[{"data":1,"prerenderedAt":101525},["ShallowReactive",2],{"sidebar-courses-with-stats":3,"wiki-derivace":1626,"course-stats-imek":3541,"course-topics-imek":3545,"backlinks-derivace":101497,"related-derivace":101522},{"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":3540},{"id":1628,"title":1629,"body":1630,"course":1128,"courses":659,"created":1129,"description":3528,"extension":661,"meta":3529,"navigation":664,"path":3530,"seo":3531,"sources":3532,"stem":3533,"tags":3534,"type":3538,"updated":677,"__hash__":3539},"topics\u002Ftopics\u002Fderivace.md","Derivace, diferenciál a extrémy funkcí jedné proměnné",{"type":9,"value":1631,"toc":3511},[1632,1635,1657,1661,1745,1748,1879,2036,2039,2122,2126,2187,2237,2246,2250,2386,2437,2441,2485,2554,2625,2633,2637,2676,2748,2752,2833,2882,2926,2930,2934,3004,3008,3058,3137,3144,3147,3200,3470,3474],[12,1633,1629],{"id":1634},"derivace-diferenciál-a-extrémy-funkcí-jedné-proměnné",[724,1636,1637,1638,1644,1645,1648,1649,1652,1653,1656],{},"Matematický aparát kurzu ",[207,1639,1643],{"className":1640,"dataFsResolvedFilePath":1641,"href":1642},[210],"courses\u002Fimek.md","\u002Fwiki\u002Fimek","ImeK",". Bez derivace se neobejdou ",[38,1646,1647],{},"mezní veličiny"," (mezní náklady, mezní příjem, mezní užitečnost), bez extrémů se neobejde ",[38,1650,1651],{},"maximalizace zisku"," ani ",[38,1654,1655],{},"minimalizace nákladů",".",[115,1658,1660],{"id":1659},"funkce-a-polynomy","Funkce a polynomy",[724,1662,1663,1664,1696,1697,1710,1711,1724,1725,1656],{},"Funkce jedné proměnné ",[883,1665,1667],{"className":1666},[886],[888,1668,1669],{"xmlns":890},[892,1670,1671,1693],{},[895,1672,1673,1676,1680,1683,1687,1690],{},[898,1674,1675],{},"y",[1677,1678,1679],"mo",{},"=",[898,1681,1682],{},"f",[1677,1684,1686],{"stretchy":1685},"false","(",[898,1688,1689],{},"x",[1677,1691,1692],{"stretchy":1685},")",[902,1694,1695],{"encoding":904},"y = f(x)"," — předpis závislosti ",[883,1698,1700],{"className":1699},[886],[888,1701,1702],{"xmlns":890},[892,1703,1704,1708],{},[895,1705,1706],{},[898,1707,1689],{},[902,1709,1689],{"encoding":904}," (nezávislá) → ",[883,1712,1714],{"className":1713},[886],[888,1715,1716],{"xmlns":890},[892,1717,1718,1722],{},[895,1719,1720],{},[898,1721,1675],{},[902,1723,1675],{"encoding":904}," (závislá). Hodnota v bodě: ",[883,1726,1728],{"className":1727},[886],[888,1729,1730],{"xmlns":890},[892,1731,1732,1742],{},[895,1733,1734,1736,1738,1740],{},[898,1735,1682],{},[1677,1737,1686],{"stretchy":1685},[898,1739,207],{},[1677,1741,1692],{"stretchy":1685},[902,1743,1744],{"encoding":904},"f(a)",[724,1746,1747],{},"Polynomy:",[120,1749,1750,1783,1827],{},[123,1751,1752],{},[152,1753,1754],{},[123,1755,1756,1757],{},"stupně: ",[883,1758,1760],{"className":1759},[886],[888,1761,1762],{"xmlns":890},[892,1763,1764,1780],{},[895,1765,1766,1768,1770,1772,1774,1777],{},[898,1767,1675],{},[1677,1769,1679],{},[898,1771,207],{},[898,1773,1689],{},[1677,1775,1776],{},"+",[898,1778,1779],{},"b",[902,1781,1782],{"encoding":904},"y = ax + b",[123,1784,1785],{},[152,1786,1787],{"start":642},[123,1788,1756,1789],{},[883,1790,1792],{"className":1791},[886],[888,1793,1794],{"xmlns":890},[892,1795,1796,1824],{},[895,1797,1798,1800,1802,1804,1813,1815,1817,1819,1821],{},[898,1799,1675],{},[1677,1801,1679],{},[898,1803,207],{},[1805,1806,1807,1809],"msup",{},[898,1808,1689],{},[1810,1811,1812],"mn",{},"2",[1677,1814,1776],{},[898,1816,1779],{},[898,1818,1689],{},[1677,1820,1776],{},[898,1822,1823],{},"c",[902,1825,1826],{"encoding":904},"y = ax^2 + bx + c",[123,1828,1829],{},[152,1830,1831],{"start":649},[123,1832,1756,1833],{},[883,1834,1836],{"className":1835},[886],[888,1837,1838],{"xmlns":890},[892,1839,1840,1876],{},[895,1841,1842,1844,1846,1848,1855,1857,1859,1865,1867,1869,1871,1873],{},[898,1843,1675],{},[1677,1845,1679],{},[898,1847,207],{},[1805,1849,1850,1852],{},[898,1851,1689],{},[1810,1853,1854],{},"3",[1677,1856,1776],{},[898,1858,1779],{},[1805,1860,1861,1863],{},[898,1862,1689],{},[1810,1864,1812],{},[1677,1866,1776],{},[898,1868,1823],{},[898,1870,1689],{},[1677,1872,1776],{},[898,1874,1875],{},"d",[902,1877,1878],{"encoding":904},"y = ax^3 + bx^2 + cx + d",[724,1880,1881,1884,1885,1942,1943,1985,1986,1656],{},[38,1882,1883],{},"Příklad rozkladu:"," ",[883,1886,1888],{"className":1887},[886],[888,1889,1890],{"xmlns":890},[892,1891,1892,1939],{},[895,1893,1894,1896,1898,1904,1907,1910,1912,1914,1917,1919,1921,1923,1925,1927,1929,1931,1933,1935,1937],{},[898,1895,1675],{},[1677,1897,1679],{},[1805,1899,1900,1902],{},[898,1901,1689],{},[1810,1903,1812],{},[1677,1905,1906],{},"−",[1810,1908,1909],{},"5",[898,1911,1689],{},[1677,1913,1776],{},[1810,1915,1916],{},"6",[1677,1918,1679],{},[1677,1920,1686],{"stretchy":1685},[898,1922,1689],{},[1677,1924,1906],{},[1810,1926,1812],{},[1677,1928,1692],{"stretchy":1685},[1677,1930,1686],{"stretchy":1685},[898,1932,1689],{},[1677,1934,1906],{},[1810,1936,1854],{},[1677,1938,1692],{"stretchy":1685},[902,1940,1941],{"encoding":904},"y = x^2 - 5x + 6 = (x-2)(x-3)",", kořeny ",[883,1944,1946],{"className":1945},[886],[888,1947,1948],{"xmlns":890},[892,1949,1950,1982],{},[895,1951,1952,1960,1962,1964,1968,1972,1978,1980],{},[1953,1954,1955,1957],"msub",{},[898,1956,1689],{},[1810,1958,1959],{},"1",[1677,1961,1679],{},[1810,1963,1812],{},[1677,1965,1967],{"separator":1966},"true",",",[1969,1970,1971],"mtext",{}," ",[1953,1973,1974,1976],{},[898,1975,1689],{},[1810,1977,1812],{},[1677,1979,1679],{},[1810,1981,1854],{},[902,1983,1984],{"encoding":904},"x_1 = 2,\\ x_2 = 3",". Vrcholový tvar ",[883,1987,1989],{"className":1988},[886],[888,1990,1991],{"xmlns":890},[892,1992,1993,2033],{},[895,1994,1995,1997,1999,2001,2003,2005,2016,2022,2024],{},[898,1996,1675],{},[1677,1998,1679],{},[1677,2000,1686],{"stretchy":1685},[898,2002,1689],{},[1677,2004,1906],{},[2006,2007,2009],"mstyle",{"scriptlevel":2008,"displaystyle":1685},"0",[2010,2011,2012,2014],"mfrac",{},[1810,2013,1909],{},[1810,2015,1812],{},[1805,2017,2018,2020],{},[1677,2019,1692],{"stretchy":1685},[1810,2021,1812],{},[1677,2023,1906],{},[2006,2025,2026],{"scriptlevel":2008,"displaystyle":1685},[2010,2027,2028,2030],{},[1810,2029,1959],{},[1810,2031,2032],{},"4",[902,2034,2035],{"encoding":904},"y = (x - \\tfrac{5}{2})^2 - \\tfrac{1}{4}",[115,2037,2038],{"id":1145},"Derivace",[724,2040,2041,2042,1348,2069,2097,2098,1656],{},"Označení ",[883,2043,2045],{"className":2044},[886],[888,2046,2047],{"xmlns":890},[892,2048,2049,2066],{},[895,2050,2051,2060,2062,2064],{},[1805,2052,2053,2055],{},[898,2054,1682],{},[1677,2056,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},"normal","0em","′",[1677,2061,1686],{"stretchy":1685},[898,2063,1689],{},[1677,2065,1692],{"stretchy":1685},[902,2067,2068],{"encoding":904},"f'(x)",[883,2070,2072],{"className":2071},[886],[888,2073,2074],{"xmlns":890},[892,2075,2076,2094],{},[895,2077,2078],{},[2006,2079,2080],{"scriptlevel":2008,"displaystyle":1966},[2010,2081,2082,2088],{},[895,2083,2084,2086],{},[898,2085,1875],{},[898,2087,1675],{},[895,2089,2090,2092],{},[898,2091,1875],{},[898,2093,1689],{},[902,2095,2096],{"encoding":904},"\\dfrac{dy}{dx}",". Hodnota v bodě: ",[883,2099,2101],{"className":2100},[886],[888,2102,2103],{"xmlns":890},[892,2104,2105,2119],{},[895,2106,2107,2113,2115,2117],{},[1805,2108,2109,2111],{},[898,2110,1682],{},[1677,2112,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,2114,1686],{"stretchy":1685},[898,2116,207],{},[1677,2118,1692],{"stretchy":1685},[902,2120,2121],{"encoding":904},"f'(a)",[198,2123,2125],{"id":2124},"geometrická-interpretace","Geometrická interpretace",[724,2127,2128,2151,2152,2155,2156,2186],{},[883,2129,2131],{"className":2130},[886],[888,2132,2133],{"xmlns":890},[892,2134,2135,2149],{},[895,2136,2137,2143,2145,2147],{},[1805,2138,2139,2141],{},[898,2140,1682],{},[1677,2142,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,2144,1686],{"stretchy":1685},[898,2146,207],{},[1677,2148,1692],{"stretchy":1685},[902,2150,2121],{"encoding":904}," = ",[38,2153,2154],{},"sklon tečny"," ke grafu funkce v bodě ",[883,2157,2159],{"className":2158},[886],[888,2160,2161],{"xmlns":890},[892,2162,2163,2183],{},[895,2164,2165,2168,2170,2172,2174,2176,2178,2180],{},[1677,2166,2167],{"stretchy":1685},"[",[898,2169,207],{},[1677,2171,1967],{"separator":1966},[898,2173,1682],{},[1677,2175,1686],{"stretchy":1685},[898,2177,207],{},[1677,2179,1692],{"stretchy":1685},[1677,2181,2182],{"stretchy":1685},"]",[902,2184,2185],{"encoding":904},"[a, f(a)]",". Rovnice tečny:",[724,2188,2189],{},[883,2190,2192],{"className":2191},[886],[888,2193,2194],{"xmlns":890},[892,2195,2196,2234],{},[895,2197,2198,2200,2202,2204,2206,2208,2210,2212,2218,2220,2222,2224,2226,2228,2230,2232],{},[898,2199,1675],{},[1677,2201,1906],{},[898,2203,1682],{},[1677,2205,1686],{"stretchy":1685},[898,2207,207],{},[1677,2209,1692],{"stretchy":1685},[1677,2211,1679],{},[1805,2213,2214,2216],{},[898,2215,1682],{},[1677,2217,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,2219,1686],{"stretchy":1685},[898,2221,207],{},[1677,2223,1692],{"stretchy":1685},[1677,2225,1686],{"stretchy":1685},[898,2227,1689],{},[1677,2229,1906],{},[898,2231,207],{},[1677,2233,1692],{"stretchy":1685},[902,2235,2236],{"encoding":904},"y - f(a) = f'(a)(x - a)",[724,2238,2239],{},[2240,2241],"img",{"alt":2242,"className":2243,"src":2245},"imek-derivace-tecna",[210,2244],"wikilink-broken","\u002Fwiki-assets\u002Fimek-derivace-tecna.jpeg",[198,2247,2249],{"id":2248},"inženýrská-interpretace","Inženýrská interpretace",[724,2251,2252,2151,2275,1884,2278,2291,2292,2305,2306,2324,2325,2338,2339,2352,2353,2366,2367,2385],{},[883,2253,2255],{"className":2254},[886],[888,2256,2257],{"xmlns":890},[892,2258,2259,2273],{},[895,2260,2261,2267,2269,2271],{},[1805,2262,2263,2265],{},[898,2264,1682],{},[1677,2266,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,2268,1686],{"stretchy":1685},[898,2270,207],{},[1677,2272,1692],{"stretchy":1685},[902,2274,2121],{"encoding":904},[38,2276,2277],{},"rychlost změny",[883,2279,2281],{"className":2280},[886],[888,2282,2283],{"xmlns":890},[892,2284,2285,2289],{},[895,2286,2287],{},[898,2288,1675],{},[902,2290,1675],{"encoding":904}," vzhledem k ",[883,2293,2295],{"className":2294},[886],[888,2296,2297],{"xmlns":890},[892,2298,2299,2303],{},[895,2300,2301],{},[898,2302,1689],{},[902,2304,1689],{"encoding":904}," v bodě ",[883,2307,2309],{"className":2308},[886],[888,2310,2311],{"xmlns":890},[892,2312,2313,2321],{},[895,2314,2315,2317,2319],{},[898,2316,1689],{},[1677,2318,1679],{},[898,2320,207],{},[902,2322,2323],{"encoding":904},"x = a","; přibližná změna ",[883,2326,2328],{"className":2327},[886],[888,2329,2330],{"xmlns":890},[892,2331,2332,2336],{},[895,2333,2334],{},[898,2335,1675],{},[902,2337,1675],{"encoding":904}," při změně ",[883,2340,2342],{"className":2341},[886],[888,2343,2344],{"xmlns":890},[892,2345,2346,2350],{},[895,2347,2348],{},[898,2349,1689],{},[902,2351,1689],{"encoding":904}," z ",[883,2354,2356],{"className":2355},[886],[888,2357,2358],{"xmlns":890},[892,2359,2360,2364],{},[895,2361,2362],{},[898,2363,207],{},[902,2365,207],{"encoding":904}," na ",[883,2368,2370],{"className":2369},[886],[888,2371,2372],{"xmlns":890},[892,2373,2374,2382],{},[895,2375,2376,2378,2380],{},[898,2377,207],{},[1677,2379,1776],{},[1810,2381,1959],{},[902,2383,2384],{"encoding":904},"a+1",":",[724,2387,2388],{},[883,2389,2391],{"className":2390},[886],[888,2392,2393],{"xmlns":890},[892,2394,2395,2434],{},[895,2396,2397,2399,2401,2403,2405,2407,2409,2412,2414,2416,2418,2420,2422,2428,2430,2432],{},[898,2398,1682],{},[1677,2400,1686],{"stretchy":1685},[898,2402,207],{},[1677,2404,1776],{},[1810,2406,1959],{},[1677,2408,1692],{"stretchy":1685},[1677,2410,2411],{},"≈",[898,2413,1682],{},[1677,2415,1686],{"stretchy":1685},[898,2417,207],{},[1677,2419,1692],{"stretchy":1685},[1677,2421,1776],{},[1805,2423,2424,2426],{},[898,2425,1682],{},[1677,2427,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,2429,1686],{"stretchy":1685},[898,2431,207],{},[1677,2433,1692],{"stretchy":1685},[902,2435,2436],{"encoding":904},"f(a+1) \\approx f(a) + f'(a)",[198,2438,2440],{"id":2439},"příklad-mezní-náklady","Příklad — mezní náklady",[724,2442,2443,2444,1656],{},"Celkové náklady ",[883,2445,2447],{"className":2446},[886],[888,2448,2449],{"xmlns":890},[892,2450,2451,2482],{},[895,2452,2453,2456,2459,2461,2464,2466,2468,2471,2473,2476],{},[898,2454,2455],{},"T",[898,2457,2458],{},"C",[1677,2460,1679],{},[1810,2462,2463],{},"1000",[1677,2465,1776],{},[1810,2467,1812],{},[898,2469,2470],{},"Q",[1677,2472,1776],{},[1810,2474,2475],{},"0,1",[1805,2477,2478,2480],{},[898,2479,2470],{},[1810,2481,1812],{},[902,2483,2484],{"encoding":904},"TC = 1000 + 2Q + 0{,}1 Q^2",[724,2486,2487,2488,2526,2527,1656],{},"Mezní náklady: ",[883,2489,2491],{"className":2490},[886],[888,2492,2493],{"xmlns":890},[892,2494,2495,2523],{},[895,2496,2497,2500,2502,2504,2506,2512,2514,2516,2518,2521],{},[898,2498,2499],{},"M",[898,2501,2458],{},[1677,2503,1679],{},[898,2505,2455],{},[1805,2507,2508,2510],{},[898,2509,2458],{},[1677,2511,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,2513,1679],{},[1810,2515,1812],{},[1677,2517,1776],{},[1810,2519,2520],{},"0,2",[898,2522,2470],{},[902,2524,2525],{"encoding":904},"MC = TC' = 2 + 0{,}2 Q",", takže ",[883,2528,2530],{"className":2529},[886],[888,2531,2532],{"xmlns":890},[892,2533,2534,2551],{},[895,2535,2536,2538,2540,2542,2545,2547,2549],{},[898,2537,2499],{},[898,2539,2458],{},[1677,2541,1686],{"stretchy":1685},[1810,2543,2544],{},"10",[1677,2546,1692],{"stretchy":1685},[1677,2548,1679],{},[1810,2550,2032],{},[902,2552,2553],{"encoding":904},"MC(10) = 4",[724,2555,2556,1884,2559,2608,2609,1884,2612,1656],{},[38,2557,2558],{},"Skutečný přírůstek:",[883,2560,2562],{"className":2561},[886],[888,2563,2564],{"xmlns":890},[892,2565,2566,2605],{},[895,2567,2568,2571,2573,2575,2577,2579,2581,2583,2586,2588,2590,2592,2594,2596,2598,2600,2602],{},[898,2569,2570],{"mathvariant":2057},"Δ",[898,2572,2455],{},[898,2574,2458],{},[1677,2576,1679],{},[898,2578,2455],{},[898,2580,2458],{},[1677,2582,1686],{"stretchy":1685},[1810,2584,2585],{},"11",[1677,2587,1692],{"stretchy":1685},[1677,2589,1906],{},[898,2591,2455],{},[898,2593,2458],{},[1677,2595,1686],{"stretchy":1685},[1810,2597,2544],{},[1677,2599,1692],{"stretchy":1685},[1677,2601,1679],{},[1810,2603,2604],{},"4,2",[902,2606,2607],{"encoding":904},"\\Delta TC = TC(11) - TC(10) = 4{,}2",". ",[38,2610,2611],{},"Přibližný (lineární):",[883,2613,2615],{"className":2614},[886],[888,2616,2617],{"xmlns":890},[892,2618,2619,2623],{},[895,2620,2621],{},[1810,2622,2032],{},[902,2624,2032],{"encoding":904},[724,2626,2627,2628,2632],{},"(Viz aplikace v ",[207,2629,2631],{"className":2630,"dataFsResolvedFilePath":827,"href":828},[210],"prijem-naklady-zisk",".)",[115,2634,2636],{"id":2635},"diferenciál","Diferenciál",[724,2638,2639],{},[883,2640,2642],{"className":2641},[886],[888,2643,2644],{"xmlns":890},[892,2645,2646,2673],{},[895,2647,2648,2650,2652,2654,2660,2662,2664,2666,2669,2671],{},[898,2649,1875],{},[898,2651,1682],{},[1677,2653,1679],{},[1805,2655,2656,2658],{},[898,2657,1682],{},[1677,2659,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,2661,1686],{"stretchy":1685},[898,2663,1689],{},[1677,2665,1692],{"stretchy":1685},[1969,2667,2668],{}," ",[898,2670,1875],{},[898,2672,1689],{},[902,2674,2675],{"encoding":904},"df = f'(x)\\, dx",[724,2677,2678,2679,2695,2696,2744,2745,1656],{},"Pro malá ",[883,2680,2682],{"className":2681},[886],[888,2683,2684],{"xmlns":890},[892,2685,2686,2692],{},[895,2687,2688,2690],{},[898,2689,1875],{},[898,2691,1689],{},[902,2693,2694],{"encoding":904},"dx"," platí: ",[883,2697,2699],{"className":2698},[886],[888,2700,2701],{"xmlns":890},[892,2702,2703,2741],{},[895,2704,2705,2707,2709,2711,2713,2715,2717,2719,2721,2723,2725,2727,2729,2731,2733,2735,2737,2739],{},[898,2706,2570],{"mathvariant":2057},[898,2708,1682],{},[1677,2710,1679],{},[898,2712,1682],{},[1677,2714,1686],{"stretchy":1685},[898,2716,1689],{},[1677,2718,1776],{},[898,2720,1875],{},[898,2722,1689],{},[1677,2724,1692],{"stretchy":1685},[1677,2726,1906],{},[898,2728,1682],{},[1677,2730,1686],{"stretchy":1685},[898,2732,1689],{},[1677,2734,1692],{"stretchy":1685},[1677,2736,2411],{},[898,2738,1875],{},[898,2740,1682],{},[902,2742,2743],{"encoding":904},"\\Delta f = f(x + dx) - f(x) \\approx df",". Diferenciál je ",[38,2746,2747],{},"lineární odhad přírůstku",[198,2749,2751],{"id":2750},"příklad","Příklad",[724,2753,2754,2785,2786,2811,2812,2832],{},[883,2755,2757],{"className":2756},[886],[888,2758,2759],{"xmlns":890},[892,2760,2761,2782],{},[895,2762,2763,2765,2767,2769,2772,2774,2776],{},[898,2764,2455],{},[898,2766,2458],{},[1677,2768,1679],{},[1810,2770,2771],{},"100",[1677,2773,1776],{},[1810,2775,2475],{},[1805,2777,2778,2780],{},[898,2779,2470],{},[1810,2781,1812],{},[902,2783,2784],{"encoding":904},"TC = 100 + 0{,}1 Q^2",", odhad změny při ",[883,2787,2789],{"className":2788},[886],[888,2790,2791],{"xmlns":890},[892,2792,2793,2808],{},[895,2794,2795,2797,2799,2802,2805],{},[898,2796,2470],{},[1677,2798,2385],{},[1810,2800,2801],{},"50",[1677,2803,2804],{},"→",[1810,2806,2807],{},"60",[902,2809,2810],{"encoding":904},"Q: 50 \\to 60"," (tj. ",[883,2813,2815],{"className":2814},[886],[888,2816,2817],{"xmlns":890},[892,2818,2819,2829],{},[895,2820,2821,2823,2825,2827],{},[898,2822,1875],{},[898,2824,2470],{},[1677,2826,1679],{},[1810,2828,2544],{},[902,2830,2831],{"encoding":904},"dQ = 10","):",[724,2834,2835],{},[883,2836,2838],{"className":2837},[886],[888,2839,2840],{"xmlns":890},[892,2841,2842,2879],{},[895,2843,2844,2846,2848,2850,2852,2854,2856,2859,2861,2863,2865,2867,2869,2871,2873,2875,2877],{},[898,2845,1875],{},[898,2847,2455],{},[898,2849,2458],{},[1677,2851,1679],{},[1810,2853,2520],{},[898,2855,2470],{},[1677,2857,2858],{},"⋅",[898,2860,1875],{},[898,2862,2470],{},[1677,2864,1679],{},[1810,2866,2520],{},[1677,2868,2858],{},[1810,2870,2801],{},[1677,2872,2858],{},[1810,2874,2544],{},[1677,2876,1679],{},[1810,2878,2771],{},[902,2880,2881],{"encoding":904},"dTC = 0{,}2 Q \\cdot dQ = 0{,}2 \\cdot 50 \\cdot 10 = 100",[724,2883,2884,2885,2908,2909,2925],{},"Přesná změna: ",[883,2886,2888],{"className":2887},[886],[888,2889,2890],{"xmlns":890},[892,2891,2892,2905],{},[895,2893,2894,2896,2898,2900,2902],{},[898,2895,2570],{"mathvariant":2057},[898,2897,2455],{},[898,2899,2458],{},[1677,2901,1679],{},[1810,2903,2904],{},"110",[902,2906,2907],{"encoding":904},"\\Delta TC = 110",". Lineární odhad mírně podstřeluje, protože ",[883,2910,2912],{"className":2911},[886],[888,2913,2914],{"xmlns":890},[892,2915,2916,2922],{},[895,2917,2918,2920],{},[898,2919,2455],{},[898,2921,2458],{},[902,2923,2924],{"encoding":904},"TC"," je konvexní.",[115,2927,2929],{"id":2928},"extrémy-funkce-jedné-proměnné","Extrémy funkce jedné proměnné",[198,2931,2933],{"id":2932},"nutná-podmínka","Nutná podmínka",[724,2935,2936,2937,2305,2957,2970,2971,2999,3000,3003],{},"Má-li ",[883,2938,2940],{"className":2939},[886],[888,2941,2942],{"xmlns":890},[892,2943,2944,2954],{},[895,2945,2946,2948,2950,2952],{},[898,2947,1682],{},[1677,2949,1686],{"stretchy":1685},[898,2951,1689],{},[1677,2953,1692],{"stretchy":1685},[902,2955,2956],{"encoding":904},"f(x)",[883,2958,2960],{"className":2959},[886],[888,2961,2962],{"xmlns":890},[892,2963,2964,2968],{},[895,2965,2966],{},[898,2967,207],{},[902,2969,207],{"encoding":904}," extrém, pak ",[883,2972,2974],{"className":2973},[886],[888,2975,2976],{"xmlns":890},[892,2977,2978,2996],{},[895,2979,2980,2986,2988,2990,2992,2994],{},[1805,2981,2982,2984],{},[898,2983,1682],{},[1677,2985,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,2987,1686],{"stretchy":1685},[898,2989,207],{},[1677,2991,1692],{"stretchy":1685},[1677,2993,1679],{},[1810,2995,2008],{},[902,2997,2998],{"encoding":904},"f'(a) = 0",". Body splňující tuto podmínku se nazývají ",[38,3001,3002],{},"stacionární"," (podezřelé) body.",[198,3005,3007],{"id":3006},"postačující-podmínka","Postačující podmínka",[724,3009,3010,3011,3024,3025,2385],{},"Pro stacionární bod ",[883,3012,3014],{"className":3013},[886],[888,3015,3016],{"xmlns":890},[892,3017,3018,3022],{},[895,3019,3020],{},[898,3021,207],{},[902,3023,207],{"encoding":904},", je-li ",[883,3026,3028],{"className":3027},[886],[888,3029,3030],{"xmlns":890},[892,3031,3032,3055],{},[895,3033,3034,3044,3046,3048,3050,3053],{},[1805,3035,3036,3038],{},[898,3037,1682],{},[895,3039,3040,3042],{},[1677,3041,2059],{"mathvariant":2057},[1677,3043,2059],{"mathvariant":2057},[1677,3045,1686],{"stretchy":1685},[898,3047,207],{},[1677,3049,1692],{"stretchy":1685},[1677,3051,3052],{"mathvariant":2057},"≠",[1810,3054,2008],{},[902,3056,3057],{"encoding":904},"f''(a) \\neq 0",[120,3059,3060,3099],{},[123,3061,3062,3095,3096],{},[883,3063,3065],{"className":3064},[886],[888,3066,3067],{"xmlns":890},[892,3068,3069,3092],{},[895,3070,3071,3081,3083,3085,3087,3090],{},[1805,3072,3073,3075],{},[898,3074,1682],{},[895,3076,3077,3079],{},[1677,3078,2059],{"mathvariant":2057},[1677,3080,2059],{"mathvariant":2057},[1677,3082,1686],{"stretchy":1685},[898,3084,207],{},[1677,3086,1692],{"stretchy":1685},[1677,3088,3089],{},">",[1810,3091,2008],{},[902,3093,3094],{"encoding":904},"f''(a) > 0"," ⇒ ",[38,3097,3098],{},"lokální minimum",[123,3100,3101,3095,3134],{},[883,3102,3104],{"className":3103},[886],[888,3105,3106],{"xmlns":890},[892,3107,3108,3131],{},[895,3109,3110,3120,3122,3124,3126,3129],{},[1805,3111,3112,3114],{},[898,3113,1682],{},[895,3115,3116,3118],{},[1677,3117,2059],{"mathvariant":2057},[1677,3119,2059],{"mathvariant":2057},[1677,3121,1686],{"stretchy":1685},[898,3123,207],{},[1677,3125,1692],{"stretchy":1685},[1677,3127,3128],{},"\u003C",[1810,3130,2008],{},[902,3132,3133],{"encoding":904},"f''(a) \u003C 0",[38,3135,3136],{},"lokální maximum",[724,3138,3139],{},[2240,3140],{"alt":3141,"className":3142,"src":3143},"imek-extremy-1d",[210,2244],"\u002Fwiki-assets\u002Fimek-extremy-1d.jpeg",[198,3145,2751],{"id":3146},"příklad-1",[724,3148,3149],{},[883,3150,3152],{"className":3151},[886],[888,3153,3154],{"xmlns":890},[892,3155,3156,3197],{},[895,3157,3158,3160,3162,3164,3166,3168,3170,3176,3178,3180,3186,3188,3191,3193,3195],{},[898,3159,1682],{},[1677,3161,1686],{"stretchy":1685},[898,3163,1689],{},[1677,3165,1692],{"stretchy":1685},[1677,3167,1679],{},[1810,3169,1812],{},[1805,3171,3172,3174],{},[898,3173,1689],{},[1810,3175,1854],{},[1677,3177,1906],{},[1810,3179,1854],{},[1805,3181,3182,3184],{},[898,3183,1689],{},[1810,3185,1812],{},[1677,3187,1906],{},[1810,3189,3190],{},"12",[898,3192,1689],{},[1677,3194,1776],{},[1810,3196,1854],{},[902,3198,3199],{"encoding":904},"f(x) = 2x^3 - 3x^2 - 12x + 3",[120,3201,3202,3313,3353,3416],{},[123,3203,3204,3276,3277],{},[883,3205,3207],{"className":3206},[886],[888,3208,3209],{"xmlns":890},[892,3210,3211,3273],{},[895,3212,3213,3219,3221,3223,3225,3227,3229,3235,3237,3239,3241,3243,3245,3247,3249,3251,3253,3255,3257,3259,3261,3263,3265,3267,3269,3271],{},[1805,3214,3215,3217],{},[898,3216,1682],{},[1677,3218,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,3220,1686],{"stretchy":1685},[898,3222,1689],{},[1677,3224,1692],{"stretchy":1685},[1677,3226,1679],{},[1810,3228,1916],{},[1805,3230,3231,3233],{},[898,3232,1689],{},[1810,3234,1812],{},[1677,3236,1906],{},[1810,3238,1916],{},[898,3240,1689],{},[1677,3242,1906],{},[1810,3244,3190],{},[1677,3246,1679],{},[1810,3248,1916],{},[1677,3250,1686],{"stretchy":1685},[898,3252,1689],{},[1677,3254,1776],{},[1810,3256,1959],{},[1677,3258,1692],{"stretchy":1685},[1677,3260,1686],{"stretchy":1685},[898,3262,1689],{},[1677,3264,1906],{},[1810,3266,1812],{},[1677,3268,1692],{"stretchy":1685},[1677,3270,1679],{},[1810,3272,2008],{},[902,3274,3275],{"encoding":904},"f'(x) = 6x^2 - 6x - 12 = 6(x+1)(x-2) = 0"," ⇒ S.B. ",[883,3278,3280],{"className":3279},[886],[888,3281,3282],{"xmlns":890},[892,3283,3284,3310],{},[895,3285,3286,3292,3294,3296,3298,3300,3306,3308],{},[1953,3287,3288,3290],{},[898,3289,1689],{},[1810,3291,1959],{},[1677,3293,1679],{},[1677,3295,1906],{},[1810,3297,1959],{},[1677,3299,1967],{"separator":1966},[1953,3301,3302,3304],{},[898,3303,1689],{},[1810,3305,1812],{},[1677,3307,1679],{},[1810,3309,1812],{},[902,3311,3312],{"encoding":904},"x_1 = -1, x_2 = 2",[123,3314,3315],{},[883,3316,3318],{"className":3317},[886],[888,3319,3320],{"xmlns":890},[892,3321,3322,3350],{},[895,3323,3324,3334,3336,3338,3340,3342,3344,3346,3348],{},[1805,3325,3326,3328],{},[898,3327,1682],{},[895,3329,3330,3332],{},[1677,3331,2059],{"mathvariant":2057},[1677,3333,2059],{"mathvariant":2057},[1677,3335,1686],{"stretchy":1685},[898,3337,1689],{},[1677,3339,1692],{"stretchy":1685},[1677,3341,1679],{},[1810,3343,3190],{},[898,3345,1689],{},[1677,3347,1906],{},[1810,3349,1916],{},[902,3351,3352],{"encoding":904},"f''(x) = 12x - 6",[123,3354,3355,3095,3396,3399,3400],{},[883,3356,3358],{"className":3357},[886],[888,3359,3360],{"xmlns":890},[892,3361,3362,3393],{},[895,3363,3364,3374,3376,3378,3380,3382,3384,3386,3389,3391],{},[1805,3365,3366,3368],{},[898,3367,1682],{},[895,3369,3370,3372],{},[1677,3371,2059],{"mathvariant":2057},[1677,3373,2059],{"mathvariant":2057},[1677,3375,1686],{"stretchy":1685},[1677,3377,1906],{},[1810,3379,1959],{},[1677,3381,1692],{"stretchy":1685},[1677,3383,1679],{},[1677,3385,1906],{},[1810,3387,3388],{},"18",[1677,3390,3128],{},[1810,3392,2008],{},[902,3394,3395],{"encoding":904},"f''(-1) = -18 \u003C 0",[38,3397,3398],{},"maximum"," v ",[883,3401,3403],{"className":3402},[886],[888,3404,3405],{"xmlns":890},[892,3406,3407,3413],{},[895,3408,3409,3411],{},[1677,3410,1906],{},[1810,3412,1959],{},[902,3414,3415],{"encoding":904},"-1",[123,3417,3418,3095,3454,3399,3457],{},[883,3419,3421],{"className":3420},[886],[888,3422,3423],{"xmlns":890},[892,3424,3425,3451],{},[895,3426,3427,3437,3439,3441,3443,3445,3447,3449],{},[1805,3428,3429,3431],{},[898,3430,1682],{},[895,3432,3433,3435],{},[1677,3434,2059],{"mathvariant":2057},[1677,3436,2059],{"mathvariant":2057},[1677,3438,1686],{"stretchy":1685},[1810,3440,1812],{},[1677,3442,1692],{"stretchy":1685},[1677,3444,1679],{},[1810,3446,3388],{},[1677,3448,3089],{},[1810,3450,2008],{},[902,3452,3453],{"encoding":904},"f''(2) = 18 > 0",[38,3455,3456],{},"minimum",[883,3458,3460],{"className":3459},[886],[888,3461,3462],{"xmlns":890},[892,3463,3464,3468],{},[895,3465,3466],{},[1810,3467,1812],{},[902,3469,1812],{"encoding":904},[115,3471,3473],{"id":3472},"navigace","Navigace",[120,3475,3476,3484,3492],{},[123,3477,3478,1884,3481],{},[38,3479,3480],{},"Předchozí:",[207,3482,757],{"className":3483,"dataFsResolvedFilePath":755,"href":756},[210],[123,3485,3486,1884,3489],{},[38,3487,3488],{},"Navazující:",[207,3490,775],{"className":3491,"dataFsResolvedFilePath":773,"href":774},[210],[123,3493,3494,1884,3497,3500,3501,3505,3506,3510],{},[38,3495,3496],{},"Souvislosti:",[207,3498,784],{"className":3499,"dataFsResolvedFilePath":782,"href":783},[210]," (rozšíření na 2D), ",[207,3502,3504],{"className":3503,"dataFsResolvedFilePath":827,"href":828},[210],"Příjem, náklady, zisk"," (aplikace mezních veličin), ",[207,3507,3509],{"className":3508,"dataFsResolvedFilePath":848,"href":849},[210],"Elasticita"," (procentní citlivost přes derivaci)",{"title":641,"searchDepth":642,"depth":642,"links":3512},[3513,3514,3519,3522,3527],{"id":1659,"depth":642,"text":1660},{"id":1145,"depth":642,"text":2038,"children":3515},[3516,3517,3518],{"id":2124,"depth":649,"text":2125},{"id":2248,"depth":649,"text":2249},{"id":2439,"depth":649,"text":2440},{"id":2635,"depth":642,"text":2636,"children":3520},[3521],{"id":2750,"depth":649,"text":2751},{"id":2928,"depth":642,"text":2929,"children":3523},[3524,3525,3526],{"id":2932,"depth":649,"text":2933},{"id":3006,"depth":649,"text":3007},{"id":3146,"depth":649,"text":2751},{"id":3472,"depth":642,"text":3473},"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":1629,"description":3528},[1135],"topics\u002Fderivace",[1128,1145,3535,3536,3537],"diferencial","extremy","mezni-naklady","topic","U4vqwJqO65hVzq9khEr5sxPHpHJLXAz_kTaaHdKCCIw","topics",{"zapisku":1625,"topics":3542,"summaries":3543,"outputs":3544},15,5,1,[3546,5245,10956,12513,13385,17669,19276,29156,38150,52217,56509,75853,87965,96924,97212],{"id":1628,"title":1629,"body":3547,"course":1128,"courses":659,"created":1129,"description":3528,"extension":661,"meta":5241,"navigation":664,"path":3530,"seo":5242,"sources":5243,"stem":3533,"tags":5244,"type":3538,"updated":677,"__hash__":3539},{"type":9,"value":3548,"toc":5224},[3549,3551,3562,3564,3634,3636,3755,3892,3894,3969,3971,4025,4074,4079,4081,4207,4256,4258,4295,4357,4421,4426,4428,4465,4531,4533,4604,4651,4689,4691,4693,4756,4758,4804,4876,4881,4883,4934,5193,5195],[12,3550,1629],{"id":1634},[724,3552,1637,3553,1644,3556,1648,3558,1652,3560,1656],{},[207,3554,1643],{"className":3555,"dataFsResolvedFilePath":1641,"href":1642},[210],[38,3557,1647],{},[38,3559,1651],{},[38,3561,1655],{},[115,3563,1660],{"id":1659},[724,3565,1663,3566,1696,3589,1710,3602,1724,3615,1656],{},[883,3567,3569],{"className":3568},[886],[888,3570,3571],{"xmlns":890},[892,3572,3573,3587],{},[895,3574,3575,3577,3579,3581,3583,3585],{},[898,3576,1675],{},[1677,3578,1679],{},[898,3580,1682],{},[1677,3582,1686],{"stretchy":1685},[898,3584,1689],{},[1677,3586,1692],{"stretchy":1685},[902,3588,1695],{"encoding":904},[883,3590,3592],{"className":3591},[886],[888,3593,3594],{"xmlns":890},[892,3595,3596,3600],{},[895,3597,3598],{},[898,3599,1689],{},[902,3601,1689],{"encoding":904},[883,3603,3605],{"className":3604},[886],[888,3606,3607],{"xmlns":890},[892,3608,3609,3613],{},[895,3610,3611],{},[898,3612,1675],{},[902,3614,1675],{"encoding":904},[883,3616,3618],{"className":3617},[886],[888,3619,3620],{"xmlns":890},[892,3621,3622,3632],{},[895,3623,3624,3626,3628,3630],{},[898,3625,1682],{},[1677,3627,1686],{"stretchy":1685},[898,3629,207],{},[1677,3631,1692],{"stretchy":1685},[902,3633,1744],{"encoding":904},[724,3635,1747],{},[120,3637,3638,3667,3706],{},[123,3639,3640],{},[152,3641,3642],{},[123,3643,1756,3644],{},[883,3645,3647],{"className":3646},[886],[888,3648,3649],{"xmlns":890},[892,3650,3651,3665],{},[895,3652,3653,3655,3657,3659,3661,3663],{},[898,3654,1675],{},[1677,3656,1679],{},[898,3658,207],{},[898,3660,1689],{},[1677,3662,1776],{},[898,3664,1779],{},[902,3666,1782],{"encoding":904},[123,3668,3669],{},[152,3670,3671],{"start":642},[123,3672,1756,3673],{},[883,3674,3676],{"className":3675},[886],[888,3677,3678],{"xmlns":890},[892,3679,3680,3704],{},[895,3681,3682,3684,3686,3688,3694,3696,3698,3700,3702],{},[898,3683,1675],{},[1677,3685,1679],{},[898,3687,207],{},[1805,3689,3690,3692],{},[898,3691,1689],{},[1810,3693,1812],{},[1677,3695,1776],{},[898,3697,1779],{},[898,3699,1689],{},[1677,3701,1776],{},[898,3703,1823],{},[902,3705,1826],{"encoding":904},[123,3707,3708],{},[152,3709,3710],{"start":649},[123,3711,1756,3712],{},[883,3713,3715],{"className":3714},[886],[888,3716,3717],{"xmlns":890},[892,3718,3719,3753],{},[895,3720,3721,3723,3725,3727,3733,3735,3737,3743,3745,3747,3749,3751],{},[898,3722,1675],{},[1677,3724,1679],{},[898,3726,207],{},[1805,3728,3729,3731],{},[898,3730,1689],{},[1810,3732,1854],{},[1677,3734,1776],{},[898,3736,1779],{},[1805,3738,3739,3741],{},[898,3740,1689],{},[1810,3742,1812],{},[1677,3744,1776],{},[898,3746,1823],{},[898,3748,1689],{},[1677,3750,1776],{},[898,3752,1875],{},[902,3754,1878],{"encoding":904},[724,3756,3757,1884,3759,1942,3812,1985,3847,1656],{},[38,3758,1883],{},[883,3760,3762],{"className":3761},[886],[888,3763,3764],{"xmlns":890},[892,3765,3766,3810],{},[895,3767,3768,3770,3772,3778,3780,3782,3784,3786,3788,3790,3792,3794,3796,3798,3800,3802,3804,3806,3808],{},[898,3769,1675],{},[1677,3771,1679],{},[1805,3773,3774,3776],{},[898,3775,1689],{},[1810,3777,1812],{},[1677,3779,1906],{},[1810,3781,1909],{},[898,3783,1689],{},[1677,3785,1776],{},[1810,3787,1916],{},[1677,3789,1679],{},[1677,3791,1686],{"stretchy":1685},[898,3793,1689],{},[1677,3795,1906],{},[1810,3797,1812],{},[1677,3799,1692],{"stretchy":1685},[1677,3801,1686],{"stretchy":1685},[898,3803,1689],{},[1677,3805,1906],{},[1810,3807,1854],{},[1677,3809,1692],{"stretchy":1685},[902,3811,1941],{"encoding":904},[883,3813,3815],{"className":3814},[886],[888,3816,3817],{"xmlns":890},[892,3818,3819,3845],{},[895,3820,3821,3827,3829,3831,3833,3835,3841,3843],{},[1953,3822,3823,3825],{},[898,3824,1689],{},[1810,3826,1959],{},[1677,3828,1679],{},[1810,3830,1812],{},[1677,3832,1967],{"separator":1966},[1969,3834,1971],{},[1953,3836,3837,3839],{},[898,3838,1689],{},[1810,3840,1812],{},[1677,3842,1679],{},[1810,3844,1854],{},[902,3846,1984],{"encoding":904},[883,3848,3850],{"className":3849},[886],[888,3851,3852],{"xmlns":890},[892,3853,3854,3890],{},[895,3855,3856,3858,3860,3862,3864,3866,3874,3880,3882],{},[898,3857,1675],{},[1677,3859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poptávky a nabídky",{"type":9,"value":5249,"toc":10917},[5250,5253,5276,5280,5307,5311,5353,5444,5488,5492,5516,5523,5527,5537,5549,5553,5582,5591,5648,5654,5657,5663,5690,5696,5794,5954,6245,6249,6329,6335,6339,6437,6503,6671,6675,6753,6784,6811,6817,6849,6927,7014,7018,7081,7087,7090,7096,7210,7295,7339,7343,7389,7396,7713,7718,7742,7771,7838,7935,7939,7946,7953,8024,8144,8228,8231,8237,8564,8568,8731,8739,8875,8883,9121,9129,9132,9137,9393,9397,9571,9705,9742,9786,9789,9919,10009,10027,10031,10038,10044,10105,10108,10132,10135,10141,10144,10150,10153,10157,10195,10253,10442,10446,10519,10525,10532,10536,10542,10684,10688,10694,10730,10735,10912],[12,5251,5247],{"id":5252},"elasticita-poptávky-a-nabídky",[5254,5255,5256],"blockquote",{},[724,5257,5258,5261,5262,5264,5265,5268,5269,5272,5273,1656],{},[883,5259,5260],{},"!abstract"," TL;DR\n",[38,5263,3509],{}," 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: ",[38,5266,5267],{},"cenovou elasticitu poptávky"," (a nabídky), ",[38,5270,5271],{},"křížově-cenovou elasticitu"," a ",[38,5274,5275],{},"důchodovou elasticitu",[115,5277,5279],{"id":5278},"úvod-motivace","Úvod — motivace",[724,5281,5282,5283,5286,5287,5290,5291,5294,5295,5298,5299,5302,5303,5306],{},"Termín ",[614,5284,5285],{},"elasticita"," (alternativně ",[614,5288,5289],{},"pružnost",") patří ke klíčovým pojmům ekonomické teorie. Slouží ke ",[38,5292,5293],{},"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 ",[614,5296,5297],{},"cenové elasticity poptávky"," (resp. ",[614,5300,5301],{},"nabídky","). Matematickým modelem míry citlivosti je elasticita funkce (viz ",[207,5304,2038],{"className":5305,"dataFsResolvedFilePath":764,"href":765},[210],").",[198,5308,5310],{"id":5309},"srovnání-trh-1-vs-trh-2","Srovnání Trh 1 vs Trh 2",[724,5312,5313,5314,5333,5334,5352],{},"Uvažujme dvě různá tržní prostředí. Zboží má na obou trzích stejnou cenu ",[883,5315,5317],{"className":5316},[886],[888,5318,5319],{"xmlns":890},[892,5320,5321,5330],{},[895,5322,5323,5326,5328],{},[898,5324,5325],{},"P",[1677,5327,1679],{},[1810,5329,2544],{},[902,5331,5332],{"encoding":904},"P=10"," a při této ceně se prodá ",[883,5335,5337],{"className":5336},[886],[888,5338,5339],{"xmlns":890},[892,5340,5341,5349],{},[895,5342,5343,5345,5347],{},[898,5344,2470],{},[1677,5346,1679],{},[1810,5348,2771],{},[902,5350,5351],{"encoding":904},"Q=100"," jednotek. Prodejce sníží cenu z 10 na 9:",[120,5354,5355,5401],{},[123,5356,5357,5360,5361,5400],{},[38,5358,5359],{},"Trh 1"," zareaguje zvýšením množství na 110 ",[883,5362,5364],{"className":5363},[886],[888,5365,5366],{"xmlns":890},[892,5367,5368,5397],{},[895,5369,5370,5373,5376,5378,5380,5383,5385,5388,5390,5392,5394],{},[1969,5371,5372],{},"  ",[1677,5374,5375],{},"⇒",[1969,5377,5372],{},[898,5379,2455],{},[898,5381,5382],{},"R",[1677,5384,1679],{},[1810,5386,5387],{},"9",[1677,5389,2858],{},[1810,5391,2904],{},[1677,5393,1679],{},[1810,5395,5396],{},"990",[902,5398,5399],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 110 = 990"," (pokles z 1000).",[123,5402,5403,5406,5407,5443],{},[38,5404,5405],{},"Trh 2"," zareaguje zvýšením množství na 120 ",[883,5408,5410],{"className":5409},[886],[888,5411,5412],{"xmlns":890},[892,5413,5414,5440],{},[895,5415,5416,5418,5420,5422,5424,5426,5428,5430,5432,5435,5437],{},[1969,5417,5372],{},[1677,5419,5375],{},[1969,5421,5372],{},[898,5423,2455],{},[898,5425,5382],{},[1677,5427,1679],{},[1810,5429,5387],{},[1677,5431,2858],{},[1810,5433,5434],{},"120",[1677,5436,1679],{},[1810,5438,5439],{},"1080",[902,5441,5442],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 120 = 1080"," (růst z 1000).",[724,5445,5446,5447,5450,5451,5454,5455,5458,5459,5462,5463,5466,5467,5483,5484,5487],{},"Závěr: snížení ceny bylo na Trhu 1 ",[38,5448,5449],{},"nerozumné",", na Trhu 2 ",[38,5452,5453],{},"rozumné",". Trh 2 je ",[38,5456,5457],{},"relativně citlivý"," na změnu ceny — říkáme, že poptávka je ",[614,5460,5461],{},"elastická"," a snížení ceny je „překompenzováno\" zvýšením poptávaného množství. Na Trhu 1 je poptávka ",[614,5464,5465],{},"neelastická"," a vyššího ",[883,5468,5470],{"className":5469},[886],[888,5471,5472],{"xmlns":890},[892,5473,5474,5480],{},[895,5475,5476,5478],{},[898,5477,2455],{},[898,5479,5382],{},[902,5481,5482],{"encoding":904},"TR"," lze naopak dosáhnout ",[614,5485,5486],{},"zvýšením"," ceny.",[198,5489,5491],{"id":5490},"hypotéza-41","Hypotéza 4.1",[5254,5493,5494],{},[724,5495,5496,5497],{},"Aby nedošlo k poklesu celkového příjmu, musí být procentní růst poptávaného množství alespoň takový, jaký je procentní pokles jeho ceny. ",[883,5498,5500],{"className":5499},[886],[888,5501,5502],{"xmlns":890},[892,5503,5504,5513],{},[895,5505,5506,5508,5511],{},[1677,5507,1686],{"stretchy":1685},[1810,5509,5510],{},"4.1",[1677,5512,1692],{"stretchy":1685},[902,5514,5515],{"encoding":904},"(4.1)",[724,5517,5518,5519,5522],{},"Rozhodující nejsou nominální změny (jsou měřeny v různých jednotkách), nýbrž ",[38,5520,5521],{},"procentní změny"," obou faktorů.",[115,5524,5526],{"id":5525},"pojem-elasticity","Pojem elasticity",[724,5528,5529,5530,5532,5533,5536],{},"Obecně ",[38,5531,5285],{}," jedné veličiny vzhledem k druhé kvantifikuje, o kolik procent se první veličina přibližně změní, když se druhá veličina změní o 1 %. Jde o ",[38,5534,5535],{},"bezrozměrnou veličinu"," — nezávislou na jednotkách, ve kterých jsou proměnné měřeny (viz čl. 1.5.1).",[5254,5538,5539],{},[724,5540,5541,5544,5545,5548],{},[883,5542,5543],{},"!info"," Intuice\nElasticitu lze číst jako ",[38,5546,5547],{},"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.",[115,5550,5552],{"id":5551},"cenová-elasticita-poptávky-jednofaktorový-model","Cenová elasticita poptávky — jednofaktorový model",[724,5554,5555,5556,5581],{},"Nechť ",[883,5557,5559],{"className":5558},[886],[888,5560,5561],{"xmlns":890},[892,5562,5563,5578],{},[895,5564,5565,5567,5569,5572,5574,5576],{},[898,5566,2470],{},[1677,5568,1679],{},[898,5570,5571],{},"D",[1677,5573,1686],{"stretchy":1685},[898,5575,5325],{},[1677,5577,1692],{"stretchy":1685},[902,5579,5580],{"encoding":904},"Q = D(P)"," je funkce poptávky (ceteris paribus). Zkoumáme podíl procentních změn",[724,5583,5584],{},[883,5585,5590],{"className":5586,"title":5588,"style":5589},[5587],"katex-error","ParseError: KaTeX parse error: \\tag works only in display equations","color:#cc0000","E^A = -\\frac{\\Delta Q\\%}{\\Delta P\\%}. \\tag{4.2}",[724,5592,5593,5594,5272,5610,5626,5627,5647],{},"Znaménko minus je korekce: změny ",[883,5595,5597],{"className":5596},[886],[888,5598,5599],{"xmlns":890},[892,5600,5601,5607],{},[895,5602,5603,5605],{},[898,5604,2570],{"mathvariant":2057},[898,5606,2470],{},[902,5608,5609],{"encoding":904},"\\Delta Q",[883,5611,5613],{"className":5612},[886],[888,5614,5615],{"xmlns":890},[892,5616,5617,5623],{},[895,5618,5619,5621],{},[898,5620,2570],{"mathvariant":2057},[898,5622,5325],{},[902,5624,5625],{"encoding":904},"\\Delta P"," mají vždy opačná znaménka, takže bez korekce by ",[883,5628,5630],{"className":5629},[886],[888,5631,5632],{"xmlns":890},[892,5633,5634,5644],{},[895,5635,5636],{},[1805,5637,5638,5641],{},[898,5639,5640],{},"E",[898,5642,5643],{},"A",[902,5645,5646],{"encoding":904},"E^A"," bylo záporné; pro pohodlí pracujeme s nezápornými hodnotami. Pro procentní změny platí",[724,5649,5650],{},[883,5651,5653],{"className":5652,"title":5588,"style":5589},[5587],"\\Delta Q\\% = \\frac{\\Delta Q}{Q}\\cdot 100, \\qquad \\Delta P\\% = \\frac{\\Delta P}{P}\\cdot 100. \\tag{4.3}",[724,5655,5656],{},"Po dosazení:",[724,5658,5659],{},[883,5660,5662],{"className":5661,"title":5588,"style":5589},[5587],"E^A = -\\frac{\\frac{\\Delta Q}{Q}}{\\frac{\\Delta P}{P}} = -\\frac{P}{Q}\\cdot \\frac{\\Delta Q}{\\Delta P}. \\tag{4.4}",[724,5664,5665,5666,5686,5687,5689],{},"Limitním přechodem ",[883,5667,5669],{"className":5668},[886],[888,5670,5671],{"xmlns":890},[892,5672,5673,5683],{},[895,5674,5675,5677,5679,5681],{},[898,5676,2570],{"mathvariant":2057},[898,5678,5325],{},[1677,5680,2804],{},[1810,5682,2008],{},[902,5684,5685],{"encoding":904},"\\Delta P \\to 0"," získáme definici ",[38,5688,5297],{}," (price elasticity of demand):",[724,5691,5692],{},[883,5693,5695],{"className":5694,"title":5588,"style":5589},[5587],"\\boxed{\\;E = E(P) = -\\frac{P}{Q}\\cdot \\frac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\frac{P}{Q}\\,Q'(P)\\;} \\tag{4.5}",[724,5697,5698,5699,5722,5723,5746,5747,5771,5772,5793],{},"kde ",[883,5700,5702],{"className":5701},[886],[888,5703,5704],{"xmlns":890},[892,5705,5706,5720],{},[895,5707,5708,5710,5712,5714,5716,5718],{},[898,5709,2470],{},[1677,5711,1679],{},[898,5713,5571],{},[1677,5715,1686],{"stretchy":1685},[898,5717,5325],{},[1677,5719,1692],{"stretchy":1685},[902,5721,5580],{"encoding":904},". Pro pevnou cenu ",[883,5724,5726],{"className":5725},[886],[888,5727,5728],{"xmlns":890},[892,5729,5730,5743],{},[895,5731,5732,5734,5736],{},[898,5733,5325],{},[1677,5735,1679],{},[1805,5737,5738,5740],{},[898,5739,5325],{},[1677,5741,5742],{},"∗",[902,5744,5745],{"encoding":904},"P = P^*"," se ",[883,5748,5750],{"className":5749},[886],[888,5751,5752],{"xmlns":890},[892,5753,5754,5768],{},[895,5755,5756,5758,5760,5766],{},[898,5757,5640],{},[1677,5759,1686],{"stretchy":1685},[1805,5761,5762,5764],{},[898,5763,5325],{},[1677,5765,5742],{},[1677,5767,1692],{"stretchy":1685},[902,5769,5770],{"encoding":904},"E(P^*)"," nazývá ",[614,5773,5774,5775],{},"elasticita poptávky při ceně ",[883,5776,5778],{"className":5777},[886],[888,5779,5780],{"xmlns":890},[892,5781,5782,5790],{},[895,5783,5784],{},[1805,5785,5786,5788],{},[898,5787,5325],{},[1677,5789,5742],{},[902,5791,5792],{"encoding":904},"P^*"," a je to vždy nezáporné číslo.",[5254,5795,5796],{},[724,5797,5798,5801,5802,5820,5821,5849,5850,5879,5880,1343,5898,1343,5916,5934,5935,5950,5951,1656],{},[883,5799,5800],{},"!warning"," Pozor na znaménko\nV (4.5) je ",[38,5803,5804,5805],{},"explicitní ",[883,5806,5808],{"className":5807},[886],[888,5809,5810],{"xmlns":890},[892,5811,5812,5818],{},[895,5813,5814,5816],{},[1677,5815,1906],{},[1810,5817,1959],{},[902,5819,3415],{"encoding":904}," právě proto, že ",[883,5822,5824],{"className":5823},[886],[888,5825,5826],{"xmlns":890},[892,5827,5828,5846],{},[895,5829,5830,5836,5838,5840,5842,5844],{},[1805,5831,5832,5834],{},[898,5833,2470],{},[1677,5835,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,5837,1686],{"stretchy":1685},[898,5839,5325],{},[1677,5841,1692],{"stretchy":1685},[1677,5843,3128],{},[1810,5845,2008],{},[902,5847,5848],{"encoding":904},"Q'(P) \u003C 0"," (poptávka klesá s cenou). Díky korekčnímu znaménku je výsledné ",[883,5851,5853],{"className":5852},[886],[888,5854,5855],{"xmlns":890},[892,5856,5857,5876],{},[895,5858,5859,5861,5863,5869,5871,5874],{},[898,5860,5640],{},[1677,5862,1686],{"stretchy":1685},[1805,5864,5865,5867],{},[898,5866,5325],{},[1677,5868,5742],{},[1677,5870,1692],{"stretchy":1685},[1677,5872,5873],{},"≥",[1810,5875,2008],{},[902,5877,5878],{"encoding":904},"E(P^*) \\ge 0"," a s touto nezápornou konvencí pracuje celá klasifikace ",[883,5881,5883],{"className":5882},[886],[888,5884,5885],{"xmlns":890},[892,5886,5887,5895],{},[895,5888,5889,5891,5893],{},[898,5890,5640],{},[1677,5892,3089],{},[1810,5894,1959],{},[902,5896,5897],{"encoding":904},"E > 1",[883,5899,5901],{"className":5900},[886],[888,5902,5903],{"xmlns":890},[892,5904,5905,5913],{},[895,5906,5907,5909,5911],{},[898,5908,5640],{},[1677,5910,3128],{},[1810,5912,1959],{},[902,5914,5915],{"encoding":904},"E \u003C 1",[883,5917,5919],{"className":5918},[886],[888,5920,5921],{"xmlns":890},[892,5922,5923,5931],{},[895,5924,5925,5927,5929],{},[898,5926,5640],{},[1677,5928,1679],{},[1810,5930,1959],{},[902,5932,5933],{"encoding":904},"E = 1",". V některých starších pramenech se ",[883,5936,5938],{"className":5937},[886],[888,5939,5940],{"xmlns":890},[892,5941,5942,5948],{},[895,5943,5944,5946],{},[1677,5945,1906],{},[1810,5947,1959],{},[902,5949,3415],{"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 ",[38,5952,5953],{},"absolutní hodnotou",[5254,5955,5956,5976],{},[724,5957,5958,5961,5962,5975],{},[883,5959,5960],{},"!tip"," Postup: jak spočítat ",[883,5963,5965],{"className":5964},[886],[888,5966,5967],{"xmlns":890},[892,5968,5969,5973],{},[895,5970,5971],{},[898,5972,5640],{},[902,5974,5640],{"encoding":904}," v bodě",[152,5977,5978,6030,6070,6123,6188],{},[123,5979,5980,5981,6004,6005,6029],{},"Zapište ",[883,5982,5984],{"className":5983},[886],[888,5985,5986],{"xmlns":890},[892,5987,5988,6002],{},[895,5989,5990,5992,5994,5996,5998,6000],{},[898,5991,2470],{},[1677,5993,1679],{},[898,5995,5571],{},[1677,5997,1686],{"stretchy":1685},[898,5999,5325],{},[1677,6001,1692],{"stretchy":1685},[902,6003,5580],{"encoding":904},". Pokud je poptávka zadaná jako ",[883,6006,6008],{"className":6007},[886],[888,6009,6010],{"xmlns":890},[892,6011,6012,6026],{},[895,6013,6014,6016,6018,6020,6022,6024],{},[898,6015,5325],{},[1677,6017,1679],{},[898,6019,5571],{},[1677,6021,1686],{"stretchy":1685},[898,6023,2470],{},[1677,6025,1692],{"stretchy":1685},[902,6027,6028],{"encoding":904},"P = D(Q)",", použijte vztah (4.9).",[123,6031,6032,6033,1656],{},"Spočítejte derivaci ",[883,6034,6036],{"className":6035},[886],[888,6037,6038],{"xmlns":890},[892,6039,6040,6067],{},[895,6041,6042,6048,6050,6052,6054,6056,6058,6060,6063,6065],{},[1805,6043,6044,6046],{},[898,6045,2470],{},[1677,6047,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,6049,1686],{"stretchy":1685},[898,6051,5325],{},[1677,6053,1692],{"stretchy":1685},[1677,6055,1679],{},[898,6057,1875],{"mathvariant":2057},[898,6059,2470],{},[898,6061,6062],{"mathvariant":2057},"\u002F",[898,6064,1875],{"mathvariant":2057},[898,6066,5325],{},[902,6068,6069],{"encoding":904},"Q'(P) = \\mathrm{d}Q\u002F\\mathrm{d}P",[123,6071,6072,6073,6090,6091,1656],{},"Dosaďte zadanou cenu ",[883,6074,6076],{"className":6075},[886],[888,6077,6078],{"xmlns":890},[892,6079,6080,6088],{},[895,6081,6082],{},[1805,6083,6084,6086],{},[898,6085,5325],{},[1677,6087,5742],{},[902,6089,5792],{"encoding":904}," a dopočítejte odpovídající ",[883,6092,6094],{"className":6093},[886],[888,6095,6096],{"xmlns":890},[892,6097,6098,6120],{},[895,6099,6100,6106,6108,6110,6112,6118],{},[1805,6101,6102,6104],{},[898,6103,2470],{},[1677,6105,5742],{},[1677,6107,1679],{},[898,6109,5571],{},[1677,6111,1686],{"stretchy":1685},[1805,6113,6114,6116],{},[898,6115,5325],{},[1677,6117,5742],{},[1677,6119,1692],{"stretchy":1685},[902,6121,6122],{"encoding":904},"Q^* = D(P^*)",[123,6124,6125,6126,1656],{},"Dosaďte do (4.5): ",[883,6127,6129],{"className":6128},[886],[888,6130,6131],{"xmlns":890},[892,6132,6133,6185],{},[895,6134,6135,6137,6139,6145,6147,6149,6151,6167,6169,6175,6177,6183],{},[898,6136,5640],{},[1677,6138,1686],{"stretchy":1685},[1805,6140,6141,6143],{},[898,6142,5325],{},[1677,6144,5742],{},[1677,6146,1692],{"stretchy":1685},[1677,6148,1679],{},[1677,6150,1906],{},[2006,6152,6153],{"scriptlevel":2008,"displaystyle":1966},[2010,6154,6155,6161],{},[1805,6156,6157,6159],{},[898,6158,5325],{},[1677,6160,5742],{},[1805,6162,6163,6165],{},[898,6164,2470],{},[1677,6166,5742],{},[1969,6168,2668],{},[1805,6170,6171,6173],{},[898,6172,2470],{},[1677,6174,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,6176,1686],{"stretchy":1685},[1805,6178,6179,6181],{},[898,6180,5325],{},[1677,6182,5742],{},[1677,6184,1692],{"stretchy":1685},[902,6186,6187],{"encoding":904},"E(P^*) = -\\dfrac{P^*}{Q^*}\\,Q'(P^*)",[123,6189,6190,6191,6208,6209,6226,6227,6244],{},"Klasifikujte: ",[883,6192,6194],{"className":6193},[886],[888,6195,6196],{"xmlns":890},[892,6197,6198,6206],{},[895,6199,6200,6202,6204],{},[898,6201,5640],{},[1677,6203,3089],{},[1810,6205,1959],{},[902,6207,5897],{"encoding":904}," elastická, ",[883,6210,6212],{"className":6211},[886],[888,6213,6214],{"xmlns":890},[892,6215,6216,6224],{},[895,6217,6218,6220,6222],{},[898,6219,5640],{},[1677,6221,1679],{},[1810,6223,1959],{},[902,6225,5933],{"encoding":904}," jednotková, ",[883,6228,6230],{"className":6229},[886],[888,6231,6232],{"xmlns":890},[892,6233,6234,6242],{},[895,6235,6236,6238,6240],{},[898,6237,5640],{},[1677,6239,3128],{},[1810,6241,1959],{},[902,6243,5915],{"encoding":904}," neelastická.",[198,6246,6248],{"id":6247},"interpretace-46","Interpretace (4.6)",[5254,6250,6251],{},[724,6252,6253,6254,6277,6278,6291,6292,6309,6310],{},"Číslo ",[883,6255,6257],{"className":6256},[886],[888,6258,6259],{"xmlns":890},[892,6260,6261,6275],{},[895,6262,6263,6265,6267,6273],{},[898,6264,5640],{},[1677,6266,1686],{"stretchy":1685},[1805,6268,6269,6271],{},[898,6270,5325],{},[1677,6272,5742],{},[1677,6274,1692],{"stretchy":1685},[902,6276,5770],{"encoding":904}," udává, o kolik % se přibližně změní poptávané množství ",[883,6279,6281],{"className":6280},[886],[888,6282,6283],{"xmlns":890},[892,6284,6285,6289],{},[895,6286,6287],{},[898,6288,2470],{},[902,6290,2470],{"encoding":904},", jestliže se cena ",[883,6293,6295],{"className":6294},[886],[888,6296,6297],{"xmlns":890},[892,6298,6299,6307],{},[895,6300,6301],{},[1805,6302,6303,6305],{},[898,6304,5325],{},[1677,6306,5742],{},[902,6308,5792],{"encoding":904}," změní o 1 %. ",[883,6311,6313],{"className":6312},[886],[888,6314,6315],{"xmlns":890},[892,6316,6317,6326],{},[895,6318,6319,6321,6324],{},[1677,6320,1686],{"stretchy":1685},[1810,6322,6323],{},"4.6",[1677,6325,1692],{"stretchy":1685},[902,6327,6328],{"encoding":904},"(4.6)",[724,6330,6331,6334],{},[38,6332,6333],{},"Historicky:"," úvahy vedoucí k hypotéze (4.1) formuloval již Cournot (1838), dnešní vymezení se připisuje Marshallovi (1881).",[198,6336,6338],{"id":6337},"příklad-41","Příklad 4.1",[724,6340,6341,6342,6376,6377,1343,6403,2385],{},"Poptávka ",[883,6343,6345],{"className":6344},[886],[888,6346,6347],{"xmlns":890},[892,6348,6349,6373],{},[895,6350,6351,6353,6355,6357,6359,6361,6363,6365,6367,6369,6371],{},[898,6352,5325],{},[1677,6354,1679],{},[898,6356,5571],{},[1677,6358,1686],{"stretchy":1685},[898,6360,2470],{},[1677,6362,1692],{"stretchy":1685},[1677,6364,1679],{},[1810,6366,2801],{},[1677,6368,1906],{},[1810,6370,1812],{},[898,6372,2470],{},[902,6374,6375],{"encoding":904},"P = D(Q) = 50 - 2Q",". Vyjádříme ",[883,6378,6380],{"className":6379},[886],[888,6381,6382],{"xmlns":890},[892,6383,6384,6400],{},[895,6385,6386,6388,6390,6393,6395,6398],{},[898,6387,2470],{},[1677,6389,1679],{},[1810,6391,6392],{},"25",[1677,6394,1906],{},[1810,6396,6397],{},"0,5",[898,6399,5325],{},[902,6401,6402],{"encoding":904},"Q = 25 - 0{,}5P",[883,6404,6406],{"className":6405},[886],[888,6407,6408],{"xmlns":890},[892,6409,6410,6434],{},[895,6411,6412,6428,6430,6432],{},[2006,6413,6414],{"scriptlevel":2008,"displaystyle":1966},[2010,6415,6416,6422],{},[895,6417,6418,6420],{},[898,6419,1875],{"mathvariant":2057},[898,6421,2470],{},[895,6423,6424,6426],{},[898,6425,1875],{"mathvariant":2057},[898,6427,5325],{},[1677,6429,1679],{},[1677,6431,1906],{},[1810,6433,6397],{},[902,6435,6436],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -0{,}5",[724,6438,6439],{},[883,6440,6442],{"className":6441},[886],[888,6443,6444],{"xmlns":890},[892,6445,6446,6500],{},[895,6447,6448,6450,6452,6454,6468,6470,6472,6474,6476,6478,6480,6498],{},[898,6449,5640],{},[1677,6451,1679],{},[1677,6453,1906],{},[2010,6455,6456,6458],{},[898,6457,5325],{},[895,6459,6460,6462,6464,6466],{},[1810,6461,6392],{},[1677,6463,1906],{},[1810,6465,6397],{},[898,6467,5325],{},[1677,6469,2858],{},[1677,6471,1686],{"stretchy":1685},[1677,6473,1906],{},[1810,6475,6397],{},[1677,6477,1692],{"stretchy":1685},[1677,6479,1679],{},[2010,6481,6482,6488],{},[895,6483,6484,6486],{},[1810,6485,6397],{},[898,6487,5325],{},[895,6489,6490,6492,6494,6496],{},[1810,6491,6392],{},[1677,6493,1906],{},[1810,6495,6397],{},[898,6497,5325],{},[898,6499,1656],{"mathvariant":2057},[902,6501,6502],{"encoding":904},"E = -\\frac{P}{25-0{,}5P}\\cdot(-0{,}5) = \\frac{0{,}5P}{25-0{,}5P}.",[724,6504,6505,6506,1343,6530,1343,6560,1343,6584,6609,6610,6633,6634,2366,6652,5306],{},"Potom ",[883,6507,6509],{"className":6508},[886],[888,6510,6511],{"xmlns":890},[892,6512,6513,6527],{},[895,6514,6515,6517,6519,6521,6523,6525],{},[898,6516,5640],{},[1677,6518,1686],{"stretchy":1685},[1810,6520,2008],{},[1677,6522,1692],{"stretchy":1685},[1677,6524,1679],{},[1810,6526,2008],{},[902,6528,6529],{"encoding":904},"E(0)=0",[883,6531,6533],{"className":6532},[886],[888,6534,6535],{"xmlns":890},[892,6536,6537,6557],{},[895,6538,6539,6541,6543,6545,6547,6549],{},[898,6540,5640],{},[1677,6542,1686],{"stretchy":1685},[1810,6544,2544],{},[1677,6546,1692],{"stretchy":1685},[1677,6548,1679],{},[2006,6550,6551],{"scriptlevel":2008,"displaystyle":1685},[2010,6552,6553,6555],{},[1810,6554,1959],{},[1810,6556,2032],{},[902,6558,6559],{"encoding":904},"E(10)=\\tfrac{1}{4}",[883,6561,6563],{"className":6562},[886],[888,6564,6565],{"xmlns":890},[892,6566,6567,6581],{},[895,6568,6569,6571,6573,6575,6577,6579],{},[898,6570,5640],{},[1677,6572,1686],{"stretchy":1685},[1810,6574,6392],{},[1677,6576,1692],{"stretchy":1685},[1677,6578,1679],{},[1810,6580,1959],{},[902,6582,6583],{"encoding":904},"E(25)=1",[883,6585,6587],{"className":6586},[886],[888,6588,6589],{"xmlns":890},[892,6590,6591,6606],{},[895,6592,6593,6595,6597,6600,6602,6604],{},[898,6594,5640],{},[1677,6596,1686],{"stretchy":1685},[1810,6598,6599],{},"40",[1677,6601,1692],{"stretchy":1685},[1677,6603,1679],{},[1810,6605,2032],{},[902,6607,6608],{"encoding":904},"E(40)=4",". Např. ",[883,6611,6613],{"className":6612},[886],[888,6614,6615],{"xmlns":890},[892,6616,6617,6631],{},[895,6618,6619,6621,6623,6625,6627,6629],{},[898,6620,5640],{},[1677,6622,1686],{"stretchy":1685},[1810,6624,6599],{},[1677,6626,1692],{"stretchy":1685},[1677,6628,1679],{},[1810,6630,2032],{},[902,6632,6608],{"encoding":904}," znamená, že zvýšení ceny o 1 % (z 40 na 40,4) způsobí pokles množství o 4 % (z ",[883,6635,6637],{"className":6636},[886],[888,6638,6639],{"xmlns":890},[892,6640,6641,6649],{},[895,6642,6643,6645,6647],{},[898,6644,2470],{},[1677,6646,1679],{},[1810,6648,1909],{},[902,6650,6651],{"encoding":904},"Q=5",[883,6653,6655],{"className":6654},[886],[888,6656,6657],{"xmlns":890},[892,6658,6659,6668],{},[895,6660,6661,6663,6665],{},[898,6662,2470],{},[1677,6664,1679],{},[1810,6666,6667],{},"4,8",[902,6669,6670],{"encoding":904},"Q=4{,}8",[198,6672,6674],{"id":6673},"oblouková-průměrná-vs-bodová-okamžitá-elasticita","Oblouková (průměrná) vs. bodová (okamžitá) elasticita",[120,6676,6677,6733],{},[123,6678,6679,6682,6683,6700,6701,1656],{},[38,6680,6681],{},"Oblouková"," (průměrná) elasticita: výraz ",[883,6684,6686],{"className":6685},[886],[888,6687,6688],{"xmlns":890},[892,6689,6690,6698],{},[895,6691,6692],{},[1805,6693,6694,6696],{},[898,6695,5640],{},[898,6697,5643],{},[902,6699,5646],{"encoding":904}," ze (4.4) vztažený k intervalu ",[883,6702,6704],{"className":6703},[886],[888,6705,6706],{"xmlns":890},[892,6707,6708,6730],{},[895,6709,6710,6713,6715,6717,6719,6721,6723,6725,6727],{},[1677,6711,6712],{"stretchy":1685},"⟨",[898,6714,5325],{},[1677,6716,1967],{"separator":1966},[1969,6718,2668],{},[898,6720,5325],{},[1677,6722,1776],{},[898,6724,2570],{"mathvariant":2057},[898,6726,5325],{},[1677,6728,6729],{"stretchy":1685},"⟩",[902,6731,6732],{"encoding":904},"\\langle P,\\, P+\\Delta P\\rangle",[123,6734,6735,6738,6739,6752],{},[38,6736,6737],{},"Bodová"," (okamžitá) elasticita: ",[883,6740,6742],{"className":6741},[886],[888,6743,6744],{"xmlns":890},[892,6745,6746,6750],{},[895,6747,6748],{},[898,6749,5640],{},[902,6751,5640],{"encoding":904}," dle (4.5) — výchozí pojem dále v textu.",[198,6754,6756,6757,6770,6771],{"id":6755},"výpočet-je-li-dáno-pp-jako-funkce-qq","Výpočet, je-li dáno ",[883,6758,6760],{"className":6759},[886],[888,6761,6762],{"xmlns":890},[892,6763,6764,6768],{},[895,6765,6766],{},[898,6767,5325],{},[902,6769,5325],{"encoding":904}," jako funkce ",[883,6772,6774],{"className":6773},[886],[888,6775,6776],{"xmlns":890},[892,6777,6778,6782],{},[895,6779,6780],{},[898,6781,2470],{},[902,6783,2470],{"encoding":904},[724,6785,6786,6787,6810],{},"Pokud je poptávka zadaná ve tvaru ",[883,6788,6790],{"className":6789},[886],[888,6791,6792],{"xmlns":890},[892,6793,6794,6808],{},[895,6795,6796,6798,6800,6802,6804,6806],{},[898,6797,5325],{},[1677,6799,1679],{},[898,6801,5571],{},[1677,6803,1686],{"stretchy":1685},[898,6805,2470],{},[1677,6807,1692],{"stretchy":1685},[902,6809,6028],{"encoding":904},", využijeme vztah pro derivaci inverzní funkce",[724,6812,6813],{},[883,6814,6816],{"className":6815,"title":5588,"style":5589},[5587],"\\frac{\\mathrm{d}Q}{\\mathrm{d}P} = \\frac{1}{\\frac{\\mathrm{d}P}{\\mathrm{d}Q}}. \\tag{4.9}",[724,6818,6819,1884,6822,6848],{},[38,6820,6821],{},"Příklad 4.3.",[883,6823,6825],{"className":6824},[886],[888,6826,6827],{"xmlns":890},[892,6828,6829,6845],{},[895,6830,6831,6833,6835,6837,6839],{},[898,6832,5325],{},[1677,6834,1679],{},[1810,6836,2771],{},[1677,6838,1906],{},[1805,6840,6841,6843],{},[898,6842,2470],{},[1810,6844,1812],{},[902,6846,6847],{"encoding":904},"P = 100 - Q^2",", ptáme se na elasticitu při ceně 36. Dostáváme",[724,6850,6851],{},[883,6852,6854],{"className":6853},[886],[888,6855,6856],{"xmlns":890},[892,6857,6858,6924],{},[895,6859,6860,6862,6864,6866,6882,6884,6896,6898,6922],{},[898,6861,5640],{},[1677,6863,1679],{},[1677,6865,1906],{},[2010,6867,6868,6880],{},[895,6869,6870,6872,6874],{},[1810,6871,2771],{},[1677,6873,1906],{},[1805,6875,6876,6878],{},[898,6877,2470],{},[1810,6879,1812],{},[898,6881,2470],{},[1677,6883,2858],{},[2010,6885,6886,6888],{},[1810,6887,1959],{},[895,6889,6890,6892,6894],{},[1677,6891,1906],{},[1810,6893,1812],{},[898,6895,2470],{},[1677,6897,1679],{},[2010,6899,6900,6912],{},[895,6901,6902,6904,6906],{},[1810,6903,2771],{},[1677,6905,1906],{},[1805,6907,6908,6910],{},[898,6909,2470],{},[1810,6911,1812],{},[895,6913,6914,6916],{},[1810,6915,1812],{},[1805,6917,6918,6920],{},[898,6919,2470],{},[1810,6921,1812],{},[898,6923,1656],{"mathvariant":2057},[902,6925,6926],{"encoding":904},"E = -\\frac{100-Q^2}{Q}\\cdot \\frac{1}{-2Q} = \\frac{100-Q^2}{2Q^2}.",[724,6928,6929,6930,6957,6958,6977,6978,1656],{},"Z rovnice ",[883,6931,6933],{"className":6932},[886],[888,6934,6935],{"xmlns":890},[892,6936,6937,6954],{},[895,6938,6939,6941,6943,6949,6951],{},[1810,6940,2771],{},[1677,6942,1906],{},[1805,6944,6945,6947],{},[898,6946,2470],{},[1810,6948,1812],{},[1677,6950,1679],{},[1810,6952,6953],{},"36",[902,6955,6956],{"encoding":904},"100 - Q^2 = 36"," plyne ",[883,6959,6961],{"className":6960},[886],[888,6962,6963],{"xmlns":890},[892,6964,6965,6974],{},[895,6966,6967,6969,6971],{},[898,6968,2470],{},[1677,6970,1679],{},[1810,6972,6973],{},"8",[902,6975,6976],{"encoding":904},"Q = 8",", tedy ",[883,6979,6981],{"className":6980},[886],[888,6982,6983],{"xmlns":890},[892,6984,6985,7011],{},[895,6986,6987,6989,6991,6993,6995,6997,7006,7008],{},[898,6988,5640],{},[1677,6990,1686],{"stretchy":1685},[1810,6992,6973],{},[1677,6994,1692],{"stretchy":1685},[1677,6996,1679],{},[2006,6998,6999],{"scriptlevel":2008,"displaystyle":1685},[2010,7000,7001,7003],{},[1810,7002,6953],{},[1810,7004,7005],{},"128",[1677,7007,1679],{},[1810,7009,7010],{},"0,281",[902,7012,7013],{"encoding":904},"E(8) = \\tfrac{36}{128} = 0{,}281",[198,7015,7017],{"id":7016},"přibližné-změny","Přibližné změny",[724,7019,7020,7021,7057,7058,7080],{},"Diferenciál ",[883,7022,7024],{"className":7023},[886],[888,7025,7026],{"xmlns":890},[892,7027,7028,7054],{},[895,7029,7030,7032,7034,7036,7042,7044,7046,7048,7050,7052],{},[898,7031,1875],{"mathvariant":2057},[898,7033,2470],{},[1677,7035,1679],{},[1805,7037,7038,7040],{},[898,7039,2470],{},[1677,7041,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,7043,1686],{"stretchy":1685},[898,7045,5325],{},[1677,7047,1692],{"stretchy":1685},[1969,7049,2668],{},[898,7051,1875],{"mathvariant":2057},[898,7053,5325],{},[902,7055,7056],{"encoding":904},"\\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P"," s ",[883,7059,7061],{"className":7060},[886],[888,7062,7063],{"xmlns":890},[892,7064,7065,7077],{},[895,7066,7067,7069,7071,7073,7075],{},[898,7068,1875],{"mathvariant":2057},[898,7070,5325],{},[1677,7072,1679],{},[898,7074,2570],{"mathvariant":2057},[898,7076,5325],{},[902,7078,7079],{"encoding":904},"\\mathrm{d}P = \\Delta P"," dává nominální odhad",[724,7082,7083],{},[883,7084,7086],{"className":7085,"title":5588,"style":5589},[5587],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P. \\tag{4.10}",[724,7088,7089],{},"Po přechodu na procentní změny (vztah (4.3)):",[724,7091,7092],{},[883,7093,7095],{"className":7094,"title":5588,"style":5589},[5587],"\\boxed{\\;\\Delta Q\\% \\approx -E(P)\\,\\Delta P\\%\\;} \\tag{4.11}",[724,7097,7098,1884,7101,7136,7137,7156,7157,7191,7192,7209],{},[38,7099,7100],{},"Příklad 4.5.",[883,7102,7104],{"className":7103},[886],[888,7105,7106],{"xmlns":890},[892,7107,7108,7133],{},[895,7109,7110,7112,7114,7116,7122,7124,7126,7128,7130],{},[898,7111,5325],{},[1677,7113,1679],{},[1677,7115,1906],{},[1805,7117,7118,7120],{},[898,7119,2470],{},[1810,7121,1812],{},[1677,7123,1906],{},[1810,7125,2032],{},[898,7127,2470],{},[1677,7129,1776],{},[1810,7131,7132],{},"96",[902,7134,7135],{"encoding":904},"P = -Q^2 - 4Q + 96",", cena ",[883,7138,7140],{"className":7139},[886],[888,7141,7142],{"xmlns":890},[892,7143,7144,7153],{},[895,7145,7146,7148,7150],{},[898,7147,5325],{},[1677,7149,1679],{},[1810,7151,7152],{},"51",[902,7154,7155],{"encoding":904},"P=51",". Z rovnice ",[883,7158,7160],{"className":7159},[886],[888,7161,7162],{"xmlns":890},[892,7163,7164,7188],{},[895,7165,7166,7168,7170,7172,7178,7180,7182,7184,7186],{},[1810,7167,7152],{},[1677,7169,1679],{},[1677,7171,1906],{},[1805,7173,7174,7176],{},[898,7175,2470],{},[1810,7177,1812],{},[1677,7179,1906],{},[1810,7181,2032],{},[898,7183,2470],{},[1677,7185,1776],{},[1810,7187,7132],{},[902,7189,7190],{"encoding":904},"51 = -Q^2-4Q+96"," volíme (kladný kořen) ",[883,7193,7195],{"className":7194},[886],[888,7196,7197],{"xmlns":890},[892,7198,7199,7207],{},[895,7200,7201,7203,7205],{},[898,7202,2470],{},[1677,7204,1679],{},[1810,7206,1909],{},[902,7208,6651],{"encoding":904},". Elasticita:",[724,7211,7212],{},[883,7213,7215],{"className":7214},[886],[888,7216,7217],{"xmlns":890},[892,7218,7219,7292],{},[895,7220,7221,7223,7225,7263,7265,7269,7271,7273,7275,7277,7279,7286,7289],{},[898,7222,5640],{},[1677,7224,1679],{},[2010,7226,7227,7247],{},[895,7228,7229,7231,7237,7239,7241,7243,7245],{},[1677,7230,1906],{},[1805,7232,7233,7235],{},[898,7234,2470],{},[1810,7236,1812],{},[1677,7238,1906],{},[1810,7240,2032],{},[898,7242,2470],{},[1677,7244,1776],{},[1810,7246,7132],{},[895,7248,7249,7251,7253,7255,7257,7259,7261],{},[898,7250,2470],{},[1677,7252,1686],{"stretchy":1685},[1810,7254,1812],{},[898,7256,2470],{},[1677,7258,1776],{},[1810,7260,2032],{},[1677,7262,1692],{"stretchy":1685},[1677,7264,1967],{"separator":1966},[7266,7267],"mspace",{"width":7268},"2em",[898,7270,5640],{},[1677,7272,1686],{"stretchy":1685},[1810,7274,1909],{},[1677,7276,1692],{"stretchy":1685},[1677,7278,1679],{},[2010,7280,7281,7283],{},[1810,7282,7152],{},[1810,7284,7285],{},"70",[1677,7287,7288],{},"≐",[1810,7290,7291],{},"0,728.",[902,7293,7294],{"encoding":904},"E = \\frac{-Q^2-4Q+96}{Q(2Q+4)}, \\qquad E(5) = \\frac{51}{70} \\doteq 0{,}728.",[724,7296,7297,7298,1656],{},"Jde o neelastickou poptávku. Zvýší-li se cena o 2 %, pak ",[883,7299,7301],{"className":7300},[886],[888,7302,7303],{"xmlns":890},[892,7304,7305,7336],{},[895,7306,7307,7309,7311,7314,7316,7318,7321,7323,7325,7327,7329,7332,7334],{},[898,7308,2570],{"mathvariant":2057},[898,7310,2470],{},[898,7312,7313],{"mathvariant":2057},"%",[1677,7315,2411],{},[1677,7317,1906],{},[1810,7319,7320],{},"0,728",[1677,7322,2858],{},[1810,7324,1812],{},[1677,7326,1679],{},[1677,7328,1906],{},[1810,7330,7331],{},"1,456",[1969,7333,2668],{},[898,7335,7313],{"mathvariant":2057},[902,7337,7338],{"encoding":904},"\\Delta Q\\% \\approx -0{,}728\\cdot 2 = -1{,}456\\,\\%",[115,7340,7342],{"id":7341},"klasifikace-elasticit-poptávky","Klasifikace elasticit poptávky",[724,7344,7345,7346,7369,7370,2385],{},"V závislosti na hodnotě ",[883,7347,7349],{"className":7348},[886],[888,7350,7351],{"xmlns":890},[892,7352,7353,7367],{},[895,7354,7355,7357,7359,7365],{},[898,7356,5640],{},[1677,7358,1686],{"stretchy":1685},[1805,7360,7361,7363],{},[898,7362,5325],{},[1677,7364,5742],{},[1677,7366,1692],{"stretchy":1685},[902,7368,5770],{"encoding":904}," mluvíme o poptávce podle následující tabulky ",[883,7371,7373],{"className":7372},[886],[888,7374,7375],{"xmlns":890},[892,7376,7377,7386],{},[895,7378,7379,7381,7384],{},[1677,7380,1686],{"stretchy":1685},[1810,7382,7383],{},"4.7",[1677,7385,1692],{"stretchy":1685},[902,7387,7388],{"encoding":904},"(4.7)",[724,7390,7391],{},[2240,7392],{"alt":7393,"className":7394,"src":7395},"imek-typy-elasticity-5panelu",[210,2244],"\u002Fwiki-assets\u002Fimek-typy-elasticity-5panelu.jpeg",[16,7397,7398,7437],{},[19,7399,7400],{},[22,7401,7402,7428,7431,7434],{},[25,7403,7404,7405],{},"Hodnota ",[883,7406,7408],{"className":7407},[886],[888,7409,7410],{"xmlns":890},[892,7411,7412,7426],{},[895,7413,7414,7416,7418,7424],{},[898,7415,5640],{},[1677,7417,1686],{"stretchy":1685},[1805,7419,7420,7422],{},[898,7421,5325],{},[1677,7423,5742],{},[1677,7425,1692],{"stretchy":1685},[902,7427,5770],{"encoding":904},[25,7429,7430],{},"Typ poptávky",[25,7432,7433],{},"Termín",[25,7435,7436],{},"Význam",[30,7438,7439,7472,7534,7609,7666],{},[22,7440,7441,7461,7466,7469],{},[35,7442,7443],{},[883,7444,7446],{"className":7445},[886],[888,7447,7448],{"xmlns":890},[892,7449,7450,7458],{},[895,7451,7452,7454,7456],{},[898,7453,5640],{},[1677,7455,1679],{},[1810,7457,2008],{},[902,7459,7460],{"encoding":904},"E = 0",[35,7462,7463],{},[38,7464,7465],{},"dokonale neelastická",[35,7467,7468],{},"perfectly inelastic",[35,7470,7471],{},"množství se nemění bez ohledu na cenu",[22,7473,7474,7498,7502,7505],{},[35,7475,7476],{},[883,7477,7479],{"className":7478},[886],[888,7480,7481],{"xmlns":890},[892,7482,7483,7495],{},[895,7484,7485,7487,7489,7491,7493],{},[1810,7486,2008],{},[1677,7488,3128],{},[898,7490,5640],{},[1677,7492,3128],{},[1810,7494,1959],{},[902,7496,7497],{"encoding":904},"0 \u003C E \u003C 1",[35,7499,7500],{},[38,7501,5465],{},[35,7503,7504],{},"inelastic",[35,7506,7507,7520,7521],{},[883,7508,7510],{"className":7509},[886],[888,7511,7512],{"xmlns":890},[892,7513,7514,7518],{},[895,7515,7516],{},[898,7517,2470],{},[902,7519,2470],{"encoding":904}," se mění pomaleji než ",[883,7522,7524],{"className":7523},[886],[888,7525,7526],{"xmlns":890},[892,7527,7528,7532],{},[895,7529,7530],{},[898,7531,5325],{},[902,7533,5325],{"encoding":904},[22,7535,7536,7555,7560,7563],{},[35,7537,7538],{},[883,7539,7541],{"className":7540},[886],[888,7542,7543],{"xmlns":890},[892,7544,7545,7553],{},[895,7546,7547,7549,7551],{},[898,7548,5640],{},[1677,7550,1679],{},[1810,7552,1959],{},[902,7554,5933],{"encoding":904},[35,7556,7557],{},[38,7558,7559],{},"jednotkově elastická",[35,7561,7562],{},"unit elastic",[35,7564,7565,7578,7579,7592,7593,7608],{},[883,7566,7568],{"className":7567},[886],[888,7569,7570],{"xmlns":890},[892,7571,7572,7576],{},[895,7573,7574],{},[898,7575,2470],{},[902,7577,2470],{"encoding":904}," i ",[883,7580,7582],{"className":7581},[886],[888,7583,7584],{"xmlns":890},[892,7585,7586,7590],{},[895,7587,7588],{},[898,7589,5325],{},[902,7591,5325],{"encoding":904}," se mění stejně rychle; ",[883,7594,7596],{"className":7595},[886],[888,7597,7598],{"xmlns":890},[892,7599,7600,7606],{},[895,7601,7602,7604],{},[898,7603,2455],{},[898,7605,5382],{},[902,7607,5482],{"encoding":904}," má maximum",[22,7610,7611,7630,7634,7637],{},[35,7612,7613],{},[883,7614,7616],{"className":7615},[886],[888,7617,7618],{"xmlns":890},[892,7619,7620,7628],{},[895,7621,7622,7624,7626],{},[898,7623,5640],{},[1677,7625,3089],{},[1810,7627,1959],{},[902,7629,5897],{"encoding":904},[35,7631,7632],{},[38,7633,5461],{},[35,7635,7636],{},"elastic",[35,7638,7639,7652,7653],{},[883,7640,7642],{"className":7641},[886],[888,7643,7644],{"xmlns":890},[892,7645,7646,7650],{},[895,7647,7648],{},[898,7649,2470],{},[902,7651,2470],{"encoding":904}," se mění rychleji než ",[883,7654,7656],{"className":7655},[886],[888,7657,7658],{"xmlns":890},[892,7659,7660,7664],{},[895,7661,7662],{},[898,7663,5325],{},[902,7665,5325],{"encoding":904},[22,7667,7668,7689,7694,7697],{},[35,7669,7670],{},[883,7671,7673],{"className":7672},[886],[888,7674,7675],{"xmlns":890},[892,7676,7677,7686],{},[895,7678,7679,7681,7683],{},[898,7680,5640],{},[1677,7682,2804],{},[898,7684,7685],{"mathvariant":2057},"∞",[902,7687,7688],{"encoding":904},"E \\to \\infty",[35,7690,7691],{},[38,7692,7693],{},"dokonale elastická",[35,7695,7696],{},"perfectly elastic",[35,7698,7699,7700],{},"sebemenší změna ceny úplně mění ",[883,7701,7703],{"className":7702},[886],[888,7704,7705],{"xmlns":890},[892,7706,7707,7711],{},[895,7708,7709],{},[898,7710,2470],{},[902,7712,2470],{"encoding":904},[724,7714,7715],{},[38,7716,7717],{},"Pravidlo růstu elasticity s cenou:",[5254,7719,7720],{},[724,7721,7722,7723],{},"S rostoucí cenou elasticita poptávky roste. ",[883,7724,7726],{"className":7725},[886],[888,7727,7728],{"xmlns":890},[892,7729,7730,7739],{},[895,7731,7732,7734,7737],{},[1677,7733,1686],{"stretchy":1685},[1810,7735,7736],{},"4.8",[1677,7738,1692],{"stretchy":1685},[902,7740,7741],{"encoding":904},"(4.8)",[724,7743,7744,7745,7748,7749,7752,7753,7770],{},"Z toho plyne, že při ",[614,7746,7747],{},"dostatečně nízkých"," cenách je poptávka neelastická a při ",[614,7750,7751],{},"dostatečně vysokých"," elastická. Existuje tedy cena ",[883,7754,7756],{"className":7755},[886],[888,7757,7758],{"xmlns":890},[892,7759,7760,7768],{},[895,7761,7762],{},[1805,7763,7764,7766],{},[898,7765,5325],{},[1677,7767,5742],{},[902,7769,5792],{"encoding":904},", při které je poptávka jednotkově elastická, a ta rozděluje reálné cenové rozpětí na obě zóny.",[5254,7772,7773,7778],{},[724,7774,7775,7777],{},[883,7776,5960],{}," Postup: jak klasifikovat poptávku",[152,7779,7780,7807,7810],{},[123,7781,7782,7783,7806],{},"Spočítejte ",[883,7784,7786],{"className":7785},[886],[888,7787,7788],{"xmlns":890},[892,7789,7790,7804],{},[895,7791,7792,7794,7796,7802],{},[898,7793,5640],{},[1677,7795,1686],{"stretchy":1685},[1805,7797,7798,7800],{},[898,7799,5325],{},[1677,7801,5742],{},[1677,7803,1692],{"stretchy":1685},[902,7805,5770],{"encoding":904}," dle (4.5).",[123,7808,7809],{},"Porovnejte s jedničkou (viz tabulka výše).",[123,7811,7812,7813,7837],{},"Chcete-li najít hranici mezi elastickou a neelastickou zónou, řešte rovnici ",[883,7814,7816],{"className":7815},[886],[888,7817,7818],{"xmlns":890},[892,7819,7820,7834],{},[895,7821,7822,7824,7826,7828,7830,7832],{},[898,7823,5640],{},[1677,7825,1686],{"stretchy":1685},[898,7827,5325],{},[1677,7829,1692],{"stretchy":1685},[1677,7831,1679],{},[1810,7833,1959],{},[902,7835,7836],{"encoding":904},"E(P) = 1"," a výsledek porovnejte s reálným cenovým rozpětím.",[724,7839,7840,7843,7844,7861,7862,7880,7881,7908,7909,1656],{},[38,7841,7842],{},"Příklad 4.2."," Pro poptávku z Příkladu 4.1: ",[883,7845,7847],{"className":7846},[886],[888,7848,7849],{"xmlns":890},[892,7850,7851,7859],{},[895,7852,7853,7855,7857],{},[898,7854,5640],{},[1677,7856,1679],{},[1810,7858,1959],{},[902,7860,5933],{"encoding":904}," pro ",[883,7863,7865],{"className":7864},[886],[888,7866,7867],{"xmlns":890},[892,7868,7869,7877],{},[895,7870,7871,7873,7875],{},[898,7872,5325],{},[1677,7874,1679],{},[1810,7876,6392],{},[902,7878,7879],{"encoding":904},"P = 25",". Podle (4.8) je poptávka neelastická pro ",[883,7882,7884],{"className":7883},[886],[888,7885,7886],{"xmlns":890},[892,7887,7888,7905],{},[895,7889,7890,7892,7895,7897,7899,7901,7903],{},[898,7891,5325],{},[1677,7893,7894],{},"∈",[1677,7896,6712],{"stretchy":1685},[1810,7898,2008],{},[1677,7900,1967],{"separator":1966},[1810,7902,6392],{},[1677,7904,1692],{"stretchy":1685},[902,7906,7907],{"encoding":904},"P \\in \\langle 0, 25)"," a elastická pro ",[883,7910,7912],{"className":7911},[886],[888,7913,7914],{"xmlns":890},[892,7915,7916,7932],{},[895,7917,7918,7920,7922,7924,7926,7928,7930],{},[898,7919,5325],{},[1677,7921,7894],{},[1677,7923,1686],{"stretchy":1685},[1810,7925,6392],{},[1677,7927,1967],{"separator":1966},[1810,7929,2801],{},[1677,7931,6729],{"stretchy":1685},[902,7933,7934],{"encoding":904},"P \\in (25, 50\\rangle",[115,7936,7938],{"id":7937},"elasticita-a-celkový-příjem","Elasticita a celkový příjem",[724,7940,7941],{},[2240,7942],{"alt":7943,"className":7944,"src":7945},"imek-elasticita-tr",[210,2244],"\u002Fwiki-assets\u002Fimek-elasticita-tr.jpeg",[724,7947,7948],{},[2240,7949],{"alt":7950,"className":7951,"src":7952},"imek-elasticita-podel-linearni-poptavky",[210,2244],"\u002Fwiki-assets\u002Fimek-elasticita-podel-linearni-poptavky.jpeg",[724,7954,7955,7956,8006,8007,8023],{},"Pro celkový příjem platí ",[883,7957,7959],{"className":7958},[886],[888,7960,7961],{"xmlns":890},[892,7962,7963,8003],{},[895,7964,7965,7967,7969,7971,7973,7975,7977,7979,7981,7983,7985,7987,7989,7991,7993,7995,7997,7999,8001],{},[898,7966,2455],{},[898,7968,5382],{},[1677,7970,1679],{},[898,7972,2455],{},[898,7974,5382],{},[1677,7976,1686],{"stretchy":1685},[898,7978,2470],{},[1677,7980,1692],{"stretchy":1685},[1677,7982,1679],{},[898,7984,5325],{},[1677,7986,2858],{},[898,7988,2470],{},[1677,7990,1679],{},[898,7992,2470],{},[1677,7994,2858],{},[898,7996,5571],{},[1677,7998,1686],{"stretchy":1685},[898,8000,2470],{},[1677,8002,1692],{"stretchy":1685},[902,8004,8005],{"encoding":904},"TR = TR(Q) = P\\cdot Q = Q\\cdot D(Q)",". Pro mezní příjem ",[883,8008,8010],{"className":8009},[886],[888,8011,8012],{"xmlns":890},[892,8013,8014,8020],{},[895,8015,8016,8018],{},[898,8017,2499],{},[898,8019,5382],{},[902,8021,8022],{"encoding":904},"MR"," odvodíme:",[724,8025,8026],{},[883,8027,8029],{"className":8028},[886],[888,8030,8031],{"xmlns":890},[892,8032,8033,8141],{},[895,8034,8035,8037,8039,8041,8043,8049,8051,8053,8055,8057,8059,8061,8063,8065,8067,8069,8071,8077,8079,8081,8083,8085,8087,8089,8091,8105,8107,8109],{},[898,8036,2499],{},[898,8038,5382],{},[1677,8040,1679],{},[898,8042,2455],{},[1805,8044,8045,8047],{},[898,8046,5382],{},[1677,8048,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,8050,1686],{"stretchy":1685},[898,8052,2470],{},[1677,8054,1692],{"stretchy":1685},[1677,8056,1679],{},[898,8058,5571],{},[1677,8060,1686],{"stretchy":1685},[898,8062,2470],{},[1677,8064,1692],{"stretchy":1685},[1677,8066,1776],{},[898,8068,2470],{},[1969,8070,2668],{},[1805,8072,8073,8075],{},[898,8074,5571],{},[1677,8076,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,8078,1686],{"stretchy":1685},[898,8080,2470],{},[1677,8082,1692],{"stretchy":1685},[1677,8084,1679],{},[898,8086,5325],{},[1677,8088,1776],{},[898,8090,2470],{},[2010,8092,8093,8099],{},[895,8094,8095,8097],{},[898,8096,1875],{"mathvariant":2057},[898,8098,5325],{},[895,8100,8101,8103],{},[898,8102,1875],{"mathvariant":2057},[898,8104,2470],{},[1677,8106,1679],{},[898,8108,5325],{},[895,8110,8111,8113,8115,8117,8123,8125,8139],{},[1677,8112,1686],{"fence":1966},[1810,8114,1959],{},[1677,8116,1776],{},[2010,8118,8119,8121],{},[898,8120,2470],{},[898,8122,5325],{},[1677,8124,2858],{},[2010,8126,8127,8133],{},[895,8128,8129,8131],{},[898,8130,1875],{"mathvariant":2057},[898,8132,5325],{},[895,8134,8135,8137],{},[898,8136,1875],{"mathvariant":2057},[898,8138,2470],{},[1677,8140,1692],{"fence":1966},[902,8142,8143],{"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)",[724,8145,8146],{},[883,8147,8149],{"className":8148},[886],[888,8150,8151],{"xmlns":890},[892,8152,8153,8225],{},[895,8154,8155,8157,8159,8201,8203,8205],{},[1677,8156,1679],{},[898,8158,5325],{},[895,8160,8161,8163,8165,8167,8199],{},[1677,8162,1686],{"fence":1966},[1810,8164,1959],{},[1677,8166,1776],{},[2010,8168,8169,8171],{},[1810,8170,1959],{},[895,8172,8173,8181,8183],{},[2006,8174,8175],{"scriptlevel":2008,"displaystyle":1685},[2010,8176,8177,8179],{},[898,8178,5325],{},[898,8180,2470],{},[1677,8182,2858],{},[2006,8184,8185],{"scriptlevel":2008,"displaystyle":1685},[2010,8186,8187,8193],{},[895,8188,8189,8191],{},[898,8190,1875],{"mathvariant":2057},[898,8192,2470],{},[895,8194,8195,8197],{},[898,8196,1875],{"mathvariant":2057},[898,8198,5325],{},[1677,8200,1692],{"fence":1966},[1677,8202,1679],{},[898,8204,5325],{},[895,8206,8207,8209,8211,8213,8223],{},[1677,8208,1686],{"fence":1966},[1810,8210,1959],{},[1677,8212,1776],{},[2010,8214,8215,8217],{},[1810,8216,1959],{},[895,8218,8219,8221],{},[1677,8220,1906],{},[898,8222,5640],{},[1677,8224,1692],{"fence":1966},[902,8226,8227],{"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)",[724,8229,8230],{},"a tedy",[724,8232,8233],{},[883,8234,8236],{"className":8235,"title":5588,"style":5589},[5587],"\\boxed{\\;MR = P\\left(1 - \\frac{1}{E}\\right) = D(Q)\\left(1 - \\frac{1}{E}\\right)\\;} \\tag{4.12}",[5254,8238,8239,8308,8558],{},[724,8240,8241,8243,8244,8278,8279,8294,8295,2385],{},[883,8242,5543],{}," Intuice: vztah ",[883,8245,8247],{"className":8246},[886],[888,8248,8249],{"xmlns":890},[892,8250,8251,8275],{},[895,8252,8253,8255,8257,8259,8261,8263,8265,8267,8269,8271,8273],{},[898,8254,2499],{},[898,8256,5382],{},[1677,8258,1679],{},[898,8260,5325],{},[1677,8262,1686],{"stretchy":1685},[1810,8264,1959],{},[1677,8266,1906],{},[1810,8268,1959],{},[898,8270,6062],{"mathvariant":2057},[898,8272,5640],{},[1677,8274,1692],{"stretchy":1685},[902,8276,8277],{"encoding":904},"MR = P(1 - 1\u002FE)","\nVztah (4.12) je „most\" mezi elasticitou a mezním příjmem — znaménko ",[883,8280,8282],{"className":8281},[886],[888,8283,8284],{"xmlns":890},[892,8285,8286,8292],{},[895,8287,8288,8290],{},[898,8289,2499],{},[898,8291,5382],{},[902,8293,8022],{"encoding":904}," jednoznačně určuje hodnota ",[883,8296,8298],{"className":8297},[886],[888,8299,8300],{"xmlns":890},[892,8301,8302,8306],{},[895,8303,8304],{},[898,8305,5640],{},[902,8307,5640],{"encoding":904},[120,8309,8310,8420,8489],{},[123,8311,8312,8329,8330,1884,8344,1884,8370,1884,8383,8403,8404,8419],{},[883,8313,8315],{"className":8314},[886],[888,8316,8317],{"xmlns":890},[892,8318,8319,8327],{},[895,8320,8321,8323,8325],{},[898,8322,5640],{},[1677,8324,3089],{},[1810,8326,1959],{},[902,8328,5897],{"encoding":904}," (elastická) ",[883,8331,8333],{"className":8332},[886],[888,8334,8335],{"xmlns":890},[892,8336,8337,8341],{},[895,8338,8339],{},[1677,8340,5375],{},[902,8342,8343],{"encoding":904},"\\Rightarrow",[883,8345,8347],{"className":8346},[886],[888,8348,8349],{"xmlns":890},[892,8350,8351,8367],{},[895,8352,8353,8355,8357,8359,8361,8363,8365],{},[1810,8354,1959],{},[1677,8356,1906],{},[1810,8358,1959],{},[898,8360,6062],{"mathvariant":2057},[898,8362,5640],{},[1677,8364,3089],{},[1810,8366,2008],{},[902,8368,8369],{"encoding":904},"1 - 1\u002FE > 0",[883,8371,8373],{"className":8372},[886],[888,8374,8375],{"xmlns":890},[892,8376,8377,8381],{},[895,8378,8379],{},[1677,8380,5375],{},[902,8382,8343],{"encoding":904},[883,8384,8386],{"className":8385},[886],[888,8387,8388],{"xmlns":890},[892,8389,8390,8400],{},[895,8391,8392,8394,8396,8398],{},[898,8393,2499],{},[898,8395,5382],{},[1677,8397,3089],{},[1810,8399,2008],{},[902,8401,8402],{"encoding":904},"MR > 0"," — ",[883,8405,8407],{"className":8406},[886],[888,8408,8409],{"xmlns":890},[892,8410,8411,8417],{},[895,8412,8413,8415],{},[898,8414,2455],{},[898,8416,5382],{},[902,8418,5482],{"encoding":904}," roste s množstvím, tj. klesá s cenou.",[123,8421,8422,8439,8440,1884,8453,8403,8473,8488],{},[883,8423,8425],{"className":8424},[886],[888,8426,8427],{"xmlns":890},[892,8428,8429,8437],{},[895,8430,8431,8433,8435],{},[898,8432,5640],{},[1677,8434,1679],{},[1810,8436,1959],{},[902,8438,5933],{"encoding":904}," (jednotková) ",[883,8441,8443],{"className":8442},[886],[888,8444,8445],{"xmlns":890},[892,8446,8447,8451],{},[895,8448,8449],{},[1677,8450,5375],{},[902,8452,8343],{"encoding":904},[883,8454,8456],{"className":8455},[886],[888,8457,8458],{"xmlns":890},[892,8459,8460,8470],{},[895,8461,8462,8464,8466,8468],{},[898,8463,2499],{},[898,8465,5382],{},[1677,8467,1679],{},[1810,8469,2008],{},[902,8471,8472],{"encoding":904},"MR = 0",[883,8474,8476],{"className":8475},[886],[888,8477,8478],{"xmlns":890},[892,8479,8480,8486],{},[895,8481,8482,8484],{},[898,8483,2455],{},[898,8485,5382],{},[902,8487,5482],{"encoding":904}," je extrém (maximum).",[123,8490,8491,8508,8509,1884,8522,8403,8542,8557],{},[883,8492,8494],{"className":8493},[886],[888,8495,8496],{"xmlns":890},[892,8497,8498,8506],{},[895,8499,8500,8502,8504],{},[898,8501,5640],{},[1677,8503,3128],{},[1810,8505,1959],{},[902,8507,5915],{"encoding":904}," (neelastická) ",[883,8510,8512],{"className":8511},[886],[888,8513,8514],{"xmlns":890},[892,8515,8516,8520],{},[895,8517,8518],{},[1677,8519,5375],{},[902,8521,8343],{"encoding":904},[883,8523,8525],{"className":8524},[886],[888,8526,8527],{"xmlns":890},[892,8528,8529,8539],{},[895,8530,8531,8533,8535,8537],{},[898,8532,2499],{},[898,8534,5382],{},[1677,8536,3128],{},[1810,8538,2008],{},[902,8540,8541],{"encoding":904},"MR \u003C 0",[883,8543,8545],{"className":8544},[886],[888,8546,8547],{"xmlns":890},[892,8548,8549,8555],{},[895,8550,8551,8553],{},[898,8552,2455],{},[898,8554,5382],{},[902,8556,5482],{"encoding":904}," klesá s množstvím, tj. roste s cenou.",[724,8559,8560,8561,1656],{},"Viz také ",[207,8562,3504],{"className":8563,"dataFsResolvedFilePath":827,"href":828},[210],[198,8565,8567],{"id":8566},"pravidla-13-odvození-z-412","Pravidla 1–3 (odvození z (4.12))",[724,8569,8570,8590,8591,8617,8618,8633,8634,8647,8648,8661,8662,8675,8676,8692,8693,1884,8708,8711,8712,8692,8728,1656],{},[38,8571,8572,8573,5306],{},"(a) Poptávka elastická (",[883,8574,8576],{"className":8575},[886],[888,8577,8578],{"xmlns":890},[892,8579,8580,8588],{},[895,8581,8582,8584,8586],{},[898,8583,5640],{},[1677,8585,3089],{},[1810,8587,1959],{},[902,8589,5897],{"encoding":904}," Z (4.12) plyne ",[883,8592,8594],{"className":8593},[886],[888,8595,8596],{"xmlns":890},[892,8597,8598,8614],{},[895,8599,8600,8602,8604,8606,8608,8610,8612],{},[898,8601,2499],{},[898,8603,5382],{},[1677,8605,1686],{"stretchy":1685},[898,8607,2470],{},[1677,8609,1692],{"stretchy":1685},[1677,8611,3089],{},[1810,8613,2008],{},[902,8615,8616],{"encoding":904},"MR(Q) > 0",", a tedy celkový příjem ",[883,8619,8621],{"className":8620},[886],[888,8622,8623],{"xmlns":890},[892,8624,8625,8631],{},[895,8626,8627,8629],{},[898,8628,2455],{},[898,8630,5382],{},[902,8632,5482],{"encoding":904}," je rostoucí funkcí ",[883,8635,8637],{"className":8636},[886],[888,8638,8639],{"xmlns":890},[892,8640,8641,8645],{},[895,8642,8643],{},[898,8644,2470],{},[902,8646,2470],{"encoding":904},". Avšak růst ",[883,8649,8651],{"className":8650},[886],[888,8652,8653],{"xmlns":890},[892,8654,8655,8659],{},[895,8656,8657],{},[898,8658,2470],{},[902,8660,2470],{"encoding":904}," je odezvou na pokles ceny ",[883,8663,8665],{"className":8664},[886],[888,8666,8667],{"xmlns":890},[892,8668,8669,8673],{},[895,8670,8671],{},[898,8672,5325],{},[902,8674,5325],{"encoding":904},". Tudíž s ",[614,8677,8678,8679],{},"poklesem ceny ",[883,8680,8682],{"className":8681},[886],[888,8683,8684],{"xmlns":890},[892,8685,8686,8690],{},[895,8687,8688],{},[898,8689,5325],{},[902,8691,5325],{"encoding":904}," celkový příjem ",[883,8694,8696],{"className":8695},[886],[888,8697,8698],{"xmlns":890},[892,8699,8700,8706],{},[895,8701,8702,8704],{},[898,8703,2455],{},[898,8705,5382],{},[902,8707,5482],{"encoding":904},[614,8709,8710],{},"roste"," a s ",[614,8713,8714,8715],{},"růstem ceny ",[883,8716,8718],{"className":8717},[886],[888,8719,8720],{"xmlns":890},[892,8721,8722,8726],{},[895,8723,8724],{},[898,8725,5325],{},[902,8727,5325],{"encoding":904},[614,8729,8730],{},"klesá",[5254,8732,8733],{},[724,8734,8735,8738],{},[38,8736,8737],{},"Pravidlo 1."," Je-li poptávka elastická, pak s poklesem ceny celkový příjem roste a s růstem ceny celkový příjem klesá.",[724,8740,8741,8590,8761,1343,8787,8802,8803,8816,8817,8830,8831,8844,8845,8692,8858,1884,8873,1656],{},[38,8742,8743,8744,5306],{},"(b) Poptávka neelastická (",[883,8745,8747],{"className":8746},[886],[888,8748,8749],{"xmlns":890},[892,8750,8751,8759],{},[895,8752,8753,8755,8757],{},[898,8754,5640],{},[1677,8756,3128],{},[1810,8758,1959],{},[902,8760,5915],{"encoding":904},[883,8762,8764],{"className":8763},[886],[888,8765,8766],{"xmlns":890},[892,8767,8768,8784],{},[895,8769,8770,8772,8774,8776,8778,8780,8782],{},[898,8771,2499],{},[898,8773,5382],{},[1677,8775,1686],{"stretchy":1685},[898,8777,2470],{},[1677,8779,1692],{"stretchy":1685},[1677,8781,3128],{},[1810,8783,2008],{},[902,8785,8786],{"encoding":904},"MR(Q) \u003C 0",[883,8788,8790],{"className":8789},[886],[888,8791,8792],{"xmlns":890},[892,8793,8794,8800],{},[895,8795,8796,8798],{},[898,8797,2455],{},[898,8799,5382],{},[902,8801,5482],{"encoding":904}," je klesající funkce ",[883,8804,8806],{"className":8805},[886],[888,8807,8808],{"xmlns":890},[892,8809,8810,8814],{},[895,8811,8812],{},[898,8813,2470],{},[902,8815,2470],{"encoding":904},", tj. s růstem ",[883,8818,8820],{"className":8819},[886],[888,8821,8822],{"xmlns":890},[892,8823,8824,8828],{},[895,8825,8826],{},[898,8827,2470],{},[902,8829,2470],{"encoding":904}," (s poklesem ceny ",[883,8832,8834],{"className":8833},[886],[888,8835,8836],{"xmlns":890},[892,8837,8838,8842],{},[895,8839,8840],{},[898,8841,5325],{},[902,8843,5325],{"encoding":904},") celkový příjem klesá. S růstem ceny ",[883,8846,8848],{"className":8847},[886],[888,8849,8850],{"xmlns":890},[892,8851,8852,8856],{},[895,8853,8854],{},[898,8855,5325],{},[902,8857,5325],{"encoding":904},[883,8859,8861],{"className":8860},[886],[888,8862,8863],{"xmlns":890},[892,8864,8865,8871],{},[895,8866,8867,8869],{},[898,8868,2455],{},[898,8870,5382],{},[902,8872,5482],{"encoding":904},[614,8874,8710],{},[5254,8876,8877],{},[724,8878,8879,8882],{},[38,8880,8881],{},"Pravidlo 2."," Je-li poptávka neelastická, pak s poklesem ceny celkový příjem klesá a s růstem ceny celkový příjem roste.",[724,8884,8885,8590,8905,8924,8925,8940,8941,9011,9012,5272,9040,9073,9074,6977,9102,9117,9118,1656],{},[38,8886,8887,8888,5306],{},"(c) Jednotková elasticita (",[883,8889,8891],{"className":8890},[886],[888,8892,8893],{"xmlns":890},[892,8894,8895,8903],{},[895,8896,8897,8899,8901],{},[898,8898,5640],{},[1677,8900,1679],{},[1810,8902,1959],{},[902,8904,5933],{"encoding":904},[883,8906,8908],{"className":8907},[886],[888,8909,8910],{"xmlns":890},[892,8911,8912,8922],{},[895,8913,8914,8916,8918,8920],{},[898,8915,2499],{},[898,8917,5382],{},[1677,8919,1679],{},[1810,8921,2008],{},[902,8923,8472],{"encoding":904}," — nutná podmínka extrému ",[883,8926,8928],{"className":8927},[886],[888,8929,8930],{"xmlns":890},[892,8931,8932,8938],{},[895,8933,8934,8936],{},[898,8935,2455],{},[898,8937,5382],{},[902,8939,5482],{"encoding":904},". Dále ",[883,8942,8944],{"className":8943},[886],[888,8945,8946],{"xmlns":890},[892,8947,8948,9008],{},[895,8949,8950,8952,8962,8964,8966,8972,8974,8980,8982,8984,8986,8988,8990,8992,9002,9004,9006],{},[898,8951,2455],{},[1805,8953,8954,8956],{},[898,8955,5382],{},[895,8957,8958,8960],{},[1677,8959,2059],{"mathvariant":2057},[1677,8961,2059],{"mathvariant":2057},[1677,8963,1679],{},[898,8965,2499],{},[1805,8967,8968,8970],{},[898,8969,5382],{},[1677,8971,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,8973,1679],{},[1805,8975,8976,8978],{},[898,8977,5571],{},[1677,8979,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,8981,1686],{"stretchy":1685},[898,8983,2470],{},[1677,8985,1692],{"stretchy":1685},[1677,8987,1776],{},[898,8989,2470],{},[1969,8991,2668],{},[1805,8993,8994,8996],{},[898,8995,5571],{},[895,8997,8998,9000],{},[1677,8999,2059],{"mathvariant":2057},[1677,9001,2059],{"mathvariant":2057},[1677,9003,1686],{"stretchy":1685},[898,9005,2470],{},[1677,9007,1692],{"stretchy":1685},[902,9009,9010],{"encoding":904},"TR'' = MR' = D'(Q) + Q\\,D''(Q)","; za normálních podmínek ",[883,9013,9015],{"className":9014},[886],[888,9016,9017],{"xmlns":890},[892,9018,9019,9037],{},[895,9020,9021,9027,9029,9031,9033,9035],{},[1805,9022,9023,9025],{},[898,9024,5571],{},[1677,9026,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,9028,1686],{"stretchy":1685},[898,9030,2470],{},[1677,9032,1692],{"stretchy":1685},[1677,9034,3128],{},[1810,9036,2008],{},[902,9038,9039],{"encoding":904},"D'(Q) \u003C 0",[883,9041,9043],{"className":9042},[886],[888,9044,9045],{"xmlns":890},[892,9046,9047,9070],{},[895,9048,9049,9059,9061,9063,9065,9068],{},[1805,9050,9051,9053],{},[898,9052,5571],{},[895,9054,9055,9057],{},[1677,9056,2059],{"mathvariant":2057},[1677,9058,2059],{"mathvariant":2057},[1677,9060,1686],{"stretchy":1685},[898,9062,2470],{},[1677,9064,1692],{"stretchy":1685},[1677,9066,9067],{},"≤",[1810,9069,2008],{},[902,9071,9072],{"encoding":904},"D''(Q) \\le 0",", odkud ",[883,9075,9077],{"className":9076},[886],[888,9078,9079],{"xmlns":890},[892,9080,9081,9099],{},[895,9082,9083,9085,9095,9097],{},[898,9084,2455],{},[1805,9086,9087,9089],{},[898,9088,5382],{},[895,9090,9091,9093],{},[1677,9092,2059],{"mathvariant":2057},[1677,9094,2059],{"mathvariant":2057},[1677,9096,3128],{},[1810,9098,2008],{},[902,9100,9101],{"encoding":904},"TR'' \u003C 0",[883,9103,9105],{"className":9104},[886],[888,9106,9107],{"xmlns":890},[892,9108,9109,9115],{},[895,9110,9111,9113],{},[898,9112,2455],{},[898,9114,5382],{},[902,9116,5482],{"encoding":904}," nabývá ",[38,9119,9120],{},"maxima",[5254,9122,9123],{},[724,9124,9125,9128],{},[38,9126,9127],{},"Pravidlo 3."," Celkový příjem nabývá maxima při ceně, pro kterou je poptávka jednotkově elastická.",[724,9130,9131],{},"Tato tři pravidla potvrzují hypotézu (4.1) a jsou klíčem k regulaci ceny za účelem zvýšení (maximalizace) celkového příjmu.",[724,9133,9134],{},[38,9135,9136],{},"Souhrnná tabulka Pravidel 1–3:",[16,9138,9139,9243],{},[19,9140,9141],{},[22,9142,9143,9146,9161,9178,9209,9240],{},[25,9144,9145],{},"Charakter poptávky",[25,9147,9148],{},[883,9149,9151],{"className":9150},[886],[888,9152,9153],{"xmlns":890},[892,9154,9155,9159],{},[895,9156,9157],{},[898,9158,5640],{},[902,9160,5640],{"encoding":904},[25,9162,9163],{},[883,9164,9166],{"className":9165},[886],[888,9167,9168],{"xmlns":890},[892,9169,9170,9176],{},[895,9171,9172,9174],{},[898,9173,2499],{},[898,9175,5382],{},[902,9177,8022],{"encoding":904},[25,9179,9180,9181,1884,9194],{},"Pokles ceny ",[883,9182,9184],{"className":9183},[886],[888,9185,9186],{"xmlns":890},[892,9187,9188,9192],{},[895,9189,9190],{},[1677,9191,5375],{},[902,9193,8343],{"encoding":904},[883,9195,9197],{"className":9196},[886],[888,9198,9199],{"xmlns":890},[892,9200,9201,9207],{},[895,9202,9203,9205],{},[898,9204,2455],{},[898,9206,5382],{},[902,9208,5482],{"encoding":904},[25,9210,9211,9212,1884,9225],{},"Růst ceny ",[883,9213,9215],{"className":9214},[886],[888,9216,9217],{"xmlns":890},[892,9218,9219,9223],{},[895,9220,9221],{},[1677,9222,5375],{},[902,9224,8343],{"encoding":904},[883,9226,9228],{"className":9227},[886],[888,9229,9230],{"xmlns":890},[892,9231,9232,9238],{},[895,9233,9234,9236],{},[898,9235,2455],{},[898,9237,5382],{},[902,9239,5482],{"encoding":904},[25,9241,9242],{},"Doporučení",[30,9244,9245,9294,9344],{},[22,9246,9247,9249,9267,9285,9287,9289],{},[35,9248,5461],{},[35,9250,9251],{},[883,9252,9254],{"className":9253},[886],[888,9255,9256],{"xmlns":890},[892,9257,9258,9264],{},[895,9259,9260,9262],{},[1677,9261,3089],{},[1810,9263,1959],{},[902,9265,9266],{"encoding":904},"> 1",[35,9268,9269],{},[883,9270,9272],{"className":9271},[886],[888,9273,9274],{"xmlns":890},[892,9275,9276,9282],{},[895,9277,9278,9280],{},[1677,9279,3089],{},[1810,9281,2008],{},[902,9283,9284],{"encoding":904},"> 0",[35,9286,8710],{},[35,9288,8730],{},[35,9290,9291],{},[38,9292,9293],{},"snížit cenu",[22,9295,9296,9299,9317,9335,9337,9339],{},[35,9297,9298],{},"jednotková",[35,9300,9301],{},[883,9302,9304],{"className":9303},[886],[888,9305,9306],{"xmlns":890},[892,9307,9308,9314],{},[895,9309,9310,9312],{},[1677,9311,1679],{},[1810,9313,1959],{},[902,9315,9316],{"encoding":904},"= 1",[35,9318,9319],{},[883,9320,9322],{"className":9321},[886],[888,9323,9324],{"xmlns":890},[892,9325,9326,9332],{},[895,9327,9328,9330],{},[1677,9329,1679],{},[1810,9331,2008],{},[902,9333,9334],{"encoding":904},"= 0",[35,9336,3398],{},[35,9338,3398],{},[35,9340,9341],{},[38,9342,9343],{},"držet cenu",[22,9345,9346,9348,9366,9384,9386,9388],{},[35,9347,5465],{},[35,9349,9350],{},[883,9351,9353],{"className":9352},[886],[888,9354,9355],{"xmlns":890},[892,9356,9357,9363],{},[895,9358,9359,9361],{},[1677,9360,3128],{},[1810,9362,1959],{},[902,9364,9365],{"encoding":904},"\u003C 1",[35,9367,9368],{},[883,9369,9371],{"className":9370},[886],[888,9372,9373],{"xmlns":890},[892,9374,9375,9381],{},[895,9376,9377,9379],{},[1677,9378,3128],{},[1810,9380,2008],{},[902,9382,9383],{"encoding":904},"\u003C 0",[35,9385,8730],{},[35,9387,8710],{},[35,9389,9390],{},[38,9391,9392],{},"zvýšit cenu",[198,9394,9396],{"id":9395},"příklad-46-aplikace-pravidel-13","Příklad 4.6 — aplikace Pravidel 1–3",[724,9398,9399,9400,9425,9426,9448,9449,9462,9463,9476,9477,9490,9491,6977,9518,9570],{},"Aplikujme pravidla 1–3 pro poptávku ",[883,9401,9403],{"className":9402},[886],[888,9404,9405],{"xmlns":890},[892,9406,9407,9423],{},[895,9408,9409,9411,9413,9415,9417],{},[898,9410,5325],{},[1677,9412,1679],{},[1810,9414,2771],{},[1677,9416,1906],{},[1805,9418,9419,9421],{},[898,9420,2470],{},[1810,9422,1812],{},[902,9424,6847],{"encoding":904},". Reálné cenové rozpětí je ",[883,9427,9429],{"className":9428},[886],[888,9430,9431],{"xmlns":890},[892,9432,9433,9445],{},[895,9434,9435,9437,9439,9441,9443],{},[1677,9436,6712],{"stretchy":1685},[1810,9438,1959],{},[1677,9440,1967],{"separator":1966},[1810,9442,2771],{},[1677,9444,6729],{"stretchy":1685},[902,9446,9447],{"encoding":904},"\\langle 1, 100\\rangle",". Pro výpočet elasticity vyjádříme ",[883,9450,9452],{"className":9451},[886],[888,9453,9454],{"xmlns":890},[892,9455,9456,9460],{},[895,9457,9458],{},[898,9459,2470],{},[902,9461,2470],{"encoding":904}," jako funkci ",[883,9464,9466],{"className":9465},[886],[888,9467,9468],{"xmlns":890},[892,9469,9470,9474],{},[895,9471,9472],{},[898,9473,5325],{},[902,9475,5325],{"encoding":904},"; pro nezáporné ",[883,9478,9480],{"className":9479},[886],[888,9481,9482],{"xmlns":890},[892,9483,9484,9488],{},[895,9485,9486],{},[898,9487,2470],{},[902,9489,2470],{"encoding":904}," je ",[883,9492,9494],{"className":9493},[886],[888,9495,9496],{"xmlns":890},[892,9497,9498,9515],{},[895,9499,9500,9502,9504],{},[898,9501,2470],{},[1677,9503,1679],{},[9505,9506,9507],"msqrt",{},[895,9508,9509,9511,9513],{},[1810,9510,2771],{},[1677,9512,1906],{},[898,9514,5325],{},[902,9516,9517],{"encoding":904},"Q = \\sqrt{100 - P}",[883,9519,9521],{"className":9520},[886],[888,9522,9523],{"xmlns":890},[892,9524,9525,9567],{},[895,9526,9527,9543,9545,9547],{},[2006,9528,9529],{"scriptlevel":2008,"displaystyle":1966},[2010,9530,9531,9537],{},[895,9532,9533,9535],{},[898,9534,1875],{"mathvariant":2057},[898,9536,2470],{},[895,9538,9539,9541],{},[898,9540,1875],{"mathvariant":2057},[898,9542,5325],{},[1677,9544,1679],{},[1677,9546,1906],{},[2006,9548,9549],{"scriptlevel":2008,"displaystyle":1966},[2010,9550,9551,9553],{},[1810,9552,1959],{},[895,9554,9555,9557],{},[1810,9556,1812],{},[9505,9558,9559],{},[895,9560,9561,9563,9565],{},[1810,9562,2771],{},[1677,9564,1906],{},[898,9566,5325],{},[902,9568,9569],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\dfrac{1}{2\\sqrt{100-P}}",". Podle (4.5):",[724,9572,9573],{},[883,9574,9576],{"className":9575},[886],[888,9577,9578],{"xmlns":890},[892,9579,9580,9702],{},[895,9581,9582,9584,9586,9588,9590,9592,9594,9600,9602,9616,9618,9620,9634,9636,9662,9664,9682,9684,9700],{},[898,9583,5640],{},[1677,9585,1686],{"stretchy":1685},[898,9587,5325],{},[1677,9589,1692],{"stretchy":1685},[1677,9591,1679],{},[1677,9593,1906],{},[2010,9595,9596,9598],{},[898,9597,5325],{},[898,9599,2470],{},[1677,9601,2858],{},[2010,9603,9604,9610],{},[895,9605,9606,9608],{},[898,9607,1875],{"mathvariant":2057},[898,9609,2470],{},[895,9611,9612,9614],{},[898,9613,1875],{"mathvariant":2057},[898,9615,5325],{},[1677,9617,1679],{},[1677,9619,1906],{},[2010,9621,9622,9624],{},[898,9623,5325],{},[9505,9625,9626],{},[895,9627,9628,9630,9632],{},[1810,9629,2771],{},[1677,9631,1906],{},[898,9633,5325],{},[1677,9635,2858],{},[895,9637,9638,9640,9642,9660],{},[1677,9639,1686],{"fence":1966},[1677,9641,1906],{},[2010,9643,9644,9646],{},[1810,9645,1959],{},[895,9647,9648,9650],{},[1810,9649,1812],{},[9505,9651,9652],{},[895,9653,9654,9656,9658],{},[1810,9655,2771],{},[1677,9657,1906],{},[898,9659,5325],{},[1677,9661,1692],{"fence":1966},[1677,9663,1679],{},[2010,9665,9666,9668],{},[898,9667,5325],{},[895,9669,9670,9672,9674,9676,9678,9680],{},[1810,9671,1812],{},[1677,9673,1686],{"stretchy":1685},[1810,9675,2771],{},[1677,9677,1906],{},[898,9679,5325],{},[1677,9681,1692],{"stretchy":1685},[1677,9683,1679],{},[2010,9685,9686,9692],{},[895,9687,9688,9690],{},[1810,9689,6397],{},[898,9691,5325],{},[895,9693,9694,9696,9698],{},[1810,9695,2771],{},[1677,9697,1906],{},[898,9699,5325],{},[898,9701,1656],{"mathvariant":2057},[902,9703,9704],{"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}.",[724,9706,9707,9708,2385],{},"Stanovíme cenu, při které je poptávka jednotkově elastická. Řešíme ",[883,9709,9711],{"className":9710},[886],[888,9712,9713],{"xmlns":890},[892,9714,9715,9739],{},[895,9716,9717,9735,9737],{},[2006,9718,9719],{"scriptlevel":2008,"displaystyle":1966},[2010,9720,9721,9727],{},[895,9722,9723,9725],{},[1810,9724,6397],{},[898,9726,5325],{},[895,9728,9729,9731,9733],{},[1810,9730,2771],{},[1677,9732,1906],{},[898,9734,5325],{},[1677,9736,1679],{},[1810,9738,1959],{},[902,9740,9741],{"encoding":904},"\\dfrac{0{,}5P}{100-P} = 1",[724,9743,9744],{},[883,9745,9747],{"className":9746},[886],[888,9748,9749],{"xmlns":890},[892,9750,9751,9783],{},[895,9752,9753,9759,9761,9768,9770,9773,9781],{},[1805,9754,9755,9757],{},[898,9756,5325],{},[1677,9758,5742],{},[1677,9760,1679],{},[2010,9762,9763,9766],{},[1810,9764,9765],{},"200",[1810,9767,1854],{},[1677,9769,7288],{},[1810,9771,9772],{},"66,",[9774,9775,9776,9778],"mover",{"accent":1966},[1810,9777,1916],{},[1677,9779,9780],{"stretchy":1966},"‾",[898,9782,1656],{"mathvariant":2057},[902,9784,9785],{"encoding":904},"P^* = \\frac{200}{3} \\doteq 66{,}\\overline{6}.",[724,9787,9788],{},"S využitím vlastnosti (4.8):",[120,9790,9791,9837,9879],{},[123,9792,9793,9794,9829,9830,9832,9833,9836],{},"Při cenách ",[883,9795,9797],{"className":9796},[886],[888,9798,9799],{"xmlns":890},[892,9800,9801,9826],{},[895,9802,9803,9805,9807,9809,9811,9814,9816,9818,9824],{},[898,9804,5325],{},[1677,9806,7894],{},[1677,9808,6712],{"stretchy":1685},[1810,9810,1959],{},[1677,9812,9813],{"separator":1966},";",[1969,9815,2668],{},[1810,9817,9772],{},[9774,9819,9820,9822],{"accent":1966},[1810,9821,1916],{},[1677,9823,9780],{"stretchy":1966},[1677,9825,1692],{"stretchy":1685},[902,9827,9828],{"encoding":904},"P \\in \\langle 1;\\, 66{,}\\overline{6})"," je poptávka ",[38,9831,5465],{}," — dle ",[614,9834,9835],{},"Pravidla 2"," přiměřené zvýšení ceny zvýší celkový příjem.",[123,9838,9793,9839,9829,9873,9832,9875,9878],{},[883,9840,9842],{"className":9841},[886],[888,9843,9844],{"xmlns":890},[892,9845,9846,9870],{},[895,9847,9848,9850,9852,9854,9856,9862,9864,9866,9868],{},[898,9849,5325],{},[1677,9851,7894],{},[1677,9853,1686],{"stretchy":1685},[1810,9855,9772],{},[9774,9857,9858,9860],{"accent":1966},[1810,9859,1916],{},[1677,9861,9780],{"stretchy":1966},[1677,9863,9813],{"separator":1966},[1969,9865,2668],{},[1810,9867,2771],{},[1677,9869,6729],{"stretchy":1685},[902,9871,9872],{"encoding":904},"P \\in (66{,}\\overline{6};\\, 100\\rangle",[38,9874,5461],{},[614,9876,9877],{},"Pravidla 1"," přiměřené snížení ceny povede ke zvýšení celkového příjmu.",[123,9880,9881,9882,9885,9886,9914,9915,9918],{},"Dle ",[614,9883,9884],{},"Pravidla 3"," je při ceně ",[883,9887,9889],{"className":9888},[886],[888,9890,9891],{"xmlns":890},[892,9892,9893,9911],{},[895,9894,9895,9901,9903,9905],{},[1805,9896,9897,9899],{},[898,9898,5325],{},[1677,9900,5742],{},[1677,9902,1679],{},[1810,9904,9772],{},[9774,9906,9907,9909],{"accent":1966},[1810,9908,1916],{},[1677,9910,9780],{"stretchy":1966},[902,9912,9913],{"encoding":904},"P^* = 66{,}\\overline{6}"," dosaženo ",[38,9916,9917],{},"maxima celkového příjmu"," ve výši",[724,9920,9921],{},[883,9922,9924],{"className":9923},[886],[888,9925,9926],{"xmlns":890},[892,9927,9928,10006],{},[895,9929,9930,9932,9934,9936,9942,9944,9946,9952,9954,9968,9970,9976,9978,9986,9988,10001,10003],{},[898,9931,2455],{},[898,9933,5382],{},[1677,9935,1686],{"stretchy":1685},[1805,9937,9938,9940],{},[898,9939,5325],{},[1677,9941,5742],{},[1677,9943,1692],{"stretchy":1685},[1677,9945,1679],{},[1805,9947,9948,9950],{},[898,9949,5325],{},[1677,9951,5742],{},[1677,9953,2858],{},[9505,9955,9956],{},[895,9957,9958,9960,9962],{},[1810,9959,2771],{},[1677,9961,1906],{},[1805,9963,9964,9966],{},[898,9965,5325],{},[1677,9967,5742],{},[1677,9969,1679],{},[2010,9971,9972,9974],{},[1810,9973,9765],{},[1810,9975,1854],{},[1677,9977,2858],{},[9505,9979,9980],{},[2010,9981,9982,9984],{},[1810,9983,2771],{},[1810,9985,1854],{},[1677,9987,1679],{},[2010,9989,9990,9993],{},[1810,9991,9992],{},"2000",[895,9994,9995,9997],{},[1810,9996,1854],{},[9505,9998,9999],{},[1810,10000,1854],{},[1677,10002,7288],{},[1810,10004,10005],{},"384,9.",[902,10007,10008],{"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.",[724,10010,10011,10012,1656],{},"Ke stejnému výsledku bychom dospěli přímým hledáním maxima funkce ",[883,10013,10015],{"className":10014},[886],[888,10016,10017],{"xmlns":890},[892,10018,10019,10025],{},[895,10020,10021,10023],{},[898,10022,2455],{},[898,10024,5382],{},[902,10026,5482],{"encoding":904},[115,10028,10030],{"id":10029},"cenová-elasticita-nabídky","Cenová elasticita nabídky",[724,10032,10033,10034,10037],{},"Analogicky se definuje ",[38,10035,10036],{},"cenová elasticita nabídky"," (price elasticity of supply):",[724,10039,10040],{},[883,10041,10043],{"className":10042,"title":5588,"style":5589},[5587],"\\boxed{\\;E = E(P) = \\frac{P}{Q}\\cdot\\frac{\\mathrm{d}Q}{\\mathrm{d}P}\\;} \\tag{4.13}",[724,10045,5698,10046,10071,10072,10104],{},[883,10047,10049],{"className":10048},[886],[888,10050,10051],{"xmlns":890},[892,10052,10053,10068],{},[895,10054,10055,10057,10059,10062,10064,10066],{},[898,10056,2470],{},[1677,10058,1679],{},[898,10060,10061],{},"S",[1677,10063,1686],{"stretchy":1685},[898,10065,5325],{},[1677,10067,1692],{"stretchy":1685},[902,10069,10070],{"encoding":904},"Q = S(P)"," je funkce nabídky. Protože nabídka je rostoucí, ",[883,10073,10075],{"className":10074},[886],[888,10076,10077],{"xmlns":890},[892,10078,10079,10101],{},[895,10080,10081,10097,10099],{},[2006,10082,10083],{"scriptlevel":2008,"displaystyle":1966},[2010,10084,10085,10091],{},[895,10086,10087,10089],{},[898,10088,1875],{"mathvariant":2057},[898,10090,2470],{},[895,10092,10093,10095],{},[898,10094,1875],{"mathvariant":2057},[898,10096,5325],{},[1677,10098,3089],{},[1810,10100,2008],{},[902,10102,10103],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} > 0",", a elasticita nabídky je vždy nezáporná — proto zde není znaménková korekce jako u poptávky.",[724,10106,10107],{},"Klasifikace na elastickou \u002F jednotkově elastickou \u002F neelastickou je analogická jako u poptávky (tabulka (4.7)). Platí paralela k (4.8):",[5254,10109,10110],{},[724,10111,10112,10113],{},"S rostoucí cenou elasticita nabídky roste. ",[883,10114,10116],{"className":10115},[886],[888,10117,10118],{"xmlns":890},[892,10119,10120,10129],{},[895,10121,10122,10124,10127],{},[1677,10123,1686],{"stretchy":1685},[1810,10125,10126],{},"4.14",[1677,10128,1692],{"stretchy":1685},[902,10130,10131],{"encoding":904},"(4.14)",[724,10133,10134],{},"Pro nominální změny platí",[724,10136,10137],{},[883,10138,10140],{"className":10139,"title":5588,"style":5589},[5587],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P, \\qquad \\mathrm{d}P = \\Delta P, \\tag{4.15}",[724,10142,10143],{},"a pro procentní změny",[724,10145,10146],{},[883,10147,10149],{"className":10148,"title":5588,"style":5589},[5587],"\\boxed{\\;\\Delta Q\\% \\approx E(P)\\,\\Delta P\\%\\;} \\tag{4.16}",[724,10151,10152],{},"(bez znaménka minus).",[198,10154,10156],{"id":10155},"příklad-47","Příklad 4.7",[724,10158,10159,10160,2385],{},"Nabídka ",[883,10161,10163],{"className":10162},[886],[888,10164,10165],{"xmlns":890},[892,10166,10167,10192],{},[895,10168,10169,10171,10173,10175,10181,10183,10185,10187,10189],{},[898,10170,2470],{},[1677,10172,1679],{},[1810,10174,2475],{},[1805,10176,10177,10179],{},[898,10178,5325],{},[1810,10180,1812],{},[1677,10182,1776],{},[1810,10184,1909],{},[898,10186,5325],{},[1677,10188,1776],{},[1810,10190,10191],{},"150",[902,10193,10194],{"encoding":904},"Q = 0{,}1P^2 + 5P + 150",[724,10196,10197],{},[883,10198,10200],{"className":10199},[886],[888,10201,10202],{"xmlns":890},[892,10203,10204,10250],{},[895,10205,10206,10208,10210,10234,10236,10238,10240,10242,10244,10246,10248],{},[898,10207,5640],{},[1677,10209,1679],{},[2010,10211,10212,10214],{},[898,10213,5325],{},[895,10215,10216,10218,10224,10226,10228,10230,10232],{},[1810,10217,2475],{},[1805,10219,10220,10222],{},[898,10221,5325],{},[1810,10223,1812],{},[1677,10225,1776],{},[1810,10227,1909],{},[898,10229,5325],{},[1677,10231,1776],{},[1810,10233,10191],{},[1969,10235,2668],{},[1677,10237,1686],{"stretchy":1685},[1810,10239,2520],{},[898,10241,5325],{},[1677,10243,1776],{},[1810,10245,1909],{},[1677,10247,1692],{"stretchy":1685},[898,10249,1656],{"mathvariant":2057},[902,10251,10252],{"encoding":904},"E = \\frac{P}{0{,}1P^2 + 5P + 150}\\,(0{,}2P + 5).",[724,10254,6505,10255,1343,10285,1343,10312,10348,10349,10374,10375,10393,10394,1656],{},[883,10256,10258],{"className":10257},[886],[888,10259,10260],{"xmlns":890},[892,10261,10262,10282],{},[895,10263,10264,10266,10268,10270,10272,10274],{},[898,10265,5640],{},[1677,10267,1686],{"stretchy":1685},[1810,10269,2544],{},[1677,10271,1692],{"stretchy":1685},[1677,10273,1679],{},[2006,10275,10276],{"scriptlevel":2008,"displaystyle":1685},[2010,10277,10278,10280],{},[1810,10279,1959],{},[1810,10281,1854],{},[902,10283,10284],{"encoding":904},"E(10) = \\tfrac{1}{3}",[883,10286,10288],{"className":10287},[886],[888,10289,10290],{"xmlns":890},[892,10291,10292,10309],{},[895,10293,10294,10296,10298,10303,10305,10307],{},[898,10295,5640],{},[1677,10297,1686],{"stretchy":1685},[9505,10299,10300],{},[1810,10301,10302],{},"1500",[1677,10304,1692],{"stretchy":1685},[1677,10306,1679],{},[1810,10308,1959],{},[902,10310,10311],{"encoding":904},"E(\\sqrt{1500}) = 1",[883,10313,10315],{"className":10314},[886],[888,10316,10317],{"xmlns":890},[892,10318,10319,10345],{},[895,10320,10321,10323,10325,10327,10329,10331,10340,10342],{},[898,10322,5640],{},[1677,10324,1686],{"stretchy":1685},[1810,10326,2771],{},[1677,10328,1692],{"stretchy":1685},[1677,10330,1679],{},[2006,10332,10333],{"scriptlevel":2008,"displaystyle":1685},[2010,10334,10335,10337],{},[1810,10336,2801],{},[1810,10338,10339],{},"33",[1677,10341,7288],{},[1810,10343,10344],{},"1,515",[902,10346,10347],{"encoding":904},"E(100) = \\tfrac{50}{33} \\doteq 1{,}515",". Dle (4.14): pro ",[883,10350,10352],{"className":10351},[886],[888,10353,10354],{"xmlns":890},[892,10355,10356,10371],{},[895,10357,10358,10360,10362,10366,10368],{},[898,10359,5325],{},[1677,10361,3089],{},[9505,10363,10364],{},[1810,10365,10302],{},[1677,10367,2411],{},[1810,10369,10370],{},"38,7",[902,10372,10373],{"encoding":904},"P > \\sqrt{1500} \\approx 38{,}7"," je nabídka elastická, pro ",[883,10376,10378],{"className":10377},[886],[888,10379,10380],{"xmlns":890},[892,10381,10382,10390],{},[895,10383,10384,10386,10388],{},[898,10385,5325],{},[1677,10387,3128],{},[1810,10389,10370],{},[902,10391,10392],{"encoding":904},"P \u003C 38{,}7"," neelastická. Zvýší-li se cena z 10 o 20 %, pak ",[883,10395,10397],{"className":10396},[886],[888,10398,10399],{"xmlns":890},[892,10400,10401,10439],{},[895,10402,10403,10405,10407,10409,10411,10419,10421,10424,10426,10429,10435,10437],{},[898,10404,2570],{"mathvariant":2057},[898,10406,2470],{},[898,10408,7313],{"mathvariant":2057},[1677,10410,2411],{},[2006,10412,10413],{"scriptlevel":2008,"displaystyle":1685},[2010,10414,10415,10417],{},[1810,10416,1959],{},[1810,10418,1854],{},[1677,10420,2858],{},[1810,10422,10423],{},"20",[1677,10425,1679],{},[1810,10427,10428],{},"6,",[9774,10430,10431,10433],{"accent":1966},[1810,10432,1916],{},[1677,10434,9780],{"stretchy":1966},[1969,10436,2668],{},[898,10438,7313],{"mathvariant":2057},[902,10440,10441],{"encoding":904},"\\Delta Q\\% \\approx \\tfrac{1}{3}\\cdot 20 = 6{,}\\overline{6}\\,\\%",[115,10443,10445],{"id":10444},"vícefaktorový-model","Vícefaktorový model",[724,10447,10448,10449,10462,10463,1884,10466,10479,10480,1884,10483,10501,10502,1884,10505,2385],{},"Předpokládejme, že poptávané množství ",[883,10450,10452],{"className":10451},[886],[888,10453,10454],{"xmlns":890},[892,10455,10456,10460],{},[895,10457,10458],{},[898,10459,2470],{},[902,10461,2470],{"encoding":904}," závisí na ",[38,10464,10465],{},"ceně základního zboží",[883,10467,10469],{"className":10468},[886],[888,10470,10471],{"xmlns":890},[892,10472,10473,10477],{},[895,10474,10475],{},[898,10476,5325],{},[902,10478,5325],{"encoding":904},", na ",[38,10481,10482],{},"ceně alternativního zboží",[883,10484,10486],{"className":10485},[886],[888,10487,10488],{"xmlns":890},[892,10489,10490,10498],{},[895,10491,10492],{},[1953,10493,10494,10496],{},[898,10495,5325],{},[898,10497,5643],{},[902,10499,10500],{"encoding":904},"P_A"," a na ",[38,10503,10504],{},"důchodu",[883,10506,10508],{"className":10507},[886],[888,10509,10510],{"xmlns":890},[892,10511,10512,10517],{},[895,10513,10514],{},[898,10515,10516],{},"Y",[902,10518,10516],{"encoding":904},[724,10520,10521],{},[883,10522,10524],{"className":10523,"title":5588,"style":5589},[5587],"Q = D(P, P_A, Y). \\tag{4.17}",[724,10526,10527,10528,10531],{},"V analogii jednofaktorového modelu pracujeme s ",[38,10529,10530],{},"parciálními derivacemi"," funkce poptávky.",[198,10533,10535],{"id":10534},"cenová-elasticita-poptávky-vícefaktorová","Cenová elasticita poptávky (vícefaktorová)",[724,10537,10538],{},[883,10539,10541],{"className":10540,"title":5588,"style":5589},[5587],"\\boxed{\\;E_P = -\\frac{P}{Q}\\,Q'_P\\;} \\tag{4.18}",[724,10543,5698,10544,10565,10566,10579,10580,2608,10602,1884,10605,10651,10652,10665,10666,10683],{},[883,10545,10547],{"className":10546},[886],[888,10548,10549],{"xmlns":890},[892,10550,10551,10562],{},[895,10552,10553],{},[10554,10555,10556,10558,10560],"msubsup",{},[898,10557,2470],{},[898,10559,5325],{},[1677,10561,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[902,10563,10564],{"encoding":904},"Q'_P"," je parciální derivace (4.17) podle ",[883,10567,10569],{"className":10568},[886],[888,10570,10571],{"xmlns":890},[892,10572,10573,10577],{},[895,10574,10575],{},[898,10576,5325],{},[902,10578,5325],{"encoding":904},". Vždy ",[883,10581,10583],{"className":10582},[886],[888,10584,10585],{"xmlns":890},[892,10586,10587,10599],{},[895,10588,10589,10595,10597],{},[1953,10590,10591,10593],{},[898,10592,5640],{},[898,10594,5325],{},[1677,10596,5873],{},[1810,10598,2008],{},[902,10600,10601],{"encoding":904},"E_P \\ge 0",[614,10603,10604],{},"Interpretace:",[883,10606,10608],{"className":10607},[886],[888,10609,10610],{"xmlns":890},[892,10611,10612,10648],{},[895,10613,10614,10620,10622,10628,10630,10638,10640,10646],{},[1953,10615,10616,10618],{},[898,10617,5640],{},[898,10619,5325],{},[1677,10621,1686],{"stretchy":1685},[1805,10623,10624,10626],{},[898,10625,5325],{},[1677,10627,5742],{},[1677,10629,1967],{"separator":1966},[10554,10631,10632,10634,10636],{},[898,10633,5325],{},[898,10635,5643],{},[1677,10637,5742],{},[1677,10639,1967],{"separator":1966},[1805,10641,10642,10644],{},[898,10643,10516],{},[1677,10645,5742],{},[1677,10647,1692],{"stretchy":1685},[902,10649,10650],{"encoding":904},"E_P(P^*, P_A^*, Y^*)"," udává přibližnou procentní změnu ",[883,10653,10655],{"className":10654},[886],[888,10656,10657],{"xmlns":890},[892,10658,10659,10663],{},[895,10660,10661],{},[898,10662,2470],{},[902,10664,2470],{"encoding":904}," při 1% změně ",[883,10667,10669],{"className":10668},[886],[888,10670,10671],{"xmlns":890},[892,10672,10673,10681],{},[895,10674,10675],{},[1805,10676,10677,10679],{},[898,10678,5325],{},[1677,10680,5742],{},[902,10682,5792],{"encoding":904},", ceteris paribus.",[198,10685,10687],{"id":10686},"křížová-křížově-cenová-elasticita-poptávky","Křížová (křížově-cenová) elasticita poptávky",[724,10689,10690],{},[883,10691,10693],{"className":10692,"title":5588,"style":5589},[5587],"\\boxed{\\;E_{P_A} = \\frac{P_A}{Q}\\,Q'_{P_A}\\;} \\tag{4.19}",[724,10695,10696,10651,10698,10711,10712,10729],{},[614,10697,10604],{},[883,10699,10701],{"className":10700},[886],[888,10702,10703],{"xmlns":890},[892,10704,10705,10709],{},[895,10706,10707],{},[898,10708,2470],{},[902,10710,2470],{"encoding":904}," základního zboží při 1% změně ceny ",[883,10713,10715],{"className":10714},[886],[888,10716,10717],{"xmlns":890},[892,10718,10719,10727],{},[895,10720,10721],{},[1953,10722,10723,10725],{},[898,10724,5325],{},[898,10726,5643],{},[902,10728,10500],{"encoding":904}," alternativního zboží (ceteris paribus).",[724,10731,10732],{},[38,10733,10734],{},"Znaménko závisí na povaze alternativního zboží:",[120,10736,10737,10825],{},[123,10738,10739,10740,10743,10744,10761,10762,1884,10775,1656],{},"Je-li alternativní zboží ",[38,10741,10742],{},"komplement",", růst ",[883,10745,10747],{"className":10746},[886],[888,10748,10749],{"xmlns":890},[892,10750,10751,10759],{},[895,10752,10753],{},[1953,10754,10755,10757],{},[898,10756,5325],{},[898,10758,5643],{},[902,10760,10500],{"encoding":904}," způsobí zdražení dvojice, pokles ",[883,10763,10765],{"className":10764},[886],[888,10766,10767],{"xmlns":890},[892,10768,10769,10773],{},[895,10770,10771],{},[898,10772,2470],{},[902,10774,2470],{"encoding":904},[883,10776,10778],{"className":10777},[886],[888,10779,10780],{"xmlns":890},[892,10781,10782,10822],{},[895,10783,10784,10786,10788,10800,10802,10804,10806,10808,10818,10820],{},[1677,10785,5375],{},[1969,10787,5372],{},[10554,10789,10790,10792,10798],{},[898,10791,2470],{},[1953,10793,10794,10796],{},[898,10795,5325],{},[898,10797,5643],{},[1677,10799,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,10801,3128],{},[1810,10803,2008],{},[1677,10805,1967],{"separator":1966},[1969,10807,5372],{},[1953,10809,10810,10812],{},[898,10811,5640],{},[1953,10813,10814,10816],{},[898,10815,5325],{},[898,10817,5643],{},[1677,10819,3128],{},[1810,10821,2008],{},[902,10823,10824],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} \u003C 0,\\; E_{P_A} \u003C 0",[123,10826,10739,10827,10743,10830,10847,10848,10861,10862,1656],{},[38,10828,10829],{},"substitut",[883,10831,10833],{"className":10832},[886],[888,10834,10835],{"xmlns":890},[892,10836,10837,10845],{},[895,10838,10839],{},[1953,10840,10841,10843],{},[898,10842,5325],{},[898,10844,5643],{},[902,10846,10500],{"encoding":904}," učiní základní zboží relativně levnější, zájem se přesune, ",[883,10849,10851],{"className":10850},[886],[888,10852,10853],{"xmlns":890},[892,10854,10855,10859],{},[895,10856,10857],{},[898,10858,2470],{},[902,10860,2470],{"encoding":904}," roste ",[883,10863,10865],{"className":10864},[886],[888,10866,10867],{"xmlns":890},[892,10868,10869,10909],{},[895,10870,10871,10873,10875,10887,10889,10891,10893,10895,10905,10907],{},[1677,10872,5375],{},[1969,10874,5372],{},[10554,10876,10877,10879,10885],{},[898,10878,2470],{},[1953,10880,10881,10883],{},[898,10882,5325],{},[898,10884,5643],{},[1677,10886,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,10888,3089],{},[1810,10890,2008],{},[1677,10892,1967],{"separator":1966},[1969,10894,5372],{},[1953,10896,10897,10899],{},[898,10898,5640],{},[1953,10900,10901,10903],{},[898,10902,5325],{},[898,10904,5643],{},[1677,10906,3089],{},[1810,10908,2008],{},[902,10910,10911],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} > 0,\\; E_{P_A} > 0",[883,10913,10916],{"className":10914,"title":10915,"style":5589},[5587],"ParseError: KaTeX parse error: Expected 'EOF', got '&' at position 9: E_{P_A} &̲> 0 \\;\\;\\Leftri…","undefined",{"title":641,"searchDepth":642,"depth":642,"links":10918},[10919,10923,10924,10932,10933,10937,10940],{"id":5278,"depth":642,"text":5279,"children":10920},[10921,10922],{"id":5309,"depth":649,"text":5310},{"id":5490,"depth":649,"text":5491},{"id":5525,"depth":642,"text":5526},{"id":5551,"depth":642,"text":5552,"children":10925},[10926,10927,10928,10929,10931],{"id":6247,"depth":649,"text":6248},{"id":6337,"depth":649,"text":6338},{"id":6673,"depth":649,"text":6674},{"id":6755,"depth":649,"text":10930},"Výpočet, je-li dáno PP jako funkce QQ",{"id":7016,"depth":649,"text":7017},{"id":7341,"depth":642,"text":7342},{"id":7937,"depth":642,"text":7938,"children":10934},[10935,10936],{"id":8566,"depth":649,"text":8567},{"id":9395,"depth":649,"text":9396},{"id":10029,"depth":642,"text":10030,"children":10938},[10939],{"id":10155,"depth":649,"text":10156},{"id":10444,"depth":642,"text":10445,"children":10941},[10942,10943],{"id":10534,"depth":649,"text":10535},{"id":10686,"depth":649,"text":10687},"2026-04-22",{},"\u002Ftopics\u002Felasticita",{"title":5247,"description":641},[1138,1136],"topics\u002Felasticita",[1128,5285,10951,10952,10953,10954],"cenova-elasticita","krizova-elasticita","duchodova-elasticita","mr-tr","c_Ilj6dK9Ey4kbyp6EKogVl_p8zmryyIur0pCOtxlhM",{"id":10957,"title":10958,"body":10959,"course":1128,"courses":659,"created":1129,"description":12501,"extension":661,"meta":12502,"navigation":664,"path":12503,"seo":12504,"sources":12505,"stem":12506,"tags":12507,"type":3538,"updated":677,"__hash__":12512},"topics\u002Ftopics\u002Ffunkce-vice-promennych.md","Kalkul funkcí více proměnných",{"type":9,"value":10960,"toc":12486},[10961,10964,11038,11045,11049,11113,11202,11206,11233,11300,11355,11359,11386,11479,11481,11513,11684,11688,11758,11806,11810,11871,11977,11992,11996,11998,12026,12091,12093,12100,12188,12213,12411,12415,12451,12453],[12,10962,10958],{"id":10963},"kalkul-funkcí-více-proměnných",[724,10965,10966,10967,10970,10971,1343,11000,1656],{},"Většina ekonomických veličin závisí na ",[38,10968,10969],{},"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 ",[883,10972,10974],{"className":10973},[886],[888,10975,10976],{"xmlns":890},[892,10977,10978,10997],{},[895,10979,10980,10983,10985,10987,10989,10991,10993,10995],{},[898,10981,10982],{},"z",[1677,10984,1679],{},[898,10986,1682],{},[1677,10988,1686],{"stretchy":1685},[898,10990,1689],{},[1677,10992,1967],{"separator":1966},[898,10994,1675],{},[1677,10996,1692],{"stretchy":1685},[902,10998,10999],{"encoding":904},"z = f(x, y)",[883,11001,11003],{"className":11002},[886],[888,11004,11005],{"xmlns":890},[892,11006,11007,11035],{},[895,11008,11009,11012,11014,11016,11018,11020,11022,11024,11026,11028,11030,11032],{},[898,11010,11011],{},"w",[1677,11013,1679],{},[898,11015,1682],{},[1677,11017,1686],{"stretchy":1685},[898,11019,1689],{},[1677,11021,1967],{"separator":1966},[898,11023,1675],{},[1677,11025,1967],{"separator":1966},[898,11027,10982],{},[1677,11029,1692],{"stretchy":1685},[1677,11031,1967],{"separator":1966},[1677,11033,11034],{},"…",[902,11036,11037],{"encoding":904},"w = f(x, y, z), \\ldots",[724,11039,11040],{},[2240,11041],{"alt":11042,"className":11043,"src":11044},"imek-funkce-2d-vrstevnice",[210,2244],"\u002Fwiki-assets\u002Fimek-funkce-2d-vrstevnice.jpeg",[115,11046,11048],{"id":11047},"indiferenční-izokvantové-křivky","Indiferenční \u002F izokvantové křivky",[724,11050,11051,11052,11079,11080,11108,11109,11112],{},"Pro ",[883,11053,11055],{"className":11054},[886],[888,11056,11057],{"xmlns":890},[892,11058,11059,11077],{},[895,11060,11061,11063,11065,11067,11069,11071,11073,11075],{},[898,11062,10982],{},[1677,11064,1679],{},[898,11066,1682],{},[1677,11068,1686],{"stretchy":1685},[898,11070,1689],{},[1677,11072,1967],{"separator":1966},[898,11074,1675],{},[1677,11076,1692],{"stretchy":1685},[902,11078,10999],{"encoding":904}," se křivkou s předpisem ",[883,11081,11083],{"className":11082},[886],[888,11084,11085],{"xmlns":890},[892,11086,11087,11105],{},[895,11088,11089,11091,11093,11095,11097,11099,11101,11103],{},[898,11090,1682],{},[1677,11092,1686],{"stretchy":1685},[898,11094,1689],{},[1677,11096,1967],{"separator":1966},[898,11098,1675],{},[1677,11100,1692],{"stretchy":1685},[1677,11102,1679],{},[898,11104,1823],{},[902,11106,11107],{"encoding":904},"f(x, y) = c"," (konstanta) rozumí ",[38,11110,11111],{},"vrstevnice"," funkce. V ekonomii:",[120,11114,11115,11162],{},[123,11116,11117,11120,11121,11157,11158,1656],{},[38,11118,11119],{},"Indiferenční křivky"," užitečnosti ",[883,11122,11124],{"className":11123},[886],[888,11125,11126],{"xmlns":890},[892,11127,11128,11154],{},[895,11129,11130,11132,11134,11140,11142,11148,11150,11152],{},[898,11131,900],{},[1677,11133,1686],{"stretchy":1685},[1953,11135,11136,11138],{},[898,11137,2470],{},[1810,11139,1959],{},[1677,11141,1967],{"separator":1966},[1953,11143,11144,11146],{},[898,11145,2470],{},[1810,11147,1812],{},[1677,11149,1692],{"stretchy":1685},[1677,11151,1679],{},[898,11153,1823],{},[902,11155,11156],{"encoding":904},"U(Q_1, Q_2) = c"," — viz ",[207,11159,11161],{"className":11160,"dataFsResolvedFilePath":878,"href":879},[210],"uzitecnost",[123,11163,11164,11167,11168,11157,11198,1656],{},[38,11165,11166],{},"Izokvanty"," produkce ",[883,11169,11171],{"className":11170},[886],[888,11172,11173],{"xmlns":890},[892,11174,11175,11195],{},[895,11176,11177,11179,11181,11184,11186,11189,11191,11193],{},[898,11178,2470],{},[1677,11180,1686],{"stretchy":1685},[898,11182,11183],{},"L",[1677,11185,1967],{"separator":1966},[898,11187,11188],{},"K",[1677,11190,1692],{"stretchy":1685},[1677,11192,1679],{},[898,11194,1823],{},[902,11196,11197],{"encoding":904},"Q(L, K) = c",[207,11199,11201],{"className":11200,"dataFsResolvedFilePath":857,"href":858},[210],"produkce",[115,11203,11205],{"id":11204},"parciální-derivace","Parciální derivace",[724,11207,11051,11208,11232],{},[883,11209,11211],{"className":11210},[886],[888,11212,11213],{"xmlns":890},[892,11214,11215,11229],{},[895,11216,11217,11219,11221,11223,11225,11227],{},[898,11218,1682],{},[1677,11220,1686],{"stretchy":1685},[898,11222,1689],{},[1677,11224,1967],{"separator":1966},[898,11226,1675],{},[1677,11228,1692],{"stretchy":1685},[902,11230,11231],{"encoding":904},"f(x, y)"," derivujeme jako kdyby druhá proměnná byla konstanta:",[724,11234,11235],{},[883,11236,11238],{"className":11237},[886],[888,11239,11240],{"xmlns":890},[892,11241,11242,11297],{},[895,11243,11244,11252,11254,11269,11271,11273,11281,11283],{},[10554,11245,11246,11248,11250],{},[898,11247,1682],{},[898,11249,1689],{},[1677,11251,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,11253,1679],{},[2010,11255,11256,11263],{},[895,11257,11258,11261],{},[898,11259,11260],{"mathvariant":2057},"∂",[898,11262,1682],{},[895,11264,11265,11267],{},[898,11266,11260],{"mathvariant":2057},[898,11268,1689],{},[1677,11270,1967],{"separator":1966},[7266,11272],{"width":7268},[10554,11274,11275,11277,11279],{},[898,11276,1682],{},[898,11278,1675],{},[1677,11280,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,11282,1679],{},[2010,11284,11285,11291],{},[895,11286,11287,11289],{},[898,11288,11260],{"mathvariant":2057},[898,11290,1682],{},[895,11292,11293,11295],{},[898,11294,11260],{"mathvariant":2057},[898,11296,1675],{},[902,11298,11299],{"encoding":904},"f'_x = \\frac{\\partial f}{\\partial x}, \\qquad f'_y = \\frac{\\partial f}{\\partial y}",[724,11301,11302,11303,1656],{},"Hodnoty v bodě: ",[883,11304,11306],{"className":11305},[886],[888,11307,11308],{"xmlns":890},[892,11309,11310,11352],{},[895,11311,11312,11320,11322,11324,11326,11328,11330,11332,11334,11342,11344,11346,11348,11350],{},[10554,11313,11314,11316,11318],{},[898,11315,1682],{},[898,11317,1689],{},[1677,11319,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,11321,1686],{"stretchy":1685},[898,11323,207],{},[1677,11325,1967],{"separator":1966},[898,11327,1779],{},[1677,11329,1692],{"stretchy":1685},[1677,11331,1967],{"separator":1966},[1969,11333,1971],{},[10554,11335,11336,11338,11340],{},[898,11337,1682],{},[898,11339,1675],{},[1677,11341,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,11343,1686],{"stretchy":1685},[898,11345,207],{},[1677,11347,1967],{"separator":1966},[898,11349,1779],{},[1677,11351,1692],{"stretchy":1685},[902,11353,11354],{"encoding":904},"f'_x(a, b),\\ f'_y(a, b)",[198,11356,11358],{"id":11357},"ekonomické-značení","Ekonomické značení",[724,11360,11361,11362,2385],{},"Pro produkční funkci ",[883,11363,11365],{"className":11364},[886],[888,11366,11367],{"xmlns":890},[892,11368,11369,11383],{},[895,11370,11371,11373,11375,11377,11379,11381],{},[898,11372,2470],{},[1677,11374,1686],{"stretchy":1685},[898,11376,11183],{},[1677,11378,1967],{"separator":1966},[898,11380,11188],{},[1677,11382,1692],{"stretchy":1685},[902,11384,11385],{"encoding":904},"Q(L, K)",[120,11387,11388,11434],{},[123,11389,11390,2151,11410,11413,11414,1692],{},[883,11391,11393],{"className":11392},[886],[888,11394,11395],{"xmlns":890},[892,11396,11397,11407],{},[895,11398,11399],{},[10554,11400,11401,11403,11405],{},[898,11402,2470],{},[898,11404,11183],{},[1677,11406,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[902,11408,11409],{"encoding":904},"Q'_L",[38,11411,11412],{},"mezní produkt práce"," (",[883,11415,11417],{"className":11416},[886],[888,11418,11419],{"xmlns":890},[892,11420,11421,11431],{},[895,11422,11423,11425],{},[898,11424,2499],{},[1953,11426,11427,11429],{},[898,11428,5325],{},[898,11430,11183],{},[902,11432,11433],{"encoding":904},"MP_L",[123,11435,11436,2151,11456,11413,11459,1692],{},[883,11437,11439],{"className":11438},[886],[888,11440,11441],{"xmlns":890},[892,11442,11443,11453],{},[895,11444,11445],{},[10554,11446,11447,11449,11451],{},[898,11448,2470],{},[898,11450,11188],{},[1677,11452,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[902,11454,11455],{"encoding":904},"Q'_K",[38,11457,11458],{},"mezní produkt kapitálu",[883,11460,11462],{"className":11461},[886],[888,11463,11464],{"xmlns":890},[892,11465,11466,11476],{},[895,11467,11468,11470],{},[898,11469,2499],{},[1953,11471,11472,11474],{},[898,11473,5325],{},[898,11475,11188],{},[902,11477,11478],{"encoding":904},"MP_K",[198,11480,2249],{"id":2248},[724,11482,11483,2385],{},[883,11484,11486],{"className":11485},[886],[888,11487,11488],{"xmlns":890},[892,11489,11490,11510],{},[895,11491,11492,11500,11502,11504,11506,11508],{},[10554,11493,11494,11496,11498],{},[898,11495,1682],{},[898,11497,1689],{},[1677,11499,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,11501,1686],{"stretchy":1685},[898,11503,207],{},[1677,11505,1967],{"separator":1966},[898,11507,1779],{},[1677,11509,1692],{"stretchy":1685},[902,11511,11512],{"encoding":904},"f'_x(a, b)",[120,11514,11515,11573],{},[123,11516,11517,11518,11531,11532,11545,11546,11572],{},"rychlost změny ",[883,11519,11521],{"className":11520},[886],[888,11522,11523],{"xmlns":890},[892,11524,11525,11529],{},[895,11526,11527],{},[898,11528,1682],{},[902,11530,1682],{"encoding":904}," vůči ",[883,11533,11535],{"className":11534},[886],[888,11536,11537],{"xmlns":890},[892,11538,11539,11543],{},[895,11540,11541],{},[898,11542,1689],{},[902,11544,1689],{"encoding":904}," při ",[883,11547,11549],{"className":11548},[886],[888,11550,11551],{"xmlns":890},[892,11552,11553,11569],{},[895,11554,11555,11557,11559,11561,11563,11565,11567],{},[898,11556,1689],{},[1677,11558,1679],{},[898,11560,207],{},[1677,11562,1967],{"separator":1966},[898,11564,1675],{},[1677,11566,1679],{},[898,11568,1779],{},[902,11570,11571],{"encoding":904},"x = a, y = b"," (kapitál fixní),",[123,11574,11575,11576,2338,11589,11602,11603,11621,11622,1656],{},"přibližná změna ",[883,11577,11579],{"className":11578},[886],[888,11580,11581],{"xmlns":890},[892,11582,11583,11587],{},[895,11584,11585],{},[898,11586,1682],{},[902,11588,1682],{"encoding":904},[883,11590,11592],{"className":11591},[886],[888,11593,11594],{"xmlns":890},[892,11595,11596,11600],{},[895,11597,11598],{},[898,11599,1689],{},[902,11601,1689],{"encoding":904}," o 1 (a pevném ",[883,11604,11606],{"className":11605},[886],[888,11607,11608],{"xmlns":890},[892,11609,11610,11618],{},[895,11611,11612,11614,11616],{},[898,11613,1675],{},[1677,11615,1679],{},[898,11617,1779],{},[902,11619,11620],{"encoding":904},"y = b","): ",[883,11623,11625],{"className":11624},[886],[888,11626,11627],{"xmlns":890},[892,11628,11629,11681],{},[895,11630,11631,11633,11635,11637,11639,11641,11643,11645,11647,11649,11651,11653,11655,11657,11659,11661,11663,11671,11673,11675,11677,11679],{},[898,11632,1682],{},[1677,11634,1686],{"stretchy":1685},[898,11636,207],{},[1677,11638,1776],{},[1810,11640,1959],{},[1677,11642,1967],{"separator":1966},[898,11644,1779],{},[1677,11646,1692],{"stretchy":1685},[1677,11648,2411],{},[898,11650,1682],{},[1677,11652,1686],{"stretchy":1685},[898,11654,207],{},[1677,11656,1967],{"separator":1966},[898,11658,1779],{},[1677,11660,1692],{"stretchy":1685},[1677,11662,1776],{},[10554,11664,11665,11667,11669],{},[898,11666,1682],{},[898,11668,1689],{},[1677,11670,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,11672,1686],{"stretchy":1685},[898,11674,207],{},[1677,11676,1967],{"separator":1966},[898,11678,1779],{},[1677,11680,1692],{"stretchy":1685},[902,11682,11683],{"encoding":904},"f(a+1, b) \\approx f(a, b) + f'_x(a, b)",[115,11685,11687],{"id":11686},"diferenciál-funkce-dvou-proměnných","Diferenciál funkce dvou proměnných",[724,11689,11690],{},[883,11691,11693],{"className":11692},[886],[888,11694,11695],{"xmlns":890},[892,11696,11697,11755],{},[895,11698,11699,11701,11703,11705,11713,11715,11717,11719,11721,11723,11725,11727,11729,11731,11739,11741,11743,11745,11747,11749,11751,11753],{},[898,11700,1875],{},[898,11702,1682],{},[1677,11704,1679],{},[10554,11706,11707,11709,11711],{},[898,11708,1682],{},[898,11710,1689],{},[1677,11712,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,11714,1686],{"stretchy":1685},[898,11716,1689],{},[1677,11718,1967],{"separator":1966},[898,11720,1675],{},[1677,11722,1692],{"stretchy":1685},[1969,11724,2668],{},[898,11726,1875],{},[898,11728,1689],{},[1677,11730,1776],{},[10554,11732,11733,11735,11737],{},[898,11734,1682],{},[898,11736,1675],{},[1677,11738,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,11740,1686],{"stretchy":1685},[898,11742,1689],{},[1677,11744,1967],{"separator":1966},[898,11746,1675],{},[1677,11748,1692],{"stretchy":1685},[1969,11750,2668],{},[898,11752,1875],{},[898,11754,1675],{},[902,11756,11757],{"encoding":904},"df = f'_x(x, y)\\, dx + f'_y(x, y)\\, dy",[724,11759,2678,11760,11782,11783,11805],{},[883,11761,11763],{"className":11762},[886],[888,11764,11765],{"xmlns":890},[892,11766,11767,11779],{},[895,11768,11769,11771,11773,11775,11777],{},[898,11770,1875],{},[898,11772,1689],{},[1677,11774,1967],{"separator":1966},[898,11776,1875],{},[898,11778,1675],{},[902,11780,11781],{"encoding":904},"dx, dy"," platí ",[883,11784,11786],{"className":11785},[886],[888,11787,11788],{"xmlns":890},[892,11789,11790,11802],{},[895,11791,11792,11794,11796,11798,11800],{},[898,11793,2570],{"mathvariant":2057},[898,11795,1682],{},[1677,11797,2411],{},[898,11799,1875],{},[898,11801,1682],{},[902,11803,11804],{"encoding":904},"\\Delta f \\approx df",". Linearizace přírůstku ve dvou směrech současně.",[115,11807,11809],{"id":11808},"implicitní-funkce","Implicitní funkce",[724,11811,11812,11813,11842,11843,11856,11857,11870],{},"Je-li vztah dán rovnicí ",[883,11814,11816],{"className":11815},[886],[888,11817,11818],{"xmlns":890},[892,11819,11820,11839],{},[895,11821,11822,11825,11827,11829,11831,11833,11835,11837],{},[898,11823,11824],{},"F",[1677,11826,1686],{"stretchy":1685},[898,11828,1689],{},[1677,11830,1967],{"separator":1966},[898,11832,1675],{},[1677,11834,1692],{"stretchy":1685},[1677,11836,1679],{},[1810,11838,2008],{},[902,11840,11841],{"encoding":904},"F(x, y) = 0"," a chceme derivaci ",[883,11844,11846],{"className":11845},[886],[888,11847,11848],{"xmlns":890},[892,11849,11850,11854],{},[895,11851,11852],{},[898,11853,1675],{},[902,11855,1675],{"encoding":904}," podle ",[883,11858,11860],{"className":11859},[886],[888,11861,11862],{"xmlns":890},[892,11863,11864,11868],{},[895,11865,11866],{},[898,11867,1689],{},[902,11869,1689],{"encoding":904}," (nebo naopak):",[724,11872,11873],{},[883,11874,11876],{"className":11875},[886],[888,11877,11878],{"xmlns":890},[892,11879,11880,11974],{},[895,11881,11882,11888,11890,11904,11906,11908,11926,11928,11930,11936,11938,11952,11954,11956],{},[1805,11883,11884,11886],{},[898,11885,1675],{},[1677,11887,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,11889,1679],{},[2010,11891,11892,11898],{},[895,11893,11894,11896],{},[898,11895,1875],{},[898,11897,1675],{},[895,11899,11900,11902],{},[898,11901,1875],{},[898,11903,1689],{},[1677,11905,1679],{},[1677,11907,1906],{},[2010,11909,11910,11918],{},[10554,11911,11912,11914,11916],{},[898,11913,11824],{},[898,11915,1689],{},[1677,11917,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[10554,11919,11920,11922,11924],{},[898,11921,11824],{},[898,11923,1675],{},[1677,11925,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,11927,1967],{"separator":1966},[7266,11929],{"width":7268},[1805,11931,11932,11934],{},[898,11933,1689],{},[1677,11935,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,11937,1679],{},[2010,11939,11940,11946],{},[895,11941,11942,11944],{},[898,11943,1875],{},[898,11945,1689],{},[895,11947,11948,11950],{},[898,11949,1875],{},[898,11951,1675],{},[1677,11953,1679],{},[1677,11955,1906],{},[2010,11957,11958,11966],{},[10554,11959,11960,11962,11964],{},[898,11961,11824],{},[898,11963,1675],{},[1677,11965,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[10554,11967,11968,11970,11972],{},[898,11969,11824],{},[898,11971,1689],{},[1677,11973,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[902,11975,11976],{"encoding":904},"y' = \\frac{dy}{dx} = -\\frac{F'_x}{F'_y}, \\qquad x' = \\frac{dx}{dy} = -\\frac{F'_y}{F'_x}",[724,11978,11979,11980,11983,11984,5272,11988,1656],{},"Tato vzorec dává ",[38,11981,11982],{},"sklon vrstevnice"," — používá se mj. pro výpočet ",[207,11985,11987],{"className":11986,"dataFsResolvedFilePath":857,"href":858},[210],"MRTS",[207,11989,11991],{"className":11990,"dataFsResolvedFilePath":878,"href":879},[210],"MRCS",[115,11993,11995],{"id":11994},"volné-extrémy-funkce-dvou-proměnných","Volné extrémy funkce dvou proměnných",[198,11997,2933],{"id":2932},[724,11999,12000,12001,12025],{},"V bodě extrému ",[883,12002,12004],{"className":12003},[886],[888,12005,12006],{"xmlns":890},[892,12007,12008,12022],{},[895,12009,12010,12012,12014,12016,12018,12020],{},[898,12011,5643],{},[1677,12013,2167],{"stretchy":1685},[898,12015,207],{},[1677,12017,1967],{"separator":1966},[898,12019,1779],{},[1677,12021,2182],{"stretchy":1685},[902,12023,12024],{"encoding":904},"A[a, b]"," musí platit současně:",[724,12027,12028],{},[883,12029,12031],{"className":12030},[886],[888,12032,12033],{"xmlns":890},[892,12034,12035,12088],{},[895,12036,12037,12045,12047,12049,12051,12053,12055,12057,12059,12061,12064,12066,12074,12076,12078,12080,12082,12084,12086],{},[10554,12038,12039,12041,12043],{},[898,12040,1682],{},[898,12042,1689],{},[1677,12044,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,12046,1686],{"stretchy":1685},[898,12048,207],{},[1677,12050,1967],{"separator":1966},[898,12052,1779],{},[1677,12054,1692],{"stretchy":1685},[1677,12056,1679],{},[1810,12058,2008],{},[1969,12060,5372],{},[1677,12062,12063],{},"∧",[1969,12065,5372],{},[10554,12067,12068,12070,12072],{},[898,12069,1682],{},[898,12071,1675],{},[1677,12073,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,12075,1686],{"stretchy":1685},[898,12077,207],{},[1677,12079,1967],{"separator":1966},[898,12081,1779],{},[1677,12083,1692],{"stretchy":1685},[1677,12085,1679],{},[1810,12087,2008],{},[902,12089,12090],{"encoding":904},"f'_x(a, b) = 0 \\;\\wedge\\; f'_y(a, b) = 0",[198,12092,3007],{"id":3006},[724,12094,12095,12096,12099],{},"Definujeme ",[38,12097,12098],{},"diskriminant"," (Hessián zjednodušeně):",[724,12101,12102],{},[883,12103,12105],{"className":12104},[886],[888,12106,12107],{"xmlns":890},[892,12108,12109,12185],{},[895,12110,12111,12113,12115,12117,12119,12121,12123,12125,12141,12143,12159,12161,12163,12179],{},[898,12112,5571],{},[1677,12114,1686],{"stretchy":1685},[898,12116,1689],{},[1677,12118,1967],{"separator":1966},[898,12120,1675],{},[1677,12122,1692],{"stretchy":1685},[1677,12124,1679],{},[10554,12126,12127,12129,12135],{},[898,12128,1682],{},[895,12130,12131,12133],{},[898,12132,1689],{},[898,12134,1689],{},[895,12136,12137,12139],{},[1677,12138,2059],{"mathvariant":2057},[1677,12140,2059],{"mathvariant":2057},[1677,12142,2858],{},[10554,12144,12145,12147,12153],{},[898,12146,1682],{},[895,12148,12149,12151],{},[898,12150,1675],{},[898,12152,1675],{},[895,12154,12155,12157],{},[1677,12156,2059],{"mathvariant":2057},[1677,12158,2059],{"mathvariant":2057},[1677,12160,1906],{},[1677,12162,1686],{"stretchy":1685},[10554,12164,12165,12167,12173],{},[898,12166,1682],{},[895,12168,12169,12171],{},[898,12170,1689],{},[898,12172,1675],{},[895,12174,12175,12177],{},[1677,12176,2059],{"mathvariant":2057},[1677,12178,2059],{"mathvariant":2057},[1805,12180,12181,12183],{},[1677,12182,1692],{"stretchy":1685},[1810,12184,1812],{},[902,12186,12187],{"encoding":904},"D(x, y) = f''_{xx} \\cdot f''_{yy} - (f''_{xy})^2",[724,12189,12190,12191,2385],{},"V podezřelém bodě ",[883,12192,12194],{"className":12193},[886],[888,12195,12196],{"xmlns":890},[892,12197,12198,12210],{},[895,12199,12200,12202,12204,12206,12208],{},[1677,12201,2167],{"stretchy":1685},[898,12203,207],{},[1677,12205,1967],{"separator":1966},[898,12207,1779],{},[1677,12209,2182],{"stretchy":1685},[902,12211,12212],{"encoding":904},"[a, b]",[152,12214,12215,12342,12378],{},[123,12216,12217,12247,12248],{},[38,12218,12219,2385],{},[883,12220,12222],{"className":12221},[886],[888,12223,12224],{"xmlns":890},[892,12225,12226,12244],{},[895,12227,12228,12230,12232,12234,12236,12238,12240,12242],{},[898,12229,5571],{},[1677,12231,1686],{"stretchy":1685},[898,12233,207],{},[1677,12235,1967],{"separator":1966},[898,12237,1779],{},[1677,12239,1692],{"stretchy":1685},[1677,12241,3089],{},[1810,12243,2008],{},[902,12245,12246],{"encoding":904},"D(a, b) > 0"," je to extrém.\n",[120,12249,12250,12296],{},[123,12251,12252,3095,12294],{},[883,12253,12255],{"className":12254},[886],[888,12256,12257],{"xmlns":890},[892,12258,12259,12291],{},[895,12260,12261,12277,12279,12281,12283,12285,12287,12289],{},[10554,12262,12263,12265,12271],{},[898,12264,1682],{},[895,12266,12267,12269],{},[898,12268,1689],{},[898,12270,1689],{},[895,12272,12273,12275],{},[1677,12274,2059],{"mathvariant":2057},[1677,12276,2059],{"mathvariant":2057},[1677,12278,1686],{"stretchy":1685},[898,12280,207],{},[1677,12282,1967],{"separator":1966},[898,12284,1779],{},[1677,12286,1692],{"stretchy":1685},[1677,12288,3089],{},[1810,12290,2008],{},[902,12292,12293],{"encoding":904},"f''_{xx}(a, b) > 0",[38,12295,3456],{},[123,12297,12298,3095,12340],{},[883,12299,12301],{"className":12300},[886],[888,12302,12303],{"xmlns":890},[892,12304,12305,12337],{},[895,12306,12307,12323,12325,12327,12329,12331,12333,12335],{},[10554,12308,12309,12311,12317],{},[898,12310,1682],{},[895,12312,12313,12315],{},[898,12314,1689],{},[898,12316,1689],{},[895,12318,12319,12321],{},[1677,12320,2059],{"mathvariant":2057},[1677,12322,2059],{"mathvariant":2057},[1677,12324,1686],{"stretchy":1685},[898,12326,207],{},[1677,12328,1967],{"separator":1966},[898,12330,1779],{},[1677,12332,1692],{"stretchy":1685},[1677,12334,3128],{},[1810,12336,2008],{},[902,12338,12339],{"encoding":904},"f''_{xx}(a, b) \u003C 0",[38,12341,3398],{},[123,12343,12344,1884,12374,12377],{},[38,12345,12346,2385],{},[883,12347,12349],{"className":12348},[886],[888,12350,12351],{"xmlns":890},[892,12352,12353,12371],{},[895,12354,12355,12357,12359,12361,12363,12365,12367,12369],{},[898,12356,5571],{},[1677,12358,1686],{"stretchy":1685},[898,12360,207],{},[1677,12362,1967],{"separator":1966},[898,12364,1779],{},[1677,12366,1692],{"stretchy":1685},[1677,12368,3128],{},[1810,12370,2008],{},[902,12372,12373],{"encoding":904},"D(a, b) \u003C 0",[38,12375,12376],{},"sedlo"," (v daném bodě extrém není).",[123,12379,12380,12410],{},[38,12381,12382,2385],{},[883,12383,12385],{"className":12384},[886],[888,12386,12387],{"xmlns":890},[892,12388,12389,12407],{},[895,12390,12391,12393,12395,12397,12399,12401,12403,12405],{},[898,12392,5571],{},[1677,12394,1686],{"stretchy":1685},[898,12396,207],{},[1677,12398,1967],{"separator":1966},[898,12400,1779],{},[1677,12402,1692],{"stretchy":1685},[1677,12404,1679],{},[1810,12406,2008],{},[902,12408,12409],{"encoding":904},"D(a, b) = 0"," podmínka nerozhoduje.",[115,12412,12414],{"id":12413},"vázané-extrémy","Vázané extrémy",[724,12416,12417,12418,12447,12448,1656],{},"Pro extrémy s omezující podmínkou ",[883,12419,12421],{"className":12420},[886],[888,12422,12423],{"xmlns":890},[892,12424,12425,12444],{},[895,12426,12427,12430,12432,12434,12436,12438,12440,12442],{},[898,12428,12429],{},"g",[1677,12431,1686],{"stretchy":1685},[898,12433,1689],{},[1677,12435,1967],{"separator":1966},[898,12437,1675],{},[1677,12439,1692],{"stretchy":1685},[1677,12441,1679],{},[1810,12443,2008],{},[902,12445,12446],{"encoding":904},"g(x, y) = 0"," se používá ",[207,12449,793],{"className":12450,"dataFsResolvedFilePath":791,"href":792},[210],[115,12452,3473],{"id":3472},[120,12454,12455,12462,12469],{},[123,12456,12457,1884,12459],{},[38,12458,3480],{},[207,12460,775],{"className":12461,"dataFsResolvedFilePath":773,"href":774},[210],[123,12463,12464,1884,12466],{},[38,12465,3488],{},[207,12467,793],{"className":12468,"dataFsResolvedFilePath":791,"href":792},[210],[123,12470,12471,1884,12473,12477,12478,12481,12482,12485],{},[38,12472,3496],{},[207,12474,12476],{"className":12475,"dataFsResolvedFilePath":857,"href":858},[210],"Produkce"," (parciální derivace = mezní produkty), ",[207,12479,880],{"className":12480,"dataFsResolvedFilePath":878,"href":879},[210]," (parciální derivace = mezní užitečnost), ",[207,12483,3509],{"className":12484,"dataFsResolvedFilePath":848,"href":849},[210]," (vícefaktorový model)",{"title":641,"searchDepth":642,"depth":642,"links":12487},[12488,12489,12493,12494,12495,12499,12500],{"id":11047,"depth":642,"text":11048},{"id":11204,"depth":642,"text":11205,"children":12490},[12491,12492],{"id":11357,"depth":649,"text":11358},{"id":2248,"depth":649,"text":2249},{"id":11686,"depth":642,"text":11687},{"id":11808,"depth":642,"text":11809},{"id":11994,"depth":642,"text":11995,"children":12496},[12497,12498],{"id":2932,"depth":649,"text":2933},{"id":3006,"depth":649,"text":3007},{"id":12413,"depth":642,"text":12414},{"id":3472,"depth":642,"text":3473},"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":10958,"description":12501},[1135],"topics\u002Ffunkce-vice-promennych",[1128,12508,3535,12509,12510,12511],"parcialni-derivace","implicitni-funkce","volne-extremy","indiferencni-krivky","iuWLbpl-7gHnuMDZKTa3RcRM2uCyFhGx9GhXHIN1R_A",{"id":12514,"title":775,"body":12515,"course":1128,"courses":659,"created":1129,"description":13371,"extension":661,"meta":13372,"navigation":664,"path":13373,"seo":13374,"sources":13375,"stem":13376,"tags":13377,"type":3538,"updated":677,"__hash__":13384},"topics\u002Ftopics\u002Fintegral.md",{"type":9,"value":12516,"toc":13361},[12517,12520,12531,12535,12580,12660,12664,12740,12782,12789,12793,12797,12826,12884,12931,12969,12973,13023,13075,13127,13171,13174,13177,13249,13252,13324,13331,13333],[12,12518,775],{"id":12519},"integrál",[724,12521,12522,12523,12526,12527,12530],{},"Druhá polovina kalkulu jedné proměnné. Slouží k ",[38,12524,12525],{},"rekonstrukci totální veličiny z mezní"," (TR z MR, TC z MC) a k výpočtu ",[38,12528,12529],{},"přebytků"," (consumer\u002Fproducer surplus).",[115,12532,12534],{"id":12533},"neurčitý-integrál","Neurčitý integrál",[724,12536,12537],{},[883,12538,12540],{"className":12539},[886],[888,12541,12542],{"xmlns":890},[892,12543,12544,12577],{},[895,12545,12546,12548,12550,12552,12554,12556,12559,12561,12563,12565,12567,12569,12571,12573,12575],{},[898,12547,11824],{},[1677,12549,1686],{"stretchy":1685},[898,12551,1689],{},[1677,12553,1692],{"stretchy":1685},[1677,12555,1679],{},[1677,12557,12558],{},"∫",[898,12560,1682],{},[1677,12562,1686],{"stretchy":1685},[898,12564,1689],{},[1677,12566,1692],{"stretchy":1685},[1969,12568,2668],{},[898,12570,1875],{},[898,12572,1689],{},[1677,12574,1776],{},[898,12576,2458],{},[902,12578,12579],{"encoding":904},"F(x) = \\int f(x)\\, dx + C",[724,12581,5698,12582,2608,12616,9490,12629,12632,12633,1343,12646,12659],{},[883,12583,12585],{"className":12584},[886],[888,12586,12587],{"xmlns":890},[892,12588,12589,12613],{},[895,12590,12591,12597,12599,12601,12603,12605,12607,12609,12611],{},[1805,12592,12593,12595],{},[898,12594,11824],{},[1677,12596,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,12598,1686],{"stretchy":1685},[898,12600,1689],{},[1677,12602,1692],{"stretchy":1685},[1677,12604,1679],{},[898,12606,1682],{},[1677,12608,1686],{"stretchy":1685},[898,12610,1689],{},[1677,12612,1692],{"stretchy":1685},[902,12614,12615],{"encoding":904},"F'(x) = f(x)",[883,12617,12619],{"className":12618},[886],[888,12620,12621],{"xmlns":890},[892,12622,12623,12627],{},[895,12624,12625],{},[898,12626,11824],{},[902,12628,11824],{"encoding":904},[38,12630,12631],{},"primitivní funkce"," k ",[883,12634,12636],{"className":12635},[886],[888,12637,12638],{"xmlns":890},[892,12639,12640,12644],{},[895,12641,12642],{},[898,12643,1682],{},[902,12645,1682],{"encoding":904},[883,12647,12649],{"className":12648},[886],[888,12650,12651],{"xmlns":890},[892,12652,12653,12657],{},[895,12654,12655],{},[898,12656,2458],{},[902,12658,2458],{"encoding":904}," konstanta.",[115,12661,12663],{"id":12662},"určitý-integrál","Určitý integrál",[724,12665,12666],{},[883,12667,12669],{"className":12668},[886],[888,12670,12671],{"xmlns":890},[892,12672,12673,12737],{},[895,12674,12675,12683,12685,12687,12689,12691,12693,12695,12697,12699,12701,12703,12705,12707,12709,12717,12719,12721,12723,12725,12727,12729,12731,12733,12735],{},[10554,12676,12677,12679,12681],{},[1677,12678,12558],{},[898,12680,207],{},[898,12682,1779],{},[898,12684,1682],{},[1677,12686,1686],{"stretchy":1685},[898,12688,1689],{},[1677,12690,1692],{"stretchy":1685},[1969,12692,2668],{},[898,12694,1875],{},[898,12696,1689],{},[1677,12698,1679],{},[1677,12700,2167],{"stretchy":1685},[898,12702,11824],{},[1677,12704,1686],{"stretchy":1685},[898,12706,1689],{},[1677,12708,1692],{"stretchy":1685},[10554,12710,12711,12713,12715],{},[1677,12712,2182],{"stretchy":1685},[898,12714,207],{},[898,12716,1779],{},[1677,12718,1679],{},[898,12720,11824],{},[1677,12722,1686],{"stretchy":1685},[898,12724,1779],{},[1677,12726,1692],{"stretchy":1685},[1677,12728,1906],{},[898,12730,11824],{},[1677,12732,1686],{"stretchy":1685},[898,12734,207],{},[1677,12736,1692],{"stretchy":1685},[902,12738,12739],{"encoding":904},"\\int_a^b f(x)\\, dx = [F(x)]_a^b = F(b) - F(a)",[724,12741,12742,12743,1884,12746,12759,12760,12781],{},"Geometricky ",[38,12744,12745],{},"plocha pod grafem",[883,12747,12749],{"className":12748},[886],[888,12750,12751],{"xmlns":890},[892,12752,12753,12757],{},[895,12754,12755],{},[898,12756,1682],{},[902,12758,1682],{"encoding":904}," na intervalu ",[883,12761,12763],{"className":12762},[886],[888,12764,12765],{"xmlns":890},[892,12766,12767,12779],{},[895,12768,12769,12771,12773,12775,12777],{},[1677,12770,2167],{"stretchy":1685},[898,12772,207],{},[1677,12774,1967],{"separator":1966},[898,12776,1779],{},[1677,12778,2182],{"stretchy":1685},[902,12780,12212],{"encoding":904}," (orientovaná).",[724,12783,12784],{},[2240,12785],{"alt":12786,"className":12787,"src":12788},"imek-integral-plocha",[210,2244],"\u002Fwiki-assets\u002Fimek-integral-plocha.jpeg",[115,12790,12792],{"id":12791},"aplikace-v-ekonomii","Aplikace v ekonomii",[198,12794,12796],{"id":12795},"příklad-tr-z-mr","Příklad — TR z MR",[724,12798,12799,12800,1656],{},"Mezní příjem ",[883,12801,12803],{"className":12802},[886],[888,12804,12805],{"xmlns":890},[892,12806,12807,12823],{},[895,12808,12809,12811,12813,12815,12817,12819,12821],{},[898,12810,2499],{},[898,12812,5382],{},[1677,12814,1679],{},[1810,12816,2771],{},[1677,12818,1906],{},[1810,12820,1812],{},[898,12822,2470],{},[902,12824,12825],{"encoding":904},"MR = 100 - 2Q",[724,12827,12828],{},[883,12829,12831],{"className":12830},[886],[888,12832,12833],{"xmlns":890},[892,12834,12835,12881],{},[895,12836,12837,12839,12841,12843,12845,12847,12849,12851,12853,12855,12857,12859,12861,12863,12865,12867,12869,12871,12877,12879],{},[898,12838,2455],{},[898,12840,5382],{},[1677,12842,1679],{},[1677,12844,12558],{},[1677,12846,1686],{"stretchy":1685},[1810,12848,2771],{},[1677,12850,1906],{},[1810,12852,1812],{},[898,12854,2470],{},[1677,12856,1692],{"stretchy":1685},[1969,12858,2668],{},[898,12860,1875],{},[898,12862,2470],{},[1677,12864,1679],{},[1810,12866,2771],{},[898,12868,2470],{},[1677,12870,1906],{},[1805,12872,12873,12875],{},[898,12874,2470],{},[1810,12876,1812],{},[1677,12878,1776],{},[898,12880,1823],{},[902,12882,12883],{"encoding":904},"TR = \\int (100 - 2Q)\\, dQ = 100Q - Q^2 + c",[724,12885,12886,12887,3095,12913,2385],{},"Okrajová podmínka ",[883,12888,12890],{"className":12889},[886],[888,12891,12892],{"xmlns":890},[892,12893,12894,12910],{},[895,12895,12896,12898,12900,12902,12904,12906,12908],{},[898,12897,2455],{},[898,12899,5382],{},[1677,12901,1686],{"stretchy":1685},[1810,12903,2008],{},[1677,12905,1692],{"stretchy":1685},[1677,12907,1679],{},[1810,12909,2008],{},[902,12911,12912],{"encoding":904},"TR(0) = 0",[883,12914,12916],{"className":12915},[886],[888,12917,12918],{"xmlns":890},[892,12919,12920,12928],{},[895,12921,12922,12924,12926],{},[898,12923,1823],{},[1677,12925,1679],{},[1810,12927,2008],{},[902,12929,12930],{"encoding":904},"c = 0",[724,12932,12933],{},[883,12934,12936],{"className":12935},[886],[888,12937,12938],{"xmlns":890},[892,12939,12940,12966],{},[895,12941,12942,12944,12946,12948,12950,12952,12954,12956,12958,12960],{},[898,12943,2455],{},[898,12945,5382],{},[1677,12947,1686],{"stretchy":1685},[898,12949,2470],{},[1677,12951,1692],{"stretchy":1685},[1677,12953,1679],{},[1810,12955,2771],{},[898,12957,2470],{},[1677,12959,1906],{},[1805,12961,12962,12964],{},[898,12963,2470],{},[1810,12965,1812],{},[902,12967,12968],{"encoding":904},"TR(Q) = 100Q - Q^2",[198,12970,12972],{"id":12971},"příklad-tc-z-mc","Příklad — TC z MC",[724,12974,12975,12976,13002,13003,1656],{},"Mezní náklady ",[883,12977,12979],{"className":12978},[886],[888,12980,12981],{"xmlns":890},[892,12982,12983,12999],{},[895,12984,12985,12987,12989,12991,12993,12995,12997],{},[898,12986,2499],{},[898,12988,2458],{},[1677,12990,1679],{},[1810,12992,1812],{},[1677,12994,1776],{},[1810,12996,2520],{},[898,12998,2470],{},[902,13000,13001],{"encoding":904},"MC = 2 + 0{,}2 Q",", fixní náklady ",[883,13004,13006],{"className":13005},[886],[888,13007,13008],{"xmlns":890},[892,13009,13010,13020],{},[895,13011,13012,13014,13016,13018],{},[898,13013,11824],{},[898,13015,2458],{},[1677,13017,1679],{},[1810,13019,2771],{},[902,13021,13022],{"encoding":904},"FC = 100",[724,13024,13025],{},[883,13026,13028],{"className":13027},[886],[888,13029,13030],{"xmlns":890},[892,13031,13032,13072],{},[895,13033,13034,13036,13038,13040,13042,13044,13046,13048,13050,13052,13054,13056,13058,13060,13062,13068,13070],{},[898,13035,2455],{},[898,13037,2458],{},[1677,13039,1679],{},[1677,13041,12558],{},[898,13043,2499],{},[898,13045,2458],{},[1969,13047,2668],{},[898,13049,1875],{},[898,13051,2470],{},[1677,13053,1679],{},[1810,13055,1812],{},[898,13057,2470],{},[1677,13059,1776],{},[1810,13061,2475],{},[1805,13063,13064,13066],{},[898,13065,2470],{},[1810,13067,1812],{},[1677,13069,1776],{},[898,13071,1823],{},[902,13073,13074],{"encoding":904},"TC = \\int MC\\, dQ = 2Q + 0{,}1 Q^2 + c",[724,13076,12886,13077,3095,13109,2385],{},[883,13078,13080],{"className":13079},[886],[888,13081,13082],{"xmlns":890},[892,13083,13084,13106],{},[895,13085,13086,13088,13090,13092,13094,13096,13098,13100,13102,13104],{},[898,13087,2455],{},[898,13089,2458],{},[1677,13091,1686],{"stretchy":1685},[1810,13093,2008],{},[1677,13095,1692],{"stretchy":1685},[1677,13097,1679],{},[898,13099,11824],{},[898,13101,2458],{},[1677,13103,1679],{},[1810,13105,2771],{},[902,13107,13108],{"encoding":904},"TC(0) = FC = 100",[883,13110,13112],{"className":13111},[886],[888,13113,13114],{"xmlns":890},[892,13115,13116,13124],{},[895,13117,13118,13120,13122],{},[898,13119,1823],{},[1677,13121,1679],{},[1810,13123,2771],{},[902,13125,13126],{"encoding":904},"c = 100",[724,13128,13129],{},[883,13130,13132],{"className":13131},[886],[888,13133,13134],{"xmlns":890},[892,13135,13136,13168],{},[895,13137,13138,13140,13142,13144,13146,13148,13150,13152,13154,13156,13158,13160,13162],{},[898,13139,2455],{},[898,13141,2458],{},[1677,13143,1686],{"stretchy":1685},[898,13145,2470],{},[1677,13147,1692],{"stretchy":1685},[1677,13149,1679],{},[1810,13151,2771],{},[1677,13153,1776],{},[1810,13155,1812],{},[898,13157,2470],{},[1677,13159,1776],{},[1810,13161,2475],{},[1805,13163,13164,13166],{},[898,13165,2470],{},[1810,13167,1812],{},[902,13169,13170],{"encoding":904},"TC(Q) = 100 + 2Q + 0{,}1 Q^2",[198,13172,820],{"id":13173},"přebytek-spotřebitele-a-výrobce",[724,13175,13176],{},"Přebytek spotřebitele:",[724,13178,13179],{},[883,13180,13182],{"className":13181},[886],[888,13183,13184],{"xmlns":890},[892,13185,13186,13246],{},[895,13187,13188,13190,13192,13194,13200,13202,13204,13216,13218,13220,13222,13224,13226,13228,13230,13232,13238,13240],{},[898,13189,2458],{},[898,13191,10061],{},[1677,13193,1686],{"stretchy":1685},[1953,13195,13196,13198],{},[898,13197,2470],{},[1810,13199,2008],{},[1677,13201,1692],{"stretchy":1685},[1677,13203,1679],{},[10554,13205,13206,13208,13210],{},[1677,13207,12558],{},[1810,13209,2008],{},[1953,13211,13212,13214],{},[898,13213,2470],{},[1810,13215,2008],{},[898,13217,5571],{},[1677,13219,1686],{"stretchy":1685},[898,13221,2470],{},[1677,13223,1692],{"stretchy":1685},[1969,13225,2668],{},[898,13227,1875],{},[898,13229,2470],{},[1677,13231,1906],{},[1953,13233,13234,13236],{},[898,13235,5325],{},[1810,13237,2008],{},[1969,13239,2668],{},[1953,13241,13242,13244],{},[898,13243,2470],{},[1810,13245,2008],{},[902,13247,13248],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\, dQ - P_0\\, Q_0",[724,13250,13251],{},"Přebytek výrobce:",[724,13253,13254],{},[883,13255,13257],{"className":13256},[886],[888,13258,13259],{"xmlns":890},[892,13260,13261,13321],{},[895,13262,13263,13265,13267,13269,13275,13277,13279,13285,13287,13293,13295,13307,13309,13311,13313,13315,13317,13319],{},[898,13264,5325],{},[898,13266,10061],{},[1677,13268,1686],{"stretchy":1685},[1953,13270,13271,13273],{},[898,13272,2470],{},[1810,13274,2008],{},[1677,13276,1692],{"stretchy":1685},[1677,13278,1679],{},[1953,13280,13281,13283],{},[898,13282,5325],{},[1810,13284,2008],{},[1969,13286,2668],{},[1953,13288,13289,13291],{},[898,13290,2470],{},[1810,13292,2008],{},[1677,13294,1906],{},[10554,13296,13297,13299,13301],{},[1677,13298,12558],{},[1810,13300,2008],{},[1953,13302,13303,13305],{},[898,13304,2470],{},[1810,13306,2008],{},[898,13308,10061],{},[1677,13310,1686],{"stretchy":1685},[898,13312,2470],{},[1677,13314,1692],{"stretchy":1685},[1969,13316,2668],{},[898,13318,1875],{},[898,13320,2470],{},[902,13322,13323],{"encoding":904},"PS(Q_0) = P_0\\, Q_0 - \\int_0^{Q_0} S(Q)\\, dQ",[724,13325,13326,13327,1656],{},"Detailně viz ",[207,13328,13330],{"className":13329,"dataFsResolvedFilePath":800,"href":801},[210],"Poptávka a nabídka",[115,13332,3473],{"id":3472},[120,13334,13335,13342,13349],{},[123,13336,13337,1884,13339],{},[38,13338,3480],{},[207,13340,766],{"className":13341,"dataFsResolvedFilePath":764,"href":765},[210],[123,13343,13344,1884,13346],{},[38,13345,3488],{},[207,13347,784],{"className":13348,"dataFsResolvedFilePath":782,"href":783},[210],[123,13350,13351,1884,13353,13356,13357,13360],{},[38,13352,3496],{},[207,13354,3504],{"className":13355,"dataFsResolvedFilePath":827,"href":828},[210]," (TR\u002FTC), ",[207,13358,13330],{"className":13359,"dataFsResolvedFilePath":800,"href":801},[210]," (přebytky CS\u002FPS)",{"title":641,"searchDepth":642,"depth":642,"links":13362},[13363,13364,13365,13370],{"id":12533,"depth":642,"text":12534},{"id":12662,"depth":642,"text":12663},{"id":12791,"depth":642,"text":12792,"children":13366},[13367,13368,13369],{"id":12795,"depth":649,"text":12796},{"id":12971,"depth":649,"text":12972},{"id":13173,"depth":649,"text":820},{"id":3472,"depth":642,"text":3473},"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":13371},[1135],"topics\u002Fintegral",[1128,13378,13379,13380,13381,13382,13383],"integral","neurcity","urcity","primitivni-funkce","tr-z-mr","tc-z-mc","H1oOmn3Z5yZ_KZm1LLzfN_DVUhYSxx7eveFc7CASwZY",{"id":13386,"title":13387,"body":13388,"course":1128,"courses":659,"created":10944,"description":641,"extension":661,"meta":17657,"navigation":664,"path":17658,"seo":17659,"sources":17660,"stem":17661,"tags":17662,"type":3538,"updated":677,"__hash__":17668},"topics\u002Ftopics\u002Fis-lm.md","IS-LM analýza — simultánní rovnováha trhu zboží a peněz",{"type":9,"value":13389,"toc":17645},[13390,13393,13397,13541,13548,13552,13622,13660,13763,13767,13797,13863,13910,13913,13982,13985,14020,14056,14060,14108,14115,14161,14207,14210,14289,14386,14469,14473,14517,14547,14553,14582,14604,14654,14707,14773,14776,14842,14871,14930,14946,15033,15131,15262,15266,15423,15572,15952,15956,15959,16018,16021,16107,16135,16173,16176,16213,16253,16287,16289,16326,16358,16456,16461,16585,16637,16719,16858,16862,16982,16989,17100,17107,17111,17586,17588],[12,13391,13387],{"id":13392},"is-lm-analýza-simultánní-rovnováha-trhu-zboží-a-peněz",[115,13394,13396],{"id":13395},"tldr","TL;DR",[724,13398,13399,13402,13403,11413,13406,13419,13420,13434,13435,13438,13439,1343,13442,13445,13446,1343,13449,13452,13453,1884,13456,13486,13487,13490,13491,1343,13505,13518,13519,13522,13523,5306],{},[38,13400,13401],{},"IS-LM"," je makroekonomický model se ",[38,13404,13405],{},"dvěma neznámými",[883,13407,13409],{"className":13408},[886],[888,13410,13411],{"xmlns":890},[892,13412,13413,13417],{},[895,13414,13415],{},[898,13416,10516],{},[902,13418,10516],{"encoding":904}," — národní důchod a ",[883,13421,13423],{"className":13422},[886],[888,13424,13425],{"xmlns":890},[892,13426,13427,13432],{},[895,13428,13429],{},[898,13430,13431],{},"r",[902,13433,13431],{"encoding":904}," — úroková míra) a ",[38,13436,13437],{},"dvěma trhy",": trhem zboží (křivka ",[38,13440,13441],{},"IS",[614,13443,13444],{},"Investment = Savings",") a trhem peněz (křivka ",[38,13447,13448],{},"LM",[614,13450,13451],{},"Liquidity of Money","). Průsečík obou křivek určuje ",[38,13454,13455],{},"simultánní rovnováhu",[883,13457,13459],{"className":13458},[886],[888,13460,13461],{"xmlns":890},[892,13462,13463,13483],{},[895,13464,13465,13467,13473,13475,13481],{},[1677,13466,1686],{"stretchy":1685},[1805,13468,13469,13471],{},[898,13470,10516],{},[898,13472,5640],{},[1677,13474,1967],{"separator":1966},[1805,13476,13477,13479],{},[898,13478,13431],{},[898,13480,5640],{},[1677,13482,1692],{"stretchy":1685},[902,13484,13485],{"encoding":904},"(Y^E, r^E)",", v níž jsou oba trhy vyvážené zároveň. Model je klíčovým nástrojem pro analýzu ",[38,13488,13489],{},"fiskální politiky"," (posun IS změnou ",[883,13492,13494],{"className":13493},[886],[888,13495,13496],{"xmlns":890},[892,13497,13498,13503],{},[895,13499,13500],{},[898,13501,13502],{},"G",[902,13504,13502],{"encoding":904},[883,13506,13508],{"className":13507},[886],[888,13509,13510],{"xmlns":890},[892,13511,13512,13516],{},[895,13513,13514],{},[898,13515,2455],{},[902,13517,2455],{"encoding":904},") a ",[38,13520,13521],{},"monetární politiky"," (posun LM změnou nabídky peněz ",[883,13524,13526],{"className":13525},[886],[888,13527,13528],{"xmlns":890},[892,13529,13530,13538],{},[895,13531,13532],{},[1805,13533,13534,13536],{},[898,13535,2499],{},[1677,13537,5742],{},[902,13539,13540],{"encoding":904},"M^*",[724,13542,13543],{},[2240,13544],{"alt":13545,"className":13546,"src":13547},"imek-is-lm-model",[210,2244],"\u002Fwiki-assets\u002Fimek-is-lm-model.jpeg",[115,13549,13551],{"id":13550},"motivace-proč-přejít-od-c-i-g-x-k-is-lm","Motivace — proč přejít od C-I-G-X k IS-LM",[724,13553,13554,13555,13559,13560,11413,13563,13586,13587,13590,13591,13607,13608,13621],{},"V modelech ",[207,13556,13558],{"className":13557,"dataFsResolvedFilePath":934,"href":935},[210],"C-I, C-I-G a C-I-G-X"," byly ",[38,13561,13562],{},"investice pokládány za konstantní",[883,13564,13566],{"className":13565},[886],[888,13567,13568],{"xmlns":890},[892,13569,13570,13583],{},[895,13571,13572,13575,13577],{},[898,13573,13574],{},"I",[1677,13576,1679],{},[1805,13578,13579,13581],{},[898,13580,13574],{},[1677,13582,5742],{},[902,13584,13585],{"encoding":904},"I = I^*","). To není realistické — investice firem závisejí na ",[38,13588,13589],{},"ceně peněz",", tedy na ",[38,13592,13593,13594],{},"úrokové míře ",[883,13595,13597],{"className":13596},[886],[888,13598,13599],{"xmlns":890},[892,13600,13601,13605],{},[895,13602,13603],{},[898,13604,13431],{},[902,13606,13431],{"encoding":904},": čím vyšší ",[883,13609,13611],{"className":13610},[886],[888,13612,13613],{"xmlns":890},[892,13614,13615,13619],{},[895,13616,13617],{},[898,13618,13431],{},[902,13620,13431],{"encoding":904},", tím dražší úvěr a tím méně investic. IS-LM analýza proto zavádí:",[120,13623,13624,13654],{},[123,13625,13626,1884,13629,13653],{},[38,13627,13628],{},"funkci investic",[883,13630,13632],{"className":13631},[886],[888,13633,13634],{"xmlns":890},[892,13635,13636,13650],{},[895,13637,13638,13640,13642,13644,13646,13648],{},[898,13639,13574],{},[1677,13641,1679],{},[898,13643,13574],{},[1677,13645,1686],{"stretchy":1685},[898,13647,13431],{},[1677,13649,1692],{"stretchy":1685},[902,13651,13652],{"encoding":904},"I = I(r)"," jako klesající funkci úrokové míry,",[123,13655,13656,13659],{},[38,13657,13658],{},"trh peněz",", jehož rovnováha (poptávka = nabídka peněz) doplňuje druhou rovnici potřebnou pro určení obou neznámých.",[5254,13661,13662],{},[724,13663,13664,13666,13667,13686,13687,13714,13715,13728,13729,13758,13759,13762],{},[883,13665,5800],{}," Pozor — dvě neznámé vyžadují dvě rovnice\nV modelech ",[883,13668,13670],{"className":13669},[886],[888,13671,13672],{"xmlns":890},[892,13673,13674,13683],{},[895,13675,13676,13678,13681],{},[898,13677,2458],{},[1969,13679,13680],{},"-",[898,13682,13574],{},[902,13684,13685],{"encoding":904},"C\\text{-}I"," až ",[883,13688,13690],{"className":13689},[886],[888,13691,13692],{"xmlns":890},[892,13693,13694,13711],{},[895,13695,13696,13698,13700,13702,13704,13706,13708],{},[898,13697,2458],{},[1969,13699,13680],{},[898,13701,13574],{},[1969,13703,13680],{},[898,13705,13502],{},[1969,13707,13680],{},[898,13709,13710],{},"X",[902,13712,13713],{"encoding":904},"C\\text{-}I\\text{-}G\\text{-}X"," byla hlavní neznámou jen ",[883,13716,13718],{"className":13717},[886],[888,13719,13720],{"xmlns":890},[892,13721,13722,13726],{},[895,13723,13724],{},[898,13725,10516],{},[902,13727,10516],{"encoding":904},". V IS-LM jsou ",[38,13730,13731,13732,5272,13745],{},"dvě neznámé ",[883,13733,13735],{"className":13734},[886],[888,13736,13737],{"xmlns":890},[892,13738,13739,13743],{},[895,13740,13741],{},[898,13742,10516],{},[902,13744,10516],{"encoding":904},[883,13746,13748],{"className":13747},[886],[888,13749,13750],{"xmlns":890},[892,13751,13752,13756],{},[895,13753,13754],{},[898,13755,13431],{},[902,13757,13431],{"encoding":904},", a proto potřebujeme ",[38,13760,13761],{},"dvě rovnice",": jednu z trhu zboží (křivka IS) a jednu z trhu peněz (křivka LM).",[115,13764,13766],{"id":13765},"funkce-investic-a-funkce-spotřeby","Funkce investic a funkce spotřeby",[724,13768,13769,13770,13783,13784,2385],{},"Lineární závislost investic ",[883,13771,13773],{"className":13772},[886],[888,13774,13775],{"xmlns":890},[892,13776,13777,13781],{},[895,13778,13779],{},[898,13780,13574],{},[902,13782,13574],{"encoding":904}," na úrokové míře ",[883,13785,13787],{"className":13786},[886],[888,13788,13789],{"xmlns":890},[892,13790,13791,13795],{},[895,13792,13793],{},[898,13794,13431],{},[902,13796,13431],{"encoding":904},[724,13798,13799],{},[883,13800,13802],{"className":13801},[886],[888,13803,13804],{"xmlns":890},[892,13805,13806,13860],{},[895,13807,13808,13810,13812,13814,13816,13818,13820,13822,13824,13826,13828,13830,13832,13834,13836,13838,13840,13842,13844,13846,13848,13851,13853,13855,13858],{},[898,13809,13574],{},[1677,13811,1679],{},[898,13813,13574],{},[1677,13815,1686],{"stretchy":1685},[898,13817,13431],{},[1677,13819,1692],{"stretchy":1685},[1677,13821,1679],{},[898,13823,1823],{},[898,13825,13431],{},[1677,13827,1776],{},[898,13829,1875],{},[1677,13831,1967],{"separator":1966},[7266,13833],{"width":7268},[898,13835,1823],{},[1677,13837,3128],{},[1810,13839,2008],{},[1677,13841,1967],{"separator":1966},[1969,13843,1971],{},[898,13845,1875],{},[1677,13847,3089],{},[1810,13849,13850],{},"0.",[7266,13852],{"width":7268},[1677,13854,1686],{"stretchy":1685},[1810,13856,13857],{},"7.11",[1677,13859,1692],{"stretchy":1685},[902,13861,13862],{"encoding":904},"I = I(r) = cr + d, \\qquad c \u003C 0,\\ d > 0. \\qquad (7.11)",[120,13864,13865,13886],{},[123,13866,13867,13885],{},[883,13868,13870],{"className":13869},[886],[888,13871,13872],{"xmlns":890},[892,13873,13874,13882],{},[895,13875,13876,13878,13880],{},[898,13877,1875],{},[1677,13879,3089],{},[1810,13881,2008],{},[902,13883,13884],{"encoding":904},"d > 0"," zřejmé,",[123,13887,13888,13906,13907,1656],{},[883,13889,13891],{"className":13890},[886],[888,13892,13893],{"xmlns":890},[892,13894,13895,13903],{},[895,13896,13897,13899,13901],{},[898,13898,1823],{},[1677,13900,3128],{},[1810,13902,2008],{},[902,13904,13905],{"encoding":904},"c \u003C 0",", protože růst úrokové míry tlumí investice — funkce investic je ",[38,13908,13909],{},"klesající",[724,13911,13912],{},"Spotřeba zůstává lineární funkcí důchodu:",[724,13914,13915],{},[883,13916,13918],{"className":13917},[886],[888,13919,13920],{"xmlns":890},[892,13921,13922,13979],{},[895,13923,13924,13926,13928,13930,13932,13934,13936,13938,13940,13942,13944,13946,13948,13950,13952,13954,13956,13958,13960,13962,13964,13966,13968,13970,13972,13974,13977],{},[898,13925,2458],{},[1677,13927,1679],{},[898,13929,2458],{},[1677,13931,1686],{"stretchy":1685},[898,13933,10516],{},[1677,13935,1692],{"stretchy":1685},[1677,13937,1679],{},[898,13939,207],{},[898,13941,10516],{},[1677,13943,1776],{},[898,13945,1779],{},[1677,13947,1967],{"separator":1966},[7266,13949],{"width":7268},[1810,13951,2008],{},[1677,13953,3128],{},[898,13955,207],{},[1677,13957,3128],{},[1810,13959,1959],{},[1677,13961,1967],{"separator":1966},[1969,13963,1971],{},[898,13965,1779],{},[1677,13967,3089],{},[1810,13969,13850],{},[7266,13971],{"width":7268},[1677,13973,1686],{"stretchy":1685},[1810,13975,13976],{},"7.12",[1677,13978,1692],{"stretchy":1685},[902,13980,13981],{"encoding":904},"C = C(Y) = aY + b, \\qquad 0 \u003C a \u003C 1,\\ b > 0. \\qquad (7.12)",[724,13983,13984],{},"Podmínka rovnováhy na trhu zboží:",[724,13986,13987],{},[883,13988,13990],{"className":13989},[886],[888,13991,13992],{"xmlns":890},[892,13993,13994,14017],{},[895,13995,13996,13998,14000,14002,14004,14006,14008,14010,14012,14015],{},[898,13997,10516],{},[1677,13999,1679],{},[898,14001,2458],{},[1677,14003,1776],{},[898,14005,13574],{},[898,14007,1656],{"mathvariant":2057},[7266,14009],{"width":7268},[1677,14011,1686],{"stretchy":1685},[1810,14013,14014],{},"7.13",[1677,14016,1692],{"stretchy":1685},[902,14018,14019],{"encoding":904},"Y = C + I. \\qquad (7.13)",[724,14021,14022,14023,1884,14026,14052,14053,1656],{},"To dává ",[38,14024,14025],{},"tři rovnice o čtyřech neznámých",[883,14027,14029],{"className":14028},[886],[888,14030,14031],{"xmlns":890},[892,14032,14033,14049],{},[895,14034,14035,14037,14039,14041,14043,14045,14047],{},[898,14036,10516],{},[1677,14038,1967],{"separator":1966},[898,14040,2458],{},[1677,14042,1967],{"separator":1966},[898,14044,13574],{},[1677,14046,1967],{"separator":1966},[898,14048,13431],{},[902,14050,14051],{"encoding":904},"Y, C, I, r",". Pro jednoznačné určení rovnováhy potřebujeme čtvrtou rovnici — odvodí se z ",[38,14054,14055],{},"rovnováhy na trhu peněz",[115,14057,14059],{"id":14058},"křivka-is-rovnováha-na-trhu-zboží","Křivka IS — rovnováha na trhu zboží",[724,14061,14062,14063,6957,14085,14103,14104,14107],{},"Podmínka (7.13) reprezentuje rovnováhu na trhu zboží, protože s ohledem na ",[883,14064,14066],{"className":14065},[886],[888,14067,14068],{"xmlns":890},[892,14069,14070,14082],{},[895,14071,14072,14074,14076,14078,14080],{},[898,14073,10516],{},[1677,14075,1679],{},[898,14077,2458],{},[1677,14079,1776],{},[898,14081,10061],{},[902,14083,14084],{"encoding":904},"Y = C + S",[883,14086,14088],{"className":14087},[886],[888,14089,14090],{"xmlns":890},[892,14091,14092,14100],{},[895,14093,14094,14096,14098],{},[898,14095,13574],{},[1677,14097,1679],{},[898,14099,10061],{},[902,14101,14102],{"encoding":904},"I = S"," (plánované ",[38,14105,14106],{},"investice = úspory","). Dosazením (7.11) a (7.12) do (7.13):",[724,14109,14110],{},[2240,14111],{"alt":14112,"className":14113,"src":14114},"imek-odvozeni-is-4panelu",[210,2244],"\u002Fwiki-assets\u002Fimek-odvozeni-is-4panelu.jpeg",[724,14116,14117],{},[883,14118,14120],{"className":14119},[886],[888,14121,14122],{"xmlns":890},[892,14123,14124,14158],{},[895,14125,14126,14128,14130,14132,14134,14136,14138,14140,14142,14144,14146,14148,14150,14152,14154,14156],{},[898,14127,10516],{},[1677,14129,1679],{},[1677,14131,1686],{"stretchy":1685},[898,14133,207],{},[898,14135,10516],{},[1677,14137,1776],{},[898,14139,1779],{},[1677,14141,1692],{"stretchy":1685},[1677,14143,1776],{},[1677,14145,1686],{"stretchy":1685},[898,14147,1823],{},[898,14149,13431],{},[1677,14151,1776],{},[898,14153,1875],{},[1677,14155,1692],{"stretchy":1685},[1677,14157,1967],{"separator":1966},[902,14159,14160],{"encoding":904},"Y = (aY + b) + (cr + d),",[724,14162,14163],{},[883,14164,14166],{"className":14165},[886],[888,14167,14168],{"xmlns":890},[892,14169,14170,14204],{},[895,14171,14172,14174,14176,14178,14180,14182,14184,14186,14188,14190,14192,14194,14196,14198,14200,14202],{},[1677,14173,1686],{"stretchy":1685},[1810,14175,1959],{},[1677,14177,1906],{},[898,14179,207],{},[1677,14181,1692],{"stretchy":1685},[898,14183,10516],{},[1677,14185,1906],{},[898,14187,1823],{},[898,14189,13431],{},[1677,14191,1906],{},[898,14193,1779],{},[1677,14195,1906],{},[898,14197,1875],{},[1677,14199,1679],{},[1810,14201,2008],{},[1677,14203,1967],{"separator":1966},[902,14205,14206],{"encoding":904},"(1 - a)Y - cr - b - d = 0,",[724,14208,14209],{},"odkud",[724,14211,14212],{},[883,14213,14215],{"className":14214},[886],[888,14216,14217],{"xmlns":890},[892,14218,14219,14286],{},[895,14220,14221,14277,14279,14281,14284],{},[14222,14223,14225],"menclose",{"notation":14224},"box",[2006,14226,14227],{"scriptlevel":2008,"displaystyle":1685},[2006,14228,14229],{"scriptlevel":2008,"displaystyle":1685},[2006,14230,14231],{"scriptlevel":2008,"displaystyle":1966},[895,14232,14233,14235,14237,14239,14251,14253,14255,14257,14275],{},[1969,14234,2668],{},[898,14236,10516],{},[1677,14238,1679],{},[2010,14240,14241,14243],{},[898,14242,1823],{},[895,14244,14245,14247,14249],{},[1810,14246,1959],{},[1677,14248,1906],{},[898,14250,207],{},[1969,14252,2668],{},[898,14254,13431],{},[1677,14256,1776],{},[2010,14258,14259,14267],{},[895,14260,14261,14263,14265],{},[898,14262,1779],{},[1677,14264,1776],{},[898,14266,1875],{},[895,14268,14269,14271,14273],{},[1810,14270,1959],{},[1677,14272,1906],{},[898,14274,207],{},[1969,14276,2668],{},[7266,14278],{"width":7268},[1677,14280,1686],{"stretchy":1685},[1810,14282,14283],{},"7.14",[1677,14285,1692],{"stretchy":1685},[902,14287,14288],{"encoding":904},"\\boxed{\\,Y = \\frac{c}{1 - a}\\,r + \\frac{b + d}{1 - a}\\,} \\qquad (7.14)",[724,14290,14291,14292,11413,14295,14298,14299,14302,14303,14305,14306,14328,14329,14357,14358,14379,14380,14382,14383,14385],{},"Tento vztah se nazývá ",[38,14293,14294],{},"funkce IS",[614,14296,14297],{},"IS schedule",") a její graf ",[38,14300,14301],{},"křivka IS",". Křivka je ",[38,14304,13909],{}," přímka v rovině ",[883,14307,14309],{"className":14308},[886],[888,14310,14311],{"xmlns":890},[892,14312,14313,14325],{},[895,14314,14315,14317,14319,14321,14323],{},[1677,14316,1686],{"stretchy":1685},[898,14318,13431],{},[1677,14320,1967],{"separator":1966},[898,14322,10516],{},[1677,14324,1692],{"stretchy":1685},[902,14326,14327],{"encoding":904},"(r, Y)",", neboť ",[883,14330,14332],{"className":14331},[886],[888,14333,14334],{"xmlns":890},[892,14335,14336,14354],{},[895,14337,14338,14350,14352],{},[2010,14339,14340,14342],{},[898,14341,1823],{},[895,14343,14344,14346,14348],{},[1810,14345,1959],{},[1677,14347,1906],{},[898,14349,207],{},[1677,14351,3128],{},[1810,14353,2008],{},[902,14355,14356],{"encoding":904},"\\frac{c}{1-a} \u003C 0"," (čitatel záporný, jmenovatel kladný). Název vyjadřuje, že křivka popisuje ty kombinace ",[883,14359,14361],{"className":14360},[886],[888,14362,14363],{"xmlns":890},[892,14364,14365,14377],{},[895,14366,14367,14369,14371,14373,14375],{},[1677,14368,1686],{"stretchy":1685},[898,14370,13431],{},[1677,14372,1967],{"separator":1966},[898,14374,10516],{},[1677,14376,1692],{"stretchy":1685},[902,14378,14327],{"encoding":904},", pro které plánované ",[38,14381,13574],{},"nvestment = ",[38,14384,10061],{},"avings.",[5254,14387,14388],{},[724,14389,14390,14392,14393,14406,14407,1884,14410,14423,14424,14437,14438,5272,14451,14464,14465,14468],{},[883,14391,5543],{}," Intuice — proč IS klesá\nNižší úroková míra ",[883,14394,14396],{"className":14395},[886],[888,14397,14398],{"xmlns":890},[892,14399,14400,14404],{},[895,14401,14402],{},[898,14403,13431],{},[902,14405,13431],{"encoding":904}," → levnější úvěr → ",[38,14408,14409],{},"více investic",[883,14411,14413],{"className":14412},[886],[888,14414,14415],{"xmlns":890},[892,14416,14417,14421],{},[895,14418,14419],{},[898,14420,13574],{},[902,14422,13574],{"encoding":904}," → vyšší agregátní poptávka → vyšší rovnovážný důchod ",[883,14425,14427],{"className":14426},[886],[888,14428,14429],{"xmlns":890},[892,14430,14431,14435],{},[895,14432,14433],{},[898,14434,10516],{},[902,14436,10516],{"encoding":904},". Vztah mezi ",[883,14439,14441],{"className":14440},[886],[888,14442,14443],{"xmlns":890},[892,14444,14445,14449],{},[895,14446,14447],{},[898,14448,13431],{},[902,14450,13431],{"encoding":904},[883,14452,14454],{"className":14453},[886],[888,14455,14456],{"xmlns":890},[892,14457,14458,14462],{},[895,14459,14460],{},[898,14461,10516],{},[902,14463,10516],{"encoding":904}," na trhu zboží je proto ",[38,14466,14467],{},"nepřímý"," (klesající křivka).",[115,14470,14472],{"id":14471},"křivka-lm-rovnováha-na-trhu-peněz","Křivka LM — rovnováha na trhu peněz",[724,14474,14475,14476,14494,14495,2608,14513,14516],{},"Rovnováha na trhu peněz: poptávka po penězích ",[883,14477,14479],{"className":14478},[886],[888,14480,14481],{"xmlns":890},[892,14482,14483,14491],{},[895,14484,14485],{},[1805,14486,14487,14489],{},[898,14488,2499],{},[898,14490,5571],{},[902,14492,14493],{"encoding":904},"M^D"," se rovná nabídce peněz ",[883,14496,14498],{"className":14497},[886],[888,14499,14500],{"xmlns":890},[892,14501,14502,14510],{},[895,14503,14504],{},[1805,14505,14506,14508],{},[898,14507,2499],{},[898,14509,10061],{},[902,14511,14512],{"encoding":904},"M^S",[38,14514,14515],{},"Nabídka"," je pod kontrolou národní banky a je pevně zadána:",[724,14518,14519],{},[883,14520,14522],{"className":14521},[886],[888,14523,14524],{"xmlns":890},[892,14525,14526,14544],{},[895,14527,14528,14534,14536,14542],{},[1805,14529,14530,14532],{},[898,14531,2499],{},[898,14533,10061],{},[1677,14535,1679],{},[1805,14537,14538,14540],{},[898,14539,2499],{},[1677,14541,5742],{},[898,14543,1656],{"mathvariant":2057},[902,14545,14546],{"encoding":904},"M^S = M^*.",[724,14548,14549,14552],{},[38,14550,14551],{},"Poptávka"," po penězích má tři zdroje:",[120,14554,14555,14564,14573],{},[123,14556,14557,11413,14560,14563],{},[38,14558,14559],{},"transakční poptávka",[614,14561,14562],{},"transactions demand",") — peníze pro nákup zboží,",[123,14565,14566,11413,14569,14572],{},[38,14567,14568],{},"opatrnostní poptávka",[614,14570,14571],{},"precautionary demand",") — peníze pro nenadálé výdaje,",[123,14574,14575,11413,14578,14581],{},[38,14576,14577],{},"spekulační poptávka",[614,14579,14580],{},"speculative demand",") — peníze pro zhodnocení (akcie, obligace).",[724,14583,14584,14585,14603],{},"Součet transakční a opatrnostní poptávky ",[883,14586,14588],{"className":14587},[886],[888,14589,14590],{"xmlns":890},[892,14591,14592,14600],{},[895,14593,14594],{},[1953,14595,14596,14598],{},[898,14597,11183],{},[1810,14599,1959],{},[902,14601,14602],{"encoding":904},"L_1"," je úměrný důchodu:",[724,14605,14606],{},[883,14607,14609],{"className":14608},[886],[888,14610,14611],{"xmlns":890},[892,14612,14613,14651],{},[895,14614,14615,14621,14623,14630,14632,14634,14636,14638,14640,14646,14648],{},[1953,14616,14617,14619],{},[898,14618,11183],{},[1810,14620,1959],{},[1677,14622,1679],{},[1953,14624,14625,14628],{},[898,14626,14627],{},"k",[1810,14629,1959],{},[898,14631,10516],{},[1677,14633,1967],{"separator":1966},[7266,14635],{"width":7268},[1810,14637,2008],{},[1677,14639,3128],{},[1953,14641,14642,14644],{},[898,14643,14627],{},[1810,14645,1959],{},[1677,14647,3128],{},[1810,14649,14650],{},"1.",[902,14652,14653],{"encoding":904},"L_1 = k_1 Y, \\qquad 0 \u003C k_1 \u003C 1.",[724,14655,14656,14657,14675,14676,1343,14689,14706],{},"Spekulační poptávka ",[883,14658,14660],{"className":14659},[886],[888,14661,14662],{"xmlns":890},[892,14663,14664,14672],{},[895,14665,14666],{},[1953,14667,14668,14670],{},[898,14669,11183],{},[1810,14671,1812],{},[902,14673,14674],{"encoding":904},"L_2"," závisí na úrokové míře (roste-li ",[883,14677,14679],{"className":14678},[886],[888,14680,14681],{"xmlns":890},[892,14682,14683,14687],{},[895,14684,14685],{},[898,14686,13431],{},[902,14688,13431],{"encoding":904},[883,14690,14692],{"className":14691},[886],[888,14693,14694],{"xmlns":890},[892,14695,14696,14704],{},[895,14697,14698],{},[1953,14699,14700,14702],{},[898,14701,11183],{},[1810,14703,1812],{},[902,14705,14674],{"encoding":904}," klesá, protože vyšší výnos obligací snižuje atraktivitu držby peněz):",[724,14708,14709],{},[883,14710,14712],{"className":14711},[886],[888,14713,14714],{"xmlns":890},[892,14715,14716,14770],{},[895,14717,14718,14724,14726,14732,14734,14736,14742,14744,14746,14752,14754,14756,14758,14760,14766,14768],{},[1953,14719,14720,14722],{},[898,14721,11183],{},[1810,14723,1812],{},[1677,14725,1679],{},[1953,14727,14728,14730],{},[898,14729,14627],{},[1810,14731,1812],{},[898,14733,13431],{},[1677,14735,1776],{},[1953,14737,14738,14740],{},[898,14739,14627],{},[1810,14741,1854],{},[1677,14743,1967],{"separator":1966},[7266,14745],{"width":7268},[1953,14747,14748,14750],{},[898,14749,14627],{},[1810,14751,1812],{},[1677,14753,3128],{},[1810,14755,2008],{},[1677,14757,1967],{"separator":1966},[1969,14759,1971],{},[1953,14761,14762,14764],{},[898,14763,14627],{},[1810,14765,1854],{},[1677,14767,3089],{},[1810,14769,13850],{},[902,14771,14772],{"encoding":904},"L_2 = k_2 r + k_3, \\qquad k_2 \u003C 0,\\ k_3 > 0.",[724,14774,14775],{},"Celková poptávka po penězích:",[724,14777,14778],{},[883,14779,14781],{"className":14780},[886],[888,14782,14783],{"xmlns":890},[892,14784,14785,14839],{},[895,14786,14787,14793,14795,14801,14803,14809,14811,14817,14819,14821,14827,14829,14831,14837],{},[1805,14788,14789,14791],{},[898,14790,2499],{},[898,14792,5571],{},[1677,14794,1679],{},[1953,14796,14797,14799],{},[898,14798,11183],{},[1810,14800,1959],{},[1677,14802,1776],{},[1953,14804,14805,14807],{},[898,14806,11183],{},[1810,14808,1812],{},[1677,14810,1679],{},[1953,14812,14813,14815],{},[898,14814,14627],{},[1810,14816,1959],{},[898,14818,10516],{},[1677,14820,1776],{},[1953,14822,14823,14825],{},[898,14824,14627],{},[1810,14826,1812],{},[898,14828,13431],{},[1677,14830,1776],{},[1953,14832,14833,14835],{},[898,14834,14627],{},[1810,14836,1854],{},[898,14838,1656],{"mathvariant":2057},[902,14840,14841],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3.",[724,14843,14844,14845,2385],{},"Podmínka rovnováhy na trhu peněz ",[883,14846,14848],{"className":14847},[886],[888,14849,14850],{"xmlns":890},[892,14851,14852,14868],{},[895,14853,14854,14860,14862],{},[1805,14855,14856,14858],{},[898,14857,2499],{},[898,14859,5571],{},[1677,14861,1679],{},[1805,14863,14864,14866],{},[898,14865,2499],{},[1677,14867,5742],{},[902,14869,14870],{"encoding":904},"M^D = M^*",[724,14872,14873],{},[883,14874,14876],{"className":14875},[886],[888,14877,14878],{"xmlns":890},[892,14879,14880,14927],{},[895,14881,14882,14888,14890,14896,14898,14900,14906,14908,14910,14916,14918,14920,14922,14925],{},[1805,14883,14884,14886],{},[898,14885,2499],{},[1677,14887,5742],{},[1677,14889,1679],{},[1953,14891,14892,14894],{},[898,14893,14627],{},[1810,14895,1959],{},[898,14897,10516],{},[1677,14899,1776],{},[1953,14901,14902,14904],{},[898,14903,14627],{},[1810,14905,1812],{},[898,14907,13431],{},[1677,14909,1776],{},[1953,14911,14912,14914],{},[898,14913,14627],{},[1810,14915,1854],{},[1677,14917,1967],{"separator":1966},[7266,14919],{"width":7268},[1677,14921,1686],{"stretchy":1685},[1810,14923,14924],{},"7.15",[1677,14926,1692],{"stretchy":1685},[902,14928,14929],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3, \\qquad (7.15)",[724,14931,14932,14933,2832],{},"po úpravě (vyjádření ",[883,14934,14936],{"className":14935},[886],[888,14937,14938],{"xmlns":890},[892,14939,14940,14944],{},[895,14941,14942],{},[898,14943,10516],{},[902,14945,10516],{"encoding":904},[724,14947,14948],{},[883,14949,14951],{"className":14950},[886],[888,14952,14953],{"xmlns":890},[892,14954,14955,15030],{},[895,14956,14957,15021,15023,15025,15028],{},[14222,14958,14959],{"notation":14224},[2006,14960,14961],{"scriptlevel":2008,"displaystyle":1685},[2006,14962,14963],{"scriptlevel":2008,"displaystyle":1685},[2006,14964,14965],{"scriptlevel":2008,"displaystyle":1966},[895,14966,14967,14969,14971,14973,14975,14989,14991,14993,14995,15019],{},[1969,14968,2668],{},[898,14970,10516],{},[1677,14972,1679],{},[1677,14974,1906],{},[2010,14976,14977,14983],{},[1953,14978,14979,14981],{},[898,14980,14627],{},[1810,14982,1812],{},[1953,14984,14985,14987],{},[898,14986,14627],{},[1810,14988,1959],{},[1969,14990,2668],{},[898,14992,13431],{},[1677,14994,1776],{},[2010,14996,14997,15013],{},[895,14998,14999,15005,15007],{},[1805,15000,15001,15003],{},[898,15002,2499],{},[1677,15004,5742],{},[1677,15006,1906],{},[1953,15008,15009,15011],{},[898,15010,14627],{},[1810,15012,1854],{},[1953,15014,15015,15017],{},[898,15016,14627],{},[1810,15018,1959],{},[1969,15020,2668],{},[7266,15022],{"width":7268},[1677,15024,1686],{"stretchy":1685},[1810,15026,15027],{},"7.16",[1677,15029,1692],{"stretchy":1685},[902,15031,15032],{"encoding":904},"\\boxed{\\,Y = -\\frac{k_2}{k_1}\\,r + \\frac{M^* - k_3}{k_1}\\,} \\qquad (7.16)",[724,15034,14291,15035,11413,15038,15041,15042,14302,15045,14305,15048,14328,15069,15101,15102,15124,15125,15127,15128,15130],{},[38,15036,15037],{},"funkce LM",[614,15039,15040],{},"LM schedule","), její graf ",[38,15043,15044],{},"křivka LM",[38,15046,15047],{},"rostoucí",[883,15049,15051],{"className":15050},[886],[888,15052,15053],{"xmlns":890},[892,15054,15055,15067],{},[895,15056,15057,15059,15061,15063,15065],{},[1677,15058,1686],{"stretchy":1685},[898,15060,13431],{},[1677,15062,1967],{"separator":1966},[898,15064,10516],{},[1677,15066,1692],{"stretchy":1685},[902,15068,14327],{"encoding":904},[883,15070,15072],{"className":15071},[886],[888,15073,15074],{"xmlns":890},[892,15075,15076,15098],{},[895,15077,15078,15080,15094,15096],{},[1677,15079,1906],{},[2010,15081,15082,15088],{},[1953,15083,15084,15086],{},[898,15085,14627],{},[1810,15087,1812],{},[1953,15089,15090,15092],{},[898,15091,14627],{},[1810,15093,1959],{},[1677,15095,3089],{},[1810,15097,2008],{},[902,15099,15100],{"encoding":904},"-\\frac{k_2}{k_1} > 0"," (čitatel kladný, protože ",[883,15103,15105],{"className":15104},[886],[888,15106,15107],{"xmlns":890},[892,15108,15109,15121],{},[895,15110,15111,15117,15119],{},[1953,15112,15113,15115],{},[898,15114,14627],{},[1810,15116,1812],{},[1677,15118,3128],{},[1810,15120,2008],{},[902,15122,15123],{"encoding":904},"k_2 \u003C 0",", jmenovatel kladný). Název: ",[38,15126,11183],{},"iquidity of ",[38,15129,2499],{},"oney.",[5254,15132,15133],{},[724,15134,15135,15137,15138,15151,15152,15180,15181,15198,15199,15212,15213,15230,15231,5272,15244,15257,15258,15261],{},[883,15136,5543],{}," Intuice — proč LM roste\nVyšší důchod ",[883,15139,15141],{"className":15140},[886],[888,15142,15143],{"xmlns":890},[892,15144,15145,15149],{},[895,15146,15147],{},[898,15148,10516],{},[902,15150,10516],{"encoding":904}," → větší transakční poptávka po penězích ",[883,15153,15155],{"className":15154},[886],[888,15156,15157],{"xmlns":890},[892,15158,15159,15177],{},[895,15160,15161,15167,15169,15175],{},[1953,15162,15163,15165],{},[898,15164,11183],{},[1810,15166,1959],{},[1677,15168,1679],{},[1953,15170,15171,15173],{},[898,15172,14627],{},[1810,15174,1959],{},[898,15176,10516],{},[902,15178,15179],{"encoding":904},"L_1 = k_1 Y"," → při pevné nabídce ",[883,15182,15184],{"className":15183},[886],[888,15185,15186],{"xmlns":890},[892,15187,15188,15196],{},[895,15189,15190],{},[1805,15191,15192,15194],{},[898,15193,2499],{},[1677,15195,5742],{},[902,15197,13540],{"encoding":904}," vzniká na trhu peněz přebytek poptávky → úroková míra ",[883,15200,15202],{"className":15201},[886],[888,15203,15204],{"xmlns":890},[892,15205,15206,15210],{},[895,15207,15208],{},[898,15209,13431],{},[902,15211,13431],{"encoding":904}," musí vzrůst, aby se spekulační poptávka ",[883,15214,15216],{"className":15215},[886],[888,15217,15218],{"xmlns":890},[892,15219,15220,15228],{},[895,15221,15222],{},[1953,15223,15224,15226],{},[898,15225,11183],{},[1810,15227,1812],{},[902,15229,14674],{"encoding":904}," stlačila a trh se vyrovnal. Vztah mezi ",[883,15232,15234],{"className":15233},[886],[888,15235,15236],{"xmlns":890},[892,15237,15238,15242],{},[895,15239,15240],{},[898,15241,10516],{},[902,15243,10516],{"encoding":904},[883,15245,15247],{"className":15246},[886],[888,15248,15249],{"xmlns":890},[892,15250,15251,15255],{},[895,15252,15253],{},[898,15254,13431],{},[902,15256,13431],{"encoding":904}," na trhu peněz je proto ",[38,15259,15260],{},"přímý"," (rostoucí křivka).",[115,15263,15265],{"id":15264},"simultánní-rovnováha-is-lm","Simultánní rovnováha IS-LM",[724,15267,15268,15269,15272,15273,1884,15276,5272,15294,1884,15297,15315,15316,15334,15335,15353,15354,15370,15371,5272,15386,15401,15402,1656],{},"Řešením ",[38,15270,15271],{},"soustavy dvou lineárních rovnic"," (7.14) a (7.15) určíme ",[38,15274,15275],{},"rovnovážný důchod",[883,15277,15279],{"className":15278},[886],[888,15280,15281],{"xmlns":890},[892,15282,15283,15291],{},[895,15284,15285],{},[1805,15286,15287,15289],{},[898,15288,10516],{},[898,15290,5640],{},[902,15292,15293],{"encoding":904},"Y^E",[38,15295,15296],{},"rovnovážnou úrokovou míru",[883,15298,15300],{"className":15299},[886],[888,15301,15302],{"xmlns":890},[892,15303,15304,15312],{},[895,15305,15306],{},[1805,15307,15308,15310],{},[898,15309,13431],{},[898,15311,5640],{},[902,15313,15314],{"encoding":904},"r^E","; zpětným dosazením do (7.11) a (7.12) pak rovnovážné investice ",[883,15317,15319],{"className":15318},[886],[888,15320,15321],{"xmlns":890},[892,15322,15323,15331],{},[895,15324,15325],{},[1805,15326,15327,15329],{},[898,15328,13574],{},[898,15330,5640],{},[902,15332,15333],{"encoding":904},"I^E"," a rovnovážnou spotřebu ",[883,15336,15338],{"className":15337},[886],[888,15339,15340],{"xmlns":890},[892,15341,15342,15350],{},[895,15343,15344],{},[1805,15345,15346,15348],{},[898,15347,2458],{},[898,15349,5640],{},[902,15351,15352],{"encoding":904},"C^E",". Graficky jde o ",[38,15355,15356,15357],{},"průsečík ",[883,15358,15360],{"className":15359},[886],[888,15361,15362],{"xmlns":890},[892,15363,15364,15368],{},[895,15365,15366],{},[898,15367,5640],{},[902,15369,5640],{"encoding":904}," křivek ",[883,15372,15374],{"className":15373},[886],[888,15375,15376],{"xmlns":890},[892,15377,15378,15384],{},[895,15379,15380,15382],{},[898,15381,13574],{},[898,15383,10061],{},[902,15385,13441],{"encoding":904},[883,15387,15389],{"className":15388},[886],[888,15390,15391],{"xmlns":890},[892,15392,15393,15399],{},[895,15394,15395,15397],{},[898,15396,11183],{},[898,15398,2499],{},[902,15400,13448],{"encoding":904}," v rovině ",[883,15403,15405],{"className":15404},[886],[888,15406,15407],{"xmlns":890},[892,15408,15409,15421],{},[895,15410,15411,15413,15415,15417,15419],{},[1677,15412,1686],{"stretchy":1685},[898,15414,13431],{},[1677,15416,1967],{"separator":1966},[898,15418,10516],{},[1677,15420,1692],{"stretchy":1685},[902,15422,14327],{"encoding":904},[724,15424,15425],{},[614,15426,15427,15428,15449,15450,15465,15466,15481,15482,15495,15496,15513,15514,13518,15527,15513,15544,15557,15558,15571],{},"Obrázek 7.6 — Schematický graf v rovině ",[883,15429,15431],{"className":15430},[886],[888,15432,15433],{"xmlns":890},[892,15434,15435,15447],{},[895,15436,15437,15439,15441,15443,15445],{},[1677,15438,1686],{"stretchy":1685},[898,15440,13431],{},[1677,15442,1967],{"separator":1966},[898,15444,10516],{},[1677,15446,1692],{"stretchy":1685},[902,15448,14327],{"encoding":904},". Rostoucí přímka ",[883,15451,15453],{"className":15452},[886],[888,15454,15455],{"xmlns":890},[892,15456,15457,15463],{},[895,15458,15459,15461],{},[898,15460,11183],{},[898,15462,2499],{},[902,15464,13448],{"encoding":904}," a klesající přímka ",[883,15467,15469],{"className":15468},[886],[888,15470,15471],{"xmlns":890},[892,15472,15473,15479],{},[895,15474,15475,15477],{},[898,15476,13574],{},[898,15478,10061],{},[902,15480,13441],{"encoding":904}," se protínají v bodě ",[883,15483,15485],{"className":15484},[886],[888,15486,15487],{"xmlns":890},[892,15488,15489,15493],{},[895,15490,15491],{},[898,15492,5640],{},[902,15494,5640],{"encoding":904}," se souřadnicemi ",[883,15497,15499],{"className":15498},[886],[888,15500,15501],{"xmlns":890},[892,15502,15503,15511],{},[895,15504,15505],{},[1805,15506,15507,15509],{},[898,15508,13431],{},[898,15510,5640],{},[902,15512,15314],{"encoding":904}," (na ose ",[883,15515,15517],{"className":15516},[886],[888,15518,15519],{"xmlns":890},[892,15520,15521,15525],{},[895,15522,15523],{},[898,15524,13431],{},[902,15526,13431],{"encoding":904},[883,15528,15530],{"className":15529},[886],[888,15531,15532],{"xmlns":890},[892,15533,15534,15542],{},[895,15535,15536],{},[1805,15537,15538,15540],{},[898,15539,10516],{},[898,15541,5640],{},[902,15543,15293],{"encoding":904},[883,15545,15547],{"className":15546},[886],[888,15548,15549],{"xmlns":890},[892,15550,15551,15555],{},[895,15552,15553],{},[898,15554,10516],{},[902,15556,10516],{"encoding":904},"); tečkované čáry z ",[883,15559,15561],{"className":15560},[886],[888,15562,15563],{"xmlns":890},[892,15564,15565,15569],{},[895,15566,15567],{},[898,15568,5640],{},[902,15570,5640],{"encoding":904}," kolmé k osám vyznačují polohu rovnovážné úrokové míry a rovnovážného národního důchodu.",[5254,15573,15574,15579],{},[724,15575,15576,15578],{},[883,15577,5960],{}," Postup — jak najít IS-LM rovnováhu",[152,15580,15581,15657,15725,15783,15856],{},[123,15582,15583,15586,15587,5272,15607,15627,15628,5272,15641,15654,15655,1656],{},[38,15584,15585],{},"Z trhu zboží (7.13)"," dosaď funkce ",[883,15588,15590],{"className":15589},[886],[888,15591,15592],{"xmlns":890},[892,15593,15594,15604],{},[895,15595,15596,15598,15600,15602],{},[898,15597,2458],{},[1677,15599,1686],{"stretchy":1685},[898,15601,10516],{},[1677,15603,1692],{"stretchy":1685},[902,15605,15606],{"encoding":904},"C(Y)",[883,15608,15610],{"className":15609},[886],[888,15611,15612],{"xmlns":890},[892,15613,15614,15624],{},[895,15615,15616,15618,15620,15622],{},[898,15617,13574],{},[1677,15619,1686],{"stretchy":1685},[898,15621,13431],{},[1677,15623,1692],{"stretchy":1685},[902,15625,15626],{"encoding":904},"I(r)"," a vyjádři vztah mezi ",[883,15629,15631],{"className":15630},[886],[888,15632,15633],{"xmlns":890},[892,15634,15635,15639],{},[895,15636,15637],{},[898,15638,10516],{},[902,15640,10516],{"encoding":904},[883,15642,15644],{"className":15643},[886],[888,15645,15646],{"xmlns":890},[892,15647,15648,15652],{},[895,15649,15650],{},[898,15651,13431],{},[902,15653,13431],{"encoding":904}," — dostaneš rovnici ",[38,15656,13441],{},[123,15658,15659,15662,15663,5272,15680,15697,15698,15654,15723,1656],{},[38,15660,15661],{},"Z trhu peněz (7.15)"," dosaď ",[883,15664,15666],{"className":15665},[886],[888,15667,15668],{"xmlns":890},[892,15669,15670,15678],{},[895,15671,15672],{},[1953,15673,15674,15676],{},[898,15675,11183],{},[1810,15677,1959],{},[902,15679,14602],{"encoding":904},[883,15681,15683],{"className":15682},[886],[888,15684,15685],{"xmlns":890},[892,15686,15687,15695],{},[895,15688,15689],{},[1953,15690,15691,15693],{},[898,15692,11183],{},[1810,15694,1812],{},[902,15696,14674],{"encoding":904}," a vztah ",[883,15699,15701],{"className":15700},[886],[888,15702,15703],{"xmlns":890},[892,15704,15705,15721],{},[895,15706,15707,15713,15715],{},[1805,15708,15709,15711],{},[898,15710,2499],{},[898,15712,5571],{},[1677,15714,1679],{},[1805,15716,15717,15719],{},[898,15718,2499],{},[1677,15720,5742],{},[902,15722,14870],{"encoding":904},[38,15724,13448],{},[123,15726,15727,15730,15731,5272,15744,15757,15758,15782],{},[38,15728,15729],{},"Vyřeš soustavu"," dvou lineárních rovnic o dvou neznámých ",[883,15732,15734],{"className":15733},[886],[888,15735,15736],{"xmlns":890},[892,15737,15738,15742],{},[895,15739,15740],{},[898,15741,10516],{},[902,15743,10516],{"encoding":904},[883,15745,15747],{"className":15746},[886],[888,15748,15749],{"xmlns":890},[892,15750,15751,15755],{},[895,15752,15753],{},[898,15754,13431],{},[902,15756,13431],{"encoding":904}," — nejsnáze substituční metodou (vyjádři z IS ",[883,15759,15761],{"className":15760},[886],[888,15762,15763],{"xmlns":890},[892,15764,15765,15779],{},[895,15766,15767,15769,15771,15773,15775,15777],{},[898,15768,10516],{},[1677,15770,1679],{},[898,15772,1682],{},[1677,15774,1686],{"stretchy":1685},[898,15776,13431],{},[1677,15778,1692],{"stretchy":1685},[902,15780,15781],{"encoding":904},"Y = f(r)"," a dosaď do LM).",[123,15784,15785,1884,15788,5272,15822,1656],{},[38,15786,15787],{},"Zpětně dopočítej",[883,15789,15791],{"className":15790},[886],[888,15792,15793],{"xmlns":890},[892,15794,15795,15819],{},[895,15796,15797,15803,15805,15807,15809,15815,15817],{},[1805,15798,15799,15801],{},[898,15800,2458],{},[898,15802,5640],{},[1677,15804,1679],{},[898,15806,207],{},[1969,15808,2668],{},[1805,15810,15811,15813],{},[898,15812,10516],{},[898,15814,5640],{},[1677,15816,1776],{},[898,15818,1779],{},[902,15820,15821],{"encoding":904},"C^E = a\\,Y^E + b",[883,15823,15825],{"className":15824},[886],[888,15826,15827],{"xmlns":890},[892,15828,15829,15853],{},[895,15830,15831,15837,15839,15841,15843,15849,15851],{},[1805,15832,15833,15835],{},[898,15834,13574],{},[898,15836,5640],{},[1677,15838,1679],{},[898,15840,1823],{},[1969,15842,2668],{},[1805,15844,15845,15847],{},[898,15846,13431],{},[898,15848,5640],{},[1677,15850,1776],{},[898,15852,1875],{},[902,15854,15855],{"encoding":904},"I^E = c\\,r^E + d",[123,15857,15858,15861,15862,15896,15897,15951],{},[38,15859,15860],{},"Ověř:"," musí platit ",[883,15863,15865],{"className":15864},[886],[888,15866,15867],{"xmlns":890},[892,15868,15869,15893],{},[895,15870,15871,15877,15879,15885,15887],{},[1805,15872,15873,15875],{},[898,15874,10516],{},[898,15876,5640],{},[1677,15878,1679],{},[1805,15880,15881,15883],{},[898,15882,2458],{},[898,15884,5640],{},[1677,15886,1776],{},[1805,15888,15889,15891],{},[898,15890,13574],{},[898,15892,5640],{},[902,15894,15895],{"encoding":904},"Y^E = C^E + I^E"," (rovnováha trhu zboží) i ",[883,15898,15900],{"className":15899},[886],[888,15901,15902],{"xmlns":890},[892,15903,15904,15948],{},[895,15905,15906,15912,15914,15920,15926,15928,15934,15940,15942],{},[1805,15907,15908,15910],{},[898,15909,2499],{},[1677,15911,5742],{},[1677,15913,1679],{},[1953,15915,15916,15918],{},[898,15917,14627],{},[1810,15919,1959],{},[1805,15921,15922,15924],{},[898,15923,10516],{},[898,15925,5640],{},[1677,15927,1776],{},[1953,15929,15930,15932],{},[898,15931,14627],{},[1810,15933,1812],{},[1805,15935,15936,15938],{},[898,15937,13431],{},[898,15939,5640],{},[1677,15941,1776],{},[1953,15943,15944,15946],{},[898,15945,14627],{},[1810,15947,1854],{},[902,15949,15950],{"encoding":904},"M^* = k_1 Y^E + k_2 r^E + k_3"," (rovnováha trhu peněz).",[115,15953,15955],{"id":15954},"příklad-76-is-lm","Příklad 7.6 (IS-LM)",[724,15957,15958],{},"Pro trh zboží jsou dány:",[120,15960,15961,15989],{},[123,15962,15963,15964,1967],{},"spotřeba ",[883,15965,15967],{"className":15966},[886],[888,15968,15969],{"xmlns":890},[892,15970,15971,15986],{},[895,15972,15973,15975,15977,15980,15982,15984],{},[898,15974,2458],{},[1677,15976,1679],{},[1810,15978,15979],{},"0,8",[898,15981,10516],{},[1677,15983,1776],{},[1810,15985,2771],{},[902,15987,15988],{"encoding":904},"C = 0{,}8Y + 100",[123,15990,15991,15992,1656],{},"investice ",[883,15993,15995],{"className":15994},[886],[888,15996,15997],{"xmlns":890},[892,15998,15999,16015],{},[895,16000,16001,16003,16005,16007,16009,16011,16013],{},[898,16002,13574],{},[1677,16004,1679],{},[1677,16006,1906],{},[1810,16008,10423],{},[898,16010,13431],{},[1677,16012,1776],{},[1810,16014,2463],{},[902,16016,16017],{"encoding":904},"I = -20r + 1000",[724,16019,16020],{},"Pro trh peněz:",[120,16022,16023,16049,16081],{},[123,16024,16025,1967],{},[883,16026,16028],{"className":16027},[886],[888,16029,16030],{"xmlns":890},[892,16031,16032,16046],{},[895,16033,16034,16040,16042,16044],{},[1953,16035,16036,16038],{},[898,16037,11183],{},[1810,16039,1959],{},[1677,16041,1679],{},[1810,16043,2475],{},[898,16045,10516],{},[902,16047,16048],{"encoding":904},"L_1 = 0{,}1Y",[123,16050,16051,1967],{},[883,16052,16054],{"className":16053},[886],[888,16055,16056],{"xmlns":890},[892,16057,16058,16078],{},[895,16059,16060,16066,16068,16070,16072,16074,16076],{},[1953,16061,16062,16064],{},[898,16063,11183],{},[1810,16065,1812],{},[1677,16067,1679],{},[1677,16069,1906],{},[1810,16071,6392],{},[898,16073,13431],{},[1677,16075,1776],{},[1810,16077,9992],{},[902,16079,16080],{"encoding":904},"L_2 = -25r + 2000",[123,16082,16083,16084,1656],{},"nabídka peněz ",[883,16085,16087],{"className":16086},[886],[888,16088,16089],{"xmlns":890},[892,16090,16091,16104],{},[895,16092,16093,16099,16101],{},[1805,16094,16095,16097],{},[898,16096,2499],{},[1677,16098,5742],{},[1677,16100,1679],{},[1810,16102,16103],{},"2375",[902,16105,16106],{"encoding":904},"M^* = 2375",[724,16108,16109,16112,16113,2385],{},[38,16110,16111],{},"Funkce IS"," — dosazením do (7.13) ",[883,16114,16116],{"className":16115},[886],[888,16117,16118],{"xmlns":890},[892,16119,16120,16132],{},[895,16121,16122,16124,16126,16128,16130],{},[898,16123,10516],{},[1677,16125,1679],{},[898,16127,2458],{},[1677,16129,1776],{},[898,16131,13574],{},[902,16133,16134],{"encoding":904},"Y = C + I",[724,16136,16137],{},[883,16138,16140],{"className":16139},[886],[888,16141,16142],{"xmlns":890},[892,16143,16144,16170],{},[895,16145,16146,16148,16150,16152,16154,16156,16158,16160,16162,16164,16166,16168],{},[898,16147,10516],{},[1677,16149,1679],{},[1810,16151,15979],{},[898,16153,10516],{},[1677,16155,1776],{},[1810,16157,2771],{},[1677,16159,1906],{},[1810,16161,10423],{},[898,16163,13431],{},[1677,16165,1776],{},[1810,16167,2463],{},[1677,16169,1967],{"separator":1966},[902,16171,16172],{"encoding":904},"Y = 0{,}8Y + 100 - 20r + 1000,",[724,16174,16175],{},"tj.",[724,16177,16178],{},[883,16179,16181],{"className":16180},[886],[888,16182,16183],{"xmlns":890},[892,16184,16185,16210],{},[895,16186,16187,16189,16191,16193,16195,16197,16199,16202,16204,16206,16208],{},[1810,16188,2520],{},[898,16190,10516],{},[1677,16192,1776],{},[1810,16194,10423],{},[898,16196,13431],{},[1677,16198,1679],{},[1810,16200,16201],{},"1100.",[7266,16203],{"width":7268},[1677,16205,1686],{"stretchy":1685},[1969,16207,13441],{},[1677,16209,1692],{"stretchy":1685},[902,16211,16212],{"encoding":904},"0{,}2Y + 20r = 1100. \\qquad (\\text{IS})",[724,16214,16215,16218,16219,2385],{},[38,16216,16217],{},"Funkce LM"," — dosazením do (7.15) ",[883,16220,16222],{"className":16221},[886],[888,16223,16224],{"xmlns":890},[892,16225,16226,16250],{},[895,16227,16228,16234,16236,16242,16244],{},[1805,16229,16230,16232],{},[898,16231,2499],{},[1677,16233,5742],{},[1677,16235,1679],{},[1953,16237,16238,16240],{},[898,16239,11183],{},[1810,16241,1959],{},[1677,16243,1776],{},[1953,16245,16246,16248],{},[898,16247,11183],{},[1810,16249,1812],{},[902,16251,16252],{"encoding":904},"M^* = L_1 + L_2",[724,16254,16255],{},[883,16256,16258],{"className":16257},[886],[888,16259,16260],{"xmlns":890},[892,16261,16262,16284],{},[895,16263,16264,16266,16268,16270,16272,16274,16276,16278,16280,16282],{},[1810,16265,16103],{},[1677,16267,1679],{},[1810,16269,2475],{},[898,16271,10516],{},[1677,16273,1906],{},[1810,16275,6392],{},[898,16277,13431],{},[1677,16279,1776],{},[1810,16281,9992],{},[1677,16283,1967],{"separator":1966},[902,16285,16286],{"encoding":904},"2375 = 0{,}1Y - 25r + 2000,",[724,16288,16175],{},[724,16290,16291],{},[883,16292,16294],{"className":16293},[886],[888,16295,16296],{"xmlns":890},[892,16297,16298,16323],{},[895,16299,16300,16302,16304,16306,16308,16310,16312,16315,16317,16319,16321],{},[1810,16301,2475],{},[898,16303,10516],{},[1677,16305,1906],{},[1810,16307,6392],{},[898,16309,13431],{},[1677,16311,1679],{},[1810,16313,16314],{},"375.",[7266,16316],{"width":7268},[1677,16318,1686],{"stretchy":1685},[1969,16320,13448],{},[1677,16322,1692],{"stretchy":1685},[902,16324,16325],{"encoding":904},"0{,}1Y - 25r = 375. \\qquad (\\text{LM})",[724,16327,16328,16331,16332,16357],{},[38,16329,16330],{},"Řešení soustavy."," Z (IS) vyjádříme ",[883,16333,16335],{"className":16334},[886],[888,16336,16337],{"xmlns":890},[892,16338,16339,16354],{},[895,16340,16341,16343,16345,16348,16350,16352],{},[898,16342,10516],{},[1677,16344,1679],{},[1810,16346,16347],{},"5500",[1677,16349,1906],{},[1810,16351,2771],{},[898,16353,13431],{},[902,16355,16356],{"encoding":904},"Y = 5500 - 100r"," a dosadíme do (LM):",[724,16359,16360],{},[883,16361,16363],{"className":16362},[886],[888,16364,16365],{"xmlns":890},[892,16366,16367,16453],{},[895,16368,16369,16371,16373,16375,16377,16379,16381,16383,16385,16387,16389,16391,16394,16396,16399,16401,16404,16406,16408,16410,16412,16414,16416,16418,16420,16422,16424,16426,16429,16431,16433,16436,16438,16440,16442,16448,16450],{},[1810,16370,2475],{},[1677,16372,1686],{"stretchy":1685},[1810,16374,16347],{},[1677,16376,1906],{},[1810,16378,2771],{},[898,16380,13431],{},[1677,16382,1692],{"stretchy":1685},[1677,16384,1906],{},[1810,16386,6392],{},[898,16388,13431],{},[1677,16390,1679],{},[1810,16392,16393],{},"375",[1969,16395,5372],{},[1677,16397,16398],{},"⟹",[1969,16400,5372],{},[1810,16402,16403],{},"550",[1677,16405,1906],{},[1810,16407,2544],{},[898,16409,13431],{},[1677,16411,1906],{},[1810,16413,6392],{},[898,16415,13431],{},[1677,16417,1679],{},[1810,16419,16393],{},[1969,16421,5372],{},[1677,16423,16398],{},[1969,16425,5372],{},[1810,16427,16428],{},"35",[898,16430,13431],{},[1677,16432,1679],{},[1810,16434,16435],{},"175",[1969,16437,5372],{},[1677,16439,16398],{},[1969,16441,5372],{},[1805,16443,16444,16446],{},[898,16445,13431],{},[898,16447,5640],{},[1677,16449,1679],{},[1810,16451,16452],{},"5.",[902,16454,16455],{"encoding":904},"0{,}1(5500 - 100r) - 25r = 375 \\;\\Longrightarrow\\; 550 - 10r - 25r = 375 \\;\\Longrightarrow\\; 35r = 175 \\;\\Longrightarrow\\; r^E = 5.",[724,16457,16458],{},[38,16459,16460],{},"Zpětné dosazení:",[120,16462,16463,16509,16546],{},[123,16464,16465,1967],{},[883,16466,16468],{"className":16467},[886],[888,16469,16470],{"xmlns":890},[892,16471,16472,16506],{},[895,16473,16474,16480,16482,16484,16486,16488,16490,16492,16494,16496,16498,16501,16503],{},[1805,16475,16476,16478],{},[898,16477,10516],{},[898,16479,5640],{},[1677,16481,1679],{},[1810,16483,16347],{},[1677,16485,1906],{},[1810,16487,2771],{},[1677,16489,2858],{},[1810,16491,1909],{},[1677,16493,1679],{},[1810,16495,16347],{},[1677,16497,1906],{},[1810,16499,16500],{},"500",[1677,16502,1679],{},[1810,16504,16505],{},"5000",[902,16507,16508],{"encoding":904},"Y^E = 5500 - 100 \\cdot 5 = 5500 - 500 = 5000",[123,16510,16511,1967],{},[883,16512,16514],{"className":16513},[886],[888,16515,16516],{"xmlns":890},[892,16517,16518,16543],{},[895,16519,16520,16526,16528,16530,16532,16534,16536,16538,16540],{},[1805,16521,16522,16524],{},[898,16523,2458],{},[898,16525,5640],{},[1677,16527,1679],{},[1810,16529,15979],{},[1677,16531,2858],{},[1810,16533,16505],{},[1677,16535,1776],{},[1810,16537,2771],{},[1677,16539,1679],{},[1810,16541,16542],{},"4100",[902,16544,16545],{"encoding":904},"C^E = 0{,}8 \\cdot 5000 + 100 = 4100",[123,16547,16548,1656],{},[883,16549,16551],{"className":16550},[886],[888,16552,16553],{"xmlns":890},[892,16554,16555,16582],{},[895,16556,16557,16563,16565,16567,16569,16571,16573,16575,16577,16579],{},[1805,16558,16559,16561],{},[898,16560,13574],{},[898,16562,5640],{},[1677,16564,1679],{},[1677,16566,1906],{},[1810,16568,10423],{},[1677,16570,2858],{},[1810,16572,1909],{},[1677,16574,1776],{},[1810,16576,2463],{},[1677,16578,1679],{},[1810,16580,16581],{},"900",[902,16583,16584],{"encoding":904},"I^E = -20 \\cdot 5 + 1000 = 900",[724,16586,16587,1884,16590,16636],{},[38,16588,16589],{},"Ověření:",[883,16591,16593],{"className":16592},[886],[888,16594,16595],{"xmlns":890},[892,16596,16597,16633],{},[895,16598,16599,16605,16607,16613,16615,16617,16619,16621,16623,16625,16627],{},[1805,16600,16601,16603],{},[898,16602,2458],{},[898,16604,5640],{},[1677,16606,1776],{},[1805,16608,16609,16611],{},[898,16610,13574],{},[898,16612,5640],{},[1677,16614,1679],{},[1810,16616,16542],{},[1677,16618,1776],{},[1810,16620,16581],{},[1677,16622,1679],{},[1810,16624,16505],{},[1677,16626,1679],{},[1805,16628,16629,16631],{},[898,16630,10516],{},[898,16632,5640],{},[902,16634,16635],{"encoding":904},"C^E + I^E = 4100 + 900 = 5000 = Y^E",". ✓",[724,16638,16639],{},[883,16640,16642],{"className":16641},[886],[888,16643,16644],{"xmlns":890},[892,16645,16646,16716],{},[895,16647,16648],{},[14222,16649,16650],{"notation":14224},[2006,16651,16652],{"scriptlevel":2008,"displaystyle":1685},[2006,16653,16654],{"scriptlevel":2008,"displaystyle":1685},[2006,16655,16656],{"scriptlevel":2008,"displaystyle":1966},[895,16657,16658,16660,16666,16668,16670,16672,16675,16681,16683,16685,16687,16689,16695,16697,16699,16701,16703,16709,16711,16714],{},[1969,16659,2668],{},[1805,16661,16662,16664],{},[898,16663,10516],{},[898,16665,5640],{},[1677,16667,1679],{},[1810,16669,16505],{},[1677,16671,1967],{"separator":1966},[7266,16673],{"width":16674},"1em",[1805,16676,16677,16679],{},[898,16678,13431],{},[898,16680,5640],{},[1677,16682,1679],{},[1810,16684,1909],{},[1677,16686,1967],{"separator":1966},[7266,16688],{"width":16674},[1805,16690,16691,16693],{},[898,16692,2458],{},[898,16694,5640],{},[1677,16696,1679],{},[1810,16698,16542],{},[1677,16700,1967],{"separator":1966},[7266,16702],{"width":16674},[1805,16704,16705,16707],{},[898,16706,13574],{},[898,16708,5640],{},[1677,16710,1679],{},[1810,16712,16713],{},"900.",[1969,16715,2668],{},[902,16717,16718],{"encoding":904},"\\boxed{\\,Y^E = 5000, \\quad r^E = 5, \\quad C^E = 4100, \\quad I^E = 900.