[{"data":1,"prerenderedAt":100377},["ShallowReactive",2],{"sidebar-courses-with-stats":3,"wiki-imek-blok-03":1626,"course-stats-imek":2231,"course-topics-imek":2235,"backlinks-imek-blok-03":100346,"related-imek-blok-03":100371},{"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":2230},{"id":1628,"title":1629,"body":1630,"course":1128,"courses":659,"created":1129,"description":1637,"extension":661,"meta":2219,"navigation":664,"path":2220,"seo":2221,"sources":2222,"stem":2223,"tags":2224,"type":2228,"updated":677,"__hash__":2229},"summaries\u002Fsummaries\u002Fimek-blok-03.md","KS 3. blok — Užitečnost a národní důchod",{"type":9,"value":1631,"toc":2213},[1632,1635,1638,1642,1758,1762,2159,2163,2199,2203],[12,1633,1629],{"id":1634},"ks-3-blok-užitečnost-a-národní-důchod",[724,1636,1637],{},"Rozcestník třetího přednáškového bloku (25 stran). Most mezi mikroekonomií (rozhodování spotřebitele) a makroekonomií (modely národní ekonomiky).",[115,1639,1641],{"id":1640},"témata-bloku-doporučené-pořadí","Témata bloku — doporučené pořadí",[152,1643,1644,1672],{},[123,1645,1646,1649,1650,1667,1668,1671],{},[207,1647,880],{"className":1648,"dataFsResolvedFilePath":878,"href":879},[210]," — pojetí kardinalistické vs. ordinalistické, model užitečnosti, mezní užitečnost (",[883,1651,1653],{"className":1652},[886],[888,1654,1655],{"xmlns":890},[892,1656,1657,1664],{},[895,1658,1659,1662],{},[898,1660,1661],{},"M",[898,1663,900],{},[902,1665,1666],{"encoding":904},"MU","), Cobb-Douglasova funkce užitečnosti, indiferenční křivky, ",[38,1669,1670],{},"MRCS",", maximalizace užitečnosti při rozpočtovém omezení (Lagrange), minimalizace výdajů (duální úloha), Marshallova vs. Hicksova poptávka.",[123,1673,1674,1677,1678,1713,1714,1744,1745,1343,1748,1343,1751,1343,1754,1757],{},[207,1675,936],{"className":1676,"dataFsResolvedFilePath":934,"href":935},[210]," — GNP ",[883,1679,1681],{"className":1680},[886],[888,1682,1683],{"xmlns":890},[892,1684,1685,1710],{},[895,1686,1687,1691,1694,1697,1700,1702,1705,1707],{},[1688,1689,1690],"mo",{},"=",[898,1692,1693],{},"C",[1688,1695,1696],{},"+",[898,1698,1699],{},"I",[1688,1701,1696],{},[898,1703,1704],{},"G",[1688,1706,1696],{},[898,1708,1709],{},"X",[902,1711,1712],{"encoding":904},"= C + I + G + X",", lineární model spotřeby, mezní sklon ke spotřebě\u002Fúsporám (",[883,1715,1717],{"className":1716},[886],[888,1718,1719],{"xmlns":890},[892,1720,1721,1741],{},[895,1722,1723,1725,1728,1730,1734,1736,1738],{},[898,1724,1661],{},[898,1726,1727],{},"P",[898,1729,1693],{},[1688,1731,1733],{"separator":1732},"true",",",[898,1735,1661],{},[898,1737,1727],{},[898,1739,1740],{},"S",[902,1742,1743],{"encoding":904},"MPC, MPS","), modely ",[38,1746,1747],{},"C-I",[38,1749,1750],{},"C-I-G",[38,1752,1753],{},"C-I-G-X",[38,1755,1756],{},"IS-LM",", multiplikátory (autonomní spotřeby, investic, mezního sklonu).",[115,1759,1761],{"id":1760},"klíčové-vzorce-na-jeden-pohled","Klíčové vzorce na jeden pohled",[120,1763,1764,1837,1894,1960,2009,2080],{},[123,1765,1766,1767,1836],{},"MRCS: ",[883,1768,1770],{"className":1769},[886],[888,1771,1772],{"xmlns":890},[892,1773,1774,1833],{},[895,1775,1776,1807,1809],{},[1777,1778,1780],"mstyle",{"scriptlevel":1779,"displaystyle":1732},"0",[1781,1782,1783,1796],"mfrac",{},[895,1784,1785,1787],{},[898,1786,1661],{},[1788,1789,1790,1792],"msub",{},[898,1791,900],{},[1793,1794,1795],"mn",{},"1",[895,1797,1798,1800],{},[898,1799,1661],{},[1788,1801,1802,1804],{},[898,1803,900],{},[1793,1805,1806],{},"2",[1688,1808,1690],{},[1777,1810,1811],{"scriptlevel":1779,"displaystyle":1732},[1781,1812,1813,1825],{},[1814,1815,1816,1818,1820],"msubsup",{},[898,1817,900],{},[1793,1819,1795],{},[1688,1821,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},"normal","0em","′",[1814,1826,1827,1829,1831],{},[898,1828,900],{},[1793,1830,1806],{},[1688,1832,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[902,1834,1835],{"encoding":904},"\\dfrac{MU_1}{MU_2} = \\dfrac{U'_1}{U'_2}"," (poměr mezních užitečností = poměr cen v optimu)",[123,1838,1839,1840],{},"Rozpočtové omezení: ",[883,1841,1843],{"className":1842},[886],[888,1844,1845],{"xmlns":890},[892,1846,1847,1891],{},[895,1848,1849,1858,1860,1868,1875,1877,1885],{},[1850,1851,1852,1855],"msup",{},[898,1853,1854],{},"Y",[1688,1856,1857],{},"∗",[1688,1859,1690],{},[1814,1861,1862,1864,1866],{},[898,1863,1727],{},[1793,1865,1795],{},[1688,1867,1857],{},[1788,1869,1870,1873],{},[898,1871,1872],{},"Q",[1793,1874,1795],{},[1688,1876,1696],{},[1814,1878,1879,1881,1883],{},[898,1880,1727],{},[1793,1882,1806],{},[1688,1884,1857],{},[1788,1886,1887,1889],{},[898,1888,1872],{},[1793,1890,1806],{},[902,1892,1893],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2",[123,1895,1896,1897,1922,1923],{},"Lineární spotřeba: ",[883,1898,1900],{"className":1899},[886],[888,1901,1902],{"xmlns":890},[892,1903,1904,1919],{},[895,1905,1906,1908,1910,1912,1914,1916],{},[898,1907,1693],{},[1688,1909,1690],{},[898,1911,207],{},[898,1913,1854],{},[1688,1915,1696],{},[898,1917,1918],{},"b",[902,1920,1921],{"encoding":904},"C = aY + b",", redukovaný tvar C-I: ",[883,1924,1926],{"className":1925},[886],[888,1927,1928],{"xmlns":890},[892,1929,1930,1957],{},[895,1931,1932,1934,1936],{},[898,1933,1854],{},[1688,1935,1690],{},[1777,1937,1938],{"scriptlevel":1779,"displaystyle":1732},[1781,1939,1940,1948],{},[895,1941,1942,1944,1946],{},[898,1943,1918],{},[1688,1945,1696],{},[898,1947,1699],{},[895,1949,1950,1952,1955],{},[1793,1951,1795],{},[1688,1953,1954],{},"−",[898,1956,207],{},[902,1958,1959],{"encoding":904},"Y = \\dfrac{b + I}{1 - a}",[123,1961,1962,1963],{},"Multiplikátor investic \u002F autonomní spotřeby: ",[883,1964,1966],{"className":1965},[886],[888,1967,1968],{"xmlns":890},[892,1969,1970,2006],{},[895,1971,1972,1980,1982,1990,1992],{},[1814,1973,1974,1976,1978],{},[898,1975,1854],{},[898,1977,1699],{},[1688,1979,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,1981,1690],{},[1814,1983,1984,1986,1988],{},[898,1985,1854],{},[898,1987,1918],{},[1688,1989,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,1991,1690],{},[1777,1993,1994],{"scriptlevel":1779,"displaystyle":1732},[1781,1995,1996,1998],{},[1793,1997,1795],{},[895,1999,2000,2002,2004],{},[1793,2001,1795],{},[1688,2003,1954],{},[898,2005,207],{},[902,2007,2008],{"encoding":904},"Y'_I = Y'_b = \\dfrac{1}{1 - a}",[123,2010,2011,2012],{},"IS: ",[883,2013,2015],{"className":2014},[886],[888,2016,2017],{"xmlns":890},[892,2018,2019,2077],{},[895,2020,2021,2023,2025,2040,2044,2047,2049,2063,2067,2069,2071,2074],{},[898,2022,1854],{},[1688,2024,1690],{},[1777,2026,2027],{"scriptlevel":1779,"displaystyle":1732},[1781,2028,2029,2032],{},[898,2030,2031],{},"c",[895,2033,2034,2036,2038],{},[1793,2035,1795],{},[1688,2037,1954],{},[898,2039,207],{},[2041,2042,2043],"mtext",{}," ",[898,2045,2046],{},"r",[1688,2048,1696],{},[1777,2050,2051],{"scriptlevel":1779,"displaystyle":1732},[1781,2052,2053,2055],{},[1793,2054,1795],{},[895,2056,2057,2059,2061],{},[1793,2058,1795],{},[1688,2060,1954],{},[898,2062,207],{},[1688,2064,2066],{"stretchy":2065},"false","(",[898,2068,1918],{},[1688,2070,1696],{},[898,2072,2073],{},"d",[1688,2075,2076],{"stretchy":2065},")",[902,2078,2079],{"encoding":904},"Y = \\dfrac{c}{1-a}\\, r + \\dfrac{1}{1-a}(b + d)",[123,2081,2082,2083],{},"LM: ",[883,2084,2086],{"className":2085},[886],[888,2087,2088],{"xmlns":890},[892,2089,2090,2156],{},[895,2091,2092,2094,2096,2098,2115,2117,2119,2121,2138,2140],{},[898,2093,1854],{},[1688,2095,1690],{},[1688,2097,1954],{},[1777,2099,2100],{"scriptlevel":1779,"displaystyle":1732},[1781,2101,2102,2109],{},[1788,2103,2104,2107],{},[898,2105,2106],{},"k",[1793,2108,1806],{},[1788,2110,2111,2113],{},[898,2112,2106],{},[1793,2114,1795],{},[2041,2116,2043],{},[898,2118,2046],{},[1688,2120,1954],{},[1777,2122,2123],{"scriptlevel":1779,"displaystyle":1732},[1781,2124,2125,2132],{},[1788,2126,2127,2129],{},[898,2128,2106],{},[1793,2130,2131],{},"3",[1788,2133,2134,2136],{},[898,2135,2106],{},[1793,2137,1795],{},[1688,2139,1696],{},[1777,2141,2142],{"scriptlevel":1779,"displaystyle":1732},[1781,2143,2144,2150],{},[1850,2145,2146,2148],{},[898,2147,1661],{},[1688,2149,1857],{},[1788,2151,2152,2154],{},[898,2153,2106],{},[1793,2155,1795],{},[902,2157,2158],{"encoding":904},"Y = -\\dfrac{k_2}{k_1}\\, r - \\dfrac{k_3}{k_1} + \\dfrac{M^*}{k_1}",[115,2160,2162],{"id":2161},"vazby","Vazby",[120,2164,2165,2175,2181],{},[123,2166,2167,2170,2171,2174],{},[38,2168,2169],{},"Předchozí blok:"," ",[207,2172,1094],{"className":2173,"dataFsResolvedFilePath":838,"href":839},[210]," — produkce (paralela izokvanty ↔ indiferenční křivky)",[123,2176,2177,2180],{},[38,2178,2179],{},"Navazující:"," — (poslední blok kurzu)",[123,2182,2183,2170,2186,1343,2190,2194,2195],{},[38,2184,2185],{},"Předpoklady:",[207,2187,2189],{"className":2188,"dataFsResolvedFilePath":791,"href":792},[210],"Lagrange",[207,2191,2193],{"className":2192,"dataFsResolvedFilePath":782,"href":783},[210],"2D kalkul"," z ",[207,2196,2198],{"className":2197,"dataFsResolvedFilePath":745,"href":746},[210],"Bloku 1",[115,2200,2202],{"id":2201},"související","Související",[120,2204,2205],{},[123,2206,2207],{},[207,2208,2212],{"className":2209,"dataFsResolvedFilePath":2210,"href":2211},[210],"courses\u002Fimek.md","\u002Fwiki\u002Fimek","Kurz ImeK",{"title":641,"searchDepth":642,"depth":642,"links":2214},[2215,2216,2217,2218],{"id":1640,"depth":642,"text":1641},{"id":1760,"depth":642,"text":1761},{"id":2161,"depth":642,"text":2162},{"id":2201,"depth":642,"text":2202},{},"\u002Fsummaries\u002Fimek-blok-03",{"title":1629,"description":1637},[1137],"summaries\u002Fimek-blok-03",[1128,2225,1144,2226,2227],"uzitecnost","is-lm","gnp","summary","Wm7uyoEKQfsPBb_MtycXHkrbnPMQuof03eH-QI7XEyQ","summaries",{"zapisku":1625,"topics":2232,"summaries":2233,"outputs":2234},15,5,1,[2236,4115,9821,11376,12248,16525,18130,28005,36999,51066,55358,74702,86814,95773,96061],{"id":2237,"title":2238,"body":2239,"course":1128,"courses":659,"created":1129,"description":4103,"extension":661,"meta":4104,"navigation":664,"path":4105,"seo":4106,"sources":4107,"stem":4108,"tags":4109,"type":4113,"updated":677,"__hash__":4114},"topics\u002Ftopics\u002Fderivace.md","Derivace, diferenciál a extrémy funkcí jedné proměnné",{"type":9,"value":2240,"toc":4086},[2241,2244,2264,2268,2347,2350,2473,2620,2623,2703,2707,2768,2818,2827,2831,2966,3017,3021,3063,3131,3202,3210,3214,3252,3324,3328,3409,3458,3502,3506,3510,3580,3584,3634,3713,3720,3723,3776,4046,4050],[12,2242,2238],{"id":2243},"derivace-diferenciál-a-extrémy-funkcí-jedné-proměnné",[724,2245,2246,2247,2251,2252,2255,2256,2259,2260,2263],{},"Matematický aparát kurzu ",[207,2248,2250],{"className":2249,"dataFsResolvedFilePath":2210,"href":2211},[210],"ImeK",". Bez derivace se neobejdou ",[38,2253,2254],{},"mezní veličiny"," (mezní náklady, mezní příjem, mezní užitečnost), bez extrémů se neobejde ",[38,2257,2258],{},"maximalizace zisku"," ani ",[38,2261,2262],{},"minimalizace nákladů",".",[115,2265,2267],{"id":2266},"funkce-a-polynomy","Funkce a polynomy",[724,2269,2270,2271,2298,2299,2312,2313,2326,2327,2263],{},"Funkce jedné proměnné ",[883,2272,2274],{"className":2273},[886],[888,2275,2276],{"xmlns":890},[892,2277,2278,2295],{},[895,2279,2280,2283,2285,2288,2290,2293],{},[898,2281,2282],{},"y",[1688,2284,1690],{},[898,2286,2287],{},"f",[1688,2289,2066],{"stretchy":2065},[898,2291,2292],{},"x",[1688,2294,2076],{"stretchy":2065},[902,2296,2297],{"encoding":904},"y = f(x)"," — předpis závislosti ",[883,2300,2302],{"className":2301},[886],[888,2303,2304],{"xmlns":890},[892,2305,2306,2310],{},[895,2307,2308],{},[898,2309,2292],{},[902,2311,2292],{"encoding":904}," (nezávislá) → ",[883,2314,2316],{"className":2315},[886],[888,2317,2318],{"xmlns":890},[892,2319,2320,2324],{},[895,2321,2322],{},[898,2323,2282],{},[902,2325,2282],{"encoding":904}," (závislá). Hodnota v bodě: ",[883,2328,2330],{"className":2329},[886],[888,2331,2332],{"xmlns":890},[892,2333,2334,2344],{},[895,2335,2336,2338,2340,2342],{},[898,2337,2287],{},[1688,2339,2066],{"stretchy":2065},[898,2341,207],{},[1688,2343,2076],{"stretchy":2065},[902,2345,2346],{"encoding":904},"f(a)",[724,2348,2349],{},"Polynomy:",[120,2351,2352,2383,2423],{},[123,2353,2354],{},[152,2355,2356],{},[123,2357,2358,2359],{},"stupně: ",[883,2360,2362],{"className":2361},[886],[888,2363,2364],{"xmlns":890},[892,2365,2366,2380],{},[895,2367,2368,2370,2372,2374,2376,2378],{},[898,2369,2282],{},[1688,2371,1690],{},[898,2373,207],{},[898,2375,2292],{},[1688,2377,1696],{},[898,2379,1918],{},[902,2381,2382],{"encoding":904},"y = ax + b",[123,2384,2385],{},[152,2386,2387],{"start":642},[123,2388,2358,2389],{},[883,2390,2392],{"className":2391},[886],[888,2393,2394],{"xmlns":890},[892,2395,2396,2420],{},[895,2397,2398,2400,2402,2404,2410,2412,2414,2416,2418],{},[898,2399,2282],{},[1688,2401,1690],{},[898,2403,207],{},[1850,2405,2406,2408],{},[898,2407,2292],{},[1793,2409,1806],{},[1688,2411,1696],{},[898,2413,1918],{},[898,2415,2292],{},[1688,2417,1696],{},[898,2419,2031],{},[902,2421,2422],{"encoding":904},"y = ax^2 + bx + c",[123,2424,2425],{},[152,2426,2427],{"start":649},[123,2428,2358,2429],{},[883,2430,2432],{"className":2431},[886],[888,2433,2434],{"xmlns":890},[892,2435,2436,2470],{},[895,2437,2438,2440,2442,2444,2450,2452,2454,2460,2462,2464,2466,2468],{},[898,2439,2282],{},[1688,2441,1690],{},[898,2443,207],{},[1850,2445,2446,2448],{},[898,2447,2292],{},[1793,2449,2131],{},[1688,2451,1696],{},[898,2453,1918],{},[1850,2455,2456,2458],{},[898,2457,2292],{},[1793,2459,1806],{},[1688,2461,1696],{},[898,2463,2031],{},[898,2465,2292],{},[1688,2467,1696],{},[898,2469,2073],{},[902,2471,2472],{"encoding":904},"y = ax^3 + bx^2 + cx + d",[724,2474,2475,2170,2478,2534,2535,2572,2573,2263],{},[38,2476,2477],{},"Příklad rozkladu:",[883,2479,2481],{"className":2480},[886],[888,2482,2483],{"xmlns":890},[892,2484,2485,2531],{},[895,2486,2487,2489,2491,2497,2499,2502,2504,2506,2509,2511,2513,2515,2517,2519,2521,2523,2525,2527,2529],{},[898,2488,2282],{},[1688,2490,1690],{},[1850,2492,2493,2495],{},[898,2494,2292],{},[1793,2496,1806],{},[1688,2498,1954],{},[1793,2500,2501],{},"5",[898,2503,2292],{},[1688,2505,1696],{},[1793,2507,2508],{},"6",[1688,2510,1690],{},[1688,2512,2066],{"stretchy":2065},[898,2514,2292],{},[1688,2516,1954],{},[1793,2518,1806],{},[1688,2520,2076],{"stretchy":2065},[1688,2522,2066],{"stretchy":2065},[898,2524,2292],{},[1688,2526,1954],{},[1793,2528,2131],{},[1688,2530,2076],{"stretchy":2065},[902,2532,2533],{"encoding":904},"y = x^2 - 5x + 6 = (x-2)(x-3)",", kořeny ",[883,2536,2538],{"className":2537},[886],[888,2539,2540],{"xmlns":890},[892,2541,2542,2569],{},[895,2543,2544,2550,2552,2554,2556,2559,2565,2567],{},[1788,2545,2546,2548],{},[898,2547,2292],{},[1793,2549,1795],{},[1688,2551,1690],{},[1793,2553,1806],{},[1688,2555,1733],{"separator":1732},[2041,2557,2558],{}," ",[1788,2560,2561,2563],{},[898,2562,2292],{},[1793,2564,1806],{},[1688,2566,1690],{},[1793,2568,2131],{},[902,2570,2571],{"encoding":904},"x_1 = 2,\\ x_2 = 3",". Vrcholový tvar ",[883,2574,2576],{"className":2575},[886],[888,2577,2578],{"xmlns":890},[892,2579,2580,2617],{},[895,2581,2582,2584,2586,2588,2590,2592,2600,2606,2608],{},[898,2583,2282],{},[1688,2585,1690],{},[1688,2587,2066],{"stretchy":2065},[898,2589,2292],{},[1688,2591,1954],{},[1777,2593,2594],{"scriptlevel":1779,"displaystyle":2065},[1781,2595,2596,2598],{},[1793,2597,2501],{},[1793,2599,1806],{},[1850,2601,2602,2604],{},[1688,2603,2076],{"stretchy":2065},[1793,2605,1806],{},[1688,2607,1954],{},[1777,2609,2610],{"scriptlevel":1779,"displaystyle":2065},[1781,2611,2612,2614],{},[1793,2613,1795],{},[1793,2615,2616],{},"4",[902,2618,2619],{"encoding":904},"y = (x - \\tfrac{5}{2})^2 - \\tfrac{1}{4}",[115,2621,2622],{"id":1145},"Derivace",[724,2624,2625,2626,1348,2650,2678,2679,2263],{},"Označení ",[883,2627,2629],{"className":2628},[886],[888,2630,2631],{"xmlns":890},[892,2632,2633,2647],{},[895,2634,2635,2641,2643,2645],{},[1850,2636,2637,2639],{},[898,2638,2287],{},[1688,2640,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,2642,2066],{"stretchy":2065},[898,2644,2292],{},[1688,2646,2076],{"stretchy":2065},[902,2648,2649],{"encoding":904},"f'(x)",[883,2651,2653],{"className":2652},[886],[888,2654,2655],{"xmlns":890},[892,2656,2657,2675],{},[895,2658,2659],{},[1777,2660,2661],{"scriptlevel":1779,"displaystyle":1732},[1781,2662,2663,2669],{},[895,2664,2665,2667],{},[898,2666,2073],{},[898,2668,2282],{},[895,2670,2671,2673],{},[898,2672,2073],{},[898,2674,2292],{},[902,2676,2677],{"encoding":904},"\\dfrac{dy}{dx}",". Hodnota v bodě: ",[883,2680,2682],{"className":2681},[886],[888,2683,2684],{"xmlns":890},[892,2685,2686,2700],{},[895,2687,2688,2694,2696,2698],{},[1850,2689,2690,2692],{},[898,2691,2287],{},[1688,2693,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,2695,2066],{"stretchy":2065},[898,2697,207],{},[1688,2699,2076],{"stretchy":2065},[902,2701,2702],{"encoding":904},"f'(a)",[198,2704,2706],{"id":2705},"geometrická-interpretace","Geometrická interpretace",[724,2708,2709,2732,2733,2736,2737,2767],{},[883,2710,2712],{"className":2711},[886],[888,2713,2714],{"xmlns":890},[892,2715,2716,2730],{},[895,2717,2718,2724,2726,2728],{},[1850,2719,2720,2722],{},[898,2721,2287],{},[1688,2723,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,2725,2066],{"stretchy":2065},[898,2727,207],{},[1688,2729,2076],{"stretchy":2065},[902,2731,2702],{"encoding":904}," = ",[38,2734,2735],{},"sklon tečny"," ke grafu funkce v bodě ",[883,2738,2740],{"className":2739},[886],[888,2741,2742],{"xmlns":890},[892,2743,2744,2764],{},[895,2745,2746,2749,2751,2753,2755,2757,2759,2761],{},[1688,2747,2748],{"stretchy":2065},"[",[898,2750,207],{},[1688,2752,1733],{"separator":1732},[898,2754,2287],{},[1688,2756,2066],{"stretchy":2065},[898,2758,207],{},[1688,2760,2076],{"stretchy":2065},[1688,2762,2763],{"stretchy":2065},"]",[902,2765,2766],{"encoding":904},"[a, f(a)]",". Rovnice tečny:",[724,2769,2770],{},[883,2771,2773],{"className":2772},[886],[888,2774,2775],{"xmlns":890},[892,2776,2777,2815],{},[895,2778,2779,2781,2783,2785,2787,2789,2791,2793,2799,2801,2803,2805,2807,2809,2811,2813],{},[898,2780,2282],{},[1688,2782,1954],{},[898,2784,2287],{},[1688,2786,2066],{"stretchy":2065},[898,2788,207],{},[1688,2790,2076],{"stretchy":2065},[1688,2792,1690],{},[1850,2794,2795,2797],{},[898,2796,2287],{},[1688,2798,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,2800,2066],{"stretchy":2065},[898,2802,207],{},[1688,2804,2076],{"stretchy":2065},[1688,2806,2066],{"stretchy":2065},[898,2808,2292],{},[1688,2810,1954],{},[898,2812,207],{},[1688,2814,2076],{"stretchy":2065},[902,2816,2817],{"encoding":904},"y - f(a) = f'(a)(x - a)",[724,2819,2820],{},[2821,2822],"img",{"alt":2823,"className":2824,"src":2826},"imek-derivace-tecna",[210,2825],"wikilink-broken","\u002Fwiki-assets\u002Fimek-derivace-tecna.jpeg",[198,2828,2830],{"id":2829},"inženýrská-interpretace","Inženýrská interpretace",[724,2832,2833,2732,2856,2170,2859,2872,2873,2886,2887,2905,2906,2919,2920,2194,2933,2946,2947,2965],{},[883,2834,2836],{"className":2835},[886],[888,2837,2838],{"xmlns":890},[892,2839,2840,2854],{},[895,2841,2842,2848,2850,2852],{},[1850,2843,2844,2846],{},[898,2845,2287],{},[1688,2847,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,2849,2066],{"stretchy":2065},[898,2851,207],{},[1688,2853,2076],{"stretchy":2065},[902,2855,2702],{"encoding":904},[38,2857,2858],{},"rychlost změny",[883,2860,2862],{"className":2861},[886],[888,2863,2864],{"xmlns":890},[892,2865,2866,2870],{},[895,2867,2868],{},[898,2869,2282],{},[902,2871,2282],{"encoding":904}," vzhledem k ",[883,2874,2876],{"className":2875},[886],[888,2877,2878],{"xmlns":890},[892,2879,2880,2884],{},[895,2881,2882],{},[898,2883,2292],{},[902,2885,2292],{"encoding":904}," v bodě ",[883,2888,2890],{"className":2889},[886],[888,2891,2892],{"xmlns":890},[892,2893,2894,2902],{},[895,2895,2896,2898,2900],{},[898,2897,2292],{},[1688,2899,1690],{},[898,2901,207],{},[902,2903,2904],{"encoding":904},"x = a","; přibližná změna ",[883,2907,2909],{"className":2908},[886],[888,2910,2911],{"xmlns":890},[892,2912,2913,2917],{},[895,2914,2915],{},[898,2916,2282],{},[902,2918,2282],{"encoding":904}," při změně ",[883,2921,2923],{"className":2922},[886],[888,2924,2925],{"xmlns":890},[892,2926,2927,2931],{},[895,2928,2929],{},[898,2930,2292],{},[902,2932,2292],{"encoding":904},[883,2934,2936],{"className":2935},[886],[888,2937,2938],{"xmlns":890},[892,2939,2940,2944],{},[895,2941,2942],{},[898,2943,207],{},[902,2945,207],{"encoding":904}," na ",[883,2948,2950],{"className":2949},[886],[888,2951,2952],{"xmlns":890},[892,2953,2954,2962],{},[895,2955,2956,2958,2960],{},[898,2957,207],{},[1688,2959,1696],{},[1793,2961,1795],{},[902,2963,2964],{"encoding":904},"a+1",":",[724,2967,2968],{},[883,2969,2971],{"className":2970},[886],[888,2972,2973],{"xmlns":890},[892,2974,2975,3014],{},[895,2976,2977,2979,2981,2983,2985,2987,2989,2992,2994,2996,2998,3000,3002,3008,3010,3012],{},[898,2978,2287],{},[1688,2980,2066],{"stretchy":2065},[898,2982,207],{},[1688,2984,1696],{},[1793,2986,1795],{},[1688,2988,2076],{"stretchy":2065},[1688,2990,2991],{},"≈",[898,2993,2287],{},[1688,2995,2066],{"stretchy":2065},[898,2997,207],{},[1688,2999,2076],{"stretchy":2065},[1688,3001,1696],{},[1850,3003,3004,3006],{},[898,3005,2287],{},[1688,3007,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,3009,2066],{"stretchy":2065},[898,3011,207],{},[1688,3013,2076],{"stretchy":2065},[902,3015,3016],{"encoding":904},"f(a+1) \\approx f(a) + f'(a)",[198,3018,3020],{"id":3019},"příklad-mezní-náklady","Příklad — mezní náklady",[724,3022,3023,3024,2263],{},"Celkové náklady ",[883,3025,3027],{"className":3026},[886],[888,3028,3029],{"xmlns":890},[892,3030,3031,3060],{},[895,3032,3033,3036,3038,3040,3043,3045,3047,3049,3051,3054],{},[898,3034,3035],{},"T",[898,3037,1693],{},[1688,3039,1690],{},[1793,3041,3042],{},"1000",[1688,3044,1696],{},[1793,3046,1806],{},[898,3048,1872],{},[1688,3050,1696],{},[1793,3052,3053],{},"0,1",[1850,3055,3056,3058],{},[898,3057,1872],{},[1793,3059,1806],{},[902,3061,3062],{"encoding":904},"TC = 1000 + 2Q + 0{,}1 Q^2",[724,3064,3065,3066,3103,3104,2263],{},"Mezní náklady: ",[883,3067,3069],{"className":3068},[886],[888,3070,3071],{"xmlns":890},[892,3072,3073,3100],{},[895,3074,3075,3077,3079,3081,3083,3089,3091,3093,3095,3098],{},[898,3076,1661],{},[898,3078,1693],{},[1688,3080,1690],{},[898,3082,3035],{},[1850,3084,3085,3087],{},[898,3086,1693],{},[1688,3088,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,3090,1690],{},[1793,3092,1806],{},[1688,3094,1696],{},[1793,3096,3097],{},"0,2",[898,3099,1872],{},[902,3101,3102],{"encoding":904},"MC = TC' = 2 + 0{,}2 Q",", takže ",[883,3105,3107],{"className":3106},[886],[888,3108,3109],{"xmlns":890},[892,3110,3111,3128],{},[895,3112,3113,3115,3117,3119,3122,3124,3126],{},[898,3114,1661],{},[898,3116,1693],{},[1688,3118,2066],{"stretchy":2065},[1793,3120,3121],{},"10",[1688,3123,2076],{"stretchy":2065},[1688,3125,1690],{},[1793,3127,2616],{},[902,3129,3130],{"encoding":904},"MC(10) = 4",[724,3132,3133,2170,3136,3185,3186,2170,3189,2263],{},[38,3134,3135],{},"Skutečný přírůstek:",[883,3137,3139],{"className":3138},[886],[888,3140,3141],{"xmlns":890},[892,3142,3143,3182],{},[895,3144,3145,3148,3150,3152,3154,3156,3158,3160,3163,3165,3167,3169,3171,3173,3175,3177,3179],{},[898,3146,3147],{"mathvariant":1822},"Δ",[898,3149,3035],{},[898,3151,1693],{},[1688,3153,1690],{},[898,3155,3035],{},[898,3157,1693],{},[1688,3159,2066],{"stretchy":2065},[1793,3161,3162],{},"11",[1688,3164,2076],{"stretchy":2065},[1688,3166,1954],{},[898,3168,3035],{},[898,3170,1693],{},[1688,3172,2066],{"stretchy":2065},[1793,3174,3121],{},[1688,3176,2076],{"stretchy":2065},[1688,3178,1690],{},[1793,3180,3181],{},"4,2",[902,3183,3184],{"encoding":904},"\\Delta TC = TC(11) - TC(10) = 4{,}2",". ",[38,3187,3188],{},"Přibližný (lineární):",[883,3190,3192],{"className":3191},[886],[888,3193,3194],{"xmlns":890},[892,3195,3196,3200],{},[895,3197,3198],{},[1793,3199,2616],{},[902,3201,2616],{"encoding":904},[724,3203,3204,3205,3209],{},"(Viz aplikace v ",[207,3206,3208],{"className":3207,"dataFsResolvedFilePath":827,"href":828},[210],"prijem-naklady-zisk",".)",[115,3211,3213],{"id":3212},"diferenciál","Diferenciál",[724,3215,3216],{},[883,3217,3219],{"className":3218},[886],[888,3220,3221],{"xmlns":890},[892,3222,3223,3249],{},[895,3224,3225,3227,3229,3231,3237,3239,3241,3243,3245,3247],{},[898,3226,2073],{},[898,3228,2287],{},[1688,3230,1690],{},[1850,3232,3233,3235],{},[898,3234,2287],{},[1688,3236,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,3238,2066],{"stretchy":2065},[898,3240,2292],{},[1688,3242,2076],{"stretchy":2065},[2041,3244,2043],{},[898,3246,2073],{},[898,3248,2292],{},[902,3250,3251],{"encoding":904},"df = f'(x)\\, dx",[724,3253,3254,3255,3271,3272,3320,3321,2263],{},"Pro malá ",[883,3256,3258],{"className":3257},[886],[888,3259,3260],{"xmlns":890},[892,3261,3262,3268],{},[895,3263,3264,3266],{},[898,3265,2073],{},[898,3267,2292],{},[902,3269,3270],{"encoding":904},"dx"," platí: ",[883,3273,3275],{"className":3274},[886],[888,3276,3277],{"xmlns":890},[892,3278,3279,3317],{},[895,3280,3281,3283,3285,3287,3289,3291,3293,3295,3297,3299,3301,3303,3305,3307,3309,3311,3313,3315],{},[898,3282,3147],{"mathvariant":1822},[898,3284,2287],{},[1688,3286,1690],{},[898,3288,2287],{},[1688,3290,2066],{"stretchy":2065},[898,3292,2292],{},[1688,3294,1696],{},[898,3296,2073],{},[898,3298,2292],{},[1688,3300,2076],{"stretchy":2065},[1688,3302,1954],{},[898,3304,2287],{},[1688,3306,2066],{"stretchy":2065},[898,3308,2292],{},[1688,3310,2076],{"stretchy":2065},[1688,3312,2991],{},[898,3314,2073],{},[898,3316,2287],{},[902,3318,3319],{"encoding":904},"\\Delta f = f(x + dx) - f(x) \\approx df",". Diferenciál je ",[38,3322,3323],{},"lineární odhad přírůstku",[198,3325,3327],{"id":3326},"příklad","Příklad",[724,3329,3330,3361,3362,3387,3388,3408],{},[883,3331,3333],{"className":3332},[886],[888,3334,3335],{"xmlns":890},[892,3336,3337,3358],{},[895,3338,3339,3341,3343,3345,3348,3350,3352],{},[898,3340,3035],{},[898,3342,1693],{},[1688,3344,1690],{},[1793,3346,3347],{},"100",[1688,3349,1696],{},[1793,3351,3053],{},[1850,3353,3354,3356],{},[898,3355,1872],{},[1793,3357,1806],{},[902,3359,3360],{"encoding":904},"TC = 100 + 0{,}1 Q^2",", odhad změny při ",[883,3363,3365],{"className":3364},[886],[888,3366,3367],{"xmlns":890},[892,3368,3369,3384],{},[895,3370,3371,3373,3375,3378,3381],{},[898,3372,1872],{},[1688,3374,2965],{},[1793,3376,3377],{},"50",[1688,3379,3380],{},"→",[1793,3382,3383],{},"60",[902,3385,3386],{"encoding":904},"Q: 50 \\to 60"," (tj. ",[883,3389,3391],{"className":3390},[886],[888,3392,3393],{"xmlns":890},[892,3394,3395,3405],{},[895,3396,3397,3399,3401,3403],{},[898,3398,2073],{},[898,3400,1872],{},[1688,3402,1690],{},[1793,3404,3121],{},[902,3406,3407],{"encoding":904},"dQ = 10","):",[724,3410,3411],{},[883,3412,3414],{"className":3413},[886],[888,3415,3416],{"xmlns":890},[892,3417,3418,3455],{},[895,3419,3420,3422,3424,3426,3428,3430,3432,3435,3437,3439,3441,3443,3445,3447,3449,3451,3453],{},[898,3421,2073],{},[898,3423,3035],{},[898,3425,1693],{},[1688,3427,1690],{},[1793,3429,3097],{},[898,3431,1872],{},[1688,3433,3434],{},"⋅",[898,3436,2073],{},[898,3438,1872],{},[1688,3440,1690],{},[1793,3442,3097],{},[1688,3444,3434],{},[1793,3446,3377],{},[1688,3448,3434],{},[1793,3450,3121],{},[1688,3452,1690],{},[1793,3454,3347],{},[902,3456,3457],{"encoding":904},"dTC = 0{,}2 Q \\cdot dQ = 0{,}2 \\cdot 50 \\cdot 10 = 100",[724,3459,3460,3461,3484,3485,3501],{},"Přesná změna: ",[883,3462,3464],{"className":3463},[886],[888,3465,3466],{"xmlns":890},[892,3467,3468,3481],{},[895,3469,3470,3472,3474,3476,3478],{},[898,3471,3147],{"mathvariant":1822},[898,3473,3035],{},[898,3475,1693],{},[1688,3477,1690],{},[1793,3479,3480],{},"110",[902,3482,3483],{"encoding":904},"\\Delta TC = 110",". Lineární odhad mírně podstřeluje, protože ",[883,3486,3488],{"className":3487},[886],[888,3489,3490],{"xmlns":890},[892,3491,3492,3498],{},[895,3493,3494,3496],{},[898,3495,3035],{},[898,3497,1693],{},[902,3499,3500],{"encoding":904},"TC"," je konvexní.",[115,3503,3505],{"id":3504},"extrémy-funkce-jedné-proměnné","Extrémy funkce jedné proměnné",[198,3507,3509],{"id":3508},"nutná-podmínka","Nutná podmínka",[724,3511,3512,3513,2886,3533,3546,3547,3575,3576,3579],{},"Má-li ",[883,3514,3516],{"className":3515},[886],[888,3517,3518],{"xmlns":890},[892,3519,3520,3530],{},[895,3521,3522,3524,3526,3528],{},[898,3523,2287],{},[1688,3525,2066],{"stretchy":2065},[898,3527,2292],{},[1688,3529,2076],{"stretchy":2065},[902,3531,3532],{"encoding":904},"f(x)",[883,3534,3536],{"className":3535},[886],[888,3537,3538],{"xmlns":890},[892,3539,3540,3544],{},[895,3541,3542],{},[898,3543,207],{},[902,3545,207],{"encoding":904}," extrém, pak ",[883,3548,3550],{"className":3549},[886],[888,3551,3552],{"xmlns":890},[892,3553,3554,3572],{},[895,3555,3556,3562,3564,3566,3568,3570],{},[1850,3557,3558,3560],{},[898,3559,2287],{},[1688,3561,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,3563,2066],{"stretchy":2065},[898,3565,207],{},[1688,3567,2076],{"stretchy":2065},[1688,3569,1690],{},[1793,3571,1779],{},[902,3573,3574],{"encoding":904},"f'(a) = 0",". Body splňující tuto podmínku se nazývají ",[38,3577,3578],{},"stacionární"," (podezřelé) body.",[198,3581,3583],{"id":3582},"postačující-podmínka","Postačující podmínka",[724,3585,3586,3587,3600,3601,2965],{},"Pro stacionární bod ",[883,3588,3590],{"className":3589},[886],[888,3591,3592],{"xmlns":890},[892,3593,3594,3598],{},[895,3595,3596],{},[898,3597,207],{},[902,3599,207],{"encoding":904},", je-li ",[883,3602,3604],{"className":3603},[886],[888,3605,3606],{"xmlns":890},[892,3607,3608,3631],{},[895,3609,3610,3620,3622,3624,3626,3629],{},[1850,3611,3612,3614],{},[898,3613,2287],{},[895,3615,3616,3618],{},[1688,3617,1824],{"mathvariant":1822},[1688,3619,1824],{"mathvariant":1822},[1688,3621,2066],{"stretchy":2065},[898,3623,207],{},[1688,3625,2076],{"stretchy":2065},[1688,3627,3628],{"mathvariant":1822},"≠",[1793,3630,1779],{},[902,3632,3633],{"encoding":904},"f''(a) \\neq 0",[120,3635,3636,3675],{},[123,3637,3638,3671,3672],{},[883,3639,3641],{"className":3640},[886],[888,3642,3643],{"xmlns":890},[892,3644,3645,3668],{},[895,3646,3647,3657,3659,3661,3663,3666],{},[1850,3648,3649,3651],{},[898,3650,2287],{},[895,3652,3653,3655],{},[1688,3654,1824],{"mathvariant":1822},[1688,3656,1824],{"mathvariant":1822},[1688,3658,2066],{"stretchy":2065},[898,3660,207],{},[1688,3662,2076],{"stretchy":2065},[1688,3664,3665],{},">",[1793,3667,1779],{},[902,3669,3670],{"encoding":904},"f''(a) > 0"," ⇒ ",[38,3673,3674],{},"lokální minimum",[123,3676,3677,3671,3710],{},[883,3678,3680],{"className":3679},[886],[888,3681,3682],{"xmlns":890},[892,3683,3684,3707],{},[895,3685,3686,3696,3698,3700,3702,3705],{},[1850,3687,3688,3690],{},[898,3689,2287],{},[895,3691,3692,3694],{},[1688,3693,1824],{"mathvariant":1822},[1688,3695,1824],{"mathvariant":1822},[1688,3697,2066],{"stretchy":2065},[898,3699,207],{},[1688,3701,2076],{"stretchy":2065},[1688,3703,3704],{},"\u003C",[1793,3706,1779],{},[902,3708,3709],{"encoding":904},"f''(a) \u003C 0",[38,3711,3712],{},"lokální maximum",[724,3714,3715],{},[2821,3716],{"alt":3717,"className":3718,"src":3719},"imek-extremy-1d",[210,2825],"\u002Fwiki-assets\u002Fimek-extremy-1d.jpeg",[198,3721,3327],{"id":3722},"příklad-1",[724,3724,3725],{},[883,3726,3728],{"className":3727},[886],[888,3729,3730],{"xmlns":890},[892,3731,3732,3773],{},[895,3733,3734,3736,3738,3740,3742,3744,3746,3752,3754,3756,3762,3764,3767,3769,3771],{},[898,3735,2287],{},[1688,3737,2066],{"stretchy":2065},[898,3739,2292],{},[1688,3741,2076],{"stretchy":2065},[1688,3743,1690],{},[1793,3745,1806],{},[1850,3747,3748,3750],{},[898,3749,2292],{},[1793,3751,2131],{},[1688,3753,1954],{},[1793,3755,2131],{},[1850,3757,3758,3760],{},[898,3759,2292],{},[1793,3761,1806],{},[1688,3763,1954],{},[1793,3765,3766],{},"12",[898,3768,2292],{},[1688,3770,1696],{},[1793,3772,2131],{},[902,3774,3775],{"encoding":904},"f(x) = 2x^3 - 3x^2 - 12x + 3",[120,3777,3778,3889,3929,3992],{},[123,3779,3780,3852,3853],{},[883,3781,3783],{"className":3782},[886],[888,3784,3785],{"xmlns":890},[892,3786,3787,3849],{},[895,3788,3789,3795,3797,3799,3801,3803,3805,3811,3813,3815,3817,3819,3821,3823,3825,3827,3829,3831,3833,3835,3837,3839,3841,3843,3845,3847],{},[1850,3790,3791,3793],{},[898,3792,2287],{},[1688,3794,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,3796,2066],{"stretchy":2065},[898,3798,2292],{},[1688,3800,2076],{"stretchy":2065},[1688,3802,1690],{},[1793,3804,2508],{},[1850,3806,3807,3809],{},[898,3808,2292],{},[1793,3810,1806],{},[1688,3812,1954],{},[1793,3814,2508],{},[898,3816,2292],{},[1688,3818,1954],{},[1793,3820,3766],{},[1688,3822,1690],{},[1793,3824,2508],{},[1688,3826,2066],{"stretchy":2065},[898,3828,2292],{},[1688,3830,1696],{},[1793,3832,1795],{},[1688,3834,2076],{"stretchy":2065},[1688,3836,2066],{"stretchy":2065},[898,3838,2292],{},[1688,3840,1954],{},[1793,3842,1806],{},[1688,3844,2076],{"stretchy":2065},[1688,3846,1690],{},[1793,3848,1779],{},[902,3850,3851],{"encoding":904},"f'(x) = 6x^2 - 6x - 12 = 6(x+1)(x-2) = 0"," ⇒ S.B. ",[883,3854,3856],{"className":3855},[886],[888,3857,3858],{"xmlns":890},[892,3859,3860,3886],{},[895,3861,3862,3868,3870,3872,3874,3876,3882,3884],{},[1788,3863,3864,3866],{},[898,3865,2292],{},[1793,3867,1795],{},[1688,3869,1690],{},[1688,3871,1954],{},[1793,3873,1795],{},[1688,3875,1733],{"separator":1732},[1788,3877,3878,3880],{},[898,3879,2292],{},[1793,3881,1806],{},[1688,3883,1690],{},[1793,3885,1806],{},[902,3887,3888],{"encoding":904},"x_1 = -1, x_2 = 2",[123,3890,3891],{},[883,3892,3894],{"className":3893},[886],[888,3895,3896],{"xmlns":890},[892,3897,3898,3926],{},[895,3899,3900,3910,3912,3914,3916,3918,3920,3922,3924],{},[1850,3901,3902,3904],{},[898,3903,2287],{},[895,3905,3906,3908],{},[1688,3907,1824],{"mathvariant":1822},[1688,3909,1824],{"mathvariant":1822},[1688,3911,2066],{"stretchy":2065},[898,3913,2292],{},[1688,3915,2076],{"stretchy":2065},[1688,3917,1690],{},[1793,3919,3766],{},[898,3921,2292],{},[1688,3923,1954],{},[1793,3925,2508],{},[902,3927,3928],{"encoding":904},"f''(x) = 12x - 6",[123,3930,3931,3671,3972,3975,3976],{},[883,3932,3934],{"className":3933},[886],[888,3935,3936],{"xmlns":890},[892,3937,3938,3969],{},[895,3939,3940,3950,3952,3954,3956,3958,3960,3962,3965,3967],{},[1850,3941,3942,3944],{},[898,3943,2287],{},[895,3945,3946,3948],{},[1688,3947,1824],{"mathvariant":1822},[1688,3949,1824],{"mathvariant":1822},[1688,3951,2066],{"stretchy":2065},[1688,3953,1954],{},[1793,3955,1795],{},[1688,3957,2076],{"stretchy":2065},[1688,3959,1690],{},[1688,3961,1954],{},[1793,3963,3964],{},"18",[1688,3966,3704],{},[1793,3968,1779],{},[902,3970,3971],{"encoding":904},"f''(-1) = -18 \u003C 0",[38,3973,3974],{},"maximum"," v ",[883,3977,3979],{"className":3978},[886],[888,3980,3981],{"xmlns":890},[892,3982,3983,3989],{},[895,3984,3985,3987],{},[1688,3986,1954],{},[1793,3988,1795],{},[902,3990,3991],{"encoding":904},"-1",[123,3993,3994,3671,4030,3975,4033],{},[883,3995,3997],{"className":3996},[886],[888,3998,3999],{"xmlns":890},[892,4000,4001,4027],{},[895,4002,4003,4013,4015,4017,4019,4021,4023,4025],{},[1850,4004,4005,4007],{},[898,4006,2287],{},[895,4008,4009,4011],{},[1688,4010,1824],{"mathvariant":1822},[1688,4012,1824],{"mathvariant":1822},[1688,4014,2066],{"stretchy":2065},[1793,4016,1806],{},[1688,4018,2076],{"stretchy":2065},[1688,4020,1690],{},[1793,4022,3964],{},[1688,4024,3665],{},[1793,4026,1779],{},[902,4028,4029],{"encoding":904},"f''(2) = 18 > 0",[38,4031,4032],{},"minimum",[883,4034,4036],{"className":4035},[886],[888,4037,4038],{"xmlns":890},[892,4039,4040,4044],{},[895,4041,4042],{},[1793,4043,1806],{},[902,4045,1806],{"encoding":904},[115,4047,4049],{"id":4048},"navigace","Navigace",[120,4051,4052,4060,4067],{},[123,4053,4054,2170,4057],{},[38,4055,4056],{},"Předchozí:",[207,4058,757],{"className":4059,"dataFsResolvedFilePath":755,"href":756},[210],[123,4061,4062,2170,4064],{},[38,4063,2179],{},[207,4065,775],{"className":4066,"dataFsResolvedFilePath":773,"href":774},[210],[123,4068,4069,2170,4072,4075,4076,4080,4081,4085],{},[38,4070,4071],{},"Souvislosti:",[207,4073,784],{"className":4074,"dataFsResolvedFilePath":782,"href":783},[210]," (rozšíření na 2D), ",[207,4077,4079],{"className":4078,"dataFsResolvedFilePath":827,"href":828},[210],"Příjem, náklady, zisk"," (aplikace mezních veličin), ",[207,4082,4084],{"className":4083,"dataFsResolvedFilePath":848,"href":849},[210],"Elasticita"," (procentní citlivost přes derivaci)",{"title":641,"searchDepth":642,"depth":642,"links":4087},[4088,4089,4094,4097,4102],{"id":2266,"depth":642,"text":2267},{"id":1145,"depth":642,"text":2622,"children":4090},[4091,4092,4093],{"id":2705,"depth":649,"text":2706},{"id":2829,"depth":649,"text":2830},{"id":3019,"depth":649,"text":3020},{"id":3212,"depth":642,"text":3213,"children":4095},[4096],{"id":3326,"depth":649,"text":3327},{"id":3504,"depth":642,"text":3505,"children":4098},[4099,4100,4101],{"id":3508,"depth":649,"text":3509},{"id":3582,"depth":649,"text":3583},{"id":3722,"depth":649,"text":3327},{"id":4048,"depth":642,"text":4049},"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":2238,"description":4103},[1135],"topics\u002Fderivace",[1128,1145,4110,4111,4112],"diferencial","extremy","mezni-naklady","topic","U4vqwJqO65hVzq9khEr5sxPHpHJLXAz_kTaaHdKCCIw",{"id":4116,"title":4117,"body":4118,"course":1128,"courses":659,"created":9809,"description":641,"extension":661,"meta":9810,"navigation":664,"path":9811,"seo":9812,"sources":9813,"stem":9814,"tags":9815,"type":4113,"updated":677,"__hash__":9820},"topics\u002Ftopics\u002Felasticita.md","Elasticita poptávky a nabídky",{"type":9,"value":4119,"toc":9782},[4120,4123,4146,4150,4177,4181,4222,4313,4357,4361,4385,4392,4396,4406,4418,4422,4451,4460,4517,4523,4526,4532,4559,4565,4662,4822,5113,5117,5197,5203,5207,5305,5371,5539,5543,5621,5652,5679,5685,5717,5795,5882,5886,5949,5955,5958,5964,6078,6163,6207,6211,6257,6264,6581,6586,6610,6639,6706,6803,6807,6814,6821,6892,7012,7096,7099,7105,7432,7436,7599,7607,7743,7751,7989,7997,8000,8005,8261,8265,8439,8573,8610,8654,8657,8787,8877,8895,8899,8906,8912,8972,8975,8999,9002,9008,9011,9017,9020,9024,9062,9120,9309,9313,9385,9391,9398,9402,9408,9549,9553,9559,9595,9600,9777],[12,4121,4117],{"id":4122},"elasticita-poptávky-a-nabídky",[4124,4125,4126],"blockquote",{},[724,4127,4128,4131,4132,4134,4135,4138,4139,4142,4143,2263],{},[883,4129,4130],{},"!abstract"," TL;DR\n",[38,4133,4084],{}," 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: ",[38,4136,4137],{},"cenovou elasticitu poptávky"," (a nabídky), ",[38,4140,4141],{},"křížově-cenovou elasticitu"," a ",[38,4144,4145],{},"důchodovou elasticitu",[115,4147,4149],{"id":4148},"úvod-motivace","Úvod — motivace",[724,4151,4152,4153,4156,4157,4160,4161,4164,4165,4168,4169,4172,4173,4176],{},"Termín ",[614,4154,4155],{},"elasticita"," (alternativně ",[614,4158,4159],{},"pružnost",") patří ke klíčovým pojmům ekonomické teorie. Slouží ke ",[38,4162,4163],{},"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 ",[614,4166,4167],{},"cenové elasticity poptávky"," (resp. ",[614,4170,4171],{},"nabídky","). Matematickým modelem míry citlivosti je elasticita funkce (viz ",[207,4174,2622],{"className":4175,"dataFsResolvedFilePath":764,"href":765},[210],").",[198,4178,4180],{"id":4179},"srovnání-trh-1-vs-trh-2","Srovnání Trh 1 vs Trh 2",[724,4182,4183,4184,4202,4203,4221],{},"Uvažujme dvě různá tržní prostředí. Zboží má na obou trzích stejnou cenu ",[883,4185,4187],{"className":4186},[886],[888,4188,4189],{"xmlns":890},[892,4190,4191,4199],{},[895,4192,4193,4195,4197],{},[898,4194,1727],{},[1688,4196,1690],{},[1793,4198,3121],{},[902,4200,4201],{"encoding":904},"P=10"," a při této ceně se prodá ",[883,4204,4206],{"className":4205},[886],[888,4207,4208],{"xmlns":890},[892,4209,4210,4218],{},[895,4211,4212,4214,4216],{},[898,4213,1872],{},[1688,4215,1690],{},[1793,4217,3347],{},[902,4219,4220],{"encoding":904},"Q=100"," jednotek. Prodejce sníží cenu z 10 na 9:",[120,4223,4224,4270],{},[123,4225,4226,4229,4230,4269],{},[38,4227,4228],{},"Trh 1"," zareaguje zvýšením množství na 110 ",[883,4231,4233],{"className":4232},[886],[888,4234,4235],{"xmlns":890},[892,4236,4237,4266],{},[895,4238,4239,4242,4245,4247,4249,4252,4254,4257,4259,4261,4263],{},[2041,4240,4241],{},"  ",[1688,4243,4244],{},"⇒",[2041,4246,4241],{},[898,4248,3035],{},[898,4250,4251],{},"R",[1688,4253,1690],{},[1793,4255,4256],{},"9",[1688,4258,3434],{},[1793,4260,3480],{},[1688,4262,1690],{},[1793,4264,4265],{},"990",[902,4267,4268],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 110 = 990"," (pokles z 1000).",[123,4271,4272,4275,4276,4312],{},[38,4273,4274],{},"Trh 2"," zareaguje zvýšením množství na 120 ",[883,4277,4279],{"className":4278},[886],[888,4280,4281],{"xmlns":890},[892,4282,4283,4309],{},[895,4284,4285,4287,4289,4291,4293,4295,4297,4299,4301,4304,4306],{},[2041,4286,4241],{},[1688,4288,4244],{},[2041,4290,4241],{},[898,4292,3035],{},[898,4294,4251],{},[1688,4296,1690],{},[1793,4298,4256],{},[1688,4300,3434],{},[1793,4302,4303],{},"120",[1688,4305,1690],{},[1793,4307,4308],{},"1080",[902,4310,4311],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 120 = 1080"," (růst z 1000).",[724,4314,4315,4316,4319,4320,4323,4324,4327,4328,4331,4332,4335,4336,4352,4353,4356],{},"Závěr: snížení ceny bylo na Trhu 1 ",[38,4317,4318],{},"nerozumné",", na Trhu 2 ",[38,4321,4322],{},"rozumné",". Trh 2 je ",[38,4325,4326],{},"relativně citlivý"," na změnu ceny — říkáme, že poptávka je ",[614,4329,4330],{},"elastická"," a snížení ceny je „překompenzováno\" zvýšením poptávaného množství. Na Trhu 1 je poptávka ",[614,4333,4334],{},"neelastická"," a vyššího ",[883,4337,4339],{"className":4338},[886],[888,4340,4341],{"xmlns":890},[892,4342,4343,4349],{},[895,4344,4345,4347],{},[898,4346,3035],{},[898,4348,4251],{},[902,4350,4351],{"encoding":904},"TR"," lze naopak dosáhnout ",[614,4354,4355],{},"zvýšením"," ceny.",[198,4358,4360],{"id":4359},"hypotéza-41","Hypotéza 4.1",[4124,4362,4363],{},[724,4364,4365,4366],{},"Aby nedošlo k poklesu celkového příjmu, musí být procentní růst poptávaného množství alespoň takový, jaký je procentní pokles jeho ceny. ",[883,4367,4369],{"className":4368},[886],[888,4370,4371],{"xmlns":890},[892,4372,4373,4382],{},[895,4374,4375,4377,4380],{},[1688,4376,2066],{"stretchy":2065},[1793,4378,4379],{},"4.1",[1688,4381,2076],{"stretchy":2065},[902,4383,4384],{"encoding":904},"(4.1)",[724,4386,4387,4388,4391],{},"Rozhodující nejsou nominální změny (jsou měřeny v různých jednotkách), nýbrž ",[38,4389,4390],{},"procentní změny"," obou faktorů.",[115,4393,4395],{"id":4394},"pojem-elasticity","Pojem elasticity",[724,4397,4398,4399,4401,4402,4405],{},"Obecně ",[38,4400,4155],{}," jedné veličiny vzhledem k druhé kvantifikuje, o kolik procent se první veličina přibližně změní, když se druhá veličina změní o 1 %. Jde o ",[38,4403,4404],{},"bezrozměrnou veličinu"," — nezávislou na jednotkách, ve kterých jsou proměnné měřeny (viz čl. 1.5.1).",[4124,4407,4408],{},[724,4409,4410,4413,4414,4417],{},[883,4411,4412],{},"!info"," Intuice\nElasticitu lze číst jako ",[38,4415,4416],{},"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.",[115,4419,4421],{"id":4420},"cenová-elasticita-poptávky-jednofaktorový-model","Cenová elasticita poptávky — jednofaktorový model",[724,4423,4424,4425,4450],{},"Nechť ",[883,4426,4428],{"className":4427},[886],[888,4429,4430],{"xmlns":890},[892,4431,4432,4447],{},[895,4433,4434,4436,4438,4441,4443,4445],{},[898,4435,1872],{},[1688,4437,1690],{},[898,4439,4440],{},"D",[1688,4442,2066],{"stretchy":2065},[898,4444,1727],{},[1688,4446,2076],{"stretchy":2065},[902,4448,4449],{"encoding":904},"Q = D(P)"," je funkce poptávky (ceteris paribus). Zkoumáme podíl procentních změn",[724,4452,4453],{},[883,4454,4459],{"className":4455,"title":4457,"style":4458},[4456],"katex-error","ParseError: KaTeX parse error: \\tag works only in display equations","color:#cc0000","E^A = -\\frac{\\Delta Q\\%}{\\Delta P\\%}. \\tag{4.2}",[724,4461,4462,4463,4142,4479,4495,4496,4516],{},"Znaménko minus je korekce: změny ",[883,4464,4466],{"className":4465},[886],[888,4467,4468],{"xmlns":890},[892,4469,4470,4476],{},[895,4471,4472,4474],{},[898,4473,3147],{"mathvariant":1822},[898,4475,1872],{},[902,4477,4478],{"encoding":904},"\\Delta Q",[883,4480,4482],{"className":4481},[886],[888,4483,4484],{"xmlns":890},[892,4485,4486,4492],{},[895,4487,4488,4490],{},[898,4489,3147],{"mathvariant":1822},[898,4491,1727],{},[902,4493,4494],{"encoding":904},"\\Delta P"," mají vždy opačná znaménka, takže bez korekce by ",[883,4497,4499],{"className":4498},[886],[888,4500,4501],{"xmlns":890},[892,4502,4503,4513],{},[895,4504,4505],{},[1850,4506,4507,4510],{},[898,4508,4509],{},"E",[898,4511,4512],{},"A",[902,4514,4515],{"encoding":904},"E^A"," bylo záporné; pro pohodlí pracujeme s nezápornými hodnotami. Pro procentní změny platí",[724,4518,4519],{},[883,4520,4522],{"className":4521,"title":4457,"style":4458},[4456],"\\Delta Q\\% = \\frac{\\Delta Q}{Q}\\cdot 100, \\qquad \\Delta P\\% = \\frac{\\Delta P}{P}\\cdot 100. \\tag{4.3}",[724,4524,4525],{},"Po dosazení:",[724,4527,4528],{},[883,4529,4531],{"className":4530,"title":4457,"style":4458},[4456],"E^A = -\\frac{\\frac{\\Delta Q}{Q}}{\\frac{\\Delta P}{P}} = -\\frac{P}{Q}\\cdot \\frac{\\Delta Q}{\\Delta P}. \\tag{4.4}",[724,4533,4534,4535,4555,4556,4558],{},"Limitním přechodem ",[883,4536,4538],{"className":4537},[886],[888,4539,4540],{"xmlns":890},[892,4541,4542,4552],{},[895,4543,4544,4546,4548,4550],{},[898,4545,3147],{"mathvariant":1822},[898,4547,1727],{},[1688,4549,3380],{},[1793,4551,1779],{},[902,4553,4554],{"encoding":904},"\\Delta P \\to 0"," získáme definici ",[38,4557,4167],{}," (price elasticity of demand):",[724,4560,4561],{},[883,4562,4564],{"className":4563,"title":4457,"style":4458},[4456],"\\boxed{\\;E = E(P) = -\\frac{P}{Q}\\cdot \\frac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\frac{P}{Q}\\,Q'(P)\\;} \\tag{4.5}",[724,4566,4567,4568,4591,4592,4614,4615,4639,4640,4661],{},"kde ",[883,4569,4571],{"className":4570},[886],[888,4572,4573],{"xmlns":890},[892,4574,4575,4589],{},[895,4576,4577,4579,4581,4583,4585,4587],{},[898,4578,1872],{},[1688,4580,1690],{},[898,4582,4440],{},[1688,4584,2066],{"stretchy":2065},[898,4586,1727],{},[1688,4588,2076],{"stretchy":2065},[902,4590,4449],{"encoding":904},". Pro pevnou cenu ",[883,4593,4595],{"className":4594},[886],[888,4596,4597],{"xmlns":890},[892,4598,4599,4611],{},[895,4600,4601,4603,4605],{},[898,4602,1727],{},[1688,4604,1690],{},[1850,4606,4607,4609],{},[898,4608,1727],{},[1688,4610,1857],{},[902,4612,4613],{"encoding":904},"P = P^*"," se ",[883,4616,4618],{"className":4617},[886],[888,4619,4620],{"xmlns":890},[892,4621,4622,4636],{},[895,4623,4624,4626,4628,4634],{},[898,4625,4509],{},[1688,4627,2066],{"stretchy":2065},[1850,4629,4630,4632],{},[898,4631,1727],{},[1688,4633,1857],{},[1688,4635,2076],{"stretchy":2065},[902,4637,4638],{"encoding":904},"E(P^*)"," nazývá ",[614,4641,4642,4643],{},"elasticita poptávky při ceně ",[883,4644,4646],{"className":4645},[886],[888,4647,4648],{"xmlns":890},[892,4649,4650,4658],{},[895,4651,4652],{},[1850,4653,4654,4656],{},[898,4655,1727],{},[1688,4657,1857],{},[902,4659,4660],{"encoding":904},"P^*"," a je to vždy nezáporné číslo.",[4124,4663,4664],{},[724,4665,4666,4669,4670,4688,4689,4717,4718,4747,4748,1343,4766,1343,4784,4802,4803,4818,4819,2263],{},[883,4667,4668],{},"!warning"," Pozor na znaménko\nV (4.5) je ",[38,4671,4672,4673],{},"explicitní ",[883,4674,4676],{"className":4675},[886],[888,4677,4678],{"xmlns":890},[892,4679,4680,4686],{},[895,4681,4682,4684],{},[1688,4683,1954],{},[1793,4685,1795],{},[902,4687,3991],{"encoding":904}," právě proto, že ",[883,4690,4692],{"className":4691},[886],[888,4693,4694],{"xmlns":890},[892,4695,4696,4714],{},[895,4697,4698,4704,4706,4708,4710,4712],{},[1850,4699,4700,4702],{},[898,4701,1872],{},[1688,4703,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,4705,2066],{"stretchy":2065},[898,4707,1727],{},[1688,4709,2076],{"stretchy":2065},[1688,4711,3704],{},[1793,4713,1779],{},[902,4715,4716],{"encoding":904},"Q'(P) \u003C 0"," (poptávka klesá s cenou). Díky korekčnímu znaménku je výsledné ",[883,4719,4721],{"className":4720},[886],[888,4722,4723],{"xmlns":890},[892,4724,4725,4744],{},[895,4726,4727,4729,4731,4737,4739,4742],{},[898,4728,4509],{},[1688,4730,2066],{"stretchy":2065},[1850,4732,4733,4735],{},[898,4734,1727],{},[1688,4736,1857],{},[1688,4738,2076],{"stretchy":2065},[1688,4740,4741],{},"≥",[1793,4743,1779],{},[902,4745,4746],{"encoding":904},"E(P^*) \\ge 0"," a s touto nezápornou konvencí pracuje celá klasifikace ",[883,4749,4751],{"className":4750},[886],[888,4752,4753],{"xmlns":890},[892,4754,4755,4763],{},[895,4756,4757,4759,4761],{},[898,4758,4509],{},[1688,4760,3665],{},[1793,4762,1795],{},[902,4764,4765],{"encoding":904},"E > 1",[883,4767,4769],{"className":4768},[886],[888,4770,4771],{"xmlns":890},[892,4772,4773,4781],{},[895,4774,4775,4777,4779],{},[898,4776,4509],{},[1688,4778,3704],{},[1793,4780,1795],{},[902,4782,4783],{"encoding":904},"E \u003C 1",[883,4785,4787],{"className":4786},[886],[888,4788,4789],{"xmlns":890},[892,4790,4791,4799],{},[895,4792,4793,4795,4797],{},[898,4794,4509],{},[1688,4796,1690],{},[1793,4798,1795],{},[902,4800,4801],{"encoding":904},"E = 1",". V některých starších pramenech se ",[883,4804,4806],{"className":4805},[886],[888,4807,4808],{"xmlns":890},[892,4809,4810,4816],{},[895,4811,4812,4814],{},[1688,4813,1954],{},[1793,4815,1795],{},[902,4817,3991],{"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 ",[38,4820,4821],{},"absolutní hodnotou",[4124,4823,4824,4844],{},[724,4825,4826,4829,4830,4843],{},[883,4827,4828],{},"!tip"," Postup: jak spočítat ",[883,4831,4833],{"className":4832},[886],[888,4834,4835],{"xmlns":890},[892,4836,4837,4841],{},[895,4838,4839],{},[898,4840,4509],{},[902,4842,4509],{"encoding":904}," v bodě",[152,4845,4846,4898,4938,4991,5056],{},[123,4847,4848,4849,4872,4873,4897],{},"Zapište ",[883,4850,4852],{"className":4851},[886],[888,4853,4854],{"xmlns":890},[892,4855,4856,4870],{},[895,4857,4858,4860,4862,4864,4866,4868],{},[898,4859,1872],{},[1688,4861,1690],{},[898,4863,4440],{},[1688,4865,2066],{"stretchy":2065},[898,4867,1727],{},[1688,4869,2076],{"stretchy":2065},[902,4871,4449],{"encoding":904},". Pokud je poptávka zadaná jako ",[883,4874,4876],{"className":4875},[886],[888,4877,4878],{"xmlns":890},[892,4879,4880,4894],{},[895,4881,4882,4884,4886,4888,4890,4892],{},[898,4883,1727],{},[1688,4885,1690],{},[898,4887,4440],{},[1688,4889,2066],{"stretchy":2065},[898,4891,1872],{},[1688,4893,2076],{"stretchy":2065},[902,4895,4896],{"encoding":904},"P = D(Q)",", použijte vztah (4.9).",[123,4899,4900,4901,2263],{},"Spočítejte derivaci ",[883,4902,4904],{"className":4903},[886],[888,4905,4906],{"xmlns":890},[892,4907,4908,4935],{},[895,4909,4910,4916,4918,4920,4922,4924,4926,4928,4931,4933],{},[1850,4911,4912,4914],{},[898,4913,1872],{},[1688,4915,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,4917,2066],{"stretchy":2065},[898,4919,1727],{},[1688,4921,2076],{"stretchy":2065},[1688,4923,1690],{},[898,4925,2073],{"mathvariant":1822},[898,4927,1872],{},[898,4929,4930],{"mathvariant":1822},"\u002F",[898,4932,2073],{"mathvariant":1822},[898,4934,1727],{},[902,4936,4937],{"encoding":904},"Q'(P) = \\mathrm{d}Q\u002F\\mathrm{d}P",[123,4939,4940,4941,4958,4959,2263],{},"Dosaďte zadanou cenu ",[883,4942,4944],{"className":4943},[886],[888,4945,4946],{"xmlns":890},[892,4947,4948,4956],{},[895,4949,4950],{},[1850,4951,4952,4954],{},[898,4953,1727],{},[1688,4955,1857],{},[902,4957,4660],{"encoding":904}," a dopočítejte odpovídající ",[883,4960,4962],{"className":4961},[886],[888,4963,4964],{"xmlns":890},[892,4965,4966,4988],{},[895,4967,4968,4974,4976,4978,4980,4986],{},[1850,4969,4970,4972],{},[898,4971,1872],{},[1688,4973,1857],{},[1688,4975,1690],{},[898,4977,4440],{},[1688,4979,2066],{"stretchy":2065},[1850,4981,4982,4984],{},[898,4983,1727],{},[1688,4985,1857],{},[1688,4987,2076],{"stretchy":2065},[902,4989,4990],{"encoding":904},"Q^* = D(P^*)",[123,4992,4993,4994,2263],{},"Dosaďte do (4.5): ",[883,4995,4997],{"className":4996},[886],[888,4998,4999],{"xmlns":890},[892,5000,5001,5053],{},[895,5002,5003,5005,5007,5013,5015,5017,5019,5035,5037,5043,5045,5051],{},[898,5004,4509],{},[1688,5006,2066],{"stretchy":2065},[1850,5008,5009,5011],{},[898,5010,1727],{},[1688,5012,1857],{},[1688,5014,2076],{"stretchy":2065},[1688,5016,1690],{},[1688,5018,1954],{},[1777,5020,5021],{"scriptlevel":1779,"displaystyle":1732},[1781,5022,5023,5029],{},[1850,5024,5025,5027],{},[898,5026,1727],{},[1688,5028,1857],{},[1850,5030,5031,5033],{},[898,5032,1872],{},[1688,5034,1857],{},[2041,5036,2043],{},[1850,5038,5039,5041],{},[898,5040,1872],{},[1688,5042,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,5044,2066],{"stretchy":2065},[1850,5046,5047,5049],{},[898,5048,1727],{},[1688,5050,1857],{},[1688,5052,2076],{"stretchy":2065},[902,5054,5055],{"encoding":904},"E(P^*) = -\\dfrac{P^*}{Q^*}\\,Q'(P^*)",[123,5057,5058,5059,5076,5077,5094,5095,5112],{},"Klasifikujte: ",[883,5060,5062],{"className":5061},[886],[888,5063,5064],{"xmlns":890},[892,5065,5066,5074],{},[895,5067,5068,5070,5072],{},[898,5069,4509],{},[1688,5071,3665],{},[1793,5073,1795],{},[902,5075,4765],{"encoding":904}," elastická, ",[883,5078,5080],{"className":5079},[886],[888,5081,5082],{"xmlns":890},[892,5083,5084,5092],{},[895,5085,5086,5088,5090],{},[898,5087,4509],{},[1688,5089,1690],{},[1793,5091,1795],{},[902,5093,4801],{"encoding":904}," jednotková, ",[883,5096,5098],{"className":5097},[886],[888,5099,5100],{"xmlns":890},[892,5101,5102,5110],{},[895,5103,5104,5106,5108],{},[898,5105,4509],{},[1688,5107,3704],{},[1793,5109,1795],{},[902,5111,4783],{"encoding":904}," neelastická.",[198,5114,5116],{"id":5115},"interpretace-46","Interpretace (4.6)",[4124,5118,5119],{},[724,5120,5121,5122,5145,5146,5159,5160,5177,5178],{},"Číslo ",[883,5123,5125],{"className":5124},[886],[888,5126,5127],{"xmlns":890},[892,5128,5129,5143],{},[895,5130,5131,5133,5135,5141],{},[898,5132,4509],{},[1688,5134,2066],{"stretchy":2065},[1850,5136,5137,5139],{},[898,5138,1727],{},[1688,5140,1857],{},[1688,5142,2076],{"stretchy":2065},[902,5144,4638],{"encoding":904}," udává, o kolik % se přibližně změní poptávané množství ",[883,5147,5149],{"className":5148},[886],[888,5150,5151],{"xmlns":890},[892,5152,5153,5157],{},[895,5154,5155],{},[898,5156,1872],{},[902,5158,1872],{"encoding":904},", jestliže se cena ",[883,5161,5163],{"className":5162},[886],[888,5164,5165],{"xmlns":890},[892,5166,5167,5175],{},[895,5168,5169],{},[1850,5170,5171,5173],{},[898,5172,1727],{},[1688,5174,1857],{},[902,5176,4660],{"encoding":904}," změní o 1 %. ",[883,5179,5181],{"className":5180},[886],[888,5182,5183],{"xmlns":890},[892,5184,5185,5194],{},[895,5186,5187,5189,5192],{},[1688,5188,2066],{"stretchy":2065},[1793,5190,5191],{},"4.6",[1688,5193,2076],{"stretchy":2065},[902,5195,5196],{"encoding":904},"(4.6)",[724,5198,5199,5202],{},[38,5200,5201],{},"Historicky:"," úvahy vedoucí k hypotéze (4.1) formuloval již Cournot (1838), dnešní vymezení se připisuje Marshallovi (1881).",[198,5204,5206],{"id":5205},"příklad-41","Příklad 4.1",[724,5208,5209,5210,5244,5245,1343,5271,2965],{},"Poptávka ",[883,5211,5213],{"className":5212},[886],[888,5214,5215],{"xmlns":890},[892,5216,5217,5241],{},[895,5218,5219,5221,5223,5225,5227,5229,5231,5233,5235,5237,5239],{},[898,5220,1727],{},[1688,5222,1690],{},[898,5224,4440],{},[1688,5226,2066],{"stretchy":2065},[898,5228,1872],{},[1688,5230,2076],{"stretchy":2065},[1688,5232,1690],{},[1793,5234,3377],{},[1688,5236,1954],{},[1793,5238,1806],{},[898,5240,1872],{},[902,5242,5243],{"encoding":904},"P = D(Q) = 50 - 2Q",". Vyjádříme ",[883,5246,5248],{"className":5247},[886],[888,5249,5250],{"xmlns":890},[892,5251,5252,5268],{},[895,5253,5254,5256,5258,5261,5263,5266],{},[898,5255,1872],{},[1688,5257,1690],{},[1793,5259,5260],{},"25",[1688,5262,1954],{},[1793,5264,5265],{},"0,5",[898,5267,1727],{},[902,5269,5270],{"encoding":904},"Q = 25 - 0{,}5P",[883,5272,5274],{"className":5273},[886],[888,5275,5276],{"xmlns":890},[892,5277,5278,5302],{},[895,5279,5280,5296,5298,5300],{},[1777,5281,5282],{"scriptlevel":1779,"displaystyle":1732},[1781,5283,5284,5290],{},[895,5285,5286,5288],{},[898,5287,2073],{"mathvariant":1822},[898,5289,1872],{},[895,5291,5292,5294],{},[898,5293,2073],{"mathvariant":1822},[898,5295,1727],{},[1688,5297,1690],{},[1688,5299,1954],{},[1793,5301,5265],{},[902,5303,5304],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -0{,}5",[724,5306,5307],{},[883,5308,5310],{"className":5309},[886],[888,5311,5312],{"xmlns":890},[892,5313,5314,5368],{},[895,5315,5316,5318,5320,5322,5336,5338,5340,5342,5344,5346,5348,5366],{},[898,5317,4509],{},[1688,5319,1690],{},[1688,5321,1954],{},[1781,5323,5324,5326],{},[898,5325,1727],{},[895,5327,5328,5330,5332,5334],{},[1793,5329,5260],{},[1688,5331,1954],{},[1793,5333,5265],{},[898,5335,1727],{},[1688,5337,3434],{},[1688,5339,2066],{"stretchy":2065},[1688,5341,1954],{},[1793,5343,5265],{},[1688,5345,2076],{"stretchy":2065},[1688,5347,1690],{},[1781,5349,5350,5356],{},[895,5351,5352,5354],{},[1793,5353,5265],{},[898,5355,1727],{},[895,5357,5358,5360,5362,5364],{},[1793,5359,5260],{},[1688,5361,1954],{},[1793,5363,5265],{},[898,5365,1727],{},[898,5367,2263],{"mathvariant":1822},[902,5369,5370],{"encoding":904},"E = -\\frac{P}{25-0{,}5P}\\cdot(-0{,}5) = \\frac{0{,}5P}{25-0{,}5P}.",[724,5372,5373,5374,1343,5398,1343,5428,1343,5452,5477,5478,5501,5502,2946,5520,4176],{},"Potom ",[883,5375,5377],{"className":5376},[886],[888,5378,5379],{"xmlns":890},[892,5380,5381,5395],{},[895,5382,5383,5385,5387,5389,5391,5393],{},[898,5384,4509],{},[1688,5386,2066],{"stretchy":2065},[1793,5388,1779],{},[1688,5390,2076],{"stretchy":2065},[1688,5392,1690],{},[1793,5394,1779],{},[902,5396,5397],{"encoding":904},"E(0)=0",[883,5399,5401],{"className":5400},[886],[888,5402,5403],{"xmlns":890},[892,5404,5405,5425],{},[895,5406,5407,5409,5411,5413,5415,5417],{},[898,5408,4509],{},[1688,5410,2066],{"stretchy":2065},[1793,5412,3121],{},[1688,5414,2076],{"stretchy":2065},[1688,5416,1690],{},[1777,5418,5419],{"scriptlevel":1779,"displaystyle":2065},[1781,5420,5421,5423],{},[1793,5422,1795],{},[1793,5424,2616],{},[902,5426,5427],{"encoding":904},"E(10)=\\tfrac{1}{4}",[883,5429,5431],{"className":5430},[886],[888,5432,5433],{"xmlns":890},[892,5434,5435,5449],{},[895,5436,5437,5439,5441,5443,5445,5447],{},[898,5438,4509],{},[1688,5440,2066],{"stretchy":2065},[1793,5442,5260],{},[1688,5444,2076],{"stretchy":2065},[1688,5446,1690],{},[1793,5448,1795],{},[902,5450,5451],{"encoding":904},"E(25)=1",[883,5453,5455],{"className":5454},[886],[888,5456,5457],{"xmlns":890},[892,5458,5459,5474],{},[895,5460,5461,5463,5465,5468,5470,5472],{},[898,5462,4509],{},[1688,5464,2066],{"stretchy":2065},[1793,5466,5467],{},"40",[1688,5469,2076],{"stretchy":2065},[1688,5471,1690],{},[1793,5473,2616],{},[902,5475,5476],{"encoding":904},"E(40)=4",". Např. ",[883,5479,5481],{"className":5480},[886],[888,5482,5483],{"xmlns":890},[892,5484,5485,5499],{},[895,5486,5487,5489,5491,5493,5495,5497],{},[898,5488,4509],{},[1688,5490,2066],{"stretchy":2065},[1793,5492,5467],{},[1688,5494,2076],{"stretchy":2065},[1688,5496,1690],{},[1793,5498,2616],{},[902,5500,5476],{"encoding":904}," znamená, že zvýšení ceny o 1 % (z 40 na 40,4) způsobí pokles množství o 4 % (z ",[883,5503,5505],{"className":5504},[886],[888,5506,5507],{"xmlns":890},[892,5508,5509,5517],{},[895,5510,5511,5513,5515],{},[898,5512,1872],{},[1688,5514,1690],{},[1793,5516,2501],{},[902,5518,5519],{"encoding":904},"Q=5",[883,5521,5523],{"className":5522},[886],[888,5524,5525],{"xmlns":890},[892,5526,5527,5536],{},[895,5528,5529,5531,5533],{},[898,5530,1872],{},[1688,5532,1690],{},[1793,5534,5535],{},"4,8",[902,5537,5538],{"encoding":904},"Q=4{,}8",[198,5540,5542],{"id":5541},"oblouková-průměrná-vs-bodová-okamžitá-elasticita","Oblouková (průměrná) vs. bodová (okamžitá) elasticita",[120,5544,5545,5601],{},[123,5546,5547,5550,5551,5568,5569,2263],{},[38,5548,5549],{},"Oblouková"," (průměrná) elasticita: výraz ",[883,5552,5554],{"className":5553},[886],[888,5555,5556],{"xmlns":890},[892,5557,5558,5566],{},[895,5559,5560],{},[1850,5561,5562,5564],{},[898,5563,4509],{},[898,5565,4512],{},[902,5567,4515],{"encoding":904}," ze (4.4) vztažený k intervalu ",[883,5570,5572],{"className":5571},[886],[888,5573,5574],{"xmlns":890},[892,5575,5576,5598],{},[895,5577,5578,5581,5583,5585,5587,5589,5591,5593,5595],{},[1688,5579,5580],{"stretchy":2065},"⟨",[898,5582,1727],{},[1688,5584,1733],{"separator":1732},[2041,5586,2043],{},[898,5588,1727],{},[1688,5590,1696],{},[898,5592,3147],{"mathvariant":1822},[898,5594,1727],{},[1688,5596,5597],{"stretchy":2065},"⟩",[902,5599,5600],{"encoding":904},"\\langle P,\\, P+\\Delta P\\rangle",[123,5602,5603,5606,5607,5620],{},[38,5604,5605],{},"Bodová"," (okamžitá) elasticita: ",[883,5608,5610],{"className":5609},[886],[888,5611,5612],{"xmlns":890},[892,5613,5614,5618],{},[895,5615,5616],{},[898,5617,4509],{},[902,5619,4509],{"encoding":904}," dle (4.5) — výchozí pojem dále v textu.",[198,5622,5624,5625,5638,5639],{"id":5623},"výpočet-je-li-dáno-pp-jako-funkce-qq","Výpočet, je-li dáno ",[883,5626,5628],{"className":5627},[886],[888,5629,5630],{"xmlns":890},[892,5631,5632,5636],{},[895,5633,5634],{},[898,5635,1727],{},[902,5637,1727],{"encoding":904}," jako funkce ",[883,5640,5642],{"className":5641},[886],[888,5643,5644],{"xmlns":890},[892,5645,5646,5650],{},[895,5647,5648],{},[898,5649,1872],{},[902,5651,1872],{"encoding":904},[724,5653,5654,5655,5678],{},"Pokud je poptávka zadaná ve tvaru ",[883,5656,5658],{"className":5657},[886],[888,5659,5660],{"xmlns":890},[892,5661,5662,5676],{},[895,5663,5664,5666,5668,5670,5672,5674],{},[898,5665,1727],{},[1688,5667,1690],{},[898,5669,4440],{},[1688,5671,2066],{"stretchy":2065},[898,5673,1872],{},[1688,5675,2076],{"stretchy":2065},[902,5677,4896],{"encoding":904},", využijeme vztah pro derivaci inverzní funkce",[724,5680,5681],{},[883,5682,5684],{"className":5683,"title":4457,"style":4458},[4456],"\\frac{\\mathrm{d}Q}{\\mathrm{d}P} = \\frac{1}{\\frac{\\mathrm{d}P}{\\mathrm{d}Q}}. \\tag{4.9}",[724,5686,5687,2170,5690,5716],{},[38,5688,5689],{},"Příklad 4.3.",[883,5691,5693],{"className":5692},[886],[888,5694,5695],{"xmlns":890},[892,5696,5697,5713],{},[895,5698,5699,5701,5703,5705,5707],{},[898,5700,1727],{},[1688,5702,1690],{},[1793,5704,3347],{},[1688,5706,1954],{},[1850,5708,5709,5711],{},[898,5710,1872],{},[1793,5712,1806],{},[902,5714,5715],{"encoding":904},"P = 100 - Q^2",", ptáme se na elasticitu při ceně 36. Dostáváme",[724,5718,5719],{},[883,5720,5722],{"className":5721},[886],[888,5723,5724],{"xmlns":890},[892,5725,5726,5792],{},[895,5727,5728,5730,5732,5734,5750,5752,5764,5766,5790],{},[898,5729,4509],{},[1688,5731,1690],{},[1688,5733,1954],{},[1781,5735,5736,5748],{},[895,5737,5738,5740,5742],{},[1793,5739,3347],{},[1688,5741,1954],{},[1850,5743,5744,5746],{},[898,5745,1872],{},[1793,5747,1806],{},[898,5749,1872],{},[1688,5751,3434],{},[1781,5753,5754,5756],{},[1793,5755,1795],{},[895,5757,5758,5760,5762],{},[1688,5759,1954],{},[1793,5761,1806],{},[898,5763,1872],{},[1688,5765,1690],{},[1781,5767,5768,5780],{},[895,5769,5770,5772,5774],{},[1793,5771,3347],{},[1688,5773,1954],{},[1850,5775,5776,5778],{},[898,5777,1872],{},[1793,5779,1806],{},[895,5781,5782,5784],{},[1793,5783,1806],{},[1850,5785,5786,5788],{},[898,5787,1872],{},[1793,5789,1806],{},[898,5791,2263],{"mathvariant":1822},[902,5793,5794],{"encoding":904},"E = -\\frac{100-Q^2}{Q}\\cdot \\frac{1}{-2Q} = \\frac{100-Q^2}{2Q^2}.",[724,5796,5797,5798,5825,5826,5845,5846,2263],{},"Z rovnice ",[883,5799,5801],{"className":5800},[886],[888,5802,5803],{"xmlns":890},[892,5804,5805,5822],{},[895,5806,5807,5809,5811,5817,5819],{},[1793,5808,3347],{},[1688,5810,1954],{},[1850,5812,5813,5815],{},[898,5814,1872],{},[1793,5816,1806],{},[1688,5818,1690],{},[1793,5820,5821],{},"36",[902,5823,5824],{"encoding":904},"100 - Q^2 = 36"," plyne ",[883,5827,5829],{"className":5828},[886],[888,5830,5831],{"xmlns":890},[892,5832,5833,5842],{},[895,5834,5835,5837,5839],{},[898,5836,1872],{},[1688,5838,1690],{},[1793,5840,5841],{},"8",[902,5843,5844],{"encoding":904},"Q = 8",", tedy ",[883,5847,5849],{"className":5848},[886],[888,5850,5851],{"xmlns":890},[892,5852,5853,5879],{},[895,5854,5855,5857,5859,5861,5863,5865,5874,5876],{},[898,5856,4509],{},[1688,5858,2066],{"stretchy":2065},[1793,5860,5841],{},[1688,5862,2076],{"stretchy":2065},[1688,5864,1690],{},[1777,5866,5867],{"scriptlevel":1779,"displaystyle":2065},[1781,5868,5869,5871],{},[1793,5870,5821],{},[1793,5872,5873],{},"128",[1688,5875,1690],{},[1793,5877,5878],{},"0,281",[902,5880,5881],{"encoding":904},"E(8) = \\tfrac{36}{128} = 0{,}281",[198,5883,5885],{"id":5884},"přibližné-změny","Přibližné změny",[724,5887,5888,5889,5925,5926,5948],{},"Diferenciál ",[883,5890,5892],{"className":5891},[886],[888,5893,5894],{"xmlns":890},[892,5895,5896,5922],{},[895,5897,5898,5900,5902,5904,5910,5912,5914,5916,5918,5920],{},[898,5899,2073],{"mathvariant":1822},[898,5901,1872],{},[1688,5903,1690],{},[1850,5905,5906,5908],{},[898,5907,1872],{},[1688,5909,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,5911,2066],{"stretchy":2065},[898,5913,1727],{},[1688,5915,2076],{"stretchy":2065},[2041,5917,2043],{},[898,5919,2073],{"mathvariant":1822},[898,5921,1727],{},[902,5923,5924],{"encoding":904},"\\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P"," s ",[883,5927,5929],{"className":5928},[886],[888,5930,5931],{"xmlns":890},[892,5932,5933,5945],{},[895,5934,5935,5937,5939,5941,5943],{},[898,5936,2073],{"mathvariant":1822},[898,5938,1727],{},[1688,5940,1690],{},[898,5942,3147],{"mathvariant":1822},[898,5944,1727],{},[902,5946,5947],{"encoding":904},"\\mathrm{d}P = \\Delta P"," dává nominální odhad",[724,5950,5951],{},[883,5952,5954],{"className":5953,"title":4457,"style":4458},[4456],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P. \\tag{4.10}",[724,5956,5957],{},"Po přechodu na procentní změny (vztah (4.3)):",[724,5959,5960],{},[883,5961,5963],{"className":5962,"title":4457,"style":4458},[4456],"\\boxed{\\;\\Delta Q\\% \\approx -E(P)\\,\\Delta P\\%\\;} \\tag{4.11}",[724,5965,5966,2170,5969,6004,6005,6024,6025,6059,6060,6077],{},[38,5967,5968],{},"Příklad 4.5.",[883,5970,5972],{"className":5971},[886],[888,5973,5974],{"xmlns":890},[892,5975,5976,6001],{},[895,5977,5978,5980,5982,5984,5990,5992,5994,5996,5998],{},[898,5979,1727],{},[1688,5981,1690],{},[1688,5983,1954],{},[1850,5985,5986,5988],{},[898,5987,1872],{},[1793,5989,1806],{},[1688,5991,1954],{},[1793,5993,2616],{},[898,5995,1872],{},[1688,5997,1696],{},[1793,5999,6000],{},"96",[902,6002,6003],{"encoding":904},"P = -Q^2 - 4Q + 96",", cena ",[883,6006,6008],{"className":6007},[886],[888,6009,6010],{"xmlns":890},[892,6011,6012,6021],{},[895,6013,6014,6016,6018],{},[898,6015,1727],{},[1688,6017,1690],{},[1793,6019,6020],{},"51",[902,6022,6023],{"encoding":904},"P=51",". Z rovnice ",[883,6026,6028],{"className":6027},[886],[888,6029,6030],{"xmlns":890},[892,6031,6032,6056],{},[895,6033,6034,6036,6038,6040,6046,6048,6050,6052,6054],{},[1793,6035,6020],{},[1688,6037,1690],{},[1688,6039,1954],{},[1850,6041,6042,6044],{},[898,6043,1872],{},[1793,6045,1806],{},[1688,6047,1954],{},[1793,6049,2616],{},[898,6051,1872],{},[1688,6053,1696],{},[1793,6055,6000],{},[902,6057,6058],{"encoding":904},"51 = -Q^2-4Q+96"," volíme (kladný kořen) ",[883,6061,6063],{"className":6062},[886],[888,6064,6065],{"xmlns":890},[892,6066,6067,6075],{},[895,6068,6069,6071,6073],{},[898,6070,1872],{},[1688,6072,1690],{},[1793,6074,2501],{},[902,6076,5519],{"encoding":904},". Elasticita:",[724,6079,6080],{},[883,6081,6083],{"className":6082},[886],[888,6084,6085],{"xmlns":890},[892,6086,6087,6160],{},[895,6088,6089,6091,6093,6131,6133,6137,6139,6141,6143,6145,6147,6154,6157],{},[898,6090,4509],{},[1688,6092,1690],{},[1781,6094,6095,6115],{},[895,6096,6097,6099,6105,6107,6109,6111,6113],{},[1688,6098,1954],{},[1850,6100,6101,6103],{},[898,6102,1872],{},[1793,6104,1806],{},[1688,6106,1954],{},[1793,6108,2616],{},[898,6110,1872],{},[1688,6112,1696],{},[1793,6114,6000],{},[895,6116,6117,6119,6121,6123,6125,6127,6129],{},[898,6118,1872],{},[1688,6120,2066],{"stretchy":2065},[1793,6122,1806],{},[898,6124,1872],{},[1688,6126,1696],{},[1793,6128,2616],{},[1688,6130,2076],{"stretchy":2065},[1688,6132,1733],{"separator":1732},[6134,6135],"mspace",{"width":6136},"2em",[898,6138,4509],{},[1688,6140,2066],{"stretchy":2065},[1793,6142,2501],{},[1688,6144,2076],{"stretchy":2065},[1688,6146,1690],{},[1781,6148,6149,6151],{},[1793,6150,6020],{},[1793,6152,6153],{},"70",[1688,6155,6156],{},"≐",[1793,6158,6159],{},"0,728.",[902,6161,6162],{"encoding":904},"E = \\frac{-Q^2-4Q+96}{Q(2Q+4)}, \\qquad E(5) = \\frac{51}{70} \\doteq 0{,}728.",[724,6164,6165,6166,2263],{},"Jde o neelastickou poptávku. Zvýší-li se cena o 2 %, pak ",[883,6167,6169],{"className":6168},[886],[888,6170,6171],{"xmlns":890},[892,6172,6173,6204],{},[895,6174,6175,6177,6179,6182,6184,6186,6189,6191,6193,6195,6197,6200,6202],{},[898,6176,3147],{"mathvariant":1822},[898,6178,1872],{},[898,6180,6181],{"mathvariant":1822},"%",[1688,6183,2991],{},[1688,6185,1954],{},[1793,6187,6188],{},"0,728",[1688,6190,3434],{},[1793,6192,1806],{},[1688,6194,1690],{},[1688,6196,1954],{},[1793,6198,6199],{},"1,456",[2041,6201,2043],{},[898,6203,6181],{"mathvariant":1822},[902,6205,6206],{"encoding":904},"\\Delta Q\\% \\approx -0{,}728\\cdot 2 = -1{,}456\\,\\%",[115,6208,6210],{"id":6209},"klasifikace-elasticit-poptávky","Klasifikace elasticit poptávky",[724,6212,6213,6214,6237,6238,2965],{},"V závislosti na hodnotě ",[883,6215,6217],{"className":6216},[886],[888,6218,6219],{"xmlns":890},[892,6220,6221,6235],{},[895,6222,6223,6225,6227,6233],{},[898,6224,4509],{},[1688,6226,2066],{"stretchy":2065},[1850,6228,6229,6231],{},[898,6230,1727],{},[1688,6232,1857],{},[1688,6234,2076],{"stretchy":2065},[902,6236,4638],{"encoding":904}," mluvíme o poptávce podle následující tabulky ",[883,6239,6241],{"className":6240},[886],[888,6242,6243],{"xmlns":890},[892,6244,6245,6254],{},[895,6246,6247,6249,6252],{},[1688,6248,2066],{"stretchy":2065},[1793,6250,6251],{},"4.7",[1688,6253,2076],{"stretchy":2065},[902,6255,6256],{"encoding":904},"(4.7)",[724,6258,6259],{},[2821,6260],{"alt":6261,"className":6262,"src":6263},"imek-typy-elasticity-5panelu",[210,2825],"\u002Fwiki-assets\u002Fimek-typy-elasticity-5panelu.jpeg",[16,6265,6266,6305],{},[19,6267,6268],{},[22,6269,6270,6296,6299,6302],{},[25,6271,6272,6273],{},"Hodnota ",[883,6274,6276],{"className":6275},[886],[888,6277,6278],{"xmlns":890},[892,6279,6280,6294],{},[895,6281,6282,6284,6286,6292],{},[898,6283,4509],{},[1688,6285,2066],{"stretchy":2065},[1850,6287,6288,6290],{},[898,6289,1727],{},[1688,6291,1857],{},[1688,6293,2076],{"stretchy":2065},[902,6295,4638],{"encoding":904},[25,6297,6298],{},"Typ poptávky",[25,6300,6301],{},"Termín",[25,6303,6304],{},"Význam",[30,6306,6307,6340,6402,6477,6534],{},[22,6308,6309,6329,6334,6337],{},[35,6310,6311],{},[883,6312,6314],{"className":6313},[886],[888,6315,6316],{"xmlns":890},[892,6317,6318,6326],{},[895,6319,6320,6322,6324],{},[898,6321,4509],{},[1688,6323,1690],{},[1793,6325,1779],{},[902,6327,6328],{"encoding":904},"E = 0",[35,6330,6331],{},[38,6332,6333],{},"dokonale neelastická",[35,6335,6336],{},"perfectly inelastic",[35,6338,6339],{},"množství se nemění bez ohledu na cenu",[22,6341,6342,6366,6370,6373],{},[35,6343,6344],{},[883,6345,6347],{"className":6346},[886],[888,6348,6349],{"xmlns":890},[892,6350,6351,6363],{},[895,6352,6353,6355,6357,6359,6361],{},[1793,6354,1779],{},[1688,6356,3704],{},[898,6358,4509],{},[1688,6360,3704],{},[1793,6362,1795],{},[902,6364,6365],{"encoding":904},"0 \u003C E \u003C 1",[35,6367,6368],{},[38,6369,4334],{},[35,6371,6372],{},"inelastic",[35,6374,6375,6388,6389],{},[883,6376,6378],{"className":6377},[886],[888,6379,6380],{"xmlns":890},[892,6381,6382,6386],{},[895,6383,6384],{},[898,6385,1872],{},[902,6387,1872],{"encoding":904}," se mění pomaleji než ",[883,6390,6392],{"className":6391},[886],[888,6393,6394],{"xmlns":890},[892,6395,6396,6400],{},[895,6397,6398],{},[898,6399,1727],{},[902,6401,1727],{"encoding":904},[22,6403,6404,6423,6428,6431],{},[35,6405,6406],{},[883,6407,6409],{"className":6408},[886],[888,6410,6411],{"xmlns":890},[892,6412,6413,6421],{},[895,6414,6415,6417,6419],{},[898,6416,4509],{},[1688,6418,1690],{},[1793,6420,1795],{},[902,6422,4801],{"encoding":904},[35,6424,6425],{},[38,6426,6427],{},"jednotkově elastická",[35,6429,6430],{},"unit elastic",[35,6432,6433,6446,6447,6460,6461,6476],{},[883,6434,6436],{"className":6435},[886],[888,6437,6438],{"xmlns":890},[892,6439,6440,6444],{},[895,6441,6442],{},[898,6443,1872],{},[902,6445,1872],{"encoding":904}," i ",[883,6448,6450],{"className":6449},[886],[888,6451,6452],{"xmlns":890},[892,6453,6454,6458],{},[895,6455,6456],{},[898,6457,1727],{},[902,6459,1727],{"encoding":904}," se mění stejně rychle; ",[883,6462,6464],{"className":6463},[886],[888,6465,6466],{"xmlns":890},[892,6467,6468,6474],{},[895,6469,6470,6472],{},[898,6471,3035],{},[898,6473,4251],{},[902,6475,4351],{"encoding":904}," má maximum",[22,6478,6479,6498,6502,6505],{},[35,6480,6481],{},[883,6482,6484],{"className":6483},[886],[888,6485,6486],{"xmlns":890},[892,6487,6488,6496],{},[895,6489,6490,6492,6494],{},[898,6491,4509],{},[1688,6493,3665],{},[1793,6495,1795],{},[902,6497,4765],{"encoding":904},[35,6499,6500],{},[38,6501,4330],{},[35,6503,6504],{},"elastic",[35,6506,6507,6520,6521],{},[883,6508,6510],{"className":6509},[886],[888,6511,6512],{"xmlns":890},[892,6513,6514,6518],{},[895,6515,6516],{},[898,6517,1872],{},[902,6519,1872],{"encoding":904}," se mění rychleji než ",[883,6522,6524],{"className":6523},[886],[888,6525,6526],{"xmlns":890},[892,6527,6528,6532],{},[895,6529,6530],{},[898,6531,1727],{},[902,6533,1727],{"encoding":904},[22,6535,6536,6557,6562,6565],{},[35,6537,6538],{},[883,6539,6541],{"className":6540},[886],[888,6542,6543],{"xmlns":890},[892,6544,6545,6554],{},[895,6546,6547,6549,6551],{},[898,6548,4509],{},[1688,6550,3380],{},[898,6552,6553],{"mathvariant":1822},"∞",[902,6555,6556],{"encoding":904},"E \\to \\infty",[35,6558,6559],{},[38,6560,6561],{},"dokonale elastická",[35,6563,6564],{},"perfectly elastic",[35,6566,6567,6568],{},"sebemenší změna ceny úplně mění ",[883,6569,6571],{"className":6570},[886],[888,6572,6573],{"xmlns":890},[892,6574,6575,6579],{},[895,6576,6577],{},[898,6578,1872],{},[902,6580,1872],{"encoding":904},[724,6582,6583],{},[38,6584,6585],{},"Pravidlo růstu elasticity s cenou:",[4124,6587,6588],{},[724,6589,6590,6591],{},"S rostoucí cenou elasticita poptávky roste. ",[883,6592,6594],{"className":6593},[886],[888,6595,6596],{"xmlns":890},[892,6597,6598,6607],{},[895,6599,6600,6602,6605],{},[1688,6601,2066],{"stretchy":2065},[1793,6603,6604],{},"4.8",[1688,6606,2076],{"stretchy":2065},[902,6608,6609],{"encoding":904},"(4.8)",[724,6611,6612,6613,6616,6617,6620,6621,6638],{},"Z toho plyne, že při ",[614,6614,6615],{},"dostatečně nízkých"," cenách je poptávka neelastická a při ",[614,6618,6619],{},"dostatečně vysokých"," elastická. Existuje tedy cena ",[883,6622,6624],{"className":6623},[886],[888,6625,6626],{"xmlns":890},[892,6627,6628,6636],{},[895,6629,6630],{},[1850,6631,6632,6634],{},[898,6633,1727],{},[1688,6635,1857],{},[902,6637,4660],{"encoding":904},", při které je poptávka jednotkově elastická, a ta rozděluje reálné cenové rozpětí na obě zóny.",[4124,6640,6641,6646],{},[724,6642,6643,6645],{},[883,6644,4828],{}," Postup: jak klasifikovat poptávku",[152,6647,6648,6675,6678],{},[123,6649,6650,6651,6674],{},"Spočítejte ",[883,6652,6654],{"className":6653},[886],[888,6655,6656],{"xmlns":890},[892,6657,6658,6672],{},[895,6659,6660,6662,6664,6670],{},[898,6661,4509],{},[1688,6663,2066],{"stretchy":2065},[1850,6665,6666,6668],{},[898,6667,1727],{},[1688,6669,1857],{},[1688,6671,2076],{"stretchy":2065},[902,6673,4638],{"encoding":904}," dle (4.5).",[123,6676,6677],{},"Porovnejte s jedničkou (viz tabulka výše).",[123,6679,6680,6681,6705],{},"Chcete-li najít hranici mezi elastickou a neelastickou zónou, řešte rovnici ",[883,6682,6684],{"className":6683},[886],[888,6685,6686],{"xmlns":890},[892,6687,6688,6702],{},[895,6689,6690,6692,6694,6696,6698,6700],{},[898,6691,4509],{},[1688,6693,2066],{"stretchy":2065},[898,6695,1727],{},[1688,6697,2076],{"stretchy":2065},[1688,6699,1690],{},[1793,6701,1795],{},[902,6703,6704],{"encoding":904},"E(P) = 1"," a výsledek porovnejte s reálným cenovým rozpětím.",[724,6707,6708,6711,6712,6729,6730,6748,6749,6776,6777,2263],{},[38,6709,6710],{},"Příklad 4.2."," Pro poptávku z Příkladu 4.1: ",[883,6713,6715],{"className":6714},[886],[888,6716,6717],{"xmlns":890},[892,6718,6719,6727],{},[895,6720,6721,6723,6725],{},[898,6722,4509],{},[1688,6724,1690],{},[1793,6726,1795],{},[902,6728,4801],{"encoding":904}," pro ",[883,6731,6733],{"className":6732},[886],[888,6734,6735],{"xmlns":890},[892,6736,6737,6745],{},[895,6738,6739,6741,6743],{},[898,6740,1727],{},[1688,6742,1690],{},[1793,6744,5260],{},[902,6746,6747],{"encoding":904},"P = 25",". Podle (4.8) je poptávka neelastická pro ",[883,6750,6752],{"className":6751},[886],[888,6753,6754],{"xmlns":890},[892,6755,6756,6773],{},[895,6757,6758,6760,6763,6765,6767,6769,6771],{},[898,6759,1727],{},[1688,6761,6762],{},"∈",[1688,6764,5580],{"stretchy":2065},[1793,6766,1779],{},[1688,6768,1733],{"separator":1732},[1793,6770,5260],{},[1688,6772,2076],{"stretchy":2065},[902,6774,6775],{"encoding":904},"P \\in \\langle 0, 25)"," a elastická pro ",[883,6778,6780],{"className":6779},[886],[888,6781,6782],{"xmlns":890},[892,6783,6784,6800],{},[895,6785,6786,6788,6790,6792,6794,6796,6798],{},[898,6787,1727],{},[1688,6789,6762],{},[1688,6791,2066],{"stretchy":2065},[1793,6793,5260],{},[1688,6795,1733],{"separator":1732},[1793,6797,3377],{},[1688,6799,5597],{"stretchy":2065},[902,6801,6802],{"encoding":904},"P \\in (25, 50\\rangle",[115,6804,6806],{"id":6805},"elasticita-a-celkový-příjem","Elasticita a celkový příjem",[724,6808,6809],{},[2821,6810],{"alt":6811,"className":6812,"src":6813},"imek-elasticita-tr",[210,2825],"\u002Fwiki-assets\u002Fimek-elasticita-tr.jpeg",[724,6815,6816],{},[2821,6817],{"alt":6818,"className":6819,"src":6820},"imek-elasticita-podel-linearni-poptavky",[210,2825],"\u002Fwiki-assets\u002Fimek-elasticita-podel-linearni-poptavky.jpeg",[724,6822,6823,6824,6874,6875,6891],{},"Pro celkový příjem platí ",[883,6825,6827],{"className":6826},[886],[888,6828,6829],{"xmlns":890},[892,6830,6831,6871],{},[895,6832,6833,6835,6837,6839,6841,6843,6845,6847,6849,6851,6853,6855,6857,6859,6861,6863,6865,6867,6869],{},[898,6834,3035],{},[898,6836,4251],{},[1688,6838,1690],{},[898,6840,3035],{},[898,6842,4251],{},[1688,6844,2066],{"stretchy":2065},[898,6846,1872],{},[1688,6848,2076],{"stretchy":2065},[1688,6850,1690],{},[898,6852,1727],{},[1688,6854,3434],{},[898,6856,1872],{},[1688,6858,1690],{},[898,6860,1872],{},[1688,6862,3434],{},[898,6864,4440],{},[1688,6866,2066],{"stretchy":2065},[898,6868,1872],{},[1688,6870,2076],{"stretchy":2065},[902,6872,6873],{"encoding":904},"TR = TR(Q) = P\\cdot Q = Q\\cdot D(Q)",". Pro mezní příjem ",[883,6876,6878],{"className":6877},[886],[888,6879,6880],{"xmlns":890},[892,6881,6882,6888],{},[895,6883,6884,6886],{},[898,6885,1661],{},[898,6887,4251],{},[902,6889,6890],{"encoding":904},"MR"," odvodíme:",[724,6893,6894],{},[883,6895,6897],{"className":6896},[886],[888,6898,6899],{"xmlns":890},[892,6900,6901,7009],{},[895,6902,6903,6905,6907,6909,6911,6917,6919,6921,6923,6925,6927,6929,6931,6933,6935,6937,6939,6945,6947,6949,6951,6953,6955,6957,6959,6973,6975,6977],{},[898,6904,1661],{},[898,6906,4251],{},[1688,6908,1690],{},[898,6910,3035],{},[1850,6912,6913,6915],{},[898,6914,4251],{},[1688,6916,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,6918,2066],{"stretchy":2065},[898,6920,1872],{},[1688,6922,2076],{"stretchy":2065},[1688,6924,1690],{},[898,6926,4440],{},[1688,6928,2066],{"stretchy":2065},[898,6930,1872],{},[1688,6932,2076],{"stretchy":2065},[1688,6934,1696],{},[898,6936,1872],{},[2041,6938,2043],{},[1850,6940,6941,6943],{},[898,6942,4440],{},[1688,6944,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,6946,2066],{"stretchy":2065},[898,6948,1872],{},[1688,6950,2076],{"stretchy":2065},[1688,6952,1690],{},[898,6954,1727],{},[1688,6956,1696],{},[898,6958,1872],{},[1781,6960,6961,6967],{},[895,6962,6963,6965],{},[898,6964,2073],{"mathvariant":1822},[898,6966,1727],{},[895,6968,6969,6971],{},[898,6970,2073],{"mathvariant":1822},[898,6972,1872],{},[1688,6974,1690],{},[898,6976,1727],{},[895,6978,6979,6981,6983,6985,6991,6993,7007],{},[1688,6980,2066],{"fence":1732},[1793,6982,1795],{},[1688,6984,1696],{},[1781,6986,6987,6989],{},[898,6988,1872],{},[898,6990,1727],{},[1688,6992,3434],{},[1781,6994,6995,7001],{},[895,6996,6997,6999],{},[898,6998,2073],{"mathvariant":1822},[898,7000,1727],{},[895,7002,7003,7005],{},[898,7004,2073],{"mathvariant":1822},[898,7006,1872],{},[1688,7008,2076],{"fence":1732},[902,7010,7011],{"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)",[724,7013,7014],{},[883,7015,7017],{"className":7016},[886],[888,7018,7019],{"xmlns":890},[892,7020,7021,7093],{},[895,7022,7023,7025,7027,7069,7071,7073],{},[1688,7024,1690],{},[898,7026,1727],{},[895,7028,7029,7031,7033,7035,7067],{},[1688,7030,2066],{"fence":1732},[1793,7032,1795],{},[1688,7034,1696],{},[1781,7036,7037,7039],{},[1793,7038,1795],{},[895,7040,7041,7049,7051],{},[1777,7042,7043],{"scriptlevel":1779,"displaystyle":2065},[1781,7044,7045,7047],{},[898,7046,1727],{},[898,7048,1872],{},[1688,7050,3434],{},[1777,7052,7053],{"scriptlevel":1779,"displaystyle":2065},[1781,7054,7055,7061],{},[895,7056,7057,7059],{},[898,7058,2073],{"mathvariant":1822},[898,7060,1872],{},[895,7062,7063,7065],{},[898,7064,2073],{"mathvariant":1822},[898,7066,1727],{},[1688,7068,2076],{"fence":1732},[1688,7070,1690],{},[898,7072,1727],{},[895,7074,7075,7077,7079,7081,7091],{},[1688,7076,2066],{"fence":1732},[1793,7078,1795],{},[1688,7080,1696],{},[1781,7082,7083,7085],{},[1793,7084,1795],{},[895,7086,7087,7089],{},[1688,7088,1954],{},[898,7090,4509],{},[1688,7092,2076],{"fence":1732},[902,7094,7095],{"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)",[724,7097,7098],{},"a tedy",[724,7100,7101],{},[883,7102,7104],{"className":7103,"title":4457,"style":4458},[4456],"\\boxed{\\;MR = P\\left(1 - \\frac{1}{E}\\right) = D(Q)\\left(1 - \\frac{1}{E}\\right)\\;} \\tag{4.12}",[4124,7106,7107,7176,7426],{},[724,7108,7109,7111,7112,7146,7147,7162,7163,2965],{},[883,7110,4412],{}," Intuice: vztah ",[883,7113,7115],{"className":7114},[886],[888,7116,7117],{"xmlns":890},[892,7118,7119,7143],{},[895,7120,7121,7123,7125,7127,7129,7131,7133,7135,7137,7139,7141],{},[898,7122,1661],{},[898,7124,4251],{},[1688,7126,1690],{},[898,7128,1727],{},[1688,7130,2066],{"stretchy":2065},[1793,7132,1795],{},[1688,7134,1954],{},[1793,7136,1795],{},[898,7138,4930],{"mathvariant":1822},[898,7140,4509],{},[1688,7142,2076],{"stretchy":2065},[902,7144,7145],{"encoding":904},"MR = P(1 - 1\u002FE)","\nVztah (4.12) je „most\" mezi elasticitou a mezním příjmem — znaménko ",[883,7148,7150],{"className":7149},[886],[888,7151,7152],{"xmlns":890},[892,7153,7154,7160],{},[895,7155,7156,7158],{},[898,7157,1661],{},[898,7159,4251],{},[902,7161,6890],{"encoding":904}," jednoznačně určuje hodnota ",[883,7164,7166],{"className":7165},[886],[888,7167,7168],{"xmlns":890},[892,7169,7170,7174],{},[895,7171,7172],{},[898,7173,4509],{},[902,7175,4509],{"encoding":904},[120,7177,7178,7288,7357],{},[123,7179,7180,7197,7198,2170,7212,2170,7238,2170,7251,7271,7272,7287],{},[883,7181,7183],{"className":7182},[886],[888,7184,7185],{"xmlns":890},[892,7186,7187,7195],{},[895,7188,7189,7191,7193],{},[898,7190,4509],{},[1688,7192,3665],{},[1793,7194,1795],{},[902,7196,4765],{"encoding":904}," (elastická) ",[883,7199,7201],{"className":7200},[886],[888,7202,7203],{"xmlns":890},[892,7204,7205,7209],{},[895,7206,7207],{},[1688,7208,4244],{},[902,7210,7211],{"encoding":904},"\\Rightarrow",[883,7213,7215],{"className":7214},[886],[888,7216,7217],{"xmlns":890},[892,7218,7219,7235],{},[895,7220,7221,7223,7225,7227,7229,7231,7233],{},[1793,7222,1795],{},[1688,7224,1954],{},[1793,7226,1795],{},[898,7228,4930],{"mathvariant":1822},[898,7230,4509],{},[1688,7232,3665],{},[1793,7234,1779],{},[902,7236,7237],{"encoding":904},"1 - 1\u002FE > 0",[883,7239,7241],{"className":7240},[886],[888,7242,7243],{"xmlns":890},[892,7244,7245,7249],{},[895,7246,7247],{},[1688,7248,4244],{},[902,7250,7211],{"encoding":904},[883,7252,7254],{"className":7253},[886],[888,7255,7256],{"xmlns":890},[892,7257,7258,7268],{},[895,7259,7260,7262,7264,7266],{},[898,7261,1661],{},[898,7263,4251],{},[1688,7265,3665],{},[1793,7267,1779],{},[902,7269,7270],{"encoding":904},"MR > 0"," — ",[883,7273,7275],{"className":7274},[886],[888,7276,7277],{"xmlns":890},[892,7278,7279,7285],{},[895,7280,7281,7283],{},[898,7282,3035],{},[898,7284,4251],{},[902,7286,4351],{"encoding":904}," roste s množstvím, tj. klesá s cenou.",[123,7289,7290,7307,7308,2170,7321,7271,7341,7356],{},[883,7291,7293],{"className":7292},[886],[888,7294,7295],{"xmlns":890},[892,7296,7297,7305],{},[895,7298,7299,7301,7303],{},[898,7300,4509],{},[1688,7302,1690],{},[1793,7304,1795],{},[902,7306,4801],{"encoding":904}," (jednotková) ",[883,7309,7311],{"className":7310},[886],[888,7312,7313],{"xmlns":890},[892,7314,7315,7319],{},[895,7316,7317],{},[1688,7318,4244],{},[902,7320,7211],{"encoding":904},[883,7322,7324],{"className":7323},[886],[888,7325,7326],{"xmlns":890},[892,7327,7328,7338],{},[895,7329,7330,7332,7334,7336],{},[898,7331,1661],{},[898,7333,4251],{},[1688,7335,1690],{},[1793,7337,1779],{},[902,7339,7340],{"encoding":904},"MR = 0",[883,7342,7344],{"className":7343},[886],[888,7345,7346],{"xmlns":890},[892,7347,7348,7354],{},[895,7349,7350,7352],{},[898,7351,3035],{},[898,7353,4251],{},[902,7355,4351],{"encoding":904}," je extrém (maximum).",[123,7358,7359,7376,7377,2170,7390,7271,7410,7425],{},[883,7360,7362],{"className":7361},[886],[888,7363,7364],{"xmlns":890},[892,7365,7366,7374],{},[895,7367,7368,7370,7372],{},[898,7369,4509],{},[1688,7371,3704],{},[1793,7373,1795],{},[902,7375,4783],{"encoding":904}," (neelastická) ",[883,7378,7380],{"className":7379},[886],[888,7381,7382],{"xmlns":890},[892,7383,7384,7388],{},[895,7385,7386],{},[1688,7387,4244],{},[902,7389,7211],{"encoding":904},[883,7391,7393],{"className":7392},[886],[888,7394,7395],{"xmlns":890},[892,7396,7397,7407],{},[895,7398,7399,7401,7403,7405],{},[898,7400,1661],{},[898,7402,4251],{},[1688,7404,3704],{},[1793,7406,1779],{},[902,7408,7409],{"encoding":904},"MR \u003C 0",[883,7411,7413],{"className":7412},[886],[888,7414,7415],{"xmlns":890},[892,7416,7417,7423],{},[895,7418,7419,7421],{},[898,7420,3035],{},[898,7422,4251],{},[902,7424,4351],{"encoding":904}," klesá s množstvím, tj. roste s cenou.",[724,7427,7428,7429,2263],{},"Viz také ",[207,7430,4079],{"className":7431,"dataFsResolvedFilePath":827,"href":828},[210],[198,7433,7435],{"id":7434},"pravidla-13-odvození-z-412","Pravidla 