1761,5752,1844],{"stretchy":1821},[902,5754,3143],{"encoding":904},[123,5756,5757,3927,5759,5761,5762],{},[38,5758,3922],{},[614,5760,3930],{},") — rozklad ",[883,5763,5765],{"className":5764},[886],[888,5766,5767],{"xmlns":890},[892,5768,5769,5799],{},[895,5770,5771,5773,5775,5785,5787],{},[898,5772,1655],{},[1761,5774,1909],{},[1681,5776,5777,5779],{},[898,5778,1655],{},[895,5780,5781,5783],{},[898,5782,1689],{},[898,5784,724],{},[1761,5786,1964],{},[1681,5788,5789,5791],{},[898,5790,1655],{},[895,5792,5793,5795,5797],{},[898,5794,1713],{},[898,5796,1716],{},[898,5798,1719],{},[902,5800,5801],{"encoding":904},"T = T_{sp} + T_{vyr}",[123,5803,5804,5827,5828,1920],{},[38,5805,5806],{},[883,5807,5809],{"className":5808},[886],[888,5810,5811],{"xmlns":890},[892,5812,5813,5825],{},[895,5814,5815],{},[1681,5816,5817,5819],{},[898,5818,1655],{},[895,5820,5821,5823],{},[898,5822,1689],{},[898,5824,724],{},[902,5826,1694],{"encoding":904}," — část daně nesená spotřebitelem (navýšení ceny nad ",[883,5829,5831],{"className":5830},[886],[888,5832,5833],{"xmlns":890},[892,5834,5835,5843],{},[895,5836,5837],{},[1824,5838,5839,5841],{},[898,5840,1839],{},[898,5842,1818],{},[902,5844,2161],{"encoding":904},[123,5846,5847,5872,5873,1920],{},[38,5848,5849],{},[883,5850,5852],{"className":5851},[886],[888,5853,5854],{"xmlns":890},[892,5855,5856,5870],{},[895,5857,5858],{},[1681,5859,5860,5862],{},[898,5861,1655],{},[895,5863,5864,5866,5868],{},[898,5865,1713],{},[898,5867,1716],{},[898,5869,1719],{},[902,5871,1722],{"encoding":904}," — část daně nesená výrobcem (pokles čisté přijímané ceny pod ",[883,5874,5876],{"className":5875},[886],[888,5877,5878],{"xmlns":890},[892,5879,5880,5888],{},[895,5881,5882],{},[1824,5883,5884,5886],{},[898,5885,1839],{},[898,5887,1818],{},[902,5889,2161],{"encoding":904},[123,5891,5892,5675,5895,1343,5924],{},[38,5893,5894],{},"Ekvivalence zdanění",[883,5896,5898],{"className":5897},[886],[888,5899,5900],{"xmlns":890},[892,5901,5902,5922],{},[895,5903,5904,5912,5914],{},[2015,5905,5906,5908,5910],{},[898,5907,1828],{},[1765,5909,1945],{},[898,5911,1818],{},[1761,5913,1909],{},[2015,5915,5916,5918,5920],{},[898,5917,1828],{},[1765,5919,2296],{},[898,5921,1818],{},[902,5923,5202],{"encoding":904},[883,5925,5927],{"className":5926},[886],[888,5928,5929],{"xmlns":890},[892,5930,5931,5955],{},[895,5932,5933,5941,5943,5945,5947],{},[2015,5934,5935,5937,5939],{},[898,5936,1839],{},[1765,5938,1945],{},[898,5940,1818],{},[1761,5942,1885],{},[898,5944,1655],{},[1761,5946,1909],{},[2015,5948,5949,5951,5953],{},[898,5950,1839],{},[1765,5952,2296],{},[898,5954,1818],{},[902,5956,5239],{"encoding":904},[123,5958,5959,5962],{},[38,5960,5961],{},"Zákonný vs. ekonomický nositel daně"," — rozdíl mezi formálním ustanovením zákona a skutečným rozdělením břemene",[1849,5964],{},[115,5966,5968],{"id":5967},"navigace","Navigace",[120,5970,5971,5979,6002,6011],{},[123,5972,5973,1989,5976],{},[38,5974,5975],{},"Kontext (hub):",[207,5977,802],{"className":5978,"dataFsResolvedFilePath":800,"href":801},[210],[123,5980,5981,1989,5984,5987,5988,5991,5992,5996,5997,6001],{},[38,5982,5983],{},"Související témata:",[207,5985,820],{"className":5986,"dataFsResolvedFilePath":818,"href":819},[210]," (daň vyvolává ztrátu blahobytu — ",[614,5989,5990],{},"deadweight loss","), ",[207,5993,5995],{"className":5994,"dataFsResolvedFilePath":764,"href":765},[210],"Derivace"," (sklony křivek, rovnovážný bod jako řešení soustavy), ",[207,5998,6000],{"className":5999,"dataFsResolvedFilePath":848,"href":849},[210],"Elasticita"," (kvantifikace, jak se daňové břemeno dělí podle citlivosti stran trhu)",[123,6003,6004,1989,6007],{},[38,6005,6006],{},"Shrnutí přednášek:",[207,6008,6010],{"className":6009,"dataFsResolvedFilePath":745,"href":746},[210],"KS — 1. blok",[123,6012,6013,1989,6016],{},[38,6014,6015],{},"Kurz:",[207,6017,6021],{"className":6018,"dataFsResolvedFilePath":6019,"href":6020},[210],"courses\u002Fimek.md","\u002Fwiki\u002Fimek","Matematická ekonomie",{"title":641,"searchDepth":642,"depth":642,"links":6023},[6024,6025,6028,6031,6035,6036,6037,6038],{"id":1744,"depth":642,"text":1745},{"id":1853,"depth":642,"text":1854,"children":6026},[6027],{"id":2268,"depth":649,"text":2269},{"id":2972,"depth":642,"text":2973,"children":6029},[6030],{"id":3453,"depth":649,"text":3454},{"id":3921,"depth":642,"text":3922,"children":6032},[6033,6034],{"id":4032,"depth":649,"text":4033},{"id":4272,"depth":649,"text":4273},{"id":4760,"depth":642,"text":4761},{"id":5363,"depth":642,"text":5364},{"id":5532,"depth":642,"text":5533},{"id":5967,"depth":642,"text":5968},"2026-04-22",{},"\u002Ftopics\u002Fzdaneni-trhu",{"title":1629,"description":641},[1138,1135],"topics\u002Fzdaneni-trhu",[1128,6046,6047,6048,6049,5371],"zdaneni","dane","danove-bremeno","posun-krivek","topic","cFuKqHgzIrqvY-l4jNdqjFEM7_ixjw33HOL0So8cPn0","topics",{"zapisku":1625,"topics":6054,"summaries":6055,"outputs":6056},15,5,1,[6058,7919,13608,15163,16035,20312,21919,31796,40787,54806,59096,78440,90552,99510,99798],{"id":6059,"title":6060,"body":6061,"course":1128,"courses":659,"created":1129,"description":7908,"extension":661,"meta":7909,"navigation":664,"path":7910,"seo":7911,"sources":7912,"stem":7913,"tags":7914,"type":6050,"updated":677,"__hash__":7918},"topics\u002Ftopics\u002Fderivace.md","Derivace, diferenciál a extrémy funkcí jedné proměnné",{"type":9,"value":6062,"toc":7891},[6063,6066,6085,6089,6167,6170,6293,6438,6440,6522,6524,6583,6633,6640,6644,6778,6829,6833,6875,6943,7014,7022,7026,7065,7137,7141,7220,7268,7312,7316,7320,7390,7394,7444,7521,7528,7531,7583,7853,7855],[12,6064,6060],{"id":6065},"derivace-diferenciál-a-extrémy-funkcí-jedné-proměnné",[724,6067,6068,6069,6073,6074,6077,6078,6081,6082,1741],{},"Matematický aparát kurzu ",[207,6070,6072],{"className":6071,"dataFsResolvedFilePath":6019,"href":6020},[210],"ImeK",". Bez derivace se neobejdou ",[38,6075,6076],{},"mezní veličiny"," (mezní náklady, mezní příjem, mezní užitečnost), bez extrémů se neobejde ",[38,6079,6080],{},"maximalizace zisku"," ani ",[38,6083,6084],{},"minimalizace nákladů",[115,6086,6088],{"id":6087},"funkce-a-polynomy","Funkce a polynomy",[724,6090,6091,6092,6118,6119,6132,6133,6146,6147,1741],{},"Funkce jedné proměnné ",[883,6093,6095],{"className":6094},[886],[888,6096,6097],{"xmlns":890},[892,6098,6099,6115],{},[895,6100,6101,6103,6105,6108,6110,6113],{},[898,6102,1716],{},[1761,6104,1909],{},[898,6106,6107],{},"f",[1761,6109,1915],{"stretchy":1821},[898,6111,6112],{},"x",[1761,6114,1920],{"stretchy":1821},[902,6116,6117],{"encoding":904},"y = f(x)"," — předpis závislosti ",[883,6120,6122],{"className":6121},[886],[888,6123,6124],{"xmlns":890},[892,6125,6126,6130],{},[895,6127,6128],{},[898,6129,6112],{},[902,6131,6112],{"encoding":904}," (nezávislá) → ",[883,6134,6136],{"className":6135},[886],[888,6137,6138],{"xmlns":890},[892,6139,6140,6144],{},[895,6141,6142],{},[898,6143,1716],{},[902,6145,1716],{"encoding":904}," (závislá). Hodnota v bodě: ",[883,6148,6150],{"className":6149},[886],[888,6151,6152],{"xmlns":890},[892,6153,6154,6164],{},[895,6155,6156,6158,6160,6162],{},[898,6157,6107],{},[1761,6159,1915],{"stretchy":1821},[898,6161,207],{},[1761,6163,1920],{"stretchy":1821},[902,6165,6166],{"encoding":904},"f(a)",[724,6168,6169],{},"Polynomy:",[120,6171,6172,6203,6243],{},[123,6173,6174],{},[152,6175,6176],{},[123,6177,6178,6179],{},"stupně: ",[883,6180,6182],{"className":6181},[886],[888,6183,6184],{"xmlns":890},[892,6185,6186,6200],{},[895,6187,6188,6190,6192,6194,6196,6198],{},[898,6189,1716],{},[1761,6191,1909],{},[898,6193,207],{},[898,6195,6112],{},[1761,6197,1964],{},[898,6199,4302],{},[902,6201,6202],{"encoding":904},"y = ax + b",[123,6204,6205],{},[152,6206,6207],{"start":642},[123,6208,6178,6209],{},[883,6210,6212],{"className":6211},[886],[888,6213,6214],{"xmlns":890},[892,6215,6216,6240],{},[895,6217,6218,6220,6222,6224,6230,6232,6234,6236,6238],{},[898,6219,1716],{},[1761,6221,1909],{},[898,6223,207],{},[1824,6225,6226,6228],{},[898,6227,6112],{},[1765,6229,2296],{},[1761,6231,1964],{},[898,6233,4302],{},[898,6235,6112],{},[1761,6237,1964],{},[898,6239,2774],{},[902,6241,6242],{"encoding":904},"y = ax^2 + bx + c",[123,6244,6245],{},[152,6246,6247],{"start":649},[123,6248,6178,6249],{},[883,6250,6252],{"className":6251},[886],[888,6253,6254],{"xmlns":890},[892,6255,6256,6290],{},[895,6257,6258,6260,6262,6264,6270,6272,6274,6280,6282,6284,6286,6288],{},[898,6259,1716],{},[1761,6261,1909],{},[898,6263,207],{},[1824,6265,6266,6268],{},[898,6267,6112],{},[1765,6269,5486],{},[1761,6271,1964],{},[898,6273,4302],{},[1824,6275,6276,6278],{},[898,6277,6112],{},[1765,6279,2296],{},[1761,6281,1964],{},[898,6283,2774],{},[898,6285,6112],{},[1761,6287,1964],{},[898,6289,4346],{},[902,6291,6292],{"encoding":904},"y = ax^3 + bx^2 + cx + d",[724,6294,6295,1989,6298,6353,6354,6390,6391,1741],{},[38,6296,6297],{},"Příklad rozkladu:",[883,6299,6301],{"className":6300},[886],[888,6302,6303],{"xmlns":890},[892,6304,6305,6350],{},[895,6306,6307,6309,6311,6317,6319,6322,6324,6326,6328,6330,6332,6334,6336,6338,6340,6342,6344,6346,6348],{},[898,6308,1716],{},[1761,6310,1909],{},[1824,6312,6313,6315],{},[898,6314,6112],{},[1765,6316,2296],{},[1761,6318,1885],{},[1765,6320,6321],{},"5",[898,6323,6112],{},[1761,6325,1964],{},[1765,6327,2340],{},[1761,6329,1909],{},[1761,6331,1915],{"stretchy":1821},[898,6333,6112],{},[1761,6335,1885],{},[1765,6337,2296],{},[1761,6339,1920],{"stretchy":1821},[1761,6341,1915],{"stretchy":1821},[898,6343,6112],{},[1761,6345,1885],{},[1765,6347,5486],{},[1761,6349,1920],{"stretchy":1821},[902,6351,6352],{"encoding":904},"y = x^2 - 5x + 6 = (x-2)(x-3)",", kořeny ",[883,6355,6357],{"className":6356},[886],[888,6358,6359],{"xmlns":890},[892,6360,6361,6387],{},[895,6362,6363,6369,6371,6373,6375,6377,6383,6385],{},[1681,6364,6365,6367],{},[898,6366,6112],{},[1765,6368,1945],{},[1761,6370,1909],{},[1765,6372,2296],{},[1761,6374,1834],{"separator":1833},[2761,6376,2763],{},[1681,6378,6379,6381],{},[898,6380,6112],{},[1765,6382,2296],{},[1761,6384,1909],{},[1765,6386,5486],{},[902,6388,6389],{"encoding":904},"x_1 = 2,\\ x_2 = 3",". Vrcholový tvar ",[883,6392,6394],{"className":6393},[886],[888,6395,6396],{"xmlns":890},[892,6397,6398,6435],{},[895,6399,6400,6402,6404,6406,6408,6410,6419,6425,6427],{},[898,6401,1716],{},[1761,6403,1909],{},[1761,6405,1915],{"stretchy":1821},[898,6407,6112],{},[1761,6409,1885],{},[6411,6412,6413],"mstyle",{"scriptlevel":1767,"displaystyle":1821},[4379,6414,6415,6417],{},[1765,6416,6321],{},[1765,6418,2296],{},[1824,6420,6421,6423],{},[1761,6422,1920],{"stretchy":1821},[1765,6424,2296],{},[1761,6426,1885],{},[6411,6428,6429],{"scriptlevel":1767,"displaystyle":1821},[4379,6430,6431,6433],{},[1765,6432,1945],{},[1765,6434,2318],{},[902,6436,6437],{"encoding":904},"y = (x - \\tfrac{5}{2})^2 - \\tfrac{1}{4}",[115,6439,5995],{"id":1145},[724,6441,6442,6443,1348,6469,6497,6498,1741],{},"Označení ",[883,6444,6446],{"className":6445},[886],[888,6447,6448],{"xmlns":890},[892,6449,6450,6466],{},[895,6451,6452,6460,6462,6464],{},[1824,6453,6454,6456],{},[898,6455,6107],{},[1761,6457,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},"0em","′",[1761,6461,1915],{"stretchy":1821},[898,6463,6112],{},[1761,6465,1920],{"stretchy":1821},[902,6467,6468],{"encoding":904},"f'(x)",[883,6470,6472],{"className":6471},[886],[888,6473,6474],{"xmlns":890},[892,6475,6476,6494],{},[895,6477,6478],{},[6411,6479,6480],{"scriptlevel":1767,"displaystyle":1833},[4379,6481,6482,6488],{},[895,6483,6484,6486],{},[898,6485,4346],{},[898,6487,1716],{},[895,6489,6490,6492],{},[898,6491,4346],{},[898,6493,6112],{},[902,6495,6496],{"encoding":904},"\\dfrac{dy}{dx}",". Hodnota v bodě: ",[883,6499,6501],{"className":6500},[886],[888,6502,6503],{"xmlns":890},[892,6504,6505,6519],{},[895,6506,6507,6513,6515,6517],{},[1824,6508,6509,6511],{},[898,6510,6107],{},[1761,6512,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,6514,1915],{"stretchy":1821},[898,6516,207],{},[1761,6518,1920],{"stretchy":1821},[902,6520,6521],{"encoding":904},"f'(a)",[198,6523,4033],{"id":4032},[724,6525,6526,6549,6550,6553,6554,6582],{},[883,6527,6529],{"className":6528},[886],[888,6530,6531],{"xmlns":890},[892,6532,6533,6547],{},[895,6534,6535,6541,6543,6545],{},[1824,6536,6537,6539],{},[898,6538,6107],{},[1761,6540,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,6542,1915],{"stretchy":1821},[898,6544,207],{},[1761,6546,1920],{"stretchy":1821},[902,6548,6521],{"encoding":904}," = ",[38,6551,6552],{},"sklon tečny"," ke grafu funkce v bodě ",[883,6555,6557],{"className":6556},[886],[888,6558,6559],{"xmlns":890},[892,6560,6561,6579],{},[895,6562,6563,6565,6567,6569,6571,6573,6575,6577],{},[1761,6564,1822],{"stretchy":1821},[898,6566,207],{},[1761,6568,1834],{"separator":1833},[898,6570,6107],{},[1761,6572,1915],{"stretchy":1821},[898,6574,207],{},[1761,6576,1920],{"stretchy":1821},[1761,6578,1844],{"stretchy":1821},[902,6580,6581],{"encoding":904},"[a, f(a)]",". Rovnice tečny:",[724,6584,6585],{},[883,6586,6588],{"className":6587},[886],[888,6589,6590],{"xmlns":890},[892,6591,6592,6630],{},[895,6593,6594,6596,6598,6600,6602,6604,6606,6608,6614,6616,6618,6620,6622,6624,6626,6628],{},[898,6595,1716],{},[1761,6597,1885],{},[898,6599,6107],{},[1761,6601,1915],{"stretchy":1821},[898,6603,207],{},[1761,6605,1920],{"stretchy":1821},[1761,6607,1909],{},[1824,6609,6610,6612],{},[898,6611,6107],{},[1761,6613,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,6615,1915],{"stretchy":1821},[898,6617,207],{},[1761,6619,1920],{"stretchy":1821},[1761,6621,1915],{"stretchy":1821},[898,6623,6112],{},[1761,6625,1885],{},[898,6627,207],{},[1761,6629,1920],{"stretchy":1821},[902,6631,6632],{"encoding":904},"y - f(a) = f'(a)(x - a)",[724,6634,6635],{},[3991,6636],{"alt":6637,"className":6638,"src":6639},"imek-derivace-tecna",[210,3995],"\u002Fwiki-assets\u002Fimek-derivace-tecna.jpeg",[198,6641,6643],{"id":6642},"inženýrská-interpretace","Inženýrská interpretace",[724,6645,6646,6549,6669,1989,6672,6685,6686,6699,6700,6718,6719,6732,6733,6746,6747,4178,6760,2506],{},[883,6647,6649],{"className":6648},[886],[888,6650,6651],{"xmlns":890},[892,6652,6653,6667],{},[895,6654,6655,6661,6663,6665],{},[1824,6656,6657,6659],{},[898,6658,6107],{},[1761,6660,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,6662,1915],{"stretchy":1821},[898,6664,207],{},[1761,6666,1920],{"stretchy":1821},[902,6668,6521],{"encoding":904},[38,6670,6671],{},"rychlost změny",[883,6673,6675],{"className":6674},[886],[888,6676,6677],{"xmlns":890},[892,6678,6679,6683],{},[895,6680,6681],{},[898,6682,1716],{},[902,6684,1716],{"encoding":904}," vzhledem k ",[883,6687,6689],{"className":6688},[886],[888,6690,6691],{"xmlns":890},[892,6692,6693,6697],{},[895,6694,6695],{},[898,6696,6112],{},[902,6698,6112],{"encoding":904}," v bodě ",[883,6701,6703],{"className":6702},[886],[888,6704,6705],{"xmlns":890},[892,6706,6707,6715],{},[895,6708,6709,6711,6713],{},[898,6710,6112],{},[1761,6712,1909],{},[898,6714,207],{},[902,6716,6717],{"encoding":904},"x = a","; přibližná změna ",[883,6720,6722],{"className":6721},[886],[888,6723,6724],{"xmlns":890},[892,6725,6726,6730],{},[895,6727,6728],{},[898,6729,1716],{},[902,6731,1716],{"encoding":904}," při změně ",[883,6734,6736],{"className":6735},[886],[888,6737,6738],{"xmlns":890},[892,6739,6740,6744],{},[895,6741,6742],{},[898,6743,6112],{},[902,6745,6112],{"encoding":904}," z ",[883,6748,6750],{"className":6749},[886],[888,6751,6752],{"xmlns":890},[892,6753,6754,6758],{},[895,6755,6756],{},[898,6757,207],{},[902,6759,207],{"encoding":904},[883,6761,6763],{"className":6762},[886],[888,6764,6765],{"xmlns":890},[892,6766,6767,6775],{},[895,6768,6769,6771,6773],{},[898,6770,207],{},[1761,6772,1964],{},[1765,6774,1945],{},[902,6776,6777],{"encoding":904},"a+1",[724,6779,6780],{},[883,6781,6783],{"className":6782},[886],[888,6784,6785],{"xmlns":890},[892,6786,6787,6826],{},[895,6788,6789,6791,6793,6795,6797,6799,6801,6804,6806,6808,6810,6812,6814,6820,6822,6824],{},[898,6790,6107],{},[1761,6792,1915],{"stretchy":1821},[898,6794,207],{},[1761,6796,1964],{},[1765,6798,1945],{},[1761,6800,1920],{"stretchy":1821},[1761,6802,6803],{},"≈",[898,6805,6107],{},[1761,6807,1915],{"stretchy":1821},[898,6809,207],{},[1761,6811,1920],{"stretchy":1821},[1761,6813,1964],{},[1824,6815,6816,6818],{},[898,6817,6107],{},[1761,6819,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,6821,1915],{"stretchy":1821},[898,6823,207],{},[1761,6825,1920],{"stretchy":1821},[902,6827,6828],{"encoding":904},"f(a+1) \\approx f(a) + f'(a)",[198,6830,6832],{"id":6831},"příklad-mezní-náklady","Příklad — mezní náklady",[724,6834,6835,6836,1741],{},"Celkové náklady ",[883,6837,6839],{"className":6838},[886],[888,6840,6841],{"xmlns":890},[892,6842,6843,6872],{},[895,6844,6845,6847,6850,6852,6855,6857,6859,6861,6863,6866],{},[898,6846,1655],{},[898,6848,6849],{},"C",[1761,6851,1909],{},[1765,6853,6854],{},"1000",[1761,6856,1964],{},[1765,6858,2296],{},[898,6860,1828],{},[1761,6862,1964],{},[1765,6864,6865],{},"0,1",[1824,6867,6868,6870],{},[898,6869,1828],{},[1765,6871,2296],{},[902,6873,6874],{"encoding":904},"TC = 1000 + 2Q + 0{,}1 Q^2",[724,6876,6877,6878,6916,6917,1741],{},"Mezní náklady: ",[883,6879,6881],{"className":6880},[886],[888,6882,6883],{"xmlns":890},[892,6884,6885,6913],{},[895,6886,6887,6890,6892,6894,6896,6902,6904,6906,6908,6911],{},[898,6888,6889],{},"M",[898,6891,6849],{},[1761,6893,1909],{},[898,6895,1655],{},[1824,6897,6898,6900],{},[898,6899,6849],{},[1761,6901,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,6903,1909],{},[1765,6905,2296],{},[1761,6907,1964],{},[1765,6909,6910],{},"0,2",[898,6912,1828],{},[902,6914,6915],{"encoding":904},"MC = TC' = 2 + 0{,}2 Q",", takže ",[883,6918,6920],{"className":6919},[886],[888,6921,6922],{"xmlns":890},[892,6923,6924,6940],{},[895,6925,6926,6928,6930,6932,6934,6936,6938],{},[898,6927,6889],{},[898,6929,6849],{},[1761,6931,1915],{"stretchy":1821},[1765,6933,2633],{},[1761,6935,1920],{"stretchy":1821},[1761,6937,1909],{},[1765,6939,2318],{},[902,6941,6942],{"encoding":904},"MC(10) = 4",[724,6944,6945,1989,6948,6997,6998,1989,7001,1741],{},[38,6946,6947],{},"Skutečný přírůstek:",[883,6949,6951],{"className":6950},[886],[888,6952,6953],{"xmlns":890},[892,6954,6955,6994],{},[895,6956,6957,6960,6962,6964,6966,6968,6970,6972,6975,6977,6979,6981,6983,6985,6987,6989,6991],{},[898,6958,6959],{"mathvariant":1969},"Δ",[898,6961,1655],{},[898,6963,6849],{},[1761,6965,1909],{},[898,6967,1655],{},[898,6969,6849],{},[1761,6971,1915],{"stretchy":1821},[1765,6973,6974],{},"11",[1761,6976,1920],{"stretchy":1821},[1761,6978,1885],{},[898,6980,1655],{},[898,6982,6849],{},[1761,6984,1915],{"stretchy":1821},[1765,6986,2633],{},[1761,6988,1920],{"stretchy":1821},[1761,6990,1909],{},[1765,6992,6993],{},"4,2",[902,6995,6996],{"encoding":904},"\\Delta TC = TC(11) - TC(10) = 4{,}2",". ",[38,6999,7000],{},"Přibližný (lineární):",[883,7002,7004],{"className":7003},[886],[888,7005,7006],{"xmlns":890},[892,7007,7008,7012],{},[895,7009,7010],{},[1765,7011,2318],{},[902,7013,2318],{"encoding":904},[724,7015,7016,7017,7021],{},"(Viz aplikace v ",[207,7018,7020],{"className":7019,"dataFsResolvedFilePath":827,"href":828},[210],"prijem-naklady-zisk",".)",[115,7023,7025],{"id":7024},"diferenciál","Diferenciál",[724,7027,7028],{},[883,7029,7031],{"className":7030},[886],[888,7032,7033],{"xmlns":890},[892,7034,7035,7062],{},[895,7036,7037,7039,7041,7043,7049,7051,7053,7055,7058,7060],{},[898,7038,4346],{},[898,7040,6107],{},[1761,7042,1909],{},[1824,7044,7045,7047],{},[898,7046,6107],{},[1761,7048,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,7050,1915],{"stretchy":1821},[898,7052,6112],{},[1761,7054,1920],{"stretchy":1821},[2761,7056,7057],{}," ",[898,7059,4346],{},[898,7061,6112],{},[902,7063,7064],{"encoding":904},"df = f'(x)\\, dx",[724,7066,7067,7068,7084,7085,7133,7134,1741],{},"Pro malá ",[883,7069,7071],{"className":7070},[886],[888,7072,7073],{"xmlns":890},[892,7074,7075,7081],{},[895,7076,7077,7079],{},[898,7078,4346],{},[898,7080,6112],{},[902,7082,7083],{"encoding":904},"dx"," platí: ",[883,7086,7088],{"className":7087},[886],[888,7089,7090],{"xmlns":890},[892,7091,7092,7130],{},[895,7093,7094,7096,7098,7100,7102,7104,7106,7108,7110,7112,7114,7116,7118,7120,7122,7124,7126,7128],{},[898,7095,6959],{"mathvariant":1969},[898,7097,6107],{},[1761,7099,1909],{},[898,7101,6107],{},[1761,7103,1915],{"stretchy":1821},[898,7105,6112],{},[1761,7107,1964],{},[898,7109,4346],{},[898,7111,6112],{},[1761,7113,1920],{"stretchy":1821},[1761,7115,1885],{},[898,7117,6107],{},[1761,7119,1915],{"stretchy":1821},[898,7121,6112],{},[1761,7123,1920],{"stretchy":1821},[1761,7125,6803],{},[898,7127,4346],{},[898,7129,6107],{},[902,7131,7132],{"encoding":904},"\\Delta f = f(x + dx) - f(x) \\approx df",". Diferenciál je ",[38,7135,7136],{},"lineární odhad přírůstku",[198,7138,7140],{"id":7139},"příklad","Příklad",[724,7142,7143,7174,7175,7199,7200,5372],{},[883,7144,7146],{"className":7145},[886],[888,7147,7148],{"xmlns":890},[892,7149,7150,7171],{},[895,7151,7152,7154,7156,7158,7161,7163,7165],{},[898,7153,1655],{},[898,7155,6849],{},[1761,7157,1909],{},[1765,7159,7160],{},"100",[1761,7162,1964],{},[1765,7164,6865],{},[1824,7166,7167,7169],{},[898,7168,1828],{},[1765,7170,2296],{},[902,7172,7173],{"encoding":904},"TC = 100 + 0{,}1 Q^2",", odhad změny při ",[883,7176,7178],{"className":7177},[886],[888,7179,7180],{"xmlns":890},[892,7181,7182,7196],{},[895,7183,7184,7186,7188,7191,7193],{},[898,7185,1828],{},[1761,7187,2506],{},[1765,7189,7190],{},"50",[1761,7192,2181],{},[1765,7194,7195],{},"60",[902,7197,7198],{"encoding":904},"Q: 50 \\to 60"," (tj. ",[883,7201,7203],{"className":7202},[886],[888,7204,7205],{"xmlns":890},[892,7206,7207,7217],{},[895,7208,7209,7211,7213,7215],{},[898,7210,4346],{},[898,7212,1828],{},[1761,7214,1909],{},[1765,7216,2633],{},[902,7218,7219],{"encoding":904},"dQ = 10",[724,7221,7222],{},[883,7223,7225],{"className":7224},[886],[888,7226,7227],{"xmlns":890},[892,7228,7229,7265],{},[895,7230,7231,7233,7235,7237,7239,7241,7243,7245,7247,7249,7251,7253,7255,7257,7259,7261,7263],{},[898,7232,4346],{},[898,7234,1655],{},[898,7236,6849],{},[1761,7238,1909],{},[1765,7240,6910],{},[898,7242,1828],{},[1761,7244,2447],{},[898,7246,4346],{},[898,7248,1828],{},[1761,7250,1909],{},[1765,7252,6910],{},[1761,7254,2447],{},[1765,7256,7190],{},[1761,7258,2447],{},[1765,7260,2633],{},[1761,7262,1909],{},[1765,7264,7160],{},[902,7266,7267],{"encoding":904},"dTC = 0{,}2 Q \\cdot dQ = 0{,}2 \\cdot 50 \\cdot 10 = 100",[724,7269,7270,7271,7294,7295,7311],{},"Přesná změna: ",[883,7272,7274],{"className":7273},[886],[888,7275,7276],{"xmlns":890},[892,7277,7278,7291],{},[895,7279,7280,7282,7284,7286,7288],{},[898,7281,6959],{"mathvariant":1969},[898,7283,1655],{},[898,7285,6849],{},[1761,7287,1909],{},[1765,7289,7290],{},"110",[902,7292,7293],{"encoding":904},"\\Delta TC = 110",". Lineární odhad mírně podstřeluje, protože ",[883,7296,7298],{"className":7297},[886],[888,7299,7300],{"xmlns":890},[892,7301,7302,7308],{},[895,7303,7304,7306],{},[898,7305,1655],{},[898,7307,6849],{},[902,7309,7310],{"encoding":904},"TC"," je konvexní.",[115,7313,7315],{"id":7314},"extrémy-funkce-jedné-proměnné","Extrémy funkce jedné proměnné",[198,7317,7319],{"id":7318},"nutná-podmínka","Nutná podmínka",[724,7321,7322,7323,6699,7343,7356,7357,7385,7386,7389],{},"Má-li ",[883,7324,7326],{"className":7325},[886],[888,7327,7328],{"xmlns":890},[892,7329,7330,7340],{},[895,7331,7332,7334,7336,7338],{},[898,7333,6107],{},[1761,7335,1915],{"stretchy":1821},[898,7337,6112],{},[1761,7339,1920],{"stretchy":1821},[902,7341,7342],{"encoding":904},"f(x)",[883,7344,7346],{"className":7345},[886],[888,7347,7348],{"xmlns":890},[892,7349,7350,7354],{},[895,7351,7352],{},[898,7353,207],{},[902,7355,207],{"encoding":904}," extrém, pak ",[883,7358,7360],{"className":7359},[886],[888,7361,7362],{"xmlns":890},[892,7363,7364,7382],{},[895,7365,7366,7372,7374,7376,7378,7380],{},[1824,7367,7368,7370],{},[898,7369,6107],{},[1761,7371,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,7373,1915],{"stretchy":1821},[898,7375,207],{},[1761,7377,1920],{"stretchy":1821},[1761,7379,1909],{},[1765,7381,1767],{},[902,7383,7384],{"encoding":904},"f'(a) = 0",". Body splňující tuto podmínku se nazývají ",[38,7387,7388],{},"stacionární"," (podezřelé) body.",[198,7391,7393],{"id":7392},"postačující-podmínka","Postačující podmínka",[724,7395,7396,7397,7410,7411,2506],{},"Pro stacionární bod ",[883,7398,7400],{"className":7399},[886],[888,7401,7402],{"xmlns":890},[892,7403,7404,7408],{},[895,7405,7406],{},[898,7407,207],{},[902,7409,207],{"encoding":904},", je-li ",[883,7412,7414],{"className":7413},[886],[888,7415,7416],{"xmlns":890},[892,7417,7418,7441],{},[895,7419,7420,7430,7432,7434,7436,7439],{},[1824,7421,7422,7424],{},[898,7423,6107],{},[895,7425,7426,7428],{},[1761,7427,6459],{"mathvariant":1969},[1761,7429,6459],{"mathvariant":1969},[1761,7431,1915],{"stretchy":1821},[898,7433,207],{},[1761,7435,1920],{"stretchy":1821},[1761,7437,7438],{"mathvariant":1969},"≠",[1765,7440,1767],{},[902,7442,7443],{"encoding":904},"f''(a) \\neq 0",[120,7445,7446,7484],{},[123,7447,7448,7480,7481],{},[883,7449,7451],{"className":7450},[886],[888,7452,7453],{"xmlns":890},[892,7454,7455,7477],{},[895,7456,7457,7467,7469,7471,7473,7475],{},[1824,7458,7459,7461],{},[898,7460,6107],{},[895,7462,7463,7465],{},[1761,7464,6459],{"mathvariant":1969},[1761,7466,6459],{"mathvariant":1969},[1761,7468,1915],{"stretchy":1821},[898,7470,207],{},[1761,7472,1920],{"stretchy":1821},[1761,7474,1763],{},[1765,7476,1767],{},[902,7478,7479],{"encoding":904},"f''(a) > 0"," ⇒ ",[38,7482,7483],{},"lokální minimum",[123,7485,7486,7480,7518],{},[883,7487,7489],{"className":7488},[886],[888,7490,7491],{"xmlns":890},[892,7492,7493,7515],{},[895,7494,7495,7505,7507,7509,7511,7513],{},[1824,7496,7497,7499],{},[898,7498,6107],{},[895,7500,7501,7503],{},[1761,7502,6459],{"mathvariant":1969},[1761,7504,6459],{"mathvariant":1969},[1761,7506,1915],{"stretchy":1821},[898,7508,207],{},[1761,7510,1920],{"stretchy":1821},[1761,7512,2058],{},[1765,7514,1767],{},[902,7516,7517],{"encoding":904},"f''(a) \u003C 0",[38,7519,7520],{},"lokální maximum",[724,7522,7523],{},[3991,7524],{"alt":7525,"className":7526,"src":7527},"imek-extremy-1d",[210,3995],"\u002Fwiki-assets\u002Fimek-extremy-1d.jpeg",[198,7529,7140],{"id":7530},"příklad-1",[724,7532,7533],{},[883,7534,7536],{"className":7535},[886],[888,7537,7538],{"xmlns":890},[892,7539,7540,7580],{},[895,7541,7542,7544,7546,7548,7550,7552,7554,7560,7562,7564,7570,7572,7574,7576,7578],{},[898,7543,6107],{},[1761,7545,1915],{"stretchy":1821},[898,7547,6112],{},[1761,7549,1920],{"stretchy":1821},[1761,7551,1909],{},[1765,7553,2296],{},[1824,7555,7556,7558],{},[898,7557,6112],{},[1765,7559,5486],{},[1761,7561,1885],{},[1765,7563,5486],{},[1824,7565,7566,7568],{},[898,7567,6112],{},[1765,7569,2296],{},[1761,7571,1885],{},[1765,7573,2291],{},[898,7575,6112],{},[1761,7577,1964],{},[1765,7579,5486],{},[902,7581,7582],{"encoding":904},"f(x) = 2x^3 - 3x^2 - 12x + 3",[120,7584,7585,7696,7736,7799],{},[123,7586,7587,7659,7660],{},[883,7588,7590],{"className":7589},[886],[888,7591,7592],{"xmlns":890},[892,7593,7594,7656],{},[895,7595,7596,7602,7604,7606,7608,7610,7612,7618,7620,7622,7624,7626,7628,7630,7632,7634,7636,7638,7640,7642,7644,7646,7648,7650,7652,7654],{},[1824,7597,7598,7600],{},[898,7599,6107],{},[1761,7601,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,7603,1915],{"stretchy":1821},[898,7605,6112],{},[1761,7607,1920],{"stretchy":1821},[1761,7609,1909],{},[1765,7611,2340],{},[1824,7613,7614,7616],{},[898,7615,6112],{},[1765,7617,2296],{},[1761,7619,1885],{},[1765,7621,2340],{},[898,7623,6112],{},[1761,7625,1885],{},[1765,7627,2291],{},[1761,7629,1909],{},[1765,7631,2340],{},[1761,7633,1915],{"stretchy":1821},[898,7635,6112],{},[1761,7637,1964],{},[1765,7639,1945],{},[1761,7641,1920],{"stretchy":1821},[1761,7643,1915],{"stretchy":1821},[898,7645,6112],{},[1761,7647,1885],{},[1765,7649,2296],{},[1761,7651,1920],{"stretchy":1821},[1761,7653,1909],{},[1765,7655,1767],{},[902,7657,7658],{"encoding":904},"f'(x) = 6x^2 - 6x - 12 = 6(x+1)(x-2) = 0"," ⇒ S.B. ",[883,7661,7663],{"className":7662},[886],[888,7664,7665],{"xmlns":890},[892,7666,7667,7693],{},[895,7668,7669,7675,7677,7679,7681,7683,7689,7691],{},[1681,7670,7671,7673],{},[898,7672,6112],{},[1765,7674,1945],{},[1761,7676,1909],{},[1761,7678,1885],{},[1765,7680,1945],{},[1761,7682,1834],{"separator":1833},[1681,7684,7685,7687],{},[898,7686,6112],{},[1765,7688,2296],{},[1761,7690,1909],{},[1765,7692,2296],{},[902,7694,7695],{"encoding":904},"x_1 = -1, x_2 = 2",[123,7697,7698],{},[883,7699,7701],{"className":7700},[886],[888,7702,7703],{"xmlns":890},[892,7704,7705,7733],{},[895,7706,7707,7717,7719,7721,7723,7725,7727,7729,7731],{},[1824,7708,7709,7711],{},[898,7710,6107],{},[895,7712,7713,7715],{},[1761,7714,6459],{"mathvariant":1969},[1761,7716,6459],{"mathvariant":1969},[1761,7718,1915],{"stretchy":1821},[898,7720,6112],{},[1761,7722,1920],{"stretchy":1821},[1761,7724,1909],{},[1765,7726,2291],{},[898,7728,6112],{},[1761,7730,1885],{},[1765,7732,2340],{},[902,7734,7735],{"encoding":904},"f''(x) = 12x - 6",[123,7737,7738,7480,7779,7782,7783],{},[883,7739,7741],{"className":7740},[886],[888,7742,7743],{"xmlns":890},[892,7744,7745,7776],{},[895,7746,7747,7757,7759,7761,7763,7765,7767,7769,7772,7774],{},[1824,7748,7749,7751],{},[898,7750,6107],{},[895,7752,7753,7755],{},[1761,7754,6459],{"mathvariant":1969},[1761,7756,6459],{"mathvariant":1969},[1761,7758,1915],{"stretchy":1821},[1761,7760,1885],{},[1765,7762,1945],{},[1761,7764,1920],{"stretchy":1821},[1761,7766,1909],{},[1761,7768,1885],{},[1765,7770,7771],{},"18",[1761,7773,2058],{},[1765,7775,1767],{},[902,7777,7778],{"encoding":904},"f''(-1) = -18 \u003C 0",[38,7780,7781],{},"maximum"," v ",[883,7784,7786],{"className":7785},[886],[888,7787,7788],{"xmlns":890},[892,7789,7790,7796],{},[895,7791,7792,7794],{},[1761,7793,1885],{},[1765,7795,1945],{},[902,7797,7798],{"encoding":904},"-1",[123,7800,7801,7480,7837,7782,7840],{},[883,7802,7804],{"className":7803},[886],[888,7805,7806],{"xmlns":890},[892,7807,7808,7834],{},[895,7809,7810,7820,7822,7824,7826,7828,7830,7832],{},[1824,7811,7812,7814],{},[898,7813,6107],{},[895,7815,7816,7818],{},[1761,7817,6459],{"mathvariant":1969},[1761,7819,6459],{"mathvariant":1969},[1761,7821,1915],{"stretchy":1821},[1765,7823,2296],{},[1761,7825,1920],{"stretchy":1821},[1761,7827,1909],{},[1765,7829,7771],{},[1761,7831,1763],{},[1765,7833,1767],{},[902,7835,7836],{"encoding":904},"f''(2) = 18 > 0",[38,7838,7839],{},"minimum",[883,7841,7843],{"className":7842},[886],[888,7844,7845],{"xmlns":890},[892,7846,7847,7851],{},[895,7848,7849],{},[1765,7850,2296],{},[902,7852,2296],{"encoding":904},[115,7854,5968],{"id":5967},[120,7856,7857,7865,7873],{},[123,7858,7859,1989,7862],{},[38,7860,7861],{},"Předchozí:",[207,7863,757],{"className":7864,"dataFsResolvedFilePath":755,"href":756},[210],[123,7866,7867,1989,7870],{},[38,7868,7869],{},"Navazující:",[207,7871,775],{"className":7872,"dataFsResolvedFilePath":773,"href":774},[210],[123,7874,7875,1989,7878,7881,7882,7886,7887,7890],{},[38,7876,7877],{},"Souvislosti:",[207,7879,784],{"className":7880,"dataFsResolvedFilePath":782,"href":783},[210]," (rozšíření na 2D), ",[207,7883,7885],{"className":7884,"dataFsResolvedFilePath":827,"href":828},[210],"Příjem, náklady, zisk"," (aplikace mezních veličin), ",[207,7888,6000],{"className":7889,"dataFsResolvedFilePath":848,"href":849},[210]," (procentní citlivost přes derivaci)",{"title":641,"searchDepth":642,"depth":642,"links":7892},[7893,7894,7899,7902,7907],{"id":6087,"depth":642,"text":6088},{"id":1145,"depth":642,"text":5995,"children":7895},[7896,7897,7898],{"id":4032,"depth":649,"text":4033},{"id":6642,"depth":649,"text":6643},{"id":6831,"depth":649,"text":6832},{"id":7024,"depth":642,"text":7025,"children":7900},[7901],{"id":7139,"depth":649,"text":7140},{"id":7314,"depth":642,"text":7315,"children":7903},[7904,7905,7906],{"id":7318,"depth":649,"text":7319},{"id":7392,"depth":649,"text":7393},{"id":7530,"depth":649,"text":7140},{"id":5967,"depth":642,"text":5968},"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":6060,"description":7908},[1135],"topics\u002Fderivace",[1128,1145,7915,7916,7917],"diferencial","extremy","mezni-naklady","U4vqwJqO65hVzq9khEr5sxPHpHJLXAz_kTaaHdKCCIw",{"id":7920,"title":7921,"body":7922,"course":1128,"courses":659,"created":6039,"description":641,"extension":661,"meta":13597,"navigation":664,"path":13598,"seo":13599,"sources":13600,"stem":13601,"tags":13602,"type":6050,"updated":677,"__hash__":13607},"topics\u002Ftopics\u002Felasticita.md","Elasticita poptávky a nabídky",{"type":9,"value":7923,"toc":13570},[7924,7927,7948,7952,7977,7981,8022,8113,8157,8161,8185,8192,8196,8206,8217,8221,8249,8258,8314,8320,8323,8329,8356,8362,8460,8619,8909,8913,8993,8999,9003,9100,9166,9334,9338,9416,9447,9474,9480,9512,9590,9674,9678,9740,9746,9749,9755,9869,9952,9996,10000,10046,10053,10370,10375,10399,10428,10495,10592,10596,10603,10610,10681,10801,10885,10888,10894,11220,11224,11387,11395,11531,11539,11777,11785,11788,11793,12049,12053,12227,12361,12398,12441,12444,12574,12664,12682,12686,12693,12699,12759,12762,12786,12789,12795,12798,12804,12807,12811,12849,12907,13096,13100,13173,13179,13186,13190,13196,13337,13341,13347,13383,13388,13565],[12,7925,7921],{"id":7926},"elasticita-poptávky-a-nabídky",[1636,7928,7929],{},[724,7930,7931,7934,7935,7937,7938,7941,7942,2068,7945,1741],{},[883,7932,7933],{},"!abstract"," TL;DR\n",[38,7936,6000],{}," 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: ",[38,7939,7940],{},"cenovou elasticitu poptávky"," (a nabídky), ",[38,7943,7944],{},"křížově-cenovou elasticitu",[38,7946,7947],{},"důchodovou elasticitu",[115,7949,7951],{"id":7950},"úvod-motivace","Úvod — motivace",[724,7953,7954,7955,7958,7959,7962,7963,7966,7967,4569,7970,7973,7974,2162],{},"Termín ",[614,7956,7957],{},"elasticita"," (alternativně ",[614,7960,7961],{},"pružnost",") patří ke klíčovým pojmům ekonomické teorie. Slouží ke ",[38,7964,7965],{},"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 ",[614,7968,7969],{},"cenové elasticity poptávky",[614,7971,7972],{},"nabídky","). Matematickým modelem míry citlivosti je elasticita funkce (viz ",[207,7975,5995],{"className":7976,"dataFsResolvedFilePath":764,"href":765},[210],[198,7978,7980],{"id":7979},"srovnání-trh-1-vs-trh-2","Srovnání Trh 1 vs Trh 2",[724,7982,7983,7984,8002,8003,8021],{},"Uvažujme dvě různá tržní prostředí. Zboží má na obou trzích stejnou cenu ",[883,7985,7987],{"className":7986},[886],[888,7988,7989],{"xmlns":890},[892,7990,7991,7999],{},[895,7992,7993,7995,7997],{},[898,7994,1839],{},[1761,7996,1909],{},[1765,7998,2633],{},[902,8000,8001],{"encoding":904},"P=10"," a při této ceně se prodá ",[883,8004,8006],{"className":8005},[886],[888,8007,8008],{"xmlns":890},[892,8009,8010,8018],{},[895,8011,8012,8014,8016],{},[898,8013,1828],{},[1761,8015,1909],{},[1765,8017,7160],{},[902,8019,8020],{"encoding":904},"Q=100"," jednotek. Prodejce sníží cenu z 10 na 9:",[120,8023,8024,8070],{},[123,8025,8026,8029,8030,8069],{},[38,8027,8028],{},"Trh 1"," zareaguje zvýšením množství na 110 ",[883,8031,8033],{"className":8032},[886],[888,8034,8035],{"xmlns":890},[892,8036,8037,8066],{},[895,8038,8039,8042,8045,8047,8049,8052,8054,8057,8059,8061,8063],{},[2761,8040,8041],{},"  ",[1761,8043,8044],{},"⇒",[2761,8046,8041],{},[898,8048,1655],{},[898,8050,8051],{},"R",[1761,8053,1909],{},[1765,8055,8056],{},"9",[1761,8058,2447],{},[1765,8060,7290],{},[1761,8062,1909],{},[1765,8064,8065],{},"990",[902,8067,8068],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 110 = 990"," (pokles z 1000).",[123,8071,8072,8075,8076,8112],{},[38,8073,8074],{},"Trh 2"," zareaguje zvýšením množství na 120 ",[883,8077,8079],{"className":8078},[886],[888,8080,8081],{"xmlns":890},[892,8082,8083,8109],{},[895,8084,8085,8087,8089,8091,8093,8095,8097,8099,8101,8104,8106],{},[2761,8086,8041],{},[1761,8088,8044],{},[2761,8090,8041],{},[898,8092,1655],{},[898,8094,8051],{},[1761,8096,1909],{},[1765,8098,8056],{},[1761,8100,2447],{},[1765,8102,8103],{},"120",[1761,8105,1909],{},[1765,8107,8108],{},"1080",[902,8110,8111],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 120 = 1080"," (růst z 1000).",[724,8114,8115,8116,8119,8120,8123,8124,8127,8128,8131,8132,8135,8136,8152,8153,8156],{},"Závěr: snížení ceny bylo na Trhu 1 ",[38,8117,8118],{},"nerozumné",", na Trhu 2 ",[38,8121,8122],{},"rozumné",". Trh 2 je ",[38,8125,8126],{},"relativně citlivý"," na změnu ceny — říkáme, že poptávka je ",[614,8129,8130],{},"elastická"," a snížení ceny je „překompenzováno\" zvýšením poptávaného množství. Na Trhu 1 je poptávka ",[614,8133,8134],{},"neelastická"," a vyššího ",[883,8137,8139],{"className":8138},[886],[888,8140,8141],{"xmlns":890},[892,8142,8143,8149],{},[895,8144,8145,8147],{},[898,8146,1655],{},[898,8148,8051],{},[902,8150,8151],{"encoding":904},"TR"," lze naopak dosáhnout ",[614,8154,8155],{},"zvýšením"," ceny.",[198,8158,8160],{"id":8159},"hypotéza-41","Hypotéza 4.1",[1636,8162,8163],{},[724,8164,8165,8166],{},"Aby nedošlo k poklesu celkového příjmu, musí být procentní růst poptávaného množství alespoň takový, jaký je procentní pokles jeho ceny. ",[883,8167,8169],{"className":8168},[886],[888,8170,8171],{"xmlns":890},[892,8172,8173,8182],{},[895,8174,8175,8177,8180],{},[1761,8176,1915],{"stretchy":1821},[1765,8178,8179],{},"4.1",[1761,8181,1920],{"stretchy":1821},[902,8183,8184],{"encoding":904},"(4.1)",[724,8186,8187,8188,8191],{},"Rozhodující nejsou nominální změny (jsou měřeny v různých jednotkách), nýbrž ",[38,8189,8190],{},"procentní změny"," obou faktorů.",[115,8193,8195],{"id":8194},"pojem-elasticity","Pojem elasticity",[724,8197,8198,8199,8201,8202,8205],{},"Obecně ",[38,8200,7957],{}," jedné veličiny vzhledem k druhé kvantifikuje, o kolik procent se první veličina přibližně změní, když se druhá veličina změní o 1 %. Jde o ",[38,8203,8204],{},"bezrozměrnou veličinu"," — nezávislou na jednotkách, ve kterých jsou proměnné měřeny (viz čl. 1.5.1).",[1636,8207,8208],{},[724,8209,8210,8212,8213,8216],{},[883,8211,1642],{}," Intuice\nElasticitu lze číst jako ",[38,8214,8215],{},"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.",[115,8218,8220],{"id":8219},"cenová-elasticita-poptávky-jednofaktorový-model","Cenová elasticita poptávky — jednofaktorový model",[724,8222,8223,8224,8248],{},"Nechť ",[883,8225,8227],{"className":8226},[886],[888,8228,8229],{"xmlns":890},[892,8230,8231,8245],{},[895,8232,8233,8235,8237,8239,8241,8243],{},[898,8234,1828],{},[1761,8236,1909],{},[898,8238,2244],{},[1761,8240,1915],{"stretchy":1821},[898,8242,1839],{},[1761,8244,1920],{"stretchy":1821},[902,8246,8247],{"encoding":904},"Q = D(P)"," je funkce poptávky (ceteris paribus). Zkoumáme podíl procentních změn",[724,8250,8251],{},[883,8252,8257],{"className":8253,"title":8255,"style":8256},[8254],"katex-error","ParseError: KaTeX parse error: \\tag works only in display equations","color:#cc0000","E^A = -\\frac{\\Delta Q\\%}{\\Delta P\\%}. \\tag{4.2}",[724,8259,8260,8261,2068,8277,8293,8294,8313],{},"Znaménko minus je korekce: změny ",[883,8262,8264],{"className":8263},[886],[888,8265,8266],{"xmlns":890},[892,8267,8268,8274],{},[895,8269,8270,8272],{},[898,8271,6959],{"mathvariant":1969},[898,8273,1828],{},[902,8275,8276],{"encoding":904},"\\Delta Q",[883,8278,8280],{"className":8279},[886],[888,8281,8282],{"xmlns":890},[892,8283,8284,8290],{},[895,8285,8286,8288],{},[898,8287,6959],{"mathvariant":1969},[898,8289,1839],{},[902,8291,8292],{"encoding":904},"\\Delta P"," mají vždy opačná znaménka, takže bez korekce by ",[883,8295,8297],{"className":8296},[886],[888,8298,8299],{"xmlns":890},[892,8300,8301,8310],{},[895,8302,8303],{},[1824,8304,8305,8307],{},[898,8306,1818],{},[898,8308,8309],{},"A",[902,8311,8312],{"encoding":904},"E^A"," bylo záporné; pro pohodlí pracujeme s nezápornými hodnotami. Pro procentní změny platí",[724,8315,8316],{},[883,8317,8319],{"className":8318,"title":8255,"style":8256},[8254],"\\Delta Q\\% = \\frac{\\Delta Q}{Q}\\cdot 100, \\qquad \\Delta P\\% = \\frac{\\Delta P}{P}\\cdot 100. \\tag{4.3}",[724,8321,8322],{},"Po dosazení:",[724,8324,8325],{},[883,8326,8328],{"className":8327,"title":8255,"style":8256},[8254],"E^A = -\\frac{\\frac{\\Delta Q}{Q}}{\\frac{\\Delta P}{P}} = -\\frac{P}{Q}\\cdot \\frac{\\Delta Q}{\\Delta P}. \\tag{4.4}",[724,8330,8331,8332,8352,8353,8355],{},"Limitním přechodem ",[883,8333,8335],{"className":8334},[886],[888,8336,8337],{"xmlns":890},[892,8338,8339,8349],{},[895,8340,8341,8343,8345,8347],{},[898,8342,6959],{"mathvariant":1969},[898,8344,1839],{},[1761,8346,2181],{},[1765,8348,1767],{},[902,8350,8351],{"encoding":904},"\\Delta P \\to 0"," získáme definici ",[38,8354,7969],{}," (price elasticity of demand):",[724,8357,8358],{},[883,8359,8361],{"className":8360,"title":8255,"style":8256},[8254],"\\boxed{\\;E = E(P) = -\\frac{P}{Q}\\cdot \\frac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\frac{P}{Q}\\,Q'(P)\\;} \\tag{4.5}",[724,8363,8364,8365,8388,8389,8412,8413,8437,8438,8459],{},"kde ",[883,8366,8368],{"className":8367},[886],[888,8369,8370],{"xmlns":890},[892,8371,8372,8386],{},[895,8373,8374,8376,8378,8380,8382,8384],{},[898,8375,1828],{},[1761,8377,1909],{},[898,8379,2244],{},[1761,8381,1915],{"stretchy":1821},[898,8383,1839],{},[1761,8385,1920],{"stretchy":1821},[902,8387,8247],{"encoding":904},". Pro pevnou cenu ",[883,8390,8392],{"className":8391},[886],[888,8393,8394],{"xmlns":890},[892,8395,8396,8409],{},[895,8397,8398,8400,8402],{},[898,8399,1839],{},[1761,8401,1909],{},[1824,8403,8404,8406],{},[898,8405,1839],{},[1761,8407,8408],{},"∗",[902,8410,8411],{"encoding":904},"P = P^*"," se ",[883,8414,8416],{"className":8415},[886],[888,8417,8418],{"xmlns":890},[892,8419,8420,8434],{},[895,8421,8422,8424,8426,8432],{},[898,8423,1818],{},[1761,8425,1915],{"stretchy":1821},[1824,8427,8428,8430],{},[898,8429,1839],{},[1761,8431,8408],{},[1761,8433,1920],{"stretchy":1821},[902,8435,8436],{"encoding":904},"E(P^*)"," nazývá ",[614,8439,8440,8441],{},"elasticita poptávky při ceně ",[883,8442,8444],{"className":8443},[886],[888,8445,8446],{"xmlns":890},[892,8447,8448,8456],{},[895,8449,8450],{},[1824,8451,8452,8454],{},[898,8453,1839],{},[1761,8455,8408],{},[902,8457,8458],{"encoding":904},"P^*"," a je to vždy nezáporné číslo.",[1636,8461,8462],{},[724,8463,8464,8466,8467,8485,8486,8514,8515,8544,8545,1343,8563,1343,8581,8599,8600,8615,8616,1741],{},[883,8465,4723],{}," Pozor na znaménko\nV (4.5) je ",[38,8468,8469,8470],{},"explicitní ",[883,8471,8473],{"className":8472},[886],[888,8474,8475],{"xmlns":890},[892,8476,8477,8483],{},[895,8478,8479,8481],{},[1761,8480,1885],{},[1765,8482,1945],{},[902,8484,7798],{"encoding":904}," právě proto, že ",[883,8487,8489],{"className":8488},[886],[888,8490,8491],{"xmlns":890},[892,8492,8493,8511],{},[895,8494,8495,8501,8503,8505,8507,8509],{},[1824,8496,8497,8499],{},[898,8498,1828],{},[1761,8500,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,8502,1915],{"stretchy":1821},[898,8504,1839],{},[1761,8506,1920],{"stretchy":1821},[1761,8508,2058],{},[1765,8510,1767],{},[902,8512,8513],{"encoding":904},"Q'(P) \u003C 0"," (poptávka klesá s cenou). Díky korekčnímu znaménku je výsledné ",[883,8516,8518],{"className":8517},[886],[888,8519,8520],{"xmlns":890},[892,8521,8522,8541],{},[895,8523,8524,8526,8528,8534,8536,8539],{},[898,8525,1818],{},[1761,8527,1915],{"stretchy":1821},[1824,8529,8530,8532],{},[898,8531,1839],{},[1761,8533,8408],{},[1761,8535,1920],{"stretchy":1821},[1761,8537,8538],{},"≥",[1765,8540,1767],{},[902,8542,8543],{"encoding":904},"E(P^*) \\ge 0"," a s touto nezápornou konvencí pracuje celá klasifikace ",[883,8546,8548],{"className":8547},[886],[888,8549,8550],{"xmlns":890},[892,8551,8552,8560],{},[895,8553,8554,8556,8558],{},[898,8555,1818],{},[1761,8557,1763],{},[1765,8559,1945],{},[902,8561,8562],{"encoding":904},"E > 1",[883,8564,8566],{"className":8565},[886],[888,8567,8568],{"xmlns":890},[892,8569,8570,8578],{},[895,8571,8572,8574,8576],{},[898,8573,1818],{},[1761,8575,2058],{},[1765,8577,1945],{},[902,8579,8580],{"encoding":904},"E \u003C 1",[883,8582,8584],{"className":8583},[886],[888,8585,8586],{"xmlns":890},[892,8587,8588,8596],{},[895,8589,8590,8592,8594],{},[898,8591,1818],{},[1761,8593,1909],{},[1765,8595,1945],{},[902,8597,8598],{"encoding":904},"E = 1",". V některých starších pramenech se ",[883,8601,8603],{"className":8602},[886],[888,8604,8605],{"xmlns":890},[892,8606,8607,8613],{},[895,8608,8609,8611],{},[1761,8610,1885],{},[1765,8612,1945],{},[902,8614,7798],{"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 ",[38,8617,8618],{},"absolutní hodnotou",[1636,8620,8621,8640],{},[724,8622,8623,8625,8626,8639],{},[883,8624,4452],{}," Postup: jak spočítat ",[883,8627,8629],{"className":8628},[886],[888,8630,8631],{"xmlns":890},[892,8632,8633,8637],{},[895,8634,8635],{},[898,8636,1818],{},[902,8638,1818],{"encoding":904}," v bodě",[152,8641,8642,8694,8734,8787,8852],{},[123,8643,8644,8645,8668,8669,8693],{},"Zapište ",[883,8646,8648],{"className":8647},[886],[888,8649,8650],{"xmlns":890},[892,8651,8652,8666],{},[895,8653,8654,8656,8658,8660,8662,8664],{},[898,8655,1828],{},[1761,8657,1909],{},[898,8659,2244],{},[1761,8661,1915],{"stretchy":1821},[898,8663,1839],{},[1761,8665,1920],{"stretchy":1821},[902,8667,8247],{"encoding":904},". Pokud je poptávka zadaná jako ",[883,8670,8672],{"className":8671},[886],[888,8673,8674],{"xmlns":890},[892,8675,8676,8690],{},[895,8677,8678,8680,8682,8684,8686,8688],{},[898,8679,1839],{},[1761,8681,1909],{},[898,8683,2244],{},[1761,8685,1915],{"stretchy":1821},[898,8687,1828],{},[1761,8689,1920],{"stretchy":1821},[902,8691,8692],{"encoding":904},"P = D(Q)",", použijte vztah (4.9).",[123,8695,8696,8697,1741],{},"Spočítejte derivaci ",[883,8698,8700],{"className":8699},[886],[888,8701,8702],{"xmlns":890},[892,8703,8704,8731],{},[895,8705,8706,8712,8714,8716,8718,8720,8722,8724,8727,8729],{},[1824,8707,8708,8710],{},[898,8709,1828],{},[1761,8711,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,8713,1915],{"stretchy":1821},[898,8715,1839],{},[1761,8717,1920],{"stretchy":1821},[1761,8719,1909],{},[898,8721,4346],{"mathvariant":1969},[898,8723,1828],{},[898,8725,8726],{"mathvariant":1969},"\u002F",[898,8728,4346],{"mathvariant":1969},[898,8730,1839],{},[902,8732,8733],{"encoding":904},"Q'(P) = \\mathrm{d}Q\u002F\\mathrm{d}P",[123,8735,8736,8737,8754,8755,1741],{},"Dosaďte zadanou cenu ",[883,8738,8740],{"className":8739},[886],[888,8741,8742],{"xmlns":890},[892,8743,8744,8752],{},[895,8745,8746],{},[1824,8747,8748,8750],{},[898,8749,1839],{},[1761,8751,8408],{},[902,8753,8458],{"encoding":904}," a dopočítejte odpovídající ",[883,8756,8758],{"className":8757},[886],[888,8759,8760],{"xmlns":890},[892,8761,8762,8784],{},[895,8763,8764,8770,8772,8774,8776,8782],{},[1824,8765,8766,8768],{},[898,8767,1828],{},[1761,8769,8408],{},[1761,8771,1909],{},[898,8773,2244],{},[1761,8775,1915],{"stretchy":1821},[1824,8777,8778,8780],{},[898,8779,1839],{},[1761,8781,8408],{},[1761,8783,1920],{"stretchy":1821},[902,8785,8786],{"encoding":904},"Q^* = D(P^*)",[123,8788,8789,8790,1741],{},"Dosaďte do (4.5): ",[883,8791,8793],{"className":8792},[886],[888,8794,8795],{"xmlns":890},[892,8796,8797,8849],{},[895,8798,8799,8801,8803,8809,8811,8813,8815,8831,8833,8839,8841,8847],{},[898,8800,1818],{},[1761,8802,1915],{"stretchy":1821},[1824,8804,8805,8807],{},[898,8806,1839],{},[1761,8808,8408],{},[1761,8810,1920],{"stretchy":1821},[1761,8812,1909],{},[1761,8814,1885],{},[6411,8816,8817],{"scriptlevel":1767,"displaystyle":1833},[4379,8818,8819,8825],{},[1824,8820,8821,8823],{},[898,8822,1839],{},[1761,8824,8408],{},[1824,8826,8827,8829],{},[898,8828,1828],{},[1761,8830,8408],{},[2761,8832,7057],{},[1824,8834,8835,8837],{},[898,8836,1828],{},[1761,8838,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,8840,1915],{"stretchy":1821},[1824,8842,8843,8845],{},[898,8844,1839],{},[1761,8846,8408],{},[1761,8848,1920],{"stretchy":1821},[902,8850,8851],{"encoding":904},"E(P^*) = -\\dfrac{P^*}{Q^*}\\,Q'(P^*)",[123,8853,8854,8855,8872,8873,8890,8891,8908],{},"Klasifikujte: ",[883,8856,8858],{"className":8857},[886],[888,8859,8860],{"xmlns":890},[892,8861,8862,8870],{},[895,8863,8864,8866,8868],{},[898,8865,1818],{},[1761,8867,1763],{},[1765,8869,1945],{},[902,8871,8562],{"encoding":904}," elastická, ",[883,8874,8876],{"className":8875},[886],[888,8877,8878],{"xmlns":890},[892,8879,8880,8888],{},[895,8881,8882,8884,8886],{},[898,8883,1818],{},[1761,8885,1909],{},[1765,8887,1945],{},[902,8889,8598],{"encoding":904}," jednotková, ",[883,8892,8894],{"className":8893},[886],[888,8895,8896],{"xmlns":890},[892,8897,8898,8906],{},[895,8899,8900,8902,8904],{},[898,8901,1818],{},[1761,8903,2058],{},[1765,8905,1945],{},[902,8907,8580],{"encoding":904}," neelastická.",[198,8910,8912],{"id":8911},"interpretace-46","Interpretace (4.6)",[1636,8914,8915],{},[724,8916,8917,8918,8941,8942,8955,8956,8973,8974],{},"Číslo ",[883,8919,8921],{"className":8920},[886],[888,8922,8923],{"xmlns":890},[892,8924,8925,8939],{},[895,8926,8927,8929,8931,8937],{},[898,8928,1818],{},[1761,8930,1915],{"stretchy":1821},[1824,8932,8933,8935],{},[898,8934,1839],{},[1761,8936,8408],{},[1761,8938,1920],{"stretchy":1821},[902,8940,8436],{"encoding":904}," udává, o kolik % se přibližně změní poptávané množství ",[883,8943,8945],{"className":8944},[886],[888,8946,8947],{"xmlns":890},[892,8948,8949,8953],{},[895,8950,8951],{},[898,8952,1828],{},[902,8954,1828],{"encoding":904},", jestliže se cena ",[883,8957,8959],{"className":8958},[886],[888,8960,8961],{"xmlns":890},[892,8962,8963,8971],{},[895,8964,8965],{},[1824,8966,8967,8969],{},[898,8968,1839],{},[1761,8970,8408],{},[902,8972,8458],{"encoding":904}," změní o 1 %. ",[883,8975,8977],{"className":8976},[886],[888,8978,8979],{"xmlns":890},[892,8980,8981,8990],{},[895,8982,8983,8985,8988],{},[1761,8984,1915],{"stretchy":1821},[1765,8986,8987],{},"4.6",[1761,8989,1920],{"stretchy":1821},[902,8991,8992],{"encoding":904},"(4.6)",[724,8994,8995,8998],{},[38,8996,8997],{},"Historicky:"," úvahy vedoucí k hypotéze (4.1) formuloval již Cournot (1838), dnešní vymezení se připisuje Marshallovi (1881).",[198,9000,9002],{"id":9001},"příklad-41","Příklad 4.1",[724,9004,9005,9006,9040,9041,1343,9066,2506],{},"Poptávka ",[883,9007,9009],{"className":9008},[886],[888,9010,9011],{"xmlns":890},[892,9012,9013,9037],{},[895,9014,9015,9017,9019,9021,9023,9025,9027,9029,9031,9033,9035],{},[898,9016,1839],{},[1761,9018,1909],{},[898,9020,2244],{},[1761,9022,1915],{"stretchy":1821},[898,9024,1828],{},[1761,9026,1920],{"stretchy":1821},[1761,9028,1909],{},[1765,9030,7190],{},[1761,9032,1885],{},[1765,9034,2296],{},[898,9036,1828],{},[902,9038,9039],{"encoding":904},"P = D(Q) = 50 - 2Q",". Vyjádříme ",[883,9042,9044],{"className":9043},[886],[888,9045,9046],{"xmlns":890},[892,9047,9048,9063],{},[895,9049,9050,9052,9054,9057,9059,9061],{},[898,9051,1828],{},[1761,9053,1909],{},[1765,9055,9056],{},"25",[1761,9058,1885],{},[1765,9060,5426],{},[898,9062,1839],{},[902,9064,9065],{"encoding":904},"Q = 25 - 0{,}5P",[883,9067,9069],{"className":9068},[886],[888,9070,9071],{"xmlns":890},[892,9072,9073,9097],{},[895,9074,9075,9091,9093,9095],{},[6411,9076,9077],{"scriptlevel":1767,"displaystyle":1833},[4379,9078,9079,9085],{},[895,9080,9081,9083],{},[898,9082,4346],{"mathvariant":1969},[898,9084,1828],{},[895,9086,9087,9089],{},[898,9088,4346],{"mathvariant":1969},[898,9090,1839],{},[1761,9092,1909],{},[1761,9094,1885],{},[1765,9096,5426],{},[902,9098,9099],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -0{,}5",[724,9101,9102],{},[883,9103,9105],{"className":9104},[886],[888,9106,9107],{"xmlns":890},[892,9108,9109,9163],{},[895,9110,9111,9113,9115,9117,9131,9133,9135,9137,9139,9141,9143,9161],{},[898,9112,1818],{},[1761,9114,1909],{},[1761,9116,1885],{},[4379,9118,9119,9121],{},[898,9120,1839],{},[895,9122,9123,9125,9127,9129],{},[1765,9124,9056],{},[1761,9126,1885],{},[1765,9128,5426],{},[898,9130,1839],{},[1761,9132,2447],{},[1761,9134,1915],{"stretchy":1821},[1761,9136,1885],{},[1765,9138,5426],{},[1761,9140,1920],{"stretchy":1821},[1761,9142,1909],{},[4379,9144,9145,9151],{},[895,9146,9147,9149],{},[1765,9148,5426],{},[898,9150,1839],{},[895,9152,9153,9155,9157,9159],{},[1765,9154,9056],{},[1761,9156,1885],{},[1765,9158,5426],{},[898,9160,1839],{},[898,9162,1741],{"mathvariant":1969},[902,9164,9165],{"encoding":904},"E = -\\frac{P}{25-0{,}5P}\\cdot(-0{,}5) = \\frac{0{,}5P}{25-0{,}5P}.",[724,9167,9168,9169,1343,9193,1343,9223,1343,9247,9272,9273,9296,9297,4178,9315,2162],{},"Potom ",[883,9170,9172],{"className":9171},[886],[888,9173,9174],{"xmlns":890},[892,9175,9176,9190],{},[895,9177,9178,9180,9182,9184,9186,9188],{},[898,9179,1818],{},[1761,9181,1915],{"stretchy":1821},[1765,9183,1767],{},[1761,9185,1920],{"stretchy":1821},[1761,9187,1909],{},[1765,9189,1767],{},[902,9191,9192],{"encoding":904},"E(0)=0",[883,9194,9196],{"className":9195},[886],[888,9197,9198],{"xmlns":890},[892,9199,9200,9220],{},[895,9201,9202,9204,9206,9208,9210,9212],{},[898,9203,1818],{},[1761,9205,1915],{"stretchy":1821},[1765,9207,2633],{},[1761,9209,1920],{"stretchy":1821},[1761,9211,1909],{},[6411,9213,9214],{"scriptlevel":1767,"displaystyle":1821},[4379,9215,9216,9218],{},[1765,9217,1945],{},[1765,9219,2318],{},[902,9221,9222],{"encoding":904},"E(10)=\\tfrac{1}{4}",[883,9224,9226],{"className":9225},[886],[888,9227,9228],{"xmlns":890},[892,9229,9230,9244],{},[895,9231,9232,9234,9236,9238,9240,9242],{},[898,9233,1818],{},[1761,9235,1915],{"stretchy":1821},[1765,9237,9056],{},[1761,9239,1920],{"stretchy":1821},[1761,9241,1909],{},[1765,9243,1945],{},[902,9245,9246],{"encoding":904},"E(25)=1",[883,9248,9250],{"className":9249},[886],[888,9251,9252],{"xmlns":890},[892,9253,9254,9269],{},[895,9255,9256,9258,9260,9263,9265,9267],{},[898,9257,1818],{},[1761,9259,1915],{"stretchy":1821},[1765,9261,9262],{},"40",[1761,9264,1920],{"stretchy":1821},[1761,9266,1909],{},[1765,9268,2318],{},[902,9270,9271],{"encoding":904},"E(40)=4",". Např. ",[883,9274,9276],{"className":9275},[886],[888,9277,9278],{"xmlns":890},[892,9279,9280,9294],{},[895,9281,9282,9284,9286,9288,9290,9292],{},[898,9283,1818],{},[1761,9285,1915],{"stretchy":1821},[1765,9287,9262],{},[1761,9289,1920],{"stretchy":1821},[1761,9291,1909],{},[1765,9293,2318],{},[902,9295,9271],{"encoding":904}," znamená, že zvýšení ceny o 1 % (z 40 na 40,4) způsobí pokles množství o 4 % (z ",[883,9298,9300],{"className":9299},[886],[888,9301,9302],{"xmlns":890},[892,9303,9304,9312],{},[895,9305,9306,9308,9310],{},[898,9307,1828],{},[1761,9309,1909],{},[1765,9311,6321],{},[902,9313,9314],{"encoding":904},"Q=5",[883,9316,9318],{"className":9317},[886],[888,9319,9320],{"xmlns":890},[892,9321,9322,9331],{},[895,9323,9324,9326,9328],{},[898,9325,1828],{},[1761,9327,1909],{},[1765,9329,9330],{},"4,8",[902,9332,9333],{"encoding":904},"Q=4{,}8",[198,9335,9337],{"id":9336},"oblouková-průměrná-vs-bodová-okamžitá-elasticita","Oblouková (průměrná) vs. bodová (okamžitá) elasticita",[120,9339,9340,9396],{},[123,9341,9342,9345,9346,9363,9364,1741],{},[38,9343,9344],{},"Oblouková"," (průměrná) elasticita: výraz ",[883,9347,9349],{"className":9348},[886],[888,9350,9351],{"xmlns":890},[892,9352,9353,9361],{},[895,9354,9355],{},[1824,9356,9357,9359],{},[898,9358,1818],{},[898,9360,8309],{},[902,9362,8312],{"encoding":904}," ze (4.4) vztažený k intervalu ",[883,9365,9367],{"className":9366},[886],[888,9368,9369],{"xmlns":890},[892,9370,9371,9393],{},[895,9372,9373,9376,9378,9380,9382,9384,9386,9388,9390],{},[1761,9374,9375],{"stretchy":1821},"⟨",[898,9377,1839],{},[1761,9379,1834],{"separator":1833},[2761,9381,7057],{},[898,9383,1839],{},[1761,9385,1964],{},[898,9387,6959],{"mathvariant":1969},[898,9389,1839],{},[1761,9391,9392],{"stretchy":1821},"⟩",[902,9394,9395],{"encoding":904},"\\langle P,\\, P+\\Delta P\\rangle",[123,9397,9398,9401,9402,9415],{},[38,9399,9400],{},"Bodová"," (okamžitá) elasticita: ",[883,9403,9405],{"className":9404},[886],[888,9406,9407],{"xmlns":890},[892,9408,9409,9413],{},[895,9410,9411],{},[898,9412,1818],{},[902,9414,1818],{"encoding":904}," dle (4.5) — výchozí pojem dále v textu.",[198,9417,9419,9420,9433,9434],{"id":9418},"výpočet-je-li-dáno-pp-jako-funkce-qq","Výpočet, je-li dáno ",[883,9421,9423],{"className":9422},[886],[888,9424,9425],{"xmlns":890},[892,9426,9427,9431],{},[895,9428,9429],{},[898,9430,1839],{},[902,9432,1839],{"encoding":904}," jako funkce ",[883,9435,9437],{"className":9436},[886],[888,9438,9439],{"xmlns":890},[892,9440,9441,9445],{},[895,9442,9443],{},[898,9444,1828],{},[902,9446,1828],{"encoding":904},[724,9448,9449,9450,9473],{},"Pokud je poptávka zadaná ve tvaru ",[883,9451,9453],{"className":9452},[886],[888,9454,9455],{"xmlns":890},[892,9456,9457,9471],{},[895,9458,9459,9461,9463,9465,9467,9469],{},[898,9460,1839],{},[1761,9462,1909],{},[898,9464,2244],{},[1761,9466,1915],{"stretchy":1821},[898,9468,1828],{},[1761,9470,1920],{"stretchy":1821},[902,9472,8692],{"encoding":904},", využijeme vztah pro derivaci inverzní funkce",[724,9475,9476],{},[883,9477,9479],{"className":9478,"title":8255,"style":8256},[8254],"\\frac{\\mathrm{d}Q}{\\mathrm{d}P} = \\frac{1}{\\frac{\\mathrm{d}P}{\\mathrm{d}Q}}. \\tag{4.9}",[724,9481,9482,1989,9485,9511],{},[38,9483,9484],{},"Příklad 4.3.",[883,9486,9488],{"className":9487},[886],[888,9489,9490],{"xmlns":890},[892,9491,9492,9508],{},[895,9493,9494,9496,9498,9500,9502],{},[898,9495,1839],{},[1761,9497,1909],{},[1765,9499,7160],{},[1761,9501,1885],{},[1824,9503,9504,9506],{},[898,9505,1828],{},[1765,9507,2296],{},[902,9509,9510],{"encoding":904},"P = 100 - Q^2",", ptáme se na elasticitu při ceně 36. Dostáváme",[724,9513,9514],{},[883,9515,9517],{"className":9516},[886],[888,9518,9519],{"xmlns":890},[892,9520,9521,9587],{},[895,9522,9523,9525,9527,9529,9545,9547,9559,9561,9585],{},[898,9524,1818],{},[1761,9526,1909],{},[1761,9528,1885],{},[4379,9530,9531,9543],{},[895,9532,9533,9535,9537],{},[1765,9534,7160],{},[1761,9536,1885],{},[1824,9538,9539,9541],{},[898,9540,1828],{},[1765,9542,2296],{},[898,9544,1828],{},[1761,9546,2447],{},[4379,9548,9549,9551],{},[1765,9550,1945],{},[895,9552,9553,9555,9557],{},[1761,9554,1885],{},[1765,9556,2296],{},[898,9558,1828],{},[1761,9560,1909],{},[4379,9562,9563,9575],{},[895,9564,9565,9567,9569],{},[1765,9566,7160],{},[1761,9568,1885],{},[1824,9570,9571,9573],{},[898,9572,1828],{},[1765,9574,2296],{},[895,9576,9577,9579],{},[1765,9578,2296],{},[1824,9580,9581,9583],{},[898,9582,1828],{},[1765,9584,2296],{},[898,9586,1741],{"mathvariant":1969},[902,9588,9589],{"encoding":904},"E = -\\frac{100-Q^2}{Q}\\cdot \\frac{1}{-2Q} = \\frac{100-Q^2}{2Q^2}.",[724,9591,9592,9593,2382,9620,2403,9638,1741],{},"Z rovnice ",[883,9594,9596],{"className":9595},[886],[888,9597,9598],{"xmlns":890},[892,9599,9600,9617],{},[895,9601,9602,9604,9606,9612,9614],{},[1765,9603,7160],{},[1761,9605,1885],{},[1824,9607,9608,9610],{},[898,9609,1828],{},[1765,9611,2296],{},[1761,9613,1909],{},[1765,9615,9616],{},"36",[902,9618,9619],{"encoding":904},"100 - Q^2 = 36",[883,9621,9623],{"className":9622},[886],[888,9624,9625],{"xmlns":890},[892,9626,9627,9635],{},[895,9628,9629,9631,9633],{},[898,9630,1828],{},[1761,9632,1909],{},[1765,9634,2454],{},[902,9636,9637],{"encoding":904},"Q = 8",[883,9639,9641],{"className":9640},[886],[888,9642,9643],{"xmlns":890},[892,9644,9645,9671],{},[895,9646,9647,9649,9651,9653,9655,9657,9666,9668],{},[898,9648,1818],{},[1761,9650,1915],{"stretchy":1821},[1765,9652,2454],{},[1761,9654,1920],{"stretchy":1821},[1761,9656,1909],{},[6411,9658,9659],{"scriptlevel":1767,"displaystyle":1821},[4379,9660,9661,9663],{},[1765,9662,9616],{},[1765,9664,9665],{},"128",[1761,9667,1909],{},[1765,9669,9670],{},"0,281",[902,9672,9673],{"encoding":904},"E(8) = \\tfrac{36}{128} = 0{,}281",[198,9675,9677],{"id":9676},"přibližné-změny","Přibližné změny",[724,9679,9680,9681,2232,9717,9739],{},"Diferenciál ",[883,9682,9684],{"className":9683},[886],[888,9685,9686],{"xmlns":890},[892,9687,9688,9714],{},[895,9689,9690,9692,9694,9696,9702,9704,9706,9708,9710,9712],{},[898,9691,4346],{"mathvariant":1969},[898,9693,1828],{},[1761,9695,1909],{},[1824,9697,9698,9700],{},[898,9699,1828],{},[1761,9701,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,9703,1915],{"stretchy":1821},[898,9705,1839],{},[1761,9707,1920],{"stretchy":1821},[2761,9709,7057],{},[898,9711,4346],{"mathvariant":1969},[898,9713,1839],{},[902,9715,9716],{"encoding":904},"\\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P",[883,9718,9720],{"className":9719},[886],[888,9721,9722],{"xmlns":890},[892,9723,9724,9736],{},[895,9725,9726,9728,9730,9732,9734],{},[898,9727,4346],{"mathvariant":1969},[898,9729,1839],{},[1761,9731,1909],{},[898,9733,6959],{"mathvariant":1969},[898,9735,1839],{},[902,9737,9738],{"encoding":904},"\\mathrm{d}P = \\Delta P"," dává nominální odhad",[724,9741,9742],{},[883,9743,9745],{"className":9744,"title":8255,"style":8256},[8254],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P. \\tag{4.10}",[724,9747,9748],{},"Po přechodu na procentní změny (vztah (4.3)):",[724,9750,9751],{},[883,9752,9754],{"className":9753,"title":8255,"style":8256},[8254],"\\boxed{\\;\\Delta Q\\% \\approx -E(P)\\,\\Delta P\\%\\;} \\tag{4.11}",[724,9756,9757,1989,9760,9795,9796,9815,9816,9850,9851,9868],{},[38,9758,9759],{},"Příklad 4.5.",[883,9761,9763],{"className":9762},[886],[888,9764,9765],{"xmlns":890},[892,9766,9767,9792],{},[895,9768,9769,9771,9773,9775,9781,9783,9785,9787,9789],{},[898,9770,1839],{},[1761,9772,1909],{},[1761,9774,1885],{},[1824,9776,9777,9779],{},[898,9778,1828],{},[1765,9780,2296],{},[1761,9782,1885],{},[1765,9784,2318],{},[898,9786,1828],{},[1761,9788,1964],{},[1765,9790,9791],{},"96",[902,9793,9794],{"encoding":904},"P = -Q^2 - 4Q + 96",", cena ",[883,9797,9799],{"className":9798},[886],[888,9800,9801],{"xmlns":890},[892,9802,9803,9812],{},[895,9804,9805,9807,9809],{},[898,9806,1839],{},[1761,9808,1909],{},[1765,9810,9811],{},"51",[902,9813,9814],{"encoding":904},"P=51",". Z rovnice ",[883,9817,9819],{"className":9818},[886],[888,9820,9821],{"xmlns":890},[892,9822,9823,9847],{},[895,9824,9825,9827,9829,9831,9837,9839,9841,9843,9845],{},[1765,9826,9811],{},[1761,9828,1909],{},[1761,9830,1885],{},[1824,9832,9833,9835],{},[898,9834,1828],{},[1765,9836,2296],{},[1761,9838,1885],{},[1765,9840,2318],{},[898,9842,1828],{},[1761,9844,1964],{},[1765,9846,9791],{},[902,9848,9849],{"encoding":904},"51 = -Q^2-4Q+96"," volíme (kladný kořen) ",[883,9852,9854],{"className":9853},[886],[888,9855,9856],{"xmlns":890},[892,9857,9858,9866],{},[895,9859,9860,9862,9864],{},[898,9861,1828],{},[1761,9863,1909],{},[1765,9865,6321],{},[902,9867,9314],{"encoding":904},". Elasticita:",[724,9870,9871],{},[883,9872,9874],{"className":9873},[886],[888,9875,9876],{"xmlns":890},[892,9877,9878,9949],{},[895,9879,9880,9882,9884,9922,9924,9926,9928,9930,9932,9934,9936,9943,9946],{},[898,9881,1818],{},[1761,9883,1909],{},[4379,9885,9886,9906],{},[895,9887,9888,9890,9896,9898,9900,9902,9904],{},[1761,9889,1885],{},[1824,9891,9892,9894],{},[898,9893,1828],{},[1765,9895,2296],{},[1761,9897,1885],{},[1765,9899,2318],{},[898,9901,1828],{},[1761,9903,1964],{},[1765,9905,9791],{},[895,9907,9908,9910,9912,9914,9916,9918,9920],{},[898,9909,1828],{},[1761,9911,1915],{"stretchy":1821},[1765,9913,2296],{},[898,9915,1828],{},[1761,9917,1964],{},[1765,9919,2318],{},[1761,9921,1920],{"stretchy":1821},[1761,9923,1834],{"separator":1833},[3315,9925],{"width":3317},[898,9927,1818],{},[1761,9929,1915],{"stretchy":1821},[1765,9931,6321],{},[1761,9933,1920],{"stretchy":1821},[1761,9935,1909],{},[4379,9937,9938,9940],{},[1765,9939,9811],{},[1765,9941,9942],{},"70",[1761,9944,9945],{},"≐",[1765,9947,9948],{},"0,728.",[902,9950,9951],{"encoding":904},"E = \\frac{-Q^2-4Q+96}{Q(2Q+4)}, \\qquad E(5) = \\frac{51}{70} \\doteq 0{,}728.",[724,9953,9954,9955,1741],{},"Jde o neelastickou poptávku. Zvýší-li se cena o 2 %, pak ",[883,9956,9958],{"className":9957},[886],[888,9959,9960],{"xmlns":890},[892,9961,9962,9993],{},[895,9963,9964,9966,9968,9971,9973,9975,9978,9980,9982,9984,9986,9989,9991],{},[898,9965,6959],{"mathvariant":1969},[898,9967,1828],{},[898,9969,9970],{"mathvariant":1969},"%",[1761,9972,6803],{},[1761,9974,1885],{},[1765,9976,9977],{},"0,728",[1761,9979,2447],{},[1765,9981,2296],{},[1761,9983,1909],{},[1761,9985,1885],{},[1765,9987,9988],{},"1,456",[2761,9990,7057],{},[898,9992,9970],{"mathvariant":1969},[902,9994,9995],{"encoding":904},"\\Delta Q\\% \\approx -0{,}728\\cdot 2 = -1{,}456\\,\\%",[115,9997,9999],{"id":9998},"klasifikace-elasticit-poptávky","Klasifikace elasticit poptávky",[724,10001,10002,10003,10026,10027,2506],{},"V závislosti na hodnotě ",[883,10004,10006],{"className":10005},[886],[888,10007,10008],{"xmlns":890},[892,10009,10010,10024],{},[895,10011,10012,10014,10016,10022],{},[898,10013,1818],{},[1761,10015,1915],{"stretchy":1821},[1824,10017,10018,10020],{},[898,10019,1839],{},[1761,10021,8408],{},[1761,10023,1920],{"stretchy":1821},[902,10025,8436],{"encoding":904}," mluvíme o poptávce podle následující tabulky ",[883,10028,10030],{"className":10029},[886],[888,10031,10032],{"xmlns":890},[892,10033,10034,10043],{},[895,10035,10036,10038,10041],{},[1761,10037,1915],{"stretchy":1821},[1765,10039,10040],{},"4.7",[1761,10042,1920],{"stretchy":1821},[902,10044,10045],{"encoding":904},"(4.7)",[724,10047,10048],{},[3991,10049],{"alt":10050,"className":10051,"src":10052},"imek-typy-elasticity-5panelu",[210,3995],"\u002Fwiki-assets\u002Fimek-typy-elasticity-5panelu.jpeg",[16,10054,10055,10094],{},[19,10056,10057],{},[22,10058,10059,10085,10088,10091],{},[25,10060,10061,10062],{},"Hodnota ",[883,10063,10065],{"className":10064},[886],[888,10066,10067],{"xmlns":890},[892,10068,10069,10083],{},[895,10070,10071,10073,10075,10081],{},[898,10072,1818],{},[1761,10074,1915],{"stretchy":1821},[1824,10076,10077,10079],{},[898,10078,1839],{},[1761,10080,8408],{},[1761,10082,1920],{"stretchy":1821},[902,10084,8436],{"encoding":904},[25,10086,10087],{},"Typ poptávky",[25,10089,10090],{},"Termín",[25,10092,10093],{},"Význam",[30,10095,10096,10129,10191,10266,10323],{},[22,10097,10098,10118,10123,10126],{},[35,10099,10100],{},[883,10101,10103],{"className":10102},[886],[888,10104,10105],{"xmlns":890},[892,10106,10107,10115],{},[895,10108,10109,10111,10113],{},[898,10110,1818],{},[1761,10112,1909],{},[1765,10114,1767],{},[902,10116,10117],{"encoding":904},"E = 0",[35,10119,10120],{},[38,10121,10122],{},"dokonale neelastická",[35,10124,10125],{},"perfectly inelastic",[35,10127,10128],{},"množství se nemění bez ohledu na cenu",[22,10130,10131,10155,10159,10162],{},[35,10132,10133],{},[883,10134,10136],{"className":10135},[886],[888,10137,10138],{"xmlns":890},[892,10139,10140,10152],{},[895,10141,10142,10144,10146,10148,10150],{},[1765,10143,1767],{},[1761,10145,2058],{},[898,10147,1818],{},[1761,10149,2058],{},[1765,10151,1945],{},[902,10153,10154],{"encoding":904},"0 \u003C E \u003C 1",[35,10156,10157],{},[38,10158,8134],{},[35,10160,10161],{},"inelastic",[35,10163,10164,10177,10178],{},[883,10165,10167],{"className":10166},[886],[888,10168,10169],{"xmlns":890},[892,10170,10171,10175],{},[895,10172,10173],{},[898,10174,1828],{},[902,10176,1828],{"encoding":904}," se mění pomaleji než ",[883,10179,10181],{"className":10180},[886],[888,10182,10183],{"xmlns":890},[892,10184,10185,10189],{},[895,10186,10187],{},[898,10188,1839],{},[902,10190,1839],{"encoding":904},[22,10192,10193,10212,10217,10220],{},[35,10194,10195],{},[883,10196,10198],{"className":10197},[886],[888,10199,10200],{"xmlns":890},[892,10201,10202,10210],{},[895,10203,10204,10206,10208],{},[898,10205,1818],{},[1761,10207,1909],{},[1765,10209,1945],{},[902,10211,8598],{"encoding":904},[35,10213,10214],{},[38,10215,10216],{},"jednotkově elastická",[35,10218,10219],{},"unit elastic",[35,10221,10222,10235,10236,10249,10250,10265],{},[883,10223,10225],{"className":10224},[886],[888,10226,10227],{"xmlns":890},[892,10228,10229,10233],{},[895,10230,10231],{},[898,10232,1828],{},[902,10234,1828],{"encoding":904}," i ",[883,10237,10239],{"className":10238},[886],[888,10240,10241],{"xmlns":890},[892,10242,10243,10247],{},[895,10244,10245],{},[898,10246,1839],{},[902,10248,1839],{"encoding":904}," se mění stejně rychle; ",[883,10251,10253],{"className":10252},[886],[888,10254,10255],{"xmlns":890},[892,10256,10257,10263],{},[895,10258,10259,10261],{},[898,10260,1655],{},[898,10262,8051],{},[902,10264,8151],{"encoding":904}," má maximum",[22,10267,10268,10287,10291,10294],{},[35,10269,10270],{},[883,10271,10273],{"className":10272},[886],[888,10274,10275],{"xmlns":890},[892,10276,10277,10285],{},[895,10278,10279,10281,10283],{},[898,10280,1818],{},[1761,10282,1763],{},[1765,10284,1945],{},[902,10286,8562],{"encoding":904},[35,10288,10289],{},[38,10290,8130],{},[35,10292,10293],{},"elastic",[35,10295,10296,10309,10310],{},[883,10297,10299],{"className":10298},[886],[888,10300,10301],{"xmlns":890},[892,10302,10303,10307],{},[895,10304,10305],{},[898,10306,1828],{},[902,10308,1828],{"encoding":904}," se mění rychleji než ",[883,10311,10313],{"className":10312},[886],[888,10314,10315],{"xmlns":890},[892,10316,10317,10321],{},[895,10318,10319],{},[898,10320,1839],{},[902,10322,1839],{"encoding":904},[22,10324,10325,10346,10351,10354],{},[35,10326,10327],{},[883,10328,10330],{"className":10329},[886],[888,10331,10332],{"xmlns":890},[892,10333,10334,10343],{},[895,10335,10336,10338,10340],{},[898,10337,1818],{},[1761,10339,2181],{},[898,10341,10342],{"mathvariant":1969},"∞",[902,10344,10345],{"encoding":904},"E \\to \\infty",[35,10347,10348],{},[38,10349,10350],{},"dokonale elastická",[35,10352,10353],{},"perfectly elastic",[35,10355,10356,10357],{},"sebemenší změna ceny úplně mění ",[883,10358,10360],{"className":10359},[886],[888,10361,10362],{"xmlns":890},[892,10363,10364,10368],{},[895,10365,10366],{},[898,10367,1828],{},[902,10369,1828],{"encoding":904},[724,10371,10372],{},[38,10373,10374],{},"Pravidlo růstu elasticity s cenou:",[1636,10376,10377],{},[724,10378,10379,10380],{},"S rostoucí cenou elasticita poptávky roste. ",[883,10381,10383],{"className":10382},[886],[888,10384,10385],{"xmlns":890},[892,10386,10387,10396],{},[895,10388,10389,10391,10394],{},[1761,10390,1915],{"stretchy":1821},[1765,10392,10393],{},"4.8",[1761,10395,1920],{"stretchy":1821},[902,10397,10398],{"encoding":904},"(4.8)",[724,10400,10401,10402,10405,10406,10409,10410,10427],{},"Z toho plyne, že při ",[614,10403,10404],{},"dostatečně nízkých"," cenách je poptávka neelastická a při ",[614,10407,10408],{},"dostatečně vysokých"," elastická. Existuje tedy cena ",[883,10411,10413],{"className":10412},[886],[888,10414,10415],{"xmlns":890},[892,10416,10417,10425],{},[895,10418,10419],{},[1824,10420,10421,10423],{},[898,10422,1839],{},[1761,10424,8408],{},[902,10426,8458],{"encoding":904},", při které je poptávka jednotkově elastická, a ta rozděluje reálné cenové rozpětí na obě zóny.",[1636,10429,10430,10435],{},[724,10431,10432,10434],{},[883,10433,4452],{}," Postup: jak klasifikovat poptávku",[152,10436,10437,10464,10467],{},[123,10438,10439,10440,10463],{},"Spočítejte ",[883,10441,10443],{"className":10442},[886],[888,10444,10445],{"xmlns":890},[892,10446,10447,10461],{},[895,10448,10449,10451,10453,10459],{},[898,10450,1818],{},[1761,10452,1915],{"stretchy":1821},[1824,10454,10455,10457],{},[898,10456,1839],{},[1761,10458,8408],{},[1761,10460,1920],{"stretchy":1821},[902,10462,8436],{"encoding":904}," dle (4.5).",[123,10465,10466],{},"Porovnejte s jedničkou (viz tabulka výše).",[123,10468,10469,10470,10494],{},"Chcete-li najít hranici mezi elastickou a neelastickou zónou, řešte rovnici ",[883,10471,10473],{"className":10472},[886],[888,10474,10475],{"xmlns":890},[892,10476,10477,10491],{},[895,10478,10479,10481,10483,10485,10487,10489],{},[898,10480,1818],{},[1761,10482,1915],{"stretchy":1821},[898,10484,1839],{},[1761,10486,1920],{"stretchy":1821},[1761,10488,1909],{},[1765,10490,1945],{},[902,10492,10493],{"encoding":904},"E(P) = 1"," a výsledek porovnejte s reálným cenovým rozpětím.",[724,10496,10497,10500,10501,10518,10519,10537,10538,10565,10566,1741],{},[38,10498,10499],{},"Příklad 4.2."," Pro poptávku z Příkladu 4.1: ",[883,10502,10504],{"className":10503},[886],[888,10505,10506],{"xmlns":890},[892,10507,10508,10516],{},[895,10509,10510,10512,10514],{},[898,10511,1818],{},[1761,10513,1909],{},[1765,10515,1945],{},[902,10517,8598],{"encoding":904}," pro ",[883,10520,10522],{"className":10521},[886],[888,10523,10524],{"xmlns":890},[892,10525,10526,10534],{},[895,10527,10528,10530,10532],{},[898,10529,1839],{},[1761,10531,1909],{},[1765,10533,9056],{},[902,10535,10536],{"encoding":904},"P = 25",". Podle (4.8) je poptávka neelastická pro ",[883,10539,10541],{"className":10540},[886],[888,10542,10543],{"xmlns":890},[892,10544,10545,10562],{},[895,10546,10547,10549,10552,10554,10556,10558,10560],{},[898,10548,1839],{},[1761,10550,10551],{},"∈",[1761,10553,9375],{"stretchy":1821},[1765,10555,1767],{},[1761,10557,1834],{"separator":1833},[1765,10559,9056],{},[1761,10561,1920],{"stretchy":1821},[902,10563,10564],{"encoding":904},"P \\in \\langle 0, 25)"," a elastická pro ",[883,10567,10569],{"className":10568},[886],[888,10570,10571],{"xmlns":890},[892,10572,10573,10589],{},[895,10574,10575,10577,10579,10581,10583,10585,10587],{},[898,10576,1839],{},[1761,10578,10551],{},[1761,10580,1915],{"stretchy":1821},[1765,10582,9056],{},[1761,10584,1834],{"separator":1833},[1765,10586,7190],{},[1761,10588,9392],{"stretchy":1821},[902,10590,10591],{"encoding":904},"P \\in (25, 50\\rangle",[115,10593,10595],{"id":10594},"elasticita-a-celkový-příjem","Elasticita a celkový příjem",[724,10597,10598],{},[3991,10599],{"alt":10600,"className":10601,"src":10602},"imek-elasticita-tr",[210,3995],"\u002Fwiki-assets\u002Fimek-elasticita-tr.jpeg",[724,10604,10605],{},[3991,10606],{"alt":10607,"className":10608,"src":10609},"imek-elasticita-podel-linearni-poptavky",[210,3995],"\u002Fwiki-assets\u002Fimek-elasticita-podel-linearni-poptavky.jpeg",[724,10611,10612,10613,10663,10664,10680],{},"Pro celkový příjem platí ",[883,10614,10616],{"className":10615},[886],[888,10617,10618],{"xmlns":890},[892,10619,10620,10660],{},[895,10621,10622,10624,10626,10628,10630,10632,10634,10636,10638,10640,10642,10644,10646,10648,10650,10652,10654,10656,10658],{},[898,10623,1655],{},[898,10625,8051],{},[1761,10627,1909],{},[898,10629,1655],{},[898,10631,8051],{},[1761,10633,1915],{"stretchy":1821},[898,10635,1828],{},[1761,10637,1920],{"stretchy":1821},[1761,10639,1909],{},[898,10641,1839],{},[1761,10643,2447],{},[898,10645,1828],{},[1761,10647,1909],{},[898,10649,1828],{},[1761,10651,2447],{},[898,10653,2244],{},[1761,10655,1915],{"stretchy":1821},[898,10657,1828],{},[1761,10659,1920],{"stretchy":1821},[902,10661,10662],{"encoding":904},"TR = TR(Q) = P\\cdot Q = Q\\cdot D(Q)",". Pro mezní příjem ",[883,10665,10667],{"className":10666},[886],[888,10668,10669],{"xmlns":890},[892,10670,10671,10677],{},[895,10672,10673,10675],{},[898,10674,6889],{},[898,10676,8051],{},[902,10678,10679],{"encoding":904},"MR"," odvodíme:",[724,10682,10683],{},[883,10684,10686],{"className":10685},[886],[888,10687,10688],{"xmlns":890},[892,10689,10690,10798],{},[895,10691,10692,10694,10696,10698,10700,10706,10708,10710,10712,10714,10716,10718,10720,10722,10724,10726,10728,10734,10736,10738,10740,10742,10744,10746,10748,10762,10764,10766],{},[898,10693,6889],{},[898,10695,8051],{},[1761,10697,1909],{},[898,10699,1655],{},[1824,10701,10702,10704],{},[898,10703,8051],{},[1761,10705,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,10707,1915],{"stretchy":1821},[898,10709,1828],{},[1761,10711,1920],{"stretchy":1821},[1761,10713,1909],{},[898,10715,2244],{},[1761,10717,1915],{"stretchy":1821},[898,10719,1828],{},[1761,10721,1920],{"stretchy":1821},[1761,10723,1964],{},[898,10725,1828],{},[2761,10727,7057],{},[1824,10729,10730,10732],{},[898,10731,2244],{},[1761,10733,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,10735,1915],{"stretchy":1821},[898,10737,1828],{},[1761,10739,1920],{"stretchy":1821},[1761,10741,1909],{},[898,10743,1839],{},[1761,10745,1964],{},[898,10747,1828],{},[4379,10749,10750,10756],{},[895,10751,10752,10754],{},[898,10753,4346],{"mathvariant":1969},[898,10755,1839],{},[895,10757,10758,10760],{},[898,10759,4346],{"mathvariant":1969},[898,10761,1828],{},[1761,10763,1909],{},[898,10765,1839],{},[895,10767,10768,10770,10772,10774,10780,10782,10796],{},[1761,10769,1915],{"fence":1833},[1765,10771,1945],{},[1761,10773,1964],{},[4379,10775,10776,10778],{},[898,10777,1828],{},[898,10779,1839],{},[1761,10781,2447],{},[4379,10783,10784,10790],{},[895,10785,10786,10788],{},[898,10787,4346],{"mathvariant":1969},[898,10789,1839],{},[895,10791,10792,10794],{},[898,10793,4346],{"mathvariant":1969},[898,10795,1828],{},[1761,10797,1920],{"fence":1833},[902,10799,10800],{"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)",[724,10802,10803],{},[883,10804,10806],{"className":10805},[886],[888,10807,10808],{"xmlns":890},[892,10809,10810,10882],{},[895,10811,10812,10814,10816,10858,10860,10862],{},[1761,10813,1909],{},[898,10815,1839],{},[895,10817,10818,10820,10822,10824,10856],{},[1761,10819,1915],{"fence":1833},[1765,10821,1945],{},[1761,10823,1964],{},[4379,10825,10826,10828],{},[1765,10827,1945],{},[895,10829,10830,10838,10840],{},[6411,10831,10832],{"scriptlevel":1767,"displaystyle":1821},[4379,10833,10834,10836],{},[898,10835,1839],{},[898,10837,1828],{},[1761,10839,2447],{},[6411,10841,10842],{"scriptlevel":1767,"displaystyle":1821},[4379,10843,10844,10850],{},[895,10845,10846,10848],{},[898,10847,4346],{"mathvariant":1969},[898,10849,1828],{},[895,10851,10852,10854],{},[898,10853,4346],{"mathvariant":1969},[898,10855,1839],{},[1761,10857,1920],{"fence":1833},[1761,10859,1909],{},[898,10861,1839],{},[895,10863,10864,10866,10868,10870,10880],{},[1761,10865,1915],{"fence":1833},[1765,10867,1945],{},[1761,10869,1964],{},[4379,10871,10872,10874],{},[1765,10873,1945],{},[895,10875,10876,10878],{},[1761,10877,1885],{},[898,10879,1818],{},[1761,10881,1920],{"fence":1833},[902,10883,10884],{"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)",[724,10886,10887],{},"a tedy",[724,10889,10890],{},[883,10891,10893],{"className":10892,"title":8255,"style":8256},[8254],"\\boxed{\\;MR = P\\left(1 - \\frac{1}{E}\\right) = D(Q)\\left(1 - \\frac{1}{E}\\right)\\;} \\tag{4.12}",[1636,10895,10896,10965,11214],{},[724,10897,10898,10900,10901,10935,10936,10951,10952,2506],{},[883,10899,1642],{}," Intuice: vztah ",[883,10902,10904],{"className":10903},[886],[888,10905,10906],{"xmlns":890},[892,10907,10908,10932],{},[895,10909,10910,10912,10914,10916,10918,10920,10922,10924,10926,10928,10930],{},[898,10911,6889],{},[898,10913,8051],{},[1761,10915,1909],{},[898,10917,1839],{},[1761,10919,1915],{"stretchy":1821},[1765,10921,1945],{},[1761,10923,1885],{},[1765,10925,1945],{},[898,10927,8726],{"mathvariant":1969},[898,10929,1818],{},[1761,10931,1920],{"stretchy":1821},[902,10933,10934],{"encoding":904},"MR = P(1 - 1\u002FE)","\nVztah (4.12) je „most\" mezi elasticitou a mezním příjmem — znaménko ",[883,10937,10939],{"className":10938},[886],[888,10940,10941],{"xmlns":890},[892,10942,10943,10949],{},[895,10944,10945,10947],{},[898,10946,6889],{},[898,10948,8051],{},[902,10950,10679],{"encoding":904}," jednoznačně určuje hodnota ",[883,10953,10955],{"className":10954},[886],[888,10956,10957],{"xmlns":890},[892,10958,10959,10963],{},[895,10960,10961],{},[898,10962,1818],{},[902,10964,1818],{"encoding":904},[120,10966,10967,11076,11145],{},[123,10968,10969,10986,10987,1989,11001,1989,11027,1989,11040,5675,11060,11075],{},[883,10970,10972],{"className":10971},[886],[888,10973,10974],{"xmlns":890},[892,10975,10976,10984],{},[895,10977,10978,10980,10982],{},[898,10979,1818],{},[1761,10981,1763],{},[1765,10983,1945],{},[902,10985,8562],{"encoding":904}," (elastická) ",[883,10988,10990],{"className":10989},[886],[888,10991,10992],{"xmlns":890},[892,10993,10994,10998],{},[895,10995,10996],{},[1761,10997,8044],{},[902,10999,11000],{"encoding":904},"\\Rightarrow",[883,11002,11004],{"className":11003},[886],[888,11005,11006],{"xmlns":890},[892,11007,11008,11024],{},[895,11009,11010,11012,11014,11016,11018,11020,11022],{},[1765,11011,1945],{},[1761,11013,1885],{},[1765,11015,1945],{},[898,11017,8726],{"mathvariant":1969},[898,11019,1818],{},[1761,11021,1763],{},[1765,11023,1767],{},[902,11025,11026],{"encoding":904},"1 - 1\u002FE > 0",[883,11028,11030],{"className":11029},[886],[888,11031,11032],{"xmlns":890},[892,11033,11034,11038],{},[895,11035,11036],{},[1761,11037,8044],{},[902,11039,11000],{"encoding":904},[883,11041,11043],{"className":11042},[886],[888,11044,11045],{"xmlns":890},[892,11046,11047,11057],{},[895,11048,11049,11051,11053,11055],{},[898,11050,6889],{},[898,11052,8051],{},[1761,11054,1763],{},[1765,11056,1767],{},[902,11058,11059],{"encoding":904},"MR > 0",[883,11061,11063],{"className":11062},[886],[888,11064,11065],{"xmlns":890},[892,11066,11067,11073],{},[895,11068,11069,11071],{},[898,11070,1655],{},[898,11072,8051],{},[902,11074,8151],{"encoding":904}," roste s množstvím, tj. klesá s cenou.",[123,11077,11078,11095,11096,1989,11109,5675,11129,11144],{},[883,11079,11081],{"className":11080},[886],[888,11082,11083],{"xmlns":890},[892,11084,11085,11093],{},[895,11086,11087,11089,11091],{},[898,11088,1818],{},[1761,11090,1909],{},[1765,11092,1945],{},[902,11094,8598],{"encoding":904}," (jednotková) ",[883,11097,11099],{"className":11098},[886],[888,11100,11101],{"xmlns":890},[892,11102,11103,11107],{},[895,11104,11105],{},[1761,11106,8044],{},[902,11108,11000],{"encoding":904},[883,11110,11112],{"className":11111},[886],[888,11113,11114],{"xmlns":890},[892,11115,11116,11126],{},[895,11117,11118,11120,11122,11124],{},[898,11119,6889],{},[898,11121,8051],{},[1761,11123,1909],{},[1765,11125,1767],{},[902,11127,11128],{"encoding":904},"MR = 0",[883,11130,11132],{"className":11131},[886],[888,11133,11134],{"xmlns":890},[892,11135,11136,11142],{},[895,11137,11138,11140],{},[898,11139,1655],{},[898,11141,8051],{},[902,11143,8151],{"encoding":904}," je extrém (maximum).",[123,11146,11147,11164,11165,1989,11178,5675,11198,11213],{},[883,11148,11150],{"className":11149},[886],[888,11151,11152],{"xmlns":890},[892,11153,11154,11162],{},[895,11155,11156,11158,11160],{},[898,11157,1818],{},[1761,11159,2058],{},[1765,11161,1945],{},[902,11163,8580],{"encoding":904}," (neelastická) ",[883,11166,11168],{"className":11167},[886],[888,11169,11170],{"xmlns":890},[892,11171,11172,11176],{},[895,11173,11174],{},[1761,11175,8044],{},[902,11177,11000],{"encoding":904},[883,11179,11181],{"className":11180},[886],[888,11182,11183],{"xmlns":890},[892,11184,11185,11195],{},[895,11186,11187,11189,11191,11193],{},[898,11188,6889],{},[898,11190,8051],{},[1761,11192,2058],{},[1765,11194,1767],{},[902,11196,11197],{"encoding":904},"MR \u003C 0",[883,11199,11201],{"className":11200},[886],[888,11202,11203],{"xmlns":890},[892,11204,11205,11211],{},[895,11206,11207,11209],{},[898,11208,1655],{},[898,11210,8051],{},[902,11212,8151],{"encoding":904}," klesá s množstvím, tj. roste s cenou.",[724,11215,11216,11217,1741],{},"Viz také ",[207,11218,7885],{"className":11219,"dataFsResolvedFilePath":827,"href":828},[210],[198,11221,11223],{"id":11222},"pravidla-13-odvození-z-412","Pravidla 1–3 (odvození z (4.12))",[724,11225,11226,11246,11247,11273,11274,11289,11290,11303,11304,11317,11318,11331,11332,11348,11349,1989,11364,11367,11368,11348,11384,1741],{},[38,11227,11228,11229,2162],{},"(a) Poptávka elastická (",[883,11230,11232],{"className":11231},[886],[888,11233,11234],{"xmlns":890},[892,11235,11236,11244],{},[895,11237,11238,11240,11242],{},[898,11239,1818],{},[1761,11241,1763],{},[1765,11243,1945],{},[902,11245,8562],{"encoding":904}," Z (4.12) plyne ",[883,11248,11250],{"className":11249},[886],[888,11251,11252],{"xmlns":890},[892,11253,11254,11270],{},[895,11255,11256,11258,11260,11262,11264,11266,11268],{},[898,11257,6889],{},[898,11259,8051],{},[1761,11261,1915],{"stretchy":1821},[898,11263,1828],{},[1761,11265,1920],{"stretchy":1821},[1761,11267,1763],{},[1765,11269,1767],{},[902,11271,11272],{"encoding":904},"MR(Q) > 0",", a tedy celkový příjem ",[883,11275,11277],{"className":11276},[886],[888,11278,11279],{"xmlns":890},[892,11280,11281,11287],{},[895,11282,11283,11285],{},[898,11284,1655],{},[898,11286,8051],{},[902,11288,8151],{"encoding":904}," je rostoucí funkcí ",[883,11291,11293],{"className":11292},[886],[888,11294,11295],{"xmlns":890},[892,11296,11297,11301],{},[895,11298,11299],{},[898,11300,1828],{},[902,11302,1828],{"encoding":904},". Avšak růst ",[883,11305,11307],{"className":11306},[886],[888,11308,11309],{"xmlns":890},[892,11310,11311,11315],{},[895,11312,11313],{},[898,11314,1828],{},[902,11316,1828],{"encoding":904}," je odezvou na pokles ceny ",[883,11319,11321],{"className":11320},[886],[888,11322,11323],{"xmlns":890},[892,11324,11325,11329],{},[895,11326,11327],{},[898,11328,1839],{},[902,11330,1839],{"encoding":904},". Tudíž s ",[614,11333,11334,11335],{},"poklesem ceny ",[883,11336,11338],{"className":11337},[886],[888,11339,11340],{"xmlns":890},[892,11341,11342,11346],{},[895,11343,11344],{},[898,11345,1839],{},[902,11347,1839],{"encoding":904}," celkový příjem ",[883,11350,11352],{"className":11351},[886],[888,11353,11354],{"xmlns":890},[892,11355,11356,11362],{},[895,11357,11358,11360],{},[898,11359,1655],{},[898,11361,8051],{},[902,11363,8151],{"encoding":904},[614,11365,11366],{},"roste"," a s ",[614,11369,11370,11371],{},"růstem ceny ",[883,11372,11374],{"className":11373},[886],[888,11375,11376],{"xmlns":890},[892,11377,11378,11382],{},[895,11379,11380],{},[898,11381,1839],{},[902,11383,1839],{"encoding":904},[614,11385,11386],{},"klesá",[1636,11388,11389],{},[724,11390,11391,11394],{},[38,11392,11393],{},"Pravidlo 1."," Je-li poptávka elastická, pak s poklesem ceny celkový příjem roste a s růstem ceny celkový příjem klesá.",[724,11396,11397,11246,11417,1343,11443,11458,11459,11472,11473,11486,11487,11500,11501,11348,11514,1989,11529,1741],{},[38,11398,11399,11400,2162],{},"(b) Poptávka neelastická (",[883,11401,11403],{"className":11402},[886],[888,11404,11405],{"xmlns":890},[892,11406,11407,11415],{},[895,11408,11409,11411,11413],{},[898,11410,1818],{},[1761,11412,2058],{},[1765,11414,1945],{},[902,11416,8580],{"encoding":904},[883,11418,11420],{"className":11419},[886],[888,11421,11422],{"xmlns":890},[892,11423,11424,11440],{},[895,11425,11426,11428,11430,11432,11434,11436,11438],{},[898,11427,6889],{},[898,11429,8051],{},[1761,11431,1915],{"stretchy":1821},[898,11433,1828],{},[1761,11435,1920],{"stretchy":1821},[1761,11437,2058],{},[1765,11439,1767],{},[902,11441,11442],{"encoding":904},"MR(Q) \u003C 0",[883,11444,11446],{"className":11445},[886],[888,11447,11448],{"xmlns":890},[892,11449,11450,11456],{},[895,11451,11452,11454],{},[898,11453,1655],{},[898,11455,8051],{},[902,11457,8151],{"encoding":904}," je klesající funkce ",[883,11460,11462],{"className":11461},[886],[888,11463,11464],{"xmlns":890},[892,11465,11466,11470],{},[895,11467,11468],{},[898,11469,1828],{},[902,11471,1828],{"encoding":904},", tj. s růstem ",[883,11474,11476],{"className":11475},[886],[888,11477,11478],{"xmlns":890},[892,11479,11480,11484],{},[895,11481,11482],{},[898,11483,1828],{},[902,11485,1828],{"encoding":904}," (s poklesem ceny ",[883,11488,11490],{"className":11489},[886],[888,11491,11492],{"xmlns":890},[892,11493,11494,11498],{},[895,11495,11496],{},[898,11497,1839],{},[902,11499,1839],{"encoding":904},") celkový příjem klesá. S růstem ceny ",[883,11502,11504],{"className":11503},[886],[888,11505,11506],{"xmlns":890},[892,11507,11508,11512],{},[895,11509,11510],{},[898,11511,1839],{},[902,11513,1839],{"encoding":904},[883,11515,11517],{"className":11516},[886],[888,11518,11519],{"xmlns":890},[892,11520,11521,11527],{},[895,11522,11523,11525],{},[898,11524,1655],{},[898,11526,8051],{},[902,11528,8151],{"encoding":904},[614,11530,11366],{},[1636,11532,11533],{},[724,11534,11535,11538],{},[38,11536,11537],{},"Pravidlo 2."," Je-li poptávka neelastická, pak s poklesem ceny celkový příjem klesá a s růstem ceny celkový příjem roste.",[724,11540,11541,11246,11561,11580,11581,11596,11597,11667,11668,2068,11696,11729,11730,2403,11758,11773,11774,1741],{},[38,11542,11543,11544,2162],{},"(c) Jednotková elasticita (",[883,11545,11547],{"className":11546},[886],[888,11548,11549],{"xmlns":890},[892,11550,11551,11559],{},[895,11552,11553,11555,11557],{},[898,11554,1818],{},[1761,11556,1909],{},[1765,11558,1945],{},[902,11560,8598],{"encoding":904},[883,11562,11564],{"className":11563},[886],[888,11565,11566],{"xmlns":890},[892,11567,11568,11578],{},[895,11569,11570,11572,11574,11576],{},[898,11571,6889],{},[898,11573,8051],{},[1761,11575,1909],{},[1765,11577,1767],{},[902,11579,11128],{"encoding":904}," — nutná podmínka extrému ",[883,11582,11584],{"className":11583},[886],[888,11585,11586],{"xmlns":890},[892,11587,11588,11594],{},[895,11589,11590,11592],{},[898,11591,1655],{},[898,11593,8051],{},[902,11595,8151],{"encoding":904},". Dále ",[883,11598,11600],{"className":11599},[886],[888,11601,11602],{"xmlns":890},[892,11603,11604,11664],{},[895,11605,11606,11608,11618,11620,11622,11628,11630,11636,11638,11640,11642,11644,11646,11648,11658,11660,11662],{},[898,11607,1655],{},[1824,11609,11610,11612],{},[898,11611,8051],{},[895,11613,11614,11616],{},[1761,11615,6459],{"mathvariant":1969},[1761,11617,6459],{"mathvariant":1969},[1761,11619,1909],{},[898,11621,6889],{},[1824,11623,11624,11626],{},[898,11625,8051],{},[1761,11627,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,11629,1909],{},[1824,11631,11632,11634],{},[898,11633,2244],{},[1761,11635,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,11637,1915],{"stretchy":1821},[898,11639,1828],{},[1761,11641,1920],{"stretchy":1821},[1761,11643,1964],{},[898,11645,1828],{},[2761,11647,7057],{},[1824,11649,11650,11652],{},[898,11651,2244],{},[895,11653,11654,11656],{},[1761,11655,6459],{"mathvariant":1969},[1761,11657,6459],{"mathvariant":1969},[1761,11659,1915],{"stretchy":1821},[898,11661,1828],{},[1761,11663,1920],{"stretchy":1821},[902,11665,11666],{"encoding":904},"TR'' = MR' = D'(Q) + Q\\,D''(Q)","; za normálních podmínek ",[883,11669,11671],{"className":11670},[886],[888,11672,11673],{"xmlns":890},[892,11674,11675,11693],{},[895,11676,11677,11683,11685,11687,11689,11691],{},[1824,11678,11679,11681],{},[898,11680,2244],{},[1761,11682,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,11684,1915],{"stretchy":1821},[898,11686,1828],{},[1761,11688,1920],{"stretchy":1821},[1761,11690,2058],{},[1765,11692,1767],{},[902,11694,11695],{"encoding":904},"D'(Q) \u003C 0",[883,11697,11699],{"className":11698},[886],[888,11700,11701],{"xmlns":890},[892,11702,11703,11726],{},[895,11704,11705,11715,11717,11719,11721,11724],{},[1824,11706,11707,11709],{},[898,11708,2244],{},[895,11710,11711,11713],{},[1761,11712,6459],{"mathvariant":1969},[1761,11714,6459],{"mathvariant":1969},[1761,11716,1915],{"stretchy":1821},[898,11718,1828],{},[1761,11720,1920],{"stretchy":1821},[1761,11722,11723],{},"≤",[1765,11725,1767],{},[902,11727,11728],{"encoding":904},"D''(Q) \\le 0",", odkud ",[883,11731,11733],{"className":11732},[886],[888,11734,11735],{"xmlns":890},[892,11736,11737,11755],{},[895,11738,11739,11741,11751,11753],{},[898,11740,1655],{},[1824,11742,11743,11745],{},[898,11744,8051],{},[895,11746,11747,11749],{},[1761,11748,6459],{"mathvariant":1969},[1761,11750,6459],{"mathvariant":1969},[1761,11752,2058],{},[1765,11754,1767],{},[902,11756,11757],{"encoding":904},"TR'' \u003C 0",[883,11759,11761],{"className":11760},[886],[888,11762,11763],{"xmlns":890},[892,11764,11765,11771],{},[895,11766,11767,11769],{},[898,11768,1655],{},[898,11770,8051],{},[902,11772,8151],{"encoding":904}," nabývá ",[38,11775,11776],{},"maxima",[1636,11778,11779],{},[724,11780,11781,11784],{},[38,11782,11783],{},"Pravidlo 3."," Celkový příjem nabývá maxima při ceně, pro kterou je poptávka jednotkově elastická.",[724,11786,11787],{},"Tato tři pravidla potvrzují hypotézu (4.1) a jsou klíčem k regulaci ceny za účelem zvýšení (maximalizace) celkového příjmu.",[724,11789,11790],{},[38,11791,11792],{},"Souhrnná tabulka Pravidel 1–3:",[16,11794,11795,11899],{},[19,11796,11797],{},[22,11798,11799,11802,11817,11834,11865,11896],{},[25,11800,11801],{},"Charakter poptávky",[25,11803,11804],{},[883,11805,11807],{"className":11806},[886],[888,11808,11809],{"xmlns":890},[892,11810,11811,11815],{},[895,11812,11813],{},[898,11814,1818],{},[902,11816,1818],{"encoding":904},[25,11818,11819],{},[883,11820,11822],{"className":11821},[886],[888,11823,11824],{"xmlns":890},[892,11825,11826,11832],{},[895,11827,11828,11830],{},[898,11829,6889],{},[898,11831,8051],{},[902,11833,10679],{"encoding":904},[25,11835,11836,11837,1989,11850],{},"Pokles ceny ",[883,11838,11840],{"className":11839},[886],[888,11841,11842],{"xmlns":890},[892,11843,11844,11848],{},[895,11845,11846],{},[1761,11847,8044],{},[902,11849,11000],{"encoding":904},[883,11851,11853],{"className":11852},[886],[888,11854,11855],{"xmlns":890},[892,11856,11857,11863],{},[895,11858,11859,11861],{},[898,11860,1655],{},[898,11862,8051],{},[902,11864,8151],{"encoding":904},[25,11866,11867,11868,1989,11881],{},"Růst ceny ",[883,11869,11871],{"className":11870},[886],[888,11872,11873],{"xmlns":890},[892,11874,11875,11879],{},[895,11876,11877],{},[1761,11878,8044],{},[902,11880,11000],{"encoding":904},[883,11882,11884],{"className":11883},[886],[888,11885,11886],{"xmlns":890},[892,11887,11888,11894],{},[895,11889,11890,11892],{},[898,11891,1655],{},[898,11893,8051],{},[902,11895,8151],{"encoding":904},[25,11897,11898],{},"Doporučení",[30,11900,11901,11950,12000],{},[22,11902,11903,11905,11923,11941,11943,11945],{},[35,11904,8130],{},[35,11906,11907],{},[883,11908,11910],{"className":11909},[886],[888,11911,11912],{"xmlns":890},[892,11913,11914,11920],{},[895,11915,11916,11918],{},[1761,11917,1763],{},[1765,11919,1945],{},[902,11921,11922],{"encoding":904},"> 1",[35,11924,11925],{},[883,11926,11928],{"className":11927},[886],[888,11929,11930],{"xmlns":890},[892,11931,11932,11938],{},[895,11933,11934,11936],{},[1761,11935,1763],{},[1765,11937,1767],{},[902,11939,11940],{"encoding":904},"> 0",[35,11942,11366],{},[35,11944,11386],{},[35,11946,11947],{},[38,11948,11949],{},"snížit cenu",[22,11951,11952,11955,11973,11991,11993,11995],{},[35,11953,11954],{},"jednotková",[35,11956,11957],{},[883,11958,11960],{"className":11959},[886],[888,11961,11962],{"xmlns":890},[892,11963,11964,11970],{},[895,11965,11966,11968],{},[1761,11967,1909],{},[1765,11969,1945],{},[902,11971,11972],{"encoding":904},"= 1",[35,11974,11975],{},[883,11976,11978],{"className":11977},[886],[888,11979,11980],{"xmlns":890},[892,11981,11982,11988],{},[895,11983,11984,11986],{},[1761,11985,1909],{},[1765,11987,1767],{},[902,11989,11990],{"encoding":904},"= 0",[35,11992,7781],{},[35,11994,7781],{},[35,11996,11997],{},[38,11998,11999],{},"držet cenu",[22,12001,12002,12004,12022,12040,12042,12044],{},[35,12003,8134],{},[35,12005,12006],{},[883,12007,12009],{"className":12008},[886],[888,12010,12011],{"xmlns":890},[892,12012,12013,12019],{},[895,12014,12015,12017],{},[1761,12016,2058],{},[1765,12018,1945],{},[902,12020,12021],{"encoding":904},"\u003C 1",[35,12023,12024],{},[883,12025,12027],{"className":12026},[886],[888,12028,12029],{"xmlns":890},[892,12030,12031,12037],{},[895,12032,12033,12035],{},[1761,12034,2058],{},[1765,12036,1767],{},[902,12038,12039],{"encoding":904},"\u003C 0",[35,12041,11386],{},[35,12043,11366],{},[35,12045,12046],{},[38,12047,12048],{},"zvýšit cenu",[198,12050,12052],{"id":12051},"příklad-46-aplikace-pravidel-13","Příklad 4.6 — aplikace Pravidel 1–3",[724,12054,12055,12056,12081,12082,12104,12105,12118,12119,12132,12133,12146,12147,2403,12174,12226],{},"Aplikujme pravidla 1–3 pro poptávku ",[883,12057,12059],{"className":12058},[886],[888,12060,12061],{"xmlns":890},[892,12062,12063,12079],{},[895,12064,12065,12067,12069,12071,12073],{},[898,12066,1839],{},[1761,12068,1909],{},[1765,12070,7160],{},[1761,12072,1885],{},[1824,12074,12075,12077],{},[898,12076,1828],{},[1765,12078,2296],{},[902,12080,9510],{"encoding":904},". Reálné cenové rozpětí je ",[883,12083,12085],{"className":12084},[886],[888,12086,12087],{"xmlns":890},[892,12088,12089,12101],{},[895,12090,12091,12093,12095,12097,12099],{},[1761,12092,9375],{"stretchy":1821},[1765,12094,1945],{},[1761,12096,1834],{"separator":1833},[1765,12098,7160],{},[1761,12100,9392],{"stretchy":1821},[902,12102,12103],{"encoding":904},"\\langle 1, 100\\rangle",". Pro výpočet elasticity vyjádříme ",[883,12106,12108],{"className":12107},[886],[888,12109,12110],{"xmlns":890},[892,12111,12112,12116],{},[895,12113,12114],{},[898,12115,1828],{},[902,12117,1828],{"encoding":904}," jako funkci ",[883,12120,12122],{"className":12121},[886],[888,12123,12124],{"xmlns":890},[892,12125,12126,12130],{},[895,12127,12128],{},[898,12129,1839],{},[902,12131,1839],{"encoding":904},"; pro nezáporné ",[883,12134,12136],{"className":12135},[886],[888,12137,12138],{"xmlns":890},[892,12139,12140,12144],{},[895,12141,12142],{},[898,12143,1828],{},[902,12145,1828],{"encoding":904}," je ",[883,12148,12150],{"className":12149},[886],[888,12151,12152],{"xmlns":890},[892,12153,12154,12171],{},[895,12155,12156,12158,12160],{},[898,12157,1828],{},[1761,12159,1909],{},[12161,12162,12163],"msqrt",{},[895,12164,12165,12167,12169],{},[1765,12166,7160],{},[1761,12168,1885],{},[898,12170,1839],{},[902,12172,12173],{"encoding":904},"Q = \\sqrt{100 - P}",[883,12175,12177],{"className":12176},[886],[888,12178,12179],{"xmlns":890},[892,12180,12181,12223],{},[895,12182,12183,12199,12201,12203],{},[6411,12184,12185],{"scriptlevel":1767,"displaystyle":1833},[4379,12186,12187,12193],{},[895,12188,12189,12191],{},[898,12190,4346],{"mathvariant":1969},[898,12192,1828],{},[895,12194,12195,12197],{},[898,12196,4346],{"mathvariant":1969},[898,12198,1839],{},[1761,12200,1909],{},[1761,12202,1885],{},[6411,12204,12205],{"scriptlevel":1767,"displaystyle":1833},[4379,12206,12207,12209],{},[1765,12208,1945],{},[895,12210,12211,12213],{},[1765,12212,2296],{},[12161,12214,12215],{},[895,12216,12217,12219,12221],{},[1765,12218,7160],{},[1761,12220,1885],{},[898,12222,1839],{},[902,12224,12225],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\dfrac{1}{2\\sqrt{100-P}}",". Podle (4.5):",[724,12228,12229],{},[883,12230,12232],{"className":12231},[886],[888,12233,12234],{"xmlns":890},[892,12235,12236,12358],{},[895,12237,12238,12240,12242,12244,12246,12248,12250,12256,12258,12272,12274,12276,12290,12292,12318,12320,12338,12340,12356],{},[898,12239,1818],{},[1761,12241,1915],{"stretchy":1821},[898,12243,1839],{},[1761,12245,1920],{"stretchy":1821},[1761,12247,1909],{},[1761,12249,1885],{},[4379,12251,12252,12254],{},[898,12253,1839],{},[898,12255,1828],{},[1761,12257,2447],{},[4379,12259,12260,12266],{},[895,12261,12262,12264],{},[898,12263,4346],{"mathvariant":1969},[898,12265,1828],{},[895,12267,12268,12270],{},[898,12269,4346],{"mathvariant":1969},[898,12271,1839],{},[1761,12273,1909],{},[1761,12275,1885],{},[4379,12277,12278,12280],{},[898,12279,1839],{},[12161,12281,12282],{},[895,12283,12284,12286,12288],{},[1765,12285,7160],{},[1761,12287,1885],{},[898,12289,1839],{},[1761,12291,2447],{},[895,12293,12294,12296,12298,12316],{},[1761,12295,1915],{"fence":1833},[1761,12297,1885],{},[4379,12299,12300,12302],{},[1765,12301,1945],{},[895,12303,12304,12306],{},[1765,12305,2296],{},[12161,12307,12308],{},[895,12309,12310,12312,12314],{},[1765,12311,7160],{},[1761,12313,1885],{},[898,12315,1839],{},[1761,12317,1920],{"fence":1833},[1761,12319,1909],{},[4379,12321,12322,12324],{},[898,12323,1839],{},[895,12325,12326,12328,12330,12332,12334,12336],{},[1765,12327,2296],{},[1761,12329,1915],{"stretchy":1821},[1765,12331,7160],{},[1761,12333,1885],{},[898,12335,1839],{},[1761,12337,1920],{"stretchy":1821},[1761,12339,1909],{},[4379,12341,12342,12348],{},[895,12343,12344,12346],{},[1765,12345,5426],{},[898,12347,1839],{},[895,12349,12350,12352,12354],{},[1765,12351,7160],{},[1761,12353,1885],{},[898,12355,1839],{},[898,12357,1741],{"mathvariant":1969},[902,12359,12360],{"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}.",[724,12362,12363,12364,2506],{},"Stanovíme cenu, při které je poptávka jednotkově elastická. Řešíme ",[883,12365,12367],{"className":12366},[886],[888,12368,12369],{"xmlns":890},[892,12370,12371,12395],{},[895,12372,12373,12391,12393],{},[6411,12374,12375],{"scriptlevel":1767,"displaystyle":1833},[4379,12376,12377,12383],{},[895,12378,12379,12381],{},[1765,12380,5426],{},[898,12382,1839],{},[895,12384,12385,12387,12389],{},[1765,12386,7160],{},[1761,12388,1885],{},[898,12390,1839],{},[1761,12392,1909],{},[1765,12394,1945],{},[902,12396,12397],{"encoding":904},"\\dfrac{0{,}5P}{100-P} = 1",[724,12399,12400],{},[883,12401,12403],{"className":12402},[886],[888,12404,12405],{"xmlns":890},[892,12406,12407,12438],{},[895,12408,12409,12415,12417,12424,12426,12429,12436],{},[1824,12410,12411,12413],{},[898,12412,1839],{},[1761,12414,8408],{},[1761,12416,1909],{},[4379,12418,12419,12422],{},[1765,12420,12421],{},"200",[1765,12423,5486],{},[1761,12425,9945],{},[1765,12427,12428],{},"66,",[2770,12430,12431,12433],{"accent":1833},[1765,12432,2340],{},[1761,12434,12435],{"stretchy":1833},"‾",[898,12437,1741],{"mathvariant":1969},[902,12439,12440],{"encoding":904},"P^* = \\frac{200}{3} \\doteq 66{,}\\overline{6}.",[724,12442,12443],{},"S využitím vlastnosti (4.8):",[120,12445,12446,12492,12534],{},[123,12447,12448,12449,12484,12485,12487,12488,12491],{},"Při cenách ",[883,12450,12452],{"className":12451},[886],[888,12453,12454],{"xmlns":890},[892,12455,12456,12481],{},[895,12457,12458,12460,12462,12464,12466,12469,12471,12473,12479],{},[898,12459,1839],{},[1761,12461,10551],{},[1761,12463,9375],{"stretchy":1821},[1765,12465,1945],{},[1761,12467,12468],{"separator":1833},";",[2761,12470,7057],{},[1765,12472,12428],{},[2770,12474,12475,12477],{"accent":1833},[1765,12476,2340],{},[1761,12478,12435],{"stretchy":1833},[1761,12480,1920],{"stretchy":1821},[902,12482,12483],{"encoding":904},"P \\in \\langle 1;\\, 66{,}\\overline{6})"," je poptávka ",[38,12486,8134],{}," — dle ",[614,12489,12490],{},"Pravidla 2"," přiměřené zvýšení ceny zvýší celkový příjem.",[123,12493,12448,12494,12484,12528,12487,12530,12533],{},[883,12495,12497],{"className":12496},[886],[888,12498,12499],{"xmlns":890},[892,12500,12501,12525],{},[895,12502,12503,12505,12507,12509,12511,12517,12519,12521,12523],{},[898,12504,1839],{},[1761,12506,10551],{},[1761,12508,1915],{"stretchy":1821},[1765,12510,12428],{},[2770,12512,12513,12515],{"accent":1833},[1765,12514,2340],{},[1761,12516,12435],{"stretchy":1833},[1761,12518,12468],{"separator":1833},[2761,12520,7057],{},[1765,12522,7160],{},[1761,12524,9392],{"stretchy":1821},[902,12526,12527],{"encoding":904},"P \\in (66{,}\\overline{6};\\, 100\\rangle",[38,12529,8130],{},[614,12531,12532],{},"Pravidla 1"," přiměřené snížení ceny povede ke zvýšení celkového příjmu.",[123,12535,12536,12537,12540,12541,12569,12570,12573],{},"Dle ",[614,12538,12539],{},"Pravidla 3"," je při ceně ",[883,12542,12544],{"className":12543},[886],[888,12545,12546],{"xmlns":890},[892,12547,12548,12566],{},[895,12549,12550,12556,12558,12560],{},[1824,12551,12552,12554],{},[898,12553,1839],{},[1761,12555,8408],{},[1761,12557,1909],{},[1765,12559,12428],{},[2770,12561,12562,12564],{"accent":1833},[1765,12563,2340],{},[1761,12565,12435],{"stretchy":1833},[902,12567,12568],{"encoding":904},"P^* = 66{,}\\overline{6}"," dosaženo ",[38,12571,12572],{},"maxima celkového příjmu"," ve výši",[724,12575,12576],{},[883,12577,12579],{"className":12578},[886],[888,12580,12581],{"xmlns":890},[892,12582,12583,12661],{},[895,12584,12585,12587,12589,12591,12597,12599,12601,12607,12609,12623,12625,12631,12633,12641,12643,12656,12658],{},[898,12586,1655],{},[898,12588,8051],{},[1761,12590,1915],{"stretchy":1821},[1824,12592,12593,12595],{},[898,12594,1839],{},[1761,12596,8408],{},[1761,12598,1920],{"stretchy":1821},[1761,12600,1909],{},[1824,12602,12603,12605],{},[898,12604,1839],{},[1761,12606,8408],{},[1761,12608,2447],{},[12161,12610,12611],{},[895,12612,12613,12615,12617],{},[1765,12614,7160],{},[1761,12616,1885],{},[1824,12618,12619,12621],{},[898,12620,1839],{},[1761,12622,8408],{},[1761,12624,1909],{},[4379,12626,12627,12629],{},[1765,12628,12421],{},[1765,12630,5486],{},[1761,12632,2447],{},[12161,12634,12635],{},[4379,12636,12637,12639],{},[1765,12638,7160],{},[1765,12640,5486],{},[1761,12642,1909],{},[4379,12644,12645,12648],{},[1765,12646,12647],{},"2000",[895,12649,12650,12652],{},[1765,12651,5486],{},[12161,12653,12654],{},[1765,12655,5486],{},[1761,12657,9945],{},[1765,12659,12660],{},"384,9.",[902,12662,12663],{"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.",[724,12665,12666,12667,1741],{},"Ke stejnému výsledku bychom dospěli přímým hledáním maxima funkce ",[883,12668,12670],{"className":12669},[886],[888,12671,12672],{"xmlns":890},[892,12673,12674,12680],{},[895,12675,12676,12678],{},[898,12677,1655],{},[898,12679,8051],{},[902,12681,8151],{"encoding":904},[115,12683,12685],{"id":12684},"cenová-elasticita-nabídky","Cenová elasticita nabídky",[724,12687,12688,12689,12692],{},"Analogicky se definuje ",[38,12690,12691],{},"cenová elasticita nabídky"," (price elasticity of supply):",[724,12694,12695],{},[883,12696,12698],{"className":12697,"title":8255,"style":8256},[8254],"\\boxed{\\;E = E(P) = \\frac{P}{Q}\\cdot\\frac{\\mathrm{d}Q}{\\mathrm{d}P}\\;} \\tag{4.13}",[724,12700,8364,12701,12725,12726,12758],{},[883,12702,12704],{"className":12703},[886],[888,12705,12706],{"xmlns":890},[892,12707,12708,12722],{},[895,12709,12710,12712,12714,12716,12718,12720],{},[898,12711,1828],{},[1761,12713,1909],{},[898,12715,1912],{},[1761,12717,1915],{"stretchy":1821},[898,12719,1839],{},[1761,12721,1920],{"stretchy":1821},[902,12723,12724],{"encoding":904},"Q = S(P)"," je funkce nabídky. Protože nabídka je rostoucí, ",[883,12727,12729],{"className":12728},[886],[888,12730,12731],{"xmlns":890},[892,12732,12733,12755],{},[895,12734,12735,12751,12753],{},[6411,12736,12737],{"scriptlevel":1767,"displaystyle":1833},[4379,12738,12739,12745],{},[895,12740,12741,12743],{},[898,12742,4346],{"mathvariant":1969},[898,12744,1828],{},[895,12746,12747,12749],{},[898,12748,4346],{"mathvariant":1969},[898,12750,1839],{},[1761,12752,1763],{},[1765,12754,1767],{},[902,12756,12757],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} > 0",", a elasticita nabídky je vždy nezáporná — proto zde není znaménková korekce jako u poptávky.",[724,12760,12761],{},"Klasifikace na elastickou \u002F jednotkově elastickou \u002F neelastickou je analogická jako u poptávky (tabulka (4.7)). Platí paralela k (4.8):",[1636,12763,12764],{},[724,12765,12766,12767],{},"S rostoucí cenou elasticita nabídky roste. ",[883,12768,12770],{"className":12769},[886],[888,12771,12772],{"xmlns":890},[892,12773,12774,12783],{},[895,12775,12776,12778,12781],{},[1761,12777,1915],{"stretchy":1821},[1765,12779,12780],{},"4.14",[1761,12782,1920],{"stretchy":1821},[902,12784,12785],{"encoding":904},"(4.14)",[724,12787,12788],{},"Pro nominální změny platí",[724,12790,12791],{},[883,12792,12794],{"className":12793,"title":8255,"style":8256},[8254],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P, \\qquad \\mathrm{d}P = \\Delta P, \\tag{4.15}",[724,12796,12797],{},"a pro procentní změny",[724,12799,12800],{},[883,12801,12803],{"className":12802,"title":8255,"style":8256},[8254],"\\boxed{\\;\\Delta Q\\% \\approx E(P)\\,\\Delta P\\%\\;} \\tag{4.16}",[724,12805,12806],{},"(bez znaménka minus).",[198,12808,12810],{"id":12809},"příklad-47","Příklad 4.7",[724,12812,12813,12814,2506],{},"Nabídka ",[883,12815,12817],{"className":12816},[886],[888,12818,12819],{"xmlns":890},[892,12820,12821,12846],{},[895,12822,12823,12825,12827,12829,12835,12837,12839,12841,12843],{},[898,12824,1828],{},[1761,12826,1909],{},[1765,12828,6865],{},[1824,12830,12831,12833],{},[898,12832,1839],{},[1765,12834,2296],{},[1761,12836,1964],{},[1765,12838,6321],{},[898,12840,1839],{},[1761,12842,1964],{},[1765,12844,12845],{},"150",[902,12847,12848],{"encoding":904},"Q = 0{,}1P^2 + 5P + 150",[724,12850,12851],{},[883,12852,12854],{"className":12853},[886],[888,12855,12856],{"xmlns":890},[892,12857,12858,12904],{},[895,12859,12860,12862,12864,12888,12890,12892,12894,12896,12898,12900,12902],{},[898,12861,1818],{},[1761,12863,1909],{},[4379,12865,12866,12868],{},[898,12867,1839],{},[895,12869,12870,12872,12878,12880,12882,12884,12886],{},[1765,12871,6865],{},[1824,12873,12874,12876],{},[898,12875,1839],{},[1765,12877,2296],{},[1761,12879,1964],{},[1765,12881,6321],{},[898,12883,1839],{},[1761,12885,1964],{},[1765,12887,12845],{},[2761,12889,7057],{},[1761,12891,1915],{"stretchy":1821},[1765,12893,6910],{},[898,12895,1839],{},[1761,12897,1964],{},[1765,12899,6321],{},[1761,12901,1920],{"stretchy":1821},[898,12903,1741],{"mathvariant":1969},[902,12905,12906],{"encoding":904},"E = \\frac{P}{0{,}1P^2 + 5P + 150}\\,(0{,}2P + 5).",[724,12908,9168,12909,1343,12939,1343,12966,13002,13003,13028,13029,13047,13048,1741],{},[883,12910,12912],{"className":12911},[886],[888,12913,12914],{"xmlns":890},[892,12915,12916,12936],{},[895,12917,12918,12920,12922,12924,12926,12928],{},[898,12919,1818],{},[1761,12921,1915],{"stretchy":1821},[1765,12923,2633],{},[1761,12925,1920],{"stretchy":1821},[1761,12927,1909],{},[6411,12929,12930],{"scriptlevel":1767,"displaystyle":1821},[4379,12931,12932,12934],{},[1765,12933,1945],{},[1765,12935,5486],{},[902,12937,12938],{"encoding":904},"E(10) = \\tfrac{1}{3}",[883,12940,12942],{"className":12941},[886],[888,12943,12944],{"xmlns":890},[892,12945,12946,12963],{},[895,12947,12948,12950,12952,12957,12959,12961],{},[898,12949,1818],{},[1761,12951,1915],{"stretchy":1821},[12161,12953,12954],{},[1765,12955,12956],{},"1500",[1761,12958,1920],{"stretchy":1821},[1761,12960,1909],{},[1765,12962,1945],{},[902,12964,12965],{"encoding":904},"E(\\sqrt{1500}) = 1",[883,12967,12969],{"className":12968},[886],[888,12970,12971],{"xmlns":890},[892,12972,12973,12999],{},[895,12974,12975,12977,12979,12981,12983,12985,12994,12996],{},[898,12976,1818],{},[1761,12978,1915],{"stretchy":1821},[1765,12980,7160],{},[1761,12982,1920],{"stretchy":1821},[1761,12984,1909],{},[6411,12986,12987],{"scriptlevel":1767,"displaystyle":1821},[4379,12988,12989,12991],{},[1765,12990,7190],{},[1765,12992,12993],{},"33",[1761,12995,9945],{},[1765,12997,12998],{},"1,515",[902,13000,13001],{"encoding":904},"E(100) = \\tfrac{50}{33} \\doteq 1{,}515",". Dle (4.14): pro ",[883,13004,13006],{"className":13005},[886],[888,13007,13008],{"xmlns":890},[892,13009,13010,13025],{},[895,13011,13012,13014,13016,13020,13022],{},[898,13013,1839],{},[1761,13015,1763],{},[12161,13017,13018],{},[1765,13019,12956],{},[1761,13021,6803],{},[1765,13023,13024],{},"38,7",[902,13026,13027],{"encoding":904},"P > \\sqrt{1500} \\approx 38{,}7"," je nabídka elastická, pro ",[883,13030,13032],{"className":13031},[886],[888,13033,13034],{"xmlns":890},[892,13035,13036,13044],{},[895,13037,13038,13040,13042],{},[898,13039,1839],{},[1761,13041,2058],{},[1765,13043,13024],{},[902,13045,13046],{"encoding":904},"P \u003C 38{,}7"," neelastická. Zvýší-li se cena z 10 o 20 %, pak ",[883,13049,13051],{"className":13050},[886],[888,13052,13053],{"xmlns":890},[892,13054,13055,13093],{},[895,13056,13057,13059,13061,13063,13065,13073,13075,13078,13080,13083,13089,13091],{},[898,13058,6959],{"mathvariant":1969},[898,13060,1828],{},[898,13062,9970],{"mathvariant":1969},[1761,13064,6803],{},[6411,13066,13067],{"scriptlevel":1767,"displaystyle":1821},[4379,13068,13069,13071],{},[1765,13070,1945],{},[1765,13072,5486],{},[1761,13074,2447],{},[1765,13076,13077],{},"20",[1761,13079,1909],{},[1765,13081,13082],{},"6,",[2770,13084,13085,13087],{"accent":1833},[1765,13086,2340],{},[1761,13088,12435],{"stretchy":1833},[2761,13090,7057],{},[898,13092,9970],{"mathvariant":1969},[902,13094,13095],{"encoding":904},"\\Delta Q\\% \\approx \\tfrac{1}{3}\\cdot 20 = 6{,}\\overline{6}\\,\\%",[115,13097,13099],{"id":13098},"vícefaktorový-model","Vícefaktorový model",[724,13101,13102,13103,13116,13117,1989,13120,13133,13134,1989,13137,13155,13156,1989,13159,2506],{},"Předpokládejme, že poptávané množství ",[883,13104,13106],{"className":13105},[886],[888,13107,13108],{"xmlns":890},[892,13109,13110,13114],{},[895,13111,13112],{},[898,13113,1828],{},[902,13115,1828],{"encoding":904}," závisí na ",[38,13118,13119],{},"ceně základního zboží",[883,13121,13123],{"className":13122},[886],[888,13124,13125],{"xmlns":890},[892,13126,13127,13131],{},[895,13128,13129],{},[898,13130,1839],{},[902,13132,1839],{"encoding":904},", na ",[38,13135,13136],{},"ceně alternativního zboží",[883,13138,13140],{"className":13139},[886],[888,13141,13142],{"xmlns":890},[892,13143,13144,13152],{},[895,13145,13146],{},[1681,13147,13148,13150],{},[898,13149,1839],{},[898,13151,8309],{},[902,13153,13154],{"encoding":904},"P_A"," a na ",[38,13157,13158],{},"důchodu",[883,13160,13162],{"className":13161},[886],[888,13163,13164],{"xmlns":890},[892,13165,13166,13171],{},[895,13167,13168],{},[898,13169,13170],{},"Y",[902,13172,13170],{"encoding":904},[724,13174,13175],{},[883,13176,13178],{"className":13177,"title":8255,"style":8256},[8254],"Q = D(P, P_A, Y). \\tag{4.17}",[724,13180,13181,13182,13185],{},"V analogii jednofaktorového modelu pracujeme s ",[38,13183,13184],{},"parciálními derivacemi"," funkce poptávky.",[198,13187,13189],{"id":13188},"cenová-elasticita-poptávky-vícefaktorová","Cenová elasticita poptávky (vícefaktorová)",[724,13191,13192],{},[883,13193,13195],{"className":13194,"title":8255,"style":8256},[8254],"\\boxed{\\;E_P = -\\frac{P}{Q}\\,Q'_P\\;} \\tag{4.18}",[724,13197,8364,13198,13218,13219,13232,13233,6997,13255,1989,13258,13304,13305,13318,13319,13336],{},[883,13199,13201],{"className":13200},[886],[888,13202,13203],{"xmlns":890},[892,13204,13205,13215],{},[895,13206,13207],{},[2015,13208,13209,13211,13213],{},[898,13210,1828],{},[898,13212,1839],{},[1761,13214,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[902,13216,13217],{"encoding":904},"Q'_P"," je parciální derivace (4.17) podle ",[883,13220,13222],{"className":13221},[886],[888,13223,13224],{"xmlns":890},[892,13225,13226,13230],{},[895,13227,13228],{},[898,13229,1839],{},[902,13231,1839],{"encoding":904},". Vždy ",[883,13234,13236],{"className":13235},[886],[888,13237,13238],{"xmlns":890},[892,13239,13240,13252],{},[895,13241,13242,13248,13250],{},[1681,13243,13244,13246],{},[898,13245,1818],{},[898,13247,1839],{},[1761,13249,8538],{},[1765,13251,1767],{},[902,13253,13254],{"encoding":904},"E_P \\ge 0",[614,13256,13257],{},"Interpretace:",[883,13259,13261],{"className":13260},[886],[888,13262,13263],{"xmlns":890},[892,13264,13265,13301],{},[895,13266,13267,13273,13275,13281,13283,13291,13293,13299],{},[1681,13268,13269,13271],{},[898,13270,1818],{},[898,13272,1839],{},[1761,13274,1915],{"stretchy":1821},[1824,13276,13277,13279],{},[898,13278,1839],{},[1761,13280,8408],{},[1761,13282,1834],{"separator":1833},[2015,13284,13285,13287,13289],{},[898,13286,1839],{},[898,13288,8309],{},[1761,13290,8408],{},[1761,13292,1834],{"separator":1833},[1824,13294,13295,13297],{},[898,13296,13170],{},[1761,13298,8408],{},[1761,13300,1920],{"stretchy":1821},[902,13302,13303],{"encoding":904},"E_P(P^*, P_A^*, Y^*)"," udává přibližnou procentní změnu ",[883,13306,13308],{"className":13307},[886],[888,13309,13310],{"xmlns":890},[892,13311,13312,13316],{},[895,13313,13314],{},[898,13315,1828],{},[902,13317,1828],{"encoding":904}," při 1% změně ",[883,13320,13322],{"className":13321},[886],[888,13323,13324],{"xmlns":890},[892,13325,13326,13334],{},[895,13327,13328],{},[1824,13329,13330,13332],{},[898,13331,1839],{},[1761,13333,8408],{},[902,13335,8458],{"encoding":904},", ceteris paribus.",[198,13338,13340],{"id":13339},"křížová-křížově-cenová-elasticita-poptávky","Křížová (křížově-cenová) elasticita poptávky",[724,13342,13343],{},[883,13344,13346],{"className":13345,"title":8255,"style":8256},[8254],"\\boxed{\\;E_{P_A} = \\frac{P_A}{Q}\\,Q'_{P_A}\\;} \\tag{4.19}",[724,13348,13349,13304,13351,13364,13365,13382],{},[614,13350,13257],{},[883,13352,13354],{"className":13353},[886],[888,13355,13356],{"xmlns":890},[892,13357,13358,13362],{},[895,13359,13360],{},[898,13361,1828],{},[902,13363,1828],{"encoding":904}," základního zboží při 1% změně ceny ",[883,13366,13368],{"className":13367},[886],[888,13369,13370],{"xmlns":890},[892,13371,13372,13380],{},[895,13373,13374],{},[1681,13375,13376,13378],{},[898,13377,1839],{},[898,13379,8309],{},[902,13381,13154],{"encoding":904}," alternativního zboží (ceteris paribus).",[724,13384,13385],{},[38,13386,13387],{},"Znaménko závisí na povaze alternativního zboží:",[120,13389,13390,13478],{},[123,13391,13392,13393,13396,13397,13414,13415,1989,13428,1741],{},"Je-li alternativní zboží ",[38,13394,13395],{},"komplement",", růst ",[883,13398,13400],{"className":13399},[886],[888,13401,13402],{"xmlns":890},[892,13403,13404,13412],{},[895,13405,13406],{},[1681,13407,13408,13410],{},[898,13409,1839],{},[898,13411,8309],{},[902,13413,13154],{"encoding":904}," způsobí zdražení dvojice, pokles ",[883,13416,13418],{"className":13417},[886],[888,13419,13420],{"xmlns":890},[892,13421,13422,13426],{},[895,13423,13424],{},[898,13425,1828],{},[902,13427,1828],{"encoding":904},[883,13429,13431],{"className":13430},[886],[888,13432,13433],{"xmlns":890},[892,13434,13435,13475],{},[895,13436,13437,13439,13441,13453,13455,13457,13459,13461,13471,13473],{},[1761,13438,8044],{},[2761,13440,8041],{},[2015,13442,13443,13445,13451],{},[898,13444,1828],{},[1681,13446,13447,13449],{},[898,13448,1839],{},[898,13450,8309],{},[1761,13452,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,13454,2058],{},[1765,13456,1767],{},[1761,13458,1834],{"separator":1833},[2761,13460,8041],{},[1681,13462,13463,13465],{},[898,13464,1818],{},[1681,13466,13467,13469],{},[898,13468,1839],{},[898,13470,8309],{},[1761,13472,2058],{},[1765,13474,1767],{},[902,13476,13477],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} \u003C 0,\\; E_{P_A} \u003C 0",[123,13479,13392,13480,13396,13483,13500,13501,13514,13515,1741],{},[38,13481,13482],{},"substitut",[883,13484,13486],{"className":13485},[886],[888,13487,13488],{"xmlns":890},[892,13489,13490,13498],{},[895,13491,13492],{},[1681,13493,13494,13496],{},[898,13495,1839],{},[898,13497,8309],{},[902,13499,13154],{"encoding":904}," učiní základní zboží relativně levnější, zájem se přesune, ",[883,13502,13504],{"className":13503},[886],[888,13505,13506],{"xmlns":890},[892,13507,13508,13512],{},[895,13509,13510],{},[898,13511,1828],{},[902,13513,1828],{"encoding":904}," roste ",[883,13516,13518],{"className":13517},[886],[888,13519,13520],{"xmlns":890},[892,13521,13522,13562],{},[895,13523,13524,13526,13528,13540,13542,13544,13546,13548,13558,13560],{},[1761,13525,8044],{},[2761,13527,8041],{},[2015,13529,13530,13532,13538],{},[898,13531,1828],{},[1681,13533,13534,13536],{},[898,13535,1839],{},[898,13537,8309],{},[1761,13539,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,13541,1763],{},[1765,13543,1767],{},[1761,13545,1834],{"separator":1833},[2761,13547,8041],{},[1681,13549,13550,13552],{},[898,13551,1818],{},[1681,13553,13554,13556],{},[898,13555,1839],{},[898,13557,8309],{},[1761,13559,1763],{},[1765,13561,1767],{},[902,13563,13564],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} > 0,\\; E_{P_A} > 0",[883,13566,13569],{"className":13567,"title":13568,"style":8256},[8254],"ParseError: KaTeX parse error: Expected 'EOF', got '&' at position 9: E_{P_A} &̲> 0 \\;\\;\\Leftri…","undefined",{"title":641,"searchDepth":642,"depth":642,"links":13571},[13572,13576,13577,13585,13586,13590,13593],{"id":7950,"depth":642,"text":7951,"children":13573},[13574,13575],{"id":7979,"depth":649,"text":7980},{"id":8159,"depth":649,"text":8160},{"id":8194,"depth":642,"text":8195},{"id":8219,"depth":642,"text":8220,"children":13578},[13579,13580,13581,13582,13584],{"id":8911,"depth":649,"text":8912},{"id":9001,"depth":649,"text":9002},{"id":9336,"depth":649,"text":9337},{"id":9418,"depth":649,"text":13583},"Výpočet, je-li dáno PP jako funkce QQ",{"id":9676,"depth":649,"text":9677},{"id":9998,"depth":642,"text":9999},{"id":10594,"depth":642,"text":10595,"children":13587},[13588,13589],{"id":11222,"depth":649,"text":11223},{"id":12051,"depth":649,"text":12052},{"id":12684,"depth":642,"text":12685,"children":13591},[13592],{"id":12809,"depth":649,"text":12810},{"id":13098,"depth":642,"text":13099,"children":13594},[13595,13596],{"id":13188,"depth":649,"text":13189},{"id":13339,"depth":649,"text":13340},{},"\u002Ftopics\u002Felasticita",{"title":7921,"description":641},[1138,1136],"topics\u002Felasticita",[1128,7957,13603,13604,13605,13606],"cenova-elasticita","krizova-elasticita","duchodova-elasticita","mr-tr","c_Ilj6dK9Ey4kbyp6EKogVl_p8zmryyIur0pCOtxlhM",{"id":13609,"title":13610,"body":13611,"course":1128,"courses":659,"created":1129,"description":15151,"extension":661,"meta":15152,"navigation":664,"path":15153,"seo":15154,"sources":15155,"stem":15156,"tags":15157,"type":6050,"updated":677,"__hash__":15162},"topics\u002Ftopics\u002Ffunkce-vice-promennych.md","Kalkul funkcí více proměnných",{"type":9,"value":13612,"toc":15136},[13613,13616,13690,13697,13701,13765,13853,13857,13884,13951,14006,14010,14037,14129,14131,14163,14334,14338,14408,14456,14460,14521,14627,14642,14646,14648,14676,14741,14743,14750,14838,14863,15061,15065,15101,15103],[12,13614,13610],{"id":13615},"kalkul-funkcí-více-proměnných",[724,13617,13618,13619,13622,13623,1343,13652,1741],{},"Většina ekonomických veličin závisí na ",[38,13620,13621],{},"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 ",[883,13624,13626],{"className":13625},[886],[888,13627,13628],{"xmlns":890},[892,13629,13630,13649],{},[895,13631,13632,13635,13637,13639,13641,13643,13645,13647],{},[898,13633,13634],{},"z",[1761,13636,1909],{},[898,13638,6107],{},[1761,13640,1915],{"stretchy":1821},[898,13642,6112],{},[1761,13644,1834],{"separator":1833},[898,13646,1716],{},[1761,13648,1920],{"stretchy":1821},[902,13650,13651],{"encoding":904},"z = f(x, y)",[883,13653,13655],{"className":13654},[886],[888,13656,13657],{"xmlns":890},[892,13658,13659,13687],{},[895,13660,13661,13664,13666,13668,13670,13672,13674,13676,13678,13680,13682,13684],{},[898,13662,13663],{},"w",[1761,13665,1909],{},[898,13667,6107],{},[1761,13669,1915],{"stretchy":1821},[898,13671,6112],{},[1761,13673,1834],{"separator":1833},[898,13675,1716],{},[1761,13677,1834],{"separator":1833},[898,13679,13634],{},[1761,13681,1920],{"stretchy":1821},[1761,13683,1834],{"separator":1833},[1761,13685,13686],{},"…",[902,13688,13689],{"encoding":904},"w = f(x, y, z), \\ldots",[724,13691,13692],{},[3991,13693],{"alt":13694,"className":13695,"src":13696},"imek-funkce-2d-vrstevnice",[210,3995],"\u002Fwiki-assets\u002Fimek-funkce-2d-vrstevnice.jpeg",[115,13698,13700],{"id":13699},"indiferenční-izokvantové-křivky","Indiferenční \u002F izokvantové křivky",[724,13702,13703,13704,13731,13732,13760,13761,13764],{},"Pro ",[883,13705,13707],{"className":13706},[886],[888,13708,13709],{"xmlns":890},[892,13710,13711,13729],{},[895,13712,13713,13715,13717,13719,13721,13723,13725,13727],{},[898,13714,13634],{},[1761,13716,1909],{},[898,13718,6107],{},[1761,13720,1915],{"stretchy":1821},[898,13722,6112],{},[1761,13724,1834],{"separator":1833},[898,13726,1716],{},[1761,13728,1920],{"stretchy":1821},[902,13730,13651],{"encoding":904}," se křivkou s předpisem ",[883,13733,13735],{"className":13734},[886],[888,13736,13737],{"xmlns":890},[892,13738,13739,13757],{},[895,13740,13741,13743,13745,13747,13749,13751,13753,13755],{},[898,13742,6107],{},[1761,13744,1915],{"stretchy":1821},[898,13746,6112],{},[1761,13748,1834],{"separator":1833},[898,13750,1716],{},[1761,13752,1920],{"stretchy":1821},[1761,13754,1909],{},[898,13756,2774],{},[902,13758,13759],{"encoding":904},"f(x, y) = c"," (konstanta) rozumí ",[38,13762,13763],{},"vrstevnice"," funkce. V ekonomii:",[120,13766,13767,13814],{},[123,13768,13769,13772,13773,13809,13810,1741],{},[38,13770,13771],{},"Indiferenční křivky"," užitečnosti ",[883,13774,13776],{"className":13775},[886],[888,13777,13778],{"xmlns":890},[892,13779,13780,13806],{},[895,13781,13782,13784,13786,13792,13794,13800,13802,13804],{},[898,13783,900],{},[1761,13785,1915],{"stretchy":1821},[1681,13787,13788,13790],{},[898,13789,1828],{},[1765,13791,1945],{},[1761,13793,1834],{"separator":1833},[1681,13795,13796,13798],{},[898,13797,1828],{},[1765,13799,2296],{},[1761,13801,1920],{"stretchy":1821},[1761,13803,1909],{},[898,13805,2774],{},[902,13807,13808],{"encoding":904},"U(Q_1, Q_2) = c"," — viz ",[207,13811,13813],{"className":13812,"dataFsResolvedFilePath":878,"href":879},[210],"uzitecnost",[123,13815,13816,13819,13820,13809,13849,1741],{},[38,13817,13818],{},"Izokvanty"," produkce ",[883,13821,13823],{"className":13822},[886],[888,13824,13825],{"xmlns":890},[892,13826,13827,13846],{},[895,13828,13829,13831,13833,13836,13838,13840,13842,13844],{},[898,13830,1828],{},[1761,13832,1915],{"stretchy":1821},[898,13834,13835],{},"L",[1761,13837,1834],{"separator":1833},[898,13839,2768],{},[1761,13841,1920],{"stretchy":1821},[1761,13843,1909],{},[898,13845,2774],{},[902,13847,13848],{"encoding":904},"Q(L, K) = c",[207,13850,13852],{"className":13851,"dataFsResolvedFilePath":857,"href":858},[210],"produkce",[115,13854,13856],{"id":13855},"parciální-derivace","Parciální derivace",[724,13858,13703,13859,13883],{},[883,13860,13862],{"className":13861},[886],[888,13863,13864],{"xmlns":890},[892,13865,13866,13880],{},[895,13867,13868,13870,13872,13874,13876,13878],{},[898,13869,6107],{},[1761,13871,1915],{"stretchy":1821},[898,13873,6112],{},[1761,13875,1834],{"separator":1833},[898,13877,1716],{},[1761,13879,1920],{"stretchy":1821},[902,13881,13882],{"encoding":904},"f(x, y)"," derivujeme jako kdyby druhá proměnná byla konstanta:",[724,13885,13886],{},[883,13887,13889],{"className":13888},[886],[888,13890,13891],{"xmlns":890},[892,13892,13893,13948],{},[895,13894,13895,13903,13905,13920,13922,13924,13932,13934],{},[2015,13896,13897,13899,13901],{},[898,13898,6107],{},[898,13900,6112],{},[1761,13902,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,13904,1909],{},[4379,13906,13907,13914],{},[895,13908,13909,13912],{},[898,13910,13911],{"mathvariant":1969},"∂",[898,13913,6107],{},[895,13915,13916,13918],{},[898,13917,13911],{"mathvariant":1969},[898,13919,6112],{},[1761,13921,1834],{"separator":1833},[3315,13923],{"width":3317},[2015,13925,13926,13928,13930],{},[898,13927,6107],{},[898,13929,1716],{},[1761,13931,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,13933,1909],{},[4379,13935,13936,13942],{},[895,13937,13938,13940],{},[898,13939,13911],{"mathvariant":1969},[898,13941,6107],{},[895,13943,13944,13946],{},[898,13945,13911],{"mathvariant":1969},[898,13947,1716],{},[902,13949,13950],{"encoding":904},"f'_x = \\frac{\\partial f}{\\partial x}, \\qquad f'_y = \\frac{\\partial f}{\\partial y}",[724,13952,13953,13954,1741],{},"Hodnoty v bodě: ",[883,13955,13957],{"className":13956},[886],[888,13958,13959],{"xmlns":890},[892,13960,13961,14003],{},[895,13962,13963,13971,13973,13975,13977,13979,13981,13983,13985,13993,13995,13997,13999,14001],{},[2015,13964,13965,13967,13969],{},[898,13966,6107],{},[898,13968,6112],{},[1761,13970,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,13972,1915],{"stretchy":1821},[898,13974,207],{},[1761,13976,1834],{"separator":1833},[898,13978,4302],{},[1761,13980,1920],{"stretchy":1821},[1761,13982,1834],{"separator":1833},[2761,13984,2763],{},[2015,13986,13987,13989,13991],{},[898,13988,6107],{},[898,13990,1716],{},[1761,13992,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,13994,1915],{"stretchy":1821},[898,13996,207],{},[1761,13998,1834],{"separator":1833},[898,14000,4302],{},[1761,14002,1920],{"stretchy":1821},[902,14004,14005],{"encoding":904},"f'_x(a, b),\\ f'_y(a, b)",[198,14007,14009],{"id":14008},"ekonomické-značení","Ekonomické značení",[724,14011,14012,14013,2506],{},"Pro produkční funkci ",[883,14014,14016],{"className":14015},[886],[888,14017,14018],{"xmlns":890},[892,14019,14020,14034],{},[895,14021,14022,14024,14026,14028,14030,14032],{},[898,14023,1828],{},[1761,14025,1915],{"stretchy":1821},[898,14027,13835],{},[1761,14029,1834],{"separator":1833},[898,14031,2768],{},[1761,14033,1920],{"stretchy":1821},[902,14035,14036],{"encoding":904},"Q(L, K)",[120,14038,14039,14084],{},[123,14040,14041,6549,14061,3927,14064,1920],{},[883,14042,14044],{"className":14043},[886],[888,14045,14046],{"xmlns":890},[892,14047,14048,14058],{},[895,14049,14050],{},[2015,14051,14052,14054,14056],{},[898,14053,1828],{},[898,14055,13835],{},[1761,14057,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[902,14059,14060],{"encoding":904},"Q'_L",[38,14062,14063],{},"mezní produkt práce",[883,14065,14067],{"className":14066},[886],[888,14068,14069],{"xmlns":890},[892,14070,14071,14081],{},[895,14072,14073,14075],{},[898,14074,6889],{},[1681,14076,14077,14079],{},[898,14078,1839],{},[898,14080,13835],{},[902,14082,14083],{"encoding":904},"MP_L",[123,14085,14086,6549,14106,3927,14109,1920],{},[883,14087,14089],{"className":14088},[886],[888,14090,14091],{"xmlns":890},[892,14092,14093,14103],{},[895,14094,14095],{},[2015,14096,14097,14099,14101],{},[898,14098,1828],{},[898,14100,2768],{},[1761,14102,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[902,14104,14105],{"encoding":904},"Q'_K",[38,14107,14108],{},"mezní produkt kapitálu",[883,14110,14112],{"className":14111},[886],[888,14113,14114],{"xmlns":890},[892,14115,14116,14126],{},[895,14117,14118,14120],{},[898,14119,6889],{},[1681,14121,14122,14124],{},[898,14123,1839],{},[898,14125,2768],{},[902,14127,14128],{"encoding":904},"MP_K",[198,14130,6643],{"id":6642},[724,14132,14133,2506],{},[883,14134,14136],{"className":14135},[886],[888,14137,14138],{"xmlns":890},[892,14139,14140,14160],{},[895,14141,14142,14150,14152,14154,14156,14158],{},[2015,14143,14144,14146,14148],{},[898,14145,6107],{},[898,14147,6112],{},[1761,14149,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,14151,1915],{"stretchy":1821},[898,14153,207],{},[1761,14155,1834],{"separator":1833},[898,14157,4302],{},[1761,14159,1920],{"stretchy":1821},[902,14161,14162],{"encoding":904},"f'_x(a, b)",[120,14164,14165,14223],{},[123,14166,14167,14168,14181,14182,14195,14196,14222],{},"rychlost změny ",[883,14169,14171],{"className":14170},[886],[888,14172,14173],{"xmlns":890},[892,14174,14175,14179],{},[895,14176,14177],{},[898,14178,6107],{},[902,14180,6107],{"encoding":904}," vůči ",[883,14183,14185],{"className":14184},[886],[888,14186,14187],{"xmlns":890},[892,14188,14189,14193],{},[895,14190,14191],{},[898,14192,6112],{},[902,14194,6112],{"encoding":904}," při ",[883,14197,14199],{"className":14198},[886],[888,14200,14201],{"xmlns":890},[892,14202,14203,14219],{},[895,14204,14205,14207,14209,14211,14213,14215,14217],{},[898,14206,6112],{},[1761,14208,1909],{},[898,14210,207],{},[1761,14212,1834],{"separator":1833},[898,14214,1716],{},[1761,14216,1909],{},[898,14218,4302],{},[902,14220,14221],{"encoding":904},"x = a, y = b"," (kapitál fixní),",[123,14224,14225,14226,6732,14239,14252,14253,14271,14272,1741],{},"přibližná změna ",[883,14227,14229],{"className":14228},[886],[888,14230,14231],{"xmlns":890},[892,14232,14233,14237],{},[895,14234,14235],{},[898,14236,6107],{},[902,14238,6107],{"encoding":904},[883,14240,14242],{"className":14241},[886],[888,14243,14244],{"xmlns":890},[892,14245,14246,14250],{},[895,14247,14248],{},[898,14249,6112],{},[902,14251,6112],{"encoding":904}," o 1 (a pevném ",[883,14254,14256],{"className":14255},[886],[888,14257,14258],{"xmlns":890},[892,14259,14260,14268],{},[895,14261,14262,14264,14266],{},[898,14263,1716],{},[1761,14265,1909],{},[898,14267,4302],{},[902,14269,14270],{"encoding":904},"y = b","): ",[883,14273,14275],{"className":14274},[886],[888,14276,14277],{"xmlns":890},[892,14278,14279,14331],{},[895,14280,14281,14283,14285,14287,14289,14291,14293,14295,14297,14299,14301,14303,14305,14307,14309,14311,14313,14321,14323,14325,14327,14329],{},[898,14282,6107],{},[1761,14284,1915],{"stretchy":1821},[898,14286,207],{},[1761,14288,1964],{},[1765,14290,1945],{},[1761,14292,1834],{"separator":1833},[898,14294,4302],{},[1761,14296,1920],{"stretchy":1821},[1761,14298,6803],{},[898,14300,6107],{},[1761,14302,1915],{"stretchy":1821},[898,14304,207],{},[1761,14306,1834],{"separator":1833},[898,14308,4302],{},[1761,14310,1920],{"stretchy":1821},[1761,14312,1964],{},[2015,14314,14315,14317,14319],{},[898,14316,6107],{},[898,14318,6112],{},[1761,14320,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,14322,1915],{"stretchy":1821},[898,14324,207],{},[1761,14326,1834],{"separator":1833},[898,14328,4302],{},[1761,14330,1920],{"stretchy":1821},[902,14332,14333],{"encoding":904},"f(a+1, b) \\approx f(a, b) + f'_x(a, b)",[115,14335,14337],{"id":14336},"diferenciál-funkce-dvou-proměnných","Diferenciál funkce dvou proměnných",[724,14339,14340],{},[883,14341,14343],{"className":14342},[886],[888,14344,14345],{"xmlns":890},[892,14346,14347,14405],{},[895,14348,14349,14351,14353,14355,14363,14365,14367,14369,14371,14373,14375,14377,14379,14381,14389,14391,14393,14395,14397,14399,14401,14403],{},[898,14350,4346],{},[898,14352,6107],{},[1761,14354,1909],{},[2015,14356,14357,14359,14361],{},[898,14358,6107],{},[898,14360,6112],{},[1761,14362,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,14364,1915],{"stretchy":1821},[898,14366,6112],{},[1761,14368,1834],{"separator":1833},[898,14370,1716],{},[1761,14372,1920],{"stretchy":1821},[2761,14374,7057],{},[898,14376,4346],{},[898,14378,6112],{},[1761,14380,1964],{},[2015,14382,14383,14385,14387],{},[898,14384,6107],{},[898,14386,1716],{},[1761,14388,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,14390,1915],{"stretchy":1821},[898,14392,6112],{},[1761,14394,1834],{"separator":1833},[898,14396,1716],{},[1761,14398,1920],{"stretchy":1821},[2761,14400,7057],{},[898,14402,4346],{},[898,14404,1716],{},[902,14406,14407],{"encoding":904},"df = f'_x(x, y)\\, dx + f'_y(x, y)\\, dy",[724,14409,7067,14410,14432,14433,14455],{},[883,14411,14413],{"className":14412},[886],[888,14414,14415],{"xmlns":890},[892,14416,14417,14429],{},[895,14418,14419,14421,14423,14425,14427],{},[898,14420,4346],{},[898,14422,6112],{},[1761,14424,1834],{"separator":1833},[898,14426,4346],{},[898,14428,1716],{},[902,14430,14431],{"encoding":904},"dx, dy"," platí ",[883,14434,14436],{"className":14435},[886],[888,14437,14438],{"xmlns":890},[892,14439,14440,14452],{},[895,14441,14442,14444,14446,14448,14450],{},[898,14443,6959],{"mathvariant":1969},[898,14445,6107],{},[1761,14447,6803],{},[898,14449,4346],{},[898,14451,6107],{},[902,14453,14454],{"encoding":904},"\\Delta f \\approx df",". Linearizace přírůstku ve dvou směrech současně.",[115,14457,14459],{"id":14458},"implicitní-funkce","Implicitní funkce",[724,14461,14462,14463,14492,14493,14506,14507,14520],{},"Je-li vztah dán rovnicí ",[883,14464,14466],{"className":14465},[886],[888,14467,14468],{"xmlns":890},[892,14469,14470,14489],{},[895,14471,14472,14475,14477,14479,14481,14483,14485,14487],{},[898,14473,14474],{},"F",[1761,14476,1915],{"stretchy":1821},[898,14478,6112],{},[1761,14480,1834],{"separator":1833},[898,14482,1716],{},[1761,14484,1920],{"stretchy":1821},[1761,14486,1909],{},[1765,14488,1767],{},[902,14490,14491],{"encoding":904},"F(x, y) = 0"," a chceme derivaci ",[883,14494,14496],{"className":14495},[886],[888,14497,14498],{"xmlns":890},[892,14499,14500,14504],{},[895,14501,14502],{},[898,14503,1716],{},[902,14505,1716],{"encoding":904}," podle ",[883,14508,14510],{"className":14509},[886],[888,14511,14512],{"xmlns":890},[892,14513,14514,14518],{},[895,14515,14516],{},[898,14517,6112],{},[902,14519,6112],{"encoding":904}," (nebo naopak):",[724,14522,14523],{},[883,14524,14526],{"className":14525},[886],[888,14527,14528],{"xmlns":890},[892,14529,14530,14624],{},[895,14531,14532,14538,14540,14554,14556,14558,14576,14578,14580,14586,14588,14602,14604,14606],{},[1824,14533,14534,14536],{},[898,14535,1716],{},[1761,14537,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,14539,1909],{},[4379,14541,14542,14548],{},[895,14543,14544,14546],{},[898,14545,4346],{},[898,14547,1716],{},[895,14549,14550,14552],{},[898,14551,4346],{},[898,14553,6112],{},[1761,14555,1909],{},[1761,14557,1885],{},[4379,14559,14560,14568],{},[2015,14561,14562,14564,14566],{},[898,14563,14474],{},[898,14565,6112],{},[1761,14567,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[2015,14569,14570,14572,14574],{},[898,14571,14474],{},[898,14573,1716],{},[1761,14575,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,14577,1834],{"separator":1833},[3315,14579],{"width":3317},[1824,14581,14582,14584],{},[898,14583,6112],{},[1761,14585,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,14587,1909],{},[4379,14589,14590,14596],{},[895,14591,14592,14594],{},[898,14593,4346],{},[898,14595,6112],{},[895,14597,14598,14600],{},[898,14599,4346],{},[898,14601,1716],{},[1761,14603,1909],{},[1761,14605,1885],{},[4379,14607,14608,14616],{},[2015,14609,14610,14612,14614],{},[898,14611,14474],{},[898,14613,1716],{},[1761,14615,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[2015,14617,14618,14620,14622],{},[898,14619,14474],{},[898,14621,6112],{},[1761,14623,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[902,14625,14626],{"encoding":904},"y' = \\frac{dy}{dx} = -\\frac{F'_x}{F'_y}, \\qquad x' = \\frac{dx}{dy} = -\\frac{F'_y}{F'_x}",[724,14628,14629,14630,14633,14634,2068,14638,1741],{},"Tato vzorec dává ",[38,14631,14632],{},"sklon vrstevnice"," — používá se mj. pro výpočet ",[207,14635,14637],{"className":14636,"dataFsResolvedFilePath":857,"href":858},[210],"MRTS",[207,14639,14641],{"className":14640,"dataFsResolvedFilePath":878,"href":879},[210],"MRCS",[115,14643,14645],{"id":14644},"volné-extrémy-funkce-dvou-proměnných","Volné extrémy funkce dvou proměnných",[198,14647,7319],{"id":7318},[724,14649,14650,14651,14675],{},"V bodě extrému ",[883,14652,14654],{"className":14653},[886],[888,14655,14656],{"xmlns":890},[892,14657,14658,14672],{},[895,14659,14660,14662,14664,14666,14668,14670],{},[898,14661,8309],{},[1761,14663,1822],{"stretchy":1821},[898,14665,207],{},[1761,14667,1834],{"separator":1833},[898,14669,4302],{},[1761,14671,1844],{"stretchy":1821},[902,14673,14674],{"encoding":904},"A[a, b]"," musí platit současně:",[724,14677,14678],{},[883,14679,14681],{"className":14680},[886],[888,14682,14683],{"xmlns":890},[892,14684,14685,14738],{},[895,14686,14687,14695,14697,14699,14701,14703,14705,14707,14709,14711,14714,14716,14724,14726,14728,14730,14732,14734,14736],{},[2015,14688,14689,14691,14693],{},[898,14690,6107],{},[898,14692,6112],{},[1761,14694,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,14696,1915],{"stretchy":1821},[898,14698,207],{},[1761,14700,1834],{"separator":1833},[898,14702,4302],{},[1761,14704,1920],{"stretchy":1821},[1761,14706,1909],{},[1765,14708,1767],{},[2761,14710,8041],{},[1761,14712,14713],{},"∧",[2761,14715,8041],{},[2015,14717,14718,14720,14722],{},[898,14719,6107],{},[898,14721,1716],{},[1761,14723,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,14725,1915],{"stretchy":1821},[898,14727,207],{},[1761,14729,1834],{"separator":1833},[898,14731,4302],{},[1761,14733,1920],{"stretchy":1821},[1761,14735,1909],{},[1765,14737,1767],{},[902,14739,14740],{"encoding":904},"f'_x(a, b) = 0 \\;\\wedge\\; f'_y(a, b) = 0",[198,14742,7393],{"id":7392},[724,14744,14745,14746,14749],{},"Definujeme ",[38,14747,14748],{},"diskriminant"," (Hessián zjednodušeně):",[724,14751,14752],{},[883,14753,14755],{"className":14754},[886],[888,14756,14757],{"xmlns":890},[892,14758,14759,14835],{},[895,14760,14761,14763,14765,14767,14769,14771,14773,14775,14791,14793,14809,14811,14813,14829],{},[898,14762,2244],{},[1761,14764,1915],{"stretchy":1821},[898,14766,6112],{},[1761,14768,1834],{"separator":1833},[898,14770,1716],{},[1761,14772,1920],{"stretchy":1821},[1761,14774,1909],{},[2015,14776,14777,14779,14785],{},[898,14778,6107],{},[895,14780,14781,14783],{},[898,14782,6112],{},[898,14784,6112],{},[895,14786,14787,14789],{},[1761,14788,6459],{"mathvariant":1969},[1761,14790,6459],{"mathvariant":1969},[1761,14792,2447],{},[2015,14794,14795,14797,14803],{},[898,14796,6107],{},[895,14798,14799,14801],{},[898,14800,1716],{},[898,14802,1716],{},[895,14804,14805,14807],{},[1761,14806,6459],{"mathvariant":1969},[1761,14808,6459],{"mathvariant":1969},[1761,14810,1885],{},[1761,14812,1915],{"stretchy":1821},[2015,14814,14815,14817,14823],{},[898,14816,6107],{},[895,14818,14819,14821],{},[898,14820,6112],{},[898,14822,1716],{},[895,14824,14825,14827],{},[1761,14826,6459],{"mathvariant":1969},[1761,14828,6459],{"mathvariant":1969},[1824,14830,14831,14833],{},[1761,14832,1920],{"stretchy":1821},[1765,14834,2296],{},[902,14836,14837],{"encoding":904},"D(x, y) = f''_{xx} \\cdot f''_{yy} - (f''_{xy})^2",[724,14839,14840,14841,2506],{},"V podezřelém bodě ",[883,14842,14844],{"className":14843},[886],[888,14845,14846],{"xmlns":890},[892,14847,14848,14860],{},[895,14849,14850,14852,14854,14856,14858],{},[1761,14851,1822],{"stretchy":1821},[898,14853,207],{},[1761,14855,1834],{"separator":1833},[898,14857,4302],{},[1761,14859,1844],{"stretchy":1821},[902,14861,14862],{"encoding":904},"[a, b]",[152,14864,14865,14992,15028],{},[123,14866,14867,14897,14898],{},[38,14868,14869,2506],{},[883,14870,14872],{"className":14871},[886],[888,14873,14874],{"xmlns":890},[892,14875,14876,14894],{},[895,14877,14878,14880,14882,14884,14886,14888,14890,14892],{},[898,14879,2244],{},[1761,14881,1915],{"stretchy":1821},[898,14883,207],{},[1761,14885,1834],{"separator":1833},[898,14887,4302],{},[1761,14889,1920],{"stretchy":1821},[1761,14891,1763],{},[1765,14893,1767],{},[902,14895,14896],{"encoding":904},"D(a, b) > 0"," je to extrém.\n",[120,14899,14900,14946],{},[123,14901,14902,7480,14944],{},[883,14903,14905],{"className":14904},[886],[888,14906,14907],{"xmlns":890},[892,14908,14909,14941],{},[895,14910,14911,14927,14929,14931,14933,14935,14937,14939],{},[2015,14912,14913,14915,14921],{},[898,14914,6107],{},[895,14916,14917,14919],{},[898,14918,6112],{},[898,14920,6112],{},[895,14922,14923,14925],{},[1761,14924,6459],{"mathvariant":1969},[1761,14926,6459],{"mathvariant":1969},[1761,14928,1915],{"stretchy":1821},[898,14930,207],{},[1761,14932,1834],{"separator":1833},[898,14934,4302],{},[1761,14936,1920],{"stretchy":1821},[1761,14938,1763],{},[1765,14940,1767],{},[902,14942,14943],{"encoding":904},"f''_{xx}(a, b) > 0",[38,14945,7839],{},[123,14947,14948,7480,14990],{},[883,14949,14951],{"className":14950},[886],[888,14952,14953],{"xmlns":890},[892,14954,14955,14987],{},[895,14956,14957,14973,14975,14977,14979,14981,14983,14985],{},[2015,14958,14959,14961,14967],{},[898,14960,6107],{},[895,14962,14963,14965],{},[898,14964,6112],{},[898,14966,6112],{},[895,14968,14969,14971],{},[1761,14970,6459],{"mathvariant":1969},[1761,14972,6459],{"mathvariant":1969},[1761,14974,1915],{"stretchy":1821},[898,14976,207],{},[1761,14978,1834],{"separator":1833},[898,14980,4302],{},[1761,14982,1920],{"stretchy":1821},[1761,14984,2058],{},[1765,14986,1767],{},[902,14988,14989],{"encoding":904},"f''_{xx}(a, b) \u003C 0",[38,14991,7781],{},[123,14993,14994,1989,15024,15027],{},[38,14995,14996,2506],{},[883,14997,14999],{"className":14998},[886],[888,15000,15001],{"xmlns":890},[892,15002,15003,15021],{},[895,15004,15005,15007,15009,15011,15013,15015,15017,15019],{},[898,15006,2244],{},[1761,15008,1915],{"stretchy":1821},[898,15010,207],{},[1761,15012,1834],{"separator":1833},[898,15014,4302],{},[1761,15016,1920],{"stretchy":1821},[1761,15018,2058],{},[1765,15020,1767],{},[902,15022,15023],{"encoding":904},"D(a, b) \u003C 0",[38,15025,15026],{},"sedlo"," (v daném bodě extrém není).",[123,15029,15030,15060],{},[38,15031,15032,2506],{},[883,15033,15035],{"className":15034},[886],[888,15036,15037],{"xmlns":890},[892,15038,15039,15057],{},[895,15040,15041,15043,15045,15047,15049,15051,15053,15055],{},[898,15042,2244],{},[1761,15044,1915],{"stretchy":1821},[898,15046,207],{},[1761,15048,1834],{"separator":1833},[898,15050,4302],{},[1761,15052,1920],{"stretchy":1821},[1761,15054,1909],{},[1765,15056,1767],{},[902,15058,15059],{"encoding":904},"D(a, b) = 0"," podmínka nerozhoduje.",[115,15062,15064],{"id":15063},"vázané-extrémy","Vázané extrémy",[724,15066,15067,15068,15097,15098,1741],{},"Pro extrémy s omezující podmínkou ",[883,15069,15071],{"className":15070},[886],[888,15072,15073],{"xmlns":890},[892,15074,15075,15094],{},[895,15076,15077,15080,15082,15084,15086,15088,15090,15092],{},[898,15078,15079],{},"g",[1761,15081,1915],{"stretchy":1821},[898,15083,6112],{},[1761,15085,1834],{"separator":1833},[898,15087,1716],{},[1761,15089,1920],{"stretchy":1821},[1761,15091,1909],{},[1765,15093,1767],{},[902,15095,15096],{"encoding":904},"g(x, y) = 0"," se používá ",[207,15099,793],{"className":15100,"dataFsResolvedFilePath":791,"href":792},[210],[115,15102,5968],{"id":5967},[120,15104,15105,15112,15119],{},[123,15106,15107,1989,15109],{},[38,15108,7861],{},[207,15110,775],{"className":15111,"dataFsResolvedFilePath":773,"href":774},[210],[123,15113,15114,1989,15116],{},[38,15115,7869],{},[207,15117,793],{"className":15118,"dataFsResolvedFilePath":791,"href":792},[210],[123,15120,15121,1989,15123,15127,15128,15131,15132,15135],{},[38,15122,7877],{},[207,15124,15126],{"className":15125,"dataFsResolvedFilePath":857,"href":858},[210],"Produkce"," (parciální derivace = mezní produkty), ",[207,15129,880],{"className":15130,"dataFsResolvedFilePath":878,"href":879},[210]," (parciální derivace = mezní užitečnost), ",[207,15133,6000],{"className":15134,"dataFsResolvedFilePath":848,"href":849},[210]," (vícefaktorový model)",{"title":641,"searchDepth":642,"depth":642,"links":15137},[15138,15139,15143,15144,15145,15149,15150],{"id":13699,"depth":642,"text":13700},{"id":13855,"depth":642,"text":13856,"children":15140},[15141,15142],{"id":14008,"depth":649,"text":14009},{"id":6642,"depth":649,"text":6643},{"id":14336,"depth":642,"text":14337},{"id":14458,"depth":642,"text":14459},{"id":14644,"depth":642,"text":14645,"children":15146},[15147,15148],{"id":7318,"depth":649,"text":7319},{"id":7392,"depth":649,"text":7393},{"id":15063,"depth":642,"text":15064},{"id":5967,"depth":642,"text":5968},"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":13610,"description":15151},[1135],"topics\u002Ffunkce-vice-promennych",[1128,15158,7915,15159,15160,15161],"parcialni-derivace","implicitni-funkce","volne-extremy","indiferencni-krivky","iuWLbpl-7gHnuMDZKTa3RcRM2uCyFhGx9GhXHIN1R_A",{"id":15164,"title":775,"body":15165,"course":1128,"courses":659,"created":1129,"description":16021,"extension":661,"meta":16022,"navigation":664,"path":16023,"seo":16024,"sources":16025,"stem":16026,"tags":16027,"type":6050,"updated":677,"__hash__":16034},"topics\u002Ftopics\u002Fintegral.md",{"type":9,"value":15166,"toc":16011},[15167,15170,15181,15185,15230,15310,15314,15390,15432,15439,15443,15447,15476,15534,15581,15619,15623,15673,15725,15777,15821,15824,15827,15899,15902,15974,15981,15983],[12,15168,775],{"id":15169},"integrál",[724,15171,15172,15173,15176,15177,15180],{},"Druhá polovina kalkulu jedné proměnné. Slouží k ",[38,15174,15175],{},"rekonstrukci totální veličiny z mezní"," (TR z MR, TC z MC) a k výpočtu ",[38,15178,15179],{},"přebytků"," (consumer\u002Fproducer surplus).",[115,15182,15184],{"id":15183},"neurčitý-integrál","Neurčitý integrál",[724,15186,15187],{},[883,15188,15190],{"className":15189},[886],[888,15191,15192],{"xmlns":890},[892,15193,15194,15227],{},[895,15195,15196,15198,15200,15202,15204,15206,15209,15211,15213,15215,15217,15219,15221,15223,15225],{},[898,15197,14474],{},[1761,15199,1915],{"stretchy":1821},[898,15201,6112],{},[1761,15203,1920],{"stretchy":1821},[1761,15205,1909],{},[1761,15207,15208],{},"∫",[898,15210,6107],{},[1761,15212,1915],{"stretchy":1821},[898,15214,6112],{},[1761,15216,1920],{"stretchy":1821},[2761,15218,7057],{},[898,15220,4346],{},[898,15222,6112],{},[1761,15224,1964],{},[898,15226,6849],{},[902,15228,15229],{"encoding":904},"F(x) = \\int f(x)\\, dx + C",[724,15231,8364,15232,6997,15266,12146,15279,15282,15283,1343,15296,15309],{},[883,15233,15235],{"className":15234},[886],[888,15236,15237],{"xmlns":890},[892,15238,15239,15263],{},[895,15240,15241,15247,15249,15251,15253,15255,15257,15259,15261],{},[1824,15242,15243,15245],{},[898,15244,14474],{},[1761,15246,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,15248,1915],{"stretchy":1821},[898,15250,6112],{},[1761,15252,1920],{"stretchy":1821},[1761,15254,1909],{},[898,15256,6107],{},[1761,15258,1915],{"stretchy":1821},[898,15260,6112],{},[1761,15262,1920],{"stretchy":1821},[902,15264,15265],{"encoding":904},"F'(x) = f(x)",[883,15267,15269],{"className":15268},[886],[888,15270,15271],{"xmlns":890},[892,15272,15273,15277],{},[895,15274,15275],{},[898,15276,14474],{},[902,15278,14474],{"encoding":904},[38,15280,15281],{},"primitivní funkce"," k ",[883,15284,15286],{"className":15285},[886],[888,15287,15288],{"xmlns":890},[892,15289,15290,15294],{},[895,15291,15292],{},[898,15293,6107],{},[902,15295,6107],{"encoding":904},[883,15297,15299],{"className":15298},[886],[888,15300,15301],{"xmlns":890},[892,15302,15303,15307],{},[895,15304,15305],{},[898,15306,6849],{},[902,15308,6849],{"encoding":904}," konstanta.",[115,15311,15313],{"id":15312},"určitý-integrál","Určitý integrál",[724,15315,15316],{},[883,15317,15319],{"className":15318},[886],[888,15320,15321],{"xmlns":890},[892,15322,15323,15387],{},[895,15324,15325,15333,15335,15337,15339,15341,15343,15345,15347,15349,15351,15353,15355,15357,15359,15367,15369,15371,15373,15375,15377,15379,15381,15383,15385],{},[2015,15326,15327,15329,15331],{},[1761,15328,15208],{},[898,15330,207],{},[898,15332,4302],{},[898,15334,6107],{},[1761,15336,1915],{"stretchy":1821},[898,15338,6112],{},[1761,15340,1920],{"stretchy":1821},[2761,15342,7057],{},[898,15344,4346],{},[898,15346,6112],{},[1761,15348,1909],{},[1761,15350,1822],{"stretchy":1821},[898,15352,14474],{},[1761,15354,1915],{"stretchy":1821},[898,15356,6112],{},[1761,15358,1920],{"stretchy":1821},[2015,15360,15361,15363,15365],{},[1761,15362,1844],{"stretchy":1821},[898,15364,207],{},[898,15366,4302],{},[1761,15368,1909],{},[898,15370,14474],{},[1761,15372,1915],{"stretchy":1821},[898,15374,4302],{},[1761,15376,1920],{"stretchy":1821},[1761,15378,1885],{},[898,15380,14474],{},[1761,15382,1915],{"stretchy":1821},[898,15384,207],{},[1761,15386,1920],{"stretchy":1821},[902,15388,15389],{"encoding":904},"\\int_a^b f(x)\\, dx = [F(x)]_a^b = F(b) - F(a)",[724,15391,15392,15393,1989,15396,15409,15410,15431],{},"Geometricky ",[38,15394,15395],{},"plocha pod grafem",[883,15397,15399],{"className":15398},[886],[888,15400,15401],{"xmlns":890},[892,15402,15403,15407],{},[895,15404,15405],{},[898,15406,6107],{},[902,15408,6107],{"encoding":904}," na intervalu ",[883,15411,15413],{"className":15412},[886],[888,15414,15415],{"xmlns":890},[892,15416,15417,15429],{},[895,15418,15419,15421,15423,15425,15427],{},[1761,15420,1822],{"stretchy":1821},[898,15422,207],{},[1761,15424,1834],{"separator":1833},[898,15426,4302],{},[1761,15428,1844],{"stretchy":1821},[902,15430,14862],{"encoding":904}," (orientovaná).",[724,15433,15434],{},[3991,15435],{"alt":15436,"className":15437,"src":15438},"imek-integral-plocha",[210,3995],"\u002Fwiki-assets\u002Fimek-integral-plocha.jpeg",[115,15440,15442],{"id":15441},"aplikace-v-ekonomii","Aplikace v ekonomii",[198,15444,15446],{"id":15445},"příklad-tr-z-mr","Příklad — TR z MR",[724,15448,15449,15450,1741],{},"Mezní příjem ",[883,15451,15453],{"className":15452},[886],[888,15454,15455],{"xmlns":890},[892,15456,15457,15473],{},[895,15458,15459,15461,15463,15465,15467,15469,15471],{},[898,15460,6889],{},[898,15462,8051],{},[1761,15464,1909],{},[1765,15466,7160],{},[1761,15468,1885],{},[1765,15470,2296],{},[898,15472,1828],{},[902,15474,15475],{"encoding":904},"MR = 100 - 2Q",[724,15477,15478],{},[883,15479,15481],{"className":15480},[886],[888,15482,15483],{"xmlns":890},[892,15484,15485,15531],{},[895,15486,15487,15489,15491,15493,15495,15497,15499,15501,15503,15505,15507,15509,15511,15513,15515,15517,15519,15521,15527,15529],{},[898,15488,1655],{},[898,15490,8051],{},[1761,15492,1909],{},[1761,15494,15208],{},[1761,15496,1915],{"stretchy":1821},[1765,15498,7160],{},[1761,15500,1885],{},[1765,15502,2296],{},[898,15504,1828],{},[1761,15506,1920],{"stretchy":1821},[2761,15508,7057],{},[898,15510,4346],{},[898,15512,1828],{},[1761,15514,1909],{},[1765,15516,7160],{},[898,15518,1828],{},[1761,15520,1885],{},[1824,15522,15523,15525],{},[898,15524,1828],{},[1765,15526,2296],{},[1761,15528,1964],{},[898,15530,2774],{},[902,15532,15533],{"encoding":904},"TR = \\int (100 - 2Q)\\, dQ = 100Q - Q^2 + c",[724,15535,15536,15537,7480,15563,2506],{},"Okrajová podmínka ",[883,15538,15540],{"className":15539},[886],[888,15541,15542],{"xmlns":890},[892,15543,15544,15560],{},[895,15545,15546,15548,15550,15552,15554,15556,15558],{},[898,15547,1655],{},[898,15549,8051],{},[1761,15551,1915],{"stretchy":1821},[1765,15553,1767],{},[1761,15555,1920],{"stretchy":1821},[1761,15557,1909],{},[1765,15559,1767],{},[902,15561,15562],{"encoding":904},"TR(0) = 0",[883,15564,15566],{"className":15565},[886],[888,15567,15568],{"xmlns":890},[892,15569,15570,15578],{},[895,15571,15572,15574,15576],{},[898,15573,2774],{},[1761,15575,1909],{},[1765,15577,1767],{},[902,15579,15580],{"encoding":904},"c = 0",[724,15582,15583],{},[883,15584,15586],{"className":15585},[886],[888,15587,15588],{"xmlns":890},[892,15589,15590,15616],{},[895,15591,15592,15594,15596,15598,15600,15602,15604,15606,15608,15610],{},[898,15593,1655],{},[898,15595,8051],{},[1761,15597,1915],{"stretchy":1821},[898,15599,1828],{},[1761,15601,1920],{"stretchy":1821},[1761,15603,1909],{},[1765,15605,7160],{},[898,15607,1828],{},[1761,15609,1885],{},[1824,15611,15612,15614],{},[898,15613,1828],{},[1765,15615,2296],{},[902,15617,15618],{"encoding":904},"TR(Q) = 100Q - Q^2",[198,15620,15622],{"id":15621},"příklad-tc-z-mc","Příklad — TC z MC",[724,15624,15625,15626,15652,15653,1741],{},"Mezní náklady ",[883,15627,15629],{"className":15628},[886],[888,15630,15631],{"xmlns":890},[892,15632,15633,15649],{},[895,15634,15635,15637,15639,15641,15643,15645,15647],{},[898,15636,6889],{},[898,15638,6849],{},[1761,15640,1909],{},[1765,15642,2296],{},[1761,15644,1964],{},[1765,15646,6910],{},[898,15648,1828],{},[902,15650,15651],{"encoding":904},"MC = 2 + 0{,}2 Q",", fixní náklady ",[883,15654,15656],{"className":15655},[886],[888,15657,15658],{"xmlns":890},[892,15659,15660,15670],{},[895,15661,15662,15664,15666,15668],{},[898,15663,14474],{},[898,15665,6849],{},[1761,15667,1909],{},[1765,15669,7160],{},[902,15671,15672],{"encoding":904},"FC = 100",[724,15674,15675],{},[883,15676,15678],{"className":15677},[886],[888,15679,15680],{"xmlns":890},[892,15681,15682,15722],{},[895,15683,15684,15686,15688,15690,15692,15694,15696,15698,15700,15702,15704,15706,15708,15710,15712,15718,15720],{},[898,15685,1655],{},[898,15687,6849],{},[1761,15689,1909],{},[1761,15691,15208],{},[898,15693,6889],{},[898,15695,6849],{},[2761,15697,7057],{},[898,15699,4346],{},[898,15701,1828],{},[1761,15703,1909],{},[1765,15705,2296],{},[898,15707,1828],{},[1761,15709,1964],{},[1765,15711,6865],{},[1824,15713,15714,15716],{},[898,15715,1828],{},[1765,15717,2296],{},[1761,15719,1964],{},[898,15721,2774],{},[902,15723,15724],{"encoding":904},"TC = \\int MC\\, dQ = 2Q + 0{,}1 Q^2 + c",[724,15726,15536,15727,7480,15759,2506],{},[883,15728,15730],{"className":15729},[886],[888,15731,15732],{"xmlns":890},[892,15733,15734,15756],{},[895,15735,15736,15738,15740,15742,15744,15746,15748,15750,15752,15754],{},[898,15737,1655],{},[898,15739,6849],{},[1761,15741,1915],{"stretchy":1821},[1765,15743,1767],{},[1761,15745,1920],{"stretchy":1821},[1761,15747,1909],{},[898,15749,14474],{},[898,15751,6849],{},[1761,15753,1909],{},[1765,15755,7160],{},[902,15757,15758],{"encoding":904},"TC(0) = FC = 100",[883,15760,15762],{"className":15761},[886],[888,15763,15764],{"xmlns":890},[892,15765,15766,15774],{},[895,15767,15768,15770,15772],{},[898,15769,2774],{},[1761,15771,1909],{},[1765,15773,7160],{},[902,15775,15776],{"encoding":904},"c = 100",[724,15778,15779],{},[883,15780,15782],{"className":15781},[886],[888,15783,15784],{"xmlns":890},[892,15785,15786,15818],{},[895,15787,15788,15790,15792,15794,15796,15798,15800,15802,15804,15806,15808,15810,15812],{},[898,15789,1655],{},[898,15791,6849],{},[1761,15793,1915],{"stretchy":1821},[898,15795,1828],{},[1761,15797,1920],{"stretchy":1821},[1761,15799,1909],{},[1765,15801,7160],{},[1761,15803,1964],{},[1765,15805,2296],{},[898,15807,1828],{},[1761,15809,1964],{},[1765,15811,6865],{},[1824,15813,15814,15816],{},[898,15815,1828],{},[1765,15817,2296],{},[902,15819,15820],{"encoding":904},"TC(Q) = 100 + 2Q + 0{,}1 Q^2",[198,15822,820],{"id":15823},"přebytek-spotřebitele-a-výrobce",[724,15825,15826],{},"Přebytek spotřebitele:",[724,15828,15829],{},[883,15830,15832],{"className":15831},[886],[888,15833,15834],{"xmlns":890},[892,15835,15836,15896],{},[895,15837,15838,15840,15842,15844,15850,15852,15854,15866,15868,15870,15872,15874,15876,15878,15880,15882,15888,15890],{},[898,15839,6849],{},[898,15841,1912],{},[1761,15843,1915],{"stretchy":1821},[1681,15845,15846,15848],{},[898,15847,1828],{},[1765,15849,1767],{},[1761,15851,1920],{"stretchy":1821},[1761,15853,1909],{},[2015,15855,15856,15858,15860],{},[1761,15857,15208],{},[1765,15859,1767],{},[1681,15861,15862,15864],{},[898,15863,1828],{},[1765,15865,1767],{},[898,15867,2244],{},[1761,15869,1915],{"stretchy":1821},[898,15871,1828],{},[1761,15873,1920],{"stretchy":1821},[2761,15875,7057],{},[898,15877,4346],{},[898,15879,1828],{},[1761,15881,1885],{},[1681,15883,15884,15886],{},[898,15885,1839],{},[1765,15887,1767],{},[2761,15889,7057],{},[1681,15891,15892,15894],{},[898,15893,1828],{},[1765,15895,1767],{},[902,15897,15898],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\, dQ - P_0\\, Q_0",[724,15900,15901],{},"Přebytek výrobce:",[724,15903,15904],{},[883,15905,15907],{"className":15906},[886],[888,15908,15909],{"xmlns":890},[892,15910,15911,15971],{},[895,15912,15913,15915,15917,15919,15925,15927,15929,15935,15937,15943,15945,15957,15959,15961,15963,15965,15967,15969],{},[898,15914,1839],{},[898,15916,1912],{},[1761,15918,1915],{"stretchy":1821},[1681,15920,15921,15923],{},[898,15922,1828],{},[1765,15924,1767],{},[1761,15926,1920],{"stretchy":1821},[1761,15928,1909],{},[1681,15930,15931,15933],{},[898,15932,1839],{},[1765,15934,1767],{},[2761,15936,7057],{},[1681,15938,15939,15941],{},[898,15940,1828],{},[1765,15942,1767],{},[1761,15944,1885],{},[2015,15946,15947,15949,15951],{},[1761,15948,15208],{},[1765,15950,1767],{},[1681,15952,15953,15955],{},[898,15954,1828],{},[1765,15956,1767],{},[898,15958,1912],{},[1761,15960,1915],{"stretchy":1821},[898,15962,1828],{},[1761,15964,1920],{"stretchy":1821},[2761,15966,7057],{},[898,15968,4346],{},[898,15970,1828],{},[902,15972,15973],{"encoding":904},"PS(Q_0) = P_0\\, Q_0 - \\int_0^{Q_0} S(Q)\\, dQ",[724,15975,15976,15977,1741],{},"Detailně viz ",[207,15978,15980],{"className":15979,"dataFsResolvedFilePath":800,"href":801},[210],"Poptávka a nabídka",[115,15982,5968],{"id":5967},[120,15984,15985,15992,15999],{},[123,15986,15987,1989,15989],{},[38,15988,7861],{},[207,15990,766],{"className":15991,"dataFsResolvedFilePath":764,"href":765},[210],[123,15993,15994,1989,15996],{},[38,15995,7869],{},[207,15997,784],{"className":15998,"dataFsResolvedFilePath":782,"href":783},[210],[123,16000,16001,1989,16003,16006,16007,16010],{},[38,16002,7877],{},[207,16004,7885],{"className":16005,"dataFsResolvedFilePath":827,"href":828},[210]," (TR\u002FTC), ",[207,16008,15980],{"className":16009,"dataFsResolvedFilePath":800,"href":801},[210]," (přebytky CS\u002FPS)",{"title":641,"searchDepth":642,"depth":642,"links":16012},[16013,16014,16015,16020],{"id":15183,"depth":642,"text":15184},{"id":15312,"depth":642,"text":15313},{"id":15441,"depth":642,"text":15442,"children":16016},[16017,16018,16019],{"id":15445,"depth":649,"text":15446},{"id":15621,"depth":649,"text":15622},{"id":15823,"depth":649,"text":820},{"id":5967,"depth":642,"text":5968},"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":16021},[1135],"topics\u002Fintegral",[1128,16028,16029,16030,16031,16032,16033],"integral","neurcity","urcity","primitivni-funkce","tr-z-mr","tc-z-mc","H1oOmn3Z5yZ_KZm1LLzfN_DVUhYSxx7eveFc7CASwZY",{"id":16036,"title":16037,"body":16038,"course":1128,"courses":659,"created":6039,"description":641,"extension":661,"meta":20300,"navigation":664,"path":20301,"seo":20302,"sources":20303,"stem":20304,"tags":20305,"type":6050,"updated":677,"__hash__":20311},"topics\u002Ftopics\u002Fis-lm.md","IS-LM analýza — simultánní rovnováha trhu zboží a peněz",{"type":9,"value":16039,"toc":20288},[16040,16043,16047,16189,16196,16200,16270,16308,16411,16415,16445,16511,16558,16561,16630,16633,16668,16704,16708,16756,16763,16809,16855,16858,16937,17034,17117,17121,17165,17195,17201,17230,17252,17302,17355,17421,17424,17490,17519,17578,17594,17681,17779,17910,17914,18071,18220,18600,18604,18607,18666,18669,18755,18783,18821,18824,18861,18901,18935,18937,18974,19006,19104,19109,19233,19285,19367,19506,19510,19630,19637,19748,19755,19757,20232,20234],[12,16041,16037],{"id":16042},"is-lm-analýza-simultánní-rovnováha-trhu-zboží-a-peněz",[115,16044,16046],{"id":16045},"tldr","TL;DR",[724,16048,16049,16052,16053,3927,16056,16069,16070,16083,16084,16087,16088,1343,16091,16094,16095,1343,16098,16101,16102,1989,16105,16135,16136,16139,16140,1343,16154,4590,16167,16170,16171,2162],{},[38,16050,16051],{},"IS-LM"," je makroekonomický model se ",[38,16054,16055],{},"dvěma neznámými",[883,16057,16059],{"className":16058},[886],[888,16060,16061],{"xmlns":890},[892,16062,16063,16067],{},[895,16064,16065],{},[898,16066,13170],{},[902,16068,13170],{"encoding":904}," — národní důchod a ",[883,16071,16073],{"className":16072},[886],[888,16074,16075],{"xmlns":890},[892,16076,16077,16081],{},[895,16078,16079],{},[898,16080,1719],{},[902,16082,1719],{"encoding":904}," — úroková míra) a ",[38,16085,16086],{},"dvěma trhy",": trhem zboží (křivka ",[38,16089,16090],{},"IS",[614,16092,16093],{},"Investment = Savings",") a trhem peněz (křivka ",[38,16096,16097],{},"LM",[614,16099,16100],{},"Liquidity of Money","). Průsečík obou křivek určuje ",[38,16103,16104],{},"simultánní rovnováhu",[883,16106,16108],{"className":16107},[886],[888,16109,16110],{"xmlns":890},[892,16111,16112,16132],{},[895,16113,16114,16116,16122,16124,16130],{},[1761,16115,1915],{"stretchy":1821},[1824,16117,16118,16120],{},[898,16119,13170],{},[898,16121,1818],{},[1761,16123,1834],{"separator":1833},[1824,16125,16126,16128],{},[898,16127,1719],{},[898,16129,1818],{},[1761,16131,1920],{"stretchy":1821},[902,16133,16134],{"encoding":904},"(Y^E, r^E)",", v níž jsou oba trhy vyvážené zároveň. Model je klíčovým nástrojem pro analýzu ",[38,16137,16138],{},"fiskální politiky"," (posun IS změnou ",[883,16141,16143],{"className":16142},[886],[888,16144,16145],{"xmlns":890},[892,16146,16147,16152],{},[895,16148,16149],{},[898,16150,16151],{},"G",[902,16153,16151],{"encoding":904},[883,16155,16157],{"className":16156},[886],[888,16158,16159],{"xmlns":890},[892,16160,16161,16165],{},[895,16162,16163],{},[898,16164,1655],{},[902,16166,1655],{"encoding":904},[38,16168,16169],{},"monetární politiky"," (posun LM změnou nabídky peněz ",[883,16172,16174],{"className":16173},[886],[888,16175,16176],{"xmlns":890},[892,16177,16178,16186],{},[895,16179,16180],{},[1824,16181,16182,16184],{},[898,16183,6889],{},[1761,16185,8408],{},[902,16187,16188],{"encoding":904},"M^*",[724,16190,16191],{},[3991,16192],{"alt":16193,"className":16194,"src":16195},"imek-is-lm-model",[210,3995],"\u002Fwiki-assets\u002Fimek-is-lm-model.jpeg",[115,16197,16199],{"id":16198},"motivace-proč-přejít-od-c-i-g-x-k-is-lm","Motivace — proč přejít od C-I-G-X k IS-LM",[724,16201,16202,16203,16207,16208,3927,16211,16234,16235,16238,16239,16255,16256,16269],{},"V modelech ",[207,16204,16206],{"className":16205,"dataFsResolvedFilePath":934,"href":935},[210],"C-I, C-I-G a C-I-G-X"," byly ",[38,16209,16210],{},"investice pokládány za konstantní",[883,16212,16214],{"className":16213},[886],[888,16215,16216],{"xmlns":890},[892,16217,16218,16231],{},[895,16219,16220,16223,16225],{},[898,16221,16222],{},"I",[1761,16224,1909],{},[1824,16226,16227,16229],{},[898,16228,16222],{},[1761,16230,8408],{},[902,16232,16233],{"encoding":904},"I = I^*","). To není realistické — investice firem závisejí na ",[38,16236,16237],{},"ceně peněz",", tedy na ",[38,16240,16241,16242],{},"úrokové míře ",[883,16243,16245],{"className":16244},[886],[888,16246,16247],{"xmlns":890},[892,16248,16249,16253],{},[895,16250,16251],{},[898,16252,1719],{},[902,16254,1719],{"encoding":904},": čím vyšší ",[883,16257,16259],{"className":16258},[886],[888,16260,16261],{"xmlns":890},[892,16262,16263,16267],{},[895,16264,16265],{},[898,16266,1719],{},[902,16268,1719],{"encoding":904},", tím dražší úvěr a tím méně investic. IS-LM analýza proto zavádí:",[120,16271,16272,16302],{},[123,16273,16274,1989,16277,16301],{},[38,16275,16276],{},"funkci investic",[883,16278,16280],{"className":16279},[886],[888,16281,16282],{"xmlns":890},[892,16283,16284,16298],{},[895,16285,16286,16288,16290,16292,16294,16296],{},[898,16287,16222],{},[1761,16289,1909],{},[898,16291,16222],{},[1761,16293,1915],{"stretchy":1821},[898,16295,1719],{},[1761,16297,1920],{"stretchy":1821},[902,16299,16300],{"encoding":904},"I = I(r)"," jako klesající funkci úrokové míry,",[123,16303,16304,16307],{},[38,16305,16306],{},"trh peněz",", jehož rovnováha (poptávka = nabídka peněz) doplňuje druhou rovnici potřebnou pro určení obou neznámých.",[1636,16309,16310],{},[724,16311,16312,16314,16315,16334,16335,16362,16363,16376,16377,16406,16407,16410],{},[883,16313,4723],{}," Pozor — dvě neznámé vyžadují dvě rovnice\nV modelech ",[883,16316,16318],{"className":16317},[886],[888,16319,16320],{"xmlns":890},[892,16321,16322,16331],{},[895,16323,16324,16326,16329],{},[898,16325,6849],{},[2761,16327,16328],{},"-",[898,16330,16222],{},[902,16332,16333],{"encoding":904},"C\\text{-}I"," až ",[883,16336,16338],{"className":16337},[886],[888,16339,16340],{"xmlns":890},[892,16341,16342,16359],{},[895,16343,16344,16346,16348,16350,16352,16354,16356],{},[898,16345,6849],{},[2761,16347,16328],{},[898,16349,16222],{},[2761,16351,16328],{},[898,16353,16151],{},[2761,16355,16328],{},[898,16357,16358],{},"X",[902,16360,16361],{"encoding":904},"C\\text{-}I\\text{-}G\\text{-}X"," byla hlavní neznámou jen ",[883,16364,16366],{"className":16365},[886],[888,16367,16368],{"xmlns":890},[892,16369,16370,16374],{},[895,16371,16372],{},[898,16373,13170],{},[902,16375,13170],{"encoding":904},". V IS-LM jsou ",[38,16378,16379,16380,2068,16393],{},"dvě neznámé ",[883,16381,16383],{"className":16382},[886],[888,16384,16385],{"xmlns":890},[892,16386,16387,16391],{},[895,16388,16389],{},[898,16390,13170],{},[902,16392,13170],{"encoding":904},[883,16394,16396],{"className":16395},[886],[888,16397,16398],{"xmlns":890},[892,16399,16400,16404],{},[895,16401,16402],{},[898,16403,1719],{},[902,16405,1719],{"encoding":904},", a proto potřebujeme ",[38,16408,16409],{},"dvě rovnice",": jednu z trhu zboží (křivka IS) a jednu z trhu peněz (křivka LM).",[115,16412,16414],{"id":16413},"funkce-investic-a-funkce-spotřeby","Funkce investic a funkce spotřeby",[724,16416,16417,16418,16431,16432,2506],{},"Lineární závislost investic ",[883,16419,16421],{"className":16420},[886],[888,16422,16423],{"xmlns":890},[892,16424,16425,16429],{},[895,16426,16427],{},[898,16428,16222],{},[902,16430,16222],{"encoding":904}," na úrokové míře ",[883,16433,16435],{"className":16434},[886],[888,16436,16437],{"xmlns":890},[892,16438,16439,16443],{},[895,16440,16441],{},[898,16442,1719],{},[902,16444,1719],{"encoding":904},[724,16446,16447],{},[883,16448,16450],{"className":16449},[886],[888,16451,16452],{"xmlns":890},[892,16453,16454,16508],{},[895,16455,16456,16458,16460,16462,16464,16466,16468,16470,16472,16474,16476,16478,16480,16482,16484,16486,16488,16490,16492,16494,16496,16499,16501,16503,16506],{},[898,16457,16222],{},[1761,16459,1909],{},[898,16461,16222],{},[1761,16463,1915],{"stretchy":1821},[898,16465,1719],{},[1761,16467,1920],{"stretchy":1821},[1761,16469,1909],{},[898,16471,2774],{},[898,16473,1719],{},[1761,16475,1964],{},[898,16477,4346],{},[1761,16479,1834],{"separator":1833},[3315,16481],{"width":3317},[898,16483,2774],{},[1761,16485,2058],{},[1765,16487,1767],{},[1761,16489,1834],{"separator":1833},[2761,16491,2763],{},[898,16493,4346],{},[1761,16495,1763],{},[1765,16497,16498],{},"0.",[3315,16500],{"width":3317},[1761,16502,1915],{"stretchy":1821},[1765,16504,16505],{},"7.11",[1761,16507,1920],{"stretchy":1821},[902,16509,16510],{"encoding":904},"I = I(r) = cr + d, \\qquad c \u003C 0,\\ d > 0. \\qquad (7.11)",[120,16512,16513,16534],{},[123,16514,16515,16533],{},[883,16516,16518],{"className":16517},[886],[888,16519,16520],{"xmlns":890},[892,16521,16522,16530],{},[895,16523,16524,16526,16528],{},[898,16525,4346],{},[1761,16527,1763],{},[1765,16529,1767],{},[902,16531,16532],{"encoding":904},"d > 0"," zřejmé,",[123,16535,16536,16554,16555,1741],{},[883,16537,16539],{"className":16538},[886],[888,16540,16541],{"xmlns":890},[892,16542,16543,16551],{},[895,16544,16545,16547,16549],{},[898,16546,2774],{},[1761,16548,2058],{},[1765,16550,1767],{},[902,16552,16553],{"encoding":904},"c \u003C 0",", protože růst úrokové míry tlumí investice — funkce investic je ",[38,16556,16557],{},"klesající",[724,16559,16560],{},"Spotřeba zůstává lineární funkcí důchodu:",[724,16562,16563],{},[883,16564,16566],{"className":16565},[886],[888,16567,16568],{"xmlns":890},[892,16569,16570,16627],{},[895,16571,16572,16574,16576,16578,16580,16582,16584,16586,16588,16590,16592,16594,16596,16598,16600,16602,16604,16606,16608,16610,16612,16614,16616,16618,16620,16622,16625],{},[898,16573,6849],{},[1761,16575,1909],{},[898,16577,6849],{},[1761,16579,1915],{"stretchy":1821},[898,16581,13170],{},[1761,16583,1920],{"stretchy":1821},[1761,16585,1909],{},[898,16587,207],{},[898,16589,13170],{},[1761,16591,1964],{},[898,16593,4302],{},[1761,16595,1834],{"separator":1833},[3315,16597],{"width":3317},[1765,16599,1767],{},[1761,16601,2058],{},[898,16603,207],{},[1761,16605,2058],{},[1765,16607,1945],{},[1761,16609,1834],{"separator":1833},[2761,16611,2763],{},[898,16613,4302],{},[1761,16615,1763],{},[1765,16617,16498],{},[3315,16619],{"width":3317},[1761,16621,1915],{"stretchy":1821},[1765,16623,16624],{},"7.12",[1761,16626,1920],{"stretchy":1821},[902,16628,16629],{"encoding":904},"C = C(Y) = aY + b, \\qquad 0 \u003C a \u003C 1,\\ b > 0. \\qquad (7.12)",[724,16631,16632],{},"Podmínka rovnováhy na trhu zboží:",[724,16634,16635],{},[883,16636,16638],{"className":16637},[886],[888,16639,16640],{"xmlns":890},[892,16641,16642,16665],{},[895,16643,16644,16646,16648,16650,16652,16654,16656,16658,16660,16663],{},[898,16645,13170],{},[1761,16647,1909],{},[898,16649,6849],{},[1761,16651,1964],{},[898,16653,16222],{},[898,16655,1741],{"mathvariant":1969},[3315,16657],{"width":3317},[1761,16659,1915],{"stretchy":1821},[1765,16661,16662],{},"7.13",[1761,16664,1920],{"stretchy":1821},[902,16666,16667],{"encoding":904},"Y = C + I. \\qquad (7.13)",[724,16669,16670,16671,1989,16674,16700,16701,1741],{},"To dává ",[38,16672,16673],{},"tři rovnice o čtyřech neznámých",[883,16675,16677],{"className":16676},[886],[888,16678,16679],{"xmlns":890},[892,16680,16681,16697],{},[895,16682,16683,16685,16687,16689,16691,16693,16695],{},[898,16684,13170],{},[1761,16686,1834],{"separator":1833},[898,16688,6849],{},[1761,16690,1834],{"separator":1833},[898,16692,16222],{},[1761,16694,1834],{"separator":1833},[898,16696,1719],{},[902,16698,16699],{"encoding":904},"Y, C, I, r",". Pro jednoznačné určení rovnováhy potřebujeme čtvrtou rovnici — odvodí se z ",[38,16702,16703],{},"rovnováhy na trhu peněz",[115,16705,16707],{"id":16706},"křivka-is-rovnováha-na-trhu-zboží","Křivka IS — rovnováha na trhu zboží",[724,16709,16710,16711,2382,16733,16751,16752,16755],{},"Podmínka (7.13) reprezentuje rovnováhu na trhu zboží, protože s ohledem na ",[883,16712,16714],{"className":16713},[886],[888,16715,16716],{"xmlns":890},[892,16717,16718,16730],{},[895,16719,16720,16722,16724,16726,16728],{},[898,16721,13170],{},[1761,16723,1909],{},[898,16725,6849],{},[1761,16727,1964],{},[898,16729,1912],{},[902,16731,16732],{"encoding":904},"Y = C + S",[883,16734,16736],{"className":16735},[886],[888,16737,16738],{"xmlns":890},[892,16739,16740,16748],{},[895,16741,16742,16744,16746],{},[898,16743,16222],{},[1761,16745,1909],{},[898,16747,1912],{},[902,16749,16750],{"encoding":904},"I = S"," (plánované ",[38,16753,16754],{},"investice = úspory","). Dosazením (7.11) a (7.12) do (7.13):",[724,16757,16758],{},[3991,16759],{"alt":16760,"className":16761,"src":16762},"imek-odvozeni-is-4panelu",[210,3995],"\u002Fwiki-assets\u002Fimek-odvozeni-is-4panelu.jpeg",[724,16764,16765],{},[883,16766,16768],{"className":16767},[886],[888,16769,16770],{"xmlns":890},[892,16771,16772,16806],{},[895,16773,16774,16776,16778,16780,16782,16784,16786,16788,16790,16792,16794,16796,16798,16800,16802,16804],{},[898,16775,13170],{},[1761,16777,1909],{},[1761,16779,1915],{"stretchy":1821},[898,16781,207],{},[898,16783,13170],{},[1761,16785,1964],{},[898,16787,4302],{},[1761,16789,1920],{"stretchy":1821},[1761,16791,1964],{},[1761,16793,1915],{"stretchy":1821},[898,16795,2774],{},[898,16797,1719],{},[1761,16799,1964],{},[898,16801,4346],{},[1761,16803,1920],{"stretchy":1821},[1761,16805,1834],{"separator":1833},[902,16807,16808],{"encoding":904},"Y = (aY + b) + (cr + d),",[724,16810,16811],{},[883,16812,16814],{"className":16813},[886],[888,16815,16816],{"xmlns":890},[892,16817,16818,16852],{},[895,16819,16820,16822,16824,16826,16828,16830,16832,16834,16836,16838,16840,16842,16844,16846,16848,16850],{},[1761,16821,1915],{"stretchy":1821},[1765,16823,1945],{},[1761,16825,1885],{},[898,16827,207],{},[1761,16829,1920],{"stretchy":1821},[898,16831,13170],{},[1761,16833,1885],{},[898,16835,2774],{},[898,16837,1719],{},[1761,16839,1885],{},[898,16841,4302],{},[1761,16843,1885],{},[898,16845,4346],{},[1761,16847,1909],{},[1765,16849,1767],{},[1761,16851,1834],{"separator":1833},[902,16853,16854],{"encoding":904},"(1 - a)Y - cr - b - d = 0,",[724,16856,16857],{},"odkud",[724,16859,16860],{},[883,16861,16863],{"className":16862},[886],[888,16864,16865],{"xmlns":890},[892,16866,16867,16934],{},[895,16868,16869,16925,16927,16929,16932],{},[16870,16871,16873],"menclose",{"notation":16872},"box",[6411,16874,16875],{"scriptlevel":1767,"displaystyle":1821},[6411,16876,16877],{"scriptlevel":1767,"displaystyle":1821},[6411,16878,16879],{"scriptlevel":1767,"displaystyle":1833},[895,16880,16881,16883,16885,16887,16899,16901,16903,16905,16923],{},[2761,16882,7057],{},[898,16884,13170],{},[1761,16886,1909],{},[4379,16888,16889,16891],{},[898,16890,2774],{},[895,16892,16893,16895,16897],{},[1765,16894,1945],{},[1761,16896,1885],{},[898,16898,207],{},[2761,16900,7057],{},[898,16902,1719],{},[1761,16904,1964],{},[4379,16906,16907,16915],{},[895,16908,16909,16911,16913],{},[898,16910,4302],{},[1761,16912,1964],{},[898,16914,4346],{},[895,16916,16917,16919,16921],{},[1765,16918,1945],{},[1761,16920,1885],{},[898,16922,207],{},[2761,16924,7057],{},[3315,16926],{"width":3317},[1761,16928,1915],{"stretchy":1821},[1765,16930,16931],{},"7.14",[1761,16933,1920],{"stretchy":1821},[902,16935,16936],{"encoding":904},"\\boxed{\\,Y = \\frac{c}{1 - a}\\,r + \\frac{b + d}{1 - a}\\,} \\qquad (7.14)",[724,16938,16939,16940,3927,16943,16946,16947,16950,16951,16953,16954,16976,16977,17005,17006,17027,17028,17030,17031,17033],{},"Tento vztah se nazývá ",[38,16941,16942],{},"funkce IS",[614,16944,16945],{},"IS schedule",") a její graf ",[38,16948,16949],{},"křivka IS",". Křivka je ",[38,16952,16557],{}," přímka v rovině ",[883,16955,16957],{"className":16956},[886],[888,16958,16959],{"xmlns":890},[892,16960,16961,16973],{},[895,16962,16963,16965,16967,16969,16971],{},[1761,16964,1915],{"stretchy":1821},[898,16966,1719],{},[1761,16968,1834],{"separator":1833},[898,16970,13170],{},[1761,16972,1920],{"stretchy":1821},[902,16974,16975],{"encoding":904},"(r, Y)",", neboť ",[883,16978,16980],{"className":16979},[886],[888,16981,16982],{"xmlns":890},[892,16983,16984,17002],{},[895,16985,16986,16998,17000],{},[4379,16987,16988,16990],{},[898,16989,2774],{},[895,16991,16992,16994,16996],{},[1765,16993,1945],{},[1761,16995,1885],{},[898,16997,207],{},[1761,16999,2058],{},[1765,17001,1767],{},[902,17003,17004],{"encoding":904},"\\frac{c}{1-a} \u003C 0"," (čitatel záporný, jmenovatel kladný). Název vyjadřuje, že křivka popisuje ty kombinace ",[883,17007,17009],{"className":17008},[886],[888,17010,17011],{"xmlns":890},[892,17012,17013,17025],{},[895,17014,17015,17017,17019,17021,17023],{},[1761,17016,1915],{"stretchy":1821},[898,17018,1719],{},[1761,17020,1834],{"separator":1833},[898,17022,13170],{},[1761,17024,1920],{"stretchy":1821},[902,17026,16975],{"encoding":904},", pro které plánované ",[38,17029,16222],{},"nvestment = ",[38,17032,1912],{},"avings.",[1636,17035,17036],{},[724,17037,17038,17040,17041,17054,17055,1989,17058,17071,17072,17085,17086,2068,17099,17112,17113,17116],{},[883,17039,1642],{}," Intuice — proč IS klesá\nNižší úroková míra ",[883,17042,17044],{"className":17043},[886],[888,17045,17046],{"xmlns":890},[892,17047,17048,17052],{},[895,17049,17050],{},[898,17051,1719],{},[902,17053,1719],{"encoding":904}," → levnější úvěr → ",[38,17056,17057],{},"více investic",[883,17059,17061],{"className":17060},[886],[888,17062,17063],{"xmlns":890},[892,17064,17065,17069],{},[895,17066,17067],{},[898,17068,16222],{},[902,17070,16222],{"encoding":904}," → vyšší agregátní poptávka → vyšší rovnovážný důchod ",[883,17073,17075],{"className":17074},[886],[888,17076,17077],{"xmlns":890},[892,17078,17079,17083],{},[895,17080,17081],{},[898,17082,13170],{},[902,17084,13170],{"encoding":904},". Vztah mezi ",[883,17087,17089],{"className":17088},[886],[888,17090,17091],{"xmlns":890},[892,17092,17093,17097],{},[895,17094,17095],{},[898,17096,1719],{},[902,17098,1719],{"encoding":904},[883,17100,17102],{"className":17101},[886],[888,17103,17104],{"xmlns":890},[892,17105,17106,17110],{},[895,17107,17108],{},[898,17109,13170],{},[902,17111,13170],{"encoding":904}," na trhu zboží je proto ",[38,17114,17115],{},"nepřímý"," (klesající křivka).",[115,17118,17120],{"id":17119},"křivka-lm-rovnováha-na-trhu-peněz","Křivka LM — rovnováha na trhu peněz",[724,17122,17123,17124,17142,17143,6997,17161,17164],{},"Rovnováha na trhu peněz: poptávka po penězích ",[883,17125,17127],{"className":17126},[886],[888,17128,17129],{"xmlns":890},[892,17130,17131,17139],{},[895,17132,17133],{},[1824,17134,17135,17137],{},[898,17136,6889],{},[898,17138,2244],{},[902,17140,17141],{"encoding":904},"M^D"," se rovná nabídce peněz ",[883,17144,17146],{"className":17145},[886],[888,17147,17148],{"xmlns":890},[892,17149,17150,17158],{},[895,17151,17152],{},[1824,17153,17154,17156],{},[898,17155,6889],{},[898,17157,1912],{},[902,17159,17160],{"encoding":904},"M^S",[38,17162,17163],{},"Nabídka"," je pod kontrolou národní banky a je pevně zadána:",[724,17166,17167],{},[883,17168,17170],{"className":17169},[886],[888,17171,17172],{"xmlns":890},[892,17173,17174,17192],{},[895,17175,17176,17182,17184,17190],{},[1824,17177,17178,17180],{},[898,17179,6889],{},[898,17181,1912],{},[1761,17183,1909],{},[1824,17185,17186,17188],{},[898,17187,6889],{},[1761,17189,8408],{},[898,17191,1741],{"mathvariant":1969},[902,17193,17194],{"encoding":904},"M^S = M^*.",[724,17196,17197,17200],{},[38,17198,17199],{},"Poptávka"," po penězích má tři zdroje:",[120,17202,17203,17212,17221],{},[123,17204,17205,3927,17208,17211],{},[38,17206,17207],{},"transakční poptávka",[614,17209,17210],{},"transactions demand",") — peníze pro nákup zboží,",[123,17213,17214,3927,17217,17220],{},[38,17215,17216],{},"opatrnostní poptávka",[614,17218,17219],{},"precautionary demand",") — peníze pro nenadálé výdaje,",[123,17222,17223,3927,17226,17229],{},[38,17224,17225],{},"spekulační poptávka",[614,17227,17228],{},"speculative demand",") — peníze pro zhodnocení (akcie, obligace).",[724,17231,17232,17233,17251],{},"Součet transakční a opatrnostní poptávky ",[883,17234,17236],{"className":17235},[886],[888,17237,17238],{"xmlns":890},[892,17239,17240,17248],{},[895,17241,17242],{},[1681,17243,17244,17246],{},[898,17245,13835],{},[1765,17247,1945],{},[902,17249,17250],{"encoding":904},"L_1"," je úměrný důchodu:",[724,17253,17254],{},[883,17255,17257],{"className":17256},[886],[888,17258,17259],{"xmlns":890},[892,17260,17261,17299],{},[895,17262,17263,17269,17271,17278,17280,17282,17284,17286,17288,17294,17296],{},[1681,17264,17265,17267],{},[898,17266,13835],{},[1765,17268,1945],{},[1761,17270,1909],{},[1681,17272,17273,17276],{},[898,17274,17275],{},"k",[1765,17277,1945],{},[898,17279,13170],{},[1761,17281,1834],{"separator":1833},[3315,17283],{"width":3317},[1765,17285,1767],{},[1761,17287,2058],{},[1681,17289,17290,17292],{},[898,17291,17275],{},[1765,17293,1945],{},[1761,17295,2058],{},[1765,17297,17298],{},"1.",[902,17300,17301],{"encoding":904},"L_1 = k_1 Y, \\qquad 0 \u003C k_1 \u003C 1.",[724,17303,17304,17305,17323,17324,1343,17337,17354],{},"Spekulační poptávka ",[883,17306,17308],{"className":17307},[886],[888,17309,17310],{"xmlns":890},[892,17311,17312,17320],{},[895,17313,17314],{},[1681,17315,17316,17318],{},[898,17317,13835],{},[1765,17319,2296],{},[902,17321,17322],{"encoding":904},"L_2"," závisí na úrokové míře (roste-li ",[883,17325,17327],{"className":17326},[886],[888,17328,17329],{"xmlns":890},[892,17330,17331,17335],{},[895,17332,17333],{},[898,17334,1719],{},[902,17336,1719],{"encoding":904},[883,17338,17340],{"className":17339},[886],[888,17341,17342],{"xmlns":890},[892,17343,17344,17352],{},[895,17345,17346],{},[1681,17347,17348,17350],{},[898,17349,13835],{},[1765,17351,2296],{},[902,17353,17322],{"encoding":904}," klesá, protože vyšší výnos obligací snižuje atraktivitu držby peněz):",[724,17356,17357],{},[883,17358,17360],{"className":17359},[886],[888,17361,17362],{"xmlns":890},[892,17363,17364,17418],{},[895,17365,17366,17372,17374,17380,17382,17384,17390,17392,17394,17400,17402,17404,17406,17408,17414,17416],{},[1681,17367,17368,17370],{},[898,17369,13835],{},[1765,17371,2296],{},[1761,17373,1909],{},[1681,17375,17376,17378],{},[898,17377,17275],{},[1765,17379,2296],{},[898,17381,1719],{},[1761,17383,1964],{},[1681,17385,17386,17388],{},[898,17387,17275],{},[1765,17389,5486],{},[1761,17391,1834],{"separator":1833},[3315,17393],{"width":3317},[1681,17395,17396,17398],{},[898,17397,17275],{},[1765,17399,2296],{},[1761,17401,2058],{},[1765,17403,1767],{},[1761,17405,1834],{"separator":1833},[2761,17407,2763],{},[1681,17409,17410,17412],{},[898,17411,17275],{},[1765,17413,5486],{},[1761,17415,1763],{},[1765,17417,16498],{},[902,17419,17420],{"encoding":904},"L_2 = k_2 r + k_3, \\qquad k_2 \u003C 0,\\ k_3 > 0.",[724,17422,17423],{},"Celková poptávka po penězích:",[724,17425,17426],{},[883,17427,17429],{"className":17428},[886],[888,17430,17431],{"xmlns":890},[892,17432,17433,17487],{},[895,17434,17435,17441,17443,17449,17451,17457,17459,17465,17467,17469,17475,17477,17479,17485],{},[1824,17436,17437,17439],{},[898,17438,6889],{},[898,17440,2244],{},[1761,17442,1909],{},[1681,17444,17445,17447],{},[898,17446,13835],{},[1765,17448,1945],{},[1761,17450,1964],{},[1681,17452,17453,17455],{},[898,17454,13835],{},[1765,17456,2296],{},[1761,17458,1909],{},[1681,17460,17461,17463],{},[898,17462,17275],{},[1765,17464,1945],{},[898,17466,13170],{},[1761,17468,1964],{},[1681,17470,17471,17473],{},[898,17472,17275],{},[1765,17474,2296],{},[898,17476,1719],{},[1761,17478,1964],{},[1681,17480,17481,17483],{},[898,17482,17275],{},[1765,17484,5486],{},[898,17486,1741],{"mathvariant":1969},[902,17488,17489],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3.",[724,17491,17492,17493,2506],{},"Podmínka rovnováhy na trhu peněz ",[883,17494,17496],{"className":17495},[886],[888,17497,17498],{"xmlns":890},[892,17499,17500,17516],{},[895,17501,17502,17508,17510],{},[1824,17503,17504,17506],{},[898,17505,6889],{},[898,17507,2244],{},[1761,17509,1909],{},[1824,17511,17512,17514],{},[898,17513,6889],{},[1761,17515,8408],{},[902,17517,17518],{"encoding":904},"M^D = M^*",[724,17520,17521],{},[883,17522,17524],{"className":17523},[886],[888,17525,17526],{"xmlns":890},[892,17527,17528,17575],{},[895,17529,17530,17536,17538,17544,17546,17548,17554,17556,17558,17564,17566,17568,17570,17573],{},[1824,17531,17532,17534],{},[898,17533,6889],{},[1761,17535,8408],{},[1761,17537,1909],{},[1681,17539,17540,17542],{},[898,17541,17275],{},[1765,17543,1945],{},[898,17545,13170],{},[1761,17547,1964],{},[1681,17549,17550,17552],{},[898,17551,17275],{},[1765,17553,2296],{},[898,17555,1719],{},[1761,17557,1964],{},[1681,17559,17560,17562],{},[898,17561,17275],{},[1765,17563,5486],{},[1761,17565,1834],{"separator":1833},[3315,17567],{"width":3317},[1761,17569,1915],{"stretchy":1821},[1765,17571,17572],{},"7.15",[1761,17574,1920],{"stretchy":1821},[902,17576,17577],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3, \\qquad (7.15)",[724,17579,17580,17581,5372],{},"po úpravě (vyjádření ",[883,17582,17584],{"className":17583},[886],[888,17585,17586],{"xmlns":890},[892,17587,17588,17592],{},[895,17589,17590],{},[898,17591,13170],{},[902,17593,13170],{"encoding":904},[724,17595,17596],{},[883,17597,17599],{"className":17598},[886],[888,17600,17601],{"xmlns":890},[892,17602,17603,17678],{},[895,17604,17605,17669,17671,17673,17676],{},[16870,17606,17607],{"notation":16872},[6411,17608,17609],{"scriptlevel":1767,"displaystyle":1821},[6411,17610,17611],{"scriptlevel":1767,"displaystyle":1821},[6411,17612,17613],{"scriptlevel":1767,"displaystyle":1833},[895,17614,17615,17617,17619,17621,17623,17637,17639,17641,17643,17667],{},[2761,17616,7057],{},[898,17618,13170],{},[1761,17620,1909],{},[1761,17622,1885],{},[4379,17624,17625,17631],{},[1681,17626,17627,17629],{},[898,17628,17275],{},[1765,17630,2296],{},[1681,17632,17633,17635],{},[898,17634,17275],{},[1765,17636,1945],{},[2761,17638,7057],{},[898,17640,1719],{},[1761,17642,1964],{},[4379,17644,17645,17661],{},[895,17646,17647,17653,17655],{},[1824,17648,17649,17651],{},[898,17650,6889],{},[1761,17652,8408],{},[1761,17654,1885],{},[1681,17656,17657,17659],{},[898,17658,17275],{},[1765,17660,5486],{},[1681,17662,17663,17665],{},[898,17664,17275],{},[1765,17666,1945],{},[2761,17668,7057],{},[3315,17670],{"width":3317},[1761,17672,1915],{"stretchy":1821},[1765,17674,17675],{},"7.16",[1761,17677,1920],{"stretchy":1821},[902,17679,17680],{"encoding":904},"\\boxed{\\,Y = -\\frac{k_2}{k_1}\\,r + \\frac{M^* - k_3}{k_1}\\,} \\qquad (7.16)",[724,17682,16939,17683,3927,17686,17689,17690,16950,17693,16953,17696,16976,17717,17749,17750,17772,17773,17775,17776,17778],{},[38,17684,17685],{},"funkce LM",[614,17687,17688],{},"LM schedule","), její graf ",[38,17691,17692],{},"křivka LM",[38,17694,17695],{},"rostoucí",[883,17697,17699],{"className":17698},[886],[888,17700,17701],{"xmlns":890},[892,17702,17703,17715],{},[895,17704,17705,17707,17709,17711,17713],{},[1761,17706,1915],{"stretchy":1821},[898,17708,1719],{},[1761,17710,1834],{"separator":1833},[898,17712,13170],{},[1761,17714,1920],{"stretchy":1821},[902,17716,16975],{"encoding":904},[883,17718,17720],{"className":17719},[886],[888,17721,17722],{"xmlns":890},[892,17723,17724,17746],{},[895,17725,17726,17728,17742,17744],{},[1761,17727,1885],{},[4379,17729,17730,17736],{},[1681,17731,17732,17734],{},[898,17733,17275],{},[1765,17735,2296],{},[1681,17737,17738,17740],{},[898,17739,17275],{},[1765,17741,1945],{},[1761,17743,1763],{},[1765,17745,1767],{},[902,17747,17748],{"encoding":904},"-\\frac{k_2}{k_1} > 0"," (čitatel kladný, protože ",[883,17751,17753],{"className":17752},[886],[888,17754,17755],{"xmlns":890},[892,17756,17757,17769],{},[895,17758,17759,17765,17767],{},[1681,17760,17761,17763],{},[898,17762,17275],{},[1765,17764,2296],{},[1761,17766,2058],{},[1765,17768,1767],{},[902,17770,17771],{"encoding":904},"k_2 \u003C 0",", jmenovatel kladný). Název: ",[38,17774,13835],{},"iquidity of ",[38,17777,6889],{},"oney.",[1636,17780,17781],{},[724,17782,17783,17785,17786,17799,17800,17828,17829,17846,17847,17860,17861,17878,17879,2068,17892,17905,17906,17909],{},[883,17784,1642],{}," Intuice — proč LM roste\nVyšší důchod ",[883,17787,17789],{"className":17788},[886],[888,17790,17791],{"xmlns":890},[892,17792,17793,17797],{},[895,17794,17795],{},[898,17796,13170],{},[902,17798,13170],{"encoding":904}," → větší transakční poptávka po penězích ",[883,17801,17803],{"className":17802},[886],[888,17804,17805],{"xmlns":890},[892,17806,17807,17825],{},[895,17808,17809,17815,17817,17823],{},[1681,17810,17811,17813],{},[898,17812,13835],{},[1765,17814,1945],{},[1761,17816,1909],{},[1681,17818,17819,17821],{},[898,17820,17275],{},[1765,17822,1945],{},[898,17824,13170],{},[902,17826,17827],{"encoding":904},"L_1 = k_1 Y"," → při pevné nabídce ",[883,17830,17832],{"className":17831},[886],[888,17833,17834],{"xmlns":890},[892,17835,17836,17844],{},[895,17837,17838],{},[1824,17839,17840,17842],{},[898,17841,6889],{},[1761,17843,8408],{},[902,17845,16188],{"encoding":904}," vzniká na trhu peněz přebytek poptávky → úroková míra ",[883,17848,17850],{"className":17849},[886],[888,17851,17852],{"xmlns":890},[892,17853,17854,17858],{},[895,17855,17856],{},[898,17857,1719],{},[902,17859,1719],{"encoding":904}," musí vzrůst, aby se spekulační poptávka ",[883,17862,17864],{"className":17863},[886],[888,17865,17866],{"xmlns":890},[892,17867,17868,17876],{},[895,17869,17870],{},[1681,17871,17872,17874],{},[898,17873,13835],{},[1765,17875,2296],{},[902,17877,17322],{"encoding":904}," stlačila a trh se vyrovnal. Vztah mezi ",[883,17880,17882],{"className":17881},[886],[888,17883,17884],{"xmlns":890},[892,17885,17886,17890],{},[895,17887,17888],{},[898,17889,13170],{},[902,17891,13170],{"encoding":904},[883,17893,17895],{"className":17894},[886],[888,17896,17897],{"xmlns":890},[892,17898,17899,17903],{},[895,17900,17901],{},[898,17902,1719],{},[902,17904,1719],{"encoding":904}," na trhu peněz je proto ",[38,17907,17908],{},"přímý"," (rostoucí křivka).",[115,17911,17913],{"id":17912},"simultánní-rovnováha-is-lm","Simultánní rovnováha IS-LM",[724,17915,17916,17917,17920,17921,1989,17924,2068,17942,1989,17945,17963,17964,17982,17983,18001,18002,18018,18019,2068,18034,18049,18050,1741],{},"Řešením ",[38,17918,17919],{},"soustavy dvou lineárních rovnic"," (7.14) a (7.15) určíme ",[38,17922,17923],{},"rovnovážný důchod",[883,17925,17927],{"className":17926},[886],[888,17928,17929],{"xmlns":890},[892,17930,17931,17939],{},[895,17932,17933],{},[1824,17934,17935,17937],{},[898,17936,13170],{},[898,17938,1818],{},[902,17940,17941],{"encoding":904},"Y^E",[38,17943,17944],{},"rovnovážnou úrokovou míru",[883,17946,17948],{"className":17947},[886],[888,17949,17950],{"xmlns":890},[892,17951,17952,17960],{},[895,17953,17954],{},[1824,17955,17956,17958],{},[898,17957,1719],{},[898,17959,1818],{},[902,17961,17962],{"encoding":904},"r^E","; zpětným dosazením do (7.11) a (7.12) pak rovnovážné investice ",[883,17965,17967],{"className":17966},[886],[888,17968,17969],{"xmlns":890},[892,17970,17971,17979],{},[895,17972,17973],{},[1824,17974,17975,17977],{},[898,17976,16222],{},[898,17978,1818],{},[902,17980,17981],{"encoding":904},"I^E"," a rovnovážnou spotřebu ",[883,17984,17986],{"className":17985},[886],[888,17987,17988],{"xmlns":890},[892,17989,17990,17998],{},[895,17991,17992],{},[1824,17993,17994,17996],{},[898,17995,6849],{},[898,17997,1818],{},[902,17999,18000],{"encoding":904},"C^E",". Graficky jde o ",[38,18003,18004,18005],{},"průsečík ",[883,18006,18008],{"className":18007},[886],[888,18009,18010],{"xmlns":890},[892,18011,18012,18016],{},[895,18013,18014],{},[898,18015,1818],{},[902,18017,1818],{"encoding":904}," křivek ",[883,18020,18022],{"className":18021},[886],[888,18023,18024],{"xmlns":890},[892,18025,18026,18032],{},[895,18027,18028,18030],{},[898,18029,16222],{},[898,18031,1912],{},[902,18033,16090],{"encoding":904},[883,18035,18037],{"className":18036},[886],[888,18038,18039],{"xmlns":890},[892,18040,18041,18047],{},[895,18042,18043,18045],{},[898,18044,13835],{},[898,18046,6889],{},[902,18048,16097],{"encoding":904}," v rovině ",[883,18051,18053],{"className":18052},[886],[888,18054,18055],{"xmlns":890},[892,18056,18057,18069],{},[895,18058,18059,18061,18063,18065,18067],{},[1761,18060,1915],{"stretchy":1821},[898,18062,1719],{},[1761,18064,1834],{"separator":1833},[898,18066,13170],{},[1761,18068,1920],{"stretchy":1821},[902,18070,16975],{"encoding":904},[724,18072,18073],{},[614,18074,18075,18076,18097,18098,18113,18114,18129,18130,18143,18144,18161,18162,4590,18175,18161,18192,18205,18206,18219],{},"Obrázek 7.6 — Schematický graf v rovině ",[883,18077,18079],{"className":18078},[886],[888,18080,18081],{"xmlns":890},[892,18082,18083,18095],{},[895,18084,18085,18087,18089,18091,18093],{},[1761,18086,1915],{"stretchy":1821},[898,18088,1719],{},[1761,18090,1834],{"separator":1833},[898,18092,13170],{},[1761,18094,1920],{"stretchy":1821},[902,18096,16975],{"encoding":904},". Rostoucí přímka ",[883,18099,18101],{"className":18100},[886],[888,18102,18103],{"xmlns":890},[892,18104,18105,18111],{},[895,18106,18107,18109],{},[898,18108,13835],{},[898,18110,6889],{},[902,18112,16097],{"encoding":904}," a klesající přímka ",[883,18115,18117],{"className":18116},[886],[888,18118,18119],{"xmlns":890},[892,18120,18121,18127],{},[895,18122,18123,18125],{},[898,18124,16222],{},[898,18126,1912],{},[902,18128,16090],{"encoding":904}," se protínají v bodě ",[883,18131,18133],{"className":18132},[886],[888,18134,18135],{"xmlns":890},[892,18136,18137,18141],{},[895,18138,18139],{},[898,18140,1818],{},[902,18142,1818],{"encoding":904}," se souřadnicemi ",[883,18145,18147],{"className":18146},[886],[888,18148,18149],{"xmlns":890},[892,18150,18151,18159],{},[895,18152,18153],{},[1824,18154,18155,18157],{},[898,18156,1719],{},[898,18158,1818],{},[902,18160,17962],{"encoding":904}," (na ose ",[883,18163,18165],{"className":18164},[886],[888,18166,18167],{"xmlns":890},[892,18168,18169,18173],{},[895,18170,18171],{},[898,18172,1719],{},[902,18174,1719],{"encoding":904},[883,18176,18178],{"className":18177},[886],[888,18179,18180],{"xmlns":890},[892,18181,18182,18190],{},[895,18183,18184],{},[1824,18185,18186,18188],{},[898,18187,13170],{},[898,18189,1818],{},[902,18191,17941],{"encoding":904},[883,18193,18195],{"className":18194},[886],[888,18196,18197],{"xmlns":890},[892,18198,18199,18203],{},[895,18200,18201],{},[898,18202,13170],{},[902,18204,13170],{"encoding":904},"); tečkované čáry z ",[883,18207,18209],{"className":18208},[886],[888,18210,18211],{"xmlns":890},[892,18212,18213,18217],{},[895,18214,18215],{},[898,18216,1818],{},[902,18218,1818],{"encoding":904}," kolmé k osám vyznačují polohu rovnovážné úrokové míry a rovnovážného národního důchodu.",[1636,18221,18222,18227],{},[724,18223,18224,18226],{},[883,18225,4452],{}," Postup — jak najít IS-LM rovnováhu",[152,18228,18229,18305,18373,18431,18504],{},[123,18230,18231,18234,18235,2068,18255,18275,18276,2068,18289,18302,18303,1741],{},[38,18232,18233],{},"Z trhu zboží (7.13)"," dosaď funkce ",[883,18236,18238],{"className":18237},[886],[888,18239,18240],{"xmlns":890},[892,18241,18242,18252],{},[895,18243,18244,18246,18248,18250],{},[898,18245,6849],{},[1761,18247,1915],{"stretchy":1821},[898,18249,13170],{},[1761,18251,1920],{"stretchy":1821},[902,18253,18254],{"encoding":904},"C(Y)",[883,18256,18258],{"className":18257},[886],[888,18259,18260],{"xmlns":890},[892,18261,18262,18272],{},[895,18263,18264,18266,18268,18270],{},[898,18265,16222],{},[1761,18267,1915],{"stretchy":1821},[898,18269,1719],{},[1761,18271,1920],{"stretchy":1821},[902,18273,18274],{"encoding":904},"I(r)"," a vyjádři vztah mezi ",[883,18277,18279],{"className":18278},[886],[888,18280,18281],{"xmlns":890},[892,18282,18283,18287],{},[895,18284,18285],{},[898,18286,13170],{},[902,18288,13170],{"encoding":904},[883,18290,18292],{"className":18291},[886],[888,18293,18294],{"xmlns":890},[892,18295,18296,18300],{},[895,18297,18298],{},[898,18299,1719],{},[902,18301,1719],{"encoding":904}," — dostaneš rovnici ",[38,18304,16090],{},[123,18306,18307,18310,18311,2068,18328,18345,18346,18302,18371,1741],{},[38,18308,18309],{},"Z trhu peněz (7.15)"," dosaď ",[883,18312,18314],{"className":18313},[886],[888,18315,18316],{"xmlns":890},[892,18317,18318,18326],{},[895,18319,18320],{},[1681,18321,18322,18324],{},[898,18323,13835],{},[1765,18325,1945],{},[902,18327,17250],{"encoding":904},[883,18329,18331],{"className":18330},[886],[888,18332,18333],{"xmlns":890},[892,18334,18335,18343],{},[895,18336,18337],{},[1681,18338,18339,18341],{},[898,18340,13835],{},[1765,18342,2296],{},[902,18344,17322],{"encoding":904}," a vztah ",[883,18347,18349],{"className":18348},[886],[888,18350,18351],{"xmlns":890},[892,18352,18353,18369],{},[895,18354,18355,18361,18363],{},[1824,18356,18357,18359],{},[898,18358,6889],{},[898,18360,2244],{},[1761,18362,1909],{},[1824,18364,18365,18367],{},[898,18366,6889],{},[1761,18368,8408],{},[902,18370,17518],{"encoding":904},[38,18372,16097],{},[123,18374,18375,18378,18379,2068,18392,18405,18406,18430],{},[38,18376,18377],{},"Vyřeš soustavu"," dvou lineárních rovnic o dvou neznámých ",[883,18380,18382],{"className":18381},[886],[888,18383,18384],{"xmlns":890},[892,18385,18386,18390],{},[895,18387,18388],{},[898,18389,13170],{},[902,18391,13170],{"encoding":904},[883,18393,18395],{"className":18394},[886],[888,18396,18397],{"xmlns":890},[892,18398,18399,18403],{},[895,18400,18401],{},[898,18402,1719],{},[902,18404,1719],{"encoding":904}," — nejsnáze substituční metodou (vyjádři z IS ",[883,18407,18409],{"className":18408},[886],[888,18410,18411],{"xmlns":890},[892,18412,18413,18427],{},[895,18414,18415,18417,18419,18421,18423,18425],{},[898,18416,13170],{},[1761,18418,1909],{},[898,18420,6107],{},[1761,18422,1915],{"stretchy":1821},[898,18424,1719],{},[1761,18426,1920],{"stretchy":1821},[902,18428,18429],{"encoding":904},"Y = f(r)"," a dosaď do LM).",[123,18432,18433,1989,18436,2068,18470,1741],{},[38,18434,18435],{},"Zpětně dopočítej",[883,18437,18439],{"className":18438},[886],[888,18440,18441],{"xmlns":890},[892,18442,18443,18467],{},[895,18444,18445,18451,18453,18455,18457,18463,18465],{},[1824,18446,18447,18449],{},[898,18448,6849],{},[898,18450,1818],{},[1761,18452,1909],{},[898,18454,207],{},[2761,18456,7057],{},[1824,18458,18459,18461],{},[898,18460,13170],{},[898,18462,1818],{},[1761,18464,1964],{},[898,18466,4302],{},[902,18468,18469],{"encoding":904},"C^E = a\\,Y^E + b",[883,18471,18473],{"className":18472},[886],[888,18474,18475],{"xmlns":890},[892,18476,18477,18501],{},[895,18478,18479,18485,18487,18489,18491,18497,18499],{},[1824,18480,18481,18483],{},[898,18482,16222],{},[898,18484,1818],{},[1761,18486,1909],{},[898,18488,2774],{},[2761,18490,7057],{},[1824,18492,18493,18495],{},[898,18494,1719],{},[898,18496,1818],{},[1761,18498,1964],{},[898,18500,4346],{},[902,18502,18503],{"encoding":904},"I^E = c\\,r^E + d",[123,18505,18506,18509,18510,18544,18545,18599],{},[38,18507,18508],{},"Ověř:"," musí platit ",[883,18511,18513],{"className":18512},[886],[888,18514,18515],{"xmlns":890},[892,18516,18517,18541],{},[895,18518,18519,18525,18527,18533,18535],{},[1824,18520,18521,18523],{},[898,18522,13170],{},[898,18524,1818],{},[1761,18526,1909],{},[1824,18528,18529,18531],{},[898,18530,6849],{},[898,18532,1818],{},[1761,18534,1964],{},[1824,18536,18537,18539],{},[898,18538,16222],{},[898,18540,1818],{},[902,18542,18543],{"encoding":904},"Y^E = C^E + I^E"," (rovnováha trhu zboží) i ",[883,18546,18548],{"className":18547},[886],[888,18549,18550],{"xmlns":890},[892,18551,18552,18596],{},[895,18553,18554,18560,18562,18568,18574,18576,18582,18588,18590],{},[1824,18555,18556,18558],{},[898,18557,6889],{},[1761,18559,8408],{},[1761,18561,1909],{},[1681,18563,18564,18566],{},[898,18565,17275],{},[1765,18567,1945],{},[1824,18569,18570,18572],{},[898,18571,13170],{},[898,18573,1818],{},[1761,18575,1964],{},[1681,18577,18578,18580],{},[898,18579,17275],{},[1765,18581,2296],{},[1824,18583,18584,18586],{},[898,18585,1719],{},[898,18587,1818],{},[1761,18589,1964],{},[1681,18591,18592,18594],{},[898,18593,17275],{},[1765,18595,5486],{},[902,18597,18598],{"encoding":904},"M^* = k_1 Y^E + k_2 r^E + k_3"," (rovnováha trhu peněz).",[115,18601,18603],{"id":18602},"příklad-76-is-lm","Příklad 7.6 (IS-LM)",[724,18605,18606],{},"Pro trh zboží jsou dány:",[120,18608,18609,18637],{},[123,18610,18611,18612,1834],{},"spotřeba ",[883,18613,18615],{"className":18614},[886],[888,18616,18617],{"xmlns":890},[892,18618,18619,18634],{},[895,18620,18621,18623,18625,18628,18630,18632],{},[898,18622,6849],{},[1761,18624,1909],{},[1765,18626,18627],{},"0,8",[898,18629,13170],{},[1761,18631,1964],{},[1765,18633,7160],{},[902,18635,18636],{"encoding":904},"C = 0{,}8Y + 100",[123,18638,18639,18640,1741],{},"investice ",[883,18641,18643],{"className":18642},[886],[888,18644,18645],{"xmlns":890},[892,18646,18647,18663],{},[895,18648,18649,18651,18653,18655,18657,18659,18661],{},[898,18650,16222],{},[1761,18652,1909],{},[1761,18654,1885],{},[1765,18656,13077],{},[898,18658,1719],{},[1761,18660,1964],{},[1765,18662,6854],{},[902,18664,18665],{"encoding":904},"I = -20r + 1000",[724,18667,18668],{},"Pro trh peněz:",[120,18670,18671,18697,18729],{},[123,18672,18673,1834],{},[883,18674,18676],{"className":18675},[886],[888,18677,18678],{"xmlns":890},[892,18679,18680,18694],{},[895,18681,18682,18688,18690,18692],{},[1681,18683,18684,18686],{},[898,18685,13835],{},[1765,18687,1945],{},[1761,18689,1909],{},[1765,18691,6865],{},[898,18693,13170],{},[902,18695,18696],{"encoding":904},"L_1 = 0{,}1Y",[123,18698,18699,1834],{},[883,18700,18702],{"className":18701},[886],[888,18703,18704],{"xmlns":890},[892,18705,18706,18726],{},[895,18707,18708,18714,18716,18718,18720,18722,18724],{},[1681,18709,18710,18712],{},[898,18711,13835],{},[1765,18713,2296],{},[1761,18715,1909],{},[1761,18717,1885],{},[1765,18719,9056],{},[898,18721,1719],{},[1761,18723,1964],{},[1765,18725,12647],{},[902,18727,18728],{"encoding":904},"L_2 = -25r + 2000",[123,18730,18731,18732,1741],{},"nabídka peněz ",[883,18733,18735],{"className":18734},[886],[888,18736,18737],{"xmlns":890},[892,18738,18739,18752],{},[895,18740,18741,18747,18749],{},[1824,18742,18743,18745],{},[898,18744,6889],{},[1761,18746,8408],{},[1761,18748,1909],{},[1765,18750,18751],{},"2375",[902,18753,18754],{"encoding":904},"M^* = 2375",[724,18756,18757,18760,18761,2506],{},[38,18758,18759],{},"Funkce IS"," — dosazením do (7.13) ",[883,18762,18764],{"className":18763},[886],[888,18765,18766],{"xmlns":890},[892,18767,18768,18780],{},[895,18769,18770,18772,18774,18776,18778],{},[898,18771,13170],{},[1761,18773,1909],{},[898,18775,6849],{},[1761,18777,1964],{},[898,18779,16222],{},[902,18781,18782],{"encoding":904},"Y = C + I",[724,18784,18785],{},[883,18786,18788],{"className":18787},[886],[888,18789,18790],{"xmlns":890},[892,18791,18792,18818],{},[895,18793,18794,18796,18798,18800,18802,18804,18806,18808,18810,18812,18814,18816],{},[898,18795,13170],{},[1761,18797,1909],{},[1765,18799,18627],{},[898,18801,13170],{},[1761,18803,1964],{},[1765,18805,7160],{},[1761,18807,1885],{},[1765,18809,13077],{},[898,18811,1719],{},[1761,18813,1964],{},[1765,18815,6854],{},[1761,18817,1834],{"separator":1833},[902,18819,18820],{"encoding":904},"Y = 0{,}8Y + 100 - 20r + 1000,",[724,18822,18823],{},"tj.",[724,18825,18826],{},[883,18827,18829],{"className":18828},[886],[888,18830,18831],{"xmlns":890},[892,18832,18833,18858],{},[895,18834,18835,18837,18839,18841,18843,18845,18847,18850,18852,18854,18856],{},[1765,18836,6910],{},[898,18838,13170],{},[1761,18840,1964],{},[1765,18842,13077],{},[898,18844,1719],{},[1761,18846,1909],{},[1765,18848,18849],{},"1100.",[3315,18851],{"width":3317},[1761,18853,1915],{"stretchy":1821},[2761,18855,16090],{},[1761,18857,1920],{"stretchy":1821},[902,18859,18860],{"encoding":904},"0{,}2Y + 20r = 1100. \\qquad (\\text{IS})",[724,18862,18863,18866,18867,2506],{},[38,18864,18865],{},"Funkce LM"," — dosazením do (7.15) ",[883,18868,18870],{"className":18869},[886],[888,18871,18872],{"xmlns":890},[892,18873,18874,18898],{},[895,18875,18876,18882,18884,18890,18892],{},[1824,18877,18878,18880],{},[898,18879,6889],{},[1761,18881,8408],{},[1761,18883,1909],{},[1681,18885,18886,18888],{},[898,18887,13835],{},[1765,18889,1945],{},[1761,18891,1964],{},[1681,18893,18894,18896],{},[898,18895,13835],{},[1765,18897,2296],{},[902,18899,18900],{"encoding":904},"M^* = L_1 + L_2",[724,18902,18903],{},[883,18904,18906],{"className":18905},[886],[888,18907,18908],{"xmlns":890},[892,18909,18910,18932],{},[895,18911,18912,18914,18916,18918,18920,18922,18924,18926,18928,18930],{},[1765,18913,18751],{},[1761,18915,1909],{},[1765,18917,6865],{},[898,18919,13170],{},[1761,18921,1885],{},[1765,18923,9056],{},[898,18925,1719],{},[1761,18927,1964],{},[1765,18929,12647],{},[1761,18931,1834],{"separator":1833},[902,18933,18934],{"encoding":904},"2375 = 0{,}1Y - 25r + 2000,",[724,18936,18823],{},[724,18938,18939],{},[883,18940,18942],{"className":18941},[886],[888,18943,18944],{"xmlns":890},[892,18945,18946,18971],{},[895,18947,18948,18950,18952,18954,18956,18958,18960,18963,18965,18967,18969],{},[1765,18949,6865],{},[898,18951,13170],{},[1761,18953,1885],{},[1765,18955,9056],{},[898,18957,1719],{},[1761,18959,1909],{},[1765,18961,18962],{},"375.",[3315,18964],{"width":3317},[1761,18966,1915],{"stretchy":1821},[2761,18968,16097],{},[1761,18970,1920],{"stretchy":1821},[902,18972,18973],{"encoding":904},"0{,}1Y - 25r = 375. \\qquad (\\text{LM})",[724,18975,18976,18979,18980,19005],{},[38,18977,18978],{},"Řešení soustavy."," Z (IS) vyjádříme ",[883,18981,18983],{"className":18982},[886],[888,18984,18985],{"xmlns":890},[892,18986,18987,19002],{},[895,18988,18989,18991,18993,18996,18998,19000],{},[898,18990,13170],{},[1761,18992,1909],{},[1765,18994,18995],{},"5500",[1761,18997,1885],{},[1765,18999,7160],{},[898,19001,1719],{},[902,19003,19004],{"encoding":904},"Y = 5500 - 100r"," a dosadíme do (LM):",[724,19007,19008],{},[883,19009,19011],{"className":19010},[886],[888,19012,19013],{"xmlns":890},[892,19014,19015,19101],{},[895,19016,19017,19019,19021,19023,19025,19027,19029,19031,19033,19035,19037,19039,19042,19044,19047,19049,19052,19054,19056,19058,19060,19062,19064,19066,19068,19070,19072,19074,19077,19079,19081,19084,19086,19088,19090,19096,19098],{},[1765,19018,6865],{},[1761,19020,1915],{"stretchy":1821},[1765,19022,18995],{},[1761,19024,1885],{},[1765,19026,7160],{},[898,19028,1719],{},[1761,19030,1920],{"stretchy":1821},[1761,19032,1885],{},[1765,19034,9056],{},[898,19036,1719],{},[1761,19038,1909],{},[1765,19040,19041],{},"375",[2761,19043,8041],{},[1761,19045,19046],{},"⟹",[2761,19048,8041],{},[1765,19050,19051],{},"550",[1761,19053,1885],{},[1765,19055,2633],{},[898,19057,1719],{},[1761,19059,1885],{},[1765,19061,9056],{},[898,19063,1719],{},[1761,19065,1909],{},[1765,19067,19041],{},[2761,19069,8041],{},[1761,19071,19046],{},[2761,19073,8041],{},[1765,19075,19076],{},"35",[898,19078,1719],{},[1761,19080,1909],{},[1765,19082,19083],{},"175",[2761,19085,8041],{},[1761,19087,19046],{},[2761,19089,8041],{},[1824,19091,19092,19094],{},[898,19093,1719],{},[898,19095,1818],{},[1761,19097,1909],{},[1765,19099,19100],{},"5.",[902,19102,19103],{"encoding":904},"0{,}1(5500 - 100r) - 25r = 375 \\;\\Longrightarrow\\; 550 - 10r - 25r = 375 \\;\\Longrightarrow\\; 35r = 175 \\;\\Longrightarrow\\; r^E = 5.",[724,19105,19106],{},[38,19107,19108],{},"Zpětné dosazení:",[120,19110,19111,19157,19194],{},[123,19112,19113,1834],{},[883,19114,19116],{"className":19115},[886],[888,19117,19118],{"xmlns":890},[892,19119,19120,19154],{},[895,19121,19122,19128,19130,19132,19134,19136,19138,19140,19142,19144,19146,19149,19151],{},[1824,19123,19124,19126],{},[898,19125,13170],{},[898,19127,1818],{},[1761,19129,1909],{},[1765,19131,18995],{},[1761,19133,1885],{},[1765,19135,7160],{},[1761,19137,2447],{},[1765,19139,6321],{},[1761,19141,1909],{},[1765,19143,18995],{},[1761,19145,1885],{},[1765,19147,19148],{},"500",[1761,19150,1909],{},[1765,19152,19153],{},"5000",[902,19155,19156],{"encoding":904},"Y^E = 5500 - 100 \\cdot 5 = 5500 - 500 = 5000",[123,19158,19159,1834],{},[883,19160,19162],{"className":19161},[886],[888,19163,19164],{"xmlns":890},[892,19165,19166,19191],{},[895,19167,19168,19174,19176,19178,19180,19182,19184,19186,19188],{},[1824,19169,19170,19172],{},[898,19171,6849],{},[898,19173,1818],{},[1761,19175,1909],{},[1765,19177,18627],{},[1761,19179,2447],{},[1765,19181,19153],{},[1761,19183,1964],{},[1765,19185,7160],{},[1761,19187,1909],{},[1765,19189,19190],{},"4100",[902,19192,19193],{"encoding":904},"C^E = 0{,}8 \\cdot 5000 + 100 = 4100",[123,19195,19196,1741],{},[883,19197,19199],{"className":19198},[886],[888,19200,19201],{"xmlns":890},[892,19202,19203,19230],{},[895,19204,19205,19211,19213,19215,19217,19219,19221,19223,19225,19227],{},[1824,19206,19207,19209],{},[898,19208,16222],{},[898,19210,1818],{},[1761,19212,1909],{},[1761,19214,1885],{},[1765,19216,13077],{},[1761,19218,2447],{},[1765,19220,6321],{},[1761,19222,1964],{},[1765,19224,6854],{},[1761,19226,1909],{},[1765,19228,19229],{},"900",[902,19231,19232],{"encoding":904},"I^E = -20 \\cdot 5 + 1000 = 900",[724,19234,19235,1989,19238,19284],{},[38,19236,19237],{},"Ověření:",[883,19239,19241],{"className":19240},[886],[888,19242,19243],{"xmlns":890},[892,19244,19245,19281],{},[895,19246,19247,19253,19255,19261,19263,19265,19267,19269,19271,19273,19275],{},[1824,19248,19249,19251],{},[898,19250,6849],{},[898,19252,1818],{},[1761,19254,1964],{},[1824,19256,19257,19259],{},[898,19258,16222],{},[898,19260,1818],{},[1761,19262,1909],{},[1765,19264,19190],{},[1761,19266,1964],{},[1765,19268,19229],{},[1761,19270,1909],{},[1765,19272,19153],{},[1761,19274,1909],{},[1824,19276,19277,19279],{},[898,19278,13170],{},[898,19280,1818],{},[902,19282,19283],{"encoding":904},"C^E + I^E = 4100 + 900 = 5000 = Y^E",". ✓",[724,19286,19287],{},[883,19288,19290],{"className":19289},[886],[888,19291,19292],{"xmlns":890},[892,19293,19294,19364],{},[895,19295,19296],{},[16870,19297,19298],{"notation":16872},[6411,19299,19300],{"scriptlevel":1767,"displaystyle":1821},[6411,19301,19302],{"scriptlevel":1767,"displaystyle":1821},[6411,19303,19304],{"scriptlevel":1767,"displaystyle":1833},[895,19305,19306,19308,19314,19316,19318,19320,19323,19329,19331,19333,19335,19337,19343,19345,19347,19349,19351,19357,19359,19362],{},[2761,19307,7057],{},[1824,19309,19310,19312],{},[898,19311,13170],{},[898,19313,1818],{},[1761,19315,1909],{},[1765,19317,19153],{},[1761,19319,1834],{"separator":1833},[3315,19321],{"width":19322},"1em",[1824,19324,19325,19327],{},[898,19326,1719],{},[898,19328,1818],{},[1761,19330,1909],{},[1765,19332,6321],{},[1761,19334,1834],{"separator":1833},[3315,19336],{"width":19322},[1824,19338,19339,19341],{},[898,19340,6849],{},[898,19342,1818],{},[1761,19344,1909],{},[1765,19346,19190],{},[1761,19348,1834],{"separator":1833},[3315,19350],{"width":19322},[1824,19352,19353,19355],{},[898,19354,16222],{},[898,19356,1818],{},[1761,19358,1909],{},[1765,19360,19361],{},"900.",[2761,19363,7057],{},[902,19365,19366],{"encoding":904},"\\boxed{\\,Y^E = 5000, \\quad r^E = 5, \\quad C^E = 4100, \\quad I^E = 900.\\,}",[724,19368,19369],{},[614,19370,19371,19372,19385,19386,19399,19400,19415,19416,19429,19430,19445,19446,19459,19460,19473,19474,1741],{},"Obrázek 7.7 — Konkrétní numerický příklad IS-LM rovnováhy. Na ose ",[883,19373,19375],{"className":19374},[886],[888,19376,19377],{"xmlns":890},[892,19378,19379,19383],{},[895,19380,19381],{},[898,19382,13170],{},[902,19384,13170],{"encoding":904}," jsou vyznačeny hodnoty 3750, 5000, 5500; na ose ",[883,19387,19389],{"className":19388},[886],[888,19390,19391],{"xmlns":890},[892,19392,19393,19397],{},[895,19394,19395],{},[898,19396,1719],{},[902,19398,1719],{"encoding":904}," hodnoty 5 a 55. Přímka ",[883,19401,19403],{"className":19402},[886],[888,19404,19405],{"xmlns":890},[892,19406,19407,19413],{},[895,19408,19409,19411],{},[898,19410,13835],{},[898,19412,6889],{},[902,19414,16097],{"encoding":904}," stoupá z oblasti nízkých ",[883,19417,19419],{"className":19418},[886],[888,19420,19421],{"xmlns":890},[892,19422,19423,19427],{},[895,19424,19425],{},[898,19426,1719],{},[902,19428,1719],{"encoding":904},", přímka ",[883,19431,19433],{"className":19432},[886],[888,19434,19435],{"xmlns":890},[892,19436,19437,19443],{},[895,19438,19439,19441],{},[898,19440,16222],{},[898,19442,1912],{},[902,19444,16090],{"encoding":904}," klesá a protíná osu ",[883,19447,19449],{"className":19448},[886],[888,19450,19451],{"xmlns":890},[892,19452,19453,19457],{},[895,19454,19455],{},[898,19456,1719],{},[902,19458,1719],{"encoding":904}," kolem hodnoty 55. Průsečík ",[883,19461,19463],{"className":19462},[886],[888,19464,19465],{"xmlns":890},[892,19466,19467,19471],{},[895,19468,19469],{},[898,19470,1818],{},[902,19472,1818],{"encoding":904}," leží v bodě ",[883,19475,19477],{"className":19476},[886],[888,19478,19479],{"xmlns":890},[892,19480,19481,19503],{},[895,19482,19483,19485,19487,19489,19491,19493,19495,19497,19499,19501],{},[1761,19484,1822],{"stretchy":1821},[898,19486,1719],{},[1761,19488,1909],{},[1765,19490,6321],{},[1761,19492,1834],{"separator":1833},[2761,19494,2763],{},[898,19496,13170],{},[1761,19498,1909],{},[1765,19500,19153],{},[1761,19502,1844],{"stretchy":1821},[902,19504,19505],{"encoding":904},"[r = 5,\\ Y = 5000]",[115,19507,19509],{"id":19508},"ekonomická-interpretace-fiskální-a-monetární-politika","Ekonomická interpretace — fiskální a monetární politika",[724,19511,19512,19515,19516,19529,19530,5675,19543,19546,19547,19565,19566,19583,19584,19601,19602,19615,19616,19629],{},[38,19513,19514],{},"Posun křivky IS (fiskální politika)."," Expanzivní fiskální politika — zvýšení vládních výdajů ",[883,19517,19519],{"className":19518},[886],[888,19520,19521],{"xmlns":890},[892,19522,19523,19527],{},[895,19524,19525],{},[898,19526,16151],{},[902,19528,16151],{"encoding":904}," nebo snížení daní ",[883,19531,19533],{"className":19532},[886],[888,19534,19535],{"xmlns":890},[892,19536,19537,19541],{},[895,19538,19539],{},[898,19540,1655],{},[902,19542,1655],{"encoding":904},[38,19544,19545],{},"posouvá IS doprava",": při dané úrokové míře vzroste rovnovážný důchod trhu zboží. Nová rovnováha ",[883,19548,19550],{"className":19549},[886],[888,19551,19552],{"xmlns":890},[892,19553,19554,19562],{},[895,19555,19556],{},[1824,19557,19558,19560],{},[898,19559,1818],{},[1761,19561,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[902,19563,19564],{"encoding":904},"E'"," má vyšší ",[883,19567,19569],{"className":19568},[886],[888,19570,19571],{"xmlns":890},[892,19572,19573,19581],{},[895,19574,19575],{},[1824,19576,19577,19579],{},[898,19578,13170],{},[898,19580,1818],{},[902,19582,17941],{"encoding":904}," i vyšší ",[883,19585,19587],{"className":19586},[886],[888,19588,19589],{"xmlns":890},[892,19590,19591,19599],{},[895,19592,19593],{},[1824,19594,19595,19597],{},[898,19596,1719],{},[898,19598,1818],{},[902,19600,17962],{"encoding":904}," (vyšší ",[883,19603,19605],{"className":19604},[886],[888,19606,19607],{"xmlns":890},[892,19608,19609,19613],{},[895,19610,19611],{},[898,19612,13170],{},[902,19614,13170],{"encoding":904}," zvedá poptávku po penězích, což tlačí ",[883,19617,19619],{"className":19618},[886],[888,19620,19621],{"xmlns":890},[892,19622,19623,19627],{},[895,19624,19625],{},[898,19626,1719],{},[902,19628,1719],{"encoding":904}," nahoru).",[724,19631,19632],{},[3991,19633],{"alt":19634,"className":19635,"src":19636},"imek-posun-is-lm-politiky",[210,3995],"\u002Fwiki-assets\u002Fimek-posun-is-lm-politiky.jpeg",[724,19638,19639,19642,19643,19660,19661,19664,19665,19682,19683,19700,19701,19714,19715,19734,19735,2162],{},[38,19640,19641],{},"Posun křivky LM (monetární politika)."," Expanzivní monetární politika — zvýšení nabídky peněz ",[883,19644,19646],{"className":19645},[886],[888,19647,19648],{"xmlns":890},[892,19649,19650,19658],{},[895,19651,19652],{},[1824,19653,19654,19656],{},[898,19655,6889],{},[1761,19657,8408],{},[902,19659,16188],{"encoding":904}," národní bankou — ",[38,19662,19663],{},"posouvá LM doprava\u002Fdolů",": při daném důchodu je trh peněz v rovnováze při nižší úrokové míře. Nová rovnováha má nižší ",[883,19666,19668],{"className":19667},[886],[888,19669,19670],{"xmlns":890},[892,19671,19672,19680],{},[895,19673,19674],{},[1824,19675,19676,19678],{},[898,19677,1719],{},[898,19679,1818],{},[902,19681,17962],{"encoding":904}," a vyšší ",[883,19684,19686],{"className":19685},[886],[888,19687,19688],{"xmlns":890},[892,19689,19690,19698],{},[895,19691,19692],{},[1824,19693,19694,19696],{},[898,19695,13170],{},[898,19697,1818],{},[902,19699,17941],{"encoding":904}," (nižší ",[883,19702,19704],{"className":19703},[886],[888,19705,19706],{"xmlns":890},[892,19707,19708,19712],{},[895,19709,19710],{},[898,19711,1719],{},[902,19713,1719],{"encoding":904}," povzbuzuje investice ",[883,19716,19718],{"className":19717},[886],[888,19719,19720],{"xmlns":890},[892,19721,19722,19732],{},[895,19723,19724,19726,19728,19730],{},[898,19725,16222],{},[1761,19727,1915],{"stretchy":1821},[898,19729,1719],{},[1761,19731,1920],{"stretchy":1821},[902,19733,18274],{"encoding":904},", ty zvedají ",[883,19736,19738],{"className":19737},[886],[888,19739,19740],{"xmlns":890},[892,19741,19742,19746],{},[895,19743,19744],{},[898,19745,13170],{},[902,19747,13170],{"encoding":904},[724,19749,19750,19751,19754],{},"IS-LM tak dává jednotný rámec pro diskusi ",[38,19752,19753],{},"dopadu obou typů politik"," na důchod a úrokovou míru současně.",[115,19756,5533],{"id":5532},[120,19758,19759,19832,19878,19960,20010,20077,20134,20175,20208],{},[123,19760,19761,5675,19794,1343,19811,19828,19829,19831],{},[38,19762,19763,19764],{},"Funkce investic ",[883,19765,19767],{"className":19766},[886],[888,19768,19769],{"xmlns":890},[892,19770,19771,19791],{},[895,19772,19773,19775,19777,19779,19781,19783,19785,19787,19789],{},[898,19774,16222],{},[1761,19776,1915],{"stretchy":1821},[898,19778,1719],{},[1761,19780,1920],{"stretchy":1821},[1761,19782,1909],{},[898,19784,2774],{},[898,19786,1719],{},[1761,19788,1964],{},[898,19790,4346],{},[902,19792,19793],{"encoding":904},"I(r) = cr + d",[883,19795,19797],{"className":19796},[886],[888,19798,19799],{"xmlns":890},[892,19800,19801,19809],{},[895,19802,19803,19805,19807],{},[898,19804,2774],{},[1761,19806,2058],{},[1765,19808,1767],{},[902,19810,16553],{"encoding":904},[883,19812,19814],{"className":19813},[886],[888,19815,19816],{"xmlns":890},[892,19817,19818,19826],{},[895,19819,19820,19822,19824],{},[898,19821,4346],{},[1761,19823,1763],{},[1765,19825,1767],{},[902,19827,16532],{"encoding":904},"; ",[38,19830,16557],{}," funkce úrokové míry.",[123,19833,19834,19837,19838,19859,19860,19877],{},[38,19835,19836],{},"Trh zboží"," — rovnováha ",[883,19839,19841],{"className":19840},[886],[888,19842,19843],{"xmlns":890},[892,19844,19845,19857],{},[895,19846,19847,19849,19851,19853,19855],{},[898,19848,13170],{},[1761,19850,1909],{},[898,19852,6849],{},[1761,19854,1964],{},[898,19856,16222],{},[902,19858,18782],{"encoding":904},", ekvivalentně ",[883,19861,19863],{"className":19862},[886],[888,19864,19865],{"xmlns":890},[892,19866,19867,19875],{},[895,19868,19869,19871,19873],{},[898,19870,16222],{},[1761,19872,1909],{},[898,19874,1912],{},[902,19876,16750],{"encoding":904}," (investice = úspory).",[123,19879,19880,3927,19883,19885,19886,19936,19937,16953,19939,1741],{},[38,19881,19882],{},"Křivka IS",[614,19884,16093],{},") — ",[883,19887,19889],{"className":19888},[886],[888,19890,19891],{"xmlns":890},[892,19892,19893,19933],{},[895,19894,19895,19897,19899,19911,19913,19915],{},[898,19896,13170],{},[1761,19898,1909],{},[4379,19900,19901,19903],{},[898,19902,2774],{},[895,19904,19905,19907,19909],{},[1765,19906,1945],{},[1761,19908,1885],{},[898,19910,207],{},[898,19912,1719],{},[1761,19914,1964],{},[4379,19916,19917,19925],{},[895,19918,19919,19921,19923],{},[898,19920,4302],{},[1761,19922,1964],{},[898,19924,4346],{},[895,19926,19927,19929,19931],{},[1765,19928,1945],{},[1761,19930,1885],{},[898,19932,207],{},[902,19934,19935],{"encoding":904},"Y = \\frac{c}{1-a}r + \\frac{b+d}{1-a}"," (7.14); ",[38,19938,16557],{},[883,19940,19942],{"className":19941},[886],[888,19943,19944],{"xmlns":890},[892,19945,19946,19958],{},[895,19947,19948,19950,19952,19954,19956],{},[1761,19949,1915],{"stretchy":1821},[898,19951,1719],{},[1761,19953,1834],{"separator":1833},[898,19955,13170],{},[1761,19957,1920],{"stretchy":1821},[902,19959,16975],{"encoding":904},[123,19961,19962,19837,19965,19991,19992,1741],{},[38,19963,19964],{},"Trh peněz",[883,19966,19968],{"className":19967},[886],[888,19969,19970],{"xmlns":890},[892,19971,19972,19988],{},[895,19973,19974,19980,19982],{},[1824,19975,19976,19978],{},[898,19977,6889],{},[898,19979,2244],{},[1761,19981,1909],{},[1824,19983,19984,19986],{},[898,19985,6889],{},[898,19987,1912],{},[902,19989,19990],{"encoding":904},"M^D = M^S"," při pevné nabídce ",[883,19993,19995],{"className":19994},[886],[888,19996,19997],{"xmlns":890},[892,19998,19999,20007],{},[895,20000,20001],{},[1824,20002,20003,20005],{},[898,20004,6889],{},[1761,20006,8408],{},[902,20008,20009],{"encoding":904},"M^* ",[123,20011,20012,5675,20015,1741],{},[38,20013,20014],{},"Transakční, opatrnostní, spekulační poptávka",[883,20016,20018],{"className":20017},[886],[888,20019,20020],{"xmlns":890},[892,20021,20022,20074],{},[895,20023,20024,20030,20032,20038,20040,20046,20048,20054,20056,20058,20064,20066,20068],{},[1824,20025,20026,20028],{},[898,20027,6889],{},[898,20029,2244],{},[1761,20031,1909],{},[1681,20033,20034,20036],{},[898,20035,13835],{},[1765,20037,1945],{},[1761,20039,1964],{},[1681,20041,20042,20044],{},[898,20043,13835],{},[1765,20045,2296],{},[1761,20047,1909],{},[1681,20049,20050,20052],{},[898,20051,17275],{},[1765,20053,1945],{},[898,20055,13170],{},[1761,20057,1964],{},[1681,20059,20060,20062],{},[898,20061,17275],{},[1765,20063,2296],{},[898,20065,1719],{},[1761,20067,1964],{},[1681,20069,20070,20072],{},[898,20071,17275],{},[1765,20073,5486],{},[902,20075,20076],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3",[123,20078,20079,3927,20082,19885,20084,20130,20131,20133],{},[38,20080,20081],{},"Křivka LM",[614,20083,16100],{},[883,20085,20087],{"className":20086},[886],[888,20088,20089],{"xmlns":890},[892,20090,20091,20127],{},[895,20092,20093,20099,20101,20107,20109,20111,20117,20119,20121],{},[1824,20094,20095,20097],{},[898,20096,6889],{},[1761,20098,8408],{},[1761,20100,1909],{},[1681,20102,20103,20105],{},[898,20104,17275],{},[1765,20106,1945],{},[898,20108,13170],{},[1761,20110,1964],{},[1681,20112,20113,20115],{},[898,20114,17275],{},[1765,20116,2296],{},[898,20118,1719],{},[1761,20120,1964],{},[1681,20122,20123,20125],{},[898,20124,17275],{},[1765,20126,5486],{},[902,20128,20129],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3"," (7.15); ",[38,20132,17695],{}," přímka.",[123,20135,20136,20139,20140,20174],{},[38,20137,20138],{},"Simultánní rovnováha"," — průsečík ",[883,20141,20143],{"className":20142},[886],[888,20144,20145],{"xmlns":890},[892,20146,20147,20171],{},[895,20148,20149,20151,20153,20155,20161,20163,20169],{},[898,20150,1818],{},[1761,20152,1909],{},[1761,20154,1915],{"stretchy":1821},[1824,20156,20157,20159],{},[898,20158,1719],{},[898,20160,1818],{},[1761,20162,1834],{"separator":1833},[1824,20164,20165,20167],{},[898,20166,13170],{},[898,20168,1818],{},[1761,20170,1920],{"stretchy":1821},[902,20172,20173],{"encoding":904},"E = (r^E, Y^E)"," křivek IS a LM.",[123,20176,20177,20180,20181,1343,20194,20207],{},[38,20178,20179],{},"Fiskální politika"," — nástroje ",[883,20182,20184],{"className":20183},[886],[888,20185,20186],{"xmlns":890},[892,20187,20188,20192],{},[895,20189,20190],{},[898,20191,16151],{},[902,20193,16151],{"encoding":904},[883,20195,20197],{"className":20196},[886],[888,20198,20199],{"xmlns":890},[892,20200,20201,20205],{},[895,20202,20203],{},[898,20204,1655],{},[902,20206,1655],{"encoding":904}," posouvající křivku IS.",[123,20209,20210,20213,20214,20231],{},[38,20211,20212],{},"Monetární politika"," — nástroj ",[883,20215,20217],{"className":20216},[886],[888,20218,20219],{"xmlns":890},[892,20220,20221,20229],{},[895,20222,20223],{},[1824,20224,20225,20227],{},[898,20226,6889],{},[1761,20228,8408],{},[902,20230,16188],{"encoding":904}," posouvající křivku LM.",[115,20233,5968],{"id":5967},[120,20235,20236,20243,20252,20262],{},[123,20237,20238,1989,20240],{},[38,20239,6015],{},[207,20241,6021],{"className":20242,"dataFsResolvedFilePath":6019,"href":6020},[210],[123,20244,20245,1989,20248],{},[38,20246,20247],{},"Přednáška:",[207,20249,20251],{"className":20250,"dataFsResolvedFilePath":868,"href":869},[210],"imek-blok-03",[123,20253,20254,1989,20257,20261],{},[38,20255,20256],{},"Nadřazené téma:",[207,20258,20260],{"className":20259,"dataFsResolvedFilePath":934,"href":935},[210],"narodni-duchod"," — makroekonomické modely C-I, C-I-G, C-I-G-X a úvod do IS-LM",[123,20263,20264,20267],{},[38,20265,20266],{},"Související:",[120,20268,20269,20275,20281],{},[123,20270,20271,20274],{},[207,20272,5371],{"className":20273,"dataFsResolvedFilePath":800,"href":801},[210]," — paralela rovnovážného bodu (průsečík dvou křivek) v mikroekonomii",[123,20276,20277,20280],{},[207,20278,1145],{"className":20279,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro směrnice IS a LM",[123,20282,20283,20287],{},[207,20284,20286],{"className":20285,"dataFsResolvedFilePath":782,"href":783},[210],"funkce-vice-promennych"," — dvě neznámé a řešení lineárních soustav",{"title":641,"searchDepth":642,"depth":642,"links":20289},[20290,20291,20292,20293,20294,20295,20296,20297,20298,20299],{"id":16045,"depth":642,"text":16046},{"id":16198,"depth":642,"text":16199},{"id":16413,"depth":642,"text":16414},{"id":16706,"depth":642,"text":16707},{"id":17119,"depth":642,"text":17120},{"id":17912,"depth":642,"text":17913},{"id":18602,"depth":642,"text":18603},{"id":19508,"depth":642,"text":19509},{"id":5532,"depth":642,"text":5533},{"id":5967,"depth":642,"text":5968},{},"\u002Ftopics\u002Fis-lm",{"title":16037,"description":641},[1138,1137],"topics\u002Fis-lm",[1128,20306,1143,20307,20308,20309,20310,20260],"is-lm","trh-zbozi","trh-penez","urokova-mira","investice","OcXqlUxNqiCsj643lVoQEu_ZWU2vH0D_lWZ_-SxoyHk",{"id":20313,"title":20314,"body":20315,"course":659,"courses":21908,"created":1129,"description":21909,"extension":661,"meta":21910,"navigation":664,"path":21911,"seo":21912,"sources":21913,"stem":21914,"tags":21915,"type":6050,"updated":677,"__hash__":21918},"topics\u002Ftopics\u002Flagrangeova-metoda.md","Lagrangeova metoda (vázané extrémy)",{"type":9,"value":20316,"toc":21896},[20317,20320,20416,20423,20443,20447,20452,20515,20534,20536,20539,20675,20677,20887,20921,21058,21062,21126,21142,21170,21174,21272,21276,21280,21333,21439,21653,21657,21700,21806,21858,21860],[12,20318,20314],{"id":20319},"lagrangeova-metoda-vázané-extrémy",[724,20321,20322,20323,4569,20346,20378,20379,20382,20383,20410,20411,20415],{},"Hledáme extrém funkce ",[883,20324,20326],{"className":20325},[886],[888,20327,20328],{"xmlns":890},[892,20329,20330,20344],{},[895,20331,20332,20334,20336,20338,20340,20342],{},[898,20333,6107],{},[1761,20335,1915],{"stretchy":1821},[898,20337,6112],{},[1761,20339,1834],{"separator":1833},[898,20341,1716],{},[1761,20343,1920],{"stretchy":1821},[902,20345,13882],{"encoding":904},[883,20347,20349],{"className":20348},[886],[888,20350,20351],{"xmlns":890},[892,20352,20353,20375],{},[895,20354,20355,20357,20359,20365,20367,20373],{},[898,20356,900],{},[1761,20358,1915],{"stretchy":1821},[1681,20360,20361,20363],{},[898,20362,1828],{},[1765,20364,1945],{},[1761,20366,1834],{"separator":1833},[1681,20368,20369,20371],{},[898,20370,1828],{},[1765,20372,2296],{},[1761,20374,1920],{"stretchy":1821},[902,20376,20377],{"encoding":904},"U(Q_1, Q_2)"," apod.) ",[38,20380,20381],{},"podmíněný"," rovnicí ",[883,20384,20386],{"className":20385},[886],[888,20387,20388],{"xmlns":890},[892,20389,20390,20408],{},[895,20391,20392,20394,20396,20398,20400,20402,20404,20406],{},[898,20393,15079],{},[1761,20395,1915],{"stretchy":1821},[898,20397,6112],{},[1761,20399,1834],{"separator":1833},[898,20401,1716],{},[1761,20403,1920],{"stretchy":1821},[1761,20405,1909],{},[1765,20407,1767],{},[902,20409,15096],{"encoding":904},". V ",[207,20412,20414],{"className":20413,"dataFsResolvedFilePath":6019,"href":6020},[210],"matematické ekonomii"," se používá pro:",[724,20417,20418],{},[3991,20419],{"alt":20420,"className":20421,"src":20422},"imek-lagrange-tecnost",[210,3995],"\u002Fwiki-assets\u002Fimek-lagrange-tecnost.jpeg",[120,20424,20425,20434,20440],{},[123,20426,20427,20430,20431,1920],{},[38,20428,20429],{},"Maximalizaci užitečnosti"," při rozpočtovém omezení (viz ",[207,20432,13813],{"className":20433,"dataFsResolvedFilePath":878,"href":879},[210],[123,20435,20436,20439],{},[38,20437,20438],{},"Minimalizaci výdajů"," při dané úrovni užitečnosti (duální úloha)",[123,20441,20442],{},"Optimalizaci produkce \u002F nákladů za omezení",[115,20444,20446],{"id":20445},"princip","Princip",[724,20448,14745,20449,2506],{},[38,20450,20451],{},"Lagrangeovu funkci",[724,20453,20454],{},[883,20455,20457],{"className":20456},[886],[888,20458,20459],{"xmlns":890},[892,20460,20461,20512],{},[895,20462,20463,20465,20467,20469,20471,20473,20475,20478,20480,20482,20484,20486,20488,20490,20492,20494,20496,20498,20500,20502,20504,20506,20508,20510],{},[898,20464,13835],{},[1761,20466,1915],{"stretchy":1821},[898,20468,6112],{},[1761,20470,1834],{"separator":1833},[898,20472,1716],{},[1761,20474,1834],{"separator":1833},[898,20476,20477],{},"λ",[1761,20479,1920],{"stretchy":1821},[1761,20481,1909],{},[898,20483,6107],{},[1761,20485,1915],{"stretchy":1821},[898,20487,6112],{},[1761,20489,1834],{"separator":1833},[898,20491,1716],{},[1761,20493,1920],{"stretchy":1821},[1761,20495,1964],{},[898,20497,20477],{},[2761,20499,7057],{},[898,20501,15079],{},[1761,20503,1915],{"stretchy":1821},[898,20505,6112],{},[1761,20507,1834],{"separator":1833},[898,20509,1716],{},[1761,20511,1920],{"stretchy":1821},[902,20513,20514],{"encoding":904},"L(x, y, \\lambda) = f(x, y) + \\lambda\\, g(x, y)",[724,20516,8364,20517,12146,20531,1741],{},[883,20518,20520],{"className":20519},[886],[888,20521,20522],{"xmlns":890},[892,20523,20524,20528],{},[895,20525,20526],{},[898,20527,20477],{},[902,20529,20530],{"encoding":904},"\\lambda",[38,20532,20533],{},"Lagrangeův multiplikátor",[115,20535,7319],{"id":7318},[724,20537,20538],{},"Řešíme soustavu:",[724,20540,20541,20589,20637],{},[883,20542,20544],{"className":20543},[886],[888,20545,20546],{"xmlns":890},[892,20547,20548,20586],{},[895,20549,20550,20558,20560,20568,20570,20572,20574,20582,20584],{},[2015,20551,20552,20554,20556],{},[898,20553,13835],{},[898,20555,6112],{},[1761,20557,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,20559,1909],{},[2015,20561,20562,20564,20566],{},[898,20563,6107],{},[898,20565,6112],{},[1761,20567,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,20569,1964],{},[898,20571,20477],{},[2761,20573,7057],{},[2015,20575,20576,20578,20580],{},[898,20577,15079],{},[898,20579,6112],{},[1761,20581,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,20583,1909],{},[1765,20585,1767],{},[902,20587,20588],{"encoding":904},"L'_x = f'_x + \\lambda\\, g'_x = 0",[883,20590,20592],{"className":20591},[886],[888,20593,20594],{"xmlns":890},[892,20595,20596,20634],{},[895,20597,20598,20606,20608,20616,20618,20620,20622,20630,20632],{},[2015,20599,20600,20602,20604],{},[898,20601,13835],{},[898,20603,1716],{},[1761,20605,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,20607,1909],{},[2015,20609,20610,20612,20614],{},[898,20611,6107],{},[898,20613,1716],{},[1761,20615,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,20617,1964],{},[898,20619,20477],{},[2761,20621,7057],{},[2015,20623,20624,20626,20628],{},[898,20625,15079],{},[898,20627,1716],{},[1761,20629,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,20631,1909],{},[1765,20633,1767],{},[902,20635,20636],{"encoding":904},"L'_y = f'_y + \\lambda\\, g'_y = 0",[883,20638,20640],{"className":20639},[886],[888,20641,20642],{"xmlns":890},[892,20643,20644,20672],{},[895,20645,20646,20654,20656,20658,20660,20662,20664,20666,20668,20670],{},[2015,20647,20648,20650,20652],{},[898,20649,13835],{},[898,20651,20477],{},[1761,20653,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,20655,1909],{},[898,20657,15079],{},[1761,20659,1915],{"stretchy":1821},[898,20661,6112],{},[1761,20663,1834],{"separator":1833},[898,20665,1716],{},[1761,20667,1920],{"stretchy":1821},[1761,20669,1909],{},[1765,20671,1767],{},[902,20673,20674],{"encoding":904},"L'_\\lambda = g(x, y) = 0",[115,20676,7393],{"id":7392},[724,20678,20679],{},[883,20680,20682],{"className":20681},[886],[888,20683,20684],{"xmlns":890},[892,20685,20686,20884],{},[895,20687,20688,20690,20692,20694,20696,20698,20700,20702,20704,20706,20708,20724,20726,20728,20744,20746,20748,20756,20762,20764,20766,20782,20784,20786,20802,20804,20806,20814,20820,20822,20824,20826,20842,20844,20846,20862,20864,20866,20874,20876],{},[898,20689,2244],{},[1761,20691,1915],{"stretchy":1821},[898,20693,6112],{},[1761,20695,1834],{"separator":1833},[898,20697,1716],{},[1761,20699,1834],{"separator":1833},[898,20701,20477],{},[1761,20703,1920],{"stretchy":1821},[1761,20705,1909],{},[1761,20707,1915],{"stretchy":1821},[2015,20709,20710,20712,20718],{},[898,20711,6107],{},[895,20713,20714,20716],{},[898,20715,6112],{},[898,20717,6112],{},[895,20719,20720,20722],{},[1761,20721,6459],{"mathvariant":1969},[1761,20723,6459],{"mathvariant":1969},[1761,20725,1964],{},[898,20727,20477],{},[2015,20729,20730,20732,20738],{},[898,20731,15079],{},[895,20733,20734,20736],{},[898,20735,6112],{},[898,20737,6112],{},[895,20739,20740,20742],{},[1761,20741,6459],{"mathvariant":1969},[1761,20743,6459],{"mathvariant":1969},[1761,20745,1920],{"stretchy":1821},[1761,20747,1915],{"stretchy":1821},[2015,20749,20750,20752,20754],{},[898,20751,15079],{},[898,20753,1716],{},[1761,20755,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1824,20757,20758,20760],{},[1761,20759,1920],{"stretchy":1821},[1765,20761,2296],{},[1761,20763,1964],{},[1761,20765,1915],{"stretchy":1821},[2015,20767,20768,20770,20776],{},[898,20769,6107],{},[895,20771,20772,20774],{},[898,20773,1716],{},[898,20775,1716],{},[895,20777,20778,20780],{},[1761,20779,6459],{"mathvariant":1969},[1761,20781,6459],{"mathvariant":1969},[1761,20783,1964],{},[898,20785,20477],{},[2015,20787,20788,20790,20796],{},[898,20789,15079],{},[895,20791,20792,20794],{},[898,20793,1716],{},[898,20795,1716],{},[895,20797,20798,20800],{},[1761,20799,6459],{"mathvariant":1969},[1761,20801,6459],{"mathvariant":1969},[1761,20803,1920],{"stretchy":1821},[1761,20805,1915],{"stretchy":1821},[2015,20807,20808,20810,20812],{},[898,20809,15079],{},[898,20811,6112],{},[1761,20813,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1824,20815,20816,20818],{},[1761,20817,1920],{"stretchy":1821},[1765,20819,2296],{},[1761,20821,1885],{},[1765,20823,2296],{},[1761,20825,1915],{"stretchy":1821},[2015,20827,20828,20830,20836],{},[898,20829,6107],{},[895,20831,20832,20834],{},[898,20833,6112],{},[898,20835,1716],{},[895,20837,20838,20840],{},[1761,20839,6459],{"mathvariant":1969},[1761,20841,6459],{"mathvariant":1969},[1761,20843,1964],{},[898,20845,20477],{},[2015,20847,20848,20850,20856],{},[898,20849,15079],{},[895,20851,20852,20854],{},[898,20853,6112],{},[898,20855,1716],{},[895,20857,20858,20860],{},[1761,20859,6459],{"mathvariant":1969},[1761,20861,6459],{"mathvariant":1969},[1761,20863,1920],{"stretchy":1821},[2761,20865,7057],{},[2015,20867,20868,20870,20872],{},[898,20869,15079],{},[898,20871,6112],{},[1761,20873,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[2761,20875,7057],{},[2015,20877,20878,20880,20882],{},[898,20879,15079],{},[898,20881,1716],{},[1761,20883,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[902,20885,20886],{"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",[724,20888,20889,20890,20920],{},"Je-li ",[883,20891,20893],{"className":20892},[886],[888,20894,20895],{"xmlns":890},[892,20896,20897,20917],{},[895,20898,20899,20901,20903,20905,20907,20909,20915],{},[1761,20900,1822],{"stretchy":1821},[898,20902,207],{},[1761,20904,1834],{"separator":1833},[898,20906,4302],{},[1761,20908,1834],{"separator":1833},[1681,20910,20911,20913],{},[898,20912,20477],{},[1765,20914,1767],{},[1761,20916,1844],{"stretchy":1821},[902,20918,20919],{"encoding":904},"[a, b, \\lambda_0]"," podezřelý bod:",[120,20922,20923,20991],{},[123,20924,20925,7480,20961,20963,20964],{},[883,20926,20928],{"className":20927},[886],[888,20929,20930],{"xmlns":890},[892,20931,20932,20958],{},[895,20933,20934,20936,20938,20940,20942,20944,20946,20952,20954,20956],{},[898,20935,2244],{},[1761,20937,1915],{"stretchy":1821},[898,20939,207],{},[1761,20941,1834],{"separator":1833},[898,20943,4302],{},[1761,20945,1834],{"separator":1833},[1681,20947,20948,20950],{},[898,20949,20477],{},[1765,20951,1767],{},[1761,20953,1920],{"stretchy":1821},[1761,20955,2058],{},[1765,20957,1767],{},[902,20959,20960],{"encoding":904},"D(a, b, \\lambda_0) \u003C 0",[38,20962,7781],{}," vázané podmínkou ",[883,20965,20967],{"className":20966},[886],[888,20968,20969],{"xmlns":890},[892,20970,20971,20989],{},[895,20972,20973,20975,20977,20979,20981,20983,20985,20987],{},[898,20974,15079],{},[1761,20976,1915],{"stretchy":1821},[898,20978,6112],{},[1761,20980,1834],{"separator":1833},[898,20982,1716],{},[1761,20984,1920],{"stretchy":1821},[1761,20986,1909],{},[1765,20988,1767],{},[902,20990,15096],{"encoding":904},[123,20992,20993,7480,21029,20963,21031],{},[883,20994,20996],{"className":20995},[886],[888,20997,20998],{"xmlns":890},[892,20999,21000,21026],{},[895,21001,21002,21004,21006,21008,21010,21012,21014,21020,21022,21024],{},[898,21003,2244],{},[1761,21005,1915],{"stretchy":1821},[898,21007,207],{},[1761,21009,1834],{"separator":1833},[898,21011,4302],{},[1761,21013,1834],{"separator":1833},[1681,21015,21016,21018],{},[898,21017,20477],{},[1765,21019,1767],{},[1761,21021,1920],{"stretchy":1821},[1761,21023,1763],{},[1765,21025,1767],{},[902,21027,21028],{"encoding":904},"D(a, b, \\lambda_0) > 0",[38,21030,7839],{},[883,21032,21034],{"className":21033},[886],[888,21035,21036],{"xmlns":890},[892,21037,21038,21056],{},[895,21039,21040,21042,21044,21046,21048,21050,21052,21054],{},[898,21041,15079],{},[1761,21043,1915],{"stretchy":1821},[898,21045,6112],{},[1761,21047,1834],{"separator":1833},[898,21049,1716],{},[1761,21051,1920],{"stretchy":1821},[1761,21053,1909],{},[1765,21055,1767],{},[902,21057,15096],{"encoding":904},[115,21059,21061],{"id":21060},"význam-multiplikátoru","Význam multiplikátoru",[724,21063,21064],{},[883,21065,21067],{"className":21066},[886],[888,21068,21069],{"xmlns":890},[892,21070,21071,21123],{},[895,21072,21073,21075,21077,21099,21101],{},[898,21074,20477],{},[1761,21076,1909],{},[4379,21078,21079,21087],{},[2015,21080,21081,21083,21085],{},[898,21082,6107],{},[898,21084,6112],{},[1761,21086,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[895,21088,21089,21091],{},[1761,21090,1885],{},[2015,21092,21093,21095,21097],{},[898,21094,15079],{},[898,21096,6112],{},[1761,21098,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,21100,1909],{},[4379,21102,21103,21111],{},[2015,21104,21105,21107,21109],{},[898,21106,6107],{},[898,21108,1716],{},[1761,21110,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[895,21112,21113,21115],{},[1761,21114,1885],{},[2015,21116,21117,21119,21121],{},[898,21118,15079],{},[898,21120,1716],{},[1761,21122,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[902,21124,21125],{"encoding":904},"\\lambda = \\frac{f'_x}{-g'_x} = \\frac{f'_y}{-g'_y}",[724,21127,21128,21141],{},[883,21129,21131],{"className":21130},[886],[888,21132,21133],{"xmlns":890},[892,21134,21135,21139],{},[895,21136,21137],{},[898,21138,20477],{},[902,21140,20530],{"encoding":904}," udává:",[120,21143,21144,21150],{},[123,21145,21146,21147],{},"konstantní ",[38,21148,21149],{},"poměr mezi mezním prospěchem a mezním nákladem",[123,21151,21152,21155,21156,21169],{},[38,21153,21154],{},"náklady příležitosti"," (opportunity cost) — o kolik vzroste optimální hodnota ",[883,21157,21159],{"className":21158},[886],[888,21160,21161],{"xmlns":890},[892,21162,21163,21167],{},[895,21164,21165],{},[898,21166,6107],{},[902,21168,6107],{"encoding":904},", uvolní-li se omezení o jednotku",[115,21171,21173],{"id":21172},"alternativní-postup","Alternativní postup",[724,21175,21176,21177,21204,21205,21229,21230,21254,21255,21268,21269,1741],{},"Lze-li z ",[883,21178,21180],{"className":21179},[886],[888,21181,21182],{"xmlns":890},[892,21183,21184,21202],{},[895,21185,21186,21188,21190,21192,21194,21196,21198,21200],{},[898,21187,15079],{},[1761,21189,1915],{"stretchy":1821},[898,21191,6112],{},[1761,21193,1834],{"separator":1833},[898,21195,1716],{},[1761,21197,1920],{"stretchy":1821},[1761,21199,1909],{},[1765,21201,1767],{},[902,21203,15096],{"encoding":904}," vyjádřit ",[883,21206,21208],{"className":21207},[886],[888,21209,21210],{"xmlns":890},[892,21211,21212,21226],{},[895,21213,21214,21216,21218,21220,21222,21224],{},[898,21215,1716],{},[1761,21217,1909],{},[898,21219,1716],{},[1761,21221,1915],{"stretchy":1821},[898,21223,6112],{},[1761,21225,1920],{"stretchy":1821},[902,21227,21228],{"encoding":904},"y = y(x)"," (nebo ",[883,21231,21233],{"className":21232},[886],[888,21234,21235],{"xmlns":890},[892,21236,21237,21251],{},[895,21238,21239,21241,21243,21245,21247,21249],{},[898,21240,6112],{},[1761,21242,1909],{},[898,21244,6112],{},[1761,21246,1915],{"stretchy":1821},[898,21248,1716],{},[1761,21250,1920],{"stretchy":1821},[902,21252,21253],{"encoding":904},"x = x(y)","), dosadíme do ",[883,21256,21258],{"className":21257},[886],[888,21259,21260],{"xmlns":890},[892,21261,21262,21266],{},[895,21263,21264],{},[898,21265,6107],{},[902,21267,6107],{"encoding":904}," a převedeme na ",[38,21270,21271],{},"extrém funkce jedné proměnné",[115,21273,21275],{"id":21274},"použití-v-imek","Použití v ImeK",[198,21277,21279],{"id":21278},"maximalizace-užitečnosti","Maximalizace užitečnosti",[724,21281,21282,21283,1741],{},"Rozpočtové omezení: ",[883,21284,21286],{"className":21285},[886],[888,21287,21288],{"xmlns":890},[892,21289,21290,21330],{},[895,21291,21292,21298,21300,21308,21314,21316,21324],{},[1824,21293,21294,21296],{},[898,21295,13170],{},[1761,21297,8408],{},[1761,21299,1909],{},[2015,21301,21302,21304,21306],{},[898,21303,1839],{},[1765,21305,1945],{},[1761,21307,8408],{},[1681,21309,21310,21312],{},[898,21311,1828],{},[1765,21313,1945],{},[1761,21315,1964],{},[2015,21317,21318,21320,21322],{},[898,21319,1839],{},[1765,21321,2296],{},[1761,21323,8408],{},[1681,21325,21326,21328],{},[898,21327,1828],{},[1765,21329,2296],{},[902,21331,21332],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2",[724,21334,21335],{},[883,21336,21338],{"className":21337},[886],[888,21339,21340],{"xmlns":890},[892,21341,21342,21436],{},[895,21343,21344,21346,21348,21354,21356,21362,21364,21366,21368,21370,21372,21374,21380,21382,21388,21390,21392,21394,21396,21402,21404,21412,21418,21420,21428,21434],{},[898,21345,13835],{},[1761,21347,1915],{"stretchy":1821},[1681,21349,21350,21352],{},[898,21351,1828],{},[1765,21353,1945],{},[1761,21355,1834],{"separator":1833},[1681,21357,21358,21360],{},[898,21359,1828],{},[1765,21361,2296],{},[1761,21363,1834],{"separator":1833},[898,21365,20477],{},[1761,21367,1920],{"stretchy":1821},[1761,21369,1909],{},[898,21371,900],{},[1761,21373,1915],{"stretchy":1821},[1681,21375,21376,21378],{},[898,21377,1828],{},[1765,21379,1945],{},[1761,21381,1834],{"separator":1833},[1681,21383,21384,21386],{},[898,21385,1828],{},[1765,21387,2296],{},[1761,21389,1920],{"stretchy":1821},[1761,21391,1964],{},[898,21393,20477],{},[1761,21395,1915],{"stretchy":1821},[1824,21397,21398,21400],{},[898,21399,13170],{},[1761,21401,8408],{},[1761,21403,1885],{},[2015,21405,21406,21408,21410],{},[898,21407,1839],{},[1765,21409,1945],{},[1761,21411,8408],{},[1681,21413,21414,21416],{},[898,21415,1828],{},[1765,21417,1945],{},[1761,21419,1885],{},[2015,21421,21422,21424,21426],{},[898,21423,1839],{},[1765,21425,2296],{},[1761,21427,8408],{},[1681,21429,21430,21432],{},[898,21431,1828],{},[1765,21433,2296],{},[1761,21435,1920],{"stretchy":1821},[902,21437,21438],{"encoding":904},"L(Q_1, Q_2, \\lambda) = U(Q_1, Q_2) + \\lambda (Y^* - P_1^* Q_1 - P_2^* Q_2)",[724,21440,21441,21442,1343,21474,1343,21506,21555,21556,21610,21611,1741],{},"Soustava: ",[883,21443,21445],{"className":21444},[886],[888,21446,21447],{"xmlns":890},[892,21448,21449,21471],{},[895,21450,21451,21459,21461,21463],{},[2015,21452,21453,21455,21457],{},[898,21454,900],{},[1765,21456,1945],{},[1761,21458,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,21460,1909],{},[898,21462,20477],{},[2015,21464,21465,21467,21469],{},[898,21466,1839],{},[1765,21468,1945],{},[1761,21470,8408],{},[902,21472,21473],{"encoding":904},"U'_1 = \\lambda P_1^*",[883,21475,21477],{"className":21476},[886],[888,21478,21479],{"xmlns":890},[892,21480,21481,21503],{},[895,21482,21483,21491,21493,21495],{},[2015,21484,21485,21487,21489],{},[898,21486,900],{},[1765,21488,2296],{},[1761,21490,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,21492,1909],{},[898,21494,20477],{},[2015,21496,21497,21499,21501],{},[898,21498,1839],{},[1765,21500,2296],{},[1761,21502,8408],{},[902,21504,21505],{"encoding":904},"U'_2 = \\lambda P_2^*",[883,21507,21509],{"className":21508},[886],[888,21510,21511],{"xmlns":890},[892,21512,21513,21553],{},[895,21514,21515,21521,21523,21531,21537,21539,21547],{},[1824,21516,21517,21519],{},[898,21518,13170],{},[1761,21520,8408],{},[1761,21522,1909],{},[2015,21524,21525,21527,21529],{},[898,21526,1839],{},[1765,21528,1945],{},[1761,21530,8408],{},[1681,21532,21533,21535],{},[898,21534,1828],{},[1765,21536,1945],{},[1761,21538,1964],{},[2015,21540,21541,21543,21545],{},[898,21542,1839],{},[1765,21544,2296],{},[1761,21546,8408],{},[1681,21548,21549,21551],{},[898,21550,1828],{},[1765,21552,2296],{},[902,21554,21332],{"encoding":904},". Z prvních dvou: ",[883,21557,21559],{"className":21558},[886],[888,21560,21561],{"xmlns":890},[892,21562,21563,21607],{},[895,21564,21565,21585,21587],{},[6411,21566,21567],{"scriptlevel":1767,"displaystyle":1821},[4379,21568,21569,21577],{},[2015,21570,21571,21573,21575],{},[898,21572,900],{},[1765,21574,1945],{},[1761,21576,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[2015,21578,21579,21581,21583],{},[898,21580,900],{},[1765,21582,2296],{},[1761,21584,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,21586,1909],{},[6411,21588,21589],{"scriptlevel":1767,"displaystyle":1821},[4379,21590,21591,21599],{},[2015,21592,21593,21595,21597],{},[898,21594,1839],{},[1765,21596,1945],{},[1761,21598,8408],{},[2015,21600,21601,21603,21605],{},[898,21602,1839],{},[1765,21604,2296],{},[1761,21606,8408],{},[902,21608,21609],{"encoding":904},"\\tfrac{U'_1}{U'_2} = \\tfrac{P_1^*}{P_2^*}",", tj. ",[883,21612,21614],{"className":21613},[886],[888,21615,21616],{"xmlns":890},[892,21617,21618,21650],{},[895,21619,21620,21622,21624,21626,21628,21630],{},[898,21621,6889],{},[898,21623,8051],{},[898,21625,6849],{},[898,21627,1912],{},[1761,21629,1909],{},[6411,21631,21632],{"scriptlevel":1767,"displaystyle":1821},[4379,21633,21634,21642],{},[2015,21635,21636,21638,21640],{},[898,21637,1839],{},[1765,21639,1945],{},[1761,21641,8408],{},[2015,21643,21644,21646,21648],{},[898,21645,1839],{},[1765,21647,2296],{},[1761,21649,8408],{},[902,21651,21652],{"encoding":904},"MRCS = \\tfrac{P_1^*}{P_2^*}",[198,21654,21656],{"id":21655},"minimalizace-výdajů","Minimalizace výdajů",[724,21658,21659,21660,1741],{},"Podmínka dané užitečnosti ",[883,21661,21663],{"className":21662},[886],[888,21664,21665],{"xmlns":890},[892,21666,21667,21697],{},[895,21668,21669,21675,21677,21679,21681,21687,21689,21695],{},[1824,21670,21671,21673],{},[898,21672,900],{},[1761,21674,8408],{},[1761,21676,1909],{},[898,21678,900],{},[1761,21680,1915],{"stretchy":1821},[1681,21682,21683,21685],{},[898,21684,1828],{},[1765,21686,1945],{},[1761,21688,1834],{"separator":1833},[1681,21690,21691,21693],{},[898,21692,1828],{},[1765,21694,2296],{},[1761,21696,1920],{"stretchy":1821},[902,21698,21699],{"encoding":904},"U^* = U(Q_1, Q_2)",[724,21701,21702],{},[883,21703,21705],{"className":21704},[886],[888,21706,21707],{"xmlns":890},[892,21708,21709,21803],{},[895,21710,21711,21713,21715,21721,21723,21729,21731,21733,21735,21737,21745,21751,21753,21761,21767,21769,21771,21773,21779,21781,21783,21785,21791,21793,21799,21801],{},[898,21712,13835],{},[1761,21714,1915],{"stretchy":1821},[1681,21716,21717,21719],{},[898,21718,1828],{},[1765,21720,1945],{},[1761,21722,1834],{"separator":1833},[1681,21724,21725,21727],{},[898,21726,1828],{},[1765,21728,2296],{},[1761,21730,1834],{"separator":1833},[898,21732,20477],{},[1761,21734,1920],{"stretchy":1821},[1761,21736,1909],{},[2015,21738,21739,21741,21743],{},[898,21740,1839],{},[1765,21742,1945],{},[1761,21744,8408],{},[1681,21746,21747,21749],{},[898,21748,1828],{},[1765,21750,1945],{},[1761,21752,1964],{},[2015,21754,21755,21757,21759],{},[898,21756,1839],{},[1765,21758,2296],{},[1761,21760,8408],{},[1681,21762,21763,21765],{},[898,21764,1828],{},[1765,21766,2296],{},[1761,21768,1964],{},[898,21770,20477],{},[1761,21772,1915],{"stretchy":1821},[1824,21774,21775,21777],{},[898,21776,900],{},[1761,21778,8408],{},[1761,21780,1885],{},[898,21782,900],{},[1761,21784,1915],{"stretchy":1821},[1681,21786,21787,21789],{},[898,21788,1828],{},[1765,21790,1945],{},[1761,21792,1834],{"separator":1833},[1681,21794,21795,21797],{},[898,21796,1828],{},[1765,21798,2296],{},[1761,21800,1920],{"stretchy":1821},[1761,21802,1920],{"stretchy":1821},[902,21804,21805],{"encoding":904},"L(Q_1, Q_2, \\lambda) = P_1^* Q_1 + P_2^* Q_2 + \\lambda (U^* - U(Q_1, Q_2))",[724,21807,21808,21809,1741],{},"Duálně dostaneme Hicksovy poptávkové funkce ",[883,21810,21812],{"className":21811},[886],[888,21813,21814],{"xmlns":890},[892,21815,21816,21855],{},[895,21817,21818,21825,21827,21833,21835,21841,21843,21849,21851,21853],{},[1681,21819,21820,21822],{},[898,21821,1828],{},[898,21823,21824],{},"i",[1761,21826,1909],{},[1681,21828,21829,21831],{},[898,21830,2244],{},[898,21832,21824],{},[1761,21834,1915],{"stretchy":1821},[1681,21836,21837,21839],{},[898,21838,1839],{},[1765,21840,1945],{},[1761,21842,1834],{"separator":1833},[1681,21844,21845,21847],{},[898,21846,1839],{},[1765,21848,2296],{},[1761,21850,1834],{"separator":1833},[898,21852,900],{},[1761,21854,1920],{"stretchy":1821},[902,21856,21857],{"encoding":904},"Q_i = D_i(P_1, P_2, U)",[115,21859,5968],{"id":5967},[120,21861,21862,21869,21876,21885],{},[123,21863,21864,1989,21866],{},[38,21865,7861],{},[207,21867,784],{"className":21868,"dataFsResolvedFilePath":782,"href":783},[210],[123,21870,21871,1989,21873],{},[38,21872,7869],{},[207,21874,15980],{"className":21875,"dataFsResolvedFilePath":800,"href":801},[210],[123,21877,21878,1989,21881,21884],{},[38,21879,21880],{},"Aplikace v kurzu:",[207,21882,880],{"className":21883,"dataFsResolvedFilePath":878,"href":879},[210]," (maximalizace užitečnosti při rozpočtovém omezení), minimalizace výdajů (duální úloha), optimalizace produkce",[123,21886,21887,1989,21889,1343,21892,21895],{},[38,21888,7877],{},[207,21890,936],{"className":21891,"dataFsResolvedFilePath":934,"href":935},[210],[207,21893,1400],{"className":21894,"dataFsResolvedFilePath":1398,"href":1399},[210]," (IpmrK)",{"title":641,"searchDepth":642,"depth":642,"links":21897},[21898,21899,21900,21901,21902,21903,21907],{"id":20445,"depth":642,"text":20446},{"id":7318,"depth":642,"text":7319},{"id":7392,"depth":642,"text":7393},{"id":21060,"depth":642,"text":21061},{"id":21172,"depth":642,"text":21173},{"id":21274,"depth":642,"text":21275,"children":21904},[21905,21906],{"id":21278,"depth":649,"text":21279},{"id":21655,"depth":649,"text":21656},{"id":5967,"depth":642,"text":5968},[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":20314,"description":21909},[1135,1137],"topics\u002Flagrangeova-metoda",[1128,1619,21916,21917],"vazane-extremy","multiplikator","PRnK6wpMGySFp-C47ico7wAs4MDBp47Titm-Obyzgow",{"id":21920,"title":936,"body":21921,"course":1128,"courses":659,"created":6039,"description":641,"extension":661,"meta":31786,"navigation":664,"path":31787,"seo":31788,"sources":31789,"stem":31790,"tags":31791,"type":6050,"updated":677,"__hash__":31795},"topics\u002Ftopics\u002Fnarodni-duchod.md",{"type":9,"value":21922,"toc":31748},[21923,21926,21928,22051,22186,22190,22193,22306,22310,22338,22385,22388,22454,22499,22502,22528,22559,22563,22567,22611,22655,22716,22771,22774,22778,22781,22828,22925,23031,23037,23114,23143,23282,23286,23315,23365,23512,23602,23606,23632,23670,23697,23735,23797,23872,23950,24008,24074,24118,24122,24180,24229,24274,24487,24607,24613,24617,24640,24644,24651,24655,24686,24721,24725,24775,24863,24905,24926,24988,25048,25052,25123,25191,25263,25378,25426,25430,25433,25474,25513,25536,25650,25814,25822,25849,25879,25882,25959,26112,26196,26535,26539,26663,26799,26935,26988,26991,27241,27322,27326,27329,27387,27419,27422,27471,27474,27545,27741,27745,27896,28126,28164,28217,28262,28265,28321,28370,28574,28664,28668,28684,28691,28860,28864,28935,29016,29096,29175,29321,29409,29413,29596,29727,29772,29869,29873,30612,30614,31665,31667],[12,21924,936],{"id":21925},"národní-důchod",[115,21927,16046],{"id":16045},[724,21929,21930,21931,1989,21935,21938,21939,1989,21942,21955,21956,21959,21960,21963,21964,21967,21968,21970,21971,1989,21973,21990,21991,22008,22009,22012,22013,2162],{},"Kapitola 7 ",[207,21932,21934],{"className":21933,"dataFsResolvedFilePath":6019,"href":6020},[210],"Matematické ekonomie",[38,21936,21937],{},"přechází z mikroekonomie do makroekonomie",": předmětem zkoumání už není jedna firma, ale celá národní ekonomika popsaná ",[38,21940,21941],{},"národním důchodem",[883,21943,21945],{"className":21944},[886],[888,21946,21947],{"xmlns":890},[892,21948,21949,21953],{},[895,21950,21951],{},[898,21952,13170],{},[902,21954,13170],{"encoding":904},". Budují se postupně bohatší modely — ",[38,21957,21958],{},"C-I"," (jen spotřeba a investice) → ",[38,21961,21962],{},"C-I-G"," (přidá vládu a zdanění) → ",[38,21965,21966],{},"C-I-G-X"," (otevře ekonomiku o čistý export) → ",[38,21969,16051],{}," (propojí trh zboží s trhem peněz přes úrokovou míru). V každém modelu hledáme ",[38,21972,17923],{},[883,21974,21976],{"className":21975},[886],[888,21977,21978],{"xmlns":890},[892,21979,21980,21988],{},[895,21981,21982],{},[1824,21983,21984,21986],{},[898,21985,13170],{},[898,21987,1818],{},[902,21989,17941],{"encoding":904}," jako řešení soustavy lineárních rovnic; citlivost ",[883,21992,21994],{"className":21993},[886],[888,21995,21996],{"xmlns":890},[892,21997,21998,22006],{},[895,21999,22000],{},[1824,22001,22002,22004],{},[898,22003,13170],{},[898,22005,1818],{},[902,22007,17941],{"encoding":904}," na exogenní veličiny popisují ",[38,22010,22011],{},"multiplikátory"," (zejména Keynesův multiplikátor investic ",[883,22014,22016],{"className":22015},[886],[888,22017,22018],{"xmlns":890},[892,22019,22020,22048],{},[895,22021,22022,22024,22026,22028,22030,22032,22034,22036,22038,22040,22042,22044,22046],{},[1765,22023,1945],{},[898,22025,8726],{"mathvariant":1969},[1761,22027,1915],{"stretchy":1821},[1765,22029,1945],{},[1761,22031,1885],{},[898,22033,207],{},[1761,22035,1920],{"stretchy":1821},[1761,22037,1909],{},[1765,22039,1945],{},[898,22041,8726],{"mathvariant":1969},[898,22043,6889],{},[898,22045,1839],{},[898,22047,1912],{},[902,22049,22050],{"encoding":904},"1\u002F(1-a) = 1\u002FMPS",[1636,22052,22053],{},[724,22054,22055,22057,22058,22061,22062,22080,22081,22111,22112,22159,22160,22162,22163,22185],{},[883,22056,1642],{}," Intuice\n",[38,22059,22060],{},"Makroekonomie je zrcadlovým obrazem mikroekonomie"," na úrovni celé ekonomiky. Mezní sklon ke spotřebě ",[883,22063,22065],{"className":22064},[886],[888,22066,22067],{"xmlns":890},[892,22068,22069,22077],{},[895,22070,22071,22073,22075],{},[898,22072,6889],{},[898,22074,1839],{},[898,22076,6849],{},[902,22078,22079],{"encoding":904},"MPC"," je „ta část dodatečné korunky důchodu, kterou domácnost utratí“; zbytek ",[883,22082,22084],{"className":22083},[886],[888,22085,22086],{"xmlns":890},[892,22087,22088,22108],{},[895,22089,22090,22092,22094,22096,22098,22100,22102,22104,22106],{},[898,22091,6889],{},[898,22093,1839],{},[898,22095,1912],{},[1761,22097,1909],{},[1765,22099,1945],{},[1761,22101,1885],{},[898,22103,6889],{},[898,22105,1839],{},[898,22107,6849],{},[902,22109,22110],{"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 ",[883,22113,22115],{"className":22114},[886],[888,22116,22117],{"xmlns":890},[892,22118,22119,22156],{},[895,22120,22121,22123,22125,22127,22129,22135,22137,22140,22142,22144,22146,22148,22150,22152,22154],{},[1765,22122,1945],{},[1761,22124,1964],{},[898,22126,207],{},[1761,22128,1964],{},[1824,22130,22131,22133],{},[898,22132,207],{},[1765,22134,2296],{},[1761,22136,1964],{},[1761,22138,22139],{},"⋯",[1761,22141,1909],{},[1765,22143,1945],{},[898,22145,8726],{"mathvariant":1969},[1761,22147,1915],{"stretchy":1821},[1765,22149,1945],{},[1761,22151,1885],{},[898,22153,207],{},[1761,22155,1920],{"stretchy":1821},[902,22157,22158],{"encoding":904},"1 + a + a^2 + \\dots = 1\u002F(1-a)","). ",[38,22161,16051],{}," 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 ",[883,22164,22166],{"className":22165},[886],[888,22167,22168],{"xmlns":890},[892,22169,22170,22182],{},[895,22171,22172,22174,22176,22178,22180],{},[1761,22173,1915],{"stretchy":1821},[898,22175,13170],{},[1761,22177,1834],{"separator":1833},[898,22179,1719],{},[1761,22181,1920],{"stretchy":1821},[902,22183,22184],{"encoding":904},"(Y, r)"," jsou oba trhy v rovnováze současně.",[115,22187,22189],{"id":22188},"úvod-cílové-znalosti-kapitoly-7","Úvod — cílové znalosti kapitoly 7",[724,22191,22192],{},"Po prostudování kapitoly by čtenář měl umět:",[120,22194,22195,22198,22201,22204,22207,22210,22213,22303],{},[123,22196,22197],{},"popsat zjednodušený model národní ekonomiky,",[123,22199,22200],{},"formulovat pojmy funkcí spotřeby a úspor spolu s jejich základními vlastnostmi,",[123,22202,22203],{},"popsat lineární model spotřeby a úspor,",[123,22205,22206],{},"stanovit mezní sklony ke spotřebě a úsporám,",[123,22208,22209],{},"vymezit pojem makroekonomické rovnováhy ve vztahu k agregátní poptávce a nabídce,",[123,22211,22212],{},"vyložit pojmy křivek agregátní poptávky, agregátní nabídky a rovnovážného bodu,",[123,22214,22215,22216,1343,22233,1343,22255,2068,22280,22302],{},"popsat modely ",[883,22217,22219],{"className":22218},[886],[888,22220,22221],{"xmlns":890},[892,22222,22223,22231],{},[895,22224,22225,22227,22229],{},[898,22226,6849],{},[2761,22228,16328],{},[898,22230,16222],{},[902,22232,16333],{"encoding":904},[883,22234,22236],{"className":22235},[886],[888,22237,22238],{"xmlns":890},[892,22239,22240,22252],{},[895,22241,22242,22244,22246,22248,22250],{},[898,22243,6849],{},[2761,22245,16328],{},[898,22247,16222],{},[2761,22249,16328],{},[898,22251,16151],{},[902,22253,22254],{"encoding":904},"C\\text{-}I\\text{-}G",[883,22256,22258],{"className":22257},[886],[888,22259,22260],{"xmlns":890},[892,22261,22262,22278],{},[895,22263,22264,22266,22268,22270,22272,22274,22276],{},[898,22265,6849],{},[2761,22267,16328],{},[898,22269,16222],{},[2761,22271,16328],{},[898,22273,16151],{},[2761,22275,16328],{},[898,22277,16358],{},[902,22279,16361],{"encoding":904},[883,22281,22283],{"className":22282},[886],[888,22284,22285],{"xmlns":890},[892,22286,22287,22299],{},[895,22288,22289,22291,22293,22295,22297],{},[898,22290,16222],{},[898,22292,1912],{},[2761,22294,16328],{},[898,22296,13835],{},[898,22298,6889],{},[902,22300,22301],{"encoding":904},"IS\\text{-}LM"," národních ekonomik a vypočítat rovnovážné veličiny,",[123,22304,22305],{},"formulovat a stanovit základní makroekonomické multiplikátory.",[115,22307,22309],{"id":22308},"gnp-a-národní-důchod","GNP a národní důchod",[724,22311,22312,1989,22315,3927,22334,22337],{},[38,22313,22314],{},"Hrubý národní produkt",[883,22316,22318],{"className":22317},[886],[888,22319,22320],{"xmlns":890},[892,22321,22322,22331],{},[895,22323,22324,22326,22329],{},[898,22325,16151],{},[898,22327,22328],{},"N",[898,22330,1839],{},[902,22332,22333],{"encoding":904},"GNP",[614,22335,22336],{},"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:",[724,22339,22340],{},[883,22341,22343],{"className":22342},[886],[888,22344,22345],{"xmlns":890},[892,22346,22347,22382],{},[895,22348,22349,22351,22353,22355,22357,22359,22361,22363,22365,22367,22369,22371,22373,22375,22377,22380],{},[898,22350,16151],{},[898,22352,22328],{},[898,22354,1839],{},[1761,22356,1909],{},[898,22358,6849],{},[1761,22360,1964],{},[898,22362,16222],{},[1761,22364,1964],{},[898,22366,16151],{},[1761,22368,1964],{},[898,22370,16358],{},[1761,22372,1834],{"separator":1833},[3315,22374],{"width":3317},[1761,22376,1915],{"stretchy":1821},[1765,22378,22379],{},"7.1",[1761,22381,1920],{"stretchy":1821},[902,22383,22384],{"encoding":904},"GNP = C + I + G + X, \\qquad (7.1)",[724,22386,22387],{},"kde",[120,22389,22390,22406,22422,22438],{},[123,22391,22392,22405],{},[883,22393,22395],{"className":22394},[886],[888,22396,22397],{"xmlns":890},[892,22398,22399,22403],{},[895,22400,22401],{},[898,22402,6849],{},[902,22404,6849],{"encoding":904}," — výdaje domácností na spotřebu,",[123,22407,22408,22421],{},[883,22409,22411],{"className":22410},[886],[888,22412,22413],{"xmlns":890},[892,22414,22415,22419],{},[895,22416,22417],{},[898,22418,16222],{},[902,22420,16222],{"encoding":904}," — hrubé domácí investice,",[123,22423,22424,22437],{},[883,22425,22427],{"className":22426},[886],[888,22428,22429],{"xmlns":890},[892,22430,22431,22435],{},[895,22432,22433],{},[898,22434,16151],{},[902,22436,16151],{"encoding":904}," — vládní výdaje,",[123,22439,22440,22453],{},[883,22441,22443],{"className":22442},[886],[888,22444,22445],{"xmlns":890},[892,22446,22447,22451],{},[895,22448,22449],{},[898,22450,16358],{},[902,22452,16358],{"encoding":904}," — čistý export.",[724,22455,22456,22457,22474,22475,22478,22479,1989,22482,3927,22495,22498],{},"K měření ",[883,22458,22460],{"className":22459},[886],[888,22461,22462],{"xmlns":890},[892,22463,22464,22472],{},[895,22465,22466,22468,22470],{},[898,22467,16151],{},[898,22469,22328],{},[898,22471,1839],{},[902,22473,22333],{"encoding":904}," se užívá ",[38,22476,22477],{},"důchodová metoda",". Jejím hlavním konstrukčním prvkem je ",[38,22480,22481],{},"národní důchod",[883,22483,22485],{"className":22484},[886],[888,22486,22487],{"xmlns":890},[892,22488,22489,22493],{},[895,22490,22491],{},[898,22492,13170],{},[902,22494,13170],{"encoding":904},[614,22496,22497],{},"national income",") — součet důchodů všech vrstev domácností, tj. tok důchodů od firem k domácnostem jako platba za pronájem výrobních faktorů.",[724,22500,22501],{},"Pro tvorbu základních makroekonomických modelů se zjednodušeně ztotožňuje hrubý národní produkt s národním důchodem (rovněž s agregátní poptávkou):",[724,22503,22504],{},[883,22505,22507],{"className":22506},[886],[888,22508,22509],{"xmlns":890},[892,22510,22511,22525],{},[895,22512,22513,22515,22517,22519,22521,22523],{},[898,22514,16151],{},[898,22516,22328],{},[898,22518,1839],{},[1761,22520,6803],{},[898,22522,13170],{},[1761,22524,1834],{"separator":1833},[902,22526,22527],{"encoding":904},"GNP \\approx Y,",[724,22529,22530,22531,3927,22534,22537,22538,22551,22552,22555,22556,1741],{},"a užívá se společného názvu ",[38,22532,22533],{},"důchod",[614,22535,22536],{},"income",") s označením ",[883,22539,22541],{"className":22540},[886],[888,22542,22543],{"xmlns":890},[892,22544,22545,22549],{},[895,22546,22547],{},[898,22548,13170],{},[902,22550,13170],{"encoding":904},". Domácnosti důchod použijí ke ",[38,22553,22554],{},"spotřebě"," zboží a služeb nebo ke tvorbě ",[38,22557,22558],{},"úspor",[115,22560,22562],{"id":22561},"spotřeba-a-úspory","Spotřeba a úspory",[198,22564,22566],{"id":22565},"funkce-spotřeby-a-úspor","Funkce spotřeby a úspor",[724,22568,22569,22570,22583,22584,22597,22598,2506],{},"Jak spotřeba ",[883,22571,22573],{"className":22572},[886],[888,22574,22575],{"xmlns":890},[892,22576,22577,22581],{},[895,22578,22579],{},[898,22580,6849],{},[902,22582,6849],{"encoding":904},", tak úspory ",[883,22585,22587],{"className":22586},[886],[888,22588,22589],{"xmlns":890},[892,22590,22591,22595],{},[895,22592,22593],{},[898,22594,1912],{},[902,22596,1912],{"encoding":904}," závisejí na důchodu ",[883,22599,22601],{"className":22600},[886],[888,22602,22603],{"xmlns":890},[892,22604,22605,22609],{},[895,22606,22607],{},[898,22608,13170],{},[902,22610,13170],{"encoding":904},[724,22612,22613],{},[883,22614,22616],{"className":22615},[886],[888,22617,22618],{"xmlns":890},[892,22619,22620,22652],{},[895,22621,22622,22624,22626,22628,22630,22632,22634,22636,22638,22640,22642,22644,22646,22648,22650],{},[898,22623,6849],{},[1761,22625,1909],{},[898,22627,6849],{},[1761,22629,1915],{"stretchy":1821},[898,22631,13170],{},[1761,22633,1920],{"stretchy":1821},[1761,22635,1834],{"separator":1833},[3315,22637],{"width":3317},[898,22639,1912],{},[1761,22641,1909],{},[898,22643,1912],{},[1761,22645,1915],{"stretchy":1821},[898,22647,13170],{},[1761,22649,1920],{"stretchy":1821},[898,22651,1741],{"mathvariant":1969},[902,22653,22654],{"encoding":904},"C = C(Y), \\qquad S = S(Y).",[724,22656,22657,12146,22676,3927,22679,5991,22682,12146,22702,3927,22705,22708,22709,2068,22712,22715],{},[883,22658,22660],{"className":22659},[886],[888,22661,22662],{"xmlns":890},[892,22663,22664,22674],{},[895,22665,22666,22668,22670,22672],{},[898,22667,6849],{},[1761,22669,1915],{"stretchy":1821},[898,22671,13170],{},[1761,22673,1920],{"stretchy":1821},[902,22675,18254],{"encoding":904},[38,22677,22678],{},"funkce spotřeby",[614,22680,22681],{},"consumption function",[883,22683,22685],{"className":22684},[886],[888,22686,22687],{"xmlns":890},[892,22688,22689,22699],{},[895,22690,22691,22693,22695,22697],{},[898,22692,1912],{},[1761,22694,1915],{"stretchy":1821},[898,22696,13170],{},[1761,22698,1920],{"stretchy":1821},[902,22700,22701],{"encoding":904},"S(Y)",[38,22703,22704],{},"funkce úspor",[614,22706,22707],{},"savings function","); jejich grafy se nazývají ",[38,22710,22711],{},"křivka spotřeby",[38,22713,22714],{},"křivka úspor",". Platí základní identita",[724,22717,22718],{},[883,22719,22721],{"className":22720},[886],[888,22722,22723],{"xmlns":890},[892,22724,22725,22768],{},[895,22726,22727,22729,22731,22733,22735,22737,22739,22741,22743,22745,22747,22749,22751,22753,22755,22757,22759,22761,22763,22766],{},[898,22728,13170],{},[1761,22730,1909],{},[898,22732,6849],{},[1761,22734,1964],{},[898,22736,1912],{},[1761,22738,1909],{},[898,22740,6849],{},[1761,22742,1915],{"stretchy":1821},[898,22744,13170],{},[1761,22746,1920],{"stretchy":1821},[1761,22748,1964],{},[898,22750,1912],{},[1761,22752,1915],{"stretchy":1821},[898,22754,13170],{},[1761,22756,1920],{"stretchy":1821},[898,22758,1741],{"mathvariant":1969},[3315,22760],{"width":3317},[1761,22762,1915],{"stretchy":1821},[1765,22764,22765],{},"7.2",[1761,22767,1920],{"stretchy":1821},[902,22769,22770],{"encoding":904},"Y = C + S = C(Y) + S(Y). \\qquad (7.2)",[724,22772,22773],{},"Známe-li jednu z funkcí, je tím určena i druhá. Obě funkce jsou rostoucí (s růstem důchodu roste spotřeba i úspory).",[198,22775,22777],{"id":22776},"lineární-model-spotřeby-a-úspor","Lineární model spotřeby a úspor",[724,22779,22780],{},"Nejjednodušší model předpokládá lineární tvar",[724,22782,22783],{},[883,22784,22786],{"className":22785},[886],[888,22787,22788],{"xmlns":890},[892,22789,22790,22825],{},[895,22791,22792,22794,22796,22798,22800,22802,22804,22806,22808,22810,22812,22814,22816,22818,22820,22823],{},[898,22793,6849],{},[1761,22795,1909],{},[898,22797,6849],{},[1761,22799,1915],{"stretchy":1821},[898,22801,13170],{},[1761,22803,1920],{"stretchy":1821},[1761,22805,1909],{},[898,22807,207],{},[898,22809,13170],{},[1761,22811,1964],{},[898,22813,4302],{},[1761,22815,1834],{"separator":1833},[3315,22817],{"width":3317},[1761,22819,1915],{"stretchy":1821},[1765,22821,22822],{},"7.3",[1761,22824,1920],{"stretchy":1821},[902,22826,22827],{"encoding":904},"C = C(Y) = aY + b, \\qquad (7.3)",[724,22829,8364,22830,2068,22848,22870,22871,22911,22912,1741],{},[883,22831,22833],{"className":22832},[886],[888,22834,22835],{"xmlns":890},[892,22836,22837,22845],{},[895,22838,22839,22841,22843],{},[898,22840,4302],{},[1761,22842,1763],{},[1765,22844,1767],{},[902,22846,22847],{"encoding":904},"b > 0",[883,22849,22851],{"className":22850},[886],[888,22852,22853],{"xmlns":890},[892,22854,22855,22867],{},[895,22856,22857,22859,22861,22863,22865],{},[1765,22858,1767],{},[1761,22860,2058],{},[898,22862,207],{},[1761,22864,2058],{},[1765,22866,1945],{},[902,22868,22869],{"encoding":904},"0 \u003C a \u003C 1",". Směrnice ",[883,22872,22874],{"className":22873},[886],[888,22875,22876],{"xmlns":890},[892,22877,22878,22908],{},[895,22879,22880,22882,22884,22891,22893,22896,22898,22900,22902,22904,22906],{},[898,22881,207],{},[1761,22883,1909],{},[895,22885,22886,22889],{},[898,22887,22888],{"mathvariant":1969},"t",[898,22890,15079],{"mathvariant":1969},[2761,22892,7057],{},[898,22894,22895],{},"α",[1761,22897,1909],{},[898,22899,6959],{"mathvariant":1969},[898,22901,6849],{},[898,22903,8726],{"mathvariant":1969},[898,22905,6959],{"mathvariant":1969},[898,22907,13170],{},[902,22909,22910],{"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 ",[883,22913,22915],{"className":22914},[886],[888,22916,22917],{"xmlns":890},[892,22918,22919,22923],{},[895,22920,22921],{},[898,22922,13170],{},[902,22924,13170],{"encoding":904},[724,22926,22927],{},[614,22928,22929,22930,22954,22955,22993,22994,23010,23011,1741],{},"Obrázek 7.1 — Přímka spotřeby ",[883,22931,22933],{"className":22932},[886],[888,22934,22935],{"xmlns":890},[892,22936,22937,22951],{},[895,22938,22939,22941,22943,22945,22947,22949],{},[898,22940,6849],{},[1761,22942,1909],{},[898,22944,207],{},[898,22946,13170],{},[1761,22948,1964],{},[898,22950,4302],{},[902,22952,22953],{"encoding":904},"C = aY + b"," se směrnicí ",[883,22956,22958],{"className":22957},[886],[888,22959,22960],{"xmlns":890},[892,22961,22962,22990],{},[895,22963,22964,22966,22968,22974,22976,22978,22980,22982,22984,22986,22988],{},[898,22965,207],{},[1761,22967,1909],{},[895,22969,22970,22972],{},[898,22971,22888],{"mathvariant":1969},[898,22973,15079],{"mathvariant":1969},[2761,22975,7057],{},[898,22977,22895],{},[1761,22979,1909],{},[898,22981,6959],{"mathvariant":1969},[898,22983,6849],{},[898,22985,8726],{"mathvariant":1969},[898,22987,6959],{"mathvariant":1969},[898,22989,13170],{},[902,22991,22992],{"encoding":904},"a = \\mathrm{tg}\\,\\alpha = \\Delta C\u002F\\Delta Y","; znázornění ",[883,22995,22997],{"className":22996},[886],[888,22998,22999],{"xmlns":890},[892,23000,23001,23007],{},[895,23002,23003,23005],{},[898,23004,6959],{"mathvariant":1969},[898,23006,6849],{},[902,23008,23009],{"encoding":904},"\\Delta C"," při jednotkovém přírůstku ",[883,23012,23014],{"className":23013},[886],[888,23015,23016],{"xmlns":890},[892,23017,23018,23028],{},[895,23019,23020,23022,23024,23026],{},[898,23021,6959],{"mathvariant":1969},[898,23023,13170],{},[1761,23025,1909],{},[1765,23027,1945],{},[902,23029,23030],{"encoding":904},"\\Delta Y = 1",[724,23032,23033,23034,2506],{},"Dosazením do (7.2) plyne ",[38,23035,23036],{},"lineární model úspor",[724,23038,23039],{},[883,23040,23042],{"className":23041},[886],[888,23043,23044],{"xmlns":890},[892,23045,23046,23111],{},[895,23047,23048,23050,23052,23054,23056,23058,23060,23062,23064,23066,23068,23070,23072,23074,23076,23078,23080,23082,23084,23086,23088,23090,23092,23094,23096,23098,23100,23102,23104,23106,23109],{},[898,23049,1912],{},[1761,23051,1909],{},[898,23053,13170],{},[1761,23055,1885],{},[898,23057,6849],{},[1761,23059,1915],{"stretchy":1821},[898,23061,13170],{},[1761,23063,1920],{"stretchy":1821},[1761,23065,1909],{},[898,23067,13170],{},[1761,23069,1885],{},[1761,23071,1915],{"stretchy":1821},[898,23073,207],{},[898,23075,13170],{},[1761,23077,1964],{},[898,23079,4302],{},[1761,23081,1920],{"stretchy":1821},[1761,23083,1909],{},[1761,23085,1915],{"stretchy":1821},[1765,23087,1945],{},[1761,23089,1885],{},[898,23091,207],{},[1761,23093,1920],{"stretchy":1821},[898,23095,13170],{},[1761,23097,1885],{},[898,23099,4302],{},[898,23101,1741],{"mathvariant":1969},[3315,23103],{"width":3317},[1761,23105,1915],{"stretchy":1821},[1765,23107,23108],{},"7.4",[1761,23110,1920],{"stretchy":1821},[902,23112,23113],{"encoding":904},"S = Y - C(Y) = Y - (aY + b) = (1 - a)Y - b. \\qquad (7.4)",[724,23115,23116,23117,2162],{},"Úspory jsou také lineární a „pomalu rostoucí“ (protože ",[883,23118,23120],{"className":23119},[886],[888,23121,23122],{"xmlns":890},[892,23123,23124,23140],{},[895,23125,23126,23128,23130,23132,23134,23136,23138],{},[1765,23127,1767],{},[1761,23129,2058],{},[1765,23131,1945],{},[1761,23133,1885],{},[898,23135,207],{},[1761,23137,2058],{},[1765,23139,1945],{},[902,23141,23142],{"encoding":904},"0 \u003C 1 - a \u003C 1",[724,23144,23145],{},[614,23146,23147,23148,2068,23171,23203,23204,6699,23217,23247,23248,6699,23266,1741],{},"Obrázek 7.2 — Přímky ",[883,23149,23151],{"className":23150},[886],[888,23152,23153],{"xmlns":890},[892,23154,23155,23169],{},[895,23156,23157,23159,23161,23163,23165,23167],{},[898,23158,6849],{},[1761,23160,1909],{},[898,23162,207],{},[898,23164,13170],{},[1761,23166,1964],{},[898,23168,4302],{},[902,23170,22953],{"encoding":904},[883,23172,23174],{"className":23173},[886],[888,23175,23176],{"xmlns":890},[892,23177,23178,23200],{},[895,23179,23180,23182,23184,23186,23188,23190,23192,23194,23196,23198],{},[898,23181,1912],{},[1761,23183,1909],{},[1761,23185,1915],{"stretchy":1821},[1765,23187,1945],{},[1761,23189,1885],{},[898,23191,207],{},[1761,23193,1920],{"stretchy":1821},[898,23195,13170],{},[1761,23197,1885],{},[898,23199,4302],{},[902,23201,23202],{"encoding":904},"S = (1-a)Y - b",". Přímka úspor protíná osu ",[883,23205,23207],{"className":23206},[886],[888,23208,23209],{"xmlns":890},[892,23210,23211,23215],{},[895,23212,23213],{},[898,23214,13170],{},[902,23216,13170],{"encoding":904},[883,23218,23220],{"className":23219},[886],[888,23221,23222],{"xmlns":890},[892,23223,23224,23244],{},[895,23225,23226,23228,23230,23232,23234,23236,23238,23240,23242],{},[898,23227,13170],{},[1761,23229,1909],{},[898,23231,4302],{},[898,23233,8726],{"mathvariant":1969},[1761,23235,1915],{"stretchy":1821},[1765,23237,1945],{},[1761,23239,1885],{},[898,23241,207],{},[1761,23243,1920],{"stretchy":1821},[902,23245,23246],{"encoding":904},"Y = b\u002F(1-a)"," a osu ",[883,23249,23251],{"className":23250},[886],[888,23252,23253],{"xmlns":890},[892,23254,23255,23263],{},[895,23256,23257,23259,23261],{},[898,23258,6849],{},[1761,23260,1834],{"separator":1833},[898,23262,1912],{},[902,23264,23265],{"encoding":904},"C, S",[883,23267,23269],{"className":23268},[886],[888,23270,23271],{"xmlns":890},[892,23272,23273,23279],{},[895,23274,23275,23277],{},[1761,23276,1885],{},[898,23278,4302],{},[902,23280,23281],{"encoding":904},"-b",[198,23283,23285],{"id":23284},"příklad-71","Příklad 7.1",[724,23287,23288,23289,23314],{},"Pro spotřebu ",[883,23290,23292],{"className":23291},[886],[888,23293,23294],{"xmlns":890},[892,23295,23296,23311],{},[895,23297,23298,23300,23302,23305,23307,23309],{},[898,23299,6849],{},[1761,23301,1909],{},[1765,23303,23304],{},"0,4",[898,23306,13170],{},[1761,23308,1964],{},[1765,23310,2633],{},[902,23312,23313],{"encoding":904},"C = 0{,}4Y + 10"," jsou úspory",[724,23316,23317],{},[883,23318,23320],{"className":23319},[886],[888,23321,23322],{"xmlns":890},[892,23323,23324,23362],{},[895,23325,23326,23328,23330,23332,23334,23336,23338,23340,23342,23344,23346,23348,23350,23352,23355,23357,23359],{},[898,23327,1912],{},[1761,23329,1909],{},[898,23331,13170],{},[1761,23333,1885],{},[898,23335,6849],{},[1761,23337,1909],{},[898,23339,13170],{},[1761,23341,1885],{},[1765,23343,23304],{},[898,23345,13170],{},[1761,23347,1885],{},[1765,23349,2633],{},[1761,23351,1909],{},[1765,23353,23354],{},"0,6",[898,23356,13170],{},[1761,23358,1885],{},[1765,23360,23361],{},"10.",[902,23363,23364],{"encoding":904},"S = Y - C = Y - 0{,}4Y - 10 = 0{,}6Y - 10.",[724,23366,23367],{},[614,23368,23369,23370,2068,23393,23417,23418,12146,23431,23455,23456,12146,23473,23489,23490,1741],{},"Obrázek 7.3 — Přímky ",[883,23371,23373],{"className":23372},[886],[888,23374,23375],{"xmlns":890},[892,23376,23377,23391],{},[895,23378,23379,23381,23383,23385,23387,23389],{},[898,23380,6849],{},[1761,23382,1909],{},[1765,23384,23304],{},[898,23386,13170],{},[1761,23388,1964],{},[1765,23390,2633],{},[902,23392,23313],{"encoding":904},[883,23394,23396],{"className":23395},[886],[888,23397,23398],{"xmlns":890},[892,23399,23400,23414],{},[895,23401,23402,23404,23406,23408,23410,23412],{},[898,23403,1912],{},[1761,23405,1909],{},[1765,23407,23354],{},[898,23409,13170],{},[1761,23411,1885],{},[1765,23413,2633],{},[902,23415,23416],{"encoding":904},"S = 0{,}6Y - 10","; průsečík přímky úspor s osou ",[883,23419,23421],{"className":23420},[886],[888,23422,23423],{"xmlns":890},[892,23424,23425,23429],{},[895,23426,23427],{},[898,23428,13170],{},[902,23430,13170],{"encoding":904},[883,23432,23434],{"className":23433},[886],[888,23435,23436],{"xmlns":890},[892,23437,23438,23452],{},[895,23439,23440,23442,23445],{},[1761,23441,6803],{},[1765,23443,23444],{},"16,",[2770,23446,23447,23449],{"accent":1833},[1765,23448,2340],{},[1761,23450,23451],{},"ˉ",[902,23453,23454],{"encoding":904},"\\approx 16{,}\\bar{6}",", s osou ",[883,23457,23459],{"className":23458},[886],[888,23460,23461],{"xmlns":890},[892,23462,23463,23471],{},[895,23464,23465,23467,23469],{},[898,23466,6849],{},[1761,23468,1834],{"separator":1833},[898,23470,1912],{},[902,23472,23265],{"encoding":904},[883,23474,23476],{"className":23475},[886],[888,23477,23478],{"xmlns":890},[892,23479,23480,23486],{},[895,23481,23482,23484],{},[1761,23483,1885],{},[1765,23485,2633],{},[902,23487,23488],{"encoding":904},"-10","; přímka spotřeby prochází bodem ",[883,23491,23493],{"className":23492},[886],[888,23494,23495],{"xmlns":890},[892,23496,23497,23509],{},[895,23498,23499,23501,23503,23505,23507],{},[1761,23500,1915],{"stretchy":1821},[1765,23502,1767],{},[1761,23504,1834],{"separator":1833},[1765,23506,2633],{},[1761,23508,1920],{"stretchy":1821},[902,23510,23511],{"encoding":904},"(0, 10)",[724,23513,23514,23515,12146,23533,23563,23564,3927,23567,23570,23571,12146,23595,3927,23598,23601],{},"Funkce úspor může nabývat záporných hodnot — pro ",[883,23516,23518],{"className":23517},[886],[888,23519,23520],{"xmlns":890},[892,23521,23522,23530],{},[895,23523,23524,23526,23528],{},[898,23525,13170],{},[1761,23527,1909],{},[1765,23529,1767],{},[902,23531,23532],{"encoding":904},"Y = 0",[883,23534,23536],{"className":23535},[886],[888,23537,23538],{"xmlns":890},[892,23539,23540,23560],{},[895,23541,23542,23544,23546,23548,23550,23552,23554,23556,23558],{},[898,23543,1912],{},[1761,23545,1915],{"stretchy":1821},[1765,23547,1767],{},[1761,23549,1920],{"stretchy":1821},[1761,23551,1909],{},[1761,23553,1885],{},[898,23555,4302],{},[1761,23557,2058],{},[1765,23559,1767],{},[902,23561,23562],{"encoding":904},"S(0) = -b \u003C 0","; hovoří se o ",[38,23565,23566],{},"autonomních úsporách",[614,23568,23569],{},"autonomous savings","). Analogicky ",[883,23572,23574],{"className":23573},[886],[888,23575,23576],{"xmlns":890},[892,23577,23578,23592],{},[895,23579,23580,23582,23584,23586,23588,23590],{},[898,23581,6849],{},[1761,23583,1915],{"stretchy":1821},[1765,23585,1767],{},[1761,23587,1920],{"stretchy":1821},[1761,23589,1909],{},[898,23591,4302],{},[902,23593,23594],{"encoding":904},"C(0) = b",[38,23596,23597],{},"autonomní spotřeba",[614,23599,23600],{},"autonomous consumption",") — spotřeba při nulovém důchodu krytá dřívějšími úsporami.",[115,23603,23605],{"id":23604},"mezní-sklon-ke-spotřebě-mpc-a-k-úsporám-mps","Mezní sklon ke spotřebě (MPC) a k úsporám (MPS)",[724,23607,23608,1989,23611,3927,23628,23631],{},[38,23609,23610],{},"Mezní sklon ke spotřebě",[883,23612,23614],{"className":23613},[886],[888,23615,23616],{"xmlns":890},[892,23617,23618,23626],{},[895,23619,23620,23622,23624],{},[898,23621,6889],{},[898,23623,1839],{},[898,23625,6849],{},[902,23627,22079],{"encoding":904},[614,23629,23630],{},"marginal propensity to consume",") je derivace spotřeby podle důchodu:",[724,23633,23634],{},[883,23635,23637],{"className":23636},[886],[888,23638,23639],{"xmlns":890},[892,23640,23641,23667],{},[895,23642,23643,23645,23647,23649,23651,23665],{},[898,23644,6889],{},[898,23646,1839],{},[898,23648,6849],{},[1761,23650,1909],{},[4379,23652,23653,23659],{},[895,23654,23655,23657],{},[898,23656,4346],{"mathvariant":1969},[898,23658,6849],{},[895,23660,23661,23663],{},[898,23662,4346],{"mathvariant":1969},[898,23664,13170],{},[898,23666,1741],{"mathvariant":1969},[902,23668,23669],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y}.",[724,23671,23672,1989,23675,3927,23693,23696],{},[38,23673,23674],{},"Mezní sklon k úsporám",[883,23676,23678],{"className":23677},[886],[888,23679,23680],{"xmlns":890},[892,23681,23682,23690],{},[895,23683,23684,23686,23688],{},[898,23685,6889],{},[898,23687,1839],{},[898,23689,1912],{},[902,23691,23692],{"encoding":904},"MPS",[614,23694,23695],{},"marginal propensity to save",") je derivace úspor podle důchodu:",[724,23698,23699],{},[883,23700,23702],{"className":23701},[886],[888,23703,23704],{"xmlns":890},[892,23705,23706,23732],{},[895,23707,23708,23710,23712,23714,23716,23730],{},[898,23709,6889],{},[898,23711,1839],{},[898,23713,1912],{},[1761,23715,1909],{},[4379,23717,23718,23724],{},[895,23719,23720,23722],{},[898,23721,4346],{"mathvariant":1969},[898,23723,1912],{},[895,23725,23726,23728],{},[898,23727,4346],{"mathvariant":1969},[898,23729,13170],{},[898,23731,1741],{"mathvariant":1969},[902,23733,23734],{"encoding":904},"MPS = \\frac{\\mathrm{d}S}{\\mathrm{d}Y}.",[724,23736,23737,23738,23796],{},"Z (7.2) plyne ",[883,23739,23741],{"className":23740},[886],[888,23742,23743],{"xmlns":890},[892,23744,23745,23793],{},[895,23746,23747,23761,23763,23777,23779],{},[4379,23748,23749,23755],{},[895,23750,23751,23753],{},[898,23752,4346],{"mathvariant":1969},[898,23754,13170],{},[895,23756,23757,23759],{},[898,23758,4346],{"mathvariant":1969},[898,23760,13170],{},[1761,23762,1909],{},[4379,23764,23765,23771],{},[895,23766,23767,23769],{},[898,23768,4346],{"mathvariant":1969},[898,23770,6849],{},[895,23772,23773,23775],{},[898,23774,4346],{"mathvariant":1969},[898,23776,13170],{},[1761,23778,1964],{},[4379,23780,23781,23787],{},[895,23782,23783,23785],{},[898,23784,4346],{"mathvariant":1969},[898,23786,1912],{},[895,23788,23789,23791],{},[898,23790,4346],{"mathvariant":1969},[898,23792,13170],{},[902,23794,23795],{"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",[724,23798,23799],{},[883,23800,23802],{"className":23801},[886],[888,23803,23804],{"xmlns":890},[892,23805,23806,23869],{},[895,23807,23808,23860,23862,23864,23867],{},[16870,23809,23810],{"notation":16872},[6411,23811,23812],{"scriptlevel":1767,"displaystyle":1821},[6411,23813,23814],{"scriptlevel":1767,"displaystyle":1821},[6411,23815,23816],{"scriptlevel":1767,"displaystyle":1833},[895,23817,23818,23820,23822,23824,23826,23828,23830,23832,23834,23836,23838,23840,23842,23844,23846,23848,23850,23852,23854,23856,23858],{},[898,23819,6889],{},[898,23821,1839],{},[898,23823,6849],{},[1761,23825,1964],{},[898,23827,6889],{},[898,23829,1839],{},[898,23831,1912],{},[1761,23833,1909],{},[1765,23835,1945],{},[1761,23837,1834],{"separator":1833},[3315,23839],{"width":3317},[898,23841,6889],{},[898,23843,1839],{},[898,23845,1912],{},[1761,23847,1909],{},[1765,23849,1945],{},[1761,23851,1885],{},[898,23853,6889],{},[898,23855,1839],{},[898,23857,6849],{},[898,23859,1741],{"mathvariant":1969},[3315,23861],{"width":3317},[1761,23863,1915],{"stretchy":1821},[1765,23865,23866],{},"7.5",[1761,23868,1920],{"stretchy":1821},[902,23870,23871],{"encoding":904},"\\boxed{MPC + MPS = 1, \\qquad MPS = 1 - MPC.} \\qquad (7.5)",[724,23873,23874,1989,23877,23900,23901,2068,23923,23949],{},[38,23875,23876],{},"Pro lineární model",[883,23878,23880],{"className":23879},[886],[888,23881,23882],{"xmlns":890},[892,23883,23884,23898],{},[895,23885,23886,23888,23890,23892,23894,23896],{},[898,23887,6849],{},[1761,23889,1909],{},[898,23891,207],{},[898,23893,13170],{},[1761,23895,1964],{},[898,23897,4302],{},[902,23899,22953],{"encoding":904}," vychází ",[883,23902,23904],{"className":23903},[886],[888,23905,23906],{"xmlns":890},[892,23907,23908,23920],{},[895,23909,23910,23912,23914,23916,23918],{},[898,23911,6889],{},[898,23913,1839],{},[898,23915,6849],{},[1761,23917,1909],{},[898,23919,207],{},[902,23921,23922],{"encoding":904},"MPC = a",[883,23924,23926],{"className":23925},[886],[888,23927,23928],{"xmlns":890},[892,23929,23930,23946],{},[895,23931,23932,23934,23936,23938,23940,23942,23944],{},[898,23933,6889],{},[898,23935,1839],{},[898,23937,1912],{},[1761,23939,1909],{},[1765,23941,1945],{},[1761,23943,1885],{},[898,23945,207],{},[902,23947,23948],{"encoding":904},"MPS = 1 - a"," — tedy směrnice přímek spotřeby a úspor.",[724,23951,23952,23955,23956,23978,23979,24007],{},[38,23953,23954],{},"Interpretace diferenciálem."," Pro pevné ",[883,23957,23959],{"className":23958},[886],[888,23960,23961],{"xmlns":890},[892,23962,23963,23975],{},[895,23964,23965,23967,23969],{},[898,23966,13170],{},[1761,23968,1909],{},[1824,23970,23971,23973],{},[898,23972,13170],{},[1761,23974,8408],{},[902,23976,23977],{"encoding":904},"Y = Y^*"," udává ",[883,23980,23982],{"className":23981},[886],[888,23983,23984],{"xmlns":890},[892,23985,23986,24004],{},[895,23987,23988,23990,23992,23994,23996,24002],{},[898,23989,6889],{},[898,23991,1839],{},[898,23993,6849],{},[1761,23995,1915],{"stretchy":1821},[1824,23997,23998,24000],{},[898,23999,13170],{},[1761,24001,8408],{},[1761,24003,1920],{"stretchy":1821},[902,24005,24006],{"encoding":904},"MPC(Y^*)"," přibližnou změnu spotřeby při jednotkovém přírůstku důchodu:",[724,24009,24010],{},[883,24011,24013],{"className":24012},[886],[888,24014,24015],{"xmlns":890},[892,24016,24017,24071],{},[895,24018,24019,24021,24023,24025,24027,24029,24031,24037,24039,24041,24043,24045,24047,24049,24051,24053,24055,24057,24059,24061,24063,24065,24067,24069],{},[898,24020,6959],{"mathvariant":1969},[898,24022,6849],{},[1761,24024,6803],{},[898,24026,4346],{"mathvariant":1969},[898,24028,6849],{},[1761,24030,1909],{},[1824,24032,24033,24035],{},[898,24034,6849],{},[1761,24036,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,24038,1915],{"stretchy":1821},[898,24040,13170],{},[1761,24042,1920],{"stretchy":1821},[2761,24044,7057],{},[898,24046,4346],{"mathvariant":1969},[898,24048,13170],{},[1761,24050,1909],{},[898,24052,6889],{},[898,24054,1839],{},[898,24056,6849],{},[1761,24058,1915],{"stretchy":1821},[898,24060,13170],{},[1761,24062,1920],{"stretchy":1821},[2761,24064,7057],{},[898,24066,4346],{"mathvariant":1969},[898,24068,13170],{},[898,24070,1741],{"mathvariant":1969},[902,24072,24073],{"encoding":904},"\\Delta C \\approx \\mathrm{d}C = C'(Y)\\,\\mathrm{d}Y = MPC(Y)\\,\\mathrm{d}Y.",[724,24075,24076,24077,24113,24114,24117],{},"Analogicky ",[883,24078,24080],{"className":24079},[886],[888,24081,24082],{"xmlns":890},[892,24083,24084,24110],{},[895,24085,24086,24088,24090,24092,24094,24096,24098,24100,24102,24104,24106,24108],{},[898,24087,6959],{"mathvariant":1969},[898,24089,1912],{},[1761,24091,6803],{},[898,24093,6889],{},[898,24095,1839],{},[898,24097,1912],{},[1761,24099,1915],{"stretchy":1821},[898,24101,13170],{},[1761,24103,1920],{"stretchy":1821},[2761,24105,7057],{},[898,24107,4346],{"mathvariant":1969},[898,24109,13170],{},[902,24111,24112],{"encoding":904},"\\Delta S \\approx MPS(Y)\\,\\mathrm{d}Y",". Viz ",[207,24115,1145],{"className":24116,"dataFsResolvedFilePath":764,"href":765},[210]," a její ekonomická interpretace.",[198,24119,24121],{"id":24120},"příklad-72","Příklad 7.2",[724,24123,23288,24124,24159,24160,24179],{},[883,24125,24127],{"className":24126},[886],[888,24128,24129],{"xmlns":890},[892,24130,24131,24156],{},[895,24132,24133,24135,24137,24140,24146,24148,24150,24152,24154],{},[898,24134,6849],{},[1761,24136,1909],{},[1765,24138,24139],{},"0,001",[1824,24141,24142,24144],{},[898,24143,13170],{},[1765,24145,2296],{},[1761,24147,1964],{},[1765,24149,6910],{},[898,24151,13170],{},[1761,24153,1964],{},[1765,24155,7190],{},[902,24157,24158],{"encoding":904},"C = 0{,}001Y^2 + 0{,}2Y + 50"," (pro ",[883,24161,24163],{"className":24162},[886],[888,24164,24165],{"xmlns":890},[892,24166,24167,24176],{},[895,24168,24169,24171,24173],{},[898,24170,13170],{},[1761,24172,2058],{},[1765,24174,24175],{},"400",[902,24177,24178],{"encoding":904},"Y \u003C 400",") platí",[724,24181,24182],{},[883,24183,24185],{"className":24184},[886],[888,24186,24187],{"xmlns":890},[892,24188,24189,24226],{},[895,24190,24191,24193,24195,24197,24199,24213,24215,24218,24220,24222,24224],{},[898,24192,6889],{},[898,24194,1839],{},[898,24196,6849],{},[1761,24198,1909],{},[4379,24200,24201,24207],{},[895,24202,24203,24205],{},[898,24204,4346],{"mathvariant":1969},[898,24206,6849],{},[895,24208,24209,24211],{},[898,24210,4346],{"mathvariant":1969},[898,24212,13170],{},[1761,24214,1909],{},[1765,24216,24217],{},"0,002",[898,24219,13170],{},[1761,24221,1964],{},[1765,24223,6910],{},[1761,24225,1834],{"separator":1833},[902,24227,24228],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y} = 0{,}002Y + 0{,}2,",[724,24230,24231],{},[883,24232,24234],{"className":24233},[886],[888,24235,24236],{"xmlns":890},[892,24237,24238,24271],{},[895,24239,24240,24242,24244,24246,24248,24250,24252,24254,24256,24258,24260,24262,24264,24266,24268],{},[898,24241,6889],{},[898,24243,1839],{},[898,24245,1912],{},[1761,24247,1909],{},[1765,24249,1945],{},[1761,24251,1885],{},[898,24253,6889],{},[898,24255,1839],{},[898,24257,6849],{},[1761,24259,1909],{},[1761,24261,1885],{},[1765,24263,24217],{},[898,24265,13170],{},[1761,24267,1964],{},[1765,24269,24270],{},"0,8.",[902,24272,24273],{"encoding":904},"MPS = 1 - MPC = -0{,}002Y + 0{,}8.",[120,24275,24276,24356,24435],{},[123,24277,24278,1343,24306,24334,24335,12146,24353,1741],{},[883,24279,24281],{"className":24280},[886],[888,24282,24283],{"xmlns":890},[892,24284,24285,24303],{},[895,24286,24287,24289,24291,24293,24295,24297,24299,24301],{},[898,24288,6889],{},[898,24290,1839],{},[898,24292,6849],{},[1761,24294,1915],{"stretchy":1821},[1765,24296,7160],{},[1761,24298,1920],{"stretchy":1821},[1761,24300,1909],{},[1765,24302,23304],{},[902,24304,24305],{"encoding":904},"MPC(100) = 0{,}4",[883,24307,24309],{"className":24308},[886],[888,24310,24311],{"xmlns":890},[892,24312,24313,24331],{},[895,24314,24315,24317,24319,24321,24323,24325,24327,24329],{},[898,24316,6889],{},[898,24318,1839],{},[898,24320,1912],{},[1761,24322,1915],{"stretchy":1821},[1765,24324,7160],{},[1761,24326,1920],{"stretchy":1821},[1761,24328,1909],{},[1765,24330,23354],{},[902,24332,24333],{"encoding":904},"MPS(100) = 0{,}6"," — při ",[883,24336,24338],{"className":24337},[886],[888,24339,24340],{"xmlns":890},[892,24341,24342,24350],{},[895,24343,24344,24346,24348],{},[898,24345,13170],{},[1761,24347,1909],{},[1765,24349,7160],{},[902,24351,24352],{"encoding":904},"Y = 100",[38,24354,24355],{},"větší sklon k úsporám",[123,24357,24358,1343,24386,24334,24414,12146,24432,1741],{},[883,24359,24361],{"className":24360},[886],[888,24362,24363],{"xmlns":890},[892,24364,24365,24383],{},[895,24366,24367,24369,24371,24373,24375,24377,24379,24381],{},[898,24368,6889],{},[898,24370,1839],{},[898,24372,6849],{},[1761,24374,1915],{"stretchy":1821},[1765,24376,12421],{},[1761,24378,1920],{"stretchy":1821},[1761,24380,1909],{},[1765,24382,23354],{},[902,24384,24385],{"encoding":904},"MPC(200) = 0{,}6",[883,24387,24389],{"className":24388},[886],[888,24390,24391],{"xmlns":890},[892,24392,24393,24411],{},[895,24394,24395,24397,24399,24401,24403,24405,24407,24409],{},[898,24396,6889],{},[898,24398,1839],{},[898,24400,1912],{},[1761,24402,1915],{"stretchy":1821},[1765,24404,12421],{},[1761,24406,1920],{"stretchy":1821},[1761,24408,1909],{},[1765,24410,23304],{},[902,24412,24413],{"encoding":904},"MPS(200) = 0{,}4",[883,24415,24417],{"className":24416},[886],[888,24418,24419],{"xmlns":890},[892,24420,24421,24429],{},[895,24422,24423,24425,24427],{},[898,24424,13170],{},[1761,24426,1909],{},[1765,24428,12421],{},[902,24430,24431],{"encoding":904},"Y = 200",[38,24433,24434],{},"větší sklon ke spotřebě",[123,24436,24437,24438,24456,24457,2162],{},"Přesně při ",[883,24439,24441],{"className":24440},[886],[888,24442,24443],{"xmlns":890},[892,24444,24445,24453],{},[895,24446,24447,24449,24451],{},[898,24448,13170],{},[1761,24450,1909],{},[1765,24452,12845],{},[902,24454,24455],{"encoding":904},"Y = 150"," se oba sklony rovnají (",[883,24458,24460],{"className":24459},[886],[888,24461,24462],{"xmlns":890},[892,24463,24464,24484],{},[895,24465,24466,24468,24470,24472,24474,24476,24478,24480,24482],{},[898,24467,6889],{},[898,24469,1839],{},[898,24471,6849],{},[1761,24473,1909],{},[898,24475,6889],{},[898,24477,1839],{},[898,24479,1912],{},[1761,24481,1909],{},[1765,24483,5426],{},[902,24485,24486],{"encoding":904},"MPC = MPS = 0{,}5",[724,24488,24489,24490,24507,24508,24522,24523,4178,24536,24550,24551,24564,24565,24606],{},"Interpretace: při ",[883,24491,24493],{"className":24492},[886],[888,24494,24495],{"xmlns":890},[892,24496,24497,24505],{},[895,24498,24499,24501,24503],{},[898,24500,13170],{},[1761,24502,1909],{},[1765,24504,7160],{},[902,24506,24352],{"encoding":904}," se spotřeba mění ",[883,24509,24511],{"className":24510},[886],[888,24512,24513],{"xmlns":890},[892,24514,24515,24519],{},[895,24516,24517],{},[1765,24518,23304],{},[902,24520,24521],{"encoding":904},"0{,}4","-krát rychleji než důchod; změní-li se důchod ze ",[883,24524,24526],{"className":24525},[886],[888,24527,24528],{"xmlns":890},[892,24529,24530,24534],{},[895,24531,24532],{},[1765,24533,7160],{},[902,24535,7160],{"encoding":904},[883,24537,24539],{"className":24538},[886],[888,24540,24541],{"xmlns":890},[892,24542,24543,24548],{},[895,24544,24545],{},[1765,24546,24547],{},"101",[902,24549,24547],{"encoding":904},", změní se spotřeba přibližně o ",[883,24552,24554],{"className":24553},[886],[888,24555,24556],{"xmlns":890},[892,24557,24558,24562],{},[895,24559,24560],{},[1765,24561,23304],{},[902,24563,24521],{"encoding":904},". Skutečná změna ",[883,24566,24568],{"className":24567},[886],[888,24569,24570],{"xmlns":890},[892,24571,24572,24603],{},[895,24573,24574,24576,24578,24580,24582,24584,24586,24588,24590,24592,24594,24596,24598,24600],{},[898,24575,6959],{"mathvariant":1969},[898,24577,6849],{},[1761,24579,1909],{},[898,24581,6849],{},[1761,24583,1915],{"stretchy":1821},[1765,24585,24547],{},[1761,24587,1920],{"stretchy":1821},[1761,24589,1885],{},[898,24591,6849],{},[1761,24593,1915],{"stretchy":1821},[1765,24595,7160],{},[1761,24597,1920],{"stretchy":1821},[1761,24599,1909],{},[1765,24601,24602],{},"0,401",[902,24604,24605],{"encoding":904},"\\Delta C = C(101) - C(100) = 0{,}401"," — aproximace diferenciálem je přesná na setiny.",[724,24608,24609,24610],{},"Obecný trend: ",[38,24611,24612],{},"s růstem důchodu se sklon ke spotřebě zvětšuje.",[115,24614,24616],{"id":24615},"makroekonomická-rovnováha","Makroekonomická rovnováha",[724,24618,24619,24620,3927,24623,24626,24627,3927,24630,4590,24633,3927,24636,24639],{},"Při modelování národní ekonomiky hraje klíčovou roli ",[38,24621,24622],{},"makroekonomická rovnováha",[614,24624,24625],{},"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 ",[38,24628,24629],{},"agregátní poptávky",[614,24631,24632],{},"aggregate demand",[38,24634,24635],{},"agregátní nabídky",[614,24637,24638],{},"aggregate supply",") — obě popisují závislost mezi cenovou hladinou a množstvím, které jsou spotřebitelé ochotni koupit (agregátními výdaji).",[115,24641,24643],{"id":24642},"model-c-i-uzavřená-ekonomika-bez-vlády","Model C-I — uzavřená ekonomika bez vlády",[724,24645,24646],{},[3991,24647],{"alt":24648,"className":24649,"src":24650},"imek-keynesian-kriz",[210,3995],"\u002Fwiki-assets\u002Fimek-keynesian-kriz.jpeg",[198,24652,24654],{"id":24653},"zadání-modelu","Zadání modelu",[724,24656,24657,24658,24671,24672,24685],{},"Nejjednodušší model uzavřené ekonomiky bez vlády obsahuje jen spotřebu ",[883,24659,24661],{"className":24660},[886],[888,24662,24663],{"xmlns":890},[892,24664,24665,24669],{},[895,24666,24667],{},[898,24668,6849],{},[902,24670,6849],{"encoding":904}," a investice ",[883,24673,24675],{"className":24674},[886],[888,24676,24677],{"xmlns":890},[892,24678,24679,24683],{},[895,24680,24681],{},[898,24682,16222],{},[902,24684,16222],{"encoding":904},". Podmínka rovnováhy:",[724,24687,24688],{},[883,24689,24691],{"className":24690},[886],[888,24692,24693],{"xmlns":890},[892,24694,24695,24718],{},[895,24696,24697,24699,24701,24703,24705,24707,24709,24711,24713,24716],{},[898,24698,13170],{},[1761,24700,1909],{},[898,24702,6849],{},[1761,24704,1964],{},[898,24706,16222],{},[898,24708,1741],{"mathvariant":1969},[3315,24710],{"width":3317},[1761,24712,1915],{"stretchy":1821},[1765,24714,24715],{},"7.6",[1761,24717,1920],{"stretchy":1821},[902,24719,24720],{"encoding":904},"Y = C + I. \\qquad (7.6)",[198,24722,24724],{"id":24723},"soustava-rovnic","Soustava rovnic",[724,24726,24727,24728,24749,24750,24774],{},"Pro pevně zadané (plánované) investice ",[883,24729,24731],{"className":24730},[886],[888,24732,24733],{"xmlns":890},[892,24734,24735,24747],{},[895,24736,24737,24739,24741],{},[898,24738,16222],{},[1761,24740,1909],{},[1824,24742,24743,24745],{},[898,24744,16222],{},[1761,24746,8408],{},[902,24748,16233],{"encoding":904}," a funkci spotřeby ",[883,24751,24753],{"className":24752},[886],[888,24754,24755],{"xmlns":890},[892,24756,24757,24771],{},[895,24758,24759,24761,24763,24765,24767,24769],{},[898,24760,6849],{},[1761,24762,1909],{},[898,24764,6849],{},[1761,24766,1915],{"stretchy":1821},[898,24768,13170],{},[1761,24770,1920],{"stretchy":1821},[902,24772,24773],{"encoding":904},"C = C(Y)"," dostáváme soustavu",[724,24776,24777],{},[883,24778,24780],{"className":24779},[886],[888,24781,24782],{"xmlns":890},[892,24783,24784,24860],{},[895,24785,24786,24851,24853,24855,24858],{},[24787,24788,24791,24823],"mtable",{"rowspacing":24789,"columnalign":24790,"columnspacing":6458},"0.25em","right left",[24792,24793,24794,24801],"mtr",{},[24795,24796,24797],"mtd",{},[6411,24798,24799],{"scriptlevel":1767,"displaystyle":1833},[898,24800,13170],{},[24795,24802,24803],{},[6411,24804,24805],{"scriptlevel":1767,"displaystyle":1833},[895,24806,24807,24809,24811,24813,24815,24821],{},[895,24808],{},[1761,24810,1909],{},[898,24812,6849],{},[1761,24814,1964],{},[1824,24816,24817,24819],{},[898,24818,16222],{},[1761,24820,8408],{},[1761,24822,1834],{"separator":1833},[24792,24824,24825,24831],{},[24795,24826,24827],{},[6411,24828,24829],{"scriptlevel":1767,"displaystyle":1833},[898,24830,6849],{},[24795,24832,24833],{},[6411,24834,24835],{"scriptlevel":1767,"displaystyle":1833},[895,24836,24837,24839,24841,24843,24845,24847,24849],{},[895,24838],{},[1761,24840,1909],{},[898,24842,6849],{},[1761,24844,1915],{"stretchy":1821},[898,24846,13170],{},[1761,24848,1920],{"stretchy":1821},[1761,24850,1834],{"separator":1833},[3315,24852],{"width":3317},[1761,24854,1915],{"stretchy":1821},[1765,24856,24857],{},"7.7",[1761,24859,1920],{"stretchy":1821},[902,24861,24862],{"encoding":904},"\\begin{aligned} Y &= C + I^*, \\\\ C &= C(Y), \\end{aligned} \\qquad (7.7)",[724,24864,24865,24866,1989,24868,2068,24885,1989,24888,1741],{},"jejímž řešením jsou ",[38,24867,17923],{},[883,24869,24871],{"className":24870},[886],[888,24872,24873],{"xmlns":890},[892,24874,24875,24883],{},[895,24876,24877],{},[1824,24878,24879,24881],{},[898,24880,13170],{},[898,24882,1818],{},[902,24884,17941],{"encoding":904},[38,24886,24887],{},"rovnovážná spotřeba",[883,24889,24891],{"className":24890},[886],[888,24892,24893],{"xmlns":890},[892,24894,24895,24903],{},[895,24896,24897],{},[1824,24898,24899,24901],{},[898,24900,6849],{},[898,24902,1818],{},[902,24904,18000],{"encoding":904},[198,24906,24908,24909],{"id":24907},"výpočet-yeye","Výpočet ",[883,24910,24912],{"className":24911},[886],[888,24913,24914],{"xmlns":890},[892,24915,24916,24924],{},[895,24917,24918],{},[1824,24919,24920,24922],{},[898,24921,13170],{},[898,24923,1818],{},[902,24925,17941],{"encoding":904},[724,24927,24928,24929,24952,24953,11729,24985],{},"Pro lineární spotřebu ",[883,24930,24932],{"className":24931},[886],[888,24933,24934],{"xmlns":890},[892,24935,24936,24950],{},[895,24937,24938,24940,24942,24944,24946,24948],{},[898,24939,6849],{},[1761,24941,1909],{},[898,24943,207],{},[898,24945,13170],{},[1761,24947,1964],{},[898,24949,4302],{},[902,24951,22953],{"encoding":904}," plyne z (7.7) rovnice ",[883,24954,24956],{"className":24955},[886],[888,24957,24958],{"xmlns":890},[892,24959,24960,24982],{},[895,24961,24962,24964,24966,24968,24970,24972,24974,24976],{},[898,24963,13170],{},[1761,24965,1909],{},[898,24967,207],{},[898,24969,13170],{},[1761,24971,1964],{},[898,24973,4302],{},[1761,24975,1964],{},[1824,24977,24978,24980],{},[898,24979,16222],{},[1761,24981,8408],{},[902,24983,24984],{"encoding":904},"Y = aY + b + I^*",[38,24986,24987],{},"redukovaný tvar",[724,24989,24990],{},[883,24991,24993],{"className":24992},[886],[888,24994,24995],{"xmlns":890},[892,24996,24997,25045],{},[895,24998,24999],{},[16870,25000,25001],{"notation":16872},[6411,25002,25003],{"scriptlevel":1767,"displaystyle":1821},[6411,25004,25005],{"scriptlevel":1767,"displaystyle":1821},[6411,25006,25007],{"scriptlevel":1767,"displaystyle":1833},[895,25008,25009,25011,25017,25019,25041,25043],{},[2761,25010,7057],{},[1824,25012,25013,25015],{},[898,25014,13170],{},[898,25016,1818],{},[1761,25018,1909],{},[4379,25020,25021,25033],{},[895,25022,25023,25025,25027],{},[898,25024,4302],{},[1761,25026,1964],{},[1824,25028,25029,25031],{},[898,25030,16222],{},[1761,25032,8408],{},[895,25034,25035,25037,25039],{},[1765,25036,1945],{},[1761,25038,1885],{},[898,25040,207],{},[898,25042,1741],{"mathvariant":1969},[2761,25044,7057],{},[902,25046,25047],{"encoding":904},"\\boxed{\\,Y^E = \\frac{b + I^*}{1 - a}.\\,}",[198,25049,25051],{"id":25050},"příklad-73","Příklad 7.3",[724,25053,25054,25055,12146,25072,2068,25096,25122],{},"V modelu ",[883,25056,25058],{"className":25057},[886],[888,25059,25060],{"xmlns":890},[892,25061,25062,25070],{},[895,25063,25064,25066,25068],{},[898,25065,6849],{},[2761,25067,16328],{},[898,25069,16222],{},[902,25071,16333],{"encoding":904},[883,25073,25075],{"className":25074},[886],[888,25076,25077],{"xmlns":890},[892,25078,25079,25093],{},[895,25080,25081,25083,25085,25087,25089,25091],{},[898,25082,6849],{},[1761,25084,1909],{},[1765,25086,23354],{},[898,25088,13170],{},[1761,25090,1964],{},[1765,25092,2633],{},[902,25094,25095],{"encoding":904},"C = 0{,}6Y + 10",[883,25097,25099],{"className":25098},[886],[888,25100,25101],{"xmlns":890},[892,25102,25103,25119],{},[895,25104,25105,25107,25109,25111,25113],{},[898,25106,16222],{},[1761,25108,1909],{},[1765,25110,2291],{},[1761,25112,1909],{},[1824,25114,25115,25117],{},[898,25116,16222],{},[1761,25118,8408],{},[902,25120,25121],{"encoding":904},"I = 12 = I^*",". Soustava",[724,25124,25125],{},[883,25126,25128],{"className":25127},[886],[888,25129,25130],{"xmlns":890},[892,25131,25132,25188],{},[24787,25133,25134,25160],{"rowspacing":24789,"columnalign":24790,"columnspacing":6458},[24792,25135,25136,25142],{},[24795,25137,25138],{},[6411,25139,25140],{"scriptlevel":1767,"displaystyle":1833},[898,25141,13170],{},[24795,25143,25144],{},[6411,25145,25146],{"scriptlevel":1767,"displaystyle":1833},[895,25147,25148,25150,25152,25154,25156,25158],{},[895,25149],{},[1761,25151,1909],{},[898,25153,6849],{},[1761,25155,1964],{},[1765,25157,2291],{},[1761,25159,1834],{"separator":1833},[24792,25161,25162,25168],{},[24795,25163,25164],{},[6411,25165,25166],{"scriptlevel":1767,"displaystyle":1833},[898,25167,6849],{},[24795,25169,25170],{},[6411,25171,25172],{"scriptlevel":1767,"displaystyle":1833},[895,25173,25174,25176,25178,25180,25182,25184,25186],{},[895,25175],{},[1761,25177,1909],{},[1765,25179,23354],{},[898,25181,13170],{},[1761,25183,1964],{},[1765,25185,2633],{},[1761,25187,1834],{"separator":1833},[902,25189,25190],{"encoding":904},"\\begin{aligned} Y &= C + 12, \\\\ C &= 0{,}6Y + 10, \\end{aligned}",[724,25192,25193,25194,1343,25217,25240,25241,2162],{},"má řešení ",[883,25195,25197],{"className":25196},[886],[888,25198,25199],{"xmlns":890},[892,25200,25201,25214],{},[895,25202,25203,25209,25211],{},[1824,25204,25205,25207],{},[898,25206,13170],{},[898,25208,1818],{},[1761,25210,1909],{},[1765,25212,25213],{},"55",[902,25215,25216],{"encoding":904},"Y^E = 55",[883,25218,25220],{"className":25219},[886],[888,25221,25222],{"xmlns":890},[892,25223,25224,25237],{},[895,25225,25226,25232,25234],{},[1824,25227,25228,25230],{},[898,25229,6849],{},[898,25231,1818],{},[1761,25233,1909],{},[1765,25235,25236],{},"43",[902,25238,25239],{"encoding":904},"C^E = 43"," (a ",[883,25242,25244],{"className":25243},[886],[888,25245,25246],{"xmlns":890},[892,25247,25248,25260],{},[895,25249,25250,25256,25258],{},[1824,25251,25252,25254],{},[898,25253,1912],{},[898,25255,1818],{},[1761,25257,1909],{},[1765,25259,2291],{},[902,25261,25262],{"encoding":904},"S^E = 12",[724,25264,25265],{},[614,25266,25267,25268,25290,25291,4590,25312,25335,25336,1741],{},"Obrázek 7.5 — Přímky ",[883,25269,25271],{"className":25270},[886],[888,25272,25273],{"xmlns":890},[892,25274,25275,25287],{},[895,25276,25277,25279,25281,25283,25285],{},[898,25278,6849],{},[1761,25280,1909],{},[898,25282,13170],{},[1761,25284,1885],{},[1765,25286,2291],{},[902,25288,25289],{"encoding":904},"C = Y - 12"," (rovnováha ",[883,25292,25294],{"className":25293},[886],[888,25295,25296],{"xmlns":890},[892,25297,25298,25310],{},[895,25299,25300,25302,25304,25306,25308],{},[898,25301,13170],{},[1761,25303,1909],{},[898,25305,6849],{},[1761,25307,1964],{},[898,25309,16222],{},[902,25311,18782],{"encoding":904},[883,25313,25315],{"className":25314},[886],[888,25316,25317],{"xmlns":890},[892,25318,25319,25333],{},[895,25320,25321,25323,25325,25327,25329,25331],{},[898,25322,6849],{},[1761,25324,1909],{},[1765,25326,23354],{},[898,25328,13170],{},[1761,25330,1964],{},[1765,25332,2633],{},[902,25334,25095],{"encoding":904}," (funkce spotřeby) se protínají v bodě ",[883,25337,25339],{"className":25338},[886],[888,25340,25341],{"xmlns":890},[892,25342,25343,25375],{},[895,25344,25345,25347,25353,25355,25361,25363,25365,25367,25369,25371,25373],{},[1761,25346,1822],{"stretchy":1821},[1824,25348,25349,25351],{},[898,25350,13170],{},[898,25352,1818],{},[1761,25354,1834],{"separator":1833},[1824,25356,25357,25359],{},[898,25358,6849],{},[898,25360,1818],{},[1761,25362,1844],{"stretchy":1821},[1761,25364,1909],{},[1761,25366,1822],{"stretchy":1821},[1765,25368,25213],{},[1761,25370,1834],{"separator":1833},[1765,25372,25236],{},[1761,25374,1844],{"stretchy":1821},[902,25376,25377],{"encoding":904},"[Y^E, C^E] = [55, 43]",[724,25379,25380,25383,25384,25401,25402,1741],{},[38,25381,25382],{},"Komentář k přechodu."," Model ",[883,25385,25387],{"className":25386},[886],[888,25388,25389],{"xmlns":890},[892,25390,25391,25399],{},[895,25392,25393,25395,25397],{},[898,25394,6849],{},[2761,25396,16328],{},[898,25398,16222],{},[902,25400,16333],{"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 ",[38,25403,25404,25405],{},"model ",[883,25406,25408],{"className":25407},[886],[888,25409,25410],{"xmlns":890},[892,25411,25412,25424],{},[895,25413,25414,25416,25418,25420,25422],{},[898,25415,6849],{},[2761,25417,16328],{},[898,25419,16222],{},[2761,25421,16328],{},[898,25423,16151],{},[902,25425,22254],{"encoding":904},[115,25427,25429],{"id":25428},"model-c-i-g-s-vládním-sektorem","Model C-I-G — s vládním sektorem",[198,25431,24654],{"id":25432},"zadání-modelu-1",[724,25434,25435,25436,25453,25454,1989,25457,3927,25470,25473],{},"Rozšíření modelu ",[883,25437,25439],{"className":25438},[886],[888,25440,25441],{"xmlns":890},[892,25442,25443,25451],{},[895,25444,25445,25447,25449],{},[898,25446,6849],{},[2761,25448,16328],{},[898,25450,16222],{},[902,25452,16333],{"encoding":904}," o ",[38,25455,25456],{},"vládní výdaje",[883,25458,25460],{"className":25459},[886],[888,25461,25462],{"xmlns":890},[892,25463,25464,25468],{},[895,25465,25466],{},[898,25467,16151],{},[902,25469,16151],{"encoding":904},[614,25471,25472],{},"government expenditure","). Podmínka rovnováhy:",[724,25475,25476],{},[883,25477,25479],{"className":25478},[886],[888,25480,25481],{"xmlns":890},[892,25482,25483,25510],{},[895,25484,25485,25487,25489,25491,25493,25495,25497,25499,25501,25503,25505,25508],{},[898,25486,13170],{},[1761,25488,1909],{},[898,25490,6849],{},[1761,25492,1964],{},[898,25494,16222],{},[1761,25496,1964],{},[898,25498,16151],{},[898,25500,1741],{"mathvariant":1969},[3315,25502],{"width":3317},[1761,25504,1915],{"stretchy":1821},[1765,25506,25507],{},"7.8",[1761,25509,1920],{"stretchy":1821},[902,25511,25512],{"encoding":904},"Y = C + I + G. \\qquad (7.8)",[724,25514,25515,25516,1989,25519,3927,25532,25535],{},"Stát se stává spotřebitelem, jehož „důchod“ získává ",[38,25517,25518],{},"zdaněním domácností",[883,25520,25522],{"className":25521},[886],[888,25523,25524],{"xmlns":890},[892,25525,25526,25530],{},[895,25527,25528],{},[898,25529,1655],{},[902,25531,1655],{"encoding":904},[614,25533,25534],{},"taxation","). Zdanění bývá:",[120,25537,25538,25571,25596],{},[123,25539,25540,25541,1834],{},"úměrné důchodu: ",[883,25542,25544],{"className":25543},[886],[888,25545,25546],{"xmlns":890},[892,25547,25548,25568],{},[895,25549,25550,25552,25554,25556,25558,25560,25562,25564,25566],{},[898,25551,1655],{},[1761,25553,1909],{},[898,25555,1655],{},[1761,25557,1915],{"stretchy":1821},[898,25559,13170],{},[1761,25561,1920],{"stretchy":1821},[1761,25563,1909],{},[898,25565,22888],{},[898,25567,13170],{},[902,25569,25570],{"encoding":904},"T = T(Y) = tY",[123,25572,25573,25574,1834],{},"fixní: ",[883,25575,25577],{"className":25576},[886],[888,25578,25579],{"xmlns":890},[892,25580,25581,25593],{},[895,25582,25583,25585,25587],{},[898,25584,1655],{},[1761,25586,1909],{},[1824,25588,25589,25591],{},[898,25590,1655],{},[1761,25592,8408],{},[902,25594,25595],{"encoding":904},"T = T^*",[123,25597,25598,25599,25627,25628,1741],{},"kombinované: ",[883,25600,25602],{"className":25601},[886],[888,25603,25604],{"xmlns":890},[892,25605,25606,25624],{},[895,25607,25608,25610,25612,25618,25620,25622],{},[898,25609,1655],{},[1761,25611,1909],{},[1824,25613,25614,25616],{},[898,25615,1655],{},[1761,25617,8408],{},[1761,25619,1964],{},[898,25621,22888],{},[898,25623,13170],{},[902,25625,25626],{"encoding":904},"T = T^* + tY",", kde ",[883,25629,25631],{"className":25630},[886],[888,25632,25633],{"xmlns":890},[892,25634,25635,25647],{},[895,25636,25637,25639,25641,25643,25645],{},[1765,25638,1767],{},[1761,25640,11723],{},[898,25642,22888],{},[1761,25644,2058],{},[1765,25646,1945],{},[902,25648,25649],{"encoding":904},"0 \\le t \u003C 1",[1636,25651,25652],{},[724,25653,25654,25656,25657,25678,25679,25682,25683,25696,25697,4590,25723,1989,25726,25752,25753,25781,25782,2068,25795,25813],{},[883,25655,4723],{}," Pozor na disponibilní důchod\nV modelu ",[883,25658,25660],{"className":25659},[886],[888,25661,25662],{"xmlns":890},[892,25663,25664,25676],{},[895,25665,25666,25668,25670,25672,25674],{},[898,25667,6849],{},[2761,25669,16328],{},[898,25671,16222],{},[2761,25673,16328],{},[898,25675,16151],{},[902,25677,22254],{"encoding":904}," je nutné ",[38,25680,25681],{},"důsledně rozlišovat dva důchody",": celkový národní důchod ",[883,25684,25686],{"className":25685},[886],[888,25687,25688],{"xmlns":890},[892,25689,25690,25694],{},[895,25691,25692],{},[898,25693,13170],{},[902,25695,13170],{"encoding":904}," (vstupuje do podmínky rovnováhy ",[883,25698,25700],{"className":25699},[886],[888,25701,25702],{"xmlns":890},[892,25703,25704,25720],{},[895,25705,25706,25708,25710,25712,25714,25716,25718],{},[898,25707,13170],{},[1761,25709,1909],{},[898,25711,6849],{},[1761,25713,1964],{},[898,25715,16222],{},[1761,25717,1964],{},[898,25719,16151],{},[902,25721,25722],{"encoding":904},"Y = C + I + G",[38,25724,25725],{},"disponibilní důchod",[883,25727,25729],{"className":25728},[886],[888,25730,25731],{"xmlns":890},[892,25732,25733,25749],{},[895,25734,25735,25741,25743,25745,25747],{},[1681,25736,25737,25739],{},[898,25738,13170],{},[898,25740,2244],{},[1761,25742,1909],{},[898,25744,13170],{},[1761,25746,1885],{},[898,25748,1655],{},[902,25750,25751],{"encoding":904},"Y_D = Y - T"," (na něm závisí spotřeba domácností, ",[883,25754,25756],{"className":25755},[886],[888,25757,25758],{"xmlns":890},[892,25759,25760,25778],{},[895,25761,25762,25764,25766,25768,25770,25776],{},[898,25763,6849],{},[1761,25765,1909],{},[898,25767,6849],{},[1761,25769,1915],{"stretchy":1821},[1681,25771,25772,25774],{},[898,25773,13170],{},[898,25775,2244],{},[1761,25777,1920],{"stretchy":1821},[902,25779,25780],{"encoding":904},"C = C(Y_D)","). Záměna ",[883,25783,25785],{"className":25784},[886],[888,25786,25787],{"xmlns":890},[892,25788,25789,25793],{},[895,25790,25791],{},[898,25792,13170],{},[902,25794,13170],{"encoding":904},[883,25796,25798],{"className":25797},[886],[888,25799,25800],{"xmlns":890},[892,25801,25802,25810],{},[895,25803,25804],{},[1681,25805,25806,25808],{},[898,25807,13170],{},[898,25809,2244],{},[902,25811,25812],{"encoding":904},"Y_D"," ve funkci spotřeby je nejčastější zdroj chyb.",[724,25815,25816,3927,25819,1920],{},[38,25817,25818],{},"Disponibilní důchod",[614,25820,25821],{},"disposable income",[724,25823,25824],{},[883,25825,25827],{"className":25826},[886],[888,25828,25829],{"xmlns":890},[892,25830,25831,25847],{},[895,25832,25833,25839,25841,25843,25845],{},[1681,25834,25835,25837],{},[898,25836,13170],{},[898,25838,2244],{},[1761,25840,1909],{},[898,25842,13170],{},[1761,25844,1885],{},[898,25846,1655],{},[902,25848,25751],{"encoding":904},[724,25850,25851,25852,1741],{},"je to, co zbývá domácnostem po zdanění. Spotřeba je pak funkcí disponibilního důchodu: ",[883,25853,25855],{"className":25854},[886],[888,25856,25857],{"xmlns":890},[892,25858,25859,25877],{},[895,25860,25861,25863,25865,25867,25869,25875],{},[898,25862,6849],{},[1761,25864,1909],{},[898,25866,6849],{},[1761,25868,1915],{"stretchy":1821},[1681,25870,25871,25873],{},[898,25872,13170],{},[898,25874,2244],{},[1761,25876,1920],{"stretchy":1821},[902,25878,25780],{"encoding":904},[198,25880,24724],{"id":25881},"soustava-rovnic-1",[724,25883,25884,25885,1343,25906,25928,25929,2506],{},"Pro pevně zadané ",[883,25886,25888],{"className":25887},[886],[888,25889,25890],{"xmlns":890},[892,25891,25892,25904],{},[895,25893,25894,25896,25898],{},[898,25895,16222],{},[1761,25897,1909],{},[1824,25899,25900,25902],{},[898,25901,16222],{},[1761,25903,8408],{},[902,25905,16233],{"encoding":904},[883,25907,25909],{"className":25908},[886],[888,25910,25911],{"xmlns":890},[892,25912,25913,25925],{},[895,25914,25915,25917,25919],{},[898,25916,16151],{},[1761,25918,1909],{},[1824,25920,25921,25923],{},[898,25922,16151],{},[1761,25924,8408],{},[902,25926,25927],{"encoding":904},"G = G^*"," dostáváme soustavu 4 rovnic o 4 neznámých ",[883,25930,25932],{"className":25931},[886],[888,25933,25934],{"xmlns":890},[892,25935,25936,25956],{},[895,25937,25938,25940,25942,25944,25946,25952,25954],{},[898,25939,13170],{},[1761,25941,1834],{"separator":1833},[898,25943,6849],{},[1761,25945,1834],{"separator":1833},[1681,25947,25948,25950],{},[898,25949,13170],{},[898,25951,2244],{},[1761,25953,1834],{"separator":1833},[898,25955,1655],{},[902,25957,25958],{"encoding":904},"Y, C, Y_D, T",[724,25960,25961],{},[883,25962,25964],{"className":25963},[886],[888,25965,25966],{"xmlns":890},[892,25967,25968,26109],{},[895,25969,25970,26100,26102,26104,26107],{},[24787,25971,25972,26010,26038,26070],{"rowspacing":24789,"columnalign":24790,"columnspacing":6458},[24792,25973,25974,25980],{},[24795,25975,25976],{},[6411,25977,25978],{"scriptlevel":1767,"displaystyle":1833},[898,25979,13170],{},[24795,25981,25982],{},[6411,25983,25984],{"scriptlevel":1767,"displaystyle":1833},[895,25985,25986,25988,25990,25992,25994,26000,26002,26008],{},[895,25987],{},[1761,25989,1909],{},[898,25991,6849],{},[1761,25993,1964],{},[1824,25995,25996,25998],{},[898,25997,16222],{},[1761,25999,8408],{},[1761,26001,1964],{},[1824,26003,26004,26006],{},[898,26005,16151],{},[1761,26007,8408],{},[1761,26009,1834],{"separator":1833},[24792,26011,26012,26018],{},[24795,26013,26014],{},[6411,26015,26016],{"scriptlevel":1767,"displaystyle":1833},[898,26017,1655],{},[24795,26019,26020],{},[6411,26021,26022],{"scriptlevel":1767,"displaystyle":1833},[895,26023,26024,26026,26028,26030,26032,26034,26036],{},[895,26025],{},[1761,26027,1909],{},[898,26029,1655],{},[1761,26031,1915],{"stretchy":1821},[898,26033,13170],{},[1761,26035,1920],{"stretchy":1821},[1761,26037,1834],{"separator":1833},[24792,26039,26040,26046],{},[24795,26041,26042],{},[6411,26043,26044],{"scriptlevel":1767,"displaystyle":1833},[898,26045,6849],{},[24795,26047,26048],{},[6411,26049,26050],{"scriptlevel":1767,"displaystyle":1833},[895,26051,26052,26054,26056,26058,26060,26066,26068],{},[895,26053],{},[1761,26055,1909],{},[898,26057,6849],{},[1761,26059,1915],{"stretchy":1821},[1681,26061,26062,26064],{},[898,26063,13170],{},[898,26065,2244],{},[1761,26067,1920],{"stretchy":1821},[1761,26069,1834],{"separator":1833},[24792,26071,26072,26082],{},[24795,26073,26074],{},[6411,26075,26076],{"scriptlevel":1767,"displaystyle":1833},[1681,26077,26078,26080],{},[898,26079,13170],{},[898,26081,2244],{},[24795,26083,26084],{},[6411,26085,26086],{"scriptlevel":1767,"displaystyle":1833},[895,26087,26088,26090,26092,26094,26096,26098],{},[895,26089],{},[1761,26091,1909],{},[898,26093,13170],{},[1761,26095,1885],{},[898,26097,1655],{},[1761,26099,1834],{"separator":1833},[3315,26101],{"width":3317},[1761,26103,1915],{"stretchy":1821},[1765,26105,26106],{},"7.9",[1761,26108,1920],{"stretchy":1821},[902,26110,26111],{"encoding":904},"\\begin{aligned} Y &= C + I^* + G^*, \\\\ T &= T(Y), \\\\ C &= C(Y_D), \\\\ Y_D &= Y - T, \\end{aligned} \\qquad (7.9)",[724,26113,26114,26115,26159,26160,1741],{},"s řešeními ",[883,26116,26118],{"className":26117},[886],[888,26119,26120],{"xmlns":890},[892,26121,26122,26156],{},[895,26123,26124,26130,26132,26138,26140,26146,26148],{},[1824,26125,26126,26128],{},[898,26127,13170],{},[898,26129,1818],{},[1761,26131,1834],{"separator":1833},[1824,26133,26134,26136],{},[898,26135,6849],{},[898,26137,1818],{},[1761,26139,1834],{"separator":1833},[1824,26141,26142,26144],{},[898,26143,1655],{},[898,26145,1818],{},[1761,26147,1834],{"separator":1833},[2015,26149,26150,26152,26154],{},[898,26151,13170],{},[898,26153,2244],{},[898,26155,1818],{},[902,26157,26158],{"encoding":904},"Y^E, C^E, T^E, Y_D^E",", případně rovnovážnými úsporami domácností ",[883,26161,26163],{"className":26162},[886],[888,26164,26165],{"xmlns":890},[892,26166,26167,26193],{},[895,26168,26169,26175,26177,26185,26187],{},[1824,26170,26171,26173],{},[898,26172,1912],{},[898,26174,1818],{},[1761,26176,1909],{},[2015,26178,26179,26181,26183],{},[898,26180,13170],{},[898,26182,2244],{},[898,26184,1818],{},[1761,26186,1885],{},[1824,26188,26189,26191],{},[898,26190,6849],{},[898,26192,1818],{},[902,26194,26195],{"encoding":904},"S^E = Y_D^E - C^E",[1636,26197,26198,26203],{},[724,26199,26200,26202],{},[883,26201,4452],{}," Postup — jak sestavit a vyřešit soustavu C-I-G",[152,26204,26205,26228,26311,26366,26456],{},[123,26206,26207,26210,26211,1741],{},[38,26208,26209],{},"Zapiš všechny 4 rovnice"," ze zadání: podmínku rovnováhy, daňovou funkci, funkci spotřeby, definici ",[883,26212,26214],{"className":26213},[886],[888,26215,26216],{"xmlns":890},[892,26217,26218,26226],{},[895,26219,26220],{},[1681,26221,26222,26224],{},[898,26223,13170],{},[898,26225,2244],{},[902,26227,25812],{"encoding":904},[123,26229,26230,26279,26280,26297,26298,1741],{},[38,26231,26232,26233,26253,26254],{},"Dosaď ",[883,26234,26236],{"className":26235},[886],[888,26237,26238],{"xmlns":890},[892,26239,26240,26250],{},[895,26241,26242,26244,26246,26248],{},[898,26243,1655],{},[1761,26245,1915],{"stretchy":1821},[898,26247,13170],{},[1761,26249,1920],{"stretchy":1821},[902,26251,26252],{"encoding":904},"T(Y)"," do ",[883,26255,26257],{"className":26256},[886],[888,26258,26259],{"xmlns":890},[892,26260,26261,26277],{},[895,26262,26263,26269,26271,26273,26275],{},[1681,26264,26265,26267],{},[898,26266,13170],{},[898,26268,2244],{},[1761,26270,1909],{},[898,26272,13170],{},[1761,26274,1885],{},[898,26276,1655],{},[902,26278,25751],{"encoding":904}," — dostaneš ",[883,26281,26283],{"className":26282},[886],[888,26284,26285],{"xmlns":890},[892,26286,26287,26295],{},[895,26288,26289],{},[1681,26290,26291,26293],{},[898,26292,13170],{},[898,26294,2244],{},[902,26296,25812],{"encoding":904}," jako lineární funkci ",[883,26299,26301],{"className":26300},[886],[888,26302,26303],{"xmlns":890},[892,26304,26305,26309],{},[895,26306,26307],{},[898,26308,13170],{},[902,26310,13170],{"encoding":904},[123,26312,26313,26279,26340,26297,26353,1741],{},[38,26314,26232,26315,26339],{},[883,26316,26318],{"className":26317},[886],[888,26319,26320],{"xmlns":890},[892,26321,26322,26336],{},[895,26323,26324,26330,26332,26334],{},[1681,26325,26326,26328],{},[898,26327,13170],{},[898,26329,2244],{},[1761,26331,1915],{"stretchy":1821},[898,26333,13170],{},[1761,26335,1920],{"stretchy":1821},[902,26337,26338],{"encoding":904},"Y_D(Y)"," do funkce spotřeby",[883,26341,26343],{"className":26342},[886],[888,26344,26345],{"xmlns":890},[892,26346,26347,26351],{},[895,26348,26349],{},[898,26350,6849],{},[902,26352,6849],{"encoding":904},[883,26354,26356],{"className":26355},[886],[888,26357,26358],{"xmlns":890},[892,26359,26360,26364],{},[895,26361,26362],{},[898,26363,13170],{},[902,26365,13170],{"encoding":904},[123,26367,26368,1989,26390,26424,26425,26438,26439,1741],{},[38,26369,26232,26370,26389],{},[883,26371,26373],{"className":26372},[886],[888,26374,26375],{"xmlns":890},[892,26376,26377,26387],{},[895,26378,26379,26381,26383,26385],{},[898,26380,6849],{},[1761,26382,1915],{"stretchy":1821},[898,26384,13170],{},[1761,26386,1920],{"stretchy":1821},[902,26388,18254],{"encoding":904}," do podmínky rovnováhy",[883,26391,26393],{"className":26392},[886],[888,26394,26395],{"xmlns":890},[892,26396,26397,26421],{},[895,26398,26399,26401,26403,26405,26407,26413,26415],{},[898,26400,13170],{},[1761,26402,1909],{},[898,26404,6849],{},[1761,26406,1964],{},[1824,26408,26409,26411],{},[898,26410,16222],{},[1761,26412,8408],{},[1761,26414,1964],{},[1824,26416,26417,26419],{},[898,26418,16151],{},[1761,26420,8408],{},[902,26422,26423],{"encoding":904},"Y = C + I^* + G^*"," — zbývá jediná rovnice o jedné neznámé ",[883,26426,26428],{"className":26427},[886],[888,26429,26430],{"xmlns":890},[892,26431,26432,26436],{},[895,26433,26434],{},[898,26435,13170],{},[902,26437,13170],{"encoding":904},", odtud ",[883,26440,26442],{"className":26441},[886],[888,26443,26444],{"xmlns":890},[892,26445,26446,26454],{},[895,26447,26448],{},[1824,26449,26450,26452],{},[898,26451,13170],{},[898,26453,1818],{},[902,26455,17941],{"encoding":904},[123,26457,26458,26461,26462,1343,26480,1343,26500,1343,26517,1741],{},[38,26459,26460],{},"Zpětným dosazením"," dopočítej ",[883,26463,26465],{"className":26464},[886],[888,26466,26467],{"xmlns":890},[892,26468,26469,26477],{},[895,26470,26471],{},[1824,26472,26473,26475],{},[898,26474,1655],{},[898,26476,1818],{},[902,26478,26479],{"encoding":904},"T^E",[883,26481,26483],{"className":26482},[886],[888,26484,26485],{"xmlns":890},[892,26486,26487,26497],{},[895,26488,26489],{},[2015,26490,26491,26493,26495],{},[898,26492,13170],{},[898,26494,2244],{},[898,26496,1818],{},[902,26498,26499],{"encoding":904},"Y_D^E",[883,26501,26503],{"className":26502},[886],[888,26504,26505],{"xmlns":890},[892,26506,26507,26515],{},[895,26508,26509],{},[1824,26510,26511,26513],{},[898,26512,6849],{},[898,26514,1818],{},[902,26516,18000],{"encoding":904},[883,26518,26520],{"className":26519},[886],[888,26521,26522],{"xmlns":890},[892,26523,26524,26532],{},[895,26525,26526],{},[1824,26527,26528,26530],{},[898,26529,1912],{},[898,26531,1818],{},[902,26533,26534],{"encoding":904},"S^E",[198,26536,26538],{"id":26537},"příklad-74","Příklad 7.4",[724,26540,25054,26541,26562,26563,1343,26594,1343,26618,1343,26640,26662],{},[883,26542,26544],{"className":26543},[886],[888,26545,26546],{"xmlns":890},[892,26547,26548,26560],{},[895,26549,26550,26552,26554,26556,26558],{},[898,26551,6849],{},[2761,26553,16328],{},[898,26555,16222],{},[2761,26557,16328],{},[898,26559,16151],{},[902,26561,22254],{"encoding":904}," jsou dány ",[883,26564,26566],{"className":26565},[886],[888,26567,26568],{"xmlns":890},[892,26569,26570,26591],{},[895,26571,26572,26574,26576,26579,26581,26587,26589],{},[898,26573,6849],{},[1761,26575,1909],{},[1765,26577,26578],{},"0,9",[2761,26580,7057],{},[1681,26582,26583,26585],{},[898,26584,13170],{},[898,26586,2244],{},[1761,26588,1964],{},[1765,26590,9942],{},[902,26592,26593],{"encoding":904},"C = 0{,}9\\,Y_D + 70",[883,26595,26597],{"className":26596},[886],[888,26598,26599],{"xmlns":890},[892,26600,26601,26615],{},[895,26602,26603,26605,26607,26609,26611,26613],{},[898,26604,1655],{},[1761,26606,1909],{},[1765,26608,6910],{},[898,26610,13170],{},[1761,26612,1964],{},[1765,26614,9056],{},[902,26616,26617],{"encoding":904},"T = 0{,}2Y + 25",[883,26619,26621],{"className":26620},[886],[888,26622,26623],{"xmlns":890},[892,26624,26625,26637],{},[895,26626,26627,26633,26635],{},[1824,26628,26629,26631],{},[898,26630,16222],{},[1761,26632,8408],{},[1761,26634,1909],{},[1765,26636,19076],{},[902,26638,26639],{"encoding":904},"I^* = 35",[883,26641,26643],{"className":26642},[886],[888,26644,26645],{"xmlns":890},[892,26646,26647,26659],{},[895,26648,26649,26655,26657],{},[1824,26650,26651,26653],{},[898,26652,16151],{},[1761,26654,8408],{},[1761,26656,1909],{},[1765,26658,13077],{},[902,26660,26661],{"encoding":904},"G^* = 20",". Soustava (7.9):",[724,26664,26665],{},[883,26666,26668],{"className":26667},[886],[888,26669,26670],{"xmlns":890},[892,26671,26672,26796],{},[24787,26673,26674,26704,26732,26766],{"rowspacing":24789,"columnalign":24790,"columnspacing":6458},[24792,26675,26676,26682],{},[24795,26677,26678],{},[6411,26679,26680],{"scriptlevel":1767,"displaystyle":1833},[898,26681,13170],{},[24795,26683,26684],{},[6411,26685,26686],{"scriptlevel":1767,"displaystyle":1833},[895,26687,26688,26690,26692,26694,26696,26698,26700,26702],{},[895,26689],{},[1761,26691,1909],{},[898,26693,6849],{},[1761,26695,1964],{},[1765,26697,19076],{},[1761,26699,1964],{},[1765,26701,13077],{},[1761,26703,1834],{"separator":1833},[24792,26705,26706,26712],{},[24795,26707,26708],{},[6411,26709,26710],{"scriptlevel":1767,"displaystyle":1833},[898,26711,1655],{},[24795,26713,26714],{},[6411,26715,26716],{"scriptlevel":1767,"displaystyle":1833},[895,26717,26718,26720,26722,26724,26726,26728,26730],{},[895,26719],{},[1761,26721,1909],{},[1765,26723,6910],{},[898,26725,13170],{},[1761,26727,1964],{},[1765,26729,9056],{},[1761,26731,1834],{"separator":1833},[24792,26733,26734,26740],{},[24795,26735,26736],{},[6411,26737,26738],{"scriptlevel":1767,"displaystyle":1833},[898,26739,6849],{},[24795,26741,26742],{},[6411,26743,26744],{"scriptlevel":1767,"displaystyle":1833},[895,26745,26746,26748,26750,26752,26754,26760,26762,26764],{},[895,26747],{},[1761,26749,1909],{},[1765,26751,26578],{},[2761,26753,7057],{},[1681,26755,26756,26758],{},[898,26757,13170],{},[898,26759,2244],{},[1761,26761,1964],{},[1765,26763,9942],{},[1761,26765,1834],{"separator":1833},[24792,26767,26768,26778],{},[24795,26769,26770],{},[6411,26771,26772],{"scriptlevel":1767,"displaystyle":1833},[1681,26773,26774,26776],{},[898,26775,13170],{},[898,26777,2244],{},[24795,26779,26780],{},[6411,26781,26782],{"scriptlevel":1767,"displaystyle":1833},[895,26783,26784,26786,26788,26790,26792,26794],{},[895,26785],{},[1761,26787,1909],{},[898,26789,13170],{},[1761,26791,1885],{},[898,26793,1655],{},[898,26795,1741],{"mathvariant":1969},[902,26797,26798],{"encoding":904},"\\begin{aligned} Y &= C + 35 + 20, \\\\ T &= 0{,}2Y + 25, \\\\ C &= 0{,}9\\,Y_D + 70, \\\\ Y_D &= Y - T. \\end{aligned}",[724,26800,26801,26804,26805,26859,26860,26906,26907,2506],{},[38,26802,26803],{},"Řešení."," Z definice ",[883,26806,26808],{"className":26807},[886],[888,26809,26810],{"xmlns":890},[892,26811,26812,26856],{},[895,26813,26814,26820,26822,26824,26826,26828,26830,26832,26834,26836,26838,26840,26842,26844,26846,26848,26850,26852,26854],{},[1681,26815,26816,26818],{},[898,26817,13170],{},[898,26819,2244],{},[1761,26821,1909],{},[898,26823,13170],{},[1761,26825,1885],{},[898,26827,1655],{},[1761,26829,1909],{},[898,26831,13170],{},[1761,26833,1885],{},[1761,26835,1915],{"stretchy":1821},[1765,26837,6910],{},[898,26839,13170],{},[1761,26841,1964],{},[1765,26843,9056],{},[1761,26845,1920],{"stretchy":1821},[1761,26847,1909],{},[1765,26849,18627],{},[898,26851,13170],{},[1761,26853,1885],{},[1765,26855,9056],{},[902,26857,26858],{"encoding":904},"Y_D = Y - T = Y - (0{,}2Y + 25) = 0{,}8Y - 25",". Dosazením do spotřeby: ",[883,26861,26863],{"className":26862},[886],[888,26864,26865],{"xmlns":890},[892,26866,26867,26903],{},[895,26868,26869,26871,26873,26875,26877,26879,26881,26883,26885,26887,26889,26891,26893,26896,26898,26900],{},[898,26870,6849],{},[1761,26872,1909],{},[1765,26874,26578],{},[1761,26876,1915],{"stretchy":1821},[1765,26878,18627],{},[898,26880,13170],{},[1761,26882,1885],{},[1765,26884,9056],{},[1761,26886,1920],{"stretchy":1821},[1761,26888,1964],{},[1765,26890,9942],{},[1761,26892,1909],{},[1765,26894,26895],{},"0,72",[898,26897,13170],{},[1761,26899,1964],{},[1765,26901,26902],{},"47,5",[902,26904,26905],{"encoding":904},"C = 0{,}9(0{,}8Y - 25) + 70 = 0{,}72Y + 47{,}5",". Dosazením do rovnovážné rovnice ",[883,26908,26910],{"className":26909},[886],[888,26911,26912],{"xmlns":890},[892,26913,26914,26932],{},[895,26915,26916,26918,26920,26922,26924,26926,26928,26930],{},[898,26917,13170],{},[1761,26919,1909],{},[1765,26921,26895],{},[898,26923,13170],{},[1761,26925,1964],{},[1765,26927,26902],{},[1761,26929,1964],{},[1765,26931,25213],{},[902,26933,26934],{"encoding":904},"Y = 0{,}72Y + 47{,}5 + 55",[724,26936,26937],{},[883,26938,26940],{"className":26939},[886],[888,26941,26942],{"xmlns":890},[892,26943,26944,26985],{},[895,26945,26946,26949,26951,26953,26956,26958,26960,26962,26968,26970,26980,26982],{},[1765,26947,26948],{},"0,28",[898,26950,13170],{},[1761,26952,1909],{},[1765,26954,26955],{},"102,5",[2761,26957,8041],{},[1761,26959,19046],{},[2761,26961,8041],{},[1824,26963,26964,26966],{},[898,26965,13170],{},[898,26967,1818],{},[1761,26969,1909],{},[6411,26971,26972],{"scriptlevel":1767,"displaystyle":1821},[4379,26973,26974,26977],{},[1765,26975,26976],{},"5125",[1765,26978,26979],{},"14",[1761,26981,9945],{},[1765,26983,26984],{},"366,071.",[902,26986,26987],{"encoding":904},"0{,}28Y = 102{,}5 \\;\\Longrightarrow\\; Y^E = \\tfrac{5125}{14} \\doteq 366{,}071.",[724,26989,26990],{},"Rovnovážné veličiny:",[120,26992,26993,27028,27080,27134,27182],{},[123,26994,26995,1834],{},[883,26996,26998],{"className":26997},[886],[888,26999,27000],{"xmlns":890},[892,27001,27002,27025],{},[895,27003,27004,27010,27012,27020,27022],{},[1824,27005,27006,27008],{},[898,27007,13170],{},[898,27009,1818],{},[1761,27011,1909],{},[6411,27013,27014],{"scriptlevel":1767,"displaystyle":1821},[4379,27015,27016,27018],{},[1765,27017,26976],{},[1765,27019,26979],{},[1761,27021,9945],{},[1765,27023,27024],{},"366,071",[902,27026,27027],{"encoding":904},"Y^E = \\tfrac{5125}{14} \\doteq 366{,}071",[123,27029,27030,1834],{},[883,27031,27033],{"className":27032},[886],[888,27034,27035],{"xmlns":890},[892,27036,27037,27077],{},[895,27038,27039,27045,27047,27049,27051,27057,27059,27061,27063,27072,27074],{},[1824,27040,27041,27043],{},[898,27042,1655],{},[898,27044,1818],{},[1761,27046,1909],{},[1765,27048,6910],{},[2761,27050,7057],{},[1824,27052,27053,27055],{},[898,27054,13170],{},[898,27056,1818],{},[1761,27058,1964],{},[1765,27060,9056],{},[1761,27062,1909],{},[6411,27064,27065],{"scriptlevel":1767,"displaystyle":1821},[4379,27066,27067,27070],{},[1765,27068,27069],{},"1375",[1765,27071,26979],{},[1761,27073,9945],{},[1765,27075,27076],{},"98,214",[902,27078,27079],{"encoding":904},"T^E = 0{,}2\\,Y^E + 25 = \\tfrac{1375}{14} \\doteq 98{,}214",[123,27081,27082,1834],{},[883,27083,27085],{"className":27084},[886],[888,27086,27087],{"xmlns":890},[892,27088,27089,27131],{},[895,27090,27091,27099,27101,27107,27109,27115,27117,27126,27128],{},[2015,27092,27093,27095,27097],{},[898,27094,13170],{},[898,27096,2244],{},[898,27098,1818],{},[1761,27100,1909],{},[1824,27102,27103,27105],{},[898,27104,13170],{},[898,27106,1818],{},[1761,27108,1885],{},[1824,27110,27111,27113],{},[898,27112,1655],{},[898,27114,1818],{},[1761,27116,1909],{},[6411,27118,27119],{"scriptlevel":1767,"displaystyle":1821},[4379,27120,27121,27124],{},[1765,27122,27123],{},"3750",[1765,27125,26979],{},[1761,27127,9945],{},[1765,27129,27130],{},"267,857",[902,27132,27133],{"encoding":904},"Y_D^E = Y^E - T^E = \\tfrac{3750}{14} \\doteq 267{,}857",[123,27135,27136,1834],{},[883,27137,27139],{"className":27138},[886],[888,27140,27141],{"xmlns":890},[892,27142,27143,27179],{},[895,27144,27145,27151,27153,27159,27161,27163,27165,27174,27176],{},[1824,27146,27147,27149],{},[898,27148,6849],{},[898,27150,1818],{},[1761,27152,1909],{},[1824,27154,27155,27157],{},[898,27156,13170],{},[898,27158,1818],{},[1761,27160,1885],{},[1765,27162,25213],{},[1761,27164,1909],{},[6411,27166,27167],{"scriptlevel":1767,"displaystyle":1821},[4379,27168,27169,27172],{},[1765,27170,27171],{},"4355",[1765,27173,26979],{},[1761,27175,9945],{},[1765,27177,27178],{},"311,071",[902,27180,27181],{"encoding":904},"C^E = Y^E - 55 = \\tfrac{4355}{14} \\doteq 311{,}071",[123,27183,27184,27240],{},[883,27185,27187],{"className":27186},[886],[888,27188,27189],{"xmlns":890},[892,27190,27191,27237],{},[895,27192,27193,27199,27201,27209,27211,27217,27219,27221,27230,27232,27234],{},[1824,27194,27195,27197],{},[898,27196,1912],{},[898,27198,1818],{},[1761,27200,1909],{},[2015,27202,27203,27205,27207],{},[898,27204,13170],{},[898,27206,2244],{},[898,27208,1818],{},[1761,27210,1885],{},[1824,27212,27213,27215],{},[898,27214,6849],{},[898,27216,1818],{},[1761,27218,1909],{},[1761,27220,1885],{},[6411,27222,27223],{"scriptlevel":1767,"displaystyle":1821},[4379,27224,27225,27228],{},[1765,27226,27227],{},"605",[1765,27229,26979],{},[1761,27231,9945],{},[1761,27233,1885],{},[1765,27235,27236],{},"43,214",[902,27238,27239],{"encoding":904},"S^E = Y_D^E - C^E = -\\tfrac{605}{14} \\doteq -43{,}214"," (záporné — domácnosti při této kalibraci čerpají úspory).",[724,27242,27243,25383,27245,27266,27267,27270,27271,27294,27295,1741],{},[38,27244,25382],{},[883,27246,27248],{"className":27247},[886],[888,27249,27250],{"xmlns":890},[892,27251,27252,27264],{},[895,27253,27254,27256,27258,27260,27262],{},[898,27255,6849],{},[2761,27257,16328],{},[898,27259,16222],{},[2761,27261,16328],{},[898,27263,16151],{},[902,27265,22254],{"encoding":904}," stále uvažuje ",[38,27268,27269],{},"uzavřenou"," ekonomiku. Reálné ekonomiky dovážejí a vyvážejí zboží — otevření ekonomiky o čistý export ",[883,27272,27274],{"className":27273},[886],[888,27275,27276],{"xmlns":890},[892,27277,27278,27291],{},[895,27279,27280,27282,27284,27287,27289],{},[898,27281,16358],{},[1761,27283,1909],{},[898,27285,27286],{},"B",[1761,27288,1885],{},[898,27290,6889],{},[902,27292,27293],{"encoding":904},"X = B - M"," dává ",[38,27296,25404,27297],{},[883,27298,27300],{"className":27299},[886],[888,27301,27302],{"xmlns":890},[892,27303,27304,27320],{},[895,27305,27306,27308,27310,27312,27314,27316,27318],{},[898,27307,6849],{},[2761,27309,16328],{},[898,27311,16222],{},[2761,27313,16328],{},[898,27315,16151],{},[2761,27317,16328],{},[898,27319,16358],{},[902,27321,16361],{"encoding":904},[115,27323,27325],{"id":27324},"model-c-i-g-x-otevřená-ekonomika","Model C-I-G-X — otevřená ekonomika",[198,27327,24654],{"id":27328},"zadání-modelu-2",[724,27330,27331,27332,1989,27335,25627,27356,27369,27370,4590,27373,27386],{},"Rozšíření o ",[38,27333,27334],{},"čistý export",[883,27336,27338],{"className":27337},[886],[888,27339,27340],{"xmlns":890},[892,27341,27342,27354],{},[895,27343,27344,27346,27348,27350,27352],{},[898,27345,16358],{},[1761,27347,1909],{},[898,27349,27286],{},[1761,27351,1885],{},[898,27353,6889],{},[902,27355,27293],{"encoding":904},[883,27357,27359],{"className":27358},[886],[888,27360,27361],{"xmlns":890},[892,27362,27363,27367],{},[895,27364,27365],{},[898,27366,27286],{},[902,27368,27286],{"encoding":904}," je hrubý export (",[614,27371,27372],{},"brutto export",[883,27374,27376],{"className":27375},[886],[888,27377,27378],{"xmlns":890},[892,27379,27380,27384],{},[895,27381,27382],{},[898,27383,6889],{},[902,27385,6889],{"encoding":904}," import. Obvyklá konstrukce: import závisí (nejčastěji je úměrný) disponibilnímu důchodu:",[724,27388,27389],{},[883,27390,27392],{"className":27391},[886],[888,27393,27394],{"xmlns":890},[892,27395,27396,27416],{},[895,27397,27398,27400,27402,27404,27406,27412,27414],{},[898,27399,6889],{},[1761,27401,1909],{},[898,27403,6889],{},[1761,27405,1915],{"stretchy":1821},[1681,27407,27408,27410],{},[898,27409,13170],{},[898,27411,2244],{},[1761,27413,1920],{"stretchy":1821},[898,27415,1741],{"mathvariant":1969},[902,27417,27418],{"encoding":904},"M = M(Y_D).",[724,27420,27421],{},"Podmínka rovnováhy:",[724,27423,27424],{},[883,27425,27427],{"className":27426},[886],[888,27428,27429],{"xmlns":890},[892,27430,27431,27468],{},[895,27432,27433,27435,27437,27439,27441,27443,27445,27447,27449,27451,27453,27455,27457,27459,27461,27464,27466],{},[898,27434,13170],{},[1761,27436,1909],{},[898,27438,6849],{},[1761,27440,1964],{},[898,27442,16222],{},[1761,27444,1964],{},[898,27446,16151],{},[1761,27448,1964],{},[898,27450,27286],{},[1761,27452,1885],{},[898,27454,6889],{},[898,27456,1741],{"mathvariant":1969},[3315,27458],{"width":3317},[1761,27460,1915],{"stretchy":1821},[1765,27462,27463],{},"7.10",[2761,27465,207],{},[1761,27467,1920],{"stretchy":1821},[902,27469,27470],{"encoding":904},"Y = C + I + G + B - M. \\qquad (7.10\\text{a})",[198,27472,24724],{"id":27473},"soustava-rovnic-2",[724,27475,25884,27476,27510,27511,2506],{},[883,27477,27479],{"className":27478},[886],[888,27480,27481],{"xmlns":890},[892,27482,27483,27507],{},[895,27484,27485,27491,27493,27499,27501],{},[1824,27486,27487,27489],{},[898,27488,16222],{},[1761,27490,8408],{},[1761,27492,1834],{"separator":1833},[1824,27494,27495,27497],{},[898,27496,16151],{},[1761,27498,8408],{},[1761,27500,1834],{"separator":1833},[1824,27502,27503,27505],{},[898,27504,27286],{},[1761,27506,8408],{},[902,27508,27509],{"encoding":904},"I^*, G^*, B^*"," dostáváme soustavu 5 rovnic o 5 neznámých ",[883,27512,27514],{"className":27513},[886],[888,27515,27516],{"xmlns":890},[892,27517,27518,27542],{},[895,27519,27520,27522,27524,27526,27528,27530,27532,27538,27540],{},[898,27521,13170],{},[1761,27523,1834],{"separator":1833},[898,27525,6849],{},[1761,27527,1834],{"separator":1833},[898,27529,1655],{},[1761,27531,1834],{"separator":1833},[1681,27533,27534,27536],{},[898,27535,13170],{},[898,27537,2244],{},[1761,27539,1834],{"separator":1833},[898,27541,6889],{},[902,27543,27544],{"encoding":904},"Y, C, T, Y_D, M",[724,27546,27547],{},[883,27548,27550],{"className":27549},[886],[888,27551,27552],{"xmlns":890},[892,27553,27554,27738],{},[895,27555,27556,27730,27732,27734,27736],{},[24787,27557,27558,27590,27620,27648,27680],{"rowspacing":24789,"columnalign":24790,"columnspacing":6458},[24792,27559,27560,27566],{},[24795,27561,27562],{},[6411,27563,27564],{"scriptlevel":1767,"displaystyle":1833},[898,27565,6849],{},[24795,27567,27568],{},[6411,27569,27570],{"scriptlevel":1767,"displaystyle":1833},[895,27571,27572,27574,27576,27578,27580,27586,27588],{},[895,27573],{},[1761,27575,1909],{},[898,27577,6849],{},[1761,27579,1915],{"stretchy":1821},[1681,27581,27582,27584],{},[898,27583,13170],{},[898,27585,2244],{},[1761,27587,1920],{"stretchy":1821},[1761,27589,1834],{"separator":1833},[24792,27591,27592,27602],{},[24795,27593,27594],{},[6411,27595,27596],{"scriptlevel":1767,"displaystyle":1833},[1681,27597,27598,27600],{},[898,27599,13170],{},[898,27601,2244],{},[24795,27603,27604],{},[6411,27605,27606],{"scriptlevel":1767,"displaystyle":1833},[895,27607,27608,27610,27612,27614,27616,27618],{},[895,27609],{},[1761,27611,1909],{},[898,27613,13170],{},[1761,27615,1885],{},[898,27617,1655],{},[1761,27619,1834],{"separator":1833},[24792,27621,27622,27628],{},[24795,27623,27624],{},[6411,27625,27626],{"scriptlevel":1767,"displaystyle":1833},[898,27627,1655],{},[24795,27629,27630],{},[6411,27631,27632],{"scriptlevel":1767,"displaystyle":1833},[895,27633,27634,27636,27638,27640,27642,27644,27646],{},[895,27635],{},[1761,27637,1909],{},[898,27639,1655],{},[1761,27641,1915],{"stretchy":1821},[898,27643,13170],{},[1761,27645,1920],{"stretchy":1821},[1761,27647,1834],{"separator":1833},[24792,27649,27650,27656],{},[24795,27651,27652],{},[6411,27653,27654],{"scriptlevel":1767,"displaystyle":1833},[898,27655,6889],{},[24795,27657,27658],{},[6411,27659,27660],{"scriptlevel":1767,"displaystyle":1833},[895,27661,27662,27664,27666,27668,27670,27676,27678],{},[895,27663],{},[1761,27665,1909],{},[898,27667,6889],{},[1761,27669,1915],{"stretchy":1821},[1681,27671,27672,27674],{},[898,27673,13170],{},[898,27675,2244],{},[1761,27677,1920],{"stretchy":1821},[1761,27679,1834],{"separator":1833},[24792,27681,27682,27688],{},[24795,27683,27684],{},[6411,27685,27686],{"scriptlevel":1767,"displaystyle":1833},[898,27687,13170],{},[24795,27689,27690],{},[6411,27691,27692],{"scriptlevel":1767,"displaystyle":1833},[895,27693,27694,27696,27698,27700,27702,27708,27710,27716,27718,27724,27726,27728],{},[895,27695],{},[1761,27697,1909],{},[898,27699,6849],{},[1761,27701,1964],{},[1824,27703,27704,27706],{},[898,27705,16222],{},[1761,27707,8408],{},[1761,27709,1964],{},[1824,27711,27712,27714],{},[898,27713,16151],{},[1761,27715,8408],{},[1761,27717,1964],{},[1824,27719,27720,27722],{},[898,27721,27286],{},[1761,27723,8408],{},[1761,27725,1885],{},[898,27727,6889],{},[898,27729,1741],{"mathvariant":1969},[3315,27731],{"width":3317},[1761,27733,1915],{"stretchy":1821},[1765,27735,27463],{},[1761,27737,1920],{"stretchy":1821},[902,27739,27740],{"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)",[198,27742,27744],{"id":27743},"příklad-75","Příklad 7.5",[724,27746,27747,27748,1343,27780,1343,27807,1343,27828,1343,27850,1343,27872,27895],{},"Dáno: ",[883,27749,27751],{"className":27750},[886],[888,27752,27753],{"xmlns":890},[892,27754,27755,27777],{},[895,27756,27757,27759,27761,27764,27766,27772,27774],{},[898,27758,6849],{},[1761,27760,1909],{},[1765,27762,27763],{},"0,75",[2761,27765,7057],{},[1681,27767,27768,27770],{},[898,27769,13170],{},[898,27771,2244],{},[1761,27773,1964],{},[1765,27775,27776],{},"750",[902,27778,27779],{"encoding":904},"C = 0{,}75\\,Y_D + 750",[883,27781,27783],{"className":27782},[886],[888,27784,27785],{"xmlns":890},[892,27786,27787,27804],{},[895,27788,27789,27791,27793,27796,27798],{},[898,27790,6889],{},[1761,27792,1909],{},[1765,27794,27795],{},"0,15",[2761,27797,7057],{},[1681,27799,27800,27802],{},[898,27801,13170],{},[898,27803,2244],{},[902,27805,27806],{"encoding":904},"M = 0{,}15\\,Y_D",[883,27808,27810],{"className":27809},[886],[888,27811,27812],{"xmlns":890},[892,27813,27814,27825],{},[895,27815,27816,27818,27820,27823],{},[898,27817,1655],{},[1761,27819,1909],{},[1765,27821,27822],{},"0,25",[898,27824,13170],{},[902,27826,27827],{"encoding":904},"T = 0{,}25Y",[883,27829,27831],{"className":27830},[886],[888,27832,27833],{"xmlns":890},[892,27834,27835,27847],{},[895,27836,27837,27843,27845],{},[1824,27838,27839,27841],{},[898,27840,16222],{},[1761,27842,8408],{},[1761,27844,1909],{},[1765,27846,19148],{},[902,27848,27849],{"encoding":904},"I^* = 500",[883,27851,27853],{"className":27852},[886],[888,27854,27855],{"xmlns":890},[892,27856,27857,27869],{},[895,27858,27859,27865,27867],{},[1824,27860,27861,27863],{},[898,27862,16151],{},[1761,27864,8408],{},[1761,27866,1909],{},[1765,27868,12845],{},[902,27870,27871],{"encoding":904},"G^* = 150",[883,27873,27875],{"className":27874},[886],[888,27876,27877],{"xmlns":890},[892,27878,27879,27892],{},[895,27880,27881,27887,27889],{},[1824,27882,27883,27885],{},[898,27884,27286],{},[1761,27886,8408],{},[1761,27888,1909],{},[1765,27890,27891],{},"800",[902,27893,27894],{"encoding":904},"B^* = 800",". Soustava:",[724,27897,27898],{},[883,27899,27901],{"className":27900},[886],[888,27902,27903],{"xmlns":890},[892,27904,27905,28123],{},[24787,27906,27907,27953,27995,28031,28073],{"rowspacing":24789,"columnalign":24790,"columnspacing":6458},[24792,27908,27909,27925],{},[24795,27910,27911],{},[6411,27912,27913],{"scriptlevel":1767,"displaystyle":1833},[895,27914,27915,27917,27919,27921,27923],{},[1761,27916,1915],{"stretchy":1821},[898,27918,1719],{},[1765,27920,1945],{},[1761,27922,1920],{"stretchy":1821},[2761,27924,2763],{},[24795,27926,27927],{},[6411,27928,27929],{"scriptlevel":1767,"displaystyle":1833},[895,27930,27931,27933,27935,27937,27939,27941,27947,27949,27951],{},[895,27932],{},[898,27934,6849],{},[1761,27936,1909],{},[1765,27938,27763],{},[2761,27940,7057],{},[1681,27942,27943,27945],{},[898,27944,13170],{},[898,27946,2244],{},[1761,27948,1964],{},[1765,27950,27776],{},[1761,27952,1834],{"separator":1833},[24792,27954,27955,27971],{},[24795,27956,27957],{},[6411,27958,27959],{"scriptlevel":1767,"displaystyle":1833},[895,27960,27961,27963,27965,27967,27969],{},[1761,27962,1915],{"stretchy":1821},[898,27964,1719],{},[1765,27966,2296],{},[1761,27968,1920],{"stretchy":1821},[2761,27970,2763],{},[24795,27972,27973],{},[6411,27974,27975],{"scriptlevel":1767,"displaystyle":1833},[895,27976,27977,27979,27985,27987,27989,27991,27993],{},[895,27978],{},[1681,27980,27981,27983],{},[898,27982,13170],{},[898,27984,2244],{},[1761,27986,1909],{},[898,27988,13170],{},[1761,27990,1885],{},[898,27992,1655],{},[1761,27994,1834],{"separator":1833},[24792,27996,27997,28013],{},[24795,27998,27999],{},[6411,28000,28001],{"scriptlevel":1767,"displaystyle":1833},[895,28002,28003,28005,28007,28009,28011],{},[1761,28004,1915],{"stretchy":1821},[898,28006,1719],{},[1765,28008,5486],{},[1761,28010,1920],{"stretchy":1821},[2761,28012,2763],{},[24795,28014,28015],{},[6411,28016,28017],{"scriptlevel":1767,"displaystyle":1833},[895,28018,28019,28021,28023,28025,28027,28029],{},[895,28020],{},[898,28022,1655],{},[1761,28024,1909],{},[1765,28026,27822],{},[898,28028,13170],{},[1761,28030,1834],{"separator":1833},[24792,28032,28033,28049],{},[24795,28034,28035],{},[6411,28036,28037],{"scriptlevel":1767,"displaystyle":1833},[895,28038,28039,28041,28043,28045,28047],{},[1761,28040,1915],{"stretchy":1821},[898,28042,1719],{},[1765,28044,2318],{},[1761,28046,1920],{"stretchy":1821},[2761,28048,2763],{},[24795,28050,28051],{},[6411,28052,28053],{"scriptlevel":1767,"displaystyle":1833},[895,28054,28055,28057,28059,28061,28063,28065,28071],{},[895,28056],{},[898,28058,6889],{},[1761,28060,1909],{},[1765,28062,27795],{},[2761,28064,7057],{},[1681,28066,28067,28069],{},[898,28068,13170],{},[898,28070,2244],{},[1761,28072,1834],{"separator":1833},[24792,28074,28075,28091],{},[24795,28076,28077],{},[6411,28078,28079],{"scriptlevel":1767,"displaystyle":1833},[895,28080,28081,28083,28085,28087,28089],{},[1761,28082,1915],{"stretchy":1821},[898,28084,1719],{},[1765,28086,6321],{},[1761,28088,1920],{"stretchy":1821},[2761,28090,2763],{},[24795,28092,28093],{},[6411,28094,28095],{"scriptlevel":1767,"displaystyle":1833},[895,28096,28097,28099,28101,28103,28105,28107,28109,28111,28113,28115,28117,28119,28121],{},[895,28098],{},[898,28100,13170],{},[1761,28102,1909],{},[898,28104,6849],{},[1761,28106,1964],{},[1765,28108,19148],{},[1761,28110,1964],{},[1765,28112,12845],{},[1761,28114,1964],{},[1765,28116,27891],{},[1761,28118,1885],{},[898,28120,6889],{},[898,28122,1741],{"mathvariant":1969},[902,28124,28125],{"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}",[724,28127,28128,28129,28163],{},"Postupná substituce — z (r3) do (r2): ",[883,28130,28132],{"className":28131},[886],[888,28133,28134],{"xmlns":890},[892,28135,28136,28160],{},[895,28137,28138,28144,28146,28148,28150,28152,28154,28156,28158],{},[1681,28139,28140,28142],{},[898,28141,13170],{},[898,28143,2244],{},[1761,28145,1909],{},[898,28147,13170],{},[1761,28149,1885],{},[1765,28151,27822],{},[898,28153,13170],{},[1761,28155,1909],{},[1765,28157,27763],{},[898,28159,13170],{},[902,28161,28162],{"encoding":904},"Y_D = Y - 0{,}25Y = 0{,}75Y",". Dosazením do (r1) a (r4):",[724,28165,28166],{},[883,28167,28169],{"className":28168},[886],[888,28170,28171],{"xmlns":890},[892,28172,28173,28214],{},[895,28174,28175,28177,28179,28181,28183,28185,28187,28189,28191,28193,28195,28197,28199,28201,28203,28206,28208,28210,28212],{},[1761,28176,1915],{"stretchy":1821},[898,28178,1719],{},[1765,28180,2340],{},[1761,28182,1920],{"stretchy":1821},[2761,28184,2763],{},[898,28186,6849],{},[1761,28188,1909],{},[1765,28190,27763],{},[1761,28192,2447],{},[1765,28194,27763],{},[898,28196,13170],{},[1761,28198,1964],{},[1765,28200,27776],{},[1761,28202,1909],{},[1765,28204,28205],{},"0,5625",[898,28207,13170],{},[1761,28209,1964],{},[1765,28211,27776],{},[1761,28213,1834],{"separator":1833},[902,28215,28216],{"encoding":904},"(r6)\\ C = 0{,}75 \\cdot 0{,}75Y + 750 = 0{,}5625Y + 750,",[724,28218,28219],{},[883,28220,28222],{"className":28221},[886],[888,28223,28224],{"xmlns":890},[892,28225,28226,28259],{},[895,28227,28228,28230,28232,28234,28236,28238,28240,28242,28244,28246,28248,28250,28252,28255,28257],{},[1761,28229,1915],{"stretchy":1821},[898,28231,1719],{},[1765,28233,5512],{},[1761,28235,1920],{"stretchy":1821},[2761,28237,2763],{},[898,28239,6889],{},[1761,28241,1909],{},[1765,28243,27795],{},[1761,28245,2447],{},[1765,28247,27763],{},[898,28249,13170],{},[1761,28251,1909],{},[1765,28253,28254],{},"0,1125",[898,28256,13170],{},[898,28258,1741],{"mathvariant":1969},[902,28260,28261],{"encoding":904},"(r7)\\ M = 0{,}15 \\cdot 0{,}75Y = 0{,}1125Y.",[724,28263,28264],{},"Dosazením do (r5):",[724,28266,28267],{},[883,28268,28270],{"className":28269},[886],[888,28271,28272],{"xmlns":890},[892,28273,28274,28318],{},[895,28275,28276,28278,28280,28282,28284,28286,28288,28290,28292,28294,28296,28298,28300,28302,28304,28306,28308,28311,28313,28315],{},[898,28277,13170],{},[1761,28279,1909],{},[1765,28281,28205],{},[898,28283,13170],{},[1761,28285,1964],{},[1765,28287,27776],{},[1761,28289,1964],{},[1765,28291,19148],{},[1761,28293,1964],{},[1765,28295,12845],{},[1761,28297,1964],{},[1765,28299,27891],{},[1761,28301,1885],{},[1765,28303,28254],{},[898,28305,13170],{},[1761,28307,1909],{},[1765,28309,28310],{},"0,45",[898,28312,13170],{},[1761,28314,1964],{},[1765,28316,28317],{},"2200.",[902,28319,28320],{"encoding":904},"Y = 0{,}5625Y + 750 + 500 + 150 + 800 - 0{,}1125Y = 0{,}45Y + 2200.",[724,28322,28323,28324,2403,28346,28369],{},"Odtud ",[883,28325,28327],{"className":28326},[886],[888,28328,28329],{"xmlns":890},[892,28330,28331,28343],{},[895,28332,28333,28336,28338,28340],{},[1765,28334,28335],{},"0,55",[898,28337,13170],{},[1761,28339,1909],{},[1765,28341,28342],{},"2200",[902,28344,28345],{"encoding":904},"0{,}55Y = 2200",[883,28347,28349],{"className":28348},[886],[888,28350,28351],{"xmlns":890},[892,28352,28353,28366],{},[895,28354,28355,28361,28363],{},[1824,28356,28357,28359],{},[898,28358,13170],{},[898,28360,1818],{},[1761,28362,1909],{},[1765,28364,28365],{},"4000",[902,28367,28368],{"encoding":904},"Y^E = 4000",". Rovnovážné veličiny:",[120,28371,28372,28395,28427,28462,28495,28531],{},[123,28373,28374,1834],{},[883,28375,28377],{"className":28376},[886],[888,28378,28379],{"xmlns":890},[892,28380,28381,28393],{},[895,28382,28383,28389,28391],{},[1824,28384,28385,28387],{},[898,28386,13170],{},[898,28388,1818],{},[1761,28390,1909],{},[1765,28392,28365],{},[902,28394,28368],{"encoding":904},[123,28396,28397,1834],{},[883,28398,28400],{"className":28399},[886],[888,28401,28402],{"xmlns":890},[892,28403,28404,28424],{},[895,28405,28406,28412,28414,28416,28418,28420,28422],{},[1824,28407,28408,28410],{},[898,28409,1655],{},[898,28411,1818],{},[1761,28413,1909],{},[1765,28415,27822],{},[1761,28417,2447],{},[1765,28419,28365],{},[1761,28421,1909],{},[1765,28423,6854],{},[902,28425,28426],{"encoding":904},"T^E = 0{,}25 \\cdot 4000 = 1000",[123,28428,28429,1834],{},[883,28430,28432],{"className":28431},[886],[888,28433,28434],{"xmlns":890},[892,28435,28436,28459],{},[895,28437,28438,28446,28448,28450,28452,28454,28456],{},[2015,28439,28440,28442,28444],{},[898,28441,13170],{},[898,28443,2244],{},[898,28445,1818],{},[1761,28447,1909],{},[1765,28449,27763],{},[1761,28451,2447],{},[1765,28453,28365],{},[1761,28455,1909],{},[1765,28457,28458],{},"3000",[902,28460,28461],{"encoding":904},"Y_D^E = 0{,}75 \\cdot 4000 = 3000",[123,28463,28464,1834],{},[883,28465,28467],{"className":28466},[886],[888,28468,28469],{"xmlns":890},[892,28470,28471,28492],{},[895,28472,28473,28479,28481,28483,28485,28487,28489],{},[1824,28474,28475,28477],{},[898,28476,6889],{},[898,28478,1818],{},[1761,28480,1909],{},[1765,28482,27795],{},[1761,28484,2447],{},[1765,28486,28458],{},[1761,28488,1909],{},[1765,28490,28491],{},"450",[902,28493,28494],{"encoding":904},"M^E = 0{,}15 \\cdot 3000 = 450",[123,28496,28497,1834],{},[883,28498,28500],{"className":28499},[886],[888,28501,28502],{"xmlns":890},[892,28503,28504,28528],{},[895,28505,28506,28512,28514,28516,28518,28520,28522,28524,28526],{},[1824,28507,28508,28510],{},[898,28509,6849],{},[898,28511,1818],{},[1761,28513,1909],{},[1765,28515,27763],{},[1761,28517,2447],{},[1765,28519,28458],{},[1761,28521,1964],{},[1765,28523,27776],{},[1761,28525,1909],{},[1765,28527,28458],{},[902,28529,28530],{"encoding":904},"C^E = 0{,}75 \\cdot 3000 + 750 = 3000",[123,28532,28533,28573],{},[883,28534,28536],{"className":28535},[886],[888,28537,28538],{"xmlns":890},[892,28539,28540,28570],{},[895,28541,28542,28548,28550,28558,28560,28566,28568],{},[1824,28543,28544,28546],{},[898,28545,1912],{},[898,28547,1818],{},[1761,28549,1909],{},[2015,28551,28552,28554,28556],{},[898,28553,13170],{},[898,28555,2244],{},[898,28557,1818],{},[1761,28559,1885],{},[1824,28561,28562,28564],{},[898,28563,6849],{},[898,28565,1818],{},[1761,28567,1909],{},[1765,28569,1767],{},[902,28571,28572],{"encoding":904},"S^E = Y_D^E - C^E = 0"," (při této kalibraci domácnosti celý disponibilní důchod spotřebují).",[724,28575,28576,28578,28579,1343,28596,2068,28617,28642,28643,28646,28647,28660,28661,1741],{},[38,28577,25382],{}," Modely ",[883,28580,28582],{"className":28581},[886],[888,28583,28584],{"xmlns":890},[892,28585,28586,28594],{},[895,28587,28588,28590,28592],{},[898,28589,6849],{},[2761,28591,16328],{},[898,28593,16222],{},[902,28595,16333],{"encoding":904},[883,28597,28599],{"className":28598},[886],[888,28600,28601],{"xmlns":890},[892,28602,28603,28615],{},[895,28604,28605,28607,28609,28611,28613],{},[898,28606,6849],{},[2761,28608,16328],{},[898,28610,16222],{},[2761,28612,16328],{},[898,28614,16151],{},[902,28616,22254],{"encoding":904},[883,28618,28620],{"className":28619},[886],[888,28621,28622],{"xmlns":890},[892,28623,28624,28640],{},[895,28625,28626,28628,28630,28632,28634,28636,28638],{},[898,28627,6849],{},[2761,28629,16328],{},[898,28631,16222],{},[2761,28633,16328],{},[898,28635,16151],{},[2761,28637,16328],{},[898,28639,16358],{},[902,28641,16361],{"encoding":904}," pokládají investice za ",[38,28644,28645],{},"konstantní",". To není realistické — investice závisejí na úrokové míře ",[883,28648,28650],{"className":28649},[886],[888,28651,28652],{"xmlns":890},[892,28653,28654,28658],{},[895,28655,28656],{},[898,28657,1719],{},[902,28659,1719],{"encoding":904},". Přidáním trhu peněz a úrokové míry vzniká ",[38,28662,28663],{},"model IS-LM",[115,28665,28667],{"id":28666},"_74-multiplikátory-pro-makroekonomické-proměnné","7.4 Multiplikátory pro makroekonomické proměnné",[724,28669,28670,28671,28675,28676,28679,28680,28683],{},"V článku ",[207,28672,28674],{"className":28673,"dataFsResolvedFilePath":827,"href":828},[210],"2.4"," (mikroekonomie) byly zavedeny multiplikátory pro mikroekonomické proměnné. ",[38,28677,28678],{},"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 ",[38,28681,28682],{},"výraznější"," než v mikroekonomických modelech.",[724,28685,28686],{},[3991,28687],{"alt":28688,"className":28689,"src":28690},"imek-multiplikatorovy-efekt-chain",[210,3995],"\u002Fwiki-assets\u002Fimek-multiplikatorovy-efekt-chain.jpeg",[724,28692,16202,28693,1343,28710,1343,28731,28756,28757,28760,28761,28779,28780,28798,28799,28817,28818,28821,28822,1343,28839,28856,28857,28859],{},[883,28694,28696],{"className":28695},[886],[888,28697,28698],{"xmlns":890},[892,28699,28700,28708],{},[895,28701,28702,28704,28706],{},[898,28703,6849],{},[2761,28705,16328],{},[898,28707,16222],{},[902,28709,16333],{"encoding":904},[883,28711,28713],{"className":28712},[886],[888,28714,28715],{"xmlns":890},[892,28716,28717,28729],{},[895,28718,28719,28721,28723,28725,28727],{},[898,28720,6849],{},[2761,28722,16328],{},[898,28724,16222],{},[2761,28726,16328],{},[898,28728,16151],{},[902,28730,22254],{"encoding":904},[883,28732,28734],{"className":28733},[886],[888,28735,28736],{"xmlns":890},[892,28737,28738,28754],{},[895,28739,28740,28742,28744,28746,28748,28750,28752],{},[898,28741,6849],{},[2761,28743,16328],{},[898,28745,16222],{},[2761,28747,16328],{},[898,28749,16151],{},[2761,28751,16328],{},[898,28753,16358],{},[902,28755,16361],{"encoding":904}," se vyšetřuje vliv změn ",[38,28758,28759],{},"exogenních"," veličin (plánovaných investic ",[883,28762,28764],{"className":28763},[886],[888,28765,28766],{"xmlns":890},[892,28767,28768,28776],{},[895,28769,28770],{},[1824,28771,28772,28774],{},[898,28773,16222],{},[1761,28775,8408],{},[902,28777,28778],{"encoding":904},"I^*",", vládních výdajů ",[883,28781,28783],{"className":28782},[886],[888,28784,28785],{"xmlns":890},[892,28786,28787,28795],{},[895,28788,28789],{},[1824,28790,28791,28793],{},[898,28792,16151],{},[1761,28794,8408],{},[902,28796,28797],{"encoding":904},"G^*",", exportu ",[883,28800,28802],{"className":28801},[886],[888,28803,28804],{"xmlns":890},[892,28805,28806,28814],{},[895,28807,28808],{},[1824,28809,28810,28812],{},[898,28811,27286],{},[1761,28813,8408],{},[902,28815,28816],{"encoding":904},"B^*",") na změny ",[38,28819,28820],{},"endogenních"," rovnovážných veličin (",[883,28823,28825],{"className":28824},[886],[888,28826,28827],{"xmlns":890},[892,28828,28829,28837],{},[895,28830,28831],{},[1824,28832,28833,28835],{},[898,28834,13170],{},[898,28836,1818],{},[902,28838,17941],{"encoding":904},[883,28840,28842],{"className":28841},[886],[888,28843,28844],{"xmlns":890},[892,28845,28846,28854],{},[895,28847,28848],{},[1824,28849,28850,28852],{},[898,28851,6849],{},[898,28853,1818],{},[902,28855,18000],{"encoding":904}," atd.). Tyto citlivosti se vyjadřují ",[38,28858,22011],{}," — parciálními derivacemi rovnovážných veličin podle exogenních veličin.",[198,28861,28863],{"id":28862},"multiplikátory-v-modelu-c-i","Multiplikátory v modelu C-I",[724,28865,24928,28866,28889,28890,28934],{},[883,28867,28869],{"className":28868},[886],[888,28870,28871],{"xmlns":890},[892,28872,28873,28887],{},[895,28874,28875,28877,28879,28881,28883,28885],{},[898,28876,6849],{},[1761,28878,1909],{},[898,28880,207],{},[898,28882,13170],{},[1761,28884,1964],{},[898,28886,4302],{},[902,28888,22953],{"encoding":904}," dává (7.7) redukovaný tvar ",[883,28891,28893],{"className":28892},[886],[888,28894,28895],{"xmlns":890},[892,28896,28897,28931],{},[895,28898,28899,28905,28907],{},[1824,28900,28901,28903],{},[898,28902,13170],{},[898,28904,1818],{},[1761,28906,1909],{},[6411,28908,28909],{"scriptlevel":1767,"displaystyle":1833},[4379,28910,28911,28923],{},[895,28912,28913,28915,28917],{},[898,28914,4302],{},[1761,28916,1964],{},[1824,28918,28919,28921],{},[898,28920,16222],{},[1761,28922,8408],{},[895,28924,28925,28927,28929],{},[1765,28926,1945],{},[1761,28928,1885],{},[898,28930,207],{},[902,28932,28933],{"encoding":904},"Y^E = \\dfrac{b + I^*}{1 - a}",". Parciální derivace:",[724,28936,28937],{},[883,28938,28940],{"className":28939},[886],[888,28941,28942],{"xmlns":890},[892,28943,28944,29013],{},[895,28945,28946,28964,28966,28996,28998],{},[4379,28947,28948,28958],{},[895,28949,28950,28952],{},[898,28951,13911],{"mathvariant":1969},[1824,28953,28954,28956],{},[898,28955,13170],{},[898,28957,1818],{},[895,28959,28960,28962],{},[898,28961,13911],{"mathvariant":1969},[898,28963,207],{},[1761,28965,1909],{},[4379,28967,28968,28980],{},[895,28969,28970,28972,28974],{},[898,28971,4302],{},[1761,28973,1964],{},[1824,28975,28976,28978],{},[898,28977,16222],{},[1761,28979,8408],{},[895,28981,28982,28984,28986,28988,28990],{},[1761,28983,1915],{"stretchy":1821},[1765,28985,1945],{},[1761,28987,1885],{},[898,28989,207],{},[1824,28991,28992,28994],{},[1761,28993,1920],{"stretchy":1821},[1765,28995,2296],{},[3315,28997],{"width":3317},[895,28999,29000,29003,29010],{},[2761,29001,29002],{},"(multiplik",[2770,29004,29005,29007],{"accent":1833},[2761,29006,207],{},[1761,29008,29009],{},"ˊ",[2761,29011,29012],{},"tor MPC)",[902,29014,29015],{"encoding":904},"\\frac{\\partial Y^E}{\\partial a} = \\frac{b + I^*}{(1 - a)^2} \\qquad \\text{(multiplikátor MPC)}",[724,29017,29018],{},[883,29019,29021],{"className":29020},[886],[888,29022,29023],{"xmlns":890},[892,29024,29025,29093],{},[895,29026,29027,29045,29047,29059,29061],{},[4379,29028,29029,29039],{},[895,29030,29031,29033],{},[898,29032,13911],{"mathvariant":1969},[1824,29034,29035,29037],{},[898,29036,13170],{},[898,29038,1818],{},[895,29040,29041,29043],{},[898,29042,13911],{"mathvariant":1969},[898,29044,4302],{},[1761,29046,1909],{},[4379,29048,29049,29051],{},[1765,29050,1945],{},[895,29052,29053,29055,29057],{},[1765,29054,1945],{},[1761,29056,1885],{},[898,29058,207],{},[3315,29060],{"width":3317},[895,29062,29063,29065,29071,29074,29081,29084,29090],{},[2761,29064,29002],{},[2770,29066,29067,29069],{"accent":1833},[2761,29068,207],{},[1761,29070,29009],{},[2761,29072,29073],{},"tor autonomn",[2770,29075,29076,29079],{"accent":1833},[2761,29077,29078],{},"ı",[1761,29080,29009],{},[2761,29082,29083],{}," spot",[2770,29085,29086,29088],{"accent":1833},[2761,29087,1719],{},[1761,29089,2777],{},[2761,29091,29092],{},"eby)",[902,29094,29095],{"encoding":904},"\\frac{\\partial Y^E}{\\partial b} = \\frac{1}{1 - a} \\qquad \\text{(multiplikátor autonomní spotřeby)}",[724,29097,29098],{},[883,29099,29101],{"className":29100},[886],[888,29102,29103],{"xmlns":890},[892,29104,29105,29172],{},[895,29106,29107,29129,29131,29143,29145,29157,29159],{},[4379,29108,29109,29119],{},[895,29110,29111,29113],{},[898,29112,13911],{"mathvariant":1969},[1824,29114,29115,29117],{},[898,29116,13170],{},[898,29118,1818],{},[895,29120,29121,29123],{},[898,29122,13911],{"mathvariant":1969},[1824,29124,29125,29127],{},[898,29126,16222],{},[1761,29128,8408],{},[1761,29130,1909],{},[4379,29132,29133,29135],{},[1765,29134,1945],{},[895,29136,29137,29139,29141],{},[1765,29138,1945],{},[1761,29140,1885],{},[898,29142,207],{},[1761,29144,1909],{},[4379,29146,29147,29149],{},[1765,29148,1945],{},[895,29150,29151,29153,29155],{},[898,29152,6889],{},[898,29154,1839],{},[898,29156,1912],{},[3315,29158],{"width":3317},[895,29160,29161,29163,29169],{},[2761,29162,29002],{},[2770,29164,29165,29167],{"accent":1833},[2761,29166,207],{},[1761,29168,29009],{},[2761,29170,29171],{},"tor investic)",[902,29173,29174],{"encoding":904},"\\frac{\\partial Y^E}{\\partial I^*} = \\frac{1}{1 - a} = \\frac{1}{MPS} \\qquad \\text{(multiplikátor investic)}",[1636,29176,29177],{},[724,29178,29179,29181,29182,29185,29186,29199,29200,29217,29218,29236,29237,29281,29282,25453,29299,29302,29303,29320],{},[883,29180,1642],{}," Intuice — proč Keynesův multiplikátor funguje\nInvestice o 1 Kč se stanou něčím ",[38,29183,29184],{},"důchodem","; z něj se utratí ",[883,29187,29189],{"className":29188},[886],[888,29190,29191],{"xmlns":890},[892,29192,29193,29197],{},[895,29194,29195],{},[898,29196,207],{},[902,29198,207],{"encoding":904}," Kč (= ",[883,29201,29203],{"className":29202},[886],[888,29204,29205],{"xmlns":890},[892,29206,29207,29215],{},[895,29208,29209,29211,29213],{},[898,29210,6889],{},[898,29212,1839],{},[898,29214,6849],{},[902,29216,22079],{"encoding":904},"), to je zase něčí důchod, z něj ",[883,29219,29221],{"className":29220},[886],[888,29222,29223],{"xmlns":890},[892,29224,29225,29233],{},[895,29226,29227],{},[1824,29228,29229,29231],{},[898,29230,207],{},[1765,29232,2296],{},[902,29234,29235],{"encoding":904},"a^2"," Kč… Součet geometrické řady ",[883,29238,29240],{"className":29239},[886],[888,29241,29242],{"xmlns":890},[892,29243,29244,29278],{},[895,29245,29246,29248,29250,29252,29254,29260,29262,29264,29266],{},[1765,29247,1945],{},[1761,29249,1964],{},[898,29251,207],{},[1761,29253,1964],{},[1824,29255,29256,29258],{},[898,29257,207],{},[1765,29259,2296],{},[1761,29261,1964],{},[1761,29263,22139],{},[1761,29265,1909],{},[4379,29267,29268,29270],{},[1765,29269,1945],{},[895,29271,29272,29274,29276],{},[1765,29273,1945],{},[1761,29275,1885],{},[898,29277,207],{},[902,29279,29280],{"encoding":904},"1 + a + a^2 + \\dots = \\frac{1}{1-a}",". Proto jedna koruna investic navíc zvedne ",[883,29283,29285],{"className":29284},[886],[888,29286,29287],{"xmlns":890},[892,29288,29289,29297],{},[895,29290,29291],{},[1824,29292,29293,29295],{},[898,29294,13170],{},[898,29296,1818],{},[902,29298,17941],{"encoding":904},[38,29300,29301],{},"více"," než korunu — čím vyšší ",[883,29304,29306],{"className":29305},[886],[888,29307,29308],{"xmlns":890},[892,29309,29310,29318],{},[895,29311,29312,29314,29316],{},[898,29313,6889],{},[898,29315,1839],{},[898,29317,6849],{},[902,29319,22079],{"encoding":904},", tím silnější multiplikační efekt.",[724,29322,29323,29326,29327,29353,29354,29357,29358,2068,29379,29404,29405,1741],{},[38,29324,29325],{},"Multiplikátor autonomní spotřeby se rovná multiplikátoru investic"," — oba činí ",[883,29328,29330],{"className":29329},[886],[888,29331,29332],{"xmlns":890},[892,29333,29334,29350],{},[895,29335,29336],{},[6411,29337,29338],{"scriptlevel":1767,"displaystyle":1821},[4379,29339,29340,29342],{},[1765,29341,1945],{},[895,29343,29344,29346,29348],{},[1765,29345,1945],{},[1761,29347,1885],{},[898,29349,207],{},[902,29351,29352],{"encoding":904},"\\tfrac{1}{1-a}",", což je standardní ",[38,29355,29356],{},"Keynesův multiplikátor",". Analogicky se v modelech ",[883,29359,29361],{"className":29360},[886],[888,29362,29363],{"xmlns":890},[892,29364,29365,29377],{},[895,29366,29367,29369,29371,29373,29375],{},[898,29368,6849],{},[2761,29370,16328],{},[898,29372,16222],{},[2761,29374,16328],{},[898,29376,16151],{},[902,29378,22254],{"encoding":904},[883,29380,29382],{"className":29381},[886],[888,29383,29384],{"xmlns":890},[892,29385,29386,29402],{},[895,29387,29388,29390,29392,29394,29396,29398,29400],{},[898,29389,6849],{},[2761,29391,16328],{},[898,29393,16222],{},[2761,29395,16328],{},[898,29397,16151],{},[2761,29399,16328],{},[898,29401,16358],{},[902,29403,16361],{"encoding":904}," zavádějí multiplikátory vládních výdajů, zdanění a exportu. Paralela k mikroekonomickým multiplikátorům viz ",[207,29406,29408],{"className":29407,"dataFsResolvedFilePath":800,"href":801},[210],"poptávka a nabídka",[115,29410,29412],{"id":29411},"is-lm-analýza-stručný-přehled","IS-LM analýza (stručný přehled)",[724,29414,16202,29415,1343,29432,2068,29453,16207,29478,3927,29481,29502,29503,1989,29506,29519,29520,2232,29549,29566,29567,29570,29571,29573,29574,29595],{},[883,29416,29418],{"className":29417},[886],[888,29419,29420],{"xmlns":890},[892,29421,29422,29430],{},[895,29423,29424,29426,29428],{},[898,29425,6849],{},[2761,29427,16328],{},[898,29429,16222],{},[902,29431,16333],{"encoding":904},[883,29433,29435],{"className":29434},[886],[888,29436,29437],{"xmlns":890},[892,29438,29439,29451],{},[895,29440,29441,29443,29445,29447,29449],{},[898,29442,6849],{},[2761,29444,16328],{},[898,29446,16222],{},[2761,29448,16328],{},[898,29450,16151],{},[902,29452,22254],{"encoding":904},[883,29454,29456],{"className":29455},[886],[888,29457,29458],{"xmlns":890},[892,29459,29460,29476],{},[895,29461,29462,29464,29466,29468,29470,29472,29474],{},[898,29463,6849],{},[2761,29465,16328],{},[898,29467,16222],{},[2761,29469,16328],{},[898,29471,16151],{},[2761,29473,16328],{},[898,29475,16358],{},[902,29477,16361],{"encoding":904},[38,29479,29480],{},"investice konstantní",[883,29482,29484],{"className":29483},[886],[888,29485,29486],{"xmlns":890},[892,29487,29488,29500],{},[895,29489,29490,29492,29494],{},[898,29491,16222],{},[1761,29493,1909],{},[1824,29495,29496,29498],{},[898,29497,16222],{},[1761,29499,8408],{},[902,29501,16233],{"encoding":904},"). Reálnější je předpoklad, že ",[38,29504,29505],{},"investice závisejí na úrokové míře",[883,29507,29509],{"className":29508},[886],[888,29510,29511],{"xmlns":890},[892,29512,29513,29517],{},[895,29514,29515],{},[898,29516,1719],{},[902,29518,1719],{"encoding":904}," — klesající funkce ",[883,29521,29523],{"className":29522},[886],[888,29524,29525],{"xmlns":890},[892,29526,29527,29547],{},[895,29528,29529,29531,29533,29535,29537,29539,29541,29543,29545],{},[898,29530,16222],{},[1761,29532,1915],{"stretchy":1821},[898,29534,1719],{},[1761,29536,1920],{"stretchy":1821},[1761,29538,1909],{},[898,29540,2774],{},[898,29542,1719],{},[1761,29544,1964],{},[898,29546,4346],{},[902,29548,19793],{"encoding":904},[883,29550,29552],{"className":29551},[886],[888,29553,29554],{"xmlns":890},[892,29555,29556,29564],{},[895,29557,29558,29560,29562],{},[898,29559,2774],{},[1761,29561,2058],{},[1765,29563,1767],{},[902,29565,16553],{"encoding":904},". Přidáním ",[38,29568,29569],{},"trhu peněz"," k trhu zboží vzniká model ",[38,29572,16051],{}," se dvěma neznámými ",[883,29575,29577],{"className":29576},[886],[888,29578,29579],{"xmlns":890},[892,29580,29581,29593],{},[895,29582,29583,29585,29587,29589,29591],{},[1761,29584,1915],{"stretchy":1821},[898,29586,13170],{},[1761,29588,1834],{"separator":1833},[898,29590,1719],{},[1761,29592,1920],{"stretchy":1821},[902,29594,22184],{"encoding":904}," a dvěma rovnicemi:",[120,29597,29598,29648],{},[123,29599,29600,3927,29602,29604,29605,29626,29627,1741],{},[38,29601,19882],{},[614,29603,16093],{},") — klesající přímka v rovině ",[883,29606,29608],{"className":29607},[886],[888,29609,29610],{"xmlns":890},[892,29611,29612,29624],{},[895,29613,29614,29616,29618,29620,29622],{},[1761,29615,1915],{"stretchy":1821},[898,29617,1719],{},[1761,29619,1834],{"separator":1833},[898,29621,13170],{},[1761,29623,1920],{"stretchy":1821},[902,29625,16975],{"encoding":904},", odvozená z rovnováhy trhu zboží ",[883,29628,29630],{"className":29629},[886],[888,29631,29632],{"xmlns":890},[892,29633,29634,29646],{},[895,29635,29636,29638,29640,29642,29644],{},[898,29637,13170],{},[1761,29639,1909],{},[898,29641,6849],{},[1761,29643,1964],{},[898,29645,16222],{},[902,29647,18782],{"encoding":904},[123,29649,29650,3927,29652,29654,29655,25627,29680,29726],{},[38,29651,20081],{},[614,29653,16100],{},") — rostoucí přímka, odvozená z rovnováhy trhu peněz ",[883,29656,29658],{"className":29657},[886],[888,29659,29660],{"xmlns":890},[892,29661,29662,29678],{},[895,29663,29664,29670,29672],{},[1824,29665,29666,29668],{},[898,29667,6889],{},[898,29669,2244],{},[1761,29671,1909],{},[1824,29673,29674,29676],{},[898,29675,6889],{},[1761,29677,8408],{},[902,29679,17518],{"encoding":904},[883,29681,29683],{"className":29682},[886],[888,29684,29685],{"xmlns":890},[892,29686,29687,29723],{},[895,29688,29689,29695,29697,29703,29705,29707,29713,29715,29717],{},[1824,29690,29691,29693],{},[898,29692,6889],{},[898,29694,2244],{},[1761,29696,1909],{},[1681,29698,29699,29701],{},[898,29700,17275],{},[1765,29702,1945],{},[898,29704,13170],{},[1761,29706,1964],{},[1681,29708,29709,29711],{},[898,29710,17275],{},[1765,29712,2296],{},[898,29714,1719],{},[1761,29716,1964],{},[1681,29718,29719,29721],{},[898,29720,17275],{},[1765,29722,5486],{},[902,29724,29725],{"encoding":904},"M^D = k_1 Y + k_2 r + k_3"," (transakční, opatrnostní a spekulační poptávka).",[724,29728,29729,1989,29732,29765,29766,29768,29769,29771],{},[38,29730,29731],{},"Simultánní rovnovážný bod",[883,29733,29735],{"className":29734},[886],[888,29736,29737],{"xmlns":890},[892,29738,29739,29763],{},[895,29740,29741,29743,29745,29747,29753,29755,29761],{},[898,29742,1818],{},[1761,29744,1909],{},[1761,29746,1915],{"stretchy":1821},[1824,29748,29749,29751],{},[898,29750,1719],{},[898,29752,1818],{},[1761,29754,1834],{"separator":1833},[1824,29756,29757,29759],{},[898,29758,13170],{},[898,29760,1818],{},[1761,29762,1920],{"stretchy":1821},[902,29764,20173],{"encoding":904}," je průsečík křivek IS a LM; určuje současně rovnovážný důchod a rovnovážnou úrokovou míru. Model slouží jako rámec pro analýzu ",[38,29767,16138],{}," (posun IS) a ",[38,29770,16169],{}," (posun LM).",[724,29773,29774],{},[38,29775,29776,29777,1343,29799,1343,29821,1343,29843,29865,29866,1741],{},"Pro detailní odvození obou křivek, řešení Příkladu 7.6 (",[883,29778,29780],{"className":29779},[886],[888,29781,29782],{"xmlns":890},[892,29783,29784,29796],{},[895,29785,29786,29792,29794],{},[1824,29787,29788,29790],{},[898,29789,13170],{},[898,29791,1818],{},[1761,29793,1909],{},[1765,29795,19153],{},[902,29797,29798],{"encoding":904},"Y^E = 5000",[883,29800,29802],{"className":29801},[886],[888,29803,29804],{"xmlns":890},[892,29805,29806,29818],{},[895,29807,29808,29814,29816],{},[1824,29809,29810,29812],{},[898,29811,1719],{},[898,29813,1818],{},[1761,29815,1909],{},[1765,29817,6321],{},[902,29819,29820],{"encoding":904},"r^E = 5",[883,29822,29824],{"className":29823},[886],[888,29825,29826],{"xmlns":890},[892,29827,29828,29840],{},[895,29829,29830,29836,29838],{},[1824,29831,29832,29834],{},[898,29833,6849],{},[898,29835,1818],{},[1761,29837,1909],{},[1765,29839,19190],{},[902,29841,29842],{"encoding":904},"C^E = 4100",[883,29844,29846],{"className":29845},[886],[888,29847,29848],{"xmlns":890},[892,29849,29850,29862],{},[895,29851,29852,29858,29860],{},[1824,29853,29854,29856],{},[898,29855,16222],{},[898,29857,1818],{},[1761,29859,1909],{},[1765,29861,19229],{},[902,29863,29864],{"encoding":904},"I^E = 900",") a ekonomickou interpretaci posunů viz ",[207,29867,945],{"className":29868,"dataFsResolvedFilePath":943,"href":944},[210],[115,29870,29872],{"id":29871},"shrnutí-kapitoly-7","Shrnutí kapitoly 7",[152,29874,29875,29939,30050,30193,30435,30503],{},[123,29876,29877,29880,29881,29903,29904,29938],{},[38,29878,29879],{},"Zjednodušený makroekonomický model"," ztotožňuje ",[883,29882,29884],{"className":29883},[886],[888,29885,29886],{"xmlns":890},[892,29887,29888,29900],{},[895,29889,29890,29892,29894,29896,29898],{},[898,29891,16151],{},[898,29893,22328],{},[898,29895,1839],{},[1761,29897,6803],{},[898,29899,13170],{},[902,29901,29902],{"encoding":904},"GNP \\approx Y"," (národní důchod). Základ: ",[883,29905,29907],{"className":29906},[886],[888,29908,29909],{"xmlns":890},[892,29910,29911,29935],{},[895,29912,29913,29915,29917,29919,29921,29923,29925,29927,29929,29931,29933],{},[898,29914,16151],{},[898,29916,22328],{},[898,29918,1839],{},[1761,29920,1909],{},[898,29922,6849],{},[1761,29924,1964],{},[898,29926,16222],{},[1761,29928,1964],{},[898,29930,16151],{},[1761,29932,1964],{},[898,29934,16358],{},[902,29936,29937],{"encoding":904},"GNP = C + I + G + X"," (7.1).",[123,29940,29941,29943,29944,29965,29966,1343,29989,30020,30021,30034,30035,1741],{},[38,29942,22562],{}," splňují ",[883,29945,29947],{"className":29946},[886],[888,29948,29949],{"xmlns":890},[892,29950,29951,29963],{},[895,29952,29953,29955,29957,29959,29961],{},[898,29954,13170],{},[1761,29956,1909],{},[898,29958,6849],{},[1761,29960,1964],{},[898,29962,1912],{},[902,29964,16732],{"encoding":904}," (7.2); lineární model ",[883,29967,29969],{"className":29968},[886],[888,29970,29971],{"xmlns":890},[892,29972,29973,29987],{},[895,29974,29975,29977,29979,29981,29983,29985],{},[898,29976,6849],{},[1761,29978,1909],{},[898,29980,207],{},[898,29982,13170],{},[1761,29984,1964],{},[898,29986,4302],{},[902,29988,22953],{"encoding":904},[883,29990,29992],{"className":29991},[886],[888,29993,29994],{"xmlns":890},[892,29995,29996,30018],{},[895,29997,29998,30000,30002,30004,30006,30008,30010,30012,30014,30016],{},[898,29999,1912],{},[1761,30001,1909],{},[1761,30003,1915],{"stretchy":1821},[1765,30005,1945],{},[1761,30007,1885],{},[898,30009,207],{},[1761,30011,1920],{"stretchy":1821},[898,30013,13170],{},[1761,30015,1885],{},[898,30017,4302],{},[902,30019,23202],{"encoding":904}," s autonomní spotřebou ",[883,30022,30024],{"className":30023},[886],[888,30025,30026],{"xmlns":890},[892,30027,30028,30032],{},[895,30029,30030],{},[898,30031,4302],{},[902,30033,4302],{"encoding":904}," a autonomními úsporami ",[883,30036,30038],{"className":30037},[886],[888,30039,30040],{"xmlns":890},[892,30041,30042,30048],{},[895,30043,30044,30046],{},[1761,30045,1885],{},[898,30047,4302],{},[902,30049,23281],{"encoding":904},[123,30051,30052,1989,30055,1343,30085,30115,30116,30146,30147,1343,30168,1741],{},[38,30053,30054],{},"Mezní sklony",[883,30056,30058],{"className":30057},[886],[888,30059,30060],{"xmlns":890},[892,30061,30062,30082],{},[895,30063,30064,30066,30068,30070,30072,30074,30076,30078,30080],{},[898,30065,6889],{},[898,30067,1839],{},[898,30069,6849],{},[1761,30071,1909],{},[898,30073,4346],{"mathvariant":1969},[898,30075,6849],{},[898,30077,8726],{"mathvariant":1969},[898,30079,4346],{"mathvariant":1969},[898,30081,13170],{},[902,30083,30084],{"encoding":904},"MPC = \\mathrm{d}C\u002F\\mathrm{d}Y",[883,30086,30088],{"className":30087},[886],[888,30089,30090],{"xmlns":890},[892,30091,30092,30112],{},[895,30093,30094,30096,30098,30100,30102,30104,30106,30108,30110],{},[898,30095,6889],{},[898,30097,1839],{},[898,30099,1912],{},[1761,30101,1909],{},[898,30103,4346],{"mathvariant":1969},[898,30105,1912],{},[898,30107,8726],{"mathvariant":1969},[898,30109,4346],{"mathvariant":1969},[898,30111,13170],{},[902,30113,30114],{"encoding":904},"MPS = \\mathrm{d}S\u002F\\mathrm{d}Y",", vazba ",[883,30117,30119],{"className":30118},[886],[888,30120,30121],{"xmlns":890},[892,30122,30123,30143],{},[895,30124,30125,30127,30129,30131,30133,30135,30137,30139,30141],{},[898,30126,6889],{},[898,30128,1839],{},[898,30130,6849],{},[1761,30132,1964],{},[898,30134,6889],{},[898,30136,1839],{},[898,30138,1912],{},[1761,30140,1909],{},[1765,30142,1945],{},[902,30144,30145],{"encoding":904},"MPC + MPS = 1"," (7.5). V lineárním modelu ",[883,30148,30150],{"className":30149},[886],[888,30151,30152],{"xmlns":890},[892,30153,30154,30166],{},[895,30155,30156,30158,30160,30162,30164],{},[898,30157,6889],{},[898,30159,1839],{},[898,30161,6849],{},[1761,30163,1909],{},[898,30165,207],{},[902,30167,23922],{"encoding":904},[883,30169,30171],{"className":30170},[886],[888,30172,30173],{"xmlns":890},[892,30174,30175,30191],{},[895,30176,30177,30179,30181,30183,30185,30187,30189],{},[898,30178,6889],{},[898,30180,1839],{},[898,30182,1912],{},[1761,30184,1909],{},[1765,30186,1945],{},[1761,30188,1885],{},[898,30190,207],{},[902,30192,23948],{"encoding":904},[123,30194,30195,30198,30199],{},[38,30196,30197],{},"Modely národní ekonomiky"," postupně bohatnou:\n",[120,30200,30201,30289,30358],{},[123,30202,30203,30220,30221,30242,30243,1834],{},[883,30204,30206],{"className":30205},[886],[888,30207,30208],{"xmlns":890},[892,30209,30210,30218],{},[895,30211,30212,30214,30216],{},[898,30213,6849],{},[2761,30215,16328],{},[898,30217,16222],{},[902,30219,16333],{"encoding":904},": ",[883,30222,30224],{"className":30223},[886],[888,30225,30226],{"xmlns":890},[892,30227,30228,30240],{},[895,30229,30230,30232,30234,30236,30238],{},[898,30231,13170],{},[1761,30233,1909],{},[898,30235,6849],{},[1761,30237,1964],{},[898,30239,16222],{},[902,30241,18782],{"encoding":904}," (uzavřená ekonomika bez vlády), ",[883,30244,30246],{"className":30245},[886],[888,30247,30248],{"xmlns":890},[892,30249,30250,30286],{},[895,30251,30252,30258,30260,30262,30264,30266,30272,30274,30276,30278,30280,30282,30284],{},[1824,30253,30254,30256],{},[898,30255,13170],{},[898,30257,1818],{},[1761,30259,1909],{},[1761,30261,1915],{"stretchy":1821},[898,30263,4302],{},[1761,30265,1964],{},[1824,30267,30268,30270],{},[898,30269,16222],{},[1761,30271,8408],{},[1761,30273,1920],{"stretchy":1821},[898,30275,8726],{"mathvariant":1969},[1761,30277,1915],{"stretchy":1821},[1765,30279,1945],{},[1761,30281,1885],{},[898,30283,207],{},[1761,30285,1920],{"stretchy":1821},[902,30287,30288],{"encoding":904},"Y^E = (b + I^*)\u002F(1-a)",[123,30290,30291,30312,30313,30332,30333,1834],{},[883,30292,30294],{"className":30293},[886],[888,30295,30296],{"xmlns":890},[892,30297,30298,30310],{},[895,30299,30300,30302,30304,30306,30308],{},[898,30301,6849],{},[2761,30303,16328],{},[898,30305,16222],{},[2761,30307,16328],{},[898,30309,16151],{},[902,30311,22254],{"encoding":904},": přidává vládu, zdanění ",[883,30314,30316],{"className":30315},[886],[888,30317,30318],{"xmlns":890},[892,30319,30320,30330],{},[895,30321,30322,30324,30326,30328],{},[898,30323,1655],{},[1761,30325,1915],{"stretchy":1821},[898,30327,13170],{},[1761,30329,1920],{"stretchy":1821},[902,30331,26252],{"encoding":904}," a disponibilní důchod ",[883,30334,30336],{"className":30335},[886],[888,30337,30338],{"xmlns":890},[892,30339,30340,30356],{},[895,30341,30342,30348,30350,30352,30354],{},[1681,30343,30344,30346],{},[898,30345,13170],{},[898,30347,2244],{},[1761,30349,1909],{},[898,30351,13170],{},[1761,30353,1885],{},[898,30355,1655],{},[902,30357,25751],{"encoding":904},[123,30359,30360,30385,30386,25627,30407,1741],{},[883,30361,30363],{"className":30362},[886],[888,30364,30365],{"xmlns":890},[892,30366,30367,30383],{},[895,30368,30369,30371,30373,30375,30377,30379,30381],{},[898,30370,6849],{},[2761,30372,16328],{},[898,30374,16222],{},[2761,30376,16328],{},[898,30378,16151],{},[2761,30380,16328],{},[898,30382,16358],{},[902,30384,16361],{"encoding":904},": otevírá ekonomiku čistým exportem ",[883,30387,30389],{"className":30388},[886],[888,30390,30391],{"xmlns":890},[892,30392,30393,30405],{},[895,30394,30395,30397,30399,30401,30403],{},[898,30396,16358],{},[1761,30398,1909],{},[898,30400,27286],{},[1761,30402,1885],{},[898,30404,6889],{},[902,30406,27293],{"encoding":904},[883,30408,30410],{"className":30409},[886],[888,30411,30412],{"xmlns":890},[892,30413,30414,30432],{},[895,30415,30416,30418,30420,30422,30424,30430],{},[898,30417,6889],{},[1761,30419,1909],{},[898,30421,6889],{},[1761,30423,1915],{"stretchy":1821},[1681,30425,30426,30428],{},[898,30427,13170],{},[898,30429,2244],{},[1761,30431,1920],{"stretchy":1821},[902,30433,30434],{"encoding":904},"M = M(Y_D)",[123,30436,30437,30440,30441,1989,30444,30502],{},[38,30438,30439],{},"Multiplikátory"," (parciální derivace rovnovážných veličin podle exogenních) — klíčový ",[38,30442,30443],{},"multiplikátor investic",[883,30445,30447],{"className":30446},[886],[888,30448,30449],{"xmlns":890},[892,30450,30451,30499],{},[895,30452,30453,30455,30461,30463,30465,30471,30473,30475,30477,30479,30481,30483,30485,30487,30489,30491,30493,30495,30497],{},[898,30454,13911],{"mathvariant":1969},[1824,30456,30457,30459],{},[898,30458,13170],{},[898,30460,1818],{},[898,30462,8726],{"mathvariant":1969},[898,30464,13911],{"mathvariant":1969},[1824,30466,30467,30469],{},[898,30468,16222],{},[1761,30470,8408],{},[1761,30472,1909],{},[1765,30474,1945],{},[898,30476,8726],{"mathvariant":1969},[1761,30478,1915],{"stretchy":1821},[1765,30480,1945],{},[1761,30482,1885],{},[898,30484,207],{},[1761,30486,1920],{"stretchy":1821},[1761,30488,1909],{},[1765,30490,1945],{},[898,30492,8726],{"mathvariant":1969},[898,30494,6889],{},[898,30496,1839],{},[898,30498,1912],{},[902,30500,30501],{"encoding":904},"\\partial Y^E\u002F\\partial I^* = 1\u002F(1-a) = 1\u002FMPS"," (Keynesův multiplikátor).",[123,30504,30505,30507,30508,30523,30524,5991,30541,30556,30557,30582,30583,1741],{},[38,30506,945],{}," doplňuje obraz o trh peněz: investice závisejí na úrokové míře, ",[883,30509,30511],{"className":30510},[886],[888,30512,30513],{"xmlns":890},[892,30514,30515,30521],{},[895,30516,30517,30519],{},[898,30518,16222],{},[898,30520,1912],{},[902,30522,16090],{"encoding":904}," popisuje rovnováhu trhu zboží (",[883,30525,30527],{"className":30526},[886],[888,30528,30529],{"xmlns":890},[892,30530,30531,30539],{},[895,30532,30533,30535,30537],{},[898,30534,16222],{},[1761,30536,1909],{},[898,30538,1912],{},[902,30540,16750],{"encoding":904},[883,30542,30544],{"className":30543},[886],[888,30545,30546],{"xmlns":890},[892,30547,30548,30554],{},[895,30549,30550,30552],{},[898,30551,13835],{},[898,30553,6889],{},[902,30555,16097],{"encoding":904}," rovnováhu trhu peněz (",[883,30558,30560],{"className":30559},[886],[888,30561,30562],{"xmlns":890},[892,30563,30564,30580],{},[895,30565,30566,30572,30574],{},[1824,30567,30568,30570],{},[898,30569,6889],{},[898,30571,2244],{},[1761,30573,1909],{},[1824,30575,30576,30578],{},[898,30577,6889],{},[1761,30579,8408],{},[902,30581,17518],{"encoding":904},"); průsečík dává ",[883,30584,30586],{"className":30585},[886],[888,30587,30588],{"xmlns":890},[892,30589,30590,30610],{},[895,30591,30592,30594,30600,30602,30608],{},[1761,30593,1915],{"stretchy":1821},[1824,30595,30596,30598],{},[898,30597,13170],{},[898,30599,1818],{},[1761,30601,1834],{"separator":1833},[1824,30603,30604,30606],{},[898,30605,1719],{},[898,30607,1818],{},[1761,30609,1920],{"stretchy":1821},[902,30611,16134],{"encoding":904},[115,30613,5533],{"id":5532},[120,30615,30616,30654,30694,30784,30866,30920,30976,31035,31070,31075,31147,31222,31308,31370,31438,31496,31549,31588],{},[123,30617,30618,5675,30621,29938],{},[38,30619,30620],{},"Hrubý národní produkt (GNP)",[883,30622,30624],{"className":30623},[886],[888,30625,30626],{"xmlns":890},[892,30627,30628,30652],{},[895,30629,30630,30632,30634,30636,30638,30640,30642,30644,30646,30648,30650],{},[898,30631,16151],{},[898,30633,22328],{},[898,30635,1839],{},[1761,30637,1909],{},[898,30639,6849],{},[1761,30641,1964],{},[898,30643,16222],{},[1761,30645,1964],{},[898,30647,16151],{},[1761,30649,1964],{},[898,30651,16358],{},[902,30653,29937],{"encoding":904},[123,30655,30656,30672,30673,1741],{},[38,30657,30658,30659],{},"Národní důchod ",[883,30660,30662],{"className":30661},[886],[888,30663,30664],{"xmlns":890},[892,30665,30666,30670],{},[895,30667,30668],{},[898,30669,13170],{},[902,30671,13170],{"encoding":904}," — součet důchodů domácností; v modelech ",[883,30674,30676],{"className":30675},[886],[888,30677,30678],{"xmlns":890},[892,30679,30680,30692],{},[895,30681,30682,30684,30686,30688,30690],{},[898,30683,16151],{},[898,30685,22328],{},[898,30687,1839],{},[1761,30689,6803],{},[898,30691,13170],{},[902,30693,29902],{"encoding":904},[123,30695,30696,30722,30723,1343,30746,1343,30767,1741],{},[38,30697,30698,30699],{},"Funkce spotřeby ",[883,30700,30702],{"className":30701},[886],[888,30703,30704],{"xmlns":890},[892,30705,30706,30720],{},[895,30707,30708,30710,30712,30714,30716,30718],{},[898,30709,6849],{},[1761,30711,1909],{},[898,30713,6849],{},[1761,30715,1915],{"stretchy":1821},[898,30717,13170],{},[1761,30719,1920],{"stretchy":1821},[902,30721,24773],{"encoding":904}," — lineární model ",[883,30724,30726],{"className":30725},[886],[888,30727,30728],{"xmlns":890},[892,30729,30730,30744],{},[895,30731,30732,30734,30736,30738,30740,30742],{},[898,30733,6849],{},[1761,30735,1909],{},[898,30737,207],{},[898,30739,13170],{},[1761,30741,1964],{},[898,30743,4302],{},[902,30745,22953],{"encoding":904},[883,30747,30749],{"className":30748},[886],[888,30750,30751],{"xmlns":890},[892,30752,30753,30765],{},[895,30754,30755,30757,30759,30761,30763],{},[1765,30756,1767],{},[1761,30758,2058],{},[898,30760,207],{},[1761,30762,2058],{},[1765,30764,1945],{},[902,30766,22869],{"encoding":904},[883,30768,30770],{"className":30769},[886],[888,30771,30772],{"xmlns":890},[892,30773,30774,30782],{},[895,30775,30776,30778,30780],{},[898,30777,4302],{},[1761,30779,1763],{},[1765,30781,1767],{},[902,30783,22847],{"encoding":904},[123,30785,30786,5675,30813,30834,30835,1741],{},[38,30787,30788,30789],{},"Funkce úspor ",[883,30790,30792],{"className":30791},[886],[888,30793,30794],{"xmlns":890},[892,30795,30796,30810],{},[895,30797,30798,30800,30802,30804,30806,30808],{},[898,30799,1912],{},[1761,30801,1909],{},[898,30803,1912],{},[1761,30805,1915],{"stretchy":1821},[898,30807,13170],{},[1761,30809,1920],{"stretchy":1821},[902,30811,30812],{"encoding":904},"S = S(Y)",[883,30814,30816],{"className":30815},[886],[888,30817,30818],{"xmlns":890},[892,30819,30820,30832],{},[895,30821,30822,30824,30826,30828,30830],{},[898,30823,13170],{},[1761,30825,1909],{},[898,30827,6849],{},[1761,30829,1964],{},[898,30831,1912],{},[902,30833,16732],{"encoding":904},"; lineární ",[883,30836,30838],{"className":30837},[886],[888,30839,30840],{"xmlns":890},[892,30841,30842,30864],{},[895,30843,30844,30846,30848,30850,30852,30854,30856,30858,30860,30862],{},[898,30845,1912],{},[1761,30847,1909],{},[1761,30849,1915],{"stretchy":1821},[1765,30851,1945],{},[1761,30853,1885],{},[898,30855,207],{},[1761,30857,1920],{"stretchy":1821},[898,30859,13170],{},[1761,30861,1885],{},[898,30863,4302],{},[902,30865,23202],{"encoding":904},[123,30867,30868,5675,30871,1343,30894,1741],{},[38,30869,30870],{},"Autonomní spotřeba\u002Fúspory",[883,30872,30874],{"className":30873},[886],[888,30875,30876],{"xmlns":890},[892,30877,30878,30892],{},[895,30879,30880,30882,30884,30886,30888,30890],{},[898,30881,6849],{},[1761,30883,1915],{"stretchy":1821},[1765,30885,1767],{},[1761,30887,1920],{"stretchy":1821},[1761,30889,1909],{},[898,30891,4302],{},[902,30893,23594],{"encoding":904},[883,30895,30897],{"className":30896},[886],[888,30898,30899],{"xmlns":890},[892,30900,30901,30917],{},[895,30902,30903,30905,30907,30909,30911,30913,30915],{},[898,30904,1912],{},[1761,30906,1915],{"stretchy":1821},[1765,30908,1767],{},[1761,30910,1920],{"stretchy":1821},[1761,30912,1909],{},[1761,30914,1885],{},[898,30916,4302],{},[902,30918,30919],{"encoding":904},"S(0) = -b",[123,30921,30922,30954,30955,2162],{},[38,30923,30924,30925],{},"Mezní sklon ke spotřebě ",[883,30926,30928],{"className":30927},[886],[888,30929,30930],{"xmlns":890},[892,30931,30932,30952],{},[895,30933,30934,30936,30938,30940,30942,30944,30946,30948,30950],{},[898,30935,6889],{},[898,30937,1839],{},[898,30939,6849],{},[1761,30941,1909],{},[898,30943,4346],{"mathvariant":1969},[898,30945,6849],{},[898,30947,8726],{"mathvariant":1969},[898,30949,4346],{"mathvariant":1969},[898,30951,13170],{},[902,30953,30084],{"encoding":904}," (v lineárním modelu ",[883,30956,30958],{"className":30957},[886],[888,30959,30960],{"xmlns":890},[892,30961,30962,30974],{},[895,30963,30964,30966,30968,30970,30972],{},[898,30965,6889],{},[898,30967,1839],{},[898,30969,6849],{},[1761,30971,1909],{},[898,30973,207],{},[902,30975,23922],{"encoding":904},[123,30977,30978,30954,31010,2162],{},[38,30979,30980,30981],{},"Mezní sklon k úsporám ",[883,30982,30984],{"className":30983},[886],[888,30985,30986],{"xmlns":890},[892,30987,30988,31008],{},[895,30989,30990,30992,30994,30996,30998,31000,31002,31004,31006],{},[898,30991,6889],{},[898,30993,1839],{},[898,30995,1912],{},[1761,30997,1909],{},[898,30999,4346],{"mathvariant":1969},[898,31001,1912],{},[898,31003,8726],{"mathvariant":1969},[898,31005,4346],{"mathvariant":1969},[898,31007,13170],{},[902,31009,30114],{"encoding":904},[883,31011,31013],{"className":31012},[886],[888,31014,31015],{"xmlns":890},[892,31016,31017,31033],{},[895,31018,31019,31021,31023,31025,31027,31029,31031],{},[898,31020,6889],{},[898,31022,1839],{},[898,31024,1912],{},[1761,31026,1909],{},[1765,31028,1945],{},[1761,31030,1885],{},[898,31032,207],{},[902,31034,23948],{"encoding":904},[123,31036,31037,1989,31040,31069],{},[38,31038,31039],{},"Vztah",[883,31041,31043],{"className":31042},[886],[888,31044,31045],{"xmlns":890},[892,31046,31047,31067],{},[895,31048,31049,31051,31053,31055,31057,31059,31061,31063,31065],{},[898,31050,6889],{},[898,31052,1839],{},[898,31054,6849],{},[1761,31056,1964],{},[898,31058,6889],{},[898,31060,1839],{},[898,31062,1912],{},[1761,31064,1909],{},[1765,31066,1945],{},[902,31068,30145],{"encoding":904}," (7.5).",[123,31071,31072,31074],{},[38,31073,24616],{}," — rovnováha agregátní poptávky a nabídky.",[123,31076,31077,31080,31081,19828,31102,1741],{},[38,31078,31079],{},"Model C-I"," — uzavřená ekonomika bez vlády; ",[883,31082,31084],{"className":31083},[886],[888,31085,31086],{"xmlns":890},[892,31087,31088,31100],{},[895,31089,31090,31092,31094,31096,31098],{},[898,31091,13170],{},[1761,31093,1909],{},[898,31095,6849],{},[1761,31097,1964],{},[898,31099,16222],{},[902,31101,18782],{"encoding":904},[883,31103,31105],{"className":31104},[886],[888,31106,31107],{"xmlns":890},[892,31108,31109,31145],{},[895,31110,31111,31117,31119,31121,31123,31125,31131,31133,31135,31137,31139,31141,31143],{},[1824,31112,31113,31115],{},[898,31114,13170],{},[898,31116,1818],{},[1761,31118,1909],{},[1761,31120,1915],{"stretchy":1821},[898,31122,4302],{},[1761,31124,1964],{},[1824,31126,31127,31129],{},[898,31128,16222],{},[1761,31130,8408],{},[1761,31132,1920],{"stretchy":1821},[898,31134,8726],{"mathvariant":1969},[1761,31136,1915],{"stretchy":1821},[1765,31138,1945],{},[1761,31140,1885],{},[898,31142,207],{},[1761,31144,1920],{"stretchy":1821},[902,31146,30288],{"encoding":904},[123,31148,31149,31152,31153,1343,31172,19828,31197,1741],{},[38,31150,31151],{},"Model C-I-G"," — ekonomika s vládou, zdaněním ",[883,31154,31156],{"className":31155},[886],[888,31157,31158],{"xmlns":890},[892,31159,31160,31170],{},[895,31161,31162,31164,31166,31168],{},[898,31163,1655],{},[1761,31165,1915],{"stretchy":1821},[898,31167,13170],{},[1761,31169,1920],{"stretchy":1821},[902,31171,26252],{"encoding":904},[883,31173,31175],{"className":31174},[886],[888,31176,31177],{"xmlns":890},[892,31178,31179,31195],{},[895,31180,31181,31187,31189,31191,31193],{},[1681,31182,31183,31185],{},[898,31184,13170],{},[898,31186,2244],{},[1761,31188,1909],{},[898,31190,13170],{},[1761,31192,1885],{},[898,31194,1655],{},[902,31196,25751],{"encoding":904},[883,31198,31200],{"className":31199},[886],[888,31201,31202],{"xmlns":890},[892,31203,31204,31220],{},[895,31205,31206,31208,31210,31212,31214,31216,31218],{},[898,31207,13170],{},[1761,31209,1909],{},[898,31211,6849],{},[1761,31213,1964],{},[898,31215,16222],{},[1761,31217,1964],{},[898,31219,16151],{},[902,31221,25722],{"encoding":904},[123,31223,31224,31227,31228,31249,31250,19828,31274,1741],{},[38,31225,31226],{},"Model C-I-G-X"," — otevřená ekonomika s čistým exportem ",[883,31229,31231],{"className":31230},[886],[888,31232,31233],{"xmlns":890},[892,31234,31235,31247],{},[895,31236,31237,31239,31241,31243,31245],{},[898,31238,16358],{},[1761,31240,1909],{},[898,31242,27286],{},[1761,31244,1885],{},[898,31246,6889],{},[902,31248,27293],{"encoding":904},", importem ",[883,31251,31253],{"className":31252},[886],[888,31254,31255],{"xmlns":890},[892,31256,31257,31271],{},[895,31258,31259,31261,31263,31269],{},[898,31260,6889],{},[1761,31262,1915],{"stretchy":1821},[1681,31264,31265,31267],{},[898,31266,13170],{},[898,31268,2244],{},[1761,31270,1920],{"stretchy":1821},[902,31272,31273],{"encoding":904},"M(Y_D)",[883,31275,31277],{"className":31276},[886],[888,31278,31279],{"xmlns":890},[892,31280,31281,31305],{},[895,31282,31283,31285,31287,31289,31291,31293,31295,31297,31299,31301,31303],{},[898,31284,13170],{},[1761,31286,1909],{},[898,31288,6849],{},[1761,31290,1964],{},[898,31292,16222],{},[1761,31294,1964],{},[898,31296,16151],{},[1761,31298,1964],{},[898,31300,27286],{},[1761,31302,1885],{},[898,31304,6889],{},[902,31306,31307],{"encoding":904},"Y = C + I + G + B - M",[123,31309,31310,5675,31313,30502],{},[38,31311,31312],{},"Multiplikátor investic",[883,31314,31316],{"className":31315},[886],[888,31317,31318],{"xmlns":890},[892,31319,31320,31368],{},[895,31321,31322,31324,31330,31332,31334,31340,31342,31344,31346,31348,31350,31352,31354,31356,31358,31360,31362,31364,31366],{},[898,31323,13911],{"mathvariant":1969},[1824,31325,31326,31328],{},[898,31327,13170],{},[898,31329,1818],{},[898,31331,8726],{"mathvariant":1969},[898,31333,13911],{"mathvariant":1969},[1824,31335,31336,31338],{},[898,31337,16222],{},[1761,31339,8408],{},[1761,31341,1909],{},[1765,31343,1945],{},[898,31345,8726],{"mathvariant":1969},[1761,31347,1915],{"stretchy":1821},[1765,31349,1945],{},[1761,31351,1885],{},[898,31353,207],{},[1761,31355,1920],{"stretchy":1821},[1761,31357,1909],{},[1765,31359,1945],{},[898,31361,8726],{"mathvariant":1969},[898,31363,6889],{},[898,31365,1839],{},[898,31367,1912],{},[902,31369,30501],{"encoding":904},[123,31371,31372,5675,31403,1343,31420,31437],{},[38,31373,19763,31374],{},[883,31375,31377],{"className":31376},[886],[888,31378,31379],{"xmlns":890},[892,31380,31381,31401],{},[895,31382,31383,31385,31387,31389,31391,31393,31395,31397,31399],{},[898,31384,16222],{},[1761,31386,1915],{"stretchy":1821},[898,31388,1719],{},[1761,31390,1920],{"stretchy":1821},[1761,31392,1909],{},[898,31394,2774],{},[898,31396,1719],{},[1761,31398,1964],{},[898,31400,4346],{},[902,31402,19793],{"encoding":904},[883,31404,31406],{"className":31405},[886],[888,31407,31408],{"xmlns":890},[892,31409,31410,31418],{},[895,31411,31412,31414,31416],{},[898,31413,2774],{},[1761,31415,2058],{},[1765,31417,1767],{},[902,31419,16553],{"encoding":904},[883,31421,31423],{"className":31422},[886],[888,31424,31425],{"xmlns":890},[892,31426,31427,31435],{},[895,31428,31429,31431,31433],{},[898,31430,4346],{},[1761,31432,1763],{},[1765,31434,1767],{},[902,31436,16532],{"encoding":904},"; klesající.",[123,31439,31440,31442,31443,31445,31446,31495],{},[38,31441,19882],{}," — rovnováha na trhu zboží (",[614,31444,16093],{},"); ",[883,31447,31449],{"className":31448},[886],[888,31450,31451],{"xmlns":890},[892,31452,31453,31493],{},[895,31454,31455,31457,31459,31471,31473,31475],{},[898,31456,13170],{},[1761,31458,1909],{},[4379,31460,31461,31463],{},[898,31462,2774],{},[895,31464,31465,31467,31469],{},[1765,31466,1945],{},[1761,31468,1885],{},[898,31470,207],{},[898,31472,1719],{},[1761,31474,1964],{},[4379,31476,31477,31485],{},[895,31478,31479,31481,31483],{},[898,31480,4302],{},[1761,31482,1964],{},[898,31484,4346],{},[895,31486,31487,31489,31491],{},[1765,31488,1945],{},[1761,31490,1885],{},[898,31492,207],{},[902,31494,19935],{"encoding":904}," (7.14); klesající.",[123,31497,31498,31500,31501,31445,31503,31548],{},[38,31499,20081],{}," — rovnováha na trhu peněz (",[614,31502,16100],{},[883,31504,31506],{"className":31505},[886],[888,31507,31508],{"xmlns":890},[892,31509,31510,31546],{},[895,31511,31512,31518,31520,31526,31528,31530,31536,31538,31540],{},[1824,31513,31514,31516],{},[898,31515,6889],{},[1761,31517,8408],{},[1761,31519,1909],{},[1681,31521,31522,31524],{},[898,31523,17275],{},[1765,31525,1945],{},[898,31527,13170],{},[1761,31529,1964],{},[1681,31531,31532,31534],{},[898,31533,17275],{},[1765,31535,2296],{},[898,31537,1719],{},[1761,31539,1964],{},[1681,31541,31542,31544],{},[898,31543,17275],{},[1765,31545,5486],{},[902,31547,20129],{"encoding":904}," (7.15); rostoucí.",[123,31550,31551,5675,31554,1741],{},[38,31552,31553],{},"Transakční, opatrnostní a spekulační poptávka po penězích",[883,31555,31557],{"className":31556},[886],[888,31558,31559],{"xmlns":890},[892,31560,31561,31585],{},[895,31562,31563,31569,31571,31577,31579],{},[1824,31564,31565,31567],{},[898,31566,6889],{},[898,31568,2244],{},[1761,31570,1909],{},[1681,31572,31573,31575],{},[898,31574,13835],{},[1765,31576,1945],{},[1761,31578,1964],{},[1681,31580,31581,31583],{},[898,31582,13835],{},[1765,31584,2296],{},[902,31586,31587],{"encoding":904},"M^D = L_1 + L_2",[123,31589,31590,20139,31592,18018,31605,2068,31620,31635,31636,1741],{},[38,31591,945],{},[883,31593,31595],{"className":31594},[886],[888,31596,31597],{"xmlns":890},[892,31598,31599,31603],{},[895,31600,31601],{},[898,31602,1818],{},[902,31604,1818],{"encoding":904},[883,31606,31608],{"className":31607},[886],[888,31609,31610],{"xmlns":890},[892,31611,31612,31618],{},[895,31613,31614,31616],{},[898,31615,16222],{},[898,31617,1912],{},[902,31619,16090],{"encoding":904},[883,31621,31623],{"className":31622},[886],[888,31624,31625],{"xmlns":890},[892,31626,31627,31633],{},[895,31628,31629,31631],{},[898,31630,13835],{},[898,31632,6889],{},[902,31634,16097],{"encoding":904}," určuje ",[883,31637,31639],{"className":31638},[886],[888,31640,31641],{"xmlns":890},[892,31642,31643,31663],{},[895,31644,31645,31647,31653,31655,31661],{},[1761,31646,1915],{"stretchy":1821},[1824,31648,31649,31651],{},[898,31650,13170],{},[898,31652,1818],{},[1761,31654,1834],{"separator":1833},[1824,31656,31657,31659],{},[898,31658,1719],{},[898,31660,1818],{},[1761,31662,1920],{"stretchy":1821},[902,31664,16134],{"encoding":904},[115,31666,5968],{"id":5967},[120,31668,31669,31676,31683],{},[123,31670,31671,1989,31673],{},[38,31672,6015],{},[207,31674,6021],{"className":31675,"dataFsResolvedFilePath":6019,"href":6020},[210],[123,31677,31678,1989,31680],{},[38,31679,20247],{},[207,31681,20251],{"className":31682,"dataFsResolvedFilePath":868,"href":869},[210],[123,31684,31685,31687],{},[38,31686,20266],{},[120,31688,31689,31695,31701,31707],{},[123,31690,31691,31694],{},[207,31692,20306],{"className":31693,"dataFsResolvedFilePath":943,"href":944},[210]," — detailní IS-LM analýza (odvození křivek, Příklad 7.6, fiskální vs monetární politika)",[123,31696,31697,31700],{},[207,31698,5371],{"className":31699,"dataFsResolvedFilePath":800,"href":801},[210]," — paralela mikroekonomických multiplikátorů (multiplikátory rovnovážné ceny a množství)",[123,31702,31703,31706],{},[207,31704,7020],{"className":31705,"dataFsResolvedFilePath":827,"href":828},[210]," — mikroekonomické analogie, článek 2.4 o multiplikátorech",[123,31708,31709,31712,31713,1343,31730,31747],{},[207,31710,1145],{"className":31711,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro ",[883,31714,31716],{"className":31715},[886],[888,31717,31718],{"xmlns":890},[892,31719,31720,31728],{},[895,31721,31722,31724,31726],{},[898,31723,6889],{},[898,31725,1839],{},[898,31727,6849],{},[902,31729,22079],{"encoding":904},[883,31731,31733],{"className":31732},[886],[888,31734,31735],{"xmlns":890},[892,31736,31737,31745],{},[895,31738,31739,31741,31743],{},[898,31740,6889],{},[898,31742,1839],{},[898,31744,1912],{},[902,31746,23692],{"encoding":904}," a interpretaci změn diferenciálem",{"title":641,"searchDepth":642,"depth":642,"links":31749},[31750,31751,31752,31753,31758,31761,31762,31769,31774,31779,31782,31783,31784,31785],{"id":16045,"depth":642,"text":16046},{"id":22188,"depth":642,"text":22189},{"id":22308,"depth":642,"text":22309},{"id":22561,"depth":642,"text":22562,"children":31754},[31755,31756,31757],{"id":22565,"depth":649,"text":22566},{"id":22776,"depth":649,"text":22777},{"id":23284,"depth":649,"text":23285},{"id":23604,"depth":642,"text":23605,"children":31759},[31760],{"id":24120,"depth":649,"text":24121},{"id":24615,"depth":642,"text":24616},{"id":24642,"depth":642,"text":24643,"children":31763},[31764,31765,31766,31768],{"id":24653,"depth":649,"text":24654},{"id":24723,"depth":649,"text":24724},{"id":24907,"depth":649,"text":31767},"Výpočet YEY^E",{"id":25050,"depth":649,"text":25051},{"id":25428,"depth":642,"text":25429,"children":31770},[31771,31772,31773],{"id":25432,"depth":649,"text":24654},{"id":25881,"depth":649,"text":24724},{"id":26537,"depth":649,"text":26538},{"id":27324,"depth":642,"text":27325,"children":31775},[31776,31777,31778],{"id":27328,"depth":649,"text":24654},{"id":27473,"depth":649,"text":24724},{"id":27743,"depth":649,"text":27744},{"id":28666,"depth":642,"text":28667,"children":31780},[31781],{"id":28862,"depth":649,"text":28863},{"id":29411,"depth":642,"text":29412},{"id":29871,"depth":642,"text":29872},{"id":5532,"depth":642,"text":5533},{"id":5967,"depth":642,"text":5968},{},"\u002Ftopics\u002Fnarodni-duchod",{"title":936,"description":641},[1138,1137],"topics\u002Fnarodni-duchod",[1128,20260,1143,31792,31793,31794,20306,21917],"gnp","mpc","mps","BMicmr68yKQbb8qpoE9KfzU5NFshq3Inq6w0tL8-GjU",{"id":31797,"title":31798,"body":31799,"course":1128,"courses":659,"created":6039,"description":641,"extension":661,"meta":40776,"navigation":664,"path":40777,"seo":40778,"sources":40779,"stem":40780,"tags":40781,"type":6050,"updated":677,"__hash__":40786},"topics\u002Ftopics\u002Foptimalizace-spotrebitele.md","Optimalizace spotřebitele — Lagrange, poptávka, minimalizace výdajů",{"type":9,"value":31800,"toc":40745},[31801,31804,31806,32035,32039,32092,32161,32273,32432,32436,32552,32556,32559,32681,32684,32877,32901,32969,33133,33151,33217,33595,33599,33606,33850,33906,33910,33975,34093,34225,34257,34377,34459,34462,34584,34777,34998,35002,35042,35147,35204,35304,35481,35611,35664,35667,35754,35758,35934,35938,35941,36026,36029,36086,36191,36195,36316,36319,36502,36505,36613,36822,37142,37190,37263,37337,37339,37563,37798,38066,38070,38073,38178,38235,38269,38316,38349,38433,38435,38667,38800,38877,38999,39154,39158,39298,39305,39529,39540,39544,39548,39653,39795,39905,40004,40008,40167,40276,40278,40671,40673],[12,31802,31798],{"id":31803},"optimalizace-spotřebitele-lagrange-poptávka-minimalizace-výdajů",[115,31805,16046],{"id":16045},[724,31807,31808,31810,31811,31845,31846,31849,31850,31881,31882,31928,31929,31932,31933,31975,31976,31994,31995,31999,32000,32030,32031,32034],{},[38,31809,913],{}," řeší, jaký svazek zboží ",[883,31812,31814],{"className":31813},[886],[888,31815,31816],{"xmlns":890},[892,31817,31818,31842],{},[895,31819,31820,31822,31830,31832,31840],{},[1761,31821,1822],{"stretchy":1821},[2015,31823,31824,31826,31828],{},[898,31825,1828],{},[1765,31827,1945],{},[1761,31829,8408],{},[1761,31831,1834],{"separator":1833},[2015,31833,31834,31836,31838],{},[898,31835,1828],{},[1765,31837,2296],{},[1761,31839,8408],{},[1761,31841,1844],{"stretchy":1821},[902,31843,31844],{"encoding":904},"[Q_1^*, Q_2^*]"," zvolit při známých cenách a důchodu. Existují dvě ekvivalentní formulace: ",[38,31847,31848],{},"primární úloha"," — maximalizace užitečnosti ",[883,31851,31853],{"className":31852},[886],[888,31854,31855],{"xmlns":890},[892,31856,31857,31879],{},[895,31858,31859,31861,31863,31869,31871,31877],{},[898,31860,900],{},[1761,31862,1915],{"stretchy":1821},[1681,31864,31865,31867],{},[898,31866,1828],{},[1765,31868,1945],{},[1761,31870,1834],{"separator":1833},[1681,31872,31873,31875],{},[898,31874,1828],{},[1765,31876,2296],{},[1761,31878,1920],{"stretchy":1821},[902,31880,20377],{"encoding":904}," při rozpočtovém omezení ",[883,31883,31885],{"className":31884},[886],[888,31886,31887],{"xmlns":890},[892,31888,31889,31925],{},[895,31890,31891,31897,31899,31905,31911,31913,31919],{},[1824,31892,31893,31895],{},[898,31894,13170],{},[1761,31896,8408],{},[1761,31898,1909],{},[1681,31900,31901,31903],{},[898,31902,1839],{},[1765,31904,1945],{},[1681,31906,31907,31909],{},[898,31908,1828],{},[1765,31910,1945],{},[1761,31912,1964],{},[1681,31914,31915,31917],{},[898,31916,1839],{},[1765,31918,2296],{},[1681,31920,31921,31923],{},[898,31922,1828],{},[1765,31924,2296],{},[902,31926,31927],{"encoding":904},"Y^* = P_1 Q_1 + P_2 Q_2",", a ",[38,31930,31931],{},"duální úloha"," — minimalizace výdajů ",[883,31934,31936],{"className":31935},[886],[888,31937,31938],{"xmlns":890},[892,31939,31940,31972],{},[895,31941,31942,31944,31946,31952,31958,31960,31966],{},[898,31943,1818],{},[1761,31945,1909],{},[1681,31947,31948,31950],{},[898,31949,1839],{},[1765,31951,1945],{},[1681,31953,31954,31956],{},[898,31955,1828],{},[1765,31957,1945],{},[1761,31959,1964],{},[1681,31961,31962,31964],{},[898,31963,1839],{},[1765,31965,2296],{},[1681,31967,31968,31970],{},[898,31969,1828],{},[1765,31971,2296],{},[902,31973,31974],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2"," při zadané hladině užitečnosti ",[883,31977,31979],{"className":31978},[886],[888,31980,31981],{"xmlns":890},[892,31982,31983,31991],{},[895,31984,31985],{},[1824,31986,31987,31989],{},[898,31988,900],{},[1761,31990,8408],{},[902,31992,31993],{"encoding":904},"U^*",". Obě úlohy se řeší ",[207,31996,31998],{"className":31997,"dataFsResolvedFilePath":791,"href":792},[210],"metodou Lagrangeových multiplikátorů"," a vedou na tentýž bod dotyku indiferenční křivky a rozpočtové přímky, v němž platí ",[883,32001,32003],{"className":32002},[886],[888,32004,32005],{"xmlns":890},[892,32006,32007,32027],{},[895,32008,32009,32011,32013,32019,32021],{},[2761,32010,14641],{},[1761,32012,1909],{},[1681,32014,32015,32017],{},[898,32016,1839],{},[1765,32018,1945],{},[898,32020,8726],{"mathvariant":1969},[1681,32022,32023,32025],{},[898,32024,1839],{},[1765,32026,2296],{},[902,32028,32029],{"encoding":904},"\\text{MRCS} = P_1\u002FP_2",". Výstupem jsou ",[38,32032,32033],{},"funkce poptávky"," — Marshallova (závislá na důchodu) a Hicksova (závislá na hladině užitečnosti).",[115,32036,32038],{"id":32037},"úvod-proč-optimalizovat","Úvod — proč optimalizovat",[724,32040,32041,32042,32060,32061,32091],{},"Racionální spotřebitel má omezený důchod a musí se rozhodnout, jak jej rozdělit mezi spotřebovávané zboží. V modelu pro dvě zboží je k dispozici částka ",[883,32043,32045],{"className":32044},[886],[888,32046,32047],{"xmlns":890},[892,32048,32049,32057],{},[895,32050,32051],{},[1824,32052,32053,32055],{},[898,32054,13170],{},[1761,32056,8408],{},[902,32058,32059],{"encoding":904},"Y^*"," a ceny ",[883,32062,32064],{"className":32063},[886],[888,32065,32066],{"xmlns":890},[892,32067,32068,32088],{},[895,32069,32070,32078,32080],{},[2015,32071,32072,32074,32076],{},[898,32073,1839],{},[1765,32075,1945],{},[1761,32077,8408],{},[1761,32079,1834],{"separator":1833},[2015,32081,32082,32084,32086],{},[898,32083,1839],{},[1765,32085,2296],{},[1761,32087,8408],{},[902,32089,32090],{"encoding":904},"P_1^*, P_2^*",", rozpočtové omezení má tvar",[883,32093,32095],{"className":32094},[886],[888,32096,32097],{"xmlns":890,"display":1930},[892,32098,32099,32158],{},[24787,32100,32102],{"width":32101},"100%",[24792,32103,32104,32107,32151,32153],{},[24795,32105],{"width":32106},"50%",[24795,32108,32109],{},[895,32110,32111,32117,32119,32127,32133,32135,32143,32149],{},[1824,32112,32113,32115],{},[898,32114,13170],{},[1761,32116,8408],{},[1761,32118,1909],{},[2015,32120,32121,32123,32125],{},[898,32122,1839],{},[1765,32124,1945],{},[1761,32126,8408],{},[1681,32128,32129,32131],{},[898,32130,1828],{},[1765,32132,1945],{},[1761,32134,1964],{},[2015,32136,32137,32139,32141],{},[898,32138,1839],{},[1765,32140,2296],{},[1761,32142,8408],{},[1681,32144,32145,32147],{},[898,32146,1828],{},[1765,32148,2296],{},[1761,32150,1834],{"separator":1833},[24795,32152],{"width":32106},[24795,32154,32155],{},[2761,32156,32157],{},"(6.12)",[902,32159,32160],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2, \\tag{6.12}",[724,32162,32163,32164,32167,32168,2068,32204,32240,32241,32254,32255,32269,32270,1741],{},"geometricky ",[38,32165,32166],{},"rozpočtová přímka (budget line)"," procházející body ",[883,32169,32171],{"className":32170},[886],[888,32172,32173],{"xmlns":890},[892,32174,32175,32201],{},[895,32176,32177,32179,32185,32187,32195,32197,32199],{},[1761,32178,1822],{"stretchy":1821},[1824,32180,32181,32183],{},[898,32182,13170],{},[1761,32184,8408],{},[898,32186,8726],{"mathvariant":1969},[2015,32188,32189,32191,32193],{},[898,32190,1839],{},[1765,32192,1945],{},[1761,32194,8408],{},[1761,32196,1834],{"separator":1833},[1765,32198,1767],{},[1761,32200,1844],{"stretchy":1821},[902,32202,32203],{"encoding":904},"[Y^*\u002FP_1^*, 0]",[883,32205,32207],{"className":32206},[886],[888,32208,32209],{"xmlns":890},[892,32210,32211,32237],{},[895,32212,32213,32215,32217,32219,32225,32227,32235],{},[1761,32214,1822],{"stretchy":1821},[1765,32216,1767],{},[1761,32218,1834],{"separator":1833},[1824,32220,32221,32223],{},[898,32222,13170],{},[1761,32224,8408],{},[898,32226,8726],{"mathvariant":1969},[2015,32228,32229,32231,32233],{},[898,32230,1839],{},[1765,32232,2296],{},[1761,32234,8408],{},[1761,32236,1844],{"stretchy":1821},[902,32238,32239],{"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 ",[883,32242,32244],{"className":32243},[886],[888,32245,32246],{"xmlns":890},[892,32247,32248,32252],{},[895,32249,32250],{},[898,32251,900],{},[902,32253,900],{"encoding":904},", indiferenční křivky a ",[883,32256,32258],{"className":32257},[886],[888,32259,32260],{"xmlns":890},[892,32261,32262,32266],{},[895,32263,32264],{},[2761,32265,14641],{},[902,32267,32268],{"encoding":904},"\\text{MRCS}"," — je shrnuta v ",[207,32271,880],{"className":32272,"dataFsResolvedFilePath":878,"href":879},[210],[1636,32274,32275],{},[724,32276,32277,32279,32280,32283,32284,32297,32298,32300,32301,32314,32315,1989,32318,32358,32359,32376,32377,32394,32395,32412,32413,32431],{},[883,32278,4723],{}," Pozor — dvě úlohy, totéž řešení\n",[38,32281,32282],{},"Primární úloha"," (max ",[883,32285,32287],{"className":32286},[886],[888,32288,32289],{"xmlns":890},[892,32290,32291,32295],{},[895,32292,32293],{},[898,32294,900],{},[902,32296,900],{"encoding":904}," při pevném rozpočtu) a ",[38,32299,31931],{}," (min ",[883,32302,32304],{"className":32303},[886],[888,32305,32306],{"xmlns":890},[892,32307,32308,32312],{},[895,32309,32310],{},[898,32311,1818],{},[902,32313,1818],{"encoding":904}," při pevné užitečnosti) vedou na ",[38,32316,32317],{},"tentýž bod",[883,32319,32321],{"className":32320},[886],[888,32322,32323],{"xmlns":890},[892,32324,32325,32355],{},[895,32326,32327,32333,32335,32343,32345,32353],{},[1824,32328,32329,32331],{},[898,32330,1828],{},[1761,32332,8408],{},[1761,32334,1822],{"stretchy":1821},[2015,32336,32337,32339,32341],{},[898,32338,1828],{},[1765,32340,1945],{},[1761,32342,8408],{},[1761,32344,1834],{"separator":1833},[2015,32346,32347,32349,32351],{},[898,32348,1828],{},[1765,32350,2296],{},[1761,32352,8408],{},[1761,32354,1844],{"stretchy":1821},[902,32356,32357],{"encoding":904},"Q^*[Q_1^*, Q_2^*]",". Rozdíl je v tom, co je „vstup\" a co „výstup\": u primární úlohy je zadán důchod ",[883,32360,32362],{"className":32361},[886],[888,32363,32364],{"xmlns":890},[892,32365,32366,32374],{},[895,32367,32368],{},[1824,32369,32370,32372],{},[898,32371,13170],{},[1761,32373,8408],{},[902,32375,32059],{"encoding":904}," a hledáme maximální ",[883,32378,32380],{"className":32379},[886],[888,32381,32382],{"xmlns":890},[892,32383,32384,32392],{},[895,32385,32386],{},[1824,32387,32388,32390],{},[898,32389,900],{},[1761,32391,8408],{},[902,32393,31993],{"encoding":904},"; u duální úlohy je zadána hladina ",[883,32396,32398],{"className":32397},[886],[888,32399,32400],{"xmlns":890},[892,32401,32402,32410],{},[895,32403,32404],{},[1824,32405,32406,32408],{},[898,32407,900],{},[1761,32409,8408],{},[902,32411,31993],{"encoding":904}," a hledáme minimální ",[883,32414,32416],{"className":32415},[886],[888,32417,32418],{"xmlns":890},[892,32419,32420,32428],{},[895,32421,32422],{},[1824,32423,32424,32426],{},[898,32425,1818],{},[1761,32427,8408],{},[902,32429,32430],{"encoding":904},"E^*",". Z pozorování je přirozenější minimalizace výdajů (výdaje lze měřit).",[115,32433,32435],{"id":32434},"maximalizace-užitečnosti-za-rozpočtového-omezení","Maximalizace užitečnosti za rozpočtového omezení",[724,32437,32438,32439,32470,32471,32547,32548,1741],{},"Úlohou je najít maximum ",[883,32440,32442],{"className":32441},[886],[888,32443,32444],{"xmlns":890},[892,32445,32446,32468],{},[895,32447,32448,32450,32452,32458,32460,32466],{},[898,32449,900],{},[1761,32451,1915],{"stretchy":1821},[1681,32453,32454,32456],{},[898,32455,1828],{},[1765,32457,1945],{},[1761,32459,1834],{"separator":1833},[1681,32461,32462,32464],{},[898,32463,1828],{},[1765,32465,2296],{},[1761,32467,1920],{"stretchy":1821},[902,32469,20377],{"encoding":904}," vázané podmínkou (6.12) ve tvaru ",[883,32472,32474],{"className":32473},[886],[888,32475,32476],{"xmlns":890},[892,32477,32478,32544],{},[895,32479,32480,32482,32484,32490,32492,32498,32500,32502,32508,32510,32518,32524,32526,32534,32540,32542],{},[898,32481,15079],{},[1761,32483,1915],{"stretchy":1821},[1681,32485,32486,32488],{},[898,32487,1828],{},[1765,32489,1945],{},[1761,32491,1834],{"separator":1833},[1681,32493,32494,32496],{},[898,32495,1828],{},[1765,32497,2296],{},[1761,32499,1920],{"stretchy":1821},[1761,32501,1909],{},[1824,32503,32504,32506],{},[898,32505,13170],{},[1761,32507,8408],{},[1761,32509,1885],{},[2015,32511,32512,32514,32516],{},[898,32513,1839],{},[1765,32515,1945],{},[1761,32517,8408],{},[1681,32519,32520,32522],{},[898,32521,1828],{},[1765,32523,1945],{},[1761,32525,1885],{},[2015,32527,32528,32530,32532],{},[898,32529,1839],{},[1765,32531,2296],{},[1761,32533,8408],{},[1681,32535,32536,32538],{},[898,32537,1828],{},[1765,32539,2296],{},[1761,32541,1909],{},[1765,32543,1767],{},[902,32545,32546],{"encoding":904},"g(Q_1, Q_2) = Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",". Použijeme ",[207,32549,32551],{"className":32550,"dataFsResolvedFilePath":791,"href":792},[210],"metodu Lagrangeových multiplikátorů",[198,32553,32555],{"id":32554},"lagrangeova-funkce-a-podmínky-optimality","Lagrangeova funkce a podmínky optimality",[724,32557,32558],{},"Sestavíme",[883,32560,32562],{"className":32561},[886],[888,32563,32564],{"xmlns":890,"display":1930},[892,32565,32566,32678],{},[24787,32567,32568],{"width":32101},[24792,32569,32570,32572,32671,32673],{},[24795,32571],{"width":32106},[24795,32573,32574],{},[895,32575,32576,32579,32581,32587,32589,32595,32597,32599,32601,32603,32605,32607,32613,32615,32621,32623,32625,32627,32629,32635,32637,32645,32651,32653,32661,32667,32669],{},[898,32577,13835],{"mathvariant":32578},"script",[1761,32580,1915],{"stretchy":1821},[1681,32582,32583,32585],{},[898,32584,1828],{},[1765,32586,1945],{},[1761,32588,1834],{"separator":1833},[1681,32590,32591,32593],{},[898,32592,1828],{},[1765,32594,2296],{},[1761,32596,1834],{"separator":1833},[898,32598,20477],{},[1761,32600,1920],{"stretchy":1821},[1761,32602,1909],{},[898,32604,900],{},[1761,32606,1915],{"stretchy":1821},[1681,32608,32609,32611],{},[898,32610,1828],{},[1765,32612,1945],{},[1761,32614,1834],{"separator":1833},[1681,32616,32617,32619],{},[898,32618,1828],{},[1765,32620,2296],{},[1761,32622,1920],{"stretchy":1821},[1761,32624,1964],{},[898,32626,20477],{},[1761,32628,1915],{"stretchy":1821},[1824,32630,32631,32633],{},[898,32632,13170],{},[1761,32634,8408],{},[1761,32636,1885],{},[2015,32638,32639,32641,32643],{},[898,32640,1839],{},[1765,32642,1945],{},[1761,32644,8408],{},[1681,32646,32647,32649],{},[898,32648,1828],{},[1765,32650,1945],{},[1761,32652,1885],{},[2015,32654,32655,32657,32659],{},[898,32656,1839],{},[1765,32658,2296],{},[1761,32660,8408],{},[1681,32662,32663,32665],{},[898,32664,1828],{},[1765,32666,2296],{},[1761,32668,1920],{"stretchy":1821},[898,32670,1741],{"mathvariant":1969},[24795,32672],{"width":32106},[24795,32674,32675],{},[2761,32676,32677],{},"(6.13)",[902,32679,32680],{"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}",[724,32682,32683],{},"Soustava prvního řádu:",[883,32685,32687],{"className":32686},[886],[888,32688,32689],{"xmlns":890,"display":1930},[892,32690,32691,32874],{},[24787,32692,32693],{"width":32101},[24792,32694,32695,32697,32867,32869],{},[24795,32696],{"width":32106},[24795,32698,32699],{},[24787,32700,32701,32751,32801],{"rowspacing":24789,"columnalign":24790,"columnspacing":6458},[24792,32702,32703,32715],{},[24795,32704,32705],{},[6411,32706,32707],{"scriptlevel":1767,"displaystyle":1833},[2015,32708,32709,32711,32713],{},[898,32710,13835],{"mathvariant":32578},[1765,32712,1945],{},[1761,32714,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[24795,32716,32717],{},[6411,32718,32719],{"scriptlevel":1767,"displaystyle":1833},[895,32720,32721,32723,32725,32733,32735,32737,32745,32747,32749],{},[895,32722],{},[1761,32724,1909],{},[2015,32726,32727,32729,32731],{},[898,32728,900],{},[1765,32730,1945],{},[1761,32732,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,32734,1885],{},[898,32736,20477],{},[2015,32738,32739,32741,32743],{},[898,32740,1839],{},[1765,32742,1945],{},[1761,32744,8408],{},[1761,32746,1909],{},[1765,32748,1767],{},[1761,32750,1834],{"separator":1833},[24792,32752,32753,32765],{},[24795,32754,32755],{},[6411,32756,32757],{"scriptlevel":1767,"displaystyle":1833},[2015,32758,32759,32761,32763],{},[898,32760,13835],{"mathvariant":32578},[1765,32762,2296],{},[1761,32764,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[24795,32766,32767],{},[6411,32768,32769],{"scriptlevel":1767,"displaystyle":1833},[895,32770,32771,32773,32775,32783,32785,32787,32795,32797,32799],{},[895,32772],{},[1761,32774,1909],{},[2015,32776,32777,32779,32781],{},[898,32778,900],{},[1765,32780,2296],{},[1761,32782,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,32784,1885],{},[898,32786,20477],{},[2015,32788,32789,32791,32793],{},[898,32790,1839],{},[1765,32792,2296],{},[1761,32794,8408],{},[1761,32796,1909],{},[1765,32798,1767],{},[1761,32800,1834],{"separator":1833},[24792,32802,32803,32815],{},[24795,32804,32805],{},[6411,32806,32807],{"scriptlevel":1767,"displaystyle":1833},[2015,32808,32809,32811,32813],{},[898,32810,13835],{"mathvariant":32578},[898,32812,20477],{},[1761,32814,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[24795,32816,32817],{},[6411,32818,32819],{"scriptlevel":1767,"displaystyle":1833},[895,32820,32821,32823,32825,32831,32833,32841,32847,32849,32857,32863,32865],{},[895,32822],{},[1761,32824,1909],{},[1824,32826,32827,32829],{},[898,32828,13170],{},[1761,32830,8408],{},[1761,32832,1885],{},[2015,32834,32835,32837,32839],{},[898,32836,1839],{},[1765,32838,1945],{},[1761,32840,8408],{},[1681,32842,32843,32845],{},[898,32844,1828],{},[1765,32846,1945],{},[1761,32848,1885],{},[2015,32850,32851,32853,32855],{},[898,32852,1839],{},[1765,32854,2296],{},[1761,32856,8408],{},[1681,32858,32859,32861],{},[898,32860,1828],{},[1765,32862,2296],{},[1761,32864,1909],{},[1765,32866,16498],{},[24795,32868],{"width":32106},[24795,32870,32871],{},[2761,32872,32873],{},"(6.14)",[902,32875,32876],{"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}",[724,32878,32879,32880,32883,32884,32897,32898,2506],{},"Díky konvexitě indiferenčních křivek je řešení ",[38,32881,32882],{},"vázaným maximem",". Z prvních dvou rovnic po vyloučení ",[883,32885,32887],{"className":32886},[886],[888,32888,32889],{"xmlns":890},[892,32890,32891,32895],{},[895,32892,32893],{},[898,32894,20477],{},[902,32896,20530],{"encoding":904}," dostáváme ",[38,32899,32900],{},"podmínku optimality",[883,32902,32904],{"className":32903},[886],[888,32905,32906],{"xmlns":890,"display":1930},[892,32907,32908,32966],{},[895,32909,32910],{},[16870,32911,32912],{"notation":16872},[6411,32913,32914],{"scriptlevel":1767,"displaystyle":1821},[6411,32915,32916],{"scriptlevel":1767,"displaystyle":1821},[6411,32917,32918],{"scriptlevel":1767,"displaystyle":1833},[895,32919,32920,32922,32924,32926,32944,32946,32964],{},[2761,32921,8041],{},[2761,32923,14641],{},[1761,32925,1909],{},[4379,32927,32928,32936],{},[2015,32929,32930,32932,32934],{},[898,32931,900],{},[1765,32933,1945],{},[1761,32935,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[2015,32937,32938,32940,32942],{},[898,32939,900],{},[1765,32941,2296],{},[1761,32943,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,32945,1909],{},[4379,32947,32948,32956],{},[2015,32949,32950,32952,32954],{},[898,32951,1839],{},[1765,32953,1945],{},[1761,32955,8408],{},[2015,32957,32958,32960,32962],{},[898,32959,1839],{},[1765,32961,2296],{},[1761,32963,8408],{},[2761,32965,8041],{},[902,32967,32968],{"encoding":904},"\\boxed{\\; \\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*} \\;}",[1636,32970,32971],{},[724,32972,32973,32975,32976,33010,33011,33014,33015,33033,33034,33052,33053,33083,33084,33101,33102,33132],{},[883,32974,1642],{}," Intuice — mezní poměr užitečnosti = mezní poměr cen\nPodmínka ",[883,32977,32979],{"className":32978},[886],[888,32980,32981],{"xmlns":890},[892,32982,32983,33007],{},[895,32984,32985,32987,32989,32997,32999],{},[2761,32986,14641],{},[1761,32988,1909],{},[2015,32990,32991,32993,32995],{},[898,32992,1839],{},[1765,32994,1945],{},[1761,32996,8408],{},[898,32998,8726],{"mathvariant":1969},[2015,33000,33001,33003,33005],{},[898,33002,1839],{},[1765,33004,2296],{},[1761,33006,8408],{},[902,33008,33009],{"encoding":904},"\\text{MRCS} = P_1^*\u002FP_2^*"," říká, že v optimu je ",[38,33012,33013],{},"sklon indiferenční křivky roven sklonu rozpočtové přímky",". Ekonomicky: spotřebitel je ochoten vyměnit ",[883,33016,33018],{"className":33017},[886],[888,33019,33020],{"xmlns":890},[892,33021,33022,33030],{},[895,33023,33024],{},[1681,33025,33026,33028],{},[898,33027,1828],{},[1765,33029,1945],{},[902,33031,33032],{"encoding":904},"Q_1"," za ",[883,33035,33037],{"className":33036},[886],[888,33038,33039],{"xmlns":890},[892,33040,33041,33049],{},[895,33042,33043],{},[1681,33044,33045,33047],{},[898,33046,1828],{},[1765,33048,2296],{},[902,33050,33051],{"encoding":904},"Q_2"," v přesně tom poměru, v jakém je trh (ceny) umožňuje vyměňovat. Kdyby ",[883,33054,33056],{"className":33055},[886],[888,33057,33058],{"xmlns":890},[892,33059,33060,33080],{},[895,33061,33062,33064,33066,33072,33074],{},[2761,33063,14641],{},[1761,33065,1763],{},[1681,33067,33068,33070],{},[898,33069,1839],{},[1765,33071,1945],{},[898,33073,8726],{"mathvariant":1969},[1681,33075,33076,33078],{},[898,33077,1839],{},[1765,33079,2296],{},[902,33081,33082],{"encoding":904},"\\text{MRCS} > P_1\u002FP_2",", vyplatilo by se nakupovat více ",[883,33085,33087],{"className":33086},[886],[888,33088,33089],{"xmlns":890},[892,33090,33091,33099],{},[895,33092,33093],{},[1681,33094,33095,33097],{},[898,33096,1828],{},[1765,33098,1945],{},[902,33100,33032],{"encoding":904}," (subjektivní ocenění převažuje nad tržním); kdyby ",[883,33103,33105],{"className":33104},[886],[888,33106,33107],{"xmlns":890},[892,33108,33109,33129],{},[895,33110,33111,33113,33115,33121,33123],{},[2761,33112,14641],{},[1761,33114,2058],{},[1681,33116,33117,33119],{},[898,33118,1839],{},[1765,33120,1945],{},[898,33122,8726],{"mathvariant":1969},[1681,33124,33125,33127],{},[898,33126,1839],{},[1765,33128,2296],{},[902,33130,33131],{"encoding":904},"\\text{MRCS} \u003C P_1\u002FP_2",", vyplatil by se opak.",[198,33134,33136,33137,33150],{"id":33135},"interpretace-λlambda-mezní-užitečnost-důchodu","Interpretace ",[883,33138,33140],{"className":33139},[886],[888,33141,33142],{"xmlns":890},[892,33143,33144,33148],{},[895,33145,33146],{},[898,33147,20477],{},[902,33149,20530],{"encoding":904}," — mezní užitečnost důchodu",[724,33152,33153,33154,33172,33173,33176,33177,33194,33195,33212,33213,33216],{},"Lagrangeův multiplikátor ",[883,33155,33157],{"className":33156},[886],[888,33158,33159],{"xmlns":890},[892,33160,33161,33169],{},[895,33162,33163],{},[1824,33164,33165,33167],{},[898,33166,20477],{},[1761,33168,8408],{},[902,33170,33171],{"encoding":904},"\\lambda^*"," představuje ",[38,33174,33175],{},"mezní užitečnost důchodu"," — přibližnou změnu maximální užitečnosti ",[883,33178,33180],{"className":33179},[886],[888,33181,33182],{"xmlns":890},[892,33183,33184,33192],{},[895,33185,33186],{},[1824,33187,33188,33190],{},[898,33189,900],{},[1761,33191,8408],{},[902,33193,31993],{"encoding":904}," při jednotkové změně důchodu ",[883,33196,33198],{"className":33197},[886],[888,33199,33200],{"xmlns":890},[892,33201,33202,33210],{},[895,33203,33204],{},[1824,33205,33206,33208],{},[898,33207,13170],{},[1761,33209,8408],{},[902,33211,32059],{"encoding":904},". Je to ",[38,33214,33215],{},"stínová cena"," rozpočtového omezení.",[1636,33218,33219,33224],{},[724,33220,33221,33223],{},[883,33222,4452],{}," Postup — maximalizace užitečnosti Lagrangeovou metodou",[152,33225,33226,33286,33373,33409,33496],{},[123,33227,33228,33231,33232,1741],{},[38,33229,33230],{},"Zapiš rozpočtové omezení"," ve tvaru ",[883,33233,33235],{"className":33234},[886],[888,33236,33237],{"xmlns":890},[892,33238,33239,33283],{},[895,33240,33241,33247,33249,33257,33263,33265,33273,33279,33281],{},[1824,33242,33243,33245],{},[898,33244,13170],{},[1761,33246,8408],{},[1761,33248,1885],{},[2015,33250,33251,33253,33255],{},[898,33252,1839],{},[1765,33254,1945],{},[1761,33256,8408],{},[1681,33258,33259,33261],{},[898,33260,1828],{},[1765,33262,1945],{},[1761,33264,1885],{},[2015,33266,33267,33269,33271],{},[898,33268,1839],{},[1765,33270,2296],{},[1761,33272,8408],{},[1681,33274,33275,33277],{},[898,33276,1828],{},[1765,33278,2296],{},[1761,33280,1909],{},[1765,33282,1767],{},[902,33284,33285],{"encoding":904},"Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",[123,33287,33288,1989,33291,1741],{},[38,33289,33290],{},"Sestav Lagrangeovu funkci",[883,33292,33294],{"className":33293},[886],[888,33295,33296],{"xmlns":890},[892,33297,33298,33370],{},[895,33299,33300,33302,33304,33306,33308,33314,33316,33322,33324,33326,33328,33330,33336,33338,33346,33352,33354,33362,33368],{},[898,33301,13835],{"mathvariant":32578},[1761,33303,1909],{},[898,33305,900],{},[1761,33307,1915],{"stretchy":1821},[1681,33309,33310,33312],{},[898,33311,1828],{},[1765,33313,1945],{},[1761,33315,1834],{"separator":1833},[1681,33317,33318,33320],{},[898,33319,1828],{},[1765,33321,2296],{},[1761,33323,1920],{"stretchy":1821},[1761,33325,1964],{},[898,33327,20477],{},[1761,33329,1915],{"stretchy":1821},[1824,33331,33332,33334],{},[898,33333,13170],{},[1761,33335,8408],{},[1761,33337,1885],{},[2015,33339,33340,33342,33344],{},[898,33341,1839],{},[1765,33343,1945],{},[1761,33345,8408],{},[1681,33347,33348,33350],{},[898,33349,1828],{},[1765,33351,1945],{},[1761,33353,1885],{},[2015,33355,33356,33358,33360],{},[898,33357,1839],{},[1765,33359,2296],{},[1761,33361,8408],{},[1681,33363,33364,33366],{},[898,33365,1828],{},[1765,33367,2296],{},[1761,33369,1920],{"stretchy":1821},[902,33371,33372],{"encoding":904},"\\mathcal{L} = U(Q_1, Q_2) + \\lambda(Y^* - P_1^* Q_1 - P_2^* Q_2)",[123,33374,33375,14506,33378,33408],{},[38,33376,33377],{},"Spočítej parciální derivace",[883,33379,33381],{"className":33380},[886],[888,33382,33383],{"xmlns":890},[892,33384,33385,33405],{},[895,33386,33387,33393,33395,33401,33403],{},[1681,33388,33389,33391],{},[898,33390,1828],{},[1765,33392,1945],{},[1761,33394,1834],{"separator":1833},[1681,33396,33397,33399],{},[898,33398,1828],{},[1765,33400,2296],{},[1761,33402,1834],{"separator":1833},[898,33404,20477],{},[902,33406,33407],{"encoding":904},"Q_1, Q_2, \\lambda"," a polož je rovny nule.",[123,33410,33411,33427,33428,33461,33462,2068,33479,1741],{},[38,33412,33413,33414],{},"Vyluč ",[883,33415,33417],{"className":33416},[886],[888,33418,33419],{"xmlns":890},[892,33420,33421,33425],{},[895,33422,33423],{},[898,33424,20477],{},[902,33426,20530],{"encoding":904}," dělením prvních dvou rovnic — dostaneš podmínku ",[883,33429,33431],{"className":33430},[886],[888,33432,33433],{"xmlns":890},[892,33434,33435,33459],{},[895,33436,33437,33439,33441,33449,33451],{},[2761,33438,14641],{},[1761,33440,1909],{},[2015,33442,33443,33445,33447],{},[898,33444,1839],{},[1765,33446,1945],{},[1761,33448,8408],{},[898,33450,8726],{"mathvariant":1969},[2015,33452,33453,33455,33457],{},[898,33454,1839],{},[1765,33456,2296],{},[1761,33458,8408],{},[902,33460,33009],{"encoding":904},", která dá vztah mezi ",[883,33463,33465],{"className":33464},[886],[888,33466,33467],{"xmlns":890},[892,33468,33469,33477],{},[895,33470,33471],{},[1681,33472,33473,33475],{},[898,33474,1828],{},[1765,33476,1945],{},[902,33478,33032],{"encoding":904},[883,33480,33482],{"className":33481},[886],[888,33483,33484],{"xmlns":890},[892,33485,33486,33494],{},[895,33487,33488],{},[1681,33489,33490,33492],{},[898,33491,1828],{},[1765,33493,2296],{},[902,33495,33051],{"encoding":904},[123,33497,33498,33501,33502,33532,33533,33550,33551,1741],{},[38,33499,33500],{},"Dosaď do rozpočtového omezení"," a vypočítej ",[883,33503,33505],{"className":33504},[886],[888,33506,33507],{"xmlns":890},[892,33508,33509,33529],{},[895,33510,33511,33519,33521],{},[2015,33512,33513,33515,33517],{},[898,33514,1828],{},[1765,33516,1945],{},[1761,33518,8408],{},[1761,33520,1834],{"separator":1833},[2015,33522,33523,33525,33527],{},[898,33524,1828],{},[1765,33526,2296],{},[1761,33528,8408],{},[902,33530,33531],{"encoding":904},"Q_1^*, Q_2^*",", případně ",[883,33534,33536],{"className":33535},[886],[888,33537,33538],{"xmlns":890},[892,33539,33540,33548],{},[895,33541,33542],{},[1824,33543,33544,33546],{},[898,33545,20477],{},[1761,33547,8408],{},[902,33549,33171],{"encoding":904}," a maximální užitečnost ",[883,33552,33554],{"className":33553},[886],[888,33555,33556],{"xmlns":890},[892,33557,33558,33592],{},[895,33559,33560,33566,33568,33570,33572,33580,33582,33590],{},[1824,33561,33562,33564],{},[898,33563,900],{},[1761,33565,8408],{},[1761,33567,1909],{},[898,33569,900],{},[1761,33571,1915],{"stretchy":1821},[2015,33573,33574,33576,33578],{},[898,33575,1828],{},[1765,33577,1945],{},[1761,33579,8408],{},[1761,33581,1834],{"separator":1833},[2015,33583,33584,33586,33588],{},[898,33585,1828],{},[1765,33587,2296],{},[1761,33589,8408],{},[1761,33591,1920],{"stretchy":1821},[902,33593,33594],{"encoding":904},"U^* = U(Q_1^*, Q_2^*)",[115,33596,33598],{"id":33597},"geometrie-optima-tečnost-ic-a-rozpočtové-přímky","Geometrie optima — tečnost IC a rozpočtové přímky",[724,33600,33601],{},[3991,33602],{"alt":33603,"className":33604,"src":33605},"imek-uzitecnost-optimum",[210,3995],"\u002Fwiki-assets\u002Fimek-uzitecnost-optimum.jpeg",[724,33607,33608],{},[614,33609,33610,33611,33660,33661,2068,33689,33717,33718,33752,33753,33792,33793,33811,33812,33830,33831,33849],{},"Obrázek 6.7 — Rozpočtová přímka ",[883,33612,33614],{"className":33613},[886],[888,33615,33616],{"xmlns":890},[892,33617,33618,33658],{},[895,33619,33620,33626,33628,33636,33642,33644,33652],{},[1824,33621,33622,33624],{},[898,33623,13170],{},[1761,33625,8408],{},[1761,33627,1909],{},[2015,33629,33630,33632,33634],{},[898,33631,1839],{},[1765,33633,1945],{},[1761,33635,8408],{},[1681,33637,33638,33640],{},[898,33639,1828],{},[1765,33641,1945],{},[1761,33643,1964],{},[2015,33645,33646,33648,33650],{},[898,33647,1839],{},[1765,33649,2296],{},[1761,33651,8408],{},[1681,33653,33654,33656],{},[898,33655,1828],{},[1765,33657,2296],{},[902,33659,21332],{"encoding":904}," protíná osy v ",[883,33662,33664],{"className":33663},[886],[888,33665,33666],{"xmlns":890},[892,33667,33668,33686],{},[895,33669,33670,33676,33678],{},[1824,33671,33672,33674],{},[898,33673,13170],{},[1761,33675,8408],{},[898,33677,8726],{"mathvariant":1969},[2015,33679,33680,33682,33684],{},[898,33681,1839],{},[1765,33683,1945],{},[1761,33685,8408],{},[902,33687,33688],{"encoding":904},"Y^*\u002FP_1^*",[883,33690,33692],{"className":33691},[886],[888,33693,33694],{"xmlns":890},[892,33695,33696,33714],{},[895,33697,33698,33704,33706],{},[1824,33699,33700,33702],{},[898,33701,13170],{},[1761,33703,8408],{},[898,33705,8726],{"mathvariant":1969},[2015,33707,33708,33710,33712],{},[898,33709,1839],{},[1765,33711,2296],{},[1761,33713,8408],{},[902,33715,33716],{"encoding":904},"Y^*\u002FP_2^*",". Tři indiferenční křivky ",[883,33719,33721],{"className":33720},[886],[888,33722,33723],{"xmlns":890},[892,33724,33725,33749],{},[895,33726,33727,33733,33735,33741,33743],{},[1681,33728,33729,33731],{},[898,33730,2774],{},[1765,33732,1945],{},[1761,33734,2058],{},[1824,33736,33737,33739],{},[898,33738,2774],{},[1761,33740,8408],{},[1761,33742,2058],{},[1681,33744,33745,33747],{},[898,33746,2774],{},[1765,33748,2296],{},[902,33750,33751],{"encoding":904},"c_1 \u003C c^* \u003C c_2",". Optimum ",[883,33754,33756],{"className":33755},[886],[888,33757,33758],{"xmlns":890},[892,33759,33760,33790],{},[895,33761,33762,33768,33770,33778,33780,33788],{},[1824,33763,33764,33766],{},[898,33765,1828],{},[1761,33767,8408],{},[1761,33769,1822],{"stretchy":1821},[2015,33771,33772,33774,33776],{},[898,33773,1828],{},[1765,33775,1945],{},[1761,33777,8408],{},[1761,33779,1834],{"separator":1833},[2015,33781,33782,33784,33786],{},[898,33783,1828],{},[1765,33785,2296],{},[1761,33787,8408],{},[1761,33789,1844],{"stretchy":1821},[902,33791,32357],{"encoding":904}," je bod dotyku rozpočtové přímky s křivkou ",[883,33794,33796],{"className":33795},[886],[888,33797,33798],{"xmlns":890},[892,33799,33800,33808],{},[895,33801,33802],{},[1824,33803,33804,33806],{},[898,33805,2774],{},[1761,33807,8408],{},[902,33809,33810],{"encoding":904},"c^*",". Křivka ",[883,33813,33815],{"className":33814},[886],[888,33816,33817],{"xmlns":890},[892,33818,33819,33827],{},[895,33820,33821],{},[1681,33822,33823,33825],{},[898,33824,2774],{},[1765,33826,1945],{},[902,33828,33829],{"encoding":904},"c_1"," je dosažitelná, ale nemaximalizuje užitečnost; křivka ",[883,33832,33834],{"className":33833},[886],[888,33835,33836],{"xmlns":890},[892,33837,33838,33846],{},[895,33839,33840],{},[1681,33841,33842,33844],{},[898,33843,2774],{},[1765,33845,2296],{},[902,33847,33848],{"encoding":904},"c_2"," není při daném důchodu dosažitelná.",[724,33851,33852,33853,33856,33857,33875,33876,33905],{},"Geometrie je jádrem intuice: přímka (rozpočet) a křivka (užitečnost) se v optimu ",[38,33854,33855],{},"dotýkají",", tj. mají v bodě ",[883,33858,33860],{"className":33859},[886],[888,33861,33862],{"xmlns":890},[892,33863,33864,33872],{},[895,33865,33866],{},[1824,33867,33868,33870],{},[898,33869,1828],{},[1761,33871,8408],{},[902,33873,33874],{"encoding":904},"Q^*"," společnou tečnu. To přímo převádí podmínku ",[883,33877,33879],{"className":33878},[886],[888,33880,33881],{"xmlns":890},[892,33882,33883,33903],{},[895,33884,33885,33887,33889,33895,33897],{},[2761,33886,14641],{},[1761,33888,1909],{},[1681,33890,33891,33893],{},[898,33892,1839],{},[1765,33894,1945],{},[898,33896,8726],{"mathvariant":1969},[1681,33898,33899,33901],{},[898,33900,1839],{},[1765,33902,2296],{},[902,33904,32029],{"encoding":904}," — poměr mezních užitečností (sklon IC) = poměr cen (sklon přímky).",[115,33907,33909],{"id":33908},"příklad-65-mrcs-pro-cobb-douglasovu-užitečnost","Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost",[724,33911,13703,33912,33974],{},[883,33913,33915],{"className":33914},[886],[888,33916,33917],{"xmlns":890},[892,33918,33919,33971],{},[895,33920,33921,33923,33925,33931,33933,33939,33941,33943,33957],{},[898,33922,900],{},[1761,33924,1915],{"stretchy":1821},[1681,33926,33927,33929],{},[898,33928,1828],{},[1765,33930,1945],{},[1761,33932,1834],{"separator":1833},[1681,33934,33935,33937],{},[898,33936,1828],{},[1765,33938,2296],{},[1761,33940,1920],{"stretchy":1821},[1761,33942,1909],{},[2015,33944,33945,33947,33949],{},[898,33946,1828],{},[1765,33948,1945],{},[895,33950,33951,33953,33955],{},[1765,33952,1945],{},[898,33954,8726],{"mathvariant":1969},[1765,33956,2296],{},[2015,33958,33959,33961,33963],{},[898,33960,1828],{},[1765,33962,2296],{},[895,33964,33965,33967,33969],{},[1765,33966,1945],{},[898,33968,8726],{"mathvariant":1969},[1765,33970,2296],{},[902,33972,33973],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F2} Q_2^{1\u002F2}"," platí",[724,33976,33977],{},[883,33978,33980],{"className":33979},[886],[888,33981,33982],{"xmlns":890},[892,33983,33984,34090],{},[895,33985,33986,33988,33990,34072,34074,34088],{},[2761,33987,14641],{},[1761,33989,1909],{},[4379,33991,33992,34032],{},[895,33993,33994,34002,34018],{},[6411,33995,33996],{"scriptlevel":1767,"displaystyle":1821},[4379,33997,33998,34000],{},[1765,33999,1945],{},[1765,34001,2296],{},[2015,34003,34004,34006,34008],{},[898,34005,1828],{},[1765,34007,1945],{},[895,34009,34010,34012,34014,34016],{},[1761,34011,1885],{},[1765,34013,1945],{},[898,34015,8726],{"mathvariant":1969},[1765,34017,2296],{},[2015,34019,34020,34022,34024],{},[898,34021,1828],{},[1765,34023,2296],{},[895,34025,34026,34028,34030],{},[1765,34027,1945],{},[898,34029,8726],{"mathvariant":1969},[1765,34031,2296],{},[895,34033,34034,34042,34056],{},[6411,34035,34036],{"scriptlevel":1767,"displaystyle":1821},[4379,34037,34038,34040],{},[1765,34039,1945],{},[1765,34041,2296],{},[2015,34043,34044,34046,34048],{},[898,34045,1828],{},[1765,34047,1945],{},[895,34049,34050,34052,34054],{},[1765,34051,1945],{},[898,34053,8726],{"mathvariant":1969},[1765,34055,2296],{},[2015,34057,34058,34060,34062],{},[898,34059,1828],{},[1765,34061,2296],{},[895,34063,34064,34066,34068,34070],{},[1761,34065,1885],{},[1765,34067,1945],{},[898,34069,8726],{"mathvariant":1969},[1765,34071,2296],{},[1761,34073,1909],{},[4379,34075,34076,34082],{},[1681,34077,34078,34080],{},[898,34079,1828],{},[1765,34081,2296],{},[1681,34083,34084,34086],{},[898,34085,1828],{},[1765,34087,1945],{},[898,34089,1741],{"mathvariant":1969},[902,34091,34092],{"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}.",[724,34094,34095,34096,6997,34141,34143,34144,34164,34165,34195,34196,1741],{},"Tedy ",[883,34097,34099],{"className":34098},[886],[888,34100,34101],{"xmlns":890},[892,34102,34103,34138],{},[895,34104,34105,34107,34109,34112,34114,34116,34118,34120,34128,34130],{},[2761,34106,14641],{},[1761,34108,1915],{"stretchy":1821},[1765,34110,34111],{},"300",[1761,34113,1834],{"separator":1833},[1765,34115,19148],{},[1761,34117,1920],{"stretchy":1821},[1761,34119,1909],{},[6411,34121,34122],{"scriptlevel":1767,"displaystyle":1821},[4379,34123,34124,34126],{},[1765,34125,19148],{},[1765,34127,34111],{},[1761,34129,1909],{},[6411,34131,34132],{"scriptlevel":1767,"displaystyle":1821},[4379,34133,34134,34136],{},[1765,34135,6321],{},[1765,34137,5486],{},[902,34139,34140],{"encoding":904},"\\text{MRCS}(300, 500) = \\tfrac{500}{300} = \\tfrac{5}{3}",[614,34142,13257],{}," zvýší-li spotřebitel nákup prvního zboží o 1 jednotku, musí snížit nákup druhého zboží přibližně o ",[883,34145,34147],{"className":34146},[886],[888,34148,34149],{"xmlns":890},[892,34150,34151,34161],{},[895,34152,34153],{},[6411,34154,34155],{"scriptlevel":1767,"displaystyle":1821},[4379,34156,34157,34159],{},[1765,34158,6321],{},[1765,34160,5486],{},[902,34162,34163],{"encoding":904},"\\tfrac{5}{3}"," jednotky, aby se užitečnost zachovala. Tato forma ",[883,34166,34168],{"className":34167},[886],[888,34169,34170],{"xmlns":890},[892,34171,34172,34192],{},[895,34173,34174,34176,34178,34184,34186],{},[2761,34175,14641],{},[1761,34177,1909],{},[1681,34179,34180,34182],{},[898,34181,1828],{},[1765,34183,2296],{},[898,34185,8726],{"mathvariant":1969},[1681,34187,34188,34190],{},[898,34189,1828],{},[1765,34191,1945],{},[902,34193,34194],{"encoding":904},"\\text{MRCS} = Q_2\u002FQ_1"," je typická pro symetrické Cobb-Douglasovy preference a vstupuje do optimalizace skrze podmínku ",[883,34197,34199],{"className":34198},[886],[888,34200,34201],{"xmlns":890},[892,34202,34203,34223],{},[895,34204,34205,34207,34209,34215,34217],{},[2761,34206,14641],{},[1761,34208,1909],{},[1681,34210,34211,34213],{},[898,34212,1839],{},[1765,34214,1945],{},[898,34216,8726],{"mathvariant":1969},[1681,34218,34219,34221],{},[898,34220,1839],{},[1765,34222,2296],{},[902,34224,32029],{"encoding":904},[115,34226,34228,34229],{"id":34227},"příklad-66-maximalizace-užitečnosti-pro-uq1q2u-q_1-q_2","Příklad 6.6 — maximalizace užitečnosti pro ",[883,34230,34232],{"className":34231},[886],[888,34233,34234],{"xmlns":890},[892,34235,34236,34254],{},[895,34237,34238,34240,34242,34248],{},[898,34239,900],{},[1761,34241,1909],{},[1681,34243,34244,34246],{},[898,34245,1828],{},[1765,34247,1945],{},[1681,34249,34250,34252],{},[898,34251,1828],{},[1765,34253,2296],{},[902,34255,34256],{"encoding":904},"U = Q_1 Q_2",[724,34258,34259,34260,1343,34306,1343,34330,1343,34354,34376],{},"Je dána ",[883,34261,34263],{"className":34262},[886],[888,34264,34265],{"xmlns":890},[892,34266,34267,34303],{},[895,34268,34269,34271,34273,34279,34281,34287,34289,34291,34297],{},[898,34270,900],{},[1761,34272,1915],{"stretchy":1821},[1681,34274,34275,34277],{},[898,34276,1828],{},[1765,34278,1945],{},[1761,34280,1834],{"separator":1833},[1681,34282,34283,34285],{},[898,34284,1828],{},[1765,34286,2296],{},[1761,34288,1920],{"stretchy":1821},[1761,34290,1909],{},[1681,34292,34293,34295],{},[898,34294,1828],{},[1765,34296,1945],{},[1681,34298,34299,34301],{},[898,34300,1828],{},[1765,34302,2296],{},[902,34304,34305],{"encoding":904},"U(Q_1, Q_2) = Q_1 Q_2",[883,34307,34309],{"className":34308},[886],[888,34310,34311],{"xmlns":890},[892,34312,34313,34327],{},[895,34314,34315,34323,34325],{},[2015,34316,34317,34319,34321],{},[898,34318,1839],{},[1765,34320,1945],{},[1761,34322,8408],{},[1761,34324,1909],{},[1765,34326,2296],{},[902,34328,34329],{"encoding":904},"P_1^* = 2",[883,34331,34333],{"className":34332},[886],[888,34334,34335],{"xmlns":890},[892,34336,34337,34351],{},[895,34338,34339,34347,34349],{},[2015,34340,34341,34343,34345],{},[898,34342,1839],{},[1765,34344,2296],{},[1761,34346,8408],{},[1761,34348,1909],{},[1765,34350,6321],{},[902,34352,34353],{"encoding":904},"P_2^* = 5",[883,34355,34357],{"className":34356},[886],[888,34358,34359],{"xmlns":890},[892,34360,34361,34373],{},[895,34362,34363,34369,34371],{},[1824,34364,34365,34367],{},[898,34366,13170],{},[1761,34368,8408],{},[1761,34370,1909],{},[1765,34372,7160],{},[902,34374,34375],{"encoding":904},"Y^* = 100",". Lagrangeova funkce:",[883,34378,34380],{"className":34379},[886],[888,34381,34382],{"xmlns":890,"display":1930},[892,34383,34384,34456],{},[895,34385,34386,34388,34390,34396,34398,34404,34406,34408,34410,34412,34418,34424,34426,34428,34430,34432,34434,34436,34442,34444,34446,34452,34454],{},[898,34387,13835],{"mathvariant":32578},[1761,34389,1915],{"stretchy":1821},[1681,34391,34392,34394],{},[898,34393,1828],{},[1765,34395,1945],{},[1761,34397,1834],{"separator":1833},[1681,34399,34400,34402],{},[898,34401,1828],{},[1765,34403,2296],{},[1761,34405,1834],{"separator":1833},[898,34407,20477],{},[1761,34409,1920],{"stretchy":1821},[1761,34411,1909],{},[1681,34413,34414,34416],{},[898,34415,1828],{},[1765,34417,1945],{},[1681,34419,34420,34422],{},[898,34421,1828],{},[1765,34423,2296],{},[1761,34425,1964],{},[898,34427,20477],{},[1761,34429,1915],{"stretchy":1821},[1765,34431,7160],{},[1761,34433,1885],{},[1765,34435,2296],{},[1681,34437,34438,34440],{},[898,34439,1828],{},[1765,34441,1945],{},[1761,34443,1885],{},[1765,34445,6321],{},[1681,34447,34448,34450],{},[898,34449,1828],{},[1765,34451,2296],{},[1761,34453,1920],{"stretchy":1821},[898,34455,1741],{"mathvariant":1969},[902,34457,34458],{"encoding":904},"\\mathcal{L}(Q_1, Q_2, \\lambda) = Q_1 Q_2 + \\lambda(100 - 2 Q_1 - 5 Q_2).",[724,34460,34461],{},"Soustava:",[883,34463,34465],{"className":34464},[886],[888,34466,34467],{"xmlns":890,"display":1930},[892,34468,34469,34581],{},[24787,34470,34471,34505,34539],{"rowspacing":24789,"columnalign":24790,"columnspacing":6458},[24792,34472,34473,34491],{},[24795,34474,34475],{},[6411,34476,34477],{"scriptlevel":1767,"displaystyle":1833},[895,34478,34479,34485,34487,34489],{},[1681,34480,34481,34483],{},[898,34482,1828],{},[1765,34484,2296],{},[1761,34486,1885],{},[1765,34488,2296],{},[898,34490,20477],{},[24795,34492,34493],{},[6411,34494,34495],{"scriptlevel":1767,"displaystyle":1833},[895,34496,34497,34499,34501,34503],{},[895,34498],{},[1761,34500,1909],{},[1765,34502,1767],{},[1761,34504,1834],{"separator":1833},[24792,34506,34507,34525],{},[24795,34508,34509],{},[6411,34510,34511],{"scriptlevel":1767,"displaystyle":1833},[895,34512,34513,34519,34521,34523],{},[1681,34514,34515,34517],{},[898,34516,1828],{},[1765,34518,1945],{},[1761,34520,1885],{},[1765,34522,6321],{},[898,34524,20477],{},[24795,34526,34527],{},[6411,34528,34529],{"scriptlevel":1767,"displaystyle":1833},[895,34530,34531,34533,34535,34537],{},[895,34532],{},[1761,34534,1909],{},[1765,34536,1767],{},[1761,34538,1834],{"separator":1833},[24792,34540,34541,34569],{},[24795,34542,34543],{},[6411,34544,34545],{"scriptlevel":1767,"displaystyle":1833},[895,34546,34547,34549,34551,34553,34559,34561,34563],{},[1765,34548,7160],{},[1761,34550,1885],{},[1765,34552,2296],{},[1681,34554,34555,34557],{},[898,34556,1828],{},[1765,34558,1945],{},[1761,34560,1885],{},[1765,34562,6321],{},[1681,34564,34565,34567],{},[898,34566,1828],{},[1765,34568,2296],{},[24795,34570,34571],{},[6411,34572,34573],{"scriptlevel":1767,"displaystyle":1833},[895,34574,34575,34577,34579],{},[895,34576],{},[1761,34578,1909],{},[1765,34580,16498],{},[902,34582,34583],{"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}",[724,34585,34586,34587,1343,34611,34635,34636,2403,34676,34694,34695,34745,34746,1741],{},"Z prvních dvou rovnic ",[883,34588,34590],{"className":34589},[886],[888,34591,34592],{"xmlns":890},[892,34593,34594,34608],{},[895,34595,34596,34602,34604,34606],{},[1681,34597,34598,34600],{},[898,34599,1828],{},[1765,34601,2296],{},[1761,34603,1909],{},[1765,34605,2296],{},[898,34607,20477],{},[902,34609,34610],{"encoding":904},"Q_2 = 2\\lambda",[883,34612,34614],{"className":34613},[886],[888,34615,34616],{"xmlns":890},[892,34617,34618,34632],{},[895,34619,34620,34626,34628,34630],{},[1681,34621,34622,34624],{},[898,34623,1828],{},[1765,34625,1945],{},[1761,34627,1909],{},[1765,34629,6321],{},[898,34631,20477],{},[902,34633,34634],{"encoding":904},"Q_1 = 5\\lambda","; dosazením do třetí ",[883,34637,34639],{"className":34638},[886],[888,34640,34641],{"xmlns":890},[892,34642,34643,34673],{},[895,34644,34645,34647,34649,34651,34653,34655,34657,34659,34661,34663,34665,34667,34669,34671],{},[1765,34646,7160],{},[1761,34648,1909],{},[1765,34650,2296],{},[1761,34652,2447],{},[1765,34654,6321],{},[898,34656,20477],{},[1761,34658,1964],{},[1765,34660,6321],{},[1761,34662,2447],{},[1765,34664,2296],{},[898,34666,20477],{},[1761,34668,1909],{},[1765,34670,13077],{},[898,34672,20477],{},[902,34674,34675],{"encoding":904},"100 = 2 \\cdot 5\\lambda + 5 \\cdot 2\\lambda = 20\\lambda",[883,34677,34679],{"className":34678},[886],[888,34680,34681],{"xmlns":890},[892,34682,34683,34691],{},[895,34684,34685,34687,34689],{},[898,34686,20477],{},[1761,34688,1909],{},[1765,34690,6321],{},[902,34692,34693],{"encoding":904},"\\lambda = 5",". Odtud ",[38,34696,34697,1343,34721],{},[883,34698,34700],{"className":34699},[886],[888,34701,34702],{"xmlns":890},[892,34703,34704,34718],{},[895,34705,34706,34714,34716],{},[2015,34707,34708,34710,34712],{},[898,34709,1828],{},[1765,34711,1945],{},[1761,34713,8408],{},[1761,34715,1909],{},[1765,34717,9056],{},[902,34719,34720],{"encoding":904},"Q_1^* = 25",[883,34722,34724],{"className":34723},[886],[888,34725,34726],{"xmlns":890},[892,34727,34728,34742],{},[895,34729,34730,34738,34740],{},[2015,34731,34732,34734,34736],{},[898,34733,1828],{},[1765,34735,2296],{},[1761,34737,8408],{},[1761,34739,1909],{},[1765,34741,2633],{},[902,34743,34744],{"encoding":904},"Q_2^* = 10",", maximální užitečnost ",[883,34747,34749],{"className":34748},[886],[888,34750,34751],{"xmlns":890},[892,34752,34753,34774],{},[895,34754,34755,34761,34763,34765,34767,34769,34771],{},[1824,34756,34757,34759],{},[898,34758,900],{},[1761,34760,8408],{},[1761,34762,1909],{},[1765,34764,9056],{},[1761,34766,2447],{},[1765,34768,2633],{},[1761,34770,1909],{},[1765,34772,34773],{},"250",[902,34775,34776],{"encoding":904},"U^* = 25 \\cdot 10 = 250",[724,34778,34779],{},[614,34780,34781,34782,32167,34820,2068,34844,34868,34869,34899,34900,34924,34925,34947,34948,1741],{},"Obrázek 6.8 — Rozpočtová přímka ",[883,34783,34785],{"className":34784},[886],[888,34786,34787],{"xmlns":890},[892,34788,34789,34817],{},[895,34790,34791,34793,34795,34797,34803,34805,34807,34813,34815],{},[1765,34792,7160],{},[1761,34794,1885],{},[1765,34796,2296],{},[1681,34798,34799,34801],{},[898,34800,1828],{},[1765,34802,1945],{},[1761,34804,1885],{},[1765,34806,6321],{},[1681,34808,34809,34811],{},[898,34810,1828],{},[1765,34812,2296],{},[1761,34814,1909],{},[1765,34816,1767],{},[902,34818,34819],{"encoding":904},"100 - 2 Q_1 - 5 Q_2 = 0",[883,34821,34823],{"className":34822},[886],[888,34824,34825],{"xmlns":890},[892,34826,34827,34841],{},[895,34828,34829,34831,34833,34835,34837,34839],{},[898,34830,8309],{},[1761,34832,1822],{"stretchy":1821},[1765,34834,1767],{},[1761,34836,1834],{"separator":1833},[1765,34838,13077],{},[1761,34840,1844],{"stretchy":1821},[902,34842,34843],{"encoding":904},"A[0, 20]",[883,34845,34847],{"className":34846},[886],[888,34848,34849],{"xmlns":890},[892,34850,34851,34865],{},[895,34852,34853,34855,34857,34859,34861,34863],{},[898,34854,27286],{},[1761,34856,1822],{"stretchy":1821},[1765,34858,7190],{},[1761,34860,1834],{"separator":1833},[1765,34862,1767],{},[1761,34864,1844],{"stretchy":1821},[902,34866,34867],{"encoding":904},"B[50, 0]","; hyperbolická indiferenční křivka ",[883,34870,34872],{"className":34871},[886],[888,34873,34874],{"xmlns":890},[892,34875,34876,34896],{},[895,34877,34878,34884,34886,34888,34890],{},[1681,34879,34880,34882],{},[898,34881,1828],{},[1765,34883,2296],{},[1761,34885,1909],{},[1765,34887,34773],{},[898,34889,8726],{"mathvariant":1969},[1681,34891,34892,34894],{},[898,34893,1828],{},[1765,34895,1945],{},[902,34897,34898],{"encoding":904},"Q_2 = 250\u002FQ_1"," se dotýká rozpočtové přímky v bodě ",[883,34901,34903],{"className":34902},[886],[888,34904,34905],{"xmlns":890},[892,34906,34907,34921],{},[895,34908,34909,34911,34913,34915,34917,34919],{},[898,34910,1818],{},[1761,34912,1822],{"stretchy":1821},[1765,34914,9056],{},[1761,34916,1834],{"separator":1833},[1765,34918,2633],{},[1761,34920,1844],{"stretchy":1821},[902,34922,34923],{"encoding":904},"E[25, 10]",". Sklon přímky ",[883,34926,34928],{"className":34927},[886],[888,34929,34930],{"xmlns":890},[892,34931,34932,34944],{},[895,34933,34934,34936],{},[1761,34935,1885],{},[6411,34937,34938],{"scriptlevel":1767,"displaystyle":1821},[4379,34939,34940,34942],{},[1765,34941,2296],{},[1765,34943,6321],{},[902,34945,34946],{"encoding":904},"-\\tfrac{2}{5}"," odpovídá ",[883,34949,34951],{"className":34950},[886],[888,34952,34953],{"xmlns":890},[892,34954,34955,34995],{},[895,34956,34957,34959,34961,34963,34965,34967,34969,34971,34973,34975,34983,34985,34987],{},[1761,34958,1885],{},[2761,34960,14641],{},[1761,34962,1915],{"stretchy":1821},[1765,34964,9056],{},[1761,34966,1834],{"separator":1833},[1765,34968,2633],{},[1761,34970,1920],{"stretchy":1821},[1761,34972,1909],{},[1761,34974,1885],{},[6411,34976,34977],{"scriptlevel":1767,"displaystyle":1821},[4379,34978,34979,34981],{},[1765,34980,2633],{},[1765,34982,9056],{},[1761,34984,1909],{},[1761,34986,1885],{},[6411,34988,34989],{"scriptlevel":1767,"displaystyle":1821},[4379,34990,34991,34993],{},[1765,34992,2296],{},[1765,34994,6321],{},[902,34996,34997],{"encoding":904},"-\\text{MRCS}(25, 10) = -\\tfrac{10}{25} = -\\tfrac{2}{5}",[115,34999,35001],{"id":35000},"funkce-poptávky-spotřebitele-marshallova","Funkce poptávky spotřebitele (Marshallova)",[724,35003,35004,35005,33033,35035,35038,35039,2506],{},"Považujeme-li v úloze ",[883,35006,35008],{"className":35007},[886],[888,35009,35010],{"xmlns":890},[892,35011,35012,35032],{},[895,35013,35014,35020,35022,35028,35030],{},[1681,35015,35016,35018],{},[898,35017,1839],{},[1765,35019,1945],{},[1761,35021,1834],{"separator":1833},[1681,35023,35024,35026],{},[898,35025,1839],{},[1765,35027,2296],{},[1761,35029,1834],{"separator":1833},[898,35031,13170],{},[902,35033,35034],{"encoding":904},"P_1, P_2, Y",[38,35036,35037],{},"parametry"," (nikoli čísla), dostáváme z první řádové podmínky ",[38,35040,35041],{},"Marshallovy poptávkové funkce",[883,35043,35045],{"className":35044},[886],[888,35046,35047],{"xmlns":890,"display":1930},[892,35048,35049,35144],{},[24787,35050,35051],{"width":32101},[24792,35052,35053,35055,35137,35139],{},[24795,35054],{"width":32106},[24795,35056,35057],{},[895,35058,35059,35065,35067,35073,35075,35081,35083,35089,35091,35093,35095,35097,35099,35105,35107,35113,35115,35121,35123,35129,35131,35133,35135],{},[1681,35060,35061,35063],{},[898,35062,1828],{},[1765,35064,1945],{},[1761,35066,1909],{},[1681,35068,35069,35071],{},[898,35070,2244],{},[1765,35072,1945],{},[1761,35074,1915],{"stretchy":1821},[1681,35076,35077,35079],{},[898,35078,1839],{},[1765,35080,1945],{},[1761,35082,1834],{"separator":1833},[1681,35084,35085,35087],{},[898,35086,1839],{},[1765,35088,2296],{},[1761,35090,1834],{"separator":1833},[898,35092,13170],{},[1761,35094,1920],{"stretchy":1821},[1761,35096,1834],{"separator":1833},[3315,35098],{"width":19322},[1681,35100,35101,35103],{},[898,35102,1828],{},[1765,35104,2296],{},[1761,35106,1909],{},[1681,35108,35109,35111],{},[898,35110,2244],{},[1765,35112,2296],{},[1761,35114,1915],{"stretchy":1821},[1681,35116,35117,35119],{},[898,35118,1839],{},[1765,35120,1945],{},[1761,35122,1834],{"separator":1833},[1681,35124,35125,35127],{},[898,35126,1839],{},[1765,35128,2296],{},[1761,35130,1834],{"separator":1833},[898,35132,13170],{},[1761,35134,1920],{"stretchy":1821},[1761,35136,1834],{"separator":1833},[24795,35138],{"width":32106},[24795,35140,35141],{},[2761,35142,35143],{},"(6.15)",[902,35145,35146],{"encoding":904},"Q_1 = D_1(P_1, P_2, Y), \\quad Q_2 = D_2(P_1, P_2, Y), \\tag{6.15}",[883,35148,35150],{"className":35149},[886],[888,35151,35152],{"xmlns":890,"display":1930},[892,35153,35154,35201],{},[24787,35155,35156],{"width":32101},[24792,35157,35158,35160,35194,35196],{},[24795,35159],{"width":32106},[24795,35161,35162],{},[895,35163,35164,35166,35168,35170,35172,35178,35180,35186,35188,35190,35192],{},[898,35165,20477],{},[1761,35167,1909],{},[898,35169,20477],{},[1761,35171,1915],{"stretchy":1821},[1681,35173,35174,35176],{},[898,35175,1839],{},[1765,35177,1945],{},[1761,35179,1834],{"separator":1833},[1681,35181,35182,35184],{},[898,35183,1839],{},[1765,35185,2296],{},[1761,35187,1834],{"separator":1833},[898,35189,13170],{},[1761,35191,1920],{"stretchy":1821},[898,35193,1741],{"mathvariant":1969},[24795,35195],{"width":32106},[24795,35197,35198],{},[2761,35199,35200],{},"(6.16)",[902,35202,35203],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, Y). \\tag{6.16}",[724,35205,35206,35236,35237,35303],{},[38,35207,35208,35209,1741],{},"Odvození pro ",[883,35210,35212],{"className":35211},[886],[888,35213,35214],{"xmlns":890},[892,35215,35216,35234],{},[895,35217,35218,35220,35222,35228],{},[898,35219,900],{},[1761,35221,1909],{},[1681,35223,35224,35226],{},[898,35225,1828],{},[1765,35227,1945],{},[1681,35229,35230,35232],{},[898,35231,1828],{},[1765,35233,2296],{},[902,35235,34256],{"encoding":904}," Lagrangeova funkce ",[883,35238,35240],{"className":35239},[886],[888,35241,35242],{"xmlns":890},[892,35243,35244,35300],{},[895,35245,35246,35248,35250,35256,35262,35264,35266,35268,35270,35272,35278,35284,35286,35292,35298],{},[898,35247,13835],{"mathvariant":32578},[1761,35249,1909],{},[1681,35251,35252,35254],{},[898,35253,1828],{},[1765,35255,1945],{},[1681,35257,35258,35260],{},[898,35259,1828],{},[1765,35261,2296],{},[1761,35263,1964],{},[898,35265,20477],{},[1761,35267,1915],{"stretchy":1821},[898,35269,13170],{},[1761,35271,1885],{},[1681,35273,35274,35276],{},[898,35275,1839],{},[1765,35277,1945],{},[1681,35279,35280,35282],{},[898,35281,1828],{},[1765,35283,1945],{},[1761,35285,1885],{},[1681,35287,35288,35290],{},[898,35289,1839],{},[1765,35291,2296],{},[1681,35293,35294,35296],{},[898,35295,1828],{},[1765,35297,2296],{},[1761,35299,1920],{"stretchy":1821},[902,35301,35302],{"encoding":904},"\\mathcal{L} = Q_1 Q_2 + \\lambda(Y - P_1 Q_1 - P_2 Q_2)"," dává soustavu",[883,35305,35307],{"className":35306},[886],[888,35308,35309],{"xmlns":890,"display":1930},[892,35310,35311,35478],{},[24787,35312,35313],{"width":32101},[24792,35314,35315,35317,35471,35473],{},[24795,35316],{"width":32106},[24795,35318,35319],{},[24787,35320,35321,35367,35413],{"rowspacing":24789,"columnalign":24790,"columnspacing":6458},[24792,35322,35323,35335],{},[24795,35324,35325],{},[6411,35326,35327],{"scriptlevel":1767,"displaystyle":1833},[2015,35328,35329,35331,35333],{},[898,35330,13835],{"mathvariant":32578},[1765,35332,1945],{},[1761,35334,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[24795,35336,35337],{},[6411,35338,35339],{"scriptlevel":1767,"displaystyle":1833},[895,35340,35341,35343,35345,35351,35353,35355,35361,35363,35365],{},[895,35342],{},[1761,35344,1909],{},[1681,35346,35347,35349],{},[898,35348,1828],{},[1765,35350,2296],{},[1761,35352,1885],{},[898,35354,20477],{},[1681,35356,35357,35359],{},[898,35358,1839],{},[1765,35360,1945],{},[1761,35362,1909],{},[1765,35364,1767],{},[1761,35366,1834],{"separator":1833},[24792,35368,35369,35381],{},[24795,35370,35371],{},[6411,35372,35373],{"scriptlevel":1767,"displaystyle":1833},[2015,35374,35375,35377,35379],{},[898,35376,13835],{"mathvariant":32578},[1765,35378,2296],{},[1761,35380,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[24795,35382,35383],{},[6411,35384,35385],{"scriptlevel":1767,"displaystyle":1833},[895,35386,35387,35389,35391,35397,35399,35401,35407,35409,35411],{},[895,35388],{},[1761,35390,1909],{},[1681,35392,35393,35395],{},[898,35394,1828],{},[1765,35396,1945],{},[1761,35398,1885],{},[898,35400,20477],{},[1681,35402,35403,35405],{},[898,35404,1839],{},[1765,35406,2296],{},[1761,35408,1909],{},[1765,35410,1767],{},[1761,35412,1834],{"separator":1833},[24792,35414,35415,35427],{},[24795,35416,35417],{},[6411,35418,35419],{"scriptlevel":1767,"displaystyle":1833},[2015,35420,35421,35423,35425],{},[898,35422,13835],{"mathvariant":32578},[898,35424,20477],{},[1761,35426,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[24795,35428,35429],{},[6411,35430,35431],{"scriptlevel":1767,"displaystyle":1833},[895,35432,35433,35435,35437,35439,35441,35447,35453,35455,35461,35467,35469],{},[895,35434],{},[1761,35436,1909],{},[898,35438,13170],{},[1761,35440,1885],{},[1681,35442,35443,35445],{},[898,35444,1839],{},[1765,35446,1945],{},[1681,35448,35449,35451],{},[898,35450,1828],{},[1765,35452,1945],{},[1761,35454,1885],{},[1681,35456,35457,35459],{},[898,35458,1839],{},[1765,35460,2296],{},[1681,35462,35463,35465],{},[898,35464,1828],{},[1765,35466,2296],{},[1761,35468,1909],{},[1765,35470,16498],{},[24795,35472],{"width":32106},[24795,35474,35475],{},[2761,35476,35477],{},"(6.17)",[902,35479,35480],{"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}",[724,35482,35483,35484,35512,35513,35541,35542,35610],{},"Z prvních dvou: ",[883,35485,35487],{"className":35486},[886],[888,35488,35489],{"xmlns":890},[892,35490,35491,35509],{},[895,35492,35493,35499,35501,35507],{},[1681,35494,35495,35497],{},[898,35496,1828],{},[1765,35498,2296],{},[1761,35500,1909],{},[1681,35502,35503,35505],{},[898,35504,1839],{},[1765,35506,1945],{},[898,35508,20477],{},[902,35510,35511],{"encoding":904},"Q_2 = P_1 \\lambda"," (6.18), ",[883,35514,35516],{"className":35515},[886],[888,35517,35518],{"xmlns":890},[892,35519,35520,35538],{},[895,35521,35522,35528,35530,35536],{},[1681,35523,35524,35526],{},[898,35525,1828],{},[1765,35527,1945],{},[1761,35529,1909],{},[1681,35531,35532,35534],{},[898,35533,1839],{},[1765,35535,2296],{},[898,35537,20477],{},[902,35539,35540],{"encoding":904},"Q_1 = P_2 \\lambda"," (6.19). Dosazením do třetí ",[883,35543,35545],{"className":35544},[886],[888,35546,35547],{"xmlns":890},[892,35548,35549,35607],{},[895,35550,35551,35553,35555,35561,35563,35569,35571,35573,35579,35581,35587,35589,35591,35593,35599,35605],{},[898,35552,13170],{},[1761,35554,1909],{},[1681,35556,35557,35559],{},[898,35558,1839],{},[1765,35560,1945],{},[1761,35562,2447],{},[1681,35564,35565,35567],{},[898,35566,1839],{},[1765,35568,2296],{},[898,35570,20477],{},[1761,35572,1964],{},[1681,35574,35575,35577],{},[898,35576,1839],{},[1765,35578,2296],{},[1761,35580,2447],{},[1681,35582,35583,35585],{},[898,35584,1839],{},[1765,35586,1945],{},[898,35588,20477],{},[1761,35590,1909],{},[1765,35592,2296],{},[1681,35594,35595,35597],{},[898,35596,1839],{},[1765,35598,1945],{},[1681,35600,35601,35603],{},[898,35602,1839],{},[1765,35604,2296],{},[898,35606,20477],{},[902,35608,35609],{"encoding":904},"Y = P_1 \\cdot P_2 \\lambda + P_2 \\cdot P_1 \\lambda = 2 P_1 P_2 \\lambda",", odtud",[883,35612,35614],{"className":35613},[886],[888,35615,35616],{"xmlns":890,"display":1930},[892,35617,35618,35661],{},[24787,35619,35620],{"width":32101},[24792,35621,35622,35624,35654,35656],{},[24795,35623],{"width":32106},[24795,35625,35626],{},[895,35627,35628,35630,35632,35652],{},[898,35629,20477],{},[1761,35631,1909],{},[4379,35633,35634,35636],{},[898,35635,13170],{},[895,35637,35638,35640,35646],{},[1765,35639,2296],{},[1681,35641,35642,35644],{},[898,35643,1839],{},[1765,35645,1945],{},[1681,35647,35648,35650],{},[898,35649,1839],{},[1765,35651,2296],{},[898,35653,1741],{"mathvariant":1969},[24795,35655],{"width":32106},[24795,35657,35658],{},[2761,35659,35660],{},"(6.20)",[902,35662,35663],{"encoding":904},"\\lambda = \\frac{Y}{2 P_1 P_2}. \\tag{6.20}",[724,35665,35666],{},"Zpětně:",[883,35668,35670],{"className":35669},[886],[888,35671,35672],{"xmlns":890,"display":1930},[892,35673,35674,35751],{},[24787,35675,35676],{"width":32101},[24792,35677,35678,35680,35744,35746],{},[24795,35679],{"width":32106},[24795,35681,35682],{},[16870,35683,35684],{"notation":16872},[6411,35685,35686],{"scriptlevel":1767,"displaystyle":1821},[6411,35687,35688],{"scriptlevel":1767,"displaystyle":1821},[6411,35689,35690],{"scriptlevel":1767,"displaystyle":1833},[895,35691,35692,35694,35700,35702,35716,35718,35720,35726,35728,35742],{},[2761,35693,8041],{},[1681,35695,35696,35698],{},[898,35697,1828],{},[1765,35699,1945],{},[1761,35701,1909],{},[4379,35703,35704,35706],{},[898,35705,13170],{},[895,35707,35708,35710],{},[1765,35709,2296],{},[1681,35711,35712,35714],{},[898,35713,1839],{},[1765,35715,1945],{},[1761,35717,1834],{"separator":1833},[3315,35719],{"width":19322},[1681,35721,35722,35724],{},[898,35723,1828],{},[1765,35725,2296],{},[1761,35727,1909],{},[4379,35729,35730,35732],{},[898,35731,13170],{},[895,35733,35734,35736],{},[1765,35735,2296],{},[1681,35737,35738,35740],{},[898,35739,1839],{},[1765,35741,2296],{},[2761,35743,8041],{},[24795,35745],{"width":32106},[24795,35747,35748],{},[2761,35749,35750],{},"(6.21)",[902,35752,35753],{"encoding":904},"\\boxed{\\; Q_1 = \\frac{Y}{2 P_1}, \\quad Q_2 = \\frac{Y}{2 P_2} \\;} \\tag{6.21}",[198,35755,35757],{"id":35756},"engelova-funkce","Engelova funkce",[724,35759,13703,35760,35763,35764,35767,35768,23900,35785,1343,35815,35845,35846,35880,35881,1343,35907,35933],{},[38,35761,35762],{},"pevné ceny"," a proměnný důchod se Marshallova poptávka stává ",[38,35765,35766],{},"Engelovou funkcí",": pro ",[883,35769,35771],{"className":35770},[886],[888,35772,35773],{"xmlns":890},[892,35774,35775,35783],{},[895,35776,35777,35779,35781],{},[898,35778,13170],{},[1761,35780,1909],{},[1765,35782,7160],{},[902,35784,24352],{"encoding":904},[883,35786,35788],{"className":35787},[886],[888,35789,35790],{"xmlns":890},[892,35791,35792,35812],{},[895,35793,35794,35800,35802,35804,35806],{},[1681,35795,35796,35798],{},[898,35797,1828],{},[1765,35799,1945],{},[1761,35801,1909],{},[1765,35803,7190],{},[898,35805,8726],{"mathvariant":1969},[1681,35807,35808,35810],{},[898,35809,1839],{},[1765,35811,1945],{},[902,35813,35814],{"encoding":904},"Q_1 = 50\u002FP_1",[883,35816,35818],{"className":35817},[886],[888,35819,35820],{"xmlns":890},[892,35821,35822,35842],{},[895,35823,35824,35830,35832,35834,35836],{},[1681,35825,35826,35828],{},[898,35827,1828],{},[1765,35829,2296],{},[1761,35831,1909],{},[1765,35833,7190],{},[898,35835,8726],{"mathvariant":1969},[1681,35837,35838,35840],{},[898,35839,1839],{},[1765,35841,2296],{},[902,35843,35844],{"encoding":904},"Q_2 = 50\u002FP_2",". Pro pevné ceny ",[883,35847,35849],{"className":35848},[886],[888,35850,35851],{"xmlns":890},[892,35852,35853,35877],{},[895,35854,35855,35861,35863,35865,35867,35873,35875],{},[1681,35856,35857,35859],{},[898,35858,1839],{},[1765,35860,1945],{},[1761,35862,1909],{},[1765,35864,2633],{},[1761,35866,1834],{"separator":1833},[1681,35868,35869,35871],{},[898,35870,1839],{},[1765,35872,2296],{},[1761,35874,1909],{},[1765,35876,13077],{},[902,35878,35879],{"encoding":904},"P_1 = 10, P_2 = 20"," dostáváme Engelovy funkce ",[883,35882,35884],{"className":35883},[886],[888,35885,35886],{"xmlns":890},[892,35887,35888,35904],{},[895,35889,35890,35896,35898,35900,35902],{},[1681,35891,35892,35894],{},[898,35893,1828],{},[1765,35895,1945],{},[1761,35897,1909],{},[898,35899,13170],{},[898,35901,8726],{"mathvariant":1969},[1765,35903,13077],{},[902,35905,35906],{"encoding":904},"Q_1 = Y\u002F20",[883,35908,35910],{"className":35909},[886],[888,35911,35912],{"xmlns":890},[892,35913,35914,35930],{},[895,35915,35916,35922,35924,35926,35928],{},[1681,35917,35918,35920],{},[898,35919,1828],{},[1765,35921,2296],{},[1761,35923,1909],{},[898,35925,13170],{},[898,35927,8726],{"mathvariant":1969},[1765,35929,9262],{},[902,35931,35932],{"encoding":904},"Q_2 = Y\u002F40"," — lineární závislost spotřebovaného množství na důchodu.",[115,35935,35937],{"id":35936},"duální-úloha-minimalizace-výdajů","Duální úloha — minimalizace výdajů",[724,35939,35940],{},"Výdaje spotřebitele jsou",[883,35942,35944],{"className":35943},[886],[888,35945,35946],{"xmlns":890,"display":1930},[892,35947,35948,36023],{},[24787,35949,35950],{"width":32101},[24792,35951,35952,35954,36016,36018],{},[24795,35953],{"width":32106},[24795,35955,35956],{},[895,35957,35958,35960,35962,35964,35966,35972,35974,35980,35982,35984,35992,35998,36000,36008,36014],{},[898,35959,1818],{},[1761,35961,1909],{},[898,35963,1818],{},[1761,35965,1915],{"stretchy":1821},[1681,35967,35968,35970],{},[898,35969,1828],{},[1765,35971,1945],{},[1761,35973,1834],{"separator":1833},[1681,35975,35976,35978],{},[898,35977,1828],{},[1765,35979,2296],{},[1761,35981,1920],{"stretchy":1821},[1761,35983,1909],{},[2015,35985,35986,35988,35990],{},[898,35987,1839],{},[1765,35989,1945],{},[1761,35991,8408],{},[1681,35993,35994,35996],{},[898,35995,1828],{},[1765,35997,1945],{},[1761,35999,1964],{},[2015,36001,36002,36004,36006],{},[898,36003,1839],{},[1765,36005,2296],{},[1761,36007,8408],{},[1681,36009,36010,36012],{},[898,36011,1828],{},[1765,36013,2296],{},[1761,36015,1834],{"separator":1833},[24795,36017],{"width":32106},[24795,36019,36020],{},[2761,36021,36022],{},"(6.22)",[902,36024,36025],{"encoding":904},"E = E(Q_1, Q_2) = P_1^* Q_1 + P_2^* Q_2, \\tag{6.22}",[724,36027,36028],{},"a je pevně zadána hladina užitečnosti",[883,36030,36032],{"className":36031},[886],[888,36033,36034],{"xmlns":890,"display":1930},[892,36035,36036,36083],{},[24787,36037,36038],{"width":32101},[24792,36039,36040,36042,36076,36078],{},[24795,36041],{"width":32106},[24795,36043,36044],{},[895,36045,36046,36052,36054,36056,36058,36064,36066,36072,36074],{},[1824,36047,36048,36050],{},[898,36049,900],{},[1761,36051,8408],{},[1761,36053,1909],{},[898,36055,900],{},[1761,36057,1915],{"stretchy":1821},[1681,36059,36060,36062],{},[898,36061,1828],{},[1765,36063,1945],{},[1761,36065,1834],{"separator":1833},[1681,36067,36068,36070],{},[898,36069,1828],{},[1765,36071,2296],{},[1761,36073,1920],{"stretchy":1821},[898,36075,1741],{"mathvariant":1969},[24795,36077],{"width":32106},[24795,36079,36080],{},[2761,36081,36082],{},"(6.23)",[902,36084,36085],{"encoding":904},"U^* = U(Q_1, Q_2). \\tag{6.23}",[724,36087,36088,36091,36092,36124,36125,1741],{},[38,36089,36090],{},"Úlohou o minimalizaci výdajů"," je najít minimum ",[883,36093,36095],{"className":36094},[886],[888,36096,36097],{"xmlns":890},[892,36098,36099,36121],{},[895,36100,36101,36103,36105,36111,36113,36119],{},[898,36102,1818],{},[1761,36104,1915],{"stretchy":1821},[1681,36106,36107,36109],{},[898,36108,1828],{},[1765,36110,1945],{},[1761,36112,1834],{"separator":1833},[1681,36114,36115,36117],{},[898,36116,1828],{},[1765,36118,2296],{},[1761,36120,1920],{"stretchy":1821},[902,36122,36123],{"encoding":904},"E(Q_1, Q_2)"," vázané podmínkou (6.23) ve tvaru ",[883,36126,36128],{"className":36127},[886],[888,36129,36130],{"xmlns":890},[892,36131,36132,36188],{},[895,36133,36134,36136,36138,36144,36146,36152,36154,36156,36162,36164,36166,36168,36174,36176,36182,36184,36186],{},[898,36135,15079],{},[1761,36137,1915],{"stretchy":1821},[1681,36139,36140,36142],{},[898,36141,1828],{},[1765,36143,1945],{},[1761,36145,1834],{"separator":1833},[1681,36147,36148,36150],{},[898,36149,1828],{},[1765,36151,2296],{},[1761,36153,1920],{"stretchy":1821},[1761,36155,1909],{},[1824,36157,36158,36160],{},[898,36159,900],{},[1761,36161,8408],{},[1761,36163,1885],{},[898,36165,900],{},[1761,36167,1915],{"stretchy":1821},[1681,36169,36170,36172],{},[898,36171,1828],{},[1765,36173,1945],{},[1761,36175,1834],{"separator":1833},[1681,36177,36178,36180],{},[898,36179,1828],{},[1765,36181,2296],{},[1761,36183,1920],{"stretchy":1821},[1761,36185,1909],{},[1765,36187,1767],{},[902,36189,36190],{"encoding":904},"g(Q_1, Q_2) = U^* - U(Q_1, Q_2) = 0",[198,36192,36194],{"id":36193},"lagrangeova-funkce","Lagrangeova funkce",[883,36196,36198],{"className":36197},[886],[888,36199,36200],{"xmlns":890,"display":1930},[892,36201,36202,36313],{},[24787,36203,36204],{"width":32101},[24792,36205,36206,36208,36306,36308],{},[24795,36207],{"width":32106},[24795,36209,36210],{},[895,36211,36212,36214,36216,36222,36224,36230,36232,36234,36236,36238,36246,36252,36254,36262,36268,36270,36272,36274,36280,36282,36284,36286,36292,36294,36300,36302,36304],{},[898,36213,13835],{"mathvariant":32578},[1761,36215,1915],{"stretchy":1821},[1681,36217,36218,36220],{},[898,36219,1828],{},[1765,36221,1945],{},[1761,36223,1834],{"separator":1833},[1681,36225,36226,36228],{},[898,36227,1828],{},[1765,36229,2296],{},[1761,36231,1834],{"separator":1833},[898,36233,20477],{},[1761,36235,1920],{"stretchy":1821},[1761,36237,1909],{},[2015,36239,36240,36242,36244],{},[898,36241,1839],{},[1765,36243,1945],{},[1761,36245,8408],{},[1681,36247,36248,36250],{},[898,36249,1828],{},[1765,36251,1945],{},[1761,36253,1964],{},[2015,36255,36256,36258,36260],{},[898,36257,1839],{},[1765,36259,2296],{},[1761,36261,8408],{},[1681,36263,36264,36266],{},[898,36265,1828],{},[1765,36267,2296],{},[1761,36269,1964],{},[898,36271,20477],{},[1761,36273,1915],{"stretchy":1821},[1824,36275,36276,36278],{},[898,36277,900],{},[1761,36279,8408],{},[1761,36281,1885],{},[898,36283,900],{},[1761,36285,1915],{"stretchy":1821},[1681,36287,36288,36290],{},[898,36289,1828],{},[1765,36291,1945],{},[1761,36293,1834],{"separator":1833},[1681,36295,36296,36298],{},[898,36297,1828],{},[1765,36299,2296],{},[1761,36301,1920],{"stretchy":1821},[1761,36303,1920],{"stretchy":1821},[898,36305,1741],{"mathvariant":1969},[24795,36307],{"width":32106},[24795,36309,36310],{},[2761,36311,36312],{},"(6.24)",[902,36314,36315],{"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}",[724,36317,36318],{},"Soustava podmínek prvního řádu:",[883,36320,36322],{"className":36321},[886],[888,36323,36324],{"xmlns":890,"display":1930},[892,36325,36326,36499],{},[24787,36327,36328],{"width":32101},[24792,36329,36330,36332,36492,36494],{},[24795,36331],{"width":32106},[24795,36333,36334],{},[24787,36335,36336,36386,36436],{"rowspacing":24789,"columnalign":24790,"columnspacing":6458},[24792,36337,36338,36350],{},[24795,36339,36340],{},[6411,36341,36342],{"scriptlevel":1767,"displaystyle":1833},[2015,36343,36344,36346,36348],{},[898,36345,13835],{"mathvariant":32578},[1765,36347,1945],{},[1761,36349,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[24795,36351,36352],{},[6411,36353,36354],{"scriptlevel":1767,"displaystyle":1833},[895,36355,36356,36358,36360,36368,36370,36372,36380,36382,36384],{},[895,36357],{},[1761,36359,1909],{},[2015,36361,36362,36364,36366],{},[898,36363,1839],{},[1765,36365,1945],{},[1761,36367,8408],{},[1761,36369,1885],{},[898,36371,20477],{},[2015,36373,36374,36376,36378],{},[898,36375,900],{},[1765,36377,1945],{},[1761,36379,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,36381,1909],{},[1765,36383,1767],{},[1761,36385,1834],{"separator":1833},[24792,36387,36388,36400],{},[24795,36389,36390],{},[6411,36391,36392],{"scriptlevel":1767,"displaystyle":1833},[2015,36393,36394,36396,36398],{},[898,36395,13835],{"mathvariant":32578},[1765,36397,2296],{},[1761,36399,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[24795,36401,36402],{},[6411,36403,36404],{"scriptlevel":1767,"displaystyle":1833},[895,36405,36406,36408,36410,36418,36420,36422,36430,36432,36434],{},[895,36407],{},[1761,36409,1909],{},[2015,36411,36412,36414,36416],{},[898,36413,1839],{},[1765,36415,2296],{},[1761,36417,8408],{},[1761,36419,1885],{},[898,36421,20477],{},[2015,36423,36424,36426,36428],{},[898,36425,900],{},[1765,36427,2296],{},[1761,36429,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,36431,1909],{},[1765,36433,1767],{},[1761,36435,1834],{"separator":1833},[24792,36437,36438,36450],{},[24795,36439,36440],{},[6411,36441,36442],{"scriptlevel":1767,"displaystyle":1833},[2015,36443,36444,36446,36448],{},[898,36445,13835],{"mathvariant":32578},[898,36447,20477],{},[1761,36449,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[24795,36451,36452],{},[6411,36453,36454],{"scriptlevel":1767,"displaystyle":1833},[895,36455,36456,36458,36460,36466,36468,36470,36472,36478,36480,36486,36488,36490],{},[895,36457],{},[1761,36459,1909],{},[1824,36461,36462,36464],{},[898,36463,900],{},[1761,36465,8408],{},[1761,36467,1885],{},[898,36469,900],{},[1761,36471,1915],{"stretchy":1821},[1681,36473,36474,36476],{},[898,36475,1828],{},[1765,36477,1945],{},[1761,36479,1834],{"separator":1833},[1681,36481,36482,36484],{},[898,36483,1828],{},[1765,36485,2296],{},[1761,36487,1920],{"stretchy":1821},[1761,36489,1909],{},[1765,36491,16498],{},[24795,36493],{"width":32106},[24795,36495,36496],{},[2761,36497,36498],{},"(6.25)",[902,36500,36501],{"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}",[724,36503,36504],{},"Postačující podmínka pro minimum (vzhledem k linearitě funkce výdajů) má tvar",[883,36506,36508],{"className":36507},[886],[888,36509,36510],{"xmlns":890,"display":1930},[892,36511,36512,36610],{},[24787,36513,36514],{"width":32101},[24792,36515,36516,36518,36603,36605],{},[24795,36517],{"width":32106},[24795,36519,36520],{},[895,36521,36522,36524,36526,36532,36534,36540,36542,36544,36546,36548,36550,36552,36601],{},[898,36523,2244],{},[1761,36525,1915],{"stretchy":1821},[1681,36527,36528,36530],{},[898,36529,1828],{},[1765,36531,1945],{},[1761,36533,1834],{"separator":1833},[1681,36535,36536,36538],{},[898,36537,1828],{},[1765,36539,2296],{},[1761,36541,1834],{"separator":1833},[898,36543,20477],{},[1761,36545,1920],{"stretchy":1821},[1761,36547,1909],{},[1761,36549,1885],{},[898,36551,20477],{},[895,36553,36554,36556,36568,36570,36583,36585,36587,36599],{},[1761,36555,1915],{"fence":1833},[2015,36557,36558,36560,36562],{},[898,36559,900],{},[1765,36561,6974],{},[895,36563,36564,36566],{},[1761,36565,6459],{"mathvariant":1969},[1761,36567,6459],{"mathvariant":1969},[1761,36569,1964],{},[2015,36571,36572,36574,36577],{},[898,36573,900],{},[1765,36575,36576],{},"22",[895,36578,36579,36581],{},[1761,36580,6459],{"mathvariant":1969},[1761,36582,6459],{"mathvariant":1969},[1761,36584,1964],{},[1765,36586,2296],{},[2015,36588,36589,36591,36593],{},[898,36590,900],{},[1765,36592,2291],{},[895,36594,36595,36597],{},[1761,36596,6459],{"mathvariant":1969},[1761,36598,6459],{"mathvariant":1969},[1761,36600,1920],{"fence":1833},[898,36602,1741],{"mathvariant":1969},[24795,36604],{"width":32106},[24795,36606,36607],{},[2761,36608,36609],{},"(6.26)",[902,36611,36612],{"encoding":904},"D(Q_1, Q_2, \\lambda) = -\\lambda \\left(U''_{11} + U''_{22} + 2 U''_{12}\\right). \\tag{6.26}",[724,36614,36615,36618,36619,36658,36659,36698,36699,36749,36750,36776,36777,36794,36795,36821],{},[38,36616,36617],{},"Geometrie (obrázek 6.9)."," Řešením je bod ",[883,36620,36622],{"className":36621},[886],[888,36623,36624],{"xmlns":890},[892,36625,36626,36656],{},[895,36627,36628,36634,36636,36644,36646,36654],{},[1824,36629,36630,36632],{},[898,36631,1828],{},[1761,36633,8408],{},[1761,36635,1822],{"stretchy":1821},[2015,36637,36638,36640,36642],{},[898,36639,1828],{},[1765,36641,1945],{},[1761,36643,8408],{},[1761,36645,1834],{"separator":1833},[2015,36647,36648,36650,36652],{},[898,36649,1828],{},[1765,36651,2296],{},[1761,36653,8408],{},[1761,36655,1844],{"stretchy":1821},[902,36657,32357],{"encoding":904}," dotyku křivky užitečnosti ",[883,36660,36662],{"className":36661},[886],[888,36663,36664],{"xmlns":890},[892,36665,36666,36696],{},[895,36667,36668,36674,36676,36678,36680,36686,36688,36694],{},[1824,36669,36670,36672],{},[898,36671,900],{},[1761,36673,8408],{},[1761,36675,1909],{},[898,36677,900],{},[1761,36679,1915],{"stretchy":1821},[1681,36681,36682,36684],{},[898,36683,1828],{},[1765,36685,1945],{},[1761,36687,1834],{"separator":1833},[1681,36689,36690,36692],{},[898,36691,1828],{},[1765,36693,2296],{},[1761,36695,1920],{"stretchy":1821},[902,36697,21699],{"encoding":904}," s přímkou výdajů ",[883,36700,36702],{"className":36701},[886],[888,36703,36704],{"xmlns":890},[892,36705,36706,36746],{},[895,36707,36708,36714,36716,36724,36730,36732,36740],{},[1824,36709,36710,36712],{},[898,36711,1818],{},[1761,36713,8408],{},[1761,36715,1909],{},[2015,36717,36718,36720,36722],{},[898,36719,1839],{},[1765,36721,1945],{},[1761,36723,8408],{},[1681,36725,36726,36728],{},[898,36727,1828],{},[1765,36729,1945],{},[1761,36731,1964],{},[2015,36733,36734,36736,36738],{},[898,36735,1839],{},[1765,36737,2296],{},[1761,36739,8408],{},[1681,36741,36742,36744],{},[898,36743,1828],{},[1765,36745,2296],{},[902,36747,36748],{"encoding":904},"E^* = P_1^* Q_1 + P_2^* Q_2",". Hladina ",[883,36751,36753],{"className":36752},[886],[888,36754,36755],{"xmlns":890},[892,36756,36757,36773],{},[895,36758,36759,36765,36767],{},[1681,36760,36761,36763],{},[898,36762,1818],{},[1765,36764,1767],{},[1761,36766,2058],{},[1824,36768,36769,36771],{},[898,36770,1818],{},[1761,36772,8408],{},[902,36774,36775],{"encoding":904},"E_0 \u003C E^*"," nestačí k dosažení ",[883,36778,36780],{"className":36779},[886],[888,36781,36782],{"xmlns":890},[892,36783,36784,36792],{},[895,36785,36786],{},[1824,36787,36788,36790],{},[898,36789,900],{},[1761,36791,8408],{},[902,36793,31993],{"encoding":904},", hladina ",[883,36796,36798],{"className":36797},[886],[888,36799,36800],{"xmlns":890},[892,36801,36802,36818],{},[895,36803,36804,36810,36812],{},[1681,36805,36806,36808],{},[898,36807,1818],{},[1765,36809,1945],{},[1761,36811,1763],{},[1824,36813,36814,36816],{},[898,36815,1818],{},[1761,36817,8408],{},[902,36819,36820],{"encoding":904},"E_1 > E^*"," je nadbytečná.",[1636,36823,36824,36829],{},[724,36825,36826,36828],{},[883,36827,4452],{}," Postup — duální úloha (minimalizace výdajů)",[152,36830,36831,36881,36967,37007,37082],{},[123,36832,36833,1989,36836,36880],{},[38,36834,36835],{},"Zapiš vazbu",[883,36837,36839],{"className":36838},[886],[888,36840,36841],{"xmlns":890},[892,36842,36843,36877],{},[895,36844,36845,36851,36853,36855,36857,36863,36865,36871,36873,36875],{},[1824,36846,36847,36849],{},[898,36848,900],{},[1761,36850,8408],{},[1761,36852,1885],{},[898,36854,900],{},[1761,36856,1915],{"stretchy":1821},[1681,36858,36859,36861],{},[898,36860,1828],{},[1765,36862,1945],{},[1761,36864,1834],{"separator":1833},[1681,36866,36867,36869],{},[898,36868,1828],{},[1765,36870,2296],{},[1761,36872,1920],{"stretchy":1821},[1761,36874,1909],{},[1765,36876,1767],{},[902,36878,36879],{"encoding":904},"U^* - U(Q_1, Q_2) = 0"," (zadaná hladina užitečnosti).",[123,36882,36883,1989,36885,1741],{},[38,36884,33290],{},[883,36886,36888],{"className":36887},[886],[888,36889,36890],{"xmlns":890},[892,36891,36892,36964],{},[895,36893,36894,36896,36898,36906,36912,36914,36922,36928,36930,36932,36934,36940,36942,36944,36946,36952,36954,36960,36962],{},[898,36895,13835],{"mathvariant":32578},[1761,36897,1909],{},[2015,36899,36900,36902,36904],{},[898,36901,1839],{},[1765,36903,1945],{},[1761,36905,8408],{},[1681,36907,36908,36910],{},[898,36909,1828],{},[1765,36911,1945],{},[1761,36913,1964],{},[2015,36915,36916,36918,36920],{},[898,36917,1839],{},[1765,36919,2296],{},[1761,36921,8408],{},[1681,36923,36924,36926],{},[898,36925,1828],{},[1765,36927,2296],{},[1761,36929,1964],{},[898,36931,20477],{},[1761,36933,1915],{"stretchy":1821},[1824,36935,36936,36938],{},[898,36937,900],{},[1761,36939,8408],{},[1761,36941,1885],{},[898,36943,900],{},[1761,36945,1915],{"stretchy":1821},[1681,36947,36948,36950],{},[898,36949,1828],{},[1765,36951,1945],{},[1761,36953,1834],{"separator":1833},[1681,36955,36956,36958],{},[898,36957,1828],{},[1765,36959,2296],{},[1761,36961,1920],{"stretchy":1821},[1761,36963,1920],{"stretchy":1821},[902,36965,36966],{"encoding":904},"\\mathcal{L} = P_1^* Q_1 + P_2^* Q_2 + \\lambda(U^* - U(Q_1, Q_2))",[123,36968,36969,36972,36973,37006],{},[38,36970,36971],{},"Derivace rovny nule",", z prvních dvou rovnic podílem dostaneš podmínku ",[883,36974,36976],{"className":36975},[886],[888,36977,36978],{"xmlns":890},[892,36979,36980,37004],{},[895,36981,36982,36984,36986,36994,36996],{},[2761,36983,14641],{},[1761,36985,1909],{},[2015,36987,36988,36990,36992],{},[898,36989,1839],{},[1765,36991,1945],{},[1761,36993,8408],{},[898,36995,8726],{"mathvariant":1969},[2015,36997,36998,37000,37002],{},[898,36999,1839],{},[1765,37001,2296],{},[1761,37003,8408],{},[902,37005,33009],{"encoding":904}," (stejná jako u maximalizace!).",[123,37008,37009,1989,37012,37052,37053,1741],{},[38,37010,37011],{},"Dosaď do vazby",[883,37013,37015],{"className":37014},[886],[888,37016,37017],{"xmlns":890},[892,37018,37019,37049],{},[895,37020,37021,37023,37025,37031,37033,37039,37041,37043],{},[898,37022,900],{},[1761,37024,1915],{"stretchy":1821},[1681,37026,37027,37029],{},[898,37028,1828],{},[1765,37030,1945],{},[1761,37032,1834],{"separator":1833},[1681,37034,37035,37037],{},[898,37036,1828],{},[1765,37038,2296],{},[1761,37040,1920],{"stretchy":1821},[1761,37042,1909],{},[1824,37044,37045,37047],{},[898,37046,900],{},[1761,37048,8408],{},[902,37050,37051],{"encoding":904},"U(Q_1, Q_2) = U^*"," a vyřeš pro ",[883,37054,37056],{"className":37055},[886],[888,37057,37058],{"xmlns":890},[892,37059,37060,37080],{},[895,37061,37062,37070,37072],{},[2015,37063,37064,37066,37068],{},[898,37065,1828],{},[1765,37067,1945],{},[1761,37069,8408],{},[1761,37071,1834],{"separator":1833},[2015,37073,37074,37076,37078],{},[898,37075,1828],{},[1765,37077,2296],{},[1761,37079,8408],{},[902,37081,33531],{"encoding":904},[123,37083,37084,1989,37087,37141],{},[38,37085,37086],{},"Vypočítej minimální výdaje",[883,37088,37090],{"className":37089},[886],[888,37091,37092],{"xmlns":890},[892,37093,37094,37138],{},[895,37095,37096,37102,37104,37112,37120,37122,37130],{},[1824,37097,37098,37100],{},[898,37099,1818],{},[1761,37101,8408],{},[1761,37103,1909],{},[2015,37105,37106,37108,37110],{},[898,37107,1839],{},[1765,37109,1945],{},[1761,37111,8408],{},[2015,37113,37114,37116,37118],{},[898,37115,1828],{},[1765,37117,1945],{},[1761,37119,8408],{},[1761,37121,1964],{},[2015,37123,37124,37126,37128],{},[898,37125,1839],{},[1765,37127,2296],{},[1761,37129,8408],{},[2015,37131,37132,37134,37136],{},[898,37133,1828],{},[1765,37135,2296],{},[1761,37137,8408],{},[902,37139,37140],{"encoding":904},"E^* = P_1^* Q_1^* + P_2^* Q_2^*"," a případně ověř druhou podmínku (6.26).",[115,37143,37145,37146],{"id":37144},"příklad-67-minimalizace-výdajů-pro-uq112q212u-q_112-q_212","Příklad 6.7 — minimalizace výdajů pro ",[883,37147,37149],{"className":37148},[886],[888,37150,37151],{"xmlns":890},[892,37152,37153,37187],{},[895,37154,37155,37157,37159,37173],{},[898,37156,900],{},[1761,37158,1909],{},[2015,37160,37161,37163,37165],{},[898,37162,1828],{},[1765,37164,1945],{},[895,37166,37167,37169,37171],{},[1765,37168,1945],{},[898,37170,8726],{"mathvariant":1969},[1765,37172,2296],{},[2015,37174,37175,37177,37179],{},[898,37176,1828],{},[1765,37178,2296],{},[895,37180,37181,37183,37185],{},[1765,37182,1945],{},[898,37184,8726],{"mathvariant":1969},[1765,37186,2296],{},[902,37188,37189],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F2}",[724,37191,37192,37193,1343,37215,1343,37239,34376],{},"Dáno ",[883,37194,37196],{"className":37195},[886],[888,37197,37198],{"xmlns":890},[892,37199,37200,37212],{},[895,37201,37202,37208,37210],{},[1824,37203,37204,37206],{},[898,37205,900],{},[1761,37207,8408],{},[1761,37209,1909],{},[1765,37211,2296],{},[902,37213,37214],{"encoding":904},"U^* = 2",[883,37216,37218],{"className":37217},[886],[888,37219,37220],{"xmlns":890},[892,37221,37222,37236],{},[895,37223,37224,37232,37234],{},[2015,37225,37226,37228,37230],{},[898,37227,1839],{},[1765,37229,1945],{},[1761,37231,8408],{},[1761,37233,1909],{},[1765,37235,27822],{},[902,37237,37238],{"encoding":904},"P_1^* = 0{,}25",[883,37240,37242],{"className":37241},[886],[888,37243,37244],{"xmlns":890},[892,37245,37246,37260],{},[895,37247,37248,37256,37258],{},[2015,37249,37250,37252,37254],{},[898,37251,1839],{},[1765,37253,2296],{},[1761,37255,8408],{},[1761,37257,1909],{},[1765,37259,1945],{},[902,37261,37262],{"encoding":904},"P_2^* = 1",[883,37264,37266],{"className":37265},[886],[888,37267,37268],{"xmlns":890,"display":1930},[892,37269,37270,37334],{},[895,37271,37272,37274,37276,37278,37284,37286,37292,37294,37296,37298,37300,37302,37316,37330,37332],{},[898,37273,13835],{"mathvariant":32578},[1761,37275,1909],{},[1765,37277,27822],{},[1681,37279,37280,37282],{},[898,37281,1828],{},[1765,37283,1945],{},[1761,37285,1964],{},[1681,37287,37288,37290],{},[898,37289,1828],{},[1765,37291,2296],{},[1761,37293,1964],{},[898,37295,20477],{},[1761,37297,1915],{"stretchy":1821},[1765,37299,2296],{},[1761,37301,1885],{},[2015,37303,37304,37306,37308],{},[898,37305,1828],{},[1765,37307,1945],{},[895,37309,37310,37312,37314],{},[1765,37311,1945],{},[898,37313,8726],{"mathvariant":1969},[1765,37315,2296],{},[2015,37317,37318,37320,37322],{},[898,37319,1828],{},[1765,37321,2296],{},[895,37323,37324,37326,37328],{},[1765,37325,1945],{},[898,37327,8726],{"mathvariant":1969},[1765,37329,2296],{},[1761,37331,1920],{"stretchy":1821},[898,37333,1741],{"mathvariant":1969},[902,37335,37336],{"encoding":904},"\\mathcal{L} = 0{,}25 Q_1 + Q_2 + \\lambda(2 - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,37338,34461],{},[883,37340,37342],{"className":37341},[886],[888,37343,37344],{"xmlns":890,"display":1930},[892,37345,37346,37560],{},[24787,37347,37348,37424,37500],{"rowspacing":24789,"columnalign":24790,"columnspacing":6458},[24792,37349,37350,37362],{},[24795,37351,37352],{},[6411,37353,37354],{"scriptlevel":1767,"displaystyle":1833},[2015,37355,37356,37358,37360],{},[898,37357,13835],{"mathvariant":32578},[1765,37359,1945],{},[1761,37361,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[24795,37363,37364],{},[6411,37365,37366],{"scriptlevel":1767,"displaystyle":1833},[895,37367,37368,37370,37372,37374,37376,37378,37380,37388,37404,37418,37420,37422],{},[895,37369],{},[1761,37371,1909],{},[1765,37373,27822],{},[1761,37375,1885],{},[898,37377,20477],{},[1761,37379,2447],{},[6411,37381,37382],{"scriptlevel":1767,"displaystyle":1821},[4379,37383,37384,37386],{},[1765,37385,1945],{},[1765,37387,2296],{},[2015,37389,37390,37392,37394],{},[898,37391,1828],{},[1765,37393,1945],{},[895,37395,37396,37398,37400,37402],{},[1761,37397,1885],{},[1765,37399,1945],{},[898,37401,8726],{"mathvariant":1969},[1765,37403,2296],{},[2015,37405,37406,37408,37410],{},[898,37407,1828],{},[1765,37409,2296],{},[895,37411,37412,37414,37416],{},[1765,37413,1945],{},[898,37415,8726],{"mathvariant":1969},[1765,37417,2296],{},[1761,37419,1909],{},[1765,37421,1767],{},[1761,37423,1834],{"separator":1833},[24792,37425,37426,37438],{},[24795,37427,37428],{},[6411,37429,37430],{"scriptlevel":1767,"displaystyle":1833},[2015,37431,37432,37434,37436],{},[898,37433,13835],{"mathvariant":32578},[1765,37435,2296],{},[1761,37437,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[24795,37439,37440],{},[6411,37441,37442],{"scriptlevel":1767,"displaystyle":1833},[895,37443,37444,37446,37448,37450,37452,37454,37456,37464,37478,37494,37496,37498],{},[895,37445],{},[1761,37447,1909],{},[1765,37449,1945],{},[1761,37451,1885],{},[898,37453,20477],{},[1761,37455,2447],{},[6411,37457,37458],{"scriptlevel":1767,"displaystyle":1821},[4379,37459,37460,37462],{},[1765,37461,1945],{},[1765,37463,2296],{},[2015,37465,37466,37468,37470],{},[898,37467,1828],{},[1765,37469,1945],{},[895,37471,37472,37474,37476],{},[1765,37473,1945],{},[898,37475,8726],{"mathvariant":1969},[1765,37477,2296],{},[2015,37479,37480,37482,37484],{},[898,37481,1828],{},[1765,37483,2296],{},[895,37485,37486,37488,37490,37492],{},[1761,37487,1885],{},[1765,37489,1945],{},[898,37491,8726],{"mathvariant":1969},[1765,37493,2296],{},[1761,37495,1909],{},[1765,37497,1767],{},[1761,37499,1834],{"separator":1833},[24792,37501,37502,37514],{},[24795,37503,37504],{},[6411,37505,37506],{"scriptlevel":1767,"displaystyle":1833},[2015,37507,37508,37510,37512],{},[898,37509,13835],{"mathvariant":32578},[898,37511,20477],{},[1761,37513,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[24795,37515,37516],{},[6411,37517,37518],{"scriptlevel":1767,"displaystyle":1833},[895,37519,37520,37522,37524,37526,37528,37542,37556,37558],{},[895,37521],{},[1761,37523,1909],{},[1765,37525,2296],{},[1761,37527,1885],{},[2015,37529,37530,37532,37534],{},[898,37531,1828],{},[1765,37533,1945],{},[895,37535,37536,37538,37540],{},[1765,37537,1945],{},[898,37539,8726],{"mathvariant":1969},[1765,37541,2296],{},[2015,37543,37544,37546,37548],{},[898,37545,1828],{},[1765,37547,2296],{},[895,37549,37550,37552,37554],{},[1765,37551,1945],{},[898,37553,8726],{"mathvariant":1969},[1765,37555,2296],{},[1761,37557,1909],{},[1765,37559,16498],{},[902,37561,37562],{"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}",[724,37564,37565,37566,21610,37596,37624,37625,2403,37687,1343,37737,37759,37760,1741],{},"Podílem prvních dvou rovnic: ",[883,37567,37569],{"className":37568},[886],[888,37570,37571],{"xmlns":890},[892,37572,37573,37593],{},[895,37574,37575,37577,37579,37585,37587],{},[1765,37576,27822],{},[1761,37578,1909],{},[1681,37580,37581,37583],{},[898,37582,1828],{},[1765,37584,2296],{},[898,37586,8726],{"mathvariant":1969},[1681,37588,37589,37591],{},[898,37590,1828],{},[1765,37592,1945],{},[902,37594,37595],{"encoding":904},"0{,}25 = Q_2 \u002F Q_1",[883,37597,37599],{"className":37598},[886],[888,37600,37601],{"xmlns":890},[892,37602,37603,37621],{},[895,37604,37605,37611,37613,37615],{},[1681,37606,37607,37609],{},[898,37608,1828],{},[1765,37610,2296],{},[1761,37612,1909],{},[1765,37614,27822],{},[1681,37616,37617,37619],{},[898,37618,1828],{},[1765,37620,1945],{},[902,37622,37623],{"encoding":904},"Q_2 = 0{,}25 Q_1",". Dosazením do třetí: ",[883,37626,37628],{"className":37627},[886],[888,37629,37630],{"xmlns":890},[892,37631,37632,37684],{},[895,37633,37634,37648,37650,37652,37658,37670,37672,37674,37680,37682],{},[2015,37635,37636,37638,37640],{},[898,37637,1828],{},[1765,37639,1945],{},[895,37641,37642,37644,37646],{},[1765,37643,1945],{},[898,37645,8726],{"mathvariant":1969},[1765,37647,2296],{},[1761,37649,1915],{"stretchy":1821},[1765,37651,27822],{},[1681,37653,37654,37656],{},[898,37655,1828],{},[1765,37657,1945],{},[1824,37659,37660,37662],{},[1761,37661,1920],{"stretchy":1821},[895,37663,37664,37666,37668],{},[1765,37665,1945],{},[898,37667,8726],{"mathvariant":1969},[1765,37669,2296],{},[1761,37671,1909],{},[1765,37673,5426],{},[1681,37675,37676,37678],{},[898,37677,1828],{},[1765,37679,1945],{},[1761,37681,1909],{},[1765,37683,2296],{},[902,37685,37686],{"encoding":904},"Q_1^{1\u002F2} (0{,}25 Q_1)^{1\u002F2} = 0{,}5 Q_1 = 2",[38,37688,37689,1343,37713],{},[883,37690,37692],{"className":37691},[886],[888,37693,37694],{"xmlns":890},[892,37695,37696,37710],{},[895,37697,37698,37706,37708],{},[2015,37699,37700,37702,37704],{},[898,37701,1828],{},[1765,37703,1945],{},[1761,37705,8408],{},[1761,37707,1909],{},[1765,37709,2318],{},[902,37711,37712],{"encoding":904},"Q_1^* = 4",[883,37714,37716],{"className":37715},[886],[888,37717,37718],{"xmlns":890},[892,37719,37720,37734],{},[895,37721,37722,37730,37732],{},[2015,37723,37724,37726,37728],{},[898,37725,1828],{},[1765,37727,2296],{},[1761,37729,8408],{},[1761,37731,1909],{},[1765,37733,1945],{},[902,37735,37736],{"encoding":904},"Q_2^* = 1",[883,37738,37740],{"className":37739},[886],[888,37741,37742],{"xmlns":890},[892,37743,37744,37756],{},[895,37745,37746,37752,37754],{},[1824,37747,37748,37750],{},[898,37749,20477],{},[1761,37751,8408],{},[1761,37753,1909],{},[1765,37755,1945],{},[902,37757,37758],{"encoding":904},"\\lambda^* = 1",". Minimální výdaje: ",[883,37761,37763],{"className":37762},[886],[888,37764,37765],{"xmlns":890},[892,37766,37767,37795],{},[895,37768,37769,37775,37777,37779,37781,37783,37785,37787,37789,37791,37793],{},[1824,37770,37771,37773],{},[898,37772,1818],{},[1761,37774,8408],{},[1761,37776,1909],{},[1765,37778,27822],{},[1761,37780,2447],{},[1765,37782,2318],{},[1761,37784,1964],{},[1765,37786,1945],{},[1761,37788,2447],{},[1765,37790,1945],{},[1761,37792,1909],{},[1765,37794,2296],{},[902,37796,37797],{"encoding":904},"E^* = 0{,}25 \\cdot 4 + 1 \\cdot 1 = 2",[724,37799,37800,37803,37804,1343,37870,1343,37936,38002,38003,38040,38041,38063,38064,1741],{},[614,37801,37802],{},"Ověření postačující podmínky"," (6.26): ",[883,37805,37807],{"className":37806},[886],[888,37808,37809],{"xmlns":890},[892,37810,37811,37867],{},[895,37812,37813,37825,37827,37829,37837,37853],{},[2015,37814,37815,37817,37819],{},[898,37816,900],{},[1765,37818,6974],{},[895,37820,37821,37823],{},[1761,37822,6459],{"mathvariant":1969},[1761,37824,6459],{"mathvariant":1969},[1761,37826,1909],{},[1761,37828,1885],{},[6411,37830,37831],{"scriptlevel":1767,"displaystyle":1821},[4379,37832,37833,37835],{},[1765,37834,1945],{},[1765,37836,2318],{},[2015,37838,37839,37841,37843],{},[898,37840,1828],{},[1765,37842,1945],{},[895,37844,37845,37847,37849,37851],{},[1761,37846,1885],{},[1765,37848,5486],{},[898,37850,8726],{"mathvariant":1969},[1765,37852,2296],{},[2015,37854,37855,37857,37859],{},[898,37856,1828],{},[1765,37858,2296],{},[895,37860,37861,37863,37865],{},[1765,37862,1945],{},[898,37864,8726],{"mathvariant":1969},[1765,37866,2296],{},[902,37868,37869],{"encoding":904},"U''_{11} = -\\tfrac{1}{4} Q_1^{-3\u002F2} Q_2^{1\u002F2}",[883,37871,37873],{"className":37872},[886],[888,37874,37875],{"xmlns":890},[892,37876,37877,37933],{},[895,37878,37879,37891,37893,37895,37903,37917],{},[2015,37880,37881,37883,37885],{},[898,37882,900],{},[1765,37884,36576],{},[895,37886,37887,37889],{},[1761,37888,6459],{"mathvariant":1969},[1761,37890,6459],{"mathvariant":1969},[1761,37892,1909],{},[1761,37894,1885],{},[6411,37896,37897],{"scriptlevel":1767,"displaystyle":1821},[4379,37898,37899,37901],{},[1765,37900,1945],{},[1765,37902,2318],{},[2015,37904,37905,37907,37909],{},[898,37906,1828],{},[1765,37908,1945],{},[895,37910,37911,37913,37915],{},[1765,37912,1945],{},[898,37914,8726],{"mathvariant":1969},[1765,37916,2296],{},[2015,37918,37919,37921,37923],{},[898,37920,1828],{},[1765,37922,2296],{},[895,37924,37925,37927,37929,37931],{},[1761,37926,1885],{},[1765,37928,5486],{},[898,37930,8726],{"mathvariant":1969},[1765,37932,2296],{},[902,37934,37935],{"encoding":904},"U''_{22} = -\\tfrac{1}{4} Q_1^{1\u002F2} Q_2^{-3\u002F2}",[883,37937,37939],{"className":37938},[886],[888,37940,37941],{"xmlns":890},[892,37942,37943,37999],{},[895,37944,37945,37957,37959,37967,37983],{},[2015,37946,37947,37949,37951],{},[898,37948,900],{},[1765,37950,2291],{},[895,37952,37953,37955],{},[1761,37954,6459],{"mathvariant":1969},[1761,37956,6459],{"mathvariant":1969},[1761,37958,1909],{},[6411,37960,37961],{"scriptlevel":1767,"displaystyle":1821},[4379,37962,37963,37965],{},[1765,37964,1945],{},[1765,37966,2318],{},[2015,37968,37969,37971,37973],{},[898,37970,1828],{},[1765,37972,1945],{},[895,37974,37975,37977,37979,37981],{},[1761,37976,1885],{},[1765,37978,1945],{},[898,37980,8726],{"mathvariant":1969},[1765,37982,2296],{},[2015,37984,37985,37987,37989],{},[898,37986,1828],{},[1765,37988,2296],{},[895,37990,37991,37993,37995,37997],{},[1761,37992,1885],{},[1765,37994,1945],{},[898,37996,8726],{"mathvariant":1969},[1765,37998,2296],{},[902,38000,38001],{"encoding":904},"U''_{12} = \\tfrac{1}{4} Q_1^{-1\u002F2} Q_2^{-1\u002F2}",". Po dosazení ",[883,38004,38006],{"className":38005},[886],[888,38007,38008],{"xmlns":890},[892,38009,38010,38037],{},[895,38011,38012,38014,38016,38018,38020,38022,38024,38026,38028,38030,38033,38035],{},[898,38013,2244],{},[1761,38015,1915],{"stretchy":1821},[1765,38017,2318],{},[1761,38019,1834],{"separator":1833},[1765,38021,1945],{},[1761,38023,1834],{"separator":1833},[1765,38025,1945],{},[1761,38027,1920],{"stretchy":1821},[1761,38029,1909],{},[1765,38031,38032],{},"0,28125",[1761,38034,1763],{},[1765,38036,1767],{},[902,38038,38039],{"encoding":904},"D(4, 1, 1) = 0{,}28125 > 0"," — v bodě ",[883,38042,38044],{"className":38043},[886],[888,38045,38046],{"xmlns":890},[892,38047,38048,38060],{},[895,38049,38050,38052,38054,38056,38058],{},[1761,38051,1822],{"stretchy":1821},[1765,38053,2318],{},[1761,38055,1834],{"separator":1833},[1765,38057,1945],{},[1761,38059,1844],{"stretchy":1821},[902,38061,38062],{"encoding":904},"[4, 1]"," je vázané ",[38,38065,7839],{},[115,38067,38069],{"id":38068},"poptávka-minimalizující-výdaje-hicksova","Poptávka minimalizující výdaje (Hicksova)",[724,38071,38072],{},"Obecně:",[883,38074,38076],{"className":38075},[886],[888,38077,38078],{"xmlns":890,"display":1930},[892,38079,38080,38175],{},[24787,38081,38082],{"width":32101},[24792,38083,38084,38086,38168,38170],{},[24795,38085],{"width":32106},[24795,38087,38088],{},[895,38089,38090,38096,38098,38104,38106,38112,38114,38120,38122,38124,38126,38128,38130,38136,38138,38144,38146,38152,38154,38160,38162,38164,38166],{},[1681,38091,38092,38094],{},[898,38093,1828],{},[1765,38095,1945],{},[1761,38097,1909],{},[1681,38099,38100,38102],{},[898,38101,2244],{},[1765,38103,1945],{},[1761,38105,1915],{"stretchy":1821},[1681,38107,38108,38110],{},[898,38109,1839],{},[1765,38111,1945],{},[1761,38113,1834],{"separator":1833},[1681,38115,38116,38118],{},[898,38117,1839],{},[1765,38119,2296],{},[1761,38121,1834],{"separator":1833},[898,38123,900],{},[1761,38125,1920],{"stretchy":1821},[1761,38127,1834],{"separator":1833},[3315,38129],{"width":19322},[1681,38131,38132,38134],{},[898,38133,1828],{},[1765,38135,2296],{},[1761,38137,1909],{},[1681,38139,38140,38142],{},[898,38141,2244],{},[1765,38143,2296],{},[1761,38145,1915],{"stretchy":1821},[1681,38147,38148,38150],{},[898,38149,1839],{},[1765,38151,1945],{},[1761,38153,1834],{"separator":1833},[1681,38155,38156,38158],{},[898,38157,1839],{},[1765,38159,2296],{},[1761,38161,1834],{"separator":1833},[898,38163,900],{},[1761,38165,1920],{"stretchy":1821},[1761,38167,1834],{"separator":1833},[24795,38169],{"width":32106},[24795,38171,38172],{},[2761,38173,38174],{},"(6.27)",[902,38176,38177],{"encoding":904},"Q_1 = D_1(P_1, P_2, U), \\quad Q_2 = D_2(P_1, P_2, U), \\tag{6.27}",[883,38179,38181],{"className":38180},[886],[888,38182,38183],{"xmlns":890,"display":1930},[892,38184,38185,38232],{},[24787,38186,38187],{"width":32101},[24792,38188,38189,38191,38225,38227],{},[24795,38190],{"width":32106},[24795,38192,38193],{},[895,38194,38195,38197,38199,38201,38203,38209,38211,38217,38219,38221,38223],{},[898,38196,20477],{},[1761,38198,1909],{},[898,38200,20477],{},[1761,38202,1915],{"stretchy":1821},[1681,38204,38205,38207],{},[898,38206,1839],{},[1765,38208,1945],{},[1761,38210,1834],{"separator":1833},[1681,38212,38213,38215],{},[898,38214,1839],{},[1765,38216,2296],{},[1761,38218,1834],{"separator":1833},[898,38220,900],{},[1761,38222,1920],{"stretchy":1821},[898,38224,1741],{"mathvariant":1969},[24795,38226],{"width":32106},[24795,38228,38229],{},[2761,38230,38231],{},"(6.28)",[902,38233,38234],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, U). \\tag{6.28}",[724,38236,38237,38238,1989,38241,38254,38255,38268],{},"Hicksova poptávka závisí na ",[38,38239,38240],{},"hladině užitečnosti",[883,38242,38244],{"className":38243},[886],[888,38245,38246],{"xmlns":890},[892,38247,38248,38252],{},[895,38249,38250],{},[898,38251,900],{},[902,38253,900],{"encoding":904}," (nikoli na důchodu ",[883,38256,38258],{"className":38257},[886],[888,38259,38260],{"xmlns":890},[892,38261,38262,38266],{},[895,38263,38264],{},[898,38265,13170],{},[902,38267,13170],{"encoding":904}," jako u Marshallovy). Fyzická interpretace: jaké množství zboží koupit při daných cenách, abych dosáhl předem stanovené úrovně uspokojení s minimálními výdaji.",[115,38270,38272,38273],{"id":38271},"příklad-68-obecné-odvození-pro-uq112q212u-q_112-q_212","Příklad 6.8 — obecné odvození pro ",[883,38274,38276],{"className":38275},[886],[888,38277,38278],{"xmlns":890},[892,38279,38280,38314],{},[895,38281,38282,38284,38286,38300],{},[898,38283,900],{},[1761,38285,1909],{},[2015,38287,38288,38290,38292],{},[898,38289,1828],{},[1765,38291,1945],{},[895,38293,38294,38296,38298],{},[1765,38295,1945],{},[898,38297,8726],{"mathvariant":1969},[1765,38299,2296],{},[2015,38301,38302,38304,38306],{},[898,38303,1828],{},[1765,38305,2296],{},[895,38307,38308,38310,38312],{},[1765,38309,1945],{},[898,38311,8726],{"mathvariant":1969},[1765,38313,2296],{},[902,38315,37189],{"encoding":904},[724,38317,38318,38348],{},[883,38319,38321],{"className":38320},[886],[888,38322,38323],{"xmlns":890},[892,38324,38325,38345],{},[895,38326,38327,38333,38335,38341,38343],{},[1681,38328,38329,38331],{},[898,38330,1839],{},[1765,38332,1945],{},[1761,38334,1834],{"separator":1833},[1681,38336,38337,38339],{},[898,38338,1839],{},[1765,38340,2296],{},[1761,38342,1834],{"separator":1833},[898,38344,900],{},[902,38346,38347],{"encoding":904},"P_1, P_2, U"," jsou parametry. Lagrangeova funkce:",[883,38350,38352],{"className":38351},[886],[888,38353,38354],{"xmlns":890,"display":1930},[892,38355,38356,38430],{},[895,38357,38358,38360,38362,38368,38374,38376,38382,38388,38390,38392,38394,38396,38398,38412,38426,38428],{},[898,38359,13835],{"mathvariant":32578},[1761,38361,1909],{},[1681,38363,38364,38366],{},[898,38365,1839],{},[1765,38367,1945],{},[1681,38369,38370,38372],{},[898,38371,1828],{},[1765,38373,1945],{},[1761,38375,1964],{},[1681,38377,38378,38380],{},[898,38379,1839],{},[1765,38381,2296],{},[1681,38383,38384,38386],{},[898,38385,1828],{},[1765,38387,2296],{},[1761,38389,1964],{},[898,38391,20477],{},[1761,38393,1915],{"stretchy":1821},[898,38395,900],{},[1761,38397,1885],{},[2015,38399,38400,38402,38404],{},[898,38401,1828],{},[1765,38403,1945],{},[895,38405,38406,38408,38410],{},[1765,38407,1945],{},[898,38409,8726],{"mathvariant":1969},[1765,38411,2296],{},[2015,38413,38414,38416,38418],{},[898,38415,1828],{},[1765,38417,2296],{},[895,38419,38420,38422,38424],{},[1765,38421,1945],{},[898,38423,8726],{"mathvariant":1969},[1765,38425,2296],{},[1761,38427,1920],{"stretchy":1821},[898,38429,1741],{"mathvariant":1969},[902,38431,38432],{"encoding":904},"\\mathcal{L} = P_1 Q_1 + P_2 Q_2 + \\lambda(U - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,38434,34461],{},[883,38436,38438],{"className":38437},[886],[888,38439,38440],{"xmlns":890,"display":1930},[892,38441,38442,38664],{},[24787,38443,38444,38524,38604],{"rowspacing":24789,"columnalign":24790,"columnspacing":6458},[24792,38445,38446,38458],{},[24795,38447,38448],{},[6411,38449,38450],{"scriptlevel":1767,"displaystyle":1833},[2015,38451,38452,38454,38456],{},[898,38453,13835],{"mathvariant":32578},[1765,38455,1945],{},[1761,38457,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[24795,38459,38460],{},[6411,38461,38462],{"scriptlevel":1767,"displaystyle":1833},[895,38463,38464,38466,38468,38474,38476,38478,38480,38488,38504,38518,38520,38522],{},[895,38465],{},[1761,38467,1909],{},[1681,38469,38470,38472],{},[898,38471,1839],{},[1765,38473,1945],{},[1761,38475,1885],{},[898,38477,20477],{},[1761,38479,2447],{},[6411,38481,38482],{"scriptlevel":1767,"displaystyle":1821},[4379,38483,38484,38486],{},[1765,38485,1945],{},[1765,38487,2296],{},[2015,38489,38490,38492,38494],{},[898,38491,1828],{},[1765,38493,1945],{},[895,38495,38496,38498,38500,38502],{},[1761,38497,1885],{},[1765,38499,1945],{},[898,38501,8726],{"mathvariant":1969},[1765,38503,2296],{},[2015,38505,38506,38508,38510],{},[898,38507,1828],{},[1765,38509,2296],{},[895,38511,38512,38514,38516],{},[1765,38513,1945],{},[898,38515,8726],{"mathvariant":1969},[1765,38517,2296],{},[1761,38519,1909],{},[1765,38521,1767],{},[1761,38523,1834],{"separator":1833},[24792,38525,38526,38538],{},[24795,38527,38528],{},[6411,38529,38530],{"scriptlevel":1767,"displaystyle":1833},[2015,38531,38532,38534,38536],{},[898,38533,13835],{"mathvariant":32578},[1765,38535,2296],{},[1761,38537,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[24795,38539,38540],{},[6411,38541,38542],{"scriptlevel":1767,"displaystyle":1833},[895,38543,38544,38546,38548,38554,38556,38558,38560,38568,38582,38598,38600,38602],{},[895,38545],{},[1761,38547,1909],{},[1681,38549,38550,38552],{},[898,38551,1839],{},[1765,38553,2296],{},[1761,38555,1885],{},[898,38557,20477],{},[1761,38559,2447],{},[6411,38561,38562],{"scriptlevel":1767,"displaystyle":1821},[4379,38563,38564,38566],{},[1765,38565,1945],{},[1765,38567,2296],{},[2015,38569,38570,38572,38574],{},[898,38571,1828],{},[1765,38573,1945],{},[895,38575,38576,38578,38580],{},[1765,38577,1945],{},[898,38579,8726],{"mathvariant":1969},[1765,38581,2296],{},[2015,38583,38584,38586,38588],{},[898,38585,1828],{},[1765,38587,2296],{},[895,38589,38590,38592,38594,38596],{},[1761,38591,1885],{},[1765,38593,1945],{},[898,38595,8726],{"mathvariant":1969},[1765,38597,2296],{},[1761,38599,1909],{},[1765,38601,1767],{},[1761,38603,1834],{"separator":1833},[24792,38605,38606,38618],{},[24795,38607,38608],{},[6411,38609,38610],{"scriptlevel":1767,"displaystyle":1833},[2015,38611,38612,38614,38616],{},[898,38613,13835],{"mathvariant":32578},[898,38615,20477],{},[1761,38617,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[24795,38619,38620],{},[6411,38621,38622],{"scriptlevel":1767,"displaystyle":1833},[895,38623,38624,38626,38628,38630,38632,38646,38660,38662],{},[895,38625],{},[1761,38627,1909],{},[898,38629,900],{},[1761,38631,1885],{},[2015,38633,38634,38636,38638],{},[898,38635,1828],{},[1765,38637,1945],{},[895,38639,38640,38642,38644],{},[1765,38641,1945],{},[898,38643,8726],{"mathvariant":1969},[1765,38645,2296],{},[2015,38647,38648,38650,38652],{},[898,38649,1828],{},[1765,38651,2296],{},[895,38653,38654,38656,38658],{},[1765,38655,1945],{},[898,38657,8726],{"mathvariant":1969},[1765,38659,2296],{},[1761,38661,1909],{},[1765,38663,16498],{},[902,38665,38666],{"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}",[724,38668,38669,38670,38740,38741,38799],{},"Podílem rovnic: ",[883,38671,38673],{"className":38672},[886],[888,38674,38675],{"xmlns":890},[892,38676,38677,38737],{},[895,38678,38679,38685,38687,38693,38695,38701,38703,38709,38711,38717,38723,38725,38731],{},[1681,38680,38681,38683],{},[898,38682,1839],{},[1765,38684,1945],{},[898,38686,8726],{"mathvariant":1969},[1681,38688,38689,38691],{},[898,38690,1839],{},[1765,38692,2296],{},[1761,38694,1909],{},[1681,38696,38697,38699],{},[898,38698,1828],{},[1765,38700,2296],{},[898,38702,8726],{"mathvariant":1969},[1681,38704,38705,38707],{},[898,38706,1828],{},[1765,38708,1945],{},[1761,38710,8044],{},[1681,38712,38713,38715],{},[898,38714,1839],{},[1765,38716,1945],{},[1681,38718,38719,38721],{},[898,38720,1828],{},[1765,38722,1945],{},[1761,38724,1909],{},[1681,38726,38727,38729],{},[898,38728,1839],{},[1765,38730,2296],{},[1681,38732,38733,38735],{},[898,38734,1828],{},[1765,38736,2296],{},[902,38738,38739],{"encoding":904},"P_1\u002FP_2 = Q_2\u002FQ_1 \\Rightarrow P_1 Q_1 = P_2 Q_2",", tedy celkové výdaje ",[883,38742,38744],{"className":38743},[886],[888,38745,38746],{"xmlns":890},[892,38747,38748,38796],{},[895,38749,38750,38752,38754,38760,38766,38768,38774,38780,38782,38784,38790],{},[898,38751,1818],{},[1761,38753,1909],{},[1681,38755,38756,38758],{},[898,38757,1839],{},[1765,38759,1945],{},[1681,38761,38762,38764],{},[898,38763,1828],{},[1765,38765,1945],{},[1761,38767,1964],{},[1681,38769,38770,38772],{},[898,38771,1839],{},[1765,38773,2296],{},[1681,38775,38776,38778],{},[898,38777,1828],{},[1765,38779,2296],{},[1761,38781,1909],{},[1765,38783,2296],{},[1681,38785,38786,38788],{},[898,38787,1839],{},[1765,38789,1945],{},[1681,38791,38792,38794],{},[898,38793,1828],{},[1765,38795,1945],{},[902,38797,38798],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2 = 2 P_1 Q_1",". Odtud",[883,38801,38803],{"className":38802},[886],[888,38804,38805],{"xmlns":890,"display":1930},[892,38806,38807,38874],{},[24787,38808,38809],{"width":32101},[24792,38810,38811,38813,38867,38869],{},[24795,38812],{"width":32106},[24795,38814,38815],{},[895,38816,38817,38823,38825,38839,38841,38843,38849,38851,38865],{},[1681,38818,38819,38821],{},[898,38820,1828],{},[1765,38822,1945],{},[1761,38824,1909],{},[4379,38826,38827,38829],{},[898,38828,1818],{},[895,38830,38831,38833],{},[1765,38832,2296],{},[1681,38834,38835,38837],{},[898,38836,1839],{},[1765,38838,1945],{},[1761,38840,1834],{"separator":1833},[3315,38842],{"width":19322},[1681,38844,38845,38847],{},[898,38846,1828],{},[1765,38848,2296],{},[1761,38850,1909],{},[4379,38852,38853,38855],{},[898,38854,1818],{},[895,38856,38857,38859],{},[1765,38858,2296],{},[1681,38860,38861,38863],{},[898,38862,1839],{},[1765,38864,2296],{},[898,38866,1741],{"mathvariant":1969},[24795,38868],{"width":32106},[24795,38870,38871],{},[2761,38872,38873],{},"(6.29)",[902,38875,38876],{"encoding":904},"Q_1 = \\frac{E}{2 P_1}, \\quad Q_2 = \\frac{E}{2 P_2}. \\tag{6.29}",[724,38878,38879,38880,21610,38962,38998],{},"Ze třetí rovnice ",[883,38881,38883],{"className":38882},[886],[888,38884,38885],{"xmlns":890},[892,38886,38887,38959],{},[895,38888,38889,38891,38893,38931,38933],{},[898,38890,900],{},[1761,38892,1909],{},[12161,38894,38895],{},[895,38896,38897,38913,38915],{},[6411,38898,38899],{"scriptlevel":1767,"displaystyle":1821},[4379,38900,38901,38903],{},[898,38902,1818],{},[895,38904,38905,38907],{},[1765,38906,2296],{},[1681,38908,38909,38911],{},[898,38910,1839],{},[1765,38912,1945],{},[1761,38914,2447],{},[6411,38916,38917],{"scriptlevel":1767,"displaystyle":1821},[4379,38918,38919,38921],{},[898,38920,1818],{},[895,38922,38923,38925],{},[1765,38924,2296],{},[1681,38926,38927,38929],{},[898,38928,1839],{},[1765,38930,2296],{},[1761,38932,1909],{},[6411,38934,38935],{"scriptlevel":1767,"displaystyle":1821},[4379,38936,38937,38939],{},[898,38938,1818],{},[895,38940,38941,38943],{},[1765,38942,2296],{},[12161,38944,38945],{},[895,38946,38947,38953],{},[1681,38948,38949,38951],{},[898,38950,1839],{},[1765,38952,1945],{},[1681,38954,38955,38957],{},[898,38956,1839],{},[1765,38958,2296],{},[902,38960,38961],{"encoding":904},"U = \\sqrt{\\tfrac{E}{2 P_1} \\cdot \\tfrac{E}{2 P_2}} = \\tfrac{E}{2\\sqrt{P_1 P_2}}",[883,38963,38965],{"className":38964},[886],[888,38966,38967],{"xmlns":890},[892,38968,38969,38995],{},[895,38970,38971,38973,38975,38977,38979],{},[898,38972,1818],{},[1761,38974,1909],{},[1765,38976,2296],{},[898,38978,900],{},[12161,38980,38981],{},[895,38982,38983,38989],{},[1681,38984,38985,38987],{},[898,38986,1839],{},[1765,38988,1945],{},[1681,38990,38991,38993],{},[898,38992,1839],{},[1765,38994,2296],{},[902,38996,38997],{"encoding":904},"E = 2 U \\sqrt{P_1 P_2}",". Dosazením:",[883,39000,39002],{"className":39001},[886],[888,39003,39004],{"xmlns":890,"display":1930},[892,39005,39006,39151],{},[24787,39007,39008],{"width":32101},[24792,39009,39010,39012,39144,39146],{},[24795,39011],{"width":32106},[24795,39013,39014],{},[16870,39015,39016],{"notation":16872},[6411,39017,39018],{"scriptlevel":1767,"displaystyle":1821},[6411,39019,39020],{"scriptlevel":1767,"displaystyle":1821},[6411,39021,39022],{"scriptlevel":1767,"displaystyle":1833},[895,39023,39024,39026,39032,39034,39036,39052,39054,39060,39062,39068,39070,39076,39078,39080,39082,39084,39086,39092,39094,39096,39112,39114,39120,39122,39128,39130,39136,39138,39140,39142],{},[2761,39025,8041],{},[1681,39027,39028,39030],{},[898,39029,1828],{},[1765,39031,1945],{},[1761,39033,1909],{},[898,39035,900],{},[12161,39037,39038],{},[4379,39039,39040,39046],{},[1681,39041,39042,39044],{},[898,39043,1839],{},[1765,39045,2296],{},[1681,39047,39048,39050],{},[898,39049,1839],{},[1765,39051,1945],{},[1761,39053,1909],{},[1681,39055,39056,39058],{},[898,39057,2244],{},[1765,39059,1945],{},[1761,39061,1915],{"stretchy":1821},[1681,39063,39064,39066],{},[898,39065,1839],{},[1765,39067,1945],{},[1761,39069,1834],{"separator":1833},[1681,39071,39072,39074],{},[898,39073,1839],{},[1765,39075,2296],{},[1761,39077,1834],{"separator":1833},[898,39079,900],{},[1761,39081,1920],{"stretchy":1821},[1761,39083,1834],{"separator":1833},[3315,39085],{"width":19322},[1681,39087,39088,39090],{},[898,39089,1828],{},[1765,39091,2296],{},[1761,39093,1909],{},[898,39095,900],{},[12161,39097,39098],{},[4379,39099,39100,39106],{},[1681,39101,39102,39104],{},[898,39103,1839],{},[1765,39105,1945],{},[1681,39107,39108,39110],{},[898,39109,1839],{},[1765,39111,2296],{},[1761,39113,1909],{},[1681,39115,39116,39118],{},[898,39117,2244],{},[1765,39119,2296],{},[1761,39121,1915],{"stretchy":1821},[1681,39123,39124,39126],{},[898,39125,1839],{},[1765,39127,1945],{},[1761,39129,1834],{"separator":1833},[1681,39131,39132,39134],{},[898,39133,1839],{},[1765,39135,2296],{},[1761,39137,1834],{"separator":1833},[898,39139,900],{},[1761,39141,1920],{"stretchy":1821},[2761,39143,8041],{},[24795,39145],{"width":32106},[24795,39147,39148],{},[2761,39149,39150],{},"(6.30)",[902,39152,39153],{"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}",[115,39155,39157],{"id":39156},"vztah-primární-a-duální-úlohy","Vztah primární a duální úlohy",[724,39159,39160,39161,39174,39175,39192,39193,39206,39207,39224,39225,39227,39228,39267,39268,39297],{},"Primární (max ",[883,39162,39164],{"className":39163},[886],[888,39165,39166],{"xmlns":890},[892,39167,39168,39172],{},[895,39169,39170],{},[898,39171,900],{},[902,39173,900],{"encoding":904}," při rozpočtu ",[883,39176,39178],{"className":39177},[886],[888,39179,39180],{"xmlns":890},[892,39181,39182,39190],{},[895,39183,39184],{},[1824,39185,39186,39188],{},[898,39187,13170],{},[1761,39189,8408],{},[902,39191,32059],{"encoding":904},") a duální (min ",[883,39194,39196],{"className":39195},[886],[888,39197,39198],{"xmlns":890},[892,39199,39200,39204],{},[895,39201,39202],{},[898,39203,1818],{},[902,39205,1818],{"encoding":904}," při užitečnosti ",[883,39208,39210],{"className":39209},[886],[888,39211,39212],{"xmlns":890},[892,39213,39214,39222],{},[895,39215,39216],{},[1824,39217,39218,39220],{},[898,39219,900],{},[1761,39221,8408],{},[902,39223,31993],{"encoding":904},") úloha jsou ",[38,39226,5329],{},": mají tentýž bod optima ",[883,39229,39231],{"className":39230},[886],[888,39232,39233],{"xmlns":890},[892,39234,39235,39265],{},[895,39236,39237,39243,39245,39253,39255,39263],{},[1824,39238,39239,39241],{},[898,39240,1828],{},[1761,39242,8408],{},[1761,39244,1822],{"stretchy":1821},[2015,39246,39247,39249,39251],{},[898,39248,1828],{},[1765,39250,1945],{},[1761,39252,8408],{},[1761,39254,1834],{"separator":1833},[2015,39256,39257,39259,39261],{},[898,39258,1828],{},[1765,39260,2296],{},[1761,39262,8408],{},[1761,39264,1844],{"stretchy":1821},[902,39266,32357],{"encoding":904}," a v obou platí ",[883,39269,39271],{"className":39270},[886],[888,39272,39273],{"xmlns":890},[892,39274,39275,39295],{},[895,39276,39277,39279,39281,39287,39289],{},[2761,39278,14641],{},[1761,39280,1909],{},[1681,39282,39283,39285],{},[898,39284,1839],{},[1765,39286,1945],{},[898,39288,8726],{"mathvariant":1969},[1681,39290,39291,39293],{},[898,39292,1839],{},[1765,39294,2296],{},[902,39296,32029],{"encoding":904},". Rozdíl je v tom, která veličina je zadána a která se optimalizuje:",[724,39299,39300],{},[3991,39301],{"alt":39302,"className":39303,"src":39304},"imek-primarni-vs-dualni",[210,3995],"\u002Fwiki-assets\u002Fimek-primarni-vs-dualni.jpeg",[120,39306,39307,39418],{},[123,39308,39309,39312,39313,39326,39327,39367,39368,1741],{},[38,39310,39311],{},"Primární"," (Marshall): zadáno ",[883,39314,39316],{"className":39315},[886],[888,39317,39318],{"xmlns":890},[892,39319,39320,39324],{},[895,39321,39322],{},[898,39323,13170],{},[902,39325,13170],{"encoding":904},", hledáme maximální ",[883,39328,39330],{"className":39329},[886],[888,39331,39332],{"xmlns":890},[892,39333,39334,39364],{},[895,39335,39336,39342,39344,39350,39352,39358,39360,39362],{},[1824,39337,39338,39340],{},[898,39339,900],{},[1761,39341,8408],{},[1761,39343,1915],{"stretchy":1821},[1681,39345,39346,39348],{},[898,39347,1839],{},[1765,39349,1945],{},[1761,39351,1834],{"separator":1833},[1681,39353,39354,39356],{},[898,39355,1839],{},[1765,39357,2296],{},[1761,39359,1834],{"separator":1833},[898,39361,13170],{},[1761,39363,1920],{"stretchy":1821},[902,39365,39366],{"encoding":904},"U^*(P_1, P_2, Y)"," a poptávku ",[883,39369,39371],{"className":39370},[886],[888,39372,39373],{"xmlns":890},[892,39374,39375,39415],{},[895,39376,39377,39383,39385,39393,39395,39401,39403,39409,39411,39413],{},[1681,39378,39379,39381],{},[898,39380,1828],{},[898,39382,21824],{},[1761,39384,1909],{},[2015,39386,39387,39389,39391],{},[898,39388,2244],{},[898,39390,21824],{},[898,39392,6889],{},[1761,39394,1915],{"stretchy":1821},[1681,39396,39397,39399],{},[898,39398,1839],{},[1765,39400,1945],{},[1761,39402,1834],{"separator":1833},[1681,39404,39405,39407],{},[898,39406,1839],{},[1765,39408,2296],{},[1761,39410,1834],{"separator":1833},[898,39412,13170],{},[1761,39414,1920],{"stretchy":1821},[902,39416,39417],{"encoding":904},"Q_i = D_i^M(P_1, P_2, Y)",[123,39419,39420,39423,39424,39437,39438,39367,39478,1741],{},[38,39421,39422],{},"Duální"," (Hicks): zadáno ",[883,39425,39427],{"className":39426},[886],[888,39428,39429],{"xmlns":890},[892,39430,39431,39435],{},[895,39432,39433],{},[898,39434,900],{},[902,39436,900],{"encoding":904},", hledáme minimální ",[883,39439,39441],{"className":39440},[886],[888,39442,39443],{"xmlns":890},[892,39444,39445,39475],{},[895,39446,39447,39453,39455,39461,39463,39469,39471,39473],{},[1824,39448,39449,39451],{},[898,39450,1818],{},[1761,39452,8408],{},[1761,39454,1915],{"stretchy":1821},[1681,39456,39457,39459],{},[898,39458,1839],{},[1765,39460,1945],{},[1761,39462,1834],{"separator":1833},[1681,39464,39465,39467],{},[898,39466,1839],{},[1765,39468,2296],{},[1761,39470,1834],{"separator":1833},[898,39472,900],{},[1761,39474,1920],{"stretchy":1821},[902,39476,39477],{"encoding":904},"E^*(P_1, P_2, U)",[883,39479,39481],{"className":39480},[886],[888,39482,39483],{"xmlns":890},[892,39484,39485,39526],{},[895,39486,39487,39493,39495,39504,39506,39512,39514,39520,39522,39524],{},[1681,39488,39489,39491],{},[898,39490,1828],{},[898,39492,21824],{},[1761,39494,1909],{},[2015,39496,39497,39499,39501],{},[898,39498,2244],{},[898,39500,21824],{},[898,39502,39503],{},"H",[1761,39505,1915],{"stretchy":1821},[1681,39507,39508,39510],{},[898,39509,1839],{},[1765,39511,1945],{},[1761,39513,1834],{"separator":1833},[1681,39515,39516,39518],{},[898,39517,1839],{},[1765,39519,2296],{},[1761,39521,1834],{"separator":1833},[898,39523,900],{},[1761,39525,1920],{"stretchy":1821},[902,39527,39528],{"encoding":904},"Q_i = D_i^H(P_1, P_2, U)",[724,39530,39531,39532,39535,39536,39539],{},"Proč se studují obě? Marshallova poptávka je ",[38,39533,39534],{},"pozorovatelná"," (lze odhadnout z dat o spotřebě a důchodech), zatímco Hicksova umožňuje čistě oddělit ",[38,39537,39538],{},"substituční efekt"," změny ceny od efektu důchodového — je klíčová pro teorii blahobytu a cenové indexy.",[115,39541,39543],{"id":39542},"úlohy-k-optimalizaci","Úlohy k optimalizaci",[198,39545,39547],{"id":39546},"maximalizace-užitečnosti-a-marshallova-poptávka","Maximalizace užitečnosti a Marshallova poptávka",[724,39549,39550,39553,39554,39586,39587,39625,39626,39652],{},[38,39551,39552],{},"6.8"," Jsou dány užitečnost ",[883,39555,39557],{"className":39556},[886],[888,39558,39559],{"xmlns":890},[892,39560,39561,39583],{},[895,39562,39563,39565,39567,39575],{},[898,39564,900],{},[1761,39566,1909],{},[2015,39568,39569,39571,39573],{},[898,39570,1828],{},[1765,39572,1945],{},[1765,39574,5426],{},[2015,39576,39577,39579,39581],{},[898,39578,1828],{},[1765,39580,2296],{},[1765,39582,5426],{},[902,39584,39585],{"encoding":904},"U = Q_1^{0{,}5} Q_2^{0{,}5}",", ceny ",[883,39588,39590],{"className":39589},[886],[888,39591,39592],{"xmlns":890},[892,39593,39594,39622],{},[895,39595,39596,39604,39606,39608,39610,39618,39620],{},[2015,39597,39598,39600,39602],{},[898,39599,1839],{},[1765,39601,1945],{},[1761,39603,8408],{},[1761,39605,1909],{},[1765,39607,2318],{},[1761,39609,1834],{"separator":1833},[2015,39611,39612,39614,39616],{},[898,39613,1839],{},[1765,39615,2296],{},[1761,39617,8408],{},[1761,39619,1909],{},[1765,39621,2633],{},[902,39623,39624],{"encoding":904},"P_1^* = 4, P_2^* = 10"," za jednotku zboží a důchod spotřebitele 200. Určete množství ",[883,39627,39629],{"className":39628},[886],[888,39630,39631],{"xmlns":890},[892,39632,39633,39649],{},[895,39634,39635,39641,39643],{},[1681,39636,39637,39639],{},[898,39638,1828],{},[1765,39640,1945],{},[1761,39642,1834],{"separator":1833},[1681,39644,39645,39647],{},[898,39646,1828],{},[1765,39648,2296],{},[902,39650,39651],{"encoding":904},"Q_1, Q_2"," maximalizující užitečnost.",[724,39654,39655,39658,39659,39701,39702,39733,39734,39756,39757,1741],{},[38,39656,39657],{},"6.9"," Jsou dány rozpočtové omezení ",[883,39660,39662],{"className":39661},[886],[888,39663,39664],{"xmlns":890},[892,39665,39666,39698],{},[895,39667,39668,39670,39672,39678,39684,39686,39692],{},[898,39669,13170],{},[1761,39671,1909],{},[1681,39673,39674,39676],{},[898,39675,1839],{},[1765,39677,1945],{},[1681,39679,39680,39682],{},[898,39681,1828],{},[1765,39683,1945],{},[1761,39685,1964],{},[1681,39687,39688,39690],{},[898,39689,1839],{},[1765,39691,2296],{},[1681,39693,39694,39696],{},[898,39695,1828],{},[1765,39697,2296],{},[902,39699,39700],{"encoding":904},"Y = P_1 Q_1 + P_2 Q_2"," a užitečnost ",[883,39703,39705],{"className":39704},[886],[888,39706,39707],{"xmlns":890},[892,39708,39709,39731],{},[895,39710,39711,39713,39715,39723],{},[898,39712,900],{},[1761,39714,1909],{},[2015,39716,39717,39719,39721],{},[898,39718,1828],{},[1765,39720,1945],{},[1765,39722,5426],{},[2015,39724,39725,39727,39729],{},[898,39726,1828],{},[1765,39728,2296],{},[1765,39730,5426],{},[902,39732,39585],{"encoding":904},". (a) Odvoďte funkce poptávky maximalizující užitečnost. (b) Najděte funkce poptávky pro důchod ",[883,39735,39737],{"className":39736},[886],[888,39738,39739],{"xmlns":890},[892,39740,39741,39753],{},[895,39742,39743,39749,39751],{},[1824,39744,39745,39747],{},[898,39746,13170],{},[1761,39748,8408],{},[1761,39750,1909],{},[1765,39752,19148],{},[902,39754,39755],{"encoding":904},"Y^* = 500",". (c) Najděte Engelovy funkce pro ceny ",[883,39758,39760],{"className":39759},[886],[888,39761,39762],{"xmlns":890},[892,39763,39764,39792],{},[895,39765,39766,39774,39776,39778,39780,39788,39790],{},[2015,39767,39768,39770,39772],{},[898,39769,1839],{},[1765,39771,1945],{},[1761,39773,8408],{},[1761,39775,1909],{},[1765,39777,6321],{},[1761,39779,1834],{"separator":1833},[2015,39781,39782,39784,39786],{},[898,39783,1839],{},[1765,39785,2296],{},[1761,39787,8408],{},[1761,39789,1909],{},[1765,39791,2633],{},[902,39793,39794],{"encoding":904},"P_1^* = 5, P_2^* = 10",[724,39796,39797,39800,39801,25627,39833,39863,39864,1741],{},[38,39798,39799],{},"6.10"," Odvoďte funkce poptávky pro Cobb-Douglasovy funkce užitečnosti ",[883,39802,39804],{"className":39803},[886],[888,39805,39806],{"xmlns":890},[892,39807,39808,39830],{},[895,39809,39810,39812,39814,39822],{},[898,39811,900],{},[1761,39813,1909],{},[2015,39815,39816,39818,39820],{},[898,39817,1828],{},[1765,39819,1945],{},[898,39821,207],{},[2015,39823,39824,39826,39828],{},[898,39825,1828],{},[1765,39827,2296],{},[898,39829,4302],{},[902,39831,39832],{"encoding":904},"U = Q_1^a Q_2^b",[883,39834,39836],{"className":39835},[886],[888,39837,39838],{"xmlns":890},[892,39839,39840,39860],{},[895,39841,39842,39844,39846,39848,39850,39852,39854,39856,39858],{},[898,39843,207],{},[1761,39845,1834],{"separator":1833},[898,39847,4302],{},[1761,39849,10551],{},[1761,39851,9375],{"stretchy":1821},[1765,39853,1767],{},[1761,39855,1834],{"separator":1833},[1765,39857,1945],{},[1761,39859,9392],{"stretchy":1821},[902,39861,39862],{"encoding":904},"a, b \\in \\langle 0, 1 \\rangle"," a rozpočtové omezení ",[883,39865,39867],{"className":39866},[886],[888,39868,39869],{"xmlns":890},[892,39870,39871,39903],{},[895,39872,39873,39875,39877,39883,39889,39891,39897],{},[898,39874,13170],{},[1761,39876,1909],{},[1681,39878,39879,39881],{},[898,39880,1839],{},[1765,39882,1945],{},[1681,39884,39885,39887],{},[898,39886,1828],{},[1765,39888,1945],{},[1761,39890,1964],{},[1681,39892,39893,39895],{},[898,39894,1839],{},[1765,39896,2296],{},[1681,39898,39899,39901],{},[898,39900,1828],{},[1765,39902,2296],{},[902,39904,39700],{"encoding":904},[724,39906,39907,39910,39911,25627,39945,39863,39963,1741],{},[38,39908,39909],{},"6.11"," Odvoďte funkce poptávky pro funkce užitečnosti CES typu ",[883,39912,39914],{"className":39913},[886],[888,39915,39916],{"xmlns":890},[892,39917,39918,39942],{},[895,39919,39920,39922,39924,39932,39934],{},[898,39921,900],{},[1761,39923,1909],{},[2015,39925,39926,39928,39930],{},[898,39927,1828],{},[1765,39929,1945],{},[898,39931,207],{},[1761,39933,1964],{},[2015,39935,39936,39938,39940],{},[898,39937,1828],{},[1765,39939,2296],{},[898,39941,207],{},[902,39943,39944],{"encoding":904},"U = Q_1^a + Q_2^a",[883,39946,39948],{"className":39947},[886],[888,39949,39950],{"xmlns":890},[892,39951,39952,39960],{},[895,39953,39954,39956,39958],{},[898,39955,207],{},[1761,39957,7438],{"mathvariant":1969},[1765,39959,1767],{},[902,39961,39962],{"encoding":904},"a \\neq 0",[883,39964,39966],{"className":39965},[886],[888,39967,39968],{"xmlns":890},[892,39969,39970,40002],{},[895,39971,39972,39974,39976,39982,39988,39990,39996],{},[898,39973,13170],{},[1761,39975,1909],{},[1681,39977,39978,39980],{},[898,39979,1839],{},[1765,39981,1945],{},[1681,39983,39984,39986],{},[898,39985,1828],{},[1765,39987,1945],{},[1761,39989,1964],{},[1681,39991,39992,39994],{},[898,39993,1839],{},[1765,39995,2296],{},[1681,39997,39998,40000],{},[898,39999,1828],{},[1765,40001,2296],{},[902,40003,39700],{"encoding":904},[198,40005,40007],{"id":40006},"minimalizace-výdajů-a-hicksova-poptávka","Minimalizace výdajů a Hicksova poptávka",[724,40009,40010,39553,40013,1343,40040,40062,40063,1343,40086,40110,40111,40136,40137,1741],{},[38,40011,40012],{},"6.12",[883,40014,40016],{"className":40015},[886],[888,40017,40018],{"xmlns":890},[892,40019,40020,40038],{},[895,40021,40022,40024,40026,40032],{},[898,40023,900],{},[1761,40025,1909],{},[1681,40027,40028,40030],{},[898,40029,1828],{},[1765,40031,1945],{},[1681,40033,40034,40036],{},[898,40035,1828],{},[1765,40037,2296],{},[902,40039,34256],{"encoding":904},[883,40041,40043],{"className":40042},[886],[888,40044,40045],{"xmlns":890},[892,40046,40047,40059],{},[895,40048,40049,40055,40057],{},[1824,40050,40051,40053],{},[898,40052,900],{},[1761,40054,8408],{},[1761,40056,1909],{},[1765,40058,2633],{},[902,40060,40061],{"encoding":904},"U^* = 10"," hladina užitečnosti a ceny ",[883,40064,40066],{"className":40065},[886],[888,40067,40068],{"xmlns":890},[892,40069,40070,40084],{},[895,40071,40072,40080,40082],{},[2015,40073,40074,40076,40078],{},[898,40075,1839],{},[1765,40077,1945],{},[1761,40079,8408],{},[1761,40081,1909],{},[1765,40083,2296],{},[902,40085,34329],{"encoding":904},[883,40087,40089],{"className":40088},[886],[888,40090,40091],{"xmlns":890},[892,40092,40093,40107],{},[895,40094,40095,40103,40105],{},[2015,40096,40097,40099,40101],{},[898,40098,1839],{},[1765,40100,2296],{},[1761,40102,8408],{},[1761,40104,1909],{},[1765,40106,2318],{},[902,40108,40109],{"encoding":904},"P_2^* = 4",". Určete množství ",[883,40112,40114],{"className":40113},[886],[888,40115,40116],{"xmlns":890},[892,40117,40118,40134],{},[895,40119,40120,40126,40128],{},[1681,40121,40122,40124],{},[898,40123,1828],{},[1765,40125,1945],{},[1761,40127,1834],{"separator":1833},[1681,40129,40130,40132],{},[898,40131,1828],{},[1765,40133,2296],{},[902,40135,39651],{"encoding":904}," minimalizující výdaje spotřebitele ",[883,40138,40140],{"className":40139},[886],[888,40141,40142],{"xmlns":890},[892,40143,40144,40164],{},[895,40145,40146,40148,40150,40156,40158],{},[898,40147,900],{},[1761,40149,1909],{},[1681,40151,40152,40154],{},[898,40153,1828],{},[1765,40155,1945],{},[1761,40157,2447],{},[1681,40159,40160,40162],{},[898,40161,1828],{},[1765,40163,2296],{},[902,40165,40166],{"encoding":904},"U = Q_1 \\cdot Q_2",[724,40168,40169,40172,40173,40214,40215,40237,40238,1741],{},[38,40170,40171],{},"6.13"," Jsou dány výdaje spotřebitele ",[883,40174,40176],{"className":40175},[886],[888,40177,40178],{"xmlns":890},[892,40179,40180,40212],{},[895,40181,40182,40184,40186,40192,40198,40200,40206],{},[898,40183,1818],{},[1761,40185,1909],{},[1681,40187,40188,40190],{},[898,40189,1839],{},[1765,40191,1945],{},[1681,40193,40194,40196],{},[898,40195,1828],{},[1765,40197,1945],{},[1761,40199,1964],{},[1681,40201,40202,40204],{},[898,40203,1839],{},[1765,40205,2296],{},[1681,40207,40208,40210],{},[898,40209,1828],{},[1765,40211,2296],{},[902,40213,31974],{"encoding":904}," a užitečnost. (a) Najděte funkce poptávky minimalizující výdaje spotřebitele. (b) Určete funkce poptávky pro užitečnost ",[883,40216,40218],{"className":40217},[886],[888,40219,40220],{"xmlns":890},[892,40221,40222,40234],{},[895,40223,40224,40230,40232],{},[1824,40225,40226,40228],{},[898,40227,900],{},[1761,40229,8408],{},[1761,40231,1909],{},[1765,40233,9056],{},[902,40235,40236],{"encoding":904},"U^* = 25"," a stanovte příslušné výdaje spotřebitele při cenách ",[883,40239,40241],{"className":40240},[886],[888,40242,40243],{"xmlns":890},[892,40244,40245,40273],{},[895,40246,40247,40255,40257,40259,40261,40269,40271],{},[2015,40248,40249,40251,40253],{},[898,40250,1839],{},[1765,40252,1945],{},[1761,40254,8408],{},[1761,40256,1909],{},[1765,40258,13077],{},[1761,40260,1834],{"separator":1833},[2015,40262,40263,40265,40267],{},[898,40264,1839],{},[1765,40266,2296],{},[1761,40268,8408],{},[1761,40270,1909],{},[1765,40272,5433],{},[902,40274,40275],{"encoding":904},"P_1^* = 20, P_2^* = 15",[115,40277,5533],{"id":5532},[120,40279,40280,40337,40376,40396,40431,40485,40490,40496,40592,40637],{},[123,40281,40282,1989,40285,40334,40335,1741],{},[38,40283,40284],{},"Rozpočtové omezení (budget constraint)",[883,40286,40288],{"className":40287},[886],[888,40289,40290],{"xmlns":890},[892,40291,40292,40332],{},[895,40293,40294,40300,40302,40310,40316,40318,40326],{},[1824,40295,40296,40298],{},[898,40297,13170],{},[1761,40299,8408],{},[1761,40301,1909],{},[2015,40303,40304,40306,40308],{},[898,40305,1839],{},[1765,40307,1945],{},[1761,40309,8408],{},[1681,40311,40312,40314],{},[898,40313,1828],{},[1765,40315,1945],{},[1761,40317,1964],{},[2015,40319,40320,40322,40324],{},[898,40321,1839],{},[1765,40323,2296],{},[1761,40325,8408],{},[1681,40327,40328,40330],{},[898,40329,1828],{},[1765,40331,2296],{},[902,40333,21332],{"encoding":904}," — (6.12); ",[38,40336,32166],{},[123,40338,40339,40342,40343,1741],{},[38,40340,40341],{},"Úloha o maximalizaci užitečnosti"," (primární) — Lagrangeova funkce (6.13), soustava (6.14), podmínka optimality ",[883,40344,40346],{"className":40345},[886],[888,40347,40348],{"xmlns":890},[892,40349,40350,40374],{},[895,40351,40352,40354,40356,40364,40366],{},[2761,40353,14641],{},[1761,40355,1909],{},[2015,40357,40358,40360,40362],{},[898,40359,1839],{},[1765,40361,1945],{},[1761,40363,8408],{},[898,40365,8726],{"mathvariant":1969},[2015,40367,40368,40370,40372],{},[898,40369,1839],{},[1765,40371,2296],{},[1761,40373,8408],{},[902,40375,33009],{"encoding":904},[123,40377,40378,40393,40394,1741],{},[38,40379,33153,40380],{},[883,40381,40383],{"className":40382},[886],[888,40384,40385],{"xmlns":890},[892,40386,40387,40391],{},[895,40388,40389],{},[898,40390,20477],{},[902,40392,20530],{"encoding":904}," — stínová cena uvolnění omezení; u maximalizace ",[38,40395,33175],{},[123,40397,40398,40401,40402,1741],{},[38,40399,40400],{},"Podmínka tečnosti"," — sklon indiferenční křivky = sklon rozpočtové přímky; ",[883,40403,40405],{"className":40404},[886],[888,40406,40407],{"xmlns":890},[892,40408,40409,40429],{},[895,40410,40411,40413,40415,40421,40423],{},[2761,40412,14641],{},[1761,40414,1909],{},[1681,40416,40417,40419],{},[898,40418,1839],{},[1765,40420,1945],{},[898,40422,8726],{"mathvariant":1969},[1681,40424,40425,40427],{},[898,40426,1839],{},[1765,40428,2296],{},[902,40430,32029],{"encoding":904},[123,40432,40433,5675,40436,40484],{},[38,40434,40435],{},"Poptávka maximalizující užitečnost (Marshallova)",[883,40437,40439],{"className":40438},[886],[888,40440,40441],{"xmlns":890},[892,40442,40443,40481],{},[895,40444,40445,40451,40453,40459,40461,40467,40469,40475,40477,40479],{},[1681,40446,40447,40449],{},[898,40448,1828],{},[898,40450,21824],{},[1761,40452,1909],{},[1681,40454,40455,40457],{},[898,40456,2244],{},[898,40458,21824],{},[1761,40460,1915],{"stretchy":1821},[1681,40462,40463,40465],{},[898,40464,1839],{},[1765,40466,1945],{},[1761,40468,1834],{"separator":1833},[1681,40470,40471,40473],{},[898,40472,1839],{},[1765,40474,2296],{},[1761,40476,1834],{"separator":1833},[898,40478,13170],{},[1761,40480,1920],{"stretchy":1821},[902,40482,40483],{"encoding":904},"Q_i = D_i(P_1, P_2, Y)"," — (6.15).",[123,40486,40487,40489],{},[38,40488,35757],{}," — poptávka jako funkce důchodu při pevných cenách.",[123,40491,40492,40495],{},[38,40493,40494],{},"Úloha o minimalizaci výdajů"," (duální) — Lagrangeova funkce (6.24), soustava (6.25), postačující podmínka (6.26).",[123,40497,40498,5675,40500,40547,40548,40591],{},[38,40499,38069],{},[883,40501,40503],{"className":40502},[886],[888,40504,40505],{"xmlns":890},[892,40506,40507,40545],{},[895,40508,40509,40515,40517,40523,40525,40531,40533,40539,40541,40543],{},[1681,40510,40511,40513],{},[898,40512,1828],{},[898,40514,21824],{},[1761,40516,1909],{},[1681,40518,40519,40521],{},[898,40520,2244],{},[898,40522,21824],{},[1761,40524,1915],{"stretchy":1821},[1681,40526,40527,40529],{},[898,40528,1839],{},[1765,40530,1945],{},[1761,40532,1834],{"separator":1833},[1681,40534,40535,40537],{},[898,40536,1839],{},[1765,40538,2296],{},[1761,40540,1834],{"separator":1833},[898,40542,900],{},[1761,40544,1920],{"stretchy":1821},[902,40546,21857],{"encoding":904}," — (6.27); obecný výsledek pro ",[883,40549,40551],{"className":40550},[886],[888,40552,40553],{"xmlns":890},[892,40554,40555,40589],{},[895,40556,40557,40559,40561,40575],{},[898,40558,900],{},[1761,40560,1909],{},[2015,40562,40563,40565,40567],{},[898,40564,1828],{},[1765,40566,1945],{},[895,40568,40569,40571,40573],{},[1765,40570,1945],{},[898,40572,8726],{"mathvariant":1969},[1765,40574,2296],{},[2015,40576,40577,40579,40581],{},[898,40578,1828],{},[1765,40580,2296],{},[895,40582,40583,40585,40587],{},[1765,40584,1945],{},[898,40586,8726],{"mathvariant":1969},[1765,40588,2296],{},[902,40590,37189],{"encoding":904},": (6.30).",[123,40593,40594,40636],{},[38,40595,40596,40597],{},"Bod dotyku ",[883,40598,40600],{"className":40599},[886],[888,40601,40602],{"xmlns":890},[892,40603,40604,40634],{},[895,40605,40606,40612,40614,40622,40624,40632],{},[1824,40607,40608,40610],{},[898,40609,1828],{},[1761,40611,8408],{},[1761,40613,1822],{"stretchy":1821},[2015,40615,40616,40618,40620],{},[898,40617,1828],{},[1765,40619,1945],{},[1761,40621,8408],{},[1761,40623,1834],{"separator":1833},[2015,40625,40626,40628,40630],{},[898,40627,1828],{},[1765,40629,2296],{},[1761,40631,8408],{},[1761,40633,1844],{"stretchy":1821},[902,40635,32357],{"encoding":904}," — řešení obou úloh; totožný pro primární i duální formulaci.",[123,40638,40639,40642,40643,40656,40657,40670],{},[38,40640,40641],{},"Dualita"," — ekvivalence max ",[883,40644,40646],{"className":40645},[886],[888,40647,40648],{"xmlns":890},[892,40649,40650,40654],{},[895,40651,40652],{},[898,40653,900],{},[902,40655,900],{"encoding":904}," a min ",[883,40658,40660],{"className":40659},[886],[888,40661,40662],{"xmlns":890},[892,40663,40664,40668],{},[895,40665,40666],{},[898,40667,1818],{},[902,40669,1818],{"encoding":904},"; Marshallova a Hicksova poptávka.",[115,40672,5968],{"id":5967},[120,40674,40675,40698,40714,40727,40738],{},[123,40676,40677,1989,40680,40683,40684,40697],{},[38,40678,40679],{},"Teorie před optimalizací:",[207,40681,880],{"className":40682,"dataFsResolvedFilePath":878,"href":879},[210]," (funkce ",[883,40685,40687],{"className":40686},[886],[888,40688,40689],{"xmlns":890},[892,40690,40691,40695],{},[895,40692,40693],{},[898,40694,900],{},[902,40696,900],{"encoding":904},", indiferenční křivky, MRCS).",[123,40699,40700,1989,40703,40706,40707,40710,40711,1741],{},[38,40701,40702],{},"Matematický aparát:",[207,40704,793],{"className":40705,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace), ",[207,40708,784],{"className":40709,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace), ",[207,40712,5995],{"className":40713,"dataFsResolvedFilePath":764,"href":765},[210],[123,40715,40716,1989,40719,40722,40723,40726],{},[38,40717,40718],{},"Paralely:",[207,40720,15126],{"className":40721,"dataFsResolvedFilePath":857,"href":858},[210]," (MRTS ↔ MRCS, izokvanty ↔ IC, Eulerova věta pro CD), ",[207,40724,15980],{"className":40725,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallova poptávka jako vstup tržního modelu).",[123,40728,40729,1989,40732,1343,40735],{},[38,40730,40731],{},"Přednášky:",[207,40733,1094],{"className":40734,"dataFsResolvedFilePath":838,"href":839},[210],[207,40736,1101],{"className":40737,"dataFsResolvedFilePath":868,"href":869},[210],[123,40739,40740,1989,40742],{},[38,40741,6015],{},[207,40743,6021],{"className":40744,"dataFsResolvedFilePath":6019,"href":6020},[210],{"title":641,"searchDepth":642,"depth":642,"links":40746},[40747,40748,40749,40754,40755,40756,40758,40761,40764,40766,40767,40769,40770,40774,40775],{"id":16045,"depth":642,"text":16046},{"id":32037,"depth":642,"text":32038},{"id":32434,"depth":642,"text":32435,"children":40750},[40751,40752],{"id":32554,"depth":649,"text":32555},{"id":33135,"depth":649,"text":40753},"Interpretace λ\\lambda — mezní užitečnost důchodu",{"id":33597,"depth":642,"text":33598},{"id":33908,"depth":642,"text":33909},{"id":34227,"depth":642,"text":40757},"Příklad 6.6 — maximalizace užitečnosti pro U=Q1Q2U = Q_1 Q_2",{"id":35000,"depth":642,"text":35001,"children":40759},[40760],{"id":35756,"depth":649,"text":35757},{"id":35936,"depth":642,"text":35937,"children":40762},[40763],{"id":36193,"depth":649,"text":36194},{"id":37144,"depth":642,"text":40765},"Příklad 6.7 — minimalizace výdajů pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":38068,"depth":642,"text":38069},{"id":38271,"depth":642,"text":40768},"Příklad 6.8 — obecné odvození pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":39156,"depth":642,"text":39157},{"id":39542,"depth":642,"text":39543,"children":40771},[40772,40773],{"id":39546,"depth":649,"text":39547},{"id":40006,"depth":649,"text":40007},{"id":5532,"depth":642,"text":5533},{"id":5967,"depth":642,"text":5968},{},"\u002Ftopics\u002Foptimalizace-spotrebitele",{"title":31798,"description":641},[1138,1137],"topics\u002Foptimalizace-spotrebitele",[1128,40782,1144,13813,40783,40784,40785],"optimalizace-spotrebitele","poptavka-spotrebitele","minimalizace-vydaju","dualita","jxXhWsWsCIcDvEqLkcWTWs-jk9CvI-eFUi2Afo7U40o",{"id":40788,"title":802,"body":40789,"course":1128,"courses":659,"created":6039,"description":641,"extension":661,"meta":54795,"navigation":664,"path":54796,"seo":54797,"sources":54798,"stem":54799,"tags":54800,"type":6050,"updated":677,"__hash__":54805},"topics\u002Ftopics\u002Fpoptavka-nabidka.md",{"type":9,"value":40790,"toc":54751},[40791,40794,40820,40824,40831,40983,40997,40999,41001,41087,41091,41127,41200,41221,41346,41356,41369,41373,41378,41408,41470,41479,41483,41545,41552,41573,41691,41768,41772,41775,41834,41949,41954,41985,42046,42094,42149,42153,42174,42198,42246,42250,42262,42266,42375,42379,42395,42436,42447,42606,42616,42621,42625,42747,42757,42764,42768,42846,42857,42937,42943,42950,43089,43096,43099,43156,43160,43238,43284,43328,43334,43447,43451,43454,43649,43653,43890,43893,44047,44200,44202,44204,44282,44285,44390,44459,44468,44472,44475,44536,44545,44549,44582,44660,44699,44703,44752,44806,44810,44839,44868,44920,44927,44981,45058,45062,45105,45170,45213,45315,45334,45336,45340,45447,45451,45518,45567,45574,45659,45663,45733,45738,45786,45974,45978,45983,46159,46164,46223,46328,46332,46359,46363,46370,46534,46621,46626,46628,46631,46725,46872,46942,47014,47016,47020,47034,47038,47170,47225,47337,47414,47418,47475,47578,47637,47798,47802,47877,47949,48047,48105,48199,48252,48273,48327,48332,48410,48458,48545,48583,48671,48824,48860,48914,48917,48919,48921,48970,48977,48985,49072,49081,49168,49175,49177,49181,49402,49404,49408,49412,49481,49532,49735,49741,49752,49820,49826,50248,50252,50316,50340,50536,50542,50556,50624,50627,50667,50890,50958,51260,51669,51746,51907,51913,51916,51991,52444,52495,52901,53006,53669,53672,53749,53757,53831,53862,53864,53868,53912,53914,53916,53920,54150,54154,54245,54250,54344,54349,54521,54525,54643,54648,54697,54699,54701],[12,40792,802],{"id":40793},"poptávka-nabídka-a-tržní-rovnováha",[1636,40795,40796],{},[724,40797,40798,40800,40801,40804,40805,40808,40809,40812,40813,40815,40816,40819],{},[883,40799,1642],{}," TL;DR\nKapitola buduje základní mikroekonomický model trhu: chování spotřebitele (",[38,40802,40803],{},"poptávka",") a výrobce (",[38,40806,40807],{},"nabídka","), jejich interakci v ",[38,40810,40811],{},"tržní rovnováze"," a kvantitativní analýzu reakce modelu na změnu exogenních proměnných (posuny, zdanění, ",[38,40814,22011],{},"). Uzavírá ji pojem ",[38,40817,40818],{},"přebytku spotřebitele a výrobce"," jako míry čistého prospěchu obou stran trhu.",[115,40821,40823],{"id":40822},"úvod-model-a-proměnné","Úvod — model a proměnné",[724,40825,40826,40827,40830],{},"Cílem je popsat chování spotřebitele a výrobce za předpokladu racionality jedince (",[614,40828,40829],{},"homo economicus","). Mezi hlavní proměnné patří:",[120,40832,40833,40850,40892,40908],{},[123,40834,40835,40836,40849],{},"cena ",[883,40837,40839],{"className":40838},[886],[888,40840,40841],{"xmlns":890},[892,40842,40843,40847],{},[895,40844,40845],{},[898,40846,1839],{},[902,40848,1839],{"encoding":904}," zkoumaného zboží,",[123,40851,40852,40853,1834],{},"ceny alternativních zboží ",[883,40854,40856],{"className":40855},[886],[888,40857,40858],{"xmlns":890},[892,40859,40860,40889],{},[895,40861,40862,40868,40870,40876,40878,40880,40882],{},[1681,40863,40864,40866],{},[898,40865,1839],{},[1765,40867,1945],{},[1761,40869,1834],{"separator":1833},[1681,40871,40872,40874],{},[898,40873,1839],{},[1765,40875,2296],{},[1761,40877,1834],{"separator":1833},[1761,40879,13686],{},[1761,40881,1834],{"separator":1833},[1681,40883,40884,40886],{},[898,40885,1839],{},[898,40887,40888],{},"n",[902,40890,40891],{"encoding":904},"P_1, P_2, \\dots, P_n",[123,40893,40894,40895,1834],{},"důchod ",[883,40896,40898],{"className":40897},[886],[888,40899,40900],{"xmlns":890},[892,40901,40902,40906],{},[895,40903,40904],{},[898,40905,13170],{},[902,40907,13170],{"encoding":904},[123,40909,40910,40911,40924,40925,40938,40939,40952,40953,40967,40968,40982],{},"preference, očekávání, populace, výrobní faktory (práce ",[883,40912,40914],{"className":40913},[886],[888,40915,40916],{"xmlns":890},[892,40917,40918,40922],{},[895,40919,40920],{},[898,40921,13835],{},[902,40923,13835],{"encoding":904},", kapitál ",[883,40926,40928],{"className":40927},[886],[888,40929,40930],{"xmlns":890},[892,40931,40932,40936],{},[895,40933,40934],{},[898,40935,2768],{},[902,40937,2768],{"encoding":904},", půda ",[883,40940,40942],{"className":40941},[886],[888,40943,40944],{"xmlns":890},[892,40945,40946,40950],{},[895,40947,40948],{},[898,40949,1818],{},[902,40951,1818],{"encoding":904},"), technologie, počet výrobců ",[883,40954,40956],{"className":40955},[886],[888,40957,40958],{"xmlns":890},[892,40959,40960,40965],{},[895,40961,40962],{},[898,40963,40964],{},"O",[902,40966,40964],{"encoding":904},", počasí ",[883,40969,40971],{"className":40970},[886],[888,40972,40973],{"xmlns":890},[892,40974,40975,40980],{},[895,40976,40977],{},[898,40978,40979],{},"W",[902,40981,40979],{"encoding":904}," atd.",[724,40984,40985,40986,40989,40990,40993,40994,1741],{},"Vybereme-li právě jeden z faktorů jako endogenní (",[614,40987,40988],{},"ceteris paribus","), hovoříme o ",[38,40991,40992],{},"jednofaktorovém modelu","; jinak jde o model ",[38,40995,40996],{},"vícefaktorový",[1849,40998],{},[115,41000,17199],{"id":40803},[1636,41002,41003],{},[724,41004,41005,41007,41008,41021,41022,41035,41036,41039,41040,41063,41064,1741],{},[883,41006,1642],{}," TL;DR\nPoptávka vyjadřuje závislost nakupovaného množství ",[883,41009,41011],{"className":41010},[886],[888,41012,41013],{"xmlns":890},[892,41014,41015,41019],{},[895,41016,41017],{},[898,41018,1828],{},[902,41020,1828],{"encoding":904}," na ceně ",[883,41023,41025],{"className":41024},[886],[888,41026,41027],{"xmlns":890},[892,41028,41029,41033],{},[895,41030,41031],{},[898,41032,1839],{},[902,41034,1839],{"encoding":904}," (případně dalších proměnných). Základní vlastností je ",[38,41037,41038],{},"zákon klesající poptávky",": při růstu ceny množství klesá. Z důvodu přehlednosti se pracuje s jednofaktorovým modelem ",[883,41041,41043],{"className":41042},[886],[888,41044,41045],{"xmlns":890},[892,41046,41047,41061],{},[895,41048,41049,41051,41053,41055,41057,41059],{},[898,41050,1828],{},[1761,41052,1909],{},[898,41054,2244],{},[1761,41056,1915],{"stretchy":1821},[898,41058,1839],{},[1761,41060,1920],{"stretchy":1821},[902,41062,8247],{"encoding":904}," a jeho lineární verzí ",[883,41065,41067],{"className":41066},[886],[888,41068,41069],{"xmlns":890},[892,41070,41071,41085],{},[895,41072,41073,41075,41077,41079,41081,41083],{},[898,41074,1839],{},[1761,41076,1909],{},[898,41078,207],{},[898,41080,1828],{},[1761,41082,1964],{},[898,41084,4302],{},[902,41086,4305],{"encoding":904},[198,41088,41090],{"id":41089},"obecný-vícefaktorový-model","Obecný vícefaktorový model",[724,41092,41093,41094,41107,41108,41121,41122,3927,41124,5372],{},"Ve vícefaktorovém modelu uvažujeme, že poptávané množství ",[883,41095,41097],{"className":41096},[886],[888,41098,41099],{"xmlns":890},[892,41100,41101,41105],{},[895,41102,41103],{},[898,41104,1828],{},[902,41106,1828],{"encoding":904}," závisí na ceně ",[883,41109,41111],{"className":41110},[886],[888,41112,41113],{"xmlns":890},[892,41114,41115,41119],{},[895,41116,41117],{},[898,41118,1839],{},[902,41120,1839],{"encoding":904},", na cenách alternativních zboží a důchodu. Závislost vyjadřuje ",[38,41123,32033],{},[614,41125,41126],{},"demand function",[883,41128,41130],{"className":41129},[886],[888,41131,41132],{"xmlns":890,"display":1930},[892,41133,41134,41197],{},[24787,41135,41136],{"width":32101},[24792,41137,41138,41140,41190,41192],{},[24795,41139],{"width":32106},[24795,41141,41142],{},[895,41143,41144,41146,41148,41150,41152,41154,41156,41162,41164,41170,41172,41174,41176,41182,41184,41186,41188],{},[898,41145,1828],{},[1761,41147,1909],{},[898,41149,2244],{},[1761,41151,1915],{"stretchy":1821},[898,41153,1839],{},[1761,41155,1834],{"separator":1833},[1681,41157,41158,41160],{},[898,41159,1839],{},[1765,41161,1945],{},[1761,41163,1834],{"separator":1833},[1681,41165,41166,41168],{},[898,41167,1839],{},[1765,41169,2296],{},[1761,41171,1834],{"separator":1833},[1761,41173,13686],{},[1761,41175,1834],{"separator":1833},[1681,41177,41178,41180],{},[898,41179,1839],{},[898,41181,40888],{},[1761,41183,1834],{"separator":1833},[898,41185,13170],{},[1761,41187,1920],{"stretchy":1821},[898,41189,1741],{"mathvariant":1969},[24795,41191],{"width":32106},[24795,41193,41194],{},[2761,41195,41196],{},"(2.1)",[902,41198,41199],{"encoding":904},"Q = D(P, P_1, P_2, \\dots, P_n, Y). \\tag{2.1}",[724,41201,41202,41203,41206,41207,41220],{},"Důležitou vlastností je ",[38,41204,41205],{},"homogenita",": změní-li se všechny nezávisle proměnné ",[883,41208,41210],{"className":41209},[886],[888,41211,41212],{"xmlns":890},[892,41213,41214,41218],{},[895,41215,41216],{},[898,41217,1719],{},[902,41219,1719],{"encoding":904},"-krát, poptávané množství se nezmění,",[883,41222,41224],{"className":41223},[886],[888,41225,41226],{"xmlns":890,"display":1930},[892,41227,41228,41343],{},[24787,41229,41230],{"width":32101},[24792,41231,41232,41234,41336,41338],{},[24795,41233],{"width":32106},[24795,41235,41236],{},[895,41237,41238,41240,41242,41244,41246,41248,41250,41252,41254,41260,41262,41264,41270,41272,41274,41276,41278,41284,41286,41288,41290,41292,41294,41296,41298,41300,41302,41308,41310,41316,41318,41320,41322,41328,41330,41332,41334],{},[898,41239,1828],{},[1761,41241,1909],{},[898,41243,2244],{},[1761,41245,1915],{"stretchy":1821},[898,41247,1719],{},[898,41249,1839],{},[1761,41251,1834],{"separator":1833},[898,41253,1719],{},[1681,41255,41256,41258],{},[898,41257,1839],{},[1765,41259,1945],{},[1761,41261,1834],{"separator":1833},[898,41263,1719],{},[1681,41265,41266,41268],{},[898,41267,1839],{},[1765,41269,2296],{},[1761,41271,1834],{"separator":1833},[1761,41273,13686],{},[1761,41275,1834],{"separator":1833},[898,41277,1719],{},[1681,41279,41280,41282],{},[898,41281,1839],{},[898,41283,40888],{},[1761,41285,1834],{"separator":1833},[898,41287,1719],{},[898,41289,13170],{},[1761,41291,1920],{"stretchy":1821},[1761,41293,1909],{},[898,41295,2244],{},[1761,41297,1915],{"stretchy":1821},[898,41299,1839],{},[1761,41301,1834],{"separator":1833},[1681,41303,41304,41306],{},[898,41305,1839],{},[1765,41307,1945],{},[1761,41309,1834],{"separator":1833},[1681,41311,41312,41314],{},[898,41313,1839],{},[1765,41315,2296],{},[1761,41317,1834],{"separator":1833},[1761,41319,13686],{},[1761,41321,1834],{"separator":1833},[1681,41323,41324,41326],{},[898,41325,1839],{},[898,41327,40888],{},[1761,41329,1834],{"separator":1833},[898,41331,13170],{},[1761,41333,1920],{"stretchy":1821},[898,41335,1741],{"mathvariant":1969},[24795,41337],{"width":32106},[24795,41339,41340],{},[2761,41341,41342],{},"(2.2)",[902,41344,41345],{"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}",[1636,41347,41348],{},[724,41349,41350,41352,41353,1741],{},[883,41351,4723],{}," Pozor\nHomogenita platí pouze v zidealizovaném vícefaktorovém modelu; ",[38,41354,41355],{},"v jednofaktorových modelech neplatí",[724,41357,41358,41359,1343,41362,2068,41365,41368],{},"Rozlišuje se poptávka ",[38,41360,41361],{},"individuální",[38,41363,41364],{},"tržní",[38,41366,41367],{},"agregátní"," (není-li specifikováno, rozumí se tržní).",[198,41370,41372],{"id":41371},"jednofaktorové-modely","Jednofaktorové modely",[41374,41375,41377],"h4",{"id":41376},"funkce-poptávky-v-užším-slova-smyslu","Funkce poptávky v užším slova smyslu",[724,41379,41380,41381,41394,41395,2506],{},"Poptávané množství ",[883,41382,41384],{"className":41383},[886],[888,41385,41386],{"xmlns":890},[892,41387,41388,41392],{},[895,41389,41390],{},[898,41391,1828],{},[902,41393,1828],{"encoding":904}," závisí pouze na ceně ",[883,41396,41398],{"className":41397},[886],[888,41399,41400],{"xmlns":890},[892,41401,41402,41406],{},[895,41403,41404],{},[898,41405,1839],{},[902,41407,1839],{"encoding":904},[883,41409,41411],{"className":41410},[886],[888,41412,41413],{"xmlns":890,"display":1930},[892,41414,41415,41467],{},[24787,41416,41417],{"width":32101},[24792,41418,41419,41421,41460,41462],{},[24795,41420],{"width":32106},[24795,41422,41423],{},[895,41424,41425,41427,41429,41431,41433,41435,41437,41439,41441,41444,41446,41448,41450,41452,41454,41456,41458],{},[898,41426,1828],{},[1761,41428,1909],{},[898,41430,2244],{},[1761,41432,1915],{"stretchy":1821},[898,41434,1839],{},[1761,41436,1920],{"stretchy":1821},[1761,41438,1834],{"separator":1833},[3315,41440],{"width":3317},[2761,41442,41443],{},"resp.",[3315,41445],{"width":3317},[898,41447,1839],{},[1761,41449,1909],{},[898,41451,2244],{},[1761,41453,1915],{"stretchy":1821},[898,41455,1828],{},[1761,41457,1920],{"stretchy":1821},[898,41459,1741],{"mathvariant":1969},[24795,41461],{"width":32106},[24795,41463,41464],{},[2761,41465,41466],{},"(2.3)",[902,41468,41469],{"encoding":904},"Q = D(P), \\qquad \\text{resp.