\\,}",[724,16720,16721],{},[614,16722,16723,16724,16737,16738,16751,16752,16767,16768,16781,16782,16797,16798,16811,16812,16825,16826,1656],{},"Obrázek 7.7 — Konkrétní numerický příklad IS-LM rovnováhy. Na ose ",[883,16725,16727],{"className":16726},[886],[888,16728,16729],{"xmlns":890},[892,16730,16731,16735],{},[895,16732,16733],{},[898,16734,10516],{},[902,16736,10516],{"encoding":904}," jsou vyznačeny hodnoty 3750, 5000, 5500; na ose ",[883,16739,16741],{"className":16740},[886],[888,16742,16743],{"xmlns":890},[892,16744,16745,16749],{},[895,16746,16747],{},[898,16748,13431],{},[902,16750,13431],{"encoding":904}," hodnoty 5 a 55. Přímka ",[883,16753,16755],{"className":16754},[886],[888,16756,16757],{"xmlns":890},[892,16758,16759,16765],{},[895,16760,16761,16763],{},[898,16762,11183],{},[898,16764,2499],{},[902,16766,13448],{"encoding":904}," stoupá z oblasti nízkých ",[883,16769,16771],{"className":16770},[886],[888,16772,16773],{"xmlns":890},[892,16774,16775,16779],{},[895,16776,16777],{},[898,16778,13431],{},[902,16780,13431],{"encoding":904},", přímka ",[883,16783,16785],{"className":16784},[886],[888,16786,16787],{"xmlns":890},[892,16788,16789,16795],{},[895,16790,16791,16793],{},[898,16792,13574],{},[898,16794,10061],{},[902,16796,13441],{"encoding":904}," klesá a protíná osu ",[883,16799,16801],{"className":16800},[886],[888,16802,16803],{"xmlns":890},[892,16804,16805,16809],{},[895,16806,16807],{},[898,16808,13431],{},[902,16810,13431],{"encoding":904}," kolem hodnoty 55. Průsečík ",[883,16813,16815],{"className":16814},[886],[888,16816,16817],{"xmlns":890},[892,16818,16819,16823],{},[895,16820,16821],{},[898,16822,5640],{},[902,16824,5640],{"encoding":904}," leží v bodě ",[883,16827,16829],{"className":16828},[886],[888,16830,16831],{"xmlns":890},[892,16832,16833,16855],{},[895,16834,16835,16837,16839,16841,16843,16845,16847,16849,16851,16853],{},[1677,16836,2167],{"stretchy":1685},[898,16838,13431],{},[1677,16840,1679],{},[1810,16842,1909],{},[1677,16844,1967],{"separator":1966},[1969,16846,1971],{},[898,16848,10516],{},[1677,16850,1679],{},[1810,16852,16505],{},[1677,16854,2182],{"stretchy":1685},[902,16856,16857],{"encoding":904},"[r = 5,\\ Y = 5000]",[115,16859,16861],{"id":16860},"ekonomická-interpretace-fiskální-a-monetární-politika","Ekonomická interpretace — fiskální a monetární politika",[724,16863,16864,16867,16868,16881,16882,8403,16895,16898,16899,16917,16918,16935,16936,16953,16954,16967,16968,16981],{},[38,16865,16866],{},"Posun křivky IS (fiskální politika)."," Expanzivní fiskální politika — zvýšení vládních výdajů ",[883,16869,16871],{"className":16870},[886],[888,16872,16873],{"xmlns":890},[892,16874,16875,16879],{},[895,16876,16877],{},[898,16878,13502],{},[902,16880,13502],{"encoding":904}," nebo snížení daní ",[883,16883,16885],{"className":16884},[886],[888,16886,16887],{"xmlns":890},[892,16888,16889,16893],{},[895,16890,16891],{},[898,16892,2455],{},[902,16894,2455],{"encoding":904},[38,16896,16897],{},"posouvá IS doprava",": při dané úrokové míře vzroste rovnovážný důchod trhu zboží. Nová rovnováha ",[883,16900,16902],{"className":16901},[886],[888,16903,16904],{"xmlns":890},[892,16905,16906,16914],{},[895,16907,16908],{},[1805,16909,16910,16912],{},[898,16911,5640],{},[1677,16913,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[902,16915,16916],{"encoding":904},"E'"," má vyšší ",[883,16919,16921],{"className":16920},[886],[888,16922,16923],{"xmlns":890},[892,16924,16925,16933],{},[895,16926,16927],{},[1805,16928,16929,16931],{},[898,16930,10516],{},[898,16932,5640],{},[902,16934,15293],{"encoding":904}," i vyšší ",[883,16937,16939],{"className":16938},[886],[888,16940,16941],{"xmlns":890},[892,16942,16943,16951],{},[895,16944,16945],{},[1805,16946,16947,16949],{},[898,16948,13431],{},[898,16950,5640],{},[902,16952,15314],{"encoding":904}," (vyšší ",[883,16955,16957],{"className":16956},[886],[888,16958,16959],{"xmlns":890},[892,16960,16961,16965],{},[895,16962,16963],{},[898,16964,10516],{},[902,16966,10516],{"encoding":904}," zvedá poptávku po penězích, což tlačí ",[883,16969,16971],{"className":16970},[886],[888,16972,16973],{"xmlns":890},[892,16974,16975,16979],{},[895,16976,16977],{},[898,16978,13431],{},[902,16980,13431],{"encoding":904}," nahoru).",[724,16983,16984],{},[2240,16985],{"alt":16986,"className":16987,"src":16988},"imek-posun-is-lm-politiky",[210,2244],"\u002Fwiki-assets\u002Fimek-posun-is-lm-politiky.jpeg",[724,16990,16991,16994,16995,17012,17013,17016,17017,17034,17035,17052,17053,17066,17067,17086,17087,5306],{},[38,16992,16993],{},"Posun křivky LM (monetární politika)."," Expanzivní monetární politika — zvýšení nabídky peněz ",[883,16996,16998],{"className":16997},[886],[888,16999,17000],{"xmlns":890},[892,17001,17002,17010],{},[895,17003,17004],{},[1805,17005,17006,17008],{},[898,17007,2499],{},[1677,17009,5742],{},[902,17011,13540],{"encoding":904}," národní bankou — ",[38,17014,17015],{},"posouvá LM doprava\u002Fdolů",": při daném důchodu je trh peněz v rovnováze při nižší úrokové míře. Nová rovnováha má nižší ",[883,17018,17020],{"className":17019},[886],[888,17021,17022],{"xmlns":890},[892,17023,17024,17032],{},[895,17025,17026],{},[1805,17027,17028,17030],{},[898,17029,13431],{},[898,17031,5640],{},[902,17033,15314],{"encoding":904}," a vyšší ",[883,17036,17038],{"className":17037},[886],[888,17039,17040],{"xmlns":890},[892,17041,17042,17050],{},[895,17043,17044],{},[1805,17045,17046,17048],{},[898,17047,10516],{},[898,17049,5640],{},[902,17051,15293],{"encoding":904}," (nižší ",[883,17054,17056],{"className":17055},[886],[888,17057,17058],{"xmlns":890},[892,17059,17060,17064],{},[895,17061,17062],{},[898,17063,13431],{},[902,17065,13431],{"encoding":904}," povzbuzuje investice ",[883,17068,17070],{"className":17069},[886],[888,17071,17072],{"xmlns":890},[892,17073,17074,17084],{},[895,17075,17076,17078,17080,17082],{},[898,17077,13574],{},[1677,17079,1686],{"stretchy":1685},[898,17081,13431],{},[1677,17083,1692],{"stretchy":1685},[902,17085,15626],{"encoding":904},", ty zvedají ",[883,17088,17090],{"className":17089},[886],[888,17091,17092],{"xmlns":890},[892,17093,17094,17098],{},[895,17095,17096],{},[898,17097,10516],{},[902,17099,10516],{"encoding":904},[724,17101,17102,17103,17106],{},"IS-LM tak dává jednotný rámec pro diskusi ",[38,17104,17105],{},"dopadu obou typů politik"," na důchod a úrokovou míru současně.",[115,17108,17110],{"id":17109},"klíčové-pojmy","Klíčové pojmy",[120,17112,17113,17186,17232,17314,17364,17431,17488,17529,17562],{},[123,17114,17115,8403,17148,1343,17165,17182,17183,17185],{},[38,17116,17117,17118],{},"Funkce investic ",[883,17119,17121],{"className":17120},[886],[888,17122,17123],{"xmlns":890},[892,17124,17125,17145],{},[895,17126,17127,17129,17131,17133,17135,17137,17139,17141,17143],{},[898,17128,13574],{},[1677,17130,1686],{"stretchy":1685},[898,17132,13431],{},[1677,17134,1692],{"stretchy":1685},[1677,17136,1679],{},[898,17138,1823],{},[898,17140,13431],{},[1677,17142,1776],{},[898,17144,1875],{},[902,17146,17147],{"encoding":904},"I(r) = cr + d",[883,17149,17151],{"className":17150},[886],[888,17152,17153],{"xmlns":890},[892,17154,17155,17163],{},[895,17156,17157,17159,17161],{},[898,17158,1823],{},[1677,17160,3128],{},[1810,17162,2008],{},[902,17164,13905],{"encoding":904},[883,17166,17168],{"className":17167},[886],[888,17169,17170],{"xmlns":890},[892,17171,17172,17180],{},[895,17173,17174,17176,17178],{},[898,17175,1875],{},[1677,17177,3089],{},[1810,17179,2008],{},[902,17181,13884],{"encoding":904},"; ",[38,17184,13909],{}," funkce úrokové míry.",[123,17187,17188,17191,17192,17213,17214,17231],{},[38,17189,17190],{},"Trh zboží"," — rovnováha ",[883,17193,17195],{"className":17194},[886],[888,17196,17197],{"xmlns":890},[892,17198,17199,17211],{},[895,17200,17201,17203,17205,17207,17209],{},[898,17202,10516],{},[1677,17204,1679],{},[898,17206,2458],{},[1677,17208,1776],{},[898,17210,13574],{},[902,17212,16134],{"encoding":904},", ekvivalentně ",[883,17215,17217],{"className":17216},[886],[888,17218,17219],{"xmlns":890},[892,17220,17221,17229],{},[895,17222,17223,17225,17227],{},[898,17224,13574],{},[1677,17226,1679],{},[898,17228,10061],{},[902,17230,14102],{"encoding":904}," (investice = úspory).",[123,17233,17234,11413,17237,17239,17240,17290,17291,14305,17293,1656],{},[38,17235,17236],{},"Křivka IS",[614,17238,13444],{},") — ",[883,17241,17243],{"className":17242},[886],[888,17244,17245],{"xmlns":890},[892,17246,17247,17287],{},[895,17248,17249,17251,17253,17265,17267,17269],{},[898,17250,10516],{},[1677,17252,1679],{},[2010,17254,17255,17257],{},[898,17256,1823],{},[895,17258,17259,17261,17263],{},[1810,17260,1959],{},[1677,17262,1906],{},[898,17264,207],{},[898,17266,13431],{},[1677,17268,1776],{},[2010,17270,17271,17279],{},[895,17272,17273,17275,17277],{},[898,17274,1779],{},[1677,17276,1776],{},[898,17278,1875],{},[895,17280,17281,17283,17285],{},[1810,17282,1959],{},[1677,17284,1906],{},[898,17286,207],{},[902,17288,17289],{"encoding":904},"Y = \\frac{c}{1-a}r + \\frac{b+d}{1-a}"," (7.14); ",[38,17292,13909],{},[883,17294,17296],{"className":17295},[886],[888,17297,17298],{"xmlns":890},[892,17299,17300,17312],{},[895,17301,17302,17304,17306,17308,17310],{},[1677,17303,1686],{"stretchy":1685},[898,17305,13431],{},[1677,17307,1967],{"separator":1966},[898,17309,10516],{},[1677,17311,1692],{"stretchy":1685},[902,17313,14327],{"encoding":904},[123,17315,17316,17191,17319,17345,17346,1656],{},[38,17317,17318],{},"Trh peněz",[883,17320,17322],{"className":17321},[886],[888,17323,17324],{"xmlns":890},[892,17325,17326,17342],{},[895,17327,17328,17334,17336],{},[1805,17329,17330,17332],{},[898,17331,2499],{},[898,17333,5571],{},[1677,17335,1679],{},[1805,17337,17338,17340],{},[898,17339,2499],{},[898,17341,10061],{},[902,17343,17344],{"encoding":904},"M^D = M^S"," při pevné nabídce ",[883,17347,17349],{"className":17348},[886],[888,17350,17351],{"xmlns":890},[892,17352,17353,17361],{},[895,17354,17355],{},[1805,17356,17357,17359],{},[898,17358,2499],{},[1677,17360,5742],{},[902,17362,17363],{"encoding":904},"M^* ",[123,17365,17366,8403,17369,1656],{},[38,17367,17368],{},"Transakční, opatrnostní, spekulační poptávka",[883,17370,17372],{"className":17371},[886],[888,17373,17374],{"xmlns":890},[892,17375,17376,17428],{},[895,17377,17378,17384,17386,17392,17394,17400,17402,17408,17410,17412,17418,17420,17422],{},[1805,17379,17380,17382],{},[898,17381,2499],{},[898,17383,5571],{},[1677,17385,1679],{},[1953,17387,17388,17390],{},[898,17389,11183],{},[1810,17391,1959],{},[1677,17393,1776],{},[1953,17395,17396,17398],{},[898,17397,11183],{},[1810,17399,1812],{},[1677,17401,1679],{},[1953,17403,17404,17406],{},[898,17405,14627],{},[1810,17407,1959],{},[898,17409,10516],{},[1677,17411,1776],{},[1953,17413,17414,17416],{},[898,17415,14627],{},[1810,17417,1812],{},[898,17419,13431],{},[1677,17421,1776],{},[1953,17423,17424,17426],{},[898,17425,14627],{},[1810,17427,1854],{},[902,17429,17430],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3",[123,17432,17433,11413,17436,17239,17438,17484,17485,17487],{},[38,17434,17435],{},"Křivka LM",[614,17437,13451],{},[883,17439,17441],{"className":17440},[886],[888,17442,17443],{"xmlns":890},[892,17444,17445,17481],{},[895,17446,17447,17453,17455,17461,17463,17465,17471,17473,17475],{},[1805,17448,17449,17451],{},[898,17450,2499],{},[1677,17452,5742],{},[1677,17454,1679],{},[1953,17456,17457,17459],{},[898,17458,14627],{},[1810,17460,1959],{},[898,17462,10516],{},[1677,17464,1776],{},[1953,17466,17467,17469],{},[898,17468,14627],{},[1810,17470,1812],{},[898,17472,13431],{},[1677,17474,1776],{},[1953,17476,17477,17479],{},[898,17478,14627],{},[1810,17480,1854],{},[902,17482,17483],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3"," (7.15); ",[38,17486,15047],{}," přímka.",[123,17489,17490,17493,17494,17528],{},[38,17491,17492],{},"Simultánní rovnováha"," — průsečík ",[883,17495,17497],{"className":17496},[886],[888,17498,17499],{"xmlns":890},[892,17500,17501,17525],{},[895,17502,17503,17505,17507,17509,17515,17517,17523],{},[898,17504,5640],{},[1677,17506,1679],{},[1677,17508,1686],{"stretchy":1685},[1805,17510,17511,17513],{},[898,17512,13431],{},[898,17514,5640],{},[1677,17516,1967],{"separator":1966},[1805,17518,17519,17521],{},[898,17520,10516],{},[898,17522,5640],{},[1677,17524,1692],{"stretchy":1685},[902,17526,17527],{"encoding":904},"E = (r^E, Y^E)"," křivek IS a LM.",[123,17530,17531,17534,17535,1343,17548,17561],{},[38,17532,17533],{},"Fiskální politika"," — nástroje ",[883,17536,17538],{"className":17537},[886],[888,17539,17540],{"xmlns":890},[892,17541,17542,17546],{},[895,17543,17544],{},[898,17545,13502],{},[902,17547,13502],{"encoding":904},[883,17549,17551],{"className":17550},[886],[888,17552,17553],{"xmlns":890},[892,17554,17555,17559],{},[895,17556,17557],{},[898,17558,2455],{},[902,17560,2455],{"encoding":904}," posouvající křivku IS.",[123,17563,17564,17567,17568,17585],{},[38,17565,17566],{},"Monetární politika"," — nástroj ",[883,17569,17571],{"className":17570},[886],[888,17572,17573],{"xmlns":890},[892,17574,17575,17583],{},[895,17576,17577],{},[1805,17578,17579,17581],{},[898,17580,2499],{},[1677,17582,5742],{},[902,17584,13540],{"encoding":904}," posouvající křivku LM.",[115,17587,3473],{"id":3472},[120,17589,17590,17599,17608,17618],{},[123,17591,17592,1884,17595],{},[38,17593,17594],{},"Kurz:",[207,17596,17598],{"className":17597,"dataFsResolvedFilePath":1641,"href":1642},[210],"Matematická ekonomie",[123,17600,17601,1884,17604],{},[38,17602,17603],{},"Přednáška:",[207,17605,17607],{"className":17606,"dataFsResolvedFilePath":868,"href":869},[210],"imek-blok-03",[123,17609,17610,1884,17613,17617],{},[38,17611,17612],{},"Nadřazené téma:",[207,17614,17616],{"className":17615,"dataFsResolvedFilePath":934,"href":935},[210],"narodni-duchod"," — makroekonomické modely C-I, C-I-G, C-I-G-X a úvod do IS-LM",[123,17619,17620,17623],{},[38,17621,17622],{},"Související:",[120,17624,17625,17632,17638],{},[123,17626,17627,17631],{},[207,17628,17630],{"className":17629,"dataFsResolvedFilePath":800,"href":801},[210],"poptavka-nabidka"," — paralela rovnovážného bodu (průsečík dvou křivek) v mikroekonomii",[123,17633,17634,17637],{},[207,17635,1145],{"className":17636,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro směrnice IS a LM",[123,17639,17640,17644],{},[207,17641,17643],{"className":17642,"dataFsResolvedFilePath":782,"href":783},[210],"funkce-vice-promennych"," — dvě neznámé a řešení lineárních soustav",{"title":641,"searchDepth":642,"depth":642,"links":17646},[17647,17648,17649,17650,17651,17652,17653,17654,17655,17656],{"id":13395,"depth":642,"text":13396},{"id":13550,"depth":642,"text":13551},{"id":13765,"depth":642,"text":13766},{"id":14058,"depth":642,"text":14059},{"id":14471,"depth":642,"text":14472},{"id":15264,"depth":642,"text":15265},{"id":15954,"depth":642,"text":15955},{"id":16860,"depth":642,"text":16861},{"id":17109,"depth":642,"text":17110},{"id":3472,"depth":642,"text":3473},{},"\u002Ftopics\u002Fis-lm",{"title":13387,"description":641},[1138,1137],"topics\u002Fis-lm",[1128,17663,1143,17664,17665,17666,17667,17616],"is-lm","trh-zbozi","trh-penez","urokova-mira","investice","OcXqlUxNqiCsj643lVoQEu_ZWU2vH0D_lWZ_-SxoyHk",{"id":17670,"title":17671,"body":17672,"course":659,"courses":19265,"created":1129,"description":19266,"extension":661,"meta":19267,"navigation":664,"path":19268,"seo":19269,"sources":19270,"stem":19271,"tags":19272,"type":3538,"updated":677,"__hash__":19275},"topics\u002Ftopics\u002Flagrangeova-metoda.md","Lagrangeova metoda (vázané extrémy)",{"type":9,"value":17673,"toc":19253},[17674,17677,17773,17780,17800,17804,17809,17872,17891,17893,17896,18032,18034,18244,18278,18415,18419,18483,18499,18527,18531,18629,18633,18637,18690,18796,19010,19014,19057,19163,19215,19217],[12,17675,17671],{"id":17676},"lagrangeova-metoda-vázané-extrémy",[724,17678,17679,17680,5298,17703,17735,17736,17739,17740,17767,17768,17772],{},"Hledáme extrém funkce ",[883,17681,17683],{"className":17682},[886],[888,17684,17685],{"xmlns":890},[892,17686,17687,17701],{},[895,17688,17689,17691,17693,17695,17697,17699],{},[898,17690,1682],{},[1677,17692,1686],{"stretchy":1685},[898,17694,1689],{},[1677,17696,1967],{"separator":1966},[898,17698,1675],{},[1677,17700,1692],{"stretchy":1685},[902,17702,11231],{"encoding":904},[883,17704,17706],{"className":17705},[886],[888,17707,17708],{"xmlns":890},[892,17709,17710,17732],{},[895,17711,17712,17714,17716,17722,17724,17730],{},[898,17713,900],{},[1677,17715,1686],{"stretchy":1685},[1953,17717,17718,17720],{},[898,17719,2470],{},[1810,17721,1959],{},[1677,17723,1967],{"separator":1966},[1953,17725,17726,17728],{},[898,17727,2470],{},[1810,17729,1812],{},[1677,17731,1692],{"stretchy":1685},[902,17733,17734],{"encoding":904},"U(Q_1, Q_2)"," apod.) ",[38,17737,17738],{},"podmíněný"," rovnicí ",[883,17741,17743],{"className":17742},[886],[888,17744,17745],{"xmlns":890},[892,17746,17747,17765],{},[895,17748,17749,17751,17753,17755,17757,17759,17761,17763],{},[898,17750,12429],{},[1677,17752,1686],{"stretchy":1685},[898,17754,1689],{},[1677,17756,1967],{"separator":1966},[898,17758,1675],{},[1677,17760,1692],{"stretchy":1685},[1677,17762,1679],{},[1810,17764,2008],{},[902,17766,12446],{"encoding":904},". V ",[207,17769,17771],{"className":17770,"dataFsResolvedFilePath":1641,"href":1642},[210],"matematické ekonomii"," se používá pro:",[724,17774,17775],{},[2240,17776],{"alt":17777,"className":17778,"src":17779},"imek-lagrange-tecnost",[210,2244],"\u002Fwiki-assets\u002Fimek-lagrange-tecnost.jpeg",[120,17781,17782,17791,17797],{},[123,17783,17784,17787,17788,1692],{},[38,17785,17786],{},"Maximalizaci užitečnosti"," při rozpočtovém omezení (viz ",[207,17789,11161],{"className":17790,"dataFsResolvedFilePath":878,"href":879},[210],[123,17792,17793,17796],{},[38,17794,17795],{},"Minimalizaci výdajů"," při dané úrovni užitečnosti (duální úloha)",[123,17798,17799],{},"Optimalizaci produkce \u002F nákladů za omezení",[115,17801,17803],{"id":17802},"princip","Princip",[724,17805,12095,17806,2385],{},[38,17807,17808],{},"Lagrangeovu funkci",[724,17810,17811],{},[883,17812,17814],{"className":17813},[886],[888,17815,17816],{"xmlns":890},[892,17817,17818,17869],{},[895,17819,17820,17822,17824,17826,17828,17830,17832,17835,17837,17839,17841,17843,17845,17847,17849,17851,17853,17855,17857,17859,17861,17863,17865,17867],{},[898,17821,11183],{},[1677,17823,1686],{"stretchy":1685},[898,17825,1689],{},[1677,17827,1967],{"separator":1966},[898,17829,1675],{},[1677,17831,1967],{"separator":1966},[898,17833,17834],{},"λ",[1677,17836,1692],{"stretchy":1685},[1677,17838,1679],{},[898,17840,1682],{},[1677,17842,1686],{"stretchy":1685},[898,17844,1689],{},[1677,17846,1967],{"separator":1966},[898,17848,1675],{},[1677,17850,1692],{"stretchy":1685},[1677,17852,1776],{},[898,17854,17834],{},[1969,17856,2668],{},[898,17858,12429],{},[1677,17860,1686],{"stretchy":1685},[898,17862,1689],{},[1677,17864,1967],{"separator":1966},[898,17866,1675],{},[1677,17868,1692],{"stretchy":1685},[902,17870,17871],{"encoding":904},"L(x, y, \\lambda) = f(x, y) + \\lambda\\, g(x, y)",[724,17873,5698,17874,9490,17888,1656],{},[883,17875,17877],{"className":17876},[886],[888,17878,17879],{"xmlns":890},[892,17880,17881,17885],{},[895,17882,17883],{},[898,17884,17834],{},[902,17886,17887],{"encoding":904},"\\lambda",[38,17889,17890],{},"Lagrangeův multiplikátor",[115,17892,2933],{"id":2932},[724,17894,17895],{},"Řešíme soustavu:",[724,17897,17898,17946,17994],{},[883,17899,17901],{"className":17900},[886],[888,17902,17903],{"xmlns":890},[892,17904,17905,17943],{},[895,17906,17907,17915,17917,17925,17927,17929,17931,17939,17941],{},[10554,17908,17909,17911,17913],{},[898,17910,11183],{},[898,17912,1689],{},[1677,17914,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,17916,1679],{},[10554,17918,17919,17921,17923],{},[898,17920,1682],{},[898,17922,1689],{},[1677,17924,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,17926,1776],{},[898,17928,17834],{},[1969,17930,2668],{},[10554,17932,17933,17935,17937],{},[898,17934,12429],{},[898,17936,1689],{},[1677,17938,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,17940,1679],{},[1810,17942,2008],{},[902,17944,17945],{"encoding":904},"L'_x = f'_x + \\lambda\\, g'_x = 0",[883,17947,17949],{"className":17948},[886],[888,17950,17951],{"xmlns":890},[892,17952,17953,17991],{},[895,17954,17955,17963,17965,17973,17975,17977,17979,17987,17989],{},[10554,17956,17957,17959,17961],{},[898,17958,11183],{},[898,17960,1675],{},[1677,17962,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,17964,1679],{},[10554,17966,17967,17969,17971],{},[898,17968,1682],{},[898,17970,1675],{},[1677,17972,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,17974,1776],{},[898,17976,17834],{},[1969,17978,2668],{},[10554,17980,17981,17983,17985],{},[898,17982,12429],{},[898,17984,1675],{},[1677,17986,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,17988,1679],{},[1810,17990,2008],{},[902,17992,17993],{"encoding":904},"L'_y = f'_y + \\lambda\\, g'_y = 0",[883,17995,17997],{"className":17996},[886],[888,17998,17999],{"xmlns":890},[892,18000,18001,18029],{},[895,18002,18003,18011,18013,18015,18017,18019,18021,18023,18025,18027],{},[10554,18004,18005,18007,18009],{},[898,18006,11183],{},[898,18008,17834],{},[1677,18010,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,18012,1679],{},[898,18014,12429],{},[1677,18016,1686],{"stretchy":1685},[898,18018,1689],{},[1677,18020,1967],{"separator":1966},[898,18022,1675],{},[1677,18024,1692],{"stretchy":1685},[1677,18026,1679],{},[1810,18028,2008],{},[902,18030,18031],{"encoding":904},"L'_\\lambda = g(x, y) = 0",[115,18033,3007],{"id":3006},[724,18035,18036],{},[883,18037,18039],{"className":18038},[886],[888,18040,18041],{"xmlns":890},[892,18042,18043,18241],{},[895,18044,18045,18047,18049,18051,18053,18055,18057,18059,18061,18063,18065,18081,18083,18085,18101,18103,18105,18113,18119,18121,18123,18139,18141,18143,18159,18161,18163,18171,18177,18179,18181,18183,18199,18201,18203,18219,18221,18223,18231,18233],{},[898,18046,5571],{},[1677,18048,1686],{"stretchy":1685},[898,18050,1689],{},[1677,18052,1967],{"separator":1966},[898,18054,1675],{},[1677,18056,1967],{"separator":1966},[898,18058,17834],{},[1677,18060,1692],{"stretchy":1685},[1677,18062,1679],{},[1677,18064,1686],{"stretchy":1685},[10554,18066,18067,18069,18075],{},[898,18068,1682],{},[895,18070,18071,18073],{},[898,18072,1689],{},[898,18074,1689],{},[895,18076,18077,18079],{},[1677,18078,2059],{"mathvariant":2057},[1677,18080,2059],{"mathvariant":2057},[1677,18082,1776],{},[898,18084,17834],{},[10554,18086,18087,18089,18095],{},[898,18088,12429],{},[895,18090,18091,18093],{},[898,18092,1689],{},[898,18094,1689],{},[895,18096,18097,18099],{},[1677,18098,2059],{"mathvariant":2057},[1677,18100,2059],{"mathvariant":2057},[1677,18102,1692],{"stretchy":1685},[1677,18104,1686],{"stretchy":1685},[10554,18106,18107,18109,18111],{},[898,18108,12429],{},[898,18110,1675],{},[1677,18112,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1805,18114,18115,18117],{},[1677,18116,1692],{"stretchy":1685},[1810,18118,1812],{},[1677,18120,1776],{},[1677,18122,1686],{"stretchy":1685},[10554,18124,18125,18127,18133],{},[898,18126,1682],{},[895,18128,18129,18131],{},[898,18130,1675],{},[898,18132,1675],{},[895,18134,18135,18137],{},[1677,18136,2059],{"mathvariant":2057},[1677,18138,2059],{"mathvariant":2057},[1677,18140,1776],{},[898,18142,17834],{},[10554,18144,18145,18147,18153],{},[898,18146,12429],{},[895,18148,18149,18151],{},[898,18150,1675],{},[898,18152,1675],{},[895,18154,18155,18157],{},[1677,18156,2059],{"mathvariant":2057},[1677,18158,2059],{"mathvariant":2057},[1677,18160,1692],{"stretchy":1685},[1677,18162,1686],{"stretchy":1685},[10554,18164,18165,18167,18169],{},[898,18166,12429],{},[898,18168,1689],{},[1677,18170,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1805,18172,18173,18175],{},[1677,18174,1692],{"stretchy":1685},[1810,18176,1812],{},[1677,18178,1906],{},[1810,18180,1812],{},[1677,18182,1686],{"stretchy":1685},[10554,18184,18185,18187,18193],{},[898,18186,1682],{},[895,18188,18189,18191],{},[898,18190,1689],{},[898,18192,1675],{},[895,18194,18195,18197],{},[1677,18196,2059],{"mathvariant":2057},[1677,18198,2059],{"mathvariant":2057},[1677,18200,1776],{},[898,18202,17834],{},[10554,18204,18205,18207,18213],{},[898,18206,12429],{},[895,18208,18209,18211],{},[898,18210,1689],{},[898,18212,1675],{},[895,18214,18215,18217],{},[1677,18216,2059],{"mathvariant":2057},[1677,18218,2059],{"mathvariant":2057},[1677,18220,1692],{"stretchy":1685},[1969,18222,2668],{},[10554,18224,18225,18227,18229],{},[898,18226,12429],{},[898,18228,1689],{},[1677,18230,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1969,18232,2668],{},[10554,18234,18235,18237,18239],{},[898,18236,12429],{},[898,18238,1675],{},[1677,18240,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[902,18242,18243],{"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",[724,18245,18246,18247,18277],{},"Je-li ",[883,18248,18250],{"className":18249},[886],[888,18251,18252],{"xmlns":890},[892,18253,18254,18274],{},[895,18255,18256,18258,18260,18262,18264,18266,18272],{},[1677,18257,2167],{"stretchy":1685},[898,18259,207],{},[1677,18261,1967],{"separator":1966},[898,18263,1779],{},[1677,18265,1967],{"separator":1966},[1953,18267,18268,18270],{},[898,18269,17834],{},[1810,18271,2008],{},[1677,18273,2182],{"stretchy":1685},[902,18275,18276],{"encoding":904},"[a, b, \\lambda_0]"," podezřelý bod:",[120,18279,18280,18348],{},[123,18281,18282,3095,18318,18320,18321],{},[883,18283,18285],{"className":18284},[886],[888,18286,18287],{"xmlns":890},[892,18288,18289,18315],{},[895,18290,18291,18293,18295,18297,18299,18301,18303,18309,18311,18313],{},[898,18292,5571],{},[1677,18294,1686],{"stretchy":1685},[898,18296,207],{},[1677,18298,1967],{"separator":1966},[898,18300,1779],{},[1677,18302,1967],{"separator":1966},[1953,18304,18305,18307],{},[898,18306,17834],{},[1810,18308,2008],{},[1677,18310,1692],{"stretchy":1685},[1677,18312,3128],{},[1810,18314,2008],{},[902,18316,18317],{"encoding":904},"D(a, b, \\lambda_0) \u003C 0",[38,18319,3398],{}," vázané podmínkou ",[883,18322,18324],{"className":18323},[886],[888,18325,18326],{"xmlns":890},[892,18327,18328,18346],{},[895,18329,18330,18332,18334,18336,18338,18340,18342,18344],{},[898,18331,12429],{},[1677,18333,1686],{"stretchy":1685},[898,18335,1689],{},[1677,18337,1967],{"separator":1966},[898,18339,1675],{},[1677,18341,1692],{"stretchy":1685},[1677,18343,1679],{},[1810,18345,2008],{},[902,18347,12446],{"encoding":904},[123,18349,18350,3095,18386,18320,18388],{},[883,18351,18353],{"className":18352},[886],[888,18354,18355],{"xmlns":890},[892,18356,18357,18383],{},[895,18358,18359,18361,18363,18365,18367,18369,18371,18377,18379,18381],{},[898,18360,5571],{},[1677,18362,1686],{"stretchy":1685},[898,18364,207],{},[1677,18366,1967],{"separator":1966},[898,18368,1779],{},[1677,18370,1967],{"separator":1966},[1953,18372,18373,18375],{},[898,18374,17834],{},[1810,18376,2008],{},[1677,18378,1692],{"stretchy":1685},[1677,18380,3089],{},[1810,18382,2008],{},[902,18384,18385],{"encoding":904},"D(a, b, \\lambda_0) > 0",[38,18387,3456],{},[883,18389,18391],{"className":18390},[886],[888,18392,18393],{"xmlns":890},[892,18394,18395,18413],{},[895,18396,18397,18399,18401,18403,18405,18407,18409,18411],{},[898,18398,12429],{},[1677,18400,1686],{"stretchy":1685},[898,18402,1689],{},[1677,18404,1967],{"separator":1966},[898,18406,1675],{},[1677,18408,1692],{"stretchy":1685},[1677,18410,1679],{},[1810,18412,2008],{},[902,18414,12446],{"encoding":904},[115,18416,18418],{"id":18417},"význam-multiplikátoru","Význam multiplikátoru",[724,18420,18421],{},[883,18422,18424],{"className":18423},[886],[888,18425,18426],{"xmlns":890},[892,18427,18428,18480],{},[895,18429,18430,18432,18434,18456,18458],{},[898,18431,17834],{},[1677,18433,1679],{},[2010,18435,18436,18444],{},[10554,18437,18438,18440,18442],{},[898,18439,1682],{},[898,18441,1689],{},[1677,18443,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[895,18445,18446,18448],{},[1677,18447,1906],{},[10554,18449,18450,18452,18454],{},[898,18451,12429],{},[898,18453,1689],{},[1677,18455,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,18457,1679],{},[2010,18459,18460,18468],{},[10554,18461,18462,18464,18466],{},[898,18463,1682],{},[898,18465,1675],{},[1677,18467,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[895,18469,18470,18472],{},[1677,18471,1906],{},[10554,18473,18474,18476,18478],{},[898,18475,12429],{},[898,18477,1675],{},[1677,18479,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[902,18481,18482],{"encoding":904},"\\lambda = \\frac{f'_x}{-g'_x} = \\frac{f'_y}{-g'_y}",[724,18484,18485,18498],{},[883,18486,18488],{"className":18487},[886],[888,18489,18490],{"xmlns":890},[892,18491,18492,18496],{},[895,18493,18494],{},[898,18495,17834],{},[902,18497,17887],{"encoding":904}," udává:",[120,18500,18501,18507],{},[123,18502,18503,18504],{},"konstantní ",[38,18505,18506],{},"poměr mezi mezním prospěchem a mezním nákladem",[123,18508,18509,18512,18513,18526],{},[38,18510,18511],{},"náklady příležitosti"," (opportunity cost) — o kolik vzroste optimální hodnota ",[883,18514,18516],{"className":18515},[886],[888,18517,18518],{"xmlns":890},[892,18519,18520,18524],{},[895,18521,18522],{},[898,18523,1682],{},[902,18525,1682],{"encoding":904},", uvolní-li se omezení o jednotku",[115,18528,18530],{"id":18529},"alternativní-postup","Alternativní postup",[724,18532,18533,18534,18561,18562,18586,18587,18611,18612,18625,18626,1656],{},"Lze-li z ",[883,18535,18537],{"className":18536},[886],[888,18538,18539],{"xmlns":890},[892,18540,18541,18559],{},[895,18542,18543,18545,18547,18549,18551,18553,18555,18557],{},[898,18544,12429],{},[1677,18546,1686],{"stretchy":1685},[898,18548,1689],{},[1677,18550,1967],{"separator":1966},[898,18552,1675],{},[1677,18554,1692],{"stretchy":1685},[1677,18556,1679],{},[1810,18558,2008],{},[902,18560,12446],{"encoding":904}," vyjádřit ",[883,18563,18565],{"className":18564},[886],[888,18566,18567],{"xmlns":890},[892,18568,18569,18583],{},[895,18570,18571,18573,18575,18577,18579,18581],{},[898,18572,1675],{},[1677,18574,1679],{},[898,18576,1675],{},[1677,18578,1686],{"stretchy":1685},[898,18580,1689],{},[1677,18582,1692],{"stretchy":1685},[902,18584,18585],{"encoding":904},"y = y(x)"," (nebo ",[883,18588,18590],{"className":18589},[886],[888,18591,18592],{"xmlns":890},[892,18593,18594,18608],{},[895,18595,18596,18598,18600,18602,18604,18606],{},[898,18597,1689],{},[1677,18599,1679],{},[898,18601,1689],{},[1677,18603,1686],{"stretchy":1685},[898,18605,1675],{},[1677,18607,1692],{"stretchy":1685},[902,18609,18610],{"encoding":904},"x = x(y)","), dosadíme do ",[883,18613,18615],{"className":18614},[886],[888,18616,18617],{"xmlns":890},[892,18618,18619,18623],{},[895,18620,18621],{},[898,18622,1682],{},[902,18624,1682],{"encoding":904}," a převedeme na ",[38,18627,18628],{},"extrém funkce jedné proměnné",[115,18630,18632],{"id":18631},"použití-v-imek","Použití v ImeK",[198,18634,18636],{"id":18635},"maximalizace-užitečnosti","Maximalizace užitečnosti",[724,18638,18639,18640,1656],{},"Rozpočtové omezení: ",[883,18641,18643],{"className":18642},[886],[888,18644,18645],{"xmlns":890},[892,18646,18647,18687],{},[895,18648,18649,18655,18657,18665,18671,18673,18681],{},[1805,18650,18651,18653],{},[898,18652,10516],{},[1677,18654,5742],{},[1677,18656,1679],{},[10554,18658,18659,18661,18663],{},[898,18660,5325],{},[1810,18662,1959],{},[1677,18664,5742],{},[1953,18666,18667,18669],{},[898,18668,2470],{},[1810,18670,1959],{},[1677,18672,1776],{},[10554,18674,18675,18677,18679],{},[898,18676,5325],{},[1810,18678,1812],{},[1677,18680,5742],{},[1953,18682,18683,18685],{},[898,18684,2470],{},[1810,18686,1812],{},[902,18688,18689],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2",[724,18691,18692],{},[883,18693,18695],{"className":18694},[886],[888,18696,18697],{"xmlns":890},[892,18698,18699,18793],{},[895,18700,18701,18703,18705,18711,18713,18719,18721,18723,18725,18727,18729,18731,18737,18739,18745,18747,18749,18751,18753,18759,18761,18769,18775,18777,18785,18791],{},[898,18702,11183],{},[1677,18704,1686],{"stretchy":1685},[1953,18706,18707,18709],{},[898,18708,2470],{},[1810,18710,1959],{},[1677,18712,1967],{"separator":1966},[1953,18714,18715,18717],{},[898,18716,2470],{},[1810,18718,1812],{},[1677,18720,1967],{"separator":1966},[898,18722,17834],{},[1677,18724,1692],{"stretchy":1685},[1677,18726,1679],{},[898,18728,900],{},[1677,18730,1686],{"stretchy":1685},[1953,18732,18733,18735],{},[898,18734,2470],{},[1810,18736,1959],{},[1677,18738,1967],{"separator":1966},[1953,18740,18741,18743],{},[898,18742,2470],{},[1810,18744,1812],{},[1677,18746,1692],{"stretchy":1685},[1677,18748,1776],{},[898,18750,17834],{},[1677,18752,1686],{"stretchy":1685},[1805,18754,18755,18757],{},[898,18756,10516],{},[1677,18758,5742],{},[1677,18760,1906],{},[10554,18762,18763,18765,18767],{},[898,18764,5325],{},[1810,18766,1959],{},[1677,18768,5742],{},[1953,18770,18771,18773],{},[898,18772,2470],{},[1810,18774,1959],{},[1677,18776,1906],{},[10554,18778,18779,18781,18783],{},[898,18780,5325],{},[1810,18782,1812],{},[1677,18784,5742],{},[1953,18786,18787,18789],{},[898,18788,2470],{},[1810,18790,1812],{},[1677,18792,1692],{"stretchy":1685},[902,18794,18795],{"encoding":904},"L(Q_1, Q_2, \\lambda) = U(Q_1, Q_2) + \\lambda (Y^* - P_1^* Q_1 - P_2^* Q_2)",[724,18797,18798,18799,1343,18831,1343,18863,18912,18913,18967,18968,1656],{},"Soustava: ",[883,18800,18802],{"className":18801},[886],[888,18803,18804],{"xmlns":890},[892,18805,18806,18828],{},[895,18807,18808,18816,18818,18820],{},[10554,18809,18810,18812,18814],{},[898,18811,900],{},[1810,18813,1959],{},[1677,18815,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,18817,1679],{},[898,18819,17834],{},[10554,18821,18822,18824,18826],{},[898,18823,5325],{},[1810,18825,1959],{},[1677,18827,5742],{},[902,18829,18830],{"encoding":904},"U'_1 = \\lambda P_1^*",[883,18832,18834],{"className":18833},[886],[888,18835,18836],{"xmlns":890},[892,18837,18838,18860],{},[895,18839,18840,18848,18850,18852],{},[10554,18841,18842,18844,18846],{},[898,18843,900],{},[1810,18845,1812],{},[1677,18847,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,18849,1679],{},[898,18851,17834],{},[10554,18853,18854,18856,18858],{},[898,18855,5325],{},[1810,18857,1812],{},[1677,18859,5742],{},[902,18861,18862],{"encoding":904},"U'_2 = \\lambda P_2^*",[883,18864,18866],{"className":18865},[886],[888,18867,18868],{"xmlns":890},[892,18869,18870,18910],{},[895,18871,18872,18878,18880,18888,18894,18896,18904],{},[1805,18873,18874,18876],{},[898,18875,10516],{},[1677,18877,5742],{},[1677,18879,1679],{},[10554,18881,18882,18884,18886],{},[898,18883,5325],{},[1810,18885,1959],{},[1677,18887,5742],{},[1953,18889,18890,18892],{},[898,18891,2470],{},[1810,18893,1959],{},[1677,18895,1776],{},[10554,18897,18898,18900,18902],{},[898,18899,5325],{},[1810,18901,1812],{},[1677,18903,5742],{},[1953,18905,18906,18908],{},[898,18907,2470],{},[1810,18909,1812],{},[902,18911,18689],{"encoding":904},". Z prvních dvou: ",[883,18914,18916],{"className":18915},[886],[888,18917,18918],{"xmlns":890},[892,18919,18920,18964],{},[895,18921,18922,18942,18944],{},[2006,18923,18924],{"scriptlevel":2008,"displaystyle":1685},[2010,18925,18926,18934],{},[10554,18927,18928,18930,18932],{},[898,18929,900],{},[1810,18931,1959],{},[1677,18933,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[10554,18935,18936,18938,18940],{},[898,18937,900],{},[1810,18939,1812],{},[1677,18941,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,18943,1679],{},[2006,18945,18946],{"scriptlevel":2008,"displaystyle":1685},[2010,18947,18948,18956],{},[10554,18949,18950,18952,18954],{},[898,18951,5325],{},[1810,18953,1959],{},[1677,18955,5742],{},[10554,18957,18958,18960,18962],{},[898,18959,5325],{},[1810,18961,1812],{},[1677,18963,5742],{},[902,18965,18966],{"encoding":904},"\\tfrac{U'_1}{U'_2} = \\tfrac{P_1^*}{P_2^*}",", tj. ",[883,18969,18971],{"className":18970},[886],[888,18972,18973],{"xmlns":890},[892,18974,18975,19007],{},[895,18976,18977,18979,18981,18983,18985,18987],{},[898,18978,2499],{},[898,18980,5382],{},[898,18982,2458],{},[898,18984,10061],{},[1677,18986,1679],{},[2006,18988,18989],{"scriptlevel":2008,"displaystyle":1685},[2010,18990,18991,18999],{},[10554,18992,18993,18995,18997],{},[898,18994,5325],{},[1810,18996,1959],{},[1677,18998,5742],{},[10554,19000,19001,19003,19005],{},[898,19002,5325],{},[1810,19004,1812],{},[1677,19006,5742],{},[902,19008,19009],{"encoding":904},"MRCS = \\tfrac{P_1^*}{P_2^*}",[198,19011,19013],{"id":19012},"minimalizace-výdajů","Minimalizace výdajů",[724,19015,19016,19017,1656],{},"Podmínka dané užitečnosti ",[883,19018,19020],{"className":19019},[886],[888,19021,19022],{"xmlns":890},[892,19023,19024,19054],{},[895,19025,19026,19032,19034,19036,19038,19044,19046,19052],{},[1805,19027,19028,19030],{},[898,19029,900],{},[1677,19031,5742],{},[1677,19033,1679],{},[898,19035,900],{},[1677,19037,1686],{"stretchy":1685},[1953,19039,19040,19042],{},[898,19041,2470],{},[1810,19043,1959],{},[1677,19045,1967],{"separator":1966},[1953,19047,19048,19050],{},[898,19049,2470],{},[1810,19051,1812],{},[1677,19053,1692],{"stretchy":1685},[902,19055,19056],{"encoding":904},"U^* = U(Q_1, Q_2)",[724,19058,19059],{},[883,19060,19062],{"className":19061},[886],[888,19063,19064],{"xmlns":890},[892,19065,19066,19160],{},[895,19067,19068,19070,19072,19078,19080,19086,19088,19090,19092,19094,19102,19108,19110,19118,19124,19126,19128,19130,19136,19138,19140,19142,19148,19150,19156,19158],{},[898,19069,11183],{},[1677,19071,1686],{"stretchy":1685},[1953,19073,19074,19076],{},[898,19075,2470],{},[1810,19077,1959],{},[1677,19079,1967],{"separator":1966},[1953,19081,19082,19084],{},[898,19083,2470],{},[1810,19085,1812],{},[1677,19087,1967],{"separator":1966},[898,19089,17834],{},[1677,19091,1692],{"stretchy":1685},[1677,19093,1679],{},[10554,19095,19096,19098,19100],{},[898,19097,5325],{},[1810,19099,1959],{},[1677,19101,5742],{},[1953,19103,19104,19106],{},[898,19105,2470],{},[1810,19107,1959],{},[1677,19109,1776],{},[10554,19111,19112,19114,19116],{},[898,19113,5325],{},[1810,19115,1812],{},[1677,19117,5742],{},[1953,19119,19120,19122],{},[898,19121,2470],{},[1810,19123,1812],{},[1677,19125,1776],{},[898,19127,17834],{},[1677,19129,1686],{"stretchy":1685},[1805,19131,19132,19134],{},[898,19133,900],{},[1677,19135,5742],{},[1677,19137,1906],{},[898,19139,900],{},[1677,19141,1686],{"stretchy":1685},[1953,19143,19144,19146],{},[898,19145,2470],{},[1810,19147,1959],{},[1677,19149,1967],{"separator":1966},[1953,19151,19152,19154],{},[898,19153,2470],{},[1810,19155,1812],{},[1677,19157,1692],{"stretchy":1685},[1677,19159,1692],{"stretchy":1685},[902,19161,19162],{"encoding":904},"L(Q_1, Q_2, \\lambda) = P_1^* Q_1 + P_2^* Q_2 + \\lambda (U^* - U(Q_1, Q_2))",[724,19164,19165,19166,1656],{},"Duálně dostaneme Hicksovy poptávkové funkce ",[883,19167,19169],{"className":19168},[886],[888,19170,19171],{"xmlns":890},[892,19172,19173,19212],{},[895,19174,19175,19182,19184,19190,19192,19198,19200,19206,19208,19210],{},[1953,19176,19177,19179],{},[898,19178,2470],{},[898,19180,19181],{},"i",[1677,19183,1679],{},[1953,19185,19186,19188],{},[898,19187,5571],{},[898,19189,19181],{},[1677,19191,1686],{"stretchy":1685},[1953,19193,19194,19196],{},[898,19195,5325],{},[1810,19197,1959],{},[1677,19199,1967],{"separator":1966},[1953,19201,19202,19204],{},[898,19203,5325],{},[1810,19205,1812],{},[1677,19207,1967],{"separator":1966},[898,19209,900],{},[1677,19211,1692],{"stretchy":1685},[902,19213,19214],{"encoding":904},"Q_i = D_i(P_1, P_2, U)",[115,19216,3473],{"id":3472},[120,19218,19219,19226,19233,19242],{},[123,19220,19221,1884,19223],{},[38,19222,3480],{},[207,19224,784],{"className":19225,"dataFsResolvedFilePath":782,"href":783},[210],[123,19227,19228,1884,19230],{},[38,19229,3488],{},[207,19231,13330],{"className":19232,"dataFsResolvedFilePath":800,"href":801},[210],[123,19234,19235,1884,19238,19241],{},[38,19236,19237],{},"Aplikace v kurzu:",[207,19239,880],{"className":19240,"dataFsResolvedFilePath":878,"href":879},[210]," (maximalizace užitečnosti při rozpočtovém omezení), minimalizace výdajů (duální úloha), optimalizace produkce",[123,19243,19244,1884,19246,1343,19249,19252],{},[38,19245,3496],{},[207,19247,936],{"className":19248,"dataFsResolvedFilePath":934,"href":935},[210],[207,19250,1400],{"className":19251,"dataFsResolvedFilePath":1398,"href":1399},[210]," (IpmrK)",{"title":641,"searchDepth":642,"depth":642,"links":19254},[19255,19256,19257,19258,19259,19260,19264],{"id":17802,"depth":642,"text":17803},{"id":2932,"depth":642,"text":2933},{"id":3006,"depth":642,"text":3007},{"id":18417,"depth":642,"text":18418},{"id":18529,"depth":642,"text":18530},{"id":18631,"depth":642,"text":18632,"children":19261},[19262,19263],{"id":18635,"depth":649,"text":18636},{"id":19012,"depth":649,"text":19013},{"id":3472,"depth":642,"text":3473},[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":17671,"description":19266},[1135,1137],"topics\u002Flagrangeova-metoda",[1128,1619,19273,19274],"vazane-extremy","multiplikator","PRnK6wpMGySFp-C47ico7wAs4MDBp47Titm-Obyzgow",{"id":19277,"title":936,"body":19278,"course":1128,"courses":659,"created":10944,"description":641,"extension":661,"meta":29146,"navigation":664,"path":29147,"seo":29148,"sources":29149,"stem":29150,"tags":29151,"type":3538,"updated":677,"__hash__":29155},"topics\u002Ftopics\u002Fnarodni-duchod.md",{"type":9,"value":19279,"toc":29108},[19280,19283,19285,19408,19543,19547,19550,19663,19667,19695,19742,19745,19811,19856,19859,19885,19916,19920,19924,19968,20012,20074,20129,20132,20136,20139,20186,20283,20389,20395,20472,20501,20640,20644,20673,20723,20870,20960,20964,20990,21028,21055,21093,21155,21230,21308,21366,21432,21476,21480,21538,21587,21632,21845,21965,21971,21975,21998,22002,22009,22013,22044,22079,22083,22133,22221,22263,22284,22346,22406,22410,22481,22549,22621,22736,22784,22788,22791,22832,22871,22894,23008,23172,23180,23207,23237,23240,23317,23470,23554,23893,23897,24021,24157,24293,24346,24349,24599,24680,24684,24687,24745,24777,24780,24829,24832,24903,25099,25103,25254,25484,25522,25575,25621,25624,25680,25729,25933,26023,26027,26043,26050,26219,26223,26294,26375,26456,26535,26681,26769,26773,26956,27087,27132,27229,27233,27972,27974,29025,29027],[12,19281,936],{"id":19282},"národní-důchod",[115,19284,13396],{"id":13395},[724,19286,19287,19288,1884,19292,19295,19296,1884,19299,19312,19313,19316,19317,19320,19321,19324,19325,19327,19328,1884,19330,19347,19348,19365,19366,19369,19370,5306],{},"Kapitola 7 ",[207,19289,19291],{"className":19290,"dataFsResolvedFilePath":1641,"href":1642},[210],"Matematické ekonomie",[38,19293,19294],{},"přechází z mikroekonomie do makroekonomie",": předmětem zkoumání už není jedna firma, ale celá národní ekonomika popsaná ",[38,19297,19298],{},"národním důchodem",[883,19300,19302],{"className":19301},[886],[888,19303,19304],{"xmlns":890},[892,19305,19306,19310],{},[895,19307,19308],{},[898,19309,10516],{},[902,19311,10516],{"encoding":904},". Budují se postupně bohatší modely — ",[38,19314,19315],{},"C-I"," (jen spotřeba a investice) → ",[38,19318,19319],{},"C-I-G"," (přidá vládu a zdanění) → ",[38,19322,19323],{},"C-I-G-X"," (otevře ekonomiku o čistý export) → ",[38,19326,13401],{}," (propojí trh zboží s trhem peněz přes úrokovou míru). V každém modelu hledáme ",[38,19329,15275],{},[883,19331,19333],{"className":19332},[886],[888,19334,19335],{"xmlns":890},[892,19336,19337,19345],{},[895,19338,19339],{},[1805,19340,19341,19343],{},[898,19342,10516],{},[898,19344,5640],{},[902,19346,15293],{"encoding":904}," jako řešení soustavy lineárních rovnic; citlivost ",[883,19349,19351],{"className":19350},[886],[888,19352,19353],{"xmlns":890},[892,19354,19355,19363],{},[895,19356,19357],{},[1805,19358,19359,19361],{},[898,19360,10516],{},[898,19362,5640],{},[902,19364,15293],{"encoding":904}," na exogenní veličiny popisují ",[38,19367,19368],{},"multiplikátory"," (zejména Keynesův multiplikátor investic ",[883,19371,19373],{"className":19372},[886],[888,19374,19375],{"xmlns":890},[892,19376,19377,19405],{},[895,19378,19379,19381,19383,19385,19387,19389,19391,19393,19395,19397,19399,19401,19403],{},[1810,19380,1959],{},[898,19382,6062],{"mathvariant":2057},[1677,19384,1686],{"stretchy":1685},[1810,19386,1959],{},[1677,19388,1906],{},[898,19390,207],{},[1677,19392,1692],{"stretchy":1685},[1677,19394,1679],{},[1810,19396,1959],{},[898,19398,6062],{"mathvariant":2057},[898,19400,2499],{},[898,19402,5325],{},[898,19404,10061],{},[902,19406,19407],{"encoding":904},"1\u002F(1-a) = 1\u002FMPS",[5254,19409,19410],{},[724,19411,19412,19414,19415,19418,19419,19437,19438,19468,19469,19516,19517,19519,19520,19542],{},[883,19413,5543],{}," Intuice\n",[38,19416,19417],{},"Makroekonomie je zrcadlovým obrazem mikroekonomie"," na úrovni celé ekonomiky. Mezní sklon ke spotřebě ",[883,19420,19422],{"className":19421},[886],[888,19423,19424],{"xmlns":890},[892,19425,19426,19434],{},[895,19427,19428,19430,19432],{},[898,19429,2499],{},[898,19431,5325],{},[898,19433,2458],{},[902,19435,19436],{"encoding":904},"MPC"," je „ta část dodatečné korunky důchodu, kterou domácnost utratí“; zbytek ",[883,19439,19441],{"className":19440},[886],[888,19442,19443],{"xmlns":890},[892,19444,19445,19465],{},[895,19446,19447,19449,19451,19453,19455,19457,19459,19461,19463],{},[898,19448,2499],{},[898,19450,5325],{},[898,19452,10061],{},[1677,19454,1679],{},[1810,19456,1959],{},[1677,19458,1906],{},[898,19460,2499],{},[898,19462,5325],{},[898,19464,2458],{},[902,19466,19467],{"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 ",[883,19470,19472],{"className":19471},[886],[888,19473,19474],{"xmlns":890},[892,19475,19476,19513],{},[895,19477,19478,19480,19482,19484,19486,19492,19494,19497,19499,19501,19503,19505,19507,19509,19511],{},[1810,19479,1959],{},[1677,19481,1776],{},[898,19483,207],{},[1677,19485,1776],{},[1805,19487,19488,19490],{},[898,19489,207],{},[1810,19491,1812],{},[1677,19493,1776],{},[1677,19495,19496],{},"⋯",[1677,19498,1679],{},[1810,19500,1959],{},[898,19502,6062],{"mathvariant":2057},[1677,19504,1686],{"stretchy":1685},[1810,19506,1959],{},[1677,19508,1906],{},[898,19510,207],{},[1677,19512,1692],{"stretchy":1685},[902,19514,19515],{"encoding":904},"1 + a + a^2 + \\dots = 1\u002F(1-a)","). ",[38,19518,13401],{}," 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 ",[883,19521,19523],{"className":19522},[886],[888,19524,19525],{"xmlns":890},[892,19526,19527,19539],{},[895,19528,19529,19531,19533,19535,19537],{},[1677,19530,1686],{"stretchy":1685},[898,19532,10516],{},[1677,19534,1967],{"separator":1966},[898,19536,13431],{},[1677,19538,1692],{"stretchy":1685},[902,19540,19541],{"encoding":904},"(Y, r)"," jsou oba trhy v rovnováze současně.",[115,19544,19546],{"id":19545},"úvod-cílové-znalosti-kapitoly-7","Úvod — cílové znalosti kapitoly 7",[724,19548,19549],{},"Po prostudování kapitoly by čtenář měl umět:",[120,19551,19552,19555,19558,19561,19564,19567,19570,19660],{},[123,19553,19554],{},"popsat zjednodušený model národní ekonomiky,",[123,19556,19557],{},"formulovat pojmy funkcí spotřeby a úspor spolu s jejich základními vlastnostmi,",[123,19559,19560],{},"popsat lineární model spotřeby a úspor,",[123,19562,19563],{},"stanovit mezní sklony ke spotřebě a úsporám,",[123,19565,19566],{},"vymezit pojem makroekonomické rovnováhy ve vztahu k agregátní poptávce a nabídce,",[123,19568,19569],{},"vyložit pojmy křivek agregátní poptávky, agregátní nabídky a rovnovážného bodu,",[123,19571,19572,19573,1343,19590,1343,19612,5272,19637,19659],{},"popsat modely ",[883,19574,19576],{"className":19575},[886],[888,19577,19578],{"xmlns":890},[892,19579,19580,19588],{},[895,19581,19582,19584,19586],{},[898,19583,2458],{},[1969,19585,13680],{},[898,19587,13574],{},[902,19589,13685],{"encoding":904},[883,19591,19593],{"className":19592},[886],[888,19594,19595],{"xmlns":890},[892,19596,19597,19609],{},[895,19598,19599,19601,19603,19605,19607],{},[898,19600,2458],{},[1969,19602,13680],{},[898,19604,13574],{},[1969,19606,13680],{},[898,19608,13502],{},[902,19610,19611],{"encoding":904},"C\\text{-}I\\text{-}G",[883,19613,19615],{"className":19614},[886],[888,19616,19617],{"xmlns":890},[892,19618,19619,19635],{},[895,19620,19621,19623,19625,19627,19629,19631,19633],{},[898,19622,2458],{},[1969,19624,13680],{},[898,19626,13574],{},[1969,19628,13680],{},[898,19630,13502],{},[1969,19632,13680],{},[898,19634,13710],{},[902,19636,13713],{"encoding":904},[883,19638,19640],{"className":19639},[886],[888,19641,19642],{"xmlns":890},[892,19643,19644,19656],{},[895,19645,19646,19648,19650,19652,19654],{},[898,19647,13574],{},[898,19649,10061],{},[1969,19651,13680],{},[898,19653,11183],{},[898,19655,2499],{},[902,19657,19658],{"encoding":904},"IS\\text{-}LM"," národních ekonomik a vypočítat rovnovážné veličiny,",[123,19661,19662],{},"formulovat a stanovit základní makroekonomické multiplikátory.",[115,19664,19666],{"id":19665},"gnp-a-národní-důchod","GNP a národní důchod",[724,19668,19669,1884,19672,11413,19691,19694],{},[38,19670,19671],{},"Hrubý národní produkt",[883,19673,19675],{"className":19674},[886],[888,19676,19677],{"xmlns":890},[892,19678,19679,19688],{},[895,19680,19681,19683,19686],{},[898,19682,13502],{},[898,19684,19685],{},"N",[898,19687,5325],{},[902,19689,19690],{"encoding":904},"GNP",[614,19692,19693],{},"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:",[724,19696,19697],{},[883,19698,19700],{"className":19699},[886],[888,19701,19702],{"xmlns":890},[892,19703,19704,19739],{},[895,19705,19706,19708,19710,19712,19714,19716,19718,19720,19722,19724,19726,19728,19730,19732,19734,19737],{},[898,19707,13502],{},[898,19709,19685],{},[898,19711,5325],{},[1677,19713,1679],{},[898,19715,2458],{},[1677,19717,1776],{},[898,19719,13574],{},[1677,19721,1776],{},[898,19723,13502],{},[1677,19725,1776],{},[898,19727,13710],{},[1677,19729,1967],{"separator":1966},[7266,19731],{"width":7268},[1677,19733,1686],{"stretchy":1685},[1810,19735,19736],{},"7.1",[1677,19738,1692],{"stretchy":1685},[902,19740,19741],{"encoding":904},"GNP = C + I + G + X, \\qquad (7.1)",[724,19743,19744],{},"kde",[120,19746,19747,19763,19779,19795],{},[123,19748,19749,19762],{},[883,19750,19752],{"className":19751},[886],[888,19753,19754],{"xmlns":890},[892,19755,19756,19760],{},[895,19757,19758],{},[898,19759,2458],{},[902,19761,2458],{"encoding":904}," — výdaje domácností na spotřebu,",[123,19764,19765,19778],{},[883,19766,19768],{"className":19767},[886],[888,19769,19770],{"xmlns":890},[892,19771,19772,19776],{},[895,19773,19774],{},[898,19775,13574],{},[902,19777,13574],{"encoding":904}," — hrubé domácí investice,",[123,19780,19781,19794],{},[883,19782,19784],{"className":19783},[886],[888,19785,19786],{"xmlns":890},[892,19787,19788,19792],{},[895,19789,19790],{},[898,19791,13502],{},[902,19793,13502],{"encoding":904}," — vládní výdaje,",[123,19796,19797,19810],{},[883,19798,19800],{"className":19799},[886],[888,19801,19802],{"xmlns":890},[892,19803,19804,19808],{},[895,19805,19806],{},[898,19807,13710],{},[902,19809,13710],{"encoding":904}," — čistý export.",[724,19812,19813,19814,19831,19832,19835,19836,1884,19839,11413,19852,19855],{},"K měření ",[883,19815,19817],{"className":19816},[886],[888,19818,19819],{"xmlns":890},[892,19820,19821,19829],{},[895,19822,19823,19825,19827],{},[898,19824,13502],{},[898,19826,19685],{},[898,19828,5325],{},[902,19830,19690],{"encoding":904}," se užívá ",[38,19833,19834],{},"důchodová metoda",". Jejím hlavním konstrukčním prvkem je ",[38,19837,19838],{},"národní důchod",[883,19840,19842],{"className":19841},[886],[888,19843,19844],{"xmlns":890},[892,19845,19846,19850],{},[895,19847,19848],{},[898,19849,10516],{},[902,19851,10516],{"encoding":904},[614,19853,19854],{},"national income",") — součet důchodů všech vrstev domácností, tj. tok důchodů od firem k domácnostem jako platba za pronájem výrobních faktorů.",[724,19857,19858],{},"Pro tvorbu základních makroekonomických modelů se zjednodušeně ztotožňuje hrubý národní produkt s národním důchodem (rovněž s agregátní poptávkou):",[724,19860,19861],{},[883,19862,19864],{"className":19863},[886],[888,19865,19866],{"xmlns":890},[892,19867,19868,19882],{},[895,19869,19870,19872,19874,19876,19878,19880],{},[898,19871,13502],{},[898,19873,19685],{},[898,19875,5325],{},[1677,19877,2411],{},[898,19879,10516],{},[1677,19881,1967],{"separator":1966},[902,19883,19884],{"encoding":904},"GNP \\approx Y,",[724,19886,19887,19888,11413,19891,19894,19895,19908,19909,19912,19913,1656],{},"a užívá se společného názvu ",[38,19889,19890],{},"důchod",[614,19892,19893],{},"income",") s označením ",[883,19896,19898],{"className":19897},[886],[888,19899,19900],{"xmlns":890},[892,19901,19902,19906],{},[895,19903,19904],{},[898,19905,10516],{},[902,19907,10516],{"encoding":904},". Domácnosti důchod použijí ke ",[38,19910,19911],{},"spotřebě"," zboží a služeb nebo ke tvorbě ",[38,19914,19915],{},"úspor",[115,19917,19919],{"id":19918},"spotřeba-a-úspory","Spotřeba a úspory",[198,19921,19923],{"id":19922},"funkce-spotřeby-a-úspor","Funkce spotřeby a úspor",[724,19925,19926,19927,19940,19941,19954,19955,2385],{},"Jak spotřeba ",[883,19928,19930],{"className":19929},[886],[888,19931,19932],{"xmlns":890},[892,19933,19934,19938],{},[895,19935,19936],{},[898,19937,2458],{},[902,19939,2458],{"encoding":904},", tak úspory ",[883,19942,19944],{"className":19943},[886],[888,19945,19946],{"xmlns":890},[892,19947,19948,19952],{},[895,19949,19950],{},[898,19951,10061],{},[902,19953,10061],{"encoding":904}," závisejí na důchodu ",[883,19956,19958],{"className":19957},[886],[888,19959,19960],{"xmlns":890},[892,19961,19962,19966],{},[895,19963,19964],{},[898,19965,10516],{},[902,19967,10516],{"encoding":904},[724,19969,19970],{},[883,19971,19973],{"className":19972},[886],[888,19974,19975],{"xmlns":890},[892,19976,19977,20009],{},[895,19978,19979,19981,19983,19985,19987,19989,19991,19993,19995,19997,19999,20001,20003,20005,20007],{},[898,19980,2458],{},[1677,19982,1679],{},[898,19984,2458],{},[1677,19986,1686],{"stretchy":1685},[898,19988,10516],{},[1677,19990,1692],{"stretchy":1685},[1677,19992,1967],{"separator":1966},[7266,19994],{"width":7268},[898,19996,10061],{},[1677,19998,1679],{},[898,20000,10061],{},[1677,20002,1686],{"stretchy":1685},[898,20004,10516],{},[1677,20006,1692],{"stretchy":1685},[898,20008,1656],{"mathvariant":2057},[902,20010,20011],{"encoding":904},"C = C(Y), \\qquad S = S(Y).",[724,20013,20014,9490,20033,11413,20036,20039,20040,9490,20060,11413,20063,20066,20067,5272,20070,20073],{},[883,20015,20017],{"className":20016},[886],[888,20018,20019],{"xmlns":890},[892,20020,20021,20031],{},[895,20022,20023,20025,20027,20029],{},[898,20024,2458],{},[1677,20026,1686],{"stretchy":1685},[898,20028,10516],{},[1677,20030,1692],{"stretchy":1685},[902,20032,15606],{"encoding":904},[38,20034,20035],{},"funkce spotřeby",[614,20037,20038],{},"consumption function","), ",[883,20041,20043],{"className":20042},[886],[888,20044,20045],{"xmlns":890},[892,20046,20047,20057],{},[895,20048,20049,20051,20053,20055],{},[898,20050,10061],{},[1677,20052,1686],{"stretchy":1685},[898,20054,10516],{},[1677,20056,1692],{"stretchy":1685},[902,20058,20059],{"encoding":904},"S(Y)",[38,20061,20062],{},"funkce úspor",[614,20064,20065],{},"savings function","); jejich grafy se nazývají ",[38,20068,20069],{},"křivka spotřeby",[38,20071,20072],{},"křivka úspor",". Platí základní identita",[724,20075,20076],{},[883,20077,20079],{"className":20078},[886],[888,20080,20081],{"xmlns":890},[892,20082,20083,20126],{},[895,20084,20085,20087,20089,20091,20093,20095,20097,20099,20101,20103,20105,20107,20109,20111,20113,20115,20117,20119,20121,20124],{},[898,20086,10516],{},[1677,20088,1679],{},[898,20090,2458],{},[1677,20092,1776],{},[898,20094,10061],{},[1677,20096,1679],{},[898,20098,2458],{},[1677,20100,1686],{"stretchy":1685},[898,20102,10516],{},[1677,20104,1692],{"stretchy":1685},[1677,20106,1776],{},[898,20108,10061],{},[1677,20110,1686],{"stretchy":1685},[898,20112,10516],{},[1677,20114,1692],{"stretchy":1685},[898,20116,1656],{"mathvariant":2057},[7266,20118],{"width":7268},[1677,20120,1686],{"stretchy":1685},[1810,20122,20123],{},"7.2",[1677,20125,1692],{"stretchy":1685},[902,20127,20128],{"encoding":904},"Y = C + S = C(Y) + S(Y). \\qquad (7.2)",[724,20130,20131],{},"Známe-li jednu z funkcí, je tím určena i druhá. Obě funkce jsou rostoucí (s růstem důchodu roste spotřeba i úspory).",[198,20133,20135],{"id":20134},"lineární-model-spotřeby-a-úspor","Lineární model spotřeby a úspor",[724,20137,20138],{},"Nejjednodušší model předpokládá lineární tvar",[724,20140,20141],{},[883,20142,20144],{"className":20143},[886],[888,20145,20146],{"xmlns":890},[892,20147,20148,20183],{},[895,20149,20150,20152,20154,20156,20158,20160,20162,20164,20166,20168,20170,20172,20174,20176,20178,20181],{},[898,20151,2458],{},[1677,20153,1679],{},[898,20155,2458],{},[1677,20157,1686],{"stretchy":1685},[898,20159,10516],{},[1677,20161,1692],{"stretchy":1685},[1677,20163,1679],{},[898,20165,207],{},[898,20167,10516],{},[1677,20169,1776],{},[898,20171,1779],{},[1677,20173,1967],{"separator":1966},[7266,20175],{"width":7268},[1677,20177,1686],{"stretchy":1685},[1810,20179,20180],{},"7.3",[1677,20182,1692],{"stretchy":1685},[902,20184,20185],{"encoding":904},"C = C(Y) = aY + b, \\qquad (7.3)",[724,20187,5698,20188,5272,20206,20228,20229,20269,20270,1656],{},[883,20189,20191],{"className":20190},[886],[888,20192,20193],{"xmlns":890},[892,20194,20195,20203],{},[895,20196,20197,20199,20201],{},[898,20198,1779],{},[1677,20200,3089],{},[1810,20202,2008],{},[902,20204,20205],{"encoding":904},"b > 0",[883,20207,20209],{"className":20208},[886],[888,20210,20211],{"xmlns":890},[892,20212,20213,20225],{},[895,20214,20215,20217,20219,20221,20223],{},[1810,20216,2008],{},[1677,20218,3128],{},[898,20220,207],{},[1677,20222,3128],{},[1810,20224,1959],{},[902,20226,20227],{"encoding":904},"0 \u003C a \u003C 1",". Směrnice ",[883,20230,20232],{"className":20231},[886],[888,20233,20234],{"xmlns":890},[892,20235,20236,20266],{},[895,20237,20238,20240,20242,20249,20251,20254,20256,20258,20260,20262,20264],{},[898,20239,207],{},[1677,20241,1679],{},[895,20243,20244,20247],{},[898,20245,20246],{"mathvariant":2057},"t",[898,20248,12429],{"mathvariant":2057},[1969,20250,2668],{},[898,20252,20253],{},"α",[1677,20255,1679],{},[898,20257,2570],{"mathvariant":2057},[898,20259,2458],{},[898,20261,6062],{"mathvariant":2057},[898,20263,2570],{"mathvariant":2057},[898,20265,10516],{},[902,20267,20268],{"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 ",[883,20271,20273],{"className":20272},[886],[888,20274,20275],{"xmlns":890},[892,20276,20277,20281],{},[895,20278,20279],{},[898,20280,10516],{},[902,20282,10516],{"encoding":904},[724,20284,20285],{},[614,20286,20287,20288,20312,20313,20351,20352,20368,20369,1656],{},"Obrázek 7.1 — Přímka spotřeby ",[883,20289,20291],{"className":20290},[886],[888,20292,20293],{"xmlns":890},[892,20294,20295,20309],{},[895,20296,20297,20299,20301,20303,20305,20307],{},[898,20298,2458],{},[1677,20300,1679],{},[898,20302,207],{},[898,20304,10516],{},[1677,20306,1776],{},[898,20308,1779],{},[902,20310,20311],{"encoding":904},"C = aY + b"," se směrnicí ",[883,20314,20316],{"className":20315},[886],[888,20317,20318],{"xmlns":890},[892,20319,20320,20348],{},[895,20321,20322,20324,20326,20332,20334,20336,20338,20340,20342,20344,20346],{},[898,20323,207],{},[1677,20325,1679],{},[895,20327,20328,20330],{},[898,20329,20246],{"mathvariant":2057},[898,20331,12429],{"mathvariant":2057},[1969,20333,2668],{},[898,20335,20253],{},[1677,20337,1679],{},[898,20339,2570],{"mathvariant":2057},[898,20341,2458],{},[898,20343,6062],{"mathvariant":2057},[898,20345,2570],{"mathvariant":2057},[898,20347,10516],{},[902,20349,20350],{"encoding":904},"a = \\mathrm{tg}\\,\\alpha = \\Delta C\u002F\\Delta Y","; znázornění ",[883,20353,20355],{"className":20354},[886],[888,20356,20357],{"xmlns":890},[892,20358,20359,20365],{},[895,20360,20361,20363],{},[898,20362,2570],{"mathvariant":2057},[898,20364,2458],{},[902,20366,20367],{"encoding":904},"\\Delta C"," při jednotkovém přírůstku ",[883,20370,20372],{"className":20371},[886],[888,20373,20374],{"xmlns":890},[892,20375,20376,20386],{},[895,20377,20378,20380,20382,20384],{},[898,20379,2570],{"mathvariant":2057},[898,20381,10516],{},[1677,20383,1679],{},[1810,20385,1959],{},[902,20387,20388],{"encoding":904},"\\Delta Y = 1",[724,20390,20391,20392,2385],{},"Dosazením do (7.2) plyne ",[38,20393,20394],{},"lineární model úspor",[724,20396,20397],{},[883,20398,20400],{"className":20399},[886],[888,20401,20402],{"xmlns":890},[892,20403,20404,20469],{},[895,20405,20406,20408,20410,20412,20414,20416,20418,20420,20422,20424,20426,20428,20430,20432,20434,20436,20438,20440,20442,20444,20446,20448,20450,20452,20454,20456,20458,20460,20462,20464,20467],{},[898,20407,10061],{},[1677,20409,1679],{},[898,20411,10516],{},[1677,20413,1906],{},[898,20415,2458],{},[1677,20417,1686],{"stretchy":1685},[898,20419,10516],{},[1677,20421,1692],{"stretchy":1685},[1677,20423,1679],{},[898,20425,10516],{},[1677,20427,1906],{},[1677,20429,1686],{"stretchy":1685},[898,20431,207],{},[898,20433,10516],{},[1677,20435,1776],{},[898,20437,1779],{},[1677,20439,1692],{"stretchy":1685},[1677,20441,1679],{},[1677,20443,1686],{"stretchy":1685},[1810,20445,1959],{},[1677,20447,1906],{},[898,20449,207],{},[1677,20451,1692],{"stretchy":1685},[898,20453,10516],{},[1677,20455,1906],{},[898,20457,1779],{},[898,20459,1656],{"mathvariant":2057},[7266,20461],{"width":7268},[1677,20463,1686],{"stretchy":1685},[1810,20465,20466],{},"7.4",[1677,20468,1692],{"stretchy":1685},[902,20470,20471],{"encoding":904},"S = Y - C(Y) = Y - (aY + b) = (1 - a)Y - b. \\qquad (7.4)",[724,20473,20474,20475,5306],{},"Úspory jsou také lineární a „pomalu rostoucí“ (protože ",[883,20476,20478],{"className":20477},[886],[888,20479,20480],{"xmlns":890},[892,20481,20482,20498],{},[895,20483,20484,20486,20488,20490,20492,20494,20496],{},[1810,20485,2008],{},[1677,20487,3128],{},[1810,20489,1959],{},[1677,20491,1906],{},[898,20493,207],{},[1677,20495,3128],{},[1810,20497,1959],{},[902,20499,20500],{"encoding":904},"0 \u003C 1 - a \u003C 1",[724,20502,20503],{},[614,20504,20505,20506,5272,20529,20561,20562,2305,20575,20605,20606,2305,20624,1656],{},"Obrázek 7.2 — Přímky ",[883,20507,20509],{"className":20508},[886],[888,20510,20511],{"xmlns":890},[892,20512,20513,20527],{},[895,20514,20515,20517,20519,20521,20523,20525],{},[898,20516,2458],{},[1677,20518,1679],{},[898,20520,207],{},[898,20522,10516],{},[1677,20524,1776],{},[898,20526,1779],{},[902,20528,20311],{"encoding":904},[883,20530,20532],{"className":20531},[886],[888,20533,20534],{"xmlns":890},[892,20535,20536,20558],{},[895,20537,20538,20540,20542,20544,20546,20548,20550,20552,20554,20556],{},[898,20539,10061],{},[1677,20541,1679],{},[1677,20543,1686],{"stretchy":1685},[1810,20545,1959],{},[1677,20547,1906],{},[898,20549,207],{},[1677,20551,1692],{"stretchy":1685},[898,20553,10516],{},[1677,20555,1906],{},[898,20557,1779],{},[902,20559,20560],{"encoding":904},"S = (1-a)Y - b",". Přímka úspor protíná osu ",[883,20563,20565],{"className":20564},[886],[888,20566,20567],{"xmlns":890},[892,20568,20569,20573],{},[895,20570,20571],{},[898,20572,10516],{},[902,20574,10516],{"encoding":904},[883,20576,20578],{"className":20577},[886],[888,20579,20580],{"xmlns":890},[892,20581,20582,20602],{},[895,20583,20584,20586,20588,20590,20592,20594,20596,20598,20600],{},[898,20585,10516],{},[1677,20587,1679],{},[898,20589,1779],{},[898,20591,6062],{"mathvariant":2057},[1677,20593,1686],{"stretchy":1685},[1810,20595,1959],{},[1677,20597,1906],{},[898,20599,207],{},[1677,20601,1692],{"stretchy":1685},[902,20603,20604],{"encoding":904},"Y = b\u002F(1-a)"," a osu ",[883,20607,20609],{"className":20608},[886],[888,20610,20611],{"xmlns":890},[892,20612,20613,20621],{},[895,20614,20615,20617,20619],{},[898,20616,2458],{},[1677,20618,1967],{"separator":1966},[898,20620,10061],{},[902,20622,20623],{"encoding":904},"C, S",[883,20625,20627],{"className":20626},[886],[888,20628,20629],{"xmlns":890},[892,20630,20631,20637],{},[895,20632,20633,20635],{},[1677,20634,1906],{},[898,20636,1779],{},[902,20638,20639],{"encoding":904},"-b",[198,20641,20643],{"id":20642},"příklad-71","Příklad 7.1",[724,20645,20646,20647,20672],{},"Pro spotřebu ",[883,20648,20650],{"className":20649},[886],[888,20651,20652],{"xmlns":890},[892,20653,20654,20669],{},[895,20655,20656,20658,20660,20663,20665,20667],{},[898,20657,2458],{},[1677,20659,1679],{},[1810,20661,20662],{},"0,4",[898,20664,10516],{},[1677,20666,1776],{},[1810,20668,2544],{},[902,20670,20671],{"encoding":904},"C = 0{,}4Y + 10"," jsou úspory",[724,20674,20675],{},[883,20676,20678],{"className":20677},[886],[888,20679,20680],{"xmlns":890},[892,20681,20682,20720],{},[895,20683,20684,20686,20688,20690,20692,20694,20696,20698,20700,20702,20704,20706,20708,20710,20713,20715,20717],{},[898,20685,10061],{},[1677,20687,1679],{},[898,20689,10516],{},[1677,20691,1906],{},[898,20693,2458],{},[1677,20695,1679],{},[898,20697,10516],{},[1677,20699,1906],{},[1810,20701,20662],{},[898,20703,10516],{},[1677,20705,1906],{},[1810,20707,2544],{},[1677,20709,1679],{},[1810,20711,20712],{},"0,6",[898,20714,10516],{},[1677,20716,1906],{},[1810,20718,20719],{},"10.",[902,20721,20722],{"encoding":904},"S = Y - C = Y - 0{,}4Y - 10 = 0{,}6Y - 10.",[724,20724,20725],{},[614,20726,20727,20728,5272,20751,20775,20776,9490,20789,20813,20814,9490,20831,20847,20848,1656],{},"Obrázek 7.3 — Přímky ",[883,20729,20731],{"className":20730},[886],[888,20732,20733],{"xmlns":890},[892,20734,20735,20749],{},[895,20736,20737,20739,20741,20743,20745,20747],{},[898,20738,2458],{},[1677,20740,1679],{},[1810,20742,20662],{},[898,20744,10516],{},[1677,20746,1776],{},[1810,20748,2544],{},[902,20750,20671],{"encoding":904},[883,20752,20754],{"className":20753},[886],[888,20755,20756],{"xmlns":890},[892,20757,20758,20772],{},[895,20759,20760,20762,20764,20766,20768,20770],{},[898,20761,10061],{},[1677,20763,1679],{},[1810,20765,20712],{},[898,20767,10516],{},[1677,20769,1906],{},[1810,20771,2544],{},[902,20773,20774],{"encoding":904},"S = 0{,}6Y - 10","; průsečík přímky úspor s osou ",[883,20777,20779],{"className":20778},[886],[888,20780,20781],{"xmlns":890},[892,20782,20783,20787],{},[895,20784,20785],{},[898,20786,10516],{},[902,20788,10516],{"encoding":904},[883,20790,20792],{"className":20791},[886],[888,20793,20794],{"xmlns":890},[892,20795,20796,20810],{},[895,20797,20798,20800,20803],{},[1677,20799,2411],{},[1810,20801,20802],{},"16,",[9774,20804,20805,20807],{"accent":1966},[1810,20806,1916],{},[1677,20808,20809],{},"ˉ",[902,20811,20812],{"encoding":904},"\\approx 16{,}\\bar{6}",", s osou ",[883,20815,20817],{"className":20816},[886],[888,20818,20819],{"xmlns":890},[892,20820,20821,20829],{},[895,20822,20823,20825,20827],{},[898,20824,2458],{},[1677,20826,1967],{"separator":1966},[898,20828,10061],{},[902,20830,20623],{"encoding":904},[883,20832,20834],{"className":20833},[886],[888,20835,20836],{"xmlns":890},[892,20837,20838,20844],{},[895,20839,20840,20842],{},[1677,20841,1906],{},[1810,20843,2544],{},[902,20845,20846],{"encoding":904},"-10","; přímka spotřeby prochází bodem ",[883,20849,20851],{"className":20850},[886],[888,20852,20853],{"xmlns":890},[892,20854,20855,20867],{},[895,20856,20857,20859,20861,20863,20865],{},[1677,20858,1686],{"stretchy":1685},[1810,20860,2008],{},[1677,20862,1967],{"separator":1966},[1810,20864,2544],{},[1677,20866,1692],{"stretchy":1685},[902,20868,20869],{"encoding":904},"(0, 10)",[724,20871,20872,20873,9490,20891,20921,20922,11413,20925,20928,20929,9490,20953,11413,20956,20959],{},"Funkce úspor může nabývat záporných hodnot — pro ",[883,20874,20876],{"className":20875},[886],[888,20877,20878],{"xmlns":890},[892,20879,20880,20888],{},[895,20881,20882,20884,20886],{},[898,20883,10516],{},[1677,20885,1679],{},[1810,20887,2008],{},[902,20889,20890],{"encoding":904},"Y = 0",[883,20892,20894],{"className":20893},[886],[888,20895,20896],{"xmlns":890},[892,20897,20898,20918],{},[895,20899,20900,20902,20904,20906,20908,20910,20912,20914,20916],{},[898,20901,10061],{},[1677,20903,1686],{"stretchy":1685},[1810,20905,2008],{},[1677,20907,1692],{"stretchy":1685},[1677,20909,1679],{},[1677,20911,1906],{},[898,20913,1779],{},[1677,20915,3128],{},[1810,20917,2008],{},[902,20919,20920],{"encoding":904},"S(0) = -b \u003C 0","; hovoří se o ",[38,20923,20924],{},"autonomních úsporách",[614,20926,20927],{},"autonomous savings","). Analogicky ",[883,20930,20932],{"className":20931},[886],[888,20933,20934],{"xmlns":890},[892,20935,20936,20950],{},[895,20937,20938,20940,20942,20944,20946,20948],{},[898,20939,2458],{},[1677,20941,1686],{"stretchy":1685},[1810,20943,2008],{},[1677,20945,1692],{"stretchy":1685},[1677,20947,1679],{},[898,20949,1779],{},[902,20951,20952],{"encoding":904},"C(0) = b",[38,20954,20955],{},"autonomní spotřeba",[614,20957,20958],{},"autonomous consumption",") — spotřeba při nulovém důchodu krytá dřívějšími úsporami.",[115,20961,20963],{"id":20962},"mezní-sklon-ke-spotřebě-mpc-a-k-úsporám-mps","Mezní sklon ke spotřebě (MPC) a k úsporám (MPS)",[724,20965,20966,1884,20969,11413,20986,20989],{},[38,20967,20968],{},"Mezní sklon ke spotřebě",[883,20970,20972],{"className":20971},[886],[888,20973,20974],{"xmlns":890},[892,20975,20976,20984],{},[895,20977,20978,20980,20982],{},[898,20979,2499],{},[898,20981,5325],{},[898,20983,2458],{},[902,20985,19436],{"encoding":904},[614,20987,20988],{},"marginal propensity to consume",") je derivace spotřeby podle důchodu:",[724,20991,20992],{},[883,20993,20995],{"className":20994},[886],[888,20996,20997],{"xmlns":890},[892,20998,20999,21025],{},[895,21000,21001,21003,21005,21007,21009,21023],{},[898,21002,2499],{},[898,21004,5325],{},[898,21006,2458],{},[1677,21008,1679],{},[2010,21010,21011,21017],{},[895,21012,21013,21015],{},[898,21014,1875],{"mathvariant":2057},[898,21016,2458],{},[895,21018,21019,21021],{},[898,21020,1875],{"mathvariant":2057},[898,21022,10516],{},[898,21024,1656],{"mathvariant":2057},[902,21026,21027],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y}.",[724,21029,21030,1884,21033,11413,21051,21054],{},[38,21031,21032],{},"Mezní sklon k úsporám",[883,21034,21036],{"className":21035},[886],[888,21037,21038],{"xmlns":890},[892,21039,21040,21048],{},[895,21041,21042,21044,21046],{},[898,21043,2499],{},[898,21045,5325],{},[898,21047,10061],{},[902,21049,21050],{"encoding":904},"MPS",[614,21052,21053],{},"marginal propensity to save",") je derivace úspor podle důchodu:",[724,21056,21057],{},[883,21058,21060],{"className":21059},[886],[888,21061,21062],{"xmlns":890},[892,21063,21064,21090],{},[895,21065,21066,21068,21070,21072,21074,21088],{},[898,21067,2499],{},[898,21069,5325],{},[898,21071,10061],{},[1677,21073,1679],{},[2010,21075,21076,21082],{},[895,21077,21078,21080],{},[898,21079,1875],{"mathvariant":2057},[898,21081,10061],{},[895,21083,21084,21086],{},[898,21085,1875],{"mathvariant":2057},[898,21087,10516],{},[898,21089,1656],{"mathvariant":2057},[902,21091,21092],{"encoding":904},"MPS = \\frac{\\mathrm{d}S}{\\mathrm{d}Y}.",[724,21094,21095,21096,21154],{},"Z (7.2) plyne ",[883,21097,21099],{"className":21098},[886],[888,21100,21101],{"xmlns":890},[892,21102,21103,21151],{},[895,21104,21105,21119,21121,21135,21137],{},[2010,21106,21107,21113],{},[895,21108,21109,21111],{},[898,21110,1875],{"mathvariant":2057},[898,21112,10516],{},[895,21114,21115,21117],{},[898,21116,1875],{"mathvariant":2057},[898,21118,10516],{},[1677,21120,1679],{},[2010,21122,21123,21129],{},[895,21124,21125,21127],{},[898,21126,1875],{"mathvariant":2057},[898,21128,2458],{},[895,21130,21131,21133],{},[898,21132,1875],{"mathvariant":2057},[898,21134,10516],{},[1677,21136,1776],{},[2010,21138,21139,21145],{},[895,21140,21141,21143],{},[898,21142,1875],{"mathvariant":2057},[898,21144,10061],{},[895,21146,21147,21149],{},[898,21148,1875],{"mathvariant":2057},[898,21150,10516],{},[902,21152,21153],{"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",[724,21156,21157],{},[883,21158,21160],{"className":21159},[886],[888,21161,21162],{"xmlns":890},[892,21163,21164,21227],{},[895,21165,21166,21218,21220,21222,21225],{},[14222,21167,21168],{"notation":14224},[2006,21169,21170],{"scriptlevel":2008,"displaystyle":1685},[2006,21171,21172],{"scriptlevel":2008,"displaystyle":1685},[2006,21173,21174],{"scriptlevel":2008,"displaystyle":1966},[895,21175,21176,21178,21180,21182,21184,21186,21188,21190,21192,21194,21196,21198,21200,21202,21204,21206,21208,21210,21212,21214,21216],{},[898,21177,2499],{},[898,21179,5325],{},[898,21181,2458],{},[1677,21183,1776],{},[898,21185,2499],{},[898,21187,5325],{},[898,21189,10061],{},[1677,21191,1679],{},[1810,21193,1959],{},[1677,21195,1967],{"separator":1966},[7266,21197],{"width":7268},[898,21199,2499],{},[898,21201,5325],{},[898,21203,10061],{},[1677,21205,1679],{},[1810,21207,1959],{},[1677,21209,1906],{},[898,21211,2499],{},[898,21213,5325],{},[898,21215,2458],{},[898,21217,1656],{"mathvariant":2057},[7266,21219],{"width":7268},[1677,21221,1686],{"stretchy":1685},[1810,21223,21224],{},"7.5",[1677,21226,1692],{"stretchy":1685},[902,21228,21229],{"encoding":904},"\\boxed{MPC + MPS = 1, \\qquad MPS = 1 - MPC.} \\qquad (7.5)",[724,21231,21232,1884,21235,21258,21259,5272,21281,21307],{},[38,21233,21234],{},"Pro lineární model",[883,21236,21238],{"className":21237},[886],[888,21239,21240],{"xmlns":890},[892,21241,21242,21256],{},[895,21243,21244,21246,21248,21250,21252,21254],{},[898,21245,2458],{},[1677,21247,1679],{},[898,21249,207],{},[898,21251,10516],{},[1677,21253,1776],{},[898,21255,1779],{},[902,21257,20311],{"encoding":904}," vychází ",[883,21260,21262],{"className":21261},[886],[888,21263,21264],{"xmlns":890},[892,21265,21266,21278],{},[895,21267,21268,21270,21272,21274,21276],{},[898,21269,2499],{},[898,21271,5325],{},[898,21273,2458],{},[1677,21275,1679],{},[898,21277,207],{},[902,21279,21280],{"encoding":904},"MPC = a",[883,21282,21284],{"className":21283},[886],[888,21285,21286],{"xmlns":890},[892,21287,21288,21304],{},[895,21289,21290,21292,21294,21296,21298,21300,21302],{},[898,21291,2499],{},[898,21293,5325],{},[898,21295,10061],{},[1677,21297,1679],{},[1810,21299,1959],{},[1677,21301,1906],{},[898,21303,207],{},[902,21305,21306],{"encoding":904},"MPS = 1 - a"," — tedy směrnice přímek spotřeby a úspor.",[724,21309,21310,21313,21314,21336,21337,21365],{},[38,21311,21312],{},"Interpretace diferenciálem."," Pro pevné ",[883,21315,21317],{"className":21316},[886],[888,21318,21319],{"xmlns":890},[892,21320,21321,21333],{},[895,21322,21323,21325,21327],{},[898,21324,10516],{},[1677,21326,1679],{},[1805,21328,21329,21331],{},[898,21330,10516],{},[1677,21332,5742],{},[902,21334,21335],{"encoding":904},"Y = Y^*"," udává ",[883,21338,21340],{"className":21339},[886],[888,21341,21342],{"xmlns":890},[892,21343,21344,21362],{},[895,21345,21346,21348,21350,21352,21354,21360],{},[898,21347,2499],{},[898,21349,5325],{},[898,21351,2458],{},[1677,21353,1686],{"stretchy":1685},[1805,21355,21356,21358],{},[898,21357,10516],{},[1677,21359,5742],{},[1677,21361,1692],{"stretchy":1685},[902,21363,21364],{"encoding":904},"MPC(Y^*)"," přibližnou změnu spotřeby při jednotkovém přírůstku důchodu:",[724,21367,21368],{},[883,21369,21371],{"className":21370},[886],[888,21372,21373],{"xmlns":890},[892,21374,21375,21429],{},[895,21376,21377,21379,21381,21383,21385,21387,21389,21395,21397,21399,21401,21403,21405,21407,21409,21411,21413,21415,21417,21419,21421,21423,21425,21427],{},[898,21378,2570],{"mathvariant":2057},[898,21380,2458],{},[1677,21382,2411],{},[898,21384,1875],{"mathvariant":2057},[898,21386,2458],{},[1677,21388,1679],{},[1805,21390,21391,21393],{},[898,21392,2458],{},[1677,21394,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,21396,1686],{"stretchy":1685},[898,21398,10516],{},[1677,21400,1692],{"stretchy":1685},[1969,21402,2668],{},[898,21404,1875],{"mathvariant":2057},[898,21406,10516],{},[1677,21408,1679],{},[898,21410,2499],{},[898,21412,5325],{},[898,21414,2458],{},[1677,21416,1686],{"stretchy":1685},[898,21418,10516],{},[1677,21420,1692],{"stretchy":1685},[1969,21422,2668],{},[898,21424,1875],{"mathvariant":2057},[898,21426,10516],{},[898,21428,1656],{"mathvariant":2057},[902,21430,21431],{"encoding":904},"\\Delta C \\approx \\mathrm{d}C = C'(Y)\\,\\mathrm{d}Y = MPC(Y)\\,\\mathrm{d}Y.",[724,21433,21434,21435,21471,21472,21475],{},"Analogicky ",[883,21436,21438],{"className":21437},[886],[888,21439,21440],{"xmlns":890},[892,21441,21442,21468],{},[895,21443,21444,21446,21448,21450,21452,21454,21456,21458,21460,21462,21464,21466],{},[898,21445,2570],{"mathvariant":2057},[898,21447,10061],{},[1677,21449,2411],{},[898,21451,2499],{},[898,21453,5325],{},[898,21455,10061],{},[1677,21457,1686],{"stretchy":1685},[898,21459,10516],{},[1677,21461,1692],{"stretchy":1685},[1969,21463,2668],{},[898,21465,1875],{"mathvariant":2057},[898,21467,10516],{},[902,21469,21470],{"encoding":904},"\\Delta S \\approx MPS(Y)\\,\\mathrm{d}Y",". Viz ",[207,21473,1145],{"className":21474,"dataFsResolvedFilePath":764,"href":765},[210]," a její ekonomická interpretace.",[198,21477,21479],{"id":21478},"příklad-72","Příklad 7.2",[724,21481,20646,21482,21517,21518,21537],{},[883,21483,21485],{"className":21484},[886],[888,21486,21487],{"xmlns":890},[892,21488,21489,21514],{},[895,21490,21491,21493,21495,21498,21504,21506,21508,21510,21512],{},[898,21492,2458],{},[1677,21494,1679],{},[1810,21496,21497],{},"0,001",[1805,21499,21500,21502],{},[898,21501,10516],{},[1810,21503,1812],{},[1677,21505,1776],{},[1810,21507,2520],{},[898,21509,10516],{},[1677,21511,1776],{},[1810,21513,2801],{},[902,21515,21516],{"encoding":904},"C = 0{,}001Y^2 + 0{,}2Y + 50"," (pro ",[883,21519,21521],{"className":21520},[886],[888,21522,21523],{"xmlns":890},[892,21524,21525,21534],{},[895,21526,21527,21529,21531],{},[898,21528,10516],{},[1677,21530,3128],{},[1810,21532,21533],{},"400",[902,21535,21536],{"encoding":904},"Y \u003C 400",") platí",[724,21539,21540],{},[883,21541,21543],{"className":21542},[886],[888,21544,21545],{"xmlns":890},[892,21546,21547,21584],{},[895,21548,21549,21551,21553,21555,21557,21571,21573,21576,21578,21580,21582],{},[898,21550,2499],{},[898,21552,5325],{},[898,21554,2458],{},[1677,21556,1679],{},[2010,21558,21559,21565],{},[895,21560,21561,21563],{},[898,21562,1875],{"mathvariant":2057},[898,21564,2458],{},[895,21566,21567,21569],{},[898,21568,1875],{"mathvariant":2057},[898,21570,10516],{},[1677,21572,1679],{},[1810,21574,21575],{},"0,002",[898,21577,10516],{},[1677,21579,1776],{},[1810,21581,2520],{},[1677,21583,1967],{"separator":1966},[902,21585,21586],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y} = 0{,}002Y + 0{,}2,",[724,21588,21589],{},[883,21590,21592],{"className":21591},[886],[888,21593,21594],{"xmlns":890},[892,21595,21596,21629],{},[895,21597,21598,21600,21602,21604,21606,21608,21610,21612,21614,21616,21618,21620,21622,21624,21626],{},[898,21599,2499],{},[898,21601,5325],{},[898,21603,10061],{},[1677,21605,1679],{},[1810,21607,1959],{},[1677,21609,1906],{},[898,21611,2499],{},[898,21613,5325],{},[898,21615,2458],{},[1677,21617,1679],{},[1677,21619,1906],{},[1810,21621,21575],{},[898,21623,10516],{},[1677,21625,1776],{},[1810,21627,21628],{},"0,8.",[902,21630,21631],{"encoding":904},"MPS = 1 - MPC = -0{,}002Y + 0{,}8.",[120,21633,21634,21714,21793],{},[123,21635,21636,1343,21664,21692,21693,9490,21711,1656],{},[883,21637,21639],{"className":21638},[886],[888,21640,21641],{"xmlns":890},[892,21642,21643,21661],{},[895,21644,21645,21647,21649,21651,21653,21655,21657,21659],{},[898,21646,2499],{},[898,21648,5325],{},[898,21650,2458],{},[1677,21652,1686],{"stretchy":1685},[1810,21654,2771],{},[1677,21656,1692],{"stretchy":1685},[1677,21658,1679],{},[1810,21660,20662],{},[902,21662,21663],{"encoding":904},"MPC(100) = 0{,}4",[883,21665,21667],{"className":21666},[886],[888,21668,21669],{"xmlns":890},[892,21670,21671,21689],{},[895,21672,21673,21675,21677,21679,21681,21683,21685,21687],{},[898,21674,2499],{},[898,21676,5325],{},[898,21678,10061],{},[1677,21680,1686],{"stretchy":1685},[1810,21682,2771],{},[1677,21684,1692],{"stretchy":1685},[1677,21686,1679],{},[1810,21688,20712],{},[902,21690,21691],{"encoding":904},"MPS(100) = 0{,}6"," — při ",[883,21694,21696],{"className":21695},[886],[888,21697,21698],{"xmlns":890},[892,21699,21700,21708],{},[895,21701,21702,21704,21706],{},[898,21703,10516],{},[1677,21705,1679],{},[1810,21707,2771],{},[902,21709,21710],{"encoding":904},"Y = 100",[38,21712,21713],{},"větší sklon k úsporám",[123,21715,21716,1343,21744,21692,21772,9490,21790,1656],{},[883,21717,21719],{"className":21718},[886],[888,21720,21721],{"xmlns":890},[892,21722,21723,21741],{},[895,21724,21725,21727,21729,21731,21733,21735,21737,21739],{},[898,21726,2499],{},[898,21728,5325],{},[898,21730,2458],{},[1677,21732,1686],{"stretchy":1685},[1810,21734,9765],{},[1677,21736,1692],{"stretchy":1685},[1677,21738,1679],{},[1810,21740,20712],{},[902,21742,21743],{"encoding":904},"MPC(200) = 0{,}6",[883,21745,21747],{"className":21746},[886],[888,21748,21749],{"xmlns":890},[892,21750,21751,21769],{},[895,21752,21753,21755,21757,21759,21761,21763,21765,21767],{},[898,21754,2499],{},[898,21756,5325],{},[898,21758,10061],{},[1677,21760,1686],{"stretchy":1685},[1810,21762,9765],{},[1677,21764,1692],{"stretchy":1685},[1677,21766,1679],{},[1810,21768,20662],{},[902,21770,21771],{"encoding":904},"MPS(200) = 0{,}4",[883,21773,21775],{"className":21774},[886],[888,21776,21777],{"xmlns":890},[892,21778,21779,21787],{},[895,21780,21781,21783,21785],{},[898,21782,10516],{},[1677,21784,1679],{},[1810,21786,9765],{},[902,21788,21789],{"encoding":904},"Y = 200",[38,21791,21792],{},"větší sklon ke spotřebě",[123,21794,21795,21796,21814,21815,5306],{},"Přesně při ",[883,21797,21799],{"className":21798},[886],[888,21800,21801],{"xmlns":890},[892,21802,21803,21811],{},[895,21804,21805,21807,21809],{},[898,21806,10516],{},[1677,21808,1679],{},[1810,21810,10191],{},[902,21812,21813],{"encoding":904},"Y = 150"," se oba sklony rovnají (",[883,21816,21818],{"className":21817},[886],[888,21819,21820],{"xmlns":890},[892,21821,21822,21842],{},[895,21823,21824,21826,21828,21830,21832,21834,21836,21838,21840],{},[898,21825,2499],{},[898,21827,5325],{},[898,21829,2458],{},[1677,21831,1679],{},[898,21833,2499],{},[898,21835,5325],{},[898,21837,10061],{},[1677,21839,1679],{},[1810,21841,6397],{},[902,21843,21844],{"encoding":904},"MPC = MPS = 0{,}5",[724,21846,21847,21848,21865,21866,21880,21881,2366,21894,21908,21909,21922,21923,21964],{},"Interpretace: při ",[883,21849,21851],{"className":21850},[886],[888,21852,21853],{"xmlns":890},[892,21854,21855,21863],{},[895,21856,21857,21859,21861],{},[898,21858,10516],{},[1677,21860,1679],{},[1810,21862,2771],{},[902,21864,21710],{"encoding":904}," se spotřeba mění ",[883,21867,21869],{"className":21868},[886],[888,21870,21871],{"xmlns":890},[892,21872,21873,21877],{},[895,21874,21875],{},[1810,21876,20662],{},[902,21878,21879],{"encoding":904},"0{,}4","-krát rychleji než důchod; změní-li se důchod ze ",[883,21882,21884],{"className":21883},[886],[888,21885,21886],{"xmlns":890},[892,21887,21888,21892],{},[895,21889,21890],{},[1810,21891,2771],{},[902,21893,2771],{"encoding":904},[883,21895,21897],{"className":21896},[886],[888,21898,21899],{"xmlns":890},[892,21900,21901,21906],{},[895,21902,21903],{},[1810,21904,21905],{},"101",[902,21907,21905],{"encoding":904},", změní se spotřeba přibližně o ",[883,21910,21912],{"className":21911},[886],[888,21913,21914],{"xmlns":890},[892,21915,21916,21920],{},[895,21917,21918],{},[1810,21919,20662],{},[902,21921,21879],{"encoding":904},". Skutečná změna ",[883,21924,21926],{"className":21925},[886],[888,21927,21928],{"xmlns":890},[892,21929,21930,21961],{},[895,21931,21932,21934,21936,21938,21940,21942,21944,21946,21948,21950,21952,21954,21956,21958],{},[898,21933,2570],{"mathvariant":2057},[898,21935,2458],{},[1677,21937,1679],{},[898,21939,2458],{},[1677,21941,1686],{"stretchy":1685},[1810,21943,21905],{},[1677,21945,1692],{"stretchy":1685},[1677,21947,1906],{},[898,21949,2458],{},[1677,21951,1686],{"stretchy":1685},[1810,21953,2771],{},[1677,21955,1692],{"stretchy":1685},[1677,21957,1679],{},[1810,21959,21960],{},"0,401",[902,21962,21963],{"encoding":904},"\\Delta C = C(101) - C(100) = 0{,}401"," — aproximace diferenciálem je přesná na setiny.",[724,21966,21967,21968],{},"Obecný trend: ",[38,21969,21970],{},"s růstem důchodu se sklon ke spotřebě zvětšuje.",[115,21972,21974],{"id":21973},"makroekonomická-rovnováha","Makroekonomická rovnováha",[724,21976,21977,21978,11413,21981,21984,21985,11413,21988,13518,21991,11413,21994,21997],{},"Při modelování národní ekonomiky hraje klíčovou roli ",[38,21979,21980],{},"makroekonomická rovnováha",[614,21982,21983],{},"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 ",[38,21986,21987],{},"agregátní poptávky",[614,21989,21990],{},"aggregate demand",[38,21992,21993],{},"agregátní nabídky",[614,21995,21996],{},"aggregate supply",") — obě popisují závislost mezi cenovou hladinou a množstvím, které jsou spotřebitelé ochotni koupit (agregátními výdaji).",[115,21999,22001],{"id":22000},"model-c-i-uzavřená-ekonomika-bez-vlády","Model C-I — uzavřená ekonomika bez vlády",[724,22003,22004],{},[2240,22005],{"alt":22006,"className":22007,"src":22008},"imek-keynesian-kriz",[210,2244],"\u002Fwiki-assets\u002Fimek-keynesian-kriz.jpeg",[198,22010,22012],{"id":22011},"zadání-modelu","Zadání modelu",[724,22014,22015,22016,22029,22030,22043],{},"Nejjednodušší model uzavřené ekonomiky bez vlády obsahuje jen spotřebu ",[883,22017,22019],{"className":22018},[886],[888,22020,22021],{"xmlns":890},[892,22022,22023,22027],{},[895,22024,22025],{},[898,22026,2458],{},[902,22028,2458],{"encoding":904}," a investice ",[883,22031,22033],{"className":22032},[886],[888,22034,22035],{"xmlns":890},[892,22036,22037,22041],{},[895,22038,22039],{},[898,22040,13574],{},[902,22042,13574],{"encoding":904},". Podmínka rovnováhy:",[724,22045,22046],{},[883,22047,22049],{"className":22048},[886],[888,22050,22051],{"xmlns":890},[892,22052,22053,22076],{},[895,22054,22055,22057,22059,22061,22063,22065,22067,22069,22071,22074],{},[898,22056,10516],{},[1677,22058,1679],{},[898,22060,2458],{},[1677,22062,1776],{},[898,22064,13574],{},[898,22066,1656],{"mathvariant":2057},[7266,22068],{"width":7268},[1677,22070,1686],{"stretchy":1685},[1810,22072,22073],{},"7.6",[1677,22075,1692],{"stretchy":1685},[902,22077,22078],{"encoding":904},"Y = C + I. \\qquad (7.6)",[198,22080,22082],{"id":22081},"soustava-rovnic","Soustava rovnic",[724,22084,22085,22086,22107,22108,22132],{},"Pro pevně zadané (plánované) investice ",[883,22087,22089],{"className":22088},[886],[888,22090,22091],{"xmlns":890},[892,22092,22093,22105],{},[895,22094,22095,22097,22099],{},[898,22096,13574],{},[1677,22098,1679],{},[1805,22100,22101,22103],{},[898,22102,13574],{},[1677,22104,5742],{},[902,22106,13585],{"encoding":904}," a funkci spotřeby ",[883,22109,22111],{"className":22110},[886],[888,22112,22113],{"xmlns":890},[892,22114,22115,22129],{},[895,22116,22117,22119,22121,22123,22125,22127],{},[898,22118,2458],{},[1677,22120,1679],{},[898,22122,2458],{},[1677,22124,1686],{"stretchy":1685},[898,22126,10516],{},[1677,22128,1692],{"stretchy":1685},[902,22130,22131],{"encoding":904},"C = C(Y)"," dostáváme soustavu",[724,22134,22135],{},[883,22136,22138],{"className":22137},[886],[888,22139,22140],{"xmlns":890},[892,22141,22142,22218],{},[895,22143,22144,22209,22211,22213,22216],{},[22145,22146,22149,22181],"mtable",{"rowspacing":22147,"columnalign":22148,"columnspacing":2058},"0.25em","right left",[22150,22151,22152,22159],"mtr",{},[22153,22154,22155],"mtd",{},[2006,22156,22157],{"scriptlevel":2008,"displaystyle":1966},[898,22158,10516],{},[22153,22160,22161],{},[2006,22162,22163],{"scriptlevel":2008,"displaystyle":1966},[895,22164,22165,22167,22169,22171,22173,22179],{},[895,22166],{},[1677,22168,1679],{},[898,22170,2458],{},[1677,22172,1776],{},[1805,22174,22175,22177],{},[898,22176,13574],{},[1677,22178,5742],{},[1677,22180,1967],{"separator":1966},[22150,22182,22183,22189],{},[22153,22184,22185],{},[2006,22186,22187],{"scriptlevel":2008,"displaystyle":1966},[898,22188,2458],{},[22153,22190,22191],{},[2006,22192,22193],{"scriptlevel":2008,"displaystyle":1966},[895,22194,22195,22197,22199,22201,22203,22205,22207],{},[895,22196],{},[1677,22198,1679],{},[898,22200,2458],{},[1677,22202,1686],{"stretchy":1685},[898,22204,10516],{},[1677,22206,1692],{"stretchy":1685},[1677,22208,1967],{"separator":1966},[7266,22210],{"width":7268},[1677,22212,1686],{"stretchy":1685},[1810,22214,22215],{},"7.7",[1677,22217,1692],{"stretchy":1685},[902,22219,22220],{"encoding":904},"\\begin{aligned} Y &= C + I^*, \\\\ C &= C(Y), \\end{aligned} \\qquad (7.7)",[724,22222,22223,22224,1884,22226,5272,22243,1884,22246,1656],{},"jejímž řešením jsou ",[38,22225,15275],{},[883,22227,22229],{"className":22228},[886],[888,22230,22231],{"xmlns":890},[892,22232,22233,22241],{},[895,22234,22235],{},[1805,22236,22237,22239],{},[898,22238,10516],{},[898,22240,5640],{},[902,22242,15293],{"encoding":904},[38,22244,22245],{},"rovnovážná spotřeba",[883,22247,22249],{"className":22248},[886],[888,22250,22251],{"xmlns":890},[892,22252,22253,22261],{},[895,22254,22255],{},[1805,22256,22257,22259],{},[898,22258,2458],{},[898,22260,5640],{},[902,22262,15352],{"encoding":904},[198,22264,22266,22267],{"id":22265},"výpočet-yeye","Výpočet ",[883,22268,22270],{"className":22269},[886],[888,22271,22272],{"xmlns":890},[892,22273,22274,22282],{},[895,22275,22276],{},[1805,22277,22278,22280],{},[898,22279,10516],{},[898,22281,5640],{},[902,22283,15293],{"encoding":904},[724,22285,22286,22287,22310,22311,9073,22343],{},"Pro lineární spotřebu ",[883,22288,22290],{"className":22289},[886],[888,22291,22292],{"xmlns":890},[892,22293,22294,22308],{},[895,22295,22296,22298,22300,22302,22304,22306],{},[898,22297,2458],{},[1677,22299,1679],{},[898,22301,207],{},[898,22303,10516],{},[1677,22305,1776],{},[898,22307,1779],{},[902,22309,20311],{"encoding":904}," plyne z (7.7) rovnice ",[883,22312,22314],{"className":22313},[886],[888,22315,22316],{"xmlns":890},[892,22317,22318,22340],{},[895,22319,22320,22322,22324,22326,22328,22330,22332,22334],{},[898,22321,10516],{},[1677,22323,1679],{},[898,22325,207],{},[898,22327,10516],{},[1677,22329,1776],{},[898,22331,1779],{},[1677,22333,1776],{},[1805,22335,22336,22338],{},[898,22337,13574],{},[1677,22339,5742],{},[902,22341,22342],{"encoding":904},"Y = aY + b + I^*",[38,22344,22345],{},"redukovaný tvar",[724,22347,22348],{},[883,22349,22351],{"className":22350},[886],[888,22352,22353],{"xmlns":890},[892,22354,22355,22403],{},[895,22356,22357],{},[14222,22358,22359],{"notation":14224},[2006,22360,22361],{"scriptlevel":2008,"displaystyle":1685},[2006,22362,22363],{"scriptlevel":2008,"displaystyle":1685},[2006,22364,22365],{"scriptlevel":2008,"displaystyle":1966},[895,22366,22367,22369,22375,22377,22399,22401],{},[1969,22368,2668],{},[1805,22370,22371,22373],{},[898,22372,10516],{},[898,22374,5640],{},[1677,22376,1679],{},[2010,22378,22379,22391],{},[895,22380,22381,22383,22385],{},[898,22382,1779],{},[1677,22384,1776],{},[1805,22386,22387,22389],{},[898,22388,13574],{},[1677,22390,5742],{},[895,22392,22393,22395,22397],{},[1810,22394,1959],{},[1677,22396,1906],{},[898,22398,207],{},[898,22400,1656],{"mathvariant":2057},[1969,22402,2668],{},[902,22404,22405],{"encoding":904},"\\boxed{\\,Y^E = \\frac{b + I^*}{1 - a}.\\,}",[198,22407,22409],{"id":22408},"příklad-73","Příklad 7.3",[724,22411,22412,22413,9490,22430,5272,22454,22480],{},"V modelu ",[883,22414,22416],{"className":22415},[886],[888,22417,22418],{"xmlns":890},[892,22419,22420,22428],{},[895,22421,22422,22424,22426],{},[898,22423,2458],{},[1969,22425,13680],{},[898,22427,13574],{},[902,22429,13685],{"encoding":904},[883,22431,22433],{"className":22432},[886],[888,22434,22435],{"xmlns":890},[892,22436,22437,22451],{},[895,22438,22439,22441,22443,22445,22447,22449],{},[898,22440,2458],{},[1677,22442,1679],{},[1810,22444,20712],{},[898,22446,10516],{},[1677,22448,1776],{},[1810,22450,2544],{},[902,22452,22453],{"encoding":904},"C = 0{,}6Y + 10",[883,22455,22457],{"className":22456},[886],[888,22458,22459],{"xmlns":890},[892,22460,22461,22477],{},[895,22462,22463,22465,22467,22469,22471],{},[898,22464,13574],{},[1677,22466,1679],{},[1810,22468,3190],{},[1677,22470,1679],{},[1805,22472,22473,22475],{},[898,22474,13574],{},[1677,22476,5742],{},[902,22478,22479],{"encoding":904},"I = 12 = I^*",". Soustava",[724,22482,22483],{},[883,22484,22486],{"className":22485},[886],[888,22487,22488],{"xmlns":890},[892,22489,22490,22546],{},[22145,22491,22492,22518],{"rowspacing":22147,"columnalign":22148,"columnspacing":2058},[22150,22493,22494,22500],{},[22153,22495,22496],{},[2006,22497,22498],{"scriptlevel":2008,"displaystyle":1966},[898,22499,10516],{},[22153,22501,22502],{},[2006,22503,22504],{"scriptlevel":2008,"displaystyle":1966},[895,22505,22506,22508,22510,22512,22514,22516],{},[895,22507],{},[1677,22509,1679],{},[898,22511,2458],{},[1677,22513,1776],{},[1810,22515,3190],{},[1677,22517,1967],{"separator":1966},[22150,22519,22520,22526],{},[22153,22521,22522],{},[2006,22523,22524],{"scriptlevel":2008,"displaystyle":1966},[898,22525,2458],{},[22153,22527,22528],{},[2006,22529,22530],{"scriptlevel":2008,"displaystyle":1966},[895,22531,22532,22534,22536,22538,22540,22542,22544],{},[895,22533],{},[1677,22535,1679],{},[1810,22537,20712],{},[898,22539,10516],{},[1677,22541,1776],{},[1810,22543,2544],{},[1677,22545,1967],{"separator":1966},[902,22547,22548],{"encoding":904},"\\begin{aligned} Y &= C + 12, \\\\ C &= 0{,}6Y + 10, \\end{aligned}",[724,22550,22551,22552,1343,22575,22598,22599,5306],{},"má řešení ",[883,22553,22555],{"className":22554},[886],[888,22556,22557],{"xmlns":890},[892,22558,22559,22572],{},[895,22560,22561,22567,22569],{},[1805,22562,22563,22565],{},[898,22564,10516],{},[898,22566,5640],{},[1677,22568,1679],{},[1810,22570,22571],{},"55",[902,22573,22574],{"encoding":904},"Y^E = 55",[883,22576,22578],{"className":22577},[886],[888,22579,22580],{"xmlns":890},[892,22581,22582,22595],{},[895,22583,22584,22590,22592],{},[1805,22585,22586,22588],{},[898,22587,2458],{},[898,22589,5640],{},[1677,22591,1679],{},[1810,22593,22594],{},"43",[902,22596,22597],{"encoding":904},"C^E = 43"," (a ",[883,22600,22602],{"className":22601},[886],[888,22603,22604],{"xmlns":890},[892,22605,22606,22618],{},[895,22607,22608,22614,22616],{},[1805,22609,22610,22612],{},[898,22611,10061],{},[898,22613,5640],{},[1677,22615,1679],{},[1810,22617,3190],{},[902,22619,22620],{"encoding":904},"S^E = 12",[724,22622,22623],{},[614,22624,22625,22626,22648,22649,13518,22670,22693,22694,1656],{},"Obrázek 7.5 — Přímky ",[883,22627,22629],{"className":22628},[886],[888,22630,22631],{"xmlns":890},[892,22632,22633,22645],{},[895,22634,22635,22637,22639,22641,22643],{},[898,22636,2458],{},[1677,22638,1679],{},[898,22640,10516],{},[1677,22642,1906],{},[1810,22644,3190],{},[902,22646,22647],{"encoding":904},"C = Y - 12"," (rovnováha ",[883,22650,22652],{"className":22651},[886],[888,22653,22654],{"xmlns":890},[892,22655,22656,22668],{},[895,22657,22658,22660,22662,22664,22666],{},[898,22659,10516],{},[1677,22661,1679],{},[898,22663,2458],{},[1677,22665,1776],{},[898,22667,13574],{},[902,22669,16134],{"encoding":904},[883,22671,22673],{"className":22672},[886],[888,22674,22675],{"xmlns":890},[892,22676,22677,22691],{},[895,22678,22679,22681,22683,22685,22687,22689],{},[898,22680,2458],{},[1677,22682,1679],{},[1810,22684,20712],{},[898,22686,10516],{},[1677,22688,1776],{},[1810,22690,2544],{},[902,22692,22453],{"encoding":904}," (funkce spotřeby) se protínají v bodě ",[883,22695,22697],{"className":22696},[886],[888,22698,22699],{"xmlns":890},[892,22700,22701,22733],{},[895,22702,22703,22705,22711,22713,22719,22721,22723,22725,22727,22729,22731],{},[1677,22704,2167],{"stretchy":1685},[1805,22706,22707,22709],{},[898,22708,10516],{},[898,22710,5640],{},[1677,22712,1967],{"separator":1966},[1805,22714,22715,22717],{},[898,22716,2458],{},[898,22718,5640],{},[1677,22720,2182],{"stretchy":1685},[1677,22722,1679],{},[1677,22724,2167],{"stretchy":1685},[1810,22726,22571],{},[1677,22728,1967],{"separator":1966},[1810,22730,22594],{},[1677,22732,2182],{"stretchy":1685},[902,22734,22735],{"encoding":904},"[Y^E, C^E] = [55, 43]",[724,22737,22738,22741,22742,22759,22760,1656],{},[38,22739,22740],{},"Komentář k přechodu."," Model ",[883,22743,22745],{"className":22744},[886],[888,22746,22747],{"xmlns":890},[892,22748,22749,22757],{},[895,22750,22751,22753,22755],{},[898,22752,2458],{},[1969,22754,13680],{},[898,22756,13574],{},[902,22758,13685],{"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 ",[38,22761,22762,22763],{},"model ",[883,22764,22766],{"className":22765},[886],[888,22767,22768],{"xmlns":890},[892,22769,22770,22782],{},[895,22771,22772,22774,22776,22778,22780],{},[898,22773,2458],{},[1969,22775,13680],{},[898,22777,13574],{},[1969,22779,13680],{},[898,22781,13502],{},[902,22783,19611],{"encoding":904},[115,22785,22787],{"id":22786},"model-c-i-g-s-vládním-sektorem","Model C-I-G — s vládním sektorem",[198,22789,22012],{"id":22790},"zadání-modelu-1",[724,22792,22793,22794,22811,22812,1884,22815,11413,22828,22831],{},"Rozšíření modelu ",[883,22795,22797],{"className":22796},[886],[888,22798,22799],{"xmlns":890},[892,22800,22801,22809],{},[895,22802,22803,22805,22807],{},[898,22804,2458],{},[1969,22806,13680],{},[898,22808,13574],{},[902,22810,13685],{"encoding":904}," o ",[38,22813,22814],{},"vládní výdaje",[883,22816,22818],{"className":22817},[886],[888,22819,22820],{"xmlns":890},[892,22821,22822,22826],{},[895,22823,22824],{},[898,22825,13502],{},[902,22827,13502],{"encoding":904},[614,22829,22830],{},"government expenditure","). Podmínka rovnováhy:",[724,22833,22834],{},[883,22835,22837],{"className":22836},[886],[888,22838,22839],{"xmlns":890},[892,22840,22841,22868],{},[895,22842,22843,22845,22847,22849,22851,22853,22855,22857,22859,22861,22863,22866],{},[898,22844,10516],{},[1677,22846,1679],{},[898,22848,2458],{},[1677,22850,1776],{},[898,22852,13574],{},[1677,22854,1776],{},[898,22856,13502],{},[898,22858,1656],{"mathvariant":2057},[7266,22860],{"width":7268},[1677,22862,1686],{"stretchy":1685},[1810,22864,22865],{},"7.8",[1677,22867,1692],{"stretchy":1685},[902,22869,22870],{"encoding":904},"Y = C + I + G. \\qquad (7.8)",[724,22872,22873,22874,1884,22877,11413,22890,22893],{},"Stát se stává spotřebitelem, jehož „důchod“ získává ",[38,22875,22876],{},"zdaněním domácností",[883,22878,22880],{"className":22879},[886],[888,22881,22882],{"xmlns":890},[892,22883,22884,22888],{},[895,22885,22886],{},[898,22887,2455],{},[902,22889,2455],{"encoding":904},[614,22891,22892],{},"taxation","). Zdanění bývá:",[120,22895,22896,22929,22954],{},[123,22897,22898,22899,1967],{},"úměrné důchodu: ",[883,22900,22902],{"className":22901},[886],[888,22903,22904],{"xmlns":890},[892,22905,22906,22926],{},[895,22907,22908,22910,22912,22914,22916,22918,22920,22922,22924],{},[898,22909,2455],{},[1677,22911,1679],{},[898,22913,2455],{},[1677,22915,1686],{"stretchy":1685},[898,22917,10516],{},[1677,22919,1692],{"stretchy":1685},[1677,22921,1679],{},[898,22923,20246],{},[898,22925,10516],{},[902,22927,22928],{"encoding":904},"T = T(Y) = tY",[123,22930,22931,22932,1967],{},"fixní: ",[883,22933,22935],{"className":22934},[886],[888,22936,22937],{"xmlns":890},[892,22938,22939,22951],{},[895,22940,22941,22943,22945],{},[898,22942,2455],{},[1677,22944,1679],{},[1805,22946,22947,22949],{},[898,22948,2455],{},[1677,22950,5742],{},[902,22952,22953],{"encoding":904},"T = T^*",[123,22955,22956,22957,22985,22986,1656],{},"kombinované: ",[883,22958,22960],{"className":22959},[886],[888,22961,22962],{"xmlns":890},[892,22963,22964,22982],{},[895,22965,22966,22968,22970,22976,22978,22980],{},[898,22967,2455],{},[1677,22969,1679],{},[1805,22971,22972,22974],{},[898,22973,2455],{},[1677,22975,5742],{},[1677,22977,1776],{},[898,22979,20246],{},[898,22981,10516],{},[902,22983,22984],{"encoding":904},"T = T^* + tY",", kde ",[883,22987,22989],{"className":22988},[886],[888,22990,22991],{"xmlns":890},[892,22992,22993,23005],{},[895,22994,22995,22997,22999,23001,23003],{},[1810,22996,2008],{},[1677,22998,9067],{},[898,23000,20246],{},[1677,23002,3128],{},[1810,23004,1959],{},[902,23006,23007],{"encoding":904},"0 \\le t \u003C 1",[5254,23009,23010],{},[724,23011,23012,23014,23015,23036,23037,23040,23041,23054,23055,13518,23081,1884,23084,23110,23111,23139,23140,5272,23153,23171],{},[883,23013,5800],{}," Pozor na disponibilní důchod\nV modelu ",[883,23016,23018],{"className":23017},[886],[888,23019,23020],{"xmlns":890},[892,23021,23022,23034],{},[895,23023,23024,23026,23028,23030,23032],{},[898,23025,2458],{},[1969,23027,13680],{},[898,23029,13574],{},[1969,23031,13680],{},[898,23033,13502],{},[902,23035,19611],{"encoding":904}," je nutné ",[38,23038,23039],{},"důsledně rozlišovat dva důchody",": celkový národní důchod ",[883,23042,23044],{"className":23043},[886],[888,23045,23046],{"xmlns":890},[892,23047,23048,23052],{},[895,23049,23050],{},[898,23051,10516],{},[902,23053,10516],{"encoding":904}," (vstupuje do podmínky rovnováhy ",[883,23056,23058],{"className":23057},[886],[888,23059,23060],{"xmlns":890},[892,23061,23062,23078],{},[895,23063,23064,23066,23068,23070,23072,23074,23076],{},[898,23065,10516],{},[1677,23067,1679],{},[898,23069,2458],{},[1677,23071,1776],{},[898,23073,13574],{},[1677,23075,1776],{},[898,23077,13502],{},[902,23079,23080],{"encoding":904},"Y = C + I + G",[38,23082,23083],{},"disponibilní důchod",[883,23085,23087],{"className":23086},[886],[888,23088,23089],{"xmlns":890},[892,23090,23091,23107],{},[895,23092,23093,23099,23101,23103,23105],{},[1953,23094,23095,23097],{},[898,23096,10516],{},[898,23098,5571],{},[1677,23100,1679],{},[898,23102,10516],{},[1677,23104,1906],{},[898,23106,2455],{},[902,23108,23109],{"encoding":904},"Y_D = Y - T"," (na něm závisí spotřeba domácností, ",[883,23112,23114],{"className":23113},[886],[888,23115,23116],{"xmlns":890},[892,23117,23118,23136],{},[895,23119,23120,23122,23124,23126,23128,23134],{},[898,23121,2458],{},[1677,23123,1679],{},[898,23125,2458],{},[1677,23127,1686],{"stretchy":1685},[1953,23129,23130,23132],{},[898,23131,10516],{},[898,23133,5571],{},[1677,23135,1692],{"stretchy":1685},[902,23137,23138],{"encoding":904},"C = C(Y_D)","). Záměna ",[883,23141,23143],{"className":23142},[886],[888,23144,23145],{"xmlns":890},[892,23146,23147,23151],{},[895,23148,23149],{},[898,23150,10516],{},[902,23152,10516],{"encoding":904},[883,23154,23156],{"className":23155},[886],[888,23157,23158],{"xmlns":890},[892,23159,23160,23168],{},[895,23161,23162],{},[1953,23163,23164,23166],{},[898,23165,10516],{},[898,23167,5571],{},[902,23169,23170],{"encoding":904},"Y_D"," ve funkci spotřeby je nejčastější zdroj chyb.",[724,23173,23174,11413,23177,1692],{},[38,23175,23176],{},"Disponibilní důchod",[614,23178,23179],{},"disposable income",[724,23181,23182],{},[883,23183,23185],{"className":23184},[886],[888,23186,23187],{"xmlns":890},[892,23188,23189,23205],{},[895,23190,23191,23197,23199,23201,23203],{},[1953,23192,23193,23195],{},[898,23194,10516],{},[898,23196,5571],{},[1677,23198,1679],{},[898,23200,10516],{},[1677,23202,1906],{},[898,23204,2455],{},[902,23206,23109],{"encoding":904},[724,23208,23209,23210,1656],{},"je to, co zbývá domácnostem po zdanění. Spotřeba je pak funkcí disponibilního důchodu: ",[883,23211,23213],{"className":23212},[886],[888,23214,23215],{"xmlns":890},[892,23216,23217,23235],{},[895,23218,23219,23221,23223,23225,23227,23233],{},[898,23220,2458],{},[1677,23222,1679],{},[898,23224,2458],{},[1677,23226,1686],{"stretchy":1685},[1953,23228,23229,23231],{},[898,23230,10516],{},[898,23232,5571],{},[1677,23234,1692],{"stretchy":1685},[902,23236,23138],{"encoding":904},[198,23238,22082],{"id":23239},"soustava-rovnic-1",[724,23241,23242,23243,1343,23264,23286,23287,2385],{},"Pro pevně zadané ",[883,23244,23246],{"className":23245},[886],[888,23247,23248],{"xmlns":890},[892,23249,23250,23262],{},[895,23251,23252,23254,23256],{},[898,23253,13574],{},[1677,23255,1679],{},[1805,23257,23258,23260],{},[898,23259,13574],{},[1677,23261,5742],{},[902,23263,13585],{"encoding":904},[883,23265,23267],{"className":23266},[886],[888,23268,23269],{"xmlns":890},[892,23270,23271,23283],{},[895,23272,23273,23275,23277],{},[898,23274,13502],{},[1677,23276,1679],{},[1805,23278,23279,23281],{},[898,23280,13502],{},[1677,23282,5742],{},[902,23284,23285],{"encoding":904},"G = G^*"," dostáváme soustavu 4 rovnic o 4 neznámých ",[883,23288,23290],{"className":23289},[886],[888,23291,23292],{"xmlns":890},[892,23293,23294,23314],{},[895,23295,23296,23298,23300,23302,23304,23310,23312],{},[898,23297,10516],{},[1677,23299,1967],{"separator":1966},[898,23301,2458],{},[1677,23303,1967],{"separator":1966},[1953,23305,23306,23308],{},[898,23307,10516],{},[898,23309,5571],{},[1677,23311,1967],{"separator":1966},[898,23313,2455],{},[902,23315,23316],{"encoding":904},"Y, C, Y_D, T",[724,23318,23319],{},[883,23320,23322],{"className":23321},[886],[888,23323,23324],{"xmlns":890},[892,23325,23326,23467],{},[895,23327,23328,23458,23460,23462,23465],{},[22145,23329,23330,23368,23396,23428],{"rowspacing":22147,"columnalign":22148,"columnspacing":2058},[22150,23331,23332,23338],{},[22153,23333,23334],{},[2006,23335,23336],{"scriptlevel":2008,"displaystyle":1966},[898,23337,10516],{},[22153,23339,23340],{},[2006,23341,23342],{"scriptlevel":2008,"displaystyle":1966},[895,23343,23344,23346,23348,23350,23352,23358,23360,23366],{},[895,23345],{},[1677,23347,1679],{},[898,23349,2458],{},[1677,23351,1776],{},[1805,23353,23354,23356],{},[898,23355,13574],{},[1677,23357,5742],{},[1677,23359,1776],{},[1805,23361,23362,23364],{},[898,23363,13502],{},[1677,23365,5742],{},[1677,23367,1967],{"separator":1966},[22150,23369,23370,23376],{},[22153,23371,23372],{},[2006,23373,23374],{"scriptlevel":2008,"displaystyle":1966},[898,23375,2455],{},[22153,23377,23378],{},[2006,23379,23380],{"scriptlevel":2008,"displaystyle":1966},[895,23381,23382,23384,23386,23388,23390,23392,23394],{},[895,23383],{},[1677,23385,1679],{},[898,23387,2455],{},[1677,23389,1686],{"stretchy":1685},[898,23391,10516],{},[1677,23393,1692],{"stretchy":1685},[1677,23395,1967],{"separator":1966},[22150,23397,23398,23404],{},[22153,23399,23400],{},[2006,23401,23402],{"scriptlevel":2008,"displaystyle":1966},[898,23403,2458],{},[22153,23405,23406],{},[2006,23407,23408],{"scriptlevel":2008,"displaystyle":1966},[895,23409,23410,23412,23414,23416,23418,23424,23426],{},[895,23411],{},[1677,23413,1679],{},[898,23415,2458],{},[1677,23417,1686],{"stretchy":1685},[1953,23419,23420,23422],{},[898,23421,10516],{},[898,23423,5571],{},[1677,23425,1692],{"stretchy":1685},[1677,23427,1967],{"separator":1966},[22150,23429,23430,23440],{},[22153,23431,23432],{},[2006,23433,23434],{"scriptlevel":2008,"displaystyle":1966},[1953,23435,23436,23438],{},[898,23437,10516],{},[898,23439,5571],{},[22153,23441,23442],{},[2006,23443,23444],{"scriptlevel":2008,"displaystyle":1966},[895,23445,23446,23448,23450,23452,23454,23456],{},[895,23447],{},[1677,23449,1679],{},[898,23451,10516],{},[1677,23453,1906],{},[898,23455,2455],{},[1677,23457,1967],{"separator":1966},[7266,23459],{"width":7268},[1677,23461,1686],{"stretchy":1685},[1810,23463,23464],{},"7.9",[1677,23466,1692],{"stretchy":1685},[902,23468,23469],{"encoding":904},"\\begin{aligned} Y &= C + I^* + G^*, \\\\ T &= T(Y), \\\\ C &= C(Y_D), \\\\ Y_D &= Y - T, \\end{aligned} \\qquad (7.9)",[724,23471,23472,23473,23517,23518,1656],{},"s řešeními ",[883,23474,23476],{"className":23475},[886],[888,23477,23478],{"xmlns":890},[892,23479,23480,23514],{},[895,23481,23482,23488,23490,23496,23498,23504,23506],{},[1805,23483,23484,23486],{},[898,23485,10516],{},[898,23487,5640],{},[1677,23489,1967],{"separator":1966},[1805,23491,23492,23494],{},[898,23493,2458],{},[898,23495,5640],{},[1677,23497,1967],{"separator":1966},[1805,23499,23500,23502],{},[898,23501,2455],{},[898,23503,5640],{},[1677,23505,1967],{"separator":1966},[10554,23507,23508,23510,23512],{},[898,23509,10516],{},[898,23511,5571],{},[898,23513,5640],{},[902,23515,23516],{"encoding":904},"Y^E, C^E, T^E, Y_D^E",", případně rovnovážnými úsporami domácností ",[883,23519,23521],{"className":23520},[886],[888,23522,23523],{"xmlns":890},[892,23524,23525,23551],{},[895,23526,23527,23533,23535,23543,23545],{},[1805,23528,23529,23531],{},[898,23530,10061],{},[898,23532,5640],{},[1677,23534,1679],{},[10554,23536,23537,23539,23541],{},[898,23538,10516],{},[898,23540,5571],{},[898,23542,5640],{},[1677,23544,1906],{},[1805,23546,23547,23549],{},[898,23548,2458],{},[898,23550,5640],{},[902,23552,23553],{"encoding":904},"S^E = Y_D^E - C^E",[5254,23555,23556,23561],{},[724,23557,23558,23560],{},[883,23559,5960],{}," Postup — jak sestavit a vyřešit soustavu C-I-G",[152,23562,23563,23586,23669,23724,23814],{},[123,23564,23565,23568,23569,1656],{},[38,23566,23567],{},"Zapiš všechny 4 rovnice"," ze zadání: podmínku rovnováhy, daňovou funkci, funkci spotřeby, definici ",[883,23570,23572],{"className":23571},[886],[888,23573,23574],{"xmlns":890},[892,23575,23576,23584],{},[895,23577,23578],{},[1953,23579,23580,23582],{},[898,23581,10516],{},[898,23583,5571],{},[902,23585,23170],{"encoding":904},[123,23587,23588,23637,23638,23655,23656,1656],{},[38,23589,23590,23591,23611,23612],{},"Dosaď ",[883,23592,23594],{"className":23593},[886],[888,23595,23596],{"xmlns":890},[892,23597,23598,23608],{},[895,23599,23600,23602,23604,23606],{},[898,23601,2455],{},[1677,23603,1686],{"stretchy":1685},[898,23605,10516],{},[1677,23607,1692],{"stretchy":1685},[902,23609,23610],{"encoding":904},"T(Y)"," do ",[883,23613,23615],{"className":23614},[886],[888,23616,23617],{"xmlns":890},[892,23618,23619,23635],{},[895,23620,23621,23627,23629,23631,23633],{},[1953,23622,23623,23625],{},[898,23624,10516],{},[898,23626,5571],{},[1677,23628,1679],{},[898,23630,10516],{},[1677,23632,1906],{},[898,23634,2455],{},[902,23636,23109],{"encoding":904}," — dostaneš ",[883,23639,23641],{"className":23640},[886],[888,23642,23643],{"xmlns":890},[892,23644,23645,23653],{},[895,23646,23647],{},[1953,23648,23649,23651],{},[898,23650,10516],{},[898,23652,5571],{},[902,23654,23170],{"encoding":904}," jako lineární funkci ",[883,23657,23659],{"className":23658},[886],[888,23660,23661],{"xmlns":890},[892,23662,23663,23667],{},[895,23664,23665],{},[898,23666,10516],{},[902,23668,10516],{"encoding":904},[123,23670,23671,23637,23698,23655,23711,1656],{},[38,23672,23590,23673,23697],{},[883,23674,23676],{"className":23675},[886],[888,23677,23678],{"xmlns":890},[892,23679,23680,23694],{},[895,23681,23682,23688,23690,23692],{},[1953,23683,23684,23686],{},[898,23685,10516],{},[898,23687,5571],{},[1677,23689,1686],{"stretchy":1685},[898,23691,10516],{},[1677,23693,1692],{"stretchy":1685},[902,23695,23696],{"encoding":904},"Y_D(Y)"," do funkce spotřeby",[883,23699,23701],{"className":23700},[886],[888,23702,23703],{"xmlns":890},[892,23704,23705,23709],{},[895,23706,23707],{},[898,23708,2458],{},[902,23710,2458],{"encoding":904},[883,23712,23714],{"className":23713},[886],[888,23715,23716],{"xmlns":890},[892,23717,23718,23722],{},[895,23719,23720],{},[898,23721,10516],{},[902,23723,10516],{"encoding":904},[123,23725,23726,1884,23748,23782,23783,23796,23797,1656],{},[38,23727,23590,23728,23747],{},[883,23729,23731],{"className":23730},[886],[888,23732,23733],{"xmlns":890},[892,23734,23735,23745],{},[895,23736,23737,23739,23741,23743],{},[898,23738,2458],{},[1677,23740,1686],{"stretchy":1685},[898,23742,10516],{},[1677,23744,1692],{"stretchy":1685},[902,23746,15606],{"encoding":904}," do podmínky rovnováhy",[883,23749,23751],{"className":23750},[886],[888,23752,23753],{"xmlns":890},[892,23754,23755,23779],{},[895,23756,23757,23759,23761,23763,23765,23771,23773],{},[898,23758,10516],{},[1677,23760,1679],{},[898,23762,2458],{},[1677,23764,1776],{},[1805,23766,23767,23769],{},[898,23768,13574],{},[1677,23770,5742],{},[1677,23772,1776],{},[1805,23774,23775,23777],{},[898,23776,13502],{},[1677,23778,5742],{},[902,23780,23781],{"encoding":904},"Y = C + I^* + G^*"," — zbývá jediná rovnice o jedné neznámé ",[883,23784,23786],{"className":23785},[886],[888,23787,23788],{"xmlns":890},[892,23789,23790,23794],{},[895,23791,23792],{},[898,23793,10516],{},[902,23795,10516],{"encoding":904},", odtud ",[883,23798,23800],{"className":23799},[886],[888,23801,23802],{"xmlns":890},[892,23803,23804,23812],{},[895,23805,23806],{},[1805,23807,23808,23810],{},[898,23809,10516],{},[898,23811,5640],{},[902,23813,15293],{"encoding":904},[123,23815,23816,23819,23820,1343,23838,1343,23858,1343,23875,1656],{},[38,23817,23818],{},"Zpětným dosazením"," dopočítej ",[883,23821,23823],{"className":23822},[886],[888,23824,23825],{"xmlns":890},[892,23826,23827,23835],{},[895,23828,23829],{},[1805,23830,23831,23833],{},[898,23832,2455],{},[898,23834,5640],{},[902,23836,23837],{"encoding":904},"T^E",[883,23839,23841],{"className":23840},[886],[888,23842,23843],{"xmlns":890},[892,23844,23845,23855],{},[895,23846,23847],{},[10554,23848,23849,23851,23853],{},[898,23850,10516],{},[898,23852,5571],{},[898,23854,5640],{},[902,23856,23857],{"encoding":904},"Y_D^E",[883,23859,23861],{"className":23860},[886],[888,23862,23863],{"xmlns":890},[892,23864,23865,23873],{},[895,23866,23867],{},[1805,23868,23869,23871],{},[898,23870,2458],{},[898,23872,5640],{},[902,23874,15352],{"encoding":904},[883,23876,23878],{"className":23877},[886],[888,23879,23880],{"xmlns":890},[892,23881,23882,23890],{},[895,23883,23884],{},[1805,23885,23886,23888],{},[898,23887,10061],{},[898,23889,5640],{},[902,23891,23892],{"encoding":904},"S^E",[198,23894,23896],{"id":23895},"příklad-74","Příklad 7.4",[724,23898,22412,23899,23920,23921,1343,23952,1343,23976,1343,23998,24020],{},[883,23900,23902],{"className":23901},[886],[888,23903,23904],{"xmlns":890},[892,23905,23906,23918],{},[895,23907,23908,23910,23912,23914,23916],{},[898,23909,2458],{},[1969,23911,13680],{},[898,23913,13574],{},[1969,23915,13680],{},[898,23917,13502],{},[902,23919,19611],{"encoding":904}," jsou dány ",[883,23922,23924],{"className":23923},[886],[888,23925,23926],{"xmlns":890},[892,23927,23928,23949],{},[895,23929,23930,23932,23934,23937,23939,23945,23947],{},[898,23931,2458],{},[1677,23933,1679],{},[1810,23935,23936],{},"0,9",[1969,23938,2668],{},[1953,23940,23941,23943],{},[898,23942,10516],{},[898,23944,5571],{},[1677,23946,1776],{},[1810,23948,7285],{},[902,23950,23951],{"encoding":904},"C = 0{,}9\\,Y_D + 70",[883,23953,23955],{"className":23954},[886],[888,23956,23957],{"xmlns":890},[892,23958,23959,23973],{},[895,23960,23961,23963,23965,23967,23969,23971],{},[898,23962,2455],{},[1677,23964,1679],{},[1810,23966,2520],{},[898,23968,10516],{},[1677,23970,1776],{},[1810,23972,6392],{},[902,23974,23975],{"encoding":904},"T = 0{,}2Y + 25",[883,23977,23979],{"className":23978},[886],[888,23980,23981],{"xmlns":890},[892,23982,23983,23995],{},[895,23984,23985,23991,23993],{},[1805,23986,23987,23989],{},[898,23988,13574],{},[1677,23990,5742],{},[1677,23992,1679],{},[1810,23994,16428],{},[902,23996,23997],{"encoding":904},"I^* = 35",[883,23999,24001],{"className":24000},[886],[888,24002,24003],{"xmlns":890},[892,24004,24005,24017],{},[895,24006,24007,24013,24015],{},[1805,24008,24009,24011],{},[898,24010,13502],{},[1677,24012,5742],{},[1677,24014,1679],{},[1810,24016,10423],{},[902,24018,24019],{"encoding":904},"G^* = 20",". Soustava (7.9):",[724,24022,24023],{},[883,24024,24026],{"className":24025},[886],[888,24027,24028],{"xmlns":890},[892,24029,24030,24154],{},[22145,24031,24032,24062,24090,24124],{"rowspacing":22147,"columnalign":22148,"columnspacing":2058},[22150,24033,24034,24040],{},[22153,24035,24036],{},[2006,24037,24038],{"scriptlevel":2008,"displaystyle":1966},[898,24039,10516],{},[22153,24041,24042],{},[2006,24043,24044],{"scriptlevel":2008,"displaystyle":1966},[895,24045,24046,24048,24050,24052,24054,24056,24058,24060],{},[895,24047],{},[1677,24049,1679],{},[898,24051,2458],{},[1677,24053,1776],{},[1810,24055,16428],{},[1677,24057,1776],{},[1810,24059,10423],{},[1677,24061,1967],{"separator":1966},[22150,24063,24064,24070],{},[22153,24065,24066],{},[2006,24067,24068],{"scriptlevel":2008,"displaystyle":1966},[898,24069,2455],{},[22153,24071,24072],{},[2006,24073,24074],{"scriptlevel":2008,"displaystyle":1966},[895,24075,24076,24078,24080,24082,24084,24086,24088],{},[895,24077],{},[1677,24079,1679],{},[1810,24081,2520],{},[898,24083,10516],{},[1677,24085,1776],{},[1810,24087,6392],{},[1677,24089,1967],{"separator":1966},[22150,24091,24092,24098],{},[22153,24093,24094],{},[2006,24095,24096],{"scriptlevel":2008,"displaystyle":1966},[898,24097,2458],{},[22153,24099,24100],{},[2006,24101,24102],{"scriptlevel":2008,"displaystyle":1966},[895,24103,24104,24106,24108,24110,24112,24118,24120,24122],{},[895,24105],{},[1677,24107,1679],{},[1810,24109,23936],{},[1969,24111,2668],{},[1953,24113,24114,24116],{},[898,24115,10516],{},[898,24117,5571],{},[1677,24119,1776],{},[1810,24121,7285],{},[1677,24123,1967],{"separator":1966},[22150,24125,24126,24136],{},[22153,24127,24128],{},[2006,24129,24130],{"scriptlevel":2008,"displaystyle":1966},[1953,24131,24132,24134],{},[898,24133,10516],{},[898,24135,5571],{},[22153,24137,24138],{},[2006,24139,24140],{"scriptlevel":2008,"displaystyle":1966},[895,24141,24142,24144,24146,24148,24150,24152],{},[895,24143],{},[1677,24145,1679],{},[898,24147,10516],{},[1677,24149,1906],{},[898,24151,2455],{},[898,24153,1656],{"mathvariant":2057},[902,24155,24156],{"encoding":904},"\\begin{aligned} Y &= C + 35 + 20, \\\\ T &= 0{,}2Y + 25, \\\\ C &= 0{,}9\\,Y_D + 70, \\\\ Y_D &= Y - T. \\end{aligned}",[724,24158,24159,24162,24163,24217,24218,24264,24265,2385],{},[38,24160,24161],{},"Řešení."," Z definice ",[883,24164,24166],{"className":24165},[886],[888,24167,24168],{"xmlns":890},[892,24169,24170,24214],{},[895,24171,24172,24178,24180,24182,24184,24186,24188,24190,24192,24194,24196,24198,24200,24202,24204,24206,24208,24210,24212],{},[1953,24173,24174,24176],{},[898,24175,10516],{},[898,24177,5571],{},[1677,24179,1679],{},[898,24181,10516],{},[1677,24183,1906],{},[898,24185,2455],{},[1677,24187,1679],{},[898,24189,10516],{},[1677,24191,1906],{},[1677,24193,1686],{"stretchy":1685},[1810,24195,2520],{},[898,24197,10516],{},[1677,24199,1776],{},[1810,24201,6392],{},[1677,24203,1692],{"stretchy":1685},[1677,24205,1679],{},[1810,24207,15979],{},[898,24209,10516],{},[1677,24211,1906],{},[1810,24213,6392],{},[902,24215,24216],{"encoding":904},"Y_D = Y - T = Y - (0{,}2Y + 25) = 0{,}8Y - 25",". Dosazením do spotřeby: ",[883,24219,24221],{"className":24220},[886],[888,24222,24223],{"xmlns":890},[892,24224,24225,24261],{},[895,24226,24227,24229,24231,24233,24235,24237,24239,24241,24243,24245,24247,24249,24251,24254,24256,24258],{},[898,24228,2458],{},[1677,24230,1679],{},[1810,24232,23936],{},[1677,24234,1686],{"stretchy":1685},[1810,24236,15979],{},[898,24238,10516],{},[1677,24240,1906],{},[1810,24242,6392],{},[1677,24244,1692],{"stretchy":1685},[1677,24246,1776],{},[1810,24248,7285],{},[1677,24250,1679],{},[1810,24252,24253],{},"0,72",[898,24255,10516],{},[1677,24257,1776],{},[1810,24259,24260],{},"47,5",[902,24262,24263],{"encoding":904},"C = 0{,}9(0{,}8Y - 25) + 70 = 0{,}72Y + 47{,}5",". Dosazením do rovnovážné rovnice ",[883,24266,24268],{"className":24267},[886],[888,24269,24270],{"xmlns":890},[892,24271,24272,24290],{},[895,24273,24274,24276,24278,24280,24282,24284,24286,24288],{},[898,24275,10516],{},[1677,24277,1679],{},[1810,24279,24253],{},[898,24281,10516],{},[1677,24283,1776],{},[1810,24285,24260],{},[1677,24287,1776],{},[1810,24289,22571],{},[902,24291,24292],{"encoding":904},"Y = 0{,}72Y + 47{,}5 + 55",[724,24294,24295],{},[883,24296,24298],{"className":24297},[886],[888,24299,24300],{"xmlns":890},[892,24301,24302,24343],{},[895,24303,24304,24307,24309,24311,24314,24316,24318,24320,24326,24328,24338,24340],{},[1810,24305,24306],{},"0,28",[898,24308,10516],{},[1677,24310,1679],{},[1810,24312,24313],{},"102,5",[1969,24315,5372],{},[1677,24317,16398],{},[1969,24319,5372],{},[1805,24321,24322,24324],{},[898,24323,10516],{},[898,24325,5640],{},[1677,24327,1679],{},[2006,24329,24330],{"scriptlevel":2008,"displaystyle":1685},[2010,24331,24332,24335],{},[1810,24333,24334],{},"5125",[1810,24336,24337],{},"14",[1677,24339,7288],{},[1810,24341,24342],{},"366,071.",[902,24344,24345],{"encoding":904},"0{,}28Y = 102{,}5 \\;\\Longrightarrow\\; Y^E = \\tfrac{5125}{14} \\doteq 366{,}071.",[724,24347,24348],{},"Rovnovážné veličiny:",[120,24350,24351,24386,24438,24492,24540],{},[123,24352,24353,1967],{},[883,24354,24356],{"className":24355},[886],[888,24357,24358],{"xmlns":890},[892,24359,24360,24383],{},[895,24361,24362,24368,24370,24378,24380],{},[1805,24363,24364,24366],{},[898,24365,10516],{},[898,24367,5640],{},[1677,24369,1679],{},[2006,24371,24372],{"scriptlevel":2008,"displaystyle":1685},[2010,24373,24374,24376],{},[1810,24375,24334],{},[1810,24377,24337],{},[1677,24379,7288],{},[1810,24381,24382],{},"366,071",[902,24384,24385],{"encoding":904},"Y^E = \\tfrac{5125}{14} \\doteq 366{,}071",[123,24387,24388,1967],{},[883,24389,24391],{"className":24390},[886],[888,24392,24393],{"xmlns":890},[892,24394,24395,24435],{},[895,24396,24397,24403,24405,24407,24409,24415,24417,24419,24421,24430,24432],{},[1805,24398,24399,24401],{},[898,24400,2455],{},[898,24402,5640],{},[1677,24404,1679],{},[1810,24406,2520],{},[1969,24408,2668],{},[1805,24410,24411,24413],{},[898,24412,10516],{},[898,24414,5640],{},[1677,24416,1776],{},[1810,24418,6392],{},[1677,24420,1679],{},[2006,24422,24423],{"scriptlevel":2008,"displaystyle":1685},[2010,24424,24425,24428],{},[1810,24426,24427],{},"1375",[1810,24429,24337],{},[1677,24431,7288],{},[1810,24433,24434],{},"98,214",[902,24436,24437],{"encoding":904},"T^E = 0{,}2\\,Y^E + 25 = \\tfrac{1375}{14} \\doteq 98{,}214",[123,24439,24440,1967],{},[883,24441,24443],{"className":24442},[886],[888,24444,24445],{"xmlns":890},[892,24446,24447,24489],{},[895,24448,24449,24457,24459,24465,24467,24473,24475,24484,24486],{},[10554,24450,24451,24453,24455],{},[898,24452,10516],{},[898,24454,5571],{},[898,24456,5640],{},[1677,24458,1679],{},[1805,24460,24461,24463],{},[898,24462,10516],{},[898,24464,5640],{},[1677,24466,1906],{},[1805,24468,24469,24471],{},[898,24470,2455],{},[898,24472,5640],{},[1677,24474,1679],{},[2006,24476,24477],{"scriptlevel":2008,"displaystyle":1685},[2010,24478,24479,24482],{},[1810,24480,24481],{},"3750",[1810,24483,24337],{},[1677,24485,7288],{},[1810,24487,24488],{},"267,857",[902,24490,24491],{"encoding":904},"Y_D^E = Y^E - T^E = \\tfrac{3750}{14} \\doteq 267{,}857",[123,24493,24494,1967],{},[883,24495,24497],{"className":24496},[886],[888,24498,24499],{"xmlns":890},[892,24500,24501,24537],{},[895,24502,24503,24509,24511,24517,24519,24521,24523,24532,24534],{},[1805,24504,24505,24507],{},[898,24506,2458],{},[898,24508,5640],{},[1677,24510,1679],{},[1805,24512,24513,24515],{},[898,24514,10516],{},[898,24516,5640],{},[1677,24518,1906],{},[1810,24520,22571],{},[1677,24522,1679],{},[2006,24524,24525],{"scriptlevel":2008,"displaystyle":1685},[2010,24526,24527,24530],{},[1810,24528,24529],{},"4355",[1810,24531,24337],{},[1677,24533,7288],{},[1810,24535,24536],{},"311,071",[902,24538,24539],{"encoding":904},"C^E = Y^E - 55 = \\tfrac{4355}{14} \\doteq 311{,}071",[123,24541,24542,24598],{},[883,24543,24545],{"className":24544},[886],[888,24546,24547],{"xmlns":890},[892,24548,24549,24595],{},[895,24550,24551,24557,24559,24567,24569,24575,24577,24579,24588,24590,24592],{},[1805,24552,24553,24555],{},[898,24554,10061],{},[898,24556,5640],{},[1677,24558,1679],{},[10554,24560,24561,24563,24565],{},[898,24562,10516],{},[898,24564,5571],{},[898,24566,5640],{},[1677,24568,1906],{},[1805,24570,24571,24573],{},[898,24572,2458],{},[898,24574,5640],{},[1677,24576,1679],{},[1677,24578,1906],{},[2006,24580,24581],{"scriptlevel":2008,"displaystyle":1685},[2010,24582,24583,24586],{},[1810,24584,24585],{},"605",[1810,24587,24337],{},[1677,24589,7288],{},[1677,24591,1906],{},[1810,24593,24594],{},"43,214",[902,24596,24597],{"encoding":904},"S^E = Y_D^E - C^E = -\\tfrac{605}{14} \\doteq -43{,}214"," (záporné — domácnosti při této kalibraci čerpají úspory).",[724,24600,24601,22741,24603,24624,24625,24628,24629,24652,24653,1656],{},[38,24602,22740],{},[883,24604,24606],{"className":24605},[886],[888,24607,24608],{"xmlns":890},[892,24609,24610,24622],{},[895,24611,24612,24614,24616,24618,24620],{},[898,24613,2458],{},[1969,24615,13680],{},[898,24617,13574],{},[1969,24619,13680],{},[898,24621,13502],{},[902,24623,19611],{"encoding":904}," stále uvažuje ",[38,24626,24627],{},"uzavřenou"," ekonomiku. Reálné ekonomiky dovážejí a vyvážejí zboží — otevření ekonomiky o čistý export ",[883,24630,24632],{"className":24631},[886],[888,24633,24634],{"xmlns":890},[892,24635,24636,24649],{},[895,24637,24638,24640,24642,24645,24647],{},[898,24639,13710],{},[1677,24641,1679],{},[898,24643,24644],{},"B",[1677,24646,1906],{},[898,24648,2499],{},[902,24650,24651],{"encoding":904},"X = B - M"," dává ",[38,24654,22762,24655],{},[883,24656,24658],{"className":24657},[886],[888,24659,24660],{"xmlns":890},[892,24661,24662,24678],{},[895,24663,24664,24666,24668,24670,24672,24674,24676],{},[898,24665,2458],{},[1969,24667,13680],{},[898,24669,13574],{},[1969,24671,13680],{},[898,24673,13502],{},[1969,24675,13680],{},[898,24677,13710],{},[902,24679,13713],{"encoding":904},[115,24681,24683],{"id":24682},"model-c-i-g-x-otevřená-ekonomika","Model C-I-G-X — otevřená ekonomika",[198,24685,22012],{"id":24686},"zadání-modelu-2",[724,24688,24689,24690,1884,24693,22985,24714,24727,24728,13518,24731,24744],{},"Rozšíření o ",[38,24691,24692],{},"čistý export",[883,24694,24696],{"className":24695},[886],[888,24697,24698],{"xmlns":890},[892,24699,24700,24712],{},[895,24701,24702,24704,24706,24708,24710],{},[898,24703,13710],{},[1677,24705,1679],{},[898,24707,24644],{},[1677,24709,1906],{},[898,24711,2499],{},[902,24713,24651],{"encoding":904},[883,24715,24717],{"className":24716},[886],[888,24718,24719],{"xmlns":890},[892,24720,24721,24725],{},[895,24722,24723],{},[898,24724,24644],{},[902,24726,24644],{"encoding":904}," je hrubý export (",[614,24729,24730],{},"brutto export",[883,24732,24734],{"className":24733},[886],[888,24735,24736],{"xmlns":890},[892,24737,24738,24742],{},[895,24739,24740],{},[898,24741,2499],{},[902,24743,2499],{"encoding":904}," import. Obvyklá konstrukce: import závisí (nejčastěji je úměrný) disponibilnímu důchodu:",[724,24746,24747],{},[883,24748,24750],{"className":24749},[886],[888,24751,24752],{"xmlns":890},[892,24753,24754,24774],{},[895,24755,24756,24758,24760,24762,24764,24770,24772],{},[898,24757,2499],{},[1677,24759,1679],{},[898,24761,2499],{},[1677,24763,1686],{"stretchy":1685},[1953,24765,24766,24768],{},[898,24767,10516],{},[898,24769,5571],{},[1677,24771,1692],{"stretchy":1685},[898,24773,1656],{"mathvariant":2057},[902,24775,24776],{"encoding":904},"M = M(Y_D).",[724,24778,24779],{},"Podmínka rovnováhy:",[724,24781,24782],{},[883,24783,24785],{"className":24784},[886],[888,24786,24787],{"xmlns":890},[892,24788,24789,24826],{},[895,24790,24791,24793,24795,24797,24799,24801,24803,24805,24807,24809,24811,24813,24815,24817,24819,24822,24824],{},[898,24792,10516],{},[1677,24794,1679],{},[898,24796,2458],{},[1677,24798,1776],{},[898,24800,13574],{},[1677,24802,1776],{},[898,24804,13502],{},[1677,24806,1776],{},[898,24808,24644],{},[1677,24810,1906],{},[898,24812,2499],{},[898,24814,1656],{"mathvariant":2057},[7266,24816],{"width":7268},[1677,24818,1686],{"stretchy":1685},[1810,24820,24821],{},"7.10",[1969,24823,207],{},[1677,24825,1692],{"stretchy":1685},[902,24827,24828],{"encoding":904},"Y = C + I + G + B - M. \\qquad (7.10\\text{a})",[198,24830,22082],{"id":24831},"soustava-rovnic-2",[724,24833,23242,24834,24868,24869,2385],{},[883,24835,24837],{"className":24836},[886],[888,24838,24839],{"xmlns":890},[892,24840,24841,24865],{},[895,24842,24843,24849,24851,24857,24859],{},[1805,24844,24845,24847],{},[898,24846,13574],{},[1677,24848,5742],{},[1677,24850,1967],{"separator":1966},[1805,24852,24853,24855],{},[898,24854,13502],{},[1677,24856,5742],{},[1677,24858,1967],{"separator":1966},[1805,24860,24861,24863],{},[898,24862,24644],{},[1677,24864,5742],{},[902,24866,24867],{"encoding":904},"I^*, G^*, B^*"," dostáváme soustavu 5 rovnic o 5 neznámých ",[883,24870,24872],{"className":24871},[886],[888,24873,24874],{"xmlns":890},[892,24875,24876,24900],{},[895,24877,24878,24880,24882,24884,24886,24888,24890,24896,24898],{},[898,24879,10516],{},[1677,24881,1967],{"separator":1966},[898,24883,2458],{},[1677,24885,1967],{"separator":1966},[898,24887,2455],{},[1677,24889,1967],{"separator":1966},[1953,24891,24892,24894],{},[898,24893,10516],{},[898,24895,5571],{},[1677,24897,1967],{"separator":1966},[898,24899,2499],{},[902,24901,24902],{"encoding":904},"Y, C, T, Y_D, M",[724,24904,24905],{},[883,24906,24908],{"className":24907},[886],[888,24909,24910],{"xmlns":890},[892,24911,24912,25096],{},[895,24913,24914,25088,25090,25092,25094],{},[22145,24915,24916,24948,24978,25006,25038],{"rowspacing":22147,"columnalign":22148,"columnspacing":2058},[22150,24917,24918,24924],{},[22153,24919,24920],{},[2006,24921,24922],{"scriptlevel":2008,"displaystyle":1966},[898,24923,2458],{},[22153,24925,24926],{},[2006,24927,24928],{"scriptlevel":2008,"displaystyle":1966},[895,24929,24930,24932,24934,24936,24938,24944,24946],{},[895,24931],{},[1677,24933,1679],{},[898,24935,2458],{},[1677,24937,1686],{"stretchy":1685},[1953,24939,24940,24942],{},[898,24941,10516],{},[898,24943,5571],{},[1677,24945,1692],{"stretchy":1685},[1677,24947,1967],{"separator":1966},[22150,24949,24950,24960],{},[22153,24951,24952],{},[2006,24953,24954],{"scriptlevel":2008,"displaystyle":1966},[1953,24955,24956,24958],{},[898,24957,10516],{},[898,24959,5571],{},[22153,24961,24962],{},[2006,24963,24964],{"scriptlevel":2008,"displaystyle":1966},[895,24965,24966,24968,24970,24972,24974,24976],{},[895,24967],{},[1677,24969,1679],{},[898,24971,10516],{},[1677,24973,1906],{},[898,24975,2455],{},[1677,24977,1967],{"separator":1966},[22150,24979,24980,24986],{},[22153,24981,24982],{},[2006,24983,24984],{"scriptlevel":2008,"displaystyle":1966},[898,24985,2455],{},[22153,24987,24988],{},[2006,24989,24990],{"scriptlevel":2008,"displaystyle":1966},[895,24991,24992,24994,24996,24998,25000,25002,25004],{},[895,24993],{},[1677,24995,1679],{},[898,24997,2455],{},[1677,24999,1686],{"stretchy":1685},[898,25001,10516],{},[1677,25003,1692],{"stretchy":1685},[1677,25005,1967],{"separator":1966},[22150,25007,25008,25014],{},[22153,25009,25010],{},[2006,25011,25012],{"scriptlevel":2008,"displaystyle":1966},[898,25013,2499],{},[22153,25015,25016],{},[2006,25017,25018],{"scriptlevel":2008,"displaystyle":1966},[895,25019,25020,25022,25024,25026,25028,25034,25036],{},[895,25021],{},[1677,25023,1679],{},[898,25025,2499],{},[1677,25027,1686],{"stretchy":1685},[1953,25029,25030,25032],{},[898,25031,10516],{},[898,25033,5571],{},[1677,25035,1692],{"stretchy":1685},[1677,25037,1967],{"separator":1966},[22150,25039,25040,25046],{},[22153,25041,25042],{},[2006,25043,25044],{"scriptlevel":2008,"displaystyle":1966},[898,25045,10516],{},[22153,25047,25048],{},[2006,25049,25050],{"scriptlevel":2008,"displaystyle":1966},[895,25051,25052,25054,25056,25058,25060,25066,25068,25074,25076,25082,25084,25086],{},[895,25053],{},[1677,25055,1679],{},[898,25057,2458],{},[1677,25059,1776],{},[1805,25061,25062,25064],{},[898,25063,13574],{},[1677,25065,5742],{},[1677,25067,1776],{},[1805,25069,25070,25072],{},[898,25071,13502],{},[1677,25073,5742],{},[1677,25075,1776],{},[1805,25077,25078,25080],{},[898,25079,24644],{},[1677,25081,5742],{},[1677,25083,1906],{},[898,25085,2499],{},[898,25087,1656],{"mathvariant":2057},[7266,25089],{"width":7268},[1677,25091,1686],{"stretchy":1685},[1810,25093,24821],{},[1677,25095,1692],{"stretchy":1685},[902,25097,25098],{"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)",[198,25100,25102],{"id":25101},"příklad-75","Příklad 7.5",[724,25104,25105,25106,1343,25138,1343,25165,1343,25186,1343,25208,1343,25230,25253],{},"Dáno: ",[883,25107,25109],{"className":25108},[886],[888,25110,25111],{"xmlns":890},[892,25112,25113,25135],{},[895,25114,25115,25117,25119,25122,25124,25130,25132],{},[898,25116,2458],{},[1677,25118,1679],{},[1810,25120,25121],{},"0,75",[1969,25123,2668],{},[1953,25125,25126,25128],{},[898,25127,10516],{},[898,25129,5571],{},[1677,25131,1776],{},[1810,25133,25134],{},"750",[902,25136,25137],{"encoding":904},"C = 0{,}75\\,Y_D + 750",[883,25139,25141],{"className":25140},[886],[888,25142,25143],{"xmlns":890},[892,25144,25145,25162],{},[895,25146,25147,25149,25151,25154,25156],{},[898,25148,2499],{},[1677,25150,1679],{},[1810,25152,25153],{},"0,15",[1969,25155,2668],{},[1953,25157,25158,25160],{},[898,25159,10516],{},[898,25161,5571],{},[902,25163,25164],{"encoding":904},"M = 0{,}15\\,Y_D",[883,25166,25168],{"className":25167},[886],[888,25169,25170],{"xmlns":890},[892,25171,25172,25183],{},[895,25173,25174,25176,25178,25181],{},[898,25175,2455],{},[1677,25177,1679],{},[1810,25179,25180],{},"0,25",[898,25182,10516],{},[902,25184,25185],{"encoding":904},"T = 0{,}25Y",[883,25187,25189],{"className":25188},[886],[888,25190,25191],{"xmlns":890},[892,25192,25193,25205],{},[895,25194,25195,25201,25203],{},[1805,25196,25197,25199],{},[898,25198,13574],{},[1677,25200,5742],{},[1677,25202,1679],{},[1810,25204,16500],{},[902,25206,25207],{"encoding":904},"I^* = 500",[883,25209,25211],{"className":25210},[886],[888,25212,25213],{"xmlns":890},[892,25214,25215,25227],{},[895,25216,25217,25223,25225],{},[1805,25218,25219,25221],{},[898,25220,13502],{},[1677,25222,5742],{},[1677,25224,1679],{},[1810,25226,10191],{},[902,25228,25229],{"encoding":904},"G^* = 150",[883,25231,25233],{"className":25232},[886],[888,25234,25235],{"xmlns":890},[892,25236,25237,25250],{},[895,25238,25239,25245,25247],{},[1805,25240,25241,25243],{},[898,25242,24644],{},[1677,25244,5742],{},[1677,25246,1679],{},[1810,25248,25249],{},"800",[902,25251,25252],{"encoding":904},"B^* = 800",". Soustava:",[724,25255,25256],{},[883,25257,25259],{"className":25258},[886],[888,25260,25261],{"xmlns":890},[892,25262,25263,25481],{},[22145,25264,25265,25311,25353,25389,25431],{"rowspacing":22147,"columnalign":22148,"columnspacing":2058},[22150,25266,25267,25283],{},[22153,25268,25269],{},[2006,25270,25271],{"scriptlevel":2008,"displaystyle":1966},[895,25272,25273,25275,25277,25279,25281],{},[1677,25274,1686],{"stretchy":1685},[898,25276,13431],{},[1810,25278,1959],{},[1677,25280,1692],{"stretchy":1685},[1969,25282,1971],{},[22153,25284,25285],{},[2006,25286,25287],{"scriptlevel":2008,"displaystyle":1966},[895,25288,25289,25291,25293,25295,25297,25299,25305,25307,25309],{},[895,25290],{},[898,25292,2458],{},[1677,25294,1679],{},[1810,25296,25121],{},[1969,25298,2668],{},[1953,25300,25301,25303],{},[898,25302,10516],{},[898,25304,5571],{},[1677,25306,1776],{},[1810,25308,25134],{},[1677,25310,1967],{"separator":1966},[22150,25312,25313,25329],{},[22153,25314,25315],{},[2006,25316,25317],{"scriptlevel":2008,"displaystyle":1966},[895,25318,25319,25321,25323,25325,25327],{},[1677,25320,1686],{"stretchy":1685},[898,25322,13431],{},[1810,25324,1812],{},[1677,25326,1692],{"stretchy":1685},[1969,25328,1971],{},[22153,25330,25331],{},[2006,25332,25333],{"scriptlevel":2008,"displaystyle":1966},[895,25334,25335,25337,25343,25345,25347,25349,25351],{},[895,25336],{},[1953,25338,25339,25341],{},[898,25340,10516],{},[898,25342,5571],{},[1677,25344,1679],{},[898,25346,10516],{},[1677,25348,1906],{},[898,25350,2455],{},[1677,25352,1967],{"separator":1966},[22150,25354,25355,25371],{},[22153,25356,25357],{},[2006,25358,25359],{"scriptlevel":2008,"displaystyle":1966},[895,25360,25361,25363,25365,25367,25369],{},[1677,25362,1686],{"stretchy":1685},[898,25364,13431],{},[1810,25366,1854],{},[1677,25368,1692],{"stretchy":1685},[1969,25370,1971],{},[22153,25372,25373],{},[2006,25374,25375],{"scriptlevel":2008,"displaystyle":1966},[895,25376,25377,25379,25381,25383,25385,25387],{},[895,25378],{},[898,25380,2455],{},[1677,25382,1679],{},[1810,25384,25180],{},[898,25386,10516],{},[1677,25388,1967],{"separator":1966},[22150,25390,25391,25407],{},[22153,25392,25393],{},[2006,25394,25395],{"scriptlevel":2008,"displaystyle":1966},[895,25396,25397,25399,25401,25403,25405],{},[1677,25398,1686],{"stretchy":1685},[898,25400,13431],{},[1810,25402,2032],{},[1677,25404,1692],{"stretchy":1685},[1969,25406,1971],{},[22153,25408,25409],{},[2006,25410,25411],{"scriptlevel":2008,"displaystyle":1966},[895,25412,25413,25415,25417,25419,25421,25423,25429],{},[895,25414],{},[898,25416,2499],{},[1677,25418,1679],{},[1810,25420,25153],{},[1969,25422,2668],{},[1953,25424,25425,25427],{},[898,25426,10516],{},[898,25428,5571],{},[1677,25430,1967],{"separator":1966},[22150,25432,25433,25449],{},[22153,25434,25435],{},[2006,25436,25437],{"scriptlevel":2008,"displaystyle":1966},[895,25438,25439,25441,25443,25445,25447],{},[1677,25440,1686],{"stretchy":1685},[898,25442,13431],{},[1810,25444,1909],{},[1677,25446,1692],{"stretchy":1685},[1969,25448,1971],{},[22153,25450,25451],{},[2006,25452,25453],{"scriptlevel":2008,"displaystyle":1966},[895,25454,25455,25457,25459,25461,25463,25465,25467,25469,25471,25473,25475,25477,25479],{},[895,25456],{},[898,25458,10516],{},[1677,25460,1679],{},[898,25462,2458],{},[1677,25464,1776],{},[1810,25466,16500],{},[1677,25468,1776],{},[1810,25470,10191],{},[1677,25472,1776],{},[1810,25474,25249],{},[1677,25476,1906],{},[898,25478,2499],{},[898,25480,1656],{"mathvariant":2057},[902,25482,25483],{"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}",[724,25485,25486,25487,25521],{},"Postupná substituce — z (r3) do (r2): ",[883,25488,25490],{"className":25489},[886],[888,25491,25492],{"xmlns":890},[892,25493,25494,25518],{},[895,25495,25496,25502,25504,25506,25508,25510,25512,25514,25516],{},[1953,25497,25498,25500],{},[898,25499,10516],{},[898,25501,5571],{},[1677,25503,1679],{},[898,25505,10516],{},[1677,25507,1906],{},[1810,25509,25180],{},[898,25511,10516],{},[1677,25513,1679],{},[1810,25515,25121],{},[898,25517,10516],{},[902,25519,25520],{"encoding":904},"Y_D = Y - 0{,}25Y = 0{,}75Y",". Dosazením do (r1) a (r4):",[724,25523,25524],{},[883,25525,25527],{"className":25526},[886],[888,25528,25529],{"xmlns":890},[892,25530,25531,25572],{},[895,25532,25533,25535,25537,25539,25541,25543,25545,25547,25549,25551,25553,25555,25557,25559,25561,25564,25566,25568,25570],{},[1677,25534,1686],{"stretchy":1685},[898,25536,13431],{},[1810,25538,1916],{},[1677,25540,1692],{"stretchy":1685},[1969,25542,1971],{},[898,25544,2458],{},[1677,25546,1679],{},[1810,25548,25121],{},[1677,25550,2858],{},[1810,25552,25121],{},[898,25554,10516],{},[1677,25556,1776],{},[1810,25558,25134],{},[1677,25560,1679],{},[1810,25562,25563],{},"0,5625",[898,25565,10516],{},[1677,25567,1776],{},[1810,25569,25134],{},[1677,25571,1967],{"separator":1966},[902,25573,25574],{"encoding":904},"(r6)\\ C = 0{,}75 \\cdot 0{,}75Y + 750 = 0{,}5625Y + 750,",[724,25576,25577],{},[883,25578,25580],{"className":25579},[886],[888,25581,25582],{"xmlns":890},[892,25583,25584,25618],{},[895,25585,25586,25588,25590,25593,25595,25597,25599,25601,25603,25605,25607,25609,25611,25614,25616],{},[1677,25587,1686],{"stretchy":1685},[898,25589,13431],{},[1810,25591,25592],{},"7",[1677,25594,1692],{"stretchy":1685},[1969,25596,1971],{},[898,25598,2499],{},[1677,25600,1679],{},[1810,25602,25153],{},[1677,25604,2858],{},[1810,25606,25121],{},[898,25608,10516],{},[1677,25610,1679],{},[1810,25612,25613],{},"0,1125",[898,25615,10516],{},[898,25617,1656],{"mathvariant":2057},[902,25619,25620],{"encoding":904},"(r7)\\ M = 0{,}15 \\cdot 0{,}75Y = 0{,}1125Y.",[724,25622,25623],{},"Dosazením do (r5):",[724,25625,25626],{},[883,25627,25629],{"className":25628},[886],[888,25630,25631],{"xmlns":890},[892,25632,25633,25677],{},[895,25634,25635,25637,25639,25641,25643,25645,25647,25649,25651,25653,25655,25657,25659,25661,25663,25665,25667,25670,25672,25674],{},[898,25636,10516],{},[1677,25638,1679],{},[1810,25640,25563],{},[898,25642,10516],{},[1677,25644,1776],{},[1810,25646,25134],{},[1677,25648,1776],{},[1810,25650,16500],{},[1677,25652,1776],{},[1810,25654,10191],{},[1677,25656,1776],{},[1810,25658,25249],{},[1677,25660,1906],{},[1810,25662,25613],{},[898,25664,10516],{},[1677,25666,1679],{},[1810,25668,25669],{},"0,45",[898,25671,10516],{},[1677,25673,1776],{},[1810,25675,25676],{},"2200.",[902,25678,25679],{"encoding":904},"Y = 0{,}5625Y + 750 + 500 + 150 + 800 - 0{,}1125Y = 0{,}45Y + 2200.",[724,25681,25682,25683,6977,25705,25728],{},"Odtud ",[883,25684,25686],{"className":25685},[886],[888,25687,25688],{"xmlns":890},[892,25689,25690,25702],{},[895,25691,25692,25695,25697,25699],{},[1810,25693,25694],{},"0,55",[898,25696,10516],{},[1677,25698,1679],{},[1810,25700,25701],{},"2200",[902,25703,25704],{"encoding":904},"0{,}55Y = 2200",[883,25706,25708],{"className":25707},[886],[888,25709,25710],{"xmlns":890},[892,25711,25712,25725],{},[895,25713,25714,25720,25722],{},[1805,25715,25716,25718],{},[898,25717,10516],{},[898,25719,5640],{},[1677,25721,1679],{},[1810,25723,25724],{},"4000",[902,25726,25727],{"encoding":904},"Y^E = 4000",". Rovnovážné veličiny:",[120,25730,25731,25754,25786,25821,25854,25890],{},[123,25732,25733,1967],{},[883,25734,25736],{"className":25735},[886],[888,25737,25738],{"xmlns":890},[892,25739,25740,25752],{},[895,25741,25742,25748,25750],{},[1805,25743,25744,25746],{},[898,25745,10516],{},[898,25747,5640],{},[1677,25749,1679],{},[1810,25751,25724],{},[902,25753,25727],{"encoding":904},[123,25755,25756,1967],{},[883,25757,25759],{"className":25758},[886],[888,25760,25761],{"xmlns":890},[892,25762,25763,25783],{},[895,25764,25765,25771,25773,25775,25777,25779,25781],{},[1805,25766,25767,25769],{},[898,25768,2455],{},[898,25770,5640],{},[1677,25772,1679],{},[1810,25774,25180],{},[1677,25776,2858],{},[1810,25778,25724],{},[1677,25780,1679],{},[1810,25782,2463],{},[902,25784,25785],{"encoding":904},"T^E = 0{,}25 \\cdot 4000 = 1000",[123,25787,25788,1967],{},[883,25789,25791],{"className":25790},[886],[888,25792,25793],{"xmlns":890},[892,25794,25795,25818],{},[895,25796,25797,25805,25807,25809,25811,25813,25815],{},[10554,25798,25799,25801,25803],{},[898,25800,10516],{},[898,25802,5571],{},[898,25804,5640],{},[1677,25806,1679],{},[1810,25808,25121],{},[1677,25810,2858],{},[1810,25812,25724],{},[1677,25814,1679],{},[1810,25816,25817],{},"3000",[902,25819,25820],{"encoding":904},"Y_D^E = 0{,}75 \\cdot 4000 = 3000",[123,25822,25823,1967],{},[883,25824,25826],{"className":25825},[886],[888,25827,25828],{"xmlns":890},[892,25829,25830,25851],{},[895,25831,25832,25838,25840,25842,25844,25846,25848],{},[1805,25833,25834,25836],{},[898,25835,2499],{},[898,25837,5640],{},[1677,25839,1679],{},[1810,25841,25153],{},[1677,25843,2858],{},[1810,25845,25817],{},[1677,25847,1679],{},[1810,25849,25850],{},"450",[902,25852,25853],{"encoding":904},"M^E = 0{,}15 \\cdot 3000 = 450",[123,25855,25856,1967],{},[883,25857,25859],{"className":25858},[886],[888,25860,25861],{"xmlns":890},[892,25862,25863,25887],{},[895,25864,25865,25871,25873,25875,25877,25879,25881,25883,25885],{},[1805,25866,25867,25869],{},[898,25868,2458],{},[898,25870,5640],{},[1677,25872,1679],{},[1810,25874,25121],{},[1677,25876,2858],{},[1810,25878,25817],{},[1677,25880,1776],{},[1810,25882,25134],{},[1677,25884,1679],{},[1810,25886,25817],{},[902,25888,25889],{"encoding":904},"C^E = 0{,}75 \\cdot 3000 + 750 = 3000",[123,25891,25892,25932],{},[883,25893,25895],{"className":25894},[886],[888,25896,25897],{"xmlns":890},[892,25898,25899,25929],{},[895,25900,25901,25907,25909,25917,25919,25925,25927],{},[1805,25902,25903,25905],{},[898,25904,10061],{},[898,25906,5640],{},[1677,25908,1679],{},[10554,25910,25911,25913,25915],{},[898,25912,10516],{},[898,25914,5571],{},[898,25916,5640],{},[1677,25918,1906],{},[1805,25920,25921,25923],{},[898,25922,2458],{},[898,25924,5640],{},[1677,25926,1679],{},[1810,25928,2008],{},[902,25930,25931],{"encoding":904},"S^E = Y_D^E - C^E = 0"," (při této kalibraci domácnosti celý disponibilní důchod spotřebují).",[724,25934,25935,25937,25938,1343,25955,5272,25976,26001,26002,26005,26006,26019,26020,1656],{},[38,25936,22740],{}," Modely ",[883,25939,25941],{"className":25940},[886],[888,25942,25943],{"xmlns":890},[892,25944,25945,25953],{},[895,25946,25947,25949,25951],{},[898,25948,2458],{},[1969,25950,13680],{},[898,25952,13574],{},[902,25954,13685],{"encoding":904},[883,25956,25958],{"className":25957},[886],[888,25959,25960],{"xmlns":890},[892,25961,25962,25974],{},[895,25963,25964,25966,25968,25970,25972],{},[898,25965,2458],{},[1969,25967,13680],{},[898,25969,13574],{},[1969,25971,13680],{},[898,25973,13502],{},[902,25975,19611],{"encoding":904},[883,25977,25979],{"className":25978},[886],[888,25980,25981],{"xmlns":890},[892,25982,25983,25999],{},[895,25984,25985,25987,25989,25991,25993,25995,25997],{},[898,25986,2458],{},[1969,25988,13680],{},[898,25990,13574],{},[1969,25992,13680],{},[898,25994,13502],{},[1969,25996,13680],{},[898,25998,13710],{},[902,26000,13713],{"encoding":904}," pokládají investice za ",[38,26003,26004],{},"konstantní",". To není realistické — investice závisejí na úrokové míře ",[883,26007,26009],{"className":26008},[886],[888,26010,26011],{"xmlns":890},[892,26012,26013,26017],{},[895,26014,26015],{},[898,26016,13431],{},[902,26018,13431],{"encoding":904},". Přidáním trhu peněz a úrokové míry vzniká ",[38,26021,26022],{},"model IS-LM",[115,26024,26026],{"id":26025},"_74-multiplikátory-pro-makroekonomické-proměnné","7.4 Multiplikátory pro makroekonomické proměnné",[724,26028,26029,26030,26034,26035,26038,26039,26042],{},"V článku ",[207,26031,26033],{"className":26032,"dataFsResolvedFilePath":827,"href":828},[210],"2.4"," (mikroekonomie) byly zavedeny multiplikátory pro mikroekonomické proměnné. ",[38,26036,26037],{},"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 ",[38,26040,26041],{},"výraznější"," než v mikroekonomických modelech.",[724,26044,26045],{},[2240,26046],{"alt":26047,"className":26048,"src":26049},"imek-multiplikatorovy-efekt-chain",[210,2244],"\u002Fwiki-assets\u002Fimek-multiplikatorovy-efekt-chain.jpeg",[724,26051,13554,26052,1343,26069,1343,26090,26115,26116,26119,26120,26138,26139,26157,26158,26176,26177,26180,26181,1343,26198,26215,26216,26218],{},[883,26053,26055],{"className":26054},[886],[888,26056,26057],{"xmlns":890},[892,26058,26059,26067],{},[895,26060,26061,26063,26065],{},[898,26062,2458],{},[1969,26064,13680],{},[898,26066,13574],{},[902,26068,13685],{"encoding":904},[883,26070,26072],{"className":26071},[886],[888,26073,26074],{"xmlns":890},[892,26075,26076,26088],{},[895,26077,26078,26080,26082,26084,26086],{},[898,26079,2458],{},[1969,26081,13680],{},[898,26083,13574],{},[1969,26085,13680],{},[898,26087,13502],{},[902,26089,19611],{"encoding":904},[883,26091,26093],{"className":26092},[886],[888,26094,26095],{"xmlns":890},[892,26096,26097,26113],{},[895,26098,26099,26101,26103,26105,26107,26109,26111],{},[898,26100,2458],{},[1969,26102,13680],{},[898,26104,13574],{},[1969,26106,13680],{},[898,26108,13502],{},[1969,26110,13680],{},[898,26112,13710],{},[902,26114,13713],{"encoding":904}," se vyšetřuje vliv změn ",[38,26117,26118],{},"exogenních"," veličin (plánovaných investic ",[883,26121,26123],{"className":26122},[886],[888,26124,26125],{"xmlns":890},[892,26126,26127,26135],{},[895,26128,26129],{},[1805,26130,26131,26133],{},[898,26132,13574],{},[1677,26134,5742],{},[902,26136,26137],{"encoding":904},"I^*",", vládních výdajů ",[883,26140,26142],{"className":26141},[886],[888,26143,26144],{"xmlns":890},[892,26145,26146,26154],{},[895,26147,26148],{},[1805,26149,26150,26152],{},[898,26151,13502],{},[1677,26153,5742],{},[902,26155,26156],{"encoding":904},"G^*",", exportu ",[883,26159,26161],{"className":26160},[886],[888,26162,26163],{"xmlns":890},[892,26164,26165,26173],{},[895,26166,26167],{},[1805,26168,26169,26171],{},[898,26170,24644],{},[1677,26172,5742],{},[902,26174,26175],{"encoding":904},"B^*",") na změny ",[38,26178,26179],{},"endogenních"," rovnovážných veličin (",[883,26182,26184],{"className":26183},[886],[888,26185,26186],{"xmlns":890},[892,26187,26188,26196],{},[895,26189,26190],{},[1805,26191,26192,26194],{},[898,26193,10516],{},[898,26195,5640],{},[902,26197,15293],{"encoding":904},[883,26199,26201],{"className":26200},[886],[888,26202,26203],{"xmlns":890},[892,26204,26205,26213],{},[895,26206,26207],{},[1805,26208,26209,26211],{},[898,26210,2458],{},[898,26212,5640],{},[902,26214,15352],{"encoding":904}," atd.). Tyto citlivosti se vyjadřují ",[38,26217,19368],{}," — parciálními derivacemi rovnovážných veličin podle exogenních veličin.",[198,26220,26222],{"id":26221},"multiplikátory-v-modelu-c-i","Multiplikátory v modelu C-I",[724,26224,22286,26225,26248,26249,26293],{},[883,26226,26228],{"className":26227},[886],[888,26229,26230],{"xmlns":890},[892,26231,26232,26246],{},[895,26233,26234,26236,26238,26240,26242,26244],{},[898,26235,2458],{},[1677,26237,1679],{},[898,26239,207],{},[898,26241,10516],{},[1677,26243,1776],{},[898,26245,1779],{},[902,26247,20311],{"encoding":904}," dává (7.7) redukovaný tvar ",[883,26250,26252],{"className":26251},[886],[888,26253,26254],{"xmlns":890},[892,26255,26256,26290],{},[895,26257,26258,26264,26266],{},[1805,26259,26260,26262],{},[898,26261,10516],{},[898,26263,5640],{},[1677,26265,1679],{},[2006,26267,26268],{"scriptlevel":2008,"displaystyle":1966},[2010,26269,26270,26282],{},[895,26271,26272,26274,26276],{},[898,26273,1779],{},[1677,26275,1776],{},[1805,26277,26278,26280],{},[898,26279,13574],{},[1677,26281,5742],{},[895,26283,26284,26286,26288],{},[1810,26285,1959],{},[1677,26287,1906],{},[898,26289,207],{},[902,26291,26292],{"encoding":904},"Y^E = \\dfrac{b + I^*}{1 - a}",". Parciální derivace:",[724,26295,26296],{},[883,26297,26299],{"className":26298},[886],[888,26300,26301],{"xmlns":890},[892,26302,26303,26372],{},[895,26304,26305,26323,26325,26355,26357],{},[2010,26306,26307,26317],{},[895,26308,26309,26311],{},[898,26310,11260],{"mathvariant":2057},[1805,26312,26313,26315],{},[898,26314,10516],{},[898,26316,5640],{},[895,26318,26319,26321],{},[898,26320,11260],{"mathvariant":2057},[898,26322,207],{},[1677,26324,1679],{},[2010,26326,26327,26339],{},[895,26328,26329,26331,26333],{},[898,26330,1779],{},[1677,26332,1776],{},[1805,26334,26335,26337],{},[898,26336,13574],{},[1677,26338,5742],{},[895,26340,26341,26343,26345,26347,26349],{},[1677,26342,1686],{"stretchy":1685},[1810,26344,1959],{},[1677,26346,1906],{},[898,26348,207],{},[1805,26350,26351,26353],{},[1677,26352,1692],{"stretchy":1685},[1810,26354,1812],{},[7266,26356],{"width":7268},[895,26358,26359,26362,26369],{},[1969,26360,26361],{},"(multiplik",[9774,26363,26364,26366],{"accent":1966},[1969,26365,207],{},[1677,26367,26368],{},"ˊ",[1969,26370,26371],{},"tor MPC)",[902,26373,26374],{"encoding":904},"\\frac{\\partial Y^E}{\\partial a} = \\frac{b + I^*}{(1 - a)^2} \\qquad \\text{(multiplikátor MPC)}",[724,26376,26377],{},[883,26378,26380],{"className":26379},[886],[888,26381,26382],{"xmlns":890},[892,26383,26384,26453],{},[895,26385,26386,26404,26406,26418,26420],{},[2010,26387,26388,26398],{},[895,26389,26390,26392],{},[898,26391,11260],{"mathvariant":2057},[1805,26393,26394,26396],{},[898,26395,10516],{},[898,26397,5640],{},[895,26399,26400,26402],{},[898,26401,11260],{"mathvariant":2057},[898,26403,1779],{},[1677,26405,1679],{},[2010,26407,26408,26410],{},[1810,26409,1959],{},[895,26411,26412,26414,26416],{},[1810,26413,1959],{},[1677,26415,1906],{},[898,26417,207],{},[7266,26419],{"width":7268},[895,26421,26422,26424,26430,26433,26440,26443,26450],{},[1969,26423,26361],{},[9774,26425,26426,26428],{"accent":1966},[1969,26427,207],{},[1677,26429,26368],{},[1969,26431,26432],{},"tor autonomn",[9774,26434,26435,26438],{"accent":1966},[1969,26436,26437],{},"ı",[1677,26439,26368],{},[1969,26441,26442],{}," spot",[9774,26444,26445,26447],{"accent":1966},[1969,26446,13431],{},[1677,26448,26449],{},"ˇ",[1969,26451,26452],{},"eby)",[902,26454,26455],{"encoding":904},"\\frac{\\partial Y^E}{\\partial b} = \\frac{1}{1 - a} \\qquad \\text{(multiplikátor autonomní spotřeby)}",[724,26457,26458],{},[883,26459,26461],{"className":26460},[886],[888,26462,26463],{"xmlns":890},[892,26464,26465,26532],{},[895,26466,26467,26489,26491,26503,26505,26517,26519],{},[2010,26468,26469,26479],{},[895,26470,26471,26473],{},[898,26472,11260],{"mathvariant":2057},[1805,26474,26475,26477],{},[898,26476,10516],{},[898,26478,5640],{},[895,26480,26481,26483],{},[898,26482,11260],{"mathvariant":2057},[1805,26484,26485,26487],{},[898,26486,13574],{},[1677,26488,5742],{},[1677,26490,1679],{},[2010,26492,26493,26495],{},[1810,26494,1959],{},[895,26496,26497,26499,26501],{},[1810,26498,1959],{},[1677,26500,1906],{},[898,26502,207],{},[1677,26504,1679],{},[2010,26506,26507,26509],{},[1810,26508,1959],{},[895,26510,26511,26513,26515],{},[898,26512,2499],{},[898,26514,5325],{},[898,26516,10061],{},[7266,26518],{"width":7268},[895,26520,26521,26523,26529],{},[1969,26522,26361],{},[9774,26524,26525,26527],{"accent":1966},[1969,26526,207],{},[1677,26528,26368],{},[1969,26530,26531],{},"tor investic)",[902,26533,26534],{"encoding":904},"\\frac{\\partial Y^E}{\\partial I^*} = \\frac{1}{1 - a} = \\frac{1}{MPS} \\qquad \\text{(multiplikátor investic)}",[5254,26536,26537],{},[724,26538,26539,26541,26542,26545,26546,26559,26560,26577,26578,26596,26597,26641,26642,22811,26659,26662,26663,26680],{},[883,26540,5543],{}," Intuice — proč Keynesův multiplikátor funguje\nInvestice o 1 Kč se stanou něčím ",[38,26543,26544],{},"důchodem","; z něj se utratí ",[883,26547,26549],{"className":26548},[886],[888,26550,26551],{"xmlns":890},[892,26552,26553,26557],{},[895,26554,26555],{},[898,26556,207],{},[902,26558,207],{"encoding":904}," Kč (= ",[883,26561,26563],{"className":26562},[886],[888,26564,26565],{"xmlns":890},[892,26566,26567,26575],{},[895,26568,26569,26571,26573],{},[898,26570,2499],{},[898,26572,5325],{},[898,26574,2458],{},[902,26576,19436],{"encoding":904},"), to je zase něčí důchod, z něj ",[883,26579,26581],{"className":26580},[886],[888,26582,26583],{"xmlns":890},[892,26584,26585,26593],{},[895,26586,26587],{},[1805,26588,26589,26591],{},[898,26590,207],{},[1810,26592,1812],{},[902,26594,26595],{"encoding":904},"a^2"," Kč… Součet geometrické řady ",[883,26598,26600],{"className":26599},[886],[888,26601,26602],{"xmlns":890},[892,26603,26604,26638],{},[895,26605,26606,26608,26610,26612,26614,26620,26622,26624,26626],{},[1810,26607,1959],{},[1677,26609,1776],{},[898,26611,207],{},[1677,26613,1776],{},[1805,26615,26616,26618],{},[898,26617,207],{},[1810,26619,1812],{},[1677,26621,1776],{},[1677,26623,19496],{},[1677,26625,1679],{},[2010,26627,26628,26630],{},[1810,26629,1959],{},[895,26631,26632,26634,26636],{},[1810,26633,1959],{},[1677,26635,1906],{},[898,26637,207],{},[902,26639,26640],{"encoding":904},"1 + a + a^2 + \\dots = \\frac{1}{1-a}",". Proto jedna koruna investic navíc zvedne ",[883,26643,26645],{"className":26644},[886],[888,26646,26647],{"xmlns":890},[892,26648,26649,26657],{},[895,26650,26651],{},[1805,26652,26653,26655],{},[898,26654,10516],{},[898,26656,5640],{},[902,26658,15293],{"encoding":904},[38,26660,26661],{},"více"," než korunu — čím vyšší ",[883,26664,26666],{"className":26665},[886],[888,26667,26668],{"xmlns":890},[892,26669,26670,26678],{},[895,26671,26672,26674,26676],{},[898,26673,2499],{},[898,26675,5325],{},[898,26677,2458],{},[902,26679,19436],{"encoding":904},", tím silnější multiplikační efekt.",[724,26682,26683,26686,26687,26713,26714,26717,26718,5272,26739,26764,26765,1656],{},[38,26684,26685],{},"Multiplikátor autonomní spotřeby se rovná multiplikátoru investic"," — oba činí ",[883,26688,26690],{"className":26689},[886],[888,26691,26692],{"xmlns":890},[892,26693,26694,26710],{},[895,26695,26696],{},[2006,26697,26698],{"scriptlevel":2008,"displaystyle":1685},[2010,26699,26700,26702],{},[1810,26701,1959],{},[895,26703,26704,26706,26708],{},[1810,26705,1959],{},[1677,26707,1906],{},[898,26709,207],{},[902,26711,26712],{"encoding":904},"\\tfrac{1}{1-a}",", což je standardní ",[38,26715,26716],{},"Keynesův multiplikátor",". Analogicky se v modelech ",[883,26719,26721],{"className":26720},[886],[888,26722,26723],{"xmlns":890},[892,26724,26725,26737],{},[895,26726,26727,26729,26731,26733,26735],{},[898,26728,2458],{},[1969,26730,13680],{},[898,26732,13574],{},[1969,26734,13680],{},[898,26736,13502],{},[902,26738,19611],{"encoding":904},[883,26740,26742],{"className":26741},[886],[888,26743,26744],{"xmlns":890},[892,26745,26746,26762],{},[895,26747,26748,26750,26752,26754,26756,26758,26760],{},[898,26749,2458],{},[1969,26751,13680],{},[898,26753,13574],{},[1969,26755,13680],{},[898,26757,13502],{},[1969,26759,13680],{},[898,26761,13710],{},[902,26763,13713],{"encoding":904}," zavádějí multiplikátory vládních výdajů, zdanění a exportu. Paralela k mikroekonomickým multiplikátorům viz ",[207,26766,26768],{"className":26767,"dataFsResolvedFilePath":800,"href":801},[210],"poptávka a nabídka",[115,26770,26772],{"id":26771},"is-lm-analýza-stručný-přehled","IS-LM analýza (stručný přehled)",[724,26774,13554,26775,1343,26792,5272,26813,13559,26838,11413,26841,26862,26863,1884,26866,26879,26880,7057,26909,26926,26927,26930,26931,26933,26934,26955],{},[883,26776,26778],{"className":26777},[886],[888,26779,26780],{"xmlns":890},[892,26781,26782,26790],{},[895,26783,26784,26786,26788],{},[898,26785,2458],{},[1969,26787,13680],{},[898,26789,13574],{},[902,26791,13685],{"encoding":904},[883,26793,26795],{"className":26794},[886],[888,26796,26797],{"xmlns":890},[892,26798,26799,26811],{},[895,26800,26801,26803,26805,26807,26809],{},[898,26802,2458],{},[1969,26804,13680],{},[898,26806,13574],{},[1969,26808,13680],{},[898,26810,13502],{},[902,26812,19611],{"encoding":904},[883,26814,26816],{"className":26815},[886],[888,26817,26818],{"xmlns":890},[892,26819,26820,26836],{},[895,26821,26822,26824,26826,26828,26830,26832,26834],{},[898,26823,2458],{},[1969,26825,13680],{},[898,26827,13574],{},[1969,26829,13680],{},[898,26831,13502],{},[1969,26833,13680],{},[898,26835,13710],{},[902,26837,13713],{"encoding":904},[38,26839,26840],{},"investice konstantní",[883,26842,26844],{"className":26843},[886],[888,26845,26846],{"xmlns":890},[892,26847,26848,26860],{},[895,26849,26850,26852,26854],{},[898,26851,13574],{},[1677,26853,1679],{},[1805,26855,26856,26858],{},[898,26857,13574],{},[1677,26859,5742],{},[902,26861,13585],{"encoding":904},"). Reálnější je předpoklad, že ",[38,26864,26865],{},"investice závisejí na úrokové míře",[883,26867,26869],{"className":26868},[886],[888,26870,26871],{"xmlns":890},[892,26872,26873,26877],{},[895,26874,26875],{},[898,26876,13431],{},[902,26878,13431],{"encoding":904}," — klesající funkce ",[883,26881,26883],{"className":26882},[886],[888,26884,26885],{"xmlns":890},[892,26886,26887,26907],{},[895,26888,26889,26891,26893,26895,26897,26899,26901,26903,26905],{},[898,26890,13574],{},[1677,26892,1686],{"stretchy":1685},[898,26894,13431],{},[1677,26896,1692],{"stretchy":1685},[1677,26898,1679],{},[898,26900,1823],{},[898,26902,13431],{},[1677,26904,1776],{},[898,26906,1875],{},[902,26908,17147],{"encoding":904},[883,26910,26912],{"className":26911},[886],[888,26913,26914],{"xmlns":890},[892,26915,26916,26924],{},[895,26917,26918,26920,26922],{},[898,26919,1823],{},[1677,26921,3128],{},[1810,26923,2008],{},[902,26925,13905],{"encoding":904},". Přidáním ",[38,26928,26929],{},"trhu peněz"," k trhu zboží vzniká model ",[38,26932,13401],{}," se dvěma neznámými ",[883,26935,26937],{"className":26936},[886],[888,26938,26939],{"xmlns":890},[892,26940,26941,26953],{},[895,26942,26943,26945,26947,26949,26951],{},[1677,26944,1686],{"stretchy":1685},[898,26946,10516],{},[1677,26948,1967],{"separator":1966},[898,26950,13431],{},[1677,26952,1692],{"stretchy":1685},[902,26954,19541],{"encoding":904}," a dvěma rovnicemi:",[120,26957,26958,27008],{},[123,26959,26960,11413,26962,26964,26965,26986,26987,1656],{},[38,26961,17236],{},[614,26963,13444],{},") — klesající přímka v rovině ",[883,26966,26968],{"className":26967},[886],[888,26969,26970],{"xmlns":890},[892,26971,26972,26984],{},[895,26973,26974,26976,26978,26980,26982],{},[1677,26975,1686],{"stretchy":1685},[898,26977,13431],{},[1677,26979,1967],{"separator":1966},[898,26981,10516],{},[1677,26983,1692],{"stretchy":1685},[902,26985,14327],{"encoding":904},", odvozená z rovnováhy trhu zboží ",[883,26988,26990],{"className":26989},[886],[888,26991,26992],{"xmlns":890},[892,26993,26994,27006],{},[895,26995,26996,26998,27000,27002,27004],{},[898,26997,10516],{},[1677,26999,1679],{},[898,27001,2458],{},[1677,27003,1776],{},[898,27005,13574],{},[902,27007,16134],{"encoding":904},[123,27009,27010,11413,27012,27014,27015,22985,27040,27086],{},[38,27011,17435],{},[614,27013,13451],{},") — rostoucí přímka, odvozená z rovnováhy trhu peněz ",[883,27016,27018],{"className":27017},[886],[888,27019,27020],{"xmlns":890},[892,27021,27022,27038],{},[895,27023,27024,27030,27032],{},[1805,27025,27026,27028],{},[898,27027,2499],{},[898,27029,5571],{},[1677,27031,1679],{},[1805,27033,27034,27036],{},[898,27035,2499],{},[1677,27037,5742],{},[902,27039,14870],{"encoding":904},[883,27041,27043],{"className":27042},[886],[888,27044,27045],{"xmlns":890},[892,27046,27047,27083],{},[895,27048,27049,27055,27057,27063,27065,27067,27073,27075,27077],{},[1805,27050,27051,27053],{},[898,27052,2499],{},[898,27054,5571],{},[1677,27056,1679],{},[1953,27058,27059,27061],{},[898,27060,14627],{},[1810,27062,1959],{},[898,27064,10516],{},[1677,27066,1776],{},[1953,27068,27069,27071],{},[898,27070,14627],{},[1810,27072,1812],{},[898,27074,13431],{},[1677,27076,1776],{},[1953,27078,27079,27081],{},[898,27080,14627],{},[1810,27082,1854],{},[902,27084,27085],{"encoding":904},"M^D = k_1 Y + k_2 r + k_3"," (transakční, opatrnostní a spekulační poptávka).",[724,27088,27089,1884,27092,27125,27126,27128,27129,27131],{},[38,27090,27091],{},"Simultánní rovnovážný bod",[883,27093,27095],{"className":27094},[886],[888,27096,27097],{"xmlns":890},[892,27098,27099,27123],{},[895,27100,27101,27103,27105,27107,27113,27115,27121],{},[898,27102,5640],{},[1677,27104,1679],{},[1677,27106,1686],{"stretchy":1685},[1805,27108,27109,27111],{},[898,27110,13431],{},[898,27112,5640],{},[1677,27114,1967],{"separator":1966},[1805,27116,27117,27119],{},[898,27118,10516],{},[898,27120,5640],{},[1677,27122,1692],{"stretchy":1685},[902,27124,17527],{"encoding":904}," je průsečík křivek IS a LM; určuje současně rovnovážný důchod a rovnovážnou úrokovou míru. Model slouží jako rámec pro analýzu ",[38,27127,13489],{}," (posun IS) a ",[38,27130,13521],{}," (posun LM).",[724,27133,27134],{},[38,27135,27136,27137,1343,27159,1343,27181,1343,27203,27225,27226,1656],{},"Pro detailní odvození obou křivek, řešení Příkladu 7.6 (",[883,27138,27140],{"className":27139},[886],[888,27141,27142],{"xmlns":890},[892,27143,27144,27156],{},[895,27145,27146,27152,27154],{},[1805,27147,27148,27150],{},[898,27149,10516],{},[898,27151,5640],{},[1677,27153,1679],{},[1810,27155,16505],{},[902,27157,27158],{"encoding":904},"Y^E = 5000",[883,27160,27162],{"className":27161},[886],[888,27163,27164],{"xmlns":890},[892,27165,27166,27178],{},[895,27167,27168,27174,27176],{},[1805,27169,27170,27172],{},[898,27171,13431],{},[898,27173,5640],{},[1677,27175,1679],{},[1810,27177,1909],{},[902,27179,27180],{"encoding":904},"r^E = 5",[883,27182,27184],{"className":27183},[886],[888,27185,27186],{"xmlns":890},[892,27187,27188,27200],{},[895,27189,27190,27196,27198],{},[1805,27191,27192,27194],{},[898,27193,2458],{},[898,27195,5640],{},[1677,27197,1679],{},[1810,27199,16542],{},[902,27201,27202],{"encoding":904},"C^E = 4100",[883,27204,27206],{"className":27205},[886],[888,27207,27208],{"xmlns":890},[892,27209,27210,27222],{},[895,27211,27212,27218,27220],{},[1805,27213,27214,27216],{},[898,27215,13574],{},[898,27217,5640],{},[1677,27219,1679],{},[1810,27221,16581],{},[902,27223,27224],{"encoding":904},"I^E = 900",") a ekonomickou interpretaci posunů viz ",[207,27227,945],{"className":27228,"dataFsResolvedFilePath":943,"href":944},[210],[115,27230,27232],{"id":27231},"shrnutí-kapitoly-7","Shrnutí kapitoly 7",[152,27234,27235,27299,27410,27553,27795,27863],{},[123,27236,27237,27240,27241,27263,27264,27298],{},[38,27238,27239],{},"Zjednodušený makroekonomický model"," ztotožňuje ",[883,27242,27244],{"className":27243},[886],[888,27245,27246],{"xmlns":890},[892,27247,27248,27260],{},[895,27249,27250,27252,27254,27256,27258],{},[898,27251,13502],{},[898,27253,19685],{},[898,27255,5325],{},[1677,27257,2411],{},[898,27259,10516],{},[902,27261,27262],{"encoding":904},"GNP \\approx Y"," (národní důchod). Základ: ",[883,27265,27267],{"className":27266},[886],[888,27268,27269],{"xmlns":890},[892,27270,27271,27295],{},[895,27272,27273,27275,27277,27279,27281,27283,27285,27287,27289,27291,27293],{},[898,27274,13502],{},[898,27276,19685],{},[898,27278,5325],{},[1677,27280,1679],{},[898,27282,2458],{},[1677,27284,1776],{},[898,27286,13574],{},[1677,27288,1776],{},[898,27290,13502],{},[1677,27292,1776],{},[898,27294,13710],{},[902,27296,27297],{"encoding":904},"GNP = C + I + G + X"," (7.1).",[123,27300,27301,27303,27304,27325,27326,1343,27349,27380,27381,27394,27395,1656],{},[38,27302,19919],{}," splňují ",[883,27305,27307],{"className":27306},[886],[888,27308,27309],{"xmlns":890},[892,27310,27311,27323],{},[895,27312,27313,27315,27317,27319,27321],{},[898,27314,10516],{},[1677,27316,1679],{},[898,27318,2458],{},[1677,27320,1776],{},[898,27322,10061],{},[902,27324,14084],{"encoding":904}," (7.2); lineární model ",[883,27327,27329],{"className":27328},[886],[888,27330,27331],{"xmlns":890},[892,27332,27333,27347],{},[895,27334,27335,27337,27339,27341,27343,27345],{},[898,27336,2458],{},[1677,27338,1679],{},[898,27340,207],{},[898,27342,10516],{},[1677,27344,1776],{},[898,27346,1779],{},[902,27348,20311],{"encoding":904},[883,27350,27352],{"className":27351},[886],[888,27353,27354],{"xmlns":890},[892,27355,27356,27378],{},[895,27357,27358,27360,27362,27364,27366,27368,27370,27372,27374,27376],{},[898,27359,10061],{},[1677,27361,1679],{},[1677,27363,1686],{"stretchy":1685},[1810,27365,1959],{},[1677,27367,1906],{},[898,27369,207],{},[1677,27371,1692],{"stretchy":1685},[898,27373,10516],{},[1677,27375,1906],{},[898,27377,1779],{},[902,27379,20560],{"encoding":904}," s autonomní spotřebou ",[883,27382,27384],{"className":27383},[886],[888,27385,27386],{"xmlns":890},[892,27387,27388,27392],{},[895,27389,27390],{},[898,27391,1779],{},[902,27393,1779],{"encoding":904}," a autonomními úsporami ",[883,27396,27398],{"className":27397},[886],[888,27399,27400],{"xmlns":890},[892,27401,27402,27408],{},[895,27403,27404,27406],{},[1677,27405,1906],{},[898,27407,1779],{},[902,27409,20639],{"encoding":904},[123,27411,27412,1884,27415,1343,27445,27475,27476,27506,27507,1343,27528,1656],{},[38,27413,27414],{},"Mezní sklony",[883,27416,27418],{"className":27417},[886],[888,27419,27420],{"xmlns":890},[892,27421,27422,27442],{},[895,27423,27424,27426,27428,27430,27432,27434,27436,27438,27440],{},[898,27425,2499],{},[898,27427,5325],{},[898,27429,2458],{},[1677,27431,1679],{},[898,27433,1875],{"mathvariant":2057},[898,27435,2458],{},[898,27437,6062],{"mathvariant":2057},[898,27439,1875],{"mathvariant":2057},[898,27441,10516],{},[902,27443,27444],{"encoding":904},"MPC = \\mathrm{d}C\u002F\\mathrm{d}Y",[883,27446,27448],{"className":27447},[886],[888,27449,27450],{"xmlns":890},[892,27451,27452,27472],{},[895,27453,27454,27456,27458,27460,27462,27464,27466,27468,27470],{},[898,27455,2499],{},[898,27457,5325],{},[898,27459,10061],{},[1677,27461,1679],{},[898,27463,1875],{"mathvariant":2057},[898,27465,10061],{},[898,27467,6062],{"mathvariant":2057},[898,27469,1875],{"mathvariant":2057},[898,27471,10516],{},[902,27473,27474],{"encoding":904},"MPS = \\mathrm{d}S\u002F\\mathrm{d}Y",", vazba ",[883,27477,27479],{"className":27478},[886],[888,27480,27481],{"xmlns":890},[892,27482,27483,27503],{},[895,27484,27485,27487,27489,27491,27493,27495,27497,27499,27501],{},[898,27486,2499],{},[898,27488,5325],{},[898,27490,2458],{},[1677,27492,1776],{},[898,27494,2499],{},[898,27496,5325],{},[898,27498,10061],{},[1677,27500,1679],{},[1810,27502,1959],{},[902,27504,27505],{"encoding":904},"MPC + MPS = 1"," (7.5). V lineárním modelu ",[883,27508,27510],{"className":27509},[886],[888,27511,27512],{"xmlns":890},[892,27513,27514,27526],{},[895,27515,27516,27518,27520,27522,27524],{},[898,27517,2499],{},[898,27519,5325],{},[898,27521,2458],{},[1677,27523,1679],{},[898,27525,207],{},[902,27527,21280],{"encoding":904},[883,27529,27531],{"className":27530},[886],[888,27532,27533],{"xmlns":890},[892,27534,27535,27551],{},[895,27536,27537,27539,27541,27543,27545,27547,27549],{},[898,27538,2499],{},[898,27540,5325],{},[898,27542,10061],{},[1677,27544,1679],{},[1810,27546,1959],{},[1677,27548,1906],{},[898,27550,207],{},[902,27552,21306],{"encoding":904},[123,27554,27555,27558,27559],{},[38,27556,27557],{},"Modely národní ekonomiky"," postupně bohatnou:\n",[120,27560,27561,27649,27718],{},[123,27562,27563,27580,27581,27602,27603,1967],{},[883,27564,27566],{"className":27565},[886],[888,27567,27568],{"xmlns":890},[892,27569,27570,27578],{},[895,27571,27572,27574,27576],{},[898,27573,2458],{},[1969,27575,13680],{},[898,27577,13574],{},[902,27579,13685],{"encoding":904},": ",[883,27582,27584],{"className":27583},[886],[888,27585,27586],{"xmlns":890},[892,27587,27588,27600],{},[895,27589,27590,27592,27594,27596,27598],{},[898,27591,10516],{},[1677,27593,1679],{},[898,27595,2458],{},[1677,27597,1776],{},[898,27599,13574],{},[902,27601,16134],{"encoding":904}," (uzavřená ekonomika bez vlády), ",[883,27604,27606],{"className":27605},[886],[888,27607,27608],{"xmlns":890},[892,27609,27610,27646],{},[895,27611,27612,27618,27620,27622,27624,27626,27632,27634,27636,27638,27640,27642,27644],{},[1805,27613,27614,27616],{},[898,27615,10516],{},[898,27617,5640],{},[1677,27619,1679],{},[1677,27621,1686],{"stretchy":1685},[898,27623,1779],{},[1677,27625,1776],{},[1805,27627,27628,27630],{},[898,27629,13574],{},[1677,27631,5742],{},[1677,27633,1692],{"stretchy":1685},[898,27635,6062],{"mathvariant":2057},[1677,27637,1686],{"stretchy":1685},[1810,27639,1959],{},[1677,27641,1906],{},[898,27643,207],{},[1677,27645,1692],{"stretchy":1685},[902,27647,27648],{"encoding":904},"Y^E = (b + I^*)\u002F(1-a)",[123,27650,27651,27672,27673,27692,27693,1967],{},[883,27652,27654],{"className":27653},[886],[888,27655,27656],{"xmlns":890},[892,27657,27658,27670],{},[895,27659,27660,27662,27664,27666,27668],{},[898,27661,2458],{},[1969,27663,13680],{},[898,27665,13574],{},[1969,27667,13680],{},[898,27669,13502],{},[902,27671,19611],{"encoding":904},": přidává vládu, zdanění ",[883,27674,27676],{"className":27675},[886],[888,27677,27678],{"xmlns":890},[892,27679,27680,27690],{},[895,27681,27682,27684,27686,27688],{},[898,27683,2455],{},[1677,27685,1686],{"stretchy":1685},[898,27687,10516],{},[1677,27689,1692],{"stretchy":1685},[902,27691,23610],{"encoding":904}," a disponibilní důchod ",[883,27694,27696],{"className":27695},[886],[888,27697,27698],{"xmlns":890},[892,27699,27700,27716],{},[895,27701,27702,27708,27710,27712,27714],{},[1953,27703,27704,27706],{},[898,27705,10516],{},[898,27707,5571],{},[1677,27709,1679],{},[898,27711,10516],{},[1677,27713,1906],{},[898,27715,2455],{},[902,27717,23109],{"encoding":904},[123,27719,27720,27745,27746,22985,27767,1656],{},[883,27721,27723],{"className":27722},[886],[888,27724,27725],{"xmlns":890},[892,27726,27727,27743],{},[895,27728,27729,27731,27733,27735,27737,27739,27741],{},[898,27730,2458],{},[1969,27732,13680],{},[898,27734,13574],{},[1969,27736,13680],{},[898,27738,13502],{},[1969,27740,13680],{},[898,27742,13710],{},[902,27744,13713],{"encoding":904},": otevírá ekonomiku čistým exportem ",[883,27747,27749],{"className":27748},[886],[888,27750,27751],{"xmlns":890},[892,27752,27753,27765],{},[895,27754,27755,27757,27759,27761,27763],{},[898,27756,13710],{},[1677,27758,1679],{},[898,27760,24644],{},[1677,27762,1906],{},[898,27764,2499],{},[902,27766,24651],{"encoding":904},[883,27768,27770],{"className":27769},[886],[888,27771,27772],{"xmlns":890},[892,27773,27774,27792],{},[895,27775,27776,27778,27780,27782,27784,27790],{},[898,27777,2499],{},[1677,27779,1679],{},[898,27781,2499],{},[1677,27783,1686],{"stretchy":1685},[1953,27785,27786,27788],{},[898,27787,10516],{},[898,27789,5571],{},[1677,27791,1692],{"stretchy":1685},[902,27793,27794],{"encoding":904},"M = M(Y_D)",[123,27796,27797,27800,27801,1884,27804,27862],{},[38,27798,27799],{},"Multiplikátory"," (parciální derivace rovnovážných veličin podle exogenních) — klíčový ",[38,27802,27803],{},"multiplikátor