1–3 (odvození z (4.12))",[724,7437,7438,7458,7459,7485,7486,7501,7502,7515,7516,7529,7530,7543,7544,7560,7561,2170,7576,7579,7580,7560,7596,2263],{},[38,7439,7440,7441,4176],{},"(a) Poptávka elastická (",[883,7442,7444],{"className":7443},[886],[888,7445,7446],{"xmlns":890},[892,7447,7448,7456],{},[895,7449,7450,7452,7454],{},[898,7451,4509],{},[1688,7453,3665],{},[1793,7455,1795],{},[902,7457,4765],{"encoding":904}," Z (4.12) plyne ",[883,7460,7462],{"className":7461},[886],[888,7463,7464],{"xmlns":890},[892,7465,7466,7482],{},[895,7467,7468,7470,7472,7474,7476,7478,7480],{},[898,7469,1661],{},[898,7471,4251],{},[1688,7473,2066],{"stretchy":2065},[898,7475,1872],{},[1688,7477,2076],{"stretchy":2065},[1688,7479,3665],{},[1793,7481,1779],{},[902,7483,7484],{"encoding":904},"MR(Q) > 0",", a tedy celkový příjem ",[883,7487,7489],{"className":7488},[886],[888,7490,7491],{"xmlns":890},[892,7492,7493,7499],{},[895,7494,7495,7497],{},[898,7496,3035],{},[898,7498,4251],{},[902,7500,4351],{"encoding":904}," je rostoucí funkcí ",[883,7503,7505],{"className":7504},[886],[888,7506,7507],{"xmlns":890},[892,7508,7509,7513],{},[895,7510,7511],{},[898,7512,1872],{},[902,7514,1872],{"encoding":904},". Avšak růst ",[883,7517,7519],{"className":7518},[886],[888,7520,7521],{"xmlns":890},[892,7522,7523,7527],{},[895,7524,7525],{},[898,7526,1872],{},[902,7528,1872],{"encoding":904}," je odezvou na pokles ceny ",[883,7531,7533],{"className":7532},[886],[888,7534,7535],{"xmlns":890},[892,7536,7537,7541],{},[895,7538,7539],{},[898,7540,1727],{},[902,7542,1727],{"encoding":904},". Tudíž s ",[614,7545,7546,7547],{},"poklesem ceny ",[883,7548,7550],{"className":7549},[886],[888,7551,7552],{"xmlns":890},[892,7553,7554,7558],{},[895,7555,7556],{},[898,7557,1727],{},[902,7559,1727],{"encoding":904}," celkový příjem ",[883,7562,7564],{"className":7563},[886],[888,7565,7566],{"xmlns":890},[892,7567,7568,7574],{},[895,7569,7570,7572],{},[898,7571,3035],{},[898,7573,4251],{},[902,7575,4351],{"encoding":904},[614,7577,7578],{},"roste"," a s ",[614,7581,7582,7583],{},"růstem ceny ",[883,7584,7586],{"className":7585},[886],[888,7587,7588],{"xmlns":890},[892,7589,7590,7594],{},[895,7591,7592],{},[898,7593,1727],{},[902,7595,1727],{"encoding":904},[614,7597,7598],{},"klesá",[4124,7600,7601],{},[724,7602,7603,7606],{},[38,7604,7605],{},"Pravidlo 1."," Je-li poptávka elastická, pak s poklesem ceny celkový příjem roste a s růstem ceny celkový příjem klesá.",[724,7608,7609,7458,7629,1343,7655,7670,7671,7684,7685,7698,7699,7712,7713,7560,7726,2170,7741,2263],{},[38,7610,7611,7612,4176],{},"(b) Poptávka neelastická (",[883,7613,7615],{"className":7614},[886],[888,7616,7617],{"xmlns":890},[892,7618,7619,7627],{},[895,7620,7621,7623,7625],{},[898,7622,4509],{},[1688,7624,3704],{},[1793,7626,1795],{},[902,7628,4783],{"encoding":904},[883,7630,7632],{"className":7631},[886],[888,7633,7634],{"xmlns":890},[892,7635,7636,7652],{},[895,7637,7638,7640,7642,7644,7646,7648,7650],{},[898,7639,1661],{},[898,7641,4251],{},[1688,7643,2066],{"stretchy":2065},[898,7645,1872],{},[1688,7647,2076],{"stretchy":2065},[1688,7649,3704],{},[1793,7651,1779],{},[902,7653,7654],{"encoding":904},"MR(Q) \u003C 0",[883,7656,7658],{"className":7657},[886],[888,7659,7660],{"xmlns":890},[892,7661,7662,7668],{},[895,7663,7664,7666],{},[898,7665,3035],{},[898,7667,4251],{},[902,7669,4351],{"encoding":904}," je klesající funkce ",[883,7672,7674],{"className":7673},[886],[888,7675,7676],{"xmlns":890},[892,7677,7678,7682],{},[895,7679,7680],{},[898,7681,1872],{},[902,7683,1872],{"encoding":904},", tj. s růstem ",[883,7686,7688],{"className":7687},[886],[888,7689,7690],{"xmlns":890},[892,7691,7692,7696],{},[895,7693,7694],{},[898,7695,1872],{},[902,7697,1872],{"encoding":904}," (s poklesem ceny ",[883,7700,7702],{"className":7701},[886],[888,7703,7704],{"xmlns":890},[892,7705,7706,7710],{},[895,7707,7708],{},[898,7709,1727],{},[902,7711,1727],{"encoding":904},") celkový příjem klesá. S růstem ceny ",[883,7714,7716],{"className":7715},[886],[888,7717,7718],{"xmlns":890},[892,7719,7720,7724],{},[895,7721,7722],{},[898,7723,1727],{},[902,7725,1727],{"encoding":904},[883,7727,7729],{"className":7728},[886],[888,7730,7731],{"xmlns":890},[892,7732,7733,7739],{},[895,7734,7735,7737],{},[898,7736,3035],{},[898,7738,4251],{},[902,7740,4351],{"encoding":904},[614,7742,7578],{},[4124,7744,7745],{},[724,7746,7747,7750],{},[38,7748,7749],{},"Pravidlo 2."," Je-li poptávka neelastická, pak s poklesem ceny celkový příjem klesá a s růstem ceny celkový příjem roste.",[724,7752,7753,7458,7773,7792,7793,7808,7809,7879,7880,4142,7908,7941,7942,5845,7970,7985,7986,2263],{},[38,7754,7755,7756,4176],{},"(c) Jednotková elasticita (",[883,7757,7759],{"className":7758},[886],[888,7760,7761],{"xmlns":890},[892,7762,7763,7771],{},[895,7764,7765,7767,7769],{},[898,7766,4509],{},[1688,7768,1690],{},[1793,7770,1795],{},[902,7772,4801],{"encoding":904},[883,7774,7776],{"className":7775},[886],[888,7777,7778],{"xmlns":890},[892,7779,7780,7790],{},[895,7781,7782,7784,7786,7788],{},[898,7783,1661],{},[898,7785,4251],{},[1688,7787,1690],{},[1793,7789,1779],{},[902,7791,7340],{"encoding":904}," — nutná podmínka extrému ",[883,7794,7796],{"className":7795},[886],[888,7797,7798],{"xmlns":890},[892,7799,7800,7806],{},[895,7801,7802,7804],{},[898,7803,3035],{},[898,7805,4251],{},[902,7807,4351],{"encoding":904},". Dále ",[883,7810,7812],{"className":7811},[886],[888,7813,7814],{"xmlns":890},[892,7815,7816,7876],{},[895,7817,7818,7820,7830,7832,7834,7840,7842,7848,7850,7852,7854,7856,7858,7860,7870,7872,7874],{},[898,7819,3035],{},[1850,7821,7822,7824],{},[898,7823,4251],{},[895,7825,7826,7828],{},[1688,7827,1824],{"mathvariant":1822},[1688,7829,1824],{"mathvariant":1822},[1688,7831,1690],{},[898,7833,1661],{},[1850,7835,7836,7838],{},[898,7837,4251],{},[1688,7839,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,7841,1690],{},[1850,7843,7844,7846],{},[898,7845,4440],{},[1688,7847,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,7849,2066],{"stretchy":2065},[898,7851,1872],{},[1688,7853,2076],{"stretchy":2065},[1688,7855,1696],{},[898,7857,1872],{},[2041,7859,2043],{},[1850,7861,7862,7864],{},[898,7863,4440],{},[895,7865,7866,7868],{},[1688,7867,1824],{"mathvariant":1822},[1688,7869,1824],{"mathvariant":1822},[1688,7871,2066],{"stretchy":2065},[898,7873,1872],{},[1688,7875,2076],{"stretchy":2065},[902,7877,7878],{"encoding":904},"TR'' = MR' = D'(Q) + Q\\,D''(Q)","; za normálních podmínek ",[883,7881,7883],{"className":7882},[886],[888,7884,7885],{"xmlns":890},[892,7886,7887,7905],{},[895,7888,7889,7895,7897,7899,7901,7903],{},[1850,7890,7891,7893],{},[898,7892,4440],{},[1688,7894,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,7896,2066],{"stretchy":2065},[898,7898,1872],{},[1688,7900,2076],{"stretchy":2065},[1688,7902,3704],{},[1793,7904,1779],{},[902,7906,7907],{"encoding":904},"D'(Q) \u003C 0",[883,7909,7911],{"className":7910},[886],[888,7912,7913],{"xmlns":890},[892,7914,7915,7938],{},[895,7916,7917,7927,7929,7931,7933,7936],{},[1850,7918,7919,7921],{},[898,7920,4440],{},[895,7922,7923,7925],{},[1688,7924,1824],{"mathvariant":1822},[1688,7926,1824],{"mathvariant":1822},[1688,7928,2066],{"stretchy":2065},[898,7930,1872],{},[1688,7932,2076],{"stretchy":2065},[1688,7934,7935],{},"≤",[1793,7937,1779],{},[902,7939,7940],{"encoding":904},"D''(Q) \\le 0",", odkud ",[883,7943,7945],{"className":7944},[886],[888,7946,7947],{"xmlns":890},[892,7948,7949,7967],{},[895,7950,7951,7953,7963,7965],{},[898,7952,3035],{},[1850,7954,7955,7957],{},[898,7956,4251],{},[895,7958,7959,7961],{},[1688,7960,1824],{"mathvariant":1822},[1688,7962,1824],{"mathvariant":1822},[1688,7964,3704],{},[1793,7966,1779],{},[902,7968,7969],{"encoding":904},"TR'' \u003C 0",[883,7971,7973],{"className":7972},[886],[888,7974,7975],{"xmlns":890},[892,7976,7977,7983],{},[895,7978,7979,7981],{},[898,7980,3035],{},[898,7982,4251],{},[902,7984,4351],{"encoding":904}," nabývá ",[38,7987,7988],{},"maxima",[4124,7990,7991],{},[724,7992,7993,7996],{},[38,7994,7995],{},"Pravidlo 3."," Celkový příjem nabývá maxima při ceně, pro kterou je poptávka jednotkově elastická.",[724,7998,7999],{},"Tato tři pravidla potvrzují hypotézu (4.1) a jsou klíčem k regulaci ceny za účelem zvýšení (maximalizace) celkového příjmu.",[724,8001,8002],{},[38,8003,8004],{},"Souhrnná tabulka Pravidel 1–3:",[16,8006,8007,8111],{},[19,8008,8009],{},[22,8010,8011,8014,8029,8046,8077,8108],{},[25,8012,8013],{},"Charakter poptávky",[25,8015,8016],{},[883,8017,8019],{"className":8018},[886],[888,8020,8021],{"xmlns":890},[892,8022,8023,8027],{},[895,8024,8025],{},[898,8026,4509],{},[902,8028,4509],{"encoding":904},[25,8030,8031],{},[883,8032,8034],{"className":8033},[886],[888,8035,8036],{"xmlns":890},[892,8037,8038,8044],{},[895,8039,8040,8042],{},[898,8041,1661],{},[898,8043,4251],{},[902,8045,6890],{"encoding":904},[25,8047,8048,8049,2170,8062],{},"Pokles ceny ",[883,8050,8052],{"className":8051},[886],[888,8053,8054],{"xmlns":890},[892,8055,8056,8060],{},[895,8057,8058],{},[1688,8059,4244],{},[902,8061,7211],{"encoding":904},[883,8063,8065],{"className":8064},[886],[888,8066,8067],{"xmlns":890},[892,8068,8069,8075],{},[895,8070,8071,8073],{},[898,8072,3035],{},[898,8074,4251],{},[902,8076,4351],{"encoding":904},[25,8078,8079,8080,2170,8093],{},"Růst ceny ",[883,8081,8083],{"className":8082},[886],[888,8084,8085],{"xmlns":890},[892,8086,8087,8091],{},[895,8088,8089],{},[1688,8090,4244],{},[902,8092,7211],{"encoding":904},[883,8094,8096],{"className":8095},[886],[888,8097,8098],{"xmlns":890},[892,8099,8100,8106],{},[895,8101,8102,8104],{},[898,8103,3035],{},[898,8105,4251],{},[902,8107,4351],{"encoding":904},[25,8109,8110],{},"Doporučení",[30,8112,8113,8162,8212],{},[22,8114,8115,8117,8135,8153,8155,8157],{},[35,8116,4330],{},[35,8118,8119],{},[883,8120,8122],{"className":8121},[886],[888,8123,8124],{"xmlns":890},[892,8125,8126,8132],{},[895,8127,8128,8130],{},[1688,8129,3665],{},[1793,8131,1795],{},[902,8133,8134],{"encoding":904},"> 1",[35,8136,8137],{},[883,8138,8140],{"className":8139},[886],[888,8141,8142],{"xmlns":890},[892,8143,8144,8150],{},[895,8145,8146,8148],{},[1688,8147,3665],{},[1793,8149,1779],{},[902,8151,8152],{"encoding":904},"> 0",[35,8154,7578],{},[35,8156,7598],{},[35,8158,8159],{},[38,8160,8161],{},"snížit cenu",[22,8163,8164,8167,8185,8203,8205,8207],{},[35,8165,8166],{},"jednotková",[35,8168,8169],{},[883,8170,8172],{"className":8171},[886],[888,8173,8174],{"xmlns":890},[892,8175,8176,8182],{},[895,8177,8178,8180],{},[1688,8179,1690],{},[1793,8181,1795],{},[902,8183,8184],{"encoding":904},"= 1",[35,8186,8187],{},[883,8188,8190],{"className":8189},[886],[888,8191,8192],{"xmlns":890},[892,8193,8194,8200],{},[895,8195,8196,8198],{},[1688,8197,1690],{},[1793,8199,1779],{},[902,8201,8202],{"encoding":904},"= 0",[35,8204,3974],{},[35,8206,3974],{},[35,8208,8209],{},[38,8210,8211],{},"držet cenu",[22,8213,8214,8216,8234,8252,8254,8256],{},[35,8215,4334],{},[35,8217,8218],{},[883,8219,8221],{"className":8220},[886],[888,8222,8223],{"xmlns":890},[892,8224,8225,8231],{},[895,8226,8227,8229],{},[1688,8228,3704],{},[1793,8230,1795],{},[902,8232,8233],{"encoding":904},"\u003C 1",[35,8235,8236],{},[883,8237,8239],{"className":8238},[886],[888,8240,8241],{"xmlns":890},[892,8242,8243,8249],{},[895,8244,8245,8247],{},[1688,8246,3704],{},[1793,8248,1779],{},[902,8250,8251],{"encoding":904},"\u003C 0",[35,8253,7598],{},[35,8255,7578],{},[35,8257,8258],{},[38,8259,8260],{},"zvýšit cenu",[198,8262,8264],{"id":8263},"příklad-46-aplikace-pravidel-13","Příklad 4.6 — aplikace Pravidel 1–3",[724,8266,8267,8268,8293,8294,8316,8317,8330,8331,8344,8345,8358,8359,5845,8386,8438],{},"Aplikujme pravidla 1–3 pro poptávku ",[883,8269,8271],{"className":8270},[886],[888,8272,8273],{"xmlns":890},[892,8274,8275,8291],{},[895,8276,8277,8279,8281,8283,8285],{},[898,8278,1727],{},[1688,8280,1690],{},[1793,8282,3347],{},[1688,8284,1954],{},[1850,8286,8287,8289],{},[898,8288,1872],{},[1793,8290,1806],{},[902,8292,5715],{"encoding":904},". Reálné cenové rozpětí je ",[883,8295,8297],{"className":8296},[886],[888,8298,8299],{"xmlns":890},[892,8300,8301,8313],{},[895,8302,8303,8305,8307,8309,8311],{},[1688,8304,5580],{"stretchy":2065},[1793,8306,1795],{},[1688,8308,1733],{"separator":1732},[1793,8310,3347],{},[1688,8312,5597],{"stretchy":2065},[902,8314,8315],{"encoding":904},"\\langle 1, 100\\rangle",". Pro výpočet elasticity vyjádříme ",[883,8318,8320],{"className":8319},[886],[888,8321,8322],{"xmlns":890},[892,8323,8324,8328],{},[895,8325,8326],{},[898,8327,1872],{},[902,8329,1872],{"encoding":904}," jako funkci ",[883,8332,8334],{"className":8333},[886],[888,8335,8336],{"xmlns":890},[892,8337,8338,8342],{},[895,8339,8340],{},[898,8341,1727],{},[902,8343,1727],{"encoding":904},"; pro nezáporné ",[883,8346,8348],{"className":8347},[886],[888,8349,8350],{"xmlns":890},[892,8351,8352,8356],{},[895,8353,8354],{},[898,8355,1872],{},[902,8357,1872],{"encoding":904}," je ",[883,8360,8362],{"className":8361},[886],[888,8363,8364],{"xmlns":890},[892,8365,8366,8383],{},[895,8367,8368,8370,8372],{},[898,8369,1872],{},[1688,8371,1690],{},[8373,8374,8375],"msqrt",{},[895,8376,8377,8379,8381],{},[1793,8378,3347],{},[1688,8380,1954],{},[898,8382,1727],{},[902,8384,8385],{"encoding":904},"Q = \\sqrt{100 - P}",[883,8387,8389],{"className":8388},[886],[888,8390,8391],{"xmlns":890},[892,8392,8393,8435],{},[895,8394,8395,8411,8413,8415],{},[1777,8396,8397],{"scriptlevel":1779,"displaystyle":1732},[1781,8398,8399,8405],{},[895,8400,8401,8403],{},[898,8402,2073],{"mathvariant":1822},[898,8404,1872],{},[895,8406,8407,8409],{},[898,8408,2073],{"mathvariant":1822},[898,8410,1727],{},[1688,8412,1690],{},[1688,8414,1954],{},[1777,8416,8417],{"scriptlevel":1779,"displaystyle":1732},[1781,8418,8419,8421],{},[1793,8420,1795],{},[895,8422,8423,8425],{},[1793,8424,1806],{},[8373,8426,8427],{},[895,8428,8429,8431,8433],{},[1793,8430,3347],{},[1688,8432,1954],{},[898,8434,1727],{},[902,8436,8437],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\dfrac{1}{2\\sqrt{100-P}}",". Podle (4.5):",[724,8440,8441],{},[883,8442,8444],{"className":8443},[886],[888,8445,8446],{"xmlns":890},[892,8447,8448,8570],{},[895,8449,8450,8452,8454,8456,8458,8460,8462,8468,8470,8484,8486,8488,8502,8504,8530,8532,8550,8552,8568],{},[898,8451,4509],{},[1688,8453,2066],{"stretchy":2065},[898,8455,1727],{},[1688,8457,2076],{"stretchy":2065},[1688,8459,1690],{},[1688,8461,1954],{},[1781,8463,8464,8466],{},[898,8465,1727],{},[898,8467,1872],{},[1688,8469,3434],{},[1781,8471,8472,8478],{},[895,8473,8474,8476],{},[898,8475,2073],{"mathvariant":1822},[898,8477,1872],{},[895,8479,8480,8482],{},[898,8481,2073],{"mathvariant":1822},[898,8483,1727],{},[1688,8485,1690],{},[1688,8487,1954],{},[1781,8489,8490,8492],{},[898,8491,1727],{},[8373,8493,8494],{},[895,8495,8496,8498,8500],{},[1793,8497,3347],{},[1688,8499,1954],{},[898,8501,1727],{},[1688,8503,3434],{},[895,8505,8506,8508,8510,8528],{},[1688,8507,2066],{"fence":1732},[1688,8509,1954],{},[1781,8511,8512,8514],{},[1793,8513,1795],{},[895,8515,8516,8518],{},[1793,8517,1806],{},[8373,8519,8520],{},[895,8521,8522,8524,8526],{},[1793,8523,3347],{},[1688,8525,1954],{},[898,8527,1727],{},[1688,8529,2076],{"fence":1732},[1688,8531,1690],{},[1781,8533,8534,8536],{},[898,8535,1727],{},[895,8537,8538,8540,8542,8544,8546,8548],{},[1793,8539,1806],{},[1688,8541,2066],{"stretchy":2065},[1793,8543,3347],{},[1688,8545,1954],{},[898,8547,1727],{},[1688,8549,2076],{"stretchy":2065},[1688,8551,1690],{},[1781,8553,8554,8560],{},[895,8555,8556,8558],{},[1793,8557,5265],{},[898,8559,1727],{},[895,8561,8562,8564,8566],{},[1793,8563,3347],{},[1688,8565,1954],{},[898,8567,1727],{},[898,8569,2263],{"mathvariant":1822},[902,8571,8572],{"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}.",[724,8574,8575,8576,2965],{},"Stanovíme cenu, při které je poptávka jednotkově elastická. Řešíme ",[883,8577,8579],{"className":8578},[886],[888,8580,8581],{"xmlns":890},[892,8582,8583,8607],{},[895,8584,8585,8603,8605],{},[1777,8586,8587],{"scriptlevel":1779,"displaystyle":1732},[1781,8588,8589,8595],{},[895,8590,8591,8593],{},[1793,8592,5265],{},[898,8594,1727],{},[895,8596,8597,8599,8601],{},[1793,8598,3347],{},[1688,8600,1954],{},[898,8602,1727],{},[1688,8604,1690],{},[1793,8606,1795],{},[902,8608,8609],{"encoding":904},"\\dfrac{0{,}5P}{100-P} = 1",[724,8611,8612],{},[883,8613,8615],{"className":8614},[886],[888,8616,8617],{"xmlns":890},[892,8618,8619,8651],{},[895,8620,8621,8627,8629,8636,8638,8641,8649],{},[1850,8622,8623,8625],{},[898,8624,1727],{},[1688,8626,1857],{},[1688,8628,1690],{},[1781,8630,8631,8634],{},[1793,8632,8633],{},"200",[1793,8635,2131],{},[1688,8637,6156],{},[1793,8639,8640],{},"66,",[8642,8643,8644,8646],"mover",{"accent":1732},[1793,8645,2508],{},[1688,8647,8648],{"stretchy":1732},"‾",[898,8650,2263],{"mathvariant":1822},[902,8652,8653],{"encoding":904},"P^* = \\frac{200}{3} \\doteq 66{,}\\overline{6}.",[724,8655,8656],{},"S využitím vlastnosti (4.8):",[120,8658,8659,8705,8747],{},[123,8660,8661,8662,8697,8698,8700,8701,8704],{},"Při cenách ",[883,8663,8665],{"className":8664},[886],[888,8666,8667],{"xmlns":890},[892,8668,8669,8694],{},[895,8670,8671,8673,8675,8677,8679,8682,8684,8686,8692],{},[898,8672,1727],{},[1688,8674,6762],{},[1688,8676,5580],{"stretchy":2065},[1793,8678,1795],{},[1688,8680,8681],{"separator":1732},";",[2041,8683,2043],{},[1793,8685,8640],{},[8642,8687,8688,8690],{"accent":1732},[1793,8689,2508],{},[1688,8691,8648],{"stretchy":1732},[1688,8693,2076],{"stretchy":2065},[902,8695,8696],{"encoding":904},"P \\in \\langle 1;\\, 66{,}\\overline{6})"," je poptávka ",[38,8699,4334],{}," — dle ",[614,8702,8703],{},"Pravidla 2"," přiměřené zvýšení ceny zvýší celkový příjem.",[123,8706,8661,8707,8697,8741,8700,8743,8746],{},[883,8708,8710],{"className":8709},[886],[888,8711,8712],{"xmlns":890},[892,8713,8714,8738],{},[895,8715,8716,8718,8720,8722,8724,8730,8732,8734,8736],{},[898,8717,1727],{},[1688,8719,6762],{},[1688,8721,2066],{"stretchy":2065},[1793,8723,8640],{},[8642,8725,8726,8728],{"accent":1732},[1793,8727,2508],{},[1688,8729,8648],{"stretchy":1732},[1688,8731,8681],{"separator":1732},[2041,8733,2043],{},[1793,8735,3347],{},[1688,8737,5597],{"stretchy":2065},[902,8739,8740],{"encoding":904},"P \\in (66{,}\\overline{6};\\, 100\\rangle",[38,8742,4330],{},[614,8744,8745],{},"Pravidla 1"," přiměřené snížení ceny povede ke zvýšení celkového příjmu.",[123,8748,8749,8750,8753,8754,8782,8783,8786],{},"Dle ",[614,8751,8752],{},"Pravidla 3"," je při ceně ",[883,8755,8757],{"className":8756},[886],[888,8758,8759],{"xmlns":890},[892,8760,8761,8779],{},[895,8762,8763,8769,8771,8773],{},[1850,8764,8765,8767],{},[898,8766,1727],{},[1688,8768,1857],{},[1688,8770,1690],{},[1793,8772,8640],{},[8642,8774,8775,8777],{"accent":1732},[1793,8776,2508],{},[1688,8778,8648],{"stretchy":1732},[902,8780,8781],{"encoding":904},"P^* = 66{,}\\overline{6}"," dosaženo ",[38,8784,8785],{},"maxima celkového příjmu"," ve výši",[724,8788,8789],{},[883,8790,8792],{"className":8791},[886],[888,8793,8794],{"xmlns":890},[892,8795,8796,8874],{},[895,8797,8798,8800,8802,8804,8810,8812,8814,8820,8822,8836,8838,8844,8846,8854,8856,8869,8871],{},[898,8799,3035],{},[898,8801,4251],{},[1688,8803,2066],{"stretchy":2065},[1850,8805,8806,8808],{},[898,8807,1727],{},[1688,8809,1857],{},[1688,8811,2076],{"stretchy":2065},[1688,8813,1690],{},[1850,8815,8816,8818],{},[898,8817,1727],{},[1688,8819,1857],{},[1688,8821,3434],{},[8373,8823,8824],{},[895,8825,8826,8828,8830],{},[1793,8827,3347],{},[1688,8829,1954],{},[1850,8831,8832,8834],{},[898,8833,1727],{},[1688,8835,1857],{},[1688,8837,1690],{},[1781,8839,8840,8842],{},[1793,8841,8633],{},[1793,8843,2131],{},[1688,8845,3434],{},[8373,8847,8848],{},[1781,8849,8850,8852],{},[1793,8851,3347],{},[1793,8853,2131],{},[1688,8855,1690],{},[1781,8857,8858,8861],{},[1793,8859,8860],{},"2000",[895,8862,8863,8865],{},[1793,8864,2131],{},[8373,8866,8867],{},[1793,8868,2131],{},[1688,8870,6156],{},[1793,8872,8873],{},"384,9.",[902,8875,8876],{"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.",[724,8878,8879,8880,2263],{},"Ke stejnému výsledku bychom dospěli přímým hledáním maxima funkce ",[883,8881,8883],{"className":8882},[886],[888,8884,8885],{"xmlns":890},[892,8886,8887,8893],{},[895,8888,8889,8891],{},[898,8890,3035],{},[898,8892,4251],{},[902,8894,4351],{"encoding":904},[115,8896,8898],{"id":8897},"cenová-elasticita-nabídky","Cenová elasticita nabídky",[724,8900,8901,8902,8905],{},"Analogicky se definuje ",[38,8903,8904],{},"cenová elasticita nabídky"," (price elasticity of supply):",[724,8907,8908],{},[883,8909,8911],{"className":8910,"title":4457,"style":4458},[4456],"\\boxed{\\;E = E(P) = \\frac{P}{Q}\\cdot\\frac{\\mathrm{d}Q}{\\mathrm{d}P}\\;} \\tag{4.13}",[724,8913,4567,8914,8938,8939,8971],{},[883,8915,8917],{"className":8916},[886],[888,8918,8919],{"xmlns":890},[892,8920,8921,8935],{},[895,8922,8923,8925,8927,8929,8931,8933],{},[898,8924,1872],{},[1688,8926,1690],{},[898,8928,1740],{},[1688,8930,2066],{"stretchy":2065},[898,8932,1727],{},[1688,8934,2076],{"stretchy":2065},[902,8936,8937],{"encoding":904},"Q = S(P)"," je funkce nabídky. Protože nabídka je rostoucí, ",[883,8940,8942],{"className":8941},[886],[888,8943,8944],{"xmlns":890},[892,8945,8946,8968],{},[895,8947,8948,8964,8966],{},[1777,8949,8950],{"scriptlevel":1779,"displaystyle":1732},[1781,8951,8952,8958],{},[895,8953,8954,8956],{},[898,8955,2073],{"mathvariant":1822},[898,8957,1872],{},[895,8959,8960,8962],{},[898,8961,2073],{"mathvariant":1822},[898,8963,1727],{},[1688,8965,3665],{},[1793,8967,1779],{},[902,8969,8970],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} > 0",", a elasticita nabídky je vždy nezáporná — proto zde není znaménková korekce jako u poptávky.",[724,8973,8974],{},"Klasifikace na elastickou \u002F jednotkově elastickou \u002F neelastickou je analogická jako u poptávky (tabulka (4.7)). Platí paralela k (4.8):",[4124,8976,8977],{},[724,8978,8979,8980],{},"S rostoucí cenou elasticita nabídky roste. ",[883,8981,8983],{"className":8982},[886],[888,8984,8985],{"xmlns":890},[892,8986,8987,8996],{},[895,8988,8989,8991,8994],{},[1688,8990,2066],{"stretchy":2065},[1793,8992,8993],{},"4.14",[1688,8995,2076],{"stretchy":2065},[902,8997,8998],{"encoding":904},"(4.14)",[724,9000,9001],{},"Pro nominální změny platí",[724,9003,9004],{},[883,9005,9007],{"className":9006,"title":4457,"style":4458},[4456],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P, \\qquad \\mathrm{d}P = \\Delta P, \\tag{4.15}",[724,9009,9010],{},"a pro procentní změny",[724,9012,9013],{},[883,9014,9016],{"className":9015,"title":4457,"style":4458},[4456],"\\boxed{\\;\\Delta Q\\% \\approx E(P)\\,\\Delta P\\%\\;} \\tag{4.16}",[724,9018,9019],{},"(bez znaménka minus).",[198,9021,9023],{"id":9022},"příklad-47","Příklad 4.7",[724,9025,9026,9027,2965],{},"Nabídka ",[883,9028,9030],{"className":9029},[886],[888,9031,9032],{"xmlns":890},[892,9033,9034,9059],{},[895,9035,9036,9038,9040,9042,9048,9050,9052,9054,9056],{},[898,9037,1872],{},[1688,9039,1690],{},[1793,9041,3053],{},[1850,9043,9044,9046],{},[898,9045,1727],{},[1793,9047,1806],{},[1688,9049,1696],{},[1793,9051,2501],{},[898,9053,1727],{},[1688,9055,1696],{},[1793,9057,9058],{},"150",[902,9060,9061],{"encoding":904},"Q = 0{,}1P^2 + 5P + 150",[724,9063,9064],{},[883,9065,9067],{"className":9066},[886],[888,9068,9069],{"xmlns":890},[892,9070,9071,9117],{},[895,9072,9073,9075,9077,9101,9103,9105,9107,9109,9111,9113,9115],{},[898,9074,4509],{},[1688,9076,1690],{},[1781,9078,9079,9081],{},[898,9080,1727],{},[895,9082,9083,9085,9091,9093,9095,9097,9099],{},[1793,9084,3053],{},[1850,9086,9087,9089],{},[898,9088,1727],{},[1793,9090,1806],{},[1688,9092,1696],{},[1793,9094,2501],{},[898,9096,1727],{},[1688,9098,1696],{},[1793,9100,9058],{},[2041,9102,2043],{},[1688,9104,2066],{"stretchy":2065},[1793,9106,3097],{},[898,9108,1727],{},[1688,9110,1696],{},[1793,9112,2501],{},[1688,9114,2076],{"stretchy":2065},[898,9116,2263],{"mathvariant":1822},[902,9118,9119],{"encoding":904},"E = \\frac{P}{0{,}1P^2 + 5P + 150}\\,(0{,}2P + 5).",[724,9121,5373,9122,1343,9152,1343,9179,9215,9216,9241,9242,9260,9261,2263],{},[883,9123,9125],{"className":9124},[886],[888,9126,9127],{"xmlns":890},[892,9128,9129,9149],{},[895,9130,9131,9133,9135,9137,9139,9141],{},[898,9132,4509],{},[1688,9134,2066],{"stretchy":2065},[1793,9136,3121],{},[1688,9138,2076],{"stretchy":2065},[1688,9140,1690],{},[1777,9142,9143],{"scriptlevel":1779,"displaystyle":2065},[1781,9144,9145,9147],{},[1793,9146,1795],{},[1793,9148,2131],{},[902,9150,9151],{"encoding":904},"E(10) = \\tfrac{1}{3}",[883,9153,9155],{"className":9154},[886],[888,9156,9157],{"xmlns":890},[892,9158,9159,9176],{},[895,9160,9161,9163,9165,9170,9172,9174],{},[898,9162,4509],{},[1688,9164,2066],{"stretchy":2065},[8373,9166,9167],{},[1793,9168,9169],{},"1500",[1688,9171,2076],{"stretchy":2065},[1688,9173,1690],{},[1793,9175,1795],{},[902,9177,9178],{"encoding":904},"E(\\sqrt{1500}) = 1",[883,9180,9182],{"className":9181},[886],[888,9183,9184],{"xmlns":890},[892,9185,9186,9212],{},[895,9187,9188,9190,9192,9194,9196,9198,9207,9209],{},[898,9189,4509],{},[1688,9191,2066],{"stretchy":2065},[1793,9193,3347],{},[1688,9195,2076],{"stretchy":2065},[1688,9197,1690],{},[1777,9199,9200],{"scriptlevel":1779,"displaystyle":2065},[1781,9201,9202,9204],{},[1793,9203,3377],{},[1793,9205,9206],{},"33",[1688,9208,6156],{},[1793,9210,9211],{},"1,515",[902,9213,9214],{"encoding":904},"E(100) = \\tfrac{50}{33} \\doteq 1{,}515",". Dle (4.14): pro ",[883,9217,9219],{"className":9218},[886],[888,9220,9221],{"xmlns":890},[892,9222,9223,9238],{},[895,9224,9225,9227,9229,9233,9235],{},[898,9226,1727],{},[1688,9228,3665],{},[8373,9230,9231],{},[1793,9232,9169],{},[1688,9234,2991],{},[1793,9236,9237],{},"38,7",[902,9239,9240],{"encoding":904},"P > \\sqrt{1500} \\approx 38{,}7"," je nabídka elastická, pro ",[883,9243,9245],{"className":9244},[886],[888,9246,9247],{"xmlns":890},[892,9248,9249,9257],{},[895,9250,9251,9253,9255],{},[898,9252,1727],{},[1688,9254,3704],{},[1793,9256,9237],{},[902,9258,9259],{"encoding":904},"P \u003C 38{,}7"," neelastická. Zvýší-li se cena z 10 o 20 %, pak ",[883,9262,9264],{"className":9263},[886],[888,9265,9266],{"xmlns":890},[892,9267,9268,9306],{},[895,9269,9270,9272,9274,9276,9278,9286,9288,9291,9293,9296,9302,9304],{},[898,9271,3147],{"mathvariant":1822},[898,9273,1872],{},[898,9275,6181],{"mathvariant":1822},[1688,9277,2991],{},[1777,9279,9280],{"scriptlevel":1779,"displaystyle":2065},[1781,9281,9282,9284],{},[1793,9283,1795],{},[1793,9285,2131],{},[1688,9287,3434],{},[1793,9289,9290],{},"20",[1688,9292,1690],{},[1793,9294,9295],{},"6,",[8642,9297,9298,9300],{"accent":1732},[1793,9299,2508],{},[1688,9301,8648],{"stretchy":1732},[2041,9303,2043],{},[898,9305,6181],{"mathvariant":1822},[902,9307,9308],{"encoding":904},"\\Delta Q\\% \\approx \\tfrac{1}{3}\\cdot 20 = 6{,}\\overline{6}\\,\\%",[115,9310,9312],{"id":9311},"vícefaktorový-model","Vícefaktorový model",[724,9314,9315,9316,9329,9330,2170,9333,9346,9347,2170,9350,9368,9369,2170,9372,2965],{},"Předpokládejme, že poptávané množství ",[883,9317,9319],{"className":9318},[886],[888,9320,9321],{"xmlns":890},[892,9322,9323,9327],{},[895,9324,9325],{},[898,9326,1872],{},[902,9328,1872],{"encoding":904}," závisí na ",[38,9331,9332],{},"ceně základního zboží",[883,9334,9336],{"className":9335},[886],[888,9337,9338],{"xmlns":890},[892,9339,9340,9344],{},[895,9341,9342],{},[898,9343,1727],{},[902,9345,1727],{"encoding":904},", na ",[38,9348,9349],{},"ceně alternativního zboží",[883,9351,9353],{"className":9352},[886],[888,9354,9355],{"xmlns":890},[892,9356,9357,9365],{},[895,9358,9359],{},[1788,9360,9361,9363],{},[898,9362,1727],{},[898,9364,4512],{},[902,9366,9367],{"encoding":904},"P_A"," a na ",[38,9370,9371],{},"důchodu",[883,9373,9375],{"className":9374},[886],[888,9376,9377],{"xmlns":890},[892,9378,9379,9383],{},[895,9380,9381],{},[898,9382,1854],{},[902,9384,1854],{"encoding":904},[724,9386,9387],{},[883,9388,9390],{"className":9389,"title":4457,"style":4458},[4456],"Q = D(P, P_A, Y). \\tag{4.17}",[724,9392,9393,9394,9397],{},"V analogii jednofaktorového modelu pracujeme s ",[38,9395,9396],{},"parciálními derivacemi"," funkce poptávky.",[198,9399,9401],{"id":9400},"cenová-elasticita-poptávky-vícefaktorová","Cenová elasticita poptávky (vícefaktorová)",[724,9403,9404],{},[883,9405,9407],{"className":9406,"title":4457,"style":4458},[4456],"\\boxed{\\;E_P = -\\frac{P}{Q}\\,Q'_P\\;} \\tag{4.18}",[724,9409,4567,9410,9430,9431,9444,9445,3185,9467,2170,9470,9516,9517,9530,9531,9548],{},[883,9411,9413],{"className":9412},[886],[888,9414,9415],{"xmlns":890},[892,9416,9417,9427],{},[895,9418,9419],{},[1814,9420,9421,9423,9425],{},[898,9422,1872],{},[898,9424,1727],{},[1688,9426,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[902,9428,9429],{"encoding":904},"Q'_P"," je parciální derivace (4.17) podle ",[883,9432,9434],{"className":9433},[886],[888,9435,9436],{"xmlns":890},[892,9437,9438,9442],{},[895,9439,9440],{},[898,9441,1727],{},[902,9443,1727],{"encoding":904},". Vždy ",[883,9446,9448],{"className":9447},[886],[888,9449,9450],{"xmlns":890},[892,9451,9452,9464],{},[895,9453,9454,9460,9462],{},[1788,9455,9456,9458],{},[898,9457,4509],{},[898,9459,1727],{},[1688,9461,4741],{},[1793,9463,1779],{},[902,9465,9466],{"encoding":904},"E_P \\ge 0",[614,9468,9469],{},"Interpretace:",[883,9471,9473],{"className":9472},[886],[888,9474,9475],{"xmlns":890},[892,9476,9477,9513],{},[895,9478,9479,9485,9487,9493,9495,9503,9505,9511],{},[1788,9480,9481,9483],{},[898,9482,4509],{},[898,9484,1727],{},[1688,9486,2066],{"stretchy":2065},[1850,9488,9489,9491],{},[898,9490,1727],{},[1688,9492,1857],{},[1688,9494,1733],{"separator":1732},[1814,9496,9497,9499,9501],{},[898,9498,1727],{},[898,9500,4512],{},[1688,9502,1857],{},[1688,9504,1733],{"separator":1732},[1850,9506,9507,9509],{},[898,9508,1854],{},[1688,9510,1857],{},[1688,9512,2076],{"stretchy":2065},[902,9514,9515],{"encoding":904},"E_P(P^*, P_A^*, Y^*)"," udává přibližnou procentní změnu ",[883,9518,9520],{"className":9519},[886],[888,9521,9522],{"xmlns":890},[892,9523,9524,9528],{},[895,9525,9526],{},[898,9527,1872],{},[902,9529,1872],{"encoding":904}," při 1% změně ",[883,9532,9534],{"className":9533},[886],[888,9535,9536],{"xmlns":890},[892,9537,9538,9546],{},[895,9539,9540],{},[1850,9541,9542,9544],{},[898,9543,1727],{},[1688,9545,1857],{},[902,9547,4660],{"encoding":904},", ceteris paribus.",[198,9550,9552],{"id":9551},"křížová-křížově-cenová-elasticita-poptávky","Křížová (křížově-cenová) elasticita poptávky",[724,9554,9555],{},[883,9556,9558],{"className":9557,"title":4457,"style":4458},[4456],"\\boxed{\\;E_{P_A} = \\frac{P_A}{Q}\\,Q'_{P_A}\\;} \\tag{4.19}",[724,9560,9561,9516,9563,9576,9577,9594],{},[614,9562,9469],{},[883,9564,9566],{"className":9565},[886],[888,9567,9568],{"xmlns":890},[892,9569,9570,9574],{},[895,9571,9572],{},[898,9573,1872],{},[902,9575,1872],{"encoding":904}," základního zboží při 1% změně ceny ",[883,9578,9580],{"className":9579},[886],[888,9581,9582],{"xmlns":890},[892,9583,9584,9592],{},[895,9585,9586],{},[1788,9587,9588,9590],{},[898,9589,1727],{},[898,9591,4512],{},[902,9593,9367],{"encoding":904}," alternativního zboží (ceteris paribus).",[724,9596,9597],{},[38,9598,9599],{},"Znaménko závisí na povaze alternativního zboží:",[120,9601,9602,9690],{},[123,9603,9604,9605,9608,9609,9626,9627,2170,9640,2263],{},"Je-li alternativní zboží ",[38,9606,9607],{},"komplement",", růst ",[883,9610,9612],{"className":9611},[886],[888,9613,9614],{"xmlns":890},[892,9615,9616,9624],{},[895,9617,9618],{},[1788,9619,9620,9622],{},[898,9621,1727],{},[898,9623,4512],{},[902,9625,9367],{"encoding":904}," způsobí zdražení dvojice, pokles ",[883,9628,9630],{"className":9629},[886],[888,9631,9632],{"xmlns":890},[892,9633,9634,9638],{},[895,9635,9636],{},[898,9637,1872],{},[902,9639,1872],{"encoding":904},[883,9641,9643],{"className":9642},[886],[888,9644,9645],{"xmlns":890},[892,9646,9647,9687],{},[895,9648,9649,9651,9653,9665,9667,9669,9671,9673,9683,9685],{},[1688,9650,4244],{},[2041,9652,4241],{},[1814,9654,9655,9657,9663],{},[898,9656,1872],{},[1788,9658,9659,9661],{},[898,9660,1727],{},[898,9662,4512],{},[1688,9664,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,9666,3704],{},[1793,9668,1779],{},[1688,9670,1733],{"separator":1732},[2041,9672,4241],{},[1788,9674,9675,9677],{},[898,9676,4509],{},[1788,9678,9679,9681],{},[898,9680,1727],{},[898,9682,4512],{},[1688,9684,3704],{},[1793,9686,1779],{},[902,9688,9689],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} \u003C 0,\\; E_{P_A} \u003C 0",[123,9691,9604,9692,9608,9695,9712,9713,9726,9727,2263],{},[38,9693,9694],{},"substitut",[883,9696,9698],{"className":9697},[886],[888,9699,9700],{"xmlns":890},[892,9701,9702,9710],{},[895,9703,9704],{},[1788,9705,9706,9708],{},[898,9707,1727],{},[898,9709,4512],{},[902,9711,9367],{"encoding":904}," učiní základní zboží relativně levnější, zájem se přesune, ",[883,9714,9716],{"className":9715},[886],[888,9717,9718],{"xmlns":890},[892,9719,9720,9724],{},[895,9721,9722],{},[898,9723,1872],{},[902,9725,1872],{"encoding":904}," roste ",[883,9728,9730],{"className":9729},[886],[888,9731,9732],{"xmlns":890},[892,9733,9734,9774],{},[895,9735,9736,9738,9740,9752,9754,9756,9758,9760,9770,9772],{},[1688,9737,4244],{},[2041,9739,4241],{},[1814,9741,9742,9744,9750],{},[898,9743,1872],{},[1788,9745,9746,9748],{},[898,9747,1727],{},[898,9749,4512],{},[1688,9751,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,9753,3665],{},[1793,9755,1779],{},[1688,9757,1733],{"separator":1732},[2041,9759,4241],{},[1788,9761,9762,9764],{},[898,9763,4509],{},[1788,9765,9766,9768],{},[898,9767,1727],{},[898,9769,4512],{},[1688,9771,3665],{},[1793,9773,1779],{},[902,9775,9776],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} > 0,\\; E_{P_A} > 0",[883,9778,9781],{"className":9779,"title":9780,"style":4458},[4456],"ParseError: KaTeX parse error: Expected 'EOF', got '&' at position 9: E_{P_A} &̲> 0 \\;\\;\\Leftri…","undefined",{"title":641,"searchDepth":642,"depth":642,"links":9783},[9784,9788,9789,9797,9798,9802,9805],{"id":4148,"depth":642,"text":4149,"children":9785},[9786,9787],{"id":4179,"depth":649,"text":4180},{"id":4359,"depth":649,"text":4360},{"id":4394,"depth":642,"text":4395},{"id":4420,"depth":642,"text":4421,"children":9790},[9791,9792,9793,9794,9796],{"id":5115,"depth":649,"text":5116},{"id":5205,"depth":649,"text":5206},{"id":5541,"depth":649,"text":5542},{"id":5623,"depth":649,"text":9795},"Výpočet, je-li dáno PP jako funkce QQ",{"id":5884,"depth":649,"text":5885},{"id":6209,"depth":642,"text":6210},{"id":6805,"depth":642,"text":6806,"children":9799},[9800,9801],{"id":7434,"depth":649,"text":7435},{"id":8263,"depth":649,"text":8264},{"id":8897,"depth":642,"text":8898,"children":9803},[9804],{"id":9022,"depth":649,"text":9023},{"id":9311,"depth":642,"text":9312,"children":9806},[9807,9808],{"id":9400,"depth":649,"text":9401},{"id":9551,"depth":649,"text":9552},"2026-04-22",{},"\u002Ftopics\u002Felasticita",{"title":4117,"description":641},[1138,1136],"topics\u002Felasticita",[1128,4155,9816,9817,9818,9819],"cenova-elasticita","krizova-elasticita","duchodova-elasticita","mr-tr","c_Ilj6dK9Ey4kbyp6EKogVl_p8zmryyIur0pCOtxlhM",{"id":9822,"title":9823,"body":9824,"course":1128,"courses":659,"created":1129,"description":11364,"extension":661,"meta":11365,"navigation":664,"path":11366,"seo":11367,"sources":11368,"stem":11369,"tags":11370,"type":4113,"updated":677,"__hash__":11375},"topics\u002Ftopics\u002Ffunkce-vice-promennych.md","Kalkul funkcí více proměnných",{"type":9,"value":9825,"toc":11349},[9826,9829,9903,9910,9914,9978,10066,10070,10097,10164,10219,10223,10250,10343,10345,10377,10548,10552,10622,10670,10674,10735,10841,10855,10859,10861,10889,10954,10956,10963,11051,11076,11274,11278,11314,11316],[12,9827,9823],{"id":9828},"kalkul-funkcí-více-proměnných",[724,9830,9831,9832,9835,9836,1343,9865,2263],{},"Většina ekonomických veličin závisí na ",[38,9833,9834],{},"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 ",[883,9837,9839],{"className":9838},[886],[888,9840,9841],{"xmlns":890},[892,9842,9843,9862],{},[895,9844,9845,9848,9850,9852,9854,9856,9858,9860],{},[898,9846,9847],{},"z",[1688,9849,1690],{},[898,9851,2287],{},[1688,9853,2066],{"stretchy":2065},[898,9855,2292],{},[1688,9857,1733],{"separator":1732},[898,9859,2282],{},[1688,9861,2076],{"stretchy":2065},[902,9863,9864],{"encoding":904},"z = f(x, y)",[883,9866,9868],{"className":9867},[886],[888,9869,9870],{"xmlns":890},[892,9871,9872,9900],{},[895,9873,9874,9877,9879,9881,9883,9885,9887,9889,9891,9893,9895,9897],{},[898,9875,9876],{},"w",[1688,9878,1690],{},[898,9880,2287],{},[1688,9882,2066],{"stretchy":2065},[898,9884,2292],{},[1688,9886,1733],{"separator":1732},[898,9888,2282],{},[1688,9890,1733],{"separator":1732},[898,9892,9847],{},[1688,9894,2076],{"stretchy":2065},[1688,9896,1733],{"separator":1732},[1688,9898,9899],{},"…",[902,9901,9902],{"encoding":904},"w = f(x, y, z), \\ldots",[724,9904,9905],{},[2821,9906],{"alt":9907,"className":9908,"src":9909},"imek-funkce-2d-vrstevnice",[210,2825],"\u002Fwiki-assets\u002Fimek-funkce-2d-vrstevnice.jpeg",[115,9911,9913],{"id":9912},"indiferenční-izokvantové-křivky","Indiferenční \u002F izokvantové křivky",[724,9915,9916,9917,9944,9945,9973,9974,9977],{},"Pro ",[883,9918,9920],{"className":9919},[886],[888,9921,9922],{"xmlns":890},[892,9923,9924,9942],{},[895,9925,9926,9928,9930,9932,9934,9936,9938,9940],{},[898,9927,9847],{},[1688,9929,1690],{},[898,9931,2287],{},[1688,9933,2066],{"stretchy":2065},[898,9935,2292],{},[1688,9937,1733],{"separator":1732},[898,9939,2282],{},[1688,9941,2076],{"stretchy":2065},[902,9943,9864],{"encoding":904}," se křivkou s předpisem ",[883,9946,9948],{"className":9947},[886],[888,9949,9950],{"xmlns":890},[892,9951,9952,9970],{},[895,9953,9954,9956,9958,9960,9962,9964,9966,9968],{},[898,9955,2287],{},[1688,9957,2066],{"stretchy":2065},[898,9959,2292],{},[1688,9961,1733],{"separator":1732},[898,9963,2282],{},[1688,9965,2076],{"stretchy":2065},[1688,9967,1690],{},[898,9969,2031],{},[902,9971,9972],{"encoding":904},"f(x, y) = c"," (konstanta) rozumí ",[38,9975,9976],{},"vrstevnice"," funkce. V ekonomii:",[120,9979,9980,10026],{},[123,9981,9982,9985,9986,10022,10023,2263],{},[38,9983,9984],{},"Indiferenční křivky"," užitečnosti ",[883,9987,9989],{"className":9988},[886],[888,9990,9991],{"xmlns":890},[892,9992,9993,10019],{},[895,9994,9995,9997,9999,10005,10007,10013,10015,10017],{},[898,9996,900],{},[1688,9998,2066],{"stretchy":2065},[1788,10000,10001,10003],{},[898,10002,1872],{},[1793,10004,1795],{},[1688,10006,1733],{"separator":1732},[1788,10008,10009,10011],{},[898,10010,1872],{},[1793,10012,1806],{},[1688,10014,2076],{"stretchy":2065},[1688,10016,1690],{},[898,10018,2031],{},[902,10020,10021],{"encoding":904},"U(Q_1, Q_2) = c"," — viz ",[207,10024,2225],{"className":10025,"dataFsResolvedFilePath":878,"href":879},[210],[123,10027,10028,10031,10032,10022,10062,2263],{},[38,10029,10030],{},"Izokvanty"," produkce ",[883,10033,10035],{"className":10034},[886],[888,10036,10037],{"xmlns":890},[892,10038,10039,10059],{},[895,10040,10041,10043,10045,10048,10050,10053,10055,10057],{},[898,10042,1872],{},[1688,10044,2066],{"stretchy":2065},[898,10046,10047],{},"L",[1688,10049,1733],{"separator":1732},[898,10051,10052],{},"K",[1688,10054,2076],{"stretchy":2065},[1688,10056,1690],{},[898,10058,2031],{},[902,10060,10061],{"encoding":904},"Q(L, K) = c",[207,10063,10065],{"className":10064,"dataFsResolvedFilePath":857,"href":858},[210],"produkce",[115,10067,10069],{"id":10068},"parciální-derivace","Parciální derivace",[724,10071,9916,10072,10096],{},[883,10073,10075],{"className":10074},[886],[888,10076,10077],{"xmlns":890},[892,10078,10079,10093],{},[895,10080,10081,10083,10085,10087,10089,10091],{},[898,10082,2287],{},[1688,10084,2066],{"stretchy":2065},[898,10086,2292],{},[1688,10088,1733],{"separator":1732},[898,10090,2282],{},[1688,10092,2076],{"stretchy":2065},[902,10094,10095],{"encoding":904},"f(x, y)"," derivujeme jako kdyby druhá proměnná byla konstanta:",[724,10098,10099],{},[883,10100,10102],{"className":10101},[886],[888,10103,10104],{"xmlns":890},[892,10105,10106,10161],{},[895,10107,10108,10116,10118,10133,10135,10137,10145,10147],{},[1814,10109,10110,10112,10114],{},[898,10111,2287],{},[898,10113,2292],{},[1688,10115,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,10117,1690],{},[1781,10119,10120,10127],{},[895,10121,10122,10125],{},[898,10123,10124],{"mathvariant":1822},"∂",[898,10126,2287],{},[895,10128,10129,10131],{},[898,10130,10124],{"mathvariant":1822},[898,10132,2292],{},[1688,10134,1733],{"separator":1732},[6134,10136],{"width":6136},[1814,10138,10139,10141,10143],{},[898,10140,2287],{},[898,10142,2282],{},[1688,10144,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,10146,1690],{},[1781,10148,10149,10155],{},[895,10150,10151,10153],{},[898,10152,10124],{"mathvariant":1822},[898,10154,2287],{},[895,10156,10157,10159],{},[898,10158,10124],{"mathvariant":1822},[898,10160,2282],{},[902,10162,10163],{"encoding":904},"f'_x = \\frac{\\partial f}{\\partial x}, \\qquad f'_y = \\frac{\\partial f}{\\partial y}",[724,10165,10166,10167,2263],{},"Hodnoty v bodě: ",[883,10168,10170],{"className":10169},[886],[888,10171,10172],{"xmlns":890},[892,10173,10174,10216],{},[895,10175,10176,10184,10186,10188,10190,10192,10194,10196,10198,10206,10208,10210,10212,10214],{},[1814,10177,10178,10180,10182],{},[898,10179,2287],{},[898,10181,2292],{},[1688,10183,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,10185,2066],{"stretchy":2065},[898,10187,207],{},[1688,10189,1733],{"separator":1732},[898,10191,1918],{},[1688,10193,2076],{"stretchy":2065},[1688,10195,1733],{"separator":1732},[2041,10197,2558],{},[1814,10199,10200,10202,10204],{},[898,10201,2287],{},[898,10203,2282],{},[1688,10205,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,10207,2066],{"stretchy":2065},[898,10209,207],{},[1688,10211,1733],{"separator":1732},[898,10213,1918],{},[1688,10215,2076],{"stretchy":2065},[902,10217,10218],{"encoding":904},"f'_x(a, b),\\ f'_y(a, b)",[198,10220,10222],{"id":10221},"ekonomické-značení","Ekonomické značení",[724,10224,10225,10226,2965],{},"Pro produkční funkci ",[883,10227,10229],{"className":10228},[886],[888,10230,10231],{"xmlns":890},[892,10232,10233,10247],{},[895,10234,10235,10237,10239,10241,10243,10245],{},[898,10236,1872],{},[1688,10238,2066],{"stretchy":2065},[898,10240,10047],{},[1688,10242,1733],{"separator":1732},[898,10244,10052],{},[1688,10246,2076],{"stretchy":2065},[902,10248,10249],{"encoding":904},"Q(L, K)",[120,10251,10252,10298],{},[123,10253,10254,2732,10274,10277,10278,2076],{},[883,10255,10257],{"className":10256},[886],[888,10258,10259],{"xmlns":890},[892,10260,10261,10271],{},[895,10262,10263],{},[1814,10264,10265,10267,10269],{},[898,10266,1872],{},[898,10268,10047],{},[1688,10270,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[902,10272,10273],{"encoding":904},"Q'_L",[38,10275,10276],{},"mezní produkt práce"," (",[883,10279,10281],{"className":10280},[886],[888,10282,10283],{"xmlns":890},[892,10284,10285,10295],{},[895,10286,10287,10289],{},[898,10288,1661],{},[1788,10290,10291,10293],{},[898,10292,1727],{},[898,10294,10047],{},[902,10296,10297],{"encoding":904},"MP_L",[123,10299,10300,2732,10320,10277,10323,2076],{},[883,10301,10303],{"className":10302},[886],[888,10304,10305],{"xmlns":890},[892,10306,10307,10317],{},[895,10308,10309],{},[1814,10310,10311,10313,10315],{},[898,10312,1872],{},[898,10314,10052],{},[1688,10316,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[902,10318,10319],{"encoding":904},"Q'_K",[38,10321,10322],{},"mezní