} \\qquad P = D(Q). \\tag{2.3}",[724,41471,41472,41473,3927,41476,2162],{},"Graf této funkce se nazývá ",[38,41474,41475],{},"křivka poptávky",[614,41477,41478],{},"demand curve",[41374,41480,41482],{"id":41481},"zákon-klesající-poptávky","Zákon klesající poptávky",[1636,41484,41485],{},[724,41486,41487],{},[38,41488,41489,41490,41503,41504,41517,41518,41503,41531,41544],{},"Roste-li cena ",[883,41491,41493],{"className":41492},[886],[888,41494,41495],{"xmlns":890},[892,41496,41497,41501],{},[895,41498,41499],{},[898,41500,1839],{},[902,41502,1839],{"encoding":904},", pak množství ",[883,41505,41507],{"className":41506},[886],[888,41508,41509],{"xmlns":890},[892,41510,41511,41515],{},[895,41512,41513],{},[898,41514,1828],{},[902,41516,1828],{"encoding":904}," klesá; klesá-li cena ",[883,41519,41521],{"className":41520},[886],[888,41522,41523],{"xmlns":890},[892,41524,41525,41529],{},[895,41526,41527],{},[898,41528,1839],{},[902,41530,1839],{"encoding":904},[883,41532,41534],{"className":41533},[886],[888,41535,41536],{"xmlns":890},[892,41537,41538,41542],{},[895,41539,41540],{},[898,41541,1828],{},[902,41543,1828],{"encoding":904}," roste.",[724,41546,41547,41548,41551],{},"Spotřebitelé jsou ochotni nakoupit větší množství za nižší cenu (mezní užitečnost — viz kap. 6). Zákon platí za ",[38,41549,41550],{},"normálních podmínek","; první kvantitativní formulaci podal Marshall (1890).",[1636,41553,41554,41559],{},[724,41555,41556,41558],{},[883,41557,1642],{}," Intuice — proč zákon platí",[120,41560,41561,41567],{},[123,41562,41563,41566],{},[38,41564,41565],{},"Substituční efekt"," — růst ceny vede ke snaze nahradit zboží jiným.",[123,41568,41569,41572],{},[38,41570,41571],{},"Důchodový efekt"," — růst ceny způsobí nevítaný úbytek reálného důchodu.",[724,41574,41575,41576,41589,41590,41603,41604,41630,41631,41657,41658,12146,41684,41687,41688,1741],{},"Každá funkce poptávky je tedy klesající. Cena ",[883,41577,41579],{"className":41578},[886],[888,41580,41581],{"xmlns":890},[892,41582,41583,41587],{},[895,41584,41585],{},[898,41586,1839],{},[902,41588,1839],{"encoding":904}," se vynáší na svislou osu, množství ",[883,41591,41593],{"className":41592},[886],[888,41594,41595],{"xmlns":890},[892,41596,41597,41601],{},[895,41598,41599],{},[898,41600,1828],{},[902,41602,1828],{"encoding":904}," na vodorovnou. Hypotetická křivka prochází body ",[883,41605,41607],{"className":41606},[886],[888,41608,41609],{"xmlns":890},[892,41610,41611,41627],{},[895,41612,41613,41615,41617,41619,41625],{},[1761,41614,1822],{"stretchy":1821},[1765,41616,1767],{},[1761,41618,1834],{"separator":1833},[1681,41620,41621,41623],{},[898,41622,1839],{},[1765,41624,1767],{},[1761,41626,1844],{"stretchy":1821},[902,41628,41629],{"encoding":904},"[0, P_0]"," (cena, při níž je zboží neprodejné) a ",[883,41632,41634],{"className":41633},[886],[888,41635,41636],{"xmlns":890},[892,41637,41638,41654],{},[895,41639,41640,41642,41648,41650,41652],{},[1761,41641,1822],{"stretchy":1821},[1681,41643,41644,41646],{},[898,41645,1828],{},[1765,41647,1767],{},[1761,41649,1834],{"separator":1833},[1765,41651,1767],{},[1761,41653,1844],{"stretchy":1821},[902,41655,41656],{"encoding":904},"[Q_0, 0]"," (teoretický objem při nulové ceně). Interval ",[883,41659,41661],{"className":41660},[886],[888,41662,41663],{"xmlns":890},[892,41664,41665,41681],{},[895,41666,41667,41669,41671,41673,41679],{},[1761,41668,1915],{"stretchy":1821},[1765,41670,1767],{},[1761,41672,1834],{"separator":1833},[1681,41674,41675,41677],{},[898,41676,1839],{},[1765,41678,1767],{},[1761,41680,1920],{"stretchy":1821},[902,41682,41683],{"encoding":904},"(0, P_0)",[38,41685,41686],{},"reálné cenové rozpětí",". Za teoretických předpokladů je křivka ",[38,41689,41690],{},"konvexní",[724,41692,41693],{},[614,41694,41695,41696,41717,41718,2068,41743,1741],{},"Obrázek 2.1: Hypotetická křivka poptávky v rovině ",[883,41697,41699],{"className":41698},[886],[888,41700,41701],{"xmlns":890},[892,41702,41703,41715],{},[895,41704,41705,41707,41709,41711,41713],{},[1761,41706,1915],{"stretchy":1821},[898,41708,1828],{},[1761,41710,1834],{"separator":1833},[898,41712,1839],{},[1761,41714,1920],{"stretchy":1821},[902,41716,4058],{"encoding":904}," — klesající, konvexní, procházející body ",[883,41719,41721],{"className":41720},[886],[888,41722,41723],{"xmlns":890},[892,41724,41725,41741],{},[895,41726,41727,41729,41731,41733,41739],{},[1761,41728,1822],{"stretchy":1821},[1765,41730,1767],{},[1761,41732,1834],{"separator":1833},[1681,41734,41735,41737],{},[898,41736,1839],{},[1765,41738,1767],{},[1761,41740,1844],{"stretchy":1821},[902,41742,41629],{"encoding":904},[883,41744,41746],{"className":41745},[886],[888,41747,41748],{"xmlns":890},[892,41749,41750,41766],{},[895,41751,41752,41754,41760,41762,41764],{},[1761,41753,1822],{"stretchy":1821},[1681,41755,41756,41758],{},[898,41757,1828],{},[1765,41759,1767],{},[1761,41761,1834],{"separator":1833},[1765,41763,1767],{},[1761,41765,1844],{"stretchy":1821},[902,41767,41656],{"encoding":904},[41374,41769,41771],{"id":41770},"lineární-model-poptávky","Lineární model poptávky",[724,41773,41774],{},"Nejjednodušší závislostí je",[883,41776,41778],{"className":41777},[886],[888,41779,41780],{"xmlns":890,"display":1930},[892,41781,41782,41831],{},[24787,41783,41784],{"width":32101},[24792,41785,41786,41788,41824,41826],{},[24795,41787],{"width":32106},[24795,41789,41790],{},[895,41791,41792,41794,41796,41798,41800,41802,41804,41806,41808,41810,41812,41814,41816,41818,41820,41822],{},[898,41793,1839],{},[1761,41795,1909],{},[898,41797,207],{},[898,41799,1828],{},[1761,41801,1964],{},[898,41803,4302],{},[1761,41805,1834],{"separator":1833},[3315,41807],{"width":3317},[898,41809,207],{},[1761,41811,2058],{},[1765,41813,1767],{},[1761,41815,1834],{"separator":1833},[2761,41817,2763],{},[898,41819,4302],{},[1761,41821,1763],{},[1765,41823,16498],{},[24795,41825],{"width":32106},[24795,41827,41828],{},[2761,41829,41830],{},"(2.4)",[902,41832,41833],{"encoding":904},"P = aQ + b, \\qquad a \u003C 0,\\ b > 0. \\tag{2.4}",[724,41835,41836,41837,25627,41873,2068,41897,12081,41923,41945,41946,1741],{},"Křivka poptávky je přímka se záporným sklonem. Alternativně ",[883,41838,41840],{"className":41839},[886],[888,41841,41842],{"xmlns":890},[892,41843,41844,41870],{},[895,41845,41846,41848,41850,41858,41860,41862],{},[898,41847,1828],{},[1761,41849,1909],{},[6411,41851,41852],{"scriptlevel":1767,"displaystyle":1821},[4379,41853,41854,41856],{},[1765,41855,1945],{},[898,41857,207],{},[898,41859,1839],{},[1761,41861,1885],{},[6411,41863,41864],{"scriptlevel":1767,"displaystyle":1821},[4379,41865,41866,41868],{},[898,41867,4302],{},[898,41869,207],{},[902,41871,41872],{"encoding":904},"Q = \\tfrac{1}{a}P - \\tfrac{b}{a}",[883,41874,41876],{"className":41875},[886],[888,41877,41878],{"xmlns":890},[892,41879,41880,41894],{},[895,41881,41882,41890,41892],{},[6411,41883,41884],{"scriptlevel":1767,"displaystyle":1821},[4379,41885,41886,41888],{},[1765,41887,1945],{},[898,41889,207],{},[1761,41891,2058],{},[1765,41893,1767],{},[902,41895,41896],{"encoding":904},"\\tfrac{1}{a} \u003C 0",[883,41898,41900],{"className":41899},[886],[888,41901,41902],{"xmlns":890},[892,41903,41904,41920],{},[895,41905,41906,41908,41916,41918],{},[1761,41907,1885],{},[6411,41909,41910],{"scriptlevel":1767,"displaystyle":1821},[4379,41911,41912,41914],{},[898,41913,4302],{},[898,41915,207],{},[1761,41917,1763],{},[1765,41919,1767],{},[902,41921,41922],{"encoding":904},"-\\tfrac{b}{a} > 0",[883,41924,41926],{"className":41925},[886],[888,41927,41928],{"xmlns":890},[892,41929,41930,41942],{},[895,41931,41932,41934,41936,41938,41940],{},[1761,41933,1915],{"stretchy":1821},[1765,41935,1767],{},[1761,41937,1834],{"separator":1833},[898,41939,4302],{},[1761,41941,1920],{"stretchy":1821},[902,41943,41944],{"encoding":904},"(0, b)",". Tento model odpovídá ",[38,41947,41948],{},"nedokonalé konkurenci",[41950,41951,41953],"h5",{"id":41952},"příklad-21","Příklad 2.1",[724,41955,41956,41958,41959,1741],{},[38,41957,2274],{}," Lineární poptávka ",[883,41960,41962],{"className":41961},[886],[888,41963,41964],{"xmlns":890},[892,41965,41966,41982],{},[895,41967,41968,41970,41972,41974,41976,41978,41980],{},[898,41969,1839],{},[1761,41971,1909],{},[1761,41973,1885],{},[1765,41975,2296],{},[898,41977,1828],{},[1761,41979,1964],{},[1765,41981,7195],{},[902,41983,41984],{"encoding":904},"P = -2Q + 60",[724,41986,41987,41989,41990,42012,42013,1741],{},[38,41988,2349],{}," Reálné cenové rozpětí je ",[883,41991,41993],{"className":41992},[886],[888,41994,41995],{"xmlns":890},[892,41996,41997,42009],{},[895,41998,41999,42001,42003,42005,42007],{},[1761,42000,1915],{"stretchy":1821},[1765,42002,1767],{},[1761,42004,1834],{"separator":1833},[1765,42006,7195],{},[1761,42008,1920],{"stretchy":1821},[902,42010,42011],{"encoding":904},"(0, 60)","; alternativní tvar je ",[883,42014,42016],{"className":42015},[886],[888,42017,42018],{"xmlns":890},[892,42019,42020,42043],{},[895,42021,42022,42024,42026,42028,42036,42038,42040],{},[898,42023,1828],{},[1761,42025,1909],{},[1761,42027,1885],{},[6411,42029,42030],{"scriptlevel":1767,"displaystyle":1821},[4379,42031,42032,42034],{},[1765,42033,1945],{},[1765,42035,2296],{},[898,42037,1839],{},[1761,42039,1964],{},[1765,42041,42042],{},"30",[902,42044,42045],{"encoding":904},"Q = -\\tfrac{1}{2}P + 30",[16,42047,42048,42071],{},[19,42049,42050],{},[22,42051,42052,42067,42069],{},[25,42053,42054],{},[883,42055,42057],{"className":42056},[886],[888,42058,42059],{"xmlns":890},[892,42060,42061,42065],{},[895,42062,42063],{},[898,42064,1839],{},[902,42066,1839],{"encoding":904},[25,42068,9262],{},[25,42070,13077],{},[30,42072,42073],{},[22,42074,42075,42090,42092],{},[35,42076,42077],{},[883,42078,42080],{"className":42079},[886],[888,42081,42082],{"xmlns":890},[892,42083,42084,42088],{},[895,42085,42086],{},[898,42087,1828],{},[902,42089,1828],{"encoding":904},[35,42091,2633],{},[35,42093,13077],{},[724,42095,42096],{},[614,42097,42098,42099,2068,42121,1741],{},"Obrázek 2.2 \u002F 2.3: Lineární poptávka — přímka s průsečíky ",[883,42100,42102],{"className":42101},[886],[888,42103,42104],{"xmlns":890},[892,42105,42106,42118],{},[895,42107,42108,42110,42112,42114,42116],{},[1761,42109,1822],{"stretchy":1821},[1765,42111,1767],{},[1761,42113,1834],{"separator":1833},[898,42115,4302],{},[1761,42117,1844],{"stretchy":1821},[902,42119,42120],{"encoding":904},"[0, b]",[883,42122,42124],{"className":42123},[886],[888,42125,42126],{"xmlns":890},[892,42127,42128,42146],{},[895,42129,42130,42132,42134,42136,42138,42140,42142,42144],{},[1761,42131,1822],{"stretchy":1821},[1761,42133,1885],{},[898,42135,4302],{},[898,42137,8726],{"mathvariant":1969},[898,42139,207],{},[1761,42141,1834],{"separator":1833},[1765,42143,1767],{},[1761,42145,1844],{"stretchy":1821},[902,42147,42148],{"encoding":904},"[-b\u002Fa, 0]",[41374,42150,42152],{"id":42151},"poptávka-při-dokonalé-konkurenci","Poptávka při dokonalé konkurenci",[724,42154,42155,42156,42173],{},"Přebírá-li každý účastník trhu pevnou tržní cenu ",[883,42157,42159],{"className":42158},[886],[888,42160,42161],{"xmlns":890},[892,42162,42163,42171],{},[895,42164,42165],{},[1824,42166,42167,42169],{},[898,42168,1839],{},[1761,42170,8408],{},[902,42172,8458],{"encoding":904},", je funkce poptávky konstantní:",[883,42175,42177],{"className":42176},[886],[888,42178,42179],{"xmlns":890,"display":1930},[892,42180,42181,42195],{},[895,42182,42183,42185,42187,42193],{},[898,42184,1839],{},[1761,42186,1909],{},[1824,42188,42189,42191],{},[898,42190,1839],{},[1761,42192,8408],{},[898,42194,1741],{"mathvariant":1969},[902,42196,42197],{"encoding":904},"P = P^*.",[724,42199,42200],{},[614,42201,42202,42203,42224,42225,1741],{},"Obrázek 2.4: Vodorovná přímka v rovině ",[883,42204,42206],{"className":42205},[886],[888,42207,42208],{"xmlns":890},[892,42209,42210,42222],{},[895,42211,42212,42214,42216,42218,42220],{},[1761,42213,1915],{"stretchy":1821},[898,42215,1828],{},[1761,42217,1834],{"separator":1833},[898,42219,1839],{},[1761,42221,1920],{"stretchy":1821},[902,42223,4058],{"encoding":904}," na úrovni ",[883,42226,42228],{"className":42227},[886],[888,42229,42230],{"xmlns":890},[892,42231,42232,42244],{},[895,42233,42234,42236,42238],{},[898,42235,1839],{},[1761,42237,1909],{},[1824,42239,42240,42242],{},[898,42241,1839],{},[1761,42243,8408],{},[902,42245,8411],{"encoding":904},[41374,42247,42249],{"id":42248},"giffenův-statek","Giffenův statek",[724,42251,42252,42253,42255,42256,42258,42259,1741],{},"Existují zboží, u nichž je křivka poptávky ",[38,42254,17695],{}," — tzv. ",[38,42257,42249],{},". Jde o případy, kdy důchodový efekt převáží substituční (klasický příklad: rýže u chudých asijských spotřebitelů). Giffenův statek patří k ",[38,42260,42261],{},"podřadnému zboží",[41950,42263,42265],{"id":42264},"příklad-22","Příklad 2.2",[724,42267,42268,42271,42272,42290,42291,42313,42314,42332,42333,42350,42351,42374],{},[38,42269,42270],{},"Zadání a popis:"," Křivka ",[883,42273,42275],{"className":42274},[886],[888,42276,42277],{"xmlns":890},[892,42278,42279,42287],{},[895,42280,42281],{},[1681,42282,42283,42285],{},[898,42284,2244],{},[1765,42286,1945],{},[902,42288,42289],{"encoding":904},"D_1"," reprezentuje poptávku rodiny po cukru s reálným cenovým rozpětím ",[883,42292,42294],{"className":42293},[886],[888,42295,42296],{"xmlns":890},[892,42297,42298,42310],{},[895,42299,42300,42302,42304,42306,42308],{},[1761,42301,1915],{"stretchy":1821},[1765,42303,1767],{},[1761,42305,1834],{"separator":1833},[1765,42307,5433],{},[1761,42309,1920],{"stretchy":1821},[902,42311,42312],{"encoding":904},"(0, 15)"," pencí za libru; je nejprve konvexní, od inflexního bodu ",[883,42315,42317],{"className":42316},[886],[888,42318,42319],{"xmlns":890},[892,42320,42321,42329],{},[895,42322,42323],{},[1681,42324,42325,42327],{},[898,42326,1828],{},[1765,42328,1767],{},[902,42330,42331],{"encoding":904},"Q_0"," konkávní, se saturací kolem 17 liber. Křivka ",[883,42334,42336],{"className":42335},[886],[888,42337,42338],{"xmlns":890},[892,42339,42340,42348],{},[895,42341,42342],{},[1681,42343,42344,42346],{},[898,42345,2244],{},[1765,42347,2296],{},[902,42349,3419],{"encoding":904}," na širším trhu je konvexní klesající z bodu ",[883,42352,42354],{"className":42353},[886],[888,42355,42356],{"xmlns":890},[892,42357,42358,42371],{},[895,42359,42360,42362,42364,42366,42369],{},[1761,42361,1822],{"stretchy":1821},[1765,42363,1767],{},[1761,42365,1834],{"separator":1833},[1765,42367,42368],{},"21",[1761,42370,1844],{"stretchy":1821},[902,42372,42373],{"encoding":904},"[0, 21]"," centů.",[198,42376,42378],{"id":42377},"engelova-funkce-závislost-na-důchodu","Engelova funkce (závislost na důchodu)",[724,42380,42381,42382,2506],{},"Druhý jednofaktorový model předpokládá závislost množství pouze na důchodu ",[883,42383,42385],{"className":42384},[886],[888,42386,42387],{"xmlns":890},[892,42388,42389,42393],{},[895,42390,42391],{},[898,42392,13170],{},[902,42394,13170],{"encoding":904},[883,42396,42398],{"className":42397},[886],[888,42399,42400],{"xmlns":890,"display":1930},[892,42401,42402,42433],{},[24787,42403,42404],{"width":32101},[24792,42405,42406,42408,42426,42428],{},[24795,42407],{"width":32106},[24795,42409,42410],{},[895,42411,42412,42414,42416,42418,42420,42422,42424],{},[898,42413,1828],{},[1761,42415,1909],{},[898,42417,1818],{},[1761,42419,1915],{"stretchy":1821},[898,42421,13170],{},[1761,42423,1920],{"stretchy":1821},[898,42425,1741],{"mathvariant":1969},[24795,42427],{"width":32106},[24795,42429,42430],{},[2761,42431,42432],{},"(2.5)",[902,42434,42435],{"encoding":904},"Q = E(Y). \\tag{2.5}",[724,42437,42438,42439,42442,42443,42446],{},"Funkce se nazývá ",[38,42440,42441],{},"Engelova",", její graf ",[38,42444,42445],{},"Engelova křivka",". Tvar závisí na typu zboží:",[120,42448,42449,42581],{},[123,42450,42451,5675,42454,42467,42468,42481,42482,42499,42500],{},[38,42452,42453],{},"Normální (superior) zboží",[883,42455,42457],{"className":42456},[886],[888,42458,42459],{"xmlns":890},[892,42460,42461,42465],{},[895,42462,42463],{},[898,42464,1828],{},[902,42466,1828],{"encoding":904}," roste s ",[883,42469,42471],{"className":42470},[886],[888,42472,42473],{"xmlns":890},[892,42474,42475,42479],{},[895,42476,42477],{},[898,42478,13170],{},[902,42480,13170],{"encoding":904},", nepřesáhne hodnotu ",[883,42483,42485],{"className":42484},[886],[888,42486,42487],{"xmlns":890},[892,42488,42489,42497],{},[895,42490,42491],{},[1681,42492,42493,42495],{},[898,42494,1828],{},[1765,42496,1767],{},[902,42498,42331],{"encoding":904},":\n",[120,42501,42502,42534],{},[123,42503,42504,42507,42508,42511,42512,1741],{},[38,42505,42506],{},"Nezbytné zboží"," (potraviny, léky) — malá citlivost, ",[38,42509,42510],{},"konkávní"," křivka, autonomní spotřeba ",[883,42513,42515],{"className":42514},[886],[888,42516,42517],{"xmlns":890},[892,42518,42519,42531],{},[895,42520,42521,42527,42529],{},[1681,42522,42523,42525],{},[898,42524,1828],{},[1765,42526,1945],{},[1761,42528,1763],{},[1765,42530,1767],{},[902,42532,42533],{"encoding":904},"Q_1 > 0",[123,42535,42536,42539,42540,42558,42559,42561,42562,1989,42579,1741],{},[38,42537,42538],{},"Luxusní zboží"," — velká citlivost až od hladiny ",[883,42541,42543],{"className":42542},[886],[888,42544,42545],{"xmlns":890},[892,42546,42547,42555],{},[895,42548,42549],{},[1681,42550,42551,42553],{},[898,42552,13170],{},[1765,42554,1945],{},[902,42556,42557],{"encoding":904},"Y_1",", křivka je nejprve ",[38,42560,41690],{}," a od ",[883,42563,42565],{"className":42564},[886],[888,42566,42567],{"xmlns":890},[892,42568,42569,42577],{},[895,42570,42571],{},[1681,42572,42573,42575],{},[898,42574,13170],{},[1765,42576,1945],{},[902,42578,42557],{"encoding":904},[38,42580,42510],{},[123,42582,42583,42586,42587,42605],{},[38,42584,42585],{},"Podřadné (inferior) zboží"," — od hladiny ",[883,42588,42590],{"className":42589},[886],[888,42591,42592],{"xmlns":890},[892,42593,42594,42602],{},[895,42595,42596],{},[1681,42597,42598,42600],{},[898,42599,13170],{},[1765,42601,1767],{},[902,42603,42604],{"encoding":904},"Y_0"," množství s růstem důchodu klesá.",[724,42607,42608,42609,42612,42613,2162],{},"Mírou citlivosti je ",[614,42610,42611],{},"důchodová elasticita"," (viz ",[207,42614,7957],{"className":42615,"dataFsResolvedFilePath":848,"href":849},[210],[724,42617,42618],{},[614,42619,42620],{},"Obrázek 2.6: Tři panely Engelových křivek — (a) nezbytné, (b) luxusní, (c) podřadné zboží.",[41374,42622,42624],{"id":42623},"intuice-co-vlastně-znamená-podřadné","Intuice — co vlastně znamená „podřadné\"?",[1636,42626,42627,42698,42741],{},[724,42628,42629,42631,42632,1989,42635,1989,42648,2232,42650,42663,42664,42667,42668,1741],{},[883,42630,4723],{}," Pozor — nezbytné ≠ podřadné\n",[38,42633,42634],{},"Nezbytné zboží:",[883,42636,42638],{"className":42637},[886],[888,42639,42640],{"xmlns":890},[892,42641,42642,42646],{},[895,42643,42644],{},[898,42645,1828],{},[902,42647,1828],{"encoding":904},[38,42649,11366],{},[883,42651,42653],{"className":42652},[886],[888,42654,42655],{"xmlns":890},[892,42656,42657,42661],{},[895,42658,42659],{},[898,42660,13170],{},[902,42662,13170],{"encoding":904},", ale ",[38,42665,42666],{},"pomaleji"," než důchod (2× plat → třeba 1,3× spotřeba). ",[883,42669,42671],{"className":42670},[886],[888,42672,42673],{"xmlns":890},[892,42674,42675,42695],{},[895,42676,42677,42683,42685,42687,42689,42691,42693],{},[1681,42678,42679,42681],{},[898,42680,1818],{},[898,42682,13170],{},[1761,42684,10551],{},[1761,42686,1915],{"stretchy":1821},[1765,42688,1767],{},[1761,42690,1834],{"separator":1833},[1765,42692,1945],{},[1761,42694,1920],{"stretchy":1821},[902,42696,42697],{"encoding":904},"E_Y \\in (0, 1)",[724,42699,42700,1989,42703,1989,42716,42718,42719,1741],{},[38,42701,42702],{},"Podřadné zboží:",[883,42704,42706],{"className":42705},[886],[888,42707,42708],{"xmlns":890},[892,42709,42710,42714],{},[895,42711,42712],{},[898,42713,1828],{},[902,42715,1828],{"encoding":904},[38,42717,11386],{}," v absolutních číslech (2× plat → třeba 0,7× spotřeba). ",[883,42720,42722],{"className":42721},[886],[888,42723,42724],{"xmlns":890},[892,42725,42726,42738],{},[895,42727,42728,42734,42736],{},[1681,42729,42730,42732],{},[898,42731,1818],{},[898,42733,13170],{},[1761,42735,2058],{},[1765,42737,1767],{},[902,42739,42740],{"encoding":904},"E_Y \u003C 0",[724,42742,42743,42744,1741],{},"Klíčový rozdíl: u podřadného zboží si při vyšším důchodu kupuješ ",[38,42745,42746],{},"méně kusů, ne jen proporčně méně",[724,42748,42749,42752,42753,42756],{},[38,42750,42751],{},"Mechanismus — substituce „nahoru\"."," Samotné zboží se nezhoršilo, jen si teď můžeš dovolit ",[38,42754,42755],{},"kvalitnější alternativu",". Růst důchodu → přesun k prémiovému substitutu → absolutní pokles nákupu „levnější verze\".",[724,42758,42759],{},[3991,42760],{"alt":42761,"className":42762,"src":42763},"imek-engelovy-krivky-3typy",[210,3995],"\u002Fwiki-assets\u002Fimek-engelovy-krivky-3typy.jpeg",[41950,42765,42767],{"id":42766},"české-příklady","České příklady",[16,42769,42770,42780],{},[19,42771,42772],{},[22,42773,42774,42777],{},[25,42775,42776],{},"Podřadné",[25,42778,42779],{},"Nahradí se za",[30,42781,42782,42790,42798,42806,42814,42822,42830,42838],{},[22,42783,42784,42787],{},[35,42785,42786],{},"Instantní polévky, ramen",[35,42788,42789],{},"Čerstvé jídlo, restaurace",[22,42791,42792,42795],{},[35,42793,42794],{},"MHD (autobus, tramvaj)",[35,42796,42797],{},"Vlastní auto, Uber, taxi",[22,42799,42800,42803],{},[35,42801,42802],{},"Mražené polotovary, pizza z mrazáku",[35,42804,42805],{},"Čerstvé suroviny, hotovky",[22,42807,42808,42811],{},[35,42809,42810],{},"Privátní značky supermarketů (K-Classic, Clever)",[35,42812,42813],{},"Značkové produkty",[22,42815,42816,42819],{},[35,42817,42818],{},"Paštika Májka, obyčejný měkký salám",[35,42820,42821],{},"Kvalitní uzeniny, šunka od kosti",[22,42823,42824,42827],{},[35,42825,42826],{},"Second hand oblečení",[35,42828,42829],{},"Nové oblečení, značky",[22,42831,42832,42835],{},[35,42833,42834],{},"Krabicové víno, nejlevnější pivo",[35,42836,42837],{},"Lahvové víno, řemeslná piva",[22,42839,42840,42843],{},[35,42841,42842],{},"Ojetá auta nižších tříd",[35,42844,42845],{},"Nová auta, prémiové značky",[1636,42847,42848],{},[724,42849,42850,42852,42853,42856],{},[883,42851,4452],{}," Test 50 milionů\nPředstav si, že vyhraješ 50 milionů. ",[38,42854,42855],{},"Čeho si najednou koupíš méně"," (nebo vůbec)? To je tvoje podřadné zboží.",[724,42858,42859,42862,42863,3927,42866,42888,42889,3927,42892,42913,42914,42932,42933,42936],{},[38,42860,42861],{},"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 ",[38,42864,42865],{},"luxus",[883,42867,42869],{"className":42868},[886],[888,42870,42871],{"xmlns":890},[892,42872,42873,42885],{},[895,42874,42875,42881,42883],{},[1681,42876,42877,42879],{},[898,42878,1818],{},[898,42880,13170],{},[1761,42882,1763],{},[1765,42884,1945],{},[902,42886,42887],{"encoding":904},"E_Y > 1","), pro manažera s 200k platem ",[38,42890,42891],{},"podřadné",[883,42893,42895],{"className":42894},[886],[888,42896,42897],{"xmlns":890},[892,42898,42899,42911],{},[895,42900,42901,42907,42909],{},[1681,42902,42903,42905],{},[898,42904,1818],{},[898,42906,13170],{},[1761,42908,2058],{},[1765,42910,1767],{},[902,42912,42740],{"encoding":904},"). Proto je ",[883,42915,42917],{"className":42916},[886],[888,42918,42919],{"xmlns":890},[892,42920,42921,42929],{},[895,42922,42923],{},[1681,42924,42925,42927],{},[898,42926,1818],{},[898,42928,13170],{},[902,42930,42931],{"encoding":904},"E_Y"," vždy ",[38,42934,42935],{},"lokální veličina"," — platí pro danou úroveň důchodu, ne absolutně.",[724,42938,42939,42940,42942],{},"Extrémním případem podřadného zboží, kde substituční efekt převáží už na straně ceny, je ",[38,42941,42249],{}," (viz níže) — tam poptávková křivka dokonce roste.",[198,42944,42946,42947,1920],{"id":42945},"posun-poptávky-shift-of-demand","Posun poptávky (",[614,42948,42949],{},"shift of demand",[724,42951,42952,42953,42971,42972,42989,42990,43003,43004,4178,43017,43039,43040,43057,43058,43084,43085,43088],{},"Při změně exogenní proměnné (např. důchodu) se celá křivka poptávky posouvá. Uvažujme normální zboží. Ceně ",[883,42954,42956],{"className":42955},[886],[888,42957,42958],{"xmlns":890},[892,42959,42960,42968],{},[895,42961,42962],{},[1681,42963,42964,42966],{},[898,42965,1839],{},[1765,42967,1767],{},[902,42969,42970],{"encoding":904},"P_0"," odpovídá množství ",[883,42973,42975],{"className":42974},[886],[888,42976,42977],{"xmlns":890},[892,42978,42979,42987],{},[895,42980,42981],{},[1681,42982,42983,42985],{},[898,42984,1828],{},[1765,42986,1767],{},[902,42988,42331],{"encoding":904}," na křivce ",[883,42991,42993],{"className":42992},[886],[888,42994,42995],{"xmlns":890},[892,42996,42997,43001],{},[895,42998,42999],{},[898,43000,2244],{},[902,43002,2244],{"encoding":904},"; vzroste-li důchod z ",[883,43005,43007],{"className":43006},[886],[888,43008,43009],{"xmlns":890},[892,43010,43011,43015],{},[895,43012,43013],{},[898,43014,13170],{},[902,43016,13170],{"encoding":904},[883,43018,43020],{"className":43019},[886],[888,43021,43022],{"xmlns":890},[892,43023,43024,43036],{},[895,43025,43026,43032,43034],{},[1681,43027,43028,43030],{},[898,43029,13170],{},[1765,43031,1945],{},[1761,43033,1763],{},[898,43035,13170],{},[902,43037,43038],{"encoding":904},"Y_1 > Y",", pak stejné ceně ",[883,43041,43043],{"className":43042},[886],[888,43044,43045],{"xmlns":890},[892,43046,43047,43055],{},[895,43048,43049],{},[1681,43050,43051,43053],{},[898,43052,1839],{},[1765,43054,1767],{},[902,43056,42970],{"encoding":904}," odpovídá vyšší ",[883,43059,43061],{"className":43060},[886],[888,43062,43063],{"xmlns":890},[892,43064,43065,43081],{},[895,43066,43067,43073,43075],{},[1681,43068,43069,43071],{},[898,43070,1828],{},[1765,43072,1945],{},[1761,43074,1763],{},[1681,43076,43077,43079],{},[898,43078,1828],{},[1765,43080,1767],{},[902,43082,43083],{"encoding":904},"Q_1 > Q_0"," — křivka se ",[38,43086,43087],{},"posouvá doprava",". Pokles důchodu vede k posunu doleva.",[724,43090,43091],{},[3991,43092],{"alt":43093,"className":43094,"src":43095},"imek-posun-vs-pohyb-po-krivce",[210,3995],"\u002Fwiki-assets\u002Fimek-posun-vs-pohyb-po-krivce.jpeg",[724,43097,43098],{},"Posun může být způsoben i jinými faktory (např. zdaněním spotřebitele — viz dále).",[724,43100,43101],{},[614,43102,43103,43104,18049,43134,43155],{},"Obrázek 2.7: Posun poptávky — tři křivky ",[883,43105,43107],{"className":43106},[886],[888,43108,43109],{"xmlns":890},[892,43110,43111,43131],{},[895,43112,43113,43119,43121,43123,43125],{},[1681,43114,43115,43117],{},[898,43116,2244],{},[1765,43118,2296],{},[1761,43120,1834],{"separator":1833},[898,43122,2244],{},[1761,43124,1834],{"separator":1833},[1681,43126,43127,43129],{},[898,43128,2244],{},[1765,43130,1945],{},[902,43132,43133],{"encoding":904},"D_2, D, D_1",[883,43135,43137],{"className":43136},[886],[888,43138,43139],{"xmlns":890},[892,43140,43141,43153],{},[895,43142,43143,43145,43147,43149,43151],{},[1761,43144,1915],{"stretchy":1821},[898,43146,1828],{},[1761,43148,1834],{"separator":1833},[898,43150,1839],{},[1761,43152,1920],{"stretchy":1821},[902,43154,4058],{"encoding":904},", šipky naznačují posuny.",[41950,43157,43159],{"id":43158},"příklad-23-zdanění-kupujícího","Příklad 2.3 — zdanění kupujícího",[724,43161,43162,43164,43165,43188,43189,43206,43207,43224,43225,1741],{},[38,43163,2274],{}," Poptávce ",[883,43166,43168],{"className":43167},[886],[888,43169,43170],{"xmlns":890},[892,43171,43172,43186],{},[895,43173,43174,43176,43178,43180,43182,43184],{},[898,43175,1839],{},[1761,43177,1909],{},[898,43179,2244],{},[1761,43181,1915],{"stretchy":1821},[898,43183,1828],{},[1761,43185,1920],{"stretchy":1821},[902,43187,8692],{"encoding":904}," odpovídá ceně ",[883,43190,43192],{"className":43191},[886],[888,43193,43194],{"xmlns":890},[892,43195,43196,43204],{},[895,43197,43198],{},[1681,43199,43200,43202],{},[898,43201,1839],{},[1765,43203,1767],{},[902,43205,42970],{"encoding":904}," množství ",[883,43208,43210],{"className":43209},[886],[888,43211,43212],{"xmlns":890},[892,43213,43214,43222],{},[895,43215,43216],{},[1681,43217,43218,43220],{},[898,43219,1828],{},[1765,43221,1767],{},[902,43223,42331],{"encoding":904},". Na kupujícího je uložena jednotková daň ",[883,43226,43228],{"className":43227},[886],[888,43229,43230],{"xmlns":890},[892,43231,43232,43236],{},[895,43233,43234],{},[898,43235,1655],{},[902,43237,1655],{"encoding":904},[724,43239,43240,43242,43243,43260,43261,43283],{},[38,43241,2349],{}," Kupující nakupuje množství ",[883,43244,43246],{"className":43245},[886],[888,43247,43248],{"xmlns":890},[892,43249,43250,43258],{},[895,43251,43252],{},[1681,43253,43254,43256],{},[898,43255,1828],{},[1765,43257,1945],{},[902,43259,33032],{"encoding":904},", které odpovídá ceně ",[883,43262,43264],{"className":43263},[886],[888,43265,43266],{"xmlns":890},[892,43267,43268,43280],{},[895,43269,43270,43276,43278],{},[1681,43271,43272,43274],{},[898,43273,1839],{},[1765,43275,1767],{},[1761,43277,1964],{},[898,43279,1655],{},[902,43281,43282],{"encoding":904},"P_0 + T"," na původní křivce. Nová poptávka je",[883,43285,43287],{"className":43286},[886],[888,43288,43289],{"xmlns":890,"display":1930},[892,43290,43291,43325],{},[895,43292,43293,43295,43297,43303,43305,43307,43309,43311,43313,43315,43317,43319,43321,43323],{},[898,43294,1839],{},[1761,43296,1909],{},[1681,43298,43299,43301],{},[898,43300,2244],{},[1765,43302,1945],{},[1761,43304,1915],{"stretchy":1821},[898,43306,1828],{},[1761,43308,1920],{"stretchy":1821},[1761,43310,1909],{},[898,43312,2244],{},[1761,43314,1915],{"stretchy":1821},[898,43316,1828],{},[1761,43318,1920],{"stretchy":1821},[1761,43320,1885],{},[898,43322,1655],{},[1761,43324,1834],{"separator":1833},[902,43326,43327],{"encoding":904},"P = D_1(Q) = D(Q) - T,",[724,43329,43330,43331,1741],{},"tj. dojde k ",[38,43332,43333],{},"posunu poptávky doleva",[724,43335,43336],{},[614,43337,43338,43339,43360,43361,1343,43378,1343,43391,43412,43413,2068,43430,1741],{},"Obrázek 2.8: Dvě klesající poptávkové přímky v ",[883,43340,43342],{"className":43341},[886],[888,43343,43344],{"xmlns":890},[892,43345,43346,43358],{},[895,43347,43348,43350,43352,43354,43356],{},[1761,43349,1915],{"stretchy":1821},[898,43351,1828],{},[1761,43353,1834],{"separator":1833},[898,43355,1839],{},[1761,43357,1920],{"stretchy":1821},[902,43359,4058],{"encoding":904},"; na svislé ose jsou vyznačeny ",[883,43362,43364],{"className":43363},[886],[888,43365,43366],{"xmlns":890},[892,43367,43368,43376],{},[895,43369,43370],{},[1681,43371,43372,43374],{},[898,43373,1839],{},[1765,43375,1767],{},[902,43377,42970],{"encoding":904},[883,43379,43381],{"className":43380},[886],[888,43382,43383],{"xmlns":890},[892,43384,43385,43389],{},[895,43386,43387],{},[898,43388,1655],{},[902,43390,1655],{"encoding":904},[883,43392,43394],{"className":43393},[886],[888,43395,43396],{"xmlns":890},[892,43397,43398,43410],{},[895,43399,43400,43406,43408],{},[1681,43401,43402,43404],{},[898,43403,1839],{},[1765,43405,1767],{},[1761,43407,1964],{},[898,43409,1655],{},[902,43411,43282],{"encoding":904},"; na vodorovné ",[883,43414,43416],{"className":43415},[886],[888,43417,43418],{"xmlns":890},[892,43419,43420,43428],{},[895,43421,43422],{},[1681,43423,43424,43426],{},[898,43425,1828],{},[1765,43427,1945],{},[902,43429,33032],{"encoding":904},[883,43431,43433],{"className":43432},[886],[888,43434,43435],{"xmlns":890},[892,43436,43437,43445],{},[895,43438,43439],{},[1681,43440,43441,43443],{},[898,43442,1828],{},[1765,43444,1767],{},[902,43446,42331],{"encoding":904},[198,43448,43450],{"id":43449},"vícekomoditní-dvoukomoditní-trh","Vícekomoditní (dvoukomoditní) trh",[724,43452,43453],{},"Uvažujme dvě tržně závislá zboží s lineárními funkcemi poptávky:",[883,43455,43457],{"className":43456},[886],[888,43458,43459],{"xmlns":890,"display":1930},[892,43460,43461,43646],{},[24787,43462,43463],{"width":32101},[24792,43464,43465,43467,43639,43641],{},[24795,43466],{"width":32106},[24795,43468,43469],{},[24787,43470,43471,43555],{"rowspacing":24789,"columnalign":24790,"columnspacing":6458},[24792,43472,43473,43483],{},[24795,43474,43475],{},[6411,43476,43477],{"scriptlevel":1767,"displaystyle":1833},[1681,43478,43479,43481],{},[898,43480,1828],{},[1765,43482,1945],{},[24795,43484,43485],{},[6411,43486,43487],{"scriptlevel":1767,"displaystyle":1833},[895,43488,43489,43491,43493,43499,43501,43507,43509,43515,43517,43519,43525,43527,43533,43539,43541,43547,43553],{},[895,43490],{},[1761,43492,1909],{},[1681,43494,43495,43497],{},[898,43496,2244],{},[1765,43498,1945],{},[1761,43500,1915],{"stretchy":1821},[1681,43502,43503,43505],{},[898,43504,1839],{},[1765,43506,1945],{},[1761,43508,1834],{"separator":1833},[1681,43510,43511,43513],{},[898,43512,1839],{},[1765,43514,2296],{},[1761,43516,1920],{"stretchy":1821},[1761,43518,1909],{},[1681,43520,43521,43523],{},[898,43522,207],{},[1765,43524,1945],{},[1761,43526,1964],{},[1681,43528,43529,43531],{},[898,43530,4302],{},[1765,43532,1945],{},[1681,43534,43535,43537],{},[898,43536,1839],{},[1765,43538,1945],{},[1761,43540,1964],{},[1681,43542,43543,43545],{},[898,43544,2774],{},[1765,43546,1945],{},[1681,43548,43549,43551],{},[898,43550,1839],{},[1765,43552,2296],{},[1761,43554,1834],{"separator":1833},[24792,43556,43557,43567],{},[24795,43558,43559],{},[6411,43560,43561],{"scriptlevel":1767,"displaystyle":1833},[1681,43562,43563,43565],{},[898,43564,1828],{},[1765,43566,2296],{},[24795,43568,43569],{},[6411,43570,43571],{"scriptlevel":1767,"displaystyle":1833},[895,43572,43573,43575,43577,43583,43585,43591,43593,43599,43601,43603,43609,43611,43617,43623,43625,43631,43637],{},[895,43574],{},[1761,43576,1909],{},[1681,43578,43579,43581],{},[898,43580,2244],{},[1765,43582,2296],{},[1761,43584,1915],{"stretchy":1821},[1681,43586,43587,43589],{},[898,43588,1839],{},[1765,43590,1945],{},[1761,43592,1834],{"separator":1833},[1681,43594,43595,43597],{},[898,43596,1839],{},[1765,43598,2296],{},[1761,43600,1920],{"stretchy":1821},[1761,43602,1909],{},[1681,43604,43605,43607],{},[898,43606,207],{},[1765,43608,2296],{},[1761,43610,1964],{},[1681,43612,43613,43615],{},[898,43614,4302],{},[1765,43616,2296],{},[1681,43618,43619,43621],{},[898,43620,1839],{},[1765,43622,1945],{},[1761,43624,1964],{},[1681,43626,43627,43629],{},[898,43628,2774],{},[1765,43630,2296],{},[1681,43632,43633,43635],{},[898,43634,1839],{},[1765,43636,2296],{},[898,43638,1741],{"mathvariant":1969},[24795,43640],{"width":32106},[24795,43642,43643],{},[2761,43644,43645],{},"(2.6)",[902,43647,43648],{"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}",[41374,43650,43652],{"id":43651},"znaménková-analýza-parametrů","Znaménková analýza parametrů",[120,43654,43655,43702,43749],{},[123,43656,43657,1343,43679,43701],{},[883,43658,43660],{"className":43659},[886],[888,43661,43662],{"xmlns":890},[892,43663,43664,43676],{},[895,43665,43666,43672,43674],{},[1681,43667,43668,43670],{},[898,43669,207],{},[1765,43671,1945],{},[1761,43673,1763],{},[1765,43675,1767],{},[902,43677,43678],{"encoding":904},"a_1 > 0",[883,43680,43682],{"className":43681},[886],[888,43683,43684],{"xmlns":890},[892,43685,43686,43698],{},[895,43687,43688,43694,43696],{},[1681,43689,43690,43692],{},[898,43691,207],{},[1765,43693,2296],{},[1761,43695,1763],{},[1765,43697,1767],{},[902,43699,43700],{"encoding":904},"a_2 > 0"," (při nulových cenách je poptávané množství kladné),",[123,43703,43704,1343,43726,43748],{},[883,43705,43707],{"className":43706},[886],[888,43708,43709],{"xmlns":890},[892,43710,43711,43723],{},[895,43712,43713,43719,43721],{},[1681,43714,43715,43717],{},[898,43716,4302],{},[1765,43718,1945],{},[1761,43720,2058],{},[1765,43722,1767],{},[902,43724,43725],{"encoding":904},"b_1 \u003C 0",[883,43727,43729],{"className":43728},[886],[888,43730,43731],{"xmlns":890},[892,43732,43733,43745],{},[895,43734,43735,43741,43743],{},[1681,43736,43737,43739],{},[898,43738,2774],{},[1765,43740,2296],{},[1761,43742,2058],{},[1765,43744,1767],{},[902,43746,43747],{"encoding":904},"c_2 \u003C 0"," (vlastní koeficienty — zákon klesající poptávky),",[123,43750,43751,43752,1343,43769,43787,43788],{},"zkřížené koeficienty ",[883,43753,43755],{"className":43754},[886],[888,43756,43757],{"xmlns":890},[892,43758,43759,43767],{},[895,43760,43761],{},[1681,43762,43763,43765],{},[898,43764,2774],{},[1765,43766,1945],{},[902,43768,33829],{"encoding":904},[883,43770,43772],{"className":43771},[886],[888,43773,43774],{"xmlns":890},[892,43775,43776,43784],{},[895,43777,43778],{},[1681,43779,43780,43782],{},[898,43781,4302],{},[1765,43783,2296],{},[902,43785,43786],{"encoding":904},"b_2"," určují povahu vztahu:\n",[120,43789,43790,43840],{},[123,43791,43792,43795,43796,1343,43818,1834],{},[38,43793,43794],{},"substituty"," (máslo vs. margarín): ",[883,43797,43799],{"className":43798},[886],[888,43800,43801],{"xmlns":890},[892,43802,43803,43815],{},[895,43804,43805,43811,43813],{},[1681,43806,43807,43809],{},[898,43808,2774],{},[1765,43810,1945],{},[1761,43812,1763],{},[1765,43814,1767],{},[902,43816,43817],{"encoding":904},"c_1 > 0",[883,43819,43821],{"className":43820},[886],[888,43822,43823],{"xmlns":890},[892,43824,43825,43837],{},[895,43826,43827,43833,43835],{},[1681,43828,43829,43831],{},[898,43830,4302],{},[1765,43832,2296],{},[1761,43834,1763],{},[1765,43836,1767],{},[902,43838,43839],{"encoding":904},"b_2 > 0",[123,43841,43842,43845,43846,1343,43868,1741],{},[38,43843,43844],{},"komplementy"," (auto vs. benzín): ",[883,43847,43849],{"className":43848},[886],[888,43850,43851],{"xmlns":890},[892,43852,43853,43865],{},[895,43854,43855,43861,43863],{},[1681,43856,43857,43859],{},[898,43858,2774],{},[1765,43860,1945],{},[1761,43862,2058],{},[1765,43864,1767],{},[902,43866,43867],{"encoding":904},"c_1 \u003C 0",[883,43869,43871],{"className":43870},[886],[888,43872,43873],{"xmlns":890},[892,43874,43875,43887],{},[895,43876,43877,43883,43885],{},[1681,43878,43879,43881],{},[898,43880,4302],{},[1765,43882,2296],{},[1761,43884,2058],{},[1765,43886,1767],{},[902,43888,43889],{"encoding":904},"b_2 \u003C 0",[724,43891,43892],{},"Schematicky:",[724,43894,43895,43898],{},[38,43896,43897],{},"Substituty",[883,43899,43901],{"className":43900},[886],[888,43902,43903],{"xmlns":890},[892,43904,43905,44044],{},[895,43906,43907,43913,43915,43930,43932,43952,43954,43974,43976,43978,43984,43986,44000,44002,44022,44024],{},[1681,43908,43909,43911],{},[898,43910,1828],{},[1765,43912,1945],{},[1761,43914,1909],{},[898,43916,43917],{},[43918,43919,43920,43928],"munder",{},[1761,43921,43922],{},[1681,43923,43924,43926],{},[898,43925,207],{},[1765,43927,1945],{},[1761,43929,1964],{"lspace":6458,"rspace":6458},[1761,43931,1964],{},[898,43933,43934],{},[43918,43935,43936,43950],{},[1761,43937,43938,43944],{},[1681,43939,43940,43942],{},[898,43941,4302],{},[1765,43943,1945],{},[1681,43945,43946,43948],{},[898,43947,1839],{},[1765,43949,1945],{},[1761,43951,1885],{"lspace":6458,"rspace":6458},[1761,43953,1964],{},[898,43955,43956],{},[43918,43957,43958,43972],{},[1761,43959,43960,43966],{},[1681,43961,43962,43964],{},[898,43963,2774],{},[1765,43965,1945],{},[1681,43967,43968,43970],{},[898,43969,1839],{},[1765,43971,2296],{},[1761,43973,1964],{"lspace":6458,"rspace":6458},[1761,43975,1834],{"separator":1833},[3315,43977],{"width":3317},[1681,43979,43980,43982],{},[898,43981,1828],{},[1765,43983,2296],{},[1761,43985,1909],{},[898,43987,43988],{},[43918,43989,43990,43998],{},[1761,43991,43992],{},[1681,43993,43994,43996],{},[898,43995,207],{},[1765,43997,2296],{},[1761,43999,1964],{"lspace":6458,"rspace":6458},[1761,44001,1964],{},[898,44003,44004],{},[43918,44005,44006,44020],{},[1761,44007,44008,44014],{},[1681,44009,44010,44012],{},[898,44011,4302],{},[1765,44013,2296],{},[1681,44015,44016,44018],{},[898,44017,1839],{},[1765,44019,1945],{},[1761,44021,1964],{"lspace":6458,"rspace":6458},[1761,44023,1964],{},[898,44025,44026],{},[43918,44027,44028,44042],{},[1761,44029,44030,44036],{},[1681,44031,44032,44034],{},[898,44033,2774],{},[1765,44035,2296],{},[1681,44037,44038,44040],{},[898,44039,1839],{},[1765,44041,2296],{},[1761,44043,1885],{"lspace":6458,"rspace":6458},[902,44045,44046],{"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}",[724,44048,44049,44052],{},[38,44050,44051],{},"Komplementy",[883,44053,44055],{"className":44054},[886],[888,44056,44057],{"xmlns":890},[892,44058,44059,44197],{},[895,44060,44061,44067,44069,44083,44085,44105,44107,44127,44129,44131,44137,44139,44153,44155,44175,44177],{},[1681,44062,44063,44065],{},[898,44064,1828],{},[1765,44066,1945],{},[1761,44068,1909],{},[898,44070,44071],{},[43918,44072,44073,44081],{},[1761,44074,44075],{},[1681,44076,44077,44079],{},[898,44078,207],{},[1765,44080,1945],{},[1761,44082,1964],{"lspace":6458,"rspace":6458},[1761,44084,1964],{},[898,44086,44087],{},[43918,44088,44089,44103],{},[1761,44090,44091,44097],{},[1681,44092,44093,44095],{},[898,44094,4302],{},[1765,44096,1945],{},[1681,44098,44099,44101],{},[898,44100,1839],{},[1765,44102,1945],{},[1761,44104,1885],{"lspace":6458,"rspace":6458},[1761,44106,1964],{},[898,44108,44109],{},[43918,44110,44111,44125],{},[1761,44112,44113,44119],{},[1681,44114,44115,44117],{},[898,44116,2774],{},[1765,44118,1945],{},[1681,44120,44121,44123],{},[898,44122,1839],{},[1765,44124,2296],{},[1761,44126,1885],{"lspace":6458,"rspace":6458},[1761,44128,1834],{"separator":1833},[3315,44130],{"width":3317},[1681,44132,44133,44135],{},[898,44134,1828],{},[1765,44136,2296],{},[1761,44138,1909],{},[898,44140,44141],{},[43918,44142,44143,44151],{},[1761,44144,44145],{},[1681,44146,44147,44149],{},[898,44148,207],{},[1765,44150,2296],{},[1761,44152,1964],{"lspace":6458,"rspace":6458},[1761,44154,1964],{},[898,44156,44157],{},[43918,44158,44159,44173],{},[1761,44160,44161,44167],{},[1681,44162,44163,44165],{},[898,44164,4302],{},[1765,44166,2296],{},[1681,44168,44169,44171],{},[898,44170,1839],{},[1765,44172,1945],{},[1761,44174,1885],{"lspace":6458,"rspace":6458},[1761,44176,1964],{},[898,44178,44179],{},[43918,44180,44181,44195],{},[1761,44182,44183,44189],{},[1681,44184,44185,44187],{},[898,44186,2774],{},[1765,44188,2296],{},[1681,44190,44191,44193],{},[898,44192,1839],{},[1765,44194,2296],{},[1761,44196,1885],{"lspace":6458,"rspace":6458},[902,44198,44199],{"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}",[1849,44201],{},[115,44203,17163],{"id":40807},[1636,44205,44206],{},[724,44207,44208,44210,44211,41021,44224,41035,44237,44240,44241,2232,44264,44281],{},[883,44209,1642],{}," TL;DR\nNabídka vyjadřuje závislost nabízeného množství ",[883,44212,44214],{"className":44213},[886],[888,44215,44216],{"xmlns":890},[892,44217,44218,44222],{},[895,44219,44220],{},[898,44221,1828],{},[902,44223,1828],{"encoding":904},[883,44225,44227],{"className":44226},[886],[888,44228,44229],{"xmlns":890},[892,44230,44231,44235],{},[895,44232,44233],{},[898,44234,1839],{},[902,44236,1839],{"encoding":904},[38,44238,44239],{},"zákon rostoucí nabídky",": při vyšší ceně je výrobce ochoten nabídnout více. Lineární model ",[883,44242,44244],{"className":44243},[886],[888,44245,44246],{"xmlns":890},[892,44247,44248,44262],{},[895,44249,44250,44252,44254,44256,44258,44260],{},[898,44251,1839],{},[1761,44253,1909],{},[898,44255,2774],{},[898,44257,1828],{},[1761,44259,1964],{},[898,44261,4346],{},[902,44263,4349],{"encoding":904},[883,44265,44267],{"className":44266},[886],[888,44268,44269],{"xmlns":890},[892,44270,44271,44279],{},[895,44272,44273,44275,44277],{},[898,44274,2774],{},[1761,44276,1763],{},[1765,44278,1767],{},[902,44280,4367],{"encoding":904}," je standardní aproximací.",[198,44283,41090],{"id":44284},"obecný-vícefaktorový-model-1",[724,44286,44287,3927,44290,44293,44294,44307,44308,40924,44321,40938,44334,44347,44348,44362,44363,40967,44376,44389],{},[38,44288,44289],{},"Nabízené množství",[614,44291,44292],{},"quantity supplied",") závisí na ceně ",[883,44295,44297],{"className":44296},[886],[888,44298,44299],{"xmlns":890},[892,44300,44301,44305],{},[895,44302,44303],{},[898,44304,1839],{},[902,44306,1839],{"encoding":904},", cenách výrobních faktorů (práce ",[883,44309,44311],{"className":44310},[886],[888,44312,44313],{"xmlns":890},[892,44314,44315,44319],{},[895,44316,44317],{},[898,44318,13835],{},[902,44320,13835],{"encoding":904},[883,44322,44324],{"className":44323},[886],[888,44325,44326],{"xmlns":890},[892,44327,44328,44332],{},[895,44329,44330],{},[898,44331,2768],{},[902,44333,2768],{"encoding":904},[883,44335,44337],{"className":44336},[886],[888,44338,44339],{"xmlns":890},[892,44340,44341,44345],{},[895,44342,44343],{},[898,44344,1818],{},[902,44346,1818],{"encoding":904},"), očekávání ",[883,44349,44351],{"className":44350},[886],[888,44352,44353],{"xmlns":890},[892,44354,44355,44360],{},[895,44356,44357],{},[898,44358,44359],{},"V",[902,44361,44359],{"encoding":904},", počtu výrobců ",[883,44364,44366],{"className":44365},[886],[888,44367,44368],{"xmlns":890},[892,44369,44370,44374],{},[895,44371,44372],{},[898,44373,40964],{},[902,44375,40964],{"encoding":904},[883,44377,44379],{"className":44378},[886],[888,44380,44381],{"xmlns":890},[892,44382,44383,44387],{},[895,44384,44385],{},[898,44386,40979],{},[902,44388,40979],{"encoding":904}," a dalších:",[883,44391,44393],{"className":44392},[886],[888,44394,44395],{"xmlns":890,"display":1930},[892,44396,44397,44456],{},[24787,44398,44399],{"width":32101},[24792,44400,44401,44403,44449,44451],{},[24795,44402],{"width":32106},[24795,44404,44405],{},[895,44406,44407,44409,44411,44413,44415,44417,44419,44421,44423,44425,44427,44429,44431,44433,44435,44437,44439,44441,44443,44445,44447],{},[898,44408,1828],{},[1761,44410,1909],{},[898,44412,1912],{},[1761,44414,1915],{"stretchy":1821},[898,44416,1839],{},[1761,44418,1834],{"separator":1833},[898,44420,13835],{},[1761,44422,1834],{"separator":1833},[898,44424,2768],{},[1761,44426,1834],{"separator":1833},[898,44428,1818],{},[1761,44430,1834],{"separator":1833},[898,44432,44359],{},[1761,44434,1834],{"separator":1833},[898,44436,40964],{},[1761,44438,1834],{"separator":1833},[898,44440,40979],{},[1761,44442,1834],{"separator":1833},[1761,44444,13686],{},[1761,44446,1920],{"stretchy":1821},[898,44448,1741],{"mathvariant":1969},[24795,44450],{"width":32106},[24795,44452,44453],{},[2761,44454,44455],{},"(2.7)",[902,44457,44458],{"encoding":904},"Q = S(P, L, K, E, V, O, W, \\ldots). \\tag{2.7}",[724,44460,42438,44461,3927,44464,44467],{},[38,44462,44463],{},"funkce nabídky",[614,44465,44466],{},"supply function",") v širším slova smyslu.",[198,44469,44471],{"id":44470},"jednofaktorový-model","Jednofaktorový model",[724,44473,44474],{},"V nejpřirozenějším jednofaktorovém modelu",[883,44476,44478],{"className":44477},[886],[888,44479,44480],{"xmlns":890,"display":1930},[892,44481,44482,44533],{},[24787,44483,44484],{"width":32101},[24792,44485,44486,44488,44526,44528],{},[24795,44487],{"width":32106},[24795,44489,44490],{},[895,44491,44492,44494,44496,44498,44500,44502,44504,44506,44508,44510,44512,44514,44516,44518,44520,44522,44524],{},[898,44493,1828],{},[1761,44495,1909],{},[898,44497,1912],{},[1761,44499,1915],{"stretchy":1821},[898,44501,1839],{},[1761,44503,1920],{"stretchy":1821},[1761,44505,1834],{"separator":1833},[3315,44507],{"width":3317},[2761,44509,41443],{},[3315,44511],{"width":3317},[898,44513,1839],{},[1761,44515,1909],{},[898,44517,1912],{},[1761,44519,1915],{"stretchy":1821},[898,44521,1828],{},[1761,44523,1920],{"stretchy":1821},[898,44525,1741],{"mathvariant":1969},[24795,44527],{"width":32106},[24795,44529,44530],{},[2761,44531,44532],{},"(2.8)",[902,44534,44535],{"encoding":904},"Q = S(P), \\qquad \\text{resp.} \\qquad P = S(Q). \\tag{2.8}",[724,44537,44538,44539,3927,44542,2162],{},"Graf je ",[38,44540,44541],{},"křivka nabídky",[614,44543,44544],{},"supply curve",[41374,44546,44548],{"id":44547},"zákon-rostoucí-nabídky","Zákon rostoucí nabídky",[1636,44550,44551],{},[724,44552,44553],{},[38,44554,41489,44555,44568,44569,41544],{},[883,44556,44558],{"className":44557},[886],[888,44559,44560],{"xmlns":890},[892,44561,44562,44566],{},[895,44563,44564],{},[898,44565,1839],{},[902,44567,1839],{"encoding":904},", pak nabízené množství ",[883,44570,44572],{"className":44571},[886],[888,44573,44574],{"xmlns":890},[892,44575,44576,44580],{},[895,44577,44578],{},[898,44579,1828],{},[902,44581,1828],{"encoding":904},[724,44583,44584,44585,44610,44611,44641,44642,44659],{},"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 ",[883,44586,44588],{"className":44587},[886],[888,44589,44590],{"xmlns":890},[892,44591,44592,44608],{},[895,44593,44594,44596,44598,44600,44606],{},[1761,44595,1822],{"stretchy":1821},[1765,44597,1767],{},[1761,44599,1834],{"separator":1833},[1681,44601,44602,44604],{},[898,44603,1839],{},[1765,44605,1767],{},[1761,44607,1844],{"stretchy":1821},[902,44609,41629],{"encoding":904}," na svislé ose (případně z ",[883,44612,44614],{"className":44613},[886],[888,44615,44616],{"xmlns":890},[892,44617,44618,44638],{},[895,44619,44620,44622,44628,44630,44636],{},[1761,44621,1822],{"stretchy":1821},[1681,44623,44624,44626],{},[898,44625,1828],{},[1765,44627,1945],{},[1761,44629,1834],{"separator":1833},[1681,44631,44632,44634],{},[898,44633,1839],{},[1765,44635,1945],{},[1761,44637,1844],{"stretchy":1821},[902,44639,44640],{"encoding":904},"[Q_1, P_1]","), kde ",[883,44643,44645],{"className":44644},[886],[888,44646,44647],{"xmlns":890},[892,44648,44649,44657],{},[895,44650,44651],{},[1681,44652,44653,44655],{},[898,44654,1839],{},[1765,44656,1767],{},[902,44658,42970],{"encoding":904}," je minimální cena, při které je výrobce ochoten vyrábět.",[724,44661,44662],{},[614,44663,44664,44665,7782,44678,1741],{},"Obrázek 2.9: Typická rostoucí křivka nabídky ",[883,44666,44668],{"className":44667},[886],[888,44669,44670],{"xmlns":890},[892,44671,44672,44676],{},[895,44673,44674],{},[898,44675,1912],{},[902,44677,1912],{"encoding":904},[883,44679,44681],{"className":44680},[886],[888,44682,44683],{"xmlns":890},[892,44684,44685,44697],{},[895,44686,44687,44689,44691,44693,44695],{},[1761,44688,1915],{"stretchy":1821},[898,44690,1828],{},[1761,44692,1834],{"separator":1833},[898,44694,1839],{},[1761,44696,1920],{"stretchy":1821},[902,44698,4058],{"encoding":904},[41374,44700,44702],{"id":44701},"lineární-model-nabídky","Lineární model nabídky",[883,44704,44706],{"className":44705},[886],[888,44707,44708],{"xmlns":890,"display":1930},[892,44709,44710,44749],{},[24787,44711,44712],{"width":32101},[24792,44713,44714,44716,44742,44744],{},[24795,44715],{"width":32106},[24795,44717,44718],{},[895,44719,44720,44722,44724,44726,44728,44730,44732,44734,44736,44738,44740],{},[898,44721,1839],{},[1761,44723,1909],{},[898,44725,2774],{},[898,44727,1828],{},[1761,44729,1964],{},[898,44731,4346],{},[1761,44733,1834],{"separator":1833},[3315,44735],{"width":3317},[898,44737,2774],{},[1761,44739,1763],{},[1765,44741,16498],{},[24795,44743],{"width":32106},[24795,44745,44746],{},[2761,44747,44748],{},"(2.9)",[902,44750,44751],{"encoding":904},"P = cQ + d, \\qquad c > 0. \\tag{2.9}",[724,44753,44754,44755,44791,44792,44805],{},"Alternativně ",[883,44756,44758],{"className":44757},[886],[888,44759,44760],{"xmlns":890},[892,44761,44762,44788],{},[895,44763,44764,44766,44768,44776,44778,44780],{},[898,44765,1828],{},[1761,44767,1909],{},[6411,44769,44770],{"scriptlevel":1767,"displaystyle":1821},[4379,44771,44772,44774],{},[1765,44773,1945],{},[898,44775,2774],{},[898,44777,1839],{},[1761,44779,1885],{},[6411,44781,44782],{"scriptlevel":1767,"displaystyle":1821},[4379,44783,44784,44786],{},[898,44785,4346],{},[898,44787,2774],{},[902,44789,44790],{"encoding":904},"Q = \\tfrac{1}{c}P - \\tfrac{d}{c}","; znaménko koeficientu u ",[883,44793,44795],{"className":44794},[886],[888,44796,44797],{"xmlns":890},[892,44798,44799,44803],{},[895,44800,44801],{},[898,44802,1839],{},[902,44804,1839],{"encoding":904}," zůstává, znaménko absolutního členu se mění.",[41950,44807,44809],{"id":44808},"příklad-25","Příklad 2.5",[724,44811,44812,44814,44815,1741],{},[38,44813,2274],{}," Lineární nabídka ",[883,44816,44818],{"className":44817},[886],[888,44819,44820],{"xmlns":890},[892,44821,44822,44836],{},[895,44823,44824,44826,44828,44830,44832,44834],{},[898,44825,1839],{},[1761,44827,1909],{},[1765,44829,5426],{},[898,44831,1828],{},[1761,44833,1964],{},[1765,44835,9056],{},[902,44837,44838],{"encoding":904},"P = 0{,}5Q + 25",[724,44840,44841,44843,44844,1741],{},[38,44842,2349],{}," Alternativní tvar ",[883,44845,44847],{"className":44846},[886],[888,44848,44849],{"xmlns":890},[892,44850,44851,44865],{},[895,44852,44853,44855,44857,44859,44861,44863],{},[898,44854,1828],{},[1761,44856,1909],{},[1765,44858,2296],{},[898,44860,1839],{},[1761,44862,1885],{},[1765,44864,7190],{},[902,44866,44867],{"encoding":904},"Q = 2P - 50",[16,44869,44870,44895],{},[19,44871,44872],{},[22,44873,44874,44889,44891,44893],{},[25,44875,44876],{},[883,44877,44879],{"className":44878},[886],[888,44880,44881],{"xmlns":890},[892,44882,44883,44887],{},[895,44884,44885],{},[898,44886,1839],{},[902,44888,1839],{"encoding":904},[25,44890,42042],{},[25,44892,19076],{},[25,44894,9262],{},[30,44896,44897],{},[22,44898,44899,44914,44916,44918],{},[35,44900,44901],{},[883,44902,44904],{"className":44903},[886],[888,44905,44906],{"xmlns":890},[892,44907,44908,44912],{},[895,44909,44910],{},[898,44911,1828],{},[902,44913,1828],{"encoding":904},[35,44915,2633],{},[35,44917,13077],{},[35,44919,42042],{},[198,44921,44923,44924,1920],{"id":44922},"posun-nabídky-shift-of-supply","Posun nabídky (",[614,44925,44926],{},"shift of supply",[724,44928,44929,44930,44933,44934,44951,44952,44977,44978,1741],{},"Posun nastává při změně exogenních proměnných — nová technologie snižuje náklady (posun ",[38,44931,44932],{},"doprava",": při stejné ceně ",[883,44935,44937],{"className":44936},[886],[888,44938,44939],{"xmlns":890},[892,44940,44941,44949],{},[895,44942,44943],{},[1681,44944,44945,44947],{},[898,44946,1839],{},[1765,44948,1767],{},[902,44950,42970],{"encoding":904}," vyrobí výrobce větší ",[883,44953,44955],{"className":44954},[886],[888,44956,44957],{"xmlns":890},[892,44958,44959,44975],{},[895,44960,44961,44967,44969],{},[1681,44962,44963,44965],{},[898,44964,1828],{},[1765,44966,1945],{},[1761,44968,1763],{},[1681,44970,44971,44973],{},[898,44972,1828],{},[1765,44974,1767],{},[902,44976,43083],{"encoding":904},"); zdražení vstupů posune křivku ",[38,44979,44980],{},"doleva",[724,44982,44983],{},[614,44984,44985,44986,44999,45000,45017,45018,45036,45037,1741],{},"Obrázek 2.11: Původní ",[883,44987,44989],{"className":44988},[886],[888,44990,44991],{"xmlns":890},[892,44992,44993,44997],{},[895,44994,44995],{},[898,44996,1912],{},[902,44998,1912],{"encoding":904},", posunuté ",[883,45001,45003],{"className":45002},[886],[888,45004,45005],{"xmlns":890},[892,45006,45007,45015],{},[895,45008,45009],{},[1681,45010,45011,45013],{},[898,45012,1912],{},[1765,45014,1945],{},[902,45016,2231],{"encoding":904}," (doprava) a ",[883,45019,45021],{"className":45020},[886],[888,45022,45023],{"xmlns":890},[892,45024,45025,45033],{},[895,45026,45027],{},[1681,45028,45029,45031],{},[898,45030,1912],{},[1765,45032,2296],{},[902,45034,45035],{"encoding":904},"S_2"," (doleva) v ",[883,45038,45040],{"className":45039},[886],[888,45041,45042],{"xmlns":890},[892,45043,45044,45056],{},[895,45045,45046,45048,45050,45052,45054],{},[1761,45047,1915],{"stretchy":1821},[898,45049,1828],{},[1761,45051,1834],{"separator":1833},[898,45053,1839],{},[1761,45055,1920],{"stretchy":1821},[902,45057,4058],{"encoding":904},[41950,45059,45061],{"id":45060},"příklad-26-zdanění-výrobce","Příklad 2.6 — zdanění výrobce",[724,45063,45064,45066,45067,45091,45092,1741],{},[38,45065,2274],{}," Nabídka ",[883,45068,45070],{"className":45069},[886],[888,45071,45072],{"xmlns":890},[892,45073,45074,45088],{},[895,45075,45076,45078,45080,45082,45084,45086],{},[898,45077,1839],{},[1761,45079,1909],{},[898,45081,1912],{},[1761,45083,1915],{"stretchy":1821},[898,45085,1828],{},[1761,45087,1920],{"stretchy":1821},[902,45089,45090],{"encoding":904},"P = S(Q)","; na výrobce je uložena jednotková daň ",[883,45093,45095],{"className":45094},[886],[888,45096,45097],{"xmlns":890},[892,45098,45099,45103],{},[895,45100,45101],{},[898,45102,1655],{},[902,45104,1655],{"encoding":904},[724,45106,45107,45109,45110,45123,45124,45141,45142,45169],{},[38,45108,2349],{}," Spotřebitel zaplatí ",[883,45111,45113],{"className":45112},[886],[888,45114,45115],{"xmlns":890},[892,45116,45117,45121],{},[895,45118,45119],{},[898,45120,1839],{},[902,45122,1839],{"encoding":904},", výrobce obdrží ",[883,45125,45127],{"className":45126},[886],[888,45128,45129],{"xmlns":890},[892,45130,45131,45139],{},[895,45132,45133,45135,45137],{},[898,45134,1839],{},[1761,45136,1885],{},[898,45138,1655],{},[902,45140,1890],{"encoding":904},". Z podmínky ",[883,45143,45145],{"className":45144},[886],[888,45146,45147],{"xmlns":890},[892,45148,45149,45167],{},[895,45150,45151,45153,45155,45157,45159,45161,45163,45165],{},[898,45152,1839],{},[1761,45154,1885],{},[898,45156,1655],{},[1761,45158,1909],{},[898,45160,1912],{},[1761,45162,1915],{"stretchy":1821},[898,45164,1828],{},[1761,45166,1920],{"stretchy":1821},[902,45168,1923],{"encoding":904}," plyne",[883,45171,45173],{"className":45172},[886],[888,45174,45175],{"xmlns":890,"display":1930},[892,45176,45177,45211],{},[895,45178,45179,45181,45183,45189,45191,45193,45195,45197,45199,45201,45203,45205,45207,45209],{},[898,45180,1839],{},[1761,45182,1909],{},[1681,45184,45185,45187],{},[898,45186,1912],{},[1765,45188,1945],{},[1761,45190,1915],{"stretchy":1821},[898,45192,1828],{},[1761,45194,1920],{"stretchy":1821},[1761,45196,1909],{},[898,45198,1912],{},[1761,45200,1915],{"stretchy":1821},[898,45202,1828],{},[1761,45204,1920],{"stretchy":1821},[1761,45206,1964],{},[898,45208,1655],{},[898,45210,1741],{"mathvariant":1969},[902,45212,1972],{"encoding":904},[724,45214,45215,45216,45229,45230,1989,45243,45245,45246,2068,45266,12146,45283,1741],{},"Křivka ",[883,45217,45219],{"className":45218},[886],[888,45220,45221],{"xmlns":890},[892,45222,45223,45227],{},[895,45224,45225],{},[898,45226,1912],{},[902,45228,1912],{"encoding":904}," se tedy posune o ",[883,45231,45233],{"className":45232},[886],[888,45234,45235],{"xmlns":890},[892,45236,45237,45241],{},[895,45238,45239],{},[898,45240,1655],{},[902,45242,1655],{"encoding":904},[38,45244,1992],{}," (tj. doleva). Např. pro ",[883,45247,45249],{"className":45248},[886],[888,45250,45251],{"xmlns":890},[892,45252,45253,45263],{},[895,45254,45255,45257,45259,45261],{},[898,45256,1839],{},[1761,45258,1909],{},[1765,45260,2296],{},[898,45262,1828],{},[902,45264,45265],{"encoding":904},"P = 2Q",[883,45267,45269],{"className":45268},[886],[888,45270,45271],{"xmlns":890},[892,45272,45273,45281],{},[895,45274,45275,45277,45279],{},[898,45276,1655],{},[1761,45278,1909],{},[1765,45280,2340],{},[902,45282,2343],{"encoding":904},[883,45284,45286],{"className":45285},[886],[888,45287,45288],{"xmlns":890},[892,45289,45290,45312],{},[895,45291,45292,45298,45300,45302,45304,45306,45308,45310],{},[1681,45293,45294,45296],{},[898,45295,1912],{},[1765,45297,1945],{},[1761,45299,2506],{},[898,45301,1839],{},[1761,45303,1909],{},[1765,45305,2296],{},[898,45307,1828],{},[1761,45309,1964],{},[1765,45311,2340],{},[902,45313,45314],{"encoding":904},"S_1: P = 2Q + 6",[724,45316,45317],{},[614,45318,45319,45320,45333],{},"Obrázek 2.12: Posun nabídky o ",[883,45321,45323],{"className":45322},[886],[888,45324,45325],{"xmlns":890},[892,45326,45327,45331],{},[895,45328,45329],{},[898,45330,1655],{},[902,45332,1655],{"encoding":904}," svisle nahoru.",[1849,45335],{},[115,45337,45339],{"id":45338},"tržní-rovnováha","Tržní rovnováha",[1636,45341,45342],{},[724,45343,45344,45346,45347,1989,45350,45381,45382,1343,45405,45428,45429,45432,45433,45446],{},[883,45345,1642],{}," TL;DR\nV ",[38,45348,45349],{},"rovnovážném bodě",[883,45351,45353],{"className":45352},[886],[888,45354,45355],{"xmlns":890},[892,45356,45357,45379],{},[895,45358,45359,45361,45363,45369,45371,45377],{},[898,45360,1818],{},[1761,45362,1822],{"stretchy":1821},[1824,45364,45365,45367],{},[898,45366,1828],{},[898,45368,1818],{},[1761,45370,1834],{"separator":1833},[1824,45372,45373,45375],{},[898,45374,1839],{},[898,45376,1818],{},[1761,45378,1844],{"stretchy":1821},[902,45380,1847],{"encoding":904}," se poptávané a nabízené množství rovnají. Najde se jako řešení soustavy ",[883,45383,45385],{"className":45384},[886],[888,45386,45387],{"xmlns":890},[892,45388,45389,45403],{},[895,45390,45391,45393,45395,45397,45399,45401],{},[898,45392,1839],{},[1761,45394,1909],{},[898,45396,2244],{},[1761,45398,1915],{"stretchy":1821},[898,45400,1828],{},[1761,45402,1920],{"stretchy":1821},[902,45404,8692],{"encoding":904},[883,45406,45408],{"className":45407},[886],[888,45409,45410],{"xmlns":890},[892,45411,45412,45426],{},[895,45413,45414,45416,45418,45420,45422,45424],{},[898,45415,1839],{},[1761,45417,1909],{},[898,45419,1912],{},[1761,45421,1915],{"stretchy":1821},[898,45423,1828],{},[1761,45425,1920],{"stretchy":1821},[902,45427,45090],{"encoding":904},". Čtyři ",[38,45430,45431],{},"pravidla komparativní statiky"," popisují, jak se ",[883,45434,45436],{"className":45435},[886],[888,45437,45438],{"xmlns":890},[892,45439,45440,45444],{},[895,45441,45442],{},[898,45443,1818],{},[902,45445,1818],{"encoding":904}," posune při změně poptávky nebo nabídky.",[198,45448,45450],{"id":45449},"definice","Definice",[724,45452,45453,3927,45455,45458,45459,1989,45462,45479,45480,45511,45512,3927,45515,2162],{},[38,45454,45339],{},[614,45456,45457],{},"market equilibrium",") je stav, kdy poptávané množství = nabízené množství. Při ",[38,45460,45461],{},"rovnovážné ceně",[883,45463,45465],{"className":45464},[886],[888,45466,45467],{"xmlns":890},[892,45468,45469,45477],{},[895,45470,45471],{},[1824,45472,45473,45475],{},[898,45474,1839],{},[898,45476,1818],{},[902,45478,2161],{"encoding":904}," není přebytek ani nedostatek zboží. Bod ",[883,45481,45483],{"className":45482},[886],[888,45484,45485],{"xmlns":890},[892,45486,45487,45509],{},[895,45488,45489,45491,45493,45499,45501,45507],{},[898,45490,1818],{},[1761,45492,1822],{"stretchy":1821},[1824,45494,45495,45497],{},[898,45496,1828],{},[898,45498,1818],{},[1761,45500,1834],{"separator":1833},[1824,45502,45503,45505],{},[898,45504,1839],{},[898,45506,1818],{},[1761,45508,1844],{"stretchy":1821},[902,45510,1847],{"encoding":904}," se nazývá ",[38,45513,45514],{},"rovnovážný bod",[614,45516,45517],{},"equilibrium point",[724,45519,45520,45521,1343,45544,1741],{},"Rovnovážný bod je průsečíkem křivek poptávky a nabídky; nalézá se jako řešení soustavy ",[883,45522,45524],{"className":45523},[886],[888,45525,45526],{"xmlns":890},[892,45527,45528,45542],{},[895,45529,45530,45532,45534,45536,45538,45540],{},[898,45531,1839],{},[1761,45533,1909],{},[898,45535,2244],{},[1761,45537,1915],{"stretchy":1821},[898,45539,1828],{},[1761,45541,1920],{"stretchy":1821},[902,45543,8692],{"encoding":904},[883,45545,45547],{"className":45546},[886],[888,45548,45549],{"xmlns":890},[892,45550,45551,45565],{},[895,45552,45553,45555,45557,45559,45561,45563],{},[898,45554,1839],{},[1761,45556,1909],{},[898,45558,1912],{},[1761,45560,1915],{"stretchy":1821},[898,45562,1828],{},[1761,45564,1920],{"stretchy":1821},[902,45566,45090],{"encoding":904},[724,45568,45569],{},[3991,45570],{"alt":45571,"className":45572,"src":45573},"imek-poptavka-nabidka-rovnovaha",[210,3995],"\u002Fwiki-assets\u002Fimek-poptavka-nabidka-rovnovaha.jpeg",[724,45575,45576],{},[614,45577,45578,45579,45592,45593,18049,45606,45627,45628,1741],{},"Obrázek 2.13: Klesající ",[883,45580,45582],{"className":45581},[886],[888,45583,45584],{"xmlns":890},[892,45585,45586,45590],{},[895,45587,45588],{},[898,45589,2244],{},[902,45591,2244],{"encoding":904}," a rostoucí ",[883,45594,45596],{"className":45595},[886],[888,45597,45598],{"xmlns":890},[892,45599,45600,45604],{},[895,45601,45602],{},[898,45603,1912],{},[902,45605,1912],{"encoding":904},[883,45607,45609],{"className":45608},[886],[888,45610,45611],{"xmlns":890},[892,45612,45613,45625],{},[895,45614,45615,45617,45619,45621,45623],{},[1761,45616,1915],{"stretchy":1821},[898,45618,1828],{},[1761,45620,1834],{"separator":1833},[898,45622,1839],{},[1761,45624,1920],{"stretchy":1821},[902,45626,4058],{"encoding":904}," protínající se v ",[883,45629,45631],{"className":45630},[886],[888,45632,45633],{"xmlns":890},[892,45634,45635,45657],{},[895,45636,45637,45639,45641,45647,45649,45655],{},[898,45638,1818],{},[1761,45640,1822],{"stretchy":1821},[1824,45642,45643,45645],{},[898,45644,1828],{},[898,45646,1818],{},[1761,45648,1834],{"separator":1833},[1824,45650,45651,45653],{},[898,45652,1839],{},[898,45654,1818],{},[1761,45656,1844],{"stretchy":1821},[902,45658,1847],{"encoding":904},[198,45660,45662],{"id":45661},"příklad-27-kvadratický-model","Příklad 2.7 (kvadratický model)",[724,45664,45665,2275,45667,2302,45701,1741],{},[38,45666,2274],{},[883,45668,45670],{"className":45669},[886],[888,45671,45672],{"xmlns":890},[892,45673,45674,45698],{},[895,45675,45676,45678,45680,45682,45688,45690,45692,45694,45696],{},[898,45677,1839],{},[1761,45679,1909],{},[1761,45681,1885],{},[1824,45683,45684,45686],{},[898,45685,1828],{},[1765,45687,2296],{},[1761,45689,1885],{},[1765,45691,2633],{},[898,45693,1828],{},[1761,45695,1964],{},[1765,45697,12845],{},[902,45699,45700],{"encoding":904},"P = -Q^2 - 10Q + 150",[883,45702,45704],{"className":45703},[886],[888,45705,45706],{"xmlns":890},[892,45707,45708,45730],{},[895,45709,45710,45712,45714,45720,45722,45724,45726,45728],{},[898,45711,1839],{},[1761,45713,1909],{},[1824,45715,45716,45718],{},[898,45717,1828],{},[1765,45719,2296],{},[1761,45721,1964],{},[1765,45723,26979],{},[898,45725,1828],{},[1761,45727,1964],{},[1765,45729,36576],{},[902,45731,45732],{"encoding":904},"P = Q^2 + 14Q + 22",[724,45734,45735,45737],{},[38,45736,2349],{}," Z rovnosti",[883,45739,45741],{"className":45740},[886],[888,45742,45743],{"xmlns":890,"display":1930},[892,45744,45745,45783],{},[895,45746,45747,45749,45755,45757,45759,45761,45763,45765,45767,45773,45775,45777,45779,45781],{},[1761,45748,1885],{},[1824,45750,45751,45753],{},[898,45752,1828],{},[1765,45754,2296],{},[1761,45756,1885],{},[1765,45758,2633],{},[898,45760,1828],{},[1761,45762,1964],{},[1765,45764,12845],{},[1761,45766,1909],{},[1824,45768,45769,45771],{},[898,45770,1828],{},[1765,45772,2296],{},[1761,45774,1964],{},[1765,45776,26979],{},[898,45778,1828],{},[1761,45780,1964],{},[1765,45782,36576],{},[902,45784,45785],{"encoding":904},"-Q^2 - 10Q + 150 = Q^2 + 14Q + 22",[724,45787,45788,45789,5715,45824,45857,45858,45875,45876,45889,45890,1343,45912,45949,45950,1741],{},"dostaneme ",[883,45790,45792],{"className":45791},[886],[888,45793,45794],{"xmlns":890},[892,45795,45796,45821],{},[895,45797,45798,45800,45806,45808,45811,45813,45815,45817,45819],{},[1765,45799,2296],{},[1824,45801,45802,45804],{},[898,45803,1828],{},[1765,45805,2296],{},[1761,45807,1964],{},[1765,45809,45810],{},"24",[898,45812,1828],{},[1761,45814,1885],{},[1765,45816,9665],{},[1761,45818,1909],{},[1765,45820,1767],{},[902,45822,45823],{"encoding":904},"2Q^2 + 24Q - 128 = 0",[883,45825,45827],{"className":45826},[886],[888,45828,45829],{"xmlns":890},[892,45830,45831,45854],{},[895,45832,45833,45839,45841,45843,45845,45847,45850,45852],{},[1824,45834,45835,45837],{},[898,45836,1828],{},[1765,45838,2296],{},[1761,45840,1964],{},[1765,45842,2291],{},[898,45844,1828],{},[1761,45846,1885],{},[1765,45848,45849],{},"64",[1761,45851,1909],{},[1765,45853,1767],{},[902,45855,45856],{"encoding":904},"Q^2 + 12Q - 64 = 0",". Kořeny jsou ",[883,45859,45861],{"className":45860},[886],[888,45862,45863],{"xmlns":890},[892,45864,45865,45872],{},[895,45866,45867,45869],{},[1761,45868,1885],{},[1765,45870,45871],{},"16",[902,45873,45874],{"encoding":904},"-16"," (nevyhovuje) a ",[883,45877,45879],{"className":45878},[886],[888,45880,45881],{"xmlns":890},[892,45882,45883,45887],{},[895,45884,45885],{},[1765,45886,2318],{},[902,45888,2318],{"encoding":904},". Tedy ",[883,45891,45893],{"className":45892},[886],[888,45894,45895],{"xmlns":890},[892,45896,45897,45909],{},[895,45898,45899,45905,45907],{},[1824,45900,45901,45903],{},[898,45902,1828],{},[898,45904,1818],{},[1761,45906,1909],{},[1765,45908,2318],{},[902,45910,45911],{"encoding":904},"Q^E = 4",[883,45913,45915],{"className":45914},[886],[888,45916,45917],{"xmlns":890},[892,45918,45919,45946],{},[895,45920,45921,45927,45929,45931,45933,45935,45937,45939,45941,45943],{},[1824,45922,45923,45925],{},[898,45924,1839],{},[898,45926,1818],{},[1761,45928,1909],{},[1761,45930,1885],{},[1765,45932,45871],{},[1761,45934,1885],{},[1765,45936,9262],{},[1761,45938,1964],{},[1765,45940,12845],{},[1761,45942,1909],{},[1765,45944,45945],{},"94",[902,45947,45948],{"encoding":904},"P^E = -16 - 40 + 150 = 94",", rovnovážný bod ",[883,45951,45953],{"className":45952},[886],[888,45954,45955],{"xmlns":890},[892,45956,45957,45971],{},[895,45958,45959,45961,45963,45965,45967,45969],{},[898,45960,1818],{},[1761,45962,1822],{"stretchy":1821},[1765,45964,2318],{},[1761,45966,1834],{"separator":1833},[1765,45968,45945],{},[1761,45970,1844],{"stretchy":1821},[902,45972,45973],{"encoding":904},"E[4, 94]",[198,45975,45977],{"id":45976},"příklad-28-dvoukomoditní-trh","Příklad 2.8 (dvoukomoditní trh)",[724,45979,45980,45982],{},[38,45981,2274],{}," Poptávky a nabídky dvou zboží",[883,45984,45986],{"className":45985},[886],[888,45987,45988],{"xmlns":890,"display":1930},[892,45989,45990,46156],{},[24787,45991,45994,46082],{"rowspacing":24789,"columnalign":45992,"columnspacing":45993},"right left right left","0em 1em 0em",[24792,45995,45996,46006,46038,46048],{},[24795,45997,45998],{},[6411,45999,46000],{"scriptlevel":1767,"displaystyle":1833},[1681,46001,46002,46004],{},[898,46003,1828],{},[1765,46005,1945],{},[24795,46007,46008],{},[6411,46009,46010],{"scriptlevel":1767,"displaystyle":1833},[895,46011,46012,46014,46016,46018,46020,46022,46028,46030,46036],{},[895,46013],{},[1761,46015,1909],{},[1765,46017,9262],{},[1761,46019,1885],{},[1765,46021,6321],{},[1681,46023,46024,46026],{},[898,46025,1839],{},[1765,46027,1945],{},[1761,46029,1885],{},[1681,46031,46032,46034],{},[898,46033,1839],{},[1765,46035,2296],{},[1761,46037,1834],{"separator":1833},[24795,46039,46040],{},[6411,46041,46042],{"scriptlevel":1767,"displaystyle":1833},[1681,46043,46044,46046],{},[898,46045,1828],{},[1765,46047,2296],{},[24795,46049,46050],{},[6411,46051,46052],{"scriptlevel":1767,"displaystyle":1833},[895,46053,46054,46056,46058,46060,46062,46064,46070,46072,46074,46080],{},[895,46055],{},[1761,46057,1909],{},[1765,46059,7190],{},[1761,46061,1885],{},[1765,46063,2296],{},[1681,46065,46066,46068],{},[898,46067,1839],{},[1765,46069,1945],{},[1761,46071,1885],{},[1765,46073,2318],{},[1681,46075,46076,46078],{},[898,46077,1839],{},[1765,46079,2296],{},[1761,46081,1834],{"separator":1833},[24792,46083,46084,46094,46120,46130],{},[24795,46085,46086],{},[6411,46087,46088],{"scriptlevel":1767,"displaystyle":1833},[1681,46089,46090,46092],{},[898,46091,1828],{},[1765,46093,1945],{},[24795,46095,46096],{},[6411,46097,46098],{"scriptlevel":1767,"displaystyle":1833},[895,46099,46100,46102,46104,46106,46108,46110,46112,46118],{},[895,46101],{},[1761,46103,1909],{},[1761,46105,1885],{},[1765,46107,5486],{},[1761,46109,1964],{},[1765,46111,2318],{},[1681,46113,46114,46116],{},[898,46115,1839],{},[1765,46117,1945],{},[1761,46119,1834],{"separator":1833},[24795,46121,46122],{},[6411,46123,46124],{"scriptlevel":1767,"displaystyle":1833},[1681,46125,46126,46128],{},[898,46127,1828],{},[1765,46129,2296],{},[24795,46131,46132],{},[6411,46133,46134],{"scriptlevel":1767,"displaystyle":1833},[895,46135,46136,46138,46140,46142,46144,46146,46148,46154],{},[895,46137],{},[1761,46139,1909],{},[1761,46141,1885],{},[1765,46143,5512],{},[1761,46145,1964],{},[1765,46147,5486],{},[1681,46149,46150,46152],{},[898,46151,1839],{},[1765,46153,2296],{},[898,46155,1741],{"mathvariant":1969},[902,46157,46158],{"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}",[724,46160,46161,46163],{},[38,46162,2349],{}," Z rovností poptávek a nabídek dostaneme",[883,46165,46167],{"className":46166},[886],[888,46168,46169],{"xmlns":890,"display":1930},[892,46170,46171,46220],{},[895,46172,46173,46175,46181,46183,46189,46191,46193,46195,46197,46199,46205,46207,46209,46215,46217],{},[1765,46174,8056],{},[1681,46176,46177,46179],{},[898,46178,1839],{},[1765,46180,1945],{},[1761,46182,1964],{},[1681,46184,46185,46187],{},[898,46186,1839],{},[1765,46188,2296],{},[1761,46190,1909],{},[1765,46192,25236],{},[1761,46194,1834],{"separator":1833},[3315,46196],{"width":3317},[1765,46198,2296],{},[1681,46200,46201,46203],{},[898,46202,1839],{},[1765,46204,1945],{},[1761,46206,1964],{},[1765,46208,5512],{},[1681,46210,46211,46213],{},[898,46212,1839],{},[1765,46214,2296],{},[1761,46216,1909],{},[1765,46218,46219],{},"57.",[902,46221,46222],{"encoding":904},"9P_1 + P_2 = 43, \\qquad 2P_1 + 7P_2 = 57.",[724,46224,46225,46226,1343,46250,46274,46275,1343,46300,46324,46325,46327],{},"Řešením je ",[883,46227,46229],{"className":46228},[886],[888,46230,46231],{"xmlns":890},[892,46232,46233,46247],{},[895,46234,46235,46243,46245],{},[2015,46236,46237,46239,46241],{},[898,46238,1839],{},[1765,46240,1945],{},[898,46242,1818],{},[1761,46244,1909],{},[1765,46246,2318],{},[902,46248,46249],{"encoding":904},"P_1^E = 4",[883,46251,46253],{"className":46252},[886],[888,46254,46255],{"xmlns":890},[892,46256,46257,46271],{},[895,46258,46259,46267,46269],{},[2015,46260,46261,46263,46265],{},[898,46262,1839],{},[1765,46264,2296],{},[898,46266,1818],{},[1761,46268,1909],{},[1765,46270,5512],{},[902,46272,46273],{"encoding":904},"P_2^E = 7","; zpětným dosazením ",[883,46276,46278],{"className":46277},[886],[888,46279,46280],{"xmlns":890},[892,46281,46282,46297],{},[895,46283,46284,46292,46294],{},[2015,46285,46286,46288,46290],{},[898,46287,1828],{},[1765,46289,1945],{},[898,46291,1818],{},[1761,46293,1909],{},[1765,46295,46296],{},"13",[902,46298,46299],{"encoding":904},"Q_1^E = 13",[883,46301,46303],{"className":46302},[886],[888,46304,46305],{"xmlns":890},[892,46306,46307,46321],{},[895,46308,46309,46317,46319],{},[2015,46310,46311,46313,46315],{},[898,46312,1828],{},[1765,46314,2296],{},[898,46316,1818],{},[1761,46318,1909],{},[1765,46320,26979],{},[902,46322,46323],{"encoding":904},"Q_2^E = 14",". Zboží jsou ",[38,46326,43844],{}," (zkřížené koeficienty v poptávce jsou záporné).",[198,46329,46331],{"id":46330},"dynamický-model-pavučinový-teorém","Dynamický model — pavučinový teorém",[724,46333,46334,46335,46352,46353,3927,46356,2162],{},"Rovnovážná cena se obecně liší od tržní ceny, která vzniká působením tržních sil v čase. Za podmínky stability se tržní cena přibližuje k ",[883,46336,46338],{"className":46337},[886],[888,46339,46340],{"xmlns":890},[892,46341,46342,46350],{},[895,46343,46344],{},[1824,46345,46346,46348],{},[898,46347,1839],{},[898,46349,1818],{},[902,46351,2161],{"encoding":904},"; mechanismus popisuje ",[38,46354,46355],{},"teorém pavučiny",[614,46357,46358],{},"cobweb model",[198,46360,46362],{"id":46361},"pravidla-komparativní-statiky-14","Pravidla komparativní statiky (1–4)",[724,46364,46365],{},[3991,46366],{"alt":46367,"className":46368,"src":46369},"imek-komparativni-statika-4pripady",[210,3995],"\u002Fwiki-assets\u002Fimek-komparativni-statika-4pripady.jpeg",[1636,46371,46372,46413,46453,46493],{},[724,46373,46374,46377,46378,10235,46395,1741],{},[38,46375,46376],{},"Pravidlo 1:"," Růst poptávky ⟹ růst ",[883,46379,46381],{"className":46380},[886],[888,46382,46383],{"xmlns":890},[892,46384,46385,46393],{},[895,46386,46387],{},[1824,46388,46389,46391],{},[898,46390,1839],{},[898,46392,1818],{},[902,46394,2161],{"encoding":904},[883,46396,46398],{"className":46397},[886],[888,46399,46400],{"xmlns":890},[892,46401,46402,46410],{},[895,46403,46404],{},[1824,46405,46406,46408],{},[898,46407,1828],{},[898,46409,1818],{},[902,46411,46412],{"encoding":904},"Q^E",[724,46414,46415,46418,46419,10235,46436,1741],{},[38,46416,46417],{},"Pravidlo 2:"," Pokles poptávky ⟹ pokles ",[883,46420,46422],{"className":46421},[886],[888,46423,46424],{"xmlns":890},[892,46425,46426,46434],{},[895,46427,46428],{},[1824,46429,46430,46432],{},[898,46431,1839],{},[898,46433,1818],{},[902,46435,2161],{"encoding":904},[883,46437,46439],{"className":46438},[886],[888,46440,46441],{"xmlns":890},[892,46442,46443,46451],{},[895,46444,46445],{},[1824,46446,46447,46449],{},[898,46448,1828],{},[898,46450,1818],{},[902,46452,46412],{"encoding":904},[724,46454,46455,46458,46459,13396,46476,1741],{},[38,46456,46457],{},"Pravidlo 3:"," Růst nabídky ⟹ pokles ",[883,46460,46462],{"className":46461},[886],[888,46463,46464],{"xmlns":890},[892,46465,46466,46474],{},[895,46467,46468],{},[1824,46469,46470,46472],{},[898,46471,1839],{},[898,46473,1818],{},[902,46475,2161],{"encoding":904},[883,46477,46479],{"className":46478},[886],[888,46480,46481],{"xmlns":890},[892,46482,46483,46491],{},[895,46484,46485],{},[1824,46486,46487,46489],{},[898,46488,1828],{},[898,46490,1818],{},[902,46492,46412],{"encoding":904},[724,46494,46495,46498,46499,46516,46517,1741],{},[38,46496,46497],{},"Pravidlo 4:"," Pokles nabídky ⟹ růst ",[883,46500,46502],{"className":46501},[886],[888,46503,46504],{"xmlns":890},[892,46505,46506,46514],{},[895,46507,46508],{},[1824,46509,46510,46512],{},[898,46511,1839],{},[898,46513,1818],{},[902,46515,2161],{"encoding":904},", pokles ",[883,46518,46520],{"className":46519},[886],[888,46521,46522],{"xmlns":890},[892,46523,46524,46532],{},[895,46525,46526],{},[1824,46527,46528,46530],{},[898,46529,1828],{},[898,46531,1818],{},[902,46533,46412],{"encoding":904},[16,46535,46536,46581],{},[19,46537,46538],{},[22,46539,46540,46543,46562],{},[25,46541,46542],{},"Změna",[25,46544,46545],{},[883,46546,46548],{"className":46547},[886],[888,46549,46550],{"xmlns":890},[892,46551,46552,46560],{},[895,46553,46554],{},[1824,46555,46556,46558],{},[898,46557,1839],{},[898,46559,1818],{},[902,46561,2161],{"encoding":904},[25,46563,46564],{},[883,46565,46567],{"className":46566},[886],[888,46568,46569],{"xmlns":890},[892,46570,46571,46579],{},[895,46572,46573],{},[1824,46574,46575,46577],{},[898,46576,1828],{},[898,46578,1818],{},[902,46580,46412],{"encoding":904},[30,46582,46583,46593,46603,46612],{},[22,46584,46585,46588,46591],{},[35,46586,46587],{},"Růst poptávky",[35,46589,46590],{},"↑",[35,46592,46590],{},[22,46594,46595,46598,46601],{},[35,46596,46597],{},"Pokles poptávky",[35,46599,46600],{},"↓",[35,46602,46600],{},[22,46604,46605,46608,46610],{},[35,46606,46607],{},"Růst nabídky",[35,46609,46600],{},[35,46611,46590],{},[22,46613,46614,46617,46619],{},[35,46615,46616],{},"Pokles nabídky",[35,46618,46590],{},[35,46620,46600],{},[724,46622,46623],{},[614,46624,46625],{},"Obrázky 2.15–2.18 ilustrují všechny čtyři situace pomocí posunu jedné z křivek.",[1849,46627],{},[115,46629,811],{"id":46630},"zdanění-trhu",[1636,46632,46633,46716],{},[724,46634,46635,1643,46637,46650,46651,6997,46664,46666,46667,40804,46688,46711,46712,46715],{},[883,46636,1642],{},[883,46638,46640],{"className":46639},[886],[888,46641,46642],{"xmlns":890},[892,46643,46644,46648],{},[895,46645,46646],{},[898,46647,1655],{},[902,46649,1655],{"encoding":904}," uložená na každou prodanou jednotku způsobí posun jedné z křivek o ",[883,46652,46654],{"className":46653},[886],[888,46655,46656],{"xmlns":890},[892,46657,46658,46662],{},[895,46659,46660],{},[898,46661,1655],{},[902,46663,1655],{"encoding":904},[38,46665,3922],{}," se dělí mezi spotřebitele (",[883,46668,46670],{"className":46669},[886],[888,46671,46672],{"xmlns":890},[892,46673,46674,46686],{},[895,46675,46676],{},[1681,46677,46678,46680],{},[898,46679,1655],{},[895,46681,46682,46684],{},[898,46683,1689],{},[898,46685,724],{},[902,46687,1694],{"encoding":904},[883,46689,46691],{"className":46690},[886],[888,46692,46693],{"xmlns":890},[892,46694,46695,46709],{},[895,46696,46697],{},[1681,46698,46699,46701],{},[898,46700,1655],{},[895,46702,46703,46705,46707],{},[898,46704,1713],{},[898,46706,1716],{},[898,46708,1719],{},[902,46710,1722],{"encoding":904},"). Klíčová vlastnost — ",[38,46713,46714],{},"ekvivalence zdanění",": výsledné rovnovážné množství i čistá cena pro výrobce jsou stejné bez ohledu na to, zda je daň uložena výrobci, či spotřebiteli.",[724,46717,46718],{},[614,46719,46720,46721,1741],{},"Pro detail, úplné odvození, Příklady 2.9 a 2.10 a geometrickou interpretaci viz ",[207,46722,46724],{"className":46723,"dataFsResolvedFilePath":809,"href":810},[210],"zdaneni-trhu",[724,46726,46727,46728,46731,46732,46757,46758,46761,46762,46787,46788,46805,46806,46845,46846,2068,46859,1741],{},"Existují dvě formy zdanění — daň uložená ",[38,46729,46730],{},"výrobci"," (posun nabídky ",[883,46733,46735],{"className":46734},[886],[888,46736,46737],{"xmlns":890},[892,46738,46739,46755],{},[895,46740,46741,46747,46749,46751,46753],{},[1681,46742,46743,46745],{},[898,46744,1912],{},[1765,46746,1945],{},[1761,46748,1909],{},[898,46750,1912],{},[1761,46752,1964],{},[898,46754,1655],{},[902,46756,4519],{"encoding":904}," svisle nahoru) a daň uložená ",[38,46759,46760],{},"spotřebiteli"," (posun poptávky ",[883,46763,46765],{"className":46764},[886],[888,46766,46767],{"xmlns":890},[892,46768,46769,46785],{},[895,46770,46771,46777,46779,46781,46783],{},[1681,46772,46773,46775],{},[898,46774,2244],{},[1765,46776,2296],{},[1761,46778,1909],{},[898,46780,2244],{},[1761,46782,1885],{},[898,46784,1655],{},[902,46786,4545],{"encoding":904}," svisle dolů). V obou případech nové rovnovážné množství ",[883,46789,46791],{"className":46790},[886],[888,46792,46793],{"xmlns":890},[892,46794,46795,46803],{},[895,46796,46797],{},[1824,46798,46799,46801],{},[898,46800,1828],{},[898,46802,1818],{},[902,46804,46412],{"encoding":904}," klesá a vzniká rozklad daně ",[883,46807,46809],{"className":46808},[886],[888,46810,46811],{"xmlns":890},[892,46812,46813,46843],{},[895,46814,46815,46817,46819,46829,46831],{},[898,46816,1655],{},[1761,46818,1909],{},[1681,46820,46821,46823],{},[898,46822,1655],{},[895,46824,46825,46827],{},[898,46826,1689],{},[898,46828,724],{},[1761,46830,1964],{},[1681,46832,46833,46835],{},[898,46834,1655],{},[895,46836,46837,46839,46841],{},[898,46838,1713],{},[898,46840,1716],{},[898,46842,1719],{},[902,46844,5801],{"encoding":904}," mezi obě strany trhu, určený relativními sklony křivek ",[883,46847,46849],{"className":46848},[886],[888,46850,46851],{"xmlns":890},[892,46852,46853,46857],{},[895,46854,46855],{},[898,46856,2244],{},[902,46858,2244],{"encoding":904},[883,46860,46862],{"className":46861},[886],[888,46863,46864],{"xmlns":890},[892,46865,46866,46870],{},[895,46867,46868],{},[898,46869,1912],{},[902,46871,1912],{"encoding":904},[724,46873,46874,46875,46878,46879,2068,46908,46941],{},"Zásadním výsledkem kapitoly je ",[38,46876,46877],{},"věta o ekvivalenci zdanění",": ať je daň uvalena formálně na kohokoli, rovnovážné množství i reálné rozdělení břemene jsou identické — ",[883,46880,46882],{"className":46881},[886],[888,46883,46884],{"xmlns":890},[892,46885,46886,46906],{},[895,46887,46888,46896,46898],{},[2015,46889,46890,46892,46894],{},[898,46891,1828],{},[1765,46893,1945],{},[898,46895,1818],{},[1761,46897,1909],{},[2015,46899,46900,46902,46904],{},[898,46901,1828],{},[1765,46903,2296],{},[898,46905,1818],{},[902,46907,5202],{"encoding":904},[883,46909,46911],{"className":46910},[886],[888,46912,46913],{"xmlns":890},[892,46914,46915,46939],{},[895,46916,46917,46925,46927,46929,46931],{},[2015,46918,46919,46921,46923],{},[898,46920,1839],{},[1765,46922,1945],{},[898,46924,1818],{},[1761,46926,1885],{},[898,46928,1655],{},[1761,46930,1909],{},[2015,46932,46933,46935,46937],{},[898,46934,1839],{},[1765,46936,2296],{},[898,46938,1818],{},[902,46940,5239],{"encoding":904},". Otázka, \"kdo má platit daň\", je tedy z hlediska trhu formální; skutečné rozdělení určuje struktura trhu, nikoli znění zákona.",[724,46943,46944,46945,46948,46949,46974,46975,47002,47003,47006,47007,47010,47011,1741],{},"Podrobný výklad, Příklady ",[38,46946,46947],{},"2.9"," (daň výrobci, ",[883,46950,46952],{"className":46951},[886],[888,46953,46954],{"xmlns":890},[892,46955,46956,46972],{},[895,46957,46958,46968,46970],{},[1681,46959,46960,46962],{},[898,46961,1655],{},[895,46963,46964,46966],{},[898,46965,1689],{},[898,46967,724],{},[1761,46969,1909],{},[1765,46971,2296],{},[902,46973,5003],{"encoding":904}," Kč, ",[883,46976,46978],{"className":46977},[886],[888,46979,46980],{"xmlns":890},[892,46981,46982,47000],{},[895,46983,46984,46996,46998],{},[1681,46985,46986,46988],{},[898,46987,1655],{},[895,46989,46990,46992,46994],{},[898,46991,1713],{},[898,46993,1716],{},[898,46995,1719],{},[1761,46997,1909],{},[1765,46999,2318],{},[902,47001,5031],{"encoding":904}," Kč) a ",[38,47004,47005],{},"2.10"," (táž daň, ale na spotřebitele), postup výpočtu rozkladu břemene a ",[38,47008,47009],{},"Obrázky 2.17–2.21"," jsou na samostatné stránce ",[207,47012,46724],{"className":47013,"dataFsResolvedFilePath":809,"href":810},[210],[1849,47015],{},[115,47017,47019],{"id":47018},"multiplikátory-pro-mikroekonomické-proměnné","Multiplikátory pro mikroekonomické proměnné",[1636,47021,47022],{},[724,47023,47024,47026,47027,47030,47031,47033],{},[883,47025,1642],{}," TL;DR\nMultiplikátory jsou ",[38,47028,47029],{},"parciální derivace redukovaného tvaru"," endogenní proměnné podle exogenních parametrů. Udávají přibližnou odezvu rovnovážného bodu na jednotkovou změnu parametru (",[614,47032,40988],{},"). Kvalitativní smysl (znaménko) je invariantní, kvantitativní závisí na konkrétních hodnotách.",[198,47035,47037],{"id":47036},"redukovaný-tvar","Redukovaný tvar",[724,47039,47040,47041,3927,47064,1343,47081,4590,47098,3927,47121,47138,47139,47169],{},"Pro lineární model ",[883,47042,47044],{"className":47043},[886],[888,47045,47046],{"xmlns":890},[892,47047,47048,47062],{},[895,47049,47050,47052,47054,47056,47058,47060],{},[898,47051,1839],{},[1761,47053,1909],{},[898,47055,207],{},[898,47057,1828],{},[1761,47059,1964],{},[898,47061,4302],{},[902,47063,4305],{"encoding":904},[883,47065,47067],{"className":47066},[886],[888,47068,47069],{"xmlns":890},[892,47070,47071,47079],{},[895,47072,47073,47075,47077],{},[898,47074,207],{},[1761,47076,2058],{},[1765,47078,1767],{},[902,47080,4323],{"encoding":904},[883,47082,47084],{"className":47083},[886],[888,47085,47086],{"xmlns":890},[892,47087,47088,47096],{},[895,47089,47090,47092,47094],{},[898,47091,4302],{},[1761,47093,1763],{},[1765,47095,1767],{},[902,47097,22847],{"encoding":904},[883,47099,47101],{"className":47100},[886],[888,47102,47103],{"xmlns":890},[892,47104,47105,47119],{},[895,47106,47107,47109,47111,47113,47115,47117],{},[898,47108,1839],{},[1761,47110,1909],{},[898,47112,2774],{},[898,47114,1828],{},[1761,47116,1964],{},[898,47118,4346],{},[902,47120,4349],{"encoding":904},[883,47122,47124],{"className":47123},[886],[888,47125,47126],{"xmlns":890},[892,47127,47128,47136],{},[895,47129,47130,47132,47134],{},[898,47131,2774],{},[1761,47133,1763],{},[1765,47135,1767],{},[902,47137,4367],{"encoding":904},") dává podmínka rovnováhy ",[883,47140,47142],{"className":47141},[886],[888,47143,47144],{"xmlns":890},[892,47145,47146,47166],{},[895,47147,47148,47150,47152,47154,47156,47158,47160,47162,47164],{},[898,47149,207],{},[898,47151,1828],{},[1761,47153,1964],{},[898,47155,4302],{},[1761,47157,1909],{},[898,47159,2774],{},[898,47161,1828],{},[1761,47163,1964],{},[898,47165,4346],{},[902,47167,47168],{"encoding":904},"aQ + b = cQ + d",", odkud",[883,47171,47173],{"className":47172},[886],[888,47174,47175],{"xmlns":890,"display":1930},[892,47176,47177,47222],{},[24787,47178,47179],{"width":32101},[24792,47180,47181,47183,47215,47217],{},[24795,47182],{"width":32106},[24795,47184,47185],{},[895,47186,47187,47193,47195,47213],{},[1824,47188,47189,47191],{},[898,47190,1828],{},[898,47192,1818],{},[1761,47194,1909],{},[4379,47196,47197,47205],{},[895,47198,47199,47201,47203],{},[898,47200,4302],{},[1761,47202,1885],{},[898,47204,4346],{},[895,47206,47207,47209,47211],{},[898,47208,2774],{},[1761,47210,1885],{},[898,47212,207],{},[898,47214,1741],{"mathvariant":1969},[24795,47216],{"width":32106},[24795,47218,47219],{},[2761,47220,47221],{},"(2.10)",[902,47223,47224],{"encoding":904},"Q^E = \\frac{b - d}{c - a}. \\tag{2.10}",[724,47226,47227,47228,3927,47230,47233,47234,47251,47252,1989,47255,47281,47282,47295,47296,47314,47315,2162],{},"Vztah (2.10) je ",[38,47229,24987],{},[614,47231,47232],{},"reduced form",") pro ",[883,47235,47237],{"className":47236},[886],[888,47238,47239],{"xmlns":890},[892,47240,47241,47249],{},[895,47242,47243],{},[1824,47244,47245,47247],{},[898,47246,1828],{},[898,47248,1818],{},[902,47250,46412],{"encoding":904},": endogenní proměnná je vyjádřena pomocí exogenních ",[38,47253,47254],{},"parametrů",[883,47256,47258],{"className":47257},[886],[888,47259,47260],{"xmlns":890},[892,47261,47262,47278],{},[895,47263,47264,47266,47268,47270,47272,47274,47276],{},[898,47265,207],{},[1761,47267,1834],{"separator":1833},[898,47269,4302],{},[1761,47271,1834],{"separator":1833},[898,47273,2774],{},[1761,47275,1834],{"separator":1833},[898,47277,4346],{},[902,47279,47280],{"encoding":904},"a, b, c, d",". Aby ",[883,47283,47285],{"className":47284},[886],[888,47286,47287],{"xmlns":890},[892,47288,47289,47293],{},[895,47290,47291],{},[898,47292,1818],{},[902,47294,1818],{"encoding":904}," ležel v 1. kvadrantu, musí platit ",[883,47297,47299],{"className":47298},[886],[888,47300,47301],{"xmlns":890},[892,47302,47303,47311],{},[895,47304,47305,47307,47309],{},[898,47306,4302],{},[1761,47308,1763],{},[898,47310,4346],{},[902,47312,47313],{"encoding":904},"b > d"," (neboť ",[883,47316,47318],{"className":47317},[886],[888,47319,47320],{"xmlns":890},[892,47321,47322,47334],{},[895,47323,47324,47326,47328,47330,47332],{},[898,47325,2774],{},[1761,47327,1885],{},[898,47329,207],{},[1761,47331,1763],{},[1765,47333,1767],{},[902,47335,47336],{"encoding":904},"c - a > 0",[724,47338,47339],{},[614,47340,47341,47342,47355,47356,47369,47370,5991,47383,45949,47400,47413],{},"Obrázek 2.22: Lineární poptávka (úsek ",[883,47343,47345],{"className":47344},[886],[888,47346,47347],{"xmlns":890},[892,47348,47349,47353],{},[895,47350,47351],{},[898,47352,4302],{},[902,47354,4302],{"encoding":904}," na ose ",[883,47357,47359],{"className":47358},[886],[888,47360,47361],{"xmlns":890},[892,47362,47363,47367],{},[895,47364,47365],{},[898,47366,1839],{},[902,47368,1839],{"encoding":904},") a nabídka (úsek ",[883,47371,47373],{"className":47372},[886],[888,47374,47375],{"xmlns":890},[892,47376,47377,47381],{},[895,47378,47379],{},[898,47380,4346],{},[902,47382,4346],{"encoding":904},[883,47384,47386],{"className":47385},[886],[888,47387,47388],{"xmlns":890},[892,47389,47390,47398],{},[895,47391,47392,47394,47396],{},[898,47393,4302],{},[1761,47395,1763],{},[898,47397,4346],{},[902,47399,47313],{"encoding":904},[883,47401,47403],{"className":47402},[886],[888,47404,47405],{"xmlns":890},[892,47406,47407,47411],{},[895,47408,47409],{},[898,47410,1818],{},[902,47412,1818],{"encoding":904}," v 1. kvadrantu.",[198,47415,47417],{"id":47416},"definice-multiplikátorů","Definice multiplikátorů",[724,47419,47420,47421,47446,47447,47460,47461,47474],{},"V komparativní statice jsou ",[883,47422,47424],{"className":47423},[886],[888,47425,47426],{"xmlns":890},[892,47427,47428,47444],{},[895,47429,47430,47432,47434,47436,47438,47440,47442],{},[898,47431,207],{},[1761,47433,1834],{"separator":1833},[898,47435,4302],{},[1761,47437,1834],{"separator":1833},[898,47439,2774],{},[1761,47441,1834],{"separator":1833},[898,47443,4346],{},[902,47445,47280],{"encoding":904}," exogenní proměnné a ",[883,47448,47450],{"className":47449},[886],[888,47451,47452],{"xmlns":890},[892,47453,47454,47458],{},[895,47455,47456],{},[898,47457,1828],{},[902,47459,1828],{"encoding":904}," endogenní. Přibližná změna ",[883,47462,47464],{"className":47463},[886],[888,47465,47466],{"xmlns":890},[892,47467,47468,47472],{},[895,47469,47470],{},[898,47471,1828],{},[902,47473,1828],{"encoding":904}," se rovná totálnímu diferenciálu:",[883,47476,47478],{"className":47477},[886],[888,47479,47480],{"xmlns":890,"display":1930},[892,47481,47482,47575],{},[24787,47483,47484],{"width":32101},[24792,47485,47486,47488,47568,47570],{},[24795,47487],{"width":32106},[24795,47489,47490],{},[895,47491,47492,47494,47496,47498,47500,47502,47504,47512,47514,47516,47518,47520,47528,47530,47532,47534,47536,47544,47546,47548,47550,47552,47560,47562,47564,47566],{},[898,47493,6959],{"mathvariant":1969},[898,47495,1828],{},[1761,47497,6803],{},[898,47499,4346],{},[898,47501,1828],{},[1761,47503,1909],{},[2015,47505,47506,47508,47510],{},[898,47507,1828],{},[898,47509,207],{},[1761,47511,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[2761,47513,7057],{},[898,47515,4346],{},[898,47517,207],{},[1761,47519,1964],{},[2015,47521,47522,47524,47526],{},[898,47523,1828],{},[898,47525,4302],{},[1761,47527,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[2761,47529,7057],{},[898,47531,4346],{},[898,47533,4302],{},[1761,47535,1964],{},[2015,47537,47538,47540,47542],{},[898,47539,1828],{},[898,47541,2774],{},[1761,47543,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[2761,47545,7057],{},[898,47547,4346],{},[898,47549,2774],{},[1761,47551,1964],{},[2015,47553,47554,47556,47558],{},[898,47555,1828],{},[898,47557,4346],{},[1761,47559,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[2761,47561,7057],{},[898,47563,4346],{},[898,47565,4346],{},[898,47567,1741],{"mathvariant":1969},[24795,47569],{"width":32106},[24795,47571,47572],{},[2761,47573,47574],{},"(2.11)",[902,47576,47577],{"encoding":904},"\\Delta Q \\approx dQ = Q'_a\\,da + Q'_b\\,db + Q'_c\\,dc + Q'_d\\,dd. \\tag{2.11}",[724,47579,47580,47581,47631,47632,3927,47634,5372],{},"Parciální derivace ",[883,47582,47584],{"className":47583},[886],[888,47585,47586],{"xmlns":890},[892,47587,47588,47628],{},[895,47589,47590,47598,47600,47608,47610,47618,47620],{},[2015,47591,47592,47594,47596],{},[898,47593,1828],{},[898,47595,207],{},[1761,47597,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,47599,1834],{"separator":1833},[2015,47601,47602,47604,47606],{},[898,47603,1828],{},[898,47605,4302],{},[1761,47607,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,47609,1834],{"separator":1833},[2015,47611,47612,47614,47616],{},[898,47613,1828],{},[898,47615,2774],{},[1761,47617,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,47619,1834],{"separator":1833},[2015,47621,47622,47624,47626],{},[898,47623,1828],{},[898,47625,4346],{},[1761,47627,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[902,47629,47630],{"encoding":904},"Q'_a, Q'_b, Q'_c, Q'_d"," se nazývají ",[38,47633,22011],{},[614,47635,47636],{},"multipliers",[883,47638,47640],{"className":47639},[886],[888,47641,47642],{"xmlns":890,"display":1930},[892,47643,47644,47795],{},[24787,47645,47646],{"width":32101},[24792,47647,47648,47650,47788,47790],{},[24795,47649],{"width":32106},[24795,47651,47652],{},[895,47653,47654,47662,47664,47690,47692,47694,47702,47704,47716,47718,47720,47728,47730,47732,47758,47760,47762,47770,47772,47774,47786],{},[2015,47655,47656,47658,47660],{},[898,47657,1828],{},[898,47659,207],{},[1761,47661,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,47663,1909],{},[4379,47665,47666,47674],{},[895,47667,47668,47670,47672],{},[898,47669,4302],{},[1761,47671,1885],{},[898,47673,4346],{},[895,47675,47676,47678,47680,47682,47684],{},[1761,47677,1915],{"stretchy":1821},[898,47679,2774],{},[1761,47681,1885],{},[898,47683,207],{},[1824,47685,47686,47688],{},[1761,47687,1920],{"stretchy":1821},[1765,47689,2296],{},[1761,47691,1834],{"separator":1833},[3315,47693],{"width":19322},[2015,47695,47696,47698,47700],{},[898,47697,1828],{},[898,47699,4302],{},[1761,47701,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,47703,1909],{},[4379,47705,47706,47708],{},[1765,47707,1945],{},[895,47709,47710,47712,47714],{},[898,47711,2774],{},[1761,47713,1885],{},[898,47715,207],{},[1761,47717,1834],{"separator":1833},[3315,47719],{"width":19322},[2015,47721,47722,47724,47726],{},[898,47723,1828],{},[898,47725,2774],{},[1761,47727,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,47729,1909],{},[1761,47731,1885],{},[4379,47733,47734,47742],{},[895,47735,47736,47738,47740],{},[898,47737,4302],{},[1761,47739,1885],{},[898,47741,4346],{},[895,47743,47744,47746,47748,47750,47752],{},[1761,47745,1915],{"stretchy":1821},[898,47747,2774],{},[1761,47749,1885],{},[898,47751,207],{},[1824,47753,47754,47756],{},[1761,47755,1920],{"stretchy":1821},[1765,47757,2296],{},[1761,47759,1834],{"separator":1833},[3315,47761],{"width":19322},[2015,47763,47764,47766,47768],{},[898,47765,1828],{},[898,47767,4346],{},[1761,47769,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,47771,1909],{},[1761,47773,1885],{},[4379,47775,47776,47778],{},[1765,47777,1945],{},[895,47779,47780,47782,47784],{},[898,47781,2774],{},[1761,47783,1885],{},[898,47785,207],{},[898,47787,1741],{"mathvariant":1969},[24795,47789],{"width":32106},[24795,47791,47792],{},[2761,47793,47794],{},"(2.12)",[902,47796,47797],{"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}",[198,47799,47801],{"id":47800},"znaménka-a-interpretace","Znaménka a interpretace",[724,47803,47804,47805,1343,47822,1343,47839,1343,47856,47873,47874,5372],{},"Za podmínek ",[883,47806,47808],{"className":47807},[886],[888,47809,47810],{"xmlns":890},[892,47811,47812,47820],{},[895,47813,47814,47816,47818],{},[898,47815,207],{},[1761,47817,2058],{},[1765,47819,1767],{},[902,47821,4323],{"encoding":904},[883,47823,47825],{"className":47824},[886],[888,47826,47827],{"xmlns":890},[892,47828,47829,47837],{},[895,47830,47831,47833,47835],{},[898,47832,4302],{},[1761,47834,1763],{},[1765,47836,1767],{},[902,47838,22847],{"encoding":904},[883,47840,47842],{"className":47841},[886],[888,47843,47844],{"xmlns":890},[892,47845,47846,47854],{},[895,47847,47848,47850,47852],{},[898,47849,2774],{},[1761,47851,1763],{},[1765,47853,1767],{},[902,47855,4367],{"encoding":904},[883,47857,47859],{"className":47858},[886],[888,47860,47861],{"xmlns":890},[892,47862,47863,47871],{},[895,47864,47865,47867,47869],{},[898,47866,4302],{},[1761,47868,1763],{},[898,47870,4346],{},[902,47872,47313],{"encoding":904}," platí (znaménka se ",[38,47875,47876],{},"nemění",[883,47878,47880],{"className":47879},[886],[888,47881,47882],{"xmlns":890,"display":1930},[892,47883,47884,47946],{},[895,47885,47886,47894,47896,47898,47900,47902,47910,47912,47914,47916,47918,47926,47928,47930,47932,47934,47942,47944],{},[2015,47887,47888,47890,47892],{},[898,47889,1828],{},[898,47891,207],{},[1761,47893,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,47895,1763],{},[1765,47897,1767],{},[1761,47899,1834],{"separator":1833},[3315,47901],{"width":3317},[2015,47903,47904,47906,47908],{},[898,47905,1828],{},[898,47907,4302],{},[1761,47909,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,47911,1763],{},[1765,47913,1767],{},[1761,47915,1834],{"separator":1833},[3315,47917],{"width":3317},[2015,47919,47920,47922,47924],{},[898,47921,1828],{},[898,47923,2774],{},[1761,47925,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,47927,2058],{},[1765,47929,1767],{},[1761,47931,1834],{"separator":1833},[3315,47933],{"width":3317},[2015,47935,47936,47938,47940],{},[898,47937,1828],{},[898,47939,4346],{},[1761,47941,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,47943,2058],{},[1765,47945,16498],{},[902,47947,47948],{"encoding":904},"Q'_a > 0, \\qquad Q'_b > 0, \\qquad Q'_c \u003C 0, \\qquad Q'_d \u003C 0.",[120,47950,47951,48010],{},[123,47952,47953,1989,47956,47976,47977,47994,47995,1343,48008,1741],{},[38,47954,47955],{},"Kvantitativní smysl:",[883,47957,47959],{"className":47958},[886],[888,47960,47961],{"xmlns":890},[892,47962,47963,47973],{},[895,47964,47965],{},[2015,47966,47967,47969,47971],{},[898,47968,1828],{},[898,47970,6112],{},[1761,47972,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[902,47974,47975],{"encoding":904},"Q'_x"," udává, o kolik přibližně vzroste ",[883,47978,47980],{"className":47979},[886],[888,47981,47982],{"xmlns":890},[892,47983,47984,47992],{},[895,47985,47986],{},[1824,47987,47988,47990],{},[898,47989,1828],{},[898,47991,1818],{},[902,47993,46412],{"encoding":904}," při jednotkové změně parametru ",[883,47996,47998],{"className":47997},[886],[888,47999,48000],{"xmlns":890},[892,48001,48002,48006],{},[895,48003,48004],{},[898,48005,6112],{},[902,48007,6112],{"encoding":904},[614,48009,40988],{},[123,48011,48012,48015,48016,48033,48034,1741],{},[38,48013,48014],{},"Kvalitativní smysl:"," znaménko určuje směr reakce ",[883,48017,48019],{"className":48018},[886],[888,48020,48021],{"xmlns":890},[892,48022,48023,48031],{},[895,48024,48025],{},[1824,48026,48027,48029],{},[898,48028,1828],{},[898,48030,1818],{},[902,48032,46412],{"encoding":904}," na růst ",[883,48035,48037],{"className":48036},[886],[888,48038,48039],{"xmlns":890},[892,48040,48041,48045],{},[895,48042,48043],{},[898,48044,6112],{},[902,48046,6112],{"encoding":904},[724,48048,48049,48050,48063,48064,47314,48081,2162],{},"Např. růst ",[883,48051,48053],{"className":48052},[886],[888,48054,48055],{"xmlns":890},[892,48056,48057,48061],{},[895,48058,48059],{},[898,48060,2774],{},[902,48062,2774],{"encoding":904}," (strmější nabídka) ⟹ pokles ",[883,48065,48067],{"className":48066},[886],[888,48068,48069],{"xmlns":890},[892,48070,48071,48079],{},[895,48072,48073],{},[1824,48074,48075,48077],{},[898,48076,1828],{},[898,48078,1818],{},[902,48080,46412],{"encoding":904},[883,48082,48084],{"className":48083},[886],[888,48085,48086],{"xmlns":890},[892,48087,48088,48102],{},[895,48089,48090,48098,48100],{},[2015,48091,48092,48094,48096],{},[898,48093,1828],{},[898,48095,2774],{},[1761,48097,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,48099,2058],{},[1765,48101,1767],{},[902,48103,48104],{"encoding":904},"Q'_c \u003C 0",[724,48106,48107],{},[614,48108,48109,48110,48130,48131,48155,48156,48178,48179,1741],{},"Obrázek 2.23: Pootočení přímky nabídky z ",[883,48111,48113],{"className":48112},[886],[888,48114,48115],{"xmlns":890},[892,48116,48117,48127],{},[895,48118,48119,48121,48123,48125],{},[898,48120,2774],{},[898,48122,1828],{},[1761,48124,1964],{},[898,48126,4346],{},[902,48128,48129],{"encoding":904},"cQ + d"," na strmější ",[883,48132,48134],{"className":48133},[886],[888,48135,48136],{"xmlns":890},[892,48137,48138,48152],{},[895,48139,48140,48146,48148,48150],{},[1681,48141,48142,48144],{},[898,48143,2774],{},[1765,48145,1945],{},[898,48147,1828],{},[1761,48149,1964],{},[898,48151,4346],{},[902,48153,48154],{"encoding":904},"c_1 Q + d"," (při ",[883,48157,48159],{"className":48158},[886],[888,48160,48161],{"xmlns":890},[892,48162,48163,48175],{},[895,48164,48165,48171,48173],{},[1681,48166,48167,48169],{},[898,48168,2774],{},[1765,48170,1945],{},[1761,48172,1763],{},[898,48174,2774],{},[902,48176,48177],{"encoding":904},"c_1 > c",") — rovnovážný bod se posouvá vlevo, ",[883,48180,48182],{"className":48181},[886],[888,48183,48184],{"xmlns":890},[892,48185,48186,48196],{},[895,48187,48188,48194],{},[1824,48189,48190,48192],{},[898,48191,1828],{},[898,48193,1818],{},[1761,48195,46600],{},[902,48197,48198],{"encoding":904},"Q^E \\downarrow",[724,48200,48201,48202,48234,48235,1741],{},"Při změně jediné proměnné se (2.11) redukuje např. na ",[883,48203,48205],{"className":48204},[886],[888,48206,48207],{"xmlns":890},[892,48208,48209,48231],{},[895,48210,48211,48213,48215,48217,48225,48227,48229],{},[898,48212,6959],{"mathvariant":1969},[898,48214,1828],{},[1761,48216,6803],{},[2015,48218,48219,48221,48223],{},[898,48220,1828],{},[898,48222,4302],{},[1761,48224,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[2761,48226,7057],{},[898,48228,4346],{},[898,48230,4302],{},[902,48232,48233],{"encoding":904},"\\Delta Q \\approx Q'_b\\,db",". Analogicky lze odvodit multiplikátory pro ",[883,48236,48238],{"className":48237},[886],[888,48239,48240],{"xmlns":890},[892,48241,48242,48250],{},[895,48243,48244],{},[1824,48245,48246,48248],{},[898,48247,1839],{},[898,48249,1818],{},[902,48251,2161],{"encoding":904},[198,48253,48255,48256],{"id":48254},"příklad-211-komparativní-statika-pro-qeqe","Příklad 2.11 — komparativní statika pro ",[883,48257,48259],{"className":48258},[886],[888,48260,48261],{"xmlns":890},[892,48262,48263,48271],{},[895,48264,48265],{},[1824,48266,48267,48269],{},[898,48268,1828],{},[898,48270,1818],{},[902,48272,46412],{"encoding":904},[724,48274,48275,2275,48277,2302,48303,1741],{},[38,48276,2274],{},[883,48278,48280],{"className":48279},[886],[888,48281,48282],{"xmlns":890},[892,48283,48284,48300],{},[895,48285,48286,48288,48290,48292,48294,48296,48298],{},[898,48287,1839],{},[1761,48289,1909],{},[1761,48291,1885],{},[1765,48293,5486],{},[898,48295,1828],{},[1761,48297,1964],{},[1765,48299,9262],{},[902,48301,48302],{"encoding":904},"P = -3Q + 40",[883,48304,48306],{"className":48305},[886],[888,48307,48308],{"xmlns":890},[892,48309,48310,48324],{},[895,48311,48312,48314,48316,48318,48320,48322],{},[898,48313,1839],{},[1761,48315,1909],{},[1765,48317,5426],{},[898,48319,1828],{},[1761,48321,1964],{},[1765,48323,2633],{},[902,48325,48326],{"encoding":904},"P = 0{,}5Q + 10",[724,48328,48329,48331],{},[38,48330,2349],{}," Rovnovážné množství",[883,48333,48335],{"className":48334},[886],[888,48336,48337],{"xmlns":890,"display":1930},[892,48338,48339,48407],{},[895,48340,48341,48347,48349,48367,48369,48393,48395,48402,48404],{},[1824,48342,48343,48345],{},[898,48344,1828],{},[898,48346,1818],{},[1761,48348,1909],{},[4379,48350,48351,48359],{},[895,48352,48353,48355,48357],{},[898,48354,4302],{},[1761,48356,1885],{},[898,48358,4346],{},[895,48360,48361,48363,48365],{},[898,48362,2774],{},[1761,48364,1885],{},[898,48366,207],{},[1761,48368,1909],{},[4379,48370,48371,48379],{},[895,48372,48373,48375,48377],{},[1765,48374,9262],{},[1761,48376,1885],{},[1765,48378,2633],{},[895,48380,48381,48383,48385,48387,48389,48391],{},[1765,48382,5426],{},[1761,48384,1885],{},[1761,48386,1915],{"stretchy":1821},[1761,48388,1885],{},[1765,48390,5486],{},[1761,48392,1920],{"stretchy":1821},[1761,48394,1909],{},[4379,48396,48397,48399],{},[1765,48398,42042],{},[1765,48400,48401],{},"3,5",[1761,48403,6803],{},[1765,48405,48406],{},"8,571.",[902,48408,48409],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\approx 8{,}571.",[724,48411,48412,48457],{},[38,48413,48414,48415,6746,48428,4178,48442,48456],{},"(a) Změna ",[883,48416,48418],{"className":48417},[886],[888,48419,48420],{"xmlns":890},[892,48421,48422,48426],{},[895,48423,48424],{},[898,48425,2774],{},[902,48427,2774],{"encoding":904},[883,48429,48431],{"className":48430},[886],[888,48432,48433],{"xmlns":890},[892,48434,48435,48439],{},[895,48436,48437],{},[1765,48438,5426],{},[902,48440,48441],{"encoding":904},"0{,}5",[883,48443,48445],{"className":48444},[886],[888,48446,48447],{"xmlns":890},[892,48448,48449,48453],{},[895,48450,48451],{},[1765,48452,23354],{},[902,48454,48455],{"encoding":904},"0{,}6"," (ceteris paribus)."," Dle (2.12):",[883,48459,48461],{"className":48460},[886],[888,48462,48463],{"xmlns":890,"display":1930},[892,48464,48465,48542],{},[895,48466,48467,48475,48477,48479,48481,48483,48485,48511,48513,48515,48517,48519,48521,48531,48533,48535,48537,48539],{},[2015,48468,48469,48471,48473],{},[898,48470,1828],{},[898,48472,2774],{},[1761,48474,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[2761,48476,7057],{},[898,48478,4346],{},[898,48480,2774],{},[1761,48482,1909],{},[1761,48484,1885],{},[4379,48486,48487,48495],{},[895,48488,48489,48491,48493],{},[898,48490,4302],{},[1761,48492,1885],{},[898,48494,4346],{},[895,48496,48497,48499,48501,48503,48505],{},[1761,48498,1915],{"stretchy":1821},[898,48500,2774],{},[1761,48502,1885],{},[898,48504,207],{},[1824,48506,48507,48509],{},[1761,48508,1920],{"stretchy":1821},[1765,48510,2296],{},[2761,48512,7057],{},[898,48514,4346],{},[898,48516,2774],{},[1761,48518,1909],{},[1761,48520,1885],{},[4379,48522,48523,48525],{},[1765,48524,42042],{},[1824,48526,48527,48529],{},[1765,48528,48401],{},[1765,48530,2296],{},[1761,48532,2447],{},[1765,48534,6865],{},[1761,48536,6803],{},[1761,48538,1885],{},[1765,48540,48541],{},"0,245.",[902,48543,48544],{"encoding":904},"Q'_c\\,dc = -\\frac{b - d}{(c - a)^2}\\,dc = -\\frac{30}{3{,}5^2}\\cdot 0{,}1 \\approx -0{,}245.",[724,48546,48547,48548,1741],{},"Nové rovnovážné množství ",[883,48549,48551],{"className":48550},[886],[888,48552,48553],{"xmlns":890},[892,48554,48555,48580],{},[895,48556,48557,48565,48567,48570,48572,48575,48577],{},[2015,48558,48559,48561,48563],{},[898,48560,1828],{},[1765,48562,1945],{},[898,48564,1818],{},[1761,48566,6803],{},[1765,48568,48569],{},"8,571",[1761,48571,1885],{},[1765,48573,48574],{},"0,245",[1761,48576,1909],{},[1765,48578,48579],{},"8,326",[902,48581,48582],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326",[724,48584,48585,48670],{},[38,48586,48587,48588,1343,48608,1343,48630,1343,48650,1741],{},"(b) Současné změny ",[883,48589,48591],{"className":48590},[886],[888,48592,48593],{"xmlns":890},[892,48594,48595,48605],{},[895,48596,48597,48599,48601,48603],{},[898,48598,4346],{},[898,48600,207],{},[1761,48602,1909],{},[1765,48604,5426],{},[902,48606,48607],{"encoding":904},"da = 0{,}5",[883,48609,48611],{"className":48610},[886],[888,48612,48613],{"xmlns":890},[892,48614,48615,48627],{},[895,48616,48617,48619,48621,48623,48625],{},[898,48618,4346],{},[898,48620,4302],{},[1761,48622,1909],{},[1761,48624,1885],{},[1765,48626,6321],{},[902,48628,48629],{"encoding":904},"db = -5",[883,48631,48633],{"className":48632},[886],[888,48634,48635],{"xmlns":890},[892,48636,48637,48647],{},[895,48638,48639,48641,48643,48645],{},[898,48640,4346],{},[898,48642,2774],{},[1761,48644,1909],{},[1765,48646,6865],{},[902,48648,48649],{"encoding":904},"dc = 0{,}1",[883,48651,48653],{"className":48652},[886],[888,48654,48655],{"xmlns":890},[892,48656,48657,48667],{},[895,48658,48659,48661,48663,48665],{},[898,48660,4346],{},[898,48662,4346],{},[1761,48664,1909],{},[1765,48666,1945],{},[902,48668,48669],{"encoding":904},"dd = 1"," Dosazením do (2.11):",[883,48672,48674],{"className":48673},[886],[888,48675,48676],{"xmlns":890,"display":1930},[892,48677,48678,48821],{},[24787,48679,48680,48762,48798],{"rowspacing":24789,"columnalign":24790,"columnspacing":6458},[24792,48681,48682,48692],{},[24795,48683,48684],{},[6411,48685,48686],{"scriptlevel":1767,"displaystyle":1833},[895,48687,48688,48690],{},[898,48689,6959],{"mathvariant":1969},[898,48691,1828],{},[24795,48693,48694],{},[6411,48695,48696],{"scriptlevel":1767,"displaystyle":1833},[895,48697,48698,48700,48702,48712,48714,48716,48718,48724,48726,48728,48730,48732,48734,48736,48746,48748,48750,48752,48758,48760],{},[895,48699],{},[1761,48701,6803],{},[4379,48703,48704,48706],{},[1765,48705,42042],{},[1824,48707,48708,48710],{},[1765,48709,48401],{},[1765,48711,2296],{},[1761,48713,2447],{},[1765,48715,5426],{},[1761,48717,1964],{},[4379,48719,48720,48722],{},[1765,48721,1945],{},[1765,48723,48401],{},[1761,48725,2447],{},[1761,48727,1915],{"stretchy":1821},[1761,48729,1885],{},[1765,48731,6321],{},[1761,48733,1920],{"stretchy":1821},[1761,48735,1885],{},[4379,48737,48738,48740],{},[1765,48739,42042],{},[1824,48741,48742,48744],{},[1765,48743,48401],{},[1765,48745,2296],{},[1761,48747,2447],{},[1765,48749,6865],{},[1761,48751,1885],{},[4379,48753,48754,48756],{},[1765,48755,1945],{},[1765,48757,48401],{},[1761,48759,2447],{},[1765,48761,1945],{},[24792,48763,48764,48770],{},[24795,48765,48766],{},[6411,48767,48768],{"scriptlevel":1767,"displaystyle":1833},[895,48769],{},[24795,48771,48772],{},[6411,48773,48774],{"scriptlevel":1767,"displaystyle":1833},[895,48775,48776,48778,48780,48783,48785,48788,48790,48793,48795],{},[895,48777],{},[1761,48779,1909],{},[1765,48781,48782],{},"1,2245",[1761,48784,1885],{},[1765,48786,48787],{},"1,4286",[1761,48789,1885],{},[1765,48791,48792],{},"0,2449",[1761,48794,1885],{},[1765,48796,48797],{},"0,2857",[24792,48799,48800,48806],{},[24795,48801,48802],{},[6411,48803,48804],{"scriptlevel":1767,"displaystyle":1833},[895,48805],{},[24795,48807,48808],{},[6411,48809,48810],{"scriptlevel":1767,"displaystyle":1833},[895,48811,48812,48814,48816,48818],{},[895,48813],{},[1761,48815,6803],{},[1761,48817,1885],{},[1765,48819,48820],{},"0,735.",[902,48822,48823],{"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}",[724,48825,34095,48826,1741],{},[883,48827,48829],{"className":48828},[886],[888,48830,48831],{"xmlns":890},[892,48832,48833,48857],{},[895,48834,48835,48843,48845,48847,48849,48852,48854],{},[2015,48836,48837,48839,48841],{},[898,48838,1828],{},[1765,48840,1945],{},[898,48842,1818],{},[1761,48844,6803],{},[1765,48846,48569],{},[1761,48848,1885],{},[1765,48850,48851],{},"0,735",[1761,48853,1909],{},[1765,48855,48856],{},"7,836",[902,48858,48859],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 = 7{,}836",[1636,48861,48862],{},[724,48863,48864,48866,48867,48890,48891,48913],{},[883,48865,4723],{}," Pozn. — oprava\nV knize je u této dílčí úlohy uvedena hodnota ",[883,48868,48870],{"className":48869},[886],[888,48871,48872],{"xmlns":890},[892,48873,48874,48887],{},[895,48875,48876,48878,48880,48882,48884],{},[898,48877,6959],{"mathvariant":1969},[898,48879,1828],{},[1761,48881,6803],{},[1761,48883,1885],{},[1765,48885,48886],{},"2,69",[902,48888,48889],{"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 ",[883,48892,48894],{"className":48893},[886],[888,48895,48896],{"xmlns":890},[892,48897,48898,48910],{},[895,48899,48900,48902,48904,48906,48908],{},[898,48901,6959],{"mathvariant":1969},[898,48903,1828],{},[1761,48905,6803],{},[1761,48907,1885],{},[1765,48909,48851],{},[902,48911,48912],{"encoding":904},"\\Delta Q \\approx -0{,}735",". Výsledek byl v této wiki opraven.",[724,48915,48916],{},"Princip multiplikátorů lze uplatnit na libovolné ekonomické proměnné — analogicky v makroekonomii (kap. 7).",[1849,48918],{},[115,48920,820],{"id":15823},[1636,48922,48923],{},[724,48924,48925,7934,48927,3927,48930,4590,48946,3927,48949,48965,48966,1741],{},[883,48926,1642],{},[38,48928,48929],{},"Přebytek spotřebitele",[883,48931,48933],{"className":48932},[886],[888,48934,48935],{"xmlns":890},[892,48936,48937,48943],{},[895,48938,48939,48941],{},[898,48940,6849],{},[898,48942,1912],{},[902,48944,48945],{"encoding":904},"CS",[38,48947,48948],{},"přebytek výrobce",[883,48950,48952],{"className":48951},[886],[888,48953,48954],{"xmlns":890},[892,48955,48956,48962],{},[895,48957,48958,48960],{},[898,48959,1839],{},[898,48961,1912],{},[902,48963,48964],{"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 ",[207,48967,48969],{"className":48968,"dataFsResolvedFilePath":818,"href":819},[210],"prebytek-spotrebitele-vyrobce",[724,48971,48972],{},[3991,48973],{"alt":48974,"className":48975,"src":48976},"imek-prebytky-cs-ps",[210,3995],"\u002Fwiki-assets\u002Fimek-prebytky-cs-ps.jpeg",[724,48978,48979,3927,48981,48984],{},[38,48980,48929],{},[614,48982,48983],{},"consumer surplus",") — rozdíl mezi ochotou platit a skutečnou platbou:",[883,48986,48988],{"className":48987},[886],[888,48989,48990],{"xmlns":890,"display":1930},[892,48991,48992,49069],{},[24787,48993,48994],{"width":32101},[24792,48995,48996,48998,49062,49064],{},[24795,48997],{"width":32106},[24795,48999,49000],{},[895,49001,49002,49004,49006,49008,49014,49016,49018,49030,49032,49034,49036,49038,49040,49042,49044,49046,49052,49054,49060],{},[898,49003,6849],{},[898,49005,1912],{},[1761,49007,1915],{"stretchy":1821},[1681,49009,49010,49012],{},[898,49011,1828],{},[1765,49013,1767],{},[1761,49015,1920],{"stretchy":1821},[1761,49017,1909],{},[2015,49019,49020,49022,49024],{},[1761,49021,15208],{},[1765,49023,1767],{},[1681,49025,49026,49028],{},[898,49027,1828],{},[1765,49029,1767],{},[898,49031,2244],{},[1761,49033,1915],{"stretchy":1821},[898,49035,1828],{},[1761,49037,1920],{"stretchy":1821},[2761,49039,7057],{},[898,49041,4346],{},[898,49043,1828],{},[1761,49045,1885],{},[1681,49047,49048,49050],{},[898,49049,1839],{},[1765,49051,1767],{},[2761,49053,7057],{},[1681,49055,49056,49058],{},[898,49057,1828],{},[1765,49059,1767],{},[898,49061,1741],{"mathvariant":1969},[24795,49063],{"width":32106},[24795,49065,49066],{},[2761,49067,49068],{},"(2.14)",[902,49070,49071],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\,dQ - P_0\\,Q_0. \\tag{2.14}",[724,49073,49074,3927,49077,49080],{},[38,49075,49076],{},"Přebytek výrobce",[614,49078,49079],{},"producer surplus",") — rozdíl mezi tržbou a minimální cenou:",[883,49082,49084],{"className":49083},[886],[888,49085,49086],{"xmlns":890,"display":1930},[892,49087,49088,49165],{},[24787,49089,49090],{"width":32101},[24792,49091,49092,49094,49158,49160],{},[24795,49093],{"width":32106},[24795,49095,49096],{},[895,49097,49098,49100,49102,49104,49110,49112,49114,49120,49122,49128,49130,49142,49144,49146,49148,49150,49152,49154,49156],{},[898,49099,1839],{},[898,49101,1912],{},[1761,49103,1915],{"stretchy":1821},[1681,49105,49106,49108],{},[898,49107,1828],{},[1765,49109,1767],{},[1761,49111,1920],{"stretchy":1821},[1761,49113,1909],{},[1681,49115,49116,49118],{},[898,49117,1839],{},[1765,49119,1767],{},[2761,49121,7057],{},[1681,49123,49124,49126],{},[898,49125,1828],{},[1765,49127,1767],{},[1761,49129,1885],{},[2015,49131,49132,49134,49136],{},[1761,49133,15208],{},[1765,49135,1767],{},[1681,49137,49138,49140],{},[898,49139,1828],{},[1765,49141,1767],{},[898,49143,1912],{},[1761,49145,1915],{"stretchy":1821},[898,49147,1828],{},[1761,49149,1920],{"stretchy":1821},[2761,49151,7057],{},[898,49153,4346],{},[898,49155,1828],{},[898,49157,1741],{"mathvariant":1969},[24795,49159],{"width":32106},[24795,49161,49162],{},[2761,49163,49164],{},"(2.15)",[902,49166,49167],{"encoding":904},"PS(Q_0) = P_0\\,Q_0 - \\int_0^{Q_0} S(Q)\\,dQ. \\tag{2.15}",[724,49169,49170,49171,1741],{},"Geometricky jde o plochy mezi rovnovážnou cenou a příslušnou křivkou; výpočet využívá aparát ",[207,49172,49174],{"className":49173,"dataFsResolvedFilePath":773,"href":774},[210],"určitého integrálu",[1849,49176],{},[115,49178,49180],{"id":49179},"příklady-z-knihy-přehled","Příklady z knihy — přehled",[120,49182,49183,49214,49219,49224,49252,49257,49286,49292,49371,49396],{},[123,49184,49185,49187,49188,49213],{},[38,49186,41953],{}," — lineární poptávka ",[883,49189,49191],{"className":49190},[886],[888,49192,49193],{"xmlns":890},[892,49194,49195,49211],{},[895,49196,49197,49199,49201,49203,49205,49207,49209],{},[898,49198,1839],{},[1761,49200,1909],{},[1761,49202,1885],{},[1765,49204,2296],{},[898,49206,1828],{},[1761,49208,1964],{},[1765,49210,7195],{},[902,49212,41984],{"encoding":904},", alternativní tvar, cenové rozpětí.",[123,49215,49216,49218],{},[38,49217,42265],{}," — empirické křivky poptávky po cukru (rodina vs. trh).",[123,49220,49221,49223],{},[38,49222,5522],{}," — posun poptávky při zdanění kupujícího.",[123,49225,49226,49228,49229,1741],{},[38,49227,44809],{}," — lineární nabídka ",[883,49230,49232],{"className":49231},[886],[888,49233,49234],{"xmlns":890},[892,49235,49236,49250],{},[895,49237,49238,49240,49242,49244,49246,49248],{},[898,49239,1839],{},[1761,49241,1909],{},[1765,49243,5426],{},[898,49245,1828],{},[1761,49247,1964],{},[1765,49249,9056],{},[902,49251,44838],{"encoding":904},[123,49253,49254,49256],{},[38,49255,5526],{}," — posun nabídky při zdanění výrobce.",[123,49258,49259,49262,49263,1741],{},[38,49260,49261],{},"Příklad 2.7"," — kvadratická rovnováha, ",[883,49264,49266],{"className":49265},[886],[888,49267,49268],{"xmlns":890},[892,49269,49270,49284],{},[895,49271,49272,49274,49276,49278,49280,49282],{},[898,49273,1818],{},[1761,49275,1822],{"stretchy":1821},[1765,49277,2318],{},[1761,49279,1834],{"separator":1833},[1765,49281,45945],{},[1761,49283,1844],{"stretchy":1821},[902,49285,45973],{"encoding":904},[123,49287,49288,49291],{},[38,49289,49290],{},"Příklad 2.8"," — dvoukomoditní trh, soustava rovnic, komplementy.",[123,49293,49294,49296,49297,49314,49315,1343,49340,49367,49368,7021],{},[38,49295,2269],{}," — daň ",[883,49298,49300],{"className":49299},[886],[888,49301,49302],{"xmlns":890},[892,49303,49304,49312],{},[895,49305,49306,49308,49310],{},[898,49307,1655],{},[1761,49309,1909],{},[1765,49311,2340],{},[902,49313,2343],{"encoding":904}," na výrobce; rozklad ",[883,49316,49318],{"className":49317},[886],[888,49319,49320],{"xmlns":890},[892,49321,49322,49338],{},[895,49323,49324,49334,49336],{},[1681,49325,49326,49328],{},[898,49327,1655],{},[895,49329,49330,49332],{},[898,49331,1689],{},[898,49333,724],{},[1761,49335,1909],{},[1765,49337,2296],{},[902,49339,5003],{"encoding":904},[883,49341,49343],{"className":49342},[886],[888,49344,49345],{"xmlns":890},[892,49346,49347,49365],{},[895,49348,49349,49361,49363],{},[1681,49350,49351,49353],{},[898,49352,1655],{},[895,49354,49355,49357,49359],{},[898,49356,1713],{},[898,49358,1716],{},[898,49360,1719],{},[1761,49362,1909],{},[1765,49364,2318],{},[902,49366,5031],{"encoding":904},". (Viz ",[207,49369,46724],{"className":49370,"dataFsResolvedFilePath":809,"href":810},[210],[123,49372,49373,49296,49375,49392,49393,7021],{},[38,49374,3454],{},[883,49376,49378],{"className":49377},[886],[888,49379,49380],{"xmlns":890},[892,49381,49382,49390],{},[895,49383,49384,49386,49388],{},[898,49385,1655],{},[1761,49387,1909],{},[1765,49389,2340],{},[902,49391,2343],{"encoding":904}," na spotřebitele; stejné čisté ceny i množství. (Viz ",[207,49394,46724],{"className":49395,"dataFsResolvedFilePath":809,"href":810},[210],[123,49397,49398,49401],{},[38,49399,49400],{},"Příklad 2.11"," — komparativní statika, multiplikátory, změny parametrů.",[1849,49403],{},[115,49405,49407],{"id":49406},"úlohy-k-samostatnému-řešení","Úlohy k samostatnému řešení",[198,49409,49411],{"id":49410},"základní-analýza-poptávky","Základní analýza poptávky",[724,49413,49414,49417,49418,49453,49454,49480],{},[38,49415,49416],{},"2.1"," Je dána poptávka ",[883,49419,49421],{"className":49420},[886],[888,49422,49423],{"xmlns":890},[892,49424,49425,49450],{},[895,49426,49427,49429,49431,49433,49435,49437,49439,49441,49444,49446,49448],{},[898,49428,1828],{},[1761,49430,1909],{},[898,49432,2244],{},[1761,49434,1915],{"stretchy":1821},[898,49436,1839],{},[1761,49438,1920],{"stretchy":1821},[1761,49440,1909],{},[1765,49442,49443],{},"75",[1761,49445,1885],{},[1765,49447,6321],{},[898,49449,1839],{},[902,49451,49452],{"encoding":904},"Q = D(P) = 75 - 5P",". (a) Načrtněte křivku poptávky. (b) Stanovte reálné cenové rozpětí. (c) Vypočtěte množství při cenách ",[883,49455,49457],{"className":49456},[886],[888,49458,49459],{"xmlns":890},[892,49460,49461,49477],{},[895,49462,49463,49465,49467,49469,49471,49473,49475],{},[1765,49464,1767],{},[1761,49466,1834],{"separator":1833},[1765,49468,6321],{},[1761,49470,1834],{"separator":1833},[1765,49472,2633],{},[1761,49474,1834],{"separator":1833},[1765,49476,5433],{},[902,49478,49479],{"encoding":904},"0, 5, 10, 15"," a výsledky vyznačte na křivku poptávky.",[724,49482,49483,49486,49487,49505,49506,5372],{},[38,49484,49485],{},"2.2"," Ověřte, že uvedené funkce vyjadřují (s případným omezením pro ",[883,49488,49490],{"className":49489},[886],[888,49491,49492],{"xmlns":890},[892,49493,49494,49502],{},[895,49495,49496,49498,49500],{},[898,49497,1839],{},[1761,49499,1834],{"separator":1833},[898,49501,1828],{},[902,49503,49504],{"encoding":904},"P, Q",") poptávku (využijte testu na zápornost derivace), charakterizujte tvar křivky poptávky a vyjádřete ve tvaru poptávky v alternativním tvaru (",[883,49507,49509],{"className":49508},[886],[888,49510,49511],{"xmlns":890},[892,49512,49513,49529],{},[895,49514,49515,49517,49519,49521,49523,49525,49527],{},[898,49516,207],{},[1761,49518,1834],{"separator":1833},[898,49520,4302],{},[1761,49522,1834],{"separator":1833},[898,49524,2774],{},[1761,49526,1763],{},[1765,49528,1767],{},[902,49530,49531],{"encoding":904},"a, b, c > 0",[120,49533,49534,49567,49598,49633,49664,49699],{},[123,49535,49536,49537],{},"(a) ",[883,49538,49540],{"className":49539},[886],[888,49541,49542],{"xmlns":890},[892,49543,49544,49564],{},[895,49545,49546,49548,49550],{},[898,49547,1828],{},[1761,49549,1909],{},[6411,49551,49552],{"scriptlevel":1767,"displaystyle":1833},[4379,49553,49554,49556],{},[898,49555,207],{},[895,49557,49558,49560,49562],{},[898,49559,1839],{},[1761,49561,1964],{},[898,49563,2774],{},[902,49565,49566],{"encoding":904},"Q = \\dfrac{a}{P + c}",[123,49568,49569,49570],{},"(b) ",[883,49571,49573],{"className":49572},[886],[888,49574,49575],{"xmlns":890},[892,49576,49577,49595],{},[895,49578,49579,49581,49583],{},[898,49580,1828],{},[1761,49582,1909],{},[12161,49584,49585],{},[895,49586,49587,49589,49591,49593],{},[898,49588,207],{},[1761,49590,1885],{},[898,49592,4302],{},[898,49594,1828],{},[902,49596,49597],{"encoding":904},"Q = \\sqrt{a - bQ}",[123,49599,49600,49601],{},"(c) ",[883,49602,49604],{"className":49603},[886],[888,49605,49606],{"xmlns":890},[892,49607,49608,49630],{},[895,49609,49610,49612,49614],{},[898,49611,1828],{},[1761,49613,1909],{},[6411,49615,49616],{"scriptlevel":1767,"displaystyle":1833},[4379,49617,49618,49628],{},[895,49619,49620,49622,49624],{},[898,49621,207],{},[1761,49623,1885],{},[12161,49625,49626],{},[898,49627,1839],{},[898,49629,4302],{},[902,49631,49632],{"encoding":904},"Q = \\dfrac{a - \\sqrt{P}}{b}",[123,49634,49635,49636],{},"(d) ",[883,49637,49639],{"className":49638},[886],[888,49640,49641],{"xmlns":890},[892,49642,49643,49661],{},[895,49644,49645,49647,49649,49651,49653,49655],{},[898,49646,1839],{},[1761,49648,1909],{},[898,49650,207],{},[1761,49652,1885],{},[898,49654,4302],{},[1824,49656,49657,49659],{},[898,49658,1828],{},[1765,49660,2296],{},[902,49662,49663],{"encoding":904},"P = a - bQ^2",[123,49665,49666,49667],{},"(e) ",[883,49668,49670],{"className":49669},[886],[888,49671,49672],{"xmlns":890},[892,49673,49674,49696],{},[895,49675,49676,49678,49680,49682,49692,49694],{},[898,49677,1828],{},[1761,49679,1909],{},[898,49681,4302],{},[1824,49683,49684,49686],{},[898,49685,1839],{},[895,49687,49688,49690],{},[1761,49689,1885],{},[898,49691,207],{},[1761,49693,1964],{},[898,49695,2774],{},[902,49697,49698],{"encoding":904},"Q = bP^{-a} + c",[123,49700,49701,49702],{},"(f) ",[883,49703,49705],{"className":49704},[886],[888,49706,49707],{"xmlns":890},[892,49708,49709,49732],{},[895,49710,49711,49713,49715,49717,49719],{},[898,49712,1828],{},[1761,49714,1909],{},[898,49716,207],{},[1761,49718,2447],{},[1824,49720,49721,49724],{},[898,49722,49723],{},"e",[895,49725,49726,49728,49730],{},[1761,49727,1885],{},[898,49729,4302],{},[898,49731,1839],{},[902,49733,49734],{"encoding":904},"Q = a \\cdot e^{-bP}",[724,49736,49737,49740],{},[38,49738,49739],{},"2.3"," Rozhodněte, jak se změní křivka poptávky, jestliže se zvýší (ceteris paribus):",[120,49742,49743,49746,49749],{},[123,49744,49745],{},"(a) Cena substitutu.",[123,49747,49748],{},"(b) Cena komplementu.",[123,49750,49751],{},"(c) Výdaje na reklamu.",[724,49753,49754,49417,49756,49790,49791,49819],{},[38,49755,28674],{},[883,49757,49759],{"className":49758},[886],[888,49760,49761],{"xmlns":890},[892,49762,49763,49787],{},[895,49764,49765,49767,49769,49771,49773,49775,49777,49779,49781,49783,49785],{},[898,49766,1839],{},[1761,49768,1909],{},[898,49770,2244],{},[1761,49772,1915],{"stretchy":1821},[898,49774,1828],{},[1761,49776,1920],{"stretchy":1821},[1761,49778,1909],{},[1765,49780,2291],{},[1761,49782,1885],{},[1765,49784,2296],{},[898,49786,1828],{},[902,49788,49789],{"encoding":904},"P = D(Q) = 12 - 2Q",". Najděte novou poptávku ",[883,49792,49794],{"className":49793},[886],[888,49795,49796],{"xmlns":890},[892,49797,49798,49816],{},[895,49799,49800,49802,49804,49810,49812,49814],{},[898,49801,1839],{},[1761,49803,1909],{},[1824,49805,49806,49808],{},[898,49807,2244],{},[1761,49809,8408],{},[1761,49811,1915],{"stretchy":1821},[898,49813,1828],{},[1761,49815,1920],{"stretchy":1821},[902,49817,49818],{"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.",[724,49821,49822,49825],{},[38,49823,49824],{},"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:",[120,49827,49828,49912,49988,50074,50162],{},[123,49829,49536,49830,1343,49870,1741],{},[883,49831,49833],{"className":49832},[886],[888,49834,49835],{"xmlns":890},[892,49836,49837,49867],{},[895,49838,49839,49845,49847,49849,49851,49853,49859,49861],{},[1681,49840,49841,49843],{},[898,49842,27286],{},[1765,49844,1945],{},[1761,49846,1909],{},[1765,49848,13077],{},[1761,49850,1885],{},[1765,49852,2318],{},[1681,49854,49855,49857],{},[898,49856,8309],{},[1765,49858,1945],{},[1761,49860,1964],{},[1681,49862,49863,49865],{},[898,49864,8309],{},[1765,49866,2296],{},[902,49868,49869],{"encoding":904},"B_1 = 20 - 4A_1 + A_2",[883,49871,49873],{"className":49872},[886],[888,49874,49875],{"xmlns":890},[892,49876,49877,49909],{},[895,49878,49879,49885,49887,49889,49891,49893,49899,49901,49903],{},[1681,49880,49881,49883],{},[898,49882,27286],{},[1765,49884,2296],{},[1761,49886,1909],{},[1765,49888,2633],{},[1761,49890,1964],{},[1765,49892,2296],{},[1681,49894,49895,49897],{},[898,49896,8309],{},[1765,49898,1945],{},[1761,49900,1885],{},[1765,49902,2318],{},[1681,49904,49905,49907],{},[898,49906,8309],{},[1765,49908,2296],{},[902,49910,49911],{"encoding":904},"B_2 = 10 + 2A_1 - 4A_2",[123,49913,49569,49914,1343,49956,1741],{},[883,49915,49917],{"className":49916},[886],[888,49918,49919],{"xmlns":890},[892,49920,49921,49953],{},[895,49922,49923,49929,49931,49933,49935,49937,49943,49945,49947],{},[1681,49924,49925,49927],{},[898,49926,27286],{},[1765,49928,1945],{},[1761,49930,1909],{},[1765,49932,7190],{},[1761,49934,1885],{},[1765,49936,2633],{},[1681,49938,49939,49941],{},[898,49940,8309],{},[1765,49942,1945],{},[1761,49944,1885],{},[1765,49946,2340],{},[1681,49948,49949,49951],{},[898,49950,8309],{},[1765,49952,2296],{},[902,49954,49955],{"encoding":904},"B_1 = 50 - 10A_1 - 6A_2",[883,49957,49959],{"className":49958},[886],[888,49960,49961],{"xmlns":890},[892,49962,49963,49985],{},[895,49964,49965,49971,49973,49975,49977,49979],{},[1681,49966,49967,49969],{},[898,49968,27286],{},[1765,49970,2296],{},[1761,49972,1909],{},[1765,49974,5433],{},[1761,49976,1885],{},[1765,49978,2633],{},[1681,49980,49981,49983],{},[898,49982,8309],{},[1765,49984,2296],{},[902,49986,49987],{"encoding":904},"B_2 = 15 - 10A_2",[123,49989,49600,49990,1343,50032,1741],{},[883,49991,49993],{"className":49992},[886],[888,49994,49995],{"xmlns":890},[892,49996,49997,50029],{},[895,49998,49999,50005,50007,50009,50011,50013,50019,50021,50023],{},[1681,50000,50001,50003],{},[898,50002,27286],{},[1765,50004,1945],{},[1761,50006,1909],{},[1765,50008,42042],{},[1761,50010,1885],{},[1765,50012,2296],{},[1681,50014,50015,50017],{},[898,50016,8309],{},[1765,50018,1945],{},[1761,50020,1885],{},[1765,50022,2318],{},[1681,50024,50025,50027],{},[898,50026,8309],{},[1765,50028,2296],{},[902,50030,50031],{"encoding":904},"B_1 = 30 - 2A_1 - 4A_2",[883,50033,50035],{"className":50034},[886],[888,50036,50037],{"xmlns":890},[892,50038,50039,50071],{},[895,50040,50041,50047,50049,50051,50053,50055,50061,50063,50065],{},[1681,50042,50043,50045],{},[898,50044,27286],{},[1765,50046,2296],{},[1761,50048,1909],{},[1765,50050,5433],{},[1761,50052,1964],{},[1765,50054,2296],{},[1681,50056,50057,50059],{},[898,50058,8309],{},[1765,50060,1945],{},[1761,50062,1885],{},[1765,50064,2296],{},[1681,50066,50067,50069],{},[898,50068,8309],{},[1765,50070,2296],{},[902,50072,50073],{"encoding":904},"B_2 = 15 + 2A_1 - 2A_2",[123,50075,49635,50076,1343,50120,1741],{},[883,50077,50079],{"className":50078},[886],[888,50080,50081],{"xmlns":890},[892,50082,50083,50117],{},[895,50084,50085,50091,50093,50095,50097,50099,50101,50107,50109,50111],{},[1681,50086,50087,50089],{},[898,50088,27286],{},[1765,50090,1945],{},[1761,50092,1909],{},[1761,50094,1885],{},[1765,50096,13077],{},[1761,50098,1885],{},[1765,50100,2296],{},[1681,50102,50103,50105],{},[898,50104,8309],{},[1765,50106,1945],{},[1761,50108,1964],{},[1765,50110,5486],{},[1681,50112,50113,50115],{},[898,50114,8309],{},[1765,50116,2296],{},[902,50118,50119],{"encoding":904},"B_1 = -20 - 2A_1 + 3A_2",[883,50121,50123],{"className":50122},[886],[888,50124,50125],{"xmlns":890},[892,50126,50127,50159],{},[895,50128,50129,50135,50137,50139,50141,50143,50149,50151,50153],{},[1681,50130,50131,50133],{},[898,50132,27286],{},[1765,50134,2296],{},[1761,50136,1909],{},[1765,50138,2633],{},[1761,50140,1964],{},[1765,50142,2296],{},[1681,50144,50145,50147],{},[898,50146,8309],{},[1765,50148,1945],{},[1761,50150,1885],{},[1765,50152,2296],{},[1681,50154,50155,50157],{},[898,50156,8309],{},[1765,50158,2296],{},[902,50160,50161],{"encoding":904},"B_2 = 10 + 2A_1 - 2A_2",[123,50163,49666,50164,1343,50206,1741],{},[883,50165,50167],{"className":50166},[886],[888,50168,50169],{"xmlns":890},[892,50170,50171,50203],{},[895,50172,50173,50179,50181,50183,50185,50187,50193,50195,50197],{},[1681,50174,50175,50177],{},[898,50176,27286],{},[1765,50178,1945],{},[1761,50180,1909],{},[1765,50182,13077],{},[1761,50184,1964],{},[1765,50186,2296],{},[1681,50188,50189,50191],{},[898,50190,8309],{},[1765,50192,1945],{},[1761,50194,1964],{},[1765,50196,2318],{},[1681,50198,50199,50201],{},[898,50200,8309],{},[1765,50202,2296],{},[902,50204,50205],{"encoding":904},"B_1 = 20 + 2A_1 + 4A_2",[883,50207,50209],{"className":50208},[886],[888,50210,50211],{"xmlns":890},[892,50212,50213,50245],{},[895,50214,50215,50221,50223,50225,50227,50229,50235,50237,50239],{},[1681,50216,50217,50219],{},[898,50218,27286],{},[1765,50220,2296],{},[1761,50222,1909],{},[1765,50224,9262],{},[1761,50226,1885],{},[1765,50228,5486],{},[1681,50230,50231,50233],{},[898,50232,8309],{},[1765,50234,1945],{},[1761,50236,1964],{},[1765,50238,6321],{},[1681,50240,50241,50243],{},[898,50242,8309],{},[1765,50244,2296],{},[902,50246,50247],{"encoding":904},"B_2 = 40 - 3A_1 + 5A_2",[198,50249,50251],{"id":50250},"základní-analýza-nabídky","Základní analýza nabídky",[724,50253,50254,50257,50258,50292,50293,50315],{},[38,50255,50256],{},"2.6"," Je dána nabídka ",[883,50259,50261],{"className":50260},[886],[888,50262,50263],{"xmlns":890},[892,50264,50265,50289],{},[895,50266,50267,50269,50271,50273,50275,50277,50279,50281,50283,50285,50287],{},[898,50268,1839],{},[1761,50270,1909],{},[898,50272,1912],{},[1761,50274,1915],{"stretchy":1821},[898,50276,1828],{},[1761,50278,1920],{"stretchy":1821},[1761,50280,1909],{},[1765,50282,13077],{},[1761,50284,1964],{},[1765,50286,6910],{},[898,50288,1828],{},[902,50290,50291],{"encoding":904},"P = S(Q) = 20 + 0{,}2Q",". (a) Načrtněte křivku nabídky. (b) Vypočtěte množství při cenách ",[883,50294,50296],{"className":50295},[886],[888,50297,50298],{"xmlns":890},[892,50299,50300,50312],{},[895,50301,50302,50304,50306,50308,50310],{},[1765,50303,9056],{},[1761,50305,1834],{"separator":1833},[1765,50307,42042],{},[1761,50309,1834],{"separator":1833},[1765,50311,19076],{},[902,50313,50314],{"encoding":904},"25, 30, 35"," a vyznačte výsledky na křivku nabídky.",[724,50317,50318,50321,50322,50339],{},[38,50319,50320],{},"2.7"," Ověřte, že zadané funkce vyjadřují (s případným omezením na ",[883,50323,50325],{"className":50324},[886],[888,50326,50327],{"xmlns":890},[892,50328,50329,50337],{},[895,50330,50331,50333,50335],{},[898,50332,1839],{},[1761,50334,1834],{"separator":1833},[898,50336,1828],{},[902,50338,49504],{"encoding":904},") nabídku (využijte testu na kladnost derivace), charakterizujte tvar křivky nabídky a vyjádřete nabídku v alternativním tvaru:",[120,50341,50342,50368,50396,50429,50463,50499],{},[123,50343,49536,50344],{},[883,50345,50347],{"className":50346},[886],[888,50348,50349],{"xmlns":890},[892,50350,50351,50365],{},[895,50352,50353,50355,50357,50359,50361,50363],{},[898,50354,1839],{},[1761,50356,1909],{},[1765,50358,42042],{},[1761,50360,1964],{},[1765,50362,2296],{},[898,50364,1828],{},[902,50366,50367],{"encoding":904},"P = 30 + 2Q",[123,50369,49569,50370],{},[883,50371,50373],{"className":50372},[886],[888,50374,50375],{"xmlns":890},[892,50376,50377,50393],{},[895,50378,50379,50381,50383,50385,50387,50389,50391],{},[898,50380,1828],{},[1761,50382,1909],{},[1761,50384,1885],{},[1765,50386,5486],{},[1761,50388,1964],{},[1765,50390,2291],{},[898,50392,1839],{},[902,50394,50395],{"encoding":904},"Q = -3 + 12P",[123,50397,49600,50398],{},[883,50399,50401],{"className":50400},[886],[888,50402,50403],{"xmlns":890},[892,50404,50405,50427],{},[895,50406,50407,50409,50411,50417,50419,50421,50423,50425],{},[898,50408,1839],{},[1761,50410,1909],{},[1824,50412,50413,50415],{},[898,50414,1828],{},[1765,50416,2296],{},[1761,50418,1964],{},[1765,50420,26979],{},[898,50422,1828],{},[1761,50424,1964],{},[1765,50426,36576],{},[902,50428,45732],{"encoding":904},[123,50430,49635,50431],{},[883,50432,50434],{"className":50433},[886],[888,50435,50436],{"xmlns":890},[892,50437,50438,50460],{},[895,50439,50440,50442,50444,50450,50452,50454,50456,50458],{},[898,50441,1839],{},[1761,50443,1909],{},[1824,50445,50446,50448],{},[898,50447,1828],{},[1765,50449,2296],{},[1761,50451,1964],{},[1765,50453,2296],{},[898,50455,1828],{},[1761,50457,1964],{},[1765,50459,2291],{},[902,50461,50462],{"encoding":904},"P = Q^2 + 2Q + 12",[123,50464,49666,50465],{},[883,50466,50468],{"className":50467},[886],[888,50469,50470],{"xmlns":890},[892,50471,50472,50496],{},[895,50473,50474,50476,50478,50480,50482,50484,50486,50488,50490],{},[898,50475,1828],{},[1761,50477,1909],{},[1765,50479,12845],{},[1761,50481,1964],{},[1765,50483,6321],{},[898,50485,1839],{},[1761,50487,1964],{},[1765,50489,6865],{},[1824,50491,50492,50494],{},[898,50493,1839],{},[1765,50495,2296],{},[902,50497,50498],{"encoding":904},"Q = 150 + 5P + 0{,}1P^2",[123,50500,49701,50501],{},[883,50502,50504],{"className":50503},[886],[888,50505,50506],{"xmlns":890},[892,50507,50508,50533],{},[895,50509,50510,50512,50514,50516,50518,50520,50522,50524,50527],{},[898,50511,1828],{},[1761,50513,1909],{},[1765,50515,5512],{},[1761,50517,1964],{},[1765,50519,6865],{},[898,50521,1839],{},[1761,50523,1964],{},[1765,50525,50526],{},"0,004",[1824,50528,50529,50531],{},[898,50530,1839],{},[1765,50532,2296],{},[902,50534,50535],{"encoding":904},"Q = 7 + 0{,}1P + 0{,}004P^2",[724,50537,50538,50541],{},[38,50539,50540],{},"2.8"," Rozhodněte, jak se změní křivka nabídky, jestliže se (ceteris paribus):",[120,50543,50544,50547,50550,50553],{},[123,50545,50546],{},"(a) Sníží ceny surovin — vstupů.",[123,50548,50549],{},"(b) Zavede nová ekologičtější technologie zvyšující výrobní náklady.",[123,50551,50552],{},"(c) Zvýší ceny všech energií.",[123,50554,50555],{},"(d) Sníží daňové odvody státu.",[724,50557,50558,50257,50560,50594,50595,50623],{},[38,50559,46947],{},[883,50561,50563],{"className":50562},[886],[888,50564,50565],{"xmlns":890},[892,50566,50567,50591],{},[895,50568,50569,50571,50573,50575,50577,50579,50581,50583,50585,50587,50589],{},[898,50570,1839],{},[1761,50572,1909],{},[898,50574,1912],{},[1761,50576,1915],{"stretchy":1821},[898,50578,1828],{},[1761,50580,1920],{"stretchy":1821},[1761,50582,1909],{},[1765,50584,5426],{},[898,50586,1828],{},[1761,50588,1964],{},[1765,50590,5433],{},[902,50592,50593],{"encoding":904},"P = S(Q) = 0{,}5Q + 15",". Najděte novou nabídku ",[883,50596,50598],{"className":50597},[886],[888,50599,50600],{"xmlns":890},[892,50601,50602,50620],{},[895,50603,50604,50606,50608,50614,50616,50618],{},[898,50605,1839],{},[1761,50607,1909],{},[1824,50609,50610,50612],{},[898,50611,1912],{},[1761,50613,8408],{},[1761,50615,1915],{"stretchy":1821},[898,50617,1828],{},[1761,50619,1920],{"stretchy":1821},[902,50621,50622],{"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.",[198,50625,45339],{"id":50626},"tržní-rovnováha-1",[724,50628,50629,50631,50632,50649,50650,2506],{},[38,50630,47005],{}," Pro zadanou poptávku a nabídku najděte rovnovážné množství ",[883,50633,50635],{"className":50634},[886],[888,50636,50637],{"xmlns":890},[892,50638,50639,50647],{},[895,50640,50641],{},[1824,50642,50643,50645],{},[898,50644,1828],{},[898,50646,1818],{},[902,50648,46412],{"encoding":904}," a rovnovážnou cenu ",[883,50651,50653],{"className":50652},[886],[888,50654,50655],{"xmlns":890},[892,50656,50657,50665],{},[895,50658,50659],{},[1824,50660,50661,50663],{},[898,50662,1839],{},[898,50664,1818],{},[902,50666,2161],{"encoding":904},[120,50668,50669,50721,50772,50831],{},[123,50670,49536,50671,1343,50697,1741],{},[883,50672,50674],{"className":50673},[886],[888,50675,50676],{"xmlns":890},[892,50677,50678,50694],{},[895,50679,50680,50682,50684,50686,50688,50690,50692],{},[898,50681,1839],{},[1761,50683,1909],{},[1761,50685,1885],{},[1765,50687,6321],{},[898,50689,1828],{},[1761,50691,1964],{},[1765,50693,5467],{},[902,50695,50696],{"encoding":904},"P = -5Q + 80",[883,50698,50700],{"className":50699},[886],[888,50701,50702],{"xmlns":890},[892,50703,50704,50718],{},[895,50705,50706,50708,50710,50712,50714,50716],{},[898,50707,1839],{},[1761,50709,1909],{},[1765,50711,2296],{},[898,50713,1828],{},[1761,50715,1964],{},[1765,50717,2633],{},[902,50719,50720],{"encoding":904},"P = 2Q + 10",[123,50722,49569,50723,1343,50749,1741],{},[883,50724,50726],{"className":50725},[886],[888,50727,50728],{"xmlns":890},[892,50729,50730,50746],{},[895,50731,50732,50734,50736,50738,50740,50742,50744],{},[898,50733,1828],{},[1761,50735,1909],{},[1761,50737,1885],{},[1765,50739,5426],{},[898,50741,1839],{},[1761,50743,1964],{},[1765,50745,9056],{},[902,50747,50748],{"encoding":904},"Q = -0{,}5P + 25",[883,50750,50752],{"className":50751},[886],[888,50753,50754],{"xmlns":890},[892,50755,50756,50770],{},[895,50757,50758,50760,50762,50764,50766,50768],{},[898,50759,1828],{},[1761,50761,1909],{},[1765,50763,2296],{},[898,50765,1839],{},[1761,50767,1885],{},[1765,50769,7190],{},[902,50771,44867],{"encoding":904},[123,50773,49600,50774,1343,50800,1741],{},[883,50775,50777],{"className":50776},[886],[888,50778,50779],{"xmlns":890},[892,50780,50781,50797],{},[895,50782,50783,50785,50787,50789,50791,50793,50795],{},[898,50784,1839],{},[1761,50786,1909],{},[1761,50788,1885],{},[1765,50790,2318],{},[898,50792,1828],{},[1761,50794,1964],{},[1765,50796,8103],{},[902,50798,50799],{"encoding":904},"P = -4Q + 120",[883,50801,50803],{"className":50802},[886],[888,50804,50805],{"xmlns":890},[892,50806,50807,50828],{},[895,50808,50809,50811,50813,50821,50823,50825],{},[898,50810,1839],{},[1761,50812,1909],{},[6411,50814,50815],{"scriptlevel":1767,"displaystyle":1821},[4379,50816,50817,50819],{},[1765,50818,1945],{},[1765,50820,5486],{},[898,50822,1828],{},[1761,50824,1964],{},[1765,50826,50827],{},"29",[902,50829,50830],{"encoding":904},"P = \\tfrac{1}{3}Q + 29",[123,50832,49635,50833,1343,50862,1741],{},[883,50834,50836],{"className":50835},[886],[888,50837,50838],{"xmlns":890},[892,50839,50840,50859],{},[895,50841,50842,50844,50846,50848,50854,50856],{},[898,50843,1839],{},[1761,50845,1909],{},[1761,50847,1885],{},[1824,50849,50850,50852],{},[898,50851,1828],{},[1765,50853,2296],{},[1761,50855,1964],{},[1765,50857,50858],{},"52",[902,50860,50861],{"encoding":904},"P = -Q^2 + 52",[883,50863,50865],{"className":50864},[886],[888,50866,50867],{"xmlns":890},[892,50868,50869,50887],{},[895,50870,50871,50873,50875,50877,50883,50885],{},[898,50872,1839],{},[1761,50874,1909],{},[1765,50876,2296],{},[1824,50878,50879,50881],{},[898,50880,1828],{},[1765,50882,2296],{},[1761,50884,1964],{},[1765,50886,2633],{},[902,50888,50889],{"encoding":904},"P = 2Q^2 + 10",[724,50891,50892,50895,50896,50926,50927,50957],{},[38,50893,50894],{},"2.11"," Pro zadanou poptávku a nabídku dvou závislých zboží najděte rovnovážná množství ",[883,50897,50899],{"className":50898},[886],[888,50900,50901],{"xmlns":890},[892,50902,50903,50923],{},[895,50904,50905,50913,50915],{},[2015,50906,50907,50909,50911],{},[898,50908,1828],{},[1765,50910,1945],{},[898,50912,1818],{},[1761,50914,1834],{"separator":1833},[2015,50916,50917,50919,50921],{},[898,50918,1828],{},[1765,50920,2296],{},[898,50922,1818],{},[902,50924,50925],{"encoding":904},"Q_1^E, Q_2^E"," a rovnovážné ceny ",[883,50928,50930],{"className":50929},[886],[888,50931,50932],{"xmlns":890},[892,50933,50934,50954],{},[895,50935,50936,50944,50946],{},[2015,50937,50938,50940,50942],{},[898,50939,1839],{},[1765,50941,1945],{},[898,50943,1818],{},[1761,50945,1834],{"separator":1833},[2015,50947,50948,50950,50952],{},[898,50949,1839],{},[1765,50951,2296],{},[898,50953,1818],{},[902,50955,50956],{"encoding":904},"P_1^E, P_2^E"," (index 1 přísluší prvnímu, index 2 druhému zboží):",[120,50959,50960,51112],{},[123,50961,49536,50962,1343,51002,1343,51044,1343,51078,1741],{},[883,50963,50965],{"className":50964},[886],[888,50966,50967],{"xmlns":890},[892,50968,50969,50999],{},[895,50970,50971,50977,50979,50981,50983,50985,50991,50993],{},[1681,50972,50973,50975],{},[898,50974,1828],{},[1765,50976,1945],{},[1761,50978,1909],{},[1765,50980,2633],{},[1761,50982,1885],{},[1765,50984,2296],{},[1681,50986,50987,50989],{},[898,50988,1839],{},[1765,50990,1945],{},[1761,50992,1964],{},[1681,50994,50995,50997],{},[898,50996,1839],{},[1765,50998,2296],{},[902,51000,51001],{"encoding":904},"Q_1 = 10 - 2P_1 + P_2",[883,51003,51005],{"className":51004},[886],[888,51006,51007],{"xmlns":890},[892,51008,51009,51041],{},[895,51010,51011,51017,51019,51021,51023,51025,51031,51033,51035],{},[1681,51012,51013,51015],{},[898,51014,1828],{},[1765,51016,2296],{},[1761,51018,1909],{},[1765,51020,6321],{},[1761,51022,1964],{},[1765,51024,2296],{},[1681,51026,51027,51029],{},[898,51028,1839],{},[1765,51030,1945],{},[1761,51032,1885],{},[1765,51034,2296],{},[1681,51036,51037,51039],{},[898,51038,1839],{},[1765,51040,2296],{},[902,51042,51043],{"encoding":904},"Q_2 = 5 + 2P_1 - 2P_2",[883,51045,51047],{"className":51046},[886],[888,51048,51049],{"xmlns":890},[892,51050,51051,51075],{},[895,51052,51053,51059,51061,51063,51065,51067,51069],{},[1681,51054,51055,51057],{},[898,51056,1828],{},[1765,51058,1945],{},[1761,51060,1909],{},[1761,51062,1885],{},[1765,51064,5486],{},[1761,51066,1964],{},[1765,51068,2296],{},[1681,51070,51071,51073],{},[898,51072,1839],{},[1765,51074,1945],{},[902,51076,51077],{"encoding":904},"Q_1 = -3 + 2P_1",[883,51079,51081],{"className":51080},[886],[888,51082,51083],{"xmlns":890},[892,51084,51085,51109],{},[895,51086,51087,51093,51095,51097,51099,51101,51103],{},[1681,51088,51089,51091],{},[898,51090,1828],{},[1765,51092,2296],{},[1761,51094,1909],{},[1761,51096,1885],{},[1765,51098,2296],{},[1761,51100,1964],{},[1765,51102,5486],{},[1681,51104,51105,51107],{},[898,51106,1839],{},[1765,51108,2296],{},[902,51110,51111],{"encoding":904},"Q_2 = -2 + 3P_2",[123,51113,49569,51114,1343,51154,1343,51196,1343,51228,1741],{},[883,51115,51117],{"className":51116},[886],[888,51118,51119],{"xmlns":890},[892,51120,51121,51151],{},[895,51122,51123,51129,51131,51133,51135,51137,51143,51145],{},[1681,51124,51125,51127],{},[898,51126,1828],{},[1765,51128,1945],{},[1761,51130,1909],{},[1765,51132,7160],{},[1761,51134,1885],{},[1765,51136,2296],{},[1681,51138,51139,51141],{},[898,51140,1839],{},[1765,51142,1945],{},[1761,51144,1964],{},[1681,51146,51147,51149],{},[898,51148,1839],{},[1765,51150,2296],{},[902,51152,51153],{"encoding":904},"Q_1 = 100 - 2P_1 + P_2",[883,51155,51157],{"className":51156},[886],[888,51158,51159],{"xmlns":890},[892,51160,51161,51193],{},[895,51162,51163,51169,51171,51173,51175,51177,51183,51185,51187],{},[1681,51164,51165,51167],{},[898,51166,1828],{},[1765,51168,2296],{},[1761,51170,1909],{},[1765,51172,6321],{},[1761,51174,1964],{},[1765,51176,2296],{},[1681,51178,51179,51181],{},[898,51180,1839],{},[1765,51182,1945],{},[1761,51184,1885],{},[1765,51186,5486],{},[1681,51188,51189,51191],{},[898,51190,1839],{},[1765,51192,2296],{},[902,51194,51195],{"encoding":904},"Q_2 = 5 + 2P_1 - 3P_2",[883,51197,51199],{"className":51198},[886],[888,51200,51201],{"xmlns":890},[892,51202,51203,51225],{},[895,51204,51205,51211,51213,51215,51217,51219],{},[1681,51206,51207,51209],{},[898,51208,1828],{},[1765,51210,1945],{},[1761,51212,1909],{},[1761,51214,1885],{},[1765,51216,2633],{},[1761,51218,1964],{},[1681,51220,51221,51223],{},[898,51222,1839],{},[1765,51224,1945],{},[902,51226,51227],{"encoding":904},"Q_1 = -10 + P_1",[883,51229,51231],{"className":51230},[886],[888,51232,51233],{"xmlns":890},[892,51234,51235,51257],{},[895,51236,51237,51243,51245,51247,51249,51251],{},[1681,51238,51239,51241],{},[898,51240,1828],{},[1765,51242,2296],{},[1761,51244,1909],{},[1765,51246,6321],{},[1761,51248,1964],{},[1765,51250,2340],{},[1681,51252,51253,51255],{},[898,51254,1839],{},[1765,51256,2296],{},[902,51258,51259],{"encoding":904},"Q_2 = 5 + 6P_2",[724,51261,51262,51265,51266,1343,51314,1343,51360,51410,51411,1343,51443,1343,51477,25627,51511,2068,51529,51547,51548,51561,51562,51588,51589,50926,51629,1741],{},[38,51263,51264],{},"2.12"," Pro tři závislá zboží jsou dány poptávky rovnicemi ",[883,51267,51269],{"className":51268},[886],[888,51270,51271],{"xmlns":890},[892,51272,51273,51311],{},[895,51274,51275,51281,51283,51285,51287,51293,51295,51297,51303,51305],{},[1681,51276,51277,51279],{},[898,51278,1828],{},[1765,51280,1945],{},[1761,51282,1909],{},[1765,51284,5433],{},[1761,51286,1885],{},[1681,51288,51289,51291],{},[898,51290,1839],{},[1765,51292,1945],{},[1761,51294,1964],{},[1765,51296,2296],{},[1681,51298,51299,51301],{},[898,51300,1839],{},[1765,51302,2296],{},[1761,51304,1964],{},[1681,51306,51307,51309],{},[898,51308,1839],{},[1765,51310,5486],{},[902,51312,51313],{"encoding":904},"Q_1 = 15 - P_1 + 2P_2 + P_3",[883,51315,51317],{"className":51316},[886],[888,51318,51319],{"xmlns":890},[892,51320,51321,51357],{},[895,51322,51323,51329,51331,51333,51335,51341,51343,51349,51351],{},[1681,51324,51325,51327],{},[898,51326,1828],{},[1765,51328,2296],{},[1761,51330,1909],{},[1765,51332,8056],{},[1761,51334,1964],{},[1681,51336,51337,51339],{},[898,51338,1839],{},[1765,51340,1945],{},[1761,51342,1885],{},[1681,51344,51345,51347],{},[898,51346,1839],{},[1765,51348,2296],{},[1761,51350,1885],{},[1681,51352,51353,51355],{},[898,51354,1839],{},[1765,51356,5486],{},[902,51358,51359],{"encoding":904},"Q_2 = 9 + P_1 - P_2 - P_3",[883,51361,51363],{"className":51362},[886],[888,51364,51365],{"xmlns":890},[892,51366,51367,51407],{},[895,51368,51369,51375,51377,51379,51381,51383,51389,51391,51397,51399,51401],{},[1681,51370,51371,51373],{},[898,51372,1828],{},[1765,51374,5486],{},[1761,51376,1909],{},[1765,51378,2454],{},[1761,51380,1964],{},[1765,51382,2296],{},[1681,51384,51385,51387],{},[898,51386,1839],{},[1765,51388,1945],{},[1761,51390,1885],{},[1681,51392,51393,51395],{},[898,51394,1839],{},[1765,51396,2296],{},[1761,51398,1885],{},[1765,51400,2318],{},[1681,51402,51403,51405],{},[898,51404,1839],{},[1765,51406,5486],{},[902,51408,51409],{"encoding":904},"Q_3 = 8 + 2P_1 - P_2 - 4P_3"," a nabídky rovnicemi ",[883,51412,51414],{"className":51413},[886],[888,51415,51416],{"xmlns":890},[892,51417,51418,51440],{},[895,51419,51420,51426,51428,51430,51432,51434],{},[1681,51421,51422,51424],{},[898,51423,1828],{},[1765,51425,1945],{},[1761,51427,1909],{},[1761,51429,1885],{},[1765,51431,5512],{},[1761,51433,1964],{},[1681,51435,51436,51438],{},[898,51437,1839],{},[1765,51439,1945],{},[902,51441,51442],{"encoding":904},"Q_1 = -7 + P_1",[883,51444,51446],{"className":51445},[886],[888,51447,51448],{"xmlns":890},[892,51449,51450,51474],{},[895,51451,51452,51458,51460,51462,51464,51466,51468],{},[1681,51453,51454,51456],{},[898,51455,1828],{},[1765,51457,2296],{},[1761,51459,1909],{},[1761,51461,1885],{},[1765,51463,2318],{},[1761,51465,1964],{},[1765,51467,2318],{},[1681,51469,51470,51472],{},[898,51471,1839],{},[1765,51473,2296],{},[902,51475,51476],{"encoding":904},"Q_2 = -4 + 4P_2",[883,51478,51480],{"className":51479},[886],[888,51481,51482],{"xmlns":890},[892,51483,51484,51508],{},[895,51485,51486,51492,51494,51496,51498,51500,51502],{},[1681,51487,51488,51490],{},[898,51489,1828],{},[1765,51491,5486],{},[1761,51493,1909],{},[1761,51495,1885],{},[1765,51497,6321],{},[1761,51499,1964],{},[1765,51501,2296],{},[1681,51503,51504,51506],{},[898,51505,1839],{},[1765,51507,5486],{},[902,51509,51510],{"encoding":904},"Q_3 = -5 + 2P_3",[883,51512,51514],{"className":51513},[886],[888,51515,51516],{"xmlns":890},[892,51517,51518,51526],{},[895,51519,51520],{},[1681,51521,51522,51524],{},[898,51523,1828],{},[898,51525,21824],{},[902,51527,51528],{"encoding":904},"Q_i",[883,51530,51532],{"className":51531},[886],[888,51533,51534],{"xmlns":890},[892,51535,51536,51544],{},[895,51537,51538],{},[1681,51539,51540,51542],{},[898,51541,1839],{},[898,51543,21824],{},[902,51545,51546],{"encoding":904},"P_i"," značí příslušné množství a ceny ",[883,51549,51551],{"className":51550},[886],[888,51552,51553],{"xmlns":890},[892,51554,51555,51559],{},[895,51556,51557],{},[898,51558,21824],{},[902,51560,21824],{"encoding":904},"-tého zboží, ",[883,51563,51565],{"className":51564},[886],[888,51566,51567],{"xmlns":890},[892,51568,51569,51585],{},[895,51570,51571,51573,51575,51577,51579,51581,51583],{},[898,51572,21824],{},[1761,51574,1909],{},[1765,51576,1945],{},[1761,51578,1834],{"separator":1833},[1765,51580,2296],{},[1761,51582,1834],{"separator":1833},[1765,51584,5486],{},[902,51586,51587],{"encoding":904},"i = 1, 2, 3",". Najděte rovnovážná množství ",[883,51590,51592],{"className":51591},[886],[888,51593,51594],{"xmlns":890},[892,51595,51596,51626],{},[895,51597,51598,51606,51608,51616,51618],{},[2015,51599,51600,51602,51604],{},[898,51601,1828],{},[1765,51603,1945],{},[898,51605,1818],{},[1761,51607,1834],{"separator":1833},[2015,51609,51610,51612,51614],{},[898,51611,1828],{},[1765,51613,2296],{},[898,51615,1818],{},[1761,51617,1834],{"separator":1833},[2015,51619,51620,51622,51624],{},[898,51621,1828],{},[1765,51623,5486],{},[898,51625,1818],{},[902,51627,51628],{"encoding":904},"Q_1^E, Q_2^E, Q_3^E",[883,51630,51632],{"className":51631},[886],[888,51633,51634],{"xmlns":890},[892,51635,51636,51666],{},[895,51637,51638,51646,51648,51656,51658],{},[2015,51639,51640,51642,51644],{},[898,51641,1839],{},[1765,51643,1945],{},[898,51645,1818],{},[1761,51647,1834],{"separator":1833},[2015,51649,51650,51652,51654],{},[898,51651,1839],{},[1765,51653,2296],{},[898,51655,1818],{},[1761,51657,1834],{"separator":1833},[2015,51659,51660,51662,51664],{},[898,51661,1839],{},[1765,51663,5486],{},[898,51665,1818],{},[902,51667,51668],{"encoding":904},"P_1^E, P_2^E, P_3^E",[724,51670,51671,51674,51675,51711,51712,1741],{},[38,51672,51673],{},"2.13"," Jsou dány poptávka ",[883,51676,51678],{"className":51677},[886],[888,51679,51680],{"xmlns":890},[892,51681,51682,51708],{},[895,51683,51684,51686,51688,51690,51692,51694,51696,51698,51700,51702,51704,51706],{},[898,51685,1839],{},[1761,51687,1909],{},[898,51689,2244],{},[1761,51691,1915],{"stretchy":1821},[898,51693,1828],{},[1761,51695,1920],{"stretchy":1821},[1761,51697,1909],{},[1761,51699,1885],{},[1765,51701,2318],{},[898,51703,1828],{},[1761,51705,1964],{},[1765,51707,5467],{},[902,51709,51710],{"encoding":904},"P = D(Q) = -4Q + 80"," a nabídka ",[883,51713,51715],{"className":51714},[886],[888,51716,51717],{"xmlns":890},[892,51718,51719,51743],{},[895,51720,51721,51723,51725,51727,51729,51731,51733,51735,51737,51739,51741],{},[898,51722,1839],{},[1761,51724,1909],{},[898,51726,1912],{},[1761,51728,1915],{"stretchy":1821},[898,51730,1828],{},[1761,51732,1920],{"stretchy":1821},[1761,51734,1909],{},[1765,51736,5486],{},[898,51738,1828],{},[1761,51740,1964],{},[1765,51742,2633],{},[902,51744,51745],{"encoding":904},"P = S(Q) = 3Q + 10",[120,51747,51748,51785,51846,51904],{},[123,51749,51750,51751,50649,51768,1741],{},"(a) Určete rovnovážné množství ",[883,51752,51754],{"className":51753},[886],[888,51755,51756],{"xmlns":890},[892,51757,51758,51766],{},[895,51759,51760],{},[1824,51761,51762,51764],{},[898,51763,1828],{},[898,51765,1818],{},[902,51767,46412],{"encoding":904},[883,51769,51771],{"className":51770},[886],[888,51772,51773],{"xmlns":890},[892,51774,51775,51783],{},[895,51776,51777],{},[1824,51778,51779,51781],{},[898,51780,1839],{},[898,51782,1818],{},[902,51784,2161],{"encoding":904},[123,51786,51787,51788,51805,51806,51825,51826,51845],{},"(b) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží výrobci daň ",[883,51789,51791],{"className":51790},[886],[888,51792,51793],{"xmlns":890},[892,51794,51795,51803],{},[895,51796,51797,51799,51801],{},[898,51798,1655],{},[1761,51800,1909],{},[1765,51802,5512],{},[902,51804,5515],{"encoding":904}," Kč na každou jednotku zboží, vypočtěte nové rovnovážné množství ",[883,51807,51809],{"className":51808},[886],[888,51810,51811],{"xmlns":890},[892,51812,51813,51823],{},[895,51814,51815],{},[2015,51816,51817,51819,51821],{},[898,51818,1828],{},[1765,51820,1945],{},[898,51822,1818],{},[902,51824,4568],{"encoding":904}," a novou rovnovážnou cenu ",[883,51827,51829],{"className":51828},[886],[888,51830,51831],{"xmlns":890},[892,51832,51833,51843],{},[895,51834,51835],{},[2015,51836,51837,51839,51841],{},[898,51838,1839],{},[1765,51840,1945],{},[898,51842,1818],{},[902,51844,2117],{"encoding":904}," a určete, kolik z daňového zatížení zaplatí výrobce a kolik spotřebitel.",[123,51847,51848,51849,51805,51866,51825,51885,51845],{},"(c) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží spotřebiteli daň ",[883,51850,51852],{"className":51851},[886],[888,51853,51854],{"xmlns":890},[892,51855,51856,51864],{},[895,51857,51858,51860,51862],{},[898,51859,1655],{},[1761,51861,1909],{},[1765,51863,5512],{},[902,51865,5515],{"encoding":904},[883,51867,51869],{"className":51868},[886],[888,51870,51871],{"xmlns":890},[892,51872,51873,51883],{},[895,51874,51875],{},[2015,51876,51877,51879,51881],{},[898,51878,1828],{},[1765,51880,2296],{},[898,51882,1818],{},[902,51884,4589],{"encoding":904},[883,51886,51888],{"className":51887},[886],[888,51889,51890],{"xmlns":890},[892,51891,51892,51902],{},[895,51893,51894],{},[2015,51895,51896,51898,51900],{},[898,51897,1839],{},[1765,51899,2296],{},[898,51901,1818],{},[902,51903,3220],{"encoding":904},[123,51905,51906],{},"(d) Proveďte analýzu dopadu daňového zatížení na spotřebitele a výrobce vyplývající z výsledků (b) a (c).",[724,51908,51909,51910,1741],{},"Viz též ",[207,51911,46724],{"className":51912,"dataFsResolvedFilePath":809,"href":810},[210],[198,51914,47019],{"id":51915},"multiplikátory-pro-mikroekonomické-proměnné-1",[724,51917,51918,51674,51921,51711,51957,1741],{},[38,51919,51920],{},"2.14",[883,51922,51924],{"className":51923},[886],[888,51925,51926],{"xmlns":890},[892,51927,51928,51954],{},[895,51929,51930,51932,51934,51936,51938,51940,51942,51944,51946,51948,51950,51952],{},[898,51931,1839],{},[1761,51933,1909],{},[898,51935,207],{},[898,51937,1828],{},[1761,51939,1964],{},[898,51941,4302],{},[1761,51943,1909],{},[1761,51945,1885],{},[1765,51947,2296],{},[898,51949,1828],{},[1761,51951,1964],{},[1765,51953,7190],{},[902,51955,51956],{"encoding":904},"P = aQ + b = -2Q + 50",[883,51958,51960],{"className":51959},[886],[888,51961,51962],{"xmlns":890},[892,51963,51964,51988],{},[895,51965,51966,51968,51970,51972,51974,51976,51978,51980,51982,51984,51986],{},[898,51967,1839],{},[1761,51969,1909],{},[898,51971,2774],{},[898,51973,1828],{},[1761,51975,1964],{},[898,51977,4346],{},[1761,51979,1909],{},[1765,51981,23354],{},[898,51983,1828],{},[1761,51985,1964],{},[1765,51987,13077],{},[902,51989,51990],{"encoding":904},"P = cQ + d = 0{,}6Q + 20",[120,51992,51993,52029,52032,52118,52171,52251,52305],{},[123,51994,51750,51995,50649,52012,1741],{},[883,51996,51998],{"className":51997},[886],[888,51999,52000],{"xmlns":890},[892,52001,52002,52010],{},[895,52003,52004],{},[1824,52005,52006,52008],{},[898,52007,1828],{},[898,52009,1818],{},[902,52011,46412],{"encoding":904},[883,52013,52015],{"className":52014},[886],[888,52016,52017],{"xmlns":890},[892,52018,52019,52027],{},[895,52020,52021],{},[1824,52022,52023,52025],{},[898,52024,1839],{},[898,52026,1818],{},[902,52028,2161],{"encoding":904},[123,52030,52031],{},"(b) Určete hodnoty multiplikátorů pro zadané parametry.",[123,52033,52034,52035,52052,52053,6746,52066,4178,52082,52098,52099,1741],{},"(c) Určete přibližnou změnu rovnovážného množství ",[883,52036,52038],{"className":52037},[886],[888,52039,52040],{"xmlns":890},[892,52041,52042,52050],{},[895,52043,52044],{},[1824,52045,52046,52048],{},[898,52047,1828],{},[898,52049,1818],{},[902,52051,46412],{"encoding":904}," odpovídající změně ",[883,52054,52056],{"className":52055},[886],[888,52057,52058],{"xmlns":890},[892,52059,52060,52064],{},[895,52061,52062],{},[898,52063,207],{},[902,52065,207],{"encoding":904},[883,52067,52069],{"className":52068},[886],[888,52070,52071],{"xmlns":890},[892,52072,52073,52079],{},[895,52074,52075,52077],{},[1761,52076,1885],{},[1765,52078,2296],{},[902,52080,52081],{"encoding":904},"-2",[883,52083,52085],{"className":52084},[886],[888,52086,52087],{"xmlns":890},[892,52088,52089,52095],{},[895,52090,52091,52093],{},[1761,52092,1885],{},[1765,52094,5486],{},[902,52096,52097],{"encoding":904},"-3"," (ceteris paribus) a stanovte nové rovnovážné množství ",[883,52100,52102],{"className":52101},[886],[888,52103,52104],{"xmlns":890},[892,52105,52106,52116],{},[895,52107,52108],{},[2015,52109,52110,52112,52114],{},[898,52111,1828],{},[1765,52113,1945],{},[898,52115,1818],{},[902,52117,4568],{"encoding":904},[123,52119,52120,52121,52052,52138,52151,52152,1741],{},"(d) Určete přibližnou změnu rovnovážného množství ",[883,52122,52124],{"className":52123},[886],[888,52125,52126],{"xmlns":890},[892,52127,52128,52136],{},[895,52129,52130],{},[1824,52131,52132,52134],{},[898,52133,1828],{},[898,52135,1818],{},[902,52137,46412],{"encoding":904},[883,52139,52141],{"className":52140},[886],[888,52142,52143],{"xmlns":890},[892,52144,52145,52149],{},[895,52146,52147],{},[898,52148,4302],{},[902,52150,4302],{"encoding":904}," z 50 na 60 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,52153,52155],{"className":52154},[886],[888,52156,52157],{"xmlns":890},[892,52158,52159,52169],{},[895,52160,52161],{},[2015,52162,52163,52165,52167],{},[898,52164,1828],{},[1765,52166,2296],{},[898,52168,1818],{},[902,52170,4589],{"encoding":904},[123,52172,52173,52174,52052,52191,6746,52204,4178,52217,52098,52231,1741],{},"(e) Určete přibližnou změnu rovnovážného množství ",[883,52175,52177],{"className":52176},[886],[888,52178,52179],{"xmlns":890},[892,52180,52181,52189],{},[895,52182,52183],{},[1824,52184,52185,52187],{},[898,52186,1828],{},[898,52188,1818],{},[902,52190,46412],{"encoding":904},[883,52192,52194],{"className":52193},[886],[888,52195,52196],{"xmlns":890},[892,52197,52198,52202],{},[895,52199,52200],{},[898,52201,2774],{},[902,52203,2774],{"encoding":904},[883,52205,52207],{"className":52206},[886],[888,52208,52209],{"xmlns":890},[892,52210,52211,52215],{},[895,52212,52213],{},[1765,52214,23354],{},[902,52216,48455],{"encoding":904},[883,52218,52220],{"className":52219},[886],[888,52221,52222],{"xmlns":890},[892,52223,52224,52228],{},[895,52225,52226],{},[1765,52227,18627],{},[902,52229,52230],{"encoding":904},"0{,}8",[883,52232,52234],{"className":52233},[886],[888,52235,52236],{"xmlns":890},[892,52237,52238,52248],{},[895,52239,52240],{},[2015,52241,52242,52244,52246],{},[898,52243,1828],{},[1765,52245,5486],{},[898,52247,1818],{},[902,52249,52250],{"encoding":904},"Q_3^E",[123,52252,52253,52254,52052,52271,52284,52285,1741],{},"(f) Určete přibližnou změnu rovnovážného množství ",[883,52255,52257],{"className":52256},[886],[888,52258,52259],{"xmlns":890},[892,52260,52261,52269],{},[895,52262,52263],{},[1824,52264,52265,52267],{},[898,52266,1828],{},[898,52268,1818],{},[902,52270,46412],{"encoding":904},[883,52272,52274],{"className":52273},[886],[888,52275,52276],{"xmlns":890},[892,52277,52278,52282],{},[895,52279,52280],{},[898,52281,4346],{},[902,52283,4346],{"encoding":904}," z 20 na 10 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,52286,52288],{"className":52287},[886],[888,52289,52290],{"xmlns":890},[892,52291,52292,52302],{},[895,52293,52294],{},[2015,52295,52296,52298,52300],{},[898,52297,1828],{},[1765,52299,2318],{},[898,52301,1818],{},[902,52303,52304],{"encoding":904},"Q_4^E",[123,52306,52307,52308,52325,52326,52339,52340,25453,52353,1343,52368,25453,52381,2068,52395,25453,52408,52423,52424,1741],{},"(g) Určete přibližnou změnu rovnovážného množství ",[883,52309,52311],{"className":52310},[886],[888,52312,52313],{"xmlns":890},[892,52314,52315,52323],{},[895,52316,52317],{},[1824,52318,52319,52321],{},[898,52320,1828],{},[898,52322,1818],{},[902,52324,46412],{"encoding":904}," odpovídající změnám ",[883,52327,52329],{"className":52328},[886],[888,52330,52331],{"xmlns":890},[892,52332,52333,52337],{},[895,52334,52335],{},[898,52336,207],{},[902,52338,207],{"encoding":904}," o 1, ",[883,52341,52343],{"className":52342},[886],[888,52344,52345],{"xmlns":890},[892,52346,52347,52351],{},[895,52348,52349],{},[898,52350,4302],{},[902,52352,4302],{"encoding":904},[883,52354,52356],{"className":52355},[886],[888,52357,52358],{"xmlns":890},[892,52359,52360,52366],{},[895,52361,52362,52364],{},[1761,52363,1885],{},[1765,52365,2633],{},[902,52367,23488],{"encoding":904},[883,52369,52371],{"className":52370},[886],[888,52372,52373],{"xmlns":890},[892,52374,52375,52379],{},[895,52376,52377],{},[898,52378,2774],{},[902,52380,2774],{"encoding":904},[883,52382,52384],{"className":52383},[886],[888,52385,52386],{"xmlns":890},[892,52387,52388,52392],{},[895,52389,52390],{},[1765,52391,6865],{},[902,52393,52394],{"encoding":904},"0{,}1",[883,52396,52398],{"className":52397},[886],[888,52399,52400],{"xmlns":890},[892,52401,52402,52406],{},[895,52403,52404],{},[898,52405,4346],{},[902,52407,4346],{"encoding":904},[883,52409,52411],{"className":52410},[886],[888,52412,52413],{"xmlns":890},[892,52414,52415,52421],{},[895,52416,52417,52419],{},[1761,52418,1885],{},[1765,52420,2633],{},[902,52422,23488],{"encoding":904}," vzhledem k zadaným hodnotám a stanovte nové rovnovážné množství ",[883,52425,52427],{"className":52426},[886],[888,52428,52429],{"xmlns":890},[892,52430,52431,52441],{},[895,52432,52433],{},[2015,52434,52435,52437,52439],{},[898,52436,1828],{},[1765,52438,6321],{},[898,52440,1818],{},[902,52442,52443],{"encoding":904},"Q_5^E",[724,52445,52446,51674,52449,51711,52472,1741],{},[38,52447,52448],{},"2.15",[883,52450,52452],{"className":52451},[886],[888,52453,52454],{"xmlns":890},[892,52455,52456,52470],{},[895,52457,52458,52460,52462,52464,52466,52468],{},[898,52459,1839],{},[1761,52461,1909],{},[898,52463,207],{},[898,52465,1828],{},[1761,52467,1964],{},[898,52469,4302],{},[902,52471,4305],{"encoding":904},[883,52473,52475],{"className":52474},[886],[888,52476,52477],{"xmlns":890},[892,52478,52479,52493],{},[895,52480,52481,52483,52485,52487,52489,52491],{},[898,52482,1839],{},[1761,52484,1909],{},[898,52486,2774],{},[898,52488,1828],{},[1761,52490,1964],{},[898,52492,4346],{},[902,52494,4349],{"encoding":904},[120,52496,52497,52572,52589,52698,52751,52805],{},[123,52498,52499,52500,52513,52514,52539,52540,52571],{},"(a) Odvoďte redukovaný tvar pro ",[883,52501,52503],{"className":52502},[886],[888,52504,52505],{"xmlns":890},[892,52506,52507,52511],{},[895,52508,52509],{},[898,52510,1839],{},[902,52512,1839],{"encoding":904},". Stanovte podmínky pro ",[883,52515,52517],{"className":52516},[886],[888,52518,52519],{"xmlns":890},[892,52520,52521,52537],{},[895,52522,52523,52525,52527,52529,52531,52533,52535],{},[898,52524,207],{},[1761,52526,1834],{"separator":1833},[898,52528,4302],{},[1761,52530,1834],{"separator":1833},[898,52532,2774],{},[1761,52534,1834],{"separator":1833},[898,52536,4346],{},[902,52538,47280],{"encoding":904}," tak, aby rovnovážný bod ",[883,52541,52543],{"className":52542},[886],[888,52544,52545],{"xmlns":890},[892,52546,52547,52569],{},[895,52548,52549,52551,52553,52559,52561,52567],{},[898,52550,1818],{},[1761,52552,1822],{"stretchy":1821},[1824,52554,52555,52557],{},[898,52556,1828],{},[898,52558,1818],{},[1761,52560,1834],{"separator":1833},[1824,52562,52563,52565],{},[898,52564,1839],{},[898,52566,1818],{},[1761,52568,1844],{"stretchy":1821},[902,52570,1847],{"encoding":904}," patřil do 1. kvadrantu (využijte obrázku 2.22).",[123,52573,52574,52575,52588],{},"(b) Vypočtěte multiplikátory pro ",[883,52576,52578],{"className":52577},[886],[888,52579,52580],{"xmlns":890},[892,52581,52582,52586],{},[895,52583,52584],{},[898,52585,1839],{},[902,52587,1839],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků 2.22, 2.23).",[123,52590,52591,52592,1343,52612,1343,52630,1343,52648,52666,52667,52684,52685,1741],{},"(c) Pro hodnoty parametrů ",[883,52593,52595],{"className":52594},[886],[888,52596,52597],{"xmlns":890},[892,52598,52599,52609],{},[895,52600,52601,52603,52605,52607],{},[898,52602,207],{},[1761,52604,1909],{},[1761,52606,1885],{},[1765,52608,2296],{},[902,52610,52611],{"encoding":904},"a = -2",[883,52613,52615],{"className":52614},[886],[888,52616,52617],{"xmlns":890},[892,52618,52619,52627],{},[895,52620,52621,52623,52625],{},[898,52622,4302],{},[1761,52624,1909],{},[1765,52626,9262],{},[902,52628,52629],{"encoding":904},"b = 40",[883,52631,52633],{"className":52632},[886],[888,52634,52635],{"xmlns":890},[892,52636,52637,52645],{},[895,52638,52639,52641,52643],{},[898,52640,2774],{},[1761,52642,1909],{},[1765,52644,5426],{},[902,52646,52647],{"encoding":904},"c = 0{,}5",[883,52649,52651],{"className":52650},[886],[888,52652,52653],{"xmlns":890},[892,52654,52655,52663],{},[895,52656,52657,52659,52661],{},[898,52658,4346],{},[1761,52660,1909],{},[1765,52662,2633],{},[902,52664,52665],{"encoding":904},"d = 10"," určete rovnovážnou cenu ",[883,52668,52670],{"className":52669},[886],[888,52671,52672],{"xmlns":890},[892,52673,52674,52682],{},[895,52675,52676],{},[1824,52677,52678,52680],{},[898,52679,1839],{},[898,52681,1818],{},[902,52683,2161],{"encoding":904}," a hodnoty multiplikátorů pro ",[883,52686,52688],{"className":52687},[886],[888,52689,52690],{"xmlns":890},[892,52691,52692,52696],{},[895,52693,52694],{},[898,52695,1839],{},[902,52697,1839],{"encoding":904},[123,52699,52700,52701,52052,52718,52731,52732,1741],{},"(d) Určete přibližnou změnu rovnovážné ceny ",[883,52702,52704],{"className":52703},[886],[888,52705,52706],{"xmlns":890},[892,52707,52708,52716],{},[895,52709,52710],{},[1824,52711,52712,52714],{},[898,52713,1839],{},[898,52715,1818],{},[902,52717,2161],{"encoding":904},[883,52719,52721],{"className":52720},[886],[888,52722,52723],{"xmlns":890},[892,52724,52725,52729],{},[895,52726,52727],{},[898,52728,207],{},[902,52730,207],{"encoding":904}," o 5 (ceteris paribus) a stanovte novou rovnovážnou cenu ",[883,52733,52735],{"className":52734},[886],[888,52736,52737],{"xmlns":890},[892,52738,52739,52749],{},[895,52740,52741],{},[2015,52742,52743,52745,52747],{},[898,52744,1839],{},[1765,52746,1945],{},[898,52748,1818],{},[902,52750,2117],{"encoding":904},[123,52752,52753,52754,52771,52772,52785,52786,1741],{},"(e) Určete přibližnou změnu rovnovážné ceny ",[883,52755,52757],{"className":52756},[886],[888,52758,52759],{"xmlns":890},[892,52760,52761,52769],{},[895,52762,52763],{},[1824,52764,52765,52767],{},[898,52766,1839],{},[898,52768,1818],{},[902,52770,2161],{"encoding":904}," odpovídající poklesu ",[883,52773,52775],{"className":52774},[886],[888,52776,52777],{"xmlns":890},[892,52778,52779,52783],{},[895,52780,52781],{},[898,52782,207],{},[902,52784,207],{"encoding":904}," o 1 a stanovte novou rovnovážnou cenu ",[883,52787,52789],{"className":52788},[886],[888,52790,52791],{"xmlns":890},[892,52792,52793,52803],{},[895,52794,52795],{},[2015,52796,52797,52799,52801],{},[898,52798,1839],{},[1765,52800,2296],{},[898,52802,1818],{},[902,52804,3220],{"encoding":904},[123,52806,52807,52808,52325,52825,52838,52839,4178,52852,2068,52867,52880,52881,1741],{},"(f) Určete přibližnou změnu rovnovážné ceny ",[883,52809,52811],{"className":52810},[886],[888,52812,52813],{"xmlns":890},[892,52814,52815,52823],{},[895,52816,52817],{},[1824,52818,52819,52821],{},[898,52820,1839],{},[898,52822,1818],{},[902,52824,2161],{"encoding":904},[883,52826,52828],{"className":52827},[886],[888,52829,52830],{"xmlns":890},[892,52831,52832,52836],{},[895,52833,52834],{},[898,52835,207],{},[902,52837,207],{"encoding":904}," na 35, ",[883,52840,52842],{"className":52841},[886],[888,52843,52844],{"xmlns":890},[892,52845,52846,52850],{},[895,52847,52848],{},[898,52849,2774],{},[902,52851,2774],{"encoding":904},[883,52853,52855],{"className":52854},[886],[888,52856,52857],{"xmlns":890},[892,52858,52859,52864],{},[895,52860,52861],{},[1765,52862,52863],{},"0,7",[902,52865,52866],{"encoding":904},"0{,}7",[883,52868,52870],{"className":52869},[886],[888,52871,52872],{"xmlns":890},[892,52873,52874,52878],{},[895,52875,52876],{},[898,52877,4346],{},[902,52879,4346],{"encoding":904}," na 12 vzhledem k hodnotám dle (d) a stanovte novou rovnovážnou cenu ",[883,52882,52884],{"className":52883},[886],[888,52885,52886],{"xmlns":890},[892,52887,52888,52898],{},[895,52889,52890],{},[2015,52891,52892,52894,52896],{},[898,52893,1839],{},[1765,52895,5486],{},[898,52897,1818],{},[902,52899,52900],{"encoding":904},"P_3^E",[724,52902,52903,51674,52906,51711,52934,25627,52962,2068,52988,1741],{},[38,52904,52905],{},"2.16",[883,52907,52909],{"className":52908},[886],[888,52910,52911],{"xmlns":890},[892,52912,52913,52931],{},[895,52914,52915,52917,52919,52921,52923,52925],{},[898,52916,1839],{},[1761,52918,1909],{},[898,52920,207],{},[1761,52922,1964],{},[898,52924,4302],{},[1824,52926,52927,52929],{},[898,52928,1828],{},[1765,52930,2296],{},[902,52932,52933],{"encoding":904},"P = a + bQ^2",[883,52935,52937],{"className":52936},[886],[888,52938,52939],{"xmlns":890},[892,52940,52941,52959],{},[895,52942,52943,52945,52947,52949,52951,52953],{},[898,52944,1839],{},[1761,52946,1909],{},[898,52948,2774],{},[1761,52950,1964],{},[898,52952,4346],{},[1824,52954,52955,52957],{},[898,52956,1828],{},[1765,52958,2296],{},[902,52960,52961],{"encoding":904},"P = c + dQ^2",[883,52963,52965],{"className":52964},[886],[888,52966,52967],{"xmlns":890},[892,52968,52969,52985],{},[895,52970,52971,52973,52975,52977,52979,52981,52983],{},[898,52972,207],{},[1761,52974,1834],{"separator":1833},[898,52976,2774],{},[1761,52978,1834],{"separator":1833},[898,52980,4346],{},[1761,52982,1763],{},[1765,52984,1767],{},[902,52986,52987],{"encoding":904},"a, c, d > 0",[883,52989,52991],{"className":52990},[886],[888,52992,52993],{"xmlns":890},[892,52994,52995,53003],{},[895,52996,52997,52999,53001],{},[898,52998,4302],{},[1761,53000,2058],{},[1765,53002,1767],{},[902,53004,53005],{"encoding":904},"b \u003C 0",[120,53007,53008,53056,53072,53179,53231,53283,53392,53408,53507,53560],{},[123,53009,52499,53010,53023,53024,53055],{},[883,53011,53013],{"className":53012},[886],[888,53014,53015],{"xmlns":890},[892,53016,53017,53021],{},[895,53018,53019],{},[898,53020,1828],{},[902,53022,1828],{"encoding":904},". Načrtněte křivky poptávky a nabídky a stanovte podmínky, aby rovnovážný bod ",[883,53025,53027],{"className":53026},[886],[888,53028,53029],{"xmlns":890},[892,53030,53031,53053],{},[895,53032,53033,53035,53037,53043,53045,53051],{},[898,53034,1818],{},[1761,53036,1822],{"stretchy":1821},[1824,53038,53039,53041],{},[898,53040,1828],{},[898,53042,1818],{},[1761,53044,1834],{"separator":1833},[1824,53046,53047,53049],{},[898,53048,1839],{},[898,53050,1818],{},[1761,53052,1844],{"stretchy":1821},[902,53054,1847],{"encoding":904}," patřil do 1. kvadrantu.",[123,53057,52574,53058,53071],{},[883,53059,53061],{"className":53060},[886],[888,53062,53063],{"xmlns":890},[892,53064,53065,53069],{},[895,53066,53067],{},[898,53068,1828],{},[902,53070,1828],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků v (b)).",[123,53073,52591,53074,1343,53092,1343,53112,1343,53130,53148,53149,52684,53166,1741],{},[883,53075,53077],{"className":53076},[886],[888,53078,53079],{"xmlns":890},[892,53080,53081,53089],{},[895,53082,53083,53085,53087],{},[898,53084,207],{},[1761,53086,1909],{},[1765,53088,7160],{},[902,53090,53091],{"encoding":904},"a = 100",[883,53093,53095],{"className":53094},[886],[888,53096,53097],{"xmlns":890},[892,53098,53099,53109],{},[895,53100,53101,53103,53105,53107],{},[898,53102,4302],{},[1761,53104,1909],{},[1761,53106,1885],{},[1765,53108,1945],{},[902,53110,53111],{"encoding":904},"b = -1",[883,53113,53115],{"className":53114},[886],[888,53116,53117],{"xmlns":890},[892,53118,53119,53127],{},[895,53120,53121,53123,53125],{},[898,53122,2774],{},[1761,53124,1909],{},[1765,53126,13077],{},[902,53128,53129],{"encoding":904},"c = 20",[883,53131,53133],{"className":53132},[886],[888,53134,53135],{"xmlns":890},[892,53136,53137,53145],{},[895,53138,53139,53141,53143],{},[898,53140,4346],{},[1761,53142,1909],{},[1765,53144,1945],{},[902,53146,53147],{"encoding":904},"d = 1"," určete rovnovážné množství ",[883,53150,53152],{"className":53151},[886],[888,53153,53154],{"xmlns":890},[892,53155,53156,53164],{},[895,53157,53158],{},[1824,53159,53160,53162],{},[898,53161,1828],{},[898,53163,1818],{},[902,53165,46412],{"encoding":904},[883,53167,53169],{"className":53168},[886],[888,53170,53171],{"xmlns":890},[892,53172,53173,53177],{},[895,53174,53175],{},[898,53176,1828],{},[902,53178,1828],{"encoding":904},[123,53180,52120,53181,52052,53198,53211,53212,1741],{},[883,53182,53184],{"className":53183},[886],[888,53185,53186],{"xmlns":890},[892,53187,53188,53196],{},[895,53189,53190],{},[1824,53191,53192,53194],{},[898,53193,1828],{},[898,53195,1818],{},[902,53197,46412],{"encoding":904},[883,53199,53201],{"className":53200},[886],[888,53202,53203],{"xmlns":890},[892,53204,53205,53209],{},[895,53206,53207],{},[898,53208,207],{},[902,53210,207],{"encoding":904}," na 110 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,53213,53215],{"className":53214},[886],[888,53216,53217],{"xmlns":890},[892,53218,53219,53229],{},[895,53220,53221],{},[2015,53222,53223,53225,53227],{},[898,53224,1828],{},[1765,53226,1945],{},[898,53228,1818],{},[902,53230,4568],{"encoding":904},[123,53232,52173,53233,52052,53250,53263,53264,1741],{},[883,53234,53236],{"className":53235},[886],[888,53237,53238],{"xmlns":890},[892,53239,53240,53248],{},[895,53241,53242],{},[1824,53243,53244,53246],{},[898,53245,1828],{},[898,53247,1818],{},[902,53249,46412],{"encoding":904},[883,53251,53253],{"className":53252},[886],[888,53254,53255],{"xmlns":890},[892,53256,53257,53261],{},[895,53258,53259],{},[898,53260,2774],{},[902,53262,2774],{"encoding":904}," na 25 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,53265,53267],{"className":53266},[886],[888,53268,53269],{"xmlns":890},[892,53270,53271,53281],{},[895,53272,53273],{},[2015,53274,53275,53277,53279],{},[898,53276,1828],{},[1765,53278,2296],{},[898,53280,1818],{},[902,53282,4589],{"encoding":904},[123,53284,52253,53285,52325,53302,53315,53316,4178,53329,53344,53345,53358,53359,53372,53373,1741],{},[883,53286,53288],{"className":53287},[886],[888,53289,53290],{"xmlns":890},[892,53291,53292,53300],{},[895,53293,53294],{},[1824,53295,53296,53298],{},[898,53297,1828],{},[898,53299,1818],{},[902,53301,46412],{"encoding":904},[883,53303,53305],{"className":53304},[886],[888,53306,53307],{"xmlns":890},[892,53308,53309,53313],{},[895,53310,53311],{},[898,53312,207],{},[902,53314,207],{"encoding":904}," na 110, poklesu ",[883,53317,53319],{"className":53318},[886],[888,53320,53321],{"xmlns":890},[892,53322,53323,53327],{},[895,53324,53325],{},[898,53326,4302],{},[902,53328,4302],{"encoding":904},[883,53330,53332],{"className":53331},[886],[888,53333,53334],{"xmlns":890},[892,53335,53336,53342],{},[895,53337,53338,53340],{},[1761,53339,1885],{},[1765,53341,2296],{},[902,53343,52081],{"encoding":904},", růstu ",[883,53346,53348],{"className":53347},[886],[888,53349,53350],{"xmlns":890},[892,53351,53352,53356],{},[895,53353,53354],{},[898,53355,2774],{},[902,53357,2774],{"encoding":904}," na 25 a růstu ",[883,53360,53362],{"className":53361},[886],[888,53363,53364],{"xmlns":890},[892,53365,53366,53370],{},[895,53367,53368],{},[898,53369,4346],{},[902,53371,4346],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte nové rovnovážné množství ",[883,53374,53376],{"className":53375},[886],[888,53377,53378],{"xmlns":890},[892,53379,53380,53390],{},[895,53381,53382],{},[2015,53383,53384,53386,53388],{},[898,53385,1828],{},[1765,53387,5486],{},[898,53389,1818],{},[902,53391,52250],{"encoding":904},[123,53393,53394,53395,53071],{},"(i) Vypočtěte multiplikátory pro ",[883,53396,53398],{"className":53397},[886],[888,53399,53400],{"xmlns":890},[892,53401,53402,53406],{},[895,53403,53404],{},[898,53405,1839],{},[902,53407,1839],{"encoding":904},[123,53409,53410,53411,52684,53428,53441,53442,52052,53459,4178,53472,53487,53488,1741],{},"(j) Pro hodnoty parametrů dle (b) určete rovnovážnou cenu ",[883,53412,53414],{"className":53413},[886],[888,53415,53416],{"xmlns":890},[892,53417,53418,53426],{},[895,53419,53420],{},[1824,53421,53422,53424],{},[898,53423,1839],{},[898,53425,1818],{},[902,53427,2161],{"encoding":904},[883,53429,53431],{"className":53430},[886],[888,53432,53433],{"xmlns":890},[892,53434,53435,53439],{},[895,53436,53437],{},[898,53438,1839],{},[902,53440,1839],{"encoding":904},", přibližnou změnu rovnovážné ceny ",[883,53443,53445],{"className":53444},[886],[888,53446,53447],{"xmlns":890},[892,53448,53449,53457],{},[895,53450,53451],{},[1824,53452,53453,53455],{},[898,53454,1839],{},[898,53456,1818],{},[902,53458,2161],{"encoding":904},[883,53460,53462],{"className":53461},[886],[888,53463,53464],{"xmlns":890},[892,53465,53466,53470],{},[895,53467,53468],{},[898,53469,207],{},[902,53471,207],{"encoding":904},[883,53473,53475],{"className":53474},[886],[888,53476,53477],{"xmlns":890},[892,53478,53479,53485],{},[895,53480,53481,53483],{},[1761,53482,1885],{},[1765,53484,5486],{},[902,53486,52097],{"encoding":904}," (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,53489,53491],{"className":53490},[886],[888,53492,53493],{"xmlns":890},[892,53494,53495,53505],{},[895,53496,53497],{},[2015,53498,53499,53501,53503],{},[898,53500,1839],{},[1765,53502,1945],{},[898,53504,1818],{},[902,53506,2117],{"encoding":904},[123,53508,53509,53510,52052,53527,53540,53541,1741],{},"(k) Určete přibližnou změnu rovnovážné ceny ",[883,53511,53513],{"className":53512},[886],[888,53514,53515],{"xmlns":890},[892,53516,53517,53525],{},[895,53518,53519],{},[1824,53520,53521,53523],{},[898,53522,1839],{},[898,53524,1818],{},[902,53526,2161],{"encoding":904},[883,53528,53530],{"className":53529},[886],[888,53531,53532],{"xmlns":890},[892,53533,53534,53538],{},[895,53535,53536],{},[898,53537,207],{},[902,53539,207],{"encoding":904}," na 2 (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,53542,53544],{"className":53543},[886],[888,53545,53546],{"xmlns":890},[892,53547,53548,53558],{},[895,53549,53550],{},[2015,53551,53552,53554,53556],{},[898,53553,1839],{},[1765,53555,2296],{},[898,53557,1818],{},[902,53559,3220],{"encoding":904},[123,53561,53562,53563,52771,53580,53593,53594,4178,53607,53344,53622,53635,53636,53649,53650,1741],{},"(l) Určete přibližnou změnu rovnovážné ceny ",[883,53564,53566],{"className":53565},[886],[888,53567,53568],{"xmlns":890},[892,53569,53570,53578],{},[895,53571,53572],{},[1824,53573,53574,53576],{},[898,53575,1839],{},[898,53577,1818],{},[902,53579,2161],{"encoding":904},[883,53581,53583],{"className":53582},[886],[888,53584,53585],{"xmlns":890},[892,53586,53587,53591],{},[895,53588,53589],{},[898,53590,207],{},[902,53592,207],{"encoding":904}," na 90, poklesu ",[883,53595,53597],{"className":53596},[886],[888,53598,53599],{"xmlns":890},[892,53600,53601,53605],{},[895,53602,53603],{},[898,53604,4302],{},[902,53606,4302],{"encoding":904},[883,53608,53610],{"className":53609},[886],[888,53611,53612],{"xmlns":890},[892,53613,53614,53620],{},[895,53615,53616,53618],{},[1761,53617,1885],{},[1765,53619,5486],{},[902,53621,52097],{"encoding":904},[883,53623,53625],{"className":53624},[886],[888,53626,53627],{"xmlns":890},[892,53628,53629,53633],{},[895,53630,53631],{},[898,53632,2774],{},[902,53634,2774],{"encoding":904}," na 30 a růstu ",[883,53637,53639],{"className":53638},[886],[888,53640,53641],{"xmlns":890},[892,53642,53643,53647],{},[895,53644,53645],{},[898,53646,4346],{},[902,53648,4346],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,53651,53653],{"className":53652},[886],[888,53654,53655],{"xmlns":890},[892,53656,53657,53667],{},[895,53658,53659],{},[2015,53660,53661,53663,53665],{},[898,53662,1839],{},[1765,53664,5486],{},[898,53666,1818],{},[902,53668,52900],{"encoding":904},[198,53670,820],{"id":53671},"přebytek-spotřebitele-a-výrobce-1",[724,53673,53674,51674,53677,51711,53713,1741],{},[38,53675,53676],{},"2.17",[883,53678,53680],{"className":53679},[886],[888,53681,53682],{"xmlns":890},[892,53683,53684,53710],{},[895,53685,53686,53688,53690,53692,53694,53696,53698,53700,53702,53704],{},[898,53687,1839],{},[1761,53689,1909],{},[898,53691,2244],{},[1761,53693,1915],{"stretchy":1821},[898,53695,1828],{},[1761,53697,1920],{"stretchy":1821},[1761,53699,1909],{},[1765,53701,19076],{},[1761,53703,1885],{},[1824,53705,53706,53708],{},[898,53707,1828],{},[1765,53709,2296],{},[902,53711,53712],{"encoding":904},"P = D(Q) = 35 - Q^2",[883,53714,53716],{"className":53715},[886],[888,53717,53718],{"xmlns":890},[892,53719,53720,53746],{},[895,53721,53722,53724,53726,53728,53730,53732,53734,53736,53738,53740],{},[898,53723,1839],{},[1761,53725,1909],{},[898,53727,1912],{},[1761,53729,1915],{"stretchy":1821},[898,53731,1828],{},[1761,53733,1920],{"stretchy":1821},[1761,53735,1909],{},[1765,53737,5486],{},[1761,53739,1964],{},[1824,53741,53742,53744],{},[898,53743,1828],{},[1765,53745,2296],{},[902,53747,53748],{"encoding":904},"P = S(Q) = 3 + Q^2",[120,53750,53751,53754],{},[123,53752,53753],{},"(a) Vypočtěte přebytek spotřebitele při množství 4.",[123,53755,53756],{},"(b) Vypočtěte přebytek výrobce při množství 4.",[724,53758,53759,51674,53762,51711,53796,1741],{},[38,53760,53761],{},"2.18",[883,53763,53765],{"className":53764},[886],[888,53766,53767],{"xmlns":890},[892,53768,53769,53793],{},[895,53770,53771,53773,53775,53777,53779,53781,53783,53785,53787,53789,53791],{},[898,53772,1839],{},[1761,53774,1909],{},[898,53776,2244],{},[1761,53778,1915],{"stretchy":1821},[898,53780,1828],{},[1761,53782,1920],{"stretchy":1821},[1761,53784,1909],{},[1765,53786,7771],{},[1761,53788,1885],{},[1765,53790,2296],{},[898,53792,1828],{},[902,53794,53795],{"encoding":904},"P = D(Q) = 18 - 2Q",[883,53797,53799],{"className":53798},[886],[888,53800,53801],{"xmlns":890},[892,53802,53803,53829],{},[895,53804,53805,53807,53809,53811,53813,53815,53817,53819,53821,53823],{},[898,53806,1839],{},[1761,53808,1909],{},[898,53810,1912],{},[1761,53812,1915],{"stretchy":1821},[898,53814,1828],{},[1761,53816,1920],{"stretchy":1821},[1761,53818,1909],{},[1765,53820,5486],{},[1761,53822,1964],{},[1824,53824,53825,53827],{},[898,53826,1828],{},[1765,53828,2296],{},[902,53830,53748],{"encoding":904},[120,53832,53833,53853,53856,53859],{},[123,53834,53835,53836,1741],{},"(a) Vypočtěte rovnovážné množství ",[883,53837,53839],{"className":53838},[886],[888,53840,53841],{"xmlns":890},[892,53842,53843,53851],{},[895,53844,53845],{},[1824,53846,53847,53849],{},[898,53848,1828],{},[898,53850,1818],{},[902,53852,46412],{"encoding":904},[123,53854,53855],{},"(b) Vypočtěte přebytek spotřebitele při rovnovážném množství.",[123,53857,53858],{},"(b) Vypočtěte přebytek výrobce při rovnovážném množství.",[123,53860,53861],{},"(c) Graficky interpretujte.",[1849,53863],{},[115,53865,53867],{"id":53866},"otázky-k-sebehodnocení","Otázky k sebehodnocení",[152,53869,53870,53873,53876,53879,53882,53885,53888,53891,53894,53897,53900,53903,53906,53909],{},[123,53871,53872],{},"Jaký je rozdíl mezi jednofaktorovým a vícefaktorovým modelem poptávky?",[123,53874,53875],{},"Vyjádřete (vícefaktorovou) funkci poptávky. Jakou má vlastnost?",[123,53877,53878],{},"Definujte funkci poptávky (jednofaktorovou). Jaká je její základní vlastnost? Zdůvodněte.",[123,53880,53881],{},"Definujte Engelovu funkci. Na čem závisí tvar příslušné Engelovy křivky?",[123,53883,53884],{},"Jaký charakter má odezva poptávky na změnu některé z exogenních proměnných?",[123,53886,53887],{},"Definujte funkci nabídky. Jaká je její základní vlastnost? Zdůvodněte.",[123,53889,53890],{},"Co znamená tržní rovnováha? Čím je reprezentována?",[123,53892,53893],{},"Jak se určí rovnovážné množství a rovnovážná cena?",[123,53895,53896],{},"Jaká jsou pravidla pro změnu rovnovážného bodu jako odezvy na posun poptávky, resp. nabídky?",[123,53898,53899],{},"K čemu slouží multiplikátory?",[123,53901,53902],{},"Jak se najde redukovaný tvar pro vybranou rovnovážnou veličinu?",[123,53904,53905],{},"Jak se vypočtou multiplikátory? Mění se jejich znaménka?",[123,53907,53908],{},"Co se rozumí přebytkem spotřebitele? Jak se vypočte?",[123,53910,53911],{},"Co se rozumí přebytkem výrobce? Jak se vypočte?",[1849,53913],{},[115,53915,5533],{"id":5532},[724,53917,53918],{},[38,53919,17199],{},[120,53921,53922,53957,53962,53992,53997,54060,54086,54091,54121,54130,54137,54143],{},[123,53923,53924,3927,53927,5991,53930,1989,53932,1343,53955],{},[38,53925,53926],{},"Poptávané množství",[614,53928,53929],{},"quantity demanded",[38,53931,32033],{},[883,53933,53935],{"className":53934},[886],[888,53936,53937],{"xmlns":890},[892,53938,53939,53953],{},[895,53940,53941,53943,53945,53947,53949,53951],{},[898,53942,1828],{},[1761,53944,1909],{},[898,53946,2244],{},[1761,53948,1915],{"stretchy":1821},[898,53950,1839],{},[1761,53952,1920],{"stretchy":1821},[902,53954,8247],{"encoding":904},[38,53956,41475],{},[123,53958,53959,53961],{},[38,53960,41482],{}," — substituční + důchodový efekt",[123,53963,53964,1989,53967],{},[38,53965,53966],{},"Reálné cenové rozpětí",[883,53968,53970],{"className":53969},[886],[888,53971,53972],{"xmlns":890},[892,53973,53974,53990],{},[895,53975,53976,53978,53980,53982,53988],{},[1761,53977,1915],{"stretchy":1821},[1765,53979,1767],{},[1761,53981,1834],{"separator":1833},[1681,53983,53984,53986],{},[898,53985,1839],{},[1765,53987,1767],{},[1761,53989,1920],{"stretchy":1821},[902,53991,41683],{"encoding":904},[123,53993,53994,15135],{},[38,53995,53996],{},"Homogenita poptávky",[123,53998,53999,1989,54002,1343,54025,1343,54042,54059],{},[38,54000,54001],{},"Lineární poptávka",[883,54003,54005],{"className":54004},[886],[888,54006,54007],{"xmlns":890},[892,54008,54009,54023],{},[895,54010,54011,54013,54015,54017,54019,54021],{},[898,54012,1839],{},[1761,54014,1909],{},[898,54016,207],{},[898,54018,1828],{},[1761,54020,1964],{},[898,54022,4302],{},[902,54024,4305],{"encoding":904},[883,54026,54028],{"className":54027},[886],[888,54029,54030],{"xmlns":890},[892,54031,54032,54040],{},[895,54033,54034,54036,54038],{},[898,54035,207],{},[1761,54037,2058],{},[1765,54039,1767],{},[902,54041,4323],{"encoding":904},[883,54043,54045],{"className":54044},[886],[888,54046,54047],{"xmlns":890},[892,54048,54049,54057],{},[895,54050,54051,54053,54055],{},[898,54052,4302],{},[1761,54054,1763],{},[1765,54056,1767],{},[902,54058,22847],{"encoding":904}," — nedokonalá konkurence",[123,54061,54062,5675,54065],{},[38,54063,54064],{},"Dokonalá konkurence",[883,54066,54068],{"className":54067},[886],[888,54069,54070],{"xmlns":890},[892,54071,54072,54084],{},[895,54073,54074,54076,54078],{},[898,54075,1839],{},[1761,54077,1909],{},[1824,54079,54080,54082],{},[898,54081,1839],{},[1761,54083,8408],{},[902,54085,8411],{"encoding":904},[123,54087,54088,54090],{},[38,54089,42249],{}," — rostoucí křivka poptávky (důchodový efekt > substituční)",[123,54092,54093,1989,54095,1343,54119],{},[38,54094,35757],{},[883,54096,54098],{"className":54097},[886],[888,54099,54100],{"xmlns":890},[892,54101,54102,54116],{},[895,54103,54104,54106,54108,54110,54112,54114],{},[898,54105,1828],{},[1761,54107,1909],{},[898,54109,1818],{},[1761,54111,1915],{"stretchy":1821},[898,54113,13170],{},[1761,54115,1920],{"stretchy":1821},[902,54117,54118],{"encoding":904},"Q = E(Y)",[38,54120,42445],{},[123,54122,54123,54126,54127,54129],{},[38,54124,54125],{},"Normální"," (nezbytné \u002F luxusní) vs. ",[38,54128,42891],{}," zboží",[123,54131,54132,2068,54134,54136],{},[38,54133,43897],{},[38,54135,43844],{}," — znaménka zkřížených koeficientů",[123,54138,54139,54142],{},[38,54140,54141],{},"Dvoukomoditní trh"," (2.6)",[123,54144,54145,3927,54148,1920],{},[38,54146,54147],{},"Posun poptávky",[614,54149,42949],{},[724,54151,54152],{},[38,54153,17163],{},[120,54155,54156,54189,54193,54238],{},[123,54157,54158,3927,54160,5991,54162,1989,54164,1343,54187],{},[38,54159,44289],{},[614,54161,44292],{},[38,54163,44463],{},[883,54165,54167],{"className":54166},[886],[888,54168,54169],{"xmlns":890},[892,54170,54171,54185],{},[895,54172,54173,54175,54177,54179,54181,54183],{},[898,54174,1828],{},[1761,54176,1909],{},[898,54178,1912],{},[1761,54180,1915],{"stretchy":1821},[898,54182,1839],{},[1761,54184,1920],{"stretchy":1821},[902,54186,12724],{"encoding":904},[38,54188,44541],{},[123,54190,54191],{},[38,54192,44548],{},[123,54194,54195,1989,54198,1343,54221],{},[38,54196,54197],{},"Lineární nabídka",[883,54199,54201],{"className":54200},[886],[888,54202,54203],{"xmlns":890},[892,54204,54205,54219],{},[895,54206,54207,54209,54211,54213,54215,54217],{},[898,54208,1839],{},[1761,54210,1909],{},[898,54212,2774],{},[898,54214,1828],{},[1761,54216,1964],{},[898,54218,4346],{},[902,54220,4349],{"encoding":904},[883,54222,54224],{"className":54223},[886],[888,54225,54226],{"xmlns":890},[892,54227,54228,54236],{},[895,54229,54230,54232,54234],{},[898,54231,2774],{},[1761,54233,1763],{},[1765,54235,1767],{},[902,54237,4367],{"encoding":904},[123,54239,54240,3927,54243,1920],{},[38,54241,54242],{},"Posun nabídky",[614,54244,44926],{},[724,54246,54247],{},[38,54248,54249],{},"Rovnováha a komparativní statika",[120,54251,54252,54331,54337],{},[123,54253,54254,3927,54256,5991,54258,1989,54261,1343,54278,1989,54281,1343,54298,1989,54300],{},[38,54255,45339],{},[614,54257,45457],{},[38,54259,54260],{},"rovnovážná cena",[883,54262,54264],{"className":54263},[886],[888,54265,54266],{"xmlns":890},[892,54267,54268,54276],{},[895,54269,54270],{},[1824,54271,54272,54274],{},[898,54273,1839],{},[898,54275,1818],{},[902,54277,2161],{"encoding":904},[38,54279,54280],{},"rovnovážné množství",[883,54282,54284],{"className":54283},[886],[888,54285,54286],{"xmlns":890},[892,54287,54288,54296],{},[895,54289,54290],{},[1824,54291,54292,54294],{},[898,54293,1828],{},[898,54295,1818],{},[902,54297,46412],{"encoding":904},[38,54299,45514],{},[883,54301,54303],{"className":54302},[886],[888,54304,54305],{"xmlns":890},[892,54306,54307,54329],{},[895,54308,54309,54311,54313,54319,54321,54327],{},[898,54310,1818],{},[1761,54312,1822],{"stretchy":1821},[1824,54314,54315,54317],{},[898,54316,1828],{},[898,54318,1818],{},[1761,54320,1834],{"separator":1833},[1824,54322,54323,54325],{},[898,54324,1839],{},[898,54326,1818],{},[1761,54328,1844],{"stretchy":1821},[902,54330,1847],{"encoding":904},[123,54332,54333,54336],{},[38,54334,54335],{},"Pravidla 1–4"," komparativní statiky",[123,54338,54339,3927,54342,1920],{},[38,54340,54341],{},"Teorém pavučiny",[614,54343,46358],{},[724,54345,54346],{},[38,54347,54348],{},"Zdanění",[120,54350,54351,54407,54455],{},[123,54352,54353,54355,54356,54381,54382,1920],{},[38,54354,54348],{}," — daň výrobci (",[883,54357,54359],{"className":54358},[886],[888,54360,54361],{"xmlns":890},[892,54362,54363,54379],{},[895,54364,54365,54371,54373,54375,54377],{},[1681,54366,54367,54369],{},[898,54368,1912],{},[1765,54370,1945],{},[1761,54372,1909],{},[898,54374,1912],{},[1761,54376,1964],{},[898,54378,1655],{},[902,54380,4519],{"encoding":904},") vs. daň spotřebiteli (",[883,54383,54385],{"className":54384},[886],[888,54386,54387],{"xmlns":890},[892,54388,54389,54405],{},[895,54390,54391,54397,54399,54401,54403],{},[1681,54392,54393,54395],{},[898,54394,2244],{},[1765,54396,2296],{},[1761,54398,1909],{},[898,54400,2244],{},[1761,54402,1885],{},[898,54404,1655],{},[902,54406,4545],{"encoding":904},[123,54408,54409,1989,54411,1343,54432],{},[38,54410,3922],{},[883,54412,54414],{"className":54413},[886],[888,54415,54416],{"xmlns":890},[892,54417,54418,54430],{},[895,54419,54420],{},[1681,54421,54422,54424],{},[898,54423,1655],{},[895,54425,54426,54428],{},[898,54427,1689],{},[898,54429,724],{},[902,54431,1694],{"encoding":904},[883,54433,54435],{"className":54434},[886],[888,54436,54437],{"xmlns":890},[892,54438,54439,54453],{},[895,54440,54441],{},[1681,54442,54443,54445],{},[898,54444,1655],{},[895,54446,54447,54449,54451],{},[898,54448,1713],{},[898,54450,1716],{},[898,54452,1719],{},[902,54454,1722],{"encoding":904},[123,54456,54457,1989,54459,1343,54488],{},[38,54458,5894],{},[883,54460,54462],{"className":54461},[886],[888,54463,54464],{"xmlns":890},[892,54465,54466,54486],{},[895,54467,54468,54476,54478],{},[2015,54469,54470,54472,54474],{},[898,54471,1828],{},[1765,54473,1945],{},[898,54475,1818],{},[1761,54477,1909],{},[2015,54479,54480,54482,54484],{},[898,54481,1828],{},[1765,54483,2296],{},[898,54485,1818],{},[902,54487,5202],{"encoding":904},[883,54489,54491],{"className":54490},[886],[888,54492,54493],{"xmlns":890},[892,54494,54495,54519],{},[895,54496,54497,54505,54507,54509,54511],{},[2015,54498,54499,54501,54503],{},[898,54500,1839],{},[1765,54502,1945],{},[898,54504,1818],{},[1761,54506,1885],{},[898,54508,1655],{},[1761,54510,1909],{},[2015,54512,54513,54515,54517],{},[898,54514,1839],{},[1765,54516,2296],{},[898,54518,1818],{},[902,54520,5239],{"encoding":904},[724,54522,54523],{},[38,54524,30439],{},[120,54526,54527,54573,54604,54609,54615,54622],{},[123,54528,54529,1989,54531],{},[38,54530,47037],{},[883,54532,54534],{"className":54533},[886],[888,54535,54536],{"xmlns":890},[892,54537,54538,54570],{},[895,54539,54540,54546,54548,54550,54552,54554,54556,54558,54560,54562,54564,54566,54568],{},[1824,54541,54542,54544],{},[898,54543,1828],{},[898,54545,1818],{},[1761,54547,1909],{},[1761,54549,1915],{"stretchy":1821},[898,54551,4302],{},[1761,54553,1885],{},[898,54555,4346],{},[1761,54557,1920],{"stretchy":1821},[898,54559,8726],{"mathvariant":1969},[1761,54561,1915],{"stretchy":1821},[898,54563,2774],{},[1761,54565,1885],{},[898,54567,207],{},[1761,54569,1920],{"stretchy":1821},[902,54571,54572],{"encoding":904},"Q^E = (b - d)\u002F(c - a)",[123,54574,54575,1989,54578,54603],{},[38,54576,54577],{},"Parametry",[883,54579,54581],{"className":54580},[886],[888,54582,54583],{"xmlns":890},[892,54584,54585,54601],{},[895,54586,54587,54589,54591,54593,54595,54597,54599],{},[898,54588,207],{},[1761,54590,1834],{"separator":1833},[898,54592,4302],{},[1761,54594,1834],{"separator":1833},[898,54596,2774],{},[1761,54598,1834],{"separator":1833},[898,54600,4346],{},[902,54602,47280],{"encoding":904}," — exogenní proměnné",[123,54605,54606],{},[38,54607,54608],{},"Endogenní \u002F exogenní proměnná",[123,54610,54611,54614],{},[38,54612,54613],{},"Multiplikátor"," — parciální derivace redukovaného tvaru",[123,54616,54617,1343,54620],{},[38,54618,54619],{},"Komparativní statika",[38,54621,40988],{},[123,54623,54624,1989,54626,54642],{},[38,54625,7025],{},[883,54627,54629],{"className":54628},[886],[888,54630,54631],{"xmlns":890},[892,54632,54633,54639],{},[895,54634,54635,54637],{},[898,54636,4346],{},[898,54638,1828],{},[902,54640,54641],{"encoding":904},"dQ"," (2.11)",[724,54644,54645],{},[38,54646,54647],{},"Přebytky a ostatní",[120,54649,54650,54688],{},[123,54651,54652,1989,54654,54669,54670,1989,54672,54687],{},[38,54653,48929],{},[883,54655,54657],{"className":54656},[886],[888,54658,54659],{"xmlns":890},[892,54660,54661,54667],{},[895,54662,54663,54665],{},[898,54664,6849],{},[898,54666,1912],{},[902,54668,48945],{"encoding":904}," (2.14), ",[38,54671,48948],{},[883,54673,54675],{"className":54674},[886],[888,54676,54677],{"xmlns":890},[892,54678,54679,54685],{},[895,54680,54681,54683],{},[898,54682,1839],{},[898,54684,1912],{},[902,54686,48964],{"encoding":904}," (2.15)",[123,54689,54690,1343,54693,54696],{},[38,54691,54692],{},"Homo economicus",[38,54694,54695],{},"Marshallova formulace"," (1890)",[1849,54698],{},[115,54700,5968],{"id":5967},[120,54702,54703,54737,54744],{},[123,54704,54705,1989,54707,54710,54711,1343,54714,54717,54718,54721,54722,54725,54726,54729,54730,54733,54734],{},[38,54706,5983],{},[207,54708,811],{"className":54709,"dataFsResolvedFilePath":809,"href":810},[210]," (dopady daně, daňové břemeno, ekvivalence), ",[207,54712,820],{"className":54713,"dataFsResolvedFilePath":818,"href":819},[210],[207,54715,5995],{"className":54716,"dataFsResolvedFilePath":764,"href":765},[210]," (zákon klesající\u002Frostoucí, monotonie), ",[207,54719,775],{"className":54720,"dataFsResolvedFilePath":773,"href":774},[210]," (CS a PS), ",[207,54723,784],{"className":54724,"dataFsResolvedFilePath":782,"href":783},[210]," (vícefaktorové modely, multiplikátory), ",[207,54727,793],{"className":54728,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace spotřebitele), ",[207,54731,6000],{"className":54732,"dataFsResolvedFilePath":848,"href":849},[210]," (důchodová a cenová citlivost), ",[207,54735,7885],{"className":54736,"dataFsResolvedFilePath":827,"href":828},[210],[123,54738,54739,1989,54741],{},[38,54740,6006],{},[207,54742,6010],{"className":54743,"dataFsResolvedFilePath":745,"href":746},[210],[123,54745,54746,1989,54748],{},[38,54747,6015],{},[207,54749,6021],{"className":54750,"dataFsResolvedFilePath":6019,"href":6020},[210],{"title":641,"searchDepth":642,"depth":642,"links":54752},[54753,54754,54762,54768,54775,54776,54783,54784,54785,54792,54793,54794],{"id":40822,"depth":642,"text":40823},{"id":40803,"depth":642,"text":17199,"children":54755},[54756,54757,54758,54759,54761],{"id":41089,"depth":649,"text":41090},{"id":41371,"depth":649,"text":41372},{"id":42377,"depth":649,"text":42378},{"id":42945,"depth":649,"text":54760},"Posun poptávky (shift of demand)",{"id":43449,"depth":649,"text":43450},{"id":40807,"depth":642,"text":17163,"children":54763},[54764,54765,54766],{"id":44284,"depth":649,"text":41090},{"id":44470,"depth":649,"text":44471},{"id":44922,"depth":649,"text":54767},"Posun nabídky (shift of supply)",{"id":45338,"depth":642,"text":45339,"children":54769},[54770,54771,54772,54773,54774],{"id":45449,"depth":649,"text":45450},{"id":45661,"depth":649,"text":45662},{"id":45976,"depth":649,"text":45977},{"id":46330,"depth":649,"text":46331},{"id":46361,"depth":649,"text":46362},{"id":46630,"depth":642,"text":811},{"id":47018,"depth":642,"text":47019,"children":54777},[54778,54779,54780,54781],{"id":47036,"depth":649,"text":47037},{"id":47416,"depth":649,"text":47417},{"id":47800,"depth":649,"text":47801},{"id":48254,"depth":649,"text":54782},"Příklad 2.11 — komparativní statika pro QEQ^E",{"id":15823,"depth":642,"text":820},{"id":49179,"depth":642,"text":49180},{"id":49406,"depth":642,"text":49407,"children":54786},[54787,54788,54789,54790,54791],{"id":49410,"depth":649,"text":49411},{"id":50250,"depth":649,"text":50251},{"id":50626,"depth":649,"text":45339},{"id":51915,"depth":649,"text":47019},{"id":53671,"depth":649,"text":820},{"id":53866,"depth":642,"text":53867},{"id":5532,"depth":642,"text":5533},{"id":5967,"depth":642,"text":5968},{},"\u002Ftopics\u002Fpoptavka-nabidka",{"title":802,"description":641},[1138,1135],"topics\u002Fpoptavka-nabidka",[1128,54801,54802,54803,21917,6046,54804],"poptavka","nabidka","rovnovaha","prebytek","VHXMOe03Z24g0HTNlL2geCMzNcnJ3vQ8m2Org-s9n8Q",{"id":54807,"title":820,"body":54808,"course":1128,"courses":659,"created":6039,"description":641,"extension":661,"meta":59085,"navigation":664,"path":59086,"seo":59087,"sources":59088,"stem":59089,"tags":59090,"type":6050,"updated":677,"__hash__":59095},"topics\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce.md",{"type":9,"value":54809,"toc":59063},[54810,54812,54880,54930,54932,54935,55193,55269,55274,55276,55295,55299,55375,55460,55462,55776,55869,55871,55890,55894,55968,56053,56056,56232,56237,56239,56659,56661,56665,56669,56905,56949,57049,57115,57118,57151,57327,57389,57519,57597,57708,57742,57940,57959,57978,58043,58047,58050,58095,58098,58216,58262,58264,58268,58615,58617,58619,58897,58899,58903,58938,58945,59017,59019,59021],[12,54811,820],{"id":15823},[1636,54813,54814],{},[724,54815,54816,7934,54818,3927,54820,54835,54836,3927,54838,54853,54854,54876,54877,1741],{},[883,54817,7933],{},[38,54819,48929],{},[883,54821,54823],{"className":54822},[886],[888,54824,54825],{"xmlns":890},[892,54826,54827,54833],{},[895,54828,54829,54831],{},[898,54830,6849],{},[898,54832,1912],{},[902,54834,48945],{"encoding":904},") je rozdíl mezi tím, co byl spotřebitel ochoten zaplatit, a tím, co skutečně zaplatil. ",[38,54837,49076],{},[883,54839,54841],{"className":54840},[886],[888,54842,54843],{"xmlns":890},[892,54844,54845,54851],{},[895,54846,54847,54849],{},[898,54848,1839],{},[898,54850,1912],{},[902,54852,48964],{"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 ",[883,54855,54857],{"className":54856},[886],[888,54858,54859],{"xmlns":890},[892,54860,54861,54873],{},[895,54862,54863,54865,54867,54869,54871],{},[898,54864,6849],{},[898,54866,1912],{},[1761,54868,1964],{},[898,54870,1839],{},[898,54872,1912],{},[902,54874,54875],{"encoding":904},"CS + PS"," měří ",[38,54878,54879],{},"celkový blahobyt trhu",[724,54881,54882,3927,54884,1343,54886,4590,54901,3927,54903,1343,54905,54920,54921,54925,54926,1741],{},[38,54883,48929],{},[614,54885,48983],{},[883,54887,54889],{"className":54888},[886],[888,54890,54891],{"xmlns":890},[892,54892,54893,54899],{},[895,54894,54895,54897],{},[898,54896,6849],{},[898,54898,1912],{},[902,54900,48945],{"encoding":904},[38,54902,48948],{},[614,54904,49079],{},[883,54906,54908],{"className":54907},[886],[888,54909,54910],{"xmlns":890},[892,54911,54912,54918],{},[895,54913,54914,54916],{},[898,54915,1839],{},[898,54917,1912],{},[902,54919,48964],{"encoding":904},") kvantifikují čistý prospěch jednotlivých stran trhu. Navazují na pojmy ",[207,54922,54924],{"className":54923,"dataFsResolvedFilePath":800,"href":801},[210],"tržní rovnováhy"," a využívají aparát ",[207,54927,54929],{"className":54928,"dataFsResolvedFilePath":773,"href":774},[210],"integrálního počtu",[1849,54931],{},[115,54933,1241],{"id":54934},"úvod",[724,54936,54937,54938,54961,54962,54985,54986,55003,55004,4569,55036,55068,55069,55095,55096,55099,55100,55103,55104,18049,55138,25627,55159,1741],{},"Je dána funkce poptávky ",[883,54939,54941],{"className":54940},[886],[888,54942,54943],{"xmlns":890},[892,54944,54945,54959],{},[895,54946,54947,54949,54951,54953,54955,54957],{},[898,54948,1839],{},[1761,54950,1909],{},[898,54952,2244],{},[1761,54954,1915],{"stretchy":1821},[898,54956,1828],{},[1761,54958,1920],{"stretchy":1821},[902,54960,8692],{"encoding":904},", resp. funkce nabídky ",[883,54963,54965],{"className":54964},[886],[888,54966,54967],{"xmlns":890},[892,54968,54969,54983],{},[895,54970,54971,54973,54975,54977,54979,54981],{},[898,54972,1839],{},[1761,54974,1909],{},[898,54976,1912],{},[1761,54978,1915],{"stretchy":1821},[898,54980,1828],{},[1761,54982,1920],{"stretchy":1821},[902,54984,45090],{"encoding":904},". Pro pevně zadané množství ",[883,54987,54989],{"className":54988},[886],[888,54990,54991],{"xmlns":890},[892,54992,54993,55001],{},[895,54994,54995],{},[1681,54996,54997,54999],{},[898,54998,1828],{},[1765,55000,1767],{},[902,55002,42331],{"encoding":904}," je odpovídající cena ",[883,55005,55007],{"className":55006},[886],[888,55008,55009],{"xmlns":890},[892,55010,55011,55033],{},[895,55012,55013,55019,55021,55023,55025,55031],{},[1681,55014,55015,55017],{},[898,55016,1839],{},[1765,55018,1767],{},[1761,55020,1909],{},[898,55022,2244],{},[1761,55024,1915],{"stretchy":1821},[1681,55026,55027,55029],{},[898,55028,1828],{},[1765,55030,1767],{},[1761,55032,1920],{"stretchy":1821},[902,55034,55035],{"encoding":904},"P_0 = D(Q_0)",[883,55037,55039],{"className":55038},[886],[888,55040,55041],{"xmlns":890},[892,55042,55043,55065],{},[895,55044,55045,55051,55053,55055,55057,55063],{},[1681,55046,55047,55049],{},[898,55048,1839],{},[1765,55050,1767],{},[1761,55052,1909],{},[898,55054,1912],{},[1761,55056,1915],{"stretchy":1821},[1681,55058,55059,55061],{},[898,55060,1828],{},[1765,55062,1767],{},[1761,55064,1920],{"stretchy":1821},[902,55066,55067],{"encoding":904},"P_0 = S(Q_0)","). Součin ",[883,55070,55072],{"className":55071},[886],[888,55073,55074],{"xmlns":890},[892,55075,55076,55092],{},[895,55077,55078,55084,55086],{},[1681,55079,55080,55082],{},[898,55081,1839],{},[1765,55083,1767],{},[2761,55085,7057],{},[1681,55087,55088,55090],{},[898,55089,1828],{},[1765,55091,1767],{},[902,55093,55094],{"encoding":904},"P_0 \\, Q_0"," reprezentuje buď ",[38,55097,55098],{},"výdaje spotřebitele",", nebo ",[38,55101,55102],{},"tržby výrobce"," a geometricky odpovídá obsahu obdélníka ",[883,55105,55107],{"className":55106},[886],[888,55108,55109],{"xmlns":890},[892,55110,55111,55135],{},[895,55112,55113,55115,55117,55123,55125,55127,55129],{},[1765,55114,1767],{},[2761,55116,7057],{},[1681,55118,55119,55121],{},[898,55120,1828],{},[1765,55122,1767],{},[2761,55124,7057],{},[898,55126,8309],{},[2761,55128,7057],{},[1681,55130,55131,55133],{},[898,55132,1839],{},[1765,55134,1767],{},[902,55136,55137],{"encoding":904},"0\\,Q_0\\,A\\,P_0",[883,55139,55141],{"className":55140},[886],[888,55142,55143],{"xmlns":890},[892,55144,55145,55157],{},[895,55146,55147,55149,55151,55153,55155],{},[1761,55148,1915],{"stretchy":1821},[898,55150,1828],{},[1761,55152,1834],{"separator":1833},[898,55154,1839],{},[1761,55156,1920],{"stretchy":1821},[902,55158,4058],{"encoding":904},[883,55160,55162],{"className":55161},[886],[888,55163,55164],{"xmlns":890},[892,55165,55166,55190],{},[895,55167,55168,55170,55172,55174,55180,55182,55188],{},[898,55169,8309],{},[1761,55171,1909],{},[1761,55173,1822],{"stretchy":1821},[1681,55175,55176,55178],{},[898,55177,1828],{},[1765,55179,1767],{},[1761,55181,1834],{"separator":1833},[1681,55183,55184,55186],{},[898,55185,1839],{},[1765,55187,1767],{},[1761,55189,1844],{"stretchy":1821},[902,55191,55192],{"encoding":904},"A = [Q_0, P_0]",[1636,55194,55195,55200,55258],{},[724,55196,55197,55199],{},[883,55198,1642],{}," Intuice",[120,55201,55202,55230],{},[123,55203,55204,55205,55208,55209,55211,55212,55229],{},"Za jednotky zboží nakoupené ",[38,55206,55207],{},"před"," posledním kusem je spotřebitel podle funkce poptávky ochoten platit ",[614,55210,29301],{}," než ",[883,55213,55215],{"className":55214},[886],[888,55216,55217],{"xmlns":890},[892,55218,55219,55227],{},[895,55220,55221],{},[1681,55222,55223,55225],{},[898,55224,1839],{},[1765,55226,1767],{},[902,55228,42970],{"encoding":904}," — rozdíl si „šetří do kapsy\" jako přebytek.",[123,55231,55232,55233,55235,55236,55239,55240,55257],{},"Za jednotky zboží prodané ",[38,55234,55207],{}," posledním kusem by výrobce podle funkce nabídky byl ochoten prodávat i za ",[614,55237,55238],{},"nižší"," cenu než ",[883,55241,55243],{"className":55242},[886],[888,55244,55245],{"xmlns":890},[892,55246,55247,55255],{},[895,55248,55249],{},[1681,55250,55251,55253],{},[898,55252,1839],{},[1765,55254,1767],{},[902,55256,42970],{"encoding":904}," — rozdíl je jeho přebytek.",[724,55259,55260,55261,55264,55265,55268],{},"Přebytek je tedy rozdíl mezi ",[614,55262,55263],{},"ochotou"," (platit \u002F prodávat) a ",[614,55266,55267],{},"skutečností"," (zaplaceno \u002F obdrženo).",[724,55270,55271],{},[3991,55272],{"alt":48974,"className":55273,"src":48976},[210,3995],[1849,55275],{},[115,55277,55279,55280,1920],{"id":55278},"přebytek-spotřebitele-cscs","Přebytek spotřebitele (",[883,55281,55283],{"className":55282},[886],[888,55284,55285],{"xmlns":890},[892,55286,55287,55293],{},[895,55288,55289,55291],{},[898,55290,6849],{},[898,55292,1912],{},[902,55294,48945],{"encoding":904},[198,55296,55298],{"id":55297},"definice-vzorec-214","Definice (vzorec 2.14)",[724,55300,55301,55302,55325,55326,55343,55344,2506],{},"Pro poptávku ",[883,55303,55305],{"className":55304},[886],[888,55306,55307],{"xmlns":890},[892,55308,55309,55323],{},[895,55310,55311,55313,55315,55317,55319,55321],{},[898,55312,1839],{},[1761,55314,1909],{},[898,55316,2244],{},[1761,55318,1915],{"stretchy":1821},[898,55320,1828],{},[1761,55322,1920],{"stretchy":1821},[902,55324,8692],{"encoding":904}," a pevně zadané ",[883,55327,55329],{"className":55328},[886],[888,55330,55331],{"xmlns":890},[892,55332,55333,55341],{},[895,55334,55335],{},[1681,55336,55337,55339],{},[898,55338,1828],{},[1765,55340,1767],{},[902,55342,42331],{"encoding":904}," s cenou ",[883,55345,55347],{"className":55346},[886],[888,55348,55349],{"xmlns":890},[892,55350,55351,55373],{},[895,55352,55353,55359,55361,55363,55365,55371],{},[1681,55354,55355,55357],{},[898,55356,1839],{},[1765,55358,1767],{},[1761,55360,1909],{},[898,55362,2244],{},[1761,55364,1915],{"stretchy":1821},[1681,55366,55367,55369],{},[898,55368,1828],{},[1765,55370,1767],{},[1761,55372,1920],{"stretchy":1821},[902,55374,55035],{"encoding":904},[883,55376,55378],{"className":55377},[886],[888,55379,55380],{"xmlns":890,"display":1930},[892,55381,55382,55458],{},[24787,55383,55384],{"width":32101},[24792,55385,55386,55388,55452,55454],{},[24795,55387],{"width":32106},[24795,55389,55390],{},[895,55391,55392,55394,55396,55398,55404,55406,55408,55420,55422,55424,55426,55428,55430,55432,55434,55436,55442,55444,55450],{},[898,55393,6849],{},[898,55395,1912],{},[1761,55397,1915],{"stretchy":1821},[1681,55399,55400,55402],{},[898,55401,1828],{},[1765,55403,1767],{},[1761,55405,1920],{"stretchy":1821},[1761,55407,1909],{},[2015,55409,55410,55412,55414],{},[1761,55411,15208],{},[1765,55413,1767],{},[1681,55415,55416,55418],{},[898,55417,1828],{},[1765,55419,1767],{},[898,55421,2244],{},[1761,55423,1915],{"stretchy":1821},[898,55425,1828],{},[1761,55427,1920],{"stretchy":1821},[2761,55429,7057],{},[898,55431,4346],{},[898,55433,1828],{},[1761,55435,1885],{},[1681,55437,55438,55440],{},[898,55439,1839],{},[1765,55441,1767],{},[2761,55443,7057],{},[1681,55445,55446,55448],{},[898,55447,1828],{},[1765,55449,1767],{},[898,55451,1741],{"mathvariant":1969},[24795,55453],{"width":32106},[24795,55455,55456],{},[2761,55457,49068],{},[902,55459,49071],{"encoding":904},[198,55461,4033],{"id":4032},[120,55463,55464,55556,55618],{},[123,55465,55466,55506,55507,55533,55534,55537,55538,55555],{},[883,55467,55469],{"className":55468},[886],[888,55470,55471],{"xmlns":890},[892,55472,55473,55503],{},[895,55474,55475],{},[6411,55476,55477,55489,55491,55493,55495,55497,55499,55501],{"scriptlevel":1767,"displaystyle":1833},[2015,55478,55479,55481,55483],{},[1761,55480,15208],{},[1765,55482,1767],{},[1681,55484,55485,55487],{},[898,55486,1828],{},[1765,55488,1767],{},[898,55490,2244],{},[1761,55492,1915],{"stretchy":1821},[898,55494,1828],{},[1761,55496,1920],{"stretchy":1821},[2761,55498,7057],{},[898,55500,4346],{},[898,55502,1828],{},[902,55504,55505],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ"," — plocha pod křivkou poptávky v intervalu ",[883,55508,55510],{"className":55509},[886],[888,55511,55512],{"xmlns":890},[892,55513,55514,55530],{},[895,55515,55516,55518,55520,55522,55528],{},[1761,55517,1822],{"stretchy":1821},[1765,55519,1767],{},[1761,55521,1834],{"separator":1833},[1681,55523,55524,55526],{},[898,55525,1828],{},[1765,55527,1767],{},[1761,55529,1844],{"stretchy":1821},[902,55531,55532],{"encoding":904},"[0, Q_0]","; představuje celkovou ",[38,55535,55536],{},"ochotu platit"," (maximální částku, kterou by spotřebitel za ",[883,55539,55541],{"className":55540},[886],[888,55542,55543],{"xmlns":890},[892,55544,55545,55553],{},[895,55546,55547],{},[1681,55548,55549,55551],{},[898,55550,1828],{},[1765,55552,1767],{},[902,55554,42331],{"encoding":904}," jednotek byl ochoten zaplatit).",[123,55557,55558,55584,55585,2162],{},[883,55559,55561],{"className":55560},[886],[888,55562,55563],{"xmlns":890},[892,55564,55565,55581],{},[895,55566,55567,55573,55575],{},[1681,55568,55569,55571],{},[898,55570,1839],{},[1765,55572,1767],{},[2761,55574,7057],{},[1681,55576,55577,55579],{},[898,55578,1828],{},[1765,55580,1767],{},[902,55582,55583],{"encoding":904},"P_0\\,Q_0"," — skutečně zaplacená částka (obdélník ",[883,55586,55588],{"className":55587},[886],[888,55589,55590],{"xmlns":890},[892,55591,55592,55616],{},[895,55593,55594,55596,55598,55604,55606,55608,55610],{},[1765,55595,1767],{},[2761,55597,7057],{},[1681,55599,55600,55602],{},[898,55601,1828],{},[1765,55603,1767],{},[2761,55605,7057],{},[898,55607,8309],{},[2761,55609,7057],{},[1681,55611,55612,55614],{},[898,55613,1839],{},[1765,55615,1767],{},[902,55617,55137],{"encoding":904},[123,55619,55620,55635,55636,55658,55659,55684,55685,25627,55711,2068,55743,1741],{},[883,55621,55623],{"className":55622},[886],[888,55624,55625],{"xmlns":890},[892,55626,55627,55633],{},[895,55628,55629,55631],{},[898,55630,6849],{},[898,55632,1912],{},[902,55634,48945],{"encoding":904}," je plocha mezi křivkou poptávky a vodorovnou přímkou ",[883,55637,55639],{"className":55638},[886],[888,55640,55641],{"xmlns":890},[892,55642,55643,55655],{},[895,55644,55645,55647,55649],{},[898,55646,1839],{},[1761,55648,1909],{},[1681,55650,55651,55653],{},[898,55652,1839],{},[1765,55654,1767],{},[902,55656,55657],{"encoding":904},"P = P_0"," v pásu ",[883,55660,55662],{"className":55661},[886],[888,55663,55664],{"xmlns":890},[892,55665,55666,55682],{},[895,55667,55668,55670,55672,55674,55680],{},[1761,55669,1822],{"stretchy":1821},[1765,55671,1767],{},[1761,55673,1834],{"separator":1833},[1681,55675,55676,55678],{},[898,55677,1828],{},[1765,55679,1767],{},[1761,55681,1844],{"stretchy":1821},[902,55683,55532],{"encoding":904}," — „křivočarý trojúhelník\" ",[883,55686,55688],{"className":55687},[886],[888,55689,55690],{"xmlns":890},[892,55691,55692,55708],{},[895,55693,55694,55700,55702,55704,55706],{},[1681,55695,55696,55698],{},[898,55697,1839],{},[1765,55699,1767],{},[2761,55701,7057],{},[898,55703,27286],{},[2761,55705,7057],{},[898,55707,8309],{},[902,55709,55710],{"encoding":904},"P_0\\,B\\,A",[883,55712,55714],{"className":55713},[886],[888,55715,55716],{"xmlns":890},[892,55717,55718,55740],{},[895,55719,55720,55722,55724,55726,55728,55730,55732,55734,55736,55738],{},[898,55721,27286],{},[1761,55723,1909],{},[1761,55725,1822],{"stretchy":1821},[1765,55727,1767],{},[1761,55729,1834],{"separator":1833},[898,55731,2244],{},[1761,55733,1915],{"stretchy":1821},[1765,55735,1767],{},[1761,55737,1920],{"stretchy":1821},[1761,55739,1844],{"stretchy":1821},[902,55741,55742],{"encoding":904},"B = [0, D(0)]",[883,55744,55746],{"className":55745},[886],[888,55747,55748],{"xmlns":890},[892,55749,55750,55774],{},[895,55751,55752,55754,55756,55758,55764,55766,55772],{},[898,55753,8309],{},[1761,55755,1909],{},[1761,55757,1822],{"stretchy":1821},[1681,55759,55760,55762],{},[898,55761,1828],{},[1765,55763,1767],{},[1761,55765,1834],{"separator":1833},[1681,55767,55768,55770],{},[898,55769,1839],{},[1765,55771,1767],{},[1761,55773,1844],{"stretchy":1821},[902,55775,55192],{"encoding":904},[724,55777,55778],{},[614,55779,55780,55781,55794,55795,55828,55829,33172,55854,1741],{},"Obrázek 2.24: Křivka poptávky ",[883,55782,55784],{"className":55783},[886],[888,55785,55786],{"xmlns":890},[892,55787,55788,55792],{},[895,55789,55790],{},[898,55791,2244],{},[902,55793,2244],{"encoding":904},", bod ",[883,55796,55798],{"className":55797},[886],[888,55799,55800],{"xmlns":890},[892,55801,55802,55826],{},[895,55803,55804,55806,55808,55810,55816,55818,55824],{},[898,55805,8309],{},[1761,55807,1909],{},[1761,55809,1822],{"stretchy":1821},[1681,55811,55812,55814],{},[898,55813,1828],{},[1765,55815,1767],{},[1761,55817,1834],{"separator":1833},[1681,55819,55820,55822],{},[898,55821,1839],{},[1765,55823,1767],{},[1761,55825,1844],{"stretchy":1821},[902,55827,55192],{"encoding":904},", vyšrafovaná plocha trojúhelníku ",[883,55830,55832],{"className":55831},[886],[888,55833,55834],{"xmlns":890},[892,55835,55836,55852],{},[895,55837,55838,55844,55846,55848,55850],{},[1681,55839,55840,55842],{},[898,55841,1839],{},[1765,55843,1767],{},[2761,55845,7057],{},[898,55847,27286],{},[2761,55849,7057],{},[898,55851,8309],{},[902,55853,55710],{"encoding":904},[883,55855,55857],{"className":55856},[886],[888,55858,55859],{"xmlns":890},[892,55860,55861,55867],{},[895,55862,55863,55865],{},[898,55864,6849],{},[898,55866,1912],{},[902,55868,48945],{"encoding":904},[1849,55870],{},[115,55872,55874,55875,1920],{"id":55873},"přebytek-výrobce-psps","Přebytek výrobce (",[883,55876,55878],{"className":55877},[886],[888,55879,55880],{"xmlns":890},[892,55881,55882,55888],{},[895,55883,55884,55886],{},[898,55885,1839],{},[898,55887,1912],{},[902,55889,48964],{"encoding":904},[198,55891,55893],{"id":55892},"definice-vzorec-215","Definice (vzorec 2.15)",[724,55895,55896,55897,55325,55920,55343,55937,2506],{},"Analogicky — pro nabídku ",[883,55898,55900],{"className":55899},[886],[888,55901,55902],{"xmlns":890},[892,55903,55904,55918],{},[895,55905,55906,55908,55910,55912,55914,55916],{},[898,55907,1839],{},[1761,55909,1909],{},[898,55911,1912],{},[1761,55913,1915],{"stretchy":1821},[898,55915,1828],{},[1761,55917,1920],{"stretchy":1821},[902,55919,45090],{"encoding":904},[883,55921,55923],{"className":55922},[886],[888,55924,55925],{"xmlns":890},[892,55926,55927,55935],{},[895,55928,55929],{},[1681,55930,55931,55933],{},[898,55932,1828],{},[1765,55934,1767],{},[902,55936,42331],{"encoding":904},[883,55938,55940],{"className":55939},[886],[888,55941,55942],{"xmlns":890},[892,55943,55944,55966],{},[895,55945,55946,55952,55954,55956,55958,55964],{},[1681,55947,55948,55950],{},[898,55949,1839],{},[1765,55951,1767],{},[1761,55953,1909],{},[898,55955,1912],{},[1761,55957,1915],{"stretchy":1821},[1681,55959,55960,55962],{},[898,55961,1828],{},[1765,55963,1767],{},[1761,55965,1920],{"stretchy":1821},[902,55967,55067],{"encoding":904},[883,55969,55971],{"className":55970},[886],[888,55972,55973],{"xmlns":890,"display":1930},[892,55974,55975,56051],{},[24787,55976,55977],{"width":32101},[24792,55978,55979,55981,56045,56047],{},[24795,55980],{"width":32106},[24795,55982,55983],{},[895,55984,55985,55987,55989,55991,55997,55999,56001,56007,56009,56015,56017,56029,56031,56033,56035,56037,56039,56041,56043],{},[898,55986,1839],{},[898,55988,1912],{},[1761,55990,1915],{"stretchy":1821},[1681,55992,55993,55995],{},[898,55994,1828],{},[1765,55996,1767],{},[1761,55998,1920],{"stretchy":1821},[1761,56000,1909],{},[1681,56002,56003,56005],{},[898,56004,1839],{},[1765,56006,1767],{},[2761,56008,7057],{},[1681,56010,56011,56013],{},[898,56012,1828],{},[1765,56014,1767],{},[1761,56016,1885],{},[2015,56018,56019,56021,56023],{},[1761,56020,15208],{},[1765,56022,1767],{},[1681,56024,56025,56027],{},[898,56026,1828],{},[1765,56028,1767],{},[898,56030,1912],{},[1761,56032,1915],{"stretchy":1821},[898,56034,1828],{},[1761,56036,1920],{"stretchy":1821},[2761,56038,7057],{},[898,56040,4346],{},[898,56042,1828],{},[898,56044,1741],{"mathvariant":1969},[24795,56046],{"width":32106},[24795,56048,56049],{},[2761,56050,49164],{},[902,56052,49167],{"encoding":904},[198,56054,4033],{"id":56055},"geometrická-interpretace-1",[120,56057,56058,56106,56167],{},[123,56059,56060,5675,56085,56088,56089,1741],{},[883,56061,56063],{"className":56062},[886],[888,56064,56065],{"xmlns":890},[892,56066,56067,56083],{},[895,56068,56069,56075,56077],{},[1681,56070,56071,56073],{},[898,56072,1839],{},[1765,56074,1767],{},[2761,56076,7057],{},[1681,56078,56079,56081],{},[898,56080,1828],{},[1765,56082,1767],{},[902,56084,55583],{"encoding":904},[38,56086,56087],{},"tržba"," výrobce za prodané množství ",[883,56090,56092],{"className":56091},[886],[888,56093,56094],{"xmlns":890},[892,56095,56096,56104],{},[895,56097,56098],{},[1681,56099,56100,56102],{},[898,56101,1828],{},[1765,56103,1767],{},[902,56105,42331],{"encoding":904},[123,56107,56108,56148,56149,56166],{},[883,56109,56111],{"className":56110},[886],[888,56112,56113],{"xmlns":890},[892,56114,56115,56145],{},[895,56116,56117],{},[6411,56118,56119,56131,56133,56135,56137,56139,56141,56143],{"scriptlevel":1767,"displaystyle":1833},[2015,56120,56121,56123,56125],{},[1761,56122,15208],{},[1765,56124,1767],{},[1681,56126,56127,56129],{},[898,56128,1828],{},[1765,56130,1767],{},[898,56132,1912],{},[1761,56134,1915],{"stretchy":1821},[898,56136,1828],{},[1761,56138,1920],{"stretchy":1821},[2761,56140,7057],{},[898,56142,4346],{},[898,56144,1828],{},[902,56146,56147],{"encoding":904},"\\displaystyle \\int_0^{Q_0} S(Q)\\,dQ"," — plocha pod křivkou nabídky; minimální částka, za kterou by byl výrobce ochoten ",[883,56150,56152],{"className":56151},[886],[888,56153,56154],{"xmlns":890},[892,56155,56156,56164],{},[895,56157,56158],{},[1681,56159,56160,56162],{},[898,56161,1828],{},[1765,56163,1767],{},[902,56165,42331],{"encoding":904}," jednotek dodat (souvisí s mezními náklady).",[123,56168,56169,56184,56185,56206,56207,1741],{},[883,56170,56172],{"className":56171},[886],[888,56173,56174],{"xmlns":890},[892,56175,56176,56182],{},[895,56177,56178,56180],{},[898,56179,1839],{},[898,56181,1912],{},[902,56183,48964],{"encoding":904}," je plocha mezi vodorovnou přímkou ",[883,56186,56188],{"className":56187},[886],[888,56189,56190],{"xmlns":890},[892,56191,56192,56204],{},[895,56193,56194,56196,56198],{},[898,56195,1839],{},[1761,56197,1909],{},[1681,56199,56200,56202],{},[898,56201,1839],{},[1765,56203,1767],{},[902,56205,55657],{"encoding":904}," a křivkou nabídky v pásu ",[883,56208,56210],{"className":56209},[886],[888,56211,56212],{"xmlns":890},[892,56213,56214,56230],{},[895,56215,56216,56218,56220,56222,56228],{},[1761,56217,1822],{"stretchy":1821},[1765,56219,1767],{},[1761,56221,1834],{"separator":1833},[1681,56223,56224,56226],{},[898,56225,1828],{},[1765,56227,1767],{},[1761,56229,1844],{"stretchy":1821},[902,56231,55532],{"encoding":904},[724,56233,56234],{},[614,56235,56236],{},"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.",[1849,56238],{},[1636,56240,56241,56246],{},[724,56242,56243,56245],{},[883,56244,4452],{}," Postup výpočtu CS a PS",[152,56247,56248,56379,56489,56518,56652],{},[123,56249,56250,56251,56268,56269,56300,56301,56332,56333,1741],{},"Zjisti (nebo si zvol) množství ",[883,56252,56254],{"className":56253},[886],[888,56255,56256],{"xmlns":890},[892,56257,56258,56266],{},[895,56259,56260],{},[1681,56261,56262,56264],{},[898,56263,1828],{},[1765,56265,1767],{},[902,56267,42331],{"encoding":904}," a odpovídající cenu ",[883,56270,56272],{"className":56271},[886],[888,56273,56274],{"xmlns":890},[892,56275,56276,56298],{},[895,56277,56278,56284,56286,56288,56290,56296],{},[1681,56279,56280,56282],{},[898,56281,1839],{},[1765,56283,1767],{},[1761,56285,1909],{},[898,56287,2244],{},[1761,56289,1915],{"stretchy":1821},[1681,56291,56292,56294],{},[898,56293,1828],{},[1765,56295,1767],{},[1761,56297,1920],{"stretchy":1821},[902,56299,55035],{"encoding":904}," resp. ",[883,56302,56304],{"className":56303},[886],[888,56305,56306],{"xmlns":890},[892,56307,56308,56330],{},[895,56309,56310,56316,56318,56320,56322,56328],{},[1681,56311,56312,56314],{},[898,56313,1839],{},[1765,56315,1767],{},[1761,56317,1909],{},[898,56319,1912],{},[1761,56321,1915],{"stretchy":1821},[1681,56323,56324,56326],{},[898,56325,1828],{},[1765,56327,1767],{},[1761,56329,1920],{"stretchy":1821},[902,56331,55067],{"encoding":904},". V rovnováze platí ",[883,56334,56336],{"className":56335},[886],[888,56337,56338],{"xmlns":890},[892,56339,56340,56376],{},[895,56341,56342,56344,56346,56352,56354,56356,56358,56360,56366,56368,56370],{},[898,56343,2244],{},[1761,56345,1915],{"stretchy":1821},[1824,56347,56348,56350],{},[898,56349,1828],{},[898,56351,1818],{},[1761,56353,1920],{"stretchy":1821},[1761,56355,1909],{},[898,56357,1912],{},[1761,56359,1915],{"stretchy":1821},[1824,56361,56362,56364],{},[898,56363,1828],{},[898,56365,1818],{},[1761,56367,1920],{"stretchy":1821},[1761,56369,1909],{},[1824,56371,56372,56374],{},[898,56373,1839],{},[898,56375,1818],{},[902,56377,56378],{"encoding":904},"D(Q^E) = S(Q^E) = P^E",[123,56380,56381,56382,24159,56420,56435,56436,24159,56474,2162],{},"Spočti určitý integrál ",[883,56383,56385],{"className":56384},[886],[888,56386,56387],{"xmlns":890},[892,56388,56389,56417],{},[895,56390,56391,56403,56405,56407,56409,56411,56413,56415],{},[2015,56392,56393,56395,56397],{},[1761,56394,15208],{},[1765,56396,1767],{},[1681,56398,56399,56401],{},[898,56400,1828],{},[1765,56402,1767],{},[898,56404,2244],{},[1761,56406,1915],{"stretchy":1821},[898,56408,1828],{},[1761,56410,1920],{"stretchy":1821},[2761,56412,7057],{},[898,56414,4346],{},[898,56416,1828],{},[902,56418,56419],{"encoding":904},"\\int_0^{Q_0} D(Q)\\,dQ",[883,56421,56423],{"className":56422},[886],[888,56424,56425],{"xmlns":890},[892,56426,56427,56433],{},[895,56428,56429,56431],{},[898,56430,6849],{},[898,56432,1912],{},[902,56434,48945],{"encoding":904},") nebo ",[883,56437,56439],{"className":56438},[886],[888,56440,56441],{"xmlns":890},[892,56442,56443,56471],{},[895,56444,56445,56457,56459,56461,56463,56465,56467,56469],{},[2015,56446,56447,56449,56451],{},[1761,56448,15208],{},[1765,56450,1767],{},[1681,56452,56453,56455],{},[898,56454,1828],{},[1765,56456,1767],{},[898,56458,1912],{},[1761,56460,1915],{"stretchy":1821},[898,56462,1828],{},[1761,56464,1920],{"stretchy":1821},[2761,56466,7057],{},[898,56468,4346],{},[898,56470,1828],{},[902,56472,56473],{"encoding":904},"\\int_0^{Q_0} S(Q)\\,dQ",[883,56475,56477],{"className":56476},[886],[888,56478,56479],{"xmlns":890},[892,56480,56481,56487],{},[895,56482,56483,56485],{},[898,56484,1839],{},[898,56486,1912],{},[902,56488,48964],{"encoding":904},[123,56490,56491,56492,1741],{},"Sestav obdélník ",[883,56493,56495],{"className":56494},[886],[888,56496,56497],{"xmlns":890},[892,56498,56499,56515],{},[895,56500,56501,56507,56509],{},[1681,56502,56503,56505],{},[898,56504,1839],{},[1765,56506,1767],{},[1761,56508,2447],{},[1681,56510,56511,56513],{},[898,56512,1828],{},[1765,56514,1767],{},[902,56516,56517],{"encoding":904},"P_0 \\cdot Q_0",[123,56519,56520,56521],{},"Dosaď:\n",[120,56522,56523,56588],{},[123,56524,56525,56583,56584,56587],{},[883,56526,56528],{"className":56527},[886],[888,56529,56530],{"xmlns":890},[892,56531,56532,56580],{},[895,56533,56534,56536,56538,56540,56552,56554,56556,56558,56560,56562,56564,56566,56568,56574],{},[898,56535,6849],{},[898,56537,1912],{},[1761,56539,1909],{},[2015,56541,56542,56544,56546],{},[1761,56543,15208],{},[1765,56545,1767],{},[1681,56547,56548,56550],{},[898,56549,1828],{},[1765,56551,1767],{},[898,56553,2244],{},[1761,56555,1915],{"stretchy":1821},[898,56557,1828],{},[1761,56559,1920],{"stretchy":1821},[2761,56561,7057],{},[898,56563,4346],{},[898,56565,1828],{},[1761,56567,1885],{},[1681,56569,56570,56572],{},[898,56571,1839],{},[1765,56573,1767],{},[1681,56575,56576,56578],{},[898,56577,1828],{},[1765,56579,1767],{},[902,56581,56582],{"encoding":904},"CS = \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0"," (integrál ",[38,56585,56586],{},"mínus"," obdélník)",[123,56589,56590,56648,56649,56651],{},[883,56591,56593],{"className":56592},[886],[888,56594,56595],{"xmlns":890},[892,56596,56597,56645],{},[895,56598,56599,56601,56603,56605,56611,56617,56619,56631,56633,56635,56637,56639,56641,56643],{},[898,56600,1839],{},[898,56602,1912],{},[1761,56604,1909],{},[1681,56606,56607,56609],{},[898,56608,1839],{},[1765,56610,1767],{},[1681,56612,56613,56615],{},[898,56614,1828],{},[1765,56616,1767],{},[1761,56618,1885],{},[2015,56620,56621,56623,56625],{},[1761,56622,15208],{},[1765,56624,1767],{},[1681,56626,56627,56629],{},[898,56628,1828],{},[1765,56630,1767],{},[898,56632,1912],{},[1761,56634,1915],{"stretchy":1821},[898,56636,1828],{},[1761,56638,1920],{"stretchy":1821},[2761,56640,7057],{},[898,56642,4346],{},[898,56644,1828],{},[902,56646,56647],{"encoding":904},"PS = P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ"," (obdélník ",[38,56650,56586],{}," integrál)",[123,56653,56654,56655,56658],{},"Kontrola znaménka: obě hodnoty musí být ",[38,56656,56657],{},"kladné",". Pokud vyjde záporná, máš prohozené pořadí.",[1849,56660],{},[115,56662,56664],{"id":56663},"příklady","Příklady",[198,56666,56668],{"id":56667},"příklad-211-komparativní-statika-pro-rovnovážné-množství","Příklad 2.11 — komparativní statika pro rovnovážné množství",[1636,56670,56671],{},[724,56672,56673,56676,56677,51711,56700,56723,56724,1343,56744,1343,56761,1343,56778,56795,56796,56872,56873,56890,56891,56904],{},[883,56674,56675],{},"!example"," Zadání\nJsou dány poptávka ",[883,56678,56680],{"className":56679},[886],[888,56681,56682],{"xmlns":890},[892,56683,56684,56698],{},[895,56685,56686,56688,56690,56692,56694,56696],{},[898,56687,1839],{},[1761,56689,1909],{},[898,56691,207],{},[898,56693,1828],{},[1761,56695,1964],{},[898,56697,4302],{},[902,56699,4305],{"encoding":904},[883,56701,56703],{"className":56702},[886],[888,56704,56705],{"xmlns":890},[892,56706,56707,56721],{},[895,56708,56709,56711,56713,56715,56717,56719],{},[898,56710,1839],{},[1761,56712,1909],{},[898,56714,2774],{},[898,56716,1828],{},[1761,56718,1964],{},[898,56720,4346],{},[902,56722,4349],{"encoding":904}," s hodnotami ",[883,56725,56727],{"className":56726},[886],[888,56728,56729],{"xmlns":890},[892,56730,56731,56741],{},[895,56732,56733,56735,56737,56739],{},[898,56734,207],{},[1761,56736,1909],{},[1761,56738,1885],{},[1765,56740,5486],{},[902,56742,56743],{"encoding":904},"a = -3",[883,56745,56747],{"className":56746},[886],[888,56748,56749],{"xmlns":890},[892,56750,56751,56759],{},[895,56752,56753,56755,56757],{},[898,56754,4302],{},[1761,56756,1909],{},[1765,56758,9262],{},[902,56760,52629],{"encoding":904},[883,56762,56764],{"className":56763},[886],[888,56765,56766],{"xmlns":890},[892,56767,56768,56776],{},[895,56769,56770,56772,56774],{},[898,56771,2774],{},[1761,56773,1909],{},[1765,56775,5426],{},[902,56777,52647],{"encoding":904},[883,56779,56781],{"className":56780},[886],[888,56782,56783],{"xmlns":890},[892,56784,56785,56793],{},[895,56786,56787,56789,56791],{},[898,56788,4346],{},[1761,56790,1909],{},[1765,56792,2633],{},[902,56794,52665],{"encoding":904},".\nRovnovážné množství:\n",[883,56797,56799],{"className":56798},[886],[888,56800,56801],{"xmlns":890},[892,56802,56803,56869],{},[895,56804,56805,56811,56813,56831,56833,56857,56859,56865,56867],{},[1824,56806,56807,56809],{},[898,56808,1828],{},[898,56810,1818],{},[1761,56812,1909],{},[4379,56814,56815,56823],{},[895,56816,56817,56819,56821],{},[898,56818,4302],{},[1761,56820,1885],{},[898,56822,4346],{},[895,56824,56825,56827,56829],{},[898,56826,2774],{},[1761,56828,1885],{},[898,56830,207],{},[1761,56832,1909],{},[4379,56834,56835,56843],{},[895,56836,56837,56839,56841],{},[1765,56838,9262],{},[1761,56840,1885],{},[1765,56842,2633],{},[895,56844,56845,56847,56849,56851,56853,56855],{},[1765,56846,5426],{},[1761,56848,1885],{},[1761,56850,1915],{"stretchy":1821},[1761,56852,1885],{},[1765,56854,5486],{},[1761,56856,1920],{"stretchy":1821},[1761,56858,1909],{},[4379,56860,56861,56863],{},[1765,56862,42042],{},[1765,56864,48401],{},[1761,56866,9945],{},[1765,56868,48406],{},[902,56870,56871],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\doteq 8{,}571.","\nZjistěte změnu ",[883,56874,56876],{"className":56875},[886],[888,56877,56878],{"xmlns":890},[892,56879,56880,56888],{},[895,56881,56882],{},[1824,56883,56884,56886],{},[898,56885,1828],{},[898,56887,1818],{},[902,56889,46412],{"encoding":904}," (a) při změně samotného parametru ",[883,56892,56894],{"className":56893},[886],[888,56895,56896],{"xmlns":890},[892,56897,56898,56902],{},[895,56899,56900],{},[898,56901,2774],{},[902,56903,2774],{"encoding":904},", (b) při současné změně všech čtyř parametrů.",[724,56906,56907],{},[38,56908,56909,56910,6746,56923,4178,56936,13336],{},"Řešení (a) — změna ",[883,56911,56913],{"className":56912},[886],[888,56914,56915],{"xmlns":890},[892,56916,56917,56921],{},[895,56918,56919],{},[898,56920,2774],{},[902,56922,2774],{"encoding":904},[883,56924,56926],{"className":56925},[886],[888,56927,56928],{"xmlns":890},[892,56929,56930,56934],{},[895,56931,56932],{},[1765,56933,5426],{},[902,56935,48441],{"encoding":904},[883,56937,56939],{"className":56938},[886],[888,56940,56941],{"xmlns":890},[892,56942,56943,56947],{},[895,56944,56945],{},[1765,56946,23354],{},[902,56948,48455],{"encoding":904},[724,56950,56951,56952,57016,57017,2506],{},"Pomocí vzorce (2.13) pro ",[883,56953,56955],{"className":56954},[886],[888,56956,56957],{"xmlns":890},[892,56958,56959,57013],{},[895,56960,56961,56981,56983,56985],{},[6411,56962,56963],{"scriptlevel":1767,"displaystyle":1833},[4379,56964,56965,56975],{},[895,56966,56967,56969],{},[898,56968,13911],{"mathvariant":1969},[1824,56970,56971,56973],{},[898,56972,1828],{},[898,56974,1818],{},[895,56976,56977,56979],{},[898,56978,13911],{"mathvariant":1969},[898,56980,2774],{},[1761,56982,1909],{},[1761,56984,1885],{},[6411,56986,56987],{"scriptlevel":1767,"displaystyle":1833},[4379,56988,56989,56997],{},[895,56990,56991,56993,56995],{},[898,56992,4302],{},[1761,56994,1885],{},[898,56996,4346],{},[895,56998,56999,57001,57003,57005,57007],{},[1761,57000,1915],{"stretchy":1821},[898,57002,2774],{},[1761,57004,1885],{},[898,57006,207],{},[1824,57008,57009,57011],{},[1761,57010,1920],{"stretchy":1821},[1765,57012,2296],{},[902,57014,57015],{"encoding":904},"\\dfrac{\\partial Q^E}{\\partial c} = -\\dfrac{b-d}{(c-a)^2}",", resp. ekvivalentně ",[883,57018,57020],{"className":57019},[886],[888,57021,57022],{"xmlns":890},[892,57023,57024,57046],{},[895,57025,57026,57028],{},[1761,57027,1885],{},[6411,57029,57030],{"scriptlevel":1767,"displaystyle":1833},[4379,57031,57032,57038],{},[1824,57033,57034,57036],{},[898,57035,1828],{},[898,57037,1818],{},[895,57039,57040,57042,57044],{},[898,57041,2774],{},[1761,57043,1885],{},[898,57045,207],{},[902,57047,57048],{"encoding":904},"-\\dfrac{Q^E}{c-a}",[883,57050,57052],{"className":57051},[886],[888,57053,57054],{"xmlns":890,"display":1930},[892,57055,57056,57112],{},[895,57057,57058,57060,57066,57068,57070,57086,57088,57090,57092,57094,57096,57102,57104,57106,57108,57110],{},[898,57059,4346],{},[1824,57061,57062,57064],{},[898,57063,1828],{},[898,57065,1818],{},[1761,57067,1909],{},[1761,57069,1885],{},[4379,57071,57072,57078],{},[1824,57073,57074,57076],{},[898,57075,1828],{},[898,57077,1818],{},[895,57079,57080,57082,57084],{},[898,57081,2774],{},[1761,57083,1885],{},[898,57085,207],{},[2761,57087,7057],{},[898,57089,4346],{},[898,57091,2774],{},[1761,57093,1909],{},[1761,57095,1885],{},[4379,57097,57098,57100],{},[1765,57099,48569],{},[1765,57101,48401],{},[1761,57103,2447],{},[1765,57105,6865],{},[1761,57107,9945],{},[1761,57109,1885],{},[1765,57111,48541],{},[902,57113,57114],{"encoding":904},"dQ^E = -\\frac{Q^E}{c - a}\\,dc = -\\frac{8{,}571}{3{,}5}\\cdot 0{,}1 \\doteq -0{,}245.",[724,57116,57117],{},"Nové rovnovážné množství:",[883,57119,57121],{"className":57120},[886],[888,57122,57123],{"xmlns":890,"display":1930},[892,57124,57125,57148],{},[895,57126,57127,57135,57137,57139,57141,57143,57145],{},[2015,57128,57129,57131,57133],{},[898,57130,1828],{},[1765,57132,1945],{},[898,57134,1818],{},[1761,57136,6803],{},[1765,57138,48569],{},[1761,57140,1885],{},[1765,57142,48574],{},[1761,57144,1909],{},[1765,57146,57147],{},"8,326.",[902,57149,57150],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326.",[724,57152,57153,1989,57156,1343,57183,1343,57205,1343,57227,2403,57249,1343,57268,1343,57289,1343,57308,1741],{},[38,57154,57155],{},"Řešení (b) — současná změna všech parametrů:",[883,57157,57159],{"className":57158},[886],[888,57160,57161],{"xmlns":890},[892,57162,57163,57180],{},[895,57164,57165,57167,57169,57171,57173,57175,57177],{},[898,57166,207],{},[1761,57168,2506],{},[1761,57170,1885],{},[1765,57172,5486],{},[1761,57174,2181],{},[1761,57176,1885],{},[1765,57178,57179],{},"2,5",[902,57181,57182],{"encoding":904},"a: -3 \\to -2{,}5",[883,57184,57186],{"className":57185},[886],[888,57187,57188],{"xmlns":890},[892,57189,57190,57202],{},[895,57191,57192,57194,57196,57198,57200],{},[898,57193,4302],{},[1761,57195,2506],{},[1765,57197,9262],{},[1761,57199,2181],{},[1765,57201,19076],{},[902,57203,57204],{"encoding":904},"b: 40 \\to 35",[883,57206,57208],{"className":57207},[886],[888,57209,57210],{"xmlns":890},[892,57211,57212,57224],{},[895,57213,57214,57216,57218,57220,57222],{},[898,57215,2774],{},[1761,57217,2506],{},[1765,57219,5426],{},[1761,57221,2181],{},[1765,57223,23354],{},[902,57225,57226],{"encoding":904},"c: 0{,}5 \\to 0{,}6",[883,57228,57230],{"className":57229},[886],[888,57231,57232],{"xmlns":890},[892,57233,57234,57246],{},[895,57235,57236,57238,57240,57242,57244],{},[898,57237,4346],{},[1761,57239,2506],{},[1765,57241,2633],{},[1761,57243,2181],{},[1765,57245,6974],{},[902,57247,57248],{"encoding":904},"d: 10 \\to 11",[883,57250,57252],{"className":57251},[886],[888,57253,57254],{"xmlns":890},[892,57255,57256,57266],{},[895,57257,57258,57260,57262,57264],{},[898,57259,4346],{},[898,57261,207],{},[1761,57263,1909],{},[1765,57265,5426],{},[902,57267,48607],{"encoding":904},[883,57269,57271],{"className":57270},[886],[888,57272,57273],{"xmlns":890},[892,57274,57275,57287],{},[895,57276,57277,57279,57281,57283,57285],{},[898,57278,4346],{},[898,57280,4302],{},[1761,57282,1909],{},[1761,57284,1885],{},[1765,57286,6321],{},[902,57288,48629],{"encoding":904},[883,57290,57292],{"className":57291},[886],[888,57293,57294],{"xmlns":890},[892,57295,57296,57306],{},[895,57297,57298,57300,57302,57304],{},[898,57299,4346],{},[898,57301,2774],{},[1761,57303,1909],{},[1765,57305,6865],{},[902,57307,48649],{"encoding":904},[883,57309,57311],{"className":57310},[886],[888,57312,57313],{"xmlns":890},[892,57314,57315,57325],{},[895,57316,57317,57319,57321,57323],{},[898,57318,4346],{},[898,57320,4346],{},[1761,57322,1909],{},[1765,57324,1945],{},[902,57326,48669],{"encoding":904},[724,57328,57329,57330,57388],{},"Totální diferenciál ",[883,57331,57333],{"className":57332},[886],[888,57334,57335],{"xmlns":890},[892,57336,57337,57385],{},[895,57338,57339,57345,57347,57349,57351,57353,57355,57357,57359,57361,57363,57365],{},[1824,57340,57341,57343],{},[898,57342,1828],{},[898,57344,1818],{},[1761,57346,1915],{"stretchy":1821},[898,57348,207],{},[1761,57350,1834],{"separator":1833},[898,57352,4302],{},[1761,57354,1834],{"separator":1833},[898,57356,2774],{},[1761,57358,1834],{"separator":1833},[898,57360,4346],{},[1761,57362,1920],{"stretchy":1821},[1761,57364,1909],{},[6411,57366,57367],{"scriptlevel":1767,"displaystyle":1833},[4379,57368,57369,57377],{},[895,57370,57371,57373,57375],{},[898,57372,4302],{},[1761,57374,1885],{},[898,57376,4346],{},[895,57378,57379,57381,57383],{},[898,57380,2774],{},[1761,57382,1885],{},[898,57384,207],{},[902,57386,57387],{"encoding":904},"Q^E(a, b, c, d) = \\dfrac{b - d}{c - a}"," podle (2.11) a (2.12):",[883,57390,57392],{"className":57391},[886],[888,57393,57394],{"xmlns":890,"display":1930},[892,57395,57396,57516],{},[895,57397,57398,57400,57406,57408,57434,57436,57438,57440,57442,57454,57456,57458,57460,57462,57488,57490,57492,57494,57496,57508,57510,57512,57514],{},[898,57399,4346],{},[1824,57401,57402,57404],{},[898,57403,1828],{},[898,57405,1818],{},[1761,57407,1909],{},[4379,57409,57410,57418],{},[895,57411,57412,57414,57416],{},[898,57413,4302],{},[1761,57415,1885],{},[898,57417,4346],{},[895,57419,57420,57422,57424,57426,57428],{},[1761,57421,1915],{"stretchy":1821},[898,57423,2774],{},[1761,57425,1885],{},[898,57427,207],{},[1824,57429,57430,57432],{},[1761,57431,1920],{"stretchy":1821},[1765,57433,2296],{},[2761,57435,7057],{},[898,57437,4346],{},[898,57439,207],{},[1761,57441,1964],{},[4379,57443,57444,57446],{},[1765,57445,1945],{},[895,57447,57448,57450,57452],{},[898,57449,2774],{},[1761,57451,1885],{},[898,57453,207],{},[2761,57455,7057],{},[898,57457,4346],{},[898,57459,4302],{},[1761,57461,1885],{},[4379,57463,57464,57472],{},[895,57465,57466,57468,57470],{},[898,57467,4302],{},[1761,57469,1885],{},[898,57471,4346],{},[895,57473,57474,57476,57478,57480,57482],{},[1761,57475,1915],{"stretchy":1821},[898,57477,2774],{},[1761,57479,1885],{},[898,57481,207],{},[1824,57483,57484,57486],{},[1761,57485,1920],{"stretchy":1821},[1765,57487,2296],{},[2761,57489,7057],{},[898,57491,4346],{},[898,57493,2774],{},[1761,57495,1885],{},[4379,57497,57498,57500],{},[1765,57499,1945],{},[895,57501,57502,57504,57506],{},[898,57503,2774],{},[1761,57505,1885],{},[898,57507,207],{},[2761,57509,7057],{},[898,57511,4346],{},[898,57513,4346],{},[898,57515,1741],{"mathvariant":1969},[902,57517,57518],{"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.",[724,57520,57521,57522,1343,57544,1343,57575,5372],{},"Dosazením číselných hodnot (",[883,57523,57525],{"className":57524},[886],[888,57526,57527],{"xmlns":890},[892,57528,57529,57541],{},[895,57530,57531,57533,57535,57537,57539],{},[898,57532,2774],{},[1761,57534,1885],{},[898,57536,207],{},[1761,57538,1909],{},[1765,57540,48401],{},[902,57542,57543],{"encoding":904},"c - a = 3{,}5",[883,57545,57547],{"className":57546},[886],[888,57548,57549],{"xmlns":890},[892,57550,57551,57572],{},[895,57552,57553,57555,57557,57559,57561,57567,57569],{},[1761,57554,1915],{"stretchy":1821},[898,57556,2774],{},[1761,57558,1885],{},[898,57560,207],{},[1824,57562,57563,57565],{},[1761,57564,1920],{"stretchy":1821},[1765,57566,2296],{},[1761,57568,1909],{},[1765,57570,57571],{},"12,25",[902,57573,57574],{"encoding":904},"(c-a)^2 = 12{,}25",[883,57576,57578],{"className":57577},[886],[888,57579,57580],{"xmlns":890},[892,57581,57582,57594],{},[895,57583,57584,57586,57588,57590,57592],{},[898,57585,4302],{},[1761,57587,1885],{},[898,57589,4346],{},[1761,57591,1909],{},[1765,57593,42042],{},[902,57595,57596],{"encoding":904},"b - d = 30",[883,57598,57600],{"className":57599},[886],[888,57601,57602],{"xmlns":890,"display":1930},[892,57603,57604,57705],{},[895,57605,57606,57608,57614,57616,57624,57626,57628,57630,57632,57640,57642,57644,57646,57648,57650,57658,57660,57662,57664,57666,57674,57676,57678,57680,57682,57685,57687,57690,57692,57694,57696,57699,57701,57703],{},[898,57607,4346],{},[1824,57609,57610,57612],{},[898,57611,1828],{},[898,57613,1818],{},[1761,57615,6803],{},[6411,57617,57618],{"scriptlevel":1767,"displaystyle":1821},[4379,57619,57620,57622],{},[1765,57621,42042],{},[1765,57623,57571],{},[1761,57625,1915],{"stretchy":1821},[1765,57627,5426],{},[1761,57629,1920],{"stretchy":1821},[1761,57631,1964],{},[6411,57633,57634],{"scriptlevel":1767,"displaystyle":1821},[4379,57635,57636,57638],{},[1765,57637,1945],{},[1765,57639,48401],{},[1761,57641,1915],{"stretchy":1821},[1761,57643,1885],{},[1765,57645,6321],{},[1761,57647,1920],{"stretchy":1821},[1761,57649,1885],{},[6411,57651,57652],{"scriptlevel":1767,"displaystyle":1821},[4379,57653,57654,57656],{},[1765,57655,42042],{},[1765,57657,57571],{},[1761,57659,1915],{"stretchy":1821},[1765,57661,6865],{},[1761,57663,1920],{"stretchy":1821},[1761,57665,1885],{},[6411,57667,57668],{"scriptlevel":1767,"displaystyle":1821},[4379,57669,57670,57672],{},[1765,57671,1945],{},[1765,57673,48401],{},[1761,57675,1915],{"stretchy":1821},[1765,57677,1945],{},[1761,57679,1920],{"stretchy":1821},[1761,57681,9945],{},[1765,57683,57684],{},"1,224",[1761,57686,1885],{},[1765,57688,57689],{},"1,429",[1761,57691,1885],{},[1765,57693,48574],{},[1761,57695,1885],{},[1765,57697,57698],{},"0,286",[1761,57700,9945],{},[1761,57702,1885],{},[1765,57704,48820],{},[902,57706,57707],{"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.",[724,57709,34095,57710,1741],{},[883,57711,57713],{"className":57712},[886],[888,57714,57715],{"xmlns":890},[892,57716,57717,57739],{},[895,57718,57719,57727,57729,57731,57733,57735,57737],{},[2015,57720,57721,57723,57725],{},[898,57722,1828],{},[1765,57724,1945],{},[898,57726,1818],{},[1761,57728,6803],{},[1765,57730,48569],{},[1761,57732,1885],{},[1765,57734,48851],{},[1761,57736,9945],{},[1765,57738,48856],{},[902,57740,57741],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 \\doteq 7{,}836",[1636,57743,57744],{},[724,57745,57746,57748,57749,57770,57771,57797,57798,57801,57802,57898,57899,57922,57923,57939],{},[883,57747,4723],{}," Pozn. k přepisu učebnice\nV původním skenu přednášky byla u části (b) uvedena hodnota ",[883,57750,57752],{"className":57751},[886],[888,57753,57754],{"xmlns":890},[892,57755,57756,57768],{},[895,57757,57758,57760,57762,57764,57766],{},[898,57759,6959],{"mathvariant":1969},[898,57761,1828],{},[1761,57763,6803],{},[1761,57765,1885],{},[1765,57767,48886],{},[902,57769,48889],{"encoding":904},", což neodpovídá součtu dílčích derivací při daných přírůstcích. Podle vlastního přepočtu vychází ",[883,57772,57774],{"className":57773},[886],[888,57775,57776],{"xmlns":890},[892,57777,57778,57794],{},[895,57779,57780,57782,57788,57790,57792],{},[898,57781,4346],{},[1824,57783,57784,57786],{},[898,57785,1828],{},[898,57787,1818],{},[1761,57789,9945],{},[1761,57791,1885],{},[1765,57793,48851],{},[902,57795,57796],{"encoding":904},"dQ^E \\doteq -0{,}735",". Totální diferenciál je navíc pouze ",[38,57799,57800],{},"lineární aproximací","; přesná změna zjištěná ze změněného vzorce\n",[883,57803,57805],{"className":57804},[886],[888,57806,57807],{"xmlns":890},[892,57808,57809,57895],{},[895,57810,57811,57819,57821,57855,57857,57881,57883,57890,57892],{},[2015,57812,57813,57815,57817],{},[898,57814,1828],{},[1765,57816,1945],{},[898,57818,1818],{},[1761,57820,1909],{},[4379,57822,57823,57839],{},[895,57824,57825,57831,57833],{},[1824,57826,57827,57829],{},[898,57828,4302],{},[1761,57830,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,57832,1885],{},[1824,57834,57835,57837],{},[898,57836,4346],{},[1761,57838,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[895,57840,57841,57847,57849],{},[1824,57842,57843,57845],{},[898,57844,2774],{},[1761,57846,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,57848,1885],{},[1824,57850,57851,57853],{},[898,57852,207],{},[1761,57854,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,57856,1909],{},[4379,57858,57859,57867],{},[895,57860,57861,57863,57865],{},[1765,57862,19076],{},[1761,57864,1885],{},[1765,57866,6974],{},[895,57868,57869,57871,57873,57875,57877,57879],{},[1765,57870,23354],{},[1761,57872,1885],{},[1761,57874,1915],{"stretchy":1821},[1761,57876,1885],{},[1765,57878,57179],{},[1761,57880,1920],{"stretchy":1821},[1761,57882,1909],{},[4379,57884,57885,57887],{},[1765,57886,45810],{},[1765,57888,57889],{},"3,1",[1761,57891,9945],{},[1765,57893,57894],{},"7,742",[902,57896,57897],{"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 ",[883,57900,57902],{"className":57901},[886],[888,57903,57904],{"xmlns":890},[892,57905,57906,57919],{},[895,57907,57908,57910,57912,57914,57916],{},[898,57909,6959],{"mathvariant":1969},[898,57911,1828],{},[1761,57913,9945],{},[1761,57915,1885],{},[1765,57917,57918],{},"0,829",[902,57920,57921],{"encoding":904},"\\Delta Q \\doteq -0{,}829"," — dobře konzistentní s diferenciálem. Hodnota ",[883,57924,57926],{"className":57925},[886],[888,57927,57928],{"xmlns":890},[892,57929,57930,57936],{},[895,57931,57932,57934],{},[1761,57933,1885],{},[1765,57935,48886],{},[902,57937,57938],{"encoding":904},"-2{,}69"," je tedy pravděpodobně chyba v zápisu.",[724,57941,57942],{},[614,57943,57944,57945,57958],{},"Příklad 2.11 je primárně o multiplikátorech pro ",[883,57946,57948],{"className":57947},[886],[888,57949,57950],{"xmlns":890},[892,57951,57952,57956],{},[895,57953,57954],{},[898,57955,1828],{},[902,57957,1828],{"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.",[198,57960,57962,57963],{"id":57961},"příklad-213-numerický-výpočet-psps","Příklad 2.13 — numerický výpočet ",[883,57964,57966],{"className":57965},[886],[888,57967,57968],{"xmlns":890},[892,57969,57970,57976],{},[895,57971,57972,57974],{},[898,57973,1839],{},[898,57975,1912],{},[902,57977,48964],{"encoding":904},[1636,57979,57980],{},[724,57981,57982,57984,57985,58019,58020,58042],{},[883,57983,56675],{}," Zadání\nPro nabídku ",[883,57986,57988],{"className":57987},[886],[888,57989,57990],{"xmlns":890},[892,57991,57992,58016],{},[895,57993,57994,57996,57998,58000,58002,58004,58006,58008,58010,58012,58014],{},[898,57995,1839],{},[1761,57997,1909],{},[898,57999,1912],{},[1761,58001,1915],{"stretchy":1821},[898,58003,1828],{},[1761,58005,1920],{"stretchy":1821},[1761,58007,1909],{},[1765,58009,2633],{},[1761,58011,1964],{},[1765,58013,2296],{},[898,58015,1828],{},[902,58017,58018],{"encoding":904},"P = S(Q) = 10 + 2Q"," a množství ",[883,58021,58023],{"className":58022},[886],[888,58024,58025],{"xmlns":890},[892,58026,58027,58039],{},[895,58028,58029,58035,58037],{},[1681,58030,58031,58033],{},[898,58032,1828],{},[1765,58034,1767],{},[1761,58036,1909],{},[1765,58038,2633],{},[902,58040,58041],{"encoding":904},"Q_0 = 10"," vypočítejte přebytek výrobce.",[724,58044,58045],{},[38,58046,26803],{},[724,58048,58049],{},"Odpovídající cena:",[883,58051,58053],{"className":58052},[886],[888,58054,58055],{"xmlns":890,"display":1930},[892,58056,58057,58092],{},[895,58058,58059,58065,58067,58069,58071,58073,58075,58077,58079,58081,58083,58085,58087,58089],{},[1681,58060,58061,58063],{},[898,58062,1839],{},[1765,58064,1767],{},[1761,58066,1909],{},[898,58068,1912],{},[1761,58070,1915],{"stretchy":1821},[1765,58072,2633],{},[1761,58074,1920],{"stretchy":1821},[1761,58076,1909],{},[1765,58078,2633],{},[1761,58080,1964],{},[1765,58082,2296],{},[1761,58084,2447],{},[1765,58086,2633],{},[1761,58088,1909],{},[1765,58090,58091],{},"30.",[902,58093,58094],{"encoding":904},"P_0 = S(10) = 10 + 2\\cdot 10 = 30.",[724,58096,58097],{},"Dle vzorce (2.15):",[883,58099,58101],{"className":58100},[886],[888,58102,58103],{"xmlns":890,"display":1930},[892,58104,58105,58213],{},[895,58106,58107,58109,58111,58113,58115,58117,58119,58125,58131,58133,58141,58143,58145,58147,58149,58151,58153,58155,58157,58159,58161,58163,58165,58167,58169,58172,58174,58176,58178,58184,58192,58194,58196,58198,58200,58202,58204,58206,58208,58210],{},[898,58108,1839],{},[898,58110,1912],{},[1761,58112,1915],{"stretchy":1821},[1765,58114,2633],{},[1761,58116,1920],{"stretchy":1821},[1761,58118,1909],{},[1681,58120,58121,58123],{},[898,58122,1839],{},[1765,58124,1767],{},[1681,58126,58127,58129],{},[898,58128,1828],{},[1765,58130,1767],{},[1761,58132,1885],{},[2015,58134,58135,58137,58139],{},[1761,58136,15208],{},[1765,58138,1767],{},[1765,58140,2633],{},[1761,58142,1915],{"stretchy":1821},[1765,58144,2633],{},[1761,58146,1964],{},[1765,58148,2296],{},[898,58150,1828],{},[1761,58152,1920],{"stretchy":1821},[2761,58154,7057],{},[898,58156,4346],{},[898,58158,1828],{},[1761,58160,1909],{},[1765,58162,2633],{},[1761,58164,2447],{},[1765,58166,42042],{},[1761,58168,1885],{},[1761,58170,1822],{"fence":1821,"stretchy":1833,"minsize":58171,"maxsize":58171},"1.8em",[1765,58173,2633],{},[898,58175,1828],{},[1761,58177,1964],{},[1824,58179,58180,58182],{},[898,58181,1828],{},[1765,58183,2296],{},[2015,58185,58186,58188,58190],{},[1761,58187,1844],{"fence":1821,"stretchy":1833,"minsize":58171,"maxsize":58171},[1765,58189,1767],{},[1765,58191,2633],{},[1761,58193,1909],{},[1765,58195,34111],{},[1761,58197,1885],{},[1761,58199,1915],{"stretchy":1821},[1765,58201,7160],{},[1761,58203,1964],{},[1765,58205,7160],{},[1761,58207,1920],{"stretchy":1821},[1761,58209,1909],{},[1765,58211,58212],{},"100.",[902,58214,58215],{"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.",[724,58217,58218,58219,58240,58241,58261],{},"Přebytek výrobce při množství ",[883,58220,58222],{"className":58221},[886],[888,58223,58224],{"xmlns":890},[892,58225,58226,58238],{},[895,58227,58228,58234,58236],{},[1681,58229,58230,58232],{},[898,58231,1828],{},[1765,58233,1767],{},[1761,58235,1909],{},[1765,58237,2633],{},[902,58239,58041],{"encoding":904}," je tedy ",[883,58242,58244],{"className":58243},[886],[888,58245,58246],{"xmlns":890},[892,58247,58248,58258],{},[895,58249,58250,58252,58254,58256],{},[898,58251,1839],{},[898,58253,1912],{},[1761,58255,1909],{},[1765,58257,7160],{},[902,58259,58260],{"encoding":904},"PS = 100"," (peněžních jednotek).",[1849,58263],{},[115,58265,58267],{"id":58266},"cheat-sheet","Cheat sheet",[16,58269,58270,58282],{},[19,58271,58272],{},[22,58273,58274,58276,58279],{},[25,58275,4780],{},[25,58277,58278],{},"Vzorec",[25,58280,58281],{},"Geometrie",[30,58283,58284,58402,58516,58584],{},[22,58285,58286,58314,58370],{},[35,58287,58288],{},[883,58289,58291],{"className":58290},[886],[888,58292,58293],{"xmlns":890},[892,58294,58295,58311],{},[895,58296,58297,58299,58301,58303,58309],{},[898,58298,6849],{},[898,58300,1912],{},[1761,58302,1915],{"stretchy":1821},[1681,58304,58305,58307],{},[898,58306,1828],{},[1765,58308,1767],{},[1761,58310,1920],{"stretchy":1821},[902,58312,58313],{"encoding":904},"CS(Q_0)",[35,58315,58316],{},[883,58317,58319],{"className":58318},[886],[888,58320,58321],{"xmlns":890},[892,58322,58323,58367],{},[895,58324,58325],{},[6411,58326,58327,58339,58341,58343,58345,58347,58349,58351,58353,58355,58361],{"scriptlevel":1767,"displaystyle":1833},[2015,58328,58329,58331,58333],{},[1761,58330,15208],{},[1765,58332,1767],{},[1681,58334,58335,58337],{},[898,58336,1828],{},[1765,58338,1767],{},[898,58340,2244],{},[1761,58342,1915],{"stretchy":1821},[898,58344,1828],{},[1761,58346,1920],{"stretchy":1821},[2761,58348,7057],{},[898,58350,4346],{},[898,58352,1828],{},[1761,58354,1885],{},[1681,58356,58357,58359],{},[898,58358,1839],{},[1765,58360,1767],{},[1681,58362,58363,58365],{},[898,58364,1828],{},[1765,58366,1767],{},[902,58368,58369],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0",[35,58371,58372,58373,58376,58377,58380,58381],{},"plocha ",[38,58374,58375],{},"pod"," křivkou poptávky, ",[38,58378,58379],{},"nad"," čárou ",[883,58382,58384],{"className":58383},[886],[888,58385,58386],{"xmlns":890},[892,58387,58388,58400],{},[895,58389,58390,58392,58394],{},[898,58391,1839],{},[1761,58393,1909],{},[1681,58395,58396,58398],{},[898,58397,1839],{},[1765,58399,1767],{},[902,58401,55657],{"encoding":904},[22,58403,58404,58432,58488],{},[35,58405,58406],{},[883,58407,58409],{"className":58408},[886],[888,58410,58411],{"xmlns":890},[892,58412,58413,58429],{},[895,58414,58415,58417,58419,58421,58427],{},[898,58416,1839],{},[898,58418,1912],{},[1761,58420,1915],{"stretchy":1821},[1681,58422,58423,58425],{},[898,58424,1828],{},[1765,58426,1767],{},[1761,58428,1920],{"stretchy":1821},[902,58430,58431],{"encoding":904},"PS(Q_0)",[35,58433,58434],{},[883,58435,58437],{"className":58436},[886],[888,58438,58439],{"xmlns":890},[892,58440,58441,58485],{},[895,58442,58443],{},[6411,58444,58445,58451,58457,58459,58471,58473,58475,58477,58479,58481,58483],{"scriptlevel":1767,"displaystyle":1833},[1681,58446,58447,58449],{},[898,58448,1839],{},[1765,58450,1767],{},[1681,58452,58453,58455],{},[898,58454,1828],{},[1765,58456,1767],{},[1761,58458,1885],{},[2015,58460,58461,58463,58465],{},[1761,58462,15208],{},[1765,58464,1767],{},[1681,58466,58467,58469],{},[898,58468,1828],{},[1765,58470,1767],{},[898,58472,1912],{},[1761,58474,1915],{"stretchy":1821},[898,58476,1828],{},[1761,58478,1920],{"stretchy":1821},[2761,58480,7057],{},[898,58482,4346],{},[898,58484,1828],{},[902,58486,58487],{"encoding":904},"\\displaystyle P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ",[35,58489,58372,58490,58492,58493,58380,58495],{},[38,58491,58379],{}," křivkou nabídky, ",[38,58494,58375],{},[883,58496,58498],{"className":58497},[886],[888,58499,58500],{"xmlns":890},[892,58501,58502,58514],{},[895,58503,58504,58506,58508],{},[898,58505,1839],{},[1761,58507,1909],{},[1681,58509,58510,58512],{},[898,58511,1839],{},[1765,58513,1767],{},[902,58515,55657],{"encoding":904},[22,58517,58518,58521,58548],{},[35,58519,58520],{},"Výdaje \u002F tržby",[35,58522,58523],{},[883,58524,58526],{"className":58525},[886],[888,58527,58528],{"xmlns":890},[892,58529,58530,58546],{},[895,58531,58532,58538,58540],{},[1681,58533,58534,58536],{},[898,58535,1839],{},[1765,58537,1767],{},[1761,58539,2447],{},[1681,58541,58542,58544],{},[898,58543,1828],{},[1765,58545,1767],{},[902,58547,56517],{"encoding":904},[35,58549,58550,58551],{},"obdélník ",[883,58552,58554],{"className":58553},[886],[888,58555,58556],{"xmlns":890},[892,58557,58558,58582],{},[895,58559,58560,58562,58564,58570,58572,58574,58576],{},[1765,58561,1767],{},[2761,58563,7057],{},[1681,58565,58566,58568],{},[898,58567,1828],{},[1765,58569,1767],{},[2761,58571,7057],{},[898,58573,8309],{},[2761,58575,7057],{},[1681,58577,58578,58580],{},[898,58579,1839],{},[1765,58581,1767],{},[902,58583,55137],{"encoding":904},[22,58585,58586,58589,58612],{},[35,58587,58588],{},"Celkový přebytek",[35,58590,58591],{},[883,58592,58594],{"className":58593},[886],[888,58595,58596],{"xmlns":890},[892,58597,58598,58610],{},[895,58599,58600,58602,58604,58606,58608],{},[898,58601,6849],{},[898,58603,1912],{},[1761,58605,1964],{},[898,58607,1839],{},[898,58609,1912],{},[902,58611,54875],{"encoding":904},[35,58613,58614],{},"součet obou ploch v rovnováze",[1849,58616],{},[115,58618,5533],{"id":5532},[120,58620,58621,58643,58665,58709,58753,58816,58844],{},[123,58622,58623,3927,58625,1343,58640,58642],{},[38,58624,48929],{},[883,58626,58628],{"className":58627},[886],[888,58629,58630],{"xmlns":890},[892,58631,58632,58638],{},[895,58633,58634,58636],{},[898,58635,6849],{},[898,58637,1912],{},[902,58639,48945],{"encoding":904},[614,58641,48983],{},") — rozdíl mezi ochotou platit a skutečnou platbou, vzorec (2.14).",[123,58644,58645,3927,58647,1343,58662,58664],{},[38,58646,49076],{},[883,58648,58650],{"className":58649},[886],[888,58651,58652],{"xmlns":890},[892,58653,58654,58660],{},[895,58655,58656,58658],{},[898,58657,1839],{},[898,58659,1912],{},[902,58661,48964],{"encoding":904},[614,58663,49079],{},") — rozdíl mezi tržbou a minimální cenou dle nabídky, vzorec (2.15).",[123,58666,58667,5675,58670,1741],{},[38,58668,58669],{},"Ochota platit",[883,58671,58673],{"className":58672},[886],[888,58674,58675],{"xmlns":890},[892,58676,58677,58707],{},[895,58678,58679],{},[6411,58680,58681,58693,58695,58697,58699,58701,58703,58705],{"scriptlevel":1767,"displaystyle":1833},[2015,58682,58683,58685,58687],{},[1761,58684,15208],{},[1765,58686,1767],{},[1681,58688,58689,58691],{},[898,58690,1828],{},[1765,58692,1767],{},[898,58694,2244],{},[1761,58696,1915],{"stretchy":1821},[898,58698,1828],{},[1761,58700,1920],{"stretchy":1821},[2761,58702,7057],{},[898,58704,4346],{},[898,58706,1828],{},[902,58708,55505],{"encoding":904},[123,58710,58711,5675,58714,1741],{},[38,58712,58713],{},"Minimální cena výrobce",[883,58715,58717],{"className":58716},[886],[888,58718,58719],{"xmlns":890},[892,58720,58721,58751],{},[895,58722,58723],{},[6411,58724,58725,58737,58739,58741,58743,58745,58747,58749],{"scriptlevel":1767,"displaystyle":1833},[2015,58726,58727,58729,58731],{},[1761,58728,15208],{},[1765,58730,1767],{},[1681,58732,58733,58735],{},[898,58734,1828],{},[1765,58736,1767],{},[898,58738,1912],{},[1761,58740,1915],{"stretchy":1821},[898,58742,1828],{},[1761,58744,1920],{"stretchy":1821},[2761,58746,7057],{},[898,58748,4346],{},[898,58750,1828],{},[902,58752,56147],{"encoding":904},[123,58754,58755,5675,58758,56648,58783,2162],{},[38,58756,58757],{},"Výdaje spotřebitele \u002F tržby výrobce",[883,58759,58761],{"className":58760},[886],[888,58762,58763],{"xmlns":890},[892,58764,58765,58781],{},[895,58766,58767,58773,58775],{},[1681,58768,58769,58771],{},[898,58770,1839],{},[1765,58772,1767],{},[2761,58774,7057],{},[1681,58776,58777,58779],{},[898,58778,1828],{},[1765,58780,1767],{},[902,58782,55583],{"encoding":904},[883,58784,58786],{"className":58785},[886],[888,58787,58788],{"xmlns":890},[892,58789,58790,58814],{},[895,58791,58792,58794,58796,58802,58804,58806,58808],{},[1765,58793,1767],{},[2761,58795,7057],{},[1681,58797,58798,58800],{},[898,58799,1828],{},[1765,58801,1767],{},[2761,58803,7057],{},[898,58805,8309],{},[2761,58807,7057],{},[1681,58809,58810,58812],{},[898,58811,1839],{},[1765,58813,1767],{},[902,58815,55137],{"encoding":904},[123,58817,58818,58821,58822,58843],{},[38,58819,58820],{},"Celkový přebytek trhu"," — součet ",[883,58823,58825],{"className":58824},[886],[888,58826,58827],{"xmlns":890},[892,58828,58829,58841],{},[895,58830,58831,58833,58835,58837,58839],{},[898,58832,6849],{},[898,58834,1912],{},[1761,58836,1964],{},[898,58838,1839],{},[898,58840,1912],{},[902,58842,54875],{"encoding":904}," v rovnovážném bodě.",[123,58845,58846,58848,58849,1343,58862,58875,58876,1741],{},[38,58847,4033],{}," — plochy ohraničené křivkami ",[883,58850,58852],{"className":58851},[886],[888,58853,58854],{"xmlns":890},[892,58855,58856,58860],{},[895,58857,58858],{},[898,58859,2244],{},[902,58861,2244],{"encoding":904},[883,58863,58865],{"className":58864},[886],[888,58866,58867],{"xmlns":890},[892,58868,58869,58873],{},[895,58870,58871],{},[898,58872,1912],{},[902,58874,1912],{"encoding":904}," a přímkou ",[883,58877,58879],{"className":58878},[886],[888,58880,58881],{"xmlns":890},[892,58882,58883,58895],{},[895,58884,58885,58887,58889],{},[898,58886,1839],{},[1761,58888,1909],{},[1681,58890,58891,58893],{},[898,58892,1839],{},[1765,58894,1767],{},[902,58896,55657],{"encoding":904},[1849,58898],{},[115,58900,58902],{"id":58901},"dopad-daně-na-přebytky-a-mrtvá-ztráta","Dopad daně na přebytky a mrtvá ztráta",[724,58904,58905,58906,58919,58920,58937],{},"Uvalení jednotkové daně ",[883,58907,58909],{"className":58908},[886],[888,58910,58911],{"xmlns":890},[892,58912,58913,58917],{},[895,58914,58915],{},[898,58916,1655],{},[902,58918,1655],{"encoding":904}," na trh posouvá rovnovážné množství pod ",[883,58921,58923],{"className":58922},[886],[888,58924,58925],{"xmlns":890},[892,58926,58927,58935],{},[895,58928,58929],{},[1824,58930,58931,58933],{},[898,58932,1828],{},[898,58934,1818],{},[902,58936,46412],{"encoding":904}," a rozkládá původní plochu přebytků na nové části.",[724,58939,58940],{},[3991,58941],{"alt":58942,"className":58943,"src":58944},"imek-prebytky-s-dani-deadweight",[210,3995],"\u002Fwiki-assets\u002Fimek-prebytky-s-dani-deadweight.jpeg",[724,58946,58947,58948,58963,58964,58979,58980,56648,58983,59007,59008,3927,59011,59013,59014,1741],{},"Přebytek spotřebitele ",[883,58949,58951],{"className":58950},[886],[888,58952,58953],{"xmlns":890},[892,58954,58955,58961],{},[895,58956,58957,58959],{},[898,58958,6849],{},[898,58960,1912],{},[902,58962,48945],{"encoding":904}," se zmenší (spotřebitelé platí víc a nakupují méně), přebytek výrobce ",[883,58965,58967],{"className":58966},[886],[888,58968,58969],{"xmlns":890},[892,58970,58971,58977],{},[895,58972,58973,58975],{},[898,58974,1839],{},[898,58976,1912],{},[902,58978,48964],{"encoding":904}," se rovněž zmenší (výrobci obdrží po odvodu méně). Stát získává ",[38,58981,58982],{},"daňový příjem",[883,58984,58986],{"className":58985},[886],[888,58987,58988],{"xmlns":890},[892,58989,58990,59004],{},[895,58991,58992,58994,58996],{},[898,58993,1655],{},[1761,58995,2447],{},[2015,58997,58998,59000,59002],{},[898,58999,1828],{},[1765,59001,1945],{},[898,59003,1818],{},[902,59005,59006],{"encoding":904},"T \\cdot Q_1^E","). Zbývající část původních přebytků — ",[38,59009,59010],{},"mrtvá ztráta",[614,59012,5990],{},", DWL) — je čistým úbytkem blahobytu, který nikdo neinkasuje, a je důsledkem transakcí, které se kvůli dani vůbec neuskuteční. Detailní rozbor viz ",[207,59015,811],{"className":59016,"dataFsResolvedFilePath":809,"href":810},[210],[1849,59018],{},[115,59020,5968],{"id":5967},[120,59022,59023,59030,59042,59049,59056],{},[123,59024,59025,1989,59027],{},[38,59026,20256],{},[207,59028,802],{"className":59029,"dataFsResolvedFilePath":800,"href":801},[210],[123,59031,59032,1989,59034,59037,59038,59041],{},[38,59033,40702],{},[207,59035,775],{"className":59036,"dataFsResolvedFilePath":773,"href":774},[210]," (určitý integrál, plocha pod křivkou), ",[207,59039,5995],{"className":59040,"dataFsResolvedFilePath":764,"href":765},[210]," (monotonie křivek)",[123,59043,59044,1989,59046],{},[38,59045,20266],{},[207,59047,7885],{"className":59048,"dataFsResolvedFilePath":827,"href":828},[210],[123,59050,59051,1989,59053],{},[38,59052,6006],{},[207,59054,6010],{"className":59055,"dataFsResolvedFilePath":745,"href":746},[210],[123,59057,59058,1989,59060],{},[38,59059,6015],{},[207,59061,6021],{"className":59062,"dataFsResolvedFilePath":6019,"href":6020},[210],{"title":641,"searchDepth":642,"depth":642,"links":59064},[59065,59066,59071,59076,59081,59082,59083,59084],{"id":54934,"depth":642,"text":1241},{"id":55278,"depth":642,"text":59067,"children":59068},"Přebytek spotřebitele (CSCS)",[59069,59070],{"id":55297,"depth":649,"text":55298},{"id":4032,"depth":649,"text":4033},{"id":55873,"depth":642,"text":59072,"children":59073},"Přebytek výrobce (PSPS)",[59074,59075],{"id":55892,"depth":649,"text":55893},{"id":56055,"depth":649,"text":4033},{"id":56663,"depth":642,"text":56664,"children":59077},[59078,59079],{"id":56667,"depth":649,"text":56668},{"id":57961,"depth":649,"text":59080},"Příklad 2.13 — numerický výpočet PSPS",{"id":58266,"depth":642,"text":58267},{"id":5532,"depth":642,"text":5533},{"id":58901,"depth":642,"text":58902},{"id":5967,"depth":642,"text":5968},{},"\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce",{"title":820,"description":641},[1138,1135],"topics\u002Fprebytek-spotrebitele-vyrobce",[1128,54804,59091,59092,16028,5371,59093,59094],"cs","ps","spotrebitel","vyrobce","FhK0gkf2tjMxSgO0-74OuedOn6U35QtJczf-f255pZs",{"id":59097,"title":59098,"body":59099,"course":1128,"courses":659,"created":6039,"description":641,"extension":661,"meta":78428,"navigation":664,"path":78429,"seo":78430,"sources":78431,"stem":78432,"tags":78433,"type":6050,"updated":677,"__hash__":78439},"topics\u002Ftopics\u002Fprijem-naklady-zisk.md","Příjem, náklady, zisk a nabídka firmy",{"type":9,"value":59100,"toc":78392},[59101,59104,59290,59292,59383,59388,59714,59718,59725,59729,59774,59841,59872,59922,59957,59961,60020,60025,60091,60209,60311,60315,60338,60416,60459,60463,60492,60559,60565,60679,60683,60763,60800,60852,61050,61114,61201,61205,61208,61287,61290,61408,61427,61492,61496,61588,61656,61697,61751,61819,61856,61860,61918,61948,62159,62231,62283,62449,62542,62577,62581,62585,62622,62687,62742,62746,62769,62858,62962,63031,63035,63132,63245,63301,63355,63413,63474,63477,63513,63578,63608,63837,63895,63929,63933,63960,64039,64153,64174,64253,64255,64363,64367,64505,64827,64831,64834,64838,64887,64891,65145,65297,65304,65377,65561,65566,65909,65913,65936,65938,65959,66018,66028,66077,66219,66293,66388,66503,66601,66719,66723,66792,66797,66909,67054,67105,67217,67259,67263,67283,67344,67371,67433,67437,67459,67528,67808,67815,67845,67852,68045,68049,68127,68132,68208,68211,68299,68375,68442,68491,68594,68667,68788,69139,69252,69354,69358,69361,69368,69371,69407,69466,69475,69624,69848,69852,69915,70094,70186,70241,70245,70301,70371,70423,70444,70525,70528,70603,70647,70651,70692,70735,70761,70765,70836,70932,70994,71046,71149,71227,71250,71279,71283,71449,71566,71638,71953,72113,72117,72168,72230,72265,72295,72395,72437,72606,72611,72707,72745,72749,72868,73169,73171,73206,73210,73214,73342,73474,73796,73984,74062,74066,74371,74484,74630,74815,74921,75153,75268,75350,75469,75567,75608,75612,75667,75811,75965,76125,76218,76412,76724,76855,76984,76988,77060,77102,77153,77155,78350,78352],[12,59102,59098],{"id":59103},"příjem-náklady-zisk-a-nabídka-firmy",[1636,59105,59106],{},[724,59107,59108,7934,59110,1989,59113,59128,59129,1989,59132,59147,59148,1989,59151,59179,59180,59202,59203,59227,59228,59250,59251,59254,59255,59271,59272,1741],{},[883,59109,7933],{},[38,59111,59112],{},"Příjem",[883,59114,59116],{"className":59115},[886],[888,59117,59118],{"xmlns":890},[892,59119,59120,59126],{},[895,59121,59122,59124],{},[898,59123,1655],{},[898,59125,8051],{},[902,59127,8151],{"encoding":904}," je to, co firma inkasuje (cena krát množství), ",[38,59130,59131],{},"náklady",[883,59133,59135],{"className":59134},[886],[888,59136,59137],{"xmlns":890},[892,59138,59139,59145],{},[895,59140,59141,59143],{},[898,59142,1655],{},[898,59144,6849],{},[902,59146,7310],{"encoding":904}," to, co vynaloží (fixní plus variabilní), a ",[38,59149,59150],{},"zisk",[883,59152,59154],{"className":59153},[886],[888,59155,59156],{"xmlns":890},[892,59157,59158,59176],{},[895,59159,59160,59162,59164,59166,59168,59170,59172,59174],{},[898,59161,1839],{},[898,59163,8051],{},[1761,59165,1909],{},[898,59167,1655],{},[898,59169,8051],{},[1761,59171,1885],{},[898,59173,1655],{},[898,59175,6849],{},[902,59177,59178],{"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: ",[883,59181,59183],{"className":59182},[886],[888,59184,59185],{"xmlns":890},[892,59186,59187,59199],{},[895,59188,59189,59191,59193,59195,59197],{},[898,59190,8309],{},[898,59192,6849],{},[1761,59194,1909],{},[898,59196,6889],{},[898,59198,6849],{},[902,59200,59201],{"encoding":904},"AC = MC"," v minimu průměrných nákladů, ",[883,59204,59206],{"className":59205},[886],[888,59207,59208],{"xmlns":890},[892,59209,59210,59224],{},[895,59211,59212,59214,59216,59218,59220,59222],{},[898,59213,8309],{},[898,59215,44359],{},[898,59217,6849],{},[1761,59219,1909],{},[898,59221,6889],{},[898,59223,6849],{},[902,59225,59226],{"encoding":904},"AVC = MC"," v minimu průměrných variabilních nákladů a ",[883,59229,59231],{"className":59230},[886],[888,59232,59233],{"xmlns":890},[892,59234,59235,59247],{},[895,59236,59237,59239,59241,59243,59245],{},[898,59238,6889],{},[898,59240,8051],{},[1761,59242,1909],{},[898,59244,6889],{},[898,59246,6849],{},[902,59248,59249],{"encoding":904},"MR = MC"," v maximu zisku. Na závěr se sestaví ",[38,59252,59253],{},"funkce nabídky firmy"," jako rostoucí část křivky ",[883,59256,59258],{"className":59257},[886],[888,59259,59260],{"xmlns":890},[892,59261,59262,59268],{},[895,59263,59264,59266],{},[898,59265,6889],{},[898,59267,6849],{},[902,59269,59270],{"encoding":904},"MC"," nad bodem minima ",[883,59273,59275],{"className":59274},[886],[888,59276,59277],{"xmlns":890},[892,59278,59279,59287],{},[895,59280,59281,59283,59285],{},[898,59282,8309],{},[898,59284,44359],{},[898,59286,6849],{},[902,59288,59289],{"encoding":904},"AVC",[115,59291,1241],{"id":54934},[724,59293,59294,59295,59298,59299,59301,59302,1343,59305,1343,59308,59310,59311,59314,59315,59318,59319,59322,59323,6746,59338,1348,59353,6746,59368,2162],{},"Kapitola 3 se zabývá dvěma základními veličinami popisujícími ekonomickou aktivitu firmy — ",[38,59296,59297],{},"příjmem"," (revenue) a ",[38,59300,59131],{}," (cost) — v jejich třech standardních podobách: celkové, průměrné a mezní. Navazuje analýzou ",[38,59303,59304],{},"zisku",[38,59306,59307],{},"bodů zvratu",[38,59309,6080],{}," a konstrukcí ",[38,59312,59313],{},"nabídkové křivky firmy",". Klíčovými matematickými nástroji jsou ",[207,59316,1145],{"className":59317,"dataFsResolvedFilePath":764,"href":765},[210]," (pro mezní veličiny) a diferenciál (pro odhad přírůstků); v několika úlohách se využívá také ",[207,59320,15169],{"className":59321,"dataFsResolvedFilePath":773,"href":774},[210]," (pro zpětnou rekonstrukci ",[883,59324,59326],{"className":59325},[886],[888,59327,59328],{"xmlns":890},[892,59329,59330,59336],{},[895,59331,59332,59334],{},[898,59333,1655],{},[898,59335,8051],{},[902,59337,8151],{"encoding":904},[883,59339,59341],{"className":59340},[886],[888,59342,59343],{"xmlns":890},[892,59344,59345,59351],{},[895,59346,59347,59349],{},[898,59348,6889],{},[898,59350,8051],{},[902,59352,10679],{"encoding":904},[883,59354,59356],{"className":59355},[886],[888,59357,59358],{"xmlns":890},[892,59359,59360,59366],{},[895,59361,59362,59364],{},[898,59363,1655],{},[898,59365,6849],{},[902,59367,7310],{"encoding":904},[883,59369,59371],{"className":59370},[886],[888,59372,59373],{"xmlns":890},[892,59374,59375,59381],{},[895,59376,59377,59379],{},[898,59378,6889],{},[898,59380,6849],{},[902,59382,59270],{"encoding":904},[724,59384,59385],{},[38,59386,59387],{},"Cílové znalosti:",[120,59389,59390,59554,59557,59560,59653,59700,59707],{},[123,59391,59392,59393,1343,59408,1343,59424,2068,59439,1343,59454,1343,59470,1343,59488,1343,59506,1343,59523,1343,59539,12468],{},"odvodit a interpretovat funkce ",[883,59394,59396],{"className":59395},[886],[888,59397,59398],{"xmlns":890},[892,59399,59400,59406],{},[895,59401,59402,59404],{},[898,59403,1655],{},[898,59405,8051],{},[902,59407,8151],{"encoding":904},[883,59409,59411],{"className":59410},[886],[888,59412,59413],{"xmlns":890},[892,59414,59415,59421],{},[895,59416,59417,59419],{},[898,59418,8309],{},[898,59420,8051],{},[902,59422,59423],{"encoding":904},"AR",[883,59425,59427],{"className":59426},[886],[888,59428,59429],{"xmlns":890},[892,59430,59431,59437],{},[895,59432,59433,59435],{},[898,59434,6889],{},[898,59436,8051],{},[902,59438,10679],{"encoding":904},[883,59440,59442],{"className":59441},[886],[888,59443,59444],{"xmlns":890},[892,59445,59446,59452],{},[895,59447,59448,59450],{},[898,59449,1655],{},[898,59451,6849],{},[902,59453,7310],{"encoding":904},[883,59455,59457],{"className":59456},[886],[888,59458,59459],{"xmlns":890},[892,59460,59461,59467],{},[895,59462,59463,59465],{},[898,59464,14474],{},[898,59466,6849],{},[902,59468,59469],{"encoding":904},"FC",[883,59471,59473],{"className":59472},[886],[888,59474,59475],{"xmlns":890},[892,59476,59477,59485],{},[895,59478,59479,59481,59483],{},[898,59480,1655],{},[898,59482,44359],{},[898,59484,6849],{},[902,59486,59487],{"encoding":904},"TVC",[883,59489,59491],{"className":59490},[886],[888,59492,59493],{"xmlns":890},[892,59494,59495,59503],{},[895,59496,59497,59499,59501],{},[898,59498,8309],{},[898,59500,14474],{},[898,59502,6849],{},[902,59504,59505],{"encoding":904},"AFC",[883,59507,59509],{"className":59508},[886],[888,59510,59511],{"xmlns":890},[892,59512,59513,59521],{},[895,59514,59515,59517,59519],{},[898,59516,8309],{},[898,59518,44359],{},[898,59520,6849],{},[902,59522,59289],{"encoding":904},[883,59524,59526],{"className":59525},[886],[888,59527,59528],{"xmlns":890},[892,59529,59530,59536],{},[895,59531,59532,59534],{},[898,59533,8309],{},[898,59535,6849],{},[902,59537,59538],{"encoding":904},"AC",[883,59540,59542],{"className":59541},[886],[888,59543,59544],{"xmlns":890},[892,59545,59546,59552],{},[895,59547,59548,59550],{},[898,59549,6889],{},[898,59551,6849],{},[902,59553,59270],{"encoding":904},[123,59555,59556],{},"porozumět vzájemným vztahům mezi průměrnou a mezní veličinou, zvláště pro lineární poptávku;",[123,59558,59559],{},"pomocí diferenciálu odhadovat změny celkových veličin;",[123,59561,59562,59563,59566,59567,5715,59609,12468],{},"osvojit si ",[38,59564,59565],{},"princip minimalizace průměrných (variabilních) nákladů"," — podmínku ",[883,59568,59570],{"className":59569},[886],[888,59571,59572],{"xmlns":890},[892,59573,59574,59606],{},[895,59575,59576,59578,59580,59582,59588,59590,59592,59594,59596,59598,59604],{},[898,59577,8309],{},[898,59579,6849],{},[1761,59581,1915],{"stretchy":1821},[1681,59583,59584,59586],{},[898,59585,1828],{},[1765,59587,1767],{},[1761,59589,1920],{"stretchy":1821},[1761,59591,1909],{},[898,59593,6889],{},[898,59595,6849],{},[1761,59597,1915],{"stretchy":1821},[1681,59599,59600,59602],{},[898,59601,1828],{},[1765,59603,1767],{},[1761,59605,1920],{"stretchy":1821},[902,59607,59608],{"encoding":904},"AC(Q_0)=MC(Q_0)",[883,59610,59612],{"className":59611},[886],[888,59613,59614],{"xmlns":890},[892,59615,59616,59650],{},[895,59617,59618,59620,59622,59624,59626,59632,59634,59636,59638,59640,59642,59648],{},[898,59619,8309],{},[898,59621,44359],{},[898,59623,6849],{},[1761,59625,1915],{"stretchy":1821},[1681,59627,59628,59630],{},[898,59629,1828],{},[1765,59631,1767],{},[1761,59633,1920],{"stretchy":1821},[1761,59635,1909],{},[898,59637,6889],{},[898,59639,6849],{},[1761,59641,1915],{"stretchy":1821},[1681,59643,59644,59646],{},[898,59645,1828],{},[1765,59647,1767],{},[1761,59649,1920],{"stretchy":1821},[902,59651,59652],{"encoding":904},"AVC(Q_0)=MC(Q_0)",[123,59654,59562,59655,59566,59658,12468],{},[38,59656,59657],{},"princip maximalizace zisku",[883,59659,59661],{"className":59660},[886],[888,59662,59663],{"xmlns":890},[892,59664,59665,59697],{},[895,59666,59667,59669,59671,59673,59679,59681,59683,59685,59687,59689,59695],{},[898,59668,6889],{},[898,59670,8051],{},[1761,59672,1915],{"stretchy":1821},[1681,59674,59675,59677],{},[898,59676,1828],{},[1765,59678,1767],{},[1761,59680,1920],{"stretchy":1821},[1761,59682,1909],{},[898,59684,6889],{},[898,59686,6849],{},[1761,59688,1915],{"stretchy":1821},[1681,59690,59691,59693],{},[898,59692,1828],{},[1765,59694,1767],{},[1761,59696,1920],{"stretchy":1821},[902,59698,59699],{"encoding":904},"MR(Q_0)=MC(Q_0)",[123,59701,59702,59703,59706],{},"stanovit ",[38,59704,59705],{},"body zvratu"," a interval zisku;",[123,59708,59709,59710,59713],{},"zkonstruovat ",[38,59711,59712],{},"funkci nabídky firmy"," na základě nákladových charakteristik.",[115,59715,59717],{"id":59716},"příjem-firmy","Příjem firmy",[724,59719,59720],{},[3991,59721],{"alt":59722,"className":59723,"src":59724},"imek-ar-mr-dvojnasobny-sklon",[210,3995],"\u002Fwiki-assets\u002Fimek-ar-mr-dvojnasobny-sklon.jpeg",[198,59726,59728],{"id":59727},"celkový-příjem","Celkový příjem",[724,59730,59731,59732,3927,59747,59750,59751,33974],{},"Celkový příjem ",[883,59733,59735],{"className":59734},[886],[888,59736,59737],{"xmlns":890},[892,59738,59739,59745],{},[895,59740,59741,59743],{},[898,59742,1655],{},[898,59744,8051],{},[902,59746,8151],{"encoding":904},[38,59748,59749],{},"total revenue",") je součin ceny a prodaného množství. Při poptávce ",[883,59752,59754],{"className":59753},[886],[888,59755,59756],{"xmlns":890},[892,59757,59758,59772],{},[895,59759,59760,59762,59764,59766,59768,59770],{},[898,59761,1839],{},[1761,59763,1909],{},[898,59765,2244],{},[1761,59767,1915],{"stretchy":1821},[898,59769,1828],{},[1761,59771,1920],{"stretchy":1821},[902,59773,8692],{"encoding":904},[883,59775,59777],{"className":59776},[886],[888,59778,59779],{"xmlns":890,"display":1930},[892,59780,59781,59838],{},[24787,59782,59783],{"width":32101},[24792,59784,59785,59787,59831,59833],{},[24795,59786],{"width":32106},[24795,59788,59789],{},[895,59790,59791,59793,59795,59797,59799,59801,59803,59805,59807,59809,59811,59813,59815,59817,59819,59821,59823,59825,59827,59829],{},[898,59792,1655],{},[898,59794,8051],{},[1761,59796,1909],{},[898,59798,1655],{},[898,59800,8051],{},[1761,59802,1915],{"stretchy":1821},[898,59804,1828],{},[1761,59806,1920],{"stretchy":1821},[1761,59808,1909],{},[898,59810,1839],{},[1761,59812,2447],{},[898,59814,1828],{},[1761,59816,1909],{},[898,59818,2244],{},[1761,59820,1915],{"stretchy":1821},[898,59822,1828],{},[1761,59824,1920],{"stretchy":1821},[1761,59826,2447],{},[898,59828,1828],{},[898,59830,1741],{"mathvariant":1969},[24795,59832],{"width":32106},[24795,59834,59835],{},[2761,59836,59837],{},"(3.1)",[902,59839,59840],{"encoding":904},"TR = TR(Q) = P \\cdot Q = D(Q) \\cdot Q.\n\\tag{3.1}",[724,59842,59843,59844,59847,59848,59871],{},"Graf funkce se nazývá ",[38,59845,59846],{},"křivka celkového příjmu"," (total revenue curve). Za předpokladu linearity poptávky, tj. ",[883,59849,59851],{"className":59850},[886],[888,59852,59853],{"xmlns":890},[892,59854,59855,59869],{},[895,59856,59857,59859,59861,59863,59865,59867],{},[898,59858,1839],{},[1761,59860,1909],{},[898,59862,207],{},[898,59864,1828],{},[1761,59866,1964],{},[898,59868,4302],{},[902,59870,4305],{"encoding":904},", je celkový příjem kvadratickou funkcí, neboť",[883,59873,59875],{"className":59874},[886],[888,59876,59877],{"xmlns":890,"display":1930},[892,59878,59879,59919],{},[895,59880,59881,59883,59885,59887,59889,59891,59893,59895,59897,59899,59901,59903,59905,59911,59913,59915,59917],{},[898,59882,1655],{},[898,59884,8051],{},[1761,59886,1909],{},[898,59888,1828],{},[1761,59890,1915],{"stretchy":1821},[898,59892,207],{},[898,59894,1828],{},[1761,59896,1964],{},[898,59898,4302],{},[1761,59900,1920],{"stretchy":1821},[1761,59902,1909],{},[898,59904,207],{},[1824,59906,59907,59909],{},[898,59908,1828],{},[1765,59910,2296],{},[1761,59912,1964],{},[898,59914,4302],{},[898,59916,1828],{},[1761,59918,1834],{"separator":1833},[902,59920,59921],{"encoding":904},"TR = Q(aQ + b) = aQ^2 + bQ,",[724,59923,59924,59925,59938,59939,59956],{},"a křivka celkového příjmu je parabola tvaru obráceného ",[883,59926,59928],{"className":59927},[886],[888,59929,59930],{"xmlns":890},[892,59931,59932,59936],{},[895,59933,59934],{},[898,59935,900],{},[902,59937,900],{"encoding":904}," (jelikož ",[883,59940,59942],{"className":59941},[886],[888,59943,59944],{"xmlns":890},[892,59945,59946,59954],{},[895,59947,59948,59950,59952],{},[898,59949,207],{},[1761,59951,2058],{},[1765,59953,1767],{},[902,59955,4323],{"encoding":904},") procházející počátkem.",[41374,59958,59960],{"id":59959},"příklad-31","Příklad 3.1",[724,59962,59963,59966,59967,60003,60004,60019],{},[38,59964,59965],{},"Zadání."," Pro poptávku ",[883,59968,59970],{"className":59969},[886],[888,59971,59972],{"xmlns":890},[892,59973,59974,60000],{},[895,59975,59976,59978,59980,59982,59984,59986,59988,59990,59992,59994,59996,59998],{},[898,59977,1839],{},[1761,59979,1909],{},[898,59981,2244],{},[1761,59983,1915],{"stretchy":1821},[898,59985,1828],{},[1761,59987,1920],{"stretchy":1821},[1761,59989,1909],{},[1761,59991,1885],{},[1765,59993,2296],{},[898,59995,1828],{},[1761,59997,1964],{},[1765,59999,7160],{},[902,60001,60002],{"encoding":904},"P = D(Q) = -2Q + 100"," určete ",[883,60005,60007],{"className":60006},[886],[888,60008,60009],{"xmlns":890},[892,60010,60011,60017],{},[895,60012,60013,60015],{},[898,60014,1655],{},[898,60016,8051],{},[902,60018,8151],{"encoding":904}," a charakterizujte jeho křivku.",[724,60021,60022,60024],{},[38,60023,26803],{}," Celkový příjem je",[883,60026,60028],{"className":60027},[886],[888,60029,60030],{"xmlns":890,"display":1930},[892,60031,60032,60088],{},[895,60033,60034,60036,60038,60040,60042,60044,60046,60048,60050,60052,60054,60056,60058,60060,60062,60064,60066,60068,60070,60072,60074,60080,60082,60084,60086],{},[898,60035,1655],{},[898,60037,8051],{},[1761,60039,1909],{},[898,60041,1655],{},[898,60043,8051],{},[1761,60045,1915],{"stretchy":1821},[898,60047,1828],{},[1761,60049,1920],{"stretchy":1821},[1761,60051,1909],{},[898,60053,1828],{},[1761,60055,1915],{"stretchy":1821},[1761,60057,1885],{},[1765,60059,2296],{},[898,60061,1828],{},[1761,60063,1964],{},[1765,60065,7160],{},[1761,60067,1920],{"stretchy":1821},[1761,60069,1909],{},[1761,60071,1885],{},[1765,60073,2296],{},[1824,60075,60076,60078],{},[898,60077,1828],{},[1765,60079,2296],{},[1761,60081,1964],{},[1765,60083,7160],{},[898,60085,1828],{},[898,60087,1741],{"mathvariant":1969},[902,60089,60090],{"encoding":904},"TR = TR(Q) = Q(-2Q + 100) = -2Q^2 + 100Q.",[724,60092,60093,60094,2068,60116,60138,60139,60157,60158,1741],{},"Křivkou je parabola (obrázek 3.1) s nulami v ",[883,60095,60097],{"className":60096},[886],[888,60098,60099],{"xmlns":890},[892,60100,60101,60113],{},[895,60102,60103,60109,60111],{},[1681,60104,60105,60107],{},[898,60106,1828],{},[1765,60108,1945],{},[1761,60110,1909],{},[1765,60112,1767],{},[902,60114,60115],{"encoding":904},"Q_1 = 0",[883,60117,60119],{"className":60118},[886],[888,60120,60121],{"xmlns":890},[892,60122,60123,60135],{},[895,60124,60125,60131,60133],{},[1681,60126,60127,60129],{},[898,60128,1828],{},[1765,60130,2296],{},[1761,60132,1909],{},[1765,60134,7190],{},[902,60136,60137],{"encoding":904},"Q_2 = 50",". Maxima dosahuje při ",[883,60140,60142],{"className":60141},[886],[888,60143,60144],{"xmlns":890},[892,60145,60146,60154],{},[895,60147,60148,60150,60152],{},[898,60149,1828],{},[1761,60151,1909],{},[1765,60153,9056],{},[902,60155,60156],{"encoding":904},"Q = 25"," ve výši ",[883,60159,60161],{"className":60160},[886],[888,60162,60163],{"xmlns":890},[892,60164,60165,60206],{},[895,60166,60167,60169,60179,60181,60183,60185,60187,60190,60192,60194,60196,60198,60200,60202,60204],{},[898,60168,1655],{},[1681,60170,60171,60173,60176],{},[898,60172,8051],{},[898,60174,60175],{},"max",[1761,60177,60178],{},"⁡",[1761,60180,1909],{},[1761,60182,1885],{},[1765,60184,2296],{},[1761,60186,2447],{},[1765,60188,60189],{},"625",[1761,60191,1964],{},[1765,60193,7160],{},[1761,60195,2447],{},[1765,60197,9056],{},[1761,60199,1909],{},[1765,60201,1945],{},[2761,60203,7057],{},[1765,60205,34773],{},[902,60207,60208],{"encoding":904},"TR_{\\max} = -2 \\cdot 625 + 100 \\cdot 25 = 1\\,250",[724,60210,60211],{},[614,60212,60213,60214,60248,60249,2068,60262,60275,60276,6699,60294,1741],{},"Obrázek 3.1: Parabola ",[883,60215,60217],{"className":60216},[886],[888,60218,60219],{"xmlns":890},[892,60220,60221,60245],{},[895,60222,60223,60225,60227,60229,60231,60233,60239,60241,60243],{},[898,60224,1655],{},[898,60226,8051],{},[1761,60228,1909],{},[1761,60230,1885],{},[1765,60232,2296],{},[1824,60234,60235,60237],{},[898,60236,1828],{},[1765,60238,2296],{},[1761,60240,1964],{},[1765,60242,7160],{},[898,60244,1828],{},[902,60246,60247],{"encoding":904},"TR = -2Q^2 + 100Q"," s nulami v ",[883,60250,60252],{"className":60251},[886],[888,60253,60254],{"xmlns":890},[892,60255,60256,60260],{},[895,60257,60258],{},[1765,60259,1767],{},[902,60261,1767],{"encoding":904},[883,60263,60265],{"className":60264},[886],[888,60266,60267],{"xmlns":890},[892,60268,60269,60273],{},[895,60270,60271],{},[1765,60272,7190],{},[902,60274,7190],{"encoding":904}," a maximem ",[883,60277,60279],{"className":60278},[886],[888,60280,60281],{"xmlns":890},[892,60282,60283,60291],{},[895,60284,60285,60287,60289],{},[1765,60286,1945],{},[2761,60288,7057],{},[1765,60290,34773],{},[902,60292,60293],{"encoding":904},"1\\,250",[883,60295,60297],{"className":60296},[886],[888,60298,60299],{"xmlns":890},[892,60300,60301,60309],{},[895,60302,60303,60305,60307],{},[898,60304,1828],{},[1761,60306,1909],{},[1765,60308,9056],{},[902,60310,60156],{"encoding":904},[198,60312,60314],{"id":60313},"průměrný-příjem","Průměrný příjem",[724,60316,60317,1989,60319,3927,60334,60337],{},[38,60318,60314],{},[883,60320,60322],{"className":60321},[886],[888,60323,60324],{"xmlns":890},[892,60325,60326,60332],{},[895,60327,60328,60330],{},[898,60329,8309],{},[898,60331,8051],{},[902,60333,59423],{"encoding":904},[38,60335,60336],{},"average revenue",") je podíl celkového příjmu a množství. Z (3.1) plyne",[883,60339,60341],{"className":60340},[886],[888,60342,60343],{"xmlns":890,"display":1930},[892,60344,60345,60413],{},[895,60346,60347,60349,60351,60353,60355,60357,60359,60361,60363,60365,60381,60383,60401,60403,60405,60407,60409,60411],{},[898,60348,8309],{},[898,60350,8051],{},[1761,60352,1909],{},[898,60354,8309],{},[898,60356,8051],{},[1761,60358,1915],{"stretchy":1821},[898,60360,1828],{},[1761,60362,1920],{"stretchy":1821},[1761,60364,1909],{},[4379,60366,60367,60379],{},[895,60368,60369,60371,60373,60375,60377],{},[898,60370,1655],{},[898,60372,8051],{},[1761,60374,1915],{"stretchy":1821},[898,60376,1828],{},[1761,60378,1920],{"stretchy":1821},[898,60380,1828],{},[1761,60382,1909],{},[4379,60384,60385,60399],{},[895,60386,60387,60389,60391,60393,60395,60397],{},[898,60388,1828],{},[2761,60390,7057],{},[898,60392,2244],{},[1761,60394,1915],{"stretchy":1821},[898,60396,1828],{},[1761,60398,1920],{"stretchy":1821},[898,60400,1828],{},[1761,60402,1909],{},[898,60404,2244],{},[1761,60406,1915],{"stretchy":1821},[898,60408,1828],{},[1761,60410,1920],{"stretchy":1821},[898,60412,1741],{"mathvariant":1969},[902,60414,60415],{"encoding":904},"AR = AR(Q) = \\frac{TR(Q)}{Q} = \\frac{Q \\, D(Q)}{Q} = D(Q).",[1636,60417,60418],{},[724,60419,60420,60423,60424,1343,60427,1741],{},[883,60421,60422],{},"!note"," Klíčové pozorování\n",[38,60425,60426],{},"Průměrný příjem se vždy rovná poptávkové funkci",[883,60428,60430],{"className":60429},[886],[888,60431,60432],{"xmlns":890},[892,60433,60434,60456],{},[895,60435,60436,60438,60440,60442,60444,60446,60448,60450,60452,60454],{},[898,60437,8309],{},[898,60439,8051],{},[1761,60441,1915],{"stretchy":1821},[898,60443,1828],{},[1761,60445,1920],{"stretchy":1821},[1761,60447,1909],{},[898,60449,2244],{},[1761,60451,1915],{"stretchy":1821},[898,60453,1828],{},[1761,60455,1920],{"stretchy":1821},[902,60457,60458],{"encoding":904},"AR(Q) = D(Q)",[198,60460,60462],{"id":60461},"mezní-příjem","Mezní příjem",[724,60464,60465,60466,1989,60469,3927,60484,60487,60488,60491],{},"Pro zkoumání dynamiky změn celkového příjmu zavádíme ",[38,60467,60468],{},"mezní příjem",[883,60470,60472],{"className":60471},[886],[888,60473,60474],{"xmlns":890},[892,60475,60476,60482],{},[895,60477,60478,60480],{},[898,60479,6889],{},[898,60481,8051],{},[902,60483,10679],{"encoding":904},[38,60485,60486],{},"marginal revenue","), definovaný jako ",[207,60489,1145],{"className":60490,"dataFsResolvedFilePath":764,"href":765},[210]," celkového příjmu podle množství:",[883,60493,60495],{"className":60494},[886],[888,60496,60497],{"xmlns":890,"display":1930},[892,60498,60499,60556],{},[24787,60500,60501],{"width":32101},[24792,60502,60503,60505,60549,60551],{},[24795,60504],{"width":32106},[24795,60506,60507],{},[895,60508,60509,60511,60513,60515,60531,60533,60535,60541,60543,60545,60547],{},[898,60510,6889],{},[898,60512,8051],{},[1761,60514,1909],{},[4379,60516,60517,60525],{},[895,60518,60519,60521,60523],{},[898,60520,4346],{"mathvariant":1969},[898,60522,1655],{},[898,60524,8051],{},[895,60526,60527,60529],{},[898,60528,4346],{"mathvariant":1969},[898,60530,1828],{},[1761,60532,1909],{},[898,60534,1655],{},[1824,60536,60537,60539],{},[898,60538,8051],{},[1761,60540,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,60542,1915],{"stretchy":1821},[898,60544,1828],{},[1761,60546,1920],{"stretchy":1821},[898,60548,1741],{"mathvariant":1969},[24795,60550],{"width":32106},[24795,60552,60553],{},[2761,60554,60555],{},"(3.2)",[902,60557,60558],{"encoding":904},"MR = \\frac{\\mathrm{d}TR}{\\mathrm{d}Q} = TR'(Q).\n\\tag{3.2}",[724,60560,60561,60562,60564],{},"Mezní příjem udává ",[38,60563,6671],{}," celkového příjmu vzhledem k množství.",[1636,60566,60567],{},[724,60568,60569,60571,60572,60598,60599,60616,60617,1741],{},[883,60570,1642],{}," Intuice — „kolik vyděláš za další kus\"\nHodnota ",[883,60573,60575],{"className":60574},[886],[888,60576,60577],{"xmlns":890},[892,60578,60579,60595],{},[895,60580,60581,60583,60585,60587,60593],{},[898,60582,6889],{},[898,60584,8051],{},[1761,60586,1915],{"stretchy":1821},[1824,60588,60589,60591],{},[898,60590,1828],{},[1761,60592,8408],{},[1761,60594,1920],{"stretchy":1821},[902,60596,60597],{"encoding":904},"MR(Q^*)"," je přibližně to, o kolik se zvýší celkový příjem, prodá-li firma jednu další jednotku nad aktuální úroveň ",[883,60600,60602],{"className":60601},[886],[888,60603,60604],{"xmlns":890},[892,60605,60606,60614],{},[895,60607,60608],{},[1824,60609,60610,60612],{},[898,60611,1828],{},[1761,60613,8408],{},[902,60615,33874],{"encoding":904},". Jinak řečeno: ",[883,60618,60620],{"className":60619},[886],[888,60621,60622],{"xmlns":890},[892,60623,60624,60676],{},[895,60625,60626,60628,60630,60632,60638,60640,60642,60644,60646,60648,60654,60656,60658,60660,60662,60664,60666,60668,60674],{},[898,60627,6889],{},[898,60629,8051],{},[1761,60631,1915],{"stretchy":1821},[1824,60633,60634,60636],{},[898,60635,1828],{},[1761,60637,8408],{},[1761,60639,1920],{"stretchy":1821},[1761,60641,6803],{},[898,60643,1655],{},[898,60645,8051],{},[1761,60647,1915],{"stretchy":1821},[1824,60649,60650,60652],{},[898,60651,1828],{},[1761,60653,8408],{},[1761,60655,1964],{},[1765,60657,1945],{},[1761,60659,1920],{"stretchy":1821},[1761,60661,1885],{},[898,60663,1655],{},[898,60665,8051],{},[1761,60667,1915],{"stretchy":1821},[1824,60669,60670,60672],{},[898,60671,1828],{},[1761,60673,8408],{},[1761,60675,1920],{"stretchy":1821},[902,60677,60678],{"encoding":904},"MR(Q^*) \\approx TR(Q^* + 1) - TR(Q^*)",[41374,60680,60682],{"id":60681},"příklad-32","Příklad 3.2",[724,60684,60685,59966,60687,60003,60721,60736,60737,1741],{},[38,60686,59965],{},[883,60688,60690],{"className":60689},[886],[888,60691,60692],{"xmlns":890},[892,60693,60694,60718],{},[895,60695,60696,60698,60700,60702,60704,60706,60708,60710,60712,60714,60716],{},[898,60697,1839],{},[1761,60699,1909],{},[898,60701,2244],{},[1761,60703,1915],{"stretchy":1821},[898,60705,1828],{},[1761,60707,1920],{"stretchy":1821},[1761,60709,1909],{},[1765,60711,7160],{},[1761,60713,1885],{},[1765,60715,2296],{},[898,60717,1828],{},[902,60719,60720],{"encoding":904},"P = D(Q) = 100 - 2Q",[883,60722,60724],{"className":60723},[886],[888,60725,60726],{"xmlns":890},[892,60727,60728,60734],{},[895,60729,60730,60732],{},[898,60731,6889],{},[898,60733,8051],{},[902,60735,10679],{"encoding":904}," a interpretujte jeho hodnoty pro ",[883,60738,60740],{"className":60739},[886],[888,60741,60742],{"xmlns":890},[892,60743,60744,60760],{},[895,60745,60746,60748,60750,60752,60754,60756,60758],{},[898,60747,1828],{},[1761,60749,1909],{},[1765,60751,5433],{},[1761,60753,1834],{"separator":1833},[1765,60755,45871],{},[1761,60757,1834],{"separator":1833},[1765,60759,13077],{},[902,60761,60762],{"encoding":904},"Q = 15, 16, 20",[724,60764,60765,1989,60767,60799],{},[38,60766,26803],{},[883,60768,60770],{"className":60769},[886],[888,60771,60772],{"xmlns":890},[892,60773,60774,60796],{},[895,60775,60776,60778,60780,60782,60784,60786,60788,60790],{},[898,60777,1655],{},[898,60779,8051],{},[1761,60781,1909],{},[1765,60783,7160],{},[898,60785,1828],{},[1761,60787,1885],{},[1765,60789,2296],{},[1824,60791,60792,60794],{},[898,60793,1828],{},[1765,60795,2296],{},[902,60797,60798],{"encoding":904},"TR = 100Q - 2Q^2",", tedy",[883,60801,60803],{"className":60802},[886],[888,60804,60805],{"xmlns":890,"display":1930},[892,60806,60807,60849],{},[895,60808,60809,60811,60813,60815,60817,60819,60821,60823,60825,60831,60837,60839,60841,60843,60845,60847],{},[898,60810,6889],{},[898,60812,8051],{},[1761,60814,1909],{},[1761,60816,1915],{"stretchy":1821},[1765,60818,7160],{},[898,60820,1828],{},[1761,60822,1885],{},[1765,60824,2296],{},[1824,60826,60827,60829],{},[898,60828,1828],{},[1765,60830,2296],{},[1824,60832,60833,60835],{},[1761,60834,1920],{"stretchy":1821},[1761,60836,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,60838,1909],{},[1765,60840,7160],{},[1761,60842,1885],{},[1765,60844,2318],{},[898,60846,1828],{},[898,60848,1741],{"mathvariant":1969},[902,60850,60851],{"encoding":904},"MR = (100Q - 2Q^2)' = 100 - 4Q.",[724,60853,13703,60854,12146,60872,60898,60899,8412,60912,60927,60928,60941,60942,25453,60955,8412,60968,60983,60984,60997,60998,61029,61030,61049],{},[883,60855,60857],{"className":60856},[886],[888,60858,60859],{"xmlns":890},[892,60860,60861,60869],{},[895,60862,60863,60865,60867],{},[898,60864,1828],{},[1761,60866,1909],{},[1765,60868,5433],{},[902,60870,60871],{"encoding":904},"Q = 15",[883,60873,60875],{"className":60874},[886],[888,60876,60877],{"xmlns":890},[892,60878,60879,60895],{},[895,60880,60881,60883,60885,60887,60889,60891,60893],{},[898,60882,6889],{},[898,60884,8051],{},[1761,60886,1915],{"stretchy":1821},[1765,60888,5433],{},[1761,60890,1920],{"stretchy":1821},[1761,60892,1909],{},[1765,60894,9262],{},[902,60896,60897],{"encoding":904},"MR(15) = 40",": při množství ",[883,60900,60902],{"className":60901},[886],[888,60903,60904],{"xmlns":890},[892,60905,60906,60910],{},[895,60907,60908],{},[1765,60909,5433],{},[902,60911,5433],{"encoding":904},[883,60913,60915],{"className":60914},[886],[888,60916,60917],{"xmlns":890},[892,60918,60919,60925],{},[895,60920,60921,60923],{},[898,60922,1655],{},[898,60924,8051],{},[902,60926,8151],{"encoding":904}," mění asi ",[883,60929,60931],{"className":60930},[886],[888,60932,60933],{"xmlns":890},[892,60934,60935,60939],{},[895,60936,60937],{},[1765,60938,9262],{},[902,60940,9262],{"encoding":904},"-krát rychleji než množství; s růstem ",[883,60943,60945],{"className":60944},[886],[888,60946,60947],{"xmlns":890},[892,60948,60949,60953],{},[895,60950,60951],{},[898,60952,1828],{},[902,60954,1828],{"encoding":904},[883,60956,60958],{"className":60957},[886],[888,60959,60960],{"xmlns":890},[892,60961,60962,60966],{},[895,60963,60964],{},[1765,60965,1945],{},[902,60967,1945],{"encoding":904},[883,60969,60971],{"className":60970},[886],[888,60972,60973],{"xmlns":890},[892,60974,60975,60981],{},[895,60976,60977,60979],{},[898,60978,1655],{},[898,60980,8051],{},[902,60982,8151],{"encoding":904}," zvýší přibližně o ",[883,60985,60987],{"className":60986},[886],[888,60988,60989],{"xmlns":890},[892,60990,60991,60995],{},[895,60992,60993],{},[1765,60994,9262],{},[902,60996,9262],{"encoding":904},", tj. ze skutečné hodnoty ",[883,60999,61001],{"className":61000},[886],[888,61002,61003],{"xmlns":890},[892,61004,61005,61026],{},[895,61006,61007,61009,61011,61013,61015,61017,61019,61021,61023],{},[898,61008,1655],{},[898,61010,8051],{},[1761,61012,1915],{"stretchy":1821},[1765,61014,5433],{},[1761,61016,1920],{"stretchy":1821},[1761,61018,1909],{},[1765,61020,1945],{},[2761,61022,7057],{},[1765,61024,61025],{},"050",[902,61027,61028],{"encoding":904},"TR(15) = 1\\,050"," na přibližně ",[883,61031,61033],{"className":61032},[886],[888,61034,61035],{"xmlns":890},[892,61036,61037,61046],{},[895,61038,61039,61041,61043],{},[1765,61040,1945],{},[2761,61042,7057],{},[1765,61044,61045],{},"090",[902,61047,61048],{"encoding":904},"1\\,090",". Skutečná změna je",[883,61051,61053],{"className":61052},[886],[888,61054,61055],{"xmlns":890,"display":1930},[892,61056,61057,61111],{},[895,61058,61059,61061,61063,61065,61067,61069,61071,61073,61075,61077,61079,61081,61083,61085,61087,61089,61091,61093,61095,61098,61100,61102,61104,61106,61108],{},[898,61060,6959],{"mathvariant":1969},[898,61062,1655],{},[898,61064,8051],{},[1761,61066,1909],{},[898,61068,1655],{},[898,61070,8051],{},[1761,61072,1915],{"stretchy":1821},[1765,61074,45871],{},[1761,61076,1920],{"stretchy":1821},[1761,61078,1885],{},[898,61080,1655],{},[898,61082,8051],{},[1761,61084,1915],{"stretchy":1821},[1765,61086,5433],{},[1761,61088,1920],{"stretchy":1821},[1761,61090,1909],{},[1765,61092,1945],{},[2761,61094,7057],{},[1765,61096,61097],{},"088",[1761,61099,1885],{},[1765,61101,1945],{},[2761,61103,7057],{},[1765,61105,61025],{},[1761,61107,1909],{},[1765,61109,61110],{},"38.",[902,61112,61113],{"encoding":904},"\\Delta TR = TR(16) - TR(15) = 1\\,088 - 1\\,050 = 38.",[724,61115,61116,61117,1343,61143,6997,61169,61184,61185,61200],{},"Podobně ",[883,61118,61120],{"className":61119},[886],[888,61121,61122],{"xmlns":890},[892,61123,61124,61140],{},[895,61125,61126,61128,61130,61132,61134,61136,61138],{},[898,61127,6889],{},[898,61129,8051],{},[1761,61131,1915],{"stretchy":1821},[1765,61133,45871],{},[1761,61135,1920],{"stretchy":1821},[1761,61137,1909],{},[1765,61139,9616],{},[902,61141,61142],{"encoding":904},"MR(16) = 36",[883,61144,61146],{"className":61145},[886],[888,61147,61148],{"xmlns":890},[892,61149,61150,61166],{},[895,61151,61152,61154,61156,61158,61160,61162,61164],{},[898,61153,6889],{},[898,61155,8051],{},[1761,61157,1915],{"stretchy":1821},[1765,61159,13077],{},[1761,61161,1920],{"stretchy":1821},[1761,61163,1909],{},[1765,61165,13077],{},[902,61167,61168],{"encoding":904},"MR(20) = 20",[883,61170,61172],{"className":61171},[886],[888,61173,61174],{"xmlns":890},[892,61175,61176,61182],{},[895,61177,61178,61180],{},[898,61179,6889],{},[898,61181,8051],{},[902,61183,10679],{"encoding":904}," je klesající funkce — rychlost změny ",[883,61186,61188],{"className":61187},[886],[888,61189,61190],{"xmlns":890},[892,61191,61192,61198],{},[895,61193,61194,61196],{},[898,61195,1655],{},[898,61197,8051],{},[902,61199,8151],{"encoding":904}," s růstem množství klesá.",[198,61202,61204],{"id":61203},"odhad-změny-tr-pomocí-diferenciálu","Odhad změny TR pomocí diferenciálu",[724,61206,61207],{},"Užitím mezního příjmu lze odhadnout změnu celkového příjmu jako odezvu na změnu množství:",[883,61209,61211],{"className":61210},[886],[888,61212,61213],{"xmlns":890,"display":1930},[892,61214,61215,61284],{},[24787,61216,61217],{"width":32101},[24792,61218,61219,61221,61277,61279],{},[24795,61220],{"width":32106},[24795,61222,61223],{},[895,61224,61225,61227,61229,61231,61233,61235,61237,61239,61241,61243,61245,61247,61249,61251,61257,61259,61261,61263,61265,61267,61269,61271,61273,61275],{},[898,61226,6959],{"mathvariant":1969},[898,61228,1655],{},[898,61230,8051],{},[2761,61232,8041],{},[1761,61234,6803],{},[2761,61236,8041],{},[898,61238,4346],{"mathvariant":1969},[898,61240,1655],{},[898,61242,8051],{},[1761,61244,1909],{},[1761,61246,1915],{"stretchy":1821},[898,61248,1655],{},[898,61250,8051],{},[1824,61252,61253,61255],{},[1761,61254,1920],{"stretchy":1821},[1761,61256,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[2761,61258,7057],{},[898,61260,4346],{"mathvariant":1969},[898,61262,1828],{},[1761,61264,1909],{},[898,61266,6889],{},[898,61268,8051],{},[2761,61270,7057],{},[898,61272,4346],{"mathvariant":1969},[898,61274,1828],{},[1761,61276,1834],{"separator":1833},[24795,61278],{"width":32106},[24795,61280,61281],{},[2761,61282,61283],{},"(3.3)",[902,61285,61286],{"encoding":904},"\\Delta TR \\;\\approx\\; \\mathrm{d}TR = (TR)' \\, \\mathrm{d}Q = MR \\, \\mathrm{d}Q,\n\\tag{3.3}",[724,61288,61289],{},"schematicky:",[883,61291,61293],{"className":61292},[886],[888,61294,61295],{"xmlns":890,"display":1930},[892,61296,61297,61405],{},[895,61298,61299,61337,61339,61341,61343,61372,61375,61403],{},[895,61300,61301,61304,61310,61313,61319,61322,61328,61334],{},[2761,61302,61303],{},"zm",[2770,61305,61306,61308],{"accent":1833},[2761,61307,49723],{},[1761,61309,2777],{},[2761,61311,61312],{},"na celkov",[2770,61314,61315,61317],{"accent":1833},[2761,61316,49723],{},[1761,61318,29009],{},[2761,61320,61321],{},"ho p",[2770,61323,61324,61326],{"accent":1833},[2761,61325,1719],{},[1761,61327,2777],{},[2770,61329,61330,61332],{"accent":1833},[2761,61331,29078],{},[1761,61333,29009],{},[2761,61335,61336],{},"jmu",[2761,61338,8041],{},[1761,61340,6803],{},[2761,61342,8041],{},[895,61344,61345,61348,61354,61357,61363,61369],{},[2761,61346,61347],{},"mezn",[2770,61349,61350,61352],{"accent":1833},[2761,61351,29078],{},[1761,61353,29009],{},[2761,61355,61356],{}," p",[2770,61358,61359,61361],{"accent":1833},[2761,61360,1719],{},[1761,61362,2777],{},[2770,61364,61365,61367],{"accent":1833},[2761,61366,29078],{},[1761,61368,29009],{},[2761,61370,61371],{},"jem",[1761,61373,61374],{},"×",[895,61376,61377,61379,61385,61388,61394,61397],{},[2761,61378,61303],{},[2770,61380,61381,61383],{"accent":1833},[2761,61382,49723],{},[1761,61384,2777],{},[2761,61386,61387],{},"na mno",[2770,61389,61390,61392],{"accent":1833},[2761,61391,13634],{},[1761,61393,2777],{},[2761,61395,61396],{},"stv",[2770,61398,61399,61401],{"accent":1833},[2761,61400,29078],{},[1761,61402,29009],{},[898,61404,1741],{"mathvariant":1969},[902,61406,61407],{"encoding":904},"\\text{změna celkového příjmu} \\;\\approx\\; \\text{mezní příjem} \\times \\text{změna množství}.",[724,61409,61410,61411,61426],{},"Pro porovnání skutečná změna ",[883,61412,61414],{"className":61413},[886],[888,61415,61416],{"xmlns":890},[892,61417,61418,61424],{},[895,61419,61420,61422],{},[898,61421,1655],{},[898,61423,8051],{},[902,61425,8151],{"encoding":904}," je",[883,61428,61430],{"className":61429},[886],[888,61431,61432],{"xmlns":890,"display":1930},[892,61433,61434,61489],{},[24787,61435,61436],{"width":32101},[24792,61437,61438,61440,61482,61484],{},[24795,61439],{"width":32106},[24795,61441,61442],{},[895,61443,61444,61446,61448,61450,61452,61454,61456,61458,61460,61462,61464,61466,61468,61470,61472,61474,61476,61478,61480],{},[898,61445,6959],{"mathvariant":1969},[898,61447,1655],{},[898,61449,8051],{},[1761,61451,1909],{},[898,61453,1655],{},[898,61455,8051],{},[1761,61457,1915],{"stretchy":1821},[898,61459,1828],{},[1761,61461,1964],{},[898,61463,4346],{"mathvariant":1969},[898,61465,1828],{},[1761,61467,1920],{"stretchy":1821},[1761,61469,1885],{},[898,61471,1655],{},[898,61473,8051],{},[1761,61475,1915],{"stretchy":1821},[898,61477,1828],{},[1761,61479,1920],{"stretchy":1821},[898,61481,1741],{"mathvariant":1969},[24795,61483],{"width":32106},[24795,61485,61486],{},[2761,61487,61488],{},"(3.4)",[902,61490,61491],{"encoding":904},"\\Delta TR = TR(Q + \\mathrm{d}Q) - TR(Q).\n\\tag{3.4}",[41374,61493,61495],{"id":61494},"příklad-33","Příklad 3.3",[724,61497,61498,61500,61501,61531,61532,6732,61547,6746,61560,4178,61573,61587],{},[38,61499,59965],{}," Pro ",[883,61502,61504],{"className":61503},[886],[888,61505,61506],{"xmlns":890},[892,61507,61508,61528],{},[895,61509,61510,61512,61514,61516,61518,61520,61522],{},[898,61511,1655],{},[898,61513,8051],{},[1761,61515,1909],{},[1765,61517,7160],{},[898,61519,1828],{},[1761,61521,1885],{},[1824,61523,61524,61526],{},[898,61525,1828],{},[1765,61527,2296],{},[902,61529,61530],{"encoding":904},"TR = 100Q - Q^2"," odhadněte změnu ",[883,61533,61535],{"className":61534},[886],[888,61536,61537],{"xmlns":890},[892,61538,61539,61545],{},[895,61540,61541,61543],{},[898,61542,1655],{},[898,61544,8051],{},[902,61546,8151],{"encoding":904},[883,61548,61550],{"className":61549},[886],[888,61551,61552],{"xmlns":890},[892,61553,61554,61558],{},[895,61555,61556],{},[898,61557,1828],{},[902,61559,1828],{"encoding":904},[883,61561,61563],{"className":61562},[886],[888,61564,61565],{"xmlns":890},[892,61566,61567,61571],{},[895,61568,61569],{},[1765,61570,7195],{},[902,61572,7195],{"encoding":904},[883,61574,61576],{"className":61575},[886],[888,61577,61578],{"xmlns":890},[892,61579,61580,61585],{},[895,61581,61582],{},[1765,61583,61584],{},"63",[902,61586,61584],{"encoding":904}," a porovnejte se skutečnou změnou.",[724,61589,61590,1989,61592,61617,61618,1343,61636,2506],{},[38,61591,26803],{},[883,61593,61595],{"className":61594},[886],[888,61596,61597],{"xmlns":890},[892,61598,61599,61615],{},[895,61600,61601,61603,61605,61607,61609,61611,61613],{},[898,61602,6889],{},[898,61604,8051],{},[1761,61606,1909],{},[1765,61608,7160],{},[1761,61610,1885],{},[1765,61612,2296],{},[898,61614,1828],{},[902,61616,15475],{"encoding":904},", tedy při ",[883,61619,61621],{"className":61620},[886],[888,61622,61623],{"xmlns":890},[892,61624,61625,61633],{},[895,61626,61627,61629,61631],{},[898,61628,1828],{},[1761,61630,1909],{},[1765,61632,7195],{},[902,61634,61635],{"encoding":904},"Q = 60",[883,61637,61639],{"className":61638},[886],[888,61640,61641],{"xmlns":890},[892,61642,61643,61653],{},[895,61644,61645,61647,61649,61651],{},[898,61646,4346],{"mathvariant":1969},[898,61648,1828],{},[1761,61650,1909],{},[1765,61652,5486],{},[902,61654,61655],{"encoding":904},"\\mathrm{d}Q = 3",[883,61657,61659],{"className":61658},[886],[888,61660,61661],{"xmlns":890,"display":1930},[892,61662,61663,61694],{},[895,61664,61665,61667,61669,61671,61673,61675,61677,61679,61681,61683,61685,61687,61689,61691],{},[898,61666,4346],{"mathvariant":1969},[898,61668,1655],{},[898,61670,8051],{},[1761,61672,1909],{},[1761,61674,1915],{"stretchy":1821},[1765,61676,7160],{},[1761,61678,1885],{},[1765,61680,8103],{},[1761,61682,1920],{"stretchy":1821},[1761,61684,2447],{},[1765,61686,5486],{},[1761,61688,1909],{},[1761,61690,1885],{},[1765,61692,61693],{},"60.",[902,61695,61696],{"encoding":904},"\\mathrm{d}TR = (100 - 120) \\cdot 3 = -60.",[724,61698,61699,61700,61730,61731,61750],{},"Celkový příjem klesne z ",[883,61701,61703],{"className":61702},[886],[888,61704,61705],{"xmlns":890},[892,61706,61707,61727],{},[895,61708,61709,61711,61713,61715,61717,61719,61721,61723,61725],{},[898,61710,1655],{},[898,61712,8051],{},[1761,61714,1915],{"stretchy":1821},[1765,61716,7195],{},[1761,61718,1920],{"stretchy":1821},[1761,61720,1909],{},[1765,61722,2296],{},[2761,61724,7057],{},[1765,61726,24175],{},[902,61728,61729],{"encoding":904},"TR(60) = 2\\,400"," přibližně na ",[883,61732,61734],{"className":61733},[886],[888,61735,61736],{"xmlns":890},[892,61737,61738,61747],{},[895,61739,61740,61742,61744],{},[1765,61741,2296],{},[2761,61743,7057],{},[1765,61745,61746],{},"340",[902,61748,61749],{"encoding":904},"2\\,340",". Skutečná změna dle (3.4):",[883,61752,61754],{"className":61753},[886],[888,61755,61756],{"xmlns":890,"display":1930},[892,61757,61758,61816],{},[895,61759,61760,61762,61764,61766,61768,61770,61772,61774,61776,61778,61780,61782,61784,61786,61788,61790,61792,61794,61796,61799,61801,61803,61805,61807,61809,61811,61814],{},[898,61761,6959],{"mathvariant":1969},[898,61763,1655],{},[898,61765,8051],{},[1761,61767,1909],{},[898,61769,1655],{},[898,61771,8051],{},[1761,61773,1915],{"stretchy":1821},[1765,61775,61584],{},[1761,61777,1920],{"stretchy":1821},[1761,61779,1885],{},[898,61781,1655],{},[898,61783,8051],{},[1761,61785,1915],{"stretchy":1821},[1765,61787,7195],{},[1761,61789,1920],{"stretchy":1821},[1761,61791,1909],{},[1765,61793,2296],{},[2761,61795,7057],{},[1765,61797,61798],{},"331",[1761,61800,1885],{},[1765,61802,2296],{},[2761,61804,7057],{},[1765,61806,24175],{},[1761,61808,1909],{},[1761,61810,1885],{},[1765,61812,61813],{},"69",[1761,61815,1834],{"separator":1833},[902,61817,61818],{"encoding":904},"\\Delta TR = TR(63) - TR(60) = 2\\,331 - 2\\,400 = -69,",[724,61820,61821,61822,61837,61838,1741],{},"tj. ",[883,61823,61825],{"className":61824},[886],[888,61826,61827],{"xmlns":890},[892,61828,61829,61835],{},[895,61830,61831,61833],{},[898,61832,1655],{},[898,61834,8051],{},[902,61836,8151],{"encoding":904}," klesne na ",[883,61839,61841],{"className":61840},[886],[888,61842,61843],{"xmlns":890},[892,61844,61845,61853],{},[895,61846,61847,61849,61851],{},[1765,61848,2296],{},[2761,61850,7057],{},[1765,61852,61798],{},[902,61854,61855],{"encoding":904},"2\\,331",[198,61857,61859],{"id":61858},"vztah-ar-a-mr-pro-lineární-poptávku","Vztah AR a MR pro lineární poptávku",[724,61861,61862,61863,14432,61886,35610],{},"Obecně pro lineární poptávku ",[883,61864,61866],{"className":61865},[886],[888,61867,61868],{"xmlns":890},[892,61869,61870,61884],{},[895,61871,61872,61874,61876,61878,61880,61882],{},[898,61873,1839],{},[1761,61875,1909],{},[898,61877,207],{},[898,61879,1828],{},[1761,61881,1964],{},[898,61883,4302],{},[902,61885,4305],{"encoding":904},[883,61887,61889],{"className":61888},[886],[888,61890,61891],{"xmlns":890},[892,61892,61893,61915],{},[895,61894,61895,61897,61899,61901,61903,61909,61911,61913],{},[898,61896,1655],{},[898,61898,8051],{},[1761,61900,1909],{},[898,61902,207],{},[1824,61904,61905,61907],{},[898,61906,1828],{},[1765,61908,2296],{},[1761,61910,1964],{},[898,61912,4302],{},[898,61914,1828],{},[902,61916,61917],{"encoding":904},"TR = aQ^2 + bQ",[883,61919,61921],{"className":61920},[886],[888,61922,61923],{"xmlns":890,"display":1930},[892,61924,61925,61945],{},[895,61926,61927,61929,61931,61933,61935,61937,61939,61941,61943],{},[898,61928,6889],{},[898,61930,8051],{},[1761,61932,1909],{},[1765,61934,2296],{},[898,61936,207],{},[898,61938,1828],{},[1761,61940,1964],{},[898,61942,4302],{},[898,61944,1741],{"mathvariant":1969},[902,61946,61947],{"encoding":904},"MR = 2aQ + b.",[724,61949,61950,61951,61966,61967,61982,61983,61996,61997,3927,62000,62016,62017,62030,62031,62046,62047,62062,62063,62078,62079,6699,62092,62122,62123,62142,62143,62158],{},"Křivky ",[883,61952,61954],{"className":61953},[886],[888,61955,61956],{"xmlns":890},[892,61957,61958,61964],{},[895,61959,61960,61962],{},[898,61961,6889],{},[898,61963,8051],{},[902,61965,10679],{"encoding":904}," a poptávky (resp. ",[883,61968,61970],{"className":61969},[886],[888,61971,61972],{"xmlns":890},[892,61973,61974,61980],{},[895,61975,61976,61978],{},[898,61977,8309],{},[898,61979,8051],{},[902,61981,59423],{"encoding":904},") jsou přímky protínající svislou osu v témže bodě ",[883,61984,61986],{"className":61985},[886],[888,61987,61988],{"xmlns":890},[892,61989,61990,61994],{},[895,61991,61992],{},[898,61993,4302],{},[902,61995,4302],{"encoding":904},", přičemž ",[38,61998,61999],{},"přímka mezního příjmu má sklon rovný dvojnásobku sklonu přímky poptávky",[883,62001,62003],{"className":62002},[886],[888,62004,62005],{"xmlns":890},[892,62006,62007,62013],{},[895,62008,62009,62011],{},[1765,62010,2296],{},[898,62012,207],{},[902,62014,62015],{"encoding":904},"2a"," vs. ",[883,62018,62020],{"className":62019},[886],[888,62021,62022],{"xmlns":890},[892,62023,62024,62028],{},[895,62025,62026],{},[898,62027,207],{},[902,62029,207],{"encoding":904},", obrázek 3.2). ",[883,62032,62034],{"className":62033},[886],[888,62035,62036],{"xmlns":890},[892,62037,62038,62044],{},[895,62039,62040,62042],{},[898,62041,6889],{},[898,62043,8051],{},[902,62045,10679],{"encoding":904}," nabývá jak kladných, tak záporných hodnot; křivka ",[883,62048,62050],{"className":62049},[886],[888,62051,62052],{"xmlns":890},[892,62053,62054,62060],{},[895,62055,62056,62058],{},[898,62057,1655],{},[898,62059,8051],{},[902,62061,8151],{"encoding":904}," nejprve roste, v bodě maxima protíná ",[883,62064,62066],{"className":62065},[886],[888,62067,62068],{"xmlns":890},[892,62069,62070,62076],{},[895,62071,62072,62074],{},[898,62073,6889],{},[898,62075,8051],{},[902,62077,10679],{"encoding":904}," osu ",[883,62080,62082],{"className":62081},[886],[888,62083,62084],{"xmlns":890},[892,62085,62086,62090],{},[895,62087,62088],{},[898,62089,1828],{},[902,62091,1828],{"encoding":904},[883,62093,62095],{"className":62094},[886],[888,62096,62097],{"xmlns":890},[892,62098,62099,62119],{},[895,62100,62101,62103,62105,62107],{},[898,62102,1828],{},[1761,62104,1909],{},[1761,62106,1885],{},[6411,62108,62109],{"scriptlevel":1767,"displaystyle":1821},[4379,62110,62111,62113],{},[898,62112,4302],{},[895,62114,62115,62117],{},[1765,62116,2296],{},[898,62118,207],{},[902,62120,62121],{"encoding":904},"Q = -\\tfrac{b}{2a}"," hodnotou ",[883,62124,62126],{"className":62125},[886],[888,62127,62128],{"xmlns":890},[892,62129,62130,62140],{},[895,62131,62132,62134,62136,62138],{},[898,62133,6889],{},[898,62135,8051],{},[1761,62137,1909],{},[1765,62139,1767],{},[902,62141,11128],{"encoding":904},", a dále ",[883,62144,62146],{"className":62145},[886],[888,62147,62148],{"xmlns":890},[892,62149,62150,62156],{},[895,62151,62152,62154],{},[898,62153,1655],{},[898,62155,8051],{},[902,62157,8151],{"encoding":904}," klesá.",[724,62160,62161,62162,62168,62169,62201,62202,62230],{},"V případě ",[38,62163,62164],{},[207,62165,62167],{"className":62166,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurence",", kdy poptávka ",[883,62170,62172],{"className":62171},[886],[888,62173,62174],{"xmlns":890},[892,62175,62176,62198],{},[895,62177,62178,62180,62182,62184,62186,62188,62190,62192],{},[898,62179,1839],{},[1761,62181,1909],{},[898,62183,2244],{},[1761,62185,1915],{"stretchy":1821},[898,62187,1828],{},[1761,62189,1920],{"stretchy":1821},[1761,62191,1909],{},[1824,62193,62194,62196],{},[898,62195,1839],{},[1761,62197,8408],{},[902,62199,62200],{"encoding":904},"P = D(Q) = P^*"," je pevná tržní cena, platí ",[883,62203,62205],{"className":62204},[886],[888,62206,62207],{"xmlns":890},[892,62208,62209,62227],{},[895,62210,62211,62213,62215,62217,62219,62221],{},[898,62212,1655],{},[898,62214,8051],{},[1761,62216,1909],{},[898,62218,1828],{},[1761,62220,2447],{},[1824,62222,62223,62225],{},[898,62224,1839],{},[1761,62226,8408],{},[902,62228,62229],{"encoding":904},"TR = Q \\cdot P^*"," a tedy",[883,62232,62234],{"className":62233},[886],[888,62235,62236],{"xmlns":890,"display":1930},[892,62237,62238,62280],{},[895,62239,62240,62242,62244,62246,62248,62250,62252,62258,62260,62262,62276,62278],{},[898,62241,6889],{},[898,62243,8051],{},[1761,62245,1909],{},[898,62247,8309],{},[898,62249,8051],{},[1761,62251,1909],{},[1824,62253,62254,62256],{},[898,62255,1839],{},[1761,62257,8408],{},[3315,62259],{"width":19322},[1761,62261,1915],{"stretchy":1821},[895,62263,62264,62267,62273],{},[2761,62265,62266],{},"obr",[2770,62268,62269,62271],{"accent":1833},[2761,62270,207],{},[1761,62272,29009],{},[2761,62274,62275],{},"zek 3.4",[1761,62277,1920],{"stretchy":1821},[898,62279,1741],{"mathvariant":1969},[902,62281,62282],{"encoding":904},"MR = AR = P^* \\quad (\\text{obrázek 3.4}).",[724,62284,62285],{},[614,62286,62287,62288,2068,62314,62342,62343,62356,62357,62372,62373,7782,62386,1343,62412,7782,62427,1741],{},"Obrázek 3.2: Přímky ",[883,62289,62291],{"className":62290},[886],[888,62292,62293],{"xmlns":890},[892,62294,62295,62311],{},[895,62296,62297,62299,62301,62303,62305,62307,62309],{},[898,62298,8309],{},[898,62300,8051],{},[1761,62302,1909],{},[898,62304,207],{},[898,62306,1828],{},[1761,62308,1964],{},[898,62310,4302],{},[902,62312,62313],{"encoding":904},"AR = aQ + b",[883,62315,62317],{"className":62316},[886],[888,62318,62319],{"xmlns":890},[892,62320,62321,62339],{},[895,62322,62323,62325,62327,62329,62331,62333,62335,62337],{},[898,62324,6889],{},[898,62326,8051],{},[1761,62328,1909],{},[1765,62330,2296],{},[898,62332,207],{},[898,62334,1828],{},[1761,62336,1964],{},[898,62338,4302],{},[902,62340,62341],{"encoding":904},"MR = 2aQ + b"," v jednom grafu; společný průsečík ",[883,62344,62346],{"className":62345},[886],[888,62347,62348],{"xmlns":890},[892,62349,62350,62354],{},[895,62351,62352],{},[898,62353,4302],{},[902,62355,4302],{"encoding":904}," se svislou osou, ",[883,62358,62360],{"className":62359},[886],[888,62361,62362],{"xmlns":890},[892,62363,62364,62370],{},[895,62365,62366,62368],{},[898,62367,6889],{},[898,62369,8051],{},[902,62371,10679],{"encoding":904}," protíná osu ",[883,62374,62376],{"className":62375},[886],[888,62377,62378],{"xmlns":890},[892,62379,62380,62384],{},[895,62381,62382],{},[898,62383,1828],{},[902,62385,1828],{"encoding":904},[883,62387,62389],{"className":62388},[886],[888,62390,62391],{"xmlns":890},[892,62392,62393,62409],{},[895,62394,62395,62397],{},[1761,62396,1885],{},[6411,62398,62399],{"scriptlevel":1767,"displaystyle":1821},[4379,62400,62401,62403],{},[898,62402,4302],{},[895,62404,62405,62407],{},[1765,62406,2296],{},[898,62408,207],{},[902,62410,62411],{"encoding":904},"-\\tfrac{b}{2a}",[883,62413,62415],{"className":62414},[886],[888,62416,62417],{"xmlns":890},[892,62418,62419,62425],{},[895,62420,62421,62423],{},[898,62422,8309],{},[898,62424,8051],{},[902,62426,59423],{"encoding":904},[883,62428,62430],{"className":62429},[886],[888,62431,62432],{"xmlns":890},[892,62433,62434,62446],{},[895,62435,62436,62438],{},[1761,62437,1885],{},[6411,62439,62440],{"scriptlevel":1767,"displaystyle":1821},[4379,62441,62442,62444],{},[898,62443,4302],{},[898,62445,207],{},[902,62447,62448],{"encoding":904},"-\\tfrac{b}{a}",[724,62450,62451],{},[614,62452,62453,62454,62485,62486,62515,62516,1741],{},"Obrázek 3.3: Parabola ",[883,62455,62457],{"className":62456},[886],[888,62458,62459],{"xmlns":890},[892,62460,62461,62483],{},[895,62462,62463,62465,62467,62469,62471,62477,62479,62481],{},[898,62464,1655],{},[898,62466,8051],{},[1761,62468,1909],{},[898,62470,207],{},[1824,62472,62473,62475],{},[898,62474,1828],{},[1765,62476,2296],{},[1761,62478,1964],{},[898,62480,4302],{},[898,62482,1828],{},[902,62484,61917],{"encoding":904}," s maximem v ",[883,62487,62489],{"className":62488},[886],[888,62490,62491],{"xmlns":890},[892,62492,62493,62513],{},[895,62494,62495,62497,62499,62501],{},[898,62496,1828],{},[1761,62498,1909],{},[1761,62500,1885],{},[6411,62502,62503],{"scriptlevel":1767,"displaystyle":1821},[4379,62504,62505,62507],{},[898,62506,4302],{},[895,62508,62509,62511],{},[1765,62510,2296],{},[898,62512,207],{},[902,62514,62121],{"encoding":904}," a nulou v ",[883,62517,62519],{"className":62518},[886],[888,62520,62521],{"xmlns":890},[892,62522,62523,62539],{},[895,62524,62525,62527,62529,62531],{},[898,62526,1828],{},[1761,62528,1909],{},[1761,62530,1885],{},[6411,62532,62533],{"scriptlevel":1767,"displaystyle":1821},[4379,62534,62535,62537],{},[898,62536,4302],{},[898,62538,207],{},[902,62540,62541],{"encoding":904},"Q = -\\tfrac{b}{a}",[724,62543,62544],{},[614,62545,62546,62547,1741],{},"Obrázek 3.4: Dokonalá konkurence — vodorovná přímka ",[883,62548,62550],{"className":62549},[886],[888,62551,62552],{"xmlns":890},[892,62553,62554,62574],{},[895,62555,62556,62558,62560,62562,62564,62566,62568],{},[898,62557,8309],{},[898,62559,8051],{},[1761,62561,1909],{},[898,62563,6889],{},[898,62565,8051],{},[1761,62567,1909],{},[1824,62569,62570,62572],{},[898,62571,1839],{},[1761,62573,8408],{},[902,62575,62576],{"encoding":904},"AR = MR = P^*",[115,62578,62580],{"id":62579},"náklady-firmy","Náklady firmy",[198,62582,62584],{"id":62583},"celkové-náklady","Celkové náklady",[724,62586,62587,1989,62589,3927,62604,62607,62608,62621],{},[38,62588,62584],{},[883,62590,62592],{"className":62591},[886],[888,62593,62594],{"xmlns":890},[892,62595,62596,62602],{},[895,62597,62598,62600],{},[898,62599,1655],{},[898,62601,6849],{},[902,62603,7310],{"encoding":904},[38,62605,62606],{},"total cost",") jsou veškeré náklady na realizaci ",[883,62609,62611],{"className":62610},[886],[888,62612,62613],{"xmlns":890},[892,62614,62615,62619],{},[895,62616,62617],{},[898,62618,1828],{},[902,62620,1828],{"encoding":904}," jednotek produkce:",[883,62623,62625],{"className":62624},[886],[888,62626,62627],{"xmlns":890,"display":1930},[892,62628,62629,62684],{},[24787,62630,62631],{"width":32101},[24792,62632,62633,62635,62677,62679],{},[24795,62634],{"width":32106},[24795,62636,62637],{},[895,62638,62639,62641,62643,62645,62647,62649,62651,62653,62655,62657,62659,62661,62663,62665,62667,62669,62671,62673,62675],{},[898,62640,1655],{},[898,62642,6849],{},[1761,62644,1909],{},[898,62646,1655],{},[898,62648,6849],{},[1761,62650,1915],{"stretchy":1821},[898,62652,1828],{},[1761,62654,1920],{"stretchy":1821},[1761,62656,1909],{},[898,62658,14474],{},[898,62660,6849],{},[1761,62662,1964],{},[898,62664,1655],{},[898,62666,44359],{},[898,62668,6849],{},[1761,62670,1915],{"stretchy":1821},[898,62672,1828],{},[1761,62674,1920],{"stretchy":1821},[1761,62676,1834],{"separator":1833},[24795,62678],{"width":32106},[24795,62680,62681],{},[2761,62682,62683],{},"(3.5)",[902,62685,62686],{"encoding":904},"TC = TC(Q) = FC + TVC(Q),\n\\tag{3.5}",[724,62688,8364,62689,62704,62705,3927,62708,4590,62711,62704,62735,3927,62738,62741],{},[883,62690,62692],{"className":62691},[886],[888,62693,62694],{"xmlns":890},[892,62695,62696,62702],{},[895,62697,62698,62700],{},[898,62699,14474],{},[898,62701,6849],{},[902,62703,59469],{"encoding":904}," jsou ",[38,62706,62707],{},"fixní náklady",[38,62709,62710],{},"fixed cost",[883,62712,62714],{"className":62713},[886],[888,62715,62716],{"xmlns":890},[892,62717,62718,62732],{},[895,62719,62720,62722,62724,62726,62728,62730],{},[898,62721,1655],{},[898,62723,44359],{},[898,62725,6849],{},[1761,62727,1915],{"stretchy":1821},[898,62729,1828],{},[1761,62731,1920],{"stretchy":1821},[902,62733,62734],{"encoding":904},"TVC(Q)",[38,62736,62737],{},"celkové variabilní náklady",[38,62739,62740],{},"total variable cost","). Celkové náklady jsou rostoucí, neboť růst množství objektivně vynutí jejich růst.",[198,62743,62745],{"id":62744},"průměrné-náklady","Průměrné náklady",[724,62747,62748,1989,62750,3927,62765,62768],{},[38,62749,62745],{},[883,62751,62753],{"className":62752},[886],[888,62754,62755],{"xmlns":890},[892,62756,62757,62763],{},[895,62758,62759,62761],{},[898,62760,8309],{},[898,62762,6849],{},[902,62764,59538],{"encoding":904},[38,62766,62767],{},"average cost",") jsou podíl celkových nákladů a množství. Z (3.5):",[883,62770,62772],{"className":62771},[886],[888,62773,62774],{"xmlns":890,"display":1930},[892,62775,62776,62855],{},[24787,62777,62778],{"width":32101},[24792,62779,62780,62782,62848,62850],{},[24795,62781],{"width":32106},[24795,62783,62784],{},[895,62785,62786,62788,62790,62792,62794,62796,62798,62800,62802,62804,62814,62816,62826,62828,62846],{},[898,62787,8309],{},[898,62789,6849],{},[1761,62791,1909],{},[898,62793,8309],{},[898,62795,6849],{},[1761,62797,1915],{"stretchy":1821},[898,62799,1828],{},[1761,62801,1920],{"stretchy":1821},[1761,62803,1909],{},[4379,62805,62806,62812],{},[895,62807,62808,62810],{},[898,62809,1655],{},[898,62811,6849],{},[898,62813,1828],{},[1761,62815,1909],{},[4379,62817,62818,62824],{},[895,62819,62820,62822],{},[898,62821,14474],{},[898,62823,6849],{},[898,62825,1828],{},[1761,62827,1964],{},[4379,62829,62830,62844],{},[895,62831,62832,62834,62836,62838,62840,62842],{},[898,62833,1655],{},[898,62835,44359],{},[898,62837,6849],{},[1761,62839,1915],{"stretchy":1821},[898,62841,1828],{},[1761,62843,1920],{"stretchy":1821},[898,62845,1828],{},[1761,62847,1834],{"separator":1833},[24795,62849],{"width":32106},[24795,62851,62852],{},[2761,62853,62854],{},"(3.6)",[902,62856,62857],{"encoding":904},"AC = AC(Q) = \\frac{TC}{Q} = \\frac{FC}{Q} + \\frac{TVC(Q)}{Q},\n\\tag{3.6}",[724,62859,8364,62860,62704,62884,1989,62887,3927,62904,4590,62907,62704,62939,1989,62942,3927,62959,5372],{},[883,62861,62863],{"className":62862},[886],[888,62864,62865],{"xmlns":890},[892,62866,62867,62881],{},[895,62868,62869],{},[6411,62870,62871],{"scriptlevel":1767,"displaystyle":1821},[4379,62872,62873,62879],{},[895,62874,62875,62877],{},[898,62876,14474],{},[898,62878,6849],{},[898,62880,1828],{},[902,62882,62883],{"encoding":904},"\\tfrac{FC}{Q}",[38,62885,62886],{},"průměrné fixní náklady",[883,62888,62890],{"className":62889},[886],[888,62891,62892],{"xmlns":890},[892,62893,62894,62902],{},[895,62895,62896,62898,62900],{},[898,62897,8309],{},[898,62899,14474],{},[898,62901,6849],{},[902,62903,59505],{"encoding":904},[38,62905,62906],{},"average fixed cost",[883,62908,62910],{"className":62909},[886],[888,62911,62912],{"xmlns":890},[892,62913,62914,62936],{},[895,62915,62916],{},[6411,62917,62918],{"scriptlevel":1767,"displaystyle":1821},[4379,62919,62920,62934],{},[895,62921,62922,62924,62926,62928,62930,62932],{},[898,62923,1655],{},[898,62925,44359],{},[898,62927,6849],{},[1761,62929,1915],{"stretchy":1821},[898,62931,1828],{},[1761,62933,1920],{"stretchy":1821},[898,62935,1828],{},[902,62937,62938],{"encoding":904},"\\tfrac{TVC(Q)}{Q}",[38,62940,62941],{},"průměrné variabilní náklady",[883,62943,62945],{"className":62944},[886],[888,62946,62947],{"xmlns":890},[892,62948,62949,62957],{},[895,62950,62951,62953,62955],{},[898,62952,8309],{},[898,62954,44359],{},[898,62956,6849],{},[902,62958,59289],{"encoding":904},[38,62960,62961],{},"average variable cost",[883,62963,62965],{"className":62964},[886],[888,62966,62967],{"xmlns":890,"display":1930},[892,62968,62969,63028],{},[24787,62970,62971],{"width":32101},[24792,62972,62973,62975,63021,63023],{},[24795,62974],{"width":32106},[24795,62976,62977],{},[895,62978,62979,62981,62983,62985,62987,62989,62991,62993,62995,62997,62999,63001,63019],{},[898,62980,8309],{},[898,62982,44359],{},[898,62984,6849],{},[1761,62986,1909],{},[898,62988,8309],{},[898,62990,44359],{},[898,62992,6849],{},[1761,62994,1915],{"stretchy":1821},[898,62996,1828],{},[1761,62998,1920],{"stretchy":1821},[1761,63000,1909],{},[4379,63002,63003,63017],{},[895,63004,63005,63007,63009,63011,63013,63015],{},[898,63006,1655],{},[898,63008,44359],{},[898,63010,6849],{},[1761,63012,1915],{"stretchy":1821},[898,63014,1828],{},[1761,63016,1920],{"stretchy":1821},[898,63018,1828],{},[898,63020,1741],{"mathvariant":1969},[24795,63022],{"width":32106},[24795,63024,63025],{},[2761,63026,63027],{},"(3.7)",[902,63029,63030],{"encoding":904},"AVC = AVC(Q) = \\frac{TVC(Q)}{Q}.\n\\tag{3.7}",[41374,63032,63034],{"id":63033},"příklad-34","Příklad 3.4",[724,63036,63037,61500,63039,2068,63064,60003,63088,2068,63103,63118,63119,1741],{},[38,63038,59965],{},[883,63040,63042],{"className":63041},[886],[888,63043,63044],{"xmlns":890},[892,63045,63046,63061],{},[895,63047,63048,63050,63052,63054,63056,63058],{},[898,63049,14474],{},[898,63051,6849],{},[1761,63053,1909],{},[1765,63055,1945],{},[2761,63057,7057],{},[1765,63059,63060],{},"000",[902,63062,63063],{"encoding":904},"FC = 1\\,000",[883,63065,63067],{"className":63066},[886],[888,63068,63069],{"xmlns":890},[892,63070,63071,63085],{},[895,63072,63073,63075,63077,63079,63081,63083],{},[898,63074,1655],{},[898,63076,44359],{},[898,63078,6849],{},[1761,63080,1909],{},[1765,63082,2318],{},[898,63084,1828],{},[902,63086,63087],{"encoding":904},"TVC = 4Q",[883,63089,63091],{"className":63090},[886],[888,63092,63093],{"xmlns":890},[892,63094,63095,63101],{},[895,63096,63097,63099],{},[898,63098,1655],{},[898,63100,6849],{},[902,63102,7310],{"encoding":904},[883,63104,63106],{"className":63105},[886],[888,63107,63108],{"xmlns":890},[892,63109,63110,63116],{},[895,63111,63112,63114],{},[898,63113,8309],{},[898,63115,6849],{},[902,63117,59538],{"encoding":904}," a jejich chování s rostoucím ",[883,63120,63122],{"className":63121},[886],[888,63123,63124],{"xmlns":890},[892,63125,63126,63130],{},[895,63127,63128],{},[898,63129,1828],{},[902,63131,1828],{"encoding":904},[724,63133,63134,1989,63136,2068,63166,63202,63203,8412,63216,63231,63232,2506],{},[38,63135,26803],{},[883,63137,63139],{"className":63138},[886],[888,63140,63141],{"xmlns":890},[892,63142,63143,63163],{},[895,63144,63145,63147,63149,63151,63153,63155,63157,63159,63161],{},[898,63146,1655],{},[898,63148,6849],{},[1761,63150,1909],{},[1765,63152,1945],{},[2761,63154,7057],{},[1765,63156,63060],{},[1761,63158,1964],{},[1765,63160,2318],{},[898,63162,1828],{},[902,63164,63165],{"encoding":904},"TC = 1\\,000 + 4Q",[883,63167,63169],{"className":63168},[886],[888,63170,63171],{"xmlns":890},[892,63172,63173,63199],{},[895,63174,63175,63177,63179,63181,63195,63197],{},[898,63176,8309],{},[898,63178,6849],{},[1761,63180,1909],{},[6411,63182,63183],{"scriptlevel":1767,"displaystyle":1821},[4379,63184,63185,63193],{},[895,63186,63187,63189,63191],{},[1765,63188,1945],{},[2761,63190,7057],{},[1765,63192,63060],{},[898,63194,1828],{},[1761,63196,1964],{},[1765,63198,2318],{},[902,63200,63201],{"encoding":904},"AC = \\tfrac{1\\,000}{Q} + 4",". S rostoucím ",[883,63204,63206],{"className":63205},[886],[888,63207,63208],{"xmlns":890},[892,63209,63210,63214],{},[895,63211,63212],{},[898,63213,1828],{},[902,63215,1828],{"encoding":904},[883,63217,63219],{"className":63218},[886],[888,63220,63221],{"xmlns":890},[892,63222,63223,63229],{},[895,63224,63225,63227],{},[898,63226,8309],{},[898,63228,6849],{},[902,63230,59538],{"encoding":904}," blíží ",[883,63233,63235],{"className":63234},[886],[888,63236,63237],{"xmlns":890},[892,63238,63239,63243],{},[895,63240,63241],{},[1765,63242,2318],{},[902,63244,2318],{"encoding":904},[883,63246,63248],{"className":63247},[886],[888,63249,63250],{"xmlns":890,"display":1930},[892,63251,63252,63298],{},[895,63253,63254,63271,63293,63295],{},[43918,63255,63256,63263],{},[895,63257,63258,63261],{},[898,63259,63260],{},"lim",[1761,63262,60178],{},[895,63264,63265,63267,63269],{},[898,63266,1828],{},[1761,63268,2181],{},[898,63270,10342],{"mathvariant":1969},[895,63272,63273,63275,63287,63289,63291],{},[1761,63274,1915],{"fence":1833},[4379,63276,63277,63285],{},[895,63278,63279,63281,63283],{},[1765,63280,1945],{},[2761,63282,7057],{},[1765,63284,63060],{},[898,63286,1828],{},[1761,63288,1964],{},[1765,63290,2318],{},[1761,63292,1920],{"fence":1833},[1761,63294,1909],{},[1765,63296,63297],{},"4.",[902,63299,63300],{"encoding":904},"\\lim_{Q \\to \\infty} \\left( \\frac{1\\,000}{Q} + 4 \\right) = 4.",[724,63302,63303,63341,63342,1741],{},[883,63304,63306],{"className":63305},[886],[888,63307,63308],{"xmlns":890},[892,63309,63310,63338],{},[895,63311,63312,63314,63316,63318,63320,63334,63336],{},[898,63313,8309],{},[898,63315,14474],{},[898,63317,6849],{},[1761,63319,1909],{},[6411,63321,63322],{"scriptlevel":1767,"displaystyle":1821},[4379,63323,63324,63332],{},[895,63325,63326,63328,63330],{},[1765,63327,1945],{},[2761,63329,7057],{},[1765,63331,63060],{},[898,63333,1828],{},[1761,63335,2181],{},[1765,63337,1767],{},[902,63339,63340],{"encoding":904},"AFC = \\tfrac{1\\,000}{Q} \\to 0"," s rostoucím ",[883,63343,63345],{"className":63344},[886],[888,63346,63347],{"xmlns":890},[892,63348,63349,63353],{},[895,63350,63351],{},[898,63352,1828],{},[902,63354,1828],{"encoding":904},[724,63356,63357],{},[614,63358,63359,63360,63389,63390,1741],{},"Obrázek 3.5: Přímka ",[883,63361,63363],{"className":63362},[886],[888,63364,63365],{"xmlns":890},[892,63366,63367,63387],{},[895,63368,63369,63371,63373,63375,63377,63379,63381,63383,63385],{},[898,63370,1655],{},[898,63372,6849],{},[1761,63374,1909],{},[1765,63376,1945],{},[2761,63378,7057],{},[1765,63380,63060],{},[1761,63382,1964],{},[1765,63384,2318],{},[898,63386,1828],{},[902,63388,63165],{"encoding":904}," protínající svislou osu ve výši ",[883,63391,63393],{"className":63392},[886],[888,63394,63395],{"xmlns":890},[892,63396,63397,63411],{},[895,63398,63399,63401,63403,63405,63407,63409],{},[898,63400,14474],{},[898,63402,6849],{},[1761,63404,1909],{},[1765,63406,1945],{},[2761,63408,7057],{},[1765,63410,63060],{},[902,63412,63063],{"encoding":904},[724,63414,63415],{},[614,63416,63417,63418,63453,63454,1741],{},"Obrázek 3.6: Hyperbola ",[883,63419,63421],{"className":63420},[886],[888,63422,63423],{"xmlns":890},[892,63424,63425,63451],{},[895,63426,63427,63429,63431,63433,63447,63449],{},[898,63428,8309],{},[898,63430,6849],{},[1761,63432,1909],{},[6411,63434,63435],{"scriptlevel":1767,"displaystyle":1821},[4379,63436,63437,63445],{},[895,63438,63439,63441,63443],{},[1765,63440,1945],{},[2761,63442,7057],{},[1765,63444,63060],{},[898,63446,1828],{},[1761,63448,1964],{},[1765,63450,2318],{},[902,63452,63201],{"encoding":904}," s vodorovnou asymptotou ",[883,63455,63457],{"className":63456},[886],[888,63458,63459],{"xmlns":890},[892,63460,63461,63471],{},[895,63462,63463,63465,63467,63469],{},[898,63464,8309],{},[898,63466,6849],{},[1761,63468,1909],{},[1765,63470,2318],{},[902,63472,63473],{"encoding":904},"AC = 4",[724,63475,63476],{},"Celkové variabilní náklady lze často vyjádřit ve tvaru",[883,63478,63480],{"className":63479},[886],[888,63481,63482],{"xmlns":890,"display":1930},[892,63483,63484,63510],{},[895,63485,63486,63488,63490,63492,63494,63496,63498,63500,63502,63504,63506,63508],{},[898,63487,1655],{},[898,63489,44359],{},[898,63491,6849],{},[1761,63493,1909],{},[898,63495,1828],{},[1761,63497,2447],{},[898,63499,44359],{},[898,63501,6849],{},[1761,63503,1915],{"stretchy":1821},[898,63505,1828],{},[1761,63507,1920],{"stretchy":1821},[1761,63509,1834],{"separator":1833},[902,63511,63512],{"encoding":904},"TVC = Q \\cdot VC(Q),",[724,63514,8364,63515,62704,63543,63546,63547,63577],{},[883,63516,63518],{"className":63517},[886],[888,63519,63520],{"xmlns":890},[892,63521,63522,63540],{},[895,63523,63524,63526,63528,63530,63532,63534,63536,63538],{},[898,63525,44359],{},[898,63527,6849],{},[1761,63529,1909],{},[898,63531,44359],{},[898,63533,6849],{},[1761,63535,1915],{"stretchy":1821},[898,63537,1828],{},[1761,63539,1920],{"stretchy":1821},[902,63541,63542],{"encoding":904},"VC = VC(Q)",[38,63544,63545],{},"variabilní náklady na jednotku množství",". Jsou-li konstantní, ",[883,63548,63550],{"className":63549},[886],[888,63551,63552],{"xmlns":890},[892,63553,63554,63574],{},[895,63555,63556,63558,63560,63562,63564,63566,63568,63570,63572],{},[898,63557,1655],{},[898,63559,44359],{},[898,63561,6849],{},[1761,63563,1915],{"stretchy":1821},[898,63565,1828],{},[1761,63567,1920],{"stretchy":1821},[1761,63569,1909],{},[898,63571,207],{},[898,63573,1828],{},[902,63575,63576],{"encoding":904},"TVC(Q) = aQ"," a nejjednodušší model nákladů má tvar",[883,63579,63581],{"className":63580},[886],[888,63582,63583],{"xmlns":890,"display":1930},[892,63584,63585,63605],{},[895,63586,63587,63589,63591,63593,63595,63597,63599,63601,63603],{},[898,63588,1655],{},[898,63590,6849],{},[1761,63592,1909],{},[898,63594,14474],{},[898,63596,6849],{},[1761,63598,1964],{},[898,63600,207],{},[898,63602,1828],{},[898,63604,1741],{"mathvariant":1969},[902,63606,63607],{"encoding":904},"TC = FC + aQ.",[724,63609,63610,63611,63626,63627,63642,63643,63666,63667,63701,63702,63453,63715,63728,63729,2068,63777,63821,63822,1741],{},"Křivkou ",[883,63612,63614],{"className":63613},[886],[888,63615,63616],{"xmlns":890},[892,63617,63618,63624],{},[895,63619,63620,63622],{},[898,63621,1655],{},[898,63623,6849],{},[902,63625,7310],{"encoding":904}," je přímka se svislým průsečíkem ",[883,63628,63630],{"className":63629},[886],[888,63631,63632],{"xmlns":890},[892,63633,63634,63640],{},[895,63635,63636,63638],{},[898,63637,14474],{},[898,63639,6849],{},[902,63641,59469],{"encoding":904}," a sklonem ",[883,63644,63646],{"className":63645},[886],[888,63647,63648],{"xmlns":890},[892,63649,63650,63663],{},[895,63651,63652,63655,63657,63659,63661],{},[898,63653,63654],{},"tan",[1761,63656,60178],{},[898,63658,22895],{},[1761,63660,1909],{},[898,63662,207],{},[902,63664,63665],{"encoding":904},"\\tan\\alpha = a"," (obrázek 3.7). Průměrné náklady tvoří hyperbolu ",[883,63668,63670],{"className":63669},[886],[888,63671,63672],{"xmlns":890},[892,63673,63674,63698],{},[895,63675,63676,63678,63680,63682,63694,63696],{},[898,63677,8309],{},[898,63679,6849],{},[1761,63681,1909],{},[6411,63683,63684],{"scriptlevel":1767,"displaystyle":1821},[4379,63685,63686,63692],{},[895,63687,63688,63690],{},[898,63689,14474],{},[898,63691,6849],{},[898,63693,1828],{},[1761,63695,1964],{},[898,63697,207],{},[902,63699,63700],{"encoding":904},"AC = \\tfrac{FC}{Q} + a"," tvaru ",[883,63703,63705],{"className":63704},[886],[888,63706,63707],{"xmlns":890},[892,63708,63709,63713],{},[895,63710,63711],{},[898,63712,13835],{},[902,63714,13835],{"encoding":904},[883,63716,63718],{"className":63717},[886],[888,63719,63720],{"xmlns":890},[892,63721,63722,63726],{},[895,63723,63724],{},[898,63725,207],{},[902,63727,207],{"encoding":904}," (obrázek 3.8). Limity ",[883,63730,63732],{"className":63731},[886],[888,63733,63734],{"xmlns":890},[892,63735,63736,63774],{},[895,63737,63738,63758,63770,63772],{},[1681,63739,63740,63746],{},[895,63741,63742,63744],{},[898,63743,63260],{},[1761,63745,60178],{},[895,63747,63748,63750,63752],{},[898,63749,1828],{},[1761,63751,2181],{},[1824,63753,63754,63756],{},[1765,63755,1767],{},[1761,63757,1964],{},[6411,63759,63760],{"scriptlevel":1767,"displaystyle":1821},[4379,63761,63762,63768],{},[895,63763,63764,63766],{},[898,63765,14474],{},[898,63767,6849],{},[898,63769,1828],{},[1761,63771,1909],{},[898,63773,10342],{"mathvariant":1969},[902,63775,63776],{"encoding":904},"\\lim_{Q \\to 0^+} \\tfrac{FC}{Q} = \\infty",[883,63778,63780],{"className":63779},[886],[888,63781,63782],{"xmlns":890},[892,63783,63784,63818],{},[895,63785,63786,63802,63814,63816],{},[1681,63787,63788,63794],{},[895,63789,63790,63792],{},[898,63791,63260],{},[1761,63793,60178],{},[895,63795,63796,63798,63800],{},[898,63797,1828],{},[1761,63799,2181],{},[898,63801,10342],{"mathvariant":1969},[6411,63803,63804],{"scriptlevel":1767,"displaystyle":1821},[4379,63805,63806,63812],{},[895,63807,63808,63810],{},[898,63809,14474],{},[898,63811,6849],{},[898,63813,1828],{},[1761,63815,1909],{},[1765,63817,1767],{},[902,63819,63820],{"encoding":904},"\\lim_{Q \\to \\infty} \\tfrac{FC}{Q} = 0"," vysvětlují, proč s rostoucí produkcí fixní náklady stále méně ovlivňují ",[883,63823,63825],{"className":63824},[886],[888,63826,63827],{"xmlns":890},[892,63828,63829,63835],{},[895,63830,63831,63833],{},[898,63832,8309],{},[898,63834,6849],{},[902,63836,59538],{"encoding":904},[724,63838,63839],{},[614,63840,63841,63842,63857,63858,63873,63874,1741],{},"Obrázek 3.7: Přímka ",[883,63843,63845],{"className":63844},[886],[888,63846,63847],{"xmlns":890},[892,63848,63849,63855],{},[895,63850,63851,63853],{},[898,63852,1655],{},[898,63854,6849],{},[902,63856,7310],{"encoding":904}," s osovým průsečíkem ve výši ",[883,63859,63861],{"className":63860},[886],[888,63862,63863],{"xmlns":890},[892,63864,63865,63871],{},[895,63866,63867,63869],{},[898,63868,14474],{},[898,63870,6849],{},[902,63872,59469],{"encoding":904}," a se sklonem ",[883,63875,63877],{"className":63876},[886],[888,63878,63879],{"xmlns":890},[892,63880,63881,63893],{},[895,63882,63883,63885,63887,63889,63891],{},[898,63884,63654],{},[1761,63886,60178],{},[898,63888,22895],{},[1761,63890,1909],{},[898,63892,207],{},[902,63894,63665],{"encoding":904},[724,63896,63897],{},[614,63898,63899,63900,63915,63916,1741],{},"Obrázek 3.8: Klesající hyperbola ",[883,63901,63903],{"className":63902},[886],[888,63904,63905],{"xmlns":890},[892,63906,63907,63913],{},[895,63908,63909,63911],{},[898,63910,8309],{},[898,63912,6849],{},[902,63914,59538],{"encoding":904}," s vodorovnou asymptotou ve výši ",[883,63917,63919],{"className":63918},[886],[888,63920,63921],{"xmlns":890},[892,63922,63923,63927],{},[895,63924,63925],{},[898,63926,207],{},[902,63928,207],{"encoding":904},[198,63930,63932],{"id":63931},"mezní-náklady","Mezní náklady",[724,63934,63935,1989,63937,3927,63952,63955,63956,63959],{},[38,63936,63932],{},[883,63938,63940],{"className":63939},[886],[888,63941,63942],{"xmlns":890},[892,63943,63944,63950],{},[895,63945,63946,63948],{},[898,63947,6889],{},[898,63949,6849],{},[902,63951,59270],{"encoding":904},[38,63953,63954],{},"marginal cost",") jsou ",[207,63957,1145],{"className":63958,"dataFsResolvedFilePath":764,"href":765},[210]," celkových nákladů podle množství:",[883,63961,63963],{"className":63962},[886],[888,63964,63965],{"xmlns":890,"display":1930},[892,63966,63967,64036],{},[24787,63968,63969],{"width":32101},[24792,63970,63971,63973,64029,64031],{},[24795,63972],{"width":32106},[24795,63974,63975],{},[895,63976,63977,63979,63981,63983,63985,63987,63989,63991,63993,63995,64011,64013,64015,64021,64023,64025,64027],{},[898,63978,6889],{},[898,63980,6849],{},[1761,63982,1909],{},[898,63984,6889],{},[898,63986,6849],{},[1761,63988,1915],{"stretchy":1821},[898,63990,1828],{},[1761,63992,1920],{"stretchy":1821},[1761,63994,1909],{},[4379,63996,63997,64005],{},[895,63998,63999,64001,64003],{},[898,64000,4346],{"mathvariant":1969},[898,64002,1655],{},[898,64004,6849],{},[895,64006,64007,64009],{},[898,64008,4346],{"mathvariant":1969},[898,64010,1828],{},[1761,64012,1909],{},[898,64014,1655],{},[1824,64016,64017,64019],{},[898,64018,6849],{},[1761,64020,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,64022,1915],{"stretchy":1821},[898,64024,1828],{},[1761,64026,1920],{"stretchy":1821},[898,64028,1741],{"mathvariant":1969},[24795,64030],{"width":32106},[24795,64032,64033],{},[2761,64034,64035],{},"(3.8)",[902,64037,64038],{"encoding":904},"MC = MC(Q) = \\frac{\\mathrm{d}TC}{\\mathrm{d}Q} = TC'(Q).