investic",[883,27805,27807],{"className":27806},[886],[888,27808,27809],{"xmlns":890},[892,27810,27811,27859],{},[895,27812,27813,27815,27821,27823,27825,27831,27833,27835,27837,27839,27841,27843,27845,27847,27849,27851,27853,27855,27857],{},[898,27814,11260],{"mathvariant":2057},[1805,27816,27817,27819],{},[898,27818,10516],{},[898,27820,5640],{},[898,27822,6062],{"mathvariant":2057},[898,27824,11260],{"mathvariant":2057},[1805,27826,27827,27829],{},[898,27828,13574],{},[1677,27830,5742],{},[1677,27832,1679],{},[1810,27834,1959],{},[898,27836,6062],{"mathvariant":2057},[1677,27838,1686],{"stretchy":1685},[1810,27840,1959],{},[1677,27842,1906],{},[898,27844,207],{},[1677,27846,1692],{"stretchy":1685},[1677,27848,1679],{},[1810,27850,1959],{},[898,27852,6062],{"mathvariant":2057},[898,27854,2499],{},[898,27856,5325],{},[898,27858,10061],{},[902,27860,27861],{"encoding":904},"\\partial Y^E\u002F\\partial I^* = 1\u002F(1-a) = 1\u002FMPS"," (Keynesův multiplikátor).",[123,27864,27865,27867,27868,27883,27884,20039,27901,27916,27917,27942,27943,1656],{},[38,27866,945],{}," doplňuje obraz o trh peněz: investice závisejí na úrokové míře, ",[883,27869,27871],{"className":27870},[886],[888,27872,27873],{"xmlns":890},[892,27874,27875,27881],{},[895,27876,27877,27879],{},[898,27878,13574],{},[898,27880,10061],{},[902,27882,13441],{"encoding":904}," popisuje rovnováhu trhu zboží (",[883,27885,27887],{"className":27886},[886],[888,27888,27889],{"xmlns":890},[892,27890,27891,27899],{},[895,27892,27893,27895,27897],{},[898,27894,13574],{},[1677,27896,1679],{},[898,27898,10061],{},[902,27900,14102],{"encoding":904},[883,27902,27904],{"className":27903},[886],[888,27905,27906],{"xmlns":890},[892,27907,27908,27914],{},[895,27909,27910,27912],{},[898,27911,11183],{},[898,27913,2499],{},[902,27915,13448],{"encoding":904}," rovnováhu trhu peněz (",[883,27918,27920],{"className":27919},[886],[888,27921,27922],{"xmlns":890},[892,27923,27924,27940],{},[895,27925,27926,27932,27934],{},[1805,27927,27928,27930],{},[898,27929,2499],{},[898,27931,5571],{},[1677,27933,1679],{},[1805,27935,27936,27938],{},[898,27937,2499],{},[1677,27939,5742],{},[902,27941,14870],{"encoding":904},"); průsečík dává ",[883,27944,27946],{"className":27945},[886],[888,27947,27948],{"xmlns":890},[892,27949,27950,27970],{},[895,27951,27952,27954,27960,27962,27968],{},[1677,27953,1686],{"stretchy":1685},[1805,27955,27956,27958],{},[898,27957,10516],{},[898,27959,5640],{},[1677,27961,1967],{"separator":1966},[1805,27963,27964,27966],{},[898,27965,13431],{},[898,27967,5640],{},[1677,27969,1692],{"stretchy":1685},[902,27971,13485],{"encoding":904},[115,27973,17110],{"id":17109},[120,27975,27976,28014,28054,28144,28226,28280,28336,28395,28430,28435,28507,28582,28668,28730,28798,28856,28909,28948],{},[123,27977,27978,8403,27981,27298],{},[38,27979,27980],{},"Hrubý národní produkt (GNP)",[883,27982,27984],{"className":27983},[886],[888,27985,27986],{"xmlns":890},[892,27987,27988,28012],{},[895,27989,27990,27992,27994,27996,27998,28000,28002,28004,28006,28008,28010],{},[898,27991,13502],{},[898,27993,19685],{},[898,27995,5325],{},[1677,27997,1679],{},[898,27999,2458],{},[1677,28001,1776],{},[898,28003,13574],{},[1677,28005,1776],{},[898,28007,13502],{},[1677,28009,1776],{},[898,28011,13710],{},[902,28013,27297],{"encoding":904},[123,28015,28016,28032,28033,1656],{},[38,28017,28018,28019],{},"Národní důchod ",[883,28020,28022],{"className":28021},[886],[888,28023,28024],{"xmlns":890},[892,28025,28026,28030],{},[895,28027,28028],{},[898,28029,10516],{},[902,28031,10516],{"encoding":904}," — součet důchodů domácností; v modelech ",[883,28034,28036],{"className":28035},[886],[888,28037,28038],{"xmlns":890},[892,28039,28040,28052],{},[895,28041,28042,28044,28046,28048,28050],{},[898,28043,13502],{},[898,28045,19685],{},[898,28047,5325],{},[1677,28049,2411],{},[898,28051,10516],{},[902,28053,27262],{"encoding":904},[123,28055,28056,28082,28083,1343,28106,1343,28127,1656],{},[38,28057,28058,28059],{},"Funkce spotřeby ",[883,28060,28062],{"className":28061},[886],[888,28063,28064],{"xmlns":890},[892,28065,28066,28080],{},[895,28067,28068,28070,28072,28074,28076,28078],{},[898,28069,2458],{},[1677,28071,1679],{},[898,28073,2458],{},[1677,28075,1686],{"stretchy":1685},[898,28077,10516],{},[1677,28079,1692],{"stretchy":1685},[902,28081,22131],{"encoding":904}," — lineární model ",[883,28084,28086],{"className":28085},[886],[888,28087,28088],{"xmlns":890},[892,28089,28090,28104],{},[895,28091,28092,28094,28096,28098,28100,28102],{},[898,28093,2458],{},[1677,28095,1679],{},[898,28097,207],{},[898,28099,10516],{},[1677,28101,1776],{},[898,28103,1779],{},[902,28105,20311],{"encoding":904},[883,28107,28109],{"className":28108},[886],[888,28110,28111],{"xmlns":890},[892,28112,28113,28125],{},[895,28114,28115,28117,28119,28121,28123],{},[1810,28116,2008],{},[1677,28118,3128],{},[898,28120,207],{},[1677,28122,3128],{},[1810,28124,1959],{},[902,28126,20227],{"encoding":904},[883,28128,28130],{"className":28129},[886],[888,28131,28132],{"xmlns":890},[892,28133,28134,28142],{},[895,28135,28136,28138,28140],{},[898,28137,1779],{},[1677,28139,3089],{},[1810,28141,2008],{},[902,28143,20205],{"encoding":904},[123,28145,28146,8403,28173,28194,28195,1656],{},[38,28147,28148,28149],{},"Funkce úspor ",[883,28150,28152],{"className":28151},[886],[888,28153,28154],{"xmlns":890},[892,28155,28156,28170],{},[895,28157,28158,28160,28162,28164,28166,28168],{},[898,28159,10061],{},[1677,28161,1679],{},[898,28163,10061],{},[1677,28165,1686],{"stretchy":1685},[898,28167,10516],{},[1677,28169,1692],{"stretchy":1685},[902,28171,28172],{"encoding":904},"S = S(Y)",[883,28174,28176],{"className":28175},[886],[888,28177,28178],{"xmlns":890},[892,28179,28180,28192],{},[895,28181,28182,28184,28186,28188,28190],{},[898,28183,10516],{},[1677,28185,1679],{},[898,28187,2458],{},[1677,28189,1776],{},[898,28191,10061],{},[902,28193,14084],{"encoding":904},"; lineární ",[883,28196,28198],{"className":28197},[886],[888,28199,28200],{"xmlns":890},[892,28201,28202,28224],{},[895,28203,28204,28206,28208,28210,28212,28214,28216,28218,28220,28222],{},[898,28205,10061],{},[1677,28207,1679],{},[1677,28209,1686],{"stretchy":1685},[1810,28211,1959],{},[1677,28213,1906],{},[898,28215,207],{},[1677,28217,1692],{"stretchy":1685},[898,28219,10516],{},[1677,28221,1906],{},[898,28223,1779],{},[902,28225,20560],{"encoding":904},[123,28227,28228,8403,28231,1343,28254,1656],{},[38,28229,28230],{},"Autonomní spotřeba\u002Fúspory",[883,28232,28234],{"className":28233},[886],[888,28235,28236],{"xmlns":890},[892,28237,28238,28252],{},[895,28239,28240,28242,28244,28246,28248,28250],{},[898,28241,2458],{},[1677,28243,1686],{"stretchy":1685},[1810,28245,2008],{},[1677,28247,1692],{"stretchy":1685},[1677,28249,1679],{},[898,28251,1779],{},[902,28253,20952],{"encoding":904},[883,28255,28257],{"className":28256},[886],[888,28258,28259],{"xmlns":890},[892,28260,28261,28277],{},[895,28262,28263,28265,28267,28269,28271,28273,28275],{},[898,28264,10061],{},[1677,28266,1686],{"stretchy":1685},[1810,28268,2008],{},[1677,28270,1692],{"stretchy":1685},[1677,28272,1679],{},[1677,28274,1906],{},[898,28276,1779],{},[902,28278,28279],{"encoding":904},"S(0) = -b",[123,28281,28282,28314,28315,5306],{},[38,28283,28284,28285],{},"Mezní sklon ke spotřebě ",[883,28286,28288],{"className":28287},[886],[888,28289,28290],{"xmlns":890},[892,28291,28292,28312],{},[895,28293,28294,28296,28298,28300,28302,28304,28306,28308,28310],{},[898,28295,2499],{},[898,28297,5325],{},[898,28299,2458],{},[1677,28301,1679],{},[898,28303,1875],{"mathvariant":2057},[898,28305,2458],{},[898,28307,6062],{"mathvariant":2057},[898,28309,1875],{"mathvariant":2057},[898,28311,10516],{},[902,28313,27444],{"encoding":904}," (v lineárním modelu ",[883,28316,28318],{"className":28317},[886],[888,28319,28320],{"xmlns":890},[892,28321,28322,28334],{},[895,28323,28324,28326,28328,28330,28332],{},[898,28325,2499],{},[898,28327,5325],{},[898,28329,2458],{},[1677,28331,1679],{},[898,28333,207],{},[902,28335,21280],{"encoding":904},[123,28337,28338,28314,28370,5306],{},[38,28339,28340,28341],{},"Mezní sklon k úsporám ",[883,28342,28344],{"className":28343},[886],[888,28345,28346],{"xmlns":890},[892,28347,28348,28368],{},[895,28349,28350,28352,28354,28356,28358,28360,28362,28364,28366],{},[898,28351,2499],{},[898,28353,5325],{},[898,28355,10061],{},[1677,28357,1679],{},[898,28359,1875],{"mathvariant":2057},[898,28361,10061],{},[898,28363,6062],{"mathvariant":2057},[898,28365,1875],{"mathvariant":2057},[898,28367,10516],{},[902,28369,27474],{"encoding":904},[883,28371,28373],{"className":28372},[886],[888,28374,28375],{"xmlns":890},[892,28376,28377,28393],{},[895,28378,28379,28381,28383,28385,28387,28389,28391],{},[898,28380,2499],{},[898,28382,5325],{},[898,28384,10061],{},[1677,28386,1679],{},[1810,28388,1959],{},[1677,28390,1906],{},[898,28392,207],{},[902,28394,21306],{"encoding":904},[123,28396,28397,1884,28400,28429],{},[38,28398,28399],{},"Vztah",[883,28401,28403],{"className":28402},[886],[888,28404,28405],{"xmlns":890},[892,28406,28407,28427],{},[895,28408,28409,28411,28413,28415,28417,28419,28421,28423,28425],{},[898,28410,2499],{},[898,28412,5325],{},[898,28414,2458],{},[1677,28416,1776],{},[898,28418,2499],{},[898,28420,5325],{},[898,28422,10061],{},[1677,28424,1679],{},[1810,28426,1959],{},[902,28428,27505],{"encoding":904}," (7.5).",[123,28431,28432,28434],{},[38,28433,21974],{}," — rovnováha agregátní poptávky a nabídky.",[123,28436,28437,28440,28441,17182,28462,1656],{},[38,28438,28439],{},"Model C-I"," — uzavřená ekonomika bez vlády; ",[883,28442,28444],{"className":28443},[886],[888,28445,28446],{"xmlns":890},[892,28447,28448,28460],{},[895,28449,28450,28452,28454,28456,28458],{},[898,28451,10516],{},[1677,28453,1679],{},[898,28455,2458],{},[1677,28457,1776],{},[898,28459,13574],{},[902,28461,16134],{"encoding":904},[883,28463,28465],{"className":28464},[886],[888,28466,28467],{"xmlns":890},[892,28468,28469,28505],{},[895,28470,28471,28477,28479,28481,28483,28485,28491,28493,28495,28497,28499,28501,28503],{},[1805,28472,28473,28475],{},[898,28474,10516],{},[898,28476,5640],{},[1677,28478,1679],{},[1677,28480,1686],{"stretchy":1685},[898,28482,1779],{},[1677,28484,1776],{},[1805,28486,28487,28489],{},[898,28488,13574],{},[1677,28490,5742],{},[1677,28492,1692],{"stretchy":1685},[898,28494,6062],{"mathvariant":2057},[1677,28496,1686],{"stretchy":1685},[1810,28498,1959],{},[1677,28500,1906],{},[898,28502,207],{},[1677,28504,1692],{"stretchy":1685},[902,28506,27648],{"encoding":904},[123,28508,28509,28512,28513,1343,28532,17182,28557,1656],{},[38,28510,28511],{},"Model C-I-G"," — ekonomika s vládou, zdaněním ",[883,28514,28516],{"className":28515},[886],[888,28517,28518],{"xmlns":890},[892,28519,28520,28530],{},[895,28521,28522,28524,28526,28528],{},[898,28523,2455],{},[1677,28525,1686],{"stretchy":1685},[898,28527,10516],{},[1677,28529,1692],{"stretchy":1685},[902,28531,23610],{"encoding":904},[883,28533,28535],{"className":28534},[886],[888,28536,28537],{"xmlns":890},[892,28538,28539,28555],{},[895,28540,28541,28547,28549,28551,28553],{},[1953,28542,28543,28545],{},[898,28544,10516],{},[898,28546,5571],{},[1677,28548,1679],{},[898,28550,10516],{},[1677,28552,1906],{},[898,28554,2455],{},[902,28556,23109],{"encoding":904},[883,28558,28560],{"className":28559},[886],[888,28561,28562],{"xmlns":890},[892,28563,28564,28580],{},[895,28565,28566,28568,28570,28572,28574,28576,28578],{},[898,28567,10516],{},[1677,28569,1679],{},[898,28571,2458],{},[1677,28573,1776],{},[898,28575,13574],{},[1677,28577,1776],{},[898,28579,13502],{},[902,28581,23080],{"encoding":904},[123,28583,28584,28587,28588,28609,28610,17182,28634,1656],{},[38,28585,28586],{},"Model C-I-G-X"," — otevřená ekonomika s čistým exportem ",[883,28589,28591],{"className":28590},[886],[888,28592,28593],{"xmlns":890},[892,28594,28595,28607],{},[895,28596,28597,28599,28601,28603,28605],{},[898,28598,13710],{},[1677,28600,1679],{},[898,28602,24644],{},[1677,28604,1906],{},[898,28606,2499],{},[902,28608,24651],{"encoding":904},", importem ",[883,28611,28613],{"className":28612},[886],[888,28614,28615],{"xmlns":890},[892,28616,28617,28631],{},[895,28618,28619,28621,28623,28629],{},[898,28620,2499],{},[1677,28622,1686],{"stretchy":1685},[1953,28624,28625,28627],{},[898,28626,10516],{},[898,28628,5571],{},[1677,28630,1692],{"stretchy":1685},[902,28632,28633],{"encoding":904},"M(Y_D)",[883,28635,28637],{"className":28636},[886],[888,28638,28639],{"xmlns":890},[892,28640,28641,28665],{},[895,28642,28643,28645,28647,28649,28651,28653,28655,28657,28659,28661,28663],{},[898,28644,10516],{},[1677,28646,1679],{},[898,28648,2458],{},[1677,28650,1776],{},[898,28652,13574],{},[1677,28654,1776],{},[898,28656,13502],{},[1677,28658,1776],{},[898,28660,24644],{},[1677,28662,1906],{},[898,28664,2499],{},[902,28666,28667],{"encoding":904},"Y = C + I + G + B - M",[123,28669,28670,8403,28673,27862],{},[38,28671,28672],{},"Multiplikátor investic",[883,28674,28676],{"className":28675},[886],[888,28677,28678],{"xmlns":890},[892,28679,28680,28728],{},[895,28681,28682,28684,28690,28692,28694,28700,28702,28704,28706,28708,28710,28712,28714,28716,28718,28720,28722,28724,28726],{},[898,28683,11260],{"mathvariant":2057},[1805,28685,28686,28688],{},[898,28687,10516],{},[898,28689,5640],{},[898,28691,6062],{"mathvariant":2057},[898,28693,11260],{"mathvariant":2057},[1805,28695,28696,28698],{},[898,28697,13574],{},[1677,28699,5742],{},[1677,28701,1679],{},[1810,28703,1959],{},[898,28705,6062],{"mathvariant":2057},[1677,28707,1686],{"stretchy":1685},[1810,28709,1959],{},[1677,28711,1906],{},[898,28713,207],{},[1677,28715,1692],{"stretchy":1685},[1677,28717,1679],{},[1810,28719,1959],{},[898,28721,6062],{"mathvariant":2057},[898,28723,2499],{},[898,28725,5325],{},[898,28727,10061],{},[902,28729,27861],{"encoding":904},[123,28731,28732,8403,28763,1343,28780,28797],{},[38,28733,17117,28734],{},[883,28735,28737],{"className":28736},[886],[888,28738,28739],{"xmlns":890},[892,28740,28741,28761],{},[895,28742,28743,28745,28747,28749,28751,28753,28755,28757,28759],{},[898,28744,13574],{},[1677,28746,1686],{"stretchy":1685},[898,28748,13431],{},[1677,28750,1692],{"stretchy":1685},[1677,28752,1679],{},[898,28754,1823],{},[898,28756,13431],{},[1677,28758,1776],{},[898,28760,1875],{},[902,28762,17147],{"encoding":904},[883,28764,28766],{"className":28765},[886],[888,28767,28768],{"xmlns":890},[892,28769,28770,28778],{},[895,28771,28772,28774,28776],{},[898,28773,1823],{},[1677,28775,3128],{},[1810,28777,2008],{},[902,28779,13905],{"encoding":904},[883,28781,28783],{"className":28782},[886],[888,28784,28785],{"xmlns":890},[892,28786,28787,28795],{},[895,28788,28789,28791,28793],{},[898,28790,1875],{},[1677,28792,3089],{},[1810,28794,2008],{},[902,28796,13884],{"encoding":904},"; klesající.",[123,28799,28800,28802,28803,28805,28806,28855],{},[38,28801,17236],{}," — rovnováha na trhu zboží (",[614,28804,13444],{},"); ",[883,28807,28809],{"className":28808},[886],[888,28810,28811],{"xmlns":890},[892,28812,28813,28853],{},[895,28814,28815,28817,28819,28831,28833,28835],{},[898,28816,10516],{},[1677,28818,1679],{},[2010,28820,28821,28823],{},[898,28822,1823],{},[895,28824,28825,28827,28829],{},[1810,28826,1959],{},[1677,28828,1906],{},[898,28830,207],{},[898,28832,13431],{},[1677,28834,1776],{},[2010,28836,28837,28845],{},[895,28838,28839,28841,28843],{},[898,28840,1779],{},[1677,28842,1776],{},[898,28844,1875],{},[895,28846,28847,28849,28851],{},[1810,28848,1959],{},[1677,28850,1906],{},[898,28852,207],{},[902,28854,17289],{"encoding":904}," (7.14); klesající.",[123,28857,28858,28860,28861,28805,28863,28908],{},[38,28859,17435],{}," — rovnováha na trhu peněz (",[614,28862,13451],{},[883,28864,28866],{"className":28865},[886],[888,28867,28868],{"xmlns":890},[892,28869,28870,28906],{},[895,28871,28872,28878,28880,28886,28888,28890,28896,28898,28900],{},[1805,28873,28874,28876],{},[898,28875,2499],{},[1677,28877,5742],{},[1677,28879,1679],{},[1953,28881,28882,28884],{},[898,28883,14627],{},[1810,28885,1959],{},[898,28887,10516],{},[1677,28889,1776],{},[1953,28891,28892,28894],{},[898,28893,14627],{},[1810,28895,1812],{},[898,28897,13431],{},[1677,28899,1776],{},[1953,28901,28902,28904],{},[898,28903,14627],{},[1810,28905,1854],{},[902,28907,17483],{"encoding":904}," (7.15); rostoucí.",[123,28910,28911,8403,28914,1656],{},[38,28912,28913],{},"Transakční, opatrnostní a spekulační poptávka po penězích",[883,28915,28917],{"className":28916},[886],[888,28918,28919],{"xmlns":890},[892,28920,28921,28945],{},[895,28922,28923,28929,28931,28937,28939],{},[1805,28924,28925,28927],{},[898,28926,2499],{},[898,28928,5571],{},[1677,28930,1679],{},[1953,28932,28933,28935],{},[898,28934,11183],{},[1810,28936,1959],{},[1677,28938,1776],{},[1953,28940,28941,28943],{},[898,28942,11183],{},[1810,28944,1812],{},[902,28946,28947],{"encoding":904},"M^D = L_1 + L_2",[123,28949,28950,17493,28952,15370,28965,5272,28980,28995,28996,1656],{},[38,28951,945],{},[883,28953,28955],{"className":28954},[886],[888,28956,28957],{"xmlns":890},[892,28958,28959,28963],{},[895,28960,28961],{},[898,28962,5640],{},[902,28964,5640],{"encoding":904},[883,28966,28968],{"className":28967},[886],[888,28969,28970],{"xmlns":890},[892,28971,28972,28978],{},[895,28973,28974,28976],{},[898,28975,13574],{},[898,28977,10061],{},[902,28979,13441],{"encoding":904},[883,28981,28983],{"className":28982},[886],[888,28984,28985],{"xmlns":890},[892,28986,28987,28993],{},[895,28988,28989,28991],{},[898,28990,11183],{},[898,28992,2499],{},[902,28994,13448],{"encoding":904}," určuje ",[883,28997,28999],{"className":28998},[886],[888,29000,29001],{"xmlns":890},[892,29002,29003,29023],{},[895,29004,29005,29007,29013,29015,29021],{},[1677,29006,1686],{"stretchy":1685},[1805,29008,29009,29011],{},[898,29010,10516],{},[898,29012,5640],{},[1677,29014,1967],{"separator":1966},[1805,29016,29017,29019],{},[898,29018,13431],{},[898,29020,5640],{},[1677,29022,1692],{"stretchy":1685},[902,29024,13485],{"encoding":904},[115,29026,3473],{"id":3472},[120,29028,29029,29036,29043],{},[123,29030,29031,1884,29033],{},[38,29032,17594],{},[207,29034,17598],{"className":29035,"dataFsResolvedFilePath":1641,"href":1642},[210],[123,29037,29038,1884,29040],{},[38,29039,17603],{},[207,29041,17607],{"className":29042,"dataFsResolvedFilePath":868,"href":869},[210],[123,29044,29045,29047],{},[38,29046,17622],{},[120,29048,29049,29055,29061,29067],{},[123,29050,29051,29054],{},[207,29052,17663],{"className":29053,"dataFsResolvedFilePath":943,"href":944},[210]," — detailní IS-LM analýza (odvození křivek, Příklad 7.6, fiskální vs monetární politika)",[123,29056,29057,29060],{},[207,29058,17630],{"className":29059,"dataFsResolvedFilePath":800,"href":801},[210]," — paralela mikroekonomických multiplikátorů (multiplikátory rovnovážné ceny a množství)",[123,29062,29063,29066],{},[207,29064,2631],{"className":29065,"dataFsResolvedFilePath":827,"href":828},[210]," — mikroekonomické analogie, článek 2.4 o multiplikátorech",[123,29068,29069,29072,29073,1343,29090,29107],{},[207,29070,1145],{"className":29071,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro ",[883,29074,29076],{"className":29075},[886],[888,29077,29078],{"xmlns":890},[892,29079,29080,29088],{},[895,29081,29082,29084,29086],{},[898,29083,2499],{},[898,29085,5325],{},[898,29087,2458],{},[902,29089,19436],{"encoding":904},[883,29091,29093],{"className":29092},[886],[888,29094,29095],{"xmlns":890},[892,29096,29097,29105],{},[895,29098,29099,29101,29103],{},[898,29100,2499],{},[898,29102,5325],{},[898,29104,10061],{},[902,29106,21050],{"encoding":904}," a interpretaci změn diferenciálem",{"title":641,"searchDepth":642,"depth":642,"links":29109},[29110,29111,29112,29113,29118,29121,29122,29129,29134,29139,29142,29143,29144,29145],{"id":13395,"depth":642,"text":13396},{"id":19545,"depth":642,"text":19546},{"id":19665,"depth":642,"text":19666},{"id":19918,"depth":642,"text":19919,"children":29114},[29115,29116,29117],{"id":19922,"depth":649,"text":19923},{"id":20134,"depth":649,"text":20135},{"id":20642,"depth":649,"text":20643},{"id":20962,"depth":642,"text":20963,"children":29119},[29120],{"id":21478,"depth":649,"text":21479},{"id":21973,"depth":642,"text":21974},{"id":22000,"depth":642,"text":22001,"children":29123},[29124,29125,29126,29128],{"id":22011,"depth":649,"text":22012},{"id":22081,"depth":649,"text":22082},{"id":22265,"depth":649,"text":29127},"Výpočet YEY^E",{"id":22408,"depth":649,"text":22409},{"id":22786,"depth":642,"text":22787,"children":29130},[29131,29132,29133],{"id":22790,"depth":649,"text":22012},{"id":23239,"depth":649,"text":22082},{"id":23895,"depth":649,"text":23896},{"id":24682,"depth":642,"text":24683,"children":29135},[29136,29137,29138],{"id":24686,"depth":649,"text":22012},{"id":24831,"depth":649,"text":22082},{"id":25101,"depth":649,"text":25102},{"id":26025,"depth":642,"text":26026,"children":29140},[29141],{"id":26221,"depth":649,"text":26222},{"id":26771,"depth":642,"text":26772},{"id":27231,"depth":642,"text":27232},{"id":17109,"depth":642,"text":17110},{"id":3472,"depth":642,"text":3473},{},"\u002Ftopics\u002Fnarodni-duchod",{"title":936,"description":641},[1138,1137],"topics\u002Fnarodni-duchod",[1128,17616,1143,29152,29153,29154,17663,19274],"gnp","mpc","mps","BMicmr68yKQbb8qpoE9KfzU5NFshq3Inq6w0tL8-GjU",{"id":29157,"title":29158,"body":29159,"course":1128,"courses":659,"created":10944,"description":641,"extension":661,"meta":38139,"navigation":664,"path":38140,"seo":38141,"sources":38142,"stem":38143,"tags":38144,"type":3538,"updated":677,"__hash__":38149},"topics\u002Ftopics\u002Foptimalizace-spotrebitele.md","Optimalizace spotřebitele — Lagrange, poptávka, minimalizace výdajů",{"type":9,"value":29160,"toc":38108},[29161,29164,29166,29395,29399,29452,29522,29634,29793,29797,29913,29917,29920,30042,30045,30238,30262,30330,30494,30512,30578,30956,30960,30967,31211,31267,31271,31336,31454,31586,31618,31738,31820,31823,31945,32138,32359,32363,32403,32508,32565,32665,32842,32972,33025,33028,33115,33119,33295,33299,33302,33387,33390,33447,33552,33556,33677,33680,33863,33866,33974,34183,34503,34551,34624,34698,34700,34924,35159,35427,35431,35434,35539,35596,35630,35677,35710,35794,35796,36028,36161,36238,36360,36515,36519,36660,36667,36891,36902,36906,36910,37015,37157,37267,37366,37370,37529,37639,37641,38034,38036],[12,29162,29158],{"id":29163},"optimalizace-spotřebitele-lagrange-poptávka-minimalizace-výdajů",[115,29165,13396],{"id":13395},[724,29167,29168,29170,29171,29205,29206,29209,29210,29241,29242,29288,29289,29292,29293,29335,29336,29354,29355,29359,29360,29390,29391,29394],{},[38,29169,913],{}," řeší, jaký svazek zboží ",[883,29172,29174],{"className":29173},[886],[888,29175,29176],{"xmlns":890},[892,29177,29178,29202],{},[895,29179,29180,29182,29190,29192,29200],{},[1677,29181,2167],{"stretchy":1685},[10554,29183,29184,29186,29188],{},[898,29185,2470],{},[1810,29187,1959],{},[1677,29189,5742],{},[1677,29191,1967],{"separator":1966},[10554,29193,29194,29196,29198],{},[898,29195,2470],{},[1810,29197,1812],{},[1677,29199,5742],{},[1677,29201,2182],{"stretchy":1685},[902,29203,29204],{"encoding":904},"[Q_1^*, Q_2^*]"," zvolit při známých cenách a důchodu. Existují dvě ekvivalentní formulace: ",[38,29207,29208],{},"primární úloha"," — maximalizace užitečnosti ",[883,29211,29213],{"className":29212},[886],[888,29214,29215],{"xmlns":890},[892,29216,29217,29239],{},[895,29218,29219,29221,29223,29229,29231,29237],{},[898,29220,900],{},[1677,29222,1686],{"stretchy":1685},[1953,29224,29225,29227],{},[898,29226,2470],{},[1810,29228,1959],{},[1677,29230,1967],{"separator":1966},[1953,29232,29233,29235],{},[898,29234,2470],{},[1810,29236,1812],{},[1677,29238,1692],{"stretchy":1685},[902,29240,17734],{"encoding":904}," při rozpočtovém omezení ",[883,29243,29245],{"className":29244},[886],[888,29246,29247],{"xmlns":890},[892,29248,29249,29285],{},[895,29250,29251,29257,29259,29265,29271,29273,29279],{},[1805,29252,29253,29255],{},[898,29254,10516],{},[1677,29256,5742],{},[1677,29258,1679],{},[1953,29260,29261,29263],{},[898,29262,5325],{},[1810,29264,1959],{},[1953,29266,29267,29269],{},[898,29268,2470],{},[1810,29270,1959],{},[1677,29272,1776],{},[1953,29274,29275,29277],{},[898,29276,5325],{},[1810,29278,1812],{},[1953,29280,29281,29283],{},[898,29282,2470],{},[1810,29284,1812],{},[902,29286,29287],{"encoding":904},"Y^* = P_1 Q_1 + P_2 Q_2",", a ",[38,29290,29291],{},"duální úloha"," — minimalizace výdajů ",[883,29294,29296],{"className":29295},[886],[888,29297,29298],{"xmlns":890},[892,29299,29300,29332],{},[895,29301,29302,29304,29306,29312,29318,29320,29326],{},[898,29303,5640],{},[1677,29305,1679],{},[1953,29307,29308,29310],{},[898,29309,5325],{},[1810,29311,1959],{},[1953,29313,29314,29316],{},[898,29315,2470],{},[1810,29317,1959],{},[1677,29319,1776],{},[1953,29321,29322,29324],{},[898,29323,5325],{},[1810,29325,1812],{},[1953,29327,29328,29330],{},[898,29329,2470],{},[1810,29331,1812],{},[902,29333,29334],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2"," při zadané hladině užitečnosti ",[883,29337,29339],{"className":29338},[886],[888,29340,29341],{"xmlns":890},[892,29342,29343,29351],{},[895,29344,29345],{},[1805,29346,29347,29349],{},[898,29348,900],{},[1677,29350,5742],{},[902,29352,29353],{"encoding":904},"U^*",". Obě úlohy se řeší ",[207,29356,29358],{"className":29357,"dataFsResolvedFilePath":791,"href":792},[210],"metodou Lagrangeových multiplikátorů"," a vedou na tentýž bod dotyku indiferenční křivky a rozpočtové přímky, v němž platí ",[883,29361,29363],{"className":29362},[886],[888,29364,29365],{"xmlns":890},[892,29366,29367,29387],{},[895,29368,29369,29371,29373,29379,29381],{},[1969,29370,11991],{},[1677,29372,1679],{},[1953,29374,29375,29377],{},[898,29376,5325],{},[1810,29378,1959],{},[898,29380,6062],{"mathvariant":2057},[1953,29382,29383,29385],{},[898,29384,5325],{},[1810,29386,1812],{},[902,29388,29389],{"encoding":904},"\\text{MRCS} = P_1\u002FP_2",". Výstupem jsou ",[38,29392,29393],{},"funkce poptávky"," — Marshallova (závislá na důchodu) a Hicksova (závislá na hladině užitečnosti).",[115,29396,29398],{"id":29397},"úvod-proč-optimalizovat","Úvod — proč optimalizovat",[724,29400,29401,29402,29420,29421,29451],{},"Racionální spotřebitel má omezený důchod a musí se rozhodnout, jak jej rozdělit mezi spotřebovávané zboží. V modelu pro dvě zboží je k dispozici částka ",[883,29403,29405],{"className":29404},[886],[888,29406,29407],{"xmlns":890},[892,29408,29409,29417],{},[895,29410,29411],{},[1805,29412,29413,29415],{},[898,29414,10516],{},[1677,29416,5742],{},[902,29418,29419],{"encoding":904},"Y^*"," a ceny ",[883,29422,29424],{"className":29423},[886],[888,29425,29426],{"xmlns":890},[892,29427,29428,29448],{},[895,29429,29430,29438,29440],{},[10554,29431,29432,29434,29436],{},[898,29433,5325],{},[1810,29435,1959],{},[1677,29437,5742],{},[1677,29439,1967],{"separator":1966},[10554,29441,29442,29444,29446],{},[898,29443,5325],{},[1810,29445,1812],{},[1677,29447,5742],{},[902,29449,29450],{"encoding":904},"P_1^*, P_2^*",", rozpočtové omezení má tvar",[883,29453,29455],{"className":29454},[886],[888,29456,29458],{"xmlns":890,"display":29457},"block",[892,29459,29460,29519],{},[22145,29461,29463],{"width":29462},"100%",[22150,29464,29465,29468,29512,29514],{},[22153,29466],{"width":29467},"50%",[22153,29469,29470],{},[895,29471,29472,29478,29480,29488,29494,29496,29504,29510],{},[1805,29473,29474,29476],{},[898,29475,10516],{},[1677,29477,5742],{},[1677,29479,1679],{},[10554,29481,29482,29484,29486],{},[898,29483,5325],{},[1810,29485,1959],{},[1677,29487,5742],{},[1953,29489,29490,29492],{},[898,29491,2470],{},[1810,29493,1959],{},[1677,29495,1776],{},[10554,29497,29498,29500,29502],{},[898,29499,5325],{},[1810,29501,1812],{},[1677,29503,5742],{},[1953,29505,29506,29508],{},[898,29507,2470],{},[1810,29509,1812],{},[1677,29511,1967],{"separator":1966},[22153,29513],{"width":29467},[22153,29515,29516],{},[1969,29517,29518],{},"(6.12)",[902,29520,29521],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2, \\tag{6.12}",[724,29523,29524,29525,29528,29529,5272,29565,29601,29602,29615,29616,29630,29631,1656],{},"geometricky ",[38,29526,29527],{},"rozpočtová přímka (budget line)"," procházející body ",[883,29530,29532],{"className":29531},[886],[888,29533,29534],{"xmlns":890},[892,29535,29536,29562],{},[895,29537,29538,29540,29546,29548,29556,29558,29560],{},[1677,29539,2167],{"stretchy":1685},[1805,29541,29542,29544],{},[898,29543,10516],{},[1677,29545,5742],{},[898,29547,6062],{"mathvariant":2057},[10554,29549,29550,29552,29554],{},[898,29551,5325],{},[1810,29553,1959],{},[1677,29555,5742],{},[1677,29557,1967],{"separator":1966},[1810,29559,2008],{},[1677,29561,2182],{"stretchy":1685},[902,29563,29564],{"encoding":904},"[Y^*\u002FP_1^*, 0]",[883,29566,29568],{"className":29567},[886],[888,29569,29570],{"xmlns":890},[892,29571,29572,29598],{},[895,29573,29574,29576,29578,29580,29586,29588,29596],{},[1677,29575,2167],{"stretchy":1685},[1810,29577,2008],{},[1677,29579,1967],{"separator":1966},[1805,29581,29582,29584],{},[898,29583,10516],{},[1677,29585,5742],{},[898,29587,6062],{"mathvariant":2057},[10554,29589,29590,29592,29594],{},[898,29591,5325],{},[1810,29593,1812],{},[1677,29595,5742],{},[1677,29597,2182],{"stretchy":1685},[902,29599,29600],{"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 ",[883,29603,29605],{"className":29604},[886],[888,29606,29607],{"xmlns":890},[892,29608,29609,29613],{},[895,29610,29611],{},[898,29612,900],{},[902,29614,900],{"encoding":904},", indiferenční křivky a ",[883,29617,29619],{"className":29618},[886],[888,29620,29621],{"xmlns":890},[892,29622,29623,29627],{},[895,29624,29625],{},[1969,29626,11991],{},[902,29628,29629],{"encoding":904},"\\text{MRCS}"," — je shrnuta v ",[207,29632,880],{"className":29633,"dataFsResolvedFilePath":878,"href":879},[210],[5254,29635,29636],{},[724,29637,29638,29640,29641,29644,29645,29658,29659,29661,29662,29675,29676,1884,29679,29719,29720,29737,29738,29755,29756,29773,29774,29792],{},[883,29639,5800],{}," Pozor — dvě úlohy, totéž řešení\n",[38,29642,29643],{},"Primární úloha"," (max ",[883,29646,29648],{"className":29647},[886],[888,29649,29650],{"xmlns":890},[892,29651,29652,29656],{},[895,29653,29654],{},[898,29655,900],{},[902,29657,900],{"encoding":904}," při pevném rozpočtu) a ",[38,29660,29291],{}," (min ",[883,29663,29665],{"className":29664},[886],[888,29666,29667],{"xmlns":890},[892,29668,29669,29673],{},[895,29670,29671],{},[898,29672,5640],{},[902,29674,5640],{"encoding":904}," při pevné užitečnosti) vedou na ",[38,29677,29678],{},"tentýž bod",[883,29680,29682],{"className":29681},[886],[888,29683,29684],{"xmlns":890},[892,29685,29686,29716],{},[895,29687,29688,29694,29696,29704,29706,29714],{},[1805,29689,29690,29692],{},[898,29691,2470],{},[1677,29693,5742],{},[1677,29695,2167],{"stretchy":1685},[10554,29697,29698,29700,29702],{},[898,29699,2470],{},[1810,29701,1959],{},[1677,29703,5742],{},[1677,29705,1967],{"separator":1966},[10554,29707,29708,29710,29712],{},[898,29709,2470],{},[1810,29711,1812],{},[1677,29713,5742],{},[1677,29715,2182],{"stretchy":1685},[902,29717,29718],{"encoding":904},"Q^*[Q_1^*, Q_2^*]",". Rozdíl je v tom, co je „vstup\" a co „výstup\": u primární úlohy je zadán důchod ",[883,29721,29723],{"className":29722},[886],[888,29724,29725],{"xmlns":890},[892,29726,29727,29735],{},[895,29728,29729],{},[1805,29730,29731,29733],{},[898,29732,10516],{},[1677,29734,5742],{},[902,29736,29419],{"encoding":904}," a hledáme maximální ",[883,29739,29741],{"className":29740},[886],[888,29742,29743],{"xmlns":890},[892,29744,29745,29753],{},[895,29746,29747],{},[1805,29748,29749,29751],{},[898,29750,900],{},[1677,29752,5742],{},[902,29754,29353],{"encoding":904},"; u duální úlohy je zadána hladina ",[883,29757,29759],{"className":29758},[886],[888,29760,29761],{"xmlns":890},[892,29762,29763,29771],{},[895,29764,29765],{},[1805,29766,29767,29769],{},[898,29768,900],{},[1677,29770,5742],{},[902,29772,29353],{"encoding":904}," a hledáme minimální ",[883,29775,29777],{"className":29776},[886],[888,29778,29779],{"xmlns":890},[892,29780,29781,29789],{},[895,29782,29783],{},[1805,29784,29785,29787],{},[898,29786,5640],{},[1677,29788,5742],{},[902,29790,29791],{"encoding":904},"E^*",". Z pozorování je přirozenější minimalizace výdajů (výdaje lze měřit).",[115,29794,29796],{"id":29795},"maximalizace-užitečnosti-za-rozpočtového-omezení","Maximalizace užitečnosti za rozpočtového omezení",[724,29798,29799,29800,29831,29832,29908,29909,1656],{},"Úlohou je najít maximum ",[883,29801,29803],{"className":29802},[886],[888,29804,29805],{"xmlns":890},[892,29806,29807,29829],{},[895,29808,29809,29811,29813,29819,29821,29827],{},[898,29810,900],{},[1677,29812,1686],{"stretchy":1685},[1953,29814,29815,29817],{},[898,29816,2470],{},[1810,29818,1959],{},[1677,29820,1967],{"separator":1966},[1953,29822,29823,29825],{},[898,29824,2470],{},[1810,29826,1812],{},[1677,29828,1692],{"stretchy":1685},[902,29830,17734],{"encoding":904}," vázané podmínkou (6.12) ve tvaru ",[883,29833,29835],{"className":29834},[886],[888,29836,29837],{"xmlns":890},[892,29838,29839,29905],{},[895,29840,29841,29843,29845,29851,29853,29859,29861,29863,29869,29871,29879,29885,29887,29895,29901,29903],{},[898,29842,12429],{},[1677,29844,1686],{"stretchy":1685},[1953,29846,29847,29849],{},[898,29848,2470],{},[1810,29850,1959],{},[1677,29852,1967],{"separator":1966},[1953,29854,29855,29857],{},[898,29856,2470],{},[1810,29858,1812],{},[1677,29860,1692],{"stretchy":1685},[1677,29862,1679],{},[1805,29864,29865,29867],{},[898,29866,10516],{},[1677,29868,5742],{},[1677,29870,1906],{},[10554,29872,29873,29875,29877],{},[898,29874,5325],{},[1810,29876,1959],{},[1677,29878,5742],{},[1953,29880,29881,29883],{},[898,29882,2470],{},[1810,29884,1959],{},[1677,29886,1906],{},[10554,29888,29889,29891,29893],{},[898,29890,5325],{},[1810,29892,1812],{},[1677,29894,5742],{},[1953,29896,29897,29899],{},[898,29898,2470],{},[1810,29900,1812],{},[1677,29902,1679],{},[1810,29904,2008],{},[902,29906,29907],{"encoding":904},"g(Q_1, Q_2) = Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",". Použijeme ",[207,29910,29912],{"className":29911,"dataFsResolvedFilePath":791,"href":792},[210],"metodu Lagrangeových multiplikátorů",[198,29914,29916],{"id":29915},"lagrangeova-funkce-a-podmínky-optimality","Lagrangeova funkce a podmínky optimality",[724,29918,29919],{},"Sestavíme",[883,29921,29923],{"className":29922},[886],[888,29924,29925],{"xmlns":890,"display":29457},[892,29926,29927,30039],{},[22145,29928,29929],{"width":29462},[22150,29930,29931,29933,30032,30034],{},[22153,29932],{"width":29467},[22153,29934,29935],{},[895,29936,29937,29940,29942,29948,29950,29956,29958,29960,29962,29964,29966,29968,29974,29976,29982,29984,29986,29988,29990,29996,29998,30006,30012,30014,30022,30028,30030],{},[898,29938,11183],{"mathvariant":29939},"script",[1677,29941,1686],{"stretchy":1685},[1953,29943,29944,29946],{},[898,29945,2470],{},[1810,29947,1959],{},[1677,29949,1967],{"separator":1966},[1953,29951,29952,29954],{},[898,29953,2470],{},[1810,29955,1812],{},[1677,29957,1967],{"separator":1966},[898,29959,17834],{},[1677,29961,1692],{"stretchy":1685},[1677,29963,1679],{},[898,29965,900],{},[1677,29967,1686],{"stretchy":1685},[1953,29969,29970,29972],{},[898,29971,2470],{},[1810,29973,1959],{},[1677,29975,1967],{"separator":1966},[1953,29977,29978,29980],{},[898,29979,2470],{},[1810,29981,1812],{},[1677,29983,1692],{"stretchy":1685},[1677,29985,1776],{},[898,29987,17834],{},[1677,29989,1686],{"stretchy":1685},[1805,29991,29992,29994],{},[898,29993,10516],{},[1677,29995,5742],{},[1677,29997,1906],{},[10554,29999,30000,30002,30004],{},[898,30001,5325],{},[1810,30003,1959],{},[1677,30005,5742],{},[1953,30007,30008,30010],{},[898,30009,2470],{},[1810,30011,1959],{},[1677,30013,1906],{},[10554,30015,30016,30018,30020],{},[898,30017,5325],{},[1810,30019,1812],{},[1677,30021,5742],{},[1953,30023,30024,30026],{},[898,30025,2470],{},[1810,30027,1812],{},[1677,30029,1692],{"stretchy":1685},[898,30031,1656],{"mathvariant":2057},[22153,30033],{"width":29467},[22153,30035,30036],{},[1969,30037,30038],{},"(6.13)",[902,30040,30041],{"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}",[724,30043,30044],{},"Soustava prvního řádu:",[883,30046,30048],{"className":30047},[886],[888,30049,30050],{"xmlns":890,"display":29457},[892,30051,30052,30235],{},[22145,30053,30054],{"width":29462},[22150,30055,30056,30058,30228,30230],{},[22153,30057],{"width":29467},[22153,30059,30060],{},[22145,30061,30062,30112,30162],{"rowspacing":22147,"columnalign":22148,"columnspacing":2058},[22150,30063,30064,30076],{},[22153,30065,30066],{},[2006,30067,30068],{"scriptlevel":2008,"displaystyle":1966},[10554,30069,30070,30072,30074],{},[898,30071,11183],{"mathvariant":29939},[1810,30073,1959],{},[1677,30075,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[22153,30077,30078],{},[2006,30079,30080],{"scriptlevel":2008,"displaystyle":1966},[895,30081,30082,30084,30086,30094,30096,30098,30106,30108,30110],{},[895,30083],{},[1677,30085,1679],{},[10554,30087,30088,30090,30092],{},[898,30089,900],{},[1810,30091,1959],{},[1677,30093,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,30095,1906],{},[898,30097,17834],{},[10554,30099,30100,30102,30104],{},[898,30101,5325],{},[1810,30103,1959],{},[1677,30105,5742],{},[1677,30107,1679],{},[1810,30109,2008],{},[1677,30111,1967],{"separator":1966},[22150,30113,30114,30126],{},[22153,30115,30116],{},[2006,30117,30118],{"scriptlevel":2008,"displaystyle":1966},[10554,30119,30120,30122,30124],{},[898,30121,11183],{"mathvariant":29939},[1810,30123,1812],{},[1677,30125,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[22153,30127,30128],{},[2006,30129,30130],{"scriptlevel":2008,"displaystyle":1966},[895,30131,30132,30134,30136,30144,30146,30148,30156,30158,30160],{},[895,30133],{},[1677,30135,1679],{},[10554,30137,30138,30140,30142],{},[898,30139,900],{},[1810,30141,1812],{},[1677,30143,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,30145,1906],{},[898,30147,17834],{},[10554,30149,30150,30152,30154],{},[898,30151,5325],{},[1810,30153,1812],{},[1677,30155,5742],{},[1677,30157,1679],{},[1810,30159,2008],{},[1677,30161,1967],{"separator":1966},[22150,30163,30164,30176],{},[22153,30165,30166],{},[2006,30167,30168],{"scriptlevel":2008,"displaystyle":1966},[10554,30169,30170,30172,30174],{},[898,30171,11183],{"mathvariant":29939},[898,30173,17834],{},[1677,30175,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[22153,30177,30178],{},[2006,30179,30180],{"scriptlevel":2008,"displaystyle":1966},[895,30181,30182,30184,30186,30192,30194,30202,30208,30210,30218,30224,30226],{},[895,30183],{},[1677,30185,1679],{},[1805,30187,30188,30190],{},[898,30189,10516],{},[1677,30191,5742],{},[1677,30193,1906],{},[10554,30195,30196,30198,30200],{},[898,30197,5325],{},[1810,30199,1959],{},[1677,30201,5742],{},[1953,30203,30204,30206],{},[898,30205,2470],{},[1810,30207,1959],{},[1677,30209,1906],{},[10554,30211,30212,30214,30216],{},[898,30213,5325],{},[1810,30215,1812],{},[1677,30217,5742],{},[1953,30219,30220,30222],{},[898,30221,2470],{},[1810,30223,1812],{},[1677,30225,1679],{},[1810,30227,13850],{},[22153,30229],{"width":29467},[22153,30231,30232],{},[1969,30233,30234],{},"(6.14)",[902,30236,30237],{"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}",[724,30239,30240,30241,30244,30245,30258,30259,2385],{},"Díky konvexitě indiferenčních křivek je řešení ",[38,30242,30243],{},"vázaným maximem",". Z prvních dvou rovnic po vyloučení ",[883,30246,30248],{"className":30247},[886],[888,30249,30250],{"xmlns":890},[892,30251,30252,30256],{},[895,30253,30254],{},[898,30255,17834],{},[902,30257,17887],{"encoding":904}," dostáváme ",[38,30260,30261],{},"podmínku optimality",[883,30263,30265],{"className":30264},[886],[888,30266,30267],{"xmlns":890,"display":29457},[892,30268,30269,30327],{},[895,30270,30271],{},[14222,30272,30273],{"notation":14224},[2006,30274,30275],{"scriptlevel":2008,"displaystyle":1685},[2006,30276,30277],{"scriptlevel":2008,"displaystyle":1685},[2006,30278,30279],{"scriptlevel":2008,"displaystyle":1966},[895,30280,30281,30283,30285,30287,30305,30307,30325],{},[1969,30282,5372],{},[1969,30284,11991],{},[1677,30286,1679],{},[2010,30288,30289,30297],{},[10554,30290,30291,30293,30295],{},[898,30292,900],{},[1810,30294,1959],{},[1677,30296,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[10554,30298,30299,30301,30303],{},[898,30300,900],{},[1810,30302,1812],{},[1677,30304,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,30306,1679],{},[2010,30308,30309,30317],{},[10554,30310,30311,30313,30315],{},[898,30312,5325],{},[1810,30314,1959],{},[1677,30316,5742],{},[10554,30318,30319,30321,30323],{},[898,30320,5325],{},[1810,30322,1812],{},[1677,30324,5742],{},[1969,30326,5372],{},[902,30328,30329],{"encoding":904},"\\boxed{\\; \\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*} \\;}",[5254,30331,30332],{},[724,30333,30334,30336,30337,30371,30372,30375,30376,30394,30395,30413,30414,30444,30445,30462,30463,30493],{},[883,30335,5543],{}," Intuice — mezní poměr užitečnosti = mezní poměr cen\nPodmínka ",[883,30338,30340],{"className":30339},[886],[888,30341,30342],{"xmlns":890},[892,30343,30344,30368],{},[895,30345,30346,30348,30350,30358,30360],{},[1969,30347,11991],{},[1677,30349,1679],{},[10554,30351,30352,30354,30356],{},[898,30353,5325],{},[1810,30355,1959],{},[1677,30357,5742],{},[898,30359,6062],{"mathvariant":2057},[10554,30361,30362,30364,30366],{},[898,30363,5325],{},[1810,30365,1812],{},[1677,30367,5742],{},[902,30369,30370],{"encoding":904},"\\text{MRCS} = P_1^*\u002FP_2^*"," říká, že v optimu je ",[38,30373,30374],{},"sklon indiferenční křivky roven sklonu rozpočtové přímky",". Ekonomicky: spotřebitel je ochoten vyměnit ",[883,30377,30379],{"className":30378},[886],[888,30380,30381],{"xmlns":890},[892,30382,30383,30391],{},[895,30384,30385],{},[1953,30386,30387,30389],{},[898,30388,2470],{},[1810,30390,1959],{},[902,30392,30393],{"encoding":904},"Q_1"," za ",[883,30396,30398],{"className":30397},[886],[888,30399,30400],{"xmlns":890},[892,30401,30402,30410],{},[895,30403,30404],{},[1953,30405,30406,30408],{},[898,30407,2470],{},[1810,30409,1812],{},[902,30411,30412],{"encoding":904},"Q_2"," v přesně tom poměru, v jakém je trh (ceny) umožňuje vyměňovat. Kdyby ",[883,30415,30417],{"className":30416},[886],[888,30418,30419],{"xmlns":890},[892,30420,30421,30441],{},[895,30422,30423,30425,30427,30433,30435],{},[1969,30424,11991],{},[1677,30426,3089],{},[1953,30428,30429,30431],{},[898,30430,5325],{},[1810,30432,1959],{},[898,30434,6062],{"mathvariant":2057},[1953,30436,30437,30439],{},[898,30438,5325],{},[1810,30440,1812],{},[902,30442,30443],{"encoding":904},"\\text{MRCS} > P_1\u002FP_2",", vyplatilo by se nakupovat více ",[883,30446,30448],{"className":30447},[886],[888,30449,30450],{"xmlns":890},[892,30451,30452,30460],{},[895,30453,30454],{},[1953,30455,30456,30458],{},[898,30457,2470],{},[1810,30459,1959],{},[902,30461,30393],{"encoding":904}," (subjektivní ocenění převažuje nad tržním); kdyby ",[883,30464,30466],{"className":30465},[886],[888,30467,30468],{"xmlns":890},[892,30469,30470,30490],{},[895,30471,30472,30474,30476,30482,30484],{},[1969,30473,11991],{},[1677,30475,3128],{},[1953,30477,30478,30480],{},[898,30479,5325],{},[1810,30481,1959],{},[898,30483,6062],{"mathvariant":2057},[1953,30485,30486,30488],{},[898,30487,5325],{},[1810,30489,1812],{},[902,30491,30492],{"encoding":904},"\\text{MRCS} \u003C P_1\u002FP_2",", vyplatil by se opak.",[198,30495,30497,30498,30511],{"id":30496},"interpretace-λlambda-mezní-užitečnost-důchodu","Interpretace ",[883,30499,30501],{"className":30500},[886],[888,30502,30503],{"xmlns":890},[892,30504,30505,30509],{},[895,30506,30507],{},[898,30508,17834],{},[902,30510,17887],{"encoding":904}," — mezní užitečnost důchodu",[724,30513,30514,30515,30533,30534,30537,30538,30555,30556,30573,30574,30577],{},"Lagrangeův multiplikátor ",[883,30516,30518],{"className":30517},[886],[888,30519,30520],{"xmlns":890},[892,30521,30522,30530],{},[895,30523,30524],{},[1805,30525,30526,30528],{},[898,30527,17834],{},[1677,30529,5742],{},[902,30531,30532],{"encoding":904},"\\lambda^*"," představuje ",[38,30535,30536],{},"mezní užitečnost důchodu"," — přibližnou změnu maximální užitečnosti ",[883,30539,30541],{"className":30540},[886],[888,30542,30543],{"xmlns":890},[892,30544,30545,30553],{},[895,30546,30547],{},[1805,30548,30549,30551],{},[898,30550,900],{},[1677,30552,5742],{},[902,30554,29353],{"encoding":904}," při jednotkové změně důchodu ",[883,30557,30559],{"className":30558},[886],[888,30560,30561],{"xmlns":890},[892,30562,30563,30571],{},[895,30564,30565],{},[1805,30566,30567,30569],{},[898,30568,10516],{},[1677,30570,5742],{},[902,30572,29419],{"encoding":904},". Je to ",[38,30575,30576],{},"stínová cena"," rozpočtového omezení.",[5254,30579,30580,30585],{},[724,30581,30582,30584],{},[883,30583,5960],{}," Postup — maximalizace užitečnosti Lagrangeovou metodou",[152,30586,30587,30647,30734,30770,30857],{},[123,30588,30589,30592,30593,1656],{},[38,30590,30591],{},"Zapiš rozpočtové omezení"," ve tvaru ",[883,30594,30596],{"className":30595},[886],[888,30597,30598],{"xmlns":890},[892,30599,30600,30644],{},[895,30601,30602,30608,30610,30618,30624,30626,30634,30640,30642],{},[1805,30603,30604,30606],{},[898,30605,10516],{},[1677,30607,5742],{},[1677,30609,1906],{},[10554,30611,30612,30614,30616],{},[898,30613,5325],{},[1810,30615,1959],{},[1677,30617,5742],{},[1953,30619,30620,30622],{},[898,30621,2470],{},[1810,30623,1959],{},[1677,30625,1906],{},[10554,30627,30628,30630,30632],{},[898,30629,5325],{},[1810,30631,1812],{},[1677,30633,5742],{},[1953,30635,30636,30638],{},[898,30637,2470],{},[1810,30639,1812],{},[1677,30641,1679],{},[1810,30643,2008],{},[902,30645,30646],{"encoding":904},"Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",[123,30648,30649,1884,30652,1656],{},[38,30650,30651],{},"Sestav Lagrangeovu funkci",[883,30653,30655],{"className":30654},[886],[888,30656,30657],{"xmlns":890},[892,30658,30659,30731],{},[895,30660,30661,30663,30665,30667,30669,30675,30677,30683,30685,30687,30689,30691,30697,30699,30707,30713,30715,30723,30729],{},[898,30662,11183],{"mathvariant":29939},[1677,30664,1679],{},[898,30666,900],{},[1677,30668,1686],{"stretchy":1685},[1953,30670,30671,30673],{},[898,30672,2470],{},[1810,30674,1959],{},[1677,30676,1967],{"separator":1966},[1953,30678,30679,30681],{},[898,30680,2470],{},[1810,30682,1812],{},[1677,30684,1692],{"stretchy":1685},[1677,30686,1776],{},[898,30688,17834],{},[1677,30690,1686],{"stretchy":1685},[1805,30692,30693,30695],{},[898,30694,10516],{},[1677,30696,5742],{},[1677,30698,1906],{},[10554,30700,30701,30703,30705],{},[898,30702,5325],{},[1810,30704,1959],{},[1677,30706,5742],{},[1953,30708,30709,30711],{},[898,30710,2470],{},[1810,30712,1959],{},[1677,30714,1906],{},[10554,30716,30717,30719,30721],{},[898,30718,5325],{},[1810,30720,1812],{},[1677,30722,5742],{},[1953,30724,30725,30727],{},[898,30726,2470],{},[1810,30728,1812],{},[1677,30730,1692],{"stretchy":1685},[902,30732,30733],{"encoding":904},"\\mathcal{L} = U(Q_1, Q_2) + \\lambda(Y^* - P_1^* Q_1 - P_2^* Q_2)",[123,30735,30736,11856,30739,30769],{},[38,30737,30738],{},"Spočítej parciální derivace",[883,30740,30742],{"className":30741},[886],[888,30743,30744],{"xmlns":890},[892,30745,30746,30766],{},[895,30747,30748,30754,30756,30762,30764],{},[1953,30749,30750,30752],{},[898,30751,2470],{},[1810,30753,1959],{},[1677,30755,1967],{"separator":1966},[1953,30757,30758,30760],{},[898,30759,2470],{},[1810,30761,1812],{},[1677,30763,1967],{"separator":1966},[898,30765,17834],{},[902,30767,30768],{"encoding":904},"Q_1, Q_2, \\lambda"," a polož je rovny nule.",[123,30771,30772,30788,30789,30822,30823,5272,30840,1656],{},[38,30773,30774,30775],{},"Vyluč ",[883,30776,30778],{"className":30777},[886],[888,30779,30780],{"xmlns":890},[892,30781,30782,30786],{},[895,30783,30784],{},[898,30785,17834],{},[902,30787,17887],{"encoding":904}," dělením prvních dvou rovnic — dostaneš podmínku ",[883,30790,30792],{"className":30791},[886],[888,30793,30794],{"xmlns":890},[892,30795,30796,30820],{},[895,30797,30798,30800,30802,30810,30812],{},[1969,30799,11991],{},[1677,30801,1679],{},[10554,30803,30804,30806,30808],{},[898,30805,5325],{},[1810,30807,1959],{},[1677,30809,5742],{},[898,30811,6062],{"mathvariant":2057},[10554,30813,30814,30816,30818],{},[898,30815,5325],{},[1810,30817,1812],{},[1677,30819,5742],{},[902,30821,30370],{"encoding":904},", která dá vztah mezi ",[883,30824,30826],{"className":30825},[886],[888,30827,30828],{"xmlns":890},[892,30829,30830,30838],{},[895,30831,30832],{},[1953,30833,30834,30836],{},[898,30835,2470],{},[1810,30837,1959],{},[902,30839,30393],{"encoding":904},[883,30841,30843],{"className":30842},[886],[888,30844,30845],{"xmlns":890},[892,30846,30847,30855],{},[895,30848,30849],{},[1953,30850,30851,30853],{},[898,30852,2470],{},[1810,30854,1812],{},[902,30856,30412],{"encoding":904},[123,30858,30859,30862,30863,30893,30894,30911,30912,1656],{},[38,30860,30861],{},"Dosaď do rozpočtového omezení"," a vypočítej ",[883,30864,30866],{"className":30865},[886],[888,30867,30868],{"xmlns":890},[892,30869,30870,30890],{},[895,30871,30872,30880,30882],{},[10554,30873,30874,30876,30878],{},[898,30875,2470],{},[1810,30877,1959],{},[1677,30879,5742],{},[1677,30881,1967],{"separator":1966},[10554,30883,30884,30886,30888],{},[898,30885,2470],{},[1810,30887,1812],{},[1677,30889,5742],{},[902,30891,30892],{"encoding":904},"Q_1^*, Q_2^*",", případně ",[883,30895,30897],{"className":30896},[886],[888,30898,30899],{"xmlns":890},[892,30900,30901,30909],{},[895,30902,30903],{},[1805,30904,30905,30907],{},[898,30906,17834],{},[1677,30908,5742],{},[902,30910,30532],{"encoding":904}," a maximální užitečnost ",[883,30913,30915],{"className":30914},[886],[888,30916,30917],{"xmlns":890},[892,30918,30919,30953],{},[895,30920,30921,30927,30929,30931,30933,30941,30943,30951],{},[1805,30922,30923,30925],{},[898,30924,900],{},[1677,30926,5742],{},[1677,30928,1679],{},[898,30930,900],{},[1677,30932,1686],{"stretchy":1685},[10554,30934,30935,30937,30939],{},[898,30936,2470],{},[1810,30938,1959],{},[1677,30940,5742],{},[1677,30942,1967],{"separator":1966},[10554,30944,30945,30947,30949],{},[898,30946,2470],{},[1810,30948,1812],{},[1677,30950,5742],{},[1677,30952,1692],{"stretchy":1685},[902,30954,30955],{"encoding":904},"U^* = U(Q_1^*, Q_2^*)",[115,30957,30959],{"id":30958},"geometrie-optima-tečnost-ic-a-rozpočtové-přímky","Geometrie optima — tečnost IC a rozpočtové přímky",[724,30961,30962],{},[2240,30963],{"alt":30964,"className":30965,"src":30966},"imek-uzitecnost-optimum",[210,2244],"\u002Fwiki-assets\u002Fimek-uzitecnost-optimum.jpeg",[724,30968,30969],{},[614,30970,30971,30972,31021,31022,5272,31050,31078,31079,31113,31114,31153,31154,31172,31173,31191,31192,31210],{},"Obrázek 6.7 — Rozpočtová přímka ",[883,30973,30975],{"className":30974},[886],[888,30976,30977],{"xmlns":890},[892,30978,30979,31019],{},[895,30980,30981,30987,30989,30997,31003,31005,31013],{},[1805,30982,30983,30985],{},[898,30984,10516],{},[1677,30986,5742],{},[1677,30988,1679],{},[10554,30990,30991,30993,30995],{},[898,30992,5325],{},[1810,30994,1959],{},[1677,30996,5742],{},[1953,30998,30999,31001],{},[898,31000,2470],{},[1810,31002,1959],{},[1677,31004,1776],{},[10554,31006,31007,31009,31011],{},[898,31008,5325],{},[1810,31010,1812],{},[1677,31012,5742],{},[1953,31014,31015,31017],{},[898,31016,2470],{},[1810,31018,1812],{},[902,31020,18689],{"encoding":904}," protíná osy v ",[883,31023,31025],{"className":31024},[886],[888,31026,31027],{"xmlns":890},[892,31028,31029,31047],{},[895,31030,31031,31037,31039],{},[1805,31032,31033,31035],{},[898,31034,10516],{},[1677,31036,5742],{},[898,31038,6062],{"mathvariant":2057},[10554,31040,31041,31043,31045],{},[898,31042,5325],{},[1810,31044,1959],{},[1677,31046,5742],{},[902,31048,31049],{"encoding":904},"Y^*\u002FP_1^*",[883,31051,31053],{"className":31052},[886],[888,31054,31055],{"xmlns":890},[892,31056,31057,31075],{},[895,31058,31059,31065,31067],{},[1805,31060,31061,31063],{},[898,31062,10516],{},[1677,31064,5742],{},[898,31066,6062],{"mathvariant":2057},[10554,31068,31069,31071,31073],{},[898,31070,5325],{},[1810,31072,1812],{},[1677,31074,5742],{},[902,31076,31077],{"encoding":904},"Y^*\u002FP_2^*",". Tři indiferenční křivky ",[883,31080,31082],{"className":31081},[886],[888,31083,31084],{"xmlns":890},[892,31085,31086,31110],{},[895,31087,31088,31094,31096,31102,31104],{},[1953,31089,31090,31092],{},[898,31091,1823],{},[1810,31093,1959],{},[1677,31095,3128],{},[1805,31097,31098,31100],{},[898,31099,1823],{},[1677,31101,5742],{},[1677,31103,3128],{},[1953,31105,31106,31108],{},[898,31107,1823],{},[1810,31109,1812],{},[902,31111,31112],{"encoding":904},"c_1 \u003C c^* \u003C c_2",". Optimum ",[883,31115,31117],{"className":31116},[886],[888,31118,31119],{"xmlns":890},[892,31120,31121,31151],{},[895,31122,31123,31129,31131,31139,31141,31149],{},[1805,31124,31125,31127],{},[898,31126,2470],{},[1677,31128,5742],{},[1677,31130,2167],{"stretchy":1685},[10554,31132,31133,31135,31137],{},[898,31134,2470],{},[1810,31136,1959],{},[1677,31138,5742],{},[1677,31140,1967],{"separator":1966},[10554,31142,31143,31145,31147],{},[898,31144,2470],{},[1810,31146,1812],{},[1677,31148,5742],{},[1677,31150,2182],{"stretchy":1685},[902,31152,29718],{"encoding":904}," je bod dotyku rozpočtové přímky s křivkou ",[883,31155,31157],{"className":31156},[886],[888,31158,31159],{"xmlns":890},[892,31160,31161,31169],{},[895,31162,31163],{},[1805,31164,31165,31167],{},[898,31166,1823],{},[1677,31168,5742],{},[902,31170,31171],{"encoding":904},"c^*",". Křivka ",[883,31174,31176],{"className":31175},[886],[888,31177,31178],{"xmlns":890},[892,31179,31180,31188],{},[895,31181,31182],{},[1953,31183,31184,31186],{},[898,31185,1823],{},[1810,31187,1959],{},[902,31189,31190],{"encoding":904},"c_1"," je dosažitelná, ale nemaximalizuje užitečnost; křivka ",[883,31193,31195],{"className":31194},[886],[888,31196,31197],{"xmlns":890},[892,31198,31199,31207],{},[895,31200,31201],{},[1953,31202,31203,31205],{},[898,31204,1823],{},[1810,31206,1812],{},[902,31208,31209],{"encoding":904},"c_2"," není při daném důchodu dosažitelná.",[724,31212,31213,31214,31217,31218,31236,31237,31266],{},"Geometrie je jádrem intuice: přímka (rozpočet) a křivka (užitečnost) se v optimu ",[38,31215,31216],{},"dotýkají",", tj. mají v bodě ",[883,31219,31221],{"className":31220},[886],[888,31222,31223],{"xmlns":890},[892,31224,31225,31233],{},[895,31226,31227],{},[1805,31228,31229,31231],{},[898,31230,2470],{},[1677,31232,5742],{},[902,31234,31235],{"encoding":904},"Q^*"," společnou tečnu. To přímo převádí podmínku ",[883,31238,31240],{"className":31239},[886],[888,31241,31242],{"xmlns":890},[892,31243,31244,31264],{},[895,31245,31246,31248,31250,31256,31258],{},[1969,31247,11991],{},[1677,31249,1679],{},[1953,31251,31252,31254],{},[898,31253,5325],{},[1810,31255,1959],{},[898,31257,6062],{"mathvariant":2057},[1953,31259,31260,31262],{},[898,31261,5325],{},[1810,31263,1812],{},[902,31265,29389],{"encoding":904}," — poměr mezních užitečností (sklon IC) = poměr cen (sklon přímky).",[115,31268,31270],{"id":31269},"příklad-65-mrcs-pro-cobb-douglasovu-užitečnost","Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost",[724,31272,11051,31273,31335],{},[883,31274,31276],{"className":31275},[886],[888,31277,31278],{"xmlns":890},[892,31279,31280,31332],{},[895,31281,31282,31284,31286,31292,31294,31300,31302,31304,31318],{},[898,31283,900],{},[1677,31285,1686],{"stretchy":1685},[1953,31287,31288,31290],{},[898,31289,2470],{},[1810,31291,1959],{},[1677,31293,1967],{"separator":1966},[1953,31295,31296,31298],{},[898,31297,2470],{},[1810,31299,1812],{},[1677,31301,1692],{"stretchy":1685},[1677,31303,1679],{},[10554,31305,31306,31308,31310],{},[898,31307,2470],{},[1810,31309,1959],{},[895,31311,31312,31314,31316],{},[1810,31313,1959],{},[898,31315,6062],{"mathvariant":2057},[1810,31317,1812],{},[10554,31319,31320,31322,31324],{},[898,31321,2470],{},[1810,31323,1812],{},[895,31325,31326,31328,31330],{},[1810,31327,1959],{},[898,31329,6062],{"mathvariant":2057},[1810,31331,1812],{},[902,31333,31334],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F2} Q_2^{1\u002F2}"," platí",[724,31337,31338],{},[883,31339,31341],{"className":31340},[886],[888,31342,31343],{"xmlns":890},[892,31344,31345,31451],{},[895,31346,31347,31349,31351,31433,31435,31449],{},[1969,31348,11991],{},[1677,31350,1679],{},[2010,31352,31353,31393],{},[895,31354,31355,31363,31379],{},[2006,31356,31357],{"scriptlevel":2008,"displaystyle":1685},[2010,31358,31359,31361],{},[1810,31360,1959],{},[1810,31362,1812],{},[10554,31364,31365,31367,31369],{},[898,31366,2470],{},[1810,31368,1959],{},[895,31370,31371,31373,31375,31377],{},[1677,31372,1906],{},[1810,31374,1959],{},[898,31376,6062],{"mathvariant":2057},[1810,31378,1812],{},[10554,31380,31381,31383,31385],{},[898,31382,2470],{},[1810,31384,1812],{},[895,31386,31387,31389,31391],{},[1810,31388,1959],{},[898,31390,6062],{"mathvariant":2057},[1810,31392,1812],{},[895,31394,31395,31403,31417],{},[2006,31396,31397],{"scriptlevel":2008,"displaystyle":1685},[2010,31398,31399,31401],{},[1810,31400,1959],{},[1810,31402,1812],{},[10554,31404,31405,31407,31409],{},[898,31406,2470],{},[1810,31408,1959],{},[895,31410,31411,31413,31415],{},[1810,31412,1959],{},[898,31414,6062],{"mathvariant":2057},[1810,31416,1812],{},[10554,31418,31419,31421,31423],{},[898,31420,2470],{},[1810,31422,1812],{},[895,31424,31425,31427,31429,31431],{},[1677,31426,1906],{},[1810,31428,1959],{},[898,31430,6062],{"mathvariant":2057},[1810,31432,1812],{},[1677,31434,1679],{},[2010,31436,31437,31443],{},[1953,31438,31439,31441],{},[898,31440,2470],{},[1810,31442,1812],{},[1953,31444,31445,31447],{},[898,31446,2470],{},[1810,31448,1959],{},[898,31450,1656],{"mathvariant":2057},[902,31452,31453],{"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}.",[724,31455,31456,31457,2608,31502,31504,31505,31525,31526,31556,31557,1656],{},"Tedy ",[883,31458,31460],{"className":31459},[886],[888,31461,31462],{"xmlns":890},[892,31463,31464,31499],{},[895,31465,31466,31468,31470,31473,31475,31477,31479,31481,31489,31491],{},[1969,31467,11991],{},[1677,31469,1686],{"stretchy":1685},[1810,31471,31472],{},"300",[1677,31474,1967],{"separator":1966},[1810,31476,16500],{},[1677,31478,1692],{"stretchy":1685},[1677,31480,1679],{},[2006,31482,31483],{"scriptlevel":2008,"displaystyle":1685},[2010,31484,31485,31487],{},[1810,31486,16500],{},[1810,31488,31472],{},[1677,31490,1679],{},[2006,31492,31493],{"scriptlevel":2008,"displaystyle":1685},[2010,31494,31495,31497],{},[1810,31496,1909],{},[1810,31498,1854],{},[902,31500,31501],{"encoding":904},"\\text{MRCS}(300, 500) = \\tfrac{500}{300} = \\tfrac{5}{3}",[614,31503,10604],{}," zvýší-li spotřebitel nákup prvního zboží o 1 jednotku, musí snížit nákup druhého zboží přibližně o ",[883,31506,31508],{"className":31507},[886],[888,31509,31510],{"xmlns":890},[892,31511,31512,31522],{},[895,31513,31514],{},[2006,31515,31516],{"scriptlevel":2008,"displaystyle":1685},[2010,31517,31518,31520],{},[1810,31519,1909],{},[1810,31521,1854],{},[902,31523,31524],{"encoding":904},"\\tfrac{5}{3}"," jednotky, aby se užitečnost zachovala. Tato forma ",[883,31527,31529],{"className":31528},[886],[888,31530,31531],{"xmlns":890},[892,31532,31533,31553],{},[895,31534,31535,31537,31539,31545,31547],{},[1969,31536,11991],{},[1677,31538,1679],{},[1953,31540,31541,31543],{},[898,31542,2470],{},[1810,31544,1812],{},[898,31546,6062],{"mathvariant":2057},[1953,31548,31549,31551],{},[898,31550,2470],{},[1810,31552,1959],{},[902,31554,31555],{"encoding":904},"\\text{MRCS} = Q_2\u002FQ_1"," je typická pro symetrické Cobb-Douglasovy preference a vstupuje do optimalizace skrze podmínku ",[883,31558,31560],{"className":31559},[886],[888,31561,31562],{"xmlns":890},[892,31563,31564,31584],{},[895,31565,31566,31568,31570,31576,31578],{},[1969,31567,11991],{},[1677,31569,1679],{},[1953,31571,31572,31574],{},[898,31573,5325],{},[1810,31575,1959],{},[898,31577,6062],{"mathvariant":2057},[1953,31579,31580,31582],{},[898,31581,5325],{},[1810,31583,1812],{},[902,31585,29389],{"encoding":904},[115,31587,31589,31590],{"id":31588},"příklad-66-maximalizace-užitečnosti-pro-uq1q2u-q_1-q_2","Příklad 6.6 — maximalizace užitečnosti pro ",[883,31591,31593],{"className":31592},[886],[888,31594,31595],{"xmlns":890},[892,31596,31597,31615],{},[895,31598,31599,31601,31603,31609],{},[898,31600,900],{},[1677,31602,1679],{},[1953,31604,31605,31607],{},[898,31606,2470],{},[1810,31608,1959],{},[1953,31610,31611,31613],{},[898,31612,2470],{},[1810,31614,1812],{},[902,31616,31617],{"encoding":904},"U = Q_1 Q_2",[724,31619,31620,31621,1343,31667,1343,31691,1343,31715,31737],{},"Je dána ",[883,31622,31624],{"className":31623},[886],[888,31625,31626],{"xmlns":890},[892,31627,31628,31664],{},[895,31629,31630,31632,31634,31640,31642,31648,31650,31652,31658],{},[898,31631,900],{},[1677,31633,1686],{"stretchy":1685},[1953,31635,31636,31638],{},[898,31637,2470],{},[1810,31639,1959],{},[1677,31641,1967],{"separator":1966},[1953,31643,31644,31646],{},[898,31645,2470],{},[1810,31647,1812],{},[1677,31649,1692],{"stretchy":1685},[1677,31651,1679],{},[1953,31653,31654,31656],{},[898,31655,2470],{},[1810,31657,1959],{},[1953,31659,31660,31662],{},[898,31661,2470],{},[1810,31663,1812],{},[902,31665,31666],{"encoding":904},"U(Q_1, Q_2) = Q_1 Q_2",[883,31668,31670],{"className":31669},[886],[888,31671,31672],{"xmlns":890},[892,31673,31674,31688],{},[895,31675,31676,31684,31686],{},[10554,31677,31678,31680,31682],{},[898,31679,5325],{},[1810,31681,1959],{},[1677,31683,5742],{},[1677,31685,1679],{},[1810,31687,1812],{},[902,31689,31690],{"encoding":904},"P_1^* = 2",[883,31692,31694],{"className":31693},[886],[888,31695,31696],{"xmlns":890},[892,31697,31698,31712],{},[895,31699,31700,31708,31710],{},[10554,31701,31702,31704,31706],{},[898,31703,5325],{},[1810,31705,1812],{},[1677,31707,5742],{},[1677,31709,1679],{},[1810,31711,1909],{},[902,31713,31714],{"encoding":904},"P_2^* = 5",[883,31716,31718],{"className":31717},[886],[888,31719,31720],{"xmlns":890},[892,31721,31722,31734],{},[895,31723,31724,31730,31732],{},[1805,31725,31726,31728],{},[898,31727,10516],{},[1677,31729,5742],{},[1677,31731,1679],{},[1810,31733,2771],{},[902,31735,31736],{"encoding":904},"Y^* = 100",". Lagrangeova funkce:",[883,31739,31741],{"className":31740},[886],[888,31742,31743],{"xmlns":890,"display":29457},[892,31744,31745,31817],{},[895,31746,31747,31749,31751,31757,31759,31765,31767,31769,31771,31773,31779,31785,31787,31789,31791,31793,31795,31797,31803,31805,31807,31813,31815],{},[898,31748,11183],{"mathvariant":29939},[1677,31750,1686],{"stretchy":1685},[1953,31752,31753,31755],{},[898,31754,2470],{},[1810,31756,1959],{},[1677,31758,1967],{"separator":1966},[1953,31760,31761,31763],{},[898,31762,2470],{},[1810,31764,1812],{},[1677,31766,1967],{"separator":1966},[898,31768,17834],{},[1677,31770,1692],{"stretchy":1685},[1677,31772,1679],{},[1953,31774,31775,31777],{},[898,31776,2470],{},[1810,31778,1959],{},[1953,31780,31781,31783],{},[898,31782,2470],{},[1810,31784,1812],{},[1677,31786,1776],{},[898,31788,17834],{},[1677,31790,1686],{"stretchy":1685},[1810,31792,2771],{},[1677,31794,1906],{},[1810,31796,1812],{},[1953,31798,31799,31801],{},[898,31800,2470],{},[1810,31802,1959],{},[1677,31804,1906],{},[1810,31806,1909],{},[1953,31808,31809,31811],{},[898,31810,2470],{},[1810,31812,1812],{},[1677,31814,1692],{"stretchy":1685},[898,31816,1656],{"mathvariant":2057},[902,31818,31819],{"encoding":904},"\\mathcal{L}(Q_1, Q_2, \\lambda) = Q_1 Q_2 + \\lambda(100 - 2 Q_1 - 5 Q_2).",[724,31821,31822],{},"Soustava:",[883,31824,31826],{"className":31825},[886],[888,31827,31828],{"xmlns":890,"display":29457},[892,31829,31830,31942],{},[22145,31831,31832,31866,31900],{"rowspacing":22147,"columnalign":22148,"columnspacing":2058},[22150,31833,31834,31852],{},[22153,31835,31836],{},[2006,31837,31838],{"scriptlevel":2008,"displaystyle":1966},[895,31839,31840,31846,31848,31850],{},[1953,31841,31842,31844],{},[898,31843,2470],{},[1810,31845,1812],{},[1677,31847,1906],{},[1810,31849,1812],{},[898,31851,17834],{},[22153,31853,31854],{},[2006,31855,31856],{"scriptlevel":2008,"displaystyle":1966},[895,31857,31858,31860,31862,31864],{},[895,31859],{},[1677,31861,1679],{},[1810,31863,2008],{},[1677,31865,1967],{"separator":1966},[22150,31867,31868,31886],{},[22153,31869,31870],{},[2006,31871,31872],{"scriptlevel":2008,"displaystyle":1966},[895,31873,31874,31880,31882,31884],{},[1953,31875,31876,31878],{},[898,31877,2470],{},[1810,31879,1959],{},[1677,31881,1906],{},[1810,31883,1909],{},[898,31885,17834],{},[22153,31887,31888],{},[2006,31889,31890],{"scriptlevel":2008,"displaystyle":1966},[895,31891,31892,31894,31896,31898],{},[895,31893],{},[1677,31895,1679],{},[1810,31897,2008],{},[1677,31899,1967],{"separator":1966},[22150,31901,31902,31930],{},[22153,31903,31904],{},[2006,31905,31906],{"scriptlevel":2008,"displaystyle":1966},[895,31907,31908,31910,31912,31914,31920,31922,31924],{},[1810,31909,2771],{},[1677,31911,1906],{},[1810,31913,1812],{},[1953,31915,31916,31918],{},[898,31917,2470],{},[1810,31919,1959],{},[1677,31921,1906],{},[1810,31923,1909],{},[1953,31925,31926,31928],{},[898,31927,2470],{},[1810,31929,1812],{},[22153,31931,31932],{},[2006,31933,31934],{"scriptlevel":2008,"displaystyle":1966},[895,31935,31936,31938,31940],{},[895,31937],{},[1677,31939,1679],{},[1810,31941,13850],{},[902,31943,31944],{"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}",[724,31946,31947,31948,1343,31972,31996,31997,6977,32037,32055,32056,32106,32107,1656],{},"Z prvních dvou rovnic ",[883,31949,31951],{"className":31950},[886],[888,31952,31953],{"xmlns":890},[892,31954,31955,31969],{},[895,31956,31957,31963,31965,31967],{},[1953,31958,31959,31961],{},[898,31960,2470],{},[1810,31962,1812],{},[1677,31964,1679],{},[1810,31966,1812],{},[898,31968,17834],{},[902,31970,31971],{"encoding":904},"Q_2 = 2\\lambda",[883,31973,31975],{"className":31974},[886],[888,31976,31977],{"xmlns":890},[892,31978,31979,31993],{},[895,31980,31981,31987,31989,31991],{},[1953,31982,31983,31985],{},[898,31984,2470],{},[1810,31986,1959],{},[1677,31988,1679],{},[1810,31990,1909],{},[898,31992,17834],{},[902,31994,31995],{"encoding":904},"Q_1 = 5\\lambda","; dosazením do třetí ",[883,31998,32000],{"className":31999},[886],[888,32001,32002],{"xmlns":890},[892,32003,32004,32034],{},[895,32005,32006,32008,32010,32012,32014,32016,32018,32020,32022,32024,32026,32028,32030,32032],{},[1810,32007,2771],{},[1677,32009,1679],{},[1810,32011,1812],{},[1677,32013,2858],{},[1810,32015,1909],{},[898,32017,17834],{},[1677,32019,1776],{},[1810,32021,1909],{},[1677,32023,2858],{},[1810,32025,1812],{},[898,32027,17834],{},[1677,32029,1679],{},[1810,32031,10423],{},[898,32033,17834],{},[902,32035,32036],{"encoding":904},"100 = 2 \\cdot 5\\lambda + 5 \\cdot 2\\lambda = 20\\lambda",[883,32038,32040],{"className":32039},[886],[888,32041,32042],{"xmlns":890},[892,32043,32044,32052],{},[895,32045,32046,32048,32050],{},[898,32047,17834],{},[1677,32049,1679],{},[1810,32051,1909],{},[902,32053,32054],{"encoding":904},"\\lambda = 5",". Odtud ",[38,32057,32058,1343,32082],{},[883,32059,32061],{"className":32060},[886],[888,32062,32063],{"xmlns":890},[892,32064,32065,32079],{},[895,32066,32067,32075,32077],{},[10554,32068,32069,32071,32073],{},[898,32070,2470],{},[1810,32072,1959],{},[1677,32074,5742],{},[1677,32076,1679],{},[1810,32078,6392],{},[902,32080,32081],{"encoding":904},"Q_1^* = 25",[883,32083,32085],{"className":32084},[886],[888,32086,32087],{"xmlns":890},[892,32088,32089,32103],{},[895,32090,32091,32099,32101],{},[10554,32092,32093,32095,32097],{},[898,32094,2470],{},[1810,32096,1812],{},[1677,32098,5742],{},[1677,32100,1679],{},[1810,32102,2544],{},[902,32104,32105],{"encoding":904},"Q_2^* = 10",", maximální užitečnost ",[883,32108,32110],{"className":32109},[886],[888,32111,32112],{"xmlns":890},[892,32113,32114,32135],{},[895,32115,32116,32122,32124,32126,32128,32130,32132],{},[1805,32117,32118,32120],{},[898,32119,900],{},[1677,32121,5742],{},[1677,32123,1679],{},[1810,32125,6392],{},[1677,32127,2858],{},[1810,32129,2544],{},[1677,32131,1679],{},[1810,32133,32134],{},"250",[902,32136,32137],{"encoding":904},"U^* = 25 \\cdot 10 = 250",[724,32139,32140],{},[614,32141,32142,32143,29528,32181,5272,32205,32229,32230,32260,32261,32285,32286,32308,32309,1656],{},"Obrázek 6.8 — Rozpočtová přímka ",[883,32144,32146],{"className":32145},[886],[888,32147,32148],{"xmlns":890},[892,32149,32150,32178],{},[895,32151,32152,32154,32156,32158,32164,32166,32168,32174,32176],{},[1810,32153,2771],{},[1677,32155,1906],{},[1810,32157,1812],{},[1953,32159,32160,32162],{},[898,32161,2470],{},[1810,32163,1959],{},[1677,32165,1906],{},[1810,32167,1909],{},[1953,32169,32170,32172],{},[898,32171,2470],{},[1810,32173,1812],{},[1677,32175,1679],{},[1810,32177,2008],{},[902,32179,32180],{"encoding":904},"100 - 2 Q_1 - 5 Q_2 = 0",[883,32182,32184],{"className":32183},[886],[888,32185,32186],{"xmlns":890},[892,32187,32188,32202],{},[895,32189,32190,32192,32194,32196,32198,32200],{},[898,32191,5643],{},[1677,32193,2167],{"stretchy":1685},[1810,32195,2008],{},[1677,32197,1967],{"separator":1966},[1810,32199,10423],{},[1677,32201,2182],{"stretchy":1685},[902,32203,32204],{"encoding":904},"A[0, 20]",[883,32206,32208],{"className":32207},[886],[888,32209,32210],{"xmlns":890},[892,32211,32212,32226],{},[895,32213,32214,32216,32218,32220,32222,32224],{},[898,32215,24644],{},[1677,32217,2167],{"stretchy":1685},[1810,32219,2801],{},[1677,32221,1967],{"separator":1966},[1810,32223,2008],{},[1677,32225,2182],{"stretchy":1685},[902,32227,32228],{"encoding":904},"B[50, 0]","; hyperbolická indiferenční křivka ",[883,32231,32233],{"className":32232},[886],[888,32234,32235],{"xmlns":890},[892,32236,32237,32257],{},[895,32238,32239,32245,32247,32249,32251],{},[1953,32240,32241,32243],{},[898,32242,2470],{},[1810,32244,1812],{},[1677,32246,1679],{},[1810,32248,32134],{},[898,32250,6062],{"mathvariant":2057},[1953,32252,32253,32255],{},[898,32254,2470],{},[1810,32256,1959],{},[902,32258,32259],{"encoding":904},"Q_2 = 250\u002FQ_1"," se dotýká rozpočtové přímky v bodě ",[883,32262,32264],{"className":32263},[886],[888,32265,32266],{"xmlns":890},[892,32267,32268,32282],{},[895,32269,32270,32272,32274,32276,32278,32280],{},[898,32271,5640],{},[1677,32273,2167],{"stretchy":1685},[1810,32275,6392],{},[1677,32277,1967],{"separator":1966},[1810,32279,2544],{},[1677,32281,2182],{"stretchy":1685},[902,32283,32284],{"encoding":904},"E[25, 10]",". Sklon přímky ",[883,32287,32289],{"className":32288},[886],[888,32290,32291],{"xmlns":890},[892,32292,32293,32305],{},[895,32294,32295,32297],{},[1677,32296,1906],{},[2006,32298,32299],{"scriptlevel":2008,"displaystyle":1685},[2010,32300,32301,32303],{},[1810,32302,1812],{},[1810,32304,1909],{},[902,32306,32307],{"encoding":904},"-\\tfrac{2}{5}"," odpovídá ",[883,32310,32312],{"className":32311},[886],[888,32313,32314],{"xmlns":890},[892,32315,32316,32356],{},[895,32317,32318,32320,32322,32324,32326,32328,32330,32332,32334,32336,32344,32346,32348],{},[1677,32319,1906],{},[1969,32321,11991],{},[1677,32323,1686],{"stretchy":1685},[1810,32325,6392],{},[1677,32327,1967],{"separator":1966},[1810,32329,2544],{},[1677,32331,1692],{"stretchy":1685},[1677,32333,1679],{},[1677,32335,1906],{},[2006,32337,32338],{"scriptlevel":2008,"displaystyle":1685},[2010,32339,32340,32342],{},[1810,32341,2544],{},[1810,32343,6392],{},[1677,32345,1679],{},[1677,32347,1906],{},[2006,32349,32350],{"scriptlevel":2008,"displaystyle":1685},[2010,32351,32352,32354],{},[1810,32353,1812],{},[1810,32355,1909],{},[902,32357,32358],{"encoding":904},"-\\text{MRCS}(25, 10) = -\\tfrac{10}{25} = -\\tfrac{2}{5}",[115,32360,32362],{"id":32361},"funkce-poptávky-spotřebitele-marshallova","Funkce poptávky spotřebitele (Marshallova)",[724,32364,32365,32366,30394,32396,32399,32400,2385],{},"Považujeme-li v úloze ",[883,32367,32369],{"className":32368},[886],[888,32370,32371],{"xmlns":890},[892,32372,32373,32393],{},[895,32374,32375,32381,32383,32389,32391],{},[1953,32376,32377,32379],{},[898,32378,5325],{},[1810,32380,1959],{},[1677,32382,1967],{"separator":1966},[1953,32384,32385,32387],{},[898,32386,5325],{},[1810,32388,1812],{},[1677,32390,1967],{"separator":1966},[898,32392,10516],{},[902,32394,32395],{"encoding":904},"P_1, P_2, Y",[38,32397,32398],{},"parametry"," (nikoli čísla), dostáváme z první řádové podmínky ",[38,32401,32402],{},"Marshallovy poptávkové funkce",[883,32404,32406],{"className":32405},[886],[888,32407,32408],{"xmlns":890,"display":29457},[892,32409,32410,32505],{},[22145,32411,32412],{"width":29462},[22150,32413,32414,32416,32498,32500],{},[22153,32415],{"width":29467},[22153,32417,32418],{},[895,32419,32420,32426,32428,32434,32436,32442,32444,32450,32452,32454,32456,32458,32460,32466,32468,32474,32476,32482,32484,32490,32492,32494,32496],{},[1953,32421,32422,32424],{},[898,32423,2470],{},[1810,32425,1959],{},[1677,32427,1679],{},[1953,32429,32430,32432],{},[898,32431,5571],{},[1810,32433,1959],{},[1677,32435,1686],{"stretchy":1685},[1953,32437,32438,32440],{},[898,32439,5325],{},[1810,32441,1959],{},[1677,32443,1967],{"separator":1966},[1953,32445,32446,32448],{},[898,32447,5325],{},[1810,32449,1812],{},[1677,32451,1967],{"separator":1966},[898,32453,10516],{},[1677,32455,1692],{"stretchy":1685},[1677,32457,1967],{"separator":1966},[7266,32459],{"width":16674},[1953,32461,32462,32464],{},[898,32463,2470],{},[1810,32465,1812],{},[1677,32467,1679],{},[1953,32469,32470,32472],{},[898,32471,5571],{},[1810,32473,1812],{},[1677,32475,1686],{"stretchy":1685},[1953,32477,32478,32480],{},[898,32479,5325],{},[1810,32481,1959],{},[1677,32483,1967],{"separator":1966},[1953,32485,32486,32488],{},[898,32487,5325],{},[1810,32489,1812],{},[1677,32491,1967],{"separator":1966},[898,32493,10516],{},[1677,32495,1692],{"stretchy":1685},[1677,32497,1967],{"separator":1966},[22153,32499],{"width":29467},[22153,32501,32502],{},[1969,32503,32504],{},"(6.15)",[902,32506,32507],{"encoding":904},"Q_1 = D_1(P_1, P_2, Y), \\quad Q_2 = D_2(P_1, P_2, Y), \\tag{6.15}",[883,32509,32511],{"className":32510},[886],[888,32512,32513],{"xmlns":890,"display":29457},[892,32514,32515,32562],{},[22145,32516,32517],{"width":29462},[22150,32518,32519,32521,32555,32557],{},[22153,32520],{"width":29467},[22153,32522,32523],{},[895,32524,32525,32527,32529,32531,32533,32539,32541,32547,32549,32551,32553],{},[898,32526,17834],{},[1677,32528,1679],{},[898,32530,17834],{},[1677,32532,1686],{"stretchy":1685},[1953,32534,32535,32537],{},[898,32536,5325],{},[1810,32538,1959],{},[1677,32540,1967],{"separator":1966},[1953,32542,32543,32545],{},[898,32544,5325],{},[1810,32546,1812],{},[1677,32548,1967],{"separator":1966},[898,32550,10516],{},[1677,32552,1692],{"stretchy":1685},[898,32554,1656],{"mathvariant":2057},[22153,32556],{"width":29467},[22153,32558,32559],{},[1969,32560,32561],{},"(6.16)",[902,32563,32564],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, Y). \\tag{6.16}",[724,32566,32567,32597,32598,32664],{},[38,32568,32569,32570,1656],{},"Odvození pro ",[883,32571,32573],{"className":32572},[886],[888,32574,32575],{"xmlns":890},[892,32576,32577,32595],{},[895,32578,32579,32581,32583,32589],{},[898,32580,900],{},[1677,32582,1679],{},[1953,32584,32585,32587],{},[898,32586,2470],{},[1810,32588,1959],{},[1953,32590,32591,32593],{},[898,32592,2470],{},[1810,32594,1812],{},[902,32596,31617],{"encoding":904}," Lagrangeova funkce ",[883,32599,32601],{"className":32600},[886],[888,32602,32603],{"xmlns":890},[892,32604,32605,32661],{},[895,32606,32607,32609,32611,32617,32623,32625,32627,32629,32631,32633,32639,32645,32647,32653,32659],{},[898,32608,11183],{"mathvariant":29939},[1677,32610,1679],{},[1953,32612,32613,32615],{},[898,32614,2470],{},[1810,32616,1959],{},[1953,32618,32619,32621],{},[898,32620,2470],{},[1810,32622,1812],{},[1677,32624,1776],{},[898,32626,17834],{},[1677,32628,1686],{"stretchy":1685},[898,32630,10516],{},[1677,32632,1906],{},[1953,32634,32635,32637],{},[898,32636,5325],{},[1810,32638,1959],{},[1953,32640,32641,32643],{},[898,32642,2470],{},[1810,32644,1959],{},[1677,32646,1906],{},[1953,32648,32649,32651],{},[898,32650,5325],{},[1810,32652,1812],{},[1953,32654,32655,32657],{},[898,32656,2470],{},[1810,32658,1812],{},[1677,32660,1692],{"stretchy":1685},[902,32662,32663],{"encoding":904},"\\mathcal{L} = Q_1 Q_2 + \\lambda(Y - P_1 Q_1 - P_2 Q_2)"," dává soustavu",[883,32666,32668],{"className":32667},[886],[888,32669,32670],{"xmlns":890,"display":29457},[892,32671,32672,32839],{},[22145,32673,32674],{"width":29462},[22150,32675,32676,32678,32832,32834],{},[22153,32677],{"width":29467},[22153,32679,32680],{},[22145,32681,32682,32728,32774],{"rowspacing":22147,"columnalign":22148,"columnspacing":2058},[22150,32683,32684,32696],{},[22153,32685,32686],{},[2006,32687,32688],{"scriptlevel":2008,"displaystyle":1966},[10554,32689,32690,32692,32694],{},[898,32691,11183],{"mathvariant":29939},[1810,32693,1959],{},[1677,32695,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[22153,32697,32698],{},[2006,32699,32700],{"scriptlevel":2008,"displaystyle":1966},[895,32701,32702,32704,32706,32712,32714,32716,32722,32724,32726],{},[895,32703],{},[1677,32705,1679],{},[1953,32707,32708,32710],{},[898,32709,2470],{},[1810,32711,1812],{},[1677,32713,1906],{},[898,32715,17834],{},[1953,32717,32718,32720],{},[898,32719,5325],{},[1810,32721,1959],{},[1677,32723,1679],{},[1810,32725,2008],{},[1677,32727,1967],{"separator":1966},[22150,32729,32730,32742],{},[22153,32731,32732],{},[2006,32733,32734],{"scriptlevel":2008,"displaystyle":1966},[10554,32735,32736,32738,32740],{},[898,32737,11183],{"mathvariant":29939},[1810,32739,1812],{},[1677,32741,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[22153,32743,32744],{},[2006,32745,32746],{"scriptlevel":2008,"displaystyle":1966},[895,32747,32748,32750,32752,32758,32760,32762,32768,32770,32772],{},[895,32749],{},[1677,32751,1679],{},[1953,32753,32754,32756],{},[898,32755,2470],{},[1810,32757,1959],{},[1677,32759,1906],{},[898,32761,17834],{},[1953,32763,32764,32766],{},[898,32765,5325],{},[1810,32767,1812],{},[1677,32769,1679],{},[1810,32771,2008],{},[1677,32773,1967],{"separator":1966},[22150,32775,32776,32788],{},[22153,32777,32778],{},[2006,32779,32780],{"scriptlevel":2008,"displaystyle":1966},[10554,32781,32782,32784,32786],{},[898,32783,11183],{"mathvariant":29939},[898,32785,17834],{},[1677,32787,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[22153,32789,32790],{},[2006,32791,32792],{"scriptlevel":2008,"displaystyle":1966},[895,32793,32794,32796,32798,32800,32802,32808,32814,32816,32822,32828,32830],{},[895,32795],{},[1677,32797,1679],{},[898,32799,10516],{},[1677,32801,1906],{},[1953,32803,32804,32806],{},[898,32805,5325],{},[1810,32807,1959],{},[1953,32809,32810,32812],{},[898,32811,2470],{},[1810,32813,1959],{},[1677,32815,1906],{},[1953,32817,32818,32820],{},[898,32819,5325],{},[1810,32821,1812],{},[1953,32823,32824,32826],{},[898,32825,2470],{},[1810,32827,1812],{},[1677,32829,1679],{},[1810,32831,13850],{},[22153,32833],{"width":29467},[22153,32835,32836],{},[1969,32837,32838],{},"(6.17)",[902,32840,32841],{"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}",[724,32843,32844,32845,32873,32874,32902,32903,32971],{},"Z prvních dvou: ",[883,32846,32848],{"className":32847},[886],[888,32849,32850],{"xmlns":890},[892,32851,32852,32870],{},[895,32853,32854,32860,32862,32868],{},[1953,32855,32856,32858],{},[898,32857,2470],{},[1810,32859,1812],{},[1677,32861,1679],{},[1953,32863,32864,32866],{},[898,32865,5325],{},[1810,32867,1959],{},[898,32869,17834],{},[902,32871,32872],{"encoding":904},"Q_2 = P_1 \\lambda"," (6.18), ",[883,32875,32877],{"className":32876},[886],[888,32878,32879],{"xmlns":890},[892,32880,32881,32899],{},[895,32882,32883,32889,32891,32897],{},[1953,32884,32885,32887],{},[898,32886,2470],{},[1810,32888,1959],{},[1677,32890,1679],{},[1953,32892,32893,32895],{},[898,32894,5325],{},[1810,32896,1812],{},[898,32898,17834],{},[902,32900,32901],{"encoding":904},"Q_1 = P_2 \\lambda"," (6.19). Dosazením do třetí ",[883,32904,32906],{"className":32905},[886],[888,32907,32908],{"xmlns":890},[892,32909,32910,32968],{},[895,32911,32912,32914,32916,32922,32924,32930,32932,32934,32940,32942,32948,32950,32952,32954,32960,32966],{},[898,32913,10516],{},[1677,32915,1679],{},[1953,32917,32918,32920],{},[898,32919,5325],{},[1810,32921,1959],{},[1677,32923,2858],{},[1953,32925,32926,32928],{},[898,32927,5325],{},[1810,32929,1812],{},[898,32931,17834],{},[1677,32933,1776],{},[1953,32935,32936,32938],{},[898,32937,5325],{},[1810,32939,1812],{},[1677,32941,2858],{},[1953,32943,32944,32946],{},[898,32945,5325],{},[1810,32947,1959],{},[898,32949,17834],{},[1677,32951,1679],{},[1810,32953,1812],{},[1953,32955,32956,32958],{},[898,32957,5325],{},[1810,32959,1959],{},[1953,32961,32962,32964],{},[898,32963,5325],{},[1810,32965,1812],{},[898,32967,17834],{},[902,32969,32970],{"encoding":904},"Y = P_1 \\cdot P_2 \\lambda + P_2 \\cdot P_1 \\lambda = 2 P_1 P_2 \\lambda",", odtud",[883,32973,32975],{"className":32974},[886],[888,32976,32977],{"xmlns":890,"display":29457},[892,32978,32979,33022],{},[22145,32980,32981],{"width":29462},[22150,32982,32983,32985,33015,33017],{},[22153,32984],{"width":29467},[22153,32986,32987],{},[895,32988,32989,32991,32993,33013],{},[898,32990,17834],{},[1677,32992,1679],{},[2010,32994,32995,32997],{},[898,32996,10516],{},[895,32998,32999,33001,33007],{},[1810,33000,1812],{},[1953,33002,33003,33005],{},[898,33004,5325],{},[1810,33006,1959],{},[1953,33008,33009,33011],{},[898,33010,5325],{},[1810,33012,1812],{},[898,33014,1656],{"mathvariant":2057},[22153,33016],{"width":29467},[22153,33018,33019],{},[1969,33020,33021],{},"(6.20)",[902,33023,33024],{"encoding":904},"\\lambda = \\frac{Y}{2 P_1 P_2}. \\tag{6.20}",[724,33026,33027],{},"Zpětně:",[883,33029,33031],{"className":33030},[886],[888,33032,33033],{"xmlns":890,"display":29457},[892,33034,33035,33112],{},[22145,33036,33037],{"width":29462},[22150,33038,33039,33041,33105,33107],{},[22153,33040],{"width":29467},[22153,33042,33043],{},[14222,33044,33045],{"notation":14224},[2006,33046,33047],{"scriptlevel":2008,"displaystyle":1685},[2006,33048,33049],{"scriptlevel":2008,"displaystyle":1685},[2006,33050,33051],{"scriptlevel":2008,"displaystyle":1966},[895,33052,33053,33055,33061,33063,33077,33079,33081,33087,33089,33103],{},[1969,33054,5372],{},[1953,33056,33057,33059],{},[898,33058,2470],{},[1810,33060,1959],{},[1677,33062,1679],{},[2010,33064,33065,33067],{},[898,33066,10516],{},[895,33068,33069,33071],{},[1810,33070,1812],{},[1953,33072,33073,33075],{},[898,33074,5325],{},[1810,33076,1959],{},[1677,33078,1967],{"separator":1966},[7266,33080],{"width":16674},[1953,33082,33083,33085],{},[898,33084,2470],{},[1810,33086,1812],{},[1677,33088,1679],{},[2010,33090,33091,33093],{},[898,33092,10516],{},[895,33094,33095,33097],{},[1810,33096,1812],{},[1953,33098,33099,33101],{},[898,33100,5325],{},[1810,33102,1812],{},[1969,33104,5372],{},[22153,33106],{"width":29467},[22153,33108,33109],{},[1969,33110,33111],{},"(6.21)",[902,33113,33114],{"encoding":904},"\\boxed{\\; Q_1 = \\frac{Y}{2 P_1}, \\quad Q_2 = \\frac{Y}{2 P_2} \\;} \\tag{6.21}",[198,33116,33118],{"id":33117},"engelova-funkce","Engelova funkce",[724,33120,11051,33121,33124,33125,33128,33129,21258,33146,1343,33176,33206,33207,33241,33242,1343,33268,33294],{},[38,33122,33123],{},"pevné ceny"," a proměnný důchod se Marshallova poptávka stává ",[38,33126,33127],{},"Engelovou funkcí",": pro ",[883,33130,33132],{"className":33131},[886],[888,33133,33134],{"xmlns":890},[892,33135,33136,33144],{},[895,33137,33138,33140,33142],{},[898,33139,10516],{},[1677,33141,1679],{},[1810,33143,2771],{},[902,33145,21710],{"encoding":904},[883,33147,33149],{"className":33148},[886],[888,33150,33151],{"xmlns":890},[892,33152,33153,33173],{},[895,33154,33155,33161,33163,33165,33167],{},[1953,33156,33157,33159],{},[898,33158,2470],{},[1810,33160,1959],{},[1677,33162,1679],{},[1810,33164,2801],{},[898,33166,6062],{"mathvariant":2057},[1953,33168,33169,33171],{},[898,33170,5325],{},[1810,33172,1959],{},[902,33174,33175],{"encoding":904},"Q_1 = 50\u002FP_1",[883,33177,33179],{"className":33178},[886],[888,33180,33181],{"xmlns":890},[892,33182,33183,33203],{},[895,33184,33185,33191,33193,33195,33197],{},[1953,33186,33187,33189],{},[898,33188,2470],{},[1810,33190,1812],{},[1677,33192,1679],{},[1810,33194,2801],{},[898,33196,6062],{"mathvariant":2057},[1953,33198,33199,33201],{},[898,33200,5325],{},[1810,33202,1812],{},[902,33204,33205],{"encoding":904},"Q_2 = 50\u002FP_2",". Pro pevné ceny ",[883,33208,33210],{"className":33209},[886],[888,33211,33212],{"xmlns":890},[892,33213,33214,33238],{},[895,33215,33216,33222,33224,33226,33228,33234,33236],{},[1953,33217,33218,33220],{},[898,33219,5325],{},[1810,33221,1959],{},[1677,33223,1679],{},[1810,33225,2544],{},[1677,33227,1967],{"separator":1966},[1953,33229,33230,33232],{},[898,33231,5325],{},[1810,33233,1812],{},[1677,33235,1679],{},[1810,33237,10423],{},[902,33239,33240],{"encoding":904},"P_1 = 10, P_2 = 20"," dostáváme Engelovy funkce ",[883,33243,33245],{"className":33244},[886],[888,33246,33247],{"xmlns":890},[892,33248,33249,33265],{},[895,33250,33251,33257,33259,33261,33263],{},[1953,33252,33253,33255],{},[898,33254,2470],{},[1810,33256,1959],{},[1677,33258,1679],{},[898,33260,10516],{},[898,33262,6062],{"mathvariant":2057},[1810,33264,10423],{},[902,33266,33267],{"encoding":904},"Q_1 = Y\u002F20",[883,33269,33271],{"className":33270},[886],[888,33272,33273],{"xmlns":890},[892,33274,33275,33291],{},[895,33276,33277,33283,33285,33287,33289],{},[1953,33278,33279,33281],{},[898,33280,2470],{},[1810,33282,1812],{},[1677,33284,1679],{},[898,33286,10516],{},[898,33288,6062],{"mathvariant":2057},[1810,33290,6599],{},[902,33292,33293],{"encoding":904},"Q_2 = Y\u002F40"," — lineární závislost spotřebovaného množství na důchodu.",[115,33296,33298],{"id":33297},"duální-úloha-minimalizace-výdajů","Duální úloha — minimalizace výdajů",[724,33300,33301],{},"Výdaje spotřebitele jsou",[883,33303,33305],{"className":33304},[886],[888,33306,33307],{"xmlns":890,"display":29457},[892,33308,33309,33384],{},[22145,33310,33311],{"width":29462},[22150,33312,33313,33315,33377,33379],{},[22153,33314],{"width":29467},[22153,33316,33317],{},[895,33318,33319,33321,33323,33325,33327,33333,33335,33341,33343,33345,33353,33359,33361,33369,33375],{},[898,33320,5640],{},[1677,33322,1679],{},[898,33324,5640],{},[1677,33326,1686],{"stretchy":1685},[1953,33328,33329,33331],{},[898,33330,2470],{},[1810,33332,1959],{},[1677,33334,1967],{"separator":1966},[1953,33336,33337,33339],{},[898,33338,2470],{},[1810,33340,1812],{},[1677,33342,1692],{"stretchy":1685},[1677,33344,1679],{},[10554,33346,33347,33349,33351],{},[898,33348,5325],{},[1810,33350,1959],{},[1677,33352,5742],{},[1953,33354,33355,33357],{},[898,33356,2470],{},[1810,33358,1959],{},[1677,33360,1776],{},[10554,33362,33363,33365,33367],{},[898,33364,5325],{},[1810,33366,1812],{},[1677,33368,5742],{},[1953,33370,33371,33373],{},[898,33372,2470],{},[1810,33374,1812],{},[1677,33376,1967],{"separator":1966},[22153,33378],{"width":29467},[22153,33380,33381],{},[1969,33382,33383],{},"(6.22)",[902,33385,33386],{"encoding":904},"E = E(Q_1, Q_2) = P_1^* Q_1 + P_2^* Q_2, \\tag{6.22}",[724,33388,33389],{},"a je pevně zadána hladina užitečnosti",[883,33391,33393],{"className":33392},[886],[888,33394,33395],{"xmlns":890,"display":29457},[892,33396,33397,33444],{},[22145,33398,33399],{"width":29462},[22150,33400,33401,33403,33437,33439],{},[22153,33402],{"width":29467},[22153,33404,33405],{},[895,33406,33407,33413,33415,33417,33419,33425,33427,33433,33435],{},[1805,33408,33409,33411],{},[898,33410,900],{},[1677,33412,5742],{},[1677,33414,1679],{},[898,33416,900],{},[1677,33418,1686],{"stretchy":1685},[1953,33420,33421,33423],{},[898,33422,2470],{},[1810,33424,1959],{},[1677,33426,1967],{"separator":1966},[1953,33428,33429,33431],{},[898,33430,2470],{},[1810,33432,1812],{},[1677,33434,1692],{"stretchy":1685},[898,33436,1656],{"mathvariant":2057},[22153,33438],{"width":29467},[22153,33440,33441],{},[1969,33442,33443],{},"(6.23)",[902,33445,33446],{"encoding":904},"U^* = U(Q_1, Q_2). \\tag{6.23}",[724,33448,33449,33452,33453,33485,33486,1656],{},[38,33450,33451],{},"Úlohou o minimalizaci výdajů"," je najít minimum ",[883,33454,33456],{"className":33455},[886],[888,33457,33458],{"xmlns":890},[892,33459,33460,33482],{},[895,33461,33462,33464,33466,33472,33474,33480],{},[898,33463,5640],{},[1677,33465,1686],{"stretchy":1685},[1953,33467,33468,33470],{},[898,33469,2470],{},[1810,33471,1959],{},[1677,33473,1967],{"separator":1966},[1953,33475,33476,33478],{},[898,33477,2470],{},[1810,33479,1812],{},[1677,33481,1692],{"stretchy":1685},[902,33483,33484],{"encoding":904},"E(Q_1, Q_2)"," vázané podmínkou (6.23) ve tvaru ",[883,33487,33489],{"className":33488},[886],[888,33490,33491],{"xmlns":890},[892,33492,33493,33549],{},[895,33494,33495,33497,33499,33505,33507,33513,33515,33517,33523,33525,33527,33529,33535,33537,33543,33545,33547],{},[898,33496,12429],{},[1677,33498,1686],{"stretchy":1685},[1953,33500,33501,33503],{},[898,33502,2470],{},[1810,33504,1959],{},[1677,33506,1967],{"separator":1966},[1953,33508,33509,33511],{},[898,33510,2470],{},[1810,33512,1812],{},[1677,33514,1692],{"stretchy":1685},[1677,33516,1679],{},[1805,33518,33519,33521],{},[898,33520,900],{},[1677,33522,5742],{},[1677,33524,1906],{},[898,33526,900],{},[1677,33528,1686],{"stretchy":1685},[1953,33530,33531,33533],{},[898,33532,2470],{},[1810,33534,1959],{},[1677,33536,1967],{"separator":1966},[1953,33538,33539,33541],{},[898,33540,2470],{},[1810,33542,1812],{},[1677,33544,1692],{"stretchy":1685},[1677,33546,1679],{},[1810,33548,2008],{},[902,33550,33551],{"encoding":904},"g(Q_1, Q_2) = U^* - U(Q_1, Q_2) = 0",[198,33553,33555],{"id":33554},"lagrangeova-funkce","Lagrangeova funkce",[883,33557,33559],{"className":33558},[886],[888,33560,33561],{"xmlns":890,"display":29457},[892,33562,33563,33674],{},[22145,33564,33565],{"width":29462},[22150,33566,33567,33569,33667,33669],{},[22153,33568],{"width":29467},[22153,33570,33571],{},[895,33572,33573,33575,33577,33583,33585,33591,33593,33595,33597,33599,33607,33613,33615,33623,33629,33631,33633,33635,33641,33643,33645,33647,33653,33655,33661,33663,33665],{},[898,33574,11183],{"mathvariant":29939},[1677,33576,1686],{"stretchy":1685},[1953,33578,33579,33581],{},[898,33580,2470],{},[1810,33582,1959],{},[1677,33584,1967],{"separator":1966},[1953,33586,33587,33589],{},[898,33588,2470],{},[1810,33590,1812],{},[1677,33592,1967],{"separator":1966},[898,33594,17834],{},[1677,33596,1692],{"stretchy":1685},[1677,33598,1679],{},[10554,33600,33601,33603,33605],{},[898,33602,5325],{},[1810,33604,1959],{},[1677,33606,5742],{},[1953,33608,33609,33611],{},[898,33610,2470],{},[1810,33612,1959],{},[1677,33614,1776],{},[10554,33616,33617,33619,33621],{},[898,33618,5325],{},[1810,33620,1812],{},[1677,33622,5742],{},[1953,33624,33625,33627],{},[898,33626,2470],{},[1810,33628,1812],{},[1677,33630,1776],{},[898,33632,17834],{},[1677,33634,1686],{"stretchy":1685},[1805,33636,33637,33639],{},[898,33638,900],{},[1677,33640,5742],{},[1677,33642,1906],{},[898,33644,900],{},[1677,33646,1686],{"stretchy":1685},[1953,33648,33649,33651],{},[898,33650,2470],{},[1810,33652,1959],{},[1677,33654,1967],{"separator":1966},[1953,33656,33657,33659],{},[898,33658,2470],{},[1810,33660,1812],{},[1677,33662,1692],{"stretchy":1685},[1677,33664,1692],{"stretchy":1685},[898,33666,1656],{"mathvariant":2057},[22153,33668],{"width":29467},[22153,33670,33671],{},[1969,33672,33673],{},"(6.24)",[902,33675,33676],{"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}",[724,33678,33679],{},"Soustava podmínek prvního řádu:",[883,33681,33683],{"className":33682},[886],[888,33684,33685],{"xmlns":890,"display":29457},[892,33686,33687,33860],{},[22145,33688,33689],{"width":29462},[22150,33690,33691,33693,33853,33855],{},[22153,33692],{"width":29467},[22153,33694,33695],{},[22145,33696,33697,33747,33797],{"rowspacing":22147,"columnalign":22148,"columnspacing":2058},[22150,33698,33699,33711],{},[22153,33700,33701],{},[2006,33702,33703],{"scriptlevel":2008,"displaystyle":1966},[10554,33704,33705,33707,33709],{},[898,33706,11183],{"mathvariant":29939},[1810,33708,1959],{},[1677,33710,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[22153,33712,33713],{},[2006,33714,33715],{"scriptlevel":2008,"displaystyle":1966},[895,33716,33717,33719,33721,33729,33731,33733,33741,33743,33745],{},[895,33718],{},[1677,33720,1679],{},[10554,33722,33723,33725,33727],{},[898,33724,5325],{},[1810,33726,1959],{},[1677,33728,5742],{},[1677,33730,1906],{},[898,33732,17834],{},[10554,33734,33735,33737,33739],{},[898,33736,900],{},[1810,33738,1959],{},[1677,33740,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,33742,1679],{},[1810,33744,2008],{},[1677,33746,1967],{"separator":1966},[22150,33748,33749,33761],{},[22153,33750,33751],{},[2006,33752,33753],{"scriptlevel":2008,"displaystyle":1966},[10554,33754,33755,33757,33759],{},[898,33756,11183],{"mathvariant":29939},[1810,33758,1812],{},[1677,33760,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[22153,33762,33763],{},[2006,33764,33765],{"scriptlevel":2008,"displaystyle":1966},[895,33766,33767,33769,33771,33779,33781,33783,33791,33793,33795],{},[895,33768],{},[1677,33770,1679],{},[10554,33772,33773,33775,33777],{},[898,33774,5325],{},[1810,33776,1812],{},[1677,33778,5742],{},[1677,33780,1906],{},[898,33782,17834],{},[10554,33784,33785,33787,33789],{},[898,33786,900],{},[1810,33788,1812],{},[1677,33790,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,33792,1679],{},[1810,33794,2008],{},[1677,33796,1967],{"separator":1966},[22150,33798,33799,33811],{},[22153,33800,33801],{},[2006,33802,33803],{"scriptlevel":2008,"displaystyle":1966},[10554,33804,33805,33807,33809],{},[898,33806,11183],{"mathvariant":29939},[898,33808,17834],{},[1677,33810,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[22153,33812,33813],{},[2006,33814,33815],{"scriptlevel":2008,"displaystyle":1966},[895,33816,33817,33819,33821,33827,33829,33831,33833,33839,33841,33847,33849,33851],{},[895,33818],{},[1677,33820,1679],{},[1805,33822,33823,33825],{},[898,33824,900],{},[1677,33826,5742],{},[1677,33828,1906],{},[898,33830,900],{},[1677,33832,1686],{"stretchy":1685},[1953,33834,33835,33837],{},[898,33836,2470],{},[1810,33838,1959],{},[1677,33840,1967],{"separator":1966},[1953,33842,33843,33845],{},[898,33844,2470],{},[1810,33846,1812],{},[1677,33848,1692],{"stretchy":1685},[1677,33850,1679],{},[1810,33852,13850],{},[22153,33854],{"width":29467},[22153,33856,33857],{},[1969,33858,33859],{},"(6.25)",[902,33861,33862],{"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}",[724,33864,33865],{},"Postačující podmínka pro minimum (vzhledem k linearitě funkce výdajů) má tvar",[883,33867,33869],{"className":33868},[886],[888,33870,33871],{"xmlns":890,"display":29457},[892,33872,33873,33971],{},[22145,33874,33875],{"width":29462},[22150,33876,33877,33879,33964,33966],{},[22153,33878],{"width":29467},[22153,33880,33881],{},[895,33882,33883,33885,33887,33893,33895,33901,33903,33905,33907,33909,33911,33913,33962],{},[898,33884,5571],{},[1677,33886,1686],{"stretchy":1685},[1953,33888,33889,33891],{},[898,33890,2470],{},[1810,33892,1959],{},[1677,33894,1967],{"separator":1966},[1953,33896,33897,33899],{},[898,33898,2470],{},[1810,33900,1812],{},[1677,33902,1967],{"separator":1966},[898,33904,17834],{},[1677,33906,1692],{"stretchy":1685},[1677,33908,1679],{},[1677,33910,1906],{},[898,33912,17834],{},[895,33914,33915,33917,33929,33931,33944,33946,33948,33960],{},[1677,33916,1686],{"fence":1966},[10554,33918,33919,33921,33923],{},[898,33920,900],{},[1810,33922,2585],{},[895,33924,33925,33927],{},[1677,33926,2059],{"mathvariant":2057},[1677,33928,2059],{"mathvariant":2057},[1677,33930,1776],{},[10554,33932,33933,33935,33938],{},[898,33934,900],{},[1810,33936,33937],{},"22",[895,33939,33940,33942],{},[1677,33941,2059],{"mathvariant":2057},[1677,33943,2059],{"mathvariant":2057},[1677,33945,1776],{},[1810,33947,1812],{},[10554,33949,33950,33952,33954],{},[898,33951,900],{},[1810,33953,3190],{},[895,33955,33956,33958],{},[1677,33957,2059],{"mathvariant":2057},[1677,33959,2059],{"mathvariant":2057},[1677,33961,1692],{"fence":1966},[898,33963,1656],{"mathvariant":2057},[22153,33965],{"width":29467},[22153,33967,33968],{},[1969,33969,33970],{},"(6.26)",[902,33972,33973],{"encoding":904},"D(Q_1, Q_2, \\lambda) = -\\lambda \\left(U''_{11} + U''_{22} + 2 U''_{12}\\right). \\tag{6.26}",[724,33975,33976,33979,33980,34019,34020,34059,34060,34110,34111,34137,34138,34155,34156,34182],{},[38,33977,33978],{},"Geometrie (obrázek 6.9)."," Řešením je bod ",[883,33981,33983],{"className":33982},[886],[888,33984,33985],{"xmlns":890},[892,33986,33987,34017],{},[895,33988,33989,33995,33997,34005,34007,34015],{},[1805,33990,33991,33993],{},[898,33992,2470],{},[1677,33994,5742],{},[1677,33996,2167],{"stretchy":1685},[10554,33998,33999,34001,34003],{},[898,34000,2470],{},[1810,34002,1959],{},[1677,34004,5742],{},[1677,34006,1967],{"separator":1966},[10554,34008,34009,34011,34013],{},[898,34010,2470],{},[1810,34012,1812],{},[1677,34014,5742],{},[1677,34016,2182],{"stretchy":1685},[902,34018,29718],{"encoding":904}," dotyku křivky užitečnosti ",[883,34021,34023],{"className":34022},[886],[888,34024,34025],{"xmlns":890},[892,34026,34027,34057],{},[895,34028,34029,34035,34037,34039,34041,34047,34049,34055],{},[1805,34030,34031,34033],{},[898,34032,900],{},[1677,34034,5742],{},[1677,34036,1679],{},[898,34038,900],{},[1677,34040,1686],{"stretchy":1685},[1953,34042,34043,34045],{},[898,34044,2470],{},[1810,34046,1959],{},[1677,34048,1967],{"separator":1966},[1953,34050,34051,34053],{},[898,34052,2470],{},[1810,34054,1812],{},[1677,34056,1692],{"stretchy":1685},[902,34058,19056],{"encoding":904}," s přímkou výdajů ",[883,34061,34063],{"className":34062},[886],[888,34064,34065],{"xmlns":890},[892,34066,34067,34107],{},[895,34068,34069,34075,34077,34085,34091,34093,34101],{},[1805,34070,34071,34073],{},[898,34072,5640],{},[1677,34074,5742],{},[1677,34076,1679],{},[10554,34078,34079,34081,34083],{},[898,34080,5325],{},[1810,34082,1959],{},[1677,34084,5742],{},[1953,34086,34087,34089],{},[898,34088,2470],{},[1810,34090,1959],{},[1677,34092,1776],{},[10554,34094,34095,34097,34099],{},[898,34096,5325],{},[1810,34098,1812],{},[1677,34100,5742],{},[1953,34102,34103,34105],{},[898,34104,2470],{},[1810,34106,1812],{},[902,34108,34109],{"encoding":904},"E^* = P_1^* Q_1 + P_2^* Q_2",". Hladina ",[883,34112,34114],{"className":34113},[886],[888,34115,34116],{"xmlns":890},[892,34117,34118,34134],{},[895,34119,34120,34126,34128],{},[1953,34121,34122,34124],{},[898,34123,5640],{},[1810,34125,2008],{},[1677,34127,3128],{},[1805,34129,34130,34132],{},[898,34131,5640],{},[1677,34133,5742],{},[902,34135,34136],{"encoding":904},"E_0 \u003C E^*"," nestačí k dosažení ",[883,34139,34141],{"className":34140},[886],[888,34142,34143],{"xmlns":890},[892,34144,34145,34153],{},[895,34146,34147],{},[1805,34148,34149,34151],{},[898,34150,900],{},[1677,34152,5742],{},[902,34154,29353],{"encoding":904},", hladina ",[883,34157,34159],{"className":34158},[886],[888,34160,34161],{"xmlns":890},[892,34162,34163,34179],{},[895,34164,34165,34171,34173],{},[1953,34166,34167,34169],{},[898,34168,5640],{},[1810,34170,1959],{},[1677,34172,3089],{},[1805,34174,34175,34177],{},[898,34176,5640],{},[1677,34178,5742],{},[902,34180,34181],{"encoding":904},"E_1 > E^*"," je nadbytečná.",[5254,34184,34185,34190],{},[724,34186,34187,34189],{},[883,34188,5960],{}," Postup — duální úloha (minimalizace výdajů)",[152,34191,34192,34242,34328,34368,34443],{},[123,34193,34194,1884,34197,34241],{},[38,34195,34196],{},"Zapiš vazbu",[883,34198,34200],{"className":34199},[886],[888,34201,34202],{"xmlns":890},[892,34203,34204,34238],{},[895,34205,34206,34212,34214,34216,34218,34224,34226,34232,34234,34236],{},[1805,34207,34208,34210],{},[898,34209,900],{},[1677,34211,5742],{},[1677,34213,1906],{},[898,34215,900],{},[1677,34217,1686],{"stretchy":1685},[1953,34219,34220,34222],{},[898,34221,2470],{},[1810,34223,1959],{},[1677,34225,1967],{"separator":1966},[1953,34227,34228,34230],{},[898,34229,2470],{},[1810,34231,1812],{},[1677,34233,1692],{"stretchy":1685},[1677,34235,1679],{},[1810,34237,2008],{},[902,34239,34240],{"encoding":904},"U^* - U(Q_1, Q_2) = 0"," (zadaná hladina užitečnosti).",[123,34243,34244,1884,34246,1656],{},[38,34245,30651],{},[883,34247,34249],{"className":34248},[886],[888,34250,34251],{"xmlns":890},[892,34252,34253,34325],{},[895,34254,34255,34257,34259,34267,34273,34275,34283,34289,34291,34293,34295,34301,34303,34305,34307,34313,34315,34321,34323],{},[898,34256,11183],{"mathvariant":29939},[1677,34258,1679],{},[10554,34260,34261,34263,34265],{},[898,34262,5325],{},[1810,34264,1959],{},[1677,34266,5742],{},[1953,34268,34269,34271],{},[898,34270,2470],{},[1810,34272,1959],{},[1677,34274,1776],{},[10554,34276,34277,34279,34281],{},[898,34278,5325],{},[1810,34280,1812],{},[1677,34282,5742],{},[1953,34284,34285,34287],{},[898,34286,2470],{},[1810,34288,1812],{},[1677,34290,1776],{},[898,34292,17834],{},[1677,34294,1686],{"stretchy":1685},[1805,34296,34297,34299],{},[898,34298,900],{},[1677,34300,5742],{},[1677,34302,1906],{},[898,34304,900],{},[1677,34306,1686],{"stretchy":1685},[1953,34308,34309,34311],{},[898,34310,2470],{},[1810,34312,1959],{},[1677,34314,1967],{"separator":1966},[1953,34316,34317,34319],{},[898,34318,2470],{},[1810,34320,1812],{},[1677,34322,1692],{"stretchy":1685},[1677,34324,1692],{"stretchy":1685},[902,34326,34327],{"encoding":904},"\\mathcal{L} = P_1^* Q_1 + P_2^* Q_2 + \\lambda(U^* - U(Q_1, Q_2))",[123,34329,34330,34333,34334,34367],{},[38,34331,34332],{},"Derivace rovny nule",", z prvních dvou rovnic podílem dostaneš podmínku ",[883,34335,34337],{"className":34336},[886],[888,34338,34339],{"xmlns":890},[892,34340,34341,34365],{},[895,34342,34343,34345,34347,34355,34357],{},[1969,34344,11991],{},[1677,34346,1679],{},[10554,34348,34349,34351,34353],{},[898,34350,5325],{},[1810,34352,1959],{},[1677,34354,5742],{},[898,34356,6062],{"mathvariant":2057},[10554,34358,34359,34361,34363],{},[898,34360,5325],{},[1810,34362,1812],{},[1677,34364,5742],{},[902,34366,30370],{"encoding":904}," (stejná jako u maximalizace!).",[123,34369,34370,1884,34373,34413,34414,1656],{},[38,34371,34372],{},"Dosaď do vazby",[883,34374,34376],{"className":34375},[886],[888,34377,34378],{"xmlns":890},[892,34379,34380,34410],{},[895,34381,34382,34384,34386,34392,34394,34400,34402,34404],{},[898,34383,900],{},[1677,34385,1686],{"stretchy":1685},[1953,34387,34388,34390],{},[898,34389,2470],{},[1810,34391,1959],{},[1677,34393,1967],{"separator":1966},[1953,34395,34396,34398],{},[898,34397,2470],{},[1810,34399,1812],{},[1677,34401,1692],{"stretchy":1685},[1677,34403,1679],{},[1805,34405,34406,34408],{},[898,34407,900],{},[1677,34409,5742],{},[902,34411,34412],{"encoding":904},"U(Q_1, Q_2) = U^*"," a vyřeš pro ",[883,34415,34417],{"className":34416},[886],[888,34418,34419],{"xmlns":890},[892,34420,34421,34441],{},[895,34422,34423,34431,34433],{},[10554,34424,34425,34427,34429],{},[898,34426,2470],{},[1810,34428,1959],{},[1677,34430,5742],{},[1677,34432,1967],{"separator":1966},[10554,34434,34435,34437,34439],{},[898,34436,2470],{},[1810,34438,1812],{},[1677,34440,5742],{},[902,34442,30892],{"encoding":904},[123,34444,34445,1884,34448,34502],{},[38,34446,34447],{},"Vypočítej minimální výdaje",[883,34449,34451],{"className":34450},[886],[888,34452,34453],{"xmlns":890},[892,34454,34455,34499],{},[895,34456,34457,34463,34465,34473,34481,34483,34491],{},[1805,34458,34459,34461],{},[898,34460,5640],{},[1677,34462,5742],{},[1677,34464,1679],{},[10554,34466,34467,34469,34471],{},[898,34468,5325],{},[1810,34470,1959],{},[1677,34472,5742],{},[10554,34474,34475,34477,34479],{},[898,34476,2470],{},[1810,34478,1959],{},[1677,34480,5742],{},[1677,34482,1776],{},[10554,34484,34485,34487,34489],{},[898,34486,5325],{},[1810,34488,1812],{},[1677,34490,5742],{},[10554,34492,34493,34495,34497],{},[898,34494,2470],{},[1810,34496,1812],{},[1677,34498,5742],{},[902,34500,34501],{"encoding":904},"E^* = P_1^* Q_1^* + P_2^* Q_2^*"," a případně ověř druhou podmínku (6.26).",[115,34504,34506,34507],{"id":34505},"příklad-67-minimalizace-výdajů-pro-uq112q212u-q_112-q_212","Příklad 6.7 — minimalizace výdajů pro ",[883,34508,34510],{"className":34509},[886],[888,34511,34512],{"xmlns":890},[892,34513,34514,34548],{},[895,34515,34516,34518,34520,34534],{},[898,34517,900],{},[1677,34519,1679],{},[10554,34521,34522,34524,34526],{},[898,34523,2470],{},[1810,34525,1959],{},[895,34527,34528,34530,34532],{},[1810,34529,1959],{},[898,34531,6062],{"mathvariant":2057},[1810,34533,1812],{},[10554,34535,34536,34538,34540],{},[898,34537,2470],{},[1810,34539,1812],{},[895,34541,34542,34544,34546],{},[1810,34543,1959],{},[898,34545,6062],{"mathvariant":2057},[1810,34547,1812],{},[902,34549,34550],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F2}",[724,34552,34553,34554,1343,34576,1343,34600,31737],{},"Dáno ",[883,34555,34557],{"className":34556},[886],[888,34558,34559],{"xmlns":890},[892,34560,34561,34573],{},[895,34562,34563,34569,34571],{},[1805,34564,34565,34567],{},[898,34566,900],{},[1677,34568,5742],{},[1677,34570,1679],{},[1810,34572,1812],{},[902,34574,34575],{"encoding":904},"U^* = 2",[883,34577,34579],{"className":34578},[886],[888,34580,34581],{"xmlns":890},[892,34582,34583,34597],{},[895,34584,34585,34593,34595],{},[10554,34586,34587,34589,34591],{},[898,34588,5325],{},[1810,34590,1959],{},[1677,34592,5742],{},[1677,34594,1679],{},[1810,34596,25180],{},[902,34598,34599],{"encoding":904},"P_1^* = 0{,}25",[883,34601,34603],{"className":34602},[886],[888,34604,34605],{"xmlns":890},[892,34606,34607,34621],{},[895,34608,34609,34617,34619],{},[10554,34610,34611,34613,34615],{},[898,34612,5325],{},[1810,34614,1812],{},[1677,34616,5742],{},[1677,34618,1679],{},[1810,34620,1959],{},[902,34622,34623],{"encoding":904},"P_2^* = 1",[883,34625,34627],{"className":34626},[886],[888,34628,34629],{"xmlns":890,"display":29457},[892,34630,34631,34695],{},[895,34632,34633,34635,34637,34639,34645,34647,34653,34655,34657,34659,34661,34663,34677,34691,34693],{},[898,34634,11183],{"mathvariant":29939},[1677,34636,1679],{},[1810,34638,25180],{},[1953,34640,34641,34643],{},[898,34642,2470],{},[1810,34644,1959],{},[1677,34646,1776],{},[1953,34648,34649,34651],{},[898,34650,2470],{},[1810,34652,1812],{},[1677,34654,1776],{},[898,34656,17834],{},[1677,34658,1686],{"stretchy":1685},[1810,34660,1812],{},[1677,34662,1906],{},[10554,34664,34665,34667,34669],{},[898,34666,2470],{},[1810,34668,1959],{},[895,34670,34671,34673,34675],{},[1810,34672,1959],{},[898,34674,6062],{"mathvariant":2057},[1810,34676,1812],{},[10554,34678,34679,34681,34683],{},[898,34680,2470],{},[1810,34682,1812],{},[895,34684,34685,34687,34689],{},[1810,34686,1959],{},[898,34688,6062],{"mathvariant":2057},[1810,34690,1812],{},[1677,34692,1692],{"stretchy":1685},[898,34694,1656],{"mathvariant":2057},[902,34696,34697],{"encoding":904},"\\mathcal{L} = 0{,}25 Q_1 + Q_2 + \\lambda(2 - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,34699,31822],{},[883,34701,34703],{"className":34702},[886],[888,34704,34705],{"xmlns":890,"display":29457},[892,34706,34707,34921],{},[22145,34708,34709,34785,34861],{"rowspacing":22147,"columnalign":22148,"columnspacing":2058},[22150,34710,34711,34723],{},[22153,34712,34713],{},[2006,34714,34715],{"scriptlevel":2008,"displaystyle":1966},[10554,34716,34717,34719,34721],{},[898,34718,11183],{"mathvariant":29939},[1810,34720,1959],{},[1677,34722,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[22153,34724,34725],{},[2006,34726,34727],{"scriptlevel":2008,"displaystyle":1966},[895,34728,34729,34731,34733,34735,34737,34739,34741,34749,34765,34779,34781,34783],{},[895,34730],{},[1677,34732,1679],{},[1810,34734,25180],{},[1677,34736,1906],{},[898,34738,17834],{},[1677,34740,2858],{},[2006,34742,34743],{"scriptlevel":2008,"displaystyle":1685},[2010,34744,34745,34747],{},[1810,34746,1959],{},[1810,34748,1812],{},[10554,34750,34751,34753,34755],{},[898,34752,2470],{},[1810,34754,1959],{},[895,34756,34757,34759,34761,34763],{},[1677,34758,1906],{},[1810,34760,1959],{},[898,34762,6062],{"mathvariant":2057},[1810,34764,1812],{},[10554,34766,34767,34769,34771],{},[898,34768,2470],{},[1810,34770,1812],{},[895,34772,34773,34775,34777],{},[1810,34774,1959],{},[898,34776,6062],{"mathvariant":2057},[1810,34778,1812],{},[1677,34780,1679],{},[1810,34782,2008],{},[1677,34784,1967],{"separator":1966},[22150,34786,34787,34799],{},[22153,34788,34789],{},[2006,34790,34791],{"scriptlevel":2008,"displaystyle":1966},[10554,34792,34793,34795,34797],{},[898,34794,11183],{"mathvariant":29939},[1810,34796,1812],{},[1677,34798,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[22153,34800,34801],{},[2006,34802,34803],{"scriptlevel":2008,"displaystyle":1966},[895,34804,34805,34807,34809,34811,34813,34815,34817,34825,34839,34855,34857,34859],{},[895,34806],{},[1677,34808,1679],{},[1810,34810,1959],{},[1677,34812,1906],{},[898,34814,17834],{},[1677,34816,2858],{},[2006,34818,34819],{"scriptlevel":2008,"displaystyle":1685},[2010,34820,34821,34823],{},[1810,34822,1959],{},[1810,34824,1812],{},[10554,34826,34827,34829,34831],{},[898,34828,2470],{},[1810,34830,1959],{},[895,34832,34833,34835,34837],{},[1810,34834,1959],{},[898,34836,6062],{"mathvariant":2057},[1810,34838,1812],{},[10554,34840,34841,34843,34845],{},[898,34842,2470],{},[1810,34844,1812],{},[895,34846,34847,34849,34851,34853],{},[1677,34848,1906],{},[1810,34850,1959],{},[898,34852,6062],{"mathvariant":2057},[1810,34854,1812],{},[1677,34856,1679],{},[1810,34858,2008],{},[1677,34860,1967],{"separator":1966},[22150,34862,34863,34875],{},[22153,34864,34865],{},[2006,34866,34867],{"scriptlevel":2008,"displaystyle":1966},[10554,34868,34869,34871,34873],{},[898,34870,11183],{"mathvariant":29939},[898,34872,17834],{},[1677,34874,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[22153,34876,34877],{},[2006,34878,34879],{"scriptlevel":2008,"displaystyle":1966},[895,34880,34881,34883,34885,34887,34889,34903,34917,34919],{},[895,34882],{},[1677,34884,1679],{},[1810,34886,1812],{},[1677,34888,1906],{},[10554,34890,34891,34893,34895],{},[898,34892,2470],{},[1810,34894,1959],{},[895,34896,34897,34899,34901],{},[1810,34898,1959],{},[898,34900,6062],{"mathvariant":2057},[1810,34902,1812],{},[10554,34904,34905,34907,34909],{},[898,34906,2470],{},[1810,34908,1812],{},[895,34910,34911,34913,34915],{},[1810,34912,1959],{},[898,34914,6062],{"mathvariant":2057},[1810,34916,1812],{},[1677,34918,1679],{},[1810,34920,13850],{},[902,34922,34923],{"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}",[724,34925,34926,34927,18967,34957,34985,34986,6977,35048,1343,35098,35120,35121,1656],{},"Podílem prvních dvou rovnic: ",[883,34928,34930],{"className":34929},[886],[888,34931,34932],{"xmlns":890},[892,34933,34934,34954],{},[895,34935,34936,34938,34940,34946,34948],{},[1810,34937,25180],{},[1677,34939,1679],{},[1953,34941,34942,34944],{},[898,34943,2470],{},[1810,34945,1812],{},[898,34947,6062],{"mathvariant":2057},[1953,34949,34950,34952],{},[898,34951,2470],{},[1810,34953,1959],{},[902,34955,34956],{"encoding":904},"0{,}25 = Q_2 \u002F Q_1",[883,34958,34960],{"className":34959},[886],[888,34961,34962],{"xmlns":890},[892,34963,34964,34982],{},[895,34965,34966,34972,34974,34976],{},[1953,34967,34968,34970],{},[898,34969,2470],{},[1810,34971,1812],{},[1677,34973,1679],{},[1810,34975,25180],{},[1953,34977,34978,34980],{},[898,34979,2470],{},[1810,34981,1959],{},[902,34983,34984],{"encoding":904},"Q_2 = 0{,}25 Q_1",". Dosazením do třetí: ",[883,34987,34989],{"className":34988},[886],[888,34990,34991],{"xmlns":890},[892,34992,34993,35045],{},[895,34994,34995,35009,35011,35013,35019,35031,35033,35035,35041,35043],{},[10554,34996,34997,34999,35001],{},[898,34998,2470],{},[1810,35000,1959],{},[895,35002,35003,35005,35007],{},[1810,35004,1959],{},[898,35006,6062],{"mathvariant":2057},[1810,35008,1812],{},[1677,35010,1686],{"stretchy":1685},[1810,35012,25180],{},[1953,35014,35015,35017],{},[898,35016,2470],{},[1810,35018,1959],{},[1805,35020,35021,35023],{},[1677,35022,1692],{"stretchy":1685},[895,35024,35025,35027,35029],{},[1810,35026,1959],{},[898,35028,6062],{"mathvariant":2057},[1810,35030,1812],{},[1677,35032,1679],{},[1810,35034,6397],{},[1953,35036,35037,35039],{},[898,35038,2470],{},[1810,35040,1959],{},[1677,35042,1679],{},[1810,35044,1812],{},[902,35046,35047],{"encoding":904},"Q_1^{1\u002F2} (0{,}25 Q_1)^{1\u002F2} = 0{,}5 Q_1 = 2",[38,35049,35050,1343,35074],{},[883,35051,35053],{"className":35052},[886],[888,35054,35055],{"xmlns":890},[892,35056,35057,35071],{},[895,35058,35059,35067,35069],{},[10554,35060,35061,35063,35065],{},[898,35062,2470],{},[1810,35064,1959],{},[1677,35066,5742],{},[1677,35068,1679],{},[1810,35070,2032],{},[902,35072,35073],{"encoding":904},"Q_1^* = 4",[883,35075,35077],{"className":35076},[886],[888,35078,35079],{"xmlns":890},[892,35080,35081,35095],{},[895,35082,35083,35091,35093],{},[10554,35084,35085,35087,35089],{},[898,35086,2470],{},[1810,35088,1812],{},[1677,35090,5742],{},[1677,35092,1679],{},[1810,35094,1959],{},[902,35096,35097],{"encoding":904},"Q_2^* = 1",[883,35099,35101],{"className":35100},[886],[888,35102,35103],{"xmlns":890},[892,35104,35105,35117],{},[895,35106,35107,35113,35115],{},[1805,35108,35109,35111],{},[898,35110,17834],{},[1677,35112,5742],{},[1677,35114,1679],{},[1810,35116,1959],{},[902,35118,35119],{"encoding":904},"\\lambda^* = 1",". Minimální výdaje: ",[883,35122,35124],{"className":35123},[886],[888,35125,35126],{"xmlns":890},[892,35127,35128,35156],{},[895,35129,35130,35136,35138,35140,35142,35144,35146,35148,35150,35152,35154],{},[1805,35131,35132,35134],{},[898,35133,5640],{},[1677,35135,5742],{},[1677,35137,1679],{},[1810,35139,25180],{},[1677,35141,2858],{},[1810,35143,2032],{},[1677,35145,1776],{},[1810,35147,1959],{},[1677,35149,2858],{},[1810,35151,1959],{},[1677,35153,1679],{},[1810,35155,1812],{},[902,35157,35158],{"encoding":904},"E^* = 0{,}25 \\cdot 4 + 1 \\cdot 1 = 2",[724,35160,35161,35164,35165,1343,35231,1343,35297,35363,35364,35401,35402,35424,35425,1656],{},[614,35162,35163],{},"Ověření postačující podmínky"," (6.26): ",[883,35166,35168],{"className":35167},[886],[888,35169,35170],{"xmlns":890},[892,35171,35172,35228],{},[895,35173,35174,35186,35188,35190,35198,35214],{},[10554,35175,35176,35178,35180],{},[898,35177,900],{},[1810,35179,2585],{},[895,35181,35182,35184],{},[1677,35183,2059],{"mathvariant":2057},[1677,35185,2059],{"mathvariant":2057},[1677,35187,1679],{},[1677,35189,1906],{},[2006,35191,35192],{"scriptlevel":2008,"displaystyle":1685},[2010,35193,35194,35196],{},[1810,35195,1959],{},[1810,35197,2032],{},[10554,35199,35200,35202,35204],{},[898,35201,2470],{},[1810,35203,1959],{},[895,35205,35206,35208,35210,35212],{},[1677,35207,1906],{},[1810,35209,1854],{},[898,35211,6062],{"mathvariant":2057},[1810,35213,1812],{},[10554,35215,35216,35218,35220],{},[898,35217,2470],{},[1810,35219,1812],{},[895,35221,35222,35224,35226],{},[1810,35223,1959],{},[898,35225,6062],{"mathvariant":2057},[1810,35227,1812],{},[902,35229,35230],{"encoding":904},"U''_{11} = -\\tfrac{1}{4} Q_1^{-3\u002F2} Q_2^{1\u002F2}",[883,35232,35234],{"className":35233},[886],[888,35235,35236],{"xmlns":890},[892,35237,35238,35294],{},[895,35239,35240,35252,35254,35256,35264,35278],{},[10554,35241,35242,35244,35246],{},[898,35243,900],{},[1810,35245,33937],{},[895,35247,35248,35250],{},[1677,35249,2059],{"mathvariant":2057},[1677,35251,2059],{"mathvariant":2057},[1677,35253,1679],{},[1677,35255,1906],{},[2006,35257,35258],{"scriptlevel":2008,"displaystyle":1685},[2010,35259,35260,35262],{},[1810,35261,1959],{},[1810,35263,2032],{},[10554,35265,35266,35268,35270],{},[898,35267,2470],{},[1810,35269,1959],{},[895,35271,35272,35274,35276],{},[1810,35273,1959],{},[898,35275,6062],{"mathvariant":2057},[1810,35277,1812],{},[10554,35279,35280,35282,35284],{},[898,35281,2470],{},[1810,35283,1812],{},[895,35285,35286,35288,35290,35292],{},[1677,35287,1906],{},[1810,35289,1854],{},[898,35291,6062],{"mathvariant":2057},[1810,35293,1812],{},[902,35295,35296],{"encoding":904},"U''_{22} = -\\tfrac{1}{4} Q_1^{1\u002F2} Q_2^{-3\u002F2}",[883,35298,35300],{"className":35299},[886],[888,35301,35302],{"xmlns":890},[892,35303,35304,35360],{},[895,35305,35306,35318,35320,35328,35344],{},[10554,35307,35308,35310,35312],{},[898,35309,900],{},[1810,35311,3190],{},[895,35313,35314,35316],{},[1677,35315,2059],{"mathvariant":2057},[1677,35317,2059],{"mathvariant":2057},[1677,35319,1679],{},[2006,35321,35322],{"scriptlevel":2008,"displaystyle":1685},[2010,35323,35324,35326],{},[1810,35325,1959],{},[1810,35327,2032],{},[10554,35329,35330,35332,35334],{},[898,35331,2470],{},[1810,35333,1959],{},[895,35335,35336,35338,35340,35342],{},[1677,35337,1906],{},[1810,35339,1959],{},[898,35341,6062],{"mathvariant":2057},[1810,35343,1812],{},[10554,35345,35346,35348,35350],{},[898,35347,2470],{},[1810,35349,1812],{},[895,35351,35352,35354,35356,35358],{},[1677,35353,1906],{},[1810,35355,1959],{},[898,35357,6062],{"mathvariant":2057},[1810,35359,1812],{},[902,35361,35362],{"encoding":904},"U''_{12} = \\tfrac{1}{4} Q_1^{-1\u002F2} Q_2^{-1\u002F2}",". Po dosazení ",[883,35365,35367],{"className":35366},[886],[888,35368,35369],{"xmlns":890},[892,35370,35371,35398],{},[895,35372,35373,35375,35377,35379,35381,35383,35385,35387,35389,35391,35394,35396],{},[898,35374,5571],{},[1677,35376,1686],{"stretchy":1685},[1810,35378,2032],{},[1677,35380,1967],{"separator":1966},[1810,35382,1959],{},[1677,35384,1967],{"separator":1966},[1810,35386,1959],{},[1677,35388,1692],{"stretchy":1685},[1677,35390,1679],{},[1810,35392,35393],{},"0,28125",[1677,35395,3089],{},[1810,35397,2008],{},[902,35399,35400],{"encoding":904},"D(4, 1, 1) = 0{,}28125 > 0"," — v bodě ",[883,35403,35405],{"className":35404},[886],[888,35406,35407],{"xmlns":890},[892,35408,35409,35421],{},[895,35410,35411,35413,35415,35417,35419],{},[1677,35412,2167],{"stretchy":1685},[1810,35414,2032],{},[1677,35416,1967],{"separator":1966},[1810,35418,1959],{},[1677,35420,2182],{"stretchy":1685},[902,35422,35423],{"encoding":904},"[4, 1]"," je vázané ",[38,35426,3456],{},[115,35428,35430],{"id":35429},"poptávka-minimalizující-výdaje-hicksova","Poptávka minimalizující výdaje (Hicksova)",[724,35432,35433],{},"Obecně:",[883,35435,35437],{"className":35436},[886],[888,35438,35439],{"xmlns":890,"display":29457},[892,35440,35441,35536],{},[22145,35442,35443],{"width":29462},[22150,35444,35445,35447,35529,35531],{},[22153,35446],{"width":29467},[22153,35448,35449],{},[895,35450,35451,35457,35459,35465,35467,35473,35475,35481,35483,35485,35487,35489,35491,35497,35499,35505,35507,35513,35515,35521,35523,35525,35527],{},[1953,35452,35453,35455],{},[898,35454,2470],{},[1810,35456,1959],{},[1677,35458,1679],{},[1953,35460,35461,35463],{},[898,35462,5571],{},[1810,35464,1959],{},[1677,35466,1686],{"stretchy":1685},[1953,35468,35469,35471],{},[898,35470,5325],{},[1810,35472,1959],{},[1677,35474,1967],{"separator":1966},[1953,35476,35477,35479],{},[898,35478,5325],{},[1810,35480,1812],{},[1677,35482,1967],{"separator":1966},[898,35484,900],{},[1677,35486,1692],{"stretchy":1685},[1677,35488,1967],{"separator":1966},[7266,35490],{"width":16674},[1953,35492,35493,35495],{},[898,35494,2470],{},[1810,35496,1812],{},[1677,35498,1679],{},[1953,35500,35501,35503],{},[898,35502,5571],{},[1810,35504,1812],{},[1677,35506,1686],{"stretchy":1685},[1953,35508,35509,35511],{},[898,35510,5325],{},[1810,35512,1959],{},[1677,35514,1967],{"separator":1966},[1953,35516,35517,35519],{},[898,35518,5325],{},[1810,35520,1812],{},[1677,35522,1967],{"separator":1966},[898,35524,900],{},[1677,35526,1692],{"stretchy":1685},[1677,35528,1967],{"separator":1966},[22153,35530],{"width":29467},[22153,35532,35533],{},[1969,35534,35535],{},"(6.27)",[902,35537,35538],{"encoding":904},"Q_1 = D_1(P_1, P_2, U), \\quad Q_2 = D_2(P_1, P_2, U), \\tag{6.27}",[883,35540,35542],{"className":35541},[886],[888,35543,35544],{"xmlns":890,"display":29457},[892,35545,35546,35593],{},[22145,35547,35548],{"width":29462},[22150,35549,35550,35552,35586,35588],{},[22153,35551],{"width":29467},[22153,35553,35554],{},[895,35555,35556,35558,35560,35562,35564,35570,35572,35578,35580,35582,35584],{},[898,35557,17834],{},[1677,35559,1679],{},[898,35561,17834],{},[1677,35563,1686],{"stretchy":1685},[1953,35565,35566,35568],{},[898,35567,5325],{},[1810,35569,1959],{},[1677,35571,1967],{"separator":1966},[1953,35573,35574,35576],{},[898,35575,5325],{},[1810,35577,1812],{},[1677,35579,1967],{"separator":1966},[898,35581,900],{},[1677,35583,1692],{"stretchy":1685},[898,35585,1656],{"mathvariant":2057},[22153,35587],{"width":29467},[22153,35589,35590],{},[1969,35591,35592],{},"(6.28)",[902,35594,35595],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, U). \\tag{6.28}",[724,35597,35598,35599,1884,35602,35615,35616,35629],{},"Hicksova poptávka závisí na ",[38,35600,35601],{},"hladině užitečnosti",[883,35603,35605],{"className":35604},[886],[888,35606,35607],{"xmlns":890},[892,35608,35609,35613],{},[895,35610,35611],{},[898,35612,900],{},[902,35614,900],{"encoding":904}," (nikoli na důchodu ",[883,35617,35619],{"className":35618},[886],[888,35620,35621],{"xmlns":890},[892,35622,35623,35627],{},[895,35624,35625],{},[898,35626,10516],{},[902,35628,10516],{"encoding":904}," jako u Marshallovy). Fyzická interpretace: jaké množství zboží koupit při daných cenách, abych dosáhl předem stanovené úrovně uspokojení s minimálními výdaji.",[115,35631,35633,35634],{"id":35632},"příklad-68-obecné-odvození-pro-uq112q212u-q_112-q_212","Příklad 6.8 — obecné odvození pro ",[883,35635,35637],{"className":35636},[886],[888,35638,35639],{"xmlns":890},[892,35640,35641,35675],{},[895,35642,35643,35645,35647,35661],{},[898,35644,900],{},[1677,35646,1679],{},[10554,35648,35649,35651,35653],{},[898,35650,2470],{},[1810,35652,1959],{},[895,35654,35655,35657,35659],{},[1810,35656,1959],{},[898,35658,6062],{"mathvariant":2057},[1810,35660,1812],{},[10554,35662,35663,35665,35667],{},[898,35664,2470],{},[1810,35666,1812],{},[895,35668,35669,35671,35673],{},[1810,35670,1959],{},[898,35672,6062],{"mathvariant":2057},[1810,35674,1812],{},[902,35676,34550],{"encoding":904},[724,35678,35679,35709],{},[883,35680,35682],{"className":35681},[886],[888,35683,35684],{"xmlns":890},[892,35685,35686,35706],{},[895,35687,35688,35694,35696,35702,35704],{},[1953,35689,35690,35692],{},[898,35691,5325],{},[1810,35693,1959],{},[1677,35695,1967],{"separator":1966},[1953,35697,35698,35700],{},[898,35699,5325],{},[1810,35701,1812],{},[1677,35703,1967],{"separator":1966},[898,35705,900],{},[902,35707,35708],{"encoding":904},"P_1, P_2, U"," jsou parametry. Lagrangeova funkce:",[883,35711,35713],{"className":35712},[886],[888,35714,35715],{"xmlns":890,"display":29457},[892,35716,35717,35791],{},[895,35718,35719,35721,35723,35729,35735,35737,35743,35749,35751,35753,35755,35757,35759,35773,35787,35789],{},[898,35720,11183],{"mathvariant":29939},[1677,35722,1679],{},[1953,35724,35725,35727],{},[898,35726,5325],{},[1810,35728,1959],{},[1953,35730,35731,35733],{},[898,35732,2470],{},[1810,35734,1959],{},[1677,35736,1776],{},[1953,35738,35739,35741],{},[898,35740,5325],{},[1810,35742,1812],{},[1953,35744,35745,35747],{},[898,35746,2470],{},[1810,35748,1812],{},[1677,35750,1776],{},[898,35752,17834],{},[1677,35754,1686],{"stretchy":1685},[898,35756,900],{},[1677,35758,1906],{},[10554,35760,35761,35763,35765],{},[898,35762,2470],{},[1810,35764,1959],{},[895,35766,35767,35769,35771],{},[1810,35768,1959],{},[898,35770,6062],{"mathvariant":2057},[1810,35772,1812],{},[10554,35774,35775,35777,35779],{},[898,35776,2470],{},[1810,35778,1812],{},[895,35780,35781,35783,35785],{},[1810,35782,1959],{},[898,35784,6062],{"mathvariant":2057},[1810,35786,1812],{},[1677,35788,1692],{"stretchy":1685},[898,35790,1656],{"mathvariant":2057},[902,35792,35793],{"encoding":904},"\\mathcal{L} = P_1 Q_1 + P_2 Q_2 + \\lambda(U - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,35795,31822],{},[883,35797,35799],{"className":35798},[886],[888,35800,35801],{"xmlns":890,"display":29457},[892,35802,35803,36025],{},[22145,35804,35805,35885,35965],{"rowspacing":22147,"columnalign":22148,"columnspacing":2058},[22150,35806,35807,35819],{},[22153,35808,35809],{},[2006,35810,35811],{"scriptlevel":2008,"displaystyle":1966},[10554,35812,35813,35815,35817],{},[898,35814,11183],{"mathvariant":29939},[1810,35816,1959],{},[1677,35818,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[22153,35820,35821],{},[2006,35822,35823],{"scriptlevel":2008,"displaystyle":1966},[895,35824,35825,35827,35829,35835,35837,35839,35841,35849,35865,35879,35881,35883],{},[895,35826],{},[1677,35828,1679],{},[1953,35830,35831,35833],{},[898,35832,5325],{},[1810,35834,1959],{},[1677,35836,1906],{},[898,35838,17834],{},[1677,35840,2858],{},[2006,35842,35843],{"scriptlevel":2008,"displaystyle":1685},[2010,35844,35845,35847],{},[1810,35846,1959],{},[1810,35848,1812],{},[10554,35850,35851,35853,35855],{},[898,35852,2470],{},[1810,35854,1959],{},[895,35856,35857,35859,35861,35863],{},[1677,35858,1906],{},[1810,35860,1959],{},[898,35862,6062],{"mathvariant":2057},[1810,35864,1812],{},[10554,35866,35867,35869,35871],{},[898,35868,2470],{},[1810,35870,1812],{},[895,35872,35873,35875,35877],{},[1810,35874,1959],{},[898,35876,6062],{"mathvariant":2057},[1810,35878,1812],{},[1677,35880,1679],{},[1810,35882,2008],{},[1677,35884,1967],{"separator":1966},[22150,35886,35887,35899],{},[22153,35888,35889],{},[2006,35890,35891],{"scriptlevel":2008,"displaystyle":1966},[10554,35892,35893,35895,35897],{},[898,35894,11183],{"mathvariant":29939},[1810,35896,1812],{},[1677,35898,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[22153,35900,35901],{},[2006,35902,35903],{"scriptlevel":2008,"displaystyle":1966},[895,35904,35905,35907,35909,35915,35917,35919,35921,35929,35943,35959,35961,35963],{},[895,35906],{},[1677,35908,1679],{},[1953,35910,35911,35913],{},[898,35912,5325],{},[1810,35914,1812],{},[1677,35916,1906],{},[898,35918,17834],{},[1677,35920,2858],{},[2006,35922,35923],{"scriptlevel":2008,"displaystyle":1685},[2010,35924,35925,35927],{},[1810,35926,1959],{},[1810,35928,1812],{},[10554,35930,35931,35933,35935],{},[898,35932,2470],{},[1810,35934,1959],{},[895,35936,35937,35939,35941],{},[1810,35938,1959],{},[898,35940,6062],{"mathvariant":2057},[1810,35942,1812],{},[10554,35944,35945,35947,35949],{},[898,35946,2470],{},[1810,35948,1812],{},[895,35950,35951,35953,35955,35957],{},[1677,35952,1906],{},[1810,35954,1959],{},[898,35956,6062],{"mathvariant":2057},[1810,35958,1812],{},[1677,35960,1679],{},[1810,35962,2008],{},[1677,35964,1967],{"separator":1966},[22150,35966,35967,35979],{},[22153,35968,35969],{},[2006,35970,35971],{"scriptlevel":2008,"displaystyle":1966},[10554,35972,35973,35975,35977],{},[898,35974,11183],{"mathvariant":29939},[898,35976,17834],{},[1677,35978,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[22153,35980,35981],{},[2006,35982,35983],{"scriptlevel":2008,"displaystyle":1966},[895,35984,35985,35987,35989,35991,35993,36007,36021,36023],{},[895,35986],{},[1677,35988,1679],{},[898,35990,900],{},[1677,35992,1906],{},[10554,35994,35995,35997,35999],{},[898,35996,2470],{},[1810,35998,1959],{},[895,36000,36001,36003,36005],{},[1810,36002,1959],{},[898,36004,6062],{"mathvariant":2057},[1810,36006,1812],{},[10554,36008,36009,36011,36013],{},[898,36010,2470],{},[1810,36012,1812],{},[895,36014,36015,36017,36019],{},[1810,36016,1959],{},[898,36018,6062],{"mathvariant":2057},[1810,36020,1812],{},[1677,36022,1679],{},[1810,36024,13850],{},[902,36026,36027],{"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}",[724,36029,36030,36031,36101,36102,36160],{},"Podílem rovnic: ",[883,36032,36034],{"className":36033},[886],[888,36035,36036],{"xmlns":890},[892,36037,36038,36098],{},[895,36039,36040,36046,36048,36054,36056,36062,36064,36070,36072,36078,36084,36086,36092],{},[1953,36041,36042,36044],{},[898,36043,5325],{},[1810,36045,1959],{},[898,36047,6062],{"mathvariant":2057},[1953,36049,36050,36052],{},[898,36051,5325],{},[1810,36053,1812],{},[1677,36055,1679],{},[1953,36057,36058,36060],{},[898,36059,2470],{},[1810,36061,1812],{},[898,36063,6062],{"mathvariant":2057},[1953,36065,36066,36068],{},[898,36067,2470],{},[1810,36069,1959],{},[1677,36071,5375],{},[1953,36073,36074,36076],{},[898,36075,5325],{},[1810,36077,1959],{},[1953,36079,36080,36082],{},[898,36081,2470],{},[1810,36083,1959],{},[1677,36085,1679],{},[1953,36087,36088,36090],{},[898,36089,5325],{},[1810,36091,1812],{},[1953,36093,36094,36096],{},[898,36095,2470],{},[1810,36097,1812],{},[902,36099,36100],{"encoding":904},"P_1\u002FP_2 = Q_2\u002FQ_1 \\Rightarrow P_1 Q_1 = P_2 Q_2",", tedy celkové výdaje ",[883,36103,36105],{"className":36104},[886],[888,36106,36107],{"xmlns":890},[892,36108,36109,36157],{},[895,36110,36111,36113,36115,36121,36127,36129,36135,36141,36143,36145,36151],{},[898,36112,5640],{},[1677,36114,1679],{},[1953,36116,36117,36119],{},[898,36118,5325],{},[1810,36120,1959],{},[1953,36122,36123,36125],{},[898,36124,2470],{},[1810,36126,1959],{},[1677,36128,1776],{},[1953,36130,36131,36133],{},[898,36132,5325],{},[1810,36134,1812],{},[1953,36136,36137,36139],{},[898,36138,2470],{},[1810,36140,1812],{},[1677,36142,1679],{},[1810,36144,1812],{},[1953,36146,36147,36149],{},[898,36148,5325],{},[1810,36150,1959],{},[1953,36152,36153,36155],{},[898,36154,2470],{},[1810,36156,1959],{},[902,36158,36159],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2 = 2 P_1 Q_1",". Odtud",[883,36162,36164],{"className":36163},[886],[888,36165,36166],{"xmlns":890,"display":29457},[892,36167,36168,36235],{},[22145,36169,36170],{"width":29462},[22150,36171,36172,36174,36228,36230],{},[22153,36173],{"width":29467},[22153,36175,36176],{},[895,36177,36178,36184,36186,36200,36202,36204,36210,36212,36226],{},[1953,36179,36180,36182],{},[898,36181,2470],{},[1810,36183,1959],{},[1677,36185,1679],{},[2010,36187,36188,36190],{},[898,36189,5640],{},[895,36191,36192,36194],{},[1810,36193,1812],{},[1953,36195,36196,36198],{},[898,36197,5325],{},[1810,36199,1959],{},[1677,36201,1967],{"separator":1966},[7266,36203],{"width":16674},[1953,36205,36206,36208],{},[898,36207,2470],{},[1810,36209,1812],{},[1677,36211,1679],{},[2010,36213,36214,36216],{},[898,36215,5640],{},[895,36217,36218,36220],{},[1810,36219,1812],{},[1953,36221,36222,36224],{},[898,36223,5325],{},[1810,36225,1812],{},[898,36227,1656],{"mathvariant":2057},[22153,36229],{"width":29467},[22153,36231,36232],{},[1969,36233,36234],{},"(6.29)",[902,36236,36237],{"encoding":904},"Q_1 = \\frac{E}{2 P_1}, \\quad Q_2 = \\frac{E}{2 P_2}. \\tag{6.29}",[724,36239,36240,36241,18967,36323,36359],{},"Ze třetí rovnice ",[883,36242,36244],{"className":36243},[886],[888,36245,36246],{"xmlns":890},[892,36247,36248,36320],{},[895,36249,36250,36252,36254,36292,36294],{},[898,36251,900],{},[1677,36253,1679],{},[9505,36255,36256],{},[895,36257,36258,36274,36276],{},[2006,36259,36260],{"scriptlevel":2008,"displaystyle":1685},[2010,36261,36262,36264],{},[898,36263,5640],{},[895,36265,36266,36268],{},[1810,36267,1812],{},[1953,36269,36270,36272],{},[898,36271,5325],{},[1810,36273,1959],{},[1677,36275,2858],{},[2006,36277,36278],{"scriptlevel":2008,"displaystyle":1685},[2010,36279,36280,36282],{},[898,36281,5640],{},[895,36283,36284,36286],{},[1810,36285,1812],{},[1953,36287,36288,36290],{},[898,36289,5325],{},[1810,36291,1812],{},[1677,36293,1679],{},[2006,36295,36296],{"scriptlevel":2008,"displaystyle":1685},[2010,36297,36298,36300],{},[898,36299,5640],{},[895,36301,36302,36304],{},[1810,36303,1812],{},[9505,36305,36306],{},[895,36307,36308,36314],{},[1953,36309,36310,36312],{},[898,36311,5325],{},[1810,36313,1959],{},[1953,36315,36316,36318],{},[898,36317,5325],{},[1810,36319,1812],{},[902,36321,36322],{"encoding":904},"U = \\sqrt{\\tfrac{E}{2 P_1} \\cdot \\tfrac{E}{2 P_2}} = \\tfrac{E}{2\\sqrt{P_1 P_2}}",[883,36324,36326],{"className":36325},[886],[888,36327,36328],{"xmlns":890},[892,36329,36330,36356],{},[895,36331,36332,36334,36336,36338,36340],{},[898,36333,5640],{},[1677,36335,1679],{},[1810,36337,1812],{},[898,36339,900],{},[9505,36341,36342],{},[895,36343,36344,36350],{},[1953,36345,36346,36348],{},[898,36347,5325],{},[1810,36349,1959],{},[1953,36351,36352,36354],{},[898,36353,5325],{},[1810,36355,1812],{},[902,36357,36358],{"encoding":904},"E = 2 U \\sqrt{P_1 P_2}",". Dosazením:",[883,36361,36363],{"className":36362},[886],[888,36364,36365],{"xmlns":890,"display":29457},[892,36366,36367,36512],{},[22145,36368,36369],{"width":29462},[22150,36370,36371,36373,36505,36507],{},[22153,36372],{"width":29467},[22153,36374,36375],{},[14222,36376,36377],{"notation":14224},[2006,36378,36379],{"scriptlevel":2008,"displaystyle":1685},[2006,36380,36381],{"scriptlevel":2008,"displaystyle":1685},[2006,36382,36383],{"scriptlevel":2008,"displaystyle":1966},[895,36384,36385,36387,36393,36395,36397,36413,36415,36421,36423,36429,36431,36437,36439,36441,36443,36445,36447,36453,36455,36457,36473,36475,36481,36483,36489,36491,36497,36499,36501,36503],{},[1969,36386,5372],{},[1953,36388,36389,36391],{},[898,36390,2470],{},[1810,36392,1959],{},[1677,36394,1679],{},[898,36396,900],{},[9505,36398,36399],{},[2010,36400,36401,36407],{},[1953,36402,36403,36405],{},[898,36404,5325],{},[1810,36406,1812],{},[1953,36408,36409,36411],{},[898,36410,5325],{},[1810,36412,1959],{},[1677,36414,1679],{},[1953,36416,36417,36419],{},[898,36418,5571],{},[1810,36420,1959],{},[1677,36422,1686],{"stretchy":1685},[1953,36424,36425,36427],{},[898,36426,5325],{},[1810,36428,1959],{},[1677,36430,1967],{"separator":1966},[1953,36432,36433,36435],{},[898,36434,5325],{},[1810,36436,1812],{},[1677,36438,1967],{"separator":1966},[898,36440,900],{},[1677,36442,1692],{"stretchy":1685},[1677,36444,1967],{"separator":1966},[7266,36446],{"width":16674},[1953,36448,36449,36451],{},[898,36450,2470],{},[1810,36452,1812],{},[1677,36454,1679],{},[898,36456,900],{},[9505,36458,36459],{},[2010,36460,36461,36467],{},[1953,36462,36463,36465],{},[898,36464,5325],{},[1810,36466,1959],{},[1953,36468,36469,36471],{},[898,36470,5325],{},[1810,36472,1812],{},[1677,36474,1679],{},[1953,36476,36477,36479],{},[898,36478,5571],{},[1810,36480,1812],{},[1677,36482,1686],{"stretchy":1685},[1953,36484,36485,36487],{},[898,36486,5325],{},[1810,36488,1959],{},[1677,36490,1967],{"separator":1966},[1953,36492,36493,36495],{},[898,36494,5325],{},[1810,36496,1812],{},[1677,36498,1967],{"separator":1966},[898,36500,900],{},[1677,36502,1692],{"stretchy":1685},[1969,36504,5372],{},[22153,36506],{"width":29467},[22153,36508,36509],{},[1969,36510,36511],{},"(6.30)",[902,36513,36514],{"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}",[115,36516,36518],{"id":36517},"vztah-primární-a-duální-úlohy","Vztah primární a duální úlohy",[724,36520,36521,36522,36535,36536,36553,36554,36567,36568,36585,36586,36589,36590,36629,36630,36659],{},"Primární (max ",[883,36523,36525],{"className":36524},[886],[888,36526,36527],{"xmlns":890},[892,36528,36529,36533],{},[895,36530,36531],{},[898,36532,900],{},[902,36534,900],{"encoding":904}," při rozpočtu ",[883,36537,36539],{"className":36538},[886],[888,36540,36541],{"xmlns":890},[892,36542,36543,36551],{},[895,36544,36545],{},[1805,36546,36547,36549],{},[898,36548,10516],{},[1677,36550,5742],{},[902,36552,29419],{"encoding":904},") a duální (min ",[883,36555,36557],{"className":36556},[886],[888,36558,36559],{"xmlns":890},[892,36560,36561,36565],{},[895,36562,36563],{},[898,36564,5640],{},[902,36566,5640],{"encoding":904}," při užitečnosti ",[883,36569,36571],{"className":36570},[886],[888,36572,36573],{"xmlns":890},[892,36574,36575,36583],{},[895,36576,36577],{},[1805,36578,36579,36581],{},[898,36580,900],{},[1677,36582,5742],{},[902,36584,29353],{"encoding":904},") úloha jsou ",[38,36587,36588],{},"ekvivalentní",": mají tentýž bod optima ",[883,36591,36593],{"className":36592},[886],[888,36594,36595],{"xmlns":890},[892,36596,36597,36627],{},[895,36598,36599,36605,36607,36615,36617,36625],{},[1805,36600,36601,36603],{},[898,36602,2470],{},[1677,36604,5742],{},[1677,36606,2167],{"stretchy":1685},[10554,36608,36609,36611,36613],{},[898,36610,2470],{},[1810,36612,1959],{},[1677,36614,5742],{},[1677,36616,1967],{"separator":1966},[10554,36618,36619,36621,36623],{},[898,36620,2470],{},[1810,36622,1812],{},[1677,36624,5742],{},[1677,36626,2182],{"stretchy":1685},[902,36628,29718],{"encoding":904}," a v obou platí ",[883,36631,36633],{"className":36632},[886],[888,36634,36635],{"xmlns":890},[892,36636,36637,36657],{},[895,36638,36639,36641,36643,36649,36651],{},[1969,36640,11991],{},[1677,36642,1679],{},[1953,36644,36645,36647],{},[898,36646,5325],{},[1810,36648,1959],{},[898,36650,6062],{"mathvariant":2057},[1953,36652,36653,36655],{},[898,36654,5325],{},[1810,36656,1812],{},[902,36658,29389],{"encoding":904},". Rozdíl je v tom, která veličina je zadána a která se optimalizuje:",[724,36661,36662],{},[2240,36663],{"alt":36664,"className":36665,"src":36666},"imek-primarni-vs-dualni",[210,2244],"\u002Fwiki-assets\u002Fimek-primarni-vs-dualni.jpeg",[120,36668,36669,36780],{},[123,36670,36671,36674,36675,36688,36689,36729,36730,1656],{},[38,36672,36673],{},"Primární"," (Marshall): zadáno ",[883,36676,36678],{"className":36677},[886],[888,36679,36680],{"xmlns":890},[892,36681,36682,36686],{},[895,36683,36684],{},[898,36685,10516],{},[902,36687,10516],{"encoding":904},", hledáme maximální ",[883,36690,36692],{"className":36691},[886],[888,36693,36694],{"xmlns":890},[892,36695,36696,36726],{},[895,36697,36698,36704,36706,36712,36714,36720,36722,36724],{},[1805,36699,36700,36702],{},[898,36701,900],{},[1677,36703,5742],{},[1677,36705,1686],{"stretchy":1685},[1953,36707,36708,36710],{},[898,36709,5325],{},[1810,36711,1959],{},[1677,36713,1967],{"separator":1966},[1953,36715,36716,36718],{},[898,36717,5325],{},[1810,36719,1812],{},[1677,36721,1967],{"separator":1966},[898,36723,10516],{},[1677,36725,1692],{"stretchy":1685},[902,36727,36728],{"encoding":904},"U^*(P_1, P_2, Y)"," a poptávku ",[883,36731,36733],{"className":36732},[886],[888,36734,36735],{"xmlns":890},[892,36736,36737,36777],{},[895,36738,36739,36745,36747,36755,36757,36763,36765,36771,36773,36775],{},[1953,36740,36741,36743],{},[898,36742,2470],{},[898,36744,19181],{},[1677,36746,1679],{},[10554,36748,36749,36751,36753],{},[898,36750,5571],{},[898,36752,19181],{},[898,36754,2499],{},[1677,36756,1686],{"stretchy":1685},[1953,36758,36759,36761],{},[898,36760,5325],{},[1810,36762,1959],{},[1677,36764,1967],{"separator":1966},[1953,36766,36767,36769],{},[898,36768,5325],{},[1810,36770,1812],{},[1677,36772,1967],{"separator":1966},[898,36774,10516],{},[1677,36776,1692],{"stretchy":1685},[902,36778,36779],{"encoding":904},"Q_i = D_i^M(P_1, P_2, Y)",[123,36781,36782,36785,36786,36799,36800,36729,36840,1656],{},[38,36783,36784],{},"Duální"," (Hicks): zadáno ",[883,36787,36789],{"className":36788},[886],[888,36790,36791],{"xmlns":890},[892,36792,36793,36797],{},[895,36794,36795],{},[898,36796,900],{},[902,36798,900],{"encoding":904},", hledáme minimální ",[883,36801,36803],{"className":36802},[886],[888,36804,36805],{"xmlns":890},[892,36806,36807,36837],{},[895,36808,36809,36815,36817,36823,36825,36831,36833,36835],{},[1805,36810,36811,36813],{},[898,36812,5640],{},[1677,36814,5742],{},[1677,36816,1686],{"stretchy":1685},[1953,36818,36819,36821],{},[898,36820,5325],{},[1810,36822,1959],{},[1677,36824,1967],{"separator":1966},[1953,36826,36827,36829],{},[898,36828,5325],{},[1810,36830,1812],{},[1677,36832,1967],{"separator":1966},[898,36834,900],{},[1677,36836,1692],{"stretchy":1685},[902,36838,36839],{"encoding":904},"E^*(P_1, P_2, U)",[883,36841,36843],{"className":36842},[886],[888,36844,36845],{"xmlns":890},[892,36846,36847,36888],{},[895,36848,36849,36855,36857,36866,36868,36874,36876,36882,36884,36886],{},[1953,36850,36851,36853],{},[898,36852,2470],{},[898,36854,19181],{},[1677,36856,1679],{},[10554,36858,36859,36861,36863],{},[898,36860,5571],{},[898,36862,19181],{},[898,36864,36865],{},"H",[1677,36867,1686],{"stretchy":1685},[1953,36869,36870,36872],{},[898,36871,5325],{},[1810,36873,1959],{},[1677,36875,1967],{"separator":1966},[1953,36877,36878,36880],{},[898,36879,5325],{},[1810,36881,1812],{},[1677,36883,1967],{"separator":1966},[898,36885,900],{},[1677,36887,1692],{"stretchy":1685},[902,36889,36890],{"encoding":904},"Q_i = D_i^H(P_1, P_2, U)",[724,36892,36893,36894,36897,36898,36901],{},"Proč se studují obě? Marshallova poptávka je ",[38,36895,36896],{},"pozorovatelná"," (lze odhadnout z dat o spotřebě a důchodech), zatímco Hicksova umožňuje čistě oddělit ",[38,36899,36900],{},"substituční efekt"," změny ceny od efektu důchodového — je klíčová pro teorii blahobytu a cenové indexy.",[115,36903,36905],{"id":36904},"úlohy-k-optimalizaci","Úlohy k optimalizaci",[198,36907,36909],{"id":36908},"maximalizace-užitečnosti-a-marshallova-poptávka","Maximalizace užitečnosti a Marshallova poptávka",[724,36911,36912,36915,36916,36948,36949,36987,36988,37014],{},[38,36913,36914],{},"6.8"," Jsou dány užitečnost ",[883,36917,36919],{"className":36918},[886],[888,36920,36921],{"xmlns":890},[892,36922,36923,36945],{},[895,36924,36925,36927,36929,36937],{},[898,36926,900],{},[1677,36928,1679],{},[10554,36930,36931,36933,36935],{},[898,36932,2470],{},[1810,36934,1959],{},[1810,36936,6397],{},[10554,36938,36939,36941,36943],{},[898,36940,2470],{},[1810,36942,1812],{},[1810,36944,6397],{},[902,36946,36947],{"encoding":904},"U = Q_1^{0{,}5} Q_2^{0{,}5}",", ceny ",[883,36950,36952],{"className":36951},[886],[888,36953,36954],{"xmlns":890},[892,36955,36956,36984],{},[895,36957,36958,36966,36968,36970,36972,36980,36982],{},[10554,36959,36960,36962,36964],{},[898,36961,5325],{},[1810,36963,1959],{},[1677,36965,5742],{},[1677,36967,1679],{},[1810,36969,2032],{},[1677,36971,1967],{"separator":1966},[10554,36973,36974,36976,36978],{},[898,36975,5325],{},[1810,36977,1812],{},[1677,36979,5742],{},[1677,36981,1679],{},[1810,36983,2544],{},[902,36985,36986],{"encoding":904},"P_1^* = 4, P_2^* = 10"," za jednotku zboží a důchod spotřebitele 200. Určete množství ",[883,36989,36991],{"className":36990},[886],[888,36992,36993],{"xmlns":890},[892,36994,36995,37011],{},[895,36996,36997,37003,37005],{},[1953,36998,36999,37001],{},[898,37000,2470],{},[1810,37002,1959],{},[1677,37004,1967],{"separator":1966},[1953,37006,37007,37009],{},[898,37008,2470],{},[1810,37010,1812],{},[902,37012,37013],{"encoding":904},"Q_1, Q_2"," maximalizující užitečnost.",[724,37016,37017,37020,37021,37063,37064,37095,37096,37118,37119,1656],{},[38,37018,37019],{},"6.9"," Jsou dány rozpočtové omezení ",[883,37022,37024],{"className":37023},[886],[888,37025,37026],{"xmlns":890},[892,37027,37028,37060],{},[895,37029,37030,37032,37034,37040,37046,37048,37054],{},[898,37031,10516],{},[1677,37033,1679],{},[1953,37035,37036,37038],{},[898,37037,5325],{},[1810,37039,1959],{},[1953,37041,37042,37044],{},[898,37043,2470],{},[1810,37045,1959],{},[1677,37047,1776],{},[1953,37049,37050,37052],{},[898,37051,5325],{},[1810,37053,1812],{},[1953,37055,37056,37058],{},[898,37057,2470],{},[1810,37059,1812],{},[902,37061,37062],{"encoding":904},"Y = P_1 Q_1 + P_2 Q_2"," a užitečnost ",[883,37065,37067],{"className":37066},[886],[888,37068,37069],{"xmlns":890},[892,37070,37071,37093],{},[895,37072,37073,37075,37077,37085],{},[898,37074,900],{},[1677,37076,1679],{},[10554,37078,37079,37081,37083],{},[898,37080,2470],{},[1810,37082,1959],{},[1810,37084,6397],{},[10554,37086,37087,37089,37091],{},[898,37088,2470],{},[1810,37090,1812],{},[1810,37092,6397],{},[902,37094,36947],{"encoding":904},". (a) Odvoďte funkce poptávky maximalizující užitečnost. (b) Najděte funkce poptávky pro důchod ",[883,37097,37099],{"className":37098},[886],[888,37100,37101],{"xmlns":890},[892,37102,37103,37115],{},[895,37104,37105,37111,37113],{},[1805,37106,37107,37109],{},[898,37108,10516],{},[1677,37110,5742],{},[1677,37112,1679],{},[1810,37114,16500],{},[902,37116,37117],{"encoding":904},"Y^* = 500",". (c) Najděte Engelovy funkce pro ceny ",[883,37120,37122],{"className":37121},[886],[888,37123,37124],{"xmlns":890},[892,37125,37126,37154],{},[895,37127,37128,37136,37138,37140,37142,37150,37152],{},[10554,37129,37130,37132,37134],{},[898,37131,5325],{},[1810,37133,1959],{},[1677,37135,5742],{},[1677,37137,1679],{},[1810,37139,1909],{},[1677,37141,1967],{"separator":1966},[10554,37143,37144,37146,37148],{},[898,37145,5325],{},[1810,37147,1812],{},[1677,37149,5742],{},[1677,37151,1679],{},[1810,37153,2544],{},[902,37155,37156],{"encoding":904},"P_1^* = 5, P_2^* = 10",[724,37158,37159,37162,37163,22985,37195,37225,37226,1656],{},[38,37160,37161],{},"6.10"," Odvoďte funkce poptávky pro Cobb-Douglasovy funkce užitečnosti ",[883,37164,37166],{"className":37165},[886],[888,37167,37168],{"xmlns":890},[892,37169,37170,37192],{},[895,37171,37172,37174,37176,37184],{},[898,37173,900],{},[1677,37175,1679],{},[10554,37177,37178,37180,37182],{},[898,37179,2470],{},[1810,37181,1959],{},[898,37183,207],{},[10554,37185,37186,37188,37190],{},[898,37187,2470],{},[1810,37189,1812],{},[898,37191,1779],{},[902,37193,37194],{"encoding":904},"U = Q_1^a Q_2^b",[883,37196,37198],{"className":37197},[886],[888,37199,37200],{"xmlns":890},[892,37201,37202,37222],{},[895,37203,37204,37206,37208,37210,37212,37214,37216,37218,37220],{},[898,37205,207],{},[1677,37207,1967],{"separator":1966},[898,37209,1779],{},[1677,37211,7894],{},[1677,37213,6712],{"stretchy":1685},[1810,37215,2008],{},[1677,37217,1967],{"separator":1966},[1810,37219,1959],{},[1677,37221,6729],{"stretchy":1685},[902,37223,37224],{"encoding":904},"a, b \\in \\langle 0, 1 \\rangle"," a rozpočtové omezení ",[883,37227,37229],{"className":37228},[886],[888,37230,37231],{"xmlns":890},[892,37232,37233,37265],{},[895,37234,37235,37237,37239,37245,37251,37253,37259],{},[898,37236,10516],{},[1677,37238,1679],{},[1953,37240,37241,37243],{},[898,37242,5325],{},[1810,37244,1959],{},[1953,37246,37247,37249],{},[898,37248,2470],{},[1810,37250,1959],{},[1677,37252,1776],{},[1953,37254,37255,37257],{},[898,37256,5325],{},[1810,37258,1812],{},[1953,37260,37261,37263],{},[898,37262,2470],{},[1810,37264,1812],{},[902,37266,37062],{"encoding":904},[724,37268,37269,37272,37273,22985,37307,37225,37325,1656],{},[38,37270,37271],{},"6.11"," Odvoďte funkce poptávky pro funkce užitečnosti CES typu ",[883,37274,37276],{"className":37275},[886],[888,37277,37278],{"xmlns":890},[892,37279,37280,37304],{},[895,37281,37282,37284,37286,37294,37296],{},[898,37283,900],{},[1677,37285,1679],{},[10554,37287,37288,37290,37292],{},[898,37289,2470],{},[1810,37291,1959],{},[898,37293,207],{},[1677,37295,1776],{},[10554,37297,37298,37300,37302],{},[898,37299,2470],{},[1810,37301,1812],{},[898,37303,207],{},[902,37305,37306],{"encoding":904},"U = Q_1^a + Q_2^a",[883,37308,37310],{"className":37309},[886],[888,37311,37312],{"xmlns":890},[892,37313,37314,37322],{},[895,37315,37316,37318,37320],{},[898,37317,207],{},[1677,37319,3052],{"mathvariant":2057},[1810,37321,2008],{},[902,37323,37324],{"encoding":904},"a \\neq 0",[883,37326,37328],{"className":37327},[886],[888,37329,37330],{"xmlns":890},[892,37331,37332,37364],{},[895,37333,37334,37336,37338,37344,37350,37352,37358],{},[898,37335,10516],{},[1677,37337,1679],{},[1953,37339,37340,37342],{},[898,37341,5325],{},[1810,37343,1959],{},[1953,37345,37346,37348],{},[898,37347,2470],{},[1810,37349,1959],{},[1677,37351,1776],{},[1953,37353,37354,37356],{},[898,37355,5325],{},[1810,37357,1812],{},[1953,37359,37360,37362],{},[898,37361,2470],{},[1810,37363,1812],{},[902,37365,37062],{"encoding":904},[198,37367,37369],{"id":37368},"minimalizace-výdajů-a-hicksova-poptávka","Minimalizace výdajů a Hicksova poptávka",[724,37371,37372,36915,37375,1343,37402,37424,37425,1343,37448,37472,37473,37498,37499,1656],{},[38,37373,37374],{},"6.12",[883,37376,37378],{"className":37377},[886],[888,37379,37380],{"xmlns":890},[892,37381,37382,37400],{},[895,37383,37384,37386,37388,37394],{},[898,37385,900],{},[1677,37387,1679],{},[1953,37389,37390,37392],{},[898,37391,2470],{},[1810,37393,1959],{},[1953,37395,37396,37398],{},[898,37397,2470],{},[1810,37399,1812],{},[902,37401,31617],{"encoding":904},[883,37403,37405],{"className":37404},[886],[888,37406,37407],{"xmlns":890},[892,37408,37409,37421],{},[895,37410,37411,37417,37419],{},[1805,37412,37413,37415],{},[898,37414,900],{},[1677,37416,5742],{},[1677,37418,1679],{},[1810,37420,2544],{},[902,37422,37423],{"encoding":904},"U^* = 10"," hladina užitečnosti a ceny ",[883,37426,37428],{"className":37427},[886],[888,37429,37430],{"xmlns":890},[892,37431,37432,37446],{},[895,37433,37434,37442,37444],{},[10554,37435,37436,37438,37440],{},[898,37437,5325],{},[1810,37439,1959],{},[1677,37441,5742],{},[1677,37443,1679],{},[1810,37445,1812],{},[902,37447,31690],{"encoding":904},[883,37449,37451],{"className":37450},[886],[888,37452,37453],{"xmlns":890},[892,37454,37455,37469],{},[895,37456,37457,37465,37467],{},[10554,37458,37459,37461,37463],{},[898,37460,5325],{},[1810,37462,1812],{},[1677,37464,5742],{},[1677,37466,1679],{},[1810,37468,2032],{},[902,37470,37471],{"encoding":904},"P_2^* = 4",". Určete množství ",[883,37474,37476],{"className":37475},[886],[888,37477,37478],{"xmlns":890},[892,37479,37480,37496],{},[895,37481,37482,37488,37490],{},[1953,37483,37484,37486],{},[898,37485,2470],{},[1810,37487,1959],{},[1677,37489,1967],{"separator":1966},[1953,37491,37492,37494],{},[898,37493,2470],{},[1810,37495,1812],{},[902,37497,37013],{"encoding":904}," minimalizující výdaje spotřebitele ",[883,37500,37502],{"className":37501},[886],[888,37503,37504],{"xmlns":890},[892,37505,37506,37526],{},[895,37507,37508,37510,37512,37518,37520],{},[898,37509,900],{},[1677,37511,1679],{},[1953,37513,37514,37516],{},[898,37515,2470],{},[1810,37517,1959],{},[1677,37519,2858],{},[1953,37521,37522,37524],{},[898,37523,2470],{},[1810,37525,1812],{},[902,37527,37528],{"encoding":904},"U = Q_1 \\cdot Q_2",[724,37530,37531,37534,37535,37576,37577,37599,37600,1656],{},[38,37532,37533],{},"6.13"," Jsou dány výdaje spotřebitele ",[883,37536,37538],{"className":37537},[886],[888,37539,37540],{"xmlns":890},[892,37541,37542,37574],{},[895,37543,37544,37546,37548,37554,37560,37562,37568],{},[898,37545,5640],{},[1677,37547,1679],{},[1953,37549,37550,37552],{},[898,37551,5325],{},[1810,37553,1959],{},[1953,37555,37556,37558],{},[898,37557,2470],{},[1810,37559,1959],{},[1677,37561,1776],{},[1953,37563,37564,37566],{},[898,37565,5325],{},[1810,37567,1812],{},[1953,37569,37570,37572],{},[898,37571,2470],{},[1810,37573,1812],{},[902,37575,29334],{"encoding":904}," a užitečnost. (a) Najděte funkce poptávky minimalizující výdaje spotřebitele. (b) Určete funkce poptávky pro užitečnost ",[883,37578,37580],{"className":37579},[886],[888,37581,37582],{"xmlns":890},[892,37583,37584,37596],{},[895,37585,37586,37592,37594],{},[1805,37587,37588,37590],{},[898,37589,900],{},[1677,37591,5742],{},[1677,37593,1679],{},[1810,37595,6392],{},[902,37597,37598],{"encoding":904},"U^* = 25"," a stanovte příslušné výdaje spotřebitele při cenách ",[883,37601,37603],{"className":37602},[886],[888,37604,37605],{"xmlns":890},[892,37606,37607,37636],{},[895,37608,37609,37617,37619,37621,37623,37631,37633],{},[10554,37610,37611,37613,37615],{},[898,37612,5325],{},[1810,37614,1959],{},[1677,37616,5742],{},[1677,37618,1679],{},[1810,37620,10423],{},[1677,37622,1967],{"separator":1966},[10554,37624,37625,37627,37629],{},[898,37626,5325],{},[1810,37628,1812],{},[1677,37630,5742],{},[1677,37632,1679],{},[1810,37634,37635],{},"15",[902,37637,37638],{"encoding":904},"P_1^* = 20, P_2^* = 15",[115,37640,17110],{"id":17109},[120,37642,37643,37700,37739,37759,37794,37848,37853,37859,37955,38000],{},[123,37644,37645,1884,37648,37697,37698,1656],{},[38,37646,37647],{},"Rozpočtové omezení (budget constraint)",[883,37649,37651],{"className":37650},[886],[888,37652,37653],{"xmlns":890},[892,37654,37655,37695],{},[895,37656,37657,37663,37665,37673,37679,37681,37689],{},[1805,37658,37659,37661],{},[898,37660,10516],{},[1677,37662,5742],{},[1677,37664,1679],{},[10554,37666,37667,37669,37671],{},[898,37668,5325],{},[1810,37670,1959],{},[1677,37672,5742],{},[1953,37674,37675,37677],{},[898,37676,2470],{},[1810,37678,1959],{},[1677,37680,1776],{},[10554,37682,37683,37685,37687],{},[898,37684,5325],{},[1810,37686,1812],{},[1677,37688,5742],{},[1953,37690,37691,37693],{},[898,37692,2470],{},[1810,37694,1812],{},[902,37696,18689],{"encoding":904}," — (6.12); ",[38,37699,29527],{},[123,37701,37702,37705,37706,1656],{},[38,37703,37704],{},"Úloha o maximalizaci užitečnosti"," (primární) — Lagrangeova funkce (6.13), soustava (6.14), podmínka optimality ",[883,37707,37709],{"className":37708},[886],[888,37710,37711],{"xmlns":890},[892,37712,37713,37737],{},[895,37714,37715,37717,37719,37727,37729],{},[1969,37716,11991],{},[1677,37718,1679],{},[10554,37720,37721,37723,37725],{},[898,37722,5325],{},[1810,37724,1959],{},[1677,37726,5742],{},[898,37728,6062],{"mathvariant":2057},[10554,37730,37731,37733,37735],{},[898,37732,5325],{},[1810,37734,1812],{},[1677,37736,5742],{},[902,37738,30370],{"encoding":904},[123,37740,37741,37756,37757,1656],{},[38,37742,30514,37743],{},[883,37744,37746],{"className":37745},[886],[888,37747,37748],{"xmlns":890},[892,37749,37750,37754],{},[895,37751,37752],{},[898,37753,17834],{},[902,37755,17887],{"encoding":904}," — stínová cena uvolnění omezení; u maximalizace ",[38,37758,30536],{},[123,37760,37761,37764,37765,1656],{},[38,37762,37763],{},"Podmínka tečnosti"," — sklon indiferenční křivky = sklon rozpočtové přímky; ",[883,37766,37768],{"className":37767},[886],[888,37769,37770],{"xmlns":890},[892,37771,37772,37792],{},[895,37773,37774,37776,37778,37784,37786],{},[1969,37775,11991],{},[1677,37777,1679],{},[1953,37779,37780,37782],{},[898,37781,5325],{},[1810,37783,1959],{},[898,37785,6062],{"mathvariant":2057},[1953,37787,37788,37790],{},[898,37789,5325],{},[1810,37791,1812],{},[902,37793,29389],{"encoding":904},[123,37795,37796,8403,37799,37847],{},[38,37797,37798],{},"Poptávka maximalizující užitečnost (Marshallova)",[883,37800,37802],{"className":37801},[886],[888,37803,37804],{"xmlns":890},[892,37805,37806,37844],{},[895,37807,37808,37814,37816,37822,37824,37830,37832,37838,37840,37842],{},[1953,37809,37810,37812],{},[898,37811,2470],{},[898,37813,19181],{},[1677,37815,1679],{},[1953,37817,37818,37820],{},[898,37819,5571],{},[898,37821,19181],{},[1677,37823,1686],{"stretchy":1685},[1953,37825,37826,37828],{},[898,37827,5325],{},[1810,37829,1959],{},[1677,37831,1967],{"separator":1966},[1953,37833,37834,37836],{},[898,37835,5325],{},[1810,37837,1812],{},[1677,37839,1967],{"separator":1966},[898,37841,10516],{},[1677,37843,1692],{"stretchy":1685},[902,37845,37846],{"encoding":904},"Q_i = D_i(P_1, P_2, Y)"," — (6.15).",[123,37849,37850,37852],{},[38,37851,33118],{}," — poptávka jako funkce důchodu při pevných cenách.",[123,37854,37855,37858],{},[38,37856,37857],{},"Úloha o minimalizaci výdajů"," (duální) — Lagrangeova funkce (6.24), soustava (6.25), postačující podmínka (6.26).",[123,37860,37861,8403,37863,37910,37911,37954],{},[38,37862,35430],{},[883,37864,37866],{"className":37865},[886],[888,37867,37868],{"xmlns":890},[892,37869,37870,37908],{},[895,37871,37872,37878,37880,37886,37888,37894,37896,37902,37904,37906],{},[1953,37873,37874,37876],{},[898,37875,2470],{},[898,37877,19181],{},[1677,37879,1679],{},[1953,37881,37882,37884],{},[898,37883,5571],{},[898,37885,19181],{},[1677,37887,1686],{"stretchy":1685},[1953,37889,37890,37892],{},[898,37891,5325],{},[1810,37893,1959],{},[1677,37895,1967],{"separator":1966},[1953,37897,37898,37900],{},[898,37899,5325],{},[1810,37901,1812],{},[1677,37903,1967],{"separator":1966},[898,37905,900],{},[1677,37907,1692],{"stretchy":1685},[902,37909,19214],{"encoding":904}," — (6.27); obecný výsledek pro ",[883,37912,37914],{"className":37913},[886],[888,37915,37916],{"xmlns":890},[892,37917,37918,37952],{},[895,37919,37920,37922,37924,37938],{},[898,37921,900],{},[1677,37923,1679],{},[10554,37925,37926,37928,37930],{},[898,37927,2470],{},[1810,37929,1959],{},[895,37931,37932,37934,37936],{},[1810,37933,1959],{},[898,37935,6062],{"mathvariant":2057},[1810,37937,1812],{},[10554,37939,37940,37942,37944],{},[898,37941,2470],{},[1810,37943,1812],{},[895,37945,37946,37948,37950],{},[1810,37947,1959],{},[898,37949,6062],{"mathvariant":2057},[1810,37951,1812],{},[902,37953,34550],{"encoding":904},": (6.30).",[123,37956,37957,37999],{},[38,37958,37959,37960],{},"Bod dotyku ",[883,37961,37963],{"className":37962},[886],[888,37964,37965],{"xmlns":890},[892,37966,37967,37997],{},[895,37968,37969,37975,37977,37985,37987,37995],{},[1805,37970,37971,37973],{},[898,37972,2470],{},[1677,37974,5742],{},[1677,37976,2167],{"stretchy":1685},[10554,37978,37979,37981,37983],{},[898,37980,2470],{},[1810,37982,1959],{},[1677,37984,5742],{},[1677,37986,1967],{"separator":1966},[10554,37988,37989,37991,37993],{},[898,37990,2470],{},[1810,37992,1812],{},[1677,37994,5742],{},[1677,37996,2182],{"stretchy":1685},[902,37998,29718],{"encoding":904}," — řešení obou úloh; totožný pro primární i duální formulaci.",[123,38001,38002,38005,38006,38019,38020,38033],{},[38,38003,38004],{},"Dualita"," — ekvivalence max ",[883,38007,38009],{"className":38008},[886],[888,38010,38011],{"xmlns":890},[892,38012,38013,38017],{},[895,38014,38015],{},[898,38016,900],{},[902,38018,900],{"encoding":904}," a min ",[883,38021,38023],{"className":38022},[886],[888,38024,38025],{"xmlns":890},[892,38026,38027,38031],{},[895,38028,38029],{},[898,38030,5640],{},[902,38032,5640],{"encoding":904},"; Marshallova a Hicksova poptávka.",[115,38035,3473],{"id":3472},[120,38037,38038,38061,38077,38090,38101],{},[123,38039,38040,1884,38043,38046,38047,38060],{},[38,38041,38042],{},"Teorie před optimalizací:",[207,38044,880],{"className":38045,"dataFsResolvedFilePath":878,"href":879},[210]," (funkce ",[883,38048,38050],{"className":38049},[886],[888,38051,38052],{"xmlns":890},[892,38053,38054,38058],{},[895,38055,38056],{},[898,38057,900],{},[902,38059,900],{"encoding":904},", indiferenční křivky, MRCS).",[123,38062,38063,1884,38066,38069,38070,38073,38074,1656],{},[38,38064,38065],{},"Matematický aparát:",[207,38067,793],{"className":38068,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace), ",[207,38071,784],{"className":38072,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace), ",[207,38075,2038],{"className":38076,"dataFsResolvedFilePath":764,"href":765},[210],[123,38078,38079,1884,38082,38085,38086,38089],{},[38,38080,38081],{},"Paralely:",[207,38083,12476],{"className":38084,"dataFsResolvedFilePath":857,"href":858},[210]," (MRTS ↔ MRCS, izokvanty ↔ IC, Eulerova věta pro CD), ",[207,38087,13330],{"className":38088,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallova poptávka jako vstup tržního modelu).",[123,38091,38092,1884,38095,1343,38098],{},[38,38093,38094],{},"Přednášky:",[207,38096,1094],{"className":38097,"dataFsResolvedFilePath":838,"href":839},[210],[207,38099,1101],{"className":38100,"dataFsResolvedFilePath":868,"href":869},[210],[123,38102,38103,1884,38105],{},[38,38104,17594],{},[207,38106,17598],{"className":38107,"dataFsResolvedFilePath":1641,"href":1642},[210],{"title":641,"searchDepth":642,"depth":642,"links":38109},[38110,38111,38112,38117,38118,38119,38121,38124,38127,38129,38130,38132,38133,38137,38138],{"id":13395,"depth":642,"text":13396},{"id":29397,"depth":642,"text":29398},{"id":29795,"depth":642,"text":29796,"children":38113},[38114,38115],{"id":29915,"depth":649,"text":29916},{"id":30496,"depth":649,"text":38116},"Interpretace λ\\lambda — mezní užitečnost důchodu",{"id":30958,"depth":642,"text":30959},{"id":31269,"depth":642,"text":31270},{"id":31588,"depth":642,"text":38120},"Příklad 6.6 — maximalizace užitečnosti pro U=Q1Q2U = Q_1 Q_2",{"id":32361,"depth":642,"text":32362,"children":38122},[38123],{"id":33117,"depth":649,"text":33118},{"id":33297,"depth":642,"text":33298,"children":38125},[38126],{"id":33554,"depth":649,"text":33555},{"id":34505,"depth":642,"text":38128},"Příklad 6.7 — minimalizace výdajů pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":35429,"depth":642,"text":35430},{"id":35632,"depth":642,"text":38131},"Příklad 6.8 — obecné odvození pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":36517,"depth":642,"text":36518},{"id":36904,"depth":642,"text":36905,"children":38134},[38135,38136],{"id":36908,"depth":649,"text":36909},{"id":37368,"depth":649,"text":37369},{"id":17109,"depth":642,"text":17110},{"id":3472,"depth":642,"text":3473},{},"\u002Ftopics\u002Foptimalizace-spotrebitele",{"title":29158,"description":641},[1138,1137],"topics\u002Foptimalizace-spotrebitele",[1128,38145,1144,11161,38146,38147,38148],"optimalizace-spotrebitele","poptavka-spotrebitele","minimalizace-vydaju","dualita","jxXhWsWsCIcDvEqLkcWTWs-jk9CvI-eFUi2Afo7U40o",{"id":38151,"title":802,"body":38152,"course":1128,"courses":659,"created":10944,"description":641,"extension":661,"meta":52205,"navigation":664,"path":52206,"seo":52207,"sources":52208,"stem":52209,"tags":52210,"type":3538,"updated":677,"__hash__":52216},"topics\u002Ftopics\u002Fpoptavka-nabidka.md",{"type":9,"value":38153,"toc":52161},[38154,38157,38183,38187,38194,38346,38360,38363,38365,38452,38456,38492,38565,38586,38711,38721,38734,38738,38743,38773,38835,38844,38848,38910,38917,38938,39056,39134,39138,39141,39200,39315,39320,39352,39414,39462,39517,39521,39542,39566,39614,39618,39630,39634,39744,39748,39764,39805,39816,39975,39985,39990,39994,40116,40126,40133,40137,40215,40226,40306,40312,40319,40458,40465,40468,40525,40529,40607,40653,40697,40703,40816,40820,40823,41018,41022,41259,41262,41416,41569,41571,41573,41653,41656,41761,41830,41839,41843,41846,41907,41916,41920,41953,42031,42070,42074,42123,42177,42181,42210,42239,42291,42298,42352,42430,42434,42477,42544,42588,42692,42711,42713,42717,42825,42829,42897,42946,42953,43038,43042,43114,43119,43167,43356,43360,43365,43541,43546,43605,43710,43714,43741,43745,43752,43916,44003,44008,44010,44013,44113,44263,44335,44409,44411,44415,44429,44433,44566,44621,44733,44810,44814,44871,44974,45033,45194,45198,45273,45345,45443,45501,45595,45648,45669,45723,45728,45806,45854,45941,45979,46067,46220,46256,46310,46313,46315,46317,46366,46373,46381,46468,46477,46564,46571,46573,46577,46802,46804,46808,46812,46881,46932,47135,47141,47152,47220,47226,47648,47652,47716,47740,47936,47942,47956,48024,48027,48067,48291,48359,48661,49070,49147,49313,49319,49322,49397,49850,49901,50307,50412,51075,51078,51155,51163,51237,51268,51270,51274,51318,51320,51322,51326,51556,51560,51651,51656,51750,51755,51928,51932,52050,52055,52104,52106,52108],[12,38155,802],{"id":38156},"poptávka-nabídka-a-tržní-rovnováha",[5254,38158,38159],{},[724,38160,38161,38163,38164,38167,38168,38171,38172,38175,38176,38178,38179,38182],{},[883,38162,5543],{}," TL;DR\nKapitola buduje základní mikroekonomický model trhu: chování spotřebitele (",[38,38165,38166],{},"poptávka",") a výrobce (",[38,38169,38170],{},"nabídka","), jejich interakci v ",[38,38173,38174],{},"tržní rovnováze"," a kvantitativní analýzu reakce modelu na změnu exogenních proměnných (posuny, zdanění, ",[38,38177,19368],{},"). Uzavírá ji pojem ",[38,38180,38181],{},"přebytku spotřebitele a výrobce"," jako míry čistého prospěchu obou stran trhu.",[115,38184,38186],{"id":38185},"úvod-model-a-proměnné","Úvod — model a proměnné",[724,38188,38189,38190,38193],{},"Cílem je popsat chování spotřebitele a výrobce za předpokladu racionality jedince (",[614,38191,38192],{},"homo economicus","). Mezi hlavní proměnné patří:",[120,38195,38196,38213,38255,38271],{},[123,38197,38198,38199,38212],{},"cena ",[883,38200,38202],{"className":38201},[886],[888,38203,38204],{"xmlns":890},[892,38205,38206,38210],{},[895,38207,38208],{},[898,38209,5325],{},[902,38211,5325],{"encoding":904}," zkoumaného zboží,",[123,38214,38215,38216,1967],{},"ceny alternativních zboží ",[883,38217,38219],{"className":38218},[886],[888,38220,38221],{"xmlns":890},[892,38222,38223,38252],{},[895,38224,38225,38231,38233,38239,38241,38243,38245],{},[1953,38226,38227,38229],{},[898,38228,5325],{},[1810,38230,1959],{},[1677,38232,1967],{"separator":1966},[1953,38234,38235,38237],{},[898,38236,5325],{},[1810,38238,1812],{},[1677,38240,1967],{"separator":1966},[1677,38242,11034],{},[1677,38244,1967],{"separator":1966},[1953,38246,38247,38249],{},[898,38248,5325],{},[898,38250,38251],{},"n",[902,38253,38254],{"encoding":904},"P_1, P_2, \\dots, P_n",[123,38256,38257,38258,1967],{},"důchod ",[883,38259,38261],{"className":38260},[886],[888,38262,38263],{"xmlns":890},[892,38264,38265,38269],{},[895,38266,38267],{},[898,38268,10516],{},[902,38270,10516],{"encoding":904},[123,38272,38273,38274,38287,38288,38301,38302,38315,38316,38330,38331,38345],{},"preference, očekávání, populace, výrobní faktory (práce ",[883,38275,38277],{"className":38276},[886],[888,38278,38279],{"xmlns":890},[892,38280,38281,38285],{},[895,38282,38283],{},[898,38284,11183],{},[902,38286,11183],{"encoding":904},", kapitál ",[883,38289,38291],{"className":38290},[886],[888,38292,38293],{"xmlns":890},[892,38294,38295,38299],{},[895,38296,38297],{},[898,38298,11188],{},[902,38300,11188],{"encoding":904},", půda ",[883,38303,38305],{"className":38304},[886],[888,38306,38307],{"xmlns":890},[892,38308,38309,38313],{},[895,38310,38311],{},[898,38312,5640],{},[902,38314,5640],{"encoding":904},"), technologie, počet výrobců ",[883,38317,38319],{"className":38318},[886],[888,38320,38321],{"xmlns":890},[892,38322,38323,38328],{},[895,38324,38325],{},[898,38326,38327],{},"O",[902,38329,38327],{"encoding":904},", počasí ",[883,38332,38334],{"className":38333},[886],[888,38335,38336],{"xmlns":890},[892,38337,38338,38343],{},[895,38339,38340],{},[898,38341,38342],{},"W",[902,38344,38342],{"encoding":904}," atd.",[724,38347,38348,38349,38352,38353,38356,38357,1656],{},"Vybereme-li právě jeden z faktorů jako endogenní (",[614,38350,38351],{},"ceteris paribus","), hovoříme o ",[38,38354,38355],{},"jednofaktorovém modelu","; jinak jde o model ",[38,38358,38359],{},"vícefaktorový",[38361,38362],"hr",{},[115,38364,14551],{"id":38166},[5254,38366,38367],{},[724,38368,38369,38371,38372,38385,38386,38399,38400,38403,38404,38427,38428,1656],{},[883,38370,5543],{}," TL;DR\nPoptávka vyjadřuje závislost nakupovaného množství ",[883,38373,38375],{"className":38374},[886],[888,38376,38377],{"xmlns":890},[892,38378,38379,38383],{},[895,38380,38381],{},[898,38382,2470],{},[902,38384,2470],{"encoding":904}," na ceně ",[883,38387,38389],{"className":38388},[886],[888,38390,38391],{"xmlns":890},[892,38392,38393,38397],{},[895,38394,38395],{},[898,38396,5325],{},[902,38398,5325],{"encoding":904}," (případně dalších proměnných). Základní vlastností je ",[38,38401,38402],{},"zákon klesající poptávky",": při růstu ceny množství klesá. Z důvodu přehlednosti se pracuje s jednofaktorovým modelem ",[883,38405,38407],{"className":38406},[886],[888,38408,38409],{"xmlns":890},[892,38410,38411,38425],{},[895,38412,38413,38415,38417,38419,38421,38423],{},[898,38414,2470],{},[1677,38416,1679],{},[898,38418,5571],{},[1677,38420,1686],{"stretchy":1685},[898,38422,5325],{},[1677,38424,1692],{"stretchy":1685},[902,38426,5580],{"encoding":904}," a jeho lineární verzí ",[883,38429,38431],{"className":38430},[886],[888,38432,38433],{"xmlns":890},[892,38434,38435,38449],{},[895,38436,38437,38439,38441,38443,38445,38447],{},[898,38438,5325],{},[1677,38440,1679],{},[898,38442,207],{},[898,38444,2470],{},[1677,38446,1776],{},[898,38448,1779],{},[902,38450,38451],{"encoding":904},"P = aQ + b",[198,38453,38455],{"id":38454},"obecný-vícefaktorový-model","Obecný vícefaktorový model",[724,38457,38458,38459,38472,38473,38486,38487,11413,38489,2832],{},"Ve vícefaktorovém modelu uvažujeme, že poptávané množství ",[883,38460,38462],{"className":38461},[886],[888,38463,38464],{"xmlns":890},[892,38465,38466,38470],{},[895,38467,38468],{},[898,38469,2470],{},[902,38471,2470],{"encoding":904}," závisí na ceně ",[883,38474,38476],{"className":38475},[886],[888,38477,38478],{"xmlns":890},[892,38479,38480,38484],{},[895,38481,38482],{},[898,38483,5325],{},[902,38485,5325],{"encoding":904},", na cenách alternativních zboží a důchodu. Závislost vyjadřuje ",[38,38488,29393],{},[614,38490,38491],{},"demand function",[883,38493,38495],{"className":38494},[886],[888,38496,38497],{"xmlns":890,"display":29457},[892,38498,38499,38562],{},[22145,38500,38501],{"width":29462},[22150,38502,38503,38505,38555,38557],{},[22153,38504],{"width":29467},[22153,38506,38507],{},[895,38508,38509,38511,38513,38515,38517,38519,38521,38527,38529,38535,38537,38539,38541,38547,38549,38551,38553],{},[898,38510,2470],{},[1677,38512,1679],{},[898,38514,5571],{},[1677,38516,1686],{"stretchy":1685},[898,38518,5325],{},[1677,38520,1967],{"separator":1966},[1953,38522,38523,38525],{},[898,38524,5325],{},[1810,38526,1959],{},[1677,38528,1967],{"separator":1966},[1953,38530,38531,38533],{},[898,38532,5325],{},[1810,38534,1812],{},[1677,38536,1967],{"separator":1966},[1677,38538,11034],{},[1677,38540,1967],{"separator":1966},[1953,38542,38543,38545],{},[898,38544,5325],{},[898,38546,38251],{},[1677,38548,1967],{"separator":1966},[898,38550,10516],{},[1677,38552,1692],{"stretchy":1685},[898,38554,1656],{"mathvariant":2057},[22153,38556],{"width":29467},[22153,38558,38559],{},[1969,38560,38561],{},"(2.1)",[902,38563,38564],{"encoding":904},"Q = D(P, P_1, P_2, \\dots, P_n, Y). \\tag{2.1}",[724,38566,38567,38568,38571,38572,38585],{},"Důležitou vlastností je ",[38,38569,38570],{},"homogenita",": změní-li se všechny nezávisle proměnné ",[883,38573,38575],{"className":38574},[886],[888,38576,38577],{"xmlns":890},[892,38578,38579,38583],{},[895,38580,38581],{},[898,38582,13431],{},[902,38584,13431],{"encoding":904},"-krát, poptávané množství se nezmění,",[883,38587,38589],{"className":38588},[886],[888,38590,38591],{"xmlns":890,"display":29457},[892,38592,38593,38708],{},[22145,38594,38595],{"width":29462},[22150,38596,38597,38599,38701,38703],{},[22153,38598],{"width":29467},[22153,38600,38601],{},[895,38602,38603,38605,38607,38609,38611,38613,38615,38617,38619,38625,38627,38629,38635,38637,38639,38641,38643,38649,38651,38653,38655,38657,38659,38661,38663,38665,38667,38673,38675,38681,38683,38685,38687,38693,38695,38697,38699],{},[898,38604,2470],{},[1677,38606,1679],{},[898,38608,5571],{},[1677,38610,1686],{"stretchy":1685},[898,38612,13431],{},[898,38614,5325],{},[1677,38616,1967],{"separator":1966},[898,38618,13431],{},[1953,38620,38621,38623],{},[898,38622,5325],{},[1810,38624,1959],{},[1677,38626,1967],{"separator":1966},[898,38628,13431],{},[1953,38630,38631,38633],{},[898,38632,5325],{},[1810,38634,1812],{},[1677,38636,1967],{"separator":1966},[1677,38638,11034],{},[1677,38640,1967],{"separator":1966},[898,38642,13431],{},[1953,38644,38645,38647],{},[898,38646,5325],{},[898,38648,38251],{},[1677,38650,1967],{"separator":1966},[898,38652,13431],{},[898,38654,10516],{},[1677,38656,1692],{"stretchy":1685},[1677,38658,1679],{},[898,38660,5571],{},[1677,38662,1686],{"stretchy":1685},[898,38664,5325],{},[1677,38666,1967],{"separator":1966},[1953,38668,38669,38671],{},[898,38670,5325],{},[1810,38672,1959],{},[1677,38674,1967],{"separator":1966},[1953,38676,38677,38679],{},[898,38678,5325],{},[1810,38680,1812],{},[1677,38682,1967],{"separator":1966},[1677,38684,11034],{},[1677,38686,1967],{"separator":1966},[1953,38688,38689,38691],{},[898,38690,5325],{},[898,38692,38251],{},[1677,38694,1967],{"separator":1966},[898,38696,10516],{},[1677,38698,1692],{"stretchy":1685},[898,38700,1656],{"mathvariant":2057},[22153,38702],{"width":29467},[22153,38704,38705],{},[1969,38706,38707],{},"(2.2)",[902,38709,38710],{"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}",[5254,38712,38713],{},[724,38714,38715,38717,38718,1656],{},[883,38716,5800],{}," Pozor\nHomogenita platí pouze v zidealizovaném vícefaktorovém modelu; ",[38,38719,38720],{},"v jednofaktorových modelech neplatí",[724,38722,38723,38724,1343,38727,5272,38730,38733],{},"Rozlišuje se poptávka ",[38,38725,38726],{},"individuální",[38,38728,38729],{},"tržní",[38,38731,38732],{},"agregátní"," (není-li specifikováno, rozumí se tržní).",[198,38735,38737],{"id":38736},"jednofaktorové-modely","Jednofaktorové modely",[38739,38740,38742],"h4",{"id":38741},"funkce-poptávky-v-užším-slova-smyslu","Funkce poptávky v užším slova smyslu",[724,38744,38745,38746,38759,38760,2385],{},"Poptávané množství ",[883,38747,38749],{"className":38748},[886],[888,38750,38751],{"xmlns":890},[892,38752,38753,38757],{},[895,38754,38755],{},[898,38756,2470],{},[902,38758,2470],{"encoding":904}," závisí pouze na ceně ",[883,38761,38763],{"className":38762},[886],[888,38764,38765],{"xmlns":890},[892,38766,38767,38771],{},[895,38768,38769],{},[898,38770,5325],{},[902,38772,5325],{"encoding":904},[883,38774,38776],{"className":38775},[886],[888,38777,38778],{"xmlns":890,"display":29457},[892,38779,38780,38832],{},[22145,38781,38782],{"width":29462},[22150,38783,38784,38786,38825,38827],{},[22153,38785],{"width":29467},[22153,38787,38788],{},[895,38789,38790,38792,38794,38796,38798,38800,38802,38804,38806,38809,38811,38813,38815,38817,38819,38821,38823],{},[898,38791,2470],{},[1677,38793,1679],{},[898,38795,5571],{},[1677,38797,1686],{"stretchy":1685},[898,38799,5325],{},[1677,38801,1692],{"stretchy":1685},[1677,38803,1967],{"separator":1966},[7266,38805],{"width":7268},[1969,38807,38808],{},"resp.",[7266,38810],{"width":7268},[898,38812,5325],{},[1677,38814,1679],{},[898,38816,5571],{},[1677,38818,1686],{"stretchy":1685},[898,38820,2470],{},[1677,38822,1692],{"stretchy":1685},[898,38824,1656],{"mathvariant":2057},[22153,38826],{"width":29467},[22153,38828,38829],{},[1969,38830,38831],{},"(2.3)",[902,38833,38834],{"encoding":904},"Q = D(P), \\qquad \\text{resp.