produkt kapitálu",[883,10324,10326],{"className":10325},[886],[888,10327,10328],{"xmlns":890},[892,10329,10330,10340],{},[895,10331,10332,10334],{},[898,10333,1661],{},[1788,10335,10336,10338],{},[898,10337,1727],{},[898,10339,10052],{},[902,10341,10342],{"encoding":904},"MP_K",[198,10344,2830],{"id":2829},[724,10346,10347,2965],{},[883,10348,10350],{"className":10349},[886],[888,10351,10352],{"xmlns":890},[892,10353,10354,10374],{},[895,10355,10356,10364,10366,10368,10370,10372],{},[1814,10357,10358,10360,10362],{},[898,10359,2287],{},[898,10361,2292],{},[1688,10363,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,10365,2066],{"stretchy":2065},[898,10367,207],{},[1688,10369,1733],{"separator":1732},[898,10371,1918],{},[1688,10373,2076],{"stretchy":2065},[902,10375,10376],{"encoding":904},"f'_x(a, b)",[120,10378,10379,10437],{},[123,10380,10381,10382,10395,10396,10409,10410,10436],{},"rychlost změny ",[883,10383,10385],{"className":10384},[886],[888,10386,10387],{"xmlns":890},[892,10388,10389,10393],{},[895,10390,10391],{},[898,10392,2287],{},[902,10394,2287],{"encoding":904}," vůči ",[883,10397,10399],{"className":10398},[886],[888,10400,10401],{"xmlns":890},[892,10402,10403,10407],{},[895,10404,10405],{},[898,10406,2292],{},[902,10408,2292],{"encoding":904}," při ",[883,10411,10413],{"className":10412},[886],[888,10414,10415],{"xmlns":890},[892,10416,10417,10433],{},[895,10418,10419,10421,10423,10425,10427,10429,10431],{},[898,10420,2292],{},[1688,10422,1690],{},[898,10424,207],{},[1688,10426,1733],{"separator":1732},[898,10428,2282],{},[1688,10430,1690],{},[898,10432,1918],{},[902,10434,10435],{"encoding":904},"x = a, y = b"," (kapitál fixní),",[123,10438,10439,10440,2919,10453,10466,10467,10485,10486,2263],{},"přibližná změna ",[883,10441,10443],{"className":10442},[886],[888,10444,10445],{"xmlns":890},[892,10446,10447,10451],{},[895,10448,10449],{},[898,10450,2287],{},[902,10452,2287],{"encoding":904},[883,10454,10456],{"className":10455},[886],[888,10457,10458],{"xmlns":890},[892,10459,10460,10464],{},[895,10461,10462],{},[898,10463,2292],{},[902,10465,2292],{"encoding":904}," o 1 (a pevném ",[883,10468,10470],{"className":10469},[886],[888,10471,10472],{"xmlns":890},[892,10473,10474,10482],{},[895,10475,10476,10478,10480],{},[898,10477,2282],{},[1688,10479,1690],{},[898,10481,1918],{},[902,10483,10484],{"encoding":904},"y = b","): ",[883,10487,10489],{"className":10488},[886],[888,10490,10491],{"xmlns":890},[892,10492,10493,10545],{},[895,10494,10495,10497,10499,10501,10503,10505,10507,10509,10511,10513,10515,10517,10519,10521,10523,10525,10527,10535,10537,10539,10541,10543],{},[898,10496,2287],{},[1688,10498,2066],{"stretchy":2065},[898,10500,207],{},[1688,10502,1696],{},[1793,10504,1795],{},[1688,10506,1733],{"separator":1732},[898,10508,1918],{},[1688,10510,2076],{"stretchy":2065},[1688,10512,2991],{},[898,10514,2287],{},[1688,10516,2066],{"stretchy":2065},[898,10518,207],{},[1688,10520,1733],{"separator":1732},[898,10522,1918],{},[1688,10524,2076],{"stretchy":2065},[1688,10526,1696],{},[1814,10528,10529,10531,10533],{},[898,10530,2287],{},[898,10532,2292],{},[1688,10534,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,10536,2066],{"stretchy":2065},[898,10538,207],{},[1688,10540,1733],{"separator":1732},[898,10542,1918],{},[1688,10544,2076],{"stretchy":2065},[902,10546,10547],{"encoding":904},"f(a+1, b) \\approx f(a, b) + f'_x(a, b)",[115,10549,10551],{"id":10550},"diferenciál-funkce-dvou-proměnných","Diferenciál funkce dvou proměnných",[724,10553,10554],{},[883,10555,10557],{"className":10556},[886],[888,10558,10559],{"xmlns":890},[892,10560,10561,10619],{},[895,10562,10563,10565,10567,10569,10577,10579,10581,10583,10585,10587,10589,10591,10593,10595,10603,10605,10607,10609,10611,10613,10615,10617],{},[898,10564,2073],{},[898,10566,2287],{},[1688,10568,1690],{},[1814,10570,10571,10573,10575],{},[898,10572,2287],{},[898,10574,2292],{},[1688,10576,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,10578,2066],{"stretchy":2065},[898,10580,2292],{},[1688,10582,1733],{"separator":1732},[898,10584,2282],{},[1688,10586,2076],{"stretchy":2065},[2041,10588,2043],{},[898,10590,2073],{},[898,10592,2292],{},[1688,10594,1696],{},[1814,10596,10597,10599,10601],{},[898,10598,2287],{},[898,10600,2282],{},[1688,10602,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,10604,2066],{"stretchy":2065},[898,10606,2292],{},[1688,10608,1733],{"separator":1732},[898,10610,2282],{},[1688,10612,2076],{"stretchy":2065},[2041,10614,2043],{},[898,10616,2073],{},[898,10618,2282],{},[902,10620,10621],{"encoding":904},"df = f'_x(x, y)\\, dx + f'_y(x, y)\\, dy",[724,10623,3254,10624,10646,10647,10669],{},[883,10625,10627],{"className":10626},[886],[888,10628,10629],{"xmlns":890},[892,10630,10631,10643],{},[895,10632,10633,10635,10637,10639,10641],{},[898,10634,2073],{},[898,10636,2292],{},[1688,10638,1733],{"separator":1732},[898,10640,2073],{},[898,10642,2282],{},[902,10644,10645],{"encoding":904},"dx, dy"," platí ",[883,10648,10650],{"className":10649},[886],[888,10651,10652],{"xmlns":890},[892,10653,10654,10666],{},[895,10655,10656,10658,10660,10662,10664],{},[898,10657,3147],{"mathvariant":1822},[898,10659,2287],{},[1688,10661,2991],{},[898,10663,2073],{},[898,10665,2287],{},[902,10667,10668],{"encoding":904},"\\Delta f \\approx df",". Linearizace přírůstku ve dvou směrech současně.",[115,10671,10673],{"id":10672},"implicitní-funkce","Implicitní funkce",[724,10675,10676,10677,10706,10707,10720,10721,10734],{},"Je-li vztah dán rovnicí ",[883,10678,10680],{"className":10679},[886],[888,10681,10682],{"xmlns":890},[892,10683,10684,10703],{},[895,10685,10686,10689,10691,10693,10695,10697,10699,10701],{},[898,10687,10688],{},"F",[1688,10690,2066],{"stretchy":2065},[898,10692,2292],{},[1688,10694,1733],{"separator":1732},[898,10696,2282],{},[1688,10698,2076],{"stretchy":2065},[1688,10700,1690],{},[1793,10702,1779],{},[902,10704,10705],{"encoding":904},"F(x, y) = 0"," a chceme derivaci ",[883,10708,10710],{"className":10709},[886],[888,10711,10712],{"xmlns":890},[892,10713,10714,10718],{},[895,10715,10716],{},[898,10717,2282],{},[902,10719,2282],{"encoding":904}," podle ",[883,10722,10724],{"className":10723},[886],[888,10725,10726],{"xmlns":890},[892,10727,10728,10732],{},[895,10729,10730],{},[898,10731,2292],{},[902,10733,2292],{"encoding":904}," (nebo naopak):",[724,10736,10737],{},[883,10738,10740],{"className":10739},[886],[888,10741,10742],{"xmlns":890},[892,10743,10744,10838],{},[895,10745,10746,10752,10754,10768,10770,10772,10790,10792,10794,10800,10802,10816,10818,10820],{},[1850,10747,10748,10750],{},[898,10749,2282],{},[1688,10751,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,10753,1690],{},[1781,10755,10756,10762],{},[895,10757,10758,10760],{},[898,10759,2073],{},[898,10761,2282],{},[895,10763,10764,10766],{},[898,10765,2073],{},[898,10767,2292],{},[1688,10769,1690],{},[1688,10771,1954],{},[1781,10773,10774,10782],{},[1814,10775,10776,10778,10780],{},[898,10777,10688],{},[898,10779,2292],{},[1688,10781,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1814,10783,10784,10786,10788],{},[898,10785,10688],{},[898,10787,2282],{},[1688,10789,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,10791,1733],{"separator":1732},[6134,10793],{"width":6136},[1850,10795,10796,10798],{},[898,10797,2292],{},[1688,10799,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,10801,1690],{},[1781,10803,10804,10810],{},[895,10805,10806,10808],{},[898,10807,2073],{},[898,10809,2292],{},[895,10811,10812,10814],{},[898,10813,2073],{},[898,10815,2282],{},[1688,10817,1690],{},[1688,10819,1954],{},[1781,10821,10822,10830],{},[1814,10823,10824,10826,10828],{},[898,10825,10688],{},[898,10827,2282],{},[1688,10829,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1814,10831,10832,10834,10836],{},[898,10833,10688],{},[898,10835,2292],{},[1688,10837,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[902,10839,10840],{"encoding":904},"y' = \\frac{dy}{dx} = -\\frac{F'_x}{F'_y}, \\qquad x' = \\frac{dx}{dy} = -\\frac{F'_y}{F'_x}",[724,10842,10843,10844,10847,10848,4142,10852,2263],{},"Tato vzorec dává ",[38,10845,10846],{},"sklon vrstevnice"," — používá se mj. pro výpočet ",[207,10849,10851],{"className":10850,"dataFsResolvedFilePath":857,"href":858},[210],"MRTS",[207,10853,1670],{"className":10854,"dataFsResolvedFilePath":878,"href":879},[210],[115,10856,10858],{"id":10857},"volné-extrémy-funkce-dvou-proměnných","Volné extrémy funkce dvou proměnných",[198,10860,3509],{"id":3508},[724,10862,10863,10864,10888],{},"V bodě extrému ",[883,10865,10867],{"className":10866},[886],[888,10868,10869],{"xmlns":890},[892,10870,10871,10885],{},[895,10872,10873,10875,10877,10879,10881,10883],{},[898,10874,4512],{},[1688,10876,2748],{"stretchy":2065},[898,10878,207],{},[1688,10880,1733],{"separator":1732},[898,10882,1918],{},[1688,10884,2763],{"stretchy":2065},[902,10886,10887],{"encoding":904},"A[a, b]"," musí platit současně:",[724,10890,10891],{},[883,10892,10894],{"className":10893},[886],[888,10895,10896],{"xmlns":890},[892,10897,10898,10951],{},[895,10899,10900,10908,10910,10912,10914,10916,10918,10920,10922,10924,10927,10929,10937,10939,10941,10943,10945,10947,10949],{},[1814,10901,10902,10904,10906],{},[898,10903,2287],{},[898,10905,2292],{},[1688,10907,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,10909,2066],{"stretchy":2065},[898,10911,207],{},[1688,10913,1733],{"separator":1732},[898,10915,1918],{},[1688,10917,2076],{"stretchy":2065},[1688,10919,1690],{},[1793,10921,1779],{},[2041,10923,4241],{},[1688,10925,10926],{},"∧",[2041,10928,4241],{},[1814,10930,10931,10933,10935],{},[898,10932,2287],{},[898,10934,2282],{},[1688,10936,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,10938,2066],{"stretchy":2065},[898,10940,207],{},[1688,10942,1733],{"separator":1732},[898,10944,1918],{},[1688,10946,2076],{"stretchy":2065},[1688,10948,1690],{},[1793,10950,1779],{},[902,10952,10953],{"encoding":904},"f'_x(a, b) = 0 \\;\\wedge\\; f'_y(a, b) = 0",[198,10955,3583],{"id":3582},[724,10957,10958,10959,10962],{},"Definujeme ",[38,10960,10961],{},"diskriminant"," (Hessián zjednodušeně):",[724,10964,10965],{},[883,10966,10968],{"className":10967},[886],[888,10969,10970],{"xmlns":890},[892,10971,10972,11048],{},[895,10973,10974,10976,10978,10980,10982,10984,10986,10988,11004,11006,11022,11024,11026,11042],{},[898,10975,4440],{},[1688,10977,2066],{"stretchy":2065},[898,10979,2292],{},[1688,10981,1733],{"separator":1732},[898,10983,2282],{},[1688,10985,2076],{"stretchy":2065},[1688,10987,1690],{},[1814,10989,10990,10992,10998],{},[898,10991,2287],{},[895,10993,10994,10996],{},[898,10995,2292],{},[898,10997,2292],{},[895,10999,11000,11002],{},[1688,11001,1824],{"mathvariant":1822},[1688,11003,1824],{"mathvariant":1822},[1688,11005,3434],{},[1814,11007,11008,11010,11016],{},[898,11009,2287],{},[895,11011,11012,11014],{},[898,11013,2282],{},[898,11015,2282],{},[895,11017,11018,11020],{},[1688,11019,1824],{"mathvariant":1822},[1688,11021,1824],{"mathvariant":1822},[1688,11023,1954],{},[1688,11025,2066],{"stretchy":2065},[1814,11027,11028,11030,11036],{},[898,11029,2287],{},[895,11031,11032,11034],{},[898,11033,2292],{},[898,11035,2282],{},[895,11037,11038,11040],{},[1688,11039,1824],{"mathvariant":1822},[1688,11041,1824],{"mathvariant":1822},[1850,11043,11044,11046],{},[1688,11045,2076],{"stretchy":2065},[1793,11047,1806],{},[902,11049,11050],{"encoding":904},"D(x, y) = f''_{xx} \\cdot f''_{yy} - (f''_{xy})^2",[724,11052,11053,11054,2965],{},"V podezřelém bodě ",[883,11055,11057],{"className":11056},[886],[888,11058,11059],{"xmlns":890},[892,11060,11061,11073],{},[895,11062,11063,11065,11067,11069,11071],{},[1688,11064,2748],{"stretchy":2065},[898,11066,207],{},[1688,11068,1733],{"separator":1732},[898,11070,1918],{},[1688,11072,2763],{"stretchy":2065},[902,11074,11075],{"encoding":904},"[a, b]",[152,11077,11078,11205,11241],{},[123,11079,11080,11110,11111],{},[38,11081,11082,2965],{},[883,11083,11085],{"className":11084},[886],[888,11086,11087],{"xmlns":890},[892,11088,11089,11107],{},[895,11090,11091,11093,11095,11097,11099,11101,11103,11105],{},[898,11092,4440],{},[1688,11094,2066],{"stretchy":2065},[898,11096,207],{},[1688,11098,1733],{"separator":1732},[898,11100,1918],{},[1688,11102,2076],{"stretchy":2065},[1688,11104,3665],{},[1793,11106,1779],{},[902,11108,11109],{"encoding":904},"D(a, b) > 0"," je to extrém.\n",[120,11112,11113,11159],{},[123,11114,11115,3671,11157],{},[883,11116,11118],{"className":11117},[886],[888,11119,11120],{"xmlns":890},[892,11121,11122,11154],{},[895,11123,11124,11140,11142,11144,11146,11148,11150,11152],{},[1814,11125,11126,11128,11134],{},[898,11127,2287],{},[895,11129,11130,11132],{},[898,11131,2292],{},[898,11133,2292],{},[895,11135,11136,11138],{},[1688,11137,1824],{"mathvariant":1822},[1688,11139,1824],{"mathvariant":1822},[1688,11141,2066],{"stretchy":2065},[898,11143,207],{},[1688,11145,1733],{"separator":1732},[898,11147,1918],{},[1688,11149,2076],{"stretchy":2065},[1688,11151,3665],{},[1793,11153,1779],{},[902,11155,11156],{"encoding":904},"f''_{xx}(a, b) > 0",[38,11158,4032],{},[123,11160,11161,3671,11203],{},[883,11162,11164],{"className":11163},[886],[888,11165,11166],{"xmlns":890},[892,11167,11168,11200],{},[895,11169,11170,11186,11188,11190,11192,11194,11196,11198],{},[1814,11171,11172,11174,11180],{},[898,11173,2287],{},[895,11175,11176,11178],{},[898,11177,2292],{},[898,11179,2292],{},[895,11181,11182,11184],{},[1688,11183,1824],{"mathvariant":1822},[1688,11185,1824],{"mathvariant":1822},[1688,11187,2066],{"stretchy":2065},[898,11189,207],{},[1688,11191,1733],{"separator":1732},[898,11193,1918],{},[1688,11195,2076],{"stretchy":2065},[1688,11197,3704],{},[1793,11199,1779],{},[902,11201,11202],{"encoding":904},"f''_{xx}(a, b) \u003C 0",[38,11204,3974],{},[123,11206,11207,2170,11237,11240],{},[38,11208,11209,2965],{},[883,11210,11212],{"className":11211},[886],[888,11213,11214],{"xmlns":890},[892,11215,11216,11234],{},[895,11217,11218,11220,11222,11224,11226,11228,11230,11232],{},[898,11219,4440],{},[1688,11221,2066],{"stretchy":2065},[898,11223,207],{},[1688,11225,1733],{"separator":1732},[898,11227,1918],{},[1688,11229,2076],{"stretchy":2065},[1688,11231,3704],{},[1793,11233,1779],{},[902,11235,11236],{"encoding":904},"D(a, b) \u003C 0",[38,11238,11239],{},"sedlo"," (v daném bodě extrém není).",[123,11242,11243,11273],{},[38,11244,11245,2965],{},[883,11246,11248],{"className":11247},[886],[888,11249,11250],{"xmlns":890},[892,11251,11252,11270],{},[895,11253,11254,11256,11258,11260,11262,11264,11266,11268],{},[898,11255,4440],{},[1688,11257,2066],{"stretchy":2065},[898,11259,207],{},[1688,11261,1733],{"separator":1732},[898,11263,1918],{},[1688,11265,2076],{"stretchy":2065},[1688,11267,1690],{},[1793,11269,1779],{},[902,11271,11272],{"encoding":904},"D(a, b) = 0"," podmínka nerozhoduje.",[115,11275,11277],{"id":11276},"vázané-extrémy","Vázané extrémy",[724,11279,11280,11281,11310,11311,2263],{},"Pro extrémy s omezující podmínkou ",[883,11282,11284],{"className":11283},[886],[888,11285,11286],{"xmlns":890},[892,11287,11288,11307],{},[895,11289,11290,11293,11295,11297,11299,11301,11303,11305],{},[898,11291,11292],{},"g",[1688,11294,2066],{"stretchy":2065},[898,11296,2292],{},[1688,11298,1733],{"separator":1732},[898,11300,2282],{},[1688,11302,2076],{"stretchy":2065},[1688,11304,1690],{},[1793,11306,1779],{},[902,11308,11309],{"encoding":904},"g(x, y) = 0"," se používá ",[207,11312,793],{"className":11313,"dataFsResolvedFilePath":791,"href":792},[210],[115,11315,4049],{"id":4048},[120,11317,11318,11325,11332],{},[123,11319,11320,2170,11322],{},[38,11321,4056],{},[207,11323,775],{"className":11324,"dataFsResolvedFilePath":773,"href":774},[210],[123,11326,11327,2170,11329],{},[38,11328,2179],{},[207,11330,793],{"className":11331,"dataFsResolvedFilePath":791,"href":792},[210],[123,11333,11334,2170,11336,11340,11341,11344,11345,11348],{},[38,11335,4071],{},[207,11337,11339],{"className":11338,"dataFsResolvedFilePath":857,"href":858},[210],"Produkce"," (parciální derivace = mezní produkty), ",[207,11342,880],{"className":11343,"dataFsResolvedFilePath":878,"href":879},[210]," (parciální derivace = mezní užitečnost), ",[207,11346,4084],{"className":11347,"dataFsResolvedFilePath":848,"href":849},[210]," (vícefaktorový model)",{"title":641,"searchDepth":642,"depth":642,"links":11350},[11351,11352,11356,11357,11358,11362,11363],{"id":9912,"depth":642,"text":9913},{"id":10068,"depth":642,"text":10069,"children":11353},[11354,11355],{"id":10221,"depth":649,"text":10222},{"id":2829,"depth":649,"text":2830},{"id":10550,"depth":642,"text":10551},{"id":10672,"depth":642,"text":10673},{"id":10857,"depth":642,"text":10858,"children":11359},[11360,11361],{"id":3508,"depth":649,"text":3509},{"id":3582,"depth":649,"text":3583},{"id":11276,"depth":642,"text":11277},{"id":4048,"depth":642,"text":4049},"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":9823,"description":11364},[1135],"topics\u002Ffunkce-vice-promennych",[1128,11371,4110,11372,11373,11374],"parcialni-derivace","implicitni-funkce","volne-extremy","indiferencni-krivky","iuWLbpl-7gHnuMDZKTa3RcRM2uCyFhGx9GhXHIN1R_A",{"id":11377,"title":775,"body":11378,"course":1128,"courses":659,"created":1129,"description":12234,"extension":661,"meta":12235,"navigation":664,"path":12236,"seo":12237,"sources":12238,"stem":12239,"tags":12240,"type":4113,"updated":677,"__hash__":12247},"topics\u002Ftopics\u002Fintegral.md",{"type":9,"value":11379,"toc":12224},[11380,11383,11394,11398,11443,11523,11527,11603,11645,11652,11656,11660,11689,11747,11794,11832,11836,11886,11938,11990,12034,12037,12040,12112,12115,12187,12194,12196],[12,11381,775],{"id":11382},"integrál",[724,11384,11385,11386,11389,11390,11393],{},"Druhá polovina kalkulu jedné proměnné. Slouží k ",[38,11387,11388],{},"rekonstrukci totální veličiny z mezní"," (TR z MR, TC z MC) a k výpočtu ",[38,11391,11392],{},"přebytků"," (consumer\u002Fproducer surplus).",[115,11395,11397],{"id":11396},"neurčitý-integrál","Neurčitý integrál",[724,11399,11400],{},[883,11401,11403],{"className":11402},[886],[888,11404,11405],{"xmlns":890},[892,11406,11407,11440],{},[895,11408,11409,11411,11413,11415,11417,11419,11422,11424,11426,11428,11430,11432,11434,11436,11438],{},[898,11410,10688],{},[1688,11412,2066],{"stretchy":2065},[898,11414,2292],{},[1688,11416,2076],{"stretchy":2065},[1688,11418,1690],{},[1688,11420,11421],{},"∫",[898,11423,2287],{},[1688,11425,2066],{"stretchy":2065},[898,11427,2292],{},[1688,11429,2076],{"stretchy":2065},[2041,11431,2043],{},[898,11433,2073],{},[898,11435,2292],{},[1688,11437,1696],{},[898,11439,1693],{},[902,11441,11442],{"encoding":904},"F(x) = \\int f(x)\\, dx + C",[724,11444,4567,11445,3185,11479,8358,11492,11495,11496,1343,11509,11522],{},[883,11446,11448],{"className":11447},[886],[888,11449,11450],{"xmlns":890},[892,11451,11452,11476],{},[895,11453,11454,11460,11462,11464,11466,11468,11470,11472,11474],{},[1850,11455,11456,11458],{},[898,11457,10688],{},[1688,11459,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,11461,2066],{"stretchy":2065},[898,11463,2292],{},[1688,11465,2076],{"stretchy":2065},[1688,11467,1690],{},[898,11469,2287],{},[1688,11471,2066],{"stretchy":2065},[898,11473,2292],{},[1688,11475,2076],{"stretchy":2065},[902,11477,11478],{"encoding":904},"F'(x) = f(x)",[883,11480,11482],{"className":11481},[886],[888,11483,11484],{"xmlns":890},[892,11485,11486,11490],{},[895,11487,11488],{},[898,11489,10688],{},[902,11491,10688],{"encoding":904},[38,11493,11494],{},"primitivní funkce"," k ",[883,11497,11499],{"className":11498},[886],[888,11500,11501],{"xmlns":890},[892,11502,11503,11507],{},[895,11504,11505],{},[898,11506,2287],{},[902,11508,2287],{"encoding":904},[883,11510,11512],{"className":11511},[886],[888,11513,11514],{"xmlns":890},[892,11515,11516,11520],{},[895,11517,11518],{},[898,11519,1693],{},[902,11521,1693],{"encoding":904}," konstanta.",[115,11524,11526],{"id":11525},"určitý-integrál","Určitý integrál",[724,11528,11529],{},[883,11530,11532],{"className":11531},[886],[888,11533,11534],{"xmlns":890},[892,11535,11536,11600],{},[895,11537,11538,11546,11548,11550,11552,11554,11556,11558,11560,11562,11564,11566,11568,11570,11572,11580,11582,11584,11586,11588,11590,11592,11594,11596,11598],{},[1814,11539,11540,11542,11544],{},[1688,11541,11421],{},[898,11543,207],{},[898,11545,1918],{},[898,11547,2287],{},[1688,11549,2066],{"stretchy":2065},[898,11551,2292],{},[1688,11553,2076],{"stretchy":2065},[2041,11555,2043],{},[898,11557,2073],{},[898,11559,2292],{},[1688,11561,1690],{},[1688,11563,2748],{"stretchy":2065},[898,11565,10688],{},[1688,11567,2066],{"stretchy":2065},[898,11569,2292],{},[1688,11571,2076],{"stretchy":2065},[1814,11573,11574,11576,11578],{},[1688,11575,2763],{"stretchy":2065},[898,11577,207],{},[898,11579,1918],{},[1688,11581,1690],{},[898,11583,10688],{},[1688,11585,2066],{"stretchy":2065},[898,11587,1918],{},[1688,11589,2076],{"stretchy":2065},[1688,11591,1954],{},[898,11593,10688],{},[1688,11595,2066],{"stretchy":2065},[898,11597,207],{},[1688,11599,2076],{"stretchy":2065},[902,11601,11602],{"encoding":904},"\\int_a^b f(x)\\, dx = [F(x)]_a^b = F(b) - F(a)",[724,11604,11605,11606,2170,11609,11622,11623,11644],{},"Geometricky ",[38,11607,11608],{},"plocha pod grafem",[883,11610,11612],{"className":11611},[886],[888,11613,11614],{"xmlns":890},[892,11615,11616,11620],{},[895,11617,11618],{},[898,11619,2287],{},[902,11621,2287],{"encoding":904}," na intervalu ",[883,11624,11626],{"className":11625},[886],[888,11627,11628],{"xmlns":890},[892,11629,11630,11642],{},[895,11631,11632,11634,11636,11638,11640],{},[1688,11633,2748],{"stretchy":2065},[898,11635,207],{},[1688,11637,1733],{"separator":1732},[898,11639,1918],{},[1688,11641,2763],{"stretchy":2065},[902,11643,11075],{"encoding":904}," (orientovaná).",[724,11646,11647],{},[2821,11648],{"alt":11649,"className":11650,"src":11651},"imek-integral-plocha",[210,2825],"\u002Fwiki-assets\u002Fimek-integral-plocha.jpeg",[115,11653,11655],{"id":11654},"aplikace-v-ekonomii","Aplikace v ekonomii",[198,11657,11659],{"id":11658},"příklad-tr-z-mr","Příklad — TR z MR",[724,11661,11662,11663,2263],{},"Mezní příjem ",[883,11664,11666],{"className":11665},[886],[888,11667,11668],{"xmlns":890},[892,11669,11670,11686],{},[895,11671,11672,11674,11676,11678,11680,11682,11684],{},[898,11673,1661],{},[898,11675,4251],{},[1688,11677,1690],{},[1793,11679,3347],{},[1688,11681,1954],{},[1793,11683,1806],{},[898,11685,1872],{},[902,11687,11688],{"encoding":904},"MR = 100 - 2Q",[724,11690,11691],{},[883,11692,11694],{"className":11693},[886],[888,11695,11696],{"xmlns":890},[892,11697,11698,11744],{},[895,11699,11700,11702,11704,11706,11708,11710,11712,11714,11716,11718,11720,11722,11724,11726,11728,11730,11732,11734,11740,11742],{},[898,11701,3035],{},[898,11703,4251],{},[1688,11705,1690],{},[1688,11707,11421],{},[1688,11709,2066],{"stretchy":2065},[1793,11711,3347],{},[1688,11713,1954],{},[1793,11715,1806],{},[898,11717,1872],{},[1688,11719,2076],{"stretchy":2065},[2041,11721,2043],{},[898,11723,2073],{},[898,11725,1872],{},[1688,11727,1690],{},[1793,11729,3347],{},[898,11731,1872],{},[1688,11733,1954],{},[1850,11735,11736,11738],{},[898,11737,1872],{},[1793,11739,1806],{},[1688,11741,1696],{},[898,11743,2031],{},[902,11745,11746],{"encoding":904},"TR = \\int (100 - 2Q)\\, dQ = 100Q - Q^2 + c",[724,11748,11749,11750,3671,11776,2965],{},"Okrajová podmínka ",[883,11751,11753],{"className":11752},[886],[888,11754,11755],{"xmlns":890},[892,11756,11757,11773],{},[895,11758,11759,11761,11763,11765,11767,11769,11771],{},[898,11760,3035],{},[898,11762,4251],{},[1688,11764,2066],{"stretchy":2065},[1793,11766,1779],{},[1688,11768,2076],{"stretchy":2065},[1688,11770,1690],{},[1793,11772,1779],{},[902,11774,11775],{"encoding":904},"TR(0) = 0",[883,11777,11779],{"className":11778},[886],[888,11780,11781],{"xmlns":890},[892,11782,11783,11791],{},[895,11784,11785,11787,11789],{},[898,11786,2031],{},[1688,11788,1690],{},[1793,11790,1779],{},[902,11792,11793],{"encoding":904},"c = 0",[724,11795,11796],{},[883,11797,11799],{"className":11798},[886],[888,11800,11801],{"xmlns":890},[892,11802,11803,11829],{},[895,11804,11805,11807,11809,11811,11813,11815,11817,11819,11821,11823],{},[898,11806,3035],{},[898,11808,4251],{},[1688,11810,2066],{"stretchy":2065},[898,11812,1872],{},[1688,11814,2076],{"stretchy":2065},[1688,11816,1690],{},[1793,11818,3347],{},[898,11820,1872],{},[1688,11822,1954],{},[1850,11824,11825,11827],{},[898,11826,1872],{},[1793,11828,1806],{},[902,11830,11831],{"encoding":904},"TR(Q) = 100Q - Q^2",[198,11833,11835],{"id":11834},"příklad-tc-z-mc","Příklad — TC z MC",[724,11837,11838,11839,11865,11866,2263],{},"Mezní náklady ",[883,11840,11842],{"className":11841},[886],[888,11843,11844],{"xmlns":890},[892,11845,11846,11862],{},[895,11847,11848,11850,11852,11854,11856,11858,11860],{},[898,11849,1661],{},[898,11851,1693],{},[1688,11853,1690],{},[1793,11855,1806],{},[1688,11857,1696],{},[1793,11859,3097],{},[898,11861,1872],{},[902,11863,11864],{"encoding":904},"MC = 2 + 0{,}2 Q",", fixní náklady ",[883,11867,11869],{"className":11868},[886],[888,11870,11871],{"xmlns":890},[892,11872,11873,11883],{},[895,11874,11875,11877,11879,11881],{},[898,11876,10688],{},[898,11878,1693],{},[1688,11880,1690],{},[1793,11882,3347],{},[902,11884,11885],{"encoding":904},"FC = 100",[724,11887,11888],{},[883,11889,11891],{"className":11890},[886],[888,11892,11893],{"xmlns":890},[892,11894,11895,11935],{},[895,11896,11897,11899,11901,11903,11905,11907,11909,11911,11913,11915,11917,11919,11921,11923,11925,11931,11933],{},[898,11898,3035],{},[898,11900,1693],{},[1688,11902,1690],{},[1688,11904,11421],{},[898,11906,1661],{},[898,11908,1693],{},[2041,11910,2043],{},[898,11912,2073],{},[898,11914,1872],{},[1688,11916,1690],{},[1793,11918,1806],{},[898,11920,1872],{},[1688,11922,1696],{},[1793,11924,3053],{},[1850,11926,11927,11929],{},[898,11928,1872],{},[1793,11930,1806],{},[1688,11932,1696],{},[898,11934,2031],{},[902,11936,11937],{"encoding":904},"TC = \\int MC\\, dQ = 2Q + 0{,}1 Q^2 + c",[724,11939,11749,11940,3671,11972,2965],{},[883,11941,11943],{"className":11942},[886],[888,11944,11945],{"xmlns":890},[892,11946,11947,11969],{},[895,11948,11949,11951,11953,11955,11957,11959,11961,11963,11965,11967],{},[898,11950,3035],{},[898,11952,1693],{},[1688,11954,2066],{"stretchy":2065},[1793,11956,1779],{},[1688,11958,2076],{"stretchy":2065},[1688,11960,1690],{},[898,11962,10688],{},[898,11964,1693],{},[1688,11966,1690],{},[1793,11968,3347],{},[902,11970,11971],{"encoding":904},"TC(0) = FC = 100",[883,11973,11975],{"className":11974},[886],[888,11976,11977],{"xmlns":890},[892,11978,11979,11987],{},[895,11980,11981,11983,11985],{},[898,11982,2031],{},[1688,11984,1690],{},[1793,11986,3347],{},[902,11988,11989],{"encoding":904},"c = 100",[724,11991,11992],{},[883,11993,11995],{"className":11994},[886],[888,11996,11997],{"xmlns":890},[892,11998,11999,12031],{},[895,12000,12001,12003,12005,12007,12009,12011,12013,12015,12017,12019,12021,12023,12025],{},[898,12002,3035],{},[898,12004,1693],{},[1688,12006,2066],{"stretchy":2065},[898,12008,1872],{},[1688,12010,2076],{"stretchy":2065},[1688,12012,1690],{},[1793,12014,3347],{},[1688,12016,1696],{},[1793,12018,1806],{},[898,12020,1872],{},[1688,12022,1696],{},[1793,12024,3053],{},[1850,12026,12027,12029],{},[898,12028,1872],{},[1793,12030,1806],{},[902,12032,12033],{"encoding":904},"TC(Q) = 100 + 2Q + 0{,}1 Q^2",[198,12035,820],{"id":12036},"přebytek-spotřebitele-a-výrobce",[724,12038,12039],{},"Přebytek spotřebitele:",[724,12041,12042],{},[883,12043,12045],{"className":12044},[886],[888,12046,12047],{"xmlns":890},[892,12048,12049,12109],{},[895,12050,12051,12053,12055,12057,12063,12065,12067,12079,12081,12083,12085,12087,12089,12091,12093,12095,12101,12103],{},[898,12052,1693],{},[898,12054,1740],{},[1688,12056,2066],{"stretchy":2065},[1788,12058,12059,12061],{},[898,12060,1872],{},[1793,12062,1779],{},[1688,12064,2076],{"stretchy":2065},[1688,12066,1690],{},[1814,12068,12069,12071,12073],{},[1688,12070,11421],{},[1793,12072,1779],{},[1788,12074,12075,12077],{},[898,12076,1872],{},[1793,12078,1779],{},[898,12080,4440],{},[1688,12082,2066],{"stretchy":2065},[898,12084,1872],{},[1688,12086,2076],{"stretchy":2065},[2041,12088,2043],{},[898,12090,2073],{},[898,12092,1872],{},[1688,12094,1954],{},[1788,12096,12097,12099],{},[898,12098,1727],{},[1793,12100,1779],{},[2041,12102,2043],{},[1788,12104,12105,12107],{},[898,12106,1872],{},[1793,12108,1779],{},[902,12110,12111],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\, dQ - P_0\\, Q_0",[724,12113,12114],{},"Přebytek výrobce:",[724,12116,12117],{},[883,12118,12120],{"className":12119},[886],[888,12121,12122],{"xmlns":890},[892,12123,12124,12184],{},[895,12125,12126,12128,12130,12132,12138,12140,12142,12148,12150,12156,12158,12170,12172,12174,12176,12178,12180,12182],{},[898,12127,1727],{},[898,12129,1740],{},[1688,12131,2066],{"stretchy":2065},[1788,12133,12134,12136],{},[898,12135,1872],{},[1793,12137,1779],{},[1688,12139,2076],{"stretchy":2065},[1688,12141,1690],{},[1788,12143,12144,12146],{},[898,12145,1727],{},[1793,12147,1779],{},[2041,12149,2043],{},[1788,12151,12152,12154],{},[898,12153,1872],{},[1793,12155,1779],{},[1688,12157,1954],{},[1814,12159,12160,12162,12164],{},[1688,12161,11421],{},[1793,12163,1779],{},[1788,12165,12166,12168],{},[898,12167,1872],{},[1793,12169,1779],{},[898,12171,1740],{},[1688,12173,2066],{"stretchy":2065},[898,12175,1872],{},[1688,12177,2076],{"stretchy":2065},[2041,12179,2043],{},[898,12181,2073],{},[898,12183,1872],{},[902,12185,12186],{"encoding":904},"PS(Q_0) = P_0\\, Q_0 - \\int_0^{Q_0} S(Q)\\, dQ",[724,12188,12189,12190,2263],{},"Detailně viz ",[207,12191,12193],{"className":12192,"dataFsResolvedFilePath":800,"href":801},[210],"Poptávka a nabídka",[115,12195,4049],{"id":4048},[120,12197,12198,12205,12212],{},[123,12199,12200,2170,12202],{},[38,12201,4056],{},[207,12203,766],{"className":12204,"dataFsResolvedFilePath":764,"href":765},[210],[123,12206,12207,2170,12209],{},[38,12208,2179],{},[207,12210,784],{"className":12211,"dataFsResolvedFilePath":782,"href":783},[210],[123,12213,12214,2170,12216,12219,12220,12223],{},[38,12215,4071],{},[207,12217,4079],{"className":12218,"dataFsResolvedFilePath":827,"href":828},[210]," (TR\u002FTC), ",[207,12221,12193],{"className":12222,"dataFsResolvedFilePath":800,"href":801},[210]," (přebytky CS\u002FPS)",{"title":641,"searchDepth":642,"depth":642,"links":12225},[12226,12227,12228,12233],{"id":11396,"depth":642,"text":11397},{"id":11525,"depth":642,"text":11526},{"id":11654,"depth":642,"text":11655,"children":12229},[12230,12231,12232],{"id":11658,"depth":649,"text":11659},{"id":11834,"depth":649,"text":11835},{"id":12036,"depth":649,"text":820},{"id":4048,"depth":642,"text":4049},"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":12234},[1135],"topics\u002Fintegral",[1128,12241,12242,12243,12244,12245,12246],"integral","neurcity","urcity","primitivni-funkce","tr-z-mr","tc-z-mc","H1oOmn3Z5yZ_KZm1LLzfN_DVUhYSxx7eveFc7CASwZY",{"id":12249,"title":12250,"body":12251,"course":1128,"courses":659,"created":9809,"description":641,"extension":661,"meta":16514,"navigation":664,"path":16515,"seo":16516,"sources":16517,"stem":16518,"tags":16519,"type":4113,"updated":677,"__hash__":16524},"topics\u002Ftopics\u002Fis-lm.md","IS-LM analýza — simultánní rovnováha trhu zboží a peněz",{"type":9,"value":12252,"toc":16502},[12253,12256,12260,12401,12408,12412,12481,12519,12621,12625,12655,12721,12768,12771,12840,12843,12878,12914,12918,12966,12973,13019,13065,13068,13147,13244,13327,13331,13375,13405,13411,13440,13462,13511,13564,13630,13633,13699,13728,13787,13803,13890,13988,14119,14123,14280,14429,14809,14813,14816,14875,14878,14964,14992,15030,15033,15070,15110,15144,15146,15183,15215,15313,15318,15442,15494,15576,15715,15719,15839,15846,15957,15964,15968,16443,16445],[12,12254,12250],{"id":12255},"is-lm-analýza-simultánní-rovnováha-trhu-zboží-a-peněz",[115,12257,12259],{"id":12258},"tldr","TL;DR",[724,12261,12262,12264,12265,10277,12268,12281,12282,12295,12296,12299,12300,1343,12303,12306,12307,1343,12310,12313,12314,2170,12317,12347,12348,12351,12352,1343,12365,12378,12379,12382,12383,4176],{},[38,12263,1756],{}," je makroekonomický model se ",[38,12266,12267],{},"dvěma neznámými",[883,12269,12271],{"className":12270},[886],[888,12272,12273],{"xmlns":890},[892,12274,12275,12279],{},[895,12276,12277],{},[898,12278,1854],{},[902,12280,1854],{"encoding":904}," — národní důchod a ",[883,12283,12285],{"className":12284},[886],[888,12286,12287],{"xmlns":890},[892,12288,12289,12293],{},[895,12290,12291],{},[898,12292,2046],{},[902,12294,2046],{"encoding":904}," — úroková míra) a ",[38,12297,12298],{},"dvěma trhy",": trhem zboží (křivka ",[38,12301,12302],{},"IS",[614,12304,12305],{},"Investment = Savings",") a trhem peněz (křivka ",[38,12308,12309],{},"LM",[614,12311,12312],{},"Liquidity of Money","). Průsečík obou křivek určuje ",[38,12315,12316],{},"simultánní rovnováhu",[883,12318,12320],{"className":12319},[886],[888,12321,12322],{"xmlns":890},[892,12323,12324,12344],{},[895,12325,12326,12328,12334,12336,12342],{},[1688,12327,2066],{"stretchy":2065},[1850,12329,12330,12332],{},[898,12331,1854],{},[898,12333,4509],{},[1688,12335,1733],{"separator":1732},[1850,12337,12338,12340],{},[898,12339,2046],{},[898,12341,4509],{},[1688,12343,2076],{"stretchy":2065},[902,12345,12346],{"encoding":904},"(Y^E, r^E)",", v níž jsou oba trhy vyvážené zároveň. Model je klíčovým nástrojem pro analýzu ",[38,12349,12350],{},"fiskální politiky"," (posun IS změnou ",[883,12353,12355],{"className":12354},[886],[888,12356,12357],{"xmlns":890},[892,12358,12359,12363],{},[895,12360,12361],{},[898,12362,1704],{},[902,12364,1704],{"encoding":904},[883,12366,12368],{"className":12367},[886],[888,12369,12370],{"xmlns":890},[892,12371,12372,12376],{},[895,12373,12374],{},[898,12375,3035],{},[902,12377,3035],{"encoding":904},") a ",[38,12380,12381],{},"monetární politiky"," (posun LM změnou nabídky peněz ",[883,12384,12386],{"className":12385},[886],[888,12387,12388],{"xmlns":890},[892,12389,12390,12398],{},[895,12391,12392],{},[1850,12393,12394,12396],{},[898,12395,1661],{},[1688,12397,1857],{},[902,12399,12400],{"encoding":904},"M^*",[724,12402,12403],{},[2821,12404],{"alt":12405,"className":12406,"src":12407},"imek-is-lm-model",[210,2825],"\u002Fwiki-assets\u002Fimek-is-lm-model.jpeg",[115,12409,12411],{"id":12410},"motivace-proč-přejít-od-c-i-g-x-k-is-lm","Motivace — proč přejít od C-I-G-X k IS-LM",[724,12413,12414,12415,12419,12420,10277,12423,12445,12446,12449,12450,12466,12467,12480],{},"V modelech ",[207,12416,12418],{"className":12417,"dataFsResolvedFilePath":934,"href":935},[210],"C-I, C-I-G a C-I-G-X"," byly ",[38,12421,12422],{},"investice pokládány za konstantní",[883,12424,12426],{"className":12425},[886],[888,12427,12428],{"xmlns":890},[892,12429,12430,12442],{},[895,12431,12432,12434,12436],{},[898,12433,1699],{},[1688,12435,1690],{},[1850,12437,12438,12440],{},[898,12439,1699],{},[1688,12441,1857],{},[902,12443,12444],{"encoding":904},"I = I^*","). To není realistické — investice firem závisejí na ",[38,12447,12448],{},"ceně peněz",", tedy na ",[38,12451,12452,12453],{},"úrokové míře ",[883,12454,12456],{"className":12455},[886],[888,12457,12458],{"xmlns":890},[892,12459,12460,12464],{},[895,12461,12462],{},[898,12463,2046],{},[902,12465,2046],{"encoding":904},": čím vyšší ",[883,12468,12470],{"className":12469},[886],[888,12471,12472],{"xmlns":890},[892,12473,12474,12478],{},[895,12475,12476],{},[898,12477,2046],{},[902,12479,2046],{"encoding":904},", tím dražší úvěr a tím méně investic. IS-LM analýza proto zavádí:",[120,12482,12483,12513],{},[123,12484,12485,2170,12488,12512],{},[38,12486,12487],{},"funkci investic",[883,12489,12491],{"className":12490},[886],[888,12492,12493],{"xmlns":890},[892,12494,12495,12509],{},[895,12496,12497,12499,12501,12503,12505,12507],{},[898,12498,1699],{},[1688,12500,1690],{},[898,12502,1699],{},[1688,12504,2066],{"stretchy":2065},[898,12506,2046],{},[1688,12508,2076],{"stretchy":2065},[902,12510,12511],{"encoding":904},"I = I(r)"," jako klesající funkci úrokové míry,",[123,12514,12515,12518],{},[38,12516,12517],{},"trh peněz",", jehož rovnováha (poptávka = nabídka peněz) doplňuje druhou rovnici potřebnou pro určení obou neznámých.",[4124,12520,12521],{},[724,12522,12523,12525,12526,12545,12546,12572,12573,12586,12587,12616,12617,12620],{},[883,12524,4668],{}," Pozor — dvě neznámé vyžadují dvě rovnice\nV modelech ",[883,12527,12529],{"className":12528},[886],[888,12530,12531],{"xmlns":890},[892,12532,12533,12542],{},[895,12534,12535,12537,12540],{},[898,12536,1693],{},[2041,12538,12539],{},"-",[898,12541,1699],{},[902,12543,12544],{"encoding":904},"C\\text{-}I"," až ",[883,12547,12549],{"className":12548},[886],[888,12550,12551],{"xmlns":890},[892,12552,12553,12569],{},[895,12554,12555,12557,12559,12561,12563,12565,12567],{},[898,12556,1693],{},[2041,12558,12539],{},[898,12560,1699],{},[2041,12562,12539],{},[898,12564,1704],{},[2041,12566,12539],{},[898,12568,1709],{},[902,12570,12571],{"encoding":904},"C\\text{-}I\\text{-}G\\text{-}X"," byla hlavní neznámou jen ",[883,12574,12576],{"className":12575},[886],[888,12577,12578],{"xmlns":890},[892,12579,12580,12584],{},[895,12581,12582],{},[898,12583,1854],{},[902,12585,1854],{"encoding":904},". V IS-LM jsou ",[38,12588,12589,12590,4142,12603],{},"dvě neznámé ",[883,12591,12593],{"className":12592},[886],[888,12594,12595],{"xmlns":890},[892,12596,12597,12601],{},[895,12598,12599],{},[898,12600,1854],{},[902,12602,1854],{"encoding":904},[883,12604,12606],{"className":12605},[886],[888,12607,12608],{"xmlns":890},[892,12609,12610,12614],{},[895,12611,12612],{},[898,12613,2046],{},[902,12615,2046],{"encoding":904},", a proto potřebujeme ",[38,12618,12619],{},"dvě rovnice",": jednu z trhu zboží (křivka IS) a jednu z trhu peněz (křivka LM).",[115,12622,12624],{"id":12623},"funkce-investic-a-funkce-spotřeby","Funkce investic a funkce spotřeby",[724,12626,12627,12628,12641,12642,2965],{},"Lineární závislost investic ",[883,12629,12631],{"className":12630},[886],[888,12632,12633],{"xmlns":890},[892,12634,12635,12639],{},[895,12636,12637],{},[898,12638,1699],{},[902,12640,1699],{"encoding":904}," na úrokové míře ",[883,12643,12645],{"className":12644},[886],[888,12646,12647],{"xmlns":890},[892,12648,12649,12653],{},[895,12650,12651],{},[898,12652,2046],{},[902,12654,2046],{"encoding":904},[724,12656,12657],{},[883,12658,12660],{"className":12659},[886],[888,12661,12662],{"xmlns":890},[892,12663,12664,12718],{},[895,12665,12666,12668,12670,12672,12674,12676,12678,12680,12682,12684,12686,12688,12690,12692,12694,12696,12698,12700,12702,12704,12706,12709,12711,12713,12716],{},[898,12667,1699],{},[1688,12669,1690],{},[898,12671,1699],{},[1688,12673,2066],{"stretchy":2065},[898,12675,2046],{},[1688,12677,2076],{"stretchy":2065},[1688,12679,1690],{},[898,12681,2031],{},[898,12683,2046],{},[1688,12685,1696],{},[898,12687,2073],{},[1688,12689,1733],{"separator":1732},[6134,12691],{"width":6136},[898,12693,2031],{},[1688,12695,3704],{},[1793,12697,1779],{},[1688,12699,1733],{"separator":1732},[2041,12701,2558],{},[898,12703,2073],{},[1688,12705,3665],{},[1793,12707,12708],{},"0.",[6134,12710],{"width":6136},[1688,12712,2066],{"stretchy":2065},[1793,12714,12715],{},"7.11",[1688,12717,2076],{"stretchy":2065},[902,12719,12720],{"encoding":904},"I = I(r) = cr + d, \\qquad c \u003C 0,\\ d > 0. \\qquad (7.11)",[120,12722,12723,12744],{},[123,12724,12725,12743],{},[883,12726,12728],{"className":12727},[886],[888,12729,12730],{"xmlns":890},[892,12731,12732,12740],{},[895,12733,12734,12736,12738],{},[898,12735,2073],{},[1688,12737,3665],{},[1793,12739,1779],{},[902,12741,12742],{"encoding":904},"d > 0"," zřejmé,",[123,12745,12746,12764,12765,2263],{},[883,12747,12749],{"className":12748},[886],[888,12750,12751],{"xmlns":890},[892,12752,12753,12761],{},[895,12754,12755,12757,12759],{},[898,12756,2031],{},[1688,12758,3704],{},[1793,12760,1779],{},[902,12762,12763],{"encoding":904},"c \u003C 0",", protože růst úrokové míry tlumí investice — funkce investic je ",[38,12766,12767],{},"klesající",[724,12769,12770],{},"Spotřeba zůstává lineární funkcí důchodu:",[724,12772,12773],{},[883,12774,12776],{"className":12775},[886],[888,12777,12778],{"xmlns":890},[892,12779,12780,12837],{},[895,12781,12782,12784,12786,12788,12790,12792,12794,12796,12798,12800,12802,12804,12806,12808,12810,12812,12814,12816,12818,12820,12822,12824,12826,12828,12830,12832,12835],{},[898,12783,1693],{},[1688,12785,1690],{},[898,12787,1693],{},[1688,12789,2066],{"stretchy":2065},[898,12791,1854],{},[1688,12793,2076],{"stretchy":2065},[1688,12795,1690],{},[898,12797,207],{},[898,12799,1854],{},[1688,12801,1696],{},[898,12803,1918],{},[1688,12805,1733],{"separator":1732},[6134,12807],{"width":6136},[1793,12809,1779],{},[1688,12811,3704],{},[898,12813,207],{},[1688,12815,3704],{},[1793,12817,1795],{},[1688,12819,1733],{"separator":1732},[2041,12821,2558],{},[898,12823,1918],{},[1688,12825,3665],{},[1793,12827,12708],{},[6134,12829],{"width":6136},[1688,12831,2066],{"stretchy":2065},[1793,12833,12834],{},"7.12",[1688,12836,2076],{"stretchy":2065},[902,12838,12839],{"encoding":904},"C = C(Y) = aY + b, \\qquad 0 \u003C a \u003C 1,\\ b > 0. \\qquad (7.12)",[724,12841,12842],{},"Podmínka rovnováhy na trhu zboží:",[724,12844,12845],{},[883,12846,12848],{"className":12847},[886],[888,12849,12850],{"xmlns":890},[892,12851,12852,12875],{},[895,12853,12854,12856,12858,12860,12862,12864,12866,12868,12870,12873],{},[898,12855,1854],{},[1688,12857,1690],{},[898,12859,1693],{},[1688,12861,1696],{},[898,12863,1699],{},[898,12865,2263],{"mathvariant":1822},[6134,12867],{"width":6136},[1688,12869,2066],{"stretchy":2065},[1793,12871,12872],{},"7.13",[1688,12874,2076],{"stretchy":2065},[902,12876,12877],{"encoding":904},"Y = C + I. \\qquad (7.13)",[724,12879,12880,12881,2170,12884,12910,12911,2263],{},"To dává ",[38,12882,12883],{},"tři rovnice o čtyřech neznámých",[883,12885,12887],{"className":12886},[886],[888,12888,12889],{"xmlns":890},[892,12890,12891,12907],{},[895,12892,12893,12895,12897,12899,12901,12903,12905],{},[898,12894,1854],{},[1688,12896,1733],{"separator":1732},[898,12898,1693],{},[1688,12900,1733],{"separator":1732},[898,12902,1699],{},[1688,12904,1733],{"separator":1732},[898,12906,2046],{},[902,12908,12909],{"encoding":904},"Y, C, I, r",". Pro jednoznačné určení rovnováhy potřebujeme čtvrtou rovnici — odvodí se z ",[38,12912,12913],{},"rovnováhy na trhu peněz",[115,12915,12917],{"id":12916},"křivka-is-rovnováha-na-trhu-zboží","Křivka IS — rovnováha na trhu zboží",[724,12919,12920,12921,5825,12943,12961,12962,12965],{},"Podmínka (7.13) reprezentuje rovnováhu na trhu zboží, protože s ohledem na ",[883,12922,12924],{"className":12923},[886],[888,12925,12926],{"xmlns":890},[892,12927,12928,12940],{},[895,12929,12930,12932,12934,12936,12938],{},[898,12931,1854],{},[1688,12933,1690],{},[898,12935,1693],{},[1688,12937,1696],{},[898,12939,1740],{},[902,12941,12942],{"encoding":904},"Y = C + S",[883,12944,12946],{"className":12945},[886],[888,12947,12948],{"xmlns":890},[892,12949,12950,12958],{},[895,12951,12952,12954,12956],{},[898,12953,1699],{},[1688,12955,1690],{},[898,12957,1740],{},[902,12959,12960],{"encoding":904},"I = S"," (plánované ",[38,12963,12964],{},"investice = úspory","). Dosazením (7.11) a (7.12) do (7.13):",[724,12967,12968],{},[2821,12969],{"alt":12970,"className":12971,"src":12972},"imek-odvozeni-is-4panelu",[210,2825],"\u002Fwiki-assets\u002Fimek-odvozeni-is-4panelu.jpeg",[724,12974,12975],{},[883,12976,12978],{"className":12977},[886],[888,12979,12980],{"xmlns":890},[892,12981,12982,13016],{},[895,12983,12984,12986,12988,12990,12992,12994,12996,12998,13000,13002,13004,13006,13008,13010,13012,13014],{},[898,12985,1854],{},[1688,12987,1690],{},[1688,12989,2066],{"stretchy":2065},[898,12991,207],{},[898,12993,1854],{},[1688,12995,1696],{},[898,12997,1918],{},[1688,12999,2076],{"stretchy":2065},[1688,13001,1696],{},[1688,13003,2066],{"stretchy":2065},[898,13005,2031],{},[898,13007,2046],{},[1688,13009,1696],{},[898,13011,2073],{},[1688,13013,2076],{"stretchy":2065},[1688,13015,1733],{"separator":1732},[902,13017,13018],{"encoding":904},"Y = (aY + b) + (cr + d),",[724,13020,13021],{},[883,13022,13024],{"className":13023},[886],[888,13025,13026],{"xmlns":890},[892,13027,13028,13062],{},[895,13029,13030,13032,13034,13036,13038,13040,13042,13044,13046,13048,13050,13052,13054,13056,13058,13060],{},[1688,13031,2066],{"stretchy":2065},[1793,13033,1795],{},[1688,13035,1954],{},[898,13037,207],{},[1688,13039,2076],{"stretchy":2065},[898,13041,1854],{},[1688,13043,1954],{},[898,13045,2031],{},[898,13047,2046],{},[1688,13049,1954],{},[898,13051,1918],{},[1688,13053,1954],{},[898,13055,2073],{},[1688,13057,1690],{},[1793,13059,1779],{},[1688,13061,1733],{"separator":1732},[902,13063,13064],{"encoding":904},"(1 - a)Y - cr - b - d = 0,",[724,13066,13067],{},"odkud",[724,13069,13070],{},[883,13071,13073],{"className":13072},[886],[888,13074,13075],{"xmlns":890},[892,13076,13077,13144],{},[895,13078,13079,13135,13137,13139,13142],{},[13080,13081,13083],"menclose",{"notation":13082},"box",[1777,13084,13085],{"scriptlevel":1779,"displaystyle":2065},[1777,13086,13087],{"scriptlevel":1779,"displaystyle":2065},[1777,13088,13089],{"scriptlevel":1779,"displaystyle":1732},[895,13090,13091,13093,13095,13097,13109,13111,13113,13115,13133],{},[2041,13092,2043],{},[898,13094,1854],{},[1688,13096,1690],{},[1781,13098,13099,13101],{},[898,13100,2031],{},[895,13102,13103,13105,13107],{},[1793,13104,1795],{},[1688,13106,1954],{},[898,13108,207],{},[2041,13110,2043],{},[898,13112,2046],{},[1688,13114,1696],{},[1781,13116,13117,13125],{},[895,13118,13119,13121,13123],{},[898,13120,1918],{},[1688,13122,1696],{},[898,13124,2073],{},[895,13126,13127,13129,13131],{},[1793,13128,1795],{},[1688,13130,1954],{},[898,13132,207],{},[2041,13134,2043],{},[6134,13136],{"width":6136},[1688,13138,2066],{"stretchy":2065},[1793,13140,13141],{},"7.14",[1688,13143,2076],{"stretchy":2065},[902,13145,13146],{"encoding":904},"\\boxed{\\,Y = \\frac{c}{1 - a}\\,r + \\frac{b + d}{1 - a}\\,} \\qquad (7.14)",[724,13148,13149,13150,10277,13153,13156,13157,13160,13161,13163,13164,13186,13187,13215,13216,13237,13238,13240,13241,13243],{},"Tento vztah se nazývá ",[38,13151,13152],{},"funkce IS",[614,13154,13155],{},"IS schedule",") a její graf ",[38,13158,13159],{},"křivka IS",". Křivka je ",[38,13162,12767],{}," přímka v rovině ",[883,13165,13167],{"className":13166},[886],[888,13168,13169],{"xmlns":890},[892,13170,13171,13183],{},[895,13172,13173,13175,13177,13179,13181],{},[1688,13174,2066],{"stretchy":2065},[898,13176,2046],{},[1688,13178,1733],{"separator":1732},[898,13180,1854],{},[1688,13182,2076],{"stretchy":2065},[902,13184,13185],{"encoding":904},"(r, Y)",", neboť ",[883,13188,13190],{"className":13189},[886],[888,13191,13192],{"xmlns":890},[892,13193,13194,13212],{},[895,13195,13196,13208,13210],{},[1781,13197,13198,13200],{},[898,13199,2031],{},[895,13201,13202,13204,13206],{},[1793,13203,1795],{},[1688,13205,1954],{},[898,13207,207],{},[1688,13209,3704],{},[1793,13211,1779],{},[902,13213,13214],{"encoding":904},"\\frac{c}{1-a} \u003C 0"," (čitatel záporný, jmenovatel kladný). Název vyjadřuje, že křivka popisuje ty kombinace ",[883,13217,13219],{"className":13218},[886],[888,13220,13221],{"xmlns":890},[892,13222,13223,13235],{},[895,13224,13225,13227,13229,13231,13233],{},[1688,13226,2066],{"stretchy":2065},[898,13228,2046],{},[1688,13230,1733],{"separator":1732},[898,13232,1854],{},[1688,13234,2076],{"stretchy":2065},[902,13236,13185],{"encoding":904},", pro které plánované ",[38,13239,1699],{},"nvestment = ",[38,13242,1740],{},"avings.",[4124,13245,13246],{},[724,13247,13248,13250,13251,13264,13265,2170,13268,13281,13282,13295,13296,4142,13309,13322,13323,13326],{},[883,13249,4412],{}," Intuice — proč IS klesá\nNižší úroková míra ",[883,13252,13254],{"className":13253},[886],[888,13255,13256],{"xmlns":890},[892,13257,13258,13262],{},[895,13259,13260],{},[898,13261,2046],{},[902,13263,2046],{"encoding":904}," → levnější úvěr → ",[38,13266,13267],{},"více investic",[883,13269,13271],{"className":13270},[886],[888,13272,13273],{"xmlns":890},[892,13274,13275,13279],{},[895,13276,13277],{},[898,13278,1699],{},[902,13280,1699],{"encoding":904}," → vyšší agregátní poptávka → vyšší rovnovážný důchod ",[883,13283,13285],{"className":13284},[886],[888,13286,13287],{"xmlns":890},[892,13288,13289,13293],{},[895,13290,13291],{},[898,13292,1854],{},[902,13294,1854],{"encoding":904},". Vztah mezi ",[883,13297,13299],{"className":13298},[886],[888,13300,13301],{"xmlns":890},[892,13302,13303,13307],{},[895,13304,13305],{},[898,13306,2046],{},[902,13308,2046],{"encoding":904},[883,13310,13312],{"className":13311},[886],[888,13313,13314],{"xmlns":890},[892,13315,13316,13320],{},[895,13317,13318],{},[898,13319,1854],{},[902,13321,1854],{"encoding":904}," na trhu zboží je proto ",[38,13324,13325],{},"nepřímý"," (klesající křivka).",[115,13328,13330],{"id":13329},"křivka-lm-rovnováha-na-trhu-peněz","Křivka LM — rovnováha na trhu peněz",[724,13332,13333,13334,13352,13353,3185,13371,13374],{},"Rovnováha na trhu peněz: poptávka po penězích ",[883,13335,13337],{"className":13336},[886],[888,13338,13339],{"xmlns":890},[892,13340,13341,13349],{},[895,13342,13343],{},[1850,13344,13345,13347],{},[898,13346,1661],{},[898,13348,4440],{},[902,13350,13351],{"encoding":904},"M^D"," se rovná nabídce peněz ",[883,13354,13356],{"className":13355},[886],[888,13357,13358],{"xmlns":890},[892,13359,13360,13368],{},[895,13361,13362],{},[1850,13363,13364,13366],{},[898,13365,1661],{},[898,13367,1740],{},[902,13369,13370],{"encoding":904},"M^S",[38,13372,13373],{},"Nabídka"," je pod kontrolou národní banky a je pevně zadána:",[724,13376,13377],{},[883,13378,13380],{"className":13379},[886],[888,13381,13382],{"xmlns":890},[892,13383,13384,13402],{},[895,13385,13386,13392,13394,13400],{},[1850,13387,13388,13390],{},[898,13389,1661],{},[898,13391,1740],{},[1688,13393,1690],{},[1850,13395,13396,13398],{},[898,13397,1661],{},[1688,13399,1857],{},[898,13401,2263],{"mathvariant":1822},[902,13403,13404],{"encoding":904},"M^S = M^*.",[724,13406,13407,13410],{},[38,13408,13409],{},"Poptávka"," po penězích má tři zdroje:",[120,13412,13413,13422,13431],{},[123,13414,13415,10277,13418,13421],{},[38,13416,13417],{},"transakční poptávka",[614,13419,13420],{},"transactions demand",") — peníze pro nákup zboží,",[123,13423,13424,10277,13427,13430],{},[38,13425,13426],{},"opatrnostní poptávka",[614,13428,13429],{},"precautionary demand",") — peníze pro nenadálé výdaje,",[123,13432,13433,10277,13436,13439],{},[38,13434,13435],{},"spekulační poptávka",[614,13437,13438],{},"speculative demand",") — peníze pro zhodnocení (akcie, obligace).",[724,13441,13442,13443,13461],{},"Součet transakční a opatrnostní poptávky ",[883,13444,13446],{"className":13445},[886],[888,13447,13448],{"xmlns":890},[892,13449,13450,13458],{},[895,13451,13452],{},[1788,13453,13454,13456],{},[898,13455,10047],{},[1793,13457,1795],{},[902,13459,13460],{"encoding":904},"L_1"," je úměrný důchodu:",[724,13463,13464],{},[883,13465,13467],{"className":13466},[886],[888,13468,13469],{"xmlns":890},[892,13470,13471,13508],{},[895,13472,13473,13479,13481,13487,13489,13491,13493,13495,13497,13503,13505],{},[1788,13474,13475,13477],{},[898,13476,10047],{},[1793,13478,1795],{},[1688,13480,1690],{},[1788,13482,13483,13485],{},[898,13484,2106],{},[1793,13486,1795],{},[898,13488,1854],{},[1688,13490,1733],{"separator":1732},[6134,13492],{"width":6136},[1793,13494,1779],{},[1688,13496,3704],{},[1788,13498,13499,13501],{},[898,13500,2106],{},[1793,13502,1795],{},[1688,13504,3704],{},[1793,13506,13507],{},"1.",[902,13509,13510],{"encoding":904},"L_1 = k_1 Y, \\qquad 0 \u003C k_1 \u003C 1.",[724,13512,13513,13514,13532,13533,1343,13546,13563],{},"Spekulační poptávka ",[883,13515,13517],{"className":13516},[886],[888,13518,13519],{"xmlns":890},[892,13520,13521,13529],{},[895,13522,13523],{},[1788,13524,13525,13527],{},[898,13526,10047],{},[1793,13528,1806],{},[902,13530,13531],{"encoding":904},"L_2"," závisí na úrokové míře (roste-li ",[883,13534,13536],{"className":13535},[886],[888,13537,13538],{"xmlns":890},[892,13539,13540,13544],{},[895,13541,13542],{},[898,13543,2046],{},[902,13545,2046],{"encoding":904},[883,13547,13549],{"className":13548},[886],[888,13550,13551],{"xmlns":890},[892,13552,13553,13561],{},[895,13554,13555],{},[1788,13556,13557,13559],{},[898,13558,10047],{},[1793,13560,1806],{},[902,13562,13531],{"encoding":904}," klesá, protože vyšší výnos obligací snižuje atraktivitu držby peněz):",[724,13565,13566],{},[883,13567,13569],{"className":13568},[886],[888,13570,13571],{"xmlns":890},[892,13572,13573,13627],{},[895,13574,13575,13581,13583,13589,13591,13593,13599,13601,13603,13609,13611,13613,13615,13617,13623,13625],{},[1788,13576,13577,13579],{},[898,13578,10047],{},[1793,13580,1806],{},[1688,13582,1690],{},[1788,13584,13585,13587],{},[898,13586,2106],{},[1793,13588,1806],{},[898,13590,2046],{},[1688,13592,1696],{},[1788,13594,13595,13597],{},[898,13596,2106],{},[1793,13598,2131],{},[1688,13600,1733],{"separator":1732},[6134,13602],{"width":6136},[1788,13604,13605,13607],{},[898,13606,2106],{},[1793,13608,1806],{},[1688,13610,3704],{},[1793,13612,1779],{},[1688,13614,1733],{"separator":1732},[2041,13616,2558],{},[1788,13618,13619,13621],{},[898,13620,2106],{},[1793,13622,2131],{},[1688,13624,3665],{},[1793,13626,12708],{},[902,13628,13629],{"encoding":904},"L_2 = k_2 r + k_3, \\qquad k_2 \u003C 0,\\ k_3 > 0.",[724,13631,13632],{},"Celková poptávka po penězích:",[724,13634,13635],{},[883,13636,13638],{"className":13637},[886],[888,13639,13640],{"xmlns":890},[892,13641,13642,13696],{},[895,13643,13644,13650,13652,13658,13660,13666,13668,13674,13676,13678,13684,13686,13688,13694],{},[1850,13645,13646,13648],{},[898,13647,1661],{},[898,13649,4440],{},[1688,13651,1690],{},[1788,13653,13654,13656],{},[898,13655,10047],{},[1793,13657,1795],{},[1688,13659,1696],{},[1788,13661,13662,13664],{},[898,13663,10047],{},[1793,13665,1806],{},[1688,13667,1690],{},[1788,13669,13670,13672],{},[898,13671,2106],{},[1793,13673,1795],{},[898,13675,1854],{},[1688,13677,1696],{},[1788,13679,13680,13682],{},[898,13681,2106],{},[1793,13683,1806],{},[898,13685,2046],{},[1688,13687,1696],{},[1788,13689,13690,13692],{},[898,13691,2106],{},[1793,13693,2131],{},[898,13695,2263],{"mathvariant":1822},[902,13697,13698],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3.",[724,13700,13701,13702,2965],{},"Podmínka rovnováhy na trhu peněz ",[883,13703,13705],{"className":13704},[886],[888,13706,13707],{"xmlns":890},[892,13708,13709,13725],{},[895,13710,13711,13717,13719],{},[1850,13712,13713,13715],{},[898,13714,1661],{},[898,13716,4440],{},[1688,13718,1690],{},[1850,13720,13721,13723],{},[898,13722,1661],{},[1688,13724,1857],{},[902,13726,13727],{"encoding":904},"M^D = M^*",[724,13729,13730],{},[883,13731,13733],{"className":13732},[886],[888,13734,13735],{"xmlns":890},[892,13736,13737,13784],{},[895,13738,13739,13745,13747,13753,13755,13757,13763,13765,13767,13773,13775,13777,13779,13782],{},[1850,13740,13741,13743],{},[898,13742,1661],{},[1688,13744,1857],{},[1688,13746,1690],{},[1788,13748,13749,13751],{},[898,13750,2106],{},[1793,13752,1795],{},[898,13754,1854],{},[1688,13756,1696],{},[1788,13758,13759,13761],{},[898,13760,2106],{},[1793,13762,1806],{},[898,13764,2046],{},[1688,13766,1696],{},[1788,13768,13769,13771],{},[898,13770,2106],{},[1793,13772,2131],{},[1688,13774,1733],{"separator":1732},[6134,13776],{"width":6136},[1688,13778,2066],{"stretchy":2065},[1793,13780,13781],{},"7.15",[1688,13783,2076],{"stretchy":2065},[902,13785,13786],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3, \\qquad (7.15)",[724,13788,13789,13790,3408],{},"po úpravě (vyjádření ",[883,13791,13793],{"className":13792},[886],[888,13794,13795],{"xmlns":890},[892,13796,13797,13801],{},[895,13798,13799],{},[898,13800,1854],{},[902,13802,1854],{"encoding":904},[724,13804,13805],{},[883,13806,13808],{"className":13807},[886],[888,13809,13810],{"xmlns":890},[892,13811,13812,13887],{},[895,13813,13814,13878,13880,13882,13885],{},[13080,13815,13816],{"notation":13082},[1777,13817,13818],{"scriptlevel":1779,"displaystyle":2065},[1777,13819,13820],{"scriptlevel":1779,"displaystyle":2065},[1777,13821,13822],{"scriptlevel":1779,"displaystyle":1732},[895,13823,13824,13826,13828,13830,13832,13846,13848,13850,13852,13876],{},[2041,13825,2043],{},[898,13827,1854],{},[1688,13829,1690],{},[1688,13831,1954],{},[1781,13833,13834,13840],{},[1788,13835,13836,13838],{},[898,13837,2106],{},[1793,13839,1806],{},[1788,13841,13842,13844],{},[898,13843,2106],{},[1793,13845,1795],{},[2041,13847,2043],{},[898,13849,2046],{},[1688,13851,1696],{},[1781,13853,13854,13870],{},[895,13855,13856,13862,13864],{},[1850,13857,13858,13860],{},[898,13859,1661],{},[1688,13861,1857],{},[1688,13863,1954],{},[1788,13865,13866,13868],{},[898,13867,2106],{},[1793,13869,2131],{},[1788,13871,13872,13874],{},[898,13873,2106],{},[1793,13875,1795],{},[2041,13877,2043],{},[6134,13879],{"width":6136},[1688,13881,2066],{"stretchy":2065},[1793,13883,13884],{},"7.16",[1688,13886,2076],{"stretchy":2065},[902,13888,13889],{"encoding":904},"\\boxed{\\,Y = -\\frac{k_2}{k_1}\\,r + \\frac{M^* - k_3}{k_1}\\,} \\qquad (7.16)",[724,13891,13149,13892,10277,13895,13898,13899,13160,13902,13163,13905,13186,13926,13958,13959,13981,13982,13984,13985,13987],{},[38,13893,13894],{},"funkce LM",[614,13896,13897],{},"LM schedule","), její graf ",[38,13900,13901],{},"křivka LM",[38,13903,13904],{},"rostoucí",[883,13906,13908],{"className":13907},[886],[888,13909,13910],{"xmlns":890},[892,13911,13912,13924],{},[895,13913,13914,13916,13918,13920,13922],{},[1688,13915,2066],{"stretchy":2065},[898,13917,2046],{},[1688,13919,1733],{"separator":1732},[898,13921,1854],{},[1688,13923,2076],{"stretchy":2065},[902,13925,13185],{"encoding":904},[883,13927,13929],{"className":13928},[886],[888,13930,13931],{"xmlns":890},[892,13932,13933,13955],{},[895,13934,13935,13937,13951,13953],{},[1688,13936,1954],{},[1781,13938,13939,13945],{},[1788,13940,13941,13943],{},[898,13942,2106],{},[1793,13944,1806],{},[1788,13946,13947,13949],{},[898,13948,2106],{},[1793,13950,1795],{},[1688,13952,3665],{},[1793,13954,1779],{},[902,13956,13957],{"encoding":904},"-\\frac{k_2}{k_1} > 0"," (čitatel kladný, protože ",[883,13960,13962],{"className":13961},[886],[888,13963,13964],{"xmlns":890},[892,13965,13966,13978],{},[895,13967,13968,13974,13976],{},[1788,13969,13970,13972],{},[898,13971,2106],{},[1793,13973,1806],{},[1688,13975,3704],{},[1793,13977,1779],{},[902,13979,13980],{"encoding":904},"k_2 \u003C 0",", jmenovatel kladný). Název: ",[38,13983,10047],{},"iquidity of ",[38,13986,1661],{},"oney.",[4124,13989,13990],{},[724,13991,13992,13994,13995,14008,14009,14037,14038,14055,14056,14069,14070,14087,14088,4142,14101,14114,14115,14118],{},[883,13993,4412],{}," Intuice — proč LM roste\nVyšší důchod ",[883,13996,13998],{"className":13997},[886],[888,13999,14000],{"xmlns":890},[892,14001,14002,14006],{},[895,14003,14004],{},[898,14005,1854],{},[902,14007,1854],{"encoding":904}," → větší transakční poptávka po penězích ",[883,14010,14012],{"className":14011},[886],[888,14013,14014],{"xmlns":890},[892,14015,14016,14034],{},[895,14017,14018,14024,14026,14032],{},[1788,14019,14020,14022],{},[898,14021,10047],{},[1793,14023,1795],{},[1688,14025,1690],{},[1788,14027,14028,14030],{},[898,14029,2106],{},[1793,14031,1795],{},[898,14033,1854],{},[902,14035,14036],{"encoding":904},"L_1 = k_1 Y"," → při pevné nabídce ",[883,14039,14041],{"className":14040},[886],[888,14042,14043],{"xmlns":890},[892,14044,14045,14053],{},[895,14046,14047],{},[1850,14048,14049,14051],{},[898,14050,1661],{},[1688,14052,1857],{},[902,14054,12400],{"encoding":904}," vzniká na trhu peněz přebytek poptávky → úroková míra ",[883,14057,14059],{"className":14058},[886],[888,14060,14061],{"xmlns":890},[892,14062,14063,14067],{},[895,14064,14065],{},[898,14066,2046],{},[902,14068,2046],{"encoding":904}," musí vzrůst, aby se spekulační poptávka ",[883,14071,14073],{"className":14072},[886],[888,14074,14075],{"xmlns":890},[892,14076,14077,14085],{},[895,14078,14079],{},[1788,14080,14081,14083],{},[898,14082,10047],{},[1793,14084,1806],{},[902,14086,13531],{"encoding":904}," stlačila a trh se vyrovnal. Vztah mezi ",[883,14089,14091],{"className":14090},[886],[888,14092,14093],{"xmlns":890},[892,14094,14095,14099],{},[895,14096,14097],{},[898,14098,1854],{},[902,14100,1854],{"encoding":904},[883,14102,14104],{"className":14103},[886],[888,14105,14106],{"xmlns":890},[892,14107,14108,14112],{},[895,14109,14110],{},[898,14111,2046],{},[902,14113,2046],{"encoding":904}," na trhu peněz je proto ",[38,14116,14117],{},"přímý"," (rostoucí křivka).",[115,14120,14122],{"id":14121},"simultánní-rovnováha-is-lm","Simultánní rovnováha IS-LM",[724,14124,14125,14126,14129,14130,2170,14133,4142,14151,2170,14154,14172,14173,14191,14192,14210,14211,14227,14228,4142,14243,14258,14259,2263],{},"Řešením ",[38,14127,14128],{},"soustavy dvou lineárních rovnic"," (7.14) a (7.15) určíme ",[38,14131,14132],{},"rovnovážný důchod",[883,14134,14136],{"className":14135},[886],[888,14137,14138],{"xmlns":890},[892,14139,14140,14148],{},[895,14141,14142],{},[1850,14143,14144,14146],{},[898,14145,1854],{},[898,14147,4509],{},[902,14149,14150],{"encoding":904},"Y^E",[38,14152,14153],{},"rovnovážnou úrokovou míru",[883,14155,14157],{"className":14156},[886],[888,14158,14159],{"xmlns":890},[892,14160,14161,14169],{},[895,14162,14163],{},[1850,14164,14165,14167],{},[898,14166,2046],{},[898,14168,4509],{},[902,14170,14171],{"encoding":904},"r^E","; zpětným dosazením do (7.11) a (7.12) pak rovnovážné investice ",[883,14174,14176],{"className":14175},[886],[888,14177,14178],{"xmlns":890},[892,14179,14180,14188],{},[895,14181,14182],{},[1850,14183,14184,14186],{},[898,14185,1699],{},[898,14187,4509],{},[902,14189,14190],{"encoding":904},"I^E"," a rovnovážnou spotřebu ",[883,14193,14195],{"className":14194},[886],[888,14196,14197],{"xmlns":890},[892,14198,14199,14207],{},[895,14200,14201],{},[1850,14202,14203,14205],{},[898,14204,1693],{},[898,14206,4509],{},[902,14208,14209],{"encoding":904},"C^E",". Graficky jde o ",[38,14212,14213,14214],{},"průsečík ",[883,14215,14217],{"className":14216},[886],[888,14218,14219],{"xmlns":890},[892,14220,14221,14225],{},[895,14222,14223],{},[898,14224,4509],{},[902,14226,4509],{"encoding":904}," křivek ",[883,14229,14231],{"className":14230},[886],[888,14232,14233],{"xmlns":890},[892,14234,14235,14241],{},[895,14236,14237,14239],{},[898,14238,1699],{},[898,14240,1740],{},[902,14242,12302],{"encoding":904},[883,14244,14246],{"className":14245},[886],[888,14247,14248],{"xmlns":890},[892,14249,14250,14256],{},[895,14251,14252,14254],{},[898,14253,10047],{},[898,14255,1661],{},[902,14257,12309],{"encoding":904}," v rovině ",[883,14260,14262],{"className":14261},[886],[888,14263,14264],{"xmlns":890},[892,14265,14266,14278],{},[895,14267,14268,14270,14272,14274,14276],{},[1688,14269,2066],{"stretchy":2065},[898,14271,2046],{},[1688,14273,1733],{"separator":1732},[898,14275,1854],{},[1688,14277,2076],{"stretchy":2065},[902,14279,13185],{"encoding":904},[724,14281,14282],{},[614,14283,14284,14285,14306,14307,14322,14323,14338,14339,14352,14353,14370,14371,12378,14384,14370,14401,14414,14415,14428],{},"Obrázek 7.6 — Schematický graf v rovině ",[883,14286,14288],{"className":14287},[886],[888,14289,14290],{"xmlns":890},[892,14291,14292,14304],{},[895,14293,14294,14296,14298,14300,14302],{},[1688,14295,2066],{"stretchy":2065},[898,14297,2046],{},[1688,14299,1733],{"separator":1732},[898,14301,1854],{},[1688,14303,2076],{"stretchy":2065},[902,14305,13185],{"encoding":904},". Rostoucí přímka ",[883,14308,14310],{"className":14309},[886],[888,14311,14312],{"xmlns":890},[892,14313,14314,14320],{},[895,14315,14316,14318],{},[898,14317,10047],{},[898,14319,1661],{},[902,14321,12309],{"encoding":904}," a klesající přímka ",[883,14324,14326],{"className":14325},[886],[888,14327,14328],{"xmlns":890},[892,14329,14330,14336],{},[895,14331,14332,14334],{},[898,14333,1699],{},[898,14335,1740],{},[902,14337,12302],{"encoding":904}," se protínají v bodě ",[883,14340,14342],{"className":14341},[886],[888,14343,14344],{"xmlns":890},[892,14345,14346,14350],{},[895,14347,14348],{},[898,14349,4509],{},[902,14351,4509],{"encoding":904}," se souřadnicemi ",[883,14354,14356],{"className":14355},[886],[888,14357,14358],{"xmlns":890},[892,14359,14360,14368],{},[895,14361,14362],{},[1850,14363,14364,14366],{},[898,14365,2046],{},[898,14367,4509],{},[902,14369,14171],{"encoding":904}," (na ose ",[883,14372,14374],{"className":14373},[886],[888,14375,14376],{"xmlns":890},[892,14377,14378,14382],{},[895,14379,14380],{},[898,14381,2046],{},[902,14383,2046],{"encoding":904},[883,14385,14387],{"className":14386},[886],[888,14388,14389],{"xmlns":890},[892,14390,14391,14399],{},[895,14392,14393],{},[1850,14394,14395,14397],{},[898,14396,1854],{},[898,14398,4509],{},[902,14400,14150],{"encoding":904},[883,14402,14404],{"className":14403},[886],[888,14405,14406],{"xmlns":890},[892,14407,14408,14412],{},[895,14409,14410],{},[898,14411,1854],{},[902,14413,1854],{"encoding":904},"); tečkované čáry z ",[883,14416,14418],{"className":14417},[886],[888,14419,14420],{"xmlns":890},[892,14421,14422,14426],{},[895,14423,14424],{},[898,14425,4509],{},[902,14427,4509],{"encoding":904}," kolmé k osám vyznačují polohu rovnovážné úrokové míry a rovnovážného národního důchodu.",[4124,14430,14431,14436],{},[724,14432,14433,14435],{},[883,14434,4828],{}," Postup — jak najít IS-LM rovnováhu",[152,14437,14438,14514,14582,14640,14713],{},[123,14439,14440,14443,14444,4142,14464,14484,14485,4142,14498,14511,14512,2263],{},[38,14441,14442],{},"Z trhu zboží (7.13)"," dosaď funkce ",[883,14445,14447],{"className":14446},[886],[888,14448,14449],{"xmlns":890},[892,14450,14451,14461],{},[895,14452,14453,14455,14457,14459],{},[898,14454,1693],{},[1688,14456,2066],{"stretchy":2065},[898,14458,1854],{},[1688,14460,2076],{"stretchy":2065},[902,14462,14463],{"encoding":904},"C(Y)",[883,14465,14467],{"className":14466},[886],[888,14468,14469],{"xmlns":890},[892,14470,14471,14481],{},[895,14472,14473,14475,14477,14479],{},[898,14474,1699],{},[1688,14476,2066],{"stretchy":2065},[898,14478,2046],{},[1688,14480,2076],{"stretchy":2065},[902,14482,14483],{"encoding":904},"I(r)"," a vyjádři vztah mezi ",[883,14486,14488],{"className":14487},[886],[888,14489,14490],{"xmlns":890},[892,14491,14492,14496],{},[895,14493,14494],{},[898,14495,1854],{},[902,14497,1854],{"encoding":904},[883,14499,14501],{"className":14500},[886],[888,14502,14503],{"xmlns":890},[892,14504,14505,14509],{},[895,14506,14507],{},[898,14508,2046],{},[902,14510,2046],{"encoding":904}," — dostaneš rovnici ",[38,14513,12302],{},[123,14515,14516,14519,14520,4142,14537,14554,14555,14511,14580,2263],{},[38,14517,14518],{},"Z trhu peněz (7.15)"," dosaď ",[883,14521,14523],{"className":14522},[886],[888,14524,14525],{"xmlns":890},[892,14526,14527,14535],{},[895,14528,14529],{},[1788,14530,14531,14533],{},[898,14532,10047],{},[1793,14534,1795],{},[902,14536,13460],{"encoding":904},[883,14538,14540],{"className":14539},[886],[888,14541,14542],{"xmlns":890},[892,14543,14544,14552],{},[895,14545,14546],{},[1788,14547,14548,14550],{},[898,14549,10047],{},[1793,14551,1806],{},[902,14553,13531],{"encoding":904}," a vztah ",[883,14556,14558],{"className":14557},[886],[888,14559,14560],{"xmlns":890},[892,14561,14562,14578],{},[895,14563,14564,14570,14572],{},[1850,14565,14566,14568],{},[898,14567,1661],{},[898,14569,4440],{},[1688,14571,1690],{},[1850,14573,14574,14576],{},[898,14575,1661],{},[1688,14577,1857],{},[902,14579,13727],{"encoding":904},[38,14581,12309],{},[123,14583,14584,14587,14588,4142,14601,14614,14615,14639],{},[38,14585,14586],{},"Vyřeš soustavu"," dvou lineárních rovnic o dvou neznámých ",[883,14589,14591],{"className":14590},[886],[888,14592,14593],{"xmlns":890},[892,14594,14595,14599],{},[895,14596,14597],{},[898,14598,1854],{},[902,14600,1854],{"encoding":904},[883,14602,14604],{"className":14603},[886],[888,14605,14606],{"xmlns":890},[892,14607,14608,14612],{},[895,14609,14610],{},[898,14611,2046],{},[902,14613,2046],{"encoding":904}," — nejsnáze substituční metodou (vyjádři z IS ",[883,14616,14618],{"className":14617},[886],[888,14619,14620],{"xmlns":890},[892,14621,14622,14636],{},[895,14623,14624,14626,14628,14630,14632,14634],{},[898,14625,1854],{},[1688,14627,1690],{},[898,14629,2287],{},[1688,14631,2066],{"stretchy":2065},[898,14633,2046],{},[1688,14635,2076],{"stretchy":2065},[902,14637,14638],{"encoding":904},"Y = f(r)"," a dosaď do LM).",[123,14641,14642,2170,14645,4142,14679,2263],{},[38,14643,14644],{},"Zpětně dopočítej",[883,14646,14648],{"className":14647},[886],[888,14649,14650],{"xmlns":890},[892,14651,14652,14676],{},[895,14653,14654,14660,14662,14664,14666,14672,14674],{},[1850,14655,14656,14658],{},[898,14657,1693],{},[898,14659,4509],{},[1688,14661,1690],{},[898,14663,207],{},[2041,14665,2043],{},[1850,14667,14668,14670],{},[898,14669,1854],{},[898,14671,4509],{},[1688,14673,1696],{},[898,14675,1918],{},[902,14677,14678],{"encoding":904},"C^E = a\\,Y^E + b",[883,14680,14682],{"className":14681},[886],[888,14683,14684],{"xmlns":890},[892,14685,14686,14710],{},[895,14687,14688,14694,14696,14698,14700,14706,14708],{},[1850,14689,14690,14692],{},[898,14691,1699],{},[898,14693,4509],{},[1688,14695,1690],{},[898,14697,2031],{},[2041,14699,2043],{},[1850,14701,14702,14704],{},[898,14703,2046],{},[898,14705,4509],{},[1688,14707,1696],{},[898,14709,2073],{},[902,14711,14712],{"encoding":904},"I^E = c\\,r^E + d",[123,14714,14715,14718,14719,14753,14754,14808],{},[38,14716,14717],{},"Ověř:"," musí platit ",[883,14720,14722],{"className":14721},[886],[888,14723,14724],{"xmlns":890},[892,14725,14726,14750],{},[895,14727,14728,14734,14736,14742,14744],{},[1850,14729,14730,14732],{},[898,14731,1854],{},[898,14733,4509],{},[1688,14735,1690],{},[1850,14737,14738,14740],{},[898,14739,1693],{},[898,14741,4509],{},[1688,14743,1696],{},[1850,14745,14746,14748],{},[898,14747,1699],{},[898,14749,4509],{},[902,14751,14752],{"encoding":904},"Y^E = C^E + I^E"," (rovnováha trhu zboží) i ",[883,14755,14757],{"className":14756},[886],[888,14758,14759],{"xmlns":890},[892,14760,14761,14805],{},[895,14762,14763,14769,14771,14777,14783,14785,14791,14797,14799],{},[1850,14764,14765,14767],{},[898,14766,1661],{},[1688,14768,1857],{},[1688,14770,1690],{},[1788,14772,14773,14775],{},[898,14774,2106],{},[1793,14776,1795],{},[1850,14778,14779,14781],{},[898,14780,1854],{},[898,14782,4509],{},[1688,14784,1696],{},[1788,14786,14787,14789],{},[898,14788,2106],{},[1793,14790,1806],{},[1850,14792,14793,14795],{},[898,14794,2046],{},[898,14796,4509],{},[1688,14798,1696],{},[1788,14800,14801,14803],{},[898,14802,2106],{},[1793,14804,2131],{},[902,14806,14807],{"encoding":904},"M^* = k_1 Y^E + k_2 r^E + k_3"," (rovnováha trhu peněz).",[115,14810,14812],{"id":14811},"příklad-76-is-lm","Příklad 7.6 (IS-LM)",[724,14814,14815],{},"Pro trh zboží jsou dány:",[120,14817,14818,14846],{},[123,14819,14820,14821,1733],{},"spotřeba ",[883,14822,14824],{"className":14823},[886],[888,14825,14826],{"xmlns":890},[892,14827,14828,14843],{},[895,14829,14830,14832,14834,14837,14839,14841],{},[898,14831,1693],{},[1688,14833,1690],{},[1793,14835,14836],{},"0,8",[898,14838,1854],{},[1688,14840,1696],{},[1793,14842,3347],{},[902,14844,14845],{"encoding":904},"C = 0{,}8Y + 100",[123,14847,14848,14849,2263],{},"investice ",[883,14850,14852],{"className":14851},[886],[888,14853,14854],{"xmlns":890},[892,14855,14856,14872],{},[895,14857,14858,14860,14862,14864,14866,14868,14870],{},[898,14859,1699],{},[1688,14861,1690],{},[1688,14863,1954],{},[1793,14865,9290],{},[898,14867,2046],{},[1688,14869,1696],{},[1793,14871,3042],{},[902,14873,14874],{"encoding":904},"I = -20r + 1000",[724,14876,14877],{},"Pro trh peněz:",[120,14879,14880,14906,14938],{},[123,14881,14882,1733],{},[883,14883,14885],{"className":14884},[886],[888,14886,14887],{"xmlns":890},[892,14888,14889,14903],{},[895,14890,14891,14897,14899,14901],{},[1788,14892,14893,14895],{},[898,14894,10047],{},[1793,14896,1795],{},[1688,14898,1690],{},[1793,14900,3053],{},[898,14902,1854],{},[902,14904,14905],{"encoding":904},"L_1 = 0{,}1Y",[123,14907,14908,1733],{},[883,14909,14911],{"className":14910},[886],[888,14912,14913],{"xmlns":890},[892,14914,14915,14935],{},[895,14916,14917,14923,14925,14927,14929,14931,14933],{},[1788,14918,14919,14921],{},[898,14920,10047],{},[1793,14922,1806],{},[1688,14924,1690],{},[1688,14926,1954],{},[1793,14928,5260],{},[898,14930,2046],{},[1688,14932,1696],{},[1793,14934,8860],{},[902,14936,14937],{"encoding":904},"L_2 = -25r + 2000",[123,14939,14940,14941,2263],{},"nabídka peněz ",[883,14942,14944],{"className":14943},[886],[888,14945,14946],{"xmlns":890},[892,14947,14948,14961],{},[895,14949,14950,14956,14958],{},[1850,14951,14952,14954],{},[898,14953,1661],{},[1688,14955,1857],{},[1688,14957,1690],{},[1793,14959,14960],{},"2375",[902,14962,14963],{"encoding":904},"M^* = 2375",[724,14965,14966,14969,14970,2965],{},[38,14967,14968],{},"Funkce IS"," — dosazením do (7.13) ",[883,14971,14973],{"className":14972},[886],[888,14974,14975],{"xmlns":890},[892,14976,14977,14989],{},[895,14978,14979,14981,14983,14985,14987],{},[898,14980,1854],{},[1688,14982,1690],{},[898,14984,1693],{},[1688,14986,1696],{},[898,14988,1699],{},[902,14990,14991],{"encoding":904},"Y = C + I",[724,14993,14994],{},[883,14995,14997],{"className":14996},[886],[888,14998,14999],{"xmlns":890},[892,15000,15001,15027],{},[895,15002,15003,15005,15007,15009,15011,15013,15015,15017,15019,15021,15023,15025],{},[898,15004,1854],{},[1688,15006,1690],{},[1793,15008,14836],{},[898,15010,1854],{},[1688,15012,1696],{},[1793,15014,3347],{},[1688,15016,1954],{},[1793,15018,9290],{},[898,15020,2046],{},[1688,15022,1696],{},[1793,15024,3042],{},[1688,15026,1733],{"separator":1732},[902,15028,15029],{"encoding":904},"Y = 0{,}8Y + 100 - 20r + 1000,",[724,15031,15032],{},"tj.",[724,15034,15035],{},[883,15036,15038],{"className":15037},[886],[888,15039,15040],{"xmlns":890},[892,15041,15042,15067],{},[895,15043,15044,15046,15048,15050,15052,15054,15056,15059,15061,15063,15065],{},[1793,15045,3097],{},[898,15047,1854],{},[1688,15049,1696],{},[1793,15051,9290],{},[898,15053,2046],{},[1688,15055,1690],{},[1793,15057,15058],{},"1100.",[6134,15060],{"width":6136},[1688,15062,2066],{"stretchy":2065},[2041,15064,12302],{},[1688,15066,2076],{"stretchy":2065},[902,15068,15069],{"encoding":904},"0{,}2Y + 20r = 1100. \\qquad (\\text{IS})",[724,15071,15072,15075,15076,2965],{},[38,15073,15074],{},"Funkce LM"," — dosazením do (7.15) ",[883,15077,15079],{"className":15078},[886],[888,15080,15081],{"xmlns":890},[892,15082,15083,15107],{},[895,15084,15085,15091,15093,15099,15101],{},[1850,15086,15087,15089],{},[898,15088,1661],{},[1688,15090,1857],{},[1688,15092,1690],{},[1788,15094,15095,15097],{},[898,15096,10047],{},[1793,15098,1795],{},[1688,15100,1696],{},[1788,15102,15103,15105],{},[898,15104,10047],{},[1793,15106,1806],{},[902,15108,15109],{"encoding":904},"M^* = L_1 + L_2",[724,15111,15112],{},[883,15113,15115],{"className":15114},[886],[888,15116,15117],{"xmlns":890},[892,15118,15119,15141],{},[895,15120,15121,15123,15125,15127,15129,15131,15133,15135,15137,15139],{},[1793,15122,14960],{},[1688,15124,1690],{},[1793,15126,3053],{},[898,15128,1854],{},[1688,15130,1954],{},[1793,15132,5260],{},[898,15134,2046],{},[1688,15136,1696],{},[1793,15138,8860],{},[1688,15140,1733],{"separator":1732},[902,15142,15143],{"encoding":904},"2375 = 0{,}1Y - 25r + 2000,",[724,15145,15032],{},[724,15147,15148],{},[883,15149,15151],{"className":15150},[886],[888,15152,15153],{"xmlns":890},[892,15154,15155,15180],{},[895,15156,15157,15159,15161,15163,15165,15167,15169,15172,15174,15176,15178],{},[1793,15158,3053],{},[898,15160,1854],{},[1688,15162,1954],{},[1793,15164,5260],{},[898,15166,2046],{},[1688,15168,1690],{},[1793,15170,15171],{},"375.",[6134,15173],{"width":6136},[1688,15175,2066],{"stretchy":2065},[2041,15177,12309],{},[1688,15179,2076],{"stretchy":2065},[902,15181,15182],{"encoding":904},"0{,}1Y - 25r = 375. \\qquad (\\text{LM})",[724,15184,15185,15188,15189,15214],{},[38,15186,15187],{},"Řešení soustavy."," Z (IS) vyjádříme ",[883,15190,15192],{"className":15191},[886],[888,15193,15194],{"xmlns":890},[892,15195,15196,15211],{},[895,15197,15198,15200,15202,15205,15207,15209],{},[898,15199,1854],{},[1688,15201,1690],{},[1793,15203,15204],{},"5500",[1688,15206,1954],{},[1793,15208,3347],{},[898,15210,2046],{},[902,15212,15213],{"encoding":904},"Y = 5500 - 100r"," a dosadíme do (LM):",[724,15216,15217],{},[883,15218,15220],{"className":15219},[886],[888,15221,15222],{"xmlns":890},[892,15223,15224,15310],{},[895,15225,15226,15228,15230,15232,15234,15236,15238,15240,15242,15244,15246,15248,15251,15253,15256,15258,15261,15263,15265,15267,15269,15271,15273,15275,15277,15279,15281,15283,15286,15288,15290,15293,15295,15297,15299,15305,15307],{},[1793,15227,3053],{},[1688,15229,2066],{"stretchy":2065},[1793,15231,15204],{},[1688,15233,1954],{},[1793,15235,3347],{},[898,15237,2046],{},[1688,15239,2076],{"stretchy":2065},[1688,15241,1954],{},[1793,15243,5260],{},[898,15245,2046],{},[1688,15247,1690],{},[1793,15249,15250],{},"375",[2041,15252,4241],{},[1688,15254,15255],{},"⟹",[2041,15257,4241],{},[1793,15259,15260],{},"550",[1688,15262,1954],{},[1793,15264,3121],{},[898,15266,2046],{},[1688,15268,1954],{},[1793,15270,5260],{},[898,15272,2046],{},[1688,15274,1690],{},[1793,15276,15250],{},[2041,15278,4241],{},[1688,15280,15255],{},[2041,15282,4241],{},[1793,15284,15285],{},"35",[898,15287,2046],{},[1688,15289,1690],{},[1793,15291,15292],{},"175",[2041,15294,4241],{},[1688,15296,15255],{},[2041,15298,4241],{},[1850,15300,15301,15303],{},[898,15302,2046],{},[898,15304,4509],{},[1688,15306,1690],{},[1793,15308,15309],{},"5.",[902,15311,15312],{"encoding":904},"0{,}1(5500 - 100r) - 25r = 375 \\;\\Longrightarrow\\; 550 - 10r - 25r = 375 \\;\\Longrightarrow\\; 35r = 175 \\;\\Longrightarrow\\; r^E = 5.",[724,15314,15315],{},[38,15316,15317],{},"Zpětné dosazení:",[120,15319,15320,15366,15403],{},[123,15321,15322,1733],{},[883,15323,15325],{"className":15324},[886],[888,15326,15327],{"xmlns":890},[892,15328,15329,15363],{},[895,15330,15331,15337,15339,15341,15343,15345,15347,15349,15351,15353,15355,15358,15360],{},[1850,15332,15333,15335],{},[898,15334,1854],{},[898,15336,4509],{},[1688,15338,1690],{},[1793,15340,15204],{},[1688,15342,1954],{},[1793,15344,3347],{},[1688,15346,3434],{},[1793,15348,2501],{},[1688,15350,1690],{},[1793,15352,15204],{},[1688,15354,1954],{},[1793,15356,15357],{},"500",[1688,15359,1690],{},[1793,15361,15362],{},"5000",[902,15364,15365],{"encoding":904},"Y^E = 5500 - 100 \\cdot 5 = 5500 - 500 = 5000",[123,15367,15368,1733],{},[883,15369,15371],{"className":15370},[886],[888,15372,15373],{"xmlns":890},[892,15374,15375,15400],{},[895,15376,15377,15383,15385,15387,15389,15391,15393,15395,15397],{},[1850,15378,15379,15381],{},[898,15380,1693],{},[898,15382,4509],{},[1688,15384,1690],{},[1793,15386,14836],{},[1688,15388,3434],{},[1793,15390,15362],{},[1688,15392,1696],{},[1793,15394,3347],{},[1688,15396,1690],{},[1793,15398,15399],{},"4100",[902,15401,15402],{"encoding":904},"C^E = 0{,}8 \\cdot 5000 + 100 = 4100",[123,15404,15405,2263],{},[883,15406,15408],{"className":15407},[886],[888,15409,15410],{"xmlns":890},[892,15411,15412,15439],{},[895,15413,15414,15420,15422,15424,15426,15428,15430,15432,15434,15436],{},[1850,15415,15416,15418],{},[898,15417,1699],{},[898,15419,4509],{},[1688,15421,1690],{},[1688,15423,1954],{},[1793,15425,9290],{},[1688,15427,3434],{},[1793,15429,2501],{},[1688,15431,1696],{},[1793,15433,3042],{},[1688,15435,1690],{},[1793,15437,15438],{},"900",[902,15440,15441],{"encoding":904},"I^E = -20 \\cdot 5 + 1000 = 900",[724,15443,15444,2170,15447,15493],{},[38,15445,15446],{},"Ověření:",[883,15448,15450],{"className":15449},[886],[888,15451,15452],{"xmlns":890},[892,15453,15454,15490],{},[895,15455,15456,15462,15464,15470,15472,15474,15476,15478,15480,15482,15484],{},[1850,15457,15458,15460],{},[898,15459,1693],{},[898,15461,4509],{},[1688,15463,1696],{},[1850,15465,15466,15468],{},[898,15467,1699],{},[898,15469,4509],{},[1688,15471,1690],{},[1793,15473,15399],{},[1688,15475,1696],{},[1793,15477,15438],{},[1688,15479,1690],{},[1793,15481,15362],{},[1688,15483,1690],{},[1850,15485,15486,15488],{},[898,15487,1854],{},[898,15489,4509],{},[902,15491,15492],{"encoding":904},"C^E + I^E = 4100 + 900 = 5000 = Y^E",". ✓",[724,15495,15496],{},[883,15497,15499],{"className":15498},[886],[888,15500,15501],{"xmlns":890},[892,15502,15503,15573],{},[895,15504,15505],{},[13080,15506,15507],{"notation":13082},[1777,15508,15509],{"scriptlevel":1779,"displaystyle":2065},[1777,15510,15511],{"scriptlevel":1779,"displaystyle":2065},[1777,15512,15513],{"scriptlevel":1779,"displaystyle":1732},[895,15514,15515,15517,15523,15525,15527,15529,15532,15538,15540,15542,15544,15546,15552,15554,15556,15558,15560,15566,15568,15571],{},[2041,15516,2043],{},[1850,15518,15519,15521],{},[898,15520,1854],{},[898,15522,4509],{},[1688,15524,1690],{},[1793,15526,15362],{},[1688,15528,1733],{"separator":1732},[6134,15530],{"width":15531},"1em",[1850,15533,15534,15536],{},[898,15535,2046],{},[898,15537,4509],{},[1688,15539,1690],{},[1793,15541,2501],{},[1688,15543,1733],{"separator":1732},[6134,15545],{"width":15531},[1850,15547,15548,15550],{},[898,15549,1693],{},[898,15551,4509],{},[1688,15553,1690],{},[1793,15555,15399],{},[1688,15557,1733],{"separator":1732},[6134,15559],{"width":15531},[1850,15561,15562,15564],{},[898,15563,1699],{},[898,15565,4509],{},[1688,15567,1690],{},[1793,15569,15570],{},"900.",[2041,15572,2043],{},[902,15574,15575],{"encoding":904},"\\boxed{\\,Y^E = 5000, \\quad r^E = 5, \\quad C^E = 4100, \\quad I^E = 900.