\n\\tag{3.8}",[1636,64040,64041],{},[724,64042,64043,64045,64046,64072,64073,64090,64091,1741],{},[883,64044,1642],{}," Intuice — „kolik stojí další kus\"\n",[883,64047,64049],{"className":64048},[886],[888,64050,64051],{"xmlns":890},[892,64052,64053,64069],{},[895,64054,64055,64057,64059,64061,64067],{},[898,64056,6889],{},[898,64058,6849],{},[1761,64060,1915],{"stretchy":1821},[1824,64062,64063,64065],{},[898,64064,1828],{},[1761,64066,8408],{},[1761,64068,1920],{"stretchy":1821},[902,64070,64071],{"encoding":904},"MC(Q^*)"," udává přibližné náklady na výrobu jedné další jednotky, když firma aktuálně produkuje ",[883,64074,64076],{"className":64075},[886],[888,64077,64078],{"xmlns":890},[892,64079,64080,64088],{},[895,64081,64082],{},[1824,64083,64084,64086],{},[898,64085,1828],{},[1761,64087,8408],{},[902,64089,33874],{"encoding":904},". Formálně ",[883,64092,64094],{"className":64093},[886],[888,64095,64096],{"xmlns":890},[892,64097,64098,64150],{},[895,64099,64100,64102,64104,64106,64112,64114,64116,64118,64120,64122,64128,64130,64132,64134,64136,64138,64140,64142,64148],{},[898,64101,6889],{},[898,64103,6849],{},[1761,64105,1915],{"stretchy":1821},[1824,64107,64108,64110],{},[898,64109,1828],{},[1761,64111,8408],{},[1761,64113,1920],{"stretchy":1821},[1761,64115,6803],{},[898,64117,1655],{},[898,64119,6849],{},[1761,64121,1915],{"stretchy":1821},[1824,64123,64124,64126],{},[898,64125,1828],{},[1761,64127,8408],{},[1761,64129,1964],{},[1765,64131,1945],{},[1761,64133,1920],{"stretchy":1821},[1761,64135,1885],{},[898,64137,1655],{},[898,64139,6849],{},[1761,64141,1915],{"stretchy":1821},[1824,64143,64144,64146],{},[898,64145,1828],{},[1761,64147,8408],{},[1761,64149,1920],{"stretchy":1821},[902,64151,64152],{"encoding":904},"MC(Q^*) \\approx TC(Q^* + 1) - TC(Q^*)",[724,64154,64155,64156,2506],{},"Analogicky ke vztahu (3.3) platí pro odhad změny ",[883,64157,64159],{"className":64158},[886],[888,64160,64161],{"xmlns":890},[892,64162,64163,64171],{},[895,64164,64165,64167,64169],{},[898,64166,6959],{"mathvariant":1969},[898,64168,1655],{},[898,64170,6849],{},[902,64172,64173],{"encoding":904},"\\Delta TC",[883,64175,64177],{"className":64176},[886],[888,64178,64179],{"xmlns":890,"display":1930},[892,64180,64181,64250],{},[24787,64182,64183],{"width":32101},[24792,64184,64185,64187,64243,64245],{},[24795,64186],{"width":32106},[24795,64188,64189],{},[895,64190,64191,64193,64195,64197,64199,64201,64203,64205,64207,64209,64211,64213,64215,64217,64223,64225,64227,64229,64231,64233,64235,64237,64239,64241],{},[898,64192,6959],{"mathvariant":1969},[898,64194,1655],{},[898,64196,6849],{},[2761,64198,8041],{},[1761,64200,6803],{},[2761,64202,8041],{},[898,64204,4346],{"mathvariant":1969},[898,64206,1655],{},[898,64208,6849],{},[1761,64210,1909],{},[1761,64212,1915],{"stretchy":1821},[898,64214,1655],{},[898,64216,6849],{},[1824,64218,64219,64221],{},[1761,64220,1920],{"stretchy":1821},[1761,64222,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[2761,64224,7057],{},[898,64226,4346],{"mathvariant":1969},[898,64228,1828],{},[1761,64230,1909],{},[898,64232,6889],{},[898,64234,6849],{},[2761,64236,7057],{},[898,64238,4346],{"mathvariant":1969},[898,64240,1828],{},[1761,64242,1834],{"separator":1833},[24795,64244],{"width":32106},[24795,64246,64247],{},[2761,64248,64249],{},"(3.9)",[902,64251,64252],{"encoding":904},"\\Delta TC \\;\\approx\\; \\mathrm{d}TC = (TC)' \\, \\mathrm{d}Q = MC \\, \\mathrm{d}Q,\n\\tag{3.9}",[724,64254,61289],{},[883,64256,64258],{"className":64257},[886],[888,64259,64260],{"xmlns":890,"display":1930},[892,64261,64262,64360],{},[895,64263,64264,64302,64304,64306,64308,64330,64332,64358],{},[895,64265,64266,64268,64274,64276,64282,64285,64291,64294],{},[2761,64267,61303],{},[2770,64269,64270,64272],{"accent":1833},[2761,64271,49723],{},[1761,64273,2777],{},[2761,64275,61312],{},[2770,64277,64278,64280],{"accent":1833},[2761,64279,1716],{},[1761,64281,29009],{},[2761,64283,64284],{},"ch n",[2770,64286,64287,64289],{"accent":1833},[2761,64288,207],{},[1761,64290,29009],{},[2761,64292,64293],{},"klad",[2770,64295,64296,64299],{"accent":1833},[2761,64297,64298],{},"u",[1761,64300,64301],{},"˚",[2761,64303,8041],{},[1761,64305,6803],{},[2761,64307,8041],{},[895,64309,64310,64312,64318,64321,64327],{},[2761,64311,61347],{},[2770,64313,64314,64316],{"accent":1833},[2761,64315,29078],{},[1761,64317,29009],{},[2761,64319,64320],{}," n",[2770,64322,64323,64325],{"accent":1833},[2761,64324,207],{},[1761,64326,29009],{},[2761,64328,64329],{},"klady",[1761,64331,61374],{},[895,64333,64334,64336,64342,64344,64350,64352],{},[2761,64335,61303],{},[2770,64337,64338,64340],{"accent":1833},[2761,64339,49723],{},[1761,64341,2777],{},[2761,64343,61387],{},[2770,64345,64346,64348],{"accent":1833},[2761,64347,13634],{},[1761,64349,2777],{},[2761,64351,61396],{},[2770,64353,64354,64356],{"accent":1833},[2761,64355,29078],{},[1761,64357,29009],{},[898,64359,1741],{"mathvariant":1969},[902,64361,64362],{"encoding":904},"\\text{změna celkových nákladů} \\;\\approx\\; \\text{mezní náklady} \\times \\text{změna množství}.",[41374,64364,64366],{"id":64365},"příklad-35","Příklad 3.5",[724,64368,64369,61500,64371,60003,64407,64422,64423,64438,64439,6746,64452,4178,64465,64478,64479,4178,64492,1741],{},[38,64370,59965],{},[883,64372,64374],{"className":64373},[886],[888,64375,64376],{"xmlns":890},[892,64377,64378,64404],{},[895,64379,64380,64382,64384,64386,64388,64390,64392,64394,64396,64398],{},[898,64381,1655],{},[898,64383,6849],{},[1761,64385,1909],{},[1765,64387,12421],{},[1761,64389,1964],{},[1765,64391,2340],{},[898,64393,1828],{},[1761,64395,1964],{},[1765,64397,2296],{},[1824,64399,64400,64402],{},[898,64401,1828],{},[1765,64403,2296],{},[902,64405,64406],{"encoding":904},"TC = 200 + 6Q + 2Q^2",[883,64408,64410],{"className":64409},[886],[888,64411,64412],{"xmlns":890},[892,64413,64414,64420],{},[895,64415,64416,64418],{},[898,64417,6889],{},[898,64419,6849],{},[902,64421,59270],{"encoding":904}," a odhadněte změny ",[883,64424,64426],{"className":64425},[886],[888,64427,64428],{"xmlns":890},[892,64429,64430,64436],{},[895,64431,64432,64434],{},[898,64433,1655],{},[898,64435,6849],{},[902,64437,7310],{"encoding":904}," při změnách ",[883,64440,64442],{"className":64441},[886],[888,64443,64444],{"xmlns":890},[892,64445,64446,64450],{},[895,64447,64448],{},[898,64449,1828],{},[902,64451,1828],{"encoding":904},[883,64453,64455],{"className":64454},[886],[888,64456,64457],{"xmlns":890},[892,64458,64459,64463],{},[895,64460,64461],{},[1765,64462,5433],{},[902,64464,5433],{"encoding":904},[883,64466,64468],{"className":64467},[886],[888,64469,64470],{"xmlns":890},[892,64471,64472,64476],{},[895,64473,64474],{},[1765,64475,45871],{},[902,64477,45871],{"encoding":904}," a z ",[883,64480,64482],{"className":64481},[886],[888,64483,64484],{"xmlns":890},[892,64485,64486,64490],{},[895,64487,64488],{},[1765,64489,5433],{},[902,64491,5433],{"encoding":904},[883,64493,64495],{"className":64494},[886],[888,64496,64497],{"xmlns":890},[892,64498,64499,64503],{},[895,64500,64501],{},[1765,64502,2291],{},[902,64504,2291],{"encoding":904},[724,64506,64507,1989,64509,6997,64535,1343,64562,64589,64590,64605,64606,64621,64622,64649,64650,64670,64671,24564,64692,64748,64749,6746,64762,4178,64775,12146,64788,1741],{},[38,64508,26803],{},[883,64510,64512],{"className":64511},[886],[888,64513,64514],{"xmlns":890},[892,64515,64516,64532],{},[895,64517,64518,64520,64522,64524,64526,64528,64530],{},[898,64519,6889],{},[898,64521,6849],{},[1761,64523,1909],{},[1765,64525,2340],{},[1761,64527,1964],{},[1765,64529,2318],{},[898,64531,1828],{},[902,64533,64534],{"encoding":904},"MC = 6 + 4Q",[883,64536,64538],{"className":64537},[886],[888,64539,64540],{"xmlns":890},[892,64541,64542,64559],{},[895,64543,64544,64546,64548,64550,64552,64554,64556],{},[898,64545,6889],{},[898,64547,6849],{},[1761,64549,1915],{"stretchy":1821},[1765,64551,5433],{},[1761,64553,1920],{"stretchy":1821},[1761,64555,1909],{},[1765,64557,64558],{},"66",[902,64560,64561],{"encoding":904},"MC(15) = 66",[883,64563,64565],{"className":64564},[886],[888,64566,64567],{"xmlns":890},[892,64568,64569,64586],{},[895,64570,64571,64573,64575,64577,64579,64581,64583],{},[898,64572,6889],{},[898,64574,6849],{},[1761,64576,1915],{"stretchy":1821},[1765,64578,13077],{},[1761,64580,1920],{"stretchy":1821},[1761,64582,1909],{},[1765,64584,64585],{},"86",[902,64587,64588],{"encoding":904},"MC(20) = 86",": s růstem množství se rychlost změny ",[883,64591,64593],{"className":64592},[886],[888,64594,64595],{"xmlns":890},[892,64596,64597,64603],{},[895,64598,64599,64601],{},[898,64600,1655],{},[898,64602,6849],{},[902,64604,7310],{"encoding":904}," zvyšuje (",[883,64607,64609],{"className":64608},[886],[888,64610,64611],{"xmlns":890},[892,64612,64613,64619],{},[895,64614,64615,64617],{},[898,64616,6889],{},[898,64618,6849],{},[902,64620,59270],{"encoding":904}," je rostoucí). Z ",[883,64623,64625],{"className":64624},[886],[888,64626,64627],{"xmlns":890},[892,64628,64629,64646],{},[895,64630,64631,64633,64635,64637,64639,64641,64643],{},[898,64632,1655],{},[898,64634,6849],{},[1761,64636,1915],{"stretchy":1821},[1765,64638,5433],{},[1761,64640,1920],{"stretchy":1821},[1761,64642,1909],{},[1765,64644,64645],{},"740",[902,64647,64648],{"encoding":904},"TC(15) = 740"," se po přírůstku ",[883,64651,64653],{"className":64652},[886],[888,64654,64655],{"xmlns":890},[892,64656,64657,64667],{},[895,64658,64659,64661,64663,64665],{},[898,64660,4346],{"mathvariant":1969},[898,64662,1828],{},[1761,64664,1909],{},[1765,64666,1945],{},[902,64668,64669],{"encoding":904},"\\mathrm{d}Q = 1"," předpokládá ",[883,64672,64674],{"className":64673},[886],[888,64675,64676],{"xmlns":890},[892,64677,64678,64689],{},[895,64679,64680,64682,64684,64686],{},[898,64681,1655],{},[898,64683,6849],{},[1761,64685,6803],{},[1765,64687,64688],{},"806",[902,64690,64691],{"encoding":904},"TC \\approx 806",[883,64693,64695],{"className":64694},[886],[888,64696,64697],{"xmlns":890},[892,64698,64699,64745],{},[895,64700,64701,64703,64705,64707,64709,64711,64713,64715,64717,64719,64721,64723,64725,64727,64729,64731,64733,64736,64738,64740,64742],{},[898,64702,6959],{"mathvariant":1969},[898,64704,1655],{},[898,64706,6849],{},[1761,64708,1909],{},[898,64710,1655],{},[898,64712,6849],{},[1761,64714,1915],{"stretchy":1821},[1765,64716,45871],{},[1761,64718,1920],{"stretchy":1821},[1761,64720,1885],{},[898,64722,1655],{},[898,64724,6849],{},[1761,64726,1915],{"stretchy":1821},[1765,64728,5433],{},[1761,64730,1920],{"stretchy":1821},[1761,64732,1909],{},[1765,64734,64735],{},"808",[1761,64737,1885],{},[1765,64739,64645],{},[1761,64741,1909],{},[1765,64743,64744],{},"68",[902,64746,64747],{"encoding":904},"\\Delta TC = TC(16) - TC(15) = 808 - 740 = 68",". Při poklesu ",[883,64750,64752],{"className":64751},[886],[888,64753,64754],{"xmlns":890},[892,64755,64756,64760],{},[895,64757,64758],{},[898,64759,1828],{},[902,64761,1828],{"encoding":904},[883,64763,64765],{"className":64764},[886],[888,64766,64767],{"xmlns":890},[892,64768,64769,64773],{},[895,64770,64771],{},[1765,64772,5433],{},[902,64774,5433],{"encoding":904},[883,64776,64778],{"className":64777},[886],[888,64779,64780],{"xmlns":890},[892,64781,64782,64786],{},[895,64783,64784],{},[1765,64785,2291],{},[902,64787,2291],{"encoding":904},[883,64789,64791],{"className":64790},[886],[888,64792,64793],{"xmlns":890},[892,64794,64795,64824],{},[895,64796,64797,64799,64801,64803,64805,64807,64809,64811,64813,64815,64817,64819,64821],{},[898,64798,6959],{"mathvariant":1969},[898,64800,1655],{},[898,64802,6849],{},[1761,64804,6803],{},[1765,64806,64558],{},[1761,64808,2447],{},[1761,64810,1915],{"stretchy":1821},[1761,64812,1885],{},[1765,64814,5486],{},[1761,64816,1920],{"stretchy":1821},[1761,64818,1909],{},[1761,64820,1885],{},[1765,64822,64823],{},"198",[902,64825,64826],{"encoding":904},"\\Delta TC \\approx 66 \\cdot (-3) = -198",[198,64828,64830],{"id":64829},"kubická-nákladová-funkce","Kubická nákladová funkce",[724,64832,64833],{},"V ekonomicky reálných situacích mají křivky nákladů charakteristické vazby a tvary.",[41374,64835,64837],{"id":64836},"příklad-36","Příklad 3.6",[724,64839,64840,61500,64842,64886],{},[38,64841,59965],{},[883,64843,64845],{"className":64844},[886],[888,64846,64847],{"xmlns":890},[892,64848,64849,64883],{},[895,64850,64851,64853,64855,64857,64859,64861,64863,64865,64867,64869,64875,64877],{},[898,64852,1655],{},[898,64854,6849],{},[1761,64856,1909],{},[1765,64858,7160],{},[1761,64860,1964],{},[1765,64862,9056],{},[898,64864,1828],{},[1761,64866,1885],{},[1765,64868,6321],{},[1824,64870,64871,64873],{},[898,64872,1828],{},[1765,64874,2296],{},[1761,64876,1964],{},[1824,64878,64879,64881],{},[898,64880,1828],{},[1765,64882,5486],{},[902,64884,64885],{"encoding":904},"TC = 100 + 25Q - 5Q^2 + Q^3"," odvoďte všechny nákladové charakteristiky.",[724,64888,64889],{},[38,64890,26803],{},[883,64892,64894],{"className":64893},[886],[888,64895,64896],{"xmlns":890,"display":1930},[892,64897,64898,65142],{},[24787,64899,64900,64926,64974,65008,65050,65100],{"rowspacing":24789,"columnalign":24790,"columnspacing":6458},[24792,64901,64902,64912],{},[24795,64903,64904],{},[6411,64905,64906],{"scriptlevel":1767,"displaystyle":1833},[895,64907,64908,64910],{},[898,64909,14474],{},[898,64911,6849],{},[24795,64913,64914],{},[6411,64915,64916],{"scriptlevel":1767,"displaystyle":1833},[895,64917,64918,64920,64922,64924],{},[895,64919],{},[1761,64921,1909],{},[1765,64923,7160],{},[1761,64925,1834],{"separator":1833},[24792,64927,64928,64940],{},[24795,64929,64930],{},[6411,64931,64932],{"scriptlevel":1767,"displaystyle":1833},[895,64933,64934,64936,64938],{},[898,64935,1655],{},[898,64937,44359],{},[898,64939,6849],{},[24795,64941,64942],{},[6411,64943,64944],{"scriptlevel":1767,"displaystyle":1833},[895,64945,64946,64948,64950,64952,64954,64956,64958,64964,64966,64972],{},[895,64947],{},[1761,64949,1909],{},[1765,64951,9056],{},[898,64953,1828],{},[1761,64955,1885],{},[1765,64957,6321],{},[1824,64959,64960,64962],{},[898,64961,1828],{},[1765,64963,2296],{},[1761,64965,1964],{},[1824,64967,64968,64970],{},[898,64969,1828],{},[1765,64971,5486],{},[1761,64973,1834],{"separator":1833},[24792,64975,64976,64988],{},[24795,64977,64978],{},[6411,64979,64980],{"scriptlevel":1767,"displaystyle":1833},[895,64981,64982,64984,64986],{},[898,64983,8309],{},[898,64985,14474],{},[898,64987,6849],{},[24795,64989,64990],{},[6411,64991,64992],{"scriptlevel":1767,"displaystyle":1833},[895,64993,64994,64996,64998,65006],{},[895,64995],{},[1761,64997,1909],{},[6411,64999,65000],{"scriptlevel":1767,"displaystyle":1821},[4379,65001,65002,65004],{},[1765,65003,7160],{},[898,65005,1828],{},[1761,65007,1834],{"separator":1833},[24792,65009,65010,65022],{},[24795,65011,65012],{},[6411,65013,65014],{"scriptlevel":1767,"displaystyle":1833},[895,65015,65016,65018,65020],{},[898,65017,8309],{},[898,65019,44359],{},[898,65021,6849],{},[24795,65023,65024],{},[6411,65025,65026],{"scriptlevel":1767,"displaystyle":1833},[895,65027,65028,65030,65032,65034,65036,65038,65040,65042,65048],{},[895,65029],{},[1761,65031,1909],{},[1765,65033,9056],{},[1761,65035,1885],{},[1765,65037,6321],{},[898,65039,1828],{},[1761,65041,1964],{},[1824,65043,65044,65046],{},[898,65045,1828],{},[1765,65047,2296],{},[1761,65049,1834],{"separator":1833},[24792,65051,65052,65062],{},[24795,65053,65054],{},[6411,65055,65056],{"scriptlevel":1767,"displaystyle":1833},[895,65057,65058,65060],{},[898,65059,8309],{},[898,65061,6849],{},[24795,65063,65064],{},[6411,65065,65066],{"scriptlevel":1767,"displaystyle":1833},[895,65067,65068,65070,65072,65080,65082,65084,65086,65088,65090,65092,65098],{},[895,65069],{},[1761,65071,1909],{},[6411,65073,65074],{"scriptlevel":1767,"displaystyle":1821},[4379,65075,65076,65078],{},[1765,65077,7160],{},[898,65079,1828],{},[1761,65081,1964],{},[1765,65083,9056],{},[1761,65085,1885],{},[1765,65087,6321],{},[898,65089,1828],{},[1761,65091,1964],{},[1824,65093,65094,65096],{},[898,65095,1828],{},[1765,65097,2296],{},[1761,65099,1834],{"separator":1833},[24792,65101,65102,65112],{},[24795,65103,65104],{},[6411,65105,65106],{"scriptlevel":1767,"displaystyle":1833},[895,65107,65108,65110],{},[898,65109,6889],{},[898,65111,6849],{},[24795,65113,65114],{},[6411,65115,65116],{"scriptlevel":1767,"displaystyle":1833},[895,65117,65118,65120,65122,65124,65126,65128,65130,65132,65134,65140],{},[895,65119],{},[1761,65121,1909],{},[1765,65123,9056],{},[1761,65125,1885],{},[1765,65127,2633],{},[898,65129,1828],{},[1761,65131,1964],{},[1765,65133,5486],{},[1824,65135,65136,65138],{},[898,65137,1828],{},[1765,65139,2296],{},[898,65141,1741],{"mathvariant":1969},[902,65143,65144],{"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}",[724,65146,65147,65148,19828,65163,19828,65178,65193,65194,65209,65210,1343,65228,65209,65245,1343,65263,65209,65278,65296],{},"Význačné body ",[883,65149,65151],{"className":65150},[886],[888,65152,65153],{"xmlns":890},[892,65154,65155,65160],{},[895,65156,65157],{},[1765,65158,65159],{},"1,67",[902,65161,65162],{"encoding":904},"1{,}67",[883,65164,65166],{"className":65165},[886],[888,65167,65168],{"xmlns":890},[892,65169,65170,65175],{},[895,65171,65172],{},[1765,65173,65174],{},"2,50",[902,65176,65177],{"encoding":904},"2{,}50",[883,65179,65181],{"className":65180},[886],[888,65182,65183],{"xmlns":890},[892,65184,65185,65190],{},[895,65186,65187],{},[1765,65188,65189],{},"4,73",[902,65191,65192],{"encoding":904},"4{,}73"," odpovídají: ",[883,65195,65197],{"className":65196},[886],[888,65198,65199],{"xmlns":890},[892,65200,65201,65207],{},[895,65202,65203,65205],{},[898,65204,6889],{},[898,65206,6849],{},[902,65208,59270],{"encoding":904}," minimum v ",[883,65211,65213],{"className":65212},[886],[888,65214,65215],{"xmlns":890},[892,65216,65217,65225],{},[895,65218,65219,65221,65223],{},[898,65220,1828],{},[1761,65222,9945],{},[1765,65224,65159],{},[902,65226,65227],{"encoding":904},"Q \\doteq 1{,}67",[883,65229,65231],{"className":65230},[886],[888,65232,65233],{"xmlns":890},[892,65234,65235,65243],{},[895,65236,65237,65239,65241],{},[898,65238,8309],{},[898,65240,44359],{},[898,65242,6849],{},[902,65244,59289],{"encoding":904},[883,65246,65248],{"className":65247},[886],[888,65249,65250],{"xmlns":890},[892,65251,65252,65260],{},[895,65253,65254,65256,65258],{},[898,65255,1828],{},[1761,65257,1909],{},[1765,65259,65174],{},[902,65261,65262],{"encoding":904},"Q = 2{,}50",[883,65264,65266],{"className":65265},[886],[888,65267,65268],{"xmlns":890},[892,65269,65270,65276],{},[895,65271,65272,65274],{},[898,65273,8309],{},[898,65275,6849],{},[902,65277,59538],{"encoding":904},[883,65279,65281],{"className":65280},[886],[888,65282,65283],{"xmlns":890},[892,65284,65285,65293],{},[895,65286,65287,65289,65291],{},[898,65288,1828],{},[1761,65290,9945],{},[1765,65292,65189],{},[902,65294,65295],{"encoding":904},"Q \\doteq 4{,}73"," (téma úlohy 3.11).",[724,65298,65299],{},[3991,65300],{"alt":65301,"className":65302,"src":65303},"imek-ac-avc-mc",[210,3995],"\u002Fwiki-assets\u002Fimek-ac-avc-mc.jpeg",[724,65305,65306],{},[614,65307,65308,65309,2068,65324,65341,65342,19828,65361,65376],{},"Obrázek 3.9: Kubické křivky ",[883,65310,65312],{"className":65311},[886],[888,65313,65314],{"xmlns":890},[892,65315,65316,65322],{},[895,65317,65318,65320],{},[898,65319,1655],{},[898,65321,6849],{},[902,65323,7310],{"encoding":904},[883,65325,65327],{"className":65326},[886],[888,65328,65329],{"xmlns":890},[892,65330,65331,65339],{},[895,65332,65333,65335,65337],{},[898,65334,1655],{},[898,65336,44359],{},[898,65338,6849],{},[902,65340,59487],{"encoding":904}," rostoucí od bodu ",[883,65343,65345],{"className":65344},[886],[888,65346,65347],{"xmlns":890},[892,65348,65349,65359],{},[895,65350,65351,65353,65355,65357],{},[898,65352,14474],{},[898,65354,6849],{},[1761,65356,1909],{},[1765,65358,7160],{},[902,65360,15672],{"encoding":904},[883,65362,65364],{"className":65363},[886],[888,65365,65366],{"xmlns":890},[892,65367,65368,65374],{},[895,65369,65370,65372],{},[898,65371,14474],{},[898,65373,6849],{},[902,65375,59469],{"encoding":904}," je vodorovná přímka.",[724,65378,65379],{},[614,65380,65381,65382,1343,65397,1343,65414,33231,65429,65442,65443,6997,65460,65475,65476,10235,65493,65508,65509,30220,65522,1343,65535,1343,65548,1741],{},"Obrázek 3.10: Křivky ",[883,65383,65385],{"className":65384},[886],[888,65386,65387],{"xmlns":890},[892,65388,65389,65395],{},[895,65390,65391,65393],{},[898,65392,8309],{},[898,65394,6849],{},[902,65396,59538],{"encoding":904},[883,65398,65400],{"className":65399},[886],[888,65401,65402],{"xmlns":890},[892,65403,65404,65412],{},[895,65405,65406,65408,65410],{},[898,65407,8309],{},[898,65409,44359],{},[898,65411,6849],{},[902,65413,59289],{"encoding":904},[883,65415,65417],{"className":65416},[886],[888,65418,65419],{"xmlns":890},[892,65420,65421,65427],{},[895,65422,65423,65425],{},[898,65424,6889],{},[898,65426,6849],{},[902,65428,59270],{"encoding":904},[883,65430,65432],{"className":65431},[886],[888,65433,65434],{"xmlns":890},[892,65435,65436,65440],{},[895,65437,65438],{},[898,65439,900],{},[902,65441,900],{"encoding":904}," a klesající hyperbola ",[883,65444,65446],{"className":65445},[886],[888,65447,65448],{"xmlns":890},[892,65449,65450,65458],{},[895,65451,65452,65454,65456],{},[898,65453,8309],{},[898,65455,14474],{},[898,65457,6849],{},[902,65459,59505],{"encoding":904},[883,65461,65463],{"className":65462},[886],[888,65464,65465],{"xmlns":890},[892,65466,65467,65473],{},[895,65468,65469,65471],{},[898,65470,6889],{},[898,65472,6849],{},[902,65474,59270],{"encoding":904}," protíná ",[883,65477,65479],{"className":65478},[886],[888,65480,65481],{"xmlns":890},[892,65482,65483,65491],{},[895,65484,65485,65487,65489],{},[898,65486,8309],{},[898,65488,44359],{},[898,65490,6849],{},[902,65492,59289],{"encoding":904},[883,65494,65496],{"className":65495},[886],[888,65497,65498],{"xmlns":890},[892,65499,65500,65506],{},[895,65501,65502,65504],{},[898,65503,8309],{},[898,65505,6849],{},[902,65507,59538],{"encoding":904}," zdola v jejich minimech; význačné hodnoty na ose ",[883,65510,65512],{"className":65511},[886],[888,65513,65514],{"xmlns":890},[892,65515,65516,65520],{},[895,65517,65518],{},[898,65519,1828],{},[902,65521,1828],{"encoding":904},[883,65523,65525],{"className":65524},[886],[888,65526,65527],{"xmlns":890},[892,65528,65529,65533],{},[895,65530,65531],{},[1765,65532,65159],{},[902,65534,65162],{"encoding":904},[883,65536,65538],{"className":65537},[886],[888,65539,65540],{"xmlns":890},[892,65541,65542,65546],{},[895,65543,65544],{},[1765,65545,65174],{},[902,65547,65177],{"encoding":904},[883,65549,65551],{"className":65550},[886],[888,65552,65553],{"xmlns":890},[892,65554,65555,65559],{},[895,65556,65557],{},[1765,65558,65189],{},[902,65560,65192],{"encoding":904},[724,65562,65563],{},[38,65564,65565],{},"Standardní vlastnosti:",[120,65567,65568,65603,65667,65735,65785,65805],{},[123,65569,65570,2068,65585,65602],{},[883,65571,65573],{"className":65572},[886],[888,65574,65575],{"xmlns":890},[892,65576,65577,65583],{},[895,65578,65579,65581],{},[898,65580,1655],{},[898,65582,6849],{},[902,65584,7310],{"encoding":904},[883,65586,65588],{"className":65587},[886],[888,65589,65590],{"xmlns":890},[892,65591,65592,65600],{},[895,65593,65594,65596,65598],{},[898,65595,1655],{},[898,65597,44359],{},[898,65599,6849],{},[902,65601,59487],{"encoding":904}," jsou kubické funkce;",[123,65604,65605,1343,65620,1343,65637,65652,65653,65666],{},[883,65606,65608],{"className":65607},[886],[888,65609,65610],{"xmlns":890},[892,65611,65612,65618],{},[895,65613,65614,65616],{},[898,65615,8309],{},[898,65617,6849],{},[902,65619,59538],{"encoding":904},[883,65621,65623],{"className":65622},[886],[888,65624,65625],{"xmlns":890},[892,65626,65627,65635],{},[895,65628,65629,65631,65633],{},[898,65630,8309],{},[898,65632,44359],{},[898,65634,6849],{},[902,65636,59289],{"encoding":904},[883,65638,65640],{"className":65639},[886],[888,65641,65642],{"xmlns":890},[892,65643,65644,65650],{},[895,65645,65646,65648],{},[898,65647,6889],{},[898,65649,6849],{},[902,65651,59270],{"encoding":904}," jsou křivky tvaru ",[883,65654,65656],{"className":65655},[886],[888,65657,65658],{"xmlns":890},[892,65659,65660,65664],{},[895,65661,65662],{},[898,65663,900],{},[902,65665,900],{"encoding":904}," (nejprve klesají, po minimu rostou);",[123,65668,65669,65684,65685,1343,65702,65719,65720,12468],{},[883,65670,65672],{"className":65671},[886],[888,65673,65674],{"xmlns":890},[892,65675,65676,65682],{},[895,65677,65678,65680],{},[898,65679,6889],{},[898,65681,6849],{},[902,65683,59270],{"encoding":904}," nabývá minima před ",[883,65686,65688],{"className":65687},[886],[888,65689,65690],{"xmlns":890},[892,65691,65692,65700],{},[895,65693,65694,65696,65698],{},[898,65695,8309],{},[898,65697,44359],{},[898,65699,6849],{},[902,65701,59289],{"encoding":904},[883,65703,65705],{"className":65704},[886],[888,65706,65707],{"xmlns":890},[892,65708,65709,65717],{},[895,65710,65711,65713,65715],{},[898,65712,8309],{},[898,65714,44359],{},[898,65716,6849],{},[902,65718,59289],{"encoding":904}," před ",[883,65721,65723],{"className":65722},[886],[888,65724,65725],{"xmlns":890},[892,65726,65727,65733],{},[895,65728,65729,65731],{},[898,65730,8309],{},[898,65732,6849],{},[902,65734,59538],{"encoding":904},[123,65736,65737,65475,65752,2068,65767,65784],{},[883,65738,65740],{"className":65739},[886],[888,65741,65742],{"xmlns":890},[892,65743,65744,65750],{},[895,65745,65746,65748],{},[898,65747,6889],{},[898,65749,6849],{},[902,65751,59270],{"encoding":904},[883,65753,65755],{"className":65754},[886],[888,65756,65757],{"xmlns":890},[892,65758,65759,65765],{},[895,65760,65761,65763],{},[898,65762,8309],{},[898,65764,6849],{},[902,65766,59538],{"encoding":904},[883,65768,65770],{"className":65769},[886],[888,65771,65772],{"xmlns":890},[892,65773,65774,65782],{},[895,65775,65776,65778,65780],{},[898,65777,8309],{},[898,65779,44359],{},[898,65781,6849],{},[902,65783,59289],{"encoding":904}," zdola právě v jejich minimech;",[123,65786,65787,65804],{},[883,65788,65790],{"className":65789},[886],[888,65791,65792],{"xmlns":890},[892,65793,65794,65802],{},[895,65795,65796,65798,65800],{},[898,65797,8309],{},[898,65799,14474],{},[898,65801,6849],{},[902,65803,59505],{"encoding":904}," je hyperbola, stále klesající;",[123,65806,65807,65839,65840,2068,65855,65872,65873,65886,65887,2162],{},[883,65808,65810],{"className":65809},[886],[888,65811,65812],{"xmlns":890},[892,65813,65814,65836],{},[895,65815,65816,65818,65820,65822,65824,65826,65828,65830,65832,65834],{},[898,65817,8309],{},[898,65819,6849],{},[1761,65821,1909],{},[898,65823,8309],{},[898,65825,14474],{},[898,65827,6849],{},[1761,65829,1964],{},[898,65831,8309],{},[898,65833,44359],{},[898,65835,6849],{},[902,65837,65838],{"encoding":904},"AC = AFC + AVC","; vzdálenost mezi ",[883,65841,65843],{"className":65842},[886],[888,65844,65845],{"xmlns":890},[892,65846,65847,65853],{},[895,65848,65849,65851],{},[898,65850,8309],{},[898,65852,6849],{},[902,65854,59538],{"encoding":904},[883,65856,65858],{"className":65857},[886],[888,65859,65860],{"xmlns":890},[892,65861,65862,65870],{},[895,65863,65864,65866,65868],{},[898,65865,8309],{},[898,65867,44359],{},[898,65869,6849],{},[902,65871,59289],{"encoding":904}," klesá s rostoucím ",[883,65874,65876],{"className":65875},[886],[888,65877,65878],{"xmlns":890},[892,65879,65880,65884],{},[895,65881,65882],{},[898,65883,1828],{},[902,65885,1828],{"encoding":904}," (protože ",[883,65888,65890],{"className":65889},[886],[888,65891,65892],{"xmlns":890},[892,65893,65894,65906],{},[895,65895,65896,65898,65900,65902,65904],{},[898,65897,8309],{},[898,65899,14474],{},[898,65901,6849],{},[1761,65903,2181],{},[1765,65905,1767],{},[902,65907,65908],{"encoding":904},"AFC \\to 0",[115,65910,65912],{"id":65911},"princip-minimalizace-průměrných-nákladů","Princip minimalizace průměrných nákladů",[724,65914,65915,65916,65919,65920,65935],{},"Častou optimalizační úlohou je ",[38,65917,65918],{},"minimalizace průměrných nákladů"," — stanovení produkce, pro niž je ",[883,65921,65923],{"className":65922},[886],[888,65924,65925],{"xmlns":890},[892,65926,65927,65933],{},[895,65928,65929,65931],{},[898,65930,8309],{},[898,65932,6849],{},[902,65934,59538],{"encoding":904}," minimální.",[198,65937,20446],{"id":20445},[724,65939,65940,65941,65958],{},"Mají-li průměrné náklady minimum v bodě ",[883,65942,65944],{"className":65943},[886],[888,65945,65946],{"xmlns":890},[892,65947,65948,65956],{},[895,65949,65950],{},[1681,65951,65952,65954],{},[898,65953,1828],{},[1765,65955,1767],{},[902,65957,42331],{"encoding":904},", pak platí",[883,65960,65962],{"className":65961},[886],[888,65963,65964],{"xmlns":890,"display":1930},[892,65965,65966,66015],{},[24787,65967,65968],{"width":32101},[24792,65969,65970,65972,66008,66010],{},[24795,65971],{"width":32106},[24795,65973,65974],{},[895,65975,65976,65978,65980,65982,65988,65990,65992,65994,65996,65998,66004,66006],{},[898,65977,8309],{},[898,65979,6849],{},[1761,65981,1915],{"stretchy":1821},[1681,65983,65984,65986],{},[898,65985,1828],{},[1765,65987,1767],{},[1761,65989,1920],{"stretchy":1821},[1761,65991,1909],{},[898,65993,6889],{},[898,65995,6849],{},[1761,65997,1915],{"stretchy":1821},[1681,65999,66000,66002],{},[898,66001,1828],{},[1765,66003,1767],{},[1761,66005,1920],{"stretchy":1821},[898,66007,1741],{"mathvariant":1969},[24795,66009],{"width":32106},[24795,66011,66012],{},[2761,66013,66014],{},"(3.10)",[902,66016,66017],{"encoding":904},"AC(Q_0) = MC(Q_0).\n\\tag{3.10}",[1636,66019,66020],{},[724,66021,66022,66024,66025],{},[883,66023,60422],{}," Princip\n",[38,66026,66027],{},"V bodě minima průměrných nákladů se průměrné náklady rovnají mezním nákladům.",[724,66029,66030,66033,66034,66076],{},[38,66031,66032],{},"Odvození."," Z ",[883,66035,66037],{"className":66036},[886],[888,66038,66039],{"xmlns":890},[892,66040,66041,66073],{},[895,66042,66043,66045,66047,66049,66051,66053,66055],{},[898,66044,8309],{},[898,66046,6849],{},[1761,66048,1915],{"stretchy":1821},[898,66050,1828],{},[1761,66052,1920],{"stretchy":1821},[1761,66054,1909],{},[6411,66056,66057],{"scriptlevel":1767,"displaystyle":1821},[4379,66058,66059,66071],{},[895,66060,66061,66063,66065,66067,66069],{},[898,66062,1655],{},[898,66064,6849],{},[1761,66066,1915],{"stretchy":1821},[898,66068,1828],{},[1761,66070,1920],{"stretchy":1821},[898,66072,1828],{},[902,66074,66075],{"encoding":904},"AC(Q) = \\tfrac{TC(Q)}{Q}"," derivací podílu plyne",[883,66078,66080],{"className":66079},[886],[888,66081,66082],{"xmlns":890,"display":1930},[892,66083,66084,66216],{},[895,66085,66086,66088,66094,66096,66098,66100,66102,66142,66144,66184,66186,66214],{},[898,66087,8309],{},[1824,66089,66090,66092],{},[898,66091,6849],{},[1761,66093,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,66095,1915],{"stretchy":1821},[898,66097,1828],{},[1761,66099,1920],{"stretchy":1821},[1761,66101,1909],{},[4379,66103,66104,66136],{},[895,66105,66106,66108,66114,66116,66118,66120,66122,66124,66126,66128,66130,66132,66134],{},[898,66107,1655],{},[1824,66109,66110,66112],{},[898,66111,6849],{},[1761,66113,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,66115,1915],{"stretchy":1821},[898,66117,1828],{},[1761,66119,1920],{"stretchy":1821},[1761,66121,2447],{},[898,66123,1828],{},[1761,66125,1885],{},[898,66127,1655],{},[898,66129,6849],{},[1761,66131,1915],{"stretchy":1821},[898,66133,1828],{},[1761,66135,1920],{"stretchy":1821},[1824,66137,66138,66140],{},[898,66139,1828],{},[1765,66141,2296],{},[1761,66143,1909],{},[4379,66145,66146,66178],{},[895,66147,66148,66150,66152,66154,66156,66158,66160,66162,66164,66166,66168,66170,66172,66174,66176],{},[898,66149,6889],{},[898,66151,6849],{},[1761,66153,1915],{"stretchy":1821},[898,66155,1828],{},[1761,66157,1920],{"stretchy":1821},[1761,66159,2447],{},[898,66161,1828],{},[1761,66163,1885],{},[898,66165,8309],{},[898,66167,6849],{},[1761,66169,1915],{"stretchy":1821},[898,66171,1828],{},[1761,66173,1920],{"stretchy":1821},[1761,66175,2447],{},[898,66177,1828],{},[1824,66179,66180,66182],{},[898,66181,1828],{},[1765,66183,2296],{},[1761,66185,1909],{},[4379,66187,66188,66212],{},[895,66189,66190,66192,66194,66196,66198,66200,66202,66204,66206,66208,66210],{},[898,66191,6889],{},[898,66193,6849],{},[1761,66195,1915],{"stretchy":1821},[898,66197,1828],{},[1761,66199,1920],{"stretchy":1821},[1761,66201,1885],{},[898,66203,8309],{},[898,66205,6849],{},[1761,66207,1915],{"stretchy":1821},[898,66209,1828],{},[1761,66211,1920],{"stretchy":1821},[898,66213,1828],{},[898,66215,1741],{"mathvariant":1969},[902,66217,66218],{"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}.",[724,66220,66221,66222,6699,66237,12146,66259,60799],{},"Nutnou podmínkou minima ",[883,66223,66225],{"className":66224},[886],[888,66226,66227],{"xmlns":890},[892,66228,66229,66235],{},[895,66230,66231,66233],{},[898,66232,8309],{},[898,66234,6849],{},[902,66236,59538],{"encoding":904},[883,66238,66240],{"className":66239},[886],[888,66241,66242],{"xmlns":890},[892,66243,66244,66256],{},[895,66245,66246,66252,66254],{},[1681,66247,66248,66250],{},[898,66249,1828],{},[1765,66251,1767],{},[1761,66253,1763],{},[1765,66255,1767],{},[902,66257,66258],{"encoding":904},"Q_0 > 0",[883,66260,66262],{"className":66261},[886],[888,66263,66264],{"xmlns":890},[892,66265,66266,66290],{},[895,66267,66268,66270,66276,66278,66284,66286,66288],{},[898,66269,8309],{},[1824,66271,66272,66274],{},[898,66273,6849],{},[1761,66275,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,66277,1915],{"stretchy":1821},[1681,66279,66280,66282],{},[898,66281,1828],{},[1765,66283,1767],{},[1761,66285,1920],{"stretchy":1821},[1761,66287,1909],{},[1765,66289,1767],{},[902,66291,66292],{"encoding":904},"AC'(Q_0) = 0",[883,66294,66296],{"className":66295},[886],[888,66297,66298],{"xmlns":890,"display":1930},[892,66299,66300,66385],{},[895,66301,66302,66342,66344,66346,66348,66351,66353,66355,66357,66359,66365,66367,66369,66371,66373,66375,66381,66383],{},[4379,66303,66304,66336],{},[895,66305,66306,66308,66310,66312,66318,66320,66322,66324,66326,66328,66334],{},[898,66307,6889],{},[898,66309,6849],{},[1761,66311,1915],{"stretchy":1821},[1681,66313,66314,66316],{},[898,66315,1828],{},[1765,66317,1767],{},[1761,66319,1920],{"stretchy":1821},[1761,66321,1885],{},[898,66323,8309],{},[898,66325,6849],{},[1761,66327,1915],{"stretchy":1821},[1681,66329,66330,66332],{},[898,66331,1828],{},[1765,66333,1767],{},[1761,66335,1920],{"stretchy":1821},[1681,66337,66338,66340],{},[898,66339,1828],{},[1765,66341,1767],{},[1761,66343,1909],{},[1765,66345,1767],{},[3315,66347],{"width":19322},[1761,66349,66350],{},"⟺",[3315,66352],{"width":19322},[898,66354,6889],{},[898,66356,6849],{},[1761,66358,1915],{"stretchy":1821},[1681,66360,66361,66363],{},[898,66362,1828],{},[1765,66364,1767],{},[1761,66366,1920],{"stretchy":1821},[1761,66368,1909],{},[898,66370,8309],{},[898,66372,6849],{},[1761,66374,1915],{"stretchy":1821},[1681,66376,66377,66379],{},[898,66378,1828],{},[1765,66380,1767],{},[1761,66382,1920],{"stretchy":1821},[898,66384,1741],{"mathvariant":1969},[902,66386,66387],{"encoding":904},"\\frac{MC(Q_0) - AC(Q_0)}{Q_0} = 0 \\quad\\Longleftrightarrow\\quad MC(Q_0) = AC(Q_0).",[724,66389,66390,1989,66393,65475,66408,66423,66424,66439,66440,12146,66457,66479,66480,66502],{},[38,66391,66392],{},"Geometrická interpretace.",[883,66394,66396],{"className":66395},[886],[888,66397,66398],{"xmlns":890},[892,66399,66400,66406],{},[895,66401,66402,66404],{},[898,66403,6889],{},[898,66405,6849],{},[902,66407,59270],{"encoding":904},[883,66409,66411],{"className":66410},[886],[888,66412,66413],{"xmlns":890},[892,66414,66415,66421],{},[895,66416,66417,66419],{},[898,66418,8309],{},[898,66420,6849],{},[902,66422,59538],{"encoding":904}," právě v bodě minima ",[883,66425,66427],{"className":66426},[886],[888,66428,66429],{"xmlns":890},[892,66430,66431,66437],{},[895,66432,66433,66435],{},[898,66434,8309],{},[898,66436,6849],{},[902,66438,59538],{"encoding":904}," (obrázek 3.10); nalevo od ",[883,66441,66443],{"className":66442},[886],[888,66444,66445],{"xmlns":890},[892,66446,66447,66455],{},[895,66448,66449],{},[1681,66450,66451,66453],{},[898,66452,1828],{},[1765,66454,1767],{},[902,66456,42331],{"encoding":904},[883,66458,66460],{"className":66459},[886],[888,66461,66462],{"xmlns":890},[892,66463,66464,66476],{},[895,66465,66466,66468,66470,66472,66474],{},[898,66467,6889],{},[898,66469,6849],{},[1761,66471,2058],{},[898,66473,8309],{},[898,66475,6849],{},[902,66477,66478],{"encoding":904},"MC \u003C AC"," (průměrné náklady klesají), napravo ",[883,66481,66483],{"className":66482},[886],[888,66484,66485],{"xmlns":890},[892,66486,66487,66499],{},[895,66488,66489,66491,66493,66495,66497],{},[898,66490,6889],{},[898,66492,6849],{},[1761,66494,1763],{},[898,66496,8309],{},[898,66498,6849],{},[902,66500,66501],{"encoding":904},"MC > AC"," (průměrné náklady rostou).",[724,66504,66505,66506,66548,66549,66566,66567,1741],{},"Za obvyklých ekonomických podmínek platí i obrácené tvrzení — jestliže ",[883,66507,66509],{"className":66508},[886],[888,66510,66511],{"xmlns":890},[892,66512,66513,66545],{},[895,66514,66515,66517,66519,66521,66527,66529,66531,66533,66535,66537,66543],{},[898,66516,8309],{},[898,66518,6849],{},[1761,66520,1915],{"stretchy":1821},[1681,66522,66523,66525],{},[898,66524,1828],{},[1765,66526,1767],{},[1761,66528,1920],{"stretchy":1821},[1761,66530,1909],{},[898,66532,6889],{},[898,66534,6849],{},[1761,66536,1915],{"stretchy":1821},[1681,66538,66539,66541],{},[898,66540,1828],{},[1765,66542,1767],{},[1761,66544,1920],{"stretchy":1821},[902,66546,66547],{"encoding":904},"AC(Q_0) = MC(Q_0)",", pak ",[883,66550,66552],{"className":66551},[886],[888,66553,66554],{"xmlns":890},[892,66555,66556,66564],{},[895,66557,66558],{},[1681,66559,66560,66562],{},[898,66561,1828],{},[1765,66563,1767],{},[902,66565,42331],{"encoding":904}," je bod minima. V praktických úlohách tedy postačí řešit rovnici ",[883,66568,66570],{"className":66569},[886],[888,66571,66572],{"xmlns":890},[892,66573,66574,66598],{},[895,66575,66576,66578,66580,66582,66584,66586,66588,66590,66592,66594,66596],{},[898,66577,8309],{},[898,66579,6849],{},[1761,66581,1915],{"stretchy":1821},[898,66583,1828],{},[1761,66585,1920],{"stretchy":1821},[1761,66587,1909],{},[898,66589,6889],{},[898,66591,6849],{},[1761,66593,1915],{"stretchy":1821},[898,66595,1828],{},[1761,66597,1920],{"stretchy":1821},[902,66599,66600],{"encoding":904},"AC(Q) = MC(Q)",[1636,66602,66603],{},[724,66604,66605,66607,66608,14432,66626,66647,66648,14432,66651,66672,66673,66688,66689,62016,66704,2162],{},[883,66606,4723],{}," Pozor — neplést s principem maxima zisku\nPro ",[38,66609,66610,66611],{},"minimum ",[883,66612,66614],{"className":66613},[886],[888,66615,66616],{"xmlns":890},[892,66617,66618,66624],{},[895,66619,66620,66622],{},[898,66621,8309],{},[898,66623,6849],{},[902,66625,59538],{"encoding":904},[883,66627,66629],{"className":66628},[886],[888,66630,66631],{"xmlns":890},[892,66632,66633,66645],{},[895,66634,66635,66637,66639,66641,66643],{},[898,66636,8309],{},[898,66638,6849],{},[1761,66640,1909],{},[898,66642,6889],{},[898,66644,6849],{},[902,66646,59201],{"encoding":904},", pro ",[38,66649,66650],{},"maximum zisku",[883,66652,66654],{"className":66653},[886],[888,66655,66656],{"xmlns":890},[892,66657,66658,66670],{},[895,66659,66660,66662,66664,66666,66668],{},[898,66661,6889],{},[898,66663,8051],{},[1761,66665,1909],{},[898,66667,6889],{},[898,66669,6849],{},[902,66671,59249],{"encoding":904},". Obě podmínky využívají ",[883,66674,66676],{"className":66675},[886],[888,66677,66678],{"xmlns":890},[892,66679,66680,66686],{},[895,66681,66682,66684],{},[898,66683,6889],{},[898,66685,6849],{},[902,66687,59270],{"encoding":904},", ale rovnají ho rozdílným veličinám (",[883,66690,66692],{"className":66691},[886],[888,66693,66694],{"xmlns":890},[892,66695,66696,66702],{},[895,66697,66698,66700],{},[898,66699,8309],{},[898,66701,6849],{},[902,66703,59538],{"encoding":904},[883,66705,66707],{"className":66706},[886],[888,66708,66709],{"xmlns":890},[892,66710,66711,66717],{},[895,66712,66713,66715],{},[898,66714,6889],{},[898,66716,8051],{},[902,66718,10679],{"encoding":904},[41374,66720,66722],{"id":66721},"příklad-37","Příklad 3.7",[724,66724,66725,61500,66727,66761,66762,66775,66776,66791],{},[38,66726,59965],{},[883,66728,66730],{"className":66729},[886],[888,66731,66732],{"xmlns":890},[892,66733,66734,66758],{},[895,66735,66736,66738,66740,66742,66748,66750,66752,66754,66756],{},[898,66737,1655],{},[898,66739,6849],{},[1761,66741,1909],{},[1824,66743,66744,66746],{},[898,66745,1828],{},[1765,66747,2296],{},[1761,66749,1964],{},[1765,66751,5486],{},[898,66753,1828],{},[1761,66755,1964],{},[1765,66757,9616],{},[902,66759,66760],{"encoding":904},"TC = Q^2 + 3Q + 36"," najděte ",[883,66763,66765],{"className":66764},[886],[888,66766,66767],{"xmlns":890},[892,66768,66769,66773],{},[895,66770,66771],{},[898,66772,1828],{},[902,66774,1828],{"encoding":904}," minimalizující ",[883,66777,66779],{"className":66778},[886],[888,66780,66781],{"xmlns":890},[892,66782,66783,66789],{},[895,66784,66785,66787],{},[898,66786,8309],{},[898,66788,6849],{},[902,66790,59538],{"encoding":904}," a ověřte princip (3.10).",[724,66793,66794,66796],{},[38,66795,26803],{}," Přímý výpočet:",[883,66798,66800],{"className":66799},[886],[888,66801,66802],{"xmlns":890,"display":1930},[892,66803,66804,66906],{},[895,66805,66806,66808,66810,66812,66834,66836,66838,66840,66842,66844,66850,66852,66854,66856,66858,66860,66866,66868,66870,66872,66882,66884,66904],{},[898,66807,8309],{},[898,66809,6849],{},[1761,66811,1909],{},[4379,66813,66814,66832],{},[895,66815,66816,66822,66824,66826,66828,66830],{},[1824,66817,66818,66820],{},[898,66819,1828],{},[1765,66821,2296],{},[1761,66823,1964],{},[1765,66825,5486],{},[898,66827,1828],{},[1761,66829,1964],{},[1765,66831,9616],{},[898,66833,1828],{},[1761,66835,1909],{},[898,66837,1828],{},[1761,66839,1964],{},[1765,66841,5486],{},[1761,66843,1964],{},[4379,66845,66846,66848],{},[1765,66847,9616],{},[898,66849,1828],{},[1761,66851,1834],{"separator":1833},[3315,66853],{"width":3317},[1761,66855,1915],{"stretchy":1821},[898,66857,8309],{},[898,66859,6849],{},[1824,66861,66862,66864],{},[1761,66863,1920],{"stretchy":1821},[1761,66865,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,66867,1909],{},[1765,66869,1945],{},[1761,66871,1885],{},[4379,66873,66874,66876],{},[1765,66875,9616],{},[1824,66877,66878,66880],{},[898,66879,1828],{},[1765,66881,2296],{},[1761,66883,1909],{},[4379,66885,66886,66898],{},[895,66887,66888,66894,66896],{},[1824,66889,66890,66892],{},[898,66891,1828],{},[1765,66893,2296],{},[1761,66895,1885],{},[1765,66897,9616],{},[1824,66899,66900,66902],{},[898,66901,1828],{},[1765,66903,2296],{},[898,66905,1741],{"mathvariant":1969},[902,66907,66908],{"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}.",[724,66910,66911,66951,66952,66976,66977,67027,67028,1741],{},[883,66912,66914],{"className":66913},[886],[888,66915,66916],{"xmlns":890},[892,66917,66918,66948],{},[895,66919,66920,66922,66924,66926,66932,66934,66936,66938,66944,66946],{},[1761,66921,1915],{"stretchy":1821},[898,66923,8309],{},[898,66925,6849],{},[1824,66927,66928,66930],{},[1761,66929,1920],{"stretchy":1821},[1761,66931,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,66933,1909],{},[1765,66935,1767],{},[1761,66937,8044],{},[1681,66939,66940,66942],{},[898,66941,1828],{},[1765,66943,1945],{},[1761,66945,1909],{},[1765,66947,2340],{},[902,66949,66950],{"encoding":904},"(AC)' = 0 \\Rightarrow Q_1 = 6"," (smysluplné), ",[883,66953,66955],{"className":66954},[886],[888,66956,66957],{"xmlns":890},[892,66958,66959,66973],{},[895,66960,66961,66967,66969,66971],{},[1681,66962,66963,66965],{},[898,66964,1828],{},[1765,66966,2296],{},[1761,66968,1909],{},[1761,66970,1885],{},[1765,66972,2340],{},[902,66974,66975],{"encoding":904},"Q_2 = -6"," (vyloučeno). ",[883,66978,66980],{"className":66979},[886],[888,66981,66982],{"xmlns":890},[892,66983,66984,67024],{},[895,66985,66986,66988,66990,66992,67002,67004,67006,67008,67010,67018,67020,67022],{},[1761,66987,1915],{"stretchy":1821},[898,66989,8309],{},[898,66991,6849],{},[1824,66993,66994,66996],{},[1761,66995,1920],{"stretchy":1821},[895,66997,66998,67000],{},[1761,66999,6459],{"mathvariant":1969},[1761,67001,6459],{"mathvariant":1969},[1761,67003,1915],{"stretchy":1821},[1765,67005,2340],{},[1761,67007,1920],{"stretchy":1821},[1761,67009,1909],{},[6411,67011,67012],{"scriptlevel":1767,"displaystyle":1821},[4379,67013,67014,67016],{},[1765,67015,1945],{},[1765,67017,5486],{},[1761,67019,1763],{},[1765,67021,1767],{},[1761,67023,8044],{},[902,67025,67026],{"encoding":904},"(AC)''(6) = \\tfrac{1}{3} > 0 \\Rightarrow"," minimum. ",[883,67029,67031],{"className":67030},[886],[888,67032,67033],{"xmlns":890},[892,67034,67035,67051],{},[895,67036,67037,67039,67041,67043,67045,67047,67049],{},[898,67038,8309],{},[898,67040,6849],{},[1761,67042,1915],{"stretchy":1821},[1765,67044,2340],{},[1761,67046,1920],{"stretchy":1821},[1761,67048,1909],{},[1765,67050,5433],{},[902,67052,67053],{"encoding":904},"AC(6) = 15",[724,67055,67056,67057,67083,67084,2506],{},"Pomocí principu: ",[883,67058,67060],{"className":67059},[886],[888,67061,67062],{"xmlns":890},[892,67063,67064,67080],{},[895,67065,67066,67068,67070,67072,67074,67076,67078],{},[898,67067,6889],{},[898,67069,6849],{},[1761,67071,1909],{},[1765,67073,2296],{},[898,67075,1828],{},[1761,67077,1964],{},[1765,67079,5486],{},[902,67081,67082],{"encoding":904},"MC = 2Q + 3",", rovnice ",[883,67085,67087],{"className":67086},[886],[888,67088,67089],{"xmlns":890},[892,67090,67091,67103],{},[895,67092,67093,67095,67097,67099,67101],{},[898,67094,8309],{},[898,67096,6849],{},[1761,67098,1909],{},[898,67100,6889],{},[898,67102,6849],{},[902,67104,59201],{"encoding":904},[883,67106,67108],{"className":67107},[886],[888,67109,67110],{"xmlns":890,"display":1930},[892,67111,67112,67214],{},[895,67113,67114,67136,67138,67140,67142,67144,67146,67148,67150,67152,67158,67160,67162,67164,67166,67168,67170,67172,67178,67180,67182,67184,67186,67188,67190,67196,67198,67200,67202,67204,67206,67208,67210,67212],{},[4379,67115,67116,67134],{},[895,67117,67118,67124,67126,67128,67130,67132],{},[1824,67119,67120,67122],{},[898,67121,1828],{},[1765,67123,2296],{},[1761,67125,1964],{},[1765,67127,5486],{},[898,67129,1828],{},[1761,67131,1964],{},[1765,67133,9616],{},[898,67135,1828],{},[1761,67137,1909],{},[1765,67139,2296],{},[898,67141,1828],{},[1761,67143,1964],{},[1765,67145,5486],{},[2761,67147,8041],{},[1761,67149,8044],{},[2761,67151,8041],{},[1824,67153,67154,67156],{},[898,67155,1828],{},[1765,67157,2296],{},[1761,67159,1964],{},[1765,67161,5486],{},[898,67163,1828],{},[1761,67165,1964],{},[1765,67167,9616],{},[1761,67169,1909],{},[1765,67171,2296],{},[1824,67173,67174,67176],{},[898,67175,1828],{},[1765,67177,2296],{},[1761,67179,1964],{},[1765,67181,5486],{},[898,67183,1828],{},[2761,67185,8041],{},[1761,67187,8044],{},[2761,67189,8041],{},[1824,67191,67192,67194],{},[898,67193,1828],{},[1765,67195,2296],{},[1761,67197,1909],{},[1765,67199,9616],{},[2761,67201,8041],{},[1761,67203,8044],{},[2761,67205,8041],{},[898,67207,1828],{},[1761,67209,1909],{},[1765,67211,2340],{},[1761,67213,1834],{"separator":1833},[902,67215,67216],{"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,",[724,67218,67219,67220,67258],{},"a ",[883,67221,67223],{"className":67222},[886],[888,67224,67225],{"xmlns":890},[892,67226,67227,67255],{},[895,67228,67229,67231,67233,67235,67237,67239,67241,67243,67245,67247,67249,67251,67253],{},[898,67230,8309],{},[898,67232,6849],{},[1761,67234,1915],{"stretchy":1821},[1765,67236,2340],{},[1761,67238,1920],{"stretchy":1821},[1761,67240,1909],{},[898,67242,6889],{},[898,67244,6849],{},[1761,67246,1915],{"stretchy":1821},[1765,67248,2340],{},[1761,67250,1920],{"stretchy":1821},[1761,67252,1909],{},[1765,67254,5433],{},[902,67256,67257],{"encoding":904},"AC(6) = MC(6) = 15",". Oba postupy dávají stejný výsledek.",[198,67260,67262],{"id":67261},"princip-minimalizace-průměrných-variabilních-nákladů","Princip minimalizace průměrných variabilních nákladů",[724,67264,67265,67266,2506],{},"Analogicky pro ",[883,67267,67269],{"className":67268},[886],[888,67270,67271],{"xmlns":890},[892,67272,67273,67281],{},[895,67274,67275,67277,67279],{},[898,67276,8309],{},[898,67278,44359],{},[898,67280,6849],{},[902,67282,59289],{"encoding":904},[883,67284,67286],{"className":67285},[886],[888,67287,67288],{"xmlns":890,"display":1930},[892,67289,67290,67341],{},[24787,67291,67292],{"width":32101},[24792,67293,67294,67296,67334,67336],{},[24795,67295],{"width":32106},[24795,67297,67298],{},[895,67299,67300,67302,67304,67306,67308,67314,67316,67318,67320,67322,67324,67330,67332],{},[898,67301,8309],{},[898,67303,44359],{},[898,67305,6849],{},[1761,67307,1915],{"stretchy":1821},[1681,67309,67310,67312],{},[898,67311,1828],{},[1765,67313,1767],{},[1761,67315,1920],{"stretchy":1821},[1761,67317,1909],{},[898,67319,6889],{},[898,67321,6849],{},[1761,67323,1915],{"stretchy":1821},[1681,67325,67326,67328],{},[898,67327,1828],{},[1765,67329,1767],{},[1761,67331,1920],{"stretchy":1821},[898,67333,1741],{"mathvariant":1969},[24795,67335],{"width":32106},[24795,67337,67338],{},[2761,67339,67340],{},"(3.11)",[902,67342,67343],{"encoding":904},"AVC(Q_0) = MC(Q_0).\n\\tag{3.11}",[1636,67345,67346],{},[724,67347,67348,66024,67350],{},[883,67349,60422],{},[38,67351,67352,67353,67370],{},"V bodě minima průměrných variabilních nákladů se ",[883,67354,67356],{"className":67355},[886],[888,67357,67358],{"xmlns":890},[892,67359,67360,67368],{},[895,67361,67362,67364,67366],{},[898,67363,8309],{},[898,67365,44359],{},[898,67367,6849],{},[902,67369,59289],{"encoding":904}," rovnají mezním nákladům.",[724,67372,67373,67374,67396,67397,1741],{},"Odvození je analogické (úloha 3.14). V obrázku 3.10 odpovídá ",[883,67375,67377],{"className":67376},[886],[888,67378,67379],{"xmlns":890},[892,67380,67381,67393],{},[895,67382,67383,67389,67391],{},[1681,67384,67385,67387],{},[898,67386,1828],{},[1765,67388,1767],{},[1761,67390,1909],{},[1765,67392,57179],{},[902,67394,67395],{"encoding":904},"Q_0 = 2{,}5",". Za obvyklých podmínek platí i obrácené tvrzení — postačí řešit rovnici ",[883,67398,67400],{"className":67399},[886],[888,67401,67402],{"xmlns":890},[892,67403,67404,67430],{},[895,67405,67406,67408,67410,67412,67414,67416,67418,67420,67422,67424,67426,67428],{},[898,67407,8309],{},[898,67409,44359],{},[898,67411,6849],{},[1761,67413,1915],{"stretchy":1821},[898,67415,1828],{},[1761,67417,1920],{"stretchy":1821},[1761,67419,1909],{},[898,67421,6889],{},[898,67423,6849],{},[1761,67425,1915],{"stretchy":1821},[898,67427,1828],{},[1761,67429,1920],{"stretchy":1821},[902,67431,67432],{"encoding":904},"AVC(Q) = MC(Q)",[115,67434,67436],{"id":67435},"zisk-a-body-zvratu","Zisk a body zvratu",[724,67438,67439,1989,67442,67458],{},[38,67440,67441],{},"Zisk",[883,67443,67445],{"className":67444},[886],[888,67446,67447],{"xmlns":890},[892,67448,67449,67455],{},[895,67450,67451,67453],{},[898,67452,1839],{},[898,67454,8051],{},[902,67456,67457],{"encoding":904},"PR"," (profit) je rozdíl celkového příjmu a celkových nákladů:",[883,67460,67462],{"className":67461},[886],[888,67463,67464],{"xmlns":890,"display":1930},[892,67465,67466,67525],{},[24787,67467,67468],{"width":32101},[24792,67469,67470,67472,67518,67520],{},[24795,67471],{"width":32106},[24795,67473,67474],{},[895,67475,67476,67478,67480,67482,67484,67486,67488,67490,67492,67494,67496,67498,67500,67502,67504,67506,67508,67510,67512,67514,67516],{},[898,67477,1839],{},[898,67479,8051],{},[1761,67481,1909],{},[898,67483,1839],{},[898,67485,8051],{},[1761,67487,1915],{"stretchy":1821},[898,67489,1828],{},[1761,67491,1920],{"stretchy":1821},[1761,67493,1909],{},[898,67495,1655],{},[898,67497,8051],{},[1761,67499,1915],{"stretchy":1821},[898,67501,1828],{},[1761,67503,1920],{"stretchy":1821},[1761,67505,1885],{},[898,67507,1655],{},[898,67509,6849],{},[1761,67511,1915],{"stretchy":1821},[898,67513,1828],{},[1761,67515,1920],{"stretchy":1821},[898,67517,1741],{"mathvariant":1969},[24795,67519],{"width":32106},[24795,67521,67522],{},[2761,67523,67524],{},"(3.12)",[902,67526,67527],{"encoding":904},"PR = PR(Q) = TR(Q) - TC(Q).\n\\tag{3.12}",[724,67529,67530,67531,2068,67546,47631,67561,67563,67564,67567,67568,67584,67585,67600,67601,67616,67617,1343,67630,67643,67644,1343,67662,67680,67681,3927,67684,67687,67688,1348,67710,12146,67732,67754,67755,12146,67785,67807],{},"Body rovnosti ",[883,67532,67534],{"className":67533},[886],[888,67535,67536],{"xmlns":890},[892,67537,67538,67544],{},[895,67539,67540,67542],{},[898,67541,1655],{},[898,67543,8051],{},[902,67545,8151],{"encoding":904},[883,67547,67549],{"className":67548},[886],[888,67550,67551],{"xmlns":890},[892,67552,67553,67559],{},[895,67554,67555,67557],{},[898,67556,1655],{},[898,67558,6849],{},[902,67560,7310],{"encoding":904},[38,67562,59705],{}," (též vyrovnání, ",[614,67565,67566],{},"break-even points","). V nejjednodušším modelu (lineární poptávka, konstantní ",[883,67569,67571],{"className":67570},[886],[888,67572,67573],{"xmlns":890},[892,67574,67575,67581],{},[895,67576,67577,67579],{},[898,67578,44359],{},[898,67580,6849],{},[902,67582,67583],{"encoding":904},"VC",") je ",[883,67586,67588],{"className":67587},[886],[888,67589,67590],{"xmlns":890},[892,67591,67592,67598],{},[895,67593,67594,67596],{},[898,67595,1655],{},[898,67597,8051],{},[902,67599,8151],{"encoding":904}," kvadratická a ",[883,67602,67604],{"className":67603},[886],[888,67605,67606],{"xmlns":890},[892,67607,67608,67614],{},[895,67609,67610,67612],{},[898,67611,1655],{},[898,67613,6849],{},[902,67615,7310],{"encoding":904}," lineární (obrázek 3.11). Křivky se protínají v bodech ",[883,67618,67620],{"className":67619},[886],[888,67621,67622],{"xmlns":890},[892,67623,67624,67628],{},[895,67625,67626],{},[898,67627,8309],{},[902,67629,8309],{"encoding":904},[883,67631,67633],{"className":67632},[886],[888,67634,67635],{"xmlns":890},[892,67636,67637,67641],{},[895,67638,67639],{},[898,67640,27286],{},[902,67642,27286],{"encoding":904}," odpovídajících množstvím ",[883,67645,67647],{"className":67646},[886],[888,67648,67649],{"xmlns":890},[892,67650,67651,67659],{},[895,67652,67653],{},[1681,67654,67655,67657],{},[898,67656,1828],{},[898,67658,8309],{},[902,67660,67661],{"encoding":904},"Q_A",[883,67663,67665],{"className":67664},[886],[888,67666,67667],{"xmlns":890},[892,67668,67669,67677],{},[895,67670,67671],{},[1681,67672,67673,67675],{},[898,67674,1828],{},[898,67676,27286],{},[902,67678,67679],{"encoding":904},"Q_B"," — firma je na ",[38,67682,67683],{},"prahu rentability",[614,67685,67686],{},"break even","). Pro ",[883,67689,67691],{"className":67690},[886],[888,67692,67693],{"xmlns":890},[892,67694,67695,67707],{},[895,67696,67697,67699,67701],{},[898,67698,1828],{},[1761,67700,2058],{},[1681,67702,67703,67705],{},[898,67704,1828],{},[898,67706,8309],{},[902,67708,67709],{"encoding":904},"Q \u003C Q_A",[883,67711,67713],{"className":67712},[886],[888,67714,67715],{"xmlns":890},[892,67716,67717,67729],{},[895,67718,67719,67721,67723],{},[898,67720,1828],{},[1761,67722,1763],{},[1681,67724,67725,67727],{},[898,67726,1828],{},[898,67728,27286],{},[902,67730,67731],{"encoding":904},"Q > Q_B",[883,67733,67735],{"className":67734},[886],[888,67736,67737],{"xmlns":890},[892,67738,67739,67751],{},[895,67740,67741,67743,67745,67747,67749],{},[898,67742,1655],{},[898,67744,6849],{},[1761,67746,1763],{},[898,67748,1655],{},[898,67750,8051],{},[902,67752,67753],{"encoding":904},"TC > TR"," (ztráta); pro ",[883,67756,67758],{"className":67757},[886],[888,67759,67760],{"xmlns":890},[892,67761,67762,67782],{},[895,67763,67764,67770,67772,67774,67776],{},[1681,67765,67766,67768],{},[898,67767,1828],{},[898,67769,8309],{},[1761,67771,2058],{},[898,67773,1828],{},[1761,67775,2058],{},[1681,67777,67778,67780],{},[898,67779,1828],{},[898,67781,27286],{},[902,67783,67784],{"encoding":904},"Q_A \u003C Q \u003C Q_B",[883,67786,67788],{"className":67787},[886],[888,67789,67790],{"xmlns":890},[892,67791,67792,67804],{},[895,67793,67794,67796,67798,67800,67802],{},[898,67795,1655],{},[898,67797,8051],{},[1761,67799,1763],{},[898,67801,1655],{},[898,67803,6849],{},[902,67805,67806],{"encoding":904},"TR > TC"," (zisk).",[1636,67809,67810],{},[724,67811,67812,67814],{},[883,67813,1642],{}," 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.",[724,67816,67817,67818,67844],{},"Body zvratu jsou řešení rovnice ",[883,67819,67821],{"className":67820},[886],[888,67822,67823],{"xmlns":890},[892,67824,67825,67841],{},[895,67826,67827,67829,67831,67833,67835,67837,67839],{},[898,67828,1839],{},[898,67830,8051],{},[1761,67832,1915],{"stretchy":1821},[898,67834,1828],{},[1761,67836,1920],{"stretchy":1821},[1761,67838,1909],{},[1765,67840,1767],{},[902,67842,67843],{"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.",[724,67846,67847],{},[3991,67848],{"alt":67849,"className":67850,"src":67851},"imek-tr-tc-body-zvratu",[210,3995],"\u002Fwiki-assets\u002Fimek-tr-tc-body-zvratu.jpeg",[724,67853,67854],{},[614,67855,67856,67857,67872,67873,67888,67889,2068,67902,47355,67915,67928,67929,2068,67946,67963,67964,67984,67985,2068,68000,10518,68015,68044],{},"Obrázek 3.11: Body zvratu — křivky ",[883,67858,67860],{"className":67859},[886],[888,67861,67862],{"xmlns":890},[892,67863,67864,67870],{},[895,67865,67866,67868],{},[898,67867,1655],{},[898,67869,8051],{},[902,67871,8151],{"encoding":904}," (obrácená parabola) a ",[883,67874,67876],{"className":67875},[886],[888,67877,67878],{"xmlns":890},[892,67879,67880,67886],{},[895,67881,67882,67884],{},[898,67883,1655],{},[898,67885,6849],{},[902,67887,7310],{"encoding":904}," (přímka) se protínají v bodech ",[883,67890,67892],{"className":67891},[886],[888,67893,67894],{"xmlns":890},[892,67895,67896,67900],{},[895,67897,67898],{},[898,67899,8309],{},[902,67901,8309],{"encoding":904},[883,67903,67905],{"className":67904},[886],[888,67906,67907],{"xmlns":890},[892,67908,67909,67913],{},[895,67910,67911],{},[898,67912,27286],{},[902,67914,27286],{"encoding":904},[883,67916,67918],{"className":67917},[886],[888,67919,67920],{"xmlns":890},[892,67921,67922,67926],{},[895,67923,67924],{},[898,67925,1828],{},[902,67927,1828],{"encoding":904}," v hodnotách ",[883,67930,67932],{"className":67931},[886],[888,67933,67934],{"xmlns":890},[892,67935,67936,67944],{},[895,67937,67938],{},[1681,67939,67940,67942],{},[898,67941,1828],{},[898,67943,8309],{},[902,67945,67661],{"encoding":904},[883,67947,67949],{"className":67948},[886],[888,67950,67951],{"xmlns":890},[892,67952,67953,67961],{},[895,67954,67955],{},[1681,67956,67957,67959],{},[898,67958,1828],{},[898,67960,27286],{},[902,67962,67679],{"encoding":904},"; maximum zisku leží mezi nimi v bodě ",[883,67965,67967],{"className":67966},[886],[888,67968,67969],{"xmlns":890},[892,67970,67971,67981],{},[895,67972,67973],{},[1681,67974,67975,67977,67979],{},[898,67976,1828],{},[898,67978,60175],{},[1761,67980,60178],{},[902,67982,67983],{"encoding":904},"Q_{\\max}","; svislá vzdálenost mezi ",[883,67986,67988],{"className":67987},[886],[888,67989,67990],{"xmlns":890},[892,67991,67992,67998],{},[895,67993,67994,67996],{},[898,67995,1655],{},[898,67997,8051],{},[902,67999,8151],{"encoding":904},[883,68001,68003],{"className":68002},[886],[888,68004,68005],{"xmlns":890},[892,68006,68007,68013],{},[895,68008,68009,68011],{},[898,68010,1655],{},[898,68012,6849],{},[902,68014,7310],{"encoding":904},[883,68016,68018],{"className":68017},[886],[888,68019,68020],{"xmlns":890},[892,68021,68022,68042],{},[895,68023,68024,68030,68032,68034,68036],{},[1681,68025,68026,68028],{},[898,68027,1828],{},[898,68029,8309],{},[1761,68031,2058],{},[898,68033,1828],{},[1761,68035,2058],{},[1681,68037,68038,68040],{},[898,68039,1828],{},[898,68041,27286],{},[902,68043,67784],{"encoding":904}," vyznačuje zisk.",[41374,68046,68048],{"id":68047},"příklad-38","Příklad 3.8",[724,68050,68051,68053,68054,1343,68074,1343,68100,68126],{},[38,68052,59965],{}," Dáno ",[883,68055,68057],{"className":68056},[886],[888,68058,68059],{"xmlns":890},[892,68060,68061,68071],{},[895,68062,68063,68065,68067,68069],{},[898,68064,14474],{},[898,68066,6849],{},[1761,68068,1909],{},[1765,68070,2318],{},[902,68072,68073],{"encoding":904},"FC = 4",[883,68075,68077],{"className":68076},[886],[888,68078,68079],{"xmlns":890},[892,68080,68081,68097],{},[895,68082,68083,68085,68087,68089,68091],{},[898,68084,1655],{},[898,68086,44359],{},[898,68088,6849],{},[1761,68090,1909],{},[1824,68092,68093,68095],{},[898,68094,1828],{},[1765,68096,2296],{},[902,68098,68099],{"encoding":904},"TVC = Q^2",[883,68101,68103],{"className":68102},[886],[888,68104,68105],{"xmlns":890},[892,68106,68107,68123],{},[895,68108,68109,68111,68113,68115,68117,68119,68121],{},[898,68110,1839],{},[1761,68112,1909],{},[1761,68114,1885],{},[1765,68116,2296],{},[898,68118,1828],{},[1761,68120,1964],{},[1765,68122,8056],{},[902,68124,68125],{"encoding":904},"P = -2Q + 9",". Určete zisk, body zvratu a bod maxima zisku.",[724,68128,68129,68131],{},[38,68130,26803],{}," Celkové náklady a příjem:",[883,68133,68135],{"className":68134},[886],[888,68136,68137],{"xmlns":890,"display":1930},[892,68138,68139,68205],{},[895,68140,68141,68143,68145,68147,68149,68151,68157,68159,68161,68163,68165,68167,68169,68171,68173,68175,68177,68179,68181,68183,68185,68187,68189,68191,68197,68199,68201,68203],{},[898,68142,1655],{},[898,68144,6849],{},[1761,68146,1909],{},[1765,68148,2318],{},[1761,68150,1964],{},[1824,68152,68153,68155],{},[898,68154,1828],{},[1765,68156,2296],{},[1761,68158,1834],{"separator":1833},[3315,68160],{"width":3317},[898,68162,1655],{},[898,68164,8051],{},[1761,68166,1909],{},[898,68168,1828],{},[1761,68170,2447],{},[1761,68172,1915],{"stretchy":1821},[1761,68174,1885],{},[1765,68176,2296],{},[898,68178,1828],{},[1761,68180,1964],{},[1765,68182,8056],{},[1761,68184,1920],{"stretchy":1821},[1761,68186,1909],{},[1761,68188,1885],{},[1765,68190,2296],{},[1824,68192,68193,68195],{},[898,68194,1828],{},[1765,68196,2296],{},[1761,68198,1964],{},[1765,68200,8056],{},[898,68202,1828],{},[898,68204,1741],{"mathvariant":1969},[902,68206,68207],{"encoding":904},"TC = 4 + Q^2, \\qquad TR = Q \\cdot (-2Q + 9) = -2Q^2 + 9Q.",[724,68209,68210],{},"Zisk dle (3.12):",[883,68212,68214],{"className":68213},[886],[888,68215,68216],{"xmlns":890,"display":1930},[892,68217,68218,68296],{},[895,68219,68220,68222,68224,68226,68228,68230,68232,68234,68236,68238,68240,68242,68244,68250,68252,68254,68256,68258,68260,68262,68264,68266,68272,68274,68276,68278,68280,68286,68288,68290,68292,68294],{},[898,68221,1839],{},[898,68223,8051],{},[1761,68225,1909],{},[898,68227,1655],{},[898,68229,8051],{},[1761,68231,1885],{},[898,68233,1655],{},[898,68235,6849],{},[1761,68237,1909],{},[1761,68239,1915],{"stretchy":1821},[1761,68241,1885],{},[1765,68243,2296],{},[1824,68245,68246,68248],{},[898,68247,1828],{},[1765,68249,2296],{},[1761,68251,1964],{},[1765,68253,8056],{},[898,68255,1828],{},[1761,68257,1920],{"stretchy":1821},[1761,68259,1885],{},[1761,68261,1915],{"stretchy":1821},[1765,68263,2318],{},[1761,68265,1964],{},[1824,68267,68268,68270],{},[898,68269,1828],{},[1765,68271,2296],{},[1761,68273,1920],{"stretchy":1821},[1761,68275,1909],{},[1761,68277,1885],{},[1765,68279,5486],{},[1824,68281,68282,68284],{},[898,68283,1828],{},[1765,68285,2296],{},[1761,68287,1964],{},[1765,68289,8056],{},[898,68291,1828],{},[1761,68293,1885],{},[1765,68295,63297],{},[902,68297,68298],{"encoding":904},"PR = TR - TC = (-2Q^2 + 9Q) - (4 + Q^2) = -3Q^2 + 9Q - 4.",[724,68300,68301,68304,68305,21610,68341,2506],{},[38,68302,68303],{},"Body zvratu"," jsou kořeny rovnice ",[883,68306,68308],{"className":68307},[886],[888,68309,68310],{"xmlns":890},[892,68311,68312,68338],{},[895,68313,68314,68316,68318,68324,68326,68328,68330,68332,68334,68336],{},[1761,68315,1885],{},[1765,68317,5486],{},[1824,68319,68320,68322],{},[898,68321,1828],{},[1765,68323,2296],{},[1761,68325,1964],{},[1765,68327,8056],{},[898,68329,1828],{},[1761,68331,1885],{},[1765,68333,2318],{},[1761,68335,1909],{},[1765,68337,1767],{},[902,68339,68340],{"encoding":904},"-3Q^2 + 9Q - 4 = 0",[883,68342,68344],{"className":68343},[886],[888,68345,68346],{"xmlns":890},[892,68347,68348,68372],{},[895,68349,68350,68352,68358,68360,68362,68364,68366,68368,68370],{},[1765,68351,5486],{},[1824,68353,68354,68356],{},[898,68355,1828],{},[1765,68357,2296],{},[1761,68359,1885],{},[1765,68361,8056],{},[898,68363,1828],{},[1761,68365,1964],{},[1765,68367,2318],{},[1761,68369,1909],{},[1765,68371,1767],{},[902,68373,68374],{"encoding":904},"3Q^2 - 9Q + 4 = 0",[883,68376,68378],{"className":68377},[886],[888,68379,68380],{"xmlns":890,"display":1930},[892,68381,68382,68439],{},[895,68383,68384,68396,68398,68421,68423,68437],{},[1681,68385,68386,68388],{},[898,68387,1828],{},[895,68389,68390,68392,68394],{},[1765,68391,1945],{},[1761,68393,1834],{"separator":1833},[1765,68395,2296],{},[1761,68397,1909],{},[4379,68399,68400,68419],{},[895,68401,68402,68404,68407],{},[1765,68403,8056],{},[1761,68405,68406],{},"±",[12161,68408,68409],{},[895,68410,68411,68414,68416],{},[1765,68412,68413],{},"81",[1761,68415,1885],{},[1765,68417,68418],{},"48",[1765,68420,2340],{},[1761,68422,1909],{},[4379,68424,68425,68435],{},[895,68426,68427,68429,68431],{},[1765,68428,8056],{},[1761,68430,68406],{},[12161,68432,68433],{},[1765,68434,12993],{},[1765,68436,2340],{},[1761,68438,1834],{"separator":1833},[902,68440,68441],{"encoding":904},"Q_{1,2} = \\frac{9 \\pm \\sqrt{81 - 48}}{6} = \\frac{9 \\pm \\sqrt{33}}{6},",[724,68443,68444,68445,2068,68468,1741],{},"numericky ",[883,68446,68448],{"className":68447},[886],[888,68449,68450],{"xmlns":890},[892,68451,68452,68465],{},[895,68453,68454,68460,68462],{},[1681,68455,68456,68458],{},[898,68457,1828],{},[1765,68459,1945],{},[1761,68461,9945],{},[1765,68463,68464],{},"0,543",[902,68466,68467],{"encoding":904},"Q_1 \\doteq 0{,}543",[883,68469,68471],{"className":68470},[886],[888,68472,68473],{"xmlns":890},[892,68474,68475,68488],{},[895,68476,68477,68483,68485],{},[1681,68478,68479,68481],{},[898,68480,1828],{},[1765,68482,2296],{},[1761,68484,9945],{},[1765,68486,68487],{},"2,457",[902,68489,68490],{"encoding":904},"Q_2 \\doteq 2{,}457",[724,68492,68493,1989,68496,11596,68541,21610,68575,68593],{},[38,68494,68495],{},"Maximum zisku.",[883,68497,68499],{"className":68498},[886],[888,68500,68501],{"xmlns":890},[892,68502,68503,68538],{},[895,68504,68505,68507,68513,68515,68517,68519,68521,68523,68525,68527,68529,68531,68533,68535],{},[898,68506,1839],{},[1824,68508,68509,68511],{},[898,68510,8051],{},[1761,68512,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,68514,1909],{},[1761,68516,1885],{},[1765,68518,2340],{},[898,68520,1828],{},[1761,68522,1964],{},[1765,68524,8056],{},[1761,68526,1909],{},[1765,68528,1767],{},[1761,68530,8044],{},[898,68532,1828],{},[1761,68534,1909],{},[1765,68536,68537],{},"1,5",[902,68539,68540],{"encoding":904},"PR' = -6Q + 9 = 0 \\Rightarrow Q = 1{,}5",[883,68542,68544],{"className":68543},[886],[888,68545,68546],{"xmlns":890},[892,68547,68548,68572],{},[895,68549,68550,68552,68562,68564,68566,68568,68570],{},[898,68551,1839],{},[1824,68553,68554,68556],{},[898,68555,8051],{},[895,68557,68558,68560],{},[1761,68559,6459],{"mathvariant":1969},[1761,68561,6459],{"mathvariant":1969},[1761,68563,1909],{},[1761,68565,1885],{},[1765,68567,2340],{},[1761,68569,2058],{},[1765,68571,1767],{},[902,68573,68574],{"encoding":904},"PR'' = -6 \u003C 0",[883,68576,68578],{"className":68577},[886],[888,68579,68580],{"xmlns":890},[892,68581,68582,68590],{},[895,68583,68584,68586,68588],{},[898,68585,1828],{},[1761,68587,1909],{},[1765,68589,68537],{},[902,68591,68592],{"encoding":904},"Q = 1{,}5"," je bod maxima s hodnotou",[883,68595,68597],{"className":68596},[886],[888,68598,68599],{"xmlns":890,"display":1930},[892,68600,68601,68664],{},[895,68602,68603,68605,68607,68609,68611,68613,68615,68617,68619,68621,68623,68625,68631,68633,68635,68637,68639,68641,68643,68645,68647,68650,68652,68655,68657,68659,68661],{},[898,68604,1839],{},[898,68606,8051],{},[1761,68608,1915],{"stretchy":1821},[1765,68610,68537],{},[1761,68612,1920],{"stretchy":1821},[1761,68614,1909],{},[1761,68616,1885],{},[1765,68618,5486],{},[1761,68620,2447],{},[1761,68622,1915],{"stretchy":1821},[1765,68624,68537],{},[1824,68626,68627,68629],{},[1761,68628,1920],{"stretchy":1821},[1765,68630,2296],{},[1761,68632,1964],{},[1765,68634,8056],{},[1761,68636,2447],{},[1765,68638,68537],{},[1761,68640,1885],{},[1765,68642,2318],{},[1761,68644,1909],{},[1761,68646,1885],{},[1765,68648,68649],{},"6,75",[1761,68651,1964],{},[1765,68653,68654],{},"13,5",[1761,68656,1885],{},[1765,68658,2318],{},[1761,68660,1909],{},[1765,68662,68663],{},"2,75.",[902,68665,68666],{"encoding":904},"PR(1{,}5) = -3 \\cdot (1{,}5)^2 + 9 \\cdot 1{,}5 - 4 = -6{,}75 + 13{,}5 - 4 = 2{,}75.",[724,68668,68669,68670,1343,68715,68768,68769,68787],{},"Pro srovnání maximum celkového příjmu (bez ohledu na náklady): ",[883,68671,68673],{"className":68672},[886],[888,68674,68675],{"xmlns":890},[892,68676,68677,68712],{},[895,68678,68679,68681,68687,68689,68691,68693,68695,68697,68699,68701,68703,68705,68707,68709],{},[898,68680,1655],{},[1824,68682,68683,68685],{},[898,68684,8051],{},[1761,68686,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,68688,1909],{},[1761,68690,1885],{},[1765,68692,2318],{},[898,68694,1828],{},[1761,68696,1964],{},[1765,68698,8056],{},[1761,68700,1909],{},[1765,68702,1767],{},[1761,68704,8044],{},[898,68706,1828],{},[1761,68708,1909],{},[1765,68710,68711],{},"2,25",[902,68713,68714],{"encoding":904},"TR' = -4Q + 9 = 0 \\Rightarrow Q = 2{,}25",[883,68716,68718],{"className":68717},[886],[888,68719,68720],{"xmlns":890},[892,68721,68722,68765],{},[895,68723,68724,68726,68734,68736,68738,68740,68742,68744,68746,68752,68754,68756,68758,68760,68762],{},[898,68725,1655],{},[1681,68727,68728,68730,68732],{},[898,68729,8051],{},[898,68731,60175],{},[1761,68733,60178],{},[1761,68735,1909],{},[1761,68737,1885],{},[1765,68739,2296],{},[1761,68741,2447],{},[1761,68743,1915],{"stretchy":1821},[1765,68745,68711],{},[1824,68747,68748,68750],{},[1761,68749,1920],{"stretchy":1821},[1765,68751,2296],{},[1761,68753,1964],{},[1765,68755,8056],{},[1761,68757,2447],{},[1765,68759,68711],{},[1761,68761,1909],{},[1765,68763,68764],{},"10,125",[902,68766,68767],{"encoding":904},"TR_{\\max} = -2 \\cdot (2{,}25)^2 + 9 \\cdot 2{,}25 = 10{,}125",". Leží vpravo od bodu maxima zisku, protože při ",[883,68770,68772],{"className":68771},[886],[888,68773,68774],{"xmlns":890},[892,68775,68776,68784],{},[895,68777,68778,68780,68782],{},[898,68779,1828],{},[1761,68781,1909],{},[1765,68783,68711],{},[902,68785,68786],{"encoding":904},"Q = 2{,}25"," rostou už náklady rychleji než příjem.",[1636,68789,68790],{},[724,68791,68792,68794,68795,1343,68817,68839,68840,1343,68857,68878,68879,68911,68912,68950,68951,6746,68969,68986,68987,2068,69015,69049,69050,11729,69088,2068,69112,1741],{},[883,68793,4723],{}," Nekonzistence v původním zdroji\nSkenovaný knižní text obsahoval v tomto příkladu dvě nesourodé hodnoty: uváděl body zvratu ",[883,68796,68798],{"className":68797},[886],[888,68799,68800],{"xmlns":890},[892,68801,68802,68814],{},[895,68803,68804,68810,68812],{},[1681,68805,68806,68808],{},[898,68807,1828],{},[1765,68809,1945],{},[1761,68811,1909],{},[1765,68813,5426],{},[902,68815,68816],{"encoding":904},"Q_1 = 0{,}5",[883,68818,68820],{"className":68819},[886],[888,68821,68822],{"xmlns":890},[892,68823,68824,68836],{},[895,68825,68826,68832,68834],{},[1681,68827,68828,68830],{},[898,68829,1828],{},[1765,68831,2296],{},[1761,68833,1909],{},[1765,68835,2318],{},[902,68837,68838],{"encoding":904},"Q_2 = 4"," (odpovídající starší verzi zadání) a zároveň maximum v ",[883,68841,68843],{"className":68842},[886],[888,68844,68845],{"xmlns":890},[892,68846,68847,68855],{},[895,68848,68849,68851,68853],{},[898,68850,1828],{},[1761,68852,1909],{},[1765,68854,68711],{},[902,68856,68786],{"encoding":904},[883,68858,68860],{"className":68859},[886],[888,68861,68862],{"xmlns":890},[892,68863,68864,68875],{},[895,68865,68866,68868,68870,68872],{},[898,68867,1839],{},[898,68869,8051],{},[1761,68871,1909],{},[1765,68873,68874],{},"6,125",[902,68876,68877],{"encoding":904},"PR = 6{,}125"," (odpovídající derivaci ",[883,68880,68882],{"className":68881},[886],[888,68883,68884],{"xmlns":890},[892,68885,68886,68908],{},[895,68887,68888,68890,68896,68898,68900,68902,68904,68906],{},[898,68889,1839],{},[1824,68891,68892,68894],{},[898,68893,8051],{},[1761,68895,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,68897,1909],{},[1761,68899,1885],{},[1765,68901,2318],{},[898,68903,1828],{},[1761,68905,1964],{},[1765,68907,8056],{},[902,68909,68910],{"encoding":904},"PR' = -4Q + 9",", tj. zisku ",[883,68913,68915],{"className":68914},[886],[888,68916,68917],{"xmlns":890},[892,68918,68919,68947],{},[895,68920,68921,68923,68925,68927,68929,68931,68937,68939,68941,68943,68945],{},[898,68922,1839],{},[898,68924,8051],{},[1761,68926,1909],{},[1761,68928,1885],{},[1765,68930,2296],{},[1824,68932,68933,68935],{},[898,68934,1828],{},[1765,68936,2296],{},[1761,68938,1964],{},[1765,68940,8056],{},[898,68942,1828],{},[1761,68944,1885],{},[1765,68946,2318],{},[902,68948,68949],{"encoding":904},"PR = -2Q^2 + 9Q - 4"," bez odčtení kvadratického členu ",[883,68952,68954],{"className":68953},[886],[888,68955,68956],{"xmlns":890},[892,68957,68958,68966],{},[895,68959,68960],{},[1824,68961,68962,68964],{},[898,68963,1828],{},[1765,68965,2296],{},[902,68967,68968],{"encoding":904},"Q^2",[883,68970,68972],{"className":68971},[886],[888,68973,68974],{"xmlns":890},[892,68975,68976,68984],{},[895,68977,68978,68980,68982],{},[898,68979,1655],{},[898,68981,44359],{},[898,68983,6849],{},[902,68985,59487],{"encoding":904},"). Zde je uvedena matematicky konzistentní verze: zadané ",[883,68988,68990],{"className":68989},[886],[888,68991,68992],{"xmlns":890},[892,68993,68994,69012],{},[895,68995,68996,68998,69000,69002,69004,69006],{},[898,68997,1655],{},[898,68999,6849],{},[1761,69001,1909],{},[1765,69003,2318],{},[1761,69005,1964],{},[1824,69007,69008,69010],{},[898,69009,1828],{},[1765,69011,2296],{},[902,69013,69014],{"encoding":904},"TC = 4 + Q^2",[883,69016,69018],{"className":69017},[886],[888,69019,69020],{"xmlns":890},[892,69021,69022,69046],{},[895,69023,69024,69026,69028,69030,69032,69034,69040,69042,69044],{},[898,69025,1655],{},[898,69027,8051],{},[1761,69029,1909],{},[1761,69031,1885],{},[1765,69033,2296],{},[1824,69035,69036,69038],{},[898,69037,1828],{},[1765,69039,2296],{},[1761,69041,1964],{},[1765,69043,8056],{},[898,69045,1828],{},[902,69047,69048],{"encoding":904},"TR = -2Q^2 + 9Q"," vedou na ",[883,69051,69053],{"className":69052},[886],[888,69054,69055],{"xmlns":890},[892,69056,69057,69085],{},[895,69058,69059,69061,69063,69065,69067,69069,69075,69077,69079,69081,69083],{},[898,69060,1839],{},[898,69062,8051],{},[1761,69064,1909],{},[1761,69066,1885],{},[1765,69068,5486],{},[1824,69070,69071,69073],{},[898,69072,1828],{},[1765,69074,2296],{},[1761,69076,1964],{},[1765,69078,8056],{},[898,69080,1828],{},[1761,69082,1885],{},[1765,69084,2318],{},[902,69086,69087],{"encoding":904},"PR = -3Q^2 + 9Q - 4",[883,69089,69091],{"className":69090},[886],[888,69092,69093],{"xmlns":890},[892,69094,69095,69109],{},[895,69096,69097,69105,69107],{},[1681,69098,69099,69101,69103],{},[898,69100,1828],{},[898,69102,60175],{},[1761,69104,60178],{},[1761,69106,1909],{},[1765,69108,68537],{},[902,69110,69111],{"encoding":904},"Q_{\\max} = 1{,}5",[883,69113,69115],{"className":69114},[886],[888,69116,69117],{"xmlns":890},[892,69118,69119,69136],{},[895,69120,69121,69123,69131,69133],{},[898,69122,1839],{},[1681,69124,69125,69127,69129],{},[898,69126,8051],{},[898,69128,60175],{},[1761,69130,60178],{},[1761,69132,1909],{},[1765,69134,69135],{},"2,75",[902,69137,69138],{"encoding":904},"PR_{\\max} = 2{,}75",[724,69140,69141],{},[614,69142,69143,69144,69171,69172,69205,69206,1343,69229,1741],{},"Obrázek 3.12: Graf ",[883,69145,69147],{"className":69146},[886],[888,69148,69149],{"xmlns":890},[892,69150,69151,69169],{},[895,69152,69153,69155,69157,69159,69161,69163],{},[898,69154,1655],{},[898,69156,6849],{},[1761,69158,1909],{},[1765,69160,2318],{},[1761,69162,1964],{},[1824,69164,69165,69167],{},[898,69166,1828],{},[1765,69168,2296],{},[902,69170,69014],{"encoding":904}," (parabola) a ",[883,69173,69175],{"className":69174},[886],[888,69176,69177],{"xmlns":890},[892,69178,69179,69203],{},[895,69180,69181,69183,69185,69187,69189,69191,69197,69199,69201],{},[898,69182,1655],{},[898,69184,8051],{},[1761,69186,1909],{},[1761,69188,1885],{},[1765,69190,2296],{},[1824,69192,69193,69195],{},[898,69194,1828],{},[1765,69196,2296],{},[1761,69198,1964],{},[1765,69200,8056],{},[898,69202,1828],{},[902,69204,69048],{"encoding":904}," (parabola); průsečíky vyznačují body zvratu ",[883,69207,69209],{"className":69208},[886],[888,69210,69211],{"xmlns":890},[892,69212,69213,69226],{},[895,69214,69215,69221,69223],{},[1681,69216,69217,69219],{},[898,69218,1828],{},[1765,69220,1945],{},[1761,69222,9945],{},[1765,69224,69225],{},"0,54",[902,69227,69228],{"encoding":904},"Q_1 \\doteq 0{,}54",[883,69230,69232],{"className":69231},[886],[888,69233,69234],{"xmlns":890},[892,69235,69236,69249],{},[895,69237,69238,69244,69246],{},[1681,69239,69240,69242],{},[898,69241,1828],{},[1765,69243,2296],{},[1761,69245,9945],{},[1765,69247,69248],{},"2,46",[902,69250,69251],{"encoding":904},"Q_2 \\doteq 2{,}46",[724,69253,69254],{},[614,69255,69256,69257,62485,69294,69311,69312,1343,69333,1741],{},"Obrázek 3.13: Graf zisku ",[883,69258,69260],{"className":69259},[886],[888,69261,69262],{"xmlns":890},[892,69263,69264,69292],{},[895,69265,69266,69268,69270,69272,69274,69276,69282,69284,69286,69288,69290],{},[898,69267,1839],{},[898,69269,8051],{},[1761,69271,1909],{},[1761,69273,1885],{},[1765,69275,5486],{},[1824,69277,69278,69280],{},[898,69279,1828],{},[1765,69281,2296],{},[1761,69283,1964],{},[1765,69285,8056],{},[898,69287,1828],{},[1761,69289,1885],{},[1765,69291,2318],{},[902,69293,69087],{"encoding":904},[883,69295,69297],{"className":69296},[886],[888,69298,69299],{"xmlns":890},[892,69300,69301,69309],{},[895,69302,69303,69305,69307],{},[898,69304,1828],{},[1761,69306,1909],{},[1765,69308,68537],{},[902,69310,68592],{"encoding":904}," a nulami ",[883,69313,69315],{"className":69314},[886],[888,69316,69317],{"xmlns":890},[892,69318,69319,69331],{},[895,69320,69321,69327,69329],{},[1681,69322,69323,69325],{},[898,69324,1828],{},[1765,69326,1945],{},[1761,69328,9945],{},[1765,69330,69225],{},[902,69332,69228],{"encoding":904},[883,69334,69336],{"className":69335},[886],[888,69337,69338],{"xmlns":890},[892,69339,69340,69352],{},[895,69341,69342,69348,69350],{},[1681,69343,69344,69346],{},[898,69345,1828],{},[1765,69347,2296],{},[1761,69349,9945],{},[1765,69351,69248],{},[902,69353,69251],{"encoding":904},[115,69355,69357],{"id":69356},"princip-maximalizace-zisku","Princip maximalizace zisku",[724,69359,69360],{},"Kromě standardního hledání extrému lze využít následující princip.",[724,69362,69363],{},[3991,69364],{"alt":69365,"className":69366,"src":69367},"imek-max-zisku-dva-pohledy",[210,3995],"\u002Fwiki-assets\u002Fimek-max-zisku-dva-pohledy.jpeg",[198,69369,20446],{"id":69370},"princip-1",[724,69372,69373,69374,6699,69389,69406],{},"Má-li zisk ",[883,69375,69377],{"className":69376},[886],[888,69378,69379],{"xmlns":890},[892,69380,69381,69387],{},[895,69382,69383,69385],{},[898,69384,1839],{},[898,69386,8051],{},[902,69388,67457],{"encoding":904},[883,69390,69392],{"className":69391},[886],[888,69393,69394],{"xmlns":890},[892,69395,69396,69404],{},[895,69397,69398],{},[1681,69399,69400,69402],{},[898,69401,1828],{},[1765,69403,1767],{},[902,69405,42331],{"encoding":904}," maximum, pak platí",[883,69408,69410],{"className":69409},[886],[888,69411,69412],{"xmlns":890,"display":1930},[892,69413,69414,69463],{},[24787,69415,69416],{"width":32101},[24792,69417,69418,69420,69456,69458],{},[24795,69419],{"width":32106},[24795,69421,69422],{},[895,69423,69424,69426,69428,69430,69436,69438,69440,69442,69444,69446,69452,69454],{},[898,69425,6889],{},[898,69427,8051],{},[1761,69429,1915],{"stretchy":1821},[1681,69431,69432,69434],{},[898,69433,1828],{},[1765,69435,1767],{},[1761,69437,1920],{"stretchy":1821},[1761,69439,1909],{},[898,69441,6889],{},[898,69443,6849],{},[1761,69445,1915],{"stretchy":1821},[1681,69447,69448,69450],{},[898,69449,1828],{},[1765,69451,1767],{},[1761,69453,1920],{"stretchy":1821},[898,69455,1741],{"mathvariant":1969},[24795,69457],{"width":32106},[24795,69459,69460],{},[2761,69461,69462],{},"(3.13)",[902,69464,69465],{"encoding":904},"MR(Q_0) = MC(Q_0).\n\\tag{3.13}",[1636,69467,69468],{},[724,69469,69470,66024,69472],{},[883,69471,60422],{},[38,69473,69474],{},"V bodě maxima zisku se mezní příjem rovná mezním nákladům.",[724,69476,69477,69480,69481,12146,69508,21610,69582,1741],{},[38,69478,69479],{},"Odvození"," (úloha 3.21): nutnou podmínkou maxima ",[883,69482,69484],{"className":69483},[886],[888,69485,69486],{"xmlns":890},[892,69487,69488,69506],{},[895,69489,69490,69492,69494,69496,69498,69500,69502,69504],{},[898,69491,1839],{},[898,69493,8051],{},[1761,69495,1909],{},[898,69497,1655],{},[898,69499,8051],{},[1761,69501,1885],{},[898,69503,1655],{},[898,69505,6849],{},[902,69507,59178],{"encoding":904},[883,69509,69511],{"className":69510},[886],[888,69512,69513],{"xmlns":890},[892,69514,69515,69579],{},[895,69516,69517,69519,69525,69527,69533,69535,69537,69539,69545,69547,69553,69555,69557,69559,69565,69567,69573,69575,69577],{},[898,69518,1839],{},[1824,69520,69521,69523],{},[898,69522,8051],{},[1761,69524,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,69526,1915],{"stretchy":1821},[1681,69528,69529,69531],{},[898,69530,1828],{},[1765,69532,1767],{},[1761,69534,1920],{"stretchy":1821},[1761,69536,1909],{},[898,69538,1655],{},[1824,69540,69541,69543],{},[898,69542,8051],{},[1761,69544,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,69546,1915],{"stretchy":1821},[1681,69548,69549,69551],{},[898,69550,1828],{},[1765,69552,1767],{},[1761,69554,1920],{"stretchy":1821},[1761,69556,1885],{},[898,69558,1655],{},[1824,69560,69561,69563],{},[898,69562,6849],{},[1761,69564,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,69566,1915],{"stretchy":1821},[1681,69568,69569,69571],{},[898,69570,1828],{},[1765,69572,1767],{},[1761,69574,1920],{"stretchy":1821},[1761,69576,1909],{},[1765,69578,1767],{},[902,69580,69581],{"encoding":904},"PR'(Q_0) = TR'(Q_0) - TC'(Q_0) = 0",[883,69583,69585],{"className":69584},[886],[888,69586,69587],{"xmlns":890},[892,69588,69589,69621],{},[895,69590,69591,69593,69595,69597,69603,69605,69607,69609,69611,69613,69619],{},[898,69592,6889],{},[898,69594,8051],{},[1761,69596,1915],{"stretchy":1821},[1681,69598,69599,69601],{},[898,69600,1828],{},[1765,69602,1767],{},[1761,69604,1920],{"stretchy":1821},[1761,69606,1909],{},[898,69608,6889],{},[898,69610,6849],{},[1761,69612,1915],{"stretchy":1821},[1681,69614,69615,69617],{},[898,69616,1828],{},[1765,69618,1767],{},[1761,69620,1920],{"stretchy":1821},[902,69622,69623],{"encoding":904},"MR(Q_0) = MC(Q_0)",[1636,69625,69626,69631],{},[724,69627,69628,69630],{},[883,69629,4452],{}," Postup — jak najít maximum zisku",[152,69632,69633,69697,69752,69789,69817],{},[123,69634,69635,69636,2068,69651,69666,69667,2162],{},"Sestavte ",[883,69637,69639],{"className":69638},[886],[888,69640,69641],{"xmlns":890},[892,69642,69643,69649],{},[895,69644,69645,69647],{},[898,69646,1655],{},[898,69648,8051],{},[902,69650,8151],{"encoding":904},[883,69652,69654],{"className":69653},[886],[888,69655,69656],{"xmlns":890},[892,69657,69658,69664],{},[895,69659,69660,69662],{},[898,69661,1655],{},[898,69663,6849],{},[902,69665,7310],{"encoding":904}," ze zadání (typicky ",[883,69668,69670],{"className":69669},[886],[888,69671,69672],{"xmlns":890},[892,69673,69674,69694],{},[895,69675,69676,69678,69680,69682,69684,69686,69688,69690,69692],{},[898,69677,1655],{},[898,69679,8051],{},[1761,69681,1909],{},[898,69683,1839],{},[1761,69685,1915],{"stretchy":1821},[898,69687,1828],{},[1761,69689,1920],{"stretchy":1821},[1761,69691,2447],{},[898,69693,1828],{},[902,69695,69696],{"encoding":904},"TR = P(Q) \\cdot Q",[123,69698,69699,69700,2068,69726,1741],{},"Vypočtěte ",[883,69701,69703],{"className":69702},[886],[888,69704,69705],{"xmlns":890},[892,69706,69707,69723],{},[895,69708,69709,69711,69713,69715,69717],{},[898,69710,6889],{},[898,69712,8051],{},[1761,69714,1909],{},[898,69716,1655],{},[1824,69718,69719,69721],{},[898,69720,8051],{},[1761,69722,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[902,69724,69725],{"encoding":904},"MR = TR'",[883,69727,69729],{"className":69728},[886],[888,69730,69731],{"xmlns":890},[892,69732,69733,69749],{},[895,69734,69735,69737,69739,69741,69743],{},[898,69736,6889],{},[898,69738,6849],{},[1761,69740,1909],{},[898,69742,1655],{},[1824,69744,69745,69747],{},[898,69746,6849],{},[1761,69748,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[902,69750,69751],{"encoding":904},"MC = TC'",[123,69753,69754,69755,1741],{},"Řešte rovnici ",[883,69756,69758],{"className":69757},[886],[888,69759,69760],{"xmlns":890},[892,69761,69762,69786],{},[895,69763,69764,69766,69768,69770,69772,69774,69776,69778,69780,69782,69784],{},[898,69765,6889],{},[898,69767,8051],{},[1761,69769,1915],{"stretchy":1821},[898,69771,1828],{},[1761,69773,1920],{"stretchy":1821},[1761,69775,1909],{},[898,69777,6889],{},[898,69779,6849],{},[1761,69781,1915],{"stretchy":1821},[898,69783,1828],{},[1761,69785,1920],{"stretchy":1821},[902,69787,69788],{"encoding":904},"MR(Q) = MC(Q)",[123,69790,69791,69792,69816],{},"Ověřte druhou derivaci ",[883,69793,69795],{"className":69794},[886],[888,69796,69797],{"xmlns":890},[892,69798,69799,69813],{},[895,69800,69801,69803],{},[898,69802,1839],{},[1824,69804,69805,69807],{},[898,69806,8051],{},[895,69808,69809,69811],{},[1761,69810,6459],{"mathvariant":1969},[1761,69812,6459],{"mathvariant":1969},[902,69814,69815],{"encoding":904},"PR''"," (nebo že má rovnice jediný ekonomicky smysluplný kořen).",[123,69818,69819,69820,69847],{},"Dosaďte do ",[883,69821,69823],{"className":69822},[886],[888,69824,69825],{"xmlns":890},[892,69826,69827,69845],{},[895,69828,69829,69831,69833,69835,69837,69839,69841,69843],{},[898,69830,1839],{},[898,69832,8051],{},[1761,69834,1909],{},[898,69836,1655],{},[898,69838,8051],{},[1761,69840,1885],{},[898,69842,1655],{},[898,69844,6849],{},[902,69846,59178],{"encoding":904}," pro hodnotu maxima.",[41374,69849,69851],{"id":69850},"příklad-39","Příklad 3.9",[724,69853,69854,59966,69856,2068,69878,69914],{},[38,69855,59965],{},[883,69857,69859],{"className":69858},[886],[888,69860,69861],{"xmlns":890},[892,69862,69863,69875],{},[895,69864,69865,69867,69869,69871,69873],{},[898,69866,1839],{},[1761,69868,1909],{},[1765,69870,42042],{},[1761,69872,1885],{},[898,69874,1828],{},[902,69876,69877],{"encoding":904},"P = 30 - Q",[883,69879,69881],{"className":69880},[886],[888,69882,69883],{"xmlns":890},[892,69884,69885,69911],{},[895,69886,69887,69889,69891,69893,69895,69901,69903,69905,69907,69909],{},[898,69888,1655],{},[898,69890,6849],{},[1761,69892,1909],{},[1765,69894,5426],{},[1824,69896,69897,69899],{},[898,69898,1828],{},[1765,69900,2296],{},[1761,69902,1964],{},[1765,69904,2340],{},[898,69906,1828],{},[1761,69908,1964],{},[1765,69910,5512],{},[902,69912,69913],{"encoding":904},"TC = 0{,}5Q^2 + 6Q + 7"," stanovte produkci maximalizující zisk.",[724,69916,69917,1989,69919,1343,69949,69987,69988,19828,70032,70066,70067,1741],{},[38,69918,26803],{},[883,69920,69922],{"className":69921},[886],[888,69923,69924],{"xmlns":890},[892,69925,69926,69946],{},[895,69927,69928,69930,69932,69934,69936,69938,69940],{},[898,69929,1655],{},[898,69931,8051],{},[1761,69933,1909],{},[1765,69935,42042],{},[898,69937,1828],{},[1761,69939,1885],{},[1824,69941,69942,69944],{},[898,69943,1828],{},[1765,69945,2296],{},[902,69947,69948],{"encoding":904},"TR = 30Q - Q^2",[883,69950,69952],{"className":69951},[886],[888,69953,69954],{"xmlns":890},[892,69955,69956,69984],{},[895,69957,69958,69960,69962,69964,69966,69968,69974,69976,69978,69980,69982],{},[898,69959,1839],{},[898,69961,8051],{},[1761,69963,1909],{},[1761,69965,1885],{},[1765,69967,68537],{},[1824,69969,69970,69972],{},[898,69971,1828],{},[1765,69973,2296],{},[1761,69975,1964],{},[1765,69977,45810],{},[898,69979,1828],{},[1761,69981,1885],{},[1765,69983,5512],{},[902,69985,69986],{"encoding":904},"PR = -1{,}5Q^2 + 24Q - 7",". Extrém: ",[883,69989,69991],{"className":69990},[886],[888,69992,69993],{"xmlns":890},[892,69994,69995,70029],{},[895,69996,69997,69999,70005,70007,70009,70011,70013,70015,70017,70019,70021,70023,70025,70027],{},[898,69998,1839],{},[1824,70000,70001,70003],{},[898,70002,8051],{},[1761,70004,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,70006,1909],{},[1761,70008,1885],{},[1765,70010,5486],{},[898,70012,1828],{},[1761,70014,1964],{},[1765,70016,45810],{},[1761,70018,1909],{},[1765,70020,1767],{},[1761,70022,8044],{},[898,70024,1828],{},[1761,70026,1909],{},[1765,70028,2454],{},[902,70030,70031],{"encoding":904},"PR' = -3Q + 24 = 0 \\Rightarrow Q = 8",[883,70033,70035],{"className":70034},[886],[888,70036,70037],{"xmlns":890},[892,70038,70039,70063],{},[895,70040,70041,70043,70053,70055,70057,70059,70061],{},[898,70042,1839],{},[1824,70044,70045,70047],{},[898,70046,8051],{},[895,70048,70049,70051],{},[1761,70050,6459],{"mathvariant":1969},[1761,70052,6459],{"mathvariant":1969},[1761,70054,1909],{},[1761,70056,1885],{},[1765,70058,5486],{},[1761,70060,2058],{},[1765,70062,1767],{},[902,70064,70065],{"encoding":904},"PR'' = -3 \u003C 0"," (maximum); ",[883,70068,70070],{"className":70069},[886],[888,70071,70072],{"xmlns":890},[892,70073,70074,70091],{},[895,70075,70076,70078,70080,70082,70084,70086,70088],{},[898,70077,1839],{},[898,70079,8051],{},[1761,70081,1915],{"stretchy":1821},[1765,70083,2454],{},[1761,70085,1920],{"stretchy":1821},[1761,70087,1909],{},[1765,70089,70090],{},"89",[902,70092,70093],{"encoding":904},"PR(8) = 89",[724,70095,70096,70097,1343,70123,19828,70147,70185],{},"Ověření principu: ",[883,70098,70100],{"className":70099},[886],[888,70101,70102],{"xmlns":890},[892,70103,70104,70120],{},[895,70105,70106,70108,70110,70112,70114,70116,70118],{},[898,70107,6889],{},[898,70109,8051],{},[1761,70111,1909],{},[1765,70113,42042],{},[1761,70115,1885],{},[1765,70117,2296],{},[898,70119,1828],{},[902,70121,70122],{"encoding":904},"MR = 30 - 2Q",[883,70124,70126],{"className":70125},[886],[888,70127,70128],{"xmlns":890},[892,70129,70130,70144],{},[895,70131,70132,70134,70136,70138,70140,70142],{},[898,70133,6889],{},[898,70135,6849],{},[1761,70137,1909],{},[898,70139,1828],{},[1761,70141,1964],{},[1765,70143,2340],{},[902,70145,70146],{"encoding":904},"MC = Q + 6",[883,70148,70150],{"className":70149},[886],[888,70151,70152],{"xmlns":890},[892,70153,70154,70182],{},[895,70155,70156,70158,70160,70162,70164,70166,70168,70170,70172,70174,70176,70178,70180],{},[898,70157,6889],{},[898,70159,8051],{},[1761,70161,1915],{"stretchy":1821},[1765,70163,2454],{},[1761,70165,1920],{"stretchy":1821},[1761,70167,1909],{},[1765,70169,26979],{},[1761,70171,1909],{},[898,70173,6889],{},[898,70175,6849],{},[1761,70177,1915],{"stretchy":1821},[1765,70179,2454],{},[1761,70181,1920],{"stretchy":1821},[902,70183,70184],{"encoding":904},"MR(8) = 14 = MC(8)",", tj. platí (3.13).",[724,70187,70188,70189,70222,70223,70240],{},"V řadě případů — má-li rovnice ",[883,70190,70192],{"className":70191},[886],[888,70193,70194],{"xmlns":890},[892,70195,70196,70220],{},[895,70197,70198,70200,70202,70204,70206,70208,70210,70212,70214,70216,70218],{},[898,70199,6889],{},[898,70201,8051],{},[1761,70203,1915],{"stretchy":1821},[898,70205,1828],{},[1761,70207,1920],{"stretchy":1821},[1761,70209,1909],{},[898,70211,6889],{},[898,70213,6849],{},[1761,70215,1915],{"stretchy":1821},[898,70217,1828],{},[1761,70219,1920],{"stretchy":1821},[902,70221,69788],{"encoding":904}," jediné ekonomicky smysluplné řešení ",[883,70224,70226],{"className":70225},[886],[888,70227,70228],{"xmlns":890},[892,70229,70230,70238],{},[895,70231,70232],{},[1681,70233,70234,70236],{},[898,70235,1828],{},[1765,70237,1767],{},[902,70239,42331],{"encoding":904}," — není třeba provádět test druhé derivace.",[41374,70242,70244],{"id":70243},"příklad-310","Příklad 3.10",[724,70246,70247,70249,70250,70254,70255,70268,70269,70300],{},[38,70248,59965],{}," Firma vyrábí minipočítače v ",[207,70251,70253],{"className":70252,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurenci",", produkuje 30 výrobků denně za ",[883,70256,70258],{"className":70257},[886],[888,70259,70260],{"xmlns":890},[892,70261,70262,70266],{},[895,70263,70264],{},[1765,70265,19229],{},[902,70267,19229],{"encoding":904}," EUR\u002Fks. ",[883,70270,70272],{"className":70271},[886],[888,70273,70274],{"xmlns":890},[892,70275,70276,70297],{},[895,70277,70278,70280,70282,70284,70286,70288,70291],{},[898,70279,1655],{},[898,70281,6849],{},[1761,70283,1909],{},[1765,70285,7190],{},[1761,70287,1964],{},[1765,70289,70290],{},"28",[1824,70292,70293,70295],{},[898,70294,1828],{},[1765,70296,2296],{},[902,70298,70299],{"encoding":904},"TC = 50 + 28Q^2",". Určete optimální denní produkci a zisk.",[724,70302,70303,1989,70305,1343,70327,1343,70347,70370],{},[38,70304,26803],{},[883,70306,70308],{"className":70307},[886],[888,70309,70310],{"xmlns":890},[892,70311,70312,70324],{},[895,70313,70314,70316,70318,70320,70322],{},[898,70315,1655],{},[898,70317,8051],{},[1761,70319,1909],{},[1765,70321,19229],{},[898,70323,1828],{},[902,70325,70326],{"encoding":904},"TR = 900Q",[883,70328,70330],{"className":70329},[886],[888,70331,70332],{"xmlns":890},[892,70333,70334,70344],{},[895,70335,70336,70338,70340,70342],{},[898,70337,6889],{},[898,70339,8051],{},[1761,70341,1909],{},[1765,70343,19229],{},[902,70345,70346],{"encoding":904},"MR = 900",[883,70348,70350],{"className":70349},[886],[888,70351,70352],{"xmlns":890},[892,70353,70354,70367],{},[895,70355,70356,70358,70360,70362,70365],{},[898,70357,6889],{},[898,70359,6849],{},[1761,70361,1909],{},[1765,70363,70364],{},"56",[898,70366,1828],{},[902,70368,70369],{"encoding":904},"MC = 56Q",". Z principu:",[883,70372,70374],{"className":70373},[886],[888,70375,70376],{"xmlns":890,"display":1930},[892,70377,70378,70420],{},[895,70379,70380,70382,70384,70386,70388,70390,70392,70394,70396,70398,70406,70408,70411,70413,70415,70417],{},[1765,70381,19229],{},[1761,70383,1909],{},[1765,70385,70364],{},[898,70387,1828],{},[2761,70389,8041],{},[1761,70391,8044],{},[2761,70393,8041],{},[898,70395,1828],{},[1761,70397,1909],{},[6411,70399,70400],{"scriptlevel":1767,"displaystyle":1821},[4379,70401,70402,70404],{},[1765,70403,19229],{},[1765,70405,70364],{},[1761,70407,9945],{},[1765,70409,70410],{},"16,07",[2761,70412,8041],{},[1761,70414,6803],{},[2761,70416,8041],{},[1765,70418,70419],{},"16.",[902,70421,70422],{"encoding":904},"900 = 56Q \\;\\Rightarrow\\; Q = \\tfrac{900}{56} \\doteq 16{,}07 \\;\\approx\\; 16.",[724,70424,70425,70426,2506],{},"Zisk při ",[883,70427,70429],{"className":70428},[886],[888,70430,70431],{"xmlns":890},[892,70432,70433,70441],{},[895,70434,70435,70437,70439],{},[898,70436,1828],{},[1761,70438,1909],{},[1765,70440,45871],{},[902,70442,70443],{"encoding":904},"Q = 16",[883,70445,70447],{"className":70446},[886],[888,70448,70449],{"xmlns":890,"display":1930},[892,70450,70451,70522],{},[895,70452,70453,70455,70457,70459,70461,70463,70465,70467,70469,70471,70473,70475,70477,70479,70481,70483,70489,70491,70493,70495,70497,70499,70501,70503,70505,70508,70510,70512,70514,70517,70520],{},[898,70454,1839],{},[898,70456,8051],{},[1761,70458,1915],{"stretchy":1821},[1765,70460,45871],{},[1761,70462,1920],{"stretchy":1821},[1761,70464,1909],{},[1765,70466,19229],{},[1761,70468,2447],{},[1765,70470,45871],{},[1761,70472,1885],{},[1761,70474,1915],{"stretchy":1821},[1765,70476,7190],{},[1761,70478,1964],{},[1765,70480,70290],{},[1761,70482,2447],{},[1824,70484,70485,70487],{},[1765,70486,45871],{},[1765,70488,2296],{},[1761,70490,1920],{"stretchy":1821},[1761,70492,1909],{},[1765,70494,26979],{},[2761,70496,7057],{},[1765,70498,24175],{},[1761,70500,1885],{},[1765,70502,5512],{},[2761,70504,7057],{},[1765,70506,70507],{},"218",[1761,70509,1909],{},[1765,70511,5512],{},[2761,70513,7057],{},[1765,70515,70516],{},"182",[2761,70518,70519],{}," EUR",[898,70521,1741],{"mathvariant":1969},[902,70523,70524],{"encoding":904},"PR(16) = 900 \\cdot 16 - (50 + 28 \\cdot 16^2) = 14\\,400 - 7\\,218 = 7\\,182 \\text{ EUR}.",[724,70526,70527],{},"Pro srovnání při původních 30 ks:",[883,70529,70531],{"className":70530},[886],[888,70532,70533],{"xmlns":890,"display":1930},[892,70534,70535,70600],{},[895,70536,70537,70539,70541,70543,70545,70547,70549,70551,70553,70555,70557,70559,70561,70563,70565,70567,70569,70571,70573,70576,70578,70580,70582,70584,70586,70588,70590,70592,70594,70596,70598],{},[898,70538,1839],{},[898,70540,8051],{},[1761,70542,1915],{"stretchy":1821},[1765,70544,42042],{},[1761,70546,1920],{"stretchy":1821},[1761,70548,1909],{},[1765,70550,19229],{},[1761,70552,2447],{},[1765,70554,42042],{},[1761,70556,1885],{},[1761,70558,1915],{"stretchy":1821},[1765,70560,7190],{},[1761,70562,1964],{},[1765,70564,70290],{},[1761,70566,2447],{},[1765,70568,19229],{},[1761,70570,1920],{"stretchy":1821},[1761,70572,1909],{},[1765,70574,70575],{},"27",[2761,70577,7057],{},[1765,70579,63060],{},[1761,70581,1885],{},[1765,70583,9056],{},[2761,70585,7057],{},[1765,70587,34773],{},[1761,70589,1909],{},[1765,70591,1945],{},[2761,70593,7057],{},[1765,70595,27776],{},[2761,70597,70519],{},[898,70599,1741],{"mathvariant":1969},[902,70601,70602],{"encoding":904},"PR(30) = 900 \\cdot 30 - (50 + 28 \\cdot 900) = 27\\,000 - 25\\,250 = 1\\,750 \\text{ EUR}.",[724,70604,70605,70608,70609,70627,70628,70646],{},[38,70606,70607],{},"Doporučení:"," vyrábět 16 ks\u002Fden se ziskem ",[883,70610,70612],{"className":70611},[886],[888,70613,70614],{"xmlns":890},[892,70615,70616,70624],{},[895,70617,70618,70620,70622],{},[1765,70619,5512],{},[2761,70621,7057],{},[1765,70623,70516],{},[902,70625,70626],{"encoding":904},"7\\,182"," EUR namísto původních ",[883,70629,70631],{"className":70630},[886],[888,70632,70633],{"xmlns":890},[892,70634,70635,70643],{},[895,70636,70637,70639,70641],{},[1765,70638,1945],{},[2761,70640,7057],{},[1765,70642,27776],{},[902,70644,70645],{"encoding":904},"1\\,750"," EUR.",[198,70648,70650],{"id":70649},"speciální-tvar-pro-pevnou-cenu","Speciální tvar pro pevnou cenu",[724,70652,70653,70654,66548,70667,70691],{},"Předpokládáme-li, že výrobce prodává za pevnou cenu ",[883,70655,70657],{"className":70656},[886],[888,70658,70659],{"xmlns":890},[892,70660,70661,70665],{},[895,70662,70663],{},[898,70664,1839],{},[902,70666,1839],{"encoding":904},[883,70668,70670],{"className":70669},[886],[888,70671,70672],{"xmlns":890},[892,70673,70674,70688],{},[895,70675,70676,70678,70680,70682,70684,70686],{},[898,70677,1655],{},[898,70679,8051],{},[1761,70681,1909],{},[898,70683,1839],{},[1761,70685,2447],{},[898,70687,1828],{},[902,70689,70690],{"encoding":904},"TR = P \\cdot Q"," a z (3.13) speciálně:",[883,70693,70695],{"className":70694},[886],[888,70696,70697],{"xmlns":890,"display":1930},[892,70698,70699,70732],{},[24787,70700,70701],{"width":32101},[24792,70702,70703,70705,70725,70727],{},[24795,70704],{"width":32106},[24795,70706,70707],{},[895,70708,70709,70711,70713,70715,70717,70719,70721,70723],{},[898,70710,1839],{},[1761,70712,1909],{},[898,70714,6889],{},[898,70716,6849],{},[1761,70718,1915],{"stretchy":1821},[898,70720,1828],{},[1761,70722,1920],{"stretchy":1821},[898,70724,1741],{"mathvariant":1969},[24795,70726],{"width":32106},[24795,70728,70729],{},[2761,70730,70731],{},"(3.14)",[902,70733,70734],{"encoding":904},"P = MC(Q).\n\\tag{3.14}",[724,70736,70737,70738,1741],{},"Výrobce musí nastavit nabízené množství tak, aby se mezní náklady rovnaly ceně. Má-li rovnice (3.14) více řešení, rozhoduje znaménko ",[883,70739,70741],{"className":70740},[886],[888,70742,70743],{"xmlns":890},[892,70744,70745,70759],{},[895,70746,70747,70749],{},[898,70748,1839],{},[1824,70750,70751,70753],{},[898,70752,8051],{},[895,70754,70755,70757],{},[1761,70756,6459],{"mathvariant":1969},[1761,70758,6459],{"mathvariant":1969},[902,70760,69815],{"encoding":904},[41374,70762,70764],{"id":70763},"příklad-311","Příklad 3.11",[724,70766,70767,61500,70769,70816,70817,70835],{},[38,70768,59965],{},[883,70770,70772],{"className":70771},[886],[888,70773,70774],{"xmlns":890},[892,70775,70776,70813],{},[895,70777,70778,70780,70782,70784,70787,70793,70795,70797,70803,70805,70807,70809,70811],{},[898,70779,1655],{},[898,70781,6849],{},[1761,70783,1909],{},[1765,70785,70786],{},"0,04",[1824,70788,70789,70791],{},[898,70790,1828],{},[1765,70792,5486],{},[1761,70794,1885],{},[1765,70796,26578],{},[1824,70798,70799,70801],{},[898,70800,1828],{},[1765,70802,2296],{},[1761,70804,1964],{},[1765,70806,2633],{},[898,70808,1828],{},[1761,70810,1964],{},[1765,70812,6321],{},[902,70814,70815],{"encoding":904},"TC = 0{,}04Q^3 - 0{,}9Q^2 + 10Q + 5"," a pevnou cenu ",[883,70818,70820],{"className":70819},[886],[888,70821,70822],{"xmlns":890},[892,70823,70824,70832],{},[895,70825,70826,70828,70830],{},[898,70827,1839],{},[1761,70829,1909],{},[1765,70831,2318],{},[902,70833,70834],{"encoding":904},"P = 4"," stanovte optimální produkci.",[724,70837,70838,70840,70841,21610,70883,70917,70918,2506],{},[38,70839,26803],{}," Z (3.14): ",[883,70842,70844],{"className":70843},[886],[888,70845,70846],{"xmlns":890},[892,70847,70848,70880],{},[895,70849,70850,70852,70854,70856,70859,70865,70867,70870,70872,70874,70876,70878],{},[898,70851,6889],{},[898,70853,6849],{},[1761,70855,1909],{},[1765,70857,70858],{},"0,12",[1824,70860,70861,70863],{},[898,70862,1828],{},[1765,70864,2296],{},[1761,70866,1885],{},[1765,70868,70869],{},"1,8",[898,70871,1828],{},[1761,70873,1964],{},[1765,70875,2633],{},[1761,70877,1909],{},[1765,70879,2318],{},[902,70881,70882],{"encoding":904},"MC = 0{,}12Q^2 - 1{,}8Q + 10 = 4",[883,70884,70886],{"className":70885},[886],[888,70887,70888],{"xmlns":890},[892,70889,70890,70914],{},[895,70891,70892,70894,70900,70902,70904,70906,70908,70910,70912],{},[1765,70893,70858],{},[1824,70895,70896,70898],{},[898,70897,1828],{},[1765,70899,2296],{},[1761,70901,1885],{},[1765,70903,70869],{},[898,70905,1828],{},[1761,70907,1964],{},[1765,70909,2340],{},[1761,70911,1909],{},[1765,70913,1767],{},[902,70915,70916],{"encoding":904},"0{,}12Q^2 - 1{,}8Q + 6 = 0",", po vydělení ",[883,70919,70921],{"className":70920},[886],[888,70922,70923],{"xmlns":890},[892,70924,70925,70929],{},[895,70926,70927],{},[1765,70928,70858],{},[902,70930,70931],{"encoding":904},"0{,}12",[883,70933,70935],{"className":70934},[886],[888,70936,70937],{"xmlns":890,"display":1930},[892,70938,70939,70991],{},[895,70940,70941,70947,70949,70951,70953,70955,70957,70959,70961,70963,70965,70967,70973,70975,70977,70979,70981,70987,70989],{},[1824,70942,70943,70945],{},[898,70944,1828],{},[1765,70946,2296],{},[1761,70948,1885],{},[1765,70950,5433],{},[898,70952,1828],{},[1761,70954,1964],{},[1765,70956,7190],{},[1761,70958,1909],{},[1765,70960,1767],{},[2761,70962,8041],{},[1761,70964,8044],{},[2761,70966,8041],{},[1681,70968,70969,70971],{},[898,70970,1828],{},[1765,70972,1945],{},[1761,70974,1909],{},[1765,70976,6321],{},[1761,70978,1834],{"separator":1833},[2761,70980,8041],{},[1681,70982,70983,70985],{},[898,70984,1828],{},[1765,70986,2296],{},[1761,70988,1909],{},[1765,70990,23361],{},[902,70992,70993],{"encoding":904},"Q^2 - 15Q + 50 = 0 \\;\\Rightarrow\\; Q_1 = 5, \\; Q_2 = 10.",[724,70995,70996,70997,2506],{},"Dále ",[883,70998,71000],{"className":70999},[886],[888,71001,71002],{"xmlns":890},[892,71003,71004,71043],{},[895,71005,71006,71008,71018,71020,71022,71024,71030,71032,71034,71037,71039,71041],{},[898,71007,1839],{},[1824,71009,71010,71012],{},[898,71011,8051],{},[895,71013,71014,71016],{},[1761,71015,6459],{"mathvariant":1969},[1761,71017,6459],{"mathvariant":1969},[1761,71019,1909],{},[1761,71021,1885],{},[898,71023,6889],{},[1824,71025,71026,71028],{},[898,71027,6849],{},[1761,71029,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,71031,1909],{},[1761,71033,1885],{},[1765,71035,71036],{},"0,24",[898,71038,1828],{},[1761,71040,1964],{},[1765,71042,70869],{},[902,71044,71045],{"encoding":904},"PR'' = -MC' = -0{,}24Q + 1{,}8",[120,71047,71048,71098],{},[123,71049,71050,71094,71095,71097],{},[883,71051,71053],{"className":71052},[886],[888,71054,71055],{"xmlns":890},[892,71056,71057,71091],{},[895,71058,71059,71061,71071,71073,71075,71077,71079,71081,71083,71085,71087,71089],{},[898,71060,1839],{},[1824,71062,71063,71065],{},[898,71064,8051],{},[895,71066,71067,71069],{},[1761,71068,6459],{"mathvariant":1969},[1761,71070,6459],{"mathvariant":1969},[1761,71072,1915],{"stretchy":1821},[1765,71074,6321],{},[1761,71076,1920],{"stretchy":1821},[1761,71078,1909],{},[1765,71080,23354],{},[1761,71082,1763],{},[1765,71084,1767],{},[2761,71086,8041],{},[1761,71088,8044],{},[2761,71090,8041],{},[902,71092,71093],{"encoding":904},"PR''(5) = 0{,}6 > 0 \\;\\Rightarrow\\;"," lokální ",[38,71096,7839],{}," zisku (minimalizace ztráty);",[123,71099,71100,71094,71146,71148],{},[883,71101,71103],{"className":71102},[886],[888,71104,71105],{"xmlns":890},[892,71106,71107,71143],{},[895,71108,71109,71111,71121,71123,71125,71127,71129,71131,71133,71135,71137,71139,71141],{},[898,71110,1839],{},[1824,71112,71113,71115],{},[898,71114,8051],{},[895,71116,71117,71119],{},[1761,71118,6459],{"mathvariant":1969},[1761,71120,6459],{"mathvariant":1969},[1761,71122,1915],{"stretchy":1821},[1765,71124,2633],{},[1761,71126,1920],{"stretchy":1821},[1761,71128,1909],{},[1761,71130,1885],{},[1765,71132,23354],{},[1761,71134,2058],{},[1765,71136,1767],{},[2761,71138,8041],{},[1761,71140,8044],{},[2761,71142,8041],{},[902,71144,71145],{"encoding":904},"PR''(10) = -0{,}6 \u003C 0 \\;\\Rightarrow\\;",[38,71147,7781],{}," zisku, avšak",[883,71150,71152],{"className":71151},[886],[888,71153,71154],{"xmlns":890,"display":1930},[892,71155,71156,71224],{},[895,71157,71158,71160,71162,71164,71166,71168,71170,71172,71174,71176,71178,71180,71182,71184,71186,71188,71190,71192,71194,71196,71198,71200,71202,71204,71206,71208,71210,71212,71214,71216,71218,71220,71222],{},[898,71159,1839],{},[898,71161,8051],{},[1761,71163,1915],{"stretchy":1821},[1765,71165,2633],{},[1761,71167,1920],{"stretchy":1821},[1761,71169,1909],{},[1765,71171,2318],{},[1761,71173,2447],{},[1765,71175,2633],{},[1761,71177,1885],{},[1761,71179,1915],{"stretchy":1821},[1765,71181,70786],{},[1761,71183,2447],{},[1765,71185,1945],{},[2761,71187,7057],{},[1765,71189,63060],{},[1761,71191,1885],{},[1765,71193,26578],{},[1761,71195,2447],{},[1765,71197,7160],{},[1761,71199,1964],{},[1765,71201,7160],{},[1761,71203,1964],{},[1765,71205,6321],{},[1761,71207,1920],{"stretchy":1821},[1761,71209,1909],{},[1765,71211,9262],{},[1761,71213,1885],{},[1765,71215,25213],{},[1761,71217,1909],{},[1761,71219,1885],{},[1765,71221,5433],{},[1761,71223,1834],{"separator":1833},[902,71225,71226],{"encoding":904},"PR(10) = 4 \\cdot 10 - (0{,}04 \\cdot 1\\,000 - 0{,}9 \\cdot 100 + 100 + 5) = 40 - 55 = -15,",[724,71228,71229,71230,1741],{},"tj. ztráta větší než ",[883,71231,71233],{"className":71232},[886],[888,71234,71235],{"xmlns":890},[892,71236,71237,71247],{},[895,71238,71239,71241,71243,71245],{},[898,71240,14474],{},[898,71242,6849],{},[1761,71244,1909],{},[1765,71246,6321],{},[902,71248,71249],{"encoding":904},"FC = 5",[724,71251,71252,71255,71256,71259,71260,1741],{},[38,71253,71254],{},"Závěr:"," firma by měla ",[38,71257,71258],{},"zastavit výrobu"," — i vypnutí provozu způsobí menší ztrátu, a to pouze ve výši ",[883,71261,71263],{"className":71262},[886],[888,71264,71265],{"xmlns":890},[892,71266,71267,71277],{},[895,71268,71269,71271,71273,71275],{},[898,71270,14474],{},[898,71272,6849],{},[1761,71274,1909],{},[1765,71276,6321],{},[902,71278,71249],{"encoding":904},[115,71280,71282],{"id":71281},"konstrukce-křivky-nabídky-firmy","Konstrukce křivky nabídky firmy",[724,71284,71285,71286,71288,71289,71304,71305,71318,71319,71345,71346,71359,71360,71377,71378,6699,71395,71398,71399,71419,71420,71435,71436,2506],{},"Důležitým završením analýzy je konstrukce ",[38,71287,59253],{},". S nabízeným množstvím rostou mezní náklady ",[883,71290,71292],{"className":71291},[886],[888,71293,71294],{"xmlns":890},[892,71295,71296,71302],{},[895,71297,71298,71300],{},[898,71299,6889],{},[898,71301,6849],{},[902,71303,59270],{"encoding":904}," a tyto určují cenu ",[883,71306,71308],{"className":71307},[886],[888,71309,71310],{"xmlns":890},[892,71311,71312,71316],{},[895,71313,71314],{},[898,71315,1839],{},[902,71317,1839],{"encoding":904},", za kterou je firma ochotna toto množství realizovat. Proto platí ",[883,71320,71322],{"className":71321},[886],[888,71323,71324],{"xmlns":890},[892,71325,71326,71342],{},[895,71327,71328,71330,71332,71334,71336,71338,71340],{},[898,71329,1839],{},[1761,71331,1909],{},[898,71333,6889],{},[898,71335,6849],{},[1761,71337,1915],{"stretchy":1821},[898,71339,1828],{},[1761,71341,1920],{"stretchy":1821},[902,71343,71344],{"encoding":904},"P = MC(Q)"," (obrázek 3.14). Cena ",[883,71347,71349],{"className":71348},[886],[888,71350,71351],{"xmlns":890},[892,71352,71353,71357],{},[895,71354,71355],{},[898,71356,1839],{},[902,71358,1839],{"encoding":904}," však nemůže být nižší než ",[883,71361,71363],{"className":71362},[886],[888,71364,71365],{"xmlns":890},[892,71366,71367,71375],{},[895,71368,71369],{},[1824,71370,71371,71373],{},[898,71372,1839],{},[1761,71374,8408],{},[902,71376,8458],{"encoding":904}," odpovídající množství ",[883,71379,71381],{"className":71380},[886],[888,71382,71383],{"xmlns":890},[892,71384,71385,71393],{},[895,71386,71387],{},[1824,71388,71389,71391],{},[898,71390,1828],{},[1761,71392,8408],{},[902,71394,33874],{"encoding":904},[38,71396,71397],{},"minima průměrných variabilních nákladů"," (fixní náklady nelze při optimalizaci zahrnout — jsou konstantní součástí nákladů i zisku). Křivka nabídky se tedy skládá z úsečky ",[883,71400,71402],{"className":71401},[886],[888,71403,71404],{"xmlns":890},[892,71405,71406,71416],{},[895,71407,71408,71410],{},[1765,71409,1767],{},[1824,71411,71412,71414],{},[898,71413,1828],{},[1761,71415,8408],{},[902,71417,71418],{"encoding":904},"0Q^*"," (kde firma nenabízí nic) a rostoucí části ",[883,71421,71423],{"className":71422},[886],[888,71424,71425],{"xmlns":890},[892,71426,71427,71433],{},[895,71428,71429,71431],{},[898,71430,6889],{},[898,71432,6849],{},[902,71434,59270],{"encoding":904}," nad bodem ",[883,71437,71439],{"className":71438},[886],[888,71440,71441],{"xmlns":890},[892,71442,71443,71447],{},[895,71444,71445],{},[898,71446,8309],{},[902,71448,8309],{"encoding":904},[883,71450,71452],{"className":71451},[886],[888,71453,71454],{"xmlns":890,"display":1930},[892,71455,71456,71563],{},[24787,71457,71458],{"width":32101},[24792,71459,71460,71462,71556,71558],{},[24795,71461],{"width":32106},[24795,71463,71464],{},[895,71465,71466,71468,71470,71472,71474,71476,71478,71480],{},[898,71467,1839],{},[1761,71469,1909],{},[898,71471,1912],{},[1761,71473,1915],{"stretchy":1821},[898,71475,1828],{},[1761,71477,1920],{"stretchy":1821},[1761,71479,1909],{},[895,71481,71482,71485],{},[1761,71483,71484],{"fence":1833},"{",[24787,71486,71489,71528],{"rowspacing":71487,"columnalign":71488,"columnspacing":19322},"0.36em","left left",[24792,71490,71491,71507],{},[24795,71492,71493],{},[6411,71494,71495],{"scriptlevel":1767,"displaystyle":1821},[895,71496,71497,71499,71501,71503,71505],{},[898,71498,6889],{},[898,71500,6849],{},[1761,71502,1915],{"stretchy":1821},[898,71504,1828],{},[1761,71506,1920],{"stretchy":1821},[24795,71508,71509],{},[6411,71510,71511],{"scriptlevel":1767,"displaystyle":1821},[895,71512,71513,71516,71518,71520,71526],{},[2761,71514,71515],{},"pro ",[898,71517,1828],{},[1761,71519,8538],{},[1824,71521,71522,71524],{},[898,71523,1828],{},[1761,71525,8408],{},[1761,71527,1834],{"separator":1833},[24792,71529,71530,71536],{},[24795,71531,71532],{},[6411,71533,71534],{"scriptlevel":1767,"displaystyle":1821},[1765,71535,1767],{},[24795,71537,71538],{},[6411,71539,71540],{"scriptlevel":1767,"displaystyle":1821},[895,71541,71542,71544,71546,71548,71554],{},[2761,71543,71515],{},[898,71545,1828],{},[1761,71547,2058],{},[1824,71549,71550,71552],{},[898,71551,1828],{},[1761,71553,8408],{},[1761,71555,1834],{"separator":1833},[24795,71557],{"width":32106},[24795,71559,71560],{},[2761,71561,71562],{},"(3.15)",[902,71564,71565],{"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}",[724,71567,8364,71568,71585,71586,71603,71604,45511,71634,71637],{},[883,71569,71571],{"className":71570},[886],[888,71572,71573],{"xmlns":890},[892,71574,71575,71583],{},[895,71576,71577],{},[1824,71578,71579,71581],{},[898,71580,1828],{},[1761,71582,8408],{},[902,71584,33874],{"encoding":904}," je bod minima ",[883,71587,71589],{"className":71588},[886],[888,71590,71591],{"xmlns":890},[892,71592,71593,71601],{},[895,71594,71595,71597,71599],{},[898,71596,8309],{},[898,71598,44359],{},[898,71600,6849],{},[902,71602,59289],{"encoding":904},". Bod ",[883,71605,71607],{"className":71606},[886],[888,71608,71609],{"xmlns":890},[892,71610,71611,71631],{},[895,71612,71613,71615,71621,71623,71629],{},[1761,71614,1915],{"stretchy":1821},[1824,71616,71617,71619],{},[898,71618,1828],{},[1761,71620,8408],{},[1761,71622,1834],{"separator":1833},[1824,71624,71625,71627],{},[898,71626,1839],{},[1761,71628,8408],{},[1761,71630,1920],{"stretchy":1821},[902,71632,71633],{"encoding":904},"(Q^*, P^*)",[38,71635,71636],{},"shutdown point"," — pod ním se firmě nevyplatí produkovat.",[1636,71639,71640,71645],{},[724,71641,71642,71644],{},[883,71643,4452],{}," Postup — jak odvodit nabídku firmy",[152,71646,71647,71696,71791,71846,71917],{},[123,71648,71649,71650,2068,71672,1741],{},"Ze zadaných nákladů určete ",[883,71651,71653],{"className":71652},[886],[888,71654,71655],{"xmlns":890},[892,71656,71657,71669],{},[895,71658,71659,71661,71663,71665,71667],{},[898,71660,6889],{},[898,71662,6849],{},[1761,71664,1915],{"stretchy":1821},[898,71666,1828],{},[1761,71668,1920],{"stretchy":1821},[902,71670,71671],{"encoding":904},"MC(Q)",[883,71673,71675],{"className":71674},[886],[888,71676,71677],{"xmlns":890},[892,71678,71679,71693],{},[895,71680,71681,71683,71685,71687,71689,71691],{},[898,71682,8309],{},[898,71684,44359],{},[898,71686,6849],{},[1761,71688,1915],{"stretchy":1821},[898,71690,1828],{},[1761,71692,1920],{"stretchy":1821},[902,71694,71695],{"encoding":904},"AVC(Q)",[123,71697,71698,71699,71716,71717,71734,71735,71767,71768,2162],{},"Najděte ",[883,71700,71702],{"className":71701},[886],[888,71703,71704],{"xmlns":890},[892,71705,71706,71714],{},[895,71707,71708],{},[1824,71709,71710,71712],{},[898,71711,1828],{},[1761,71713,8408],{},[902,71715,33874],{"encoding":904}," jako bod minima ",[883,71718,71720],{"className":71719},[886],[888,71721,71722],{"xmlns":890},[892,71723,71724,71732],{},[895,71725,71726,71728,71730],{},[898,71727,8309],{},[898,71729,44359],{},[898,71731,6849],{},[902,71733,59289],{"encoding":904}," (řešením ",[883,71736,71738],{"className":71737},[886],[888,71739,71740],{"xmlns":890},[892,71741,71742,71764],{},[895,71743,71744,71746,71748,71754,71756,71758,71760,71762],{},[898,71745,8309],{},[898,71747,44359],{},[1824,71749,71750,71752],{},[898,71751,6849],{},[1761,71753,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,71755,1915],{"stretchy":1821},[898,71757,1828],{},[1761,71759,1920],{"stretchy":1821},[1761,71761,1909],{},[1765,71763,1767],{},[902,71765,71766],{"encoding":904},"AVC'(Q) = 0",", případně rovnice ",[883,71769,71771],{"className":71770},[886],[888,71772,71773],{"xmlns":890},[892,71774,71775,71789],{},[895,71776,71777,71779,71781,71783,71785,71787],{},[898,71778,8309],{},[898,71780,44359],{},[898,71782,6849],{},[1761,71784,1909],{},[898,71786,6889],{},[898,71788,6849],{},[902,71790,59226],{"encoding":904},[123,71792,69699,71793,71845],{},[883,71794,71796],{"className":71795},[886],[888,71797,71798],{"xmlns":890},[892,71799,71800,71842],{},[895,71801,71802,71808,71810,71812,71814,71816,71822,71824,71826,71828,71830,71832,71834,71840],{},[1824,71803,71804,71806],{},[898,71805,1839],{},[1761,71807,8408],{},[1761,71809,1909],{},[898,71811,6889],{},[898,71813,6849],{},[1761,71815,1915],{"stretchy":1821},[1824,71817,71818,71820],{},[898,71819,1828],{},[1761,71821,8408],{},[1761,71823,1920],{"stretchy":1821},[1761,71825,1909],{},[898,71827,8309],{},[898,71829,44359],{},[898,71831,6849],{},[1761,71833,1915],{"stretchy":1821},[1824,71835,71836,71838],{},[898,71837,1828],{},[1761,71839,8408],{},[1761,71841,1920],{"stretchy":1821},[902,71843,71844],{"encoding":904},"P^* = MC(Q^*) = AVC(Q^*)"," — minimální cenu nabídky.",[123,71847,71848,71849,10518,71881,71903,71904,1741],{},"Zapište nabídku: ",[883,71850,71852],{"className":71851},[886],[888,71853,71854],{"xmlns":890},[892,71855,71856,71878],{},[895,71857,71858,71860,71862,71864,71866,71868,71870,71872,71874,71876],{},[898,71859,1912],{},[1761,71861,1915],{"stretchy":1821},[898,71863,1828],{},[1761,71865,1920],{"stretchy":1821},[1761,71867,1909],{},[898,71869,6889],{},[898,71871,6849],{},[1761,71873,1915],{"stretchy":1821},[898,71875,1828],{},[1761,71877,1920],{"stretchy":1821},[902,71879,71880],{"encoding":904},"S(Q) = MC(Q)",[883,71882,71884],{"className":71883},[886],[888,71885,71886],{"xmlns":890},[892,71887,71888,71900],{},[895,71889,71890,71892,71894],{},[898,71891,1828],{},[1761,71893,8538],{},[1824,71895,71896,71898],{},[898,71897,1828],{},[1761,71899,8408],{},[902,71901,71902],{"encoding":904},"Q \\geq Q^*",", jinak ",[883,71905,71907],{"className":71906},[886],[888,71908,71909],{"xmlns":890},[892,71910,71911,71915],{},[895,71912,71913],{},[1765,71914,1767],{},[902,71916,1767],{"encoding":904},[123,71918,71919,71920,71952],{},"V případě potřeby vyjádřete inverzi ",[883,71921,71923],{"className":71922},[886],[888,71924,71925],{"xmlns":890},[892,71926,71927,71949],{},[895,71928,71929,71931,71933,71943,71945,71947],{},[898,71930,1828],{},[1761,71932,1909],{},[1824,71934,71935,71937],{},[898,71936,1912],{},[895,71938,71939,71941],{},[1761,71940,1885],{},[1765,71942,1945],{},[1761,71944,1915],{"stretchy":1821},[898,71946,1839],{},[1761,71948,1920],{"stretchy":1821},[902,71950,71951],{"encoding":904},"Q = S^{-1}(P)"," doplněním na čtverec.",[724,71954,71955],{},[614,71956,71957,71958,1343,71973,2068,71990,33231,72005,72018,72019,72044,72045,72058,72059,72076,72077,72094,72095,72112],{},"Obrázek 3.14: Křivky ",[883,71959,71961],{"className":71960},[886],[888,71962,71963],{"xmlns":890},[892,71964,71965,71971],{},[895,71966,71967,71969],{},[898,71968,8309],{},[898,71970,6849],{},[902,71972,59538],{"encoding":904},[883,71974,71976],{"className":71975},[886],[888,71977,71978],{"xmlns":890},[892,71979,71980,71988],{},[895,71981,71982,71984,71986],{},[898,71983,8309],{},[898,71985,44359],{},[898,71987,6849],{},[902,71989,59289],{"encoding":904},[883,71991,71993],{"className":71992},[886],[888,71994,71995],{"xmlns":890},[892,71996,71997,72003],{},[895,71998,71999,72001],{},[898,72000,6889],{},[898,72002,6849],{},[902,72004,59270],{"encoding":904},[883,72006,72008],{"className":72007},[886],[888,72009,72010],{"xmlns":890},[892,72011,72012,72016],{},[895,72013,72014],{},[898,72015,900],{},[902,72017,900],{"encoding":904},"; křivka nabídky ",[883,72020,72022],{"className":72021},[886],[888,72023,72024],{"xmlns":890},[892,72025,72026,72042],{},[895,72027,72028,72030,72032,72034,72036,72038,72040],{},[898,72029,1839],{},[1761,72031,1909],{},[898,72033,6889],{},[898,72035,6849],{},[1761,72037,1915],{"stretchy":1821},[898,72039,1828],{},[1761,72041,1920],{"stretchy":1821},[902,72043,71344],{"encoding":904}," začíná v bodě ",[883,72046,72048],{"className":72047},[886],[888,72049,72050],{"xmlns":890},[892,72051,72052,72056],{},[895,72053,72054],{},[898,72055,8309],{},[902,72057,8309],{"encoding":904}," odpovídajícím minimu ",[883,72060,72062],{"className":72061},[886],[888,72063,72064],{"xmlns":890},[892,72065,72066,72074],{},[895,72067,72068,72070,72072],{},[898,72069,8309],{},[898,72071,44359],{},[898,72073,6849],{},[902,72075,59289],{"encoding":904}," při ceně ",[883,72078,72080],{"className":72079},[886],[888,72081,72082],{"xmlns":890},[892,72083,72084,72092],{},[895,72085,72086],{},[1824,72087,72088,72090],{},[898,72089,1839],{},[1761,72091,8408],{},[902,72093,8458],{"encoding":904}," (minimální cena nabídky); pod ",[883,72096,72098],{"className":72097},[886],[888,72099,72100],{"xmlns":890},[892,72101,72102,72110],{},[895,72103,72104],{},[1824,72105,72106,72108],{},[898,72107,1828],{},[1761,72109,8408],{},[902,72111,33874],{"encoding":904}," je nabídka nulová.",[41374,72114,72116],{"id":72115},"příklad-312","Příklad 3.12",[724,72118,72119,61500,72121,72167],{},[38,72120,59965],{},[883,72122,72124],{"className":72123},[886],[888,72125,72126],{"xmlns":890},[892,72127,72128,72164],{},[895,72129,72130,72132,72134,72136,72138,72144,72146,72148,72154,72156,72158,72160,72162],{},[898,72131,1655],{},[898,72133,6849],{},[1761,72135,1909],{},[1765,72137,6865],{},[1824,72139,72140,72142],{},[898,72141,1828],{},[1765,72143,5486],{},[1761,72145,1885],{},[1765,72147,2296],{},[1824,72149,72150,72152],{},[898,72151,1828],{},[1765,72153,2296],{},[1761,72155,1964],{},[1765,72157,5433],{},[898,72159,1828],{},[1761,72161,1964],{},[1765,72163,2633],{},[902,72165,72166],{"encoding":904},"TC = 0{,}1Q^3 - 2Q^2 + 15Q + 10"," odvoďte funkci nabídky firmy.",[724,72169,72170,1989,72172,72209,72210,2506],{},[38,72171,26803],{},[883,72173,72175],{"className":72174},[886],[888,72176,72177],{"xmlns":890},[892,72178,72179,72206],{},[895,72180,72181,72183,72185,72187,72190,72196,72198,72200,72202,72204],{},[898,72182,6889],{},[898,72184,6849],{},[1761,72186,1909],{},[1765,72188,72189],{},"0,3",[1824,72191,72192,72194],{},[898,72193,1828],{},[1765,72195,2296],{},[1761,72197,1885],{},[1765,72199,2318],{},[898,72201,1828],{},[1761,72203,1964],{},[1765,72205,5433],{},[902,72207,72208],{"encoding":904},"MC = 0{,}3Q^2 - 4Q + 15",", takže z ",[883,72211,72213],{"className":72212},[886],[888,72214,72215],{"xmlns":890},[892,72216,72217,72227],{},[895,72218,72219,72221,72223,72225],{},[898,72220,1839],{},[1761,72222,1909],{},[898,72224,6889],{},[898,72226,6849],{},[902,72228,72229],{"encoding":904},"P = MC",[883,72231,72233],{"className":72232},[886],[888,72234,72235],{"xmlns":890,"display":1930},[892,72236,72237,72262],{},[895,72238,72239,72241,72243,72245,72251,72253,72255,72257,72259],{},[898,72240,1839],{},[1761,72242,1909],{},[1765,72244,72189],{},[1824,72246,72247,72249],{},[898,72248,1828],{},[1765,72250,2296],{},[1761,72252,1885],{},[1765,72254,2318],{},[898,72256,1828],{},[1761,72258,1964],{},[1765,72260,72261],{},"15.",[902,72263,72264],{"encoding":904},"P = 0{,}3Q^2 - 4Q + 15.",[724,72266,72267,72268,9433,72281,72294],{},"Vyjádření ",[883,72269,72271],{"className":72270},[886],[888,72272,72273],{"xmlns":890},[892,72274,72275,72279],{},[895,72276,72277],{},[898,72278,1828],{},[902,72280,1828],{"encoding":904},[883,72282,72284],{"className":72283},[886],[888,72285,72286],{"xmlns":890},[892,72287,72288,72292],{},[895,72289,72290],{},[898,72291,1839],{},[902,72293,1839],{"encoding":904}," doplněním na čtverec:",[883,72296,72298],{"className":72297},[886],[888,72299,72300],{"xmlns":890,"display":1930},[892,72301,72302,72392],{},[895,72303,72304,72306,72308,72310,72348,72350,72352,72374,72376,72390],{},[898,72305,1839],{},[1761,72307,1909],{},[1765,72309,72189],{},[895,72311,72312,72314,72336,72338,72346],{},[1761,72313,1915],{"fence":1833},[1824,72315,72316,72334],{},[895,72317,72318,72320,72322,72324,72332],{},[1761,72319,1915],{"fence":1833},[898,72321,1828],{},[1761,72323,1885],{},[6411,72325,72326],{"scriptlevel":1767,"displaystyle":1821},[4379,72327,72328,72330],{},[1765,72329,13077],{},[1765,72331,5486],{},[1761,72333,1920],{"fence":1833},[1765,72335,2296],{},[1761,72337,1964],{},[6411,72339,72340],{"scriptlevel":1767,"displaystyle":1821},[4379,72341,72342,72344],{},[1765,72343,7190],{},[1765,72345,8056],{},[1761,72347,1920],{"fence":1833},[1761,72349,1834],{"separator":1833},[3315,72351],{"width":3317},[1824,72353,72354,72372],{},[895,72355,72356,72358,72360,72362,72370],{},[1761,72357,1915],{"fence":1833},[898,72359,1828],{},[1761,72361,1885],{},[6411,72363,72364],{"scriptlevel":1767,"displaystyle":1821},[4379,72365,72366,72368],{},[1765,72367,13077],{},[1765,72369,5486],{},[1761,72371,1920],{"fence":1833},[1765,72373,2296],{},[1761,72375,1909],{},[4379,72377,72378,72388],{},[895,72379,72380,72382,72384,72386],{},[1765,72381,42042],{},[898,72383,1839],{},[1761,72385,1885],{},[1765,72387,7190],{},[1765,72389,8056],{},[1761,72391,1834],{"separator":1833},[902,72393,72394],{"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},",[883,72396,72398],{"className":72397},[886],[888,72399,72400],{"xmlns":890,"display":1930},[892,72401,72402,72434],{},[895,72403,72404,72406,72408,72414,72416,72432],{},[898,72405,1828],{},[1761,72407,1909],{},[4379,72409,72410,72412],{},[1765,72411,13077],{},[1765,72413,5486],{},[1761,72415,1964],{},[4379,72417,72418,72430],{},[12161,72419,72420],{},[895,72421,72422,72424,72426,72428],{},[1765,72423,42042],{},[898,72425,1839],{},[1761,72427,1885],{},[1765,72429,7190],{},[1765,72431,5486],{},[898,72433,1741],{"mathvariant":1969},[902,72435,72436],{"encoding":904},"Q = \\frac{20}{3} + \\frac{\\sqrt{30P - 50}}{3}.",[724,72438,70996,72439,1343,72477,1343,72525,72559,72560,1741],{},[883,72440,72442],{"className":72441},[886],[888,72443,72444],{"xmlns":890},[892,72445,72446,72474],{},[895,72447,72448,72450,72452,72454,72456,72458,72464,72466,72468,72470,72472],{},[898,72449,8309],{},[898,72451,44359],{},[898,72453,6849],{},[1761,72455,1909],{},[1765,72457,6865],{},[1824,72459,72460,72462],{},[898,72461,1828],{},[1765,72463,2296],{},[1761,72465,1885],{},[1765,72467,2296],{},[898,72469,1828],{},[1761,72471,1964],{},[1765,72473,5433],{},[902,72475,72476],{"encoding":904},"AVC = 0{,}1Q^2 - 2Q + 15",[883,72478,72480],{"className":72479},[886],[888,72481,72482],{"xmlns":890},[892,72483,72484,72522],{},[895,72485,72486,72488,72490,72496,72498,72500,72502,72504,72506,72508,72510,72512,72518,72520],{},[898,72487,8309],{},[898,72489,44359],{},[1824,72491,72492,72494],{},[898,72493,6849],{},[1761,72495,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,72497,1909],{},[1765,72499,6910],{},[898,72501,1828],{},[1761,72503,1885],{},[1765,72505,2296],{},[1761,72507,1909],{},[1765,72509,1767],{},[1761,72511,8044],{},[1824,72513,72514,72516],{},[898,72515,1828],{},[1761,72517,8408],{},[1761,72519,1909],{},[1765,72521,2633],{},[902,72523,72524],{"encoding":904},"AVC' = 0{,}2Q - 2 = 0 \\Rightarrow Q^* = 10",[883,72526,72528],{"className":72527},[886],[888,72529,72530],{"xmlns":890},[892,72531,72532,72556],{},[895,72533,72534,72536,72538,72548,72550,72552,72554],{},[898,72535,8309],{},[898,72537,44359],{},[1824,72539,72540,72542],{},[898,72541,6849],{},[895,72543,72544,72546],{},[1761,72545,6459],{"mathvariant":1969},[1761,72547,6459],{"mathvariant":1969},[1761,72549,1909],{},[1765,72551,6910],{},[1761,72553,1763],{},[1765,72555,1767],{},[902,72557,72558],{"encoding":904},"AVC'' = 0{,}2 > 0"," (minimum). Minimální cena nabídky ",[883,72561,72563],{"className":72562},[886],[888,72564,72565],{"xmlns":890},[892,72566,72567,72603],{},[895,72568,72569,72575,72577,72579,72581,72583,72585,72587,72589,72591,72593,72595,72597,72599,72601],{},[1824,72570,72571,72573],{},[898,72572,1839],{},[1761,72574,8408],{},[1761,72576,1909],{},[898,72578,6889],{},[898,72580,6849],{},[1761,72582,1915],{"stretchy":1821},[1765,72584,2633],{},[1761,72586,1920],{"stretchy":1821},[1761,72588,1909],{},[1765,72590,42042],{},[1761,72592,1885],{},[1765,72594,9262],{},[1761,72596,1964],{},[1765,72598,5433],{},[1761,72600,1909],{},[1765,72602,6321],{},[902,72604,72605],{"encoding":904},"P^* = MC(10) = 30 - 40 + 15 = 5",[724,72607,72608],{},[38,72609,72610],{},"Závěr.",[883,72612,72614],{"className":72613},[886],[888,72615,72616],{"xmlns":890,"display":1930},[892,72617,72618,72704],{},[895,72619,72620,72622,72624,72626,72628,72630,72632,72634],{},[898,72621,1839],{},[1761,72623,1909],{},[898,72625,1912],{},[1761,72627,1915],{"stretchy":1821},[898,72629,1828],{},[1761,72631,1920],{"stretchy":1821},[1761,72633,1909],{},[895,72635,72636,72638],{},[1761,72637,71484],{"fence":1833},[24787,72639,72640,72682],{"rowspacing":71487,"columnalign":71488,"columnspacing":19322},[24792,72641,72642,72666],{},[24795,72643,72644],{},[6411,72645,72646],{"scriptlevel":1767,"displaystyle":1821},[895,72647,72648,72650,72656,72658,72660,72662,72664],{},[1765,72649,72189],{},[1824,72651,72652,72654],{},[898,72653,1828],{},[1765,72655,2296],{},[1761,72657,1885],{},[1765,72659,2318],{},[898,72661,1828],{},[1761,72663,1964],{},[1765,72665,5433],{},[24795,72667,72668],{},[6411,72669,72670],{"scriptlevel":1767,"displaystyle":1821},[895,72671,72672,72674,72676,72678,72680],{},[2761,72673,71515],{},[898,72675,1828],{},[1761,72677,8538],{},[1765,72679,2633],{},[1761,72681,1834],{"separator":1833},[24792,72683,72684,72690],{},[24795,72685,72686],{},[6411,72687,72688],{"scriptlevel":1767,"displaystyle":1821},[1765,72689,1767],{},[24795,72691,72692],{},[6411,72693,72694],{"scriptlevel":1767,"displaystyle":1821},[895,72695,72696,72698,72700,72702],{},[2761,72697,71515],{},[898,72699,1828],{},[1761,72701,2058],{},[1765,72703,23361],{},[902,72705,72706],{"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}",[724,72708,72709],{},[614,72710,72711,72712,72727,72728,1741],{},"Obrázek 3.15: Grafická ilustrace nabídky firmy odvozené z části křivky ",[883,72713,72715],{"className":72714},[886],[888,72716,72717],{"xmlns":890},[892,72718,72719,72725],{},[895,72720,72721,72723],{},[898,72722,6889],{},[898,72724,6849],{},[902,72726,59270],{"encoding":904}," ležící nad minimem ",[883,72729,72731],{"className":72730},[886],[888,72732,72733],{"xmlns":890},[892,72734,72735,72743],{},[895,72736,72737,72739,72741],{},[898,72738,8309],{},[898,72740,44359],{},[898,72742,6849],{},[902,72744,59289],{"encoding":904},[115,72746,72748],{"id":72747},"shrnutí-kapitoly-3","Shrnutí kapitoly 3",[724,72750,72751,72752,72756,72757,72772,72773,72793,72794,2068,72797,72800,72801,72803,72804,23978,72826,72828,72829,2068,72831,62704,72834,1989,72837,5715,72852,72867],{},"Celkový příjem je součin ceny a množství, kde cena je dána funkcí ",[207,72753,72755],{"className":72754,"dataFsResolvedFilePath":800,"href":801},[210],"poptávky",". Pro lineární poptávku je ",[883,72758,72760],{"className":72759},[886],[888,72761,72762],{"xmlns":890},[892,72763,72764,72770],{},[895,72765,72766,72768],{},[898,72767,1655],{},[898,72769,8051],{},[902,72771,8151],{"encoding":904}," kvadratická. Průměrný příjem je podíl ",[883,72774,72776],{"className":72775},[886],[888,72777,72778],{"xmlns":890},[892,72779,72780,72790],{},[895,72781,72782,72784,72786,72788],{},[898,72783,1655],{},[898,72785,8051],{},[898,72787,8726],{"mathvariant":1969},[898,72789,1828],{},[902,72791,72792],{"encoding":904},"TR\u002FQ"," a rovná se poptávkové funkci. Celkové náklady se skládají z ",[38,72795,72796],{},"fixních",[38,72798,72799],{},"celkových variabilních"," nákladů. Průměrné veličiny jsou jejich podíly s množstvím. ",[38,72802,68303],{}," identifikují, kdy se firma nachází na prahu rentability. Rozdíl ",[883,72805,72807],{"className":72806},[886],[888,72808,72809],{"xmlns":890},[892,72810,72811,72823],{},[895,72812,72813,72815,72817,72819,72821],{},[898,72814,1655],{},[898,72816,8051],{},[1761,72818,1885],{},[898,72820,1655],{},[898,72822,6849],{},[902,72824,72825],{"encoding":904},"TR - TC",[38,72827,59150],{},"; klíčový je výpočet produkce, která zisk maximalizuje. ",[38,72830,60462],{},[38,72832,72833],{},"mezní náklady",[207,72835,1145],{"className":72836,"dataFsResolvedFilePath":764,"href":765},[210],[883,72838,72840],{"className":72839},[886],[888,72841,72842],{"xmlns":890},[892,72843,72844,72850],{},[895,72845,72846,72848],{},[898,72847,1655],{},[898,72849,8051],{},[902,72851,8151],{"encoding":904},[883,72853,72855],{"className":72854},[886],[888,72856,72857],{"xmlns":890},[892,72858,72859,72865],{},[895,72860,72861,72863],{},[898,72862,1655],{},[898,72864,6849],{},[902,72866,7310],{"encoding":904}," podle produkce; udávají rychlosti změn, resp. přibližné změny odpovídající jednotkové změně produkce.",[120,72869,72870,72932,72998,73060],{},[123,72871,72872,72875,72876,14432,72891,1741],{},[38,72873,72874],{},"Princip minimalizace průměrných nákladů:"," v bodě minima ",[883,72877,72879],{"className":72878},[886],[888,72880,72881],{"xmlns":890},[892,72882,72883,72889],{},[895,72884,72885,72887],{},[898,72886,8309],{},[898,72888,6849],{},[902,72890,59538],{"encoding":904},[883,72892,72894],{"className":72893},[886],[888,72895,72896],{"xmlns":890},[892,72897,72898,72930],{},[895,72899,72900,72902,72904,72906,72912,72914,72916,72918,72920,72922,72928],{},[898,72901,8309],{},[898,72903,6849],{},[1761,72905,1915],{"stretchy":1821},[1681,72907,72908,72910],{},[898,72909,1828],{},[1765,72911,1767],{},[1761,72913,1920],{"stretchy":1821},[1761,72915,1909],{},[898,72917,6889],{},[898,72919,6849],{},[1761,72921,1915],{"stretchy":1821},[1681,72923,72924,72926],{},[898,72925,1828],{},[1765,72927,1767],{},[1761,72929,1920],{"stretchy":1821},[902,72931,66547],{"encoding":904},[123,72933,72934,72875,72937,14432,72954,1741],{},[38,72935,72936],{},"Princip minimalizace průměrných variabilních nákladů:",[883,72938,72940],{"className":72939},[886],[888,72941,72942],{"xmlns":890},[892,72943,72944,72952],{},[895,72945,72946,72948,72950],{},[898,72947,8309],{},[898,72949,44359],{},[898,72951,6849],{},[902,72953,59289],{"encoding":904},[883,72955,72957],{"className":72956},[886],[888,72958,72959],{"xmlns":890},[892,72960,72961,72995],{},[895,72962,72963,72965,72967,72969,72971,72977,72979,72981,72983,72985,72987,72993],{},[898,72964,8309],{},[898,72966,44359],{},[898,72968,6849],{},[1761,72970,1915],{"stretchy":1821},[1681,72972,72973,72975],{},[898,72974,1828],{},[1765,72976,1767],{},[1761,72978,1920],{"stretchy":1821},[1761,72980,1909],{},[898,72982,6889],{},[898,72984,6849],{},[1761,72986,1915],{"stretchy":1821},[1681,72988,72989,72991],{},[898,72990,1828],{},[1765,72992,1767],{},[1761,72994,1920],{"stretchy":1821},[902,72996,72997],{"encoding":904},"AVC(Q_0) = MC(Q_0)",[123,72999,73000,73003,73004,14432,73019,1741],{},[38,73001,73002],{},"Princip maximalizace zisku:"," v bodě maxima ",[883,73005,73007],{"className":73006},[886],[888,73008,73009],{"xmlns":890},[892,73010,73011,73017],{},[895,73012,73013,73015],{},[898,73014,1839],{},[898,73016,8051],{},[902,73018,67457],{"encoding":904},[883,73020,73022],{"className":73021},[886],[888,73023,73024],{"xmlns":890},[892,73025,73026,73058],{},[895,73027,73028,73030,73032,73034,73040,73042,73044,73046,73048,73050,73056],{},[898,73029,6889],{},[898,73031,8051],{},[1761,73033,1915],{"stretchy":1821},[1681,73035,73036,73038],{},[898,73037,1828],{},[1765,73039,1767],{},[1761,73041,1920],{"stretchy":1821},[1761,73043,1909],{},[898,73045,6889],{},[898,73047,6849],{},[1761,73049,1915],{"stretchy":1821},[1681,73051,73052,73054],{},[898,73053,1828],{},[1765,73055,1767],{},[1761,73057,1920],{"stretchy":1821},[902,73059,69623],{"encoding":904},[123,73061,73062,1989,73065,10518,73101,71903,73122,25627,73135,71585,73152,1741],{},[38,73063,73064],{},"Funkce nabídky firmy:",[883,73066,73068],{"className":73067},[886],[888,73069,73070],{"xmlns":890},[892,73071,73072,73098],{},[895,73073,73074,73076,73078,73080,73082,73084,73086,73088,73090,73092,73094,73096],{},[898,73075,1839],{},[1761,73077,1909],{},[898,73079,1912],{},[1761,73081,1915],{"stretchy":1821},[898,73083,1828],{},[1761,73085,1920],{"stretchy":1821},[1761,73087,1909],{},[898,73089,6889],{},[898,73091,6849],{},[1761,73093,1915],{"stretchy":1821},[898,73095,1828],{},[1761,73097,1920],{"stretchy":1821},[902,73099,73100],{"encoding":904},"P = S(Q) = MC(Q)",[883,73102,73104],{"className":73103},[886],[888,73105,73106],{"xmlns":890},[892,73107,73108,73120],{},[895,73109,73110,73112,73114],{},[898,73111,1828],{},[1761,73113,8538],{},[1824,73115,73116,73118],{},[898,73117,1828],{},[1761,73119,8408],{},[902,73121,71902],{"encoding":904},[883,73123,73125],{"className":73124},[886],[888,73126,73127],{"xmlns":890},[892,73128,73129,73133],{},[895,73130,73131],{},[1765,73132,1767],{},[902,73134,1767],{"encoding":904},[883,73136,73138],{"className":73137},[886],[888,73139,73140],{"xmlns":890},[892,73141,73142,73150],{},[895,73143,73144],{},[1824,73145,73146,73148],{},[898,73147,1828],{},[1761,73149,8408],{},[902,73151,33874],{"encoding":904},[883,73153,73155],{"className":73154},[886],[888,73156,73157],{"xmlns":890},[892,73158,73159,73167],{},[895,73160,73161,73163,73165],{},[898,73162,8309],{},[898,73164,44359],{},[898,73166,6849],{},[902,73168,59289],{"encoding":904},[115,73170,53867],{"id":53866},[152,73172,73173,73176,73179,73182,73185,73188,73191,73194,73197,73200,73203],{},[123,73174,73175],{},"Jaký je vztah pro celkový příjem v podmínkách dokonalé konkurence?",[123,73177,73178],{},"Jaký tvar má křivka celkového příjmu pro lineární poptávku?",[123,73180,73181],{},"Jak se vypočte mezní příjem a co udává?",[123,73183,73184],{},"Z jakých složek se skládají celkové náklady?",[123,73186,73187],{},"Jak se stanoví celkové náklady, známe-li náklady mezní?",[123,73189,73190],{},"Jaký je trend průměrných fixních nákladů a průměrných nákladů, roste-li produkce?",[123,73192,73193],{},"Jak se stanoví přibližně změna celkových nákladů?",[123,73195,73196],{},"Jak se vypočte zisk?",[123,73198,73199],{},"Jaká vlastnost platí v bodě maxima zisku?",[123,73201,73202],{},"Co jsou body zvratu? Jak se najdou?",[123,73204,73205],{},"Z jakých nákladových charakteristik se vychází při konstrukci nabídky?",[115,73207,73209],{"id":73208},"úlohy-31328","Úlohy 3.1–3.28",[198,73211,73213],{"id":73212},"příjem-3135","Příjem (3.1–3.5)",[724,73215,73216,49417,73219,73247,73248,73263,73264,73279,73280,73295,73296,1343,73311,1343,73326,73341],{},[38,73217,73218],{},"3.1",[883,73220,73222],{"className":73221},[886],[888,73223,73224],{"xmlns":890},[892,73225,73226,73244],{},[895,73227,73228,73230,73232,73234,73236,73238,73240,73242],{},[898,73229,1839],{},[1761,73231,1909],{},[898,73233,2244],{},[1761,73235,1915],{"stretchy":1821},[898,73237,1828],{},[1761,73239,1920],{"stretchy":1821},[1761,73241,1909],{},[1765,73243,7160],{},[902,73245,73246],{"encoding":904},"P = D(Q) = 100",". (a) Rozhodněte, v jakých podmínkách konkurence zadaná poptávka platí. (b) Najděte celkový příjem ",[883,73249,73251],{"className":73250},[886],[888,73252,73253],{"xmlns":890},[892,73254,73255,73261],{},[895,73256,73257,73259],{},[898,73258,1655],{},[898,73260,8051],{},[902,73262,8151],{"encoding":904},", průměrný příjem ",[883,73265,73267],{"className":73266},[886],[888,73268,73269],{"xmlns":890},[892,73270,73271,73277],{},[895,73272,73273,73275],{},[898,73274,8309],{},[898,73276,8051],{},[902,73278,59423],{"encoding":904}," a mezní příjem ",[883,73281,73283],{"className":73282},[886],[888,73284,73285],{"xmlns":890},[892,73286,73287,73293],{},[895,73288,73289,73291],{},[898,73290,6889],{},[898,73292,8051],{},[902,73294,10679],{"encoding":904},". (c) Vypočtěte ",[883,73297,73299],{"className":73298},[886],[888,73300,73301],{"xmlns":890},[892,73302,73303,73309],{},[895,73304,73305,73307],{},[898,73306,1655],{},[898,73308,8051],{},[902,73310,8151],{"encoding":904},[883,73312,73314],{"className":73313},[886],[888,73315,73316],{"xmlns":890},[892,73317,73318,73324],{},[895,73319,73320,73322],{},[898,73321,8309],{},[898,73323,8051],{},[902,73325,59423],{"encoding":904},[883,73327,73329],{"className":73328},[886],[888,73330,73331],{"xmlns":890},[892,73332,73333,73339],{},[895,73334,73335,73337],{},[898,73336,6889],{},[898,73338,8051],{},[902,73340,10679],{"encoding":904}," při množství 20. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,73343,73344,49417,73347,73247,73383,73263,73398,73279,73413,73295,73428,1343,73443,1343,73458,73473],{},[38,73345,73346],{},"3.2",[883,73348,73350],{"className":73349},[886],[888,73351,73352],{"xmlns":890},[892,73353,73354,73380],{},[895,73355,73356,73358,73360,73362,73364,73366,73368,73370,73372,73374,73376,73378],{},[898,73357,1839],{},[1761,73359,1909],{},[898,73361,2244],{},[1761,73363,1915],{"stretchy":1821},[898,73365,1828],{},[1761,73367,1920],{"stretchy":1821},[1761,73369,1909],{},[1761,73371,1885],{},[1765,73373,5426],{},[898,73375,1828],{},[1761,73377,1964],{},[1765,73379,13077],{},[902,73381,73382],{"encoding":904},"P = D(Q) = -0{,}5Q + 20",[883,73384,73386],{"className":73385},[886],[888,73387,73388],{"xmlns":890},[892,73389,73390,73396],{},[895,73391,73392,73394],{},[898,73393,1655],{},[898,73395,8051],{},[902,73397,8151],{"encoding":904},[883,73399,73401],{"className":73400},[886],[888,73402,73403],{"xmlns":890},[892,73404,73405,73411],{},[895,73406,73407,73409],{},[898,73408,8309],{},[898,73410,8051],{},[902,73412,59423],{"encoding":904},[883,73414,73416],{"className":73415},[886],[888,73417,73418],{"xmlns":890},[892,73419,73420,73426],{},[895,73421,73422,73424],{},[898,73423,6889],{},[898,73425,8051],{},[902,73427,10679],{"encoding":904},[883,73429,73431],{"className":73430},[886],[888,73432,73433],{"xmlns":890},[892,73434,73435,73441],{},[895,73436,73437,73439],{},[898,73438,1655],{},[898,73440,8051],{},[902,73442,8151],{"encoding":904},[883,73444,73446],{"className":73445},[886],[888,73447,73448],{"xmlns":890},[892,73449,73450,73456],{},[895,73451,73452,73454],{},[898,73453,8309],{},[898,73455,8051],{},[902,73457,59423],{"encoding":904},[883,73459,73461],{"className":73460},[886],[888,73462,73463],{"xmlns":890},[892,73464,73465,73471],{},[895,73466,73467,73469],{},[898,73468,6889],{},[898,73470,8051],{},[902,73472,10679],{"encoding":904}," při množství 10. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,73475,73476,49417,73479,73516,73517,73263,73532,73279,73547,73562,73563,10518,73578,73604,73605,73620,73621,1343,73636,10518,73651,73604,73676,73691,73692,73705,73706,73721,73722,73737,73738,1343,73751,1343,73766,1343,73781,1741],{},[38,73477,73478],{},"3.3",[883,73480,73482],{"className":73481},[886],[888,73483,73484],{"xmlns":890},[892,73485,73486,73513],{},[895,73487,73488,73490,73492,73494,73496,73498,73500,73502,73505,73507],{},[898,73489,1839],{},[1761,73491,1909],{},[898,73493,2244],{},[1761,73495,1915],{"stretchy":1821},[898,73497,1828],{},[1761,73499,1920],{"stretchy":1821},[1761,73501,1909],{},[1765,73503,73504],{},"1200",[1761,73506,1885],{},[1824,73508,73509,73511],{},[898,73510,1828],{},[1765,73512,2296],{},[902,73514,73515],{"encoding":904},"P = D(Q) = 1200 - Q^2",". (a) Najděte celkový příjem ",[883,73518,73520],{"className":73519},[886],[888,73521,73522],{"xmlns":890},[892,73523,73524,73530],{},[895,73525,73526,73528],{},[898,73527,1655],{},[898,73529,8051],{},[902,73531,8151],{"encoding":904},[883,73533,73535],{"className":73534},[886],[888,73536,73537],{"xmlns":890},[892,73538,73539,73545],{},[895,73540,73541,73543],{},[898,73542,8309],{},[898,73544,8051],{},[902,73546,59423],{"encoding":904},[883,73548,73550],{"className":73549},[886],[888,73551,73552],{"xmlns":890},[892,73553,73554,73560],{},[895,73555,73556,73558],{},[898,73557,6889],{},[898,73559,8051],{},[902,73561,10679],{"encoding":904},". (b) Vypočtěte ",[883,73564,73566],{"className":73565},[886],[888,73567,73568],{"xmlns":890},[892,73569,73570,73576],{},[895,73571,73572,73574],{},[898,73573,1655],{},[898,73575,8051],{},[902,73577,8151],{"encoding":904},[883,73579,73581],{"className":73580},[886],[888,73582,73583],{"xmlns":890},[892,73584,73585,73601],{},[895,73586,73587,73589,73591,73593,73595,73597,73599],{},[898,73588,1828],{},[1761,73590,1909],{},[1765,73592,2633],{},[1761,73594,1834],{"separator":1833},[1765,73596,13077],{},[1761,73598,1834],{"separator":1833},[1765,73600,42042],{},[902,73602,73603],{"encoding":904},"Q = 10, 20, 30"," a rozhodněte, kdy ",[883,73606,73608],{"className":73607},[886],[888,73609,73610],{"xmlns":890},[892,73611,73612,73618],{},[895,73613,73614,73616],{},[898,73615,1655],{},[898,73617,8051],{},[902,73619,8151],{"encoding":904}," roste, resp. klesá. (c) Vypočtěte ",[883,73622,73624],{"className":73623},[886],[888,73625,73626],{"xmlns":890},[892,73627,73628,73634],{},[895,73629,73630,73632],{},[898,73631,8309],{},[898,73633,8051],{},[902,73635,59423],{"encoding":904},[883,73637,73639],{"className":73638},[886],[888,73640,73641],{"xmlns":890},[892,73642,73643,73649],{},[895,73644,73645,73647],{},[898,73646,6889],{},[898,73648,8051],{},[902,73650,10679],{"encoding":904},[883,73652,73654],{"className":73653},[886],[888,73655,73656],{"xmlns":890},[892,73657,73658,73674],{},[895,73659,73660,73662,73664,73666,73668,73670,73672],{},[898,73661,1828],{},[1761,73663,1909],{},[1765,73665,2633],{},[1761,73667,1834],{"separator":1833},[1765,73669,13077],{},[1761,73671,1834],{"separator":1833},[1765,73673,42042],{},[902,73675,73603],{"encoding":904},[883,73677,73679],{"className":73678},[886],[888,73680,73681],{"xmlns":890},[892,73682,73683,73689],{},[895,73684,73685,73687],{},[898,73686,6889],{},[898,73688,8051],{},[902,73690,10679],{"encoding":904}," roste, resp. klesá. (d) Vypočtěte ",[883,73693,73695],{"className":73694},[886],[888,73696,73697],{"xmlns":890},[892,73698,73699,73703],{},[895,73700,73701],{},[898,73702,1828],{},[902,73704,1828],{"encoding":904},", které maximalizuje ",[883,73707,73709],{"className":73708},[886],[888,73710,73711],{"xmlns":890},[892,73712,73713,73719],{},[895,73714,73715,73717],{},[898,73716,1655],{},[898,73718,8051],{},[902,73720,8151],{"encoding":904}," a stanovte příslušnou hodnotu maxima ",[883,73723,73725],{"className":73724},[886],[888,73726,73727],{"xmlns":890},[892,73728,73729,73735],{},[895,73730,73731,73733],{},[898,73732,1655],{},[898,73734,8051],{},[902,73736,8151],{"encoding":904},". (e) Určete (je užitečné vyšetřit i jejich průběhy). (f) Charakterizujte geometricky křivky ",[883,73739,73741],{"className":73740},[886],[888,73742,73743],{"xmlns":890},[892,73744,73745,73749],{},[895,73746,73747],{},[898,73748,2244],{},[902,73750,2244],{"encoding":904},[883,73752,73754],{"className":73753},[886],[888,73755,73756],{"xmlns":890},[892,73757,73758,73764],{},[895,73759,73760,73762],{},[898,73761,1655],{},[898,73763,8051],{},[902,73765,8151],{"encoding":904},[883,73767,73769],{"className":73768},[886],[888,73770,73771],{"xmlns":890},[892,73772,73773,73779],{},[895,73774,73775,73777],{},[898,73776,8309],{},[898,73778,8051],{},[902,73780,59423],{"encoding":904},[883,73782,73784],{"className":73783},[886],[888,73785,73786],{"xmlns":890},[892,73787,73788,73794],{},[895,73789,73790,73792],{},[898,73791,6889],{},[898,73793,8051],{},[902,73795,10679],{"encoding":904},[724,73797,73798,73801,73802,73832,73833,73848,73849,14195,73862,1343,73880,1343,73897,73915,73916,73938,73939,73954,73955,73968,73969,1741],{},[38,73799,73800],{},"3.4"," Je dán celkový příjem ",[883,73803,73805],{"className":73804},[886],[888,73806,73807],{"xmlns":890},[892,73808,73809,73829],{},[895,73810,73811,73813,73815,73817,73819,73821,73823],{},[898,73812,1655],{},[898,73814,8051],{},[1761,73816,1909],{},[1765,73818,73504],{},[898,73820,1828],{},[1761,73822,1885],{},[1824,73824,73825,73827],{},[898,73826,1828],{},[1765,73828,5486],{},[902,73830,73831],{"encoding":904},"TR = 1200Q - Q^3",". (a) Určete, jak rychle se (přibližně) mění ",[883,73834,73836],{"className":73835},[886],[888,73837,73838],{"xmlns":890},[892,73839,73840,73846],{},[895,73841,73842,73844],{},[898,73843,1655],{},[898,73845,8051],{},[902,73847,8151],{"encoding":904}," vzhledem ke ",[883,73850,73852],{"className":73851},[886],[888,73853,73854],{"xmlns":890},[892,73855,73856,73860],{},[895,73857,73858],{},[898,73859,1828],{},[902,73861,1828],{"encoding":904},[883,73863,73865],{"className":73864},[886],[888,73866,73867],{"xmlns":890},[892,73868,73869,73877],{},[895,73870,73871,73873,73875],{},[898,73872,1828],{},[1761,73874,1909],{},[1765,73876,6321],{},[902,73878,73879],{"encoding":904},"Q = 5",[883,73881,73883],{"className":73882},[886],[888,73884,73885],{"xmlns":890},[892,73886,73887,73895],{},[895,73888,73889,73891,73893],{},[898,73890,1828],{},[1761,73892,1909],{},[1765,73894,2454],{},[902,73896,9637],{"encoding":904},[883,73898,73900],{"className":73899},[886],[888,73901,73902],{"xmlns":890},[892,73903,73904,73912],{},[895,73905,73906,73908,73910],{},[898,73907,1828],{},[1761,73909,1909],{},[1765,73911,2291],{},[902,73913,73914],{"encoding":904},"Q = 12"," a charakterizujte dynamiku změn. (b) Vypočtěte a ekonomicky interpretujte ",[883,73917,73919],{"className":73918},[886],[888,73920,73921],{"xmlns":890},[892,73922,73923,73935],{},[895,73924,73925,73927,73929,73931,73933],{},[898,73926,6889],{},[898,73928,8051],{},[1761,73930,1915],{"stretchy":1821},[1765,73932,2633],{},[1761,73934,1920],{"stretchy":1821},[902,73936,73937],{"encoding":904},"MR(10)",". (c) Odhadněte, o kolik se přibližně změní ",[883,73940,73942],{"className":73941},[886],[888,73943,73944],{"xmlns":890},[892,73945,73946,73952],{},[895,73947,73948,73950],{},[898,73949,1655],{},[898,73951,8051],{},[902,73953,8151],{"encoding":904},", jestliže se ",[883,73956,73958],{"className":73957},[886],[888,73959,73960],{"xmlns":890},[892,73961,73962,73966],{},[895,73963,73964],{},[898,73965,1828],{},[902,73967,1828],{"encoding":904}," změní z 10 na 12 a porovnejte se skutečnou změnou ",[883,73970,73972],{"className":73971},[886],[888,73973,73974],{"xmlns":890},[892,73975,73976,73982],{},[895,73977,73978,73980],{},[898,73979,1655],{},[898,73981,8051],{},[902,73983,8151],{"encoding":904},[724,73985,73986,73989,73990,74016,74017,74032,74033,73954,74048,74061],{},[38,73987,73988],{},"3.5"," Je dán mezní příjem ",[883,73991,73993],{"className":73992},[886],[888,73994,73995],{"xmlns":890},[892,73996,73997,74013],{},[895,73998,73999,74001,74003,74005,74007,74009,74011],{},[898,74000,6889],{},[898,74002,8051],{},[1761,74004,1909],{},[1761,74006,1885],{},[898,74008,1828],{},[1761,74010,1964],{},[1765,74012,13077],{},[902,74014,74015],{"encoding":904},"MR = -Q + 20",". (a) Určete celkový příjem ",[883,74018,74020],{"className":74019},[886],[888,74021,74022],{"xmlns":890},[892,74023,74024,74030],{},[895,74025,74026,74028],{},[898,74027,1655],{},[898,74029,8051],{},[902,74031,8151],{"encoding":904},". (b) Vypočtěte změnu ",[883,74034,74036],{"className":74035},[886],[888,74037,74038],{"xmlns":890},[892,74039,74040,74046],{},[895,74041,74042,74044],{},[898,74043,1655],{},[898,74045,8051],{},[902,74047,8151],{"encoding":904},[883,74049,74051],{"className":74050},[886],[888,74052,74053],{"xmlns":890},[892,74054,74055,74059],{},[895,74056,74057],{},[898,74058,1828],{},[902,74060,1828],{"encoding":904}," změní z 8 na 12.",[198,74063,74065],{"id":74064},"náklady-36316","Náklady (3.6–3.16)",[724,74067,74068,74071,74072,74112,74113,74128,74129,74146,74147,74164,74165,74180,74181,74196,74197,73562,74212,1343,74227,1343,74244,1343,74261,1343,74276,1343,74291,10518,74306,74324,74325,1343,74340,1343,74355,74370],{},[38,74069,74070],{},"3.6"," Jsou dány celkové náklady ",[883,74073,74075],{"className":74074},[886],[888,74076,74077],{"xmlns":890},[892,74078,74079,74109],{},[895,74080,74081,74083,74085,74087,74089,74091,74093,74095,74097],{},[898,74082,1655],{},[898,74084,6849],{},[1761,74086,1909],{},[1765,74088,7160],{},[1761,74090,1964],{},[1765,74092,2296],{},[898,74094,1828],{},[1761,74096,1964],{},[6411,74098,74099],{"scriptlevel":1767,"displaystyle":1821},[4379,74100,74101,74107],{},[1824,74102,74103,74105],{},[898,74104,1828],{},[1765,74106,2296],{},[1765,74108,2633],{},[902,74110,74111],{"encoding":904},"TC = 100 + 2Q + \\tfrac{Q^2}{10}",". (a) Určete fixní náklady ",[883,74114,74116],{"className":74115},[886],[888,74117,74118],{"xmlns":890},[892,74119,74120,74126],{},[895,74121,74122,74124],{},[898,74123,14474],{},[898,74125,6849],{},[902,74127,59469],{"encoding":904},", celkové variabilní náklady ",[883,74130,74132],{"className":74131},[886],[888,74133,74134],{"xmlns":890},[892,74135,74136,74144],{},[895,74137,74138,74140,74142],{},[898,74139,1655],{},[898,74141,44359],{},[898,74143,6849],{},[902,74145,59487],{"encoding":904},", průměrné variabilní náklady ",[883,74148,74150],{"className":74149},[886],[888,74151,74152],{"xmlns":890},[892,74153,74154,74162],{},[895,74155,74156,74158,74160],{},[898,74157,8309],{},[898,74159,44359],{},[898,74161,6849],{},[902,74163,59289],{"encoding":904},", variabilní náklady na jednotku ",[883,74166,74168],{"className":74167},[886],[888,74169,74170],{"xmlns":890},[892,74171,74172,74178],{},[895,74173,74174,74176],{},[898,74175,44359],{},[898,74177,6849],{},[902,74179,67583],{"encoding":904},", průměrné náklady ",[883,74182,74184],{"className":74183},[886],[888,74185,74186],{"xmlns":890},[892,74187,74188,74194],{},[895,74189,74190,74192],{},[898,74191,8309],{},[898,74193,6849],{},[902,74195,59538],{"encoding":904}," a mezní náklady ",[883,74198,74200],{"className":74199},[886],[888,74201,74202],{"xmlns":890},[892,74203,74204,74210],{},[895,74205,74206,74208],{},[898,74207,6889],{},[898,74209,6849],{},[902,74211,59270],{"encoding":904},[883,74213,74215],{"className":74214},[886],[888,74216,74217],{"xmlns":890},[892,74218,74219,74225],{},[895,74220,74221,74223],{},[898,74222,1655],{},[898,74224,6849],{},[902,74226,7310],{"encoding":904},[883,74228,74230],{"className":74229},[886],[888,74231,74232],{"xmlns":890},[892,74233,74234,74242],{},[895,74235,74236,74238,74240],{},[898,74237,1655],{},[898,74239,44359],{},[898,74241,6849],{},[902,74243,59487],{"encoding":904},[883,74245,74247],{"className":74246},[886],[888,74248,74249],{"xmlns":890},[892,74250,74251,74259],{},[895,74252,74253,74255,74257],{},[898,74254,8309],{},[898,74256,44359],{},[898,74258,6849],{},[902,74260,59289],{"encoding":904},[883,74262,74264],{"className":74263},[886],[888,74265,74266],{"xmlns":890},[892,74267,74268,74274],{},[895,74269,74270,74272],{},[898,74271,44359],{},[898,74273,6849],{},[902,74275,67583],{"encoding":904},[883,74277,74279],{"className":74278},[886],[888,74280,74281],{"xmlns":890},[892,74282,74283,74289],{},[895,74284,74285,74287],{},[898,74286,8309],{},[898,74288,6849],{},[902,74290,59538],{"encoding":904},[883,74292,74294],{"className":74293},[886],[888,74295,74296],{"xmlns":890},[892,74297,74298,74304],{},[895,74299,74300,74302],{},[898,74301,6889],{},[898,74303,6849],{},[902,74305,59270],{"encoding":904},[883,74307,74309],{"className":74308},[886],[888,74310,74311],{"xmlns":890},[892,74312,74313,74321],{},[895,74314,74315,74317,74319],{},[898,74316,1828],{},[1761,74318,1909],{},[1765,74320,7190],{},[902,74322,74323],{"encoding":904},"Q = 50",". (c) Rozhodněte, kdy ",[883,74326,74328],{"className":74327},[886],[888,74329,74330],{"xmlns":890},[892,74331,74332,74338],{},[895,74333,74334,74336],{},[898,74335,1655],{},[898,74337,6849],{},[902,74339,7310],{"encoding":904},[883,74341,74343],{"className":74342},[886],[888,74344,74345],{"xmlns":890},[892,74346,74347,74353],{},[895,74348,74349,74351],{},[898,74350,8309],{},[898,74352,6849],{},[902,74354,59538],{"encoding":904},[883,74356,74358],{"className":74357},[886],[888,74359,74360],{"xmlns":890},[892,74361,74362,74368],{},[895,74363,74364,74366],{},[898,74365,6889],{},[898,74367,6849],{},[902,74369,59270],{"encoding":904}," rostou, resp. klesají.",[724,74372,74373,74376,74377,74196,74407,74422,74423,74438,74439,1343,74454,1343,74469,1741],{},[38,74374,74375],{},"3.7"," Jsou dány průměrné náklady ",[883,74378,74380],{"className":74379},[886],[888,74381,74382],{"xmlns":890},[892,74383,74384,74404],{},[895,74385,74386,74388,74390,74392,74400,74402],{},[898,74387,8309],{},[898,74389,6849],{},[1761,74391,1909],{},[6411,74393,74394],{"scriptlevel":1767,"displaystyle":1821},[4379,74395,74396,74398],{},[1765,74397,7160],{},[898,74399,1828],{},[1761,74401,1964],{},[1765,74403,13077],{},[902,74405,74406],{"encoding":904},"AC = \\tfrac{100}{Q} + 20",[883,74408,74410],{"className":74409},[886],[888,74411,74412],{"xmlns":890},[892,74413,74414,74420],{},[895,74415,74416,74418],{},[898,74417,6889],{},[898,74419,6849],{},[902,74421,59270],{"encoding":904},". (a) Určete celkové náklady ",[883,74424,74426],{"className":74425},[886],[888,74427,74428],{"xmlns":890},[892,74429,74430,74436],{},[895,74431,74432,74434],{},[898,74433,1655],{},[898,74435,6849],{},[902,74437,7310],{"encoding":904},". (b) Načrtněte a geometricky charakterizujte křivky ",[883,74440,74442],{"className":74441},[886],[888,74443,74444],{"xmlns":890},[892,74445,74446,74452],{},[895,74447,74448,74450],{},[898,74449,8309],{},[898,74451,6849],{},[902,74453,59538],{"encoding":904},[883,74455,74457],{"className":74456},[886],[888,74458,74459],{"xmlns":890},[892,74460,74461,74467],{},[895,74462,74463,74465],{},[898,74464,1655],{},[898,74466,6849],{},[902,74468,7310],{"encoding":904},[883,74470,74472],{"className":74471},[886],[888,74473,74474],{"xmlns":890},[892,74475,74476,74482],{},[895,74477,74478,74480],{},[898,74479,6889],{},[898,74481,6849],{},[902,74483,59270],{"encoding":904},[724,74485,74486,74071,74489,74533,74534,1343,74551,1343,74566,1343,74583,1343,74598,1343,74615,1741],{},[38,74487,74488],{},"3.8",[883,74490,74492],{"className":74491},[886],[888,74493,74494],{"xmlns":890},[892,74495,74496,74530],{},[895,74497,74498,74500,74502,74504,74506,74508,74510,74512,74514,74516,74522,74524],{},[898,74499,1655],{},[898,74501,6849],{},[1761,74503,1909],{},[1765,74505,5467],{},[1761,74507,1964],{},[1765,74509,42042],{},[898,74511,1828],{},[1761,74513,1885],{},[1765,74515,2340],{},[1824,74517,74518,74520],{},[898,74519,1828],{},[1765,74521,2296],{},[1761,74523,1964],{},[1824,74525,74526,74528],{},[898,74527,1828],{},[1765,74529,5486],{},[902,74531,74532],{"encoding":904},"TC = 80 + 30Q - 6Q^2 + Q^3",". Určete ",[883,74535,74537],{"className":74536},[886],[888,74538,74539],{"xmlns":890},[892,74540,74541,74549],{},[895,74542,74543,74545,74547],{},[898,74544,1655],{},[898,74546,44359],{},[898,74548,6849],{},[902,74550,59487],{"encoding":904},[883,74552,74554],{"className":74553},[886],[888,74555,74556],{"xmlns":890},[892,74557,74558,74564],{},[895,74559,74560,74562],{},[898,74561,14474],{},[898,74563,6849],{},[902,74565,59469],{"encoding":904},[883,74567,74569],{"className":74568},[886],[888,74570,74571],{"xmlns":890},[892,74572,74573,74581],{},[895,74574,74575,74577,74579],{},[898,74576,8309],{},[898,74578,44359],{},[898,74580,6849],{},[902,74582,59289],{"encoding":904},[883,74584,74586],{"className":74585},[886],[888,74587,74588],{"xmlns":890},[892,74589,74590,74596],{},[895,74591,74592,74594],{},[898,74593,8309],{},[898,74595,6849],{},[902,74597,59538],{"encoding":904},[883,74599,74601],{"className":74600},[886],[888,74602,74603],{"xmlns":890},[892,74604,74605,74613],{},[895,74606,74607,74609,74611],{},[898,74608,8309],{},[898,74610,14474],{},[898,74612,6849],{},[902,74614,59505],{"encoding":904},[883,74616,74618],{"className":74617},[886],[888,74619,74620],{"xmlns":890},[892,74621,74622,74628],{},[895,74623,74624,74626],{},[898,74625,6889],{},[898,74627,6849],{},[902,74629,59270],{"encoding":904},[724,74631,74632,74071,74635,74665,74666,73848,74681,10518,74694,1343,74712,1343,74730,73915,74748,73938,74770,74785,74786,74799,74800,1741],{},[38,74633,74634],{},"3.9",[883,74636,74638],{"className":74637},[886],[888,74639,74640],{"xmlns":890},[892,74641,74642,74662],{},[895,74643,74644,74646,74648,74650,74652,74654,74656],{},[898,74645,1655],{},[898,74647,6849],{},[1761,74649,1909],{},[1765,74651,19148],{},[1761,74653,1964],{},[1765,74655,23354],{},[1824,74657,74658,74660],{},[898,74659,1828],{},[1765,74661,2296],{},[902,74663,74664],{"encoding":904},"TC = 500 + 0{,}6Q^2",". (a) Určete, jak rychle se přibližně mění ",[883,74667,74669],{"className":74668},[886],[888,74670,74671],{"xmlns":890},[892,74672,74673,74679],{},[895,74674,74675,74677],{},[898,74676,1655],{},[898,74678,6849],{},[902,74680,7310],{"encoding":904},[883,74682,74684],{"className":74683},[886],[888,74685,74686],{"xmlns":890},[892,74687,74688,74692],{},[895,74689,74690],{},[898,74691,1828],{},[902,74693,1828],{"encoding":904},[883,74695,74697],{"className":74696},[886],[888,74698,74699],{"xmlns":890},[892,74700,74701,74709],{},[895,74702,74703,74705,74707],{},[898,74704,1828],{},[1761,74706,1909],{},[1765,74708,2633],{},[902,74710,74711],{"encoding":904},"Q = 10",[883,74713,74715],{"className":74714},[886],[888,74716,74717],{"xmlns":890},[892,74718,74719,74727],{},[895,74720,74721,74723,74725],{},[898,74722,1828],{},[1761,74724,1909],{},[1765,74726,13077],{},[902,74728,74729],{"encoding":904},"Q = 20",[883,74731,74733],{"className":74732},[886],[888,74734,74735],{"xmlns":890},[892,74736,74737,74745],{},[895,74738,74739,74741,74743],{},[898,74740,1828],{},[1761,74742,1909],{},[1765,74744,42042],{},[902,74746,74747],{"encoding":904},"Q = 30",[883,74749,74751],{"className":74750},[886],[888,74752,74753],{"xmlns":890},[892,74754,74755,74767],{},[895,74756,74757,74759,74761,74763,74765],{},[898,74758,6889],{},[898,74760,6849],{},[1761,74762,1915],{"stretchy":1821},[1765,74764,5433],{},[1761,74766,1920],{"stretchy":1821},[902,74768,74769],{"encoding":904},"MC(15)",[883,74771,74773],{"className":74772},[886],[888,74774,74775],{"xmlns":890},[892,74776,74777,74783],{},[895,74778,74779,74781],{},[898,74780,1655],{},[898,74782,6849],{},[902,74784,7310],{"encoding":904}," v důsledku změny ",[883,74787,74789],{"className":74788},[886],[888,74790,74791],{"xmlns":890},[892,74792,74793,74797],{},[895,74794,74795],{},[898,74796,1828],{},[902,74798,1828],{"encoding":904}," z 15 na 20 a porovnejte se skutečnou změnou ",[883,74801,74803],{"className":74802},[886],[888,74804,74805],{"xmlns":890},[892,74806,74807,74813],{},[895,74808,74809,74811],{},[898,74810,1655],{},[898,74812,6849],{},[902,74814,7310],{"encoding":904},[724,74816,74817,74820,74821,74422,74857,74872,74873,74032,74892,74785,74907,74920],{},[38,74818,74819],{},"3.10"," Jsou dány mezní náklady ",[883,74822,74824],{"className":74823},[886],[888,74825,74826],{"xmlns":890},[892,74827,74828,74854],{},[895,74829,74830,74832,74834,74836,74838,74840,74842,74844,74846,74848],{},[898,74831,6889],{},[898,74833,6849],{},[1761,74835,1909],{},[1765,74837,7195],{},[1761,74839,1885],{},[1765,74841,45871],{},[898,74843,1828],{},[1761,74845,1964],{},[1765,74847,68537],{},[1824,74849,74850,74852],{},[898,74851,1828],{},[1765,74853,2296],{},[902,74855,74856],{"encoding":904},"MC = 60 - 16Q + 1{,}5Q^2",[883,74858,74860],{"className":74859},[886],[888,74861,74862],{"xmlns":890},[892,74863,74864,74870],{},[895,74865,74866,74868],{},[898,74867,1655],{},[898,74869,6849],{},[902,74871,7310],{"encoding":904},", jestliže fixní náklady ",[883,74874,74876],{"className":74875},[886],[888,74877,74878],{"xmlns":890},[892,74879,74880,74890],{},[895,74881,74882,74884,74886,74888],{},[898,74883,14474],{},[898,74885,6849],{},[1761,74887,1909],{},[1765,74889,7160],{},[902,74891,15672],{"encoding":904},[883,74893,74895],{"className":74894},[886],[888,74896,74897],{"xmlns":890},[892,74898,74899,74905],{},[895,74900,74901,74903],{},[898,74902,1655],{},[898,74904,6849],{},[902,74906,7310],{"encoding":904},[883,74908,74910],{"className":74909},[886],[888,74911,74912],{"xmlns":890},[892,74913,74914,74918],{},[895,74915,74916],{},[898,74917,1828],{},[902,74919,1828],{"encoding":904}," z 15 na 20.",[724,74922,74923,74071,74926,74969,74970,74983,74984,74999,75000,75015,75016,74983,75029,74999,75046,75063,75064,74983,75077,74999,75092,75107,75108,75128,75129,75152],{},[38,74924,74925],{},"3.11",[883,74927,74929],{"className":74928},[886],[888,74930,74931],{"xmlns":890},[892,74932,74933,74967],{},[895,74934,74935,74937,74939,74941,74943,74945,74947,74949,74951,74953,74959,74961],{},[898,74936,1655],{},[898,74938,6849],{},[1761,74940,1909],{},[1765,74942,7160],{},[1761,74944,1964],{},[1765,74946,9056],{},[898,74948,1828],{},[1761,74950,1885],{},[1765,74952,6321],{},[1824,74954,74955,74957],{},[898,74956,1828],{},[1765,74958,2296],{},[1761,74960,1964],{},[1824,74962,74963,74965],{},[898,74964,1828],{},[1765,74966,5486],{},[902,74968,64885],{"encoding":904},". (a) Určete ",[883,74971,74973],{"className":74972},[886],[888,74974,74975],{"xmlns":890},[892,74976,74977,74981],{},[895,74978,74979],{},[898,74980,1828],{},[902,74982,1828],{"encoding":904},", které minimalizuje ",[883,74985,74987],{"className":74986},[886],[888,74988,74989],{"xmlns":890},[892,74990,74991,74997],{},[895,74992,74993,74995],{},[898,74994,6889],{},[898,74996,6849],{},[902,74998,59270],{"encoding":904}," a stanovte příslušnou hodnotu minima ",[883,75001,75003],{"className":75002},[886],[888,75004,75005],{"xmlns":890},[892,75006,75007,75013],{},[895,75008,75009,75011],{},[898,75010,6889],{},[898,75012,6849],{},[902,75014,59270],{"encoding":904},". (b) Určete ",[883,75017,75019],{"className":75018},[886],[888,75020,75021],{"xmlns":890},[892,75022,75023,75027],{},[895,75024,75025],{},[898,75026,1828],{},[902,75028,1828],{"encoding":904},[883,75030,75032],{"className":75031},[886],[888,75033,75034],{"xmlns":890},[892,75035,75036,75044],{},[895,75037,75038,75040,75042],{},[898,75039,8309],{},[898,75041,44359],{},[898,75043,6849],{},[902,75045,59289],{"encoding":904},[883,75047,75049],{"className":75048},[886],[888,75050,75051],{"xmlns":890},[892,75052,75053,75061],{},[895,75054,75055,75057,75059],{},[898,75056,8309],{},[898,75058,44359],{},[898,75060,6849],{},[902,75062,59289],{"encoding":904},". (c) Určete ",[883,75065,75067],{"className":75066},[886],[888,75068,75069],{"xmlns":890},[892,75070,75071,75075],{},[895,75072,75073],{},[898,75074,1828],{},[902,75076,1828],{"encoding":904},[883,75078,75080],{"className":75079},[886],[888,75081,75082],{"xmlns":890},[892,75083,75084,75090],{},[895,75085,75086,75088],{},[898,75087,8309],{},[898,75089,6849],{},[902,75091,59538],{"encoding":904},[883,75093,75095],{"className":75094},[886],[888,75096,75097],{"xmlns":890},[892,75098,75099,75105],{},[895,75100,75101,75103],{},[898,75102,8309],{},[898,75104,6849],{},[902,75106,59538],{"encoding":904}," (rada: hledaný kořen ",[883,75109,75111],{"className":75110},[886],[888,75112,75113],{"xmlns":890},[892,75114,75115,75125],{},[895,75116,75117,75119],{},[898,75118,8309],{},[1824,75120,75121,75123],{},[898,75122,6849],{},[1761,75124,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[902,75126,75127],{"encoding":904},"AC'"," určete přibližně, patří do ",[883,75130,75132],{"className":75131},[886],[888,75133,75134],{"xmlns":890},[892,75135,75136,75149],{},[895,75137,75138,75140,75143,75145,75147],{},[1761,75139,1915],{"stretchy":1821},[1765,75141,75142],{},"4,7",[1761,75144,12468],{"separator":1833},[1765,75146,9330],{},[1761,75148,1920],{"stretchy":1821},[902,75150,75151],{"encoding":904},"(4{,}7; 4{,}8)",", zpřesněte).",[724,75154,75155,75158,75159,6699,75187,75204,75205,25627,75246,75267],{},[38,75156,75157],{},"3.12"," Dokažte, že mají-li průměrné náklady ",[883,75160,75162],{"className":75161},[886],[888,75163,75164],{"xmlns":890},[892,75165,75166,75184],{},[895,75167,75168,75170,75172,75174,75176,75178,75180,75182],{},[898,75169,8309],{},[898,75171,6849],{},[1761,75173,1909],{},[898,75175,8309],{},[898,75177,6849],{},[1761,75179,1915],{"stretchy":1821},[898,75181,1828],{},[1761,75183,1920],{"stretchy":1821},[902,75185,75186],{"encoding":904},"AC = AC(Q)",[883,75188,75190],{"className":75189},[886],[888,75191,75192],{"xmlns":890},[892,75193,75194,75202],{},[895,75195,75196],{},[1681,75197,75198,75200],{},[898,75199,1828],{},[1765,75201,1767],{},[902,75203,42331],{"encoding":904}," minimum, pak platí ",[883,75206,75208],{"className":75207},[886],[888,75209,75210],{"xmlns":890},[892,75211,75212,75244],{},[895,75213,75214,75216,75218,75220,75226,75228,75230,75232,75234,75236,75242],{},[898,75215,8309],{},[898,75217,6849],{},[1761,75219,1915],{"stretchy":1821},[1681,75221,75222,75224],{},[898,75223,1828],{},[1765,75225,1767],{},[1761,75227,1920],{"stretchy":1821},[1761,75229,1909],{},[898,75231,6889],{},[898,75233,6849],{},[1761,75235,1915],{"stretchy":1821},[1681,75237,75238,75240],{},[898,75239,1828],{},[1765,75241,1767],{},[1761,75243,1920],{"stretchy":1821},[902,75245,66547],{"encoding":904},[883,75247,75249],{"className":75248},[886],[888,75250,75251],{"xmlns":890},[892,75252,75253,75265],{},[895,75254,75255,75257,75259,75261,75263],{},[898,75256,6889],{},[898,75258,6849],{},[1761,75260,1915],{"stretchy":1821},[898,75262,1828],{},[1761,75264,1920],{"stretchy":1821},[902,75266,71671],{"encoding":904}," jsou mezní náklady.",[724,75269,75270,74071,75273,74533,75307,74983,75320,74999,75335,1741],{},[38,75271,75272],{},"3.13",[883,75274,75276],{"className":75275},[886],[888,75277,75278],{"xmlns":890},[892,75279,75280,75304],{},[895,75281,75282,75284,75286,75288,75294,75296,75298,75300,75302],{},[898,75283,1655],{},[898,75285,6849],{},[1761,75287,1909],{},[1824,75289,75290,75292],{},[898,75291,1828],{},[1765,75293,2296],{},[1761,75295,1964],{},[1765,75297,2296],{},[898,75299,1828],{},[1761,75301,1964],{},[1765,75303,9056],{},[902,75305,75306],{"encoding":904},"TC = Q^2 + 2Q + 25",[883,75308,75310],{"className":75309},[886],[888,75311,75312],{"xmlns":890},[892,75313,75314,75318],{},[895,75315,75316],{},[898,75317,1828],{},[902,75319,1828],{"encoding":904},[883,75321,75323],{"className":75322},[886],[888,75324,75325],{"xmlns":890},[892,75326,75327,75333],{},[895,75328,75329,75331],{},[898,75330,8309],{},[898,75332,6849],{},[902,75334,59538],{"encoding":904},[883,75336,75338],{"className":75337},[886],[888,75339,75340],{"xmlns":890},[892,75341,75342,75348],{},[895,75343,75344,75346],{},[898,75345,8309],{},[898,75347,6849],{},[902,75349,59538],{"encoding":904},[724,75351,75352,75355,75356,6699,75388,75204,75405,25627,75448,75267],{},[38,75353,75354],{},"3.14"," Dokažte, že mají-li průměrné variabilní náklady ",[883,75357,75359],{"className":75358},[886],[888,75360,75361],{"xmlns":890},[892,75362,75363,75385],{},[895,75364,75365,75367,75369,75371,75373,75375,75377,75379,75381,75383],{},[898,75366,8309],{},[898,75368,44359],{},[898,75370,6849],{},[1761,75372,1909],{},[898,75374,8309],{},[898,75376,44359],{},[898,75378,6849],{},[1761,75380,1915],{"stretchy":1821},[898,75382,1828],{},[1761,75384,1920],{"stretchy":1821},[902,75386,75387],{"encoding":904},"AVC = AVC(Q)",[883,75389,75391],{"className":75390},[886],[888,75392,75393],{"xmlns":890},[892,75394,75395,75403],{},[895,75396,75397],{},[1681,75398,75399,75401],{},[898,75400,1828],{},[1765,75402,1767],{},[902,75404,42331],{"encoding":904},[883,75406,75408],{"className":75407},[886],[888,75409,75410],{"xmlns":890},[892,75411,75412,75446],{},[895,75413,75414,75416,75418,75420,75422,75428,75430,75432,75434,75436,75438,75444],{},[898,75415,8309],{},[898,75417,44359],{},[898,75419,6849],{},[1761,75421,1915],{"stretchy":1821},[1681,75423,75424,75426],{},[898,75425,1828],{},[1765,75427,1767],{},[1761,75429,1920],{"stretchy":1821},[1761,75431,1909],{},[898,75433,6889],{},[898,75435,6849],{},[1761,75437,1915],{"stretchy":1821},[1681,75439,75440,75442],{},[898,75441,1828],{},[1765,75443,1767],{},[1761,75445,1920],{"stretchy":1821},[902,75447,72997],{"encoding":904},[883,75449,75451],{"className":75450},[886],[888,75452,75453],{"xmlns":890},[892,75454,75455,75467],{},[895,75456,75457,75459,75461,75463,75465],{},[898,75458,6889],{},[898,75460,6849],{},[1761,75462,1915],{"stretchy":1821},[898,75464,1828],{},[1761,75466,1920],{"stretchy":1821},[902,75468,71671],{"encoding":904},[724,75470,75471,74071,75474,74533,75520,74983,75533,74999,75550,1741],{},[38,75472,75473],{},"3.15",[883,75475,75477],{"className":75476},[886],[888,75478,75479],{"xmlns":890},[892,75480,75481,75517],{},[895,75482,75483,75485,75487,75489,75491,75493,75495,75497,75499,75501,75507,75509,75511],{},[898,75484,1655],{},[898,75486,6849],{},[1761,75488,1909],{},[1765,75490,7190],{},[1761,75492,1964],{},[1765,75494,5433],{},[898,75496,1828],{},[1761,75498,1885],{},[1765,75500,2296],{},[1824,75502,75503,75505],{},[898,75504,1828],{},[1765,75506,2296],{},[1761,75508,1964],{},[1765,75510,6910],{},[1824,75512,75513,75515],{},[898,75514,1828],{},[1765,75516,5486],{},[902,75518,75519],{"encoding":904},"TC = 50 + 15Q - 2Q^2 + 0{,}2Q^3",[883,75521,75523],{"className":75522},[886],[888,75524,75525],{"xmlns":890},[892,75526,75527,75531],{},[895,75528,75529],{},[898,75530,1828],{},[902,75532,1828],{"encoding":904},[883,75534,75536],{"className":75535},[886],[888,75537,75538],{"xmlns":890},[892,75539,75540,75548],{},[895,75541,75542,75544,75546],{},[898,75543,8309],{},[898,75545,44359],{},[898,75547,6849],{},[902,75549,59289],{"encoding":904},[883,75551,75553],{"className":75552},[886],[888,75554,75555],{"xmlns":890},[892,75556,75557,75565],{},[895,75558,75559,75561,75563],{},[898,75560,8309],{},[898,75562,44359],{},[898,75564,6849],{},[902,75566,59289],{"encoding":904},[724,75568,75569,75572,75573,75586,75587,75607],{},[38,75570,75571],{},"3.16"," Celkové náklady na výstavbu domu o ",[883,75574,75576],{"className":75575},[886],[888,75577,75578],{"xmlns":890},[892,75579,75580,75584],{},[895,75581,75582],{},[898,75583,6112],{},[902,75585,6112],{"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 ",[883,75588,75590],{"className":75589},[886],[888,75591,75592],{"xmlns":890},[892,75593,75594,75604],{},[895,75595,75596,75598,75600,75602],{},[1765,75597,2633],{},[2761,75599,7057],{},[1765,75601,63060],{},[898,75603,6112],{},[902,75605,75606],{"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.",[198,75609,75611],{"id":75610},"zisk-body-zvratu-317325","Zisk, body zvratu (3.17–3.25)",[724,75613,75614,75617,75618,2068,75640,75666],{},[38,75615,75616],{},"3.17"," Jsou dány ",[883,75619,75621],{"className":75620},[886],[888,75622,75623],{"xmlns":890},[892,75624,75625,75637],{},[895,75626,75627,75629,75631,75633,75635],{},[898,75628,1655],{},[898,75630,8051],{},[1761,75632,1909],{},[1765,75634,2633],{},[898,75636,1828],{},[902,75638,75639],{"encoding":904},"TR = 10Q",[883,75641,75643],{"className":75642},[886],[888,75644,75645],{"xmlns":890},[892,75646,75647,75663],{},[895,75648,75649,75651,75653,75655,75657,75659,75661],{},[898,75650,1655],{},[898,75652,6849],{},[1761,75654,1909],{},[1765,75656,7160],{},[1761,75658,1964],{},[1765,75660,6321],{},[898,75662,1828],{},[902,75664,75665],{"encoding":904},"TC = 100 + 5Q",". Určete body zvratu a geometricky výsledek interpretujte.",[724,75668,75669,75672,75673,10235,75688,75703,75704,1343,75726,25627,75753,75775,75776,75810],{},[38,75670,75671],{},"3.18"," Odvoďte, že jestliže ",[883,75674,75676],{"className":75675},[886],[888,75677,75678],{"xmlns":890},[892,75679,75680,75686],{},[895,75681,75682,75684],{},[898,75683,1655],{},[898,75685,8051],{},[902,75687,8151],{"encoding":904},[883,75689,75691],{"className":75690},[886],[888,75692,75693],{"xmlns":890},[892,75694,75695,75701],{},[895,75696,75697,75699],{},[898,75698,1655],{},[898,75700,6849],{},[902,75702,7310],{"encoding":904}," jsou lineární tvaru ",[883,75705,75707],{"className":75706},[886],[888,75708,75709],{"xmlns":890},[892,75710,75711,75723],{},[895,75712,75713,75715,75717,75719,75721],{},[898,75714,1655],{},[898,75716,8051],{},[1761,75718,1909],{},[898,75720,724],{},[898,75722,1828],{},[902,75724,75725],{"encoding":904},"TR = pQ",[883,75727,75729],{"className":75728},[886],[888,75730,75731],{"xmlns":890},[892,75732,75733,75750],{},[895,75734,75735,75737,75739,75741,75744,75746,75748],{},[898,75736,1655],{},[898,75738,6849],{},[1761,75740,1909],{},[898,75742,75743],{},"m",[1761,75745,1964],{},[898,75747,40888],{},[898,75749,1828],{},[902,75751,75752],{"encoding":904},"TC = m + nQ",[883,75754,75756],{"className":75755},[886],[888,75757,75758],{"xmlns":890},[892,75759,75760,75772],{},[895,75761,75762,75764,75766,75768,75770],{},[898,75763,75743],{},[1761,75765,1834],{"separator":1833},[898,75767,40888],{},[1761,75769,1834],{"separator":1833},[898,75771,724],{},[902,75773,75774],{"encoding":904},"m, n, p"," jsou pevně zadány, pak existuje jediný bod zvratu ",[883,75777,75779],{"className":75778},[886],[888,75780,75781],{"xmlns":890},[892,75782,75783,75807],{},[895,75784,75785,75791,75793],{},[1824,75786,75787,75789],{},[898,75788,1828],{},[1761,75790,8408],{},[1761,75792,1909],{},[6411,75794,75795],{"scriptlevel":1767,"displaystyle":1821},[4379,75796,75797,75799],{},[898,75798,75743],{},[895,75800,75801,75803,75805],{},[898,75802,724],{},[1761,75804,1885],{},[898,75806,40888],{},[902,75808,75809],{"encoding":904},"Q^* = \\tfrac{m}{p - n}"," a proveďte diskusi podmínek. Načrtněte obrázek.",[724,75812,75813,75617,75816,2068,75850,74969,75876,75889,75890,73721,75905,75920,75921,73705,75934,73721,75949,75964],{},[38,75814,75815],{},"3.19",[883,75817,75819],{"className":75818},[886],[888,75820,75821],{"xmlns":890},[892,75822,75823,75847],{},[895,75824,75825,75827,75829,75831,75833,75835,75841,75843,75845],{},[898,75826,1655],{},[898,75828,8051],{},[1761,75830,1909],{},[1761,75832,1885],{},[1765,75834,2296],{},[1824,75836,75837,75839],{},[898,75838,1828],{},[1765,75840,2296],{},[1761,75842,1964],{},[1765,75844,26979],{},[898,75846,1828],{},[902,75848,75849],{"encoding":904},"TR = -2Q^2 + 14Q",[883,75851,75853],{"className":75852},[886],[888,75854,75855],{"xmlns":890},[892,75856,75857,75873],{},[895,75858,75859,75861,75863,75865,75867,75869,75871],{},[898,75860,1655],{},[898,75862,6849],{},[1761,75864,1909],{},[1765,75866,2296],{},[898,75868,1828],{},[1761,75870,1964],{},[1765,75872,2633],{},[902,75874,75875],{"encoding":904},"TC = 2Q + 10",[883,75877,75879],{"className":75878},[886],[888,75880,75881],{"xmlns":890},[892,75882,75883,75887],{},[895,75884,75885],{},[898,75886,1828],{},[902,75888,1828],{"encoding":904},", které maximalizuje zisk ",[883,75891,75893],{"className":75892},[886],[888,75894,75895],{"xmlns":890},[892,75896,75897,75903],{},[895,75898,75899,75901],{},[898,75900,1839],{},[898,75902,8051],{},[902,75904,67457],{"encoding":904},[883,75906,75908],{"className":75907},[886],[888,75909,75910],{"xmlns":890},[892,75911,75912,75918],{},[895,75913,75914,75916],{},[898,75915,1839],{},[898,75917,8051],{},[902,75919,67457],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku. (c) Určete ",[883,75922,75924],{"className":75923},[886],[888,75925,75926],{"xmlns":890},[892,75927,75928,75932],{},[895,75929,75930],{},[898,75931,1828],{},[902,75933,1828],{"encoding":904},[883,75935,75937],{"className":75936},[886],[888,75938,75939],{"xmlns":890},[892,75940,75941,75947],{},[895,75942,75943,75945],{},[898,75944,1655],{},[898,75946,8051],{},[902,75948,8151],{"encoding":904},[883,75950,75952],{"className":75951},[886],[888,75953,75954],{"xmlns":890},[892,75955,75956,75962],{},[895,75957,75958,75960],{},[898,75959,1655],{},[898,75961,8051],{},[902,75963,8151],{"encoding":904},". (d) Graficky interpretujte.",[724,75966,75967,51674,75970,1343,75996,1343,76015,74969,76035,75889,76048,73721,76063,76078,76079,76101,76102,75152],{},[38,75968,75969],{},"3.20",[883,75971,75973],{"className":75972},[886],[888,75974,75975],{"xmlns":890},[892,75976,75977,75993],{},[895,75978,75979,75981,75983,75985,75987],{},[898,75980,1839],{},[1761,75982,1909],{},[1765,75984,24175],{},[1761,75986,1885],{},[1824,75988,75989,75991],{},[898,75990,1828],{},[1765,75992,2296],{},[902,75994,75995],{"encoding":904},"P = 400 - Q^2",[883,75997,75999],{"className":75998},[886],[888,76000,76001],{"xmlns":890},[892,76002,76003,76013],{},[895,76004,76005,76007,76009,76011],{},[898,76006,14474],{},[898,76008,6849],{},[1761,76010,1909],{},[1765,76012,7160],{},[902,76014,15672],{"encoding":904},[883,76016,76018],{"className":76017},[886],[888,76019,76020],{"xmlns":890},[892,76021,76022,76032],{},[895,76023,76024,76026,76028,76030],{},[898,76025,6889],{},[898,76027,6849],{},[1761,76029,1909],{},[1765,76031,13077],{},[902,76033,76034],{"encoding":904},"MC = 20",[883,76036,76038],{"className":76037},[886],[888,76039,76040],{"xmlns":890},[892,76041,76042,76046],{},[895,76043,76044],{},[898,76045,1828],{},[902,76047,1828],{"encoding":904},[883,76049,76051],{"className":76050},[886],[888,76052,76053],{"xmlns":890},[892,76054,76055,76061],{},[895,76056,76057,76059],{},[898,76058,1839],{},[898,76060,8051],{},[902,76062,67457],{"encoding":904},[883,76064,76066],{"className":76065},[886],[888,76067,76068],{"xmlns":890},[892,76069,76070,76076],{},[895,76071,76072,76074],{},[898,76073,1839],{},[898,76075,8051],{},[902,76077,67457],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku (rada: jeden z bodů zvratu patří do ",[883,76080,76082],{"className":76081},[886],[888,76083,76084],{"xmlns":890},[892,76085,76086,76098],{},[895,76087,76088,76090,76092,76094,76096],{},[1761,76089,1915],{"stretchy":1821},[1765,76091,1767],{},[1761,76093,1834],{"separator":1833},[1765,76095,1945],{},[1761,76097,1920],{"stretchy":1821},[902,76099,76100],{"encoding":904},"(0, 1)",", druhý do ",[883,76103,76105],{"className":76104},[886],[888,76106,76107],{"xmlns":890},[892,76108,76109,76122],{},[895,76110,76111,76113,76116,76118,76120],{},[1761,76112,1915],{"stretchy":1821},[1765,76114,76115],{},"19",[1761,76117,1834],{"separator":1833},[1765,76119,13077],{},[1761,76121,1920],{"stretchy":1821},[902,76123,76124],{"encoding":904},"(19, 20)",[724,76126,76127,76130,76131,6699,76159,76176,76177,1741],{},[38,76128,76129],{},"3.21"," Dokažte, že má-li zisk ",[883,76132,76134],{"className":76133},[886],[888,76135,76136],{"xmlns":890},[892,76137,76138,76156],{},[895,76139,76140,76142,76144,76146,76148,76150,76152,76154],{},[898,76141,1839],{},[898,76143,8051],{},[1761,76145,1909],{},[898,76147,1839],{},[898,76149,8051],{},[1761,76151,1915],{"stretchy":1821},[898,76153,1828],{},[1761,76155,1920],{"stretchy":1821},[902,76157,76158],{"encoding":904},"PR = PR(Q)",[883,76160,76162],{"className":76161},[886],[888,76163,76164],{"xmlns":890},[892,76165,76166,76174],{},[895,76167,76168],{},[1681,76169,76170,76172],{},[898,76171,1828],{},[1765,76173,1767],{},[902,76175,42331],{"encoding":904}," maximum, pak platí ",[883,76178,76180],{"className":76179},[886],[888,76181,76182],{"xmlns":890},[892,76183,76184,76216],{},[895,76185,76186,76188,76190,76192,76198,76200,76202,76204,76206,76208,76214],{},[898,76187,6889],{},[898,76189,8051],{},[1761,76191,1915],{"stretchy":1821},[1681,76193,76194,76196],{},[898,76195,1828],{},[1765,76197,1767],{},[1761,76199,1920],{"stretchy":1821},[1761,76201,1909],{},[898,76203,6889],{},[898,76205,6849],{},[1761,76207,1915],{"stretchy":1821},[1681,76209,76210,76212],{},[898,76211,1828],{},[1765,76213,1767],{},[1761,76215,1920],{"stretchy":1821},[902,76217,69623],{"encoding":904},[724,76219,76220,76223,76224,2068,76239,60003,76254,75889,76267,76282,76283,1343,76310,76347,76348,1343,76375,1741],{},[38,76221,76222],{},"3.22"," Pro zadané ",[883,76225,76227],{"className":76226},[886],[888,76228,76229],{"xmlns":890},[892,76230,76231,76237],{},[895,76232,76233,76235],{},[898,76234,6889],{},[898,76236,8051],{},[902,76238,10679],{"encoding":904},[883,76240,76242],{"className":76241},[886],[888,76243,76244],{"xmlns":890},[892,76245,76246,76252],{},[895,76247,76248,76250],{},[898,76249,6889],{},[898,76251,6849],{},[902,76253,59270],{"encoding":904},[883,76255,76257],{"className":76256},[886],[888,76258,76259],{"xmlns":890},[892,76260,76261,76265],{},[895,76262,76263],{},[898,76264,1828],{},[902,76266,1828],{"encoding":904},[883,76268,76270],{"className":76269},[886],[888,76271,76272],{"xmlns":890},[892,76273,76274,76280],{},[895,76275,76276,76278],{},[898,76277,1839],{},[898,76279,8051],{},[902,76281,67457],{"encoding":904},". (a) ",[883,76284,76286],{"className":76285},[886],[888,76287,76288],{"xmlns":890},[892,76289,76290,76307],{},[895,76291,76292,76294,76296,76298,76301,76303,76305],{},[898,76293,6889],{},[898,76295,8051],{},[1761,76297,1909],{},[1765,76299,76300],{},"236",[1761,76302,1885],{},[1765,76304,45871],{},[898,76306,1828],{},[902,76308,76309],{"encoding":904},"MR = 236 - 16Q",[883,76311,76313],{"className":76312},[886],[888,76314,76315],{"xmlns":890},[892,76316,76317,76344],{},[895,76318,76319,76321,76323,76325,76327,76333,76335,76338,76340,76342],{},[898,76320,6889],{},[898,76322,6849],{},[1761,76324,1909],{},[1765,76326,5486],{},[1824,76328,76329,76331],{},[898,76330,1828],{},[1765,76332,2296],{},[1761,76334,1885],{},[1765,76336,76337],{},"32",[898,76339,1828],{},[1761,76341,1964],{},[1765,76343,9791],{},[902,76345,76346],{"encoding":904},"MC = 3Q^2 - 32Q + 96",". (b) ",[883,76349,76351],{"className":76350},[886],[888,76352,76353],{"xmlns":890},[892,76354,76355,76372],{},[895,76356,76357,76359,76361,76363,76366,76368,76370],{},[898,76358,6889],{},[898,76360,8051],{},[1761,76362,1909],{},[1765,76364,76365],{},"280",[1761,76367,1885],{},[1765,76369,13077],{},[898,76371,1828],{},[902,76373,76374],{"encoding":904},"MR = 280 - 20Q",[883,76376,76378],{"className":76377},[886],[888,76379,76380],{"xmlns":890},[892,76381,76382,76409],{},[895,76383,76384,76386,76388,76390,76393,76399,76401,76403,76405,76407],{},[898,76385,6889],{},[898,76387,6849],{},[1761,76389,1909],{},[1765,76391,76392],{},"1,6",[1824,76394,76395,76397],{},[898,76396,1828],{},[1765,76398,2296],{},[1761,76400,1885],{},[1765,76402,5433],{},[898,76404,1828],{},[1761,76406,1964],{},[1765,76408,7195],{},[902,76410,76411],{"encoding":904},"MC = 1{,}6Q^2 - 15Q + 60",[724,76413,76414,76223,76417,2068,76432,60003,76447,73705,76460,73721,76475,76282,76490,1343,76521,76347,76557,1343,76589,76633,76634,1343,76666,1741],{},[38,76415,76416],{},"3.23",[883,76418,76420],{"className":76419},[886],[888,76421,76422],{"xmlns":890},[892,76423,76424,76430],{},[895,76425,76426,76428],{},[898,76427,1655],{},[898,76429,8051],{},[902,76431,8151],{"encoding":904},[883,76433,76435],{"className":76434},[886],[888,76436,76437],{"xmlns":890},[892,76438,76439,76445],{},[895,76440,76441,76443],{},[898,76442,1655],{},[898,76444,6849],{},[902,76446,7310],{"encoding":904},[883,76448,76450],{"className":76449},[886],[888,76451,76452],{"xmlns":890},[892,76453,76454,76458],{},[895,76455,76456],{},[898,76457,1828],{},[902,76459,1828],{"encoding":904},[883,76461,76463],{"className":76462},[886],[888,76464,76465],{"xmlns":890},[892,76466,76467,76473],{},[895,76468,76469,76471],{},[898,76470,1839],{},[898,76472,8051],{},[902,76474,67457],{"encoding":904},[883,76476,76478],{"className":76477},[886],[888,76479,76480],{"xmlns":890},[892,76481,76482,76488],{},[895,76483,76484,76486],{},[898,76485,1839],{},[898,76487,8051],{},[902,76489,67457],{"encoding":904},[883,76491,76493],{"className":76492},[886],[888,76494,76495],{"xmlns":890},[892,76496,76497,76518],{},[895,76498,76499,76501,76503,76505,76508,76510,76512],{},[898,76500,1655],{},[898,76502,8051],{},[1761,76504,1909],{},[1765,76506,76507],{},"125",[898,76509,1828],{},[1761,76511,1885],{},[1824,76513,76514,76516],{},[898,76515,1828],{},[1765,76517,2296],{},[902,76519,76520],{"encoding":904},"TR = 125Q - Q^2",[883,76522,76524],{"className":76523},[886],[888,76525,76526],{"xmlns":890},[892,76527,76528,76554],{},[895,76529,76530,76532,76534,76536,76538,76540,76542,76544,76546,76548],{},[898,76531,1655],{},[898,76533,6849],{},[1761,76535,1909],{},[1765,76537,19148],{},[1761,76539,1964],{},[1765,76541,6321],{},[898,76543,1828],{},[1761,76545,1964],{},[1765,76547,5426],{},[1824,76549,76550,76552],{},[898,76551,1828],{},[1765,76553,2296],{},[902,76555,76556],{"encoding":904},"TC = 500 + 5Q + 0{,}5Q^2",[883,76558,76560],{"className":76559},[886],[888,76561,76562],{"xmlns":890},[892,76563,76564,76586],{},[895,76565,76566,76568,76570,76572,76574,76576,76578,76580],{},[898,76567,1655],{},[898,76569,8051],{},[1761,76571,1909],{},[1765,76573,13077],{},[898,76575,1828],{},[1761,76577,1885],{},[1765,76579,2296],{},[1824,76581,76582,76584],{},[898,76583,1828],{},[1765,76585,2296],{},[902,76587,76588],{"encoding":904},"TR = 20Q - 2Q^2",[883,76590,76592],{"className":76591},[886],[888,76593,76594],{"xmlns":890},[892,76595,76596,76630],{},[895,76597,76598,76600,76602,76604,76606,76608,76610,76612,76614,76616,76622,76624],{},[898,76599,1655],{},[898,76601,6849],{},[1761,76603,1909],{},[1765,76605,2296],{},[1761,76607,1964],{},[1765,76609,13077],{},[898,76611,1828],{},[1761,76613,1885],{},[1765,76615,2454],{},[1824,76617,76618,76620],{},[898,76619,1828],{},[1765,76621,2296],{},[1761,76623,1964],{},[1824,76625,76626,76628],{},[898,76627,1828],{},[1765,76629,5486],{},[902,76631,76632],{"encoding":904},"TC = 2 + 20Q - 8Q^2 + Q^3",". (c) ",[883,76635,76637],{"className":76636},[886],[888,76638,76639],{"xmlns":890},[892,76640,76641,76663],{},[895,76642,76643,76645,76647,76649,76651,76653,76655,76657],{},[898,76644,1655],{},[898,76646,8051],{},[1761,76648,1909],{},[1765,76650,2318],{},[898,76652,1828],{},[1761,76654,1885],{},[1765,76656,27822],{},[1824,76658,76659,76661],{},[898,76660,1828],{},[1765,76662,2296],{},[902,76664,76665],{"encoding":904},"TR = 4Q - 0{,}25Q^2",[883,76667,76669],{"className":76668},[886],[888,76670,76671],{"xmlns":890},[892,76672,76673,76721],{},[895,76674,76675,76677,76679,76681,76683,76685,76687,76689,76691,76707,76709],{},[898,76676,1655],{},[898,76678,6849],{},[1761,76680,1909],{},[1765,76682,2318],{},[1761,76684,1964],{},[1765,76686,2296],{},[898,76688,1828],{},[1761,76690,1885],{},[6411,76692,76693],{"scriptlevel":1767,"displaystyle":1821},[4379,76694,76695,76705],{},[895,76696,76697,76699],{},[1765,76698,5486],{},[1824,76700,76701,76703],{},[898,76702,1828],{},[1765,76704,2296],{},[1765,76706,2633],{},[1761,76708,1964],{},[6411,76710,76711],{"scriptlevel":1767,"displaystyle":1821},[4379,76712,76713,76719],{},[1824,76714,76715,76717],{},[898,76716,1828],{},[1765,76718,5486],{},[1765,76720,13077],{},[902,76722,76723],{"encoding":904},"TC = 4 + 2Q - \\tfrac{3Q^2}{10} + \\tfrac{Q^3}{20}",[724,76725,76726,76729,76730,76760,76761,76793,76794,25627,76824,76854],{},[38,76727,76728],{},"3.24"," Firma řeší problém stanovení cen pro malé a velké odběratele za účelem maximalizace zisku. Poptávka pro maloodběratele je ",[883,76731,76733],{"className":76732},[886],[888,76734,76735],{"xmlns":890},[892,76736,76737,76757],{},[895,76738,76739,76745,76747,76749,76751],{},[1681,76740,76741,76743],{},[898,76742,1839],{},[1765,76744,1945],{},[1761,76746,1909],{},[1765,76748,19148],{},[1761,76750,1885],{},[1681,76752,76753,76755],{},[898,76754,1828],{},[1765,76756,1945],{},[902,76758,76759],{"encoding":904},"P_1 = 500 - Q_1",", pro velkoodběratele ",[883,76762,76764],{"className":76763},[886],[888,76765,76766],{"xmlns":890},[892,76767,76768,76790],{},[895,76769,76770,76776,76778,76780,76782,76784],{},[1681,76771,76772,76774],{},[898,76773,1839],{},[1765,76775,2296],{},[1761,76777,1909],{},[1765,76779,34111],{},[1761,76781,1885],{},[1765,76783,68537],{},[1681,76785,76786,76788],{},[898,76787,1828],{},[1765,76789,2296],{},[902,76791,76792],{"encoding":904},"P_2 = 300 - 1{,}5Q_2",". Celkové náklady firmy jsou ",[883,76795,76797],{"className":76796},[886],[888,76798,76799],{"xmlns":890},[892,76800,76801,76821],{},[895,76802,76803,76805,76807,76809,76811,76813,76815,76817,76819],{},[898,76804,1655],{},[898,76806,6849],{},[1761,76808,1909],{},[1765,76810,7190],{},[2761,76812,7057],{},[1765,76814,63060],{},[1761,76816,1964],{},[1765,76818,13077],{},[898,76820,1828],{},[902,76822,76823],{"encoding":904},"TC = 50\\,000 + 20Q",[883,76825,76827],{"className":76826},[886],[888,76828,76829],{"xmlns":890},[892,76830,76831,76851],{},[895,76832,76833,76835,76837,76843,76845],{},[898,76834,1828],{},[1761,76836,1909],{},[1681,76838,76839,76841],{},[898,76840,1828],{},[1765,76842,1945],{},[1761,76844,1964],{},[1681,76846,76847,76849],{},[898,76848,1828],{},[1765,76850,2296],{},[902,76852,76853],{"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.",[724,76856,76857,76860,76861,76891,76892,76793,76924,25627,76954,76983],{},[38,76858,76859],{},"3.25"," Firma řeší problém stanovení cen pro domácí a zahraniční trh za účelem maximalizace zisku. Poptávka pro domácí trh je ",[883,76862,76864],{"className":76863},[886],[888,76865,76866],{"xmlns":890},[892,76867,76868,76888],{},[895,76869,76870,76876,76878,76880,76882],{},[1681,76871,76872,76874],{},[898,76873,1839],{},[1765,76875,1945],{},[1761,76877,1909],{},[1765,76879,34111],{},[1761,76881,1885],{},[1681,76883,76884,76886],{},[898,76885,1828],{},[1765,76887,1945],{},[902,76889,76890],{"encoding":904},"P_1 = 300 - Q_1",", pro zahraniční trh ",[883,76893,76895],{"className":76894},[886],[888,76896,76897],{"xmlns":890},[892,76898,76899,76921],{},[895,76900,76901,76907,76909,76911,76913,76915],{},[1681,76902,76903,76905],{},[898,76904,1839],{},[1765,76906,2296],{},[1761,76908,1909],{},[1765,76910,12421],{},[1761,76912,1885],{},[1765,76914,5426],{},[1681,76916,76917,76919],{},[898,76918,1828],{},[1765,76920,2296],{},[902,76922,76923],{"encoding":904},"P_2 = 200 - 0{,}5Q_2",[883,76925,76927],{"className":76926},[886],[888,76928,76929],{"xmlns":890},[892,76930,76931,76951],{},[895,76932,76933,76935,76937,76939,76941,76943,76945,76947,76949],{},[898,76934,1655],{},[898,76936,6849],{},[1761,76938,1909],{},[1765,76940,6321],{},[2761,76942,7057],{},[1765,76944,63060],{},[1761,76946,1964],{},[1765,76948,7160],{},[898,76950,1828],{},[902,76952,76953],{"encoding":904},"TC = 5\\,000 + 100Q",[883,76955,76957],{"className":76956},[886],[888,76958,76959],{"xmlns":890},[892,76960,76961,76981],{},[895,76962,76963,76965,76967,76973,76975],{},[898,76964,1828],{},[1761,76966,1909],{},[1681,76968,76969,76971],{},[898,76970,1828],{},[1765,76972,1945],{},[1761,76974,1964],{},[1681,76976,76977,76979],{},[898,76978,1828],{},[1765,76980,2296],{},[902,76982,76853],{"encoding":904},". Stanovte ceny, při kterých firma maximalizuje zisk: (a) s cenovou diskriminací, (b) bez cenové diskriminace. Porovnejte zisk firmy v obou případech.",[198,76985,76987],{"id":76986},"konstrukce-nabídky-326328","Konstrukce nabídky (3.26–3.28)",[724,76989,76990,76993,76994,77041,77042,77059],{},[38,76991,76992],{},"3.26"," Jsou dány celkové variabilní náklady ",[883,76995,76997],{"className":76996},[886],[888,76998,76999],{"xmlns":890},[892,77000,77001,77038],{},[895,77002,77003,77005,77007,77009,77011,77014,77020,77022,77025,77031,77033,77036],{},[898,77004,1655],{},[898,77006,44359],{},[898,77008,6849],{},[1761,77010,1909],{},[1765,77012,77013],{},"0,85",[1824,77015,77016,77018],{},[898,77017,1828],{},[1765,77019,5486],{},[1761,77021,1885],{},[1765,77023,77024],{},"11,9",[1824,77026,77027,77029],{},[898,77028,1828],{},[1765,77030,2296],{},[1761,77032,1964],{},[1765,77034,77035],{},"102",[898,77037,1828],{},[902,77039,77040],{"encoding":904},"TVC = 0{,}85Q^3 - 11{,}9Q^2 + 102Q",". Určete minimální cenu ",[883,77043,77045],{"className":77044},[886],[888,77046,77047],{"xmlns":890},[892,77048,77049,77057],{},[895,77050,77051],{},[1824,77052,77053,77055],{},[898,77054,1839],{},[1761,77056,8408],{},[902,77058,8458],{"encoding":904}," nabídky a konstruujte nabídku. Graficky interpretujte.",[724,77061,77062,74820,77065,77101],{},[38,77063,77064],{},"3.27",[883,77066,77068],{"className":77067},[886],[888,77069,77070],{"xmlns":890},[892,77071,77072,77098],{},[895,77073,77074,77076,77078,77080,77082,77088,77090,77092,77094,77096],{},[898,77075,6889],{},[898,77077,6849],{},[1761,77079,1909],{},[1765,77081,6993],{},[1824,77083,77084,77086],{},[898,77085,1828],{},[1765,77087,2296],{},[1761,77089,1885],{},[1765,77091,68418],{},[898,77093,1828],{},[1761,77095,1964],{},[1765,77097,34773],{},[902,77099,77100],{"encoding":904},"MC = 4{,}2Q^2 - 48Q + 250",". Konstruujte nabídku.",[724,77103,77104,74071,77107,77101],{},[38,77105,77106],{},"3.28",[883,77108,77110],{"className":77109},[886],[888,77111,77112],{"xmlns":890},[892,77113,77114,77150],{},[895,77115,77116,77118,77120,77122,77124,77130,77132,77134,77140,77142,77144,77146,77148],{},[898,77117,1655],{},[898,77119,6849],{},[1761,77121,1909],{},[1765,77123,5426],{},[1824,77125,77126,77128],{},[898,77127,1828],{},[1765,77129,5486],{},[1761,77131,1885],{},[1765,77133,5512],{},[1824,77135,77136,77138],{},[898,77137,1828],{},[1765,77139,2296],{},[1761,77141,1964],{},[1765,77143,7195],{},[898,77145,1828],{},[1761,77147,1964],{},[1765,77149,19148],{},[902,77151,77152],{"encoding":904},"TC = 0{,}5Q^3 - 7Q^2 + 60Q + 500",[115,77154,5533],{"id":5532},[120,77156,77157,77185,77230,77302,77367,77407,77499,77605,77645,77759,77852,77916,77948,78008,78014,78078,78127,78181,78289,78344],{},[123,77158,77159,1989,77161,77184],{},[38,77160,59728],{},[883,77162,77164],{"className":77163},[886],[888,77165,77166],{"xmlns":890},[892,77167,77168,77182],{},[895,77169,77170,77172,77174,77176,77178,77180],{},[898,77171,1655],{},[898,77173,8051],{},[1761,77175,1909],{},[898,77177,1839],{},[1761,77179,2447],{},[898,77181,1828],{},[902,77183,70690],{"encoding":904}," — křivka celkového příjmu (total revenue curve).",[123,77186,77187,1989,77189,77229],{},[38,77188,60314],{},[883,77190,77192],{"className":77191},[886],[888,77193,77194],{"xmlns":890},[892,77195,77196,77226],{},[895,77197,77198,77200,77202,77204,77216,77218,77220,77222,77224],{},[898,77199,8309],{},[898,77201,8051],{},[1761,77203,1909],{},[6411,77205,77206],{"scriptlevel":1767,"displaystyle":1821},[4379,77207,77208,77214],{},[895,77209,77210,77212],{},[898,77211,1655],{},[898,77213,8051],{},[898,77215,1828],{},[1761,77217,1909],{},[898,77219,2244],{},[1761,77221,1915],{"stretchy":1821},[898,77223,1828],{},[1761,77225,1920],{"stretchy":1821},[902,77227,77228],{"encoding":904},"AR = \\tfrac{TR}{Q} = D(Q)"," — shoduje se s poptávkovou funkcí.",[123,77231,77232,1989,77234,77270,77271,77286,77287,1741],{},[38,77233,60462],{},[883,77235,77237],{"className":77236},[886],[888,77238,77239],{"xmlns":890},[892,77240,77241,77267],{},[895,77242,77243,77245,77247,77249],{},[898,77244,6889],{},[898,77246,8051],{},[1761,77248,1909],{},[6411,77250,77251],{"scriptlevel":1767,"displaystyle":1821},[4379,77252,77253,77261],{},[895,77254,77255,77257,77259],{},[898,77256,4346],{"mathvariant":1969},[898,77258,1655],{},[898,77260,8051],{},[895,77262,77263,77265],{},[898,77264,4346],{"mathvariant":1969},[898,77266,1828],{},[902,77268,77269],{"encoding":904},"MR = \\tfrac{\\mathrm{d}TR}{\\mathrm{d}Q}"," — rychlost změny ",[883,77272,77274],{"className":77273},[886],[888,77275,77276],{"xmlns":890},[892,77277,77278,77284],{},[895,77279,77280,77282],{},[898,77281,1655],{},[898,77283,8051],{},[902,77285,8151],{"encoding":904},"; pro lineární poptávku má sklon dvojnásobný vůči ",[883,77288,77290],{"className":77289},[886],[888,77291,77292],{"xmlns":890},[892,77293,77294,77300],{},[895,77295,77296,77298],{},[898,77297,8309],{},[898,77299,8051],{},[902,77301,59423],{"encoding":904},[123,77303,77304,1989,77307,1343,77337,1741],{},[38,77305,77306],{},"Diferenciál příjmu\u002Fnákladů",[883,77308,77310],{"className":77309},[886],[888,77311,77312],{"xmlns":890},[892,77313,77314,77334],{},[895,77315,77316,77318,77320,77322,77324,77326,77328,77330,77332],{},[898,77317,6959],{"mathvariant":1969},[898,77319,1655],{},[898,77321,8051],{},[1761,77323,6803],{},[898,77325,6889],{},[898,77327,8051],{},[2761,77329,7057],{},[898,77331,4346],{"mathvariant":1969},[898,77333,1828],{},[902,77335,77336],{"encoding":904},"\\Delta TR \\approx MR \\, \\mathrm{d}Q",[883,77338,77340],{"className":77339},[886],[888,77341,77342],{"xmlns":890},[892,77343,77344,77364],{},[895,77345,77346,77348,77350,77352,77354,77356,77358,77360,77362],{},[898,77347,6959],{"mathvariant":1969},[898,77349,1655],{},[898,77351,6849],{},[1761,77353,6803],{},[898,77355,6889],{},[898,77357,6849],{},[2761,77359,7057],{},[898,77361,4346],{"mathvariant":1969},[898,77363,1828],{},[902,77365,77366],{"encoding":904},"\\Delta TC \\approx MC \\, \\mathrm{d}Q",[123,77368,77369,1989,77371,1741],{},[38,77370,62584],{},[883,77372,77374],{"className":77373},[886],[888,77375,77376],{"xmlns":890},[892,77377,77378,77404],{},[895,77379,77380,77382,77384,77386,77388,77390,77392,77394,77396,77398,77400,77402],{},[898,77381,1655],{},[898,77383,6849],{},[1761,77385,1909],{},[898,77387,14474],{},[898,77389,6849],{},[1761,77391,1964],{},[898,77393,1655],{},[898,77395,44359],{},[898,77397,6849],{},[1761,77399,1915],{"stretchy":1821},[898,77401,1828],{},[1761,77403,1920],{"stretchy":1821},[902,77405,77406],{"encoding":904},"TC = FC + TVC(Q)",[123,77408,77409,1989,77412,1343,77427,1989,77429,1343,77452,1989,77455,1741],{},[38,77410,77411],{},"Fixní náklady",[883,77413,77415],{"className":77414},[886],[888,77416,77417],{"xmlns":890},[892,77418,77419,77425],{},[895,77420,77421,77423],{},[898,77422,14474],{},[898,77424,6849],{},[902,77426,59469],{"encoding":904},[38,77428,62737],{},[883,77430,77432],{"className":77431},[886],[888,77433,77434],{"xmlns":890},[892,77435,77436,77450],{},[895,77437,77438,77440,77442,77444,77446,77448],{},[898,77439,1655],{},[898,77441,44359],{},[898,77443,6849],{},[1761,77445,1915],{"stretchy":1821},[898,77447,1828],{},[1761,77449,1920],{"stretchy":1821},[902,77451,62734],{"encoding":904},[38,77453,77454],{},"variabilní náklady na jednotku",[883,77456,77458],{"className":77457},[886],[888,77459,77460],{"xmlns":890},[892,77461,77462,77496],{},[895,77463,77464,77466,77468,77470,77472,77474,77476],{},[898,77465,44359],{},[898,77467,6849],{},[1761,77469,1915],{"stretchy":1821},[898,77471,1828],{},[1761,77473,1920],{"stretchy":1821},[1761,77475,1909],{},[6411,77477,77478],{"scriptlevel":1767,"displaystyle":1821},[4379,77479,77480,77494],{},[895,77481,77482,77484,77486,77488,77490,77492],{},[898,77483,1655],{},[898,77485,44359],{},[898,77487,6849],{},[1761,77489,1915],{"stretchy":1821},[898,77491,1828],{},[1761,77493,1920],{"stretchy":1821},[898,77495,1828],{},[902,77497,77498],{"encoding":904},"VC(Q) = \\tfrac{TVC(Q)}{Q}",[123,77500,77501,1989,77503,1343,77533,1989,77536,1343,77568,1989,77571,1741],{},[38,77502,62745],{},[883,77504,77506],{"className":77505},[886],[888,77507,77508],{"xmlns":890},[892,77509,77510,77530],{},[895,77511,77512,77514,77516,77518],{},[898,77513,8309],{},[898,77515,6849],{},[1761,77517,1909],{},[6411,77519,77520],{"scriptlevel":1767,"displaystyle":1821},[4379,77521,77522,77528],{},[895,77523,77524,77526],{},[898,77525,1655],{},[898,77527,6849],{},[898,77529,1828],{},[902,77531,77532],{"encoding":904},"AC = \\tfrac{TC}{Q}",[38,77534,77535],{},"průměrné fixní",[883,77537,77539],{"className":77538},[886],[888,77540,77541],{"xmlns":890},[892,77542,77543,77565],{},[895,77544,77545,77547,77549,77551,77553],{},[898,77546,8309],{},[898,77548,14474],{},[898,77550,6849],{},[1761,77552,1909],{},[6411,77554,77555],{"scriptlevel":1767,"displaystyle":1821},[4379,77556,77557,77563],{},[895,77558,77559,77561],{},[898,77560,14474],{},[898,77562,6849],{},[898,77564,1828],{},[902,77566,77567],{"encoding":904},"AFC = \\tfrac{FC}{Q}",[38,77569,77570],{},"průměrné variabilní",[883,77572,77574],{"className":77573},[886],[888,77575,77576],{"xmlns":890},[892,77577,77578,77602],{},[895,77579,77580,77582,77584,77586,77588],{},[898,77581,8309],{},[898,77583,44359],{},[898,77585,6849],{},[1761,77587,1909],{},[6411,77589,77590],{"scriptlevel":1767,"displaystyle":1821},[4379,77591,77592,77600],{},[895,77593,77594,77596,77598],{},[898,77595,1655],{},[898,77597,44359],{},[898,77599,6849],{},[898,77601,1828],{},[902,77603,77604],{"encoding":904},"AVC = \\tfrac{TVC}{Q}",[123,77606,77607,1989,77609,1741],{},[38,77608,63932],{},[883,77610,77612],{"className":77611},[886],[888,77613,77614],{"xmlns":890},[892,77615,77616,77642],{},[895,77617,77618,77620,77622,77624],{},[898,77619,6889],{},[898,77621,6849],{},[1761,77623,1909],{},[6411,77625,77626],{"scriptlevel":1767,"displaystyle":1821},[4379,77627,77628,77636],{},[895,77629,77630,77632,77634],{},[898,77631,4346],{"mathvariant":1969},[898,77633,1655],{},[898,77635,6849],{},[895,77637,77638,77640],{},[898,77639,4346],{"mathvariant":1969},[898,77641,1828],{},[902,77643,77644],{"encoding":904},"MC = \\tfrac{\\mathrm{d}TC}{\\mathrm{d}Q}",[123,77646,77647,1989,77649,77697,77698,77711,77712,1343,77727,1343,77744,1741],{},[38,77648,64830],{},[883,77650,77652],{"className":77651},[886],[888,77653,77654],{"xmlns":890},[892,77655,77656,77694],{},[895,77657,77658,77660,77662,77664,77666,77668,77670,77672,77674,77676,77678,77684,77686,77688],{},[898,77659,1655],{},[898,77661,6849],{},[1761,77663,1909],{},[898,77665,14474],{},[898,77667,6849],{},[1761,77669,1964],{},[898,77671,207],{},[898,77673,1828],{},[1761,77675,1964],{},[898,77677,4302],{},[1824,77679,77680,77682],{},[898,77681,1828],{},[1765,77683,2296],{},[1761,77685,1964],{},[898,77687,2774],{},[1824,77689,77690,77692],{},[898,77691,1828],{},[1765,77693,5486],{},[902,77695,77696],{"encoding":904},"TC = FC + aQ + bQ^2 + cQ^3"," — „standardní\" tvar s ",[883,77699,77701],{"className":77700},[886],[888,77702,77703],{"xmlns":890},[892,77704,77705,77709],{},[895,77706,77707],{},[898,77708,900],{},[902,77710,900],{"encoding":904},"-průběhem ",[883,77713,77715],{"className":77714},[886],[888,77716,77717],{"xmlns":890},[892,77718,77719,77725],{},[895,77720,77721,77723],{},[898,77722,8309],{},[898,77724,6849],{},[902,77726,59538],{"encoding":904},[883,77728,77730],{"className":77729},[886],[888,77731,77732],{"xmlns":890},[892,77733,77734,77742],{},[895,77735,77736,77738,77740],{},[898,77737,8309],{},[898,77739,44359],{},[898,77741,6849],{},[902,77743,59289],{"encoding":904},[883,77745,77747],{"className":77746},[886],[888,77748,77749],{"xmlns":890},[892,77750,77751,77757],{},[895,77752,77753,77755],{},[898,77754,6889],{},[898,77756,6849],{},[902,77758,59270],{"encoding":904},[123,77760,77761,77763,77764,14432,77779,77820,77821,65475,77836,77851],{},[38,77762,65912],{},": v bodě minima ",[883,77765,77767],{"className":77766},[886],[888,77768,77769],{"xmlns":890},[892,77770,77771,77777],{},[895,77772,77773,77775],{},[898,77774,8309],{},[898,77776,6849],{},[902,77778,59538],{"encoding":904},[883,77780,77782],{"className":77781},[886],[888,77783,77784],{"xmlns":890},[892,77785,77786,77818],{},[895,77787,77788,77790,77792,77794,77800,77802,77804,77806,77808,77810,77816],{},[898,77789,8309],{},[898,77791,6849],{},[1761,77793,1915],{"stretchy":1821},[1681,77795,77796,77798],{},[898,77797,1828],{},[1765,77799,1767],{},[1761,77801,1920],{"stretchy":1821},[1761,77803,1909],{},[898,77805,6889],{},[898,77807,6849],{},[1761,77809,1915],{"stretchy":1821},[1681,77811,77812,77814],{},[898,77813,1828],{},[1765,77815,1767],{},[1761,77817,1920],{"stretchy":1821},[902,77819,66547],{"encoding":904},"; geometricky ",[883,77822,77824],{"className":77823},[886],[888,77825,77826],{"xmlns":890},[892,77827,77828,77834],{},[895,77829,77830,77832],{},[898,77831,6889],{},[898,77833,6849],{},[902,77835,59270],{"encoding":904},[883,77837,77839],{"className":77838},[886],[888,77840,77841],{"xmlns":890},[892,77842,77843,77849],{},[895,77844,77845,77847],{},[898,77846,8309],{},[898,77848,6849],{},[902,77850,59538],{"encoding":904}," v jejím minimu.",[123,77853,77854,77763,77856,14432,77873,1741],{},[38,77855,67262],{},[883,77857,77859],{"className":77858},[886],[888,77860,77861],{"xmlns":890},[892,77862,77863,77871],{},[895,77864,77865,77867,77869],{},[898,77866,8309],{},[898,77868,44359],{},[898,77870,6849],{},[902,77872,59289],{"encoding":904},[883,77874,77876],{"className":77875},[886],[888,77877,77878],{"xmlns":890},[892,77879,77880,77914],{},[895,77881,77882,77884,77886,77888,77890,77896,77898,77900,77902,77904,77906,77912],{},[898,77883,8309],{},[898,77885,44359],{},[898,77887,6849],{},[1761,77889,1915],{"stretchy":1821},[1681,77891,77892,77894],{},[898,77893,1828],{},[1765,77895,1767],{},[1761,77897,1920],{"stretchy":1821},[1761,77899,1909],{},[898,77901,6889],{},[898,77903,6849],{},[1761,77905,1915],{"stretchy":1821},[1681,77907,77908,77910],{},[898,77909,1828],{},[1765,77911,1767],{},[1761,77913,1920],{"stretchy":1821},[902,77915,72997],{"encoding":904},[123,77917,77918,1989,77920,77947],{},[38,77919,67441],{},[883,77921,77923],{"className":77922},[886],[888,77924,77925],{"xmlns":890},[892,77926,77927,77945],{},[895,77928,77929,77931,77933,77935,77937,77939,77941,77943],{},[898,77930,1839],{},[898,77932,8051],{},[1761,77934,1909],{},[898,77936,1655],{},[898,77938,8051],{},[1761,77940,1885],{},[898,77942,1655],{},[898,77944,6849],{},[902,77946,59178],{"encoding":904}," — rozdíl mezi celkovým příjmem a celkovými náklady.",[123,77949,77950,3927,77952,77954,77955,77981,77982,78007],{},[38,77951,68303],{},[614,77953,67566],{},") — hodnoty ",[883,77956,77958],{"className":77957},[886],[888,77959,77960],{"xmlns":890},[892,77961,77962,77978],{},[895,77963,77964,77970,77972],{},[1681,77965,77966,77968],{},[898,77967,1828],{},[898,77969,8309],{},[1761,77971,1834],{"separator":1833},[1681,77973,77974,77976],{},[898,77975,1828],{},[898,77977,27286],{},[902,77979,77980],{"encoding":904},"Q_A, Q_B"," splňující ",[883,77983,77985],{"className":77984},[886],[888,77986,77987],{"xmlns":890},[892,77988,77989,78005],{},[895,77990,77991,77993,77995,77997,77999,78001,78003],{},[898,77992,1839],{},[898,77994,8051],{},[1761,77996,1915],{"stretchy":1821},[898,77998,1828],{},[1761,78000,1920],{"stretchy":1821},[1761,78002,1909],{},[1765,78004,1767],{},[902,78006,67843],{"encoding":904},"; oddělují pásma ztráty a zisku.",[123,78009,78010,78013],{},[38,78011,78012],{},"Práh rentability"," — stav firmy v bodě zvratu.",[123,78015,78016,78018,78019,14432,78036,78077],{},[38,78017,69357],{}," — v bodě maxima zisku ",[883,78020,78022],{"className":78021},[886],[888,78023,78024],{"xmlns":890},[892,78025,78026,78034],{},[895,78027,78028],{},[1681,78029,78030,78032],{},[898,78031,1828],{},[1765,78033,1767],{},[902,78035,42331],{"encoding":904},[883,78037,78039],{"className":78038},[886],[888,78040,78041],{"xmlns":890},[892,78042,78043,78075],{},[895,78044,78045,78047,78049,78051,78057,78059,78061,78063,78065,78067,78073],{},[898,78046,6889],{},[898,78048,8051],{},[1761,78050,1915],{"stretchy":1821},[1681,78052,78053,78055],{},[898,78054,1828],{},[1765,78056,1767],{},[1761,78058,1920],{"stretchy":1821},[1761,78060,1909],{},[898,78062,6889],{},[898,78064,6849],{},[1761,78066,1915],{"stretchy":1821},[1681,78068,78069,78071],{},[898,78070,1828],{},[1765,78072,1767],{},[1761,78074,1920],{"stretchy":1821},[902,78076,69623],{"encoding":904}," (3.13).",[123,78079,78080,24334,78082,14432,78101,78126],{},[38,78081,70650],{},[883,78083,78085],{"className":78084},[886],[888,78086,78087],{"xmlns":890},[892,78088,78089,78098],{},[895,78090,78091,78093,78095],{},[898,78092,1839],{},[1761,78094,1909],{},[2761,78096,78097],{},"konst",[902,78099,78100],{"encoding":904},"P = \\text{konst}",[883,78102,78104],{"className":78103},[886],[888,78105,78106],{"xmlns":890},[892,78107,78108,78124],{},[895,78109,78110,78112,78114,78116,78118,78120,78122],{},[898,78111,1839],{},[1761,78113,1909],{},[898,78115,6889],{},[898,78117,6849],{},[1761,78119,1915],{"stretchy":1821},[898,78121,1828],{},[1761,78123,1920],{"stretchy":1821},[902,78125,71344],{"encoding":904}," (3.14).",[123,78128,78129,78132,78133,78162,78163,78180],{},[38,78130,78131],{},"Shutdown point"," — bod ",[883,78134,78136],{"className":78135},[886],[888,78137,78138],{"xmlns":890},[892,78139,78140,78160],{},[895,78141,78142,78144,78150,78152,78158],{},[1761,78143,1915],{"stretchy":1821},[1824,78145,78146,78148],{},[898,78147,1828],{},[1761,78149,8408],{},[1761,78151,1834],{"separator":1833},[1824,78153,78154,78156],{},[898,78155,1839],{},[1761,78157,8408],{},[1761,78159,1920],{"stretchy":1821},[902,78161,71633],{"encoding":904}," v minimu ",[883,78164,78166],{"className":78165},[886],[888,78167,78168],{"xmlns":890},[892,78169,78170,78178],{},[895,78171,78172,78174,78176],{},[898,78173,8309],{},[898,78175,44359],{},[898,78177,6849],{},[902,78179,59289],{"encoding":904},"; pod ním se firmě nevyplatí produkovat.",[123,78182,78183,1989,78186,10518,78221,71903,78242,78255,78256,78271,78272,1741],{},[38,78184,78185],{},"Funkce nabídky firmy",[883,78187,78189],{"className":78188},[886],[888,78190,78191],{"xmlns":890},[892,78192,78193,78219],{},[895,78194,78195,78197,78199,78201,78203,78205,78207,78209,78211,78213,78215,78217],{},[898,78196,1839],{},[1761,78198,1909],{},[898,78200,1912],{},[1761,78202,1915],{"stretchy":1821},[898,78204,1828],{},[1761,78206,1920],{"stretchy":1821},[1761,78208,1909],{},[898,78210,6889],{},[898,78212,6849],{},[1761,78214,1915],{"stretchy":1821},[898,78216,1828],{},[1761,78218,1920],{"stretchy":1821},[902,78220,73100],{"encoding":904},[883,78222,78224],{"className":78223},[886],[888,78225,78226],{"xmlns":890},[892,78227,78228,78240],{},[895,78229,78230,78232,78234],{},[898,78231,1828],{},[1761,78233,8538],{},[1824,78235,78236,78238],{},[898,78237,1828],{},[1761,78239,8408],{},[902,78241,71902],{"encoding":904},[883,78243,78245],{"className":78244},[886],[888,78246,78247],{"xmlns":890},[892,78248,78249,78253],{},[895,78250,78251],{},[1765,78252,1767],{},[902,78254,1767],{"encoding":904}," (3.15); vychází z rostoucí části ",[883,78257,78259],{"className":78258},[886],[888,78260,78261],{"xmlns":890},[892,78262,78263,78269],{},[895,78264,78265,78267],{},[898,78266,6889],{},[898,78268,6849],{},[902,78270,59270],{"encoding":904}," nad minimem ",[883,78273,78275],{"className":78274},[886],[888,78276,78277],{"xmlns":890},[892,78278,78279,78287],{},[895,78280,78281,78283,78285],{},[898,78282,8309],{},[898,78284,44359],{},[898,78286,6849],{},[902,78288,59289],{"encoding":904},[123,78290,78291,5675,78293,78314,78315,1741],{},[38,78292,54064],{},[883,78294,78296],{"className":78295},[886],[888,78297,78298],{"xmlns":890},[892,78299,78300,78312],{},[895,78301,78302,78304,78306],{},[898,78303,1839],{},[1761,78305,1909],{},[1824,78307,78308,78310],{},[898,78309,1839],{},[1761,78311,8408],{},[902,78313,8411],{"encoding":904}," konstantní ⇒ ",[883,78316,78318],{"className":78317},[886],[888,78319,78320],{"xmlns":890},[892,78321,78322,78342],{},[895,78323,78324,78326,78328,78330,78332,78334,78336],{},[898,78325,8309],{},[898,78327,8051],{},[1761,78329,1909],{},[898,78331,6889],{},[898,78333,8051],{},[1761,78335,1909],{},[1824,78337,78338,78340],{},[898,78339,1839],{},[1761,78341,8408],{},[902,78343,62576],{"encoding":904},[123,78345,78346,78349],{},[38,78347,78348],{},"Cenová diskriminace"," — stanovení odlišných cen pro různé segmenty trhu za účelem maximalizace zisku (úlohy 3.24–3.25).",[115,78351,5968],{"id":5967},[120,78353,78354,78373,78385],{},[123,78355,78356,1989,78358,1343,78361,1343,78364,1343,78367,1343,78370],{},[38,78357,5983],{},[207,78359,15980],{"className":78360,"dataFsResolvedFilePath":800,"href":801},[210],[207,78362,6000],{"className":78363,"dataFsResolvedFilePath":848,"href":849},[210],[207,78365,5995],{"className":78366,"dataFsResolvedFilePath":764,"href":765},[210],[207,78368,775],{"className":78369,"dataFsResolvedFilePath":773,"href":774},[210],[207,78371,859],{"className":78372,"dataFsResolvedFilePath":857,"href":858},[210],[123,78374,78375,1989,78377,1343,78381],{},[38,78376,40731],{},[207,78378,78380],{"className":78379,"dataFsResolvedFilePath":745,"href":746},[210],"KS 1. blok — souhrn",[207,78382,78384],{"className":78383,"dataFsResolvedFilePath":838,"href":839},[210],"KS 2. blok — souhrn",[123,78386,78387,1989,78389],{},[38,78388,6015],{},[207,78390,6021],{"className":78391,"dataFsResolvedFilePath":6019,"href":6020},[210],{"title":641,"searchDepth":642,"depth":642,"links":78393},[78394,78395,78402,78408,78412,78413,78417,78418,78419,78420,78426,78427],{"id":54934,"depth":642,"text":1241},{"id":59716,"depth":642,"text":59717,"children":78396},[78397,78398,78399,78400,78401],{"id":59727,"depth":649,"text":59728},{"id":60313,"depth":649,"text":60314},{"id":60461,"depth":649,"text":60462},{"id":61203,"depth":649,"text":61204},{"id":61858,"depth":649,"text":61859},{"id":62579,"depth":642,"text":62580,"children":78403},[78404,78405,78406,78407],{"id":62583,"depth":649,"text":62584},{"id":62744,"depth":649,"text":62745},{"id":63931,"depth":649,"text":63932},{"id":64829,"depth":649,"text":64830},{"id":65911,"depth":642,"text":65912,"children":78409},[78410,78411],{"id":20445,"depth":649,"text":20446},{"id":67261,"depth":649,"text":67262},{"id":67435,"depth":642,"text":67436},{"id":69356,"depth":642,"text":69357,"children":78414},[78415,78416],{"id":69370,"depth":649,"text":20446},{"id":70649,"depth":649,"text":70650},{"id":71281,"depth":642,"text":71282},{"id":72747,"depth":642,"text":72748},{"id":53866,"depth":642,"text":53867},{"id":73208,"depth":642,"text":73209,"children":78421},[78422,78423,78424,78425],{"id":73212,"depth":649,"text":73213},{"id":74064,"depth":649,"text":74065},{"id":75610,"depth":649,"text":75611},{"id":76986,"depth":649,"text":76987},{"id":5532,"depth":642,"text":5533},{"id":5967,"depth":642,"text":5968},{},"\u002Ftopics\u002Fprijem-naklady-zisk",{"title":59098,"description":641},[1138,1135],"topics\u002Fprijem-naklady-zisk",[1128,78434,78435,59150,78436,78437,78438],"prijem","naklady","body-zvratu","maximalizace-zisku","nabidka-firmy","0d2CjMGyTT-GeTvSE65iXk5mUJ-650ilVskfuGcRAwI",{"id":78441,"title":78442,"body":78443,"course":1128,"courses":659,"created":6039,"description":641,"extension":661,"meta":90540,"navigation":664,"path":90541,"seo":90542,"sources":90543,"stem":90544,"tags":90545,"type":6050,"updated":677,"__hash__":90551},"topics\u002Ftopics\u002Fprodukce.md","Produkce — produkční funkce, Cobb-Douglas, MRTS",{"type":9,"value":78444,"toc":90497},[78445,78448,78804,78808,78811,78879,78931,78941,78945,78979,79020,79044,79067,79096,79163,79270,79313,79370,79445,79490,79494,79502,79510,79513,79778,79829,79909,79979,80002,80030,80075,80097,80101,80108,80157,80183,80334,80337,80374,80537,80645,80649,80686,80761,80830,80949,81071,81152,81158,81199,81272,81365,81369,81405,81493,81607,81712,81797,81937,81941,81989,82034,82040,82044,82047,82098,82148,82155,82221,82354,82399,82403,82424,82803,82898,82915,82969,82973,83055,83139,83309,83312,83355,83422,83496,83500,83505,83574,83582,83591,83669,83735,83740,83835,83878,83883,83931,83936,83984,84102,84185,84223,84326,84385,84526,84530,84573,84646,84670,84724,84731,84733,84778,84823,84834,84839,84875,84937,84960,84969,85070,85137,85210,85217,85308,85370,85406,85463,85522,85707,85803,85807,85811,85890,85895,86019,86105,86111,86221,86258,86349,86447,86450,86454,86520,86557,86679,86731,86735,86763,86815,86889,86994,87018,87077,87081,87099,87242,87390,87392,87427,87431,87433,87523,87653,87779,87871,87946,87950,88066,88170,88360,88396,88490,88496,88609,88912,88918,89036,89135,89211,89213,90375,90377],[12,78446,78442],{"id":78447},"produkce-produkční-funkce-cobb-douglas-mrts",[1636,78449,78450],{},[724,78451,78452,7934,78454,78456,78457,40924,78470,78483,78484,20410,78497,3927,78499,78523,78524,1989,78526,2068,78560,1989,78563,78591,78592,14432,78612,78642,78643,3927,78646,78674,78675,78678,78679,78709,78710,78740,78741,1989,78744,78784,78785,78803],{},[883,78453,7933],{},[38,78455,859],{}," popisuje vztah mezi vstupy (práce ",[883,78458,78460],{"className":78459},[886],[888,78461,78462],{"xmlns":890},[892,78463,78464,78468],{},[895,78465,78466],{},[898,78467,13835],{},[902,78469,13835],{"encoding":904},[883,78471,78473],{"className":78472},[886],[888,78474,78475],{"xmlns":890},[892,78476,78477,78481],{},[895,78478,78479],{},[898,78480,2768],{},[902,78482,2768],{"encoding":904},") a výstupem ",[883,78485,78487],{"className":78486},[886],[888,78488,78489],{"xmlns":890},[892,78490,78491,78495],{},[895,78492,78493],{},[898,78494,1828],{},[902,78496,1828],{"encoding":904},[38,78498,40992],{},[883,78500,78502],{"className":78501},[886],[888,78503,78504],{"xmlns":890},[892,78505,78506,78520],{},[895,78507,78508,78510,78512,78514,78516,78518],{},[898,78509,1828],{},[1761,78511,1909],{},[898,78513,1828],{},[1761,78515,1915],{"stretchy":1821},[898,78517,13835],{},[1761,78519,1920],{"stretchy":1821},[902,78521,78522],{"encoding":904},"Q = Q(L)",") studujeme ",[614,78525,14063],{},[883,78527,78529],{"className":78528},[886],[888,78530,78531],{"xmlns":890},[892,78532,78533,78557],{},[895,78534,78535,78537,78543,78545,78551,78553,78555],{},[898,78536,6889],{},[1681,78538,78539,78541],{},[898,78540,1839],{},[898,78542,13835],{},[1761,78544,1909],{},[1824,78546,78547,78549],{},[898,78548,1828],{},[1761,78550,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,78552,1915],{"stretchy":1821},[898,78554,13835],{},[1761,78556,1920],{"stretchy":1821},[902,78558,78559],{"encoding":904},"MP_L = Q'(L)",[614,78561,78562],{},"průměrný produkt",[883,78564,78566],{"className":78565},[886],[888,78567,78568],{"xmlns":890},[892,78569,78570,78588],{},[895,78571,78572,78574,78580,78582,78584,78586],{},[898,78573,8309],{},[1681,78575,78576,78578],{},[898,78577,1839],{},[898,78579,13835],{},[1761,78581,1909],{},[898,78583,1828],{},[898,78585,8726],{"mathvariant":1969},[898,78587,13835],{},[902,78589,78590],{"encoding":904},"AP_L = Q\u002FL","; v maximu ",[883,78593,78595],{"className":78594},[886],[888,78596,78597],{"xmlns":890},[892,78598,78599,78609],{},[895,78600,78601,78603],{},[898,78602,8309],{},[1681,78604,78605,78607],{},[898,78606,1839],{},[898,78608,13835],{},[902,78610,78611],{"encoding":904},"AP_L",[883,78613,78615],{"className":78614},[886],[888,78616,78617],{"xmlns":890},[892,78618,78619,78639],{},[895,78620,78621,78623,78629,78631,78633],{},[898,78622,6889],{},[1681,78624,78625,78627],{},[898,78626,1839],{},[898,78628,13835],{},[1761,78630,1909],{},[898,78632,8309],{},[1681,78634,78635,78637],{},[898,78636,1839],{},[898,78638,13835],{},[902,78640,78641],{"encoding":904},"MP_L = AP_L",". Ve ",[38,78644,78645],{},"dvoufaktorovém modelu",[883,78647,78649],{"className":78648},[886],[888,78650,78651],{"xmlns":890},[892,78652,78653,78671],{},[895,78654,78655,78657,78659,78661,78663,78665,78667,78669],{},[898,78656,1828],{},[1761,78658,1909],{},[898,78660,1828],{},[1761,78662,1915],{"stretchy":1821},[898,78664,13835],{},[1761,78666,1834],{"separator":1833},[898,78668,2768],{},[1761,78670,1920],{"stretchy":1821},[902,78672,78673],{"encoding":904},"Q = Q(L,K)",") dominují ",[38,78676,78677],{},"Cobb-Douglasovy"," funkce ",[883,78680,78682],{"className":78681},[886],[888,78683,78684],{"xmlns":890},[892,78685,78686,78706],{},[895,78687,78688,78690,78692,78694,78700],{},[898,78689,1828],{},[1761,78691,1909],{},[898,78693,8309],{},[1824,78695,78696,78698],{},[898,78697,13835],{},[898,78699,207],{},[1824,78701,78702,78704],{},[898,78703,2768],{},[898,78705,4302],{},[902,78707,78708],{"encoding":904},"Q = AL^a K^b","; mezní produkty ",[883,78711,78713],{"className":78712},[886],[888,78714,78715],{"xmlns":890},[892,78716,78717,78737],{},[895,78718,78719,78721,78727,78729,78731],{},[898,78720,6889],{},[1681,78722,78723,78725],{},[898,78724,1839],{},[898,78726,13835],{},[1761,78728,1834],{"separator":1833},[898,78730,6889],{},[1681,78732,78733,78735],{},[898,78734,1839],{},[898,78736,2768],{},[902,78738,78739],{"encoding":904},"MP_L, MP_K"," jsou parciální derivace a jejich podíl dává ",[38,78742,78743],{},"mezní míru technické substituce",[883,78745,78747],{"className":78746},[886],[888,78748,78749],{"xmlns":890},[892,78750,78751,78781],{},[895,78752,78753,78755,78757,78759,78761,78763,78765,78771,78773,78775],{},[898,78754,6889],{},[898,78756,8051],{},[898,78758,1655],{},[898,78760,1912],{},[1761,78762,1909],{},[898,78764,6889],{},[1681,78766,78767,78769],{},[898,78768,1839],{},[898,78770,13835],{},[898,78772,8726],{"mathvariant":1969},[898,78774,6889],{},[1681,78776,78777,78779],{},[898,78778,1839],{},[898,78780,2768],{},[902,78782,78783],{"encoding":904},"MRTS = MP_L\u002FMP_K"," — sklon izokvanty. Součet exponentů ",[883,78786,78788],{"className":78787},[886],[888,78789,78790],{"xmlns":890},[892,78791,78792,78800],{},[895,78793,78794,78796,78798],{},[898,78795,207],{},[1761,78797,1964],{},[898,78799,4302],{},[902,78801,78802],{"encoding":904},"a+b"," určuje typ výnosů z rozsahu.",[115,78805,78807],{"id":78806},"úvod-cílové-znalosti-kapitoly-5","Úvod — cílové znalosti kapitoly 5",[724,78809,78810],{},"Po prostudování kapitoly 5 student umí:",[120,78812,78813,78819,78829,78835,78841,78846,78852,78862,78867,78873],{},[123,78814,78815,78816,1834],{},"popsat ",[38,78817,78818],{},"jednofaktorový model produkce",[123,78820,78821,78822,2068,78825,78828],{},"vypočítat ",[38,78823,78824],{},"mezní",[38,78826,78827],{},"průměrný produkt práce"," a ekonomicky je interpretovat,",[123,78830,78831,78832,1834],{},"charakterizovat průběh ",[38,78833,78834],{},"křivky produkce",[123,78836,78837,78838,1834],{},"formulovat ",[38,78839,78840],{},"princip maximalizace průměrného produktu práce",[123,78842,78815,78843,1834],{},[38,78844,78845],{},"dvoufaktorový model produkce",[123,78847,78848,78849,1834],{},"uvést tvar ",[38,78850,78851],{},"Cobb–Douglasových produkčních funkcí",[123,78853,78854,78855,1343,78857,1343,78859,1834],{},"vyložit, co jsou ",[38,78856,28645],{},[38,78858,17695],{},[38,78860,78861],{},"klesající výnosy z rozsahu",[123,78863,78821,78864,78828],{},[38,78865,78866],{},"mezní produkty práce a kapitálu",[123,78868,78869,78870,1834],{},"najít ",[38,78871,78872],{},"izokvanty",[123,78874,78821,78875,78878],{},[38,78876,78877],{},"mezní míru technické substituce (MRTS)"," a ekonomicky ji interpretovat.",[724,78880,78881,78882,78885,78886,78889,78890,1989,78893,1343,78906,1989,78909,2068,78922,78925,78926,78928,78929,1741],{},"Každý proces produkce je určován ",[38,78883,78884],{},"faktory"," (též ",[38,78887,78888],{},"vstupy",") produkce. K hlavním patří ",[38,78891,78892],{},"práce",[883,78894,78896],{"className":78895},[886],[888,78897,78898],{"xmlns":890},[892,78899,78900,78904],{},[895,78901,78902],{},[898,78903,13835],{},[902,78905,13835],{"encoding":904},[38,78907,78908],{},"kapitál",[883,78910,78912],{"className":78911},[886],[888,78913,78914],{"xmlns":890},[892,78915,78916,78920],{},[895,78917,78918],{},[898,78919,2768],{},[902,78921,2768],{"encoding":904},[38,78923,78924],{},"půda",". Při modelování se půda obvykle považuje za dlouhodobě konstantní, takže endogenními faktory zůstávají práce a kapitál. Je-li kapitál neměnný, hovoříme o ",[38,78927,40992],{}," (produkce závisí jen na práci); v opačném případě o ",[38,78930,78645],{},[724,78932,78933,78934,1343,78937,78940],{},"Související matematický aparát: ",[207,78935,5995],{"className":78936,"dataFsResolvedFilePath":764,"href":765},[210],[207,78938,784],{"className":78939,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace a totální diferenciál).",[115,78942,78944],{"id":78943},"jednofaktorový-model-produkce","Jednofaktorový model produkce",[724,78946,78947,78948,78961,78962,78975,78976],{},"Uvažujeme proces v krátkém období, kdy kapitál lze považovat za konstantní. Závislost produkce ",[883,78949,78951],{"className":78950},[886],[888,78952,78953],{"xmlns":890},[892,78954,78955,78959],{},[895,78956,78957],{},[898,78958,1828],{},[902,78960,1828],{"encoding":904}," na práci ",[883,78963,78965],{"className":78964},[886],[888,78966,78967],{"xmlns":890},[892,78968,78969,78973],{},[895,78970,78971],{},[898,78972,13835],{},[902,78974,13835],{"encoding":904}," vyjadřuje ",[38,78977,78978],{},"produkční funkce",[883,78980,78982],{"className":78981},[886],[888,78983,78984],{"xmlns":890,"display":1930},[892,78985,78986,79017],{},[24787,78987,78988],{"width":32101},[24792,78989,78990,78992,79010,79012],{},[24795,78991],{"width":32106},[24795,78993,78994],{},[895,78995,78996,78998,79000,79002,79004,79006,79008],{},[898,78997,1828],{},[1761,78999,1909],{},[898,79001,1828],{},[1761,79003,1915],{"stretchy":1821},[898,79005,13835],{},[1761,79007,1920],{"stretchy":1821},[1761,79009,1834],{"separator":1833},[24795,79011],{"width":32106},[24795,79013,79014],{},[2761,79015,79016],{},"(5.1)",[902,79018,79019],{"encoding":904},"Q = Q(L), \\tag{5.1}",[724,79021,79022,79023,3927,79026,79029,79030,79043],{},"jejíž graf se nazývá ",[38,79024,79025],{},"křivka produkce",[614,79027,79028],{},"production curve","). Práce ",[883,79031,79033],{"className":79032},[886],[888,79034,79035],{"xmlns":890},[892,79036,79037,79041],{},[895,79038,79039],{},[898,79040,13835],{},[902,79042,13835],{"encoding":904}," se měří počtem pracovníků, případně počtem pracovních hodin.",[115,79045,79047,79048,1920],{"id":79046},"mezní-produkt-práce-mplmp_l","Mezní produkt práce (",[883,79049,79051],{"className":79050},[886],[888,79052,79053],{"xmlns":890},[892,79054,79055,79065],{},[895,79056,79057,79059],{},[898,79058,6889],{},[1681,79060,79061,79063],{},[898,79062,1839],{},[898,79064,13835],{},[902,79066,14083],{"encoding":904},[724,79068,79069,3927,79072,79075,79076,79095],{},[38,79070,79071],{},"Mezní produkt práce",[614,79073,79074],{},"marginal product of labour",") ",[883,79077,79079],{"className":79078},[886],[888,79080,79081],{"xmlns":890},[892,79082,79083,79093],{},[895,79084,79085,79087],{},[898,79086,6889],{},[1681,79088,79089,79091],{},[898,79090,1839],{},[898,79092,13835],{},[902,79094,14083],{"encoding":904}," je derivace produkce podle práce:",[883,79097,79099],{"className":79098},[886],[888,79100,79101],{"xmlns":890,"display":1930},[892,79102,79103,79160],{},[24787,79104,79105],{"width":32101},[24792,79106,79107,79109,79153,79155],{},[24795,79108],{"width":32106},[24795,79110,79111],{},[895,79112,79113,79115,79121,79123,79137,79139,79145,79147,79149,79151],{},[898,79114,6889],{},[1681,79116,79117,79119],{},[898,79118,1839],{},[898,79120,13835],{},[1761,79122,1909],{},[4379,79124,79125,79131],{},[895,79126,79127,79129],{},[898,79128,4346],{},[898,79130,1828],{},[895,79132,79133,79135],{},[898,79134,4346],{},[898,79136,13835],{},[1761,79138,1909],{},[1824,79140,79141,79143],{},[898,79142,1828],{},[1761,79144,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,79146,1915],{"stretchy":1821},[898,79148,13835],{},[1761,79150,1920],{"stretchy":1821},[898,79152,1741],{"mathvariant":1969},[24795,79154],{"width":32106},[24795,79156,79157],{},[2761,79158,79159],{},"(5.2)",[902,79161,79162],{"encoding":904},"MP_L = \\frac{dQ}{dL} = Q'(L). \\tag{5.2}",[724,79164,79165,79166,23978,79184,79212,79213,79230,79231,4178,79248,2162],{},"Pro pevnou hodnotu ",[883,79167,79169],{"className":79168},[886],[888,79170,79171],{"xmlns":890},[892,79172,79173,79181],{},[895,79174,79175],{},[1824,79176,79177,79179],{},[898,79178,13835],{},[1761,79180,8408],{},[902,79182,79183],{"encoding":904},"L^*",[883,79185,79187],{"className":79186},[886],[888,79188,79189],{"xmlns":890},[892,79190,79191,79209],{},[895,79192,79193,79199,79201,79207],{},[1824,79194,79195,79197],{},[898,79196,1828],{},[1761,79198,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,79200,1915],{"stretchy":1821},[1824,79202,79203,79205],{},[898,79204,13835],{},[1761,79206,8408],{},[1761,79208,1920],{"stretchy":1821},[902,79210,79211],{"encoding":904},"Q'(L^*)"," rychlost změny produkce vzhledem k práci v bodě ",[883,79214,79216],{"className":79215},[886],[888,79217,79218],{"xmlns":890},[892,79219,79220,79228],{},[895,79221,79222],{},[1824,79223,79224,79226],{},[898,79225,13835],{},[1761,79227,8408],{},[902,79229,79183],{"encoding":904},", resp. přibližnou změnu produkce odpovídající jednotkové změně práce (z ",[883,79232,79234],{"className":79233},[886],[888,79235,79236],{"xmlns":890},[892,79237,79238,79246],{},[895,79239,79240],{},[1824,79241,79242,79244],{},[898,79243,13835],{},[1761,79245,8408],{},[902,79247,79183],{"encoding":904},[883,79249,79251],{"className":79250},[886],[888,79252,79253],{"xmlns":890},[892,79254,79255,79267],{},[895,79256,79257,79263,79265],{},[1824,79258,79259,79261],{},[898,79260,13835],{},[1761,79262,8408],{},[1761,79264,1964],{},[1765,79266,1945],{},[902,79268,79269],{"encoding":904},"L^*+1",[1636,79271,79272],{},[724,79273,79274,22057,79276,79295,79296,79299,79300,1741],{},[883,79275,1642],{},[883,79277,79279],{"className":79278},[886],[888,79280,79281],{"xmlns":890},[892,79282,79283,79293],{},[895,79284,79285,79287],{},[898,79286,6889],{},[1681,79288,79289,79291],{},[898,79290,1839],{},[898,79292,13835],{},[902,79294,14083],{"encoding":904}," odpovídá na otázku „",[38,79297,79298],{},"kolik produkce přibude, když přidám jednoho dalšího pracovníka"," (při neměnném kapitálu)?\". Je to sklon křivky produkce v bodě ",[883,79301,79303],{"className":79302},[886],[888,79304,79305],{"xmlns":890},[892,79306,79307,79311],{},[895,79308,79309],{},[898,79310,13835],{},[902,79312,13835],{"encoding":904},[724,79314,79315,79318,79319,79335,79336,4178,79349,79369],{},[38,79316,79317],{},"Přibližná změna produkce"," pro změnu práce o ",[883,79320,79322],{"className":79321},[886],[888,79323,79324],{"xmlns":890},[892,79325,79326,79332],{},[895,79327,79328,79330],{},[898,79329,4346],{},[898,79331,13835],{},[902,79333,79334],{"encoding":904},"dL"," (z ",[883,79337,79339],{"className":79338},[886],[888,79340,79341],{"xmlns":890},[892,79342,79343,79347],{},[895,79344,79345],{},[898,79346,13835],{},[902,79348,13835],{"encoding":904},[883,79350,79352],{"className":79351},[886],[888,79353,79354],{"xmlns":890},[892,79355,79356,79366],{},[895,79357,79358,79360,79362,79364],{},[898,79359,13835],{},[1761,79361,1964],{},[898,79363,4346],{},[898,79365,13835],{},[902,79367,79368],{"encoding":904},"L+dL",") pomocí diferenciálu:",[883,79371,79373],{"className":79372},[886],[888,79374,79375],{"xmlns":890,"display":1930},[892,79376,79377,79442],{},[24787,79378,79379],{"width":32101},[24792,79380,79381,79383,79435,79437],{},[24795,79382],{"width":32106},[24795,79384,79385],{},[895,79386,79387,79389,79391,79393,79395,79397,79399,79405,79407,79409,79411,79413,79415,79417,79419,79421,79427,79429,79431,79433],{},[898,79388,6959],{"mathvariant":1969},[898,79390,1828],{},[1761,79392,6803],{},[898,79394,4346],{},[898,79396,1828],{},[1761,79398,1909],{},[1824,79400,79401,79403],{},[898,79402,1828],{},[1761,79404,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,79406,1915],{"stretchy":1821},[898,79408,13835],{},[1761,79410,1920],{"stretchy":1821},[2761,79412,7057],{},[898,79414,4346],{},[898,79416,13835],{},[1761,79418,1909],{},[898,79420,6889],{},[1681,79422,79423,79425],{},[898,79424,1839],{},[898,79426,13835],{},[2761,79428,7057],{},[898,79430,4346],{},[898,79432,13835],{},[898,79434,1741],{"mathvariant":1969},[24795,79436],{"width":32106},[24795,79438,79439],{},[2761,79440,79441],{},"(5.3)",[902,79443,79444],{"encoding":904},"\\Delta Q \\approx dQ = Q'(L)\\,dL = MP_L\\,dL. \\tag{5.3}",[724,79446,79447,79448,1741],{},"Skutečná změna je ",[883,79449,79451],{"className":79450},[886],[888,79452,79453],{"xmlns":890},[892,79454,79455,79487],{},[895,79456,79457,79459,79461,79463,79465,79467,79469,79471,79473,79475,79477,79479,79481,79483,79485],{},[898,79458,6959],{"mathvariant":1969},[898,79460,1828],{},[1761,79462,1909],{},[898,79464,1828],{},[1761,79466,1915],{"stretchy":1821},[898,79468,13835],{},[1761,79470,1964],{},[898,79472,4346],{},[898,79474,13835],{},[1761,79476,1920],{"stretchy":1821},[1761,79478,1885],{},[898,79480,1828],{},[1761,79482,1915],{"stretchy":1821},[898,79484,13835],{},[1761,79486,1920],{"stretchy":1821},[902,79488,79489],{"encoding":904},"\\Delta Q = Q(L+dL) - Q(L)",[198,79491,79493],{"id":79492},"zákon-klesajících-mezních-výnosů","Zákon klesajících mezních výnosů",[724,79495,79496,3927,79499,5372],{},[38,79497,79498],{},"Zákon klesajících výnosů",[614,79500,79501],{},"law of diminishing marginal productivity",[1636,79503,79504],{},[724,79505,79506,79507,79509],{},"Roste-li postupně některý ze vstupů (",[614,79508,40988],{},"), budou přírůstky výstupu od jistého bodu klesat.",[724,79511,79512],{},"Typická křivka produkce (Obrázek 5.2) má dvě fáze:",[724,79514,79515,79516,1989,79537,79556,79557,79607,79608,79610,79611,1989,79631,79650,79651,79607,79683,6997,79685,79704,79705,25627,79722,79756,79757,12146,79774,79777],{},"1° ",[38,79517,79518,79519,2506],{},"Do bodu ",[883,79520,79522],{"className":79521},[886],[888,79523,79524],{"xmlns":890},[892,79525,79526,79534],{},[895,79527,79528],{},[1681,79529,79530,79532],{},[898,79531,13835],{},[1765,79533,1767],{},[902,79535,79536],{"encoding":904},"L_0",[883,79538,79540],{"className":79539},[886],[888,79541,79542],{"xmlns":890},[892,79543,79544,79554],{},[895,79545,79546,79548],{},[898,79547,6889],{},[1681,79549,79550,79552],{},[898,79551,1839],{},[898,79553,13835],{},[902,79555,14083],{"encoding":904}," roste, tj. ",[883,79558,79560],{"className":79559},[886],[888,79561,79562],{"xmlns":890},[892,79563,79564,79604],{},[895,79565,79566,79568,79570,79576,79582,79584,79594,79596,79598,79600,79602],{},[1761,79567,1915],{"stretchy":1821},[898,79569,6889],{},[1681,79571,79572,79574],{},[898,79573,1839],{},[898,79575,13835],{},[1824,79577,79578,79580],{},[1761,79579,1920],{"stretchy":1821},[1761,79581,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,79583,1909],{},[1824,79585,79586,79588],{},[898,79587,1828],{},[895,79589,79590,79592],{},[1761,79591,6459],{"mathvariant":1969},[1761,79593,6459],{"mathvariant":1969},[1761,79595,1915],{"stretchy":1821},[898,79597,13835],{},[1761,79599,1920],{"stretchy":1821},[1761,79601,1763],{},[1765,79603,1767],{},[902,79605,79606],{"encoding":904},"(MP_L)' = Q''(L) > 0"," — křivka produkce je ",[38,79609,41690],{},".\n2° ",[38,79612,79613,79614,2506],{},"Od bodu ",[883,79615,79617],{"className":79616},[886],[888,79618,79619],{"xmlns":890},[892,79620,79621,79629],{},[895,79622,79623],{},[1681,79624,79625,79627],{},[898,79626,13835],{},[1765,79628,1767],{},[902,79630,79536],{"encoding":904},[883,79632,79634],{"className":79633},[886],[888,79635,79636],{"xmlns":890},[892,79637,79638,79648],{},[895,79639,79640,79642],{},[898,79641,6889],{},[1681,79643,79644,79646],{},[898,79645,1839],{},[898,79647,13835],{},[902,79649,14083],{"encoding":904}," klesá, ",[883,79652,79654],{"className":79653},[886],[888,79655,79656],{"xmlns":890},[892,79657,79658,79680],{},[895,79659,79660,79670,79672,79674,79676,79678],{},[1824,79661,79662,79664],{},[898,79663,1828],{},[895,79665,79666,79668],{},[1761,79667,6459],{"mathvariant":1969},[1761,79669,6459],{"mathvariant":1969},[1761,79671,1915],{"stretchy":1821},[898,79673,13835],{},[1761,79675,1920],{"stretchy":1821},[1761,79677,2058],{},[1765,79679,1767],{},[902,79681,79682],{"encoding":904},"Q''(L) \u003C 0",[38,79684,42510],{},[883,79686,79688],{"className":79687},[886],[888,79689,79690],{"xmlns":890},[892,79691,79692,79702],{},[895,79693,79694,79696],{},[898,79695,6889],{},[1681,79697,79698,79700],{},[898,79699,1839],{},[898,79701,13835],{},[902,79703,14083],{"encoding":904}," v kladných hodnotách klesá do bodu ",[883,79706,79708],{"className":79707},[886],[888,79709,79710],{"xmlns":890},[892,79711,79712,79720],{},[895,79713,79714],{},[1681,79715,79716,79718],{},[898,79717,13835],{},[1765,79719,1945],{},[902,79721,17250],{"encoding":904},[883,79723,79725],{"className":79724},[886],[888,79726,79727],{"xmlns":890},[892,79728,79729,79753],{},[895,79730,79731,79733,79739,79741,79747,79749,79751],{},[898,79732,6889],{},[1681,79734,79735,79737],{},[898,79736,1839],{},[898,79738,13835],{},[1761,79740,1915],{"stretchy":1821},[1681,79742,79743,79745],{},[898,79744,13835],{},[1765,79746,1945],{},[1761,79748,1920],{"stretchy":1821},[1761,79750,1909],{},[1765,79752,1767],{},[902,79754,79755],{"encoding":904},"MP_L(L_1) = 0"," (maximum produkce), a dále pokračuje v záporných hodnotách. Bod ",[883,79758,79760],{"className":79759},[886],[888,79761,79762],{"xmlns":890},[892,79763,79764,79772],{},[895,79765,79766],{},[1681,79767,79768,79770],{},[898,79769,13835],{},[1765,79771,1767],{},[902,79773,79536],{"encoding":904},[38,79775,79776],{},"inflexním bodem"," produkční funkce.",[724,79779,79780,79781,14432,79798,1741],{},"Matematicky: zákon klesajících výnosů znamená, že od určitého ",[883,79782,79784],{"className":79783},[886],[888,79785,79786],{"xmlns":890},[892,79787,79788,79796],{},[895,79789,79790],{},[1681,79791,79792,79794],{},[898,79793,13835],{},[1765,79795,1767],{},[902,79797,79536],{"encoding":904},[883,79799,79801],{"className":79800},[886],[888,79802,79803],{"xmlns":890},[892,79804,79805,79827],{},[895,79806,79807,79817,79819,79821,79823,79825],{},[1824,79808,79809,79811],{},[898,79810,1828],{},[895,79812,79813,79815],{},[1761,79814,6459],{"mathvariant":1969},[1761,79816,6459],{"mathvariant":1969},[1761,79818,1915],{"stretchy":1821},[898,79820,13835],{},[1761,79822,1920],{"stretchy":1821},[1761,79824,2058],{},[1765,79826,1767],{},[902,79828,79682],{"encoding":904},[724,79830,79831,1989,79834,2232,79874,1343,79891,79908],{},[38,79832,79833],{},"Typický polynom třetího stupně:",[883,79835,79837],{"className":79836},[886],[888,79838,79839],{"xmlns":890},[892,79840,79841,79871],{},[895,79842,79843,79845,79847,79849,79851,79853,79855,79861,79863,79865],{},[898,79844,1828],{},[1761,79846,1915],{"stretchy":1821},[898,79848,13835],{},[1761,79850,1920],{"stretchy":1821},[1761,79852,1909],{},[898,79854,207],{},[1824,79856,79857,79859],{},[898,79858,13835],{},[1765,79860,5486],{},[1761,79862,1964],{},[898,79864,4302],{},[1824,79866,79867,79869],{},[898,79868,13835],{},[1765,79870,2296],{},[902,79872,79873],{"encoding":904},"Q(L) = aL^3 + bL^2",[883,79875,79877],{"className":79876},[886],[888,79878,79879],{"xmlns":890},[892,79880,79881,79889],{},[895,79882,79883,79885,79887],{},[898,79884,207],{},[1761,79886,2058],{},[1765,79888,1767],{},[902,79890,4323],{"encoding":904},[883,79892,79894],{"className":79893},[886],[888,79895,79896],{"xmlns":890},[892,79897,79898,79906],{},[895,79899,79900,79902,79904],{},[898,79901,4302],{},[1761,79903,1763],{},[1765,79905,1767],{},[902,79907,22847],{"encoding":904},". Pak",[883,79910,79912],{"className":79911},[886],[888,79913,79914],{"xmlns":890,"display":1930},[892,79915,79916,79976],{},[895,79917,79918,79924,79926,79928,79936,79944,79946,79948,79954,79956,79958,79966,79974],{},[1681,79919,79920,79922],{},[898,79921,13835],{},[1765,79923,1767],{},[1761,79925,1909],{},[1761,79927,1885],{},[6411,79929,79930],{"scriptlevel":1767,"displaystyle":1821},[4379,79931,79932,79934],{},[1765,79933,1945],{},[1765,79935,5486],{},[6411,79937,79938],{"scriptlevel":1767,"displaystyle":1821},[4379,79939,79940,79942],{},[898,79941,4302],{},[898,79943,207],{},[1761,79945,1834],{"separator":1833},[3315,79947],{"width":3317},[1681,79949,79950,79952],{},[898,79951,13835],{},[1765,79953,1945],{},[1761,79955,1909],{},[1761,79957,1885],{},[6411,79959,79960],{"scriptlevel":1767,"displaystyle":1821},[4379,79961,79962,79964],{},[1765,79963,2296],{},[1765,79965,5486],{},[6411,79967,79968],{"scriptlevel":1767,"displaystyle":1821},[4379,79969,79970,79972],{},[898,79971,4302],{},[898,79973,207],{},[898,79975,1741],{"mathvariant":1969},[902,79977,79978],{"encoding":904},"L_0 = -\\tfrac{1}{3}\\tfrac{b}{a}, \\qquad L_1 = -\\tfrac{2}{3}\\tfrac{b}{a}.",[115,79980,79982,79983,1920],{"id":79981},"průměrný-produkt-práce-aplap_l","Průměrný produkt práce (",[883,79984,79986],{"className":79985},[886],[888,79987,79988],{"xmlns":890},[892,79989,79990,80000],{},[895,79991,79992,79994],{},[898,79993,8309],{},[1681,79995,79996,79998],{},[898,79997,1839],{},[898,79999,13835],{},[902,80001,78611],{"encoding":904},[724,80003,80004,3927,80007,79075,80010,80029],{},[38,80005,80006],{},"Průměrný produkt práce",[614,80008,80009],{},"average product of labour",[883,80011,80013],{"className":80012},[886],[888,80014,80015],{"xmlns":890},[892,80016,80017,80027],{},[895,80018,80019,80021],{},[898,80020,8309],{},[1681,80022,80023,80025],{},[898,80024,1839],{},[898,80026,13835],{},[902,80028,78611],{"encoding":904}," je podíl produkce a práce:",[883,80031,80033],{"className":80032},[886],[888,80034,80035],{"xmlns":890,"display":1930},[892,80036,80037,80072],{},[24787,80038,80039],{"width":32101},[24792,80040,80041,80043,80065,80067],{},[24795,80042],{"width":32106},[24795,80044,80045],{},[895,80046,80047,80049,80055,80057,80063],{},[898,80048,8309],{},[1681,80050,80051,80053],{},[898,80052,1839],{},[898,80054,13835],{},[1761,80056,1909],{},[4379,80058,80059,80061],{},[898,80060,1828],{},[898,80062,13835],{},[898,80064,1741],{"mathvariant":1969},[24795,80066],{"width":32106},[24795,80068,80069],{},[2761,80070,80071],{},"(5.4)",[902,80073,80074],{"encoding":904},"AP_L = \\frac{Q}{L}. \\tag{5.4}",[724,80076,80077,80078,1741],{},"Je to nejjednodušší míra produktivity práce. Cílem optimalizace je maximalizace ",[883,80079,80081],{"className":80080},[886],[888,80082,80083],{"xmlns":890},[892,80084,80085,80095],{},[895,80086,80087,80089],{},[898,80088,8309],{},[1681,80090,80091,80093],{},[898,80092,1839],{},[898,80094,13835],{},[902,80096,78611],{"encoding":904},[115,80098,80100],{"id":80099},"princip-maximalizace-průměrného-produktu-práce","Princip maximalizace průměrného produktu práce",[724,80102,80103],{},[3991,80104],{"alt":80105,"className":80106,"src":80107},"imek-q-mpl-apl-tripanel",[210,3995],"\u002Fwiki-assets\u002Fimek-q-mpl-apl-tripanel.jpeg",[1636,80109,80110],{},[724,80111,80112,80115,80116,6699,80135,80152,80153],{},[38,80113,80114],{},"Princip:"," Má-li ",[883,80117,80119],{"className":80118},[886],[888,80120,80121],{"xmlns":890},[892,80122,80123,80133],{},[895,80124,80125,80127],{},[898,80126,8309],{},[1681,80128,80129,80131],{},[898,80130,1839],{},[898,80132,13835],{},[902,80134,78611],{"encoding":904},[883,80136,80138],{"className":80137},[886],[888,80139,80140],{"xmlns":890},[892,80141,80142,80150],{},[895,80143,80144],{},[1681,80145,80146,80148],{},[898,80147,13835],{},[1765,80149,1767],{},[902,80151,79536],{"encoding":904}," maximum, pak platí\n",[883,80154,80156],{"className":80155,"title":8255,"style":8256},[8254],"MP_L(L_0) = AP_L(L_0). \\tag{5.5}",[724,80158,80159,80160,80163,80164,1989,80168,1741],{},"Slovně: ",[38,80161,80162],{},"v bodě maxima průměrného produktu práce se mezní produkt práce rovná průměrnému produktu práce."," Jde o analogii ",[207,80165,80167],{"className":80166,"dataFsResolvedFilePath":827,"href":828},[210],"principu minimalizace průměrných nákladů",[883,80169,80171],{"className":80170},[886],[888,80172,80173],{"xmlns":890},[892,80174,80175,80181],{},[895,80176,80177,80179],{},[898,80178,8309],{},[898,80180,6849],{},[902,80182,59538],{"encoding":904},[1636,80184,80185,80209],{},[724,80186,80187,80189,80190],{},[883,80188,4452],{}," Postup — jak najít max ",[883,80191,80193],{"className":80192},[886],[888,80194,80195],{"xmlns":890},[892,80196,80197,80207],{},[895,80198,80199,80201],{},[898,80200,8309],{},[1681,80202,80203,80205],{},[898,80204,1839],{},[898,80206,13835],{},[902,80208,78611],{"encoding":904},[152,80210,80211,80249,80331],{},[123,80212,80213,80214,80248],{},"Napište ",[883,80215,80217],{"className":80216},[886],[888,80218,80219],{"xmlns":890},[892,80220,80221,80245],{},[895,80222,80223,80225,80231,80233,80235,80237,80239,80241,80243],{},[898,80224,8309],{},[1681,80226,80227,80229],{},[898,80228,1839],{},[898,80230,13835],{},[1761,80232,1909],{},[898,80234,1828],{},[1761,80236,1915],{"stretchy":1821},[898,80238,13835],{},[1761,80240,1920],{"stretchy":1821},[898,80242,8726],{"mathvariant":1969},[898,80244,13835],{},[902,80246,80247],{"encoding":904},"AP_L = Q(L)\u002FL"," a zderivujte.",[123,80250,80251,80252,80284,80285,80288,80289,1741],{},"Položte ",[883,80253,80255],{"className":80254},[886],[888,80256,80257],{"xmlns":890},[892,80258,80259,80281],{},[895,80260,80261,80263,80265,80271,80277,80279],{},[1761,80262,1915],{"stretchy":1821},[898,80264,8309],{},[1681,80266,80267,80269],{},[898,80268,1839],{},[898,80270,13835],{},[1824,80272,80273,80275],{},[1761,80274,1920],{"stretchy":1821},[1761,80276,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,80278,1909],{},[1765,80280,1767],{},[902,80282,80283],{"encoding":904},"(AP_L)' = 0"," a vyřešte. ",[614,80286,80287],{},"Zkratka:"," můžete rovnou řešit ",[883,80290,80292],{"className":80291},[886],[888,80293,80294],{"xmlns":890},[892,80295,80296,80328],{},[895,80297,80298,80300,80306,80308,80310,80312,80314,80316,80322,80324,80326],{},[898,80299,6889],{},[1681,80301,80302,80304],{},[898,80303,1839],{},[898,80305,13835],{},[1761,80307,1915],{"stretchy":1821},[898,80309,13835],{},[1761,80311,1920],{"stretchy":1821},[1761,80313,1909],{},[898,80315,8309],{},[1681,80317,80318,80320],{},[898,80319,1839],{},[898,80321,13835],{},[1761,80323,1915],{"stretchy":1821},[898,80325,13835],{},[1761,80327,1920],{"stretchy":1821},[902,80329,80330],{"encoding":904},"MP_L(L) = AP_L(L)",[123,80332,80333],{},"Ověřte 2. derivací (či grafem), že jde o maximum.",[198,80335,69479],{"id":80336},"odvození",[724,80338,80339,80340,80373],{},"Z ",[883,80341,80343],{"className":80342},[886],[888,80344,80345],{"xmlns":890},[892,80346,80347,80371],{},[895,80348,80349,80351,80357,80359,80361,80363,80365,80367,80369],{},[898,80350,8309],{},[1681,80352,80353,80355],{},[898,80354,1839],{},[898,80356,13835],{},[1761,80358,1909],{},[898,80360,1828],{},[1761,80362,1915],{"stretchy":1821},[898,80364,13835],{},[1761,80366,1920],{"stretchy":1821},[898,80368,8726],{"mathvariant":1969},[898,80370,13835],{},[902,80372,80247],{"encoding":904}," a derivace podílu:",[883,80375,80377],{"className":80376},[886],[888,80378,80379],{"xmlns":890,"display":1930},[892,80380,80381,80534],{},[895,80382,80383,80385,80387,80393,80399,80401,80403,80405,80407,80447,80449,80455,80489,80491,80497,80500,80502,80508,80510,80512,80514,80516,80518,80524,80526,80528,80530,80532],{},[1761,80384,1915],{"stretchy":1821},[898,80386,8309],{},[1681,80388,80389,80391],{},[898,80390,1839],{},[898,80392,13835],{},[1824,80394,80395,80397],{},[1761,80396,1920],{"stretchy":1821},[1761,80398,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,80400,1915],{"stretchy":1821},[898,80402,13835],{},[1761,80404,1920],{"stretchy":1821},[1761,80406,1909],{},[4379,80408,80409,80441],{},[895,80410,80411,80417,80419,80421,80423,80425,80427,80429,80431,80433,80435,80437,80439],{},[1824,80412,80413,80415],{},[898,80414,1828],{},[1761,80416,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,80418,1915],{"stretchy":1821},[898,80420,13835],{},[1761,80422,1920],{"stretchy":1821},[1761,80424,2447],{},[898,80426,13835],{},[1761,80428,1885],{},[898,80430,1828],{},[1761,80432,1915],{"stretchy":1821},[898,80434,13835],{},[1761,80436,1920],{"stretchy":1821},[1761,80438,2447],{},[1765,80440,1945],{},[1824,80442,80443,80445],{},[898,80444,13835],{},[1765,80446,2296],{},[1761,80448,1909],{},[4379,80450,80451,80453],{},[1765,80452,1945],{},[898,80454,13835],{},[895,80456,80457,80459,80465,80467,80469,80471,80473,80487],{},[1761,80458,1915],{"fence":1833},[1824,80460,80461,80463],{},[898,80462,1828],{},[1761,80464,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,80466,1915],{"stretchy":1821},[898,80468,13835],{},[1761,80470,1920],{"stretchy":1821},[1761,80472,1885],{},[4379,80474,80475,80485],{},[895,80476,80477,80479,80481,80483],{},[898,80478,1828],{},[1761,80480,1915],{"stretchy":1821},[898,80482,13835],{},[1761,80484,1920],{"stretchy":1821},[898,80486,13835],{},[1761,80488,1920],{"fence":1833},[1761,80490,1909],{},[4379,80492,80493,80495],{},[1765,80494,1945],{},[898,80496,13835],{},[1761,80498,1915],{"fence":1833,"stretchy":1833,"minsize":80499,"maxsize":80499},"1.2em",[898,80501,6889],{},[1681,80503,80504,80506],{},[898,80505,1839],{},[898,80507,13835],{},[1761,80509,1915],{"stretchy":1821},[898,80511,13835],{},[1761,80513,1920],{"stretchy":1821},[1761,80515,1885],{},[898,80517,8309],{},[1681,80519,80520,80522],{},[898,80521,1839],{},[898,80523,13835],{},[1761,80525,1915],{"stretchy":1821},[898,80527,13835],{},[1761,80529,1920],{"stretchy":1821},[1761,80531,1920],{"fence":1833,"stretchy":1833,"minsize":80499,"maxsize":80499},[898,80533,1741],{"mathvariant":1969},[902,80535,80536],{"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).",[724,80538,13703,80539,12146,80561,80644],{},[883,80540,80542],{"className":80541},[886],[888,80543,80544],{"xmlns":890},[892,80545,80546,80558],{},[895,80547,80548,80554,80556],{},[1681,80549,80550,80552],{},[898,80551,13835],{},[1765,80553,1767],{},[1761,80555,1763],{},[1765,80557,1767],{},[902,80559,80560],{"encoding":904},"L_0 > 0",[883,80562,80564],{"className":80563},[886],[888,80565,80566],{"xmlns":890},[892,80567,80568,80641],{},[895,80569,80570,80572,80574,80580,80586,80588,80594,80596,80598,80600,80603,80605,80611,80613,80619,80621,80623,80625,80631,80633,80639],{},[1761,80571,1915],{"stretchy":1821},[898,80573,8309],{},[1681,80575,80576,80578],{},[898,80577,1839],{},[898,80579,13835],{},[1824,80581,80582,80584],{},[1761,80583,1920],{"stretchy":1821},[1761,80585,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,80587,1915],{"stretchy":1821},[1681,80589,80590,80592],{},[898,80591,13835],{},[1765,80593,1767],{},[1761,80595,1920],{"stretchy":1821},[1761,80597,1909],{},[1765,80599,1767],{},[1761,80601,80602],{},"⇔",[898,80604,6889],{},[1681,80606,80607,80609],{},[898,80608,1839],{},[898,80610,13835],{},[1761,80612,1915],{"stretchy":1821},[1681,80614,80615,80617],{},[898,80616,13835],{},[1765,80618,1767],{},[1761,80620,1920],{"stretchy":1821},[1761,80622,1909],{},[898,80624,8309],{},[1681,80626,80627,80629],{},[898,80628,1839],{},[898,80630,13835],{},[1761,80632,1915],{"stretchy":1821},[1681,80634,80635,80637],{},[898,80636,13835],{},[1765,80638,1767],{},[1761,80640,1920],{"stretchy":1821},[902,80642,80643],{"encoding":904},"(AP_L)'(L_0) = 0 \\Leftrightarrow MP_L(L_0) = AP_L(L_0)",", čímž je (5.5) dokázáno.",[198,80646,80648],{"id":80647},"příklad-51","Příklad 5.1",[724,80650,80651,80652,1741],{},"Je dána produkce ",[883,80653,80655],{"className":80654},[886],[888,80656,80657],{"xmlns":890},[892,80658,80659,80683],{},[895,80660,80661,80663,80665,80667,80673,80675,80677],{},[898,80662,1828],{},[1761,80664,1909],{},[1765,80666,2340],{},[1824,80668,80669,80671],{},[898,80670,13835],{},[1765,80672,2296],{},[1761,80674,1885],{},[1765,80676,6910],{},[1824,80678,80679,80681],{},[898,80680,13835],{},[1765,80682,5486],{},[902,80684,80685],{"encoding":904},"Q = 6L^2 - 0{,}2L^3",[724,80687,80688,61500,80691,80741,80742,1741],{},[38,80689,80690],{},"(a)",[883,80692,80694],{"className":80693},[886],[888,80695,80696],{"xmlns":890},[892,80697,80698,80738],{},[895,80699,80700,80702,80704,80706,80708,80710,80712,80714,80716,80718,80720,80722,80724,80726,80728,80730,80732,80734,80736],{},[898,80701,13835],{},[1761,80703,1909],{},[1765,80705,2296],{},[1761,80707,1834],{"separator":1833},[1765,80709,6321],{},[1761,80711,1834],{"separator":1833},[1765,80713,2454],{},[1761,80715,1834],{"separator":1833},[1765,80717,2633],{},[1761,80719,1834],{"separator":1833},[1765,80721,26979],{},[1761,80723,1834],{"separator":1833},[1765,80725,7771],{},[1761,80727,1834],{"separator":1833},[1765,80729,13077],{},[1761,80731,1834],{"separator":1833},[1765,80733,42368],{},[1761,80735,1834],{"separator":1833},[1765,80737,9056],{},[902,80739,80740],{"encoding":904},"L = 2, 5, 8, 10, 14, 18, 20, 21, 25"," určíme ",[883,80743,80745],{"className":80744},[886],[888,80746,80747],{"xmlns":890},[892,80748,80749,80759],{},[895,80750,80751,80753],{},[898,80752,6889],{},[1681,80754,80755,80757],{},[898,80756,1839],{},[898,80758,13835],{},[902,80760,14083],{"encoding":904},[724,80762,80763,80764,38998],{},"Podle (5.2): ",[883,80765,80767],{"className":80766},[886],[888,80768,80769],{"xmlns":890},[892,80770,80771,80827],{},[895,80772,80773,80775,80781,80783,80789,80791,80793,80795,80797,80799,80801,80803,80805,80811,80813,80815,80817,80819,80821,80823,80825],{},[898,80774,6889],{},[1681,80776,80777,80779],{},[898,80778,1839],{},[898,80780,13835],{},[1761,80782,1909],{},[1824,80784,80785,80787],{},[898,80786,1828],{},[1761,80788,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,80790,1915],{"stretchy":1821},[898,80792,13835],{},[1761,80794,1920],{"stretchy":1821},[1761,80796,1909],{},[1765,80798,2291],{},[898,80800,13835],{},[1761,80802,1885],{},[1765,80804,23354],{},[1824,80806,80807,80809],{},[898,80808,13835],{},[1765,80810,2296],{},[1761,80812,1909],{},[898,80814,13835],{},[1761,80816,1915],{"stretchy":1821},[1765,80818,2291],{},[1761,80820,1885],{},[1765,80822,23354],{},[898,80824,13835],{},[1761,80826,1920],{"stretchy":1821},[902,80828,80829],{"encoding":904},"MP_L = Q'(L) = 12L - 0{,}6L^2 = L(12 - 0{,}6L)",[16,80831,80832,80869],{},[19,80833,80834],{},[22,80835,80836,80851,80853,80855,80857,80859,80861,80863,80865,80867],{},[25,80837,80838],{},[883,80839,80841],{"className":80840},[886],[888,80842,80843],{"xmlns":890},[892,80844,80845,80849],{},[895,80846,80847],{},[898,80848,13835],{},[902,80850,13835],{"encoding":904},[25,80852,2296],{},[25,80854,6321],{},[25,80856,2454],{},[25,80858,2633],{},[25,80860,26979],{},[25,80862,7771],{},[25,80864,13077],{},[25,80866,42368],{},[25,80868,9056],{},[30,80870,80871],{},[22,80872,80873,80894,80897,80900,80903,80905,80908,80910,80912,80931],{},[35,80874,80875],{},[883,80876,80878],{"className":80877},[886],[888,80879,80880],{"xmlns":890},[892,80881,80882,80892],{},[895,80883,80884,80886],{},[898,80885,6889],{},[1681,80887,80888,80890],{},[898,80889,1839],{},[898,80891,13835],{},[902,80893,14083],{"encoding":904},[35,80895,80896],{},"21,6",[35,80898,80899],{},"45",[35,80901,80902],{},"57,6",[35,80904,7195],{},[35,80906,80907],{},"50,4",[35,80909,80896],{},[35,80911,1767],{},[35,80913,80914],{},[883,80915,80917],{"className":80916},[886],[888,80918,80919],{"xmlns":890},[892,80920,80921,80928],{},[895,80922,80923,80925],{},[1761,80924,1885],{},[1765,80926,80927],{},"12,6",[902,80929,80930],{"encoding":904},"-12{,}6",[35,80932,80933],{},[883,80934,80936],{"className":80935},[886],[888,80937,80938],{"xmlns":890},[892,80939,80940,80946],{},[895,80941,80942,80944],{},[1761,80943,1885],{},[1765,80945,49443],{},[902,80947,80948],{"encoding":904},"-75",[724,80950,80951,80970,80971,80989,80990,81007,81008,81026,81027,81051,81052,81070],{},[883,80952,80954],{"className":80953},[886],[888,80955,80956],{"xmlns":890},[892,80957,80958,80968],{},[895,80959,80960,80962],{},[898,80961,6889],{},[1681,80963,80964,80966],{},[898,80965,1839],{},[898,80967,13835],{},[902,80969,14083],{"encoding":904}," nabývá maxima pro ",[883,80972,80974],{"className":80973},[886],[888,80975,80976],{"xmlns":890},[892,80977,80978,80986],{},[895,80979,80980,80982,80984],{},[898,80981,13835],{},[1761,80983,1909],{},[1765,80985,2633],{},[902,80987,80988],{"encoding":904},"L = 10"," (60 jednotek\u002Fprac.). Od ",[883,80991,80993],{"className":80992},[886],[888,80994,80995],{"xmlns":890},[892,80996,80997,81005],{},[895,80998,80999,81001,81003],{},[898,81000,13835],{},[1761,81002,1909],{},[1765,81004,2633],{},[902,81006,80988],{"encoding":904}," přírůstky klesají, v ",[883,81009,81011],{"className":81010},[886],[888,81012,81013],{"xmlns":890},[892,81014,81015,81023],{},[895,81016,81017,81019,81021],{},[898,81018,13835],{},[1761,81020,1909],{},[1765,81022,13077],{},[902,81024,81025],{"encoding":904},"L = 20"," produkce přestává růst (maximum ",[883,81028,81030],{"className":81029},[886],[888,81031,81032],{"xmlns":890},[892,81033,81034,81048],{},[895,81035,81036,81038,81040,81042,81044,81046],{},[898,81037,1828],{},[1761,81039,1915],{"stretchy":1821},[1765,81041,13077],{},[1761,81043,1920],{"stretchy":1821},[1761,81045,1909],{},[1765,81047,27891],{},[902,81049,81050],{"encoding":904},"Q(20) = 800","), od ",[883,81053,81055],{"className":81054},[886],[888,81056,81057],{"xmlns":890},[892,81058,81059,81067],{},[895,81060,81061,81063,81065],{},[898,81062,13835],{},[1761,81064,1763],{},[1765,81066,13077],{},[902,81068,81069],{"encoding":904},"L > 20"," produkce klesá (fyzické přeplnění pracoviště při neměnném kapitálu).",[724,81072,81073],{},[614,81074,81075,81076,81116,81117,6699,81135,1741],{},"Obrázek 5.1 — graf produkce ",[883,81077,81079],{"className":81078},[886],[888,81080,81081],{"xmlns":890},[892,81082,81083,81113],{},[895,81084,81085,81087,81089,81091,81093,81095,81097,81103,81105,81107],{},[898,81086,1828],{},[1761,81088,1915],{"stretchy":1821},[898,81090,13835],{},[1761,81092,1920],{"stretchy":1821},[1761,81094,1909],{},[1765,81096,2340],{},[1824,81098,81099,81101],{},[898,81100,13835],{},[1765,81102,2296],{},[1761,81104,1885],{},[1765,81106,6910],{},[1824,81108,81109,81111],{},[898,81110,13835],{},[1765,81112,5486],{},[902,81114,81115],{"encoding":904},"Q(L) = 6L^2 - 0{,}2L^3"," s maximem ",[883,81118,81120],{"className":81119},[886],[888,81121,81122],{"xmlns":890},[892,81123,81124,81132],{},[895,81125,81126,81128,81130],{},[898,81127,1828],{},[1761,81129,1909],{},[1765,81131,27891],{},[902,81133,81134],{"encoding":904},"Q = 800",[883,81136,81138],{"className":81137},[886],[888,81139,81140],{"xmlns":890},[892,81141,81142,81150],{},[895,81143,81144,81146,81148],{},[898,81145,13835],{},[1761,81147,1909],{},[1765,81149,13077],{},[902,81151,81025],{"encoding":904},[724,81153,81154,81157],{},[38,81155,81156],{},"(b)"," Přibližná změna produkce při růstu pracovníků z 6 na 9.",[724,81159,81160,81161,1343,81179,2506],{},"Podle (5.3) s ",[883,81162,81164],{"className":81163},[886],[888,81165,81166],{"xmlns":890},[892,81167,81168,81176],{},[895,81169,81170,81172,81174],{},[898,81171,13835],{},[1761,81173,1909],{},[1765,81175,2340],{},[902,81177,81178],{"encoding":904},"L = 6",[883,81180,81182],{"className":81181},[886],[888,81183,81184],{"xmlns":890},[892,81185,81186,81196],{},[895,81187,81188,81190,81192,81194],{},[898,81189,4346],{},[898,81191,13835],{},[1761,81193,1909],{},[1765,81195,5486],{},[902,81197,81198],{"encoding":904},"dL = 3",[883,81200,81202],{"className":81201},[886],[888,81203,81204],{"xmlns":890,"display":1930},[892,81205,81206,81269],{},[895,81207,81208,81210,81212,81214,81216,81222,81224,81226,81228,81230,81232,81234,81236,81238,81240,81242,81244,81246,81248,81250,81252,81254,81256,81258,81260,81262,81264,81266],{},[898,81209,4346],{},[898,81211,1828],{},[1761,81213,1909],{},[898,81215,6889],{},[1681,81217,81218,81220],{},[898,81219,1839],{},[898,81221,13835],{},[1761,81223,1915],{"stretchy":1821},[1765,81225,2340],{},[1761,81227,1920],{"stretchy":1821},[1761,81229,2447],{},[1765,81231,5486],{},[1761,81233,1909],{},[1761,81235,1915],{"stretchy":1821},[1765,81237,2291],{},[1761,81239,2447],{},[1765,81241,2340],{},[1761,81243,1885],{},[1765,81245,23354],{},[1761,81247,2447],{},[1765,81249,9616],{},[1761,81251,1920],{"stretchy":1821},[1761,81253,2447],{},[1765,81255,5486],{},[1761,81257,1909],{},[1765,81259,80907],{},[1761,81261,2447],{},[1765,81263,5486],{},[1761,81265,1909],{},[1765,81267,81268],{},"151,2.",[902,81270,81271],{"encoding":904},"dQ = MP_L(6)\\cdot 3 = (12\\cdot 6 - 0{,}6\\cdot 36)\\cdot 3 = 50{,}4 \\cdot 3 = 151{,}2.",[724,81273,81274,81275,61730,81300,81314,81315,1741],{},"Produkce vzroste z ",[883,81276,81278],{"className":81277},[886],[888,81279,81280],{"xmlns":890},[892,81281,81282,81297],{},[895,81283,81284,81286,81288,81290,81292,81294],{},[898,81285,1828],{},[1761,81287,1915],{"stretchy":1821},[1765,81289,2340],{},[1761,81291,1920],{"stretchy":1821},[1761,81293,1909],{},[1765,81295,81296],{},"172,8",[902,81298,81299],{"encoding":904},"Q(6) = 172{,}8",[883,81301,81303],{"className":81302},[886],[888,81304,81305],{"xmlns":890},[892,81306,81307,81312],{},[895,81308,81309],{},[1765,81310,81311],{},"324",[902,81313,81311],{"encoding":904},". Skutečná hodnota: ",[883,81316,81318],{"className":81317},[886],[888,81319,81320],{"xmlns":890},[892,81321,81322,81362],{},[895,81323,81324,81326,81328,81330,81332,81334,81336,81338,81340,81342,81344,81346,81348,81350,81353,81355,81357,81359],{},[898,81325,6959],{"mathvariant":1969},[898,81327,1828],{},[1761,81329,1909],{},[898,81331,1828],{},[1761,81333,1915],{"stretchy":1821},[1765,81335,8056],{},[1761,81337,1920],{"stretchy":1821},[1761,81339,1885],{},[898,81341,1828],{},[1761,81343,1915],{"stretchy":1821},[1765,81345,2340],{},[1761,81347,1920],{"stretchy":1821},[1761,81349,1909],{},[1765,81351,81352],{},"340,2",[1761,81354,1885],{},[1765,81356,81296],{},[1761,81358,1909],{},[1765,81360,81361],{},"167,4",[902,81363,81364],{"encoding":904},"\\Delta Q = Q(9) - Q(6) = 340{,}2 - 172{,}8 = 167{,}4",[198,81366,81368],{"id":81367},"příklad-52","Příklad 5.2",[724,81370,81371,81372,1741],{},"Ověříme princip (5.5) pro ",[883,81373,81375],{"className":81374},[886],[888,81376,81377],{"xmlns":890},[892,81378,81379,81403],{},[895,81380,81381,81383,81385,81387,81393,81395,81397],{},[898,81382,1828],{},[1761,81384,1909],{},[1765,81386,2340],{},[1824,81388,81389,81391],{},[898,81390,13835],{},[1765,81392,2296],{},[1761,81394,1885],{},[1765,81396,6910],{},[1824,81398,81399,81401],{},[898,81400,13835],{},[1765,81402,5486],{},[902,81404,80685],{"encoding":904},[883,81406,81408],{"className":81407},[886],[888,81409,81410],{"xmlns":890,"display":1930},[892,81411,81412,81490],{},[895,81413,81414,81416,81422,81424,81430,81432,81434,81436,81438,81440,81446,81448,81450,81452,81460,81462,81464,81466,81468,81470,81472,81474,81476,81478,81480,81486,81488],{},[898,81415,8309],{},[1681,81417,81418,81420],{},[898,81419,1839],{},[898,81421,13835],{},[1761,81423,1909],{},[4379,81425,81426,81428],{},[898,81427,1828],{},[898,81429,13835],{},[1761,81431,1909],{},[1765,81433,2340],{},[898,81435,13835],{},[1761,81437,1885],{},[1765,81439,6910],{},[1824,81441,81442,81444],{},[898,81443,13835],{},[1765,81445,2296],{},[1761,81447,1834],{"separator":1833},[3315,81449],{"width":19322},[898,81451,8309],{},[2015,81453,81454,81456,81458],{},[898,81455,1839],{},[898,81457,13835],{},[1761,81459,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,81461,1909],{},[1765,81463,2340],{},[1761,81465,1885],{},[1765,81467,23304],{},[898,81469,13835],{},[1761,81471,1909],{},[1765,81473,1767],{},[2761,81475,8041],{},[1761,81477,8044],{},[2761,81479,8041],{},[1681,81481,81482,81484],{},[898,81483,13835],{},[1765,81485,1767],{},[1761,81487,1909],{},[1765,81489,72261],{},[902,81491,81492],{"encoding":904},"AP_L = \\frac{Q}{L} = 6L - 0{,}2L^2, \\quad AP_L' = 6 - 0{,}4L = 0 \\;\\Rightarrow\\; L_0 = 15.",[724,81494,81495,81531,81532,81550,81551,1741],{},[883,81496,81498],{"className":81497},[886],[888,81499,81500],{"xmlns":890},[892,81501,81502,81528],{},[895,81503,81504,81506,81518,81520,81522,81524,81526],{},[898,81505,8309],{},[2015,81507,81508,81510,81512],{},[898,81509,1839],{},[898,81511,13835],{},[895,81513,81514,81516],{},[1761,81515,6459],{"mathvariant":1969},[1761,81517,6459],{"mathvariant":1969},[1761,81519,1909],{},[1761,81521,1885],{},[1765,81523,23304],{},[1761,81525,2058],{},[1765,81527,1767],{},[902,81529,81530],{"encoding":904},"AP_L'' = -0{,}4 \u003C 0",", takže v ",[883,81533,81535],{"className":81534},[886],[888,81536,81537],{"xmlns":890},[892,81538,81539,81547],{},[895,81540,81541,81543,81545],{},[898,81542,13835],{},[1761,81544,1909],{},[1765,81546,5433],{},[902,81548,81549],{"encoding":904},"L = 15"," je maximum, ",[883,81552,81554],{"className":81553},[886],[888,81555,81556],{"xmlns":890},[892,81557,81558,81604],{},[895,81559,81560,81562,81568,81570,81572,81574,81576,81578,81580,81582,81584,81586,81588,81591,81593,81596,81598,81600,81602],{},[898,81561,8309],{},[1681,81563,81564,81566],{},[898,81565,1839],{},[898,81567,13835],{},[1761,81569,1915],{"stretchy":1821},[1765,81571,5433],{},[1761,81573,1920],{"stretchy":1821},[1761,81575,1909],{},[1765,81577,2340],{},[1761,81579,2447],{},[1765,81581,5433],{},[1761,81583,1885],{},[1765,81585,6910],{},[1761,81587,2447],{},[1765,81589,81590],{},"225",[1761,81592,1909],{},[1765,81594,81595],{},"90",[1761,81597,1885],{},[1765,81599,80899],{},[1761,81601,1909],{},[1765,81603,80899],{},[902,81605,81606],{"encoding":904},"AP_L(15) = 6\\cdot 15 - 0{,}2\\cdot 225 = 90 - 45 = 45",[724,81608,81609,45889,81665,81711],{},[883,81610,81612],{"className":81611},[886],[888,81613,81614],{"xmlns":890},[892,81615,81616,81662],{},[895,81617,81618,81620,81626,81628,81630,81632,81634,81636,81638,81640,81642,81644,81646,81648,81650,81653,81655,81658,81660],{},[898,81619,6889],{},[1681,81621,81622,81624],{},[898,81623,1839],{},[898,81625,13835],{},[1761,81627,1915],{"stretchy":1821},[1765,81629,5433],{},[1761,81631,1920],{"stretchy":1821},[1761,81633,1909],{},[1765,81635,2291],{},[1761,81637,2447],{},[1765,81639,5433],{},[1761,81641,1885],{},[1765,81643,23354],{},[1761,81645,2447],{},[1765,81647,81590],{},[1761,81649,1909],{},[1765,81651,81652],{},"180",[1761,81654,1885],{},[1765,81656,81657],{},"135",[1761,81659,1909],{},[1765,81661,80899],{},[902,81663,81664],{"encoding":904},"MP_L(15) = 12\\cdot 15 - 0{,}6\\cdot 225 = 180 - 135 = 45",[883,81666,81668],{"className":81667},[886],[888,81669,81670],{"xmlns":890},[892,81671,81672,81708],{},[895,81673,81674,81676,81682,81684,81686,81688,81690,81692,81698,81700,81702,81704,81706],{},[898,81675,6889],{},[1681,81677,81678,81680],{},[898,81679,1839],{},[898,81681,13835],{},[1761,81683,1915],{"stretchy":1821},[1765,81685,5433],{},[1761,81687,1920],{"stretchy":1821},[1761,81689,1909],{},[898,81691,8309],{},[1681,81693,81694,81696],{},[898,81695,1839],{},[898,81697,13835],{},[1761,81699,1915],{"stretchy":1821},[1765,81701,5433],{},[1761,81703,1920],{"stretchy":1821},[1761,81705,1909],{},[1765,81707,80899],{},[902,81709,81710],{"encoding":904},"MP_L(15) = AP_L(15) = 45",", jak požaduje (5.5).",[724,81713,81714,81717,81718,21610,81747,1741],{},[38,81715,81716],{},"Zkratka bez hledání extrému:"," stačí řešit ",[883,81719,81721],{"className":81720},[886],[888,81722,81723],{"xmlns":890},[892,81724,81725,81745],{},[895,81726,81727,81729,81735,81737,81739],{},[898,81728,6889],{},[1681,81730,81731,81733],{},[898,81732,1839],{},[898,81734,13835],{},[1761,81736,1909],{},[898,81738,8309],{},[1681,81740,81741,81743],{},[898,81742,1839],{},[898,81744,13835],{},[902,81746,78641],{"encoding":904},[883,81748,81750],{"className":81749},[886],[888,81751,81752],{"xmlns":890},[892,81753,81754,81794],{},[895,81755,81756,81758,81760,81762,81764,81770,81772,81774,81776,81778,81780,81786,81788,81790,81792],{},[1765,81757,2291],{},[898,81759,13835],{},[1761,81761,1885],{},[1765,81763,23354],{},[1824,81765,81766,81768],{},[898,81767,13835],{},[1765,81769,2296],{},[1761,81771,1909],{},[1765,81773,2340],{},[898,81775,13835],{},[1761,81777,1885],{},[1765,81779,6910],{},[1824,81781,81782,81784],{},[898,81783,13835],{},[1765,81785,2296],{},[1761,81787,8044],{},[898,81789,13835],{},[1761,81791,1909],{},[1765,81793,5433],{},[902,81795,81796],{"encoding":904},"12L - 0{,}6L^2 = 6L - 0{,}2L^2 \\Rightarrow L = 15",[724,81798,81799],{},[614,81800,81801,81802,81821,81822,4590,81840,81859,81860,81878,81879,81896,81897,81916,81917,81936],{},"Obrázek 5.3 — křivky ",[883,81803,81805],{"className":81804},[886],[888,81806,81807],{"xmlns":890},[892,81808,81809,81819],{},[895,81810,81811,81813],{},[898,81812,6889],{},[1681,81814,81815,81817],{},[898,81816,1839],{},[898,81818,13835],{},[902,81820,14083],{"encoding":904}," (max 60 při ",[883,81823,81825],{"className":81824},[886],[888,81826,81827],{"xmlns":890},[892,81828,81829,81837],{},[895,81830,81831,81833,81835],{},[898,81832,13835],{},[1761,81834,1909],{},[1765,81836,2633],{},[902,81838,81839],{"encoding":904},"L=10",[883,81841,81843],{"className":81842},[886],[888,81844,81845],{"xmlns":890},[892,81846,81847,81857],{},[895,81848,81849,81851],{},[898,81850,8309],{},[1681,81852,81853,81855],{},[898,81854,1839],{},[898,81856,13835],{},[902,81858,78611],{"encoding":904}," (max 45 při ",[883,81861,81863],{"className":81862},[886],[888,81864,81865],{"xmlns":890},[892,81866,81867,81875],{},[895,81868,81869,81871,81873],{},[898,81870,13835],{},[1761,81872,1909],{},[1765,81874,5433],{},[902,81876,81877],{"encoding":904},"L=15","), průsečík v ",[883,81880,81882],{"className":81881},[886],[888,81883,81884],{"xmlns":890},[892,81885,81886,81894],{},[895,81887,81888,81890,81892],{},[898,81889,13835],{},[1761,81891,1909],{},[1765,81893,5433],{},[902,81895,81549],{"encoding":904},". Nalevo od 15 leží ",[883,81898,81900],{"className":81899},[886],[888,81901,81902],{"xmlns":890},[892,81903,81904,81914],{},[895,81905,81906,81908],{},[898,81907,6889],{},[1681,81909,81910,81912],{},[898,81911,1839],{},[898,81913,13835],{},[902,81915,14083],{"encoding":904}," nad ",[883,81918,81920],{"className":81919},[886],[888,81921,81922],{"xmlns":890},[892,81923,81924,81934],{},[895,81925,81926,81928],{},[898,81927,8309],{},[1681,81929,81930,81932],{},[898,81931,1839],{},[898,81933,13835],{},[902,81935,78611],{"encoding":904},", napravo pod ní.",[115,81938,81940],{"id":81939},"dvoufaktorový-model-produkce","Dvoufaktorový model produkce",[724,81942,81943,81944,4178,81957,1989,81960,10235,81973,1989,81976,2506],{},"V dvoufaktorovém modelu závisí produkce ",[883,81945,81947],{"className":81946},[886],[888,81948,81949],{"xmlns":890},[892,81950,81951,81955],{},[895,81952,81953],{},[898,81954,1828],{},[902,81956,1828],{"encoding":904},[38,81958,81959],{},"práci",[883,81961,81963],{"className":81962},[886],[888,81964,81965],{"xmlns":890},[892,81966,81967,81971],{},[895,81968,81969],{},[898,81970,13835],{},[902,81972,13835],{"encoding":904},[38,81974,81975],{},"kapitálu",[883,81977,81979],{"className":81978},[886],[888,81980,81981],{"xmlns":890},[892,81982,81983,81987],{},[895,81984,81985],{},[898,81986,2768],{},[902,81988,2768],{"encoding":904},[883,81990,81992],{"className":81991},[886],[888,81993,81994],{"xmlns":890,"display":1930},[892,81995,81996,82031],{},[24787,81997,81998],{"width":32101},[24792,81999,82000,82002,82024,82026],{},[24795,82001],{"width":32106},[24795,82003,82004],{},[895,82005,82006,82008,82010,82012,82014,82016,82018,82020,82022],{},[898,82007,1828],{},[1761,82009,1909],{},[898,82011,1828],{},[1761,82013,1915],{"stretchy":1821},[898,82015,13835],{},[1761,82017,1834],{"separator":1833},[898,82019,2768],{},[1761,82021,1920],{"stretchy":1821},[898,82023,1741],{"mathvariant":1969},[24795,82025],{"width":32106},[24795,82027,82028],{},[2761,82029,82030],{},"(5.6)",[902,82032,82033],{"encoding":904},"Q = Q(L, K). \\tag{5.6}",[724,82035,82036,82037,82039],{},"Půda je nadále standardní exogenní proměnnou. Vztah (5.6) se nazývá ",[38,82038,78978],{}," (v širším smyslu oproti jednofaktorovému modelu).",[115,82041,82043],{"id":82042},"cobb-douglasova-produkční-funkce","Cobb-Douglasova produkční funkce",[724,82045,82046],{},"Široce používané produkční funkce mají tvar",[883,82048,82050],{"className":82049},[886],[888,82051,82052],{"xmlns":890,"display":1930},[892,82053,82054,82095],{},[24787,82055,82056],{"width":32101},[24792,82057,82058,82060,82088,82090],{},[24795,82059],{"width":32106},[24795,82061,82062],{},[895,82063,82064,82066,82068,82070,82072,82078,82080,82086],{},[898,82065,1828],{},[1761,82067,1909],{},[898,82069,8309],{},[2761,82071,7057],{},[1824,82073,82074,82076],{},[898,82075,13835],{},[898,82077,207],{},[2761,82079,7057],{},[1824,82081,82082,82084],{},[898,82083,2768],{},[898,82085,4302],{},[1761,82087,1834],{"separator":1833},[24795,82089],{"width":32106},[24795,82091,82092],{},[2761,82093,82094],{},"(5.7)",[902,82096,82097],{"encoding":904},"Q = A\\,L^a\\,K^b, \\tag{5.7}",[724,82099,8364,82100,82122,82123,82125,82126,1741],{},[883,82101,82103],{"className":82102},[886],[888,82104,82105],{"xmlns":890},[892,82106,82107,82119],{},[895,82108,82109,82111,82113,82115,82117],{},[898,82110,8309],{},[1761,82112,1834],{"separator":1833},[898,82114,207],{},[1761,82116,1834],{"separator":1833},[898,82118,4302],{},[902,82120,82121],{"encoding":904},"A, a, b"," jsou kladné konstanty. Nazývají se ",[38,82124,78677],{}," (poprvé publikovány v roce 1939). V ekonomických analýzách zpravidla ",[883,82127,82129],{"className":82128},[886],[888,82130,82131],{"xmlns":890},[892,82132,82133,82145],{},[895,82134,82135,82137,82139,82141,82143],{},[898,82136,207],{},[1761,82138,1834],{"separator":1833},[898,82140,4302],{},[1761,82142,2058],{},[1765,82144,1945],{},[902,82146,82147],{"encoding":904},"a, b \u003C 1",[724,82149,82150],{},[3991,82151],{"alt":82152,"className":82153,"src":82154},"imek-vynosy-z-rozsahu-3typy",[210,3995],"\u002Fwiki-assets\u002Fimek-vynosy-z-rozsahu-3typy.jpeg",[724,82156,82157,82158,82161,82162,4178,82175,82191,82192,4178,82205,2506],{},"Reflektují ekonomickou zákonitost, že ",[38,82159,82160],{},"proporcionální změny vstupů mají odezvu v proporcionální změně výstupu",". Změní-li se práce z ",[883,82163,82165],{"className":82164},[886],[888,82166,82167],{"xmlns":890},[892,82168,82169,82173],{},[895,82170,82171],{},[898,82172,13835],{},[902,82174,13835],{"encoding":904},[883,82176,82178],{"className":82177},[886],[888,82179,82180],{"xmlns":890},[892,82181,82182,82188],{},[895,82183,82184,82186],{},[898,82185,1719],{},[898,82187,13835],{},[902,82189,82190],{"encoding":904},"rL"," a kapitál z ",[883,82193,82195],{"className":82194},[886],[888,82196,82197],{"xmlns":890},[892,82198,82199,82203],{},[895,82200,82201],{},[898,82202,2768],{},[902,82204,2768],{"encoding":904},[883,82206,82208],{"className":82207},[886],[888,82209,82210],{"xmlns":890},[892,82211,82212,82218],{},[895,82213,82214,82216],{},[898,82215,1719],{},[898,82217,2768],{},[902,82219,82220],{"encoding":904},"rK",[883,82222,82224],{"className":82223},[886],[888,82225,82226],{"xmlns":890,"display":1930},[892,82227,82228,82351],{},[24787,82229,82230],{"width":32101},[24792,82231,82232,82234,82344,82346],{},[24795,82233],{"width":32106},[24795,82235,82236],{},[895,82237,82238,82240,82242,82244,82246,82248,82250,82252,82254,82256,82258,82260,82262,82264,82270,82272,82274,82276,82282,82284,82286,82288,82300,82302,82308,82314,82316,82328,82330,82332,82334,82336,82338,82340,82342],{},[898,82239,1828],{},[1761,82241,1915],{"stretchy":1821},[898,82243,1719],{},[898,82245,13835],{},[1761,82247,1834],{"separator":1833},[898,82249,1719],{},[898,82251,2768],{},[1761,82253,1920],{"stretchy":1821},[1761,82255,1909],{},[898,82257,8309],{},[1761,82259,1915],{"stretchy":1821},[898,82261,1719],{},[898,82263,13835],{},[1824,82265,82266,82268],{},[1761,82267,1920],{"stretchy":1821},[898,82269,207],{},[1761,82271,1915],{"stretchy":1821},[898,82273,1719],{},[898,82275,2768],{},[1824,82277,82278,82280],{},[1761,82279,1920],{"stretchy":1821},[898,82281,4302],{},[1761,82283,1909],{},[898,82285,8309],{},[2761,82287,7057],{},[1824,82289,82290,82292],{},[898,82291,1719],{},[895,82293,82294,82296,82298],{},[898,82295,207],{},[1761,82297,1964],{},[898,82299,4302],{},[2761,82301,7057],{},[1824,82303,82304,82306],{},[898,82305,13835],{},[898,82307,207],{},[1824,82309,82310,82312],{},[898,82311,2768],{},[898,82313,4302],{},[1761,82315,1909],{},[1824,82317,82318,82320],{},[898,82319,1719],{},[895,82321,82322,82324,82326],{},[898,82323,207],{},[1761,82325,1964],{},[898,82327,4302],{},[2761,82329,7057],{},[898,82331,1828],{},[1761,82333,1915],{"stretchy":1821},[898,82335,13835],{},[1761,82337,1834],{"separator":1833},[898,82339,2768],{},[1761,82341,1920],{"stretchy":1821},[898,82343,1741],{"mathvariant":1969},[24795,82345],{"width":32106},[24795,82347,82348],{},[2761,82349,82350],{},"(5.8)",[902,82352,82353],{"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}",[724,82355,82356,82357],{},"Volně: ",[38,82358,82359,82360,82373,82374,82398],{},"změní-li se vstupy ",[883,82361,82363],{"className":82362},[886],[888,82364,82365],{"xmlns":890},[892,82366,82367,82371],{},[895,82368,82369],{},[898,82370,1719],{},[902,82372,1719],{"encoding":904},"-krát, změní se výstup ",[883,82375,82377],{"className":82376},[886],[888,82378,82379],{"xmlns":890},[892,82380,82381,82395],{},[895,82382,82383],{},[1824,82384,82385,82387],{},[898,82386,1719],{},[895,82388,82389,82391,82393],{},[898,82390,207],{},[1761,82392,1964],{},[898,82394,4302],{},[902,82396,82397],{"encoding":904},"r^{a+b}","-krát.",[198,82400,82402],{"id":82401},"výnosy-z-rozsahu","Výnosy z rozsahu",[724,82404,82405,82406,82423],{},"Součet exponentů ",[883,82407,82409],{"className":82408},[886],[888,82410,82411],{"xmlns":890},[892,82412,82413,82421],{},[895,82414,82415,82417,82419],{},[898,82416,207],{},[1761,82418,1964],{},[898,82420,4302],{},[902,82422,78802],{"encoding":904}," určuje typ výnosů z rozsahu:",[16,82425,82426,82455],{},[19,82427,82428],{},[22,82429,82430,82433,82436,82453],{},[25,82431,82432],{},"Typ",[25,82434,82435],{},"Podmínka",[25,82437,82438,82439,82452],{},"Chování produkce při ",[883,82440,82442],{"className":82441},[886],[888,82443,82444],{"xmlns":890},[892,82445,82446,82450],{},[895,82447,82448],{},[898,82449,1719],{},[902,82451,1719],{"encoding":904},"-násobném zvýšení vstupů",[25,82454,7140],{},[30,82456,82457,82568,82683],{},[22,82458,82459,82467,82491,82524],{},[35,82460,79515,82461,3927,82464,1920],{},[38,82462,82463],{},"Konstantní",[614,82465,82466],{},"constant returns",[35,82468,82469],{},[883,82470,82472],{"className":82471},[886],[888,82473,82474],{"xmlns":890},[892,82475,82476,82488],{},[895,82477,82478,82480,82482,82484,82486],{},[898,82479,207],{},[1761,82481,1964],{},[898,82483,4302],{},[1761,82485,1909],{},[1765,82487,1945],{},[902,82489,82490],{"encoding":904},"a+b = 1",[35,82492,82493,82506,82507,1989,82510,82523],{},[883,82494,82496],{"className":82495},[886],[888,82497,82498],{"xmlns":890},[892,82499,82500,82504],{},[895,82501,82502],{},[898,82503,1828],{},[902,82505,1828],{"encoding":904}," vzroste ",[38,82508,82509],{},"přesně",[883,82511,82513],{"className":82512},[886],[888,82514,82515],{"xmlns":890},[892,82516,82517,82521],{},[895,82518,82519],{},[898,82520,1719],{},[902,82522,1719],{"encoding":904},"-krát",[35,82525,82526],{},[883,82527,82529],{"className":82528},[886],[888,82530,82531],{"xmlns":890},[892,82532,82533,82565],{},[895,82534,82535,82537,82539,82541,82553],{},[898,82536,1828],{},[1761,82538,1909],{},[1765,82540,2296],{},[1824,82542,82543,82545],{},[898,82544,13835],{},[895,82546,82547,82549,82551],{},[1765,82548,1945],{},[898,82550,8726],{"mathvariant":1969},[1765,82552,2318],{},[1824,82554,82555,82557],{},[898,82556,2768],{},[895,82558,82559,82561,82563],{},[1765,82560,5486],{},[898,82562,8726],{"mathvariant":1969},[1765,82564,2318],{},[902,82566,82567],{"encoding":904},"Q = 2L^{1\u002F4}K^{3\u002F4}",[22,82569,82570,82579,82603,82633],{},[35,82571,82572,82573,3927,82576,1920],{},"2° ",[38,82574,82575],{},"Rostoucí",[614,82577,82578],{},"increasing returns",[35,82580,82581],{},[883,82582,82584],{"className":82583},[886],[888,82585,82586],{"xmlns":890},[892,82587,82588,82600],{},[895,82589,82590,82592,82594,82596,82598],{},[898,82591,207],{},[1761,82593,1964],{},[898,82595,4302],{},[1761,82597,1763],{},[1765,82599,1945],{},[902,82601,82602],{"encoding":904},"a+b > 1",[35,82604,82605,82506,82618,55211,82620,82523],{},[883,82606,82608],{"className":82607},[886],[888,82609,82610],{"xmlns":890},[892,82611,82612,82616],{},[895,82613,82614],{},[898,82615,1828],{},[902,82617,1828],{"encoding":904},[38,82619,29301],{},[883,82621,82623],{"className":82622},[886],[888,82624,82625],{"xmlns":890},[892,82626,82627,82631],{},[895,82628,82629],{},[898,82630,1719],{},[902,82632,1719],{"encoding":904},[35,82634,82635,3927,82661,1920],{},[883,82636,82638],{"className":82637},[886],[888,82639,82640],{"xmlns":890},[892,82641,82642,82658],{},[895,82643,82644,82646,82648,82650,82652],{},[898,82645,1828],{},[1761,82647,1909],{},[1765,82649,5512],{},[898,82651,13835],{},[1824,82653,82654,82656],{},[898,82655,2768],{},[1765,82657,2296],{},[902,82659,82660],{"encoding":904},"Q = 7LK^2",[883,82662,82664],{"className":82663},[886],[888,82665,82666],{"xmlns":890},[892,82667,82668,82680],{},[895,82669,82670,82672,82674,82676,82678],{},[898,82671,207],{},[1761,82673,1964],{},[898,82675,4302],{},[1761,82677,1909],{},[1765,82679,5486],{},[902,82681,82682],{"encoding":904},"a+b = 3",[22,82684,82685,82694,82718,82749],{},[35,82686,82687,82688,3927,82691,1920],{},"3° ",[38,82689,82690],{},"Klesající",[614,82692,82693],{},"decreasing returns",[35,82695,82696],{},[883,82697,82699],{"className":82698},[886],[888,82700,82701],{"xmlns":890},[892,82702,82703,82715],{},[895,82704,82705,82707,82709,82711,82713],{},[898,82706,207],{},[1761,82708,1964],{},[898,82710,4302],{},[1761,82712,2058],{},[1765,82714,1945],{},[902,82716,82717],{"encoding":904},"a+b \u003C 1",[35,82719,82720,82506,82733,55211,82736,82523],{},[883,82721,82723],{"className":82722},[886],[888,82724,82725],{"xmlns":890},[892,82726,82727,82731],{},[895,82728,82729],{},[898,82730,1828],{},[902,82732,1828],{"encoding":904},[38,82734,82735],{},"méně",[883,82737,82739],{"className":82738},[886],[888,82740,82741],{"xmlns":890},[892,82742,82743,82747],{},[895,82744,82745],{},[898,82746,1719],{},[902,82748,1719],{"encoding":904},[35,82750,82751,3927,82781,1920],{},[883,82752,82754],{"className":82753},[886],[888,82755,82756],{"xmlns":890},[892,82757,82758,82778],{},[895,82759,82760,82762,82764,82766,82772],{},[898,82761,1828],{},[1761,82763,1909],{},[1765,82765,2633],{},[1824,82767,82768,82770],{},[898,82769,13835],{},[1765,82771,72189],{},[1824,82773,82774,82776],{},[898,82775,2768],{},[1765,82777,5426],{},[902,82779,82780],{"encoding":904},"Q = 10L^{0{,}3}K^{0{,}5}",[883,82782,82784],{"className":82783},[886],[888,82785,82786],{"xmlns":890},[892,82787,82788,82800],{},[895,82789,82790,82792,82794,82796,82798],{},[898,82791,207],{},[1761,82793,1964],{},[898,82795,4302],{},[1761,82797,1909],{},[1765,82799,18627],{},[902,82801,82802],{"encoding":904},"a+b = 0{,}8",[1636,82804,82805],{},[724,82806,82807,82809,82810,82827,82828,82831,82832,1989,82835,82871,82872,82894,82895,1741],{},[883,82808,4723],{}," Pozor\nSoučet ",[883,82811,82813],{"className":82812},[886],[888,82814,82815],{"xmlns":890},[892,82816,82817,82825],{},[895,82818,82819,82821,82823],{},[898,82820,207],{},[1761,82822,1964],{},[898,82824,4302],{},[902,82826,78802],{"encoding":904}," neudává velikost produkce, ale ",[38,82829,82830],{},"elasticitu vůči škálování vstupů",". Speciálně ",[38,82833,82834],{},"ryzí Cobb-Douglas",[883,82836,82838],{"className":82837},[886],[888,82839,82840],{"xmlns":890},[892,82841,82842,82868],{},[895,82843,82844,82846,82848,82850,82856],{},[898,82845,1828],{},[1761,82847,1909],{},[898,82849,8309],{},[1824,82851,82852,82854],{},[898,82853,13835],{},[898,82855,207],{},[1824,82857,82858,82860],{},[898,82859,2768],{},[895,82861,82862,82864,82866],{},[1765,82863,1945],{},[1761,82865,1885],{},[898,82867,207],{},[902,82869,82870],{"encoding":904},"Q = AL^a K^{1-a}"," má ",[883,82873,82875],{"className":82874},[886],[888,82876,82877],{"xmlns":890},[892,82878,82879,82891],{},[895,82880,82881,82883,82885,82887,82889],{},[898,82882,4302],{},[1761,82884,1909],{},[1765,82886,1945],{},[1761,82888,1885],{},[898,82890,207],{},[902,82892,82893],{"encoding":904},"b = 1-a",", tedy vždy ",[38,82896,82897],{},"konstantní výnosy z rozsahu",[198,82899,82901,82902],{"id":82900},"parametr-efektivity-aa","Parametr efektivity ",[883,82903,82905],{"className":82904},[886],[888,82906,82907],{"xmlns":890},[892,82908,82909,82913],{},[895,82910,82911],{},[898,82912,8309],{},[902,82914,8309],{"encoding":904},[724,82916,82917,82918,82931,82932,82945,82946,82964,82965,82968],{},"Konstanta ",[883,82919,82921],{"className":82920},[886],[888,82922,82923],{"xmlns":890},[892,82924,82925,82929],{},[895,82926,82927],{},[898,82928,8309],{},[902,82930,8309],{"encoding":904}," v (5.7) proporcionálně ovlivňuje úroveň produkce ",[883,82933,82935],{"className":82934},[886],[888,82936,82937],{"xmlns":890},[892,82938,82939,82943],{},[895,82940,82941],{},[898,82942,1828],{},[902,82944,1828],{"encoding":904}," při pevně zadaných ",[883,82947,82949],{"className":82948},[886],[888,82950,82951],{"xmlns":890},[892,82952,82953,82961],{},[895,82954,82955,82957,82959],{},[898,82956,13835],{},[1761,82958,1834],{"separator":1833},[898,82960,2768],{},[902,82962,82963],{"encoding":904},"L, K",", a lze ji proto chápat jako ",[38,82966,82967],{},"parametr efektivity"," — indikátor stavu technologie.",[198,82970,82972],{"id":82971},"příklad-53","Příklad 5.3",[724,82974,82975,82976,82871,83018,83020,83021,1741],{},"Produkční funkce ",[883,82977,82979],{"className":82978},[886],[888,82980,82981],{"xmlns":890},[892,82982,82983,83015],{},[895,82984,82985,82987,82989,82991,83003],{},[898,82986,1828],{},[1761,82988,1909],{},[1765,82990,2296],{},[1824,82992,82993,82995],{},[898,82994,13835],{},[895,82996,82997,82999,83001],{},[1765,82998,1945],{},[898,83000,8726],{"mathvariant":1969},[1765,83002,2318],{},[1824,83004,83005,83007],{},[898,83006,2768],{},[895,83008,83009,83011,83013],{},[1765,83010,5486],{},[898,83012,8726],{"mathvariant":1969},[1765,83014,2318],{},[902,83016,83017],{"encoding":904},"Q = 2L^{1\u002F4} K^{3\u002F4}",[38,83019,28645],{}," výnosy z rozsahu, neboť ",[883,83022,83024],{"className":83023},[886],[888,83025,83026],{"xmlns":890},[892,83027,83028,83052],{},[895,83029,83030,83038,83040,83048,83050],{},[6411,83031,83032],{"scriptlevel":1767,"displaystyle":1821},[4379,83033,83034,83036],{},[1765,83035,1945],{},[1765,83037,2318],{},[1761,83039,1964],{},[6411,83041,83042],{"scriptlevel":1767,"displaystyle":1821},[4379,83043,83044,83046],{},[1765,83045,5486],{},[1765,83047,2318],{},[1761,83049,1909],{},[1765,83051,1945],{},[902,83053,83054],{"encoding":904},"\\tfrac{1}{4} + \\tfrac{3}{4} = 1",[724,83056,83057,83058,10235,83071,83084,83085,1989,83098,83138],{},"Změní-li se ",[883,83059,83061],{"className":83060},[886],[888,83062,83063],{"xmlns":890},[892,83064,83065,83069],{},[895,83066,83067],{},[898,83068,13835],{},[902,83070,13835],{"encoding":904},[883,83072,83074],{"className":83073},[886],[888,83075,83076],{"xmlns":890},[892,83077,83078,83082],{},[895,83079,83080],{},[898,83081,2768],{},[902,83083,2768],{"encoding":904}," čtyřnásobně, změní se ",[883,83086,83088],{"className":83087},[886],[888,83089,83090],{"xmlns":890},[892,83091,83092,83096],{},[895,83093,83094],{},[898,83095,1828],{},[902,83097,1828],{"encoding":904},[883,83099,83101],{"className":83100},[886],[888,83102,83103],{"xmlns":890},[892,83104,83105,83135],{},[895,83106,83107,83127,83129],{},[1824,83108,83109,83111],{},[1765,83110,2318],{},[895,83112,83113,83115,83117,83119,83121,83123,83125],{},[1765,83114,1945],{},[898,83116,8726],{"mathvariant":1969},[1765,83118,2318],{},[1761,83120,1964],{},[1765,83122,5486],{},[898,83124,8726],{"mathvariant":1969},[1765,83126,2318],{},[1761,83128,1909],{},[1824,83130,83131,83133],{},[1765,83132,2318],{},[1765,83134,1945],{},[902,83136,83137],{"encoding":904},"4^{1\u002F4 + 3\u002F4} = 4^1","-krát:",[883,83140,83142],{"className":83141},[886],[888,83143,83144],{"xmlns":890,"display":1930},[892,83145,83146,83306],{},[895,83147,83148,83150,83152,83154,83156,83158,83160,83162,83164,83166,83168,83170,83172,83174,83186,83188,83190,83192,83204,83206,83208,83210,83230,83242,83254,83256,83258,83260,83262,83274,83286,83288,83290,83292,83294,83296,83298,83300,83302,83304],{},[898,83149,1828],{},[1761,83151,1915],{"stretchy":1821},[1765,83153,2318],{},[898,83155,13835],{},[1761,83157,1834],{"separator":1833},[1765,83159,2318],{},[898,83161,2768],{},[1761,83163,1920],{"stretchy":1821},[1761,83165,1909],{},[1765,83167,2296],{},[1761,83169,1915],{"stretchy":1821},[1765,83171,2318],{},[898,83173,13835],{},[1824,83175,83176,83178],{},[1761,83177,1920],{"stretchy":1821},[895,83179,83180,83182,83184],{},[1765,83181,1945],{},[898,83183,8726],{"mathvariant":1969},[1765,83185,2318],{},[1761,83187,1915],{"stretchy":1821},[1765,83189,2318],{},[898,83191,2768],{},[1824,83193,83194,83196],{},[1761,83195,1920],{"stretchy":1821},[895,83197,83198,83200,83202],{},[1765,83199,5486],{},[898,83201,8726],{"mathvariant":1969},[1765,83203,2318],{},[1761,83205,1909],{},[1765,83207,2296],{},[1761,83209,2447],{},[1824,83211,83212,83214],{},[1765,83213,2318],{},[895,83215,83216,83218,83220,83222,83224,83226,83228],{},[1765,83217,1945],{},[898,83219,8726],{"mathvariant":1969},[1765,83221,2318],{},[1761,83223,1964],{},[1765,83225,5486],{},[898,83227,8726],{"mathvariant":1969},[1765,83229,2318],{},[1824,83231,83232,83234],{},[898,83233,13835],{},[895,83235,83236,83238,83240],{},[1765,83237,1945],{},[898,83239,8726],{"mathvariant":1969},[1765,83241,2318],{},[1824,83243,83244,83246],{},[898,83245,2768],{},[895,83247,83248,83250,83252],{},[1765,83249,5486],{},[898,83251,8726],{"mathvariant":1969},[1765,83253,2318],{},[1761,83255,1909],{},[1765,83257,2318],{},[1761,83259,2447],{},[1765,83261,2296],{},[1824,83263,83264,83266],{},[898,83265,13835],{},[895,83267,83268,83270,83272],{},[1765,83269,1945],{},[898,83271,8726],{"mathvariant":1969},[1765,83273,2318],{},[1824,83275,83276,83278],{},[898,83277,2768],{},[895,83279,83280,83282,83284],{},[1765,83281,5486],{},[898,83283,8726],{"mathvariant":1969},[1765,83285,2318],{},[1761,83287,1909],{},[1765,83289,2318],{},[2761,83291,7057],{},[898,83293,1828],{},[1761,83295,1915],{"stretchy":1821},[898,83297,13835],{},[1761,83299,1834],{"separator":1833},[898,83301,2768],{},[1761,83303,1920],{"stretchy":1821},[898,83305,1741],{"mathvariant":1969},[902,83307,83308],{"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).",[198,83310,83311],{"id":41205},"Homogenita",[724,83313,83314,83315,12146,83338,83354],{},"Funkce ",[883,83316,83318],{"className":83317},[886],[888,83319,83320],{"xmlns":890},[892,83321,83322,83336],{},[895,83323,83324,83326,83328,83330,83332,83334],{},[898,83325,1828],{},[1761,83327,1915],{"stretchy":1821},[898,83329,13835],{},[1761,83331,1834],{"separator":1833},[898,83333,2768],{},[1761,83335,1920],{"stretchy":1821},[902,83337,14036],{"encoding":904},[38,83339,83340,83341],{},"homogenní stupně ",[883,83342,83344],{"className":83343},[886],[888,83345,83346],{"xmlns":890},[892,83347,83348,83352],{},[895,83349,83350],{},[898,83351,40888],{},[902,83353,40888],{"encoding":904},", jestliže",[883,83356,83358],{"className":83357},[886],[888,83359,83360],{"xmlns":890,"display":1930},[892,83361,83362,83419],{},[24787,83363,83364],{"width":32101},[24792,83365,83366,83368,83412,83414],{},[24795,83367],{"width":32106},[24795,83369,83370],{},[895,83371,83372,83374,83376,83378,83380,83382,83384,83386,83388,83390,83396,83398,83400,83402,83404,83406,83408,83410],{},[898,83373,1828],{},[1761,83375,1915],{"stretchy":1821},[898,83377,1719],{},[898,83379,13835],{},[1761,83381,1834],{"separator":1833},[898,83383,1719],{},[898,83385,2768],{},[1761,83387,1920],{"stretchy":1821},[1761,83389,1909],{},[1824,83391,83392,83394],{},[898,83393,1719],{},[898,83395,40888],{},[2761,83397,7057],{},[898,83399,1828],{},[1761,83401,1915],{"stretchy":1821},[898,83403,13835],{},[1761,83405,1834],{"separator":1833},[898,83407,2768],{},[1761,83409,1920],{"stretchy":1821},[1761,83411,1834],{"separator":1833},[24795,83413],{"width":32106},[24795,83415,83416],{},[2761,83417,83418],{},"(5.10)",[902,83420,83421],{"encoding":904},"Q(rL, rK) = r^n\\,Q(L, K), \\tag{5.10}",[724,83423,8364,83424,83442,83443,83461,83462,47631,83475,83478,83479,1741],{},[883,83425,83427],{"className":83426},[886],[888,83428,83429],{"xmlns":890},[892,83430,83431,83439],{},[895,83432,83433,83435,83437],{},[898,83434,40888],{},[1761,83436,8538],{},[1765,83438,1767],{},[902,83440,83441],{"encoding":904},"n \\geq 0"," je celé číslo a ",[883,83444,83446],{"className":83445},[886],[888,83447,83448],{"xmlns":890},[892,83449,83450,83458],{},[895,83451,83452,83454,83456],{},[898,83453,1719],{},[1761,83455,1763],{},[1765,83457,1767],{},[902,83459,83460],{"encoding":904},"r > 0",". Homogenní funkce stupně ",[883,83463,83465],{"className":83464},[886],[888,83466,83467],{"xmlns":890},[892,83468,83469,83473],{},[895,83470,83471],{},[1765,83472,1945],{},[902,83474,1945],{"encoding":904},[38,83476,83477],{},"lineárně homogenní",". Cobb-Douglasovy funkce jsou homogenní stupně ",[883,83480,83482],{"className":83481},[886],[888,83483,83484],{"xmlns":890},[892,83485,83486,83494],{},[895,83487,83488,83490,83492],{},[898,83489,207],{},[1761,83491,1964],{},[898,83493,4302],{},[902,83495,78802],{"encoding":904},[115,83497,83499],{"id":83498},"ryzí-cobb-douglas-a-ces","Ryzí Cobb-Douglas a CES",[724,83501,83502],{},[38,83503,83504],{},"Ryzí Cobb-Douglasovy funkce:",[883,83506,83508],{"className":83507},[886],[888,83509,83510],{"xmlns":890,"display":1930},[892,83511,83512,83571],{},[24787,83513,83514],{"width":32101},[24792,83515,83516,83518,83564,83566],{},[24795,83517],{"width":32106},[24795,83519,83520],{},[895,83521,83522,83524,83526,83528,83530,83536,83538,83550,83552,83554,83556,83558,83560,83562],{},[898,83523,1828],{},[1761,83525,1909],{},[898,83527,8309],{},[2761,83529,7057],{},[1824,83531,83532,83534],{},[898,83533,13835],{},[898,83535,207],{},[2761,83537,7057],{},[1824,83539,83540,83542],{},[898,83541,2768],{},[895,83543,83544,83546,83548],{},[1765,83545,1945],{},[1761,83547,1885],{},[898,83549,207],{},[1761,83551,1834],{"separator":1833},[3315,83553],{"width":19322},[1765,83555,1767],{},[1761,83557,2058],{},[898,83559,207],{},[1761,83561,2058],{},[1765,83563,17298],{},[24795,83565],{"width":32106},[24795,83567,83568],{},[2761,83569,83570],{},"(5.9)",[902,83572,83573],{"encoding":904},"Q = A\\,L^a\\,K^{1-a}, \\quad 0 \u003C a \u003C 1. \\tag{5.9}",[724,83575,83576,83577,83579,83580,1741],{},"Mají vždy ",[38,83578,82897],{}," a jsou ",[38,83581,83477],{},[724,83583,83584,3927,83587,83590],{},[38,83585,83586],{},"CES produkční funkce",[614,83588,83589],{},"Constant Elasticity of Substitution",", 1961):",[883,83592,83594],{"className":83593},[886],[888,83595,83596],{"xmlns":890,"display":1930},[892,83597,83598,83666],{},[895,83599,83600,83602,83604,83606,83664],{},[898,83601,1828],{},[1761,83603,1909],{},[898,83605,8309],{},[1824,83607,83608,83652],{},[895,83609,83610,83612,83614,83616,83618,83620,83622,83624,83634,83636,83638,83640,83650],{},[1761,83611,1822],{"fence":1833},[1761,83613,1915],{"stretchy":1821},[1765,83615,1945],{},[1761,83617,1885],{},[898,83619,207],{},[1761,83621,1920],{"stretchy":1821},[2761,83623,7057],{},[1824,83625,83626,83628],{},[898,83627,13835],{},[895,83629,83630,83632],{},[1761,83631,1885],{},[898,83633,4302],{},[1761,83635,1964],{},[898,83637,207],{},[2761,83639,7057],{},[1824,83641,83642,83644],{},[898,83643,2768],{},[895,83645,83646,83648],{},[1761,83647,1885],{},[898,83649,4302],{},[1761,83651,1844],{"fence":1833},[895,83653,83654,83656],{},[1761,83655,1885],{},[6411,83657,83658],{"scriptlevel":1767,"displaystyle":1821},[4379,83659,83660,83662],{},[1765,83661,1945],{},[898,83663,4302],{},[1761,83665,1834],{"separator":1833},[902,83667,83668],{"encoding":904},"Q = A\\left[(1-a)\\,L^{-b} + a\\,K^{-b}\\right]^{-\\tfrac{1}{b}},",[724,83670,8364,83671,1343,83689,1343,83710,83734],{},[883,83672,83674],{"className":83673},[886],[888,83675,83676],{"xmlns":890},[892,83677,83678,83686],{},[895,83679,83680,83682,83684],{},[898,83681,8309],{},[1761,83683,1763],{},[1765,83685,1767],{},[902,83687,83688],{"encoding":904},"A > 0",[883,83690,83692],{"className":83691},[886],[888,83693,83694],{"xmlns":890},[892,83695,83696,83708],{},[895,83697,83698,83700,83702,83704,83706],{},[1765,83699,1767],{},[1761,83701,2058],{},[898,83703,207],{},[1761,83705,2058],{},[1765,83707,1945],{},[902,83709,22869],{"encoding":904},[883,83711,83713],{"className":83712},[886],[888,83714,83715],{"xmlns":890},[892,83716,83717,83731],{},[895,83718,83719,83721,83723,83725,83727,83729],{},[1761,83720,1885],{},[1765,83722,1945],{},[1761,83724,2058],{},[898,83726,4302],{},[1761,83728,7438],{"mathvariant":1969},[1765,83730,1767],{},[902,83732,83733],{"encoding":904},"-1 \u003C b \\neq 0",". Cobb-Douglasovy funkce jsou jejich zvláštním případem.",[724,83736,83737],{},[38,83738,83739],{},"Další typy:",[120,83741,83742,83784],{},[123,83743,83744,1989,83747,83783],{},[38,83745,83746],{},"Lineární:",[883,83748,83750],{"className":83749},[886],[888,83751,83752],{"xmlns":890},[892,83753,83754,83780],{},[895,83755,83756,83758,83760,83762,83764,83766,83768,83770,83772,83774,83776,83778],{},[898,83757,1828],{},[1761,83759,1915],{"stretchy":1821},[898,83761,13835],{},[1761,83763,1834],{"separator":1833},[898,83765,2768],{},[1761,83767,1920],{"stretchy":1821},[1761,83769,1909],{},[898,83771,207],{},[898,83773,13835],{},[1761,83775,1964],{},[898,83777,4302],{},[898,83779,2768],{},[902,83781,83782],{"encoding":904},"Q(L, K) = aL + bK"," — dokonalé substituty.",[123,83785,83786,1989,83789,83834],{},[38,83787,83788],{},"Leontiefova:",[883,83790,83792],{"className":83791},[886],[888,83793,83794],{"xmlns":890},[892,83795,83796,83831],{},[895,83797,83798,83800,83802,83804,83806,83808,83810,83812,83815,83817,83819,83821,83823,83825,83827,83829],{},[898,83799,1828],{},[1761,83801,1915],{"stretchy":1821},[898,83803,13835],{},[1761,83805,1834],{"separator":1833},[898,83807,2768],{},[1761,83809,1920],{"stretchy":1821},[1761,83811,1909],{},[898,83813,83814],{},"min",[1761,83816,60178],{},[1761,83818,1915],{"stretchy":1821},[898,83820,207],{},[898,83822,13835],{},[1761,83824,1834],{"separator":1833},[898,83826,4302],{},[898,83828,2768],{},[1761,83830,1920],{"stretchy":1821},[902,83832,83833],{"encoding":904},"Q(L, K) = \\min(aL, bK)"," — dokonalé komplementy (fixní proporce).",[115,83836,83838,83839,1343,83858,83877],{"id":83837},"mezní-produkty-mplmp_l-mpkmp_k-a-totální-diferenciál","Mezní produkty ",[883,83840,83842],{"className":83841},[886],[888,83843,83844],{"xmlns":890},[892,83845,83846,83856],{},[895,83847,83848,83850],{},[898,83849,6889],{},[1681,83851,83852,83854],{},[898,83853,1839],{},[898,83855,13835],{},[902,83857,14083],{"encoding":904},[883,83859,83861],{"className":83860},[886],[888,83862,83863],{"xmlns":890},[892,83864,83865,83875],{},[895,83866,83867,83869],{},[898,83868,6889],{},[1681,83870,83871,83873],{},[898,83872,1839],{},[898,83874,2768],{},[902,83876,14128],{"encoding":904}," a totální diferenciál",[724,83879,83880],{},[38,83881,83882],{},"Mezní produkt práce:",[883,83884,83886],{"className":83885},[886],[888,83887,83888],{"xmlns":890,"display":1930},[892,83889,83890,83928],{},[895,83891,83892,83894,83900,83902,83910,83912,83926],{},[898,83893,6889],{},[1681,83895,83896,83898],{},[898,83897,1839],{},[898,83899,13835],{},[1761,83901,1909],{},[2015,83903,83904,83906,83908],{},[898,83905,1828],{},[898,83907,13835],{},[1761,83909,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,83911,1909],{},[4379,83913,83914,83920],{},[895,83915,83916,83918],{},[898,83917,13911],{"mathvariant":1969},[898,83919,1828],{},[895,83921,83922,83924],{},[898,83923,13911],{"mathvariant":1969},[898,83925,13835],{},[898,83927,1741],{"mathvariant":1969},[902,83929,83930],{"encoding":904},"MP_L = Q'_L = \\frac{\\partial Q}{\\partial L}.",[724,83932,83933],{},[38,83934,83935],{},"Mezní produkt kapitálu:",[883,83937,83939],{"className":83938},[886],[888,83940,83941],{"xmlns":890,"display":1930},[892,83942,83943,83981],{},[895,83944,83945,83947,83953,83955,83963,83965,83979],{},[898,83946,6889],{},[1681,83948,83949,83951],{},[898,83950,1839],{},[898,83952,2768],{},[1761,83954,1909],{},[2015,83956,83957,83959,83961],{},[898,83958,1828],{},[898,83960,2768],{},[1761,83962,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,83964,1909],{},[4379,83966,83967,83973],{},[895,83968,83969,83971],{},[898,83970,13911],{"mathvariant":1969},[898,83972,1828],{},[895,83974,83975,83977],{},[898,83976,13911],{"mathvariant":1969},[898,83978,2768],{},[898,83980,1741],{"mathvariant":1969},[902,83982,83983],{"encoding":904},"MP_K = Q'_K = \\frac{\\partial Q}{\\partial K}.",[724,83985,83986,84016,84017,84038,84039,84057,84058,84071,84072,1741],{},[883,83987,83989],{"className":83988},[886],[888,83990,83991],{"xmlns":890},[892,83992,83993,84013],{},[895,83994,83995,83997,84003,84005,84007,84009,84011],{},[898,83996,6889],{},[1681,83998,83999,84001],{},[898,84000,1839],{},[898,84002,13835],{},[1761,84004,1915],{"stretchy":1821},[898,84006,207],{},[1761,84008,1834],{"separator":1833},[898,84010,4302],{},[1761,84012,1920],{"stretchy":1821},[902,84014,84015],{"encoding":904},"MP_L(a, b)"," udává rychlost změny produkce vzhledem k práci v bodě ",[883,84018,84020],{"className":84019},[886],[888,84021,84022],{"xmlns":890},[892,84023,84024,84036],{},[895,84025,84026,84028,84030,84032,84034],{},[1761,84027,1822],{"stretchy":1821},[898,84029,207],{},[1761,84031,1834],{"separator":1833},[898,84033,4302],{},[1761,84035,1844],{"stretchy":1821},[902,84037,14862],{"encoding":904}," (na hladině ",[883,84040,84042],{"className":84041},[886],[888,84043,84044],{"xmlns":890},[892,84045,84046,84054],{},[895,84047,84048,84050,84052],{},[898,84049,2768],{},[1761,84051,1909],{},[898,84053,4302],{},[902,84055,84056],{"encoding":904},"K = b","), resp. přibližnou změnu produkce při jednotkové změně ",[883,84059,84061],{"className":84060},[886],[888,84062,84063],{"xmlns":890},[892,84064,84065,84069],{},[895,84066,84067],{},[898,84068,13835],{},[902,84070,13835],{"encoding":904},". Analogicky ",[883,84073,84075],{"className":84074},[886],[888,84076,84077],{"xmlns":890},[892,84078,84079,84099],{},[895,84080,84081,84083,84089,84091,84093,84095,84097],{},[898,84082,6889],{},[1681,84084,84085,84087],{},[898,84086,1839],{},[898,84088,2768],{},[1761,84090,1915],{"stretchy":1821},[898,84092,207],{},[1761,84094,1834],{"separator":1833},[898,84096,4302],{},[1761,84098,1920],{"stretchy":1821},[902,84100,84101],{"encoding":904},"MP_K(a, b)",[1636,84103,84104,84108],{},[724,84105,84106,55199],{},[883,84107,1642],{},[120,84109,84110,84148],{},[123,84111,84112,30220,84131],{},[883,84113,84115],{"className":84114},[886],[888,84116,84117],{"xmlns":890},[892,84118,84119,84129],{},[895,84120,84121,84123],{},[898,84122,6889],{},[1681,84124,84125,84127],{},[898,84126,1839],{},[898,84128,13835],{},[902,84130,14083],{"encoding":904},[614,84132,84133,84134,84147],{},"„o kolik vzroste ",[883,84135,84137],{"className":84136},[886],[888,84138,84139],{"xmlns":890},[892,84140,84141,84145],{},[895,84142,84143],{},[898,84144,1828],{},[902,84146,1828],{"encoding":904},", když přidám jednu jednotku práce (a kapitál držím pevně)?\"",[123,84149,84150,30220,84169],{},[883,84151,84153],{"className":84152},[886],[888,84154,84155],{"xmlns":890},[892,84156,84157,84167],{},[895,84158,84159,84161],{},[898,84160,6889],{},[1681,84162,84163,84165],{},[898,84164,1839],{},[898,84166,2768],{},[902,84168,14128],{"encoding":904},[614,84170,84133,84171,84184],{},[883,84172,84174],{"className":84173},[886],[888,84175,84176],{"xmlns":890},[892,84177,84178,84182],{},[895,84179,84180],{},[898,84181,1828],{},[902,84183,1828],{"encoding":904},", když přidám jednu jednotku kapitálu (a práci držím pevně)?\"",[724,84186,84187,84190,84191,84206,84207,2506],{},[38,84188,84189],{},"Totální diferenciál"," — přibližná změna produkce při změně práce o ",[883,84192,84194],{"className":84193},[886],[888,84195,84196],{"xmlns":890},[892,84197,84198,84204],{},[895,84199,84200,84202],{},[898,84201,4346],{},[898,84203,13835],{},[902,84205,79334],{"encoding":904}," a kapitálu o ",[883,84208,84210],{"className":84209},[886],[888,84211,84212],{"xmlns":890},[892,84213,84214,84220],{},[895,84215,84216,84218],{},[898,84217,4346],{},[898,84219,2768],{},[902,84221,84222],{"encoding":904},"dK",[883,84224,84226],{"className":84225},[886],[888,84227,84228],{"xmlns":890,"display":1930},[892,84229,84230,84323],{},[24787,84231,84232],{"width":32101},[24792,84233,84234,84236,84316,84318],{},[24795,84235],{"width":32106},[24795,84237,84238],{},[895,84239,84240,84242,84244,84246,84248,84250,84252,84260,84262,84264,84266,84268,84276,84278,84280,84282,84284,84286,84292,84294,84296,84298,84300,84302,84308,84310,84312,84314],{},[898,84241,6959],{"mathvariant":1969},[898,84243,1828],{},[1761,84245,6803],{},[898,84247,4346],{},[898,84249,1828],{},[1761,84251,1909],{},[2015,84253,84254,84256,84258],{},[898,84255,1828],{},[898,84257,13835],{},[1761,84259,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[2761,84261,7057],{},[898,84263,4346],{},[898,84265,13835],{},[1761,84267,1964],{},[2015,84269,84270,84272,84274],{},[898,84271,1828],{},[898,84273,2768],{},[1761,84275,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[2761,84277,7057],{},[898,84279,4346],{},[898,84281,2768],{},[1761,84283,1909],{},[898,84285,6889],{},[1681,84287,84288,84290],{},[898,84289,1839],{},[898,84291,13835],{},[2761,84293,7057],{},[898,84295,4346],{},[898,84297,13835],{},[1761,84299,1964],{},[898,84301,6889],{},[1681,84303,84304,84306],{},[898,84305,1839],{},[898,84307,2768],{},[2761,84309,7057],{},[898,84311,4346],{},[898,84313,2768],{},[898,84315,1741],{"mathvariant":1969},[24795,84317],{"width":32106},[24795,84319,84320],{},[2761,84321,84322],{},"(5.11)",[902,84324,84325],{"encoding":904},"\\Delta Q \\approx dQ = Q'_L\\,dL + Q'_K\\,dK = MP_L\\,dL + MP_K\\,dK. \\tag{5.11}",[724,84327,84328,84329,1741],{},"Skutečná změna: ",[883,84330,84332],{"className":84331},[886],[888,84333,84334],{"xmlns":890},[892,84335,84336,84382],{},[895,84337,84338,84340,84342,84344,84346,84348,84350,84352,84354,84356,84358,84360,84362,84364,84366,84368,84370,84372,84374,84376,84378,84380],{},[898,84339,6959],{"mathvariant":1969},[898,84341,1828],{},[1761,84343,1909],{},[898,84345,1828],{},[1761,84347,1915],{"stretchy":1821},[898,84349,13835],{},[1761,84351,1964],{},[898,84353,4346],{},[898,84355,13835],{},[1761,84357,1834],{"separator":1833},[898,84359,2768],{},[1761,84361,1964],{},[898,84363,4346],{},[898,84365,2768],{},[1761,84367,1920],{"stretchy":1821},[1761,84369,1885],{},[898,84371,1828],{},[1761,84373,1915],{"stretchy":1821},[898,84375,13835],{},[1761,84377,1834],{"separator":1833},[898,84379,2768],{},[1761,84381,1920],{"stretchy":1821},[902,84383,84384],{"encoding":904},"\\Delta Q = Q(L+dL, K+dK) - Q(L, K)",[724,84386,84387,84389,84390,84408,84409,84422,84423,84442,84443,84475,84476,84508,84509,1741],{},[38,84388,79498],{}," platí ve 2F modelu pro oba vstupy: pro pevné ",[883,84391,84393],{"className":84392},[886],[888,84394,84395],{"xmlns":890},[892,84396,84397,84405],{},[895,84398,84399],{},[1681,84400,84401,84403],{},[898,84402,2768],{},[1765,84404,1767],{},[902,84406,84407],{"encoding":904},"K_0"," se od jistého ",[883,84410,84412],{"className":84411},[886],[888,84413,84414],{"xmlns":890},[892,84415,84416,84420],{},[895,84417,84418],{},[898,84419,13835],{},[902,84421,13835],{"encoding":904}," stane ",[883,84424,84426],{"className":84425},[886],[888,84427,84428],{"xmlns":890},[892,84429,84430,84440],{},[895,84431,84432,84434],{},[898,84433,6889],{},[1681,84435,84436,84438],{},[898,84437,1839],{},[898,84439,13835],{},[902,84441,14083],{"encoding":904}," klesající (",[883,84444,84446],{"className":84445},[886],[888,84447,84448],{"xmlns":890},[892,84449,84450,84472],{},[895,84451,84452,84468,84470],{},[2015,84453,84454,84456,84462],{},[898,84455,1828],{},[895,84457,84458,84460],{},[898,84459,13835],{},[898,84461,13835],{},[895,84463,84464,84466],{},[1761,84465,6459],{"mathvariant":1969},[1761,84467,6459],{"mathvariant":1969},[1761,84469,2058],{},[1765,84471,1767],{},[902,84473,84474],{"encoding":904},"Q''_{LL} \u003C 0","); analogicky ",[883,84477,84479],{"className":84478},[886],[888,84480,84481],{"xmlns":890},[892,84482,84483,84505],{},[895,84484,84485,84501,84503],{},[2015,84486,84487,84489,84495],{},[898,84488,1828],{},[895,84490,84491,84493],{},[898,84492,2768],{},[898,84494,2768],{},[895,84496,84497,84499],{},[1761,84498,6459],{"mathvariant":1969},[1761,84500,6459],{"mathvariant":1969},[1761,84502,2058],{},[1765,84504,1767],{},[902,84506,84507],{"encoding":904},"Q''_{KK} \u003C 0"," pro pevné ",[883,84510,84512],{"className":84511},[886],[888,84513,84514],{"xmlns":890},[892,84515,84516,84524],{},[895,84517,84518],{},[1681,84519,84520,84522],{},[898,84521,13835],{},[1765,84523,1767],{},[902,84525,79536],{"encoding":904},[115,84527,84529],{"id":84528},"eulerova-věta-pro-homogenní-funkce","Eulerova věta pro homogenní funkce",[724,84531,84532,84535,84536,84559,84560,33974],{},[38,84533,84534],{},"Eulerova věta"," (úloha 5.10): pro homogenní funkci ",[883,84537,84539],{"className":84538},[886],[888,84540,84541],{"xmlns":890},[892,84542,84543,84557],{},[895,84544,84545,84547,84549,84551,84553,84555],{},[898,84546,1828],{},[1761,84548,1915],{"stretchy":1821},[898,84550,13835],{},[1761,84552,1834],{"separator":1833},[898,84554,2768],{},[1761,84556,1920],{"stretchy":1821},[902,84558,14036],{"encoding":904}," stupně ",[883,84561,84563],{"className":84562},[886],[888,84564,84565],{"xmlns":890},[892,84566,84567,84571],{},[895,84568,84569],{},[898,84570,40888],{},[902,84572,40888],{"encoding":904},[883,84574,84576],{"className":84575},[886],[888,84577,84578],{"xmlns":890,"display":1930},[892,84579,84580,84643],{},[24787,84581,84582],{"width":32101},[24792,84583,84584,84586,84636,84638],{},[24795,84585],{"width":32106},[24795,84587,84588],{},[895,84589,84590,84592,84594,84602,84604,84606,84608,84616,84618,84620,84622,84624,84626,84628,84630,84632,84634],{},[898,84591,13835],{},[2761,84593,7057],{},[2015,84595,84596,84598,84600],{},[898,84597,1828],{},[898,84599,13835],{},[1761,84601,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,84603,1964],{},[898,84605,2768],{},[2761,84607,7057],{},[2015,84609,84610,84612,84614],{},[898,84611,1828],{},[898,84613,2768],{},[1761,84615,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,84617,1909],{},[898,84619,40888],{},[2761,84621,7057],{},[898,84623,1828],{},[1761,84625,1915],{"stretchy":1821},[898,84627,13835],{},[1761,84629,1834],{"separator":1833},[898,84631,2768],{},[1761,84633,1920],{"stretchy":1821},[898,84635,1741],{"mathvariant":1969},[24795,84637],{"width":32106},[24795,84639,84640],{},[2761,84641,84642],{},"(5.12)",[902,84644,84645],{"encoding":904},"L\\,Q'_L + K\\,Q'_K = n\\,Q(L, K). \\tag{5.12}",[724,84647,84648,84669],{},[38,84649,84650,84651],{},"Speciální případ ",[883,84652,84654],{"className":84653},[886],[888,84655,84656],{"xmlns":890},[892,84657,84658,84666],{},[895,84659,84660,84662,84664],{},[898,84661,40888],{},[1761,84663,1909],{},[1765,84665,1945],{},[902,84667,84668],{"encoding":904},"n = 1"," (konstantní výnosy z rozsahu):",[883,84671,84673],{"className":84672},[886],[888,84674,84675],{"xmlns":890,"display":1930},[892,84676,84677,84721],{},[895,84678,84679,84681,84683,84685,84691,84693,84695,84697,84699,84705,84707,84709,84711,84713,84715,84717,84719],{},[898,84680,13835],{},[1761,84682,2447],{},[898,84684,6889],{},[1681,84686,84687,84689],{},[898,84688,1839],{},[898,84690,13835],{},[1761,84692,1964],{},[898,84694,2768],{},[1761,84696,2447],{},[898,84698,6889],{},[1681,84700,84701,84703],{},[898,84702,1839],{},[898,84704,2768],{},[1761,84706,1909],{},[898,84708,1828],{},[1761,84710,1915],{"stretchy":1821},[898,84712,13835],{},[1761,84714,1834],{"separator":1833},[898,84716,2768],{},[1761,84718,1920],{"stretchy":1821},[898,84720,1741],{"mathvariant":1969},[902,84722,84723],{"encoding":904},"L\\cdot MP_L + K\\cdot MP_K = Q(L, K).",[724,84725,84726,84727,84730],{},"Slovně — ",[38,84728,84729],{},"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).",[115,84732,13818],{"id":78872},[724,84734,84735,3927,84737,84740,84741,84763,84764,2506],{},[38,84736,13818],{},[614,84738,84739],{},"isoquants",") jsou křivky stejné produkce — množina dvojic ",[883,84742,84744],{"className":84743},[886],[888,84745,84746],{"xmlns":890},[892,84747,84748,84760],{},[895,84749,84750,84752,84754,84756,84758],{},[1761,84751,1822],{"stretchy":1821},[898,84753,13835],{},[1761,84755,1834],{"separator":1833},[898,84757,2768],{},[1761,84759,1844],{"stretchy":1821},[902,84761,84762],{"encoding":904},"[L, K]",", pro něž produkční funkce nabývá pevně zvolené hodnoty ",[883,84765,84767],{"className":84766},[886],[888,84768,84769],{"xmlns":890},[892,84770,84771,84776],{},[895,84772,84773],{},[898,84774,84775],{},"q",[902,84777,84775],{"encoding":904},[883,84779,84781],{"className":84780},[886],[888,84782,84783],{"xmlns":890,"display":1930},[892,84784,84785,84820],{},[24787,84786,84787],{"width":32101},[24792,84788,84789,84791,84813,84815],{},[24795,84790],{"width":32106},[24795,84792,84793],{},[895,84794,84795,84797,84799,84801,84803,84805,84807,84809,84811],{},[898,84796,1828],{},[1761,84798,1915],{"stretchy":1821},[898,84800,13835],{},[1761,84802,1834],{"separator":1833},[898,84804,2768],{},[1761,84806,1920],{"stretchy":1821},[1761,84808,1909],{},[898,84810,84775],{},[898,84812,1741],{"mathvariant":1969},[24795,84814],{"width":32106},[24795,84816,84817],{},[2761,84818,84819],{},"(5.13)",[902,84821,84822],{"encoding":904},"Q(L, K) = q. \\tag{5.13}",[724,84824,84825,84826,84829,84830,2162],{},"Jsou to ",[38,84827,84828],{},"indiferenční křivky"," produkční funkce (analogie s indiferenčními křivkami u ",[207,84831,84833],{"className":84832,"dataFsResolvedFilePath":878,"href":879},[210],"užitečnosti",[724,84835,84836],{},[38,84837,84838],{},"Vlastnosti izokvant Cobb-Douglasových funkcí:",[120,84840,84841,84846,84851,84856],{},[123,84842,84843,84845],{},[38,84844,16557],{}," — pokles kapitálu vyžaduje kompenzující růst práce k udržení produkce;",[123,84847,84848,84850],{},[38,84849,41690],{}," (úloha 5.14);",[123,84852,84853,12468],{},[38,84854,84855],{},"neprotínají se",[123,84857,84858,84859,8412,84872,1741],{},"s rostoucím ",[883,84860,84862],{"className":84861},[886],[888,84863,84864],{"xmlns":890},[892,84865,84866,84870],{},[895,84867,84868],{},[898,84869,84775],{},[902,84871,84775],{"encoding":904},[38,84873,84874],{},"vzdalují od počátku",[724,84876,84877],{},[614,84878,84879,84880,84902,84903,1741],{},"Obrázek 5.4 — izokvanty Cobb-Douglasovy funkce v rovině ",[883,84881,84883],{"className":84882},[886],[888,84884,84885],{"xmlns":890},[892,84886,84887,84899],{},[895,84888,84889,84891,84893,84895,84897],{},[1761,84890,1915],{"stretchy":1821},[898,84892,13835],{},[1761,84894,1834],{"separator":1833},[898,84896,2768],{},[1761,84898,1920],{"stretchy":1821},[902,84900,84901],{"encoding":904},"(L, K)",": tři klesající konvexní křivky pro ",[883,84904,84906],{"className":84905},[886],[888,84907,84908],{"xmlns":890},[892,84909,84910,84934],{},[895,84911,84912,84918,84920,84926,84928],{},[1681,84913,84914,84916],{},[898,84915,84775],{},[1765,84917,1945],{},[1761,84919,2058],{},[1681,84921,84922,84924],{},[898,84923,84775],{},[1765,84925,1767],{},[1761,84927,2058],{},[1681,84929,84930,84932],{},[898,84931,84775],{},[1765,84933,2296],{},[902,84935,84936],{"encoding":904},"q_1 \u003C q_0 \u003C q_2",[115,84938,84940,84941,1920],{"id":84939},"mezní-míra-technické-substituce-mrtsmrts","Mezní míra technické substituce (",[883,84942,84944],{"className":84943},[886],[888,84945,84946],{"xmlns":890},[892,84947,84948,84958],{},[895,84949,84950,84952,84954,84956],{},[898,84951,6889],{},[898,84953,8051],{},[898,84955,1655],{},[898,84957,1912],{},[902,84959,14637],{"encoding":904},[724,84961,84962,3927,84965,84968],{},[38,84963,84964],{},"Mezní míra technické substituce",[614,84966,84967],{},"marginal rate of technical substitution",") je podíl mezních produktů:",[883,84970,84972],{"className":84971},[886],[888,84973,84974],{"xmlns":890,"display":1930},[892,84975,84976,85067],{},[24787,84977,84978],{"width":32101},[24792,84979,84980,84982,85060,85062],{},[24795,84981],{"width":32106},[24795,84983,84984],{},[895,84985,84986,84988,84990,84992,84994,84996,84998,85000,85002,85004,85006,85008,85010,85012,85014,85016,85038,85040,85058],{},[898,84987,6889],{},[898,84989,8051],{},[898,84991,1655],{},[898,84993,1912],{},[1761,84995,1909],{},[898,84997,6889],{},[898,84999,8051],{},[898,85001,1655],{},[898,85003,1912],{},[1761,85005,1915],{"stretchy":1821},[898,85007,13835],{},[1761,85009,1834],{"separator":1833},[898,85011,2768],{},[1761,85013,1920],{"stretchy":1821},[1761,85015,1909],{},[4379,85017,85018,85028],{},[895,85019,85020,85022],{},[898,85021,6889],{},[1681,85023,85024,85026],{},[898,85025,1839],{},[898,85027,13835],{},[895,85029,85030,85032],{},[898,85031,6889],{},[1681,85033,85034,85036],{},[898,85035,1839],{},[898,85037,2768],{},[1761,85039,1909],{},[4379,85041,85042,85050],{},[2015,85043,85044,85046,85048],{},[898,85045,1828],{},[898,85047,13835],{},[1761,85049,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[2015,85051,85052,85054,85056],{},[898,85053,1828],{},[898,85055,2768],{},[1761,85057,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[898,85059,1741],{"mathvariant":1969},[24795,85061],{"width":32106},[24795,85063,85064],{},[2761,85065,85066],{},"(5.14)",[902,85068,85069],{"encoding":904},"MRTS = MRTS(L, K) = \\frac{MP_L}{MP_K} = \\frac{Q'_L}{Q'_K}. \\tag{5.14}",[724,85071,85072,1989,85074,85104,85105,85136],{},[38,85073,13257],{},[883,85075,85077],{"className":85076},[886],[888,85078,85079],{"xmlns":890},[892,85080,85081,85101],{},[895,85082,85083,85085,85087,85089,85091,85093,85095,85097,85099],{},[898,85084,6889],{},[898,85086,8051],{},[898,85088,1655],{},[898,85090,1912],{},[1761,85092,1915],{"stretchy":1821},[898,85094,13835],{},[1761,85096,1834],{"separator":1833},[898,85098,2768],{},[1761,85100,1920],{"stretchy":1821},[902,85102,85103],{"encoding":904},"MRTS(L, K)"," udává, ",[38,85106,85107,85108,85121,85122,85135],{},"o kolik se musí přibližně změnit kapitál ",[883,85109,85111],{"className":85110},[886],[888,85112,85113],{"xmlns":890},[892,85114,85115,85119],{},[895,85116,85117],{},[898,85118,2768],{},[902,85120,2768],{"encoding":904},", jestliže se práce ",[883,85123,85125],{"className":85124},[886],[888,85126,85127],{"xmlns":890},[892,85128,85129,85133],{},[895,85130,85131],{},[898,85132,13835],{},[902,85134,13835],{"encoding":904}," změní o jednotku, aby byla zachována produkce"," (pohyb po izokvantě).",[1636,85138,85139],{},[724,85140,85141,22057,85143,85162,85163,85200,85201,85204,85205,85209],{},[883,85142,1642],{},[883,85144,85146],{"className":85145},[886],[888,85147,85148],{"xmlns":890},[892,85149,85150,85160],{},[895,85151,85152,85154,85156,85158],{},[898,85153,6889],{},[898,85155,8051],{},[898,85157,1655],{},[898,85159,1912],{},[902,85161,14637],{"encoding":904}," říká: ",[614,85164,85165,85166,85185,85186,85199],{},"„jednu jednotku práce musím nahradit přibližně ",[883,85167,85169],{"className":85168},[886],[888,85170,85171],{"xmlns":890},[892,85172,85173,85183],{},[895,85174,85175,85177,85179,85181],{},[898,85176,6889],{},[898,85178,8051],{},[898,85180,1655],{},[898,85182,1912],{},[902,85184,14637],{"encoding":904}," jednotkami kapitálu, aby produkce ",[883,85187,85189],{"className":85188},[886],[888,85190,85191],{"xmlns":890},[892,85192,85193,85197],{},[895,85194,85195],{},[898,85196,1828],{},[902,85198,1828],{"encoding":904}," zůstala stejná.\""," Je to ",[38,85202,85203],{},"směnný kurz mezi vstupy"," při zachování produkce — přesná analogie ",[207,85206,85208],{"className":85207,"dataFsResolvedFilePath":878,"href":879},[210],"MRCS z teorie užitečnosti",", kde nahrazujeme spotřební statky při zachování užitku.",[724,85211,85212],{},[3991,85213],{"alt":85214,"className":85215,"src":85216},"imek-izokvanty-mrts",[210,3995],"\u002Fwiki-assets\u002Fimek-izokvanty-mrts.jpeg",[724,85218,85219,85222,85223,12146,85253,85275,85276,5372],{},[38,85220,85221],{},"Geometrická interpretace:"," sklon tečny k izokvantě v bodě ",[883,85224,85226],{"className":85225},[886],[888,85227,85228],{"xmlns":890},[892,85229,85230,85250],{},[895,85231,85232,85234,85240,85242,85248],{},[1761,85233,1822],{"stretchy":1821},[1681,85235,85236,85238],{},[898,85237,13835],{},[1765,85239,1767],{},[1761,85241,1834],{"separator":1833},[1681,85243,85244,85246],{},[898,85245,2768],{},[1765,85247,1767],{},[1761,85249,1844],{"stretchy":1821},[902,85251,85252],{"encoding":904},"[L_0, K_0]",[883,85254,85256],{"className":85255},[886],[888,85257,85258],{"xmlns":890},[892,85259,85260,85272],{},[895,85261,85262,85264,85266,85268,85270],{},[1761,85263,1885],{},[898,85265,6889],{},[898,85267,8051],{},[898,85269,1655],{},[898,85271,1912],{},[902,85273,85274],{"encoding":904},"-MRTS",". Z derivace implicitní funkce (při ",[883,85277,85279],{"className":85278},[886],[888,85280,85281],{"xmlns":890},[892,85282,85283,85305],{},[895,85284,85285,85287,85289,85291,85293,85295,85297,85299],{},[898,85286,1828],{},[1761,85288,1915],{"stretchy":1821},[898,85290,13835],{},[1761,85292,1834],{"separator":1833},[898,85294,2768],{},[1761,85296,1920],{"stretchy":1821},[1761,85298,1909],{},[1681,85300,85301,85303],{},[898,85302,84775],{},[1765,85304,1767],{},[902,85306,85307],{"encoding":904},"Q(L,K) = q_0",[883,85309,85311],{"className":85310},[886],[888,85312,85313],{"xmlns":890,"display":1930},[892,85314,85315,85367],{},[895,85316,85317,85331,85333,85335,85353,85355,85357,85359,85361,85363,85365],{},[4379,85318,85319,85325],{},[895,85320,85321,85323],{},[898,85322,4346],{},[898,85324,2768],{},[895,85326,85327,85329],{},[898,85328,4346],{},[898,85330,13835],{},[1761,85332,1909],{},[1761,85334,1885],{},[4379,85336,85337,85345],{},[2015,85338,85339,85341,85343],{},[898,85340,1828],{},[898,85342,13835],{},[1761,85344,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[2015,85346,85347,85349,85351],{},[898,85348,1828],{},[898,85350,2768],{},[1761,85352,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,85354,1909],{},[1761,85356,1885],{},[898,85358,6889],{},[898,85360,8051],{},[898,85362,1655],{},[898,85364,1912],{},[898,85366,1741],{"mathvariant":1969},[902,85368,85369],{"encoding":904},"\\frac{dK}{dL} = -\\frac{Q'_L}{Q'_K} = -MRTS.",[724,85371,85372,85373,85388,85389,85405],{},"Změní-li se práce o ",[883,85374,85376],{"className":85375},[886],[888,85377,85378],{"xmlns":890},[892,85379,85380,85386],{},[895,85381,85382,85384],{},[898,85383,4346],{},[898,85385,13835],{},[902,85387,79334],{"encoding":904},", lze pro odhad změny kapitálu ",[883,85390,85392],{"className":85391},[886],[888,85393,85394],{"xmlns":890},[892,85395,85396,85402],{},[895,85397,85398,85400],{},[898,85399,6959],{"mathvariant":1969},[898,85401,2768],{},[902,85403,85404],{"encoding":904},"\\Delta K"," k udržení produkce použít diferenciál:",[883,85407,85409],{"className":85408},[886],[888,85410,85411],{"xmlns":890,"display":1930},[892,85412,85413,85460],{},[24787,85414,85415],{"width":32101},[24792,85416,85417,85419,85453,85455],{},[24795,85418],{"width":32106},[24795,85420,85421],{},[895,85422,85423,85425,85427,85429,85431,85433,85435,85437,85439,85441,85443,85445,85447,85449,85451],{},[898,85424,6959],{"mathvariant":1969},[898,85426,2768],{},[1761,85428,6803],{},[898,85430,4346],{},[898,85432,2768],{},[1761,85434,1909],{},[1761,85436,1885],{},[898,85438,6889],{},[898,85440,8051],{},[898,85442,1655],{},[898,85444,1912],{},[2761,85446,7057],{},[898,85448,4346],{},[898,85450,13835],{},[1761,85452,1834],{"separator":1833},[24795,85454],{"width":32106},[24795,85456,85457],{},[2761,85458,85459],{},"(5.15)",[902,85461,85462],{"encoding":904},"\\Delta K \\approx dK = -MRTS\\,dL, \\tag{5.15}",[883,85464,85466],{"className":85465},[886],[888,85467,85468],{"xmlns":890,"display":1930},[892,85469,85470,85519],{},[24787,85471,85472],{"width":32101},[24792,85473,85474,85476,85512,85514],{},[24795,85475],{"width":32106},[24795,85477,85478],{},[895,85479,85480,85482,85484,85486,85504,85506,85508,85510],{},[898,85481,4346],{},[898,85483,13835],{},[1761,85485,1909],{},[4379,85487,85488,85494],{},[895,85489,85490,85492],{},[1761,85491,1885],{},[1765,85493,1945],{},[895,85495,85496,85498,85500,85502],{},[898,85497,6889],{},[898,85499,8051],{},[898,85501,1655],{},[898,85503,1912],{},[2761,85505,7057],{},[898,85507,4346],{},[898,85509,2768],{},[898,85511,1741],{"mathvariant":1969},[24795,85513],{"width":32106},[24795,85515,85516],{},[2761,85517,85518],{},"(5.16)",[902,85520,85521],{"encoding":904},"dL = \\frac{-1}{MRTS}\\,dK. \\tag{5.16}",[1636,85523,85524,85548],{},[724,85525,85526,85528,85529],{},[883,85527,4452],{}," Postup — jak spočítat ",[883,85530,85532],{"className":85531},[886],[888,85533,85534],{"xmlns":890},[892,85535,85536,85546],{},[895,85537,85538,85540,85542,85544],{},[898,85539,6889],{},[898,85541,8051],{},[898,85543,1655],{},[898,85545,1912],{},[902,85547,14637],{"encoding":904},[152,85549,85550,85591,85634,85666],{},[123,85551,85552,85553,2068,85572,1741],{},"Vypočtěte parciální derivace ",[883,85554,85556],{"className":85555},[886],[888,85557,85558],{"xmlns":890},[892,85559,85560,85570],{},[895,85561,85562],{},[2015,85563,85564,85566,85568],{},[898,85565,1828],{},[898,85567,13835],{},[1761,85569,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[902,85571,14060],{"encoding":904},[883,85573,85575],{"className":85574},[886],[888,85576,85577],{"xmlns":890},[892,85578,85579,85589],{},[895,85580,85581],{},[2015,85582,85583,85585,85587],{},[898,85584,1828],{},[898,85586,2768],{},[1761,85588,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[902,85590,14105],{"encoding":904},[123,85592,69819,85593,85633],{},[883,85594,85596],{"className":85595},[886],[888,85597,85598],{"xmlns":890},[892,85599,85600,85630],{},[895,85601,85602,85604,85606,85608,85610,85612,85620,85622],{},[898,85603,6889],{},[898,85605,8051],{},[898,85607,1655],{},[898,85609,1912],{},[1761,85611,1909],{},[2015,85613,85614,85616,85618],{},[898,85615,1828],{},[898,85617,13835],{},[1761,85619,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[898,85621,8726],{"mathvariant":1969},[2015,85623,85624,85626,85628],{},[898,85625,1828],{},[898,85627,2768],{},[1761,85629,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[902,85631,85632],{"encoding":904},"MRTS = Q'_L \u002F Q'_K"," (zlomek zjednodušte).",[123,85635,85636,85637,1741],{},"Případně dosaďte konkrétní ",[883,85638,85640],{"className":85639},[886],[888,85641,85642],{"xmlns":890},[892,85643,85644,85664],{},[895,85645,85646,85648,85654,85656,85662],{},[1761,85647,1822],{"stretchy":1821},[1681,85649,85650,85652],{},[898,85651,13835],{},[1765,85653,1767],{},[1761,85655,1834],{"separator":1833},[1681,85657,85658,85660],{},[898,85659,2768],{},[1765,85661,1767],{},[1761,85663,1844],{"stretchy":1821},[902,85665,85252],{"encoding":904},[123,85667,85668,85669,85703,85704,85706],{},"Pro odhad substituce použijte ",[883,85670,85672],{"className":85671},[886],[888,85673,85674],{"xmlns":890},[892,85675,85676,85700],{},[895,85677,85678,85680,85682,85684,85686,85688,85690,85692,85694,85696,85698],{},[898,85679,6959],{"mathvariant":1969},[898,85681,2768],{},[1761,85683,6803],{},[1761,85685,1885],{},[898,85687,6889],{},[898,85689,8051],{},[898,85691,1655],{},[898,85693,1912],{},[1761,85695,2447],{},[898,85697,6959],{"mathvariant":1969},[898,85699,13835],{},[902,85701,85702],{"encoding":904},"\\Delta K \\approx -MRTS \\cdot \\Delta L"," (znaménko ",[38,85705,56586],{}," — substituce, ne doplnění).",[724,85708,85709],{},[614,85710,85711,85712,85744,85745,6699,85758,19828,85787,85802],{},"Obrázek 5.7 — izokvanta ",[883,85713,85715],{"className":85714},[886],[888,85716,85717],{"xmlns":890},[892,85718,85719,85741],{},[895,85720,85721,85727,85729,85731,85733,85735,85737,85739],{},[1681,85722,85723,85725],{},[898,85724,84775],{},[1765,85726,1767],{},[1761,85728,1909],{},[898,85730,1828],{},[1761,85732,1915],{"stretchy":1821},[898,85734,13835],{},[1761,85736,1834],{"separator":1833},[898,85738,2768],{},[1761,85740,1920],{"stretchy":1821},[902,85742,85743],{"encoding":904},"q_0 = Q(L,K)"," s tečnou ",[883,85746,85748],{"className":85747},[886],[888,85749,85750],{"xmlns":890},[892,85751,85752,85756],{},[895,85753,85754],{},[898,85755,22888],{},[902,85757,22888],{"encoding":904},[883,85759,85761],{"className":85760},[886],[888,85762,85763],{"xmlns":890},[892,85764,85765,85785],{},[895,85766,85767,85769,85775,85777,85783],{},[1761,85768,1822],{"stretchy":1821},[1681,85770,85771,85773],{},[898,85772,13835],{},[1765,85774,1767],{},[1761,85776,1834],{"separator":1833},[1681,85778,85779,85781],{},[898,85780,2768],{},[1765,85782,1767],{},[1761,85784,1844],{"stretchy":1821},[902,85786,85252],{"encoding":904},[883,85788,85790],{"className":85789},[886],[888,85791,85792],{"xmlns":890},[892,85793,85794,85800],{},[895,85795,85796,85798],{},[898,85797,6959],{"mathvariant":1969},[898,85799,2768],{},[902,85801,85404],{"encoding":904}," odhadnut diferenciálem (záporně vzatý sklon tečny).",[115,85804,85806],{"id":85805},"příklady-dvoufaktorový-model","Příklady (dvoufaktorový model)",[198,85808,85810],{"id":85809},"příklad-54","Příklad 5.4",[724,85812,80651,85813,1343,85855,1343,85872,1741],{},[883,85814,85816],{"className":85815},[886],[888,85817,85818],{"xmlns":890},[892,85819,85820,85852],{},[895,85821,85822,85824,85826,85828,85840],{},[898,85823,1828],{},[1761,85825,1909],{},[1765,85827,5433],{},[1824,85829,85830,85832],{},[898,85831,13835],{},[895,85833,85834,85836,85838],{},[1765,85835,1945],{},[898,85837,8726],{"mathvariant":1969},[1765,85839,2296],{},[1824,85841,85842,85844],{},[898,85843,2768],{},[895,85845,85846,85848,85850],{},[1765,85847,1945],{},[898,85849,8726],{"mathvariant":1969},[1765,85851,5486],{},[902,85853,85854],{"encoding":904},"Q = 15 L^{1\u002F2} K^{1\u002F3}",[883,85856,85858],{"className":85857},[886],[888,85859,85860],{"xmlns":890},[892,85861,85862,85870],{},[895,85863,85864,85866,85868],{},[898,85865,13835],{},[1761,85867,1909],{},[1765,85869,13077],{},[902,85871,81025],{"encoding":904},[883,85873,85875],{"className":85874},[886],[888,85876,85877],{"xmlns":890},[892,85878,85879,85887],{},[895,85880,85881,85883,85885],{},[898,85882,2768],{},[1761,85884,1909],{},[1765,85886,7160],{},[902,85888,85889],{"encoding":904},"K = 100",[724,85891,85892],{},[38,85893,85894],{},"(a) Rychlost změny produkce vzhledem k práci.",[883,85896,85898],{"className":85897},[886],[888,85899,85900],{"xmlns":890,"display":1930},[892,85901,85902,86016],{},[895,85903,85904,85906,85912,85914,85922,85924,85932,85946,85958,85960,85962,85964,85970,85972,85974,85976,85978,85980,85982,85990,85992,86002,86004,86011,86013],{},[898,85905,6889],{},[1681,85907,85908,85910],{},[898,85909,1839],{},[898,85911,13835],{},[1761,85913,1909],{},[2015,85915,85916,85918,85920],{},[898,85917,1828],{},[898,85919,13835],{},[1761,85921,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,85923,1909],{},[6411,85925,85926],{"scriptlevel":1767,"displaystyle":1821},[4379,85927,85928,85930],{},[1765,85929,5433],{},[1765,85931,2296],{},[1824,85933,85934,85936],{},[898,85935,13835],{},[895,85937,85938,85940,85942,85944],{},[1761,85939,1885],{},[1765,85941,1945],{},[898,85943,8726],{"mathvariant":1969},[1765,85945,2296],{},[1824,85947,85948,85950],{},[898,85949,2768],{},[895,85951,85952,85954,85956],{},[1765,85953,1945],{},[898,85955,8726],{"mathvariant":1969},[1765,85957,5486],{},[1761,85959,1834],{"separator":1833},[3315,85961],{"width":19322},[898,85963,6889],{},[1681,85965,85966,85968],{},[898,85967,1839],{},[898,85969,13835],{},[1761,85971,1915],{"stretchy":1821},[1765,85973,13077],{},[1761,85975,1834],{"separator":1833},[1765,85977,7160],{},[1761,85979,1920],{"stretchy":1821},[1761,85981,1909],{},[6411,85983,85984],{"scriptlevel":1767,"displaystyle":1821},[4379,85985,85986,85988],{},[1765,85987,5433],{},[1765,85989,2296],{},[1761,85991,2447],{},[6411,85993,85994],{"scriptlevel":1767,"displaystyle":1821},[4379,85995,85996,85998],{},[1765,85997,1945],{},[12161,85999,86000],{},[1765,86001,13077],{},[1761,86003,2447],{},[86005,86006,86007,86009],"mroot",{},[1765,86008,7160],{},[1765,86010,5486],{},[1761,86012,6803],{},[1765,86014,86015],{},"7,153.",[902,86017,86018],{"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.",[724,86020,86021,86022,48155,86044,14271,86061,86082,86083,86104],{},"Přibližná změna při ",[883,86023,86025],{"className":86024},[886],[888,86026,86027],{"xmlns":890},[892,86028,86029,86041],{},[895,86030,86031,86033,86035,86037,86039],{},[898,86032,13835],{},[1761,86034,2506],{},[1765,86036,13077],{},[1761,86038,2181],{},[1765,86040,42368],{},[902,86042,86043],{"encoding":904},"L: 20 \\to 21",[883,86045,86047],{"className":86046},[886],[888,86048,86049],{"xmlns":890},[892,86050,86051,86059],{},[895,86052,86053,86055,86057],{},[898,86054,2768],{},[1761,86056,1909],{},[1765,86058,7160],{},[902,86060,85889],{"encoding":904},[883,86062,86064],{"className":86063},[886],[888,86065,86066],{"xmlns":890},[892,86067,86068,86079],{},[895,86069,86070,86072,86074,86076],{},[898,86071,6959],{"mathvariant":1969},[898,86073,1828],{},[1761,86075,6803],{},[1765,86077,86078],{},"7,153",[902,86080,86081],{"encoding":904},"\\Delta Q \\approx 7{,}153",". Skutečně ",[883,86084,86086],{"className":86085},[886],[888,86087,86088],{"xmlns":890},[892,86089,86090,86101],{},[895,86091,86092,86094,86096,86098],{},[898,86093,6959],{"mathvariant":1969},[898,86095,1828],{},[1761,86097,6803],{},[1765,86099,86100],{},"26,888",[902,86102,86103],{"encoding":904},"\\Delta Q \\approx 26{,}888"," (dle knihy; zaokrouhlení v konkrétním výpočtu).",[724,86106,86107,86110],{},[38,86108,86109],{},"(b) Pokles kapitálu o 1"," (z 100 na 99).",[883,86112,86114],{"className":86113},[886],[888,86115,86116],{"xmlns":890,"display":1930},[892,86117,86118,86218],{},[895,86119,86120,86122,86128,86130,86138,86140,86142,86154,86168,86170,86172,86174,86180,86182,86184,86186,86188,86190,86192,86194,86198,86200,86213,86215],{},[898,86121,6889],{},[1681,86123,86124,86126],{},[898,86125,1839],{},[898,86127,2768],{},[1761,86129,1909],{},[2015,86131,86132,86134,86136],{},[898,86133,1828],{},[898,86135,2768],{},[1761,86137,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,86139,1909],{},[1765,86141,6321],{},[1824,86143,86144,86146],{},[898,86145,13835],{},[895,86147,86148,86150,86152],{},[1765,86149,1945],{},[898,86151,8726],{"mathvariant":1969},[1765,86153,2296],{},[1824,86155,86156,86158],{},[898,86157,2768],{},[895,86159,86160,86162,86164,86166],{},[1761,86161,1885],{},[1765,86163,2296],{},[898,86165,8726],{"mathvariant":1969},[1765,86167,5486],{},[1761,86169,1834],{"separator":1833},[3315,86171],{"width":19322},[898,86173,6889],{},[1681,86175,86176,86178],{},[898,86177,1839],{},[898,86179,2768],{},[1761,86181,1915],{"stretchy":1821},[1765,86183,13077],{},[1761,86185,1834],{"separator":1833},[1765,86187,7160],{},[1761,86189,1920],{"stretchy":1821},[1761,86191,1909],{},[1765,86193,6321],{},[12161,86195,86196],{},[1765,86197,13077],{},[1761,86199,2447],{},[6411,86201,86202],{"scriptlevel":1767,"displaystyle":1821},[4379,86203,86204,86206],{},[1765,86205,1945],{},[86005,86207,86208,86211],{},[1765,86209,86210],{},"10000",[1765,86212,5486],{},[1761,86214,6803],{},[1765,86216,86217],{},"4,525.",[902,86219,86220],{"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.",[724,86222,86223,86224,4178,86241,2162],{},"Produkce poklesne přibližně o 4,525 (z ",[883,86225,86227],{"className":86226},[886],[888,86228,86229],{"xmlns":890},[892,86230,86231,86238],{},[895,86232,86233,86235],{},[1761,86234,6803],{},[1765,86236,86237],{},"905,126",[902,86239,86240],{"encoding":904},"\\approx 905{,}126",[883,86242,86244],{"className":86243},[886],[888,86245,86246],{"xmlns":890},[892,86247,86248,86255],{},[895,86249,86250,86252],{},[1761,86251,6803],{},[1765,86253,86254],{},"900,601",[902,86256,86257],{"encoding":904},"\\approx 900{,}601",[724,86259,86260,7199,86307,1343,86329,2162],{},[38,86261,86262,86263,2068,86285],{},"(c) Změna ",[883,86264,86266],{"className":86265},[886],[888,86267,86268],{"xmlns":890},[892,86269,86270,86282],{},[895,86271,86272,86274,86276,86278,86280],{},[898,86273,13835],{},[1761,86275,2506],{},[1765,86277,13077],{},[1761,86279,2181],{},[1765,86281,5433],{},[902,86283,86284],{"encoding":904},"L: 20 \\to 15",[883,86286,86288],{"className":86287},[886],[888,86289,86290],{"xmlns":890},[892,86291,86292,86304],{},[895,86293,86294,86296,86298,86300,86302],{},[898,86295,2768],{},[1761,86297,2506],{},[1765,86299,7160],{},[1761,86301,2181],{},[1765,86303,12845],{},[902,86305,86306],{"encoding":904},"K: 100 \\to 150",[883,86308,86310],{"className":86309},[886],[888,86311,86312],{"xmlns":890},[892,86313,86314,86326],{},[895,86315,86316,86318,86320,86322,86324],{},[898,86317,4346],{},[898,86319,13835],{},[1761,86321,1909],{},[1761,86323,1885],{},[1765,86325,6321],{},[902,86327,86328],{"encoding":904},"dL = -5",[883,86330,86332],{"className":86331},[886],[888,86333,86334],{"xmlns":890},[892,86335,86336,86346],{},[895,86337,86338,86340,86342,86344],{},[898,86339,4346],{},[898,86341,2768],{},[1761,86343,1909],{},[1765,86345,7190],{},[902,86347,86348],{"encoding":904},"dK = 50",[883,86350,86352],{"className":86351},[886],[888,86353,86354],{"xmlns":890,"display":1930},[892,86355,86356,86444],{},[895,86357,86358,86360,86362,86364,86366,86372,86374,86376,86378,86380,86382,86384,86386,86388,86390,86392,86394,86396,86402,86404,86406,86408,86410,86412,86414,86416,86418,86420,86422,86424,86426,86428,86430,86432,86435,86437,86439,86441],{},[898,86359,4346],{},[898,86361,1828],{},[1761,86363,1909],{},[898,86365,6889],{},[1681,86367,86368,86370],{},[898,86369,1839],{},[898,86371,13835],{},[1761,86373,1915],{"stretchy":1821},[1765,86375,13077],{},[1761,86377,1834],{"separator":1833},[1765,86379,7160],{},[1761,86381,1920],{"stretchy":1821},[1761,86383,2447],{},[1761,86385,1915],{"stretchy":1821},[1761,86387,1885],{},[1765,86389,6321],{},[1761,86391,1920],{"stretchy":1821},[1761,86393,1964],{},[898,86395,6889],{},[1681,86397,86398,86400],{},[898,86399,1839],{},[898,86401,2768],{},[1761,86403,1915],{"stretchy":1821},[1765,86405,13077],{},[1761,86407,1834],{"separator":1833},[1765,86409,7160],{},[1761,86411,1920],{"stretchy":1821},[1761,86413,2447],{},[1765,86415,7190],{},[1761,86417,1909],{},[1765,86419,86078],{},[1761,86421,2447],{},[1761,86423,1915],{"stretchy":1821},[1761,86425,1885],{},[1765,86427,6321],{},[1761,86429,1920],{"stretchy":1821},[1761,86431,1964],{},[1765,86433,86434],{},"4,525",[1761,86436,2447],{},[1765,86438,7190],{},[1761,86440,6803],{},[1765,86442,86443],{},"190,485.",[902,86445,86446],{"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.",[724,86448,86449],{},"Produkce vzroste přibližně z 905,126 na 995,611.",[198,86451,86453],{"id":86452},"příklad-55","Příklad 5.5",[724,86455,86456,86457,86493,86494,1741],{},"Pro produkci ",[883,86458,86460],{"className":86459},[886],[888,86461,86462],{"xmlns":890},[892,86463,86464,86490],{},[895,86465,86466,86468,86470,86472,86474,86476,86478,86480,86486],{},[898,86467,1828],{},[1761,86469,1915],{"stretchy":1821},[898,86471,13835],{},[1761,86473,1834],{"separator":1833},[898,86475,2768],{},[1761,86477,1920],{"stretchy":1821},[1761,86479,1909],{},[86005,86481,86482,86484],{},[898,86483,13835],{},[1765,86485,5486],{},[12161,86487,86488],{},[898,86489,2768],{},[902,86491,86492],{"encoding":904},"Q(L, K) = \\sqrt[3]{L}\\sqrt{K}"," mají izokvanty rovnici ",[883,86495,86497],{"className":86496},[886],[888,86498,86499],{"xmlns":890},[892,86500,86501,86517],{},[895,86502,86503,86509,86513,86515],{},[86005,86504,86505,86507],{},[898,86506,13835],{},[1765,86508,5486],{},[12161,86510,86511],{},[898,86512,2768],{},[1761,86514,1909],{},[898,86516,84775],{},[902,86518,86519],{"encoding":904},"\\sqrt[3]{L}\\sqrt{K} = q",[724,86521,86522,86523,1741],{},"Umocněním na druhou: ",[883,86524,86526],{"className":86525},[886],[888,86527,86528],{"xmlns":890},[892,86529,86530,86554],{},[895,86531,86532,86534,86536,86542,86544],{},[898,86533,2768],{},[1761,86535,1909],{},[1824,86537,86538,86540],{},[898,86539,84775],{},[1765,86541,2296],{},[898,86543,8726],{"mathvariant":1969},[86005,86545,86546,86552],{},[1824,86547,86548,86550],{},[898,86549,13835],{},[1765,86551,2296],{},[1765,86553,5486],{},[902,86555,86556],{"encoding":904},"K = q^2 \u002F \\sqrt[3]{L^2}",[120,86558,86559,86599,86639],{},[123,86560,86561],{},[883,86562,86564],{"className":86563},[886],[888,86565,86566],{"xmlns":890},[892,86567,86568,86596],{},[895,86569,86570,86572,86574,86576,86578,86580,86582,86584,86586],{},[898,86571,84775],{},[1761,86573,1909],{},[1765,86575,1945],{},[1761,86577,8044],{},[898,86579,2768],{},[1761,86581,1909],{},[1765,86583,1945],{},[898,86585,8726],{"mathvariant":1969},[86005,86587,86588,86594],{},[1824,86589,86590,86592],{},[898,86591,13835],{},[1765,86593,2296],{},[1765,86595,5486],{},[902,86597,86598],{"encoding":904},"q = 1 \\Rightarrow K = 1\u002F\\sqrt[3]{L^2}",[123,86600,86601],{},[883,86602,86604],{"className":86603},[886],[888,86605,86606],{"xmlns":890},[892,86607,86608,86636],{},[895,86609,86610,86612,86614,86616,86618,86620,86622,86624,86626],{},[898,86611,84775],{},[1761,86613,1909],{},[1765,86615,2296],{},[1761,86617,8044],{},[898,86619,2768],{},[1761,86621,1909],{},[1765,86623,2318],{},[898,86625,8726],{"mathvariant":1969},[86005,86627,86628,86634],{},[1824,86629,86630,86632],{},[898,86631,13835],{},[1765,86633,2296],{},[1765,86635,5486],{},[902,86637,86638],{"encoding":904},"q = 2 \\Rightarrow K = 4\u002F\\sqrt[3]{L^2}",[123,86640,86641],{},[883,86642,86644],{"className":86643},[886],[888,86645,86646],{"xmlns":890},[892,86647,86648,86676],{},[895,86649,86650,86652,86654,86656,86658,86660,86662,86664,86666],{},[898,86651,84775],{},[1761,86653,1909],{},[1765,86655,5486],{},[1761,86657,8044],{},[898,86659,2768],{},[1761,86661,1909],{},[1765,86663,8056],{},[898,86665,8726],{"mathvariant":1969},[86005,86667,86668,86674],{},[1824,86669,86670,86672],{},[898,86671,13835],{},[1765,86673,2296],{},[1765,86675,5486],{},[902,86677,86678],{"encoding":904},"q = 3 \\Rightarrow K = 9\u002F\\sqrt[3]{L^2}",[724,86680,86681],{},[614,86682,86683,86684,10518,86705,1741],{},"Obrázek 5.5 — tři klesající konvexní izokvanty v rovině ",[883,86685,86687],{"className":86686},[886],[888,86688,86689],{"xmlns":890},[892,86690,86691,86703],{},[895,86692,86693,86695,86697,86699,86701],{},[1761,86694,1915],{"stretchy":1821},[898,86696,13835],{},[1761,86698,1834],{"separator":1833},[898,86700,2768],{},[1761,86702,1920],{"stretchy":1821},[902,86704,84901],{"encoding":904},[883,86706,86708],{"className":86707},[886],[888,86709,86710],{"xmlns":890},[892,86711,86712,86728],{},[895,86713,86714,86716,86718,86720,86722,86724,86726],{},[898,86715,84775],{},[1761,86717,1909],{},[1765,86719,1945],{},[1761,86721,1834],{"separator":1833},[1765,86723,2296],{},[1761,86725,1834],{"separator":1833},[1765,86727,5486],{},[902,86729,86730],{"encoding":904},"q = 1, 2, 3",[198,86732,86734],{"id":86733},"příklad-56","Příklad 5.6",[724,86736,80651,86737,1741],{},[883,86738,86740],{"className":86739},[886],[888,86741,86742],{"xmlns":890},[892,86743,86744,86760],{},[895,86745,86746,86748,86750,86752,86754,86756],{},[898,86747,1828],{},[1761,86749,1909],{},[1765,86751,2296],{},[898,86753,13835],{},[1761,86755,1964],{},[12161,86757,86758],{},[898,86759,2768],{},[902,86761,86762],{"encoding":904},"Q = 2L + \\sqrt{K}",[883,86764,86766],{"className":86765},[886],[888,86767,86768],{"xmlns":890,"display":1930},[892,86769,86770,86812],{},[895,86771,86772,86774,86780,86782,86784,86786,86788,86790,86796,86798,86810],{},[898,86773,6889],{},[1681,86775,86776,86778],{},[898,86777,1839],{},[898,86779,13835],{},[1761,86781,1909],{},[1765,86783,2296],{},[1761,86785,1834],{"separator":1833},[3315,86787],{"width":3317},[898,86789,6889],{},[1681,86791,86792,86794],{},[898,86793,1839],{},[898,86795,2768],{},[1761,86797,1909],{},[4379,86799,86800,86802],{},[1765,86801,1945],{},[895,86803,86804,86806],{},[1765,86805,2296],{},[12161,86807,86808],{},[898,86809,2768],{},[898,86811,1741],{"mathvariant":1969},[902,86813,86814],{"encoding":904},"MP_L = 2, \\qquad MP_K = \\frac{1}{2\\sqrt{K}}.",[883,86816,86818],{"className":86817},[886],[888,86819,86820],{"xmlns":890,"display":1930},[892,86821,86822,86886],{},[895,86823,86824,86826,86828,86830,86832,86834,86856,86858,86876,86878,86880,86884],{},[898,86825,6889],{},[898,86827,8051],{},[898,86829,1655],{},[898,86831,1912],{},[1761,86833,1909],{},[4379,86835,86836,86846],{},[895,86837,86838,86840],{},[898,86839,6889],{},[1681,86841,86842,86844],{},[898,86843,1839],{},[898,86845,13835],{},[895,86847,86848,86850],{},[898,86849,6889],{},[1681,86851,86852,86854],{},[898,86853,1839],{},[898,86855,2768],{},[1761,86857,1909],{},[4379,86859,86860,86862],{},[1765,86861,2296],{},[6411,86863,86864],{"scriptlevel":1767,"displaystyle":1821},[4379,86865,86866,86868],{},[1765,86867,1945],{},[895,86869,86870,86872],{},[1765,86871,2296],{},[12161,86873,86874],{},[898,86875,2768],{},[1761,86877,1909],{},[1765,86879,2318],{},[12161,86881,86882],{},[898,86883,2768],{},[898,86885,1741],{"mathvariant":1969},[902,86887,86888],{"encoding":904},"MRTS = \\frac{MP_L}{MP_K} = \\frac{2}{\\tfrac{1}{2\\sqrt{K}}} = 4\\sqrt{K}.",[724,86890,86891,86892,86935,86936,86975,86976,1741],{},"Například ",[883,86893,86895],{"className":86894},[886],[888,86896,86897],{"xmlns":890},[892,86898,86899,86932],{},[895,86900,86901,86903,86905,86907,86909,86911,86913,86915,86917,86919,86921,86923,86927,86929],{},[898,86902,6889],{},[898,86904,8051],{},[898,86906,1655],{},[898,86908,1912],{},[1761,86910,1915],{"stretchy":1821},[1765,86912,2318],{},[1761,86914,1834],{"separator":1833},[1765,86916,5512],{},[1761,86918,1920],{"stretchy":1821},[1761,86920,1909],{},[1765,86922,2318],{},[12161,86924,86925],{},[1765,86926,5512],{},[1761,86928,6803],{},[1765,86930,86931],{},"10,58",[902,86933,86934],{"encoding":904},"MRTS(4, 7) = 4\\sqrt{7} \\approx 10{,}58",". Klesne-li práce z 4 na 3, je k udržení produkce ",[883,86937,86939],{"className":86938},[886],[888,86940,86941],{"xmlns":890},[892,86942,86943,86972],{},[895,86944,86945,86947,86949,86951,86953,86955,86957,86959,86961,86963,86967,86969],{},[898,86946,1828],{},[1761,86948,1915],{"stretchy":1821},[1765,86950,2318],{},[1761,86952,1834],{"separator":1833},[1765,86954,5512],{},[1761,86956,1920],{"stretchy":1821},[1761,86958,1909],{},[1765,86960,2454],{},[1761,86962,1964],{},[12161,86964,86965],{},[1765,86966,5512],{},[1761,86968,6803],{},[1765,86970,86971],{},"10,646",[902,86973,86974],{"encoding":904},"Q(4,7) = 8 + \\sqrt{7} \\approx 10{,}646"," třeba zvýšit kapitál přibližně o ",[883,86977,86979],{"className":86978},[886],[888,86980,86981],{"xmlns":890},[892,86982,86983,86991],{},[895,86984,86985,86987],{},[1765,86986,2318],{},[12161,86988,86989],{},[1765,86990,5512],{},[902,86992,86993],{"encoding":904},"4\\sqrt{7}",[724,86995,86996,86997,87017],{},"Pokud se práce naopak zvýší ze 4 na 6 (",[883,86998,87000],{"className":86999},[886],[888,87001,87002],{"xmlns":890},[892,87003,87004,87014],{},[895,87005,87006,87008,87010,87012],{},[898,87007,4346],{},[898,87009,13835],{},[1761,87011,1909],{},[1765,87013,2296],{},[902,87015,87016],{"encoding":904},"dL = 2","), k udržení produkce stačí snížit kapitál o",[883,87019,87021],{"className":87020},[886],[888,87022,87023],{"xmlns":890,"display":1930},[892,87024,87025,87074],{},[895,87026,87027,87029,87031,87033,87035,87037,87039,87041,87043,87045,87047,87049,87051,87053,87055,87057,87059,87061,87063,87067,87069,87071],{},[898,87028,4346],{},[898,87030,2768],{},[1761,87032,1909],{},[1761,87034,1885],{},[898,87036,6889],{},[898,87038,8051],{},[898,87040,1655],{},[898,87042,1912],{},[1761,87044,1915],{"stretchy":1821},[1765,87046,2318],{},[1761,87048,1834],{"separator":1833},[1765,87050,5512],{},[1761,87052,1920],{"stretchy":1821},[1761,87054,2447],{},[1765,87056,2296],{},[1761,87058,1909],{},[1761,87060,1885],{},[1765,87062,2454],{},[12161,87064,87065],{},[1765,87066,5512],{},[1761,87068,6803],{},[1761,87070,1885],{},[1765,87072,87073],{},"21,17.",[902,87075,87076],{"encoding":904},"dK = -MRTS(4,7)\\cdot 2 = -8\\sqrt{7} \\approx -21{,}17.",[115,87078,87080],{"id":87079},"shrnutí-kapitoly-5","Shrnutí kapitoly 5",[724,87082,87083,87084,1343,87086,2068,87088,87090,87091,87094,87095,87098],{},"Hlavními faktory produkce jsou ",[38,87085,78892],{},[38,87087,78908],{},[38,87089,78924],{},"; půda je standardní exogenní proměnná. Přicházejí proto v úvahu ",[38,87092,87093],{},"jednofaktorový"," (pouze práce) a ",[38,87096,87097],{},"dvoufaktorový"," (práce + kapitál) model.",[724,87100,87101,87102,87105,87106,87108,87109,87111,87112,30220,87115,87134,87135,87152,87153,87170,87171,87193,87194,8412,87213,1741],{},"V ",[38,87103,87104],{},"1F modelu"," se definuje ",[38,87107,14063],{}," (derivace produkce podle práce) a ",[38,87110,78827],{}," (podíl produkce a práce). Produkční funkce má typický tvar díky ",[38,87113,87114],{},"zákonu klesajících výnosů",[883,87116,87118],{"className":87117},[886],[888,87119,87120],{"xmlns":890},[892,87121,87122,87132],{},[895,87123,87124,87126],{},[898,87125,6889],{},[1681,87127,87128,87130],{},[898,87129,1839],{},[898,87131,13835],{},[902,87133,14083],{"encoding":904}," nejprve roste, od inflexního bodu ",[883,87136,87138],{"className":87137},[886],[888,87139,87140],{"xmlns":890},[892,87141,87142,87150],{},[895,87143,87144],{},[1681,87145,87146,87148],{},[898,87147,13835],{},[1765,87149,1767],{},[902,87151,79536],{"encoding":904}," klesá a v bodě ",[883,87154,87156],{"className":87155},[886],[888,87157,87158],{"xmlns":890},[892,87159,87160,87168],{},[895,87161,87162],{},[1681,87163,87164,87166],{},[898,87165,13835],{},[1765,87167,1945],{},[902,87169,17250],{"encoding":904}," dosahuje nuly (maximum produkce). Platí ",[38,87172,87173,87174],{},"princip maximalizace ",[883,87175,87177],{"className":87176},[886],[888,87178,87179],{"xmlns":890},[892,87180,87181,87191],{},[895,87182,87183,87185],{},[898,87184,8309],{},[1681,87186,87187,87189],{},[898,87188,1839],{},[898,87190,13835],{},[902,87192,78611],{"encoding":904},": v bodě maxima ",[883,87195,87197],{"className":87196},[886],[888,87198,87199],{"xmlns":890},[892,87200,87201,87211],{},[895,87202,87203,87205],{},[898,87204,8309],{},[1681,87206,87207,87209],{},[898,87208,1839],{},[898,87210,13835],{},[902,87212,78611],{"encoding":904},[883,87214,87216],{"className":87215},[886],[888,87217,87218],{"xmlns":890},[892,87219,87220,87240],{},[895,87221,87222,87224,87230,87232,87234],{},[898,87223,6889],{},[1681,87225,87226,87228],{},[898,87227,1839],{},[898,87229,13835],{},[1761,87231,1909],{},[898,87233,8309],{},[1681,87235,87236,87238],{},[898,87237,1839],{},[898,87239,13835],{},[902,87241,78641],{"encoding":904},[724,87243,87244,87245,87248,87249,1989,87252,87281,87282,87299,87300,87303,87304,87333,87334,87336,87337,12146,87367,87389],{},"Ve ",[38,87246,87247],{},"2F modelu"," se obvykle používají ",[38,87250,87251],{},"Cobb-Douglasovy funkce",[883,87253,87255],{"className":87254},[886],[888,87256,87257],{"xmlns":890},[892,87258,87259,87279],{},[895,87260,87261,87263,87265,87267,87273],{},[898,87262,1828],{},[1761,87264,1909],{},[898,87266,8309],{},[1824,87268,87269,87271],{},[898,87270,13835],{},[898,87272,207],{},[1824,87274,87275,87277],{},[898,87276,2768],{},[898,87278,4302],{},[902,87280,78708],{"encoding":904},", které reflektují proporcionalitu změn vstupů a výstupu. Podle ",[883,87283,87285],{"className":87284},[886],[888,87286,87287],{"xmlns":890},[892,87288,87289,87297],{},[895,87290,87291,87293,87295],{},[898,87292,207],{},[1761,87294,1964],{},[898,87296,4302],{},[902,87298,78802],{"encoding":904}," rozlišujeme ",[38,87301,87302],{},"konstantní, rostoucí, klesající výnosy z rozsahu",". Mezní produkty ",[883,87305,87307],{"className":87306},[886],[888,87308,87309],{"xmlns":890},[892,87310,87311,87331],{},[895,87312,87313,87315,87321,87323,87325],{},[898,87314,6889],{},[1681,87316,87317,87319],{},[898,87318,1839],{},[898,87320,13835],{},[1761,87322,1834],{"separator":1833},[898,87324,6889],{},[1681,87326,87327,87329],{},[898,87328,1839],{},[898,87330,2768],{},[902,87332,78739],{"encoding":904}," jsou parciální derivace, totální diferenciál dává přibližnou změnu produkce. ",[38,87335,13818],{}," jsou indiferenční křivky produkční funkce. Podíl ",[883,87338,87340],{"className":87339},[886],[888,87341,87342],{"xmlns":890},[892,87343,87344,87364],{},[895,87345,87346,87348,87354,87356,87358],{},[898,87347,6889],{},[1681,87349,87350,87352],{},[898,87351,1839],{},[898,87353,13835],{},[898,87355,8726],{"mathvariant":1969},[898,87357,6889],{},[1681,87359,87360,87362],{},[898,87361,1839],{},[898,87363,2768],{},[902,87365,87366],{"encoding":904},"MP_L\u002FMP_K",[38,87368,87369,87370,1920],{},"mezní míra technické substituce (",[883,87371,87373],{"className":87372},[886],[888,87374,87375],{"xmlns":890},[892,87376,87377,87387],{},[895,87378,87379,87381,87383,87385],{},[898,87380,6889],{},[898,87382,8051],{},[898,87384,1655],{},[898,87386,1912],{},[902,87388,14637],{"encoding":904}," — udává, o kolik se musí změnit kapitál při jednotkové změně práce pro zachování produkce.",[115,87391,53867],{"id":53866},[152,87393,87394,87397,87400,87403,87406,87409,87412,87415,87418,87421,87424],{},[123,87395,87396],{},"Jaké jsou faktory produkce?",[123,87398,87399],{},"Jak se dospěje k jednofaktorovému a dvoufaktorovému modelu produkce?",[123,87401,87402],{},"Jak je zadána produkční funkce u jednofaktorového modelu?",[123,87404,87405],{},"Co udává mezní produkt práce?",[123,87407,87408],{},"Co musí respektovat průběh křivky produkce?",[123,87410,87411],{},"Jak lze matematicky vyjádřit zákon klesajících výnosů?",[123,87413,87414],{},"Jaký základní ekonomický požadavek respektují Cobb-Douglasovy funkce?",[123,87416,87417],{},"Jak se vypočtou mezní produkty práce a kapitálu?",[123,87419,87420],{},"Jak se stanoví přibližná změna produkce v závislosti na změnách práce a kapitálu?",[123,87422,87423],{},"Co vyjadřují izokvanty? Jaké jsou jejich typické vlastnosti?",[123,87425,87426],{},"Jak se vypočte mezní míra technické substituce a co vyjadřuje?",[115,87428,87430],{"id":87429},"úlohy-51517","Úlohy 5.1–5.17",[198,87432,44471],{"id":44470},[724,87434,87435,87438,87439,87461,87462,1343,87482,1343,87502,87522],{},[38,87436,87437],{},"5.1"," Je dána produkce ",[883,87440,87442],{"className":87441},[886],[888,87443,87444],{"xmlns":890},[892,87445,87446,87458],{},[895,87447,87448,87450,87452,87454],{},[898,87449,1828],{},[1761,87451,1909],{},[1765,87453,2633],{},[12161,87455,87456],{},[898,87457,13835],{},[902,87459,87460],{"encoding":904},"Q = 10\\sqrt{L}",". (a) Vypočtěte ",[883,87463,87465],{"className":87464},[886],[888,87466,87467],{"xmlns":890},[892,87468,87469,87479],{},[895,87470,87471,87473,87475,87477],{},[898,87472,1828],{},[1761,87474,1915],{"stretchy":1821},[1765,87476,1945],{},[1761,87478,1920],{"stretchy":1821},[902,87480,87481],{"encoding":904},"Q(1)",[883,87483,87485],{"className":87484},[886],[888,87486,87487],{"xmlns":890},[892,87488,87489,87499],{},[895,87490,87491,87493,87495,87497],{},[898,87492,1828],{},[1761,87494,1915],{"stretchy":1821},[1765,87496,2318],{},[1761,87498,1920],{"stretchy":1821},[902,87500,87501],{"encoding":904},"Q(4)",[883,87503,87505],{"className":87504},[886],[888,87506,87507],{"xmlns":890},[892,87508,87509,87519],{},[895,87510,87511,87513,87515,87517],{},[898,87512,1828],{},[1761,87514,1915],{"stretchy":1821},[1765,87516,8056],{},[1761,87518,1920],{"stretchy":1821},[902,87520,87521],{"encoding":904},"Q(9)",". (b) Rozhodněte, kdy produkce roste, resp. klesá. (c) Rozhodněte, kdy je křivka produkce konvexní, resp. konkávní. (d) Načrtněte křivku produkce.",[724,87524,87525,87438,87528,87564,87565,87578,87579,87598,87599,87625,87626,4178,87639,87652],{},[38,87526,87527],{},"5.2",[883,87529,87531],{"className":87530},[886],[888,87532,87533],{"xmlns":890},[892,87534,87535,87561],{},[895,87536,87537,87539,87541,87543,87545,87551,87553,87555],{},[898,87538,1828],{},[1761,87540,1909],{},[1761,87542,1885],{},[1765,87544,6865],{},[1824,87546,87547,87549],{},[898,87548,13835],{},[1765,87550,5486],{},[1761,87552,1964],{},[1765,87554,8056],{},[1824,87556,87557,87559],{},[898,87558,13835],{},[1765,87560,2296],{},[902,87562,87563],{"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 ",[883,87566,87568],{"className":87567},[886],[888,87569,87570],{"xmlns":890},[892,87571,87572,87576],{},[895,87573,87574],{},[898,87575,13835],{},[902,87577,13835],{"encoding":904}," (počet pracovníků), které maximalizuje produkci a stanovte příslušné maximum produkce. (d) Načrtněte křivku produkce. (e) Najděte mezní produkt práce ",[883,87580,87582],{"className":87581},[886],[888,87583,87584],{"xmlns":890},[892,87585,87586,87596],{},[895,87587,87588,87590],{},[898,87589,6889],{},[1681,87591,87592,87594],{},[898,87593,1839],{},[898,87595,13835],{},[902,87597,14083],{"encoding":904},". (f) Vypočtěte ",[883,87600,87602],{"className":87601},[886],[888,87603,87604],{"xmlns":890},[892,87605,87606,87622],{},[895,87607,87608,87610,87616,87618,87620],{},[898,87609,6889],{},[1681,87611,87612,87614],{},[898,87613,1839],{},[898,87615,13835],{},[1761,87617,1915],{"stretchy":1821},[1765,87619,2633],{},[1761,87621,1920],{"stretchy":1821},[902,87623,87624],{"encoding":904},"MP_L(10)"," a ekonomicky interpretujte. (g) Určete přibližnou změnu produkce v důsledku zvýšení počtu pracovníků z ",[883,87627,87629],{"className":87628},[886],[888,87630,87631],{"xmlns":890},[892,87632,87633,87637],{},[895,87634,87635],{},[1765,87636,2633],{},[902,87638,2633],{"encoding":904},[883,87640,87642],{"className":87641},[886],[888,87643,87644],{"xmlns":890},[892,87645,87646,87650],{},[895,87647,87648],{},[1765,87649,46296],{},[902,87651,46296],{"encoding":904}," a porovnejte se skutečnou změnou produkce.",[724,87654,87655,87658,87659,87681,87682,87710,87711,87742,87743,1741],{},[38,87656,87657],{},"5.3"," Pro zadanou produkci ověřte platnost zákona klesajících výnosů a charakterizujte vlastnosti mezního produktu práce:\n(a) ",[883,87660,87662],{"className":87661},[886],[888,87663,87664],{"xmlns":890},[892,87665,87666,87678],{},[895,87667,87668,87670,87672,87674],{},[898,87669,1828],{},[1761,87671,1909],{},[1765,87673,19148],{},[12161,87675,87676],{},[898,87677,13835],{},[902,87679,87680],{"encoding":904},"Q = 500\\sqrt{L}",".\n(b) ",[883,87683,87685],{"className":87684},[886],[888,87686,87687],{"xmlns":890},[892,87688,87689,87707],{},[895,87690,87691,87693,87695,87697,87701,87703,87705],{},[898,87692,1828],{},[1761,87694,1909],{},[1765,87696,34111],{},[12161,87698,87699],{},[898,87700,13835],{},[1761,87702,1885],{},[1765,87704,2318],{},[898,87706,13835],{},[902,87708,87709],{"encoding":904},"Q = 300\\sqrt{L} - 4L",".\n(c) ",[883,87712,87714],{"className":87713},[886],[888,87715,87716],{"xmlns":890},[892,87717,87718,87739],{},[895,87719,87720,87722,87724,87726,87728,87730,87733],{},[898,87721,1828],{},[1761,87723,1909],{},[1765,87725,7190],{},[898,87727,13835],{},[1761,87729,1885],{},[1765,87731,87732],{},"0,01",[1824,87734,87735,87737],{},[898,87736,13835],{},[1765,87738,2296],{},[902,87740,87741],{"encoding":904},"Q = 50L - 0{,}01 L^{2}",".