} \\qquad P = D(Q). \\tag{2.3}",[724,38836,38837,38838,11413,38841,5306],{},"Graf této funkce se nazývá ",[38,38839,38840],{},"křivka poptávky",[614,38842,38843],{},"demand curve",[38739,38845,38847],{"id":38846},"zákon-klesající-poptávky","Zákon klesající poptávky",[5254,38849,38850],{},[724,38851,38852],{},[38,38853,38854,38855,38868,38869,38882,38883,38868,38896,38909],{},"Roste-li cena ",[883,38856,38858],{"className":38857},[886],[888,38859,38860],{"xmlns":890},[892,38861,38862,38866],{},[895,38863,38864],{},[898,38865,5325],{},[902,38867,5325],{"encoding":904},", pak množství ",[883,38870,38872],{"className":38871},[886],[888,38873,38874],{"xmlns":890},[892,38875,38876,38880],{},[895,38877,38878],{},[898,38879,2470],{},[902,38881,2470],{"encoding":904}," klesá; klesá-li cena ",[883,38884,38886],{"className":38885},[886],[888,38887,38888],{"xmlns":890},[892,38889,38890,38894],{},[895,38891,38892],{},[898,38893,5325],{},[902,38895,5325],{"encoding":904},[883,38897,38899],{"className":38898},[886],[888,38900,38901],{"xmlns":890},[892,38902,38903,38907],{},[895,38904,38905],{},[898,38906,2470],{},[902,38908,2470],{"encoding":904}," roste.",[724,38911,38912,38913,38916],{},"Spotřebitelé jsou ochotni nakoupit větší množství za nižší cenu (mezní užitečnost — viz kap. 6). Zákon platí za ",[38,38914,38915],{},"normálních podmínek","; první kvantitativní formulaci podal Marshall (1890).",[5254,38918,38919,38924],{},[724,38920,38921,38923],{},[883,38922,5543],{}," Intuice — proč zákon platí",[120,38925,38926,38932],{},[123,38927,38928,38931],{},[38,38929,38930],{},"Substituční efekt"," — růst ceny vede ke snaze nahradit zboží jiným.",[123,38933,38934,38937],{},[38,38935,38936],{},"Důchodový efekt"," — růst ceny způsobí nevítaný úbytek reálného důchodu.",[724,38939,38940,38941,38954,38955,38968,38969,38995,38996,39022,39023,9490,39049,39052,39053,1656],{},"Každá funkce poptávky je tedy klesající. Cena ",[883,38942,38944],{"className":38943},[886],[888,38945,38946],{"xmlns":890},[892,38947,38948,38952],{},[895,38949,38950],{},[898,38951,5325],{},[902,38953,5325],{"encoding":904}," se vynáší na svislou osu, množství ",[883,38956,38958],{"className":38957},[886],[888,38959,38960],{"xmlns":890},[892,38961,38962,38966],{},[895,38963,38964],{},[898,38965,2470],{},[902,38967,2470],{"encoding":904}," na vodorovnou. Hypotetická křivka prochází body ",[883,38970,38972],{"className":38971},[886],[888,38973,38974],{"xmlns":890},[892,38975,38976,38992],{},[895,38977,38978,38980,38982,38984,38990],{},[1677,38979,2167],{"stretchy":1685},[1810,38981,2008],{},[1677,38983,1967],{"separator":1966},[1953,38985,38986,38988],{},[898,38987,5325],{},[1810,38989,2008],{},[1677,38991,2182],{"stretchy":1685},[902,38993,38994],{"encoding":904},"[0, P_0]"," (cena, při níž je zboží neprodejné) a ",[883,38997,38999],{"className":38998},[886],[888,39000,39001],{"xmlns":890},[892,39002,39003,39019],{},[895,39004,39005,39007,39013,39015,39017],{},[1677,39006,2167],{"stretchy":1685},[1953,39008,39009,39011],{},[898,39010,2470],{},[1810,39012,2008],{},[1677,39014,1967],{"separator":1966},[1810,39016,2008],{},[1677,39018,2182],{"stretchy":1685},[902,39020,39021],{"encoding":904},"[Q_0, 0]"," (teoretický objem při nulové ceně). Interval ",[883,39024,39026],{"className":39025},[886],[888,39027,39028],{"xmlns":890},[892,39029,39030,39046],{},[895,39031,39032,39034,39036,39038,39044],{},[1677,39033,1686],{"stretchy":1685},[1810,39035,2008],{},[1677,39037,1967],{"separator":1966},[1953,39039,39040,39042],{},[898,39041,5325],{},[1810,39043,2008],{},[1677,39045,1692],{"stretchy":1685},[902,39047,39048],{"encoding":904},"(0, P_0)",[38,39050,39051],{},"reálné cenové rozpětí",". Za teoretických předpokladů je křivka ",[38,39054,39055],{},"konvexní",[724,39057,39058],{},[614,39059,39060,39061,39083,39084,5272,39109,1656],{},"Obrázek 2.1: Hypotetická křivka poptávky v rovině ",[883,39062,39064],{"className":39063},[886],[888,39065,39066],{"xmlns":890},[892,39067,39068,39080],{},[895,39069,39070,39072,39074,39076,39078],{},[1677,39071,1686],{"stretchy":1685},[898,39073,2470],{},[1677,39075,1967],{"separator":1966},[898,39077,5325],{},[1677,39079,1692],{"stretchy":1685},[902,39081,39082],{"encoding":904},"(Q, P)"," — klesající, konvexní, procházející body ",[883,39085,39087],{"className":39086},[886],[888,39088,39089],{"xmlns":890},[892,39090,39091,39107],{},[895,39092,39093,39095,39097,39099,39105],{},[1677,39094,2167],{"stretchy":1685},[1810,39096,2008],{},[1677,39098,1967],{"separator":1966},[1953,39100,39101,39103],{},[898,39102,5325],{},[1810,39104,2008],{},[1677,39106,2182],{"stretchy":1685},[902,39108,38994],{"encoding":904},[883,39110,39112],{"className":39111},[886],[888,39113,39114],{"xmlns":890},[892,39115,39116,39132],{},[895,39117,39118,39120,39126,39128,39130],{},[1677,39119,2167],{"stretchy":1685},[1953,39121,39122,39124],{},[898,39123,2470],{},[1810,39125,2008],{},[1677,39127,1967],{"separator":1966},[1810,39129,2008],{},[1677,39131,2182],{"stretchy":1685},[902,39133,39021],{"encoding":904},[38739,39135,39137],{"id":39136},"lineární-model-poptávky","Lineární model poptávky",[724,39139,39140],{},"Nejjednodušší závislostí je",[883,39142,39144],{"className":39143},[886],[888,39145,39146],{"xmlns":890,"display":29457},[892,39147,39148,39197],{},[22145,39149,39150],{"width":29462},[22150,39151,39152,39154,39190,39192],{},[22153,39153],{"width":29467},[22153,39155,39156],{},[895,39157,39158,39160,39162,39164,39166,39168,39170,39172,39174,39176,39178,39180,39182,39184,39186,39188],{},[898,39159,5325],{},[1677,39161,1679],{},[898,39163,207],{},[898,39165,2470],{},[1677,39167,1776],{},[898,39169,1779],{},[1677,39171,1967],{"separator":1966},[7266,39173],{"width":7268},[898,39175,207],{},[1677,39177,3128],{},[1810,39179,2008],{},[1677,39181,1967],{"separator":1966},[1969,39183,1971],{},[898,39185,1779],{},[1677,39187,3089],{},[1810,39189,13850],{},[22153,39191],{"width":29467},[22153,39193,39194],{},[1969,39195,39196],{},"(2.4)",[902,39198,39199],{"encoding":904},"P = aQ + b, \\qquad a \u003C 0,\\ b > 0. \\tag{2.4}",[724,39201,39202,39203,22985,39239,5272,39263,9425,39289,39311,39312,1656],{},"Křivka poptávky je přímka se záporným sklonem. Alternativně ",[883,39204,39206],{"className":39205},[886],[888,39207,39208],{"xmlns":890},[892,39209,39210,39236],{},[895,39211,39212,39214,39216,39224,39226,39228],{},[898,39213,2470],{},[1677,39215,1679],{},[2006,39217,39218],{"scriptlevel":2008,"displaystyle":1685},[2010,39219,39220,39222],{},[1810,39221,1959],{},[898,39223,207],{},[898,39225,5325],{},[1677,39227,1906],{},[2006,39229,39230],{"scriptlevel":2008,"displaystyle":1685},[2010,39231,39232,39234],{},[898,39233,1779],{},[898,39235,207],{},[902,39237,39238],{"encoding":904},"Q = \\tfrac{1}{a}P - \\tfrac{b}{a}",[883,39240,39242],{"className":39241},[886],[888,39243,39244],{"xmlns":890},[892,39245,39246,39260],{},[895,39247,39248,39256,39258],{},[2006,39249,39250],{"scriptlevel":2008,"displaystyle":1685},[2010,39251,39252,39254],{},[1810,39253,1959],{},[898,39255,207],{},[1677,39257,3128],{},[1810,39259,2008],{},[902,39261,39262],{"encoding":904},"\\tfrac{1}{a} \u003C 0",[883,39264,39266],{"className":39265},[886],[888,39267,39268],{"xmlns":890},[892,39269,39270,39286],{},[895,39271,39272,39274,39282,39284],{},[1677,39273,1906],{},[2006,39275,39276],{"scriptlevel":2008,"displaystyle":1685},[2010,39277,39278,39280],{},[898,39279,1779],{},[898,39281,207],{},[1677,39283,3089],{},[1810,39285,2008],{},[902,39287,39288],{"encoding":904},"-\\tfrac{b}{a} > 0",[883,39290,39292],{"className":39291},[886],[888,39293,39294],{"xmlns":890},[892,39295,39296,39308],{},[895,39297,39298,39300,39302,39304,39306],{},[1677,39299,1686],{"stretchy":1685},[1810,39301,2008],{},[1677,39303,1967],{"separator":1966},[898,39305,1779],{},[1677,39307,1692],{"stretchy":1685},[902,39309,39310],{"encoding":904},"(0, b)",". Tento model odpovídá ",[38,39313,39314],{},"nedokonalé konkurenci",[39316,39317,39319],"h5",{"id":39318},"příklad-21","Příklad 2.1",[724,39321,39322,39325,39326,1656],{},[38,39323,39324],{},"Zadání:"," Lineární poptávka ",[883,39327,39329],{"className":39328},[886],[888,39330,39331],{"xmlns":890},[892,39332,39333,39349],{},[895,39334,39335,39337,39339,39341,39343,39345,39347],{},[898,39336,5325],{},[1677,39338,1679],{},[1677,39340,1906],{},[1810,39342,1812],{},[898,39344,2470],{},[1677,39346,1776],{},[1810,39348,2807],{},[902,39350,39351],{"encoding":904},"P = -2Q + 60",[724,39353,39354,39357,39358,39380,39381,1656],{},[38,39355,39356],{},"Řešení:"," Reálné cenové rozpětí je ",[883,39359,39361],{"className":39360},[886],[888,39362,39363],{"xmlns":890},[892,39364,39365,39377],{},[895,39366,39367,39369,39371,39373,39375],{},[1677,39368,1686],{"stretchy":1685},[1810,39370,2008],{},[1677,39372,1967],{"separator":1966},[1810,39374,2807],{},[1677,39376,1692],{"stretchy":1685},[902,39378,39379],{"encoding":904},"(0, 60)","; alternativní tvar je ",[883,39382,39384],{"className":39383},[886],[888,39385,39386],{"xmlns":890},[892,39387,39388,39411],{},[895,39389,39390,39392,39394,39396,39404,39406,39408],{},[898,39391,2470],{},[1677,39393,1679],{},[1677,39395,1906],{},[2006,39397,39398],{"scriptlevel":2008,"displaystyle":1685},[2010,39399,39400,39402],{},[1810,39401,1959],{},[1810,39403,1812],{},[898,39405,5325],{},[1677,39407,1776],{},[1810,39409,39410],{},"30",[902,39412,39413],{"encoding":904},"Q = -\\tfrac{1}{2}P + 30",[16,39415,39416,39439],{},[19,39417,39418],{},[22,39419,39420,39435,39437],{},[25,39421,39422],{},[883,39423,39425],{"className":39424},[886],[888,39426,39427],{"xmlns":890},[892,39428,39429,39433],{},[895,39430,39431],{},[898,39432,5325],{},[902,39434,5325],{"encoding":904},[25,39436,6599],{},[25,39438,10423],{},[30,39440,39441],{},[22,39442,39443,39458,39460],{},[35,39444,39445],{},[883,39446,39448],{"className":39447},[886],[888,39449,39450],{"xmlns":890},[892,39451,39452,39456],{},[895,39453,39454],{},[898,39455,2470],{},[902,39457,2470],{"encoding":904},[35,39459,2544],{},[35,39461,10423],{},[724,39463,39464],{},[614,39465,39466,39467,5272,39489,1656],{},"Obrázek 2.2 \u002F 2.3: Lineární poptávka — přímka s průsečíky ",[883,39468,39470],{"className":39469},[886],[888,39471,39472],{"xmlns":890},[892,39473,39474,39486],{},[895,39475,39476,39478,39480,39482,39484],{},[1677,39477,2167],{"stretchy":1685},[1810,39479,2008],{},[1677,39481,1967],{"separator":1966},[898,39483,1779],{},[1677,39485,2182],{"stretchy":1685},[902,39487,39488],{"encoding":904},"[0, b]",[883,39490,39492],{"className":39491},[886],[888,39493,39494],{"xmlns":890},[892,39495,39496,39514],{},[895,39497,39498,39500,39502,39504,39506,39508,39510,39512],{},[1677,39499,2167],{"stretchy":1685},[1677,39501,1906],{},[898,39503,1779],{},[898,39505,6062],{"mathvariant":2057},[898,39507,207],{},[1677,39509,1967],{"separator":1966},[1810,39511,2008],{},[1677,39513,2182],{"stretchy":1685},[902,39515,39516],{"encoding":904},"[-b\u002Fa, 0]",[38739,39518,39520],{"id":39519},"poptávka-při-dokonalé-konkurenci","Poptávka při dokonalé konkurenci",[724,39522,39523,39524,39541],{},"Přebírá-li každý účastník trhu pevnou tržní cenu ",[883,39525,39527],{"className":39526},[886],[888,39528,39529],{"xmlns":890},[892,39530,39531,39539],{},[895,39532,39533],{},[1805,39534,39535,39537],{},[898,39536,5325],{},[1677,39538,5742],{},[902,39540,5792],{"encoding":904},", je funkce poptávky konstantní:",[883,39543,39545],{"className":39544},[886],[888,39546,39547],{"xmlns":890,"display":29457},[892,39548,39549,39563],{},[895,39550,39551,39553,39555,39561],{},[898,39552,5325],{},[1677,39554,1679],{},[1805,39556,39557,39559],{},[898,39558,5325],{},[1677,39560,5742],{},[898,39562,1656],{"mathvariant":2057},[902,39564,39565],{"encoding":904},"P = P^*.",[724,39567,39568],{},[614,39569,39570,39571,39592,39593,1656],{},"Obrázek 2.4: Vodorovná přímka v rovině ",[883,39572,39574],{"className":39573},[886],[888,39575,39576],{"xmlns":890},[892,39577,39578,39590],{},[895,39579,39580,39582,39584,39586,39588],{},[1677,39581,1686],{"stretchy":1685},[898,39583,2470],{},[1677,39585,1967],{"separator":1966},[898,39587,5325],{},[1677,39589,1692],{"stretchy":1685},[902,39591,39082],{"encoding":904}," na úrovni ",[883,39594,39596],{"className":39595},[886],[888,39597,39598],{"xmlns":890},[892,39599,39600,39612],{},[895,39601,39602,39604,39606],{},[898,39603,5325],{},[1677,39605,1679],{},[1805,39607,39608,39610],{},[898,39609,5325],{},[1677,39611,5742],{},[902,39613,5745],{"encoding":904},[38739,39615,39617],{"id":39616},"giffenův-statek","Giffenův statek",[724,39619,39620,39621,39623,39624,39626,39627,1656],{},"Existují zboží, u nichž je křivka poptávky ",[38,39622,15047],{}," — tzv. ",[38,39625,39617],{},". Jde o případy, kdy důchodový efekt převáží substituční (klasický příklad: rýže u chudých asijských spotřebitelů). Giffenův statek patří k ",[38,39628,39629],{},"podřadnému zboží",[39316,39631,39633],{"id":39632},"příklad-22","Příklad 2.2",[724,39635,39636,39639,39640,39658,39659,39681,39682,39700,39701,39719,39720,39743],{},[38,39637,39638],{},"Zadání a popis:"," Křivka ",[883,39641,39643],{"className":39642},[886],[888,39644,39645],{"xmlns":890},[892,39646,39647,39655],{},[895,39648,39649],{},[1953,39650,39651,39653],{},[898,39652,5571],{},[1810,39654,1959],{},[902,39656,39657],{"encoding":904},"D_1"," reprezentuje poptávku rodiny po cukru s reálným cenovým rozpětím ",[883,39660,39662],{"className":39661},[886],[888,39663,39664],{"xmlns":890},[892,39665,39666,39678],{},[895,39667,39668,39670,39672,39674,39676],{},[1677,39669,1686],{"stretchy":1685},[1810,39671,2008],{},[1677,39673,1967],{"separator":1966},[1810,39675,37635],{},[1677,39677,1692],{"stretchy":1685},[902,39679,39680],{"encoding":904},"(0, 15)"," pencí za libru; je nejprve konvexní, od inflexního bodu ",[883,39683,39685],{"className":39684},[886],[888,39686,39687],{"xmlns":890},[892,39688,39689,39697],{},[895,39690,39691],{},[1953,39692,39693,39695],{},[898,39694,2470],{},[1810,39696,2008],{},[902,39698,39699],{"encoding":904},"Q_0"," konkávní, se saturací kolem 17 liber. Křivka ",[883,39702,39704],{"className":39703},[886],[888,39705,39706],{"xmlns":890},[892,39707,39708,39716],{},[895,39709,39710],{},[1953,39711,39712,39714],{},[898,39713,5571],{},[1810,39715,1812],{},[902,39717,39718],{"encoding":904},"D_2"," na širším trhu je konvexní klesající z bodu ",[883,39721,39723],{"className":39722},[886],[888,39724,39725],{"xmlns":890},[892,39726,39727,39740],{},[895,39728,39729,39731,39733,39735,39738],{},[1677,39730,2167],{"stretchy":1685},[1810,39732,2008],{},[1677,39734,1967],{"separator":1966},[1810,39736,39737],{},"21",[1677,39739,2182],{"stretchy":1685},[902,39741,39742],{"encoding":904},"[0, 21]"," centů.",[198,39745,39747],{"id":39746},"engelova-funkce-závislost-na-důchodu","Engelova funkce (závislost na důchodu)",[724,39749,39750,39751,2385],{},"Druhý jednofaktorový model předpokládá závislost množství pouze na důchodu ",[883,39752,39754],{"className":39753},[886],[888,39755,39756],{"xmlns":890},[892,39757,39758,39762],{},[895,39759,39760],{},[898,39761,10516],{},[902,39763,10516],{"encoding":904},[883,39765,39767],{"className":39766},[886],[888,39768,39769],{"xmlns":890,"display":29457},[892,39770,39771,39802],{},[22145,39772,39773],{"width":29462},[22150,39774,39775,39777,39795,39797],{},[22153,39776],{"width":29467},[22153,39778,39779],{},[895,39780,39781,39783,39785,39787,39789,39791,39793],{},[898,39782,2470],{},[1677,39784,1679],{},[898,39786,5640],{},[1677,39788,1686],{"stretchy":1685},[898,39790,10516],{},[1677,39792,1692],{"stretchy":1685},[898,39794,1656],{"mathvariant":2057},[22153,39796],{"width":29467},[22153,39798,39799],{},[1969,39800,39801],{},"(2.5)",[902,39803,39804],{"encoding":904},"Q = E(Y). \\tag{2.5}",[724,39806,39807,39808,39811,39812,39815],{},"Funkce se nazývá ",[38,39809,39810],{},"Engelova",", její graf ",[38,39813,39814],{},"Engelova křivka",". Tvar závisí na typu zboží:",[120,39817,39818,39950],{},[123,39819,39820,8403,39823,39836,39837,39850,39851,39868,39869],{},[38,39821,39822],{},"Normální (superior) zboží",[883,39824,39826],{"className":39825},[886],[888,39827,39828],{"xmlns":890},[892,39829,39830,39834],{},[895,39831,39832],{},[898,39833,2470],{},[902,39835,2470],{"encoding":904}," roste s ",[883,39838,39840],{"className":39839},[886],[888,39841,39842],{"xmlns":890},[892,39843,39844,39848],{},[895,39845,39846],{},[898,39847,10516],{},[902,39849,10516],{"encoding":904},", nepřesáhne hodnotu ",[883,39852,39854],{"className":39853},[886],[888,39855,39856],{"xmlns":890},[892,39857,39858,39866],{},[895,39859,39860],{},[1953,39861,39862,39864],{},[898,39863,2470],{},[1810,39865,2008],{},[902,39867,39699],{"encoding":904},":\n",[120,39870,39871,39903],{},[123,39872,39873,39876,39877,39880,39881,1656],{},[38,39874,39875],{},"Nezbytné zboží"," (potraviny, léky) — malá citlivost, ",[38,39878,39879],{},"konkávní"," křivka, autonomní spotřeba ",[883,39882,39884],{"className":39883},[886],[888,39885,39886],{"xmlns":890},[892,39887,39888,39900],{},[895,39889,39890,39896,39898],{},[1953,39891,39892,39894],{},[898,39893,2470],{},[1810,39895,1959],{},[1677,39897,3089],{},[1810,39899,2008],{},[902,39901,39902],{"encoding":904},"Q_1 > 0",[123,39904,39905,39908,39909,39927,39928,39930,39931,1884,39948,1656],{},[38,39906,39907],{},"Luxusní zboží"," — velká citlivost až od hladiny ",[883,39910,39912],{"className":39911},[886],[888,39913,39914],{"xmlns":890},[892,39915,39916,39924],{},[895,39917,39918],{},[1953,39919,39920,39922],{},[898,39921,10516],{},[1810,39923,1959],{},[902,39925,39926],{"encoding":904},"Y_1",", křivka je nejprve ",[38,39929,39055],{}," a od ",[883,39932,39934],{"className":39933},[886],[888,39935,39936],{"xmlns":890},[892,39937,39938,39946],{},[895,39939,39940],{},[1953,39941,39942,39944],{},[898,39943,10516],{},[1810,39945,1959],{},[902,39947,39926],{"encoding":904},[38,39949,39879],{},[123,39951,39952,39955,39956,39974],{},[38,39953,39954],{},"Podřadné (inferior) zboží"," — od hladiny ",[883,39957,39959],{"className":39958},[886],[888,39960,39961],{"xmlns":890},[892,39962,39963,39971],{},[895,39964,39965],{},[1953,39966,39967,39969],{},[898,39968,10516],{},[1810,39970,2008],{},[902,39972,39973],{"encoding":904},"Y_0"," množství s růstem důchodu klesá.",[724,39976,39977,39978,39981,39982,5306],{},"Mírou citlivosti je ",[614,39979,39980],{},"důchodová elasticita"," (viz ",[207,39983,5285],{"className":39984,"dataFsResolvedFilePath":848,"href":849},[210],[724,39986,39987],{},[614,39988,39989],{},"Obrázek 2.6: Tři panely Engelových křivek — (a) nezbytné, (b) luxusní, (c) podřadné zboží.",[38739,39991,39993],{"id":39992},"intuice-co-vlastně-znamená-podřadné","Intuice — co vlastně znamená „podřadné\"?",[5254,39995,39996,40067,40110],{},[724,39997,39998,40000,40001,1884,40004,1884,40017,7057,40019,40032,40033,40036,40037,1656],{},[883,39999,5800],{}," Pozor — nezbytné ≠ podřadné\n",[38,40002,40003],{},"Nezbytné zboží:",[883,40005,40007],{"className":40006},[886],[888,40008,40009],{"xmlns":890},[892,40010,40011,40015],{},[895,40012,40013],{},[898,40014,2470],{},[902,40016,2470],{"encoding":904},[38,40018,8710],{},[883,40020,40022],{"className":40021},[886],[888,40023,40024],{"xmlns":890},[892,40025,40026,40030],{},[895,40027,40028],{},[898,40029,10516],{},[902,40031,10516],{"encoding":904},", ale ",[38,40034,40035],{},"pomaleji"," než důchod (2× plat → třeba 1,3× spotřeba). ",[883,40038,40040],{"className":40039},[886],[888,40041,40042],{"xmlns":890},[892,40043,40044,40064],{},[895,40045,40046,40052,40054,40056,40058,40060,40062],{},[1953,40047,40048,40050],{},[898,40049,5640],{},[898,40051,10516],{},[1677,40053,7894],{},[1677,40055,1686],{"stretchy":1685},[1810,40057,2008],{},[1677,40059,1967],{"separator":1966},[1810,40061,1959],{},[1677,40063,1692],{"stretchy":1685},[902,40065,40066],{"encoding":904},"E_Y \\in (0, 1)",[724,40068,40069,1884,40072,1884,40085,40087,40088,1656],{},[38,40070,40071],{},"Podřadné zboží:",[883,40073,40075],{"className":40074},[886],[888,40076,40077],{"xmlns":890},[892,40078,40079,40083],{},[895,40080,40081],{},[898,40082,2470],{},[902,40084,2470],{"encoding":904},[38,40086,8730],{}," v absolutních číslech (2× plat → třeba 0,7× spotřeba). ",[883,40089,40091],{"className":40090},[886],[888,40092,40093],{"xmlns":890},[892,40094,40095,40107],{},[895,40096,40097,40103,40105],{},[1953,40098,40099,40101],{},[898,40100,5640],{},[898,40102,10516],{},[1677,40104,3128],{},[1810,40106,2008],{},[902,40108,40109],{"encoding":904},"E_Y \u003C 0",[724,40111,40112,40113,1656],{},"Klíčový rozdíl: u podřadného zboží si při vyšším důchodu kupuješ ",[38,40114,40115],{},"méně kusů, ne jen proporčně méně",[724,40117,40118,40121,40122,40125],{},[38,40119,40120],{},"Mechanismus — substituce „nahoru\"."," Samotné zboží se nezhoršilo, jen si teď můžeš dovolit ",[38,40123,40124],{},"kvalitnější alternativu",". Růst důchodu → přesun k prémiovému substitutu → absolutní pokles nákupu „levnější verze\".",[724,40127,40128],{},[2240,40129],{"alt":40130,"className":40131,"src":40132},"imek-engelovy-krivky-3typy",[210,2244],"\u002Fwiki-assets\u002Fimek-engelovy-krivky-3typy.jpeg",[39316,40134,40136],{"id":40135},"české-příklady","České příklady",[16,40138,40139,40149],{},[19,40140,40141],{},[22,40142,40143,40146],{},[25,40144,40145],{},"Podřadné",[25,40147,40148],{},"Nahradí se za",[30,40150,40151,40159,40167,40175,40183,40191,40199,40207],{},[22,40152,40153,40156],{},[35,40154,40155],{},"Instantní polévky, ramen",[35,40157,40158],{},"Čerstvé jídlo, restaurace",[22,40160,40161,40164],{},[35,40162,40163],{},"MHD (autobus, tramvaj)",[35,40165,40166],{},"Vlastní auto, Uber, taxi",[22,40168,40169,40172],{},[35,40170,40171],{},"Mražené polotovary, pizza z mrazáku",[35,40173,40174],{},"Čerstvé suroviny, hotovky",[22,40176,40177,40180],{},[35,40178,40179],{},"Privátní značky supermarketů (K-Classic, Clever)",[35,40181,40182],{},"Značkové produkty",[22,40184,40185,40188],{},[35,40186,40187],{},"Paštika Májka, obyčejný měkký salám",[35,40189,40190],{},"Kvalitní uzeniny, šunka od kosti",[22,40192,40193,40196],{},[35,40194,40195],{},"Second hand oblečení",[35,40197,40198],{},"Nové oblečení, značky",[22,40200,40201,40204],{},[35,40202,40203],{},"Krabicové víno, nejlevnější pivo",[35,40205,40206],{},"Lahvové víno, řemeslná piva",[22,40208,40209,40212],{},[35,40210,40211],{},"Ojetá auta nižších tříd",[35,40213,40214],{},"Nová auta, prémiové značky",[5254,40216,40217],{},[724,40218,40219,40221,40222,40225],{},[883,40220,5960],{}," Test 50 milionů\nPředstav si, že vyhraješ 50 milionů. ",[38,40223,40224],{},"Čeho si najednou koupíš méně"," (nebo vůbec)? To je tvoje podřadné zboží.",[724,40227,40228,40231,40232,11413,40235,40257,40258,11413,40261,40282,40283,40301,40302,40305],{},[38,40229,40230],{},"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 ",[38,40233,40234],{},"luxus",[883,40236,40238],{"className":40237},[886],[888,40239,40240],{"xmlns":890},[892,40241,40242,40254],{},[895,40243,40244,40250,40252],{},[1953,40245,40246,40248],{},[898,40247,5640],{},[898,40249,10516],{},[1677,40251,3089],{},[1810,40253,1959],{},[902,40255,40256],{"encoding":904},"E_Y > 1","), pro manažera s 200k platem ",[38,40259,40260],{},"podřadné",[883,40262,40264],{"className":40263},[886],[888,40265,40266],{"xmlns":890},[892,40267,40268,40280],{},[895,40269,40270,40276,40278],{},[1953,40271,40272,40274],{},[898,40273,5640],{},[898,40275,10516],{},[1677,40277,3128],{},[1810,40279,2008],{},[902,40281,40109],{"encoding":904},"). Proto je ",[883,40284,40286],{"className":40285},[886],[888,40287,40288],{"xmlns":890},[892,40289,40290,40298],{},[895,40291,40292],{},[1953,40293,40294,40296],{},[898,40295,5640],{},[898,40297,10516],{},[902,40299,40300],{"encoding":904},"E_Y"," vždy ",[38,40303,40304],{},"lokální veličina"," — platí pro danou úroveň důchodu, ne absolutně.",[724,40307,40308,40309,40311],{},"Extrémním případem podřadného zboží, kde substituční efekt převáží už na straně ceny, je ",[38,40310,39617],{}," (viz níže) — tam poptávková křivka dokonce roste.",[198,40313,40315,40316,1692],{"id":40314},"posun-poptávky-shift-of-demand","Posun poptávky (",[614,40317,40318],{},"shift of demand",[724,40320,40321,40322,40340,40341,40358,40359,40372,40373,2366,40386,40408,40409,40426,40427,40453,40454,40457],{},"Při změně exogenní proměnné (např. důchodu) se celá křivka poptávky posouvá. Uvažujme normální zboží. Ceně ",[883,40323,40325],{"className":40324},[886],[888,40326,40327],{"xmlns":890},[892,40328,40329,40337],{},[895,40330,40331],{},[1953,40332,40333,40335],{},[898,40334,5325],{},[1810,40336,2008],{},[902,40338,40339],{"encoding":904},"P_0"," odpovídá množství ",[883,40342,40344],{"className":40343},[886],[888,40345,40346],{"xmlns":890},[892,40347,40348,40356],{},[895,40349,40350],{},[1953,40351,40352,40354],{},[898,40353,2470],{},[1810,40355,2008],{},[902,40357,39699],{"encoding":904}," na křivce ",[883,40360,40362],{"className":40361},[886],[888,40363,40364],{"xmlns":890},[892,40365,40366,40370],{},[895,40367,40368],{},[898,40369,5571],{},[902,40371,5571],{"encoding":904},"; vzroste-li důchod z ",[883,40374,40376],{"className":40375},[886],[888,40377,40378],{"xmlns":890},[892,40379,40380,40384],{},[895,40381,40382],{},[898,40383,10516],{},[902,40385,10516],{"encoding":904},[883,40387,40389],{"className":40388},[886],[888,40390,40391],{"xmlns":890},[892,40392,40393,40405],{},[895,40394,40395,40401,40403],{},[1953,40396,40397,40399],{},[898,40398,10516],{},[1810,40400,1959],{},[1677,40402,3089],{},[898,40404,10516],{},[902,40406,40407],{"encoding":904},"Y_1 > Y",", pak stejné ceně ",[883,40410,40412],{"className":40411},[886],[888,40413,40414],{"xmlns":890},[892,40415,40416,40424],{},[895,40417,40418],{},[1953,40419,40420,40422],{},[898,40421,5325],{},[1810,40423,2008],{},[902,40425,40339],{"encoding":904}," odpovídá vyšší ",[883,40428,40430],{"className":40429},[886],[888,40431,40432],{"xmlns":890},[892,40433,40434,40450],{},[895,40435,40436,40442,40444],{},[1953,40437,40438,40440],{},[898,40439,2470],{},[1810,40441,1959],{},[1677,40443,3089],{},[1953,40445,40446,40448],{},[898,40447,2470],{},[1810,40449,2008],{},[902,40451,40452],{"encoding":904},"Q_1 > Q_0"," — křivka se ",[38,40455,40456],{},"posouvá doprava",". Pokles důchodu vede k posunu doleva.",[724,40459,40460],{},[2240,40461],{"alt":40462,"className":40463,"src":40464},"imek-posun-vs-pohyb-po-krivce",[210,2244],"\u002Fwiki-assets\u002Fimek-posun-vs-pohyb-po-krivce.jpeg",[724,40466,40467],{},"Posun může být způsoben i jinými faktory (např. zdaněním spotřebitele — viz dále).",[724,40469,40470],{},[614,40471,40472,40473,15401,40503,40524],{},"Obrázek 2.7: Posun poptávky — tři křivky ",[883,40474,40476],{"className":40475},[886],[888,40477,40478],{"xmlns":890},[892,40479,40480,40500],{},[895,40481,40482,40488,40490,40492,40494],{},[1953,40483,40484,40486],{},[898,40485,5571],{},[1810,40487,1812],{},[1677,40489,1967],{"separator":1966},[898,40491,5571],{},[1677,40493,1967],{"separator":1966},[1953,40495,40496,40498],{},[898,40497,5571],{},[1810,40499,1959],{},[902,40501,40502],{"encoding":904},"D_2, D, D_1",[883,40504,40506],{"className":40505},[886],[888,40507,40508],{"xmlns":890},[892,40509,40510,40522],{},[895,40511,40512,40514,40516,40518,40520],{},[1677,40513,1686],{"stretchy":1685},[898,40515,2470],{},[1677,40517,1967],{"separator":1966},[898,40519,5325],{},[1677,40521,1692],{"stretchy":1685},[902,40523,39082],{"encoding":904},", šipky naznačují posuny.",[39316,40526,40528],{"id":40527},"příklad-23-zdanění-kupujícího","Příklad 2.3 — zdanění kupujícího",[724,40530,40531,40533,40534,40557,40558,40575,40576,40593,40594,1656],{},[38,40532,39324],{}," Poptávce ",[883,40535,40537],{"className":40536},[886],[888,40538,40539],{"xmlns":890},[892,40540,40541,40555],{},[895,40542,40543,40545,40547,40549,40551,40553],{},[898,40544,5325],{},[1677,40546,1679],{},[898,40548,5571],{},[1677,40550,1686],{"stretchy":1685},[898,40552,2470],{},[1677,40554,1692],{"stretchy":1685},[902,40556,6028],{"encoding":904}," odpovídá ceně ",[883,40559,40561],{"className":40560},[886],[888,40562,40563],{"xmlns":890},[892,40564,40565,40573],{},[895,40566,40567],{},[1953,40568,40569,40571],{},[898,40570,5325],{},[1810,40572,2008],{},[902,40574,40339],{"encoding":904}," množství ",[883,40577,40579],{"className":40578},[886],[888,40580,40581],{"xmlns":890},[892,40582,40583,40591],{},[895,40584,40585],{},[1953,40586,40587,40589],{},[898,40588,2470],{},[1810,40590,2008],{},[902,40592,39699],{"encoding":904},". Na kupujícího je uložena jednotková daň ",[883,40595,40597],{"className":40596},[886],[888,40598,40599],{"xmlns":890},[892,40600,40601,40605],{},[895,40602,40603],{},[898,40604,2455],{},[902,40606,2455],{"encoding":904},[724,40608,40609,40611,40612,40629,40630,40652],{},[38,40610,39356],{}," Kupující nakupuje množství ",[883,40613,40615],{"className":40614},[886],[888,40616,40617],{"xmlns":890},[892,40618,40619,40627],{},[895,40620,40621],{},[1953,40622,40623,40625],{},[898,40624,2470],{},[1810,40626,1959],{},[902,40628,30393],{"encoding":904},", které odpovídá ceně ",[883,40631,40633],{"className":40632},[886],[888,40634,40635],{"xmlns":890},[892,40636,40637,40649],{},[895,40638,40639,40645,40647],{},[1953,40640,40641,40643],{},[898,40642,5325],{},[1810,40644,2008],{},[1677,40646,1776],{},[898,40648,2455],{},[902,40650,40651],{"encoding":904},"P_0 + T"," na původní křivce. Nová poptávka je",[883,40654,40656],{"className":40655},[886],[888,40657,40658],{"xmlns":890,"display":29457},[892,40659,40660,40694],{},[895,40661,40662,40664,40666,40672,40674,40676,40678,40680,40682,40684,40686,40688,40690,40692],{},[898,40663,5325],{},[1677,40665,1679],{},[1953,40667,40668,40670],{},[898,40669,5571],{},[1810,40671,1959],{},[1677,40673,1686],{"stretchy":1685},[898,40675,2470],{},[1677,40677,1692],{"stretchy":1685},[1677,40679,1679],{},[898,40681,5571],{},[1677,40683,1686],{"stretchy":1685},[898,40685,2470],{},[1677,40687,1692],{"stretchy":1685},[1677,40689,1906],{},[898,40691,2455],{},[1677,40693,1967],{"separator":1966},[902,40695,40696],{"encoding":904},"P = D_1(Q) = D(Q) - T,",[724,40698,40699,40700,1656],{},"tj. dojde k ",[38,40701,40702],{},"posunu poptávky doleva",[724,40704,40705],{},[614,40706,40707,40708,40729,40730,1343,40747,1343,40760,40781,40782,5272,40799,1656],{},"Obrázek 2.8: Dvě klesající poptávkové přímky v ",[883,40709,40711],{"className":40710},[886],[888,40712,40713],{"xmlns":890},[892,40714,40715,40727],{},[895,40716,40717,40719,40721,40723,40725],{},[1677,40718,1686],{"stretchy":1685},[898,40720,2470],{},[1677,40722,1967],{"separator":1966},[898,40724,5325],{},[1677,40726,1692],{"stretchy":1685},[902,40728,39082],{"encoding":904},"; na svislé ose jsou vyznačeny ",[883,40731,40733],{"className":40732},[886],[888,40734,40735],{"xmlns":890},[892,40736,40737,40745],{},[895,40738,40739],{},[1953,40740,40741,40743],{},[898,40742,5325],{},[1810,40744,2008],{},[902,40746,40339],{"encoding":904},[883,40748,40750],{"className":40749},[886],[888,40751,40752],{"xmlns":890},[892,40753,40754,40758],{},[895,40755,40756],{},[898,40757,2455],{},[902,40759,2455],{"encoding":904},[883,40761,40763],{"className":40762},[886],[888,40764,40765],{"xmlns":890},[892,40766,40767,40779],{},[895,40768,40769,40775,40777],{},[1953,40770,40771,40773],{},[898,40772,5325],{},[1810,40774,2008],{},[1677,40776,1776],{},[898,40778,2455],{},[902,40780,40651],{"encoding":904},"; na vodorovné ",[883,40783,40785],{"className":40784},[886],[888,40786,40787],{"xmlns":890},[892,40788,40789,40797],{},[895,40790,40791],{},[1953,40792,40793,40795],{},[898,40794,2470],{},[1810,40796,1959],{},[902,40798,30393],{"encoding":904},[883,40800,40802],{"className":40801},[886],[888,40803,40804],{"xmlns":890},[892,40805,40806,40814],{},[895,40807,40808],{},[1953,40809,40810,40812],{},[898,40811,2470],{},[1810,40813,2008],{},[902,40815,39699],{"encoding":904},[198,40817,40819],{"id":40818},"vícekomoditní-dvoukomoditní-trh","Vícekomoditní (dvoukomoditní) trh",[724,40821,40822],{},"Uvažujme dvě tržně závislá zboží s lineárními funkcemi poptávky:",[883,40824,40826],{"className":40825},[886],[888,40827,40828],{"xmlns":890,"display":29457},[892,40829,40830,41015],{},[22145,40831,40832],{"width":29462},[22150,40833,40834,40836,41008,41010],{},[22153,40835],{"width":29467},[22153,40837,40838],{},[22145,40839,40840,40924],{"rowspacing":22147,"columnalign":22148,"columnspacing":2058},[22150,40841,40842,40852],{},[22153,40843,40844],{},[2006,40845,40846],{"scriptlevel":2008,"displaystyle":1966},[1953,40847,40848,40850],{},[898,40849,2470],{},[1810,40851,1959],{},[22153,40853,40854],{},[2006,40855,40856],{"scriptlevel":2008,"displaystyle":1966},[895,40857,40858,40860,40862,40868,40870,40876,40878,40884,40886,40888,40894,40896,40902,40908,40910,40916,40922],{},[895,40859],{},[1677,40861,1679],{},[1953,40863,40864,40866],{},[898,40865,5571],{},[1810,40867,1959],{},[1677,40869,1686],{"stretchy":1685},[1953,40871,40872,40874],{},[898,40873,5325],{},[1810,40875,1959],{},[1677,40877,1967],{"separator":1966},[1953,40879,40880,40882],{},[898,40881,5325],{},[1810,40883,1812],{},[1677,40885,1692],{"stretchy":1685},[1677,40887,1679],{},[1953,40889,40890,40892],{},[898,40891,207],{},[1810,40893,1959],{},[1677,40895,1776],{},[1953,40897,40898,40900],{},[898,40899,1779],{},[1810,40901,1959],{},[1953,40903,40904,40906],{},[898,40905,5325],{},[1810,40907,1959],{},[1677,40909,1776],{},[1953,40911,40912,40914],{},[898,40913,1823],{},[1810,40915,1959],{},[1953,40917,40918,40920],{},[898,40919,5325],{},[1810,40921,1812],{},[1677,40923,1967],{"separator":1966},[22150,40925,40926,40936],{},[22153,40927,40928],{},[2006,40929,40930],{"scriptlevel":2008,"displaystyle":1966},[1953,40931,40932,40934],{},[898,40933,2470],{},[1810,40935,1812],{},[22153,40937,40938],{},[2006,40939,40940],{"scriptlevel":2008,"displaystyle":1966},[895,40941,40942,40944,40946,40952,40954,40960,40962,40968,40970,40972,40978,40980,40986,40992,40994,41000,41006],{},[895,40943],{},[1677,40945,1679],{},[1953,40947,40948,40950],{},[898,40949,5571],{},[1810,40951,1812],{},[1677,40953,1686],{"stretchy":1685},[1953,40955,40956,40958],{},[898,40957,5325],{},[1810,40959,1959],{},[1677,40961,1967],{"separator":1966},[1953,40963,40964,40966],{},[898,40965,5325],{},[1810,40967,1812],{},[1677,40969,1692],{"stretchy":1685},[1677,40971,1679],{},[1953,40973,40974,40976],{},[898,40975,207],{},[1810,40977,1812],{},[1677,40979,1776],{},[1953,40981,40982,40984],{},[898,40983,1779],{},[1810,40985,1812],{},[1953,40987,40988,40990],{},[898,40989,5325],{},[1810,40991,1959],{},[1677,40993,1776],{},[1953,40995,40996,40998],{},[898,40997,1823],{},[1810,40999,1812],{},[1953,41001,41002,41004],{},[898,41003,5325],{},[1810,41005,1812],{},[898,41007,1656],{"mathvariant":2057},[22153,41009],{"width":29467},[22153,41011,41012],{},[1969,41013,41014],{},"(2.6)",[902,41016,41017],{"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}",[38739,41019,41021],{"id":41020},"znaménková-analýza-parametrů","Znaménková analýza parametrů",[120,41023,41024,41071,41118],{},[123,41025,41026,1343,41048,41070],{},[883,41027,41029],{"className":41028},[886],[888,41030,41031],{"xmlns":890},[892,41032,41033,41045],{},[895,41034,41035,41041,41043],{},[1953,41036,41037,41039],{},[898,41038,207],{},[1810,41040,1959],{},[1677,41042,3089],{},[1810,41044,2008],{},[902,41046,41047],{"encoding":904},"a_1 > 0",[883,41049,41051],{"className":41050},[886],[888,41052,41053],{"xmlns":890},[892,41054,41055,41067],{},[895,41056,41057,41063,41065],{},[1953,41058,41059,41061],{},[898,41060,207],{},[1810,41062,1812],{},[1677,41064,3089],{},[1810,41066,2008],{},[902,41068,41069],{"encoding":904},"a_2 > 0"," (při nulových cenách je poptávané množství kladné),",[123,41072,41073,1343,41095,41117],{},[883,41074,41076],{"className":41075},[886],[888,41077,41078],{"xmlns":890},[892,41079,41080,41092],{},[895,41081,41082,41088,41090],{},[1953,41083,41084,41086],{},[898,41085,1779],{},[1810,41087,1959],{},[1677,41089,3128],{},[1810,41091,2008],{},[902,41093,41094],{"encoding":904},"b_1 \u003C 0",[883,41096,41098],{"className":41097},[886],[888,41099,41100],{"xmlns":890},[892,41101,41102,41114],{},[895,41103,41104,41110,41112],{},[1953,41105,41106,41108],{},[898,41107,1823],{},[1810,41109,1812],{},[1677,41111,3128],{},[1810,41113,2008],{},[902,41115,41116],{"encoding":904},"c_2 \u003C 0"," (vlastní koeficienty — zákon klesající poptávky),",[123,41119,41120,41121,1343,41138,41156,41157],{},"zkřížené koeficienty ",[883,41122,41124],{"className":41123},[886],[888,41125,41126],{"xmlns":890},[892,41127,41128,41136],{},[895,41129,41130],{},[1953,41131,41132,41134],{},[898,41133,1823],{},[1810,41135,1959],{},[902,41137,31190],{"encoding":904},[883,41139,41141],{"className":41140},[886],[888,41142,41143],{"xmlns":890},[892,41144,41145,41153],{},[895,41146,41147],{},[1953,41148,41149,41151],{},[898,41150,1779],{},[1810,41152,1812],{},[902,41154,41155],{"encoding":904},"b_2"," určují povahu vztahu:\n",[120,41158,41159,41209],{},[123,41160,41161,41164,41165,1343,41187,1967],{},[38,41162,41163],{},"substituty"," (máslo vs. margarín): ",[883,41166,41168],{"className":41167},[886],[888,41169,41170],{"xmlns":890},[892,41171,41172,41184],{},[895,41173,41174,41180,41182],{},[1953,41175,41176,41178],{},[898,41177,1823],{},[1810,41179,1959],{},[1677,41181,3089],{},[1810,41183,2008],{},[902,41185,41186],{"encoding":904},"c_1 > 0",[883,41188,41190],{"className":41189},[886],[888,41191,41192],{"xmlns":890},[892,41193,41194,41206],{},[895,41195,41196,41202,41204],{},[1953,41197,41198,41200],{},[898,41199,1779],{},[1810,41201,1812],{},[1677,41203,3089],{},[1810,41205,2008],{},[902,41207,41208],{"encoding":904},"b_2 > 0",[123,41210,41211,41214,41215,1343,41237,1656],{},[38,41212,41213],{},"komplementy"," (auto vs. benzín): ",[883,41216,41218],{"className":41217},[886],[888,41219,41220],{"xmlns":890},[892,41221,41222,41234],{},[895,41223,41224,41230,41232],{},[1953,41225,41226,41228],{},[898,41227,1823],{},[1810,41229,1959],{},[1677,41231,3128],{},[1810,41233,2008],{},[902,41235,41236],{"encoding":904},"c_1 \u003C 0",[883,41238,41240],{"className":41239},[886],[888,41241,41242],{"xmlns":890},[892,41243,41244,41256],{},[895,41245,41246,41252,41254],{},[1953,41247,41248,41250],{},[898,41249,1779],{},[1810,41251,1812],{},[1677,41253,3128],{},[1810,41255,2008],{},[902,41257,41258],{"encoding":904},"b_2 \u003C 0",[724,41260,41261],{},"Schematicky:",[724,41263,41264,41267],{},[38,41265,41266],{},"Substituty",[883,41268,41270],{"className":41269},[886],[888,41271,41272],{"xmlns":890},[892,41273,41274,41413],{},[895,41275,41276,41282,41284,41299,41301,41321,41323,41343,41345,41347,41353,41355,41369,41371,41391,41393],{},[1953,41277,41278,41280],{},[898,41279,2470],{},[1810,41281,1959],{},[1677,41283,1679],{},[898,41285,41286],{},[41287,41288,41289,41297],"munder",{},[1677,41290,41291],{},[1953,41292,41293,41295],{},[898,41294,207],{},[1810,41296,1959],{},[1677,41298,1776],{"lspace":2058,"rspace":2058},[1677,41300,1776],{},[898,41302,41303],{},[41287,41304,41305,41319],{},[1677,41306,41307,41313],{},[1953,41308,41309,41311],{},[898,41310,1779],{},[1810,41312,1959],{},[1953,41314,41315,41317],{},[898,41316,5325],{},[1810,41318,1959],{},[1677,41320,1906],{"lspace":2058,"rspace":2058},[1677,41322,1776],{},[898,41324,41325],{},[41287,41326,41327,41341],{},[1677,41328,41329,41335],{},[1953,41330,41331,41333],{},[898,41332,1823],{},[1810,41334,1959],{},[1953,41336,41337,41339],{},[898,41338,5325],{},[1810,41340,1812],{},[1677,41342,1776],{"lspace":2058,"rspace":2058},[1677,41344,1967],{"separator":1966},[7266,41346],{"width":7268},[1953,41348,41349,41351],{},[898,41350,2470],{},[1810,41352,1812],{},[1677,41354,1679],{},[898,41356,41357],{},[41287,41358,41359,41367],{},[1677,41360,41361],{},[1953,41362,41363,41365],{},[898,41364,207],{},[1810,41366,1812],{},[1677,41368,1776],{"lspace":2058,"rspace":2058},[1677,41370,1776],{},[898,41372,41373],{},[41287,41374,41375,41389],{},[1677,41376,41377,41383],{},[1953,41378,41379,41381],{},[898,41380,1779],{},[1810,41382,1812],{},[1953,41384,41385,41387],{},[898,41386,5325],{},[1810,41388,1959],{},[1677,41390,1776],{"lspace":2058,"rspace":2058},[1677,41392,1776],{},[898,41394,41395],{},[41287,41396,41397,41411],{},[1677,41398,41399,41405],{},[1953,41400,41401,41403],{},[898,41402,1823],{},[1810,41404,1812],{},[1953,41406,41407,41409],{},[898,41408,5325],{},[1810,41410,1812],{},[1677,41412,1906],{"lspace":2058,"rspace":2058},[902,41414,41415],{"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}",[724,41417,41418,41421],{},[38,41419,41420],{},"Komplementy",[883,41422,41424],{"className":41423},[886],[888,41425,41426],{"xmlns":890},[892,41427,41428,41566],{},[895,41429,41430,41436,41438,41452,41454,41474,41476,41496,41498,41500,41506,41508,41522,41524,41544,41546],{},[1953,41431,41432,41434],{},[898,41433,2470],{},[1810,41435,1959],{},[1677,41437,1679],{},[898,41439,41440],{},[41287,41441,41442,41450],{},[1677,41443,41444],{},[1953,41445,41446,41448],{},[898,41447,207],{},[1810,41449,1959],{},[1677,41451,1776],{"lspace":2058,"rspace":2058},[1677,41453,1776],{},[898,41455,41456],{},[41287,41457,41458,41472],{},[1677,41459,41460,41466],{},[1953,41461,41462,41464],{},[898,41463,1779],{},[1810,41465,1959],{},[1953,41467,41468,41470],{},[898,41469,5325],{},[1810,41471,1959],{},[1677,41473,1906],{"lspace":2058,"rspace":2058},[1677,41475,1776],{},[898,41477,41478],{},[41287,41479,41480,41494],{},[1677,41481,41482,41488],{},[1953,41483,41484,41486],{},[898,41485,1823],{},[1810,41487,1959],{},[1953,41489,41490,41492],{},[898,41491,5325],{},[1810,41493,1812],{},[1677,41495,1906],{"lspace":2058,"rspace":2058},[1677,41497,1967],{"separator":1966},[7266,41499],{"width":7268},[1953,41501,41502,41504],{},[898,41503,2470],{},[1810,41505,1812],{},[1677,41507,1679],{},[898,41509,41510],{},[41287,41511,41512,41520],{},[1677,41513,41514],{},[1953,41515,41516,41518],{},[898,41517,207],{},[1810,41519,1812],{},[1677,41521,1776],{"lspace":2058,"rspace":2058},[1677,41523,1776],{},[898,41525,41526],{},[41287,41527,41528,41542],{},[1677,41529,41530,41536],{},[1953,41531,41532,41534],{},[898,41533,1779],{},[1810,41535,1812],{},[1953,41537,41538,41540],{},[898,41539,5325],{},[1810,41541,1959],{},[1677,41543,1906],{"lspace":2058,"rspace":2058},[1677,41545,1776],{},[898,41547,41548],{},[41287,41549,41550,41564],{},[1677,41551,41552,41558],{},[1953,41553,41554,41556],{},[898,41555,1823],{},[1810,41557,1812],{},[1953,41559,41560,41562],{},[898,41561,5325],{},[1810,41563,1812],{},[1677,41565,1906],{"lspace":2058,"rspace":2058},[902,41567,41568],{"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}",[38361,41570],{},[115,41572,14515],{"id":38170},[5254,41574,41575],{},[724,41576,41577,41579,41580,38385,41593,38399,41606,41609,41610,7057,41634,41652],{},[883,41578,5543],{}," TL;DR\nNabídka vyjadřuje závislost nabízeného množství ",[883,41581,41583],{"className":41582},[886],[888,41584,41585],{"xmlns":890},[892,41586,41587,41591],{},[895,41588,41589],{},[898,41590,2470],{},[902,41592,2470],{"encoding":904},[883,41594,41596],{"className":41595},[886],[888,41597,41598],{"xmlns":890},[892,41599,41600,41604],{},[895,41601,41602],{},[898,41603,5325],{},[902,41605,5325],{"encoding":904},[38,41607,41608],{},"zákon rostoucí nabídky",": při vyšší ceně je výrobce ochoten nabídnout více. Lineární model ",[883,41611,41613],{"className":41612},[886],[888,41614,41615],{"xmlns":890},[892,41616,41617,41631],{},[895,41618,41619,41621,41623,41625,41627,41629],{},[898,41620,5325],{},[1677,41622,1679],{},[898,41624,1823],{},[898,41626,2470],{},[1677,41628,1776],{},[898,41630,1875],{},[902,41632,41633],{"encoding":904},"P = cQ + d",[883,41635,41637],{"className":41636},[886],[888,41638,41639],{"xmlns":890},[892,41640,41641,41649],{},[895,41642,41643,41645,41647],{},[898,41644,1823],{},[1677,41646,3089],{},[1810,41648,2008],{},[902,41650,41651],{"encoding":904},"c > 0"," je standardní aproximací.",[198,41654,38455],{"id":41655},"obecný-vícefaktorový-model-1",[724,41657,41658,11413,41661,41664,41665,41678,41679,38287,41692,38301,41705,41718,41719,41733,41734,38330,41747,41760],{},[38,41659,41660],{},"Nabízené množství",[614,41662,41663],{},"quantity supplied",") závisí na ceně ",[883,41666,41668],{"className":41667},[886],[888,41669,41670],{"xmlns":890},[892,41671,41672,41676],{},[895,41673,41674],{},[898,41675,5325],{},[902,41677,5325],{"encoding":904},", cenách výrobních faktorů (práce ",[883,41680,41682],{"className":41681},[886],[888,41683,41684],{"xmlns":890},[892,41685,41686,41690],{},[895,41687,41688],{},[898,41689,11183],{},[902,41691,11183],{"encoding":904},[883,41693,41695],{"className":41694},[886],[888,41696,41697],{"xmlns":890},[892,41698,41699,41703],{},[895,41700,41701],{},[898,41702,11188],{},[902,41704,11188],{"encoding":904},[883,41706,41708],{"className":41707},[886],[888,41709,41710],{"xmlns":890},[892,41711,41712,41716],{},[895,41713,41714],{},[898,41715,5640],{},[902,41717,5640],{"encoding":904},"), očekávání ",[883,41720,41722],{"className":41721},[886],[888,41723,41724],{"xmlns":890},[892,41725,41726,41731],{},[895,41727,41728],{},[898,41729,41730],{},"V",[902,41732,41730],{"encoding":904},", počtu výrobců ",[883,41735,41737],{"className":41736},[886],[888,41738,41739],{"xmlns":890},[892,41740,41741,41745],{},[895,41742,41743],{},[898,41744,38327],{},[902,41746,38327],{"encoding":904},[883,41748,41750],{"className":41749},[886],[888,41751,41752],{"xmlns":890},[892,41753,41754,41758],{},[895,41755,41756],{},[898,41757,38342],{},[902,41759,38342],{"encoding":904}," a dalších:",[883,41762,41764],{"className":41763},[886],[888,41765,41766],{"xmlns":890,"display":29457},[892,41767,41768,41827],{},[22145,41769,41770],{"width":29462},[22150,41771,41772,41774,41820,41822],{},[22153,41773],{"width":29467},[22153,41775,41776],{},[895,41777,41778,41780,41782,41784,41786,41788,41790,41792,41794,41796,41798,41800,41802,41804,41806,41808,41810,41812,41814,41816,41818],{},[898,41779,2470],{},[1677,41781,1679],{},[898,41783,10061],{},[1677,41785,1686],{"stretchy":1685},[898,41787,5325],{},[1677,41789,1967],{"separator":1966},[898,41791,11183],{},[1677,41793,1967],{"separator":1966},[898,41795,11188],{},[1677,41797,1967],{"separator":1966},[898,41799,5640],{},[1677,41801,1967],{"separator":1966},[898,41803,41730],{},[1677,41805,1967],{"separator":1966},[898,41807,38327],{},[1677,41809,1967],{"separator":1966},[898,41811,38342],{},[1677,41813,1967],{"separator":1966},[1677,41815,11034],{},[1677,41817,1692],{"stretchy":1685},[898,41819,1656],{"mathvariant":2057},[22153,41821],{"width":29467},[22153,41823,41824],{},[1969,41825,41826],{},"(2.7)",[902,41828,41829],{"encoding":904},"Q = S(P, L, K, E, V, O, W, \\ldots). \\tag{2.7}",[724,41831,39807,41832,11413,41835,41838],{},[38,41833,41834],{},"funkce nabídky",[614,41836,41837],{},"supply function",") v širším slova smyslu.",[198,41840,41842],{"id":41841},"jednofaktorový-model","Jednofaktorový model",[724,41844,41845],{},"V nejpřirozenějším jednofaktorovém modelu",[883,41847,41849],{"className":41848},[886],[888,41850,41851],{"xmlns":890,"display":29457},[892,41852,41853,41904],{},[22145,41854,41855],{"width":29462},[22150,41856,41857,41859,41897,41899],{},[22153,41858],{"width":29467},[22153,41860,41861],{},[895,41862,41863,41865,41867,41869,41871,41873,41875,41877,41879,41881,41883,41885,41887,41889,41891,41893,41895],{},[898,41864,2470],{},[1677,41866,1679],{},[898,41868,10061],{},[1677,41870,1686],{"stretchy":1685},[898,41872,5325],{},[1677,41874,1692],{"stretchy":1685},[1677,41876,1967],{"separator":1966},[7266,41878],{"width":7268},[1969,41880,38808],{},[7266,41882],{"width":7268},[898,41884,5325],{},[1677,41886,1679],{},[898,41888,10061],{},[1677,41890,1686],{"stretchy":1685},[898,41892,2470],{},[1677,41894,1692],{"stretchy":1685},[898,41896,1656],{"mathvariant":2057},[22153,41898],{"width":29467},[22153,41900,41901],{},[1969,41902,41903],{},"(2.8)",[902,41905,41906],{"encoding":904},"Q = S(P), \\qquad \\text{resp.} \\qquad P = S(Q). \\tag{2.8}",[724,41908,41909,41910,11413,41913,5306],{},"Graf je ",[38,41911,41912],{},"křivka nabídky",[614,41914,41915],{},"supply curve",[38739,41917,41919],{"id":41918},"zákon-rostoucí-nabídky","Zákon rostoucí nabídky",[5254,41921,41922],{},[724,41923,41924],{},[38,41925,38854,41926,41939,41940,38909],{},[883,41927,41929],{"className":41928},[886],[888,41930,41931],{"xmlns":890},[892,41932,41933,41937],{},[895,41934,41935],{},[898,41936,5325],{},[902,41938,5325],{"encoding":904},", pak nabízené množství ",[883,41941,41943],{"className":41942},[886],[888,41944,41945],{"xmlns":890},[892,41946,41947,41951],{},[895,41948,41949],{},[898,41950,2470],{},[902,41952,2470],{"encoding":904},[724,41954,41955,41956,41981,41982,42012,42013,42030],{},"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 ",[883,41957,41959],{"className":41958},[886],[888,41960,41961],{"xmlns":890},[892,41962,41963,41979],{},[895,41964,41965,41967,41969,41971,41977],{},[1677,41966,2167],{"stretchy":1685},[1810,41968,2008],{},[1677,41970,1967],{"separator":1966},[1953,41972,41973,41975],{},[898,41974,5325],{},[1810,41976,2008],{},[1677,41978,2182],{"stretchy":1685},[902,41980,38994],{"encoding":904}," na svislé ose (případně z ",[883,41983,41985],{"className":41984},[886],[888,41986,41987],{"xmlns":890},[892,41988,41989,42009],{},[895,41990,41991,41993,41999,42001,42007],{},[1677,41992,2167],{"stretchy":1685},[1953,41994,41995,41997],{},[898,41996,2470],{},[1810,41998,1959],{},[1677,42000,1967],{"separator":1966},[1953,42002,42003,42005],{},[898,42004,5325],{},[1810,42006,1959],{},[1677,42008,2182],{"stretchy":1685},[902,42010,42011],{"encoding":904},"[Q_1, P_1]","), kde ",[883,42014,42016],{"className":42015},[886],[888,42017,42018],{"xmlns":890},[892,42019,42020,42028],{},[895,42021,42022],{},[1953,42023,42024,42026],{},[898,42025,5325],{},[1810,42027,2008],{},[902,42029,40339],{"encoding":904}," je minimální cena, při které je výrobce ochoten vyrábět.",[724,42032,42033],{},[614,42034,42035,42036,3399,42049,1656],{},"Obrázek 2.9: Typická rostoucí křivka nabídky ",[883,42037,42039],{"className":42038},[886],[888,42040,42041],{"xmlns":890},[892,42042,42043,42047],{},[895,42044,42045],{},[898,42046,10061],{},[902,42048,10061],{"encoding":904},[883,42050,42052],{"className":42051},[886],[888,42053,42054],{"xmlns":890},[892,42055,42056,42068],{},[895,42057,42058,42060,42062,42064,42066],{},[1677,42059,1686],{"stretchy":1685},[898,42061,2470],{},[1677,42063,1967],{"separator":1966},[898,42065,5325],{},[1677,42067,1692],{"stretchy":1685},[902,42069,39082],{"encoding":904},[38739,42071,42073],{"id":42072},"lineární-model-nabídky","Lineární model nabídky",[883,42075,42077],{"className":42076},[886],[888,42078,42079],{"xmlns":890,"display":29457},[892,42080,42081,42120],{},[22145,42082,42083],{"width":29462},[22150,42084,42085,42087,42113,42115],{},[22153,42086],{"width":29467},[22153,42088,42089],{},[895,42090,42091,42093,42095,42097,42099,42101,42103,42105,42107,42109,42111],{},[898,42092,5325],{},[1677,42094,1679],{},[898,42096,1823],{},[898,42098,2470],{},[1677,42100,1776],{},[898,42102,1875],{},[1677,42104,1967],{"separator":1966},[7266,42106],{"width":7268},[898,42108,1823],{},[1677,42110,3089],{},[1810,42112,13850],{},[22153,42114],{"width":29467},[22153,42116,42117],{},[1969,42118,42119],{},"(2.9)",[902,42121,42122],{"encoding":904},"P = cQ + d, \\qquad c > 0. \\tag{2.9}",[724,42124,42125,42126,42162,42163,42176],{},"Alternativně ",[883,42127,42129],{"className":42128},[886],[888,42130,42131],{"xmlns":890},[892,42132,42133,42159],{},[895,42134,42135,42137,42139,42147,42149,42151],{},[898,42136,2470],{},[1677,42138,1679],{},[2006,42140,42141],{"scriptlevel":2008,"displaystyle":1685},[2010,42142,42143,42145],{},[1810,42144,1959],{},[898,42146,1823],{},[898,42148,5325],{},[1677,42150,1906],{},[2006,42152,42153],{"scriptlevel":2008,"displaystyle":1685},[2010,42154,42155,42157],{},[898,42156,1875],{},[898,42158,1823],{},[902,42160,42161],{"encoding":904},"Q = \\tfrac{1}{c}P - \\tfrac{d}{c}","; znaménko koeficientu u ",[883,42164,42166],{"className":42165},[886],[888,42167,42168],{"xmlns":890},[892,42169,42170,42174],{},[895,42171,42172],{},[898,42173,5325],{},[902,42175,5325],{"encoding":904}," zůstává, znaménko absolutního členu se mění.",[39316,42178,42180],{"id":42179},"příklad-25","Příklad 2.5",[724,42182,42183,42185,42186,1656],{},[38,42184,39324],{}," Lineární nabídka ",[883,42187,42189],{"className":42188},[886],[888,42190,42191],{"xmlns":890},[892,42192,42193,42207],{},[895,42194,42195,42197,42199,42201,42203,42205],{},[898,42196,5325],{},[1677,42198,1679],{},[1810,42200,6397],{},[898,42202,2470],{},[1677,42204,1776],{},[1810,42206,6392],{},[902,42208,42209],{"encoding":904},"P = 0{,}5Q + 25",[724,42211,42212,42214,42215,1656],{},[38,42213,39356],{}," Alternativní tvar ",[883,42216,42218],{"className":42217},[886],[888,42219,42220],{"xmlns":890},[892,42221,42222,42236],{},[895,42223,42224,42226,42228,42230,42232,42234],{},[898,42225,2470],{},[1677,42227,1679],{},[1810,42229,1812],{},[898,42231,5325],{},[1677,42233,1906],{},[1810,42235,2801],{},[902,42237,42238],{"encoding":904},"Q = 2P - 50",[16,42240,42241,42266],{},[19,42242,42243],{},[22,42244,42245,42260,42262,42264],{},[25,42246,42247],{},[883,42248,42250],{"className":42249},[886],[888,42251,42252],{"xmlns":890},[892,42253,42254,42258],{},[895,42255,42256],{},[898,42257,5325],{},[902,42259,5325],{"encoding":904},[25,42261,39410],{},[25,42263,16428],{},[25,42265,6599],{},[30,42267,42268],{},[22,42269,42270,42285,42287,42289],{},[35,42271,42272],{},[883,42273,42275],{"className":42274},[886],[888,42276,42277],{"xmlns":890},[892,42278,42279,42283],{},[895,42280,42281],{},[898,42282,2470],{},[902,42284,2470],{"encoding":904},[35,42286,2544],{},[35,42288,10423],{},[35,42290,39410],{},[198,42292,42294,42295,1692],{"id":42293},"posun-nabídky-shift-of-supply","Posun nabídky (",[614,42296,42297],{},"shift of supply",[724,42299,42300,42301,42304,42305,42322,42323,42348,42349,1656],{},"Posun nastává při změně exogenních proměnných — nová technologie snižuje náklady (posun ",[38,42302,42303],{},"doprava",": při stejné ceně ",[883,42306,42308],{"className":42307},[886],[888,42309,42310],{"xmlns":890},[892,42311,42312,42320],{},[895,42313,42314],{},[1953,42315,42316,42318],{},[898,42317,5325],{},[1810,42319,2008],{},[902,42321,40339],{"encoding":904}," vyrobí výrobce větší ",[883,42324,42326],{"className":42325},[886],[888,42327,42328],{"xmlns":890},[892,42329,42330,42346],{},[895,42331,42332,42338,42340],{},[1953,42333,42334,42336],{},[898,42335,2470],{},[1810,42337,1959],{},[1677,42339,3089],{},[1953,42341,42342,42344],{},[898,42343,2470],{},[1810,42345,2008],{},[902,42347,40452],{"encoding":904},"); zdražení vstupů posune křivku ",[38,42350,42351],{},"doleva",[724,42353,42354],{},[614,42355,42356,42357,42370,42371,42389,42390,42408,42409,1656],{},"Obrázek 2.11: Původní ",[883,42358,42360],{"className":42359},[886],[888,42361,42362],{"xmlns":890},[892,42363,42364,42368],{},[895,42365,42366],{},[898,42367,10061],{},[902,42369,10061],{"encoding":904},", posunuté ",[883,42372,42374],{"className":42373},[886],[888,42375,42376],{"xmlns":890},[892,42377,42378,42386],{},[895,42379,42380],{},[1953,42381,42382,42384],{},[898,42383,10061],{},[1810,42385,1959],{},[902,42387,42388],{"encoding":904},"S_1"," (doprava) a ",[883,42391,42393],{"className":42392},[886],[888,42394,42395],{"xmlns":890},[892,42396,42397,42405],{},[895,42398,42399],{},[1953,42400,42401,42403],{},[898,42402,10061],{},[1810,42404,1812],{},[902,42406,42407],{"encoding":904},"S_2"," (doleva) v ",[883,42410,42412],{"className":42411},[886],[888,42413,42414],{"xmlns":890},[892,42415,42416,42428],{},[895,42417,42418,42420,42422,42424,42426],{},[1677,42419,1686],{"stretchy":1685},[898,42421,2470],{},[1677,42423,1967],{"separator":1966},[898,42425,5325],{},[1677,42427,1692],{"stretchy":1685},[902,42429,39082],{"encoding":904},[39316,42431,42433],{"id":42432},"příklad-26-zdanění-výrobce","Příklad 2.6 — zdanění výrobce",[724,42435,42436,42438,42439,42463,42464,1656],{},[38,42437,39324],{}," Nabídka ",[883,42440,42442],{"className":42441},[886],[888,42443,42444],{"xmlns":890},[892,42445,42446,42460],{},[895,42447,42448,42450,42452,42454,42456,42458],{},[898,42449,5325],{},[1677,42451,1679],{},[898,42453,10061],{},[1677,42455,1686],{"stretchy":1685},[898,42457,2470],{},[1677,42459,1692],{"stretchy":1685},[902,42461,42462],{"encoding":904},"P = S(Q)","; na výrobce je uložena jednotková daň ",[883,42465,42467],{"className":42466},[886],[888,42468,42469],{"xmlns":890},[892,42470,42471,42475],{},[895,42472,42473],{},[898,42474,2455],{},[902,42476,2455],{"encoding":904},[724,42478,42479,42481,42482,42495,42496,42514,42515,42543],{},[38,42480,39356],{}," Spotřebitel zaplatí ",[883,42483,42485],{"className":42484},[886],[888,42486,42487],{"xmlns":890},[892,42488,42489,42493],{},[895,42490,42491],{},[898,42492,5325],{},[902,42494,5325],{"encoding":904},", výrobce obdrží ",[883,42497,42499],{"className":42498},[886],[888,42500,42501],{"xmlns":890},[892,42502,42503,42511],{},[895,42504,42505,42507,42509],{},[898,42506,5325],{},[1677,42508,1906],{},[898,42510,2455],{},[902,42512,42513],{"encoding":904},"P - T",". Z podmínky ",[883,42516,42518],{"className":42517},[886],[888,42519,42520],{"xmlns":890},[892,42521,42522,42540],{},[895,42523,42524,42526,42528,42530,42532,42534,42536,42538],{},[898,42525,5325],{},[1677,42527,1906],{},[898,42529,2455],{},[1677,42531,1679],{},[898,42533,10061],{},[1677,42535,1686],{"stretchy":1685},[898,42537,2470],{},[1677,42539,1692],{"stretchy":1685},[902,42541,42542],{"encoding":904},"P - T = S(Q)"," plyne",[883,42545,42547],{"className":42546},[886],[888,42548,42549],{"xmlns":890,"display":29457},[892,42550,42551,42585],{},[895,42552,42553,42555,42557,42563,42565,42567,42569,42571,42573,42575,42577,42579,42581,42583],{},[898,42554,5325],{},[1677,42556,1679],{},[1953,42558,42559,42561],{},[898,42560,10061],{},[1810,42562,1959],{},[1677,42564,1686],{"stretchy":1685},[898,42566,2470],{},[1677,42568,1692],{"stretchy":1685},[1677,42570,1679],{},[898,42572,10061],{},[1677,42574,1686],{"stretchy":1685},[898,42576,2470],{},[1677,42578,1692],{"stretchy":1685},[1677,42580,1776],{},[898,42582,2455],{},[898,42584,1656],{"mathvariant":2057},[902,42586,42587],{"encoding":904},"P = S_1(Q) = S(Q) + T.",[724,42589,42590,42591,42604,42605,1884,42618,42621,42622,5272,42642,9490,42660,1656],{},"Křivka ",[883,42592,42594],{"className":42593},[886],[888,42595,42596],{"xmlns":890},[892,42597,42598,42602],{},[895,42599,42600],{},[898,42601,10061],{},[902,42603,10061],{"encoding":904}," se tedy posune o ",[883,42606,42608],{"className":42607},[886],[888,42609,42610],{"xmlns":890},[892,42611,42612,42616],{},[895,42613,42614],{},[898,42615,2455],{},[902,42617,2455],{"encoding":904},[38,42619,42620],{},"svisle nahoru"," (tj. doleva). Např. pro ",[883,42623,42625],{"className":42624},[886],[888,42626,42627],{"xmlns":890},[892,42628,42629,42639],{},[895,42630,42631,42633,42635,42637],{},[898,42632,5325],{},[1677,42634,1679],{},[1810,42636,1812],{},[898,42638,2470],{},[902,42640,42641],{"encoding":904},"P = 2Q",[883,42643,42645],{"className":42644},[886],[888,42646,42647],{"xmlns":890},[892,42648,42649,42657],{},[895,42650,42651,42653,42655],{},[898,42652,2455],{},[1677,42654,1679],{},[1810,42656,1916],{},[902,42658,42659],{"encoding":904},"T = 6",[883,42661,42663],{"className":42662},[886],[888,42664,42665],{"xmlns":890},[892,42666,42667,42689],{},[895,42668,42669,42675,42677,42679,42681,42683,42685,42687],{},[1953,42670,42671,42673],{},[898,42672,10061],{},[1810,42674,1959],{},[1677,42676,2385],{},[898,42678,5325],{},[1677,42680,1679],{},[1810,42682,1812],{},[898,42684,2470],{},[1677,42686,1776],{},[1810,42688,1916],{},[902,42690,42691],{"encoding":904},"S_1: P = 2Q + 6",[724,42693,42694],{},[614,42695,42696,42697,42710],{},"Obrázek 2.12: Posun nabídky o ",[883,42698,42700],{"className":42699},[886],[888,42701,42702],{"xmlns":890},[892,42703,42704,42708],{},[895,42705,42706],{},[898,42707,2455],{},[902,42709,2455],{"encoding":904}," svisle nahoru.",[38361,42712],{},[115,42714,42716],{"id":42715},"tržní-rovnováha","Tržní rovnováha",[5254,42718,42719],{},[724,42720,42721,42723,42724,1884,42727,42759,42760,1343,42783,42806,42807,42810,42811,42824],{},[883,42722,5543],{}," TL;DR\nV ",[38,42725,42726],{},"rovnovážném bodě",[883,42728,42730],{"className":42729},[886],[888,42731,42732],{"xmlns":890},[892,42733,42734,42756],{},[895,42735,42736,42738,42740,42746,42748,42754],{},[898,42737,5640],{},[1677,42739,2167],{"stretchy":1685},[1805,42741,42742,42744],{},[898,42743,2470],{},[898,42745,5640],{},[1677,42747,1967],{"separator":1966},[1805,42749,42750,42752],{},[898,42751,5325],{},[898,42753,5640],{},[1677,42755,2182],{"stretchy":1685},[902,42757,42758],{"encoding":904},"E[Q^E, P^E]"," se poptávané a nabízené množství rovnají. Najde se jako řešení soustavy ",[883,42761,42763],{"className":42762},[886],[888,42764,42765],{"xmlns":890},[892,42766,42767,42781],{},[895,42768,42769,42771,42773,42775,42777,42779],{},[898,42770,5325],{},[1677,42772,1679],{},[898,42774,5571],{},[1677,42776,1686],{"stretchy":1685},[898,42778,2470],{},[1677,42780,1692],{"stretchy":1685},[902,42782,6028],{"encoding":904},[883,42784,42786],{"className":42785},[886],[888,42787,42788],{"xmlns":890},[892,42789,42790,42804],{},[895,42791,42792,42794,42796,42798,42800,42802],{},[898,42793,5325],{},[1677,42795,1679],{},[898,42797,10061],{},[1677,42799,1686],{"stretchy":1685},[898,42801,2470],{},[1677,42803,1692],{"stretchy":1685},[902,42805,42462],{"encoding":904},". Čtyři ",[38,42808,42809],{},"pravidla komparativní statiky"," popisují, jak se ",[883,42812,42814],{"className":42813},[886],[888,42815,42816],{"xmlns":890},[892,42817,42818,42822],{},[895,42819,42820],{},[898,42821,5640],{},[902,42823,5640],{"encoding":904}," posune při změně poptávky nebo nabídky.",[198,42826,42828],{"id":42827},"definice","Definice",[724,42830,42831,11413,42833,42836,42837,1884,42840,42858,42859,42890,42891,11413,42894,5306],{},[38,42832,42716],{},[614,42834,42835],{},"market equilibrium",") je stav, kdy poptávané množství = nabízené množství. Při ",[38,42838,42839],{},"rovnovážné ceně",[883,42841,42843],{"className":42842},[886],[888,42844,42845],{"xmlns":890},[892,42846,42847,42855],{},[895,42848,42849],{},[1805,42850,42851,42853],{},[898,42852,5325],{},[898,42854,5640],{},[902,42856,42857],{"encoding":904},"P^E"," není přebytek ani nedostatek zboží. Bod ",[883,42860,42862],{"className":42861},[886],[888,42863,42864],{"xmlns":890},[892,42865,42866,42888],{},[895,42867,42868,42870,42872,42878,42880,42886],{},[898,42869,5640],{},[1677,42871,2167],{"stretchy":1685},[1805,42873,42874,42876],{},[898,42875,2470],{},[898,42877,5640],{},[1677,42879,1967],{"separator":1966},[1805,42881,42882,42884],{},[898,42883,5325],{},[898,42885,5640],{},[1677,42887,2182],{"stretchy":1685},[902,42889,42758],{"encoding":904}," se nazývá ",[38,42892,42893],{},"rovnovážný bod",[614,42895,42896],{},"equilibrium point",[724,42898,42899,42900,1343,42923,1656],{},"Rovnovážný bod je průsečíkem křivek poptávky a nabídky; nalézá se jako řešení soustavy ",[883,42901,42903],{"className":42902},[886],[888,42904,42905],{"xmlns":890},[892,42906,42907,42921],{},[895,42908,42909,42911,42913,42915,42917,42919],{},[898,42910,5325],{},[1677,42912,1679],{},[898,42914,5571],{},[1677,42916,1686],{"stretchy":1685},[898,42918,2470],{},[1677,42920,1692],{"stretchy":1685},[902,42922,6028],{"encoding":904},[883,42924,42926],{"className":42925},[886],[888,42927,42928],{"xmlns":890},[892,42929,42930,42944],{},[895,42931,42932,42934,42936,42938,42940,42942],{},[898,42933,5325],{},[1677,42935,1679],{},[898,42937,10061],{},[1677,42939,1686],{"stretchy":1685},[898,42941,2470],{},[1677,42943,1692],{"stretchy":1685},[902,42945,42462],{"encoding":904},[724,42947,42948],{},[2240,42949],{"alt":42950,"className":42951,"src":42952},"imek-poptavka-nabidka-rovnovaha",[210,2244],"\u002Fwiki-assets\u002Fimek-poptavka-nabidka-rovnovaha.jpeg",[724,42954,42955],{},[614,42956,42957,42958,42971,42972,15401,42985,43006,43007,1656],{},"Obrázek 2.13: Klesající ",[883,42959,42961],{"className":42960},[886],[888,42962,42963],{"xmlns":890},[892,42964,42965,42969],{},[895,42966,42967],{},[898,42968,5571],{},[902,42970,5571],{"encoding":904}," a rostoucí ",[883,42973,42975],{"className":42974},[886],[888,42976,42977],{"xmlns":890},[892,42978,42979,42983],{},[895,42980,42981],{},[898,42982,10061],{},[902,42984,10061],{"encoding":904},[883,42986,42988],{"className":42987},[886],[888,42989,42990],{"xmlns":890},[892,42991,42992,43004],{},[895,42993,42994,42996,42998,43000,43002],{},[1677,42995,1686],{"stretchy":1685},[898,42997,2470],{},[1677,42999,1967],{"separator":1966},[898,43001,5325],{},[1677,43003,1692],{"stretchy":1685},[902,43005,39082],{"encoding":904}," protínající se v ",[883,43008,43010],{"className":43009},[886],[888,43011,43012],{"xmlns":890},[892,43013,43014,43036],{},[895,43015,43016,43018,43020,43026,43028,43034],{},[898,43017,5640],{},[1677,43019,2167],{"stretchy":1685},[1805,43021,43022,43024],{},[898,43023,2470],{},[898,43025,5640],{},[1677,43027,1967],{"separator":1966},[1805,43029,43030,43032],{},[898,43031,5325],{},[898,43033,5640],{},[1677,43035,2182],{"stretchy":1685},[902,43037,42758],{"encoding":904},[198,43039,43041],{"id":43040},"příklad-27-kvadratický-model","Příklad 2.7 (kvadratický model)",[724,43043,43044,43046,43047,43081,43082,1656],{},[38,43045,39324],{}," Poptávka ",[883,43048,43050],{"className":43049},[886],[888,43051,43052],{"xmlns":890},[892,43053,43054,43078],{},[895,43055,43056,43058,43060,43062,43068,43070,43072,43074,43076],{},[898,43057,5325],{},[1677,43059,1679],{},[1677,43061,1906],{},[1805,43063,43064,43066],{},[898,43065,2470],{},[1810,43067,1812],{},[1677,43069,1906],{},[1810,43071,2544],{},[898,43073,2470],{},[1677,43075,1776],{},[1810,43077,10191],{},[902,43079,43080],{"encoding":904},"P = -Q^2 - 10Q + 150",", nabídka ",[883,43083,43085],{"className":43084},[886],[888,43086,43087],{"xmlns":890},[892,43088,43089,43111],{},[895,43090,43091,43093,43095,43101,43103,43105,43107,43109],{},[898,43092,5325],{},[1677,43094,1679],{},[1805,43096,43097,43099],{},[898,43098,2470],{},[1810,43100,1812],{},[1677,43102,1776],{},[1810,43104,24337],{},[898,43106,2470],{},[1677,43108,1776],{},[1810,43110,33937],{},[902,43112,43113],{"encoding":904},"P = Q^2 + 14Q + 22",[724,43115,43116,43118],{},[38,43117,39356],{}," Z rovnosti",[883,43120,43122],{"className":43121},[886],[888,43123,43124],{"xmlns":890,"display":29457},[892,43125,43126,43164],{},[895,43127,43128,43130,43136,43138,43140,43142,43144,43146,43148,43154,43156,43158,43160,43162],{},[1677,43129,1906],{},[1805,43131,43132,43134],{},[898,43133,2470],{},[1810,43135,1812],{},[1677,43137,1906],{},[1810,43139,2544],{},[898,43141,2470],{},[1677,43143,1776],{},[1810,43145,10191],{},[1677,43147,1679],{},[1805,43149,43150,43152],{},[898,43151,2470],{},[1810,43153,1812],{},[1677,43155,1776],{},[1810,43157,24337],{},[898,43159,2470],{},[1677,43161,1776],{},[1810,43163,33937],{},[902,43165,43166],{"encoding":904},"-Q^2 - 10Q + 150 = Q^2 + 14Q + 22",[724,43168,43169,43170,43205,43206,43239,43240,43257,43258,43271,43272,1343,43294,43331,43332,1656],{},"dostaneme ",[883,43171,43173],{"className":43172},[886],[888,43174,43175],{"xmlns":890},[892,43176,43177,43202],{},[895,43178,43179,43181,43187,43189,43192,43194,43196,43198,43200],{},[1810,43180,1812],{},[1805,43182,43183,43185],{},[898,43184,2470],{},[1810,43186,1812],{},[1677,43188,1776],{},[1810,43190,43191],{},"24",[898,43193,2470],{},[1677,43195,1906],{},[1810,43197,7005],{},[1677,43199,1679],{},[1810,43201,2008],{},[902,43203,43204],{"encoding":904},"2Q^2 + 24Q - 128 = 0",", resp. ",[883,43207,43209],{"className":43208},[886],[888,43210,43211],{"xmlns":890},[892,43212,43213,43236],{},[895,43214,43215,43221,43223,43225,43227,43229,43232,43234],{},[1805,43216,43217,43219],{},[898,43218,2470],{},[1810,43220,1812],{},[1677,43222,1776],{},[1810,43224,3190],{},[898,43226,2470],{},[1677,43228,1906],{},[1810,43230,43231],{},"64",[1677,43233,1679],{},[1810,43235,2008],{},[902,43237,43238],{"encoding":904},"Q^2 + 12Q - 64 = 0",". Kořeny jsou ",[883,43241,43243],{"className":43242},[886],[888,43244,43245],{"xmlns":890},[892,43246,43247,43254],{},[895,43248,43249,43251],{},[1677,43250,1906],{},[1810,43252,43253],{},"16",[902,43255,43256],{"encoding":904},"-16"," (nevyhovuje) a ",[883,43259,43261],{"className":43260},[886],[888,43262,43263],{"xmlns":890},[892,43264,43265,43269],{},[895,43266,43267],{},[1810,43268,2032],{},[902,43270,2032],{"encoding":904},". Tedy ",[883,43273,43275],{"className":43274},[886],[888,43276,43277],{"xmlns":890},[892,43278,43279,43291],{},[895,43280,43281,43287,43289],{},[1805,43282,43283,43285],{},[898,43284,2470],{},[898,43286,5640],{},[1677,43288,1679],{},[1810,43290,2032],{},[902,43292,43293],{"encoding":904},"Q^E = 4",[883,43295,43297],{"className":43296},[886],[888,43298,43299],{"xmlns":890},[892,43300,43301,43328],{},[895,43302,43303,43309,43311,43313,43315,43317,43319,43321,43323,43325],{},[1805,43304,43305,43307],{},[898,43306,5325],{},[898,43308,5640],{},[1677,43310,1679],{},[1677,43312,1906],{},[1810,43314,43253],{},[1677,43316,1906],{},[1810,43318,6599],{},[1677,43320,1776],{},[1810,43322,10191],{},[1677,43324,1679],{},[1810,43326,43327],{},"94",[902,43329,43330],{"encoding":904},"P^E = -16 - 40 + 150 = 94",", rovnovážný bod ",[883,43333,43335],{"className":43334},[886],[888,43336,43337],{"xmlns":890},[892,43338,43339,43353],{},[895,43340,43341,43343,43345,43347,43349,43351],{},[898,43342,5640],{},[1677,43344,2167],{"stretchy":1685},[1810,43346,2032],{},[1677,43348,1967],{"separator":1966},[1810,43350,43327],{},[1677,43352,2182],{"stretchy":1685},[902,43354,43355],{"encoding":904},"E[4, 94]",[198,43357,43359],{"id":43358},"příklad-28-dvoukomoditní-trh","Příklad 2.8 (dvoukomoditní trh)",[724,43361,43362,43364],{},[38,43363,39324],{}," Poptávky a nabídky dvou zboží",[883,43366,43368],{"className":43367},[886],[888,43369,43370],{"xmlns":890,"display":29457},[892,43371,43372,43538],{},[22145,43373,43376,43464],{"rowspacing":22147,"columnalign":43374,"columnspacing":43375},"right left right left","0em 1em 0em",[22150,43377,43378,43388,43420,43430],{},[22153,43379,43380],{},[2006,43381,43382],{"scriptlevel":2008,"displaystyle":1966},[1953,43383,43384,43386],{},[898,43385,2470],{},[1810,43387,1959],{},[22153,43389,43390],{},[2006,43391,43392],{"scriptlevel":2008,"displaystyle":1966},[895,43393,43394,43396,43398,43400,43402,43404,43410,43412,43418],{},[895,43395],{},[1677,43397,1679],{},[1810,43399,6599],{},[1677,43401,1906],{},[1810,43403,1909],{},[1953,43405,43406,43408],{},[898,43407,5325],{},[1810,43409,1959],{},[1677,43411,1906],{},[1953,43413,43414,43416],{},[898,43415,5325],{},[1810,43417,1812],{},[1677,43419,1967],{"separator":1966},[22153,43421,43422],{},[2006,43423,43424],{"scriptlevel":2008,"displaystyle":1966},[1953,43425,43426,43428],{},[898,43427,2470],{},[1810,43429,1812],{},[22153,43431,43432],{},[2006,43433,43434],{"scriptlevel":2008,"displaystyle":1966},[895,43435,43436,43438,43440,43442,43444,43446,43452,43454,43456,43462],{},[895,43437],{},[1677,43439,1679],{},[1810,43441,2801],{},[1677,43443,1906],{},[1810,43445,1812],{},[1953,43447,43448,43450],{},[898,43449,5325],{},[1810,43451,1959],{},[1677,43453,1906],{},[1810,43455,2032],{},[1953,43457,43458,43460],{},[898,43459,5325],{},[1810,43461,1812],{},[1677,43463,1967],{"separator":1966},[22150,43465,43466,43476,43502,43512],{},[22153,43467,43468],{},[2006,43469,43470],{"scriptlevel":2008,"displaystyle":1966},[1953,43471,43472,43474],{},[898,43473,2470],{},[1810,43475,1959],{},[22153,43477,43478],{},[2006,43479,43480],{"scriptlevel":2008,"displaystyle":1966},[895,43481,43482,43484,43486,43488,43490,43492,43494,43500],{},[895,43483],{},[1677,43485,1679],{},[1677,43487,1906],{},[1810,43489,1854],{},[1677,43491,1776],{},[1810,43493,2032],{},[1953,43495,43496,43498],{},[898,43497,5325],{},[1810,43499,1959],{},[1677,43501,1967],{"separator":1966},[22153,43503,43504],{},[2006,43505,43506],{"scriptlevel":2008,"displaystyle":1966},[1953,43507,43508,43510],{},[898,43509,2470],{},[1810,43511,1812],{},[22153,43513,43514],{},[2006,43515,43516],{"scriptlevel":2008,"displaystyle":1966},[895,43517,43518,43520,43522,43524,43526,43528,43530,43536],{},[895,43519],{},[1677,43521,1679],{},[1677,43523,1906],{},[1810,43525,25592],{},[1677,43527,1776],{},[1810,43529,1854],{},[1953,43531,43532,43534],{},[898,43533,5325],{},[1810,43535,1812],{},[898,43537,1656],{"mathvariant":2057},[902,43539,43540],{"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}",[724,43542,43543,43545],{},[38,43544,39356],{}," Z rovností poptávek a nabídek dostaneme",[883,43547,43549],{"className":43548},[886],[888,43550,43551],{"xmlns":890,"display":29457},[892,43552,43553,43602],{},[895,43554,43555,43557,43563,43565,43571,43573,43575,43577,43579,43581,43587,43589,43591,43597,43599],{},[1810,43556,5387],{},[1953,43558,43559,43561],{},[898,43560,5325],{},[1810,43562,1959],{},[1677,43564,1776],{},[1953,43566,43567,43569],{},[898,43568,5325],{},[1810,43570,1812],{},[1677,43572,1679],{},[1810,43574,22594],{},[1677,43576,1967],{"separator":1966},[7266,43578],{"width":7268},[1810,43580,1812],{},[1953,43582,43583,43585],{},[898,43584,5325],{},[1810,43586,1959],{},[1677,43588,1776],{},[1810,43590,25592],{},[1953,43592,43593,43595],{},[898,43594,5325],{},[1810,43596,1812],{},[1677,43598,1679],{},[1810,43600,43601],{},"57.",[902,43603,43604],{"encoding":904},"9P_1 + P_2 = 43, \\qquad 2P_1 + 7P_2 = 57.",[724,43606,43607,43608,1343,43632,43656,43657,1343,43682,43706,43707,43709],{},"Řešením je ",[883,43609,43611],{"className":43610},[886],[888,43612,43613],{"xmlns":890},[892,43614,43615,43629],{},[895,43616,43617,43625,43627],{},[10554,43618,43619,43621,43623],{},[898,43620,5325],{},[1810,43622,1959],{},[898,43624,5640],{},[1677,43626,1679],{},[1810,43628,2032],{},[902,43630,43631],{"encoding":904},"P_1^E = 4",[883,43633,43635],{"className":43634},[886],[888,43636,43637],{"xmlns":890},[892,43638,43639,43653],{},[895,43640,43641,43649,43651],{},[10554,43642,43643,43645,43647],{},[898,43644,5325],{},[1810,43646,1812],{},[898,43648,5640],{},[1677,43650,1679],{},[1810,43652,25592],{},[902,43654,43655],{"encoding":904},"P_2^E = 7","; zpětným dosazením ",[883,43658,43660],{"className":43659},[886],[888,43661,43662],{"xmlns":890},[892,43663,43664,43679],{},[895,43665,43666,43674,43676],{},[10554,43667,43668,43670,43672],{},[898,43669,2470],{},[1810,43671,1959],{},[898,43673,5640],{},[1677,43675,1679],{},[1810,43677,43678],{},"13",[902,43680,43681],{"encoding":904},"Q_1^E = 13",[883,43683,43685],{"className":43684},[886],[888,43686,43687],{"xmlns":890},[892,43688,43689,43703],{},[895,43690,43691,43699,43701],{},[10554,43692,43693,43695,43697],{},[898,43694,2470],{},[1810,43696,1812],{},[898,43698,5640],{},[1677,43700,1679],{},[1810,43702,24337],{},[902,43704,43705],{"encoding":904},"Q_2^E = 14",". Zboží jsou ",[38,43708,41213],{}," (zkřížené koeficienty v poptávce jsou záporné).",[198,43711,43713],{"id":43712},"dynamický-model-pavučinový-teorém","Dynamický model — pavučinový teorém",[724,43715,43716,43717,43734,43735,11413,43738,5306],{},"Rovnovážná cena se obecně liší od tržní ceny, která vzniká působením tržních sil v čase. Za podmínky stability se tržní cena přibližuje k ",[883,43718,43720],{"className":43719},[886],[888,43721,43722],{"xmlns":890},[892,43723,43724,43732],{},[895,43725,43726],{},[1805,43727,43728,43730],{},[898,43729,5325],{},[898,43731,5640],{},[902,43733,42857],{"encoding":904},"; mechanismus popisuje ",[38,43736,43737],{},"teorém pavučiny",[614,43739,43740],{},"cobweb model",[198,43742,43744],{"id":43743},"pravidla-komparativní-statiky-14","Pravidla komparativní statiky (1–4)",[724,43746,43747],{},[2240,43748],{"alt":43749,"className":43750,"src":43751},"imek-komparativni-statika-4pripady",[210,2244],"\u002Fwiki-assets\u002Fimek-komparativni-statika-4pripady.jpeg",[5254,43753,43754,43795,43835,43875],{},[724,43755,43756,43759,43760,7578,43777,1656],{},[38,43757,43758],{},"Pravidlo 1:"," Růst poptávky ⟹ růst ",[883,43761,43763],{"className":43762},[886],[888,43764,43765],{"xmlns":890},[892,43766,43767,43775],{},[895,43768,43769],{},[1805,43770,43771,43773],{},[898,43772,5325],{},[898,43774,5640],{},[902,43776,42857],{"encoding":904},[883,43778,43780],{"className":43779},[886],[888,43781,43782],{"xmlns":890},[892,43783,43784,43792],{},[895,43785,43786],{},[1805,43787,43788,43790],{},[898,43789,2470],{},[898,43791,5640],{},[902,43793,43794],{"encoding":904},"Q^E",[724,43796,43797,43800,43801,7578,43818,1656],{},[38,43798,43799],{},"Pravidlo 2:"," Pokles poptávky ⟹ pokles ",[883,43802,43804],{"className":43803},[886],[888,43805,43806],{"xmlns":890},[892,43807,43808,43816],{},[895,43809,43810],{},[1805,43811,43812,43814],{},[898,43813,5325],{},[898,43815,5640],{},[902,43817,42857],{"encoding":904},[883,43819,43821],{"className":43820},[886],[888,43822,43823],{"xmlns":890},[892,43824,43825,43833],{},[895,43826,43827],{},[1805,43828,43829,43831],{},[898,43830,2470],{},[898,43832,5640],{},[902,43834,43794],{"encoding":904},[724,43836,43837,43840,43841,10743,43858,1656],{},[38,43838,43839],{},"Pravidlo 3:"," Růst nabídky ⟹ pokles ",[883,43842,43844],{"className":43843},[886],[888,43845,43846],{"xmlns":890},[892,43847,43848,43856],{},[895,43849,43850],{},[1805,43851,43852,43854],{},[898,43853,5325],{},[898,43855,5640],{},[902,43857,42857],{"encoding":904},[883,43859,43861],{"className":43860},[886],[888,43862,43863],{"xmlns":890},[892,43864,43865,43873],{},[895,43866,43867],{},[1805,43868,43869,43871],{},[898,43870,2470],{},[898,43872,5640],{},[902,43874,43794],{"encoding":904},[724,43876,43877,43880,43881,43898,43899,1656],{},[38,43878,43879],{},"Pravidlo 4:"," Pokles nabídky ⟹ růst ",[883,43882,43884],{"className":43883},[886],[888,43885,43886],{"xmlns":890},[892,43887,43888,43896],{},[895,43889,43890],{},[1805,43891,43892,43894],{},[898,43893,5325],{},[898,43895,5640],{},[902,43897,42857],{"encoding":904},", pokles ",[883,43900,43902],{"className":43901},[886],[888,43903,43904],{"xmlns":890},[892,43905,43906,43914],{},[895,43907,43908],{},[1805,43909,43910,43912],{},[898,43911,2470],{},[898,43913,5640],{},[902,43915,43794],{"encoding":904},[16,43917,43918,43963],{},[19,43919,43920],{},[22,43921,43922,43925,43944],{},[25,43923,43924],{},"Změna",[25,43926,43927],{},[883,43928,43930],{"className":43929},[886],[888,43931,43932],{"xmlns":890},[892,43933,43934,43942],{},[895,43935,43936],{},[1805,43937,43938,43940],{},[898,43939,5325],{},[898,43941,5640],{},[902,43943,42857],{"encoding":904},[25,43945,43946],{},[883,43947,43949],{"className":43948},[886],[888,43950,43951],{"xmlns":890},[892,43952,43953,43961],{},[895,43954,43955],{},[1805,43956,43957,43959],{},[898,43958,2470],{},[898,43960,5640],{},[902,43962,43794],{"encoding":904},[30,43964,43965,43975,43985,43994],{},[22,43966,43967,43970,43973],{},[35,43968,43969],{},"Růst poptávky",[35,43971,43972],{},"↑",[35,43974,43972],{},[22,43976,43977,43980,43983],{},[35,43978,43979],{},"Pokles poptávky",[35,43981,43982],{},"↓",[35,43984,43982],{},[22,43986,43987,43990,43992],{},[35,43988,43989],{},"Růst nabídky",[35,43991,43982],{},[35,43993,43972],{},[22,43995,43996,43999,44001],{},[35,43997,43998],{},"Pokles nabídky",[35,44000,43972],{},[35,44002,43982],{},[724,44004,44005],{},[614,44006,44007],{},"Obrázky 2.15–2.18 ilustrují všechny čtyři situace pomocí posunu jedné z křivek.",[38361,44009],{},[115,44011,811],{"id":44012},"zdanění-trhu",[5254,44014,44015,44104],{},[724,44016,44017,44019,44020,44033,44034,2608,44047,44050,44051,38167,44074,44099,44100,44103],{},[883,44018,5543],{}," TL;DR\nJednotková daň ",[883,44021,44023],{"className":44022},[886],[888,44024,44025],{"xmlns":890},[892,44026,44027,44031],{},[895,44028,44029],{},[898,44030,2455],{},[902,44032,2455],{"encoding":904}," uložená na každou prodanou jednotku způsobí posun jedné z křivek o ",[883,44035,44037],{"className":44036},[886],[888,44038,44039],{"xmlns":890},[892,44040,44041,44045],{},[895,44042,44043],{},[898,44044,2455],{},[902,44046,2455],{"encoding":904},[38,44048,44049],{},"Daňové břemeno"," se dělí mezi spotřebitele (",[883,44052,44054],{"className":44053},[886],[888,44055,44056],{"xmlns":890},[892,44057,44058,44071],{},[895,44059,44060],{},[1953,44061,44062,44064],{},[898,44063,2455],{},[895,44065,44066,44069],{},[898,44067,44068],{},"s",[898,44070,724],{},[902,44072,44073],{"encoding":904},"T_{sp}",[883,44075,44077],{"className":44076},[886],[888,44078,44079],{"xmlns":890},[892,44080,44081,44096],{},[895,44082,44083],{},[1953,44084,44085,44087],{},[898,44086,2455],{},[895,44088,44089,44092,44094],{},[898,44090,44091],{},"v",[898,44093,1675],{},[898,44095,13431],{},[902,44097,44098],{"encoding":904},"T_{vyr}","). Klíčová vlastnost — ",[38,44101,44102],{},"ekvivalence zdanění",": výsledné rovnovážné množství i čistá cena pro výrobce jsou stejné bez ohledu na to, zda je daň uložena výrobci, či spotřebiteli.",[724,44105,44106],{},[614,44107,44108,44109,1656],{},"Pro detail, úplné odvození, Příklady 2.9 a 2.10 a geometrickou interpretaci viz ",[207,44110,44112],{"className":44111,"dataFsResolvedFilePath":809,"href":810},[210],"zdaneni-trhu",[724,44114,44115,44116,44119,44120,44146,44147,44150,44151,44177,44178,44195,44196,44236,44237,5272,44250,1656],{},"Existují dvě formy zdanění — daň uložená ",[38,44117,44118],{},"výrobci"," (posun nabídky ",[883,44121,44123],{"className":44122},[886],[888,44124,44125],{"xmlns":890},[892,44126,44127,44143],{},[895,44128,44129,44135,44137,44139,44141],{},[1953,44130,44131,44133],{},[898,44132,10061],{},[1810,44134,1959],{},[1677,44136,1679],{},[898,44138,10061],{},[1677,44140,1776],{},[898,44142,2455],{},[902,44144,44145],{"encoding":904},"S_1 = S + T"," svisle nahoru) a daň uložená ",[38,44148,44149],{},"spotřebiteli"," (posun poptávky ",[883,44152,44154],{"className":44153},[886],[888,44155,44156],{"xmlns":890},[892,44157,44158,44174],{},[895,44159,44160,44166,44168,44170,44172],{},[1953,44161,44162,44164],{},[898,44163,5571],{},[1810,44165,1812],{},[1677,44167,1679],{},[898,44169,5571],{},[1677,44171,1906],{},[898,44173,2455],{},[902,44175,44176],{"encoding":904},"D_2 = D - T"," svisle dolů). V obou případech nové rovnovážné množství ",[883,44179,44181],{"className":44180},[886],[888,44182,44183],{"xmlns":890},[892,44184,44185,44193],{},[895,44186,44187],{},[1805,44188,44189,44191],{},[898,44190,2470],{},[898,44192,5640],{},[902,44194,43794],{"encoding":904}," klesá a vzniká rozklad daně ",[883,44197,44199],{"className":44198},[886],[888,44200,44201],{"xmlns":890},[892,44202,44203,44233],{},[895,44204,44205,44207,44209,44219,44221],{},[898,44206,2455],{},[1677,44208,1679],{},[1953,44210,44211,44213],{},[898,44212,2455],{},[895,44214,44215,44217],{},[898,44216,44068],{},[898,44218,724],{},[1677,44220,1776],{},[1953,44222,44223,44225],{},[898,44224,2455],{},[895,44226,44227,44229,44231],{},[898,44228,44091],{},[898,44230,1675],{},[898,44232,13431],{},[902,44234,44235],{"encoding":904},"T = T_{sp} + T_{vyr}"," mezi obě strany trhu, určený relativními sklony křivek ",[883,44238,44240],{"className":44239},[886],[888,44241,44242],{"xmlns":890},[892,44243,44244,44248],{},[895,44245,44246],{},[898,44247,5571],{},[902,44249,5571],{"encoding":904},[883,44251,44253],{"className":44252},[886],[888,44254,44255],{"xmlns":890},[892,44256,44257,44261],{},[895,44258,44259],{},[898,44260,10061],{},[902,44262,10061],{"encoding":904},[724,44264,44265,44266,44269,44270,5272,44300,44334],{},"Zásadním výsledkem kapitoly je ",[38,44267,44268],{},"věta o ekvivalenci zdanění",": ať je daň uvalena formálně na kohokoli, rovnovážné množství i reálné rozdělení břemene jsou identické — ",[883,44271,44273],{"className":44272},[886],[888,44274,44275],{"xmlns":890},[892,44276,44277,44297],{},[895,44278,44279,44287,44289],{},[10554,44280,44281,44283,44285],{},[898,44282,2470],{},[1810,44284,1959],{},[898,44286,5640],{},[1677,44288,1679],{},[10554,44290,44291,44293,44295],{},[898,44292,2470],{},[1810,44294,1812],{},[898,44296,5640],{},[902,44298,44299],{"encoding":904},"Q_1^E = Q_2^E",[883,44301,44303],{"className":44302},[886],[888,44304,44305],{"xmlns":890},[892,44306,44307,44331],{},[895,44308,44309,44317,44319,44321,44323],{},[10554,44310,44311,44313,44315],{},[898,44312,5325],{},[1810,44314,1959],{},[898,44316,5640],{},[1677,44318,1906],{},[898,44320,2455],{},[1677,44322,1679],{},[10554,44324,44325,44327,44329],{},[898,44326,5325],{},[1810,44328,1812],{},[898,44330,5640],{},[902,44332,44333],{"encoding":904},"P_1^E - T = P_2^E",". Otázka, \"kdo má platit daň\", je tedy z hlediska trhu formální; skutečné rozdělení určuje struktura trhu, nikoli znění zákona.",[724,44336,44337,44338,44341,44342,44368,44369,44397,44398,44401,44402,44405,44406,1656],{},"Podrobný výklad, Příklady ",[38,44339,44340],{},"2.9"," (daň výrobci, ",[883,44343,44345],{"className":44344},[886],[888,44346,44347],{"xmlns":890},[892,44348,44349,44365],{},[895,44350,44351,44361,44363],{},[1953,44352,44353,44355],{},[898,44354,2455],{},[895,44356,44357,44359],{},[898,44358,44068],{},[898,44360,724],{},[1677,44362,1679],{},[1810,44364,1812],{},[902,44366,44367],{"encoding":904},"T_{sp} = 2"," Kč, ",[883,44370,44372],{"className":44371},[886],[888,44373,44374],{"xmlns":890},[892,44375,44376,44394],{},[895,44377,44378,44390,44392],{},[1953,44379,44380,44382],{},[898,44381,2455],{},[895,44383,44384,44386,44388],{},[898,44385,44091],{},[898,44387,1675],{},[898,44389,13431],{},[1677,44391,1679],{},[1810,44393,2032],{},[902,44395,44396],{"encoding":904},"T_{vyr} = 4"," Kč) a ",[38,44399,44400],{},"2.10"," (táž daň, ale na spotřebitele), postup výpočtu rozkladu břemene a ",[38,44403,44404],{},"Obrázky 2.17–2.21"," jsou na samostatné stránce ",[207,44407,44112],{"className":44408,"dataFsResolvedFilePath":809,"href":810},[210],[38361,44410],{},[115,44412,44414],{"id":44413},"multiplikátory-pro-mikroekonomické-proměnné","Multiplikátory pro mikroekonomické proměnné",[5254,44416,44417],{},[724,44418,44419,44421,44422,44425,44426,44428],{},[883,44420,5543],{}," TL;DR\nMultiplikátory jsou ",[38,44423,44424],{},"parciální derivace redukovaného tvaru"," endogenní proměnné podle exogenních parametrů. Udávají přibližnou odezvu rovnovážného bodu na jednotkovou změnu parametru (",[614,44427,38351],{},"). Kvalitativní smysl (znaménko) je invariantní, kvantitativní závisí na konkrétních hodnotách.",[198,44430,44432],{"id":44431},"redukovaný-tvar","Redukovaný tvar",[724,44434,44435,44436,11413,44459,1343,44477,13518,44494,11413,44517,44534,44535,44565],{},"Pro lineární model ",[883,44437,44439],{"className":44438},[886],[888,44440,44441],{"xmlns":890},[892,44442,44443,44457],{},[895,44444,44445,44447,44449,44451,44453,44455],{},[898,44446,5325],{},[1677,44448,1679],{},[898,44450,207],{},[898,44452,2470],{},[1677,44454,1776],{},[898,44456,1779],{},[902,44458,38451],{"encoding":904},[883,44460,44462],{"className":44461},[886],[888,44463,44464],{"xmlns":890},[892,44465,44466,44474],{},[895,44467,44468,44470,44472],{},[898,44469,207],{},[1677,44471,3128],{},[1810,44473,2008],{},[902,44475,44476],{"encoding":904},"a \u003C 0",[883,44478,44480],{"className":44479},[886],[888,44481,44482],{"xmlns":890},[892,44483,44484,44492],{},[895,44485,44486,44488,44490],{},[898,44487,1779],{},[1677,44489,3089],{},[1810,44491,2008],{},[902,44493,20205],{"encoding":904},[883,44495,44497],{"className":44496},[886],[888,44498,44499],{"xmlns":890},[892,44500,44501,44515],{},[895,44502,44503,44505,44507,44509,44511,44513],{},[898,44504,5325],{},[1677,44506,1679],{},[898,44508,1823],{},[898,44510,2470],{},[1677,44512,1776],{},[898,44514,1875],{},[902,44516,41633],{"encoding":904},[883,44518,44520],{"className":44519},[886],[888,44521,44522],{"xmlns":890},[892,44523,44524,44532],{},[895,44525,44526,44528,44530],{},[898,44527,1823],{},[1677,44529,3089],{},[1810,44531,2008],{},[902,44533,41651],{"encoding":904},") dává podmínka rovnováhy ",[883,44536,44538],{"className":44537},[886],[888,44539,44540],{"xmlns":890},[892,44541,44542,44562],{},[895,44543,44544,44546,44548,44550,44552,44554,44556,44558,44560],{},[898,44545,207],{},[898,44547,2470],{},[1677,44549,1776],{},[898,44551,1779],{},[1677,44553,1679],{},[898,44555,1823],{},[898,44557,2470],{},[1677,44559,1776],{},[898,44561,1875],{},[902,44563,44564],{"encoding":904},"aQ + b = cQ + d",", odkud",[883,44567,44569],{"className":44568},[886],[888,44570,44571],{"xmlns":890,"display":29457},[892,44572,44573,44618],{},[22145,44574,44575],{"width":29462},[22150,44576,44577,44579,44611,44613],{},[22153,44578],{"width":29467},[22153,44580,44581],{},[895,44582,44583,44589,44591,44609],{},[1805,44584,44585,44587],{},[898,44586,2470],{},[898,44588,5640],{},[1677,44590,1679],{},[2010,44592,44593,44601],{},[895,44594,44595,44597,44599],{},[898,44596,1779],{},[1677,44598,1906],{},[898,44600,1875],{},[895,44602,44603,44605,44607],{},[898,44604,1823],{},[1677,44606,1906],{},[898,44608,207],{},[898,44610,1656],{"mathvariant":2057},[22153,44612],{"width":29467},[22153,44614,44615],{},[1969,44616,44617],{},"(2.10)",[902,44619,44620],{"encoding":904},"Q^E = \\frac{b - d}{c - a}. \\tag{2.10}",[724,44622,44623,44624,11413,44626,44629,44630,44647,44648,1884,44651,44677,44678,44691,44692,44710,44711,5306],{},"Vztah (2.10) je ",[38,44625,22345],{},[614,44627,44628],{},"reduced form",") pro ",[883,44631,44633],{"className":44632},[886],[888,44634,44635],{"xmlns":890},[892,44636,44637,44645],{},[895,44638,44639],{},[1805,44640,44641,44643],{},[898,44642,2470],{},[898,44644,5640],{},[902,44646,43794],{"encoding":904},": endogenní proměnná je vyjádřena pomocí exogenních ",[38,44649,44650],{},"parametrů",[883,44652,44654],{"className":44653},[886],[888,44655,44656],{"xmlns":890},[892,44657,44658,44674],{},[895,44659,44660,44662,44664,44666,44668,44670,44672],{},[898,44661,207],{},[1677,44663,1967],{"separator":1966},[898,44665,1779],{},[1677,44667,1967],{"separator":1966},[898,44669,1823],{},[1677,44671,1967],{"separator":1966},[898,44673,1875],{},[902,44675,44676],{"encoding":904},"a, b, c, d",". Aby ",[883,44679,44681],{"className":44680},[886],[888,44682,44683],{"xmlns":890},[892,44684,44685,44689],{},[895,44686,44687],{},[898,44688,5640],{},[902,44690,5640],{"encoding":904}," ležel v 1. kvadrantu, musí platit ",[883,44693,44695],{"className":44694},[886],[888,44696,44697],{"xmlns":890},[892,44698,44699,44707],{},[895,44700,44701,44703,44705],{},[898,44702,1779],{},[1677,44704,3089],{},[898,44706,1875],{},[902,44708,44709],{"encoding":904},"b > d"," (neboť ",[883,44712,44714],{"className":44713},[886],[888,44715,44716],{"xmlns":890},[892,44717,44718,44730],{},[895,44719,44720,44722,44724,44726,44728],{},[898,44721,1823],{},[1677,44723,1906],{},[898,44725,207],{},[1677,44727,3089],{},[1810,44729,2008],{},[902,44731,44732],{"encoding":904},"c - a > 0",[724,44734,44735],{},[614,44736,44737,44738,44751,44752,44765,44766,20039,44779,43331,44796,44809],{},"Obrázek 2.22: Lineární poptávka (úsek ",[883,44739,44741],{"className":44740},[886],[888,44742,44743],{"xmlns":890},[892,44744,44745,44749],{},[895,44746,44747],{},[898,44748,1779],{},[902,44750,1779],{"encoding":904}," na ose ",[883,44753,44755],{"className":44754},[886],[888,44756,44757],{"xmlns":890},[892,44758,44759,44763],{},[895,44760,44761],{},[898,44762,5325],{},[902,44764,5325],{"encoding":904},") a nabídka (úsek ",[883,44767,44769],{"className":44768},[886],[888,44770,44771],{"xmlns":890},[892,44772,44773,44777],{},[895,44774,44775],{},[898,44776,1875],{},[902,44778,1875],{"encoding":904},[883,44780,44782],{"className":44781},[886],[888,44783,44784],{"xmlns":890},[892,44785,44786,44794],{},[895,44787,44788,44790,44792],{},[898,44789,1779],{},[1677,44791,3089],{},[898,44793,1875],{},[902,44795,44709],{"encoding":904},[883,44797,44799],{"className":44798},[886],[888,44800,44801],{"xmlns":890},[892,44802,44803,44807],{},[895,44804,44805],{},[898,44806,5640],{},[902,44808,5640],{"encoding":904}," v 1. kvadrantu.",[198,44811,44813],{"id":44812},"definice-multiplikátorů","Definice multiplikátorů",[724,44815,44816,44817,44842,44843,44856,44857,44870],{},"V komparativní statice jsou ",[883,44818,44820],{"className":44819},[886],[888,44821,44822],{"xmlns":890},[892,44823,44824,44840],{},[895,44825,44826,44828,44830,44832,44834,44836,44838],{},[898,44827,207],{},[1677,44829,1967],{"separator":1966},[898,44831,1779],{},[1677,44833,1967],{"separator":1966},[898,44835,1823],{},[1677,44837,1967],{"separator":1966},[898,44839,1875],{},[902,44841,44676],{"encoding":904}," exogenní proměnné a ",[883,44844,44846],{"className":44845},[886],[888,44847,44848],{"xmlns":890},[892,44849,44850,44854],{},[895,44851,44852],{},[898,44853,2470],{},[902,44855,2470],{"encoding":904}," endogenní. Přibližná změna ",[883,44858,44860],{"className":44859},[886],[888,44861,44862],{"xmlns":890},[892,44863,44864,44868],{},[895,44865,44866],{},[898,44867,2470],{},[902,44869,2470],{"encoding":904}," se rovná totálnímu diferenciálu:",[883,44872,44874],{"className":44873},[886],[888,44875,44876],{"xmlns":890,"display":29457},[892,44877,44878,44971],{},[22145,44879,44880],{"width":29462},[22150,44881,44882,44884,44964,44966],{},[22153,44883],{"width":29467},[22153,44885,44886],{},[895,44887,44888,44890,44892,44894,44896,44898,44900,44908,44910,44912,44914,44916,44924,44926,44928,44930,44932,44940,44942,44944,44946,44948,44956,44958,44960,44962],{},[898,44889,2570],{"mathvariant":2057},[898,44891,2470],{},[1677,44893,2411],{},[898,44895,1875],{},[898,44897,2470],{},[1677,44899,1679],{},[10554,44901,44902,44904,44906],{},[898,44903,2470],{},[898,44905,207],{},[1677,44907,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1969,44909,2668],{},[898,44911,1875],{},[898,44913,207],{},[1677,44915,1776],{},[10554,44917,44918,44920,44922],{},[898,44919,2470],{},[898,44921,1779],{},[1677,44923,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1969,44925,2668],{},[898,44927,1875],{},[898,44929,1779],{},[1677,44931,1776],{},[10554,44933,44934,44936,44938],{},[898,44935,2470],{},[898,44937,1823],{},[1677,44939,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1969,44941,2668],{},[898,44943,1875],{},[898,44945,1823],{},[1677,44947,1776],{},[10554,44949,44950,44952,44954],{},[898,44951,2470],{},[898,44953,1875],{},[1677,44955,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1969,44957,2668],{},[898,44959,1875],{},[898,44961,1875],{},[898,44963,1656],{"mathvariant":2057},[22153,44965],{"width":29467},[22153,44967,44968],{},[1969,44969,44970],{},"(2.11)",[902,44972,44973],{"encoding":904},"\\Delta Q \\approx dQ = Q'_a\\,da + Q'_b\\,db + Q'_c\\,dc + Q'_d\\,dd. \\tag{2.11}",[724,44975,44976,44977,45027,45028,11413,45030,2832],{},"Parciální derivace ",[883,44978,44980],{"className":44979},[886],[888,44981,44982],{"xmlns":890},[892,44983,44984,45024],{},[895,44985,44986,44994,44996,45004,45006,45014,45016],{},[10554,44987,44988,44990,44992],{},[898,44989,2470],{},[898,44991,207],{},[1677,44993,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,44995,1967],{"separator":1966},[10554,44997,44998,45000,45002],{},[898,44999,2470],{},[898,45001,1779],{},[1677,45003,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,45005,1967],{"separator":1966},[10554,45007,45008,45010,45012],{},[898,45009,2470],{},[898,45011,1823],{},[1677,45013,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,45015,1967],{"separator":1966},[10554,45017,45018,45020,45022],{},[898,45019,2470],{},[898,45021,1875],{},[1677,45023,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[902,45025,45026],{"encoding":904},"Q'_a, Q'_b, Q'_c, Q'_d"," se nazývají ",[38,45029,19368],{},[614,45031,45032],{},"multipliers",[883,45034,45036],{"className":45035},[886],[888,45037,45038],{"xmlns":890,"display":29457},[892,45039,45040,45191],{},[22145,45041,45042],{"width":29462},[22150,45043,45044,45046,45184,45186],{},[22153,45045],{"width":29467},[22153,45047,45048],{},[895,45049,45050,45058,45060,45086,45088,45090,45098,45100,45112,45114,45116,45124,45126,45128,45154,45156,45158,45166,45168,45170,45182],{},[10554,45051,45052,45054,45056],{},[898,45053,2470],{},[898,45055,207],{},[1677,45057,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,45059,1679],{},[2010,45061,45062,45070],{},[895,45063,45064,45066,45068],{},[898,45065,1779],{},[1677,45067,1906],{},[898,45069,1875],{},[895,45071,45072,45074,45076,45078,45080],{},[1677,45073,1686],{"stretchy":1685},[898,45075,1823],{},[1677,45077,1906],{},[898,45079,207],{},[1805,45081,45082,45084],{},[1677,45083,1692],{"stretchy":1685},[1810,45085,1812],{},[1677,45087,1967],{"separator":1966},[7266,45089],{"width":16674},[10554,45091,45092,45094,45096],{},[898,45093,2470],{},[898,45095,1779],{},[1677,45097,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,45099,1679],{},[2010,45101,45102,45104],{},[1810,45103,1959],{},[895,45105,45106,45108,45110],{},[898,45107,1823],{},[1677,45109,1906],{},[898,45111,207],{},[1677,45113,1967],{"separator":1966},[7266,45115],{"width":16674},[10554,45117,45118,45120,45122],{},[898,45119,2470],{},[898,45121,1823],{},[1677,45123,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,45125,1679],{},[1677,45127,1906],{},[2010,45129,45130,45138],{},[895,45131,45132,45134,45136],{},[898,45133,1779],{},[1677,45135,1906],{},[898,45137,1875],{},[895,45139,45140,45142,45144,45146,45148],{},[1677,45141,1686],{"stretchy":1685},[898,45143,1823],{},[1677,45145,1906],{},[898,45147,207],{},[1805,45149,45150,45152],{},[1677,45151,1692],{"stretchy":1685},[1810,45153,1812],{},[1677,45155,1967],{"separator":1966},[7266,45157],{"width":16674},[10554,45159,45160,45162,45164],{},[898,45161,2470],{},[898,45163,1875],{},[1677,45165,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,45167,1679],{},[1677,45169,1906],{},[2010,45171,45172,45174],{},[1810,45173,1959],{},[895,45175,45176,45178,45180],{},[898,45177,1823],{},[1677,45179,1906],{},[898,45181,207],{},[898,45183,1656],{"mathvariant":2057},[22153,45185],{"width":29467},[22153,45187,45188],{},[1969,45189,45190],{},"(2.12)",[902,45192,45193],{"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}",[198,45195,45197],{"id":45196},"znaménka-a-interpretace","Znaménka a interpretace",[724,45199,45200,45201,1343,45218,1343,45235,1343,45252,45269,45270,2832],{},"Za podmínek ",[883,45202,45204],{"className":45203},[886],[888,45205,45206],{"xmlns":890},[892,45207,45208,45216],{},[895,45209,45210,45212,45214],{},[898,45211,207],{},[1677,45213,3128],{},[1810,45215,2008],{},[902,45217,44476],{"encoding":904},[883,45219,45221],{"className":45220},[886],[888,45222,45223],{"xmlns":890},[892,45224,45225,45233],{},[895,45226,45227,45229,45231],{},[898,45228,1779],{},[1677,45230,3089],{},[1810,45232,2008],{},[902,45234,20205],{"encoding":904},[883,45236,45238],{"className":45237},[886],[888,45239,45240],{"xmlns":890},[892,45241,45242,45250],{},[895,45243,45244,45246,45248],{},[898,45245,1823],{},[1677,45247,3089],{},[1810,45249,2008],{},[902,45251,41651],{"encoding":904},[883,45253,45255],{"className":45254},[886],[888,45256,45257],{"xmlns":890},[892,45258,45259,45267],{},[895,45260,45261,45263,45265],{},[898,45262,1779],{},[1677,45264,3089],{},[898,45266,1875],{},[902,45268,44709],{"encoding":904}," platí (znaménka se ",[38,45271,45272],{},"nemění",[883,45274,45276],{"className":45275},[886],[888,45277,45278],{"xmlns":890,"display":29457},[892,45279,45280,45342],{},[895,45281,45282,45290,45292,45294,45296,45298,45306,45308,45310,45312,45314,45322,45324,45326,45328,45330,45338,45340],{},[10554,45283,45284,45286,45288],{},[898,45285,2470],{},[898,45287,207],{},[1677,45289,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,45291,3089],{},[1810,45293,2008],{},[1677,45295,1967],{"separator":1966},[7266,45297],{"width":7268},[10554,45299,45300,45302,45304],{},[898,45301,2470],{},[898,45303,1779],{},[1677,45305,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,45307,3089],{},[1810,45309,2008],{},[1677,45311,1967],{"separator":1966},[7266,45313],{"width":7268},[10554,45315,45316,45318,45320],{},[898,45317,2470],{},[898,45319,1823],{},[1677,45321,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,45323,3128],{},[1810,45325,2008],{},[1677,45327,1967],{"separator":1966},[7266,45329],{"width":7268},[10554,45331,45332,45334,45336],{},[898,45333,2470],{},[898,45335,1875],{},[1677,45337,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,45339,3128],{},[1810,45341,13850],{},[902,45343,45344],{"encoding":904},"Q'_a > 0, \\qquad Q'_b > 0, \\qquad Q'_c \u003C 0, \\qquad Q'_d \u003C 0.",[120,45346,45347,45406],{},[123,45348,45349,1884,45352,45372,45373,45390,45391,1343,45404,1656],{},[38,45350,45351],{},"Kvantitativní smysl:",[883,45353,45355],{"className":45354},[886],[888,45356,45357],{"xmlns":890},[892,45358,45359,45369],{},[895,45360,45361],{},[10554,45362,45363,45365,45367],{},[898,45364,2470],{},[898,45366,1689],{},[1677,45368,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[902,45370,45371],{"encoding":904},"Q'_x"," udává, o kolik přibližně vzroste ",[883,45374,45376],{"className":45375},[886],[888,45377,45378],{"xmlns":890},[892,45379,45380,45388],{},[895,45381,45382],{},[1805,45383,45384,45386],{},[898,45385,2470],{},[898,45387,5640],{},[902,45389,43794],{"encoding":904}," při jednotkové změně parametru ",[883,45392,45394],{"className":45393},[886],[888,45395,45396],{"xmlns":890},[892,45397,45398,45402],{},[895,45399,45400],{},[898,45401,1689],{},[902,45403,1689],{"encoding":904},[614,45405,38351],{},[123,45407,45408,45411,45412,45429,45430,1656],{},[38,45409,45410],{},"Kvalitativní smysl:"," znaménko určuje směr reakce ",[883,45413,45415],{"className":45414},[886],[888,45416,45417],{"xmlns":890},[892,45418,45419,45427],{},[895,45420,45421],{},[1805,45422,45423,45425],{},[898,45424,2470],{},[898,45426,5640],{},[902,45428,43794],{"encoding":904}," na růst ",[883,45431,45433],{"className":45432},[886],[888,45434,45435],{"xmlns":890},[892,45436,45437,45441],{},[895,45438,45439],{},[898,45440,1689],{},[902,45442,1689],{"encoding":904},[724,45444,45445,45446,45459,45460,44710,45477,5306],{},"Např. růst ",[883,45447,45449],{"className":45448},[886],[888,45450,45451],{"xmlns":890},[892,45452,45453,45457],{},[895,45454,45455],{},[898,45456,1823],{},[902,45458,1823],{"encoding":904}," (strmější nabídka) ⟹ pokles ",[883,45461,45463],{"className":45462},[886],[888,45464,45465],{"xmlns":890},[892,45466,45467,45475],{},[895,45468,45469],{},[1805,45470,45471,45473],{},[898,45472,2470],{},[898,45474,5640],{},[902,45476,43794],{"encoding":904},[883,45478,45480],{"className":45479},[886],[888,45481,45482],{"xmlns":890},[892,45483,45484,45498],{},[895,45485,45486,45494,45496],{},[10554,45487,45488,45490,45492],{},[898,45489,2470],{},[898,45491,1823],{},[1677,45493,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,45495,3128],{},[1810,45497,2008],{},[902,45499,45500],{"encoding":904},"Q'_c \u003C 0",[724,45502,45503],{},[614,45504,45505,45506,45526,45527,45551,45552,45574,45575,1656],{},"Obrázek 2.23: Pootočení přímky nabídky z ",[883,45507,45509],{"className":45508},[886],[888,45510,45511],{"xmlns":890},[892,45512,45513,45523],{},[895,45514,45515,45517,45519,45521],{},[898,45516,1823],{},[898,45518,2470],{},[1677,45520,1776],{},[898,45522,1875],{},[902,45524,45525],{"encoding":904},"cQ + d"," na strmější ",[883,45528,45530],{"className":45529},[886],[888,45531,45532],{"xmlns":890},[892,45533,45534,45548],{},[895,45535,45536,45542,45544,45546],{},[1953,45537,45538,45540],{},[898,45539,1823],{},[1810,45541,1959],{},[898,45543,2470],{},[1677,45545,1776],{},[898,45547,1875],{},[902,45549,45550],{"encoding":904},"c_1 Q + d"," (při ",[883,45553,45555],{"className":45554},[886],[888,45556,45557],{"xmlns":890},[892,45558,45559,45571],{},[895,45560,45561,45567,45569],{},[1953,45562,45563,45565],{},[898,45564,1823],{},[1810,45566,1959],{},[1677,45568,3089],{},[898,45570,1823],{},[902,45572,45573],{"encoding":904},"c_1 > c",") — rovnovážný bod se posouvá vlevo, ",[883,45576,45578],{"className":45577},[886],[888,45579,45580],{"xmlns":890},[892,45581,45582,45592],{},[895,45583,45584,45590],{},[1805,45585,45586,45588],{},[898,45587,2470],{},[898,45589,5640],{},[1677,45591,43982],{},[902,45593,45594],{"encoding":904},"Q^E \\downarrow",[724,45596,45597,45598,45630,45631,1656],{},"Při změně jediné proměnné se (2.11) redukuje např. na ",[883,45599,45601],{"className":45600},[886],[888,45602,45603],{"xmlns":890},[892,45604,45605,45627],{},[895,45606,45607,45609,45611,45613,45621,45623,45625],{},[898,45608,2570],{"mathvariant":2057},[898,45610,2470],{},[1677,45612,2411],{},[10554,45614,45615,45617,45619],{},[898,45616,2470],{},[898,45618,1779],{},[1677,45620,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1969,45622,2668],{},[898,45624,1875],{},[898,45626,1779],{},[902,45628,45629],{"encoding":904},"\\Delta Q \\approx Q'_b\\,db",". Analogicky lze odvodit multiplikátory pro ",[883,45632,45634],{"className":45633},[886],[888,45635,45636],{"xmlns":890},[892,45637,45638,45646],{},[895,45639,45640],{},[1805,45641,45642,45644],{},[898,45643,5325],{},[898,45645,5640],{},[902,45647,42857],{"encoding":904},[198,45649,45651,45652],{"id":45650},"příklad-211-komparativní-statika-pro-qeqe","Příklad 2.11 — komparativní statika pro ",[883,45653,45655],{"className":45654},[886],[888,45656,45657],{"xmlns":890},[892,45658,45659,45667],{},[895,45660,45661],{},[1805,45662,45663,45665],{},[898,45664,2470],{},[898,45666,5640],{},[902,45668,43794],{"encoding":904},[724,45670,45671,43046,45673,43081,45699,1656],{},[38,45672,39324],{},[883,45674,45676],{"className":45675},[886],[888,45677,45678],{"xmlns":890},[892,45679,45680,45696],{},[895,45681,45682,45684,45686,45688,45690,45692,45694],{},[898,45683,5325],{},[1677,45685,1679],{},[1677,45687,1906],{},[1810,45689,1854],{},[898,45691,2470],{},[1677,45693,1776],{},[1810,45695,6599],{},[902,45697,45698],{"encoding":904},"P = -3Q + 40",[883,45700,45702],{"className":45701},[886],[888,45703,45704],{"xmlns":890},[892,45705,45706,45720],{},[895,45707,45708,45710,45712,45714,45716,45718],{},[898,45709,5325],{},[1677,45711,1679],{},[1810,45713,6397],{},[898,45715,2470],{},[1677,45717,1776],{},[1810,45719,2544],{},[902,45721,45722],{"encoding":904},"P = 0{,}5Q + 10",[724,45724,45725,45727],{},[38,45726,39356],{}," Rovnovážné množství",[883,45729,45731],{"className":45730},[886],[888,45732,45733],{"xmlns":890,"display":29457},[892,45734,45735,45803],{},[895,45736,45737,45743,45745,45763,45765,45789,45791,45798,45800],{},[1805,45738,45739,45741],{},[898,45740,2470],{},[898,45742,5640],{},[1677,45744,1679],{},[2010,45746,45747,45755],{},[895,45748,45749,45751,45753],{},[898,45750,1779],{},[1677,45752,1906],{},[898,45754,1875],{},[895,45756,45757,45759,45761],{},[898,45758,1823],{},[1677,45760,1906],{},[898,45762,207],{},[1677,45764,1679],{},[2010,45766,45767,45775],{},[895,45768,45769,45771,45773],{},[1810,45770,6599],{},[1677,45772,1906],{},[1810,45774,2544],{},[895,45776,45777,45779,45781,45783,45785,45787],{},[1810,45778,6397],{},[1677,45780,1906],{},[1677,45782,1686],{"stretchy":1685},[1677,45784,1906],{},[1810,45786,1854],{},[1677,45788,1692],{"stretchy":1685},[1677,45790,1679],{},[2010,45792,45793,45795],{},[1810,45794,39410],{},[1810,45796,45797],{},"3,5",[1677,45799,2411],{},[1810,45801,45802],{},"8,571.",[902,45804,45805],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\approx 8{,}571.",[724,45807,45808,45853],{},[38,45809,45810,45811,2352,45824,2366,45838,45852],{},"(a) Změna ",[883,45812,45814],{"className":45813},[886],[888,45815,45816],{"xmlns":890},[892,45817,45818,45822],{},[895,45819,45820],{},[898,45821,1823],{},[902,45823,1823],{"encoding":904},[883,45825,45827],{"className":45826},[886],[888,45828,45829],{"xmlns":890},[892,45830,45831,45835],{},[895,45832,45833],{},[1810,45834,6397],{},[902,45836,45837],{"encoding":904},"0{,}5",[883,45839,45841],{"className":45840},[886],[888,45842,45843],{"xmlns":890},[892,45844,45845,45849],{},[895,45846,45847],{},[1810,45848,20712],{},[902,45850,45851],{"encoding":904},"0{,}6"," (ceteris paribus)."," Dle (2.12):",[883,45855,45857],{"className":45856},[886],[888,45858,45859],{"xmlns":890,"display":29457},[892,45860,45861,45938],{},[895,45862,45863,45871,45873,45875,45877,45879,45881,45907,45909,45911,45913,45915,45917,45927,45929,45931,45933,45935],{},[10554,45864,45865,45867,45869],{},[898,45866,2470],{},[898,45868,1823],{},[1677,45870,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1969,45872,2668],{},[898,45874,1875],{},[898,45876,1823],{},[1677,45878,1679],{},[1677,45880,1906],{},[2010,45882,45883,45891],{},[895,45884,45885,45887,45889],{},[898,45886,1779],{},[1677,45888,1906],{},[898,45890,1875],{},[895,45892,45893,45895,45897,45899,45901],{},[1677,45894,1686],{"stretchy":1685},[898,45896,1823],{},[1677,45898,1906],{},[898,45900,207],{},[1805,45902,45903,45905],{},[1677,45904,1692],{"stretchy":1685},[1810,45906,1812],{},[1969,45908,2668],{},[898,45910,1875],{},[898,45912,1823],{},[1677,45914,1679],{},[1677,45916,1906],{},[2010,45918,45919,45921],{},[1810,45920,39410],{},[1805,45922,45923,45925],{},[1810,45924,45797],{},[1810,45926,1812],{},[1677,45928,2858],{},[1810,45930,2475],{},[1677,45932,2411],{},[1677,45934,1906],{},[1810,45936,45937],{},"0,245.",[902,45939,45940],{"encoding":904},"Q'_c\\,dc = -\\frac{b - d}{(c - a)^2}\\,dc = -\\frac{30}{3{,}5^2}\\cdot 0{,}1 \\approx -0{,}245.",[724,45942,45943,45944,1656],{},"Nové rovnovážné množství ",[883,45945,45947],{"className":45946},[886],[888,45948,45949],{"xmlns":890},[892,45950,45951,45976],{},[895,45952,45953,45961,45963,45966,45968,45971,45973],{},[10554,45954,45955,45957,45959],{},[898,45956,2470],{},[1810,45958,1959],{},[898,45960,5640],{},[1677,45962,2411],{},[1810,45964,45965],{},"8,571",[1677,45967,1906],{},[1810,45969,45970],{},"0,245",[1677,45972,1679],{},[1810,45974,45975],{},"8,326",[902,45977,45978],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326",[724,45980,45981,46066],{},[38,45982,45983,45984,1343,46004,1343,46026,1343,46046,1656],{},"(b) Současné změny ",[883,45985,45987],{"className":45986},[886],[888,45988,45989],{"xmlns":890},[892,45990,45991,46001],{},[895,45992,45993,45995,45997,45999],{},[898,45994,1875],{},[898,45996,207],{},[1677,45998,1679],{},[1810,46000,6397],{},[902,46002,46003],{"encoding":904},"da = 0{,}5",[883,46005,46007],{"className":46006},[886],[888,46008,46009],{"xmlns":890},[892,46010,46011,46023],{},[895,46012,46013,46015,46017,46019,46021],{},[898,46014,1875],{},[898,46016,1779],{},[1677,46018,1679],{},[1677,46020,1906],{},[1810,46022,1909],{},[902,46024,46025],{"encoding":904},"db = -5",[883,46027,46029],{"className":46028},[886],[888,46030,46031],{"xmlns":890},[892,46032,46033,46043],{},[895,46034,46035,46037,46039,46041],{},[898,46036,1875],{},[898,46038,1823],{},[1677,46040,1679],{},[1810,46042,2475],{},[902,46044,46045],{"encoding":904},"dc = 0{,}1",[883,46047,46049],{"className":46048},[886],[888,46050,46051],{"xmlns":890},[892,46052,46053,46063],{},[895,46054,46055,46057,46059,46061],{},[898,46056,1875],{},[898,46058,1875],{},[1677,46060,1679],{},[1810,46062,1959],{},[902,46064,46065],{"encoding":904},"dd = 1"," Dosazením do (2.11):",[883,46068,46070],{"className":46069},[886],[888,46071,46072],{"xmlns":890,"display":29457},[892,46073,46074,46217],{},[22145,46075,46076,46158,46194],{"rowspacing":22147,"columnalign":22148,"columnspacing":2058},[22150,46077,46078,46088],{},[22153,46079,46080],{},[2006,46081,46082],{"scriptlevel":2008,"displaystyle":1966},[895,46083,46084,46086],{},[898,46085,2570],{"mathvariant":2057},[898,46087,2470],{},[22153,46089,46090],{},[2006,46091,46092],{"scriptlevel":2008,"displaystyle":1966},[895,46093,46094,46096,46098,46108,46110,46112,46114,46120,46122,46124,46126,46128,46130,46132,46142,46144,46146,46148,46154,46156],{},[895,46095],{},[1677,46097,2411],{},[2010,46099,46100,46102],{},[1810,46101,39410],{},[1805,46103,46104,46106],{},[1810,46105,45797],{},[1810,46107,1812],{},[1677,46109,2858],{},[1810,46111,6397],{},[1677,46113,1776],{},[2010,46115,46116,46118],{},[1810,46117,1959],{},[1810,46119,45797],{},[1677,46121,2858],{},[1677,46123,1686],{"stretchy":1685},[1677,46125,1906],{},[1810,46127,1909],{},[1677,46129,1692],{"stretchy":1685},[1677,46131,1906],{},[2010,46133,46134,46136],{},[1810,46135,39410],{},[1805,46137,46138,46140],{},[1810,46139,45797],{},[1810,46141,1812],{},[1677,46143,2858],{},[1810,46145,2475],{},[1677,46147,1906],{},[2010,46149,46150,46152],{},[1810,46151,1959],{},[1810,46153,45797],{},[1677,46155,2858],{},[1810,46157,1959],{},[22150,46159,46160,46166],{},[22153,46161,46162],{},[2006,46163,46164],{"scriptlevel":2008,"displaystyle":1966},[895,46165],{},[22153,46167,46168],{},[2006,46169,46170],{"scriptlevel":2008,"displaystyle":1966},[895,46171,46172,46174,46176,46179,46181,46184,46186,46189,46191],{},[895,46173],{},[1677,46175,1679],{},[1810,46177,46178],{},"1,2245",[1677,46180,1906],{},[1810,46182,46183],{},"1,4286",[1677,46185,1906],{},[1810,46187,46188],{},"0,2449",[1677,46190,1906],{},[1810,46192,46193],{},"0,2857",[22150,46195,46196,46202],{},[22153,46197,46198],{},[2006,46199,46200],{"scriptlevel":2008,"displaystyle":1966},[895,46201],{},[22153,46203,46204],{},[2006,46205,46206],{"scriptlevel":2008,"displaystyle":1966},[895,46207,46208,46210,46212,46214],{},[895,46209],{},[1677,46211,2411],{},[1677,46213,1906],{},[1810,46215,46216],{},"0,735.",[902,46218,46219],{"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}",[724,46221,31456,46222,1656],{},[883,46223,46225],{"className":46224},[886],[888,46226,46227],{"xmlns":890},[892,46228,46229,46253],{},[895,46230,46231,46239,46241,46243,46245,46248,46250],{},[10554,46232,46233,46235,46237],{},[898,46234,2470],{},[1810,46236,1959],{},[898,46238,5640],{},[1677,46240,2411],{},[1810,46242,45965],{},[1677,46244,1906],{},[1810,46246,46247],{},"0,735",[1677,46249,1679],{},[1810,46251,46252],{},"7,836",[902,46254,46255],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 = 7{,}836",[5254,46257,46258],{},[724,46259,46260,46262,46263,46286,46287,46309],{},[883,46261,5800],{}," Pozn. — oprava\nV knize je u této dílčí úlohy uvedena hodnota ",[883,46264,46266],{"className":46265},[886],[888,46267,46268],{"xmlns":890},[892,46269,46270,46283],{},[895,46271,46272,46274,46276,46278,46280],{},[898,46273,2570],{"mathvariant":2057},[898,46275,2470],{},[1677,46277,2411],{},[1677,46279,1906],{},[1810,46281,46282],{},"2,69",[902,46284,46285],{"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 ",[883,46288,46290],{"className":46289},[886],[888,46291,46292],{"xmlns":890},[892,46293,46294,46306],{},[895,46295,46296,46298,46300,46302,46304],{},[898,46297,2570],{"mathvariant":2057},[898,46299,2470],{},[1677,46301,2411],{},[1677,46303,1906],{},[1810,46305,46247],{},[902,46307,46308],{"encoding":904},"\\Delta Q \\approx -0{,}735",". Výsledek byl v této wiki opraven.",[724,46311,46312],{},"Princip multiplikátorů lze uplatnit na libovolné ekonomické proměnné — analogicky v makroekonomii (kap. 7).",[38361,46314],{},[115,46316,820],{"id":13173},[5254,46318,46319],{},[724,46320,46321,5261,46323,11413,46326,13518,46342,11413,46345,46361,46362,1656],{},[883,46322,5543],{},[38,46324,46325],{},"Přebytek spotřebitele",[883,46327,46329],{"className":46328},[886],[888,46330,46331],{"xmlns":890},[892,46332,46333,46339],{},[895,46334,46335,46337],{},[898,46336,2458],{},[898,46338,10061],{},[902,46340,46341],{"encoding":904},"CS",[38,46343,46344],{},"přebytek výrobce",[883,46346,46348],{"className":46347},[886],[888,46349,46350],{"xmlns":890},[892,46351,46352,46358],{},[895,46353,46354,46356],{},[898,46355,5325],{},[898,46357,10061],{},[902,46359,46360],{"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 ",[207,46363,46365],{"className":46364,"dataFsResolvedFilePath":818,"href":819},[210],"prebytek-spotrebitele-vyrobce",[724,46367,46368],{},[2240,46369],{"alt":46370,"className":46371,"src":46372},"imek-prebytky-cs-ps",[210,2244],"\u002Fwiki-assets\u002Fimek-prebytky-cs-ps.jpeg",[724,46374,46375,11413,46377,46380],{},[38,46376,46325],{},[614,46378,46379],{},"consumer surplus",") — rozdíl mezi ochotou platit a skutečnou platbou:",[883,46382,46384],{"className":46383},[886],[888,46385,46386],{"xmlns":890,"display":29457},[892,46387,46388,46465],{},[22145,46389,46390],{"width":29462},[22150,46391,46392,46394,46458,46460],{},[22153,46393],{"width":29467},[22153,46395,46396],{},[895,46397,46398,46400,46402,46404,46410,46412,46414,46426,46428,46430,46432,46434,46436,46438,46440,46442,46448,46450,46456],{},[898,46399,2458],{},[898,46401,10061],{},[1677,46403,1686],{"stretchy":1685},[1953,46405,46406,46408],{},[898,46407,2470],{},[1810,46409,2008],{},[1677,46411,1692],{"stretchy":1685},[1677,46413,1679],{},[10554,46415,46416,46418,46420],{},[1677,46417,12558],{},[1810,46419,2008],{},[1953,46421,46422,46424],{},[898,46423,2470],{},[1810,46425,2008],{},[898,46427,5571],{},[1677,46429,1686],{"stretchy":1685},[898,46431,2470],{},[1677,46433,1692],{"stretchy":1685},[1969,46435,2668],{},[898,46437,1875],{},[898,46439,2470],{},[1677,46441,1906],{},[1953,46443,46444,46446],{},[898,46445,5325],{},[1810,46447,2008],{},[1969,46449,2668],{},[1953,46451,46452,46454],{},[898,46453,2470],{},[1810,46455,2008],{},[898,46457,1656],{"mathvariant":2057},[22153,46459],{"width":29467},[22153,46461,46462],{},[1969,46463,46464],{},"(2.14)",[902,46466,46467],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\,dQ - P_0\\,Q_0. \\tag{2.14}",[724,46469,46470,11413,46473,46476],{},[38,46471,46472],{},"Přebytek výrobce",[614,46474,46475],{},"producer surplus",") — rozdíl mezi tržbou a minimální cenou:",[883,46478,46480],{"className":46479},[886],[888,46481,46482],{"xmlns":890,"display":29457},[892,46483,46484,46561],{},[22145,46485,46486],{"width":29462},[22150,46487,46488,46490,46554,46556],{},[22153,46489],{"width":29467},[22153,46491,46492],{},[895,46493,46494,46496,46498,46500,46506,46508,46510,46516,46518,46524,46526,46538,46540,46542,46544,46546,46548,46550,46552],{},[898,46495,5325],{},[898,46497,10061],{},[1677,46499,1686],{"stretchy":1685},[1953,46501,46502,46504],{},[898,46503,2470],{},[1810,46505,2008],{},[1677,46507,1692],{"stretchy":1685},[1677,46509,1679],{},[1953,46511,46512,46514],{},[898,46513,5325],{},[1810,46515,2008],{},[1969,46517,2668],{},[1953,46519,46520,46522],{},[898,46521,2470],{},[1810,46523,2008],{},[1677,46525,1906],{},[10554,46527,46528,46530,46532],{},[1677,46529,12558],{},[1810,46531,2008],{},[1953,46533,46534,46536],{},[898,46535,2470],{},[1810,46537,2008],{},[898,46539,10061],{},[1677,46541,1686],{"stretchy":1685},[898,46543,2470],{},[1677,46545,1692],{"stretchy":1685},[1969,46547,2668],{},[898,46549,1875],{},[898,46551,2470],{},[898,46553,1656],{"mathvariant":2057},[22153,46555],{"width":29467},[22153,46557,46558],{},[1969,46559,46560],{},"(2.15)",[902,46562,46563],{"encoding":904},"PS(Q_0) = P_0\\,Q_0 - \\int_0^{Q_0} S(Q)\\,dQ. \\tag{2.15}",[724,46565,46566,46567,1656],{},"Geometricky jde o plochy mezi rovnovážnou cenou a příslušnou křivkou; výpočet využívá aparát ",[207,46568,46570],{"className":46569,"dataFsResolvedFilePath":773,"href":774},[210],"určitého integrálu",[38361,46572],{},[115,46574,46576],{"id":46575},"příklady-z-knihy-přehled","Příklady z knihy — přehled",[120,46578,46579,46610,46615,46621,46649,46655,46684,46690,46770,46796],{},[123,46580,46581,46583,46584,46609],{},[38,46582,39319],{}," — lineární poptávka ",[883,46585,46587],{"className":46586},[886],[888,46588,46589],{"xmlns":890},[892,46590,46591,46607],{},[895,46592,46593,46595,46597,46599,46601,46603,46605],{},[898,46594,5325],{},[1677,46596,1679],{},[1677,46598,1906],{},[1810,46600,1812],{},[898,46602,2470],{},[1677,46604,1776],{},[1810,46606,2807],{},[902,46608,39351],{"encoding":904},", alternativní tvar, cenové rozpětí.",[123,46611,46612,46614],{},[38,46613,39633],{}," — empirické křivky poptávky po cukru (rodina vs. trh).",[123,46616,46617,46620],{},[38,46618,46619],{},"Příklad 2.3"," — posun poptávky při zdanění kupujícího.",[123,46622,46623,46625,46626,1656],{},[38,46624,42180],{}," — lineární nabídka ",[883,46627,46629],{"className":46628},[886],[888,46630,46631],{"xmlns":890},[892,46632,46633,46647],{},[895,46634,46635,46637,46639,46641,46643,46645],{},[898,46636,5325],{},[1677,46638,1679],{},[1810,46640,6397],{},[898,46642,2470],{},[1677,46644,1776],{},[1810,46646,6392],{},[902,46648,42209],{"encoding":904},[123,46650,46651,46654],{},[38,46652,46653],{},"Příklad 2.6"," — posun nabídky při zdanění výrobce.",[123,46656,46657,46660,46661,1656],{},[38,46658,46659],{},"Příklad 2.7"," — kvadratická rovnováha, ",[883,46662,46664],{"className":46663},[886],[888,46665,46666],{"xmlns":890},[892,46667,46668,46682],{},[895,46669,46670,46672,46674,46676,46678,46680],{},[898,46671,5640],{},[1677,46673,2167],{"stretchy":1685},[1810,46675,2032],{},[1677,46677,1967],{"separator":1966},[1810,46679,43327],{},[1677,46681,2182],{"stretchy":1685},[902,46683,43355],{"encoding":904},[123,46685,46686,46689],{},[38,46687,46688],{},"Příklad 2.8"," — dvoukomoditní trh, soustava rovnic, komplementy.",[123,46691,46692,46695,46696,46713,46714,1343,46739,46766,46767,2632],{},[38,46693,46694],{},"Příklad 2.9"," — daň ",[883,46697,46699],{"className":46698},[886],[888,46700,46701],{"xmlns":890},[892,46702,46703,46711],{},[895,46704,46705,46707,46709],{},[898,46706,2455],{},[1677,46708,1679],{},[1810,46710,1916],{},[902,46712,42659],{"encoding":904}," na výrobce; rozklad ",[883,46715,46717],{"className":46716},[886],[888,46718,46719],{"xmlns":890},[892,46720,46721,46737],{},[895,46722,46723,46733,46735],{},[1953,46724,46725,46727],{},[898,46726,2455],{},[895,46728,46729,46731],{},[898,46730,44068],{},[898,46732,724],{},[1677,46734,1679],{},[1810,46736,1812],{},[902,46738,44367],{"encoding":904},[883,46740,46742],{"className":46741},[886],[888,46743,46744],{"xmlns":890},[892,46745,46746,46764],{},[895,46747,46748,46760,46762],{},[1953,46749,46750,46752],{},[898,46751,2455],{},[895,46753,46754,46756,46758],{},[898,46755,44091],{},[898,46757,1675],{},[898,46759,13431],{},[1677,46761,1679],{},[1810,46763,2032],{},[902,46765,44396],{"encoding":904},". (Viz ",[207,46768,44112],{"className":46769,"dataFsResolvedFilePath":809,"href":810},[210],[123,46771,46772,46695,46775,46792,46793,2632],{},[38,46773,46774],{},"Příklad 2.10",[883,46776,46778],{"className":46777},[886],[888,46779,46780],{"xmlns":890},[892,46781,46782,46790],{},[895,46783,46784,46786,46788],{},[898,46785,2455],{},[1677,46787,1679],{},[1810,46789,1916],{},[902,46791,42659],{"encoding":904}," na spotřebitele; stejné čisté ceny i množství. (Viz ",[207,46794,44112],{"className":46795,"dataFsResolvedFilePath":809,"href":810},[210],[123,46797,46798,46801],{},[38,46799,46800],{},"Příklad 2.11"," — komparativní statika, multiplikátory, změny parametrů.",[38361,46803],{},[115,46805,46807],{"id":46806},"úlohy-k-samostatnému-řešení","Úlohy k samostatnému řešení",[198,46809,46811],{"id":46810},"základní-analýza-poptávky","Základní analýza poptávky",[724,46813,46814,46817,46818,46853,46854,46880],{},[38,46815,46816],{},"2.1"," Je dána poptávka ",[883,46819,46821],{"className":46820},[886],[888,46822,46823],{"xmlns":890},[892,46824,46825,46850],{},[895,46826,46827,46829,46831,46833,46835,46837,46839,46841,46844,46846,46848],{},[898,46828,2470],{},[1677,46830,1679],{},[898,46832,5571],{},[1677,46834,1686],{"stretchy":1685},[898,46836,5325],{},[1677,46838,1692],{"stretchy":1685},[1677,46840,1679],{},[1810,46842,46843],{},"75",[1677,46845,1906],{},[1810,46847,1909],{},[898,46849,5325],{},[902,46851,46852],{"encoding":904},"Q = D(P) = 75 - 5P",". (a) Načrtněte křivku poptávky. (b) Stanovte reálné cenové rozpětí. (c) Vypočtěte množství při cenách ",[883,46855,46857],{"className":46856},[886],[888,46858,46859],{"xmlns":890},[892,46860,46861,46877],{},[895,46862,46863,46865,46867,46869,46871,46873,46875],{},[1810,46864,2008],{},[1677,46866,1967],{"separator":1966},[1810,46868,1909],{},[1677,46870,1967],{"separator":1966},[1810,46872,2544],{},[1677,46874,1967],{"separator":1966},[1810,46876,37635],{},[902,46878,46879],{"encoding":904},"0, 5, 10, 15"," a výsledky vyznačte na křivku poptávky.",[724,46882,46883,46886,46887,46905,46906,2832],{},[38,46884,46885],{},"2.2"," Ověřte, že uvedené funkce vyjadřují (s případným omezením pro ",[883,46888,46890],{"className":46889},[886],[888,46891,46892],{"xmlns":890},[892,46893,46894,46902],{},[895,46895,46896,46898,46900],{},[898,46897,5325],{},[1677,46899,1967],{"separator":1966},[898,46901,2470],{},[902,46903,46904],{"encoding":904},"P, Q",") poptávku (využijte testu na zápornost derivace), charakterizujte tvar křivky poptávky a vyjádřete ve tvaru poptávky v alternativním tvaru (",[883,46907,46909],{"className":46908},[886],[888,46910,46911],{"xmlns":890},[892,46912,46913,46929],{},[895,46914,46915,46917,46919,46921,46923,46925,46927],{},[898,46916,207],{},[1677,46918,1967],{"separator":1966},[898,46920,1779],{},[1677,46922,1967],{"separator":1966},[898,46924,1823],{},[1677,46926,3089],{},[1810,46928,2008],{},[902,46930,46931],{"encoding":904},"a, b, c > 0",[120,46933,46934,46967,46998,47033,47064,47099],{},[123,46935,46936,46937],{},"(a) ",[883,46938,46940],{"className":46939},[886],[888,46941,46942],{"xmlns":890},[892,46943,46944,46964],{},[895,46945,46946,46948,46950],{},[898,46947,2470],{},[1677,46949,1679],{},[2006,46951,46952],{"scriptlevel":2008,"displaystyle":1966},[2010,46953,46954,46956],{},[898,46955,207],{},[895,46957,46958,46960,46962],{},[898,46959,5325],{},[1677,46961,1776],{},[898,46963,1823],{},[902,46965,46966],{"encoding":904},"Q = \\dfrac{a}{P + c}",[123,46968,46969,46970],{},"(b) ",[883,46971,46973],{"className":46972},[886],[888,46974,46975],{"xmlns":890},[892,46976,46977,46995],{},[895,46978,46979,46981,46983],{},[898,46980,2470],{},[1677,46982,1679],{},[9505,46984,46985],{},[895,46986,46987,46989,46991,46993],{},[898,46988,207],{},[1677,46990,1906],{},[898,46992,1779],{},[898,46994,2470],{},[902,46996,46997],{"encoding":904},"Q = \\sqrt{a - bQ}",[123,46999,47000,47001],{},"(c) ",[883,47002,47004],{"className":47003},[886],[888,47005,47006],{"xmlns":890},[892,47007,47008,47030],{},[895,47009,47010,47012,47014],{},[898,47011,2470],{},[1677,47013,1679],{},[2006,47015,47016],{"scriptlevel":2008,"displaystyle":1966},[2010,47017,47018,47028],{},[895,47019,47020,47022,47024],{},[898,47021,207],{},[1677,47023,1906],{},[9505,47025,47026],{},[898,47027,5325],{},[898,47029,1779],{},[902,47031,47032],{"encoding":904},"Q = \\dfrac{a - \\sqrt{P}}{b}",[123,47034,47035,47036],{},"(d) ",[883,47037,47039],{"className":47038},[886],[888,47040,47041],{"xmlns":890},[892,47042,47043,47061],{},[895,47044,47045,47047,47049,47051,47053,47055],{},[898,47046,5325],{},[1677,47048,1679],{},[898,47050,207],{},[1677,47052,1906],{},[898,47054,1779],{},[1805,47056,47057,47059],{},[898,47058,2470],{},[1810,47060,1812],{},[902,47062,47063],{"encoding":904},"P = a - bQ^2",[123,47065,47066,47067],{},"(e) ",[883,47068,47070],{"className":47069},[886],[888,47071,47072],{"xmlns":890},[892,47073,47074,47096],{},[895,47075,47076,47078,47080,47082,47092,47094],{},[898,47077,2470],{},[1677,47079,1679],{},[898,47081,1779],{},[1805,47083,47084,47086],{},[898,47085,5325],{},[895,47087,47088,47090],{},[1677,47089,1906],{},[898,47091,207],{},[1677,47093,1776],{},[898,47095,1823],{},[902,47097,47098],{"encoding":904},"Q = bP^{-a} + c",[123,47100,47101,47102],{},"(f) ",[883,47103,47105],{"className":47104},[886],[888,47106,47107],{"xmlns":890},[892,47108,47109,47132],{},[895,47110,47111,47113,47115,47117,47119],{},[898,47112,2470],{},[1677,47114,1679],{},[898,47116,207],{},[1677,47118,2858],{},[1805,47120,47121,47124],{},[898,47122,47123],{},"e",[895,47125,47126,47128,47130],{},[1677,47127,1906],{},[898,47129,1779],{},[898,47131,5325],{},[902,47133,47134],{"encoding":904},"Q = a \\cdot e^{-bP}",[724,47136,47137,47140],{},[38,47138,47139],{},"2.3"," Rozhodněte, jak se změní křivka poptávky, jestliže se zvýší (ceteris paribus):",[120,47142,47143,47146,47149],{},[123,47144,47145],{},"(a) Cena substitutu.",[123,47147,47148],{},"(b) Cena komplementu.",[123,47150,47151],{},"(c) Výdaje na reklamu.",[724,47153,47154,46817,47156,47190,47191,47219],{},[38,47155,26033],{},[883,47157,47159],{"className":47158},[886],[888,47160,47161],{"xmlns":890},[892,47162,47163,47187],{},[895,47164,47165,47167,47169,47171,47173,47175,47177,47179,47181,47183,47185],{},[898,47166,5325],{},[1677,47168,1679],{},[898,47170,5571],{},[1677,47172,1686],{"stretchy":1685},[898,47174,2470],{},[1677,47176,1692],{"stretchy":1685},[1677,47178,1679],{},[1810,47180,3190],{},[1677,47182,1906],{},[1810,47184,1812],{},[898,47186,2470],{},[902,47188,47189],{"encoding":904},"P = D(Q) = 12 - 2Q",". Najděte novou poptávku ",[883,47192,47194],{"className":47193},[886],[888,47195,47196],{"xmlns":890},[892,47197,47198,47216],{},[895,47199,47200,47202,47204,47210,47212,47214],{},[898,47201,5325],{},[1677,47203,1679],{},[1805,47205,47206,47208],{},[898,47207,5571],{},[1677,47209,5742],{},[1677,47211,1686],{"stretchy":1685},[898,47213,2470],{},[1677,47215,1692],{"stretchy":1685},[902,47217,47218],{"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.",[724,47221,47222,47225],{},[38,47223,47224],{},"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:",[120,47227,47228,47312,47388,47474,47562],{},[123,47229,46936,47230,1343,47270,1656],{},[883,47231,47233],{"className":47232},[886],[888,47234,47235],{"xmlns":890},[892,47236,47237,47267],{},[895,47238,47239,47245,47247,47249,47251,47253,47259,47261],{},[1953,47240,47241,47243],{},[898,47242,24644],{},[1810,47244,1959],{},[1677,47246,1679],{},[1810,47248,10423],{},[1677,47250,1906],{},[1810,47252,2032],{},[1953,47254,47255,47257],{},[898,47256,5643],{},[1810,47258,1959],{},[1677,47260,1776],{},[1953,47262,47263,47265],{},[898,47264,5643],{},[1810,47266,1812],{},[902,47268,47269],{"encoding":904},"B_1 = 20 - 4A_1 + A_2",[883,47271,47273],{"className":47272},[886],[888,47274,47275],{"xmlns":890},[892,47276,47277,47309],{},[895,47278,47279,47285,47287,47289,47291,47293,47299,47301,47303],{},[1953,47280,47281,47283],{},[898,47282,24644],{},[1810,47284,1812],{},[1677,47286,1679],{},[1810,47288,2544],{},[1677,47290,1776],{},[1810,47292,1812],{},[1953,47294,47295,47297],{},[898,47296,5643],{},[1810,47298,1959],{},[1677,47300,1906],{},[1810,47302,2032],{},[1953,47304,47305,47307],{},[898,47306,5643],{},[1810,47308,1812],{},[902,47310,47311],{"encoding":904},"B_2 = 10 + 2A_1 - 4A_2",[123,47313,46969,47314,1343,47356,1656],{},[883,47315,47317],{"className":47316},[886],[888,47318,47319],{"xmlns":890},[892,47320,47321,47353],{},[895,47322,47323,47329,47331,47333,47335,47337,47343,47345,47347],{},[1953,47324,47325,47327],{},[898,47326,24644],{},[1810,47328,1959],{},[1677,47330,1679],{},[1810,47332,2801],{},[1677,47334,1906],{},[1810,47336,2544],{},[1953,47338,47339,47341],{},[898,47340,5643],{},[1810,47342,1959],{},[1677,47344,1906],{},[1810,47346,1916],{},[1953,47348,47349,47351],{},[898,47350,5643],{},[1810,47352,1812],{},[902,47354,47355],{"encoding":904},"B_1 = 50 - 10A_1 - 6A_2",[883,47357,47359],{"className":47358},[886],[888,47360,47361],{"xmlns":890},[892,47362,47363,47385],{},[895,47364,47365,47371,47373,47375,47377,47379],{},[1953,47366,47367,47369],{},[898,47368,24644],{},[1810,47370,1812],{},[1677,47372,1679],{},[1810,47374,37635],{},[1677,47376,1906],{},[1810,47378,2544],{},[1953,47380,47381,47383],{},[898,47382,5643],{},[1810,47384,1812],{},[902,47386,47387],{"encoding":904},"B_2 = 15 - 10A_2",[123,47389,47000,47390,1343,47432,1656],{},[883,47391,47393],{"className":47392},[886],[888,47394,47395],{"xmlns":890},[892,47396,47397,47429],{},[895,47398,47399,47405,47407,47409,47411,47413,47419,47421,47423],{},[1953,47400,47401,47403],{},[898,47402,24644],{},[1810,47404,1959],{},[1677,47406,1679],{},[1810,47408,39410],{},[1677,47410,1906],{},[1810,47412,1812],{},[1953,47414,47415,47417],{},[898,47416,5643],{},[1810,47418,1959],{},[1677,47420,1906],{},[1810,47422,2032],{},[1953,47424,47425,47427],{},[898,47426,5643],{},[1810,47428,1812],{},[902,47430,47431],{"encoding":904},"B_1 = 30 - 2A_1 - 4A_2",[883,47433,47435],{"className":47434},[886],[888,47436,47437],{"xmlns":890},[892,47438,47439,47471],{},[895,47440,47441,47447,47449,47451,47453,47455,47461,47463,47465],{},[1953,47442,47443,47445],{},[898,47444,24644],{},[1810,47446,1812],{},[1677,47448,1679],{},[1810,47450,37635],{},[1677,47452,1776],{},[1810,47454,1812],{},[1953,47456,47457,47459],{},[898,47458,5643],{},[1810,47460,1959],{},[1677,47462,1906],{},[1810,47464,1812],{},[1953,47466,47467,47469],{},[898,47468,5643],{},[1810,47470,1812],{},[902,47472,47473],{"encoding":904},"B_2 = 15 + 2A_1 - 2A_2",[123,47475,47035,47476,1343,47520,1656],{},[883,47477,47479],{"className":47478},[886],[888,47480,47481],{"xmlns":890},[892,47482,47483,47517],{},[895,47484,47485,47491,47493,47495,47497,47499,47501,47507,47509,47511],{},[1953,47486,47487,47489],{},[898,47488,24644],{},[1810,47490,1959],{},[1677,47492,1679],{},[1677,47494,1906],{},[1810,47496,10423],{},[1677,47498,1906],{},[1810,47500,1812],{},[1953,47502,47503,47505],{},[898,47504,5643],{},[1810,47506,1959],{},[1677,47508,1776],{},[1810,47510,1854],{},[1953,47512,47513,47515],{},[898,47514,5643],{},[1810,47516,1812],{},[902,47518,47519],{"encoding":904},"B_1 = -20 - 2A_1 + 3A_2",[883,47521,47523],{"className":47522},[886],[888,47524,47525],{"xmlns":890},[892,47526,47527,47559],{},[895,47528,47529,47535,47537,47539,47541,47543,47549,47551,47553],{},[1953,47530,47531,47533],{},[898,47532,24644],{},[1810,47534,1812],{},[1677,47536,1679],{},[1810,47538,2544],{},[1677,47540,1776],{},[1810,47542,1812],{},[1953,47544,47545,47547],{},[898,47546,5643],{},[1810,47548,1959],{},[1677,47550,1906],{},[1810,47552,1812],{},[1953,47554,47555,47557],{},[898,47556,5643],{},[1810,47558,1812],{},[902,47560,47561],{"encoding":904},"B_2 = 10 + 2A_1 - 2A_2",[123,47563,47066,47564,1343,47606,1656],{},[883,47565,47567],{"className":47566},[886],[888,47568,47569],{"xmlns":890},[892,47570,47571,47603],{},[895,47572,47573,47579,47581,47583,47585,47587,47593,47595,47597],{},[1953,47574,47575,47577],{},[898,47576,24644],{},[1810,47578,1959],{},[1677,47580,1679],{},[1810,47582,10423],{},[1677,47584,1776],{},[1810,47586,1812],{},[1953,47588,47589,47591],{},[898,47590,5643],{},[1810,47592,1959],{},[1677,47594,1776],{},[1810,47596,2032],{},[1953,47598,47599,47601],{},[898,47600,5643],{},[1810,47602,1812],{},[902,47604,47605],{"encoding":904},"B_1 = 20 + 2A_1 + 4A_2",[883,47607,47609],{"className":47608},[886],[888,47610,47611],{"xmlns":890},[892,47612,47613,47645],{},[895,47614,47615,47621,47623,47625,47627,47629,47635,47637,47639],{},[1953,47616,47617,47619],{},[898,47618,24644],{},[1810,47620,1812],{},[1677,47622,1679],{},[1810,47624,6599],{},[1677,47626,1906],{},[1810,47628,1854],{},[1953,47630,47631,47633],{},[898,47632,5643],{},[1810,47634,1959],{},[1677,47636,1776],{},[1810,47638,1909],{},[1953,47640,47641,47643],{},[898,47642,5643],{},[1810,47644,1812],{},[902,47646,47647],{"encoding":904},"B_2 = 40 - 3A_1 + 5A_2",[198,47649,47651],{"id":47650},"základní-analýza-nabídky","Základní analýza nabídky",[724,47653,47654,47657,47658,47692,47693,47715],{},[38,47655,47656],{},"2.6"," Je dána nabídka ",[883,47659,47661],{"className":47660},[886],[888,47662,47663],{"xmlns":890},[892,47664,47665,47689],{},[895,47666,47667,47669,47671,47673,47675,47677,47679,47681,47683,47685,47687],{},[898,47668,5325],{},[1677,47670,1679],{},[898,47672,10061],{},[1677,47674,1686],{"stretchy":1685},[898,47676,2470],{},[1677,47678,1692],{"stretchy":1685},[1677,47680,1679],{},[1810,47682,10423],{},[1677,47684,1776],{},[1810,47686,2520],{},[898,47688,2470],{},[902,47690,47691],{"encoding":904},"P = S(Q) = 20 + 0{,}2Q",". (a) Načrtněte křivku nabídky. (b) Vypočtěte množství při cenách ",[883,47694,47696],{"className":47695},[886],[888,47697,47698],{"xmlns":890},[892,47699,47700,47712],{},[895,47701,47702,47704,47706,47708,47710],{},[1810,47703,6392],{},[1677,47705,1967],{"separator":1966},[1810,47707,39410],{},[1677,47709,1967],{"separator":1966},[1810,47711,16428],{},[902,47713,47714],{"encoding":904},"25, 30, 35"," a vyznačte výsledky na křivku nabídky.",[724,47717,47718,47721,47722,47739],{},[38,47719,47720],{},"2.7"," Ověřte, že zadané funkce vyjadřují (s případným omezením na ",[883,47723,47725],{"className":47724},[886],[888,47726,47727],{"xmlns":890},[892,47728,47729,47737],{},[895,47730,47731,47733,47735],{},[898,47732,5325],{},[1677,47734,1967],{"separator":1966},[898,47736,2470],{},[902,47738,46904],{"encoding":904},") nabídku (využijte testu na kladnost derivace), charakterizujte tvar křivky nabídky a vyjádřete nabídku v alternativním tvaru:",[120,47741,47742,47768,47796,47829,47863,47899],{},[123,47743,46936,47744],{},[883,47745,47747],{"className":47746},[886],[888,47748,47749],{"xmlns":890},[892,47750,47751,47765],{},[895,47752,47753,47755,47757,47759,47761,47763],{},[898,47754,5325],{},[1677,47756,1679],{},[1810,47758,39410],{},[1677,47760,1776],{},[1810,47762,1812],{},[898,47764,2470],{},[902,47766,47767],{"encoding":904},"P = 30 + 2Q",[123,47769,46969,47770],{},[883,47771,47773],{"className":47772},[886],[888,47774,47775],{"xmlns":890},[892,47776,47777,47793],{},[895,47778,47779,47781,47783,47785,47787,47789,47791],{},[898,47780,2470],{},[1677,47782,1679],{},[1677,47784,1906],{},[1810,47786,1854],{},[1677,47788,1776],{},[1810,47790,3190],{},[898,47792,5325],{},[902,47794,47795],{"encoding":904},"Q = -3 + 12P",[123,47797,47000,47798],{},[883,47799,47801],{"className":47800},[886],[888,47802,47803],{"xmlns":890},[892,47804,47805,47827],{},[895,47806,47807,47809,47811,47817,47819,47821,47823,47825],{},[898,47808,5325],{},[1677,47810,1679],{},[1805,47812,47813,47815],{},[898,47814,2470],{},[1810,47816,1812],{},[1677,47818,1776],{},[1810,47820,24337],{},[898,47822,2470],{},[1677,47824,1776],{},[1810,47826,33937],{},[902,47828,43113],{"encoding":904},[123,47830,47035,47831],{},[883,47832,47834],{"className":47833},[886],[888,47835,47836],{"xmlns":890},[892,47837,47838,47860],{},[895,47839,47840,47842,47844,47850,47852,47854,47856,47858],{},[898,47841,5325],{},[1677,47843,1679],{},[1805,47845,47846,47848],{},[898,47847,2470],{},[1810,47849,1812],{},[1677,47851,1776],{},[1810,47853,1812],{},[898,47855,2470],{},[1677,47857,1776],{},[1810,47859,3190],{},[902,47861,47862],{"encoding":904},"P = Q^2 + 2Q + 12",[123,47864,47066,47865],{},[883,47866,47868],{"className":47867},[886],[888,47869,47870],{"xmlns":890},[892,47871,47872,47896],{},[895,47873,47874,47876,47878,47880,47882,47884,47886,47888,47890],{},[898,47875,2470],{},[1677,47877,1679],{},[1810,47879,10191],{},[1677,47881,1776],{},[1810,47883,1909],{},[898,47885,5325],{},[1677,47887,1776],{},[1810,47889,2475],{},[1805,47891,47892,47894],{},[898,47893,5325],{},[1810,47895,1812],{},[902,47897,47898],{"encoding":904},"Q = 150 + 5P + 0{,}1P^2",[123,47900,47101,47901],{},[883,47902,47904],{"className":47903},[886],[888,47905,47906],{"xmlns":890},[892,47907,47908,47933],{},[895,47909,47910,47912,47914,47916,47918,47920,47922,47924,47927],{},[898,47911,2470],{},[1677,47913,1679],{},[1810,47915,25592],{},[1677,47917,1776],{},[1810,47919,2475],{},[898,47921,5325],{},[1677,47923,1776],{},[1810,47925,47926],{},"0,004",[1805,47928,47929,47931],{},[898,47930,5325],{},[1810,47932,1812],{},[902,47934,47935],{"encoding":904},"Q = 7 + 0{,}1P + 0{,}004P^2",[724,47937,47938,47941],{},[38,47939,47940],{},"2.8"," Rozhodněte, jak se změní křivka nabídky, jestliže se (ceteris paribus):",[120,47943,47944,47947,47950,47953],{},[123,47945,47946],{},"(a) Sníží ceny surovin — vstupů.",[123,47948,47949],{},"(b) Zavede nová ekologičtější technologie zvyšující výrobní náklady.",[123,47951,47952],{},"(c) Zvýší ceny všech energií.",[123,47954,47955],{},"(d) Sníží daňové odvody státu.",[724,47957,47958,47657,47960,47994,47995,48023],{},[38,47959,44340],{},[883,47961,47963],{"className":47962},[886],[888,47964,47965],{"xmlns":890},[892,47966,47967,47991],{},[895,47968,47969,47971,47973,47975,47977,47979,47981,47983,47985,47987,47989],{},[898,47970,5325],{},[1677,47972,1679],{},[898,47974,10061],{},[1677,47976,1686],{"stretchy":1685},[898,47978,2470],{},[1677,47980,1692],{"stretchy":1685},[1677,47982,1679],{},[1810,47984,6397],{},[898,47986,2470],{},[1677,47988,1776],{},[1810,47990,37635],{},[902,47992,47993],{"encoding":904},"P = S(Q) = 0{,}5Q + 15",". Najděte novou nabídku ",[883,47996,47998],{"className":47997},[886],[888,47999,48000],{"xmlns":890},[892,48001,48002,48020],{},[895,48003,48004,48006,48008,48014,48016,48018],{},[898,48005,5325],{},[1677,48007,1679],{},[1805,48009,48010,48012],{},[898,48011,10061],{},[1677,48013,5742],{},[1677,48015,1686],{"stretchy":1685},[898,48017,2470],{},[1677,48019,1692],{"stretchy":1685},[902,48021,48022],{"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.",[198,48025,42716],{"id":48026},"tržní-rovnováha-1",[724,48028,48029,48031,48032,48049,48050,2385],{},[38,48030,44400],{}," Pro zadanou poptávku a nabídku najděte rovnovážné množství ",[883,48033,48035],{"className":48034},[886],[888,48036,48037],{"xmlns":890},[892,48038,48039,48047],{},[895,48040,48041],{},[1805,48042,48043,48045],{},[898,48044,2470],{},[898,48046,5640],{},[902,48048,43794],{"encoding":904}," a rovnovážnou cenu ",[883,48051,48053],{"className":48052},[886],[888,48054,48055],{"xmlns":890},[892,48056,48057,48065],{},[895,48058,48059],{},[1805,48060,48061,48063],{},[898,48062,5325],{},[898,48064,5640],{},[902,48066,42857],{"encoding":904},[120,48068,48069,48122,48173,48232],{},[123,48070,46936,48071,1343,48098,1656],{},[883,48072,48074],{"className":48073},[886],[888,48075,48076],{"xmlns":890},[892,48077,48078,48095],{},[895,48079,48080,48082,48084,48086,48088,48090,48092],{},[898,48081,5325],{},[1677,48083,1679],{},[1677,48085,1906],{},[1810,48087,1909],{},[898,48089,2470],{},[1677,48091,1776],{},[1810,48093,48094],{},"80",[902,48096,48097],{"encoding":904},"P = -5Q + 80",[883,48099,48101],{"className":48100},[886],[888,48102,48103],{"xmlns":890},[892,48104,48105,48119],{},[895,48106,48107,48109,48111,48113,48115,48117],{},[898,48108,5325],{},[1677,48110,1679],{},[1810,48112,1812],{},[898,48114,2470],{},[1677,48116,1776],{},[1810,48118,2544],{},[902,48120,48121],{"encoding":904},"P = 2Q + 10",[123,48123,46969,48124,1343,48150,1656],{},[883,48125,48127],{"className":48126},[886],[888,48128,48129],{"xmlns":890},[892,48130,48131,48147],{},[895,48132,48133,48135,48137,48139,48141,48143,48145],{},[898,48134,2470],{},[1677,48136,1679],{},[1677,48138,1906],{},[1810,48140,6397],{},[898,48142,5325],{},[1677,48144,1776],{},[1810,48146,6392],{},[902,48148,48149],{"encoding":904},"Q = -0{,}5P + 25",[883,48151,48153],{"className":48152},[886],[888,48154,48155],{"xmlns":890},[892,48156,48157,48171],{},[895,48158,48159,48161,48163,48165,48167,48169],{},[898,48160,2470],{},[1677,48162,1679],{},[1810,48164,1812],{},[898,48166,5325],{},[1677,48168,1906],{},[1810,48170,2801],{},[902,48172,42238],{"encoding":904},[123,48174,47000,48175,1343,48201,1656],{},[883,48176,48178],{"className":48177},[886],[888,48179,48180],{"xmlns":890},[892,48181,48182,48198],{},[895,48183,48184,48186,48188,48190,48192,48194,48196],{},[898,48185,5325],{},[1677,48187,1679],{},[1677,48189,1906],{},[1810,48191,2032],{},[898,48193,2470],{},[1677,48195,1776],{},[1810,48197,5434],{},[902,48199,48200],{"encoding":904},"P = -4Q + 120",[883,48202,48204],{"className":48203},[886],[888,48205,48206],{"xmlns":890},[892,48207,48208,48229],{},[895,48209,48210,48212,48214,48222,48224,48226],{},[898,48211,5325],{},[1677,48213,1679],{},[2006,48215,48216],{"scriptlevel":2008,"displaystyle":1685},[2010,48217,48218,48220],{},[1810,48219,1959],{},[1810,48221,1854],{},[898,48223,2470],{},[1677,48225,1776],{},[1810,48227,48228],{},"29",[902,48230,48231],{"encoding":904},"P = \\tfrac{1}{3}Q + 29",[123,48233,47035,48234,1343,48263,1656],{},[883,48235,48237],{"className":48236},[886],[888,48238,48239],{"xmlns":890},[892,48240,48241,48260],{},[895,48242,48243,48245,48247,48249,48255,48257],{},[898,48244,5325],{},[1677,48246,1679],{},[1677,48248,1906],{},[1805,48250,48251,48253],{},[898,48252,2470],{},[1810,48254,1812],{},[1677,48256,1776],{},[1810,48258,48259],{},"52",[902,48261,48262],{"encoding":904},"P = -Q^2 + 52",[883,48264,48266],{"className":48265},[886],[888,48267,48268],{"xmlns":890},[892,48269,48270,48288],{},[895,48271,48272,48274,48276,48278,48284,48286],{},[898,48273,5325],{},[1677,48275,1679],{},[1810,48277,1812],{},[1805,48279,48280,48282],{},[898,48281,2470],{},[1810,48283,1812],{},[1677,48285,1776],{},[1810,48287,2544],{},[902,48289,48290],{"encoding":904},"P = 2Q^2 + 10",[724,48292,48293,48296,48297,48327,48328,48358],{},[38,48294,48295],{},"2.11"," Pro zadanou poptávku a nabídku dvou závislých zboží najděte rovnovážná množství ",[883,48298,48300],{"className":48299},[886],[888,48301,48302],{"xmlns":890},[892,48303,48304,48324],{},[895,48305,48306,48314,48316],{},[10554,48307,48308,48310,48312],{},[898,48309,2470],{},[1810,48311,1959],{},[898,48313,5640],{},[1677,48315,1967],{"separator":1966},[10554,48317,48318,48320,48322],{},[898,48319,2470],{},[1810,48321,1812],{},[898,48323,5640],{},[902,48325,48326],{"encoding":904},"Q_1^E, Q_2^E"," a rovnovážné ceny ",[883,48329,48331],{"className":48330},[886],[888,48332,48333],{"xmlns":890},[892,48334,48335,48355],{},[895,48336,48337,48345,48347],{},[10554,48338,48339,48341,48343],{},[898,48340,5325],{},[1810,48342,1959],{},[898,48344,5640],{},[1677,48346,1967],{"separator":1966},[10554,48348,48349,48351,48353],{},[898,48350,5325],{},[1810,48352,1812],{},[898,48354,5640],{},[902,48356,48357],{"encoding":904},"P_1^E, P_2^E"," (index 1 přísluší prvnímu, index 2 druhému zboží):",[120,48360,48361,48513],{},[123,48362,46936,48363,1343,48403,1343,48445,1343,48479,1656],{},[883,48364,48366],{"className":48365},[886],[888,48367,48368],{"xmlns":890},[892,48369,48370,48400],{},[895,48371,48372,48378,48380,48382,48384,48386,48392,48394],{},[1953,48373,48374,48376],{},[898,48375,2470],{},[1810,48377,1959],{},[1677,48379,1679],{},[1810,48381,2544],{},[1677,48383,1906],{},[1810,48385,1812],{},[1953,48387,48388,48390],{},[898,48389,5325],{},[1810,48391,1959],{},[1677,48393,1776],{},[1953,48395,48396,48398],{},[898,48397,5325],{},[1810,48399,1812],{},[902,48401,48402],{"encoding":904},"Q_1 = 10 - 2P_1 + P_2",[883,48404,48406],{"className":48405},[886],[888,48407,48408],{"xmlns":890},[892,48409,48410,48442],{},[895,48411,48412,48418,48420,48422,48424,48426,48432,48434,48436],{},[1953,48413,48414,48416],{},[898,48415,2470],{},[1810,48417,1812],{},[1677,48419,1679],{},[1810,48421,1909],{},[1677,48423,1776],{},[1810,48425,1812],{},[1953,48427,48428,48430],{},[898,48429,5325],{},[1810,48431,1959],{},[1677,48433,1906],{},[1810,48435,1812],{},[1953,48437,48438,48440],{},[898,48439,5325],{},[1810,48441,1812],{},[902,48443,48444],{"encoding":904},"Q_2 = 5 + 2P_1 - 2P_2",[883,48446,48448],{"className":48447},[886],[888,48449,48450],{"xmlns":890},[892,48451,48452,48476],{},[895,48453,48454,48460,48462,48464,48466,48468,48470],{},[1953,48455,48456,48458],{},[898,48457,2470],{},[1810,48459,1959],{},[1677,48461,1679],{},[1677,48463,1906],{},[1810,48465,1854],{},[1677,48467,1776],{},[1810,48469,1812],{},[1953,48471,48472,48474],{},[898,48473,5325],{},[1810,48475,1959],{},[902,48477,48478],{"encoding":904},"Q_1 = -3 + 2P_1",[883,48480,48482],{"className":48481},[886],[888,48483,48484],{"xmlns":890},[892,48485,48486,48510],{},[895,48487,48488,48494,48496,48498,48500,48502,48504],{},[1953,48489,48490,48492],{},[898,48491,2470],{},[1810,48493,1812],{},[1677,48495,1679],{},[1677,48497,1906],{},[1810,48499,1812],{},[1677,48501,1776],{},[1810,48503,1854],{},[1953,48505,48506,48508],{},[898,48507,5325],{},[1810,48509,1812],{},[902,48511,48512],{"encoding":904},"Q_2 = -2 + 3P_2",[123,48514,46969,48515,1343,48555,1343,48597,1343,48629,1656],{},[883,48516,48518],{"className":48517},[886],[888,48519,48520],{"xmlns":890},[892,48521,48522,48552],{},[895,48523,48524,48530,48532,48534,48536,48538,48544,48546],{},[1953,48525,48526,48528],{},[898,48527,2470],{},[1810,48529,1959],{},[1677,48531,1679],{},[1810,48533,2771],{},[1677,48535,1906],{},[1810,48537,1812],{},[1953,48539,48540,48542],{},[898,48541,5325],{},[1810,48543,1959],{},[1677,48545,1776],{},[1953,48547,48548,48550],{},[898,48549,5325],{},[1810,48551,1812],{},[902,48553,48554],{"encoding":904},"Q_1 = 100 - 2P_1 + P_2",[883,48556,48558],{"className":48557},[886],[888,48559,48560],{"xmlns":890},[892,48561,48562,48594],{},[895,48563,48564,48570,48572,48574,48576,48578,48584,48586,48588],{},[1953,48565,48566,48568],{},[898,48567,2470],{},[1810,48569,1812],{},[1677,48571,1679],{},[1810,48573,1909],{},[1677,48575,1776],{},[1810,48577,1812],{},[1953,48579,48580,48582],{},[898,48581,5325],{},[1810,48583,1959],{},[1677,48585,1906],{},[1810,48587,1854],{},[1953,48589,48590,48592],{},[898,48591,5325],{},[1810,48593,1812],{},[902,48595,48596],{"encoding":904},"Q_2 = 5 + 2P_1 - 3P_2",[883,48598,48600],{"className":48599},[886],[888,48601,48602],{"xmlns":890},[892,48603,48604,48626],{},[895,48605,48606,48612,48614,48616,48618,48620],{},[1953,48607,48608,48610],{},[898,48609,2470],{},[1810,48611,1959],{},[1677,48613,1679],{},[1677,48615,1906],{},[1810,48617,2544],{},[1677,48619,1776],{},[1953,48621,48622,48624],{},[898,48623,5325],{},[1810,48625,1959],{},[902,48627,48628],{"encoding":904},"Q_1 = -10 + P_1",[883,48630,48632],{"className":48631},[886],[888,48633,48634],{"xmlns":890},[892,48635,48636,48658],{},[895,48637,48638,48644,48646,48648,48650,48652],{},[1953,48639,48640,48642],{},[898,48641,2470],{},[1810,48643,1812],{},[1677,48645,1679],{},[1810,48647,1909],{},[1677,48649,1776],{},[1810,48651,1916],{},[1953,48653,48654,48656],{},[898,48655,5325],{},[1810,48657,1812],{},[902,48659,48660],{"encoding":904},"Q_2 = 5 + 6P_2",[724,48662,48663,48666,48667,1343,48715,1343,48761,48811,48812,1343,48844,1343,48878,22985,48912,5272,48930,48948,48949,48962,48963,48989,48990,48327,49030,1656],{},[38,48664,48665],{},"2.12"," Pro tři závislá zboží jsou dány poptávky rovnicemi ",[883,48668,48670],{"className":48669},[886],[888,48671,48672],{"xmlns":890},[892,48673,48674,48712],{},[895,48675,48676,48682,48684,48686,48688,48694,48696,48698,48704,48706],{},[1953,48677,48678,48680],{},[898,48679,2470],{},[1810,48681,1959],{},[1677,48683,1679],{},[1810,48685,37635],{},[1677,48687,1906],{},[1953,48689,48690,48692],{},[898,48691,5325],{},[1810,48693,1959],{},[1677,48695,1776],{},[1810,48697,1812],{},[1953,48699,48700,48702],{},[898,48701,5325],{},[1810,48703,1812],{},[1677,48705,1776],{},[1953,48707,48708,48710],{},[898,48709,5325],{},[1810,48711,1854],{},[902,48713,48714],{"encoding":904},"Q_1 = 15 - P_1 + 2P_2 + P_3",[883,48716,48718],{"className":48717},[886],[888,48719,48720],{"xmlns":890},[892,48721,48722,48758],{},[895,48723,48724,48730,48732,48734,48736,48742,48744,48750,48752],{},[1953,48725,48726,48728],{},[898,48727,2470],{},[1810,48729,1812],{},[1677,48731,1679],{},[1810,48733,5387],{},[1677,48735,1776],{},[1953,48737,48738,48740],{},[898,48739,5325],{},[1810,48741,1959],{},[1677,48743,1906],{},[1953,48745,48746,48748],{},[898,48747,5325],{},[1810,48749,1812],{},[1677,48751,1906],{},[1953,48753,48754,48756],{},[898,48755,5325],{},[1810,48757,1854],{},[902,48759,48760],{"encoding":904},"Q_2 = 9 + P_1 - P_2 - P_3",[883,48762,48764],{"className":48763},[886],[888,48765,48766],{"xmlns":890},[892,48767,48768,48808],{},[895,48769,48770,48776,48778,48780,48782,48784,48790,48792,48798,48800,48802],{},[1953,48771,48772,48774],{},[898,48773,2470],{},[1810,48775,1854],{},[1677,48777,1679],{},[1810,48779,6973],{},[1677,48781,1776],{},[1810,48783,1812],{},[1953,48785,48786,48788],{},[898,48787,5325],{},[1810,48789,1959],{},[1677,48791,1906],{},[1953,48793,48794,48796],{},[898,48795,5325],{},[1810,48797,1812],{},[1677,48799,1906],{},[1810,48801,2032],{},[1953,48803,48804,48806],{},[898,48805,5325],{},[1810,48807,1854],{},[902,48809,48810],{"encoding":904},"Q_3 = 8 + 2P_1 - P_2 - 4P_3"," a nabídky rovnicemi ",[883,48813,48815],{"className":48814},[886],[888,48816,48817],{"xmlns":890},[892,48818,48819,48841],{},[895,48820,48821,48827,48829,48831,48833,48835],{},[1953,48822,48823,48825],{},[898,48824,2470],{},[1810,48826,1959],{},[1677,48828,1679],{},[1677,48830,1906],{},[1810,48832,25592],{},[1677,48834,1776],{},[1953,48836,48837,48839],{},[898,48838,5325],{},[1810,48840,1959],{},[902,48842,48843],{"encoding":904},"Q_1 = -7 + P_1",[883,48845,48847],{"className":48846},[886],[888,48848,48849],{"xmlns":890},[892,48850,48851,48875],{},[895,48852,48853,48859,48861,48863,48865,48867,48869],{},[1953,48854,48855,48857],{},[898,48856,2470],{},[1810,48858,1812],{},[1677,48860,1679],{},[1677,48862,1906],{},[1810,48864,2032],{},[1677,48866,1776],{},[1810,48868,2032],{},[1953,48870,48871,48873],{},[898,48872,5325],{},[1810,48874,1812],{},[902,48876,48877],{"encoding":904},"Q_2 = -4 + 4P_2",[883,48879,48881],{"className":48880},[886],[888,48882,48883],{"xmlns":890},[892,48884,48885,48909],{},[895,48886,48887,48893,48895,48897,48899,48901,48903],{},[1953,48888,48889,48891],{},[898,48890,2470],{},[1810,48892,1854],{},[1677,48894,1679],{},[1677,48896,1906],{},[1810,48898,1909],{},[1677,48900,1776],{},[1810,48902,1812],{},[1953,48904,48905,48907],{},[898,48906,5325],{},[1810,48908,1854],{},[902,48910,48911],{"encoding":904},"Q_3 = -5 + 2P_3",[883,48913,48915],{"className":48914},[886],[888,48916,48917],{"xmlns":890},[892,48918,48919,48927],{},[895,48920,48921],{},[1953,48922,48923,48925],{},[898,48924,2470],{},[898,48926,19181],{},[902,48928,48929],{"encoding":904},"Q_i",[883,48931,48933],{"className":48932},[886],[888,48934,48935],{"xmlns":890},[892,48936,48937,48945],{},[895,48938,48939],{},[1953,48940,48941,48943],{},[898,48942,5325],{},[898,48944,19181],{},[902,48946,48947],{"encoding":904},"P_i"," značí příslušné množství a ceny ",[883,48950,48952],{"className":48951},[886],[888,48953,48954],{"xmlns":890},[892,48955,48956,48960],{},[895,48957,48958],{},[898,48959,19181],{},[902,48961,19181],{"encoding":904},"-tého zboží, ",[883,48964,48966],{"className":48965},[886],[888,48967,48968],{"xmlns":890},[892,48969,48970,48986],{},[895,48971,48972,48974,48976,48978,48980,48982,48984],{},[898,48973,19181],{},[1677,48975,1679],{},[1810,48977,1959],{},[1677,48979,1967],{"separator":1966},[1810,48981,1812],{},[1677,48983,1967],{"separator":1966},[1810,48985,1854],{},[902,48987,48988],{"encoding":904},"i = 1, 2, 3",". Najděte rovnovážná množství ",[883,48991,48993],{"className":48992},[886],[888,48994,48995],{"xmlns":890},[892,48996,48997,49027],{},[895,48998,48999,49007,49009,49017,49019],{},[10554,49000,49001,49003,49005],{},[898,49002,2470],{},[1810,49004,1959],{},[898,49006,5640],{},[1677,49008,1967],{"separator":1966},[10554,49010,49011,49013,49015],{},[898,49012,2470],{},[1810,49014,1812],{},[898,49016,5640],{},[1677,49018,1967],{"separator":1966},[10554,49020,49021,49023,49025],{},[898,49022,2470],{},[1810,49024,1854],{},[898,49026,5640],{},[902,49028,49029],{"encoding":904},"Q_1^E, Q_2^E, Q_3^E",[883,49031,49033],{"className":49032},[886],[888,49034,49035],{"xmlns":890},[892,49036,49037,49067],{},[895,49038,49039,49047,49049,49057,49059],{},[10554,49040,49041,49043,49045],{},[898,49042,5325],{},[1810,49044,1959],{},[898,49046,5640],{},[1677,49048,1967],{"separator":1966},[10554,49050,49051,49053,49055],{},[898,49052,5325],{},[1810,49054,1812],{},[898,49056,5640],{},[1677,49058,1967],{"separator":1966},[10554,49060,49061,49063,49065],{},[898,49062,5325],{},[1810,49064,1854],{},[898,49066,5640],{},[902,49068,49069],{"encoding":904},"P_1^E, P_2^E, P_3^E",[724,49071,49072,49075,49076,49112,49113,1656],{},[38,49073,49074],{},"2.13"," Jsou dány poptávka ",[883,49077,49079],{"className":49078},[886],[888,49080,49081],{"xmlns":890},[892,49082,49083,49109],{},[895,49084,49085,49087,49089,49091,49093,49095,49097,49099,49101,49103,49105,49107],{},[898,49086,5325],{},[1677,49088,1679],{},[898,49090,5571],{},[1677,49092,1686],{"stretchy":1685},[898,49094,2470],{},[1677,49096,1692],{"stretchy":1685},[1677,49098,1679],{},[1677,49100,1906],{},[1810,49102,2032],{},[898,49104,2470],{},[1677,49106,1776],{},[1810,49108,48094],{},[902,49110,49111],{"encoding":904},"P = D(Q) = -4Q + 80"," a nabídka ",[883,49114,49116],{"className":49115},[886],[888,49117,49118],{"xmlns":890},[892,49119,49120,49144],{},[895,49121,49122,49124,49126,49128,49130,49132,49134,49136,49138,49140,49142],{},[898,49123,5325],{},[1677,49125,1679],{},[898,49127,10061],{},[1677,49129,1686],{"stretchy":1685},[898,49131,2470],{},[1677,49133,1692],{"stretchy":1685},[1677,49135,1679],{},[1810,49137,1854],{},[898,49139,2470],{},[1677,49141,1776],{},[1810,49143,2544],{},[902,49145,49146],{"encoding":904},"P = S(Q) = 3Q + 10",[120,49148,49149,49186,49250,49310],{},[123,49150,49151,49152,48049,49169,1656],{},"(a) Určete rovnovážné množství ",[883,49153,49155],{"className":49154},[886],[888,49156,49157],{"xmlns":890},[892,49158,49159,49167],{},[895,49160,49161],{},[1805,49162,49163,49165],{},[898,49164,2470],{},[898,49166,5640],{},[902,49168,43794],{"encoding":904},[883,49170,49172],{"className":49171},[886],[888,49173,49174],{"xmlns":890},[892,49175,49176,49184],{},[895,49177,49178],{},[1805,49179,49180,49182],{},[898,49181,5325],{},[898,49183,5640],{},[902,49185,42857],{"encoding":904},[123,49187,49188,49189,49207,49208,49228,49229,49249],{},"(b) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží výrobci daň ",[883,49190,49192],{"className":49191},[886],[888,49193,49194],{"xmlns":890},[892,49195,49196,49204],{},[895,49197,49198,49200,49202],{},[898,49199,2455],{},[1677,49201,1679],{},[1810,49203,25592],{},[902,49205,49206],{"encoding":904},"T = 7"," Kč na každou jednotku zboží, vypočtěte nové rovnovážné množství ",[883,49209,49211],{"className":49210},[886],[888,49212,49213],{"xmlns":890},[892,49214,49215,49225],{},[895,49216,49217],{},[10554,49218,49219,49221,49223],{},[898,49220,2470],{},[1810,49222,1959],{},[898,49224,5640],{},[902,49226,49227],{"encoding":904},"Q_1^E"," a novou rovnovážnou cenu ",[883,49230,49232],{"className":49231},[886],[888,49233,49234],{"xmlns":890},[892,49235,49236,49246],{},[895,49237,49238],{},[10554,49239,49240,49242,49244],{},[898,49241,5325],{},[1810,49243,1959],{},[898,49245,5640],{},[902,49247,49248],{"encoding":904},"P_1^E"," a určete, kolik z daňového zatížení zaplatí výrobce a kolik spotřebitel.",[123,49251,49252,49253,49207,49270,49228,49290,49249],{},"(c) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží spotřebiteli daň ",[883,49254,49256],{"className":49255},[886],[888,49257,49258],{"xmlns":890},[892,49259,49260,49268],{},[895,49261,49262,49264,49266],{},[898,49263,2455],{},[1677,49265,1679],{},[1810,49267,25592],{},[902,49269,49206],{"encoding":904},[883,49271,49273],{"className":49272},[886],[888,49274,49275],{"xmlns":890},[892,49276,49277,49287],{},[895,49278,49279],{},[10554,49280,49281,49283,49285],{},[898,49282,2470],{},[1810,49284,1812],{},[898,49286,5640],{},[902,49288,49289],{"encoding":904},"Q_2^E",[883,49291,49293],{"className":49292},[886],[888,49294,49295],{"xmlns":890},[892,49296,49297,49307],{},[895,49298,49299],{},[10554,49300,49301,49303,49305],{},[898,49302,5325],{},[1810,49304,1812],{},[898,49306,5640],{},[902,49308,49309],{"encoding":904},"P_2^E",[123,49311,49312],{},"(d) Proveďte analýzu dopadu daňového zatížení na spotřebitele a výrobce vyplývající z výsledků (b) a (c).",[724,49314,49315,49316,1656],{},"Viz též ",[207,49317,44112],{"className":49318,"dataFsResolvedFilePath":809,"href":810},[210],[198,49320,44414],{"id":49321},"multiplikátory-pro-mikroekonomické-proměnné-1",[724,49323,49324,49075,49327,49112,49363,1656],{},[38,49325,49326],{},"2.14",[883,49328,49330],{"className":49329},[886],[888,49331,49332],{"xmlns":890},[892,49333,49334,49360],{},[895,49335,49336,49338,49340,49342,49344,49346,49348,49350,49352,49354,49356,49358],{},[898,49337,5325],{},[1677,49339,1679],{},[898,49341,207],{},[898,49343,2470],{},[1677,49345,1776],{},[898,49347,1779],{},[1677,49349,1679],{},[1677,49351,1906],{},[1810,49353,1812],{},[898,49355,2470],{},[1677,49357,1776],{},[1810,49359,2801],{},[902,49361,49362],{"encoding":904},"P = aQ + b = -2Q + 50",[883,49364,49366],{"className":49365},[886],[888,49367,49368],{"xmlns":890},[892,49369,49370,49394],{},[895,49371,49372,49374,49376,49378,49380,49382,49384,49386,49388,49390,49392],{},[898,49373,5325],{},[1677,49375,1679],{},[898,49377,1823],{},[898,49379,2470],{},[1677,49381,1776],{},[898,49383,1875],{},[1677,49385,1679],{},[1810,49387,20712],{},[898,49389,2470],{},[1677,49391,1776],{},[1810,49393,10423],{},[902,49395,49396],{"encoding":904},"P = cQ + d = 0{,}6Q + 20",[120,49398,49399,49435,49438,49524,49577,49657,49711],{},[123,49400,49151,49401,48049,49418,1656],{},[883,49402,49404],{"className":49403},[886],[888,49405,49406],{"xmlns":890},[892,49407,49408,49416],{},[895,49409,49410],{},[1805,49411,49412,49414],{},[898,49413,2470],{},[898,49415,5640],{},[902,49417,43794],{"encoding":904},[883,49419,49421],{"className":49420},[886],[888,49422,49423],{"xmlns":890},[892,49424,49425,49433],{},[895,49426,49427],{},[1805,49428,49429,49431],{},[898,49430,5325],{},[898,49432,5640],{},[902,49434,42857],{"encoding":904},[123,49436,49437],{},"(b) Určete hodnoty multiplikátorů pro zadané parametry.",[123,49439,49440,49441,49458,49459,2352,49472,2366,49488,49504,49505,1656],{},"(c) Určete přibližnou změnu rovnovážného množství ",[883,49442,49444],{"className":49443},[886],[888,49445,49446],{"xmlns":890},[892,49447,49448,49456],{},[895,49449,49450],{},[1805,49451,49452,49454],{},[898,49453,2470],{},[898,49455,5640],{},[902,49457,43794],{"encoding":904}," odpovídající změně ",[883,49460,49462],{"className":49461},[886],[888,49463,49464],{"xmlns":890},[892,49465,49466,49470],{},[895,49467,49468],{},[898,49469,207],{},[902,49471,207],{"encoding":904},[883,49473,49475],{"className":49474},[886],[888,49476,49477],{"xmlns":890},[892,49478,49479,49485],{},[895,49480,49481,49483],{},[1677,49482,1906],{},[1810,49484,1812],{},[902,49486,49487],{"encoding":904},"-2",[883,49489,49491],{"className":49490},[886],[888,49492,49493],{"xmlns":890},[892,49494,49495,49501],{},[895,49496,49497,49499],{},[1677,49498,1906],{},[1810,49500,1854],{},[902,49502,49503],{"encoding":904},"-3"," (ceteris paribus) a stanovte nové rovnovážné množství ",[883,49506,49508],{"className":49507},[886],[888,49509,49510],{"xmlns":890},[892,49511,49512,49522],{},[895,49513,49514],{},[10554,49515,49516,49518,49520],{},[898,49517,2470],{},[1810,49519,1959],{},[898,49521,5640],{},[902,49523,49227],{"encoding":904},[123,49525,49526,49527,49458,49544,49557,49558,1656],{},"(d) Určete přibližnou změnu rovnovážného množství ",[883,49528,49530],{"className":49529},[886],[888,49531,49532],{"xmlns":890},[892,49533,49534,49542],{},[895,49535,49536],{},[1805,49537,49538,49540],{},[898,49539,2470],{},[898,49541,5640],{},[902,49543,43794],{"encoding":904},[883,49545,49547],{"className":49546},[886],[888,49548,49549],{"xmlns":890},[892,49550,49551,49555],{},[895,49552,49553],{},[898,49554,1779],{},[902,49556,1779],{"encoding":904}," z 50 na 60 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,49559,49561],{"className":49560},[886],[888,49562,49563],{"xmlns":890},[892,49564,49565,49575],{},[895,49566,49567],{},[10554,49568,49569,49571,49573],{},[898,49570,2470],{},[1810,49572,1812],{},[898,49574,5640],{},[902,49576,49289],{"encoding":904},[123,49578,49579,49580,49458,49597,2352,49610,2366,49623,49504,49637,1656],{},"(e) Určete přibližnou změnu rovnovážného množství ",[883,49581,49583],{"className":49582},[886],[888,49584,49585],{"xmlns":890},[892,49586,49587,49595],{},[895,49588,49589],{},[1805,49590,49591,49593],{},[898,49592,2470],{},[898,49594,5640],{},[902,49596,43794],{"encoding":904},[883,49598,49600],{"className":49599},[886],[888,49601,49602],{"xmlns":890},[892,49603,49604,49608],{},[895,49605,49606],{},[898,49607,1823],{},[902,49609,1823],{"encoding":904},[883,49611,49613],{"className":49612},[886],[888,49614,49615],{"xmlns":890},[892,49616,49617,49621],{},[895,49618,49619],{},[1810,49620,20712],{},[902,49622,45851],{"encoding":904},[883,49624,49626],{"className":49625},[886],[888,49627,49628],{"xmlns":890},[892,49629,49630,49634],{},[895,49631,49632],{},[1810,49633,15979],{},[902,49635,49636],{"encoding":904},"0{,}8",[883,49638,49640],{"className":49639},[886],[888,49641,49642],{"xmlns":890},[892,49643,49644,49654],{},[895,49645,49646],{},[10554,49647,49648,49650,49652],{},[898,49649,2470],{},[1810,49651,1854],{},[898,49653,5640],{},[902,49655,49656],{"encoding":904},"Q_3^E",[123,49658,49659,49660,49458,49677,49690,49691,1656],{},"(f) Určete přibližnou změnu rovnovážného množství ",[883,49661,49663],{"className":49662},[886],[888,49664,49665],{"xmlns":890},[892,49666,49667,49675],{},[895,49668,49669],{},[1805,49670,49671,49673],{},[898,49672,2470],{},[898,49674,5640],{},[902,49676,43794],{"encoding":904},[883,49678,49680],{"className":49679},[886],[888,49681,49682],{"xmlns":890},[892,49683,49684,49688],{},[895,49685,49686],{},[898,49687,1875],{},[902,49689,1875],{"encoding":904}," z 20 na 10 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,49692,49694],{"className":49693},[886],[888,49695,49696],{"xmlns":890},[892,49697,49698,49708],{},[895,49699,49700],{},[10554,49701,49702,49704,49706],{},[898,49703,2470],{},[1810,49705,2032],{},[898,49707,5640],{},[902,49709,49710],{"encoding":904},"Q_4^E",[123,49712,49713,49714,49731,49732,49745,49746,22811,49759,1343,49774,22811,49787,5272,49801,22811,49814,49829,49830,1656],{},"(g) Určete přibližnou změnu rovnovážného množství ",[883,49715,49717],{"className":49716},[886],[888,49718,49719],{"xmlns":890},[892,49720,49721,49729],{},[895,49722,49723],{},[1805,49724,49725,49727],{},[898,49726,2470],{},[898,49728,5640],{},[902,49730,43794],{"encoding":904}," odpovídající změnám ",[883,49733,49735],{"className":49734},[886],[888,49736,49737],{"xmlns":890},[892,49738,49739,49743],{},[895,49740,49741],{},[898,49742,207],{},[902,49744,207],{"encoding":904}," o 1, ",[883,49747,49749],{"className":49748},[886],[888,49750,49751],{"xmlns":890},[892,49752,49753,49757],{},[895,49754,49755],{},[898,49756,1779],{},[902,49758,1779],{"encoding":904},[883,49760,49762],{"className":49761},[886],[888,49763,49764],{"xmlns":890},[892,49765,49766,49772],{},[895,49767,49768,49770],{},[1677,49769,1906],{},[1810,49771,2544],{},[902,49773,20846],{"encoding":904},[883,49775,49777],{"className":49776},[886],[888,49778,49779],{"xmlns":890},[892,49780,49781,49785],{},[895,49782,49783],{},[898,49784,1823],{},[902,49786,1823],{"encoding":904},[883,49788,49790],{"className":49789},[886],[888,49791,49792],{"xmlns":890},[892,49793,49794,49798],{},[895,49795,49796],{},[1810,49797,2475],{},[902,49799,49800],{"encoding":904},"0{,}1",[883,49802,49804],{"className":49803},[886],[888,49805,49806],{"xmlns":890},[892,49807,49808,49812],{},[895,49809,49810],{},[898,49811,1875],{},[902,49813,1875],{"encoding":904},[883,49815,49817],{"className":49816},[886],[888,49818,49819],{"xmlns":890},[892,49820,49821,49827],{},[895,49822,49823,49825],{},[1677,49824,1906],{},[1810,49826,2544],{},[902,49828,20846],{"encoding":904}," vzhledem k zadaným hodnotám a stanovte nové rovnovážné množství ",[883,49831,49833],{"className":49832},[886],[888,49834,49835],{"xmlns":890},[892,49836,49837,49847],{},[895,49838,49839],{},[10554,49840,49841,49843,49845],{},[898,49842,2470],{},[1810,49844,1909],{},[898,49846,5640],{},[902,49848,49849],{"encoding":904},"Q_5^E",[724,49851,49852,49075,49855,49112,49878,1656],{},[38,49853,49854],{},"2.15",[883,49856,49858],{"className":49857},[886],[888,49859,49860],{"xmlns":890},[892,49861,49862,49876],{},[895,49863,49864,49866,49868,49870,49872,49874],{},[898,49865,5325],{},[1677,49867,1679],{},[898,49869,207],{},[898,49871,2470],{},[1677,49873,1776],{},[898,49875,1779],{},[902,49877,38451],{"encoding":904},[883,49879,49881],{"className":49880},[886],[888,49882,49883],{"xmlns":890},[892,49884,49885,49899],{},[895,49886,49887,49889,49891,49893,49895,49897],{},[898,49888,5325],{},[1677,49890,1679],{},[898,49892,1823],{},[898,49894,2470],{},[1677,49896,1776],{},[898,49898,1875],{},[902,49900,41633],{"encoding":904},[120,49902,49903,49978,49995,50104,50157,50211],{},[123,49904,49905,49906,49919,49920,49945,49946,49977],{},"(a) Odvoďte redukovaný tvar pro ",[883,49907,49909],{"className":49908},[886],[888,49910,49911],{"xmlns":890},[892,49912,49913,49917],{},[895,49914,49915],{},[898,49916,5325],{},[902,49918,5325],{"encoding":904},". Stanovte podmínky pro ",[883,49921,49923],{"className":49922},[886],[888,49924,49925],{"xmlns":890},[892,49926,49927,49943],{},[895,49928,49929,49931,49933,49935,49937,49939,49941],{},[898,49930,207],{},[1677,49932,1967],{"separator":1966},[898,49934,1779],{},[1677,49936,1967],{"separator":1966},[898,49938,1823],{},[1677,49940,1967],{"separator":1966},[898,49942,1875],{},[902,49944,44676],{"encoding":904}," tak, aby rovnovážný bod ",[883,49947,49949],{"className":49948},[886],[888,49950,49951],{"xmlns":890},[892,49952,49953,49975],{},[895,49954,49955,49957,49959,49965,49967,49973],{},[898,49956,5640],{},[1677,49958,2167],{"stretchy":1685},[1805,49960,49961,49963],{},[898,49962,2470],{},[898,49964,5640],{},[1677,49966,1967],{"separator":1966},[1805,49968,49969,49971],{},[898,49970,5325],{},[898,49972,5640],{},[1677,49974,2182],{"stretchy":1685},[902,49976,42758],{"encoding":904}," patřil do 1. kvadrantu (využijte obrázku 2.22).",[123,49979,49980,49981,49994],{},"(b) Vypočtěte multiplikátory pro ",[883,49982,49984],{"className":49983},[886],[888,49985,49986],{"xmlns":890},[892,49987,49988,49992],{},[895,49989,49990],{},[898,49991,5325],{},[902,49993,5325],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků 2.22, 2.23).",[123,49996,49997,49998,1343,50018,1343,50036,1343,50054,50072,50073,50090,50091,1656],{},"(c) Pro hodnoty parametrů ",[883,49999,50001],{"className":50000},[886],[888,50002,50003],{"xmlns":890},[892,50004,50005,50015],{},[895,50006,50007,50009,50011,50013],{},[898,50008,207],{},[1677,50010,1679],{},[1677,50012,1906],{},[1810,50014,1812],{},[902,50016,50017],{"encoding":904},"a = -2",[883,50019,50021],{"className":50020},[886],[888,50022,50023],{"xmlns":890},[892,50024,50025,50033],{},[895,50026,50027,50029,50031],{},[898,50028,1779],{},[1677,50030,1679],{},[1810,50032,6599],{},[902,50034,50035],{"encoding":904},"b = 40",[883,50037,50039],{"className":50038},[886],[888,50040,50041],{"xmlns":890},[892,50042,50043,50051],{},[895,50044,50045,50047,50049],{},[898,50046,1823],{},[1677,50048,1679],{},[1810,50050,6397],{},[902,50052,50053],{"encoding":904},"c = 0{,}5",[883,50055,50057],{"className":50056},[886],[888,50058,50059],{"xmlns":890},[892,50060,50061,50069],{},[895,50062,50063,50065,50067],{},[898,50064,1875],{},[1677,50066,1679],{},[1810,50068,2544],{},[902,50070,50071],{"encoding":904},"d = 10"," určete rovnovážnou cenu ",[883,50074,50076],{"className":50075},[886],[888,50077,50078],{"xmlns":890},[892,50079,50080,50088],{},[895,50081,50082],{},[1805,50083,50084,50086],{},[898,50085,5325],{},[898,50087,5640],{},[902,50089,42857],{"encoding":904}," a hodnoty multiplikátorů pro ",[883,50092,50094],{"className":50093},[886],[888,50095,50096],{"xmlns":890},[892,50097,50098,50102],{},[895,50099,50100],{},[898,50101,5325],{},[902,50103,5325],{"encoding":904},[123,50105,50106,50107,49458,50124,50137,50138,1656],{},"(d) Určete přibližnou změnu rovnovážné ceny ",[883,50108,50110],{"className":50109},[886],[888,50111,50112],{"xmlns":890},[892,50113,50114,50122],{},[895,50115,50116],{},[1805,50117,50118,50120],{},[898,50119,5325],{},[898,50121,5640],{},[902,50123,42857],{"encoding":904},[883,50125,50127],{"className":50126},[886],[888,50128,50129],{"xmlns":890},[892,50130,50131,50135],{},[895,50132,50133],{},[898,50134,207],{},[902,50136,207],{"encoding":904}," o 5 (ceteris paribus) a stanovte novou rovnovážnou cenu ",[883,50139,50141],{"className":50140},[886],[888,50142,50143],{"xmlns":890},[892,50144,50145,50155],{},[895,50146,50147],{},[10554,50148,50149,50151,50153],{},[898,50150,5325],{},[1810,50152,1959],{},[898,50154,5640],{},[902,50156,49248],{"encoding":904},[123,50158,50159,50160,50177,50178,50191,50192,1656],{},"(e) Určete přibližnou změnu rovnovážné ceny ",[883,50161,50163],{"className":50162},[886],[888,50164,50165],{"xmlns":890},[892,50166,50167,50175],{},[895,50168,50169],{},[1805,50170,50171,50173],{},[898,50172,5325],{},[898,50174,5640],{},[902,50176,42857],{"encoding":904}," odpovídající poklesu ",[883,50179,50181],{"className":50180},[886],[888,50182,50183],{"xmlns":890},[892,50184,50185,50189],{},[895,50186,50187],{},[898,50188,207],{},[902,50190,207],{"encoding":904}," o 1 a stanovte novou rovnovážnou cenu ",[883,50193,50195],{"className":50194},[886],[888,50196,50197],{"xmlns":890},[892,50198,50199,50209],{},[895,50200,50201],{},[10554,50202,50203,50205,50207],{},[898,50204,5325],{},[1810,50206,1812],{},[898,50208,5640],{},[902,50210,49309],{"encoding":904},[123,50212,50213,50214,49731,50231,50244,50245,2366,50258,5272,50273,50286,50287,1656],{},"(f) Určete přibližnou změnu rovnovážné ceny ",[883,50215,50217],{"className":50216},[886],[888,50218,50219],{"xmlns":890},[892,50220,50221,50229],{},[895,50222,50223],{},[1805,50224,50225,50227],{},[898,50226,5325],{},[898,50228,5640],{},[902,50230,42857],{"encoding":904},[883,50232,50234],{"className":50233},[886],[888,50235,50236],{"xmlns":890},[892,50237,50238,50242],{},[895,50239,50240],{},[898,50241,207],{},[902,50243,207],{"encoding":904}," na 35, ",[883,50246,50248],{"className":50247},[886],[888,50249,50250],{"xmlns":890},[892,50251,50252,50256],{},[895,50253,50254],{},[898,50255,1823],{},[902,50257,1823],{"encoding":904},[883,50259,50261],{"className":50260},[886],[888,50262,50263],{"xmlns":890},[892,50264,50265,50270],{},[895,50266,50267],{},[1810,50268,50269],{},"0,7",[902,50271,50272],{"encoding":904},"0{,}7",[883,50274,50276],{"className":50275},[886],[888,50277,50278],{"xmlns":890},[892,50279,50280,50284],{},[895,50281,50282],{},[898,50283,1875],{},[902,50285,1875],{"encoding":904}," na 12 vzhledem k hodnotám dle (d) a stanovte novou rovnovážnou cenu ",[883,50288,50290],{"className":50289},[886],[888,50291,50292],{"xmlns":890},[892,50293,50294,50304],{},[895,50295,50296],{},[10554,50297,50298,50300,50302],{},[898,50299,5325],{},[1810,50301,1854],{},[898,50303,5640],{},[902,50305,50306],{"encoding":904},"P_3^E",[724,50308,50309,49075,50312,49112,50340,22985,50368,5272,50394,1656],{},[38,50310,50311],{},"2.16",[883,50313,50315],{"className":50314},[886],[888,50316,50317],{"xmlns":890},[892,50318,50319,50337],{},[895,50320,50321,50323,50325,50327,50329,50331],{},[898,50322,5325],{},[1677,50324,1679],{},[898,50326,207],{},[1677,50328,1776],{},[898,50330,1779],{},[1805,50332,50333,50335],{},[898,50334,2470],{},[1810,50336,1812],{},[902,50338,50339],{"encoding":904},"P = a + bQ^2",[883,50341,50343],{"className":50342},[886],[888,50344,50345],{"xmlns":890},[892,50346,50347,50365],{},[895,50348,50349,50351,50353,50355,50357,50359],{},[898,50350,5325],{},[1677,50352,1679],{},[898,50354,1823],{},[1677,50356,1776],{},[898,50358,1875],{},[1805,50360,50361,50363],{},[898,50362,2470],{},[1810,50364,1812],{},[902,50366,50367],{"encoding":904},"P = c + dQ^2",[883,50369,50371],{"className":50370},[886],[888,50372,50373],{"xmlns":890},[892,50374,50375,50391],{},[895,50376,50377,50379,50381,50383,50385,50387,50389],{},[898,50378,207],{},[1677,50380,1967],{"separator":1966},[898,50382,1823],{},[1677,50384,1967],{"separator":1966},[898,50386,1875],{},[1677,50388,3089],{},[1810,50390,2008],{},[902,50392,50393],{"encoding":904},"a, c, d > 0",[883,50395,50397],{"className":50396},[886],[888,50398,50399],{"xmlns":890},[892,50400,50401,50409],{},[895,50402,50403,50405,50407],{},[898,50404,1779],{},[1677,50406,3128],{},[1810,50408,2008],{},[902,50410,50411],{"encoding":904},"b \u003C 0",[120,50413,50414,50462,50478,50585,50637,50689,50798,50814,50913,50966],{},[123,50415,49905,50416,50429,50430,50461],{},[883,50417,50419],{"className":50418},[886],[888,50420,50421],{"xmlns":890},[892,50422,50423,50427],{},[895,50424,50425],{},[898,50426,2470],{},[902,50428,2470],{"encoding":904},". Načrtněte křivky poptávky a nabídky a stanovte podmínky, aby rovnovážný bod ",[883,50431,50433],{"className":50432},[886],[888,50434,50435],{"xmlns":890},[892,50436,50437,50459],{},[895,50438,50439,50441,50443,50449,50451,50457],{},[898,50440,5640],{},[1677,50442,2167],{"stretchy":1685},[1805,50444,50445,50447],{},[898,50446,2470],{},[898,50448,5640],{},[1677,50450,1967],{"separator":1966},[1805,50452,50453,50455],{},[898,50454,5325],{},[898,50456,5640],{},[1677,50458,2182],{"stretchy":1685},[902,50460,42758],{"encoding":904}," patřil do 1. kvadrantu.",[123,50463,49980,50464,50477],{},[883,50465,50467],{"className":50466},[886],[888,50468,50469],{"xmlns":890},[892,50470,50471,50475],{},[895,50472,50473],{},[898,50474,2470],{},[902,50476,2470],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků v (b)).",[123,50479,49997,50480,1343,50498,1343,50518,1343,50536,50554,50555,50090,50572,1656],{},[883,50481,50483],{"className":50482},[886],[888,50484,50485],{"xmlns":890},[892,50486,50487,50495],{},[895,50488,50489,50491,50493],{},[898,50490,207],{},[1677,50492,1679],{},[1810,50494,2771],{},[902,50496,50497],{"encoding":904},"a = 100",[883,50499,50501],{"className":50500},[886],[888,50502,50503],{"xmlns":890},[892,50504,50505,50515],{},[895,50506,50507,50509,50511,50513],{},[898,50508,1779],{},[1677,50510,1679],{},[1677,50512,1906],{},[1810,50514,1959],{},[902,50516,50517],{"encoding":904},"b = -1",[883,50519,50521],{"className":50520},[886],[888,50522,50523],{"xmlns":890},[892,50524,50525,50533],{},[895,50526,50527,50529,50531],{},[898,50528,1823],{},[1677,50530,1679],{},[1810,50532,10423],{},[902,50534,50535],{"encoding":904},"c = 20",[883,50537,50539],{"className":50538},[886],[888,50540,50541],{"xmlns":890},[892,50542,50543,50551],{},[895,50544,50545,50547,50549],{},[898,50546,1875],{},[1677,50548,1679],{},[1810,50550,1959],{},[902,50552,50553],{"encoding":904},"d = 1"," určete rovnovážné množství ",[883,50556,50558],{"className":50557},[886],[888,50559,50560],{"xmlns":890},[892,50561,50562,50570],{},[895,50563,50564],{},[1805,50565,50566,50568],{},[898,50567,2470],{},[898,50569,5640],{},[902,50571,43794],{"encoding":904},[883,50573,50575],{"className":50574},[886],[888,50576,50577],{"xmlns":890},[892,50578,50579,50583],{},[895,50580,50581],{},[898,50582,2470],{},[902,50584,2470],{"encoding":904},[123,50586,49526,50587,49458,50604,50617,50618,1656],{},[883,50588,50590],{"className":50589},[886],[888,50591,50592],{"xmlns":890},[892,50593,50594,50602],{},[895,50595,50596],{},[1805,50597,50598,50600],{},[898,50599,2470],{},[898,50601,5640],{},[902,50603,43794],{"encoding":904},[883,50605,50607],{"className":50606},[886],[888,50608,50609],{"xmlns":890},[892,50610,50611,50615],{},[895,50612,50613],{},[898,50614,207],{},[902,50616,207],{"encoding":904}," na 110 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,50619,50621],{"className":50620},[886],[888,50622,50623],{"xmlns":890},[892,50624,50625,50635],{},[895,50626,50627],{},[10554,50628,50629,50631,50633],{},[898,50630,2470],{},[1810,50632,1959],{},[898,50634,5640],{},[902,50636,49227],{"encoding":904},[123,50638,49579,50639,49458,50656,50669,50670,1656],{},[883,50640,50642],{"className":50641},[886],[888,50643,50644],{"xmlns":890},[892,50645,50646,50654],{},[895,50647,50648],{},[1805,50649,50650,50652],{},[898,50651,2470],{},[898,50653,5640],{},[902,50655,43794],{"encoding":904},[883,50657,50659],{"className":50658},[886],[888,50660,50661],{"xmlns":890},[892,50662,50663,50667],{},[895,50664,50665],{},[898,50666,1823],{},[902,50668,1823],{"encoding":904}," na 25 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,50671,50673],{"className":50672},[886],[888,50674,50675],{"xmlns":890},[892,50676,50677,50687],{},[895,50678,50679],{},[10554,50680,50681,50683,50685],{},[898,50682,2470],{},[1810,50684,1812],{},[898,50686,5640],{},[902,50688,49289],{"encoding":904},[123,50690,49659,50691,49731,50708,50721,50722,2366,50735,50750,50751,50764,50765,50778,50779,1656],{},[883,50692,50694],{"className":50693},[886],[888,50695,50696],{"xmlns":890},[892,50697,50698,50706],{},[895,50699,50700],{},[1805,50701,50702,50704],{},[898,50703,2470],{},[898,50705,5640],{},[902,50707,43794],{"encoding":904},[883,50709,50711],{"className":50710},[886],[888,50712,50713],{"xmlns":890},[892,50714,50715,50719],{},[895,50716,50717],{},[898,50718,207],{},[902,50720,207],{"encoding":904}," na 110, poklesu ",[883,50723,50725],{"className":50724},[886],[888,50726,50727],{"xmlns":890},[892,50728,50729,50733],{},[895,50730,50731],{},[898,50732,1779],{},[902,50734,1779],{"encoding":904},[883,50736,50738],{"className":50737},[886],[888,50739,50740],{"xmlns":890},[892,50741,50742,50748],{},[895,50743,50744,50746],{},[1677,50745,1906],{},[1810,50747,1812],{},[902,50749,49487],{"encoding":904},", růstu ",[883,50752,50754],{"className":50753},[886],[888,50755,50756],{"xmlns":890},[892,50757,50758,50762],{},[895,50759,50760],{},[898,50761,1823],{},[902,50763,1823],{"encoding":904}," na 25 a růstu ",[883,50766,50768],{"className":50767},[886],[888,50769,50770],{"xmlns":890},[892,50771,50772,50776],{},[895,50773,50774],{},[898,50775,1875],{},[902,50777,1875],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte nové rovnovážné množství ",[883,50780,50782],{"className":50781},[886],[888,50783,50784],{"xmlns":890},[892,50785,50786,50796],{},[895,50787,50788],{},[10554,50789,50790,50792,50794],{},[898,50791,2470],{},[1810,50793,1854],{},[898,50795,5640],{},[902,50797,49656],{"encoding":904},[123,50799,50800,50801,50477],{},"(i) Vypočtěte multiplikátory pro ",[883,50802,50804],{"className":50803},[886],[888,50805,50806],{"xmlns":890},[892,50807,50808,50812],{},[895,50809,50810],{},[898,50811,5325],{},[902,50813,5325],{"encoding":904},[123,50815,50816,50817,50090,50834,50847,50848,49458,50865,2366,50878,50893,50894,1656],{},"(j) Pro hodnoty parametrů dle (b) určete rovnovážnou cenu ",[883,50818,50820],{"className":50819},[886],[888,50821,50822],{"xmlns":890},[892,50823,50824,50832],{},[895,50825,50826],{},[1805,50827,50828,50830],{},[898,50829,5325],{},[898,50831,5640],{},[902,50833,42857],{"encoding":904},[883,50835,50837],{"className":50836},[886],[888,50838,50839],{"xmlns":890},[892,50840,50841,50845],{},[895,50842,50843],{},[898,50844,5325],{},[902,50846,5325],{"encoding":904},", přibližnou změnu rovnovážné ceny ",[883,50849,50851],{"className":50850},[886],[888,50852,50853],{"xmlns":890},[892,50854,50855,50863],{},[895,50856,50857],{},[1805,50858,50859,50861],{},[898,50860,5325],{},[898,50862,5640],{},[902,50864,42857],{"encoding":904},[883,50866,50868],{"className":50867},[886],[888,50869,50870],{"xmlns":890},[892,50871,50872,50876],{},[895,50873,50874],{},[898,50875,207],{},[902,50877,207],{"encoding":904},[883,50879,50881],{"className":50880},[886],[888,50882,50883],{"xmlns":890},[892,50884,50885,50891],{},[895,50886,50887,50889],{},[1677,50888,1906],{},[1810,50890,1854],{},[902,50892,49503],{"encoding":904}," (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,50895,50897],{"className":50896},[886],[888,50898,50899],{"xmlns":890},[892,50900,50901,50911],{},[895,50902,50903],{},[10554,50904,50905,50907,50909],{},[898,50906,5325],{},[1810,50908,1959],{},[898,50910,5640],{},[902,50912,49248],{"encoding":904},[123,50914,50915,50916,49458,50933,50946,50947,1656],{},"(k) Určete přibližnou změnu rovnovážné ceny ",[883,50917,50919],{"className":50918},[886],[888,50920,50921],{"xmlns":890},[892,50922,50923,50931],{},[895,50924,50925],{},[1805,50926,50927,50929],{},[898,50928,5325],{},[898,50930,5640],{},[902,50932,42857],{"encoding":904},[883,50934,50936],{"className":50935},[886],[888,50937,50938],{"xmlns":890},[892,50939,50940,50944],{},[895,50941,50942],{},[898,50943,207],{},[902,50945,207],{"encoding":904}," na 2 (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,50948,50950],{"className":50949},[886],[888,50951,50952],{"xmlns":890},[892,50953,50954,50964],{},[895,50955,50956],{},[10554,50957,50958,50960,50962],{},[898,50959,5325],{},[1810,50961,1812],{},[898,50963,5640],{},[902,50965,49309],{"encoding":904},[123,50967,50968,50969,50177,50986,50999,51000,2366,51013,50750,51028,51041,51042,51055,51056,1656],{},"(l) Určete přibližnou změnu rovnovážné ceny ",[883,50970,50972],{"className":50971},[886],[888,50973,50974],{"xmlns":890},[892,50975,50976,50984],{},[895,50977,50978],{},[1805,50979,50980,50982],{},[898,50981,5325],{},[898,50983,5640],{},[902,50985,42857],{"encoding":904},[883,50987,50989],{"className":50988},[886],[888,50990,50991],{"xmlns":890},[892,50992,50993,50997],{},[895,50994,50995],{},[898,50996,207],{},[902,50998,207],{"encoding":904}," na 90, poklesu ",[883,51001,51003],{"className":51002},[886],[888,51004,51005],{"xmlns":890},[892,51006,51007,51011],{},[895,51008,51009],{},[898,51010,1779],{},[902,51012,1779],{"encoding":904},[883,51014,51016],{"className":51015},[886],[888,51017,51018],{"xmlns":890},[892,51019,51020,51026],{},[895,51021,51022,51024],{},[1677,51023,1906],{},[1810,51025,1854],{},[902,51027,49503],{"encoding":904},[883,51029,51031],{"className":51030},[886],[888,51032,51033],{"xmlns":890},[892,51034,51035,51039],{},[895,51036,51037],{},[898,51038,1823],{},[902,51040,1823],{"encoding":904}," na 30 a růstu ",[883,51043,51045],{"className":51044},[886],[888,51046,51047],{"xmlns":890},[892,51048,51049,51053],{},[895,51050,51051],{},[898,51052,1875],{},[902,51054,1875],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,51057,51059],{"className":51058},[886],[888,51060,51061],{"xmlns":890},[892,51062,51063,51073],{},[895,51064,51065],{},[10554,51066,51067,51069,51071],{},[898,51068,5325],{},[1810,51070,1854],{},[898,51072,5640],{},[902,51074,50306],{"encoding":904},[198,51076,820],{"id":51077},"přebytek-spotřebitele-a-výrobce-1",[724,51079,51080,49075,51083,49112,51119,1656],{},[38,51081,51082],{},"2.17",[883,51084,51086],{"className":51085},[886],[888,51087,51088],{"xmlns":890},[892,51089,51090,51116],{},[895,51091,51092,51094,51096,51098,51100,51102,51104,51106,51108,51110],{},[898,51093,5325],{},[1677,51095,1679],{},[898,51097,5571],{},[1677,51099,1686],{"stretchy":1685},[898,51101,2470],{},[1677,51103,1692],{"stretchy":1685},[1677,51105,1679],{},[1810,51107,16428],{},[1677,51109,1906],{},[1805,51111,51112,51114],{},[898,51113,2470],{},[1810,51115,1812],{},[902,51117,51118],{"encoding":904},"P = D(Q) = 35 - Q^2",[883,51120,51122],{"className":51121},[886],[888,51123,51124],{"xmlns":890},[892,51125,51126,51152],{},[895,51127,51128,51130,51132,51134,51136,51138,51140,51142,51144,51146],{},[898,51129,5325],{},[1677,51131,1679],{},[898,51133,10061],{},[1677,51135,1686],{"stretchy":1685},[898,51137,2470],{},[1677,51139,1692],{"stretchy":1685},[1677,51141,1679],{},[1810,51143,1854],{},[1677,51145,1776],{},[1805,51147,51148,51150],{},[898,51149,2470],{},[1810,51151,1812],{},[902,51153,51154],{"encoding":904},"P = S(Q) = 3 + Q^2",[120,51156,51157,51160],{},[123,51158,51159],{},"(a) Vypočtěte přebytek spotřebitele při množství 4.",[123,51161,51162],{},"(b) Vypočtěte přebytek výrobce při množství 4.",[724,51164,51165,49075,51168,49112,51202,1656],{},[38,51166,51167],{},"2.18",[883,51169,51171],{"className":51170},[886],[888,51172,51173],{"xmlns":890},[892,51174,51175,51199],{},[895,51176,51177,51179,51181,51183,51185,51187,51189,51191,51193,51195,51197],{},[898,51178,5325],{},[1677,51180,1679],{},[898,51182,5571],{},[1677,51184,1686],{"stretchy":1685},[898,51186,2470],{},[1677,51188,1692],{"stretchy":1685},[1677,51190,1679],{},[1810,51192,3388],{},[1677,51194,1906],{},[1810,51196,1812],{},[898,51198,2470],{},[902,51200,51201],{"encoding":904},"P = D(Q) = 18 - 2Q",[883,51203,51205],{"className":51204},[886],[888,51206,51207],{"xmlns":890},[892,51208,51209,51235],{},[895,51210,51211,51213,51215,51217,51219,51221,51223,51225,51227,51229],{},[898,51212,5325],{},[1677,51214,1679],{},[898,51216,10061],{},[1677,51218,1686],{"stretchy":1685},[898,51220,2470],{},[1677,51222,1692],{"stretchy":1685},[1677,51224,1679],{},[1810,51226,1854],{},[1677,51228,1776],{},[1805,51230,51231,51233],{},[898,51232,2470],{},[1810,51234,1812],{},[902,51236,51154],{"encoding":904},[120,51238,51239,51259,51262,51265],{},[123,51240,51241,51242,1656],{},"(a) Vypočtěte rovnovážné množství ",[883,51243,51245],{"className":51244},[886],[888,51246,51247],{"xmlns":890},[892,51248,51249,51257],{},[895,51250,51251],{},[1805,51252,51253,51255],{},[898,51254,2470],{},[898,51256,5640],{},[902,51258,43794],{"encoding":904},[123,51260,51261],{},"(b) Vypočtěte přebytek spotřebitele při rovnovážném množství.",[123,51263,51264],{},"(b) Vypočtěte přebytek výrobce při rovnovážném množství.",[123,51266,51267],{},"(c) Graficky interpretujte.",[38361,51269],{},[115,51271,51273],{"id":51272},"otázky-k-sebehodnocení","Otázky k sebehodnocení",[152,51275,51276,51279,51282,51285,51288,51291,51294,51297,51300,51303,51306,51309,51312,51315],{},[123,51277,51278],{},"Jaký je rozdíl mezi jednofaktorovým a vícefaktorovým modelem poptávky?",[123,51280,51281],{},"Vyjádřete (vícefaktorovou) funkci poptávky. Jakou má vlastnost?",[123,51283,51284],{},"Definujte funkci poptávky (jednofaktorovou). Jaká je její základní vlastnost? Zdůvodněte.",[123,51286,51287],{},"Definujte Engelovu funkci. Na čem závisí tvar příslušné Engelovy křivky?",[123,51289,51290],{},"Jaký charakter má odezva poptávky na změnu některé z exogenních proměnných?",[123,51292,51293],{},"Definujte funkci nabídky. Jaká je její základní vlastnost? Zdůvodněte.",[123,51295,51296],{},"Co znamená tržní rovnováha? Čím je reprezentována?",[123,51298,51299],{},"Jak se určí rovnovážné množství a rovnovážná cena?",[123,51301,51302],{},"Jaká jsou pravidla pro změnu rovnovážného bodu jako odezvy na posun poptávky, resp. nabídky?",[123,51304,51305],{},"K čemu slouží multiplikátory?",[123,51307,51308],{},"Jak se najde redukovaný tvar pro vybranou rovnovážnou veličinu?",[123,51310,51311],{},"Jak se vypočtou multiplikátory? Mění se jejich znaménka?",[123,51313,51314],{},"Co se rozumí přebytkem spotřebitele? Jak se vypočte?",[123,51316,51317],{},"Co se rozumí přebytkem výrobce? Jak se vypočte?",[38361,51319],{},[115,51321,17110],{"id":17109},[724,51323,51324],{},[38,51325,14551],{},[120,51327,51328,51363,51368,51398,51403,51466,51492,51497,51527,51536,51543,51549],{},[123,51329,51330,11413,51333,20039,51336,1884,51338,1343,51361],{},[38,51331,51332],{},"Poptávané množství",[614,51334,51335],{},"quantity demanded",[38,51337,29393],{},[883,51339,51341],{"className":51340},[886],[888,51342,51343],{"xmlns":890},[892,51344,51345,51359],{},[895,51346,51347,51349,51351,51353,51355,51357],{},[898,51348,2470],{},[1677,51350,1679],{},[898,51352,5571],{},[1677,51354,1686],{"stretchy":1685},[898,51356,5325],{},[1677,51358,1692],{"stretchy":1685},[902,51360,5580],{"encoding":904},[38,51362,38840],{},[123,51364,51365,51367],{},[38,51366,38847],{}," — substituční + důchodový efekt",[123,51369,51370,1884,51373],{},[38,51371,51372],{},"Reálné cenové rozpětí",[883,51374,51376],{"className":51375},[886],[888,51377,51378],{"xmlns":890},[892,51379,51380,51396],{},[895,51381,51382,51384,51386,51388,51394],{},[1677,51383,1686],{"stretchy":1685},[1810,51385,2008],{},[1677,51387,1967],{"separator":1966},[1953,51389,51390,51392],{},[898,51391,5325],{},[1810,51393,2008],{},[1677,51395,1692],{"stretchy":1685},[902,51397,39048],{"encoding":904},[123,51399,51400,12485],{},[38,51401,51402],{},"Homogenita poptávky",[123,51404,51405,1884,51408,1343,51431,1343,51448,51465],{},[38,51406,51407],{},"Lineární poptávka",[883,51409,51411],{"className":51410},[886],[888,51412,51413],{"xmlns":890},[892,51414,51415,51429],{},[895,51416,51417,51419,51421,51423,51425,51427],{},[898,51418,5325],{},[1677,51420,1679],{},[898,51422,207],{},[898,51424,2470],{},[1677,51426,1776],{},[898,51428,1779],{},[902,51430,38451],{"encoding":904},[883,51432,51434],{"className":51433},[886],[888,51435,51436],{"xmlns":890},[892,51437,51438,51446],{},[895,51439,51440,51442,51444],{},[898,51441,207],{},[1677,51443,3128],{},[1810,51445,2008],{},[902,51447,44476],{"encoding":904},[883,51449,51451],{"className":51450},[886],[888,51452,51453],{"xmlns":890},[892,51454,51455,51463],{},[895,51456,51457,51459,51461],{},[898,51458,1779],{},[1677,51460,3089],{},[1810,51462,2008],{},[902,51464,20205],{"encoding":904}," — nedokonalá konkurence",[123,51467,51468,8403,51471],{},[38,51469,51470],{},"Dokonalá konkurence",[883,51472,51474],{"className":51473},[886],[888,51475,51476],{"xmlns":890},[892,51477,51478,51490],{},[895,51479,51480,51482,51484],{},[898,51481,5325],{},[1677,51483,1679],{},[1805,51485,51486,51488],{},[898,51487,5325],{},[1677,51489,5742],{},[902,51491,5745],{"encoding":904},[123,51493,51494,51496],{},[38,51495,39617],{}," — rostoucí křivka poptávky (důchodový efekt > substituční)",[123,51498,51499,1884,51501,1343,51525],{},[38,51500,33118],{},[883,51502,51504],{"className":51503},[886],[888,51505,51506],{"xmlns":890},[892,51507,51508,51522],{},[895,51509,51510,51512,51514,51516,51518,51520],{},[898,51511,2470],{},[1677,51513,1679],{},[898,51515,5640],{},[1677,51517,1686],{"stretchy":1685},[898,51519,10516],{},[1677,51521,1692],{"stretchy":1685},[902,51523,51524],{"encoding":904},"Q = E(Y)",[38,51526,39814],{},[123,51528,51529,51532,51533,51535],{},[38,51530,51531],{},"Normální"," (nezbytné \u002F luxusní) vs. ",[38,51534,40260],{}," zboží",[123,51537,51538,5272,51540,51542],{},[38,51539,41266],{},[38,51541,41213],{}," — znaménka zkřížených koeficientů",[123,51544,51545,51548],{},[38,51546,51547],{},"Dvoukomoditní trh"," (2.6)",[123,51550,51551,11413,51554,1692],{},[38,51552,51553],{},"Posun poptávky",[614,51555,40318],{},[724,51557,51558],{},[38,51559,14515],{},[120,51561,51562,51595,51599,51644],{},[123,51563,51564,11413,51566,20039,51568,1884,51570,1343,51593],{},[38,51565,41660],{},[614,51567,41663],{},[38,51569,41834],{},[883,51571,51573],{"className":51572},[886],[888,51574,51575],{"xmlns":890},[892,51576,51577,51591],{},[895,51578,51579,51581,51583,51585,51587,51589],{},[898,51580,2470],{},[1677,51582,1679],{},[898,51584,10061],{},[1677,51586,1686],{"stretchy":1685},[898,51588,5325],{},[1677,51590,1692],{"stretchy":1685},[902,51592,10070],{"encoding":904},[38,51594,41912],{},[123,51596,51597],{},[38,51598,41919],{},[123,51600,51601,1884,51604,1343,51627],{},[38,51602,51603],{},"Lineární nabídka",[883,51605,51607],{"className":51606},[886],[888,51608,51609],{"xmlns":890},[892,51610,51611,51625],{},[895,51612,51613,51615,51617,51619,51621,51623],{},[898,51614,5325],{},[1677,51616,1679],{},[898,51618,1823],{},[898,51620,2470],{},[1677,51622,1776],{},[898,51624,1875],{},[902,51626,41633],{"encoding":904},[883,51628,51630],{"className":51629},[886],[888,51631,51632],{"xmlns":890},[892,51633,51634,51642],{},[895,51635,51636,51638,51640],{},[898,51637,1823],{},[1677,51639,3089],{},[1810,51641,2008],{},[902,51643,41651],{"encoding":904},[123,51645,51646,11413,51649,1692],{},[38,51647,51648],{},"Posun nabídky",[614,51650,42297],{},[724,51652,51653],{},[38,51654,51655],{},"Rovnováha a komparativní statika",[120,51657,51658,51737,51743],{},[123,51659,51660,11413,51662,20039,51664,1884,51667,1343,51684,1884,51687,1343,51704,1884,51706],{},[38,51661,42716],{},[614,51663,42835],{},[38,51665,51666],{},"rovnovážná cena",[883,51668,51670],{"className":51669},[886],[888,51671,51672],{"xmlns":890},[892,51673,51674,51682],{},[895,51675,51676],{},[1805,51677,51678,51680],{},[898,51679,5325],{},[898,51681,5640],{},[902,51683,42857],{"encoding":904},[38,51685,51686],{},"rovnovážné množství",[883,51688,51690],{"className":51689},[886],[888,51691,51692],{"xmlns":890},[892,51693,51694,51702],{},[895,51695,51696],{},[1805,51697,51698,51700],{},[898,51699,2470],{},[898,51701,5640],{},[902,51703,43794],{"encoding":904},[38,51705,42893],{},[883,51707,51709],{"className":51708},[886],[888,51710,51711],{"xmlns":890},[892,51712,51713,51735],{},[895,51714,51715,51717,51719,51725,51727,51733],{},[898,51716,5640],{},[1677,51718,2167],{"stretchy":1685},[1805,51720,51721,51723],{},[898,51722,2470],{},[898,51724,5640],{},[1677,51726,1967],{"separator":1966},[1805,51728,51729,51731],{},[898,51730,5325],{},[898,51732,5640],{},[1677,51734,2182],{"stretchy":1685},[902,51736,42758],{"encoding":904},[123,51738,51739,51742],{},[38,51740,51741],{},"Pravidla 1–4"," komparativní statiky",[123,51744,51745,11413,51748,1692],{},[38,51746,51747],{},"Teorém pavučiny",[614,51749,43740],{},[724,51751,51752],{},[38,51753,51754],{},"Zdanění",[120,51756,51757,51813,51861],{},[123,51758,51759,51761,51762,51787,51788,1692],{},[38,51760,51754],{}," — daň výrobci (",[883,51763,51765],{"className":51764},[886],[888,51766,51767],{"xmlns":890},[892,51768,51769,51785],{},[895,51770,51771,51777,51779,51781,51783],{},[1953,51772,51773,51775],{},[898,51774,10061],{},[1810,51776,1959],{},[1677,51778,1679],{},[898,51780,10061],{},[1677,51782,1776],{},[898,51784,2455],{},[902,51786,44145],{"encoding":904},") vs. daň spotřebiteli (",[883,51789,51791],{"className":51790},[886],[888,51792,51793],{"xmlns":890},[892,51794,51795,51811],{},[895,51796,51797,51803,51805,51807,51809],{},[1953,51798,51799,51801],{},[898,51800,5571],{},[1810,51802,1812],{},[1677,51804,1679],{},[898,51806,5571],{},[1677,51808,1906],{},[898,51810,2455],{},[902,51812,44176],{"encoding":904},[123,51814,51815,1884,51817,1343,51838],{},[38,51816,44049],{},[883,51818,51820],{"className":51819},[886],[888,51821,51822],{"xmlns":890},[892,51823,51824,51836],{},[895,51825,51826],{},[1953,51827,51828,51830],{},[898,51829,2455],{},[895,51831,51832,51834],{},[898,51833,44068],{},[898,51835,724],{},[902,51837,44073],{"encoding":904},[883,51839,51841],{"className":51840},[886],[888,51842,51843],{"xmlns":890},[892,51844,51845,51859],{},[895,51846,51847],{},[1953,51848,51849,51851],{},[898,51850,2455],{},[895,51852,51853,51855,51857],{},[898,51854,44091],{},[898,51856,1675],{},[898,51858,13431],{},[902,51860,44098],{"encoding":904},[123,51862,51863,1884,51866,1343,51895],{},[38,51864,51865],{},"Ekvivalence zdanění",[883,51867,51869],{"className":51868},[886],[888,51870,51871],{"xmlns":890},[892,51872,51873,51893],{},[895,51874,51875,51883,51885],{},[10554,51876,51877,51879,51881],{},[898,51878,2470],{},[1810,51880,1959],{},[898,51882,5640],{},[1677,51884,1679],{},[10554,51886,51887,51889,51891],{},[898,51888,2470],{},[1810,51890,1812],{},[898,51892,5640],{},[902,51894,44299],{"encoding":904},[883,51896,51898],{"className":51897},[886],[888,51899,51900],{"xmlns":890},[892,51901,51902,51926],{},[895,51903,51904,51912,51914,51916,51918],{},[10554,51905,51906,51908,51910],{},[898,51907,5325],{},[1810,51909,1959],{},[898,51911,5640],{},[1677,51913,1906],{},[898,51915,2455],{},[1677,51917,1679],{},[10554,51919,51920,51922,51924],{},[898,51921,5325],{},[1810,51923,1812],{},[898,51925,5640],{},[902,51927,44333],{"encoding":904},[724,51929,51930],{},[38,51931,27799],{},[120,51933,51934,51980,52011,52016,52022,52029],{},[123,51935,51936,1884,51938],{},[38,51937,44432],{},[883,51939,51941],{"className":51940},[886],[888,51942,51943],{"xmlns":890},[892,51944,51945,51977],{},[895,51946,51947,51953,51955,51957,51959,51961,51963,51965,51967,51969,51971,51973,51975],{},[1805,51948,51949,51951],{},[898,51950,2470],{},[898,51952,5640],{},[1677,51954,1679],{},[1677,51956,1686],{"stretchy":1685},[898,51958,1779],{},[1677,51960,1906],{},[898,51962,1875],{},[1677,51964,1692],{"stretchy":1685},[898,51966,6062],{"mathvariant":2057},[1677,51968,1686],{"stretchy":1685},[898,51970,1823],{},[1677,51972,1906],{},[898,51974,207],{},[1677,51976,1692],{"stretchy":1685},[902,51978,51979],{"encoding":904},"Q^E = (b - d)\u002F(c - a)",[123,51981,51982,1884,51985,52010],{},[38,51983,51984],{},"Parametry",[883,51986,51988],{"className":51987},[886],[888,51989,51990],{"xmlns":890},[892,51991,51992,52008],{},[895,51993,51994,51996,51998,52000,52002,52004,52006],{},[898,51995,207],{},[1677,51997,1967],{"separator":1966},[898,51999,1779],{},[1677,52001,1967],{"separator":1966},[898,52003,1823],{},[1677,52005,1967],{"separator":1966},[898,52007,1875],{},[902,52009,44676],{"encoding":904}," — exogenní proměnné",[123,52012,52013],{},[38,52014,52015],{},"Endogenní \u002F exogenní proměnná",[123,52017,52018,52021],{},[38,52019,52020],{},"Multiplikátor"," — parciální derivace redukovaného tvaru",[123,52023,52024,1343,52027],{},[38,52025,52026],{},"Komparativní statika",[38,52028,38351],{},[123,52030,52031,1884,52033,52049],{},[38,52032,2636],{},[883,52034,52036],{"className":52035},[886],[888,52037,52038],{"xmlns":890},[892,52039,52040,52046],{},[895,52041,52042,52044],{},[898,52043,1875],{},[898,52045,2470],{},[902,52047,52048],{"encoding":904},"dQ"," (2.11)",[724,52051,52052],{},[38,52053,52054],{},"Přebytky a ostatní",[120,52056,52057,52095],{},[123,52058,52059,1884,52061,52076,52077,1884,52079,52094],{},[38,52060,46325],{},[883,52062,52064],{"className":52063},[886],[888,52065,52066],{"xmlns":890},[892,52067,52068,52074],{},[895,52069,52070,52072],{},[898,52071,2458],{},[898,52073,10061],{},[902,52075,46341],{"encoding":904}," (2.14), ",[38,52078,46344],{},[883,52080,52082],{"className":52081},[886],[888,52083,52084],{"xmlns":890},[892,52085,52086,52092],{},[895,52087,52088,52090],{},[898,52089,5325],{},[898,52091,10061],{},[902,52093,46360],{"encoding":904}," (2.15)",[123,52096,52097,1343,52100,52103],{},[38,52098,52099],{},"Homo economicus",[38,52101,52102],{},"Marshallova formulace"," (1890)",[38361,52105],{},[115,52107,3473],{"id":3472},[120,52109,52110,52145,52154],{},[123,52111,52112,1884,52115,52118,52119,1343,52122,52125,52126,52129,52130,52133,52134,52137,52138,52141,52142],{},[38,52113,52114],{},"Související témata:",[207,52116,811],{"className":52117,"dataFsResolvedFilePath":809,"href":810},[210]," (dopady daně, daňové břemeno, ekvivalence), ",[207,52120,820],{"className":52121,"dataFsResolvedFilePath":818,"href":819},[210],[207,52123,2038],{"className":52124,"dataFsResolvedFilePath":764,"href":765},[210]," (zákon klesající\u002Frostoucí, monotonie), ",[207,52127,775],{"className":52128,"dataFsResolvedFilePath":773,"href":774},[210]," (CS a PS), ",[207,52131,784],{"className":52132,"dataFsResolvedFilePath":782,"href":783},[210]," (vícefaktorové modely, multiplikátory), ",[207,52135,793],{"className":52136,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace spotřebitele), ",[207,52139,3509],{"className":52140,"dataFsResolvedFilePath":848,"href":849},[210]," (důchodová a cenová citlivost), ",[207,52143,3504],{"className":52144,"dataFsResolvedFilePath":827,"href":828},[210],[123,52146,52147,1884,52150],{},[38,52148,52149],{},"Shrnutí přednášek:",[207,52151,52153],{"className":52152,"dataFsResolvedFilePath":745,"href":746},[210],"KS — 1. blok",[123,52155,52156,1884,52158],{},[38,52157,17594],{},[207,52159,17598],{"className":52160,"dataFsResolvedFilePath":1641,"href":1642},[210],{"title":641,"searchDepth":642,"depth":642,"links":52162},[52163,52164,52172,52178,52185,52186,52193,52194,52195,52202,52203,52204],{"id":38185,"depth":642,"text":38186},{"id":38166,"depth":642,"text":14551,"children":52165},[52166,52167,52168,52169,52171],{"id":38454,"depth":649,"text":38455},{"id":38736,"depth":649,"text":38737},{"id":39746,"depth":649,"text":39747},{"id":40314,"depth":649,"text":52170},"Posun poptávky (shift of demand)",{"id":40818,"depth":649,"text":40819},{"id":38170,"depth":642,"text":14515,"children":52173},[52174,52175,52176],{"id":41655,"depth":649,"text":38455},{"id":41841,"depth":649,"text":41842},{"id":42293,"depth":649,"text":52177},"Posun nabídky (shift of supply)",{"id":42715,"depth":642,"text":42716,"children":52179},[52180,52181,52182,52183,52184],{"id":42827,"depth":649,"text":42828},{"id":43040,"depth":649,"text":43041},{"id":43358,"depth":649,"text":43359},{"id":43712,"depth":649,"text":43713},{"id":43743,"depth":649,"text":43744},{"id":44012,"depth":642,"text":811},{"id":44413,"depth":642,"text":44414,"children":52187},[52188,52189,52190,52191],{"id":44431,"depth":649,"text":44432},{"id":44812,"depth":649,"text":44813},{"id":45196,"depth":649,"text":45197},{"id":45650,"depth":649,"text":52192},"Příklad 2.11 — komparativní statika pro QEQ^E",{"id":13173,"depth":642,"text":820},{"id":46575,"depth":642,"text":46576},{"id":46806,"depth":642,"text":46807,"children":52196},[52197,52198,52199,52200,52201],{"id":46810,"depth":649,"text":46811},{"id":47650,"depth":649,"text":47651},{"id":48026,"depth":649,"text":42716},{"id":49321,"depth":649,"text":44414},{"id":51077,"depth":649,"text":820},{"id":51272,"depth":642,"text":51273},{"id":17109,"depth":642,"text":17110},{"id":3472,"depth":642,"text":3473},{},"\u002Ftopics\u002Fpoptavka-nabidka",{"title":802,"description":641},[1138,1135],"topics\u002Fpoptavka-nabidka",[1128,52211,52212,52213,19274,52214,52215],"poptavka","nabidka","rovnovaha","zdaneni","prebytek","VHXMOe03Z24g0HTNlL2geCMzNcnJ3vQ8m2Org-s9n8Q",{"id":52218,"title":820,"body":52219,"course":1128,"courses":659,"created":10944,"description":641,"extension":661,"meta":56498,"navigation":664,"path":56499,"seo":56500,"sources":56501,"stem":56502,"tags":56503,"type":3538,"updated":677,"__hash__":56508},"topics\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce.md",{"type":9,"value":52220,"toc":56476},[52221,52223,52291,52341,52343,52346,52604,52680,52685,52687,52706,52710,52786,52871,52873,53187,53280,53282,53301,53305,53379,53464,53467,53643,53648,53650,54070,54072,54076,54080,54316,54360,54460,54526,54529,54562,54738,54800,54930,55008,55119,55153,55351,55370,55389,55454,55458,55461,55506,55509,55627,55673,55675,55679,56027,56029,56031,56309,56311,56315,56350,56357,56430,56432,56434],[12,52222,820],{"id":13173},[5254,52224,52225],{},[724,52226,52227,5261,52229,11413,52231,52246,52247,11413,52249,52264,52265,52287,52288,1656],{},[883,52228,5260],{},[38,52230,46325],{},[883,52232,52234],{"className":52233},[886],[888,52235,52236],{"xmlns":890},[892,52237,52238,52244],{},[895,52239,52240,52242],{},[898,52241,2458],{},[898,52243,10061],{},[902,52245,46341],{"encoding":904},") je rozdíl mezi tím, co byl spotřebitel ochoten zaplatit, a tím, co skutečně zaplatil. ",[38,52248,46472],{},[883,52250,52252],{"className":52251},[886],[888,52253,52254],{"xmlns":890},[892,52255,52256,52262],{},[895,52257,52258,52260],{},[898,52259,5325],{},[898,52261,10061],{},[902,52263,46360],{"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 ",[883,52266,52268],{"className":52267},[886],[888,52269,52270],{"xmlns":890},[892,52271,52272,52284],{},[895,52273,52274,52276,52278,52280,52282],{},[898,52275,2458],{},[898,52277,10061],{},[1677,52279,1776],{},[898,52281,5325],{},[898,52283,10061],{},[902,52285,52286],{"encoding":904},"CS + PS"," měří ",[38,52289,52290],{},"celkový blahobyt trhu",[724,52292,52293,11413,52295,1343,52297,13518,52312,11413,52314,1343,52316,52331,52332,52336,52337,1656],{},[38,52294,46325],{},[614,52296,46379],{},[883,52298,52300],{"className":52299},[886],[888,52301,52302],{"xmlns":890},[892,52303,52304,52310],{},[895,52305,52306,52308],{},[898,52307,2458],{},[898,52309,10061],{},[902,52311,46341],{"encoding":904},[38,52313,46344],{},[614,52315,46475],{},[883,52317,52319],{"className":52318},[886],[888,52320,52321],{"xmlns":890},[892,52322,52323,52329],{},[895,52324,52325,52327],{},[898,52326,5325],{},[898,52328,10061],{},[902,52330,46360],{"encoding":904},") kvantifikují čistý prospěch jednotlivých stran trhu. Navazují na pojmy ",[207,52333,52335],{"className":52334,"dataFsResolvedFilePath":800,"href":801},[210],"tržní rovnováhy"," a využívají aparát ",[207,52338,52340],{"className":52339,"dataFsResolvedFilePath":773,"href":774},[210],"integrálního počtu",[38361,52342],{},[115,52344,1241],{"id":52345},"úvod",[724,52347,52348,52349,52372,52373,52396,52397,52414,52415,5298,52447,52479,52480,52506,52507,52510,52511,52514,52515,15401,52549,22985,52570,1656],{},"Je dána funkce poptávky ",[883,52350,52352],{"className":52351},[886],[888,52353,52354],{"xmlns":890},[892,52355,52356,52370],{},[895,52357,52358,52360,52362,52364,52366,52368],{},[898,52359,5325],{},[1677,52361,1679],{},[898,52363,5571],{},[1677,52365,1686],{"stretchy":1685},[898,52367,2470],{},[1677,52369,1692],{"stretchy":1685},[902,52371,6028],{"encoding":904},", resp. funkce nabídky ",[883,52374,52376],{"className":52375},[886],[888,52377,52378],{"xmlns":890},[892,52379,52380,52394],{},[895,52381,52382,52384,52386,52388,52390,52392],{},[898,52383,5325],{},[1677,52385,1679],{},[898,52387,10061],{},[1677,52389,1686],{"stretchy":1685},[898,52391,2470],{},[1677,52393,1692],{"stretchy":1685},[902,52395,42462],{"encoding":904},". Pro pevně zadané množství ",[883,52398,52400],{"className":52399},[886],[888,52401,52402],{"xmlns":890},[892,52403,52404,52412],{},[895,52405,52406],{},[1953,52407,52408,52410],{},[898,52409,2470],{},[1810,52411,2008],{},[902,52413,39699],{"encoding":904}," je odpovídající cena ",[883,52416,52418],{"className":52417},[886],[888,52419,52420],{"xmlns":890},[892,52421,52422,52444],{},[895,52423,52424,52430,52432,52434,52436,52442],{},[1953,52425,52426,52428],{},[898,52427,5325],{},[1810,52429,2008],{},[1677,52431,1679],{},[898,52433,5571],{},[1677,52435,1686],{"stretchy":1685},[1953,52437,52438,52440],{},[898,52439,2470],{},[1810,52441,2008],{},[1677,52443,1692],{"stretchy":1685},[902,52445,52446],{"encoding":904},"P_0 = D(Q_0)",[883,52448,52450],{"className":52449},[886],[888,52451,52452],{"xmlns":890},[892,52453,52454,52476],{},[895,52455,52456,52462,52464,52466,52468,52474],{},[1953,52457,52458,52460],{},[898,52459,5325],{},[1810,52461,2008],{},[1677,52463,1679],{},[898,52465,10061],{},[1677,52467,1686],{"stretchy":1685},[1953,52469,52470,52472],{},[898,52471,2470],{},[1810,52473,2008],{},[1677,52475,1692],{"stretchy":1685},[902,52477,52478],{"encoding":904},"P_0 = S(Q_0)","). Součin ",[883,52481,52483],{"className":52482},[886],[888,52484,52485],{"xmlns":890},[892,52486,52487,52503],{},[895,52488,52489,52495,52497],{},[1953,52490,52491,52493],{},[898,52492,5325],{},[1810,52494,2008],{},[1969,52496,2668],{},[1953,52498,52499,52501],{},[898,52500,2470],{},[1810,52502,2008],{},[902,52504,52505],{"encoding":904},"P_0 \\, Q_0"," reprezentuje buď ",[38,52508,52509],{},"výdaje spotřebitele",", nebo ",[38,52512,52513],{},"tržby výrobce"," a geometricky odpovídá obsahu obdélníka ",[883,52516,52518],{"className":52517},[886],[888,52519,52520],{"xmlns":890},[892,52521,52522,52546],{},[895,52523,52524,52526,52528,52534,52536,52538,52540],{},[1810,52525,2008],{},[1969,52527,2668],{},[1953,52529,52530,52532],{},[898,52531,2470],{},[1810,52533,2008],{},[1969,52535,2668],{},[898,52537,5643],{},[1969,52539,2668],{},[1953,52541,52542,52544],{},[898,52543,5325],{},[1810,52545,2008],{},[902,52547,52548],{"encoding":904},"0\\,Q_0\\,A\\,P_0",[883,52550,52552],{"className":52551},[886],[888,52553,52554],{"xmlns":890},[892,52555,52556,52568],{},[895,52557,52558,52560,52562,52564,52566],{},[1677,52559,1686],{"stretchy":1685},[898,52561,2470],{},[1677,52563,1967],{"separator":1966},[898,52565,5325],{},[1677,52567,1692],{"stretchy":1685},[902,52569,39082],{"encoding":904},[883,52571,52573],{"className":52572},[886],[888,52574,52575],{"xmlns":890},[892,52576,52577,52601],{},[895,52578,52579,52581,52583,52585,52591,52593,52599],{},[898,52580,5643],{},[1677,52582,1679],{},[1677,52584,2167],{"stretchy":1685},[1953,52586,52587,52589],{},[898,52588,2470],{},[1810,52590,2008],{},[1677,52592,1967],{"separator":1966},[1953,52594,52595,52597],{},[898,52596,5325],{},[1810,52598,2008],{},[1677,52600,2182],{"stretchy":1685},[902,52602,52603],{"encoding":904},"A = [Q_0, P_0]",[5254,52605,52606,52611,52669],{},[724,52607,52608,52610],{},[883,52609,5543],{}," Intuice",[120,52612,52613,52641],{},[123,52614,52615,52616,52619,52620,52622,52623,52640],{},"Za jednotky zboží nakoupené ",[38,52617,52618],{},"před"," posledním kusem je spotřebitel podle funkce poptávky ochoten platit ",[614,52621,26661],{}," než ",[883,52624,52626],{"className":52625},[886],[888,52627,52628],{"xmlns":890},[892,52629,52630,52638],{},[895,52631,52632],{},[1953,52633,52634,52636],{},[898,52635,5325],{},[1810,52637,2008],{},[902,52639,40339],{"encoding":904}," — rozdíl si „šetří do kapsy\" jako přebytek.",[123,52642,52643,52644,52646,52647,52650,52651,52668],{},"Za jednotky zboží prodané ",[38,52645,52618],{}," posledním kusem by výrobce podle funkce nabídky byl ochoten prodávat i za ",[614,52648,52649],{},"nižší"," cenu než ",[883,52652,52654],{"className":52653},[886],[888,52655,52656],{"xmlns":890},[892,52657,52658,52666],{},[895,52659,52660],{},[1953,52661,52662,52664],{},[898,52663,5325],{},[1810,52665,2008],{},[902,52667,40339],{"encoding":904}," — rozdíl je jeho přebytek.",[724,52670,52671,52672,52675,52676,52679],{},"Přebytek je tedy rozdíl mezi ",[614,52673,52674],{},"ochotou"," (platit \u002F prodávat) a ",[614,52677,52678],{},"skutečností"," (zaplaceno \u002F obdrženo).",[724,52681,52682],{},[2240,52683],{"alt":46370,"className":52684,"src":46372},[210,2244],[38361,52686],{},[115,52688,52690,52691,1692],{"id":52689},"přebytek-spotřebitele-cscs","Přebytek spotřebitele (",[883,52692,52694],{"className":52693},[886],[888,52695,52696],{"xmlns":890},[892,52697,52698,52704],{},[895,52699,52700,52702],{},[898,52701,2458],{},[898,52703,10061],{},[902,52705,46341],{"encoding":904},[198,52707,52709],{"id":52708},"definice-vzorec-214","Definice (vzorec 2.14)",[724,52711,52712,52713,52736,52737,52754,52755,2385],{},"Pro poptávku ",[883,52714,52716],{"className":52715},[886],[888,52717,52718],{"xmlns":890},[892,52719,52720,52734],{},[895,52721,52722,52724,52726,52728,52730,52732],{},[898,52723,5325],{},[1677,52725,1679],{},[898,52727,5571],{},[1677,52729,1686],{"stretchy":1685},[898,52731,2470],{},[1677,52733,1692],{"stretchy":1685},[902,52735,6028],{"encoding":904}," a pevně zadané ",[883,52738,52740],{"className":52739},[886],[888,52741,52742],{"xmlns":890},[892,52743,52744,52752],{},[895,52745,52746],{},[1953,52747,52748,52750],{},[898,52749,2470],{},[1810,52751,2008],{},[902,52753,39699],{"encoding":904}," s cenou ",[883,52756,52758],{"className":52757},[886],[888,52759,52760],{"xmlns":890},[892,52761,52762,52784],{},[895,52763,52764,52770,52772,52774,52776,52782],{},[1953,52765,52766,52768],{},[898,52767,5325],{},[1810,52769,2008],{},[1677,52771,1679],{},[898,52773,5571],{},[1677,52775,1686],{"stretchy":1685},[1953,52777,52778,52780],{},[898,52779,2470],{},[1810,52781,2008],{},[1677,52783,1692],{"stretchy":1685},[902,52785,52446],{"encoding":904},[883,52787,52789],{"className":52788},[886],[888,52790,52791],{"xmlns":890,"display":29457},[892,52792,52793,52869],{},[22145,52794,52795],{"width":29462},[22150,52796,52797,52799,52863,52865],{},[22153,52798],{"width":29467},[22153,52800,52801],{},[895,52802,52803,52805,52807,52809,52815,52817,52819,52831,52833,52835,52837,52839,52841,52843,52845,52847,52853,52855,52861],{},[898,52804,2458],{},[898,52806,10061],{},[1677,52808,1686],{"stretchy":1685},[1953,52810,52811,52813],{},[898,52812,2470],{},[1810,52814,2008],{},[1677,52816,1692],{"stretchy":1685},[1677,52818,1679],{},[10554,52820,52821,52823,52825],{},[1677,52822,12558],{},[1810,52824,2008],{},[1953,52826,52827,52829],{},[898,52828,2470],{},[1810,52830,2008],{},[898,52832,5571],{},[1677,52834,1686],{"stretchy":1685},[898,52836,2470],{},[1677,52838,1692],{"stretchy":1685},[1969,52840,2668],{},[898,52842,1875],{},[898,52844,2470],{},[1677,52846,1906],{},[1953,52848,52849,52851],{},[898,52850,5325],{},[1810,52852,2008],{},[1969,52854,2668],{},[1953,52856,52857,52859],{},[898,52858,2470],{},[1810,52860,2008],{},[898,52862,1656],{"mathvariant":2057},[22153,52864],{"width":29467},[22153,52866,52867],{},[1969,52868,46464],{},[902,52870,46467],{"encoding":904},[198,52872,2125],{"id":2124},[120,52874,52875,52967,53029],{},[123,52876,52877,52917,52918,52944,52945,52948,52949,52966],{},[883,52878,52880],{"className":52879},[886],[888,52881,52882],{"xmlns":890},[892,52883,52884,52914],{},[895,52885,52886],{},[2006,52887,52888,52900,52902,52904,52906,52908,52910,52912],{"scriptlevel":2008,"displaystyle":1966},[10554,52889,52890,52892,52894],{},[1677,52891,12558],{},[1810,52893,2008],{},[1953,52895,52896,52898],{},[898,52897,2470],{},[1810,52899,2008],{},[898,52901,5571],{},[1677,52903,1686],{"stretchy":1685},[898,52905,2470],{},[1677,52907,1692],{"stretchy":1685},[1969,52909,2668],{},[898,52911,1875],{},[898,52913,2470],{},[902,52915,52916],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ"," — plocha pod křivkou poptávky v intervalu ",[883,52919,52921],{"className":52920},[886],[888,52922,52923],{"xmlns":890},[892,52924,52925,52941],{},[895,52926,52927,52929,52931,52933,52939],{},[1677,52928,2167],{"stretchy":1685},[1810,52930,2008],{},[1677,52932,1967],{"separator":1966},[1953,52934,52935,52937],{},[898,52936,2470],{},[1810,52938,2008],{},[1677,52940,2182],{"stretchy":1685},[902,52942,52943],{"encoding":904},"[0, Q_0]","; představuje celkovou ",[38,52946,52947],{},"ochotu platit"," (maximální částku, kterou by spotřebitel za ",[883,52950,52952],{"className":52951},[886],[888,52953,52954],{"xmlns":890},[892,52955,52956,52964],{},[895,52957,52958],{},[1953,52959,52960,52962],{},[898,52961,2470],{},[1810,52963,2008],{},[902,52965,39699],{"encoding":904}," jednotek byl ochoten zaplatit).",[123,52968,52969,52995,52996,5306],{},[883,52970,52972],{"className":52971},[886],[888,52973,52974],{"xmlns":890},[892,52975,52976,52992],{},[895,52977,52978,52984,52986],{},[1953,52979,52980,52982],{},[898,52981,5325],{},[1810,52983,2008],{},[1969,52985,2668],{},[1953,52987,52988,52990],{},[898,52989,2470],{},[1810,52991,2008],{},[902,52993,52994],{"encoding":904},"P_0\\,Q_0"," — skutečně zaplacená částka (obdélník ",[883,52997,52999],{"className":52998},[886],[888,53000,53001],{"xmlns":890},[892,53002,53003,53027],{},[895,53004,53005,53007,53009,53015,53017,53019,53021],{},[1810,53006,2008],{},[1969,53008,2668],{},[1953,53010,53011,53013],{},[898,53012,2470],{},[1810,53014,2008],{},[1969,53016,2668],{},[898,53018,5643],{},[1969,53020,2668],{},[1953,53022,53023,53025],{},[898,53024,5325],{},[1810,53026,2008],{},[902,53028,52548],{"encoding":904},[123,53030,53031,53046,53047,53069,53070,53095,53096,22985,53122,5272,53154,1656],{},[883,53032,53034],{"className":53033},[886],[888,53035,53036],{"xmlns":890},[892,53037,53038,53044],{},[895,53039,53040,53042],{},[898,53041,2458],{},[898,53043,10061],{},[902,53045,46341],{"encoding":904}," je plocha mezi křivkou poptávky a vodorovnou přímkou ",[883,53048,53050],{"className":53049},[886],[888,53051,53052],{"xmlns":890},[892,53053,53054,53066],{},[895,53055,53056,53058,53060],{},[898,53057,5325],{},[1677,53059,1679],{},[1953,53061,53062,53064],{},[898,53063,5325],{},[1810,53065,2008],{},[902,53067,53068],{"encoding":904},"P = P_0"," v pásu ",[883,53071,53073],{"className":53072},[886],[888,53074,53075],{"xmlns":890},[892,53076,53077,53093],{},[895,53078,53079,53081,53083,53085,53091],{},[1677,53080,2167],{"stretchy":1685},[1810,53082,2008],{},[1677,53084,1967],{"separator":1966},[1953,53086,53087,53089],{},[898,53088,2470],{},[1810,53090,2008],{},[1677,53092,2182],{"stretchy":1685},[902,53094,52943],{"encoding":904}," — „křivočarý trojúhelník\" ",[883,53097,53099],{"className":53098},[886],[888,53100,53101],{"xmlns":890},[892,53102,53103,53119],{},[895,53104,53105,53111,53113,53115,53117],{},[1953,53106,53107,53109],{},[898,53108,5325],{},[1810,53110,2008],{},[1969,53112,2668],{},[898,53114,24644],{},[1969,53116,2668],{},[898,53118,5643],{},[902,53120,53121],{"encoding":904},"P_0\\,B\\,A",[883,53123,53125],{"className":53124},[886],[888,53126,53127],{"xmlns":890},[892,53128,53129,53151],{},[895,53130,53131,53133,53135,53137,53139,53141,53143,53145,53147,53149],{},[898,53132,24644],{},[1677,53134,1679],{},[1677,53136,2167],{"stretchy":1685},[1810,53138,2008],{},[1677,53140,1967],{"separator":1966},[898,53142,5571],{},[1677,53144,1686],{"stretchy":1685},[1810,53146,2008],{},[1677,53148,1692],{"stretchy":1685},[1677,53150,2182],{"stretchy":1685},[902,53152,53153],{"encoding":904},"B = [0, D(0)]",[883,53155,53157],{"className":53156},[886],[888,53158,53159],{"xmlns":890},[892,53160,53161,53185],{},[895,53162,53163,53165,53167,53169,53175,53177,53183],{},[898,53164,5643],{},[1677,53166,1679],{},[1677,53168,2167],{"stretchy":1685},[1953,53170,53171,53173],{},[898,53172,2470],{},[1810,53174,2008],{},[1677,53176,1967],{"separator":1966},[1953,53178,53179,53181],{},[898,53180,5325],{},[1810,53182,2008],{},[1677,53184,2182],{"stretchy":1685},[902,53186,52603],{"encoding":904},[724,53188,53189],{},[614,53190,53191,53192,53205,53206,53239,53240,30533,53265,1656],{},"Obrázek 2.24: Křivka poptávky ",[883,53193,53195],{"className":53194},[886],[888,53196,53197],{"xmlns":890},[892,53198,53199,53203],{},[895,53200,53201],{},[898,53202,5571],{},[902,53204,5571],{"encoding":904},", bod ",[883,53207,53209],{"className":53208},[886],[888,53210,53211],{"xmlns":890},[892,53212,53213,53237],{},[895,53214,53215,53217,53219,53221,53227,53229,53235],{},[898,53216,5643],{},[1677,53218,1679],{},[1677,53220,2167],{"stretchy":1685},[1953,53222,53223,53225],{},[898,53224,2470],{},[1810,53226,2008],{},[1677,53228,1967],{"separator":1966},[1953,53230,53231,53233],{},[898,53232,5325],{},[1810,53234,2008],{},[1677,53236,2182],{"stretchy":1685},[902,53238,52603],{"encoding":904},", vyšrafovaná plocha trojúhelníku ",[883,53241,53243],{"className":53242},[886],[888,53244,53245],{"xmlns":890},[892,53246,53247,53263],{},[895,53248,53249,53255,53257,53259,53261],{},[1953,53250,53251,53253],{},[898,53252,5325],{},[1810,53254,2008],{},[1969,53256,2668],{},[898,53258,24644],{},[1969,53260,2668],{},[898,53262,5643],{},[902,53264,53121],{"encoding":904},[883,53266,53268],{"className":53267},[886],[888,53269,53270],{"xmlns":890},[892,53271,53272,53278],{},[895,53273,53274,53276],{},[898,53275,2458],{},[898,53277,10061],{},[902,53279,46341],{"encoding":904},[38361,53281],{},[115,53283,53285,53286,1692],{"id":53284},"přebytek-výrobce-psps","Přebytek výrobce (",[883,53287,53289],{"className":53288},[886],[888,53290,53291],{"xmlns":890},[892,53292,53293,53299],{},[895,53294,53295,53297],{},[898,53296,5325],{},[898,53298,10061],{},[902,53300,46360],{"encoding":904},[198,53302,53304],{"id":53303},"definice-vzorec-215","Definice (vzorec 2.15)",[724,53306,53307,53308,52736,53331,52754,53348,2385],{},"Analogicky — pro nabídku ",[883,53309,53311],{"className":53310},[886],[888,53312,53313],{"xmlns":890},[892,53314,53315,53329],{},[895,53316,53317,53319,53321,53323,53325,53327],{},[898,53318,5325],{},[1677,53320,1679],{},[898,53322,10061],{},[1677,53324,1686],{"stretchy":1685},[898,53326,2470],{},[1677,53328,1692],{"stretchy":1685},[902,53330,42462],{"encoding":904},[883,53332,53334],{"className":53333},[886],[888,53335,53336],{"xmlns":890},[892,53337,53338,53346],{},[895,53339,53340],{},[1953,53341,53342,53344],{},[898,53343,2470],{},[1810,53345,2008],{},[902,53347,39699],{"encoding":904},[883,53349,53351],{"className":53350},[886],[888,53352,53353],{"xmlns":890},[892,53354,53355,53377],{},[895,53356,53357,53363,53365,53367,53369,53375],{},[1953,53358,53359,53361],{},[898,53360,5325],{},[1810,53362,2008],{},[1677,53364,1679],{},[898,53366,10061],{},[1677,53368,1686],{"stretchy":1685},[1953,53370,53371,53373],{},[898,53372,2470],{},[1810,53374,2008],{},[1677,53376,1692],{"stretchy":1685},[902,53378,52478],{"encoding":904},[883,53380,53382],{"className":53381},[886],[888,53383,53384],{"xmlns":890,"display":29457},[892,53385,53386,53462],{},[22145,53387,53388],{"width":29462},[22150,53389,53390,53392,53456,53458],{},[22153,53391],{"width":29467},[22153,53393,53394],{},[895,53395,53396,53398,53400,53402,53408,53410,53412,53418,53420,53426,53428,53440,53442,53444,53446,53448,53450,53452,53454],{},[898,53397,5325],{},[898,53399,10061],{},[1677,53401,1686],{"stretchy":1685},[1953,53403,53404,53406],{},[898,53405,2470],{},[1810,53407,2008],{},[1677,53409,1692],{"stretchy":1685},[1677,53411,1679],{},[1953,53413,53414,53416],{},[898,53415,5325],{},[1810,53417,2008],{},[1969,53419,2668],{},[1953,53421,53422,53424],{},[898,53423,2470],{},[1810,53425,2008],{},[1677,53427,1906],{},[10554,53429,53430,53432,53434],{},[1677,53431,12558],{},[1810,53433,2008],{},[1953,53435,53436,53438],{},[898,53437,2470],{},[1810,53439,2008],{},[898,53441,10061],{},[1677,53443,1686],{"stretchy":1685},[898,53445,2470],{},[1677,53447,1692],{"stretchy":1685},[1969,53449,2668],{},[898,53451,1875],{},[898,53453,2470],{},[898,53455,1656],{"mathvariant":2057},[22153,53457],{"width":29467},[22153,53459,53460],{},[1969,53461,46560],{},[902,53463,46563],{"encoding":904},[198,53465,2125],{"id":53466},"geometrická-interpretace-1",[120,53468,53469,53517,53578],{},[123,53470,53471,8403,53496,53499,53500,1656],{},[883,53472,53474],{"className":53473},[886],[888,53475,53476],{"xmlns":890},[892,53477,53478,53494],{},[895,53479,53480,53486,53488],{},[1953,53481,53482,53484],{},[898,53483,5325],{},[1810,53485,2008],{},[1969,53487,2668],{},[1953,53489,53490,53492],{},[898,53491,2470],{},[1810,53493,2008],{},[902,53495,52994],{"encoding":904},[38,53497,53498],{},"tržba"," výrobce za prodané množství ",[883,53501,53503],{"className":53502},[886],[888,53504,53505],{"xmlns":890},[892,53506,53507,53515],{},[895,53508,53509],{},[1953,53510,53511,53513],{},[898,53512,2470],{},[1810,53514,2008],{},[902,53516,39699],{"encoding":904},[123,53518,53519,53559,53560,53577],{},[883,53520,53522],{"className":53521},[886],[888,53523,53524],{"xmlns":890},[892,53525,53526,53556],{},[895,53527,53528],{},[2006,53529,53530,53542,53544,53546,53548,53550,53552,53554],{"scriptlevel":2008,"displaystyle":1966},[10554,53531,53532,53534,53536],{},[1677,53533,12558],{},[1810,53535,2008],{},[1953,53537,53538,53540],{},[898,53539,2470],{},[1810,53541,2008],{},[898,53543,10061],{},[1677,53545,1686],{"stretchy":1685},[898,53547,2470],{},[1677,53549,1692],{"stretchy":1685},[1969,53551,2668],{},[898,53553,1875],{},[898,53555,2470],{},[902,53557,53558],{"encoding":904},"\\displaystyle \\int_0^{Q_0} S(Q)\\,dQ"," — plocha pod křivkou nabídky; minimální částka, za kterou by byl výrobce ochoten ",[883,53561,53563],{"className":53562},[886],[888,53564,53565],{"xmlns":890},[892,53566,53567,53575],{},[895,53568,53569],{},[1953,53570,53571,53573],{},[898,53572,2470],{},[1810,53574,2008],{},[902,53576,39699],{"encoding":904}," jednotek dodat (souvisí s mezními náklady).",[123,53579,53580,53595,53596,53617,53618,1656],{},[883,53581,53583],{"className":53582},[886],[888,53584,53585],{"xmlns":890},[892,53586,53587,53593],{},[895,53588,53589,53591],{},[898,53590,5325],{},[898,53592,10061],{},[902,53594,46360],{"encoding":904}," je plocha mezi vodorovnou přímkou ",[883,53597,53599],{"className":53598},[886],[888,53600,53601],{"xmlns":890},[892,53602,53603,53615],{},[895,53604,53605,53607,53609],{},[898,53606,5325],{},[1677,53608,1679],{},[1953,53610,53611,53613],{},[898,53612,5325],{},[1810,53614,2008],{},[902,53616,53068],{"encoding":904}," a křivkou nabídky v pásu ",[883,53619,53621],{"className":53620},[886],[888,53622,53623],{"xmlns":890},[892,53624,53625,53641],{},[895,53626,53627,53629,53631,53633,53639],{},[1677,53628,2167],{"stretchy":1685},[1810,53630,2008],{},[1677,53632,1967],{"separator":1966},[1953,53634,53635,53637],{},[898,53636,2470],{},[1810,53638,2008],{},[1677,53640,2182],{"stretchy":1685},[902,53642,52943],{"encoding":904},[724,53644,53645],{},[614,53646,53647],{},"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.",[38361,53649],{},[5254,53651,53652,53657],{},[724,53653,53654,53656],{},[883,53655,5960],{}," Postup výpočtu CS a PS",[152,53658,53659,53790,53900,53929,54063],{},[123,53660,53661,53662,53679,53680,53711,53712,53743,53744,1656],{},"Zjisti (nebo si zvol) množství ",[883,53663,53665],{"className":53664},[886],[888,53666,53667],{"xmlns":890},[892,53668,53669,53677],{},[895,53670,53671],{},[1953,53672,53673,53675],{},[898,53674,2470],{},[1810,53676,2008],{},[902,53678,39699],{"encoding":904}," a odpovídající cenu ",[883,53681,53683],{"className":53682},[886],[888,53684,53685],{"xmlns":890},[892,53686,53687,53709],{},[895,53688,53689,53695,53697,53699,53701,53707],{},[1953,53690,53691,53693],{},[898,53692,5325],{},[1810,53694,2008],{},[1677,53696,1679],{},[898,53698,5571],{},[1677,53700,1686],{"stretchy":1685},[1953,53702,53703,53705],{},[898,53704,2470],{},[1810,53706,2008],{},[1677,53708,1692],{"stretchy":1685},[902,53710,52446],{"encoding":904}," resp. ",[883,53713,53715],{"className":53714},[886],[888,53716,53717],{"xmlns":890},[892,53718,53719,53741],{},[895,53720,53721,53727,53729,53731,53733,53739],{},[1953,53722,53723,53725],{},[898,53724,5325],{},[1810,53726,2008],{},[1677,53728,1679],{},[898,53730,10061],{},[1677,53732,1686],{"stretchy":1685},[1953,53734,53735,53737],{},[898,53736,2470],{},[1810,53738,2008],{},[1677,53740,1692],{"stretchy":1685},[902,53742,52478],{"encoding":904},". V rovnováze platí ",[883,53745,53747],{"className":53746},[886],[888,53748,53749],{"xmlns":890},[892,53750,53751,53787],{},[895,53752,53753,53755,53757,53763,53765,53767,53769,53771,53777,53779,53781],{},[898,53754,5571],{},[1677,53756,1686],{"stretchy":1685},[1805,53758,53759,53761],{},[898,53760,2470],{},[898,53762,5640],{},[1677,53764,1692],{"stretchy":1685},[1677,53766,1679],{},[898,53768,10061],{},[1677,53770,1686],{"stretchy":1685},[1805,53772,53773,53775],{},[898,53774,2470],{},[898,53776,5640],{},[1677,53778,1692],{"stretchy":1685},[1677,53780,1679],{},[1805,53782,53783,53785],{},[898,53784,5325],{},[898,53786,5640],{},[902,53788,53789],{"encoding":904},"D(Q^E) = S(Q^E) = P^E",[123,53791,53792,53793,21517,53831,53846,53847,21517,53885,5306],{},"Spočti určitý integrál ",[883,53794,53796],{"className":53795},[886],[888,53797,53798],{"xmlns":890},[892,53799,53800,53828],{},[895,53801,53802,53814,53816,53818,53820,53822,53824,53826],{},[10554,53803,53804,53806,53808],{},[1677,53805,12558],{},[1810,53807,2008],{},[1953,53809,53810,53812],{},[898,53811,2470],{},[1810,53813,2008],{},[898,53815,5571],{},[1677,53817,1686],{"stretchy":1685},[898,53819,2470],{},[1677,53821,1692],{"stretchy":1685},[1969,53823,2668],{},[898,53825,1875],{},[898,53827,2470],{},[902,53829,53830],{"encoding":904},"\\int_0^{Q_0} D(Q)\\,dQ",[883,53832,53834],{"className":53833},[886],[888,53835,53836],{"xmlns":890},[892,53837,53838,53844],{},[895,53839,53840,53842],{},[898,53841,2458],{},[898,53843,10061],{},[902,53845,46341],{"encoding":904},") nebo ",[883,53848,53850],{"className":53849},[886],[888,53851,53852],{"xmlns":890},[892,53853,53854,53882],{},[895,53855,53856,53868,53870,53872,53874,53876,53878,53880],{},[10554,53857,53858,53860,53862],{},[1677,53859,12558],{},[1810,53861,2008],{},[1953,53863,53864,53866],{},[898,53865,2470],{},[1810,53867,2008],{},[898,53869,10061],{},[1677,53871,1686],{"stretchy":1685},[898,53873,2470],{},[1677,53875,1692],{"stretchy":1685},[1969,53877,2668],{},[898,53879,1875],{},[898,53881,2470],{},[902,53883,53884],{"encoding":904},"\\int_0^{Q_0} S(Q)\\,dQ",[883,53886,53888],{"className":53887},[886],[888,53889,53890],{"xmlns":890},[892,53891,53892,53898],{},[895,53893,53894,53896],{},[898,53895,5325],{},[898,53897,10061],{},[902,53899,46360],{"encoding":904},[123,53901,53902,53903,1656],{},"Sestav obdélník ",[883,53904,53906],{"className":53905},[886],[888,53907,53908],{"xmlns":890},[892,53909,53910,53926],{},[895,53911,53912,53918,53920],{},[1953,53913,53914,53916],{},[898,53915,5325],{},[1810,53917,2008],{},[1677,53919,2858],{},[1953,53921,53922,53924],{},[898,53923,2470],{},[1810,53925,2008],{},[902,53927,53928],{"encoding":904},"P_0 \\cdot Q_0",[123,53930,53931,53932],{},"Dosaď:\n",[120,53933,53934,53999],{},[123,53935,53936,53994,53995,53998],{},[883,53937,53939],{"className":53938},[886],[888,53940,53941],{"xmlns":890},[892,53942,53943,53991],{},[895,53944,53945,53947,53949,53951,53963,53965,53967,53969,53971,53973,53975,53977,53979,53985],{},[898,53946,2458],{},[898,53948,10061],{},[1677,53950,1679],{},[10554,53952,53953,53955,53957],{},[1677,53954,12558],{},[1810,53956,2008],{},[1953,53958,53959,53961],{},[898,53960,2470],{},[1810,53962,2008],{},[898,53964,5571],{},[1677,53966,1686],{"stretchy":1685},[898,53968,2470],{},[1677,53970,1692],{"stretchy":1685},[1969,53972,2668],{},[898,53974,1875],{},[898,53976,2470],{},[1677,53978,1906],{},[1953,53980,53981,53983],{},[898,53982,5325],{},[1810,53984,2008],{},[1953,53986,53987,53989],{},[898,53988,2470],{},[1810,53990,2008],{},[902,53992,53993],{"encoding":904},"CS = \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0"," (integrál ",[38,53996,53997],{},"mínus"," obdélník)",[123,54000,54001,54059,54060,54062],{},[883,54002,54004],{"className":54003},[886],[888,54005,54006],{"xmlns":890},[892,54007,54008,54056],{},[895,54009,54010,54012,54014,54016,54022,54028,54030,54042,54044,54046,54048,54050,54052,54054],{},[898,54011,5325],{},[898,54013,10061],{},[1677,54015,1679],{},[1953,54017,54018,54020],{},[898,54019,5325],{},[1810,54021,2008],{},[1953,54023,54024,54026],{},[898,54025,2470],{},[1810,54027,2008],{},[1677,54029,1906],{},[10554,54031,54032,54034,54036],{},[1677,54033,12558],{},[1810,54035,2008],{},[1953,54037,54038,54040],{},[898,54039,2470],{},[1810,54041,2008],{},[898,54043,10061],{},[1677,54045,1686],{"stretchy":1685},[898,54047,2470],{},[1677,54049,1692],{"stretchy":1685},[1969,54051,2668],{},[898,54053,1875],{},[898,54055,2470],{},[902,54057,54058],{"encoding":904},"PS = P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ"," (obdélník ",[38,54061,53997],{}," integrál)",[123,54064,54065,54066,54069],{},"Kontrola znaménka: obě hodnoty musí být ",[38,54067,54068],{},"kladné",". Pokud vyjde záporná, máš prohozené pořadí.",[38361,54071],{},[115,54073,54075],{"id":54074},"příklady","Příklady",[198,54077,54079],{"id":54078},"příklad-211-komparativní-statika-pro-rovnovážné-množství","Příklad 2.11 — komparativní statika pro rovnovážné množství",[5254,54081,54082],{},[724,54083,54084,54087,54088,49112,54111,54134,54135,1343,54155,1343,54172,1343,54189,54206,54207,54283,54284,54301,54302,54315],{},[883,54085,54086],{},"!example"," Zadání\nJsou dány poptávka ",[883,54089,54091],{"className":54090},[886],[888,54092,54093],{"xmlns":890},[892,54094,54095,54109],{},[895,54096,54097,54099,54101,54103,54105,54107],{},[898,54098,5325],{},[1677,54100,1679],{},[898,54102,207],{},[898,54104,2470],{},[1677,54106,1776],{},[898,54108,1779],{},[902,54110,38451],{"encoding":904},[883,54112,54114],{"className":54113},[886],[888,54115,54116],{"xmlns":890},[892,54117,54118,54132],{},[895,54119,54120,54122,54124,54126,54128,54130],{},[898,54121,5325],{},[1677,54123,1679],{},[898,54125,1823],{},[898,54127,2470],{},[1677,54129,1776],{},[898,54131,1875],{},[902,54133,41633],{"encoding":904}," s hodnotami ",[883,54136,54138],{"className":54137},[886],[888,54139,54140],{"xmlns":890},[892,54141,54142,54152],{},[895,54143,54144,54146,54148,54150],{},[898,54145,207],{},[1677,54147,1679],{},[1677,54149,1906],{},[1810,54151,1854],{},[902,54153,54154],{"encoding":904},"a = -3",[883,54156,54158],{"className":54157},[886],[888,54159,54160],{"xmlns":890},[892,54161,54162,54170],{},[895,54163,54164,54166,54168],{},[898,54165,1779],{},[1677,54167,1679],{},[1810,54169,6599],{},[902,54171,50035],{"encoding":904},[883,54173,54175],{"className":54174},[886],[888,54176,54177],{"xmlns":890},[892,54178,54179,54187],{},[895,54180,54181,54183,54185],{},[898,54182,1823],{},[1677,54184,1679],{},[1810,54186,6397],{},[902,54188,50053],{"encoding":904},[883,54190,54192],{"className":54191},[886],[888,54193,54194],{"xmlns":890},[892,54195,54196,54204],{},[895,54197,54198,54200,54202],{},[898,54199,1875],{},[1677,54201,1679],{},[1810,54203,2544],{},[902,54205,50071],{"encoding":904},".