\\,}",[724,15577,15578],{},[614,15579,15580,15581,15594,15595,15608,15609,15624,15625,15638,15639,15654,15655,15668,15669,15682,15683,2263],{},"Obrázek 7.7 — Konkrétní numerický příklad IS-LM rovnováhy. Na ose ",[883,15582,15584],{"className":15583},[886],[888,15585,15586],{"xmlns":890},[892,15587,15588,15592],{},[895,15589,15590],{},[898,15591,1854],{},[902,15593,1854],{"encoding":904}," jsou vyznačeny hodnoty 3750, 5000, 5500; na ose ",[883,15596,15598],{"className":15597},[886],[888,15599,15600],{"xmlns":890},[892,15601,15602,15606],{},[895,15603,15604],{},[898,15605,2046],{},[902,15607,2046],{"encoding":904}," hodnoty 5 a 55. Přímka ",[883,15610,15612],{"className":15611},[886],[888,15613,15614],{"xmlns":890},[892,15615,15616,15622],{},[895,15617,15618,15620],{},[898,15619,10047],{},[898,15621,1661],{},[902,15623,12309],{"encoding":904}," stoupá z oblasti nízkých ",[883,15626,15628],{"className":15627},[886],[888,15629,15630],{"xmlns":890},[892,15631,15632,15636],{},[895,15633,15634],{},[898,15635,2046],{},[902,15637,2046],{"encoding":904},", přímka ",[883,15640,15642],{"className":15641},[886],[888,15643,15644],{"xmlns":890},[892,15645,15646,15652],{},[895,15647,15648,15650],{},[898,15649,1699],{},[898,15651,1740],{},[902,15653,12302],{"encoding":904}," klesá a protíná osu ",[883,15656,15658],{"className":15657},[886],[888,15659,15660],{"xmlns":890},[892,15661,15662,15666],{},[895,15663,15664],{},[898,15665,2046],{},[902,15667,2046],{"encoding":904}," kolem hodnoty 55. Průsečík ",[883,15670,15672],{"className":15671},[886],[888,15673,15674],{"xmlns":890},[892,15675,15676,15680],{},[895,15677,15678],{},[898,15679,4509],{},[902,15681,4509],{"encoding":904}," leží v bodě ",[883,15684,15686],{"className":15685},[886],[888,15687,15688],{"xmlns":890},[892,15689,15690,15712],{},[895,15691,15692,15694,15696,15698,15700,15702,15704,15706,15708,15710],{},[1688,15693,2748],{"stretchy":2065},[898,15695,2046],{},[1688,15697,1690],{},[1793,15699,2501],{},[1688,15701,1733],{"separator":1732},[2041,15703,2558],{},[898,15705,1854],{},[1688,15707,1690],{},[1793,15709,15362],{},[1688,15711,2763],{"stretchy":2065},[902,15713,15714],{"encoding":904},"[r = 5,\\ Y = 5000]",[115,15716,15718],{"id":15717},"ekonomická-interpretace-fiskální-a-monetární-politika","Ekonomická interpretace — fiskální a monetární politika",[724,15720,15721,15724,15725,15738,15739,7271,15752,15755,15756,15774,15775,15792,15793,15810,15811,15824,15825,15838],{},[38,15722,15723],{},"Posun křivky IS (fiskální politika)."," Expanzivní fiskální politika — zvýšení vládních výdajů ",[883,15726,15728],{"className":15727},[886],[888,15729,15730],{"xmlns":890},[892,15731,15732,15736],{},[895,15733,15734],{},[898,15735,1704],{},[902,15737,1704],{"encoding":904}," nebo snížení daní ",[883,15740,15742],{"className":15741},[886],[888,15743,15744],{"xmlns":890},[892,15745,15746,15750],{},[895,15747,15748],{},[898,15749,3035],{},[902,15751,3035],{"encoding":904},[38,15753,15754],{},"posouvá IS doprava",": při dané úrokové míře vzroste rovnovážný důchod trhu zboží. Nová rovnováha ",[883,15757,15759],{"className":15758},[886],[888,15760,15761],{"xmlns":890},[892,15762,15763,15771],{},[895,15764,15765],{},[1850,15766,15767,15769],{},[898,15768,4509],{},[1688,15770,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[902,15772,15773],{"encoding":904},"E'"," má vyšší ",[883,15776,15778],{"className":15777},[886],[888,15779,15780],{"xmlns":890},[892,15781,15782,15790],{},[895,15783,15784],{},[1850,15785,15786,15788],{},[898,15787,1854],{},[898,15789,4509],{},[902,15791,14150],{"encoding":904}," i vyšší ",[883,15794,15796],{"className":15795},[886],[888,15797,15798],{"xmlns":890},[892,15799,15800,15808],{},[895,15801,15802],{},[1850,15803,15804,15806],{},[898,15805,2046],{},[898,15807,4509],{},[902,15809,14171],{"encoding":904}," (vyšší ",[883,15812,15814],{"className":15813},[886],[888,15815,15816],{"xmlns":890},[892,15817,15818,15822],{},[895,15819,15820],{},[898,15821,1854],{},[902,15823,1854],{"encoding":904}," zvedá poptávku po penězích, což tlačí ",[883,15826,15828],{"className":15827},[886],[888,15829,15830],{"xmlns":890},[892,15831,15832,15836],{},[895,15833,15834],{},[898,15835,2046],{},[902,15837,2046],{"encoding":904}," nahoru).",[724,15840,15841],{},[2821,15842],{"alt":15843,"className":15844,"src":15845},"imek-posun-is-lm-politiky",[210,2825],"\u002Fwiki-assets\u002Fimek-posun-is-lm-politiky.jpeg",[724,15847,15848,15851,15852,15869,15870,15873,15874,15891,15892,15909,15910,15923,15924,15943,15944,4176],{},[38,15849,15850],{},"Posun křivky LM (monetární politika)."," Expanzivní monetární politika — zvýšení nabídky peněz ",[883,15853,15855],{"className":15854},[886],[888,15856,15857],{"xmlns":890},[892,15858,15859,15867],{},[895,15860,15861],{},[1850,15862,15863,15865],{},[898,15864,1661],{},[1688,15866,1857],{},[902,15868,12400],{"encoding":904}," národní bankou — ",[38,15871,15872],{},"posouvá LM doprava\u002Fdolů",": při daném důchodu je trh peněz v rovnováze při nižší úrokové míře. Nová rovnováha má nižší ",[883,15875,15877],{"className":15876},[886],[888,15878,15879],{"xmlns":890},[892,15880,15881,15889],{},[895,15882,15883],{},[1850,15884,15885,15887],{},[898,15886,2046],{},[898,15888,4509],{},[902,15890,14171],{"encoding":904}," a vyšší ",[883,15893,15895],{"className":15894},[886],[888,15896,15897],{"xmlns":890},[892,15898,15899,15907],{},[895,15900,15901],{},[1850,15902,15903,15905],{},[898,15904,1854],{},[898,15906,4509],{},[902,15908,14150],{"encoding":904}," (nižší ",[883,15911,15913],{"className":15912},[886],[888,15914,15915],{"xmlns":890},[892,15916,15917,15921],{},[895,15918,15919],{},[898,15920,2046],{},[902,15922,2046],{"encoding":904}," povzbuzuje investice ",[883,15925,15927],{"className":15926},[886],[888,15928,15929],{"xmlns":890},[892,15930,15931,15941],{},[895,15932,15933,15935,15937,15939],{},[898,15934,1699],{},[1688,15936,2066],{"stretchy":2065},[898,15938,2046],{},[1688,15940,2076],{"stretchy":2065},[902,15942,14483],{"encoding":904},", ty zvedají ",[883,15945,15947],{"className":15946},[886],[888,15948,15949],{"xmlns":890},[892,15950,15951,15955],{},[895,15952,15953],{},[898,15954,1854],{},[902,15956,1854],{"encoding":904},[724,15958,15959,15960,15963],{},"IS-LM tak dává jednotný rámec pro diskusi ",[38,15961,15962],{},"dopadu obou typů politik"," na důchod a úrokovou míru současně.",[115,15965,15967],{"id":15966},"klíčové-pojmy","Klíčové pojmy",[120,15969,15970,16043,16089,16171,16221,16288,16345,16386,16419],{},[123,15971,15972,7271,16005,1343,16022,16039,16040,16042],{},[38,15973,15974,15975],{},"Funkce investic ",[883,15976,15978],{"className":15977},[886],[888,15979,15980],{"xmlns":890},[892,15981,15982,16002],{},[895,15983,15984,15986,15988,15990,15992,15994,15996,15998,16000],{},[898,15985,1699],{},[1688,15987,2066],{"stretchy":2065},[898,15989,2046],{},[1688,15991,2076],{"stretchy":2065},[1688,15993,1690],{},[898,15995,2031],{},[898,15997,2046],{},[1688,15999,1696],{},[898,16001,2073],{},[902,16003,16004],{"encoding":904},"I(r) = cr + d",[883,16006,16008],{"className":16007},[886],[888,16009,16010],{"xmlns":890},[892,16011,16012,16020],{},[895,16013,16014,16016,16018],{},[898,16015,2031],{},[1688,16017,3704],{},[1793,16019,1779],{},[902,16021,12763],{"encoding":904},[883,16023,16025],{"className":16024},[886],[888,16026,16027],{"xmlns":890},[892,16028,16029,16037],{},[895,16030,16031,16033,16035],{},[898,16032,2073],{},[1688,16034,3665],{},[1793,16036,1779],{},[902,16038,12742],{"encoding":904},"; ",[38,16041,12767],{}," funkce úrokové míry.",[123,16044,16045,16048,16049,16070,16071,16088],{},[38,16046,16047],{},"Trh zboží"," — rovnováha ",[883,16050,16052],{"className":16051},[886],[888,16053,16054],{"xmlns":890},[892,16055,16056,16068],{},[895,16057,16058,16060,16062,16064,16066],{},[898,16059,1854],{},[1688,16061,1690],{},[898,16063,1693],{},[1688,16065,1696],{},[898,16067,1699],{},[902,16069,14991],{"encoding":904},", ekvivalentně ",[883,16072,16074],{"className":16073},[886],[888,16075,16076],{"xmlns":890},[892,16077,16078,16086],{},[895,16079,16080,16082,16084],{},[898,16081,1699],{},[1688,16083,1690],{},[898,16085,1740],{},[902,16087,12960],{"encoding":904}," (investice = úspory).",[123,16090,16091,10277,16094,16096,16097,16147,16148,13163,16150,2263],{},[38,16092,16093],{},"Křivka IS",[614,16095,12305],{},") — ",[883,16098,16100],{"className":16099},[886],[888,16101,16102],{"xmlns":890},[892,16103,16104,16144],{},[895,16105,16106,16108,16110,16122,16124,16126],{},[898,16107,1854],{},[1688,16109,1690],{},[1781,16111,16112,16114],{},[898,16113,2031],{},[895,16115,16116,16118,16120],{},[1793,16117,1795],{},[1688,16119,1954],{},[898,16121,207],{},[898,16123,2046],{},[1688,16125,1696],{},[1781,16127,16128,16136],{},[895,16129,16130,16132,16134],{},[898,16131,1918],{},[1688,16133,1696],{},[898,16135,2073],{},[895,16137,16138,16140,16142],{},[1793,16139,1795],{},[1688,16141,1954],{},[898,16143,207],{},[902,16145,16146],{"encoding":904},"Y = \\frac{c}{1-a}r + \\frac{b+d}{1-a}"," (7.14); ",[38,16149,12767],{},[883,16151,16153],{"className":16152},[886],[888,16154,16155],{"xmlns":890},[892,16156,16157,16169],{},[895,16158,16159,16161,16163,16165,16167],{},[1688,16160,2066],{"stretchy":2065},[898,16162,2046],{},[1688,16164,1733],{"separator":1732},[898,16166,1854],{},[1688,16168,2076],{"stretchy":2065},[902,16170,13185],{"encoding":904},[123,16172,16173,16048,16176,16202,16203,2263],{},[38,16174,16175],{},"Trh peněz",[883,16177,16179],{"className":16178},[886],[888,16180,16181],{"xmlns":890},[892,16182,16183,16199],{},[895,16184,16185,16191,16193],{},[1850,16186,16187,16189],{},[898,16188,1661],{},[898,16190,4440],{},[1688,16192,1690],{},[1850,16194,16195,16197],{},[898,16196,1661],{},[898,16198,1740],{},[902,16200,16201],{"encoding":904},"M^D = M^S"," při pevné nabídce ",[883,16204,16206],{"className":16205},[886],[888,16207,16208],{"xmlns":890},[892,16209,16210,16218],{},[895,16211,16212],{},[1850,16213,16214,16216],{},[898,16215,1661],{},[1688,16217,1857],{},[902,16219,16220],{"encoding":904},"M^* ",[123,16222,16223,7271,16226,2263],{},[38,16224,16225],{},"Transakční, opatrnostní, spekulační poptávka",[883,16227,16229],{"className":16228},[886],[888,16230,16231],{"xmlns":890},[892,16232,16233,16285],{},[895,16234,16235,16241,16243,16249,16251,16257,16259,16265,16267,16269,16275,16277,16279],{},[1850,16236,16237,16239],{},[898,16238,1661],{},[898,16240,4440],{},[1688,16242,1690],{},[1788,16244,16245,16247],{},[898,16246,10047],{},[1793,16248,1795],{},[1688,16250,1696],{},[1788,16252,16253,16255],{},[898,16254,10047],{},[1793,16256,1806],{},[1688,16258,1690],{},[1788,16260,16261,16263],{},[898,16262,2106],{},[1793,16264,1795],{},[898,16266,1854],{},[1688,16268,1696],{},[1788,16270,16271,16273],{},[898,16272,2106],{},[1793,16274,1806],{},[898,16276,2046],{},[1688,16278,1696],{},[1788,16280,16281,16283],{},[898,16282,2106],{},[1793,16284,2131],{},[902,16286,16287],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3",[123,16289,16290,10277,16293,16096,16295,16341,16342,16344],{},[38,16291,16292],{},"Křivka LM",[614,16294,12312],{},[883,16296,16298],{"className":16297},[886],[888,16299,16300],{"xmlns":890},[892,16301,16302,16338],{},[895,16303,16304,16310,16312,16318,16320,16322,16328,16330,16332],{},[1850,16305,16306,16308],{},[898,16307,1661],{},[1688,16309,1857],{},[1688,16311,1690],{},[1788,16313,16314,16316],{},[898,16315,2106],{},[1793,16317,1795],{},[898,16319,1854],{},[1688,16321,1696],{},[1788,16323,16324,16326],{},[898,16325,2106],{},[1793,16327,1806],{},[898,16329,2046],{},[1688,16331,1696],{},[1788,16333,16334,16336],{},[898,16335,2106],{},[1793,16337,2131],{},[902,16339,16340],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3"," (7.15); ",[38,16343,13904],{}," přímka.",[123,16346,16347,16350,16351,16385],{},[38,16348,16349],{},"Simultánní rovnováha"," — průsečík ",[883,16352,16354],{"className":16353},[886],[888,16355,16356],{"xmlns":890},[892,16357,16358,16382],{},[895,16359,16360,16362,16364,16366,16372,16374,16380],{},[898,16361,4509],{},[1688,16363,1690],{},[1688,16365,2066],{"stretchy":2065},[1850,16367,16368,16370],{},[898,16369,2046],{},[898,16371,4509],{},[1688,16373,1733],{"separator":1732},[1850,16375,16376,16378],{},[898,16377,1854],{},[898,16379,4509],{},[1688,16381,2076],{"stretchy":2065},[902,16383,16384],{"encoding":904},"E = (r^E, Y^E)"," křivek IS a LM.",[123,16387,16388,16391,16392,1343,16405,16418],{},[38,16389,16390],{},"Fiskální politika"," — nástroje ",[883,16393,16395],{"className":16394},[886],[888,16396,16397],{"xmlns":890},[892,16398,16399,16403],{},[895,16400,16401],{},[898,16402,1704],{},[902,16404,1704],{"encoding":904},[883,16406,16408],{"className":16407},[886],[888,16409,16410],{"xmlns":890},[892,16411,16412,16416],{},[895,16413,16414],{},[898,16415,3035],{},[902,16417,3035],{"encoding":904}," posouvající křivku IS.",[123,16420,16421,16424,16425,16442],{},[38,16422,16423],{},"Monetární politika"," — nástroj ",[883,16426,16428],{"className":16427},[886],[888,16429,16430],{"xmlns":890},[892,16431,16432,16440],{},[895,16433,16434],{},[1850,16435,16436,16438],{},[898,16437,1661],{},[1688,16439,1857],{},[902,16441,12400],{"encoding":904}," posouvající křivku LM.",[115,16444,4049],{"id":4048},[120,16446,16447,16456,16465,16475],{},[123,16448,16449,2170,16452],{},[38,16450,16451],{},"Kurz:",[207,16453,16455],{"className":16454,"dataFsResolvedFilePath":2210,"href":2211},[210],"Matematická ekonomie",[123,16457,16458,2170,16461],{},[38,16459,16460],{},"Přednáška:",[207,16462,16464],{"className":16463,"dataFsResolvedFilePath":868,"href":869},[210],"imek-blok-03",[123,16466,16467,2170,16470,16474],{},[38,16468,16469],{},"Nadřazené téma:",[207,16471,16473],{"className":16472,"dataFsResolvedFilePath":934,"href":935},[210],"narodni-duchod"," — makroekonomické modely C-I, C-I-G, C-I-G-X a úvod do IS-LM",[123,16476,16477,16480],{},[38,16478,16479],{},"Související:",[120,16481,16482,16489,16495],{},[123,16483,16484,16488],{},[207,16485,16487],{"className":16486,"dataFsResolvedFilePath":800,"href":801},[210],"poptavka-nabidka"," — paralela rovnovážného bodu (průsečík dvou křivek) v mikroekonomii",[123,16490,16491,16494],{},[207,16492,1145],{"className":16493,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro směrnice IS a LM",[123,16496,16497,16501],{},[207,16498,16500],{"className":16499,"dataFsResolvedFilePath":782,"href":783},[210],"funkce-vice-promennych"," — dvě neznámé a řešení lineárních soustav",{"title":641,"searchDepth":642,"depth":642,"links":16503},[16504,16505,16506,16507,16508,16509,16510,16511,16512,16513],{"id":12258,"depth":642,"text":12259},{"id":12410,"depth":642,"text":12411},{"id":12623,"depth":642,"text":12624},{"id":12916,"depth":642,"text":12917},{"id":13329,"depth":642,"text":13330},{"id":14121,"depth":642,"text":14122},{"id":14811,"depth":642,"text":14812},{"id":15717,"depth":642,"text":15718},{"id":15966,"depth":642,"text":15967},{"id":4048,"depth":642,"text":4049},{},"\u002Ftopics\u002Fis-lm",{"title":12250,"description":641},[1138,1137],"topics\u002Fis-lm",[1128,2226,1143,16520,16521,16522,16523,16473],"trh-zbozi","trh-penez","urokova-mira","investice","OcXqlUxNqiCsj643lVoQEu_ZWU2vH0D_lWZ_-SxoyHk",{"id":16526,"title":16527,"body":16528,"course":659,"courses":18119,"created":1129,"description":18120,"extension":661,"meta":18121,"navigation":664,"path":18122,"seo":18123,"sources":18124,"stem":18125,"tags":18126,"type":4113,"updated":677,"__hash__":18129},"topics\u002Ftopics\u002Flagrangeova-metoda.md","Lagrangeova metoda (vázané extrémy)",{"type":9,"value":16529,"toc":18107},[16530,16533,16629,16636,16656,16660,16665,16728,16747,16749,16752,16888,16890,17100,17134,17271,17275,17339,17355,17383,17387,17485,17489,17493,17544,17650,17864,17868,17911,18017,18069,18071],[12,16531,16527],{"id":16532},"lagrangeova-metoda-vázané-extrémy",[724,16534,16535,16536,4168,16559,16591,16592,16595,16596,16623,16624,16628],{},"Hledáme extrém funkce ",[883,16537,16539],{"className":16538},[886],[888,16540,16541],{"xmlns":890},[892,16542,16543,16557],{},[895,16544,16545,16547,16549,16551,16553,16555],{},[898,16546,2287],{},[1688,16548,2066],{"stretchy":2065},[898,16550,2292],{},[1688,16552,1733],{"separator":1732},[898,16554,2282],{},[1688,16556,2076],{"stretchy":2065},[902,16558,10095],{"encoding":904},[883,16560,16562],{"className":16561},[886],[888,16563,16564],{"xmlns":890},[892,16565,16566,16588],{},[895,16567,16568,16570,16572,16578,16580,16586],{},[898,16569,900],{},[1688,16571,2066],{"stretchy":2065},[1788,16573,16574,16576],{},[898,16575,1872],{},[1793,16577,1795],{},[1688,16579,1733],{"separator":1732},[1788,16581,16582,16584],{},[898,16583,1872],{},[1793,16585,1806],{},[1688,16587,2076],{"stretchy":2065},[902,16589,16590],{"encoding":904},"U(Q_1, Q_2)"," apod.) ",[38,16593,16594],{},"podmíněný"," rovnicí ",[883,16597,16599],{"className":16598},[886],[888,16600,16601],{"xmlns":890},[892,16602,16603,16621],{},[895,16604,16605,16607,16609,16611,16613,16615,16617,16619],{},[898,16606,11292],{},[1688,16608,2066],{"stretchy":2065},[898,16610,2292],{},[1688,16612,1733],{"separator":1732},[898,16614,2282],{},[1688,16616,2076],{"stretchy":2065},[1688,16618,1690],{},[1793,16620,1779],{},[902,16622,11309],{"encoding":904},". V ",[207,16625,16627],{"className":16626,"dataFsResolvedFilePath":2210,"href":2211},[210],"matematické ekonomii"," se používá pro:",[724,16630,16631],{},[2821,16632],{"alt":16633,"className":16634,"src":16635},"imek-lagrange-tecnost",[210,2825],"\u002Fwiki-assets\u002Fimek-lagrange-tecnost.jpeg",[120,16637,16638,16647,16653],{},[123,16639,16640,16643,16644,2076],{},[38,16641,16642],{},"Maximalizaci užitečnosti"," při rozpočtovém omezení (viz ",[207,16645,2225],{"className":16646,"dataFsResolvedFilePath":878,"href":879},[210],[123,16648,16649,16652],{},[38,16650,16651],{},"Minimalizaci výdajů"," při dané úrovni užitečnosti (duální úloha)",[123,16654,16655],{},"Optimalizaci produkce \u002F nákladů za omezení",[115,16657,16659],{"id":16658},"princip","Princip",[724,16661,10958,16662,2965],{},[38,16663,16664],{},"Lagrangeovu funkci",[724,16666,16667],{},[883,16668,16670],{"className":16669},[886],[888,16671,16672],{"xmlns":890},[892,16673,16674,16725],{},[895,16675,16676,16678,16680,16682,16684,16686,16688,16691,16693,16695,16697,16699,16701,16703,16705,16707,16709,16711,16713,16715,16717,16719,16721,16723],{},[898,16677,10047],{},[1688,16679,2066],{"stretchy":2065},[898,16681,2292],{},[1688,16683,1733],{"separator":1732},[898,16685,2282],{},[1688,16687,1733],{"separator":1732},[898,16689,16690],{},"λ",[1688,16692,2076],{"stretchy":2065},[1688,16694,1690],{},[898,16696,2287],{},[1688,16698,2066],{"stretchy":2065},[898,16700,2292],{},[1688,16702,1733],{"separator":1732},[898,16704,2282],{},[1688,16706,2076],{"stretchy":2065},[1688,16708,1696],{},[898,16710,16690],{},[2041,16712,2043],{},[898,16714,11292],{},[1688,16716,2066],{"stretchy":2065},[898,16718,2292],{},[1688,16720,1733],{"separator":1732},[898,16722,2282],{},[1688,16724,2076],{"stretchy":2065},[902,16726,16727],{"encoding":904},"L(x, y, \\lambda) = f(x, y) + \\lambda\\, g(x, y)",[724,16729,4567,16730,8358,16744,2263],{},[883,16731,16733],{"className":16732},[886],[888,16734,16735],{"xmlns":890},[892,16736,16737,16741],{},[895,16738,16739],{},[898,16740,16690],{},[902,16742,16743],{"encoding":904},"\\lambda",[38,16745,16746],{},"Lagrangeův multiplikátor",[115,16748,3509],{"id":3508},[724,16750,16751],{},"Řešíme soustavu:",[724,16753,16754,16802,16850],{},[883,16755,16757],{"className":16756},[886],[888,16758,16759],{"xmlns":890},[892,16760,16761,16799],{},[895,16762,16763,16771,16773,16781,16783,16785,16787,16795,16797],{},[1814,16764,16765,16767,16769],{},[898,16766,10047],{},[898,16768,2292],{},[1688,16770,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,16772,1690],{},[1814,16774,16775,16777,16779],{},[898,16776,2287],{},[898,16778,2292],{},[1688,16780,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,16782,1696],{},[898,16784,16690],{},[2041,16786,2043],{},[1814,16788,16789,16791,16793],{},[898,16790,11292],{},[898,16792,2292],{},[1688,16794,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,16796,1690],{},[1793,16798,1779],{},[902,16800,16801],{"encoding":904},"L'_x = f'_x + \\lambda\\, g'_x = 0",[883,16803,16805],{"className":16804},[886],[888,16806,16807],{"xmlns":890},[892,16808,16809,16847],{},[895,16810,16811,16819,16821,16829,16831,16833,16835,16843,16845],{},[1814,16812,16813,16815,16817],{},[898,16814,10047],{},[898,16816,2282],{},[1688,16818,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,16820,1690],{},[1814,16822,16823,16825,16827],{},[898,16824,2287],{},[898,16826,2282],{},[1688,16828,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,16830,1696],{},[898,16832,16690],{},[2041,16834,2043],{},[1814,16836,16837,16839,16841],{},[898,16838,11292],{},[898,16840,2282],{},[1688,16842,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,16844,1690],{},[1793,16846,1779],{},[902,16848,16849],{"encoding":904},"L'_y = f'_y + \\lambda\\, g'_y = 0",[883,16851,16853],{"className":16852},[886],[888,16854,16855],{"xmlns":890},[892,16856,16857,16885],{},[895,16858,16859,16867,16869,16871,16873,16875,16877,16879,16881,16883],{},[1814,16860,16861,16863,16865],{},[898,16862,10047],{},[898,16864,16690],{},[1688,16866,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,16868,1690],{},[898,16870,11292],{},[1688,16872,2066],{"stretchy":2065},[898,16874,2292],{},[1688,16876,1733],{"separator":1732},[898,16878,2282],{},[1688,16880,2076],{"stretchy":2065},[1688,16882,1690],{},[1793,16884,1779],{},[902,16886,16887],{"encoding":904},"L'_\\lambda = g(x, y) = 0",[115,16889,3583],{"id":3582},[724,16891,16892],{},[883,16893,16895],{"className":16894},[886],[888,16896,16897],{"xmlns":890},[892,16898,16899,17097],{},[895,16900,16901,16903,16905,16907,16909,16911,16913,16915,16917,16919,16921,16937,16939,16941,16957,16959,16961,16969,16975,16977,16979,16995,16997,16999,17015,17017,17019,17027,17033,17035,17037,17039,17055,17057,17059,17075,17077,17079,17087,17089],{},[898,16902,4440],{},[1688,16904,2066],{"stretchy":2065},[898,16906,2292],{},[1688,16908,1733],{"separator":1732},[898,16910,2282],{},[1688,16912,1733],{"separator":1732},[898,16914,16690],{},[1688,16916,2076],{"stretchy":2065},[1688,16918,1690],{},[1688,16920,2066],{"stretchy":2065},[1814,16922,16923,16925,16931],{},[898,16924,2287],{},[895,16926,16927,16929],{},[898,16928,2292],{},[898,16930,2292],{},[895,16932,16933,16935],{},[1688,16934,1824],{"mathvariant":1822},[1688,16936,1824],{"mathvariant":1822},[1688,16938,1696],{},[898,16940,16690],{},[1814,16942,16943,16945,16951],{},[898,16944,11292],{},[895,16946,16947,16949],{},[898,16948,2292],{},[898,16950,2292],{},[895,16952,16953,16955],{},[1688,16954,1824],{"mathvariant":1822},[1688,16956,1824],{"mathvariant":1822},[1688,16958,2076],{"stretchy":2065},[1688,16960,2066],{"stretchy":2065},[1814,16962,16963,16965,16967],{},[898,16964,11292],{},[898,16966,2282],{},[1688,16968,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1850,16970,16971,16973],{},[1688,16972,2076],{"stretchy":2065},[1793,16974,1806],{},[1688,16976,1696],{},[1688,16978,2066],{"stretchy":2065},[1814,16980,16981,16983,16989],{},[898,16982,2287],{},[895,16984,16985,16987],{},[898,16986,2282],{},[898,16988,2282],{},[895,16990,16991,16993],{},[1688,16992,1824],{"mathvariant":1822},[1688,16994,1824],{"mathvariant":1822},[1688,16996,1696],{},[898,16998,16690],{},[1814,17000,17001,17003,17009],{},[898,17002,11292],{},[895,17004,17005,17007],{},[898,17006,2282],{},[898,17008,2282],{},[895,17010,17011,17013],{},[1688,17012,1824],{"mathvariant":1822},[1688,17014,1824],{"mathvariant":1822},[1688,17016,2076],{"stretchy":2065},[1688,17018,2066],{"stretchy":2065},[1814,17020,17021,17023,17025],{},[898,17022,11292],{},[898,17024,2292],{},[1688,17026,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1850,17028,17029,17031],{},[1688,17030,2076],{"stretchy":2065},[1793,17032,1806],{},[1688,17034,1954],{},[1793,17036,1806],{},[1688,17038,2066],{"stretchy":2065},[1814,17040,17041,17043,17049],{},[898,17042,2287],{},[895,17044,17045,17047],{},[898,17046,2292],{},[898,17048,2282],{},[895,17050,17051,17053],{},[1688,17052,1824],{"mathvariant":1822},[1688,17054,1824],{"mathvariant":1822},[1688,17056,1696],{},[898,17058,16690],{},[1814,17060,17061,17063,17069],{},[898,17062,11292],{},[895,17064,17065,17067],{},[898,17066,2292],{},[898,17068,2282],{},[895,17070,17071,17073],{},[1688,17072,1824],{"mathvariant":1822},[1688,17074,1824],{"mathvariant":1822},[1688,17076,2076],{"stretchy":2065},[2041,17078,2043],{},[1814,17080,17081,17083,17085],{},[898,17082,11292],{},[898,17084,2292],{},[1688,17086,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[2041,17088,2043],{},[1814,17090,17091,17093,17095],{},[898,17092,11292],{},[898,17094,2282],{},[1688,17096,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[902,17098,17099],{"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",[724,17101,17102,17103,17133],{},"Je-li ",[883,17104,17106],{"className":17105},[886],[888,17107,17108],{"xmlns":890},[892,17109,17110,17130],{},[895,17111,17112,17114,17116,17118,17120,17122,17128],{},[1688,17113,2748],{"stretchy":2065},[898,17115,207],{},[1688,17117,1733],{"separator":1732},[898,17119,1918],{},[1688,17121,1733],{"separator":1732},[1788,17123,17124,17126],{},[898,17125,16690],{},[1793,17127,1779],{},[1688,17129,2763],{"stretchy":2065},[902,17131,17132],{"encoding":904},"[a, b, \\lambda_0]"," podezřelý bod:",[120,17135,17136,17204],{},[123,17137,17138,3671,17174,17176,17177],{},[883,17139,17141],{"className":17140},[886],[888,17142,17143],{"xmlns":890},[892,17144,17145,17171],{},[895,17146,17147,17149,17151,17153,17155,17157,17159,17165,17167,17169],{},[898,17148,4440],{},[1688,17150,2066],{"stretchy":2065},[898,17152,207],{},[1688,17154,1733],{"separator":1732},[898,17156,1918],{},[1688,17158,1733],{"separator":1732},[1788,17160,17161,17163],{},[898,17162,16690],{},[1793,17164,1779],{},[1688,17166,2076],{"stretchy":2065},[1688,17168,3704],{},[1793,17170,1779],{},[902,17172,17173],{"encoding":904},"D(a, b, \\lambda_0) \u003C 0",[38,17175,3974],{}," vázané podmínkou ",[883,17178,17180],{"className":17179},[886],[888,17181,17182],{"xmlns":890},[892,17183,17184,17202],{},[895,17185,17186,17188,17190,17192,17194,17196,17198,17200],{},[898,17187,11292],{},[1688,17189,2066],{"stretchy":2065},[898,17191,2292],{},[1688,17193,1733],{"separator":1732},[898,17195,2282],{},[1688,17197,2076],{"stretchy":2065},[1688,17199,1690],{},[1793,17201,1779],{},[902,17203,11309],{"encoding":904},[123,17205,17206,3671,17242,17176,17244],{},[883,17207,17209],{"className":17208},[886],[888,17210,17211],{"xmlns":890},[892,17212,17213,17239],{},[895,17214,17215,17217,17219,17221,17223,17225,17227,17233,17235,17237],{},[898,17216,4440],{},[1688,17218,2066],{"stretchy":2065},[898,17220,207],{},[1688,17222,1733],{"separator":1732},[898,17224,1918],{},[1688,17226,1733],{"separator":1732},[1788,17228,17229,17231],{},[898,17230,16690],{},[1793,17232,1779],{},[1688,17234,2076],{"stretchy":2065},[1688,17236,3665],{},[1793,17238,1779],{},[902,17240,17241],{"encoding":904},"D(a, b, \\lambda_0) > 0",[38,17243,4032],{},[883,17245,17247],{"className":17246},[886],[888,17248,17249],{"xmlns":890},[892,17250,17251,17269],{},[895,17252,17253,17255,17257,17259,17261,17263,17265,17267],{},[898,17254,11292],{},[1688,17256,2066],{"stretchy":2065},[898,17258,2292],{},[1688,17260,1733],{"separator":1732},[898,17262,2282],{},[1688,17264,2076],{"stretchy":2065},[1688,17266,1690],{},[1793,17268,1779],{},[902,17270,11309],{"encoding":904},[115,17272,17274],{"id":17273},"význam-multiplikátoru","Význam multiplikátoru",[724,17276,17277],{},[883,17278,17280],{"className":17279},[886],[888,17281,17282],{"xmlns":890},[892,17283,17284,17336],{},[895,17285,17286,17288,17290,17312,17314],{},[898,17287,16690],{},[1688,17289,1690],{},[1781,17291,17292,17300],{},[1814,17293,17294,17296,17298],{},[898,17295,2287],{},[898,17297,2292],{},[1688,17299,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[895,17301,17302,17304],{},[1688,17303,1954],{},[1814,17305,17306,17308,17310],{},[898,17307,11292],{},[898,17309,2292],{},[1688,17311,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,17313,1690],{},[1781,17315,17316,17324],{},[1814,17317,17318,17320,17322],{},[898,17319,2287],{},[898,17321,2282],{},[1688,17323,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[895,17325,17326,17328],{},[1688,17327,1954],{},[1814,17329,17330,17332,17334],{},[898,17331,11292],{},[898,17333,2282],{},[1688,17335,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[902,17337,17338],{"encoding":904},"\\lambda = \\frac{f'_x}{-g'_x} = \\frac{f'_y}{-g'_y}",[724,17340,17341,17354],{},[883,17342,17344],{"className":17343},[886],[888,17345,17346],{"xmlns":890},[892,17347,17348,17352],{},[895,17349,17350],{},[898,17351,16690],{},[902,17353,16743],{"encoding":904}," udává:",[120,17356,17357,17363],{},[123,17358,17359,17360],{},"konstantní ",[38,17361,17362],{},"poměr mezi mezním prospěchem a mezním nákladem",[123,17364,17365,17368,17369,17382],{},[38,17366,17367],{},"náklady příležitosti"," (opportunity cost) — o kolik vzroste optimální hodnota ",[883,17370,17372],{"className":17371},[886],[888,17373,17374],{"xmlns":890},[892,17375,17376,17380],{},[895,17377,17378],{},[898,17379,2287],{},[902,17381,2287],{"encoding":904},", uvolní-li se omezení o jednotku",[115,17384,17386],{"id":17385},"alternativní-postup","Alternativní postup",[724,17388,17389,17390,17417,17418,17442,17443,17467,17468,17481,17482,2263],{},"Lze-li z ",[883,17391,17393],{"className":17392},[886],[888,17394,17395],{"xmlns":890},[892,17396,17397,17415],{},[895,17398,17399,17401,17403,17405,17407,17409,17411,17413],{},[898,17400,11292],{},[1688,17402,2066],{"stretchy":2065},[898,17404,2292],{},[1688,17406,1733],{"separator":1732},[898,17408,2282],{},[1688,17410,2076],{"stretchy":2065},[1688,17412,1690],{},[1793,17414,1779],{},[902,17416,11309],{"encoding":904}," vyjádřit ",[883,17419,17421],{"className":17420},[886],[888,17422,17423],{"xmlns":890},[892,17424,17425,17439],{},[895,17426,17427,17429,17431,17433,17435,17437],{},[898,17428,2282],{},[1688,17430,1690],{},[898,17432,2282],{},[1688,17434,2066],{"stretchy":2065},[898,17436,2292],{},[1688,17438,2076],{"stretchy":2065},[902,17440,17441],{"encoding":904},"y = y(x)"," (nebo ",[883,17444,17446],{"className":17445},[886],[888,17447,17448],{"xmlns":890},[892,17449,17450,17464],{},[895,17451,17452,17454,17456,17458,17460,17462],{},[898,17453,2292],{},[1688,17455,1690],{},[898,17457,2292],{},[1688,17459,2066],{"stretchy":2065},[898,17461,2282],{},[1688,17463,2076],{"stretchy":2065},[902,17465,17466],{"encoding":904},"x = x(y)","), dosadíme do ",[883,17469,17471],{"className":17470},[886],[888,17472,17473],{"xmlns":890},[892,17474,17475,17479],{},[895,17476,17477],{},[898,17478,2287],{},[902,17480,2287],{"encoding":904}," a převedeme na ",[38,17483,17484],{},"extrém funkce jedné proměnné",[115,17486,17488],{"id":17487},"použití-v-imek","Použití v ImeK",[198,17490,17492],{"id":17491},"maximalizace-užitečnosti","Maximalizace užitečnosti",[724,17494,1839,17495,2263],{},[883,17496,17498],{"className":17497},[886],[888,17499,17500],{"xmlns":890},[892,17501,17502,17542],{},[895,17503,17504,17510,17512,17520,17526,17528,17536],{},[1850,17505,17506,17508],{},[898,17507,1854],{},[1688,17509,1857],{},[1688,17511,1690],{},[1814,17513,17514,17516,17518],{},[898,17515,1727],{},[1793,17517,1795],{},[1688,17519,1857],{},[1788,17521,17522,17524],{},[898,17523,1872],{},[1793,17525,1795],{},[1688,17527,1696],{},[1814,17529,17530,17532,17534],{},[898,17531,1727],{},[1793,17533,1806],{},[1688,17535,1857],{},[1788,17537,17538,17540],{},[898,17539,1872],{},[1793,17541,1806],{},[902,17543,1893],{"encoding":904},[724,17545,17546],{},[883,17547,17549],{"className":17548},[886],[888,17550,17551],{"xmlns":890},[892,17552,17553,17647],{},[895,17554,17555,17557,17559,17565,17567,17573,17575,17577,17579,17581,17583,17585,17591,17593,17599,17601,17603,17605,17607,17613,17615,17623,17629,17631,17639,17645],{},[898,17556,10047],{},[1688,17558,2066],{"stretchy":2065},[1788,17560,17561,17563],{},[898,17562,1872],{},[1793,17564,1795],{},[1688,17566,1733],{"separator":1732},[1788,17568,17569,17571],{},[898,17570,1872],{},[1793,17572,1806],{},[1688,17574,1733],{"separator":1732},[898,17576,16690],{},[1688,17578,2076],{"stretchy":2065},[1688,17580,1690],{},[898,17582,900],{},[1688,17584,2066],{"stretchy":2065},[1788,17586,17587,17589],{},[898,17588,1872],{},[1793,17590,1795],{},[1688,17592,1733],{"separator":1732},[1788,17594,17595,17597],{},[898,17596,1872],{},[1793,17598,1806],{},[1688,17600,2076],{"stretchy":2065},[1688,17602,1696],{},[898,17604,16690],{},[1688,17606,2066],{"stretchy":2065},[1850,17608,17609,17611],{},[898,17610,1854],{},[1688,17612,1857],{},[1688,17614,1954],{},[1814,17616,17617,17619,17621],{},[898,17618,1727],{},[1793,17620,1795],{},[1688,17622,1857],{},[1788,17624,17625,17627],{},[898,17626,1872],{},[1793,17628,1795],{},[1688,17630,1954],{},[1814,17632,17633,17635,17637],{},[898,17634,1727],{},[1793,17636,1806],{},[1688,17638,1857],{},[1788,17640,17641,17643],{},[898,17642,1872],{},[1793,17644,1806],{},[1688,17646,2076],{"stretchy":2065},[902,17648,17649],{"encoding":904},"L(Q_1, Q_2, \\lambda) = U(Q_1, Q_2) + \\lambda (Y^* - P_1^* Q_1 - P_2^* Q_2)",[724,17651,17652,17653,1343,17685,1343,17717,17766,17767,17821,17822,2263],{},"Soustava: ",[883,17654,17656],{"className":17655},[886],[888,17657,17658],{"xmlns":890},[892,17659,17660,17682],{},[895,17661,17662,17670,17672,17674],{},[1814,17663,17664,17666,17668],{},[898,17665,900],{},[1793,17667,1795],{},[1688,17669,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,17671,1690],{},[898,17673,16690],{},[1814,17675,17676,17678,17680],{},[898,17677,1727],{},[1793,17679,1795],{},[1688,17681,1857],{},[902,17683,17684],{"encoding":904},"U'_1 = \\lambda P_1^*",[883,17686,17688],{"className":17687},[886],[888,17689,17690],{"xmlns":890},[892,17691,17692,17714],{},[895,17693,17694,17702,17704,17706],{},[1814,17695,17696,17698,17700],{},[898,17697,900],{},[1793,17699,1806],{},[1688,17701,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,17703,1690],{},[898,17705,16690],{},[1814,17707,17708,17710,17712],{},[898,17709,1727],{},[1793,17711,1806],{},[1688,17713,1857],{},[902,17715,17716],{"encoding":904},"U'_2 = \\lambda P_2^*",[883,17718,17720],{"className":17719},[886],[888,17721,17722],{"xmlns":890},[892,17723,17724,17764],{},[895,17725,17726,17732,17734,17742,17748,17750,17758],{},[1850,17727,17728,17730],{},[898,17729,1854],{},[1688,17731,1857],{},[1688,17733,1690],{},[1814,17735,17736,17738,17740],{},[898,17737,1727],{},[1793,17739,1795],{},[1688,17741,1857],{},[1788,17743,17744,17746],{},[898,17745,1872],{},[1793,17747,1795],{},[1688,17749,1696],{},[1814,17751,17752,17754,17756],{},[898,17753,1727],{},[1793,17755,1806],{},[1688,17757,1857],{},[1788,17759,17760,17762],{},[898,17761,1872],{},[1793,17763,1806],{},[902,17765,1893],{"encoding":904},". Z prvních dvou: ",[883,17768,17770],{"className":17769},[886],[888,17771,17772],{"xmlns":890},[892,17773,17774,17818],{},[895,17775,17776,17796,17798],{},[1777,17777,17778],{"scriptlevel":1779,"displaystyle":2065},[1781,17779,17780,17788],{},[1814,17781,17782,17784,17786],{},[898,17783,900],{},[1793,17785,1795],{},[1688,17787,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1814,17789,17790,17792,17794],{},[898,17791,900],{},[1793,17793,1806],{},[1688,17795,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,17797,1690],{},[1777,17799,17800],{"scriptlevel":1779,"displaystyle":2065},[1781,17801,17802,17810],{},[1814,17803,17804,17806,17808],{},[898,17805,1727],{},[1793,17807,1795],{},[1688,17809,1857],{},[1814,17811,17812,17814,17816],{},[898,17813,1727],{},[1793,17815,1806],{},[1688,17817,1857],{},[902,17819,17820],{"encoding":904},"\\tfrac{U'_1}{U'_2} = \\tfrac{P_1^*}{P_2^*}",", tj. ",[883,17823,17825],{"className":17824},[886],[888,17826,17827],{"xmlns":890},[892,17828,17829,17861],{},[895,17830,17831,17833,17835,17837,17839,17841],{},[898,17832,1661],{},[898,17834,4251],{},[898,17836,1693],{},[898,17838,1740],{},[1688,17840,1690],{},[1777,17842,17843],{"scriptlevel":1779,"displaystyle":2065},[1781,17844,17845,17853],{},[1814,17846,17847,17849,17851],{},[898,17848,1727],{},[1793,17850,1795],{},[1688,17852,1857],{},[1814,17854,17855,17857,17859],{},[898,17856,1727],{},[1793,17858,1806],{},[1688,17860,1857],{},[902,17862,17863],{"encoding":904},"MRCS = \\tfrac{P_1^*}{P_2^*}",[198,17865,17867],{"id":17866},"minimalizace-výdajů","Minimalizace výdajů",[724,17869,17870,17871,2263],{},"Podmínka dané užitečnosti ",[883,17872,17874],{"className":17873},[886],[888,17875,17876],{"xmlns":890},[892,17877,17878,17908],{},[895,17879,17880,17886,17888,17890,17892,17898,17900,17906],{},[1850,17881,17882,17884],{},[898,17883,900],{},[1688,17885,1857],{},[1688,17887,1690],{},[898,17889,900],{},[1688,17891,2066],{"stretchy":2065},[1788,17893,17894,17896],{},[898,17895,1872],{},[1793,17897,1795],{},[1688,17899,1733],{"separator":1732},[1788,17901,17902,17904],{},[898,17903,1872],{},[1793,17905,1806],{},[1688,17907,2076],{"stretchy":2065},[902,17909,17910],{"encoding":904},"U^* = U(Q_1, Q_2)",[724,17912,17913],{},[883,17914,17916],{"className":17915},[886],[888,17917,17918],{"xmlns":890},[892,17919,17920,18014],{},[895,17921,17922,17924,17926,17932,17934,17940,17942,17944,17946,17948,17956,17962,17964,17972,17978,17980,17982,17984,17990,17992,17994,17996,18002,18004,18010,18012],{},[898,17923,10047],{},[1688,17925,2066],{"stretchy":2065},[1788,17927,17928,17930],{},[898,17929,1872],{},[1793,17931,1795],{},[1688,17933,1733],{"separator":1732},[1788,17935,17936,17938],{},[898,17937,1872],{},[1793,17939,1806],{},[1688,17941,1733],{"separator":1732},[898,17943,16690],{},[1688,17945,2076],{"stretchy":2065},[1688,17947,1690],{},[1814,17949,17950,17952,17954],{},[898,17951,1727],{},[1793,17953,1795],{},[1688,17955,1857],{},[1788,17957,17958,17960],{},[898,17959,1872],{},[1793,17961,1795],{},[1688,17963,1696],{},[1814,17965,17966,17968,17970],{},[898,17967,1727],{},[1793,17969,1806],{},[1688,17971,1857],{},[1788,17973,17974,17976],{},[898,17975,1872],{},[1793,17977,1806],{},[1688,17979,1696],{},[898,17981,16690],{},[1688,17983,2066],{"stretchy":2065},[1850,17985,17986,17988],{},[898,17987,900],{},[1688,17989,1857],{},[1688,17991,1954],{},[898,17993,900],{},[1688,17995,2066],{"stretchy":2065},[1788,17997,17998,18000],{},[898,17999,1872],{},[1793,18001,1795],{},[1688,18003,1733],{"separator":1732},[1788,18005,18006,18008],{},[898,18007,1872],{},[1793,18009,1806],{},[1688,18011,2076],{"stretchy":2065},[1688,18013,2076],{"stretchy":2065},[902,18015,18016],{"encoding":904},"L(Q_1, Q_2, \\lambda) = P_1^* Q_1 + P_2^* Q_2 + \\lambda (U^* - U(Q_1, Q_2))",[724,18018,18019,18020,2263],{},"Duálně dostaneme Hicksovy poptávkové funkce ",[883,18021,18023],{"className":18022},[886],[888,18024,18025],{"xmlns":890},[892,18026,18027,18066],{},[895,18028,18029,18036,18038,18044,18046,18052,18054,18060,18062,18064],{},[1788,18030,18031,18033],{},[898,18032,1872],{},[898,18034,18035],{},"i",[1688,18037,1690],{},[1788,18039,18040,18042],{},[898,18041,4440],{},[898,18043,18035],{},[1688,18045,2066],{"stretchy":2065},[1788,18047,18048,18050],{},[898,18049,1727],{},[1793,18051,1795],{},[1688,18053,1733],{"separator":1732},[1788,18055,18056,18058],{},[898,18057,1727],{},[1793,18059,1806],{},[1688,18061,1733],{"separator":1732},[898,18063,900],{},[1688,18065,2076],{"stretchy":2065},[902,18067,18068],{"encoding":904},"Q_i = D_i(P_1, P_2, U)",[115,18070,4049],{"id":4048},[120,18072,18073,18080,18087,18096],{},[123,18074,18075,2170,18077],{},[38,18076,4056],{},[207,18078,784],{"className":18079,"dataFsResolvedFilePath":782,"href":783},[210],[123,18081,18082,2170,18084],{},[38,18083,2179],{},[207,18085,12193],{"className":18086,"dataFsResolvedFilePath":800,"href":801},[210],[123,18088,18089,2170,18092,18095],{},[38,18090,18091],{},"Aplikace v kurzu:",[207,18093,880],{"className":18094,"dataFsResolvedFilePath":878,"href":879},[210]," (maximalizace užitečnosti při rozpočtovém omezení), minimalizace výdajů (duální úloha), optimalizace produkce",[123,18097,18098,2170,18100,1343,18103,18106],{},[38,18099,4071],{},[207,18101,936],{"className":18102,"dataFsResolvedFilePath":934,"href":935},[210],[207,18104,1400],{"className":18105,"dataFsResolvedFilePath":1398,"href":1399},[210]," (IpmrK)",{"title":641,"searchDepth":642,"depth":642,"links":18108},[18109,18110,18111,18112,18113,18114,18118],{"id":16658,"depth":642,"text":16659},{"id":3508,"depth":642,"text":3509},{"id":3582,"depth":642,"text":3583},{"id":17273,"depth":642,"text":17274},{"id":17385,"depth":642,"text":17386},{"id":17487,"depth":642,"text":17488,"children":18115},[18116,18117],{"id":17491,"depth":649,"text":17492},{"id":17866,"depth":649,"text":17867},{"id":4048,"depth":642,"text":4049},[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":16527,"description":18120},[1135,1137],"topics\u002Flagrangeova-metoda",[1128,1619,18127,18128],"vazane-extremy","multiplikator","PRnK6wpMGySFp-C47ico7wAs4MDBp47Titm-Obyzgow",{"id":18131,"title":936,"body":18132,"course":1128,"courses":659,"created":9809,"description":641,"extension":661,"meta":27996,"navigation":664,"path":27997,"seo":27998,"sources":27999,"stem":28000,"tags":28001,"type":4113,"updated":677,"__hash__":28004},"topics\u002Ftopics\u002Fnarodni-duchod.md",{"type":9,"value":18133,"toc":27958},[18134,18137,18139,18259,18394,18398,18401,18514,18518,18546,18593,18596,18662,18707,18710,18736,18767,18771,18775,18819,18863,18925,18980,18983,18987,18990,19037,19134,19239,19245,19322,19351,19490,19494,19523,19573,19720,19810,19814,19840,19878,19905,19943,20005,20080,20158,20216,20282,20326,20330,20388,20437,20482,20695,20815,20821,20825,20848,20852,20859,20863,20894,20929,20933,20983,21071,21113,21134,21196,21256,21260,21331,21399,21471,21586,21634,21638,21641,21682,21721,21744,21858,22022,22030,22057,22087,22090,22167,22320,22404,22743,22747,22871,23007,23143,23196,23199,23449,23530,23534,23537,23595,23627,23630,23679,23682,23753,23949,23953,24104,24334,24372,24425,24471,24474,24530,24579,24783,24873,24877,24893,24900,25069,25073,25144,25225,25306,25385,25531,25619,25623,25806,25937,25982,26079,26083,26822,26824,27875,27877],[12,18135,936],{"id":18136},"národní-důchod",[115,18138,12259],{"id":12258},[724,18140,18141,18142,2170,18146,18149,18150,2170,18153,18166,18167,18169,18170,18172,18173,18175,18176,18178,18179,2170,18181,18198,18199,18216,18217,18220,18221,4176],{},"Kapitola 7 ",[207,18143,18145],{"className":18144,"dataFsResolvedFilePath":2210,"href":2211},[210],"Matematické ekonomie",[38,18147,18148],{},"přechází z mikroekonomie do makroekonomie",": předmětem zkoumání už není jedna firma, ale celá národní ekonomika popsaná ",[38,18151,18152],{},"národním důchodem",[883,18154,18156],{"className":18155},[886],[888,18157,18158],{"xmlns":890},[892,18159,18160,18164],{},[895,18161,18162],{},[898,18163,1854],{},[902,18165,1854],{"encoding":904},". Budují se postupně bohatší modely — ",[38,18168,1747],{}," (jen spotřeba a investice) → ",[38,18171,1750],{}," (přidá vládu a zdanění) → ",[38,18174,1753],{}," (otevře ekonomiku o čistý export) → ",[38,18177,1756],{}," (propojí trh zboží s trhem peněz přes úrokovou míru). V každém modelu hledáme ",[38,18180,14132],{},[883,18182,18184],{"className":18183},[886],[888,18185,18186],{"xmlns":890},[892,18187,18188,18196],{},[895,18189,18190],{},[1850,18191,18192,18194],{},[898,18193,1854],{},[898,18195,4509],{},[902,18197,14150],{"encoding":904}," jako řešení soustavy lineárních rovnic; citlivost ",[883,18200,18202],{"className":18201},[886],[888,18203,18204],{"xmlns":890},[892,18205,18206,18214],{},[895,18207,18208],{},[1850,18209,18210,18212],{},[898,18211,1854],{},[898,18213,4509],{},[902,18215,14150],{"encoding":904}," na exogenní veličiny popisují ",[38,18218,18219],{},"multiplikátory"," (zejména Keynesův multiplikátor investic ",[883,18222,18224],{"className":18223},[886],[888,18225,18226],{"xmlns":890},[892,18227,18228,18256],{},[895,18229,18230,18232,18234,18236,18238,18240,18242,18244,18246,18248,18250,18252,18254],{},[1793,18231,1795],{},[898,18233,4930],{"mathvariant":1822},[1688,18235,2066],{"stretchy":2065},[1793,18237,1795],{},[1688,18239,1954],{},[898,18241,207],{},[1688,18243,2076],{"stretchy":2065},[1688,18245,1690],{},[1793,18247,1795],{},[898,18249,4930],{"mathvariant":1822},[898,18251,1661],{},[898,18253,1727],{},[898,18255,1740],{},[902,18257,18258],{"encoding":904},"1\u002F(1-a) = 1\u002FMPS",[4124,18260,18261],{},[724,18262,18263,18265,18266,18269,18270,18288,18289,18319,18320,18367,18368,18370,18371,18393],{},[883,18264,4412],{}," Intuice\n",[38,18267,18268],{},"Makroekonomie je zrcadlovým obrazem mikroekonomie"," na úrovni celé ekonomiky. Mezní sklon ke spotřebě ",[883,18271,18273],{"className":18272},[886],[888,18274,18275],{"xmlns":890},[892,18276,18277,18285],{},[895,18278,18279,18281,18283],{},[898,18280,1661],{},[898,18282,1727],{},[898,18284,1693],{},[902,18286,18287],{"encoding":904},"MPC"," je „ta část dodatečné korunky důchodu, kterou domácnost utratí“; zbytek ",[883,18290,18292],{"className":18291},[886],[888,18293,18294],{"xmlns":890},[892,18295,18296,18316],{},[895,18297,18298,18300,18302,18304,18306,18308,18310,18312,18314],{},[898,18299,1661],{},[898,18301,1727],{},[898,18303,1740],{},[1688,18305,1690],{},[1793,18307,1795],{},[1688,18309,1954],{},[898,18311,1661],{},[898,18313,1727],{},[898,18315,1693],{},[902,18317,18318],{"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 ",[883,18321,18323],{"className":18322},[886],[888,18324,18325],{"xmlns":890},[892,18326,18327,18364],{},[895,18328,18329,18331,18333,18335,18337,18343,18345,18348,18350,18352,18354,18356,18358,18360,18362],{},[1793,18330,1795],{},[1688,18332,1696],{},[898,18334,207],{},[1688,18336,1696],{},[1850,18338,18339,18341],{},[898,18340,207],{},[1793,18342,1806],{},[1688,18344,1696],{},[1688,18346,18347],{},"⋯",[1688,18349,1690],{},[1793,18351,1795],{},[898,18353,4930],{"mathvariant":1822},[1688,18355,2066],{"stretchy":2065},[1793,18357,1795],{},[1688,18359,1954],{},[898,18361,207],{},[1688,18363,2076],{"stretchy":2065},[902,18365,18366],{"encoding":904},"1 + a + a^2 + \\dots = 1\u002F(1-a)","). ",[38,18369,1756],{}," 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 ",[883,18372,18374],{"className":18373},[886],[888,18375,18376],{"xmlns":890},[892,18377,18378,18390],{},[895,18379,18380,18382,18384,18386,18388],{},[1688,18381,2066],{"stretchy":2065},[898,18383,1854],{},[1688,18385,1733],{"separator":1732},[898,18387,2046],{},[1688,18389,2076],{"stretchy":2065},[902,18391,18392],{"encoding":904},"(Y, r)"," jsou oba trhy v rovnováze současně.",[115,18395,18397],{"id":18396},"úvod-cílové-znalosti-kapitoly-7","Úvod — cílové znalosti kapitoly 7",[724,18399,18400],{},"Po prostudování kapitoly by čtenář měl umět:",[120,18402,18403,18406,18409,18412,18415,18418,18421,18511],{},[123,18404,18405],{},"popsat zjednodušený model národní ekonomiky,",[123,18407,18408],{},"formulovat pojmy funkcí spotřeby a úspor spolu s jejich základními vlastnostmi,",[123,18410,18411],{},"popsat lineární model spotřeby a úspor,",[123,18413,18414],{},"stanovit mezní sklony ke spotřebě a úsporám,",[123,18416,18417],{},"vymezit pojem makroekonomické rovnováhy ve vztahu k agregátní poptávce a nabídce,",[123,18419,18420],{},"vyložit pojmy křivek agregátní poptávky, agregátní nabídky a rovnovážného bodu,",[123,18422,18423,18424,1343,18441,1343,18463,4142,18488,18510],{},"popsat modely ",[883,18425,18427],{"className":18426},[886],[888,18428,18429],{"xmlns":890},[892,18430,18431,18439],{},[895,18432,18433,18435,18437],{},[898,18434,1693],{},[2041,18436,12539],{},[898,18438,1699],{},[902,18440,12544],{"encoding":904},[883,18442,18444],{"className":18443},[886],[888,18445,18446],{"xmlns":890},[892,18447,18448,18460],{},[895,18449,18450,18452,18454,18456,18458],{},[898,18451,1693],{},[2041,18453,12539],{},[898,18455,1699],{},[2041,18457,12539],{},[898,18459,1704],{},[902,18461,18462],{"encoding":904},"C\\text{-}I\\text{-}G",[883,18464,18466],{"className":18465},[886],[888,18467,18468],{"xmlns":890},[892,18469,18470,18486],{},[895,18471,18472,18474,18476,18478,18480,18482,18484],{},[898,18473,1693],{},[2041,18475,12539],{},[898,18477,1699],{},[2041,18479,12539],{},[898,18481,1704],{},[2041,18483,12539],{},[898,18485,1709],{},[902,18487,12571],{"encoding":904},[883,18489,18491],{"className":18490},[886],[888,18492,18493],{"xmlns":890},[892,18494,18495,18507],{},[895,18496,18497,18499,18501,18503,18505],{},[898,18498,1699],{},[898,18500,1740],{},[2041,18502,12539],{},[898,18504,10047],{},[898,18506,1661],{},[902,18508,18509],{"encoding":904},"IS\\text{-}LM"," národních