\n(d) ",[883,87744,87746],{"className":87745},[886],[888,87747,87748],{"xmlns":890},[892,87749,87750,87776],{},[895,87751,87752,87754,87756,87758,87760,87766,87768,87770],{},[898,87753,1828],{},[1761,87755,1909],{},[1761,87757,1885],{},[1765,87759,72189],{},[1824,87761,87762,87764],{},[898,87763,13835],{},[1765,87765,5486],{},[1761,87767,1964],{},[1765,87769,8056],{},[1824,87771,87772,87774],{},[898,87773,13835],{},[1765,87775,2296],{},[902,87777,87778],{"encoding":904},"Q = -0{,}3 L^{3} + 9 L^{2}",[724,87780,87781,87784,87785,6699,87804,76176,87821,1741],{},[38,87782,87783],{},"5.4"," Dokažte, že má-li průměrný produkt práce ",[883,87786,87788],{"className":87787},[886],[888,87789,87790],{"xmlns":890},[892,87791,87792,87802],{},[895,87793,87794,87796],{},[898,87795,8309],{},[1681,87797,87798,87800],{},[898,87799,1839],{},[898,87801,13835],{},[902,87803,78611],{"encoding":904},[883,87805,87807],{"className":87806},[886],[888,87808,87809],{"xmlns":890},[892,87810,87811,87819],{},[895,87812,87813],{},[1681,87814,87815,87817],{},[898,87816,13835],{},[1765,87818,1767],{},[902,87820,79536],{"encoding":904},[883,87822,87824],{"className":87823},[886],[888,87825,87826],{"xmlns":890},[892,87827,87828,87868],{},[895,87829,87830,87832,87838,87840,87846,87848,87850,87852,87858,87860,87866],{},[898,87831,8309],{},[1681,87833,87834,87836],{},[898,87835,1839],{},[898,87837,13835],{},[1761,87839,1915],{"stretchy":1821},[1681,87841,87842,87844],{},[898,87843,13835],{},[1765,87845,1767],{},[1761,87847,1920],{"stretchy":1821},[1761,87849,1909],{},[898,87851,6889],{},[1681,87853,87854,87856],{},[898,87855,1839],{},[898,87857,13835],{},[1761,87859,1915],{"stretchy":1821},[1681,87861,87862,87864],{},[898,87863,13835],{},[1765,87865,1767],{},[1761,87867,1920],{"stretchy":1821},[902,87869,87870],{"encoding":904},"AP_L(L_0) = MP_L(L_0)",[724,87872,87873,87438,87876,25627,87912,87925,87926,87945],{},[38,87874,87875],{},"5.5",[883,87877,87879],{"className":87878},[886],[888,87880,87881],{"xmlns":890},[892,87882,87883,87909],{},[895,87884,87885,87887,87889,87891,87893,87899,87901,87903],{},[898,87886,1828],{},[1761,87888,1909],{},[1761,87890,1885],{},[1765,87892,6910],{},[1824,87894,87895,87897],{},[898,87896,13835],{},[1765,87898,5486],{},[1761,87900,1964],{},[1765,87902,2291],{},[1824,87904,87905,87907],{},[898,87906,13835],{},[1765,87908,2296],{},[902,87910,87911],{"encoding":904},"Q = -0{,}2 L^{3} + 12 L^{2}",[883,87913,87915],{"className":87914},[886],[888,87916,87917],{"xmlns":890},[892,87918,87919,87923],{},[895,87920,87921],{},[898,87922,13835],{},[902,87924,13835],{"encoding":904}," je počet pracovníků. (a) Určete počet pracovníků, při kterém je dosaženo nejvyšší produktivity práce (= maximálního průměrného produktu práce ",[883,87927,87929],{"className":87928},[886],[888,87930,87931],{"xmlns":890},[892,87932,87933,87943],{},[895,87934,87935,87937],{},[898,87936,8309],{},[1681,87938,87939,87941],{},[898,87940,1839],{},[898,87942,13835],{},[902,87944,78611],{"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.",[198,87947,87949],{"id":87948},"dvoufaktorový-model","Dvoufaktorový model",[724,87951,87952,87955,87956,87681,87982,87710,88024,1741],{},[38,87953,87954],{},"5.6"," Pro zadanou produkci rozhodněte, jaké výnosy z rozsahu představují:\n(a) ",[883,87957,87959],{"className":87958},[886],[888,87960,87961],{"xmlns":890},[892,87962,87963,87979],{},[895,87964,87965,87967,87969,87971,87973],{},[898,87966,1828],{},[1761,87968,1909],{},[1765,87970,5512],{},[898,87972,13835],{},[1824,87974,87975,87977],{},[898,87976,2768],{},[1765,87978,2296],{},[902,87980,87981],{"encoding":904},"Q = 7 L K^{2}",[883,87983,87985],{"className":87984},[886],[888,87986,87987],{"xmlns":890},[892,87988,87989,88021],{},[895,87990,87991,87993,87995,87997,88009],{},[898,87992,1828],{},[1761,87994,1909],{},[1765,87996,7190],{},[1824,87998,87999,88001],{},[898,88000,13835],{},[895,88002,88003,88005,88007],{},[1765,88004,2296],{},[898,88006,8726],{"mathvariant":1969},[1765,88008,5486],{},[1824,88010,88011,88013],{},[898,88012,2768],{},[895,88014,88015,88017,88019],{},[1765,88016,1945],{},[898,88018,8726],{"mathvariant":1969},[1765,88020,5486],{},[902,88022,88023],{"encoding":904},"Q = 50 L^{2\u002F3} K^{1\u002F3}",[883,88025,88027],{"className":88026},[886],[888,88028,88029],{"xmlns":890},[892,88030,88031,88063],{},[895,88032,88033,88035,88037,88039,88051],{},[898,88034,1828],{},[1761,88036,1909],{},[1765,88038,7771],{},[1824,88040,88041,88043],{},[898,88042,13835],{},[895,88044,88045,88047,88049],{},[1765,88046,5486],{},[898,88048,8726],{"mathvariant":1969},[1765,88050,6321],{},[1824,88052,88053,88055],{},[898,88054,2768],{},[895,88056,88057,88059,88061],{},[1765,88058,2296],{},[898,88060,8726],{"mathvariant":1969},[1765,88062,6321],{},[902,88064,88065],{"encoding":904},"Q = 18 L^{3\u002F5} K^{2\u002F5}",[724,88067,88068,87438,88071,88113,88114,1343,88132,88151,88152,88169],{},[38,88069,88070],{},"5.7",[883,88072,88074],{"className":88073},[886],[888,88075,88076],{"xmlns":890},[892,88077,88078,88110],{},[895,88079,88080,88082,88084,88086,88098],{},[898,88081,1828],{},[1761,88083,1909],{},[1765,88085,2633],{},[1824,88087,88088,88090],{},[898,88089,13835],{},[895,88091,88092,88094,88096],{},[1765,88093,1945],{},[898,88095,8726],{"mathvariant":1969},[1765,88097,2296],{},[1824,88099,88100,88102],{},[898,88101,2768],{},[895,88103,88104,88106,88108],{},[1765,88105,1945],{},[898,88107,8726],{"mathvariant":1969},[1765,88109,2296],{},[902,88111,88112],{"encoding":904},"Q = 10 L^{1\u002F2} K^{1\u002F2}",". (a) Vypočtěte produkci pro ",[883,88115,88117],{"className":88116},[886],[888,88118,88119],{"xmlns":890},[892,88120,88121,88129],{},[895,88122,88123,88125,88127],{},[898,88124,13835],{},[1761,88126,1909],{},[1765,88128,24175],{},[902,88130,88131],{"encoding":904},"L = 400",[883,88133,88135],{"className":88134},[886],[888,88136,88137],{"xmlns":890},[892,88138,88139,88148],{},[895,88140,88141,88143,88145],{},[898,88142,2768],{},[1761,88144,1909],{},[1765,88146,88147],{},"17576",[902,88149,88150],{"encoding":904},"K = 17576",". (b) Rozhodněte o tom, jaké výnosy z rozsahu představuje a vyložte, jak se změní produkce, jestliže se vstupy ",[883,88153,88155],{"className":88154},[886],[888,88156,88157],{"xmlns":890},[892,88158,88159,88167],{},[895,88160,88161,88163,88165],{},[898,88162,13835],{},[1761,88164,1834],{"separator":1833},[898,88166,2768],{},[902,88168,82963],{"encoding":904}," zdvojnásobí.",[724,88171,88172,88175,88176,88113,88207,1343,88225,73562,88243,88273,88274,88304,88305,4178,88318,88332,88333,4178,88346,88359],{},[38,88173,88174],{},"5.8"," V jedné empirické studii (40. léta 20. století) ze sektoru manufaktur odhadli Cobb a Douglas produkci ze zjištěných údajů ve tvaru ",[883,88177,88179],{"className":88178},[886],[888,88180,88181],{"xmlns":890},[892,88182,88183,88204],{},[895,88184,88185,88187,88189,88192,88198],{},[898,88186,1828],{},[1761,88188,1909],{},[1765,88190,88191],{},"1,01",[1824,88193,88194,88196],{},[898,88195,13835],{},[1765,88197,27763],{},[1824,88199,88200,88202],{},[898,88201,2768],{},[1765,88203,27822],{},[902,88205,88206],{"encoding":904},"Q = 1{,}01 L^{0{,}75} K^{0{,}25}",[883,88208,88210],{"className":88209},[886],[888,88211,88212],{"xmlns":890},[892,88213,88214,88222],{},[895,88215,88216,88218,88220],{},[898,88217,13835],{},[1761,88219,1909],{},[1765,88221,34773],{},[902,88223,88224],{"encoding":904},"L = 250",[883,88226,88228],{"className":88227},[886],[888,88229,88230],{"xmlns":890},[892,88231,88232,88240],{},[895,88233,88234,88236,88238],{},[898,88235,2768],{},[1761,88237,1909],{},[1765,88239,6854],{},[902,88241,88242],{"encoding":904},"K = 1000",[883,88244,88246],{"className":88245},[886],[888,88247,88248],{"xmlns":890},[892,88249,88250,88270],{},[895,88251,88252,88254,88260,88262,88264,88266,88268],{},[898,88253,6889],{},[1681,88255,88256,88258],{},[898,88257,1839],{},[898,88259,13835],{},[1761,88261,1915],{"stretchy":1821},[1765,88263,34773],{},[1761,88265,1834],{"separator":1833},[1765,88267,6854],{},[1761,88269,1920],{"stretchy":1821},[902,88271,88272],{"encoding":904},"MP_L(250, 1000)"," a výsledek ekonomicky interpretujte. (c) Vypočtěte ",[883,88275,88277],{"className":88276},[886],[888,88278,88279],{"xmlns":890},[892,88280,88281,88301],{},[895,88282,88283,88285,88291,88293,88295,88297,88299],{},[898,88284,6889],{},[1681,88286,88287,88289],{},[898,88288,1839],{},[898,88290,2768],{},[1761,88292,1915],{"stretchy":1821},[1765,88294,34773],{},[1761,88296,1834],{"separator":1833},[1765,88298,6854],{},[1761,88300,1920],{"stretchy":1821},[902,88302,88303],{"encoding":904},"MP_K(250, 1000)"," a výsledek ekonomicky interpretujte. (d) Odhadněte změnu produkce v důsledku zvýšení ",[883,88306,88308],{"className":88307},[886],[888,88309,88310],{"xmlns":890},[892,88311,88312,88316],{},[895,88313,88314],{},[898,88315,13835],{},[902,88317,13835],{"encoding":904},[883,88319,88321],{"className":88320},[886],[888,88322,88323],{"xmlns":890},[892,88324,88325,88330],{},[895,88326,88327],{},[1765,88328,88329],{},"260",[902,88331,88329],{"encoding":904}," a současném poklesu ",[883,88334,88336],{"className":88335},[886],[888,88337,88338],{"xmlns":890},[892,88339,88340,88344],{},[895,88341,88342],{},[898,88343,2768],{},[902,88345,2768],{"encoding":904},[883,88347,88349],{"className":88348},[886],[888,88350,88351],{"xmlns":890},[892,88352,88353,88357],{},[895,88354,88355],{},[1765,88356,19229],{},[902,88358,19229],{"encoding":904}," vzhledem k hladině dle (a) a porovnejte se skutečnou změnou produkce.",[724,88361,88362,88365,88366,1741],{},[38,88363,88364],{},"5.9"," Ověřte platnost zákona klesajících výnosů pro produkci ",[883,88367,88369],{"className":88368},[886],[888,88370,88371],{"xmlns":890},[892,88372,88373,88393],{},[895,88374,88375,88377,88379,88381,88387],{},[898,88376,1828],{},[1761,88378,1909],{},[1765,88380,2633],{},[1824,88382,88383,88385],{},[898,88384,13835],{},[1765,88386,72189],{},[1824,88388,88389,88391],{},[898,88390,2768],{},[1765,88392,5426],{},[902,88394,88395],{"encoding":904},"Q = 10 L^{0{,}3} K^{0{,}5}",[724,88397,88398,88401,88402,84559,88425,14432,88438,3927,88488,2162],{},[38,88399,88400],{},"5.10"," Dokažte, že pro homogenní funkci ",[883,88403,88405],{"className":88404},[886],[888,88406,88407],{"xmlns":890},[892,88408,88409,88423],{},[895,88410,88411,88413,88415,88417,88419,88421],{},[898,88412,1828],{},[1761,88414,1915],{"stretchy":1821},[898,88416,13835],{},[1761,88418,1834],{"separator":1833},[898,88420,2768],{},[1761,88422,1920],{"stretchy":1821},[902,88424,14036],{"encoding":904},[883,88426,88428],{"className":88427},[886],[888,88429,88430],{"xmlns":890},[892,88431,88432,88436],{},[895,88433,88434],{},[898,88435,40888],{},[902,88437,40888],{"encoding":904},[883,88439,88441],{"className":88440},[886],[888,88442,88443],{"xmlns":890},[892,88444,88445,88485],{},[895,88446,88447,88449,88457,88459,88461,88469,88471,88473,88475,88477,88479,88481,88483],{},[898,88448,13835],{},[2015,88450,88451,88453,88455],{},[898,88452,1828],{},[898,88454,13835],{},[1761,88456,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,88458,1964],{},[898,88460,2768],{},[2015,88462,88463,88465,88467],{},[898,88464,1828],{},[898,88466,2768],{},[1761,88468,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,88470,1909],{},[898,88472,40888],{},[898,88474,1828],{},[1761,88476,1915],{"stretchy":1821},[898,88478,13835],{},[1761,88480,1834],{"separator":1833},[898,88482,2768],{},[1761,88484,1920],{"stretchy":1821},[902,88486,88487],{"encoding":904},"L Q'_L + K Q'_K = n Q(L, K)",[614,88489,84534],{},[724,88491,88492,88495],{},[38,88493,88494],{},"5.11"," Ověřte platnost Eulerovy věty (úloha 5.10) pro Cobb-Douglasovu produkční funkci.",[724,88497,88498,87438,88501,88541,88542,1343,88564,1343,88586,88608],{},[38,88499,88500],{},"5.12",[883,88502,88504],{"className":88503},[886],[888,88505,88506],{"xmlns":890},[892,88507,88508,88538],{},[895,88509,88510,88512,88514,88526],{},[898,88511,1828],{},[1761,88513,1909],{},[1824,88515,88516,88518],{},[898,88517,13835],{},[895,88519,88520,88522,88524],{},[1765,88521,1945],{},[898,88523,8726],{"mathvariant":1969},[1765,88525,5486],{},[1824,88527,88528,88530],{},[898,88529,2768],{},[895,88531,88532,88534,88536],{},[1765,88533,1945],{},[898,88535,8726],{"mathvariant":1969},[1765,88537,2318],{},[902,88539,88540],{"encoding":904},"Q = L^{1\u002F3} K^{1\u002F4}",". (a) Najděte rovnici izokvant. (b) Najděte rovnici izokvant pro produkci ",[883,88543,88545],{"className":88544},[886],[888,88546,88547],{"xmlns":890},[892,88548,88549,88561],{},[895,88550,88551,88557,88559],{},[1681,88552,88553,88555],{},[898,88554,84775],{},[1765,88556,1767],{},[1761,88558,1909],{},[1765,88560,1945],{},[902,88562,88563],{"encoding":904},"q_0 = 1",[883,88565,88567],{"className":88566},[886],[888,88568,88569],{"xmlns":890},[892,88570,88571,88583],{},[895,88572,88573,88579,88581],{},[1681,88574,88575,88577],{},[898,88576,84775],{},[1765,88578,1945],{},[1761,88580,1909],{},[1765,88582,2296],{},[902,88584,88585],{"encoding":904},"q_1 = 2",[883,88587,88589],{"className":88588},[886],[888,88590,88591],{"xmlns":890},[892,88592,88593,88605],{},[895,88594,88595,88601,88603],{},[1681,88596,88597,88599],{},[898,88598,84775],{},[1765,88600,2296],{},[1761,88602,1909],{},[1765,88604,5486],{},[902,88606,88607],{"encoding":904},"q_2 = 3",". (c) Načrtněte izokvanty.",[724,88610,88611,87438,88614,88654,88655,1343,88683,1343,88711,1343,88739,1343,88768,1343,88797,1343,88826,1343,88855,1343,88884,1741],{},[38,88612,88613],{},"5.13",[883,88615,88617],{"className":88616},[886],[888,88618,88619],{"xmlns":890},[892,88620,88621,88651],{},[895,88622,88623,88625,88627,88639],{},[898,88624,1828],{},[1761,88626,1909],{},[1824,88628,88629,88631],{},[898,88630,13835],{},[895,88632,88633,88635,88637],{},[1765,88634,1945],{},[898,88636,8726],{"mathvariant":1969},[1765,88638,5486],{},[1824,88640,88641,88643],{},[898,88642,2768],{},[895,88644,88645,88647,88649],{},[1765,88646,1945],{},[898,88648,8726],{"mathvariant":1969},[1765,88650,2296],{},[902,88652,88653],{"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): ",[883,88656,88658],{"className":88657},[886],[888,88659,88660],{"xmlns":890},[892,88661,88662,88680],{},[895,88663,88664,88670,88672,88674,88676,88678],{},[1681,88665,88666,88668],{},[898,88667,8309],{},[1765,88669,1945],{},[1761,88671,1822],{"stretchy":1821},[1765,88673,1945],{},[1761,88675,12468],{"separator":1833},[1765,88677,1945],{},[1761,88679,1844],{"stretchy":1821},[902,88681,88682],{"encoding":904},"A_1[1; 1]",[883,88684,88686],{"className":88685},[886],[888,88687,88688],{"xmlns":890},[892,88689,88690,88708],{},[895,88691,88692,88698,88700,88702,88704,88706],{},[1681,88693,88694,88696],{},[898,88695,8309],{},[1765,88697,2296],{},[1761,88699,1822],{"stretchy":1821},[1765,88701,1945],{},[1761,88703,12468],{"separator":1833},[1765,88705,2454],{},[1761,88707,1844],{"stretchy":1821},[902,88709,88710],{"encoding":904},"A_2[1; 8]",[883,88712,88714],{"className":88713},[886],[888,88715,88716],{"xmlns":890},[892,88717,88718,88736],{},[895,88719,88720,88726,88728,88730,88732,88734],{},[1681,88721,88722,88724],{},[898,88723,8309],{},[1765,88725,5486],{},[1761,88727,1822],{"stretchy":1821},[1765,88729,1945],{},[1761,88731,12468],{"separator":1833},[1765,88733,70575],{},[1761,88735,1844],{"stretchy":1821},[902,88737,88738],{"encoding":904},"A_3[1; 27]",[883,88740,88742],{"className":88741},[886],[888,88743,88744],{"xmlns":890},[892,88745,88746,88765],{},[895,88747,88748,88754,88756,88758,88760,88763],{},[1681,88749,88750,88752],{},[898,88751,8309],{},[1765,88753,2318],{},[1761,88755,1822],{"stretchy":1821},[1765,88757,2296],{},[1761,88759,12468],{"separator":1833},[1765,88761,88762],{},"0,353",[1761,88764,1844],{"stretchy":1821},[902,88766,88767],{"encoding":904},"A_4[2; 0{,}353]",[883,88769,88771],{"className":88770},[886],[888,88772,88773],{"xmlns":890},[892,88774,88775,88794],{},[895,88776,88777,88783,88785,88787,88789,88792],{},[1681,88778,88779,88781],{},[898,88780,8309],{},[1765,88782,6321],{},[1761,88784,1822],{"stretchy":1821},[1765,88786,2296],{},[1761,88788,12468],{"separator":1833},[1765,88790,88791],{},"2,828",[1761,88793,1844],{"stretchy":1821},[902,88795,88796],{"encoding":904},"A_5[2; 2{,}828]",[883,88798,88800],{"className":88799},[886],[888,88801,88802],{"xmlns":890},[892,88803,88804,88823],{},[895,88805,88806,88812,88814,88816,88818,88821],{},[1681,88807,88808,88810],{},[898,88809,8309],{},[1765,88811,2340],{},[1761,88813,1822],{"stretchy":1821},[1765,88815,2296],{},[1761,88817,12468],{"separator":1833},[1765,88819,88820],{},"9,545",[1761,88822,1844],{"stretchy":1821},[902,88824,88825],{"encoding":904},"A_6[2; 9{,}545]",[883,88827,88829],{"className":88828},[886],[888,88830,88831],{"xmlns":890},[892,88832,88833,88852],{},[895,88834,88835,88841,88843,88845,88847,88850],{},[1681,88836,88837,88839],{},[898,88838,8309],{},[1765,88840,5512],{},[1761,88842,1822],{"stretchy":1821},[1765,88844,68537],{},[1761,88846,12468],{"separator":1833},[1765,88848,88849],{},"0,544",[1761,88851,1844],{"stretchy":1821},[902,88853,88854],{"encoding":904},"A_7[1{,}5; 0{,}544]",[883,88856,88858],{"className":88857},[886],[888,88859,88860],{"xmlns":890},[892,88861,88862,88881],{},[895,88863,88864,88870,88872,88874,88876,88879],{},[1681,88865,88866,88868],{},[898,88867,8309],{},[1765,88869,2454],{},[1761,88871,1822],{"stretchy":1821},[1765,88873,68537],{},[1761,88875,12468],{"separator":1833},[1765,88877,88878],{},"14,696",[1761,88880,1844],{"stretchy":1821},[902,88882,88883],{"encoding":904},"A_8[1{,}5; 14{,}696]",[883,88885,88887],{"className":88886},[886],[888,88888,88889],{"xmlns":890},[892,88890,88891,88909],{},[895,88892,88893,88899,88901,88903,88905,88907],{},[1681,88894,88895,88897],{},[898,88896,8309],{},[1765,88898,8056],{},[1761,88900,1822],{"stretchy":1821},[1765,88902,2296],{},[1761,88904,12468],{"separator":1833},[1765,88906,6321],{},[1761,88908,1844],{"stretchy":1821},[902,88910,88911],{"encoding":904},"A_9[2; 5]",[724,88913,88914,88917],{},[38,88915,88916],{},"5.14"," Dokažte, že izokvanty Cobb-Douglasovy produkční funkce jsou klesající a konvexní.",[724,88919,88920,88923,88924,88954,88955,88968,88969,88982,88983,73295,89002,89021,89022,1741],{},[38,88921,88922],{},"5.15"," Produkce firmy je dána vztahem ",[883,88925,88927],{"className":88926},[886],[888,88928,88929],{"xmlns":890},[892,88930,88931,88951],{},[895,88932,88933,88935,88937,88939,88945],{},[898,88934,1828],{},[1761,88936,1909],{},[1765,88938,2296],{},[1824,88940,88941,88943],{},[898,88942,13835],{},[1765,88944,5426],{},[1824,88946,88947,88949],{},[898,88948,2768],{},[1765,88950,27822],{},[902,88952,88953],{"encoding":904},"Q = 2 L^{0{,}5} K^{0{,}25}",". (a) Vypočtěte produkci, mezní produkt práce a mezní produkt kapitálu, zaměstnává-li firma ",[883,88956,88958],{"className":88957},[886],[888,88959,88960],{"xmlns":890},[892,88961,88962,88966],{},[895,88963,88964],{},[1765,88965,7160],{},[902,88967,7160],{"encoding":904}," pracovníků a disponuje-li ",[883,88970,88972],{"className":88971},[886],[888,88973,88974],{"xmlns":890},[892,88975,88976,88980],{},[895,88977,88978],{},[1765,88979,68413],{},[902,88981,68413],{"encoding":904}," jednotkami kapitálu. (b) Určete mezní míru technické substituce ",[883,88984,88986],{"className":88985},[886],[888,88987,88988],{"xmlns":890},[892,88989,88990,89000],{},[895,88991,88992,88994,88996,88998],{},[898,88993,6889],{},[898,88995,8051],{},[898,88997,1655],{},[898,88999,1912],{},[902,89001,14637],{"encoding":904},[883,89003,89005],{"className":89004},[886],[888,89006,89007],{"xmlns":890},[892,89008,89009,89019],{},[895,89010,89011,89013,89015,89017],{},[898,89012,6889],{},[898,89014,8051],{},[898,89016,1655],{},[898,89018,1912],{},[902,89020,14637],{"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 ",[883,89023,89025],{"className":89024},[886],[888,89026,89027],{"xmlns":890},[892,89028,89029,89034],{},[895,89030,89031],{},[1765,89032,89033],{},"95",[902,89035,89033],{"encoding":904},[724,89037,89038,87438,89041,74969,89073,89092,89093,89106,89107,89120,89121,89134],{},[38,89039,89040],{},"5.16",[883,89042,89044],{"className":89043},[886],[888,89045,89046],{"xmlns":890},[892,89047,89048,89070],{},[895,89049,89050,89052,89054,89060,89062,89064],{},[898,89051,1828],{},[1761,89053,1909],{},[1824,89055,89056,89058],{},[898,89057,2768],{},[1765,89059,2296],{},[1761,89061,1964],{},[1765,89063,2296],{},[1824,89065,89066,89068],{},[898,89067,13835],{},[1765,89069,2296],{},[902,89071,89072],{"encoding":904},"Q = K^{2} + 2 L^{2}",[883,89074,89076],{"className":89075},[886],[888,89077,89078],{"xmlns":890},[892,89079,89080,89090],{},[895,89081,89082,89084,89086,89088],{},[898,89083,6889],{},[898,89085,8051],{},[898,89087,1655],{},[898,89089,1912],{},[902,89091,14637],{"encoding":904},". (b) Odhadněte změnu práce potřebné k udržení produkce, která je realizována ",[883,89094,89096],{"className":89095},[886],[888,89097,89098],{"xmlns":890},[892,89099,89100,89104],{},[895,89101,89102],{},[1765,89103,7190],{},[902,89105,7190],{"encoding":904}," pracovníky a ",[883,89108,89110],{"className":89109},[886],[888,89111,89112],{"xmlns":890},[892,89113,89114,89118],{},[895,89115,89116],{},[1765,89117,81595],{},[902,89119,81595],{"encoding":904}," jednotkami kapitálu, jestliže se kapitál sníží na ",[883,89122,89124],{"className":89123},[886],[888,89125,89126],{"xmlns":890},[892,89127,89128,89132],{},[895,89129,89130],{},[1765,89131,5467],{},[902,89133,5467],{"encoding":904}," jednotek.",[724,89136,89137,89140,89141,14432,89171,1741],{},[38,89138,89139],{},"5.17"," Odvoďte, že pro Cobb-Douglasovu produkční funkci ",[883,89142,89144],{"className":89143},[886],[888,89145,89146],{"xmlns":890},[892,89147,89148,89168],{},[895,89149,89150,89152,89154,89156,89162],{},[898,89151,1828],{},[1761,89153,1909],{},[898,89155,8309],{},[1824,89157,89158,89160],{},[898,89159,13835],{},[898,89161,207],{},[1824,89163,89164,89166],{},[898,89165,2768],{},[898,89167,4302],{},[902,89169,89170],{"encoding":904},"Q = A L^{a} K^{b}",[883,89172,89174],{"className":89173},[886],[888,89175,89176],{"xmlns":890},[892,89177,89178,89208],{},[895,89179,89180,89182,89184,89186,89188,89190,89198,89200],{},[898,89181,6889],{},[898,89183,8051],{},[898,89185,1655],{},[898,89187,1912],{},[1761,89189,1909],{},[6411,89191,89192],{"scriptlevel":1767,"displaystyle":1821},[4379,89193,89194,89196],{},[898,89195,207],{},[898,89197,4302],{},[1761,89199,2447],{},[6411,89201,89202],{"scriptlevel":1767,"displaystyle":1821},[4379,89203,89204,89206],{},[898,89205,2768],{},[898,89207,13835],{},[902,89209,89210],{"encoding":904},"MRTS = \\tfrac{a}{b}\\cdot \\tfrac{K}{L}",[115,89212,5533],{"id":5532},[120,89214,89215,89248,89275,89284,89334,89365,89418,89441,89496,89569,89647,89690,89722,89755,89796,89868,89929,89995,90012,90085,90151,90203,90259,90293,90336],{},[123,89216,89217,89220,89221,40924,89234,89247],{},[38,89218,89219],{},"Faktory (vstupy) produkce:"," práce ",[883,89222,89224],{"className":89223},[886],[888,89225,89226],{"xmlns":890},[892,89227,89228,89232],{},[895,89229,89230],{},[898,89231,13835],{},[902,89233,13835],{"encoding":904},[883,89235,89237],{"className":89236},[886],[888,89238,89239],{"xmlns":890},[892,89240,89241,89245],{},[895,89242,89243],{},[898,89244,2768],{},[902,89246,2768],{"encoding":904},", půda.",[123,89249,89250,5675,89252,1741],{},[38,89251,44471],{},[883,89253,89255],{"className":89254},[886],[888,89256,89257],{"xmlns":890},[892,89258,89259,89273],{},[895,89260,89261,89263,89265,89267,89269,89271],{},[898,89262,1828],{},[1761,89264,1909],{},[898,89266,1828],{},[1761,89268,1915],{"stretchy":1821},[898,89270,13835],{},[1761,89272,1920],{"stretchy":1821},[902,89274,78522],{"encoding":904},[123,89276,89277,3927,89279,4590,89282,1741],{},[38,89278,859],{},[614,89280,89281],{},"production function",[38,89283,79025],{},[123,89285,89286,1989,89288,1741],{},[38,89287,79071],{},[883,89289,89291],{"className":89290},[886],[888,89292,89293],{"xmlns":890},[892,89294,89295,89331],{},[895,89296,89297,89299,89305,89307,89309,89311,89313,89315,89317,89319,89325,89327,89329],{},[898,89298,6889],{},[1681,89300,89301,89303],{},[898,89302,1839],{},[898,89304,13835],{},[1761,89306,1909],{},[898,89308,4346],{},[898,89310,1828],{},[898,89312,8726],{"mathvariant":1969},[898,89314,4346],{},[898,89316,13835],{},[1761,89318,1909],{},[1824,89320,89321,89323],{},[898,89322,1828],{},[1761,89324,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,89326,1915],{"stretchy":1821},[898,89328,13835],{},[1761,89330,1920],{"stretchy":1821},[902,89332,89333],{"encoding":904},"MP_L = dQ\u002FdL = Q'(L)",[123,89335,89336,1989,89338,1741],{},[38,89337,80006],{},[883,89339,89341],{"className":89340},[886],[888,89342,89343],{"xmlns":890},[892,89344,89345,89363],{},[895,89346,89347,89349,89355,89357,89359,89361],{},[898,89348,8309],{},[1681,89350,89351,89353],{},[898,89352,1839],{},[898,89354,13835],{},[1761,89356,1909],{},[898,89358,1828],{},[898,89360,8726],{"mathvariant":1969},[898,89362,13835],{},[902,89364,78590],{"encoding":904},[123,89366,89367,89369,89370,14432,89387,1741],{},[38,89368,79493],{}," — od určitého ",[883,89371,89373],{"className":89372},[886],[888,89374,89375],{"xmlns":890},[892,89376,89377,89385],{},[895,89378,89379],{},[1681,89380,89381,89383],{},[898,89382,13835],{},[1765,89384,1767],{},[902,89386,79536],{"encoding":904},[883,89388,89390],{"className":89389},[886],[888,89391,89392],{"xmlns":890},[892,89393,89394,89416],{},[895,89395,89396,89406,89408,89410,89412,89414],{},[1824,89397,89398,89400],{},[898,89399,1828],{},[895,89401,89402,89404],{},[1761,89403,6459],{"mathvariant":1969},[1761,89405,6459],{"mathvariant":1969},[1761,89407,1915],{"stretchy":1821},[898,89409,13835],{},[1761,89411,1920],{"stretchy":1821},[1761,89413,2058],{},[1765,89415,1767],{},[902,89417,79682],{"encoding":904},[123,89419,89420,1989,89423,89440],{},[38,89421,89422],{},"Inflexní bod",[883,89424,89426],{"className":89425},[886],[888,89427,89428],{"xmlns":890},[892,89429,89430,89438],{},[895,89431,89432],{},[1681,89433,89434,89436],{},[898,89435,13835],{},[1765,89437,1767],{},[902,89439,79536],{"encoding":904}," — přechod z konvexity do konkavity.",[123,89442,89443,1989,89446,5675,89463,1741],{},[38,89444,89445],{},"Bod maxima produkce",[883,89447,89449],{"className":89448},[886],[888,89450,89451],{"xmlns":890},[892,89452,89453,89461],{},[895,89454,89455],{},[1681,89456,89457,89459],{},[898,89458,13835],{},[1765,89460,1945],{},[902,89462,17250],{"encoding":904},[883,89464,89466],{"className":89465},[886],[888,89467,89468],{"xmlns":890},[892,89469,89470,89494],{},[895,89471,89472,89474,89480,89482,89488,89490,89492],{},[898,89473,6889],{},[1681,89475,89476,89478],{},[898,89477,1839],{},[898,89479,13835],{},[1761,89481,1915],{"stretchy":1821},[1681,89483,89484,89486],{},[898,89485,13835],{},[1765,89487,1945],{},[1761,89489,1920],{"stretchy":1821},[1761,89491,1909],{},[1765,89493,1767],{},[902,89495,79755],{"encoding":904},[123,89497,89498,89520,89521,14432,89540,1741],{},[38,89499,89500,89501],{},"Princip maximalizace ",[883,89502,89504],{"className":89503},[886],[888,89505,89506],{"xmlns":890},[892,89507,89508,89518],{},[895,89509,89510,89512],{},[898,89511,8309],{},[1681,89513,89514,89516],{},[898,89515,1839],{},[898,89517,13835],{},[902,89519,78611],{"encoding":904}," — v bodě maxima ",[883,89522,89524],{"className":89523},[886],[888,89525,89526],{"xmlns":890},[892,89527,89528,89538],{},[895,89529,89530,89532],{},[898,89531,8309],{},[1681,89533,89534,89536],{},[898,89535,1839],{},[898,89537,13835],{},[902,89539,78611],{"encoding":904},[883,89541,89543],{"className":89542},[886],[888,89544,89545],{"xmlns":890},[892,89546,89547,89567],{},[895,89548,89549,89551,89557,89559,89561],{},[898,89550,6889],{},[1681,89552,89553,89555],{},[898,89554,1839],{},[898,89556,13835],{},[1761,89558,1909],{},[898,89560,8309],{},[1681,89562,89563,89565],{},[898,89564,1839],{},[898,89566,13835],{},[902,89568,78641],{"encoding":904},[123,89570,89571,1989,89574,1343,89613,1343,89630,1741],{},[38,89572,89573],{},"Polynomiální produkční funkce",[883,89575,89577],{"className":89576},[886],[888,89578,89579],{"xmlns":890},[892,89580,89581,89611],{},[895,89582,89583,89585,89587,89589,89591,89593,89595,89601,89603,89605],{},[898,89584,1828],{},[1761,89586,1915],{"stretchy":1821},[898,89588,13835],{},[1761,89590,1920],{"stretchy":1821},[1761,89592,1909],{},[898,89594,207],{},[1824,89596,89597,89599],{},[898,89598,13835],{},[1765,89600,5486],{},[1761,89602,1964],{},[898,89604,4302],{},[1824,89606,89607,89609],{},[898,89608,13835],{},[1765,89610,2296],{},[902,89612,79873],{"encoding":904},[883,89614,89616],{"className":89615},[886],[888,89617,89618],{"xmlns":890},[892,89619,89620,89628],{},[895,89621,89622,89624,89626],{},[898,89623,207],{},[1761,89625,2058],{},[1765,89627,1767],{},[902,89629,4323],{"encoding":904},[883,89631,89633],{"className":89632},[886],[888,89634,89635],{"xmlns":890},[892,89636,89637,89645],{},[895,89638,89639,89641,89643],{},[898,89640,4302],{},[1761,89642,1763],{},[1765,89644,1767],{},[902,89646,22847],{"encoding":904},[123,89648,89649,1989,89652,1741],{},[38,89650,89651],{},"Diferenciál produkce",[883,89653,89655],{"className":89654},[886],[888,89656,89657],{"xmlns":890},[892,89658,89659,89687],{},[895,89660,89661,89663,89665,89667,89669,89671,89673,89675,89681,89683,89685],{},[898,89662,6959],{"mathvariant":1969},[898,89664,1828],{},[1761,89666,6803],{},[898,89668,4346],{},[898,89670,1828],{},[1761,89672,1909],{},[898,89674,6889],{},[1681,89676,89677,89679],{},[898,89678,1839],{},[898,89680,13835],{},[2761,89682,7057],{},[898,89684,4346],{},[898,89686,13835],{},[902,89688,89689],{"encoding":904},"\\Delta Q \\approx dQ = MP_L\\,dL",[123,89691,89692,5675,89694,1741],{},[38,89693,87949],{},[883,89695,89697],{"className":89696},[886],[888,89698,89699],{"xmlns":890},[892,89700,89701,89719],{},[895,89702,89703,89705,89707,89709,89711,89713,89715,89717],{},[898,89704,1828],{},[1761,89706,1909],{},[898,89708,1828],{},[1761,89710,1915],{"stretchy":1821},[898,89712,13835],{},[1761,89714,1834],{"separator":1833},[898,89716,2768],{},[1761,89718,1920],{"stretchy":1821},[902,89720,89721],{"encoding":904},"Q = Q(L, K)",[123,89723,89724,5675,89726,1741],{},[38,89725,82043],{},[883,89727,89729],{"className":89728},[886],[888,89730,89731],{"xmlns":890},[892,89732,89733,89753],{},[895,89734,89735,89737,89739,89741,89747],{},[898,89736,1828],{},[1761,89738,1909],{},[898,89740,8309],{},[1824,89742,89743,89745],{},[898,89744,13835],{},[898,89746,207],{},[1824,89748,89749,89751],{},[898,89750,2768],{},[898,89752,4302],{},[902,89754,78708],{"encoding":904},[123,89756,89757,5675,89760,89795],{},[38,89758,89759],{},"Ryzí Cobb-Douglas",[883,89761,89763],{"className":89762},[886],[888,89764,89765],{"xmlns":890},[892,89766,89767,89793],{},[895,89768,89769,89771,89773,89775,89781],{},[898,89770,1828],{},[1761,89772,1909],{},[898,89774,8309],{},[1824,89776,89777,89779],{},[898,89778,13835],{},[898,89780,207],{},[1824,89782,89783,89785],{},[898,89784,2768],{},[895,89786,89787,89789,89791],{},[1765,89788,1945],{},[1761,89790,1885],{},[898,89792,207],{},[902,89794,82870],{"encoding":904}," (konstantní výnosy).",[123,89797,89798,5675,89800,1741],{},[38,89799,83586],{},[883,89801,89803],{"className":89802},[886],[888,89804,89805],{"xmlns":890},[892,89806,89807,89865],{},[895,89808,89809,89811,89813,89815,89817,89819,89821,89823,89825,89827,89837,89839,89841,89851],{},[898,89810,1828],{},[1761,89812,1909],{},[898,89814,8309],{},[1761,89816,1822],{"stretchy":1821},[1761,89818,1915],{"stretchy":1821},[1765,89820,1945],{},[1761,89822,1885],{},[898,89824,207],{},[1761,89826,1920],{"stretchy":1821},[1824,89828,89829,89831],{},[898,89830,13835],{},[895,89832,89833,89835],{},[1761,89834,1885],{},[898,89836,4302],{},[1761,89838,1964],{},[898,89840,207],{},[1824,89842,89843,89845],{},[898,89844,2768],{},[895,89846,89847,89849],{},[1761,89848,1885],{},[898,89850,4302],{},[1824,89852,89853,89855],{},[1761,89854,1844],{"stretchy":1821},[895,89856,89857,89859,89861,89863],{},[1761,89858,1885],{},[1765,89860,1945],{},[898,89862,8726],{"mathvariant":1969},[898,89864,4302],{},[902,89866,89867],{"encoding":904},"Q = A[(1-a)L^{-b} + aK^{-b}]^{-1\u002Fb}",[123,89869,89870,3927,89873,4590,89895,3927,89898,89928],{},[38,89871,89872],{},"Lineární",[883,89874,89876],{"className":89875},[886],[888,89877,89878],{"xmlns":890},[892,89879,89880,89892],{},[895,89881,89882,89884,89886,89888,89890],{},[898,89883,207],{},[898,89885,13835],{},[1761,89887,1964],{},[898,89889,4302],{},[898,89891,2768],{},[902,89893,89894],{"encoding":904},"aL + bK",[38,89896,89897],{},"Leontiefova",[883,89899,89901],{"className":89900},[886],[888,89902,89903],{"xmlns":890},[892,89904,89905,89925],{},[895,89906,89907,89909,89911,89913,89915,89917,89919,89921,89923],{},[898,89908,83814],{},[1761,89910,60178],{},[1761,89912,1915],{"stretchy":1821},[898,89914,207],{},[898,89916,13835],{},[1761,89918,1834],{"separator":1833},[898,89920,4302],{},[898,89922,2768],{},[1761,89924,1920],{"stretchy":1821},[902,89926,89927],{"encoding":904},"\\min(aL, bK)",") produkční funkce.",[123,89930,89931,5675,89947,1741],{},[38,89932,89933,89934],{},"Homogenita stupně ",[883,89935,89937],{"className":89936},[886],[888,89938,89939],{"xmlns":890},[892,89940,89941,89945],{},[895,89942,89943],{},[898,89944,40888],{},[902,89946,40888],{"encoding":904},[883,89948,89950],{"className":89949},[886],[888,89951,89952],{"xmlns":890},[892,89953,89954,89992],{},[895,89955,89956,89958,89960,89962,89964,89966,89968,89970,89972,89974,89980,89982,89984,89986,89988,89990],{},[898,89957,1828],{},[1761,89959,1915],{"stretchy":1821},[898,89961,1719],{},[898,89963,13835],{},[1761,89965,1834],{"separator":1833},[898,89967,1719],{},[898,89969,2768],{},[1761,89971,1920],{"stretchy":1821},[1761,89973,1909],{},[1824,89975,89976,89978],{},[898,89977,1719],{},[898,89979,40888],{},[898,89981,1828],{},[1761,89983,1915],{"stretchy":1821},[898,89985,13835],{},[1761,89987,1834],{"separator":1833},[898,89989,2768],{},[1761,89991,1920],{"stretchy":1821},[902,89993,89994],{"encoding":904},"Q(rL, rK) = r^n Q(L, K)",[123,89996,89997,82968],{},[38,89998,82901,89999],{},[883,90000,90002],{"className":90001},[886],[888,90003,90004],{"xmlns":890},[892,90005,90006,90010],{},[895,90007,90008],{},[898,90009,8309],{},[902,90011,8309],{"encoding":904},[123,90013,90014,90016,90017,90039,90040,90062,90063,2162],{},[38,90015,82402],{}," — konstantní (",[883,90018,90020],{"className":90019},[886],[888,90021,90022],{"xmlns":890},[892,90023,90024,90036],{},[895,90025,90026,90028,90030,90032,90034],{},[898,90027,207],{},[1761,90029,1964],{},[898,90031,4302],{},[1761,90033,1909],{},[1765,90035,1945],{},[902,90037,90038],{"encoding":904},"a+b=1","), rostoucí (",[883,90041,90043],{"className":90042},[886],[888,90044,90045],{"xmlns":890},[892,90046,90047,90059],{},[895,90048,90049,90051,90053,90055,90057],{},[898,90050,207],{},[1761,90052,1964],{},[898,90054,4302],{},[1761,90056,1763],{},[1765,90058,1945],{},[902,90060,90061],{"encoding":904},"a+b>1","), klesající (",[883,90064,90066],{"className":90065},[886],[888,90067,90068],{"xmlns":890},[892,90069,90070,90082],{},[895,90071,90072,90074,90076,90078,90080],{},[898,90073,207],{},[1761,90075,1964],{},[898,90077,4302],{},[1761,90079,2058],{},[1765,90081,1945],{},[902,90083,90084],{"encoding":904},"a+b\u003C1",[123,90086,90087,1989,90089,1343,90119,1989,90121,1741],{},[38,90088,79071],{},[883,90090,90092],{"className":90091},[886],[888,90093,90094],{"xmlns":890},[892,90095,90096,90116],{},[895,90097,90098,90100,90106,90108],{},[898,90099,6889],{},[1681,90101,90102,90104],{},[898,90103,1839],{},[898,90105,13835],{},[1761,90107,1909],{},[2015,90109,90110,90112,90114],{},[898,90111,1828],{},[898,90113,13835],{},[1761,90115,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[902,90117,90118],{"encoding":904},"MP_L = Q'_L",[38,90120,81975],{},[883,90122,90124],{"className":90123},[886],[888,90125,90126],{"xmlns":890},[892,90127,90128,90148],{},[895,90129,90130,90132,90138,90140],{},[898,90131,6889],{},[1681,90133,90134,90136],{},[898,90135,1839],{},[898,90137,2768],{},[1761,90139,1909],{},[2015,90141,90142,90144,90146],{},[898,90143,1828],{},[898,90145,2768],{},[1761,90147,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[902,90149,90150],{"encoding":904},"MP_K = Q'_K",[123,90152,90153,1989,90155,1741],{},[38,90154,84189],{},[883,90156,90158],{"className":90157},[886],[888,90159,90160],{"xmlns":890},[892,90161,90162,90200],{},[895,90163,90164,90166,90168,90170,90172,90178,90180,90182,90184,90186,90188,90194,90196,90198],{},[898,90165,4346],{},[898,90167,1828],{},[1761,90169,1909],{},[898,90171,6889],{},[1681,90173,90174,90176],{},[898,90175,1839],{},[898,90177,13835],{},[2761,90179,7057],{},[898,90181,4346],{},[898,90183,13835],{},[1761,90185,1964],{},[898,90187,6889],{},[1681,90189,90190,90192],{},[898,90191,1839],{},[898,90193,2768],{},[2761,90195,7057],{},[898,90197,4346],{},[898,90199,2768],{},[902,90201,90202],{"encoding":904},"dQ = MP_L\\,dL + MP_K\\,dK",[123,90204,90205,5675,90207,1741],{},[38,90206,84534],{},[883,90208,90210],{"className":90209},[886],[888,90211,90212],{"xmlns":890},[892,90213,90214,90256],{},[895,90215,90216,90218,90226,90228,90230,90238,90240,90242,90244,90246,90248,90250,90252,90254],{},[898,90217,13835],{},[2015,90219,90220,90222,90224],{},[898,90221,1828],{},[898,90223,13835],{},[1761,90225,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,90227,1964],{},[898,90229,2768],{},[2015,90231,90232,90234,90236],{},[898,90233,1828],{},[898,90235,2768],{},[1761,90237,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,90239,1909],{},[898,90241,40888],{},[2761,90243,7057],{},[898,90245,1828],{},[1761,90247,1915],{"stretchy":1821},[898,90249,13835],{},[1761,90251,1834],{"separator":1833},[898,90253,2768],{},[1761,90255,1920],{"stretchy":1821},[902,90257,90258],{"encoding":904},"L Q'_L + K Q'_K = n\\,Q(L,K)",[123,90260,90261,90264,90265,1741],{},[38,90262,90263],{},"Izokvanta"," — křivka ",[883,90266,90268],{"className":90267},[886],[888,90269,90270],{"xmlns":890},[892,90271,90272,90290],{},[895,90273,90274,90276,90278,90280,90282,90284,90286,90288],{},[898,90275,1828],{},[1761,90277,1915],{"stretchy":1821},[898,90279,13835],{},[1761,90281,1834],{"separator":1833},[898,90283,2768],{},[1761,90285,1920],{"stretchy":1821},[1761,90287,1909],{},[898,90289,84775],{},[902,90291,90292],{"encoding":904},"Q(L, K) = q",[123,90294,90295,1989,90297,1741],{},[38,90296,84964],{},[883,90298,90300],{"className":90299},[886],[888,90301,90302],{"xmlns":890},[892,90303,90304,90334],{},[895,90305,90306,90308,90310,90312,90314,90316,90318,90324,90326,90328],{},[898,90307,6889],{},[898,90309,8051],{},[898,90311,1655],{},[898,90313,1912],{},[1761,90315,1909],{},[898,90317,6889],{},[1681,90319,90320,90322],{},[898,90321,1839],{},[898,90323,13835],{},[898,90325,8726],{"mathvariant":1969},[898,90327,6889],{},[1681,90329,90330,90332],{},[898,90331,1839],{},[898,90333,2768],{},[902,90335,78783],{"encoding":904},[123,90337,90338,1989,90341,1741],{},[38,90339,90340],{},"Substituční vztah",[883,90342,90344],{"className":90343},[886],[888,90345,90346],{"xmlns":890},[892,90347,90348,90372],{},[895,90349,90350,90352,90354,90356,90358,90360,90362,90364,90366,90368,90370],{},[898,90351,6959],{"mathvariant":1969},[898,90353,2768],{},[1761,90355,6803],{},[1761,90357,1885],{},[898,90359,6889],{},[898,90361,8051],{},[898,90363,1655],{},[898,90365,1912],{},[2761,90367,7057],{},[898,90369,4346],{},[898,90371,13835],{},[902,90373,90374],{"encoding":904},"\\Delta K \\approx -MRTS\\,dL",[115,90376,5968],{"id":5967},[120,90378,90379,90476,90483,90490],{},[123,90380,90381,1989,90383,90386,90387,1343,90390,90393,90394,90397,90398,90417,90418,5991,90437,90440,90441,90460,90461,2162],{},[38,90382,5983],{},[207,90384,784],{"className":90385,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace, totální diferenciál), ",[207,90388,5995],{"className":90389,"dataFsResolvedFilePath":764,"href":765},[210],[207,90391,793],{"className":90392,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace produkce s rozpočtovým omezením), ",[207,90395,880],{"className":90396,"dataFsResolvedFilePath":878,"href":879},[210]," (paralela: izokvanty ↔ indiferenční křivky, ",[883,90399,90401],{"className":90400},[886],[888,90402,90403],{"xmlns":890},[892,90404,90405,90415],{},[895,90406,90407,90409,90411,90413],{},[898,90408,6889],{},[898,90410,8051],{},[898,90412,1655],{},[898,90414,1912],{},[902,90416,14637],{"encoding":904}," ↔ ",[883,90419,90421],{"className":90420},[886],[888,90422,90423],{"xmlns":890},[892,90424,90425,90435],{},[895,90426,90427,90429,90431,90433],{},[898,90428,6889],{},[898,90430,8051],{},[898,90432,6849],{},[898,90434,1912],{},[902,90436,14641],{"encoding":904},[207,90438,7885],{"className":90439,"dataFsResolvedFilePath":827,"href":828},[210]," (analogie principu max ",[883,90442,90444],{"className":90443},[886],[888,90445,90446],{"xmlns":890},[892,90447,90448,90458],{},[895,90449,90450,90452],{},[898,90451,8309],{},[1681,90453,90454,90456],{},[898,90455,1839],{},[898,90457,13835],{},[902,90459,78611],{"encoding":904}," ↔ min ",[883,90462,90464],{"className":90463},[886],[888,90465,90466],{"xmlns":890},[892,90467,90468,90474],{},[895,90469,90470,90472],{},[898,90471,8309],{},[898,90473,6849],{},[902,90475,59538],{"encoding":904},[123,90477,90478,1989,90480,1741],{},[38,90479,7861],{},[207,90481,6000],{"className":90482,"dataFsResolvedFilePath":848,"href":849},[210],[123,90484,90485,1989,90487,1741],{},[38,90486,20247],{},[207,90488,1094],{"className":90489,"dataFsResolvedFilePath":838,"href":839},[210],[123,90491,90492,1989,90494,1741],{},[38,90493,6015],{},[207,90495,6021],{"className":90496,"dataFsResolvedFilePath":6019,"href":6020},[210],{"title":641,"searchDepth":642,"depth":642,"links":90498},[90499,90500,90501,90505,90507,90512,90513,90520,90521,90523,90524,90525,90527,90532,90533,90534,90538,90539],{"id":78806,"depth":642,"text":78807},{"id":78943,"depth":642,"text":78944},{"id":79046,"depth":642,"text":90502,"children":90503},"Mezní produkt práce (MPLMP_L)",[90504],{"id":79492,"depth":649,"text":79493},{"id":79981,"depth":642,"text":90506},"Průměrný produkt práce (APLAP_L)",{"id":80099,"depth":642,"text":80100,"children":90508},[90509,90510,90511],{"id":80336,"depth":649,"text":69479},{"id":80647,"depth":649,"text":80648},{"id":81367,"depth":649,"text":81368},{"id":81939,"depth":642,"text":81940},{"id":82042,"depth":642,"text":82043,"children":90514},[90515,90516,90518,90519],{"id":82401,"depth":649,"text":82402},{"id":82900,"depth":649,"text":90517},"Parametr efektivity AA",{"id":82971,"depth":649,"text":82972},{"id":41205,"depth":649,"text":83311},{"id":83498,"depth":642,"text":83499},{"id":83837,"depth":642,"text":90522},"Mezní produkty MPLMP_L, MPKMP_K a totální diferenciál",{"id":84528,"depth":642,"text":84529},{"id":78872,"depth":642,"text":13818},{"id":84939,"depth":642,"text":90526},"Mezní míra technické substituce (MRTSMRTS)",{"id":85805,"depth":642,"text":85806,"children":90528},[90529,90530,90531],{"id":85809,"depth":649,"text":85810},{"id":86452,"depth":649,"text":86453},{"id":86733,"depth":649,"text":86734},{"id":87079,"depth":642,"text":87080},{"id":53866,"depth":642,"text":53867},{"id":87429,"depth":642,"text":87430,"children":90535},[90536,90537],{"id":44470,"depth":649,"text":44471},{"id":87948,"depth":649,"text":87949},{"id":5532,"depth":642,"text":5533},{"id":5967,"depth":642,"text":5968},{},"\u002Ftopics\u002Fprodukce",{"title":78442,"description":641},[1138,1136],"topics\u002Fprodukce",[1128,13852,90546,90547,90548,78872,90549,90550],"produkcni-funkce","mpl-apl","cobb-douglas","mrts","euler","ZO2oG_qVOhQee90SJRry02Lau2bGvK2gaOFbwchTg1Y",{"id":90553,"title":90554,"body":90555,"course":1128,"courses":659,"created":6039,"description":641,"extension":661,"meta":99501,"navigation":664,"path":99502,"seo":99503,"sources":99504,"stem":99505,"tags":99506,"type":6050,"updated":677,"__hash__":99509},"topics\u002Ftopics\u002Fuzitecnost.md","Užitečnost, Cobb-Douglasova funkce užitečnosti a optimalizace spotřebitele",{"type":9,"value":90556,"toc":99475},[90557,90560,90562,90759,90768,90772,90775,90828,90832,90843,90847,90850,90867,90990,90996,91140,91150,91154,91189,91227,91275,91332,91392,91434,92010,92014,92097,92206,92299,92557,92560,92613,92724,92806,92810,92821,93054,93109,93115,93155,93218,93229,93420,93526,93679,93727,93732,93846,93884,94010,94056,94083,94160,94235,94315,94445,94506,94594,94598,94601,94670,94753,94760,94820,95130,95134,95140,95193,95209,95260,95398,95474,95587,95904,95908,95915,96075,96134,96138,96160,96257,96378,96492,96515,96578,96635,96887,96895,96899,96906,97160,97210,97266,97269,97433,97437,97535,97537,97569,97573,97706,97948,98132,98300,98607,98740,98927,98939,98941,99376,99378],[12,90558,90554],{"id":90559},"užitečnost-cobb-douglasova-funkce-užitečnosti-a-optimalizace-spotřebitele",[115,90561,16046],{"id":16045},[724,90563,90564,1989,90566,90597,90598,90601,90602,90632,90633,90651,90652,90692,90693,90696,90697,90710,90711,32283,90714,90727,90728,90741,90742,90755,90756,1741],{},[38,90565,880],{},[883,90567,90569],{"className":90568},[886],[888,90570,90571],{"xmlns":890},[892,90572,90573,90595],{},[895,90574,90575,90577,90579,90585,90587,90593],{},[898,90576,900],{},[1761,90578,1915],{"stretchy":1821},[1681,90580,90581,90583],{},[898,90582,1828],{},[1765,90584,1945],{},[1761,90586,1834],{"separator":1833},[1681,90588,90589,90591],{},[898,90590,1828],{},[1765,90592,2296],{},[1761,90594,1920],{"stretchy":1821},[902,90596,20377],{"encoding":904}," je číselné vyjádření uspokojení spotřebitele ze svazku zboží — v ordinalistickém přístupu slouží jen k ",[38,90599,90600],{},"uspořádání"," svazků (nikoli k měření v jednotkách). Klíčové nástroje jsou mezní užitečnosti ",[883,90603,90605],{"className":90604},[886],[888,90606,90607],{"xmlns":890},[892,90608,90609,90629],{},[895,90610,90611,90613,90619,90621],{},[898,90612,6889],{},[1681,90614,90615,90617],{},[898,90616,900],{},[898,90618,21824],{},[1761,90620,1909],{},[2015,90622,90623,90625,90627],{},[898,90624,900],{},[898,90626,21824],{},[1761,90628,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[902,90630,90631],{"encoding":904},"MU_i = U'_i",", indiferenční křivky ",[883,90634,90636],{"className":90635},[886],[888,90637,90638],{"xmlns":890},[892,90639,90640,90648],{},[895,90641,90642,90644,90646],{},[898,90643,900],{},[1761,90645,1909],{},[898,90647,2774],{},[902,90649,90650],{"encoding":904},"U = c"," a mezní míra komoditní substituce ",[883,90653,90655],{"className":90654},[886],[888,90656,90657],{"xmlns":890},[892,90658,90659,90689],{},[895,90660,90661,90663,90665,90667,90669,90671,90673,90679,90681,90683],{},[898,90662,6889],{},[898,90664,8051],{},[898,90666,6849],{},[898,90668,1912],{},[1761,90670,1909],{},[898,90672,6889],{},[1681,90674,90675,90677],{},[898,90676,900],{},[1765,90678,1945],{},[898,90680,8726],{"mathvariant":1969},[898,90682,6889],{},[1681,90684,90685,90687],{},[898,90686,900],{},[1765,90688,2296],{},[902,90690,90691],{"encoding":904},"MRCS = MU_1\u002FMU_2",". Tato stránka pokrývá ",[38,90694,90695],{},"teorii užitečnosti"," — funkce ",[883,90698,90700],{"className":90699},[886],[888,90701,90702],{"xmlns":890},[892,90703,90704,90708],{},[895,90705,90706],{},[898,90707,900],{},[902,90709,900],{"encoding":904},", její vlastnosti, Cobb-Douglasův tvar, indiferenční křivky a MRCS. ",[38,90712,90713],{},"Optimalizaci spotřebitele",[883,90715,90717],{"className":90716},[886],[888,90718,90719],{"xmlns":890},[892,90720,90721,90725],{},[895,90722,90723],{},[898,90724,900],{},[902,90726,900],{"encoding":904}," při rozpočtu, min ",[883,90729,90731],{"className":90730},[886],[888,90732,90733],{"xmlns":890},[892,90734,90735,90739],{},[895,90736,90737],{},[898,90738,1818],{},[902,90740,1818],{"encoding":904}," při dané ",[883,90743,90745],{"className":90744},[886],[888,90746,90747],{"xmlns":890},[892,90748,90749,90753],{},[895,90750,90751],{},[898,90752,900],{},[902,90754,900],{"encoding":904},", Lagrange, funkce poptávky) viz ",[207,90757,913],{"className":90758,"dataFsResolvedFilePath":911,"href":912},[210],[724,90760,90761,90762,90764,90765,1741],{},"Kapitola 6 knihy ",[614,90763,6021],{}," — model rozhodování spotřebitele. Zde: funkce užitečnosti, indiferenční křivky, mezní míra komoditní substituce. Navazující optimalizace je v ",[207,90766,40782],{"className":90767,"dataFsResolvedFilePath":911,"href":912},[210],[115,90769,90771],{"id":90770},"úvod-cílové-znalosti-kapitoly-6","Úvod — cílové znalosti kapitoly 6",[724,90773,90774],{},"Po prostudování této kapitoly byste měli umět:",[120,90776,90777,90783,90792,90797,90800,90806,90812,90815,90821],{},[123,90778,90779,90780,1834],{},"vyložit, co se rozumí termínem ",[38,90781,90782],{},"užitečnost",[123,90784,90785,90786,2068,90789,1834],{},"definovat pojmy ",[38,90787,90788],{},"svazek zboží",[38,90790,90791],{},"funkce užitečnosti",[123,90793,78821,90794,78828],{},[38,90795,90796],{},"mezní užitečnosti",[123,90798,90799],{},"vyjmenovat základní vlastnosti funkcí užitečnosti,",[123,90801,78848,90802,90805],{},[38,90803,90804],{},"Cobb-Douglasových"," funkcí užitečnosti,",[123,90807,78869,90808,90811],{},[38,90809,90810],{},"křivky užitečnosti"," (indiferenční křivky),",[123,90813,90814],{},"vyjmenovat jejich základní vlastnosti,",[123,90816,78821,90817,90820],{},[38,90818,90819],{},"mezní míru komoditní substituce"," a ekonomicky ji interpretovat,",[123,90822,90823,90824,90827],{},"řešit ",[38,90825,90826],{},"optimalizační úlohy"," s ohledem na užitečnost.",[115,90829,90831],{"id":90830},"_61-pojetí-užitečnosti","6.1 Pojetí užitečnosti",[724,90833,90834,90835,90838,90839,90842],{},"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 ",[207,90836,1665],{"className":90837,"dataFsResolvedFilePath":800,"href":801},[210],". Centrálním pojmem je ",[38,90840,90841],{},"užitečnost (utility)"," — vše, co vede spotřebitele k nákupu zboží (uspokojení, potěšení, splnění přání, pohodlí).",[198,90844,90846],{"id":90845},"kardinalistický-vs-ordinalistický-přístup","Kardinalistický vs. ordinalistický přístup",[724,90848,90849],{},"Historicky se vyvíjela dvě pojetí „měření\" užitečnosti:",[120,90851,90852,90858],{},[123,90853,90854,90857],{},[38,90855,90856],{},"Kardinalistický přístup"," (19. století — Gossen, Jevons, Walras): užitečnost měřena kvantitativně (např. peněžními jednotkami). Tento přístup se ukázal být nevýhodný.",[123,90859,90860,90863,90864,90866],{},[38,90861,90862],{},"Ordinalistický přístup"," (v současnosti preferovaný): postačuje ",[38,90865,90600],{}," svazků zboží podle preferencí; kvantitativní číselné hodnocení užitečnosti se nepožaduje.",[1636,90868,90869],{},[724,90870,90871,90873,90874,90877,90878,1989,90891,90894,90895,2068,90908,90927,90928,1343,90954,90981,90982,90985,90986,90989],{},[883,90872,4723],{}," Pozor — ordinalisté užitečnost ",[38,90875,90876],{},"neměří","\nV ordinalistickém přístupu hodnoty funkce ",[883,90879,90881],{"className":90880},[886],[888,90882,90883],{"xmlns":890},[892,90884,90885,90889],{},[895,90886,90887],{},[898,90888,900],{},[902,90890,900],{"encoding":904},[38,90892,90893],{},"nemají samostatný ekonomický význam"," — slouží pouze k uspořádání svazků. Dvě funkce ",[883,90896,90898],{"className":90897},[886],[888,90899,90900],{"xmlns":890},[892,90901,90902,90906],{},[895,90903,90904],{},[898,90905,900],{},[902,90907,900],{"encoding":904},[883,90909,90911],{"className":90910},[886],[888,90912,90913],{"xmlns":890},[892,90914,90915,90924],{},[895,90916,90917],{},[2770,90918,90919,90921],{"accent":1833},[898,90920,900],{},[1761,90922,90923],{},"~",[902,90925,90926],{"encoding":904},"\\tilde U"," reprezentují tytéž preference, jsou-li navzájem monotónní transformací (např. ",[883,90929,90931],{"className":90930},[886],[888,90932,90933],{"xmlns":890},[892,90934,90935,90951],{},[895,90936,90937,90943,90945],{},[2770,90938,90939,90941],{"accent":1833},[898,90940,900],{},[1761,90942,90923],{},[1761,90944,1909],{},[1824,90946,90947,90949],{},[898,90948,900],{},[1765,90950,2296],{},[902,90952,90953],{"encoding":904},"\\tilde U = U^2",[883,90955,90957],{"className":90956},[886],[888,90958,90959],{"xmlns":890},[892,90960,90961,90978],{},[895,90962,90963,90969,90971,90974,90976],{},[2770,90964,90965,90967],{"accent":1833},[898,90966,900],{},[1761,90968,90923],{},[1761,90970,1909],{},[898,90972,90973],{},"ln",[1761,90975,60178],{},[898,90977,900],{},[902,90979,90980],{"encoding":904},"\\tilde U = \\ln U","). Výroky typu „užitečnost je 250 jednotek\" proto samy o sobě nic neříkají — smysl mají jen ",[38,90983,90984],{},"porovnání"," mezi svazky a ",[38,90987,90988],{},"poměry"," mezních veličin.",[724,90991,90992,90993,2506],{},"Ordinalistický přístup vychází z ",[38,90994,90995],{},"pěti hlavních předpokladů",[152,90997,90998,91004,91010,91128,91134],{},[123,90999,91000,91003],{},[38,91001,91002],{},"Racionalita."," Spotřebitel jedná racionálně — snaží se maximalizovat své uspokojení (užitečnost) s ohledem na daný důchod a tržní ceny; disponuje všemi potřebnými informacemi.",[123,91005,91006,91009],{},[38,91007,91008],{},"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.",[123,91011,91012,91015,91016,65719,91029,91042,91043,65719,91056,6997,91069,91072,91073,2068,91092,66548,91110,1741],{},[38,91013,91014],{},"Konzistence a tranzitivita."," Preferuje-li v jisté době svazek ",[883,91017,91019],{"className":91018},[886],[888,91020,91021],{"xmlns":890},[892,91022,91023,91027],{},[895,91024,91025],{},[898,91026,8309],{},[902,91028,8309],{"encoding":904},[883,91030,91032],{"className":91031},[886],[888,91033,91034],{"xmlns":890},[892,91035,91036,91040],{},[895,91037,91038],{},[898,91039,27286],{},[902,91041,27286],{"encoding":904},", nebude jindy preferovat ",[883,91044,91046],{"className":91045},[886],[888,91047,91048],{"xmlns":890},[892,91049,91050,91054],{},[895,91051,91052],{},[898,91053,27286],{},[902,91055,27286],{"encoding":904},[883,91057,91059],{"className":91058},[886],[888,91060,91061],{"xmlns":890},[892,91062,91063,91067],{},[895,91064,91065],{},[898,91066,8309],{},[902,91068,8309],{"encoding":904},[38,91070,91071],{},"Tranzitivita",": pokud ",[883,91074,91076],{"className":91075},[886],[888,91077,91078],{"xmlns":890},[892,91079,91080,91089],{},[895,91081,91082,91084,91087],{},[898,91083,8309],{},[1761,91085,91086],{},"≻",[898,91088,27286],{},[902,91090,91091],{"encoding":904},"A \\succ B",[883,91093,91095],{"className":91094},[886],[888,91096,91097],{"xmlns":890},[892,91098,91099,91107],{},[895,91100,91101,91103,91105],{},[898,91102,27286],{},[1761,91104,91086],{},[898,91106,6849],{},[902,91108,91109],{"encoding":904},"B \\succ C",[883,91111,91113],{"className":91112},[886],[888,91114,91115],{"xmlns":890},[892,91116,91117,91125],{},[895,91118,91119,91121,91123],{},[898,91120,8309],{},[1761,91122,91086],{},[898,91124,6849],{},[902,91126,91127],{"encoding":904},"A \\succ C",[123,91129,91130,91133],{},[38,91131,91132],{},"Rostoucí užitečnost."," Uspokojení roste s množstvím zboží.",[123,91135,91136,91139],{},[38,91137,91138],{},"Klesající mezní užitečnost."," „Přírůstky\" uspokojení klesají s růstem množství zboží.",[724,91141,91142,91143,91146,91147,1741],{},"K naplnění předpokladů je ordinalistický přístup založen na pojmech ",[614,91144,91145],{},"preference"," a na příbuzné ",[614,91148,91149],{},"funkci užitečnosti",[115,91151,91153],{"id":91152},"_62-model-užitečnosti-svazek-zboží-a-funkce-užitečnosti","6.2 Model užitečnosti — svazek zboží a funkce užitečnosti",[724,91155,91156,91157,91170,91171,91174,91175,91188],{},"Uvažujme ",[883,91158,91160],{"className":91159},[886],[888,91161,91162],{"xmlns":890},[892,91163,91164,91168],{},[895,91165,91166],{},[898,91167,40888],{},[902,91169,40888],{"encoding":904}," různých zboží. ",[38,91172,91173],{},"Svazek zboží (bundle of goods)"," je uspořádaná ",[883,91176,91178],{"className":91177},[886],[888,91179,91180],{"xmlns":890},[892,91181,91182,91186],{},[895,91183,91184],{},[898,91185,40888],{},[902,91187,40888],{"encoding":904},"-tice",[724,91190,91191],{},[883,91192,91194],{"className":91193},[886],[888,91195,91196],{"xmlns":890},[892,91197,91198,91224],{},[895,91199,91200,91202,91208,91210,91212,91214,91220,91222],{},[1761,91201,1915],{"stretchy":1821},[1681,91203,91204,91206],{},[898,91205,1828],{},[1765,91207,1945],{},[1761,91209,1834],{"separator":1833},[1761,91211,13686],{},[1761,91213,1834],{"separator":1833},[1681,91215,91216,91218],{},[898,91217,1828],{},[898,91219,40888],{},[1761,91221,1920],{"stretchy":1821},[1761,91223,1834],{"separator":1833},[902,91225,91226],{"encoding":904},"(Q_1, \\dots, Q_n),",[724,91228,8364,91229,91246,91247,91260,91261,91264,91265,91268,91269,91272,91273,2506],{},[883,91230,91232],{"className":91231},[886],[888,91233,91234],{"xmlns":890},[892,91235,91236,91244],{},[895,91237,91238],{},[1681,91239,91240,91242],{},[898,91241,1828],{},[898,91243,21824],{},[902,91245,51528],{"encoding":904}," značí množství ",[883,91248,91250],{"className":91249},[886],[888,91251,91252],{"xmlns":890},[892,91253,91254,91258],{},[895,91255,91256],{},[898,91257,21824],{},[902,91259,21824],{"encoding":904},"-tého zboží. Spotřebitel je schopen svazky ",[38,91262,91263],{},"uspořádat"," s rostoucí užitečností, případně je prohlásit za ",[38,91266,91267],{},"indiferentní"," (tj. stejně užitečné). Tím je definována ",[38,91270,91271],{},"relace preference",". Preferenci vyjadřujeme číselně: svazku preferovanému přiřadíme větší číslo, indiferentním svazkům stejné číslo. Dostáváme ",[38,91274,91149],{},[883,91276,91278],{"className":91277},[886],[888,91279,91280],{"xmlns":890,"display":1930},[892,91281,91282,91329],{},[24787,91283,91284],{"width":32101},[24792,91285,91286,91288,91322,91324],{},[24795,91287],{"width":32106},[24795,91289,91290],{},[895,91291,91292,91294,91296,91298,91300,91306,91308,91310,91312,91318,91320],{},[898,91293,900],{},[1761,91295,1909],{},[898,91297,900],{},[1761,91299,1915],{"stretchy":1821},[1681,91301,91302,91304],{},[898,91303,1828],{},[1765,91305,1945],{},[1761,91307,1834],{"separator":1833},[1761,91309,13686],{},[1761,91311,1834],{"separator":1833},[1681,91313,91314,91316],{},[898,91315,1828],{},[898,91317,40888],{},[1761,91319,1920],{"stretchy":1821},[1761,91321,1834],{"separator":1833},[24795,91323],{"width":32106},[24795,91325,91326],{},[2761,91327,91328],{},"(6.1)",[902,91330,91331],{"encoding":904},"U = U(Q_1, \\dots, Q_n), \\tag{6.1}",[724,91333,8364,91334,91364,91365,91387,91388,91391],{},[883,91335,91337],{"className":91336},[886],[888,91338,91339],{"xmlns":890},[892,91340,91341,91361],{},[895,91342,91343,91349,91351,91353,91355],{},[1681,91344,91345,91347],{},[898,91346,1828],{},[1765,91348,1945],{},[1761,91350,1834],{"separator":1833},[1761,91352,13686],{},[1761,91354,1834],{"separator":1833},[1681,91356,91357,91359],{},[898,91358,1828],{},[898,91360,40888],{},[902,91362,91363],{"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 ",[883,91366,91368],{"className":91367},[886],[888,91369,91370],{"xmlns":890},[892,91371,91372,91384],{},[895,91373,91374,91376,91378],{},[898,91375,900],{},[1761,91377,1834],{"separator":1833},[2770,91379,91380,91382],{"accent":1833},[898,91381,900],{},[1761,91383,90923],{},[902,91385,91386],{"encoding":904},"U, \\tilde U"," reprezentují stejné preference, pokud mezi nimi existuje ",[38,91389,91390],{},"monotónní transformace"," zachovávající pořadí.",[724,91393,91394,91395,5675,91398,1741],{},"Dále se omezíme na funkce pro ",[38,91396,91397],{},"dvě zboží",[883,91399,91401],{"className":91400},[886],[888,91402,91403],{"xmlns":890},[892,91404,91405,91431],{},[895,91406,91407,91409,91411,91413,91415,91421,91423,91429],{},[898,91408,900],{},[1761,91410,1909],{},[898,91412,900],{},[1761,91414,1915],{"stretchy":1821},[1681,91416,91417,91419],{},[898,91418,1828],{},[1765,91420,1945],{},[1761,91422,1834],{"separator":1833},[1681,91424,91425,91427],{},[898,91426,1828],{},[1765,91428,2296],{},[1761,91430,1920],{"stretchy":1821},[902,91432,91433],{"encoding":904},"U = U(Q_1, Q_2)",[1636,91435,91436,91511],{},[724,91437,91438,91440,91441,2506],{},[883,91439,56675],{}," Příklad 6.1 — uspořádání a indiference\nPro ",[883,91442,91444],{"className":91443},[886],[888,91445,91446],{"xmlns":890},[892,91447,91448,91508],{},[895,91449,91450,91452,91454,91456,91458,91464,91466,91472,91474,91480,91482,91484,91486],{},[898,91451,900],{},[1761,91453,1909],{},[898,91455,900],{},[1761,91457,1915],{"stretchy":1821},[1681,91459,91460,91462],{},[898,91461,1828],{},[1765,91463,1945],{},[1761,91465,1834],{"separator":1833},[1681,91467,91468,91470],{},[898,91469,1828],{},[1765,91471,2296],{},[1761,91473,1834],{"separator":1833},[1681,91475,91476,91478],{},[898,91477,1828],{},[1765,91479,5486],{},[1761,91481,1920],{"stretchy":1821},[1761,91483,1909],{},[1765,91485,2296],{},[12161,91487,91488],{},[895,91489,91490,91496,91502],{},[1681,91491,91492,91494],{},[898,91493,1828],{},[1765,91495,1945],{},[1681,91497,91498,91500],{},[898,91499,1828],{},[1765,91501,2296],{},[1681,91503,91504,91506],{},[898,91505,1828],{},[1765,91507,5486],{},[902,91509,91510],{"encoding":904},"U = U(Q_1, Q_2, Q_3) = 2\\sqrt{Q_1 Q_2 Q_3}",[120,91512,91513,91706],{},[123,91514,91515,91516,91542,91543,16976,91569,2068,91628,2403,91688,12468],{},"svazek ",[883,91517,91519],{"className":91518},[886],[888,91520,91521],{"xmlns":890},[892,91522,91523,91539],{},[895,91524,91525,91527,91529,91531,91533,91535,91537],{},[1761,91526,1915],{"stretchy":1821},[1765,91528,45871],{},[1761,91530,1834],{"separator":1833},[1765,91532,2318],{},[1761,91534,1834],{"separator":1833},[1765,91536,45849],{},[1761,91538,1920],{"stretchy":1821},[902,91540,91541],{"encoding":904},"(16, 4, 64)"," je preferován před ",[883,91544,91546],{"className":91545},[886],[888,91547,91548],{"xmlns":890},[892,91549,91550,91566],{},[895,91551,91552,91554,91556,91558,91560,91562,91564],{},[1761,91553,1915],{"stretchy":1821},[1765,91555,8056],{},[1761,91557,1834],{"separator":1833},[1765,91559,8056],{},[1761,91561,1834],{"separator":1833},[1765,91563,70575],{},[1761,91565,1920],{"stretchy":1821},[902,91567,91568],{"encoding":904},"(9, 9, 27)",[883,91570,91572],{"className":91571},[886],[888,91573,91574],{"xmlns":890},[892,91575,91576,91625],{},[895,91577,91578,91580,91582,91584,91586,91588,91590,91592,91594,91596,91598,91612,91614,91616,91621,91623],{},[898,91579,900],{},[1761,91581,1915],{"stretchy":1821},[1765,91583,45871],{},[1761,91585,1834],{"separator":1833},[1765,91587,2318],{},[1761,91589,1834],{"separator":1833},[1765,91591,45849],{},[1761,91593,1920],{"stretchy":1821},[1761,91595,1909],{},[1765,91597,2296],{},[12161,91599,91600],{},[895,91601,91602,91604,91606,91608,91610],{},[1765,91603,45871],{},[1761,91605,2447],{},[1765,91607,2318],{},[1761,91609,2447],{},[1765,91611,45849],{},[1761,91613,1909],{},[1765,91615,2296],{},[12161,91617,91618],{},[1765,91619,91620],{},"4096",[1761,91622,1909],{},[1765,91624,9665],{},[902,91626,91627],{"encoding":904},"U(16,4,64) = 2\\sqrt{16 \\cdot 4 \\cdot 64} = 2\\sqrt{4096} = 128",[883,91629,91631],{"className":91630},[886],[888,91632,91633],{"xmlns":890},[892,91634,91635,91685],{},[895,91636,91637,91639,91641,91643,91645,91647,91649,91651,91653,91655,91657,91671,91673,91675,91680,91682],{},[898,91638,900],{},[1761,91640,1915],{"stretchy":1821},[1765,91642,8056],{},[1761,91644,1834],{"separator":1833},[1765,91646,8056],{},[1761,91648,1834],{"separator":1833},[1765,91650,70575],{},[1761,91652,1920],{"stretchy":1821},[1761,91654,1909],{},[1765,91656,2296],{},[12161,91658,91659],{},[895,91660,91661,91663,91665,91667,91669],{},[1765,91662,8056],{},[1761,91664,2447],{},[1765,91666,8056],{},[1761,91668,2447],{},[1765,91670,70575],{},[1761,91672,1909],{},[1765,91674,2296],{},[12161,91676,91677],{},[1765,91678,91679],{},"2187",[1761,91681,9945],{},[1765,91683,91684],{},"93,53",[902,91686,91687],{"encoding":904},"U(9,9,27) = 2\\sqrt{9 \\cdot 9 \\cdot 27} = 2\\sqrt{2187} \\doteq 93{,}53",[883,91689,91691],{"className":91690},[886],[888,91692,91693],{"xmlns":890},[892,91694,91695,91703],{},[895,91696,91697,91699,91701],{},[1765,91698,9665],{},[1761,91700,1763],{},[1765,91702,91684],{},[902,91704,91705],{"encoding":904},"128 > 93{,}53",[123,91707,91708,91709,2068,91735,91761,91762,2068,91802,91843,91844,91890,91891,2068,91917,6916,91943,2068,91961,91979,91980,1741],{},"svazky ",[883,91710,91712],{"className":91711},[886],[888,91713,91714],{"xmlns":890},[892,91715,91716,91732],{},[895,91717,91718,91720,91722,91724,91726,91728,91730],{},[1761,91719,1915],{"stretchy":1821},[1765,91721,2318],{},[1761,91723,1834],{"separator":1833},[1765,91725,2454],{},[1761,91727,1834],{"separator":1833},[1765,91729,2296],{},[1761,91731,1920],{"stretchy":1821},[902,91733,91734],{"encoding":904},"(4, 8, 2)",[883,91736,91738],{"className":91737},[886],[888,91739,91740],{"xmlns":890},[892,91741,91742,91758],{},[895,91743,91744,91746,91748,91750,91752,91754,91756],{},[1761,91745,1915],{"stretchy":1821},[1765,91747,45849],{},[1761,91749,1834],{"separator":1833},[1765,91751,1945],{},[1761,91753,1834],{"separator":1833},[1765,91755,2318],{},[1761,91757,1920],{"stretchy":1821},[902,91759,91760],{"encoding":904},"(64, 1, 4)"," jsou indiferentní, protože ",[883,91763,91765],{"className":91764},[886],[888,91766,91767],{"xmlns":890},[892,91768,91769,91799],{},[895,91770,91771,91773,91775,91777,91779,91781,91783,91785,91787,91789,91791,91795,91797],{},[898,91772,900],{},[1761,91774,1915],{"stretchy":1821},[1765,91776,2318],{},[1761,91778,1834],{"separator":1833},[1765,91780,2454],{},[1761,91782,1834],{"separator":1833},[1765,91784,2296],{},[1761,91786,1920],{"stretchy":1821},[1761,91788,1909],{},[1765,91790,2296],{},[12161,91792,91793],{},[1765,91794,45849],{},[1761,91796,1909],{},[1765,91798,45871],{},[902,91800,91801],{"encoding":904},"U(4,8,2) = 2\\sqrt{64} = 16",[883,91803,91805],{"className":91804},[886],[888,91806,91807],{"xmlns":890},[892,91808,91809,91840],{},[895,91810,91811,91813,91815,91817,91819,91821,91823,91825,91827,91829,91831,91836,91838],{},[898,91812,900],{},[1761,91814,1915],{"stretchy":1821},[1765,91816,45849],{},[1761,91818,1834],{"separator":1833},[1765,91820,1945],{},[1761,91822,1834],{"separator":1833},[1765,91824,2318],{},[1761,91826,1920],{"stretchy":1821},[1761,91828,1909],{},[1765,91830,2296],{},[12161,91832,91833],{},[1765,91834,91835],{},"256",[1761,91837,1909],{},[1765,91839,76337],{},[902,91841,91842],{"encoding":904},"U(64,1,4) = 2\\sqrt{256} = 32"," — jsou stejně užitečné mezi sebou, pokud ",[883,91845,91847],{"className":91846},[886],[888,91848,91849],{"xmlns":890},[892,91850,91851,91887],{},[895,91852,91853,91855,91857,91859,91861,91863,91865,91867,91869,91871,91873,91875,91877,91879,91881,91883,91885],{},[898,91854,900],{},[1761,91856,1915],{"stretchy":1821},[1765,91858,2318],{},[1761,91860,1834],{"separator":1833},[1765,91862,2454],{},[1761,91864,1834],{"separator":1833},[1765,91866,2296],{},[1761,91868,1920],{"stretchy":1821},[1761,91870,1909],{},[898,91872,900],{},[1761,91874,1915],{"stretchy":1821},[1765,91876,45849],{},[1761,91878,1834],{"separator":1833},[1765,91880,1945],{},[1761,91882,1834],{"separator":1833},[1765,91884,2318],{},[1761,91886,1920],{"stretchy":1821},[902,91888,91889],{"encoding":904},"U(4,8,2) = U(64,1,4)","; ověření: ",[883,91892,91894],{"className":91893},[886],[888,91895,91896],{"xmlns":890},[892,91897,91898,91914],{},[895,91899,91900,91902,91904,91906,91908,91910,91912],{},[1765,91901,2318],{},[1761,91903,2447],{},[1765,91905,2454],{},[1761,91907,2447],{},[1765,91909,2296],{},[1761,91911,1909],{},[1765,91913,45849],{},[902,91915,91916],{"encoding":904},"4 \\cdot 8 \\cdot 2 = 64",[883,91918,91920],{"className":91919},[886],[888,91921,91922],{"xmlns":890},[892,91923,91924,91940],{},[895,91925,91926,91928,91930,91932,91934,91936,91938],{},[1765,91927,45849],{},[1761,91929,2447],{},[1765,91931,1945],{},[1761,91933,2447],{},[1765,91935,2318],{},[1761,91937,1909],{},[1765,91939,91835],{},[902,91941,91942],{"encoding":904},"64 \\cdot 1 \\cdot 4 = 256",[883,91944,91946],{"className":91945},[886],[888,91947,91948],{"xmlns":890},[892,91949,91950,91958],{},[895,91951,91952,91954,91956],{},[898,91953,900],{},[1761,91955,1909],{},[1765,91957,45871],{},[902,91959,91960],{"encoding":904},"U = 16",[883,91962,91964],{"className":91963},[886],[888,91965,91966],{"xmlns":890},[892,91967,91968,91976],{},[895,91969,91970,91972,91974],{},[898,91971,900],{},[1761,91973,1909],{},[1765,91975,76337],{},[902,91977,91978],{"encoding":904},"U = 32"," — nejsou indiferentní. Správně indiferentní jsou svazky s týmž součinem ",[883,91981,91983],{"className":91982},[886],[888,91984,91985],{"xmlns":890},[892,91986,91987,92007],{},[895,91988,91989,91995,92001],{},[1681,91990,91991,91993],{},[898,91992,1828],{},[1765,91994,1945],{},[1681,91996,91997,91999],{},[898,91998,1828],{},[1765,92000,2296],{},[1681,92002,92003,92005],{},[898,92004,1828],{},[1765,92006,5486],{},[902,92008,92009],{"encoding":904},"Q_1 Q_2 Q_3",[115,92011,92013],{"id":92012},"mezní-užitečnost-mu","Mezní užitečnost (MU)",[724,92015,92016,92017,12146,92052,1989,92055,5715,92072,3927,92089,92092,92093,92096],{},"Pro funkci užitečnosti ",[883,92018,92020],{"className":92019},[886],[888,92021,92022],{"xmlns":890},[892,92023,92024,92050],{},[895,92025,92026,92028,92030,92032,92034,92040,92042,92048],{},[898,92027,900],{},[1761,92029,1909],{},[898,92031,900],{},[1761,92033,1915],{"stretchy":1821},[1681,92035,92036,92038],{},[898,92037,1828],{},[1765,92039,1945],{},[1761,92041,1834],{"separator":1833},[1681,92043,92044,92046],{},[898,92045,1828],{},[1765,92047,2296],{},[1761,92049,1920],{"stretchy":1821},[902,92051,91433],{"encoding":904},[38,92053,92054],{},"mezní užitečnost",[883,92056,92058],{"className":92057},[886],[888,92059,92060],{"xmlns":890},[892,92061,92062,92070],{},[895,92063,92064],{},[1681,92065,92066,92068],{},[898,92067,1828],{},[1765,92069,1945],{},[902,92071,33032],{"encoding":904},[883,92073,92075],{"className":92074},[886],[888,92076,92077],{"xmlns":890},[892,92078,92079,92087],{},[895,92080,92081],{},[1681,92082,92083,92085],{},[898,92084,1828],{},[1765,92086,2296],{},[902,92088,33051],{"encoding":904},[38,92090,92091],{},"marginal utility",") parciální ",[207,92094,1145],{"className":92095,"dataFsResolvedFilePath":764,"href":765},[210]," užitečnosti podle příslušné proměnné:",[883,92098,92100],{"className":92099},[886],[888,92101,92102],{"xmlns":890,"display":1930},[892,92103,92104,92203],{},[24787,92105,92106],{"width":32101},[24792,92107,92108,92110,92196,92198],{},[24795,92109],{"width":32106},[24795,92111,92112],{},[895,92113,92114,92116,92122,92124,92132,92134,92152,92154,92156,92158,92164,92166,92174,92176,92194],{},[898,92115,6889],{},[1681,92117,92118,92120],{},[898,92119,900],{},[1765,92121,1945],{},[1761,92123,1909],{},[2015,92125,92126,92128,92130],{},[898,92127,900],{},[1765,92129,1945],{},[1761,92131,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,92133,1909],{},[4379,92135,92136,92142],{},[895,92137,92138,92140],{},[898,92139,13911],{"mathvariant":1969},[898,92141,900],{},[895,92143,92144,92146],{},[898,92145,13911],{"mathvariant":1969},[1681,92147,92148,92150],{},[898,92149,1828],{},[1765,92151,1945],{},[1761,92153,1834],{"separator":1833},[3315,92155],{"width":19322},[898,92157,6889],{},[1681,92159,92160,92162],{},[898,92161,900],{},[1765,92163,2296],{},[1761,92165,1909],{},[2015,92167,92168,92170,92172],{},[898,92169,900],{},[1765,92171,2296],{},[1761,92173,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,92175,1909],{},[4379,92177,92178,92184],{},[895,92179,92180,92182],{},[898,92181,13911],{"mathvariant":1969},[898,92183,900],{},[895,92185,92186,92188],{},[898,92187,13911],{"mathvariant":1969},[1681,92189,92190,92192],{},[898,92191,1828],{},[1765,92193,2296],{},[898,92195,1741],{"mathvariant":1969},[24795,92197],{"width":32106},[24795,92199,92200],{},[2761,92201,92202],{},"(6.2)",[902,92204,92205],{"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}",[724,92207,92208,92209,92243,92244,92274,92275,1989,92278,1741],{},"Pro pevné ",[883,92210,92212],{"className":92211},[886],[888,92213,92214],{"xmlns":890},[892,92215,92216,92240],{},[895,92217,92218,92224,92226,92228,92230,92236,92238],{},[1681,92219,92220,92222],{},[898,92221,1828],{},[1765,92223,1945],{},[1761,92225,1909],{},[898,92227,207],{},[1761,92229,1834],{"separator":1833},[1681,92231,92232,92234],{},[898,92233,1828],{},[1765,92235,2296],{},[1761,92237,1909],{},[898,92239,4302],{},[902,92241,92242],{"encoding":904},"Q_1 = a, Q_2 = b"," se hodnota ",[883,92245,92247],{"className":92246},[886],[888,92248,92249],{"xmlns":890},[892,92250,92251,92271],{},[895,92252,92253,92255,92261,92263,92265,92267,92269],{},[898,92254,6889],{},[1681,92256,92257,92259],{},[898,92258,900],{},[1765,92260,1945],{},[1761,92262,1915],{"stretchy":1821},[898,92264,207],{},[1761,92266,1834],{"separator":1833},[898,92268,4302],{},[1761,92270,1920],{"stretchy":1821},[902,92272,92273],{"encoding":904},"MU_1(a, b)"," nazývá mezní užitečnost ",[38,92276,92277],{},"v bodě (na hladině)",[883,92279,92281],{"className":92280},[886],[888,92282,92283],{"xmlns":890},[892,92284,92285,92297],{},[895,92286,92287,92289,92291,92293,92295],{},[1761,92288,1822],{"stretchy":1821},[898,92290,207],{},[1761,92292,1834],{"separator":1833},[898,92294,4302],{},[1761,92296,1844],{"stretchy":1821},[902,92298,14862],{"encoding":904},[1636,92300,92301],{},[724,92302,92303,92305,92306,92336,92365,92366,6685,92379,6699,92396,92417,92418,6746,92435,4178,92448,92465,92466,92488,92489,92518,92519,10518,92539,92556],{},[883,92304,1642],{}," Intuice — co říká ",[883,92307,92309],{"className":92308},[886],[888,92310,92311],{"xmlns":890},[892,92312,92313,92333],{},[895,92314,92315,92317,92323,92325,92327,92329,92331],{},[898,92316,6889],{},[1681,92318,92319,92321],{},[898,92320,900],{},[1765,92322,1945],{},[1761,92324,1915],{"stretchy":1821},[898,92326,207],{},[1761,92328,1834],{"separator":1833},[898,92330,4302],{},[1761,92332,1920],{"stretchy":1821},[902,92334,92335],{"encoding":904},"MU_1(a,b)",[883,92337,92339],{"className":92338},[886],[888,92340,92341],{"xmlns":890},[892,92342,92343,92363],{},[895,92344,92345,92347,92353,92355,92357,92359,92361],{},[898,92346,6889],{},[1681,92348,92349,92351],{},[898,92350,900],{},[1765,92352,1945],{},[1761,92354,1915],{"stretchy":1821},[898,92356,207],{},[1761,92358,1834],{"separator":1833},[898,92360,4302],{},[1761,92362,1920],{"stretchy":1821},[902,92364,92273],{"encoding":904}," je rychlost změny ",[883,92367,92369],{"className":92368},[886],[888,92370,92371],{"xmlns":890},[892,92372,92373,92377],{},[895,92374,92375],{},[898,92376,900],{},[902,92378,900],{"encoding":904},[883,92380,92382],{"className":92381},[886],[888,92383,92384],{"xmlns":890},[892,92385,92386,92394],{},[895,92387,92388],{},[1681,92389,92390,92392],{},[898,92391,1828],{},[1765,92393,1945],{},[902,92395,33032],{"encoding":904},[883,92397,92399],{"className":92398},[886],[888,92400,92401],{"xmlns":890},[892,92402,92403,92415],{},[895,92404,92405,92407,92409,92411,92413],{},[1761,92406,1822],{"stretchy":1821},[898,92408,207],{},[1761,92410,1834],{"separator":1833},[898,92412,4302],{},[1761,92414,1844],{"stretchy":1821},[902,92416,14862],{"encoding":904},". Přibližně: změní-li se ",[883,92419,92421],{"className":92420},[886],[888,92422,92423],{"xmlns":890},[892,92424,92425,92433],{},[895,92426,92427],{},[1681,92428,92429,92431],{},[898,92430,1828],{},[1765,92432,1945],{},[902,92434,33032],{"encoding":904},[883,92436,92438],{"className":92437},[886],[888,92439,92440],{"xmlns":890},[892,92441,92442,92446],{},[895,92443,92444],{},[898,92445,207],{},[902,92447,207],{"encoding":904},[883,92449,92451],{"className":92450},[886],[888,92452,92453],{"xmlns":890},[892,92454,92455,92463],{},[895,92456,92457,92459,92461],{},[898,92458,207],{},[1761,92460,1964],{},[1765,92462,1945],{},[902,92464,6777],{"encoding":904}," při pevném ",[883,92467,92469],{"className":92468},[886],[888,92470,92471],{"xmlns":890},[892,92472,92473,92485],{},[895,92474,92475,92481,92483],{},[1681,92476,92477,92479],{},[898,92478,1828],{},[1765,92480,2296],{},[1761,92482,1909],{},[898,92484,4302],{},[902,92486,92487],{"encoding":904},"Q_2 = b",", změní se užitečnost zhruba o ",[883,92490,92492],{"className":92491},[886],[888,92493,92494],{"xmlns":890},[892,92495,92496,92516],{},[895,92497,92498,92500,92506,92508,92510,92512,92514],{},[898,92499,6889],{},[1681,92501,92502,92504],{},[898,92503,900],{},[1765,92505,1945],{},[1761,92507,1915],{"stretchy":1821},[898,92509,207],{},[1761,92511,1834],{"separator":1833},[898,92513,4302],{},[1761,92515,1920],{"stretchy":1821},[902,92517,92273],{"encoding":904},". Stejně tak ",[883,92520,92522],{"className":92521},[886],[888,92523,92524],{"xmlns":890},[892,92525,92526,92536],{},[895,92527,92528,92530],{},[898,92529,6889],{},[1681,92531,92532,92534],{},[898,92533,900],{},[1765,92535,2296],{},[902,92537,92538],{"encoding":904},"MU_2",[883,92540,92542],{"className":92541},[886],[888,92543,92544],{"xmlns":890},[892,92545,92546,92554],{},[895,92547,92548],{},[1681,92549,92550,92552],{},[898,92551,1828],{},[1765,92553,2296],{},[902,92555,33051],{"encoding":904},". Mezní užitečnost tedy odpovídá „užitku z další jednotky\" a podle předpokladu 5 s množstvím klesá.",[198,92558,84189],{"id":92559},"totální-diferenciál",[724,92561,92562,92563,52325,92579,92609,92610,2506],{},"Přibližnou změnu užitečnosti ",[883,92564,92566],{"className":92565},[886],[888,92567,92568],{"xmlns":890},[892,92569,92570,92576],{},[895,92571,92572,92574],{},[898,92573,6959],{"mathvariant":1969},[898,92575,900],{},[902,92577,92578],{"encoding":904},"\\Delta U",[883,92580,92582],{"className":92581},[886],[888,92583,92584],{"xmlns":890},[892,92585,92586,92606],{},[895,92587,92588,92590,92596,92598,92600],{},[898,92589,4346],{"mathvariant":1969},[1681,92591,92592,92594],{},[898,92593,1828],{},[1765,92595,1945],{},[1761,92597,1834],{"separator":1833},[898,92599,4346],{"mathvariant":1969},[1681,92601,92602,92604],{},[898,92603,1828],{},[1765,92605,2296],{},[902,92607,92608],{"encoding":904},"\\mathrm{d} Q_1, \\mathrm{d} Q_2"," stanovíme pomocí ",[38,92611,92612],{},"totálního diferenciálu",[883,92614,92616],{"className":92615},[886],[888,92617,92618],{"xmlns":890,"display":1930},[892,92619,92620,92721],{},[24787,92621,92622],{"width":32101},[24792,92623,92624,92626,92714,92716],{},[24795,92625],{"width":32106},[24795,92627,92628],{},[895,92629,92630,92632,92634,92636,92638,92640,92642,92650,92652,92658,92660,92668,92670,92676,92678,92680,92686,92688,92694,92696,92698,92704,92706,92712],{},[898,92631,6959],{"mathvariant":1969},[898,92633,900],{},[1761,92635,6803],{},[898,92637,4346],{"mathvariant":1969},[898,92639,900],{},[1761,92641,1909],{},[2015,92643,92644,92646,92648],{},[898,92645,900],{},[1765,92647,1945],{},[1761,92649,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[898,92651,4346],{"mathvariant":1969},[1681,92653,92654,92656],{},[898,92655,1828],{},[1765,92657,1945],{},[1761,92659,1964],{},[2015,92661,92662,92664,92666],{},[898,92663,900],{},[1765,92665,2296],{},[1761,92667,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[898,92669,4346],{"mathvariant":1969},[1681,92671,92672,92674],{},[898,92673,1828],{},[1765,92675,2296],{},[1761,92677,1909],{},[898,92679,6889],{},[1681,92681,92682,92684],{},[898,92683,900],{},[1765,92685,1945],{},[898,92687,4346],{"mathvariant":1969},[1681,92689,92690,92692],{},[898,92691,1828],{},[1765,92693,1945],{},[1761,92695,1964],{},[898,92697,6889],{},[1681,92699,92700,92702],{},[898,92701,900],{},[1765,92703,2296],{},[898,92705,4346],{"mathvariant":1969},[1681,92707,92708,92710],{},[898,92709,1828],{},[1765,92711,2296],{},[898,92713,1741],{"mathvariant":1969},[24795,92715],{"width":32106},[24795,92717,92718],{},[2761,92719,92720],{},"(6.3)",[902,92722,92723],{"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}",[724,92725,79447,92726,1741],{},[883,92727,92729],{"className":92728},[886],[888,92730,92731],{"xmlns":890},[892,92732,92733,92803],{},[895,92734,92735,92737,92739,92741,92743,92745,92751,92753,92755,92761,92763,92769,92771,92773,92779,92781,92783,92785,92787,92793,92795,92801],{},[898,92736,6959],{"mathvariant":1969},[898,92738,900],{},[1761,92740,1909],{},[898,92742,900],{},[1761,92744,1915],{"stretchy":1821},[1681,92746,92747,92749],{},[898,92748,1828],{},[1765,92750,1945],{},[1761,92752,1964],{},[898,92754,4346],{"mathvariant":1969},[1681,92756,92757,92759],{},[898,92758,1828],{},[1765,92760,1945],{},[1761,92762,1834],{"separator":1833},[1681,92764,92765,92767],{},[898,92766,1828],{},[1765,92768,2296],{},[1761,92770,1964],{},[898,92772,4346],{"mathvariant":1969},[1681,92774,92775,92777],{},[898,92776,1828],{},[1765,92778,2296],{},[1761,92780,1920],{"stretchy":1821},[1761,92782,1885],{},[898,92784,900],{},[1761,92786,1915],{"stretchy":1821},[1681,92788,92789,92791],{},[898,92790,1828],{},[1765,92792,1945],{},[1761,92794,1834],{"separator":1833},[1681,92796,92797,92799],{},[898,92798,1828],{},[1765,92800,2296],{},[1761,92802,1920],{"stretchy":1821},[902,92804,92805],{"encoding":904},"\\Delta U = U(Q_1 + \\mathrm{d} Q_1, Q_2 + \\mathrm{d} Q_2) - U(Q_1, Q_2)",[115,92807,92809],{"id":92808},"vlastnosti-funkce-užitečnosti","Vlastnosti funkce užitečnosti",[724,92811,92812,92813,92816,92817,92820],{},"Funkce užitečnosti musí vyjadřovat dva ekonomicky zásadní předpoklady — ",[38,92814,92815],{},"rostoucí užitečnost"," (předpoklad 4) a ",[38,92818,92819],{},"klesající mezní užitečnost"," (předpoklad 5).",[724,92822,92823,92826,92827,5715,92853,92879,92880,1343,92912,92944,92945,2068,92999,93053],{},[38,92824,92825],{},"Předpoklad 4"," (rostoucí užitečnost) znamená, že při pevně zadaných ",[883,92828,92830],{"className":92829},[886],[888,92831,92832],{"xmlns":890},[892,92833,92834,92850],{},[895,92835,92836,92842,92844],{},[1681,92837,92838,92840],{},[898,92839,1828],{},[1765,92841,2296],{},[1761,92843,1909],{},[1681,92845,92846,92848],{},[898,92847,207],{},[1765,92849,1767],{},[902,92851,92852],{"encoding":904},"Q_2 = a_0",[883,92854,92856],{"className":92855},[886],[888,92857,92858],{"xmlns":890},[892,92859,92860,92876],{},[895,92861,92862,92868,92870],{},[1681,92863,92864,92866],{},[898,92865,1828],{},[1765,92867,1945],{},[1761,92869,1909],{},[1681,92871,92872,92874],{},[898,92873,4302],{},[1765,92875,1767],{},[902,92877,92878],{"encoding":904},"Q_1 = b_0"," jsou funkce jedné proměnné ",[883,92881,92883],{"className":92882},[886],[888,92884,92885],{"xmlns":890},[892,92886,92887,92909],{},[895,92888,92889,92891,92893,92899,92901,92907],{},[898,92890,900],{},[1761,92892,1915],{"stretchy":1821},[1681,92894,92895,92897],{},[898,92896,1828],{},[1765,92898,1945],{},[1761,92900,1834],{"separator":1833},[1681,92902,92903,92905],{},[898,92904,207],{},[1765,92906,1767],{},[1761,92908,1920],{"stretchy":1821},[902,92910,92911],{"encoding":904},"U(Q_1, a_0)",[883,92913,92915],{"className":92914},[886],[888,92916,92917],{"xmlns":890},[892,92918,92919,92941],{},[895,92920,92921,92923,92925,92931,92933,92939],{},[898,92922,900],{},[1761,92924,1915],{"stretchy":1821},[1681,92926,92927,92929],{},[898,92928,4302],{},[1765,92930,1767],{},[1761,92932,1834],{"separator":1833},[1681,92934,92935,92937],{},[898,92936,1828],{},[1765,92938,2296],{},[1761,92940,1920],{"stretchy":1821},[902,92942,92943],{"encoding":904},"U(b_0, Q_2)"," rostoucí. To platí, jestliže ",[883,92946,92948],{"className":92947},[886],[888,92949,92950],{"xmlns":890},[892,92951,92952,92996],{},[895,92953,92954,92992,92994],{},[6411,92955,92956],{"scriptlevel":1767,"displaystyle":1833},[4379,92957,92958,92982],{},[895,92959,92960,92962,92964,92966,92972,92974,92980],{},[898,92961,4346],{"mathvariant":1969},[898,92963,900],{},[1761,92965,1915],{"stretchy":1821},[1681,92967,92968,92970],{},[898,92969,1828],{},[1765,92971,1945],{},[1761,92973,1834],{"separator":1833},[1681,92975,92976,92978],{},[898,92977,207],{},[1765,92979,1767],{},[1761,92981,1920],{"stretchy":1821},[895,92983,92984,92986],{},[898,92985,4346],{"mathvariant":1969},[1681,92987,92988,92990],{},[898,92989,1828],{},[1765,92991,1945],{},[1761,92993,1763],{},[1765,92995,1767],{},[902,92997,92998],{"encoding":904},"\\dfrac{\\mathrm{d} U(Q_1, a_0)}{\\mathrm{d} Q_1} > 0",[883,93000,93002],{"className":93001},[886],[888,93003,93004],{"xmlns":890},[892,93005,93006,93050],{},[895,93007,93008,93046,93048],{},[6411,93009,93010],{"scriptlevel":1767,"displaystyle":1833},[4379,93011,93012,93036],{},[895,93013,93014,93016,93018,93020,93026,93028,93034],{},[898,93015,4346],{"mathvariant":1969},[898,93017,900],{},[1761,93019,1915],{"stretchy":1821},[1681,93021,93022,93024],{},[898,93023,4302],{},[1765,93025,1767],{},[1761,93027,1834],{"separator":1833},[1681,93029,93030,93032],{},[898,93031,1828],{},[1765,93033,2296],{},[1761,93035,1920],{"stretchy":1821},[895,93037,93038,93040],{},[898,93039,4346],{"mathvariant":1969},[1681,93041,93042,93044],{},[898,93043,1828],{},[1765,93045,2296],{},[1761,93047,1763],{},[1765,93049,1767],{},[902,93051,93052],{"encoding":904},"\\dfrac{\\mathrm{d} U(b_0, Q_2)}{\\mathrm{d} Q_2} > 0",", tj.",[883,93055,93057],{"className":93056},[886],[888,93058,93059],{"xmlns":890,"display":1930},[892,93060,93061,93106],{},[24787,93062,93063],{"width":32101},[24792,93064,93065,93067,93099,93101],{},[24795,93066],{"width":32106},[24795,93068,93069],{},[895,93070,93071,93079,93081,93083,93085,93087,93095,93097],{},[2015,93072,93073,93075,93077],{},[898,93074,900],{},[1765,93076,1945],{},[1761,93078,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,93080,1763],{},[1765,93082,1767],{},[1761,93084,1834],{"separator":1833},[3315,93086],{"width":19322},[2015,93088,93089,93091,93093],{},[898,93090,900],{},[1765,93092,2296],{},[1761,93094,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,93096,1763],{},[1765,93098,16498],{},[24795,93100],{"width":32106},[24795,93102,93103],{},[2761,93104,93105],{},"(6.4)",[902,93107,93108],{"encoding":904},"U'_1 > 0, \\quad U'_2 > 0. \\tag{6.4}",[724,93110,93111,93112,93114],{},"Tedy mezní užitečnosti obou zboží jsou ",[38,93113,56657],{}," — užitečnost roste s množstvím každého zboží.",[724,93116,93117,93120,93121,93151,93152,2506],{},[38,93118,93119],{},"Předpoklad 5"," (klesající mezní užitečnost) požaduje, aby ",[883,93122,93124],{"className":93123},[886],[888,93125,93126],{"xmlns":890},[892,93127,93128,93148],{},[895,93129,93130,93138,93140],{},[2015,93131,93132,93134,93136],{},[898,93133,900],{},[1765,93135,1945],{},[1761,93137,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,93139,1834],{"separator":1833},[2015,93141,93142,93144,93146],{},[898,93143,900],{},[1765,93145,2296],{},[1761,93147,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[902,93149,93150],{"encoding":904},"U'_1, U'_2"," byly klesající funkce. To znamená, že jejich parciální derivace podle příslušné proměnné jsou ",[38,93153,93154],{},"záporné",[883,93156,93158],{"className":93157},[886],[888,93159,93160],{"xmlns":890,"display":1930},[892,93161,93162,93215],{},[24787,93163,93164],{"width":32101},[24792,93165,93166,93168,93208,93210],{},[24795,93167],{"width":32106},[24795,93169,93170],{},[895,93171,93172,93184,93186,93188,93190,93192,93204,93206],{},[2015,93173,93174,93176,93178],{},[898,93175,900],{},[1765,93177,6974],{},[895,93179,93180,93182],{},[1761,93181,6459],{"mathvariant":1969},[1761,93183,6459],{"mathvariant":1969},[1761,93185,2058],{},[1765,93187,1767],{},[1761,93189,1834],{"separator":1833},[3315,93191],{"width":19322},[2015,93193,93194,93196,93198],{},[898,93195,900],{},[1765,93197,36576],{},[895,93199,93200,93202],{},[1761,93201,6459],{"mathvariant":1969},[1761,93203,6459],{"mathvariant":1969},[1761,93205,2058],{},[1765,93207,16498],{},[24795,93209],{"width":32106},[24795,93211,93212],{},[2761,93213,93214],{},"(6.5)",[902,93216,93217],{"encoding":904},"U''_{11} \u003C 0, \\quad U''_{22} \u003C 0. \\tag{6.5}",[724,93219,93220,93221,93224,93225,1741],{},"Podmínka (6.5) je známa jako ",[38,93222,93223],{},"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 ",[207,93226,93228],{"className":93227,"dataFsResolvedFilePath":857,"href":858},[210],"produkční teorie",[724,93230,93231,93232,2068,93264,93296,93297,2068,93323,93349,93350,93378,93379,2068,93381,93383,93384,93419],{},"Podmínky (6.4), (6.5) určují tvary křivek ",[883,93233,93235],{"className":93234},[886],[888,93236,93237],{"xmlns":890},[892,93238,93239,93261],{},[895,93240,93241,93243,93245,93251,93253,93259],{},[898,93242,900],{},[1761,93244,1915],{"stretchy":1821},[1681,93246,93247,93249],{},[898,93248,1828],{},[1765,93250,1945],{},[1761,93252,1834],{"separator":1833},[1681,93254,93255,93257],{},[898,93256,4302],{},[1765,93258,1767],{},[1761,93260,1920],{"stretchy":1821},[902,93262,93263],{"encoding":904},"U(Q_1, b_0)",[883,93265,93267],{"className":93266},[886],[888,93268,93269],{"xmlns":890},[892,93270,93271,93293],{},[895,93272,93273,93275,93277,93283,93285,93291],{},[898,93274,900],{},[1761,93276,1915],{"stretchy":1821},[1681,93278,93279,93281],{},[898,93280,207],{},[1765,93282,1767],{},[1761,93284,1834],{"separator":1833},[1681,93286,93287,93289],{},[898,93288,1828],{},[1765,93290,2296],{},[1761,93292,1920],{"stretchy":1821},[902,93294,93295],{"encoding":904},"U(a_0, Q_2)"," v souřadnicových rovinách ",[883,93298,93300],{"className":93299},[886],[888,93301,93302],{"xmlns":890},[892,93303,93304,93320],{},[895,93305,93306,93308,93310,93312,93318],{},[1761,93307,1915],{"stretchy":1821},[898,93309,900],{},[1761,93311,1834],{"separator":1833},[1681,93313,93314,93316],{},[898,93315,1828],{},[1765,93317,1945],{},[1761,93319,1920],{"stretchy":1821},[902,93321,93322],{"encoding":904},"(U, Q_1)",[883,93324,93326],{"className":93325},[886],[888,93327,93328],{"xmlns":890},[892,93329,93330,93346],{},[895,93331,93332,93334,93336,93338,93344],{},[1761,93333,1915],{"stretchy":1821},[898,93335,900],{},[1761,93337,1834],{"separator":1833},[1681,93339,93340,93342],{},[898,93341,1828],{},[1765,93343,2296],{},[1761,93345,1920],{"stretchy":1821},[902,93347,93348],{"encoding":904},"(U, Q_2)"," (obrázek 6.1). Tyto křivky procházejí počátkem (neboť obvykle ",[883,93351,93353],{"className":93352},[886],[888,93354,93355],{"xmlns":890},[892,93356,93357,93375],{},[895,93358,93359,93361,93363,93365,93367,93369,93371,93373],{},[898,93360,900],{},[1761,93362,1915],{"stretchy":1821},[1765,93364,1767],{},[1761,93366,1834],{"separator":1833},[1765,93368,1767],{},[1761,93370,1920],{"stretchy":1821},[1761,93372,1909],{},[1765,93374,1767],{},[902,93376,93377],{"encoding":904},"U(0, 0) = 0","), jsou ",[38,93380,17695],{},[38,93382,42510],{},". Typický tvar grafu ",[883,93385,93387],{"className":93386},[886],[888,93388,93389],{"xmlns":890},[892,93390,93391,93417],{},[895,93392,93393,93395,93397,93399,93401,93407,93409,93415],{},[898,93394,900],{},[1761,93396,1909],{},[898,93398,900],{},[1761,93400,1915],{"stretchy":1821},[1681,93402,93403,93405],{},[898,93404,1828],{},[1765,93406,1945],{},[1761,93408,1834],{"separator":1833},[1681,93410,93411,93413],{},[898,93412,1828],{},[1765,93414,2296],{},[1761,93416,1920],{"stretchy":1821},[902,93418,91433],{"encoding":904}," — plocha v prostoru — je na obrázku 6.2.",[724,93421,93422],{},[614,93423,93424,93425,92465,93453,93474,93475,92465,93503,93525],{},"Obrázek 6.1 — typické průběhy funkce užitečnosti ",[883,93426,93428],{"className":93427},[886],[888,93429,93430],{"xmlns":890},[892,93431,93432,93450],{},[895,93433,93434,93436,93438,93444,93446,93448],{},[898,93435,900],{},[1761,93437,1915],{"stretchy":1821},[1681,93439,93440,93442],{},[898,93441,1828],{},[1765,93443,1945],{},[1761,93445,1834],{"separator":1833},[898,93447,4302],{},[1761,93449,1920],{"stretchy":1821},[902,93451,93452],{"encoding":904},"U(Q_1, b)",[883,93454,93456],{"className":93455},[886],[888,93457,93458],{"xmlns":890},[892,93459,93460,93472],{},[895,93461,93462,93468,93470],{},[1681,93463,93464,93466],{},[898,93465,1828],{},[1765,93467,2296],{},[1761,93469,1909],{},[898,93471,4302],{},[902,93473,92487],{"encoding":904}," (vlevo) a ",[883,93476,93478],{"className":93477},[886],[888,93479,93480],{"xmlns":890},[892,93481,93482,93500],{},[895,93483,93484,93486,93488,93490,93492,93498],{},[898,93485,900],{},[1761,93487,1915],{"stretchy":1821},[898,93489,207],{},[1761,93491,1834],{"separator":1833},[1681,93493,93494,93496],{},[898,93495,1828],{},[1765,93497,2296],{},[1761,93499,1920],{"stretchy":1821},[902,93501,93502],{"encoding":904},"U(a, Q_2)",[883,93504,93506],{"className":93505},[886],[888,93507,93508],{"xmlns":890},[892,93509,93510,93522],{},[895,93511,93512,93518,93520],{},[1681,93513,93514,93516],{},[898,93515,1828],{},[1765,93517,1945],{},[1761,93519,1909],{},[898,93521,207],{},[902,93523,93524],{"encoding":904},"Q_1 = a"," (vpravo) pro různé hladiny druhé proměnné.",[724,93527,93528],{},[614,93529,93530,93531,93566,93567,93597,93598,2068,93621,93643,93644,1741],{},"Obrázek 6.2 — plocha funkce užitečnosti ",[883,93532,93534],{"className":93533},[886],[888,93535,93536],{"xmlns":890},[892,93537,93538,93564],{},[895,93539,93540,93542,93544,93546,93548,93554,93556,93562],{},[898,93541,900],{},[1761,93543,1909],{},[898,93545,900],{},[1761,93547,1915],{"stretchy":1821},[1681,93549,93550,93552],{},[898,93551,1828],{},[1765,93553,1945],{},[1761,93555,1834],{"separator":1833},[1681,93557,93558,93560],{},[898,93559,1828],{},[1765,93561,2296],{},[1761,93563,1920],{"stretchy":1821},[902,93565,91433],{"encoding":904}," nad rovinou ",[883,93568,93570],{"className":93569},[886],[888,93571,93572],{"xmlns":890},[892,93573,93574,93594],{},[895,93575,93576,93578,93584,93586,93592],{},[1761,93577,1915],{"stretchy":1821},[1681,93579,93580,93582],{},[898,93581,1828],{},[1765,93583,1945],{},[1761,93585,1834],{"separator":1833},[1681,93587,93588,93590],{},[898,93589,1828],{},[1765,93591,2296],{},[1761,93593,1920],{"stretchy":1821},[902,93595,93596],{"encoding":904},"(Q_1, Q_2)"," s řezy rovinami ",[883,93599,93601],{"className":93600},[886],[888,93602,93603],{"xmlns":890},[892,93604,93605,93618],{},[895,93606,93607,93613,93615],{},[1681,93608,93609,93611],{},[898,93610,1828],{},[1765,93612,1945],{},[1761,93614,1909],{},[2761,93616,93617],{},"const",[902,93619,93620],{"encoding":904},"Q_1 = \\text{const}",[883,93622,93624],{"className":93623},[886],[888,93625,93626],{"xmlns":890},[892,93627,93628,93640],{},[895,93629,93630,93636,93638],{},[1681,93631,93632,93634],{},[898,93633,1828],{},[1765,93635,2296],{},[1761,93637,1909],{},[2761,93639,93617],{},[902,93641,93642],{"encoding":904},"Q_2 = \\text{const}"," a s křivkou ",[883,93645,93647],{"className":93646},[886],[888,93648,93649],{"xmlns":890},[892,93650,93651,93677],{},[895,93652,93653,93655,93657,93663,93665,93671,93673,93675],{},[898,93654,900],{},[1761,93656,1915],{"stretchy":1821},[1681,93658,93659,93661],{},[898,93660,1828],{},[1765,93662,1945],{},[1761,93664,1834],{"separator":1833},[1681,93666,93667,93669],{},[898,93668,1828],{},[1765,93670,2296],{},[1761,93672,1920],{"stretchy":1821},[1761,93674,1909],{},[898,93676,2774],{},[902,93678,13808],{"encoding":904},[198,93680,93682,93683],{"id":93681},"příklad-62-ověření-vlastností-a-dopočet-pro-uq112q213u-q_112-q_213","Příklad 6.2 — ověření vlastností a dopočet pro ",[883,93684,93686],{"className":93685},[886],[888,93687,93688],{"xmlns":890},[892,93689,93690,93724],{},[895,93691,93692,93694,93696,93710],{},[898,93693,900],{},[1761,93695,1909],{},[2015,93697,93698,93700,93702],{},[898,93699,1828],{},[1765,93701,1945],{},[895,93703,93704,93706,93708],{},[1765,93705,1945],{},[898,93707,8726],{"mathvariant":1969},[1765,93709,2296],{},[2015,93711,93712,93714,93716],{},[898,93713,1828],{},[1765,93715,2296],{},[895,93717,93718,93720,93722],{},[1765,93719,1945],{},[898,93721,8726],{"mathvariant":1969},[1765,93723,5486],{},[902,93725,93726],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F3}",[724,93728,93729],{},[38,93730,93731],{},"Ověření (6.4) a (6.5).",[883,93733,93735],{"className":93734},[886],[888,93736,93737],{"xmlns":890,"display":1930},[892,93738,93739,93843],{},[895,93740,93741,93749,93751,93759,93775,93789,93791,93793,93801,93803,93811,93825,93841],{},[2015,93742,93743,93745,93747],{},[898,93744,900],{},[1765,93746,1945],{},[1761,93748,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,93750,1909],{},[6411,93752,93753],{"scriptlevel":1767,"displaystyle":1821},[4379,93754,93755,93757],{},[1765,93756,1945],{},[1765,93758,2296],{},[2015,93760,93761,93763,93765],{},[898,93762,1828],{},[1765,93764,1945],{},[895,93766,93767,93769,93771,93773],{},[1761,93768,1885],{},[1765,93770,1945],{},[898,93772,8726],{"mathvariant":1969},[1765,93774,2296],{},[2015,93776,93777,93779,93781],{},[898,93778,1828],{},[1765,93780,2296],{},[895,93782,93783,93785,93787],{},[1765,93784,1945],{},[898,93786,8726],{"mathvariant":1969},[1765,93788,5486],{},[1761,93790,1834],{"separator":1833},[3315,93792],{"width":19322},[2015,93794,93795,93797,93799],{},[898,93796,900],{},[1765,93798,2296],{},[1761,93800,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,93802,1909],{},[6411,93804,93805],{"scriptlevel":1767,"displaystyle":1821},[4379,93806,93807,93809],{},[1765,93808,1945],{},[1765,93810,5486],{},[2015,93812,93813,93815,93817],{},[898,93814,1828],{},[1765,93816,1945],{},[895,93818,93819,93821,93823],{},[1765,93820,1945],{},[898,93822,8726],{"mathvariant":1969},[1765,93824,2296],{},[2015,93826,93827,93829,93831],{},[898,93828,1828],{},[1765,93830,2296],{},[895,93832,93833,93835,93837,93839],{},[1761,93834,1885],{},[1765,93836,2296],{},[898,93838,8726],{"mathvariant":1969},[1765,93840,5486],{},[1761,93842,1834],{"separator":1833},[902,93844,93845],{"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},",[724,93847,93848,93849,93883],{},"zřejmě ",[883,93850,93852],{"className":93851},[886],[888,93853,93854],{"xmlns":890},[892,93855,93856,93880],{},[895,93857,93858,93866,93868,93876,93878],{},[2015,93859,93860,93862,93864],{},[898,93861,900],{},[1765,93863,1945],{},[1761,93865,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,93867,1834],{"separator":1833},[2015,93869,93870,93872,93874],{},[898,93871,900],{},[1765,93873,2296],{},[1761,93875,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,93877,1763],{},[1765,93879,1767],{},[902,93881,93882],{"encoding":904},"U'_1, U'_2 > 0"," a platí (6.4). Dále:",[883,93885,93887],{"className":93886},[886],[888,93888,93889],{"xmlns":890,"display":1930},[892,93890,93891,94007],{},[895,93892,93893,93905,93907,93909,93917,93933,93947,93949,93951,93963,93965,93967,93975,93989,94005],{},[2015,93894,93895,93897,93899],{},[898,93896,900],{},[1765,93898,6974],{},[895,93900,93901,93903],{},[1761,93902,6459],{"mathvariant":1969},[1761,93904,6459],{"mathvariant":1969},[1761,93906,1909],{},[1761,93908,1885],{},[6411,93910,93911],{"scriptlevel":1767,"displaystyle":1821},[4379,93912,93913,93915],{},[1765,93914,1945],{},[1765,93916,2318],{},[2015,93918,93919,93921,93923],{},[898,93920,1828],{},[1765,93922,1945],{},[895,93924,93925,93927,93929,93931],{},[1761,93926,1885],{},[1765,93928,5486],{},[898,93930,8726],{"mathvariant":1969},[1765,93932,2296],{},[2015,93934,93935,93937,93939],{},[898,93936,1828],{},[1765,93938,2296],{},[895,93940,93941,93943,93945],{},[1765,93942,1945],{},[898,93944,8726],{"mathvariant":1969},[1765,93946,5486],{},[1761,93948,1834],{"separator":1833},[3315,93950],{"width":19322},[2015,93952,93953,93955,93957],{},[898,93954,900],{},[1765,93956,36576],{},[895,93958,93959,93961],{},[1761,93960,6459],{"mathvariant":1969},[1761,93962,6459],{"mathvariant":1969},[1761,93964,1909],{},[1761,93966,1885],{},[6411,93968,93969],{"scriptlevel":1767,"displaystyle":1821},[4379,93970,93971,93973],{},[1765,93972,2296],{},[1765,93974,8056],{},[2015,93976,93977,93979,93981],{},[898,93978,1828],{},[1765,93980,1945],{},[895,93982,93983,93985,93987],{},[1765,93984,1945],{},[898,93986,8726],{"mathvariant":1969},[1765,93988,2296],{},[2015,93990,93991,93993,93995],{},[898,93992,1828],{},[1765,93994,2296],{},[895,93996,93997,93999,94001,94003],{},[1761,93998,1885],{},[1765,94000,6321],{},[898,94002,8726],{"mathvariant":1969},[1765,94004,5486],{},[1761,94006,1834],{"separator":1833},[902,94008,94009],{"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},",[724,94011,94012,94013,94055],{},"opět ",[883,94014,94016],{"className":94015},[886],[888,94017,94018],{"xmlns":890},[892,94019,94020,94052],{},[895,94021,94022,94034,94036,94048,94050],{},[2015,94023,94024,94026,94028],{},[898,94025,900],{},[1765,94027,6974],{},[895,94029,94030,94032],{},[1761,94031,6459],{"mathvariant":1969},[1761,94033,6459],{"mathvariant":1969},[1761,94035,1834],{"separator":1833},[2015,94037,94038,94040,94042],{},[898,94039,900],{},[1765,94041,36576],{},[895,94043,94044,94046],{},[1761,94045,6459],{"mathvariant":1969},[1761,94047,6459],{"mathvariant":1969},[1761,94049,2058],{},[1765,94051,1767],{},[902,94053,94054],{"encoding":904},"U''_{11}, U''_{22} \u003C 0",", platí (6.5).",[724,94057,94058],{},[38,94059,94060,94061,1741],{},"(a) Mezní užitečnosti v bodě ",[883,94062,94064],{"className":94063},[886],[888,94065,94066],{"xmlns":890},[892,94067,94068,94080],{},[895,94069,94070,94072,94074,94076,94078],{},[1761,94071,1822],{"stretchy":1821},[1765,94073,7160],{},[1761,94075,1834],{"separator":1833},[1765,94077,12421],{},[1761,94079,1844],{"stretchy":1821},[902,94081,94082],{"encoding":904},"[100, 200]",[883,94084,94086],{"className":94085},[886],[888,94087,94088],{"xmlns":890,"display":1930},[892,94089,94090,94157],{},[895,94091,94092,94094,94100,94102,94104,94106,94108,94110,94112,94120,94122,94136,94138,94150,94152,94155],{},[898,94093,6889],{},[1681,94095,94096,94098],{},[898,94097,900],{},[1765,94099,1945],{},[1761,94101,1915],{"stretchy":1821},[1765,94103,7160],{},[1761,94105,1834],{"separator":1833},[1765,94107,12421],{},[1761,94109,1920],{"stretchy":1821},[1761,94111,1909],{},[6411,94113,94114],{"scriptlevel":1767,"displaystyle":1821},[4379,94115,94116,94118],{},[1765,94117,1945],{},[1765,94119,2296],{},[1761,94121,2447],{},[1824,94123,94124,94126],{},[1765,94125,7160],{},[895,94127,94128,94130,94132,94134],{},[1761,94129,1885],{},[1765,94131,1945],{},[898,94133,8726],{"mathvariant":1969},[1765,94135,2296],{},[1761,94137,2447],{},[1824,94139,94140,94142],{},[1765,94141,12421],{},[895,94143,94144,94146,94148],{},[1765,94145,1945],{},[898,94147,8726],{"mathvariant":1969},[1765,94149,5486],{},[1761,94151,9945],{},[1765,94153,94154],{},"0,4204",[1761,94156,1834],{"separator":1833},[902,94158,94159],{"encoding":904},"MU_1(100, 200) = \\tfrac{1}{2} \\cdot 100^{-1\u002F2} \\cdot 200^{1\u002F3} \\doteq 0{,}4204,",[883,94161,94163],{"className":94162},[886],[888,94164,94165],{"xmlns":890,"display":1930},[892,94166,94167,94232],{},[895,94168,94169,94171,94177,94179,94181,94183,94185,94187,94189,94197,94199,94211,94213,94227,94229],{},[898,94170,6889],{},[1681,94172,94173,94175],{},[898,94174,900],{},[1765,94176,2296],{},[1761,94178,1915],{"stretchy":1821},[1765,94180,7160],{},[1761,94182,1834],{"separator":1833},[1765,94184,12421],{},[1761,94186,1920],{"stretchy":1821},[1761,94188,1909],{},[6411,94190,94191],{"scriptlevel":1767,"displaystyle":1821},[4379,94192,94193,94195],{},[1765,94194,1945],{},[1765,94196,5486],{},[1761,94198,2447],{},[1824,94200,94201,94203],{},[1765,94202,7160],{},[895,94204,94205,94207,94209],{},[1765,94206,1945],{},[898,94208,8726],{"mathvariant":1969},[1765,94210,2296],{},[1761,94212,2447],{},[1824,94214,94215,94217],{},[1765,94216,12421],{},[895,94218,94219,94221,94223,94225],{},[1761,94220,1885],{},[1765,94222,2296],{},[898,94224,8726],{"mathvariant":1969},[1765,94226,5486],{},[1761,94228,9945],{},[1765,94230,94231],{},"0,63067.",[902,94233,94234],{"encoding":904},"MU_2(100, 200) = \\tfrac{1}{3} \\cdot 100^{1\u002F2} \\cdot 200^{-2\u002F3} \\doteq 0{,}63067.",[724,94236,94237,1989,94239,94274,94275,94296,94297,94314],{},[614,94238,13257],{},[883,94240,94242],{"className":94241},[886],[888,94243,94244],{"xmlns":890},[892,94245,94246,94271],{},[895,94247,94248,94250,94256,94258,94260,94262,94264,94266,94268],{},[898,94249,6889],{},[1681,94251,94252,94254],{},[898,94253,900],{},[1765,94255,2296],{},[1761,94257,1915],{"stretchy":1821},[1765,94259,7160],{},[1761,94261,1834],{"separator":1833},[1765,94263,12421],{},[1761,94265,1920],{"stretchy":1821},[1761,94267,9945],{},[1765,94269,94270],{},"0,63067",[902,94272,94273],{"encoding":904},"MU_2(100, 200) \\doteq 0{,}63067"," znamená, že na hladině ",[883,94276,94278],{"className":94277},[886],[888,94279,94280],{"xmlns":890},[892,94281,94282,94294],{},[895,94283,94284,94286,94288,94290,94292],{},[1761,94285,1822],{"stretchy":1821},[1765,94287,7160],{},[1761,94289,1834],{"separator":1833},[1765,94291,12421],{},[1761,94293,1844],{"stretchy":1821},[902,94295,94082],{"encoding":904}," roste užitečnost při jednotkové změně ",[883,94298,94300],{"className":94299},[886],[888,94301,94302],{"xmlns":890},[892,94303,94304,94312],{},[895,94305,94306],{},[1681,94307,94308,94310],{},[898,94309,1828],{},[1765,94311,2296],{},[902,94313,33051],{"encoding":904}," přibližně o 0,63067.",[724,94316,94317,94336,94337,43206,94358,94375,94376,94402,94403,94420,94421,5372],{},[38,94318,94319,94320,94335],{},"(b) Odhad změny ",[883,94321,94323],{"className":94322},[886],[888,94324,94325],{"xmlns":890},[892,94326,94327,94333],{},[895,94328,94329,94331],{},[898,94330,6959],{"mathvariant":1969},[898,94332,900],{},[902,94334,92578],{"encoding":904}," pomocí totálního diferenciálu (6.3)."," Klesne-li vzhledem k hladině ",[883,94338,94340],{"className":94339},[886],[888,94341,94342],{"xmlns":890},[892,94343,94344,94356],{},[895,94345,94346,94348,94350,94352,94354],{},[1761,94347,1822],{"stretchy":1821},[1765,94349,7160],{},[1761,94351,1834],{"separator":1833},[1765,94353,12421],{},[1761,94355,1844],{"stretchy":1821},[902,94357,94082],{"encoding":904},[883,94359,94361],{"className":94360},[886],[888,94362,94363],{"xmlns":890},[892,94364,94365,94373],{},[895,94366,94367],{},[1681,94368,94369,94371],{},[898,94370,1828],{},[1765,94372,1945],{},[902,94374,33032],{"encoding":904}," na 98 (tj. ",[883,94377,94379],{"className":94378},[886],[888,94380,94381],{"xmlns":890},[892,94382,94383,94399],{},[895,94384,94385,94387,94393,94395,94397],{},[898,94386,4346],{"mathvariant":1969},[1681,94388,94389,94391],{},[898,94390,1828],{},[1765,94392,1945],{},[1761,94394,1909],{},[1761,94396,1885],{},[1765,94398,2296],{},[902,94400,94401],{"encoding":904},"\\mathrm{d} Q_1 = -2",") a vzroste-li ",[883,94404,94406],{"className":94405},[886],[888,94407,94408],{"xmlns":890},[892,94409,94410,94418],{},[895,94411,94412],{},[1681,94413,94414,94416],{},[898,94415,1828],{},[1765,94417,2296],{},[902,94419,33051],{"encoding":904}," o 3 (tj. ",[883,94422,94424],{"className":94423},[886],[888,94425,94426],{"xmlns":890},[892,94427,94428,94442],{},[895,94429,94430,94432,94438,94440],{},[898,94431,4346],{"mathvariant":1969},[1681,94433,94434,94436],{},[898,94435,1828],{},[1765,94437,2296],{},[1761,94439,1909],{},[1765,94441,5486],{},[902,94443,94444],{"encoding":904},"\\mathrm{d} Q_2 = 3",[883,94446,94448],{"className":94447},[886],[888,94449,94450],{"xmlns":890,"display":1930},[892,94451,94452,94503],{},[895,94453,94454,94456,94458,94460,94462,94464,94466,94468,94470,94472,94474,94476,94478,94480,94482,94484,94486,94488,94490,94493,94495,94498,94500],{},[898,94455,6959],{"mathvariant":1969},[898,94457,900],{},[1761,94459,6803],{},[898,94461,4346],{"mathvariant":1969},[898,94463,900],{},[1761,94465,1909],{},[1765,94467,94154],{},[1761,94469,2447],{},[1761,94471,1915],{"stretchy":1821},[1761,94473,1885],{},[1765,94475,2296],{},[1761,94477,1920],{"stretchy":1821},[1761,94479,1964],{},[1765,94481,94270],{},[1761,94483,2447],{},[1765,94485,5486],{},[1761,94487,1909],{},[1761,94489,1885],{},[1765,94491,94492],{},"0,8408",[1761,94494,1964],{},[1765,94496,94497],{},"1,89201",[1761,94499,9945],{},[1765,94501,94502],{},"1,05.",[902,94504,94505],{"encoding":904},"\\Delta U \\approx \\mathrm{d} U = 0{,}4204 \\cdot (-2) + 0{,}63067 \\cdot 3 = -0{,}8408 + 1{,}89201 \\doteq 1{,}05.",[724,94507,94508,94509,94512,94513,94564,94565,1741],{},"Užitečnost se tedy zvýší přibližně o ",[38,94510,94511],{},"1,05",". Skutečná změna je ",[883,94514,94516],{"className":94515},[886],[888,94517,94518],{"xmlns":890},[892,94519,94520,94561],{},[895,94521,94522,94524,94526,94528,94530,94532,94535,94537,94540,94542,94544,94546,94548,94550,94552,94554,94556,94558],{},[898,94523,6959],{"mathvariant":1969},[898,94525,900],{},[1761,94527,1909],{},[898,94529,900],{},[1761,94531,1915],{"stretchy":1821},[1765,94533,94534],{},"98",[1761,94536,1834],{"separator":1833},[1765,94538,94539],{},"203",[1761,94541,1920],{"stretchy":1821},[1761,94543,1885],{},[898,94545,900],{},[1761,94547,1915],{"stretchy":1821},[1765,94549,7160],{},[1761,94551,1834],{"separator":1833},[1765,94553,12421],{},[1761,94555,1920],{"stretchy":1821},[1761,94557,9945],{},[1765,94559,94560],{},"1,031",[902,94562,94563],{"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 ",[883,94566,94568],{"className":94567},[886],[888,94569,94570],{"xmlns":890},[892,94571,94572,94592],{},[895,94573,94574,94576,94582,94584,94586],{},[898,94575,4346],{"mathvariant":1969},[1681,94577,94578,94580],{},[898,94579,1828],{},[1765,94581,1945],{},[1761,94583,1834],{"separator":1833},[898,94585,4346],{"mathvariant":1969},[1681,94587,94588,94590],{},[898,94589,1828],{},[1765,94591,2296],{},[902,94593,92608],{"encoding":904},[115,94595,94597],{"id":94596},"cobb-douglasova-funkce-užitečnosti","Cobb-Douglasova funkce užitečnosti",[724,94599,94600],{},"Nejčastěji používané funkce užitečnosti mají tvar",[883,94602,94604],{"className":94603},[886],[888,94605,94606],{"xmlns":890,"display":1930},[892,94607,94608,94667],{},[24787,94609,94610],{"width":32101},[24792,94611,94612,94614,94660,94662],{},[24795,94613],{"width":32106},[24795,94615,94616],{},[895,94617,94618,94620,94622,94628,94630,94636,94638,94640,94648,94650,94658],{},[898,94619,900],{},[1761,94621,1915],{"stretchy":1821},[1681,94623,94624,94626],{},[898,94625,1828],{},[1765,94627,1945],{},[1761,94629,1834],{"separator":1833},[1681,94631,94632,94634],{},[898,94633,1828],{},[1765,94635,2296],{},[1761,94637,1920],{"stretchy":1821},[1761,94639,1909],{},[2015,94641,94642,94644,94646],{},[898,94643,1828],{},[1765,94645,1945],{},[898,94647,207],{},[1761,94649,2447],{},[2015,94651,94652,94654,94656],{},[898,94653,1828],{},[1765,94655,2296],{},[898,94657,4302],{},[1761,94659,1834],{"separator":1833},[24795,94661],{"width":32106},[24795,94663,94664],{},[2761,94665,94666],{},"(6.6)",[902,94668,94669],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^b, \\tag{6.6}",[724,94671,8364,94672,94690,94691,94693,94694,94698,94699,94729,94730,94752],{},[883,94673,94675],{"className":94674},[886],[888,94676,94677],{"xmlns":890},[892,94678,94679,94687],{},[895,94680,94681,94683,94685],{},[898,94682,207],{},[1761,94684,1834],{"separator":1833},[898,94686,4302],{},[902,94688,94689],{"encoding":904},"a, b"," jsou kladná čísla; nazývají se ",[38,94692,78677],{}," (v příbuznosti s produkčními funkcemi — viz ",[207,94695,94697],{"className":94696,"dataFsResolvedFilePath":857,"href":858},[210],"kapitola 5","). Obvykle se volí ",[883,94700,94702],{"className":94701},[886],[888,94703,94704],{"xmlns":890},[892,94705,94706,94726],{},[895,94707,94708,94710,94712,94714,94716,94718,94720,94722,94724],{},[898,94709,207],{},[1761,94711,1834],{"separator":1833},[898,94713,4302],{},[1761,94715,10551],{},[1761,94717,1915],{"stretchy":1821},[1765,94719,1767],{},[1761,94721,1834],{"separator":1833},[1765,94723,1945],{},[1761,94725,1920],{"stretchy":1821},[902,94727,94728],{"encoding":904},"a, b \\in (0, 1)",", často se klade ",[883,94731,94733],{"className":94732},[886],[888,94734,94735],{"xmlns":890},[892,94736,94737,94749],{},[895,94738,94739,94741,94743,94745,94747],{},[898,94740,4302],{},[1761,94742,1909],{},[1765,94744,1945],{},[1761,94746,1885],{},[898,94748,207],{},[902,94750,94751],{"encoding":904},"b = 1 - a",", čímž (6.6) přejde na tvar",[724,94754,94755],{},[3991,94756],{"alt":94757,"className":94758,"src":94759},"imek-cobb-douglas-3d-plus-ic",[210,3995],"\u002Fwiki-assets\u002Fimek-cobb-douglas-3d-plus-ic.jpeg",[883,94761,94763],{"className":94762},[886],[888,94764,94765],{"xmlns":890,"display":1930},[892,94766,94767,94817],{},[895,94768,94769,94771,94773,94779,94781,94787,94789,94791,94799,94801,94815],{},[898,94770,900],{},[1761,94772,1915],{"stretchy":1821},[1681,94774,94775,94777],{},[898,94776,1828],{},[1765,94778,1945],{},[1761,94780,1834],{"separator":1833},[1681,94782,94783,94785],{},[898,94784,1828],{},[1765,94786,2296],{},[1761,94788,1920],{"stretchy":1821},[1761,94790,1909],{},[2015,94792,94793,94795,94797],{},[898,94794,1828],{},[1765,94796,1945],{},[898,94798,207],{},[1761,94800,2447],{},[2015,94802,94803,94805,94807],{},[898,94804,1828],{},[1765,94806,2296],{},[895,94808,94809,94811,94813],{},[1765,94810,1945],{},[1761,94812,1885],{},[898,94814,207],{},[898,94816,1741],{"mathvariant":1969},[902,94818,94819],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^{1-a}.",[1636,94821,94822,94871,94993,95127],{},[724,94823,94824,94826,94827],{},[883,94825,56675],{}," Příklad 6.3 — ověření vlastností pro ",[883,94828,94830],{"className":94829},[886],[888,94831,94832],{"xmlns":890},[892,94833,94834,94868],{},[895,94835,94836,94838,94840,94854],{},[898,94837,900],{},[1761,94839,1909],{},[2015,94841,94842,94844,94846],{},[898,94843,1828],{},[1765,94845,1945],{},[895,94847,94848,94850,94852],{},[1765,94849,1945],{},[898,94851,8726],{"mathvariant":1969},[1765,94853,2318],{},[2015,94855,94856,94858,94860],{},[898,94857,1828],{},[1765,94859,2296],{},[895,94861,94862,94864,94866],{},[1765,94863,5486],{},[898,94865,8726],{"mathvariant":1969},[1765,94867,2318],{},[902,94869,94870],{"encoding":904},"U = Q_1^{1\u002F4} Q_2^{3\u002F4}",[883,94872,94874],{"className":94873},[886],[888,94875,94876],{"xmlns":890,"display":1930},[892,94877,94878,94990],{},[895,94879,94880,94888,94890,94898,94914,94928,94930,94932,94934,94936,94944,94946,94954,94968,94984,94986,94988],{},[2015,94881,94882,94884,94886],{},[898,94883,900],{},[1765,94885,1945],{},[1761,94887,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,94889,1909],{},[6411,94891,94892],{"scriptlevel":1767,"displaystyle":1821},[4379,94893,94894,94896],{},[1765,94895,1945],{},[1765,94897,2318],{},[2015,94899,94900,94902,94904],{},[898,94901,1828],{},[1765,94903,1945],{},[895,94905,94906,94908,94910,94912],{},[1761,94907,1885],{},[1765,94909,5486],{},[898,94911,8726],{"mathvariant":1969},[1765,94913,2318],{},[2015,94915,94916,94918,94920],{},[898,94917,1828],{},[1765,94919,2296],{},[895,94921,94922,94924,94926],{},[1765,94923,5486],{},[898,94925,8726],{"mathvariant":1969},[1765,94927,2318],{},[1761,94929,1763],{},[1765,94931,1767],{},[1761,94933,1834],{"separator":1833},[3315,94935],{"width":19322},[2015,94937,94938,94940,94942],{},[898,94939,900],{},[1765,94941,2296],{},[1761,94943,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,94945,1909],{},[6411,94947,94948],{"scriptlevel":1767,"displaystyle":1821},[4379,94949,94950,94952],{},[1765,94951,5486],{},[1765,94953,2318],{},[2015,94955,94956,94958,94960],{},[898,94957,1828],{},[1765,94959,1945],{},[895,94961,94962,94964,94966],{},[1765,94963,1945],{},[898,94965,8726],{"mathvariant":1969},[1765,94967,2318],{},[2015,94969,94970,94972,94974],{},[898,94971,1828],{},[1765,94973,2296],{},[895,94975,94976,94978,94980,94982],{},[1761,94977,1885],{},[1765,94979,1945],{},[898,94981,8726],{"mathvariant":1969},[1765,94983,2318],{},[1761,94985,1763],{},[1765,94987,1767],{},[1761,94989,1834],{"separator":1833},[902,94991,94992],{"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,",[883,94994,94996],{"className":94995},[886],[888,94997,94998],{"xmlns":890,"display":1930},[892,94999,95000,95124],{},[895,95001,95002,95014,95016,95018,95026,95042,95056,95058,95060,95062,95064,95076,95078,95080,95088,95102,95118,95120,95122],{},[2015,95003,95004,95006,95008],{},[898,95005,900],{},[1765,95007,6974],{},[895,95009,95010,95012],{},[1761,95011,6459],{"mathvariant":1969},[1761,95013,6459],{"mathvariant":1969},[1761,95015,1909],{},[1761,95017,1885],{},[6411,95019,95020],{"scriptlevel":1767,"displaystyle":1821},[4379,95021,95022,95024],{},[1765,95023,5486],{},[1765,95025,45871],{},[2015,95027,95028,95030,95032],{},[898,95029,1828],{},[1765,95031,1945],{},[895,95033,95034,95036,95038,95040],{},[1761,95035,1885],{},[1765,95037,5512],{},[898,95039,8726],{"mathvariant":1969},[1765,95041,2318],{},[2015,95043,95044,95046,95048],{},[898,95045,1828],{},[1765,95047,2296],{},[895,95049,95050,95052,95054],{},[1765,95051,5486],{},[898,95053,8726],{"mathvariant":1969},[1765,95055,2318],{},[1761,95057,2058],{},[1765,95059,1767],{},[1761,95061,1834],{"separator":1833},[3315,95063],{"width":19322},[2015,95065,95066,95068,95070],{},[898,95067,900],{},[1765,95069,36576],{},[895,95071,95072,95074],{},[1761,95073,6459],{"mathvariant":1969},[1761,95075,6459],{"mathvariant":1969},[1761,95077,1909],{},[1761,95079,1885],{},[6411,95081,95082],{"scriptlevel":1767,"displaystyle":1821},[4379,95083,95084,95086],{},[1765,95085,5486],{},[1765,95087,45871],{},[2015,95089,95090,95092,95094],{},[898,95091,1828],{},[1765,95093,1945],{},[895,95095,95096,95098,95100],{},[1765,95097,1945],{},[898,95099,8726],{"mathvariant":1969},[1765,95101,2318],{},[2015,95103,95104,95106,95108],{},[898,95105,1828],{},[1765,95107,2296],{},[895,95109,95110,95112,95114,95116],{},[1761,95111,1885],{},[1765,95113,6321],{},[898,95115,8726],{"mathvariant":1969},[1765,95117,2318],{},[1761,95119,2058],{},[1765,95121,1767],{},[1761,95123,1834],{"separator":1833},[902,95125,95126],{"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,",[724,95128,95129],{},"tedy podmínky (6.4) i (6.5) jsou splněny.",[115,95131,95133],{"id":95132},"indiferenční-křivky-křivky-užitečnosti-a-jejich-vlastnosti","Indiferenční křivky (křivky užitečnosti) a jejich vlastnosti",[724,95135,95136,95139],{},[38,95137,95138],{},"Křivky užitečnosti"," (utility curves) jsou indiferenční křivky funkce užitečnosti. Jsou dány rovnicí",[883,95141,95143],{"className":95142},[886],[888,95144,95145],{"xmlns":890,"display":1930},[892,95146,95147,95190],{},[24787,95148,95149],{"width":32101},[24792,95150,95151,95153,95183,95185],{},[24795,95152],{"width":32106},[24795,95154,95155],{},[895,95156,95157,95159,95161,95167,95169,95175,95177,95179,95181],{},[898,95158,900],{},[1761,95160,1915],{"stretchy":1821},[1681,95162,95163,95165],{},[898,95164,1828],{},[1765,95166,1945],{},[1761,95168,1834],{"separator":1833},[1681,95170,95171,95173],{},[898,95172,1828],{},[1765,95174,2296],{},[1761,95176,1920],{"stretchy":1821},[1761,95178,1909],{},[898,95180,2774],{},[1761,95182,1834],{"separator":1833},[24795,95184],{"width":32106},[24795,95186,95187],{},[2761,95188,95189],{},"(6.7)",[902,95191,95192],{"encoding":904},"U(Q_1, Q_2) = c, \\tag{6.7}",[724,95194,8364,95195,95208],{},[883,95196,95198],{"className":95197},[886],[888,95199,95200],{"xmlns":890},[892,95201,95202,95206],{},[895,95203,95204],{},[898,95205,2774],{},[902,95207,2774],{"encoding":904}," je kladná konstanta. Pro Cobb-Douglasovu funkci:",[883,95210,95212],{"className":95211},[886],[888,95213,95214],{"xmlns":890,"display":1930},[892,95215,95216,95257],{},[24787,95217,95218],{"width":32101},[24792,95219,95220,95222,95250,95252],{},[24795,95221],{"width":32106},[24795,95223,95224],{},[895,95225,95226,95234,95236,95244,95246,95248],{},[2015,95227,95228,95230,95232],{},[898,95229,1828],{},[1765,95231,1945],{},[898,95233,207],{},[1761,95235,2447],{},[2015,95237,95238,95240,95242],{},[898,95239,1828],{},[1765,95241,2296],{},[898,95243,4302],{},[1761,95245,1909],{},[898,95247,2774],{},[898,95249,1741],{"mathvariant":1969},[24795,95251],{"width":32106},[24795,95253,95254],{},[2761,95255,95256],{},"(6.8)",[902,95258,95259],{"encoding":904},"Q_1^a \\cdot Q_2^b = c. \\tag{6.8}",[724,95261,95262,95263,8412,95293,1989,95296,95309,95310,95345,95346,95363,95364,95393,95394,95397],{},"Body na téže křivce užitečnosti reprezentují kombinace ",[883,95264,95266],{"className":95265},[886],[888,95267,95268],{"xmlns":890},[892,95269,95270,95290],{},[895,95271,95272,95274,95280,95282,95288],{},[1761,95273,1822],{"stretchy":1821},[1681,95275,95276,95278],{},[898,95277,1828],{},[1765,95279,1945],{},[1761,95281,1834],{"separator":1833},[1681,95283,95284,95286],{},[898,95285,1828],{},[1765,95287,2296],{},[1761,95289,1844],{"stretchy":1821},[902,95291,95292],{"encoding":904},"[Q_1, Q_2]",[38,95294,95295],{},"stejnou úrovní uspokojení",[883,95297,95299],{"className":95298},[886],[888,95300,95301],{"xmlns":890},[892,95302,95303,95307],{},[895,95304,95305],{},[898,95306,2774],{},[902,95308,2774],{"encoding":904},". Křivky užitečnosti vznikají jako průsečnice plochy ",[883,95311,95313],{"className":95312},[886],[888,95314,95315],{"xmlns":890},[892,95316,95317,95343],{},[895,95318,95319,95321,95323,95325,95327,95333,95335,95341],{},[898,95320,900],{},[1761,95322,1909],{},[898,95324,900],{},[1761,95326,1915],{"stretchy":1821},[1681,95328,95329,95331],{},[898,95330,1828],{},[1765,95332,1945],{},[1761,95334,1834],{"separator":1833},[1681,95336,95337,95339],{},[898,95338,1828],{},[1765,95340,2296],{},[1761,95342,1920],{"stretchy":1821},[902,95344,91433],{"encoding":904}," s rovinami ",[883,95347,95349],{"className":95348},[886],[888,95350,95351],{"xmlns":890},[892,95352,95353,95361],{},[895,95354,95355,95357,95359],{},[898,95356,900],{},[1761,95358,1909],{},[898,95360,2774],{},[902,95362,90650],{"encoding":904}," rovnoběžnými s rovinou ",[883,95365,95367],{"className":95366},[886],[888,95368,95369],{"xmlns":890},[892,95370,95371,95391],{},[895,95372,95373,95375,95381,95383,95389],{},[1761,95374,1915],{"stretchy":1821},[1681,95376,95377,95379],{},[898,95378,1828],{},[1765,95380,1945],{},[1761,95382,1834],{"separator":1833},[1681,95384,95385,95387],{},[898,95386,1828],{},[1765,95388,2296],{},[1761,95390,1920],{"stretchy":1821},[902,95392,93596],{"encoding":904}," (obrázek 6.2). Jsou v příbuznosti s ",[38,95395,95396],{},"izokvantami"," produkčních funkcí.",[724,95399,95400],{},[614,95401,95402,95403,93474,95421,95439,95440,1741],{},"Obrázek 6.3 — typický tvar křivek užitečnosti pro Cobb-Douglasovu funkci pro ",[883,95404,95406],{"className":95405},[886],[888,95407,95408],{"xmlns":890},[892,95409,95410,95418],{},[895,95411,95412,95414,95416],{},[898,95413,207],{},[1761,95415,2058],{},[898,95417,4302],{},[902,95419,95420],{"encoding":904},"a \u003C b",[883,95422,95424],{"className":95423},[886],[888,95425,95426],{"xmlns":890},[892,95427,95428,95436],{},[895,95429,95430,95432,95434],{},[898,95431,207],{},[1761,95433,1763],{},[898,95435,4302],{},[902,95437,95438],{"encoding":904},"a > b"," (vpravo); různé hladiny ",[883,95441,95443],{"className":95442},[886],[888,95444,95445],{"xmlns":890},[892,95446,95447,95471],{},[895,95448,95449,95455,95457,95463,95465],{},[1681,95450,95451,95453],{},[898,95452,2774],{},[1765,95454,1767],{},[1761,95456,2058],{},[1681,95458,95459,95461],{},[898,95460,2774],{},[1765,95462,1945],{},[1761,95464,2058],{},[1681,95466,95467,95469],{},[898,95468,2774],{},[1765,95470,2296],{},[902,95472,95473],{"encoding":904},"c_0 \u003C c_1 \u003C c_2",[724,95475,95476],{},[614,95477,95478,95479,95508,95509,95567,95568,95586],{},"Obrázek 6.4 — soustava křivek užitečnosti pro tři hladiny (10, 20, 30) v rovině ",[883,95480,95482],{"className":95481},[886],[888,95483,95484],{"xmlns":890},[892,95485,95486,95506],{},[895,95487,95488,95490,95496,95498,95504],{},[1761,95489,1915],{"stretchy":1821},[1681,95491,95492,95494],{},[898,95493,1828],{},[1765,95495,1945],{},[1761,95497,1834],{"separator":1833},[1681,95499,95500,95502],{},[898,95501,1828],{},[1765,95503,2296],{},[1761,95505,1920],{"stretchy":1821},[902,95507,93596],{"encoding":904},"; body ",[883,95510,95512],{"className":95511},[886],[888,95513,95514],{"xmlns":890},[892,95515,95516,95564],{},[895,95517,95518,95520,95522,95524,95530,95532,95538,95540,95542,95544,95546,95548,95554,95556,95562],{},[898,95519,8309],{},[1761,95521,1909],{},[1761,95523,1822],{"stretchy":1821},[1681,95525,95526,95528],{},[898,95527,207],{},[1765,95529,1945],{},[1761,95531,1834],{"separator":1833},[1681,95533,95534,95536],{},[898,95535,207],{},[1765,95537,2296],{},[1761,95539,1844],{"stretchy":1821},[1761,95541,1834],{"separator":1833},[898,95543,27286],{},[1761,95545,1909],{},[1761,95547,1822],{"stretchy":1821},[1681,95549,95550,95552],{},[898,95551,4302],{},[1765,95553,1945],{},[1761,95555,1834],{"separator":1833},[1681,95557,95558,95560],{},[898,95559,4302],{},[1765,95561,2296],{},[1761,95563,1844],{"stretchy":1821},[902,95565,95566],{"encoding":904},"A = [a_1, a_2], B = [b_1, b_2]"," leží na téže křivce (hladina 10), body ",[883,95569,95571],{"className":95570},[886],[888,95572,95573],{"xmlns":890},[892,95574,95575,95583],{},[895,95576,95577,95579,95581],{},[898,95578,6849],{},[1761,95580,1834],{"separator":1833},[898,95582,2244],{},[902,95584,95585],{"encoding":904},"C, D"," na vyšší hladině.",[1636,95588,95589],{},[724,95590,95591,95593,95594,95656,95657,95701,95702,95736,95737,30220,95755,95736,95809,30220,95827,95903],{},[883,95592,56675],{}," Příklad 6.4 — rovnice křivek užitečnosti\nPro ",[883,95595,95597],{"className":95596},[886],[888,95598,95599],{"xmlns":890},[892,95600,95601,95653],{},[895,95602,95603,95605,95607,95613,95615,95621,95623,95625,95639],{},[898,95604,900],{},[1761,95606,1915],{"stretchy":1821},[1681,95608,95609,95611],{},[898,95610,1828],{},[1765,95612,1945],{},[1761,95614,1834],{"separator":1833},[1681,95616,95617,95619],{},[898,95618,1828],{},[1765,95620,2296],{},[1761,95622,1920],{"stretchy":1821},[1761,95624,1909],{},[2015,95626,95627,95629,95631],{},[898,95628,1828],{},[1765,95630,1945],{},[895,95632,95633,95635,95637],{},[1765,95634,1945],{},[898,95636,8726],{"mathvariant":1969},[1765,95638,2318],{},[2015,95640,95641,95643,95645],{},[898,95642,1828],{},[1765,95644,2296],{},[895,95646,95647,95649,95651],{},[1765,95648,5486],{},[898,95650,8726],{"mathvariant":1969},[1765,95652,2318],{},[902,95654,95655],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F4} Q_2^{3\u002F4}"," mají křivky užitečnosti rovnici ",[883,95658,95660],{"className":95659},[886],[888,95661,95662],{"xmlns":890},[892,95663,95664,95698],{},[895,95665,95666,95680,95694,95696],{},[2015,95667,95668,95670,95672],{},[898,95669,1828],{},[1765,95671,1945],{},[895,95673,95674,95676,95678],{},[1765,95675,1945],{},[898,95677,8726],{"mathvariant":1969},[1765,95679,2318],{},[2015,95681,95682,95684,95686],{},[898,95683,1828],{},[1765,95685,2296],{},[895,95687,95688,95690,95692],{},[1765,95689,5486],{},[898,95691,8726],{"mathvariant":1969},[1765,95693,2318],{},[1761,95695,1909],{},[898,95697,2774],{},[902,95699,95700],{"encoding":904},"Q_1^{1\u002F4} Q_2^{3\u002F4} = c",". Umocněním na čtvrtou mocninu dostáváme ",[883,95703,95705],{"className":95704},[886],[888,95706,95707],{"xmlns":890},[892,95708,95709,95733],{},[895,95710,95711,95717,95725,95727],{},[1681,95712,95713,95715],{},[898,95714,1828],{},[1765,95716,1945],{},[2015,95718,95719,95721,95723],{},[898,95720,1828],{},[1765,95722,2296],{},[1765,95724,5486],{},[1761,95726,1909],{},[1824,95728,95729,95731],{},[898,95730,2774],{},[1765,95732,2318],{},[902,95734,95735],{"encoding":904},"Q_1 Q_2^{3} = c^{4}",". Pro ",[883,95738,95740],{"className":95739},[886],[888,95741,95742],{"xmlns":890},[892,95743,95744,95752],{},[895,95745,95746,95748,95750],{},[898,95747,2774],{},[1761,95749,1909],{},[1765,95751,1945],{},[902,95753,95754],{"encoding":904},"c = 1",[883,95756,95758],{"className":95757},[886],[888,95759,95760],{"xmlns":890},[892,95761,95762,95806],{},[895,95763,95764,95770,95772,95788,95790],{},[1681,95765,95766,95768],{},[898,95767,1828],{},[1765,95769,2296],{},[1761,95771,1909],{},[2015,95773,95774,95776,95778],{},[898,95775,1828],{},[1765,95777,1945],{},[895,95779,95780,95782,95784,95786],{},[1761,95781,1885],{},[1765,95783,1945],{},[898,95785,8726],{"mathvariant":1969},[1765,95787,5486],{},[1761,95789,1909],{},[6411,95791,95792],{"scriptlevel":1767,"displaystyle":1833},[4379,95793,95794,95796],{},[1765,95795,1945],{},[86005,95797,95798,95804],{},[1681,95799,95800,95802],{},[898,95801,1828],{},[1765,95803,1945],{},[1765,95805,5486],{},[902,95807,95808],{"encoding":904},"Q_2 = Q_1^{-1\u002F3} = \\dfrac{1}{\\sqrt[3]{Q_1}}",[883,95810,95812],{"className":95811},[886],[888,95813,95814],{"xmlns":890},[892,95815,95816,95824],{},[895,95817,95818,95820,95822],{},[898,95819,2774],{},[1761,95821,1909],{},[1765,95823,2296],{},[902,95825,95826],{"encoding":904},"c = 2",[883,95828,95830],{"className":95829},[886],[888,95831,95832],{"xmlns":890},[892,95833,95834,95900],{},[895,95835,95836,95842,95844,95856,95858,95874,95876],{},[1681,95837,95838,95840],{},[898,95839,1828],{},[1765,95841,2296],{},[1761,95843,1909],{},[1824,95845,95846,95848],{},[1765,95847,2296],{},[895,95849,95850,95852,95854],{},[1765,95851,2318],{},[898,95853,8726],{"mathvariant":1969},[1765,95855,5486],{},[1761,95857,2447],{},[2015,95859,95860,95862,95864],{},[898,95861,1828],{},[1765,95863,1945],{},[895,95865,95866,95868,95870,95872],{},[1761,95867,1885],{},[1765,95869,1945],{},[898,95871,8726],{"mathvariant":1969},[1765,95873,5486],{},[1761,95875,1909],{},[6411,95877,95878],{"scriptlevel":1767,"displaystyle":1833},[4379,95879,95880,95890],{},[895,95881,95882,95884],{},[1765,95883,2296],{},[86005,95885,95886,95888],{},[1765,95887,2296],{},[1765,95889,5486],{},[86005,95891,95892,95898],{},[1681,95893,95894,95896],{},[898,95895,1828],{},[1765,95897,1945],{},[1765,95899,5486],{},[902,95901,95902],{"encoding":904},"Q_2 = 2^{4\u002F3} \\cdot Q_1^{-1\u002F3} = \\dfrac{2 \\sqrt[3]{2}}{\\sqrt[3]{Q_1}}"," (obrázek 6.5).",[198,95905,95907],{"id":95906},"čtyři-vlastnosti-křivek-užitečnosti","Čtyři vlastnosti křivek užitečnosti",[724,95909,95910],{},[3991,95911],{"alt":95912,"className":95913,"src":95914},"imek-ic-4vlastnosti-anotovane",[210,3995],"\u002Fwiki-assets\u002Fimek-ic-4vlastnosti-anotovane.jpeg",[1636,95916,95917,95926,95973,96017,96023,96029],{},[724,95918,95919,95921,95922,95925],{},[883,95920,4723],{}," Čtyři základní vlastnosti indiferenčních křivek\n",[38,95923,95924],{},"1° Klesající."," Je-li nakoupeno méně jednoho zboží, je k dosažení stejného uspokojení třeba kompenzovat větším množstvím druhého zboží. Sklon tečny je",[724,95927,95928],{},[883,95929,95931],{"className":95930},[886],[888,95932,95933],{"xmlns":890},[892,95934,95935,95970],{},[895,95936,95937,95940,95942,95944,95946,95948,95966,95968],{},[898,95938,95939],{"mathvariant":1969},"tg",[1761,95941,60178],{},[898,95943,22895],{},[1761,95945,1909],{},[1761,95947,1885],{},[4379,95949,95950,95958],{},[2015,95951,95952,95954,95956],{},[898,95953,900],{},[1765,95955,1945],{},[1761,95957,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[2015,95959,95960,95962,95964],{},[898,95961,900],{},[1765,95963,2296],{},[1761,95965,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,95967,2058],{},[1765,95969,1767],{},[902,95971,95972],{"encoding":904},"\\operatorname{tg} \\alpha = -\\frac{U'_1}{U'_2} \u003C 0",[724,95974,95975,95976,96016],{},"(derivace implicitně zadané funkce ",[883,95977,95979],{"className":95978},[886],[888,95980,95981],{"xmlns":890},[892,95982,95983,96013],{},[895,95984,95985,95987,95989,95995,95997,96003,96005,96007,96009,96011],{},[898,95986,900],{},[1761,95988,1915],{"stretchy":1821},[1681,95990,95991,95993],{},[898,95992,1828],{},[1765,95994,1945],{},[1761,95996,1834],{"separator":1833},[1681,95998,95999,96001],{},[898,96000,1828],{},[1765,96002,2296],{},[1761,96004,1920],{"stretchy":1821},[1761,96006,1885],{},[898,96008,2774],{},[1761,96010,1909],{},[1765,96012,1767],{},[902,96014,96015],{"encoding":904},"U(Q_1, Q_2) - c = 0","). Ze záporné derivace plyne klesající průběh.",[724,96018,96019,96022],{},[38,96020,96021],{},"2° Neprotínají se."," V průsečíku by týž svazek ležel na dvou různých hladinách užitečnosti, což je spor.",[724,96024,96025,96028],{},[38,96026,96027],{},"3° Čím vzdálenější od počátku, tím vyšší užitečnost"," (obrázek 6.4).",[724,96030,96031,96034,96035,96053,96054,96070,96071,96074],{},[38,96032,96033],{},"4° Konvexní."," Pro každé dva body ",[883,96036,96038],{"className":96037},[886],[888,96039,96040],{"xmlns":890},[892,96041,96042,96050],{},[895,96043,96044,96046,96048],{},[898,96045,8309],{},[1761,96047,1834],{"separator":1833},[898,96049,27286],{},[902,96051,96052],{"encoding":904},"A, B"," na téže křivce leží vnitřní body úsečky ",[883,96055,96057],{"className":96056},[886],[888,96058,96059],{"xmlns":890},[892,96060,96061,96067],{},[895,96062,96063,96065],{},[898,96064,8309],{},[898,96066,27286],{},[902,96068,96069],{"encoding":904},"AB"," ve ",[38,96072,96073],{},"vyšší"," hladině užitečnosti (tj. „nad\" křivkou) — vyjadřuje to preferenci smíšených svazků před krajními.",[724,96076,96077],{},[614,96078,96079,96080,96115,96116,1741],{},"Obrázek 6.6 — klesající a konvexní průběh ",[883,96081,96083],{"className":96082},[886],[888,96084,96085],{"xmlns":890},[892,96086,96087,96113],{},[895,96088,96089,96091,96093,96099,96101,96107,96109,96111],{},[898,96090,900],{},[1761,96092,1915],{"stretchy":1821},[1681,96094,96095,96097],{},[898,96096,1828],{},[1765,96098,1945],{},[1761,96100,1834],{"separator":1833},[1681,96102,96103,96105],{},[898,96104,1828],{},[1765,96106,2296],{},[1761,96108,1920],{"stretchy":1821},[1761,96110,1909],{},[898,96112,2774],{},[902,96114,13808],{"encoding":904}," s tečnou se sklonem ",[883,96117,96119],{"className":96118},[886],[888,96120,96121],{"xmlns":890},[892,96122,96123,96131],{},[895,96124,96125,96127,96129],{},[898,96126,95939],{"mathvariant":1969},[1761,96128,60178],{},[898,96130,22895],{},[902,96132,96133],{"encoding":904},"\\operatorname{tg}\\alpha",[115,96135,96137],{"id":96136},"mezní-míra-komoditní-substituce-mrcs","Mezní míra komoditní substituce (MRCS)",[724,96139,96140,1989,96143,3927,96156,96159],{},[38,96141,96142],{},"Mezní míra komoditní substituce",[883,96144,96146],{"className":96145},[886],[888,96147,96148],{"xmlns":890},[892,96149,96150,96154],{},[895,96151,96152],{},[2761,96153,14641],{},[902,96155,32268],{"encoding":904},[38,96157,96158],{},"marginal rate of commodity substitution",") je podíl mezních užitečností:",[883,96161,96163],{"className":96162},[886],[888,96164,96165],{"xmlns":890,"display":1930},[892,96166,96167,96254],{},[24787,96168,96169],{"width":32101},[24792,96170,96171,96173,96247,96249],{},[24795,96172],{"width":32106},[24795,96174,96175],{},[895,96176,96177,96179,96181,96183,96185,96191,96193,96199,96201,96203,96225,96227,96245],{},[2761,96178,14641],{},[1761,96180,1909],{},[2761,96182,14641],{},[1761,96184,1915],{"stretchy":1821},[1681,96186,96187,96189],{},[898,96188,1828],{},[1765,96190,1945],{},[1761,96192,1834],{"separator":1833},[1681,96194,96195,96197],{},[898,96196,1828],{},[1765,96198,2296],{},[1761,96200,1920],{"stretchy":1821},[1761,96202,1909],{},[4379,96204,96205,96215],{},[895,96206,96207,96209],{},[898,96208,6889],{},[1681,96210,96211,96213],{},[898,96212,900],{},[1765,96214,1945],{},[895,96216,96217,96219],{},[898,96218,6889],{},[1681,96220,96221,96223],{},[898,96222,900],{},[1765,96224,2296],{},[1761,96226,1909],{},[4379,96228,96229,96237],{},[2015,96230,96231,96233,96235],{},[898,96232,900],{},[1765,96234,1945],{},[1761,96236,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[2015,96238,96239,96241,96243],{},[898,96240,900],{},[1765,96242,2296],{},[1761,96244,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[898,96246,1741],{"mathvariant":1969},[24795,96248],{"width":32106},[24795,96250,96251],{},[2761,96252,96253],{},"(6.9)",[902,96255,96256],{"encoding":904},"\\text{MRCS} = \\text{MRCS}(Q_1, Q_2) = \\frac{MU_1}{MU_2} = \\frac{U'_1}{U'_2}. \\tag{6.9}",[724,96258,96259,96260,96294,96295,96327,96328,96363,96364,96377],{},"Geometricky: ",[883,96261,96263],{"className":96262},[886],[888,96264,96265],{"xmlns":890},[892,96266,96267,96291],{},[895,96268,96269,96271],{},[1761,96270,1885],{},[6411,96272,96273],{"scriptlevel":1767,"displaystyle":1821},[4379,96274,96275,96283],{},[2015,96276,96277,96279,96281],{},[898,96278,900],{},[1765,96280,1945],{},[1761,96282,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[2015,96284,96285,96287,96289],{},[898,96286,900],{},[1765,96288,2296],{},[1761,96290,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[902,96292,96293],{"encoding":904},"-\\tfrac{U'_1}{U'_2}"," je derivace funkce ",[883,96296,96298],{"className":96297},[886],[888,96299,96300],{"xmlns":890},[892,96301,96302,96324],{},[895,96303,96304,96310,96312,96314,96316,96322],{},[1681,96305,96306,96308],{},[898,96307,1828],{},[1765,96309,2296],{},[1761,96311,1909],{},[898,96313,6107],{},[1761,96315,1915],{"stretchy":1821},[1681,96317,96318,96320],{},[898,96319,1828],{},[1765,96321,1945],{},[1761,96323,1920],{"stretchy":1821},[902,96325,96326],{"encoding":904},"Q_2 = f(Q_1)"," zadané implicitně rovnicí ",[883,96329,96331],{"className":96330},[886],[888,96332,96333],{"xmlns":890},[892,96334,96335,96361],{},[895,96336,96337,96339,96341,96347,96349,96355,96357,96359],{},[898,96338,900],{},[1761,96340,1915],{"stretchy":1821},[1681,96342,96343,96345],{},[898,96344,1828],{},[1765,96346,1945],{},[1761,96348,1834],{"separator":1833},[1681,96350,96351,96353],{},[898,96352,1828],{},[1765,96354,2296],{},[1761,96356,1920],{"stretchy":1821},[1761,96358,1909],{},[898,96360,2774],{},[902,96362,13808],{"encoding":904},". Protože je vždy záporná (křivka je klesající), bereme absolutní hodnotu a kladný ",[883,96365,96367],{"className":96366},[886],[888,96368,96369],{"xmlns":890},[892,96370,96371,96375],{},[895,96372,96373],{},[2761,96374,14641],{},[902,96376,32268],{"encoding":904}," chápeme jako velikost kompenzace.",[1636,96379,96380],{},[724,96381,96382,96384,96385,12146,96417,96455,96456,96473,96474,96491],{},[883,96383,1642],{}," Intuice — MRCS jako sklon indiferenční křivky\n",[883,96386,96388],{"className":96387},[886],[888,96389,96390],{"xmlns":890},[892,96391,96392,96414],{},[895,96393,96394,96396,96398,96404,96406,96412],{},[2761,96395,14641],{},[1761,96397,1915],{"stretchy":1821},[1681,96399,96400,96402],{},[898,96401,1828],{},[1765,96403,1945],{},[1761,96405,1834],{"separator":1833},[1681,96407,96408,96410],{},[898,96409,1828],{},[1765,96411,2296],{},[1761,96413,1920],{"stretchy":1821},[902,96415,96416],{"encoding":904},"\\text{MRCS}(Q_1, Q_2)",[38,96418,96419,96420,33033,96437,96454],{},"míra, jakou je spotřebitel ochoten zaměnit ",[883,96421,96423],{"className":96422},[886],[888,96424,96425],{"xmlns":890},[892,96426,96427,96435],{},[895,96428,96429],{},[1681,96430,96431,96433],{},[898,96432,1828],{},[1765,96434,1945],{},[902,96436,33032],{"encoding":904},[883,96438,96440],{"className":96439},[886],[888,96441,96442],{"xmlns":890},[892,96443,96444,96452],{},[895,96445,96446],{},[1681,96447,96448,96450],{},[898,96449,1828],{},[1765,96451,2296],{},[902,96453,33051],{"encoding":904}," při zachování užitečnosti"," — tedy kolik jednotek ",[883,96457,96459],{"className":96458},[886],[888,96460,96461],{"xmlns":890},[892,96462,96463,96471],{},[895,96464,96465],{},[1681,96466,96467,96469],{},[898,96468,1828],{},[1765,96470,2296],{},[902,96472,33051],{"encoding":904}," „obětuje\" za jednu jednotku ",[883,96475,96477],{"className":96476},[886],[888,96478,96479],{"xmlns":890},[892,96480,96481,96489],{},[895,96482,96483],{},[1681,96484,96485,96487],{},[898,96486,1828],{},[1765,96488,1945],{},[902,96490,33032],{"encoding":904}," navíc, aby zůstal na téže indiferenční křivce. Geometricky jde o absolutní hodnotu sklonu tečny k indiferenční křivce v daném bodě.",[724,96493,96494,96495,33974],{},"Pro obecnou změnu ",[883,96496,96498],{"className":96497},[886],[888,96499,96500],{"xmlns":890},[892,96501,96502,96512],{},[895,96503,96504,96506],{},[898,96505,4346],{"mathvariant":1969},[1681,96507,96508,96510],{},[898,96509,1828],{},[1765,96511,1945],{},[902,96513,96514],{"encoding":904},"\\mathrm{d} Q_1",[883,96516,96518],{"className":96517},[886],[888,96519,96520],{"xmlns":890,"display":1930},[892,96521,96522,96575],{},[24787,96523,96524],{"width":32101},[24792,96525,96526,96528,96568,96570],{},[24795,96527],{"width":32106},[24795,96529,96530],{},[895,96531,96532,96534,96540,96542,96544,96550,96552,96554,96556,96558,96560,96566],{},[898,96533,6959],{"mathvariant":1969},[1681,96535,96536,96538],{},[898,96537,1828],{},[1765,96539,2296],{},[1761,96541,6803],{},[898,96543,4346],{"mathvariant":1969},[1681,96545,96546,96548],{},[898,96547,1828],{},[1765,96549,2296],{},[1761,96551,1909],{},[1761,96553,1885],{},[2761,96555,14641],{},[1761,96557,2447],{},[898,96559,4346],{"mathvariant":1969},[1681,96561,96562,96564],{},[898,96563,1828],{},[1765,96565,1945],{},[1761,96567,1834],{"separator":1833},[24795,96569],{"width":32106},[24795,96571,96572],{},[2761,96573,96574],{},"(6.10)",[902,96576,96577],{"encoding":904},"\\Delta Q_2 \\approx \\mathrm{d} Q_2 = -\\text{MRCS} \\cdot \\mathrm{d} Q_1, \\tag{6.10}",[883,96579,96581],{"className":96580},[886],[888,96582,96583],{"xmlns":890,"display":1930},[892,96584,96585,96632],{},[24787,96586,96587],{"width":32101},[24792,96588,96589,96591,96625,96627],{},[24795,96590],{"width":32106},[24795,96592,96593],{},[895,96594,96595,96597,96603,96605,96607,96613,96615,96617,96623],{},[898,96596,4346],{"mathvariant":1969},[1681,96598,96599,96601],{},[898,96600,1828],{},[1765,96602,1945],{},[1761,96604,1909],{},[1761,96606,1885],{},[4379,96608,96609,96611],{},[1765,96610,1945],{},[2761,96612,14641],{},[2761,96614,7057],{},[898,96616,4346],{"mathvariant":1969},[1681,96618,96619,96621],{},[898,96620,1828],{},[1765,96622,2296],{},[898,96624,1741],{"mathvariant":1969},[24795,96626],{"width":32106},[24795,96628,96629],{},[2761,96630,96631],{},"(6.11)",[902,96633,96634],{"encoding":904},"\\mathrm{d} Q_1 = -\\frac{1}{\\text{MRCS}}\\, \\mathrm{d} Q_2. \\tag{6.11}",[1636,96636,96637,96703,96820],{},[724,96638,96639,96641,96642,33974],{},[883,96640,56675],{}," Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost\nPro ",[883,96643,96645],{"className":96644},[886],[888,96646,96647],{"xmlns":890},[892,96648,96649,96701],{},[895,96650,96651,96653,96655,96661,96663,96669,96671,96673,96687],{},[898,96652,900],{},[1761,96654,1915],{"stretchy":1821},[1681,96656,96657,96659],{},[898,96658,1828],{},[1765,96660,1945],{},[1761,96662,1834],{"separator":1833},[1681,96664,96665,96667],{},[898,96666,1828],{},[1765,96668,2296],{},[1761,96670,1920],{"stretchy":1821},[1761,96672,1909],{},[2015,96674,96675,96677,96679],{},[898,96676,1828],{},[1765,96678,1945],{},[895,96680,96681,96683,96685],{},[1765,96682,1945],{},[898,96684,8726],{"mathvariant":1969},[1765,96686,2296],{},[2015,96688,96689,96691,96693],{},[898,96690,1828],{},[1765,96692,2296],{},[895,96694,96695,96697,96699],{},[1765,96696,1945],{},[898,96698,8726],{"mathvariant":1969},[1765,96700,2296],{},[902,96702,33973],{"encoding":904},[724,96704,96705],{},[883,96706,96708],{"className":96707},[886],[888,96709,96710],{"xmlns":890},[892,96711,96712,96818],{},[895,96713,96714,96716,96718,96800,96802,96816],{},[2761,96715,14641],{},[1761,96717,1909],{},[4379,96719,96720,96760],{},[895,96721,96722,96730,96746],{},[6411,96723,96724],{"scriptlevel":1767,"displaystyle":1821},[4379,96725,96726,96728],{},[1765,96727,1945],{},[1765,96729,2296],{},[2015,96731,96732,96734,96736],{},[898,96733,1828],{},[1765,96735,1945],{},[895,96737,96738,96740,96742,96744],{},[1761,96739,1885],{},[1765,96741,1945],{},[898,96743,8726],{"mathvariant":1969},[1765,96745,2296],{},[2015,96747,96748,96750,96752],{},[898,96749,1828],{},[1765,96751,2296],{},[895,96753,96754,96756,96758],{},[1765,96755,1945],{},[898,96757,8726],{"mathvariant":1969},[1765,96759,2296],{},[895,96761,96762,96770,96784],{},[6411,96763,96764],{"scriptlevel":1767,"displaystyle":1821},[4379,96765,96766,96768],{},[1765,96767,1945],{},[1765,96769,2296],{},[2015,96771,96772,96774,96776],{},[898,96773,1828],{},[1765,96775,1945],{},[895,96777,96778,96780,96782],{},[1765,96779,1945],{},[898,96781,8726],{"mathvariant":1969},[1765,96783,2296],{},[2015,96785,96786,96788,96790],{},[898,96787,1828],{},[1765,96789,2296],{},[895,96791,96792,96794,96796,96798],{},[1761,96793,1885],{},[1765,96795,1945],{},[898,96797,8726],{"mathvariant":1969},[1765,96799,2296],{},[1761,96801,1909],{},[4379,96803,96804,96810],{},[1681,96805,96806,96808],{},[898,96807,1828],{},[1765,96809,2296],{},[1681,96811,96812,96814],{},[898,96813,1828],{},[1765,96815,1945],{},[898,96817,1741],{"mathvariant":1969},[902,96819,34092],{"encoding":904},[724,96821,34095,96822,6997,96865,34143,96867,96886],{},[883,96823,96825],{"className":96824},[886],[888,96826,96827],{"xmlns":890},[892,96828,96829,96863],{},[895,96830,96831,96833,96835,96837,96839,96841,96843,96845,96853,96855],{},[2761,96832,14641],{},[1761,96834,1915],{"stretchy":1821},[1765,96836,34111],{},[1761,96838,1834],{"separator":1833},[1765,96840,19148],{},[1761,96842,1920],{"stretchy":1821},[1761,96844,1909],{},[6411,96846,96847],{"scriptlevel":1767,"displaystyle":1821},[4379,96848,96849,96851],{},[1765,96850,19148],{},[1765,96852,34111],{},[1761,96854,1909],{},[6411,96856,96857],{"scriptlevel":1767,"displaystyle":1821},[4379,96858,96859,96861],{},[1765,96860,6321],{},[1765,96862,5486],{},[902,96864,34140],{"encoding":904},[614,96866,13257],{},[883,96868,96870],{"className":96869},[886],[888,96871,96872],{"xmlns":890},[892,96873,96874,96884],{},[895,96875,96876],{},[6411,96877,96878],{"scriptlevel":1767,"displaystyle":1821},[4379,96879,96880,96882],{},[1765,96881,6321],{},[1765,96883,5486],{},[902,96885,34163],{"encoding":904}," jednotky, aby se užitečnost zachovala.",[724,96888,96889,96890,96894],{},"(Paralelou je ",[207,96891,96893],{"className":96892,"dataFsResolvedFilePath":857,"href":858},[210],"mezní míra technické substituce MRTS"," z produkční teorie.)",[115,96896,96898],{"id":96897},"_63-64-optimalizace-spotřebitele-přehled","6.3 – 6.4 Optimalizace spotřebitele — přehled",[724,96900,96901,96902,96905],{},"Rámcově se v kapitole 6 studují ",[38,96903,96904],{},"dvě vázané optimalizační úlohy"," s užitečností:",[120,96907,96908,97044],{},[123,96909,96910,96912,96913,14195,96944,1989,96947,96996,96997,1741],{},[38,96911,32282],{}," — maximalizace ",[883,96914,96916],{"className":96915},[886],[888,96917,96918],{"xmlns":890},[892,96919,96920,96942],{},[895,96921,96922,96924,96926,96932,96934,96940],{},[898,96923,900],{},[1761,96925,1915],{"stretchy":1821},[1681,96927,96928,96930],{},[898,96929,1828],{},[1765,96931,1945],{},[1761,96933,1834],{"separator":1833},[1681,96935,96936,96938],{},[898,96937,1828],{},[1765,96939,2296],{},[1761,96941,1920],{"stretchy":1821},[902,96943,20377],{"encoding":904},[38,96945,96946],{},"rozpočtovém omezení",[883,96948,96950],{"className":96949},[886],[888,96951,96952],{"xmlns":890},[892,96953,96954,96994],{},[895,96955,96956,96962,96964,96972,96978,96980,96988],{},[1824,96957,96958,96960],{},[898,96959,13170],{},[1761,96961,8408],{},[1761,96963,1909],{},[2015,96965,96966,96968,96970],{},[898,96967,1839],{},[1765,96969,1945],{},[1761,96971,8408],{},[1681,96973,96974,96976],{},[898,96975,1828],{},[1765,96977,1945],{},[1761,96979,1964],{},[2015,96981,96982,96984,96986],{},[898,96983,1839],{},[1765,96985,2296],{},[1761,96987,8408],{},[1681,96989,96990,96992],{},[898,96991,1828],{},[1765,96993,2296],{},[902,96995,21332],{"encoding":904},". Výstupem je Marshallova poptávka ",[883,96998,97000],{"className":96999},[886],[888,97001,97002],{"xmlns":890},[892,97003,97004,97042],{},[895,97005,97006,97012,97014,97020,97022,97028,97030,97036,97038,97040],{},[1681,97007,97008,97010],{},[898,97009,1828],{},[898,97011,21824],{},[1761,97013,1909],{},[1681,97015,97016,97018],{},[898,97017,2244],{},[898,97019,21824],{},[1761,97021,1915],{"stretchy":1821},[1681,97023,97024,97026],{},[898,97025,1839],{},[1765,97027,1945],{},[1761,97029,1834],{"separator":1833},[1681,97031,97032,97034],{},[898,97033,1839],{},[1765,97035,2296],{},[1761,97037,1834],{"separator":1833},[898,97039,13170],{},[1761,97041,1920],{"stretchy":1821},[902,97043,40483],{"encoding":904},[123,97045,97046,31932,97049,31975,97095,97112,97113,1741],{},[38,97047,97048],{},"Duální úloha",[883,97050,97052],{"className":97051},[886],[888,97053,97054],{"xmlns":890},[892,97055,97056,97092],{},[895,97057,97058,97060,97062,97070,97076,97078,97086],{},[898,97059,1818],{},[1761,97061,1909],{},[2015,97063,97064,97066,97068],{},[898,97065,1839],{},[1765,97067,1945],{},[1761,97069,8408],{},[1681,97071,97072,97074],{},[898,97073,1828],{},[1765,97075,1945],{},[1761,97077,1964],{},[2015,97079,97080,97082,97084],{},[898,97081,1839],{},[1765,97083,2296],{},[1761,97085,8408],{},[1681,97087,97088,97090],{},[898,97089,1828],{},[1765,97091,2296],{},[902,97093,97094],{"encoding":904},"E = P_1^* Q_1 + P_2^* Q_2",[883,97096,97098],{"className":97097},[886],[888,97099,97100],{"xmlns":890},[892,97101,97102,97110],{},[895,97103,97104],{},[1824,97105,97106,97108],{},[898,97107,900],{},[1761,97109,8408],{},[902,97111,31993],{"encoding":904},". Výstupem je Hicksova poptávka ",[883,97114,97116],{"className":97115},[886],[888,97117,97118],{"xmlns":890},[892,97119,97120,97158],{},[895,97121,97122,97128,97130,97136,97138,97144,97146,97152,97154,97156],{},[1681,97123,97124,97126],{},[898,97125,1828],{},[898,97127,21824],{},[1761,97129,1909],{},[1681,97131,97132,97134],{},[898,97133,2244],{},[898,97135,21824],{},[1761,97137,1915],{"stretchy":1821},[1681,97139,97140,97142],{},[898,97141,1839],{},[1765,97143,1945],{},[1761,97145,1834],{"separator":1833},[1681,97147,97148,97150],{},[898,97149,1839],{},[1765,97151,2296],{},[1761,97153,1834],{"separator":1833},[898,97155,900],{},[1761,97157,1920],{"stretchy":1821},[902,97159,21857],{"encoding":904},[724,97161,97162,97163,97166,97167,1989,97170,97209],{},"Obě úlohy se řeší ",[207,97164,31998],{"className":97165,"dataFsResolvedFilePath":791,"href":792},[210]," a vedou na ",[38,97168,97169],{},"tentýž bod dotyku",[883,97171,97173],{"className":97172},[886],[888,97174,97175],{"xmlns":890},[892,97176,97177,97207],{},[895,97178,97179,97185,97187,97195,97197,97205],{},[1824,97180,97181,97183],{},[898,97182,1828],{},[1761,97184,8408],{},[1761,97186,1822],{"stretchy":1821},[2015,97188,97189,97191,97193],{},[898,97190,1828],{},[1765,97192,1945],{},[1761,97194,8408],{},[1761,97196,1834],{"separator":1833},[2015,97198,97199,97201,97203],{},[898,97200,1828],{},[1765,97202,2296],{},[1761,97204,8408],{},[1761,97206,1844],{"stretchy":1821},[902,97208,32357],{"encoding":904}," indiferenční křivky a rozpočtové přímky (resp. přímky výdajů), v němž platí podmínka optimality",[883,97211,97213],{"className":97212},[886],[888,97214,97215],{"xmlns":890,"display":1930},[892,97216,97217,97263],{},[895,97218,97219,97221,97223,97241,97243,97261],{},[2761,97220,14641],{},[1761,97222,1909],{},[4379,97224,97225,97233],{},[2015,97226,97227,97229,97231],{},[898,97228,900],{},[1765,97230,1945],{},[1761,97232,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[2015,97234,97235,97237,97239],{},[898,97236,900],{},[1765,97238,2296],{},[1761,97240,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,97242,1909],{},[4379,97244,97245,97253],{},[2015,97246,97247,97249,97251],{},[898,97248,1839],{},[1765,97250,1945],{},[1761,97252,8408],{},[2015,97254,97255,97257,97259],{},[898,97256,1839],{},[1765,97258,2296],{},[1761,97260,8408],{},[898,97262,1741],{"mathvariant":1969},[902,97264,97265],{"encoding":904},"\\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*}.",[724,97267,97268],{},"Poměr mezních užitečností se rovná poměru cen — sklon indiferenční křivky v optimu se rovná sklonu rozpočtové přímky.",[1636,97270,97271],{},[724,97272,97273,97275,97276,97279,97280,97283,97284,97311,97312,97346,97347,97381,97382,97425,97426,97429,97430,1741],{},[883,97274,1642],{}," Pro detailní postup viz ",[207,97277,40782],{"className":97278,"dataFsResolvedFilePath":911,"href":912},[210],"\nKompletní odvození obou úloh Lagrangeovou metodou, geometrická interpretace, řešené ",[38,97281,97282],{},"Příklady 6.5–6.8"," (MRCS pro Cobb-Douglase, maximalizace ",[883,97285,97287],{"className":97286},[886],[888,97288,97289],{"xmlns":890},[892,97290,97291,97309],{},[895,97292,97293,97295,97297,97303],{},[898,97294,900],{},[1761,97296,1909],{},[1681,97298,97299,97301],{},[898,97300,1828],{},[1765,97302,1945],{},[1681,97304,97305,97307],{},[898,97306,1828],{},[1765,97308,2296],{},[902,97310,34256],{"encoding":904}," s výsledkem ",[883,97313,97315],{"className":97314},[886],[888,97316,97317],{"xmlns":890},[892,97318,97319,97343],{},[895,97320,97321,97327,97329,97331,97333,97339,97341],{},[1681,97322,97323,97325],{},[898,97324,1828],{},[1765,97326,1945],{},[1761,97328,1909],{},[1765,97330,9056],{},[1761,97332,1834],{"separator":1833},[1681,97334,97335,97337],{},[898,97336,1828],{},[1765,97338,2296],{},[1761,97340,1909],{},[1765,97342,2633],{},[902,97344,97345],{"encoding":904},"Q_1 = 25, Q_2 = 10","; minimalizace výdajů s ",[883,97348,97350],{"className":97349},[886],[888,97351,97352],{"xmlns":890},[892,97353,97354,97378],{},[895,97355,97356,97362,97364,97366,97368,97374,97376],{},[1681,97357,97358,97360],{},[898,97359,1828],{},[1765,97361,1945],{},[1761,97363,1909],{},[1765,97365,2318],{},[1761,97367,1834],{"separator":1833},[1681,97369,97370,97372],{},[898,97371,1828],{},[1765,97373,2296],{},[1761,97375,1909],{},[1765,97377,1945],{},[902,97379,97380],{"encoding":904},"Q_1 = 4, Q_2 = 1","; obecná Hicksova poptávka pro ",[883,97383,97385],{"className":97384},[886],[888,97386,97387],{"xmlns":890},[892,97388,97389,97423],{},[895,97390,97391,97393,97395,97409],{},[898,97392,900],{},[1761,97394,1909],{},[2015,97396,97397,97399,97401],{},[898,97398,1828],{},[1765,97400,1945],{},[895,97402,97403,97405,97407],{},[1765,97404,1945],{},[898,97406,8726],{"mathvariant":1969},[1765,97408,2296],{},[2015,97410,97411,97413,97415],{},[898,97412,1828],{},[1765,97414,2296],{},[895,97416,97417,97419,97421],{},[1765,97418,1945],{},[898,97420,8726],{"mathvariant":1969},[1765,97422,2296],{},[902,97424,37189],{"encoding":904},"), odvození Marshallovy i Hicksovy funkce poptávky a Engelových funkcí, vztah dualita primární ↔ duální úlohy a úlohy ",[38,97427,97428],{},"6.8–6.13"," jsou na stránce ",[207,97431,31798],{"className":97432,"dataFsResolvedFilePath":911,"href":912},[210],[115,97434,97436],{"id":97435},"shrnutí-kapitoly-6","Shrnutí kapitoly 6",[724,97438,97439,97440,97453,97454,97456,97457,97459,97460,97462,97463,97465,97466,97468,97469,97471,97472,1989,97474,97509,97510,97523,97524,97527,97528,97531,97532,1741],{},"Každá ",[883,97441,97443],{"className":97442},[886],[888,97444,97445],{"xmlns":890},[892,97446,97447,97451],{},[895,97448,97449],{},[898,97450,40888],{},[902,97452,40888],{"encoding":904},"-tice množství jednotlivých zboží je ",[38,97455,90788],{},". Přiřadíme-li každému svazku kladné číslo (jeho užitečnost), můžeme svazky uspořádat podle rostoucí užitečnosti; svazky se stejnou užitečností jsou indiferentní. Tím je definována ",[38,97458,91271],{}," a současně ",[38,97461,90791],{},". Její parciální derivace (podle jednotlivých množství) jsou ",[38,97464,90796],{}," — přibližná změna užitečnosti při jednotkové změně příslušného zboží. Aby funkce mohla být funkcí užitečnosti, musejí být její první parciální derivace ",[38,97467,56657],{}," (6.4) a druhé parciální derivace ",[38,97470,93154],{}," (6.5 — zákon klesající mezní užitečnosti). ",[38,97473,13771],{},[883,97475,97477],{"className":97476},[886],[888,97478,97479],{"xmlns":890},[892,97480,97481,97507],{},[895,97482,97483,97485,97487,97493,97495,97501,97503,97505],{},[898,97484,900],{},[1761,97486,1915],{"stretchy":1821},[1681,97488,97489,97491],{},[898,97490,1828],{},[1765,97492,1945],{},[1761,97494,1834],{"separator":1833},[1681,97496,97497,97499],{},[898,97498,1828],{},[1765,97500,2296],{},[1761,97502,1920],{"stretchy":1821},[1761,97504,1909],{},[898,97506,2774],{},[902,97508,13808],{"encoding":904}," jsou klesající, neprotínající se, vzdálenější od počátku mají vyšší užitečnost a jsou konvexní. ",[883,97511,97513],{"className":97512},[886],[888,97514,97515],{"xmlns":890},[892,97516,97517,97521],{},[895,97518,97519],{},[2761,97520,14641],{},[902,97522,32268],{"encoding":904}," = podíl mezních užitečností udává náhradu jednoho zboží druhým při zachování užitečnosti. Na tento teoretický základ navazují optimalizační úlohy (",[38,97525,97526],{},"maximalizace užitečnosti"," a duální ",[38,97529,97530],{},"minimalizace výdajů",") řešené Lagrangeovou metodou — viz ",[207,97533,40782],{"className":97534,"dataFsResolvedFilePath":911,"href":912},[210],[115,97536,53867],{"id":53866},[152,97538,97539,97542,97545,97548,97551,97554,97557,97560,97563,97566],{},[123,97540,97541],{},"Co se zahrnuje pod termín užitečnost?",[123,97543,97544],{},"Co se rozumí svazkem zboží? Které svazky zboží jsou indiferentní?",[123,97546,97547],{},"Jak souvisejí hodnoty funkce užitečnosti s preferencí svazků?",[123,97549,97550],{},"Jak se vypočítá mezní užitečnost?",[123,97552,97553],{},"Jak lze ekonomicky interpretovat fakt, že mezní užitečnost určitého zboží se rovná 2,5?",[123,97555,97556],{},"Jaké vlastnosti musí mít funkce více proměnných, aby mohla být funkcí užitečnosti?",[123,97558,97559],{},"Které jsou nejčastěji používané funkce užitečnosti?",[123,97561,97562],{},"Jakou rovnici mají křivky užitečnosti? Co platí v bodech ležících na téže křivce užitečnosti?",[123,97564,97565],{},"Proč mají křivky užitečnosti záporný sklon?",[123,97567,97568],{},"Jak se vypočte mezní míra komoditní substituce? Vysvětlete, co vypočtená hodnota vyjadřuje.",[115,97570,97572],{"id":97571},"úlohy-teorie-užitečnosti-61-67","Úlohy — teorie užitečnosti (6.1 – 6.7)",[724,97574,97575,97578,97579,87461,97621,1343,97649,1343,97677,97705],{},[38,97576,97577],{},"6.1"," Užitečnost pro tři zboží — hudbu, čokoládu a sýr je dána vztahem ",[883,97580,97582],{"className":97581},[886],[888,97583,97584],{"xmlns":890},[892,97585,97586,97618],{},[895,97587,97588,97590,97592,97598,97600,97602,97608,97610,97612],{},[898,97589,900],{},[1761,97591,1909],{},[1681,97593,97594,97596],{},[898,97595,1828],{},[1765,97597,1945],{},[1761,97599,1964],{},[1765,97601,68537],{},[1681,97603,97604,97606],{},[898,97605,1828],{},[1765,97607,2296],{},[1761,97609,1964],{},[1765,97611,2296],{},[1681,97613,97614,97616],{},[898,97615,1828],{},[1765,97617,5486],{},[902,97619,97620],{"encoding":904},"U = Q_1 + 1{,}5 Q_2 + 2 Q_3",[883,97622,97624],{"className":97623},[886],[888,97625,97626],{"xmlns":890},[892,97627,97628,97646],{},[895,97629,97630,97632,97634,97636,97638,97640,97642,97644],{},[898,97631,900],{},[1761,97633,1915],{"stretchy":1821},[1765,97635,2318],{},[1761,97637,1834],{"separator":1833},[1765,97639,2296],{},[1761,97641,1834],{"separator":1833},[1765,97643,2296],{},[1761,97645,1920],{"stretchy":1821},[902,97647,97648],{"encoding":904},"U(4, 2, 2)",[883,97650,97652],{"className":97651},[886],[888,97653,97654],{"xmlns":890},[892,97655,97656,97674],{},[895,97657,97658,97660,97662,97664,97666,97668,97670,97672],{},[898,97659,900],{},[1761,97661,1915],{"stretchy":1821},[1765,97663,1945],{},[1761,97665,1834],{"separator":1833},[1765,97667,2318],{},[1761,97669,1834],{"separator":1833},[1765,97671,2296],{},[1761,97673,1920],{"stretchy":1821},[902,97675,97676],{"encoding":904},"U(1, 4, 2)",[883,97678,97680],{"className":97679},[886],[888,97681,97682],{"xmlns":890},[892,97683,97684,97702],{},[895,97685,97686,97688,97690,97692,97694,97696,97698,97700],{},[898,97687,900],{},[1761,97689,1915],{"stretchy":1821},[1765,97691,2296],{},[1761,97693,1834],{"separator":1833},[1765,97695,5486],{},[1761,97697,1834],{"separator":1833},[1765,97699,1945],{},[1761,97701,1920],{"stretchy":1821},[902,97703,97704],{"encoding":904},"U(2, 3, 1)",". (b) Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků v (a).",[724,97707,97708,97711,97712,97764,97765,1343,97791,1343,97817,1343,97843,1343,97869,1343,97895,1343,97921,97947],{},[38,97709,97710],{},"6.2"," Je dána užitečnost ",[883,97713,97715],{"className":97714},[886],[888,97716,97717],{"xmlns":890},[892,97718,97719,97761],{},[895,97720,97721,97723,97725,97727,97741,97755],{},[898,97722,900],{},[1761,97724,1909],{},[1765,97726,2296],{},[2015,97728,97729,97731,97733],{},[898,97730,1828],{},[1765,97732,1945],{},[895,97734,97735,97737,97739],{},[1765,97736,1945],{},[898,97738,8726],{"mathvariant":1969},[1765,97740,5486],{},[2015,97742,97743,97745,97747],{},[898,97744,1828],{},[1765,97746,2296],{},[895,97748,97749,97751,97753],{},[1765,97750,1945],{},[898,97752,8726],{"mathvariant":1969},[1765,97754,2296],{},[1681,97756,97757,97759],{},[898,97758,1828],{},[1765,97760,5486],{},[902,97762,97763],{"encoding":904},"U = 2 Q_1^{1\u002F3} Q_2^{1\u002F2} Q_3"," pro tři zboží. Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků ",[883,97766,97768],{"className":97767},[886],[888,97769,97770],{"xmlns":890},[892,97771,97772,97788],{},[895,97773,97774,97776,97778,97780,97782,97784,97786],{},[1761,97775,1915],{"stretchy":1821},[1765,97777,9616],{},[1761,97779,1834],{"separator":1833},[1765,97781,70575],{},[1761,97783,1834],{"separator":1833},[1765,97785,2633],{},[1761,97787,1920],{"stretchy":1821},[902,97789,97790],{"encoding":904},"(36, 27, 10)",[883,97792,97794],{"className":97793},[886],[888,97795,97796],{"xmlns":890},[892,97797,97798,97814],{},[895,97799,97800,97802,97804,97806,97808,97810,97812],{},[1761,97801,1915],{"stretchy":1821},[1765,97803,45849],{},[1761,97805,1834],{"separator":1833},[1765,97807,2454],{},[1761,97809,1834],{"separator":1833},[1765,97811,13077],{},[1761,97813,1920],{"stretchy":1821},[902,97815,97816],{"encoding":904},"(64, 8, 20)",[883,97818,97820],{"className":97819},[886],[888,97821,97822],{"xmlns":890},[892,97823,97824,97840],{},[895,97825,97826,97828,97830,97832,97834,97836,97838],{},[1761,97827,1915],{"stretchy":1821},[1765,97829,9056],{},[1761,97831,1834],{"separator":1833},[1765,97833,45849],{},[1761,97835,1834],{"separator":1833},[1765,97837,2454],{},[1761,97839,1920],{"stretchy":1821},[902,97841,97842],{"encoding":904},"(25, 64, 8)",[883,97844,97846],{"className":97845},[886],[888,97847,97848],{"xmlns":890},[892,97849,97850,97866],{},[895,97851,97852,97854,97856,97858,97860,97862,97864],{},[1761,97853,1915],{"stretchy":1821},[1765,97855,2318],{},[1761,97857,1834],{"separator":1833},[1765,97859,76507],{},[1761,97861,1834],{"separator":1833},[1765,97863,2340],{},[1761,97865,1920],{"stretchy":1821},[902,97867,97868],{"encoding":904},"(4, 125, 6)",[883,97870,97872],{"className":97871},[886],[888,97873,97874],{"xmlns":890},[892,97875,97876,97892],{},[895,97877,97878,97880,97882,97884,97886,97888,97890],{},[1761,97879,1915],{"stretchy":1821},[1765,97881,8056],{},[1761,97883,1834],{"separator":1833},[1765,97885,9262],{},[1761,97887,1834],{"separator":1833},[1765,97889,2291],{},[1761,97891,1920],{"stretchy":1821},[902,97893,97894],{"encoding":904},"(9, 40, 12)",[883,97896,97898],{"className":97897},[886],[888,97899,97900],{"xmlns":890},[892,97901,97902,97918],{},[895,97903,97904,97906,97908,97910,97912,97914,97916],{},[1761,97905,1915],{"stretchy":1821},[1765,97907,8056],{},[1761,97909,1834],{"separator":1833},[1765,97911,45849],{},[1761,97913,1834],{"separator":1833},[1765,97915,6321],{},[1761,97917,1920],{"stretchy":1821},[902,97919,97920],{"encoding":904},"(9, 64, 5)",[883,97922,97924],{"className":97923},[886],[888,97925,97926],{"xmlns":890},[892,97927,97928,97944],{},[895,97929,97930,97932,97934,97936,97938,97940,97942],{},[1761,97931,1915],{"stretchy":1821},[1765,97933,45849],{},[1761,97935,1834],{"separator":1833},[1765,97937,2454],{},[1761,97939,1834],{"separator":1833},[1765,97941,2633],{},[1761,97943,1920],{"stretchy":1821},[902,97945,97946],{"encoding":904},"(64, 8, 10)"," a uspořádejte je s neklesající užitečností.",[724,97949,97950,97711,97953,97996,97997,98031,98032,10518,98062,98095,98096,98113,98114,98131],{},[38,97951,97952],{},"6.3",[883,97954,97956],{"className":97955},[886],[888,97957,97958],{"xmlns":890},[892,97959,97960,97994],{},[895,97961,97962,97964,97966,97980],{},[898,97963,900],{},[1761,97965,1909],{},[2015,97967,97968,97970,97972],{},[898,97969,1828],{},[1765,97971,1945],{},[895,97973,97974,97976,97978],{},[1765,97975,1945],{},[898,97977,8726],{"mathvariant":1969},[1765,97979,2296],{},[2015,97981,97982,97984,97986],{},[898,97983,1828],{},[1765,97985,2296],{},[895,97987,97988,97990,97992],{},[1765,97989,1945],{},[898,97991,8726],{"mathvariant":1969},[1765,97993,2296],{},[902,97995,37189],{"encoding":904},". (a) Vypočtěte užitečnost pro ",[883,97998,98000],{"className":97999},[886],[888,98001,98002],{"xmlns":890},[892,98003,98004,98028],{},[895,98005,98006,98012,98014,98016,98018,98024,98026],{},[1681,98007,98008,98010],{},[898,98009,1828],{},[1765,98011,1945],{},[1761,98013,1909],{},[1765,98015,7190],{},[1761,98017,1834],{"separator":1833},[1681,98019,98020,98022],{},[898,98021,1828],{},[1765,98023,2296],{},[1761,98025,1909],{},[1765,98027,5467],{},[902,98029,98030],{"encoding":904},"Q_1 = 50, Q_2 = 80",". (b) Určete mezní užitečnosti ",[883,98033,98035],{"className":98034},[886],[888,98036,98037],{"xmlns":890},[892,98038,98039,98059],{},[895,98040,98041,98043,98049,98051,98053],{},[898,98042,6889],{},[1681,98044,98045,98047],{},[898,98046,900],{},[1765,98048,1945],{},[1761,98050,1834],{"separator":1833},[898,98052,6889],{},[1681,98054,98055,98057],{},[898,98056,900],{},[1765,98058,2296],{},[902,98060,98061],{"encoding":904},"MU_1, MU_2",[883,98063,98065],{"className":98064},[886],[888,98066,98067],{"xmlns":890},[892,98068,98069,98093],{},[895,98070,98071,98077,98079,98081,98083,98089,98091],{},[1681,98072,98073,98075],{},[898,98074,1828],{},[1765,98076,1945],{},[1761,98078,1909],{},[1765,98080,7190],{},[1761,98082,1834],{"separator":1833},[1681,98084,98085,98087],{},[898,98086,1828],{},[1765,98088,2296],{},[1761,98090,1909],{},[1765,98092,5467],{},[902,98094,98030],{"encoding":904}," a výsledky ekonomicky interpretujte. (d) Odhadněte změnu užitečnosti v důsledku změny ",[883,98097,98099],{"className":98098},[886],[888,98100,98101],{"xmlns":890},[892,98102,98103,98111],{},[895,98104,98105],{},[1681,98106,98107,98109],{},[898,98108,1828],{},[1765,98110,1945],{},[902,98112,33032],{"encoding":904}," na 60 a poklesu ",[883,98115,98117],{"className":98116},[886],[888,98118,98119],{"xmlns":890},[892,98120,98121,98129],{},[895,98122,98123],{},[1681,98124,98125,98127],{},[898,98126,1828],{},[1765,98128,2296],{},[902,98130,33051],{"encoding":904}," o 5 vzhledem k hladině dle (a) a porovnejte se skutečnou změnou užitečnosti.",[724,98133,98134,98137,98138,98199,98200,1741],{},[38,98135,98136],{},"6.4"," Je dána funkce ",[883,98139,98141],{"className":98140},[886],[888,98142,98143],{"xmlns":890},[892,98144,98145,98197],{},[895,98146,98147,98149,98151,98157,98159,98165,98167,98169,98183],{},[898,98148,900],{},[1761,98150,1915],{"stretchy":1821},[1681,98152,98153,98155],{},[898,98154,1828],{},[1765,98156,1945],{},[1761,98158,1834],{"separator":1833},[1681,98160,98161,98163],{},[898,98162,1828],{},[1765,98164,2296],{},[1761,98166,1920],{"stretchy":1821},[1761,98168,1909],{},[2015,98170,98171,98173,98175],{},[898,98172,1828],{},[1765,98174,1945],{},[895,98176,98177,98179,98181],{},[1765,98178,1945],{},[898,98180,8726],{"mathvariant":1969},[1765,98182,2296],{},[2015,98184,98185,98187,98189],{},[898,98186,1828],{},[1765,98188,2296],{},[895,98190,98191,98193,98195],{},[1765,98192,1945],{},[898,98194,8726],{"mathvariant":1969},[1765,98196,2296],{},[902,98198,33973],{"encoding":904},". (a) Ověřte, že tato funkce vykazuje vlastnosti funkce užitečnosti. (b) Najděte a načrtněte křivky ",[883,98201,98203],{"className":98202},[886],[888,98204,98205],{"xmlns":890},[892,98206,98207,98297],{},[895,98208,98209,98211,98213,98219,98221,98223,98225,98227,98229,98231,98237,98239,98241,98243,98245,98247,98249,98251,98253,98259,98261,98263,98265,98267,98269,98271,98277,98279,98281,98283,98285,98287,98289,98295],{},[898,98210,900],{},[1761,98212,1915],{"stretchy":1821},[1681,98214,98215,98217],{},[898,98216,1828],{},[1765,98218,1945],{},[1761,98220,1834],{"separator":1833},[1765,98222,1945],{},[1761,98224,1920],{"stretchy":1821},[1761,98226,1834],{"separator":1833},[898,98228,900],{},[1761,98230,1915],{"stretchy":1821},[1681,98232,98233,98235],{},[898,98234,1828],{},[1765,98236,1945],{},[1761,98238,1834],{"separator":1833},[1765,98240,2296],{},[1761,98242,1920],{"stretchy":1821},[1761,98244,1834],{"separator":1833},[898,98246,900],{},[1761,98248,1915],{"stretchy":1821},[1765,98250,1945],{},[1761,98252,1834],{"separator":1833},[1681,98254,98255,98257],{},[898,98256,1828],{},[1765,98258,2296],{},[1761,98260,1920],{"stretchy":1821},[1761,98262,1834],{"separator":1833},[898,98264,900],{},[1761,98266,1915],{"stretchy":1821},[1765,98268,2296],{},[1761,98270,1834],{"separator":1833},[1681,98272,98273,98275],{},[898,98274,1828],{},[1765,98276,2296],{},[1761,98278,1920],{"stretchy":1821},[1761,98280,1834],{"separator":1833},[898,98282,900],{},[1761,98284,1915],{"stretchy":1821},[1765,98286,5486],{},[1761,98288,1834],{"separator":1833},[1681,98290,98291,98293],{},[898,98292,1828],{},[1765,98294,2296],{},[1761,98296,1920],{"stretchy":1821},[902,98298,98299],{"encoding":904},"U(Q_1, 1), U(Q_1, 2), U(1, Q_2), U(2, Q_2), U(3, Q_2)",[724,98301,98302,97711,98305,98349,98350,98458,98459,1343,98484,1343,98509,98551,98552,1343,98581,98606],{},[38,98303,98304],{},"6.5",[883,98306,98308],{"className":98307},[886],[888,98309,98310],{"xmlns":890},[892,98311,98312,98346],{},[895,98313,98314,98316,98318,98332],{},[898,98315,900],{},[1761,98317,1909],{},[2015,98319,98320,98322,98324],{},[898,98321,1828],{},[1765,98323,1945],{},[895,98325,98326,98328,98330],{},[1765,98327,2296],{},[898,98329,8726],{"mathvariant":1969},[1765,98331,5486],{},[2015,98333,98334,98336,98338],{},[898,98335,1828],{},[1765,98337,2296],{},[895,98339,98340,98342,98344],{},[1765,98341,1945],{},[898,98343,8726],{"mathvariant":1969},[1765,98345,5486],{},[902,98347,98348],{"encoding":904},"U = Q_1^{2\u002F3} Q_2^{1\u002F3}",". (a) Najděte rovnici křivek užitečnosti. (b) Určete a načrtněte křivky ",[883,98351,98353],{"className":98352},[886],[888,98354,98355],{"xmlns":890},[892,98356,98357,98455],{},[895,98358,98359,98361,98363,98369,98371,98377,98379,98381,98383,98385,98387,98389,98395,98397,98399,98401,98403,98405,98407,98413,98415,98417,98419,98421,98423,98425,98427,98429,98435,98437,98439,98441,98443,98445,98447,98453],{},[898,98360,900],{},[1761,98362,1915],{"stretchy":1821},[1681,98364,98365,98367],{},[898,98366,1828],{},[1765,98368,1945],{},[1761,98370,1834],{"separator":1833},[1681,98372,98373,98375],{},[898,98374,1828],{},[1765,98376,2296],{},[1761,98378,1920],{"stretchy":1821},[1761,98380,1909],{},[1765,98382,2296],{},[1761,98384,1834],{"separator":1833},[898,98386,900],{},[1761,98388,1915],{"stretchy":1821},[1681,98390,98391,98393],{},[898,98392,1828],{},[1765,98394,1945],{},[1761,98396,1834],{"separator":1833},[1765,98398,5486],{},[1761,98400,1920],{"stretchy":1821},[1761,98402,1834],{"separator":1833},[898,98404,900],{},[1761,98406,1915],{"stretchy":1821},[1681,98408,98409,98411],{},[898,98410,1828],{},[1765,98412,1945],{},[1761,98414,1834],{"separator":1833},[1765,98416,2296],{},[1761,98418,1920],{"stretchy":1821},[1761,98420,1834],{"separator":1833},[898,98422,900],{},[1761,98424,1915],{"stretchy":1821},[1765,98426,2296],{},[1761,98428,1834],{"separator":1833},[1681,98430,98431,98433],{},[898,98432,1828],{},[1765,98434,2296],{},[1761,98436,1920],{"stretchy":1821},[1761,98438,1834],{"separator":1833},[898,98440,900],{},[1761,98442,1915],{"stretchy":1821},[1765,98444,5486],{},[1761,98446,1834],{"separator":1833},[1681,98448,98449,98451],{},[898,98450,1828],{},[1765,98452,2296],{},[1761,98454,1920],{"stretchy":1821},[902,98456,98457],{"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 ",[883,98460,98462],{"className":98461},[886],[888,98463,98464],{"xmlns":890},[892,98465,98466,98481],{},[895,98467,98468,98470,98472,98474,98476,98479],{},[898,98469,8309],{},[1761,98471,1822],{"stretchy":1821},[1765,98473,68537],{},[1761,98475,12468],{"separator":1833},[1765,98477,98478],{},"3,555",[1761,98480,1844],{"stretchy":1821},[902,98482,98483],{"encoding":904},"A[1{,}5; 3{,}555]",[883,98485,98487],{"className":98486},[886],[888,98488,98489],{"xmlns":890},[892,98490,98491,98506],{},[895,98492,98493,98495,98497,98499,98501,98504],{},[898,98494,27286],{},[1761,98496,1822],{"stretchy":1821},[1765,98498,57179],{},[1761,98500,12468],{"separator":1833},[1765,98502,98503],{},"1,28",[1761,98505,1844],{"stretchy":1821},[902,98507,98508],{"encoding":904},"B[2{,}5; 1{,}28]",[883,98510,98512],{"className":98511},[886],[888,98513,98514],{"xmlns":890},[892,98515,98516,98548],{},[895,98517,98518,98520,98522,98524,98526,98528,98530,98536,98538,98540,98542,98544,98546],{},[898,98519,6849],{},[1761,98521,1822],{"stretchy":1821},[1765,98523,2296],{},[1761,98525,12468],{"separator":1833},[898,98527,900],{},[1761,98529,1915],{"stretchy":1821},[1681,98531,98532,98534],{},[898,98533,1828],{},[1765,98535,1945],{},[1761,98537,1834],{"separator":1833},[1765,98539,5486],{},[1761,98541,1920],{"stretchy":1821},[1761,98543,1909],{},[1765,98545,5486],{},[1761,98547,1844],{"stretchy":1821},[902,98549,98550],{"encoding":904},"C[2; U(Q_1, 3) = 3]"," (c) Leží některé z bodů ",[883,98553,98555],{"className":98554},[886],[888,98556,98557],{"xmlns":890},[892,98558,98559,98578],{},[895,98560,98561,98563,98565,98567,98569,98571,98573,98576],{},[898,98562,2244],{},[1761,98564,1822],{"stretchy":1821},[1765,98566,5486],{},[1761,98568,12468],{"separator":1833},[1765,98570,1945],{},[1761,98572,12468],{"separator":1833},[1765,98574,98575],{},"0,832",[1761,98577,1844],{"stretchy":1821},[902,98579,98580],{"encoding":904},"D[3; 1; 0{,}832]",[883,98582,98584],{"className":98583},[886],[888,98585,98586],{"xmlns":890},[892,98587,98588,98603],{},[895,98589,98590,98592,98594,98596,98598,98601],{},[898,98591,1818],{},[1761,98593,1822],{"stretchy":1821},[1765,98595,57179],{},[1761,98597,12468],{"separator":1833},[1765,98599,98600],{},"4,32",[1761,98602,1844],{"stretchy":1821},[902,98604,98605],{"encoding":904},"E[2{,}5; 4{,}32]"," na téže křivce užitečnosti? Když ano, určete ji.",[724,98608,98609,97711,98612,98655,98656,10518,98669,98703,98704,98721,98722,98739],{},[38,98610,98611],{},"6.6",[883,98613,98615],{"className":98614},[886],[888,98616,98617],{"xmlns":890},[892,98618,98619,98653],{},[895,98620,98621,98623,98625,98639],{},[898,98622,900],{},[1761,98624,1909],{},[2015,98626,98627,98629,98631],{},[898,98628,1828],{},[1765,98630,1945],{},[895,98632,98633,98635,98637],{},[1765,98634,2296],{},[898,98636,8726],{"mathvariant":1969},[1765,98638,5486],{},[2015,98640,98641,98643,98645],{},[898,98642,1828],{},[1765,98644,2296],{},[895,98646,98647,98649,98651],{},[1765,98648,1945],{},[898,98650,8726],{"mathvariant":1969},[1765,98652,5486],{},[902,98654,98348],{"encoding":904},". (a) Najděte mezní míru komoditní substituce ",[883,98657,98659],{"className":98658},[886],[888,98660,98661],{"xmlns":890},[892,98662,98663,98667],{},[895,98664,98665],{},[2761,98666,14641],{},[902,98668,32268],{"encoding":904},[883,98670,98672],{"className":98671},[886],[888,98673,98674],{"xmlns":890},[892,98675,98676,98700],{},[895,98677,98678,98684,98686,98688,98690,98696,98698],{},[1681,98679,98680,98682],{},[898,98681,1828],{},[1765,98683,1945],{},[1761,98685,1909],{},[1765,98687,7160],{},[1761,98689,1834],{"separator":1833},[1681,98691,98692,98694],{},[898,98693,1828],{},[1765,98695,2296],{},[1761,98697,1909],{},[1765,98699,12421],{},[902,98701,98702],{"encoding":904},"Q_1 = 100, Q_2 = 200"," a výsledek ekonomicky interpretujte. (c) Odhadněte, o kolik je třeba změnit ",[883,98705,98707],{"className":98706},[886],[888,98708,98709],{"xmlns":890},[892,98710,98711,98719],{},[895,98712,98713],{},[1681,98714,98715,98717],{},[898,98716,1828],{},[1765,98718,1945],{},[902,98720,33032],{"encoding":904},", poklesne-li ",[883,98723,98725],{"className":98724},[886],[888,98726,98727],{"xmlns":890},[892,98728,98729,98737],{},[895,98730,98731],{},[1681,98732,98733,98735],{},[898,98734,1828],{},[1765,98736,2296],{},[902,98738,33051],{"encoding":904}," o 5 vzhledem k hladině dle (b).",[724,98741,98742,98745,98746,98763,98764,98781,98782,98814,98815,98840,98841,98854,98855,1343,98879,1343,98903,1741],{},[38,98743,98744],{},"6.7"," Míra uspokojení z nákupu množství ",[883,98747,98749],{"className":98748},[886],[888,98750,98751],{"xmlns":890},[892,98752,98753,98761],{},[895,98754,98755],{},[1681,98756,98757,98759],{},[898,98758,1828],{},[1765,98760,1945],{},[902,98762,33032],{"encoding":904}," nealko nápojů a množství ",[883,98765,98767],{"className":98766},[886],[888,98768,98769],{"xmlns":890},[892,98770,98771,98779],{},[895,98772,98773],{},[1681,98774,98775,98777],{},[898,98776,1828],{},[1765,98778,2296],{},[902,98780,33051],{"encoding":904}," hamburgerů za týden je dána funkcí užitečnosti ",[883,98783,98785],{"className":98784},[886],[888,98786,98787],{"xmlns":890},[892,98788,98789,98811],{},[895,98790,98791,98793,98795],{},[898,98792,900],{},[1761,98794,1909],{},[12161,98796,98797],{},[895,98798,98799,98805],{},[1681,98800,98801,98803],{},[898,98802,1828],{},[1765,98804,1945],{},[1681,98806,98807,98809],{},[898,98808,1828],{},[1765,98810,2296],{},[902,98812,98813],{"encoding":904},"U = \\sqrt{Q_1 Q_2}",". (a) Najděte vztah pro hodnoty ",[883,98816,98818],{"className":98817},[886],[888,98819,98820],{"xmlns":890},[892,98821,98822,98838],{},[895,98823,98824,98830,98832],{},[1681,98825,98826,98828],{},[898,98827,1828],{},[1765,98829,1945],{},[1761,98831,1834],{"separator":1833},[1681,98833,98834,98836],{},[898,98835,1828],{},[1765,98837,2296],{},[902,98839,39651],{"encoding":904},", pro něž je dosaženo užitečnosti 10 a uveďte několik takových dvojic hodnot. (b) Najděte ",[883,98842,98844],{"className":98843},[886],[888,98845,98846],{"xmlns":890},[892,98847,98848,98852],{},[895,98849,98850],{},[2761,98851,14641],{},[902,98853,32268],{"encoding":904}," na křivce nalezené v (a). (c) Ekonomicky interpretujte smysl ",[883,98856,98858],{"className":98857},[886],[888,98859,98860],{"xmlns":890},[892,98861,98862,98876],{},[895,98863,98864,98866,98868,98870,98872,98874],{},[2761,98865,14641],{},[1761,98867,1915],{"stretchy":1821},[1765,98869,6321],{},[1761,98871,1834],{"separator":1833},[1765,98873,13077],{},[1761,98875,1920],{"stretchy":1821},[902,98877,98878],{"encoding":904},"\\text{MRCS}(5, 20)",[883,98880,98882],{"className":98881},[886],[888,98883,98884],{"xmlns":890},[892,98885,98886,98900],{},[895,98887,98888,98890,98892,98894,98896,98898],{},[2761,98889,14641],{},[1761,98891,1915],{"stretchy":1821},[1765,98893,13077],{},[1761,98895,1834],{"separator":1833},[1765,98897,6321],{},[1761,98899,1920],{"stretchy":1821},[902,98901,98902],{"encoding":904},"\\text{MRCS}(20, 5)",[883,98904,98906],{"className":98905},[886],[888,98907,98908],{"xmlns":890},[892,98909,98910,98924],{},[895,98911,98912,98914,98916,98918,98920,98922],{},[2761,98913,14641],{},[1761,98915,1915],{"stretchy":1821},[1765,98917,2296],{},[1761,98919,1834],{"separator":1833},[1765,98921,7190],{},[1761,98923,1920],{"stretchy":1821},[902,98925,98926],{"encoding":904},"\\text{MRCS}(2, 50)",[1636,98928,98929],{},[724,98930,98931,98933,98934,1741],{},[883,98932,4452],{}," Úlohy 6.8 – 6.13 (optimalizace, Lagrange, poptávka)\nÚlohy navázané na maximalizaci užitečnosti, minimalizaci výdajů a odvození Marshallových\u002FHicksových funkcí poptávky jsou na stránce ",[207,98935,98938],{"className":98936,"dataFsResolvedFilePath":911,"href":98937},[210],"\u002Fwiki\u002Foptimalizace-spotrebitele#Úlohy k optimalizaci","Optimalizace spotřebitele — Úlohy",[115,98940,5533],{"id":5532},[120,98942,98943,98949,98954,98960,99013,99023,99069,99124,99187,99244,99299,99338],{},[123,98944,98945,98948],{},[38,98946,98947],{},"Užitečnost (utility)"," — ordinálně měřený ukazatel uspokojení spotřebitele ze svazku zboží.",[123,98950,98951,98953],{},[38,98952,90846],{}," — historická pojetí užitečnosti; v současnosti se preferuje ordinalistický.",[123,98955,98956,98959],{},[38,98957,98958],{},"Pět předpokladů chování spotřebitele"," — racionalita, ordinalita, konzistence a tranzitivita, rostoucí užitečnost, klesající mezní užitečnost.",[123,98961,98962,98964,98965,98978,98979,1741],{},[38,98963,91173],{}," — uspořádaná ",[883,98966,98968],{"className":98967},[886],[888,98969,98970],{"xmlns":890},[892,98971,98972,98976],{},[895,98973,98974],{},[898,98975,40888],{},[902,98977,40888],{"encoding":904},"-tice ",[883,98980,98982],{"className":98981},[886],[888,98983,98984],{"xmlns":890},[892,98985,98986,99010],{},[895,98987,98988,98990,98996,98998,99000,99002,99008],{},[1761,98989,1915],{"stretchy":1821},[1681,98991,98992,98994],{},[898,98993,1828],{},[1765,98995,1945],{},[1761,98997,1834],{"separator":1833},[1761,98999,13686],{},[1761,99001,1834],{"separator":1833},[1681,99003,99004,99006],{},[898,99005,1828],{},[898,99007,40888],{},[1761,99009,1920],{"stretchy":1821},[902,99011,99012],{"encoding":904},"(Q_1, \\dots, Q_n)",[123,99014,99015,99018,99019,99022],{},[38,99016,99017],{},"Relace preference"," — uspořádání svazků podle užitečnosti; ",[38,99020,99021],{},"indiferentní svazky"," mají stejnou užitečnost.",[123,99024,99025,1989,99028,99068],{},[38,99026,99027],{},"Funkce užitečnosti",[883,99029,99031],{"className":99030},[886],[888,99032,99033],{"xmlns":890},[892,99034,99035,99065],{},[895,99036,99037,99039,99041,99043,99045,99051,99053,99055,99057,99063],{},[898,99038,900],{},[1761,99040,1909],{},[898,99042,900],{},[1761,99044,1915],{"stretchy":1821},[1681,99046,99047,99049],{},[898,99048,1828],{},[1765,99050,1945],{},[1761,99052,1834],{"separator":1833},[1761,99054,13686],{},[1761,99056,1834],{"separator":1833},[1681,99058,99059,99061],{},[898,99060,1828],{},[898,99062,40888],{},[1761,99064,1920],{"stretchy":1821},[902,99066,99067],{"encoding":904},"U = U(Q_1, \\dots, Q_n)"," — vzorec (6.1); ekvivalentní až na monotónní transformaci.",[123,99070,99071,1989,99074,99103,99104,1989,99107,99123],{},[38,99072,99073],{},"Mezní užitečnost",[883,99075,99077],{"className":99076},[886],[888,99078,99079],{"xmlns":890},[892,99080,99081,99101],{},[895,99082,99083,99085,99091,99093],{},[898,99084,6889],{},[1681,99086,99087,99089],{},[898,99088,900],{},[898,99090,21824],{},[1761,99092,1909],{},[2015,99094,99095,99097,99099],{},[898,99096,900],{},[898,99098,21824],{},[1761,99100,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[902,99102,90631],{"encoding":904}," — vzorec (6.2); ",[38,99105,99106],{},"totální diferenciál",[883,99108,99110],{"className":99109},[886],[888,99111,99112],{"xmlns":890},[892,99113,99114,99120],{},[895,99115,99116,99118],{},[898,99117,4346],{"mathvariant":1969},[898,99119,900],{},[902,99121,99122],{"encoding":904},"\\mathrm{d} U"," — (6.3).",[123,99125,99126,99128,99129,99153,99154,99186],{},[38,99127,92809],{}," — (6.4) ",[883,99130,99132],{"className":99131},[886],[888,99133,99134],{"xmlns":890},[892,99135,99136,99150],{},[895,99137,99138,99146,99148],{},[2015,99139,99140,99142,99144],{},[898,99141,900],{},[898,99143,21824],{},[1761,99145,6459],{"mathvariant":1969,"lspace":6458,"rspace":6458},[1761,99147,1763],{},[1765,99149,1767],{},[902,99151,99152],{"encoding":904},"U'_i > 0",", (6.5) ",[883,99155,99157],{"className":99156},[886],[888,99158,99159],{"xmlns":890},[892,99160,99161,99183],{},[895,99162,99163,99179,99181],{},[2015,99164,99165,99167,99173],{},[898,99166,900],{},[895,99168,99169,99171],{},[898,99170,21824],{},[898,99172,21824],{},[895,99174,99175,99177],{},[1761,99176,6459],{"mathvariant":1969},[1761,99178,6459],{"mathvariant":1969},[1761,99180,2058],{},[1765,99182,1767],{},[902,99184,99185],{"encoding":904},"U''_{ii} \u003C 0"," (zákon klesající mezní užitečnosti).",[123,99188,99189,1989,99191,99222,99223,1741],{},[38,99190,94597],{},[883,99192,99194],{"className":99193},[886],[888,99195,99196],{"xmlns":890},[892,99197,99198,99220],{},[895,99199,99200,99202,99204,99212],{},[898,99201,900],{},[1761,99203,1909],{},[2015,99205,99206,99208,99210],{},[898,99207,1828],{},[1765,99209,1945],{},[898,99211,207],{},[2015,99213,99214,99216,99218],{},[898,99215,1828],{},[1765,99217,2296],{},[898,99219,4302],{},[902,99221,39832],{"encoding":904}," — (6.6), speciálně ",[883,99224,99226],{"className":99225},[886],[888,99227,99228],{"xmlns":890},[892,99229,99230,99242],{},[895,99231,99232,99234,99236,99238,99240],{},[898,99233,4302],{},[1761,99235,1909],{},[1765,99237,1945],{},[1761,99239,1885],{},[898,99241,207],{},[902,99243,94751],{"encoding":904},[123,99245,99246,1989,99249,99284,99285,99298],{},[38,99247,99248],{},"Křivky užitečnosti (indiferenční)",[883,99250,99252],{"className":99251},[886],[888,99253,99254],{"xmlns":890},[892,99255,99256,99282],{},[895,99257,99258,99260,99262,99268,99270,99276,99278,99280],{},[898,99259,900],{},[1761,99261,1915],{"stretchy":1821},[1681,99263,99264,99266],{},[898,99265,1828],{},[1765,99267,1945],{},[1761,99269,1834],{"separator":1833},[1681,99271,99272,99274],{},[898,99273,1828],{},[1765,99275,2296],{},[1761,99277,1920],{"stretchy":1821},[1761,99279,1909],{},[898,99281,2774],{},[902,99283,13808],{"encoding":904}," — (6.7), (6.8); čtyři vlastnosti: klesající, neprotínající se, vzdálenější od počátku = vyšší ",[883,99286,99288],{"className":99287},[886],[888,99289,99290],{"xmlns":890},[892,99291,99292,99296],{},[895,99293,99294],{},[898,99295,900],{},[902,99297,900],{"encoding":904},", konvexní.",[123,99300,99301,1989,99303,99337],{},[38,99302,96142],{},[883,99304,99306],{"className":99305},[886],[888,99307,99308],{"xmlns":890},[892,99309,99310,99334],{},[895,99311,99312,99314,99316,99318,99324,99326,99328],{},[2761,99313,14641],{},[1761,99315,1909],{},[898,99317,6889],{},[1681,99319,99320,99322],{},[898,99321,900],{},[1765,99323,1945],{},[898,99325,8726],{"mathvariant":1969},[898,99327,6889],{},[1681,99329,99330,99332],{},[898,99331,900],{},[1765,99333,2296],{},[902,99335,99336],{"encoding":904},"\\text{MRCS} = MU_1 \u002F MU_2"," — (6.9); vztahy (6.10), (6.11).",[123,99339,99340,1989,99343,13809,99372,99375],{},[38,99341,99342],{},"Podmínka optimality",[883,99344,99346],{"className":99345},[886],[888,99347,99348],{"xmlns":890},[892,99349,99350,99370],{},[895,99351,99352,99354,99356,99362,99364],{},[2761,99353,14641],{},[1761,99355,1909],{},[1681,99357,99358,99360],{},[898,99359,1839],{},[1765,99361,1945],{},[898,99363,8726],{"mathvariant":1969},[1681,99365,99366,99368],{},[898,99367,1839],{},[1765,99369,2296],{},[902,99371,32029],{"encoding":904},[207,99373,40782],{"className":99374,"dataFsResolvedFilePath":911,"href":912},[210]," pro plné odvození.",[115,99377,5968],{"id":5967},[120,99379,99380,99417,99458,99468],{},[123,99381,99382,1989,99385,99388,99389,99402,99403,99416],{},[38,99383,99384],{},"Navazující téma:",[207,99386,913],{"className":99387,"dataFsResolvedFilePath":911,"href":912},[210]," (Lagrange, max ",[883,99390,99392],{"className":99391},[886],[888,99393,99394],{"xmlns":890},[892,99395,99396,99400],{},[895,99397,99398],{},[898,99399,900],{},[902,99401,900],{"encoding":904},", min ",[883,99404,99406],{"className":99405},[886],[888,99407,99408],{"xmlns":890},[892,99409,99410,99414],{},[895,99411,99412],{},[898,99413,1818],{},[902,99415,1818],{"encoding":904},", funkce poptávky, Příklady 6.5–6.8, úlohy 6.8–6.13).",[123,99418,99419,1989,99422,15131,99425,90386,99428,99431,99432,99435,99436,5991,99454,99457],{},[38,99420,99421],{},"Související pojmy:",[207,99423,784],{"className":99424,"dataFsResolvedFilePath":782,"href":783},[210],[207,99426,5995],{"className":99427,"dataFsResolvedFilePath":764,"href":765},[210],[207,99429,15126],{"className":99430,"dataFsResolvedFilePath":857,"href":858},[210]," (paralela: MRCS ↔ MRTS, izokvanty ↔ indiferenční křivky, Cobb-Douglas), ",[207,99433,15980],{"className":99434,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallovy poptávkové funkce ",[883,99437,99439],{"className":99438},[886],[888,99440,99441],{"xmlns":890},[892,99442,99443,99451],{},[895,99444,99445],{},[1681,99446,99447,99449],{},[898,99448,2244],{},[898,99450,21824],{},[902,99452,99453],{"encoding":904},"D_i",[207,99455,793],{"className":99456,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace — nástroj pro navazující téma).",[123,99459,99460,1989,99462,1343,99465],{},[38,99461,40731],{},[207,99463,1094],{"className":99464,"dataFsResolvedFilePath":838,"href":839},[210],[207,99466,1101],{"className":99467,"dataFsResolvedFilePath":868,"href":869},[210],[123,99469,99470,1989,99472],{},[38,99471,6015],{},[207,99473,6021],{"className":99474,"dataFsResolvedFilePath":6019,"href":6020},[210],{"title":641,"searchDepth":642,"depth":642,"links":99476},[99477,99478,99479,99482,99483,99486,99490,99491,99494,99495,99496,99497,99498,99499,99500],{"id":16045,"depth":642,"text":16046},{"id":90770,"depth":642,"text":90771},{"id":90830,"depth":642,"text":90831,"children":99480},[99481],{"id":90845,"depth":649,"text":90846},{"id":91152,"depth":642,"text":91153},{"id":92012,"depth":642,"text":92013,"children":99484},[99485],{"id":92559,"depth":649,"text":84189},{"id":92808,"depth":642,"text":92809,"children":99487},[99488],{"id":93681,"depth":649,"text":99489},"Příklad 6.2 — ověření vlastností a dopočet pro U=Q11\u002F2Q21\u002F3U = Q_1^{1\u002F2} Q_2^{1\u002F3}",{"id":94596,"depth":642,"text":94597},{"id":95132,"depth":642,"text":95133,"children":99492},[99493],{"id":95906,"depth":649,"text":95907},{"id":96136,"depth":642,"text":96137},{"id":96897,"depth":642,"text":96898},{"id":97435,"depth":642,"text":97436},{"id":53866,"depth":642,"text":53867},{"id":97571,"depth":642,"text":97572},{"id":5532,"depth":642,"text":5533},{"id":5967,"depth":642,"text":5968},{},"\u002Ftopics\u002Fuzitecnost",{"title":90554,"description":641},[1138,1137],"topics\u002Fuzitecnost",[1128,13813,99507,90548,15161,99508],"mezni-uzitecnost","mrcs","xXggD9rfV5faUAk1b2B3YYbozpQLu-pObiMaZX5f7yI",{"id":99511,"title":757,"body":99512,"course":1128,"courses":659,"created":1129,"description":99785,"extension":661,"meta":99786,"navigation":664,"path":99787,"seo":99788,"sources":99789,"stem":99790,"tags":99791,"type":6050,"updated":677,"__hash__":99797},"topics\u002Ftopics\u002Fzaklady-matematicke-ekonomie.md",{"type":9,"value":99513,"toc":99777},[99514,99517,99524,99531,99535,99545,99547,99581,99585,99628,99631,99689,99693,99723,99727,99748,99750],[12,99515,757],{"id":99516},"základy-matematické-ekonomie",[724,99518,99519,99520,99523],{},"Úvodní pojmy a princip modelování v ",[207,99521,20414],{"className":99522,"dataFsResolvedFilePath":6019,"href":6020},[210],". Slouží jako vstupní bod pro celý kurz — bez těchto pojmů nedávají další kapitoly smysl.",[724,99525,99526],{},[3991,99527],{"alt":99528,"className":99529,"src":99530},"imek-model-promenne",[210,3995],"\u002Fwiki-assets\u002Fimek-model-promenne.jpeg",[115,99532,99534],{"id":99533},"co-je-matematická-ekonomie","Co je matematická ekonomie",[724,99536,99537,99540,99541,99544],{},[38,99538,99539],{},"Vědní disciplína",", která ekonomické vztahy vyjadřuje ",[38,99542,99543],{},"exaktními (matematickými) prostředky"," a provádí jejich analýzu. Cílem není jen popis, ale i predikce a optimalizace.",[115,99546,5533],{"id":5532},[120,99548,99549,99555,99561,99567,99576],{},[123,99550,99551,99554],{},[38,99552,99553],{},"Model"," — zjednodušený obraz reálné situace nebo jevu. Vždy jde o redukci skutečnosti, ne její kopii.",[123,99556,99557,99560],{},[38,99558,99559],{},"Endogenní proměnné"," — zahrnuté do modelu, mohou se měnit (vysvětlované).",[123,99562,99563,99566],{},[38,99564,99565],{},"Exogenní proměnné"," — nejsou v modelu zahrnuté (potenciálně by mohly), berou se jako dané.",[123,99568,99569,5675,99572,99575],{},[38,99570,99571],{},"Ceteris paribus",[614,99573,99574],{},"za jinak stejných podmínek",". Sledujeme změnu jedné proměnné, ostatní fixní.",[123,99577,99578,99580],{},[38,99579,54619],{}," — odezva endogenních proměnných na změnu některé exogenní.",[115,99582,99584],{"id":99583},"ilustrace-funkce-poptávky","Ilustrace — funkce poptávky",[724,99586,99587,99627],{},[883,99588,99590],{"className":99589},[886],[888,99591,99592],{"xmlns":890},[892,99593,99594,99624],{},[895,99595,99596,99598,99600,99602,99604,99606,99608,99610,99612,99614,99616,99618,99620,99622],{},[898,99597,1828],{},[1761,99599,1909],{},[898,99601,2244],{},[1761,99603,1915],{"stretchy":1821},[898,99605,1839],{},[1761,99607,1834],{"separator":1833},[898,99609,13170],{},[1761,99611,1834],{"separator":1833},[898,99613,22328],{},[1761,99615,1834],{"separator":1833},[898,99617,900],{},[1761,99619,1834],{"separator":1833},[1761,99621,13686],{},[1761,99623,1920],{"stretchy":1821},[902,99625,99626],{"encoding":904},"Q = D(P, Y, N, U, \\ldots)"," — plná (vícefaktorová) funkce poptávky.",[724,99629,99630],{},"Zjednodušení:",[120,99632,99633,99661],{},[123,99634,99635,1989,99638],{},[38,99636,99637],{},"Jednofaktorový model:",[883,99639,99641],{"className":99640},[886],[888,99642,99643],{"xmlns":890},[892,99644,99645,99659],{},[895,99646,99647,99649,99651,99653,99655,99657],{},[898,99648,1828],{},[1761,99650,1909],{},[898,99652,2244],{},[1761,99654,1915],{"stretchy":1821},[898,99656,1839],{},[1761,99658,1920],{"stretchy":1821},[902,99660,8247],{"encoding":904},[123,99662,99663,1989,99666],{},[38,99664,99665],{},"Inverzní zápis:",[883,99667,99669],{"className":99668},[886],[888,99670,99671],{"xmlns":890},[892,99672,99673,99687],{},[895,99674,99675,99677,99679,99681,99683,99685],{},[898,99676,1839],{},[1761,99678,1909],{},[898,99680,2244],{},[1761,99682,1915],{"stretchy":1821},[898,99684,1828],{},[1761,99686,1920],{"stretchy":1821},[902,99688,8692],{"encoding":904},[115,99690,99692],{"id":99691},"principy-řešení-ekonomických-úloh","Principy řešení ekonomických úloh",[152,99694,99695,99704],{},[123,99696,99697,99700,99701,2162],{},[38,99698,99699],{},"Princip rovnováhy"," — hledáme stav, kdy se protichůdné síly vyrovnají (např. tržní rovnováha, viz ",[207,99702,5371],{"className":99703,"dataFsResolvedFilePath":800,"href":801},[210],[123,99705,99706,99709,99710,99713,99714,99717,99718,99722],{},[38,99707,99708],{},"Princip optimalizace"," — hledáme extrém účelové funkce, případně vázaný omezujícími podmínkami (viz ",[207,99711,1145],{"className":99712,"dataFsResolvedFilePath":764,"href":765},[210]," pro 1D, ",[207,99715,20286],{"className":99716,"dataFsResolvedFilePath":782,"href":783},[210]," pro 2D, ",[207,99719,99721],{"className":99720,"dataFsResolvedFilePath":791,"href":792},[210],"lagrangeova-metoda"," pro vázané extrémy).",[115,99724,99726],{"id":99725},"konvence-z-přednášek","Konvence z přednášek",[120,99728,99729,99736,99742],{},[123,99730,99731,99732,99735],{},"Symbol ",[99733,99734,6803],"code",{}," pro přibližné rovnosti (typicky linearizace přes diferenciál).",[123,99737,99738,99739,1741],{},"Numerické výsledky ",[38,99740,99741],{},"na 3 desetinná místa",[123,99743,7954,99744,99747],{},[614,99745,99746],{},"jednotková změna"," má standardní význam (změna o 1).",[115,99749,5968],{"id":5967},[120,99751,99752,99757,99765],{},[123,99753,99754,99756],{},[38,99755,7861],{}," —",[123,99758,99759,1989,99761],{},[38,99760,7869],{},[207,99762,99764],{"className":99763,"dataFsResolvedFilePath":764,"href":765},[210],"Derivace a diferenciál",[123,99766,99767,1989,99769,1343,99773],{},[38,99768,7877],{},[207,99770,99772],{"className":99771,"dataFsResolvedFilePath":745,"href":746},[210],"Souhrn KS 1. blok",[207,99774,99776],{"className":99775,"dataFsResolvedFilePath":6019,"href":6020},[210],"kurz ImeK",{"title":641,"searchDepth":642,"depth":642,"links":99778},[99779,99780,99781,99782,99783,99784],{"id":99533,"depth":642,"text":99534},{"id":5532,"depth":642,"text":5533},{"id":99583,"depth":642,"text":99584},{"id":99691,"depth":642,"text":99692},{"id":99725,"depth":642,"text":99726},{"id":5967,"depth":642,"text":5968},"Úvodní pojmy a princip modelování v matematické ekonomii. Slouží jako vstupní bod pro celý kurz — bez těchto pojmů nedávají další kapitoly 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nabidka|Poptávka, nabídka a tržní rovnováha]] — modely D a S, rovnováha, multiplikátory - \u003C\u003Czdaneni-trhu>> — daň výrobci vs. spotřebiteli, rozklad daňového břemene, ekvivalence - [[prebytek-spotre …",{"slug":103849,"path":959,"title":103850,"snippet":103851},"imek-vzorce-prehled","ImeK — kompletní přehled vzorců se zdroji a intuicí","… regulace) blahobyt snižuje (mrtvá ztráta). --- ## 12. Zdanění trhu **Základní téma:** \u003C\u003Czdaneni-trhu>> ### Posun křivek při zdanění $$P = S_1(Q) = S(Q) + T \\quad \\text{(daň výrobci)}$$ $$P …",{"slug":5371,"path":801,"title":802,"snippet":103853},"\u003C!-- updated: 2026-04-22 — sekce „Zdanění trhu\" vyčleněna do \u003C\u003Czdaneni-trhu>> --> # Poptávka, nabídka a tržní rovnováha > [!info] TL;DR > Kapitola buduje základní mi …",{"slug":48969,"path":819,"title":820,"snippet":103855},"… uje, a je důsledkem transakcí, které se kvůli dani vůbec neuskuteční. Detailní rozbor viz \u003C\u003Czdaneni-trhu>>. --- ## Navigace - **Nadřazené téma:** [[poptavka-nabidka|Poptávka, nabídka a tržní ro …",[103857,103860,103861],{"slug":103858,"title":103859,"path":746,"sharedTags":642},"imek-blok-01","KS 1. blok — Kalkul a mikroekonomie",{"slug":5371,"title":802,"path":801,"sharedTags":642},{"slug":48969,"title":820,"path":819,"sharedTags":642},1777154974091]