\nRovnovážné množství:\n",[883,54208,54210],{"className":54209},[886],[888,54211,54212],{"xmlns":890},[892,54213,54214,54280],{},[895,54215,54216,54222,54224,54242,54244,54268,54270,54276,54278],{},[1805,54217,54218,54220],{},[898,54219,2470],{},[898,54221,5640],{},[1677,54223,1679],{},[2010,54225,54226,54234],{},[895,54227,54228,54230,54232],{},[898,54229,1779],{},[1677,54231,1906],{},[898,54233,1875],{},[895,54235,54236,54238,54240],{},[898,54237,1823],{},[1677,54239,1906],{},[898,54241,207],{},[1677,54243,1679],{},[2010,54245,54246,54254],{},[895,54247,54248,54250,54252],{},[1810,54249,6599],{},[1677,54251,1906],{},[1810,54253,2544],{},[895,54255,54256,54258,54260,54262,54264,54266],{},[1810,54257,6397],{},[1677,54259,1906],{},[1677,54261,1686],{"stretchy":1685},[1677,54263,1906],{},[1810,54265,1854],{},[1677,54267,1692],{"stretchy":1685},[1677,54269,1679],{},[2010,54271,54272,54274],{},[1810,54273,39410],{},[1810,54275,45797],{},[1677,54277,7288],{},[1810,54279,45802],{},[902,54281,54282],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\doteq 8{,}571.","\nZjistěte změnu ",[883,54285,54287],{"className":54286},[886],[888,54288,54289],{"xmlns":890},[892,54290,54291,54299],{},[895,54292,54293],{},[1805,54294,54295,54297],{},[898,54296,2470],{},[898,54298,5640],{},[902,54300,43794],{"encoding":904}," (a) při změně samotného parametru ",[883,54303,54305],{"className":54304},[886],[888,54306,54307],{"xmlns":890},[892,54308,54309,54313],{},[895,54310,54311],{},[898,54312,1823],{},[902,54314,1823],{"encoding":904},", (b) při současné změně všech čtyř parametrů.",[724,54317,54318],{},[38,54319,54320,54321,2352,54334,2366,54347,10683],{},"Řešení (a) — změna ",[883,54322,54324],{"className":54323},[886],[888,54325,54326],{"xmlns":890},[892,54327,54328,54332],{},[895,54329,54330],{},[898,54331,1823],{},[902,54333,1823],{"encoding":904},[883,54335,54337],{"className":54336},[886],[888,54338,54339],{"xmlns":890},[892,54340,54341,54345],{},[895,54342,54343],{},[1810,54344,6397],{},[902,54346,45837],{"encoding":904},[883,54348,54350],{"className":54349},[886],[888,54351,54352],{"xmlns":890},[892,54353,54354,54358],{},[895,54355,54356],{},[1810,54357,20712],{},[902,54359,45851],{"encoding":904},[724,54361,54362,54363,54427,54428,2385],{},"Pomocí vzorce (2.13) pro ",[883,54364,54366],{"className":54365},[886],[888,54367,54368],{"xmlns":890},[892,54369,54370,54424],{},[895,54371,54372,54392,54394,54396],{},[2006,54373,54374],{"scriptlevel":2008,"displaystyle":1966},[2010,54375,54376,54386],{},[895,54377,54378,54380],{},[898,54379,11260],{"mathvariant":2057},[1805,54381,54382,54384],{},[898,54383,2470],{},[898,54385,5640],{},[895,54387,54388,54390],{},[898,54389,11260],{"mathvariant":2057},[898,54391,1823],{},[1677,54393,1679],{},[1677,54395,1906],{},[2006,54397,54398],{"scriptlevel":2008,"displaystyle":1966},[2010,54399,54400,54408],{},[895,54401,54402,54404,54406],{},[898,54403,1779],{},[1677,54405,1906],{},[898,54407,1875],{},[895,54409,54410,54412,54414,54416,54418],{},[1677,54411,1686],{"stretchy":1685},[898,54413,1823],{},[1677,54415,1906],{},[898,54417,207],{},[1805,54419,54420,54422],{},[1677,54421,1692],{"stretchy":1685},[1810,54423,1812],{},[902,54425,54426],{"encoding":904},"\\dfrac{\\partial Q^E}{\\partial c} = -\\dfrac{b-d}{(c-a)^2}",", resp. ekvivalentně ",[883,54429,54431],{"className":54430},[886],[888,54432,54433],{"xmlns":890},[892,54434,54435,54457],{},[895,54436,54437,54439],{},[1677,54438,1906],{},[2006,54440,54441],{"scriptlevel":2008,"displaystyle":1966},[2010,54442,54443,54449],{},[1805,54444,54445,54447],{},[898,54446,2470],{},[898,54448,5640],{},[895,54450,54451,54453,54455],{},[898,54452,1823],{},[1677,54454,1906],{},[898,54456,207],{},[902,54458,54459],{"encoding":904},"-\\dfrac{Q^E}{c-a}",[883,54461,54463],{"className":54462},[886],[888,54464,54465],{"xmlns":890,"display":29457},[892,54466,54467,54523],{},[895,54468,54469,54471,54477,54479,54481,54497,54499,54501,54503,54505,54507,54513,54515,54517,54519,54521],{},[898,54470,1875],{},[1805,54472,54473,54475],{},[898,54474,2470],{},[898,54476,5640],{},[1677,54478,1679],{},[1677,54480,1906],{},[2010,54482,54483,54489],{},[1805,54484,54485,54487],{},[898,54486,2470],{},[898,54488,5640],{},[895,54490,54491,54493,54495],{},[898,54492,1823],{},[1677,54494,1906],{},[898,54496,207],{},[1969,54498,2668],{},[898,54500,1875],{},[898,54502,1823],{},[1677,54504,1679],{},[1677,54506,1906],{},[2010,54508,54509,54511],{},[1810,54510,45965],{},[1810,54512,45797],{},[1677,54514,2858],{},[1810,54516,2475],{},[1677,54518,7288],{},[1677,54520,1906],{},[1810,54522,45937],{},[902,54524,54525],{"encoding":904},"dQ^E = -\\frac{Q^E}{c - a}\\,dc = -\\frac{8{,}571}{3{,}5}\\cdot 0{,}1 \\doteq -0{,}245.",[724,54527,54528],{},"Nové rovnovážné množství:",[883,54530,54532],{"className":54531},[886],[888,54533,54534],{"xmlns":890,"display":29457},[892,54535,54536,54559],{},[895,54537,54538,54546,54548,54550,54552,54554,54556],{},[10554,54539,54540,54542,54544],{},[898,54541,2470],{},[1810,54543,1959],{},[898,54545,5640],{},[1677,54547,2411],{},[1810,54549,45965],{},[1677,54551,1906],{},[1810,54553,45970],{},[1677,54555,1679],{},[1810,54557,54558],{},"8,326.",[902,54560,54561],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326.",[724,54563,54564,1884,54567,1343,54594,1343,54616,1343,54638,6977,54660,1343,54679,1343,54700,1343,54719,1656],{},[38,54565,54566],{},"Řešení (b) — současná změna všech parametrů:",[883,54568,54570],{"className":54569},[886],[888,54571,54572],{"xmlns":890},[892,54573,54574,54591],{},[895,54575,54576,54578,54580,54582,54584,54586,54588],{},[898,54577,207],{},[1677,54579,2385],{},[1677,54581,1906],{},[1810,54583,1854],{},[1677,54585,2804],{},[1677,54587,1906],{},[1810,54589,54590],{},"2,5",[902,54592,54593],{"encoding":904},"a: -3 \\to -2{,}5",[883,54595,54597],{"className":54596},[886],[888,54598,54599],{"xmlns":890},[892,54600,54601,54613],{},[895,54602,54603,54605,54607,54609,54611],{},[898,54604,1779],{},[1677,54606,2385],{},[1810,54608,6599],{},[1677,54610,2804],{},[1810,54612,16428],{},[902,54614,54615],{"encoding":904},"b: 40 \\to 35",[883,54617,54619],{"className":54618},[886],[888,54620,54621],{"xmlns":890},[892,54622,54623,54635],{},[895,54624,54625,54627,54629,54631,54633],{},[898,54626,1823],{},[1677,54628,2385],{},[1810,54630,6397],{},[1677,54632,2804],{},[1810,54634,20712],{},[902,54636,54637],{"encoding":904},"c: 0{,}5 \\to 0{,}6",[883,54639,54641],{"className":54640},[886],[888,54642,54643],{"xmlns":890},[892,54644,54645,54657],{},[895,54646,54647,54649,54651,54653,54655],{},[898,54648,1875],{},[1677,54650,2385],{},[1810,54652,2544],{},[1677,54654,2804],{},[1810,54656,2585],{},[902,54658,54659],{"encoding":904},"d: 10 \\to 11",[883,54661,54663],{"className":54662},[886],[888,54664,54665],{"xmlns":890},[892,54666,54667,54677],{},[895,54668,54669,54671,54673,54675],{},[898,54670,1875],{},[898,54672,207],{},[1677,54674,1679],{},[1810,54676,6397],{},[902,54678,46003],{"encoding":904},[883,54680,54682],{"className":54681},[886],[888,54683,54684],{"xmlns":890},[892,54685,54686,54698],{},[895,54687,54688,54690,54692,54694,54696],{},[898,54689,1875],{},[898,54691,1779],{},[1677,54693,1679],{},[1677,54695,1906],{},[1810,54697,1909],{},[902,54699,46025],{"encoding":904},[883,54701,54703],{"className":54702},[886],[888,54704,54705],{"xmlns":890},[892,54706,54707,54717],{},[895,54708,54709,54711,54713,54715],{},[898,54710,1875],{},[898,54712,1823],{},[1677,54714,1679],{},[1810,54716,2475],{},[902,54718,46045],{"encoding":904},[883,54720,54722],{"className":54721},[886],[888,54723,54724],{"xmlns":890},[892,54725,54726,54736],{},[895,54727,54728,54730,54732,54734],{},[898,54729,1875],{},[898,54731,1875],{},[1677,54733,1679],{},[1810,54735,1959],{},[902,54737,46065],{"encoding":904},[724,54739,54740,54741,54799],{},"Totální diferenciál ",[883,54742,54744],{"className":54743},[886],[888,54745,54746],{"xmlns":890},[892,54747,54748,54796],{},[895,54749,54750,54756,54758,54760,54762,54764,54766,54768,54770,54772,54774,54776],{},[1805,54751,54752,54754],{},[898,54753,2470],{},[898,54755,5640],{},[1677,54757,1686],{"stretchy":1685},[898,54759,207],{},[1677,54761,1967],{"separator":1966},[898,54763,1779],{},[1677,54765,1967],{"separator":1966},[898,54767,1823],{},[1677,54769,1967],{"separator":1966},[898,54771,1875],{},[1677,54773,1692],{"stretchy":1685},[1677,54775,1679],{},[2006,54777,54778],{"scriptlevel":2008,"displaystyle":1966},[2010,54779,54780,54788],{},[895,54781,54782,54784,54786],{},[898,54783,1779],{},[1677,54785,1906],{},[898,54787,1875],{},[895,54789,54790,54792,54794],{},[898,54791,1823],{},[1677,54793,1906],{},[898,54795,207],{},[902,54797,54798],{"encoding":904},"Q^E(a, b, c, d) = \\dfrac{b - d}{c - a}"," podle (2.11) a (2.12):",[883,54801,54803],{"className":54802},[886],[888,54804,54805],{"xmlns":890,"display":29457},[892,54806,54807,54927],{},[895,54808,54809,54811,54817,54819,54845,54847,54849,54851,54853,54865,54867,54869,54871,54873,54899,54901,54903,54905,54907,54919,54921,54923,54925],{},[898,54810,1875],{},[1805,54812,54813,54815],{},[898,54814,2470],{},[898,54816,5640],{},[1677,54818,1679],{},[2010,54820,54821,54829],{},[895,54822,54823,54825,54827],{},[898,54824,1779],{},[1677,54826,1906],{},[898,54828,1875],{},[895,54830,54831,54833,54835,54837,54839],{},[1677,54832,1686],{"stretchy":1685},[898,54834,1823],{},[1677,54836,1906],{},[898,54838,207],{},[1805,54840,54841,54843],{},[1677,54842,1692],{"stretchy":1685},[1810,54844,1812],{},[1969,54846,2668],{},[898,54848,1875],{},[898,54850,207],{},[1677,54852,1776],{},[2010,54854,54855,54857],{},[1810,54856,1959],{},[895,54858,54859,54861,54863],{},[898,54860,1823],{},[1677,54862,1906],{},[898,54864,207],{},[1969,54866,2668],{},[898,54868,1875],{},[898,54870,1779],{},[1677,54872,1906],{},[2010,54874,54875,54883],{},[895,54876,54877,54879,54881],{},[898,54878,1779],{},[1677,54880,1906],{},[898,54882,1875],{},[895,54884,54885,54887,54889,54891,54893],{},[1677,54886,1686],{"stretchy":1685},[898,54888,1823],{},[1677,54890,1906],{},[898,54892,207],{},[1805,54894,54895,54897],{},[1677,54896,1692],{"stretchy":1685},[1810,54898,1812],{},[1969,54900,2668],{},[898,54902,1875],{},[898,54904,1823],{},[1677,54906,1906],{},[2010,54908,54909,54911],{},[1810,54910,1959],{},[895,54912,54913,54915,54917],{},[898,54914,1823],{},[1677,54916,1906],{},[898,54918,207],{},[1969,54920,2668],{},[898,54922,1875],{},[898,54924,1875],{},[898,54926,1656],{"mathvariant":2057},[902,54928,54929],{"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.",[724,54931,54932,54933,1343,54955,1343,54986,2832],{},"Dosazením číselných hodnot (",[883,54934,54936],{"className":54935},[886],[888,54937,54938],{"xmlns":890},[892,54939,54940,54952],{},[895,54941,54942,54944,54946,54948,54950],{},[898,54943,1823],{},[1677,54945,1906],{},[898,54947,207],{},[1677,54949,1679],{},[1810,54951,45797],{},[902,54953,54954],{"encoding":904},"c - a = 3{,}5",[883,54956,54958],{"className":54957},[886],[888,54959,54960],{"xmlns":890},[892,54961,54962,54983],{},[895,54963,54964,54966,54968,54970,54972,54978,54980],{},[1677,54965,1686],{"stretchy":1685},[898,54967,1823],{},[1677,54969,1906],{},[898,54971,207],{},[1805,54973,54974,54976],{},[1677,54975,1692],{"stretchy":1685},[1810,54977,1812],{},[1677,54979,1679],{},[1810,54981,54982],{},"12,25",[902,54984,54985],{"encoding":904},"(c-a)^2 = 12{,}25",[883,54987,54989],{"className":54988},[886],[888,54990,54991],{"xmlns":890},[892,54992,54993,55005],{},[895,54994,54995,54997,54999,55001,55003],{},[898,54996,1779],{},[1677,54998,1906],{},[898,55000,1875],{},[1677,55002,1679],{},[1810,55004,39410],{},[902,55006,55007],{"encoding":904},"b - d = 30",[883,55009,55011],{"className":55010},[886],[888,55012,55013],{"xmlns":890,"display":29457},[892,55014,55015,55116],{},[895,55016,55017,55019,55025,55027,55035,55037,55039,55041,55043,55051,55053,55055,55057,55059,55061,55069,55071,55073,55075,55077,55085,55087,55089,55091,55093,55096,55098,55101,55103,55105,55107,55110,55112,55114],{},[898,55018,1875],{},[1805,55020,55021,55023],{},[898,55022,2470],{},[898,55024,5640],{},[1677,55026,2411],{},[2006,55028,55029],{"scriptlevel":2008,"displaystyle":1685},[2010,55030,55031,55033],{},[1810,55032,39410],{},[1810,55034,54982],{},[1677,55036,1686],{"stretchy":1685},[1810,55038,6397],{},[1677,55040,1692],{"stretchy":1685},[1677,55042,1776],{},[2006,55044,55045],{"scriptlevel":2008,"displaystyle":1685},[2010,55046,55047,55049],{},[1810,55048,1959],{},[1810,55050,45797],{},[1677,55052,1686],{"stretchy":1685},[1677,55054,1906],{},[1810,55056,1909],{},[1677,55058,1692],{"stretchy":1685},[1677,55060,1906],{},[2006,55062,55063],{"scriptlevel":2008,"displaystyle":1685},[2010,55064,55065,55067],{},[1810,55066,39410],{},[1810,55068,54982],{},[1677,55070,1686],{"stretchy":1685},[1810,55072,2475],{},[1677,55074,1692],{"stretchy":1685},[1677,55076,1906],{},[2006,55078,55079],{"scriptlevel":2008,"displaystyle":1685},[2010,55080,55081,55083],{},[1810,55082,1959],{},[1810,55084,45797],{},[1677,55086,1686],{"stretchy":1685},[1810,55088,1959],{},[1677,55090,1692],{"stretchy":1685},[1677,55092,7288],{},[1810,55094,55095],{},"1,224",[1677,55097,1906],{},[1810,55099,55100],{},"1,429",[1677,55102,1906],{},[1810,55104,45970],{},[1677,55106,1906],{},[1810,55108,55109],{},"0,286",[1677,55111,7288],{},[1677,55113,1906],{},[1810,55115,46216],{},[902,55117,55118],{"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.",[724,55120,31456,55121,1656],{},[883,55122,55124],{"className":55123},[886],[888,55125,55126],{"xmlns":890},[892,55127,55128,55150],{},[895,55129,55130,55138,55140,55142,55144,55146,55148],{},[10554,55131,55132,55134,55136],{},[898,55133,2470],{},[1810,55135,1959],{},[898,55137,5640],{},[1677,55139,2411],{},[1810,55141,45965],{},[1677,55143,1906],{},[1810,55145,46247],{},[1677,55147,7288],{},[1810,55149,46252],{},[902,55151,55152],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 \\doteq 7{,}836",[5254,55154,55155],{},[724,55156,55157,55159,55160,55181,55182,55208,55209,55212,55213,55309,55310,55333,55334,55350],{},[883,55158,5800],{}," Pozn. k přepisu učebnice\nV původním skenu přednášky byla u části (b) uvedena hodnota ",[883,55161,55163],{"className":55162},[886],[888,55164,55165],{"xmlns":890},[892,55166,55167,55179],{},[895,55168,55169,55171,55173,55175,55177],{},[898,55170,2570],{"mathvariant":2057},[898,55172,2470],{},[1677,55174,2411],{},[1677,55176,1906],{},[1810,55178,46282],{},[902,55180,46285],{"encoding":904},", což neodpovídá součtu dílčích derivací při daných přírůstcích. Podle vlastního přepočtu vychází ",[883,55183,55185],{"className":55184},[886],[888,55186,55187],{"xmlns":890},[892,55188,55189,55205],{},[895,55190,55191,55193,55199,55201,55203],{},[898,55192,1875],{},[1805,55194,55195,55197],{},[898,55196,2470],{},[898,55198,5640],{},[1677,55200,7288],{},[1677,55202,1906],{},[1810,55204,46247],{},[902,55206,55207],{"encoding":904},"dQ^E \\doteq -0{,}735",". Totální diferenciál je navíc pouze ",[38,55210,55211],{},"lineární aproximací","; přesná změna zjištěná ze změněného vzorce\n",[883,55214,55216],{"className":55215},[886],[888,55217,55218],{"xmlns":890},[892,55219,55220,55306],{},[895,55221,55222,55230,55232,55266,55268,55292,55294,55301,55303],{},[10554,55223,55224,55226,55228],{},[898,55225,2470],{},[1810,55227,1959],{},[898,55229,5640],{},[1677,55231,1679],{},[2010,55233,55234,55250],{},[895,55235,55236,55242,55244],{},[1805,55237,55238,55240],{},[898,55239,1779],{},[1677,55241,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,55243,1906],{},[1805,55245,55246,55248],{},[898,55247,1875],{},[1677,55249,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[895,55251,55252,55258,55260],{},[1805,55253,55254,55256],{},[898,55255,1823],{},[1677,55257,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,55259,1906],{},[1805,55261,55262,55264],{},[898,55263,207],{},[1677,55265,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,55267,1679],{},[2010,55269,55270,55278],{},[895,55271,55272,55274,55276],{},[1810,55273,16428],{},[1677,55275,1906],{},[1810,55277,2585],{},[895,55279,55280,55282,55284,55286,55288,55290],{},[1810,55281,20712],{},[1677,55283,1906],{},[1677,55285,1686],{"stretchy":1685},[1677,55287,1906],{},[1810,55289,54590],{},[1677,55291,1692],{"stretchy":1685},[1677,55293,1679],{},[2010,55295,55296,55298],{},[1810,55297,43191],{},[1810,55299,55300],{},"3,1",[1677,55302,7288],{},[1810,55304,55305],{},"7,742",[902,55307,55308],{"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 ",[883,55311,55313],{"className":55312},[886],[888,55314,55315],{"xmlns":890},[892,55316,55317,55330],{},[895,55318,55319,55321,55323,55325,55327],{},[898,55320,2570],{"mathvariant":2057},[898,55322,2470],{},[1677,55324,7288],{},[1677,55326,1906],{},[1810,55328,55329],{},"0,829",[902,55331,55332],{"encoding":904},"\\Delta Q \\doteq -0{,}829"," — dobře konzistentní s diferenciálem. Hodnota ",[883,55335,55337],{"className":55336},[886],[888,55338,55339],{"xmlns":890},[892,55340,55341,55347],{},[895,55342,55343,55345],{},[1677,55344,1906],{},[1810,55346,46282],{},[902,55348,55349],{"encoding":904},"-2{,}69"," je tedy pravděpodobně chyba v zápisu.",[724,55352,55353],{},[614,55354,55355,55356,55369],{},"Příklad 2.11 je primárně o multiplikátorech pro ",[883,55357,55359],{"className":55358},[886],[888,55360,55361],{"xmlns":890},[892,55362,55363,55367],{},[895,55364,55365],{},[898,55366,2470],{},[902,55368,2470],{"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.",[198,55371,55373,55374],{"id":55372},"příklad-213-numerický-výpočet-psps","Příklad 2.13 — numerický výpočet ",[883,55375,55377],{"className":55376},[886],[888,55378,55379],{"xmlns":890},[892,55380,55381,55387],{},[895,55382,55383,55385],{},[898,55384,5325],{},[898,55386,10061],{},[902,55388,46360],{"encoding":904},[5254,55390,55391],{},[724,55392,55393,55395,55396,55430,55431,55453],{},[883,55394,54086],{}," Zadání\nPro nabídku ",[883,55397,55399],{"className":55398},[886],[888,55400,55401],{"xmlns":890},[892,55402,55403,55427],{},[895,55404,55405,55407,55409,55411,55413,55415,55417,55419,55421,55423,55425],{},[898,55406,5325],{},[1677,55408,1679],{},[898,55410,10061],{},[1677,55412,1686],{"stretchy":1685},[898,55414,2470],{},[1677,55416,1692],{"stretchy":1685},[1677,55418,1679],{},[1810,55420,2544],{},[1677,55422,1776],{},[1810,55424,1812],{},[898,55426,2470],{},[902,55428,55429],{"encoding":904},"P = S(Q) = 10 + 2Q"," a množství ",[883,55432,55434],{"className":55433},[886],[888,55435,55436],{"xmlns":890},[892,55437,55438,55450],{},[895,55439,55440,55446,55448],{},[1953,55441,55442,55444],{},[898,55443,2470],{},[1810,55445,2008],{},[1677,55447,1679],{},[1810,55449,2544],{},[902,55451,55452],{"encoding":904},"Q_0 = 10"," vypočítejte přebytek výrobce.",[724,55455,55456],{},[38,55457,24161],{},[724,55459,55460],{},"Odpovídající cena:",[883,55462,55464],{"className":55463},[886],[888,55465,55466],{"xmlns":890,"display":29457},[892,55467,55468,55503],{},[895,55469,55470,55476,55478,55480,55482,55484,55486,55488,55490,55492,55494,55496,55498,55500],{},[1953,55471,55472,55474],{},[898,55473,5325],{},[1810,55475,2008],{},[1677,55477,1679],{},[898,55479,10061],{},[1677,55481,1686],{"stretchy":1685},[1810,55483,2544],{},[1677,55485,1692],{"stretchy":1685},[1677,55487,1679],{},[1810,55489,2544],{},[1677,55491,1776],{},[1810,55493,1812],{},[1677,55495,2858],{},[1810,55497,2544],{},[1677,55499,1679],{},[1810,55501,55502],{},"30.",[902,55504,55505],{"encoding":904},"P_0 = S(10) = 10 + 2\\cdot 10 = 30.",[724,55507,55508],{},"Dle vzorce (2.15):",[883,55510,55512],{"className":55511},[886],[888,55513,55514],{"xmlns":890,"display":29457},[892,55515,55516,55624],{},[895,55517,55518,55520,55522,55524,55526,55528,55530,55536,55542,55544,55552,55554,55556,55558,55560,55562,55564,55566,55568,55570,55572,55574,55576,55578,55580,55583,55585,55587,55589,55595,55603,55605,55607,55609,55611,55613,55615,55617,55619,55621],{},[898,55519,5325],{},[898,55521,10061],{},[1677,55523,1686],{"stretchy":1685},[1810,55525,2544],{},[1677,55527,1692],{"stretchy":1685},[1677,55529,1679],{},[1953,55531,55532,55534],{},[898,55533,5325],{},[1810,55535,2008],{},[1953,55537,55538,55540],{},[898,55539,2470],{},[1810,55541,2008],{},[1677,55543,1906],{},[10554,55545,55546,55548,55550],{},[1677,55547,12558],{},[1810,55549,2008],{},[1810,55551,2544],{},[1677,55553,1686],{"stretchy":1685},[1810,55555,2544],{},[1677,55557,1776],{},[1810,55559,1812],{},[898,55561,2470],{},[1677,55563,1692],{"stretchy":1685},[1969,55565,2668],{},[898,55567,1875],{},[898,55569,2470],{},[1677,55571,1679],{},[1810,55573,2544],{},[1677,55575,2858],{},[1810,55577,39410],{},[1677,55579,1906],{},[1677,55581,2167],{"fence":1685,"stretchy":1966,"minsize":55582,"maxsize":55582},"1.8em",[1810,55584,2544],{},[898,55586,2470],{},[1677,55588,1776],{},[1805,55590,55591,55593],{},[898,55592,2470],{},[1810,55594,1812],{},[10554,55596,55597,55599,55601],{},[1677,55598,2182],{"fence":1685,"stretchy":1966,"minsize":55582,"maxsize":55582},[1810,55600,2008],{},[1810,55602,2544],{},[1677,55604,1679],{},[1810,55606,31472],{},[1677,55608,1906],{},[1677,55610,1686],{"stretchy":1685},[1810,55612,2771],{},[1677,55614,1776],{},[1810,55616,2771],{},[1677,55618,1692],{"stretchy":1685},[1677,55620,1679],{},[1810,55622,55623],{},"100.",[902,55625,55626],{"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.",[724,55628,55629,55630,55651,55652,55672],{},"Přebytek výrobce při množství ",[883,55631,55633],{"className":55632},[886],[888,55634,55635],{"xmlns":890},[892,55636,55637,55649],{},[895,55638,55639,55645,55647],{},[1953,55640,55641,55643],{},[898,55642,2470],{},[1810,55644,2008],{},[1677,55646,1679],{},[1810,55648,2544],{},[902,55650,55452],{"encoding":904}," je tedy ",[883,55653,55655],{"className":55654},[886],[888,55656,55657],{"xmlns":890},[892,55658,55659,55669],{},[895,55660,55661,55663,55665,55667],{},[898,55662,5325],{},[898,55664,10061],{},[1677,55666,1679],{},[1810,55668,2771],{},[902,55670,55671],{"encoding":904},"PS = 100"," (peněžních jednotek).",[38361,55674],{},[115,55676,55678],{"id":55677},"cheat-sheet","Cheat sheet",[16,55680,55681,55694],{},[19,55682,55683],{},[22,55684,55685,55688,55691],{},[25,55686,55687],{},"Veličina",[25,55689,55690],{},"Vzorec",[25,55692,55693],{},"Geometrie",[30,55695,55696,55814,55928,55996],{},[22,55697,55698,55726,55782],{},[35,55699,55700],{},[883,55701,55703],{"className":55702},[886],[888,55704,55705],{"xmlns":890},[892,55706,55707,55723],{},[895,55708,55709,55711,55713,55715,55721],{},[898,55710,2458],{},[898,55712,10061],{},[1677,55714,1686],{"stretchy":1685},[1953,55716,55717,55719],{},[898,55718,2470],{},[1810,55720,2008],{},[1677,55722,1692],{"stretchy":1685},[902,55724,55725],{"encoding":904},"CS(Q_0)",[35,55727,55728],{},[883,55729,55731],{"className":55730},[886],[888,55732,55733],{"xmlns":890},[892,55734,55735,55779],{},[895,55736,55737],{},[2006,55738,55739,55751,55753,55755,55757,55759,55761,55763,55765,55767,55773],{"scriptlevel":2008,"displaystyle":1966},[10554,55740,55741,55743,55745],{},[1677,55742,12558],{},[1810,55744,2008],{},[1953,55746,55747,55749],{},[898,55748,2470],{},[1810,55750,2008],{},[898,55752,5571],{},[1677,55754,1686],{"stretchy":1685},[898,55756,2470],{},[1677,55758,1692],{"stretchy":1685},[1969,55760,2668],{},[898,55762,1875],{},[898,55764,2470],{},[1677,55766,1906],{},[1953,55768,55769,55771],{},[898,55770,5325],{},[1810,55772,2008],{},[1953,55774,55775,55777],{},[898,55776,2470],{},[1810,55778,2008],{},[902,55780,55781],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0",[35,55783,55784,55785,55788,55789,55792,55793],{},"plocha ",[38,55786,55787],{},"pod"," křivkou poptávky, ",[38,55790,55791],{},"nad"," čárou ",[883,55794,55796],{"className":55795},[886],[888,55797,55798],{"xmlns":890},[892,55799,55800,55812],{},[895,55801,55802,55804,55806],{},[898,55803,5325],{},[1677,55805,1679],{},[1953,55807,55808,55810],{},[898,55809,5325],{},[1810,55811,2008],{},[902,55813,53068],{"encoding":904},[22,55815,55816,55844,55900],{},[35,55817,55818],{},[883,55819,55821],{"className":55820},[886],[888,55822,55823],{"xmlns":890},[892,55824,55825,55841],{},[895,55826,55827,55829,55831,55833,55839],{},[898,55828,5325],{},[898,55830,10061],{},[1677,55832,1686],{"stretchy":1685},[1953,55834,55835,55837],{},[898,55836,2470],{},[1810,55838,2008],{},[1677,55840,1692],{"stretchy":1685},[902,55842,55843],{"encoding":904},"PS(Q_0)",[35,55845,55846],{},[883,55847,55849],{"className":55848},[886],[888,55850,55851],{"xmlns":890},[892,55852,55853,55897],{},[895,55854,55855],{},[2006,55856,55857,55863,55869,55871,55883,55885,55887,55889,55891,55893,55895],{"scriptlevel":2008,"displaystyle":1966},[1953,55858,55859,55861],{},[898,55860,5325],{},[1810,55862,2008],{},[1953,55864,55865,55867],{},[898,55866,2470],{},[1810,55868,2008],{},[1677,55870,1906],{},[10554,55872,55873,55875,55877],{},[1677,55874,12558],{},[1810,55876,2008],{},[1953,55878,55879,55881],{},[898,55880,2470],{},[1810,55882,2008],{},[898,55884,10061],{},[1677,55886,1686],{"stretchy":1685},[898,55888,2470],{},[1677,55890,1692],{"stretchy":1685},[1969,55892,2668],{},[898,55894,1875],{},[898,55896,2470],{},[902,55898,55899],{"encoding":904},"\\displaystyle P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ",[35,55901,55784,55902,55904,55905,55792,55907],{},[38,55903,55791],{}," křivkou nabídky, ",[38,55906,55787],{},[883,55908,55910],{"className":55909},[886],[888,55911,55912],{"xmlns":890},[892,55913,55914,55926],{},[895,55915,55916,55918,55920],{},[898,55917,5325],{},[1677,55919,1679],{},[1953,55921,55922,55924],{},[898,55923,5325],{},[1810,55925,2008],{},[902,55927,53068],{"encoding":904},[22,55929,55930,55933,55960],{},[35,55931,55932],{},"Výdaje \u002F tržby",[35,55934,55935],{},[883,55936,55938],{"className":55937},[886],[888,55939,55940],{"xmlns":890},[892,55941,55942,55958],{},[895,55943,55944,55950,55952],{},[1953,55945,55946,55948],{},[898,55947,5325],{},[1810,55949,2008],{},[1677,55951,2858],{},[1953,55953,55954,55956],{},[898,55955,2470],{},[1810,55957,2008],{},[902,55959,53928],{"encoding":904},[35,55961,55962,55963],{},"obdélník ",[883,55964,55966],{"className":55965},[886],[888,55967,55968],{"xmlns":890},[892,55969,55970,55994],{},[895,55971,55972,55974,55976,55982,55984,55986,55988],{},[1810,55973,2008],{},[1969,55975,2668],{},[1953,55977,55978,55980],{},[898,55979,2470],{},[1810,55981,2008],{},[1969,55983,2668],{},[898,55985,5643],{},[1969,55987,2668],{},[1953,55989,55990,55992],{},[898,55991,5325],{},[1810,55993,2008],{},[902,55995,52548],{"encoding":904},[22,55997,55998,56001,56024],{},[35,55999,56000],{},"Celkový přebytek",[35,56002,56003],{},[883,56004,56006],{"className":56005},[886],[888,56007,56008],{"xmlns":890},[892,56009,56010,56022],{},[895,56011,56012,56014,56016,56018,56020],{},[898,56013,2458],{},[898,56015,10061],{},[1677,56017,1776],{},[898,56019,5325],{},[898,56021,10061],{},[902,56023,52286],{"encoding":904},[35,56025,56026],{},"součet obou ploch v rovnováze",[38361,56028],{},[115,56030,17110],{"id":17109},[120,56032,56033,56055,56077,56121,56165,56228,56256],{},[123,56034,56035,11413,56037,1343,56052,56054],{},[38,56036,46325],{},[883,56038,56040],{"className":56039},[886],[888,56041,56042],{"xmlns":890},[892,56043,56044,56050],{},[895,56045,56046,56048],{},[898,56047,2458],{},[898,56049,10061],{},[902,56051,46341],{"encoding":904},[614,56053,46379],{},") — rozdíl mezi ochotou platit a skutečnou platbou, vzorec (2.14).",[123,56056,56057,11413,56059,1343,56074,56076],{},[38,56058,46472],{},[883,56060,56062],{"className":56061},[886],[888,56063,56064],{"xmlns":890},[892,56065,56066,56072],{},[895,56067,56068,56070],{},[898,56069,5325],{},[898,56071,10061],{},[902,56073,46360],{"encoding":904},[614,56075,46475],{},") — rozdíl mezi tržbou a minimální cenou dle nabídky, vzorec (2.15).",[123,56078,56079,8403,56082,1656],{},[38,56080,56081],{},"Ochota platit",[883,56083,56085],{"className":56084},[886],[888,56086,56087],{"xmlns":890},[892,56088,56089,56119],{},[895,56090,56091],{},[2006,56092,56093,56105,56107,56109,56111,56113,56115,56117],{"scriptlevel":2008,"displaystyle":1966},[10554,56094,56095,56097,56099],{},[1677,56096,12558],{},[1810,56098,2008],{},[1953,56100,56101,56103],{},[898,56102,2470],{},[1810,56104,2008],{},[898,56106,5571],{},[1677,56108,1686],{"stretchy":1685},[898,56110,2470],{},[1677,56112,1692],{"stretchy":1685},[1969,56114,2668],{},[898,56116,1875],{},[898,56118,2470],{},[902,56120,52916],{"encoding":904},[123,56122,56123,8403,56126,1656],{},[38,56124,56125],{},"Minimální cena výrobce",[883,56127,56129],{"className":56128},[886],[888,56130,56131],{"xmlns":890},[892,56132,56133,56163],{},[895,56134,56135],{},[2006,56136,56137,56149,56151,56153,56155,56157,56159,56161],{"scriptlevel":2008,"displaystyle":1966},[10554,56138,56139,56141,56143],{},[1677,56140,12558],{},[1810,56142,2008],{},[1953,56144,56145,56147],{},[898,56146,2470],{},[1810,56148,2008],{},[898,56150,10061],{},[1677,56152,1686],{"stretchy":1685},[898,56154,2470],{},[1677,56156,1692],{"stretchy":1685},[1969,56158,2668],{},[898,56160,1875],{},[898,56162,2470],{},[902,56164,53558],{"encoding":904},[123,56166,56167,8403,56170,54059,56195,5306],{},[38,56168,56169],{},"Výdaje spotřebitele \u002F tržby výrobce",[883,56171,56173],{"className":56172},[886],[888,56174,56175],{"xmlns":890},[892,56176,56177,56193],{},[895,56178,56179,56185,56187],{},[1953,56180,56181,56183],{},[898,56182,5325],{},[1810,56184,2008],{},[1969,56186,2668],{},[1953,56188,56189,56191],{},[898,56190,2470],{},[1810,56192,2008],{},[902,56194,52994],{"encoding":904},[883,56196,56198],{"className":56197},[886],[888,56199,56200],{"xmlns":890},[892,56201,56202,56226],{},[895,56203,56204,56206,56208,56214,56216,56218,56220],{},[1810,56205,2008],{},[1969,56207,2668],{},[1953,56209,56210,56212],{},[898,56211,2470],{},[1810,56213,2008],{},[1969,56215,2668],{},[898,56217,5643],{},[1969,56219,2668],{},[1953,56221,56222,56224],{},[898,56223,5325],{},[1810,56225,2008],{},[902,56227,52548],{"encoding":904},[123,56229,56230,56233,56234,56255],{},[38,56231,56232],{},"Celkový přebytek trhu"," — součet ",[883,56235,56237],{"className":56236},[886],[888,56238,56239],{"xmlns":890},[892,56240,56241,56253],{},[895,56242,56243,56245,56247,56249,56251],{},[898,56244,2458],{},[898,56246,10061],{},[1677,56248,1776],{},[898,56250,5325],{},[898,56252,10061],{},[902,56254,52286],{"encoding":904}," v rovnovážném bodě.",[123,56257,56258,56260,56261,1343,56274,56287,56288,1656],{},[38,56259,2125],{}," — plochy ohraničené křivkami ",[883,56262,56264],{"className":56263},[886],[888,56265,56266],{"xmlns":890},[892,56267,56268,56272],{},[895,56269,56270],{},[898,56271,5571],{},[902,56273,5571],{"encoding":904},[883,56275,56277],{"className":56276},[886],[888,56278,56279],{"xmlns":890},[892,56280,56281,56285],{},[895,56282,56283],{},[898,56284,10061],{},[902,56286,10061],{"encoding":904}," a přímkou ",[883,56289,56291],{"className":56290},[886],[888,56292,56293],{"xmlns":890},[892,56294,56295,56307],{},[895,56296,56297,56299,56301],{},[898,56298,5325],{},[1677,56300,1679],{},[1953,56302,56303,56305],{},[898,56304,5325],{},[1810,56306,2008],{},[902,56308,53068],{"encoding":904},[38361,56310],{},[115,56312,56314],{"id":56313},"dopad-daně-na-přebytky-a-mrtvá-ztráta","Dopad daně na přebytky a mrtvá ztráta",[724,56316,56317,56318,56331,56332,56349],{},"Uvalení jednotkové daně ",[883,56319,56321],{"className":56320},[886],[888,56322,56323],{"xmlns":890},[892,56324,56325,56329],{},[895,56326,56327],{},[898,56328,2455],{},[902,56330,2455],{"encoding":904}," na trh posouvá rovnovážné množství pod ",[883,56333,56335],{"className":56334},[886],[888,56336,56337],{"xmlns":890},[892,56338,56339,56347],{},[895,56340,56341],{},[1805,56342,56343,56345],{},[898,56344,2470],{},[898,56346,5640],{},[902,56348,43794],{"encoding":904}," a rozkládá původní plochu přebytků na nové části.",[724,56351,56352],{},[2240,56353],{"alt":56354,"className":56355,"src":56356},"imek-prebytky-s-dani-deadweight",[210,2244],"\u002Fwiki-assets\u002Fimek-prebytky-s-dani-deadweight.jpeg",[724,56358,56359,56360,56375,56376,56391,56392,54059,56395,56419,56420,11413,56423,56426,56427,1656],{},"Přebytek spotřebitele ",[883,56361,56363],{"className":56362},[886],[888,56364,56365],{"xmlns":890},[892,56366,56367,56373],{},[895,56368,56369,56371],{},[898,56370,2458],{},[898,56372,10061],{},[902,56374,46341],{"encoding":904}," se zmenší (spotřebitelé platí víc a nakupují méně), přebytek výrobce ",[883,56377,56379],{"className":56378},[886],[888,56380,56381],{"xmlns":890},[892,56382,56383,56389],{},[895,56384,56385,56387],{},[898,56386,5325],{},[898,56388,10061],{},[902,56390,46360],{"encoding":904}," se rovněž zmenší (výrobci obdrží po odvodu méně). Stát získává ",[38,56393,56394],{},"daňový příjem",[883,56396,56398],{"className":56397},[886],[888,56399,56400],{"xmlns":890},[892,56401,56402,56416],{},[895,56403,56404,56406,56408],{},[898,56405,2455],{},[1677,56407,2858],{},[10554,56409,56410,56412,56414],{},[898,56411,2470],{},[1810,56413,1959],{},[898,56415,5640],{},[902,56417,56418],{"encoding":904},"T \\cdot Q_1^E","). Zbývající část původních přebytků — ",[38,56421,56422],{},"mrtvá ztráta",[614,56424,56425],{},"deadweight loss",", DWL) — je čistým úbytkem blahobytu, který nikdo neinkasuje, a je důsledkem transakcí, které se kvůli dani vůbec neuskuteční. Detailní rozbor viz ",[207,56428,811],{"className":56429,"dataFsResolvedFilePath":809,"href":810},[210],[38361,56431],{},[115,56433,3473],{"id":3472},[120,56435,56436,56443,56455,56462,56469],{},[123,56437,56438,1884,56440],{},[38,56439,17612],{},[207,56441,802],{"className":56442,"dataFsResolvedFilePath":800,"href":801},[210],[123,56444,56445,1884,56447,56450,56451,56454],{},[38,56446,38065],{},[207,56448,775],{"className":56449,"dataFsResolvedFilePath":773,"href":774},[210]," (určitý integrál, plocha pod křivkou), ",[207,56452,2038],{"className":56453,"dataFsResolvedFilePath":764,"href":765},[210]," (monotonie křivek)",[123,56456,56457,1884,56459],{},[38,56458,17622],{},[207,56460,3504],{"className":56461,"dataFsResolvedFilePath":827,"href":828},[210],[123,56463,56464,1884,56466],{},[38,56465,52149],{},[207,56467,52153],{"className":56468,"dataFsResolvedFilePath":745,"href":746},[210],[123,56470,56471,1884,56473],{},[38,56472,17594],{},[207,56474,17598],{"className":56475,"dataFsResolvedFilePath":1641,"href":1642},[210],{"title":641,"searchDepth":642,"depth":642,"links":56477},[56478,56479,56484,56489,56494,56495,56496,56497],{"id":52345,"depth":642,"text":1241},{"id":52689,"depth":642,"text":56480,"children":56481},"Přebytek spotřebitele (CSCS)",[56482,56483],{"id":52708,"depth":649,"text":52709},{"id":2124,"depth":649,"text":2125},{"id":53284,"depth":642,"text":56485,"children":56486},"Přebytek výrobce (PSPS)",[56487,56488],{"id":53303,"depth":649,"text":53304},{"id":53466,"depth":649,"text":2125},{"id":54074,"depth":642,"text":54075,"children":56490},[56491,56492],{"id":54078,"depth":649,"text":54079},{"id":55372,"depth":649,"text":56493},"Příklad 2.13 — numerický výpočet PSPS",{"id":55677,"depth":642,"text":55678},{"id":17109,"depth":642,"text":17110},{"id":56313,"depth":642,"text":56314},{"id":3472,"depth":642,"text":3473},{},"\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce",{"title":820,"description":641},[1138,1135],"topics\u002Fprebytek-spotrebitele-vyrobce",[1128,52215,56504,56505,13378,17630,56506,56507],"cs","ps","spotrebitel","vyrobce","FhK0gkf2tjMxSgO0-74OuedOn6U35QtJczf-f255pZs",{"id":56510,"title":56511,"body":56512,"course":1128,"courses":659,"created":10944,"description":641,"extension":661,"meta":75841,"navigation":664,"path":75842,"seo":75843,"sources":75844,"stem":75845,"tags":75846,"type":3538,"updated":677,"__hash__":75852},"topics\u002Ftopics\u002Fprijem-naklady-zisk.md","Příjem, náklady, zisk a nabídka firmy",{"type":9,"value":56513,"toc":75805},[56514,56517,56703,56705,56796,56801,57127,57131,57138,57142,57187,57254,57285,57335,57370,57374,57433,57438,57504,57622,57724,57728,57751,57829,57872,57876,57905,57972,57978,58092,58096,58176,58213,58265,58463,58527,58614,58618,58621,58700,58703,58821,58840,58905,58909,59001,59069,59110,59164,59232,59269,59273,59331,59361,59572,59644,59696,59862,59955,59990,59994,59998,60035,60100,60155,60159,60182,60271,60375,60444,60448,60545,60658,60714,60768,60826,60887,60890,60926,60991,61021,61250,61308,61342,61346,61373,61452,61566,61587,61666,61668,61776,61780,61918,62240,62244,62247,62251,62300,62304,62558,62710,62717,62790,62974,62979,63322,63326,63349,63351,63372,63431,63441,63490,63632,63706,63801,63916,64014,64132,64136,64205,64210,64322,64467,64518,64630,64672,64676,64696,64757,64784,64846,64850,64872,64941,65221,65228,65258,65265,65458,65462,65540,65545,65621,65624,65712,65788,65855,65904,66007,66080,66201,66552,66665,66767,66771,66774,66781,66784,66820,66879,66888,67037,67261,67265,67328,67507,67599,67654,67658,67714,67784,67836,67857,67938,67941,68016,68060,68064,68105,68148,68174,68178,68249,68345,68407,68459,68562,68640,68663,68692,68696,68862,68979,69051,69366,69526,69530,69581,69643,69678,69708,69808,69850,70019,70024,70120,70158,70162,70281,70582,70584,70619,70623,70627,70755,70887,71209,71397,71475,71479,71784,71897,72043,72228,72334,72566,72681,72763,72882,72980,73021,73025,73080,73224,73378,73538,73631,73825,74137,74268,74397,74401,74473,74515,74566,74568,75763,75765],[12,56515,56511],{"id":56516},"příjem-náklady-zisk-a-nabídka-firmy",[5254,56518,56519],{},[724,56520,56521,5261,56523,1884,56526,56541,56542,1884,56545,56560,56561,1884,56564,56592,56593,56615,56616,56640,56641,56663,56664,56667,56668,56684,56685,1656],{},[883,56522,5260],{},[38,56524,56525],{},"Příjem",[883,56527,56529],{"className":56528},[886],[888,56530,56531],{"xmlns":890},[892,56532,56533,56539],{},[895,56534,56535,56537],{},[898,56536,2455],{},[898,56538,5382],{},[902,56540,5482],{"encoding":904}," je to, co firma inkasuje (cena krát množství), ",[38,56543,56544],{},"náklady",[883,56546,56548],{"className":56547},[886],[888,56549,56550],{"xmlns":890},[892,56551,56552,56558],{},[895,56553,56554,56556],{},[898,56555,2455],{},[898,56557,2458],{},[902,56559,2924],{"encoding":904}," to, co vynaloží (fixní plus variabilní), a ",[38,56562,56563],{},"zisk",[883,56565,56567],{"className":56566},[886],[888,56568,56569],{"xmlns":890},[892,56570,56571,56589],{},[895,56572,56573,56575,56577,56579,56581,56583,56585,56587],{},[898,56574,5325],{},[898,56576,5382],{},[1677,56578,1679],{},[898,56580,2455],{},[898,56582,5382],{},[1677,56584,1906],{},[898,56586,2455],{},[898,56588,2458],{},[902,56590,56591],{"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: ",[883,56594,56596],{"className":56595},[886],[888,56597,56598],{"xmlns":890},[892,56599,56600,56612],{},[895,56601,56602,56604,56606,56608,56610],{},[898,56603,5643],{},[898,56605,2458],{},[1677,56607,1679],{},[898,56609,2499],{},[898,56611,2458],{},[902,56613,56614],{"encoding":904},"AC = MC"," v minimu průměrných nákladů, ",[883,56617,56619],{"className":56618},[886],[888,56620,56621],{"xmlns":890},[892,56622,56623,56637],{},[895,56624,56625,56627,56629,56631,56633,56635],{},[898,56626,5643],{},[898,56628,41730],{},[898,56630,2458],{},[1677,56632,1679],{},[898,56634,2499],{},[898,56636,2458],{},[902,56638,56639],{"encoding":904},"AVC = MC"," v minimu průměrných variabilních nákladů a ",[883,56642,56644],{"className":56643},[886],[888,56645,56646],{"xmlns":890},[892,56647,56648,56660],{},[895,56649,56650,56652,56654,56656,56658],{},[898,56651,2499],{},[898,56653,5382],{},[1677,56655,1679],{},[898,56657,2499],{},[898,56659,2458],{},[902,56661,56662],{"encoding":904},"MR = MC"," v maximu zisku. Na závěr se sestaví ",[38,56665,56666],{},"funkce nabídky firmy"," jako rostoucí část křivky ",[883,56669,56671],{"className":56670},[886],[888,56672,56673],{"xmlns":890},[892,56674,56675,56681],{},[895,56676,56677,56679],{},[898,56678,2499],{},[898,56680,2458],{},[902,56682,56683],{"encoding":904},"MC"," nad bodem minima ",[883,56686,56688],{"className":56687},[886],[888,56689,56690],{"xmlns":890},[892,56691,56692,56700],{},[895,56693,56694,56696,56698],{},[898,56695,5643],{},[898,56697,41730],{},[898,56699,2458],{},[902,56701,56702],{"encoding":904},"AVC",[115,56704,1241],{"id":52345},[724,56706,56707,56708,56711,56712,56714,56715,1343,56718,1343,56721,56723,56724,56727,56728,56731,56732,56735,56736,2352,56751,1348,56766,2352,56781,5306],{},"Kapitola 3 se zabývá dvěma základními veličinami popisujícími ekonomickou aktivitu firmy — ",[38,56709,56710],{},"příjmem"," (revenue) a ",[38,56713,56544],{}," (cost) — v jejich třech standardních podobách: celkové, průměrné a mezní. Navazuje analýzou ",[38,56716,56717],{},"zisku",[38,56719,56720],{},"bodů zvratu",[38,56722,1651],{}," a konstrukcí ",[38,56725,56726],{},"nabídkové křivky firmy",". Klíčovými matematickými nástroji jsou ",[207,56729,1145],{"className":56730,"dataFsResolvedFilePath":764,"href":765},[210]," (pro mezní veličiny) a diferenciál (pro odhad přírůstků); v několika úlohách se využívá také ",[207,56733,12519],{"className":56734,"dataFsResolvedFilePath":773,"href":774},[210]," (pro zpětnou rekonstrukci ",[883,56737,56739],{"className":56738},[886],[888,56740,56741],{"xmlns":890},[892,56742,56743,56749],{},[895,56744,56745,56747],{},[898,56746,2455],{},[898,56748,5382],{},[902,56750,5482],{"encoding":904},[883,56752,56754],{"className":56753},[886],[888,56755,56756],{"xmlns":890},[892,56757,56758,56764],{},[895,56759,56760,56762],{},[898,56761,2499],{},[898,56763,5382],{},[902,56765,8022],{"encoding":904},[883,56767,56769],{"className":56768},[886],[888,56770,56771],{"xmlns":890},[892,56772,56773,56779],{},[895,56774,56775,56777],{},[898,56776,2455],{},[898,56778,2458],{},[902,56780,2924],{"encoding":904},[883,56782,56784],{"className":56783},[886],[888,56785,56786],{"xmlns":890},[892,56787,56788,56794],{},[895,56789,56790,56792],{},[898,56791,2499],{},[898,56793,2458],{},[902,56795,56683],{"encoding":904},[724,56797,56798],{},[38,56799,56800],{},"Cílové znalosti:",[120,56802,56803,56967,56970,56973,57066,57113,57120],{},[123,56804,56805,56806,1343,56821,1343,56837,5272,56852,1343,56867,1343,56883,1343,56901,1343,56919,1343,56936,1343,56952,9813],{},"odvodit a interpretovat funkce ",[883,56807,56809],{"className":56808},[886],[888,56810,56811],{"xmlns":890},[892,56812,56813,56819],{},[895,56814,56815,56817],{},[898,56816,2455],{},[898,56818,5382],{},[902,56820,5482],{"encoding":904},[883,56822,56824],{"className":56823},[886],[888,56825,56826],{"xmlns":890},[892,56827,56828,56834],{},[895,56829,56830,56832],{},[898,56831,5643],{},[898,56833,5382],{},[902,56835,56836],{"encoding":904},"AR",[883,56838,56840],{"className":56839},[886],[888,56841,56842],{"xmlns":890},[892,56843,56844,56850],{},[895,56845,56846,56848],{},[898,56847,2499],{},[898,56849,5382],{},[902,56851,8022],{"encoding":904},[883,56853,56855],{"className":56854},[886],[888,56856,56857],{"xmlns":890},[892,56858,56859,56865],{},[895,56860,56861,56863],{},[898,56862,2455],{},[898,56864,2458],{},[902,56866,2924],{"encoding":904},[883,56868,56870],{"className":56869},[886],[888,56871,56872],{"xmlns":890},[892,56873,56874,56880],{},[895,56875,56876,56878],{},[898,56877,11824],{},[898,56879,2458],{},[902,56881,56882],{"encoding":904},"FC",[883,56884,56886],{"className":56885},[886],[888,56887,56888],{"xmlns":890},[892,56889,56890,56898],{},[895,56891,56892,56894,56896],{},[898,56893,2455],{},[898,56895,41730],{},[898,56897,2458],{},[902,56899,56900],{"encoding":904},"TVC",[883,56902,56904],{"className":56903},[886],[888,56905,56906],{"xmlns":890},[892,56907,56908,56916],{},[895,56909,56910,56912,56914],{},[898,56911,5643],{},[898,56913,11824],{},[898,56915,2458],{},[902,56917,56918],{"encoding":904},"AFC",[883,56920,56922],{"className":56921},[886],[888,56923,56924],{"xmlns":890},[892,56925,56926,56934],{},[895,56927,56928,56930,56932],{},[898,56929,5643],{},[898,56931,41730],{},[898,56933,2458],{},[902,56935,56702],{"encoding":904},[883,56937,56939],{"className":56938},[886],[888,56940,56941],{"xmlns":890},[892,56942,56943,56949],{},[895,56944,56945,56947],{},[898,56946,5643],{},[898,56948,2458],{},[902,56950,56951],{"encoding":904},"AC",[883,56953,56955],{"className":56954},[886],[888,56956,56957],{"xmlns":890},[892,56958,56959,56965],{},[895,56960,56961,56963],{},[898,56962,2499],{},[898,56964,2458],{},[902,56966,56683],{"encoding":904},[123,56968,56969],{},"porozumět vzájemným vztahům mezi průměrnou a mezní veličinou, zvláště pro lineární poptávku;",[123,56971,56972],{},"pomocí diferenciálu odhadovat změny celkových veličin;",[123,56974,56975,56976,56979,56980,43205,57022,9813],{},"osvojit si ",[38,56977,56978],{},"princip minimalizace průměrných (variabilních) nákladů"," — podmínku ",[883,56981,56983],{"className":56982},[886],[888,56984,56985],{"xmlns":890},[892,56986,56987,57019],{},[895,56988,56989,56991,56993,56995,57001,57003,57005,57007,57009,57011,57017],{},[898,56990,5643],{},[898,56992,2458],{},[1677,56994,1686],{"stretchy":1685},[1953,56996,56997,56999],{},[898,56998,2470],{},[1810,57000,2008],{},[1677,57002,1692],{"stretchy":1685},[1677,57004,1679],{},[898,57006,2499],{},[898,57008,2458],{},[1677,57010,1686],{"stretchy":1685},[1953,57012,57013,57015],{},[898,57014,2470],{},[1810,57016,2008],{},[1677,57018,1692],{"stretchy":1685},[902,57020,57021],{"encoding":904},"AC(Q_0)=MC(Q_0)",[883,57023,57025],{"className":57024},[886],[888,57026,57027],{"xmlns":890},[892,57028,57029,57063],{},[895,57030,57031,57033,57035,57037,57039,57045,57047,57049,57051,57053,57055,57061],{},[898,57032,5643],{},[898,57034,41730],{},[898,57036,2458],{},[1677,57038,1686],{"stretchy":1685},[1953,57040,57041,57043],{},[898,57042,2470],{},[1810,57044,2008],{},[1677,57046,1692],{"stretchy":1685},[1677,57048,1679],{},[898,57050,2499],{},[898,57052,2458],{},[1677,57054,1686],{"stretchy":1685},[1953,57056,57057,57059],{},[898,57058,2470],{},[1810,57060,2008],{},[1677,57062,1692],{"stretchy":1685},[902,57064,57065],{"encoding":904},"AVC(Q_0)=MC(Q_0)",[123,57067,56975,57068,56979,57071,9813],{},[38,57069,57070],{},"princip maximalizace zisku",[883,57072,57074],{"className":57073},[886],[888,57075,57076],{"xmlns":890},[892,57077,57078,57110],{},[895,57079,57080,57082,57084,57086,57092,57094,57096,57098,57100,57102,57108],{},[898,57081,2499],{},[898,57083,5382],{},[1677,57085,1686],{"stretchy":1685},[1953,57087,57088,57090],{},[898,57089,2470],{},[1810,57091,2008],{},[1677,57093,1692],{"stretchy":1685},[1677,57095,1679],{},[898,57097,2499],{},[898,57099,2458],{},[1677,57101,1686],{"stretchy":1685},[1953,57103,57104,57106],{},[898,57105,2470],{},[1810,57107,2008],{},[1677,57109,1692],{"stretchy":1685},[902,57111,57112],{"encoding":904},"MR(Q_0)=MC(Q_0)",[123,57114,57115,57116,57119],{},"stanovit ",[38,57117,57118],{},"body zvratu"," a interval zisku;",[123,57121,57122,57123,57126],{},"zkonstruovat ",[38,57124,57125],{},"funkci nabídky firmy"," na základě nákladových charakteristik.",[115,57128,57130],{"id":57129},"příjem-firmy","Příjem firmy",[724,57132,57133],{},[2240,57134],{"alt":57135,"className":57136,"src":57137},"imek-ar-mr-dvojnasobny-sklon",[210,2244],"\u002Fwiki-assets\u002Fimek-ar-mr-dvojnasobny-sklon.jpeg",[198,57139,57141],{"id":57140},"celkový-příjem","Celkový příjem",[724,57143,57144,57145,11413,57160,57163,57164,31335],{},"Celkový příjem ",[883,57146,57148],{"className":57147},[886],[888,57149,57150],{"xmlns":890},[892,57151,57152,57158],{},[895,57153,57154,57156],{},[898,57155,2455],{},[898,57157,5382],{},[902,57159,5482],{"encoding":904},[38,57161,57162],{},"total revenue",") je součin ceny a prodaného množství. Při poptávce ",[883,57165,57167],{"className":57166},[886],[888,57168,57169],{"xmlns":890},[892,57170,57171,57185],{},[895,57172,57173,57175,57177,57179,57181,57183],{},[898,57174,5325],{},[1677,57176,1679],{},[898,57178,5571],{},[1677,57180,1686],{"stretchy":1685},[898,57182,2470],{},[1677,57184,1692],{"stretchy":1685},[902,57186,6028],{"encoding":904},[883,57188,57190],{"className":57189},[886],[888,57191,57192],{"xmlns":890,"display":29457},[892,57193,57194,57251],{},[22145,57195,57196],{"width":29462},[22150,57197,57198,57200,57244,57246],{},[22153,57199],{"width":29467},[22153,57201,57202],{},[895,57203,57204,57206,57208,57210,57212,57214,57216,57218,57220,57222,57224,57226,57228,57230,57232,57234,57236,57238,57240,57242],{},[898,57205,2455],{},[898,57207,5382],{},[1677,57209,1679],{},[898,57211,2455],{},[898,57213,5382],{},[1677,57215,1686],{"stretchy":1685},[898,57217,2470],{},[1677,57219,1692],{"stretchy":1685},[1677,57221,1679],{},[898,57223,5325],{},[1677,57225,2858],{},[898,57227,2470],{},[1677,57229,1679],{},[898,57231,5571],{},[1677,57233,1686],{"stretchy":1685},[898,57235,2470],{},[1677,57237,1692],{"stretchy":1685},[1677,57239,2858],{},[898,57241,2470],{},[898,57243,1656],{"mathvariant":2057},[22153,57245],{"width":29467},[22153,57247,57248],{},[1969,57249,57250],{},"(3.1)",[902,57252,57253],{"encoding":904},"TR = TR(Q) = P \\cdot Q = D(Q) \\cdot Q.\n\\tag{3.1}",[724,57255,57256,57257,57260,57261,57284],{},"Graf funkce se nazývá ",[38,57258,57259],{},"křivka celkového příjmu"," (total revenue curve). Za předpokladu linearity poptávky, tj. ",[883,57262,57264],{"className":57263},[886],[888,57265,57266],{"xmlns":890},[892,57267,57268,57282],{},[895,57269,57270,57272,57274,57276,57278,57280],{},[898,57271,5325],{},[1677,57273,1679],{},[898,57275,207],{},[898,57277,2470],{},[1677,57279,1776],{},[898,57281,1779],{},[902,57283,38451],{"encoding":904},", je celkový příjem kvadratickou funkcí, neboť",[883,57286,57288],{"className":57287},[886],[888,57289,57290],{"xmlns":890,"display":29457},[892,57291,57292,57332],{},[895,57293,57294,57296,57298,57300,57302,57304,57306,57308,57310,57312,57314,57316,57318,57324,57326,57328,57330],{},[898,57295,2455],{},[898,57297,5382],{},[1677,57299,1679],{},[898,57301,2470],{},[1677,57303,1686],{"stretchy":1685},[898,57305,207],{},[898,57307,2470],{},[1677,57309,1776],{},[898,57311,1779],{},[1677,57313,1692],{"stretchy":1685},[1677,57315,1679],{},[898,57317,207],{},[1805,57319,57320,57322],{},[898,57321,2470],{},[1810,57323,1812],{},[1677,57325,1776],{},[898,57327,1779],{},[898,57329,2470],{},[1677,57331,1967],{"separator":1966},[902,57333,57334],{"encoding":904},"TR = Q(aQ + b) = aQ^2 + bQ,",[724,57336,57337,57338,57351,57352,57369],{},"a křivka celkového příjmu je parabola tvaru obráceného ",[883,57339,57341],{"className":57340},[886],[888,57342,57343],{"xmlns":890},[892,57344,57345,57349],{},[895,57346,57347],{},[898,57348,900],{},[902,57350,900],{"encoding":904}," (jelikož ",[883,57353,57355],{"className":57354},[886],[888,57356,57357],{"xmlns":890},[892,57358,57359,57367],{},[895,57360,57361,57363,57365],{},[898,57362,207],{},[1677,57364,3128],{},[1810,57366,2008],{},[902,57368,44476],{"encoding":904},") procházející počátkem.",[38739,57371,57373],{"id":57372},"příklad-31","Příklad 3.1",[724,57375,57376,57379,57380,57416,57417,57432],{},[38,57377,57378],{},"Zadání."," Pro poptávku ",[883,57381,57383],{"className":57382},[886],[888,57384,57385],{"xmlns":890},[892,57386,57387,57413],{},[895,57388,57389,57391,57393,57395,57397,57399,57401,57403,57405,57407,57409,57411],{},[898,57390,5325],{},[1677,57392,1679],{},[898,57394,5571],{},[1677,57396,1686],{"stretchy":1685},[898,57398,2470],{},[1677,57400,1692],{"stretchy":1685},[1677,57402,1679],{},[1677,57404,1906],{},[1810,57406,1812],{},[898,57408,2470],{},[1677,57410,1776],{},[1810,57412,2771],{},[902,57414,57415],{"encoding":904},"P = D(Q) = -2Q + 100"," určete ",[883,57418,57420],{"className":57419},[886],[888,57421,57422],{"xmlns":890},[892,57423,57424,57430],{},[895,57425,57426,57428],{},[898,57427,2455],{},[898,57429,5382],{},[902,57431,5482],{"encoding":904}," a charakterizujte jeho křivku.",[724,57434,57435,57437],{},[38,57436,24161],{}," Celkový příjem je",[883,57439,57441],{"className":57440},[886],[888,57442,57443],{"xmlns":890,"display":29457},[892,57444,57445,57501],{},[895,57446,57447,57449,57451,57453,57455,57457,57459,57461,57463,57465,57467,57469,57471,57473,57475,57477,57479,57481,57483,57485,57487,57493,57495,57497,57499],{},[898,57448,2455],{},[898,57450,5382],{},[1677,57452,1679],{},[898,57454,2455],{},[898,57456,5382],{},[1677,57458,1686],{"stretchy":1685},[898,57460,2470],{},[1677,57462,1692],{"stretchy":1685},[1677,57464,1679],{},[898,57466,2470],{},[1677,57468,1686],{"stretchy":1685},[1677,57470,1906],{},[1810,57472,1812],{},[898,57474,2470],{},[1677,57476,1776],{},[1810,57478,2771],{},[1677,57480,1692],{"stretchy":1685},[1677,57482,1679],{},[1677,57484,1906],{},[1810,57486,1812],{},[1805,57488,57489,57491],{},[898,57490,2470],{},[1810,57492,1812],{},[1677,57494,1776],{},[1810,57496,2771],{},[898,57498,2470],{},[898,57500,1656],{"mathvariant":2057},[902,57502,57503],{"encoding":904},"TR = TR(Q) = Q(-2Q + 100) = -2Q^2 + 100Q.",[724,57505,57506,57507,5272,57529,57551,57552,57570,57571,1656],{},"Křivkou je parabola (obrázek 3.1) s nulami v ",[883,57508,57510],{"className":57509},[886],[888,57511,57512],{"xmlns":890},[892,57513,57514,57526],{},[895,57515,57516,57522,57524],{},[1953,57517,57518,57520],{},[898,57519,2470],{},[1810,57521,1959],{},[1677,57523,1679],{},[1810,57525,2008],{},[902,57527,57528],{"encoding":904},"Q_1 = 0",[883,57530,57532],{"className":57531},[886],[888,57533,57534],{"xmlns":890},[892,57535,57536,57548],{},[895,57537,57538,57544,57546],{},[1953,57539,57540,57542],{},[898,57541,2470],{},[1810,57543,1812],{},[1677,57545,1679],{},[1810,57547,2801],{},[902,57549,57550],{"encoding":904},"Q_2 = 50",". Maxima dosahuje při ",[883,57553,57555],{"className":57554},[886],[888,57556,57557],{"xmlns":890},[892,57558,57559,57567],{},[895,57560,57561,57563,57565],{},[898,57562,2470],{},[1677,57564,1679],{},[1810,57566,6392],{},[902,57568,57569],{"encoding":904},"Q = 25"," ve výši ",[883,57572,57574],{"className":57573},[886],[888,57575,57576],{"xmlns":890},[892,57577,57578,57619],{},[895,57579,57580,57582,57592,57594,57596,57598,57600,57603,57605,57607,57609,57611,57613,57615,57617],{},[898,57581,2455],{},[1953,57583,57584,57586,57589],{},[898,57585,5382],{},[898,57587,57588],{},"max",[1677,57590,57591],{},"⁡",[1677,57593,1679],{},[1677,57595,1906],{},[1810,57597,1812],{},[1677,57599,2858],{},[1810,57601,57602],{},"625",[1677,57604,1776],{},[1810,57606,2771],{},[1677,57608,2858],{},[1810,57610,6392],{},[1677,57612,1679],{},[1810,57614,1959],{},[1969,57616,2668],{},[1810,57618,32134],{},[902,57620,57621],{"encoding":904},"TR_{\\max} = -2 \\cdot 625 + 100 \\cdot 25 = 1\\,250",[724,57623,57624],{},[614,57625,57626,57627,57661,57662,5272,57675,57688,57689,2305,57707,1656],{},"Obrázek 3.1: Parabola ",[883,57628,57630],{"className":57629},[886],[888,57631,57632],{"xmlns":890},[892,57633,57634,57658],{},[895,57635,57636,57638,57640,57642,57644,57646,57652,57654,57656],{},[898,57637,2455],{},[898,57639,5382],{},[1677,57641,1679],{},[1677,57643,1906],{},[1810,57645,1812],{},[1805,57647,57648,57650],{},[898,57649,2470],{},[1810,57651,1812],{},[1677,57653,1776],{},[1810,57655,2771],{},[898,57657,2470],{},[902,57659,57660],{"encoding":904},"TR = -2Q^2 + 100Q"," s nulami v ",[883,57663,57665],{"className":57664},[886],[888,57666,57667],{"xmlns":890},[892,57668,57669,57673],{},[895,57670,57671],{},[1810,57672,2008],{},[902,57674,2008],{"encoding":904},[883,57676,57678],{"className":57677},[886],[888,57679,57680],{"xmlns":890},[892,57681,57682,57686],{},[895,57683,57684],{},[1810,57685,2801],{},[902,57687,2801],{"encoding":904}," a maximem ",[883,57690,57692],{"className":57691},[886],[888,57693,57694],{"xmlns":890},[892,57695,57696,57704],{},[895,57697,57698,57700,57702],{},[1810,57699,1959],{},[1969,57701,2668],{},[1810,57703,32134],{},[902,57705,57706],{"encoding":904},"1\\,250",[883,57708,57710],{"className":57709},[886],[888,57711,57712],{"xmlns":890},[892,57713,57714,57722],{},[895,57715,57716,57718,57720],{},[898,57717,2470],{},[1677,57719,1679],{},[1810,57721,6392],{},[902,57723,57569],{"encoding":904},[198,57725,57727],{"id":57726},"průměrný-příjem","Průměrný příjem",[724,57729,57730,1884,57732,11413,57747,57750],{},[38,57731,57727],{},[883,57733,57735],{"className":57734},[886],[888,57736,57737],{"xmlns":890},[892,57738,57739,57745],{},[895,57740,57741,57743],{},[898,57742,5643],{},[898,57744,5382],{},[902,57746,56836],{"encoding":904},[38,57748,57749],{},"average revenue",") je podíl celkového příjmu a množství. Z (3.1) plyne",[883,57752,57754],{"className":57753},[886],[888,57755,57756],{"xmlns":890,"display":29457},[892,57757,57758,57826],{},[895,57759,57760,57762,57764,57766,57768,57770,57772,57774,57776,57778,57794,57796,57814,57816,57818,57820,57822,57824],{},[898,57761,5643],{},[898,57763,5382],{},[1677,57765,1679],{},[898,57767,5643],{},[898,57769,5382],{},[1677,57771,1686],{"stretchy":1685},[898,57773,2470],{},[1677,57775,1692],{"stretchy":1685},[1677,57777,1679],{},[2010,57779,57780,57792],{},[895,57781,57782,57784,57786,57788,57790],{},[898,57783,2455],{},[898,57785,5382],{},[1677,57787,1686],{"stretchy":1685},[898,57789,2470],{},[1677,57791,1692],{"stretchy":1685},[898,57793,2470],{},[1677,57795,1679],{},[2010,57797,57798,57812],{},[895,57799,57800,57802,57804,57806,57808,57810],{},[898,57801,2470],{},[1969,57803,2668],{},[898,57805,5571],{},[1677,57807,1686],{"stretchy":1685},[898,57809,2470],{},[1677,57811,1692],{"stretchy":1685},[898,57813,2470],{},[1677,57815,1679],{},[898,57817,5571],{},[1677,57819,1686],{"stretchy":1685},[898,57821,2470],{},[1677,57823,1692],{"stretchy":1685},[898,57825,1656],{"mathvariant":2057},[902,57827,57828],{"encoding":904},"AR = AR(Q) = \\frac{TR(Q)}{Q} = \\frac{Q \\, D(Q)}{Q} = D(Q).",[5254,57830,57831],{},[724,57832,57833,57836,57837,1343,57840,1656],{},[883,57834,57835],{},"!note"," Klíčové pozorování\n",[38,57838,57839],{},"Průměrný příjem se vždy rovná poptávkové funkci",[883,57841,57843],{"className":57842},[886],[888,57844,57845],{"xmlns":890},[892,57846,57847,57869],{},[895,57848,57849,57851,57853,57855,57857,57859,57861,57863,57865,57867],{},[898,57850,5643],{},[898,57852,5382],{},[1677,57854,1686],{"stretchy":1685},[898,57856,2470],{},[1677,57858,1692],{"stretchy":1685},[1677,57860,1679],{},[898,57862,5571],{},[1677,57864,1686],{"stretchy":1685},[898,57866,2470],{},[1677,57868,1692],{"stretchy":1685},[902,57870,57871],{"encoding":904},"AR(Q) = D(Q)",[198,57873,57875],{"id":57874},"mezní-příjem","Mezní příjem",[724,57877,57878,57879,1884,57882,11413,57897,57900,57901,57904],{},"Pro zkoumání dynamiky změn celkového příjmu zavádíme ",[38,57880,57881],{},"mezní příjem",[883,57883,57885],{"className":57884},[886],[888,57886,57887],{"xmlns":890},[892,57888,57889,57895],{},[895,57890,57891,57893],{},[898,57892,2499],{},[898,57894,5382],{},[902,57896,8022],{"encoding":904},[38,57898,57899],{},"marginal revenue","), definovaný jako ",[207,57902,1145],{"className":57903,"dataFsResolvedFilePath":764,"href":765},[210]," celkového příjmu podle množství:",[883,57906,57908],{"className":57907},[886],[888,57909,57910],{"xmlns":890,"display":29457},[892,57911,57912,57969],{},[22145,57913,57914],{"width":29462},[22150,57915,57916,57918,57962,57964],{},[22153,57917],{"width":29467},[22153,57919,57920],{},[895,57921,57922,57924,57926,57928,57944,57946,57948,57954,57956,57958,57960],{},[898,57923,2499],{},[898,57925,5382],{},[1677,57927,1679],{},[2010,57929,57930,57938],{},[895,57931,57932,57934,57936],{},[898,57933,1875],{"mathvariant":2057},[898,57935,2455],{},[898,57937,5382],{},[895,57939,57940,57942],{},[898,57941,1875],{"mathvariant":2057},[898,57943,2470],{},[1677,57945,1679],{},[898,57947,2455],{},[1805,57949,57950,57952],{},[898,57951,5382],{},[1677,57953,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,57955,1686],{"stretchy":1685},[898,57957,2470],{},[1677,57959,1692],{"stretchy":1685},[898,57961,1656],{"mathvariant":2057},[22153,57963],{"width":29467},[22153,57965,57966],{},[1969,57967,57968],{},"(3.2)",[902,57970,57971],{"encoding":904},"MR = \\frac{\\mathrm{d}TR}{\\mathrm{d}Q} = TR'(Q).\n\\tag{3.2}",[724,57973,57974,57975,57977],{},"Mezní příjem udává ",[38,57976,2277],{}," celkového příjmu vzhledem k množství.",[5254,57979,57980],{},[724,57981,57982,57984,57985,58011,58012,58029,58030,1656],{},[883,57983,5543],{}," Intuice — „kolik vyděláš za další kus\"\nHodnota ",[883,57986,57988],{"className":57987},[886],[888,57989,57990],{"xmlns":890},[892,57991,57992,58008],{},[895,57993,57994,57996,57998,58000,58006],{},[898,57995,2499],{},[898,57997,5382],{},[1677,57999,1686],{"stretchy":1685},[1805,58001,58002,58004],{},[898,58003,2470],{},[1677,58005,5742],{},[1677,58007,1692],{"stretchy":1685},[902,58009,58010],{"encoding":904},"MR(Q^*)"," je přibližně to, o kolik se zvýší celkový příjem, prodá-li firma jednu další jednotku nad aktuální úroveň ",[883,58013,58015],{"className":58014},[886],[888,58016,58017],{"xmlns":890},[892,58018,58019,58027],{},[895,58020,58021],{},[1805,58022,58023,58025],{},[898,58024,2470],{},[1677,58026,5742],{},[902,58028,31235],{"encoding":904},". Jinak řečeno: ",[883,58031,58033],{"className":58032},[886],[888,58034,58035],{"xmlns":890},[892,58036,58037,58089],{},[895,58038,58039,58041,58043,58045,58051,58053,58055,58057,58059,58061,58067,58069,58071,58073,58075,58077,58079,58081,58087],{},[898,58040,2499],{},[898,58042,5382],{},[1677,58044,1686],{"stretchy":1685},[1805,58046,58047,58049],{},[898,58048,2470],{},[1677,58050,5742],{},[1677,58052,1692],{"stretchy":1685},[1677,58054,2411],{},[898,58056,2455],{},[898,58058,5382],{},[1677,58060,1686],{"stretchy":1685},[1805,58062,58063,58065],{},[898,58064,2470],{},[1677,58066,5742],{},[1677,58068,1776],{},[1810,58070,1959],{},[1677,58072,1692],{"stretchy":1685},[1677,58074,1906],{},[898,58076,2455],{},[898,58078,5382],{},[1677,58080,1686],{"stretchy":1685},[1805,58082,58083,58085],{},[898,58084,2470],{},[1677,58086,5742],{},[1677,58088,1692],{"stretchy":1685},[902,58090,58091],{"encoding":904},"MR(Q^*) \\approx TR(Q^* + 1) - TR(Q^*)",[38739,58093,58095],{"id":58094},"příklad-32","Příklad 3.2",[724,58097,58098,57379,58100,57416,58134,58149,58150,1656],{},[38,58099,57378],{},[883,58101,58103],{"className":58102},[886],[888,58104,58105],{"xmlns":890},[892,58106,58107,58131],{},[895,58108,58109,58111,58113,58115,58117,58119,58121,58123,58125,58127,58129],{},[898,58110,5325],{},[1677,58112,1679],{},[898,58114,5571],{},[1677,58116,1686],{"stretchy":1685},[898,58118,2470],{},[1677,58120,1692],{"stretchy":1685},[1677,58122,1679],{},[1810,58124,2771],{},[1677,58126,1906],{},[1810,58128,1812],{},[898,58130,2470],{},[902,58132,58133],{"encoding":904},"P = D(Q) = 100 - 2Q",[883,58135,58137],{"className":58136},[886],[888,58138,58139],{"xmlns":890},[892,58140,58141,58147],{},[895,58142,58143,58145],{},[898,58144,2499],{},[898,58146,5382],{},[902,58148,8022],{"encoding":904}," a interpretujte jeho hodnoty pro ",[883,58151,58153],{"className":58152},[886],[888,58154,58155],{"xmlns":890},[892,58156,58157,58173],{},[895,58158,58159,58161,58163,58165,58167,58169,58171],{},[898,58160,2470],{},[1677,58162,1679],{},[1810,58164,37635],{},[1677,58166,1967],{"separator":1966},[1810,58168,43253],{},[1677,58170,1967],{"separator":1966},[1810,58172,10423],{},[902,58174,58175],{"encoding":904},"Q = 15, 16, 20",[724,58177,58178,1884,58180,58212],{},[38,58179,24161],{},[883,58181,58183],{"className":58182},[886],[888,58184,58185],{"xmlns":890},[892,58186,58187,58209],{},[895,58188,58189,58191,58193,58195,58197,58199,58201,58203],{},[898,58190,2455],{},[898,58192,5382],{},[1677,58194,1679],{},[1810,58196,2771],{},[898,58198,2470],{},[1677,58200,1906],{},[1810,58202,1812],{},[1805,58204,58205,58207],{},[898,58206,2470],{},[1810,58208,1812],{},[902,58210,58211],{"encoding":904},"TR = 100Q - 2Q^2",", tedy",[883,58214,58216],{"className":58215},[886],[888,58217,58218],{"xmlns":890,"display":29457},[892,58219,58220,58262],{},[895,58221,58222,58224,58226,58228,58230,58232,58234,58236,58238,58244,58250,58252,58254,58256,58258,58260],{},[898,58223,2499],{},[898,58225,5382],{},[1677,58227,1679],{},[1677,58229,1686],{"stretchy":1685},[1810,58231,2771],{},[898,58233,2470],{},[1677,58235,1906],{},[1810,58237,1812],{},[1805,58239,58240,58242],{},[898,58241,2470],{},[1810,58243,1812],{},[1805,58245,58246,58248],{},[1677,58247,1692],{"stretchy":1685},[1677,58249,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,58251,1679],{},[1810,58253,2771],{},[1677,58255,1906],{},[1810,58257,2032],{},[898,58259,2470],{},[898,58261,1656],{"mathvariant":2057},[902,58263,58264],{"encoding":904},"MR = (100Q - 2Q^2)' = 100 - 4Q.",[724,58266,11051,58267,9490,58285,58311,58312,5746,58325,58340,58341,58354,58355,22811,58368,5746,58381,58396,58397,58410,58411,58442,58443,58462],{},[883,58268,58270],{"className":58269},[886],[888,58271,58272],{"xmlns":890},[892,58273,58274,58282],{},[895,58275,58276,58278,58280],{},[898,58277,2470],{},[1677,58279,1679],{},[1810,58281,37635],{},[902,58283,58284],{"encoding":904},"Q = 15",[883,58286,58288],{"className":58287},[886],[888,58289,58290],{"xmlns":890},[892,58291,58292,58308],{},[895,58293,58294,58296,58298,58300,58302,58304,58306],{},[898,58295,2499],{},[898,58297,5382],{},[1677,58299,1686],{"stretchy":1685},[1810,58301,37635],{},[1677,58303,1692],{"stretchy":1685},[1677,58305,1679],{},[1810,58307,6599],{},[902,58309,58310],{"encoding":904},"MR(15) = 40",": při množství ",[883,58313,58315],{"className":58314},[886],[888,58316,58317],{"xmlns":890},[892,58318,58319,58323],{},[895,58320,58321],{},[1810,58322,37635],{},[902,58324,37635],{"encoding":904},[883,58326,58328],{"className":58327},[886],[888,58329,58330],{"xmlns":890},[892,58331,58332,58338],{},[895,58333,58334,58336],{},[898,58335,2455],{},[898,58337,5382],{},[902,58339,5482],{"encoding":904}," mění asi ",[883,58342,58344],{"className":58343},[886],[888,58345,58346],{"xmlns":890},[892,58347,58348,58352],{},[895,58349,58350],{},[1810,58351,6599],{},[902,58353,6599],{"encoding":904},"-krát rychleji než množství; s růstem ",[883,58356,58358],{"className":58357},[886],[888,58359,58360],{"xmlns":890},[892,58361,58362,58366],{},[895,58363,58364],{},[898,58365,2470],{},[902,58367,2470],{"encoding":904},[883,58369,58371],{"className":58370},[886],[888,58372,58373],{"xmlns":890},[892,58374,58375,58379],{},[895,58376,58377],{},[1810,58378,1959],{},[902,58380,1959],{"encoding":904},[883,58382,58384],{"className":58383},[886],[888,58385,58386],{"xmlns":890},[892,58387,58388,58394],{},[895,58389,58390,58392],{},[898,58391,2455],{},[898,58393,5382],{},[902,58395,5482],{"encoding":904}," zvýší přibližně o ",[883,58398,58400],{"className":58399},[886],[888,58401,58402],{"xmlns":890},[892,58403,58404,58408],{},[895,58405,58406],{},[1810,58407,6599],{},[902,58409,6599],{"encoding":904},", tj. ze skutečné hodnoty ",[883,58412,58414],{"className":58413},[886],[888,58415,58416],{"xmlns":890},[892,58417,58418,58439],{},[895,58419,58420,58422,58424,58426,58428,58430,58432,58434,58436],{},[898,58421,2455],{},[898,58423,5382],{},[1677,58425,1686],{"stretchy":1685},[1810,58427,37635],{},[1677,58429,1692],{"stretchy":1685},[1677,58431,1679],{},[1810,58433,1959],{},[1969,58435,2668],{},[1810,58437,58438],{},"050",[902,58440,58441],{"encoding":904},"TR(15) = 1\\,050"," na přibližně ",[883,58444,58446],{"className":58445},[886],[888,58447,58448],{"xmlns":890},[892,58449,58450,58459],{},[895,58451,58452,58454,58456],{},[1810,58453,1959],{},[1969,58455,2668],{},[1810,58457,58458],{},"090",[902,58460,58461],{"encoding":904},"1\\,090",". Skutečná změna je",[883,58464,58466],{"className":58465},[886],[888,58467,58468],{"xmlns":890,"display":29457},[892,58469,58470,58524],{},[895,58471,58472,58474,58476,58478,58480,58482,58484,58486,58488,58490,58492,58494,58496,58498,58500,58502,58504,58506,58508,58511,58513,58515,58517,58519,58521],{},[898,58473,2570],{"mathvariant":2057},[898,58475,2455],{},[898,58477,5382],{},[1677,58479,1679],{},[898,58481,2455],{},[898,58483,5382],{},[1677,58485,1686],{"stretchy":1685},[1810,58487,43253],{},[1677,58489,1692],{"stretchy":1685},[1677,58491,1906],{},[898,58493,2455],{},[898,58495,5382],{},[1677,58497,1686],{"stretchy":1685},[1810,58499,37635],{},[1677,58501,1692],{"stretchy":1685},[1677,58503,1679],{},[1810,58505,1959],{},[1969,58507,2668],{},[1810,58509,58510],{},"088",[1677,58512,1906],{},[1810,58514,1959],{},[1969,58516,2668],{},[1810,58518,58438],{},[1677,58520,1679],{},[1810,58522,58523],{},"38.",[902,58525,58526],{"encoding":904},"\\Delta TR = TR(16) - TR(15) = 1\\,088 - 1\\,050 = 38.",[724,58528,58529,58530,1343,58556,2608,58582,58597,58598,58613],{},"Podobně ",[883,58531,58533],{"className":58532},[886],[888,58534,58535],{"xmlns":890},[892,58536,58537,58553],{},[895,58538,58539,58541,58543,58545,58547,58549,58551],{},[898,58540,2499],{},[898,58542,5382],{},[1677,58544,1686],{"stretchy":1685},[1810,58546,43253],{},[1677,58548,1692],{"stretchy":1685},[1677,58550,1679],{},[1810,58552,6953],{},[902,58554,58555],{"encoding":904},"MR(16) = 36",[883,58557,58559],{"className":58558},[886],[888,58560,58561],{"xmlns":890},[892,58562,58563,58579],{},[895,58564,58565,58567,58569,58571,58573,58575,58577],{},[898,58566,2499],{},[898,58568,5382],{},[1677,58570,1686],{"stretchy":1685},[1810,58572,10423],{},[1677,58574,1692],{"stretchy":1685},[1677,58576,1679],{},[1810,58578,10423],{},[902,58580,58581],{"encoding":904},"MR(20) = 20",[883,58583,58585],{"className":58584},[886],[888,58586,58587],{"xmlns":890},[892,58588,58589,58595],{},[895,58590,58591,58593],{},[898,58592,2499],{},[898,58594,5382],{},[902,58596,8022],{"encoding":904}," je klesající funkce — rychlost změny ",[883,58599,58601],{"className":58600},[886],[888,58602,58603],{"xmlns":890},[892,58604,58605,58611],{},[895,58606,58607,58609],{},[898,58608,2455],{},[898,58610,5382],{},[902,58612,5482],{"encoding":904}," s růstem množství klesá.",[198,58615,58617],{"id":58616},"odhad-změny-tr-pomocí-diferenciálu","Odhad změny TR pomocí diferenciálu",[724,58619,58620],{},"Užitím mezního příjmu lze odhadnout změnu celkového příjmu jako odezvu na změnu množství:",[883,58622,58624],{"className":58623},[886],[888,58625,58626],{"xmlns":890,"display":29457},[892,58627,58628,58697],{},[22145,58629,58630],{"width":29462},[22150,58631,58632,58634,58690,58692],{},[22153,58633],{"width":29467},[22153,58635,58636],{},[895,58637,58638,58640,58642,58644,58646,58648,58650,58652,58654,58656,58658,58660,58662,58664,58670,58672,58674,58676,58678,58680,58682,58684,58686,58688],{},[898,58639,2570],{"mathvariant":2057},[898,58641,2455],{},[898,58643,5382],{},[1969,58645,5372],{},[1677,58647,2411],{},[1969,58649,5372],{},[898,58651,1875],{"mathvariant":2057},[898,58653,2455],{},[898,58655,5382],{},[1677,58657,1679],{},[1677,58659,1686],{"stretchy":1685},[898,58661,2455],{},[898,58663,5382],{},[1805,58665,58666,58668],{},[1677,58667,1692],{"stretchy":1685},[1677,58669,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1969,58671,2668],{},[898,58673,1875],{"mathvariant":2057},[898,58675,2470],{},[1677,58677,1679],{},[898,58679,2499],{},[898,58681,5382],{},[1969,58683,2668],{},[898,58685,1875],{"mathvariant":2057},[898,58687,2470],{},[1677,58689,1967],{"separator":1966},[22153,58691],{"width":29467},[22153,58693,58694],{},[1969,58695,58696],{},"(3.3)",[902,58698,58699],{"encoding":904},"\\Delta TR \\;\\approx\\; \\mathrm{d}TR = (TR)' \\, \\mathrm{d}Q = MR \\, \\mathrm{d}Q,\n\\tag{3.3}",[724,58701,58702],{},"schematicky:",[883,58704,58706],{"className":58705},[886],[888,58707,58708],{"xmlns":890,"display":29457},[892,58709,58710,58818],{},[895,58711,58712,58750,58752,58754,58756,58785,58788,58816],{},[895,58713,58714,58717,58723,58726,58732,58735,58741,58747],{},[1969,58715,58716],{},"zm",[9774,58718,58719,58721],{"accent":1966},[1969,58720,47123],{},[1677,58722,26449],{},[1969,58724,58725],{},"na celkov",[9774,58727,58728,58730],{"accent":1966},[1969,58729,47123],{},[1677,58731,26368],{},[1969,58733,58734],{},"ho p",[9774,58736,58737,58739],{"accent":1966},[1969,58738,13431],{},[1677,58740,26449],{},[9774,58742,58743,58745],{"accent":1966},[1969,58744,26437],{},[1677,58746,26368],{},[1969,58748,58749],{},"jmu",[1969,58751,5372],{},[1677,58753,2411],{},[1969,58755,5372],{},[895,58757,58758,58761,58767,58770,58776,58782],{},[1969,58759,58760],{},"mezn",[9774,58762,58763,58765],{"accent":1966},[1969,58764,26437],{},[1677,58766,26368],{},[1969,58768,58769],{}," p",[9774,58771,58772,58774],{"accent":1966},[1969,58773,13431],{},[1677,58775,26449],{},[9774,58777,58778,58780],{"accent":1966},[1969,58779,26437],{},[1677,58781,26368],{},[1969,58783,58784],{},"jem",[1677,58786,58787],{},"×",[895,58789,58790,58792,58798,58801,58807,58810],{},[1969,58791,58716],{},[9774,58793,58794,58796],{"accent":1966},[1969,58795,47123],{},[1677,58797,26449],{},[1969,58799,58800],{},"na mno",[9774,58802,58803,58805],{"accent":1966},[1969,58804,10982],{},[1677,58806,26449],{},[1969,58808,58809],{},"stv",[9774,58811,58812,58814],{"accent":1966},[1969,58813,26437],{},[1677,58815,26368],{},[898,58817,1656],{"mathvariant":2057},[902,58819,58820],{"encoding":904},"\\text{změna celkového příjmu} \\;\\approx\\; \\text{mezní příjem} \\times \\text{změna množství}.",[724,58822,58823,58824,58839],{},"Pro porovnání skutečná změna ",[883,58825,58827],{"className":58826},[886],[888,58828,58829],{"xmlns":890},[892,58830,58831,58837],{},[895,58832,58833,58835],{},[898,58834,2455],{},[898,58836,5382],{},[902,58838,5482],{"encoding":904}," je",[883,58841,58843],{"className":58842},[886],[888,58844,58845],{"xmlns":890,"display":29457},[892,58846,58847,58902],{},[22145,58848,58849],{"width":29462},[22150,58850,58851,58853,58895,58897],{},[22153,58852],{"width":29467},[22153,58854,58855],{},[895,58856,58857,58859,58861,58863,58865,58867,58869,58871,58873,58875,58877,58879,58881,58883,58885,58887,58889,58891,58893],{},[898,58858,2570],{"mathvariant":2057},[898,58860,2455],{},[898,58862,5382],{},[1677,58864,1679],{},[898,58866,2455],{},[898,58868,5382],{},[1677,58870,1686],{"stretchy":1685},[898,58872,2470],{},[1677,58874,1776],{},[898,58876,1875],{"mathvariant":2057},[898,58878,2470],{},[1677,58880,1692],{"stretchy":1685},[1677,58882,1906],{},[898,58884,2455],{},[898,58886,5382],{},[1677,58888,1686],{"stretchy":1685},[898,58890,2470],{},[1677,58892,1692],{"stretchy":1685},[898,58894,1656],{"mathvariant":2057},[22153,58896],{"width":29467},[22153,58898,58899],{},[1969,58900,58901],{},"(3.4)",[902,58903,58904],{"encoding":904},"\\Delta TR = TR(Q + \\mathrm{d}Q) - TR(Q).\n\\tag{3.4}",[38739,58906,58908],{"id":58907},"příklad-33","Příklad 3.3",[724,58910,58911,58913,58914,58944,58945,2338,58960,2352,58973,2366,58986,59000],{},[38,58912,57378],{}," Pro ",[883,58915,58917],{"className":58916},[886],[888,58918,58919],{"xmlns":890},[892,58920,58921,58941],{},[895,58922,58923,58925,58927,58929,58931,58933,58935],{},[898,58924,2455],{},[898,58926,5382],{},[1677,58928,1679],{},[1810,58930,2771],{},[898,58932,2470],{},[1677,58934,1906],{},[1805,58936,58937,58939],{},[898,58938,2470],{},[1810,58940,1812],{},[902,58942,58943],{"encoding":904},"TR = 100Q - Q^2"," odhadněte změnu ",[883,58946,58948],{"className":58947},[886],[888,58949,58950],{"xmlns":890},[892,58951,58952,58958],{},[895,58953,58954,58956],{},[898,58955,2455],{},[898,58957,5382],{},[902,58959,5482],{"encoding":904},[883,58961,58963],{"className":58962},[886],[888,58964,58965],{"xmlns":890},[892,58966,58967,58971],{},[895,58968,58969],{},[898,58970,2470],{},[902,58972,2470],{"encoding":904},[883,58974,58976],{"className":58975},[886],[888,58977,58978],{"xmlns":890},[892,58979,58980,58984],{},[895,58981,58982],{},[1810,58983,2807],{},[902,58985,2807],{"encoding":904},[883,58987,58989],{"className":58988},[886],[888,58990,58991],{"xmlns":890},[892,58992,58993,58998],{},[895,58994,58995],{},[1810,58996,58997],{},"63",[902,58999,58997],{"encoding":904}," a porovnejte se skutečnou změnou.",[724,59002,59003,1884,59005,59030,59031,1343,59049,2385],{},[38,59004,24161],{},[883,59006,59008],{"className":59007},[886],[888,59009,59010],{"xmlns":890},[892,59011,59012,59028],{},[895,59013,59014,59016,59018,59020,59022,59024,59026],{},[898,59015,2499],{},[898,59017,5382],{},[1677,59019,1679],{},[1810,59021,2771],{},[1677,59023,1906],{},[1810,59025,1812],{},[898,59027,2470],{},[902,59029,12825],{"encoding":904},", tedy při ",[883,59032,59034],{"className":59033},[886],[888,59035,59036],{"xmlns":890},[892,59037,59038,59046],{},[895,59039,59040,59042,59044],{},[898,59041,2470],{},[1677,59043,1679],{},[1810,59045,2807],{},[902,59047,59048],{"encoding":904},"Q = 60",[883,59050,59052],{"className":59051},[886],[888,59053,59054],{"xmlns":890},[892,59055,59056,59066],{},[895,59057,59058,59060,59062,59064],{},[898,59059,1875],{"mathvariant":2057},[898,59061,2470],{},[1677,59063,1679],{},[1810,59065,1854],{},[902,59067,59068],{"encoding":904},"\\mathrm{d}Q = 3",[883,59070,59072],{"className":59071},[886],[888,59073,59074],{"xmlns":890,"display":29457},[892,59075,59076,59107],{},[895,59077,59078,59080,59082,59084,59086,59088,59090,59092,59094,59096,59098,59100,59102,59104],{},[898,59079,1875],{"mathvariant":2057},[898,59081,2455],{},[898,59083,5382],{},[1677,59085,1679],{},[1677,59087,1686],{"stretchy":1685},[1810,59089,2771],{},[1677,59091,1906],{},[1810,59093,5434],{},[1677,59095,1692],{"stretchy":1685},[1677,59097,2858],{},[1810,59099,1854],{},[1677,59101,1679],{},[1677,59103,1906],{},[1810,59105,59106],{},"60.",[902,59108,59109],{"encoding":904},"\\mathrm{d}TR = (100 - 120) \\cdot 3 = -60.",[724,59111,59112,59113,59143,59144,59163],{},"Celkový příjem klesne z ",[883,59114,59116],{"className":59115},[886],[888,59117,59118],{"xmlns":890},[892,59119,59120,59140],{},[895,59121,59122,59124,59126,59128,59130,59132,59134,59136,59138],{},[898,59123,2455],{},[898,59125,5382],{},[1677,59127,1686],{"stretchy":1685},[1810,59129,2807],{},[1677,59131,1692],{"stretchy":1685},[1677,59133,1679],{},[1810,59135,1812],{},[1969,59137,2668],{},[1810,59139,21533],{},[902,59141,59142],{"encoding":904},"TR(60) = 2\\,400"," přibližně na ",[883,59145,59147],{"className":59146},[886],[888,59148,59149],{"xmlns":890},[892,59150,59151,59160],{},[895,59152,59153,59155,59157],{},[1810,59154,1812],{},[1969,59156,2668],{},[1810,59158,59159],{},"340",[902,59161,59162],{"encoding":904},"2\\,340",". Skutečná změna dle (3.4):",[883,59165,59167],{"className":59166},[886],[888,59168,59169],{"xmlns":890,"display":29457},[892,59170,59171,59229],{},[895,59172,59173,59175,59177,59179,59181,59183,59185,59187,59189,59191,59193,59195,59197,59199,59201,59203,59205,59207,59209,59212,59214,59216,59218,59220,59222,59224,59227],{},[898,59174,2570],{"mathvariant":2057},[898,59176,2455],{},[898,59178,5382],{},[1677,59180,1679],{},[898,59182,2455],{},[898,59184,5382],{},[1677,59186,1686],{"stretchy":1685},[1810,59188,58997],{},[1677,59190,1692],{"stretchy":1685},[1677,59192,1906],{},[898,59194,2455],{},[898,59196,5382],{},[1677,59198,1686],{"stretchy":1685},[1810,59200,2807],{},[1677,59202,1692],{"stretchy":1685},[1677,59204,1679],{},[1810,59206,1812],{},[1969,59208,2668],{},[1810,59210,59211],{},"331",[1677,59213,1906],{},[1810,59215,1812],{},[1969,59217,2668],{},[1810,59219,21533],{},[1677,59221,1679],{},[1677,59223,1906],{},[1810,59225,59226],{},"69",[1677,59228,1967],{"separator":1966},[902,59230,59231],{"encoding":904},"\\Delta TR = TR(63) - TR(60) = 2\\,331 - 2\\,400 = -69,",[724,59233,59234,59235,59250,59251,1656],{},"tj. ",[883,59236,59238],{"className":59237},[886],[888,59239,59240],{"xmlns":890},[892,59241,59242,59248],{},[895,59243,59244,59246],{},[898,59245,2455],{},[898,59247,5382],{},[902,59249,5482],{"encoding":904}," klesne na ",[883,59252,59254],{"className":59253},[886],[888,59255,59256],{"xmlns":890},[892,59257,59258,59266],{},[895,59259,59260,59262,59264],{},[1810,59261,1812],{},[1969,59263,2668],{},[1810,59265,59211],{},[902,59267,59268],{"encoding":904},"2\\,331",[198,59270,59272],{"id":59271},"vztah-ar-a-mr-pro-lineární-poptávku","Vztah AR a MR pro lineární poptávku",[724,59274,59275,59276,11782,59299,32971],{},"Obecně pro lineární poptávku ",[883,59277,59279],{"className":59278},[886],[888,59280,59281],{"xmlns":890},[892,59282,59283,59297],{},[895,59284,59285,59287,59289,59291,59293,59295],{},[898,59286,5325],{},[1677,59288,1679],{},[898,59290,207],{},[898,59292,2470],{},[1677,59294,1776],{},[898,59296,1779],{},[902,59298,38451],{"encoding":904},[883,59300,59302],{"className":59301},[886],[888,59303,59304],{"xmlns":890},[892,59305,59306,59328],{},[895,59307,59308,59310,59312,59314,59316,59322,59324,59326],{},[898,59309,2455],{},[898,59311,5382],{},[1677,59313,1679],{},[898,59315,207],{},[1805,59317,59318,59320],{},[898,59319,2470],{},[1810,59321,1812],{},[1677,59323,1776],{},[898,59325,1779],{},[898,59327,2470],{},[902,59329,59330],{"encoding":904},"TR = aQ^2 + bQ",[883,59332,59334],{"className":59333},[886],[888,59335,59336],{"xmlns":890,"display":29457},[892,59337,59338,59358],{},[895,59339,59340,59342,59344,59346,59348,59350,59352,59354,59356],{},[898,59341,2499],{},[898,59343,5382],{},[1677,59345,1679],{},[1810,59347,1812],{},[898,59349,207],{},[898,59351,2470],{},[1677,59353,1776],{},[898,59355,1779],{},[898,59357,1656],{"mathvariant":2057},[902,59359,59360],{"encoding":904},"MR = 2aQ + b.",[724,59362,59363,59364,59379,59380,59395,59396,59409,59410,11413,59413,59429,59430,59443,59444,59459,59460,59475,59476,59491,59492,2305,59505,59535,59536,59555,59556,59571],{},"Křivky ",[883,59365,59367],{"className":59366},[886],[888,59368,59369],{"xmlns":890},[892,59370,59371,59377],{},[895,59372,59373,59375],{},[898,59374,2499],{},[898,59376,5382],{},[902,59378,8022],{"encoding":904}," a poptávky (resp. ",[883,59381,59383],{"className":59382},[886],[888,59384,59385],{"xmlns":890},[892,59386,59387,59393],{},[895,59388,59389,59391],{},[898,59390,5643],{},[898,59392,5382],{},[902,59394,56836],{"encoding":904},") jsou přímky protínající svislou osu v témže bodě ",[883,59397,59399],{"className":59398},[886],[888,59400,59401],{"xmlns":890},[892,59402,59403,59407],{},[895,59404,59405],{},[898,59406,1779],{},[902,59408,1779],{"encoding":904},", přičemž ",[38,59411,59412],{},"přímka mezního příjmu má sklon rovný dvojnásobku sklonu přímky poptávky",[883,59414,59416],{"className":59415},[886],[888,59417,59418],{"xmlns":890},[892,59419,59420,59426],{},[895,59421,59422,59424],{},[1810,59423,1812],{},[898,59425,207],{},[902,59427,59428],{"encoding":904},"2a"," vs. ",[883,59431,59433],{"className":59432},[886],[888,59434,59435],{"xmlns":890},[892,59436,59437,59441],{},[895,59438,59439],{},[898,59440,207],{},[902,59442,207],{"encoding":904},", obrázek 3.2). ",[883,59445,59447],{"className":59446},[886],[888,59448,59449],{"xmlns":890},[892,59450,59451,59457],{},[895,59452,59453,59455],{},[898,59454,2499],{},[898,59456,5382],{},[902,59458,8022],{"encoding":904}," nabývá jak kladných, tak záporných hodnot; křivka ",[883,59461,59463],{"className":59462},[886],[888,59464,59465],{"xmlns":890},[892,59466,59467,59473],{},[895,59468,59469,59471],{},[898,59470,2455],{},[898,59472,5382],{},[902,59474,5482],{"encoding":904}," nejprve roste, v bodě maxima protíná ",[883,59477,59479],{"className":59478},[886],[888,59480,59481],{"xmlns":890},[892,59482,59483,59489],{},[895,59484,59485,59487],{},[898,59486,2499],{},[898,59488,5382],{},[902,59490,8022],{"encoding":904}," osu ",[883,59493,59495],{"className":59494},[886],[888,59496,59497],{"xmlns":890},[892,59498,59499,59503],{},[895,59500,59501],{},[898,59502,2470],{},[902,59504,2470],{"encoding":904},[883,59506,59508],{"className":59507},[886],[888,59509,59510],{"xmlns":890},[892,59511,59512,59532],{},[895,59513,59514,59516,59518,59520],{},[898,59515,2470],{},[1677,59517,1679],{},[1677,59519,1906],{},[2006,59521,59522],{"scriptlevel":2008,"displaystyle":1685},[2010,59523,59524,59526],{},[898,59525,1779],{},[895,59527,59528,59530],{},[1810,59529,1812],{},[898,59531,207],{},[902,59533,59534],{"encoding":904},"Q = -\\tfrac{b}{2a}"," hodnotou ",[883,59537,59539],{"className":59538},[886],[888,59540,59541],{"xmlns":890},[892,59542,59543,59553],{},[895,59544,59545,59547,59549,59551],{},[898,59546,2499],{},[898,59548,5382],{},[1677,59550,1679],{},[1810,59552,2008],{},[902,59554,8472],{"encoding":904},", a dále ",[883,59557,59559],{"className":59558},[886],[888,59560,59561],{"xmlns":890},[892,59562,59563,59569],{},[895,59564,59565,59567],{},[898,59566,2455],{},[898,59568,5382],{},[902,59570,5482],{"encoding":904}," klesá.",[724,59573,59574,59575,59581,59582,59614,59615,59643],{},"V případě ",[38,59576,59577],{},[207,59578,59580],{"className":59579,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurence",", kdy poptávka ",[883,59583,59585],{"className":59584},[886],[888,59586,59587],{"xmlns":890},[892,59588,59589,59611],{},[895,59590,59591,59593,59595,59597,59599,59601,59603,59605],{},[898,59592,5325],{},[1677,59594,1679],{},[898,59596,5571],{},[1677,59598,1686],{"stretchy":1685},[898,59600,2470],{},[1677,59602,1692],{"stretchy":1685},[1677,59604,1679],{},[1805,59606,59607,59609],{},[898,59608,5325],{},[1677,59610,5742],{},[902,59612,59613],{"encoding":904},"P = D(Q) = P^*"," je pevná tržní cena, platí ",[883,59616,59618],{"className":59617},[886],[888,59619,59620],{"xmlns":890},[892,59621,59622,59640],{},[895,59623,59624,59626,59628,59630,59632,59634],{},[898,59625,2455],{},[898,59627,5382],{},[1677,59629,1679],{},[898,59631,2470],{},[1677,59633,2858],{},[1805,59635,59636,59638],{},[898,59637,5325],{},[1677,59639,5742],{},[902,59641,59642],{"encoding":904},"TR = Q \\cdot P^*"," a tedy",[883,59645,59647],{"className":59646},[886],[888,59648,59649],{"xmlns":890,"display":29457},[892,59650,59651,59693],{},[895,59652,59653,59655,59657,59659,59661,59663,59665,59671,59673,59675,59689,59691],{},[898,59654,2499],{},[898,59656,5382],{},[1677,59658,1679],{},[898,59660,5643],{},[898,59662,5382],{},[1677,59664,1679],{},[1805,59666,59667,59669],{},[898,59668,5325],{},[1677,59670,5742],{},[7266,59672],{"width":16674},[1677,59674,1686],{"stretchy":1685},[895,59676,59677,59680,59686],{},[1969,59678,59679],{},"obr",[9774,59681,59682,59684],{"accent":1966},[1969,59683,207],{},[1677,59685,26368],{},[1969,59687,59688],{},"zek 3.4",[1677,59690,1692],{"stretchy":1685},[898,59692,1656],{"mathvariant":2057},[902,59694,59695],{"encoding":904},"MR = AR = P^* \\quad (\\text{obrázek 3.4}).",[724,59697,59698],{},[614,59699,59700,59701,5272,59727,59755,59756,59769,59770,59785,59786,3399,59799,1343,59825,3399,59840,1656],{},"Obrázek 3.2: Přímky ",[883,59702,59704],{"className":59703},[886],[888,59705,59706],{"xmlns":890},[892,59707,59708,59724],{},[895,59709,59710,59712,59714,59716,59718,59720,59722],{},[898,59711,5643],{},[898,59713,5382],{},[1677,59715,1679],{},[898,59717,207],{},[898,59719,2470],{},[1677,59721,1776],{},[898,59723,1779],{},[902,59725,59726],{"encoding":904},"AR = aQ + b",[883,59728,59730],{"className":59729},[886],[888,59731,59732],{"xmlns":890},[892,59733,59734,59752],{},[895,59735,59736,59738,59740,59742,59744,59746,59748,59750],{},[898,59737,2499],{},[898,59739,5382],{},[1677,59741,1679],{},[1810,59743,1812],{},[898,59745,207],{},[898,59747,2470],{},[1677,59749,1776],{},[898,59751,1779],{},[902,59753,59754],{"encoding":904},"MR = 2aQ + b"," v jednom grafu; společný průsečík ",[883,59757,59759],{"className":59758},[886],[888,59760,59761],{"xmlns":890},[892,59762,59763,59767],{},[895,59764,59765],{},[898,59766,1779],{},[902,59768,1779],{"encoding":904}," se svislou osou, ",[883,59771,59773],{"className":59772},[886],[888,59774,59775],{"xmlns":890},[892,59776,59777,59783],{},[895,59778,59779,59781],{},[898,59780,2499],{},[898,59782,5382],{},[902,59784,8022],{"encoding":904}," protíná osu ",[883,59787,59789],{"className":59788},[886],[888,59790,59791],{"xmlns":890},[892,59792,59793,59797],{},[895,59794,59795],{},[898,59796,2470],{},[902,59798,2470],{"encoding":904},[883,59800,59802],{"className":59801},[886],[888,59803,59804],{"xmlns":890},[892,59805,59806,59822],{},[895,59807,59808,59810],{},[1677,59809,1906],{},[2006,59811,59812],{"scriptlevel":2008,"displaystyle":1685},[2010,59813,59814,59816],{},[898,59815,1779],{},[895,59817,59818,59820],{},[1810,59819,1812],{},[898,59821,207],{},[902,59823,59824],{"encoding":904},"-\\tfrac{b}{2a}",[883,59826,59828],{"className":59827},[886],[888,59829,59830],{"xmlns":890},[892,59831,59832,59838],{},[895,59833,59834,59836],{},[898,59835,5643],{},[898,59837,5382],{},[902,59839,56836],{"encoding":904},[883,59841,59843],{"className":59842},[886],[888,59844,59845],{"xmlns":890},[892,59846,59847,59859],{},[895,59848,59849,59851],{},[1677,59850,1906],{},[2006,59852,59853],{"scriptlevel":2008,"displaystyle":1685},[2010,59854,59855,59857],{},[898,59856,1779],{},[898,59858,207],{},[902,59860,59861],{"encoding":904},"-\\tfrac{b}{a}",[724,59863,59864],{},[614,59865,59866,59867,59898,59899,59928,59929,1656],{},"Obrázek 3.3: Parabola ",[883,59868,59870],{"className":59869},[886],[888,59871,59872],{"xmlns":890},[892,59873,59874,59896],{},[895,59875,59876,59878,59880,59882,59884,59890,59892,59894],{},[898,59877,2455],{},[898,59879,5382],{},[1677,59881,1679],{},[898,59883,207],{},[1805,59885,59886,59888],{},[898,59887,2470],{},[1810,59889,1812],{},[1677,59891,1776],{},[898,59893,1779],{},[898,59895,2470],{},[902,59897,59330],{"encoding":904}," s maximem v ",[883,59900,59902],{"className":59901},[886],[888,59903,59904],{"xmlns":890},[892,59905,59906,59926],{},[895,59907,59908,59910,59912,59914],{},[898,59909,2470],{},[1677,59911,1679],{},[1677,59913,1906],{},[2006,59915,59916],{"scriptlevel":2008,"displaystyle":1685},[2010,59917,59918,59920],{},[898,59919,1779],{},[895,59921,59922,59924],{},[1810,59923,1812],{},[898,59925,207],{},[902,59927,59534],{"encoding":904}," a nulou v ",[883,59930,59932],{"className":59931},[886],[888,59933,59934],{"xmlns":890},[892,59935,59936,59952],{},[895,59937,59938,59940,59942,59944],{},[898,59939,2470],{},[1677,59941,1679],{},[1677,59943,1906],{},[2006,59945,59946],{"scriptlevel":2008,"displaystyle":1685},[2010,59947,59948,59950],{},[898,59949,1779],{},[898,59951,207],{},[902,59953,59954],{"encoding":904},"Q = -\\tfrac{b}{a}",[724,59956,59957],{},[614,59958,59959,59960,1656],{},"Obrázek 3.4: Dokonalá konkurence — vodorovná přímka ",[883,59961,59963],{"className":59962},[886],[888,59964,59965],{"xmlns":890},[892,59966,59967,59987],{},[895,59968,59969,59971,59973,59975,59977,59979,59981],{},[898,59970,5643],{},[898,59972,5382],{},[1677,59974,1679],{},[898,59976,2499],{},[898,59978,5382],{},[1677,59980,1679],{},[1805,59982,59983,59985],{},[898,59984,5325],{},[1677,59986,5742],{},[902,59988,59989],{"encoding":904},"AR = MR = P^*",[115,59991,59993],{"id":59992},"náklady-firmy","Náklady firmy",[198,59995,59997],{"id":59996},"celkové-náklady","Celkové náklady",[724,59999,60000,1884,60002,11413,60017,60020,60021,60034],{},[38,60001,59997],{},[883,60003,60005],{"className":60004},[886],[888,60006,60007],{"xmlns":890},[892,60008,60009,60015],{},[895,60010,60011,60013],{},[898,60012,2455],{},[898,60014,2458],{},[902,60016,2924],{"encoding":904},[38,60018,60019],{},"total cost",") jsou veškeré náklady na realizaci ",[883,60022,60024],{"className":60023},[886],[888,60025,60026],{"xmlns":890},[892,60027,60028,60032],{},[895,60029,60030],{},[898,60031,2470],{},[902,60033,2470],{"encoding":904}," jednotek produkce:",[883,60036,60038],{"className":60037},[886],[888,60039,60040],{"xmlns":890,"display":29457},[892,60041,60042,60097],{},[22145,60043,60044],{"width":29462},[22150,60045,60046,60048,60090,60092],{},[22153,60047],{"width":29467},[22153,60049,60050],{},[895,60051,60052,60054,60056,60058,60060,60062,60064,60066,60068,60070,60072,60074,60076,60078,60080,60082,60084,60086,60088],{},[898,60053,2455],{},[898,60055,2458],{},[1677,60057,1679],{},[898,60059,2455],{},[898,60061,2458],{},[1677,60063,1686],{"stretchy":1685},[898,60065,2470],{},[1677,60067,1692],{"stretchy":1685},[1677,60069,1679],{},[898,60071,11824],{},[898,60073,2458],{},[1677,60075,1776],{},[898,60077,2455],{},[898,60079,41730],{},[898,60081,2458],{},[1677,60083,1686],{"stretchy":1685},[898,60085,2470],{},[1677,60087,1692],{"stretchy":1685},[1677,60089,1967],{"separator":1966},[22153,60091],{"width":29467},[22153,60093,60094],{},[1969,60095,60096],{},"(3.5)",[902,60098,60099],{"encoding":904},"TC = TC(Q) = FC + TVC(Q),\n\\tag{3.5}",[724,60101,5698,60102,60117,60118,11413,60121,13518,60124,60117,60148,11413,60151,60154],{},[883,60103,60105],{"className":60104},[886],[888,60106,60107],{"xmlns":890},[892,60108,60109,60115],{},[895,60110,60111,60113],{},[898,60112,11824],{},[898,60114,2458],{},[902,60116,56882],{"encoding":904}," jsou ",[38,60119,60120],{},"fixní náklady",[38,60122,60123],{},"fixed cost",[883,60125,60127],{"className":60126},[886],[888,60128,60129],{"xmlns":890},[892,60130,60131,60145],{},[895,60132,60133,60135,60137,60139,60141,60143],{},[898,60134,2455],{},[898,60136,41730],{},[898,60138,2458],{},[1677,60140,1686],{"stretchy":1685},[898,60142,2470],{},[1677,60144,1692],{"stretchy":1685},[902,60146,60147],{"encoding":904},"TVC(Q)",[38,60149,60150],{},"celkové variabilní náklady",[38,60152,60153],{},"total variable cost","). Celkové náklady jsou rostoucí, neboť růst množství objektivně vynutí jejich růst.",[198,60156,60158],{"id":60157},"průměrné-náklady","Průměrné náklady",[724,60160,60161,1884,60163,11413,60178,60181],{},[38,60162,60158],{},[883,60164,60166],{"className":60165},[886],[888,60167,60168],{"xmlns":890},[892,60169,60170,60176],{},[895,60171,60172,60174],{},[898,60173,5643],{},[898,60175,2458],{},[902,60177,56951],{"encoding":904},[38,60179,60180],{},"average cost",") jsou podíl celkových nákladů a množství. Z (3.5):",[883,60183,60185],{"className":60184},[886],[888,60186,60187],{"xmlns":890,"display":29457},[892,60188,60189,60268],{},[22145,60190,60191],{"width":29462},[22150,60192,60193,60195,60261,60263],{},[22153,60194],{"width":29467},[22153,60196,60197],{},[895,60198,60199,60201,60203,60205,60207,60209,60211,60213,60215,60217,60227,60229,60239,60241,60259],{},[898,60200,5643],{},[898,60202,2458],{},[1677,60204,1679],{},[898,60206,5643],{},[898,60208,2458],{},[1677,60210,1686],{"stretchy":1685},[898,60212,2470],{},[1677,60214,1692],{"stretchy":1685},[1677,60216,1679],{},[2010,60218,60219,60225],{},[895,60220,60221,60223],{},[898,60222,2455],{},[898,60224,2458],{},[898,60226,2470],{},[1677,60228,1679],{},[2010,60230,60231,60237],{},[895,60232,60233,60235],{},[898,60234,11824],{},[898,60236,2458],{},[898,60238,2470],{},[1677,60240,1776],{},[2010,60242,60243,60257],{},[895,60244,60245,60247,60249,60251,60253,60255],{},[898,60246,2455],{},[898,60248,41730],{},[898,60250,2458],{},[1677,60252,1686],{"stretchy":1685},[898,60254,2470],{},[1677,60256,1692],{"stretchy":1685},[898,60258,2470],{},[1677,60260,1967],{"separator":1966},[22153,60262],{"width":29467},[22153,60264,60265],{},[1969,60266,60267],{},"(3.6)",[902,60269,60270],{"encoding":904},"AC = AC(Q) = \\frac{TC}{Q} = \\frac{FC}{Q} + \\frac{TVC(Q)}{Q},\n\\tag{3.6}",[724,60272,5698,60273,60117,60297,1884,60300,11413,60317,13518,60320,60117,60352,1884,60355,11413,60372,2832],{},[883,60274,60276],{"className":60275},[886],[888,60277,60278],{"xmlns":890},[892,60279,60280,60294],{},[895,60281,60282],{},[2006,60283,60284],{"scriptlevel":2008,"displaystyle":1685},[2010,60285,60286,60292],{},[895,60287,60288,60290],{},[898,60289,11824],{},[898,60291,2458],{},[898,60293,2470],{},[902,60295,60296],{"encoding":904},"\\tfrac{FC}{Q}",[38,60298,60299],{},"průměrné fixní náklady",[883,60301,60303],{"className":60302},[886],[888,60304,60305],{"xmlns":890},[892,60306,60307,60315],{},[895,60308,60309,60311,60313],{},[898,60310,5643],{},[898,60312,11824],{},[898,60314,2458],{},[902,60316,56918],{"encoding":904},[38,60318,60319],{},"average fixed cost",[883,60321,60323],{"className":60322},[886],[888,60324,60325],{"xmlns":890},[892,60326,60327,60349],{},[895,60328,60329],{},[2006,60330,60331],{"scriptlevel":2008,"displaystyle":1685},[2010,60332,60333,60347],{},[895,60334,60335,60337,60339,60341,60343,60345],{},[898,60336,2455],{},[898,60338,41730],{},[898,60340,2458],{},[1677,60342,1686],{"stretchy":1685},[898,60344,2470],{},[1677,60346,1692],{"stretchy":1685},[898,60348,2470],{},[902,60350,60351],{"encoding":904},"\\tfrac{TVC(Q)}{Q}",[38,60353,60354],{},"průměrné variabilní náklady",[883,60356,60358],{"className":60357},[886],[888,60359,60360],{"xmlns":890},[892,60361,60362,60370],{},[895,60363,60364,60366,60368],{},[898,60365,5643],{},[898,60367,41730],{},[898,60369,2458],{},[902,60371,56702],{"encoding":904},[38,60373,60374],{},"average variable cost",[883,60376,60378],{"className":60377},[886],[888,60379,60380],{"xmlns":890,"display":29457},[892,60381,60382,60441],{},[22145,60383,60384],{"width":29462},[22150,60385,60386,60388,60434,60436],{},[22153,60387],{"width":29467},[22153,60389,60390],{},[895,60391,60392,60394,60396,60398,60400,60402,60404,60406,60408,60410,60412,60414,60432],{},[898,60393,5643],{},[898,60395,41730],{},[898,60397,2458],{},[1677,60399,1679],{},[898,60401,5643],{},[898,60403,41730],{},[898,60405,2458],{},[1677,60407,1686],{"stretchy":1685},[898,60409,2470],{},[1677,60411,1692],{"stretchy":1685},[1677,60413,1679],{},[2010,60415,60416,60430],{},[895,60417,60418,60420,60422,60424,60426,60428],{},[898,60419,2455],{},[898,60421,41730],{},[898,60423,2458],{},[1677,60425,1686],{"stretchy":1685},[898,60427,2470],{},[1677,60429,1692],{"stretchy":1685},[898,60431,2470],{},[898,60433,1656],{"mathvariant":2057},[22153,60435],{"width":29467},[22153,60437,60438],{},[1969,60439,60440],{},"(3.7)",[902,60442,60443],{"encoding":904},"AVC = AVC(Q) = \\frac{TVC(Q)}{Q}.\n\\tag{3.7}",[38739,60445,60447],{"id":60446},"příklad-34","Příklad 3.4",[724,60449,60450,58913,60452,5272,60477,57416,60501,5272,60516,60531,60532,1656],{},[38,60451,57378],{},[883,60453,60455],{"className":60454},[886],[888,60456,60457],{"xmlns":890},[892,60458,60459,60474],{},[895,60460,60461,60463,60465,60467,60469,60471],{},[898,60462,11824],{},[898,60464,2458],{},[1677,60466,1679],{},[1810,60468,1959],{},[1969,60470,2668],{},[1810,60472,60473],{},"000",[902,60475,60476],{"encoding":904},"FC = 1\\,000",[883,60478,60480],{"className":60479},[886],[888,60481,60482],{"xmlns":890},[892,60483,60484,60498],{},[895,60485,60486,60488,60490,60492,60494,60496],{},[898,60487,2455],{},[898,60489,41730],{},[898,60491,2458],{},[1677,60493,1679],{},[1810,60495,2032],{},[898,60497,2470],{},[902,60499,60500],{"encoding":904},"TVC = 4Q",[883,60502,60504],{"className":60503},[886],[888,60505,60506],{"xmlns":890},[892,60507,60508,60514],{},[895,60509,60510,60512],{},[898,60511,2455],{},[898,60513,2458],{},[902,60515,2924],{"encoding":904},[883,60517,60519],{"className":60518},[886],[888,60520,60521],{"xmlns":890},[892,60522,60523,60529],{},[895,60524,60525,60527],{},[898,60526,5643],{},[898,60528,2458],{},[902,60530,56951],{"encoding":904}," a jejich chování s rostoucím ",[883,60533,60535],{"className":60534},[886],[888,60536,60537],{"xmlns":890},[892,60538,60539,60543],{},[895,60540,60541],{},[898,60542,2470],{},[902,60544,2470],{"encoding":904},[724,60546,60547,1884,60549,5272,60579,60615,60616,5746,60629,60644,60645,2385],{},[38,60548,24161],{},[883,60550,60552],{"className":60551},[886],[888,60553,60554],{"xmlns":890},[892,60555,60556,60576],{},[895,60557,60558,60560,60562,60564,60566,60568,60570,60572,60574],{},[898,60559,2455],{},[898,60561,2458],{},[1677,60563,1679],{},[1810,60565,1959],{},[1969,60567,2668],{},[1810,60569,60473],{},[1677,60571,1776],{},[1810,60573,2032],{},[898,60575,2470],{},[902,60577,60578],{"encoding":904},"TC = 1\\,000 + 4Q",[883,60580,60582],{"className":60581},[886],[888,60583,60584],{"xmlns":890},[892,60585,60586,60612],{},[895,60587,60588,60590,60592,60594,60608,60610],{},[898,60589,5643],{},[898,60591,2458],{},[1677,60593,1679],{},[2006,60595,60596],{"scriptlevel":2008,"displaystyle":1685},[2010,60597,60598,60606],{},[895,60599,60600,60602,60604],{},[1810,60601,1959],{},[1969,60603,2668],{},[1810,60605,60473],{},[898,60607,2470],{},[1677,60609,1776],{},[1810,60611,2032],{},[902,60613,60614],{"encoding":904},"AC = \\tfrac{1\\,000}{Q} + 4",". S rostoucím ",[883,60617,60619],{"className":60618},[886],[888,60620,60621],{"xmlns":890},[892,60622,60623,60627],{},[895,60624,60625],{},[898,60626,2470],{},[902,60628,2470],{"encoding":904},[883,60630,60632],{"className":60631},[886],[888,60633,60634],{"xmlns":890},[892,60635,60636,60642],{},[895,60637,60638,60640],{},[898,60639,5643],{},[898,60641,2458],{},[902,60643,56951],{"encoding":904}," blíží ",[883,60646,60648],{"className":60647},[886],[888,60649,60650],{"xmlns":890},[892,60651,60652,60656],{},[895,60653,60654],{},[1810,60655,2032],{},[902,60657,2032],{"encoding":904},[883,60659,60661],{"className":60660},[886],[888,60662,60663],{"xmlns":890,"display":29457},[892,60664,60665,60711],{},[895,60666,60667,60684,60706,60708],{},[41287,60668,60669,60676],{},[895,60670,60671,60674],{},[898,60672,60673],{},"lim",[1677,60675,57591],{},[895,60677,60678,60680,60682],{},[898,60679,2470],{},[1677,60681,2804],{},[898,60683,7685],{"mathvariant":2057},[895,60685,60686,60688,60700,60702,60704],{},[1677,60687,1686],{"fence":1966},[2010,60689,60690,60698],{},[895,60691,60692,60694,60696],{},[1810,60693,1959],{},[1969,60695,2668],{},[1810,60697,60473],{},[898,60699,2470],{},[1677,60701,1776],{},[1810,60703,2032],{},[1677,60705,1692],{"fence":1966},[1677,60707,1679],{},[1810,60709,60710],{},"4.",[902,60712,60713],{"encoding":904},"\\lim_{Q \\to \\infty} \\left( \\frac{1\\,000}{Q} + 4 \\right) = 4.",[724,60715,60716,60754,60755,1656],{},[883,60717,60719],{"className":60718},[886],[888,60720,60721],{"xmlns":890},[892,60722,60723,60751],{},[895,60724,60725,60727,60729,60731,60733,60747,60749],{},[898,60726,5643],{},[898,60728,11824],{},[898,60730,2458],{},[1677,60732,1679],{},[2006,60734,60735],{"scriptlevel":2008,"displaystyle":1685},[2010,60736,60737,60745],{},[895,60738,60739,60741,60743],{},[1810,60740,1959],{},[1969,60742,2668],{},[1810,60744,60473],{},[898,60746,2470],{},[1677,60748,2804],{},[1810,60750,2008],{},[902,60752,60753],{"encoding":904},"AFC = \\tfrac{1\\,000}{Q} \\to 0"," s rostoucím ",[883,60756,60758],{"className":60757},[886],[888,60759,60760],{"xmlns":890},[892,60761,60762,60766],{},[895,60763,60764],{},[898,60765,2470],{},[902,60767,2470],{"encoding":904},[724,60769,60770],{},[614,60771,60772,60773,60802,60803,1656],{},"Obrázek 3.5: Přímka ",[883,60774,60776],{"className":60775},[886],[888,60777,60778],{"xmlns":890},[892,60779,60780,60800],{},[895,60781,60782,60784,60786,60788,60790,60792,60794,60796,60798],{},[898,60783,2455],{},[898,60785,2458],{},[1677,60787,1679],{},[1810,60789,1959],{},[1969,60791,2668],{},[1810,60793,60473],{},[1677,60795,1776],{},[1810,60797,2032],{},[898,60799,2470],{},[902,60801,60578],{"encoding":904}," protínající svislou osu ve výši ",[883,60804,60806],{"className":60805},[886],[888,60807,60808],{"xmlns":890},[892,60809,60810,60824],{},[895,60811,60812,60814,60816,60818,60820,60822],{},[898,60813,11824],{},[898,60815,2458],{},[1677,60817,1679],{},[1810,60819,1959],{},[1969,60821,2668],{},[1810,60823,60473],{},[902,60825,60476],{"encoding":904},[724,60827,60828],{},[614,60829,60830,60831,60866,60867,1656],{},"Obrázek 3.6: Hyperbola ",[883,60832,60834],{"className":60833},[886],[888,60835,60836],{"xmlns":890},[892,60837,60838,60864],{},[895,60839,60840,60842,60844,60846,60860,60862],{},[898,60841,5643],{},[898,60843,2458],{},[1677,60845,1679],{},[2006,60847,60848],{"scriptlevel":2008,"displaystyle":1685},[2010,60849,60850,60858],{},[895,60851,60852,60854,60856],{},[1810,60853,1959],{},[1969,60855,2668],{},[1810,60857,60473],{},[898,60859,2470],{},[1677,60861,1776],{},[1810,60863,2032],{},[902,60865,60614],{"encoding":904}," s vodorovnou asymptotou ",[883,60868,60870],{"className":60869},[886],[888,60871,60872],{"xmlns":890},[892,60873,60874,60884],{},[895,60875,60876,60878,60880,60882],{},[898,60877,5643],{},[898,60879,2458],{},[1677,60881,1679],{},[1810,60883,2032],{},[902,60885,60886],{"encoding":904},"AC = 4",[724,60888,60889],{},"Celkové variabilní náklady lze často vyjádřit ve tvaru",[883,60891,60893],{"className":60892},[886],[888,60894,60895],{"xmlns":890,"display":29457},[892,60896,60897,60923],{},[895,60898,60899,60901,60903,60905,60907,60909,60911,60913,60915,60917,60919,60921],{},[898,60900,2455],{},[898,60902,41730],{},[898,60904,2458],{},[1677,60906,1679],{},[898,60908,2470],{},[1677,60910,2858],{},[898,60912,41730],{},[898,60914,2458],{},[1677,60916,1686],{"stretchy":1685},[898,60918,2470],{},[1677,60920,1692],{"stretchy":1685},[1677,60922,1967],{"separator":1966},[902,60924,60925],{"encoding":904},"TVC = Q \\cdot VC(Q),",[724,60927,5698,60928,60117,60956,60959,60960,60990],{},[883,60929,60931],{"className":60930},[886],[888,60932,60933],{"xmlns":890},[892,60934,60935,60953],{},[895,60936,60937,60939,60941,60943,60945,60947,60949,60951],{},[898,60938,41730],{},[898,60940,2458],{},[1677,60942,1679],{},[898,60944,41730],{},[898,60946,2458],{},[1677,60948,1686],{"stretchy":1685},[898,60950,2470],{},[1677,60952,1692],{"stretchy":1685},[902,60954,60955],{"encoding":904},"VC = VC(Q)",[38,60957,60958],{},"variabilní náklady na jednotku množství",". Jsou-li konstantní, ",[883,60961,60963],{"className":60962},[886],[888,60964,60965],{"xmlns":890},[892,60966,60967,60987],{},[895,60968,60969,60971,60973,60975,60977,60979,60981,60983,60985],{},[898,60970,2455],{},[898,60972,41730],{},[898,60974,2458],{},[1677,60976,1686],{"stretchy":1685},[898,60978,2470],{},[1677,60980,1692],{"stretchy":1685},[1677,60982,1679],{},[898,60984,207],{},[898,60986,2470],{},[902,60988,60989],{"encoding":904},"TVC(Q) = aQ"," a nejjednodušší model nákladů má tvar",[883,60992,60994],{"className":60993},[886],[888,60995,60996],{"xmlns":890,"display":29457},[892,60997,60998,61018],{},[895,60999,61000,61002,61004,61006,61008,61010,61012,61014,61016],{},[898,61001,2455],{},[898,61003,2458],{},[1677,61005,1679],{},[898,61007,11824],{},[898,61009,2458],{},[1677,61011,1776],{},[898,61013,207],{},[898,61015,2470],{},[898,61017,1656],{"mathvariant":2057},[902,61019,61020],{"encoding":904},"TC = FC + aQ.",[724,61022,61023,61024,61039,61040,61055,61056,61079,61080,61114,61115,60866,61128,61141,61142,5272,61190,61234,61235,1656],{},"Křivkou ",[883,61025,61027],{"className":61026},[886],[888,61028,61029],{"xmlns":890},[892,61030,61031,61037],{},[895,61032,61033,61035],{},[898,61034,2455],{},[898,61036,2458],{},[902,61038,2924],{"encoding":904}," je přímka se svislým průsečíkem ",[883,61041,61043],{"className":61042},[886],[888,61044,61045],{"xmlns":890},[892,61046,61047,61053],{},[895,61048,61049,61051],{},[898,61050,11824],{},[898,61052,2458],{},[902,61054,56882],{"encoding":904}," a sklonem ",[883,61057,61059],{"className":61058},[886],[888,61060,61061],{"xmlns":890},[892,61062,61063,61076],{},[895,61064,61065,61068,61070,61072,61074],{},[898,61066,61067],{},"tan",[1677,61069,57591],{},[898,61071,20253],{},[1677,61073,1679],{},[898,61075,207],{},[902,61077,61078],{"encoding":904},"\\tan\\alpha = a"," (obrázek 3.7). Průměrné náklady tvoří hyperbolu ",[883,61081,61083],{"className":61082},[886],[888,61084,61085],{"xmlns":890},[892,61086,61087,61111],{},[895,61088,61089,61091,61093,61095,61107,61109],{},[898,61090,5643],{},[898,61092,2458],{},[1677,61094,1679],{},[2006,61096,61097],{"scriptlevel":2008,"displaystyle":1685},[2010,61098,61099,61105],{},[895,61100,61101,61103],{},[898,61102,11824],{},[898,61104,2458],{},[898,61106,2470],{},[1677,61108,1776],{},[898,61110,207],{},[902,61112,61113],{"encoding":904},"AC = \\tfrac{FC}{Q} + a"," tvaru ",[883,61116,61118],{"className":61117},[886],[888,61119,61120],{"xmlns":890},[892,61121,61122,61126],{},[895,61123,61124],{},[898,61125,11183],{},[902,61127,11183],{"encoding":904},[883,61129,61131],{"className":61130},[886],[888,61132,61133],{"xmlns":890},[892,61134,61135,61139],{},[895,61136,61137],{},[898,61138,207],{},[902,61140,207],{"encoding":904}," (obrázek 3.8). Limity ",[883,61143,61145],{"className":61144},[886],[888,61146,61147],{"xmlns":890},[892,61148,61149,61187],{},[895,61150,61151,61171,61183,61185],{},[1953,61152,61153,61159],{},[895,61154,61155,61157],{},[898,61156,60673],{},[1677,61158,57591],{},[895,61160,61161,61163,61165],{},[898,61162,2470],{},[1677,61164,2804],{},[1805,61166,61167,61169],{},[1810,61168,2008],{},[1677,61170,1776],{},[2006,61172,61173],{"scriptlevel":2008,"displaystyle":1685},[2010,61174,61175,61181],{},[895,61176,61177,61179],{},[898,61178,11824],{},[898,61180,2458],{},[898,61182,2470],{},[1677,61184,1679],{},[898,61186,7685],{"mathvariant":2057},[902,61188,61189],{"encoding":904},"\\lim_{Q \\to 0^+} \\tfrac{FC}{Q} = \\infty",[883,61191,61193],{"className":61192},[886],[888,61194,61195],{"xmlns":890},[892,61196,61197,61231],{},[895,61198,61199,61215,61227,61229],{},[1953,61200,61201,61207],{},[895,61202,61203,61205],{},[898,61204,60673],{},[1677,61206,57591],{},[895,61208,61209,61211,61213],{},[898,61210,2470],{},[1677,61212,2804],{},[898,61214,7685],{"mathvariant":2057},[2006,61216,61217],{"scriptlevel":2008,"displaystyle":1685},[2010,61218,61219,61225],{},[895,61220,61221,61223],{},[898,61222,11824],{},[898,61224,2458],{},[898,61226,2470],{},[1677,61228,1679],{},[1810,61230,2008],{},[902,61232,61233],{"encoding":904},"\\lim_{Q \\to \\infty} \\tfrac{FC}{Q} = 0"," vysvětlují, proč s rostoucí produkcí fixní náklady stále méně ovlivňují ",[883,61236,61238],{"className":61237},[886],[888,61239,61240],{"xmlns":890},[892,61241,61242,61248],{},[895,61243,61244,61246],{},[898,61245,5643],{},[898,61247,2458],{},[902,61249,56951],{"encoding":904},[724,61251,61252],{},[614,61253,61254,61255,61270,61271,61286,61287,1656],{},"Obrázek 3.7: Přímka ",[883,61256,61258],{"className":61257},[886],[888,61259,61260],{"xmlns":890},[892,61261,61262,61268],{},[895,61263,61264,61266],{},[898,61265,2455],{},[898,61267,2458],{},[902,61269,2924],{"encoding":904}," s osovým průsečíkem ve výši ",[883,61272,61274],{"className":61273},[886],[888,61275,61276],{"xmlns":890},[892,61277,61278,61284],{},[895,61279,61280,61282],{},[898,61281,11824],{},[898,61283,2458],{},[902,61285,56882],{"encoding":904}," a se sklonem ",[883,61288,61290],{"className":61289},[886],[888,61291,61292],{"xmlns":890},[892,61293,61294,61306],{},[895,61295,61296,61298,61300,61302,61304],{},[898,61297,61067],{},[1677,61299,57591],{},[898,61301,20253],{},[1677,61303,1679],{},[898,61305,207],{},[902,61307,61078],{"encoding":904},[724,61309,61310],{},[614,61311,61312,61313,61328,61329,1656],{},"Obrázek 3.8: Klesající hyperbola ",[883,61314,61316],{"className":61315},[886],[888,61317,61318],{"xmlns":890},[892,61319,61320,61326],{},[895,61321,61322,61324],{},[898,61323,5643],{},[898,61325,2458],{},[902,61327,56951],{"encoding":904}," s vodorovnou asymptotou ve výši ",[883,61330,61332],{"className":61331},[886],[888,61333,61334],{"xmlns":890},[892,61335,61336,61340],{},[895,61337,61338],{},[898,61339,207],{},[902,61341,207],{"encoding":904},[198,61343,61345],{"id":61344},"mezní-náklady","Mezní náklady",[724,61347,61348,1884,61350,11413,61365,61368,61369,61372],{},[38,61349,61345],{},[883,61351,61353],{"className":61352},[886],[888,61354,61355],{"xmlns":890},[892,61356,61357,61363],{},[895,61358,61359,61361],{},[898,61360,2499],{},[898,61362,2458],{},[902,61364,56683],{"encoding":904},[38,61366,61367],{},"marginal cost",") jsou ",[207,61370,1145],{"className":61371,"dataFsResolvedFilePath":764,"href":765},[210]," celkových nákladů podle množství:",[883,61374,61376],{"className":61375},[886],[888,61377,61378],{"xmlns":890,"display":29457},[892,61379,61380,61449],{},[22145,61381,61382],{"width":29462},[22150,61383,61384,61386,61442,61444],{},[22153,61385],{"width":29467},[22153,61387,61388],{},[895,61389,61390,61392,61394,61396,61398,61400,61402,61404,61406,61408,61424,61426,61428,61434,61436,61438,61440],{},[898,61391,2499],{},[898,61393,2458],{},[1677,61395,1679],{},[898,61397,2499],{},[898,61399,2458],{},[1677,61401,1686],{"stretchy":1685},[898,61403,2470],{},[1677,61405,1692],{"stretchy":1685},[1677,61407,1679],{},[2010,61409,61410,61418],{},[895,61411,61412,61414,61416],{},[898,61413,1875],{"mathvariant":2057},[898,61415,2455],{},[898,61417,2458],{},[895,61419,61420,61422],{},[898,61421,1875],{"mathvariant":2057},[898,61423,2470],{},[1677,61425,1679],{},[898,61427,2455],{},[1805,61429,61430,61432],{},[898,61431,2458],{},[1677,61433,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,61435,1686],{"stretchy":1685},[898,61437,2470],{},[1677,61439,1692],{"stretchy":1685},[898,61441,1656],{"mathvariant":2057},[22153,61443],{"width":29467},[22153,61445,61446],{},[1969,61447,61448],{},"(3.8)",[902,61450,61451],{"encoding":904},"MC = MC(Q) = \\frac{\\mathrm{d}TC}{\\mathrm{d}Q} = TC'(Q).\n\\tag{3.8}",[5254,61453,61454],{},[724,61455,61456,61458,61459,61485,61486,61503,61504,1656],{},[883,61457,5543],{}," Intuice — „kolik stojí další kus\"\n",[883,61460,61462],{"className":61461},[886],[888,61463,61464],{"xmlns":890},[892,61465,61466,61482],{},[895,61467,61468,61470,61472,61474,61480],{},[898,61469,2499],{},[898,61471,2458],{},[1677,61473,1686],{"stretchy":1685},[1805,61475,61476,61478],{},[898,61477,2470],{},[1677,61479,5742],{},[1677,61481,1692],{"stretchy":1685},[902,61483,61484],{"encoding":904},"MC(Q^*)"," udává přibližné náklady na výrobu jedné další jednotky, když firma aktuálně produkuje ",[883,61487,61489],{"className":61488},[886],[888,61490,61491],{"xmlns":890},[892,61492,61493,61501],{},[895,61494,61495],{},[1805,61496,61497,61499],{},[898,61498,2470],{},[1677,61500,5742],{},[902,61502,31235],{"encoding":904},". Formálně ",[883,61505,61507],{"className":61506},[886],[888,61508,61509],{"xmlns":890},[892,61510,61511,61563],{},[895,61512,61513,61515,61517,61519,61525,61527,61529,61531,61533,61535,61541,61543,61545,61547,61549,61551,61553,61555,61561],{},[898,61514,2499],{},[898,61516,2458],{},[1677,61518,1686],{"stretchy":1685},[1805,61520,61521,61523],{},[898,61522,2470],{},[1677,61524,5742],{},[1677,61526,1692],{"stretchy":1685},[1677,61528,2411],{},[898,61530,2455],{},[898,61532,2458],{},[1677,61534,1686],{"stretchy":1685},[1805,61536,61537,61539],{},[898,61538,2470],{},[1677,61540,5742],{},[1677,61542,1776],{},[1810,61544,1959],{},[1677,61546,1692],{"stretchy":1685},[1677,61548,1906],{},[898,61550,2455],{},[898,61552,2458],{},[1677,61554,1686],{"stretchy":1685},[1805,61556,61557,61559],{},[898,61558,2470],{},[1677,61560,5742],{},[1677,61562,1692],{"stretchy":1685},[902,61564,61565],{"encoding":904},"MC(Q^*) \\approx TC(Q^* + 1) - TC(Q^*)",[724,61567,61568,61569,2385],{},"Analogicky ke vztahu (3.3) platí pro odhad změny ",[883,61570,61572],{"className":61571},[886],[888,61573,61574],{"xmlns":890},[892,61575,61576,61584],{},[895,61577,61578,61580,61582],{},[898,61579,2570],{"mathvariant":2057},[898,61581,2455],{},[898,61583,2458],{},[902,61585,61586],{"encoding":904},"\\Delta TC",[883,61588,61590],{"className":61589},[886],[888,61591,61592],{"xmlns":890,"display":29457},[892,61593,61594,61663],{},[22145,61595,61596],{"width":29462},[22150,61597,61598,61600,61656,61658],{},[22153,61599],{"width":29467},[22153,61601,61602],{},[895,61603,61604,61606,61608,61610,61612,61614,61616,61618,61620,61622,61624,61626,61628,61630,61636,61638,61640,61642,61644,61646,61648,61650,61652,61654],{},[898,61605,2570],{"mathvariant":2057},[898,61607,2455],{},[898,61609,2458],{},[1969,61611,5372],{},[1677,61613,2411],{},[1969,61615,5372],{},[898,61617,1875],{"mathvariant":2057},[898,61619,2455],{},[898,61621,2458],{},[1677,61623,1679],{},[1677,61625,1686],{"stretchy":1685},[898,61627,2455],{},[898,61629,2458],{},[1805,61631,61632,61634],{},[1677,61633,1692],{"stretchy":1685},[1677,61635,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1969,61637,2668],{},[898,61639,1875],{"mathvariant":2057},[898,61641,2470],{},[1677,61643,1679],{},[898,61645,2499],{},[898,61647,2458],{},[1969,61649,2668],{},[898,61651,1875],{"mathvariant":2057},[898,61653,2470],{},[1677,61655,1967],{"separator":1966},[22153,61657],{"width":29467},[22153,61659,61660],{},[1969,61661,61662],{},"(3.9)",[902,61664,61665],{"encoding":904},"\\Delta TC \\;\\approx\\; \\mathrm{d}TC = (TC)' \\, \\mathrm{d}Q = MC \\, \\mathrm{d}Q,\n\\tag{3.9}",[724,61667,58702],{},[883,61669,61671],{"className":61670},[886],[888,61672,61673],{"xmlns":890,"display":29457},[892,61674,61675,61773],{},[895,61676,61677,61715,61717,61719,61721,61743,61745,61771],{},[895,61678,61679,61681,61687,61689,61695,61698,61704,61707],{},[1969,61680,58716],{},[9774,61682,61683,61685],{"accent":1966},[1969,61684,47123],{},[1677,61686,26449],{},[1969,61688,58725],{},[9774,61690,61691,61693],{"accent":1966},[1969,61692,1675],{},[1677,61694,26368],{},[1969,61696,61697],{},"ch n",[9774,61699,61700,61702],{"accent":1966},[1969,61701,207],{},[1677,61703,26368],{},[1969,61705,61706],{},"klad",[9774,61708,61709,61712],{"accent":1966},[1969,61710,61711],{},"u",[1677,61713,61714],{},"˚",[1969,61716,5372],{},[1677,61718,2411],{},[1969,61720,5372],{},[895,61722,61723,61725,61731,61734,61740],{},[1969,61724,58760],{},[9774,61726,61727,61729],{"accent":1966},[1969,61728,26437],{},[1677,61730,26368],{},[1969,61732,61733],{}," n",[9774,61735,61736,61738],{"accent":1966},[1969,61737,207],{},[1677,61739,26368],{},[1969,61741,61742],{},"klady",[1677,61744,58787],{},[895,61746,61747,61749,61755,61757,61763,61765],{},[1969,61748,58716],{},[9774,61750,61751,61753],{"accent":1966},[1969,61752,47123],{},[1677,61754,26449],{},[1969,61756,58800],{},[9774,61758,61759,61761],{"accent":1966},[1969,61760,10982],{},[1677,61762,26449],{},[1969,61764,58809],{},[9774,61766,61767,61769],{"accent":1966},[1969,61768,26437],{},[1677,61770,26368],{},[898,61772,1656],{"mathvariant":2057},[902,61774,61775],{"encoding":904},"\\text{změna celkových nákladů} \\;\\approx\\; \\text{mezní náklady} \\times \\text{změna množství}.",[38739,61777,61779],{"id":61778},"příklad-35","Příklad 3.5",[724,61781,61782,58913,61784,57416,61820,61835,61836,61851,61852,2352,61865,2366,61878,61891,61892,2366,61905,1656],{},[38,61783,57378],{},[883,61785,61787],{"className":61786},[886],[888,61788,61789],{"xmlns":890},[892,61790,61791,61817],{},[895,61792,61793,61795,61797,61799,61801,61803,61805,61807,61809,61811],{},[898,61794,2455],{},[898,61796,2458],{},[1677,61798,1679],{},[1810,61800,9765],{},[1677,61802,1776],{},[1810,61804,1916],{},[898,61806,2470],{},[1677,61808,1776],{},[1810,61810,1812],{},[1805,61812,61813,61815],{},[898,61814,2470],{},[1810,61816,1812],{},[902,61818,61819],{"encoding":904},"TC = 200 + 6Q + 2Q^2",[883,61821,61823],{"className":61822},[886],[888,61824,61825],{"xmlns":890},[892,61826,61827,61833],{},[895,61828,61829,61831],{},[898,61830,2499],{},[898,61832,2458],{},[902,61834,56683],{"encoding":904}," a odhadněte změny ",[883,61837,61839],{"className":61838},[886],[888,61840,61841],{"xmlns":890},[892,61842,61843,61849],{},[895,61844,61845,61847],{},[898,61846,2455],{},[898,61848,2458],{},[902,61850,2924],{"encoding":904}," při změnách ",[883,61853,61855],{"className":61854},[886],[888,61856,61857],{"xmlns":890},[892,61858,61859,61863],{},[895,61860,61861],{},[898,61862,2470],{},[902,61864,2470],{"encoding":904},[883,61866,61868],{"className":61867},[886],[888,61869,61870],{"xmlns":890},[892,61871,61872,61876],{},[895,61873,61874],{},[1810,61875,37635],{},[902,61877,37635],{"encoding":904},[883,61879,61881],{"className":61880},[886],[888,61882,61883],{"xmlns":890},[892,61884,61885,61889],{},[895,61886,61887],{},[1810,61888,43253],{},[902,61890,43253],{"encoding":904}," a z ",[883,61893,61895],{"className":61894},[886],[888,61896,61897],{"xmlns":890},[892,61898,61899,61903],{},[895,61900,61901],{},[1810,61902,37635],{},[902,61904,37635],{"encoding":904},[883,61906,61908],{"className":61907},[886],[888,61909,61910],{"xmlns":890},[892,61911,61912,61916],{},[895,61913,61914],{},[1810,61915,3190],{},[902,61917,3190],{"encoding":904},[724,61919,61920,1884,61922,2608,61948,1343,61975,62002,62003,62018,62019,62034,62035,62062,62063,62083,62084,21922,62105,62161,62162,2352,62175,2366,62188,9490,62201,1656],{},[38,61921,24161],{},[883,61923,61925],{"className":61924},[886],[888,61926,61927],{"xmlns":890},[892,61928,61929,61945],{},[895,61930,61931,61933,61935,61937,61939,61941,61943],{},[898,61932,2499],{},[898,61934,2458],{},[1677,61936,1679],{},[1810,61938,1916],{},[1677,61940,1776],{},[1810,61942,2032],{},[898,61944,2470],{},[902,61946,61947],{"encoding":904},"MC = 6 + 4Q",[883,61949,61951],{"className":61950},[886],[888,61952,61953],{"xmlns":890},[892,61954,61955,61972],{},[895,61956,61957,61959,61961,61963,61965,61967,61969],{},[898,61958,2499],{},[898,61960,2458],{},[1677,61962,1686],{"stretchy":1685},[1810,61964,37635],{},[1677,61966,1692],{"stretchy":1685},[1677,61968,1679],{},[1810,61970,61971],{},"66",[902,61973,61974],{"encoding":904},"MC(15) = 66",[883,61976,61978],{"className":61977},[886],[888,61979,61980],{"xmlns":890},[892,61981,61982,61999],{},[895,61983,61984,61986,61988,61990,61992,61994,61996],{},[898,61985,2499],{},[898,61987,2458],{},[1677,61989,1686],{"stretchy":1685},[1810,61991,10423],{},[1677,61993,1692],{"stretchy":1685},[1677,61995,1679],{},[1810,61997,61998],{},"86",[902,62000,62001],{"encoding":904},"MC(20) = 86",": s růstem množství se rychlost změny ",[883,62004,62006],{"className":62005},[886],[888,62007,62008],{"xmlns":890},[892,62009,62010,62016],{},[895,62011,62012,62014],{},[898,62013,2455],{},[898,62015,2458],{},[902,62017,2924],{"encoding":904}," zvyšuje (",[883,62020,62022],{"className":62021},[886],[888,62023,62024],{"xmlns":890},[892,62025,62026,62032],{},[895,62027,62028,62030],{},[898,62029,2499],{},[898,62031,2458],{},[902,62033,56683],{"encoding":904}," je rostoucí). Z ",[883,62036,62038],{"className":62037},[886],[888,62039,62040],{"xmlns":890},[892,62041,62042,62059],{},[895,62043,62044,62046,62048,62050,62052,62054,62056],{},[898,62045,2455],{},[898,62047,2458],{},[1677,62049,1686],{"stretchy":1685},[1810,62051,37635],{},[1677,62053,1692],{"stretchy":1685},[1677,62055,1679],{},[1810,62057,62058],{},"740",[902,62060,62061],{"encoding":904},"TC(15) = 740"," se po přírůstku ",[883,62064,62066],{"className":62065},[886],[888,62067,62068],{"xmlns":890},[892,62069,62070,62080],{},[895,62071,62072,62074,62076,62078],{},[898,62073,1875],{"mathvariant":2057},[898,62075,2470],{},[1677,62077,1679],{},[1810,62079,1959],{},[902,62081,62082],{"encoding":904},"\\mathrm{d}Q = 1"," předpokládá ",[883,62085,62087],{"className":62086},[886],[888,62088,62089],{"xmlns":890},[892,62090,62091,62102],{},[895,62092,62093,62095,62097,62099],{},[898,62094,2455],{},[898,62096,2458],{},[1677,62098,2411],{},[1810,62100,62101],{},"806",[902,62103,62104],{"encoding":904},"TC \\approx 806",[883,62106,62108],{"className":62107},[886],[888,62109,62110],{"xmlns":890},[892,62111,62112,62158],{},[895,62113,62114,62116,62118,62120,62122,62124,62126,62128,62130,62132,62134,62136,62138,62140,62142,62144,62146,62149,62151,62153,62155],{},[898,62115,2570],{"mathvariant":2057},[898,62117,2455],{},[898,62119,2458],{},[1677,62121,1679],{},[898,62123,2455],{},[898,62125,2458],{},[1677,62127,1686],{"stretchy":1685},[1810,62129,43253],{},[1677,62131,1692],{"stretchy":1685},[1677,62133,1906],{},[898,62135,2455],{},[898,62137,2458],{},[1677,62139,1686],{"stretchy":1685},[1810,62141,37635],{},[1677,62143,1692],{"stretchy":1685},[1677,62145,1679],{},[1810,62147,62148],{},"808",[1677,62150,1906],{},[1810,62152,62058],{},[1677,62154,1679],{},[1810,62156,62157],{},"68",[902,62159,62160],{"encoding":904},"\\Delta TC = TC(16) - TC(15) = 808 - 740 = 68",". Při poklesu ",[883,62163,62165],{"className":62164},[886],[888,62166,62167],{"xmlns":890},[892,62168,62169,62173],{},[895,62170,62171],{},[898,62172,2470],{},[902,62174,2470],{"encoding":904},[883,62176,62178],{"className":62177},[886],[888,62179,62180],{"xmlns":890},[892,62181,62182,62186],{},[895,62183,62184],{},[1810,62185,37635],{},[902,62187,37635],{"encoding":904},[883,62189,62191],{"className":62190},[886],[888,62192,62193],{"xmlns":890},[892,62194,62195,62199],{},[895,62196,62197],{},[1810,62198,3190],{},[902,62200,3190],{"encoding":904},[883,62202,62204],{"className":62203},[886],[888,62205,62206],{"xmlns":890},[892,62207,62208,62237],{},[895,62209,62210,62212,62214,62216,62218,62220,62222,62224,62226,62228,62230,62232,62234],{},[898,62211,2570],{"mathvariant":2057},[898,62213,2455],{},[898,62215,2458],{},[1677,62217,2411],{},[1810,62219,61971],{},[1677,62221,2858],{},[1677,62223,1686],{"stretchy":1685},[1677,62225,1906],{},[1810,62227,1854],{},[1677,62229,1692],{"stretchy":1685},[1677,62231,1679],{},[1677,62233,1906],{},[1810,62235,62236],{},"198",[902,62238,62239],{"encoding":904},"\\Delta TC \\approx 66 \\cdot (-3) = -198",[198,62241,62243],{"id":62242},"kubická-nákladová-funkce","Kubická nákladová funkce",[724,62245,62246],{},"V ekonomicky reálných situacích mají křivky nákladů charakteristické vazby a tvary.",[38739,62248,62250],{"id":62249},"příklad-36","Příklad 3.6",[724,62252,62253,58913,62255,62299],{},[38,62254,57378],{},[883,62256,62258],{"className":62257},[886],[888,62259,62260],{"xmlns":890},[892,62261,62262,62296],{},[895,62263,62264,62266,62268,62270,62272,62274,62276,62278,62280,62282,62288,62290],{},[898,62265,2455],{},[898,62267,2458],{},[1677,62269,1679],{},[1810,62271,2771],{},[1677,62273,1776],{},[1810,62275,6392],{},[898,62277,2470],{},[1677,62279,1906],{},[1810,62281,1909],{},[1805,62283,62284,62286],{},[898,62285,2470],{},[1810,62287,1812],{},[1677,62289,1776],{},[1805,62291,62292,62294],{},[898,62293,2470],{},[1810,62295,1854],{},[902,62297,62298],{"encoding":904},"TC = 100 + 25Q - 5Q^2 + Q^3"," odvoďte všechny nákladové charakteristiky.",[724,62301,62302],{},[38,62303,24161],{},[883,62305,62307],{"className":62306},[886],[888,62308,62309],{"xmlns":890,"display":29457},[892,62310,62311,62555],{},[22145,62312,62313,62339,62387,62421,62463,62513],{"rowspacing":22147,"columnalign":22148,"columnspacing":2058},[22150,62314,62315,62325],{},[22153,62316,62317],{},[2006,62318,62319],{"scriptlevel":2008,"displaystyle":1966},[895,62320,62321,62323],{},[898,62322,11824],{},[898,62324,2458],{},[22153,62326,62327],{},[2006,62328,62329],{"scriptlevel":2008,"displaystyle":1966},[895,62330,62331,62333,62335,62337],{},[895,62332],{},[1677,62334,1679],{},[1810,62336,2771],{},[1677,62338,1967],{"separator":1966},[22150,62340,62341,62353],{},[22153,62342,62343],{},[2006,62344,62345],{"scriptlevel":2008,"displaystyle":1966},[895,62346,62347,62349,62351],{},[898,62348,2455],{},[898,62350,41730],{},[898,62352,2458],{},[22153,62354,62355],{},[2006,62356,62357],{"scriptlevel":2008,"displaystyle":1966},[895,62358,62359,62361,62363,62365,62367,62369,62371,62377,62379,62385],{},[895,62360],{},[1677,62362,1679],{},[1810,62364,6392],{},[898,62366,2470],{},[1677,62368,1906],{},[1810,62370,1909],{},[1805,62372,62373,62375],{},[898,62374,2470],{},[1810,62376,1812],{},[1677,62378,1776],{},[1805,62380,62381,62383],{},[898,62382,2470],{},[1810,62384,1854],{},[1677,62386,1967],{"separator":1966},[22150,62388,62389,62401],{},[22153,62390,62391],{},[2006,62392,62393],{"scriptlevel":2008,"displaystyle":1966},[895,62394,62395,62397,62399],{},[898,62396,5643],{},[898,62398,11824],{},[898,62400,2458],{},[22153,62402,62403],{},[2006,62404,62405],{"scriptlevel":2008,"displaystyle":1966},[895,62406,62407,62409,62411,62419],{},[895,62408],{},[1677,62410,1679],{},[2006,62412,62413],{"scriptlevel":2008,"displaystyle":1685},[2010,62414,62415,62417],{},[1810,62416,2771],{},[898,62418,2470],{},[1677,62420,1967],{"separator":1966},[22150,62422,62423,62435],{},[22153,62424,62425],{},[2006,62426,62427],{"scriptlevel":2008,"displaystyle":1966},[895,62428,62429,62431,62433],{},[898,62430,5643],{},[898,62432,41730],{},[898,62434,2458],{},[22153,62436,62437],{},[2006,62438,62439],{"scriptlevel":2008,"displaystyle":1966},[895,62440,62441,62443,62445,62447,62449,62451,62453,62455,62461],{},[895,62442],{},[1677,62444,1679],{},[1810,62446,6392],{},[1677,62448,1906],{},[1810,62450,1909],{},[898,62452,2470],{},[1677,62454,1776],{},[1805,62456,62457,62459],{},[898,62458,2470],{},[1810,62460,1812],{},[1677,62462,1967],{"separator":1966},[22150,62464,62465,62475],{},[22153,62466,62467],{},[2006,62468,62469],{"scriptlevel":2008,"displaystyle":1966},[895,62470,62471,62473],{},[898,62472,5643],{},[898,62474,2458],{},[22153,62476,62477],{},[2006,62478,62479],{"scriptlevel":2008,"displaystyle":1966},[895,62480,62481,62483,62485,62493,62495,62497,62499,62501,62503,62505,62511],{},[895,62482],{},[1677,62484,1679],{},[2006,62486,62487],{"scriptlevel":2008,"displaystyle":1685},[2010,62488,62489,62491],{},[1810,62490,2771],{},[898,62492,2470],{},[1677,62494,1776],{},[1810,62496,6392],{},[1677,62498,1906],{},[1810,62500,1909],{},[898,62502,2470],{},[1677,62504,1776],{},[1805,62506,62507,62509],{},[898,62508,2470],{},[1810,62510,1812],{},[1677,62512,1967],{"separator":1966},[22150,62514,62515,62525],{},[22153,62516,62517],{},[2006,62518,62519],{"scriptlevel":2008,"displaystyle":1966},[895,62520,62521,62523],{},[898,62522,2499],{},[898,62524,2458],{},[22153,62526,62527],{},[2006,62528,62529],{"scriptlevel":2008,"displaystyle":1966},[895,62530,62531,62533,62535,62537,62539,62541,62543,62545,62547,62553],{},[895,62532],{},[1677,62534,1679],{},[1810,62536,6392],{},[1677,62538,1906],{},[1810,62540,2544],{},[898,62542,2470],{},[1677,62544,1776],{},[1810,62546,1854],{},[1805,62548,62549,62551],{},[898,62550,2470],{},[1810,62552,1812],{},[898,62554,1656],{"mathvariant":2057},[902,62556,62557],{"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}",[724,62559,62560,62561,17182,62576,17182,62591,62606,62607,62622,62623,1343,62641,62622,62658,1343,62676,62622,62691,62709],{},"Význačné body ",[883,62562,62564],{"className":62563},[886],[888,62565,62566],{"xmlns":890},[892,62567,62568,62573],{},[895,62569,62570],{},[1810,62571,62572],{},"1,67",[902,62574,62575],{"encoding":904},"1{,}67",[883,62577,62579],{"className":62578},[886],[888,62580,62581],{"xmlns":890},[892,62582,62583,62588],{},[895,62584,62585],{},[1810,62586,62587],{},"2,50",[902,62589,62590],{"encoding":904},"2{,}50",[883,62592,62594],{"className":62593},[886],[888,62595,62596],{"xmlns":890},[892,62597,62598,62603],{},[895,62599,62600],{},[1810,62601,62602],{},"4,73",[902,62604,62605],{"encoding":904},"4{,}73"," odpovídají: ",[883,62608,62610],{"className":62609},[886],[888,62611,62612],{"xmlns":890},[892,62613,62614,62620],{},[895,62615,62616,62618],{},[898,62617,2499],{},[898,62619,2458],{},[902,62621,56683],{"encoding":904}," minimum v ",[883,62624,62626],{"className":62625},[886],[888,62627,62628],{"xmlns":890},[892,62629,62630,62638],{},[895,62631,62632,62634,62636],{},[898,62633,2470],{},[1677,62635,7288],{},[1810,62637,62572],{},[902,62639,62640],{"encoding":904},"Q \\doteq 1{,}67",[883,62642,62644],{"className":62643},[886],[888,62645,62646],{"xmlns":890},[892,62647,62648,62656],{},[895,62649,62650,62652,62654],{},[898,62651,5643],{},[898,62653,41730],{},[898,62655,2458],{},[902,62657,56702],{"encoding":904},[883,62659,62661],{"className":62660},[886],[888,62662,62663],{"xmlns":890},[892,62664,62665,62673],{},[895,62666,62667,62669,62671],{},[898,62668,2470],{},[1677,62670,1679],{},[1810,62672,62587],{},[902,62674,62675],{"encoding":904},"Q = 2{,}50",[883,62677,62679],{"className":62678},[886],[888,62680,62681],{"xmlns":890},[892,62682,62683,62689],{},[895,62684,62685,62687],{},[898,62686,5643],{},[898,62688,2458],{},[902,62690,56951],{"encoding":904},[883,62692,62694],{"className":62693},[886],[888,62695,62696],{"xmlns":890},[892,62697,62698,62706],{},[895,62699,62700,62702,62704],{},[898,62701,2470],{},[1677,62703,7288],{},[1810,62705,62602],{},[902,62707,62708],{"encoding":904},"Q \\doteq 4{,}73"," (téma úlohy 3.11).",[724,62711,62712],{},[2240,62713],{"alt":62714,"className":62715,"src":62716},"imek-ac-avc-mc",[210,2244],"\u002Fwiki-assets\u002Fimek-ac-avc-mc.jpeg",[724,62718,62719],{},[614,62720,62721,62722,5272,62737,62754,62755,17182,62774,62789],{},"Obrázek 3.9: Kubické křivky ",[883,62723,62725],{"className":62724},[886],[888,62726,62727],{"xmlns":890},[892,62728,62729,62735],{},[895,62730,62731,62733],{},[898,62732,2455],{},[898,62734,2458],{},[902,62736,2924],{"encoding":904},[883,62738,62740],{"className":62739},[886],[888,62741,62742],{"xmlns":890},[892,62743,62744,62752],{},[895,62745,62746,62748,62750],{},[898,62747,2455],{},[898,62749,41730],{},[898,62751,2458],{},[902,62753,56900],{"encoding":904}," rostoucí od bodu ",[883,62756,62758],{"className":62757},[886],[888,62759,62760],{"xmlns":890},[892,62761,62762,62772],{},[895,62763,62764,62766,62768,62770],{},[898,62765,11824],{},[898,62767,2458],{},[1677,62769,1679],{},[1810,62771,2771],{},[902,62773,13022],{"encoding":904},[883,62775,62777],{"className":62776},[886],[888,62778,62779],{"xmlns":890},[892,62780,62781,62787],{},[895,62782,62783,62785],{},[898,62784,11824],{},[898,62786,2458],{},[902,62788,56882],{"encoding":904}," je vodorovná přímka.",[724,62791,62792],{},[614,62793,62794,62795,1343,62810,1343,62827,30592,62842,62855,62856,2608,62873,62888,62889,7578,62906,62921,62922,27580,62935,1343,62948,1343,62961,1656],{},"Obrázek 3.10: Křivky ",[883,62796,62798],{"className":62797},[886],[888,62799,62800],{"xmlns":890},[892,62801,62802,62808],{},[895,62803,62804,62806],{},[898,62805,5643],{},[898,62807,2458],{},[902,62809,56951],{"encoding":904},[883,62811,62813],{"className":62812},[886],[888,62814,62815],{"xmlns":890},[892,62816,62817,62825],{},[895,62818,62819,62821,62823],{},[898,62820,5643],{},[898,62822,41730],{},[898,62824,2458],{},[902,62826,56702],{"encoding":904},[883,62828,62830],{"className":62829},[886],[888,62831,62832],{"xmlns":890},[892,62833,62834,62840],{},[895,62835,62836,62838],{},[898,62837,2499],{},[898,62839,2458],{},[902,62841,56683],{"encoding":904},[883,62843,62845],{"className":62844},[886],[888,62846,62847],{"xmlns":890},[892,62848,62849,62853],{},[895,62850,62851],{},[898,62852,900],{},[902,62854,900],{"encoding":904}," a klesající hyperbola ",[883,62857,62859],{"className":62858},[886],[888,62860,62861],{"xmlns":890},[892,62862,62863,62871],{},[895,62864,62865,62867,62869],{},[898,62866,5643],{},[898,62868,11824],{},[898,62870,2458],{},[902,62872,56918],{"encoding":904},[883,62874,62876],{"className":62875},[886],[888,62877,62878],{"xmlns":890},[892,62879,62880,62886],{},[895,62881,62882,62884],{},[898,62883,2499],{},[898,62885,2458],{},[902,62887,56683],{"encoding":904}," protíná ",[883,62890,62892],{"className":62891},[886],[888,62893,62894],{"xmlns":890},[892,62895,62896,62904],{},[895,62897,62898,62900,62902],{},[898,62899,5643],{},[898,62901,41730],{},[898,62903,2458],{},[902,62905,56702],{"encoding":904},[883,62907,62909],{"className":62908},[886],[888,62910,62911],{"xmlns":890},[892,62912,62913,62919],{},[895,62914,62915,62917],{},[898,62916,5643],{},[898,62918,2458],{},[902,62920,56951],{"encoding":904}," zdola v jejich minimech; význačné hodnoty na ose ",[883,62923,62925],{"className":62924},[886],[888,62926,62927],{"xmlns":890},[892,62928,62929,62933],{},[895,62930,62931],{},[898,62932,2470],{},[902,62934,2470],{"encoding":904},[883,62936,62938],{"className":62937},[886],[888,62939,62940],{"xmlns":890},[892,62941,62942,62946],{},[895,62943,62944],{},[1810,62945,62572],{},[902,62947,62575],{"encoding":904},[883,62949,62951],{"className":62950},[886],[888,62952,62953],{"xmlns":890},[892,62954,62955,62959],{},[895,62956,62957],{},[1810,62958,62587],{},[902,62960,62590],{"encoding":904},[883,62962,62964],{"className":62963},[886],[888,62965,62966],{"xmlns":890},[892,62967,62968,62972],{},[895,62969,62970],{},[1810,62971,62602],{},[902,62973,62605],{"encoding":904},[724,62975,62976],{},[38,62977,62978],{},"Standardní vlastnosti:",[120,62980,62981,63016,63080,63148,63198,63218],{},[123,62982,62983,5272,62998,63015],{},[883,62984,62986],{"className":62985},[886],[888,62987,62988],{"xmlns":890},[892,62989,62990,62996],{},[895,62991,62992,62994],{},[898,62993,2455],{},[898,62995,2458],{},[902,62997,2924],{"encoding":904},[883,62999,63001],{"className":63000},[886],[888,63002,63003],{"xmlns":890},[892,63004,63005,63013],{},[895,63006,63007,63009,63011],{},[898,63008,2455],{},[898,63010,41730],{},[898,63012,2458],{},[902,63014,56900],{"encoding":904}," jsou kubické funkce;",[123,63017,63018,1343,63033,1343,63050,63065,63066,63079],{},[883,63019,63021],{"className":63020},[886],[888,63022,63023],{"xmlns":890},[892,63024,63025,63031],{},[895,63026,63027,63029],{},[898,63028,5643],{},[898,63030,2458],{},[902,63032,56951],{"encoding":904},[883,63034,63036],{"className":63035},[886],[888,63037,63038],{"xmlns":890},[892,63039,63040,63048],{},[895,63041,63042,63044,63046],{},[898,63043,5643],{},[898,63045,41730],{},[898,63047,2458],{},[902,63049,56702],{"encoding":904},[883,63051,63053],{"className":63052},[886],[888,63054,63055],{"xmlns":890},[892,63056,63057,63063],{},[895,63058,63059,63061],{},[898,63060,2499],{},[898,63062,2458],{},[902,63064,56683],{"encoding":904}," jsou křivky tvaru ",[883,63067,63069],{"className":63068},[886],[888,63070,63071],{"xmlns":890},[892,63072,63073,63077],{},[895,63074,63075],{},[898,63076,900],{},[902,63078,900],{"encoding":904}," (nejprve klesají, po minimu rostou);",[123,63081,63082,63097,63098,1343,63115,63132,63133,9813],{},[883,63083,63085],{"className":63084},[886],[888,63086,63087],{"xmlns":890},[892,63088,63089,63095],{},[895,63090,63091,63093],{},[898,63092,2499],{},[898,63094,2458],{},[902,63096,56683],{"encoding":904}," nabývá minima před ",[883,63099,63101],{"className":63100},[886],[888,63102,63103],{"xmlns":890},[892,63104,63105,63113],{},[895,63106,63107,63109,63111],{},[898,63108,5643],{},[898,63110,41730],{},[898,63112,2458],{},[902,63114,56702],{"encoding":904},[883,63116,63118],{"className":63117},[886],[888,63119,63120],{"xmlns":890},[892,63121,63122,63130],{},[895,63123,63124,63126,63128],{},[898,63125,5643],{},[898,63127,41730],{},[898,63129,2458],{},[902,63131,56702],{"encoding":904}," před ",[883,63134,63136],{"className":63135},[886],[888,63137,63138],{"xmlns":890},[892,63139,63140,63146],{},[895,63141,63142,63144],{},[898,63143,5643],{},[898,63145,2458],{},[902,63147,56951],{"encoding":904},[123,63149,63150,62888,63165,5272,63180,63197],{},[883,63151,63153],{"className":63152},[886],[888,63154,63155],{"xmlns":890},[892,63156,63157,63163],{},[895,63158,63159,63161],{},[898,63160,2499],{},[898,63162,2458],{},[902,63164,56683],{"encoding":904},[883,63166,63168],{"className":63167},[886],[888,63169,63170],{"xmlns":890},[892,63171,63172,63178],{},[895,63173,63174,63176],{},[898,63175,5643],{},[898,63177,2458],{},[902,63179,56951],{"encoding":904},[883,63181,63183],{"className":63182},[886],[888,63184,63185],{"xmlns":890},[892,63186,63187,63195],{},[895,63188,63189,63191,63193],{},[898,63190,5643],{},[898,63192,41730],{},[898,63194,2458],{},[902,63196,56702],{"encoding":904}," zdola právě v jejich minimech;",[123,63199,63200,63217],{},[883,63201,63203],{"className":63202},[886],[888,63204,63205],{"xmlns":890},[892,63206,63207,63215],{},[895,63208,63209,63211,63213],{},[898,63210,5643],{},[898,63212,11824],{},[898,63214,2458],{},[902,63216,56918],{"encoding":904}," je hyperbola, stále klesající;",[123,63219,63220,63252,63253,5272,63268,63285,63286,63299,63300,5306],{},[883,63221,63223],{"className":63222},[886],[888,63224,63225],{"xmlns":890},[892,63226,63227,63249],{},[895,63228,63229,63231,63233,63235,63237,63239,63241,63243,63245,63247],{},[898,63230,5643],{},[898,63232,2458],{},[1677,63234,1679],{},[898,63236,5643],{},[898,63238,11824],{},[898,63240,2458],{},[1677,63242,1776],{},[898,63244,5643],{},[898,63246,41730],{},[898,63248,2458],{},[902,63250,63251],{"encoding":904},"AC = AFC + AVC","; vzdálenost mezi ",[883,63254,63256],{"className":63255},[886],[888,63257,63258],{"xmlns":890},[892,63259,63260,63266],{},[895,63261,63262,63264],{},[898,63263,5643],{},[898,63265,2458],{},[902,63267,56951],{"encoding":904},[883,63269,63271],{"className":63270},[886],[888,63272,63273],{"xmlns":890},[892,63274,63275,63283],{},[895,63276,63277,63279,63281],{},[898,63278,5643],{},[898,63280,41730],{},[898,63282,2458],{},[902,63284,56702],{"encoding":904}," klesá s rostoucím ",[883,63287,63289],{"className":63288},[886],[888,63290,63291],{"xmlns":890},[892,63292,63293,63297],{},[895,63294,63295],{},[898,63296,2470],{},[902,63298,2470],{"encoding":904}," (protože ",[883,63301,63303],{"className":63302},[886],[888,63304,63305],{"xmlns":890},[892,63306,63307,63319],{},[895,63308,63309,63311,63313,63315,63317],{},[898,63310,5643],{},[898,63312,11824],{},[898,63314,2458],{},[1677,63316,2804],{},[1810,63318,2008],{},[902,63320,63321],{"encoding":904},"AFC \\to 0",[115,63323,63325],{"id":63324},"princip-minimalizace-průměrných-nákladů","Princip minimalizace průměrných nákladů",[724,63327,63328,63329,63332,63333,63348],{},"Častou optimalizační úlohou je ",[38,63330,63331],{},"minimalizace průměrných nákladů"," — stanovení produkce, pro niž je ",[883,63334,63336],{"className":63335},[886],[888,63337,63338],{"xmlns":890},[892,63339,63340,63346],{},[895,63341,63342,63344],{},[898,63343,5643],{},[898,63345,2458],{},[902,63347,56951],{"encoding":904}," minimální.",[198,63350,17803],{"id":17802},[724,63352,63353,63354,63371],{},"Mají-li průměrné náklady minimum v bodě ",[883,63355,63357],{"className":63356},[886],[888,63358,63359],{"xmlns":890},[892,63360,63361,63369],{},[895,63362,63363],{},[1953,63364,63365,63367],{},[898,63366,2470],{},[1810,63368,2008],{},[902,63370,39699],{"encoding":904},", pak platí",[883,63373,63375],{"className":63374},[886],[888,63376,63377],{"xmlns":890,"display":29457},[892,63378,63379,63428],{},[22145,63380,63381],{"width":29462},[22150,63382,63383,63385,63421,63423],{},[22153,63384],{"width":29467},[22153,63386,63387],{},[895,63388,63389,63391,63393,63395,63401,63403,63405,63407,63409,63411,63417,63419],{},[898,63390,5643],{},[898,63392,2458],{},[1677,63394,1686],{"stretchy":1685},[1953,63396,63397,63399],{},[898,63398,2470],{},[1810,63400,2008],{},[1677,63402,1692],{"stretchy":1685},[1677,63404,1679],{},[898,63406,2499],{},[898,63408,2458],{},[1677,63410,1686],{"stretchy":1685},[1953,63412,63413,63415],{},[898,63414,2470],{},[1810,63416,2008],{},[1677,63418,1692],{"stretchy":1685},[898,63420,1656],{"mathvariant":2057},[22153,63422],{"width":29467},[22153,63424,63425],{},[1969,63426,63427],{},"(3.10)",[902,63429,63430],{"encoding":904},"AC(Q_0) = MC(Q_0).\n\\tag{3.10}",[5254,63432,63433],{},[724,63434,63435,63437,63438],{},[883,63436,57835],{}," Princip\n",[38,63439,63440],{},"V bodě minima průměrných nákladů se průměrné náklady rovnají mezním nákladům.",[724,63442,63443,63446,63447,63489],{},[38,63444,63445],{},"Odvození."," Z ",[883,63448,63450],{"className":63449},[886],[888,63451,63452],{"xmlns":890},[892,63453,63454,63486],{},[895,63455,63456,63458,63460,63462,63464,63466,63468],{},[898,63457,5643],{},[898,63459,2458],{},[1677,63461,1686],{"stretchy":1685},[898,63463,2470],{},[1677,63465,1692],{"stretchy":1685},[1677,63467,1679],{},[2006,63469,63470],{"scriptlevel":2008,"displaystyle":1685},[2010,63471,63472,63484],{},[895,63473,63474,63476,63478,63480,63482],{},[898,63475,2455],{},[898,63477,2458],{},[1677,63479,1686],{"stretchy":1685},[898,63481,2470],{},[1677,63483,1692],{"stretchy":1685},[898,63485,2470],{},[902,63487,63488],{"encoding":904},"AC(Q) = \\tfrac{TC(Q)}{Q}"," derivací podílu plyne",[883,63491,63493],{"className":63492},[886],[888,63494,63495],{"xmlns":890,"display":29457},[892,63496,63497,63629],{},[895,63498,63499,63501,63507,63509,63511,63513,63515,63555,63557,63597,63599,63627],{},[898,63500,5643],{},[1805,63502,63503,63505],{},[898,63504,2458],{},[1677,63506,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,63508,1686],{"stretchy":1685},[898,63510,2470],{},[1677,63512,1692],{"stretchy":1685},[1677,63514,1679],{},[2010,63516,63517,63549],{},[895,63518,63519,63521,63527,63529,63531,63533,63535,63537,63539,63541,63543,63545,63547],{},[898,63520,2455],{},[1805,63522,63523,63525],{},[898,63524,2458],{},[1677,63526,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,63528,1686],{"stretchy":1685},[898,63530,2470],{},[1677,63532,1692],{"stretchy":1685},[1677,63534,2858],{},[898,63536,2470],{},[1677,63538,1906],{},[898,63540,2455],{},[898,63542,2458],{},[1677,63544,1686],{"stretchy":1685},[898,63546,2470],{},[1677,63548,1692],{"stretchy":1685},[1805,63550,63551,63553],{},[898,63552,2470],{},[1810,63554,1812],{},[1677,63556,1679],{},[2010,63558,63559,63591],{},[895,63560,63561,63563,63565,63567,63569,63571,63573,63575,63577,63579,63581,63583,63585,63587,63589],{},[898,63562,2499],{},[898,63564,2458],{},[1677,63566,1686],{"stretchy":1685},[898,63568,2470],{},[1677,63570,1692],{"stretchy":1685},[1677,63572,2858],{},[898,63574,2470],{},[1677,63576,1906],{},[898,63578,5643],{},[898,63580,2458],{},[1677,63582,1686],{"stretchy":1685},[898,63584,2470],{},[1677,63586,1692],{"stretchy":1685},[1677,63588,2858],{},[898,63590,2470],{},[1805,63592,63593,63595],{},[898,63594,2470],{},[1810,63596,1812],{},[1677,63598,1679],{},[2010,63600,63601,63625],{},[895,63602,63603,63605,63607,63609,63611,63613,63615,63617,63619,63621,63623],{},[898,63604,2499],{},[898,63606,2458],{},[1677,63608,1686],{"stretchy":1685},[898,63610,2470],{},[1677,63612,1692],{"stretchy":1685},[1677,63614,1906],{},[898,63616,5643],{},[898,63618,2458],{},[1677,63620,1686],{"stretchy":1685},[898,63622,2470],{},[1677,63624,1692],{"stretchy":1685},[898,63626,2470],{},[898,63628,1656],{"mathvariant":2057},[902,63630,63631],{"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}.",[724,63633,63634,63635,2305,63650,9490,63672,58212],{},"Nutnou podmínkou minima ",[883,63636,63638],{"className":63637},[886],[888,63639,63640],{"xmlns":890},[892,63641,63642,63648],{},[895,63643,63644,63646],{},[898,63645,5643],{},[898,63647,2458],{},[902,63649,56951],{"encoding":904},[883,63651,63653],{"className":63652},[886],[888,63654,63655],{"xmlns":890},[892,63656,63657,63669],{},[895,63658,63659,63665,63667],{},[1953,63660,63661,63663],{},[898,63662,2470],{},[1810,63664,2008],{},[1677,63666,3089],{},[1810,63668,2008],{},[902,63670,63671],{"encoding":904},"Q_0 > 0",[883,63673,63675],{"className":63674},[886],[888,63676,63677],{"xmlns":890},[892,63678,63679,63703],{},[895,63680,63681,63683,63689,63691,63697,63699,63701],{},[898,63682,5643],{},[1805,63684,63685,63687],{},[898,63686,2458],{},[1677,63688,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,63690,1686],{"stretchy":1685},[1953,63692,63693,63695],{},[898,63694,2470],{},[1810,63696,2008],{},[1677,63698,1692],{"stretchy":1685},[1677,63700,1679],{},[1810,63702,2008],{},[902,63704,63705],{"encoding":904},"AC'(Q_0) = 0",[883,63707,63709],{"className":63708},[886],[888,63710,63711],{"xmlns":890,"display":29457},[892,63712,63713,63798],{},[895,63714,63715,63755,63757,63759,63761,63764,63766,63768,63770,63772,63778,63780,63782,63784,63786,63788,63794,63796],{},[2010,63716,63717,63749],{},[895,63718,63719,63721,63723,63725,63731,63733,63735,63737,63739,63741,63747],{},[898,63720,2499],{},[898,63722,2458],{},[1677,63724,1686],{"stretchy":1685},[1953,63726,63727,63729],{},[898,63728,2470],{},[1810,63730,2008],{},[1677,63732,1692],{"stretchy":1685},[1677,63734,1906],{},[898,63736,5643],{},[898,63738,2458],{},[1677,63740,1686],{"stretchy":1685},[1953,63742,63743,63745],{},[898,63744,2470],{},[1810,63746,2008],{},[1677,63748,1692],{"stretchy":1685},[1953,63750,63751,63753],{},[898,63752,2470],{},[1810,63754,2008],{},[1677,63756,1679],{},[1810,63758,2008],{},[7266,63760],{"width":16674},[1677,63762,63763],{},"⟺",[7266,63765],{"width":16674},[898,63767,2499],{},[898,63769,2458],{},[1677,63771,1686],{"stretchy":1685},[1953,63773,63774,63776],{},[898,63775,2470],{},[1810,63777,2008],{},[1677,63779,1692],{"stretchy":1685},[1677,63781,1679],{},[898,63783,5643],{},[898,63785,2458],{},[1677,63787,1686],{"stretchy":1685},[1953,63789,63790,63792],{},[898,63791,2470],{},[1810,63793,2008],{},[1677,63795,1692],{"stretchy":1685},[898,63797,1656],{"mathvariant":2057},[902,63799,63800],{"encoding":904},"\\frac{MC(Q_0) - AC(Q_0)}{Q_0} = 0 \\quad\\Longleftrightarrow\\quad MC(Q_0) = AC(Q_0).",[724,63802,63803,1884,63806,62888,63821,63836,63837,63852,63853,9490,63870,63892,63893,63915],{},[38,63804,63805],{},"Geometrická interpretace.",[883,63807,63809],{"className":63808},[886],[888,63810,63811],{"xmlns":890},[892,63812,63813,63819],{},[895,63814,63815,63817],{},[898,63816,2499],{},[898,63818,2458],{},[902,63820,56683],{"encoding":904},[883,63822,63824],{"className":63823},[886],[888,63825,63826],{"xmlns":890},[892,63827,63828,63834],{},[895,63829,63830,63832],{},[898,63831,5643],{},[898,63833,2458],{},[902,63835,56951],{"encoding":904}," právě v bodě minima ",[883,63838,63840],{"className":63839},[886],[888,63841,63842],{"xmlns":890},[892,63843,63844,63850],{},[895,63845,63846,63848],{},[898,63847,5643],{},[898,63849,2458],{},[902,63851,56951],{"encoding":904}," (obrázek 3.10); nalevo od ",[883,63854,63856],{"className":63855},[886],[888,63857,63858],{"xmlns":890},[892,63859,63860,63868],{},[895,63861,63862],{},[1953,63863,63864,63866],{},[898,63865,2470],{},[1810,63867,2008],{},[902,63869,39699],{"encoding":904},[883,63871,63873],{"className":63872},[886],[888,63874,63875],{"xmlns":890},[892,63876,63877,63889],{},[895,63878,63879,63881,63883,63885,63887],{},[898,63880,2499],{},[898,63882,2458],{},[1677,63884,3128],{},[898,63886,5643],{},[898,63888,2458],{},[902,63890,63891],{"encoding":904},"MC \u003C AC"," (průměrné náklady klesají), napravo ",[883,63894,63896],{"className":63895},[886],[888,63897,63898],{"xmlns":890},[892,63899,63900,63912],{},[895,63901,63902,63904,63906,63908,63910],{},[898,63903,2499],{},[898,63905,2458],{},[1677,63907,3089],{},[898,63909,5643],{},[898,63911,2458],{},[902,63913,63914],{"encoding":904},"MC > AC"," (průměrné náklady rostou).",[724,63917,63918,63919,63961,63962,63979,63980,1656],{},"Za obvyklých ekonomických podmínek platí i obrácené tvrzení — jestliže ",[883,63920,63922],{"className":63921},[886],[888,63923,63924],{"xmlns":890},[892,63925,63926,63958],{},[895,63927,63928,63930,63932,63934,63940,63942,63944,63946,63948,63950,63956],{},[898,63929,5643],{},[898,63931,2458],{},[1677,63933,1686],{"stretchy":1685},[1953,63935,63936,63938],{},[898,63937,2470],{},[1810,63939,2008],{},[1677,63941,1692],{"stretchy":1685},[1677,63943,1679],{},[898,63945,2499],{},[898,63947,2458],{},[1677,63949,1686],{"stretchy":1685},[1953,63951,63952,63954],{},[898,63953,2470],{},[1810,63955,2008],{},[1677,63957,1692],{"stretchy":1685},[902,63959,63960],{"encoding":904},"AC(Q_0) = MC(Q_0)",", pak ",[883,63963,63965],{"className":63964},[886],[888,63966,63967],{"xmlns":890},[892,63968,63969,63977],{},[895,63970,63971],{},[1953,63972,63973,63975],{},[898,63974,2470],{},[1810,63976,2008],{},[902,63978,39699],{"encoding":904}," je bod minima. V praktických úlohách tedy postačí řešit rovnici ",[883,63981,63983],{"className":63982},[886],[888,63984,63985],{"xmlns":890},[892,63986,63987,64011],{},[895,63988,63989,63991,63993,63995,63997,63999,64001,64003,64005,64007,64009],{},[898,63990,5643],{},[898,63992,2458],{},[1677,63994,1686],{"stretchy":1685},[898,63996,2470],{},[1677,63998,1692],{"stretchy":1685},[1677,64000,1679],{},[898,64002,2499],{},[898,64004,2458],{},[1677,64006,1686],{"stretchy":1685},[898,64008,2470],{},[1677,64010,1692],{"stretchy":1685},[902,64012,64013],{"encoding":904},"AC(Q) = MC(Q)",[5254,64015,64016],{},[724,64017,64018,64020,64021,11782,64039,64060,64061,11782,64064,64085,64086,64101,64102,59429,64117,5306],{},[883,64019,5800],{}," Pozor — neplést s principem maxima zisku\nPro ",[38,64022,64023,64024],{},"minimum ",[883,64025,64027],{"className":64026},[886],[888,64028,64029],{"xmlns":890},[892,64030,64031,64037],{},[895,64032,64033,64035],{},[898,64034,5643],{},[898,64036,2458],{},[902,64038,56951],{"encoding":904},[883,64040,64042],{"className":64041},[886],[888,64043,64044],{"xmlns":890},[892,64045,64046,64058],{},[895,64047,64048,64050,64052,64054,64056],{},[898,64049,5643],{},[898,64051,2458],{},[1677,64053,1679],{},[898,64055,2499],{},[898,64057,2458],{},[902,64059,56614],{"encoding":904},", pro ",[38,64062,64063],{},"maximum zisku",[883,64065,64067],{"className":64066},[886],[888,64068,64069],{"xmlns":890},[892,64070,64071,64083],{},[895,64072,64073,64075,64077,64079,64081],{},[898,64074,2499],{},[898,64076,5382],{},[1677,64078,1679],{},[898,64080,2499],{},[898,64082,2458],{},[902,64084,56662],{"encoding":904},". Obě podmínky využívají ",[883,64087,64089],{"className":64088},[886],[888,64090,64091],{"xmlns":890},[892,64092,64093,64099],{},[895,64094,64095,64097],{},[898,64096,2499],{},[898,64098,2458],{},[902,64100,56683],{"encoding":904},", ale rovnají ho rozdílným veličinám (",[883,64103,64105],{"className":64104},[886],[888,64106,64107],{"xmlns":890},[892,64108,64109,64115],{},[895,64110,64111,64113],{},[898,64112,5643],{},[898,64114,2458],{},[902,64116,56951],{"encoding":904},[883,64118,64120],{"className":64119},[886],[888,64121,64122],{"xmlns":890},[892,64123,64124,64130],{},[895,64125,64126,64128],{},[898,64127,2499],{},[898,64129,5382],{},[902,64131,8022],{"encoding":904},[38739,64133,64135],{"id":64134},"příklad-37","Příklad 3.7",[724,64137,64138,58913,64140,64174,64175,64188,64189,64204],{},[38,64139,57378],{},[883,64141,64143],{"className":64142},[886],[888,64144,64145],{"xmlns":890},[892,64146,64147,64171],{},[895,64148,64149,64151,64153,64155,64161,64163,64165,64167,64169],{},[898,64150,2455],{},[898,64152,2458],{},[1677,64154,1679],{},[1805,64156,64157,64159],{},[898,64158,2470],{},[1810,64160,1812],{},[1677,64162,1776],{},[1810,64164,1854],{},[898,64166,2470],{},[1677,64168,1776],{},[1810,64170,6953],{},[902,64172,64173],{"encoding":904},"TC = Q^2 + 3Q + 36"," najděte ",[883,64176,64178],{"className":64177},[886],[888,64179,64180],{"xmlns":890},[892,64181,64182,64186],{},[895,64183,64184],{},[898,64185,2470],{},[902,64187,2470],{"encoding":904}," minimalizující ",[883,64190,64192],{"className":64191},[886],[888,64193,64194],{"xmlns":890},[892,64195,64196,64202],{},[895,64197,64198,64200],{},[898,64199,5643],{},[898,64201,2458],{},[902,64203,56951],{"encoding":904}," a ověřte princip (3.10).",[724,64206,64207,64209],{},[38,64208,24161],{}," Přímý výpočet:",[883,64211,64213],{"className":64212},[886],[888,64214,64215],{"xmlns":890,"display":29457},[892,64216,64217,64319],{},[895,64218,64219,64221,64223,64225,64247,64249,64251,64253,64255,64257,64263,64265,64267,64269,64271,64273,64279,64281,64283,64285,64295,64297,64317],{},[898,64220,5643],{},[898,64222,2458],{},[1677,64224,1679],{},[2010,64226,64227,64245],{},[895,64228,64229,64235,64237,64239,64241,64243],{},[1805,64230,64231,64233],{},[898,64232,2470],{},[1810,64234,1812],{},[1677,64236,1776],{},[1810,64238,1854],{},[898,64240,2470],{},[1677,64242,1776],{},[1810,64244,6953],{},[898,64246,2470],{},[1677,64248,1679],{},[898,64250,2470],{},[1677,64252,1776],{},[1810,64254,1854],{},[1677,64256,1776],{},[2010,64258,64259,64261],{},[1810,64260,6953],{},[898,64262,2470],{},[1677,64264,1967],{"separator":1966},[7266,64266],{"width":7268},[1677,64268,1686],{"stretchy":1685},[898,64270,5643],{},[898,64272,2458],{},[1805,64274,64275,64277],{},[1677,64276,1692],{"stretchy":1685},[1677,64278,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,64280,1679],{},[1810,64282,1959],{},[1677,64284,1906],{},[2010,64286,64287,64289],{},[1810,64288,6953],{},[1805,64290,64291,64293],{},[898,64292,2470],{},[1810,64294,1812],{},[1677,64296,1679],{},[2010,64298,64299,64311],{},[895,64300,64301,64307,64309],{},[1805,64302,64303,64305],{},[898,64304,2470],{},[1810,64306,1812],{},[1677,64308,1906],{},[1810,64310,6953],{},[1805,64312,64313,64315],{},[898,64314,2470],{},[1810,64316,1812],{},[898,64318,1656],{"mathvariant":2057},[902,64320,64321],{"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}.",[724,64323,64324,64364,64365,64389,64390,64440,64441,1656],{},[883,64325,64327],{"className":64326},[886],[888,64328,64329],{"xmlns":890},[892,64330,64331,64361],{},[895,64332,64333,64335,64337,64339,64345,64347,64349,64351,64357,64359],{},[1677,64334,1686],{"stretchy":1685},[898,64336,5643],{},[898,64338,2458],{},[1805,64340,64341,64343],{},[1677,64342,1692],{"stretchy":1685},[1677,64344,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,64346,1679],{},[1810,64348,2008],{},[1677,64350,5375],{},[1953,64352,64353,64355],{},[898,64354,2470],{},[1810,64356,1959],{},[1677,64358,1679],{},[1810,64360,1916],{},[902,64362,64363],{"encoding":904},"(AC)' = 0 \\Rightarrow Q_1 = 6"," (smysluplné), ",[883,64366,64368],{"className":64367},[886],[888,64369,64370],{"xmlns":890},[892,64371,64372,64386],{},[895,64373,64374,64380,64382,64384],{},[1953,64375,64376,64378],{},[898,64377,2470],{},[1810,64379,1812],{},[1677,64381,1679],{},[1677,64383,1906],{},[1810,64385,1916],{},[902,64387,64388],{"encoding":904},"Q_2 = -6"," (vyloučeno). ",[883,64391,64393],{"className":64392},[886],[888,64394,64395],{"xmlns":890},[892,64396,64397,64437],{},[895,64398,64399,64401,64403,64405,64415,64417,64419,64421,64423,64431,64433,64435],{},[1677,64400,1686],{"stretchy":1685},[898,64402,5643],{},[898,64404,2458],{},[1805,64406,64407,64409],{},[1677,64408,1692],{"stretchy":1685},[895,64410,64411,64413],{},[1677,64412,2059],{"mathvariant":2057},[1677,64414,2059],{"mathvariant":2057},[1677,64416,1686],{"stretchy":1685},[1810,64418,1916],{},[1677,64420,1692],{"stretchy":1685},[1677,64422,1679],{},[2006,64424,64425],{"scriptlevel":2008,"displaystyle":1685},[2010,64426,64427,64429],{},[1810,64428,1959],{},[1810,64430,1854],{},[1677,64432,3089],{},[1810,64434,2008],{},[1677,64436,5375],{},[902,64438,64439],{"encoding":904},"(AC)''(6) = \\tfrac{1}{3} > 0 \\Rightarrow"," minimum. ",[883,64442,64444],{"className":64443},[886],[888,64445,64446],{"xmlns":890},[892,64447,64448,64464],{},[895,64449,64450,64452,64454,64456,64458,64460,64462],{},[898,64451,5643],{},[898,64453,2458],{},[1677,64455,1686],{"stretchy":1685},[1810,64457,1916],{},[1677,64459,1692],{"stretchy":1685},[1677,64461,1679],{},[1810,64463,37635],{},[902,64465,64466],{"encoding":904},"AC(6) = 15",[724,64468,64469,64470,64496,64497,2385],{},"Pomocí principu: ",[883,64471,64473],{"className":64472},[886],[888,64474,64475],{"xmlns":890},[892,64476,64477,64493],{},[895,64478,64479,64481,64483,64485,64487,64489,64491],{},[898,64480,2499],{},[898,64482,2458],{},[1677,64484,1679],{},[1810,64486,1812],{},[898,64488,2470],{},[1677,64490,1776],{},[1810,64492,1854],{},[902,64494,64495],{"encoding":904},"MC = 2Q + 3",", rovnice ",[883,64498,64500],{"className":64499},[886],[888,64501,64502],{"xmlns":890},[892,64503,64504,64516],{},[895,64505,64506,64508,64510,64512,64514],{},[898,64507,5643],{},[898,64509,2458],{},[1677,64511,1679],{},[898,64513,2499],{},[898,64515,2458],{},[902,64517,56614],{"encoding":904},[883,64519,64521],{"className":64520},[886],[888,64522,64523],{"xmlns":890,"display":29457},[892,64524,64525,64627],{},[895,64526,64527,64549,64551,64553,64555,64557,64559,64561,64563,64565,64571,64573,64575,64577,64579,64581,64583,64585,64591,64593,64595,64597,64599,64601,64603,64609,64611,64613,64615,64617,64619,64621,64623,64625],{},[2010,64528,64529,64547],{},[895,64530,64531,64537,64539,64541,64543,64545],{},[1805,64532,64533,64535],{},[898,64534,2470],{},[1810,64536,1812],{},[1677,64538,1776],{},[1810,64540,1854],{},[898,64542,2470],{},[1677,64544,1776],{},[1810,64546,6953],{},[898,64548,2470],{},[1677,64550,1679],{},[1810,64552,1812],{},[898,64554,2470],{},[1677,64556,1776],{},[1810,64558,1854],{},[1969,64560,5372],{},[1677,64562,5375],{},[1969,64564,5372],{},[1805,64566,64567,64569],{},[898,64568,2470],{},[1810,64570,1812],{},[1677,64572,1776],{},[1810,64574,1854],{},[898,64576,2470],{},[1677,64578,1776],{},[1810,64580,6953],{},[1677,64582,1679],{},[1810,64584,1812],{},[1805,64586,64587,64589],{},[898,64588,2470],{},[1810,64590,1812],{},[1677,64592,1776],{},[1810,64594,1854],{},[898,64596,2470],{},[1969,64598,5372],{},[1677,64600,5375],{},[1969,64602,5372],{},[1805,64604,64605,64607],{},[898,64606,2470],{},[1810,64608,1812],{},[1677,64610,1679],{},[1810,64612,6953],{},[1969,64614,5372],{},[1677,64616,5375],{},[1969,64618,5372],{},[898,64620,2470],{},[1677,64622,1679],{},[1810,64624,1916],{},[1677,64626,1967],{"separator":1966},[902,64628,64629],{"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,",[724,64631,64632,64633,64671],{},"a ",[883,64634,64636],{"className":64635},[886],[888,64637,64638],{"xmlns":890},[892,64639,64640,64668],{},[895,64641,64642,64644,64646,64648,64650,64652,64654,64656,64658,64660,64662,64664,64666],{},[898,64643,5643],{},[898,64645,2458],{},[1677,64647,1686],{"stretchy":1685},[1810,64649,1916],{},[1677,64651,1692],{"stretchy":1685},[1677,64653,1679],{},[898,64655,2499],{},[898,64657,2458],{},[1677,64659,1686],{"stretchy":1685},[1810,64661,1916],{},[1677,64663,1692],{"stretchy":1685},[1677,64665,1679],{},[1810,64667,37635],{},[902,64669,64670],{"encoding":904},"AC(6) = MC(6) = 15",". Oba postupy dávají stejný výsledek.",[198,64673,64675],{"id":64674},"princip-minimalizace-průměrných-variabilních-nákladů","Princip minimalizace průměrných variabilních nákladů",[724,64677,64678,64679,2385],{},"Analogicky pro ",[883,64680,64682],{"className":64681},[886],[888,64683,64684],{"xmlns":890},[892,64685,64686,64694],{},[895,64687,64688,64690,64692],{},[898,64689,5643],{},[898,64691,41730],{},[898,64693,2458],{},[902,64695,56702],{"encoding":904},[883,64697,64699],{"className":64698},[886],[888,64700,64701],{"xmlns":890,"display":29457},[892,64702,64703,64754],{},[22145,64704,64705],{"width":29462},[22150,64706,64707,64709,64747,64749],{},[22153,64708],{"width":29467},[22153,64710,64711],{},[895,64712,64713,64715,64717,64719,64721,64727,64729,64731,64733,64735,64737,64743,64745],{},[898,64714,5643],{},[898,64716,41730],{},[898,64718,2458],{},[1677,64720,1686],{"stretchy":1685},[1953,64722,64723,64725],{},[898,64724,2470],{},[1810,64726,2008],{},[1677,64728,1692],{"stretchy":1685},[1677,64730,1679],{},[898,64732,2499],{},[898,64734,2458],{},[1677,64736,1686],{"stretchy":1685},[1953,64738,64739,64741],{},[898,64740,2470],{},[1810,64742,2008],{},[1677,64744,1692],{"stretchy":1685},[898,64746,1656],{"mathvariant":2057},[22153,64748],{"width":29467},[22153,64750,64751],{},[1969,64752,64753],{},"(3.11)",[902,64755,64756],{"encoding":904},"AVC(Q_0) = MC(Q_0).\n\\tag{3.11}",[5254,64758,64759],{},[724,64760,64761,63437,64763],{},[883,64762,57835],{},[38,64764,64765,64766,64783],{},"V bodě minima průměrných variabilních nákladů se ",[883,64767,64769],{"className":64768},[886],[888,64770,64771],{"xmlns":890},[892,64772,64773,64781],{},[895,64774,64775,64777,64779],{},[898,64776,5643],{},[898,64778,41730],{},[898,64780,2458],{},[902,64782,56702],{"encoding":904}," rovnají mezním nákladům.",[724,64785,64786,64787,64809,64810,1656],{},"Odvození je analogické (úloha 3.14). V obrázku 3.10 odpovídá ",[883,64788,64790],{"className":64789},[886],[888,64791,64792],{"xmlns":890},[892,64793,64794,64806],{},[895,64795,64796,64802,64804],{},[1953,64797,64798,64800],{},[898,64799,2470],{},[1810,64801,2008],{},[1677,64803,1679],{},[1810,64805,54590],{},[902,64807,64808],{"encoding":904},"Q_0 = 2{,}5",". Za obvyklých podmínek platí i obrácené tvrzení — postačí řešit rovnici ",[883,64811,64813],{"className":64812},[886],[888,64814,64815],{"xmlns":890},[892,64816,64817,64843],{},[895,64818,64819,64821,64823,64825,64827,64829,64831,64833,64835,64837,64839,64841],{},[898,64820,5643],{},[898,64822,41730],{},[898,64824,2458],{},[1677,64826,1686],{"stretchy":1685},[898,64828,2470],{},[1677,64830,1692],{"stretchy":1685},[1677,64832,1679],{},[898,64834,2499],{},[898,64836,2458],{},[1677,64838,1686],{"stretchy":1685},[898,64840,2470],{},[1677,64842,1692],{"stretchy":1685},[902,64844,64845],{"encoding":904},"AVC(Q) = MC(Q)",[115,64847,64849],{"id":64848},"zisk-a-body-zvratu","Zisk a body zvratu",[724,64851,64852,1884,64855,64871],{},[38,64853,64854],{},"Zisk",[883,64856,64858],{"className":64857},[886],[888,64859,64860],{"xmlns":890},[892,64861,64862,64868],{},[895,64863,64864,64866],{},[898,64865,5325],{},[898,64867,5382],{},[902,64869,64870],{"encoding":904},"PR"," (profit) je rozdíl celkového příjmu a celkových nákladů:",[883,64873,64875],{"className":64874},[886],[888,64876,64877],{"xmlns":890,"display":29457},[892,64878,64879,64938],{},[22145,64880,64881],{"width":29462},[22150,64882,64883,64885,64931,64933],{},[22153,64884],{"width":29467},[22153,64886,64887],{},[895,64888,64889,64891,64893,64895,64897,64899,64901,64903,64905,64907,64909,64911,64913,64915,64917,64919,64921,64923,64925,64927,64929],{},[898,64890,5325],{},[898,64892,5382],{},[1677,64894,1679],{},[898,64896,5325],{},[898,64898,5382],{},[1677,64900,1686],{"stretchy":1685},[898,64902,2470],{},[1677,64904,1692],{"stretchy":1685},[1677,64906,1679],{},[898,64908,2455],{},[898,64910,5382],{},[1677,64912,1686],{"stretchy":1685},[898,64914,2470],{},[1677,64916,1692],{"stretchy":1685},[1677,64918,1906],{},[898,64920,2455],{},[898,64922,2458],{},[1677,64924,1686],{"stretchy":1685},[898,64926,2470],{},[1677,64928,1692],{"stretchy":1685},[898,64930,1656],{"mathvariant":2057},[22153,64932],{"width":29467},[22153,64934,64935],{},[1969,64936,64937],{},"(3.12)",[902,64939,64940],{"encoding":904},"PR = PR(Q) = TR(Q) - TC(Q).