ekonomik a vypočítat rovnovážné veličiny,",[123,18512,18513],{},"formulovat a stanovit základní makroekonomické multiplikátory.",[115,18515,18517],{"id":18516},"gnp-a-národní-důchod","GNP a národní důchod",[724,18519,18520,2170,18523,10277,18542,18545],{},[38,18521,18522],{},"Hrubý národní produkt",[883,18524,18526],{"className":18525},[886],[888,18527,18528],{"xmlns":890},[892,18529,18530,18539],{},[895,18531,18532,18534,18537],{},[898,18533,1704],{},[898,18535,18536],{},"N",[898,18538,1727],{},[902,18540,18541],{"encoding":904},"GNP",[614,18543,18544],{},"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:",[724,18547,18548],{},[883,18549,18551],{"className":18550},[886],[888,18552,18553],{"xmlns":890},[892,18554,18555,18590],{},[895,18556,18557,18559,18561,18563,18565,18567,18569,18571,18573,18575,18577,18579,18581,18583,18585,18588],{},[898,18558,1704],{},[898,18560,18536],{},[898,18562,1727],{},[1688,18564,1690],{},[898,18566,1693],{},[1688,18568,1696],{},[898,18570,1699],{},[1688,18572,1696],{},[898,18574,1704],{},[1688,18576,1696],{},[898,18578,1709],{},[1688,18580,1733],{"separator":1732},[6134,18582],{"width":6136},[1688,18584,2066],{"stretchy":2065},[1793,18586,18587],{},"7.1",[1688,18589,2076],{"stretchy":2065},[902,18591,18592],{"encoding":904},"GNP = C + I + G + X, \\qquad (7.1)",[724,18594,18595],{},"kde",[120,18597,18598,18614,18630,18646],{},[123,18599,18600,18613],{},[883,18601,18603],{"className":18602},[886],[888,18604,18605],{"xmlns":890},[892,18606,18607,18611],{},[895,18608,18609],{},[898,18610,1693],{},[902,18612,1693],{"encoding":904}," — výdaje domácností na spotřebu,",[123,18615,18616,18629],{},[883,18617,18619],{"className":18618},[886],[888,18620,18621],{"xmlns":890},[892,18622,18623,18627],{},[895,18624,18625],{},[898,18626,1699],{},[902,18628,1699],{"encoding":904}," — hrubé domácí investice,",[123,18631,18632,18645],{},[883,18633,18635],{"className":18634},[886],[888,18636,18637],{"xmlns":890},[892,18638,18639,18643],{},[895,18640,18641],{},[898,18642,1704],{},[902,18644,1704],{"encoding":904}," — vládní výdaje,",[123,18647,18648,18661],{},[883,18649,18651],{"className":18650},[886],[888,18652,18653],{"xmlns":890},[892,18654,18655,18659],{},[895,18656,18657],{},[898,18658,1709],{},[902,18660,1709],{"encoding":904}," — čistý export.",[724,18663,18664,18665,18682,18683,18686,18687,2170,18690,10277,18703,18706],{},"K měření ",[883,18666,18668],{"className":18667},[886],[888,18669,18670],{"xmlns":890},[892,18671,18672,18680],{},[895,18673,18674,18676,18678],{},[898,18675,1704],{},[898,18677,18536],{},[898,18679,1727],{},[902,18681,18541],{"encoding":904}," se užívá ",[38,18684,18685],{},"důchodová metoda",". Jejím hlavním konstrukčním prvkem je ",[38,18688,18689],{},"národní důchod",[883,18691,18693],{"className":18692},[886],[888,18694,18695],{"xmlns":890},[892,18696,18697,18701],{},[895,18698,18699],{},[898,18700,1854],{},[902,18702,1854],{"encoding":904},[614,18704,18705],{},"national income",") — součet důchodů všech vrstev domácností, tj. tok důchodů od firem k domácnostem jako platba za pronájem výrobních faktorů.",[724,18708,18709],{},"Pro tvorbu základních makroekonomických modelů se zjednodušeně ztotožňuje hrubý národní produkt s národním důchodem (rovněž s agregátní poptávkou):",[724,18711,18712],{},[883,18713,18715],{"className":18714},[886],[888,18716,18717],{"xmlns":890},[892,18718,18719,18733],{},[895,18720,18721,18723,18725,18727,18729,18731],{},[898,18722,1704],{},[898,18724,18536],{},[898,18726,1727],{},[1688,18728,2991],{},[898,18730,1854],{},[1688,18732,1733],{"separator":1732},[902,18734,18735],{"encoding":904},"GNP \\approx Y,",[724,18737,18738,18739,10277,18742,18745,18746,18759,18760,18763,18764,2263],{},"a užívá se společného názvu ",[38,18740,18741],{},"důchod",[614,18743,18744],{},"income",") s označením ",[883,18747,18749],{"className":18748},[886],[888,18750,18751],{"xmlns":890},[892,18752,18753,18757],{},[895,18754,18755],{},[898,18756,1854],{},[902,18758,1854],{"encoding":904},". Domácnosti důchod použijí ke ",[38,18761,18762],{},"spotřebě"," zboží a služeb nebo ke tvorbě ",[38,18765,18766],{},"úspor",[115,18768,18770],{"id":18769},"spotřeba-a-úspory","Spotřeba a úspory",[198,18772,18774],{"id":18773},"funkce-spotřeby-a-úspor","Funkce spotřeby a úspor",[724,18776,18777,18778,18791,18792,18805,18806,2965],{},"Jak spotřeba ",[883,18779,18781],{"className":18780},[886],[888,18782,18783],{"xmlns":890},[892,18784,18785,18789],{},[895,18786,18787],{},[898,18788,1693],{},[902,18790,1693],{"encoding":904},", tak úspory ",[883,18793,18795],{"className":18794},[886],[888,18796,18797],{"xmlns":890},[892,18798,18799,18803],{},[895,18800,18801],{},[898,18802,1740],{},[902,18804,1740],{"encoding":904}," závisejí na důchodu ",[883,18807,18809],{"className":18808},[886],[888,18810,18811],{"xmlns":890},[892,18812,18813,18817],{},[895,18814,18815],{},[898,18816,1854],{},[902,18818,1854],{"encoding":904},[724,18820,18821],{},[883,18822,18824],{"className":18823},[886],[888,18825,18826],{"xmlns":890},[892,18827,18828,18860],{},[895,18829,18830,18832,18834,18836,18838,18840,18842,18844,18846,18848,18850,18852,18854,18856,18858],{},[898,18831,1693],{},[1688,18833,1690],{},[898,18835,1693],{},[1688,18837,2066],{"stretchy":2065},[898,18839,1854],{},[1688,18841,2076],{"stretchy":2065},[1688,18843,1733],{"separator":1732},[6134,18845],{"width":6136},[898,18847,1740],{},[1688,18849,1690],{},[898,18851,1740],{},[1688,18853,2066],{"stretchy":2065},[898,18855,1854],{},[1688,18857,2076],{"stretchy":2065},[898,18859,2263],{"mathvariant":1822},[902,18861,18862],{"encoding":904},"C = C(Y), \\qquad S = S(Y).",[724,18864,18865,8358,18884,10277,18887,18890,18891,8358,18911,10277,18914,18917,18918,4142,18921,18924],{},[883,18866,18868],{"className":18867},[886],[888,18869,18870],{"xmlns":890},[892,18871,18872,18882],{},[895,18873,18874,18876,18878,18880],{},[898,18875,1693],{},[1688,18877,2066],{"stretchy":2065},[898,18879,1854],{},[1688,18881,2076],{"stretchy":2065},[902,18883,14463],{"encoding":904},[38,18885,18886],{},"funkce spotřeby",[614,18888,18889],{},"consumption function","), ",[883,18892,18894],{"className":18893},[886],[888,18895,18896],{"xmlns":890},[892,18897,18898,18908],{},[895,18899,18900,18902,18904,18906],{},[898,18901,1740],{},[1688,18903,2066],{"stretchy":2065},[898,18905,1854],{},[1688,18907,2076],{"stretchy":2065},[902,18909,18910],{"encoding":904},"S(Y)",[38,18912,18913],{},"funkce úspor",[614,18915,18916],{},"savings function","); jejich grafy se nazývají ",[38,18919,18920],{},"křivka spotřeby",[38,18922,18923],{},"křivka úspor",". Platí základní identita",[724,18926,18927],{},[883,18928,18930],{"className":18929},[886],[888,18931,18932],{"xmlns":890},[892,18933,18934,18977],{},[895,18935,18936,18938,18940,18942,18944,18946,18948,18950,18952,18954,18956,18958,18960,18962,18964,18966,18968,18970,18972,18975],{},[898,18937,1854],{},[1688,18939,1690],{},[898,18941,1693],{},[1688,18943,1696],{},[898,18945,1740],{},[1688,18947,1690],{},[898,18949,1693],{},[1688,18951,2066],{"stretchy":2065},[898,18953,1854],{},[1688,18955,2076],{"stretchy":2065},[1688,18957,1696],{},[898,18959,1740],{},[1688,18961,2066],{"stretchy":2065},[898,18963,1854],{},[1688,18965,2076],{"stretchy":2065},[898,18967,2263],{"mathvariant":1822},[6134,18969],{"width":6136},[1688,18971,2066],{"stretchy":2065},[1793,18973,18974],{},"7.2",[1688,18976,2076],{"stretchy":2065},[902,18978,18979],{"encoding":904},"Y = C + S = C(Y) + S(Y). \\qquad (7.2)",[724,18981,18982],{},"Známe-li jednu z funkcí, je tím určena i druhá. Obě funkce jsou rostoucí (s růstem důchodu roste spotřeba i úspory).",[198,18984,18986],{"id":18985},"lineární-model-spotřeby-a-úspor","Lineární model spotřeby a úspor",[724,18988,18989],{},"Nejjednodušší model předpokládá lineární tvar",[724,18991,18992],{},[883,18993,18995],{"className":18994},[886],[888,18996,18997],{"xmlns":890},[892,18998,18999,19034],{},[895,19000,19001,19003,19005,19007,19009,19011,19013,19015,19017,19019,19021,19023,19025,19027,19029,19032],{},[898,19002,1693],{},[1688,19004,1690],{},[898,19006,1693],{},[1688,19008,2066],{"stretchy":2065},[898,19010,1854],{},[1688,19012,2076],{"stretchy":2065},[1688,19014,1690],{},[898,19016,207],{},[898,19018,1854],{},[1688,19020,1696],{},[898,19022,1918],{},[1688,19024,1733],{"separator":1732},[6134,19026],{"width":6136},[1688,19028,2066],{"stretchy":2065},[1793,19030,19031],{},"7.3",[1688,19033,2076],{"stretchy":2065},[902,19035,19036],{"encoding":904},"C = C(Y) = aY + b, \\qquad (7.3)",[724,19038,4567,19039,4142,19057,19079,19080,19120,19121,2263],{},[883,19040,19042],{"className":19041},[886],[888,19043,19044],{"xmlns":890},[892,19045,19046,19054],{},[895,19047,19048,19050,19052],{},[898,19049,1918],{},[1688,19051,3665],{},[1793,19053,1779],{},[902,19055,19056],{"encoding":904},"b > 0",[883,19058,19060],{"className":19059},[886],[888,19061,19062],{"xmlns":890},[892,19063,19064,19076],{},[895,19065,19066,19068,19070,19072,19074],{},[1793,19067,1779],{},[1688,19069,3704],{},[898,19071,207],{},[1688,19073,3704],{},[1793,19075,1795],{},[902,19077,19078],{"encoding":904},"0 \u003C a \u003C 1",". Směrnice ",[883,19081,19083],{"className":19082},[886],[888,19084,19085],{"xmlns":890},[892,19086,19087,19117],{},[895,19088,19089,19091,19093,19100,19102,19105,19107,19109,19111,19113,19115],{},[898,19090,207],{},[1688,19092,1690],{},[895,19094,19095,19098],{},[898,19096,19097],{"mathvariant":1822},"t",[898,19099,11292],{"mathvariant":1822},[2041,19101,2043],{},[898,19103,19104],{},"α",[1688,19106,1690],{},[898,19108,3147],{"mathvariant":1822},[898,19110,1693],{},[898,19112,4930],{"mathvariant":1822},[898,19114,3147],{"mathvariant":1822},[898,19116,1854],{},[902,19118,19119],{"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 ",[883,19122,19124],{"className":19123},[886],[888,19125,19126],{"xmlns":890},[892,19127,19128,19132],{},[895,19129,19130],{},[898,19131,1854],{},[902,19133,1854],{"encoding":904},[724,19135,19136],{},[614,19137,19138,19139,19162,19163,19201,19202,19218,19219,2263],{},"Obrázek 7.1 — Přímka spotřeby ",[883,19140,19142],{"className":19141},[886],[888,19143,19144],{"xmlns":890},[892,19145,19146,19160],{},[895,19147,19148,19150,19152,19154,19156,19158],{},[898,19149,1693],{},[1688,19151,1690],{},[898,19153,207],{},[898,19155,1854],{},[1688,19157,1696],{},[898,19159,1918],{},[902,19161,1921],{"encoding":904}," se směrnicí ",[883,19164,19166],{"className":19165},[886],[888,19167,19168],{"xmlns":890},[892,19169,19170,19198],{},[895,19171,19172,19174,19176,19182,19184,19186,19188,19190,19192,19194,19196],{},[898,19173,207],{},[1688,19175,1690],{},[895,19177,19178,19180],{},[898,19179,19097],{"mathvariant":1822},[898,19181,11292],{"mathvariant":1822},[2041,19183,2043],{},[898,19185,19104],{},[1688,19187,1690],{},[898,19189,3147],{"mathvariant":1822},[898,19191,1693],{},[898,19193,4930],{"mathvariant":1822},[898,19195,3147],{"mathvariant":1822},[898,19197,1854],{},[902,19199,19200],{"encoding":904},"a = \\mathrm{tg}\\,\\alpha = \\Delta C\u002F\\Delta Y","; znázornění ",[883,19203,19205],{"className":19204},[886],[888,19206,19207],{"xmlns":890},[892,19208,19209,19215],{},[895,19210,19211,19213],{},[898,19212,3147],{"mathvariant":1822},[898,19214,1693],{},[902,19216,19217],{"encoding":904},"\\Delta C"," při jednotkovém přírůstku ",[883,19220,19222],{"className":19221},[886],[888,19223,19224],{"xmlns":890},[892,19225,19226,19236],{},[895,19227,19228,19230,19232,19234],{},[898,19229,3147],{"mathvariant":1822},[898,19231,1854],{},[1688,19233,1690],{},[1793,19235,1795],{},[902,19237,19238],{"encoding":904},"\\Delta Y = 1",[724,19240,19241,19242,2965],{},"Dosazením do (7.2) plyne ",[38,19243,19244],{},"lineární model úspor",[724,19246,19247],{},[883,19248,19250],{"className":19249},[886],[888,19251,19252],{"xmlns":890},[892,19253,19254,19319],{},[895,19255,19256,19258,19260,19262,19264,19266,19268,19270,19272,19274,19276,19278,19280,19282,19284,19286,19288,19290,19292,19294,19296,19298,19300,19302,19304,19306,19308,19310,19312,19314,19317],{},[898,19257,1740],{},[1688,19259,1690],{},[898,19261,1854],{},[1688,19263,1954],{},[898,19265,1693],{},[1688,19267,2066],{"stretchy":2065},[898,19269,1854],{},[1688,19271,2076],{"stretchy":2065},[1688,19273,1690],{},[898,19275,1854],{},[1688,19277,1954],{},[1688,19279,2066],{"stretchy":2065},[898,19281,207],{},[898,19283,1854],{},[1688,19285,1696],{},[898,19287,1918],{},[1688,19289,2076],{"stretchy":2065},[1688,19291,1690],{},[1688,19293,2066],{"stretchy":2065},[1793,19295,1795],{},[1688,19297,1954],{},[898,19299,207],{},[1688,19301,2076],{"stretchy":2065},[898,19303,1854],{},[1688,19305,1954],{},[898,19307,1918],{},[898,19309,2263],{"mathvariant":1822},[6134,19311],{"width":6136},[1688,19313,2066],{"stretchy":2065},[1793,19315,19316],{},"7.4",[1688,19318,2076],{"stretchy":2065},[902,19320,19321],{"encoding":904},"S = Y - C(Y) = Y - (aY + b) = (1 - a)Y - b. \\qquad (7.4)",[724,19323,19324,19325,4176],{},"Úspory jsou také lineární a „pomalu rostoucí“ (protože ",[883,19326,19328],{"className":19327},[886],[888,19329,19330],{"xmlns":890},[892,19331,19332,19348],{},[895,19333,19334,19336,19338,19340,19342,19344,19346],{},[1793,19335,1779],{},[1688,19337,3704],{},[1793,19339,1795],{},[1688,19341,1954],{},[898,19343,207],{},[1688,19345,3704],{},[1793,19347,1795],{},[902,19349,19350],{"encoding":904},"0 \u003C 1 - a \u003C 1",[724,19352,19353],{},[614,19354,19355,19356,4142,19379,19411,19412,2886,19425,19455,19456,2886,19474,2263],{},"Obrázek 7.2 — Přímky ",[883,19357,19359],{"className":19358},[886],[888,19360,19361],{"xmlns":890},[892,19362,19363,19377],{},[895,19364,19365,19367,19369,19371,19373,19375],{},[898,19366,1693],{},[1688,19368,1690],{},[898,19370,207],{},[898,19372,1854],{},[1688,19374,1696],{},[898,19376,1918],{},[902,19378,1921],{"encoding":904},[883,19380,19382],{"className":19381},[886],[888,19383,19384],{"xmlns":890},[892,19385,19386,19408],{},[895,19387,19388,19390,19392,19394,19396,19398,19400,19402,19404,19406],{},[898,19389,1740],{},[1688,19391,1690],{},[1688,19393,2066],{"stretchy":2065},[1793,19395,1795],{},[1688,19397,1954],{},[898,19399,207],{},[1688,19401,2076],{"stretchy":2065},[898,19403,1854],{},[1688,19405,1954],{},[898,19407,1918],{},[902,19409,19410],{"encoding":904},"S = (1-a)Y - b",". Přímka úspor protíná osu ",[883,19413,19415],{"className":19414},[886],[888,19416,19417],{"xmlns":890},[892,19418,19419,19423],{},[895,19420,19421],{},[898,19422,1854],{},[902,19424,1854],{"encoding":904},[883,19426,19428],{"className":19427},[886],[888,19429,19430],{"xmlns":890},[892,19431,19432,19452],{},[895,19433,19434,19436,19438,19440,19442,19444,19446,19448,19450],{},[898,19435,1854],{},[1688,19437,1690],{},[898,19439,1918],{},[898,19441,4930],{"mathvariant":1822},[1688,19443,2066],{"stretchy":2065},[1793,19445,1795],{},[1688,19447,1954],{},[898,19449,207],{},[1688,19451,2076],{"stretchy":2065},[902,19453,19454],{"encoding":904},"Y = b\u002F(1-a)"," a osu ",[883,19457,19459],{"className":19458},[886],[888,19460,19461],{"xmlns":890},[892,19462,19463,19471],{},[895,19464,19465,19467,19469],{},[898,19466,1693],{},[1688,19468,1733],{"separator":1732},[898,19470,1740],{},[902,19472,19473],{"encoding":904},"C, S",[883,19475,19477],{"className":19476},[886],[888,19478,19479],{"xmlns":890},[892,19480,19481,19487],{},[895,19482,19483,19485],{},[1688,19484,1954],{},[898,19486,1918],{},[902,19488,19489],{"encoding":904},"-b",[198,19491,19493],{"id":19492},"příklad-71","Příklad 7.1",[724,19495,19496,19497,19522],{},"Pro spotřebu ",[883,19498,19500],{"className":19499},[886],[888,19501,19502],{"xmlns":890},[892,19503,19504,19519],{},[895,19505,19506,19508,19510,19513,19515,19517],{},[898,19507,1693],{},[1688,19509,1690],{},[1793,19511,19512],{},"0,4",[898,19514,1854],{},[1688,19516,1696],{},[1793,19518,3121],{},[902,19520,19521],{"encoding":904},"C = 0{,}4Y + 10"," jsou úspory",[724,19524,19525],{},[883,19526,19528],{"className":19527},[886],[888,19529,19530],{"xmlns":890},[892,19531,19532,19570],{},[895,19533,19534,19536,19538,19540,19542,19544,19546,19548,19550,19552,19554,19556,19558,19560,19563,19565,19567],{},[898,19535,1740],{},[1688,19537,1690],{},[898,19539,1854],{},[1688,19541,1954],{},[898,19543,1693],{},[1688,19545,1690],{},[898,19547,1854],{},[1688,19549,1954],{},[1793,19551,19512],{},[898,19553,1854],{},[1688,19555,1954],{},[1793,19557,3121],{},[1688,19559,1690],{},[1793,19561,19562],{},"0,6",[898,19564,1854],{},[1688,19566,1954],{},[1793,19568,19569],{},"10.",[902,19571,19572],{"encoding":904},"S = Y - C = Y - 0{,}4Y - 10 = 0{,}6Y - 10.",[724,19574,19575],{},[614,19576,19577,19578,4142,19601,19625,19626,8358,19639,19663,19664,8358,19681,19697,19698,2263],{},"Obrázek 7.3 — Přímky ",[883,19579,19581],{"className":19580},[886],[888,19582,19583],{"xmlns":890},[892,19584,19585,19599],{},[895,19586,19587,19589,19591,19593,19595,19597],{},[898,19588,1693],{},[1688,19590,1690],{},[1793,19592,19512],{},[898,19594,1854],{},[1688,19596,1696],{},[1793,19598,3121],{},[902,19600,19521],{"encoding":904},[883,19602,19604],{"className":19603},[886],[888,19605,19606],{"xmlns":890},[892,19607,19608,19622],{},[895,19609,19610,19612,19614,19616,19618,19620],{},[898,19611,1740],{},[1688,19613,1690],{},[1793,19615,19562],{},[898,19617,1854],{},[1688,19619,1954],{},[1793,19621,3121],{},[902,19623,19624],{"encoding":904},"S = 0{,}6Y - 10","; průsečík přímky úspor s osou ",[883,19627,19629],{"className":19628},[886],[888,19630,19631],{"xmlns":890},[892,19632,19633,19637],{},[895,19634,19635],{},[898,19636,1854],{},[902,19638,1854],{"encoding":904},[883,19640,19642],{"className":19641},[886],[888,19643,19644],{"xmlns":890},[892,19645,19646,19660],{},[895,19647,19648,19650,19653],{},[1688,19649,2991],{},[1793,19651,19652],{},"16,",[8642,19654,19655,19657],{"accent":1732},[1793,19656,2508],{},[1688,19658,19659],{},"ˉ",[902,19661,19662],{"encoding":904},"\\approx 16{,}\\bar{6}",", s osou ",[883,19665,19667],{"className":19666},[886],[888,19668,19669],{"xmlns":890},[892,19670,19671,19679],{},[895,19672,19673,19675,19677],{},[898,19674,1693],{},[1688,19676,1733],{"separator":1732},[898,19678,1740],{},[902,19680,19473],{"encoding":904},[883,19682,19684],{"className":19683},[886],[888,19685,19686],{"xmlns":890},[892,19687,19688,19694],{},[895,19689,19690,19692],{},[1688,19691,1954],{},[1793,19693,3121],{},[902,19695,19696],{"encoding":904},"-10","; přímka spotřeby prochází bodem ",[883,19699,19701],{"className":19700},[886],[888,19702,19703],{"xmlns":890},[892,19704,19705,19717],{},[895,19706,19707,19709,19711,19713,19715],{},[1688,19708,2066],{"stretchy":2065},[1793,19710,1779],{},[1688,19712,1733],{"separator":1732},[1793,19714,3121],{},[1688,19716,2076],{"stretchy":2065},[902,19718,19719],{"encoding":904},"(0, 10)",[724,19721,19722,19723,8358,19741,19771,19772,10277,19775,19778,19779,8358,19803,10277,19806,19809],{},"Funkce úspor může nabývat záporných hodnot — pro ",[883,19724,19726],{"className":19725},[886],[888,19727,19728],{"xmlns":890},[892,19729,19730,19738],{},[895,19731,19732,19734,19736],{},[898,19733,1854],{},[1688,19735,1690],{},[1793,19737,1779],{},[902,19739,19740],{"encoding":904},"Y = 0",[883,19742,19744],{"className":19743},[886],[888,19745,19746],{"xmlns":890},[892,19747,19748,19768],{},[895,19749,19750,19752,19754,19756,19758,19760,19762,19764,19766],{},[898,19751,1740],{},[1688,19753,2066],{"stretchy":2065},[1793,19755,1779],{},[1688,19757,2076],{"stretchy":2065},[1688,19759,1690],{},[1688,19761,1954],{},[898,19763,1918],{},[1688,19765,3704],{},[1793,19767,1779],{},[902,19769,19770],{"encoding":904},"S(0) = -b \u003C 0","; hovoří se o ",[38,19773,19774],{},"autonomních úsporách",[614,19776,19777],{},"autonomous savings","). Analogicky ",[883,19780,19782],{"className":19781},[886],[888,19783,19784],{"xmlns":890},[892,19785,19786,19800],{},[895,19787,19788,19790,19792,19794,19796,19798],{},[898,19789,1693],{},[1688,19791,2066],{"stretchy":2065},[1793,19793,1779],{},[1688,19795,2076],{"stretchy":2065},[1688,19797,1690],{},[898,19799,1918],{},[902,19801,19802],{"encoding":904},"C(0) = b",[38,19804,19805],{},"autonomní spotřeba",[614,19807,19808],{},"autonomous consumption",") — spotřeba při nulovém důchodu krytá dřívějšími úsporami.",[115,19811,19813],{"id":19812},"mezní-sklon-ke-spotřebě-mpc-a-k-úsporám-mps","Mezní sklon ke spotřebě (MPC) a k úsporám (MPS)",[724,19815,19816,2170,19819,10277,19836,19839],{},[38,19817,19818],{},"Mezní sklon ke spotřebě",[883,19820,19822],{"className":19821},[886],[888,19823,19824],{"xmlns":890},[892,19825,19826,19834],{},[895,19827,19828,19830,19832],{},[898,19829,1661],{},[898,19831,1727],{},[898,19833,1693],{},[902,19835,18287],{"encoding":904},[614,19837,19838],{},"marginal propensity to consume",") je derivace spotřeby podle důchodu:",[724,19841,19842],{},[883,19843,19845],{"className":19844},[886],[888,19846,19847],{"xmlns":890},[892,19848,19849,19875],{},[895,19850,19851,19853,19855,19857,19859,19873],{},[898,19852,1661],{},[898,19854,1727],{},[898,19856,1693],{},[1688,19858,1690],{},[1781,19860,19861,19867],{},[895,19862,19863,19865],{},[898,19864,2073],{"mathvariant":1822},[898,19866,1693],{},[895,19868,19869,19871],{},[898,19870,2073],{"mathvariant":1822},[898,19872,1854],{},[898,19874,2263],{"mathvariant":1822},[902,19876,19877],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y}.",[724,19879,19880,2170,19883,10277,19901,19904],{},[38,19881,19882],{},"Mezní sklon k úsporám",[883,19884,19886],{"className":19885},[886],[888,19887,19888],{"xmlns":890},[892,19889,19890,19898],{},[895,19891,19892,19894,19896],{},[898,19893,1661],{},[898,19895,1727],{},[898,19897,1740],{},[902,19899,19900],{"encoding":904},"MPS",[614,19902,19903],{},"marginal propensity to save",") je derivace úspor podle důchodu:",[724,19906,19907],{},[883,19908,19910],{"className":19909},[886],[888,19911,19912],{"xmlns":890},[892,19913,19914,19940],{},[895,19915,19916,19918,19920,19922,19924,19938],{},[898,19917,1661],{},[898,19919,1727],{},[898,19921,1740],{},[1688,19923,1690],{},[1781,19925,19926,19932],{},[895,19927,19928,19930],{},[898,19929,2073],{"mathvariant":1822},[898,19931,1740],{},[895,19933,19934,19936],{},[898,19935,2073],{"mathvariant":1822},[898,19937,1854],{},[898,19939,2263],{"mathvariant":1822},[902,19941,19942],{"encoding":904},"MPS = \\frac{\\mathrm{d}S}{\\mathrm{d}Y}.",[724,19944,19945,19946,20004],{},"Z (7.2) plyne ",[883,19947,19949],{"className":19948},[886],[888,19950,19951],{"xmlns":890},[892,19952,19953,20001],{},[895,19954,19955,19969,19971,19985,19987],{},[1781,19956,19957,19963],{},[895,19958,19959,19961],{},[898,19960,2073],{"mathvariant":1822},[898,19962,1854],{},[895,19964,19965,19967],{},[898,19966,2073],{"mathvariant":1822},[898,19968,1854],{},[1688,19970,1690],{},[1781,19972,19973,19979],{},[895,19974,19975,19977],{},[898,19976,2073],{"mathvariant":1822},[898,19978,1693],{},[895,19980,19981,19983],{},[898,19982,2073],{"mathvariant":1822},[898,19984,1854],{},[1688,19986,1696],{},[1781,19988,19989,19995],{},[895,19990,19991,19993],{},[898,19992,2073],{"mathvariant":1822},[898,19994,1740],{},[895,19996,19997,19999],{},[898,19998,2073],{"mathvariant":1822},[898,20000,1854],{},[902,20002,20003],{"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",[724,20006,20007],{},[883,20008,20010],{"className":20009},[886],[888,20011,20012],{"xmlns":890},[892,20013,20014,20077],{},[895,20015,20016,20068,20070,20072,20075],{},[13080,20017,20018],{"notation":13082},[1777,20019,20020],{"scriptlevel":1779,"displaystyle":2065},[1777,20021,20022],{"scriptlevel":1779,"displaystyle":2065},[1777,20023,20024],{"scriptlevel":1779,"displaystyle":1732},[895,20025,20026,20028,20030,20032,20034,20036,20038,20040,20042,20044,20046,20048,20050,20052,20054,20056,20058,20060,20062,20064,20066],{},[898,20027,1661],{},[898,20029,1727],{},[898,20031,1693],{},[1688,20033,1696],{},[898,20035,1661],{},[898,20037,1727],{},[898,20039,1740],{},[1688,20041,1690],{},[1793,20043,1795],{},[1688,20045,1733],{"separator":1732},[6134,20047],{"width":6136},[898,20049,1661],{},[898,20051,1727],{},[898,20053,1740],{},[1688,20055,1690],{},[1793,20057,1795],{},[1688,20059,1954],{},[898,20061,1661],{},[898,20063,1727],{},[898,20065,1693],{},[898,20067,2263],{"mathvariant":1822},[6134,20069],{"width":6136},[1688,20071,2066],{"stretchy":2065},[1793,20073,20074],{},"7.5",[1688,20076,2076],{"stretchy":2065},[902,20078,20079],{"encoding":904},"\\boxed{MPC + MPS = 1, \\qquad MPS = 1 - MPC.} \\qquad (7.5)",[724,20081,20082,2170,20085,20108,20109,4142,20131,20157],{},[38,20083,20084],{},"Pro lineární model",[883,20086,20088],{"className":20087},[886],[888,20089,20090],{"xmlns":890},[892,20091,20092,20106],{},[895,20093,20094,20096,20098,20100,20102,20104],{},[898,20095,1693],{},[1688,20097,1690],{},[898,20099,207],{},[898,20101,1854],{},[1688,20103,1696],{},[898,20105,1918],{},[902,20107,1921],{"encoding":904}," vychází ",[883,20110,20112],{"className":20111},[886],[888,20113,20114],{"xmlns":890},[892,20115,20116,20128],{},[895,20117,20118,20120,20122,20124,20126],{},[898,20119,1661],{},[898,20121,1727],{},[898,20123,1693],{},[1688,20125,1690],{},[898,20127,207],{},[902,20129,20130],{"encoding":904},"MPC = a",[883,20132,20134],{"className":20133},[886],[888,20135,20136],{"xmlns":890},[892,20137,20138,20154],{},[895,20139,20140,20142,20144,20146,20148,20150,20152],{},[898,20141,1661],{},[898,20143,1727],{},[898,20145,1740],{},[1688,20147,1690],{},[1793,20149,1795],{},[1688,20151,1954],{},[898,20153,207],{},[902,20155,20156],{"encoding":904},"MPS = 1 - a"," — tedy směrnice přímek spotřeby a úspor.",[724,20159,20160,20163,20164,20186,20187,20215],{},[38,20161,20162],{},"Interpretace diferenciálem."," Pro pevné ",[883,20165,20167],{"className":20166},[886],[888,20168,20169],{"xmlns":890},[892,20170,20171,20183],{},[895,20172,20173,20175,20177],{},[898,20174,1854],{},[1688,20176,1690],{},[1850,20178,20179,20181],{},[898,20180,1854],{},[1688,20182,1857],{},[902,20184,20185],{"encoding":904},"Y = Y^*"," udává ",[883,20188,20190],{"className":20189},[886],[888,20191,20192],{"xmlns":890},[892,20193,20194,20212],{},[895,20195,20196,20198,20200,20202,20204,20210],{},[898,20197,1661],{},[898,20199,1727],{},[898,20201,1693],{},[1688,20203,2066],{"stretchy":2065},[1850,20205,20206,20208],{},[898,20207,1854],{},[1688,20209,1857],{},[1688,20211,2076],{"stretchy":2065},[902,20213,20214],{"encoding":904},"MPC(Y^*)"," přibližnou změnu spotřeby při jednotkovém přírůstku důchodu:",[724,20217,20218],{},[883,20219,20221],{"className":20220},[886],[888,20222,20223],{"xmlns":890},[892,20224,20225,20279],{},[895,20226,20227,20229,20231,20233,20235,20237,20239,20245,20247,20249,20251,20253,20255,20257,20259,20261,20263,20265,20267,20269,20271,20273,20275,20277],{},[898,20228,3147],{"mathvariant":1822},[898,20230,1693],{},[1688,20232,2991],{},[898,20234,2073],{"mathvariant":1822},[898,20236,1693],{},[1688,20238,1690],{},[1850,20240,20241,20243],{},[898,20242,1693],{},[1688,20244,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,20246,2066],{"stretchy":2065},[898,20248,1854],{},[1688,20250,2076],{"stretchy":2065},[2041,20252,2043],{},[898,20254,2073],{"mathvariant":1822},[898,20256,1854],{},[1688,20258,1690],{},[898,20260,1661],{},[898,20262,1727],{},[898,20264,1693],{},[1688,20266,2066],{"stretchy":2065},[898,20268,1854],{},[1688,20270,2076],{"stretchy":2065},[2041,20272,2043],{},[898,20274,2073],{"mathvariant":1822},[898,20276,1854],{},[898,20278,2263],{"mathvariant":1822},[902,20280,20281],{"encoding":904},"\\Delta C \\approx \\mathrm{d}C = C'(Y)\\,\\mathrm{d}Y = MPC(Y)\\,\\mathrm{d}Y.",[724,20283,20284,20285,20321,20322,20325],{},"Analogicky ",[883,20286,20288],{"className":20287},[886],[888,20289,20290],{"xmlns":890},[892,20291,20292,20318],{},[895,20293,20294,20296,20298,20300,20302,20304,20306,20308,20310,20312,20314,20316],{},[898,20295,3147],{"mathvariant":1822},[898,20297,1740],{},[1688,20299,2991],{},[898,20301,1661],{},[898,20303,1727],{},[898,20305,1740],{},[1688,20307,2066],{"stretchy":2065},[898,20309,1854],{},[1688,20311,2076],{"stretchy":2065},[2041,20313,2043],{},[898,20315,2073],{"mathvariant":1822},[898,20317,1854],{},[902,20319,20320],{"encoding":904},"\\Delta S \\approx MPS(Y)\\,\\mathrm{d}Y",". Viz ",[207,20323,1145],{"className":20324,"dataFsResolvedFilePath":764,"href":765},[210]," a její ekonomická interpretace.",[198,20327,20329],{"id":20328},"příklad-72","Příklad 7.2",[724,20331,19496,20332,20367,20368,20387],{},[883,20333,20335],{"className":20334},[886],[888,20336,20337],{"xmlns":890},[892,20338,20339,20364],{},[895,20340,20341,20343,20345,20348,20354,20356,20358,20360,20362],{},[898,20342,1693],{},[1688,20344,1690],{},[1793,20346,20347],{},"0,001",[1850,20349,20350,20352],{},[898,20351,1854],{},[1793,20353,1806],{},[1688,20355,1696],{},[1793,20357,3097],{},[898,20359,1854],{},[1688,20361,1696],{},[1793,20363,3377],{},[902,20365,20366],{"encoding":904},"C = 0{,}001Y^2 + 0{,}2Y + 50"," (pro ",[883,20369,20371],{"className":20370},[886],[888,20372,20373],{"xmlns":890},[892,20374,20375,20384],{},[895,20376,20377,20379,20381],{},[898,20378,1854],{},[1688,20380,3704],{},[1793,20382,20383],{},"400",[902,20385,20386],{"encoding":904},"Y \u003C 400",") platí",[724,20389,20390],{},[883,20391,20393],{"className":20392},[886],[888,20394,20395],{"xmlns":890},[892,20396,20397,20434],{},[895,20398,20399,20401,20403,20405,20407,20421,20423,20426,20428,20430,20432],{},[898,20400,1661],{},[898,20402,1727],{},[898,20404,1693],{},[1688,20406,1690],{},[1781,20408,20409,20415],{},[895,20410,20411,20413],{},[898,20412,2073],{"mathvariant":1822},[898,20414,1693],{},[895,20416,20417,20419],{},[898,20418,2073],{"mathvariant":1822},[898,20420,1854],{},[1688,20422,1690],{},[1793,20424,20425],{},"0,002",[898,20427,1854],{},[1688,20429,1696],{},[1793,20431,3097],{},[1688,20433,1733],{"separator":1732},[902,20435,20436],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y} = 0{,}002Y + 0{,}2,",[724,20438,20439],{},[883,20440,20442],{"className":20441},[886],[888,20443,20444],{"xmlns":890},[892,20445,20446,20479],{},[895,20447,20448,20450,20452,20454,20456,20458,20460,20462,20464,20466,20468,20470,20472,20474,20476],{},[898,20449,1661],{},[898,20451,1727],{},[898,20453,1740],{},[1688,20455,1690],{},[1793,20457,1795],{},[1688,20459,1954],{},[898,20461,1661],{},[898,20463,1727],{},[898,20465,1693],{},[1688,20467,1690],{},[1688,20469,1954],{},[1793,20471,20425],{},[898,20473,1854],{},[1688,20475,1696],{},[1793,20477,20478],{},"0,8.",[902,20480,20481],{"encoding":904},"MPS = 1 - MPC = -0{,}002Y + 0{,}8.",[120,20483,20484,20564,20643],{},[123,20485,20486,1343,20514,20542,20543,8358,20561,2263],{},[883,20487,20489],{"className":20488},[886],[888,20490,20491],{"xmlns":890},[892,20492,20493,20511],{},[895,20494,20495,20497,20499,20501,20503,20505,20507,20509],{},[898,20496,1661],{},[898,20498,1727],{},[898,20500,1693],{},[1688,20502,2066],{"stretchy":2065},[1793,20504,3347],{},[1688,20506,2076],{"stretchy":2065},[1688,20508,1690],{},[1793,20510,19512],{},[902,20512,20513],{"encoding":904},"MPC(100) = 0{,}4",[883,20515,20517],{"className":20516},[886],[888,20518,20519],{"xmlns":890},[892,20520,20521,20539],{},[895,20522,20523,20525,20527,20529,20531,20533,20535,20537],{},[898,20524,1661],{},[898,20526,1727],{},[898,20528,1740],{},[1688,20530,2066],{"stretchy":2065},[1793,20532,3347],{},[1688,20534,2076],{"stretchy":2065},[1688,20536,1690],{},[1793,20538,19562],{},[902,20540,20541],{"encoding":904},"MPS(100) = 0{,}6"," — při ",[883,20544,20546],{"className":20545},[886],[888,20547,20548],{"xmlns":890},[892,20549,20550,20558],{},[895,20551,20552,20554,20556],{},[898,20553,1854],{},[1688,20555,1690],{},[1793,20557,3347],{},[902,20559,20560],{"encoding":904},"Y = 100",[38,20562,20563],{},"větší sklon k úsporám",[123,20565,20566,1343,20594,20542,20622,8358,20640,2263],{},[883,20567,20569],{"className":20568},[886],[888,20570,20571],{"xmlns":890},[892,20572,20573,20591],{},[895,20574,20575,20577,20579,20581,20583,20585,20587,20589],{},[898,20576,1661],{},[898,20578,1727],{},[898,20580,1693],{},[1688,20582,2066],{"stretchy":2065},[1793,20584,8633],{},[1688,20586,2076],{"stretchy":2065},[1688,20588,1690],{},[1793,20590,19562],{},[902,20592,20593],{"encoding":904},"MPC(200) = 0{,}6",[883,20595,20597],{"className":20596},[886],[888,20598,20599],{"xmlns":890},[892,20600,20601,20619],{},[895,20602,20603,20605,20607,20609,20611,20613,20615,20617],{},[898,20604,1661],{},[898,20606,1727],{},[898,20608,1740],{},[1688,20610,2066],{"stretchy":2065},[1793,20612,8633],{},[1688,20614,2076],{"stretchy":2065},[1688,20616,1690],{},[1793,20618,19512],{},[902,20620,20621],{"encoding":904},"MPS(200) = 0{,}4",[883,20623,20625],{"className":20624},[886],[888,20626,20627],{"xmlns":890},[892,20628,20629,20637],{},[895,20630,20631,20633,20635],{},[898,20632,1854],{},[1688,20634,1690],{},[1793,20636,8633],{},[902,20638,20639],{"encoding":904},"Y = 200",[38,20641,20642],{},"větší sklon ke spotřebě",[123,20644,20645,20646,20664,20665,4176],{},"Přesně při ",[883,20647,20649],{"className":20648},[886],[888,20650,20651],{"xmlns":890},[892,20652,20653,20661],{},[895,20654,20655,20657,20659],{},[898,20656,1854],{},[1688,20658,1690],{},[1793,20660,9058],{},[902,20662,20663],{"encoding":904},"Y = 150"," se oba sklony rovnají (",[883,20666,20668],{"className":20667},[886],[888,20669,20670],{"xmlns":890},[892,20671,20672,20692],{},[895,20673,20674,20676,20678,20680,20682,20684,20686,20688,20690],{},[898,20675,1661],{},[898,20677,1727],{},[898,20679,1693],{},[1688,20681,1690],{},[898,20683,1661],{},[898,20685,1727],{},[898,20687,1740],{},[1688,20689,1690],{},[1793,20691,5265],{},[902,20693,20694],{"encoding":904},"MPC = MPS = 0{,}5",[724,20696,20697,20698,20715,20716,20730,20731,2946,20744,20758,20759,20772,20773,20814],{},"Interpretace: při ",[883,20699,20701],{"className":20700},[886],[888,20702,20703],{"xmlns":890},[892,20704,20705,20713],{},[895,20706,20707,20709,20711],{},[898,20708,1854],{},[1688,20710,1690],{},[1793,20712,3347],{},[902,20714,20560],{"encoding":904}," se spotřeba mění ",[883,20717,20719],{"className":20718},[886],[888,20720,20721],{"xmlns":890},[892,20722,20723,20727],{},[895,20724,20725],{},[1793,20726,19512],{},[902,20728,20729],{"encoding":904},"0{,}4","-krát rychleji než důchod; změní-li se důchod ze ",[883,20732,20734],{"className":20733},[886],[888,20735,20736],{"xmlns":890},[892,20737,20738,20742],{},[895,20739,20740],{},[1793,20741,3347],{},[902,20743,3347],{"encoding":904},[883,20745,20747],{"className":20746},[886],[888,20748,20749],{"xmlns":890},[892,20750,20751,20756],{},[895,20752,20753],{},[1793,20754,20755],{},"101",[902,20757,20755],{"encoding":904},", změní se spotřeba přibližně o ",[883,20760,20762],{"className":20761},[886],[888,20763,20764],{"xmlns":890},[892,20765,20766,20770],{},[895,20767,20768],{},[1793,20769,19512],{},[902,20771,20729],{"encoding":904},". Skutečná změna ",[883,20774,20776],{"className":20775},[886],[888,20777,20778],{"xmlns":890},[892,20779,20780,20811],{},[895,20781,20782,20784,20786,20788,20790,20792,20794,20796,20798,20800,20802,20804,20806,20808],{},[898,20783,3147],{"mathvariant":1822},[898,20785,1693],{},[1688,20787,1690],{},[898,20789,1693],{},[1688,20791,2066],{"stretchy":2065},[1793,20793,20755],{},[1688,20795,2076],{"stretchy":2065},[1688,20797,1954],{},[898,20799,1693],{},[1688,20801,2066],{"stretchy":2065},[1793,20803,3347],{},[1688,20805,2076],{"stretchy":2065},[1688,20807,1690],{},[1793,20809,20810],{},"0,401",[902,20812,20813],{"encoding":904},"\\Delta C = C(101) - C(100) = 0{,}401"," — aproximace diferenciálem je přesná na setiny.",[724,20816,20817,20818],{},"Obecný trend: ",[38,20819,20820],{},"s růstem důchodu se sklon ke spotřebě zvětšuje.",[115,20822,20824],{"id":20823},"makroekonomická-rovnováha","Makroekonomická rovnováha",[724,20826,20827,20828,10277,20831,20834,20835,10277,20838,12378,20841,10277,20844,20847],{},"Při modelování národní ekonomiky hraje klíčovou roli ",[38,20829,20830],{},"makroekonomická rovnováha",[614,20832,20833],{},"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 ",[38,20836,20837],{},"agregátní poptávky",[614,20839,20840],{},"aggregate demand",[38,20842,20843],{},"agregátní nabídky",[614,20845,20846],{},"aggregate supply",") — obě popisují závislost mezi cenovou hladinou a množstvím, které jsou spotřebitelé ochotni koupit (agregátními výdaji).",[115,20849,20851],{"id":20850},"model-c-i-uzavřená-ekonomika-bez-vlády","Model C-I — uzavřená ekonomika bez vlády",[724,20853,20854],{},[2821,20855],{"alt":20856,"className":20857,"src":20858},"imek-keynesian-kriz",[210,2825],"\u002Fwiki-assets\u002Fimek-keynesian-kriz.jpeg",[198,20860,20862],{"id":20861},"zadání-modelu","Zadání modelu",[724,20864,20865,20866,20879,20880,20893],{},"Nejjednodušší model uzavřené ekonomiky bez vlády obsahuje jen spotřebu ",[883,20867,20869],{"className":20868},[886],[888,20870,20871],{"xmlns":890},[892,20872,20873,20877],{},[895,20874,20875],{},[898,20876,1693],{},[902,20878,1693],{"encoding":904}," a investice ",[883,20881,20883],{"className":20882},[886],[888,20884,20885],{"xmlns":890},[892,20886,20887,20891],{},[895,20888,20889],{},[898,20890,1699],{},[902,20892,1699],{"encoding":904},". Podmínka rovnováhy:",[724,20895,20896],{},[883,20897,20899],{"className":20898},[886],[888,20900,20901],{"xmlns":890},[892,20902,20903,20926],{},[895,20904,20905,20907,20909,20911,20913,20915,20917,20919,20921,20924],{},[898,20906,1854],{},[1688,20908,1690],{},[898,20910,1693],{},[1688,20912,1696],{},[898,20914,1699],{},[898,20916,2263],{"mathvariant":1822},[6134,20918],{"width":6136},[1688,20920,2066],{"stretchy":2065},[1793,20922,20923],{},"7.6",[1688,20925,2076],{"stretchy":2065},[902,20927,20928],{"encoding":904},"Y = C + I. \\qquad (7.6)",[198,20930,20932],{"id":20931},"soustava-rovnic","Soustava rovnic",[724,20934,20935,20936,20957,20958,20982],{},"Pro pevně zadané (plánované) investice ",[883,20937,20939],{"className":20938},[886],[888,20940,20941],{"xmlns":890},[892,20942,20943,20955],{},[895,20944,20945,20947,20949],{},[898,20946,1699],{},[1688,20948,1690],{},[1850,20950,20951,20953],{},[898,20952,1699],{},[1688,20954,1857],{},[902,20956,12444],{"encoding":904}," a funkci spotřeby ",[883,20959,20961],{"className":20960},[886],[888,20962,20963],{"xmlns":890},[892,20964,20965,20979],{},[895,20966,20967,20969,20971,20973,20975,20977],{},[898,20968,1693],{},[1688,20970,1690],{},[898,20972,1693],{},[1688,20974,2066],{"stretchy":2065},[898,20976,1854],{},[1688,20978,2076],{"stretchy":2065},[902,20980,20981],{"encoding":904},"C = C(Y)"," dostáváme soustavu",[724,20984,20985],{},[883,20986,20988],{"className":20987},[886],[888,20989,20990],{"xmlns":890},[892,20991,20992,21068],{},[895,20993,20994,21059,21061,21063,21066],{},[20995,20996,20999,21031],"mtable",{"rowspacing":20997,"columnalign":20998,"columnspacing":1823},"0.25em","right left",[21000,21001,21002,21009],"mtr",{},[21003,21004,21005],"mtd",{},[1777,21006,21007],{"scriptlevel":1779,"displaystyle":1732},[898,21008,1854],{},[21003,21010,21011],{},[1777,21012,21013],{"scriptlevel":1779,"displaystyle":1732},[895,21014,21015,21017,21019,21021,21023,21029],{},[895,21016],{},[1688,21018,1690],{},[898,21020,1693],{},[1688,21022,1696],{},[1850,21024,21025,21027],{},[898,21026,1699],{},[1688,21028,1857],{},[1688,21030,1733],{"separator":1732},[21000,21032,21033,21039],{},[21003,21034,21035],{},[1777,21036,21037],{"scriptlevel":1779,"displaystyle":1732},[898,21038,1693],{},[21003,21040,21041],{},[1777,21042,21043],{"scriptlevel":1779,"displaystyle":1732},[895,21044,21045,21047,21049,21051,21053,21055,21057],{},[895,21046],{},[1688,21048,1690],{},[898,21050,1693],{},[1688,21052,2066],{"stretchy":2065},[898,21054,1854],{},[1688,21056,2076],{"stretchy":2065},[1688,21058,1733],{"separator":1732},[6134,21060],{"width":6136},[1688,21062,2066],{"stretchy":2065},[1793,21064,21065],{},"7.7",[1688,21067,2076],{"stretchy":2065},[902,21069,21070],{"encoding":904},"\\begin{aligned} Y &= C + I^*, \\\\ C &= C(Y), \\end{aligned} \\qquad (7.7)",[724,21072,21073,21074,2170,21076,4142,21093,2170,21096,2263],{},"jejímž řešením jsou ",[38,21075,14132],{},[883,21077,21079],{"className":21078},[886],[888,21080,21081],{"xmlns":890},[892,21082,21083,21091],{},[895,21084,21085],{},[1850,21086,21087,21089],{},[898,21088,1854],{},[898,21090,4509],{},[902,21092,14150],{"encoding":904},[38,21094,21095],{},"rovnovážná spotřeba",[883,21097,21099],{"className":21098},[886],[888,21100,21101],{"xmlns":890},[892,21102,21103,21111],{},[895,21104,21105],{},[1850,21106,21107,21109],{},[898,21108,1693],{},[898,21110,4509],{},[902,21112,14209],{"encoding":904},[198,21114,21116,21117],{"id":21115},"výpočet-yeye","Výpočet ",[883,21118,21120],{"className":21119},[886],[888,21121,21122],{"xmlns":890},[892,21123,21124,21132],{},[895,21125,21126],{},[1850,21127,21128,21130],{},[898,21129,1854],{},[898,21131,4509],{},[902,21133,14150],{"encoding":904},[724,21135,21136,21137,21160,21161,7941,21193],{},"Pro lineární spotřebu ",[883,21138,21140],{"className":21139},[886],[888,21141,21142],{"xmlns":890},[892,21143,21144,21158],{},[895,21145,21146,21148,21150,21152,21154,21156],{},[898,21147,1693],{},[1688,21149,1690],{},[898,21151,207],{},[898,21153,1854],{},[1688,21155,1696],{},[898,21157,1918],{},[902,21159,1921],{"encoding":904}," plyne z (7.7) rovnice ",[883,21162,21164],{"className":21163},[886],[888,21165,21166],{"xmlns":890},[892,21167,21168,21190],{},[895,21169,21170,21172,21174,21176,21178,21180,21182,21184],{},[898,21171,1854],{},[1688,21173,1690],{},[898,21175,207],{},[898,21177,1854],{},[1688,21179,1696],{},[898,21181,1918],{},[1688,21183,1696],{},[1850,21185,21186,21188],{},[898,21187,1699],{},[1688,21189,1857],{},[902,21191,21192],{"encoding":904},"Y = aY + b + I^*",[38,21194,21195],{},"redukovaný tvar",[724,21197,21198],{},[883,21199,21201],{"className":21200},[886],[888,21202,21203],{"xmlns":890},[892,21204,21205,21253],{},[895,21206,21207],{},[13080,21208,21209],{"notation":13082},[1777,21210,21211],{"scriptlevel":1779,"displaystyle":2065},[1777,21212,21213],{"scriptlevel":1779,"displaystyle":2065},[1777,21214,21215],{"scriptlevel":1779,"displaystyle":1732},[895,21216,21217,21219,21225,21227,21249,21251],{},[2041,21218,2043],{},[1850,21220,21221,21223],{},[898,21222,1854],{},[898,21224,4509],{},[1688,21226,1690],{},[1781,21228,21229,21241],{},[895,21230,21231,21233,21235],{},[898,21232,1918],{},[1688,21234,1696],{},[1850,21236,21237,21239],{},[898,21238,1699],{},[1688,21240,1857],{},[895,21242,21243,21245,21247],{},[1793,21244,1795],{},[1688,21246,1954],{},[898,21248,207],{},[898,21250,2263],{"mathvariant":1822},[2041,21252,2043],{},[902,21254,21255],{"encoding":904},"\\boxed{\\,Y^E = \\frac{b + I^*}{1 - a}.