\n\\tag{3.12}",[724,64942,64943,64944,5272,64959,45027,64974,64976,64977,64980,64981,64997,64998,65013,65014,65029,65030,1343,65043,65056,65057,1343,65075,65093,65094,11413,65097,65100,65101,1348,65123,9490,65145,65167,65168,9490,65198,65220],{},"Body rovnosti ",[883,64945,64947],{"className":64946},[886],[888,64948,64949],{"xmlns":890},[892,64950,64951,64957],{},[895,64952,64953,64955],{},[898,64954,2455],{},[898,64956,5382],{},[902,64958,5482],{"encoding":904},[883,64960,64962],{"className":64961},[886],[888,64963,64964],{"xmlns":890},[892,64965,64966,64972],{},[895,64967,64968,64970],{},[898,64969,2455],{},[898,64971,2458],{},[902,64973,2924],{"encoding":904},[38,64975,57118],{}," (též vyrovnání, ",[614,64978,64979],{},"break-even points","). V nejjednodušším modelu (lineární poptávka, konstantní ",[883,64982,64984],{"className":64983},[886],[888,64985,64986],{"xmlns":890},[892,64987,64988,64994],{},[895,64989,64990,64992],{},[898,64991,41730],{},[898,64993,2458],{},[902,64995,64996],{"encoding":904},"VC",") je ",[883,64999,65001],{"className":65000},[886],[888,65002,65003],{"xmlns":890},[892,65004,65005,65011],{},[895,65006,65007,65009],{},[898,65008,2455],{},[898,65010,5382],{},[902,65012,5482],{"encoding":904}," kvadratická a ",[883,65015,65017],{"className":65016},[886],[888,65018,65019],{"xmlns":890},[892,65020,65021,65027],{},[895,65022,65023,65025],{},[898,65024,2455],{},[898,65026,2458],{},[902,65028,2924],{"encoding":904}," lineární (obrázek 3.11). Křivky se protínají v bodech ",[883,65031,65033],{"className":65032},[886],[888,65034,65035],{"xmlns":890},[892,65036,65037,65041],{},[895,65038,65039],{},[898,65040,5643],{},[902,65042,5643],{"encoding":904},[883,65044,65046],{"className":65045},[886],[888,65047,65048],{"xmlns":890},[892,65049,65050,65054],{},[895,65051,65052],{},[898,65053,24644],{},[902,65055,24644],{"encoding":904}," odpovídajících množstvím ",[883,65058,65060],{"className":65059},[886],[888,65061,65062],{"xmlns":890},[892,65063,65064,65072],{},[895,65065,65066],{},[1953,65067,65068,65070],{},[898,65069,2470],{},[898,65071,5643],{},[902,65073,65074],{"encoding":904},"Q_A",[883,65076,65078],{"className":65077},[886],[888,65079,65080],{"xmlns":890},[892,65081,65082,65090],{},[895,65083,65084],{},[1953,65085,65086,65088],{},[898,65087,2470],{},[898,65089,24644],{},[902,65091,65092],{"encoding":904},"Q_B"," — firma je na ",[38,65095,65096],{},"prahu rentability",[614,65098,65099],{},"break even","). Pro ",[883,65102,65104],{"className":65103},[886],[888,65105,65106],{"xmlns":890},[892,65107,65108,65120],{},[895,65109,65110,65112,65114],{},[898,65111,2470],{},[1677,65113,3128],{},[1953,65115,65116,65118],{},[898,65117,2470],{},[898,65119,5643],{},[902,65121,65122],{"encoding":904},"Q \u003C Q_A",[883,65124,65126],{"className":65125},[886],[888,65127,65128],{"xmlns":890},[892,65129,65130,65142],{},[895,65131,65132,65134,65136],{},[898,65133,2470],{},[1677,65135,3089],{},[1953,65137,65138,65140],{},[898,65139,2470],{},[898,65141,24644],{},[902,65143,65144],{"encoding":904},"Q > Q_B",[883,65146,65148],{"className":65147},[886],[888,65149,65150],{"xmlns":890},[892,65151,65152,65164],{},[895,65153,65154,65156,65158,65160,65162],{},[898,65155,2455],{},[898,65157,2458],{},[1677,65159,3089],{},[898,65161,2455],{},[898,65163,5382],{},[902,65165,65166],{"encoding":904},"TC > TR"," (ztráta); pro ",[883,65169,65171],{"className":65170},[886],[888,65172,65173],{"xmlns":890},[892,65174,65175,65195],{},[895,65176,65177,65183,65185,65187,65189],{},[1953,65178,65179,65181],{},[898,65180,2470],{},[898,65182,5643],{},[1677,65184,3128],{},[898,65186,2470],{},[1677,65188,3128],{},[1953,65190,65191,65193],{},[898,65192,2470],{},[898,65194,24644],{},[902,65196,65197],{"encoding":904},"Q_A \u003C Q \u003C Q_B",[883,65199,65201],{"className":65200},[886],[888,65202,65203],{"xmlns":890},[892,65204,65205,65217],{},[895,65206,65207,65209,65211,65213,65215],{},[898,65208,2455],{},[898,65210,5382],{},[1677,65212,3089],{},[898,65214,2455],{},[898,65216,2458],{},[902,65218,65219],{"encoding":904},"TR > TC"," (zisk).",[5254,65222,65223],{},[724,65224,65225,65227],{},[883,65226,5543],{}," 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.",[724,65229,65230,65231,65257],{},"Body zvratu jsou řešení rovnice ",[883,65232,65234],{"className":65233},[886],[888,65235,65236],{"xmlns":890},[892,65237,65238,65254],{},[895,65239,65240,65242,65244,65246,65248,65250,65252],{},[898,65241,5325],{},[898,65243,5382],{},[1677,65245,1686],{"stretchy":1685},[898,65247,2470],{},[1677,65249,1692],{"stretchy":1685},[1677,65251,1679],{},[1810,65253,2008],{},[902,65255,65256],{"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.",[724,65259,65260],{},[2240,65261],{"alt":65262,"className":65263,"src":65264},"imek-tr-tc-body-zvratu",[210,2244],"\u002Fwiki-assets\u002Fimek-tr-tc-body-zvratu.jpeg",[724,65266,65267],{},[614,65268,65269,65270,65285,65286,65301,65302,5272,65315,44751,65328,65341,65342,5272,65359,65376,65377,65397,65398,5272,65413,7861,65428,65457],{},"Obrázek 3.11: Body zvratu — křivky ",[883,65271,65273],{"className":65272},[886],[888,65274,65275],{"xmlns":890},[892,65276,65277,65283],{},[895,65278,65279,65281],{},[898,65280,2455],{},[898,65282,5382],{},[902,65284,5482],{"encoding":904}," (obrácená parabola) a ",[883,65287,65289],{"className":65288},[886],[888,65290,65291],{"xmlns":890},[892,65292,65293,65299],{},[895,65294,65295,65297],{},[898,65296,2455],{},[898,65298,2458],{},[902,65300,2924],{"encoding":904}," (přímka) se protínají v bodech ",[883,65303,65305],{"className":65304},[886],[888,65306,65307],{"xmlns":890},[892,65308,65309,65313],{},[895,65310,65311],{},[898,65312,5643],{},[902,65314,5643],{"encoding":904},[883,65316,65318],{"className":65317},[886],[888,65319,65320],{"xmlns":890},[892,65321,65322,65326],{},[895,65323,65324],{},[898,65325,24644],{},[902,65327,24644],{"encoding":904},[883,65329,65331],{"className":65330},[886],[888,65332,65333],{"xmlns":890},[892,65334,65335,65339],{},[895,65336,65337],{},[898,65338,2470],{},[902,65340,2470],{"encoding":904}," v hodnotách ",[883,65343,65345],{"className":65344},[886],[888,65346,65347],{"xmlns":890},[892,65348,65349,65357],{},[895,65350,65351],{},[1953,65352,65353,65355],{},[898,65354,2470],{},[898,65356,5643],{},[902,65358,65074],{"encoding":904},[883,65360,65362],{"className":65361},[886],[888,65363,65364],{"xmlns":890},[892,65365,65366,65374],{},[895,65367,65368],{},[1953,65369,65370,65372],{},[898,65371,2470],{},[898,65373,24644],{},[902,65375,65092],{"encoding":904},"; maximum zisku leží mezi nimi v bodě ",[883,65378,65380],{"className":65379},[886],[888,65381,65382],{"xmlns":890},[892,65383,65384,65394],{},[895,65385,65386],{},[1953,65387,65388,65390,65392],{},[898,65389,2470],{},[898,65391,57588],{},[1677,65393,57591],{},[902,65395,65396],{"encoding":904},"Q_{\\max}","; svislá vzdálenost mezi ",[883,65399,65401],{"className":65400},[886],[888,65402,65403],{"xmlns":890},[892,65404,65405,65411],{},[895,65406,65407,65409],{},[898,65408,2455],{},[898,65410,5382],{},[902,65412,5482],{"encoding":904},[883,65414,65416],{"className":65415},[886],[888,65417,65418],{"xmlns":890},[892,65419,65420,65426],{},[895,65421,65422,65424],{},[898,65423,2455],{},[898,65425,2458],{},[902,65427,2924],{"encoding":904},[883,65429,65431],{"className":65430},[886],[888,65432,65433],{"xmlns":890},[892,65434,65435,65455],{},[895,65436,65437,65443,65445,65447,65449],{},[1953,65438,65439,65441],{},[898,65440,2470],{},[898,65442,5643],{},[1677,65444,3128],{},[898,65446,2470],{},[1677,65448,3128],{},[1953,65450,65451,65453],{},[898,65452,2470],{},[898,65454,24644],{},[902,65456,65197],{"encoding":904}," vyznačuje zisk.",[38739,65459,65461],{"id":65460},"příklad-38","Příklad 3.8",[724,65463,65464,65466,65467,1343,65487,1343,65513,65539],{},[38,65465,57378],{}," Dáno ",[883,65468,65470],{"className":65469},[886],[888,65471,65472],{"xmlns":890},[892,65473,65474,65484],{},[895,65475,65476,65478,65480,65482],{},[898,65477,11824],{},[898,65479,2458],{},[1677,65481,1679],{},[1810,65483,2032],{},[902,65485,65486],{"encoding":904},"FC = 4",[883,65488,65490],{"className":65489},[886],[888,65491,65492],{"xmlns":890},[892,65493,65494,65510],{},[895,65495,65496,65498,65500,65502,65504],{},[898,65497,2455],{},[898,65499,41730],{},[898,65501,2458],{},[1677,65503,1679],{},[1805,65505,65506,65508],{},[898,65507,2470],{},[1810,65509,1812],{},[902,65511,65512],{"encoding":904},"TVC = Q^2",[883,65514,65516],{"className":65515},[886],[888,65517,65518],{"xmlns":890},[892,65519,65520,65536],{},[895,65521,65522,65524,65526,65528,65530,65532,65534],{},[898,65523,5325],{},[1677,65525,1679],{},[1677,65527,1906],{},[1810,65529,1812],{},[898,65531,2470],{},[1677,65533,1776],{},[1810,65535,5387],{},[902,65537,65538],{"encoding":904},"P = -2Q + 9",". Určete zisk, body zvratu a bod maxima zisku.",[724,65541,65542,65544],{},[38,65543,24161],{}," Celkové náklady a příjem:",[883,65546,65548],{"className":65547},[886],[888,65549,65550],{"xmlns":890,"display":29457},[892,65551,65552,65618],{},[895,65553,65554,65556,65558,65560,65562,65564,65570,65572,65574,65576,65578,65580,65582,65584,65586,65588,65590,65592,65594,65596,65598,65600,65602,65604,65610,65612,65614,65616],{},[898,65555,2455],{},[898,65557,2458],{},[1677,65559,1679],{},[1810,65561,2032],{},[1677,65563,1776],{},[1805,65565,65566,65568],{},[898,65567,2470],{},[1810,65569,1812],{},[1677,65571,1967],{"separator":1966},[7266,65573],{"width":7268},[898,65575,2455],{},[898,65577,5382],{},[1677,65579,1679],{},[898,65581,2470],{},[1677,65583,2858],{},[1677,65585,1686],{"stretchy":1685},[1677,65587,1906],{},[1810,65589,1812],{},[898,65591,2470],{},[1677,65593,1776],{},[1810,65595,5387],{},[1677,65597,1692],{"stretchy":1685},[1677,65599,1679],{},[1677,65601,1906],{},[1810,65603,1812],{},[1805,65605,65606,65608],{},[898,65607,2470],{},[1810,65609,1812],{},[1677,65611,1776],{},[1810,65613,5387],{},[898,65615,2470],{},[898,65617,1656],{"mathvariant":2057},[902,65619,65620],{"encoding":904},"TC = 4 + Q^2, \\qquad TR = Q \\cdot (-2Q + 9) = -2Q^2 + 9Q.",[724,65622,65623],{},"Zisk dle (3.12):",[883,65625,65627],{"className":65626},[886],[888,65628,65629],{"xmlns":890,"display":29457},[892,65630,65631,65709],{},[895,65632,65633,65635,65637,65639,65641,65643,65645,65647,65649,65651,65653,65655,65657,65663,65665,65667,65669,65671,65673,65675,65677,65679,65685,65687,65689,65691,65693,65699,65701,65703,65705,65707],{},[898,65634,5325],{},[898,65636,5382],{},[1677,65638,1679],{},[898,65640,2455],{},[898,65642,5382],{},[1677,65644,1906],{},[898,65646,2455],{},[898,65648,2458],{},[1677,65650,1679],{},[1677,65652,1686],{"stretchy":1685},[1677,65654,1906],{},[1810,65656,1812],{},[1805,65658,65659,65661],{},[898,65660,2470],{},[1810,65662,1812],{},[1677,65664,1776],{},[1810,65666,5387],{},[898,65668,2470],{},[1677,65670,1692],{"stretchy":1685},[1677,65672,1906],{},[1677,65674,1686],{"stretchy":1685},[1810,65676,2032],{},[1677,65678,1776],{},[1805,65680,65681,65683],{},[898,65682,2470],{},[1810,65684,1812],{},[1677,65686,1692],{"stretchy":1685},[1677,65688,1679],{},[1677,65690,1906],{},[1810,65692,1854],{},[1805,65694,65695,65697],{},[898,65696,2470],{},[1810,65698,1812],{},[1677,65700,1776],{},[1810,65702,5387],{},[898,65704,2470],{},[1677,65706,1906],{},[1810,65708,60710],{},[902,65710,65711],{"encoding":904},"PR = TR - TC = (-2Q^2 + 9Q) - (4 + Q^2) = -3Q^2 + 9Q - 4.",[724,65713,65714,65717,65718,18967,65754,2385],{},[38,65715,65716],{},"Body zvratu"," jsou kořeny rovnice ",[883,65719,65721],{"className":65720},[886],[888,65722,65723],{"xmlns":890},[892,65724,65725,65751],{},[895,65726,65727,65729,65731,65737,65739,65741,65743,65745,65747,65749],{},[1677,65728,1906],{},[1810,65730,1854],{},[1805,65732,65733,65735],{},[898,65734,2470],{},[1810,65736,1812],{},[1677,65738,1776],{},[1810,65740,5387],{},[898,65742,2470],{},[1677,65744,1906],{},[1810,65746,2032],{},[1677,65748,1679],{},[1810,65750,2008],{},[902,65752,65753],{"encoding":904},"-3Q^2 + 9Q - 4 = 0",[883,65755,65757],{"className":65756},[886],[888,65758,65759],{"xmlns":890},[892,65760,65761,65785],{},[895,65762,65763,65765,65771,65773,65775,65777,65779,65781,65783],{},[1810,65764,1854],{},[1805,65766,65767,65769],{},[898,65768,2470],{},[1810,65770,1812],{},[1677,65772,1906],{},[1810,65774,5387],{},[898,65776,2470],{},[1677,65778,1776],{},[1810,65780,2032],{},[1677,65782,1679],{},[1810,65784,2008],{},[902,65786,65787],{"encoding":904},"3Q^2 - 9Q + 4 = 0",[883,65789,65791],{"className":65790},[886],[888,65792,65793],{"xmlns":890,"display":29457},[892,65794,65795,65852],{},[895,65796,65797,65809,65811,65834,65836,65850],{},[1953,65798,65799,65801],{},[898,65800,2470],{},[895,65802,65803,65805,65807],{},[1810,65804,1959],{},[1677,65806,1967],{"separator":1966},[1810,65808,1812],{},[1677,65810,1679],{},[2010,65812,65813,65832],{},[895,65814,65815,65817,65820],{},[1810,65816,5387],{},[1677,65818,65819],{},"±",[9505,65821,65822],{},[895,65823,65824,65827,65829],{},[1810,65825,65826],{},"81",[1677,65828,1906],{},[1810,65830,65831],{},"48",[1810,65833,1916],{},[1677,65835,1679],{},[2010,65837,65838,65848],{},[895,65839,65840,65842,65844],{},[1810,65841,5387],{},[1677,65843,65819],{},[9505,65845,65846],{},[1810,65847,10339],{},[1810,65849,1916],{},[1677,65851,1967],{"separator":1966},[902,65853,65854],{"encoding":904},"Q_{1,2} = \\frac{9 \\pm \\sqrt{81 - 48}}{6} = \\frac{9 \\pm \\sqrt{33}}{6},",[724,65856,65857,65858,5272,65881,1656],{},"numericky ",[883,65859,65861],{"className":65860},[886],[888,65862,65863],{"xmlns":890},[892,65864,65865,65878],{},[895,65866,65867,65873,65875],{},[1953,65868,65869,65871],{},[898,65870,2470],{},[1810,65872,1959],{},[1677,65874,7288],{},[1810,65876,65877],{},"0,543",[902,65879,65880],{"encoding":904},"Q_1 \\doteq 0{,}543",[883,65882,65884],{"className":65883},[886],[888,65885,65886],{"xmlns":890},[892,65887,65888,65901],{},[895,65889,65890,65896,65898],{},[1953,65891,65892,65894],{},[898,65893,2470],{},[1810,65895,1812],{},[1677,65897,7288],{},[1810,65899,65900],{},"2,457",[902,65902,65903],{"encoding":904},"Q_2 \\doteq 2{,}457",[724,65905,65906,1884,65909,8940,65954,18967,65988,66006],{},[38,65907,65908],{},"Maximum zisku.",[883,65910,65912],{"className":65911},[886],[888,65913,65914],{"xmlns":890},[892,65915,65916,65951],{},[895,65917,65918,65920,65926,65928,65930,65932,65934,65936,65938,65940,65942,65944,65946,65948],{},[898,65919,5325],{},[1805,65921,65922,65924],{},[898,65923,5382],{},[1677,65925,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,65927,1679],{},[1677,65929,1906],{},[1810,65931,1916],{},[898,65933,2470],{},[1677,65935,1776],{},[1810,65937,5387],{},[1677,65939,1679],{},[1810,65941,2008],{},[1677,65943,5375],{},[898,65945,2470],{},[1677,65947,1679],{},[1810,65949,65950],{},"1,5",[902,65952,65953],{"encoding":904},"PR' = -6Q + 9 = 0 \\Rightarrow Q = 1{,}5",[883,65955,65957],{"className":65956},[886],[888,65958,65959],{"xmlns":890},[892,65960,65961,65985],{},[895,65962,65963,65965,65975,65977,65979,65981,65983],{},[898,65964,5325],{},[1805,65966,65967,65969],{},[898,65968,5382],{},[895,65970,65971,65973],{},[1677,65972,2059],{"mathvariant":2057},[1677,65974,2059],{"mathvariant":2057},[1677,65976,1679],{},[1677,65978,1906],{},[1810,65980,1916],{},[1677,65982,3128],{},[1810,65984,2008],{},[902,65986,65987],{"encoding":904},"PR'' = -6 \u003C 0",[883,65989,65991],{"className":65990},[886],[888,65992,65993],{"xmlns":890},[892,65994,65995,66003],{},[895,65996,65997,65999,66001],{},[898,65998,2470],{},[1677,66000,1679],{},[1810,66002,65950],{},[902,66004,66005],{"encoding":904},"Q = 1{,}5"," je bod maxima s hodnotou",[883,66008,66010],{"className":66009},[886],[888,66011,66012],{"xmlns":890,"display":29457},[892,66013,66014,66077],{},[895,66015,66016,66018,66020,66022,66024,66026,66028,66030,66032,66034,66036,66038,66044,66046,66048,66050,66052,66054,66056,66058,66060,66063,66065,66068,66070,66072,66074],{},[898,66017,5325],{},[898,66019,5382],{},[1677,66021,1686],{"stretchy":1685},[1810,66023,65950],{},[1677,66025,1692],{"stretchy":1685},[1677,66027,1679],{},[1677,66029,1906],{},[1810,66031,1854],{},[1677,66033,2858],{},[1677,66035,1686],{"stretchy":1685},[1810,66037,65950],{},[1805,66039,66040,66042],{},[1677,66041,1692],{"stretchy":1685},[1810,66043,1812],{},[1677,66045,1776],{},[1810,66047,5387],{},[1677,66049,2858],{},[1810,66051,65950],{},[1677,66053,1906],{},[1810,66055,2032],{},[1677,66057,1679],{},[1677,66059,1906],{},[1810,66061,66062],{},"6,75",[1677,66064,1776],{},[1810,66066,66067],{},"13,5",[1677,66069,1906],{},[1810,66071,2032],{},[1677,66073,1679],{},[1810,66075,66076],{},"2,75.",[902,66078,66079],{"encoding":904},"PR(1{,}5) = -3 \\cdot (1{,}5)^2 + 9 \\cdot 1{,}5 - 4 = -6{,}75 + 13{,}5 - 4 = 2{,}75.",[724,66081,66082,66083,1343,66128,66181,66182,66200],{},"Pro srovnání maximum celkového příjmu (bez ohledu na náklady): ",[883,66084,66086],{"className":66085},[886],[888,66087,66088],{"xmlns":890},[892,66089,66090,66125],{},[895,66091,66092,66094,66100,66102,66104,66106,66108,66110,66112,66114,66116,66118,66120,66122],{},[898,66093,2455],{},[1805,66095,66096,66098],{},[898,66097,5382],{},[1677,66099,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,66101,1679],{},[1677,66103,1906],{},[1810,66105,2032],{},[898,66107,2470],{},[1677,66109,1776],{},[1810,66111,5387],{},[1677,66113,1679],{},[1810,66115,2008],{},[1677,66117,5375],{},[898,66119,2470],{},[1677,66121,1679],{},[1810,66123,66124],{},"2,25",[902,66126,66127],{"encoding":904},"TR' = -4Q + 9 = 0 \\Rightarrow Q = 2{,}25",[883,66129,66131],{"className":66130},[886],[888,66132,66133],{"xmlns":890},[892,66134,66135,66178],{},[895,66136,66137,66139,66147,66149,66151,66153,66155,66157,66159,66165,66167,66169,66171,66173,66175],{},[898,66138,2455],{},[1953,66140,66141,66143,66145],{},[898,66142,5382],{},[898,66144,57588],{},[1677,66146,57591],{},[1677,66148,1679],{},[1677,66150,1906],{},[1810,66152,1812],{},[1677,66154,2858],{},[1677,66156,1686],{"stretchy":1685},[1810,66158,66124],{},[1805,66160,66161,66163],{},[1677,66162,1692],{"stretchy":1685},[1810,66164,1812],{},[1677,66166,1776],{},[1810,66168,5387],{},[1677,66170,2858],{},[1810,66172,66124],{},[1677,66174,1679],{},[1810,66176,66177],{},"10,125",[902,66179,66180],{"encoding":904},"TR_{\\max} = -2 \\cdot (2{,}25)^2 + 9 \\cdot 2{,}25 = 10{,}125",". Leží vpravo od bodu maxima zisku, protože při ",[883,66183,66185],{"className":66184},[886],[888,66186,66187],{"xmlns":890},[892,66188,66189,66197],{},[895,66190,66191,66193,66195],{},[898,66192,2470],{},[1677,66194,1679],{},[1810,66196,66124],{},[902,66198,66199],{"encoding":904},"Q = 2{,}25"," rostou už náklady rychleji než příjem.",[5254,66202,66203],{},[724,66204,66205,66207,66208,1343,66230,66252,66253,1343,66270,66291,66292,66324,66325,66363,66364,2352,66382,66399,66400,5272,66428,66462,66463,9073,66501,5272,66525,1656],{},[883,66206,5800],{}," Nekonzistence v původním zdroji\nSkenovaný knižní text obsahoval v tomto příkladu dvě nesourodé hodnoty: uváděl body zvratu ",[883,66209,66211],{"className":66210},[886],[888,66212,66213],{"xmlns":890},[892,66214,66215,66227],{},[895,66216,66217,66223,66225],{},[1953,66218,66219,66221],{},[898,66220,2470],{},[1810,66222,1959],{},[1677,66224,1679],{},[1810,66226,6397],{},[902,66228,66229],{"encoding":904},"Q_1 = 0{,}5",[883,66231,66233],{"className":66232},[886],[888,66234,66235],{"xmlns":890},[892,66236,66237,66249],{},[895,66238,66239,66245,66247],{},[1953,66240,66241,66243],{},[898,66242,2470],{},[1810,66244,1812],{},[1677,66246,1679],{},[1810,66248,2032],{},[902,66250,66251],{"encoding":904},"Q_2 = 4"," (odpovídající starší verzi zadání) a zároveň maximum v ",[883,66254,66256],{"className":66255},[886],[888,66257,66258],{"xmlns":890},[892,66259,66260,66268],{},[895,66261,66262,66264,66266],{},[898,66263,2470],{},[1677,66265,1679],{},[1810,66267,66124],{},[902,66269,66199],{"encoding":904},[883,66271,66273],{"className":66272},[886],[888,66274,66275],{"xmlns":890},[892,66276,66277,66288],{},[895,66278,66279,66281,66283,66285],{},[898,66280,5325],{},[898,66282,5382],{},[1677,66284,1679],{},[1810,66286,66287],{},"6,125",[902,66289,66290],{"encoding":904},"PR = 6{,}125"," (odpovídající derivaci ",[883,66293,66295],{"className":66294},[886],[888,66296,66297],{"xmlns":890},[892,66298,66299,66321],{},[895,66300,66301,66303,66309,66311,66313,66315,66317,66319],{},[898,66302,5325],{},[1805,66304,66305,66307],{},[898,66306,5382],{},[1677,66308,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,66310,1679],{},[1677,66312,1906],{},[1810,66314,2032],{},[898,66316,2470],{},[1677,66318,1776],{},[1810,66320,5387],{},[902,66322,66323],{"encoding":904},"PR' = -4Q + 9",", tj. zisku ",[883,66326,66328],{"className":66327},[886],[888,66329,66330],{"xmlns":890},[892,66331,66332,66360],{},[895,66333,66334,66336,66338,66340,66342,66344,66350,66352,66354,66356,66358],{},[898,66335,5325],{},[898,66337,5382],{},[1677,66339,1679],{},[1677,66341,1906],{},[1810,66343,1812],{},[1805,66345,66346,66348],{},[898,66347,2470],{},[1810,66349,1812],{},[1677,66351,1776],{},[1810,66353,5387],{},[898,66355,2470],{},[1677,66357,1906],{},[1810,66359,2032],{},[902,66361,66362],{"encoding":904},"PR = -2Q^2 + 9Q - 4"," bez odčtení kvadratického členu ",[883,66365,66367],{"className":66366},[886],[888,66368,66369],{"xmlns":890},[892,66370,66371,66379],{},[895,66372,66373],{},[1805,66374,66375,66377],{},[898,66376,2470],{},[1810,66378,1812],{},[902,66380,66381],{"encoding":904},"Q^2",[883,66383,66385],{"className":66384},[886],[888,66386,66387],{"xmlns":890},[892,66388,66389,66397],{},[895,66390,66391,66393,66395],{},[898,66392,2455],{},[898,66394,41730],{},[898,66396,2458],{},[902,66398,56900],{"encoding":904},"). Zde je uvedena matematicky konzistentní verze: zadané ",[883,66401,66403],{"className":66402},[886],[888,66404,66405],{"xmlns":890},[892,66406,66407,66425],{},[895,66408,66409,66411,66413,66415,66417,66419],{},[898,66410,2455],{},[898,66412,2458],{},[1677,66414,1679],{},[1810,66416,2032],{},[1677,66418,1776],{},[1805,66420,66421,66423],{},[898,66422,2470],{},[1810,66424,1812],{},[902,66426,66427],{"encoding":904},"TC = 4 + Q^2",[883,66429,66431],{"className":66430},[886],[888,66432,66433],{"xmlns":890},[892,66434,66435,66459],{},[895,66436,66437,66439,66441,66443,66445,66447,66453,66455,66457],{},[898,66438,2455],{},[898,66440,5382],{},[1677,66442,1679],{},[1677,66444,1906],{},[1810,66446,1812],{},[1805,66448,66449,66451],{},[898,66450,2470],{},[1810,66452,1812],{},[1677,66454,1776],{},[1810,66456,5387],{},[898,66458,2470],{},[902,66460,66461],{"encoding":904},"TR = -2Q^2 + 9Q"," vedou na ",[883,66464,66466],{"className":66465},[886],[888,66467,66468],{"xmlns":890},[892,66469,66470,66498],{},[895,66471,66472,66474,66476,66478,66480,66482,66488,66490,66492,66494,66496],{},[898,66473,5325],{},[898,66475,5382],{},[1677,66477,1679],{},[1677,66479,1906],{},[1810,66481,1854],{},[1805,66483,66484,66486],{},[898,66485,2470],{},[1810,66487,1812],{},[1677,66489,1776],{},[1810,66491,5387],{},[898,66493,2470],{},[1677,66495,1906],{},[1810,66497,2032],{},[902,66499,66500],{"encoding":904},"PR = -3Q^2 + 9Q - 4",[883,66502,66504],{"className":66503},[886],[888,66505,66506],{"xmlns":890},[892,66507,66508,66522],{},[895,66509,66510,66518,66520],{},[1953,66511,66512,66514,66516],{},[898,66513,2470],{},[898,66515,57588],{},[1677,66517,57591],{},[1677,66519,1679],{},[1810,66521,65950],{},[902,66523,66524],{"encoding":904},"Q_{\\max} = 1{,}5",[883,66526,66528],{"className":66527},[886],[888,66529,66530],{"xmlns":890},[892,66531,66532,66549],{},[895,66533,66534,66536,66544,66546],{},[898,66535,5325],{},[1953,66537,66538,66540,66542],{},[898,66539,5382],{},[898,66541,57588],{},[1677,66543,57591],{},[1677,66545,1679],{},[1810,66547,66548],{},"2,75",[902,66550,66551],{"encoding":904},"PR_{\\max} = 2{,}75",[724,66553,66554],{},[614,66555,66556,66557,66584,66585,66618,66619,1343,66642,1656],{},"Obrázek 3.12: Graf ",[883,66558,66560],{"className":66559},[886],[888,66561,66562],{"xmlns":890},[892,66563,66564,66582],{},[895,66565,66566,66568,66570,66572,66574,66576],{},[898,66567,2455],{},[898,66569,2458],{},[1677,66571,1679],{},[1810,66573,2032],{},[1677,66575,1776],{},[1805,66577,66578,66580],{},[898,66579,2470],{},[1810,66581,1812],{},[902,66583,66427],{"encoding":904}," (parabola) a ",[883,66586,66588],{"className":66587},[886],[888,66589,66590],{"xmlns":890},[892,66591,66592,66616],{},[895,66593,66594,66596,66598,66600,66602,66604,66610,66612,66614],{},[898,66595,2455],{},[898,66597,5382],{},[1677,66599,1679],{},[1677,66601,1906],{},[1810,66603,1812],{},[1805,66605,66606,66608],{},[898,66607,2470],{},[1810,66609,1812],{},[1677,66611,1776],{},[1810,66613,5387],{},[898,66615,2470],{},[902,66617,66461],{"encoding":904}," (parabola); průsečíky vyznačují body zvratu ",[883,66620,66622],{"className":66621},[886],[888,66623,66624],{"xmlns":890},[892,66625,66626,66639],{},[895,66627,66628,66634,66636],{},[1953,66629,66630,66632],{},[898,66631,2470],{},[1810,66633,1959],{},[1677,66635,7288],{},[1810,66637,66638],{},"0,54",[902,66640,66641],{"encoding":904},"Q_1 \\doteq 0{,}54",[883,66643,66645],{"className":66644},[886],[888,66646,66647],{"xmlns":890},[892,66648,66649,66662],{},[895,66650,66651,66657,66659],{},[1953,66652,66653,66655],{},[898,66654,2470],{},[1810,66656,1812],{},[1677,66658,7288],{},[1810,66660,66661],{},"2,46",[902,66663,66664],{"encoding":904},"Q_2 \\doteq 2{,}46",[724,66666,66667],{},[614,66668,66669,66670,59898,66707,66724,66725,1343,66746,1656],{},"Obrázek 3.13: Graf zisku ",[883,66671,66673],{"className":66672},[886],[888,66674,66675],{"xmlns":890},[892,66676,66677,66705],{},[895,66678,66679,66681,66683,66685,66687,66689,66695,66697,66699,66701,66703],{},[898,66680,5325],{},[898,66682,5382],{},[1677,66684,1679],{},[1677,66686,1906],{},[1810,66688,1854],{},[1805,66690,66691,66693],{},[898,66692,2470],{},[1810,66694,1812],{},[1677,66696,1776],{},[1810,66698,5387],{},[898,66700,2470],{},[1677,66702,1906],{},[1810,66704,2032],{},[902,66706,66500],{"encoding":904},[883,66708,66710],{"className":66709},[886],[888,66711,66712],{"xmlns":890},[892,66713,66714,66722],{},[895,66715,66716,66718,66720],{},[898,66717,2470],{},[1677,66719,1679],{},[1810,66721,65950],{},[902,66723,66005],{"encoding":904}," a nulami ",[883,66726,66728],{"className":66727},[886],[888,66729,66730],{"xmlns":890},[892,66731,66732,66744],{},[895,66733,66734,66740,66742],{},[1953,66735,66736,66738],{},[898,66737,2470],{},[1810,66739,1959],{},[1677,66741,7288],{},[1810,66743,66638],{},[902,66745,66641],{"encoding":904},[883,66747,66749],{"className":66748},[886],[888,66750,66751],{"xmlns":890},[892,66752,66753,66765],{},[895,66754,66755,66761,66763],{},[1953,66756,66757,66759],{},[898,66758,2470],{},[1810,66760,1812],{},[1677,66762,7288],{},[1810,66764,66661],{},[902,66766,66664],{"encoding":904},[115,66768,66770],{"id":66769},"princip-maximalizace-zisku","Princip maximalizace zisku",[724,66772,66773],{},"Kromě standardního hledání extrému lze využít následující princip.",[724,66775,66776],{},[2240,66777],{"alt":66778,"className":66779,"src":66780},"imek-max-zisku-dva-pohledy",[210,2244],"\u002Fwiki-assets\u002Fimek-max-zisku-dva-pohledy.jpeg",[198,66782,17803],{"id":66783},"princip-1",[724,66785,66786,66787,2305,66802,66819],{},"Má-li zisk ",[883,66788,66790],{"className":66789},[886],[888,66791,66792],{"xmlns":890},[892,66793,66794,66800],{},[895,66795,66796,66798],{},[898,66797,5325],{},[898,66799,5382],{},[902,66801,64870],{"encoding":904},[883,66803,66805],{"className":66804},[886],[888,66806,66807],{"xmlns":890},[892,66808,66809,66817],{},[895,66810,66811],{},[1953,66812,66813,66815],{},[898,66814,2470],{},[1810,66816,2008],{},[902,66818,39699],{"encoding":904}," maximum, pak platí",[883,66821,66823],{"className":66822},[886],[888,66824,66825],{"xmlns":890,"display":29457},[892,66826,66827,66876],{},[22145,66828,66829],{"width":29462},[22150,66830,66831,66833,66869,66871],{},[22153,66832],{"width":29467},[22153,66834,66835],{},[895,66836,66837,66839,66841,66843,66849,66851,66853,66855,66857,66859,66865,66867],{},[898,66838,2499],{},[898,66840,5382],{},[1677,66842,1686],{"stretchy":1685},[1953,66844,66845,66847],{},[898,66846,2470],{},[1810,66848,2008],{},[1677,66850,1692],{"stretchy":1685},[1677,66852,1679],{},[898,66854,2499],{},[898,66856,2458],{},[1677,66858,1686],{"stretchy":1685},[1953,66860,66861,66863],{},[898,66862,2470],{},[1810,66864,2008],{},[1677,66866,1692],{"stretchy":1685},[898,66868,1656],{"mathvariant":2057},[22153,66870],{"width":29467},[22153,66872,66873],{},[1969,66874,66875],{},"(3.13)",[902,66877,66878],{"encoding":904},"MR(Q_0) = MC(Q_0).\n\\tag{3.13}",[5254,66880,66881],{},[724,66882,66883,63437,66885],{},[883,66884,57835],{},[38,66886,66887],{},"V bodě maxima zisku se mezní příjem rovná mezním nákladům.",[724,66889,66890,66893,66894,9490,66921,18967,66995,1656],{},[38,66891,66892],{},"Odvození"," (úloha 3.21): nutnou podmínkou maxima ",[883,66895,66897],{"className":66896},[886],[888,66898,66899],{"xmlns":890},[892,66900,66901,66919],{},[895,66902,66903,66905,66907,66909,66911,66913,66915,66917],{},[898,66904,5325],{},[898,66906,5382],{},[1677,66908,1679],{},[898,66910,2455],{},[898,66912,5382],{},[1677,66914,1906],{},[898,66916,2455],{},[898,66918,2458],{},[902,66920,56591],{"encoding":904},[883,66922,66924],{"className":66923},[886],[888,66925,66926],{"xmlns":890},[892,66927,66928,66992],{},[895,66929,66930,66932,66938,66940,66946,66948,66950,66952,66958,66960,66966,66968,66970,66972,66978,66980,66986,66988,66990],{},[898,66931,5325],{},[1805,66933,66934,66936],{},[898,66935,5382],{},[1677,66937,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,66939,1686],{"stretchy":1685},[1953,66941,66942,66944],{},[898,66943,2470],{},[1810,66945,2008],{},[1677,66947,1692],{"stretchy":1685},[1677,66949,1679],{},[898,66951,2455],{},[1805,66953,66954,66956],{},[898,66955,5382],{},[1677,66957,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,66959,1686],{"stretchy":1685},[1953,66961,66962,66964],{},[898,66963,2470],{},[1810,66965,2008],{},[1677,66967,1692],{"stretchy":1685},[1677,66969,1906],{},[898,66971,2455],{},[1805,66973,66974,66976],{},[898,66975,2458],{},[1677,66977,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,66979,1686],{"stretchy":1685},[1953,66981,66982,66984],{},[898,66983,2470],{},[1810,66985,2008],{},[1677,66987,1692],{"stretchy":1685},[1677,66989,1679],{},[1810,66991,2008],{},[902,66993,66994],{"encoding":904},"PR'(Q_0) = TR'(Q_0) - TC'(Q_0) = 0",[883,66996,66998],{"className":66997},[886],[888,66999,67000],{"xmlns":890},[892,67001,67002,67034],{},[895,67003,67004,67006,67008,67010,67016,67018,67020,67022,67024,67026,67032],{},[898,67005,2499],{},[898,67007,5382],{},[1677,67009,1686],{"stretchy":1685},[1953,67011,67012,67014],{},[898,67013,2470],{},[1810,67015,2008],{},[1677,67017,1692],{"stretchy":1685},[1677,67019,1679],{},[898,67021,2499],{},[898,67023,2458],{},[1677,67025,1686],{"stretchy":1685},[1953,67027,67028,67030],{},[898,67029,2470],{},[1810,67031,2008],{},[1677,67033,1692],{"stretchy":1685},[902,67035,67036],{"encoding":904},"MR(Q_0) = MC(Q_0)",[5254,67038,67039,67044],{},[724,67040,67041,67043],{},[883,67042,5960],{}," Postup — jak najít maximum zisku",[152,67045,67046,67110,67165,67202,67230],{},[123,67047,67048,67049,5272,67064,67079,67080,5306],{},"Sestavte ",[883,67050,67052],{"className":67051},[886],[888,67053,67054],{"xmlns":890},[892,67055,67056,67062],{},[895,67057,67058,67060],{},[898,67059,2455],{},[898,67061,5382],{},[902,67063,5482],{"encoding":904},[883,67065,67067],{"className":67066},[886],[888,67068,67069],{"xmlns":890},[892,67070,67071,67077],{},[895,67072,67073,67075],{},[898,67074,2455],{},[898,67076,2458],{},[902,67078,2924],{"encoding":904}," ze zadání (typicky ",[883,67081,67083],{"className":67082},[886],[888,67084,67085],{"xmlns":890},[892,67086,67087,67107],{},[895,67088,67089,67091,67093,67095,67097,67099,67101,67103,67105],{},[898,67090,2455],{},[898,67092,5382],{},[1677,67094,1679],{},[898,67096,5325],{},[1677,67098,1686],{"stretchy":1685},[898,67100,2470],{},[1677,67102,1692],{"stretchy":1685},[1677,67104,2858],{},[898,67106,2470],{},[902,67108,67109],{"encoding":904},"TR = P(Q) \\cdot Q",[123,67111,67112,67113,5272,67139,1656],{},"Vypočtěte ",[883,67114,67116],{"className":67115},[886],[888,67117,67118],{"xmlns":890},[892,67119,67120,67136],{},[895,67121,67122,67124,67126,67128,67130],{},[898,67123,2499],{},[898,67125,5382],{},[1677,67127,1679],{},[898,67129,2455],{},[1805,67131,67132,67134],{},[898,67133,5382],{},[1677,67135,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[902,67137,67138],{"encoding":904},"MR = TR'",[883,67140,67142],{"className":67141},[886],[888,67143,67144],{"xmlns":890},[892,67145,67146,67162],{},[895,67147,67148,67150,67152,67154,67156],{},[898,67149,2499],{},[898,67151,2458],{},[1677,67153,1679],{},[898,67155,2455],{},[1805,67157,67158,67160],{},[898,67159,2458],{},[1677,67161,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[902,67163,67164],{"encoding":904},"MC = TC'",[123,67166,67167,67168,1656],{},"Řešte rovnici ",[883,67169,67171],{"className":67170},[886],[888,67172,67173],{"xmlns":890},[892,67174,67175,67199],{},[895,67176,67177,67179,67181,67183,67185,67187,67189,67191,67193,67195,67197],{},[898,67178,2499],{},[898,67180,5382],{},[1677,67182,1686],{"stretchy":1685},[898,67184,2470],{},[1677,67186,1692],{"stretchy":1685},[1677,67188,1679],{},[898,67190,2499],{},[898,67192,2458],{},[1677,67194,1686],{"stretchy":1685},[898,67196,2470],{},[1677,67198,1692],{"stretchy":1685},[902,67200,67201],{"encoding":904},"MR(Q) = MC(Q)",[123,67203,67204,67205,67229],{},"Ověřte druhou derivaci ",[883,67206,67208],{"className":67207},[886],[888,67209,67210],{"xmlns":890},[892,67211,67212,67226],{},[895,67213,67214,67216],{},[898,67215,5325],{},[1805,67217,67218,67220],{},[898,67219,5382],{},[895,67221,67222,67224],{},[1677,67223,2059],{"mathvariant":2057},[1677,67225,2059],{"mathvariant":2057},[902,67227,67228],{"encoding":904},"PR''"," (nebo že má rovnice jediný ekonomicky smysluplný kořen).",[123,67231,67232,67233,67260],{},"Dosaďte do ",[883,67234,67236],{"className":67235},[886],[888,67237,67238],{"xmlns":890},[892,67239,67240,67258],{},[895,67241,67242,67244,67246,67248,67250,67252,67254,67256],{},[898,67243,5325],{},[898,67245,5382],{},[1677,67247,1679],{},[898,67249,2455],{},[898,67251,5382],{},[1677,67253,1906],{},[898,67255,2455],{},[898,67257,2458],{},[902,67259,56591],{"encoding":904}," pro hodnotu maxima.",[38739,67262,67264],{"id":67263},"příklad-39","Příklad 3.9",[724,67266,67267,57379,67269,5272,67291,67327],{},[38,67268,57378],{},[883,67270,67272],{"className":67271},[886],[888,67273,67274],{"xmlns":890},[892,67275,67276,67288],{},[895,67277,67278,67280,67282,67284,67286],{},[898,67279,5325],{},[1677,67281,1679],{},[1810,67283,39410],{},[1677,67285,1906],{},[898,67287,2470],{},[902,67289,67290],{"encoding":904},"P = 30 - Q",[883,67292,67294],{"className":67293},[886],[888,67295,67296],{"xmlns":890},[892,67297,67298,67324],{},[895,67299,67300,67302,67304,67306,67308,67314,67316,67318,67320,67322],{},[898,67301,2455],{},[898,67303,2458],{},[1677,67305,1679],{},[1810,67307,6397],{},[1805,67309,67310,67312],{},[898,67311,2470],{},[1810,67313,1812],{},[1677,67315,1776],{},[1810,67317,1916],{},[898,67319,2470],{},[1677,67321,1776],{},[1810,67323,25592],{},[902,67325,67326],{"encoding":904},"TC = 0{,}5Q^2 + 6Q + 7"," stanovte produkci maximalizující zisk.",[724,67329,67330,1884,67332,1343,67362,67400,67401,17182,67445,67479,67480,1656],{},[38,67331,24161],{},[883,67333,67335],{"className":67334},[886],[888,67336,67337],{"xmlns":890},[892,67338,67339,67359],{},[895,67340,67341,67343,67345,67347,67349,67351,67353],{},[898,67342,2455],{},[898,67344,5382],{},[1677,67346,1679],{},[1810,67348,39410],{},[898,67350,2470],{},[1677,67352,1906],{},[1805,67354,67355,67357],{},[898,67356,2470],{},[1810,67358,1812],{},[902,67360,67361],{"encoding":904},"TR = 30Q - Q^2",[883,67363,67365],{"className":67364},[886],[888,67366,67367],{"xmlns":890},[892,67368,67369,67397],{},[895,67370,67371,67373,67375,67377,67379,67381,67387,67389,67391,67393,67395],{},[898,67372,5325],{},[898,67374,5382],{},[1677,67376,1679],{},[1677,67378,1906],{},[1810,67380,65950],{},[1805,67382,67383,67385],{},[898,67384,2470],{},[1810,67386,1812],{},[1677,67388,1776],{},[1810,67390,43191],{},[898,67392,2470],{},[1677,67394,1906],{},[1810,67396,25592],{},[902,67398,67399],{"encoding":904},"PR = -1{,}5Q^2 + 24Q - 7",". Extrém: ",[883,67402,67404],{"className":67403},[886],[888,67405,67406],{"xmlns":890},[892,67407,67408,67442],{},[895,67409,67410,67412,67418,67420,67422,67424,67426,67428,67430,67432,67434,67436,67438,67440],{},[898,67411,5325],{},[1805,67413,67414,67416],{},[898,67415,5382],{},[1677,67417,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,67419,1679],{},[1677,67421,1906],{},[1810,67423,1854],{},[898,67425,2470],{},[1677,67427,1776],{},[1810,67429,43191],{},[1677,67431,1679],{},[1810,67433,2008],{},[1677,67435,5375],{},[898,67437,2470],{},[1677,67439,1679],{},[1810,67441,6973],{},[902,67443,67444],{"encoding":904},"PR' = -3Q + 24 = 0 \\Rightarrow Q = 8",[883,67446,67448],{"className":67447},[886],[888,67449,67450],{"xmlns":890},[892,67451,67452,67476],{},[895,67453,67454,67456,67466,67468,67470,67472,67474],{},[898,67455,5325],{},[1805,67457,67458,67460],{},[898,67459,5382],{},[895,67461,67462,67464],{},[1677,67463,2059],{"mathvariant":2057},[1677,67465,2059],{"mathvariant":2057},[1677,67467,1679],{},[1677,67469,1906],{},[1810,67471,1854],{},[1677,67473,3128],{},[1810,67475,2008],{},[902,67477,67478],{"encoding":904},"PR'' = -3 \u003C 0"," (maximum); ",[883,67481,67483],{"className":67482},[886],[888,67484,67485],{"xmlns":890},[892,67486,67487,67504],{},[895,67488,67489,67491,67493,67495,67497,67499,67501],{},[898,67490,5325],{},[898,67492,5382],{},[1677,67494,1686],{"stretchy":1685},[1810,67496,6973],{},[1677,67498,1692],{"stretchy":1685},[1677,67500,1679],{},[1810,67502,67503],{},"89",[902,67505,67506],{"encoding":904},"PR(8) = 89",[724,67508,67509,67510,1343,67536,17182,67560,67598],{},"Ověření principu: ",[883,67511,67513],{"className":67512},[886],[888,67514,67515],{"xmlns":890},[892,67516,67517,67533],{},[895,67518,67519,67521,67523,67525,67527,67529,67531],{},[898,67520,2499],{},[898,67522,5382],{},[1677,67524,1679],{},[1810,67526,39410],{},[1677,67528,1906],{},[1810,67530,1812],{},[898,67532,2470],{},[902,67534,67535],{"encoding":904},"MR = 30 - 2Q",[883,67537,67539],{"className":67538},[886],[888,67540,67541],{"xmlns":890},[892,67542,67543,67557],{},[895,67544,67545,67547,67549,67551,67553,67555],{},[898,67546,2499],{},[898,67548,2458],{},[1677,67550,1679],{},[898,67552,2470],{},[1677,67554,1776],{},[1810,67556,1916],{},[902,67558,67559],{"encoding":904},"MC = Q + 6",[883,67561,67563],{"className":67562},[886],[888,67564,67565],{"xmlns":890},[892,67566,67567,67595],{},[895,67568,67569,67571,67573,67575,67577,67579,67581,67583,67585,67587,67589,67591,67593],{},[898,67570,2499],{},[898,67572,5382],{},[1677,67574,1686],{"stretchy":1685},[1810,67576,6973],{},[1677,67578,1692],{"stretchy":1685},[1677,67580,1679],{},[1810,67582,24337],{},[1677,67584,1679],{},[898,67586,2499],{},[898,67588,2458],{},[1677,67590,1686],{"stretchy":1685},[1810,67592,6973],{},[1677,67594,1692],{"stretchy":1685},[902,67596,67597],{"encoding":904},"MR(8) = 14 = MC(8)",", tj. platí (3.13).",[724,67600,67601,67602,67635,67636,67653],{},"V řadě případů — má-li rovnice ",[883,67603,67605],{"className":67604},[886],[888,67606,67607],{"xmlns":890},[892,67608,67609,67633],{},[895,67610,67611,67613,67615,67617,67619,67621,67623,67625,67627,67629,67631],{},[898,67612,2499],{},[898,67614,5382],{},[1677,67616,1686],{"stretchy":1685},[898,67618,2470],{},[1677,67620,1692],{"stretchy":1685},[1677,67622,1679],{},[898,67624,2499],{},[898,67626,2458],{},[1677,67628,1686],{"stretchy":1685},[898,67630,2470],{},[1677,67632,1692],{"stretchy":1685},[902,67634,67201],{"encoding":904}," jediné ekonomicky smysluplné řešení ",[883,67637,67639],{"className":67638},[886],[888,67640,67641],{"xmlns":890},[892,67642,67643,67651],{},[895,67644,67645],{},[1953,67646,67647,67649],{},[898,67648,2470],{},[1810,67650,2008],{},[902,67652,39699],{"encoding":904}," — není třeba provádět test druhé derivace.",[38739,67655,67657],{"id":67656},"příklad-310","Příklad 3.10",[724,67659,67660,67662,67663,67667,67668,67681,67682,67713],{},[38,67661,57378],{}," Firma vyrábí minipočítače v ",[207,67664,67666],{"className":67665,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurenci",", produkuje 30 výrobků denně za ",[883,67669,67671],{"className":67670},[886],[888,67672,67673],{"xmlns":890},[892,67674,67675,67679],{},[895,67676,67677],{},[1810,67678,16581],{},[902,67680,16581],{"encoding":904}," EUR\u002Fks. ",[883,67683,67685],{"className":67684},[886],[888,67686,67687],{"xmlns":890},[892,67688,67689,67710],{},[895,67690,67691,67693,67695,67697,67699,67701,67704],{},[898,67692,2455],{},[898,67694,2458],{},[1677,67696,1679],{},[1810,67698,2801],{},[1677,67700,1776],{},[1810,67702,67703],{},"28",[1805,67705,67706,67708],{},[898,67707,2470],{},[1810,67709,1812],{},[902,67711,67712],{"encoding":904},"TC = 50 + 28Q^2",". Určete optimální denní produkci a zisk.",[724,67715,67716,1884,67718,1343,67740,1343,67760,67783],{},[38,67717,24161],{},[883,67719,67721],{"className":67720},[886],[888,67722,67723],{"xmlns":890},[892,67724,67725,67737],{},[895,67726,67727,67729,67731,67733,67735],{},[898,67728,2455],{},[898,67730,5382],{},[1677,67732,1679],{},[1810,67734,16581],{},[898,67736,2470],{},[902,67738,67739],{"encoding":904},"TR = 900Q",[883,67741,67743],{"className":67742},[886],[888,67744,67745],{"xmlns":890},[892,67746,67747,67757],{},[895,67748,67749,67751,67753,67755],{},[898,67750,2499],{},[898,67752,5382],{},[1677,67754,1679],{},[1810,67756,16581],{},[902,67758,67759],{"encoding":904},"MR = 900",[883,67761,67763],{"className":67762},[886],[888,67764,67765],{"xmlns":890},[892,67766,67767,67780],{},[895,67768,67769,67771,67773,67775,67778],{},[898,67770,2499],{},[898,67772,2458],{},[1677,67774,1679],{},[1810,67776,67777],{},"56",[898,67779,2470],{},[902,67781,67782],{"encoding":904},"MC = 56Q",". Z principu:",[883,67785,67787],{"className":67786},[886],[888,67788,67789],{"xmlns":890,"display":29457},[892,67790,67791,67833],{},[895,67792,67793,67795,67797,67799,67801,67803,67805,67807,67809,67811,67819,67821,67824,67826,67828,67830],{},[1810,67794,16581],{},[1677,67796,1679],{},[1810,67798,67777],{},[898,67800,2470],{},[1969,67802,5372],{},[1677,67804,5375],{},[1969,67806,5372],{},[898,67808,2470],{},[1677,67810,1679],{},[2006,67812,67813],{"scriptlevel":2008,"displaystyle":1685},[2010,67814,67815,67817],{},[1810,67816,16581],{},[1810,67818,67777],{},[1677,67820,7288],{},[1810,67822,67823],{},"16,07",[1969,67825,5372],{},[1677,67827,2411],{},[1969,67829,5372],{},[1810,67831,67832],{},"16.",[902,67834,67835],{"encoding":904},"900 = 56Q \\;\\Rightarrow\\; Q = \\tfrac{900}{56} \\doteq 16{,}07 \\;\\approx\\; 16.",[724,67837,67838,67839,2385],{},"Zisk při ",[883,67840,67842],{"className":67841},[886],[888,67843,67844],{"xmlns":890},[892,67845,67846,67854],{},[895,67847,67848,67850,67852],{},[898,67849,2470],{},[1677,67851,1679],{},[1810,67853,43253],{},[902,67855,67856],{"encoding":904},"Q = 16",[883,67858,67860],{"className":67859},[886],[888,67861,67862],{"xmlns":890,"display":29457},[892,67863,67864,67935],{},[895,67865,67866,67868,67870,67872,67874,67876,67878,67880,67882,67884,67886,67888,67890,67892,67894,67896,67902,67904,67906,67908,67910,67912,67914,67916,67918,67921,67923,67925,67927,67930,67933],{},[898,67867,5325],{},[898,67869,5382],{},[1677,67871,1686],{"stretchy":1685},[1810,67873,43253],{},[1677,67875,1692],{"stretchy":1685},[1677,67877,1679],{},[1810,67879,16581],{},[1677,67881,2858],{},[1810,67883,43253],{},[1677,67885,1906],{},[1677,67887,1686],{"stretchy":1685},[1810,67889,2801],{},[1677,67891,1776],{},[1810,67893,67703],{},[1677,67895,2858],{},[1805,67897,67898,67900],{},[1810,67899,43253],{},[1810,67901,1812],{},[1677,67903,1692],{"stretchy":1685},[1677,67905,1679],{},[1810,67907,24337],{},[1969,67909,2668],{},[1810,67911,21533],{},[1677,67913,1906],{},[1810,67915,25592],{},[1969,67917,2668],{},[1810,67919,67920],{},"218",[1677,67922,1679],{},[1810,67924,25592],{},[1969,67926,2668],{},[1810,67928,67929],{},"182",[1969,67931,67932],{}," EUR",[898,67934,1656],{"mathvariant":2057},[902,67936,67937],{"encoding":904},"PR(16) = 900 \\cdot 16 - (50 + 28 \\cdot 16^2) = 14\\,400 - 7\\,218 = 7\\,182 \\text{ EUR}.",[724,67939,67940],{},"Pro srovnání při původních 30 ks:",[883,67942,67944],{"className":67943},[886],[888,67945,67946],{"xmlns":890,"display":29457},[892,67947,67948,68013],{},[895,67949,67950,67952,67954,67956,67958,67960,67962,67964,67966,67968,67970,67972,67974,67976,67978,67980,67982,67984,67986,67989,67991,67993,67995,67997,67999,68001,68003,68005,68007,68009,68011],{},[898,67951,5325],{},[898,67953,5382],{},[1677,67955,1686],{"stretchy":1685},[1810,67957,39410],{},[1677,67959,1692],{"stretchy":1685},[1677,67961,1679],{},[1810,67963,16581],{},[1677,67965,2858],{},[1810,67967,39410],{},[1677,67969,1906],{},[1677,67971,1686],{"stretchy":1685},[1810,67973,2801],{},[1677,67975,1776],{},[1810,67977,67703],{},[1677,67979,2858],{},[1810,67981,16581],{},[1677,67983,1692],{"stretchy":1685},[1677,67985,1679],{},[1810,67987,67988],{},"27",[1969,67990,2668],{},[1810,67992,60473],{},[1677,67994,1906],{},[1810,67996,6392],{},[1969,67998,2668],{},[1810,68000,32134],{},[1677,68002,1679],{},[1810,68004,1959],{},[1969,68006,2668],{},[1810,68008,25134],{},[1969,68010,67932],{},[898,68012,1656],{"mathvariant":2057},[902,68014,68015],{"encoding":904},"PR(30) = 900 \\cdot 30 - (50 + 28 \\cdot 900) = 27\\,000 - 25\\,250 = 1\\,750 \\text{ EUR}.",[724,68017,68018,68021,68022,68040,68041,68059],{},[38,68019,68020],{},"Doporučení:"," vyrábět 16 ks\u002Fden se ziskem ",[883,68023,68025],{"className":68024},[886],[888,68026,68027],{"xmlns":890},[892,68028,68029,68037],{},[895,68030,68031,68033,68035],{},[1810,68032,25592],{},[1969,68034,2668],{},[1810,68036,67929],{},[902,68038,68039],{"encoding":904},"7\\,182"," EUR namísto původních ",[883,68042,68044],{"className":68043},[886],[888,68045,68046],{"xmlns":890},[892,68047,68048,68056],{},[895,68049,68050,68052,68054],{},[1810,68051,1959],{},[1969,68053,2668],{},[1810,68055,25134],{},[902,68057,68058],{"encoding":904},"1\\,750"," EUR.",[198,68061,68063],{"id":68062},"speciální-tvar-pro-pevnou-cenu","Speciální tvar pro pevnou cenu",[724,68065,68066,68067,63961,68080,68104],{},"Předpokládáme-li, že výrobce prodává za pevnou cenu ",[883,68068,68070],{"className":68069},[886],[888,68071,68072],{"xmlns":890},[892,68073,68074,68078],{},[895,68075,68076],{},[898,68077,5325],{},[902,68079,5325],{"encoding":904},[883,68081,68083],{"className":68082},[886],[888,68084,68085],{"xmlns":890},[892,68086,68087,68101],{},[895,68088,68089,68091,68093,68095,68097,68099],{},[898,68090,2455],{},[898,68092,5382],{},[1677,68094,1679],{},[898,68096,5325],{},[1677,68098,2858],{},[898,68100,2470],{},[902,68102,68103],{"encoding":904},"TR = P \\cdot Q"," a z (3.13) speciálně:",[883,68106,68108],{"className":68107},[886],[888,68109,68110],{"xmlns":890,"display":29457},[892,68111,68112,68145],{},[22145,68113,68114],{"width":29462},[22150,68115,68116,68118,68138,68140],{},[22153,68117],{"width":29467},[22153,68119,68120],{},[895,68121,68122,68124,68126,68128,68130,68132,68134,68136],{},[898,68123,5325],{},[1677,68125,1679],{},[898,68127,2499],{},[898,68129,2458],{},[1677,68131,1686],{"stretchy":1685},[898,68133,2470],{},[1677,68135,1692],{"stretchy":1685},[898,68137,1656],{"mathvariant":2057},[22153,68139],{"width":29467},[22153,68141,68142],{},[1969,68143,68144],{},"(3.14)",[902,68146,68147],{"encoding":904},"P = MC(Q).\n\\tag{3.14}",[724,68149,68150,68151,1656],{},"Výrobce musí nastavit nabízené množství tak, aby se mezní náklady rovnaly ceně. Má-li rovnice (3.14) více řešení, rozhoduje znaménko ",[883,68152,68154],{"className":68153},[886],[888,68155,68156],{"xmlns":890},[892,68157,68158,68172],{},[895,68159,68160,68162],{},[898,68161,5325],{},[1805,68163,68164,68166],{},[898,68165,5382],{},[895,68167,68168,68170],{},[1677,68169,2059],{"mathvariant":2057},[1677,68171,2059],{"mathvariant":2057},[902,68173,67228],{"encoding":904},[38739,68175,68177],{"id":68176},"příklad-311","Příklad 3.11",[724,68179,68180,58913,68182,68229,68230,68248],{},[38,68181,57378],{},[883,68183,68185],{"className":68184},[886],[888,68186,68187],{"xmlns":890},[892,68188,68189,68226],{},[895,68190,68191,68193,68195,68197,68200,68206,68208,68210,68216,68218,68220,68222,68224],{},[898,68192,2455],{},[898,68194,2458],{},[1677,68196,1679],{},[1810,68198,68199],{},"0,04",[1805,68201,68202,68204],{},[898,68203,2470],{},[1810,68205,1854],{},[1677,68207,1906],{},[1810,68209,23936],{},[1805,68211,68212,68214],{},[898,68213,2470],{},[1810,68215,1812],{},[1677,68217,1776],{},[1810,68219,2544],{},[898,68221,2470],{},[1677,68223,1776],{},[1810,68225,1909],{},[902,68227,68228],{"encoding":904},"TC = 0{,}04Q^3 - 0{,}9Q^2 + 10Q + 5"," a pevnou cenu ",[883,68231,68233],{"className":68232},[886],[888,68234,68235],{"xmlns":890},[892,68236,68237,68245],{},[895,68238,68239,68241,68243],{},[898,68240,5325],{},[1677,68242,1679],{},[1810,68244,2032],{},[902,68246,68247],{"encoding":904},"P = 4"," stanovte optimální produkci.",[724,68250,68251,68253,68254,18967,68296,68330,68331,2385],{},[38,68252,24161],{}," Z (3.14): ",[883,68255,68257],{"className":68256},[886],[888,68258,68259],{"xmlns":890},[892,68260,68261,68293],{},[895,68262,68263,68265,68267,68269,68272,68278,68280,68283,68285,68287,68289,68291],{},[898,68264,2499],{},[898,68266,2458],{},[1677,68268,1679],{},[1810,68270,68271],{},"0,12",[1805,68273,68274,68276],{},[898,68275,2470],{},[1810,68277,1812],{},[1677,68279,1906],{},[1810,68281,68282],{},"1,8",[898,68284,2470],{},[1677,68286,1776],{},[1810,68288,2544],{},[1677,68290,1679],{},[1810,68292,2032],{},[902,68294,68295],{"encoding":904},"MC = 0{,}12Q^2 - 1{,}8Q + 10 = 4",[883,68297,68299],{"className":68298},[886],[888,68300,68301],{"xmlns":890},[892,68302,68303,68327],{},[895,68304,68305,68307,68313,68315,68317,68319,68321,68323,68325],{},[1810,68306,68271],{},[1805,68308,68309,68311],{},[898,68310,2470],{},[1810,68312,1812],{},[1677,68314,1906],{},[1810,68316,68282],{},[898,68318,2470],{},[1677,68320,1776],{},[1810,68322,1916],{},[1677,68324,1679],{},[1810,68326,2008],{},[902,68328,68329],{"encoding":904},"0{,}12Q^2 - 1{,}8Q + 6 = 0",", po vydělení ",[883,68332,68334],{"className":68333},[886],[888,68335,68336],{"xmlns":890},[892,68337,68338,68342],{},[895,68339,68340],{},[1810,68341,68271],{},[902,68343,68344],{"encoding":904},"0{,}12",[883,68346,68348],{"className":68347},[886],[888,68349,68350],{"xmlns":890,"display":29457},[892,68351,68352,68404],{},[895,68353,68354,68360,68362,68364,68366,68368,68370,68372,68374,68376,68378,68380,68386,68388,68390,68392,68394,68400,68402],{},[1805,68355,68356,68358],{},[898,68357,2470],{},[1810,68359,1812],{},[1677,68361,1906],{},[1810,68363,37635],{},[898,68365,2470],{},[1677,68367,1776],{},[1810,68369,2801],{},[1677,68371,1679],{},[1810,68373,2008],{},[1969,68375,5372],{},[1677,68377,5375],{},[1969,68379,5372],{},[1953,68381,68382,68384],{},[898,68383,2470],{},[1810,68385,1959],{},[1677,68387,1679],{},[1810,68389,1909],{},[1677,68391,1967],{"separator":1966},[1969,68393,5372],{},[1953,68395,68396,68398],{},[898,68397,2470],{},[1810,68399,1812],{},[1677,68401,1679],{},[1810,68403,20719],{},[902,68405,68406],{"encoding":904},"Q^2 - 15Q + 50 = 0 \\;\\Rightarrow\\; Q_1 = 5, \\; Q_2 = 10.",[724,68408,68409,68410,2385],{},"Dále ",[883,68411,68413],{"className":68412},[886],[888,68414,68415],{"xmlns":890},[892,68416,68417,68456],{},[895,68418,68419,68421,68431,68433,68435,68437,68443,68445,68447,68450,68452,68454],{},[898,68420,5325],{},[1805,68422,68423,68425],{},[898,68424,5382],{},[895,68426,68427,68429],{},[1677,68428,2059],{"mathvariant":2057},[1677,68430,2059],{"mathvariant":2057},[1677,68432,1679],{},[1677,68434,1906],{},[898,68436,2499],{},[1805,68438,68439,68441],{},[898,68440,2458],{},[1677,68442,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,68444,1679],{},[1677,68446,1906],{},[1810,68448,68449],{},"0,24",[898,68451,2470],{},[1677,68453,1776],{},[1810,68455,68282],{},[902,68457,68458],{"encoding":904},"PR'' = -MC' = -0{,}24Q + 1{,}8",[120,68460,68461,68511],{},[123,68462,68463,68507,68508,68510],{},[883,68464,68466],{"className":68465},[886],[888,68467,68468],{"xmlns":890},[892,68469,68470,68504],{},[895,68471,68472,68474,68484,68486,68488,68490,68492,68494,68496,68498,68500,68502],{},[898,68473,5325],{},[1805,68475,68476,68478],{},[898,68477,5382],{},[895,68479,68480,68482],{},[1677,68481,2059],{"mathvariant":2057},[1677,68483,2059],{"mathvariant":2057},[1677,68485,1686],{"stretchy":1685},[1810,68487,1909],{},[1677,68489,1692],{"stretchy":1685},[1677,68491,1679],{},[1810,68493,20712],{},[1677,68495,3089],{},[1810,68497,2008],{},[1969,68499,5372],{},[1677,68501,5375],{},[1969,68503,5372],{},[902,68505,68506],{"encoding":904},"PR''(5) = 0{,}6 > 0 \\;\\Rightarrow\\;"," lokální ",[38,68509,3456],{}," zisku (minimalizace ztráty);",[123,68512,68513,68507,68559,68561],{},[883,68514,68516],{"className":68515},[886],[888,68517,68518],{"xmlns":890},[892,68519,68520,68556],{},[895,68521,68522,68524,68534,68536,68538,68540,68542,68544,68546,68548,68550,68552,68554],{},[898,68523,5325],{},[1805,68525,68526,68528],{},[898,68527,5382],{},[895,68529,68530,68532],{},[1677,68531,2059],{"mathvariant":2057},[1677,68533,2059],{"mathvariant":2057},[1677,68535,1686],{"stretchy":1685},[1810,68537,2544],{},[1677,68539,1692],{"stretchy":1685},[1677,68541,1679],{},[1677,68543,1906],{},[1810,68545,20712],{},[1677,68547,3128],{},[1810,68549,2008],{},[1969,68551,5372],{},[1677,68553,5375],{},[1969,68555,5372],{},[902,68557,68558],{"encoding":904},"PR''(10) = -0{,}6 \u003C 0 \\;\\Rightarrow\\;",[38,68560,3398],{}," zisku, avšak",[883,68563,68565],{"className":68564},[886],[888,68566,68567],{"xmlns":890,"display":29457},[892,68568,68569,68637],{},[895,68570,68571,68573,68575,68577,68579,68581,68583,68585,68587,68589,68591,68593,68595,68597,68599,68601,68603,68605,68607,68609,68611,68613,68615,68617,68619,68621,68623,68625,68627,68629,68631,68633,68635],{},[898,68572,5325],{},[898,68574,5382],{},[1677,68576,1686],{"stretchy":1685},[1810,68578,2544],{},[1677,68580,1692],{"stretchy":1685},[1677,68582,1679],{},[1810,68584,2032],{},[1677,68586,2858],{},[1810,68588,2544],{},[1677,68590,1906],{},[1677,68592,1686],{"stretchy":1685},[1810,68594,68199],{},[1677,68596,2858],{},[1810,68598,1959],{},[1969,68600,2668],{},[1810,68602,60473],{},[1677,68604,1906],{},[1810,68606,23936],{},[1677,68608,2858],{},[1810,68610,2771],{},[1677,68612,1776],{},[1810,68614,2771],{},[1677,68616,1776],{},[1810,68618,1909],{},[1677,68620,1692],{"stretchy":1685},[1677,68622,1679],{},[1810,68624,6599],{},[1677,68626,1906],{},[1810,68628,22571],{},[1677,68630,1679],{},[1677,68632,1906],{},[1810,68634,37635],{},[1677,68636,1967],{"separator":1966},[902,68638,68639],{"encoding":904},"PR(10) = 4 \\cdot 10 - (0{,}04 \\cdot 1\\,000 - 0{,}9 \\cdot 100 + 100 + 5) = 40 - 55 = -15,",[724,68641,68642,68643,1656],{},"tj. ztráta větší než ",[883,68644,68646],{"className":68645},[886],[888,68647,68648],{"xmlns":890},[892,68649,68650,68660],{},[895,68651,68652,68654,68656,68658],{},[898,68653,11824],{},[898,68655,2458],{},[1677,68657,1679],{},[1810,68659,1909],{},[902,68661,68662],{"encoding":904},"FC = 5",[724,68664,68665,68668,68669,68672,68673,1656],{},[38,68666,68667],{},"Závěr:"," firma by měla ",[38,68670,68671],{},"zastavit výrobu"," — i vypnutí provozu způsobí menší ztrátu, a to pouze ve výši ",[883,68674,68676],{"className":68675},[886],[888,68677,68678],{"xmlns":890},[892,68679,68680,68690],{},[895,68681,68682,68684,68686,68688],{},[898,68683,11824],{},[898,68685,2458],{},[1677,68687,1679],{},[1810,68689,1909],{},[902,68691,68662],{"encoding":904},[115,68693,68695],{"id":68694},"konstrukce-křivky-nabídky-firmy","Konstrukce křivky nabídky firmy",[724,68697,68698,68699,68701,68702,68717,68718,68731,68732,68758,68759,68772,68773,68790,68791,2305,68808,68811,68812,68832,68833,68848,68849,2385],{},"Důležitým završením analýzy je konstrukce ",[38,68700,56666],{},". S nabízeným množstvím rostou mezní náklady ",[883,68703,68705],{"className":68704},[886],[888,68706,68707],{"xmlns":890},[892,68708,68709,68715],{},[895,68710,68711,68713],{},[898,68712,2499],{},[898,68714,2458],{},[902,68716,56683],{"encoding":904}," a tyto určují cenu ",[883,68719,68721],{"className":68720},[886],[888,68722,68723],{"xmlns":890},[892,68724,68725,68729],{},[895,68726,68727],{},[898,68728,5325],{},[902,68730,5325],{"encoding":904},", za kterou je firma ochotna toto množství realizovat. Proto platí ",[883,68733,68735],{"className":68734},[886],[888,68736,68737],{"xmlns":890},[892,68738,68739,68755],{},[895,68740,68741,68743,68745,68747,68749,68751,68753],{},[898,68742,5325],{},[1677,68744,1679],{},[898,68746,2499],{},[898,68748,2458],{},[1677,68750,1686],{"stretchy":1685},[898,68752,2470],{},[1677,68754,1692],{"stretchy":1685},[902,68756,68757],{"encoding":904},"P = MC(Q)"," (obrázek 3.14). Cena ",[883,68760,68762],{"className":68761},[886],[888,68763,68764],{"xmlns":890},[892,68765,68766,68770],{},[895,68767,68768],{},[898,68769,5325],{},[902,68771,5325],{"encoding":904}," však nemůže být nižší než ",[883,68774,68776],{"className":68775},[886],[888,68777,68778],{"xmlns":890},[892,68779,68780,68788],{},[895,68781,68782],{},[1805,68783,68784,68786],{},[898,68785,5325],{},[1677,68787,5742],{},[902,68789,5792],{"encoding":904}," odpovídající množství ",[883,68792,68794],{"className":68793},[886],[888,68795,68796],{"xmlns":890},[892,68797,68798,68806],{},[895,68799,68800],{},[1805,68801,68802,68804],{},[898,68803,2470],{},[1677,68805,5742],{},[902,68807,31235],{"encoding":904},[38,68809,68810],{},"minima průměrných variabilních nákladů"," (fixní náklady nelze při optimalizaci zahrnout — jsou konstantní součástí nákladů i zisku). Křivka nabídky se tedy skládá z úsečky ",[883,68813,68815],{"className":68814},[886],[888,68816,68817],{"xmlns":890},[892,68818,68819,68829],{},[895,68820,68821,68823],{},[1810,68822,2008],{},[1805,68824,68825,68827],{},[898,68826,2470],{},[1677,68828,5742],{},[902,68830,68831],{"encoding":904},"0Q^*"," (kde firma nenabízí nic) a rostoucí části ",[883,68834,68836],{"className":68835},[886],[888,68837,68838],{"xmlns":890},[892,68839,68840,68846],{},[895,68841,68842,68844],{},[898,68843,2499],{},[898,68845,2458],{},[902,68847,56683],{"encoding":904}," nad bodem ",[883,68850,68852],{"className":68851},[886],[888,68853,68854],{"xmlns":890},[892,68855,68856,68860],{},[895,68857,68858],{},[898,68859,5643],{},[902,68861,5643],{"encoding":904},[883,68863,68865],{"className":68864},[886],[888,68866,68867],{"xmlns":890,"display":29457},[892,68868,68869,68976],{},[22145,68870,68871],{"width":29462},[22150,68872,68873,68875,68969,68971],{},[22153,68874],{"width":29467},[22153,68876,68877],{},[895,68878,68879,68881,68883,68885,68887,68889,68891,68893],{},[898,68880,5325],{},[1677,68882,1679],{},[898,68884,10061],{},[1677,68886,1686],{"stretchy":1685},[898,68888,2470],{},[1677,68890,1692],{"stretchy":1685},[1677,68892,1679],{},[895,68894,68895,68898],{},[1677,68896,68897],{"fence":1966},"{",[22145,68899,68902,68941],{"rowspacing":68900,"columnalign":68901,"columnspacing":16674},"0.36em","left left",[22150,68903,68904,68920],{},[22153,68905,68906],{},[2006,68907,68908],{"scriptlevel":2008,"displaystyle":1685},[895,68909,68910,68912,68914,68916,68918],{},[898,68911,2499],{},[898,68913,2458],{},[1677,68915,1686],{"stretchy":1685},[898,68917,2470],{},[1677,68919,1692],{"stretchy":1685},[22153,68921,68922],{},[2006,68923,68924],{"scriptlevel":2008,"displaystyle":1685},[895,68925,68926,68929,68931,68933,68939],{},[1969,68927,68928],{},"pro ",[898,68930,2470],{},[1677,68932,5873],{},[1805,68934,68935,68937],{},[898,68936,2470],{},[1677,68938,5742],{},[1677,68940,1967],{"separator":1966},[22150,68942,68943,68949],{},[22153,68944,68945],{},[2006,68946,68947],{"scriptlevel":2008,"displaystyle":1685},[1810,68948,2008],{},[22153,68950,68951],{},[2006,68952,68953],{"scriptlevel":2008,"displaystyle":1685},[895,68954,68955,68957,68959,68961,68967],{},[1969,68956,68928],{},[898,68958,2470],{},[1677,68960,3128],{},[1805,68962,68963,68965],{},[898,68964,2470],{},[1677,68966,5742],{},[1677,68968,1967],{"separator":1966},[22153,68970],{"width":29467},[22153,68972,68973],{},[1969,68974,68975],{},"(3.15)",[902,68977,68978],{"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}",[724,68980,5698,68981,68998,68999,69016,69017,42890,69047,69050],{},[883,68982,68984],{"className":68983},[886],[888,68985,68986],{"xmlns":890},[892,68987,68988,68996],{},[895,68989,68990],{},[1805,68991,68992,68994],{},[898,68993,2470],{},[1677,68995,5742],{},[902,68997,31235],{"encoding":904}," je bod minima ",[883,69000,69002],{"className":69001},[886],[888,69003,69004],{"xmlns":890},[892,69005,69006,69014],{},[895,69007,69008,69010,69012],{},[898,69009,5643],{},[898,69011,41730],{},[898,69013,2458],{},[902,69015,56702],{"encoding":904},". Bod ",[883,69018,69020],{"className":69019},[886],[888,69021,69022],{"xmlns":890},[892,69023,69024,69044],{},[895,69025,69026,69028,69034,69036,69042],{},[1677,69027,1686],{"stretchy":1685},[1805,69029,69030,69032],{},[898,69031,2470],{},[1677,69033,5742],{},[1677,69035,1967],{"separator":1966},[1805,69037,69038,69040],{},[898,69039,5325],{},[1677,69041,5742],{},[1677,69043,1692],{"stretchy":1685},[902,69045,69046],{"encoding":904},"(Q^*, P^*)",[38,69048,69049],{},"shutdown point"," — pod ním se firmě nevyplatí produkovat.",[5254,69052,69053,69058],{},[724,69054,69055,69057],{},[883,69056,5960],{}," Postup — jak odvodit nabídku firmy",[152,69059,69060,69109,69204,69259,69330],{},[123,69061,69062,69063,5272,69085,1656],{},"Ze zadaných nákladů určete ",[883,69064,69066],{"className":69065},[886],[888,69067,69068],{"xmlns":890},[892,69069,69070,69082],{},[895,69071,69072,69074,69076,69078,69080],{},[898,69073,2499],{},[898,69075,2458],{},[1677,69077,1686],{"stretchy":1685},[898,69079,2470],{},[1677,69081,1692],{"stretchy":1685},[902,69083,69084],{"encoding":904},"MC(Q)",[883,69086,69088],{"className":69087},[886],[888,69089,69090],{"xmlns":890},[892,69091,69092,69106],{},[895,69093,69094,69096,69098,69100,69102,69104],{},[898,69095,5643],{},[898,69097,41730],{},[898,69099,2458],{},[1677,69101,1686],{"stretchy":1685},[898,69103,2470],{},[1677,69105,1692],{"stretchy":1685},[902,69107,69108],{"encoding":904},"AVC(Q)",[123,69110,69111,69112,69129,69130,69147,69148,69180,69181,5306],{},"Najděte ",[883,69113,69115],{"className":69114},[886],[888,69116,69117],{"xmlns":890},[892,69118,69119,69127],{},[895,69120,69121],{},[1805,69122,69123,69125],{},[898,69124,2470],{},[1677,69126,5742],{},[902,69128,31235],{"encoding":904}," jako bod minima ",[883,69131,69133],{"className":69132},[886],[888,69134,69135],{"xmlns":890},[892,69136,69137,69145],{},[895,69138,69139,69141,69143],{},[898,69140,5643],{},[898,69142,41730],{},[898,69144,2458],{},[902,69146,56702],{"encoding":904}," (řešením ",[883,69149,69151],{"className":69150},[886],[888,69152,69153],{"xmlns":890},[892,69154,69155,69177],{},[895,69156,69157,69159,69161,69167,69169,69171,69173,69175],{},[898,69158,5643],{},[898,69160,41730],{},[1805,69162,69163,69165],{},[898,69164,2458],{},[1677,69166,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,69168,1686],{"stretchy":1685},[898,69170,2470],{},[1677,69172,1692],{"stretchy":1685},[1677,69174,1679],{},[1810,69176,2008],{},[902,69178,69179],{"encoding":904},"AVC'(Q) = 0",", případně rovnice ",[883,69182,69184],{"className":69183},[886],[888,69185,69186],{"xmlns":890},[892,69187,69188,69202],{},[895,69189,69190,69192,69194,69196,69198,69200],{},[898,69191,5643],{},[898,69193,41730],{},[898,69195,2458],{},[1677,69197,1679],{},[898,69199,2499],{},[898,69201,2458],{},[902,69203,56639],{"encoding":904},[123,69205,67112,69206,69258],{},[883,69207,69209],{"className":69208},[886],[888,69210,69211],{"xmlns":890},[892,69212,69213,69255],{},[895,69214,69215,69221,69223,69225,69227,69229,69235,69237,69239,69241,69243,69245,69247,69253],{},[1805,69216,69217,69219],{},[898,69218,5325],{},[1677,69220,5742],{},[1677,69222,1679],{},[898,69224,2499],{},[898,69226,2458],{},[1677,69228,1686],{"stretchy":1685},[1805,69230,69231,69233],{},[898,69232,2470],{},[1677,69234,5742],{},[1677,69236,1692],{"stretchy":1685},[1677,69238,1679],{},[898,69240,5643],{},[898,69242,41730],{},[898,69244,2458],{},[1677,69246,1686],{"stretchy":1685},[1805,69248,69249,69251],{},[898,69250,2470],{},[1677,69252,5742],{},[1677,69254,1692],{"stretchy":1685},[902,69256,69257],{"encoding":904},"P^* = MC(Q^*) = AVC(Q^*)"," — minimální cenu nabídky.",[123,69260,69261,69262,7861,69294,69316,69317,1656],{},"Zapište nabídku: ",[883,69263,69265],{"className":69264},[886],[888,69266,69267],{"xmlns":890},[892,69268,69269,69291],{},[895,69270,69271,69273,69275,69277,69279,69281,69283,69285,69287,69289],{},[898,69272,10061],{},[1677,69274,1686],{"stretchy":1685},[898,69276,2470],{},[1677,69278,1692],{"stretchy":1685},[1677,69280,1679],{},[898,69282,2499],{},[898,69284,2458],{},[1677,69286,1686],{"stretchy":1685},[898,69288,2470],{},[1677,69290,1692],{"stretchy":1685},[902,69292,69293],{"encoding":904},"S(Q) = MC(Q)",[883,69295,69297],{"className":69296},[886],[888,69298,69299],{"xmlns":890},[892,69300,69301,69313],{},[895,69302,69303,69305,69307],{},[898,69304,2470],{},[1677,69306,5873],{},[1805,69308,69309,69311],{},[898,69310,2470],{},[1677,69312,5742],{},[902,69314,69315],{"encoding":904},"Q \\geq Q^*",", jinak ",[883,69318,69320],{"className":69319},[886],[888,69321,69322],{"xmlns":890},[892,69323,69324,69328],{},[895,69325,69326],{},[1810,69327,2008],{},[902,69329,2008],{"encoding":904},[123,69331,69332,69333,69365],{},"V případě potřeby vyjádřete inverzi ",[883,69334,69336],{"className":69335},[886],[888,69337,69338],{"xmlns":890},[892,69339,69340,69362],{},[895,69341,69342,69344,69346,69356,69358,69360],{},[898,69343,2470],{},[1677,69345,1679],{},[1805,69347,69348,69350],{},[898,69349,10061],{},[895,69351,69352,69354],{},[1677,69353,1906],{},[1810,69355,1959],{},[1677,69357,1686],{"stretchy":1685},[898,69359,5325],{},[1677,69361,1692],{"stretchy":1685},[902,69363,69364],{"encoding":904},"Q = S^{-1}(P)"," doplněním na čtverec.",[724,69367,69368],{},[614,69369,69370,69371,1343,69386,5272,69403,30592,69418,69431,69432,69457,69458,69471,69472,69489,69490,69507,69508,69525],{},"Obrázek 3.14: Křivky ",[883,69372,69374],{"className":69373},[886],[888,69375,69376],{"xmlns":890},[892,69377,69378,69384],{},[895,69379,69380,69382],{},[898,69381,5643],{},[898,69383,2458],{},[902,69385,56951],{"encoding":904},[883,69387,69389],{"className":69388},[886],[888,69390,69391],{"xmlns":890},[892,69392,69393,69401],{},[895,69394,69395,69397,69399],{},[898,69396,5643],{},[898,69398,41730],{},[898,69400,2458],{},[902,69402,56702],{"encoding":904},[883,69404,69406],{"className":69405},[886],[888,69407,69408],{"xmlns":890},[892,69409,69410,69416],{},[895,69411,69412,69414],{},[898,69413,2499],{},[898,69415,2458],{},[902,69417,56683],{"encoding":904},[883,69419,69421],{"className":69420},[886],[888,69422,69423],{"xmlns":890},[892,69424,69425,69429],{},[895,69426,69427],{},[898,69428,900],{},[902,69430,900],{"encoding":904},"; křivka nabídky ",[883,69433,69435],{"className":69434},[886],[888,69436,69437],{"xmlns":890},[892,69438,69439,69455],{},[895,69440,69441,69443,69445,69447,69449,69451,69453],{},[898,69442,5325],{},[1677,69444,1679],{},[898,69446,2499],{},[898,69448,2458],{},[1677,69450,1686],{"stretchy":1685},[898,69452,2470],{},[1677,69454,1692],{"stretchy":1685},[902,69456,68757],{"encoding":904}," začíná v bodě ",[883,69459,69461],{"className":69460},[886],[888,69462,69463],{"xmlns":890},[892,69464,69465,69469],{},[895,69466,69467],{},[898,69468,5643],{},[902,69470,5643],{"encoding":904}," odpovídajícím minimu ",[883,69473,69475],{"className":69474},[886],[888,69476,69477],{"xmlns":890},[892,69478,69479,69487],{},[895,69480,69481,69483,69485],{},[898,69482,5643],{},[898,69484,41730],{},[898,69486,2458],{},[902,69488,56702],{"encoding":904}," při ceně ",[883,69491,69493],{"className":69492},[886],[888,69494,69495],{"xmlns":890},[892,69496,69497,69505],{},[895,69498,69499],{},[1805,69500,69501,69503],{},[898,69502,5325],{},[1677,69504,5742],{},[902,69506,5792],{"encoding":904}," (minimální cena nabídky); pod ",[883,69509,69511],{"className":69510},[886],[888,69512,69513],{"xmlns":890},[892,69514,69515,69523],{},[895,69516,69517],{},[1805,69518,69519,69521],{},[898,69520,2470],{},[1677,69522,5742],{},[902,69524,31235],{"encoding":904}," je nabídka nulová.",[38739,69527,69529],{"id":69528},"příklad-312","Příklad 3.12",[724,69531,69532,58913,69534,69580],{},[38,69533,57378],{},[883,69535,69537],{"className":69536},[886],[888,69538,69539],{"xmlns":890},[892,69540,69541,69577],{},[895,69542,69543,69545,69547,69549,69551,69557,69559,69561,69567,69569,69571,69573,69575],{},[898,69544,2455],{},[898,69546,2458],{},[1677,69548,1679],{},[1810,69550,2475],{},[1805,69552,69553,69555],{},[898,69554,2470],{},[1810,69556,1854],{},[1677,69558,1906],{},[1810,69560,1812],{},[1805,69562,69563,69565],{},[898,69564,2470],{},[1810,69566,1812],{},[1677,69568,1776],{},[1810,69570,37635],{},[898,69572,2470],{},[1677,69574,1776],{},[1810,69576,2544],{},[902,69578,69579],{"encoding":904},"TC = 0{,}1Q^3 - 2Q^2 + 15Q + 10"," odvoďte funkci nabídky firmy.",[724,69582,69583,1884,69585,69622,69623,2385],{},[38,69584,24161],{},[883,69586,69588],{"className":69587},[886],[888,69589,69590],{"xmlns":890},[892,69591,69592,69619],{},[895,69593,69594,69596,69598,69600,69603,69609,69611,69613,69615,69617],{},[898,69595,2499],{},[898,69597,2458],{},[1677,69599,1679],{},[1810,69601,69602],{},"0,3",[1805,69604,69605,69607],{},[898,69606,2470],{},[1810,69608,1812],{},[1677,69610,1906],{},[1810,69612,2032],{},[898,69614,2470],{},[1677,69616,1776],{},[1810,69618,37635],{},[902,69620,69621],{"encoding":904},"MC = 0{,}3Q^2 - 4Q + 15",", takže z ",[883,69624,69626],{"className":69625},[886],[888,69627,69628],{"xmlns":890},[892,69629,69630,69640],{},[895,69631,69632,69634,69636,69638],{},[898,69633,5325],{},[1677,69635,1679],{},[898,69637,2499],{},[898,69639,2458],{},[902,69641,69642],{"encoding":904},"P = MC",[883,69644,69646],{"className":69645},[886],[888,69647,69648],{"xmlns":890,"display":29457},[892,69649,69650,69675],{},[895,69651,69652,69654,69656,69658,69664,69666,69668,69670,69672],{},[898,69653,5325],{},[1677,69655,1679],{},[1810,69657,69602],{},[1805,69659,69660,69662],{},[898,69661,2470],{},[1810,69663,1812],{},[1677,69665,1906],{},[1810,69667,2032],{},[898,69669,2470],{},[1677,69671,1776],{},[1810,69673,69674],{},"15.",[902,69676,69677],{"encoding":904},"P = 0{,}3Q^2 - 4Q + 15.",[724,69679,69680,69681,6770,69694,69707],{},"Vyjádření ",[883,69682,69684],{"className":69683},[886],[888,69685,69686],{"xmlns":890},[892,69687,69688,69692],{},[895,69689,69690],{},[898,69691,2470],{},[902,69693,2470],{"encoding":904},[883,69695,69697],{"className":69696},[886],[888,69698,69699],{"xmlns":890},[892,69700,69701,69705],{},[895,69702,69703],{},[898,69704,5325],{},[902,69706,5325],{"encoding":904}," doplněním na čtverec:",[883,69709,69711],{"className":69710},[886],[888,69712,69713],{"xmlns":890,"display":29457},[892,69714,69715,69805],{},[895,69716,69717,69719,69721,69723,69761,69763,69765,69787,69789,69803],{},[898,69718,5325],{},[1677,69720,1679],{},[1810,69722,69602],{},[895,69724,69725,69727,69749,69751,69759],{},[1677,69726,1686],{"fence":1966},[1805,69728,69729,69747],{},[895,69730,69731,69733,69735,69737,69745],{},[1677,69732,1686],{"fence":1966},[898,69734,2470],{},[1677,69736,1906],{},[2006,69738,69739],{"scriptlevel":2008,"displaystyle":1685},[2010,69740,69741,69743],{},[1810,69742,10423],{},[1810,69744,1854],{},[1677,69746,1692],{"fence":1966},[1810,69748,1812],{},[1677,69750,1776],{},[2006,69752,69753],{"scriptlevel":2008,"displaystyle":1685},[2010,69754,69755,69757],{},[1810,69756,2801],{},[1810,69758,5387],{},[1677,69760,1692],{"fence":1966},[1677,69762,1967],{"separator":1966},[7266,69764],{"width":7268},[1805,69766,69767,69785],{},[895,69768,69769,69771,69773,69775,69783],{},[1677,69770,1686],{"fence":1966},[898,69772,2470],{},[1677,69774,1906],{},[2006,69776,69777],{"scriptlevel":2008,"displaystyle":1685},[2010,69778,69779,69781],{},[1810,69780,10423],{},[1810,69782,1854],{},[1677,69784,1692],{"fence":1966},[1810,69786,1812],{},[1677,69788,1679],{},[2010,69790,69791,69801],{},[895,69792,69793,69795,69797,69799],{},[1810,69794,39410],{},[898,69796,5325],{},[1677,69798,1906],{},[1810,69800,2801],{},[1810,69802,5387],{},[1677,69804,1967],{"separator":1966},[902,69806,69807],{"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},",[883,69809,69811],{"className":69810},[886],[888,69812,69813],{"xmlns":890,"display":29457},[892,69814,69815,69847],{},[895,69816,69817,69819,69821,69827,69829,69845],{},[898,69818,2470],{},[1677,69820,1679],{},[2010,69822,69823,69825],{},[1810,69824,10423],{},[1810,69826,1854],{},[1677,69828,1776],{},[2010,69830,69831,69843],{},[9505,69832,69833],{},[895,69834,69835,69837,69839,69841],{},[1810,69836,39410],{},[898,69838,5325],{},[1677,69840,1906],{},[1810,69842,2801],{},[1810,69844,1854],{},[898,69846,1656],{"mathvariant":2057},[902,69848,69849],{"encoding":904},"Q = \\frac{20}{3} + \\frac{\\sqrt{30P - 50}}{3}.",[724,69851,68409,69852,1343,69890,1343,69938,69972,69973,1656],{},[883,69853,69855],{"className":69854},[886],[888,69856,69857],{"xmlns":890},[892,69858,69859,69887],{},[895,69860,69861,69863,69865,69867,69869,69871,69877,69879,69881,69883,69885],{},[898,69862,5643],{},[898,69864,41730],{},[898,69866,2458],{},[1677,69868,1679],{},[1810,69870,2475],{},[1805,69872,69873,69875],{},[898,69874,2470],{},[1810,69876,1812],{},[1677,69878,1906],{},[1810,69880,1812],{},[898,69882,2470],{},[1677,69884,1776],{},[1810,69886,37635],{},[902,69888,69889],{"encoding":904},"AVC = 0{,}1Q^2 - 2Q + 15",[883,69891,69893],{"className":69892},[886],[888,69894,69895],{"xmlns":890},[892,69896,69897,69935],{},[895,69898,69899,69901,69903,69909,69911,69913,69915,69917,69919,69921,69923,69925,69931,69933],{},[898,69900,5643],{},[898,69902,41730],{},[1805,69904,69905,69907],{},[898,69906,2458],{},[1677,69908,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,69910,1679],{},[1810,69912,2520],{},[898,69914,2470],{},[1677,69916,1906],{},[1810,69918,1812],{},[1677,69920,1679],{},[1810,69922,2008],{},[1677,69924,5375],{},[1805,69926,69927,69929],{},[898,69928,2470],{},[1677,69930,5742],{},[1677,69932,1679],{},[1810,69934,2544],{},[902,69936,69937],{"encoding":904},"AVC' = 0{,}2Q - 2 = 0 \\Rightarrow Q^* = 10",[883,69939,69941],{"className":69940},[886],[888,69942,69943],{"xmlns":890},[892,69944,69945,69969],{},[895,69946,69947,69949,69951,69961,69963,69965,69967],{},[898,69948,5643],{},[898,69950,41730],{},[1805,69952,69953,69955],{},[898,69954,2458],{},[895,69956,69957,69959],{},[1677,69958,2059],{"mathvariant":2057},[1677,69960,2059],{"mathvariant":2057},[1677,69962,1679],{},[1810,69964,2520],{},[1677,69966,3089],{},[1810,69968,2008],{},[902,69970,69971],{"encoding":904},"AVC'' = 0{,}2 > 0"," (minimum). Minimální cena nabídky ",[883,69974,69976],{"className":69975},[886],[888,69977,69978],{"xmlns":890},[892,69979,69980,70016],{},[895,69981,69982,69988,69990,69992,69994,69996,69998,70000,70002,70004,70006,70008,70010,70012,70014],{},[1805,69983,69984,69986],{},[898,69985,5325],{},[1677,69987,5742],{},[1677,69989,1679],{},[898,69991,2499],{},[898,69993,2458],{},[1677,69995,1686],{"stretchy":1685},[1810,69997,2544],{},[1677,69999,1692],{"stretchy":1685},[1677,70001,1679],{},[1810,70003,39410],{},[1677,70005,1906],{},[1810,70007,6599],{},[1677,70009,1776],{},[1810,70011,37635],{},[1677,70013,1679],{},[1810,70015,1909],{},[902,70017,70018],{"encoding":904},"P^* = MC(10) = 30 - 40 + 15 = 5",[724,70020,70021],{},[38,70022,70023],{},"Závěr.",[883,70025,70027],{"className":70026},[886],[888,70028,70029],{"xmlns":890,"display":29457},[892,70030,70031,70117],{},[895,70032,70033,70035,70037,70039,70041,70043,70045,70047],{},[898,70034,5325],{},[1677,70036,1679],{},[898,70038,10061],{},[1677,70040,1686],{"stretchy":1685},[898,70042,2470],{},[1677,70044,1692],{"stretchy":1685},[1677,70046,1679],{},[895,70048,70049,70051],{},[1677,70050,68897],{"fence":1966},[22145,70052,70053,70095],{"rowspacing":68900,"columnalign":68901,"columnspacing":16674},[22150,70054,70055,70079],{},[22153,70056,70057],{},[2006,70058,70059],{"scriptlevel":2008,"displaystyle":1685},[895,70060,70061,70063,70069,70071,70073,70075,70077],{},[1810,70062,69602],{},[1805,70064,70065,70067],{},[898,70066,2470],{},[1810,70068,1812],{},[1677,70070,1906],{},[1810,70072,2032],{},[898,70074,2470],{},[1677,70076,1776],{},[1810,70078,37635],{},[22153,70080,70081],{},[2006,70082,70083],{"scriptlevel":2008,"displaystyle":1685},[895,70084,70085,70087,70089,70091,70093],{},[1969,70086,68928],{},[898,70088,2470],{},[1677,70090,5873],{},[1810,70092,2544],{},[1677,70094,1967],{"separator":1966},[22150,70096,70097,70103],{},[22153,70098,70099],{},[2006,70100,70101],{"scriptlevel":2008,"displaystyle":1685},[1810,70102,2008],{},[22153,70104,70105],{},[2006,70106,70107],{"scriptlevel":2008,"displaystyle":1685},[895,70108,70109,70111,70113,70115],{},[1969,70110,68928],{},[898,70112,2470],{},[1677,70114,3128],{},[1810,70116,20719],{},[902,70118,70119],{"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}",[724,70121,70122],{},[614,70123,70124,70125,70140,70141,1656],{},"Obrázek 3.15: Grafická ilustrace nabídky firmy odvozené z části křivky ",[883,70126,70128],{"className":70127},[886],[888,70129,70130],{"xmlns":890},[892,70131,70132,70138],{},[895,70133,70134,70136],{},[898,70135,2499],{},[898,70137,2458],{},[902,70139,56683],{"encoding":904}," ležící nad minimem ",[883,70142,70144],{"className":70143},[886],[888,70145,70146],{"xmlns":890},[892,70147,70148,70156],{},[895,70149,70150,70152,70154],{},[898,70151,5643],{},[898,70153,41730],{},[898,70155,2458],{},[902,70157,56702],{"encoding":904},[115,70159,70161],{"id":70160},"shrnutí-kapitoly-3","Shrnutí kapitoly 3",[724,70163,70164,70165,70169,70170,70185,70186,70206,70207,5272,70210,70213,70214,70216,70217,21336,70239,70241,70242,5272,70244,60117,70247,1884,70250,43205,70265,70280],{},"Celkový příjem je součin ceny a množství, kde cena je dána funkcí ",[207,70166,70168],{"className":70167,"dataFsResolvedFilePath":800,"href":801},[210],"poptávky",". Pro lineární poptávku je ",[883,70171,70173],{"className":70172},[886],[888,70174,70175],{"xmlns":890},[892,70176,70177,70183],{},[895,70178,70179,70181],{},[898,70180,2455],{},[898,70182,5382],{},[902,70184,5482],{"encoding":904}," kvadratická. Průměrný příjem je podíl ",[883,70187,70189],{"className":70188},[886],[888,70190,70191],{"xmlns":890},[892,70192,70193,70203],{},[895,70194,70195,70197,70199,70201],{},[898,70196,2455],{},[898,70198,5382],{},[898,70200,6062],{"mathvariant":2057},[898,70202,2470],{},[902,70204,70205],{"encoding":904},"TR\u002FQ"," a rovná se poptávkové funkci. Celkové náklady se skládají z ",[38,70208,70209],{},"fixních",[38,70211,70212],{},"celkových variabilních"," nákladů. Průměrné veličiny jsou jejich podíly s množstvím. ",[38,70215,65716],{}," identifikují, kdy se firma nachází na prahu rentability. Rozdíl ",[883,70218,70220],{"className":70219},[886],[888,70221,70222],{"xmlns":890},[892,70223,70224,70236],{},[895,70225,70226,70228,70230,70232,70234],{},[898,70227,2455],{},[898,70229,5382],{},[1677,70231,1906],{},[898,70233,2455],{},[898,70235,2458],{},[902,70237,70238],{"encoding":904},"TR - TC",[38,70240,56563],{},"; klíčový je výpočet produkce, která zisk maximalizuje. ",[38,70243,57875],{},[38,70245,70246],{},"mezní náklady",[207,70248,1145],{"className":70249,"dataFsResolvedFilePath":764,"href":765},[210],[883,70251,70253],{"className":70252},[886],[888,70254,70255],{"xmlns":890},[892,70256,70257,70263],{},[895,70258,70259,70261],{},[898,70260,2455],{},[898,70262,5382],{},[902,70264,5482],{"encoding":904},[883,70266,70268],{"className":70267},[886],[888,70269,70270],{"xmlns":890},[892,70271,70272,70278],{},[895,70273,70274,70276],{},[898,70275,2455],{},[898,70277,2458],{},[902,70279,2924],{"encoding":904}," podle produkce; udávají rychlosti změn, resp. přibližné změny odpovídající jednotkové změně produkce.",[120,70282,70283,70345,70411,70473],{},[123,70284,70285,70288,70289,11782,70304,1656],{},[38,70286,70287],{},"Princip minimalizace průměrných nákladů:"," v bodě minima ",[883,70290,70292],{"className":70291},[886],[888,70293,70294],{"xmlns":890},[892,70295,70296,70302],{},[895,70297,70298,70300],{},[898,70299,5643],{},[898,70301,2458],{},[902,70303,56951],{"encoding":904},[883,70305,70307],{"className":70306},[886],[888,70308,70309],{"xmlns":890},[892,70310,70311,70343],{},[895,70312,70313,70315,70317,70319,70325,70327,70329,70331,70333,70335,70341],{},[898,70314,5643],{},[898,70316,2458],{},[1677,70318,1686],{"stretchy":1685},[1953,70320,70321,70323],{},[898,70322,2470],{},[1810,70324,2008],{},[1677,70326,1692],{"stretchy":1685},[1677,70328,1679],{},[898,70330,2499],{},[898,70332,2458],{},[1677,70334,1686],{"stretchy":1685},[1953,70336,70337,70339],{},[898,70338,2470],{},[1810,70340,2008],{},[1677,70342,1692],{"stretchy":1685},[902,70344,63960],{"encoding":904},[123,70346,70347,70288,70350,11782,70367,1656],{},[38,70348,70349],{},"Princip minimalizace průměrných variabilních nákladů:",[883,70351,70353],{"className":70352},[886],[888,70354,70355],{"xmlns":890},[892,70356,70357,70365],{},[895,70358,70359,70361,70363],{},[898,70360,5643],{},[898,70362,41730],{},[898,70364,2458],{},[902,70366,56702],{"encoding":904},[883,70368,70370],{"className":70369},[886],[888,70371,70372],{"xmlns":890},[892,70373,70374,70408],{},[895,70375,70376,70378,70380,70382,70384,70390,70392,70394,70396,70398,70400,70406],{},[898,70377,5643],{},[898,70379,41730],{},[898,70381,2458],{},[1677,70383,1686],{"stretchy":1685},[1953,70385,70386,70388],{},[898,70387,2470],{},[1810,70389,2008],{},[1677,70391,1692],{"stretchy":1685},[1677,70393,1679],{},[898,70395,2499],{},[898,70397,2458],{},[1677,70399,1686],{"stretchy":1685},[1953,70401,70402,70404],{},[898,70403,2470],{},[1810,70405,2008],{},[1677,70407,1692],{"stretchy":1685},[902,70409,70410],{"encoding":904},"AVC(Q_0) = MC(Q_0)",[123,70412,70413,70416,70417,11782,70432,1656],{},[38,70414,70415],{},"Princip maximalizace zisku:"," v bodě maxima ",[883,70418,70420],{"className":70419},[886],[888,70421,70422],{"xmlns":890},[892,70423,70424,70430],{},[895,70425,70426,70428],{},[898,70427,5325],{},[898,70429,5382],{},[902,70431,64870],{"encoding":904},[883,70433,70435],{"className":70434},[886],[888,70436,70437],{"xmlns":890},[892,70438,70439,70471],{},[895,70440,70441,70443,70445,70447,70453,70455,70457,70459,70461,70463,70469],{},[898,70442,2499],{},[898,70444,5382],{},[1677,70446,1686],{"stretchy":1685},[1953,70448,70449,70451],{},[898,70450,2470],{},[1810,70452,2008],{},[1677,70454,1692],{"stretchy":1685},[1677,70456,1679],{},[898,70458,2499],{},[898,70460,2458],{},[1677,70462,1686],{"stretchy":1685},[1953,70464,70465,70467],{},[898,70466,2470],{},[1810,70468,2008],{},[1677,70470,1692],{"stretchy":1685},[902,70472,67036],{"encoding":904},[123,70474,70475,1884,70478,7861,70514,69316,70535,22985,70548,68998,70565,1656],{},[38,70476,70477],{},"Funkce nabídky firmy:",[883,70479,70481],{"className":70480},[886],[888,70482,70483],{"xmlns":890},[892,70484,70485,70511],{},[895,70486,70487,70489,70491,70493,70495,70497,70499,70501,70503,70505,70507,70509],{},[898,70488,5325],{},[1677,70490,1679],{},[898,70492,10061],{},[1677,70494,1686],{"stretchy":1685},[898,70496,2470],{},[1677,70498,1692],{"stretchy":1685},[1677,70500,1679],{},[898,70502,2499],{},[898,70504,2458],{},[1677,70506,1686],{"stretchy":1685},[898,70508,2470],{},[1677,70510,1692],{"stretchy":1685},[902,70512,70513],{"encoding":904},"P = S(Q) = MC(Q)",[883,70515,70517],{"className":70516},[886],[888,70518,70519],{"xmlns":890},[892,70520,70521,70533],{},[895,70522,70523,70525,70527],{},[898,70524,2470],{},[1677,70526,5873],{},[1805,70528,70529,70531],{},[898,70530,2470],{},[1677,70532,5742],{},[902,70534,69315],{"encoding":904},[883,70536,70538],{"className":70537},[886],[888,70539,70540],{"xmlns":890},[892,70541,70542,70546],{},[895,70543,70544],{},[1810,70545,2008],{},[902,70547,2008],{"encoding":904},[883,70549,70551],{"className":70550},[886],[888,70552,70553],{"xmlns":890},[892,70554,70555,70563],{},[895,70556,70557],{},[1805,70558,70559,70561],{},[898,70560,2470],{},[1677,70562,5742],{},[902,70564,31235],{"encoding":904},[883,70566,70568],{"className":70567},[886],[888,70569,70570],{"xmlns":890},[892,70571,70572,70580],{},[895,70573,70574,70576,70578],{},[898,70575,5643],{},[898,70577,41730],{},[898,70579,2458],{},[902,70581,56702],{"encoding":904},[115,70583,51273],{"id":51272},[152,70585,70586,70589,70592,70595,70598,70601,70604,70607,70610,70613,70616],{},[123,70587,70588],{},"Jaký je vztah pro celkový příjem v podmínkách dokonalé konkurence?",[123,70590,70591],{},"Jaký tvar má křivka celkového příjmu pro lineární poptávku?",[123,70593,70594],{},"Jak se vypočte mezní příjem a co udává?",[123,70596,70597],{},"Z jakých složek se skládají celkové náklady?",[123,70599,70600],{},"Jak se stanoví celkové náklady, známe-li náklady mezní?",[123,70602,70603],{},"Jaký je trend průměrných fixních nákladů a průměrných nákladů, roste-li produkce?",[123,70605,70606],{},"Jak se stanoví přibližně změna celkových nákladů?",[123,70608,70609],{},"Jak se vypočte zisk?",[123,70611,70612],{},"Jaká vlastnost platí v bodě maxima zisku?",[123,70614,70615],{},"Co jsou body zvratu? Jak se najdou?",[123,70617,70618],{},"Z jakých nákladových charakteristik se vychází při konstrukci nabídky?",[115,70620,70622],{"id":70621},"úlohy-31328","Úlohy 3.1–3.28",[198,70624,70626],{"id":70625},"příjem-3135","Příjem (3.1–3.5)",[724,70628,70629,46817,70632,70660,70661,70676,70677,70692,70693,70708,70709,1343,70724,1343,70739,70754],{},[38,70630,70631],{},"3.1",[883,70633,70635],{"className":70634},[886],[888,70636,70637],{"xmlns":890},[892,70638,70639,70657],{},[895,70640,70641,70643,70645,70647,70649,70651,70653,70655],{},[898,70642,5325],{},[1677,70644,1679],{},[898,70646,5571],{},[1677,70648,1686],{"stretchy":1685},[898,70650,2470],{},[1677,70652,1692],{"stretchy":1685},[1677,70654,1679],{},[1810,70656,2771],{},[902,70658,70659],{"encoding":904},"P = D(Q) = 100",". (a) Rozhodněte, v jakých podmínkách konkurence zadaná poptávka platí. (b) Najděte celkový příjem ",[883,70662,70664],{"className":70663},[886],[888,70665,70666],{"xmlns":890},[892,70667,70668,70674],{},[895,70669,70670,70672],{},[898,70671,2455],{},[898,70673,5382],{},[902,70675,5482],{"encoding":904},", průměrný příjem ",[883,70678,70680],{"className":70679},[886],[888,70681,70682],{"xmlns":890},[892,70683,70684,70690],{},[895,70685,70686,70688],{},[898,70687,5643],{},[898,70689,5382],{},[902,70691,56836],{"encoding":904}," a mezní příjem ",[883,70694,70696],{"className":70695},[886],[888,70697,70698],{"xmlns":890},[892,70699,70700,70706],{},[895,70701,70702,70704],{},[898,70703,2499],{},[898,70705,5382],{},[902,70707,8022],{"encoding":904},". (c) Vypočtěte ",[883,70710,70712],{"className":70711},[886],[888,70713,70714],{"xmlns":890},[892,70715,70716,70722],{},[895,70717,70718,70720],{},[898,70719,2455],{},[898,70721,5382],{},[902,70723,5482],{"encoding":904},[883,70725,70727],{"className":70726},[886],[888,70728,70729],{"xmlns":890},[892,70730,70731,70737],{},[895,70732,70733,70735],{},[898,70734,5643],{},[898,70736,5382],{},[902,70738,56836],{"encoding":904},[883,70740,70742],{"className":70741},[886],[888,70743,70744],{"xmlns":890},[892,70745,70746,70752],{},[895,70747,70748,70750],{},[898,70749,2499],{},[898,70751,5382],{},[902,70753,8022],{"encoding":904}," při množství 20. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,70756,70757,46817,70760,70660,70796,70676,70811,70692,70826,70708,70841,1343,70856,1343,70871,70886],{},[38,70758,70759],{},"3.2",[883,70761,70763],{"className":70762},[886],[888,70764,70765],{"xmlns":890},[892,70766,70767,70793],{},[895,70768,70769,70771,70773,70775,70777,70779,70781,70783,70785,70787,70789,70791],{},[898,70770,5325],{},[1677,70772,1679],{},[898,70774,5571],{},[1677,70776,1686],{"stretchy":1685},[898,70778,2470],{},[1677,70780,1692],{"stretchy":1685},[1677,70782,1679],{},[1677,70784,1906],{},[1810,70786,6397],{},[898,70788,2470],{},[1677,70790,1776],{},[1810,70792,10423],{},[902,70794,70795],{"encoding":904},"P = D(Q) = -0{,}5Q + 20",[883,70797,70799],{"className":70798},[886],[888,70800,70801],{"xmlns":890},[892,70802,70803,70809],{},[895,70804,70805,70807],{},[898,70806,2455],{},[898,70808,5382],{},[902,70810,5482],{"encoding":904},[883,70812,70814],{"className":70813},[886],[888,70815,70816],{"xmlns":890},[892,70817,70818,70824],{},[895,70819,70820,70822],{},[898,70821,5643],{},[898,70823,5382],{},[902,70825,56836],{"encoding":904},[883,70827,70829],{"className":70828},[886],[888,70830,70831],{"xmlns":890},[892,70832,70833,70839],{},[895,70834,70835,70837],{},[898,70836,2499],{},[898,70838,5382],{},[902,70840,8022],{"encoding":904},[883,70842,70844],{"className":70843},[886],[888,70845,70846],{"xmlns":890},[892,70847,70848,70854],{},[895,70849,70850,70852],{},[898,70851,2455],{},[898,70853,5382],{},[902,70855,5482],{"encoding":904},[883,70857,70859],{"className":70858},[886],[888,70860,70861],{"xmlns":890},[892,70862,70863,70869],{},[895,70864,70865,70867],{},[898,70866,5643],{},[898,70868,5382],{},[902,70870,56836],{"encoding":904},[883,70872,70874],{"className":70873},[886],[888,70875,70876],{"xmlns":890},[892,70877,70878,70884],{},[895,70879,70880,70882],{},[898,70881,2499],{},[898,70883,5382],{},[902,70885,8022],{"encoding":904}," při množství 10. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,70888,70889,46817,70892,70929,70930,70676,70945,70692,70960,70975,70976,7861,70991,71017,71018,71033,71034,1343,71049,7861,71064,71017,71089,71104,71105,71118,71119,71134,71135,71150,71151,1343,71164,1343,71179,1343,71194,1656],{},[38,70890,70891],{},"3.3",[883,70893,70895],{"className":70894},[886],[888,70896,70897],{"xmlns":890},[892,70898,70899,70926],{},[895,70900,70901,70903,70905,70907,70909,70911,70913,70915,70918,70920],{},[898,70902,5325],{},[1677,70904,1679],{},[898,70906,5571],{},[1677,70908,1686],{"stretchy":1685},[898,70910,2470],{},[1677,70912,1692],{"stretchy":1685},[1677,70914,1679],{},[1810,70916,70917],{},"1200",[1677,70919,1906],{},[1805,70921,70922,70924],{},[898,70923,2470],{},[1810,70925,1812],{},[902,70927,70928],{"encoding":904},"P = D(Q) = 1200 - Q^2",". (a) Najděte celkový příjem ",[883,70931,70933],{"className":70932},[886],[888,70934,70935],{"xmlns":890},[892,70936,70937,70943],{},[895,70938,70939,70941],{},[898,70940,2455],{},[898,70942,5382],{},[902,70944,5482],{"encoding":904},[883,70946,70948],{"className":70947},[886],[888,70949,70950],{"xmlns":890},[892,70951,70952,70958],{},[895,70953,70954,70956],{},[898,70955,5643],{},[898,70957,5382],{},[902,70959,56836],{"encoding":904},[883,70961,70963],{"className":70962},[886],[888,70964,70965],{"xmlns":890},[892,70966,70967,70973],{},[895,70968,70969,70971],{},[898,70970,2499],{},[898,70972,5382],{},[902,70974,8022],{"encoding":904},". (b) Vypočtěte ",[883,70977,70979],{"className":70978},[886],[888,70980,70981],{"xmlns":890},[892,70982,70983,70989],{},[895,70984,70985,70987],{},[898,70986,2455],{},[898,70988,5382],{},[902,70990,5482],{"encoding":904},[883,70992,70994],{"className":70993},[886],[888,70995,70996],{"xmlns":890},[892,70997,70998,71014],{},[895,70999,71000,71002,71004,71006,71008,71010,71012],{},[898,71001,2470],{},[1677,71003,1679],{},[1810,71005,2544],{},[1677,71007,1967],{"separator":1966},[1810,71009,10423],{},[1677,71011,1967],{"separator":1966},[1810,71013,39410],{},[902,71015,71016],{"encoding":904},"Q = 10, 20, 30"," a rozhodněte, kdy ",[883,71019,71021],{"className":71020},[886],[888,71022,71023],{"xmlns":890},[892,71024,71025,71031],{},[895,71026,71027,71029],{},[898,71028,2455],{},[898,71030,5382],{},[902,71032,5482],{"encoding":904}," roste, resp. klesá. (c) Vypočtěte ",[883,71035,71037],{"className":71036},[886],[888,71038,71039],{"xmlns":890},[892,71040,71041,71047],{},[895,71042,71043,71045],{},[898,71044,5643],{},[898,71046,5382],{},[902,71048,56836],{"encoding":904},[883,71050,71052],{"className":71051},[886],[888,71053,71054],{"xmlns":890},[892,71055,71056,71062],{},[895,71057,71058,71060],{},[898,71059,2499],{},[898,71061,5382],{},[902,71063,8022],{"encoding":904},[883,71065,71067],{"className":71066},[886],[888,71068,71069],{"xmlns":890},[892,71070,71071,71087],{},[895,71072,71073,71075,71077,71079,71081,71083,71085],{},[898,71074,2470],{},[1677,71076,1679],{},[1810,71078,2544],{},[1677,71080,1967],{"separator":1966},[1810,71082,10423],{},[1677,71084,1967],{"separator":1966},[1810,71086,39410],{},[902,71088,71016],{"encoding":904},[883,71090,71092],{"className":71091},[886],[888,71093,71094],{"xmlns":890},[892,71095,71096,71102],{},[895,71097,71098,71100],{},[898,71099,2499],{},[898,71101,5382],{},[902,71103,8022],{"encoding":904}," roste, resp. klesá. (d) Vypočtěte ",[883,71106,71108],{"className":71107},[886],[888,71109,71110],{"xmlns":890},[892,71111,71112,71116],{},[895,71113,71114],{},[898,71115,2470],{},[902,71117,2470],{"encoding":904},", které maximalizuje ",[883,71120,71122],{"className":71121},[886],[888,71123,71124],{"xmlns":890},[892,71125,71126,71132],{},[895,71127,71128,71130],{},[898,71129,2455],{},[898,71131,5382],{},[902,71133,5482],{"encoding":904}," a stanovte příslušnou hodnotu maxima ",[883,71136,71138],{"className":71137},[886],[888,71139,71140],{"xmlns":890},[892,71141,71142,71148],{},[895,71143,71144,71146],{},[898,71145,2455],{},[898,71147,5382],{},[902,71149,5482],{"encoding":904},". (e) Určete (je užitečné vyšetřit i jejich průběhy). (f) Charakterizujte geometricky křivky ",[883,71152,71154],{"className":71153},[886],[888,71155,71156],{"xmlns":890},[892,71157,71158,71162],{},[895,71159,71160],{},[898,71161,5571],{},[902,71163,5571],{"encoding":904},[883,71165,71167],{"className":71166},[886],[888,71168,71169],{"xmlns":890},[892,71170,71171,71177],{},[895,71172,71173,71175],{},[898,71174,2455],{},[898,71176,5382],{},[902,71178,5482],{"encoding":904},[883,71180,71182],{"className":71181},[886],[888,71183,71184],{"xmlns":890},[892,71185,71186,71192],{},[895,71187,71188,71190],{},[898,71189,5643],{},[898,71191,5382],{},[902,71193,56836],{"encoding":904},[883,71195,71197],{"className":71196},[886],[888,71198,71199],{"xmlns":890},[892,71200,71201,71207],{},[895,71202,71203,71205],{},[898,71204,2499],{},[898,71206,5382],{},[902,71208,8022],{"encoding":904},[724,71210,71211,71214,71215,71245,71246,71261,71262,11545,71275,1343,71293,1343,71310,71328,71329,71351,71352,71367,71368,71381,71382,1656],{},[38,71212,71213],{},"3.4"," Je dán celkový příjem ",[883,71216,71218],{"className":71217},[886],[888,71219,71220],{"xmlns":890},[892,71221,71222,71242],{},[895,71223,71224,71226,71228,71230,71232,71234,71236],{},[898,71225,2455],{},[898,71227,5382],{},[1677,71229,1679],{},[1810,71231,70917],{},[898,71233,2470],{},[1677,71235,1906],{},[1805,71237,71238,71240],{},[898,71239,2470],{},[1810,71241,1854],{},[902,71243,71244],{"encoding":904},"TR = 1200Q - Q^3",". (a) Určete, jak rychle se (přibližně) mění ",[883,71247,71249],{"className":71248},[886],[888,71250,71251],{"xmlns":890},[892,71252,71253,71259],{},[895,71254,71255,71257],{},[898,71256,2455],{},[898,71258,5382],{},[902,71260,5482],{"encoding":904}," vzhledem ke ",[883,71263,71265],{"className":71264},[886],[888,71266,71267],{"xmlns":890},[892,71268,71269,71273],{},[895,71270,71271],{},[898,71272,2470],{},[902,71274,2470],{"encoding":904},[883,71276,71278],{"className":71277},[886],[888,71279,71280],{"xmlns":890},[892,71281,71282,71290],{},[895,71283,71284,71286,71288],{},[898,71285,2470],{},[1677,71287,1679],{},[1810,71289,1909],{},[902,71291,71292],{"encoding":904},"Q = 5",[883,71294,71296],{"className":71295},[886],[888,71297,71298],{"xmlns":890},[892,71299,71300,71308],{},[895,71301,71302,71304,71306],{},[898,71303,2470],{},[1677,71305,1679],{},[1810,71307,6973],{},[902,71309,6976],{"encoding":904},[883,71311,71313],{"className":71312},[886],[888,71314,71315],{"xmlns":890},[892,71316,71317,71325],{},[895,71318,71319,71321,71323],{},[898,71320,2470],{},[1677,71322,1679],{},[1810,71324,3190],{},[902,71326,71327],{"encoding":904},"Q = 12"," a charakterizujte dynamiku změn. (b) Vypočtěte a ekonomicky interpretujte ",[883,71330,71332],{"className":71331},[886],[888,71333,71334],{"xmlns":890},[892,71335,71336,71348],{},[895,71337,71338,71340,71342,71344,71346],{},[898,71339,2499],{},[898,71341,5382],{},[1677,71343,1686],{"stretchy":1685},[1810,71345,2544],{},[1677,71347,1692],{"stretchy":1685},[902,71349,71350],{"encoding":904},"MR(10)",". (c) Odhadněte, o kolik se přibližně změní ",[883,71353,71355],{"className":71354},[886],[888,71356,71357],{"xmlns":890},[892,71358,71359,71365],{},[895,71360,71361,71363],{},[898,71362,2455],{},[898,71364,5382],{},[902,71366,5482],{"encoding":904},", jestliže se ",[883,71369,71371],{"className":71370},[886],[888,71372,71373],{"xmlns":890},[892,71374,71375,71379],{},[895,71376,71377],{},[898,71378,2470],{},[902,71380,2470],{"encoding":904}," změní z 10 na 12 a porovnejte se skutečnou změnou ",[883,71383,71385],{"className":71384},[886],[888,71386,71387],{"xmlns":890},[892,71388,71389,71395],{},[895,71390,71391,71393],{},[898,71392,2455],{},[898,71394,5382],{},[902,71396,5482],{"encoding":904},[724,71398,71399,71402,71403,71429,71430,71445,71446,71367,71461,71474],{},[38,71400,71401],{},"3.5"," Je dán mezní příjem ",[883,71404,71406],{"className":71405},[886],[888,71407,71408],{"xmlns":890},[892,71409,71410,71426],{},[895,71411,71412,71414,71416,71418,71420,71422,71424],{},[898,71413,2499],{},[898,71415,5382],{},[1677,71417,1679],{},[1677,71419,1906],{},[898,71421,2470],{},[1677,71423,1776],{},[1810,71425,10423],{},[902,71427,71428],{"encoding":904},"MR = -Q + 20",". (a) Určete celkový příjem ",[883,71431,71433],{"className":71432},[886],[888,71434,71435],{"xmlns":890},[892,71436,71437,71443],{},[895,71438,71439,71441],{},[898,71440,2455],{},[898,71442,5382],{},[902,71444,5482],{"encoding":904},". (b) Vypočtěte změnu ",[883,71447,71449],{"className":71448},[886],[888,71450,71451],{"xmlns":890},[892,71452,71453,71459],{},[895,71454,71455,71457],{},[898,71456,2455],{},[898,71458,5382],{},[902,71460,5482],{"encoding":904},[883,71462,71464],{"className":71463},[886],[888,71465,71466],{"xmlns":890},[892,71467,71468,71472],{},[895,71469,71470],{},[898,71471,2470],{},[902,71473,2470],{"encoding":904}," změní z 8 na 12.",[198,71476,71478],{"id":71477},"náklady-36316","Náklady (3.6–3.16)",[724,71480,71481,71484,71485,71525,71526,71541,71542,71559,71560,71577,71578,71593,71594,71609,71610,70975,71625,1343,71640,1343,71657,1343,71674,1343,71689,1343,71704,7861,71719,71737,71738,1343,71753,1343,71768,71783],{},[38,71482,71483],{},"3.6"," Jsou dány celkové náklady ",[883,71486,71488],{"className":71487},[886],[888,71489,71490],{"xmlns":890},[892,71491,71492,71522],{},[895,71493,71494,71496,71498,71500,71502,71504,71506,71508,71510],{},[898,71495,2455],{},[898,71497,2458],{},[1677,71499,1679],{},[1810,71501,2771],{},[1677,71503,1776],{},[1810,71505,1812],{},[898,71507,2470],{},[1677,71509,1776],{},[2006,71511,71512],{"scriptlevel":2008,"displaystyle":1685},[2010,71513,71514,71520],{},[1805,71515,71516,71518],{},[898,71517,2470],{},[1810,71519,1812],{},[1810,71521,2544],{},[902,71523,71524],{"encoding":904},"TC = 100 + 2Q + \\tfrac{Q^2}{10}",". (a) Určete fixní náklady ",[883,71527,71529],{"className":71528},[886],[888,71530,71531],{"xmlns":890},[892,71532,71533,71539],{},[895,71534,71535,71537],{},[898,71536,11824],{},[898,71538,2458],{},[902,71540,56882],{"encoding":904},", celkové variabilní náklady ",[883,71543,71545],{"className":71544},[886],[888,71546,71547],{"xmlns":890},[892,71548,71549,71557],{},[895,71550,71551,71553,71555],{},[898,71552,2455],{},[898,71554,41730],{},[898,71556,2458],{},[902,71558,56900],{"encoding":904},", průměrné variabilní náklady ",[883,71561,71563],{"className":71562},[886],[888,71564,71565],{"xmlns":890},[892,71566,71567,71575],{},[895,71568,71569,71571,71573],{},[898,71570,5643],{},[898,71572,41730],{},[898,71574,2458],{},[902,71576,56702],{"encoding":904},", variabilní náklady na jednotku ",[883,71579,71581],{"className":71580},[886],[888,71582,71583],{"xmlns":890},[892,71584,71585,71591],{},[895,71586,71587,71589],{},[898,71588,41730],{},[898,71590,2458],{},[902,71592,64996],{"encoding":904},", průměrné náklady ",[883,71595,71597],{"className":71596},[886],[888,71598,71599],{"xmlns":890},[892,71600,71601,71607],{},[895,71602,71603,71605],{},[898,71604,5643],{},[898,71606,2458],{},[902,71608,56951],{"encoding":904}," a mezní náklady ",[883,71611,71613],{"className":71612},[886],[888,71614,71615],{"xmlns":890},[892,71616,71617,71623],{},[895,71618,71619,71621],{},[898,71620,2499],{},[898,71622,2458],{},[902,71624,56683],{"encoding":904},[883,71626,71628],{"className":71627},[886],[888,71629,71630],{"xmlns":890},[892,71631,71632,71638],{},[895,71633,71634,71636],{},[898,71635,2455],{},[898,71637,2458],{},[902,71639,2924],{"encoding":904},[883,71641,71643],{"className":71642},[886],[888,71644,71645],{"xmlns":890},[892,71646,71647,71655],{},[895,71648,71649,71651,71653],{},[898,71650,2455],{},[898,71652,41730],{},[898,71654,2458],{},[902,71656,56900],{"encoding":904},[883,71658,71660],{"className":71659},[886],[888,71661,71662],{"xmlns":890},[892,71663,71664,71672],{},[895,71665,71666,71668,71670],{},[898,71667,5643],{},[898,71669,41730],{},[898,71671,2458],{},[902,71673,56702],{"encoding":904},[883,71675,71677],{"className":71676},[886],[888,71678,71679],{"xmlns":890},[892,71680,71681,71687],{},[895,71682,71683,71685],{},[898,71684,41730],{},[898,71686,2458],{},[902,71688,64996],{"encoding":904},[883,71690,71692],{"className":71691},[886],[888,71693,71694],{"xmlns":890},[892,71695,71696,71702],{},[895,71697,71698,71700],{},[898,71699,5643],{},[898,71701,2458],{},[902,71703,56951],{"encoding":904},[883,71705,71707],{"className":71706},[886],[888,71708,71709],{"xmlns":890},[892,71710,71711,71717],{},[895,71712,71713,71715],{},[898,71714,2499],{},[898,71716,2458],{},[902,71718,56683],{"encoding":904},[883,71720,71722],{"className":71721},[886],[888,71723,71724],{"xmlns":890},[892,71725,71726,71734],{},[895,71727,71728,71730,71732],{},[898,71729,2470],{},[1677,71731,1679],{},[1810,71733,2801],{},[902,71735,71736],{"encoding":904},"Q = 50",". (c) Rozhodněte, kdy ",[883,71739,71741],{"className":71740},[886],[888,71742,71743],{"xmlns":890},[892,71744,71745,71751],{},[895,71746,71747,71749],{},[898,71748,2455],{},[898,71750,2458],{},[902,71752,2924],{"encoding":904},[883,71754,71756],{"className":71755},[886],[888,71757,71758],{"xmlns":890},[892,71759,71760,71766],{},[895,71761,71762,71764],{},[898,71763,5643],{},[898,71765,2458],{},[902,71767,56951],{"encoding":904},[883,71769,71771],{"className":71770},[886],[888,71772,71773],{"xmlns":890},[892,71774,71775,71781],{},[895,71776,71777,71779],{},[898,71778,2499],{},[898,71780,2458],{},[902,71782,56683],{"encoding":904}," rostou, resp. klesají.",[724,71785,71786,71789,71790,71609,71820,71835,71836,71851,71852,1343,71867,1343,71882,1656],{},[38,71787,71788],{},"3.7"," Jsou dány průměrné náklady ",[883,71791,71793],{"className":71792},[886],[888,71794,71795],{"xmlns":890},[892,71796,71797,71817],{},[895,71798,71799,71801,71803,71805,71813,71815],{},[898,71800,5643],{},[898,71802,2458],{},[1677,71804,1679],{},[2006,71806,71807],{"scriptlevel":2008,"displaystyle":1685},[2010,71808,71809,71811],{},[1810,71810,2771],{},[898,71812,2470],{},[1677,71814,1776],{},[1810,71816,10423],{},[902,71818,71819],{"encoding":904},"AC = \\tfrac{100}{Q} + 20",[883,71821,71823],{"className":71822},[886],[888,71824,71825],{"xmlns":890},[892,71826,71827,71833],{},[895,71828,71829,71831],{},[898,71830,2499],{},[898,71832,2458],{},[902,71834,56683],{"encoding":904},". (a) Určete celkové náklady ",[883,71837,71839],{"className":71838},[886],[888,71840,71841],{"xmlns":890},[892,71842,71843,71849],{},[895,71844,71845,71847],{},[898,71846,2455],{},[898,71848,2458],{},[902,71850,2924],{"encoding":904},". (b) Načrtněte a geometricky charakterizujte křivky ",[883,71853,71855],{"className":71854},[886],[888,71856,71857],{"xmlns":890},[892,71858,71859,71865],{},[895,71860,71861,71863],{},[898,71862,5643],{},[898,71864,2458],{},[902,71866,56951],{"encoding":904},[883,71868,71870],{"className":71869},[886],[888,71871,71872],{"xmlns":890},[892,71873,71874,71880],{},[895,71875,71876,71878],{},[898,71877,2455],{},[898,71879,2458],{},[902,71881,2924],{"encoding":904},[883,71883,71885],{"className":71884},[886],[888,71886,71887],{"xmlns":890},[892,71888,71889,71895],{},[895,71890,71891,71893],{},[898,71892,2499],{},[898,71894,2458],{},[902,71896,56683],{"encoding":904},[724,71898,71899,71484,71902,71946,71947,1343,71964,1343,71979,1343,71996,1343,72011,1343,72028,1656],{},[38,71900,71901],{},"3.8",[883,71903,71905],{"className":71904},[886],[888,71906,71907],{"xmlns":890},[892,71908,71909,71943],{},[895,71910,71911,71913,71915,71917,71919,71921,71923,71925,71927,71929,71935,71937],{},[898,71912,2455],{},[898,71914,2458],{},[1677,71916,1679],{},[1810,71918,48094],{},[1677,71920,1776],{},[1810,71922,39410],{},[898,71924,2470],{},[1677,71926,1906],{},[1810,71928,1916],{},[1805,71930,71931,71933],{},[898,71932,2470],{},[1810,71934,1812],{},[1677,71936,1776],{},[1805,71938,71939,71941],{},[898,71940,2470],{},[1810,71942,1854],{},[902,71944,71945],{"encoding":904},"TC = 80 + 30Q - 6Q^2 + Q^3",". Určete ",[883,71948,71950],{"className":71949},[886],[888,71951,71952],{"xmlns":890},[892,71953,71954,71962],{},[895,71955,71956,71958,71960],{},[898,71957,2455],{},[898,71959,41730],{},[898,71961,2458],{},[902,71963,56900],{"encoding":904},[883,71965,71967],{"className":71966},[886],[888,71968,71969],{"xmlns":890},[892,71970,71971,71977],{},[895,71972,71973,71975],{},[898,71974,11824],{},[898,71976,2458],{},[902,71978,56882],{"encoding":904},[883,71980,71982],{"className":71981},[886],[888,71983,71984],{"xmlns":890},[892,71985,71986,71994],{},[895,71987,71988,71990,71992],{},[898,71989,5643],{},[898,71991,41730],{},[898,71993,2458],{},[902,71995,56702],{"encoding":904},[883,71997,71999],{"className":71998},[886],[888,72000,72001],{"xmlns":890},[892,72002,72003,72009],{},[895,72004,72005,72007],{},[898,72006,5643],{},[898,72008,2458],{},[902,72010,56951],{"encoding":904},[883,72012,72014],{"className":72013},[886],[888,72015,72016],{"xmlns":890},[892,72017,72018,72026],{},[895,72019,72020,72022,72024],{},[898,72021,5643],{},[898,72023,11824],{},[898,72025,2458],{},[902,72027,56918],{"encoding":904},[883,72029,72031],{"className":72030},[886],[888,72032,72033],{"xmlns":890},[892,72034,72035,72041],{},[895,72036,72037,72039],{},[898,72038,2499],{},[898,72040,2458],{},[902,72042,56683],{"encoding":904},[724,72044,72045,71484,72048,72078,72079,71261,72094,7861,72107,1343,72125,1343,72143,71328,72161,71351,72183,72198,72199,72212,72213,1656],{},[38,72046,72047],{},"3.9",[883,72049,72051],{"className":72050},[886],[888,72052,72053],{"xmlns":890},[892,72054,72055,72075],{},[895,72056,72057,72059,72061,72063,72065,72067,72069],{},[898,72058,2455],{},[898,72060,2458],{},[1677,72062,1679],{},[1810,72064,16500],{},[1677,72066,1776],{},[1810,72068,20712],{},[1805,72070,72071,72073],{},[898,72072,2470],{},[1810,72074,1812],{},[902,72076,72077],{"encoding":904},"TC = 500 + 0{,}6Q^2",". (a) Určete, jak rychle se přibližně mění ",[883,72080,72082],{"className":72081},[886],[888,72083,72084],{"xmlns":890},[892,72085,72086,72092],{},[895,72087,72088,72090],{},[898,72089,2455],{},[898,72091,2458],{},[902,72093,2924],{"encoding":904},[883,72095,72097],{"className":72096},[886],[888,72098,72099],{"xmlns":890},[892,72100,72101,72105],{},[895,72102,72103],{},[898,72104,2470],{},[902,72106,2470],{"encoding":904},[883,72108,72110],{"className":72109},[886],[888,72111,72112],{"xmlns":890},[892,72113,72114,72122],{},[895,72115,72116,72118,72120],{},[898,72117,2470],{},[1677,72119,1679],{},[1810,72121,2544],{},[902,72123,72124],{"encoding":904},"Q = 10",[883,72126,72128],{"className":72127},[886],[888,72129,72130],{"xmlns":890},[892,72131,72132,72140],{},[895,72133,72134,72136,72138],{},[898,72135,2470],{},[1677,72137,1679],{},[1810,72139,10423],{},[902,72141,72142],{"encoding":904},"Q = 20",[883,72144,72146],{"className":72145},[886],[888,72147,72148],{"xmlns":890},[892,72149,72150,72158],{},[895,72151,72152,72154,72156],{},[898,72153,2470],{},[1677,72155,1679],{},[1810,72157,39410],{},[902,72159,72160],{"encoding":904},"Q = 30",[883,72162,72164],{"className":72163},[886],[888,72165,72166],{"xmlns":890},[892,72167,72168,72180],{},[895,72169,72170,72172,72174,72176,72178],{},[898,72171,2499],{},[898,72173,2458],{},[1677,72175,1686],{"stretchy":1685},[1810,72177,37635],{},[1677,72179,1692],{"stretchy":1685},[902,72181,72182],{"encoding":904},"MC(15)",[883,72184,72186],{"className":72185},[886],[888,72187,72188],{"xmlns":890},[892,72189,72190,72196],{},[895,72191,72192,72194],{},[898,72193,2455],{},[898,72195,2458],{},[902,72197,2924],{"encoding":904}," v důsledku změny ",[883,72200,72202],{"className":72201},[886],[888,72203,72204],{"xmlns":890},[892,72205,72206,72210],{},[895,72207,72208],{},[898,72209,2470],{},[902,72211,2470],{"encoding":904}," z 15 na 20 a porovnejte se skutečnou změnou ",[883,72214,72216],{"className":72215},[886],[888,72217,72218],{"xmlns":890},[892,72219,72220,72226],{},[895,72221,72222,72224],{},[898,72223,2455],{},[898,72225,2458],{},[902,72227,2924],{"encoding":904},[724,72229,72230,72233,72234,71835,72270,72285,72286,71445,72305,72198,72320,72333],{},[38,72231,72232],{},"3.10"," Jsou dány mezní náklady ",[883,72235,72237],{"className":72236},[886],[888,72238,72239],{"xmlns":890},[892,72240,72241,72267],{},[895,72242,72243,72245,72247,72249,72251,72253,72255,72257,72259,72261],{},[898,72244,2499],{},[898,72246,2458],{},[1677,72248,1679],{},[1810,72250,2807],{},[1677,72252,1906],{},[1810,72254,43253],{},[898,72256,2470],{},[1677,72258,1776],{},[1810,72260,65950],{},[1805,72262,72263,72265],{},[898,72264,2470],{},[1810,72266,1812],{},[902,72268,72269],{"encoding":904},"MC = 60 - 16Q + 1{,}5Q^2",[883,72271,72273],{"className":72272},[886],[888,72274,72275],{"xmlns":890},[892,72276,72277,72283],{},[895,72278,72279,72281],{},[898,72280,2455],{},[898,72282,2458],{},[902,72284,2924],{"encoding":904},", jestliže fixní náklady ",[883,72287,72289],{"className":72288},[886],[888,72290,72291],{"xmlns":890},[892,72292,72293,72303],{},[895,72294,72295,72297,72299,72301],{},[898,72296,11824],{},[898,72298,2458],{},[1677,72300,1679],{},[1810,72302,2771],{},[902,72304,13022],{"encoding":904},[883,72306,72308],{"className":72307},[886],[888,72309,72310],{"xmlns":890},[892,72311,72312,72318],{},[895,72313,72314,72316],{},[898,72315,2455],{},[898,72317,2458],{},[902,72319,2924],{"encoding":904},[883,72321,72323],{"className":72322},[886],[888,72324,72325],{"xmlns":890},[892,72326,72327,72331],{},[895,72328,72329],{},[898,72330,2470],{},[902,72332,2470],{"encoding":904}," z 15 na 20.",[724,72335,72336,71484,72339,72382,72383,72396,72397,72412,72413,72428,72429,72396,72442,72412,72459,72476,72477,72396,72490,72412,72505,72520,72521,72541,72542,72565],{},[38,72337,72338],{},"3.11",[883,72340,72342],{"className":72341},[886],[888,72343,72344],{"xmlns":890},[892,72345,72346,72380],{},[895,72347,72348,72350,72352,72354,72356,72358,72360,72362,72364,72366,72372,72374],{},[898,72349,2455],{},[898,72351,2458],{},[1677,72353,1679],{},[1810,72355,2771],{},[1677,72357,1776],{},[1810,72359,6392],{},[898,72361,2470],{},[1677,72363,1906],{},[1810,72365,1909],{},[1805,72367,72368,72370],{},[898,72369,2470],{},[1810,72371,1812],{},[1677,72373,1776],{},[1805,72375,72376,72378],{},[898,72377,2470],{},[1810,72379,1854],{},[902,72381,62298],{"encoding":904},". (a) Určete ",[883,72384,72386],{"className":72385},[886],[888,72387,72388],{"xmlns":890},[892,72389,72390,72394],{},[895,72391,72392],{},[898,72393,2470],{},[902,72395,2470],{"encoding":904},", které minimalizuje ",[883,72398,72400],{"className":72399},[886],[888,72401,72402],{"xmlns":890},[892,72403,72404,72410],{},[895,72405,72406,72408],{},[898,72407,2499],{},[898,72409,2458],{},[902,72411,56683],{"encoding":904}," a stanovte příslušnou hodnotu minima ",[883,72414,72416],{"className":72415},[886],[888,72417,72418],{"xmlns":890},[892,72419,72420,72426],{},[895,72421,72422,72424],{},[898,72423,2499],{},[898,72425,2458],{},[902,72427,56683],{"encoding":904},". (b) Určete ",[883,72430,72432],{"className":72431},[886],[888,72433,72434],{"xmlns":890},[892,72435,72436,72440],{},[895,72437,72438],{},[898,72439,2470],{},[902,72441,2470],{"encoding":904},[883,72443,72445],{"className":72444},[886],[888,72446,72447],{"xmlns":890},[892,72448,72449,72457],{},[895,72450,72451,72453,72455],{},[898,72452,5643],{},[898,72454,41730],{},[898,72456,2458],{},[902,72458,56702],{"encoding":904},[883,72460,72462],{"className":72461},[886],[888,72463,72464],{"xmlns":890},[892,72465,72466,72474],{},[895,72467,72468,72470,72472],{},[898,72469,5643],{},[898,72471,41730],{},[898,72473,2458],{},[902,72475,56702],{"encoding":904},". (c) Určete ",[883,72478,72480],{"className":72479},[886],[888,72481,72482],{"xmlns":890},[892,72483,72484,72488],{},[895,72485,72486],{},[898,72487,2470],{},[902,72489,2470],{"encoding":904},[883,72491,72493],{"className":72492},[886],[888,72494,72495],{"xmlns":890},[892,72496,72497,72503],{},[895,72498,72499,72501],{},[898,72500,5643],{},[898,72502,2458],{},[902,72504,56951],{"encoding":904},[883,72506,72508],{"className":72507},[886],[888,72509,72510],{"xmlns":890},[892,72511,72512,72518],{},[895,72513,72514,72516],{},[898,72515,5643],{},[898,72517,2458],{},[902,72519,56951],{"encoding":904}," (rada: hledaný kořen ",[883,72522,72524],{"className":72523},[886],[888,72525,72526],{"xmlns":890},[892,72527,72528,72538],{},[895,72529,72530,72532],{},[898,72531,5643],{},[1805,72533,72534,72536],{},[898,72535,2458],{},[1677,72537,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[902,72539,72540],{"encoding":904},"AC'"," určete přibližně, patří do ",[883,72543,72545],{"className":72544},[886],[888,72546,72547],{"xmlns":890},[892,72548,72549,72562],{},[895,72550,72551,72553,72556,72558,72560],{},[1677,72552,1686],{"stretchy":1685},[1810,72554,72555],{},"4,7",[1677,72557,9813],{"separator":1966},[1810,72559,6667],{},[1677,72561,1692],{"stretchy":1685},[902,72563,72564],{"encoding":904},"(4{,}7; 4{,}8)",", zpřesněte).",[724,72567,72568,72571,72572,2305,72600,72617,72618,22985,72659,72680],{},[38,72569,72570],{},"3.12"," Dokažte, že mají-li průměrné náklady ",[883,72573,72575],{"className":72574},[886],[888,72576,72577],{"xmlns":890},[892,72578,72579,72597],{},[895,72580,72581,72583,72585,72587,72589,72591,72593,72595],{},[898,72582,5643],{},[898,72584,2458],{},[1677,72586,1679],{},[898,72588,5643],{},[898,72590,2458],{},[1677,72592,1686],{"stretchy":1685},[898,72594,2470],{},[1677,72596,1692],{"stretchy":1685},[902,72598,72599],{"encoding":904},"AC = AC(Q)",[883,72601,72603],{"className":72602},[886],[888,72604,72605],{"xmlns":890},[892,72606,72607,72615],{},[895,72608,72609],{},[1953,72610,72611,72613],{},[898,72612,2470],{},[1810,72614,2008],{},[902,72616,39699],{"encoding":904}," minimum, pak platí ",[883,72619,72621],{"className":72620},[886],[888,72622,72623],{"xmlns":890},[892,72624,72625,72657],{},[895,72626,72627,72629,72631,72633,72639,72641,72643,72645,72647,72649,72655],{},[898,72628,5643],{},[898,72630,2458],{},[1677,72632,1686],{"stretchy":1685},[1953,72634,72635,72637],{},[898,72636,2470],{},[1810,72638,2008],{},[1677,72640,1692],{"stretchy":1685},[1677,72642,1679],{},[898,72644,2499],{},[898,72646,2458],{},[1677,72648,1686],{"stretchy":1685},[1953,72650,72651,72653],{},[898,72652,2470],{},[1810,72654,2008],{},[1677,72656,1692],{"stretchy":1685},[902,72658,63960],{"encoding":904},[883,72660,72662],{"className":72661},[886],[888,72663,72664],{"xmlns":890},[892,72665,72666,72678],{},[895,72667,72668,72670,72672,72674,72676],{},[898,72669,2499],{},[898,72671,2458],{},[1677,72673,1686],{"stretchy":1685},[898,72675,2470],{},[1677,72677,1692],{"stretchy":1685},[902,72679,69084],{"encoding":904}," jsou mezní náklady.",[724,72682,72683,71484,72686,71946,72720,72396,72733,72412,72748,1656],{},[38,72684,72685],{},"3.13",[883,72687,72689],{"className":72688},[886],[888,72690,72691],{"xmlns":890},[892,72692,72693,72717],{},[895,72694,72695,72697,72699,72701,72707,72709,72711,72713,72715],{},[898,72696,2455],{},[898,72698,2458],{},[1677,72700,1679],{},[1805,72702,72703,72705],{},[898,72704,2470],{},[1810,72706,1812],{},[1677,72708,1776],{},[1810,72710,1812],{},[898,72712,2470],{},[1677,72714,1776],{},[1810,72716,6392],{},[902,72718,72719],{"encoding":904},"TC = Q^2 + 2Q + 25",[883,72721,72723],{"className":72722},[886],[888,72724,72725],{"xmlns":890},[892,72726,72727,72731],{},[895,72728,72729],{},[898,72730,2470],{},[902,72732,2470],{"encoding":904},[883,72734,72736],{"className":72735},[886],[888,72737,72738],{"xmlns":890},[892,72739,72740,72746],{},[895,72741,72742,72744],{},[898,72743,5643],{},[898,72745,2458],{},[902,72747,56951],{"encoding":904},[883,72749,72751],{"className":72750},[886],[888,72752,72753],{"xmlns":890},[892,72754,72755,72761],{},[895,72756,72757,72759],{},[898,72758,5643],{},[898,72760,2458],{},[902,72762,56951],{"encoding":904},[724,72764,72765,72768,72769,2305,72801,72617,72818,22985,72861,72680],{},[38,72766,72767],{},"3.14"," Dokažte, že mají-li průměrné variabilní náklady ",[883,72770,72772],{"className":72771},[886],[888,72773,72774],{"xmlns":890},[892,72775,72776,72798],{},[895,72777,72778,72780,72782,72784,72786,72788,72790,72792,72794,72796],{},[898,72779,5643],{},[898,72781,41730],{},[898,72783,2458],{},[1677,72785,1679],{},[898,72787,5643],{},[898,72789,41730],{},[898,72791,2458],{},[1677,72793,1686],{"stretchy":1685},[898,72795,2470],{},[1677,72797,1692],{"stretchy":1685},[902,72799,72800],{"encoding":904},"AVC = AVC(Q)",[883,72802,72804],{"className":72803},[886],[888,72805,72806],{"xmlns":890},[892,72807,72808,72816],{},[895,72809,72810],{},[1953,72811,72812,72814],{},[898,72813,2470],{},[1810,72815,2008],{},[902,72817,39699],{"encoding":904},[883,72819,72821],{"className":72820},[886],[888,72822,72823],{"xmlns":890},[892,72824,72825,72859],{},[895,72826,72827,72829,72831,72833,72835,72841,72843,72845,72847,72849,72851,72857],{},[898,72828,5643],{},[898,72830,41730],{},[898,72832,2458],{},[1677,72834,1686],{"stretchy":1685},[1953,72836,72837,72839],{},[898,72838,2470],{},[1810,72840,2008],{},[1677,72842,1692],{"stretchy":1685},[1677,72844,1679],{},[898,72846,2499],{},[898,72848,2458],{},[1677,72850,1686],{"stretchy":1685},[1953,72852,72853,72855],{},[898,72854,2470],{},[1810,72856,2008],{},[1677,72858,1692],{"stretchy":1685},[902,72860,70410],{"encoding":904},[883,72862,72864],{"className":72863},[886],[888,72865,72866],{"xmlns":890},[892,72867,72868,72880],{},[895,72869,72870,72872,72874,72876,72878],{},[898,72871,2499],{},[898,72873,2458],{},[1677,72875,1686],{"stretchy":1685},[898,72877,2470],{},[1677,72879,1692],{"stretchy":1685},[902,72881,69084],{"encoding":904},[724,72883,72884,71484,72887,71946,72933,72396,72946,72412,72963,1656],{},[38,72885,72886],{},"3.15",[883,72888,72890],{"className":72889},[886],[888,72891,72892],{"xmlns":890},[892,72893,72894,72930],{},[895,72895,72896,72898,72900,72902,72904,72906,72908,72910,72912,72914,72920,72922,72924],{},[898,72897,2455],{},[898,72899,2458],{},[1677,72901,1679],{},[1810,72903,2801],{},[1677,72905,1776],{},[1810,72907,37635],{},[898,72909,2470],{},[1677,72911,1906],{},[1810,72913,1812],{},[1805,72915,72916,72918],{},[898,72917,2470],{},[1810,72919,1812],{},[1677,72921,1776],{},[1810,72923,2520],{},[1805,72925,72926,72928],{},[898,72927,2470],{},[1810,72929,1854],{},[902,72931,72932],{"encoding":904},"TC = 50 + 15Q - 2Q^2 + 0{,}2Q^3",[883,72934,72936],{"className":72935},[886],[888,72937,72938],{"xmlns":890},[892,72939,72940,72944],{},[895,72941,72942],{},[898,72943,2470],{},[902,72945,2470],{"encoding":904},[883,72947,72949],{"className":72948},[886],[888,72950,72951],{"xmlns":890},[892,72952,72953,72961],{},[895,72954,72955,72957,72959],{},[898,72956,5643],{},[898,72958,41730],{},[898,72960,2458],{},[902,72962,56702],{"encoding":904},[883,72964,72966],{"className":72965},[886],[888,72967,72968],{"xmlns":890},[892,72969,72970,72978],{},[895,72971,72972,72974,72976],{},[898,72973,5643],{},[898,72975,41730],{},[898,72977,2458],{},[902,72979,56702],{"encoding":904},[724,72981,72982,72985,72986,72999,73000,73020],{},[38,72983,72984],{},"3.16"," Celkové náklady na výstavbu domu o ",[883,72987,72989],{"className":72988},[886],[888,72990,72991],{"xmlns":890},[892,72992,72993,72997],{},[895,72994,72995],{},[898,72996,1689],{},[902,72998,1689],{"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 ",[883,73001,73003],{"className":73002},[886],[888,73004,73005],{"xmlns":890},[892,73006,73007,73017],{},[895,73008,73009,73011,73013,73015],{},[1810,73010,2544],{},[1969,73012,2668],{},[1810,73014,60473],{},[898,73016,1689],{},[902,73018,73019],{"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.",[198,73022,73024],{"id":73023},"zisk-body-zvratu-317325","Zisk, body zvratu (3.17–3.25)",[724,73026,73027,73030,73031,5272,73053,73079],{},[38,73028,73029],{},"3.17"," Jsou dány ",[883,73032,73034],{"className":73033},[886],[888,73035,73036],{"xmlns":890},[892,73037,73038,73050],{},[895,73039,73040,73042,73044,73046,73048],{},[898,73041,2455],{},[898,73043,5382],{},[1677,73045,1679],{},[1810,73047,2544],{},[898,73049,2470],{},[902,73051,73052],{"encoding":904},"TR = 10Q",[883,73054,73056],{"className":73055},[886],[888,73057,73058],{"xmlns":890},[892,73059,73060,73076],{},[895,73061,73062,73064,73066,73068,73070,73072,73074],{},[898,73063,2455],{},[898,73065,2458],{},[1677,73067,1679],{},[1810,73069,2771],{},[1677,73071,1776],{},[1810,73073,1909],{},[898,73075,2470],{},[902,73077,73078],{"encoding":904},"TC = 100 + 5Q",". Určete body zvratu a geometricky výsledek interpretujte.",[724,73081,73082,73085,73086,7578,73101,73116,73117,1343,73139,22985,73166,73188,73189,73223],{},[38,73083,73084],{},"3.18"," Odvoďte, že jestliže ",[883,73087,73089],{"className":73088},[886],[888,73090,73091],{"xmlns":890},[892,73092,73093,73099],{},[895,73094,73095,73097],{},[898,73096,2455],{},[898,73098,5382],{},[902,73100,5482],{"encoding":904},[883,73102,73104],{"className":73103},[886],[888,73105,73106],{"xmlns":890},[892,73107,73108,73114],{},[895,73109,73110,73112],{},[898,73111,2455],{},[898,73113,2458],{},[902,73115,2924],{"encoding":904}," jsou lineární tvaru ",[883,73118,73120],{"className":73119},[886],[888,73121,73122],{"xmlns":890},[892,73123,73124,73136],{},[895,73125,73126,73128,73130,73132,73134],{},[898,73127,2455],{},[898,73129,5382],{},[1677,73131,1679],{},[898,73133,724],{},[898,73135,2470],{},[902,73137,73138],{"encoding":904},"TR = pQ",[883,73140,73142],{"className":73141},[886],[888,73143,73144],{"xmlns":890},[892,73145,73146,73163],{},[895,73147,73148,73150,73152,73154,73157,73159,73161],{},[898,73149,2455],{},[898,73151,2458],{},[1677,73153,1679],{},[898,73155,73156],{},"m",[1677,73158,1776],{},[898,73160,38251],{},[898,73162,2470],{},[902,73164,73165],{"encoding":904},"TC = m + nQ",[883,73167,73169],{"className":73168},[886],[888,73170,73171],{"xmlns":890},[892,73172,73173,73185],{},[895,73174,73175,73177,73179,73181,73183],{},[898,73176,73156],{},[1677,73178,1967],{"separator":1966},[898,73180,38251],{},[1677,73182,1967],{"separator":1966},[898,73184,724],{},[902,73186,73187],{"encoding":904},"m, n, p"," jsou pevně zadány, pak existuje jediný bod zvratu ",[883,73190,73192],{"className":73191},[886],[888,73193,73194],{"xmlns":890},[892,73195,73196,73220],{},[895,73197,73198,73204,73206],{},[1805,73199,73200,73202],{},[898,73201,2470],{},[1677,73203,5742],{},[1677,73205,1679],{},[2006,73207,73208],{"scriptlevel":2008,"displaystyle":1685},[2010,73209,73210,73212],{},[898,73211,73156],{},[895,73213,73214,73216,73218],{},[898,73215,724],{},[1677,73217,1906],{},[898,73219,38251],{},[902,73221,73222],{"encoding":904},"Q^* = \\tfrac{m}{p - n}"," a proveďte diskusi podmínek. Načrtněte obrázek.",[724,73225,73226,73030,73229,5272,73263,72382,73289,73302,73303,71134,73318,73333,73334,71118,73347,71134,73362,73377],{},[38,73227,73228],{},"3.19",[883,73230,73232],{"className":73231},[886],[888,73233,73234],{"xmlns":890},[892,73235,73236,73260],{},[895,73237,73238,73240,73242,73244,73246,73248,73254,73256,73258],{},[898,73239,2455],{},[898,73241,5382],{},[1677,73243,1679],{},[1677,73245,1906],{},[1810,73247,1812],{},[1805,73249,73250,73252],{},[898,73251,2470],{},[1810,73253,1812],{},[1677,73255,1776],{},[1810,73257,24337],{},[898,73259,2470],{},[902,73261,73262],{"encoding":904},"TR = -2Q^2 + 14Q",[883,73264,73266],{"className":73265},[886],[888,73267,73268],{"xmlns":890},[892,73269,73270,73286],{},[895,73271,73272,73274,73276,73278,73280,73282,73284],{},[898,73273,2455],{},[898,73275,2458],{},[1677,73277,1679],{},[1810,73279,1812],{},[898,73281,2470],{},[1677,73283,1776],{},[1810,73285,2544],{},[902,73287,73288],{"encoding":904},"TC = 2Q + 10",[883,73290,73292],{"className":73291},[886],[888,73293,73294],{"xmlns":890},[892,73295,73296,73300],{},[895,73297,73298],{},[898,73299,2470],{},[902,73301,2470],{"encoding":904},", které maximalizuje zisk ",[883,73304,73306],{"className":73305},[886],[888,73307,73308],{"xmlns":890},[892,73309,73310,73316],{},[895,73311,73312,73314],{},[898,73313,5325],{},[898,73315,5382],{},[902,73317,64870],{"encoding":904},[883,73319,73321],{"className":73320},[886],[888,73322,73323],{"xmlns":890},[892,73324,73325,73331],{},[895,73326,73327,73329],{},[898,73328,5325],{},[898,73330,5382],{},[902,73332,64870],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku. (c) Určete ",[883,73335,73337],{"className":73336},[886],[888,73338,73339],{"xmlns":890},[892,73340,73341,73345],{},[895,73342,73343],{},[898,73344,2470],{},[902,73346,2470],{"encoding":904},[883,73348,73350],{"className":73349},[886],[888,73351,73352],{"xmlns":890},[892,73353,73354,73360],{},[895,73355,73356,73358],{},[898,73357,2455],{},[898,73359,5382],{},[902,73361,5482],{"encoding":904},[883,73363,73365],{"className":73364},[886],[888,73366,73367],{"xmlns":890},[892,73368,73369,73375],{},[895,73370,73371,73373],{},[898,73372,2455],{},[898,73374,5382],{},[902,73376,5482],{"encoding":904},". (d) Graficky interpretujte.",[724,73379,73380,49075,73383,1343,73409,1343,73428,72382,73448,73302,73461,71134,73476,73491,73492,73514,73515,72565],{},[38,73381,73382],{},"3.20",[883,73384,73386],{"className":73385},[886],[888,73387,73388],{"xmlns":890},[892,73389,73390,73406],{},[895,73391,73392,73394,73396,73398,73400],{},[898,73393,5325],{},[1677,73395,1679],{},[1810,73397,21533],{},[1677,73399,1906],{},[1805,73401,73402,73404],{},[898,73403,2470],{},[1810,73405,1812],{},[902,73407,73408],{"encoding":904},"P = 400 - Q^2",[883,73410,73412],{"className":73411},[886],[888,73413,73414],{"xmlns":890},[892,73415,73416,73426],{},[895,73417,73418,73420,73422,73424],{},[898,73419,11824],{},[898,73421,2458],{},[1677,73423,1679],{},[1810,73425,2771],{},[902,73427,13022],{"encoding":904},[883,73429,73431],{"className":73430},[886],[888,73432,73433],{"xmlns":890},[892,73434,73435,73445],{},[895,73436,73437,73439,73441,73443],{},[898,73438,2499],{},[898,73440,2458],{},[1677,73442,1679],{},[1810,73444,10423],{},[902,73446,73447],{"encoding":904},"MC = 20",[883,73449,73451],{"className":73450},[886],[888,73452,73453],{"xmlns":890},[892,73454,73455,73459],{},[895,73456,73457],{},[898,73458,2470],{},[902,73460,2470],{"encoding":904},[883,73462,73464],{"className":73463},[886],[888,73465,73466],{"xmlns":890},[892,73467,73468,73474],{},[895,73469,73470,73472],{},[898,73471,5325],{},[898,73473,5382],{},[902,73475,64870],{"encoding":904},[883,73477,73479],{"className":73478},[886],[888,73480,73481],{"xmlns":890},[892,73482,73483,73489],{},[895,73484,73485,73487],{},[898,73486,5325],{},[898,73488,5382],{},[902,73490,64870],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku (rada: jeden z bodů zvratu patří do ",[883,73493,73495],{"className":73494},[886],[888,73496,73497],{"xmlns":890},[892,73498,73499,73511],{},[895,73500,73501,73503,73505,73507,73509],{},[1677,73502,1686],{"stretchy":1685},[1810,73504,2008],{},[1677,73506,1967],{"separator":1966},[1810,73508,1959],{},[1677,73510,1692],{"stretchy":1685},[902,73512,73513],{"encoding":904},"(0, 1)",", druhý do ",[883,73516,73518],{"className":73517},[886],[888,73519,73520],{"xmlns":890},[892,73521,73522,73535],{},[895,73523,73524,73526,73529,73531,73533],{},[1677,73525,1686],{"stretchy":1685},[1810,73527,73528],{},"19",[1677,73530,1967],{"separator":1966},[1810,73532,10423],{},[1677,73534,1692],{"stretchy":1685},[902,73536,73537],{"encoding":904},"(19, 20)",[724,73539,73540,73543,73544,2305,73572,73589,73590,1656],{},[38,73541,73542],{},"3.21"," Dokažte, že má-li zisk ",[883,73545,73547],{"className":73546},[886],[888,73548,73549],{"xmlns":890},[892,73550,73551,73569],{},[895,73552,73553,73555,73557,73559,73561,73563,73565,73567],{},[898,73554,5325],{},[898,73556,5382],{},[1677,73558,1679],{},[898,73560,5325],{},[898,73562,5382],{},[1677,73564,1686],{"stretchy":1685},[898,73566,2470],{},[1677,73568,1692],{"stretchy":1685},[902,73570,73571],{"encoding":904},"PR = PR(Q)",[883,73573,73575],{"className":73574},[886],[888,73576,73577],{"xmlns":890},[892,73578,73579,73587],{},[895,73580,73581],{},[1953,73582,73583,73585],{},[898,73584,2470],{},[1810,73586,2008],{},[902,73588,39699],{"encoding":904}," maximum, pak platí ",[883,73591,73593],{"className":73592},[886],[888,73594,73595],{"xmlns":890},[892,73596,73597,73629],{},[895,73598,73599,73601,73603,73605,73611,73613,73615,73617,73619,73621,73627],{},[898,73600,2499],{},[898,73602,5382],{},[1677,73604,1686],{"stretchy":1685},[1953,73606,73607,73609],{},[898,73608,2470],{},[1810,73610,2008],{},[1677,73612,1692],{"stretchy":1685},[1677,73614,1679],{},[898,73616,2499],{},[898,73618,2458],{},[1677,73620,1686],{"stretchy":1685},[1953,73622,73623,73625],{},[898,73624,2470],{},[1810,73626,2008],{},[1677,73628,1692],{"stretchy":1685},[902,73630,67036],{"encoding":904},[724,73632,73633,73636,73637,5272,73652,57416,73667,73302,73680,73695,73696,1343,73723,73760,73761,1343,73788,1656],{},[38,73634,73635],{},"3.22"," Pro zadané ",[883,73638,73640],{"className":73639},[886],[888,73641,73642],{"xmlns":890},[892,73643,73644,73650],{},[895,73645,73646,73648],{},[898,73647,2499],{},[898,73649,5382],{},[902,73651,8022],{"encoding":904},[883,73653,73655],{"className":73654},[886],[888,73656,73657],{"xmlns":890},[892,73658,73659,73665],{},[895,73660,73661,73663],{},[898,73662,2499],{},[898,73664,2458],{},[902,73666,56683],{"encoding":904},[883,73668,73670],{"className":73669},[886],[888,73671,73672],{"xmlns":890},[892,73673,73674,73678],{},[895,73675,73676],{},[898,73677,2470],{},[902,73679,2470],{"encoding":904},[883,73681,73683],{"className":73682},[886],[888,73684,73685],{"xmlns":890},[892,73686,73687,73693],{},[895,73688,73689,73691],{},[898,73690,5325],{},[898,73692,5382],{},[902,73694,64870],{"encoding":904},". (a) ",[883,73697,73699],{"className":73698},[886],[888,73700,73701],{"xmlns":890},[892,73702,73703,73720],{},[895,73704,73705,73707,73709,73711,73714,73716,73718],{},[898,73706,2499],{},[898,73708,5382],{},[1677,73710,1679],{},[1810,73712,73713],{},"236",[1677,73715,1906],{},[1810,73717,43253],{},[898,73719,2470],{},[902,73721,73722],{"encoding":904},"MR = 236 - 16Q",[883,73724,73726],{"className":73725},[886],[888,73727,73728],{"xmlns":890},[892,73729,73730,73757],{},[895,73731,73732,73734,73736,73738,73740,73746,73748,73751,73753,73755],{},[898,73733,2499],{},[898,73735,2458],{},[1677,73737,1679],{},[1810,73739,1854],{},[1805,73741,73742,73744],{},[898,73743,2470],{},[1810,73745,1812],{},[1677,73747,1906],{},[1810,73749,73750],{},"32",[898,73752,2470],{},[1677,73754,1776],{},[1810,73756,7132],{},[902,73758,73759],{"encoding":904},"MC = 3Q^2 - 32Q + 96",". (b) ",[883,73762,73764],{"className":73763},[886],[888,73765,73766],{"xmlns":890},[892,73767,73768,73785],{},[895,73769,73770,73772,73774,73776,73779,73781,73783],{},[898,73771,2499],{},[898,73773,5382],{},[1677,73775,1679],{},[1810,73777,73778],{},"280",[1677,73780,1906],{},[1810,73782,10423],{},[898,73784,2470],{},[902,73786,73787],{"encoding":904},"MR = 280 - 20Q",[883,73789,73791],{"className":73790},[886],[888,73792,73793],{"xmlns":890},[892,73794,73795,73822],{},[895,73796,73797,73799,73801,73803,73806,73812,73814,73816,73818,73820],{},[898,73798,2499],{},[898,73800,2458],{},[1677,73802,1679],{},[1810,73804,73805],{},"1,6",[1805,73807,73808,73810],{},[898,73809,2470],{},[1810,73811,1812],{},[1677,73813,1906],{},[1810,73815,37635],{},[898,73817,2470],{},[1677,73819,1776],{},[1810,73821,2807],{},[902,73823,73824],{"encoding":904},"MC = 1{,}6Q^2 - 15Q + 60",[724,73826,73827,73636,73830,5272,73845,57416,73860,71118,73873,71134,73888,73695,73903,1343,73934,73760,73970,1343,74002,74046,74047,1343,74079,1656],{},[38,73828,73829],{},"3.23",[883,73831,73833],{"className":73832},[886],[888,73834,73835],{"xmlns":890},[892,73836,73837,73843],{},[895,73838,73839,73841],{},[898,73840,2455],{},[898,73842,5382],{},[902,73844,5482],{"encoding":904},[883,73846,73848],{"className":73847},[886],[888,73849,73850],{"xmlns":890},[892,73851,73852,73858],{},[895,73853,73854,73856],{},[898,73855,2455],{},[898,73857,2458],{},[902,73859,2924],{"encoding":904},[883,73861,73863],{"className":73862},[886],[888,73864,73865],{"xmlns":890},[892,73866,73867,73871],{},[895,73868,73869],{},[898,73870,2470],{},[902,73872,2470],{"encoding":904},[883,73874,73876],{"className":73875},[886],[888,73877,73878],{"xmlns":890},[892,73879,73880,73886],{},[895,73881,73882,73884],{},[898,73883,5325],{},[898,73885,5382],{},[902,73887,64870],{"encoding":904},[883,73889,73891],{"className":73890},[886],[888,73892,73893],{"xmlns":890},[892,73894,73895,73901],{},[895,73896,73897,73899],{},[898,73898,5325],{},[898,73900,5382],{},[902,73902,64870],{"encoding":904},[883,73904,73906],{"className":73905},[886],[888,73907,73908],{"xmlns":890},[892,73909,73910,73931],{},[895,73911,73912,73914,73916,73918,73921,73923,73925],{},[898,73913,2455],{},[898,73915,5382],{},[1677,73917,1679],{},[1810,73919,73920],{},"125",[898,73922,2470],{},[1677,73924,1906],{},[1805,73926,73927,73929],{},[898,73928,2470],{},[1810,73930,1812],{},[902,73932,73933],{"encoding":904},"TR = 125Q - Q^2",[883,73935,73937],{"className":73936},[886],[888,73938,73939],{"xmlns":890},[892,73940,73941,73967],{},[895,73942,73943,73945,73947,73949,73951,73953,73955,73957,73959,73961],{},[898,73944,2455],{},[898,73946,2458],{},[1677,73948,1679],{},[1810,73950,16500],{},[1677,73952,1776],{},[1810,73954,1909],{},[898,73956,2470],{},[1677,73958,1776],{},[1810,73960,6397],{},[1805,73962,73963,73965],{},[898,73964,2470],{},[1810,73966,1812],{},[902,73968,73969],{"encoding":904},"TC = 500 + 5Q + 0{,}5Q^2",[883,73971,73973],{"className":73972},[886],[888,73974,73975],{"xmlns":890},[892,73976,73977,73999],{},[895,73978,73979,73981,73983,73985,73987,73989,73991,73993],{},[898,73980,2455],{},[898,73982,5382],{},[1677,73984,1679],{},[1810,73986,10423],{},[898,73988,2470],{},[1677,73990,1906],{},[1810,73992,1812],{},[1805,73994,73995,73997],{},[898,73996,2470],{},[1810,73998,1812],{},[902,74000,74001],{"encoding":904},"TR = 20Q - 2Q^2",[883,74003,74005],{"className":74004},[886],[888,74006,74007],{"xmlns":890},[892,74008,74009,74043],{},[895,74010,74011,74013,74015,74017,74019,74021,74023,74025,74027,74029,74035,74037],{},[898,74012,2455],{},[898,74014,2458],{},[1677,74016,1679],{},[1810,74018,1812],{},[1677,74020,1776],{},[1810,74022,10423],{},[898,74024,2470],{},[1677,74026,1906],{},[1810,74028,6973],{},[1805,74030,74031,74033],{},[898,74032,2470],{},[1810,74034,1812],{},[1677,74036,1776],{},[1805,74038,74039,74041],{},[898,74040,2470],{},[1810,74042,1854],{},[902,74044,74045],{"encoding":904},"TC = 2 + 20Q - 8Q^2 + Q^3",". (c) ",[883,74048,74050],{"className":74049},[886],[888,74051,74052],{"xmlns":890},[892,74053,74054,74076],{},[895,74055,74056,74058,74060,74062,74064,74066,74068,74070],{},[898,74057,2455],{},[898,74059,5382],{},[1677,74061,1679],{},[1810,74063,2032],{},[898,74065,2470],{},[1677,74067,1906],{},[1810,74069,25180],{},[1805,74071,74072,74074],{},[898,74073,2470],{},[1810,74075,1812],{},[902,74077,74078],{"encoding":904},"TR = 4Q - 0{,}25Q^2",[883,74080,74082],{"className":74081},[886],[888,74083,74084],{"xmlns":890},[892,74085,74086,74134],{},[895,74087,74088,74090,74092,74094,74096,74098,74100,74102,74104,74120,74122],{},[898,74089,2455],{},[898,74091,2458],{},[1677,74093,1679],{},[1810,74095,2032],{},[1677,74097,1776],{},[1810,74099,1812],{},[898,74101,2470],{},[1677,74103,1906],{},[2006,74105,74106],{"scriptlevel":2008,"displaystyle":1685},[2010,74107,74108,74118],{},[895,74109,74110,74112],{},[1810,74111,1854],{},[1805,74113,74114,74116],{},[898,74115,2470],{},[1810,74117,1812],{},[1810,74119,2544],{},[1677,74121,1776],{},[2006,74123,74124],{"scriptlevel":2008,"displaystyle":1685},[2010,74125,74126,74132],{},[1805,74127,74128,74130],{},[898,74129,2470],{},[1810,74131,1854],{},[1810,74133,10423],{},[902,74135,74136],{"encoding":904},"TC = 4 + 2Q - \\tfrac{3Q^2}{10} + \\tfrac{Q^3}{20}",[724,74138,74139,74142,74143,74173,74174,74206,74207,22985,74237,74267],{},[38,74140,74141],{},"3.24"," Firma řeší problém stanovení cen pro malé a velké odběratele za účelem maximalizace zisku. Poptávka pro maloodběratele je ",[883,74144,74146],{"className":74145},[886],[888,74147,74148],{"xmlns":890},[892,74149,74150,74170],{},[895,74151,74152,74158,74160,74162,74164],{},[1953,74153,74154,74156],{},[898,74155,5325],{},[1810,74157,1959],{},[1677,74159,1679],{},[1810,74161,16500],{},[1677,74163,1906],{},[1953,74165,74166,74168],{},[898,74167,2470],{},[1810,74169,1959],{},[902,74171,74172],{"encoding":904},"P_1 = 500 - Q_1",", pro velkoodběratele ",[883,74175,74177],{"className":74176},[886],[888,74178,74179],{"xmlns":890},[892,74180,74181,74203],{},[895,74182,74183,74189,74191,74193,74195,74197],{},[1953,74184,74185,74187],{},[898,74186,5325],{},[1810,74188,1812],{},[1677,74190,1679],{},[1810,74192,31472],{},[1677,74194,1906],{},[1810,74196,65950],{},[1953,74198,74199,74201],{},[898,74200,2470],{},[1810,74202,1812],{},[902,74204,74205],{"encoding":904},"P_2 = 300 - 1{,}5Q_2",". Celkové náklady firmy jsou ",[883,74208,74210],{"className":74209},[886],[888,74211,74212],{"xmlns":890},[892,74213,74214,74234],{},[895,74215,74216,74218,74220,74222,74224,74226,74228,74230,74232],{},[898,74217,2455],{},[898,74219,2458],{},[1677,74221,1679],{},[1810,74223,2801],{},[1969,74225,2668],{},[1810,74227,60473],{},[1677,74229,1776],{},[1810,74231,10423],{},[898,74233,2470],{},[902,74235,74236],{"encoding":904},"TC = 50\\,000 + 20Q",[883,74238,74240],{"className":74239},[886],[888,74241,74242],{"xmlns":890},[892,74243,74244,74264],{},[895,74245,74246,74248,74250,74256,74258],{},[898,74247,2470],{},[1677,74249,1679],{},[1953,74251,74252,74254],{},[898,74253,2470],{},[1810,74255,1959],{},[1677,74257,1776],{},[1953,74259,74260,74262],{},[898,74261,2470],{},[1810,74263,1812],{},[902,74265,74266],{"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.",[724,74269,74270,74273,74274,74304,74305,74206,74337,22985,74367,74396],{},[38,74271,74272],{},"3.25"," Firma řeší problém stanovení cen pro domácí a zahraniční trh za účelem maximalizace zisku. Poptávka pro domácí trh je ",[883,74275,74277],{"className":74276},[886],[888,74278,74279],{"xmlns":890},[892,74280,74281,74301],{},[895,74282,74283,74289,74291,74293,74295],{},[1953,74284,74285,74287],{},[898,74286,5325],{},[1810,74288,1959],{},[1677,74290,1679],{},[1810,74292,31472],{},[1677,74294,1906],{},[1953,74296,74297,74299],{},[898,74298,2470],{},[1810,74300,1959],{},[902,74302,74303],{"encoding":904},"P_1 = 300 - Q_1",", pro zahraniční trh ",[883,74306,74308],{"className":74307},[886],[888,74309,74310],{"xmlns":890},[892,74311,74312,74334],{},[895,74313,74314,74320,74322,74324,74326,74328],{},[1953,74315,74316,74318],{},[898,74317,5325],{},[1810,74319,1812],{},[1677,74321,1679],{},[1810,74323,9765],{},[1677,74325,1906],{},[1810,74327,6397],{},[1953,74329,74330,74332],{},[898,74331,2470],{},[1810,74333,1812],{},[902,74335,74336],{"encoding":904},"P_2 = 200 - 0{,}5Q_2",[883,74338,74340],{"className":74339},[886],[888,74341,74342],{"xmlns":890},[892,74343,74344,74364],{},[895,74345,74346,74348,74350,74352,74354,74356,74358,74360,74362],{},[898,74347,2455],{},[898,74349,2458],{},[1677,74351,1679],{},[1810,74353,1909],{},[1969,74355,2668],{},[1810,74357,60473],{},[1677,74359,1776],{},[1810,74361,2771],{},[898,74363,2470],{},[902,74365,74366],{"encoding":904},"TC = 5\\,000 + 100Q",[883,74368,74370],{"className":74369},[886],[888,74371,74372],{"xmlns":890},[892,74373,74374,74394],{},[895,74375,74376,74378,74380,74386,74388],{},[898,74377,2470],{},[1677,74379,1679],{},[1953,74381,74382,74384],{},[898,74383,2470],{},[1810,74385,1959],{},[1677,74387,1776],{},[1953,74389,74390,74392],{},[898,74391,2470],{},[1810,74393,1812],{},[902,74395,74266],{"encoding":904},". Stanovte ceny, při kterých firma maximalizuje zisk: (a) s cenovou diskriminací, (b) bez cenové diskriminace. Porovnejte zisk firmy v obou případech.",[198,74398,74400],{"id":74399},"konstrukce-nabídky-326328","Konstrukce nabídky (3.26–3.28)",[724,74402,74403,74406,74407,74454,74455,74472],{},[38,74404,74405],{},"3.26"," Jsou dány celkové variabilní náklady ",[883,74408,74410],{"className":74409},[886],[888,74411,74412],{"xmlns":890},[892,74413,74414,74451],{},[895,74415,74416,74418,74420,74422,74424,74427,74433,74435,74438,74444,74446,74449],{},[898,74417,2455],{},[898,74419,41730],{},[898,74421,2458],{},[1677,74423,1679],{},[1810,74425,74426],{},"0,85",[1805,74428,74429,74431],{},[898,74430,2470],{},[1810,74432,1854],{},[1677,74434,1906],{},[1810,74436,74437],{},"11,9",[1805,74439,74440,74442],{},[898,74441,2470],{},[1810,74443,1812],{},[1677,74445,1776],{},[1810,74447,74448],{},"102",[898,74450,2470],{},[902,74452,74453],{"encoding":904},"TVC = 0{,}85Q^3 - 11{,}9Q^2 + 102Q",". Určete minimální cenu ",[883,74456,74458],{"className":74457},[886],[888,74459,74460],{"xmlns":890},[892,74461,74462,74470],{},[895,74463,74464],{},[1805,74465,74466,74468],{},[898,74467,5325],{},[1677,74469,5742],{},[902,74471,5792],{"encoding":904}," nabídky a konstruujte nabídku. Graficky interpretujte.",[724,74474,74475,72233,74478,74514],{},[38,74476,74477],{},"3.27",[883,74479,74481],{"className":74480},[886],[888,74482,74483],{"xmlns":890},[892,74484,74485,74511],{},[895,74486,74487,74489,74491,74493,74495,74501,74503,74505,74507,74509],{},[898,74488,2499],{},[898,74490,2458],{},[1677,74492,1679],{},[1810,74494,2604],{},[1805,74496,74497,74499],{},[898,74498,2470],{},[1810,74500,1812],{},[1677,74502,1906],{},[1810,74504,65831],{},[898,74506,2470],{},[1677,74508,1776],{},[1810,74510,32134],{},[902,74512,74513],{"encoding":904},"MC = 4{,}2Q^2 - 48Q + 250",". Konstruujte nabídku.",[724,74516,74517,71484,74520,74514],{},[38,74518,74519],{},"3.28",[883,74521,74523],{"className":74522},[886],[888,74524,74525],{"xmlns":890},[892,74526,74527,74563],{},[895,74528,74529,74531,74533,74535,74537,74543,74545,74547,74553,74555,74557,74559,74561],{},[898,74530,2455],{},[898,74532,2458],{},[1677,74534,1679],{},[1810,74536,6397],{},[1805,74538,74539,74541],{},[898,74540,2470],{},[1810,74542,1854],{},[1677,74544,1906],{},[1810,74546,25592],{},[1805,74548,74549,74551],{},[898,74550,2470],{},[1810,74552,1812],{},[1677,74554,1776],{},[1810,74556,2807],{},[898,74558,2470],{},[1677,74560,1776],{},[1810,74562,16500],{},[902,74564,74565],{"encoding":904},"TC = 0{,}5Q^3 - 7Q^2 + 60Q + 500",[115,74567,17110],{"id":17109},[120,74569,74570,74598,74643,74715,74780,74820,74912,75018,75058,75172,75265,75329,75361,75421,75427,75491,75540,75594,75702,75757],{},[123,74571,74572,1884,74574,74597],{},[38,74573,57141],{},[883,74575,74577],{"className":74576},[886],[888,74578,74579],{"xmlns":890},[892,74580,74581,74595],{},[895,74582,74583,74585,74587,74589,74591,74593],{},[898,74584,2455],{},[898,74586,5382],{},[1677,74588,1679],{},[898,74590,5325],{},[1677,74592,2858],{},[898,74594,2470],{},[902,74596,68103],{"encoding":904}," — křivka celkového příjmu (total revenue curve).",[123,74599,74600,1884,74602,74642],{},[38,74601,57727],{},[883,74603,74605],{"className":74604},[886],[888,74606,74607],{"xmlns":890},[892,74608,74609,74639],{},[895,74610,74611,74613,74615,74617,74629,74631,74633,74635,74637],{},[898,74612,5643],{},[898,74614,5382],{},[1677,74616,1679],{},[2006,74618,74619],{"scriptlevel":2008,"displaystyle":1685},[2010,74620,74621,74627],{},[895,74622,74623,74625],{},[898,74624,2455],{},[898,74626,5382],{},[898,74628,2470],{},[1677,74630,1679],{},[898,74632,5571],{},[1677,74634,1686],{"stretchy":1685},[898,74636,2470],{},[1677,74638,1692],{"stretchy":1685},[902,74640,74641],{"encoding":904},"AR = \\tfrac{TR}{Q} = D(Q)"," — shoduje se s poptávkovou funkcí.",[123,74644,74645,1884,74647,74683,74684,74699,74700,1656],{},[38,74646,57875],{},[883,74648,74650],{"className":74649},[886],[888,74651,74652],{"xmlns":890},[892,74653,74654,74680],{},[895,74655,74656,74658,74660,74662],{},[898,74657,2499],{},[898,74659,5382],{},[1677,74661,1679],{},[2006,74663,74664],{"scriptlevel":2008,"displaystyle":1685},[2010,74665,74666,74674],{},[895,74667,74668,74670,74672],{},[898,74669,1875],{"mathvariant":2057},[898,74671,2455],{},[898,74673,5382],{},[895,74675,74676,74678],{},[898,74677,1875],{"mathvariant":2057},[898,74679,2470],{},[902,74681,74682],{"encoding":904},"MR = \\tfrac{\\mathrm{d}TR}{\\mathrm{d}Q}"," — rychlost změny ",[883,74685,74687],{"className":74686},[886],[888,74688,74689],{"xmlns":890},[892,74690,74691,74697],{},[895,74692,74693,74695],{},[898,74694,2455],{},[898,74696,5382],{},[902,74698,5482],{"encoding":904},"; pro lineární poptávku má sklon dvojnásobný vůči ",[883,74701,74703],{"className":74702},[886],[888,74704,74705],{"xmlns":890},[892,74706,74707,74713],{},[895,74708,74709,74711],{},[898,74710,5643],{},[898,74712,5382],{},[902,74714,56836],{"encoding":904},[123,74716,74717,1884,74720,1343,74750,1656],{},[38,74718,74719],{},"Diferenciál příjmu\u002Fnákladů",[883,74721,74723],{"className":74722},[886],[888,74724,74725],{"xmlns":890},[892,74726,74727,74747],{},[895,74728,74729,74731,74733,74735,74737,74739,74741,74743,74745],{},[898,74730,2570],{"mathvariant":2057},[898,74732,2455],{},[898,74734,5382],{},[1677,74736,2411],{},[898,74738,2499],{},[898,74740,5382],{},[1969,74742,2668],{},[898,74744,1875],{"mathvariant":2057},[898,74746,2470],{},[902,74748,74749],{"encoding":904},"\\Delta TR \\approx MR \\, \\mathrm{d}Q",[883,74751,74753],{"className":74752},[886],[888,74754,74755],{"xmlns":890},[892,74756,74757,74777],{},[895,74758,74759,74761,74763,74765,74767,74769,74771,74773,74775],{},[898,74760,2570],{"mathvariant":2057},[898,74762,2455],{},[898,74764,2458],{},[1677,74766,2411],{},[898,74768,2499],{},[898,74770,2458],{},[1969,74772,2668],{},[898,74774,1875],{"mathvariant":2057},[898,74776,2470],{},[902,74778,74779],{"encoding":904},"\\Delta TC \\approx MC \\, \\mathrm{d}Q",[123,74781,74782,1884,74784,1656],{},[38,74783,59997],{},[883,74785,74787],{"className":74786},[886],[888,74788,74789],{"xmlns":890},[892,74790,74791,74817],{},[895,74792,74793,74795,74797,74799,74801,74803,74805,74807,74809,74811,74813,74815],{},[898,74794,2455],{},[898,74796,2458],{},[1677,74798,1679],{},[898,74800,11824],{},[898,74802,2458],{},[1677,74804,1776],{},[898,74806,2455],{},[898,74808,41730],{},[898,74810,2458],{},[1677,74812,1686],{"stretchy":1685},[898,74814,2470],{},[1677,74816,1692],{"stretchy":1685},[902,74818,74819],{"encoding":904},"TC = FC + TVC(Q)",[123,74821,74822,1884,74825,1343,74840,1884,74842,1343,74865,1884,74868,1656],{},[38,74823,74824],{},"Fixní náklady",[883,74826,74828],{"className":74827},[886],[888,74829,74830],{"xmlns":890},[892,74831,74832,74838],{},[895,74833,74834,74836],{},[898,74835,11824],{},[898,74837,2458],{},[902,74839,56882],{"encoding":904},[38,74841,60150],{},[883,74843,74845],{"className":74844},[886],[888,74846,74847],{"xmlns":890},[892,74848,74849,74863],{},[895,74850,74851,74853,74855,74857,74859,74861],{},[898,74852,2455],{},[898,74854,41730],{},[898,74856,2458],{},[1677,74858,1686],{"stretchy":1685},[898,74860,2470],{},[1677,74862,1692],{"stretchy":1685},[902,74864,60147],{"encoding":904},[38,74866,74867],{},"variabilní náklady na jednotku",[883,74869,74871],{"className":74870},[886],[888,74872,74873],{"xmlns":890},[892,74874,74875,74909],{},[895,74876,74877,74879,74881,74883,74885,74887,74889],{},[898,74878,41730],{},[898,74880,2458],{},[1677,74882,1686],{"stretchy":1685},[898,74884,2470],{},[1677,74886,1692],{"stretchy":1685},[1677,74888,1679],{},[2006,74890,74891],{"scriptlevel":2008,"displaystyle":1685},[2010,74892,74893,74907],{},[895,74894,74895,74897,74899,74901,74903,74905],{},[898,74896,2455],{},[898,74898,41730],{},[898,74900,2458],{},[1677,74902,1686],{"stretchy":1685},[898,74904,2470],{},[1677,74906,1692],{"stretchy":1685},[898,74908,2470],{},[902,74910,74911],{"encoding":904},"VC(Q) = \\tfrac{TVC(Q)}{Q}",[123,74913,74914,1884,74916,1343,74946,1884,74949,1343,74981,1884,74984,1656],{},[38,74915,60158],{},[883,74917,74919],{"className":74918},[886],[888,74920,74921],{"xmlns":890},[892,74922,74923,74943],{},[895,74924,74925,74927,74929,74931],{},[898,74926,5643],{},[898,74928,2458],{},[1677,74930,1679],{},[2006,74932,74933],{"scriptlevel":2008,"displaystyle":1685},[2010,74934,74935,74941],{},[895,74936,74937,74939],{},[898,74938,2455],{},[898,74940,2458],{},[898,74942,2470],{},[902,74944,74945],{"encoding":904},"AC = \\tfrac{TC}{Q}",[38,74947,74948],{},"průměrné fixní",[883,74950,74952],{"className":74951},[886],[888,74953,74954],{"xmlns":890},[892,74955,74956,74978],{},[895,74957,74958,74960,74962,74964,74966],{},[898,74959,5643],{},[898,74961,11824],{},[898,74963,2458],{},[1677,74965,1679],{},[2006,74967,74968],{"scriptlevel":2008,"displaystyle":1685},[2010,74969,74970,74976],{},[895,74971,74972,74974],{},[898,74973,11824],{},[898,74975,2458],{},[898,74977,2470],{},[902,74979,74980],{"encoding":904},"AFC = \\tfrac{FC}{Q}",[38,74982,74983],{},"průměrné variabilní",[883,74985,74987],{"className":74986},[886],[888,74988,74989],{"xmlns":890},[892,74990,74991,75015],{},[895,74992,74993,74995,74997,74999,75001],{},[898,74994,5643],{},[898,74996,41730],{},[898,74998,2458],{},[1677,75000,1679],{},[2006,75002,75003],{"scriptlevel":2008,"displaystyle":1685},[2010,75004,75005,75013],{},[895,75006,75007,75009,75011],{},[898,75008,2455],{},[898,75010,41730],{},[898,75012,2458],{},[898,75014,2470],{},[902,75016,75017],{"encoding":904},"AVC = \\tfrac{TVC}{Q}",[123,75019,75020,1884,75022,1656],{},[38,75021,61345],{},[883,75023,75025],{"className":75024},[886],[888,75026,75027],{"xmlns":890},[892,75028,75029,75055],{},[895,75030,75031,75033,75035,75037],{},[898,75032,2499],{},[898,75034,2458],{},[1677,75036,1679],{},[2006,75038,75039],{"scriptlevel":2008,"displaystyle":1685},[2010,75040,75041,75049],{},[895,75042,75043,75045,75047],{},[898,75044,1875],{"mathvariant":2057},[898,75046,2455],{},[898,75048,2458],{},[895,75050,75051,75053],{},[898,75052,1875],{"mathvariant":2057},[898,75054,2470],{},[902,75056,75057],{"encoding":904},"MC = \\tfrac{\\mathrm{d}TC}{\\mathrm{d}Q}",[123,75059,75060,1884,75062,75110,75111,75124,75125,1343,75140,1343,75157,1656],{},[38,75061,62243],{},[883,75063,75065],{"className":75064},[886],[888,75066,75067],{"xmlns":890},[892,75068,75069,75107],{},[895,75070,75071,75073,75075,75077,75079,75081,75083,75085,75087,75089,75091,75097,75099,75101],{},[898,75072,2455],{},[898,75074,2458],{},[1677,75076,1679],{},[898,75078,11824],{},[898,75080,2458],{},[1677,75082,1776],{},[898,75084,207],{},[898,75086,2470],{},[1677,75088,1776],{},[898,75090,1779],{},[1805,75092,75093,75095],{},[898,75094,2470],{},[1810,75096,1812],{},[1677,75098,1776],{},[898,75100,1823],{},[1805,75102,75103,75105],{},[898,75104,2470],{},[1810,75106,1854],{},[902,75108,75109],{"encoding":904},"TC = FC + aQ + bQ^2 + cQ^3"," — „standardní\" tvar s ",[883,75112,75114],{"className":75113},[886],[888,75115,75116],{"xmlns":890},[892,75117,75118,75122],{},[895,75119,75120],{},[898,75121,900],{},[902,75123,900],{"encoding":904},"-průběhem ",[883,75126,75128],{"className":75127},[886],[888,75129,75130],{"xmlns":890},[892,75131,75132,75138],{},[895,75133,75134,75136],{},[898,75135,5643],{},[898,75137,2458],{},[902,75139,56951],{"encoding":904},[883,75141,75143],{"className":75142},[886],[888,75144,75145],{"xmlns":890},[892,75146,75147,75155],{},[895,75148,75149,75151,75153],{},[898,75150,5643],{},[898,75152,41730],{},[898,75154,2458],{},[902,75156,56702],{"encoding":904},[883,75158,75160],{"className":75159},[886],[888,75161,75162],{"xmlns":890},[892,75163,75164,75170],{},[895,75165,75166,75168],{},[898,75167,2499],{},[898,75169,2458],{},[902,75171,56683],{"encoding":904},[123,75173,75174,75176,75177,11782,75192,75233,75234,62888,75249,75264],{},[38,75175,63325],{},": v bodě minima ",[883,75178,75180],{"className":75179},[886],[888,75181,75182],{"xmlns":890},[892,75183,75184,75190],{},[895,75185,75186,75188],{},[898,75187,5643],{},[898,75189,2458],{},[902,75191,56951],{"encoding":904},[883,75193,75195],{"className":75194},[886],[888,75196,75197],{"xmlns":890},[892,75198,75199,75231],{},[895,75200,75201,75203,75205,75207,75213,75215,75217,75219,75221,75223,75229],{},[898,75202,5643],{},[898,75204,2458],{},[1677,75206,1686],{"stretchy":1685},[1953,75208,75209,75211],{},[898,75210,2470],{},[1810,75212,2008],{},[1677,75214,1692],{"stretchy":1685},[1677,75216,1679],{},[898,75218,2499],{},[898,75220,2458],{},[1677,75222,1686],{"stretchy":1685},[1953,75224,75225,75227],{},[898,75226,2470],{},[1810,75228,2008],{},[1677,75230,1692],{"stretchy":1685},[902,75232,63960],{"encoding":904},"; geometricky ",[883,75235,75237],{"className":75236},[886],[888,75238,75239],{"xmlns":890},[892,75240,75241,75247],{},[895,75242,75243,75245],{},[898,75244,2499],{},[898,75246,2458],{},[902,75248,56683],{"encoding":904},[883,75250,75252],{"className":75251},[886],[888,75253,75254],{"xmlns":890},[892,75255,75256,75262],{},[895,75257,75258,75260],{},[898,75259,5643],{},[898,75261,2458],{},[902,75263,56951],{"encoding":904}," v jejím minimu.",[123,75266,75267,75176,75269,11782,75286,1656],{},[38,75268,64675],{},[883,75270,75272],{"className":75271},[886],[888,75273,75274],{"xmlns":890},[892,75275,75276,75284],{},[895,75277,75278,75280,75282],{},[898,75279,5643],{},[898,75281,41730],{},[898,75283,2458],{},[902,75285,56702],{"encoding":904},[883,75287,75289],{"className":75288},[886],[888,75290,75291],{"xmlns":890},[892,75292,75293,75327],{},[895,75294,75295,75297,75299,75301,75303,75309,75311,75313,75315,75317,75319,75325],{},[898,75296,5643],{},[898,75298,41730],{},[898,75300,2458],{},[1677,75302,1686],{"stretchy":1685},[1953,75304,75305,75307],{},[898,75306,2470],{},[1810,75308,2008],{},[1677,75310,1692],{"stretchy":1685},[1677,75312,1679],{},[898,75314,2499],{},[898,75316,2458],{},[1677,75318,1686],{"stretchy":1685},[1953,75320,75321,75323],{},[898,75322,2470],{},[1810,75324,2008],{},[1677,75326,1692],{"stretchy":1685},[902,75328,70410],{"encoding":904},[123,75330,75331,1884,75333,75360],{},[38,75332,64854],{},[883,75334,75336],{"className":75335},[886],[888,75337,75338],{"xmlns":890},[892,75339,75340,75358],{},[895,75341,75342,75344,75346,75348,75350,75352,75354,75356],{},[898,75343,5325],{},[898,75345,5382],{},[1677,75347,1679],{},[898,75349,2455],{},[898,75351,5382],{},[1677,75353,1906],{},[898,75355,2455],{},[898,75357,2458],{},[902,75359,56591],{"encoding":904}," — rozdíl mezi celkovým příjmem a celkovými náklady.",[123,75362,75363,11413,75365,75367,75368,75394,75395,75420],{},[38,75364,65716],{},[614,75366,64979],{},") — hodnoty ",[883,75369,75371],{"className":75370},[886],[888,75372,75373],{"xmlns":890},[892,75374,75375,75391],{},[895,75376,75377,75383,75385],{},[1953,75378,75379,75381],{},[898,75380,2470],{},[898,75382,5643],{},[1677,75384,1967],{"separator":1966},[1953,75386,75387,75389],{},[898,75388,2470],{},[898,75390,24644],{},[902,75392,75393],{"encoding":904},"Q_A, Q_B"," splňující ",[883,75396,75398],{"className":75397},[886],[888,75399,75400],{"xmlns":890},[892,75401,75402,75418],{},[895,75403,75404,75406,75408,75410,75412,75414,75416],{},[898,75405,5325],{},[898,75407,5382],{},[1677,75409,1686],{"stretchy":1685},[898,75411,2470],{},[1677,75413,1692],{"stretchy":1685},[1677,75415,1679],{},[1810,75417,2008],{},[902,75419,65256],{"encoding":904},"; oddělují pásma ztráty a zisku.",[123,75422,75423,75426],{},[38,75424,75425],{},"Práh rentability"," — stav firmy v bodě zvratu.",[123,75428,75429,75431,75432,11782,75449,75490],{},[38,75430,66770],{}," — v bodě maxima zisku ",[883,75433,75435],{"className":75434},[886],[888,75436,75437],{"xmlns":890},[892,75438,75439,75447],{},[895,75440,75441],{},[1953,75442,75443,75445],{},[898,75444,2470],{},[1810,75446,2008],{},[902,75448,39699],{"encoding":904},[883,75450,75452],{"className":75451},[886],[888,75453,75454],{"xmlns":890},[892,75455,75456,75488],{},[895,75457,75458,75460,75462,75464,75470,75472,75474,75476,75478,75480,75486],{},[898,75459,2499],{},[898,75461,5382],{},[1677,75463,1686],{"stretchy":1685},[1953,75465,75466,75468],{},[898,75467,2470],{},[1810,75469,2008],{},[1677,75471,1692],{"stretchy":1685},[1677,75473,1679],{},[898,75475,2499],{},[898,75477,2458],{},[1677,75479,1686],{"stretchy":1685},[1953,75481,75482,75484],{},[898,75483,2470],{},[1810,75485,2008],{},[1677,75487,1692],{"stretchy":1685},[902,75489,67036],{"encoding":904}," (3.13).",[123,75492,75493,21692,75495,11782,75514,75539],{},[38,75494,68063],{},[883,75496,75498],{"className":75497},[886],[888,75499,75500],{"xmlns":890},[892,75501,75502,75511],{},[895,75503,75504,75506,75508],{},[898,75505,5325],{},[1677,75507,1679],{},[1969,75509,75510],{},"konst",[902,75512,75513],{"encoding":904},"P = \\text{konst}",[883,75515,75517],{"className":75516},[886],[888,75518,75519],{"xmlns":890},[892,75520,75521,75537],{},[895,75522,75523,75525,75527,75529,75531,75533,75535],{},[898,75524,5325],{},[1677,75526,1679],{},[898,75528,2499],{},[898,75530,2458],{},[1677,75532,1686],{"stretchy":1685},[898,75534,2470],{},[1677,75536,1692],{"stretchy":1685},[902,75538,68757],{"encoding":904}," (3.14).",[123,75541,75542,75545,75546,75575,75576,75593],{},[38,75543,75544],{},"Shutdown point"," — bod ",[883,75547,75549],{"className":75548},[886],[888,75550,75551],{"xmlns":890},[892,75552,75553,75573],{},[895,75554,75555,75557,75563,75565,75571],{},[1677,75556,1686],{"stretchy":1685},[1805,75558,75559,75561],{},[898,75560,2470],{},[1677,75562,5742],{},[1677,75564,1967],{"separator":1966},[1805,75566,75567,75569],{},[898,75568,5325],{},[1677,75570,5742],{},[1677,75572,1692],{"stretchy":1685},[902,75574,69046],{"encoding":904}," v minimu ",[883,75577,75579],{"className":75578},[886],[888,75580,75581],{"xmlns":890},[892,75582,75583,75591],{},[895,75584,75585,75587,75589],{},[898,75586,5643],{},[898,75588,41730],{},[898,75590,2458],{},[902,75592,56702],{"encoding":904},"; pod ním se firmě nevyplatí produkovat.",[123,75595,75596,1884,75599,7861,75634,69316,75655,75668,75669,75684,75685,1656],{},[38,75597,75598],{},"Funkce nabídky firmy",[883,75600,75602],{"className":75601},[886],[888,75603,75604],{"xmlns":890},[892,75605,75606,75632],{},[895,75607,75608,75610,75612,75614,75616,75618,75620,75622,75624,75626,75628,75630],{},[898,75609,5325],{},[1677,75611,1679],{},[898,75613,10061],{},[1677,75615,1686],{"stretchy":1685},[898,75617,2470],{},[1677,75619,1692],{"stretchy":1685},[1677,75621,1679],{},[898,75623,2499],{},[898,75625,2458],{},[1677,75627,1686],{"stretchy":1685},[898,75629,2470],{},[1677,75631,1692],{"stretchy":1685},[902,75633,70513],{"encoding":904},[883,75635,75637],{"className":75636},[886],[888,75638,75639],{"xmlns":890},[892,75640,75641,75653],{},[895,75642,75643,75645,75647],{},[898,75644,2470],{},[1677,75646,5873],{},[1805,75648,75649,75651],{},[898,75650,2470],{},[1677,75652,5742],{},[902,75654,69315],{"encoding":904},[883,75656,75658],{"className":75657},[886],[888,75659,75660],{"xmlns":890},[892,75661,75662,75666],{},[895,75663,75664],{},[1810,75665,2008],{},[902,75667,2008],{"encoding":904}," (3.15); vychází z rostoucí části ",[883,75670,75672],{"className":75671},[886],[888,75673,75674],{"xmlns":890},[892,75675,75676,75682],{},[895,75677,75678,75680],{},[898,75679,2499],{},[898,75681,2458],{},[902,75683,56683],{"encoding":904}," nad minimem ",[883,75686,75688],{"className":75687},[886],[888,75689,75690],{"xmlns":890},[892,75691,75692,75700],{},[895,75693,75694,75696,75698],{},[898,75695,5643],{},[898,75697,41730],{},[898,75699,2458],{},[902,75701,56702],{"encoding":904},[123,75703,75704,8403,75706,75727,75728,1656],{},[38,75705,51470],{},[883,75707,75709],{"className":75708},[886],[888,75710,75711],{"xmlns":890},[892,75712,75713,75725],{},[895,75714,75715,75717,75719],{},[898,75716,5325],{},[1677,75718,1679],{},[1805,75720,75721,75723],{},[898,75722,5325],{},[1677,75724,5742],{},[902,75726,5745],{"encoding":904}," konstantní ⇒ ",[883,75729,75731],{"className":75730},[886],[888,75732,75733],{"xmlns":890},[892,75734,75735,75755],{},[895,75736,75737,75739,75741,75743,75745,75747,75749],{},[898,75738,5643],{},[898,75740,5382],{},[1677,75742,1679],{},[898,75744,2499],{},[898,75746,5382],{},[1677,75748,1679],{},[1805,75750,75751,75753],{},[898,75752,5325],{},[1677,75754,5742],{},[902,75756,59989],{"encoding":904},[123,75758,75759,75762],{},[38,75760,75761],{},"Cenová diskriminace"," — stanovení odlišných cen pro různé segmenty trhu za účelem maximalizace zisku (úlohy 3.24–3.25).",[115,75764,3473],{"id":3472},[120,75766,75767,75786,75798],{},[123,75768,75769,1884,75771,1343,75774,1343,75777,1343,75780,1343,75783],{},[38,75770,52114],{},[207,75772,13330],{"className":75773,"dataFsResolvedFilePath":800,"href":801},[210],[207,75775,3509],{"className":75776,"dataFsResolvedFilePath":848,"href":849},[210],[207,75778,2038],{"className":75779,"dataFsResolvedFilePath":764,"href":765},[210],[207,75781,775],{"className":75782,"dataFsResolvedFilePath":773,"href":774},[210],[207,75784,859],{"className":75785,"dataFsResolvedFilePath":857,"href":858},[210],[123,75787,75788,1884,75790,1343,75794],{},[38,75789,38094],{},[207,75791,75793],{"className":75792,"dataFsResolvedFilePath":745,"href":746},[210],"KS 1. blok — souhrn",[207,75795,75797],{"className":75796,"dataFsResolvedFilePath":838,"href":839},[210],"KS 2. blok — souhrn",[123,75799,75800,1884,75802],{},[38,75801,17594],{},[207,75803,17598],{"className":75804,"dataFsResolvedFilePath":1641,"href":1642},[210],{"title":641,"searchDepth":642,"depth":642,"links":75806},[75807,75808,75815,75821,75825,75826,75830,75831,75832,75833,75839,75840],{"id":52345,"depth":642,"text":1241},{"id":57129,"depth":642,"text":57130,"children":75809},[75810,75811,75812,75813,75814],{"id":57140,"depth":649,"text":57141},{"id":57726,"depth":649,"text":57727},{"id":57874,"depth":649,"text":57875},{"id":58616,"depth":649,"text":58617},{"id":59271,"depth":649,"text":59272},{"id":59992,"depth":642,"text":59993,"children":75816},[75817,75818,75819,75820],{"id":59996,"depth":649,"text":59997},{"id":60157,"depth":649,"text":60158},{"id":61344,"depth":649,"text":61345},{"id":62242,"depth":649,"text":62243},{"id":63324,"depth":642,"text":63325,"children":75822},[75823,75824],{"id":17802,"depth":649,"text":17803},{"id":64674,"depth":649,"text":64675},{"id":64848,"depth":642,"text":64849},{"id":66769,"depth":642,"text":66770,"children":75827},[75828,75829],{"id":66783,"depth":649,"text":17803},{"id":68062,"depth":649,"text":68063},{"id":68694,"depth":642,"text":68695},{"id":70160,"depth":642,"text":70161},{"id":51272,"depth":642,"text":51273},{"id":70621,"depth":642,"text":70622,"children":75834},[75835,75836,75837,75838],{"id":70625,"depth":649,"text":70626},{"id":71477,"depth":649,"text":71478},{"id":73023,"depth":649,"text":73024},{"id":74399,"depth":649,"text":74400},{"id":17109,"depth":642,"text":17110},{"id":3472,"depth":642,"text":3473},{},"\u002Ftopics\u002Fprijem-naklady-zisk",{"title":56511,"description":641},[1138,1135],"topics\u002Fprijem-naklady-zisk",[1128,75847,75848,56563,75849,75850,75851],"prijem","naklady","body-zvratu","maximalizace-zisku","nabidka-firmy","0d2CjMGyTT-GeTvSE65iXk5mUJ-650ilVskfuGcRAwI",{"id":75854,"title":75855,"body":75856,"course":1128,"courses":659,"created":10944,"description":641,"extension":661,"meta":87953,"navigation":664,"path":87954,"seo":87955,"sources":87956,"stem":87957,"tags":87958,"type":3538,"updated":677,"__hash__":87964},"topics\u002Ftopics\u002Fprodukce.md","Produkce — produkční funkce, Cobb-Douglas, MRTS",{"type":9,"value":75857,"toc":87910},[75858,75861,76217,76221,76224,76292,76344,76354,76358,76392,76433,76457,76480,76509,76576,76683,76726,76783,76858,76903,76907,76915,76923,76926,77191,77242,77322,77392,77415,77443,77488,77510,77514,77521,77570,77596,77747,77750,77787,77950,78058,78062,78099,78174,78243,78362,78484,78565,78571,78612,78685,78778,78782,78818,78906,79020,79125,79210,79350,79354,79402,79447,79453,79457,79460,79511,79561,79568,79634,79767,79812,79816,79837,80216,80311,80328,80382,80386,80468,80552,80722,80725,80768,80835,80909,80913,80918,80987,80995,81004,81082,81148,81153,81248,81291,81296,81344,81349,81397,81515,81598,81636,81739,81798,81939,81943,81986,82059,82083,82137,82144,82146,82191,82236,82247,82252,82288,82350,82373,82382,82483,82550,82623,82630,82721,82783,82819,82876,82935,83120,83216,83220,83224,83303,83308,83432,83518,83524,83634,83671,83762,83860,83863,83867,83933,83970,84092,84144,84148,84176,84228,84302,84407,84431,84490,84494,84512,84655,84803,84805,84840,84844,84846,84936,85066,85192,85284,85359,85363,85479,85583,85773,85809,85903,85909,86022,86325,86331,86449,86548,86624,86626,87788,87790],[12,75859,75855],{"id":75860},"produkce-produkční-funkce-cobb-douglas-mrts",[5254,75862,75863],{},[724,75864,75865,5261,75867,75869,75870,38287,75883,75896,75897,17767,75910,11413,75912,75936,75937,1884,75939,5272,75973,1884,75976,76004,76005,11782,76025,76055,76056,11413,76059,76087,76088,76091,76092,76122,76123,76153,76154,1884,76157,76197,76198,76216],{},[883,75866,5260],{},[38,75868,859],{}," popisuje vztah mezi vstupy (práce ",[883,75871,75873],{"className":75872},[886],[888,75874,75875],{"xmlns":890},[892,75876,75877,75881],{},[895,75878,75879],{},[898,75880,11183],{},[902,75882,11183],{"encoding":904},[883,75884,75886],{"className":75885},[886],[888,75887,75888],{"xmlns":890},[892,75889,75890,75894],{},[895,75891,75892],{},[898,75893,11188],{},[902,75895,11188],{"encoding":904},") a výstupem ",[883,75898,75900],{"className":75899},[886],[888,75901,75902],{"xmlns":890},[892,75903,75904,75908],{},[895,75905,75906],{},[898,75907,2470],{},[902,75909,2470],{"encoding":904},[38,75911,38355],{},[883,75913,75915],{"className":75914},[886],[888,75916,75917],{"xmlns":890},[892,75918,75919,75933],{},[895,75920,75921,75923,75925,75927,75929,75931],{},[898,75922,2470],{},[1677,75924,1679],{},[898,75926,2470],{},[1677,75928,1686],{"stretchy":1685},[898,75930,11183],{},[1677,75932,1692],{"stretchy":1685},[902,75934,75935],{"encoding":904},"Q = Q(L)",") studujeme ",[614,75938,11412],{},[883,75940,75942],{"className":75941},[886],[888,75943,75944],{"xmlns":890},[892,75945,75946,75970],{},[895,75947,75948,75950,75956,75958,75964,75966,75968],{},[898,75949,2499],{},[1953,75951,75952,75954],{},[898,75953,5325],{},[898,75955,11183],{},[1677,75957,1679],{},[1805,75959,75960,75962],{},[898,75961,2470],{},[1677,75963,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,75965,1686],{"stretchy":1685},[898,75967,11183],{},[1677,75969,1692],{"stretchy":1685},[902,75971,75972],{"encoding":904},"MP_L = Q'(L)",[614,75974,75975],{},"průměrný produkt",[883,75977,75979],{"className":75978},[886],[888,75980,75981],{"xmlns":890},[892,75982,75983,76001],{},[895,75984,75985,75987,75993,75995,75997,75999],{},[898,75986,5643],{},[1953,75988,75989,75991],{},[898,75990,5325],{},[898,75992,11183],{},[1677,75994,1679],{},[898,75996,2470],{},[898,75998,6062],{"mathvariant":2057},[898,76000,11183],{},[902,76002,76003],{"encoding":904},"AP_L = Q\u002FL","; v maximu ",[883,76006,76008],{"className":76007},[886],[888,76009,76010],{"xmlns":890},[892,76011,76012,76022],{},[895,76013,76014,76016],{},[898,76015,5643],{},[1953,76017,76018,76020],{},[898,76019,5325],{},[898,76021,11183],{},[902,76023,76024],{"encoding":904},"AP_L",[883,76026,76028],{"className":76027},[886],[888,76029,76030],{"xmlns":890},[892,76031,76032,76052],{},[895,76033,76034,76036,76042,76044,76046],{},[898,76035,2499],{},[1953,76037,76038,76040],{},[898,76039,5325],{},[898,76041,11183],{},[1677,76043,1679],{},[898,76045,5643],{},[1953,76047,76048,76050],{},[898,76049,5325],{},[898,76051,11183],{},[902,76053,76054],{"encoding":904},"MP_L = AP_L",". Ve ",[38,76057,76058],{},"dvoufaktorovém modelu",[883,76060,76062],{"className":76061},[886],[888,76063,76064],{"xmlns":890},[892,76065,76066,76084],{},[895,76067,76068,76070,76072,76074,76076,76078,76080,76082],{},[898,76069,2470],{},[1677,76071,1679],{},[898,76073,2470],{},[1677,76075,1686],{"stretchy":1685},[898,76077,11183],{},[1677,76079,1967],{"separator":1966},[898,76081,11188],{},[1677,76083,1692],{"stretchy":1685},[902,76085,76086],{"encoding":904},"Q = Q(L,K)",") dominují ",[38,76089,76090],{},"Cobb-Douglasovy"," funkce ",[883,76093,76095],{"className":76094},[886],[888,76096,76097],{"xmlns":890},[892,76098,76099,76119],{},[895,76100,76101,76103,76105,76107,76113],{},[898,76102,2470],{},[1677,76104,1679],{},[898,76106,5643],{},[1805,76108,76109,76111],{},[898,76110,11183],{},[898,76112,207],{},[1805,76114,76115,76117],{},[898,76116,11188],{},[898,76118,1779],{},[902,76120,76121],{"encoding":904},"Q = AL^a K^b","; mezní produkty ",[883,76124,76126],{"className":76125},[886],[888,76127,76128],{"xmlns":890},[892,76129,76130,76150],{},[895,76131,76132,76134,76140,76142,76144],{},[898,76133,2499],{},[1953,76135,76136,76138],{},[898,76137,5325],{},[898,76139,11183],{},[1677,76141,1967],{"separator":1966},[898,76143,2499],{},[1953,76145,76146,76148],{},[898,76147,5325],{},[898,76149,11188],{},[902,76151,76152],{"encoding":904},"MP_L, MP_K"," jsou parciální derivace a jejich podíl dává ",[38,76155,76156],{},"mezní míru technické substituce",[883,76158,76160],{"className":76159},[886],[888,76161,76162],{"xmlns":890},[892,76163,76164,76194],{},[895,76165,76166,76168,76170,76172,76174,76176,76178,76184,76186,76188],{},[898,76167,2499],{},[898,76169,5382],{},[898,76171,2455],{},[898,76173,10061],{},[1677,76175,1679],{},[898,76177,2499],{},[1953,76179,76180,76182],{},[898,76181,5325],{},[898,76183,11183],{},[898,76185,6062],{"mathvariant":2057},[898,76187,2499],{},[1953,76189,76190,76192],{},[898,76191,5325],{},[898,76193,11188],{},[902,76195,76196],{"encoding":904},"MRTS = MP_L\u002FMP_K"," — sklon izokvanty. Součet exponentů ",[883,76199,76201],{"className":76200},[886],[888,76202,76203],{"xmlns":890},[892,76204,76205,76213],{},[895,76206,76207,76209,76211],{},[898,76208,207],{},[1677,76210,1776],{},[898,76212,1779],{},[902,76214,76215],{"encoding":904},"a+b"," určuje typ výnosů z rozsahu.",[115,76218,76220],{"id":76219},"úvod-cílové-znalosti-kapitoly-5","Úvod — cílové znalosti kapitoly 5",[724,76222,76223],{},"Po prostudování kapitoly 5 student umí:",[120,76225,76226,76232,76242,76248,76254,76259,76265,76275,76280,76286],{},[123,76227,76228,76229,1967],{},"popsat ",[38,76230,76231],{},"jednofaktorový model produkce",[123,76233,76234,76235,5272,76238,76241],{},"vypočítat ",[38,76236,76237],{},"mezní",[38,76239,76240],{},"průměrný produkt práce"," a ekonomicky je interpretovat,",[123,76243,76244,76245,1967],{},"charakterizovat průběh ",[38,76246,76247],{},"křivky produkce",[123,76249,76250,76251,1967],{},"formulovat ",[38,76252,76253],{},"princip maximalizace průměrného produktu práce",[123,76255,76228,76256,1967],{},[38,76257,76258],{},"dvoufaktorový model produkce",[123,76260,76261,76262,1967],{},"uvést tvar ",[38,76263,76264],{},"Cobb–Douglasových produkčních funkcí",[123,76266,76267,76268,1343,76270,1343,76272,1967],{},"vyložit, co jsou ",[38,76269,26004],{},[38,76271,15047],{},[38,76273,76274],{},"klesající výnosy z rozsahu",[123,76276,76234,76277,76241],{},[38,76278,76279],{},"mezní produkty práce a kapitálu",[123,76281,76282,76283,1967],{},"najít ",[38,76284,76285],{},"izokvanty",[123,76287,76234,76288,76291],{},[38,76289,76290],{},"mezní míru technické substituce (MRTS)"," a ekonomicky ji interpretovat.",[724,76293,76294,76295,76298,76299,76302,76303,1884,76306,1343,76319,1884,76322,5272,76335,76338,76339,76341,76342,1656],{},"Každý proces produkce je určován ",[38,76296,76297],{},"faktory"," (též ",[38,76300,76301],{},"vstupy",") produkce. K hlavním patří ",[38,76304,76305],{},"práce",[883,76307,76309],{"className":76308},[886],[888,76310,76311],{"xmlns":890},[892,76312,76313,76317],{},[895,76314,76315],{},[898,76316,11183],{},[902,76318,11183],{"encoding":904},[38,76320,76321],{},"kapitál",[883,76323,76325],{"className":76324},[886],[888,76326,76327],{"xmlns":890},[892,76328,76329,76333],{},[895,76330,76331],{},[898,76332,11188],{},[902,76334,11188],{"encoding":904},[38,76336,76337],{},"půda",". Při modelování se půda obvykle považuje za dlouhodobě konstantní, takže endogenními faktory zůstávají práce a kapitál. Je-li kapitál neměnný, hovoříme o ",[38,76340,38355],{}," (produkce závisí jen na práci); v opačném případě o ",[38,76343,76058],{},[724,76345,76346,76347,1343,76350,76353],{},"Související matematický aparát: ",[207,76348,2038],{"className":76349,"dataFsResolvedFilePath":764,"href":765},[210],[207,76351,784],{"className":76352,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace a totální diferenciál).",[115,76355,76357],{"id":76356},"jednofaktorový-model-produkce","Jednofaktorový model produkce",[724,76359,76360,76361,76374,76375,76388,76389],{},"Uvažujeme proces v krátkém období, kdy kapitál lze považovat za konstantní. Závislost produkce ",[883,76362,76364],{"className":76363},[886],[888,76365,76366],{"xmlns":890},[892,76367,76368,76372],{},[895,76369,76370],{},[898,76371,2470],{},[902,76373,2470],{"encoding":904}," na práci ",[883,76376,76378],{"className":76377},[886],[888,76379,76380],{"xmlns":890},[892,76381,76382,76386],{},[895,76383,76384],{},[898,76385,11183],{},[902,76387,11183],{"encoding":904}," vyjadřuje ",[38,76390,76391],{},"produkční funkce",[883,76393,76395],{"className":76394},[886],[888,76396,76397],{"xmlns":890,"display":29457},[892,76398,76399,76430],{},[22145,76400,76401],{"width":29462},[22150,76402,76403,76405,76423,76425],{},[22153,76404],{"width":29467},[22153,76406,76407],{},[895,76408,76409,76411,76413,76415,76417,76419,76421],{},[898,76410,2470],{},[1677,76412,1679],{},[898,76414,2470],{},[1677,76416,1686],{"stretchy":1685},[898,76418,11183],{},[1677,76420,1692],{"stretchy":1685},[1677,76422,1967],{"separator":1966},[22153,76424],{"width":29467},[22153,76426,76427],{},[1969,76428,76429],{},"(5.1)",[902,76431,76432],{"encoding":904},"Q = Q(L), \\tag{5.1}",[724,76434,76435,76436,11413,76439,76442,76443,76456],{},"jejíž graf se nazývá ",[38,76437,76438],{},"křivka produkce",[614,76440,76441],{},"production curve","). Práce ",[883,76444,76446],{"className":76445},[886],[888,76447,76448],{"xmlns":890},[892,76449,76450,76454],{},[895,76451,76452],{},[898,76453,11183],{},[902,76455,11183],{"encoding":904}," se měří počtem pracovníků, případně počtem pracovních hodin.",[115,76458,76460,76461,1692],{"id":76459},"mezní-produkt-práce-mplmp_l","Mezní produkt práce (",[883,76462,76464],{"className":76463},[886],[888,76465,76466],{"xmlns":890},[892,76467,76468,76478],{},[895,76469,76470,76472],{},[898,76471,2499],{},[1953,76473,76474,76476],{},[898,76475,5325],{},[898,76477,11183],{},[902,76479,11433],{"encoding":904},[724,76481,76482,11413,76485,76488,76489,76508],{},[38,76483,76484],{},"Mezní produkt práce",[614,76486,76487],{},"marginal product of labour",") ",[883,76490,76492],{"className":76491},[886],[888,76493,76494],{"xmlns":890},[892,76495,76496,76506],{},[895,76497,76498,76500],{},[898,76499,2499],{},[1953,76501,76502,76504],{},[898,76503,5325],{},[898,76505,11183],{},[902,76507,11433],{"encoding":904}," je derivace produkce podle práce:",[883,76510,76512],{"className":76511},[886],[888,76513,76514],{"xmlns":890,"display":29457},[892,76515,76516,76573],{},[22145,76517,76518],{"width":29462},[22150,76519,76520,76522,76566,76568],{},[22153,76521],{"width":29467},[22153,76523,76524],{},[895,76525,76526,76528,76534,76536,76550,76552,76558,76560,76562,76564],{},[898,76527,2499],{},[1953,76529,76530,76532],{},[898,76531,5325],{},[898,76533,11183],{},[1677,76535,1679],{},[2010,76537,76538,76544],{},[895,76539,76540,76542],{},[898,76541,1875],{},[898,76543,2470],{},[895,76545,76546,76548],{},[898,76547,1875],{},[898,76549,11183],{},[1677,76551,1679],{},[1805,76553,76554,76556],{},[898,76555,2470],{},[1677,76557,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,76559,1686],{"stretchy":1685},[898,76561,11183],{},[1677,76563,1692],{"stretchy":1685},[898,76565,1656],{"mathvariant":2057},[22153,76567],{"width":29467},[22153,76569,76570],{},[1969,76571,76572],{},"(5.2)",[902,76574,76575],{"encoding":904},"MP_L = \\frac{dQ}{dL} = Q'(L). \\tag{5.2}",[724,76577,76578,76579,21336,76597,76625,76626,76643,76644,2366,76661,5306],{},"Pro pevnou hodnotu ",[883,76580,76582],{"className":76581},[886],[888,76583,76584],{"xmlns":890},[892,76585,76586,76594],{},[895,76587,76588],{},[1805,76589,76590,76592],{},[898,76591,11183],{},[1677,76593,5742],{},[902,76595,76596],{"encoding":904},"L^*",[883,76598,76600],{"className":76599},[886],[888,76601,76602],{"xmlns":890},[892,76603,76604,76622],{},[895,76605,76606,76612,76614,76620],{},[1805,76607,76608,76610],{},[898,76609,2470],{},[1677,76611,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,76613,1686],{"stretchy":1685},[1805,76615,76616,76618],{},[898,76617,11183],{},[1677,76619,5742],{},[1677,76621,1692],{"stretchy":1685},[902,76623,76624],{"encoding":904},"Q'(L^*)"," rychlost změny produkce vzhledem k práci v bodě ",[883,76627,76629],{"className":76628},[886],[888,76630,76631],{"xmlns":890},[892,76632,76633,76641],{},[895,76634,76635],{},[1805,76636,76637,76639],{},[898,76638,11183],{},[1677,76640,5742],{},[902,76642,76596],{"encoding":904},", resp. přibližnou změnu produkce odpovídající jednotkové změně práce (z ",[883,76645,76647],{"className":76646},[886],[888,76648,76649],{"xmlns":890},[892,76650,76651,76659],{},[895,76652,76653],{},[1805,76654,76655,76657],{},[898,76656,11183],{},[1677,76658,5742],{},[902,76660,76596],{"encoding":904},[883,76662,76664],{"className":76663},[886],[888,76665,76666],{"xmlns":890},[892,76667,76668,76680],{},[895,76669,76670,76676,76678],{},[1805,76671,76672,76674],{},[898,76673,11183],{},[1677,76675,5742],{},[1677,76677,1776],{},[1810,76679,1959],{},[902,76681,76682],{"encoding":904},"L^*+1",[5254,76684,76685],{},[724,76686,76687,19414,76689,76708,76709,76712,76713,1656],{},[883,76688,5543],{},[883,76690,76692],{"className":76691},[886],[888,76693,76694],{"xmlns":890},[892,76695,76696,76706],{},[895,76697,76698,76700],{},[898,76699,2499],{},[1953,76701,76702,76704],{},[898,76703,5325],{},[898,76705,11183],{},[902,76707,11433],{"encoding":904}," odpovídá na otázku „",[38,76710,76711],{},"kolik produkce přibude, když přidám jednoho dalšího pracovníka"," (při neměnném kapitálu)?\". Je to sklon křivky produkce v bodě ",[883,76714,76716],{"className":76715},[886],[888,76717,76718],{"xmlns":890},[892,76719,76720,76724],{},[895,76721,76722],{},[898,76723,11183],{},[902,76725,11183],{"encoding":904},[724,76727,76728,76731,76732,76748,76749,2366,76762,76782],{},[38,76729,76730],{},"Přibližná změna produkce"," pro změnu práce o ",[883,76733,76735],{"className":76734},[886],[888,76736,76737],{"xmlns":890},[892,76738,76739,76745],{},[895,76740,76741,76743],{},[898,76742,1875],{},[898,76744,11183],{},[902,76746,76747],{"encoding":904},"dL"," (z ",[883,76750,76752],{"className":76751},[886],[888,76753,76754],{"xmlns":890},[892,76755,76756,76760],{},[895,76757,76758],{},[898,76759,11183],{},[902,76761,11183],{"encoding":904},[883,76763,76765],{"className":76764},[886],[888,76766,76767],{"xmlns":890},[892,76768,76769,76779],{},[895,76770,76771,76773,76775,76777],{},[898,76772,11183],{},[1677,76774,1776],{},[898,76776,1875],{},[898,76778,11183],{},[902,76780,76781],{"encoding":904},"L+dL",") pomocí diferenciálu:",[883,76784,76786],{"className":76785},[886],[888,76787,76788],{"xmlns":890,"display":29457},[892,76789,76790,76855],{},[22145,76791,76792],{"width":29462},[22150,76793,76794,76796,76848,76850],{},[22153,76795],{"width":29467},[22153,76797,76798],{},[895,76799,76800,76802,76804,76806,76808,76810,76812,76818,76820,76822,76824,76826,76828,76830,76832,76834,76840,76842,76844,76846],{},[898,76801,2570],{"mathvariant":2057},[898,76803,2470],{},[1677,76805,2411],{},[898,76807,1875],{},[898,76809,2470],{},[1677,76811,1679],{},[1805,76813,76814,76816],{},[898,76815,2470],{},[1677,76817,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,76819,1686],{"stretchy":1685},[898,76821,11183],{},[1677,76823,1692],{"stretchy":1685},[1969,76825,2668],{},[898,76827,1875],{},[898,76829,11183],{},[1677,76831,1679],{},[898,76833,2499],{},[1953,76835,76836,76838],{},[898,76837,5325],{},[898,76839,11183],{},[1969,76841,2668],{},[898,76843,1875],{},[898,76845,11183],{},[898,76847,1656],{"mathvariant":2057},[22153,76849],{"width":29467},[22153,76851,76852],{},[1969,76853,76854],{},"(5.3)",[902,76856,76857],{"encoding":904},"\\Delta Q \\approx dQ = Q'(L)\\,dL = MP_L\\,dL. \\tag{5.3}",[724,76859,76860,76861,1656],{},"Skutečná změna je ",[883,76862,76864],{"className":76863},[886],[888,76865,76866],{"xmlns":890},[892,76867,76868,76900],{},[895,76869,76870,76872,76874,76876,76878,76880,76882,76884,76886,76888,76890,76892,76894,76896,76898],{},[898,76871,2570],{"mathvariant":2057},[898,76873,2470],{},[1677,76875,1679],{},[898,76877,2470],{},[1677,76879,1686],{"stretchy":1685},[898,76881,11183],{},[1677,76883,1776],{},[898,76885,1875],{},[898,76887,11183],{},[1677,76889,1692],{"stretchy":1685},[1677,76891,1906],{},[898,76893,2470],{},[1677,76895,1686],{"stretchy":1685},[898,76897,11183],{},[1677,76899,1692],{"stretchy":1685},[902,76901,76902],{"encoding":904},"\\Delta Q = Q(L+dL) - Q(L)",[198,76904,76906],{"id":76905},"zákon-klesajících-mezních-výnosů","Zákon klesajících mezních výnosů",[724,76908,76909,11413,76912,2832],{},[38,76910,76911],{},"Zákon klesajících výnosů",[614,76913,76914],{},"law of diminishing marginal productivity",[5254,76916,76917],{},[724,76918,76919,76920,76922],{},"Roste-li postupně některý ze vstupů (",[614,76921,38351],{},"), budou přírůstky výstupu od jistého bodu klesat.",[724,76924,76925],{},"Typická křivka produkce (Obrázek 5.2) má dvě fáze:",[724,76927,76928,76929,1884,76950,76969,76970,77020,77021,77023,77024,1884,77044,77063,77064,77020,77096,2608,77098,77117,77118,22985,77135,77169,77170,9490,77187,77190],{},"1° ",[38,76930,76931,76932,2385],{},"Do bodu ",[883,76933,76935],{"className":76934},[886],[888,76936,76937],{"xmlns":890},[892,76938,76939,76947],{},[895,76940,76941],{},[1953,76942,76943,76945],{},[898,76944,11183],{},[1810,76946,2008],{},[902,76948,76949],{"encoding":904},"L_0",[883,76951,76953],{"className":76952},[886],[888,76954,76955],{"xmlns":890},[892,76956,76957,76967],{},[895,76958,76959,76961],{},[898,76960,2499],{},[1953,76962,76963,76965],{},[898,76964,5325],{},[898,76966,11183],{},[902,76968,11433],{"encoding":904}," roste, tj. ",[883,76971,76973],{"className":76972},[886],[888,76974,76975],{"xmlns":890},[892,76976,76977,77017],{},[895,76978,76979,76981,76983,76989,76995,76997,77007,77009,77011,77013,77015],{},[1677,76980,1686],{"stretchy":1685},[898,76982,2499],{},[1953,76984,76985,76987],{},[898,76986,5325],{},[898,76988,11183],{},[1805,76990,76991,76993],{},[1677,76992,1692],{"stretchy":1685},[1677,76994,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,76996,1679],{},[1805,76998,76999,77001],{},[898,77000,2470],{},[895,77002,77003,77005],{},[1677,77004,2059],{"mathvariant":2057},[1677,77006,2059],{"mathvariant":2057},[1677,77008,1686],{"stretchy":1685},[898,77010,11183],{},[1677,77012,1692],{"stretchy":1685},[1677,77014,3089],{},[1810,77016,2008],{},[902,77018,77019],{"encoding":904},"(MP_L)' = Q''(L) > 0"," — křivka produkce je ",[38,77022,39055],{},".\n2° ",[38,77025,77026,77027,2385],{},"Od bodu ",[883,77028,77030],{"className":77029},[886],[888,77031,77032],{"xmlns":890},[892,77033,77034,77042],{},[895,77035,77036],{},[1953,77037,77038,77040],{},[898,77039,11183],{},[1810,77041,2008],{},[902,77043,76949],{"encoding":904},[883,77045,77047],{"className":77046},[886],[888,77048,77049],{"xmlns":890},[892,77050,77051,77061],{},[895,77052,77053,77055],{},[898,77054,2499],{},[1953,77056,77057,77059],{},[898,77058,5325],{},[898,77060,11183],{},[902,77062,11433],{"encoding":904}," klesá, ",[883,77065,77067],{"className":77066},[886],[888,77068,77069],{"xmlns":890},[892,77070,77071,77093],{},[895,77072,77073,77083,77085,77087,77089,77091],{},[1805,77074,77075,77077],{},[898,77076,2470],{},[895,77078,77079,77081],{},[1677,77080,2059],{"mathvariant":2057},[1677,77082,2059],{"mathvariant":2057},[1677,77084,1686],{"stretchy":1685},[898,77086,11183],{},[1677,77088,1692],{"stretchy":1685},[1677,77090,3128],{},[1810,77092,2008],{},[902,77094,77095],{"encoding":904},"Q''(L) \u003C 0",[38,77097,39879],{},[883,77099,77101],{"className":77100},[886],[888,77102,77103],{"xmlns":890},[892,77104,77105,77115],{},[895,77106,77107,77109],{},[898,77108,2499],{},[1953,77110,77111,77113],{},[898,77112,5325],{},[898,77114,11183],{},[902,77116,11433],{"encoding":904}," v kladných hodnotách klesá do bodu ",[883,77119,77121],{"className":77120},[886],[888,77122,77123],{"xmlns":890},[892,77124,77125,77133],{},[895,77126,77127],{},[1953,77128,77129,77131],{},[898,77130,11183],{},[1810,77132,1959],{},[902,77134,14602],{"encoding":904},[883,77136,77138],{"className":77137},[886],[888,77139,77140],{"xmlns":890},[892,77141,77142,77166],{},[895,77143,77144,77146,77152,77154,77160,77162,77164],{},[898,77145,2499],{},[1953,77147,77148,77150],{},[898,77149,5325],{},[898,77151,11183],{},[1677,77153,1686],{"stretchy":1685},[1953,77155,77156,77158],{},[898,77157,11183],{},[1810,77159,1959],{},[1677,77161,1692],{"stretchy":1685},[1677,77163,1679],{},[1810,77165,2008],{},[902,77167,77168],{"encoding":904},"MP_L(L_1) = 0"," (maximum produkce), a dále pokračuje v záporných hodnotách. Bod ",[883,77171,77173],{"className":77172},[886],[888,77174,77175],{"xmlns":890},[892,77176,77177,77185],{},[895,77178,77179],{},[1953,77180,77181,77183],{},[898,77182,11183],{},[1810,77184,2008],{},[902,77186,76949],{"encoding":904},[38,77188,77189],{},"inflexním bodem"," produkční funkce.",[724,77192,77193,77194,11782,77211,1656],{},"Matematicky: zákon klesajících výnosů znamená, že od určitého ",[883,77195,77197],{"className":77196},[886],[888,77198,77199],{"xmlns":890},[892,77200,77201,77209],{},[895,77202,77203],{},[1953,77204,77205,77207],{},[898,77206,11183],{},[1810,77208,2008],{},[902,77210,76949],{"encoding":904},[883,77212,77214],{"className":77213},[886],[888,77215,77216],{"xmlns":890},[892,77217,77218,77240],{},[895,77219,77220,77230,77232,77234,77236,77238],{},[1805,77221,77222,77224],{},[898,77223,2470],{},[895,77225,77226,77228],{},[1677,77227,2059],{"mathvariant":2057},[1677,77229,2059],{"mathvariant":2057},[1677,77231,1686],{"stretchy":1685},[898,77233,11183],{},[1677,77235,1692],{"stretchy":1685},[1677,77237,3128],{},[1810,77239,2008],{},[902,77241,77095],{"encoding":904},[724,77243,77244,1884,77247,7057,77287,1343,77304,77321],{},[38,77245,77246],{},"Typický polynom třetího stupně:",[883,77248,77250],{"className":77249},[886],[888,77251,77252],{"xmlns":890},[892,77253,77254,77284],{},[895,77255,77256,77258,77260,77262,77264,77266,77268,77274,77276,77278],{},[898,77257,2470],{},[1677,77259,1686],{"stretchy":1685},[898,77261,11183],{},[1677,77263,1692],{"stretchy":1685},[1677,77265,1679],{},[898,77267,207],{},[1805,77269,77270,77272],{},[898,77271,11183],{},[1810,77273,1854],{},[1677,77275,1776],{},[898,77277,1779],{},[1805,77279,77280,77282],{},[898,77281,11183],{},[1810,77283,1812],{},[902,77285,77286],{"encoding":904},"Q(L) = aL^3 + bL^2",[883,77288,77290],{"className":77289},[886],[888,77291,77292],{"xmlns":890},[892,77293,77294,77302],{},[895,77295,77296,77298,77300],{},[898,77297,207],{},[1677,77299,3128],{},[1810,77301,2008],{},[902,77303,44476],{"encoding":904},[883,77305,77307],{"className":77306},[886],[888,77308,77309],{"xmlns":890},[892,77310,77311,77319],{},[895,77312,77313,77315,77317],{},[898,77314,1779],{},[1677,77316,3089],{},[1810,77318,2008],{},[902,77320,20205],{"encoding":904},". Pak",[883,77323,77325],{"className":77324},[886],[888,77326,77327],{"xmlns":890,"display":29457},[892,77328,77329,77389],{},[895,77330,77331,77337,77339,77341,77349,77357,77359,77361,77367,77369,77371,77379,77387],{},[1953,77332,77333,77335],{},[898,77334,11183],{},[1810,77336,2008],{},[1677,77338,1679],{},[1677,77340,1906],{},[2006,77342,77343],{"scriptlevel":2008,"displaystyle":1685},[2010,77344,77345,77347],{},[1810,77346,1959],{},[1810,77348,1854],{},[2006,77350,77351],{"scriptlevel":2008,"displaystyle":1685},[2010,77352,77353,77355],{},[898,77354,1779],{},[898,77356,207],{},[1677,77358,1967],{"separator":1966},[7266,77360],{"width":7268},[1953,77362,77363,77365],{},[898,77364,11183],{},[1810,77366,1959],{},[1677,77368,1679],{},[1677,77370,1906],{},[2006,77372,77373],{"scriptlevel":2008,"displaystyle":1685},[2010,77374,77375,77377],{},[1810,77376,1812],{},[1810,77378,1854],{},[2006,77380,77381],{"scriptlevel":2008,"displaystyle":1685},[2010,77382,77383,77385],{},[898,77384,1779],{},[898,77386,207],{},[898,77388,1656],{"mathvariant":2057},[902,77390,77391],{"encoding":904},"L_0 = -\\tfrac{1}{3}\\tfrac{b}{a}, \\qquad L_1 = -\\tfrac{2}{3}\\tfrac{b}{a}.",[115,77393,77395,77396,1692],{"id":77394},"průměrný-produkt-práce-aplap_l","Průměrný produkt práce (",[883,77397,77399],{"className":77398},[886],[888,77400,77401],{"xmlns":890},[892,77402,77403,77413],{},[895,77404,77405,77407],{},[898,77406,5643],{},[1953,77408,77409,77411],{},[898,77410,5325],{},[898,77412,11183],{},[902,77414,76024],{"encoding":904},[724,77416,77417,11413,77420,76488,77423,77442],{},[38,77418,77419],{},"Průměrný produkt práce",[614,77421,77422],{},"average product of labour",[883,77424,77426],{"className":77425},[886],[888,77427,77428],{"xmlns":890},[892,77429,77430,77440],{},[895,77431,77432,77434],{},[898,77433,5643],{},[1953,77435,77436,77438],{},[898,77437,5325],{},[898,77439,11183],{},[902,77441,76024],{"encoding":904}," je podíl produkce a práce:",[883,77444,77446],{"className":77445},[886],[888,77447,77448],{"xmlns":890,"display":29457},[892,77449,77450,77485],{},[22145,77451,77452],{"width":29462},[22150,77453,77454,77456,77478,77480],{},[22153,77455],{"width":29467},[22153,77457,77458],{},[895,77459,77460,77462,77468,77470,77476],{},[898,77461,5643],{},[1953,77463,77464,77466],{},[898,77465,5325],{},[898,77467,11183],{},[1677,77469,1679],{},[2010,77471,77472,77474],{},[898,77473,2470],{},[898,77475,11183],{},[898,77477,1656],{"mathvariant":2057},[22153,77479],{"width":29467},[22153,77481,77482],{},[1969,77483,77484],{},"(5.4)",[902,77486,77487],{"encoding":904},"AP_L = \\frac{Q}{L}. \\tag{5.4}",[724,77489,77490,77491,1656],{},"Je to nejjednodušší míra produktivity práce. Cílem optimalizace je maximalizace ",[883,77492,77494],{"className":77493},[886],[888,77495,77496],{"xmlns":890},[892,77497,77498,77508],{},[895,77499,77500,77502],{},[898,77501,5643],{},[1953,77503,77504,77506],{},[898,77505,5325],{},[898,77507,11183],{},[902,77509,76024],{"encoding":904},[115,77511,77513],{"id":77512},"princip-maximalizace-průměrného-produktu-práce","Princip maximalizace průměrného produktu práce",[724,77515,77516],{},[2240,77517],{"alt":77518,"className":77519,"src":77520},"imek-q-mpl-apl-tripanel",[210,2244],"\u002Fwiki-assets\u002Fimek-q-mpl-apl-tripanel.jpeg",[5254,77522,77523],{},[724,77524,77525,77528,77529,2305,77548,77565,77566],{},[38,77526,77527],{},"Princip:"," Má-li ",[883,77530,77532],{"className":77531},[886],[888,77533,77534],{"xmlns":890},[892,77535,77536,77546],{},[895,77537,77538,77540],{},[898,77539,5643],{},[1953,77541,77542,77544],{},[898,77543,5325],{},[898,77545,11183],{},[902,77547,76024],{"encoding":904},[883,77549,77551],{"className":77550},[886],[888,77552,77553],{"xmlns":890},[892,77554,77555,77563],{},[895,77556,77557],{},[1953,77558,77559,77561],{},[898,77560,11183],{},[1810,77562,2008],{},[902,77564,76949],{"encoding":904}," maximum, pak platí\n",[883,77567,77569],{"className":77568,"title":5588,"style":5589},[5587],"MP_L(L_0) = AP_L(L_0). \\tag{5.5}",[724,77571,77572,77573,77576,77577,1884,77581,1656],{},"Slovně: ",[38,77574,77575],{},"v bodě maxima průměrného produktu práce se mezní produkt práce rovná průměrnému produktu práce."," Jde o analogii ",[207,77578,77580],{"className":77579,"dataFsResolvedFilePath":827,"href":828},[210],"principu minimalizace průměrných nákladů",[883,77582,77584],{"className":77583},[886],[888,77585,77586],{"xmlns":890},[892,77587,77588,77594],{},[895,77589,77590,77592],{},[898,77591,5643],{},[898,77593,2458],{},[902,77595,56951],{"encoding":904},[5254,77597,77598,77622],{},[724,77599,77600,77602,77603],{},[883,77601,5960],{}," Postup — jak najít max ",[883,77604,77606],{"className":77605},[886],[888,77607,77608],{"xmlns":890},[892,77609,77610,77620],{},[895,77611,77612,77614],{},[898,77613,5643],{},[1953,77615,77616,77618],{},[898,77617,5325],{},[898,77619,11183],{},[902,77621,76024],{"encoding":904},[152,77623,77624,77662,77744],{},[123,77625,77626,77627,77661],{},"Napište ",[883,77628,77630],{"className":77629},[886],[888,77631,77632],{"xmlns":890},[892,77633,77634,77658],{},[895,77635,77636,77638,77644,77646,77648,77650,77652,77654,77656],{},[898,77637,5643],{},[1953,77639,77640,77642],{},[898,77641,5325],{},[898,77643,11183],{},[1677,77645,1679],{},[898,77647,2470],{},[1677,77649,1686],{"stretchy":1685},[898,77651,11183],{},[1677,77653,1692],{"stretchy":1685},[898,77655,6062],{"mathvariant":2057},[898,77657,11183],{},[902,77659,77660],{"encoding":904},"AP_L = Q(L)\u002FL"," a zderivujte.",[123,77663,77664,77665,77697,77698,77701,77702,1656],{},"Položte ",[883,77666,77668],{"className":77667},[886],[888,77669,77670],{"xmlns":890},[892,77671,77672,77694],{},[895,77673,77674,77676,77678,77684,77690,77692],{},[1677,77675,1686],{"stretchy":1685},[898,77677,5643],{},[1953,77679,77680,77682],{},[898,77681,5325],{},[898,77683,11183],{},[1805,77685,77686,77688],{},[1677,77687,1692],{"stretchy":1685},[1677,77689,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,77691,1679],{},[1810,77693,2008],{},[902,77695,77696],{"encoding":904},"(AP_L)' = 0"," a vyřešte. ",[614,77699,77700],{},"Zkratka:"," můžete rovnou řešit ",[883,77703,77705],{"className":77704},[886],[888,77706,77707],{"xmlns":890},[892,77708,77709,77741],{},[895,77710,77711,77713,77719,77721,77723,77725,77727,77729,77735,77737,77739],{},[898,77712,2499],{},[1953,77714,77715,77717],{},[898,77716,5325],{},[898,77718,11183],{},[1677,77720,1686],{"stretchy":1685},[898,77722,11183],{},[1677,77724,1692],{"stretchy":1685},[1677,77726,1679],{},[898,77728,5643],{},[1953,77730,77731,77733],{},[898,77732,5325],{},[898,77734,11183],{},[1677,77736,1686],{"stretchy":1685},[898,77738,11183],{},[1677,77740,1692],{"stretchy":1685},[902,77742,77743],{"encoding":904},"MP_L(L) = AP_L(L)",[123,77745,77746],{},"Ověřte 2. derivací (či grafem), že jde o maximum.",[198,77748,66892],{"id":77749},"odvození",[724,77751,77752,77753,77786],{},"Z ",[883,77754,77756],{"className":77755},[886],[888,77757,77758],{"xmlns":890},[892,77759,77760,77784],{},[895,77761,77762,77764,77770,77772,77774,77776,77778,77780,77782],{},[898,77763,5643],{},[1953,77765,77766,77768],{},[898,77767,5325],{},[898,77769,11183],{},[1677,77771,1679],{},[898,77773,2470],{},[1677,77775,1686],{"stretchy":1685},[898,77777,11183],{},[1677,77779,1692],{"stretchy":1685},[898,77781,6062],{"mathvariant":2057},[898,77783,11183],{},[902,77785,77660],{"encoding":904}," a derivace podílu:",[883,77788,77790],{"className":77789},[886],[888,77791,77792],{"xmlns":890,"display":29457},[892,77793,77794,77947],{},[895,77795,77796,77798,77800,77806,77812,77814,77816,77818,77820,77860,77862,77868,77902,77904,77910,77913,77915,77921,77923,77925,77927,77929,77931,77937,77939,77941,77943,77945],{},[1677,77797,1686],{"stretchy":1685},[898,77799,5643],{},[1953,77801,77802,77804],{},[898,77803,5325],{},[898,77805,11183],{},[1805,77807,77808,77810],{},[1677,77809,1692],{"stretchy":1685},[1677,77811,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,77813,1686],{"stretchy":1685},[898,77815,11183],{},[1677,77817,1692],{"stretchy":1685},[1677,77819,1679],{},[2010,77821,77822,77854],{},[895,77823,77824,77830,77832,77834,77836,77838,77840,77842,77844,77846,77848,77850,77852],{},[1805,77825,77826,77828],{},[898,77827,2470],{},[1677,77829,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,77831,1686],{"stretchy":1685},[898,77833,11183],{},[1677,77835,1692],{"stretchy":1685},[1677,77837,2858],{},[898,77839,11183],{},[1677,77841,1906],{},[898,77843,2470],{},[1677,77845,1686],{"stretchy":1685},[898,77847,11183],{},[1677,77849,1692],{"stretchy":1685},[1677,77851,2858],{},[1810,77853,1959],{},[1805,77855,77856,77858],{},[898,77857,11183],{},[1810,77859,1812],{},[1677,77861,1679],{},[2010,77863,77864,77866],{},[1810,77865,1959],{},[898,77867,11183],{},[895,77869,77870,77872,77878,77880,77882,77884,77886,77900],{},[1677,77871,1686],{"fence":1966},[1805,77873,77874,77876],{},[898,77875,2470],{},[1677,77877,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,77879,1686],{"stretchy":1685},[898,77881,11183],{},[1677,77883,1692],{"stretchy":1685},[1677,77885,1906],{},[2010,77887,77888,77898],{},[895,77889,77890,77892,77894,77896],{},[898,77891,2470],{},[1677,77893,1686],{"stretchy":1685},[898,77895,11183],{},[1677,77897,1692],{"stretchy":1685},[898,77899,11183],{},[1677,77901,1692],{"fence":1966},[1677,77903,1679],{},[2010,77905,77906,77908],{},[1810,77907,1959],{},[898,77909,11183],{},[1677,77911,1686],{"fence":1966,"stretchy":1966,"minsize":77912,"maxsize":77912},"1.2em",[898,77914,2499],{},[1953,77916,77917,77919],{},[898,77918,5325],{},[898,77920,11183],{},[1677,77922,1686],{"stretchy":1685},[898,77924,11183],{},[1677,77926,1692],{"stretchy":1685},[1677,77928,1906],{},[898,77930,5643],{},[1953,77932,77933,77935],{},[898,77934,5325],{},[898,77936,11183],{},[1677,77938,1686],{"stretchy":1685},[898,77940,11183],{},[1677,77942,1692],{"stretchy":1685},[1677,77944,1692],{"fence":1966,"stretchy":1966,"minsize":77912,"maxsize":77912},[898,77946,1656],{"mathvariant":2057},[902,77948,77949],{"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).",[724,77951,11051,77952,9490,77974,78057],{},[883,77953,77955],{"className":77954},[886],[888,77956,77957],{"xmlns":890},[892,77958,77959,77971],{},[895,77960,77961,77967,77969],{},[1953,77962,77963,77965],{},[898,77964,11183],{},[1810,77966,2008],{},[1677,77968,3089],{},[1810,77970,2008],{},[902,77972,77973],{"encoding":904},"L_0 > 0",[883,77975,77977],{"className":77976},[886],[888,77978,77979],{"xmlns":890},[892,77980,77981,78054],{},[895,77982,77983,77985,77987,77993,77999,78001,78007,78009,78011,78013,78016,78018,78024,78026,78032,78034,78036,78038,78044,78046,78052],{},[1677,77984,1686],{"stretchy":1685},[898,77986,5643],{},[1953,77988,77989,77991],{},[898,77990,5325],{},[898,77992,11183],{},[1805,77994,77995,77997],{},[1677,77996,1692],{"stretchy":1685},[1677,77998,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,78000,1686],{"stretchy":1685},[1953,78002,78003,78005],{},[898,78004,11183],{},[1810,78006,2008],{},[1677,78008,1692],{"stretchy":1685},[1677,78010,1679],{},[1810,78012,2008],{},[1677,78014,78015],{},"⇔",[898,78017,2499],{},[1953,78019,78020,78022],{},[898,78021,5325],{},[898,78023,11183],{},[1677,78025,1686],{"stretchy":1685},[1953,78027,78028,78030],{},[898,78029,11183],{},[1810,78031,2008],{},[1677,78033,1692],{"stretchy":1685},[1677,78035,1679],{},[898,78037,5643],{},[1953,78039,78040,78042],{},[898,78041,5325],{},[898,78043,11183],{},[1677,78045,1686],{"stretchy":1685},[1953,78047,78048,78050],{},[898,78049,11183],{},[1810,78051,2008],{},[1677,78053,1692],{"stretchy":1685},[902,78055,78056],{"encoding":904},"(AP_L)'(L_0) = 0 \\Leftrightarrow MP_L(L_0) = AP_L(L_0)",", čímž je (5.5) dokázáno.",[198,78059,78061],{"id":78060},"příklad-51","Příklad 5.1",[724,78063,78064,78065,1656],{},"Je dána produkce ",[883,78066,78068],{"className":78067},[886],[888,78069,78070],{"xmlns":890},[892,78071,78072,78096],{},[895,78073,78074,78076,78078,78080,78086,78088,78090],{},[898,78075,2470],{},[1677,78077,1679],{},[1810,78079,1916],{},[1805,78081,78082,78084],{},[898,78083,11183],{},[1810,78085,1812],{},[1677,78087,1906],{},[1810,78089,2520],{},[1805,78091,78092,78094],{},[898,78093,11183],{},[1810,78095,1854],{},[902,78097,78098],{"encoding":904},"Q = 6L^2 - 0{,}2L^3",[724,78100,78101,58913,78104,78154,78155,1656],{},[38,78102,78103],{},"(a)",[883,78105,78107],{"className":78106},[886],[888,78108,78109],{"xmlns":890},[892,78110,78111,78151],{},[895,78112,78113,78115,78117,78119,78121,78123,78125,78127,78129,78131,78133,78135,78137,78139,78141,78143,78145,78147,78149],{},[898,78114,11183],{},[1677,78116,1679],{},[1810,78118,1812],{},[1677,78120,1967],{"separator":1966},[1810,78122,1909],{},[1677,78124,1967],{"separator":1966},[1810,78126,6973],{},[1677,78128,1967],{"separator":1966},[1810,78130,2544],{},[1677,78132,1967],{"separator":1966},[1810,78134,24337],{},[1677,78136,1967],{"separator":1966},[1810,78138,3388],{},[1677,78140,1967],{"separator":1966},[1810,78142,10423],{},[1677,78144,1967],{"separator":1966},[1810,78146,39737],{},[1677,78148,1967],{"separator":1966},[1810,78150,6392],{},[902,78152,78153],{"encoding":904},"L = 2, 5, 8, 10, 14, 18, 20, 21, 25"," určíme ",[883,78156,78158],{"className":78157},[886],[888,78159,78160],{"xmlns":890},[892,78161,78162,78172],{},[895,78163,78164,78166],{},[898,78165,2499],{},[1953,78167,78168,78170],{},[898,78169,5325],{},[898,78171,11183],{},[902,78173,11433],{"encoding":904},[724,78175,78176,78177,36359],{},"Podle (5.2): ",[883,78178,78180],{"className":78179},[886],[888,78181,78182],{"xmlns":890},[892,78183,78184,78240],{},[895,78185,78186,78188,78194,78196,78202,78204,78206,78208,78210,78212,78214,78216,78218,78224,78226,78228,78230,78232,78234,78236,78238],{},[898,78187,2499],{},[1953,78189,78190,78192],{},[898,78191,5325],{},[898,78193,11183],{},[1677,78195,1679],{},[1805,78197,78198,78200],{},[898,78199,2470],{},[1677,78201,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,78203,1686],{"stretchy":1685},[898,78205,11183],{},[1677,78207,1692],{"stretchy":1685},[1677,78209,1679],{},[1810,78211,3190],{},[898,78213,11183],{},[1677,78215,1906],{},[1810,78217,20712],{},[1805,78219,78220,78222],{},[898,78221,11183],{},[1810,78223,1812],{},[1677,78225,1679],{},[898,78227,11183],{},[1677,78229,1686],{"stretchy":1685},[1810,78231,3190],{},[1677,78233,1906],{},[1810,78235,20712],{},[898,78237,11183],{},[1677,78239,1692],{"stretchy":1685},[902,78241,78242],{"encoding":904},"MP_L = Q'(L) = 12L - 0{,}6L^2 = L(12 - 0{,}6L)",[16,78244,78245,78282],{},[19,78246,78247],{},[22,78248,78249,78264,78266,78268,78270,78272,78274,78276,78278,78280],{},[25,78250,78251],{},[883,78252,78254],{"className":78253},[886],[888,78255,78256],{"xmlns":890},[892,78257,78258,78262],{},[895,78259,78260],{},[898,78261,11183],{},[902,78263,11183],{"encoding":904},[25,78265,1812],{},[25,78267,1909],{},[25,78269,6973],{},[25,78271,2544],{},[25,78273,24337],{},[25,78275,3388],{},[25,78277,10423],{},[25,78279,39737],{},[25,78281,6392],{},[30,78283,78284],{},[22,78285,78286,78307,78310,78313,78316,78318,78321,78323,78325,78344],{},[35,78287,78288],{},[883,78289,78291],{"className":78290},[886],[888,78292,78293],{"xmlns":890},[892,78294,78295,78305],{},[895,78296,78297,78299],{},[898,78298,2499],{},[1953,78300,78301,78303],{},[898,78302,5325],{},[898,78304,11183],{},[902,78306,11433],{"encoding":904},[35,78308,78309],{},"21,6",[35,78311,78312],{},"45",[35,78314,78315],{},"57,6",[35,78317,2807],{},[35,78319,78320],{},"50,4",[35,78322,78309],{},[35,78324,2008],{},[35,78326,78327],{},[883,78328,78330],{"className":78329},[886],[888,78331,78332],{"xmlns":890},[892,78333,78334,78341],{},[895,78335,78336,78338],{},[1677,78337,1906],{},[1810,78339,78340],{},"12,6",[902,78342,78343],{"encoding":904},"-12{,}6",[35,78345,78346],{},[883,78347,78349],{"className":78348},[886],[888,78350,78351],{"xmlns":890},[892,78352,78353,78359],{},[895,78354,78355,78357],{},[1677,78356,1906],{},[1810,78358,46843],{},[902,78360,78361],{"encoding":904},"-75",[724,78363,78364,78383,78384,78402,78403,78420,78421,78439,78440,78464,78465,78483],{},[883,78365,78367],{"className":78366},[886],[888,78368,78369],{"xmlns":890},[892,78370,78371,78381],{},[895,78372,78373,78375],{},[898,78374,2499],{},[1953,78376,78377,78379],{},[898,78378,5325],{},[898,78380,11183],{},[902,78382,11433],{"encoding":904}," nabývá maxima pro ",[883,78385,78387],{"className":78386},[886],[888,78388,78389],{"xmlns":890},[892,78390,78391,78399],{},[895,78392,78393,78395,78397],{},[898,78394,11183],{},[1677,78396,1679],{},[1810,78398,2544],{},[902,78400,78401],{"encoding":904},"L = 10"," (60 jednotek\u002Fprac.). Od ",[883,78404,78406],{"className":78405},[886],[888,78407,78408],{"xmlns":890},[892,78409,78410,78418],{},[895,78411,78412,78414,78416],{},[898,78413,11183],{},[1677,78415,1679],{},[1810,78417,2544],{},[902,78419,78401],{"encoding":904}," přírůstky klesají, v ",[883,78422,78424],{"className":78423},[886],[888,78425,78426],{"xmlns":890},[892,78427,78428,78436],{},[895,78429,78430,78432,78434],{},[898,78431,11183],{},[1677,78433,1679],{},[1810,78435,10423],{},[902,78437,78438],{"encoding":904},"L = 20"," produkce přestává růst (maximum ",[883,78441,78443],{"className":78442},[886],[888,78444,78445],{"xmlns":890},[892,78446,78447,78461],{},[895,78448,78449,78451,78453,78455,78457,78459],{},[898,78450,2470],{},[1677,78452,1686],{"stretchy":1685},[1810,78454,10423],{},[1677,78456,1692],{"stretchy":1685},[1677,78458,1679],{},[1810,78460,25249],{},[902,78462,78463],{"encoding":904},"Q(20) = 800","), od ",[883,78466,78468],{"className":78467},[886],[888,78469,78470],{"xmlns":890},[892,78471,78472,78480],{},[895,78473,78474,78476,78478],{},[898,78475,11183],{},[1677,78477,3089],{},[1810,78479,10423],{},[902,78481,78482],{"encoding":904},"L > 20"," produkce klesá (fyzické přeplnění pracoviště při neměnném kapitálu).",[724,78485,78486],{},[614,78487,78488,78489,78529,78530,2305,78548,1656],{},"Obrázek 5.1 — graf produkce ",[883,78490,78492],{"className":78491},[886],[888,78493,78494],{"xmlns":890},[892,78495,78496,78526],{},[895,78497,78498,78500,78502,78504,78506,78508,78510,78516,78518,78520],{},[898,78499,2470],{},[1677,78501,1686],{"stretchy":1685},[898,78503,11183],{},[1677,78505,1692],{"stretchy":1685},[1677,78507,1679],{},[1810,78509,1916],{},[1805,78511,78512,78514],{},[898,78513,11183],{},[1810,78515,1812],{},[1677,78517,1906],{},[1810,78519,2520],{},[1805,78521,78522,78524],{},[898,78523,11183],{},[1810,78525,1854],{},[902,78527,78528],{"encoding":904},"Q(L) = 6L^2 - 0{,}2L^3"," s maximem ",[883,78531,78533],{"className":78532},[886],[888,78534,78535],{"xmlns":890},[892,78536,78537,78545],{},[895,78538,78539,78541,78543],{},[898,78540,2470],{},[1677,78542,1679],{},[1810,78544,25249],{},[902,78546,78547],{"encoding":904},"Q = 800",[883,78549,78551],{"className":78550},[886],[888,78552,78553],{"xmlns":890},[892,78554,78555,78563],{},[895,78556,78557,78559,78561],{},[898,78558,11183],{},[1677,78560,1679],{},[1810,78562,10423],{},[902,78564,78438],{"encoding":904},[724,78566,78567,78570],{},[38,78568,78569],{},"(b)"," Přibližná změna produkce při růstu pracovníků z 6 na 9.",[724,78572,78573,78574,1343,78592,2385],{},"Podle (5.3) s ",[883,78575,78577],{"className":78576},[886],[888,78578,78579],{"xmlns":890},[892,78580,78581,78589],{},[895,78582,78583,78585,78587],{},[898,78584,11183],{},[1677,78586,1679],{},[1810,78588,1916],{},[902,78590,78591],{"encoding":904},"L = 6",[883,78593,78595],{"className":78594},[886],[888,78596,78597],{"xmlns":890},[892,78598,78599,78609],{},[895,78600,78601,78603,78605,78607],{},[898,78602,1875],{},[898,78604,11183],{},[1677,78606,1679],{},[1810,78608,1854],{},[902,78610,78611],{"encoding":904},"dL = 3",[883,78613,78615],{"className":78614},[886],[888,78616,78617],{"xmlns":890,"display":29457},[892,78618,78619,78682],{},[895,78620,78621,78623,78625,78627,78629,78635,78637,78639,78641,78643,78645,78647,78649,78651,78653,78655,78657,78659,78661,78663,78665,78667,78669,78671,78673,78675,78677,78679],{},[898,78622,1875],{},[898,78624,2470],{},[1677,78626,1679],{},[898,78628,2499],{},[1953,78630,78631,78633],{},[898,78632,5325],{},[898,78634,11183],{},[1677,78636,1686],{"stretchy":1685},[1810,78638,1916],{},[1677,78640,1692],{"stretchy":1685},[1677,78642,2858],{},[1810,78644,1854],{},[1677,78646,1679],{},[1677,78648,1686],{"stretchy":1685},[1810,78650,3190],{},[1677,78652,2858],{},[1810,78654,1916],{},[1677,78656,1906],{},[1810,78658,20712],{},[1677,78660,2858],{},[1810,78662,6953],{},[1677,78664,1692],{"stretchy":1685},[1677,78666,2858],{},[1810,78668,1854],{},[1677,78670,1679],{},[1810,78672,78320],{},[1677,78674,2858],{},[1810,78676,1854],{},[1677,78678,1679],{},[1810,78680,78681],{},"151,2.",[902,78683,78684],{"encoding":904},"dQ = MP_L(6)\\cdot 3 = (12\\cdot 6 - 0{,}6\\cdot 36)\\cdot 3 = 50{,}4 \\cdot 3 = 151{,}2.",[724,78686,78687,78688,59143,78713,78727,78728,1656],{},"Produkce vzroste z ",[883,78689,78691],{"className":78690},[886],[888,78692,78693],{"xmlns":890},[892,78694,78695,78710],{},[895,78696,78697,78699,78701,78703,78705,78707],{},[898,78698,2470],{},[1677,78700,1686],{"stretchy":1685},[1810,78702,1916],{},[1677,78704,1692],{"stretchy":1685},[1677,78706,1679],{},[1810,78708,78709],{},"172,8",[902,78711,78712],{"encoding":904},"Q(6) = 172{,}8",[883,78714,78716],{"className":78715},[886],[888,78717,78718],{"xmlns":890},[892,78719,78720,78725],{},[895,78721,78722],{},[1810,78723,78724],{},"324",[902,78726,78724],{"encoding":904},". Skutečná hodnota: ",[883,78729,78731],{"className":78730},[886],[888,78732,78733],{"xmlns":890},[892,78734,78735,78775],{},[895,78736,78737,78739,78741,78743,78745,78747,78749,78751,78753,78755,78757,78759,78761,78763,78766,78768,78770,78772],{},[898,78738,2570],{"mathvariant":2057},[898,78740,2470],{},[1677,78742,1679],{},[898,78744,2470],{},[1677,78746,1686],{"stretchy":1685},[1810,78748,5387],{},[1677,78750,1692],{"stretchy":1685},[1677,78752,1906],{},[898,78754,2470],{},[1677,78756,1686],{"stretchy":1685},[1810,78758,1916],{},[1677,78760,1692],{"stretchy":1685},[1677,78762,1679],{},[1810,78764,78765],{},"340,2",[1677,78767,1906],{},[1810,78769,78709],{},[1677,78771,1679],{},[1810,78773,78774],{},"167,4",[902,78776,78777],{"encoding":904},"\\Delta Q = Q(9) - Q(6) = 340{,}2 - 172{,}8 = 167{,}4",[198,78779,78781],{"id":78780},"příklad-52","Příklad 5.2",[724,78783,78784,78785,1656],{},"Ověříme princip (5.5) pro ",[883,78786,78788],{"className":78787},[886],[888,78789,78790],{"xmlns":890},[892,78791,78792,78816],{},[895,78793,78794,78796,78798,78800,78806,78808,78810],{},[898,78795,2470],{},[1677,78797,1679],{},[1810,78799,1916],{},[1805,78801,78802,78804],{},[898,78803,11183],{},[1810,78805,1812],{},[1677,78807,1906],{},[1810,78809,2520],{},[1805,78811,78812,78814],{},[898,78813,11183],{},[1810,78815,1854],{},[902,78817,78098],{"encoding":904},[883,78819,78821],{"className":78820},[886],[888,78822,78823],{"xmlns":890,"display":29457},[892,78824,78825,78903],{},[895,78826,78827,78829,78835,78837,78843,78845,78847,78849,78851,78853,78859,78861,78863,78865,78873,78875,78877,78879,78881,78883,78885,78887,78889,78891,78893,78899,78901],{},[898,78828,5643],{},[1953,78830,78831,78833],{},[898,78832,5325],{},[898,78834,11183],{},[1677,78836,1679],{},[2010,78838,78839,78841],{},[898,78840,2470],{},[898,78842,11183],{},[1677,78844,1679],{},[1810,78846,1916],{},[898,78848,11183],{},[1677,78850,1906],{},[1810,78852,2520],{},[1805,78854,78855,78857],{},[898,78856,11183],{},[1810,78858,1812],{},[1677,78860,1967],{"separator":1966},[7266,78862],{"width":16674},[898,78864,5643],{},[10554,78866,78867,78869,78871],{},[898,78868,5325],{},[898,78870,11183],{},[1677,78872,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,78874,1679],{},[1810,78876,1916],{},[1677,78878,1906],{},[1810,78880,20662],{},[898,78882,11183],{},[1677,78884,1679],{},[1810,78886,2008],{},[1969,78888,5372],{},[1677,78890,5375],{},[1969,78892,5372],{},[1953,78894,78895,78897],{},[898,78896,11183],{},[1810,78898,2008],{},[1677,78900,1679],{},[1810,78902,69674],{},[902,78904,78905],{"encoding":904},"AP_L = \\frac{Q}{L} = 6L - 0{,}2L^2, \\quad AP_L' = 6 - 0{,}4L = 0 \\;\\Rightarrow\\; L_0 = 15.",[724,78907,78908,78944,78945,78963,78964,1656],{},[883,78909,78911],{"className":78910},[886],[888,78912,78913],{"xmlns":890},[892,78914,78915,78941],{},[895,78916,78917,78919,78931,78933,78935,78937,78939],{},[898,78918,5643],{},[10554,78920,78921,78923,78925],{},[898,78922,5325],{},[898,78924,11183],{},[895,78926,78927,78929],{},[1677,78928,2059],{"mathvariant":2057},[1677,78930,2059],{"mathvariant":2057},[1677,78932,1679],{},[1677,78934,1906],{},[1810,78936,20662],{},[1677,78938,3128],{},[1810,78940,2008],{},[902,78942,78943],{"encoding":904},"AP_L'' = -0{,}4 \u003C 0",", takže v ",[883,78946,78948],{"className":78947},[886],[888,78949,78950],{"xmlns":890},[892,78951,78952,78960],{},[895,78953,78954,78956,78958],{},[898,78955,11183],{},[1677,78957,1679],{},[1810,78959,37635],{},[902,78961,78962],{"encoding":904},"L = 15"," je maximum, ",[883,78965,78967],{"className":78966},[886],[888,78968,78969],{"xmlns":890},[892,78970,78971,79017],{},[895,78972,78973,78975,78981,78983,78985,78987,78989,78991,78993,78995,78997,78999,79001,79004,79006,79009,79011,79013,79015],{},[898,78974,5643],{},[1953,78976,78977,78979],{},[898,78978,5325],{},[898,78980,11183],{},[1677,78982,1686],{"stretchy":1685},[1810,78984,37635],{},[1677,78986,1692],{"stretchy":1685},[1677,78988,1679],{},[1810,78990,1916],{},[1677,78992,2858],{},[1810,78994,37635],{},[1677,78996,1906],{},[1810,78998,2520],{},[1677,79000,2858],{},[1810,79002,79003],{},"225",[1677,79005,1679],{},[1810,79007,79008],{},"90",[1677,79010,1906],{},[1810,79012,78312],{},[1677,79014,1679],{},[1810,79016,78312],{},[902,79018,79019],{"encoding":904},"AP_L(15) = 6\\cdot 15 - 0{,}2\\cdot 225 = 90 - 45 = 45",[724,79021,79022,43271,79078,79124],{},[883,79023,79025],{"className":79024},[886],[888,79026,79027],{"xmlns":890},[892,79028,79029,79075],{},[895,79030,79031,79033,79039,79041,79043,79045,79047,79049,79051,79053,79055,79057,79059,79061,79063,79066,79068,79071,79073],{},[898,79032,2499],{},[1953,79034,79035,79037],{},[898,79036,5325],{},[898,79038,11183],{},[1677,79040,1686],{"stretchy":1685},[1810,79042,37635],{},[1677,79044,1692],{"stretchy":1685},[1677,79046,1679],{},[1810,79048,3190],{},[1677,79050,2858],{},[1810,79052,37635],{},[1677,79054,1906],{},[1810,79056,20712],{},[1677,79058,2858],{},[1810,79060,79003],{},[1677,79062,1679],{},[1810,79064,79065],{},"180",[1677,79067,1906],{},[1810,79069,79070],{},"135",[1677,79072,1679],{},[1810,79074,78312],{},[902,79076,79077],{"encoding":904},"MP_L(15) = 12\\cdot 15 - 0{,}6\\cdot 225 = 180 - 135 = 45",[883,79079,79081],{"className":79080},[886],[888,79082,79083],{"xmlns":890},[892,79084,79085,79121],{},[895,79086,79087,79089,79095,79097,79099,79101,79103,79105,79111,79113,79115,79117,79119],{},[898,79088,2499],{},[1953,79090,79091,79093],{},[898,79092,5325],{},[898,79094,11183],{},[1677,79096,1686],{"stretchy":1685},[1810,79098,37635],{},[1677,79100,1692],{"stretchy":1685},[1677,79102,1679],{},[898,79104,5643],{},[1953,79106,79107,79109],{},[898,79108,5325],{},[898,79110,11183],{},[1677,79112,1686],{"stretchy":1685},[1810,79114,37635],{},[1677,79116,1692],{"stretchy":1685},[1677,79118,1679],{},[1810,79120,78312],{},[902,79122,79123],{"encoding":904},"MP_L(15) = AP_L(15) = 45",", jak požaduje (5.5).",[724,79126,79127,79130,79131,18967,79160,1656],{},[38,79128,79129],{},"Zkratka bez hledání extrému:"," stačí řešit ",[883,79132,79134],{"className":79133},[886],[888,79135,79136],{"xmlns":890},[892,79137,79138,79158],{},[895,79139,79140,79142,79148,79150,79152],{},[898,79141,2499],{},[1953,79143,79144,79146],{},[898,79145,5325],{},[898,79147,11183],{},[1677,79149,1679],{},[898,79151,5643],{},[1953,79153,79154,79156],{},[898,79155,5325],{},[898,79157,11183],{},[902,79159,76054],{"encoding":904},[883,79161,79163],{"className":79162},[886],[888,79164,79165],{"xmlns":890},[892,79166,79167,79207],{},[895,79168,79169,79171,79173,79175,79177,79183,79185,79187,79189,79191,79193,79199,79201,79203,79205],{},[1810,79170,3190],{},[898,79172,11183],{},[1677,79174,1906],{},[1810,79176,20712],{},[1805,79178,79179,79181],{},[898,79180,11183],{},[1810,79182,1812],{},[1677,79184,1679],{},[1810,79186,1916],{},[898,79188,11183],{},[1677,79190,1906],{},[1810,79192,2520],{},[1805,79194,79195,79197],{},[898,79196,11183],{},[1810,79198,1812],{},[1677,79200,5375],{},[898,79202,11183],{},[1677,79204,1679],{},[1810,79206,37635],{},[902,79208,79209],{"encoding":904},"12L - 0{,}6L^2 = 6L - 0{,}2L^2 \\Rightarrow L = 15",[724,79211,79212],{},[614,79213,79214,79215,79234,79235,13518,79253,79272,79273,79291,79292,79309,79310,79329,79330,79349],{},"Obrázek 5.3 — křivky ",[883,79216,79218],{"className":79217},[886],[888,79219,79220],{"xmlns":890},[892,79221,79222,79232],{},[895,79223,79224,79226],{},[898,79225,2499],{},[1953,79227,79228,79230],{},[898,79229,5325],{},[898,79231,11183],{},[902,79233,11433],{"encoding":904}," (max 60 při ",[883,79236,79238],{"className":79237},[886],[888,79239,79240],{"xmlns":890},[892,79241,79242,79250],{},[895,79243,79244,79246,79248],{},[898,79245,11183],{},[1677,79247,1679],{},[1810,79249,2544],{},[902,79251,79252],{"encoding":904},"L=10",[883,79254,79256],{"className":79255},[886],[888,79257,79258],{"xmlns":890},[892,79259,79260,79270],{},[895,79261,79262,79264],{},[898,79263,5643],{},[1953,79265,79266,79268],{},[898,79267,5325],{},[898,79269,11183],{},[902,79271,76024],{"encoding":904}," (max 45 při ",[883,79274,79276],{"className":79275},[886],[888,79277,79278],{"xmlns":890},[892,79279,79280,79288],{},[895,79281,79282,79284,79286],{},[898,79283,11183],{},[1677,79285,1679],{},[1810,79287,37635],{},[902,79289,79290],{"encoding":904},"L=15","), průsečík v ",[883,79293,79295],{"className":79294},[886],[888,79296,79297],{"xmlns":890},[892,79298,79299,79307],{},[895,79300,79301,79303,79305],{},[898,79302,11183],{},[1677,79304,1679],{},[1810,79306,37635],{},[902,79308,78962],{"encoding":904},". Nalevo od 15 leží ",[883,79311,79313],{"className":79312},[886],[888,79314,79315],{"xmlns":890},[892,79316,79317,79327],{},[895,79318,79319,79321],{},[898,79320,2499],{},[1953,79322,79323,79325],{},[898,79324,5325],{},[898,79326,11183],{},[902,79328,11433],{"encoding":904}," nad ",[883,79331,79333],{"className":79332},[886],[888,79334,79335],{"xmlns":890},[892,79336,79337,79347],{},[895,79338,79339,79341],{},[898,79340,5643],{},[1953,79342,79343,79345],{},[898,79344,5325],{},[898,79346,11183],{},[902,79348,76024],{"encoding":904},", napravo pod ní.",[115,79351,79353],{"id":79352},"dvoufaktorový-model-produkce","Dvoufaktorový model produkce",[724,79355,79356,79357,2366,79370,1884,79373,7578,79386,1884,79389,2385],{},"V dvoufaktorovém modelu závisí produkce ",[883,79358,79360],{"className":79359},[886],[888,79361,79362],{"xmlns":890},[892,79363,79364,79368],{},[895,79365,79366],{},[898,79367,2470],{},[902,79369,2470],{"encoding":904},[38,79371,79372],{},"práci",[883,79374,79376],{"className":79375},[886],[888,79377,79378],{"xmlns":890},[892,79379,79380,79384],{},[895,79381,79382],{},[898,79383,11183],{},[902,79385,11183],{"encoding":904},[38,79387,79388],{},"kapitálu",[883,79390,79392],{"className":79391},[886],[888,79393,79394],{"xmlns":890},[892,79395,79396,79400],{},[895,79397,79398],{},[898,79399,11188],{},[902,79401,11188],{"encoding":904},[883,79403,79405],{"className":79404},[886],[888,79406,79407],{"xmlns":890,"display":29457},[892,79408,79409,79444],{},[22145,79410,79411],{"width":29462},[22150,79412,79413,79415,79437,79439],{},[22153,79414],{"width":29467},[22153,79416,79417],{},[895,79418,79419,79421,79423,79425,79427,79429,79431,79433,79435],{},[898,79420,2470],{},[1677,79422,1679],{},[898,79424,2470],{},[1677,79426,1686],{"stretchy":1685},[898,79428,11183],{},[1677,79430,1967],{"separator":1966},[898,79432,11188],{},[1677,79434,1692],{"stretchy":1685},[898,79436,1656],{"mathvariant":2057},[22153,79438],{"width":29467},[22153,79440,79441],{},[1969,79442,79443],{},"(5.6)",[902,79445,79446],{"encoding":904},"Q = Q(L, K). \\tag{5.6}",[724,79448,79449,79450,79452],{},"Půda je nadále standardní exogenní proměnnou. Vztah (5.6) se nazývá ",[38,79451,76391],{}," (v širším smyslu oproti jednofaktorovému modelu).",[115,79454,79456],{"id":79455},"cobb-douglasova-produkční-funkce","Cobb-Douglasova produkční funkce",[724,79458,79459],{},"Široce používané produkční funkce mají tvar",[883,79461,79463],{"className":79462},[886],[888,79464,79465],{"xmlns":890,"display":29457},[892,79466,79467,79508],{},[22145,79468,79469],{"width":29462},[22150,79470,79471,79473,79501,79503],{},[22153,79472],{"width":29467},[22153,79474,79475],{},[895,79476,79477,79479,79481,79483,79485,79491,79493,79499],{},[898,79478,2470],{},[1677,79480,1679],{},[898,79482,5643],{},[1969,79484,2668],{},[1805,79486,79487,79489],{},[898,79488,11183],{},[898,79490,207],{},[1969,79492,2668],{},[1805,79494,79495,79497],{},[898,79496,11188],{},[898,79498,1779],{},[1677,79500,1967],{"separator":1966},[22153,79502],{"width":29467},[22153,79504,79505],{},[1969,79506,79507],{},"(5.7)",[902,79509,79510],{"encoding":904},"Q = A\\,L^a\\,K^b, \\tag{5.7}",[724,79512,5698,79513,79535,79536,79538,79539,1656],{},[883,79514,79516],{"className":79515},[886],[888,79517,79518],{"xmlns":890},[892,79519,79520,79532],{},[895,79521,79522,79524,79526,79528,79530],{},[898,79523,5643],{},[1677,79525,1967],{"separator":1966},[898,79527,207],{},[1677,79529,1967],{"separator":1966},[898,79531,1779],{},[902,79533,79534],{"encoding":904},"A, a, b"," jsou kladné konstanty. Nazývají se ",[38,79537,76090],{}," (poprvé publikovány v roce 1939). V ekonomických analýzách zpravidla ",[883,79540,79542],{"className":79541},[886],[888,79543,79544],{"xmlns":890},[892,79545,79546,79558],{},[895,79547,79548,79550,79552,79554,79556],{},[898,79549,207],{},[1677,79551,1967],{"separator":1966},[898,79553,1779],{},[1677,79555,3128],{},[1810,79557,1959],{},[902,79559,79560],{"encoding":904},"a, b \u003C 1",[724,79562,79563],{},[2240,79564],{"alt":79565,"className":79566,"src":79567},"imek-vynosy-z-rozsahu-3typy",[210,2244],"\u002Fwiki-assets\u002Fimek-vynosy-z-rozsahu-3typy.jpeg",[724,79569,79570,79571,79574,79575,2366,79588,79604,79605,2366,79618,2385],{},"Reflektují ekonomickou zákonitost, že ",[38,79572,79573],{},"proporcionální změny vstupů mají odezvu v proporcionální změně výstupu",". Změní-li se práce z ",[883,79576,79578],{"className":79577},[886],[888,79579,79580],{"xmlns":890},[892,79581,79582,79586],{},[895,79583,79584],{},[898,79585,11183],{},[902,79587,11183],{"encoding":904},[883,79589,79591],{"className":79590},[886],[888,79592,79593],{"xmlns":890},[892,79594,79595,79601],{},[895,79596,79597,79599],{},[898,79598,13431],{},[898,79600,11183],{},[902,79602,79603],{"encoding":904},"rL"," a kapitál z ",[883,79606,79608],{"className":79607},[886],[888,79609,79610],{"xmlns":890},[892,79611,79612,79616],{},[895,79613,79614],{},[898,79615,11188],{},[902,79617,11188],{"encoding":904},[883,79619,79621],{"className":79620},[886],[888,79622,79623],{"xmlns":890},[892,79624,79625,79631],{},[895,79626,79627,79629],{},[898,79628,13431],{},[898,79630,11188],{},[902,79632,79633],{"encoding":904},"rK",[883,79635,79637],{"className":79636},[886],[888,79638,79639],{"xmlns":890,"display":29457},[892,79640,79641,79764],{},[22145,79642,79643],{"width":29462},[22150,79644,79645,79647,79757,79759],{},[22153,79646],{"width":29467},[22153,79648,79649],{},[895,79650,79651,79653,79655,79657,79659,79661,79663,79665,79667,79669,79671,79673,79675,79677,79683,79685,79687,79689,79695,79697,79699,79701,79713,79715,79721,79727,79729,79741,79743,79745,79747,79749,79751,79753,79755],{},[898,79652,2470],{},[1677,79654,1686],{"stretchy":1685},[898,79656,13431],{},[898,79658,11183],{},[1677,79660,1967],{"separator":1966},[898,79662,13431],{},[898,79664,11188],{},[1677,79666,1692],{"stretchy":1685},[1677,79668,1679],{},[898,79670,5643],{},[1677,79672,1686],{"stretchy":1685},[898,79674,13431],{},[898,79676,11183],{},[1805,79678,79679,79681],{},[1677,79680,1692],{"stretchy":1685},[898,79682,207],{},[1677,79684,1686],{"stretchy":1685},[898,79686,13431],{},[898,79688,11188],{},[1805,79690,79691,79693],{},[1677,79692,1692],{"stretchy":1685},[898,79694,1779],{},[1677,79696,1679],{},[898,79698,5643],{},[1969,79700,2668],{},[1805,79702,79703,79705],{},[898,79704,13431],{},[895,79706,79707,79709,79711],{},[898,79708,207],{},[1677,79710,1776],{},[898,79712,1779],{},[1969,79714,2668],{},[1805,79716,79717,79719],{},[898,79718,11183],{},[898,79720,207],{},[1805,79722,79723,79725],{},[898,79724,11188],{},[898,79726,1779],{},[1677,79728,1679],{},[1805,79730,79731,79733],{},[898,79732,13431],{},[895,79734,79735,79737,79739],{},[898,79736,207],{},[1677,79738,1776],{},[898,79740,1779],{},[1969,79742,2668],{},[898,79744,2470],{},[1677,79746,1686],{"stretchy":1685},[898,79748,11183],{},[1677,79750,1967],{"separator":1966},[898,79752,11188],{},[1677,79754,1692],{"stretchy":1685},[898,79756,1656],{"mathvariant":2057},[22153,79758],{"width":29467},[22153,79760,79761],{},[1969,79762,79763],{},"(5.8)",[902,79765,79766],{"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}",[724,79768,79769,79770],{},"Volně: ",[38,79771,79772,79773,79786,79787,79811],{},"změní-li se vstupy ",[883,79774,79776],{"className":79775},[886],[888,79777,79778],{"xmlns":890},[892,79779,79780,79784],{},[895,79781,79782],{},[898,79783,13431],{},[902,79785,13431],{"encoding":904},"-krát, změní se výstup ",[883,79788,79790],{"className":79789},[886],[888,79791,79792],{"xmlns":890},[892,79793,79794,79808],{},[895,79795,79796],{},[1805,79797,79798,79800],{},[898,79799,13431],{},[895,79801,79802,79804,79806],{},[898,79803,207],{},[1677,79805,1776],{},[898,79807,1779],{},[902,79809,79810],{"encoding":904},"r^{a+b}","-krát.",[198,79813,79815],{"id":79814},"výnosy-z-rozsahu","Výnosy z rozsahu",[724,79817,79818,79819,79836],{},"Součet exponentů ",[883,79820,79822],{"className":79821},[886],[888,79823,79824],{"xmlns":890},[892,79825,79826,79834],{},[895,79827,79828,79830,79832],{},[898,79829,207],{},[1677,79831,1776],{},[898,79833,1779],{},[902,79835,76215],{"encoding":904}," určuje typ výnosů z rozsahu:",[16,79838,79839,79868],{},[19,79840,79841],{},[22,79842,79843,79846,79849,79866],{},[25,79844,79845],{},"Typ",[25,79847,79848],{},"Podmínka",[25,79850,79851,79852,79865],{},"Chování produkce při ",[883,79853,79855],{"className":79854},[886],[888,79856,79857],{"xmlns":890},[892,79858,79859,79863],{},[895,79860,79861],{},[898,79862,13431],{},[902,79864,13431],{"encoding":904},"-násobném zvýšení vstupů",[25,79867,2751],{},[30,79869,79870,79981,80096],{},[22,79871,79872,79880,79904,79937],{},[35,79873,76928,79874,11413,79877,1692],{},[38,79875,79876],{},"Konstantní",[614,79878,79879],{},"constant returns",[35,79881,79882],{},[883,79883,79885],{"className":79884},[886],[888,79886,79887],{"xmlns":890},[892,79888,79889,79901],{},[895,79890,79891,79893,79895,79897,79899],{},[898,79892,207],{},[1677,79894,1776],{},[898,79896,1779],{},[1677,79898,1679],{},[1810,79900,1959],{},[902,79902,79903],{"encoding":904},"a+b = 1",[35,79905,79906,79919,79920,1884,79923,79936],{},[883,79907,79909],{"className":79908},[886],[888,79910,79911],{"xmlns":890},[892,79912,79913,79917],{},[895,79914,79915],{},[898,79916,2470],{},[902,79918,2470],{"encoding":904}," vzroste ",[38,79921,79922],{},"přesně",[883,79924,79926],{"className":79925},[886],[888,79927,79928],{"xmlns":890},[892,79929,79930,79934],{},[895,79931,79932],{},[898,79933,13431],{},[902,79935,13431],{"encoding":904},"-krát",[35,79938,79939],{},[883,79940,79942],{"className":79941},[886],[888,79943,79944],{"xmlns":890},[892,79945,79946,79978],{},[895,79947,79948,79950,79952,79954,79966],{},[898,79949,2470],{},[1677,79951,1679],{},[1810,79953,1812],{},[1805,79955,79956,79958],{},[898,79957,11183],{},[895,79959,79960,79962,79964],{},[1810,79961,1959],{},[898,79963,6062],{"mathvariant":2057},[1810,79965,2032],{},[1805,79967,79968,79970],{},[898,79969,11188],{},[895,79971,79972,79974,79976],{},[1810,79973,1854],{},[898,79975,6062],{"mathvariant":2057},[1810,79977,2032],{},[902,79979,79980],{"encoding":904},"Q = 2L^{1\u002F4}K^{3\u002F4}",[22,79982,79983,79992,80016,80046],{},[35,79984,79985,79986,11413,79989,1692],{},"2° ",[38,79987,79988],{},"Rostoucí",[614,79990,79991],{},"increasing returns",[35,79993,79994],{},[883,79995,79997],{"className":79996},[886],[888,79998,79999],{"xmlns":890},[892,80000,80001,80013],{},[895,80002,80003,80005,80007,80009,80011],{},[898,80004,207],{},[1677,80006,1776],{},[898,80008,1779],{},[1677,80010,3089],{},[1810,80012,1959],{},[902,80014,80015],{"encoding":904},"a+b > 1",[35,80017,80018,79919,80031,52622,80033,79936],{},[883,80019,80021],{"className":80020},[886],[888,80022,80023],{"xmlns":890},[892,80024,80025,80029],{},[895,80026,80027],{},[898,80028,2470],{},[902,80030,2470],{"encoding":904},[38,80032,26661],{},[883,80034,80036],{"className":80035},[886],[888,80037,80038],{"xmlns":890},[892,80039,80040,80044],{},[895,80041,80042],{},[898,80043,13431],{},[902,80045,13431],{"encoding":904},[35,80047,80048,11413,80074,1692],{},[883,80049,80051],{"className":80050},[886],[888,80052,80053],{"xmlns":890},[892,80054,80055,80071],{},[895,80056,80057,80059,80061,80063,80065],{},[898,80058,2470],{},[1677,80060,1679],{},[1810,80062,25592],{},[898,80064,11183],{},[1805,80066,80067,80069],{},[898,80068,11188],{},[1810,80070,1812],{},[902,80072,80073],{"encoding":904},"Q = 7LK^2",[883,80075,80077],{"className":80076},[886],[888,80078,80079],{"xmlns":890},[892,80080,80081,80093],{},[895,80082,80083,80085,80087,80089,80091],{},[898,80084,207],{},[1677,80086,1776],{},[898,80088,1779],{},[1677,80090,1679],{},[1810,80092,1854],{},[902,80094,80095],{"encoding":904},"a+b = 3",[22,80097,80098,80107,80131,80162],{},[35,80099,80100,80101,11413,80104,1692],{},"3° ",[38,80102,80103],{},"Klesající",[614,80105,80106],{},"decreasing returns",[35,80108,80109],{},[883,80110,80112],{"className":80111},[886],[888,80113,80114],{"xmlns":890},[892,80115,80116,80128],{},[895,80117,80118,80120,80122,80124,80126],{},[898,80119,207],{},[1677,80121,1776],{},[898,80123,1779],{},[1677,80125,3128],{},[1810,80127,1959],{},[902,80129,80130],{"encoding":904},"a+b \u003C 1",[35,80132,80133,79919,80146,52622,80149,79936],{},[883,80134,80136],{"className":80135},[886],[888,80137,80138],{"xmlns":890},[892,80139,80140,80144],{},[895,80141,80142],{},[898,80143,2470],{},[902,80145,2470],{"encoding":904},[38,80147,80148],{},"méně",[883,80150,80152],{"className":80151},[886],[888,80153,80154],{"xmlns":890},[892,80155,80156,80160],{},[895,80157,80158],{},[898,80159,13431],{},[902,80161,13431],{"encoding":904},[35,80163,80164,11413,80194,1692],{},[883,80165,80167],{"className":80166},[886],[888,80168,80169],{"xmlns":890},[892,80170,80171,80191],{},[895,80172,80173,80175,80177,80179,80185],{},[898,80174,2470],{},[1677,80176,1679],{},[1810,80178,2544],{},[1805,80180,80181,80183],{},[898,80182,11183],{},[1810,80184,69602],{},[1805,80186,80187,80189],{},[898,80188,11188],{},[1810,80190,6397],{},[902,80192,80193],{"encoding":904},"Q = 10L^{0{,}3}K^{0{,}5}",[883,80195,80197],{"className":80196},[886],[888,80198,80199],{"xmlns":890},[892,80200,80201,80213],{},[895,80202,80203,80205,80207,80209,80211],{},[898,80204,207],{},[1677,80206,1776],{},[898,80208,1779],{},[1677,80210,1679],{},[1810,80212,15979],{},[902,80214,80215],{"encoding":904},"a+b = 0{,}8",[5254,80217,80218],{},[724,80219,80220,80222,80223,80240,80241,80244,80245,1884,80248,80284,80285,80307,80308,1656],{},[883,80221,5800],{}," Pozor\nSoučet ",[883,80224,80226],{"className":80225},[886],[888,80227,80228],{"xmlns":890},[892,80229,80230,80238],{},[895,80231,80232,80234,80236],{},[898,80233,207],{},[1677,80235,1776],{},[898,80237,1779],{},[902,80239,76215],{"encoding":904}," neudává velikost produkce, ale ",[38,80242,80243],{},"elasticitu vůči škálování vstupů",". Speciálně ",[38,80246,80247],{},"ryzí Cobb-Douglas",[883,80249,80251],{"className":80250},[886],[888,80252,80253],{"xmlns":890},[892,80254,80255,80281],{},[895,80256,80257,80259,80261,80263,80269],{},[898,80258,2470],{},[1677,80260,1679],{},[898,80262,5643],{},[1805,80264,80265,80267],{},[898,80266,11183],{},[898,80268,207],{},[1805,80270,80271,80273],{},[898,80272,11188],{},[895,80274,80275,80277,80279],{},[1810,80276,1959],{},[1677,80278,1906],{},[898,80280,207],{},[902,80282,80283],{"encoding":904},"Q = AL^a K^{1-a}"," má ",[883,80286,80288],{"className":80287},[886],[888,80289,80290],{"xmlns":890},[892,80291,80292,80304],{},[895,80293,80294,80296,80298,80300,80302],{},[898,80295,1779],{},[1677,80297,1679],{},[1810,80299,1959],{},[1677,80301,1906],{},[898,80303,207],{},[902,80305,80306],{"encoding":904},"b = 1-a",", tedy vždy ",[38,80309,80310],{},"konstantní výnosy z rozsahu",[198,80312,80314,80315],{"id":80313},"parametr-efektivity-aa","Parametr efektivity ",[883,80316,80318],{"className":80317},[886],[888,80319,80320],{"xmlns":890},[892,80321,80322,80326],{},[895,80323,80324],{},[898,80325,5643],{},[902,80327,5643],{"encoding":904},[724,80329,80330,80331,80344,80345,80358,80359,80377,80378,80381],{},"Konstanta ",[883,80332,80334],{"className":80333},[886],[888,80335,80336],{"xmlns":890},[892,80337,80338,80342],{},[895,80339,80340],{},[898,80341,5643],{},[902,80343,5643],{"encoding":904}," v (5.7) proporcionálně ovlivňuje úroveň produkce ",[883,80346,80348],{"className":80347},[886],[888,80349,80350],{"xmlns":890},[892,80351,80352,80356],{},[895,80353,80354],{},[898,80355,2470],{},[902,80357,2470],{"encoding":904}," při pevně zadaných ",[883,80360,80362],{"className":80361},[886],[888,80363,80364],{"xmlns":890},[892,80365,80366,80374],{},[895,80367,80368,80370,80372],{},[898,80369,11183],{},[1677,80371,1967],{"separator":1966},[898,80373,11188],{},[902,80375,80376],{"encoding":904},"L, K",", a lze ji proto chápat jako ",[38,80379,80380],{},"parametr efektivity"," — indikátor stavu technologie.",[198,80383,80385],{"id":80384},"příklad-53","Příklad 5.3",[724,80387,80388,80389,80284,80431,80433,80434,1656],{},"Produkční funkce ",[883,80390,80392],{"className":80391},[886],[888,80393,80394],{"xmlns":890},[892,80395,80396,80428],{},[895,80397,80398,80400,80402,80404,80416],{},[898,80399,2470],{},[1677,80401,1679],{},[1810,80403,1812],{},[1805,80405,80406,80408],{},[898,80407,11183],{},[895,80409,80410,80412,80414],{},[1810,80411,1959],{},[898,80413,6062],{"mathvariant":2057},[1810,80415,2032],{},[1805,80417,80418,80420],{},[898,80419,11188],{},[895,80421,80422,80424,80426],{},[1810,80423,1854],{},[898,80425,6062],{"mathvariant":2057},[1810,80427,2032],{},[902,80429,80430],{"encoding":904},"Q = 2L^{1\u002F4} K^{3\u002F4}",[38,80432,26004],{}," výnosy z rozsahu, neboť ",[883,80435,80437],{"className":80436},[886],[888,80438,80439],{"xmlns":890},[892,80440,80441,80465],{},[895,80442,80443,80451,80453,80461,80463],{},[2006,80444,80445],{"scriptlevel":2008,"displaystyle":1685},[2010,80446,80447,80449],{},[1810,80448,1959],{},[1810,80450,2032],{},[1677,80452,1776],{},[2006,80454,80455],{"scriptlevel":2008,"displaystyle":1685},[2010,80456,80457,80459],{},[1810,80458,1854],{},[1810,80460,2032],{},[1677,80462,1679],{},[1810,80464,1959],{},[902,80466,80467],{"encoding":904},"\\tfrac{1}{4} + \\tfrac{3}{4} = 1",[724,80469,80470,80471,7578,80484,80497,80498,1884,80511,80551],{},"Změní-li se ",[883,80472,80474],{"className":80473},[886],[888,80475,80476],{"xmlns":890},[892,80477,80478,80482],{},[895,80479,80480],{},[898,80481,11183],{},[902,80483,11183],{"encoding":904},[883,80485,80487],{"className":80486},[886],[888,80488,80489],{"xmlns":890},[892,80490,80491,80495],{},[895,80492,80493],{},[898,80494,11188],{},[902,80496,11188],{"encoding":904}," čtyřnásobně, změní se ",[883,80499,80501],{"className":80500},[886],[888,80502,80503],{"xmlns":890},[892,80504,80505,80509],{},[895,80506,80507],{},[898,80508,2470],{},[902,80510,2470],{"encoding":904},[883,80512,80514],{"className":80513},[886],[888,80515,80516],{"xmlns":890},[892,80517,80518,80548],{},[895,80519,80520,80540,80542],{},[1805,80521,80522,80524],{},[1810,80523,2032],{},[895,80525,80526,80528,80530,80532,80534,80536,80538],{},[1810,80527,1959],{},[898,80529,6062],{"mathvariant":2057},[1810,80531,2032],{},[1677,80533,1776],{},[1810,80535,1854],{},[898,80537,6062],{"mathvariant":2057},[1810,80539,2032],{},[1677,80541,1679],{},[1805,80543,80544,80546],{},[1810,80545,2032],{},[1810,80547,1959],{},[902,80549,80550],{"encoding":904},"4^{1\u002F4 + 3\u002F4} = 4^1","-krát:",[883,80553,80555],{"className":80554},[886],[888,80556,80557],{"xmlns":890,"display":29457},[892,80558,80559,80719],{},[895,80560,80561,80563,80565,80567,80569,80571,80573,80575,80577,80579,80581,80583,80585,80587,80599,80601,80603,80605,80617,80619,80621,80623,80643,80655,80667,80669,80671,80673,80675,80687,80699,80701,80703,80705,80707,80709,80711,80713,80715,80717],{},[898,80562,2470],{},[1677,80564,1686],{"stretchy":1685},[1810,80566,2032],{},[898,80568,11183],{},[1677,80570,1967],{"separator":1966},[1810,80572,2032],{},[898,80574,11188],{},[1677,80576,1692],{"stretchy":1685},[1677,80578,1679],{},[1810,80580,1812],{},[1677,80582,1686],{"stretchy":1685},[1810,80584,2032],{},[898,80586,11183],{},[1805,80588,80589,80591],{},[1677,80590,1692],{"stretchy":1685},[895,80592,80593,80595,80597],{},[1810,80594,1959],{},[898,80596,6062],{"mathvariant":2057},[1810,80598,2032],{},[1677,80600,1686],{"stretchy":1685},[1810,80602,2032],{},[898,80604,11188],{},[1805,80606,80607,80609],{},[1677,80608,1692],{"stretchy":1685},[895,80610,80611,80613,80615],{},[1810,80612,1854],{},[898,80614,6062],{"mathvariant":2057},[1810,80616,2032],{},[1677,80618,1679],{},[1810,80620,1812],{},[1677,80622,2858],{},[1805,80624,80625,80627],{},[1810,80626,2032],{},[895,80628,80629,80631,80633,80635,80637,80639,80641],{},[1810,80630,1959],{},[898,80632,6062],{"mathvariant":2057},[1810,80634,2032],{},[1677,80636,1776],{},[1810,80638,1854],{},[898,80640,6062],{"mathvariant":2057},[1810,80642,2032],{},[1805,80644,80645,80647],{},[898,80646,11183],{},[895,80648,80649,80651,80653],{},[1810,80650,1959],{},[898,80652,6062],{"mathvariant":2057},[1810,80654,2032],{},[1805,80656,80657,80659],{},[898,80658,11188],{},[895,80660,80661,80663,80665],{},[1810,80662,1854],{},[898,80664,6062],{"mathvariant":2057},[1810,80666,2032],{},[1677,80668,1679],{},[1810,80670,2032],{},[1677,80672,2858],{},[1810,80674,1812],{},[1805,80676,80677,80679],{},[898,80678,11183],{},[895,80680,80681,80683,80685],{},[1810,80682,1959],{},[898,80684,6062],{"mathvariant":2057},[1810,80686,2032],{},[1805,80688,80689,80691],{},[898,80690,11188],{},[895,80692,80693,80695,80697],{},[1810,80694,1854],{},[898,80696,6062],{"mathvariant":2057},[1810,80698,2032],{},[1677,80700,1679],{},[1810,80702,2032],{},[1969,80704,2668],{},[898,80706,2470],{},[1677,80708,1686],{"stretchy":1685},[898,80710,11183],{},[1677,80712,1967],{"separator":1966},[898,80714,11188],{},[1677,80716,1692],{"stretchy":1685},[898,80718,1656],{"mathvariant":2057},[902,80720,80721],{"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).",[198,80723,80724],{"id":38570},"Homogenita",[724,80726,80727,80728,9490,80751,80767],{},"Funkce ",[883,80729,80731],{"className":80730},[886],[888,80732,80733],{"xmlns":890},[892,80734,80735,80749],{},[895,80736,80737,80739,80741,80743,80745,80747],{},[898,80738,2470],{},[1677,80740,1686],{"stretchy":1685},[898,80742,11183],{},[1677,80744,1967],{"separator":1966},[898,80746,11188],{},[1677,80748,1692],{"stretchy":1685},[902,80750,11385],{"encoding":904},[38,80752,80753,80754],{},"homogenní stupně ",[883,80755,80757],{"className":80756},[886],[888,80758,80759],{"xmlns":890},[892,80760,80761,80765],{},[895,80762,80763],{},[898,80764,38251],{},[902,80766,38251],{"encoding":904},", jestliže",[883,80769,80771],{"className":80770},[886],[888,80772,80773],{"xmlns":890,"display":29457},[892,80774,80775,80832],{},[22145,80776,80777],{"width":29462},[22150,80778,80779,80781,80825,80827],{},[22153,80780],{"width":29467},[22153,80782,80783],{},[895,80784,80785,80787,80789,80791,80793,80795,80797,80799,80801,80803,80809,80811,80813,80815,80817,80819,80821,80823],{},[898,80786,2470],{},[1677,80788,1686],{"stretchy":1685},[898,80790,13431],{},[898,80792,11183],{},[1677,80794,1967],{"separator":1966},[898,80796,13431],{},[898,80798,11188],{},[1677,80800,1692],{"stretchy":1685},[1677,80802,1679],{},[1805,80804,80805,80807],{},[898,80806,13431],{},[898,80808,38251],{},[1969,80810,2668],{},[898,80812,2470],{},[1677,80814,1686],{"stretchy":1685},[898,80816,11183],{},[1677,80818,1967],{"separator":1966},[898,80820,11188],{},[1677,80822,1692],{"stretchy":1685},[1677,80824,1967],{"separator":1966},[22153,80826],{"width":29467},[22153,80828,80829],{},[1969,80830,80831],{},"(5.10)",[902,80833,80834],{"encoding":904},"Q(rL, rK) = r^n\\,Q(L, K), \\tag{5.10}",[724,80836,5698,80837,80855,80856,80874,80875,45027,80888,80891,80892,1656],{},[883,80838,80840],{"className":80839},[886],[888,80841,80842],{"xmlns":890},[892,80843,80844,80852],{},[895,80845,80846,80848,80850],{},[898,80847,38251],{},[1677,80849,5873],{},[1810,80851,2008],{},[902,80853,80854],{"encoding":904},"n \\geq 0"," je celé číslo a ",[883,80857,80859],{"className":80858},[886],[888,80860,80861],{"xmlns":890},[892,80862,80863,80871],{},[895,80864,80865,80867,80869],{},[898,80866,13431],{},[1677,80868,3089],{},[1810,80870,2008],{},[902,80872,80873],{"encoding":904},"r > 0",". Homogenní funkce stupně ",[883,80876,80878],{"className":80877},[886],[888,80879,80880],{"xmlns":890},[892,80881,80882,80886],{},[895,80883,80884],{},[1810,80885,1959],{},[902,80887,1959],{"encoding":904},[38,80889,80890],{},"lineárně homogenní",". Cobb-Douglasovy funkce jsou homogenní stupně ",[883,80893,80895],{"className":80894},[886],[888,80896,80897],{"xmlns":890},[892,80898,80899,80907],{},[895,80900,80901,80903,80905],{},[898,80902,207],{},[1677,80904,1776],{},[898,80906,1779],{},[902,80908,76215],{"encoding":904},[115,80910,80912],{"id":80911},"ryzí-cobb-douglas-a-ces","Ryzí Cobb-Douglas a CES",[724,80914,80915],{},[38,80916,80917],{},"Ryzí Cobb-Douglasovy funkce:",[883,80919,80921],{"className":80920},[886],[888,80922,80923],{"xmlns":890,"display":29457},[892,80924,80925,80984],{},[22145,80926,80927],{"width":29462},[22150,80928,80929,80931,80977,80979],{},[22153,80930],{"width":29467},[22153,80932,80933],{},[895,80934,80935,80937,80939,80941,80943,80949,80951,80963,80965,80967,80969,80971,80973,80975],{},[898,80936,2470],{},[1677,80938,1679],{},[898,80940,5643],{},[1969,80942,2668],{},[1805,80944,80945,80947],{},[898,80946,11183],{},[898,80948,207],{},[1969,80950,2668],{},[1805,80952,80953,80955],{},[898,80954,11188],{},[895,80956,80957,80959,80961],{},[1810,80958,1959],{},[1677,80960,1906],{},[898,80962,207],{},[1677,80964,1967],{"separator":1966},[7266,80966],{"width":16674},[1810,80968,2008],{},[1677,80970,3128],{},[898,80972,207],{},[1677,80974,3128],{},[1810,80976,14650],{},[22153,80978],{"width":29467},[22153,80980,80981],{},[1969,80982,80983],{},"(5.9)",[902,80985,80986],{"encoding":904},"Q = A\\,L^a\\,K^{1-a}, \\quad 0 \u003C a \u003C 1. \\tag{5.9}",[724,80988,80989,80990,80992,80993,1656],{},"Mají vždy ",[38,80991,80310],{}," a jsou ",[38,80994,80890],{},[724,80996,80997,11413,81000,81003],{},[38,80998,80999],{},"CES produkční funkce",[614,81001,81002],{},"Constant Elasticity of Substitution",", 1961):",[883,81005,81007],{"className":81006},[886],[888,81008,81009],{"xmlns":890,"display":29457},[892,81010,81011,81079],{},[895,81012,81013,81015,81017,81019,81077],{},[898,81014,2470],{},[1677,81016,1679],{},[898,81018,5643],{},[1805,81020,81021,81065],{},[895,81022,81023,81025,81027,81029,81031,81033,81035,81037,81047,81049,81051,81053,81063],{},[1677,81024,2167],{"fence":1966},[1677,81026,1686],{"stretchy":1685},[1810,81028,1959],{},[1677,81030,1906],{},[898,81032,207],{},[1677,81034,1692],{"stretchy":1685},[1969,81036,2668],{},[1805,81038,81039,81041],{},[898,81040,11183],{},[895,81042,81043,81045],{},[1677,81044,1906],{},[898,81046,1779],{},[1677,81048,1776],{},[898,81050,207],{},[1969,81052,2668],{},[1805,81054,81055,81057],{},[898,81056,11188],{},[895,81058,81059,81061],{},[1677,81060,1906],{},[898,81062,1779],{},[1677,81064,2182],{"fence":1966},[895,81066,81067,81069],{},[1677,81068,1906],{},[2006,81070,81071],{"scriptlevel":2008,"displaystyle":1685},[2010,81072,81073,81075],{},[1810,81074,1959],{},[898,81076,1779],{},[1677,81078,1967],{"separator":1966},[902,81080,81081],{"encoding":904},"Q = A\\left[(1-a)\\,L^{-b} + a\\,K^{-b}\\right]^{-\\tfrac{1}{b}},",[724,81083,5698,81084,1343,81102,1343,81123,81147],{},[883,81085,81087],{"className":81086},[886],[888,81088,81089],{"xmlns":890},[892,81090,81091,81099],{},[895,81092,81093,81095,81097],{},[898,81094,5643],{},[1677,81096,3089],{},[1810,81098,2008],{},[902,81100,81101],{"encoding":904},"A > 0",[883,81103,81105],{"className":81104},[886],[888,81106,81107],{"xmlns":890},[892,81108,81109,81121],{},[895,81110,81111,81113,81115,81117,81119],{},[1810,81112,2008],{},[1677,81114,3128],{},[898,81116,207],{},[1677,81118,3128],{},[1810,81120,1959],{},[902,81122,20227],{"encoding":904},[883,81124,81126],{"className":81125},[886],[888,81127,81128],{"xmlns":890},[892,81129,81130,81144],{},[895,81131,81132,81134,81136,81138,81140,81142],{},[1677,81133,1906],{},[1810,81135,1959],{},[1677,81137,3128],{},[898,81139,1779],{},[1677,81141,3052],{"mathvariant":2057},[1810,81143,2008],{},[902,81145,81146],{"encoding":904},"-1 \u003C b \\neq 0",". Cobb-Douglasovy funkce jsou jejich zvláštním případem.",[724,81149,81150],{},[38,81151,81152],{},"Další typy:",[120,81154,81155,81197],{},[123,81156,81157,1884,81160,81196],{},[38,81158,81159],{},"Lineární:",[883,81161,81163],{"className":81162},[886],[888,81164,81165],{"xmlns":890},[892,81166,81167,81193],{},[895,81168,81169,81171,81173,81175,81177,81179,81181,81183,81185,81187,81189,81191],{},[898,81170,2470],{},[1677,81172,1686],{"stretchy":1685},[898,81174,11183],{},[1677,81176,1967],{"separator":1966},[898,81178,11188],{},[1677,81180,1692],{"stretchy":1685},[1677,81182,1679],{},[898,81184,207],{},[898,81186,11183],{},[1677,81188,1776],{},[898,81190,1779],{},[898,81192,11188],{},[902,81194,81195],{"encoding":904},"Q(L, K) = aL + bK"," — dokonalé substituty.",[123,81198,81199,1884,81202,81247],{},[38,81200,81201],{},"Leontiefova:",[883,81203,81205],{"className":81204},[886],[888,81206,81207],{"xmlns":890},[892,81208,81209,81244],{},[895,81210,81211,81213,81215,81217,81219,81221,81223,81225,81228,81230,81232,81234,81236,81238,81240,81242],{},[898,81212,2470],{},[1677,81214,1686],{"stretchy":1685},[898,81216,11183],{},[1677,81218,1967],{"separator":1966},[898,81220,11188],{},[1677,81222,1692],{"stretchy":1685},[1677,81224,1679],{},[898,81226,81227],{},"min",[1677,81229,57591],{},[1677,81231,1686],{"stretchy":1685},[898,81233,207],{},[898,81235,11183],{},[1677,81237,1967],{"separator":1966},[898,81239,1779],{},[898,81241,11188],{},[1677,81243,1692],{"stretchy":1685},[902,81245,81246],{"encoding":904},"Q(L, K) = \\min(aL, bK)"," — dokonalé komplementy (fixní proporce).",[115,81249,81251,81252,1343,81271,81290],{"id":81250},"mezní-produkty-mplmp_l-mpkmp_k-a-totální-diferenciál","Mezní produkty ",[883,81253,81255],{"className":81254},[886],[888,81256,81257],{"xmlns":890},[892,81258,81259,81269],{},[895,81260,81261,81263],{},[898,81262,2499],{},[1953,81264,81265,81267],{},[898,81266,5325],{},[898,81268,11183],{},[902,81270,11433],{"encoding":904},[883,81272,81274],{"className":81273},[886],[888,81275,81276],{"xmlns":890},[892,81277,81278,81288],{},[895,81279,81280,81282],{},[898,81281,2499],{},[1953,81283,81284,81286],{},[898,81285,5325],{},[898,81287,11188],{},[902,81289,11478],{"encoding":904}," a totální diferenciál",[724,81292,81293],{},[38,81294,81295],{},"Mezní produkt práce:",[883,81297,81299],{"className":81298},[886],[888,81300,81301],{"xmlns":890,"display":29457},[892,81302,81303,81341],{},[895,81304,81305,81307,81313,81315,81323,81325,81339],{},[898,81306,2499],{},[1953,81308,81309,81311],{},[898,81310,5325],{},[898,81312,11183],{},[1677,81314,1679],{},[10554,81316,81317,81319,81321],{},[898,81318,2470],{},[898,81320,11183],{},[1677,81322,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,81324,1679],{},[2010,81326,81327,81333],{},[895,81328,81329,81331],{},[898,81330,11260],{"mathvariant":2057},[898,81332,2470],{},[895,81334,81335,81337],{},[898,81336,11260],{"mathvariant":2057},[898,81338,11183],{},[898,81340,1656],{"mathvariant":2057},[902,81342,81343],{"encoding":904},"MP_L = Q'_L = \\frac{\\partial Q}{\\partial L}.",[724,81345,81346],{},[38,81347,81348],{},"Mezní produkt kapitálu:",[883,81350,81352],{"className":81351},[886],[888,81353,81354],{"xmlns":890,"display":29457},[892,81355,81356,81394],{},[895,81357,81358,81360,81366,81368,81376,81378,81392],{},[898,81359,2499],{},[1953,81361,81362,81364],{},[898,81363,5325],{},[898,81365,11188],{},[1677,81367,1679],{},[10554,81369,81370,81372,81374],{},[898,81371,2470],{},[898,81373,11188],{},[1677,81375,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,81377,1679],{},[2010,81379,81380,81386],{},[895,81381,81382,81384],{},[898,81383,11260],{"mathvariant":2057},[898,81385,2470],{},[895,81387,81388,81390],{},[898,81389,11260],{"mathvariant":2057},[898,81391,11188],{},[898,81393,1656],{"mathvariant":2057},[902,81395,81396],{"encoding":904},"MP_K = Q'_K = \\frac{\\partial Q}{\\partial K}.",[724,81398,81399,81429,81430,81451,81452,81470,81471,81484,81485,1656],{},[883,81400,81402],{"className":81401},[886],[888,81403,81404],{"xmlns":890},[892,81405,81406,81426],{},[895,81407,81408,81410,81416,81418,81420,81422,81424],{},[898,81409,2499],{},[1953,81411,81412,81414],{},[898,81413,5325],{},[898,81415,11183],{},[1677,81417,1686],{"stretchy":1685},[898,81419,207],{},[1677,81421,1967],{"separator":1966},[898,81423,1779],{},[1677,81425,1692],{"stretchy":1685},[902,81427,81428],{"encoding":904},"MP_L(a, b)"," udává rychlost změny produkce vzhledem k práci v bodě ",[883,81431,81433],{"className":81432},[886],[888,81434,81435],{"xmlns":890},[892,81436,81437,81449],{},[895,81438,81439,81441,81443,81445,81447],{},[1677,81440,2167],{"stretchy":1685},[898,81442,207],{},[1677,81444,1967],{"separator":1966},[898,81446,1779],{},[1677,81448,2182],{"stretchy":1685},[902,81450,12212],{"encoding":904}," (na hladině ",[883,81453,81455],{"className":81454},[886],[888,81456,81457],{"xmlns":890},[892,81458,81459,81467],{},[895,81460,81461,81463,81465],{},[898,81462,11188],{},[1677,81464,1679],{},[898,81466,1779],{},[902,81468,81469],{"encoding":904},"K = b","), resp. přibližnou změnu produkce při jednotkové změně ",[883,81472,81474],{"className":81473},[886],[888,81475,81476],{"xmlns":890},[892,81477,81478,81482],{},[895,81479,81480],{},[898,81481,11183],{},[902,81483,11183],{"encoding":904},". Analogicky ",[883,81486,81488],{"className":81487},[886],[888,81489,81490],{"xmlns":890},[892,81491,81492,81512],{},[895,81493,81494,81496,81502,81504,81506,81508,81510],{},[898,81495,2499],{},[1953,81497,81498,81500],{},[898,81499,5325],{},[898,81501,11188],{},[1677,81503,1686],{"stretchy":1685},[898,81505,207],{},[1677,81507,1967],{"separator":1966},[898,81509,1779],{},[1677,81511,1692],{"stretchy":1685},[902,81513,81514],{"encoding":904},"MP_K(a, b)",[5254,81516,81517,81521],{},[724,81518,81519,52610],{},[883,81520,5543],{},[120,81522,81523,81561],{},[123,81524,81525,27580,81544],{},[883,81526,81528],{"className":81527},[886],[888,81529,81530],{"xmlns":890},[892,81531,81532,81542],{},[895,81533,81534,81536],{},[898,81535,2499],{},[1953,81537,81538,81540],{},[898,81539,5325],{},[898,81541,11183],{},[902,81543,11433],{"encoding":904},[614,81545,81546,81547,81560],{},"„o kolik vzroste ",[883,81548,81550],{"className":81549},[886],[888,81551,81552],{"xmlns":890},[892,81553,81554,81558],{},[895,81555,81556],{},[898,81557,2470],{},[902,81559,2470],{"encoding":904},", když přidám jednu jednotku práce (a kapitál držím pevně)?\"",[123,81562,81563,27580,81582],{},[883,81564,81566],{"className":81565},[886],[888,81567,81568],{"xmlns":890},[892,81569,81570,81580],{},[895,81571,81572,81574],{},[898,81573,2499],{},[1953,81575,81576,81578],{},[898,81577,5325],{},[898,81579,11188],{},[902,81581,11478],{"encoding":904},[614,81583,81546,81584,81597],{},[883,81585,81587],{"className":81586},[886],[888,81588,81589],{"xmlns":890},[892,81590,81591,81595],{},[895,81592,81593],{},[898,81594,2470],{},[902,81596,2470],{"encoding":904},", když přidám jednu jednotku kapitálu (a práci držím pevně)?\"",[724,81599,81600,81603,81604,81619,81620,2385],{},[38,81601,81602],{},"Totální diferenciál"," — přibližná změna produkce při změně práce o ",[883,81605,81607],{"className":81606},[886],[888,81608,81609],{"xmlns":890},[892,81610,81611,81617],{},[895,81612,81613,81615],{},[898,81614,1875],{},[898,81616,11183],{},[902,81618,76747],{"encoding":904}," a kapitálu o ",[883,81621,81623],{"className":81622},[886],[888,81624,81625],{"xmlns":890},[892,81626,81627,81633],{},[895,81628,81629,81631],{},[898,81630,1875],{},[898,81632,11188],{},[902,81634,81635],{"encoding":904},"dK",[883,81637,81639],{"className":81638},[886],[888,81640,81641],{"xmlns":890,"display":29457},[892,81642,81643,81736],{},[22145,81644,81645],{"width":29462},[22150,81646,81647,81649,81729,81731],{},[22153,81648],{"width":29467},[22153,81650,81651],{},[895,81652,81653,81655,81657,81659,81661,81663,81665,81673,81675,81677,81679,81681,81689,81691,81693,81695,81697,81699,81705,81707,81709,81711,81713,81715,81721,81723,81725,81727],{},[898,81654,2570],{"mathvariant":2057},[898,81656,2470],{},[1677,81658,2411],{},[898,81660,1875],{},[898,81662,2470],{},[1677,81664,1679],{},[10554,81666,81667,81669,81671],{},[898,81668,2470],{},[898,81670,11183],{},[1677,81672,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1969,81674,2668],{},[898,81676,1875],{},[898,81678,11183],{},[1677,81680,1776],{},[10554,81682,81683,81685,81687],{},[898,81684,2470],{},[898,81686,11188],{},[1677,81688,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1969,81690,2668],{},[898,81692,1875],{},[898,81694,11188],{},[1677,81696,1679],{},[898,81698,2499],{},[1953,81700,81701,81703],{},[898,81702,5325],{},[898,81704,11183],{},[1969,81706,2668],{},[898,81708,1875],{},[898,81710,11183],{},[1677,81712,1776],{},[898,81714,2499],{},[1953,81716,81717,81719],{},[898,81718,5325],{},[898,81720,11188],{},[1969,81722,2668],{},[898,81724,1875],{},[898,81726,11188],{},[898,81728,1656],{"mathvariant":2057},[22153,81730],{"width":29467},[22153,81732,81733],{},[1969,81734,81735],{},"(5.11)",[902,81737,81738],{"encoding":904},"\\Delta Q \\approx dQ = Q'_L\\,dL + Q'_K\\,dK = MP_L\\,dL + MP_K\\,dK. \\tag{5.11}",[724,81740,81741,81742,1656],{},"Skutečná změna: ",[883,81743,81745],{"className":81744},[886],[888,81746,81747],{"xmlns":890},[892,81748,81749,81795],{},[895,81750,81751,81753,81755,81757,81759,81761,81763,81765,81767,81769,81771,81773,81775,81777,81779,81781,81783,81785,81787,81789,81791,81793],{},[898,81752,2570],{"mathvariant":2057},[898,81754,2470],{},[1677,81756,1679],{},[898,81758,2470],{},[1677,81760,1686],{"stretchy":1685},[898,81762,11183],{},[1677,81764,1776],{},[898,81766,1875],{},[898,81768,11183],{},[1677,81770,1967],{"separator":1966},[898,81772,11188],{},[1677,81774,1776],{},[898,81776,1875],{},[898,81778,11188],{},[1677,81780,1692],{"stretchy":1685},[1677,81782,1906],{},[898,81784,2470],{},[1677,81786,1686],{"stretchy":1685},[898,81788,11183],{},[1677,81790,1967],{"separator":1966},[898,81792,11188],{},[1677,81794,1692],{"stretchy":1685},[902,81796,81797],{"encoding":904},"\\Delta Q = Q(L+dL, K+dK) - Q(L, K)",[724,81799,81800,81802,81803,81821,81822,81835,81836,81855,81856,81888,81889,81921,81922,1656],{},[38,81801,76911],{}," platí ve 2F modelu pro oba vstupy: pro pevné ",[883,81804,81806],{"className":81805},[886],[888,81807,81808],{"xmlns":890},[892,81809,81810,81818],{},[895,81811,81812],{},[1953,81813,81814,81816],{},[898,81815,11188],{},[1810,81817,2008],{},[902,81819,81820],{"encoding":904},"K_0"," se od jistého ",[883,81823,81825],{"className":81824},[886],[888,81826,81827],{"xmlns":890},[892,81828,81829,81833],{},[895,81830,81831],{},[898,81832,11183],{},[902,81834,11183],{"encoding":904}," stane ",[883,81837,81839],{"className":81838},[886],[888,81840,81841],{"xmlns":890},[892,81842,81843,81853],{},[895,81844,81845,81847],{},[898,81846,2499],{},[1953,81848,81849,81851],{},[898,81850,5325],{},[898,81852,11183],{},[902,81854,11433],{"encoding":904}," klesající (",[883,81857,81859],{"className":81858},[886],[888,81860,81861],{"xmlns":890},[892,81862,81863,81885],{},[895,81864,81865,81881,81883],{},[10554,81866,81867,81869,81875],{},[898,81868,2470],{},[895,81870,81871,81873],{},[898,81872,11183],{},[898,81874,11183],{},[895,81876,81877,81879],{},[1677,81878,2059],{"mathvariant":2057},[1677,81880,2059],{"mathvariant":2057},[1677,81882,3128],{},[1810,81884,2008],{},[902,81886,81887],{"encoding":904},"Q''_{LL} \u003C 0","); analogicky ",[883,81890,81892],{"className":81891},[886],[888,81893,81894],{"xmlns":890},[892,81895,81896,81918],{},[895,81897,81898,81914,81916],{},[10554,81899,81900,81902,81908],{},[898,81901,2470],{},[895,81903,81904,81906],{},[898,81905,11188],{},[898,81907,11188],{},[895,81909,81910,81912],{},[1677,81911,2059],{"mathvariant":2057},[1677,81913,2059],{"mathvariant":2057},[1677,81915,3128],{},[1810,81917,2008],{},[902,81919,81920],{"encoding":904},"Q''_{KK} \u003C 0"," pro pevné ",[883,81923,81925],{"className":81924},[886],[888,81926,81927],{"xmlns":890},[892,81928,81929,81937],{},[895,81930,81931],{},[1953,81932,81933,81935],{},[898,81934,11183],{},[1810,81936,2008],{},[902,81938,76949],{"encoding":904},[115,81940,81942],{"id":81941},"eulerova-věta-pro-homogenní-funkce","Eulerova věta pro homogenní funkce",[724,81944,81945,81948,81949,81972,81973,31335],{},[38,81946,81947],{},"Eulerova věta"," (úloha 5.10): pro homogenní funkci ",[883,81950,81952],{"className":81951},[886],[888,81953,81954],{"xmlns":890},[892,81955,81956,81970],{},[895,81957,81958,81960,81962,81964,81966,81968],{},[898,81959,2470],{},[1677,81961,1686],{"stretchy":1685},[898,81963,11183],{},[1677,81965,1967],{"separator":1966},[898,81967,11188],{},[1677,81969,1692],{"stretchy":1685},[902,81971,11385],{"encoding":904}," stupně ",[883,81974,81976],{"className":81975},[886],[888,81977,81978],{"xmlns":890},[892,81979,81980,81984],{},[895,81981,81982],{},[898,81983,38251],{},[902,81985,38251],{"encoding":904},[883,81987,81989],{"className":81988},[886],[888,81990,81991],{"xmlns":890,"display":29457},[892,81992,81993,82056],{},[22145,81994,81995],{"width":29462},[22150,81996,81997,81999,82049,82051],{},[22153,81998],{"width":29467},[22153,82000,82001],{},[895,82002,82003,82005,82007,82015,82017,82019,82021,82029,82031,82033,82035,82037,82039,82041,82043,82045,82047],{},[898,82004,11183],{},[1969,82006,2668],{},[10554,82008,82009,82011,82013],{},[898,82010,2470],{},[898,82012,11183],{},[1677,82014,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,82016,1776],{},[898,82018,11188],{},[1969,82020,2668],{},[10554,82022,82023,82025,82027],{},[898,82024,2470],{},[898,82026,11188],{},[1677,82028,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,82030,1679],{},[898,82032,38251],{},[1969,82034,2668],{},[898,82036,2470],{},[1677,82038,1686],{"stretchy":1685},[898,82040,11183],{},[1677,82042,1967],{"separator":1966},[898,82044,11188],{},[1677,82046,1692],{"stretchy":1685},[898,82048,1656],{"mathvariant":2057},[22153,82050],{"width":29467},[22153,82052,82053],{},[1969,82054,82055],{},"(5.12)",[902,82057,82058],{"encoding":904},"L\\,Q'_L + K\\,Q'_K = n\\,Q(L, K). \\tag{5.12}",[724,82060,82061,82082],{},[38,82062,82063,82064],{},"Speciální případ ",[883,82065,82067],{"className":82066},[886],[888,82068,82069],{"xmlns":890},[892,82070,82071,82079],{},[895,82072,82073,82075,82077],{},[898,82074,38251],{},[1677,82076,1679],{},[1810,82078,1959],{},[902,82080,82081],{"encoding":904},"n = 1"," (konstantní výnosy z rozsahu):",[883,82084,82086],{"className":82085},[886],[888,82087,82088],{"xmlns":890,"display":29457},[892,82089,82090,82134],{},[895,82091,82092,82094,82096,82098,82104,82106,82108,82110,82112,82118,82120,82122,82124,82126,82128,82130,82132],{},[898,82093,11183],{},[1677,82095,2858],{},[898,82097,2499],{},[1953,82099,82100,82102],{},[898,82101,5325],{},[898,82103,11183],{},[1677,82105,1776],{},[898,82107,11188],{},[1677,82109,2858],{},[898,82111,2499],{},[1953,82113,82114,82116],{},[898,82115,5325],{},[898,82117,11188],{},[1677,82119,1679],{},[898,82121,2470],{},[1677,82123,1686],{"stretchy":1685},[898,82125,11183],{},[1677,82127,1967],{"separator":1966},[898,82129,11188],{},[1677,82131,1692],{"stretchy":1685},[898,82133,1656],{"mathvariant":2057},[902,82135,82136],{"encoding":904},"L\\cdot MP_L + K\\cdot MP_K = Q(L, K).",[724,82138,82139,82140,82143],{},"Slovně — ",[38,82141,82142],{},"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).",[115,82145,11166],{"id":76285},[724,82147,82148,11413,82150,82153,82154,82176,82177,2385],{},[38,82149,11166],{},[614,82151,82152],{},"isoquants",") jsou křivky stejné produkce — množina dvojic ",[883,82155,82157],{"className":82156},[886],[888,82158,82159],{"xmlns":890},[892,82160,82161,82173],{},[895,82162,82163,82165,82167,82169,82171],{},[1677,82164,2167],{"stretchy":1685},[898,82166,11183],{},[1677,82168,1967],{"separator":1966},[898,82170,11188],{},[1677,82172,2182],{"stretchy":1685},[902,82174,82175],{"encoding":904},"[L, K]",", pro něž produkční funkce nabývá pevně zvolené hodnoty ",[883,82178,82180],{"className":82179},[886],[888,82181,82182],{"xmlns":890},[892,82183,82184,82189],{},[895,82185,82186],{},[898,82187,82188],{},"q",[902,82190,82188],{"encoding":904},[883,82192,82194],{"className":82193},[886],[888,82195,82196],{"xmlns":890,"display":29457},[892,82197,82198,82233],{},[22145,82199,82200],{"width":29462},[22150,82201,82202,82204,82226,82228],{},[22153,82203],{"width":29467},[22153,82205,82206],{},[895,82207,82208,82210,82212,82214,82216,82218,82220,82222,82224],{},[898,82209,2470],{},[1677,82211,1686],{"stretchy":1685},[898,82213,11183],{},[1677,82215,1967],{"separator":1966},[898,82217,11188],{},[1677,82219,1692],{"stretchy":1685},[1677,82221,1679],{},[898,82223,82188],{},[898,82225,1656],{"mathvariant":2057},[22153,82227],{"width":29467},[22153,82229,82230],{},[1969,82231,82232],{},"(5.13)",[902,82234,82235],{"encoding":904},"Q(L, K) = q. \\tag{5.13}",[724,82237,82238,82239,82242,82243,5306],{},"Jsou to ",[38,82240,82241],{},"indiferenční křivky"," produkční funkce (analogie s indiferenčními křivkami u ",[207,82244,82246],{"className":82245,"dataFsResolvedFilePath":878,"href":879},[210],"užitečnosti",[724,82248,82249],{},[38,82250,82251],{},"Vlastnosti izokvant Cobb-Douglasových funkcí:",[120,82253,82254,82259,82264,82269],{},[123,82255,82256,82258],{},[38,82257,13909],{}," — pokles kapitálu vyžaduje kompenzující růst práce k udržení produkce;",[123,82260,82261,82263],{},[38,82262,39055],{}," (úloha 5.14);",[123,82265,82266,9813],{},[38,82267,82268],{},"neprotínají se",[123,82270,82271,82272,5746,82285,1656],{},"s rostoucím ",[883,82273,82275],{"className":82274},[886],[888,82276,82277],{"xmlns":890},[892,82278,82279,82283],{},[895,82280,82281],{},[898,82282,82188],{},[902,82284,82188],{"encoding":904},[38,82286,82287],{},"vzdalují od počátku",[724,82289,82290],{},[614,82291,82292,82293,82315,82316,1656],{},"Obrázek 5.4 — izokvanty Cobb-Douglasovy funkce v rovině ",[883,82294,82296],{"className":82295},[886],[888,82297,82298],{"xmlns":890},[892,82299,82300,82312],{},[895,82301,82302,82304,82306,82308,82310],{},[1677,82303,1686],{"stretchy":1685},[898,82305,11183],{},[1677,82307,1967],{"separator":1966},[898,82309,11188],{},[1677,82311,1692],{"stretchy":1685},[902,82313,82314],{"encoding":904},"(L, K)",": tři klesající konvexní křivky pro ",[883,82317,82319],{"className":82318},[886],[888,82320,82321],{"xmlns":890},[892,82322,82323,82347],{},[895,82324,82325,82331,82333,82339,82341],{},[1953,82326,82327,82329],{},[898,82328,82188],{},[1810,82330,1959],{},[1677,82332,3128],{},[1953,82334,82335,82337],{},[898,82336,82188],{},[1810,82338,2008],{},[1677,82340,3128],{},[1953,82342,82343,82345],{},[898,82344,82188],{},[1810,82346,1812],{},[902,82348,82349],{"encoding":904},"q_1 \u003C q_0 \u003C q_2",[115,82351,82353,82354,1692],{"id":82352},"mezní-míra-technické-substituce-mrtsmrts","Mezní míra technické substituce (",[883,82355,82357],{"className":82356},[886],[888,82358,82359],{"xmlns":890},[892,82360,82361,82371],{},[895,82362,82363,82365,82367,82369],{},[898,82364,2499],{},[898,82366,5382],{},[898,82368,2455],{},[898,82370,10061],{},[902,82372,11987],{"encoding":904},[724,82374,82375,11413,82378,82381],{},[38,82376,82377],{},"Mezní míra technické substituce",[614,82379,82380],{},"marginal rate of technical substitution",") je podíl mezních produktů:",[883,82383,82385],{"className":82384},[886],[888,82386,82387],{"xmlns":890,"display":29457},[892,82388,82389,82480],{},[22145,82390,82391],{"width":29462},[22150,82392,82393,82395,82473,82475],{},[22153,82394],{"width":29467},[22153,82396,82397],{},[895,82398,82399,82401,82403,82405,82407,82409,82411,82413,82415,82417,82419,82421,82423,82425,82427,82429,82451,82453,82471],{},[898,82400,2499],{},[898,82402,5382],{},[898,82404,2455],{},[898,82406,10061],{},[1677,82408,1679],{},[898,82410,2499],{},[898,82412,5382],{},[898,82414,2455],{},[898,82416,10061],{},[1677,82418,1686],{"stretchy":1685},[898,82420,11183],{},[1677,82422,1967],{"separator":1966},[898,82424,11188],{},[1677,82426,1692],{"stretchy":1685},[1677,82428,1679],{},[2010,82430,82431,82441],{},[895,82432,82433,82435],{},[898,82434,2499],{},[1953,82436,82437,82439],{},[898,82438,5325],{},[898,82440,11183],{},[895,82442,82443,82445],{},[898,82444,2499],{},[1953,82446,82447,82449],{},[898,82448,5325],{},[898,82450,11188],{},[1677,82452,1679],{},[2010,82454,82455,82463],{},[10554,82456,82457,82459,82461],{},[898,82458,2470],{},[898,82460,11183],{},[1677,82462,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[10554,82464,82465,82467,82469],{},[898,82466,2470],{},[898,82468,11188],{},[1677,82470,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[898,82472,1656],{"mathvariant":2057},[22153,82474],{"width":29467},[22153,82476,82477],{},[1969,82478,82479],{},"(5.14)",[902,82481,82482],{"encoding":904},"MRTS = MRTS(L, K) = \\frac{MP_L}{MP_K} = \\frac{Q'_L}{Q'_K}. \\tag{5.14}",[724,82484,82485,1884,82487,82517,82518,82549],{},[38,82486,10604],{},[883,82488,82490],{"className":82489},[886],[888,82491,82492],{"xmlns":890},[892,82493,82494,82514],{},[895,82495,82496,82498,82500,82502,82504,82506,82508,82510,82512],{},[898,82497,2499],{},[898,82499,5382],{},[898,82501,2455],{},[898,82503,10061],{},[1677,82505,1686],{"stretchy":1685},[898,82507,11183],{},[1677,82509,1967],{"separator":1966},[898,82511,11188],{},[1677,82513,1692],{"stretchy":1685},[902,82515,82516],{"encoding":904},"MRTS(L, K)"," udává, ",[38,82519,82520,82521,82534,82535,82548],{},"o kolik se musí přibližně změnit kapitál ",[883,82522,82524],{"className":82523},[886],[888,82525,82526],{"xmlns":890},[892,82527,82528,82532],{},[895,82529,82530],{},[898,82531,11188],{},[902,82533,11188],{"encoding":904},", jestliže se práce ",[883,82536,82538],{"className":82537},[886],[888,82539,82540],{"xmlns":890},[892,82541,82542,82546],{},[895,82543,82544],{},[898,82545,11183],{},[902,82547,11183],{"encoding":904}," změní o jednotku, aby byla zachována produkce"," (pohyb po izokvantě).",[5254,82551,82552],{},[724,82553,82554,19414,82556,82575,82576,82613,82614,82617,82618,82622],{},[883,82555,5543],{},[883,82557,82559],{"className":82558},[886],[888,82560,82561],{"xmlns":890},[892,82562,82563,82573],{},[895,82564,82565,82567,82569,82571],{},[898,82566,2499],{},[898,82568,5382],{},[898,82570,2455],{},[898,82572,10061],{},[902,82574,11987],{"encoding":904}," říká: ",[614,82577,82578,82579,82598,82599,82612],{},"„jednu jednotku práce musím nahradit přibližně ",[883,82580,82582],{"className":82581},[886],[888,82583,82584],{"xmlns":890},[892,82585,82586,82596],{},[895,82587,82588,82590,82592,82594],{},[898,82589,2499],{},[898,82591,5382],{},[898,82593,2455],{},[898,82595,10061],{},[902,82597,11987],{"encoding":904}," jednotkami kapitálu, aby produkce ",[883,82600,82602],{"className":82601},[886],[888,82603,82604],{"xmlns":890},[892,82605,82606,82610],{},[895,82607,82608],{},[898,82609,2470],{},[902,82611,2470],{"encoding":904}," zůstala stejná.\""," Je to ",[38,82615,82616],{},"směnný kurz mezi vstupy"," při zachování produkce — přesná analogie ",[207,82619,82621],{"className":82620,"dataFsResolvedFilePath":878,"href":879},[210],"MRCS z teorie užitečnosti",", kde nahrazujeme spotřební statky při zachování užitku.",[724,82624,82625],{},[2240,82626],{"alt":82627,"className":82628,"src":82629},"imek-izokvanty-mrts",[210,2244],"\u002Fwiki-assets\u002Fimek-izokvanty-mrts.jpeg",[724,82631,82632,82635,82636,9490,82666,82688,82689,2832],{},[38,82633,82634],{},"Geometrická interpretace:"," sklon tečny k izokvantě v bodě ",[883,82637,82639],{"className":82638},[886],[888,82640,82641],{"xmlns":890},[892,82642,82643,82663],{},[895,82644,82645,82647,82653,82655,82661],{},[1677,82646,2167],{"stretchy":1685},[1953,82648,82649,82651],{},[898,82650,11183],{},[1810,82652,2008],{},[1677,82654,1967],{"separator":1966},[1953,82656,82657,82659],{},[898,82658,11188],{},[1810,82660,2008],{},[1677,82662,2182],{"stretchy":1685},[902,82664,82665],{"encoding":904},"[L_0, K_0]",[883,82667,82669],{"className":82668},[886],[888,82670,82671],{"xmlns":890},[892,82672,82673,82685],{},[895,82674,82675,82677,82679,82681,82683],{},[1677,82676,1906],{},[898,82678,2499],{},[898,82680,5382],{},[898,82682,2455],{},[898,82684,10061],{},[902,82686,82687],{"encoding":904},"-MRTS",". Z derivace implicitní funkce (při ",[883,82690,82692],{"className":82691},[886],[888,82693,82694],{"xmlns":890},[892,82695,82696,82718],{},[895,82697,82698,82700,82702,82704,82706,82708,82710,82712],{},[898,82699,2470],{},[1677,82701,1686],{"stretchy":1685},[898,82703,11183],{},[1677,82705,1967],{"separator":1966},[898,82707,11188],{},[1677,82709,1692],{"stretchy":1685},[1677,82711,1679],{},[1953,82713,82714,82716],{},[898,82715,82188],{},[1810,82717,2008],{},[902,82719,82720],{"encoding":904},"Q(L,K) = q_0",[883,82722,82724],{"className":82723},[886],[888,82725,82726],{"xmlns":890,"display":29457},[892,82727,82728,82780],{},[895,82729,82730,82744,82746,82748,82766,82768,82770,82772,82774,82776,82778],{},[2010,82731,82732,82738],{},[895,82733,82734,82736],{},[898,82735,1875],{},[898,82737,11188],{},[895,82739,82740,82742],{},[898,82741,1875],{},[898,82743,11183],{},[1677,82745,1679],{},[1677,82747,1906],{},[2010,82749,82750,82758],{},[10554,82751,82752,82754,82756],{},[898,82753,2470],{},[898,82755,11183],{},[1677,82757,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[10554,82759,82760,82762,82764],{},[898,82761,2470],{},[898,82763,11188],{},[1677,82765,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,82767,1679],{},[1677,82769,1906],{},[898,82771,2499],{},[898,82773,5382],{},[898,82775,2455],{},[898,82777,10061],{},[898,82779,1656],{"mathvariant":2057},[902,82781,82782],{"encoding":904},"\\frac{dK}{dL} = -\\frac{Q'_L}{Q'_K} = -MRTS.",[724,82784,82785,82786,82801,82802,82818],{},"Změní-li se práce o ",[883,82787,82789],{"className":82788},[886],[888,82790,82791],{"xmlns":890},[892,82792,82793,82799],{},[895,82794,82795,82797],{},[898,82796,1875],{},[898,82798,11183],{},[902,82800,76747],{"encoding":904},", lze pro odhad změny kapitálu ",[883,82803,82805],{"className":82804},[886],[888,82806,82807],{"xmlns":890},[892,82808,82809,82815],{},[895,82810,82811,82813],{},[898,82812,2570],{"mathvariant":2057},[898,82814,11188],{},[902,82816,82817],{"encoding":904},"\\Delta K"," k udržení produkce použít diferenciál:",[883,82820,82822],{"className":82821},[886],[888,82823,82824],{"xmlns":890,"display":29457},[892,82825,82826,82873],{},[22145,82827,82828],{"width":29462},[22150,82829,82830,82832,82866,82868],{},[22153,82831],{"width":29467},[22153,82833,82834],{},[895,82835,82836,82838,82840,82842,82844,82846,82848,82850,82852,82854,82856,82858,82860,82862,82864],{},[898,82837,2570],{"mathvariant":2057},[898,82839,11188],{},[1677,82841,2411],{},[898,82843,1875],{},[898,82845,11188],{},[1677,82847,1679],{},[1677,82849,1906],{},[898,82851,2499],{},[898,82853,5382],{},[898,82855,2455],{},[898,82857,10061],{},[1969,82859,2668],{},[898,82861,1875],{},[898,82863,11183],{},[1677,82865,1967],{"separator":1966},[22153,82867],{"width":29467},[22153,82869,82870],{},[1969,82871,82872],{},"(5.15)",[902,82874,82875],{"encoding":904},"\\Delta K \\approx dK = -MRTS\\,dL, \\tag{5.15}",[883,82877,82879],{"className":82878},[886],[888,82880,82881],{"xmlns":890,"display":29457},[892,82882,82883,82932],{},[22145,82884,82885],{"width":29462},[22150,82886,82887,82889,82925,82927],{},[22153,82888],{"width":29467},[22153,82890,82891],{},[895,82892,82893,82895,82897,82899,82917,82919,82921,82923],{},[898,82894,1875],{},[898,82896,11183],{},[1677,82898,1679],{},[2010,82900,82901,82907],{},[895,82902,82903,82905],{},[1677,82904,1906],{},[1810,82906,1959],{},[895,82908,82909,82911,82913,82915],{},[898,82910,2499],{},[898,82912,5382],{},[898,82914,2455],{},[898,82916,10061],{},[1969,82918,2668],{},[898,82920,1875],{},[898,82922,11188],{},[898,82924,1656],{"mathvariant":2057},[22153,82926],{"width":29467},[22153,82928,82929],{},[1969,82930,82931],{},"(5.16)",[902,82933,82934],{"encoding":904},"dL = \\frac{-1}{MRTS}\\,dK. \\tag{5.16}",[5254,82936,82937,82961],{},[724,82938,82939,82941,82942],{},[883,82940,5960],{}," Postup — jak spočítat ",[883,82943,82945],{"className":82944},[886],[888,82946,82947],{"xmlns":890},[892,82948,82949,82959],{},[895,82950,82951,82953,82955,82957],{},[898,82952,2499],{},[898,82954,5382],{},[898,82956,2455],{},[898,82958,10061],{},[902,82960,11987],{"encoding":904},[152,82962,82963,83004,83047,83079],{},[123,82964,82965,82966,5272,82985,1656],{},"Vypočtěte parciální derivace ",[883,82967,82969],{"className":82968},[886],[888,82970,82971],{"xmlns":890},[892,82972,82973,82983],{},[895,82974,82975],{},[10554,82976,82977,82979,82981],{},[898,82978,2470],{},[898,82980,11183],{},[1677,82982,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[902,82984,11409],{"encoding":904},[883,82986,82988],{"className":82987},[886],[888,82989,82990],{"xmlns":890},[892,82991,82992,83002],{},[895,82993,82994],{},[10554,82995,82996,82998,83000],{},[898,82997,2470],{},[898,82999,11188],{},[1677,83001,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[902,83003,11455],{"encoding":904},[123,83005,67232,83006,83046],{},[883,83007,83009],{"className":83008},[886],[888,83010,83011],{"xmlns":890},[892,83012,83013,83043],{},[895,83014,83015,83017,83019,83021,83023,83025,83033,83035],{},[898,83016,2499],{},[898,83018,5382],{},[898,83020,2455],{},[898,83022,10061],{},[1677,83024,1679],{},[10554,83026,83027,83029,83031],{},[898,83028,2470],{},[898,83030,11183],{},[1677,83032,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[898,83034,6062],{"mathvariant":2057},[10554,83036,83037,83039,83041],{},[898,83038,2470],{},[898,83040,11188],{},[1677,83042,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[902,83044,83045],{"encoding":904},"MRTS = Q'_L \u002F Q'_K"," (zlomek zjednodušte).",[123,83048,83049,83050,1656],{},"Případně dosaďte konkrétní ",[883,83051,83053],{"className":83052},[886],[888,83054,83055],{"xmlns":890},[892,83056,83057,83077],{},[895,83058,83059,83061,83067,83069,83075],{},[1677,83060,2167],{"stretchy":1685},[1953,83062,83063,83065],{},[898,83064,11183],{},[1810,83066,2008],{},[1677,83068,1967],{"separator":1966},[1953,83070,83071,83073],{},[898,83072,11188],{},[1810,83074,2008],{},[1677,83076,2182],{"stretchy":1685},[902,83078,82665],{"encoding":904},[123,83080,83081,83082,83116,83117,83119],{},"Pro odhad substituce použijte ",[883,83083,83085],{"className":83084},[886],[888,83086,83087],{"xmlns":890},[892,83088,83089,83113],{},[895,83090,83091,83093,83095,83097,83099,83101,83103,83105,83107,83109,83111],{},[898,83092,2570],{"mathvariant":2057},[898,83094,11188],{},[1677,83096,2411],{},[1677,83098,1906],{},[898,83100,2499],{},[898,83102,5382],{},[898,83104,2455],{},[898,83106,10061],{},[1677,83108,2858],{},[898,83110,2570],{"mathvariant":2057},[898,83112,11183],{},[902,83114,83115],{"encoding":904},"\\Delta K \\approx -MRTS \\cdot \\Delta L"," (znaménko ",[38,83118,53997],{}," — substituce, ne doplnění).",[724,83121,83122],{},[614,83123,83124,83125,83157,83158,2305,83171,17182,83200,83215],{},"Obrázek 5.7 — izokvanta ",[883,83126,83128],{"className":83127},[886],[888,83129,83130],{"xmlns":890},[892,83131,83132,83154],{},[895,83133,83134,83140,83142,83144,83146,83148,83150,83152],{},[1953,83135,83136,83138],{},[898,83137,82188],{},[1810,83139,2008],{},[1677,83141,1679],{},[898,83143,2470],{},[1677,83145,1686],{"stretchy":1685},[898,83147,11183],{},[1677,83149,1967],{"separator":1966},[898,83151,11188],{},[1677,83153,1692],{"stretchy":1685},[902,83155,83156],{"encoding":904},"q_0 = Q(L,K)"," s tečnou ",[883,83159,83161],{"className":83160},[886],[888,83162,83163],{"xmlns":890},[892,83164,83165,83169],{},[895,83166,83167],{},[898,83168,20246],{},[902,83170,20246],{"encoding":904},[883,83172,83174],{"className":83173},[886],[888,83175,83176],{"xmlns":890},[892,83177,83178,83198],{},[895,83179,83180,83182,83188,83190,83196],{},[1677,83181,2167],{"stretchy":1685},[1953,83183,83184,83186],{},[898,83185,11183],{},[1810,83187,2008],{},[1677,83189,1967],{"separator":1966},[1953,83191,83192,83194],{},[898,83193,11188],{},[1810,83195,2008],{},[1677,83197,2182],{"stretchy":1685},[902,83199,82665],{"encoding":904},[883,83201,83203],{"className":83202},[886],[888,83204,83205],{"xmlns":890},[892,83206,83207,83213],{},[895,83208,83209,83211],{},[898,83210,2570],{"mathvariant":2057},[898,83212,11188],{},[902,83214,82817],{"encoding":904}," odhadnut diferenciálem (záporně vzatý sklon tečny).",[115,83217,83219],{"id":83218},"příklady-dvoufaktorový-model","Příklady (dvoufaktorový model)",[198,83221,83223],{"id":83222},"příklad-54","Příklad 5.4",[724,83225,78064,83226,1343,83268,1343,83285,1656],{},[883,83227,83229],{"className":83228},[886],[888,83230,83231],{"xmlns":890},[892,83232,83233,83265],{},[895,83234,83235,83237,83239,83241,83253],{},[898,83236,2470],{},[1677,83238,1679],{},[1810,83240,37635],{},[1805,83242,83243,83245],{},[898,83244,11183],{},[895,83246,83247,83249,83251],{},[1810,83248,1959],{},[898,83250,6062],{"mathvariant":2057},[1810,83252,1812],{},[1805,83254,83255,83257],{},[898,83256,11188],{},[895,83258,83259,83261,83263],{},[1810,83260,1959],{},[898,83262,6062],{"mathvariant":2057},[1810,83264,1854],{},[902,83266,83267],{"encoding":904},"Q = 15 L^{1\u002F2} K^{1\u002F3}",[883,83269,83271],{"className":83270},[886],[888,83272,83273],{"xmlns":890},[892,83274,83275,83283],{},[895,83276,83277,83279,83281],{},[898,83278,11183],{},[1677,83280,1679],{},[1810,83282,10423],{},[902,83284,78438],{"encoding":904},[883,83286,83288],{"className":83287},[886],[888,83289,83290],{"xmlns":890},[892,83291,83292,83300],{},[895,83293,83294,83296,83298],{},[898,83295,11188],{},[1677,83297,1679],{},[1810,83299,2771],{},[902,83301,83302],{"encoding":904},"K = 100",[724,83304,83305],{},[38,83306,83307],{},"(a) Rychlost změny produkce vzhledem k práci.",[883,83309,83311],{"className":83310},[886],[888,83312,83313],{"xmlns":890,"display":29457},[892,83314,83315,83429],{},[895,83316,83317,83319,83325,83327,83335,83337,83345,83359,83371,83373,83375,83377,83383,83385,83387,83389,83391,83393,83395,83403,83405,83415,83417,83424,83426],{},[898,83318,2499],{},[1953,83320,83321,83323],{},[898,83322,5325],{},[898,83324,11183],{},[1677,83326,1679],{},[10554,83328,83329,83331,83333],{},[898,83330,2470],{},[898,83332,11183],{},[1677,83334,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,83336,1679],{},[2006,83338,83339],{"scriptlevel":2008,"displaystyle":1685},[2010,83340,83341,83343],{},[1810,83342,37635],{},[1810,83344,1812],{},[1805,83346,83347,83349],{},[898,83348,11183],{},[895,83350,83351,83353,83355,83357],{},[1677,83352,1906],{},[1810,83354,1959],{},[898,83356,6062],{"mathvariant":2057},[1810,83358,1812],{},[1805,83360,83361,83363],{},[898,83362,11188],{},[895,83364,83365,83367,83369],{},[1810,83366,1959],{},[898,83368,6062],{"mathvariant":2057},[1810,83370,1854],{},[1677,83372,1967],{"separator":1966},[7266,83374],{"width":16674},[898,83376,2499],{},[1953,83378,83379,83381],{},[898,83380,5325],{},[898,83382,11183],{},[1677,83384,1686],{"stretchy":1685},[1810,83386,10423],{},[1677,83388,1967],{"separator":1966},[1810,83390,2771],{},[1677,83392,1692],{"stretchy":1685},[1677,83394,1679],{},[2006,83396,83397],{"scriptlevel":2008,"displaystyle":1685},[2010,83398,83399,83401],{},[1810,83400,37635],{},[1810,83402,1812],{},[1677,83404,2858],{},[2006,83406,83407],{"scriptlevel":2008,"displaystyle":1685},[2010,83408,83409,83411],{},[1810,83410,1959],{},[9505,83412,83413],{},[1810,83414,10423],{},[1677,83416,2858],{},[83418,83419,83420,83422],"mroot",{},[1810,83421,2771],{},[1810,83423,1854],{},[1677,83425,2411],{},[1810,83427,83428],{},"7,153.",[902,83430,83431],{"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.",[724,83433,83434,83435,45551,83457,11621,83474,83495,83496,83517],{},"Přibližná změna při ",[883,83436,83438],{"className":83437},[886],[888,83439,83440],{"xmlns":890},[892,83441,83442,83454],{},[895,83443,83444,83446,83448,83450,83452],{},[898,83445,11183],{},[1677,83447,2385],{},[1810,83449,10423],{},[1677,83451,2804],{},[1810,83453,39737],{},[902,83455,83456],{"encoding":904},"L: 20 \\to 21",[883,83458,83460],{"className":83459},[886],[888,83461,83462],{"xmlns":890},[892,83463,83464,83472],{},[895,83465,83466,83468,83470],{},[898,83467,11188],{},[1677,83469,1679],{},[1810,83471,2771],{},[902,83473,83302],{"encoding":904},[883,83475,83477],{"className":83476},[886],[888,83478,83479],{"xmlns":890},[892,83480,83481,83492],{},[895,83482,83483,83485,83487,83489],{},[898,83484,2570],{"mathvariant":2057},[898,83486,2470],{},[1677,83488,2411],{},[1810,83490,83491],{},"7,153",[902,83493,83494],{"encoding":904},"\\Delta Q \\approx 7{,}153",". Skutečně ",[883,83497,83499],{"className":83498},[886],[888,83500,83501],{"xmlns":890},[892,83502,83503,83514],{},[895,83504,83505,83507,83509,83511],{},[898,83506,2570],{"mathvariant":2057},[898,83508,2470],{},[1677,83510,2411],{},[1810,83512,83513],{},"26,888",[902,83515,83516],{"encoding":904},"\\Delta Q \\approx 26{,}888"," (dle knihy; zaokrouhlení v konkrétním výpočtu).",[724,83519,83520,83523],{},[38,83521,83522],{},"(b) Pokles kapitálu o 1"," (z 100 na 99).",[883,83525,83527],{"className":83526},[886],[888,83528,83529],{"xmlns":890,"display":29457},[892,83530,83531,83631],{},[895,83532,83533,83535,83541,83543,83551,83553,83555,83567,83581,83583,83585,83587,83593,83595,83597,83599,83601,83603,83605,83607,83611,83613,83626,83628],{},[898,83534,2499],{},[1953,83536,83537,83539],{},[898,83538,5325],{},[898,83540,11188],{},[1677,83542,1679],{},[10554,83544,83545,83547,83549],{},[898,83546,2470],{},[898,83548,11188],{},[1677,83550,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,83552,1679],{},[1810,83554,1909],{},[1805,83556,83557,83559],{},[898,83558,11183],{},[895,83560,83561,83563,83565],{},[1810,83562,1959],{},[898,83564,6062],{"mathvariant":2057},[1810,83566,1812],{},[1805,83568,83569,83571],{},[898,83570,11188],{},[895,83572,83573,83575,83577,83579],{},[1677,83574,1906],{},[1810,83576,1812],{},[898,83578,6062],{"mathvariant":2057},[1810,83580,1854],{},[1677,83582,1967],{"separator":1966},[7266,83584],{"width":16674},[898,83586,2499],{},[1953,83588,83589,83591],{},[898,83590,5325],{},[898,83592,11188],{},[1677,83594,1686],{"stretchy":1685},[1810,83596,10423],{},[1677,83598,1967],{"separator":1966},[1810,83600,2771],{},[1677,83602,1692],{"stretchy":1685},[1677,83604,1679],{},[1810,83606,1909],{},[9505,83608,83609],{},[1810,83610,10423],{},[1677,83612,2858],{},[2006,83614,83615],{"scriptlevel":2008,"displaystyle":1685},[2010,83616,83617,83619],{},[1810,83618,1959],{},[83418,83620,83621,83624],{},[1810,83622,83623],{},"10000",[1810,83625,1854],{},[1677,83627,2411],{},[1810,83629,83630],{},"4,525.",[902,83632,83633],{"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.",[724,83635,83636,83637,2366,83654,5306],{},"Produkce poklesne přibližně o 4,525 (z ",[883,83638,83640],{"className":83639},[886],[888,83641,83642],{"xmlns":890},[892,83643,83644,83651],{},[895,83645,83646,83648],{},[1677,83647,2411],{},[1810,83649,83650],{},"905,126",[902,83652,83653],{"encoding":904},"\\approx 905{,}126",[883,83655,83657],{"className":83656},[886],[888,83658,83659],{"xmlns":890},[892,83660,83661,83668],{},[895,83662,83663,83665],{},[1677,83664,2411],{},[1810,83666,83667],{},"900,601",[902,83669,83670],{"encoding":904},"\\approx 900{,}601",[724,83672,83673,2811,83720,1343,83742,5306],{},[38,83674,83675,83676,5272,83698],{},"(c) Změna ",[883,83677,83679],{"className":83678},[886],[888,83680,83681],{"xmlns":890},[892,83682,83683,83695],{},[895,83684,83685,83687,83689,83691,83693],{},[898,83686,11183],{},[1677,83688,2385],{},[1810,83690,10423],{},[1677,83692,2804],{},[1810,83694,37635],{},[902,83696,83697],{"encoding":904},"L: 20 \\to 15",[883,83699,83701],{"className":83700},[886],[888,83702,83703],{"xmlns":890},[892,83704,83705,83717],{},[895,83706,83707,83709,83711,83713,83715],{},[898,83708,11188],{},[1677,83710,2385],{},[1810,83712,2771],{},[1677,83714,2804],{},[1810,83716,10191],{},[902,83718,83719],{"encoding":904},"K: 100 \\to 150",[883,83721,83723],{"className":83722},[886],[888,83724,83725],{"xmlns":890},[892,83726,83727,83739],{},[895,83728,83729,83731,83733,83735,83737],{},[898,83730,1875],{},[898,83732,11183],{},[1677,83734,1679],{},[1677,83736,1906],{},[1810,83738,1909],{},[902,83740,83741],{"encoding":904},"dL = -5",[883,83743,83745],{"className":83744},[886],[888,83746,83747],{"xmlns":890},[892,83748,83749,83759],{},[895,83750,83751,83753,83755,83757],{},[898,83752,1875],{},[898,83754,11188],{},[1677,83756,1679],{},[1810,83758,2801],{},[902,83760,83761],{"encoding":904},"dK = 50",[883,83763,83765],{"className":83764},[886],[888,83766,83767],{"xmlns":890,"display":29457},[892,83768,83769,83857],{},[895,83770,83771,83773,83775,83777,83779,83785,83787,83789,83791,83793,83795,83797,83799,83801,83803,83805,83807,83809,83815,83817,83819,83821,83823,83825,83827,83829,83831,83833,83835,83837,83839,83841,83843,83845,83848,83850,83852,83854],{},[898,83772,1875],{},[898,83774,2470],{},[1677,83776,1679],{},[898,83778,2499],{},[1953,83780,83781,83783],{},[898,83782,5325],{},[898,83784,11183],{},[1677,83786,1686],{"stretchy":1685},[1810,83788,10423],{},[1677,83790,1967],{"separator":1966},[1810,83792,2771],{},[1677,83794,1692],{"stretchy":1685},[1677,83796,2858],{},[1677,83798,1686],{"stretchy":1685},[1677,83800,1906],{},[1810,83802,1909],{},[1677,83804,1692],{"stretchy":1685},[1677,83806,1776],{},[898,83808,2499],{},[1953,83810,83811,83813],{},[898,83812,5325],{},[898,83814,11188],{},[1677,83816,1686],{"stretchy":1685},[1810,83818,10423],{},[1677,83820,1967],{"separator":1966},[1810,83822,2771],{},[1677,83824,1692],{"stretchy":1685},[1677,83826,2858],{},[1810,83828,2801],{},[1677,83830,1679],{},[1810,83832,83491],{},[1677,83834,2858],{},[1677,83836,1686],{"stretchy":1685},[1677,83838,1906],{},[1810,83840,1909],{},[1677,83842,1692],{"stretchy":1685},[1677,83844,1776],{},[1810,83846,83847],{},"4,525",[1677,83849,2858],{},[1810,83851,2801],{},[1677,83853,2411],{},[1810,83855,83856],{},"190,485.",[902,83858,83859],{"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.",[724,83861,83862],{},"Produkce vzroste přibližně z 905,126 na 995,611.",[198,83864,83866],{"id":83865},"příklad-55","Příklad 5.5",[724,83868,83869,83870,83906,83907,1656],{},"Pro produkci ",[883,83871,83873],{"className":83872},[886],[888,83874,83875],{"xmlns":890},[892,83876,83877,83903],{},[895,83878,83879,83881,83883,83885,83887,83889,83891,83893,83899],{},[898,83880,2470],{},[1677,83882,1686],{"stretchy":1685},[898,83884,11183],{},[1677,83886,1967],{"separator":1966},[898,83888,11188],{},[1677,83890,1692],{"stretchy":1685},[1677,83892,1679],{},[83418,83894,83895,83897],{},[898,83896,11183],{},[1810,83898,1854],{},[9505,83900,83901],{},[898,83902,11188],{},[902,83904,83905],{"encoding":904},"Q(L, K) = \\sqrt[3]{L}\\sqrt{K}"," mají izokvanty rovnici ",[883,83908,83910],{"className":83909},[886],[888,83911,83912],{"xmlns":890},[892,83913,83914,83930],{},[895,83915,83916,83922,83926,83928],{},[83418,83917,83918,83920],{},[898,83919,11183],{},[1810,83921,1854],{},[9505,83923,83924],{},[898,83925,11188],{},[1677,83927,1679],{},[898,83929,82188],{},[902,83931,83932],{"encoding":904},"\\sqrt[3]{L}\\sqrt{K} = q",[724,83934,83935,83936,1656],{},"Umocněním na druhou: ",[883,83937,83939],{"className":83938},[886],[888,83940,83941],{"xmlns":890},[892,83942,83943,83967],{},[895,83944,83945,83947,83949,83955,83957],{},[898,83946,11188],{},[1677,83948,1679],{},[1805,83950,83951,83953],{},[898,83952,82188],{},[1810,83954,1812],{},[898,83956,6062],{"mathvariant":2057},[83418,83958,83959,83965],{},[1805,83960,83961,83963],{},[898,83962,11183],{},[1810,83964,1812],{},[1810,83966,1854],{},[902,83968,83969],{"encoding":904},"K = q^2 \u002F \\sqrt[3]{L^2}",[120,83971,83972,84012,84052],{},[123,83973,83974],{},[883,83975,83977],{"className":83976},[886],[888,83978,83979],{"xmlns":890},[892,83980,83981,84009],{},[895,83982,83983,83985,83987,83989,83991,83993,83995,83997,83999],{},[898,83984,82188],{},[1677,83986,1679],{},[1810,83988,1959],{},[1677,83990,5375],{},[898,83992,11188],{},[1677,83994,1679],{},[1810,83996,1959],{},[898,83998,6062],{"mathvariant":2057},[83418,84000,84001,84007],{},[1805,84002,84003,84005],{},[898,84004,11183],{},[1810,84006,1812],{},[1810,84008,1854],{},[902,84010,84011],{"encoding":904},"q = 1 \\Rightarrow K = 1\u002F\\sqrt[3]{L^2}",[123,84013,84014],{},[883,84015,84017],{"className":84016},[886],[888,84018,84019],{"xmlns":890},[892,84020,84021,84049],{},[895,84022,84023,84025,84027,84029,84031,84033,84035,84037,84039],{},[898,84024,82188],{},[1677,84026,1679],{},[1810,84028,1812],{},[1677,84030,5375],{},[898,84032,11188],{},[1677,84034,1679],{},[1810,84036,2032],{},[898,84038,6062],{"mathvariant":2057},[83418,84040,84041,84047],{},[1805,84042,84043,84045],{},[898,84044,11183],{},[1810,84046,1812],{},[1810,84048,1854],{},[902,84050,84051],{"encoding":904},"q = 2 \\Rightarrow K = 4\u002F\\sqrt[3]{L^2}",[123,84053,84054],{},[883,84055,84057],{"className":84056},[886],[888,84058,84059],{"xmlns":890},[892,84060,84061,84089],{},[895,84062,84063,84065,84067,84069,84071,84073,84075,84077,84079],{},[898,84064,82188],{},[1677,84066,1679],{},[1810,84068,1854],{},[1677,84070,5375],{},[898,84072,11188],{},[1677,84074,1679],{},[1810,84076,5387],{},[898,84078,6062],{"mathvariant":2057},[83418,84080,84081,84087],{},[1805,84082,84083,84085],{},[898,84084,11183],{},[1810,84086,1812],{},[1810,84088,1854],{},[902,84090,84091],{"encoding":904},"q = 3 \\Rightarrow K = 9\u002F\\sqrt[3]{L^2}",[724,84093,84094],{},[614,84095,84096,84097,7861,84118,1656],{},"Obrázek 5.5 — tři klesající konvexní izokvanty v rovině ",[883,84098,84100],{"className":84099},[886],[888,84101,84102],{"xmlns":890},[892,84103,84104,84116],{},[895,84105,84106,84108,84110,84112,84114],{},[1677,84107,1686],{"stretchy":1685},[898,84109,11183],{},[1677,84111,1967],{"separator":1966},[898,84113,11188],{},[1677,84115,1692],{"stretchy":1685},[902,84117,82314],{"encoding":904},[883,84119,84121],{"className":84120},[886],[888,84122,84123],{"xmlns":890},[892,84124,84125,84141],{},[895,84126,84127,84129,84131,84133,84135,84137,84139],{},[898,84128,82188],{},[1677,84130,1679],{},[1810,84132,1959],{},[1677,84134,1967],{"separator":1966},[1810,84136,1812],{},[1677,84138,1967],{"separator":1966},[1810,84140,1854],{},[902,84142,84143],{"encoding":904},"q = 1, 2, 3",[198,84145,84147],{"id":84146},"příklad-56","Příklad 5.6",[724,84149,78064,84150,1656],{},[883,84151,84153],{"className":84152},[886],[888,84154,84155],{"xmlns":890},[892,84156,84157,84173],{},[895,84158,84159,84161,84163,84165,84167,84169],{},[898,84160,2470],{},[1677,84162,1679],{},[1810,84164,1812],{},[898,84166,11183],{},[1677,84168,1776],{},[9505,84170,84171],{},[898,84172,11188],{},[902,84174,84175],{"encoding":904},"Q = 2L + \\sqrt{K}",[883,84177,84179],{"className":84178},[886],[888,84180,84181],{"xmlns":890,"display":29457},[892,84182,84183,84225],{},[895,84184,84185,84187,84193,84195,84197,84199,84201,84203,84209,84211,84223],{},[898,84186,2499],{},[1953,84188,84189,84191],{},[898,84190,5325],{},[898,84192,11183],{},[1677,84194,1679],{},[1810,84196,1812],{},[1677,84198,1967],{"separator":1966},[7266,84200],{"width":7268},[898,84202,2499],{},[1953,84204,84205,84207],{},[898,84206,5325],{},[898,84208,11188],{},[1677,84210,1679],{},[2010,84212,84213,84215],{},[1810,84214,1959],{},[895,84216,84217,84219],{},[1810,84218,1812],{},[9505,84220,84221],{},[898,84222,11188],{},[898,84224,1656],{"mathvariant":2057},[902,84226,84227],{"encoding":904},"MP_L = 2, \\qquad MP_K = \\frac{1}{2\\sqrt{K}}.",[883,84229,84231],{"className":84230},[886],[888,84232,84233],{"xmlns":890,"display":29457},[892,84234,84235,84299],{},[895,84236,84237,84239,84241,84243,84245,84247,84269,84271,84289,84291,84293,84297],{},[898,84238,2499],{},[898,84240,5382],{},[898,84242,2455],{},[898,84244,10061],{},[1677,84246,1679],{},[2010,84248,84249,84259],{},[895,84250,84251,84253],{},[898,84252,2499],{},[1953,84254,84255,84257],{},[898,84256,5325],{},[898,84258,11183],{},[895,84260,84261,84263],{},[898,84262,2499],{},[1953,84264,84265,84267],{},[898,84266,5325],{},[898,84268,11188],{},[1677,84270,1679],{},[2010,84272,84273,84275],{},[1810,84274,1812],{},[2006,84276,84277],{"scriptlevel":2008,"displaystyle":1685},[2010,84278,84279,84281],{},[1810,84280,1959],{},[895,84282,84283,84285],{},[1810,84284,1812],{},[9505,84286,84287],{},[898,84288,11188],{},[1677,84290,1679],{},[1810,84292,2032],{},[9505,84294,84295],{},[898,84296,11188],{},[898,84298,1656],{"mathvariant":2057},[902,84300,84301],{"encoding":904},"MRTS = \\frac{MP_L}{MP_K} = \\frac{2}{\\tfrac{1}{2\\sqrt{K}}} = 4\\sqrt{K}.",[724,84303,84304,84305,84348,84349,84388,84389,1656],{},"Například ",[883,84306,84308],{"className":84307},[886],[888,84309,84310],{"xmlns":890},[892,84311,84312,84345],{},[895,84313,84314,84316,84318,84320,84322,84324,84326,84328,84330,84332,84334,84336,84340,84342],{},[898,84315,2499],{},[898,84317,5382],{},[898,84319,2455],{},[898,84321,10061],{},[1677,84323,1686],{"stretchy":1685},[1810,84325,2032],{},[1677,84327,1967],{"separator":1966},[1810,84329,25592],{},[1677,84331,1692],{"stretchy":1685},[1677,84333,1679],{},[1810,84335,2032],{},[9505,84337,84338],{},[1810,84339,25592],{},[1677,84341,2411],{},[1810,84343,84344],{},"10,58",[902,84346,84347],{"encoding":904},"MRTS(4, 7) = 4\\sqrt{7} \\approx 10{,}58",". Klesne-li práce z 4 na 3, je k udržení produkce ",[883,84350,84352],{"className":84351},[886],[888,84353,84354],{"xmlns":890},[892,84355,84356,84385],{},[895,84357,84358,84360,84362,84364,84366,84368,84370,84372,84374,84376,84380,84382],{},[898,84359,2470],{},[1677,84361,1686],{"stretchy":1685},[1810,84363,2032],{},[1677,84365,1967],{"separator":1966},[1810,84367,25592],{},[1677,84369,1692],{"stretchy":1685},[1677,84371,1679],{},[1810,84373,6973],{},[1677,84375,1776],{},[9505,84377,84378],{},[1810,84379,25592],{},[1677,84381,2411],{},[1810,84383,84384],{},"10,646",[902,84386,84387],{"encoding":904},"Q(4,7) = 8 + \\sqrt{7} \\approx 10{,}646"," třeba zvýšit kapitál přibližně o ",[883,84390,84392],{"className":84391},[886],[888,84393,84394],{"xmlns":890},[892,84395,84396,84404],{},[895,84397,84398,84400],{},[1810,84399,2032],{},[9505,84401,84402],{},[1810,84403,25592],{},[902,84405,84406],{"encoding":904},"4\\sqrt{7}",[724,84408,84409,84410,84430],{},"Pokud se práce naopak zvýší ze 4 na 6 (",[883,84411,84413],{"className":84412},[886],[888,84414,84415],{"xmlns":890},[892,84416,84417,84427],{},[895,84418,84419,84421,84423,84425],{},[898,84420,1875],{},[898,84422,11183],{},[1677,84424,1679],{},[1810,84426,1812],{},[902,84428,84429],{"encoding":904},"dL = 2","), k udržení produkce stačí snížit kapitál o",[883,84432,84434],{"className":84433},[886],[888,84435,84436],{"xmlns":890,"display":29457},[892,84437,84438,84487],{},[895,84439,84440,84442,84444,84446,84448,84450,84452,84454,84456,84458,84460,84462,84464,84466,84468,84470,84472,84474,84476,84480,84482,84484],{},[898,84441,1875],{},[898,84443,11188],{},[1677,84445,1679],{},[1677,84447,1906],{},[898,84449,2499],{},[898,84451,5382],{},[898,84453,2455],{},[898,84455,10061],{},[1677,84457,1686],{"stretchy":1685},[1810,84459,2032],{},[1677,84461,1967],{"separator":1966},[1810,84463,25592],{},[1677,84465,1692],{"stretchy":1685},[1677,84467,2858],{},[1810,84469,1812],{},[1677,84471,1679],{},[1677,84473,1906],{},[1810,84475,6973],{},[9505,84477,84478],{},[1810,84479,25592],{},[1677,84481,2411],{},[1677,84483,1906],{},[1810,84485,84486],{},"21,17.",[902,84488,84489],{"encoding":904},"dK = -MRTS(4,7)\\cdot 2 = -8\\sqrt{7} \\approx -21{,}17.",[115,84491,84493],{"id":84492},"shrnutí-kapitoly-5","Shrnutí kapitoly 5",[724,84495,84496,84497,1343,84499,5272,84501,84503,84504,84507,84508,84511],{},"Hlavními faktory produkce jsou ",[38,84498,76305],{},[38,84500,76321],{},[38,84502,76337],{},"; půda je standardní exogenní proměnná. Přicházejí proto v úvahu ",[38,84505,84506],{},"jednofaktorový"," (pouze práce) a ",[38,84509,84510],{},"dvoufaktorový"," (práce + kapitál) model.",[724,84513,84514,84515,84518,84519,84521,84522,84524,84525,27580,84528,84547,84548,84565,84566,84583,84584,84606,84607,5746,84626,1656],{},"V ",[38,84516,84517],{},"1F modelu"," se definuje ",[38,84520,11412],{}," (derivace produkce podle práce) a ",[38,84523,76240],{}," (podíl produkce a práce). Produkční funkce má typický tvar díky ",[38,84526,84527],{},"zákonu klesajících výnosů",[883,84529,84531],{"className":84530},[886],[888,84532,84533],{"xmlns":890},[892,84534,84535,84545],{},[895,84536,84537,84539],{},[898,84538,2499],{},[1953,84540,84541,84543],{},[898,84542,5325],{},[898,84544,11183],{},[902,84546,11433],{"encoding":904}," nejprve roste, od inflexního bodu ",[883,84549,84551],{"className":84550},[886],[888,84552,84553],{"xmlns":890},[892,84554,84555,84563],{},[895,84556,84557],{},[1953,84558,84559,84561],{},[898,84560,11183],{},[1810,84562,2008],{},[902,84564,76949],{"encoding":904}," klesá a v bodě ",[883,84567,84569],{"className":84568},[886],[888,84570,84571],{"xmlns":890},[892,84572,84573,84581],{},[895,84574,84575],{},[1953,84576,84577,84579],{},[898,84578,11183],{},[1810,84580,1959],{},[902,84582,14602],{"encoding":904}," dosahuje nuly (maximum produkce). Platí ",[38,84585,84586,84587],{},"princip maximalizace ",[883,84588,84590],{"className":84589},[886],[888,84591,84592],{"xmlns":890},[892,84593,84594,84604],{},[895,84595,84596,84598],{},[898,84597,5643],{},[1953,84599,84600,84602],{},[898,84601,5325],{},[898,84603,11183],{},[902,84605,76024],{"encoding":904},": v bodě maxima ",[883,84608,84610],{"className":84609},[886],[888,84611,84612],{"xmlns":890},[892,84613,84614,84624],{},[895,84615,84616,84618],{},[898,84617,5643],{},[1953,84619,84620,84622],{},[898,84621,5325],{},[898,84623,11183],{},[902,84625,76024],{"encoding":904},[883,84627,84629],{"className":84628},[886],[888,84630,84631],{"xmlns":890},[892,84632,84633,84653],{},[895,84634,84635,84637,84643,84645,84647],{},[898,84636,2499],{},[1953,84638,84639,84641],{},[898,84640,5325],{},[898,84642,11183],{},[1677,84644,1679],{},[898,84646,5643],{},[1953,84648,84649,84651],{},[898,84650,5325],{},[898,84652,11183],{},[902,84654,76054],{"encoding":904},[724,84656,84657,84658,84661,84662,1884,84665,84694,84695,84712,84713,84716,84717,84746,84747,84749,84750,9490,84780,84802],{},"Ve ",[38,84659,84660],{},"2F modelu"," se obvykle používají ",[38,84663,84664],{},"Cobb-Douglasovy funkce",[883,84666,84668],{"className":84667},[886],[888,84669,84670],{"xmlns":890},[892,84671,84672,84692],{},[895,84673,84674,84676,84678,84680,84686],{},[898,84675,2470],{},[1677,84677,1679],{},[898,84679,5643],{},[1805,84681,84682,84684],{},[898,84683,11183],{},[898,84685,207],{},[1805,84687,84688,84690],{},[898,84689,11188],{},[898,84691,1779],{},[902,84693,76121],{"encoding":904},", které reflektují proporcionalitu změn vstupů a výstupu. Podle ",[883,84696,84698],{"className":84697},[886],[888,84699,84700],{"xmlns":890},[892,84701,84702,84710],{},[895,84703,84704,84706,84708],{},[898,84705,207],{},[1677,84707,1776],{},[898,84709,1779],{},[902,84711,76215],{"encoding":904}," rozlišujeme ",[38,84714,84715],{},"konstantní, rostoucí, klesající výnosy z rozsahu",". Mezní produkty ",[883,84718,84720],{"className":84719},[886],[888,84721,84722],{"xmlns":890},[892,84723,84724,84744],{},[895,84725,84726,84728,84734,84736,84738],{},[898,84727,2499],{},[1953,84729,84730,84732],{},[898,84731,5325],{},[898,84733,11183],{},[1677,84735,1967],{"separator":1966},[898,84737,2499],{},[1953,84739,84740,84742],{},[898,84741,5325],{},[898,84743,11188],{},[902,84745,76152],{"encoding":904}," jsou parciální derivace, totální diferenciál dává přibližnou změnu produkce. ",[38,84748,11166],{}," jsou indiferenční křivky produkční funkce. Podíl ",[883,84751,84753],{"className":84752},[886],[888,84754,84755],{"xmlns":890},[892,84756,84757,84777],{},[895,84758,84759,84761,84767,84769,84771],{},[898,84760,2499],{},[1953,84762,84763,84765],{},[898,84764,5325],{},[898,84766,11183],{},[898,84768,6062],{"mathvariant":2057},[898,84770,2499],{},[1953,84772,84773,84775],{},[898,84774,5325],{},[898,84776,11188],{},[902,84778,84779],{"encoding":904},"MP_L\u002FMP_K",[38,84781,84782,84783,1692],{},"mezní míra technické substituce (",[883,84784,84786],{"className":84785},[886],[888,84787,84788],{"xmlns":890},[892,84789,84790,84800],{},[895,84791,84792,84794,84796,84798],{},[898,84793,2499],{},[898,84795,5382],{},[898,84797,2455],{},[898,84799,10061],{},[902,84801,11987],{"encoding":904}," — udává, o kolik se musí změnit kapitál při jednotkové změně práce pro zachování produkce.",[115,84804,51273],{"id":51272},[152,84806,84807,84810,84813,84816,84819,84822,84825,84828,84831,84834,84837],{},[123,84808,84809],{},"Jaké jsou faktory produkce?",[123,84811,84812],{},"Jak se dospěje k jednofaktorovému a dvoufaktorovému modelu produkce?",[123,84814,84815],{},"Jak je zadána produkční funkce u jednofaktorového modelu?",[123,84817,84818],{},"Co udává mezní produkt práce?",[123,84820,84821],{},"Co musí respektovat průběh křivky produkce?",[123,84823,84824],{},"Jak lze matematicky vyjádřit zákon klesajících výnosů?",[123,84826,84827],{},"Jaký základní ekonomický požadavek respektují Cobb-Douglasovy funkce?",[123,84829,84830],{},"Jak se vypočtou mezní produkty práce a kapitálu?",[123,84832,84833],{},"Jak se stanoví přibližná změna produkce v závislosti na změnách práce a kapitálu?",[123,84835,84836],{},"Co vyjadřují izokvanty? Jaké jsou jejich typické vlastnosti?",[123,84838,84839],{},"Jak se vypočte mezní míra technické substituce a co vyjadřuje?",[115,84841,84843],{"id":84842},"úlohy-51517","Úlohy 5.1–5.17",[198,84845,41842],{"id":41841},[724,84847,84848,84851,84852,84874,84875,1343,84895,1343,84915,84935],{},[38,84849,84850],{},"5.1"," Je dána produkce ",[883,84853,84855],{"className":84854},[886],[888,84856,84857],{"xmlns":890},[892,84858,84859,84871],{},[895,84860,84861,84863,84865,84867],{},[898,84862,2470],{},[1677,84864,1679],{},[1810,84866,2544],{},[9505,84868,84869],{},[898,84870,11183],{},[902,84872,84873],{"encoding":904},"Q = 10\\sqrt{L}",". (a) Vypočtěte ",[883,84876,84878],{"className":84877},[886],[888,84879,84880],{"xmlns":890},[892,84881,84882,84892],{},[895,84883,84884,84886,84888,84890],{},[898,84885,2470],{},[1677,84887,1686],{"stretchy":1685},[1810,84889,1959],{},[1677,84891,1692],{"stretchy":1685},[902,84893,84894],{"encoding":904},"Q(1)",[883,84896,84898],{"className":84897},[886],[888,84899,84900],{"xmlns":890},[892,84901,84902,84912],{},[895,84903,84904,84906,84908,84910],{},[898,84905,2470],{},[1677,84907,1686],{"stretchy":1685},[1810,84909,2032],{},[1677,84911,1692],{"stretchy":1685},[902,84913,84914],{"encoding":904},"Q(4)",[883,84916,84918],{"className":84917},[886],[888,84919,84920],{"xmlns":890},[892,84921,84922,84932],{},[895,84923,84924,84926,84928,84930],{},[898,84925,2470],{},[1677,84927,1686],{"stretchy":1685},[1810,84929,5387],{},[1677,84931,1692],{"stretchy":1685},[902,84933,84934],{"encoding":904},"Q(9)",". (b) Rozhodněte, kdy produkce roste, resp. klesá. (c) Rozhodněte, kdy je křivka produkce konvexní, resp. konkávní. (d) Načrtněte křivku produkce.",[724,84937,84938,84851,84941,84977,84978,84991,84992,85011,85012,85038,85039,2366,85052,85065],{},[38,84939,84940],{},"5.2",[883,84942,84944],{"className":84943},[886],[888,84945,84946],{"xmlns":890},[892,84947,84948,84974],{},[895,84949,84950,84952,84954,84956,84958,84964,84966,84968],{},[898,84951,2470],{},[1677,84953,1679],{},[1677,84955,1906],{},[1810,84957,2475],{},[1805,84959,84960,84962],{},[898,84961,11183],{},[1810,84963,1854],{},[1677,84965,1776],{},[1810,84967,5387],{},[1805,84969,84970,84972],{},[898,84971,11183],{},[1810,84973,1812],{},[902,84975,84976],{"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 ",[883,84979,84981],{"className":84980},[886],[888,84982,84983],{"xmlns":890},[892,84984,84985,84989],{},[895,84986,84987],{},[898,84988,11183],{},[902,84990,11183],{"encoding":904}," (počet pracovníků), které maximalizuje produkci a stanovte příslušné maximum produkce. (d) Načrtněte křivku produkce. (e) Najděte mezní produkt práce ",[883,84993,84995],{"className":84994},[886],[888,84996,84997],{"xmlns":890},[892,84998,84999,85009],{},[895,85000,85001,85003],{},[898,85002,2499],{},[1953,85004,85005,85007],{},[898,85006,5325],{},[898,85008,11183],{},[902,85010,11433],{"encoding":904},". (f) Vypočtěte ",[883,85013,85015],{"className":85014},[886],[888,85016,85017],{"xmlns":890},[892,85018,85019,85035],{},[895,85020,85021,85023,85029,85031,85033],{},[898,85022,2499],{},[1953,85024,85025,85027],{},[898,85026,5325],{},[898,85028,11183],{},[1677,85030,1686],{"stretchy":1685},[1810,85032,2544],{},[1677,85034,1692],{"stretchy":1685},[902,85036,85037],{"encoding":904},"MP_L(10)"," a ekonomicky interpretujte. (g) Určete přibližnou změnu produkce v důsledku zvýšení počtu pracovníků z ",[883,85040,85042],{"className":85041},[886],[888,85043,85044],{"xmlns":890},[892,85045,85046,85050],{},[895,85047,85048],{},[1810,85049,2544],{},[902,85051,2544],{"encoding":904},[883,85053,85055],{"className":85054},[886],[888,85056,85057],{"xmlns":890},[892,85058,85059,85063],{},[895,85060,85061],{},[1810,85062,43678],{},[902,85064,43678],{"encoding":904}," a porovnejte se skutečnou změnou produkce.",[724,85067,85068,85071,85072,85094,85095,85123,85124,85155,85156,1656],{},[38,85069,85070],{},"5.3"," Pro zadanou produkci ověřte platnost zákona klesajících výnosů a charakterizujte vlastnosti mezního produktu práce:\n(a) ",[883,85073,85075],{"className":85074},[886],[888,85076,85077],{"xmlns":890},[892,85078,85079,85091],{},[895,85080,85081,85083,85085,85087],{},[898,85082,2470],{},[1677,85084,1679],{},[1810,85086,16500],{},[9505,85088,85089],{},[898,85090,11183],{},[902,85092,85093],{"encoding":904},"Q = 500\\sqrt{L}",".\n(b) ",[883,85096,85098],{"className":85097},[886],[888,85099,85100],{"xmlns":890},[892,85101,85102,85120],{},[895,85103,85104,85106,85108,85110,85114,85116,85118],{},[898,85105,2470],{},[1677,85107,1679],{},[1810,85109,31472],{},[9505,85111,85112],{},[898,85113,11183],{},[1677,85115,1906],{},[1810,85117,2032],{},[898,85119,11183],{},[902,85121,85122],{"encoding":904},"Q = 300\\sqrt{L} - 4L",".\n(c) ",[883,85125,85127],{"className":85126},[886],[888,85128,85129],{"xmlns":890},[892,85130,85131,85152],{},[895,85132,85133,85135,85137,85139,85141,85143,85146],{},[898,85134,2470],{},[1677,85136,1679],{},[1810,85138,2801],{},[898,85140,11183],{},[1677,85142,1906],{},[1810,85144,85145],{},"0,01",[1805,85147,85148,85150],{},[898,85149,11183],{},[1810,85151,1812],{},[902,85153,85154],{"encoding":904},"Q = 50L - 0{,}01 L^{2}",".\n(d) ",[883,85157,85159],{"className":85158},[886],[888,85160,85161],{"xmlns":890},[892,85162,85163,85189],{},[895,85164,85165,85167,85169,85171,85173,85179,85181,85183],{},[898,85166,2470],{},[1677,85168,1679],{},[1677,85170,1906],{},[1810,85172,69602],{},[1805,85174,85175,85177],{},[898,85176,11183],{},[1810,85178,1854],{},[1677,85180,1776],{},[1810,85182,5387],{},[1805,85184,85185,85187],{},[898,85186,11183],{},[1810,85188,1812],{},[902,85190,85191],{"encoding":904},"Q = -0{,}3 L^{3} + 9 L^{2}",[724,85193,85194,85197,85198,2305,85217,73589,85234,1656],{},[38,85195,85196],{},"5.4"," Dokažte, že má-li průměrný produkt práce ",[883,85199,85201],{"className":85200},[886],[888,85202,85203],{"xmlns":890},[892,85204,85205,85215],{},[895,85206,85207,85209],{},[898,85208,5643],{},[1953,85210,85211,85213],{},[898,85212,5325],{},[898,85214,11183],{},[902,85216,76024],{"encoding":904},[883,85218,85220],{"className":85219},[886],[888,85221,85222],{"xmlns":890},[892,85223,85224,85232],{},[895,85225,85226],{},[1953,85227,85228,85230],{},[898,85229,11183],{},[1810,85231,2008],{},[902,85233,76949],{"encoding":904},[883,85235,85237],{"className":85236},[886],[888,85238,85239],{"xmlns":890},[892,85240,85241,85281],{},[895,85242,85243,85245,85251,85253,85259,85261,85263,85265,85271,85273,85279],{},[898,85244,5643],{},[1953,85246,85247,85249],{},[898,85248,5325],{},[898,85250,11183],{},[1677,85252,1686],{"stretchy":1685},[1953,85254,85255,85257],{},[898,85256,11183],{},[1810,85258,2008],{},[1677,85260,1692],{"stretchy":1685},[1677,85262,1679],{},[898,85264,2499],{},[1953,85266,85267,85269],{},[898,85268,5325],{},[898,85270,11183],{},[1677,85272,1686],{"stretchy":1685},[1953,85274,85275,85277],{},[898,85276,11183],{},[1810,85278,2008],{},[1677,85280,1692],{"stretchy":1685},[902,85282,85283],{"encoding":904},"AP_L(L_0) = MP_L(L_0)",[724,85285,85286,84851,85289,22985,85325,85338,85339,85358],{},[38,85287,85288],{},"5.5",[883,85290,85292],{"className":85291},[886],[888,85293,85294],{"xmlns":890},[892,85295,85296,85322],{},[895,85297,85298,85300,85302,85304,85306,85312,85314,85316],{},[898,85299,2470],{},[1677,85301,1679],{},[1677,85303,1906],{},[1810,85305,2520],{},[1805,85307,85308,85310],{},[898,85309,11183],{},[1810,85311,1854],{},[1677,85313,1776],{},[1810,85315,3190],{},[1805,85317,85318,85320],{},[898,85319,11183],{},[1810,85321,1812],{},[902,85323,85324],{"encoding":904},"Q = -0{,}2 L^{3} + 12 L^{2}",[883,85326,85328],{"className":85327},[886],[888,85329,85330],{"xmlns":890},[892,85331,85332,85336],{},[895,85333,85334],{},[898,85335,11183],{},[902,85337,11183],{"encoding":904}," je počet pracovníků. (a) Určete počet pracovníků, při kterém je dosaženo nejvyšší produktivity práce (= maximálního průměrného produktu práce ",[883,85340,85342],{"className":85341},[886],[888,85343,85344],{"xmlns":890},[892,85345,85346,85356],{},[895,85347,85348,85350],{},[898,85349,5643],{},[1953,85351,85352,85354],{},[898,85353,5325],{},[898,85355,11183],{},[902,85357,76024],{"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.",[198,85360,85362],{"id":85361},"dvoufaktorový-model","Dvoufaktorový model",[724,85364,85365,85368,85369,85094,85395,85123,85437,1656],{},[38,85366,85367],{},"5.6"," Pro zadanou produkci rozhodněte, jaké výnosy z rozsahu představují:\n(a) ",[883,85370,85372],{"className":85371},[886],[888,85373,85374],{"xmlns":890},[892,85375,85376,85392],{},[895,85377,85378,85380,85382,85384,85386],{},[898,85379,2470],{},[1677,85381,1679],{},[1810,85383,25592],{},[898,85385,11183],{},[1805,85387,85388,85390],{},[898,85389,11188],{},[1810,85391,1812],{},[902,85393,85394],{"encoding":904},"Q = 7 L K^{2}",[883,85396,85398],{"className":85397},[886],[888,85399,85400],{"xmlns":890},[892,85401,85402,85434],{},[895,85403,85404,85406,85408,85410,85422],{},[898,85405,2470],{},[1677,85407,1679],{},[1810,85409,2801],{},[1805,85411,85412,85414],{},[898,85413,11183],{},[895,85415,85416,85418,85420],{},[1810,85417,1812],{},[898,85419,6062],{"mathvariant":2057},[1810,85421,1854],{},[1805,85423,85424,85426],{},[898,85425,11188],{},[895,85427,85428,85430,85432],{},[1810,85429,1959],{},[898,85431,6062],{"mathvariant":2057},[1810,85433,1854],{},[902,85435,85436],{"encoding":904},"Q = 50 L^{2\u002F3} K^{1\u002F3}",[883,85438,85440],{"className":85439},[886],[888,85441,85442],{"xmlns":890},[892,85443,85444,85476],{},[895,85445,85446,85448,85450,85452,85464],{},[898,85447,2470],{},[1677,85449,1679],{},[1810,85451,3388],{},[1805,85453,85454,85456],{},[898,85455,11183],{},[895,85457,85458,85460,85462],{},[1810,85459,1854],{},[898,85461,6062],{"mathvariant":2057},[1810,85463,1909],{},[1805,85465,85466,85468],{},[898,85467,11188],{},[895,85469,85470,85472,85474],{},[1810,85471,1812],{},[898,85473,6062],{"mathvariant":2057},[1810,85475,1909],{},[902,85477,85478],{"encoding":904},"Q = 18 L^{3\u002F5} K^{2\u002F5}",[724,85480,85481,84851,85484,85526,85527,1343,85545,85564,85565,85582],{},[38,85482,85483],{},"5.7",[883,85485,85487],{"className":85486},[886],[888,85488,85489],{"xmlns":890},[892,85490,85491,85523],{},[895,85492,85493,85495,85497,85499,85511],{},[898,85494,2470],{},[1677,85496,1679],{},[1810,85498,2544],{},[1805,85500,85501,85503],{},[898,85502,11183],{},[895,85504,85505,85507,85509],{},[1810,85506,1959],{},[898,85508,6062],{"mathvariant":2057},[1810,85510,1812],{},[1805,85512,85513,85515],{},[898,85514,11188],{},[895,85516,85517,85519,85521],{},[1810,85518,1959],{},[898,85520,6062],{"mathvariant":2057},[1810,85522,1812],{},[902,85524,85525],{"encoding":904},"Q = 10 L^{1\u002F2} K^{1\u002F2}",". (a) Vypočtěte produkci pro ",[883,85528,85530],{"className":85529},[886],[888,85531,85532],{"xmlns":890},[892,85533,85534,85542],{},[895,85535,85536,85538,85540],{},[898,85537,11183],{},[1677,85539,1679],{},[1810,85541,21533],{},[902,85543,85544],{"encoding":904},"L = 400",[883,85546,85548],{"className":85547},[886],[888,85549,85550],{"xmlns":890},[892,85551,85552,85561],{},[895,85553,85554,85556,85558],{},[898,85555,11188],{},[1677,85557,1679],{},[1810,85559,85560],{},"17576",[902,85562,85563],{"encoding":904},"K = 17576",". (b) Rozhodněte o tom, jaké výnosy z rozsahu představuje a vyložte, jak se změní produkce, jestliže se vstupy ",[883,85566,85568],{"className":85567},[886],[888,85569,85570],{"xmlns":890},[892,85571,85572,85580],{},[895,85573,85574,85576,85578],{},[898,85575,11183],{},[1677,85577,1967],{"separator":1966},[898,85579,11188],{},[902,85581,80376],{"encoding":904}," zdvojnásobí.",[724,85584,85585,85588,85589,85526,85620,1343,85638,70975,85656,85686,85687,85717,85718,2366,85731,85745,85746,2366,85759,85772],{},[38,85586,85587],{},"5.8"," V jedné empirické studii (40. léta 20. století) ze sektoru manufaktur odhadli Cobb a Douglas produkci ze zjištěných údajů ve tvaru ",[883,85590,85592],{"className":85591},[886],[888,85593,85594],{"xmlns":890},[892,85595,85596,85617],{},[895,85597,85598,85600,85602,85605,85611],{},[898,85599,2470],{},[1677,85601,1679],{},[1810,85603,85604],{},"1,01",[1805,85606,85607,85609],{},[898,85608,11183],{},[1810,85610,25121],{},[1805,85612,85613,85615],{},[898,85614,11188],{},[1810,85616,25180],{},[902,85618,85619],{"encoding":904},"Q = 1{,}01 L^{0{,}75} K^{0{,}25}",[883,85621,85623],{"className":85622},[886],[888,85624,85625],{"xmlns":890},[892,85626,85627,85635],{},[895,85628,85629,85631,85633],{},[898,85630,11183],{},[1677,85632,1679],{},[1810,85634,32134],{},[902,85636,85637],{"encoding":904},"L = 250",[883,85639,85641],{"className":85640},[886],[888,85642,85643],{"xmlns":890},[892,85644,85645,85653],{},[895,85646,85647,85649,85651],{},[898,85648,11188],{},[1677,85650,1679],{},[1810,85652,2463],{},[902,85654,85655],{"encoding":904},"K = 1000",[883,85657,85659],{"className":85658},[886],[888,85660,85661],{"xmlns":890},[892,85662,85663,85683],{},[895,85664,85665,85667,85673,85675,85677,85679,85681],{},[898,85666,2499],{},[1953,85668,85669,85671],{},[898,85670,5325],{},[898,85672,11183],{},[1677,85674,1686],{"stretchy":1685},[1810,85676,32134],{},[1677,85678,1967],{"separator":1966},[1810,85680,2463],{},[1677,85682,1692],{"stretchy":1685},[902,85684,85685],{"encoding":904},"MP_L(250, 1000)"," a výsledek ekonomicky interpretujte. (c) Vypočtěte ",[883,85688,85690],{"className":85689},[886],[888,85691,85692],{"xmlns":890},[892,85693,85694,85714],{},[895,85695,85696,85698,85704,85706,85708,85710,85712],{},[898,85697,2499],{},[1953,85699,85700,85702],{},[898,85701,5325],{},[898,85703,11188],{},[1677,85705,1686],{"stretchy":1685},[1810,85707,32134],{},[1677,85709,1967],{"separator":1966},[1810,85711,2463],{},[1677,85713,1692],{"stretchy":1685},[902,85715,85716],{"encoding":904},"MP_K(250, 1000)"," a výsledek ekonomicky interpretujte. (d) Odhadněte změnu produkce v důsledku zvýšení ",[883,85719,85721],{"className":85720},[886],[888,85722,85723],{"xmlns":890},[892,85724,85725,85729],{},[895,85726,85727],{},[898,85728,11183],{},[902,85730,11183],{"encoding":904},[883,85732,85734],{"className":85733},[886],[888,85735,85736],{"xmlns":890},[892,85737,85738,85743],{},[895,85739,85740],{},[1810,85741,85742],{},"260",[902,85744,85742],{"encoding":904}," a současném poklesu ",[883,85747,85749],{"className":85748},[886],[888,85750,85751],{"xmlns":890},[892,85752,85753,85757],{},[895,85754,85755],{},[898,85756,11188],{},[902,85758,11188],{"encoding":904},[883,85760,85762],{"className":85761},[886],[888,85763,85764],{"xmlns":890},[892,85765,85766,85770],{},[895,85767,85768],{},[1810,85769,16581],{},[902,85771,16581],{"encoding":904}," vzhledem k hladině dle (a) a porovnejte se skutečnou změnou produkce.",[724,85774,85775,85778,85779,1656],{},[38,85776,85777],{},"5.9"," Ověřte platnost zákona klesajících výnosů pro produkci ",[883,85780,85782],{"className":85781},[886],[888,85783,85784],{"xmlns":890},[892,85785,85786,85806],{},[895,85787,85788,85790,85792,85794,85800],{},[898,85789,2470],{},[1677,85791,1679],{},[1810,85793,2544],{},[1805,85795,85796,85798],{},[898,85797,11183],{},[1810,85799,69602],{},[1805,85801,85802,85804],{},[898,85803,11188],{},[1810,85805,6397],{},[902,85807,85808],{"encoding":904},"Q = 10 L^{0{,}3} K^{0{,}5}",[724,85810,85811,85814,85815,81972,85838,11782,85851,11413,85901,5306],{},[38,85812,85813],{},"5.10"," Dokažte, že pro homogenní funkci ",[883,85816,85818],{"className":85817},[886],[888,85819,85820],{"xmlns":890},[892,85821,85822,85836],{},[895,85823,85824,85826,85828,85830,85832,85834],{},[898,85825,2470],{},[1677,85827,1686],{"stretchy":1685},[898,85829,11183],{},[1677,85831,1967],{"separator":1966},[898,85833,11188],{},[1677,85835,1692],{"stretchy":1685},[902,85837,11385],{"encoding":904},[883,85839,85841],{"className":85840},[886],[888,85842,85843],{"xmlns":890},[892,85844,85845,85849],{},[895,85846,85847],{},[898,85848,38251],{},[902,85850,38251],{"encoding":904},[883,85852,85854],{"className":85853},[886],[888,85855,85856],{"xmlns":890},[892,85857,85858,85898],{},[895,85859,85860,85862,85870,85872,85874,85882,85884,85886,85888,85890,85892,85894,85896],{},[898,85861,11183],{},[10554,85863,85864,85866,85868],{},[898,85865,2470],{},[898,85867,11183],{},[1677,85869,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,85871,1776],{},[898,85873,11188],{},[10554,85875,85876,85878,85880],{},[898,85877,2470],{},[898,85879,11188],{},[1677,85881,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,85883,1679],{},[898,85885,38251],{},[898,85887,2470],{},[1677,85889,1686],{"stretchy":1685},[898,85891,11183],{},[1677,85893,1967],{"separator":1966},[898,85895,11188],{},[1677,85897,1692],{"stretchy":1685},[902,85899,85900],{"encoding":904},"L Q'_L + K Q'_K = n Q(L, K)",[614,85902,81947],{},[724,85904,85905,85908],{},[38,85906,85907],{},"5.11"," Ověřte platnost Eulerovy věty (úloha 5.10) pro Cobb-Douglasovu produkční funkci.",[724,85910,85911,84851,85914,85954,85955,1343,85977,1343,85999,86021],{},[38,85912,85913],{},"5.12",[883,85915,85917],{"className":85916},[886],[888,85918,85919],{"xmlns":890},[892,85920,85921,85951],{},[895,85922,85923,85925,85927,85939],{},[898,85924,2470],{},[1677,85926,1679],{},[1805,85928,85929,85931],{},[898,85930,11183],{},[895,85932,85933,85935,85937],{},[1810,85934,1959],{},[898,85936,6062],{"mathvariant":2057},[1810,85938,1854],{},[1805,85940,85941,85943],{},[898,85942,11188],{},[895,85944,85945,85947,85949],{},[1810,85946,1959],{},[898,85948,6062],{"mathvariant":2057},[1810,85950,2032],{},[902,85952,85953],{"encoding":904},"Q = L^{1\u002F3} K^{1\u002F4}",". (a) Najděte rovnici izokvant. (b) Najděte rovnici izokvant pro produkci ",[883,85956,85958],{"className":85957},[886],[888,85959,85960],{"xmlns":890},[892,85961,85962,85974],{},[895,85963,85964,85970,85972],{},[1953,85965,85966,85968],{},[898,85967,82188],{},[1810,85969,2008],{},[1677,85971,1679],{},[1810,85973,1959],{},[902,85975,85976],{"encoding":904},"q_0 = 1",[883,85978,85980],{"className":85979},[886],[888,85981,85982],{"xmlns":890},[892,85983,85984,85996],{},[895,85985,85986,85992,85994],{},[1953,85987,85988,85990],{},[898,85989,82188],{},[1810,85991,1959],{},[1677,85993,1679],{},[1810,85995,1812],{},[902,85997,85998],{"encoding":904},"q_1 = 2",[883,86000,86002],{"className":86001},[886],[888,86003,86004],{"xmlns":890},[892,86005,86006,86018],{},[895,86007,86008,86014,86016],{},[1953,86009,86010,86012],{},[898,86011,82188],{},[1810,86013,1812],{},[1677,86015,1679],{},[1810,86017,1854],{},[902,86019,86020],{"encoding":904},"q_2 = 3",". (c) Načrtněte izokvanty.",[724,86023,86024,84851,86027,86067,86068,1343,86096,1343,86124,1343,86152,1343,86181,1343,86210,1343,86239,1343,86268,1343,86297,1656],{},[38,86025,86026],{},"5.13",[883,86028,86030],{"className":86029},[886],[888,86031,86032],{"xmlns":890},[892,86033,86034,86064],{},[895,86035,86036,86038,86040,86052],{},[898,86037,2470],{},[1677,86039,1679],{},[1805,86041,86042,86044],{},[898,86043,11183],{},[895,86045,86046,86048,86050],{},[1810,86047,1959],{},[898,86049,6062],{"mathvariant":2057},[1810,86051,1854],{},[1805,86053,86054,86056],{},[898,86055,11188],{},[895,86057,86058,86060,86062],{},[1810,86059,1959],{},[898,86061,6062],{"mathvariant":2057},[1810,86063,1812],{},[902,86065,86066],{"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): ",[883,86069,86071],{"className":86070},[886],[888,86072,86073],{"xmlns":890},[892,86074,86075,86093],{},[895,86076,86077,86083,86085,86087,86089,86091],{},[1953,86078,86079,86081],{},[898,86080,5643],{},[1810,86082,1959],{},[1677,86084,2167],{"stretchy":1685},[1810,86086,1959],{},[1677,86088,9813],{"separator":1966},[1810,86090,1959],{},[1677,86092,2182],{"stretchy":1685},[902,86094,86095],{"encoding":904},"A_1[1; 1]",[883,86097,86099],{"className":86098},[886],[888,86100,86101],{"xmlns":890},[892,86102,86103,86121],{},[895,86104,86105,86111,86113,86115,86117,86119],{},[1953,86106,86107,86109],{},[898,86108,5643],{},[1810,86110,1812],{},[1677,86112,2167],{"stretchy":1685},[1810,86114,1959],{},[1677,86116,9813],{"separator":1966},[1810,86118,6973],{},[1677,86120,2182],{"stretchy":1685},[902,86122,86123],{"encoding":904},"A_2[1; 8]",[883,86125,86127],{"className":86126},[886],[888,86128,86129],{"xmlns":890},[892,86130,86131,86149],{},[895,86132,86133,86139,86141,86143,86145,86147],{},[1953,86134,86135,86137],{},[898,86136,5643],{},[1810,86138,1854],{},[1677,86140,2167],{"stretchy":1685},[1810,86142,1959],{},[1677,86144,9813],{"separator":1966},[1810,86146,67988],{},[1677,86148,2182],{"stretchy":1685},[902,86150,86151],{"encoding":904},"A_3[1; 27]",[883,86153,86155],{"className":86154},[886],[888,86156,86157],{"xmlns":890},[892,86158,86159,86178],{},[895,86160,86161,86167,86169,86171,86173,86176],{},[1953,86162,86163,86165],{},[898,86164,5643],{},[1810,86166,2032],{},[1677,86168,2167],{"stretchy":1685},[1810,86170,1812],{},[1677,86172,9813],{"separator":1966},[1810,86174,86175],{},"0,353",[1677,86177,2182],{"stretchy":1685},[902,86179,86180],{"encoding":904},"A_4[2; 0{,}353]",[883,86182,86184],{"className":86183},[886],[888,86185,86186],{"xmlns":890},[892,86187,86188,86207],{},[895,86189,86190,86196,86198,86200,86202,86205],{},[1953,86191,86192,86194],{},[898,86193,5643],{},[1810,86195,1909],{},[1677,86197,2167],{"stretchy":1685},[1810,86199,1812],{},[1677,86201,9813],{"separator":1966},[1810,86203,86204],{},"2,828",[1677,86206,2182],{"stretchy":1685},[902,86208,86209],{"encoding":904},"A_5[2; 2{,}828]",[883,86211,86213],{"className":86212},[886],[888,86214,86215],{"xmlns":890},[892,86216,86217,86236],{},[895,86218,86219,86225,86227,86229,86231,86234],{},[1953,86220,86221,86223],{},[898,86222,5643],{},[1810,86224,1916],{},[1677,86226,2167],{"stretchy":1685},[1810,86228,1812],{},[1677,86230,9813],{"separator":1966},[1810,86232,86233],{},"9,545",[1677,86235,2182],{"stretchy":1685},[902,86237,86238],{"encoding":904},"A_6[2; 9{,}545]",[883,86240,86242],{"className":86241},[886],[888,86243,86244],{"xmlns":890},[892,86245,86246,86265],{},[895,86247,86248,86254,86256,86258,86260,86263],{},[1953,86249,86250,86252],{},[898,86251,5643],{},[1810,86253,25592],{},[1677,86255,2167],{"stretchy":1685},[1810,86257,65950],{},[1677,86259,9813],{"separator":1966},[1810,86261,86262],{},"0,544",[1677,86264,2182],{"stretchy":1685},[902,86266,86267],{"encoding":904},"A_7[1{,}5; 0{,}544]",[883,86269,86271],{"className":86270},[886],[888,86272,86273],{"xmlns":890},[892,86274,86275,86294],{},[895,86276,86277,86283,86285,86287,86289,86292],{},[1953,86278,86279,86281],{},[898,86280,5643],{},[1810,86282,6973],{},[1677,86284,2167],{"stretchy":1685},[1810,86286,65950],{},[1677,86288,9813],{"separator":1966},[1810,86290,86291],{},"14,696",[1677,86293,2182],{"stretchy":1685},[902,86295,86296],{"encoding":904},"A_8[1{,}5; 14{,}696]",[883,86298,86300],{"className":86299},[886],[888,86301,86302],{"xmlns":890},[892,86303,86304,86322],{},[895,86305,86306,86312,86314,86316,86318,86320],{},[1953,86307,86308,86310],{},[898,86309,5643],{},[1810,86311,5387],{},[1677,86313,2167],{"stretchy":1685},[1810,86315,1812],{},[1677,86317,9813],{"separator":1966},[1810,86319,1909],{},[1677,86321,2182],{"stretchy":1685},[902,86323,86324],{"encoding":904},"A_9[2; 5]",[724,86326,86327,86330],{},[38,86328,86329],{},"5.14"," Dokažte, že izokvanty Cobb-Douglasovy produkční funkce jsou klesající a konvexní.",[724,86332,86333,86336,86337,86367,86368,86381,86382,86395,86396,70708,86415,86434,86435,1656],{},[38,86334,86335],{},"5.15"," Produkce firmy je dána vztahem ",[883,86338,86340],{"className":86339},[886],[888,86341,86342],{"xmlns":890},[892,86343,86344,86364],{},[895,86345,86346,86348,86350,86352,86358],{},[898,86347,2470],{},[1677,86349,1679],{},[1810,86351,1812],{},[1805,86353,86354,86356],{},[898,86355,11183],{},[1810,86357,6397],{},[1805,86359,86360,86362],{},[898,86361,11188],{},[1810,86363,25180],{},[902,86365,86366],{"encoding":904},"Q = 2 L^{0{,}5} K^{0{,}25}",". (a) Vypočtěte produkci, mezní produkt práce a mezní produkt kapitálu, zaměstnává-li firma ",[883,86369,86371],{"className":86370},[886],[888,86372,86373],{"xmlns":890},[892,86374,86375,86379],{},[895,86376,86377],{},[1810,86378,2771],{},[902,86380,2771],{"encoding":904}," pracovníků a disponuje-li ",[883,86383,86385],{"className":86384},[886],[888,86386,86387],{"xmlns":890},[892,86388,86389,86393],{},[895,86390,86391],{},[1810,86392,65826],{},[902,86394,65826],{"encoding":904}," jednotkami kapitálu. (b) Určete mezní míru technické substituce ",[883,86397,86399],{"className":86398},[886],[888,86400,86401],{"xmlns":890},[892,86402,86403,86413],{},[895,86404,86405,86407,86409,86411],{},[898,86406,2499],{},[898,86408,5382],{},[898,86410,2455],{},[898,86412,10061],{},[902,86414,11987],{"encoding":904},[883,86416,86418],{"className":86417},[886],[888,86419,86420],{"xmlns":890},[892,86421,86422,86432],{},[895,86423,86424,86426,86428,86430],{},[898,86425,2499],{},[898,86427,5382],{},[898,86429,2455],{},[898,86431,10061],{},[902,86433,11987],{"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 ",[883,86436,86438],{"className":86437},[886],[888,86439,86440],{"xmlns":890},[892,86441,86442,86447],{},[895,86443,86444],{},[1810,86445,86446],{},"95",[902,86448,86446],{"encoding":904},[724,86450,86451,84851,86454,72382,86486,86505,86506,86519,86520,86533,86534,86547],{},[38,86452,86453],{},"5.16",[883,86455,86457],{"className":86456},[886],[888,86458,86459],{"xmlns":890},[892,86460,86461,86483],{},[895,86462,86463,86465,86467,86473,86475,86477],{},[898,86464,2470],{},[1677,86466,1679],{},[1805,86468,86469,86471],{},[898,86470,11188],{},[1810,86472,1812],{},[1677,86474,1776],{},[1810,86476,1812],{},[1805,86478,86479,86481],{},[898,86480,11183],{},[1810,86482,1812],{},[902,86484,86485],{"encoding":904},"Q = K^{2} + 2 L^{2}",[883,86487,86489],{"className":86488},[886],[888,86490,86491],{"xmlns":890},[892,86492,86493,86503],{},[895,86494,86495,86497,86499,86501],{},[898,86496,2499],{},[898,86498,5382],{},[898,86500,2455],{},[898,86502,10061],{},[902,86504,11987],{"encoding":904},". (b) Odhadněte změnu práce potřebné k udržení produkce, která je realizována ",[883,86507,86509],{"className":86508},[886],[888,86510,86511],{"xmlns":890},[892,86512,86513,86517],{},[895,86514,86515],{},[1810,86516,2801],{},[902,86518,2801],{"encoding":904}," pracovníky a ",[883,86521,86523],{"className":86522},[886],[888,86524,86525],{"xmlns":890},[892,86526,86527,86531],{},[895,86528,86529],{},[1810,86530,79008],{},[902,86532,79008],{"encoding":904}," jednotkami kapitálu, jestliže se kapitál sníží na ",[883,86535,86537],{"className":86536},[886],[888,86538,86539],{"xmlns":890},[892,86540,86541,86545],{},[895,86542,86543],{},[1810,86544,48094],{},[902,86546,48094],{"encoding":904}," jednotek.",[724,86549,86550,86553,86554,11782,86584,1656],{},[38,86551,86552],{},"5.17"," Odvoďte, že pro Cobb-Douglasovu produkční funkci ",[883,86555,86557],{"className":86556},[886],[888,86558,86559],{"xmlns":890},[892,86560,86561,86581],{},[895,86562,86563,86565,86567,86569,86575],{},[898,86564,2470],{},[1677,86566,1679],{},[898,86568,5643],{},[1805,86570,86571,86573],{},[898,86572,11183],{},[898,86574,207],{},[1805,86576,86577,86579],{},[898,86578,11188],{},[898,86580,1779],{},[902,86582,86583],{"encoding":904},"Q = A L^{a} K^{b}",[883,86585,86587],{"className":86586},[886],[888,86588,86589],{"xmlns":890},[892,86590,86591,86621],{},[895,86592,86593,86595,86597,86599,86601,86603,86611,86613],{},[898,86594,2499],{},[898,86596,5382],{},[898,86598,2455],{},[898,86600,10061],{},[1677,86602,1679],{},[2006,86604,86605],{"scriptlevel":2008,"displaystyle":1685},[2010,86606,86607,86609],{},[898,86608,207],{},[898,86610,1779],{},[1677,86612,2858],{},[2006,86614,86615],{"scriptlevel":2008,"displaystyle":1685},[2010,86616,86617,86619],{},[898,86618,11188],{},[898,86620,11183],{},[902,86622,86623],{"encoding":904},"MRTS = \\tfrac{a}{b}\\cdot \\tfrac{K}{L}",[115,86625,17110],{"id":17109},[120,86627,86628,86661,86688,86697,86747,86778,86831,86854,86909,86982,87060,87103,87135,87168,87209,87281,87342,87408,87425,87498,87564,87616,87672,87706,87749],{},[123,86629,86630,86633,86634,38287,86647,86660],{},[38,86631,86632],{},"Faktory (vstupy) produkce:"," práce ",[883,86635,86637],{"className":86636},[886],[888,86638,86639],{"xmlns":890},[892,86640,86641,86645],{},[895,86642,86643],{},[898,86644,11183],{},[902,86646,11183],{"encoding":904},[883,86648,86650],{"className":86649},[886],[888,86651,86652],{"xmlns":890},[892,86653,86654,86658],{},[895,86655,86656],{},[898,86657,11188],{},[902,86659,11188],{"encoding":904},", půda.",[123,86662,86663,8403,86665,1656],{},[38,86664,41842],{},[883,86666,86668],{"className":86667},[886],[888,86669,86670],{"xmlns":890},[892,86671,86672,86686],{},[895,86673,86674,86676,86678,86680,86682,86684],{},[898,86675,2470],{},[1677,86677,1679],{},[898,86679,2470],{},[1677,86681,1686],{"stretchy":1685},[898,86683,11183],{},[1677,86685,1692],{"stretchy":1685},[902,86687,75935],{"encoding":904},[123,86689,86690,11413,86692,13518,86695,1656],{},[38,86691,859],{},[614,86693,86694],{},"production function",[38,86696,76438],{},[123,86698,86699,1884,86701,1656],{},[38,86700,76484],{},[883,86702,86704],{"className":86703},[886],[888,86705,86706],{"xmlns":890},[892,86707,86708,86744],{},[895,86709,86710,86712,86718,86720,86722,86724,86726,86728,86730,86732,86738,86740,86742],{},[898,86711,2499],{},[1953,86713,86714,86716],{},[898,86715,5325],{},[898,86717,11183],{},[1677,86719,1679],{},[898,86721,1875],{},[898,86723,2470],{},[898,86725,6062],{"mathvariant":2057},[898,86727,1875],{},[898,86729,11183],{},[1677,86731,1679],{},[1805,86733,86734,86736],{},[898,86735,2470],{},[1677,86737,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,86739,1686],{"stretchy":1685},[898,86741,11183],{},[1677,86743,1692],{"stretchy":1685},[902,86745,86746],{"encoding":904},"MP_L = dQ\u002FdL = Q'(L)",[123,86748,86749,1884,86751,1656],{},[38,86750,77419],{},[883,86752,86754],{"className":86753},[886],[888,86755,86756],{"xmlns":890},[892,86757,86758,86776],{},[895,86759,86760,86762,86768,86770,86772,86774],{},[898,86761,5643],{},[1953,86763,86764,86766],{},[898,86765,5325],{},[898,86767,11183],{},[1677,86769,1679],{},[898,86771,2470],{},[898,86773,6062],{"mathvariant":2057},[898,86775,11183],{},[902,86777,76003],{"encoding":904},[123,86779,86780,86782,86783,11782,86800,1656],{},[38,86781,76906],{}," — od určitého ",[883,86784,86786],{"className":86785},[886],[888,86787,86788],{"xmlns":890},[892,86789,86790,86798],{},[895,86791,86792],{},[1953,86793,86794,86796],{},[898,86795,11183],{},[1810,86797,2008],{},[902,86799,76949],{"encoding":904},[883,86801,86803],{"className":86802},[886],[888,86804,86805],{"xmlns":890},[892,86806,86807,86829],{},[895,86808,86809,86819,86821,86823,86825,86827],{},[1805,86810,86811,86813],{},[898,86812,2470],{},[895,86814,86815,86817],{},[1677,86816,2059],{"mathvariant":2057},[1677,86818,2059],{"mathvariant":2057},[1677,86820,1686],{"stretchy":1685},[898,86822,11183],{},[1677,86824,1692],{"stretchy":1685},[1677,86826,3128],{},[1810,86828,2008],{},[902,86830,77095],{"encoding":904},[123,86832,86833,1884,86836,86853],{},[38,86834,86835],{},"Inflexní bod",[883,86837,86839],{"className":86838},[886],[888,86840,86841],{"xmlns":890},[892,86842,86843,86851],{},[895,86844,86845],{},[1953,86846,86847,86849],{},[898,86848,11183],{},[1810,86850,2008],{},[902,86852,76949],{"encoding":904}," — přechod z konvexity do konkavity.",[123,86855,86856,1884,86859,8403,86876,1656],{},[38,86857,86858],{},"Bod maxima produkce",[883,86860,86862],{"className":86861},[886],[888,86863,86864],{"xmlns":890},[892,86865,86866,86874],{},[895,86867,86868],{},[1953,86869,86870,86872],{},[898,86871,11183],{},[1810,86873,1959],{},[902,86875,14602],{"encoding":904},[883,86877,86879],{"className":86878},[886],[888,86880,86881],{"xmlns":890},[892,86882,86883,86907],{},[895,86884,86885,86887,86893,86895,86901,86903,86905],{},[898,86886,2499],{},[1953,86888,86889,86891],{},[898,86890,5325],{},[898,86892,11183],{},[1677,86894,1686],{"stretchy":1685},[1953,86896,86897,86899],{},[898,86898,11183],{},[1810,86900,1959],{},[1677,86902,1692],{"stretchy":1685},[1677,86904,1679],{},[1810,86906,2008],{},[902,86908,77168],{"encoding":904},[123,86910,86911,86933,86934,11782,86953,1656],{},[38,86912,86913,86914],{},"Princip maximalizace ",[883,86915,86917],{"className":86916},[886],[888,86918,86919],{"xmlns":890},[892,86920,86921,86931],{},[895,86922,86923,86925],{},[898,86924,5643],{},[1953,86926,86927,86929],{},[898,86928,5325],{},[898,86930,11183],{},[902,86932,76024],{"encoding":904}," — v bodě maxima ",[883,86935,86937],{"className":86936},[886],[888,86938,86939],{"xmlns":890},[892,86940,86941,86951],{},[895,86942,86943,86945],{},[898,86944,5643],{},[1953,86946,86947,86949],{},[898,86948,5325],{},[898,86950,11183],{},[902,86952,76024],{"encoding":904},[883,86954,86956],{"className":86955},[886],[888,86957,86958],{"xmlns":890},[892,86959,86960,86980],{},[895,86961,86962,86964,86970,86972,86974],{},[898,86963,2499],{},[1953,86965,86966,86968],{},[898,86967,5325],{},[898,86969,11183],{},[1677,86971,1679],{},[898,86973,5643],{},[1953,86975,86976,86978],{},[898,86977,5325],{},[898,86979,11183],{},[902,86981,76054],{"encoding":904},[123,86983,86984,1884,86987,1343,87026,1343,87043,1656],{},[38,86985,86986],{},"Polynomiální produkční funkce",[883,86988,86990],{"className":86989},[886],[888,86991,86992],{"xmlns":890},[892,86993,86994,87024],{},[895,86995,86996,86998,87000,87002,87004,87006,87008,87014,87016,87018],{},[898,86997,2470],{},[1677,86999,1686],{"stretchy":1685},[898,87001,11183],{},[1677,87003,1692],{"stretchy":1685},[1677,87005,1679],{},[898,87007,207],{},[1805,87009,87010,87012],{},[898,87011,11183],{},[1810,87013,1854],{},[1677,87015,1776],{},[898,87017,1779],{},[1805,87019,87020,87022],{},[898,87021,11183],{},[1810,87023,1812],{},[902,87025,77286],{"encoding":904},[883,87027,87029],{"className":87028},[886],[888,87030,87031],{"xmlns":890},[892,87032,87033,87041],{},[895,87034,87035,87037,87039],{},[898,87036,207],{},[1677,87038,3128],{},[1810,87040,2008],{},[902,87042,44476],{"encoding":904},[883,87044,87046],{"className":87045},[886],[888,87047,87048],{"xmlns":890},[892,87049,87050,87058],{},[895,87051,87052,87054,87056],{},[898,87053,1779],{},[1677,87055,3089],{},[1810,87057,2008],{},[902,87059,20205],{"encoding":904},[123,87061,87062,1884,87065,1656],{},[38,87063,87064],{},"Diferenciál produkce",[883,87066,87068],{"className":87067},[886],[888,87069,87070],{"xmlns":890},[892,87071,87072,87100],{},[895,87073,87074,87076,87078,87080,87082,87084,87086,87088,87094,87096,87098],{},[898,87075,2570],{"mathvariant":2057},[898,87077,2470],{},[1677,87079,2411],{},[898,87081,1875],{},[898,87083,2470],{},[1677,87085,1679],{},[898,87087,2499],{},[1953,87089,87090,87092],{},[898,87091,5325],{},[898,87093,11183],{},[1969,87095,2668],{},[898,87097,1875],{},[898,87099,11183],{},[902,87101,87102],{"encoding":904},"\\Delta Q \\approx dQ = MP_L\\,dL",[123,87104,87105,8403,87107,1656],{},[38,87106,85362],{},[883,87108,87110],{"className":87109},[886],[888,87111,87112],{"xmlns":890},[892,87113,87114,87132],{},[895,87115,87116,87118,87120,87122,87124,87126,87128,87130],{},[898,87117,2470],{},[1677,87119,1679],{},[898,87121,2470],{},[1677,87123,1686],{"stretchy":1685},[898,87125,11183],{},[1677,87127,1967],{"separator":1966},[898,87129,11188],{},[1677,87131,1692],{"stretchy":1685},[902,87133,87134],{"encoding":904},"Q = Q(L, K)",[123,87136,87137,8403,87139,1656],{},[38,87138,79456],{},[883,87140,87142],{"className":87141},[886],[888,87143,87144],{"xmlns":890},[892,87145,87146,87166],{},[895,87147,87148,87150,87152,87154,87160],{},[898,87149,2470],{},[1677,87151,1679],{},[898,87153,5643],{},[1805,87155,87156,87158],{},[898,87157,11183],{},[898,87159,207],{},[1805,87161,87162,87164],{},[898,87163,11188],{},[898,87165,1779],{},[902,87167,76121],{"encoding":904},[123,87169,87170,8403,87173,87208],{},[38,87171,87172],{},"Ryzí Cobb-Douglas",[883,87174,87176],{"className":87175},[886],[888,87177,87178],{"xmlns":890},[892,87179,87180,87206],{},[895,87181,87182,87184,87186,87188,87194],{},[898,87183,2470],{},[1677,87185,1679],{},[898,87187,5643],{},[1805,87189,87190,87192],{},[898,87191,11183],{},[898,87193,207],{},[1805,87195,87196,87198],{},[898,87197,11188],{},[895,87199,87200,87202,87204],{},[1810,87201,1959],{},[1677,87203,1906],{},[898,87205,207],{},[902,87207,80283],{"encoding":904}," (konstantní výnosy).",[123,87210,87211,8403,87213,1656],{},[38,87212,80999],{},[883,87214,87216],{"className":87215},[886],[888,87217,87218],{"xmlns":890},[892,87219,87220,87278],{},[895,87221,87222,87224,87226,87228,87230,87232,87234,87236,87238,87240,87250,87252,87254,87264],{},[898,87223,2470],{},[1677,87225,1679],{},[898,87227,5643],{},[1677,87229,2167],{"stretchy":1685},[1677,87231,1686],{"stretchy":1685},[1810,87233,1959],{},[1677,87235,1906],{},[898,87237,207],{},[1677,87239,1692],{"stretchy":1685},[1805,87241,87242,87244],{},[898,87243,11183],{},[895,87245,87246,87248],{},[1677,87247,1906],{},[898,87249,1779],{},[1677,87251,1776],{},[898,87253,207],{},[1805,87255,87256,87258],{},[898,87257,11188],{},[895,87259,87260,87262],{},[1677,87261,1906],{},[898,87263,1779],{},[1805,87265,87266,87268],{},[1677,87267,2182],{"stretchy":1685},[895,87269,87270,87272,87274,87276],{},[1677,87271,1906],{},[1810,87273,1959],{},[898,87275,6062],{"mathvariant":2057},[898,87277,1779],{},[902,87279,87280],{"encoding":904},"Q = A[(1-a)L^{-b} + aK^{-b}]^{-1\u002Fb}",[123,87282,87283,11413,87286,13518,87308,11413,87311,87341],{},[38,87284,87285],{},"Lineární",[883,87287,87289],{"className":87288},[886],[888,87290,87291],{"xmlns":890},[892,87292,87293,87305],{},[895,87294,87295,87297,87299,87301,87303],{},[898,87296,207],{},[898,87298,11183],{},[1677,87300,1776],{},[898,87302,1779],{},[898,87304,11188],{},[902,87306,87307],{"encoding":904},"aL + bK",[38,87309,87310],{},"Leontiefova",[883,87312,87314],{"className":87313},[886],[888,87315,87316],{"xmlns":890},[892,87317,87318,87338],{},[895,87319,87320,87322,87324,87326,87328,87330,87332,87334,87336],{},[898,87321,81227],{},[1677,87323,57591],{},[1677,87325,1686],{"stretchy":1685},[898,87327,207],{},[898,87329,11183],{},[1677,87331,1967],{"separator":1966},[898,87333,1779],{},[898,87335,11188],{},[1677,87337,1692],{"stretchy":1685},[902,87339,87340],{"encoding":904},"\\min(aL, bK)",") produkční funkce.",[123,87343,87344,8403,87360,1656],{},[38,87345,87346,87347],{},"Homogenita stupně ",[883,87348,87350],{"className":87349},[886],[888,87351,87352],{"xmlns":890},[892,87353,87354,87358],{},[895,87355,87356],{},[898,87357,38251],{},[902,87359,38251],{"encoding":904},[883,87361,87363],{"className":87362},[886],[888,87364,87365],{"xmlns":890},[892,87366,87367,87405],{},[895,87368,87369,87371,87373,87375,87377,87379,87381,87383,87385,87387,87393,87395,87397,87399,87401,87403],{},[898,87370,2470],{},[1677,87372,1686],{"stretchy":1685},[898,87374,13431],{},[898,87376,11183],{},[1677,87378,1967],{"separator":1966},[898,87380,13431],{},[898,87382,11188],{},[1677,87384,1692],{"stretchy":1685},[1677,87386,1679],{},[1805,87388,87389,87391],{},[898,87390,13431],{},[898,87392,38251],{},[898,87394,2470],{},[1677,87396,1686],{"stretchy":1685},[898,87398,11183],{},[1677,87400,1967],{"separator":1966},[898,87402,11188],{},[1677,87404,1692],{"stretchy":1685},[902,87406,87407],{"encoding":904},"Q(rL, rK) = r^n Q(L, K)",[123,87409,87410,80381],{},[38,87411,80314,87412],{},[883,87413,87415],{"className":87414},[886],[888,87416,87417],{"xmlns":890},[892,87418,87419,87423],{},[895,87420,87421],{},[898,87422,5643],{},[902,87424,5643],{"encoding":904},[123,87426,87427,87429,87430,87452,87453,87475,87476,5306],{},[38,87428,79815],{}," — konstantní (",[883,87431,87433],{"className":87432},[886],[888,87434,87435],{"xmlns":890},[892,87436,87437,87449],{},[895,87438,87439,87441,87443,87445,87447],{},[898,87440,207],{},[1677,87442,1776],{},[898,87444,1779],{},[1677,87446,1679],{},[1810,87448,1959],{},[902,87450,87451],{"encoding":904},"a+b=1","), rostoucí (",[883,87454,87456],{"className":87455},[886],[888,87457,87458],{"xmlns":890},[892,87459,87460,87472],{},[895,87461,87462,87464,87466,87468,87470],{},[898,87463,207],{},[1677,87465,1776],{},[898,87467,1779],{},[1677,87469,3089],{},[1810,87471,1959],{},[902,87473,87474],{"encoding":904},"a+b>1","), klesající (",[883,87477,87479],{"className":87478},[886],[888,87480,87481],{"xmlns":890},[892,87482,87483,87495],{},[895,87484,87485,87487,87489,87491,87493],{},[898,87486,207],{},[1677,87488,1776],{},[898,87490,1779],{},[1677,87492,3128],{},[1810,87494,1959],{},[902,87496,87497],{"encoding":904},"a+b\u003C1",[123,87499,87500,1884,87502,1343,87532,1884,87534,1656],{},[38,87501,76484],{},[883,87503,87505],{"className":87504},[886],[888,87506,87507],{"xmlns":890},[892,87508,87509,87529],{},[895,87510,87511,87513,87519,87521],{},[898,87512,2499],{},[1953,87514,87515,87517],{},[898,87516,5325],{},[898,87518,11183],{},[1677,87520,1679],{},[10554,87522,87523,87525,87527],{},[898,87524,2470],{},[898,87526,11183],{},[1677,87528,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[902,87530,87531],{"encoding":904},"MP_L = Q'_L",[38,87533,79388],{},[883,87535,87537],{"className":87536},[886],[888,87538,87539],{"xmlns":890},[892,87540,87541,87561],{},[895,87542,87543,87545,87551,87553],{},[898,87544,2499],{},[1953,87546,87547,87549],{},[898,87548,5325],{},[898,87550,11188],{},[1677,87552,1679],{},[10554,87554,87555,87557,87559],{},[898,87556,2470],{},[898,87558,11188],{},[1677,87560,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[902,87562,87563],{"encoding":904},"MP_K = Q'_K",[123,87565,87566,1884,87568,1656],{},[38,87567,81602],{},[883,87569,87571],{"className":87570},[886],[888,87572,87573],{"xmlns":890},[892,87574,87575,87613],{},[895,87576,87577,87579,87581,87583,87585,87591,87593,87595,87597,87599,87601,87607,87609,87611],{},[898,87578,1875],{},[898,87580,2470],{},[1677,87582,1679],{},[898,87584,2499],{},[1953,87586,87587,87589],{},[898,87588,5325],{},[898,87590,11183],{},[1969,87592,2668],{},[898,87594,1875],{},[898,87596,11183],{},[1677,87598,1776],{},[898,87600,2499],{},[1953,87602,87603,87605],{},[898,87604,5325],{},[898,87606,11188],{},[1969,87608,2668],{},[898,87610,1875],{},[898,87612,11188],{},[902,87614,87615],{"encoding":904},"dQ = MP_L\\,dL + MP_K\\,dK",[123,87617,87618,8403,87620,1656],{},[38,87619,81947],{},[883,87621,87623],{"className":87622},[886],[888,87624,87625],{"xmlns":890},[892,87626,87627,87669],{},[895,87628,87629,87631,87639,87641,87643,87651,87653,87655,87657,87659,87661,87663,87665,87667],{},[898,87630,11183],{},[10554,87632,87633,87635,87637],{},[898,87634,2470],{},[898,87636,11183],{},[1677,87638,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,87640,1776],{},[898,87642,11188],{},[10554,87644,87645,87647,87649],{},[898,87646,2470],{},[898,87648,11188],{},[1677,87650,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,87652,1679],{},[898,87654,38251],{},[1969,87656,2668],{},[898,87658,2470],{},[1677,87660,1686],{"stretchy":1685},[898,87662,11183],{},[1677,87664,1967],{"separator":1966},[898,87666,11188],{},[1677,87668,1692],{"stretchy":1685},[902,87670,87671],{"encoding":904},"L Q'_L + K Q'_K = n\\,Q(L,K)",[123,87673,87674,87677,87678,1656],{},[38,87675,87676],{},"Izokvanta"," — křivka ",[883,87679,87681],{"className":87680},[886],[888,87682,87683],{"xmlns":890},[892,87684,87685,87703],{},[895,87686,87687,87689,87691,87693,87695,87697,87699,87701],{},[898,87688,2470],{},[1677,87690,1686],{"stretchy":1685},[898,87692,11183],{},[1677,87694,1967],{"separator":1966},[898,87696,11188],{},[1677,87698,1692],{"stretchy":1685},[1677,87700,1679],{},[898,87702,82188],{},[902,87704,87705],{"encoding":904},"Q(L, K) = q",[123,87707,87708,1884,87710,1656],{},[38,87709,82377],{},[883,87711,87713],{"className":87712},[886],[888,87714,87715],{"xmlns":890},[892,87716,87717,87747],{},[895,87718,87719,87721,87723,87725,87727,87729,87731,87737,87739,87741],{},[898,87720,2499],{},[898,87722,5382],{},[898,87724,2455],{},[898,87726,10061],{},[1677,87728,1679],{},[898,87730,2499],{},[1953,87732,87733,87735],{},[898,87734,5325],{},[898,87736,11183],{},[898,87738,6062],{"mathvariant":2057},[898,87740,2499],{},[1953,87742,87743,87745],{},[898,87744,5325],{},[898,87746,11188],{},[902,87748,76196],{"encoding":904},[123,87750,87751,1884,87754,1656],{},[38,87752,87753],{},"Substituční vztah",[883,87755,87757],{"className":87756},[886],[888,87758,87759],{"xmlns":890},[892,87760,87761,87785],{},[895,87762,87763,87765,87767,87769,87771,87773,87775,87777,87779,87781,87783],{},[898,87764,2570],{"mathvariant":2057},[898,87766,11188],{},[1677,87768,2411],{},[1677,87770,1906],{},[898,87772,2499],{},[898,87774,5382],{},[898,87776,2455],{},[898,87778,10061],{},[1969,87780,2668],{},[898,87782,1875],{},[898,87784,11183],{},[902,87786,87787],{"encoding":904},"\\Delta K \\approx -MRTS\\,dL",[115,87789,3473],{"id":3472},[120,87791,87792,87889,87896,87903],{},[123,87793,87794,1884,87796,87799,87800,1343,87803,87806,87807,87810,87811,87830,87831,20039,87850,87853,87854,87873,87874,5306],{},[38,87795,52114],{},[207,87797,784],{"className":87798,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace, totální diferenciál), ",[207,87801,2038],{"className":87802,"dataFsResolvedFilePath":764,"href":765},[210],[207,87804,793],{"className":87805,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace produkce s rozpočtovým omezením), ",[207,87808,880],{"className":87809,"dataFsResolvedFilePath":878,"href":879},[210]," (paralela: izokvanty ↔ indiferenční křivky, ",[883,87812,87814],{"className":87813},[886],[888,87815,87816],{"xmlns":890},[892,87817,87818,87828],{},[895,87819,87820,87822,87824,87826],{},[898,87821,2499],{},[898,87823,5382],{},[898,87825,2455],{},[898,87827,10061],{},[902,87829,11987],{"encoding":904}," ↔ ",[883,87832,87834],{"className":87833},[886],[888,87835,87836],{"xmlns":890},[892,87837,87838,87848],{},[895,87839,87840,87842,87844,87846],{},[898,87841,2499],{},[898,87843,5382],{},[898,87845,2458],{},[898,87847,10061],{},[902,87849,11991],{"encoding":904},[207,87851,3504],{"className":87852,"dataFsResolvedFilePath":827,"href":828},[210]," (analogie principu max ",[883,87855,87857],{"className":87856},[886],[888,87858,87859],{"xmlns":890},[892,87860,87861,87871],{},[895,87862,87863,87865],{},[898,87864,5643],{},[1953,87866,87867,87869],{},[898,87868,5325],{},[898,87870,11183],{},[902,87872,76024],{"encoding":904}," ↔ min ",[883,87875,87877],{"className":87876},[886],[888,87878,87879],{"xmlns":890},[892,87880,87881,87887],{},[895,87882,87883,87885],{},[898,87884,5643],{},[898,87886,2458],{},[902,87888,56951],{"encoding":904},[123,87890,87891,1884,87893,1656],{},[38,87892,3480],{},[207,87894,3509],{"className":87895,"dataFsResolvedFilePath":848,"href":849},[210],[123,87897,87898,1884,87900,1656],{},[38,87899,17603],{},[207,87901,1094],{"className":87902,"dataFsResolvedFilePath":838,"href":839},[210],[123,87904,87905,1884,87907,1656],{},[38,87906,17594],{},[207,87908,17598],{"className":87909,"dataFsResolvedFilePath":1641,"href":1642},[210],{"title":641,"searchDepth":642,"depth":642,"links":87911},[87912,87913,87914,87918,87920,87925,87926,87933,87934,87936,87937,87938,87940,87945,87946,87947,87951,87952],{"id":76219,"depth":642,"text":76220},{"id":76356,"depth":642,"text":76357},{"id":76459,"depth":642,"text":87915,"children":87916},"Mezní produkt práce (MPLMP_L)",[87917],{"id":76905,"depth":649,"text":76906},{"id":77394,"depth":642,"text":87919},"Průměrný produkt práce (APLAP_L)",{"id":77512,"depth":642,"text":77513,"children":87921},[87922,87923,87924],{"id":77749,"depth":649,"text":66892},{"id":78060,"depth":649,"text":78061},{"id":78780,"depth":649,"text":78781},{"id":79352,"depth":642,"text":79353},{"id":79455,"depth":642,"text":79456,"children":87927},[87928,87929,87931,87932],{"id":79814,"depth":649,"text":79815},{"id":80313,"depth":649,"text":87930},"Parametr efektivity AA",{"id":80384,"depth":649,"text":80385},{"id":38570,"depth":649,"text":80724},{"id":80911,"depth":642,"text":80912},{"id":81250,"depth":642,"text":87935},"Mezní produkty MPLMP_L, MPKMP_K a totální diferenciál",{"id":81941,"depth":642,"text":81942},{"id":76285,"depth":642,"text":11166},{"id":82352,"depth":642,"text":87939},"Mezní míra technické substituce (MRTSMRTS)",{"id":83218,"depth":642,"text":83219,"children":87941},[87942,87943,87944],{"id":83222,"depth":649,"text":83223},{"id":83865,"depth":649,"text":83866},{"id":84146,"depth":649,"text":84147},{"id":84492,"depth":642,"text":84493},{"id":51272,"depth":642,"text":51273},{"id":84842,"depth":642,"text":84843,"children":87948},[87949,87950],{"id":41841,"depth":649,"text":41842},{"id":85361,"depth":649,"text":85362},{"id":17109,"depth":642,"text":17110},{"id":3472,"depth":642,"text":3473},{},"\u002Ftopics\u002Fprodukce",{"title":75855,"description":641},[1138,1136],"topics\u002Fprodukce",[1128,11201,87959,87960,87961,76285,87962,87963],"produkcni-funkce","mpl-apl","cobb-douglas","mrts","euler","ZO2oG_qVOhQee90SJRry02Lau2bGvK2gaOFbwchTg1Y",{"id":87966,"title":87967,"body":87968,"course":1128,"courses":659,"created":10944,"description":641,"extension":661,"meta":96915,"navigation":664,"path":96916,"seo":96917,"sources":96918,"stem":96919,"tags":96920,"type":3538,"updated":677,"__hash__":96923},"topics\u002Ftopics\u002Fuzitecnost.md","Užitečnost, Cobb-Douglasova funkce užitečnosti a optimalizace spotřebitele",{"type":9,"value":87969,"toc":96889},[87970,87973,87975,88172,88181,88185,88188,88241,88245,88257,88261,88264,88281,88404,88410,88554,88564,88568,88603,88641,88689,88746,88806,88848,89424,89428,89511,89620,89713,89971,89974,90027,90138,90220,90224,90235,90468,90523,90529,90569,90632,90643,90834,90940,91093,91141,91146,91260,91298,91424,91470,91497,91574,91649,91729,91859,91920,92008,92012,92015,92084,92167,92174,92234,92544,92548,92554,92607,92623,92674,92812,92888,93001,93318,93322,93329,93489,93548,93552,93574,93671,93792,93906,93929,93992,94049,94301,94309,94313,94320,94574,94624,94680,94683,94847,94851,94949,94951,94983,94987,95120,95362,95546,95714,96021,96154,96341,96353,96355,96790,96792],[12,87971,87967],{"id":87972},"užitečnost-cobb-douglasova-funkce-užitečnosti-a-optimalizace-spotřebitele",[115,87974,13396],{"id":13395},[724,87976,87977,1884,87979,88010,88011,88014,88015,88045,88046,88064,88065,88105,88106,88109,88110,88123,88124,29644,88127,88140,88141,88154,88155,88168,88169,1656],{},[38,87978,880],{},[883,87980,87982],{"className":87981},[886],[888,87983,87984],{"xmlns":890},[892,87985,87986,88008],{},[895,87987,87988,87990,87992,87998,88000,88006],{},[898,87989,900],{},[1677,87991,1686],{"stretchy":1685},[1953,87993,87994,87996],{},[898,87995,2470],{},[1810,87997,1959],{},[1677,87999,1967],{"separator":1966},[1953,88001,88002,88004],{},[898,88003,2470],{},[1810,88005,1812],{},[1677,88007,1692],{"stretchy":1685},[902,88009,17734],{"encoding":904}," je číselné vyjádření uspokojení spotřebitele ze svazku zboží — v ordinalistickém přístupu slouží jen k ",[38,88012,88013],{},"uspořádání"," svazků (nikoli k měření v jednotkách). Klíčové nástroje jsou mezní užitečnosti ",[883,88016,88018],{"className":88017},[886],[888,88019,88020],{"xmlns":890},[892,88021,88022,88042],{},[895,88023,88024,88026,88032,88034],{},[898,88025,2499],{},[1953,88027,88028,88030],{},[898,88029,900],{},[898,88031,19181],{},[1677,88033,1679],{},[10554,88035,88036,88038,88040],{},[898,88037,900],{},[898,88039,19181],{},[1677,88041,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[902,88043,88044],{"encoding":904},"MU_i = U'_i",", indiferenční křivky ",[883,88047,88049],{"className":88048},[886],[888,88050,88051],{"xmlns":890},[892,88052,88053,88061],{},[895,88054,88055,88057,88059],{},[898,88056,900],{},[1677,88058,1679],{},[898,88060,1823],{},[902,88062,88063],{"encoding":904},"U = c"," a mezní míra komoditní substituce ",[883,88066,88068],{"className":88067},[886],[888,88069,88070],{"xmlns":890},[892,88071,88072,88102],{},[895,88073,88074,88076,88078,88080,88082,88084,88086,88092,88094,88096],{},[898,88075,2499],{},[898,88077,5382],{},[898,88079,2458],{},[898,88081,10061],{},[1677,88083,1679],{},[898,88085,2499],{},[1953,88087,88088,88090],{},[898,88089,900],{},[1810,88091,1959],{},[898,88093,6062],{"mathvariant":2057},[898,88095,2499],{},[1953,88097,88098,88100],{},[898,88099,900],{},[1810,88101,1812],{},[902,88103,88104],{"encoding":904},"MRCS = MU_1\u002FMU_2",". Tato stránka pokrývá ",[38,88107,88108],{},"teorii užitečnosti"," — funkce ",[883,88111,88113],{"className":88112},[886],[888,88114,88115],{"xmlns":890},[892,88116,88117,88121],{},[895,88118,88119],{},[898,88120,900],{},[902,88122,900],{"encoding":904},", její vlastnosti, Cobb-Douglasův tvar, indiferenční křivky a MRCS. ",[38,88125,88126],{},"Optimalizaci spotřebitele",[883,88128,88130],{"className":88129},[886],[888,88131,88132],{"xmlns":890},[892,88133,88134,88138],{},[895,88135,88136],{},[898,88137,900],{},[902,88139,900],{"encoding":904}," při rozpočtu, min ",[883,88142,88144],{"className":88143},[886],[888,88145,88146],{"xmlns":890},[892,88147,88148,88152],{},[895,88149,88150],{},[898,88151,5640],{},[902,88153,5640],{"encoding":904}," při dané ",[883,88156,88158],{"className":88157},[886],[888,88159,88160],{"xmlns":890},[892,88161,88162,88166],{},[895,88163,88164],{},[898,88165,900],{},[902,88167,900],{"encoding":904},", Lagrange, funkce poptávky) viz ",[207,88170,913],{"className":88171,"dataFsResolvedFilePath":911,"href":912},[210],[724,88173,88174,88175,88177,88178,1656],{},"Kapitola 6 knihy ",[614,88176,17598],{}," — model rozhodování spotřebitele. Zde: funkce užitečnosti, indiferenční křivky, mezní míra komoditní substituce. Navazující optimalizace je v ",[207,88179,38145],{"className":88180,"dataFsResolvedFilePath":911,"href":912},[210],[115,88182,88184],{"id":88183},"úvod-cílové-znalosti-kapitoly-6","Úvod — cílové znalosti kapitoly 6",[724,88186,88187],{},"Po prostudování této kapitoly byste měli umět:",[120,88189,88190,88196,88205,88210,88213,88219,88225,88228,88234],{},[123,88191,88192,88193,1967],{},"vyložit, co se rozumí termínem ",[38,88194,88195],{},"užitečnost",[123,88197,88198,88199,5272,88202,1967],{},"definovat pojmy ",[38,88200,88201],{},"svazek zboží",[38,88203,88204],{},"funkce užitečnosti",[123,88206,76234,88207,76241],{},[38,88208,88209],{},"mezní užitečnosti",[123,88211,88212],{},"vyjmenovat základní vlastnosti funkcí užitečnosti,",[123,88214,76261,88215,88218],{},[38,88216,88217],{},"Cobb-Douglasových"," funkcí užitečnosti,",[123,88220,76282,88221,88224],{},[38,88222,88223],{},"křivky užitečnosti"," (indiferenční křivky),",[123,88226,88227],{},"vyjmenovat jejich základní vlastnosti,",[123,88229,76234,88230,88233],{},[38,88231,88232],{},"mezní míru komoditní substituce"," a ekonomicky ji interpretovat,",[123,88235,88236,88237,88240],{},"řešit ",[38,88238,88239],{},"optimalizační úlohy"," s ohledem na užitečnost.",[115,88242,88244],{"id":88243},"_61-pojetí-užitečnosti","6.1 Pojetí užitečnosti",[724,88246,88247,88248,88252,88253,88256],{},"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 ",[207,88249,88251],{"className":88250,"dataFsResolvedFilePath":800,"href":801},[210],"poptávku",". Centrálním pojmem je ",[38,88254,88255],{},"užitečnost (utility)"," — vše, co vede spotřebitele k nákupu zboží (uspokojení, potěšení, splnění přání, pohodlí).",[198,88258,88260],{"id":88259},"kardinalistický-vs-ordinalistický-přístup","Kardinalistický vs. ordinalistický přístup",[724,88262,88263],{},"Historicky se vyvíjela dvě pojetí „měření\" užitečnosti:",[120,88265,88266,88272],{},[123,88267,88268,88271],{},[38,88269,88270],{},"Kardinalistický přístup"," (19. století — Gossen, Jevons, Walras): užitečnost měřena kvantitativně (např. peněžními jednotkami). Tento přístup se ukázal být nevýhodný.",[123,88273,88274,88277,88278,88280],{},[38,88275,88276],{},"Ordinalistický přístup"," (v současnosti preferovaný): postačuje ",[38,88279,88013],{}," svazků zboží podle preferencí; kvantitativní číselné hodnocení užitečnosti se nepožaduje.",[5254,88282,88283],{},[724,88284,88285,88287,88288,88291,88292,1884,88305,88308,88309,5272,88322,88341,88342,1343,88368,88395,88396,88399,88400,88403],{},[883,88286,5800],{}," Pozor — ordinalisté užitečnost ",[38,88289,88290],{},"neměří","\nV ordinalistickém přístupu hodnoty funkce ",[883,88293,88295],{"className":88294},[886],[888,88296,88297],{"xmlns":890},[892,88298,88299,88303],{},[895,88300,88301],{},[898,88302,900],{},[902,88304,900],{"encoding":904},[38,88306,88307],{},"nemají samostatný ekonomický význam"," — slouží pouze k uspořádání svazků. Dvě funkce ",[883,88310,88312],{"className":88311},[886],[888,88313,88314],{"xmlns":890},[892,88315,88316,88320],{},[895,88317,88318],{},[898,88319,900],{},[902,88321,900],{"encoding":904},[883,88323,88325],{"className":88324},[886],[888,88326,88327],{"xmlns":890},[892,88328,88329,88338],{},[895,88330,88331],{},[9774,88332,88333,88335],{"accent":1966},[898,88334,900],{},[1677,88336,88337],{},"~",[902,88339,88340],{"encoding":904},"\\tilde U"," reprezentují tytéž preference, jsou-li navzájem monotónní transformací (např. ",[883,88343,88345],{"className":88344},[886],[888,88346,88347],{"xmlns":890},[892,88348,88349,88365],{},[895,88350,88351,88357,88359],{},[9774,88352,88353,88355],{"accent":1966},[898,88354,900],{},[1677,88356,88337],{},[1677,88358,1679],{},[1805,88360,88361,88363],{},[898,88362,900],{},[1810,88364,1812],{},[902,88366,88367],{"encoding":904},"\\tilde U = U^2",[883,88369,88371],{"className":88370},[886],[888,88372,88373],{"xmlns":890},[892,88374,88375,88392],{},[895,88376,88377,88383,88385,88388,88390],{},[9774,88378,88379,88381],{"accent":1966},[898,88380,900],{},[1677,88382,88337],{},[1677,88384,1679],{},[898,88386,88387],{},"ln",[1677,88389,57591],{},[898,88391,900],{},[902,88393,88394],{"encoding":904},"\\tilde U = \\ln U","). Výroky typu „užitečnost je 250 jednotek\" proto samy o sobě nic neříkají — smysl mají jen ",[38,88397,88398],{},"porovnání"," mezi svazky a ",[38,88401,88402],{},"poměry"," mezních veličin.",[724,88405,88406,88407,2385],{},"Ordinalistický přístup vychází z ",[38,88408,88409],{},"pěti hlavních předpokladů",[152,88411,88412,88418,88424,88542,88548],{},[123,88413,88414,88417],{},[38,88415,88416],{},"Racionalita."," Spotřebitel jedná racionálně — snaží se maximalizovat své uspokojení (užitečnost) s ohledem na daný důchod a tržní ceny; disponuje všemi potřebnými informacemi.",[123,88419,88420,88423],{},[38,88421,88422],{},"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.",[123,88425,88426,88429,88430,63132,88443,88456,88457,63132,88470,2608,88483,88486,88487,5272,88506,63961,88524,1656],{},[38,88427,88428],{},"Konzistence a tranzitivita."," Preferuje-li v jisté době svazek ",[883,88431,88433],{"className":88432},[886],[888,88434,88435],{"xmlns":890},[892,88436,88437,88441],{},[895,88438,88439],{},[898,88440,5643],{},[902,88442,5643],{"encoding":904},[883,88444,88446],{"className":88445},[886],[888,88447,88448],{"xmlns":890},[892,88449,88450,88454],{},[895,88451,88452],{},[898,88453,24644],{},[902,88455,24644],{"encoding":904},", nebude jindy preferovat ",[883,88458,88460],{"className":88459},[886],[888,88461,88462],{"xmlns":890},[892,88463,88464,88468],{},[895,88465,88466],{},[898,88467,24644],{},[902,88469,24644],{"encoding":904},[883,88471,88473],{"className":88472},[886],[888,88474,88475],{"xmlns":890},[892,88476,88477,88481],{},[895,88478,88479],{},[898,88480,5643],{},[902,88482,5643],{"encoding":904},[38,88484,88485],{},"Tranzitivita",": pokud ",[883,88488,88490],{"className":88489},[886],[888,88491,88492],{"xmlns":890},[892,88493,88494,88503],{},[895,88495,88496,88498,88501],{},[898,88497,5643],{},[1677,88499,88500],{},"≻",[898,88502,24644],{},[902,88504,88505],{"encoding":904},"A \\succ B",[883,88507,88509],{"className":88508},[886],[888,88510,88511],{"xmlns":890},[892,88512,88513,88521],{},[895,88514,88515,88517,88519],{},[898,88516,24644],{},[1677,88518,88500],{},[898,88520,2458],{},[902,88522,88523],{"encoding":904},"B \\succ C",[883,88525,88527],{"className":88526},[886],[888,88528,88529],{"xmlns":890},[892,88530,88531,88539],{},[895,88532,88533,88535,88537],{},[898,88534,5643],{},[1677,88536,88500],{},[898,88538,2458],{},[902,88540,88541],{"encoding":904},"A \\succ C",[123,88543,88544,88547],{},[38,88545,88546],{},"Rostoucí užitečnost."," Uspokojení roste s množstvím zboží.",[123,88549,88550,88553],{},[38,88551,88552],{},"Klesající mezní užitečnost."," „Přírůstky\" uspokojení klesají s růstem množství zboží.",[724,88555,88556,88557,88560,88561,1656],{},"K naplnění předpokladů je ordinalistický přístup založen na pojmech ",[614,88558,88559],{},"preference"," a na příbuzné ",[614,88562,88563],{},"funkci užitečnosti",[115,88565,88567],{"id":88566},"_62-model-užitečnosti-svazek-zboží-a-funkce-užitečnosti","6.2 Model užitečnosti — svazek zboží a funkce užitečnosti",[724,88569,88570,88571,88584,88585,88588,88589,88602],{},"Uvažujme ",[883,88572,88574],{"className":88573},[886],[888,88575,88576],{"xmlns":890},[892,88577,88578,88582],{},[895,88579,88580],{},[898,88581,38251],{},[902,88583,38251],{"encoding":904}," různých zboží. ",[38,88586,88587],{},"Svazek zboží (bundle of goods)"," je uspořádaná ",[883,88590,88592],{"className":88591},[886],[888,88593,88594],{"xmlns":890},[892,88595,88596,88600],{},[895,88597,88598],{},[898,88599,38251],{},[902,88601,38251],{"encoding":904},"-tice",[724,88604,88605],{},[883,88606,88608],{"className":88607},[886],[888,88609,88610],{"xmlns":890},[892,88611,88612,88638],{},[895,88613,88614,88616,88622,88624,88626,88628,88634,88636],{},[1677,88615,1686],{"stretchy":1685},[1953,88617,88618,88620],{},[898,88619,2470],{},[1810,88621,1959],{},[1677,88623,1967],{"separator":1966},[1677,88625,11034],{},[1677,88627,1967],{"separator":1966},[1953,88629,88630,88632],{},[898,88631,2470],{},[898,88633,38251],{},[1677,88635,1692],{"stretchy":1685},[1677,88637,1967],{"separator":1966},[902,88639,88640],{"encoding":904},"(Q_1, \\dots, Q_n),",[724,88642,5698,88643,88660,88661,88674,88675,88678,88679,88682,88683,88686,88687,2385],{},[883,88644,88646],{"className":88645},[886],[888,88647,88648],{"xmlns":890},[892,88649,88650,88658],{},[895,88651,88652],{},[1953,88653,88654,88656],{},[898,88655,2470],{},[898,88657,19181],{},[902,88659,48929],{"encoding":904}," značí množství ",[883,88662,88664],{"className":88663},[886],[888,88665,88666],{"xmlns":890},[892,88667,88668,88672],{},[895,88669,88670],{},[898,88671,19181],{},[902,88673,19181],{"encoding":904},"-tého zboží. Spotřebitel je schopen svazky ",[38,88676,88677],{},"uspořádat"," s rostoucí užitečností, případně je prohlásit za ",[38,88680,88681],{},"indiferentní"," (tj. stejně užitečné). Tím je definována ",[38,88684,88685],{},"relace preference",". Preferenci vyjadřujeme číselně: svazku preferovanému přiřadíme větší číslo, indiferentním svazkům stejné číslo. Dostáváme ",[38,88688,88563],{},[883,88690,88692],{"className":88691},[886],[888,88693,88694],{"xmlns":890,"display":29457},[892,88695,88696,88743],{},[22145,88697,88698],{"width":29462},[22150,88699,88700,88702,88736,88738],{},[22153,88701],{"width":29467},[22153,88703,88704],{},[895,88705,88706,88708,88710,88712,88714,88720,88722,88724,88726,88732,88734],{},[898,88707,900],{},[1677,88709,1679],{},[898,88711,900],{},[1677,88713,1686],{"stretchy":1685},[1953,88715,88716,88718],{},[898,88717,2470],{},[1810,88719,1959],{},[1677,88721,1967],{"separator":1966},[1677,88723,11034],{},[1677,88725,1967],{"separator":1966},[1953,88727,88728,88730],{},[898,88729,2470],{},[898,88731,38251],{},[1677,88733,1692],{"stretchy":1685},[1677,88735,1967],{"separator":1966},[22153,88737],{"width":29467},[22153,88739,88740],{},[1969,88741,88742],{},"(6.1)",[902,88744,88745],{"encoding":904},"U = U(Q_1, \\dots, Q_n), \\tag{6.1}",[724,88747,5698,88748,88778,88779,88801,88802,88805],{},[883,88749,88751],{"className":88750},[886],[888,88752,88753],{"xmlns":890},[892,88754,88755,88775],{},[895,88756,88757,88763,88765,88767,88769],{},[1953,88758,88759,88761],{},[898,88760,2470],{},[1810,88762,1959],{},[1677,88764,1967],{"separator":1966},[1677,88766,11034],{},[1677,88768,1967],{"separator":1966},[1953,88770,88771,88773],{},[898,88772,2470],{},[898,88774,38251],{},[902,88776,88777],{"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 ",[883,88780,88782],{"className":88781},[886],[888,88783,88784],{"xmlns":890},[892,88785,88786,88798],{},[895,88787,88788,88790,88792],{},[898,88789,900],{},[1677,88791,1967],{"separator":1966},[9774,88793,88794,88796],{"accent":1966},[898,88795,900],{},[1677,88797,88337],{},[902,88799,88800],{"encoding":904},"U, \\tilde U"," reprezentují stejné preference, pokud mezi nimi existuje ",[38,88803,88804],{},"monotónní transformace"," zachovávající pořadí.",[724,88807,88808,88809,8403,88812,1656],{},"Dále se omezíme na funkce pro ",[38,88810,88811],{},"dvě zboží",[883,88813,88815],{"className":88814},[886],[888,88816,88817],{"xmlns":890},[892,88818,88819,88845],{},[895,88820,88821,88823,88825,88827,88829,88835,88837,88843],{},[898,88822,900],{},[1677,88824,1679],{},[898,88826,900],{},[1677,88828,1686],{"stretchy":1685},[1953,88830,88831,88833],{},[898,88832,2470],{},[1810,88834,1959],{},[1677,88836,1967],{"separator":1966},[1953,88838,88839,88841],{},[898,88840,2470],{},[1810,88842,1812],{},[1677,88844,1692],{"stretchy":1685},[902,88846,88847],{"encoding":904},"U = U(Q_1, Q_2)",[5254,88849,88850,88925],{},[724,88851,88852,88854,88855,2385],{},[883,88853,54086],{}," Příklad 6.1 — uspořádání a indiference\nPro ",[883,88856,88858],{"className":88857},[886],[888,88859,88860],{"xmlns":890},[892,88861,88862,88922],{},[895,88863,88864,88866,88868,88870,88872,88878,88880,88886,88888,88894,88896,88898,88900],{},[898,88865,900],{},[1677,88867,1679],{},[898,88869,900],{},[1677,88871,1686],{"stretchy":1685},[1953,88873,88874,88876],{},[898,88875,2470],{},[1810,88877,1959],{},[1677,88879,1967],{"separator":1966},[1953,88881,88882,88884],{},[898,88883,2470],{},[1810,88885,1812],{},[1677,88887,1967],{"separator":1966},[1953,88889,88890,88892],{},[898,88891,2470],{},[1810,88893,1854],{},[1677,88895,1692],{"stretchy":1685},[1677,88897,1679],{},[1810,88899,1812],{},[9505,88901,88902],{},[895,88903,88904,88910,88916],{},[1953,88905,88906,88908],{},[898,88907,2470],{},[1810,88909,1959],{},[1953,88911,88912,88914],{},[898,88913,2470],{},[1810,88915,1812],{},[1953,88917,88918,88920],{},[898,88919,2470],{},[1810,88921,1854],{},[902,88923,88924],{"encoding":904},"U = U(Q_1, Q_2, Q_3) = 2\\sqrt{Q_1 Q_2 Q_3}",[120,88926,88927,89120],{},[123,88928,88929,88930,88956,88957,14328,88983,5272,89042,6977,89102,9813],{},"svazek ",[883,88931,88933],{"className":88932},[886],[888,88934,88935],{"xmlns":890},[892,88936,88937,88953],{},[895,88938,88939,88941,88943,88945,88947,88949,88951],{},[1677,88940,1686],{"stretchy":1685},[1810,88942,43253],{},[1677,88944,1967],{"separator":1966},[1810,88946,2032],{},[1677,88948,1967],{"separator":1966},[1810,88950,43231],{},[1677,88952,1692],{"stretchy":1685},[902,88954,88955],{"encoding":904},"(16, 4, 64)"," je preferován před ",[883,88958,88960],{"className":88959},[886],[888,88961,88962],{"xmlns":890},[892,88963,88964,88980],{},[895,88965,88966,88968,88970,88972,88974,88976,88978],{},[1677,88967,1686],{"stretchy":1685},[1810,88969,5387],{},[1677,88971,1967],{"separator":1966},[1810,88973,5387],{},[1677,88975,1967],{"separator":1966},[1810,88977,67988],{},[1677,88979,1692],{"stretchy":1685},[902,88981,88982],{"encoding":904},"(9, 9, 27)",[883,88984,88986],{"className":88985},[886],[888,88987,88988],{"xmlns":890},[892,88989,88990,89039],{},[895,88991,88992,88994,88996,88998,89000,89002,89004,89006,89008,89010,89012,89026,89028,89030,89035,89037],{},[898,88993,900],{},[1677,88995,1686],{"stretchy":1685},[1810,88997,43253],{},[1677,88999,1967],{"separator":1966},[1810,89001,2032],{},[1677,89003,1967],{"separator":1966},[1810,89005,43231],{},[1677,89007,1692],{"stretchy":1685},[1677,89009,1679],{},[1810,89011,1812],{},[9505,89013,89014],{},[895,89015,89016,89018,89020,89022,89024],{},[1810,89017,43253],{},[1677,89019,2858],{},[1810,89021,2032],{},[1677,89023,2858],{},[1810,89025,43231],{},[1677,89027,1679],{},[1810,89029,1812],{},[9505,89031,89032],{},[1810,89033,89034],{},"4096",[1677,89036,1679],{},[1810,89038,7005],{},[902,89040,89041],{"encoding":904},"U(16,4,64) = 2\\sqrt{16 \\cdot 4 \\cdot 64} = 2\\sqrt{4096} = 128",[883,89043,89045],{"className":89044},[886],[888,89046,89047],{"xmlns":890},[892,89048,89049,89099],{},[895,89050,89051,89053,89055,89057,89059,89061,89063,89065,89067,89069,89071,89085,89087,89089,89094,89096],{},[898,89052,900],{},[1677,89054,1686],{"stretchy":1685},[1810,89056,5387],{},[1677,89058,1967],{"separator":1966},[1810,89060,5387],{},[1677,89062,1967],{"separator":1966},[1810,89064,67988],{},[1677,89066,1692],{"stretchy":1685},[1677,89068,1679],{},[1810,89070,1812],{},[9505,89072,89073],{},[895,89074,89075,89077,89079,89081,89083],{},[1810,89076,5387],{},[1677,89078,2858],{},[1810,89080,5387],{},[1677,89082,2858],{},[1810,89084,67988],{},[1677,89086,1679],{},[1810,89088,1812],{},[9505,89090,89091],{},[1810,89092,89093],{},"2187",[1677,89095,7288],{},[1810,89097,89098],{},"93,53",[902,89100,89101],{"encoding":904},"U(9,9,27) = 2\\sqrt{9 \\cdot 9 \\cdot 27} = 2\\sqrt{2187} \\doteq 93{,}53",[883,89103,89105],{"className":89104},[886],[888,89106,89107],{"xmlns":890},[892,89108,89109,89117],{},[895,89110,89111,89113,89115],{},[1810,89112,7005],{},[1677,89114,3089],{},[1810,89116,89098],{},[902,89118,89119],{"encoding":904},"128 > 93{,}53",[123,89121,89122,89123,5272,89149,89175,89176,5272,89216,89257,89258,89304,89305,5272,89331,2526,89357,5272,89375,89393,89394,1656],{},"svazky ",[883,89124,89126],{"className":89125},[886],[888,89127,89128],{"xmlns":890},[892,89129,89130,89146],{},[895,89131,89132,89134,89136,89138,89140,89142,89144],{},[1677,89133,1686],{"stretchy":1685},[1810,89135,2032],{},[1677,89137,1967],{"separator":1966},[1810,89139,6973],{},[1677,89141,1967],{"separator":1966},[1810,89143,1812],{},[1677,89145,1692],{"stretchy":1685},[902,89147,89148],{"encoding":904},"(4, 8, 2)",[883,89150,89152],{"className":89151},[886],[888,89153,89154],{"xmlns":890},[892,89155,89156,89172],{},[895,89157,89158,89160,89162,89164,89166,89168,89170],{},[1677,89159,1686],{"stretchy":1685},[1810,89161,43231],{},[1677,89163,1967],{"separator":1966},[1810,89165,1959],{},[1677,89167,1967],{"separator":1966},[1810,89169,2032],{},[1677,89171,1692],{"stretchy":1685},[902,89173,89174],{"encoding":904},"(64, 1, 4)"," jsou indiferentní, protože ",[883,89177,89179],{"className":89178},[886],[888,89180,89181],{"xmlns":890},[892,89182,89183,89213],{},[895,89184,89185,89187,89189,89191,89193,89195,89197,89199,89201,89203,89205,89209,89211],{},[898,89186,900],{},[1677,89188,1686],{"stretchy":1685},[1810,89190,2032],{},[1677,89192,1967],{"separator":1966},[1810,89194,6973],{},[1677,89196,1967],{"separator":1966},[1810,89198,1812],{},[1677,89200,1692],{"stretchy":1685},[1677,89202,1679],{},[1810,89204,1812],{},[9505,89206,89207],{},[1810,89208,43231],{},[1677,89210,1679],{},[1810,89212,43253],{},[902,89214,89215],{"encoding":904},"U(4,8,2) = 2\\sqrt{64} = 16",[883,89217,89219],{"className":89218},[886],[888,89220,89221],{"xmlns":890},[892,89222,89223,89254],{},[895,89224,89225,89227,89229,89231,89233,89235,89237,89239,89241,89243,89245,89250,89252],{},[898,89226,900],{},[1677,89228,1686],{"stretchy":1685},[1810,89230,43231],{},[1677,89232,1967],{"separator":1966},[1810,89234,1959],{},[1677,89236,1967],{"separator":1966},[1810,89238,2032],{},[1677,89240,1692],{"stretchy":1685},[1677,89242,1679],{},[1810,89244,1812],{},[9505,89246,89247],{},[1810,89248,89249],{},"256",[1677,89251,1679],{},[1810,89253,73750],{},[902,89255,89256],{"encoding":904},"U(64,1,4) = 2\\sqrt{256} = 32"," — jsou stejně užitečné mezi sebou, pokud ",[883,89259,89261],{"className":89260},[886],[888,89262,89263],{"xmlns":890},[892,89264,89265,89301],{},[895,89266,89267,89269,89271,89273,89275,89277,89279,89281,89283,89285,89287,89289,89291,89293,89295,89297,89299],{},[898,89268,900],{},[1677,89270,1686],{"stretchy":1685},[1810,89272,2032],{},[1677,89274,1967],{"separator":1966},[1810,89276,6973],{},[1677,89278,1967],{"separator":1966},[1810,89280,1812],{},[1677,89282,1692],{"stretchy":1685},[1677,89284,1679],{},[898,89286,900],{},[1677,89288,1686],{"stretchy":1685},[1810,89290,43231],{},[1677,89292,1967],{"separator":1966},[1810,89294,1959],{},[1677,89296,1967],{"separator":1966},[1810,89298,2032],{},[1677,89300,1692],{"stretchy":1685},[902,89302,89303],{"encoding":904},"U(4,8,2) = U(64,1,4)","; ověření: ",[883,89306,89308],{"className":89307},[886],[888,89309,89310],{"xmlns":890},[892,89311,89312,89328],{},[895,89313,89314,89316,89318,89320,89322,89324,89326],{},[1810,89315,2032],{},[1677,89317,2858],{},[1810,89319,6973],{},[1677,89321,2858],{},[1810,89323,1812],{},[1677,89325,1679],{},[1810,89327,43231],{},[902,89329,89330],{"encoding":904},"4 \\cdot 8 \\cdot 2 = 64",[883,89332,89334],{"className":89333},[886],[888,89335,89336],{"xmlns":890},[892,89337,89338,89354],{},[895,89339,89340,89342,89344,89346,89348,89350,89352],{},[1810,89341,43231],{},[1677,89343,2858],{},[1810,89345,1959],{},[1677,89347,2858],{},[1810,89349,2032],{},[1677,89351,1679],{},[1810,89353,89249],{},[902,89355,89356],{"encoding":904},"64 \\cdot 1 \\cdot 4 = 256",[883,89358,89360],{"className":89359},[886],[888,89361,89362],{"xmlns":890},[892,89363,89364,89372],{},[895,89365,89366,89368,89370],{},[898,89367,900],{},[1677,89369,1679],{},[1810,89371,43253],{},[902,89373,89374],{"encoding":904},"U = 16",[883,89376,89378],{"className":89377},[886],[888,89379,89380],{"xmlns":890},[892,89381,89382,89390],{},[895,89383,89384,89386,89388],{},[898,89385,900],{},[1677,89387,1679],{},[1810,89389,73750],{},[902,89391,89392],{"encoding":904},"U = 32"," — nejsou indiferentní. Správně indiferentní jsou svazky s týmž součinem ",[883,89395,89397],{"className":89396},[886],[888,89398,89399],{"xmlns":890},[892,89400,89401,89421],{},[895,89402,89403,89409,89415],{},[1953,89404,89405,89407],{},[898,89406,2470],{},[1810,89408,1959],{},[1953,89410,89411,89413],{},[898,89412,2470],{},[1810,89414,1812],{},[1953,89416,89417,89419],{},[898,89418,2470],{},[1810,89420,1854],{},[902,89422,89423],{"encoding":904},"Q_1 Q_2 Q_3",[115,89425,89427],{"id":89426},"mezní-užitečnost-mu","Mezní užitečnost (MU)",[724,89429,89430,89431,9490,89466,1884,89469,43205,89486,11413,89503,89506,89507,89510],{},"Pro funkci užitečnosti ",[883,89432,89434],{"className":89433},[886],[888,89435,89436],{"xmlns":890},[892,89437,89438,89464],{},[895,89439,89440,89442,89444,89446,89448,89454,89456,89462],{},[898,89441,900],{},[1677,89443,1679],{},[898,89445,900],{},[1677,89447,1686],{"stretchy":1685},[1953,89449,89450,89452],{},[898,89451,2470],{},[1810,89453,1959],{},[1677,89455,1967],{"separator":1966},[1953,89457,89458,89460],{},[898,89459,2470],{},[1810,89461,1812],{},[1677,89463,1692],{"stretchy":1685},[902,89465,88847],{"encoding":904},[38,89467,89468],{},"mezní užitečnost",[883,89470,89472],{"className":89471},[886],[888,89473,89474],{"xmlns":890},[892,89475,89476,89484],{},[895,89477,89478],{},[1953,89479,89480,89482],{},[898,89481,2470],{},[1810,89483,1959],{},[902,89485,30393],{"encoding":904},[883,89487,89489],{"className":89488},[886],[888,89490,89491],{"xmlns":890},[892,89492,89493,89501],{},[895,89494,89495],{},[1953,89496,89497,89499],{},[898,89498,2470],{},[1810,89500,1812],{},[902,89502,30412],{"encoding":904},[38,89504,89505],{},"marginal utility",") parciální ",[207,89508,1145],{"className":89509,"dataFsResolvedFilePath":764,"href":765},[210]," užitečnosti podle příslušné proměnné:",[883,89512,89514],{"className":89513},[886],[888,89515,89516],{"xmlns":890,"display":29457},[892,89517,89518,89617],{},[22145,89519,89520],{"width":29462},[22150,89521,89522,89524,89610,89612],{},[22153,89523],{"width":29467},[22153,89525,89526],{},[895,89527,89528,89530,89536,89538,89546,89548,89566,89568,89570,89572,89578,89580,89588,89590,89608],{},[898,89529,2499],{},[1953,89531,89532,89534],{},[898,89533,900],{},[1810,89535,1959],{},[1677,89537,1679],{},[10554,89539,89540,89542,89544],{},[898,89541,900],{},[1810,89543,1959],{},[1677,89545,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,89547,1679],{},[2010,89549,89550,89556],{},[895,89551,89552,89554],{},[898,89553,11260],{"mathvariant":2057},[898,89555,900],{},[895,89557,89558,89560],{},[898,89559,11260],{"mathvariant":2057},[1953,89561,89562,89564],{},[898,89563,2470],{},[1810,89565,1959],{},[1677,89567,1967],{"separator":1966},[7266,89569],{"width":16674},[898,89571,2499],{},[1953,89573,89574,89576],{},[898,89575,900],{},[1810,89577,1812],{},[1677,89579,1679],{},[10554,89581,89582,89584,89586],{},[898,89583,900],{},[1810,89585,1812],{},[1677,89587,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,89589,1679],{},[2010,89591,89592,89598],{},[895,89593,89594,89596],{},[898,89595,11260],{"mathvariant":2057},[898,89597,900],{},[895,89599,89600,89602],{},[898,89601,11260],{"mathvariant":2057},[1953,89603,89604,89606],{},[898,89605,2470],{},[1810,89607,1812],{},[898,89609,1656],{"mathvariant":2057},[22153,89611],{"width":29467},[22153,89613,89614],{},[1969,89615,89616],{},"(6.2)",[902,89618,89619],{"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}",[724,89621,89622,89623,89657,89658,89688,89689,1884,89692,1656],{},"Pro pevné ",[883,89624,89626],{"className":89625},[886],[888,89627,89628],{"xmlns":890},[892,89629,89630,89654],{},[895,89631,89632,89638,89640,89642,89644,89650,89652],{},[1953,89633,89634,89636],{},[898,89635,2470],{},[1810,89637,1959],{},[1677,89639,1679],{},[898,89641,207],{},[1677,89643,1967],{"separator":1966},[1953,89645,89646,89648],{},[898,89647,2470],{},[1810,89649,1812],{},[1677,89651,1679],{},[898,89653,1779],{},[902,89655,89656],{"encoding":904},"Q_1 = a, Q_2 = b"," se hodnota ",[883,89659,89661],{"className":89660},[886],[888,89662,89663],{"xmlns":890},[892,89664,89665,89685],{},[895,89666,89667,89669,89675,89677,89679,89681,89683],{},[898,89668,2499],{},[1953,89670,89671,89673],{},[898,89672,900],{},[1810,89674,1959],{},[1677,89676,1686],{"stretchy":1685},[898,89678,207],{},[1677,89680,1967],{"separator":1966},[898,89682,1779],{},[1677,89684,1692],{"stretchy":1685},[902,89686,89687],{"encoding":904},"MU_1(a, b)"," nazývá mezní užitečnost ",[38,89690,89691],{},"v bodě (na hladině)",[883,89693,89695],{"className":89694},[886],[888,89696,89697],{"xmlns":890},[892,89698,89699,89711],{},[895,89700,89701,89703,89705,89707,89709],{},[1677,89702,2167],{"stretchy":1685},[898,89704,207],{},[1677,89706,1967],{"separator":1966},[898,89708,1779],{},[1677,89710,2182],{"stretchy":1685},[902,89712,12212],{"encoding":904},[5254,89714,89715],{},[724,89716,89717,89719,89720,89750,89779,89780,2291,89793,2305,89810,89831,89832,2352,89849,2366,89862,89879,89880,89902,89903,89932,89933,7861,89953,89970],{},[883,89718,5543],{}," Intuice — co říká ",[883,89721,89723],{"className":89722},[886],[888,89724,89725],{"xmlns":890},[892,89726,89727,89747],{},[895,89728,89729,89731,89737,89739,89741,89743,89745],{},[898,89730,2499],{},[1953,89732,89733,89735],{},[898,89734,900],{},[1810,89736,1959],{},[1677,89738,1686],{"stretchy":1685},[898,89740,207],{},[1677,89742,1967],{"separator":1966},[898,89744,1779],{},[1677,89746,1692],{"stretchy":1685},[902,89748,89749],{"encoding":904},"MU_1(a,b)",[883,89751,89753],{"className":89752},[886],[888,89754,89755],{"xmlns":890},[892,89756,89757,89777],{},[895,89758,89759,89761,89767,89769,89771,89773,89775],{},[898,89760,2499],{},[1953,89762,89763,89765],{},[898,89764,900],{},[1810,89766,1959],{},[1677,89768,1686],{"stretchy":1685},[898,89770,207],{},[1677,89772,1967],{"separator":1966},[898,89774,1779],{},[1677,89776,1692],{"stretchy":1685},[902,89778,89687],{"encoding":904}," je rychlost změny ",[883,89781,89783],{"className":89782},[886],[888,89784,89785],{"xmlns":890},[892,89786,89787,89791],{},[895,89788,89789],{},[898,89790,900],{},[902,89792,900],{"encoding":904},[883,89794,89796],{"className":89795},[886],[888,89797,89798],{"xmlns":890},[892,89799,89800,89808],{},[895,89801,89802],{},[1953,89803,89804,89806],{},[898,89805,2470],{},[1810,89807,1959],{},[902,89809,30393],{"encoding":904},[883,89811,89813],{"className":89812},[886],[888,89814,89815],{"xmlns":890},[892,89816,89817,89829],{},[895,89818,89819,89821,89823,89825,89827],{},[1677,89820,2167],{"stretchy":1685},[898,89822,207],{},[1677,89824,1967],{"separator":1966},[898,89826,1779],{},[1677,89828,2182],{"stretchy":1685},[902,89830,12212],{"encoding":904},". Přibližně: změní-li se ",[883,89833,89835],{"className":89834},[886],[888,89836,89837],{"xmlns":890},[892,89838,89839,89847],{},[895,89840,89841],{},[1953,89842,89843,89845],{},[898,89844,2470],{},[1810,89846,1959],{},[902,89848,30393],{"encoding":904},[883,89850,89852],{"className":89851},[886],[888,89853,89854],{"xmlns":890},[892,89855,89856,89860],{},[895,89857,89858],{},[898,89859,207],{},[902,89861,207],{"encoding":904},[883,89863,89865],{"className":89864},[886],[888,89866,89867],{"xmlns":890},[892,89868,89869,89877],{},[895,89870,89871,89873,89875],{},[898,89872,207],{},[1677,89874,1776],{},[1810,89876,1959],{},[902,89878,2384],{"encoding":904}," při pevném ",[883,89881,89883],{"className":89882},[886],[888,89884,89885],{"xmlns":890},[892,89886,89887,89899],{},[895,89888,89889,89895,89897],{},[1953,89890,89891,89893],{},[898,89892,2470],{},[1810,89894,1812],{},[1677,89896,1679],{},[898,89898,1779],{},[902,89900,89901],{"encoding":904},"Q_2 = b",", změní se užitečnost zhruba o ",[883,89904,89906],{"className":89905},[886],[888,89907,89908],{"xmlns":890},[892,89909,89910,89930],{},[895,89911,89912,89914,89920,89922,89924,89926,89928],{},[898,89913,2499],{},[1953,89915,89916,89918],{},[898,89917,900],{},[1810,89919,1959],{},[1677,89921,1686],{"stretchy":1685},[898,89923,207],{},[1677,89925,1967],{"separator":1966},[898,89927,1779],{},[1677,89929,1692],{"stretchy":1685},[902,89931,89687],{"encoding":904},". Stejně tak ",[883,89934,89936],{"className":89935},[886],[888,89937,89938],{"xmlns":890},[892,89939,89940,89950],{},[895,89941,89942,89944],{},[898,89943,2499],{},[1953,89945,89946,89948],{},[898,89947,900],{},[1810,89949,1812],{},[902,89951,89952],{"encoding":904},"MU_2",[883,89954,89956],{"className":89955},[886],[888,89957,89958],{"xmlns":890},[892,89959,89960,89968],{},[895,89961,89962],{},[1953,89963,89964,89966],{},[898,89965,2470],{},[1810,89967,1812],{},[902,89969,30412],{"encoding":904},". Mezní užitečnost tedy odpovídá „užitku z další jednotky\" a podle předpokladu 5 s množstvím klesá.",[198,89972,81602],{"id":89973},"totální-diferenciál",[724,89975,89976,89977,49731,89993,90023,90024,2385],{},"Přibližnou změnu užitečnosti ",[883,89978,89980],{"className":89979},[886],[888,89981,89982],{"xmlns":890},[892,89983,89984,89990],{},[895,89985,89986,89988],{},[898,89987,2570],{"mathvariant":2057},[898,89989,900],{},[902,89991,89992],{"encoding":904},"\\Delta U",[883,89994,89996],{"className":89995},[886],[888,89997,89998],{"xmlns":890},[892,89999,90000,90020],{},[895,90001,90002,90004,90010,90012,90014],{},[898,90003,1875],{"mathvariant":2057},[1953,90005,90006,90008],{},[898,90007,2470],{},[1810,90009,1959],{},[1677,90011,1967],{"separator":1966},[898,90013,1875],{"mathvariant":2057},[1953,90015,90016,90018],{},[898,90017,2470],{},[1810,90019,1812],{},[902,90021,90022],{"encoding":904},"\\mathrm{d} Q_1, \\mathrm{d} Q_2"," stanovíme pomocí ",[38,90025,90026],{},"totálního diferenciálu",[883,90028,90030],{"className":90029},[886],[888,90031,90032],{"xmlns":890,"display":29457},[892,90033,90034,90135],{},[22145,90035,90036],{"width":29462},[22150,90037,90038,90040,90128,90130],{},[22153,90039],{"width":29467},[22153,90041,90042],{},[895,90043,90044,90046,90048,90050,90052,90054,90056,90064,90066,90072,90074,90082,90084,90090,90092,90094,90100,90102,90108,90110,90112,90118,90120,90126],{},[898,90045,2570],{"mathvariant":2057},[898,90047,900],{},[1677,90049,2411],{},[898,90051,1875],{"mathvariant":2057},[898,90053,900],{},[1677,90055,1679],{},[10554,90057,90058,90060,90062],{},[898,90059,900],{},[1810,90061,1959],{},[1677,90063,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[898,90065,1875],{"mathvariant":2057},[1953,90067,90068,90070],{},[898,90069,2470],{},[1810,90071,1959],{},[1677,90073,1776],{},[10554,90075,90076,90078,90080],{},[898,90077,900],{},[1810,90079,1812],{},[1677,90081,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[898,90083,1875],{"mathvariant":2057},[1953,90085,90086,90088],{},[898,90087,2470],{},[1810,90089,1812],{},[1677,90091,1679],{},[898,90093,2499],{},[1953,90095,90096,90098],{},[898,90097,900],{},[1810,90099,1959],{},[898,90101,1875],{"mathvariant":2057},[1953,90103,90104,90106],{},[898,90105,2470],{},[1810,90107,1959],{},[1677,90109,1776],{},[898,90111,2499],{},[1953,90113,90114,90116],{},[898,90115,900],{},[1810,90117,1812],{},[898,90119,1875],{"mathvariant":2057},[1953,90121,90122,90124],{},[898,90123,2470],{},[1810,90125,1812],{},[898,90127,1656],{"mathvariant":2057},[22153,90129],{"width":29467},[22153,90131,90132],{},[1969,90133,90134],{},"(6.3)",[902,90136,90137],{"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}",[724,90139,76860,90140,1656],{},[883,90141,90143],{"className":90142},[886],[888,90144,90145],{"xmlns":890},[892,90146,90147,90217],{},[895,90148,90149,90151,90153,90155,90157,90159,90165,90167,90169,90175,90177,90183,90185,90187,90193,90195,90197,90199,90201,90207,90209,90215],{},[898,90150,2570],{"mathvariant":2057},[898,90152,900],{},[1677,90154,1679],{},[898,90156,900],{},[1677,90158,1686],{"stretchy":1685},[1953,90160,90161,90163],{},[898,90162,2470],{},[1810,90164,1959],{},[1677,90166,1776],{},[898,90168,1875],{"mathvariant":2057},[1953,90170,90171,90173],{},[898,90172,2470],{},[1810,90174,1959],{},[1677,90176,1967],{"separator":1966},[1953,90178,90179,90181],{},[898,90180,2470],{},[1810,90182,1812],{},[1677,90184,1776],{},[898,90186,1875],{"mathvariant":2057},[1953,90188,90189,90191],{},[898,90190,2470],{},[1810,90192,1812],{},[1677,90194,1692],{"stretchy":1685},[1677,90196,1906],{},[898,90198,900],{},[1677,90200,1686],{"stretchy":1685},[1953,90202,90203,90205],{},[898,90204,2470],{},[1810,90206,1959],{},[1677,90208,1967],{"separator":1966},[1953,90210,90211,90213],{},[898,90212,2470],{},[1810,90214,1812],{},[1677,90216,1692],{"stretchy":1685},[902,90218,90219],{"encoding":904},"\\Delta U = U(Q_1 + \\mathrm{d} Q_1, Q_2 + \\mathrm{d} Q_2) - U(Q_1, Q_2)",[115,90221,90223],{"id":90222},"vlastnosti-funkce-užitečnosti","Vlastnosti funkce užitečnosti",[724,90225,90226,90227,90230,90231,90234],{},"Funkce užitečnosti musí vyjadřovat dva ekonomicky zásadní předpoklady — ",[38,90228,90229],{},"rostoucí užitečnost"," (předpoklad 4) a ",[38,90232,90233],{},"klesající mezní užitečnost"," (předpoklad 5).",[724,90236,90237,90240,90241,43205,90267,90293,90294,1343,90326,90358,90359,5272,90413,90467],{},[38,90238,90239],{},"Předpoklad 4"," (rostoucí užitečnost) znamená, že při pevně zadaných ",[883,90242,90244],{"className":90243},[886],[888,90245,90246],{"xmlns":890},[892,90247,90248,90264],{},[895,90249,90250,90256,90258],{},[1953,90251,90252,90254],{},[898,90253,2470],{},[1810,90255,1812],{},[1677,90257,1679],{},[1953,90259,90260,90262],{},[898,90261,207],{},[1810,90263,2008],{},[902,90265,90266],{"encoding":904},"Q_2 = a_0",[883,90268,90270],{"className":90269},[886],[888,90271,90272],{"xmlns":890},[892,90273,90274,90290],{},[895,90275,90276,90282,90284],{},[1953,90277,90278,90280],{},[898,90279,2470],{},[1810,90281,1959],{},[1677,90283,1679],{},[1953,90285,90286,90288],{},[898,90287,1779],{},[1810,90289,2008],{},[902,90291,90292],{"encoding":904},"Q_1 = b_0"," jsou funkce jedné proměnné ",[883,90295,90297],{"className":90296},[886],[888,90298,90299],{"xmlns":890},[892,90300,90301,90323],{},[895,90302,90303,90305,90307,90313,90315,90321],{},[898,90304,900],{},[1677,90306,1686],{"stretchy":1685},[1953,90308,90309,90311],{},[898,90310,2470],{},[1810,90312,1959],{},[1677,90314,1967],{"separator":1966},[1953,90316,90317,90319],{},[898,90318,207],{},[1810,90320,2008],{},[1677,90322,1692],{"stretchy":1685},[902,90324,90325],{"encoding":904},"U(Q_1, a_0)",[883,90327,90329],{"className":90328},[886],[888,90330,90331],{"xmlns":890},[892,90332,90333,90355],{},[895,90334,90335,90337,90339,90345,90347,90353],{},[898,90336,900],{},[1677,90338,1686],{"stretchy":1685},[1953,90340,90341,90343],{},[898,90342,1779],{},[1810,90344,2008],{},[1677,90346,1967],{"separator":1966},[1953,90348,90349,90351],{},[898,90350,2470],{},[1810,90352,1812],{},[1677,90354,1692],{"stretchy":1685},[902,90356,90357],{"encoding":904},"U(b_0, Q_2)"," rostoucí. To platí, jestliže ",[883,90360,90362],{"className":90361},[886],[888,90363,90364],{"xmlns":890},[892,90365,90366,90410],{},[895,90367,90368,90406,90408],{},[2006,90369,90370],{"scriptlevel":2008,"displaystyle":1966},[2010,90371,90372,90396],{},[895,90373,90374,90376,90378,90380,90386,90388,90394],{},[898,90375,1875],{"mathvariant":2057},[898,90377,900],{},[1677,90379,1686],{"stretchy":1685},[1953,90381,90382,90384],{},[898,90383,2470],{},[1810,90385,1959],{},[1677,90387,1967],{"separator":1966},[1953,90389,90390,90392],{},[898,90391,207],{},[1810,90393,2008],{},[1677,90395,1692],{"stretchy":1685},[895,90397,90398,90400],{},[898,90399,1875],{"mathvariant":2057},[1953,90401,90402,90404],{},[898,90403,2470],{},[1810,90405,1959],{},[1677,90407,3089],{},[1810,90409,2008],{},[902,90411,90412],{"encoding":904},"\\dfrac{\\mathrm{d} U(Q_1, a_0)}{\\mathrm{d} Q_1} > 0",[883,90414,90416],{"className":90415},[886],[888,90417,90418],{"xmlns":890},[892,90419,90420,90464],{},[895,90421,90422,90460,90462],{},[2006,90423,90424],{"scriptlevel":2008,"displaystyle":1966},[2010,90425,90426,90450],{},[895,90427,90428,90430,90432,90434,90440,90442,90448],{},[898,90429,1875],{"mathvariant":2057},[898,90431,900],{},[1677,90433,1686],{"stretchy":1685},[1953,90435,90436,90438],{},[898,90437,1779],{},[1810,90439,2008],{},[1677,90441,1967],{"separator":1966},[1953,90443,90444,90446],{},[898,90445,2470],{},[1810,90447,1812],{},[1677,90449,1692],{"stretchy":1685},[895,90451,90452,90454],{},[898,90453,1875],{"mathvariant":2057},[1953,90455,90456,90458],{},[898,90457,2470],{},[1810,90459,1812],{},[1677,90461,3089],{},[1810,90463,2008],{},[902,90465,90466],{"encoding":904},"\\dfrac{\\mathrm{d} U(b_0, Q_2)}{\\mathrm{d} Q_2} > 0",", tj.",[883,90469,90471],{"className":90470},[886],[888,90472,90473],{"xmlns":890,"display":29457},[892,90474,90475,90520],{},[22145,90476,90477],{"width":29462},[22150,90478,90479,90481,90513,90515],{},[22153,90480],{"width":29467},[22153,90482,90483],{},[895,90484,90485,90493,90495,90497,90499,90501,90509,90511],{},[10554,90486,90487,90489,90491],{},[898,90488,900],{},[1810,90490,1959],{},[1677,90492,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,90494,3089],{},[1810,90496,2008],{},[1677,90498,1967],{"separator":1966},[7266,90500],{"width":16674},[10554,90502,90503,90505,90507],{},[898,90504,900],{},[1810,90506,1812],{},[1677,90508,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,90510,3089],{},[1810,90512,13850],{},[22153,90514],{"width":29467},[22153,90516,90517],{},[1969,90518,90519],{},"(6.4)",[902,90521,90522],{"encoding":904},"U'_1 > 0, \\quad U'_2 > 0. \\tag{6.4}",[724,90524,90525,90526,90528],{},"Tedy mezní užitečnosti obou zboží jsou ",[38,90527,54068],{}," — užitečnost roste s množstvím každého zboží.",[724,90530,90531,90534,90535,90565,90566,2385],{},[38,90532,90533],{},"Předpoklad 5"," (klesající mezní užitečnost) požaduje, aby ",[883,90536,90538],{"className":90537},[886],[888,90539,90540],{"xmlns":890},[892,90541,90542,90562],{},[895,90543,90544,90552,90554],{},[10554,90545,90546,90548,90550],{},[898,90547,900],{},[1810,90549,1959],{},[1677,90551,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,90553,1967],{"separator":1966},[10554,90555,90556,90558,90560],{},[898,90557,900],{},[1810,90559,1812],{},[1677,90561,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[902,90563,90564],{"encoding":904},"U'_1, U'_2"," byly klesající funkce. To znamená, že jejich parciální derivace podle příslušné proměnné jsou ",[38,90567,90568],{},"záporné",[883,90570,90572],{"className":90571},[886],[888,90573,90574],{"xmlns":890,"display":29457},[892,90575,90576,90629],{},[22145,90577,90578],{"width":29462},[22150,90579,90580,90582,90622,90624],{},[22153,90581],{"width":29467},[22153,90583,90584],{},[895,90585,90586,90598,90600,90602,90604,90606,90618,90620],{},[10554,90587,90588,90590,90592],{},[898,90589,900],{},[1810,90591,2585],{},[895,90593,90594,90596],{},[1677,90595,2059],{"mathvariant":2057},[1677,90597,2059],{"mathvariant":2057},[1677,90599,3128],{},[1810,90601,2008],{},[1677,90603,1967],{"separator":1966},[7266,90605],{"width":16674},[10554,90607,90608,90610,90612],{},[898,90609,900],{},[1810,90611,33937],{},[895,90613,90614,90616],{},[1677,90615,2059],{"mathvariant":2057},[1677,90617,2059],{"mathvariant":2057},[1677,90619,3128],{},[1810,90621,13850],{},[22153,90623],{"width":29467},[22153,90625,90626],{},[1969,90627,90628],{},"(6.5)",[902,90630,90631],{"encoding":904},"U''_{11} \u003C 0, \\quad U''_{22} \u003C 0. \\tag{6.5}",[724,90633,90634,90635,90638,90639,1656],{},"Podmínka (6.5) je známa jako ",[38,90636,90637],{},"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 ",[207,90640,90642],{"className":90641,"dataFsResolvedFilePath":857,"href":858},[210],"produkční teorie",[724,90644,90645,90646,5272,90678,90710,90711,5272,90737,90763,90764,90792,90793,5272,90795,90797,90798,90833],{},"Podmínky (6.4), (6.5) určují tvary křivek ",[883,90647,90649],{"className":90648},[886],[888,90650,90651],{"xmlns":890},[892,90652,90653,90675],{},[895,90654,90655,90657,90659,90665,90667,90673],{},[898,90656,900],{},[1677,90658,1686],{"stretchy":1685},[1953,90660,90661,90663],{},[898,90662,2470],{},[1810,90664,1959],{},[1677,90666,1967],{"separator":1966},[1953,90668,90669,90671],{},[898,90670,1779],{},[1810,90672,2008],{},[1677,90674,1692],{"stretchy":1685},[902,90676,90677],{"encoding":904},"U(Q_1, b_0)",[883,90679,90681],{"className":90680},[886],[888,90682,90683],{"xmlns":890},[892,90684,90685,90707],{},[895,90686,90687,90689,90691,90697,90699,90705],{},[898,90688,900],{},[1677,90690,1686],{"stretchy":1685},[1953,90692,90693,90695],{},[898,90694,207],{},[1810,90696,2008],{},[1677,90698,1967],{"separator":1966},[1953,90700,90701,90703],{},[898,90702,2470],{},[1810,90704,1812],{},[1677,90706,1692],{"stretchy":1685},[902,90708,90709],{"encoding":904},"U(a_0, Q_2)"," v souřadnicových rovinách ",[883,90712,90714],{"className":90713},[886],[888,90715,90716],{"xmlns":890},[892,90717,90718,90734],{},[895,90719,90720,90722,90724,90726,90732],{},[1677,90721,1686],{"stretchy":1685},[898,90723,900],{},[1677,90725,1967],{"separator":1966},[1953,90727,90728,90730],{},[898,90729,2470],{},[1810,90731,1959],{},[1677,90733,1692],{"stretchy":1685},[902,90735,90736],{"encoding":904},"(U, Q_1)",[883,90738,90740],{"className":90739},[886],[888,90741,90742],{"xmlns":890},[892,90743,90744,90760],{},[895,90745,90746,90748,90750,90752,90758],{},[1677,90747,1686],{"stretchy":1685},[898,90749,900],{},[1677,90751,1967],{"separator":1966},[1953,90753,90754,90756],{},[898,90755,2470],{},[1810,90757,1812],{},[1677,90759,1692],{"stretchy":1685},[902,90761,90762],{"encoding":904},"(U, Q_2)"," (obrázek 6.1). Tyto křivky procházejí počátkem (neboť obvykle ",[883,90765,90767],{"className":90766},[886],[888,90768,90769],{"xmlns":890},[892,90770,90771,90789],{},[895,90772,90773,90775,90777,90779,90781,90783,90785,90787],{},[898,90774,900],{},[1677,90776,1686],{"stretchy":1685},[1810,90778,2008],{},[1677,90780,1967],{"separator":1966},[1810,90782,2008],{},[1677,90784,1692],{"stretchy":1685},[1677,90786,1679],{},[1810,90788,2008],{},[902,90790,90791],{"encoding":904},"U(0, 0) = 0","), jsou ",[38,90794,15047],{},[38,90796,39879],{},". Typický tvar grafu ",[883,90799,90801],{"className":90800},[886],[888,90802,90803],{"xmlns":890},[892,90804,90805,90831],{},[895,90806,90807,90809,90811,90813,90815,90821,90823,90829],{},[898,90808,900],{},[1677,90810,1679],{},[898,90812,900],{},[1677,90814,1686],{"stretchy":1685},[1953,90816,90817,90819],{},[898,90818,2470],{},[1810,90820,1959],{},[1677,90822,1967],{"separator":1966},[1953,90824,90825,90827],{},[898,90826,2470],{},[1810,90828,1812],{},[1677,90830,1692],{"stretchy":1685},[902,90832,88847],{"encoding":904}," — plocha v prostoru — je na obrázku 6.2.",[724,90835,90836],{},[614,90837,90838,90839,89879,90867,90888,90889,89879,90917,90939],{},"Obrázek 6.1 — typické průběhy funkce užitečnosti ",[883,90840,90842],{"className":90841},[886],[888,90843,90844],{"xmlns":890},[892,90845,90846,90864],{},[895,90847,90848,90850,90852,90858,90860,90862],{},[898,90849,900],{},[1677,90851,1686],{"stretchy":1685},[1953,90853,90854,90856],{},[898,90855,2470],{},[1810,90857,1959],{},[1677,90859,1967],{"separator":1966},[898,90861,1779],{},[1677,90863,1692],{"stretchy":1685},[902,90865,90866],{"encoding":904},"U(Q_1, b)",[883,90868,90870],{"className":90869},[886],[888,90871,90872],{"xmlns":890},[892,90873,90874,90886],{},[895,90875,90876,90882,90884],{},[1953,90877,90878,90880],{},[898,90879,2470],{},[1810,90881,1812],{},[1677,90883,1679],{},[898,90885,1779],{},[902,90887,89901],{"encoding":904}," (vlevo) a ",[883,90890,90892],{"className":90891},[886],[888,90893,90894],{"xmlns":890},[892,90895,90896,90914],{},[895,90897,90898,90900,90902,90904,90906,90912],{},[898,90899,900],{},[1677,90901,1686],{"stretchy":1685},[898,90903,207],{},[1677,90905,1967],{"separator":1966},[1953,90907,90908,90910],{},[898,90909,2470],{},[1810,90911,1812],{},[1677,90913,1692],{"stretchy":1685},[902,90915,90916],{"encoding":904},"U(a, Q_2)",[883,90918,90920],{"className":90919},[886],[888,90921,90922],{"xmlns":890},[892,90923,90924,90936],{},[895,90925,90926,90932,90934],{},[1953,90927,90928,90930],{},[898,90929,2470],{},[1810,90931,1959],{},[1677,90933,1679],{},[898,90935,207],{},[902,90937,90938],{"encoding":904},"Q_1 = a"," (vpravo) pro různé hladiny druhé proměnné.",[724,90941,90942],{},[614,90943,90944,90945,90980,90981,91011,91012,5272,91035,91057,91058,1656],{},"Obrázek 6.2 — plocha funkce užitečnosti ",[883,90946,90948],{"className":90947},[886],[888,90949,90950],{"xmlns":890},[892,90951,90952,90978],{},[895,90953,90954,90956,90958,90960,90962,90968,90970,90976],{},[898,90955,900],{},[1677,90957,1679],{},[898,90959,900],{},[1677,90961,1686],{"stretchy":1685},[1953,90963,90964,90966],{},[898,90965,2470],{},[1810,90967,1959],{},[1677,90969,1967],{"separator":1966},[1953,90971,90972,90974],{},[898,90973,2470],{},[1810,90975,1812],{},[1677,90977,1692],{"stretchy":1685},[902,90979,88847],{"encoding":904}," nad rovinou ",[883,90982,90984],{"className":90983},[886],[888,90985,90986],{"xmlns":890},[892,90987,90988,91008],{},[895,90989,90990,90992,90998,91000,91006],{},[1677,90991,1686],{"stretchy":1685},[1953,90993,90994,90996],{},[898,90995,2470],{},[1810,90997,1959],{},[1677,90999,1967],{"separator":1966},[1953,91001,91002,91004],{},[898,91003,2470],{},[1810,91005,1812],{},[1677,91007,1692],{"stretchy":1685},[902,91009,91010],{"encoding":904},"(Q_1, Q_2)"," s řezy rovinami ",[883,91013,91015],{"className":91014},[886],[888,91016,91017],{"xmlns":890},[892,91018,91019,91032],{},[895,91020,91021,91027,91029],{},[1953,91022,91023,91025],{},[898,91024,2470],{},[1810,91026,1959],{},[1677,91028,1679],{},[1969,91030,91031],{},"const",[902,91033,91034],{"encoding":904},"Q_1 = \\text{const}",[883,91036,91038],{"className":91037},[886],[888,91039,91040],{"xmlns":890},[892,91041,91042,91054],{},[895,91043,91044,91050,91052],{},[1953,91045,91046,91048],{},[898,91047,2470],{},[1810,91049,1812],{},[1677,91051,1679],{},[1969,91053,91031],{},[902,91055,91056],{"encoding":904},"Q_2 = \\text{const}"," a s křivkou ",[883,91059,91061],{"className":91060},[886],[888,91062,91063],{"xmlns":890},[892,91064,91065,91091],{},[895,91066,91067,91069,91071,91077,91079,91085,91087,91089],{},[898,91068,900],{},[1677,91070,1686],{"stretchy":1685},[1953,91072,91073,91075],{},[898,91074,2470],{},[1810,91076,1959],{},[1677,91078,1967],{"separator":1966},[1953,91080,91081,91083],{},[898,91082,2470],{},[1810,91084,1812],{},[1677,91086,1692],{"stretchy":1685},[1677,91088,1679],{},[898,91090,1823],{},[902,91092,11156],{"encoding":904},[198,91094,91096,91097],{"id":91095},"příklad-62-ověření-vlastností-a-dopočet-pro-uq112q213u-q_112-q_213","Příklad 6.2 — ověření vlastností a dopočet pro ",[883,91098,91100],{"className":91099},[886],[888,91101,91102],{"xmlns":890},[892,91103,91104,91138],{},[895,91105,91106,91108,91110,91124],{},[898,91107,900],{},[1677,91109,1679],{},[10554,91111,91112,91114,91116],{},[898,91113,2470],{},[1810,91115,1959],{},[895,91117,91118,91120,91122],{},[1810,91119,1959],{},[898,91121,6062],{"mathvariant":2057},[1810,91123,1812],{},[10554,91125,91126,91128,91130],{},[898,91127,2470],{},[1810,91129,1812],{},[895,91131,91132,91134,91136],{},[1810,91133,1959],{},[898,91135,6062],{"mathvariant":2057},[1810,91137,1854],{},[902,91139,91140],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F3}",[724,91142,91143],{},[38,91144,91145],{},"Ověření (6.4) a (6.5).",[883,91147,91149],{"className":91148},[886],[888,91150,91151],{"xmlns":890,"display":29457},[892,91152,91153,91257],{},[895,91154,91155,91163,91165,91173,91189,91203,91205,91207,91215,91217,91225,91239,91255],{},[10554,91156,91157,91159,91161],{},[898,91158,900],{},[1810,91160,1959],{},[1677,91162,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,91164,1679],{},[2006,91166,91167],{"scriptlevel":2008,"displaystyle":1685},[2010,91168,91169,91171],{},[1810,91170,1959],{},[1810,91172,1812],{},[10554,91174,91175,91177,91179],{},[898,91176,2470],{},[1810,91178,1959],{},[895,91180,91181,91183,91185,91187],{},[1677,91182,1906],{},[1810,91184,1959],{},[898,91186,6062],{"mathvariant":2057},[1810,91188,1812],{},[10554,91190,91191,91193,91195],{},[898,91192,2470],{},[1810,91194,1812],{},[895,91196,91197,91199,91201],{},[1810,91198,1959],{},[898,91200,6062],{"mathvariant":2057},[1810,91202,1854],{},[1677,91204,1967],{"separator":1966},[7266,91206],{"width":16674},[10554,91208,91209,91211,91213],{},[898,91210,900],{},[1810,91212,1812],{},[1677,91214,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,91216,1679],{},[2006,91218,91219],{"scriptlevel":2008,"displaystyle":1685},[2010,91220,91221,91223],{},[1810,91222,1959],{},[1810,91224,1854],{},[10554,91226,91227,91229,91231],{},[898,91228,2470],{},[1810,91230,1959],{},[895,91232,91233,91235,91237],{},[1810,91234,1959],{},[898,91236,6062],{"mathvariant":2057},[1810,91238,1812],{},[10554,91240,91241,91243,91245],{},[898,91242,2470],{},[1810,91244,1812],{},[895,91246,91247,91249,91251,91253],{},[1677,91248,1906],{},[1810,91250,1812],{},[898,91252,6062],{"mathvariant":2057},[1810,91254,1854],{},[1677,91256,1967],{"separator":1966},[902,91258,91259],{"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},",[724,91261,91262,91263,91297],{},"zřejmě ",[883,91264,91266],{"className":91265},[886],[888,91267,91268],{"xmlns":890},[892,91269,91270,91294],{},[895,91271,91272,91280,91282,91290,91292],{},[10554,91273,91274,91276,91278],{},[898,91275,900],{},[1810,91277,1959],{},[1677,91279,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,91281,1967],{"separator":1966},[10554,91283,91284,91286,91288],{},[898,91285,900],{},[1810,91287,1812],{},[1677,91289,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,91291,3089],{},[1810,91293,2008],{},[902,91295,91296],{"encoding":904},"U'_1, U'_2 > 0"," a platí (6.4). Dále:",[883,91299,91301],{"className":91300},[886],[888,91302,91303],{"xmlns":890,"display":29457},[892,91304,91305,91421],{},[895,91306,91307,91319,91321,91323,91331,91347,91361,91363,91365,91377,91379,91381,91389,91403,91419],{},[10554,91308,91309,91311,91313],{},[898,91310,900],{},[1810,91312,2585],{},[895,91314,91315,91317],{},[1677,91316,2059],{"mathvariant":2057},[1677,91318,2059],{"mathvariant":2057},[1677,91320,1679],{},[1677,91322,1906],{},[2006,91324,91325],{"scriptlevel":2008,"displaystyle":1685},[2010,91326,91327,91329],{},[1810,91328,1959],{},[1810,91330,2032],{},[10554,91332,91333,91335,91337],{},[898,91334,2470],{},[1810,91336,1959],{},[895,91338,91339,91341,91343,91345],{},[1677,91340,1906],{},[1810,91342,1854],{},[898,91344,6062],{"mathvariant":2057},[1810,91346,1812],{},[10554,91348,91349,91351,91353],{},[898,91350,2470],{},[1810,91352,1812],{},[895,91354,91355,91357,91359],{},[1810,91356,1959],{},[898,91358,6062],{"mathvariant":2057},[1810,91360,1854],{},[1677,91362,1967],{"separator":1966},[7266,91364],{"width":16674},[10554,91366,91367,91369,91371],{},[898,91368,900],{},[1810,91370,33937],{},[895,91372,91373,91375],{},[1677,91374,2059],{"mathvariant":2057},[1677,91376,2059],{"mathvariant":2057},[1677,91378,1679],{},[1677,91380,1906],{},[2006,91382,91383],{"scriptlevel":2008,"displaystyle":1685},[2010,91384,91385,91387],{},[1810,91386,1812],{},[1810,91388,5387],{},[10554,91390,91391,91393,91395],{},[898,91392,2470],{},[1810,91394,1959],{},[895,91396,91397,91399,91401],{},[1810,91398,1959],{},[898,91400,6062],{"mathvariant":2057},[1810,91402,1812],{},[10554,91404,91405,91407,91409],{},[898,91406,2470],{},[1810,91408,1812],{},[895,91410,91411,91413,91415,91417],{},[1677,91412,1906],{},[1810,91414,1909],{},[898,91416,6062],{"mathvariant":2057},[1810,91418,1854],{},[1677,91420,1967],{"separator":1966},[902,91422,91423],{"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},",[724,91425,91426,91427,91469],{},"opět ",[883,91428,91430],{"className":91429},[886],[888,91431,91432],{"xmlns":890},[892,91433,91434,91466],{},[895,91435,91436,91448,91450,91462,91464],{},[10554,91437,91438,91440,91442],{},[898,91439,900],{},[1810,91441,2585],{},[895,91443,91444,91446],{},[1677,91445,2059],{"mathvariant":2057},[1677,91447,2059],{"mathvariant":2057},[1677,91449,1967],{"separator":1966},[10554,91451,91452,91454,91456],{},[898,91453,900],{},[1810,91455,33937],{},[895,91457,91458,91460],{},[1677,91459,2059],{"mathvariant":2057},[1677,91461,2059],{"mathvariant":2057},[1677,91463,3128],{},[1810,91465,2008],{},[902,91467,91468],{"encoding":904},"U''_{11}, U''_{22} \u003C 0",", platí (6.5).",[724,91471,91472],{},[38,91473,91474,91475,1656],{},"(a) Mezní užitečnosti v bodě ",[883,91476,91478],{"className":91477},[886],[888,91479,91480],{"xmlns":890},[892,91481,91482,91494],{},[895,91483,91484,91486,91488,91490,91492],{},[1677,91485,2167],{"stretchy":1685},[1810,91487,2771],{},[1677,91489,1967],{"separator":1966},[1810,91491,9765],{},[1677,91493,2182],{"stretchy":1685},[902,91495,91496],{"encoding":904},"[100, 200]",[883,91498,91500],{"className":91499},[886],[888,91501,91502],{"xmlns":890,"display":29457},[892,91503,91504,91571],{},[895,91505,91506,91508,91514,91516,91518,91520,91522,91524,91526,91534,91536,91550,91552,91564,91566,91569],{},[898,91507,2499],{},[1953,91509,91510,91512],{},[898,91511,900],{},[1810,91513,1959],{},[1677,91515,1686],{"stretchy":1685},[1810,91517,2771],{},[1677,91519,1967],{"separator":1966},[1810,91521,9765],{},[1677,91523,1692],{"stretchy":1685},[1677,91525,1679],{},[2006,91527,91528],{"scriptlevel":2008,"displaystyle":1685},[2010,91529,91530,91532],{},[1810,91531,1959],{},[1810,91533,1812],{},[1677,91535,2858],{},[1805,91537,91538,91540],{},[1810,91539,2771],{},[895,91541,91542,91544,91546,91548],{},[1677,91543,1906],{},[1810,91545,1959],{},[898,91547,6062],{"mathvariant":2057},[1810,91549,1812],{},[1677,91551,2858],{},[1805,91553,91554,91556],{},[1810,91555,9765],{},[895,91557,91558,91560,91562],{},[1810,91559,1959],{},[898,91561,6062],{"mathvariant":2057},[1810,91563,1854],{},[1677,91565,7288],{},[1810,91567,91568],{},"0,4204",[1677,91570,1967],{"separator":1966},[902,91572,91573],{"encoding":904},"MU_1(100, 200) = \\tfrac{1}{2} \\cdot 100^{-1\u002F2} \\cdot 200^{1\u002F3} \\doteq 0{,}4204,",[883,91575,91577],{"className":91576},[886],[888,91578,91579],{"xmlns":890,"display":29457},[892,91580,91581,91646],{},[895,91582,91583,91585,91591,91593,91595,91597,91599,91601,91603,91611,91613,91625,91627,91641,91643],{},[898,91584,2499],{},[1953,91586,91587,91589],{},[898,91588,900],{},[1810,91590,1812],{},[1677,91592,1686],{"stretchy":1685},[1810,91594,2771],{},[1677,91596,1967],{"separator":1966},[1810,91598,9765],{},[1677,91600,1692],{"stretchy":1685},[1677,91602,1679],{},[2006,91604,91605],{"scriptlevel":2008,"displaystyle":1685},[2010,91606,91607,91609],{},[1810,91608,1959],{},[1810,91610,1854],{},[1677,91612,2858],{},[1805,91614,91615,91617],{},[1810,91616,2771],{},[895,91618,91619,91621,91623],{},[1810,91620,1959],{},[898,91622,6062],{"mathvariant":2057},[1810,91624,1812],{},[1677,91626,2858],{},[1805,91628,91629,91631],{},[1810,91630,9765],{},[895,91632,91633,91635,91637,91639],{},[1677,91634,1906],{},[1810,91636,1812],{},[898,91638,6062],{"mathvariant":2057},[1810,91640,1854],{},[1677,91642,7288],{},[1810,91644,91645],{},"0,63067.",[902,91647,91648],{"encoding":904},"MU_2(100, 200) = \\tfrac{1}{3} \\cdot 100^{1\u002F2} \\cdot 200^{-2\u002F3} \\doteq 0{,}63067.",[724,91650,91651,1884,91653,91688,91689,91710,91711,91728],{},[614,91652,10604],{},[883,91654,91656],{"className":91655},[886],[888,91657,91658],{"xmlns":890},[892,91659,91660,91685],{},[895,91661,91662,91664,91670,91672,91674,91676,91678,91680,91682],{},[898,91663,2499],{},[1953,91665,91666,91668],{},[898,91667,900],{},[1810,91669,1812],{},[1677,91671,1686],{"stretchy":1685},[1810,91673,2771],{},[1677,91675,1967],{"separator":1966},[1810,91677,9765],{},[1677,91679,1692],{"stretchy":1685},[1677,91681,7288],{},[1810,91683,91684],{},"0,63067",[902,91686,91687],{"encoding":904},"MU_2(100, 200) \\doteq 0{,}63067"," znamená, že na hladině ",[883,91690,91692],{"className":91691},[886],[888,91693,91694],{"xmlns":890},[892,91695,91696,91708],{},[895,91697,91698,91700,91702,91704,91706],{},[1677,91699,2167],{"stretchy":1685},[1810,91701,2771],{},[1677,91703,1967],{"separator":1966},[1810,91705,9765],{},[1677,91707,2182],{"stretchy":1685},[902,91709,91496],{"encoding":904}," roste užitečnost při jednotkové změně ",[883,91712,91714],{"className":91713},[886],[888,91715,91716],{"xmlns":890},[892,91717,91718,91726],{},[895,91719,91720],{},[1953,91721,91722,91724],{},[898,91723,2470],{},[1810,91725,1812],{},[902,91727,30412],{"encoding":904}," přibližně o 0,63067.",[724,91730,91731,91750,91751,40575,91772,91789,91790,91816,91817,91834,91835,2832],{},[38,91732,91733,91734,91749],{},"(b) Odhad změny ",[883,91735,91737],{"className":91736},[886],[888,91738,91739],{"xmlns":890},[892,91740,91741,91747],{},[895,91742,91743,91745],{},[898,91744,2570],{"mathvariant":2057},[898,91746,900],{},[902,91748,89992],{"encoding":904}," pomocí totálního diferenciálu (6.3)."," Klesne-li vzhledem k hladině ",[883,91752,91754],{"className":91753},[886],[888,91755,91756],{"xmlns":890},[892,91757,91758,91770],{},[895,91759,91760,91762,91764,91766,91768],{},[1677,91761,2167],{"stretchy":1685},[1810,91763,2771],{},[1677,91765,1967],{"separator":1966},[1810,91767,9765],{},[1677,91769,2182],{"stretchy":1685},[902,91771,91496],{"encoding":904},[883,91773,91775],{"className":91774},[886],[888,91776,91777],{"xmlns":890},[892,91778,91779,91787],{},[895,91780,91781],{},[1953,91782,91783,91785],{},[898,91784,2470],{},[1810,91786,1959],{},[902,91788,30393],{"encoding":904}," na 98 (tj. ",[883,91791,91793],{"className":91792},[886],[888,91794,91795],{"xmlns":890},[892,91796,91797,91813],{},[895,91798,91799,91801,91807,91809,91811],{},[898,91800,1875],{"mathvariant":2057},[1953,91802,91803,91805],{},[898,91804,2470],{},[1810,91806,1959],{},[1677,91808,1679],{},[1677,91810,1906],{},[1810,91812,1812],{},[902,91814,91815],{"encoding":904},"\\mathrm{d} Q_1 = -2",") a vzroste-li ",[883,91818,91820],{"className":91819},[886],[888,91821,91822],{"xmlns":890},[892,91823,91824,91832],{},[895,91825,91826],{},[1953,91827,91828,91830],{},[898,91829,2470],{},[1810,91831,1812],{},[902,91833,30412],{"encoding":904}," o 3 (tj. ",[883,91836,91838],{"className":91837},[886],[888,91839,91840],{"xmlns":890},[892,91841,91842,91856],{},[895,91843,91844,91846,91852,91854],{},[898,91845,1875],{"mathvariant":2057},[1953,91847,91848,91850],{},[898,91849,2470],{},[1810,91851,1812],{},[1677,91853,1679],{},[1810,91855,1854],{},[902,91857,91858],{"encoding":904},"\\mathrm{d} Q_2 = 3",[883,91860,91862],{"className":91861},[886],[888,91863,91864],{"xmlns":890,"display":29457},[892,91865,91866,91917],{},[895,91867,91868,91870,91872,91874,91876,91878,91880,91882,91884,91886,91888,91890,91892,91894,91896,91898,91900,91902,91904,91907,91909,91912,91914],{},[898,91869,2570],{"mathvariant":2057},[898,91871,900],{},[1677,91873,2411],{},[898,91875,1875],{"mathvariant":2057},[898,91877,900],{},[1677,91879,1679],{},[1810,91881,91568],{},[1677,91883,2858],{},[1677,91885,1686],{"stretchy":1685},[1677,91887,1906],{},[1810,91889,1812],{},[1677,91891,1692],{"stretchy":1685},[1677,91893,1776],{},[1810,91895,91684],{},[1677,91897,2858],{},[1810,91899,1854],{},[1677,91901,1679],{},[1677,91903,1906],{},[1810,91905,91906],{},"0,8408",[1677,91908,1776],{},[1810,91910,91911],{},"1,89201",[1677,91913,7288],{},[1810,91915,91916],{},"1,05.",[902,91918,91919],{"encoding":904},"\\Delta U \\approx \\mathrm{d} U = 0{,}4204 \\cdot (-2) + 0{,}63067 \\cdot 3 = -0{,}8408 + 1{,}89201 \\doteq 1{,}05.",[724,91921,91922,91923,91926,91927,91978,91979,1656],{},"Užitečnost se tedy zvýší přibližně o ",[38,91924,91925],{},"1,05",". Skutečná změna je ",[883,91928,91930],{"className":91929},[886],[888,91931,91932],{"xmlns":890},[892,91933,91934,91975],{},[895,91935,91936,91938,91940,91942,91944,91946,91949,91951,91954,91956,91958,91960,91962,91964,91966,91968,91970,91972],{},[898,91937,2570],{"mathvariant":2057},[898,91939,900],{},[1677,91941,1679],{},[898,91943,900],{},[1677,91945,1686],{"stretchy":1685},[1810,91947,91948],{},"98",[1677,91950,1967],{"separator":1966},[1810,91952,91953],{},"203",[1677,91955,1692],{"stretchy":1685},[1677,91957,1906],{},[898,91959,900],{},[1677,91961,1686],{"stretchy":1685},[1810,91963,2771],{},[1677,91965,1967],{"separator":1966},[1810,91967,9765],{},[1677,91969,1692],{"stretchy":1685},[1677,91971,7288],{},[1810,91973,91974],{},"1,031",[902,91976,91977],{"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 ",[883,91980,91982],{"className":91981},[886],[888,91983,91984],{"xmlns":890},[892,91985,91986,92006],{},[895,91987,91988,91990,91996,91998,92000],{},[898,91989,1875],{"mathvariant":2057},[1953,91991,91992,91994],{},[898,91993,2470],{},[1810,91995,1959],{},[1677,91997,1967],{"separator":1966},[898,91999,1875],{"mathvariant":2057},[1953,92001,92002,92004],{},[898,92003,2470],{},[1810,92005,1812],{},[902,92007,90022],{"encoding":904},[115,92009,92011],{"id":92010},"cobb-douglasova-funkce-užitečnosti","Cobb-Douglasova funkce užitečnosti",[724,92013,92014],{},"Nejčastěji používané funkce užitečnosti mají tvar",[883,92016,92018],{"className":92017},[886],[888,92019,92020],{"xmlns":890,"display":29457},[892,92021,92022,92081],{},[22145,92023,92024],{"width":29462},[22150,92025,92026,92028,92074,92076],{},[22153,92027],{"width":29467},[22153,92029,92030],{},[895,92031,92032,92034,92036,92042,92044,92050,92052,92054,92062,92064,92072],{},[898,92033,900],{},[1677,92035,1686],{"stretchy":1685},[1953,92037,92038,92040],{},[898,92039,2470],{},[1810,92041,1959],{},[1677,92043,1967],{"separator":1966},[1953,92045,92046,92048],{},[898,92047,2470],{},[1810,92049,1812],{},[1677,92051,1692],{"stretchy":1685},[1677,92053,1679],{},[10554,92055,92056,92058,92060],{},[898,92057,2470],{},[1810,92059,1959],{},[898,92061,207],{},[1677,92063,2858],{},[10554,92065,92066,92068,92070],{},[898,92067,2470],{},[1810,92069,1812],{},[898,92071,1779],{},[1677,92073,1967],{"separator":1966},[22153,92075],{"width":29467},[22153,92077,92078],{},[1969,92079,92080],{},"(6.6)",[902,92082,92083],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^b, \\tag{6.6}",[724,92085,5698,92086,92104,92105,92107,92108,92112,92113,92143,92144,92166],{},[883,92087,92089],{"className":92088},[886],[888,92090,92091],{"xmlns":890},[892,92092,92093,92101],{},[895,92094,92095,92097,92099],{},[898,92096,207],{},[1677,92098,1967],{"separator":1966},[898,92100,1779],{},[902,92102,92103],{"encoding":904},"a, b"," jsou kladná čísla; nazývají se ",[38,92106,76090],{}," (v příbuznosti s produkčními funkcemi — viz ",[207,92109,92111],{"className":92110,"dataFsResolvedFilePath":857,"href":858},[210],"kapitola 5","). Obvykle se volí ",[883,92114,92116],{"className":92115},[886],[888,92117,92118],{"xmlns":890},[892,92119,92120,92140],{},[895,92121,92122,92124,92126,92128,92130,92132,92134,92136,92138],{},[898,92123,207],{},[1677,92125,1967],{"separator":1966},[898,92127,1779],{},[1677,92129,7894],{},[1677,92131,1686],{"stretchy":1685},[1810,92133,2008],{},[1677,92135,1967],{"separator":1966},[1810,92137,1959],{},[1677,92139,1692],{"stretchy":1685},[902,92141,92142],{"encoding":904},"a, b \\in (0, 1)",", často se klade ",[883,92145,92147],{"className":92146},[886],[888,92148,92149],{"xmlns":890},[892,92150,92151,92163],{},[895,92152,92153,92155,92157,92159,92161],{},[898,92154,1779],{},[1677,92156,1679],{},[1810,92158,1959],{},[1677,92160,1906],{},[898,92162,207],{},[902,92164,92165],{"encoding":904},"b = 1 - a",", čímž (6.6) přejde na tvar",[724,92168,92169],{},[2240,92170],{"alt":92171,"className":92172,"src":92173},"imek-cobb-douglas-3d-plus-ic",[210,2244],"\u002Fwiki-assets\u002Fimek-cobb-douglas-3d-plus-ic.jpeg",[883,92175,92177],{"className":92176},[886],[888,92178,92179],{"xmlns":890,"display":29457},[892,92180,92181,92231],{},[895,92182,92183,92185,92187,92193,92195,92201,92203,92205,92213,92215,92229],{},[898,92184,900],{},[1677,92186,1686],{"stretchy":1685},[1953,92188,92189,92191],{},[898,92190,2470],{},[1810,92192,1959],{},[1677,92194,1967],{"separator":1966},[1953,92196,92197,92199],{},[898,92198,2470],{},[1810,92200,1812],{},[1677,92202,1692],{"stretchy":1685},[1677,92204,1679],{},[10554,92206,92207,92209,92211],{},[898,92208,2470],{},[1810,92210,1959],{},[898,92212,207],{},[1677,92214,2858],{},[10554,92216,92217,92219,92221],{},[898,92218,2470],{},[1810,92220,1812],{},[895,92222,92223,92225,92227],{},[1810,92224,1959],{},[1677,92226,1906],{},[898,92228,207],{},[898,92230,1656],{"mathvariant":2057},[902,92232,92233],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^{1-a}.",[5254,92235,92236,92285,92407,92541],{},[724,92237,92238,92240,92241],{},[883,92239,54086],{}," Příklad 6.3 — ověření vlastností pro ",[883,92242,92244],{"className":92243},[886],[888,92245,92246],{"xmlns":890},[892,92247,92248,92282],{},[895,92249,92250,92252,92254,92268],{},[898,92251,900],{},[1677,92253,1679],{},[10554,92255,92256,92258,92260],{},[898,92257,2470],{},[1810,92259,1959],{},[895,92261,92262,92264,92266],{},[1810,92263,1959],{},[898,92265,6062],{"mathvariant":2057},[1810,92267,2032],{},[10554,92269,92270,92272,92274],{},[898,92271,2470],{},[1810,92273,1812],{},[895,92275,92276,92278,92280],{},[1810,92277,1854],{},[898,92279,6062],{"mathvariant":2057},[1810,92281,2032],{},[902,92283,92284],{"encoding":904},"U = Q_1^{1\u002F4} Q_2^{3\u002F4}",[883,92286,92288],{"className":92287},[886],[888,92289,92290],{"xmlns":890,"display":29457},[892,92291,92292,92404],{},[895,92293,92294,92302,92304,92312,92328,92342,92344,92346,92348,92350,92358,92360,92368,92382,92398,92400,92402],{},[10554,92295,92296,92298,92300],{},[898,92297,900],{},[1810,92299,1959],{},[1677,92301,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,92303,1679],{},[2006,92305,92306],{"scriptlevel":2008,"displaystyle":1685},[2010,92307,92308,92310],{},[1810,92309,1959],{},[1810,92311,2032],{},[10554,92313,92314,92316,92318],{},[898,92315,2470],{},[1810,92317,1959],{},[895,92319,92320,92322,92324,92326],{},[1677,92321,1906],{},[1810,92323,1854],{},[898,92325,6062],{"mathvariant":2057},[1810,92327,2032],{},[10554,92329,92330,92332,92334],{},[898,92331,2470],{},[1810,92333,1812],{},[895,92335,92336,92338,92340],{},[1810,92337,1854],{},[898,92339,6062],{"mathvariant":2057},[1810,92341,2032],{},[1677,92343,3089],{},[1810,92345,2008],{},[1677,92347,1967],{"separator":1966},[7266,92349],{"width":16674},[10554,92351,92352,92354,92356],{},[898,92353,900],{},[1810,92355,1812],{},[1677,92357,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,92359,1679],{},[2006,92361,92362],{"scriptlevel":2008,"displaystyle":1685},[2010,92363,92364,92366],{},[1810,92365,1854],{},[1810,92367,2032],{},[10554,92369,92370,92372,92374],{},[898,92371,2470],{},[1810,92373,1959],{},[895,92375,92376,92378,92380],{},[1810,92377,1959],{},[898,92379,6062],{"mathvariant":2057},[1810,92381,2032],{},[10554,92383,92384,92386,92388],{},[898,92385,2470],{},[1810,92387,1812],{},[895,92389,92390,92392,92394,92396],{},[1677,92391,1906],{},[1810,92393,1959],{},[898,92395,6062],{"mathvariant":2057},[1810,92397,2032],{},[1677,92399,3089],{},[1810,92401,2008],{},[1677,92403,1967],{"separator":1966},[902,92405,92406],{"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,",[883,92408,92410],{"className":92409},[886],[888,92411,92412],{"xmlns":890,"display":29457},[892,92413,92414,92538],{},[895,92415,92416,92428,92430,92432,92440,92456,92470,92472,92474,92476,92478,92490,92492,92494,92502,92516,92532,92534,92536],{},[10554,92417,92418,92420,92422],{},[898,92419,900],{},[1810,92421,2585],{},[895,92423,92424,92426],{},[1677,92425,2059],{"mathvariant":2057},[1677,92427,2059],{"mathvariant":2057},[1677,92429,1679],{},[1677,92431,1906],{},[2006,92433,92434],{"scriptlevel":2008,"displaystyle":1685},[2010,92435,92436,92438],{},[1810,92437,1854],{},[1810,92439,43253],{},[10554,92441,92442,92444,92446],{},[898,92443,2470],{},[1810,92445,1959],{},[895,92447,92448,92450,92452,92454],{},[1677,92449,1906],{},[1810,92451,25592],{},[898,92453,6062],{"mathvariant":2057},[1810,92455,2032],{},[10554,92457,92458,92460,92462],{},[898,92459,2470],{},[1810,92461,1812],{},[895,92463,92464,92466,92468],{},[1810,92465,1854],{},[898,92467,6062],{"mathvariant":2057},[1810,92469,2032],{},[1677,92471,3128],{},[1810,92473,2008],{},[1677,92475,1967],{"separator":1966},[7266,92477],{"width":16674},[10554,92479,92480,92482,92484],{},[898,92481,900],{},[1810,92483,33937],{},[895,92485,92486,92488],{},[1677,92487,2059],{"mathvariant":2057},[1677,92489,2059],{"mathvariant":2057},[1677,92491,1679],{},[1677,92493,1906],{},[2006,92495,92496],{"scriptlevel":2008,"displaystyle":1685},[2010,92497,92498,92500],{},[1810,92499,1854],{},[1810,92501,43253],{},[10554,92503,92504,92506,92508],{},[898,92505,2470],{},[1810,92507,1959],{},[895,92509,92510,92512,92514],{},[1810,92511,1959],{},[898,92513,6062],{"mathvariant":2057},[1810,92515,2032],{},[10554,92517,92518,92520,92522],{},[898,92519,2470],{},[1810,92521,1812],{},[895,92523,92524,92526,92528,92530],{},[1677,92525,1906],{},[1810,92527,1909],{},[898,92529,6062],{"mathvariant":2057},[1810,92531,2032],{},[1677,92533,3128],{},[1810,92535,2008],{},[1677,92537,1967],{"separator":1966},[902,92539,92540],{"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,",[724,92542,92543],{},"tedy podmínky (6.4) i (6.5) jsou splněny.",[115,92545,92547],{"id":92546},"indiferenční-křivky-křivky-užitečnosti-a-jejich-vlastnosti","Indiferenční křivky (křivky užitečnosti) a jejich vlastnosti",[724,92549,92550,92553],{},[38,92551,92552],{},"Křivky užitečnosti"," (utility curves) jsou indiferenční křivky funkce užitečnosti. Jsou dány rovnicí",[883,92555,92557],{"className":92556},[886],[888,92558,92559],{"xmlns":890,"display":29457},[892,92560,92561,92604],{},[22145,92562,92563],{"width":29462},[22150,92564,92565,92567,92597,92599],{},[22153,92566],{"width":29467},[22153,92568,92569],{},[895,92570,92571,92573,92575,92581,92583,92589,92591,92593,92595],{},[898,92572,900],{},[1677,92574,1686],{"stretchy":1685},[1953,92576,92577,92579],{},[898,92578,2470],{},[1810,92580,1959],{},[1677,92582,1967],{"separator":1966},[1953,92584,92585,92587],{},[898,92586,2470],{},[1810,92588,1812],{},[1677,92590,1692],{"stretchy":1685},[1677,92592,1679],{},[898,92594,1823],{},[1677,92596,1967],{"separator":1966},[22153,92598],{"width":29467},[22153,92600,92601],{},[1969,92602,92603],{},"(6.7)",[902,92605,92606],{"encoding":904},"U(Q_1, Q_2) = c, \\tag{6.7}",[724,92608,5698,92609,92622],{},[883,92610,92612],{"className":92611},[886],[888,92613,92614],{"xmlns":890},[892,92615,92616,92620],{},[895,92617,92618],{},[898,92619,1823],{},[902,92621,1823],{"encoding":904}," je kladná konstanta. Pro Cobb-Douglasovu funkci:",[883,92624,92626],{"className":92625},[886],[888,92627,92628],{"xmlns":890,"display":29457},[892,92629,92630,92671],{},[22145,92631,92632],{"width":29462},[22150,92633,92634,92636,92664,92666],{},[22153,92635],{"width":29467},[22153,92637,92638],{},[895,92639,92640,92648,92650,92658,92660,92662],{},[10554,92641,92642,92644,92646],{},[898,92643,2470],{},[1810,92645,1959],{},[898,92647,207],{},[1677,92649,2858],{},[10554,92651,92652,92654,92656],{},[898,92653,2470],{},[1810,92655,1812],{},[898,92657,1779],{},[1677,92659,1679],{},[898,92661,1823],{},[898,92663,1656],{"mathvariant":2057},[22153,92665],{"width":29467},[22153,92667,92668],{},[1969,92669,92670],{},"(6.8)",[902,92672,92673],{"encoding":904},"Q_1^a \\cdot Q_2^b = c. \\tag{6.8}",[724,92675,92676,92677,5746,92707,1884,92710,92723,92724,92759,92760,92777,92778,92807,92808,92811],{},"Body na téže křivce užitečnosti reprezentují kombinace ",[883,92678,92680],{"className":92679},[886],[888,92681,92682],{"xmlns":890},[892,92683,92684,92704],{},[895,92685,92686,92688,92694,92696,92702],{},[1677,92687,2167],{"stretchy":1685},[1953,92689,92690,92692],{},[898,92691,2470],{},[1810,92693,1959],{},[1677,92695,1967],{"separator":1966},[1953,92697,92698,92700],{},[898,92699,2470],{},[1810,92701,1812],{},[1677,92703,2182],{"stretchy":1685},[902,92705,92706],{"encoding":904},"[Q_1, Q_2]",[38,92708,92709],{},"stejnou úrovní uspokojení",[883,92711,92713],{"className":92712},[886],[888,92714,92715],{"xmlns":890},[892,92716,92717,92721],{},[895,92718,92719],{},[898,92720,1823],{},[902,92722,1823],{"encoding":904},". Křivky užitečnosti vznikají jako průsečnice plochy ",[883,92725,92727],{"className":92726},[886],[888,92728,92729],{"xmlns":890},[892,92730,92731,92757],{},[895,92732,92733,92735,92737,92739,92741,92747,92749,92755],{},[898,92734,900],{},[1677,92736,1679],{},[898,92738,900],{},[1677,92740,1686],{"stretchy":1685},[1953,92742,92743,92745],{},[898,92744,2470],{},[1810,92746,1959],{},[1677,92748,1967],{"separator":1966},[1953,92750,92751,92753],{},[898,92752,2470],{},[1810,92754,1812],{},[1677,92756,1692],{"stretchy":1685},[902,92758,88847],{"encoding":904}," s rovinami ",[883,92761,92763],{"className":92762},[886],[888,92764,92765],{"xmlns":890},[892,92766,92767,92775],{},[895,92768,92769,92771,92773],{},[898,92770,900],{},[1677,92772,1679],{},[898,92774,1823],{},[902,92776,88063],{"encoding":904}," rovnoběžnými s rovinou ",[883,92779,92781],{"className":92780},[886],[888,92782,92783],{"xmlns":890},[892,92784,92785,92805],{},[895,92786,92787,92789,92795,92797,92803],{},[1677,92788,1686],{"stretchy":1685},[1953,92790,92791,92793],{},[898,92792,2470],{},[1810,92794,1959],{},[1677,92796,1967],{"separator":1966},[1953,92798,92799,92801],{},[898,92800,2470],{},[1810,92802,1812],{},[1677,92804,1692],{"stretchy":1685},[902,92806,91010],{"encoding":904}," (obrázek 6.2). Jsou v příbuznosti s ",[38,92809,92810],{},"izokvantami"," produkčních funkcí.",[724,92813,92814],{},[614,92815,92816,92817,90888,92835,92853,92854,1656],{},"Obrázek 6.3 — typický tvar křivek užitečnosti pro Cobb-Douglasovu funkci pro ",[883,92818,92820],{"className":92819},[886],[888,92821,92822],{"xmlns":890},[892,92823,92824,92832],{},[895,92825,92826,92828,92830],{},[898,92827,207],{},[1677,92829,3128],{},[898,92831,1779],{},[902,92833,92834],{"encoding":904},"a \u003C b",[883,92836,92838],{"className":92837},[886],[888,92839,92840],{"xmlns":890},[892,92841,92842,92850],{},[895,92843,92844,92846,92848],{},[898,92845,207],{},[1677,92847,3089],{},[898,92849,1779],{},[902,92851,92852],{"encoding":904},"a > b"," (vpravo); různé hladiny ",[883,92855,92857],{"className":92856},[886],[888,92858,92859],{"xmlns":890},[892,92860,92861,92885],{},[895,92862,92863,92869,92871,92877,92879],{},[1953,92864,92865,92867],{},[898,92866,1823],{},[1810,92868,2008],{},[1677,92870,3128],{},[1953,92872,92873,92875],{},[898,92874,1823],{},[1810,92876,1959],{},[1677,92878,3128],{},[1953,92880,92881,92883],{},[898,92882,1823],{},[1810,92884,1812],{},[902,92886,92887],{"encoding":904},"c_0 \u003C c_1 \u003C c_2",[724,92889,92890],{},[614,92891,92892,92893,92922,92923,92981,92982,93000],{},"Obrázek 6.4 — soustava křivek užitečnosti pro tři hladiny (10, 20, 30) v rovině ",[883,92894,92896],{"className":92895},[886],[888,92897,92898],{"xmlns":890},[892,92899,92900,92920],{},[895,92901,92902,92904,92910,92912,92918],{},[1677,92903,1686],{"stretchy":1685},[1953,92905,92906,92908],{},[898,92907,2470],{},[1810,92909,1959],{},[1677,92911,1967],{"separator":1966},[1953,92913,92914,92916],{},[898,92915,2470],{},[1810,92917,1812],{},[1677,92919,1692],{"stretchy":1685},[902,92921,91010],{"encoding":904},"; body ",[883,92924,92926],{"className":92925},[886],[888,92927,92928],{"xmlns":890},[892,92929,92930,92978],{},[895,92931,92932,92934,92936,92938,92944,92946,92952,92954,92956,92958,92960,92962,92968,92970,92976],{},[898,92933,5643],{},[1677,92935,1679],{},[1677,92937,2167],{"stretchy":1685},[1953,92939,92940,92942],{},[898,92941,207],{},[1810,92943,1959],{},[1677,92945,1967],{"separator":1966},[1953,92947,92948,92950],{},[898,92949,207],{},[1810,92951,1812],{},[1677,92953,2182],{"stretchy":1685},[1677,92955,1967],{"separator":1966},[898,92957,24644],{},[1677,92959,1679],{},[1677,92961,2167],{"stretchy":1685},[1953,92963,92964,92966],{},[898,92965,1779],{},[1810,92967,1959],{},[1677,92969,1967],{"separator":1966},[1953,92971,92972,92974],{},[898,92973,1779],{},[1810,92975,1812],{},[1677,92977,2182],{"stretchy":1685},[902,92979,92980],{"encoding":904},"A = [a_1, a_2], B = [b_1, b_2]"," leží na téže křivce (hladina 10), body ",[883,92983,92985],{"className":92984},[886],[888,92986,92987],{"xmlns":890},[892,92988,92989,92997],{},[895,92990,92991,92993,92995],{},[898,92992,2458],{},[1677,92994,1967],{"separator":1966},[898,92996,5571],{},[902,92998,92999],{"encoding":904},"C, D"," na vyšší hladině.",[5254,93002,93003],{},[724,93004,93005,93007,93008,93070,93071,93115,93116,93150,93151,27580,93169,93150,93223,27580,93241,93317],{},[883,93006,54086],{}," Příklad 6.4 — rovnice křivek užitečnosti\nPro ",[883,93009,93011],{"className":93010},[886],[888,93012,93013],{"xmlns":890},[892,93014,93015,93067],{},[895,93016,93017,93019,93021,93027,93029,93035,93037,93039,93053],{},[898,93018,900],{},[1677,93020,1686],{"stretchy":1685},[1953,93022,93023,93025],{},[898,93024,2470],{},[1810,93026,1959],{},[1677,93028,1967],{"separator":1966},[1953,93030,93031,93033],{},[898,93032,2470],{},[1810,93034,1812],{},[1677,93036,1692],{"stretchy":1685},[1677,93038,1679],{},[10554,93040,93041,93043,93045],{},[898,93042,2470],{},[1810,93044,1959],{},[895,93046,93047,93049,93051],{},[1810,93048,1959],{},[898,93050,6062],{"mathvariant":2057},[1810,93052,2032],{},[10554,93054,93055,93057,93059],{},[898,93056,2470],{},[1810,93058,1812],{},[895,93060,93061,93063,93065],{},[1810,93062,1854],{},[898,93064,6062],{"mathvariant":2057},[1810,93066,2032],{},[902,93068,93069],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F4} Q_2^{3\u002F4}"," mají křivky užitečnosti rovnici ",[883,93072,93074],{"className":93073},[886],[888,93075,93076],{"xmlns":890},[892,93077,93078,93112],{},[895,93079,93080,93094,93108,93110],{},[10554,93081,93082,93084,93086],{},[898,93083,2470],{},[1810,93085,1959],{},[895,93087,93088,93090,93092],{},[1810,93089,1959],{},[898,93091,6062],{"mathvariant":2057},[1810,93093,2032],{},[10554,93095,93096,93098,93100],{},[898,93097,2470],{},[1810,93099,1812],{},[895,93101,93102,93104,93106],{},[1810,93103,1854],{},[898,93105,6062],{"mathvariant":2057},[1810,93107,2032],{},[1677,93109,1679],{},[898,93111,1823],{},[902,93113,93114],{"encoding":904},"Q_1^{1\u002F4} Q_2^{3\u002F4} = c",". Umocněním na čtvrtou mocninu dostáváme ",[883,93117,93119],{"className":93118},[886],[888,93120,93121],{"xmlns":890},[892,93122,93123,93147],{},[895,93124,93125,93131,93139,93141],{},[1953,93126,93127,93129],{},[898,93128,2470],{},[1810,93130,1959],{},[10554,93132,93133,93135,93137],{},[898,93134,2470],{},[1810,93136,1812],{},[1810,93138,1854],{},[1677,93140,1679],{},[1805,93142,93143,93145],{},[898,93144,1823],{},[1810,93146,2032],{},[902,93148,93149],{"encoding":904},"Q_1 Q_2^{3} = c^{4}",". Pro ",[883,93152,93154],{"className":93153},[886],[888,93155,93156],{"xmlns":890},[892,93157,93158,93166],{},[895,93159,93160,93162,93164],{},[898,93161,1823],{},[1677,93163,1679],{},[1810,93165,1959],{},[902,93167,93168],{"encoding":904},"c = 1",[883,93170,93172],{"className":93171},[886],[888,93173,93174],{"xmlns":890},[892,93175,93176,93220],{},[895,93177,93178,93184,93186,93202,93204],{},[1953,93179,93180,93182],{},[898,93181,2470],{},[1810,93183,1812],{},[1677,93185,1679],{},[10554,93187,93188,93190,93192],{},[898,93189,2470],{},[1810,93191,1959],{},[895,93193,93194,93196,93198,93200],{},[1677,93195,1906],{},[1810,93197,1959],{},[898,93199,6062],{"mathvariant":2057},[1810,93201,1854],{},[1677,93203,1679],{},[2006,93205,93206],{"scriptlevel":2008,"displaystyle":1966},[2010,93207,93208,93210],{},[1810,93209,1959],{},[83418,93211,93212,93218],{},[1953,93213,93214,93216],{},[898,93215,2470],{},[1810,93217,1959],{},[1810,93219,1854],{},[902,93221,93222],{"encoding":904},"Q_2 = Q_1^{-1\u002F3} = \\dfrac{1}{\\sqrt[3]{Q_1}}",[883,93224,93226],{"className":93225},[886],[888,93227,93228],{"xmlns":890},[892,93229,93230,93238],{},[895,93231,93232,93234,93236],{},[898,93233,1823],{},[1677,93235,1679],{},[1810,93237,1812],{},[902,93239,93240],{"encoding":904},"c = 2",[883,93242,93244],{"className":93243},[886],[888,93245,93246],{"xmlns":890},[892,93247,93248,93314],{},[895,93249,93250,93256,93258,93270,93272,93288,93290],{},[1953,93251,93252,93254],{},[898,93253,2470],{},[1810,93255,1812],{},[1677,93257,1679],{},[1805,93259,93260,93262],{},[1810,93261,1812],{},[895,93263,93264,93266,93268],{},[1810,93265,2032],{},[898,93267,6062],{"mathvariant":2057},[1810,93269,1854],{},[1677,93271,2858],{},[10554,93273,93274,93276,93278],{},[898,93275,2470],{},[1810,93277,1959],{},[895,93279,93280,93282,93284,93286],{},[1677,93281,1906],{},[1810,93283,1959],{},[898,93285,6062],{"mathvariant":2057},[1810,93287,1854],{},[1677,93289,1679],{},[2006,93291,93292],{"scriptlevel":2008,"displaystyle":1966},[2010,93293,93294,93304],{},[895,93295,93296,93298],{},[1810,93297,1812],{},[83418,93299,93300,93302],{},[1810,93301,1812],{},[1810,93303,1854],{},[83418,93305,93306,93312],{},[1953,93307,93308,93310],{},[898,93309,2470],{},[1810,93311,1959],{},[1810,93313,1854],{},[902,93315,93316],{"encoding":904},"Q_2 = 2^{4\u002F3} \\cdot Q_1^{-1\u002F3} = \\dfrac{2 \\sqrt[3]{2}}{\\sqrt[3]{Q_1}}"," (obrázek 6.5).",[198,93319,93321],{"id":93320},"čtyři-vlastnosti-křivek-užitečnosti","Čtyři vlastnosti křivek užitečnosti",[724,93323,93324],{},[2240,93325],{"alt":93326,"className":93327,"src":93328},"imek-ic-4vlastnosti-anotovane",[210,2244],"\u002Fwiki-assets\u002Fimek-ic-4vlastnosti-anotovane.jpeg",[5254,93330,93331,93340,93387,93431,93437,93443],{},[724,93332,93333,93335,93336,93339],{},[883,93334,5800],{}," Čtyři základní vlastnosti indiferenčních křivek\n",[38,93337,93338],{},"1° Klesající."," Je-li nakoupeno méně jednoho zboží, je k dosažení stejného uspokojení třeba kompenzovat větším množstvím druhého zboží. Sklon tečny je",[724,93341,93342],{},[883,93343,93345],{"className":93344},[886],[888,93346,93347],{"xmlns":890},[892,93348,93349,93384],{},[895,93350,93351,93354,93356,93358,93360,93362,93380,93382],{},[898,93352,93353],{"mathvariant":2057},"tg",[1677,93355,57591],{},[898,93357,20253],{},[1677,93359,1679],{},[1677,93361,1906],{},[2010,93363,93364,93372],{},[10554,93365,93366,93368,93370],{},[898,93367,900],{},[1810,93369,1959],{},[1677,93371,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[10554,93373,93374,93376,93378],{},[898,93375,900],{},[1810,93377,1812],{},[1677,93379,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,93381,3128],{},[1810,93383,2008],{},[902,93385,93386],{"encoding":904},"\\operatorname{tg} \\alpha = -\\frac{U'_1}{U'_2} \u003C 0",[724,93388,93389,93390,93430],{},"(derivace implicitně zadané funkce ",[883,93391,93393],{"className":93392},[886],[888,93394,93395],{"xmlns":890},[892,93396,93397,93427],{},[895,93398,93399,93401,93403,93409,93411,93417,93419,93421,93423,93425],{},[898,93400,900],{},[1677,93402,1686],{"stretchy":1685},[1953,93404,93405,93407],{},[898,93406,2470],{},[1810,93408,1959],{},[1677,93410,1967],{"separator":1966},[1953,93412,93413,93415],{},[898,93414,2470],{},[1810,93416,1812],{},[1677,93418,1692],{"stretchy":1685},[1677,93420,1906],{},[898,93422,1823],{},[1677,93424,1679],{},[1810,93426,2008],{},[902,93428,93429],{"encoding":904},"U(Q_1, Q_2) - c = 0","). Ze záporné derivace plyne klesající průběh.",[724,93432,93433,93436],{},[38,93434,93435],{},"2° Neprotínají se."," V průsečíku by týž svazek ležel na dvou různých hladinách užitečnosti, což je spor.",[724,93438,93439,93442],{},[38,93440,93441],{},"3° Čím vzdálenější od počátku, tím vyšší užitečnost"," (obrázek 6.4).",[724,93444,93445,93448,93449,93467,93468,93484,93485,93488],{},[38,93446,93447],{},"4° Konvexní."," Pro každé dva body ",[883,93450,93452],{"className":93451},[886],[888,93453,93454],{"xmlns":890},[892,93455,93456,93464],{},[895,93457,93458,93460,93462],{},[898,93459,5643],{},[1677,93461,1967],{"separator":1966},[898,93463,24644],{},[902,93465,93466],{"encoding":904},"A, B"," na téže křivce leží vnitřní body úsečky ",[883,93469,93471],{"className":93470},[886],[888,93472,93473],{"xmlns":890},[892,93474,93475,93481],{},[895,93476,93477,93479],{},[898,93478,5643],{},[898,93480,24644],{},[902,93482,93483],{"encoding":904},"AB"," ve ",[38,93486,93487],{},"vyšší"," hladině užitečnosti (tj. „nad\" křivkou) — vyjadřuje to preferenci smíšených svazků před krajními.",[724,93490,93491],{},[614,93492,93493,93494,93529,93530,1656],{},"Obrázek 6.6 — klesající a konvexní průběh ",[883,93495,93497],{"className":93496},[886],[888,93498,93499],{"xmlns":890},[892,93500,93501,93527],{},[895,93502,93503,93505,93507,93513,93515,93521,93523,93525],{},[898,93504,900],{},[1677,93506,1686],{"stretchy":1685},[1953,93508,93509,93511],{},[898,93510,2470],{},[1810,93512,1959],{},[1677,93514,1967],{"separator":1966},[1953,93516,93517,93519],{},[898,93518,2470],{},[1810,93520,1812],{},[1677,93522,1692],{"stretchy":1685},[1677,93524,1679],{},[898,93526,1823],{},[902,93528,11156],{"encoding":904}," s tečnou se sklonem ",[883,93531,93533],{"className":93532},[886],[888,93534,93535],{"xmlns":890},[892,93536,93537,93545],{},[895,93538,93539,93541,93543],{},[898,93540,93353],{"mathvariant":2057},[1677,93542,57591],{},[898,93544,20253],{},[902,93546,93547],{"encoding":904},"\\operatorname{tg}\\alpha",[115,93549,93551],{"id":93550},"mezní-míra-komoditní-substituce-mrcs","Mezní míra komoditní substituce (MRCS)",[724,93553,93554,1884,93557,11413,93570,93573],{},[38,93555,93556],{},"Mezní míra komoditní substituce",[883,93558,93560],{"className":93559},[886],[888,93561,93562],{"xmlns":890},[892,93563,93564,93568],{},[895,93565,93566],{},[1969,93567,11991],{},[902,93569,29629],{"encoding":904},[38,93571,93572],{},"marginal rate of commodity substitution",") je podíl mezních užitečností:",[883,93575,93577],{"className":93576},[886],[888,93578,93579],{"xmlns":890,"display":29457},[892,93580,93581,93668],{},[22145,93582,93583],{"width":29462},[22150,93584,93585,93587,93661,93663],{},[22153,93586],{"width":29467},[22153,93588,93589],{},[895,93590,93591,93593,93595,93597,93599,93605,93607,93613,93615,93617,93639,93641,93659],{},[1969,93592,11991],{},[1677,93594,1679],{},[1969,93596,11991],{},[1677,93598,1686],{"stretchy":1685},[1953,93600,93601,93603],{},[898,93602,2470],{},[1810,93604,1959],{},[1677,93606,1967],{"separator":1966},[1953,93608,93609,93611],{},[898,93610,2470],{},[1810,93612,1812],{},[1677,93614,1692],{"stretchy":1685},[1677,93616,1679],{},[2010,93618,93619,93629],{},[895,93620,93621,93623],{},[898,93622,2499],{},[1953,93624,93625,93627],{},[898,93626,900],{},[1810,93628,1959],{},[895,93630,93631,93633],{},[898,93632,2499],{},[1953,93634,93635,93637],{},[898,93636,900],{},[1810,93638,1812],{},[1677,93640,1679],{},[2010,93642,93643,93651],{},[10554,93644,93645,93647,93649],{},[898,93646,900],{},[1810,93648,1959],{},[1677,93650,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[10554,93652,93653,93655,93657],{},[898,93654,900],{},[1810,93656,1812],{},[1677,93658,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[898,93660,1656],{"mathvariant":2057},[22153,93662],{"width":29467},[22153,93664,93665],{},[1969,93666,93667],{},"(6.9)",[902,93669,93670],{"encoding":904},"\\text{MRCS} = \\text{MRCS}(Q_1, Q_2) = \\frac{MU_1}{MU_2} = \\frac{U'_1}{U'_2}. \\tag{6.9}",[724,93672,93673,93674,93708,93709,93741,93742,93777,93778,93791],{},"Geometricky: ",[883,93675,93677],{"className":93676},[886],[888,93678,93679],{"xmlns":890},[892,93680,93681,93705],{},[895,93682,93683,93685],{},[1677,93684,1906],{},[2006,93686,93687],{"scriptlevel":2008,"displaystyle":1685},[2010,93688,93689,93697],{},[10554,93690,93691,93693,93695],{},[898,93692,900],{},[1810,93694,1959],{},[1677,93696,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[10554,93698,93699,93701,93703],{},[898,93700,900],{},[1810,93702,1812],{},[1677,93704,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[902,93706,93707],{"encoding":904},"-\\tfrac{U'_1}{U'_2}"," je derivace funkce ",[883,93710,93712],{"className":93711},[886],[888,93713,93714],{"xmlns":890},[892,93715,93716,93738],{},[895,93717,93718,93724,93726,93728,93730,93736],{},[1953,93719,93720,93722],{},[898,93721,2470],{},[1810,93723,1812],{},[1677,93725,1679],{},[898,93727,1682],{},[1677,93729,1686],{"stretchy":1685},[1953,93731,93732,93734],{},[898,93733,2470],{},[1810,93735,1959],{},[1677,93737,1692],{"stretchy":1685},[902,93739,93740],{"encoding":904},"Q_2 = f(Q_1)"," zadané implicitně rovnicí ",[883,93743,93745],{"className":93744},[886],[888,93746,93747],{"xmlns":890},[892,93748,93749,93775],{},[895,93750,93751,93753,93755,93761,93763,93769,93771,93773],{},[898,93752,900],{},[1677,93754,1686],{"stretchy":1685},[1953,93756,93757,93759],{},[898,93758,2470],{},[1810,93760,1959],{},[1677,93762,1967],{"separator":1966},[1953,93764,93765,93767],{},[898,93766,2470],{},[1810,93768,1812],{},[1677,93770,1692],{"stretchy":1685},[1677,93772,1679],{},[898,93774,1823],{},[902,93776,11156],{"encoding":904},". Protože je vždy záporná (křivka je klesající), bereme absolutní hodnotu a kladný ",[883,93779,93781],{"className":93780},[886],[888,93782,93783],{"xmlns":890},[892,93784,93785,93789],{},[895,93786,93787],{},[1969,93788,11991],{},[902,93790,29629],{"encoding":904}," chápeme jako velikost kompenzace.",[5254,93793,93794],{},[724,93795,93796,93798,93799,9490,93831,93869,93870,93887,93888,93905],{},[883,93797,5543],{}," Intuice — MRCS jako sklon indiferenční křivky\n",[883,93800,93802],{"className":93801},[886],[888,93803,93804],{"xmlns":890},[892,93805,93806,93828],{},[895,93807,93808,93810,93812,93818,93820,93826],{},[1969,93809,11991],{},[1677,93811,1686],{"stretchy":1685},[1953,93813,93814,93816],{},[898,93815,2470],{},[1810,93817,1959],{},[1677,93819,1967],{"separator":1966},[1953,93821,93822,93824],{},[898,93823,2470],{},[1810,93825,1812],{},[1677,93827,1692],{"stretchy":1685},[902,93829,93830],{"encoding":904},"\\text{MRCS}(Q_1, Q_2)",[38,93832,93833,93834,30394,93851,93868],{},"míra, jakou je spotřebitel ochoten zaměnit ",[883,93835,93837],{"className":93836},[886],[888,93838,93839],{"xmlns":890},[892,93840,93841,93849],{},[895,93842,93843],{},[1953,93844,93845,93847],{},[898,93846,2470],{},[1810,93848,1959],{},[902,93850,30393],{"encoding":904},[883,93852,93854],{"className":93853},[886],[888,93855,93856],{"xmlns":890},[892,93857,93858,93866],{},[895,93859,93860],{},[1953,93861,93862,93864],{},[898,93863,2470],{},[1810,93865,1812],{},[902,93867,30412],{"encoding":904}," při zachování užitečnosti"," — tedy kolik jednotek ",[883,93871,93873],{"className":93872},[886],[888,93874,93875],{"xmlns":890},[892,93876,93877,93885],{},[895,93878,93879],{},[1953,93880,93881,93883],{},[898,93882,2470],{},[1810,93884,1812],{},[902,93886,30412],{"encoding":904}," „obětuje\" za jednu jednotku ",[883,93889,93891],{"className":93890},[886],[888,93892,93893],{"xmlns":890},[892,93894,93895,93903],{},[895,93896,93897],{},[1953,93898,93899,93901],{},[898,93900,2470],{},[1810,93902,1959],{},[902,93904,30393],{"encoding":904}," navíc, aby zůstal na téže indiferenční křivce. Geometricky jde o absolutní hodnotu sklonu tečny k indiferenční křivce v daném bodě.",[724,93907,93908,93909,31335],{},"Pro obecnou změnu ",[883,93910,93912],{"className":93911},[886],[888,93913,93914],{"xmlns":890},[892,93915,93916,93926],{},[895,93917,93918,93920],{},[898,93919,1875],{"mathvariant":2057},[1953,93921,93922,93924],{},[898,93923,2470],{},[1810,93925,1959],{},[902,93927,93928],{"encoding":904},"\\mathrm{d} Q_1",[883,93930,93932],{"className":93931},[886],[888,93933,93934],{"xmlns":890,"display":29457},[892,93935,93936,93989],{},[22145,93937,93938],{"width":29462},[22150,93939,93940,93942,93982,93984],{},[22153,93941],{"width":29467},[22153,93943,93944],{},[895,93945,93946,93948,93954,93956,93958,93964,93966,93968,93970,93972,93974,93980],{},[898,93947,2570],{"mathvariant":2057},[1953,93949,93950,93952],{},[898,93951,2470],{},[1810,93953,1812],{},[1677,93955,2411],{},[898,93957,1875],{"mathvariant":2057},[1953,93959,93960,93962],{},[898,93961,2470],{},[1810,93963,1812],{},[1677,93965,1679],{},[1677,93967,1906],{},[1969,93969,11991],{},[1677,93971,2858],{},[898,93973,1875],{"mathvariant":2057},[1953,93975,93976,93978],{},[898,93977,2470],{},[1810,93979,1959],{},[1677,93981,1967],{"separator":1966},[22153,93983],{"width":29467},[22153,93985,93986],{},[1969,93987,93988],{},"(6.10)",[902,93990,93991],{"encoding":904},"\\Delta Q_2 \\approx \\mathrm{d} Q_2 = -\\text{MRCS} \\cdot \\mathrm{d} Q_1, \\tag{6.10}",[883,93993,93995],{"className":93994},[886],[888,93996,93997],{"xmlns":890,"display":29457},[892,93998,93999,94046],{},[22145,94000,94001],{"width":29462},[22150,94002,94003,94005,94039,94041],{},[22153,94004],{"width":29467},[22153,94006,94007],{},[895,94008,94009,94011,94017,94019,94021,94027,94029,94031,94037],{},[898,94010,1875],{"mathvariant":2057},[1953,94012,94013,94015],{},[898,94014,2470],{},[1810,94016,1959],{},[1677,94018,1679],{},[1677,94020,1906],{},[2010,94022,94023,94025],{},[1810,94024,1959],{},[1969,94026,11991],{},[1969,94028,2668],{},[898,94030,1875],{"mathvariant":2057},[1953,94032,94033,94035],{},[898,94034,2470],{},[1810,94036,1812],{},[898,94038,1656],{"mathvariant":2057},[22153,94040],{"width":29467},[22153,94042,94043],{},[1969,94044,94045],{},"(6.11)",[902,94047,94048],{"encoding":904},"\\mathrm{d} Q_1 = -\\frac{1}{\\text{MRCS}}\\, \\mathrm{d} Q_2. \\tag{6.11}",[5254,94050,94051,94117,94234],{},[724,94052,94053,94055,94056,31335],{},[883,94054,54086],{}," Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost\nPro ",[883,94057,94059],{"className":94058},[886],[888,94060,94061],{"xmlns":890},[892,94062,94063,94115],{},[895,94064,94065,94067,94069,94075,94077,94083,94085,94087,94101],{},[898,94066,900],{},[1677,94068,1686],{"stretchy":1685},[1953,94070,94071,94073],{},[898,94072,2470],{},[1810,94074,1959],{},[1677,94076,1967],{"separator":1966},[1953,94078,94079,94081],{},[898,94080,2470],{},[1810,94082,1812],{},[1677,94084,1692],{"stretchy":1685},[1677,94086,1679],{},[10554,94088,94089,94091,94093],{},[898,94090,2470],{},[1810,94092,1959],{},[895,94094,94095,94097,94099],{},[1810,94096,1959],{},[898,94098,6062],{"mathvariant":2057},[1810,94100,1812],{},[10554,94102,94103,94105,94107],{},[898,94104,2470],{},[1810,94106,1812],{},[895,94108,94109,94111,94113],{},[1810,94110,1959],{},[898,94112,6062],{"mathvariant":2057},[1810,94114,1812],{},[902,94116,31334],{"encoding":904},[724,94118,94119],{},[883,94120,94122],{"className":94121},[886],[888,94123,94124],{"xmlns":890},[892,94125,94126,94232],{},[895,94127,94128,94130,94132,94214,94216,94230],{},[1969,94129,11991],{},[1677,94131,1679],{},[2010,94133,94134,94174],{},[895,94135,94136,94144,94160],{},[2006,94137,94138],{"scriptlevel":2008,"displaystyle":1685},[2010,94139,94140,94142],{},[1810,94141,1959],{},[1810,94143,1812],{},[10554,94145,94146,94148,94150],{},[898,94147,2470],{},[1810,94149,1959],{},[895,94151,94152,94154,94156,94158],{},[1677,94153,1906],{},[1810,94155,1959],{},[898,94157,6062],{"mathvariant":2057},[1810,94159,1812],{},[10554,94161,94162,94164,94166],{},[898,94163,2470],{},[1810,94165,1812],{},[895,94167,94168,94170,94172],{},[1810,94169,1959],{},[898,94171,6062],{"mathvariant":2057},[1810,94173,1812],{},[895,94175,94176,94184,94198],{},[2006,94177,94178],{"scriptlevel":2008,"displaystyle":1685},[2010,94179,94180,94182],{},[1810,94181,1959],{},[1810,94183,1812],{},[10554,94185,94186,94188,94190],{},[898,94187,2470],{},[1810,94189,1959],{},[895,94191,94192,94194,94196],{},[1810,94193,1959],{},[898,94195,6062],{"mathvariant":2057},[1810,94197,1812],{},[10554,94199,94200,94202,94204],{},[898,94201,2470],{},[1810,94203,1812],{},[895,94205,94206,94208,94210,94212],{},[1677,94207,1906],{},[1810,94209,1959],{},[898,94211,6062],{"mathvariant":2057},[1810,94213,1812],{},[1677,94215,1679],{},[2010,94217,94218,94224],{},[1953,94219,94220,94222],{},[898,94221,2470],{},[1810,94223,1812],{},[1953,94225,94226,94228],{},[898,94227,2470],{},[1810,94229,1959],{},[898,94231,1656],{"mathvariant":2057},[902,94233,31453],{"encoding":904},[724,94235,31456,94236,2608,94279,31504,94281,94300],{},[883,94237,94239],{"className":94238},[886],[888,94240,94241],{"xmlns":890},[892,94242,94243,94277],{},[895,94244,94245,94247,94249,94251,94253,94255,94257,94259,94267,94269],{},[1969,94246,11991],{},[1677,94248,1686],{"stretchy":1685},[1810,94250,31472],{},[1677,94252,1967],{"separator":1966},[1810,94254,16500],{},[1677,94256,1692],{"stretchy":1685},[1677,94258,1679],{},[2006,94260,94261],{"scriptlevel":2008,"displaystyle":1685},[2010,94262,94263,94265],{},[1810,94264,16500],{},[1810,94266,31472],{},[1677,94268,1679],{},[2006,94270,94271],{"scriptlevel":2008,"displaystyle":1685},[2010,94272,94273,94275],{},[1810,94274,1909],{},[1810,94276,1854],{},[902,94278,31501],{"encoding":904},[614,94280,10604],{},[883,94282,94284],{"className":94283},[886],[888,94285,94286],{"xmlns":890},[892,94287,94288,94298],{},[895,94289,94290],{},[2006,94291,94292],{"scriptlevel":2008,"displaystyle":1685},[2010,94293,94294,94296],{},[1810,94295,1909],{},[1810,94297,1854],{},[902,94299,31524],{"encoding":904}," jednotky, aby se užitečnost zachovala.",[724,94302,94303,94304,94308],{},"(Paralelou je ",[207,94305,94307],{"className":94306,"dataFsResolvedFilePath":857,"href":858},[210],"mezní míra technické substituce MRTS"," z produkční teorie.)",[115,94310,94312],{"id":94311},"_63-64-optimalizace-spotřebitele-přehled","6.3 – 6.4 Optimalizace spotřebitele — přehled",[724,94314,94315,94316,94319],{},"Rámcově se v kapitole 6 studují ",[38,94317,94318],{},"dvě vázané optimalizační úlohy"," s užitečností:",[120,94321,94322,94458],{},[123,94323,94324,94326,94327,11545,94358,1884,94361,94410,94411,1656],{},[38,94325,29643],{}," — maximalizace ",[883,94328,94330],{"className":94329},[886],[888,94331,94332],{"xmlns":890},[892,94333,94334,94356],{},[895,94335,94336,94338,94340,94346,94348,94354],{},[898,94337,900],{},[1677,94339,1686],{"stretchy":1685},[1953,94341,94342,94344],{},[898,94343,2470],{},[1810,94345,1959],{},[1677,94347,1967],{"separator":1966},[1953,94349,94350,94352],{},[898,94351,2470],{},[1810,94353,1812],{},[1677,94355,1692],{"stretchy":1685},[902,94357,17734],{"encoding":904},[38,94359,94360],{},"rozpočtovém omezení",[883,94362,94364],{"className":94363},[886],[888,94365,94366],{"xmlns":890},[892,94367,94368,94408],{},[895,94369,94370,94376,94378,94386,94392,94394,94402],{},[1805,94371,94372,94374],{},[898,94373,10516],{},[1677,94375,5742],{},[1677,94377,1679],{},[10554,94379,94380,94382,94384],{},[898,94381,5325],{},[1810,94383,1959],{},[1677,94385,5742],{},[1953,94387,94388,94390],{},[898,94389,2470],{},[1810,94391,1959],{},[1677,94393,1776],{},[10554,94395,94396,94398,94400],{},[898,94397,5325],{},[1810,94399,1812],{},[1677,94401,5742],{},[1953,94403,94404,94406],{},[898,94405,2470],{},[1810,94407,1812],{},[902,94409,18689],{"encoding":904},". Výstupem je Marshallova poptávka ",[883,94412,94414],{"className":94413},[886],[888,94415,94416],{"xmlns":890},[892,94417,94418,94456],{},[895,94419,94420,94426,94428,94434,94436,94442,94444,94450,94452,94454],{},[1953,94421,94422,94424],{},[898,94423,2470],{},[898,94425,19181],{},[1677,94427,1679],{},[1953,94429,94430,94432],{},[898,94431,5571],{},[898,94433,19181],{},[1677,94435,1686],{"stretchy":1685},[1953,94437,94438,94440],{},[898,94439,5325],{},[1810,94441,1959],{},[1677,94443,1967],{"separator":1966},[1953,94445,94446,94448],{},[898,94447,5325],{},[1810,94449,1812],{},[1677,94451,1967],{"separator":1966},[898,94453,10516],{},[1677,94455,1692],{"stretchy":1685},[902,94457,37846],{"encoding":904},[123,94459,94460,29292,94463,29335,94509,94526,94527,1656],{},[38,94461,94462],{},"Duální úloha",[883,94464,94466],{"className":94465},[886],[888,94467,94468],{"xmlns":890},[892,94469,94470,94506],{},[895,94471,94472,94474,94476,94484,94490,94492,94500],{},[898,94473,5640],{},[1677,94475,1679],{},[10554,94477,94478,94480,94482],{},[898,94479,5325],{},[1810,94481,1959],{},[1677,94483,5742],{},[1953,94485,94486,94488],{},[898,94487,2470],{},[1810,94489,1959],{},[1677,94491,1776],{},[10554,94493,94494,94496,94498],{},[898,94495,5325],{},[1810,94497,1812],{},[1677,94499,5742],{},[1953,94501,94502,94504],{},[898,94503,2470],{},[1810,94505,1812],{},[902,94507,94508],{"encoding":904},"E = P_1^* Q_1 + P_2^* Q_2",[883,94510,94512],{"className":94511},[886],[888,94513,94514],{"xmlns":890},[892,94515,94516,94524],{},[895,94517,94518],{},[1805,94519,94520,94522],{},[898,94521,900],{},[1677,94523,5742],{},[902,94525,29353],{"encoding":904},". Výstupem je Hicksova poptávka ",[883,94528,94530],{"className":94529},[886],[888,94531,94532],{"xmlns":890},[892,94533,94534,94572],{},[895,94535,94536,94542,94544,94550,94552,94558,94560,94566,94568,94570],{},[1953,94537,94538,94540],{},[898,94539,2470],{},[898,94541,19181],{},[1677,94543,1679],{},[1953,94545,94546,94548],{},[898,94547,5571],{},[898,94549,19181],{},[1677,94551,1686],{"stretchy":1685},[1953,94553,94554,94556],{},[898,94555,5325],{},[1810,94557,1959],{},[1677,94559,1967],{"separator":1966},[1953,94561,94562,94564],{},[898,94563,5325],{},[1810,94565,1812],{},[1677,94567,1967],{"separator":1966},[898,94569,900],{},[1677,94571,1692],{"stretchy":1685},[902,94573,19214],{"encoding":904},[724,94575,94576,94577,94580,94581,1884,94584,94623],{},"Obě úlohy se řeší ",[207,94578,29358],{"className":94579,"dataFsResolvedFilePath":791,"href":792},[210]," a vedou na ",[38,94582,94583],{},"tentýž bod dotyku",[883,94585,94587],{"className":94586},[886],[888,94588,94589],{"xmlns":890},[892,94590,94591,94621],{},[895,94592,94593,94599,94601,94609,94611,94619],{},[1805,94594,94595,94597],{},[898,94596,2470],{},[1677,94598,5742],{},[1677,94600,2167],{"stretchy":1685},[10554,94602,94603,94605,94607],{},[898,94604,2470],{},[1810,94606,1959],{},[1677,94608,5742],{},[1677,94610,1967],{"separator":1966},[10554,94612,94613,94615,94617],{},[898,94614,2470],{},[1810,94616,1812],{},[1677,94618,5742],{},[1677,94620,2182],{"stretchy":1685},[902,94622,29718],{"encoding":904}," indiferenční křivky a rozpočtové přímky (resp. přímky výdajů), v němž platí podmínka optimality",[883,94625,94627],{"className":94626},[886],[888,94628,94629],{"xmlns":890,"display":29457},[892,94630,94631,94677],{},[895,94632,94633,94635,94637,94655,94657,94675],{},[1969,94634,11991],{},[1677,94636,1679],{},[2010,94638,94639,94647],{},[10554,94640,94641,94643,94645],{},[898,94642,900],{},[1810,94644,1959],{},[1677,94646,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[10554,94648,94649,94651,94653],{},[898,94650,900],{},[1810,94652,1812],{},[1677,94654,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,94656,1679],{},[2010,94658,94659,94667],{},[10554,94660,94661,94663,94665],{},[898,94662,5325],{},[1810,94664,1959],{},[1677,94666,5742],{},[10554,94668,94669,94671,94673],{},[898,94670,5325],{},[1810,94672,1812],{},[1677,94674,5742],{},[898,94676,1656],{"mathvariant":2057},[902,94678,94679],{"encoding":904},"\\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*}.",[724,94681,94682],{},"Poměr mezních užitečností se rovná poměru cen — sklon indiferenční křivky v optimu se rovná sklonu rozpočtové přímky.",[5254,94684,94685],{},[724,94686,94687,94689,94690,94693,94694,94697,94698,94725,94726,94760,94761,94795,94796,94839,94840,94843,94844,1656],{},[883,94688,5543],{}," Pro detailní postup viz ",[207,94691,38145],{"className":94692,"dataFsResolvedFilePath":911,"href":912},[210],"\nKompletní odvození obou úloh Lagrangeovou metodou, geometrická interpretace, řešené ",[38,94695,94696],{},"Příklady 6.5–6.8"," (MRCS pro Cobb-Douglase, maximalizace ",[883,94699,94701],{"className":94700},[886],[888,94702,94703],{"xmlns":890},[892,94704,94705,94723],{},[895,94706,94707,94709,94711,94717],{},[898,94708,900],{},[1677,94710,1679],{},[1953,94712,94713,94715],{},[898,94714,2470],{},[1810,94716,1959],{},[1953,94718,94719,94721],{},[898,94720,2470],{},[1810,94722,1812],{},[902,94724,31617],{"encoding":904}," s výsledkem ",[883,94727,94729],{"className":94728},[886],[888,94730,94731],{"xmlns":890},[892,94732,94733,94757],{},[895,94734,94735,94741,94743,94745,94747,94753,94755],{},[1953,94736,94737,94739],{},[898,94738,2470],{},[1810,94740,1959],{},[1677,94742,1679],{},[1810,94744,6392],{},[1677,94746,1967],{"separator":1966},[1953,94748,94749,94751],{},[898,94750,2470],{},[1810,94752,1812],{},[1677,94754,1679],{},[1810,94756,2544],{},[902,94758,94759],{"encoding":904},"Q_1 = 25, Q_2 = 10","; minimalizace výdajů s ",[883,94762,94764],{"className":94763},[886],[888,94765,94766],{"xmlns":890},[892,94767,94768,94792],{},[895,94769,94770,94776,94778,94780,94782,94788,94790],{},[1953,94771,94772,94774],{},[898,94773,2470],{},[1810,94775,1959],{},[1677,94777,1679],{},[1810,94779,2032],{},[1677,94781,1967],{"separator":1966},[1953,94783,94784,94786],{},[898,94785,2470],{},[1810,94787,1812],{},[1677,94789,1679],{},[1810,94791,1959],{},[902,94793,94794],{"encoding":904},"Q_1 = 4, Q_2 = 1","; obecná Hicksova poptávka pro ",[883,94797,94799],{"className":94798},[886],[888,94800,94801],{"xmlns":890},[892,94802,94803,94837],{},[895,94804,94805,94807,94809,94823],{},[898,94806,900],{},[1677,94808,1679],{},[10554,94810,94811,94813,94815],{},[898,94812,2470],{},[1810,94814,1959],{},[895,94816,94817,94819,94821],{},[1810,94818,1959],{},[898,94820,6062],{"mathvariant":2057},[1810,94822,1812],{},[10554,94824,94825,94827,94829],{},[898,94826,2470],{},[1810,94828,1812],{},[895,94830,94831,94833,94835],{},[1810,94832,1959],{},[898,94834,6062],{"mathvariant":2057},[1810,94836,1812],{},[902,94838,34550],{"encoding":904},"), odvození Marshallovy i Hicksovy funkce poptávky a Engelových funkcí, vztah dualita primární ↔ duální úlohy a úlohy ",[38,94841,94842],{},"6.8–6.13"," jsou na stránce ",[207,94845,29158],{"className":94846,"dataFsResolvedFilePath":911,"href":912},[210],[115,94848,94850],{"id":94849},"shrnutí-kapitoly-6","Shrnutí kapitoly 6",[724,94852,94853,94854,94867,94868,94870,94871,94873,94874,94876,94877,94879,94880,94882,94883,94885,94886,1884,94888,94923,94924,94937,94938,94941,94942,94945,94946,1656],{},"Každá ",[883,94855,94857],{"className":94856},[886],[888,94858,94859],{"xmlns":890},[892,94860,94861,94865],{},[895,94862,94863],{},[898,94864,38251],{},[902,94866,38251],{"encoding":904},"-tice množství jednotlivých zboží je ",[38,94869,88201],{},". Přiřadíme-li každému svazku kladné číslo (jeho užitečnost), můžeme svazky uspořádat podle rostoucí užitečnosti; svazky se stejnou užitečností jsou indiferentní. Tím je definována ",[38,94872,88685],{}," a současně ",[38,94875,88204],{},". Její parciální derivace (podle jednotlivých množství) jsou ",[38,94878,88209],{}," — přibližná změna užitečnosti při jednotkové změně příslušného zboží. Aby funkce mohla být funkcí užitečnosti, musejí být její první parciální derivace ",[38,94881,54068],{}," (6.4) a druhé parciální derivace ",[38,94884,90568],{}," (6.5 — zákon klesající mezní užitečnosti). ",[38,94887,11119],{},[883,94889,94891],{"className":94890},[886],[888,94892,94893],{"xmlns":890},[892,94894,94895,94921],{},[895,94896,94897,94899,94901,94907,94909,94915,94917,94919],{},[898,94898,900],{},[1677,94900,1686],{"stretchy":1685},[1953,94902,94903,94905],{},[898,94904,2470],{},[1810,94906,1959],{},[1677,94908,1967],{"separator":1966},[1953,94910,94911,94913],{},[898,94912,2470],{},[1810,94914,1812],{},[1677,94916,1692],{"stretchy":1685},[1677,94918,1679],{},[898,94920,1823],{},[902,94922,11156],{"encoding":904}," jsou klesající, neprotínající se, vzdálenější od počátku mají vyšší užitečnost a jsou konvexní. ",[883,94925,94927],{"className":94926},[886],[888,94928,94929],{"xmlns":890},[892,94930,94931,94935],{},[895,94932,94933],{},[1969,94934,11991],{},[902,94936,29629],{"encoding":904}," = podíl mezních užitečností udává náhradu jednoho zboží druhým při zachování užitečnosti. Na tento teoretický základ navazují optimalizační úlohy (",[38,94939,94940],{},"maximalizace užitečnosti"," a duální ",[38,94943,94944],{},"minimalizace výdajů",") řešené Lagrangeovou metodou — viz ",[207,94947,38145],{"className":94948,"dataFsResolvedFilePath":911,"href":912},[210],[115,94950,51273],{"id":51272},[152,94952,94953,94956,94959,94962,94965,94968,94971,94974,94977,94980],{},[123,94954,94955],{},"Co se zahrnuje pod termín užitečnost?",[123,94957,94958],{},"Co se rozumí svazkem zboží? Které svazky zboží jsou indiferentní?",[123,94960,94961],{},"Jak souvisejí hodnoty funkce užitečnosti s preferencí svazků?",[123,94963,94964],{},"Jak se vypočítá mezní užitečnost?",[123,94966,94967],{},"Jak lze ekonomicky interpretovat fakt, že mezní užitečnost určitého zboží se rovná 2,5?",[123,94969,94970],{},"Jaké vlastnosti musí mít funkce více proměnných, aby mohla být funkcí užitečnosti?",[123,94972,94973],{},"Které jsou nejčastěji používané funkce užitečnosti?",[123,94975,94976],{},"Jakou rovnici mají křivky užitečnosti? Co platí v bodech ležících na téže křivce užitečnosti?",[123,94978,94979],{},"Proč mají křivky užitečnosti záporný sklon?",[123,94981,94982],{},"Jak se vypočte mezní míra komoditní substituce? Vysvětlete, co vypočtená hodnota vyjadřuje.",[115,94984,94986],{"id":94985},"úlohy-teorie-užitečnosti-61-67","Úlohy — teorie užitečnosti (6.1 – 6.7)",[724,94988,94989,94992,94993,84874,95035,1343,95063,1343,95091,95119],{},[38,94990,94991],{},"6.1"," Užitečnost pro tři zboží — hudbu, čokoládu a sýr je dána vztahem ",[883,94994,94996],{"className":94995},[886],[888,94997,94998],{"xmlns":890},[892,94999,95000,95032],{},[895,95001,95002,95004,95006,95012,95014,95016,95022,95024,95026],{},[898,95003,900],{},[1677,95005,1679],{},[1953,95007,95008,95010],{},[898,95009,2470],{},[1810,95011,1959],{},[1677,95013,1776],{},[1810,95015,65950],{},[1953,95017,95018,95020],{},[898,95019,2470],{},[1810,95021,1812],{},[1677,95023,1776],{},[1810,95025,1812],{},[1953,95027,95028,95030],{},[898,95029,2470],{},[1810,95031,1854],{},[902,95033,95034],{"encoding":904},"U = Q_1 + 1{,}5 Q_2 + 2 Q_3",[883,95036,95038],{"className":95037},[886],[888,95039,95040],{"xmlns":890},[892,95041,95042,95060],{},[895,95043,95044,95046,95048,95050,95052,95054,95056,95058],{},[898,95045,900],{},[1677,95047,1686],{"stretchy":1685},[1810,95049,2032],{},[1677,95051,1967],{"separator":1966},[1810,95053,1812],{},[1677,95055,1967],{"separator":1966},[1810,95057,1812],{},[1677,95059,1692],{"stretchy":1685},[902,95061,95062],{"encoding":904},"U(4, 2, 2)",[883,95064,95066],{"className":95065},[886],[888,95067,95068],{"xmlns":890},[892,95069,95070,95088],{},[895,95071,95072,95074,95076,95078,95080,95082,95084,95086],{},[898,95073,900],{},[1677,95075,1686],{"stretchy":1685},[1810,95077,1959],{},[1677,95079,1967],{"separator":1966},[1810,95081,2032],{},[1677,95083,1967],{"separator":1966},[1810,95085,1812],{},[1677,95087,1692],{"stretchy":1685},[902,95089,95090],{"encoding":904},"U(1, 4, 2)",[883,95092,95094],{"className":95093},[886],[888,95095,95096],{"xmlns":890},[892,95097,95098,95116],{},[895,95099,95100,95102,95104,95106,95108,95110,95112,95114],{},[898,95101,900],{},[1677,95103,1686],{"stretchy":1685},[1810,95105,1812],{},[1677,95107,1967],{"separator":1966},[1810,95109,1854],{},[1677,95111,1967],{"separator":1966},[1810,95113,1959],{},[1677,95115,1692],{"stretchy":1685},[902,95117,95118],{"encoding":904},"U(2, 3, 1)",". (b) Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků v (a).",[724,95121,95122,95125,95126,95178,95179,1343,95205,1343,95231,1343,95257,1343,95283,1343,95309,1343,95335,95361],{},[38,95123,95124],{},"6.2"," Je dána užitečnost ",[883,95127,95129],{"className":95128},[886],[888,95130,95131],{"xmlns":890},[892,95132,95133,95175],{},[895,95134,95135,95137,95139,95141,95155,95169],{},[898,95136,900],{},[1677,95138,1679],{},[1810,95140,1812],{},[10554,95142,95143,95145,95147],{},[898,95144,2470],{},[1810,95146,1959],{},[895,95148,95149,95151,95153],{},[1810,95150,1959],{},[898,95152,6062],{"mathvariant":2057},[1810,95154,1854],{},[10554,95156,95157,95159,95161],{},[898,95158,2470],{},[1810,95160,1812],{},[895,95162,95163,95165,95167],{},[1810,95164,1959],{},[898,95166,6062],{"mathvariant":2057},[1810,95168,1812],{},[1953,95170,95171,95173],{},[898,95172,2470],{},[1810,95174,1854],{},[902,95176,95177],{"encoding":904},"U = 2 Q_1^{1\u002F3} Q_2^{1\u002F2} Q_3"," pro tři zboží. Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků ",[883,95180,95182],{"className":95181},[886],[888,95183,95184],{"xmlns":890},[892,95185,95186,95202],{},[895,95187,95188,95190,95192,95194,95196,95198,95200],{},[1677,95189,1686],{"stretchy":1685},[1810,95191,6953],{},[1677,95193,1967],{"separator":1966},[1810,95195,67988],{},[1677,95197,1967],{"separator":1966},[1810,95199,2544],{},[1677,95201,1692],{"stretchy":1685},[902,95203,95204],{"encoding":904},"(36, 27, 10)",[883,95206,95208],{"className":95207},[886],[888,95209,95210],{"xmlns":890},[892,95211,95212,95228],{},[895,95213,95214,95216,95218,95220,95222,95224,95226],{},[1677,95215,1686],{"stretchy":1685},[1810,95217,43231],{},[1677,95219,1967],{"separator":1966},[1810,95221,6973],{},[1677,95223,1967],{"separator":1966},[1810,95225,10423],{},[1677,95227,1692],{"stretchy":1685},[902,95229,95230],{"encoding":904},"(64, 8, 20)",[883,95232,95234],{"className":95233},[886],[888,95235,95236],{"xmlns":890},[892,95237,95238,95254],{},[895,95239,95240,95242,95244,95246,95248,95250,95252],{},[1677,95241,1686],{"stretchy":1685},[1810,95243,6392],{},[1677,95245,1967],{"separator":1966},[1810,95247,43231],{},[1677,95249,1967],{"separator":1966},[1810,95251,6973],{},[1677,95253,1692],{"stretchy":1685},[902,95255,95256],{"encoding":904},"(25, 64, 8)",[883,95258,95260],{"className":95259},[886],[888,95261,95262],{"xmlns":890},[892,95263,95264,95280],{},[895,95265,95266,95268,95270,95272,95274,95276,95278],{},[1677,95267,1686],{"stretchy":1685},[1810,95269,2032],{},[1677,95271,1967],{"separator":1966},[1810,95273,73920],{},[1677,95275,1967],{"separator":1966},[1810,95277,1916],{},[1677,95279,1692],{"stretchy":1685},[902,95281,95282],{"encoding":904},"(4, 125, 6)",[883,95284,95286],{"className":95285},[886],[888,95287,95288],{"xmlns":890},[892,95289,95290,95306],{},[895,95291,95292,95294,95296,95298,95300,95302,95304],{},[1677,95293,1686],{"stretchy":1685},[1810,95295,5387],{},[1677,95297,1967],{"separator":1966},[1810,95299,6599],{},[1677,95301,1967],{"separator":1966},[1810,95303,3190],{},[1677,95305,1692],{"stretchy":1685},[902,95307,95308],{"encoding":904},"(9, 40, 12)",[883,95310,95312],{"className":95311},[886],[888,95313,95314],{"xmlns":890},[892,95315,95316,95332],{},[895,95317,95318,95320,95322,95324,95326,95328,95330],{},[1677,95319,1686],{"stretchy":1685},[1810,95321,5387],{},[1677,95323,1967],{"separator":1966},[1810,95325,43231],{},[1677,95327,1967],{"separator":1966},[1810,95329,1909],{},[1677,95331,1692],{"stretchy":1685},[902,95333,95334],{"encoding":904},"(9, 64, 5)",[883,95336,95338],{"className":95337},[886],[888,95339,95340],{"xmlns":890},[892,95341,95342,95358],{},[895,95343,95344,95346,95348,95350,95352,95354,95356],{},[1677,95345,1686],{"stretchy":1685},[1810,95347,43231],{},[1677,95349,1967],{"separator":1966},[1810,95351,6973],{},[1677,95353,1967],{"separator":1966},[1810,95355,2544],{},[1677,95357,1692],{"stretchy":1685},[902,95359,95360],{"encoding":904},"(64, 8, 10)"," a uspořádejte je s neklesající užitečností.",[724,95363,95364,95125,95367,95410,95411,95445,95446,7861,95476,95509,95510,95527,95528,95545],{},[38,95365,95366],{},"6.3",[883,95368,95370],{"className":95369},[886],[888,95371,95372],{"xmlns":890},[892,95373,95374,95408],{},[895,95375,95376,95378,95380,95394],{},[898,95377,900],{},[1677,95379,1679],{},[10554,95381,95382,95384,95386],{},[898,95383,2470],{},[1810,95385,1959],{},[895,95387,95388,95390,95392],{},[1810,95389,1959],{},[898,95391,6062],{"mathvariant":2057},[1810,95393,1812],{},[10554,95395,95396,95398,95400],{},[898,95397,2470],{},[1810,95399,1812],{},[895,95401,95402,95404,95406],{},[1810,95403,1959],{},[898,95405,6062],{"mathvariant":2057},[1810,95407,1812],{},[902,95409,34550],{"encoding":904},". (a) Vypočtěte užitečnost pro ",[883,95412,95414],{"className":95413},[886],[888,95415,95416],{"xmlns":890},[892,95417,95418,95442],{},[895,95419,95420,95426,95428,95430,95432,95438,95440],{},[1953,95421,95422,95424],{},[898,95423,2470],{},[1810,95425,1959],{},[1677,95427,1679],{},[1810,95429,2801],{},[1677,95431,1967],{"separator":1966},[1953,95433,95434,95436],{},[898,95435,2470],{},[1810,95437,1812],{},[1677,95439,1679],{},[1810,95441,48094],{},[902,95443,95444],{"encoding":904},"Q_1 = 50, Q_2 = 80",". (b) Určete mezní užitečnosti ",[883,95447,95449],{"className":95448},[886],[888,95450,95451],{"xmlns":890},[892,95452,95453,95473],{},[895,95454,95455,95457,95463,95465,95467],{},[898,95456,2499],{},[1953,95458,95459,95461],{},[898,95460,900],{},[1810,95462,1959],{},[1677,95464,1967],{"separator":1966},[898,95466,2499],{},[1953,95468,95469,95471],{},[898,95470,900],{},[1810,95472,1812],{},[902,95474,95475],{"encoding":904},"MU_1, MU_2",[883,95477,95479],{"className":95478},[886],[888,95480,95481],{"xmlns":890},[892,95482,95483,95507],{},[895,95484,95485,95491,95493,95495,95497,95503,95505],{},[1953,95486,95487,95489],{},[898,95488,2470],{},[1810,95490,1959],{},[1677,95492,1679],{},[1810,95494,2801],{},[1677,95496,1967],{"separator":1966},[1953,95498,95499,95501],{},[898,95500,2470],{},[1810,95502,1812],{},[1677,95504,1679],{},[1810,95506,48094],{},[902,95508,95444],{"encoding":904}," a výsledky ekonomicky interpretujte. (d) Odhadněte změnu užitečnosti v důsledku změny ",[883,95511,95513],{"className":95512},[886],[888,95514,95515],{"xmlns":890},[892,95516,95517,95525],{},[895,95518,95519],{},[1953,95520,95521,95523],{},[898,95522,2470],{},[1810,95524,1959],{},[902,95526,30393],{"encoding":904}," na 60 a poklesu ",[883,95529,95531],{"className":95530},[886],[888,95532,95533],{"xmlns":890},[892,95534,95535,95543],{},[895,95536,95537],{},[1953,95538,95539,95541],{},[898,95540,2470],{},[1810,95542,1812],{},[902,95544,30412],{"encoding":904}," o 5 vzhledem k hladině dle (a) a porovnejte se skutečnou změnou užitečnosti.",[724,95547,95548,95551,95552,95613,95614,1656],{},[38,95549,95550],{},"6.4"," Je dána funkce ",[883,95553,95555],{"className":95554},[886],[888,95556,95557],{"xmlns":890},[892,95558,95559,95611],{},[895,95560,95561,95563,95565,95571,95573,95579,95581,95583,95597],{},[898,95562,900],{},[1677,95564,1686],{"stretchy":1685},[1953,95566,95567,95569],{},[898,95568,2470],{},[1810,95570,1959],{},[1677,95572,1967],{"separator":1966},[1953,95574,95575,95577],{},[898,95576,2470],{},[1810,95578,1812],{},[1677,95580,1692],{"stretchy":1685},[1677,95582,1679],{},[10554,95584,95585,95587,95589],{},[898,95586,2470],{},[1810,95588,1959],{},[895,95590,95591,95593,95595],{},[1810,95592,1959],{},[898,95594,6062],{"mathvariant":2057},[1810,95596,1812],{},[10554,95598,95599,95601,95603],{},[898,95600,2470],{},[1810,95602,1812],{},[895,95604,95605,95607,95609],{},[1810,95606,1959],{},[898,95608,6062],{"mathvariant":2057},[1810,95610,1812],{},[902,95612,31334],{"encoding":904},". (a) Ověřte, že tato funkce vykazuje vlastnosti funkce užitečnosti. (b) Najděte a načrtněte křivky ",[883,95615,95617],{"className":95616},[886],[888,95618,95619],{"xmlns":890},[892,95620,95621,95711],{},[895,95622,95623,95625,95627,95633,95635,95637,95639,95641,95643,95645,95651,95653,95655,95657,95659,95661,95663,95665,95667,95673,95675,95677,95679,95681,95683,95685,95691,95693,95695,95697,95699,95701,95703,95709],{},[898,95624,900],{},[1677,95626,1686],{"stretchy":1685},[1953,95628,95629,95631],{},[898,95630,2470],{},[1810,95632,1959],{},[1677,95634,1967],{"separator":1966},[1810,95636,1959],{},[1677,95638,1692],{"stretchy":1685},[1677,95640,1967],{"separator":1966},[898,95642,900],{},[1677,95644,1686],{"stretchy":1685},[1953,95646,95647,95649],{},[898,95648,2470],{},[1810,95650,1959],{},[1677,95652,1967],{"separator":1966},[1810,95654,1812],{},[1677,95656,1692],{"stretchy":1685},[1677,95658,1967],{"separator":1966},[898,95660,900],{},[1677,95662,1686],{"stretchy":1685},[1810,95664,1959],{},[1677,95666,1967],{"separator":1966},[1953,95668,95669,95671],{},[898,95670,2470],{},[1810,95672,1812],{},[1677,95674,1692],{"stretchy":1685},[1677,95676,1967],{"separator":1966},[898,95678,900],{},[1677,95680,1686],{"stretchy":1685},[1810,95682,1812],{},[1677,95684,1967],{"separator":1966},[1953,95686,95687,95689],{},[898,95688,2470],{},[1810,95690,1812],{},[1677,95692,1692],{"stretchy":1685},[1677,95694,1967],{"separator":1966},[898,95696,900],{},[1677,95698,1686],{"stretchy":1685},[1810,95700,1854],{},[1677,95702,1967],{"separator":1966},[1953,95704,95705,95707],{},[898,95706,2470],{},[1810,95708,1812],{},[1677,95710,1692],{"stretchy":1685},[902,95712,95713],{"encoding":904},"U(Q_1, 1), U(Q_1, 2), U(1, Q_2), U(2, Q_2), U(3, Q_2)",[724,95715,95716,95125,95719,95763,95764,95872,95873,1343,95898,1343,95923,95965,95966,1343,95995,96020],{},[38,95717,95718],{},"6.5",[883,95720,95722],{"className":95721},[886],[888,95723,95724],{"xmlns":890},[892,95725,95726,95760],{},[895,95727,95728,95730,95732,95746],{},[898,95729,900],{},[1677,95731,1679],{},[10554,95733,95734,95736,95738],{},[898,95735,2470],{},[1810,95737,1959],{},[895,95739,95740,95742,95744],{},[1810,95741,1812],{},[898,95743,6062],{"mathvariant":2057},[1810,95745,1854],{},[10554,95747,95748,95750,95752],{},[898,95749,2470],{},[1810,95751,1812],{},[895,95753,95754,95756,95758],{},[1810,95755,1959],{},[898,95757,6062],{"mathvariant":2057},[1810,95759,1854],{},[902,95761,95762],{"encoding":904},"U = Q_1^{2\u002F3} Q_2^{1\u002F3}",". (a) Najděte rovnici křivek užitečnosti. (b) Určete a načrtněte křivky ",[883,95765,95767],{"className":95766},[886],[888,95768,95769],{"xmlns":890},[892,95770,95771,95869],{},[895,95772,95773,95775,95777,95783,95785,95791,95793,95795,95797,95799,95801,95803,95809,95811,95813,95815,95817,95819,95821,95827,95829,95831,95833,95835,95837,95839,95841,95843,95849,95851,95853,95855,95857,95859,95861,95867],{},[898,95774,900],{},[1677,95776,1686],{"stretchy":1685},[1953,95778,95779,95781],{},[898,95780,2470],{},[1810,95782,1959],{},[1677,95784,1967],{"separator":1966},[1953,95786,95787,95789],{},[898,95788,2470],{},[1810,95790,1812],{},[1677,95792,1692],{"stretchy":1685},[1677,95794,1679],{},[1810,95796,1812],{},[1677,95798,1967],{"separator":1966},[898,95800,900],{},[1677,95802,1686],{"stretchy":1685},[1953,95804,95805,95807],{},[898,95806,2470],{},[1810,95808,1959],{},[1677,95810,1967],{"separator":1966},[1810,95812,1854],{},[1677,95814,1692],{"stretchy":1685},[1677,95816,1967],{"separator":1966},[898,95818,900],{},[1677,95820,1686],{"stretchy":1685},[1953,95822,95823,95825],{},[898,95824,2470],{},[1810,95826,1959],{},[1677,95828,1967],{"separator":1966},[1810,95830,1812],{},[1677,95832,1692],{"stretchy":1685},[1677,95834,1967],{"separator":1966},[898,95836,900],{},[1677,95838,1686],{"stretchy":1685},[1810,95840,1812],{},[1677,95842,1967],{"separator":1966},[1953,95844,95845,95847],{},[898,95846,2470],{},[1810,95848,1812],{},[1677,95850,1692],{"stretchy":1685},[1677,95852,1967],{"separator":1966},[898,95854,900],{},[1677,95856,1686],{"stretchy":1685},[1810,95858,1854],{},[1677,95860,1967],{"separator":1966},[1953,95862,95863,95865],{},[898,95864,2470],{},[1810,95866,1812],{},[1677,95868,1692],{"stretchy":1685},[902,95870,95871],{"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 ",[883,95874,95876],{"className":95875},[886],[888,95877,95878],{"xmlns":890},[892,95879,95880,95895],{},[895,95881,95882,95884,95886,95888,95890,95893],{},[898,95883,5643],{},[1677,95885,2167],{"stretchy":1685},[1810,95887,65950],{},[1677,95889,9813],{"separator":1966},[1810,95891,95892],{},"3,555",[1677,95894,2182],{"stretchy":1685},[902,95896,95897],{"encoding":904},"A[1{,}5; 3{,}555]",[883,95899,95901],{"className":95900},[886],[888,95902,95903],{"xmlns":890},[892,95904,95905,95920],{},[895,95906,95907,95909,95911,95913,95915,95918],{},[898,95908,24644],{},[1677,95910,2167],{"stretchy":1685},[1810,95912,54590],{},[1677,95914,9813],{"separator":1966},[1810,95916,95917],{},"1,28",[1677,95919,2182],{"stretchy":1685},[902,95921,95922],{"encoding":904},"B[2{,}5; 1{,}28]",[883,95924,95926],{"className":95925},[886],[888,95927,95928],{"xmlns":890},[892,95929,95930,95962],{},[895,95931,95932,95934,95936,95938,95940,95942,95944,95950,95952,95954,95956,95958,95960],{},[898,95933,2458],{},[1677,95935,2167],{"stretchy":1685},[1810,95937,1812],{},[1677,95939,9813],{"separator":1966},[898,95941,900],{},[1677,95943,1686],{"stretchy":1685},[1953,95945,95946,95948],{},[898,95947,2470],{},[1810,95949,1959],{},[1677,95951,1967],{"separator":1966},[1810,95953,1854],{},[1677,95955,1692],{"stretchy":1685},[1677,95957,1679],{},[1810,95959,1854],{},[1677,95961,2182],{"stretchy":1685},[902,95963,95964],{"encoding":904},"C[2; U(Q_1, 3) = 3]"," (c) Leží některé z bodů ",[883,95967,95969],{"className":95968},[886],[888,95970,95971],{"xmlns":890},[892,95972,95973,95992],{},[895,95974,95975,95977,95979,95981,95983,95985,95987,95990],{},[898,95976,5571],{},[1677,95978,2167],{"stretchy":1685},[1810,95980,1854],{},[1677,95982,9813],{"separator":1966},[1810,95984,1959],{},[1677,95986,9813],{"separator":1966},[1810,95988,95989],{},"0,832",[1677,95991,2182],{"stretchy":1685},[902,95993,95994],{"encoding":904},"D[3; 1; 0{,}832]",[883,95996,95998],{"className":95997},[886],[888,95999,96000],{"xmlns":890},[892,96001,96002,96017],{},[895,96003,96004,96006,96008,96010,96012,96015],{},[898,96005,5640],{},[1677,96007,2167],{"stretchy":1685},[1810,96009,54590],{},[1677,96011,9813],{"separator":1966},[1810,96013,96014],{},"4,32",[1677,96016,2182],{"stretchy":1685},[902,96018,96019],{"encoding":904},"E[2{,}5; 4{,}32]"," na téže křivce užitečnosti? Když ano, určete ji.",[724,96022,96023,95125,96026,96069,96070,7861,96083,96117,96118,96135,96136,96153],{},[38,96024,96025],{},"6.6",[883,96027,96029],{"className":96028},[886],[888,96030,96031],{"xmlns":890},[892,96032,96033,96067],{},[895,96034,96035,96037,96039,96053],{},[898,96036,900],{},[1677,96038,1679],{},[10554,96040,96041,96043,96045],{},[898,96042,2470],{},[1810,96044,1959],{},[895,96046,96047,96049,96051],{},[1810,96048,1812],{},[898,96050,6062],{"mathvariant":2057},[1810,96052,1854],{},[10554,96054,96055,96057,96059],{},[898,96056,2470],{},[1810,96058,1812],{},[895,96060,96061,96063,96065],{},[1810,96062,1959],{},[898,96064,6062],{"mathvariant":2057},[1810,96066,1854],{},[902,96068,95762],{"encoding":904},". (a) Najděte mezní míru komoditní substituce ",[883,96071,96073],{"className":96072},[886],[888,96074,96075],{"xmlns":890},[892,96076,96077,96081],{},[895,96078,96079],{},[1969,96080,11991],{},[902,96082,29629],{"encoding":904},[883,96084,96086],{"className":96085},[886],[888,96087,96088],{"xmlns":890},[892,96089,96090,96114],{},[895,96091,96092,96098,96100,96102,96104,96110,96112],{},[1953,96093,96094,96096],{},[898,96095,2470],{},[1810,96097,1959],{},[1677,96099,1679],{},[1810,96101,2771],{},[1677,96103,1967],{"separator":1966},[1953,96105,96106,96108],{},[898,96107,2470],{},[1810,96109,1812],{},[1677,96111,1679],{},[1810,96113,9765],{},[902,96115,96116],{"encoding":904},"Q_1 = 100, Q_2 = 200"," a výsledek ekonomicky interpretujte. (c) Odhadněte, o kolik je třeba změnit ",[883,96119,96121],{"className":96120},[886],[888,96122,96123],{"xmlns":890},[892,96124,96125,96133],{},[895,96126,96127],{},[1953,96128,96129,96131],{},[898,96130,2470],{},[1810,96132,1959],{},[902,96134,30393],{"encoding":904},", poklesne-li ",[883,96137,96139],{"className":96138},[886],[888,96140,96141],{"xmlns":890},[892,96142,96143,96151],{},[895,96144,96145],{},[1953,96146,96147,96149],{},[898,96148,2470],{},[1810,96150,1812],{},[902,96152,30412],{"encoding":904}," o 5 vzhledem k hladině dle (b).",[724,96155,96156,96159,96160,96177,96178,96195,96196,96228,96229,96254,96255,96268,96269,1343,96293,1343,96317,1656],{},[38,96157,96158],{},"6.7"," Míra uspokojení z nákupu množství ",[883,96161,96163],{"className":96162},[886],[888,96164,96165],{"xmlns":890},[892,96166,96167,96175],{},[895,96168,96169],{},[1953,96170,96171,96173],{},[898,96172,2470],{},[1810,96174,1959],{},[902,96176,30393],{"encoding":904}," nealko nápojů a množství ",[883,96179,96181],{"className":96180},[886],[888,96182,96183],{"xmlns":890},[892,96184,96185,96193],{},[895,96186,96187],{},[1953,96188,96189,96191],{},[898,96190,2470],{},[1810,96192,1812],{},[902,96194,30412],{"encoding":904}," hamburgerů za týden je dána funkcí užitečnosti ",[883,96197,96199],{"className":96198},[886],[888,96200,96201],{"xmlns":890},[892,96202,96203,96225],{},[895,96204,96205,96207,96209],{},[898,96206,900],{},[1677,96208,1679],{},[9505,96210,96211],{},[895,96212,96213,96219],{},[1953,96214,96215,96217],{},[898,96216,2470],{},[1810,96218,1959],{},[1953,96220,96221,96223],{},[898,96222,2470],{},[1810,96224,1812],{},[902,96226,96227],{"encoding":904},"U = \\sqrt{Q_1 Q_2}",". (a) Najděte vztah pro hodnoty ",[883,96230,96232],{"className":96231},[886],[888,96233,96234],{"xmlns":890},[892,96235,96236,96252],{},[895,96237,96238,96244,96246],{},[1953,96239,96240,96242],{},[898,96241,2470],{},[1810,96243,1959],{},[1677,96245,1967],{"separator":1966},[1953,96247,96248,96250],{},[898,96249,2470],{},[1810,96251,1812],{},[902,96253,37013],{"encoding":904},", pro něž je dosaženo užitečnosti 10 a uveďte několik takových dvojic hodnot. (b) Najděte ",[883,96256,96258],{"className":96257},[886],[888,96259,96260],{"xmlns":890},[892,96261,96262,96266],{},[895,96263,96264],{},[1969,96265,11991],{},[902,96267,29629],{"encoding":904}," na křivce nalezené v (a). (c) Ekonomicky interpretujte smysl ",[883,96270,96272],{"className":96271},[886],[888,96273,96274],{"xmlns":890},[892,96275,96276,96290],{},[895,96277,96278,96280,96282,96284,96286,96288],{},[1969,96279,11991],{},[1677,96281,1686],{"stretchy":1685},[1810,96283,1909],{},[1677,96285,1967],{"separator":1966},[1810,96287,10423],{},[1677,96289,1692],{"stretchy":1685},[902,96291,96292],{"encoding":904},"\\text{MRCS}(5, 20)",[883,96294,96296],{"className":96295},[886],[888,96297,96298],{"xmlns":890},[892,96299,96300,96314],{},[895,96301,96302,96304,96306,96308,96310,96312],{},[1969,96303,11991],{},[1677,96305,1686],{"stretchy":1685},[1810,96307,10423],{},[1677,96309,1967],{"separator":1966},[1810,96311,1909],{},[1677,96313,1692],{"stretchy":1685},[902,96315,96316],{"encoding":904},"\\text{MRCS}(20, 5)",[883,96318,96320],{"className":96319},[886],[888,96321,96322],{"xmlns":890},[892,96323,96324,96338],{},[895,96325,96326,96328,96330,96332,96334,96336],{},[1969,96327,11991],{},[1677,96329,1686],{"stretchy":1685},[1810,96331,1812],{},[1677,96333,1967],{"separator":1966},[1810,96335,2801],{},[1677,96337,1692],{"stretchy":1685},[902,96339,96340],{"encoding":904},"\\text{MRCS}(2, 50)",[5254,96342,96343],{},[724,96344,96345,96347,96348,1656],{},[883,96346,5960],{}," Úlohy 6.8 – 6.13 (optimalizace, Lagrange, poptávka)\nÚlohy navázané na maximalizaci užitečnosti, minimalizaci výdajů a odvození Marshallových\u002FHicksových funkcí poptávky jsou na stránce ",[207,96349,96352],{"className":96350,"dataFsResolvedFilePath":911,"href":96351},[210],"\u002Fwiki\u002Foptimalizace-spotrebitele#Úlohy k optimalizaci","Optimalizace spotřebitele — Úlohy",[115,96354,17110],{"id":17109},[120,96356,96357,96363,96368,96374,96427,96437,96483,96538,96601,96658,96713,96752],{},[123,96358,96359,96362],{},[38,96360,96361],{},"Užitečnost (utility)"," — ordinálně měřený ukazatel uspokojení spotřebitele ze svazku zboží.",[123,96364,96365,96367],{},[38,96366,88260],{}," — historická pojetí užitečnosti; v současnosti se preferuje ordinalistický.",[123,96369,96370,96373],{},[38,96371,96372],{},"Pět předpokladů chování spotřebitele"," — racionalita, ordinalita, konzistence a tranzitivita, rostoucí užitečnost, klesající mezní užitečnost.",[123,96375,96376,96378,96379,96392,96393,1656],{},[38,96377,88587],{}," — uspořádaná ",[883,96380,96382],{"className":96381},[886],[888,96383,96384],{"xmlns":890},[892,96385,96386,96390],{},[895,96387,96388],{},[898,96389,38251],{},[902,96391,38251],{"encoding":904},"-tice ",[883,96394,96396],{"className":96395},[886],[888,96397,96398],{"xmlns":890},[892,96399,96400,96424],{},[895,96401,96402,96404,96410,96412,96414,96416,96422],{},[1677,96403,1686],{"stretchy":1685},[1953,96405,96406,96408],{},[898,96407,2470],{},[1810,96409,1959],{},[1677,96411,1967],{"separator":1966},[1677,96413,11034],{},[1677,96415,1967],{"separator":1966},[1953,96417,96418,96420],{},[898,96419,2470],{},[898,96421,38251],{},[1677,96423,1692],{"stretchy":1685},[902,96425,96426],{"encoding":904},"(Q_1, \\dots, Q_n)",[123,96428,96429,96432,96433,96436],{},[38,96430,96431],{},"Relace preference"," — uspořádání svazků podle užitečnosti; ",[38,96434,96435],{},"indiferentní svazky"," mají stejnou užitečnost.",[123,96438,96439,1884,96442,96482],{},[38,96440,96441],{},"Funkce užitečnosti",[883,96443,96445],{"className":96444},[886],[888,96446,96447],{"xmlns":890},[892,96448,96449,96479],{},[895,96450,96451,96453,96455,96457,96459,96465,96467,96469,96471,96477],{},[898,96452,900],{},[1677,96454,1679],{},[898,96456,900],{},[1677,96458,1686],{"stretchy":1685},[1953,96460,96461,96463],{},[898,96462,2470],{},[1810,96464,1959],{},[1677,96466,1967],{"separator":1966},[1677,96468,11034],{},[1677,96470,1967],{"separator":1966},[1953,96472,96473,96475],{},[898,96474,2470],{},[898,96476,38251],{},[1677,96478,1692],{"stretchy":1685},[902,96480,96481],{"encoding":904},"U = U(Q_1, \\dots, Q_n)"," — vzorec (6.1); ekvivalentní až na monotónní transformaci.",[123,96484,96485,1884,96488,96517,96518,1884,96521,96537],{},[38,96486,96487],{},"Mezní užitečnost",[883,96489,96491],{"className":96490},[886],[888,96492,96493],{"xmlns":890},[892,96494,96495,96515],{},[895,96496,96497,96499,96505,96507],{},[898,96498,2499],{},[1953,96500,96501,96503],{},[898,96502,900],{},[898,96504,19181],{},[1677,96506,1679],{},[10554,96508,96509,96511,96513],{},[898,96510,900],{},[898,96512,19181],{},[1677,96514,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[902,96516,88044],{"encoding":904}," — vzorec (6.2); ",[38,96519,96520],{},"totální diferenciál",[883,96522,96524],{"className":96523},[886],[888,96525,96526],{"xmlns":890},[892,96527,96528,96534],{},[895,96529,96530,96532],{},[898,96531,1875],{"mathvariant":2057},[898,96533,900],{},[902,96535,96536],{"encoding":904},"\\mathrm{d} U"," — (6.3).",[123,96539,96540,96542,96543,96567,96568,96600],{},[38,96541,90223],{}," — (6.4) ",[883,96544,96546],{"className":96545},[886],[888,96547,96548],{"xmlns":890},[892,96549,96550,96564],{},[895,96551,96552,96560,96562],{},[10554,96553,96554,96556,96558],{},[898,96555,900],{},[898,96557,19181],{},[1677,96559,2059],{"mathvariant":2057,"lspace":2058,"rspace":2058},[1677,96561,3089],{},[1810,96563,2008],{},[902,96565,96566],{"encoding":904},"U'_i > 0",", (6.5) ",[883,96569,96571],{"className":96570},[886],[888,96572,96573],{"xmlns":890},[892,96574,96575,96597],{},[895,96576,96577,96593,96595],{},[10554,96578,96579,96581,96587],{},[898,96580,900],{},[895,96582,96583,96585],{},[898,96584,19181],{},[898,96586,19181],{},[895,96588,96589,96591],{},[1677,96590,2059],{"mathvariant":2057},[1677,96592,2059],{"mathvariant":2057},[1677,96594,3128],{},[1810,96596,2008],{},[902,96598,96599],{"encoding":904},"U''_{ii} \u003C 0"," (zákon klesající mezní užitečnosti).",[123,96602,96603,1884,96605,96636,96637,1656],{},[38,96604,92011],{},[883,96606,96608],{"className":96607},[886],[888,96609,96610],{"xmlns":890},[892,96611,96612,96634],{},[895,96613,96614,96616,96618,96626],{},[898,96615,900],{},[1677,96617,1679],{},[10554,96619,96620,96622,96624],{},[898,96621,2470],{},[1810,96623,1959],{},[898,96625,207],{},[10554,96627,96628,96630,96632],{},[898,96629,2470],{},[1810,96631,1812],{},[898,96633,1779],{},[902,96635,37194],{"encoding":904}," — (6.6), speciálně ",[883,96638,96640],{"className":96639},[886],[888,96641,96642],{"xmlns":890},[892,96643,96644,96656],{},[895,96645,96646,96648,96650,96652,96654],{},[898,96647,1779],{},[1677,96649,1679],{},[1810,96651,1959],{},[1677,96653,1906],{},[898,96655,207],{},[902,96657,92165],{"encoding":904},[123,96659,96660,1884,96663,96698,96699,96712],{},[38,96661,96662],{},"Křivky užitečnosti (indiferenční)",[883,96664,96666],{"className":96665},[886],[888,96667,96668],{"xmlns":890},[892,96669,96670,96696],{},[895,96671,96672,96674,96676,96682,96684,96690,96692,96694],{},[898,96673,900],{},[1677,96675,1686],{"stretchy":1685},[1953,96677,96678,96680],{},[898,96679,2470],{},[1810,96681,1959],{},[1677,96683,1967],{"separator":1966},[1953,96685,96686,96688],{},[898,96687,2470],{},[1810,96689,1812],{},[1677,96691,1692],{"stretchy":1685},[1677,96693,1679],{},[898,96695,1823],{},[902,96697,11156],{"encoding":904}," — (6.7), (6.8); čtyři vlastnosti: klesající, neprotínající se, vzdálenější od počátku = vyšší ",[883,96700,96702],{"className":96701},[886],[888,96703,96704],{"xmlns":890},[892,96705,96706,96710],{},[895,96707,96708],{},[898,96709,900],{},[902,96711,900],{"encoding":904},", konvexní.",[123,96714,96715,1884,96717,96751],{},[38,96716,93556],{},[883,96718,96720],{"className":96719},[886],[888,96721,96722],{"xmlns":890},[892,96723,96724,96748],{},[895,96725,96726,96728,96730,96732,96738,96740,96742],{},[1969,96727,11991],{},[1677,96729,1679],{},[898,96731,2499],{},[1953,96733,96734,96736],{},[898,96735,900],{},[1810,96737,1959],{},[898,96739,6062],{"mathvariant":2057},[898,96741,2499],{},[1953,96743,96744,96746],{},[898,96745,900],{},[1810,96747,1812],{},[902,96749,96750],{"encoding":904},"\\text{MRCS} = MU_1 \u002F MU_2"," — (6.9); vztahy (6.10), (6.11).",[123,96753,96754,1884,96757,11157,96786,96789],{},[38,96755,96756],{},"Podmínka optimality",[883,96758,96760],{"className":96759},[886],[888,96761,96762],{"xmlns":890},[892,96763,96764,96784],{},[895,96765,96766,96768,96770,96776,96778],{},[1969,96767,11991],{},[1677,96769,1679],{},[1953,96771,96772,96774],{},[898,96773,5325],{},[1810,96775,1959],{},[898,96777,6062],{"mathvariant":2057},[1953,96779,96780,96782],{},[898,96781,5325],{},[1810,96783,1812],{},[902,96785,29389],{"encoding":904},[207,96787,38145],{"className":96788,"dataFsResolvedFilePath":911,"href":912},[210]," pro plné odvození.",[115,96791,3473],{"id":3472},[120,96793,96794,96831,96872,96882],{},[123,96795,96796,1884,96799,96802,96803,96816,96817,96830],{},[38,96797,96798],{},"Navazující téma:",[207,96800,913],{"className":96801,"dataFsResolvedFilePath":911,"href":912},[210]," (Lagrange, max ",[883,96804,96806],{"className":96805},[886],[888,96807,96808],{"xmlns":890},[892,96809,96810,96814],{},[895,96811,96812],{},[898,96813,900],{},[902,96815,900],{"encoding":904},", min ",[883,96818,96820],{"className":96819},[886],[888,96821,96822],{"xmlns":890},[892,96823,96824,96828],{},[895,96825,96826],{},[898,96827,5640],{},[902,96829,5640],{"encoding":904},", funkce poptávky, Příklady 6.5–6.8, úlohy 6.8–6.13).",[123,96832,96833,1884,96836,12481,96839,87799,96842,96845,96846,96849,96850,20039,96868,96871],{},[38,96834,96835],{},"Související pojmy:",[207,96837,784],{"className":96838,"dataFsResolvedFilePath":782,"href":783},[210],[207,96840,2038],{"className":96841,"dataFsResolvedFilePath":764,"href":765},[210],[207,96843,12476],{"className":96844,"dataFsResolvedFilePath":857,"href":858},[210]," (paralela: MRCS ↔ MRTS, izokvanty ↔ indiferenční křivky, Cobb-Douglas), ",[207,96847,13330],{"className":96848,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallovy poptávkové funkce ",[883,96851,96853],{"className":96852},[886],[888,96854,96855],{"xmlns":890},[892,96856,96857,96865],{},[895,96858,96859],{},[1953,96860,96861,96863],{},[898,96862,5571],{},[898,96864,19181],{},[902,96866,96867],{"encoding":904},"D_i",[207,96869,793],{"className":96870,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace — nástroj pro navazující téma).",[123,96873,96874,1884,96876,1343,96879],{},[38,96875,38094],{},[207,96877,1094],{"className":96878,"dataFsResolvedFilePath":838,"href":839},[210],[207,96880,1101],{"className":96881,"dataFsResolvedFilePath":868,"href":869},[210],[123,96883,96884,1884,96886],{},[38,96885,17594],{},[207,96887,17598],{"className":96888,"dataFsResolvedFilePath":1641,"href":1642},[210],{"title":641,"searchDepth":642,"depth":642,"links":96890},[96891,96892,96893,96896,96897,96900,96904,96905,96908,96909,96910,96911,96912,96913,96914],{"id":13395,"depth":642,"text":13396},{"id":88183,"depth":642,"text":88184},{"id":88243,"depth":642,"text":88244,"children":96894},[96895],{"id":88259,"depth":649,"text":88260},{"id":88566,"depth":642,"text":88567},{"id":89426,"depth":642,"text":89427,"children":96898},[96899],{"id":89973,"depth":649,"text":81602},{"id":90222,"depth":642,"text":90223,"children":96901},[96902],{"id":91095,"depth":649,"text":96903},"Příklad 6.2 — ověření vlastností a dopočet pro U=Q11\u002F2Q21\u002F3U = Q_1^{1\u002F2} Q_2^{1\u002F3}",{"id":92010,"depth":642,"text":92011},{"id":92546,"depth":642,"text":92547,"children":96906},[96907],{"id":93320,"depth":649,"text":93321},{"id":93550,"depth":642,"text":93551},{"id":94311,"depth":642,"text":94312},{"id":94849,"depth":642,"text":94850},{"id":51272,"depth":642,"text":51273},{"id":94985,"depth":642,"text":94986},{"id":17109,"depth":642,"text":17110},{"id":3472,"depth":642,"text":3473},{},"\u002Ftopics\u002Fuzitecnost",{"title":87967,"description":641},[1138,1137],"topics\u002Fuzitecnost",[1128,11161,96921,87961,12511,96922],"mezni-uzitecnost","mrcs","xXggD9rfV5faUAk1b2B3YYbozpQLu-pObiMaZX5f7yI",{"id":96925,"title":757,"body":96926,"course":1128,"courses":659,"created":1129,"description":97199,"extension":661,"meta":97200,"navigation":664,"path":97201,"seo":97202,"sources":97203,"stem":97204,"tags":97205,"type":3538,"updated":677,"__hash__":97211},"topics\u002Ftopics\u002Fzaklady-matematicke-ekonomie.md",{"type":9,"value":96927,"toc":97191},[96928,96931,96938,96945,96949,96959,96961,96995,96999,97042,97045,97103,97107,97137,97141,97162,97164],[12,96929,757],{"id":96930},"základy-matematické-ekonomie",[724,96932,96933,96934,96937],{},"Úvodní pojmy a princip modelování v ",[207,96935,17771],{"className":96936,"dataFsResolvedFilePath":1641,"href":1642},[210],". Slouží jako vstupní bod pro celý kurz — bez těchto pojmů nedávají další kapitoly smysl.",[724,96939,96940],{},[2240,96941],{"alt":96942,"className":96943,"src":96944},"imek-model-promenne",[210,2244],"\u002Fwiki-assets\u002Fimek-model-promenne.jpeg",[115,96946,96948],{"id":96947},"co-je-matematická-ekonomie","Co je matematická ekonomie",[724,96950,96951,96954,96955,96958],{},[38,96952,96953],{},"Vědní disciplína",", která ekonomické vztahy vyjadřuje ",[38,96956,96957],{},"exaktními (matematickými) prostředky"," a provádí jejich analýzu. Cílem není jen popis, ale i predikce a optimalizace.",[115,96960,17110],{"id":17109},[120,96962,96963,96969,96975,96981,96990],{},[123,96964,96965,96968],{},[38,96966,96967],{},"Model"," — zjednodušený obraz reálné situace nebo jevu. Vždy jde o redukci skutečnosti, ne její kopii.",[123,96970,96971,96974],{},[38,96972,96973],{},"Endogenní proměnné"," — zahrnuté do modelu, mohou se měnit (vysvětlované).",[123,96976,96977,96980],{},[38,96978,96979],{},"Exogenní proměnné"," — nejsou v modelu zahrnuté (potenciálně by mohly), berou se jako dané.",[123,96982,96983,8403,96986,96989],{},[38,96984,96985],{},"Ceteris paribus",[614,96987,96988],{},"za jinak stejných podmínek",". Sledujeme změnu jedné proměnné, ostatní fixní.",[123,96991,96992,96994],{},[38,96993,52026],{}," — odezva endogenních proměnných na změnu některé exogenní.",[115,96996,96998],{"id":96997},"ilustrace-funkce-poptávky","Ilustrace — funkce poptávky",[724,97000,97001,97041],{},[883,97002,97004],{"className":97003},[886],[888,97005,97006],{"xmlns":890},[892,97007,97008,97038],{},[895,97009,97010,97012,97014,97016,97018,97020,97022,97024,97026,97028,97030,97032,97034,97036],{},[898,97011,2470],{},[1677,97013,1679],{},[898,97015,5571],{},[1677,97017,1686],{"stretchy":1685},[898,97019,5325],{},[1677,97021,1967],{"separator":1966},[898,97023,10516],{},[1677,97025,1967],{"separator":1966},[898,97027,19685],{},[1677,97029,1967],{"separator":1966},[898,97031,900],{},[1677,97033,1967],{"separator":1966},[1677,97035,11034],{},[1677,97037,1692],{"stretchy":1685},[902,97039,97040],{"encoding":904},"Q = D(P, Y, N, U, \\ldots)"," — plná (vícefaktorová) funkce poptávky.",[724,97043,97044],{},"Zjednodušení:",[120,97046,97047,97075],{},[123,97048,97049,1884,97052],{},[38,97050,97051],{},"Jednofaktorový model:",[883,97053,97055],{"className":97054},[886],[888,97056,97057],{"xmlns":890},[892,97058,97059,97073],{},[895,97060,97061,97063,97065,97067,97069,97071],{},[898,97062,2470],{},[1677,97064,1679],{},[898,97066,5571],{},[1677,97068,1686],{"stretchy":1685},[898,97070,5325],{},[1677,97072,1692],{"stretchy":1685},[902,97074,5580],{"encoding":904},[123,97076,97077,1884,97080],{},[38,97078,97079],{},"Inverzní zápis:",[883,97081,97083],{"className":97082},[886],[888,97084,97085],{"xmlns":890},[892,97086,97087,97101],{},[895,97088,97089,97091,97093,97095,97097,97099],{},[898,97090,5325],{},[1677,97092,1679],{},[898,97094,5571],{},[1677,97096,1686],{"stretchy":1685},[898,97098,2470],{},[1677,97100,1692],{"stretchy":1685},[902,97102,6028],{"encoding":904},[115,97104,97106],{"id":97105},"principy-řešení-ekonomických-úloh","Principy řešení ekonomických úloh",[152,97108,97109,97118],{},[123,97110,97111,97114,97115,5306],{},[38,97112,97113],{},"Princip rovnováhy"," — hledáme stav, kdy se protichůdné síly vyrovnají (např. tržní rovnováha, viz ",[207,97116,17630],{"className":97117,"dataFsResolvedFilePath":800,"href":801},[210],[123,97119,97120,97123,97124,97127,97128,97131,97132,97136],{},[38,97121,97122],{},"Princip optimalizace"," — hledáme extrém účelové funkce, případně vázaný omezujícími podmínkami (viz ",[207,97125,1145],{"className":97126,"dataFsResolvedFilePath":764,"href":765},[210]," pro 1D, ",[207,97129,17643],{"className":97130,"dataFsResolvedFilePath":782,"href":783},[210]," pro 2D, ",[207,97133,97135],{"className":97134,"dataFsResolvedFilePath":791,"href":792},[210],"lagrangeova-metoda"," pro vázané extrémy).",[115,97138,97140],{"id":97139},"konvence-z-přednášek","Konvence z přednášek",[120,97142,97143,97150,97156],{},[123,97144,97145,97146,97149],{},"Symbol ",[97147,97148,2411],"code",{}," pro přibližné rovnosti (typicky linearizace přes diferenciál).",[123,97151,97152,97153,1656],{},"Numerické výsledky ",[38,97154,97155],{},"na 3 desetinná místa",[123,97157,5282,97158,97161],{},[614,97159,97160],{},"jednotková změna"," má standardní význam (změna o 1).",[115,97163,3473],{"id":3472},[120,97165,97166,97171,97179],{},[123,97167,97168,97170],{},[38,97169,3480],{}," —",[123,97172,97173,1884,97175],{},[38,97174,3488],{},[207,97176,97178],{"className":97177,"dataFsResolvedFilePath":764,"href":765},[210],"Derivace a diferenciál",[123,97180,97181,1884,97183,1343,97187],{},[38,97182,3496],{},[207,97184,97186],{"className":97185,"dataFsResolvedFilePath":745,"href":746},[210],"Souhrn KS 1. blok",[207,97188,97190],{"className":97189,"dataFsResolvedFilePath":1641,"href":1642},[210],"kurz ImeK",{"title":641,"searchDepth":642,"depth":642,"links":97192},[97193,97194,97195,97196,97197,97198],{"id":96947,"depth":642,"text":96948},{"id":17109,"depth":642,"text":17110},{"id":96997,"depth":642,"text":96998},{"id":97105,"depth":642,"text":97106},{"id":97139,"depth":642,"text":97140},{"id":3472,"depth":642,"text":3473},"Úvodní pojmy a princip modelování v matematické ekonomii. Slouží jako vstupní bod pro celý kurz — bez těchto pojmů nedávají další kapitoly smysl.",{},"\u002Ftopics\u002Fzaklady-matematicke-ekonomie",{"title":757,"description":97199},[1135],"topics\u002Fzaklady-matematicke-ekonomie",[1128,97206,97207,97208,97209,97210],"model","endogenni","exogenni","ceteris-paribus","komparativni-statika","UZ1xD3l_gK41y8KlCBmpjprMOjIWmHZR8WZt-takTSI",{"id":97213,"title":97214,"body":97215,"course":1128,"courses":659,"created":10944,"description":641,"extension":661,"meta":101487,"navigation":664,"path":101488,"seo":101489,"sources":101490,"stem":101491,"tags":101492,"type":3538,"updated":677,"__hash__":101496},"topics\u002Ftopics\u002Fzdaneni-trhu.md","Zdanění trhu — dopady daně na rovnováhu",{"type":9,"value":97216,"toc":101470},[97217,97220,97314,97318,97340,97354,97406,97408,97412,97475,97518,97537,97700,97799,97802,97869,97873,98002,98041,98071,98183,98228,98294,98347,98423,98479,98481,98485,98549,98593,98613,98774,98777,98861,98958,98961,99027,99031,99080,99106,99211,99275,99280,99376,99423,99425,99428,99450,99492,99499,99532,99534,99605,99659,99768,99772,99861,99937,100201,100239,100241,100245,100248,100255,100566,100569,100627,100807,100836,100838,100842,100848,100986,100995,100997,100999,101424,101426,101428],[12,97218,97214],{"id":97219},"zdanění-trhu-dopady-daně-na-rovnováhu",[5254,97221,97222],{},[724,97223,97224,44019,97226,97239,97240,97243,97244,97246,97247,97250,97251,97272,97273,97296,97297,97300,97301,1656],{},[883,97225,5543],{},[883,97227,97229],{"className":97228},[886],[888,97230,97231],{"xmlns":890},[892,97232,97233,97237],{},[895,97234,97235],{},[898,97236,2455],{},[902,97238,2455],{"encoding":904}," uložená na každou prodanou jednotku zboží posouvá jednu z křivek — ",[38,97241,97242],{},"nabídku"," (je-li daň uložena výrobci) nebo ",[38,97245,88251],{}," (je-li uložena spotřebiteli). Výsledné ",[38,97248,97249],{},"daňové břemeno"," se dělí mezi obě strany trhu na ",[883,97252,97254],{"className":97253},[886],[888,97255,97256],{"xmlns":890},[892,97257,97258,97270],{},[895,97259,97260],{},[1953,97261,97262,97264],{},[898,97263,2455],{},[895,97265,97266,97268],{},[898,97267,44068],{},[898,97269,724],{},[902,97271,44073],{"encoding":904}," (spotřebitel) a ",[883,97274,97276],{"className":97275},[886],[888,97277,97278],{"xmlns":890},[892,97279,97280,97294],{},[895,97281,97282],{},[1953,97283,97284,97286],{},[898,97285,2455],{},[895,97287,97288,97290,97292],{},[898,97289,44091],{},[898,97291,1675],{},[898,97293,13431],{},[902,97295,44098],{"encoding":904}," (výrobce). Klíčovým zjištěním je ",[38,97298,97299],{},"ekvivalence obou přístupů",": rovnovážné množství i čistá cena pro výrobce jsou v obou režimech totožné; liší se pouze nominální cena na trhu o ",[883,97302,97304],{"className":97303},[886],[888,97305,97306],{"xmlns":890},[892,97307,97308,97312],{},[895,97309,97310],{},[898,97311,2455],{},[902,97313,2455],{"encoding":904},[115,97315,97317],{"id":97316},"dvě-formy-zdanění","Dvě formy zdanění",[724,97319,97320,97321,97339],{},"Uvažujme jednotkovou daň ",[883,97322,97324],{"className":97323},[886],[888,97325,97326],{"xmlns":890},[892,97327,97328,97336],{},[895,97329,97330,97332,97334],{},[898,97331,2455],{},[1677,97333,3089],{},[1810,97335,2008],{},[902,97337,97338],{"encoding":904},"T > 0"," (Kč na kus), kterou stát ukládá na každou prodanou jednotku zboží. Daň může být uložena buď:",[120,97341,97342,97348],{},[123,97343,97344,97347],{},[38,97345,97346],{},"(a) výrobci"," — výrobce ji musí odvést státu z každé prodané jednotky,",[123,97349,97350,97353],{},[38,97351,97352],{},"(b) spotřebiteli"," — spotřebitel ji platí navíc k ceně, kterou si účtuje prodejce.",[724,97355,97356,97357,97370,97371,97374,97375,1656],{},"V obou případech dochází k posunu jedné z křivek o ",[883,97358,97360],{"className":97359},[886],[888,97361,97362],{"xmlns":890},[892,97363,97364,97368],{},[895,97365,97366],{},[898,97367,2455],{},[902,97369,2455],{"encoding":904}," svisle (buď nabídky nahoru, nebo poptávky dolů) a k rozdělení ",[38,97372,97373],{},"daňového břemene"," mezi spotřebitele a výrobce. Výchozí rovnovážný bod bez daně označujeme ",[883,97376,97378],{"className":97377},[886],[888,97379,97380],{"xmlns":890},[892,97381,97382,97404],{},[895,97383,97384,97386,97388,97394,97396,97402],{},[898,97385,5640],{},[1677,97387,2167],{"stretchy":1685},[1805,97389,97390,97392],{},[898,97391,2470],{},[898,97393,5640],{},[1677,97395,1967],{"separator":1966},[1805,97397,97398,97400],{},[898,97399,5325],{},[898,97401,5640],{},[1677,97403,2182],{"stretchy":1685},[902,97405,42758],{"encoding":904},[38361,97407],{},[115,97409,97411],{"id":97410},"daň-uložená-výrobci","Daň uložená výrobci",[724,97413,97414,97415,97428,97429,97446,97447,97474],{},"Je-li daň ",[883,97416,97418],{"className":97417},[886],[888,97419,97420],{"xmlns":890},[892,97421,97422,97426],{},[895,97423,97424],{},[898,97425,2455],{},[902,97427,2455],{"encoding":904}," uložena výrobci, pak z podmínky, že výrobce za každou prodanou jednotku obdrží ",[883,97430,97432],{"className":97431},[886],[888,97433,97434],{"xmlns":890},[892,97435,97436,97444],{},[895,97437,97438,97440,97442],{},[898,97439,5325],{},[1677,97441,1906],{},[898,97443,2455],{},[902,97445,42513],{"encoding":904}," (hrubá cena mínus odvod), plyne z rovnice ",[883,97448,97450],{"className":97449},[886],[888,97451,97452],{"xmlns":890},[892,97453,97454,97472],{},[895,97455,97456,97458,97460,97462,97464,97466,97468,97470],{},[898,97457,5325],{},[1677,97459,1906],{},[898,97461,2455],{},[1677,97463,1679],{},[898,97465,10061],{},[1677,97467,1686],{"stretchy":1685},[898,97469,2470],{},[1677,97471,1692],{"stretchy":1685},[902,97473,42542],{"encoding":904}," nová funkce nabídky:",[883,97476,97478],{"className":97477},[886],[888,97479,97480],{"xmlns":890,"display":29457},[892,97481,97482,97516],{},[895,97483,97484,97486,97488,97494,97496,97498,97500,97502,97504,97506,97508,97510,97512,97514],{},[898,97485,5325],{},[1677,97487,1679],{},[1953,97489,97490,97492],{},[898,97491,10061],{},[1810,97493,1959],{},[1677,97495,1686],{"stretchy":1685},[898,97497,2470],{},[1677,97499,1692],{"stretchy":1685},[1677,97501,1679],{},[898,97503,10061],{},[1677,97505,1686],{"stretchy":1685},[898,97507,2470],{},[1677,97509,1692],{"stretchy":1685},[1677,97511,1776],{},[898,97513,2455],{},[898,97515,1656],{"mathvariant":2057},[902,97517,42587],{"encoding":904},[724,97519,97520,97521,1884,97534,97536],{},"Nabídka se tedy posouvá o ",[883,97522,97524],{"className":97523},[886],[888,97525,97526],{"xmlns":890},[892,97527,97528,97532],{},[895,97529,97530],{},[898,97531,2455],{},[902,97533,2455],{"encoding":904},[38,97535,42620],{}," (ekvivalentně doleva). Poptávka se nemění.",[724,97538,97539,97540,97580,97581,5272,97609,97637,97638,97657,97658,97682,97683,5306],{},"Nový rovnovážný bod ",[883,97541,97543],{"className":97542},[886],[888,97544,97545],{"xmlns":890},[892,97546,97547,97577],{},[895,97548,97549,97555,97557,97565,97567,97575],{},[1953,97550,97551,97553],{},[898,97552,5640],{},[1810,97554,1959],{},[1677,97556,2167],{"stretchy":1685},[10554,97558,97559,97561,97563],{},[898,97560,2470],{},[1810,97562,1959],{},[898,97564,5640],{},[1677,97566,1967],{"separator":1966},[10554,97568,97569,97571,97573],{},[898,97570,5325],{},[1810,97572,1959],{},[898,97574,5640],{},[1677,97576,2182],{"stretchy":1685},[902,97578,97579],{"encoding":904},"E_1[Q_1^E, P_1^E]"," splňuje ",[883,97582,97584],{"className":97583},[886],[888,97585,97586],{"xmlns":890},[892,97587,97588,97606],{},[895,97589,97590,97598,97600],{},[10554,97591,97592,97594,97596],{},[898,97593,2470],{},[1810,97595,1959],{},[898,97597,5640],{},[1677,97599,3128],{},[1805,97601,97602,97604],{},[898,97603,2470],{},[898,97605,5640],{},[902,97607,97608],{"encoding":904},"Q_1^E \u003C Q^E",[883,97610,97612],{"className":97611},[886],[888,97613,97614],{"xmlns":890},[892,97615,97616,97634],{},[895,97617,97618,97626,97628],{},[10554,97619,97620,97622,97624],{},[898,97621,5325],{},[1810,97623,1959],{},[898,97625,5640],{},[1677,97627,3089],{},[1805,97629,97630,97632],{},[898,97631,5325],{},[898,97633,5640],{},[902,97635,97636],{"encoding":904},"P_1^E > P^E",". Spotřebitel platí ",[883,97639,97641],{"className":97640},[886],[888,97642,97643],{"xmlns":890},[892,97644,97645,97655],{},[895,97646,97647],{},[10554,97648,97649,97651,97653],{},[898,97650,5325],{},[1810,97652,1959],{},[898,97654,5640],{},[902,97656,49248],{"encoding":904},", výrobci ale zůstává pouze čistá cena ",[883,97659,97661],{"className":97660},[886],[888,97662,97663],{"xmlns":890},[892,97664,97665,97679],{},[895,97666,97667,97675,97677],{},[10554,97668,97669,97671,97673],{},[898,97670,5325],{},[1810,97672,1959],{},[898,97674,5640],{},[1677,97676,1906],{},[898,97678,2455],{},[902,97680,97681],{"encoding":904},"P_1^E - T"," (ta je nižší než původní rovnovážná ",[883,97684,97686],{"className":97685},[886],[888,97687,97688],{"xmlns":890},[892,97689,97690,97698],{},[895,97691,97692],{},[1805,97693,97694,97696],{},[898,97695,5325],{},[898,97697,5640],{},[902,97699,42857],{"encoding":904},[724,97701,97702],{},[614,97703,97704,97705,97735,97736,97749,97750,7057,97767,97780,97781,1656],{},"Obrázek 2.17 (resp. 2.18): Posun ",[883,97706,97708],{"className":97707},[886],[888,97709,97710],{"xmlns":890},[892,97711,97712,97732],{},[895,97713,97714,97716,97718,97724,97726,97728,97730],{},[898,97715,10061],{},[1677,97717,2804],{},[1953,97719,97720,97722],{},[898,97721,10061],{},[1810,97723,1959],{},[1677,97725,1679],{},[898,97727,10061],{},[1677,97729,1776],{},[898,97731,2455],{},[902,97733,97734],{"encoding":904},"S \\to S_1 = S + T","; svislá vzdálenost mezi křivkami je přesně ",[883,97737,97739],{"className":97738},[886],[888,97740,97741],{"xmlns":890},[892,97742,97743,97747],{},[895,97744,97745],{},[898,97746,2455],{},[902,97748,2455],{"encoding":904},". Průsečík ",[883,97751,97753],{"className":97752},[886],[888,97754,97755],{"xmlns":890},[892,97756,97757,97765],{},[895,97758,97759],{},[1953,97760,97761,97763],{},[898,97762,10061],{},[1810,97764,1959],{},[902,97766,42388],{"encoding":904},[883,97768,97770],{"className":97769},[886],[888,97771,97772],{"xmlns":890},[892,97773,97774,97778],{},[895,97775,97776],{},[898,97777,5571],{},[902,97779,5571],{"encoding":904}," je nový rovnovážný bod ",[883,97782,97784],{"className":97783},[886],[888,97785,97786],{"xmlns":890},[892,97787,97788,97796],{},[895,97789,97790],{},[1953,97791,97792,97794],{},[898,97793,5640],{},[1810,97795,1959],{},[902,97797,97798],{"encoding":904},"E_1",[198,97800,46694],{"id":97801},"příklad-29",[724,97803,97804,43046,97806,43081,97830,97850,97851,97868],{},[38,97805,39324],{},[883,97807,97809],{"className":97808},[886],[888,97810,97811],{"xmlns":890},[892,97812,97813,97827],{},[895,97814,97815,97817,97819,97821,97823,97825],{},[898,97816,5325],{},[1677,97818,1679],{},[1810,97820,3190],{},[1677,97822,1906],{},[1810,97824,1812],{},[898,97826,2470],{},[902,97828,97829],{"encoding":904},"P = 12 - 2Q",[883,97831,97833],{"className":97832},[886],[888,97834,97835],{"xmlns":890},[892,97836,97837,97847],{},[895,97838,97839,97841,97843,97845],{},[898,97840,5325],{},[1677,97842,1679],{},[1810,97844,2032],{},[898,97846,2470],{},[902,97848,97849],{"encoding":904},"P = 4Q",". Na výrobce je uložena jednotková daň ",[883,97852,97854],{"className":97853},[886],[888,97855,97856],{"xmlns":890},[892,97857,97858,97866],{},[895,97859,97860,97862,97864],{},[898,97861,2455],{},[1677,97863,1679],{},[1810,97865,1916],{},[902,97867,42659],{"encoding":904}," Kč.",[724,97870,97871],{},[38,97872,39356],{},[724,97874,97875,97878,97879,6957,97905,6977,97925,1343,97947,97977,97978,1656],{},[614,97876,97877],{},"Bez daně."," Z rovnosti ",[883,97880,97882],{"className":97881},[886],[888,97883,97884],{"xmlns":890},[892,97885,97886,97902],{},[895,97887,97888,97890,97892,97894,97896,97898,97900],{},[1810,97889,3190],{},[1677,97891,1906],{},[1810,97893,1812],{},[898,97895,2470],{},[1677,97897,1679],{},[1810,97899,2032],{},[898,97901,2470],{},[902,97903,97904],{"encoding":904},"12 - 2Q = 4Q",[883,97906,97908],{"className":97907},[886],[888,97909,97910],{"xmlns":890},[892,97911,97912,97922],{},[895,97913,97914,97916,97918,97920],{},[1810,97915,1916],{},[898,97917,2470],{},[1677,97919,1679],{},[1810,97921,3190],{},[902,97923,97924],{"encoding":904},"6Q = 12",[883,97926,97928],{"className":97927},[886],[888,97929,97930],{"xmlns":890},[892,97931,97932,97944],{},[895,97933,97934,97940,97942],{},[1805,97935,97936,97938],{},[898,97937,2470],{},[898,97939,5640],{},[1677,97941,1679],{},[1810,97943,1812],{},[902,97945,97946],{"encoding":904},"Q^E = 2",[883,97948,97950],{"className":97949},[886],[888,97951,97952],{"xmlns":890},[892,97953,97954,97974],{},[895,97955,97956,97962,97964,97966,97968,97970,97972],{},[1805,97957,97958,97960],{},[898,97959,5325],{},[898,97961,5640],{},[1677,97963,1679],{},[1810,97965,2032],{},[1677,97967,2858],{},[1810,97969,1812],{},[1677,97971,1679],{},[1810,97973,6973],{},[902,97975,97976],{"encoding":904},"P^E = 4 \\cdot 2 = 8",". Rovnovážný bod ",[883,97979,97981],{"className":97980},[886],[888,97982,97983],{"xmlns":890},[892,97984,97985,97999],{},[895,97986,97987,97989,97991,97993,97995,97997],{},[898,97988,5640],{},[1677,97990,2167],{"stretchy":1685},[1810,97992,1812],{},[1677,97994,1967],{"separator":1966},[1810,97996,6973],{},[1677,97998,2182],{"stretchy":1685},[902,98000,98001],{"encoding":904},"E[2, 8]",[724,98003,98004,98007,98008,98040],{},[614,98005,98006],{},"S daní uloženou výrobci."," Nová nabídka je ",[883,98009,98011],{"className":98010},[886],[888,98012,98013],{"xmlns":890},[892,98014,98015,98037],{},[895,98016,98017,98023,98025,98027,98029,98031,98033,98035],{},[1953,98018,98019,98021],{},[898,98020,10061],{},[1810,98022,1959],{},[1677,98024,2385],{},[898,98026,5325],{},[1677,98028,1679],{},[1810,98030,2032],{},[898,98032,2470],{},[1677,98034,1776],{},[1810,98036,1916],{},[902,98038,98039],{"encoding":904},"S_1: P = 4Q + 6",". Z rovnice",[883,98042,98044],{"className":98043},[886],[888,98045,98046],{"xmlns":890,"display":29457},[892,98047,98048,98068],{},[895,98049,98050,98052,98054,98056,98058,98060,98062,98064,98066],{},[1810,98051,3190],{},[1677,98053,1906],{},[1810,98055,1812],{},[898,98057,2470],{},[1677,98059,1679],{},[1810,98061,2032],{},[898,98063,2470],{},[1677,98065,1776],{},[1810,98067,1916],{},[902,98069,98070],{"encoding":904},"12 - 2Q = 4Q + 6",[724,98072,98073,98074,6977,98094,1343,98118,98154,98155,1656],{},"plyne ",[883,98075,98077],{"className":98076},[886],[888,98078,98079],{"xmlns":890},[892,98080,98081,98091],{},[895,98082,98083,98085,98087,98089],{},[1810,98084,1916],{},[898,98086,2470],{},[1677,98088,1679],{},[1810,98090,1916],{},[902,98092,98093],{"encoding":904},"6Q = 6",[883,98095,98097],{"className":98096},[886],[888,98098,98099],{"xmlns":890},[892,98100,98101,98115],{},[895,98102,98103,98111,98113],{},[10554,98104,98105,98107,98109],{},[898,98106,2470],{},[1810,98108,1959],{},[898,98110,5640],{},[1677,98112,1679],{},[1810,98114,1959],{},[902,98116,98117],{"encoding":904},"Q_1^E = 1",[883,98119,98121],{"className":98120},[886],[888,98122,98123],{"xmlns":890},[892,98124,98125,98151],{},[895,98126,98127,98135,98137,98139,98141,98143,98145,98147,98149],{},[10554,98128,98129,98131,98133],{},[898,98130,5325],{},[1810,98132,1959],{},[898,98134,5640],{},[1677,98136,1679],{},[1810,98138,2032],{},[1677,98140,2858],{},[1810,98142,1959],{},[1677,98144,1776],{},[1810,98146,1916],{},[1677,98148,1679],{},[1810,98150,2544],{},[902,98152,98153],{"encoding":904},"P_1^E = 4 \\cdot 1 + 6 = 10",". Nový rovnovážný bod ",[883,98156,98158],{"className":98157},[886],[888,98159,98160],{"xmlns":890},[892,98161,98162,98180],{},[895,98163,98164,98170,98172,98174,98176,98178],{},[1953,98165,98166,98168],{},[898,98167,5640],{},[1810,98169,1959],{},[1677,98171,2167],{"stretchy":1685},[1810,98173,1959],{},[1677,98175,1967],{"separator":1966},[1810,98177,2544],{},[1677,98179,2182],{"stretchy":1685},[902,98181,98182],{"encoding":904},"E_1[1, 10]",[724,98184,98185,98188,98189,98213,98214,98227],{},[614,98186,98187],{},"Rozklad daňového břemene."," Spotřebitel platí ",[883,98190,98192],{"className":98191},[886],[888,98193,98194],{"xmlns":890},[892,98195,98196,98210],{},[895,98197,98198,98206,98208],{},[10554,98199,98200,98202,98204],{},[898,98201,5325],{},[1810,98203,1959],{},[898,98205,5640],{},[1677,98207,1679],{},[1810,98209,2544],{},[902,98211,98212],{"encoding":904},"P_1^E = 10"," Kč namísto původních ",[883,98215,98217],{"className":98216},[886],[888,98218,98219],{"xmlns":890},[892,98220,98221,98225],{},[895,98222,98223],{},[1810,98224,6973],{},[902,98226,6973],{"encoding":904},", navýšení je",[883,98229,98231],{"className":98230},[886],[888,98232,98233],{"xmlns":890,"display":29457},[892,98234,98235,98291],{},[895,98236,98237,98247,98249,98257,98259,98265,98267,98269,98271,98273,98275,98277,98279,98289],{},[1953,98238,98239,98241],{},[898,98240,2455],{},[895,98242,98243,98245],{},[898,98244,44068],{},[898,98246,724],{},[1677,98248,1679],{},[10554,98250,98251,98253,98255],{},[898,98252,5325],{},[1810,98254,1959],{},[898,98256,5640],{},[1677,98258,1906],{},[1805,98260,98261,98263],{},[898,98262,5325],{},[898,98264,5640],{},[1677,98266,1679],{},[1810,98268,2544],{},[1677,98270,1906],{},[1810,98272,6973],{},[1677,98274,1679],{},[1810,98276,1812],{},[1969,98278,1971],{},[895,98280,98281,98283],{},[1969,98282,11188],{},[9774,98284,98285,98287],{"accent":1966},[1969,98286,1823],{},[1677,98288,26449],{},[898,98290,1656],{"mathvariant":2057},[902,98292,98293],{"encoding":904},"T_{sp} = P_1^E - P^E = 10 - 8 = 2\\ \\text{Kč}.",[724,98295,98296,98297,98213,98333,98346],{},"Výrobci zůstává čistá cena ",[883,98298,98300],{"className":98299},[886],[888,98301,98302],{"xmlns":890},[892,98303,98304,98330],{},[895,98305,98306,98314,98316,98318,98320,98322,98324,98326,98328],{},[10554,98307,98308,98310,98312],{},[898,98309,5325],{},[1810,98311,1959],{},[898,98313,5640],{},[1677,98315,1906],{},[898,98317,2455],{},[1677,98319,1679],{},[1810,98321,2544],{},[1677,98323,1906],{},[1810,98325,1916],{},[1677,98327,1679],{},[1810,98329,2032],{},[902,98331,98332],{"encoding":904},"P_1^E - T = 10 - 6 = 4",[883,98334,98336],{"className":98335},[886],[888,98337,98338],{"xmlns":890},[892,98339,98340,98344],{},[895,98341,98342],{},[1810,98343,6973],{},[902,98345,6973],{"encoding":904},", pokles je",[883,98348,98350],{"className":98349},[886],[888,98351,98352],{"xmlns":890,"display":29457},[892,98353,98354,98420],{},[895,98355,98356,98368,98370,98376,98378,98380,98388,98390,98392,98394,98396,98398,98400,98402,98404,98406,98408,98418],{},[1953,98357,98358,98360],{},[898,98359,2455],{},[895,98361,98362,98364,98366],{},[898,98363,44091],{},[898,98365,1675],{},[898,98367,13431],{},[1677,98369,1679],{},[1805,98371,98372,98374],{},[898,98373,5325],{},[898,98375,5640],{},[1677,98377,1906],{},[1677,98379,1686],{"stretchy":1685},[10554,98381,98382,98384,98386],{},[898,98383,5325],{},[1810,98385,1959],{},[898,98387,5640],{},[1677,98389,1906],{},[898,98391,2455],{},[1677,98393,1692],{"stretchy":1685},[1677,98395,1679],{},[1810,98397,6973],{},[1677,98399,1906],{},[1810,98401,2032],{},[1677,98403,1679],{},[1810,98405,2032],{},[1969,98407,1971],{},[895,98409,98410,98412],{},[1969,98411,11188],{},[9774,98413,98414,98416],{"accent":1966},[1969,98415,1823],{},[1677,98417,26449],{},[898,98419,1656],{"mathvariant":2057},[902,98421,98422],{"encoding":904},"T_{vyr} = P^E - (P_1^E - T) = 8 - 4 = 4\\ \\text{Kč}.",[724,98424,98425,98426,98478],{},"Kontrola: ",[883,98427,98429],{"className":98428},[886],[888,98430,98431],{"xmlns":890},[892,98432,98433,98475],{},[895,98434,98435,98445,98447,98459,98461,98463,98465,98467,98469,98471,98473],{},[1953,98436,98437,98439],{},[898,98438,2455],{},[895,98440,98441,98443],{},[898,98442,44068],{},[898,98444,724],{},[1677,98446,1776],{},[1953,98448,98449,98451],{},[898,98450,2455],{},[895,98452,98453,98455,98457],{},[898,98454,44091],{},[898,98456,1675],{},[898,98458,13431],{},[1677,98460,1679],{},[1810,98462,1812],{},[1677,98464,1776],{},[1810,98466,2032],{},[1677,98468,1679],{},[1810,98470,1916],{},[1677,98472,1679],{},[898,98474,2455],{},[902,98476,98477],{"encoding":904},"T_{sp} + T_{vyr} = 2 + 4 = 6 = T",". Spotřebitel nese třetinu daně, výrobce dvě třetiny.",[38361,98480],{},[115,98482,98484],{"id":98483},"daň-uložená-spotřebiteli","Daň uložená spotřebiteli",[724,98486,97414,98487,98500,98501,98519,98520,98548],{},[883,98488,98490],{"className":98489},[886],[888,98491,98492],{"xmlns":890},[892,98493,98494,98498],{},[895,98495,98496],{},[898,98497,2455],{},[902,98499,2455],{"encoding":904}," uložena spotřebiteli, pak spotřebitel platí celkem ",[883,98502,98504],{"className":98503},[886],[888,98505,98506],{"xmlns":890},[892,98507,98508,98516],{},[895,98509,98510,98512,98514],{},[898,98511,5325],{},[1677,98513,1776],{},[898,98515,2455],{},[902,98517,98518],{"encoding":904},"P + T"," (cena prodejce plus daň). Z podmínky ",[883,98521,98523],{"className":98522},[886],[888,98524,98525],{"xmlns":890},[892,98526,98527,98545],{},[895,98528,98529,98531,98533,98535,98537,98539,98541,98543],{},[898,98530,5325],{},[1677,98532,1776],{},[898,98534,2455],{},[1677,98536,1679],{},[898,98538,5571],{},[1677,98540,1686],{"stretchy":1685},[898,98542,2470],{},[1677,98544,1692],{"stretchy":1685},[902,98546,98547],{"encoding":904},"P + T = D(Q)"," plyne nová funkce poptávky:",[883,98550,98552],{"className":98551},[886],[888,98553,98554],{"xmlns":890,"display":29457},[892,98555,98556,98590],{},[895,98557,98558,98560,98562,98568,98570,98572,98574,98576,98578,98580,98582,98584,98586,98588],{},[898,98559,5325],{},[1677,98561,1679],{},[1953,98563,98564,98566],{},[898,98565,5571],{},[1810,98567,1812],{},[1677,98569,1686],{"stretchy":1685},[898,98571,2470],{},[1677,98573,1692],{"stretchy":1685},[1677,98575,1679],{},[898,98577,5571],{},[1677,98579,1686],{"stretchy":1685},[898,98581,2470],{},[1677,98583,1692],{"stretchy":1685},[1677,98585,1906],{},[898,98587,2455],{},[898,98589,1656],{"mathvariant":2057},[902,98591,98592],{"encoding":904},"P = D_2(Q) = D(Q) - T.",[724,98594,98595,98596,1884,98609,98612],{},"Poptávka se tedy posouvá o ",[883,98597,98599],{"className":98598},[886],[888,98600,98601],{"xmlns":890},[892,98602,98603,98607],{},[895,98604,98605],{},[898,98606,2455],{},[902,98608,2455],{"encoding":904},[38,98610,98611],{},"svisle dolů",". Nabídka se nemění.",[724,98614,97539,98615,97580,98655,5272,98683,98711,98712,98731,98732,98756,98757,5306],{},[883,98616,98618],{"className":98617},[886],[888,98619,98620],{"xmlns":890},[892,98621,98622,98652],{},[895,98623,98624,98630,98632,98640,98642,98650],{},[1953,98625,98626,98628],{},[898,98627,5640],{},[1810,98629,1812],{},[1677,98631,2167],{"stretchy":1685},[10554,98633,98634,98636,98638],{},[898,98635,2470],{},[1810,98637,1812],{},[898,98639,5640],{},[1677,98641,1967],{"separator":1966},[10554,98643,98644,98646,98648],{},[898,98645,5325],{},[1810,98647,1812],{},[898,98649,5640],{},[1677,98651,2182],{"stretchy":1685},[902,98653,98654],{"encoding":904},"E_2[Q_2^E, P_2^E]",[883,98656,98658],{"className":98657},[886],[888,98659,98660],{"xmlns":890},[892,98661,98662,98680],{},[895,98663,98664,98672,98674],{},[10554,98665,98666,98668,98670],{},[898,98667,2470],{},[1810,98669,1812],{},[898,98671,5640],{},[1677,98673,3128],{},[1805,98675,98676,98678],{},[898,98677,2470],{},[898,98679,5640],{},[902,98681,98682],{"encoding":904},"Q_2^E \u003C Q^E",[883,98684,98686],{"className":98685},[886],[888,98687,98688],{"xmlns":890},[892,98689,98690,98708],{},[895,98691,98692,98700,98702],{},[10554,98693,98694,98696,98698],{},[898,98695,5325],{},[1810,98697,1812],{},[898,98699,5640],{},[1677,98701,3128],{},[1805,98703,98704,98706],{},[898,98705,5325],{},[898,98707,5640],{},[902,98709,98710],{"encoding":904},"P_2^E \u003C P^E",". Výrobce obdrží ",[883,98713,98715],{"className":98714},[886],[888,98716,98717],{"xmlns":890},[892,98718,98719,98729],{},[895,98720,98721],{},[10554,98722,98723,98725,98727],{},[898,98724,5325],{},[1810,98726,1812],{},[898,98728,5640],{},[902,98730,49309],{"encoding":904},", spotřebitel platí celkem ",[883,98733,98735],{"className":98734},[886],[888,98736,98737],{"xmlns":890},[892,98738,98739,98753],{},[895,98740,98741,98749,98751],{},[10554,98742,98743,98745,98747],{},[898,98744,5325],{},[1810,98746,1812],{},[898,98748,5640],{},[1677,98750,1776],{},[898,98752,2455],{},[902,98754,98755],{"encoding":904},"P_2^E + T"," (tato částka je vyšší než původní ",[883,98758,98760],{"className":98759},[886],[888,98761,98762],{"xmlns":890},[892,98763,98764,98772],{},[895,98765,98766],{},[1805,98767,98768,98770],{},[898,98769,5325],{},[898,98771,5640],{},[902,98773,42857],{"encoding":904},[724,98775,98776],{},"Daňové břemeno:",[883,98778,98780],{"className":98779},[886],[888,98781,98782],{"xmlns":890,"display":29457},[892,98783,98784,98858],{},[895,98785,98786,98796,98798,98800,98808,98810,98812,98814,98816,98822,98824,98826,98838,98840,98846,98848,98856],{},[1953,98787,98788,98790],{},[898,98789,2455],{},[895,98791,98792,98794],{},[898,98793,44068],{},[898,98795,724],{},[1677,98797,1679],{},[1677,98799,1686],{"stretchy":1685},[10554,98801,98802,98804,98806],{},[898,98803,5325],{},[1810,98805,1812],{},[898,98807,5640],{},[1677,98809,1776],{},[898,98811,2455],{},[1677,98813,1692],{"stretchy":1685},[1677,98815,1906],{},[1805,98817,98818,98820],{},[898,98819,5325],{},[898,98821,5640],{},[1677,98823,1967],{"separator":1966},[7266,98825],{"width":7268},[1953,98827,98828,98830],{},[898,98829,2455],{},[895,98831,98832,98834,98836],{},[898,98833,44091],{},[898,98835,1675],{},[898,98837,13431],{},[1677,98839,1679],{},[1805,98841,98842,98844],{},[898,98843,5325],{},[898,98845,5640],{},[1677,98847,1906],{},[10554,98849,98850,98852,98854],{},[898,98851,5325],{},[1810,98853,1812],{},[898,98855,5640],{},[898,98857,1656],{"mathvariant":2057},[902,98859,98860],{"encoding":904},"T_{sp} = (P_2^E + T) - P^E, \\qquad T_{vyr} = P^E - P_2^E.",[724,98862,98863],{},[614,98864,98865,98866,98896,98897,97749,98910,7057,98927,97780,98940,1656],{},"Obrázek 2.19: Posun ",[883,98867,98869],{"className":98868},[886],[888,98870,98871],{"xmlns":890},[892,98872,98873,98893],{},[895,98874,98875,98877,98879,98885,98887,98889,98891],{},[898,98876,5571],{},[1677,98878,2804],{},[1953,98880,98881,98883],{},[898,98882,5571],{},[1810,98884,1812],{},[1677,98886,1679],{},[898,98888,5571],{},[1677,98890,1906],{},[898,98892,2455],{},[902,98894,98895],{"encoding":904},"D \\to D_2 = D - T","; svislá vzdálenost mezi poptávkovými křivkami je ",[883,98898,98900],{"className":98899},[886],[888,98901,98902],{"xmlns":890},[892,98903,98904,98908],{},[895,98905,98906],{},[898,98907,2455],{},[902,98909,2455],{"encoding":904},[883,98911,98913],{"className":98912},[886],[888,98914,98915],{"xmlns":890},[892,98916,98917,98925],{},[895,98918,98919],{},[1953,98920,98921,98923],{},[898,98922,5571],{},[1810,98924,1812],{},[902,98926,39718],{"encoding":904},[883,98928,98930],{"className":98929},[886],[888,98931,98932],{"xmlns":890},[892,98933,98934,98938],{},[895,98935,98936],{},[898,98937,10061],{},[902,98939,10061],{"encoding":904},[883,98941,98943],{"className":98942},[886],[888,98944,98945],{"xmlns":890},[892,98946,98947,98955],{},[895,98948,98949],{},[1953,98950,98951,98953],{},[898,98952,5640],{},[1810,98954,1812],{},[902,98956,98957],{"encoding":904},"E_2",[198,98959,46774],{"id":98960},"příklad-210",[724,98962,98963,98965,98966,43081,98989,99008,99009,99026],{},[38,98964,39324],{}," Pokračuje z Příkladu 2.9 — stejný trh, poptávka ",[883,98967,98969],{"className":98968},[886],[888,98970,98971],{"xmlns":890},[892,98972,98973,98987],{},[895,98974,98975,98977,98979,98981,98983,98985],{},[898,98976,5325],{},[1677,98978,1679],{},[1810,98980,3190],{},[1677,98982,1906],{},[1810,98984,1812],{},[898,98986,2470],{},[902,98988,97829],{"encoding":904},[883,98990,98992],{"className":98991},[886],[888,98993,98994],{"xmlns":890},[892,98995,98996,99006],{},[895,98997,98998,99000,99002,99004],{},[898,98999,5325],{},[1677,99001,1679],{},[1810,99003,2032],{},[898,99005,2470],{},[902,99007,97849],{"encoding":904},". Daň ",[883,99010,99012],{"className":99011},[886],[888,99013,99014],{"xmlns":890},[892,99015,99016,99024],{},[895,99017,99018,99020,99022],{},[898,99019,2455],{},[1677,99021,1679],{},[1810,99023,1916],{},[902,99025,42659],{"encoding":904}," Kč je tentokrát uložena na spotřebitele.",[724,99028,99029],{},[38,99030,39356],{},[724,99032,99033,99034,98040],{},"Nová poptávka je ",[883,99035,99037],{"className":99036},[886],[888,99038,99039],{"xmlns":890},[892,99040,99041,99077],{},[895,99042,99043,99049,99051,99053,99055,99057,99059,99061,99063,99065,99067,99069,99071,99073,99075],{},[1953,99044,99045,99047],{},[898,99046,5571],{},[1810,99048,1812],{},[1677,99050,2385],{},[898,99052,5325],{},[1677,99054,1679],{},[1810,99056,3190],{},[1677,99058,1906],{},[1810,99060,1812],{},[898,99062,2470],{},[1677,99064,1906],{},[1810,99066,1916],{},[1677,99068,1679],{},[1810,99070,1916],{},[1677,99072,1906],{},[1810,99074,1812],{},[898,99076,2470],{},[902,99078,99079],{"encoding":904},"D_2: P = 12 - 2Q - 6 = 6 - 2Q",[883,99081,99083],{"className":99082},[886],[888,99084,99085],{"xmlns":890,"display":29457},[892,99086,99087,99103],{},[895,99088,99089,99091,99093,99095,99097,99099,99101],{},[1810,99090,1916],{},[1677,99092,1906],{},[1810,99094,1812],{},[898,99096,2470],{},[1677,99098,1679],{},[1810,99100,2032],{},[898,99102,2470],{},[902,99104,99105],{"encoding":904},"6 - 2Q = 4Q",[724,99107,98073,99108,6977,99127,1343,99151,98154,99183,1656],{},[883,99109,99111],{"className":99110},[886],[888,99112,99113],{"xmlns":890},[892,99114,99115,99125],{},[895,99116,99117,99119,99121,99123],{},[1810,99118,1916],{},[898,99120,2470],{},[1677,99122,1679],{},[1810,99124,1916],{},[902,99126,98093],{"encoding":904},[883,99128,99130],{"className":99129},[886],[888,99131,99132],{"xmlns":890},[892,99133,99134,99148],{},[895,99135,99136,99144,99146],{},[10554,99137,99138,99140,99142],{},[898,99139,2470],{},[1810,99141,1812],{},[898,99143,5640],{},[1677,99145,1679],{},[1810,99147,1959],{},[902,99149,99150],{"encoding":904},"Q_2^E = 1",[883,99152,99154],{"className":99153},[886],[888,99155,99156],{"xmlns":890},[892,99157,99158,99180],{},[895,99159,99160,99168,99170,99172,99174,99176,99178],{},[10554,99161,99162,99164,99166],{},[898,99163,5325],{},[1810,99165,1812],{},[898,99167,5640],{},[1677,99169,1679],{},[1810,99171,2032],{},[1677,99173,2858],{},[1810,99175,1959],{},[1677,99177,1679],{},[1810,99179,2032],{},[902,99181,99182],{"encoding":904},"P_2^E = 4 \\cdot 1 = 4",[883,99184,99186],{"className":99185},[886],[888,99187,99188],{"xmlns":890},[892,99189,99190,99208],{},[895,99191,99192,99198,99200,99202,99204,99206],{},[1953,99193,99194,99196],{},[898,99195,5640],{},[1810,99197,1812],{},[1677,99199,2167],{"stretchy":1685},[1810,99201,1959],{},[1677,99203,1967],{"separator":1966},[1810,99205,2032],{},[1677,99207,2182],{"stretchy":1685},[902,99209,99210],{"encoding":904},"E_2[1, 4]",[724,99212,99213,99214,99250,99251,97868],{},"Spotřebitel platí celkem ",[883,99215,99217],{"className":99216},[886],[888,99218,99219],{"xmlns":890},[892,99220,99221,99247],{},[895,99222,99223,99231,99233,99235,99237,99239,99241,99243,99245],{},[10554,99224,99225,99227,99229],{},[898,99226,5325],{},[1810,99228,1812],{},[898,99230,5640],{},[1677,99232,1776],{},[898,99234,2455],{},[1677,99236,1679],{},[1810,99238,2032],{},[1677,99240,1776],{},[1810,99242,1916],{},[1677,99244,1679],{},[1810,99246,2544],{},[902,99248,99249],{"encoding":904},"P_2^E + T = 4 + 6 = 10"," Kč; výrobce obdrží ",[883,99252,99254],{"className":99253},[886],[888,99255,99256],{"xmlns":890},[892,99257,99258,99272],{},[895,99259,99260,99268,99270],{},[10554,99261,99262,99264,99266],{},[898,99263,5325],{},[1810,99265,1812],{},[898,99267,5640],{},[1677,99269,1679],{},[1810,99271,2032],{},[902,99273,99274],{"encoding":904},"P_2^E = 4",[724,99276,99277],{},[614,99278,99279],{},"Rozklad daňového břemene:",[883,99281,99283],{"className":99282},[886],[888,99284,99285],{"xmlns":890,"display":29457},[892,99286,99287,99373],{},[895,99288,99289,99299,99301,99303,99305,99307,99309,99311,99313,99315,99317,99319,99321,99331,99333,99335,99347,99349,99351,99353,99355,99357,99359,99361,99371],{},[1953,99290,99291,99293],{},[898,99292,2455],{},[895,99294,99295,99297],{},[898,99296,44068],{},[898,99298,724],{},[1677,99300,1679],{},[1677,99302,1686],{"stretchy":1685},[1810,99304,2032],{},[1677,99306,1776],{},[1810,99308,1916],{},[1677,99310,1692],{"stretchy":1685},[1677,99312,1906],{},[1810,99314,6973],{},[1677,99316,1679],{},[1810,99318,1812],{},[1969,99320,1971],{},[895,99322,99323,99325],{},[1969,99324,11188],{},[9774,99326,99327,99329],{"accent":1966},[1969,99328,1823],{},[1677,99330,26449],{},[1677,99332,1967],{"separator":1966},[7266,99334],{"width":7268},[1953,99336,99337,99339],{},[898,99338,2455],{},[895,99340,99341,99343,99345],{},[898,99342,44091],{},[898,99344,1675],{},[898,99346,13431],{},[1677,99348,1679],{},[1810,99350,6973],{},[1677,99352,1906],{},[1810,99354,2032],{},[1677,99356,1679],{},[1810,99358,2032],{},[1969,99360,1971],{},[895,99362,99363,99365],{},[1969,99364,11188],{},[9774,99366,99367,99369],{"accent":1966},[1969,99368,1823],{},[1677,99370,26449],{},[898,99372,1656],{"mathvariant":2057},[902,99374,99375],{"encoding":904},"T_{sp} = (4 + 6) - 8 = 2\\ \\text{Kč}, \\qquad T_{vyr} = 8 - 4 = 4\\ \\text{Kč}.",[724,99377,99378,99379,1656],{},"Opět ",[883,99380,99382],{"className":99381},[886],[888,99383,99384],{"xmlns":890},[892,99385,99386,99420],{},[895,99387,99388,99398,99400,99412,99414,99416,99418],{},[1953,99389,99390,99392],{},[898,99391,2455],{},[895,99393,99394,99396],{},[898,99395,44068],{},[898,99397,724],{},[1677,99399,1776],{},[1953,99401,99402,99404],{},[898,99403,2455],{},[895,99405,99406,99408,99410],{},[898,99407,44091],{},[898,99409,1675],{},[898,99411,13431],{},[1677,99413,1679],{},[1810,99415,1916],{},[1677,99417,1679],{},[898,99419,2455],{},[902,99421,99422],{"encoding":904},"T_{sp} + T_{vyr} = 6 = T",[38361,99424],{},[115,99426,44049],{"id":99427},"daňové-břemeno",[724,99429,99430,11413,99432,99435,99436,99449],{},[38,99431,44049],{},[614,99433,99434],{},"tax burden",") je rozdělení zaplacené daně ",[883,99437,99439],{"className":99438},[886],[888,99440,99441],{"xmlns":890},[892,99442,99443,99447],{},[895,99444,99445],{},[898,99446,2455],{},[902,99448,2455],{"encoding":904}," mezi spotřebitele a výrobce:",[883,99451,99453],{"className":99452},[886],[888,99454,99455],{"xmlns":890,"display":29457},[892,99456,99457,99489],{},[895,99458,99459,99461,99463,99473,99475,99487],{},[898,99460,2455],{},[1677,99462,1679],{},[1953,99464,99465,99467],{},[898,99466,2455],{},[895,99468,99469,99471],{},[898,99470,44068],{},[898,99472,724],{},[1677,99474,1776],{},[1953,99476,99477,99479],{},[898,99478,2455],{},[895,99480,99481,99483,99485],{},[898,99482,44091],{},[898,99484,1675],{},[898,99486,13431],{},[898,99488,1656],{"mathvariant":2057},[902,99490,99491],{"encoding":904},"T = T_{sp} + T_{vyr}.",[724,99493,99494],{},[2240,99495],{"alt":99496,"className":99497,"src":99498},"imek-dan-rozklad-bremene-sklony",[210,2244],"\u002Fwiki-assets\u002Fimek-dan-rozklad-bremene-sklony.jpeg",[5254,99500,99501],{},[724,99502,99503,99505,99506,5272,99519,1656],{},[883,99504,5543],{}," 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 ",[883,99507,99509],{"className":99508},[886],[888,99510,99511],{"xmlns":890},[892,99512,99513,99517],{},[895,99514,99515],{},[898,99516,5571],{},[902,99518,5571],{"encoding":904},[883,99520,99522],{"className":99521},[886],[888,99523,99524],{"xmlns":890},[892,99525,99526,99530],{},[895,99527,99528],{},[898,99529,10061],{},[902,99531,10061],{"encoding":904},[198,99533,2125],{"id":2124},[724,99535,99536,99537,99558,99559,99572,99573,99590,99591,99604],{},"V grafu ",[883,99538,99540],{"className":99539},[886],[888,99541,99542],{"xmlns":890},[892,99543,99544,99556],{},[895,99545,99546,99548,99550,99552,99554],{},[1677,99547,1686],{"stretchy":1685},[898,99549,2470],{},[1677,99551,1967],{"separator":1966},[898,99553,5325],{},[1677,99555,1692],{"stretchy":1685},[902,99557,39082],{"encoding":904}," je svislá vzdálenost mezi původní a posunutou křivkou právě ",[883,99560,99562],{"className":99561},[886],[888,99563,99564],{"xmlns":890},[892,99565,99566,99570],{},[895,99567,99568],{},[898,99569,2455],{},[902,99571,2455],{"encoding":904},". Vedeme-li v novém rovnovážném bodě vodorovnou přímku na úrovni původní rovnovážné ceny ",[883,99574,99576],{"className":99575},[886],[888,99577,99578],{"xmlns":890},[892,99579,99580,99588],{},[895,99581,99582],{},[1805,99583,99584,99586],{},[898,99585,5325],{},[898,99587,5640],{},[902,99589,42857],{"encoding":904},", rozdělí se úsečka ",[883,99592,99594],{"className":99593},[886],[888,99595,99596],{"xmlns":890},[892,99597,99598,99602],{},[895,99599,99600],{},[898,99601,2455],{},[902,99603,2455],{"encoding":904}," na dvě části:",[120,99606,99607,99632],{},[123,99608,99609,99610,99631],{},"horní část odpovídá ",[883,99611,99613],{"className":99612},[886],[888,99614,99615],{"xmlns":890},[892,99616,99617,99629],{},[895,99618,99619],{},[1953,99620,99621,99623],{},[898,99622,2455],{},[895,99624,99625,99627],{},[898,99626,44068],{},[898,99628,724],{},[902,99630,44073],{"encoding":904}," (o kolik vzrostla cena placená spotřebitelem),",[123,99633,99634,99635,99658],{},"dolní část odpovídá ",[883,99636,99638],{"className":99637},[886],[888,99639,99640],{"xmlns":890},[892,99641,99642,99656],{},[895,99643,99644],{},[1953,99645,99646,99648],{},[898,99647,2455],{},[895,99649,99650,99652,99654],{},[898,99651,44091],{},[898,99653,1675],{},[898,99655,13431],{},[902,99657,44098],{"encoding":904}," (o kolik klesla cena přijímaná výrobcem).",[724,99660,99661],{},[614,99662,99663,99664,2366,99677,99698,99699,99722,99723,5272,99744,99767],{},"Obrázky 2.20 a 2.21: Ilustrace rozkladu svislé vzdálenosti ",[883,99665,99667],{"className":99666},[886],[888,99668,99669],{"xmlns":890},[892,99670,99671,99675],{},[895,99672,99673],{},[898,99674,2455],{},[902,99676,2455],{"encoding":904},[883,99678,99680],{"className":99679},[886],[888,99681,99682],{"xmlns":890},[892,99683,99684,99696],{},[895,99685,99686],{},[1953,99687,99688,99690],{},[898,99689,2455],{},[895,99691,99692,99694],{},[898,99693,44068],{},[898,99695,724],{},[902,99697,44073],{"encoding":904}," (nahoře) a ",[883,99700,99702],{"className":99701},[886],[888,99703,99704],{"xmlns":890},[892,99705,99706,99720],{},[895,99707,99708],{},[1953,99709,99710,99712],{},[898,99711,2455],{},[895,99713,99714,99716,99718],{},[898,99715,44091],{},[898,99717,1675],{},[898,99719,13431],{},[902,99721,44098],{"encoding":904}," (dole). Obrázek 2.21 porovnává obě varianty — daň výrobci vs. daň spotřebiteli — a ukazuje, že velikost ",[883,99724,99726],{"className":99725},[886],[888,99727,99728],{"xmlns":890},[892,99729,99730,99742],{},[895,99731,99732],{},[1953,99733,99734,99736],{},[898,99735,2455],{},[895,99737,99738,99740],{},[898,99739,44068],{},[898,99741,724],{},[902,99743,44073],{"encoding":904},[883,99745,99747],{"className":99746},[886],[888,99748,99749],{"xmlns":890},[892,99750,99751,99765],{},[895,99752,99753],{},[1953,99754,99755,99757],{},[898,99756,2455],{},[895,99758,99759,99761,99763],{},[898,99760,44091],{},[898,99762,1675],{},[898,99764,13431],{},[902,99766,44098],{"encoding":904}," je v obou případech stejná.",[198,99769,99771],{"id":99770},"sklony-křivek-a-rozklad","Sklony křivek a rozklad",[724,99773,99774,99775,99778,99779,11413,99802,99819,99820,11413,99843,99860],{},"Platí obecně: ",[38,99776,99777],{},"čím strmější křivka (menší elasticita), tím větší část daně nese daná strana trhu."," Pro lineární poptávku ",[883,99780,99782],{"className":99781},[886],[888,99783,99784],{"xmlns":890},[892,99785,99786,99800],{},[895,99787,99788,99790,99792,99794,99796,99798],{},[898,99789,5325],{},[1677,99791,1679],{},[898,99793,207],{},[898,99795,2470],{},[1677,99797,1776],{},[898,99799,1779],{},[902,99801,38451],{"encoding":904},[883,99803,99805],{"className":99804},[886],[888,99806,99807],{"xmlns":890},[892,99808,99809,99817],{},[895,99810,99811,99813,99815],{},[898,99812,207],{},[1677,99814,3128],{},[1810,99816,2008],{},[902,99818,44476],{"encoding":904},") a lineární nabídku ",[883,99821,99823],{"className":99822},[886],[888,99824,99825],{"xmlns":890},[892,99826,99827,99841],{},[895,99828,99829,99831,99833,99835,99837,99839],{},[898,99830,5325],{},[1677,99832,1679],{},[898,99834,1823],{},[898,99836,2470],{},[1677,99838,1776],{},[898,99840,1875],{},[902,99842,41633],{"encoding":904},[883,99844,99846],{"className":99845},[886],[888,99847,99848],{"xmlns":890},[892,99849,99850,99858],{},[895,99851,99852,99854,99856],{},[898,99853,1823],{},[1677,99855,3089],{},[1810,99857,2008],{},[902,99859,41651],{"encoding":904},") lze rozklad odvodit pomocí multiplikátorů a platí",[883,99862,99864],{"className":99863},[886],[888,99865,99866],{"xmlns":890,"display":29457},[892,99867,99868,99934],{},[895,99869,99870,99894,99896,99906,99908,99932],{},[2010,99871,99872,99882],{},[1953,99873,99874,99876],{},[898,99875,2455],{},[895,99877,99878,99880],{},[898,99879,44068],{},[898,99881,724],{},[1953,99883,99884,99886],{},[898,99885,2455],{},[895,99887,99888,99890,99892],{},[898,99889,44091],{},[898,99891,1675],{},[898,99893,13431],{},[1677,99895,1679],{},[2010,99897,99898,99900],{},[898,99899,1823],{},[895,99901,99902,99904],{},[1677,99903,1906],{},[898,99905,207],{},[1677,99907,1679],{},[2010,99909,99910,99922],{},[895,99911,99912,99915,99918,99920],{},[898,99913,99914],{"mathvariant":2057},"∣",[1969,99916,99917],{},"sklon ",[898,99919,10061],{},[898,99921,99914],{"mathvariant":2057},[895,99923,99924,99926,99928,99930],{},[898,99925,99914],{"mathvariant":2057},[1969,99927,99917],{},[898,99929,5571],{},[898,99931,99914],{"mathvariant":2057},[898,99933,1656],{"mathvariant":2057},[902,99935,99936],{"encoding":904},"\\frac{T_{sp}}{T_{vyr}} = \\frac{c}{-a} = \\frac{|\\text{sklon } S|}{|\\text{sklon } D|}.",[5254,99938,99939,99944],{},[724,99940,99941,99943],{},[883,99942,5960],{}," Postup výpočtu rozkladu",[152,99945,99946,99981,100034,100113],{},[123,99947,99948,99949,99980],{},"Spočti rovnovážný bod ",[883,99950,99952],{"className":99951},[886],[888,99953,99954],{"xmlns":890},[892,99955,99956,99978],{},[895,99957,99958,99960,99962,99968,99970,99976],{},[898,99959,5640],{},[1677,99961,2167],{"stretchy":1685},[1805,99963,99964,99966],{},[898,99965,2470],{},[898,99967,5640],{},[1677,99969,1967],{"separator":1966},[1805,99971,99972,99974],{},[898,99973,5325],{},[898,99975,5640],{},[1677,99977,2182],{"stretchy":1685},[902,99979,42758],{"encoding":904}," bez daně.",[123,99982,99983,99984,1348,100009,5306],{},"Urči posunutou křivku (",[883,99985,99987],{"className":99986},[886],[888,99988,99989],{"xmlns":890},[892,99990,99991,100007],{},[895,99992,99993,99999,100001,100003,100005],{},[1953,99994,99995,99997],{},[898,99996,10061],{},[1810,99998,1959],{},[1677,100000,1679],{},[898,100002,10061],{},[1677,100004,1776],{},[898,100006,2455],{},[902,100008,44145],{"encoding":904},[883,100010,100012],{"className":100011},[886],[888,100013,100014],{"xmlns":890},[892,100015,100016,100032],{},[895,100017,100018,100024,100026,100028,100030],{},[1953,100019,100020,100022],{},[898,100021,5571],{},[1810,100023,1812],{},[1677,100025,1679],{},[898,100027,5571],{},[1677,100029,1906],{},[898,100031,2455],{},[902,100033,44176],{"encoding":904},[123,100035,100036,100037,5298,100056,13518,100075,5298,100094,5306],{},"Vyřeš novou rovnovážnou rovnici — získáš ",[883,100038,100040],{"className":100039},[886],[888,100041,100042],{"xmlns":890},[892,100043,100044,100054],{},[895,100045,100046],{},[10554,100047,100048,100050,100052],{},[898,100049,2470],{},[1810,100051,1959],{},[898,100053,5640],{},[902,100055,49227],{"encoding":904},[883,100057,100059],{"className":100058},[886],[888,100060,100061],{"xmlns":890},[892,100062,100063,100073],{},[895,100064,100065],{},[10554,100066,100067,100069,100071],{},[898,100068,2470],{},[1810,100070,1812],{},[898,100072,5640],{},[902,100074,49289],{"encoding":904},[883,100076,100078],{"className":100077},[886],[888,100079,100080],{"xmlns":890},[892,100081,100082,100092],{},[895,100083,100084],{},[10554,100085,100086,100088,100090],{},[898,100087,5325],{},[1810,100089,1959],{},[898,100091,5640],{},[902,100093,49248],{"encoding":904},[883,100095,100097],{"className":100096},[886],[888,100098,100099],{"xmlns":890},[892,100100,100101,100111],{},[895,100102,100103],{},[10554,100104,100105,100107,100109],{},[898,100106,5325],{},[1810,100108,1812],{},[898,100110,5640],{},[902,100112,49309],{"encoding":904},[123,100114,100115,100116,5272,100137,100160,100161,1656],{},"Dopočítej ",[883,100117,100119],{"className":100118},[886],[888,100120,100121],{"xmlns":890},[892,100122,100123,100135],{},[895,100124,100125],{},[1953,100126,100127,100129],{},[898,100128,2455],{},[895,100130,100131,100133],{},[898,100132,44068],{},[898,100134,724],{},[902,100136,44073],{"encoding":904},[883,100138,100140],{"className":100139},[886],[888,100141,100142],{"xmlns":890},[892,100143,100144,100158],{},[895,100145,100146],{},[1953,100147,100148,100150],{},[898,100149,2455],{},[895,100151,100152,100154,100156],{},[898,100153,44091],{},[898,100155,1675],{},[898,100157,13431],{},[902,100159,44098],{"encoding":904}," z definice, vždy ověř ",[883,100162,100164],{"className":100163},[886],[888,100165,100166],{"xmlns":890},[892,100167,100168,100198],{},[895,100169,100170,100180,100182,100194,100196],{},[1953,100171,100172,100174],{},[898,100173,2455],{},[895,100175,100176,100178],{},[898,100177,44068],{},[898,100179,724],{},[1677,100181,1776],{},[1953,100183,100184,100186],{},[898,100185,2455],{},[895,100187,100188,100190,100192],{},[898,100189,44091],{},[898,100191,1675],{},[898,100193,13431],{},[1677,100195,1679],{},[898,100197,2455],{},[902,100199,100200],{"encoding":904},"T_{sp} + T_{vyr} = T",[5254,100202,100203],{},[724,100204,100205,100207,100208,100211,100212,5272,100225,100238],{},[883,100206,5800],{}," Pozor — zákonný vs. ekonomický nositel daně\nI když zákon ukládá daň formálně pouze jedné straně (výrobci nebo spotřebiteli), ",[38,100209,100210],{},"ekonomicky ji vždy nesou obě strany",". Skutečné rozdělení určují sklony ",[883,100213,100215],{"className":100214},[886],[888,100216,100217],{"xmlns":890},[892,100218,100219,100223],{},[895,100220,100221],{},[898,100222,5571],{},[902,100224,5571],{"encoding":904},[883,100226,100228],{"className":100227},[886],[888,100229,100230],{"xmlns":890},[892,100231,100232,100236],{},[895,100233,100234],{},[898,100235,10061],{},[902,100237,10061],{"encoding":904},", nikoli paragrafové znění zákona. Kupující a prodávající tak fakticky platí daň bez ohledu na to, na koho je uvalena.",[38361,100240],{},[115,100242,100244],{"id":100243},"ekvivalence-obou-přístupů","Ekvivalence obou přístupů",[724,100246,100247],{},"Porovnáním Příkladu 2.9 (daň výrobci) a Příkladu 2.10 (daň spotřebiteli) zjistíme:",[724,100249,100250],{},[2240,100251],{"alt":100252,"className":100253,"src":100254},"imek-dan-ekvivalence-vyrobce-spotrebitel",[210,2244],"\u002Fwiki-assets\u002Fimek-dan-ekvivalence-vyrobce-spotrebitel.jpeg",[16,100256,100257,100269],{},[19,100258,100259],{},[22,100260,100261,100263,100266],{},[25,100262,55687],{},[25,100264,100265],{},"(a) daň výrobci",[25,100267,100268],{},"(b) daň spotřebiteli",[30,100270,100271,100326,100393,100453],{},[22,100272,100273,100276,100301],{},[35,100274,100275],{},"Rovnovážné množství",[35,100277,100278],{},[883,100279,100281],{"className":100280},[886],[888,100282,100283],{"xmlns":890},[892,100284,100285,100299],{},[895,100286,100287,100295,100297],{},[10554,100288,100289,100291,100293],{},[898,100290,2470],{},[1810,100292,1959],{},[898,100294,5640],{},[1677,100296,1679],{},[1810,100298,1959],{},[902,100300,98117],{"encoding":904},[35,100302,100303],{},[883,100304,100306],{"className":100305},[886],[888,100307,100308],{"xmlns":890},[892,100309,100310,100324],{},[895,100311,100312,100320,100322],{},[10554,100313,100314,100316,100318],{},[898,100315,2470],{},[1810,100317,1812],{},[898,100319,5640],{},[1677,100321,1679],{},[1810,100323,1959],{},[902,100325,99150],{"encoding":904},[22,100327,100328,100331,100356],{},[35,100329,100330],{},"Cena placená spotřebitelem",[35,100332,100333],{},[883,100334,100336],{"className":100335},[886],[888,100337,100338],{"xmlns":890},[892,100339,100340,100354],{},[895,100341,100342,100350,100352],{},[10554,100343,100344,100346,100348],{},[898,100345,5325],{},[1810,100347,1959],{},[898,100349,5640],{},[1677,100351,1679],{},[1810,100353,2544],{},[902,100355,98212],{"encoding":904},[35,100357,100358],{},[883,100359,100361],{"className":100360},[886],[888,100362,100363],{"xmlns":890},[892,100364,100365,100391],{},[895,100366,100367,100375,100377,100379,100381,100383,100385,100387,100389],{},[10554,100368,100369,100371,100373],{},[898,100370,5325],{},[1810,100372,1812],{},[898,100374,5640],{},[1677,100376,1776],{},[898,100378,2455],{},[1677,100380,1679],{},[1810,100382,2032],{},[1677,100384,1776],{},[1810,100386,1916],{},[1677,100388,1679],{},[1810,100390,2544],{},[902,100392,99249],{"encoding":904},[22,100394,100395,100398,100428],{},[35,100396,100397],{},"Cena přijímaná výrobcem",[35,100399,100400],{},[883,100401,100403],{"className":100402},[886],[888,100404,100405],{"xmlns":890},[892,100406,100407,100425],{},[895,100408,100409,100417,100419,100421,100423],{},[10554,100410,100411,100413,100415],{},[898,100412,5325],{},[1810,100414,1959],{},[898,100416,5640],{},[1677,100418,1906],{},[898,100420,2455],{},[1677,100422,1679],{},[1810,100424,2032],{},[902,100426,100427],{"encoding":904},"P_1^E - T = 4",[35,100429,100430],{},[883,100431,100433],{"className":100432},[886],[888,100434,100435],{"xmlns":890},[892,100436,100437,100451],{},[895,100438,100439,100447,100449],{},[10554,100440,100441,100443,100445],{},[898,100442,5325],{},[1810,100444,1812],{},[898,100446,5640],{},[1677,100448,1679],{},[1810,100450,2032],{},[902,100452,99274],{"encoding":904},[22,100454,100455,100458,100512],{},[35,100456,100457],{},"Rozklad břemene",[35,100459,100460,1343,100485],{},[883,100461,100463],{"className":100462},[886],[888,100464,100465],{"xmlns":890},[892,100466,100467,100483],{},[895,100468,100469,100479,100481],{},[1953,100470,100471,100473],{},[898,100472,2455],{},[895,100474,100475,100477],{},[898,100476,44068],{},[898,100478,724],{},[1677,100480,1679],{},[1810,100482,1812],{},[902,100484,44367],{"encoding":904},[883,100486,100488],{"className":100487},[886],[888,100489,100490],{"xmlns":890},[892,100491,100492,100510],{},[895,100493,100494,100506,100508],{},[1953,100495,100496,100498],{},[898,100497,2455],{},[895,100499,100500,100502,100504],{},[898,100501,44091],{},[898,100503,1675],{},[898,100505,13431],{},[1677,100507,1679],{},[1810,100509,2032],{},[902,100511,44396],{"encoding":904},[35,100513,100514,1343,100539],{},[883,100515,100517],{"className":100516},[886],[888,100518,100519],{"xmlns":890},[892,100520,100521,100537],{},[895,100522,100523,100533,100535],{},[1953,100524,100525,100527],{},[898,100526,2455],{},[895,100528,100529,100531],{},[898,100530,44068],{},[898,100532,724],{},[1677,100534,1679],{},[1810,100536,1812],{},[902,100538,44367],{"encoding":904},[883,100540,100542],{"className":100541},[886],[888,100543,100544],{"xmlns":890},[892,100545,100546,100564],{},[895,100547,100548,100560,100562],{},[1953,100549,100550,100552],{},[898,100551,2455],{},[895,100553,100554,100556,100558],{},[898,100555,44091],{},[898,100557,1675],{},[898,100559,13431],{},[1677,100561,1679],{},[1810,100563,2032],{},[902,100565,44396],{"encoding":904},[724,100567,100568],{},"Výsledek je v obou režimech reálně totožný — liší se pouze to, kterou cenu nazveme \"tržní\":",[883,100570,100572],{"className":100571},[886],[888,100573,100574],{"xmlns":890,"display":29457},[892,100575,100576,100624],{},[895,100577,100578,100586,100588,100596,100598,100600,100608,100610,100612,100614,100622],{},[10554,100579,100580,100582,100584],{},[898,100581,2470],{},[1810,100583,1959],{},[898,100585,5640],{},[1677,100587,1679],{},[10554,100589,100590,100592,100594],{},[898,100591,2470],{},[1810,100593,1812],{},[898,100595,5640],{},[1677,100597,1967],{"separator":1966},[7266,100599],{"width":7268},[10554,100601,100602,100604,100606],{},[898,100603,5325],{},[1810,100605,1959],{},[898,100607,5640],{},[1677,100609,1906],{},[898,100611,2455],{},[1677,100613,1679],{},[10554,100615,100616,100618,100620],{},[898,100617,5325],{},[1810,100619,1812],{},[898,100621,5640],{},[898,100623,1656],{"mathvariant":2057},[902,100625,100626],{"encoding":904},"Q_1^E = Q_2^E, \\qquad P_1^E - T = P_2^E.",[5254,100628,100629,100648,100802],{},[724,100630,100631,100633,100634,100647],{},[883,100632,5960],{}," Věta o ekvivalenci zdanění\nNezávisle na tom, zda je jednotková daň ",[883,100635,100637],{"className":100636},[886],[888,100638,100639],{"xmlns":890},[892,100640,100641,100645],{},[895,100642,100643],{},[898,100644,2455],{},[902,100646,2455],{"encoding":904}," uložena výrobci, nebo spotřebiteli, se po jejím uložení rovnají:",[120,100649,100650,100682,100718,100755],{},[123,100651,100652,100653,1967],{},"rovnovážná množství obou režimů, ",[883,100654,100656],{"className":100655},[886],[888,100657,100658],{"xmlns":890},[892,100659,100660,100680],{},[895,100661,100662,100670,100672],{},[10554,100663,100664,100666,100668],{},[898,100665,2470],{},[1810,100667,1959],{},[898,100669,5640],{},[1677,100671,1679],{},[10554,100673,100674,100676,100678],{},[898,100675,2470],{},[1810,100677,1812],{},[898,100679,5640],{},[902,100681,44299],{"encoding":904},[123,100683,100684,100685,1967],{},"čistá cena přijímaná výrobcem, ",[883,100686,100688],{"className":100687},[886],[888,100689,100690],{"xmlns":890},[892,100691,100692,100716],{},[895,100693,100694,100702,100704,100706,100708],{},[10554,100695,100696,100698,100700],{},[898,100697,5325],{},[1810,100699,1959],{},[898,100701,5640],{},[1677,100703,1906],{},[898,100705,2455],{},[1677,100707,1679],{},[10554,100709,100710,100712,100714],{},[898,100711,5325],{},[1810,100713,1812],{},[898,100715,5640],{},[902,100717,44333],{"encoding":904},[123,100719,100720,100721,1967],{},"celková cena placená spotřebitelem, ",[883,100722,100724],{"className":100723},[886],[888,100725,100726],{"xmlns":890},[892,100727,100728,100752],{},[895,100729,100730,100738,100740,100748,100750],{},[10554,100731,100732,100734,100736],{},[898,100733,5325],{},[1810,100735,1959],{},[898,100737,5640],{},[1677,100739,1679],{},[10554,100741,100742,100744,100746],{},[898,100743,5325],{},[1810,100745,1812],{},[898,100747,5640],{},[1677,100749,1776],{},[898,100751,2455],{},[902,100753,100754],{"encoding":904},"P_1^E = P_2^E + T",[123,100756,100757,100758,5272,100779,1656],{},"rozklad daňového břemene ",[883,100759,100761],{"className":100760},[886],[888,100762,100763],{"xmlns":890},[892,100764,100765,100777],{},[895,100766,100767],{},[1953,100768,100769,100771],{},[898,100770,2455],{},[895,100772,100773,100775],{},[898,100774,44068],{},[898,100776,724],{},[902,100778,44073],{"encoding":904},[883,100780,100782],{"className":100781},[886],[888,100783,100784],{"xmlns":890},[892,100785,100786,100800],{},[895,100787,100788],{},[1953,100789,100790,100792],{},[898,100791,2455],{},[895,100793,100794,100796,100798],{},[898,100795,44091],{},[898,100797,1675],{},[898,100799,13431],{},[902,100801,44098],{"encoding":904},[724,100803,100804,100805,1656],{},"Z hlediska reálných dopadů na trh (objem transakcí, reálné platby stran) jsou tedy obě formy zdanění ",[38,100806,36588],{},[724,100808,100809,100810,5272,100823,5306],{},"Ekvivalence má zásadní politickou implikaci: otázka, \"kdo má platit daň\", je z hlediska trhu formální — skutečné rozdělení určuje struktura trhu (sklony ",[883,100811,100813],{"className":100812},[886],[888,100814,100815],{"xmlns":890},[892,100816,100817,100821],{},[895,100818,100819],{},[898,100820,5571],{},[902,100822,5571],{"encoding":904},[883,100824,100826],{"className":100825},[886],[888,100827,100828],{"xmlns":890},[892,100829,100830,100834],{},[895,100831,100832],{},[898,100833,10061],{},[902,100835,10061],{"encoding":904},[38361,100837],{},[115,100839,100841],{"id":100840},"úlohy","Úlohy",[724,100843,100844,100845,2832],{},"Z kapitoly 2 se zdanění týkají zejména následující úlohy (zadání v hub-page ",[207,100846,17630],{"className":100847,"dataFsResolvedFilePath":800,"href":801},[210],[120,100849,100850,100880,100911],{},[123,100851,100852,100855,100856,100879],{},[38,100853,100854],{},"Úloha 2.4"," — Poptávka ",[883,100857,100859],{"className":100858},[886],[888,100860,100861],{"xmlns":890},[892,100862,100863,100877],{},[895,100864,100865,100867,100869,100871,100873,100875],{},[898,100866,5325],{},[1677,100868,1679],{},[1810,100870,3190],{},[1677,100872,1906],{},[1810,100874,1812],{},[898,100876,2470],{},[902,100878,97829],{"encoding":904},"; najděte novou poptávku po uložení daně 6 Kč na kupujícího.",[123,100881,100882,100885,100886,100910],{},[38,100883,100884],{},"Úloha 2.9"," — Nabídka ",[883,100887,100889],{"className":100888},[886],[888,100890,100891],{"xmlns":890},[892,100892,100893,100907],{},[895,100894,100895,100897,100899,100901,100903,100905],{},[898,100896,5325],{},[1677,100898,1679],{},[1810,100900,6397],{},[898,100902,2470],{},[1677,100904,1776],{},[1810,100906,37635],{},[902,100908,100909],{"encoding":904},"P = 0{,}5Q + 15","; najděte novou nabídku po uložení daně 5 Kč na výrobce.",[123,100912,100913,100916,100917,5272,100943,100967,100968,100985],{},[38,100914,100915],{},"Úloha 2.13"," — Komplexní úloha se zadáním ",[883,100918,100920],{"className":100919},[886],[888,100921,100922],{"xmlns":890},[892,100923,100924,100940],{},[895,100925,100926,100928,100930,100932,100934,100936,100938],{},[898,100927,5325],{},[1677,100929,1679],{},[1677,100931,1906],{},[1810,100933,2032],{},[898,100935,2470],{},[1677,100937,1776],{},[1810,100939,48094],{},[902,100941,100942],{"encoding":904},"P = -4Q + 80",[883,100944,100946],{"className":100945},[886],[888,100947,100948],{"xmlns":890},[892,100949,100950,100964],{},[895,100951,100952,100954,100956,100958,100960,100962],{},[898,100953,5325],{},[1677,100955,1679],{},[1810,100957,1854],{},[898,100959,2470],{},[1677,100961,1776],{},[1810,100963,2544],{},[902,100965,100966],{"encoding":904},"P = 3Q + 10",": rovnováha, daň ",[883,100969,100971],{"className":100970},[886],[888,100972,100973],{"xmlns":890},[892,100974,100975,100983],{},[895,100976,100977,100979,100981],{},[898,100978,2455],{},[1677,100980,1679],{},[1810,100982,25592],{},[902,100984,49206],{"encoding":904}," Kč uložená postupně výrobci i spotřebiteli, rozklad daňového břemene a analýza ekvivalence.",[724,100987,100988,100989,100991,100992,100994],{},"Související úvodní příklady posunu křivek při zdanění: ",[38,100990,46619],{}," (posun poptávky při zdanění kupujícího) a ",[38,100993,46653],{}," (posun nabídky při zdanění výrobce).",[38361,100996],{},[115,100998,17110],{"id":17109},[120,101000,101001,101020,101078,101135,101218,101264,101307,101352,101418],{},[123,101002,101003,1884,101006,101019],{},[38,101004,101005],{},"Jednotková daň",[883,101007,101009],{"className":101008},[886],[888,101010,101011],{"xmlns":890},[892,101012,101013,101017],{},[895,101014,101015],{},[898,101016,2455],{},[902,101018,2455],{"encoding":904}," — fixní částka na každou prodanou jednotku zboží",[123,101021,101022,101024,101025,101063,101064,101077],{},[38,101023,97411],{}," — posun nabídky ",[883,101026,101028],{"className":101027},[886],[888,101029,101030],{"xmlns":890},[892,101031,101032,101060],{},[895,101033,101034,101040,101042,101044,101046,101048,101050,101052,101054,101056,101058],{},[1953,101035,101036,101038],{},[898,101037,10061],{},[1810,101039,1959],{},[1677,101041,1686],{"stretchy":1685},[898,101043,2470],{},[1677,101045,1692],{"stretchy":1685},[1677,101047,1679],{},[898,101049,10061],{},[1677,101051,1686],{"stretchy":1685},[898,101053,2470],{},[1677,101055,1692],{"stretchy":1685},[1677,101057,1776],{},[898,101059,2455],{},[902,101061,101062],{"encoding":904},"S_1(Q) = S(Q) + T"," (o ",[883,101065,101067],{"className":101066},[886],[888,101068,101069],{"xmlns":890},[892,101070,101071,101075],{},[895,101072,101073],{},[898,101074,2455],{},[902,101076,2455],{"encoding":904}," svisle nahoru)",[123,101079,101080,101082,101083,101063,101121,101134],{},[38,101081,98484],{}," — posun poptávky ",[883,101084,101086],{"className":101085},[886],[888,101087,101088],{"xmlns":890},[892,101089,101090,101118],{},[895,101091,101092,101098,101100,101102,101104,101106,101108,101110,101112,101114,101116],{},[1953,101093,101094,101096],{},[898,101095,5571],{},[1810,101097,1812],{},[1677,101099,1686],{"stretchy":1685},[898,101101,2470],{},[1677,101103,1692],{"stretchy":1685},[1677,101105,1679],{},[898,101107,5571],{},[1677,101109,1686],{"stretchy":1685},[898,101111,2470],{},[1677,101113,1692],{"stretchy":1685},[1677,101115,1906],{},[898,101117,2455],{},[902,101119,101120],{"encoding":904},"D_2(Q) = D(Q) - T",[883,101122,101124],{"className":101123},[886],[888,101125,101126],{"xmlns":890},[892,101127,101128,101132],{},[895,101129,101130],{},[898,101131,2455],{},[902,101133,2455],{"encoding":904}," svisle dolů)",[123,101136,101137,8403,101140,43205,101179],{},[38,101138,101139],{},"Rovnovážný bod s daní",[883,101141,101143],{"className":101142},[886],[888,101144,101145],{"xmlns":890},[892,101146,101147,101177],{},[895,101148,101149,101155,101157,101165,101167,101175],{},[1953,101150,101151,101153],{},[898,101152,5640],{},[1810,101154,1959],{},[1677,101156,2167],{"stretchy":1685},[10554,101158,101159,101161,101163],{},[898,101160,2470],{},[1810,101162,1959],{},[898,101164,5640],{},[1677,101166,1967],{"separator":1966},[10554,101168,101169,101171,101173],{},[898,101170,5325],{},[1810,101172,1959],{},[898,101174,5640],{},[1677,101176,2182],{"stretchy":1685},[902,101178,97579],{"encoding":904},[883,101180,101182],{"className":101181},[886],[888,101183,101184],{"xmlns":890},[892,101185,101186,101216],{},[895,101187,101188,101194,101196,101204,101206,101214],{},[1953,101189,101190,101192],{},[898,101191,5640],{},[1810,101193,1812],{},[1677,101195,2167],{"stretchy":1685},[10554,101197,101198,101200,101202],{},[898,101199,2470],{},[1810,101201,1812],{},[898,101203,5640],{},[1677,101205,1967],{"separator":1966},[10554,101207,101208,101210,101212],{},[898,101209,5325],{},[1810,101211,1812],{},[898,101213,5640],{},[1677,101215,2182],{"stretchy":1685},[902,101217,98654],{"encoding":904},[123,101219,101220,11413,101222,101224,101225],{},[38,101221,44049],{},[614,101223,99434],{},") — rozklad ",[883,101226,101228],{"className":101227},[886],[888,101229,101230],{"xmlns":890},[892,101231,101232,101262],{},[895,101233,101234,101236,101238,101248,101250],{},[898,101235,2455],{},[1677,101237,1679],{},[1953,101239,101240,101242],{},[898,101241,2455],{},[895,101243,101244,101246],{},[898,101245,44068],{},[898,101247,724],{},[1677,101249,1776],{},[1953,101251,101252,101254],{},[898,101253,2455],{},[895,101255,101256,101258,101260],{},[898,101257,44091],{},[898,101259,1675],{},[898,101261,13431],{},[902,101263,44235],{"encoding":904},[123,101265,101266,101289,101290,1692],{},[38,101267,101268],{},[883,101269,101271],{"className":101270},[886],[888,101272,101273],{"xmlns":890},[892,101274,101275,101287],{},[895,101276,101277],{},[1953,101278,101279,101281],{},[898,101280,2455],{},[895,101282,101283,101285],{},[898,101284,44068],{},[898,101286,724],{},[902,101288,44073],{"encoding":904}," — část daně nesená spotřebitelem (navýšení ceny nad ",[883,101291,101293],{"className":101292},[886],[888,101294,101295],{"xmlns":890},[892,101296,101297,101305],{},[895,101298,101299],{},[1805,101300,101301,101303],{},[898,101302,5325],{},[898,101304,5640],{},[902,101306,42857],{"encoding":904},[123,101308,101309,101334,101335,1692],{},[38,101310,101311],{},[883,101312,101314],{"className":101313},[886],[888,101315,101316],{"xmlns":890},[892,101317,101318,101332],{},[895,101319,101320],{},[1953,101321,101322,101324],{},[898,101323,2455],{},[895,101325,101326,101328,101330],{},[898,101327,44091],{},[898,101329,1675],{},[898,101331,13431],{},[902,101333,44098],{"encoding":904}," — část daně nesená výrobcem (pokles čisté přijímané ceny pod ",[883,101336,101338],{"className":101337},[886],[888,101339,101340],{"xmlns":890},[892,101341,101342,101350],{},[895,101343,101344],{},[1805,101345,101346,101348],{},[898,101347,5325],{},[898,101349,5640],{},[902,101351,42857],{"encoding":904},[123,101353,101354,8403,101356,1343,101385],{},[38,101355,51865],{},[883,101357,101359],{"className":101358},[886],[888,101360,101361],{"xmlns":890},[892,101362,101363,101383],{},[895,101364,101365,101373,101375],{},[10554,101366,101367,101369,101371],{},[898,101368,2470],{},[1810,101370,1959],{},[898,101372,5640],{},[1677,101374,1679],{},[10554,101376,101377,101379,101381],{},[898,101378,2470],{},[1810,101380,1812],{},[898,101382,5640],{},[902,101384,44299],{"encoding":904},[883,101386,101388],{"className":101387},[886],[888,101389,101390],{"xmlns":890},[892,101391,101392,101416],{},[895,101393,101394,101402,101404,101406,101408],{},[10554,101395,101396,101398,101400],{},[898,101397,5325],{},[1810,101399,1959],{},[898,101401,5640],{},[1677,101403,1906],{},[898,101405,2455],{},[1677,101407,1679],{},[10554,101409,101410,101412,101414],{},[898,101411,5325],{},[1810,101413,1812],{},[898,101415,5640],{},[902,101417,44333],{"encoding":904},[123,101419,101420,101423],{},[38,101421,101422],{},"Zákonný vs. ekonomický nositel daně"," — rozdíl mezi formálním ustanovením zákona a skutečným rozdělením břemene",[38361,101425],{},[115,101427,3473],{"id":3472},[120,101429,101430,101438,101456,101463],{},[123,101431,101432,1884,101435],{},[38,101433,101434],{},"Kontext (hub):",[207,101436,802],{"className":101437,"dataFsResolvedFilePath":800,"href":801},[210],[123,101439,101440,1884,101442,101445,101446,20039,101448,101451,101452,101455],{},[38,101441,52114],{},[207,101443,820],{"className":101444,"dataFsResolvedFilePath":818,"href":819},[210]," (daň vyvolává ztrátu blahobytu — ",[614,101447,56425],{},[207,101449,2038],{"className":101450,"dataFsResolvedFilePath":764,"href":765},[210]," (sklony křivek, rovnovážný bod jako řešení soustavy), ",[207,101453,3509],{"className":101454,"dataFsResolvedFilePath":848,"href":849},[210]," (kvantifikace, jak se daňové břemeno dělí podle citlivosti stran trhu)",[123,101457,101458,1884,101460],{},[38,101459,52149],{},[207,101461,52153],{"className":101462,"dataFsResolvedFilePath":745,"href":746},[210],[123,101464,101465,1884,101467],{},[38,101466,17594],{},[207,101468,17598],{"className":101469,"dataFsResolvedFilePath":1641,"href":1642},[210],{"title":641,"searchDepth":642,"depth":642,"links":101471},[101472,101473,101476,101479,101483,101484,101485,101486],{"id":97316,"depth":642,"text":97317},{"id":97410,"depth":642,"text":97411,"children":101474},[101475],{"id":97801,"depth":649,"text":46694},{"id":98483,"depth":642,"text":98484,"children":101477},[101478],{"id":98960,"depth":649,"text":46774},{"id":99427,"depth":642,"text":44049,"children":101480},[101481,101482],{"id":2124,"depth":649,"text":2125},{"id":99770,"depth":649,"text":99771},{"id":100243,"depth":642,"text":100244},{"id":100840,"depth":642,"text":100841},{"id":17109,"depth":642,"text":17110},{"id":3472,"depth":642,"text":3473},{},"\u002Ftopics\u002Fzdaneni-trhu",{"title":97214,"description":641},[1138,1135],"topics\u002Fzdaneni-trhu",[1128,52214,101493,101494,101495,17630],"dane","danove-bremeno","posun-krivek","cFuKqHgzIrqvY-l4jNdqjFEM7_ixjw33HOL0So8cPn0",[101498,101500,101502,101506,101510,101514,101518,101520],{"slug":5285,"path":849,"title":5247,"snippet":101499},"… ptávky* (resp. *nabídky*). Matematickým modelem míry citlivosti je elasticita funkce (viz \u003C\u003Cderivace>>). ### Srovnání Trh 1 vs Trh 2 Uvažujme dvě různá tržní prostředí. Zboží má na obou trzí …",{"slug":1128,"path":1642,"title":681,"snippet":101501},"… ekonomie]] — model, endogenní\u002Fexogenní proměnné, ceteris paribus, komparativní statika - \u003C\u003Cderivace>> — geometrická a inženýrská interpretace, mezní veličiny - Integrál — neurčit …",{"slug":101503,"path":746,"title":101504,"snippet":101505},"imek-blok-01","KS 1. blok — Kalkul a mikroekonomie","… l, endogenní\u002Fexogenní proměnné, ceteris paribus, komparativní statika, principy řešení 2. \u003C\u003Cderivace>> — funkce, polynomy, derivace (geom.\u002Finženýrská interpretace), tečna, diferenciál jako lin …",{"slug":101507,"path":839,"title":101508,"snippet":101509},"imek-blok-02","KS 2. blok — Elasticita a produkce","… ot MP_K = Q$ ## Vazby - **Předchozí blok:** KS 1. blok — kalkul (zejm. \u003C\u003Cderivace>> a funkce-vice-promennych je nutný předpoklad) - **Navazující blok:** [[imek-blok-03|K …",{"slug":101511,"path":1109,"title":101512,"snippet":101513},"imek-kniha","Kniha — *Úvod do matematické ekonomie pro ekonomy*","… ce, derivace, integrály, Lagrange). Teorie je pokryta v zaklady-matematicke-ekonomie, \u003C\u003Cderivace>>, integral, funkce-vice-promennych, lagrangeova-metoda ze zdrojů ve vysokoškol …",{"slug":101515,"path":959,"title":101516,"snippet":101517},"imek-vzorce-prehled","ImeK — kompletní přehled vzorců se zdroji a intuicí","… j:** Kniha Mezník — Úvod do matematické ekonomie - **Matematický aparát:** \u003C\u003Cderivace>>, Integrál, Funkce více proměnných, [[lagrangeova- …",{"slug":13378,"path":774,"title":775,"snippet":101519},"… Q$$ Detailně viz Poptávka a nabídka. ## Navigace - **Předchozí:** \u003C\u003Cderivace>> - **Navazující:** Funkce více proměnných - **Souvislosti:** [[ …",{"slug":17663,"path":944,"title":13387,"snippet":101521},"… optavka-nabidka]] — paralela rovnovážného bodu (průsečík dvou křivek) v mikroekonomii - \u003C\u003Cderivace>> — matematický základ pro směrnice IS a LM - funkce-vice-promennych — dvě neznámé a …",[101523,101524],{"slug":17643,"title":10958,"path":783,"sharedTags":642},{"slug":101503,"title":101504,"path":746,"sharedTags":642},1777154952615]