\\,}",[198,21257,21259],{"id":21258},"příklad-73","Příklad 7.3",[724,21261,21262,21263,8358,21280,4142,21304,21330],{},"V modelu ",[883,21264,21266],{"className":21265},[886],[888,21267,21268],{"xmlns":890},[892,21269,21270,21278],{},[895,21271,21272,21274,21276],{},[898,21273,1693],{},[2041,21275,12539],{},[898,21277,1699],{},[902,21279,12544],{"encoding":904},[883,21281,21283],{"className":21282},[886],[888,21284,21285],{"xmlns":890},[892,21286,21287,21301],{},[895,21288,21289,21291,21293,21295,21297,21299],{},[898,21290,1693],{},[1688,21292,1690],{},[1793,21294,19562],{},[898,21296,1854],{},[1688,21298,1696],{},[1793,21300,3121],{},[902,21302,21303],{"encoding":904},"C = 0{,}6Y + 10",[883,21305,21307],{"className":21306},[886],[888,21308,21309],{"xmlns":890},[892,21310,21311,21327],{},[895,21312,21313,21315,21317,21319,21321],{},[898,21314,1699],{},[1688,21316,1690],{},[1793,21318,3766],{},[1688,21320,1690],{},[1850,21322,21323,21325],{},[898,21324,1699],{},[1688,21326,1857],{},[902,21328,21329],{"encoding":904},"I = 12 = I^*",". Soustava",[724,21332,21333],{},[883,21334,21336],{"className":21335},[886],[888,21337,21338],{"xmlns":890},[892,21339,21340,21396],{},[20995,21341,21342,21368],{"rowspacing":20997,"columnalign":20998,"columnspacing":1823},[21000,21343,21344,21350],{},[21003,21345,21346],{},[1777,21347,21348],{"scriptlevel":1779,"displaystyle":1732},[898,21349,1854],{},[21003,21351,21352],{},[1777,21353,21354],{"scriptlevel":1779,"displaystyle":1732},[895,21355,21356,21358,21360,21362,21364,21366],{},[895,21357],{},[1688,21359,1690],{},[898,21361,1693],{},[1688,21363,1696],{},[1793,21365,3766],{},[1688,21367,1733],{"separator":1732},[21000,21369,21370,21376],{},[21003,21371,21372],{},[1777,21373,21374],{"scriptlevel":1779,"displaystyle":1732},[898,21375,1693],{},[21003,21377,21378],{},[1777,21379,21380],{"scriptlevel":1779,"displaystyle":1732},[895,21381,21382,21384,21386,21388,21390,21392,21394],{},[895,21383],{},[1688,21385,1690],{},[1793,21387,19562],{},[898,21389,1854],{},[1688,21391,1696],{},[1793,21393,3121],{},[1688,21395,1733],{"separator":1732},[902,21397,21398],{"encoding":904},"\\begin{aligned} Y &= C + 12, \\\\ C &= 0{,}6Y + 10, \\end{aligned}",[724,21400,21401,21402,1343,21425,21448,21449,4176],{},"má řešení ",[883,21403,21405],{"className":21404},[886],[888,21406,21407],{"xmlns":890},[892,21408,21409,21422],{},[895,21410,21411,21417,21419],{},[1850,21412,21413,21415],{},[898,21414,1854],{},[898,21416,4509],{},[1688,21418,1690],{},[1793,21420,21421],{},"55",[902,21423,21424],{"encoding":904},"Y^E = 55",[883,21426,21428],{"className":21427},[886],[888,21429,21430],{"xmlns":890},[892,21431,21432,21445],{},[895,21433,21434,21440,21442],{},[1850,21435,21436,21438],{},[898,21437,1693],{},[898,21439,4509],{},[1688,21441,1690],{},[1793,21443,21444],{},"43",[902,21446,21447],{"encoding":904},"C^E = 43"," (a ",[883,21450,21452],{"className":21451},[886],[888,21453,21454],{"xmlns":890},[892,21455,21456,21468],{},[895,21457,21458,21464,21466],{},[1850,21459,21460,21462],{},[898,21461,1740],{},[898,21463,4509],{},[1688,21465,1690],{},[1793,21467,3766],{},[902,21469,21470],{"encoding":904},"S^E = 12",[724,21472,21473],{},[614,21474,21475,21476,21498,21499,12378,21520,21543,21544,2263],{},"Obrázek 7.5 — Přímky ",[883,21477,21479],{"className":21478},[886],[888,21480,21481],{"xmlns":890},[892,21482,21483,21495],{},[895,21484,21485,21487,21489,21491,21493],{},[898,21486,1693],{},[1688,21488,1690],{},[898,21490,1854],{},[1688,21492,1954],{},[1793,21494,3766],{},[902,21496,21497],{"encoding":904},"C = Y - 12"," (rovnováha ",[883,21500,21502],{"className":21501},[886],[888,21503,21504],{"xmlns":890},[892,21505,21506,21518],{},[895,21507,21508,21510,21512,21514,21516],{},[898,21509,1854],{},[1688,21511,1690],{},[898,21513,1693],{},[1688,21515,1696],{},[898,21517,1699],{},[902,21519,14991],{"encoding":904},[883,21521,21523],{"className":21522},[886],[888,21524,21525],{"xmlns":890},[892,21526,21527,21541],{},[895,21528,21529,21531,21533,21535,21537,21539],{},[898,21530,1693],{},[1688,21532,1690],{},[1793,21534,19562],{},[898,21536,1854],{},[1688,21538,1696],{},[1793,21540,3121],{},[902,21542,21303],{"encoding":904}," (funkce spotřeby) se protínají v bodě ",[883,21545,21547],{"className":21546},[886],[888,21548,21549],{"xmlns":890},[892,21550,21551,21583],{},[895,21552,21553,21555,21561,21563,21569,21571,21573,21575,21577,21579,21581],{},[1688,21554,2748],{"stretchy":2065},[1850,21556,21557,21559],{},[898,21558,1854],{},[898,21560,4509],{},[1688,21562,1733],{"separator":1732},[1850,21564,21565,21567],{},[898,21566,1693],{},[898,21568,4509],{},[1688,21570,2763],{"stretchy":2065},[1688,21572,1690],{},[1688,21574,2748],{"stretchy":2065},[1793,21576,21421],{},[1688,21578,1733],{"separator":1732},[1793,21580,21444],{},[1688,21582,2763],{"stretchy":2065},[902,21584,21585],{"encoding":904},"[Y^E, C^E] = [55, 43]",[724,21587,21588,21591,21592,21609,21610,2263],{},[38,21589,21590],{},"Komentář k přechodu."," Model ",[883,21593,21595],{"className":21594},[886],[888,21596,21597],{"xmlns":890},[892,21598,21599,21607],{},[895,21600,21601,21603,21605],{},[898,21602,1693],{},[2041,21604,12539],{},[898,21606,1699],{},[902,21608,12544],{"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 ",[38,21611,21612,21613],{},"model ",[883,21614,21616],{"className":21615},[886],[888,21617,21618],{"xmlns":890},[892,21619,21620,21632],{},[895,21621,21622,21624,21626,21628,21630],{},[898,21623,1693],{},[2041,21625,12539],{},[898,21627,1699],{},[2041,21629,12539],{},[898,21631,1704],{},[902,21633,18462],{"encoding":904},[115,21635,21637],{"id":21636},"model-c-i-g-s-vládním-sektorem","Model C-I-G — s vládním sektorem",[198,21639,20862],{"id":21640},"zadání-modelu-1",[724,21642,21643,21644,21661,21662,2170,21665,10277,21678,21681],{},"Rozšíření modelu ",[883,21645,21647],{"className":21646},[886],[888,21648,21649],{"xmlns":890},[892,21650,21651,21659],{},[895,21652,21653,21655,21657],{},[898,21654,1693],{},[2041,21656,12539],{},[898,21658,1699],{},[902,21660,12544],{"encoding":904}," o ",[38,21663,21664],{},"vládní výdaje",[883,21666,21668],{"className":21667},[886],[888,21669,21670],{"xmlns":890},[892,21671,21672,21676],{},[895,21673,21674],{},[898,21675,1704],{},[902,21677,1704],{"encoding":904},[614,21679,21680],{},"government expenditure","). Podmínka rovnováhy:",[724,21683,21684],{},[883,21685,21687],{"className":21686},[886],[888,21688,21689],{"xmlns":890},[892,21690,21691,21718],{},[895,21692,21693,21695,21697,21699,21701,21703,21705,21707,21709,21711,21713,21716],{},[898,21694,1854],{},[1688,21696,1690],{},[898,21698,1693],{},[1688,21700,1696],{},[898,21702,1699],{},[1688,21704,1696],{},[898,21706,1704],{},[898,21708,2263],{"mathvariant":1822},[6134,21710],{"width":6136},[1688,21712,2066],{"stretchy":2065},[1793,21714,21715],{},"7.8",[1688,21717,2076],{"stretchy":2065},[902,21719,21720],{"encoding":904},"Y = C + I + G. \\qquad (7.8)",[724,21722,21723,21724,2170,21727,10277,21740,21743],{},"Stát se stává spotřebitelem, jehož „důchod“ získává ",[38,21725,21726],{},"zdaněním domácností",[883,21728,21730],{"className":21729},[886],[888,21731,21732],{"xmlns":890},[892,21733,21734,21738],{},[895,21735,21736],{},[898,21737,3035],{},[902,21739,3035],{"encoding":904},[614,21741,21742],{},"taxation","). Zdanění bývá:",[120,21745,21746,21779,21804],{},[123,21747,21748,21749,1733],{},"úměrné důchodu: ",[883,21750,21752],{"className":21751},[886],[888,21753,21754],{"xmlns":890},[892,21755,21756,21776],{},[895,21757,21758,21760,21762,21764,21766,21768,21770,21772,21774],{},[898,21759,3035],{},[1688,21761,1690],{},[898,21763,3035],{},[1688,21765,2066],{"stretchy":2065},[898,21767,1854],{},[1688,21769,2076],{"stretchy":2065},[1688,21771,1690],{},[898,21773,19097],{},[898,21775,1854],{},[902,21777,21778],{"encoding":904},"T = T(Y) = tY",[123,21780,21781,21782,1733],{},"fixní: ",[883,21783,21785],{"className":21784},[886],[888,21786,21787],{"xmlns":890},[892,21788,21789,21801],{},[895,21790,21791,21793,21795],{},[898,21792,3035],{},[1688,21794,1690],{},[1850,21796,21797,21799],{},[898,21798,3035],{},[1688,21800,1857],{},[902,21802,21803],{"encoding":904},"T = T^*",[123,21805,21806,21807,21835,21836,2263],{},"kombinované: ",[883,21808,21810],{"className":21809},[886],[888,21811,21812],{"xmlns":890},[892,21813,21814,21832],{},[895,21815,21816,21818,21820,21826,21828,21830],{},[898,21817,3035],{},[1688,21819,1690],{},[1850,21821,21822,21824],{},[898,21823,3035],{},[1688,21825,1857],{},[1688,21827,1696],{},[898,21829,19097],{},[898,21831,1854],{},[902,21833,21834],{"encoding":904},"T = T^* + tY",", kde ",[883,21837,21839],{"className":21838},[886],[888,21840,21841],{"xmlns":890},[892,21842,21843,21855],{},[895,21844,21845,21847,21849,21851,21853],{},[1793,21846,1779],{},[1688,21848,7935],{},[898,21850,19097],{},[1688,21852,3704],{},[1793,21854,1795],{},[902,21856,21857],{"encoding":904},"0 \\le t \u003C 1",[4124,21859,21860],{},[724,21861,21862,21864,21865,21886,21887,21890,21891,21904,21905,12378,21931,2170,21934,21960,21961,21989,21990,4142,22003,22021],{},[883,21863,4668],{}," Pozor na disponibilní důchod\nV modelu ",[883,21866,21868],{"className":21867},[886],[888,21869,21870],{"xmlns":890},[892,21871,21872,21884],{},[895,21873,21874,21876,21878,21880,21882],{},[898,21875,1693],{},[2041,21877,12539],{},[898,21879,1699],{},[2041,21881,12539],{},[898,21883,1704],{},[902,21885,18462],{"encoding":904}," je nutné ",[38,21888,21889],{},"důsledně rozlišovat dva důchody",": celkový národní důchod ",[883,21892,21894],{"className":21893},[886],[888,21895,21896],{"xmlns":890},[892,21897,21898,21902],{},[895,21899,21900],{},[898,21901,1854],{},[902,21903,1854],{"encoding":904}," (vstupuje do podmínky rovnováhy ",[883,21906,21908],{"className":21907},[886],[888,21909,21910],{"xmlns":890},[892,21911,21912,21928],{},[895,21913,21914,21916,21918,21920,21922,21924,21926],{},[898,21915,1854],{},[1688,21917,1690],{},[898,21919,1693],{},[1688,21921,1696],{},[898,21923,1699],{},[1688,21925,1696],{},[898,21927,1704],{},[902,21929,21930],{"encoding":904},"Y = C + I + G",[38,21932,21933],{},"disponibilní důchod",[883,21935,21937],{"className":21936},[886],[888,21938,21939],{"xmlns":890},[892,21940,21941,21957],{},[895,21942,21943,21949,21951,21953,21955],{},[1788,21944,21945,21947],{},[898,21946,1854],{},[898,21948,4440],{},[1688,21950,1690],{},[898,21952,1854],{},[1688,21954,1954],{},[898,21956,3035],{},[902,21958,21959],{"encoding":904},"Y_D = Y - T"," (na něm závisí spotřeba domácností, ",[883,21962,21964],{"className":21963},[886],[888,21965,21966],{"xmlns":890},[892,21967,21968,21986],{},[895,21969,21970,21972,21974,21976,21978,21984],{},[898,21971,1693],{},[1688,21973,1690],{},[898,21975,1693],{},[1688,21977,2066],{"stretchy":2065},[1788,21979,21980,21982],{},[898,21981,1854],{},[898,21983,4440],{},[1688,21985,2076],{"stretchy":2065},[902,21987,21988],{"encoding":904},"C = C(Y_D)","). Záměna ",[883,21991,21993],{"className":21992},[886],[888,21994,21995],{"xmlns":890},[892,21996,21997,22001],{},[895,21998,21999],{},[898,22000,1854],{},[902,22002,1854],{"encoding":904},[883,22004,22006],{"className":22005},[886],[888,22007,22008],{"xmlns":890},[892,22009,22010,22018],{},[895,22011,22012],{},[1788,22013,22014,22016],{},[898,22015,1854],{},[898,22017,4440],{},[902,22019,22020],{"encoding":904},"Y_D"," ve funkci spotřeby je nejčastější zdroj chyb.",[724,22023,22024,10277,22027,2076],{},[38,22025,22026],{},"Disponibilní důchod",[614,22028,22029],{},"disposable income",[724,22031,22032],{},[883,22033,22035],{"className":22034},[886],[888,22036,22037],{"xmlns":890},[892,22038,22039,22055],{},[895,22040,22041,22047,22049,22051,22053],{},[1788,22042,22043,22045],{},[898,22044,1854],{},[898,22046,4440],{},[1688,22048,1690],{},[898,22050,1854],{},[1688,22052,1954],{},[898,22054,3035],{},[902,22056,21959],{"encoding":904},[724,22058,22059,22060,2263],{},"je to, co zbývá domácnostem po zdanění. Spotřeba je pak funkcí disponibilního důchodu: ",[883,22061,22063],{"className":22062},[886],[888,22064,22065],{"xmlns":890},[892,22066,22067,22085],{},[895,22068,22069,22071,22073,22075,22077,22083],{},[898,22070,1693],{},[1688,22072,1690],{},[898,22074,1693],{},[1688,22076,2066],{"stretchy":2065},[1788,22078,22079,22081],{},[898,22080,1854],{},[898,22082,4440],{},[1688,22084,2076],{"stretchy":2065},[902,22086,21988],{"encoding":904},[198,22088,20932],{"id":22089},"soustava-rovnic-1",[724,22091,22092,22093,1343,22114,22136,22137,2965],{},"Pro pevně zadané ",[883,22094,22096],{"className":22095},[886],[888,22097,22098],{"xmlns":890},[892,22099,22100,22112],{},[895,22101,22102,22104,22106],{},[898,22103,1699],{},[1688,22105,1690],{},[1850,22107,22108,22110],{},[898,22109,1699],{},[1688,22111,1857],{},[902,22113,12444],{"encoding":904},[883,22115,22117],{"className":22116},[886],[888,22118,22119],{"xmlns":890},[892,22120,22121,22133],{},[895,22122,22123,22125,22127],{},[898,22124,1704],{},[1688,22126,1690],{},[1850,22128,22129,22131],{},[898,22130,1704],{},[1688,22132,1857],{},[902,22134,22135],{"encoding":904},"G = G^*"," dostáváme soustavu 4 rovnic o 4 neznámých ",[883,22138,22140],{"className":22139},[886],[888,22141,22142],{"xmlns":890},[892,22143,22144,22164],{},[895,22145,22146,22148,22150,22152,22154,22160,22162],{},[898,22147,1854],{},[1688,22149,1733],{"separator":1732},[898,22151,1693],{},[1688,22153,1733],{"separator":1732},[1788,22155,22156,22158],{},[898,22157,1854],{},[898,22159,4440],{},[1688,22161,1733],{"separator":1732},[898,22163,3035],{},[902,22165,22166],{"encoding":904},"Y, C, Y_D, T",[724,22168,22169],{},[883,22170,22172],{"className":22171},[886],[888,22173,22174],{"xmlns":890},[892,22175,22176,22317],{},[895,22177,22178,22308,22310,22312,22315],{},[20995,22179,22180,22218,22246,22278],{"rowspacing":20997,"columnalign":20998,"columnspacing":1823},[21000,22181,22182,22188],{},[21003,22183,22184],{},[1777,22185,22186],{"scriptlevel":1779,"displaystyle":1732},[898,22187,1854],{},[21003,22189,22190],{},[1777,22191,22192],{"scriptlevel":1779,"displaystyle":1732},[895,22193,22194,22196,22198,22200,22202,22208,22210,22216],{},[895,22195],{},[1688,22197,1690],{},[898,22199,1693],{},[1688,22201,1696],{},[1850,22203,22204,22206],{},[898,22205,1699],{},[1688,22207,1857],{},[1688,22209,1696],{},[1850,22211,22212,22214],{},[898,22213,1704],{},[1688,22215,1857],{},[1688,22217,1733],{"separator":1732},[21000,22219,22220,22226],{},[21003,22221,22222],{},[1777,22223,22224],{"scriptlevel":1779,"displaystyle":1732},[898,22225,3035],{},[21003,22227,22228],{},[1777,22229,22230],{"scriptlevel":1779,"displaystyle":1732},[895,22231,22232,22234,22236,22238,22240,22242,22244],{},[895,22233],{},[1688,22235,1690],{},[898,22237,3035],{},[1688,22239,2066],{"stretchy":2065},[898,22241,1854],{},[1688,22243,2076],{"stretchy":2065},[1688,22245,1733],{"separator":1732},[21000,22247,22248,22254],{},[21003,22249,22250],{},[1777,22251,22252],{"scriptlevel":1779,"displaystyle":1732},[898,22253,1693],{},[21003,22255,22256],{},[1777,22257,22258],{"scriptlevel":1779,"displaystyle":1732},[895,22259,22260,22262,22264,22266,22268,22274,22276],{},[895,22261],{},[1688,22263,1690],{},[898,22265,1693],{},[1688,22267,2066],{"stretchy":2065},[1788,22269,22270,22272],{},[898,22271,1854],{},[898,22273,4440],{},[1688,22275,2076],{"stretchy":2065},[1688,22277,1733],{"separator":1732},[21000,22279,22280,22290],{},[21003,22281,22282],{},[1777,22283,22284],{"scriptlevel":1779,"displaystyle":1732},[1788,22285,22286,22288],{},[898,22287,1854],{},[898,22289,4440],{},[21003,22291,22292],{},[1777,22293,22294],{"scriptlevel":1779,"displaystyle":1732},[895,22295,22296,22298,22300,22302,22304,22306],{},[895,22297],{},[1688,22299,1690],{},[898,22301,1854],{},[1688,22303,1954],{},[898,22305,3035],{},[1688,22307,1733],{"separator":1732},[6134,22309],{"width":6136},[1688,22311,2066],{"stretchy":2065},[1793,22313,22314],{},"7.9",[1688,22316,2076],{"stretchy":2065},[902,22318,22319],{"encoding":904},"\\begin{aligned} Y &= C + I^* + G^*, \\\\ T &= T(Y), \\\\ C &= C(Y_D), \\\\ Y_D &= Y - T, \\end{aligned} \\qquad (7.9)",[724,22321,22322,22323,22367,22368,2263],{},"s řešeními ",[883,22324,22326],{"className":22325},[886],[888,22327,22328],{"xmlns":890},[892,22329,22330,22364],{},[895,22331,22332,22338,22340,22346,22348,22354,22356],{},[1850,22333,22334,22336],{},[898,22335,1854],{},[898,22337,4509],{},[1688,22339,1733],{"separator":1732},[1850,22341,22342,22344],{},[898,22343,1693],{},[898,22345,4509],{},[1688,22347,1733],{"separator":1732},[1850,22349,22350,22352],{},[898,22351,3035],{},[898,22353,4509],{},[1688,22355,1733],{"separator":1732},[1814,22357,22358,22360,22362],{},[898,22359,1854],{},[898,22361,4440],{},[898,22363,4509],{},[902,22365,22366],{"encoding":904},"Y^E, C^E, T^E, Y_D^E",", případně rovnovážnými úsporami domácností ",[883,22369,22371],{"className":22370},[886],[888,22372,22373],{"xmlns":890},[892,22374,22375,22401],{},[895,22376,22377,22383,22385,22393,22395],{},[1850,22378,22379,22381],{},[898,22380,1740],{},[898,22382,4509],{},[1688,22384,1690],{},[1814,22386,22387,22389,22391],{},[898,22388,1854],{},[898,22390,4440],{},[898,22392,4509],{},[1688,22394,1954],{},[1850,22396,22397,22399],{},[898,22398,1693],{},[898,22400,4509],{},[902,22402,22403],{"encoding":904},"S^E = Y_D^E - C^E",[4124,22405,22406,22411],{},[724,22407,22408,22410],{},[883,22409,4828],{}," Postup — jak sestavit a vyřešit soustavu C-I-G",[152,22412,22413,22436,22519,22574,22664],{},[123,22414,22415,22418,22419,2263],{},[38,22416,22417],{},"Zapiš všechny 4 rovnice"," ze zadání: podmínku rovnováhy, daňovou funkci, funkci spotřeby, definici ",[883,22420,22422],{"className":22421},[886],[888,22423,22424],{"xmlns":890},[892,22425,22426,22434],{},[895,22427,22428],{},[1788,22429,22430,22432],{},[898,22431,1854],{},[898,22433,4440],{},[902,22435,22020],{"encoding":904},[123,22437,22438,22487,22488,22505,22506,2263],{},[38,22439,22440,22441,22461,22462],{},"Dosaď ",[883,22442,22444],{"className":22443},[886],[888,22445,22446],{"xmlns":890},[892,22447,22448,22458],{},[895,22449,22450,22452,22454,22456],{},[898,22451,3035],{},[1688,22453,2066],{"stretchy":2065},[898,22455,1854],{},[1688,22457,2076],{"stretchy":2065},[902,22459,22460],{"encoding":904},"T(Y)"," do ",[883,22463,22465],{"className":22464},[886],[888,22466,22467],{"xmlns":890},[892,22468,22469,22485],{},[895,22470,22471,22477,22479,22481,22483],{},[1788,22472,22473,22475],{},[898,22474,1854],{},[898,22476,4440],{},[1688,22478,1690],{},[898,22480,1854],{},[1688,22482,1954],{},[898,22484,3035],{},[902,22486,21959],{"encoding":904}," — dostaneš ",[883,22489,22491],{"className":22490},[886],[888,22492,22493],{"xmlns":890},[892,22494,22495,22503],{},[895,22496,22497],{},[1788,22498,22499,22501],{},[898,22500,1854],{},[898,22502,4440],{},[902,22504,22020],{"encoding":904}," jako lineární funkci ",[883,22507,22509],{"className":22508},[886],[888,22510,22511],{"xmlns":890},[892,22512,22513,22517],{},[895,22514,22515],{},[898,22516,1854],{},[902,22518,1854],{"encoding":904},[123,22520,22521,22487,22548,22505,22561,2263],{},[38,22522,22440,22523,22547],{},[883,22524,22526],{"className":22525},[886],[888,22527,22528],{"xmlns":890},[892,22529,22530,22544],{},[895,22531,22532,22538,22540,22542],{},[1788,22533,22534,22536],{},[898,22535,1854],{},[898,22537,4440],{},[1688,22539,2066],{"stretchy":2065},[898,22541,1854],{},[1688,22543,2076],{"stretchy":2065},[902,22545,22546],{"encoding":904},"Y_D(Y)"," do funkce spotřeby",[883,22549,22551],{"className":22550},[886],[888,22552,22553],{"xmlns":890},[892,22554,22555,22559],{},[895,22556,22557],{},[898,22558,1693],{},[902,22560,1693],{"encoding":904},[883,22562,22564],{"className":22563},[886],[888,22565,22566],{"xmlns":890},[892,22567,22568,22572],{},[895,22569,22570],{},[898,22571,1854],{},[902,22573,1854],{"encoding":904},[123,22575,22576,2170,22598,22632,22633,22646,22647,2263],{},[38,22577,22440,22578,22597],{},[883,22579,22581],{"className":22580},[886],[888,22582,22583],{"xmlns":890},[892,22584,22585,22595],{},[895,22586,22587,22589,22591,22593],{},[898,22588,1693],{},[1688,22590,2066],{"stretchy":2065},[898,22592,1854],{},[1688,22594,2076],{"stretchy":2065},[902,22596,14463],{"encoding":904}," do podmínky rovnováhy",[883,22599,22601],{"className":22600},[886],[888,22602,22603],{"xmlns":890},[892,22604,22605,22629],{},[895,22606,22607,22609,22611,22613,22615,22621,22623],{},[898,22608,1854],{},[1688,22610,1690],{},[898,22612,1693],{},[1688,22614,1696],{},[1850,22616,22617,22619],{},[898,22618,1699],{},[1688,22620,1857],{},[1688,22622,1696],{},[1850,22624,22625,22627],{},[898,22626,1704],{},[1688,22628,1857],{},[902,22630,22631],{"encoding":904},"Y = C + I^* + G^*"," — zbývá jediná rovnice o jedné neznámé ",[883,22634,22636],{"className":22635},[886],[888,22637,22638],{"xmlns":890},[892,22639,22640,22644],{},[895,22641,22642],{},[898,22643,1854],{},[902,22645,1854],{"encoding":904},", odtud ",[883,22648,22650],{"className":22649},[886],[888,22651,22652],{"xmlns":890},[892,22653,22654,22662],{},[895,22655,22656],{},[1850,22657,22658,22660],{},[898,22659,1854],{},[898,22661,4509],{},[902,22663,14150],{"encoding":904},[123,22665,22666,22669,22670,1343,22688,1343,22708,1343,22725,2263],{},[38,22667,22668],{},"Zpětným dosazením"," dopočítej ",[883,22671,22673],{"className":22672},[886],[888,22674,22675],{"xmlns":890},[892,22676,22677,22685],{},[895,22678,22679],{},[1850,22680,22681,22683],{},[898,22682,3035],{},[898,22684,4509],{},[902,22686,22687],{"encoding":904},"T^E",[883,22689,22691],{"className":22690},[886],[888,22692,22693],{"xmlns":890},[892,22694,22695,22705],{},[895,22696,22697],{},[1814,22698,22699,22701,22703],{},[898,22700,1854],{},[898,22702,4440],{},[898,22704,4509],{},[902,22706,22707],{"encoding":904},"Y_D^E",[883,22709,22711],{"className":22710},[886],[888,22712,22713],{"xmlns":890},[892,22714,22715,22723],{},[895,22716,22717],{},[1850,22718,22719,22721],{},[898,22720,1693],{},[898,22722,4509],{},[902,22724,14209],{"encoding":904},[883,22726,22728],{"className":22727},[886],[888,22729,22730],{"xmlns":890},[892,22731,22732,22740],{},[895,22733,22734],{},[1850,22735,22736,22738],{},[898,22737,1740],{},[898,22739,4509],{},[902,22741,22742],{"encoding":904},"S^E",[198,22744,22746],{"id":22745},"příklad-74","Příklad 7.4",[724,22748,21262,22749,22770,22771,1343,22802,1343,22826,1343,22848,22870],{},[883,22750,22752],{"className":22751},[886],[888,22753,22754],{"xmlns":890},[892,22755,22756,22768],{},[895,22757,22758,22760,22762,22764,22766],{},[898,22759,1693],{},[2041,22761,12539],{},[898,22763,1699],{},[2041,22765,12539],{},[898,22767,1704],{},[902,22769,18462],{"encoding":904}," jsou dány ",[883,22772,22774],{"className":22773},[886],[888,22775,22776],{"xmlns":890},[892,22777,22778,22799],{},[895,22779,22780,22782,22784,22787,22789,22795,22797],{},[898,22781,1693],{},[1688,22783,1690],{},[1793,22785,22786],{},"0,9",[2041,22788,2043],{},[1788,22790,22791,22793],{},[898,22792,1854],{},[898,22794,4440],{},[1688,22796,1696],{},[1793,22798,6153],{},[902,22800,22801],{"encoding":904},"C = 0{,}9\\,Y_D + 70",[883,22803,22805],{"className":22804},[886],[888,22806,22807],{"xmlns":890},[892,22808,22809,22823],{},[895,22810,22811,22813,22815,22817,22819,22821],{},[898,22812,3035],{},[1688,22814,1690],{},[1793,22816,3097],{},[898,22818,1854],{},[1688,22820,1696],{},[1793,22822,5260],{},[902,22824,22825],{"encoding":904},"T = 0{,}2Y + 25",[883,22827,22829],{"className":22828},[886],[888,22830,22831],{"xmlns":890},[892,22832,22833,22845],{},[895,22834,22835,22841,22843],{},[1850,22836,22837,22839],{},[898,22838,1699],{},[1688,22840,1857],{},[1688,22842,1690],{},[1793,22844,15285],{},[902,22846,22847],{"encoding":904},"I^* = 35",[883,22849,22851],{"className":22850},[886],[888,22852,22853],{"xmlns":890},[892,22854,22855,22867],{},[895,22856,22857,22863,22865],{},[1850,22858,22859,22861],{},[898,22860,1704],{},[1688,22862,1857],{},[1688,22864,1690],{},[1793,22866,9290],{},[902,22868,22869],{"encoding":904},"G^* = 20",". Soustava (7.9):",[724,22872,22873],{},[883,22874,22876],{"className":22875},[886],[888,22877,22878],{"xmlns":890},[892,22879,22880,23004],{},[20995,22881,22882,22912,22940,22974],{"rowspacing":20997,"columnalign":20998,"columnspacing":1823},[21000,22883,22884,22890],{},[21003,22885,22886],{},[1777,22887,22888],{"scriptlevel":1779,"displaystyle":1732},[898,22889,1854],{},[21003,22891,22892],{},[1777,22893,22894],{"scriptlevel":1779,"displaystyle":1732},[895,22895,22896,22898,22900,22902,22904,22906,22908,22910],{},[895,22897],{},[1688,22899,1690],{},[898,22901,1693],{},[1688,22903,1696],{},[1793,22905,15285],{},[1688,22907,1696],{},[1793,22909,9290],{},[1688,22911,1733],{"separator":1732},[21000,22913,22914,22920],{},[21003,22915,22916],{},[1777,22917,22918],{"scriptlevel":1779,"displaystyle":1732},[898,22919,3035],{},[21003,22921,22922],{},[1777,22923,22924],{"scriptlevel":1779,"displaystyle":1732},[895,22925,22926,22928,22930,22932,22934,22936,22938],{},[895,22927],{},[1688,22929,1690],{},[1793,22931,3097],{},[898,22933,1854],{},[1688,22935,1696],{},[1793,22937,5260],{},[1688,22939,1733],{"separator":1732},[21000,22941,22942,22948],{},[21003,22943,22944],{},[1777,22945,22946],{"scriptlevel":1779,"displaystyle":1732},[898,22947,1693],{},[21003,22949,22950],{},[1777,22951,22952],{"scriptlevel":1779,"displaystyle":1732},[895,22953,22954,22956,22958,22960,22962,22968,22970,22972],{},[895,22955],{},[1688,22957,1690],{},[1793,22959,22786],{},[2041,22961,2043],{},[1788,22963,22964,22966],{},[898,22965,1854],{},[898,22967,4440],{},[1688,22969,1696],{},[1793,22971,6153],{},[1688,22973,1733],{"separator":1732},[21000,22975,22976,22986],{},[21003,22977,22978],{},[1777,22979,22980],{"scriptlevel":1779,"displaystyle":1732},[1788,22981,22982,22984],{},[898,22983,1854],{},[898,22985,4440],{},[21003,22987,22988],{},[1777,22989,22990],{"scriptlevel":1779,"displaystyle":1732},[895,22991,22992,22994,22996,22998,23000,23002],{},[895,22993],{},[1688,22995,1690],{},[898,22997,1854],{},[1688,22999,1954],{},[898,23001,3035],{},[898,23003,2263],{"mathvariant":1822},[902,23005,23006],{"encoding":904},"\\begin{aligned} Y &= C + 35 + 20, \\\\ T &= 0{,}2Y + 25, \\\\ C &= 0{,}9\\,Y_D + 70, \\\\ Y_D &= Y - T. \\end{aligned}",[724,23008,23009,23012,23013,23067,23068,23114,23115,2965],{},[38,23010,23011],{},"Řešení."," Z definice ",[883,23014,23016],{"className":23015},[886],[888,23017,23018],{"xmlns":890},[892,23019,23020,23064],{},[895,23021,23022,23028,23030,23032,23034,23036,23038,23040,23042,23044,23046,23048,23050,23052,23054,23056,23058,23060,23062],{},[1788,23023,23024,23026],{},[898,23025,1854],{},[898,23027,4440],{},[1688,23029,1690],{},[898,23031,1854],{},[1688,23033,1954],{},[898,23035,3035],{},[1688,23037,1690],{},[898,23039,1854],{},[1688,23041,1954],{},[1688,23043,2066],{"stretchy":2065},[1793,23045,3097],{},[898,23047,1854],{},[1688,23049,1696],{},[1793,23051,5260],{},[1688,23053,2076],{"stretchy":2065},[1688,23055,1690],{},[1793,23057,14836],{},[898,23059,1854],{},[1688,23061,1954],{},[1793,23063,5260],{},[902,23065,23066],{"encoding":904},"Y_D = Y - T = Y - (0{,}2Y + 25) = 0{,}8Y - 25",". Dosazením do spotřeby: ",[883,23069,23071],{"className":23070},[886],[888,23072,23073],{"xmlns":890},[892,23074,23075,23111],{},[895,23076,23077,23079,23081,23083,23085,23087,23089,23091,23093,23095,23097,23099,23101,23104,23106,23108],{},[898,23078,1693],{},[1688,23080,1690],{},[1793,23082,22786],{},[1688,23084,2066],{"stretchy":2065},[1793,23086,14836],{},[898,23088,1854],{},[1688,23090,1954],{},[1793,23092,5260],{},[1688,23094,2076],{"stretchy":2065},[1688,23096,1696],{},[1793,23098,6153],{},[1688,23100,1690],{},[1793,23102,23103],{},"0,72",[898,23105,1854],{},[1688,23107,1696],{},[1793,23109,23110],{},"47,5",[902,23112,23113],{"encoding":904},"C = 0{,}9(0{,}8Y - 25) + 70 = 0{,}72Y + 47{,}5",". Dosazením do rovnovážné rovnice ",[883,23116,23118],{"className":23117},[886],[888,23119,23120],{"xmlns":890},[892,23121,23122,23140],{},[895,23123,23124,23126,23128,23130,23132,23134,23136,23138],{},[898,23125,1854],{},[1688,23127,1690],{},[1793,23129,23103],{},[898,23131,1854],{},[1688,23133,1696],{},[1793,23135,23110],{},[1688,23137,1696],{},[1793,23139,21421],{},[902,23141,23142],{"encoding":904},"Y = 0{,}72Y + 47{,}5 + 55",[724,23144,23145],{},[883,23146,23148],{"className":23147},[886],[888,23149,23150],{"xmlns":890},[892,23151,23152,23193],{},[895,23153,23154,23157,23159,23161,23164,23166,23168,23170,23176,23178,23188,23190],{},[1793,23155,23156],{},"0,28",[898,23158,1854],{},[1688,23160,1690],{},[1793,23162,23163],{},"102,5",[2041,23165,4241],{},[1688,23167,15255],{},[2041,23169,4241],{},[1850,23171,23172,23174],{},[898,23173,1854],{},[898,23175,4509],{},[1688,23177,1690],{},[1777,23179,23180],{"scriptlevel":1779,"displaystyle":2065},[1781,23181,23182,23185],{},[1793,23183,23184],{},"5125",[1793,23186,23187],{},"14",[1688,23189,6156],{},[1793,23191,23192],{},"366,071.",[902,23194,23195],{"encoding":904},"0{,}28Y = 102{,}5 \\;\\Longrightarrow\\; Y^E = \\tfrac{5125}{14} \\doteq 366{,}071.",[724,23197,23198],{},"Rovnovážné veličiny:",[120,23200,23201,23236,23288,23342,23390],{},[123,23202,23203,1733],{},[883,23204,23206],{"className":23205},[886],[888,23207,23208],{"xmlns":890},[892,23209,23210,23233],{},[895,23211,23212,23218,23220,23228,23230],{},[1850,23213,23214,23216],{},[898,23215,1854],{},[898,23217,4509],{},[1688,23219,1690],{},[1777,23221,23222],{"scriptlevel":1779,"displaystyle":2065},[1781,23223,23224,23226],{},[1793,23225,23184],{},[1793,23227,23187],{},[1688,23229,6156],{},[1793,23231,23232],{},"366,071",[902,23234,23235],{"encoding":904},"Y^E = \\tfrac{5125}{14} \\doteq 366{,}071",[123,23237,23238,1733],{},[883,23239,23241],{"className":23240},[886],[888,23242,23243],{"xmlns":890},[892,23244,23245,23285],{},[895,23246,23247,23253,23255,23257,23259,23265,23267,23269,23271,23280,23282],{},[1850,23248,23249,23251],{},[898,23250,3035],{},[898,23252,4509],{},[1688,23254,1690],{},[1793,23256,3097],{},[2041,23258,2043],{},[1850,23260,23261,23263],{},[898,23262,1854],{},[898,23264,4509],{},[1688,23266,1696],{},[1793,23268,5260],{},[1688,23270,1690],{},[1777,23272,23273],{"scriptlevel":1779,"displaystyle":2065},[1781,23274,23275,23278],{},[1793,23276,23277],{},"1375",[1793,23279,23187],{},[1688,23281,6156],{},[1793,23283,23284],{},"98,214",[902,23286,23287],{"encoding":904},"T^E = 0{,}2\\,Y^E + 25 = \\tfrac{1375}{14} \\doteq 98{,}214",[123,23289,23290,1733],{},[883,23291,23293],{"className":23292},[886],[888,23294,23295],{"xmlns":890},[892,23296,23297,23339],{},[895,23298,23299,23307,23309,23315,23317,23323,23325,23334,23336],{},[1814,23300,23301,23303,23305],{},[898,23302,1854],{},[898,23304,4440],{},[898,23306,4509],{},[1688,23308,1690],{},[1850,23310,23311,23313],{},[898,23312,1854],{},[898,23314,4509],{},[1688,23316,1954],{},[1850,23318,23319,23321],{},[898,23320,3035],{},[898,23322,4509],{},[1688,23324,1690],{},[1777,23326,23327],{"scriptlevel":1779,"displaystyle":2065},[1781,23328,23329,23332],{},[1793,23330,23331],{},"3750",[1793,23333,23187],{},[1688,23335,6156],{},[1793,23337,23338],{},"267,857",[902,23340,23341],{"encoding":904},"Y_D^E = Y^E - T^E = \\tfrac{3750}{14} \\doteq 267{,}857",[123,23343,23344,1733],{},[883,23345,23347],{"className":23346},[886],[888,23348,23349],{"xmlns":890},[892,23350,23351,23387],{},[895,23352,23353,23359,23361,23367,23369,23371,23373,23382,23384],{},[1850,23354,23355,23357],{},[898,23356,1693],{},[898,23358,4509],{},[1688,23360,1690],{},[1850,23362,23363,23365],{},[898,23364,1854],{},[898,23366,4509],{},[1688,23368,1954],{},[1793,23370,21421],{},[1688,23372,1690],{},[1777,23374,23375],{"scriptlevel":1779,"displaystyle":2065},[1781,23376,23377,23380],{},[1793,23378,23379],{},"4355",[1793,23381,23187],{},[1688,23383,6156],{},[1793,23385,23386],{},"311,071",[902,23388,23389],{"encoding":904},"C^E = Y^E - 55 = \\tfrac{4355}{14} \\doteq 311{,}071",[123,23391,23392,23448],{},[883,23393,23395],{"className":23394},[886],[888,23396,23397],{"xmlns":890},[892,23398,23399,23445],{},[895,23400,23401,23407,23409,23417,23419,23425,23427,23429,23438,23440,23442],{},[1850,23402,23403,23405],{},[898,23404,1740],{},[898,23406,4509],{},[1688,23408,1690],{},[1814,23410,23411,23413,23415],{},[898,23412,1854],{},[898,23414,4440],{},[898,23416,4509],{},[1688,23418,1954],{},[1850,23420,23421,23423],{},[898,23422,1693],{},[898,23424,4509],{},[1688,23426,1690],{},[1688,23428,1954],{},[1777,23430,23431],{"scriptlevel":1779,"displaystyle":2065},[1781,23432,23433,23436],{},[1793,23434,23435],{},"605",[1793,23437,23187],{},[1688,23439,6156],{},[1688,23441,1954],{},[1793,23443,23444],{},"43,214",[902,23446,23447],{"encoding":904},"S^E = Y_D^E - C^E = -\\tfrac{605}{14} \\doteq -43{,}214"," (záporné — domácnosti při této kalibraci čerpají úspory).",[724,23450,23451,21591,23453,23474,23475,23478,23479,23502,23503,2263],{},[38,23452,21590],{},[883,23454,23456],{"className":23455},[886],[888,23457,23458],{"xmlns":890},[892,23459,23460,23472],{},[895,23461,23462,23464,23466,23468,23470],{},[898,23463,1693],{},[2041,23465,12539],{},[898,23467,1699],{},[2041,23469,12539],{},[898,23471,1704],{},[902,23473,18462],{"encoding":904}," stále uvažuje ",[38,23476,23477],{},"uzavřenou"," ekonomiku. Reálné ekonomiky dovážejí a vyvážejí zboží — otevření ekonomiky o čistý export ",[883,23480,23482],{"className":23481},[886],[888,23483,23484],{"xmlns":890},[892,23485,23486,23499],{},[895,23487,23488,23490,23492,23495,23497],{},[898,23489,1709],{},[1688,23491,1690],{},[898,23493,23494],{},"B",[1688,23496,1954],{},[898,23498,1661],{},[902,23500,23501],{"encoding":904},"X = B - M"," dává ",[38,23504,21612,23505],{},[883,23506,23508],{"className":23507},[886],[888,23509,23510],{"xmlns":890},[892,23511,23512,23528],{},[895,23513,23514,23516,23518,23520,23522,23524,23526],{},[898,23515,1693],{},[2041,23517,12539],{},[898,23519,1699],{},[2041,23521,12539],{},[898,23523,1704],{},[2041,23525,12539],{},[898,23527,1709],{},[902,23529,12571],{"encoding":904},[115,23531,23533],{"id":23532},"model-c-i-g-x-otevřená-ekonomika","Model C-I-G-X — otevřená ekonomika",[198,23535,20862],{"id":23536},"zadání-modelu-2",[724,23538,23539,23540,2170,23543,21835,23564,23577,23578,12378,23581,23594],{},"Rozšíření o ",[38,23541,23542],{},"čistý export",[883,23544,23546],{"className":23545},[886],[888,23547,23548],{"xmlns":890},[892,23549,23550,23562],{},[895,23551,23552,23554,23556,23558,23560],{},[898,23553,1709],{},[1688,23555,1690],{},[898,23557,23494],{},[1688,23559,1954],{},[898,23561,1661],{},[902,23563,23501],{"encoding":904},[883,23565,23567],{"className":23566},[886],[888,23568,23569],{"xmlns":890},[892,23570,23571,23575],{},[895,23572,23573],{},[898,23574,23494],{},[902,23576,23494],{"encoding":904}," je hrubý export (",[614,23579,23580],{},"brutto export",[883,23582,23584],{"className":23583},[886],[888,23585,23586],{"xmlns":890},[892,23587,23588,23592],{},[895,23589,23590],{},[898,23591,1661],{},[902,23593,1661],{"encoding":904}," import. Obvyklá konstrukce: import závisí (nejčastěji je úměrný) disponibilnímu důchodu:",[724,23596,23597],{},[883,23598,23600],{"className":23599},[886],[888,23601,23602],{"xmlns":890},[892,23603,23604,23624],{},[895,23605,23606,23608,23610,23612,23614,23620,23622],{},[898,23607,1661],{},[1688,23609,1690],{},[898,23611,1661],{},[1688,23613,2066],{"stretchy":2065},[1788,23615,23616,23618],{},[898,23617,1854],{},[898,23619,4440],{},[1688,23621,2076],{"stretchy":2065},[898,23623,2263],{"mathvariant":1822},[902,23625,23626],{"encoding":904},"M = M(Y_D).",[724,23628,23629],{},"Podmínka rovnováhy:",[724,23631,23632],{},[883,23633,23635],{"className":23634},[886],[888,23636,23637],{"xmlns":890},[892,23638,23639,23676],{},[895,23640,23641,23643,23645,23647,23649,23651,23653,23655,23657,23659,23661,23663,23665,23667,23669,23672,23674],{},[898,23642,1854],{},[1688,23644,1690],{},[898,23646,1693],{},[1688,23648,1696],{},[898,23650,1699],{},[1688,23652,1696],{},[898,23654,1704],{},[1688,23656,1696],{},[898,23658,23494],{},[1688,23660,1954],{},[898,23662,1661],{},[898,23664,2263],{"mathvariant":1822},[6134,23666],{"width":6136},[1688,23668,2066],{"stretchy":2065},[1793,23670,23671],{},"7.10",[2041,23673,207],{},[1688,23675,2076],{"stretchy":2065},[902,23677,23678],{"encoding":904},"Y = C + I + G + B - M. \\qquad (7.10\\text{a})",[198,23680,20932],{"id":23681},"soustava-rovnic-2",[724,23683,22092,23684,23718,23719,2965],{},[883,23685,23687],{"className":23686},[886],[888,23688,23689],{"xmlns":890},[892,23690,23691,23715],{},[895,23692,23693,23699,23701,23707,23709],{},[1850,23694,23695,23697],{},[898,23696,1699],{},[1688,23698,1857],{},[1688,23700,1733],{"separator":1732},[1850,23702,23703,23705],{},[898,23704,1704],{},[1688,23706,1857],{},[1688,23708,1733],{"separator":1732},[1850,23710,23711,23713],{},[898,23712,23494],{},[1688,23714,1857],{},[902,23716,23717],{"encoding":904},"I^*, G^*, B^*"," dostáváme soustavu 5 rovnic o 5 neznámých ",[883,23720,23722],{"className":23721},[886],[888,23723,23724],{"xmlns":890},[892,23725,23726,23750],{},[895,23727,23728,23730,23732,23734,23736,23738,23740,23746,23748],{},[898,23729,1854],{},[1688,23731,1733],{"separator":1732},[898,23733,1693],{},[1688,23735,1733],{"separator":1732},[898,23737,3035],{},[1688,23739,1733],{"separator":1732},[1788,23741,23742,23744],{},[898,23743,1854],{},[898,23745,4440],{},[1688,23747,1733],{"separator":1732},[898,23749,1661],{},[902,23751,23752],{"encoding":904},"Y, C, T, Y_D, M",[724,23754,23755],{},[883,23756,23758],{"className":23757},[886],[888,23759,23760],{"xmlns":890},[892,23761,23762,23946],{},[895,23763,23764,23938,23940,23942,23944],{},[20995,23765,23766,23798,23828,23856,23888],{"rowspacing":20997,"columnalign":20998,"columnspacing":1823},[21000,23767,23768,23774],{},[21003,23769,23770],{},[1777,23771,23772],{"scriptlevel":1779,"displaystyle":1732},[898,23773,1693],{},[21003,23775,23776],{},[1777,23777,23778],{"scriptlevel":1779,"displaystyle":1732},[895,23779,23780,23782,23784,23786,23788,23794,23796],{},[895,23781],{},[1688,23783,1690],{},[898,23785,1693],{},[1688,23787,2066],{"stretchy":2065},[1788,23789,23790,23792],{},[898,23791,1854],{},[898,23793,4440],{},[1688,23795,2076],{"stretchy":2065},[1688,23797,1733],{"separator":1732},[21000,23799,23800,23810],{},[21003,23801,23802],{},[1777,23803,23804],{"scriptlevel":1779,"displaystyle":1732},[1788,23805,23806,23808],{},[898,23807,1854],{},[898,23809,4440],{},[21003,23811,23812],{},[1777,23813,23814],{"scriptlevel":1779,"displaystyle":1732},[895,23815,23816,23818,23820,23822,23824,23826],{},[895,23817],{},[1688,23819,1690],{},[898,23821,1854],{},[1688,23823,1954],{},[898,23825,3035],{},[1688,23827,1733],{"separator":1732},[21000,23829,23830,23836],{},[21003,23831,23832],{},[1777,23833,23834],{"scriptlevel":1779,"displaystyle":1732},[898,23835,3035],{},[21003,23837,23838],{},[1777,23839,23840],{"scriptlevel":1779,"displaystyle":1732},[895,23841,23842,23844,23846,23848,23850,23852,23854],{},[895,23843],{},[1688,23845,1690],{},[898,23847,3035],{},[1688,23849,2066],{"stretchy":2065},[898,23851,1854],{},[1688,23853,2076],{"stretchy":2065},[1688,23855,1733],{"separator":1732},[21000,23857,23858,23864],{},[21003,23859,23860],{},[1777,23861,23862],{"scriptlevel":1779,"displaystyle":1732},[898,23863,1661],{},[21003,23865,23866],{},[1777,23867,23868],{"scriptlevel":1779,"displaystyle":1732},[895,23869,23870,23872,23874,23876,23878,23884,23886],{},[895,23871],{},[1688,23873,1690],{},[898,23875,1661],{},[1688,23877,2066],{"stretchy":2065},[1788,23879,23880,23882],{},[898,23881,1854],{},[898,23883,4440],{},[1688,23885,2076],{"stretchy":2065},[1688,23887,1733],{"separator":1732},[21000,23889,23890,23896],{},[21003,23891,23892],{},[1777,23893,23894],{"scriptlevel":1779,"displaystyle":1732},[898,23895,1854],{},[21003,23897,23898],{},[1777,23899,23900],{"scriptlevel":1779,"displaystyle":1732},[895,23901,23902,23904,23906,23908,23910,23916,23918,23924,23926,23932,23934,23936],{},[895,23903],{},[1688,23905,1690],{},[898,23907,1693],{},[1688,23909,1696],{},[1850,23911,23912,23914],{},[898,23913,1699],{},[1688,23915,1857],{},[1688,23917,1696],{},[1850,23919,23920,23922],{},[898,23921,1704],{},[1688,23923,1857],{},[1688,23925,1696],{},[1850,23927,23928,23930],{},[898,23929,23494],{},[1688,23931,1857],{},[1688,23933,1954],{},[898,23935,1661],{},[898,23937,2263],{"mathvariant":1822},[6134,23939],{"width":6136},[1688,23941,2066],{"stretchy":2065},[1793,23943,23671],{},[1688,23945,2076],{"stretchy":2065},[902,23947,23948],{"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)",[198,23950,23952],{"id":23951},"příklad-75","Příklad 7.5",[724,23954,23955,23956,1343,23988,1343,24015,1343,24036,1343,24058,1343,24080,24103],{},"Dáno: ",[883,23957,23959],{"className":23958},[886],[888,23960,23961],{"xmlns":890},[892,23962,23963,23985],{},[895,23964,23965,23967,23969,23972,23974,23980,23982],{},[898,23966,1693],{},[1688,23968,1690],{},[1793,23970,23971],{},"0,75",[2041,23973,2043],{},[1788,23975,23976,23978],{},[898,23977,1854],{},[898,23979,4440],{},[1688,23981,1696],{},[1793,23983,23984],{},"750",[902,23986,23987],{"encoding":904},"C = 0{,}75\\,Y_D + 750",[883,23989,23991],{"className":23990},[886],[888,23992,23993],{"xmlns":890},[892,23994,23995,24012],{},[895,23996,23997,23999,24001,24004,24006],{},[898,23998,1661],{},[1688,24000,1690],{},[1793,24002,24003],{},"0,15",[2041,24005,2043],{},[1788,24007,24008,24010],{},[898,24009,1854],{},[898,24011,4440],{},[902,24013,24014],{"encoding":904},"M = 0{,}15\\,Y_D",[883,24016,24018],{"className":24017},[886],[888,24019,24020],{"xmlns":890},[892,24021,24022,24033],{},[895,24023,24024,24026,24028,24031],{},[898,24025,3035],{},[1688,24027,1690],{},[1793,24029,24030],{},"0,25",[898,24032,1854],{},[902,24034,24035],{"encoding":904},"T = 0{,}25Y",[883,24037,24039],{"className":24038},[886],[888,24040,24041],{"xmlns":890},[892,24042,24043,24055],{},[895,24044,24045,24051,24053],{},[1850,24046,24047,24049],{},[898,24048,1699],{},[1688,24050,1857],{},[1688,24052,1690],{},[1793,24054,15357],{},[902,24056,24057],{"encoding":904},"I^* = 500",[883,24059,24061],{"className":24060},[886],[888,24062,24063],{"xmlns":890},[892,24064,24065,24077],{},[895,24066,24067,24073,24075],{},[1850,24068,24069,24071],{},[898,24070,1704],{},[1688,24072,1857],{},[1688,24074,1690],{},[1793,24076,9058],{},[902,24078,24079],{"encoding":904},"G^* = 150",[883,24081,24083],{"className":24082},[886],[888,24084,24085],{"xmlns":890},[892,24086,24087,24100],{},[895,24088,24089,24095,24097],{},[1850,24090,24091,24093],{},[898,24092,23494],{},[1688,24094,1857],{},[1688,24096,1690],{},[1793,24098,24099],{},"800",[902,24101,24102],{"encoding":904},"B^* = 800",". Soustava:",[724,24105,24106],{},[883,24107,24109],{"className":24108},[886],[888,24110,24111],{"xmlns":890},[892,24112,24113,24331],{},[20995,24114,24115,24161,24203,24239,24281],{"rowspacing":20997,"columnalign":20998,"columnspacing":1823},[21000,24116,24117,24133],{},[21003,24118,24119],{},[1777,24120,24121],{"scriptlevel":1779,"displaystyle":1732},[895,24122,24123,24125,24127,24129,24131],{},[1688,24124,2066],{"stretchy":2065},[898,24126,2046],{},[1793,24128,1795],{},[1688,24130,2076],{"stretchy":2065},[2041,24132,2558],{},[21003,24134,24135],{},[1777,24136,24137],{"scriptlevel":1779,"displaystyle":1732},[895,24138,24139,24141,24143,24145,24147,24149,24155,24157,24159],{},[895,24140],{},[898,24142,1693],{},[1688,24144,1690],{},[1793,24146,23971],{},[2041,24148,2043],{},[1788,24150,24151,24153],{},[898,24152,1854],{},[898,24154,4440],{},[1688,24156,1696],{},[1793,24158,23984],{},[1688,24160,1733],{"separator":1732},[21000,24162,24163,24179],{},[21003,24164,24165],{},[1777,24166,24167],{"scriptlevel":1779,"displaystyle":1732},[895,24168,24169,24171,24173,24175,24177],{},[1688,24170,2066],{"stretchy":2065},[898,24172,2046],{},[1793,24174,1806],{},[1688,24176,2076],{"stretchy":2065},[2041,24178,2558],{},[21003,24180,24181],{},[1777,24182,24183],{"scriptlevel":1779,"displaystyle":1732},[895,24184,24185,24187,24193,24195,24197,24199,24201],{},[895,24186],{},[1788,24188,24189,24191],{},[898,24190,1854],{},[898,24192,4440],{},[1688,24194,1690],{},[898,24196,1854],{},[1688,24198,1954],{},[898,24200,3035],{},[1688,24202,1733],{"separator":1732},[21000,24204,24205,24221],{},[21003,24206,24207],{},[1777,24208,24209],{"scriptlevel":1779,"displaystyle":1732},[895,24210,24211,24213,24215,24217,24219],{},[1688,24212,2066],{"stretchy":2065},[898,24214,2046],{},[1793,24216,2131],{},[1688,24218,2076],{"stretchy":2065},[2041,24220,2558],{},[21003,24222,24223],{},[1777,24224,24225],{"scriptlevel":1779,"displaystyle":1732},[895,24226,24227,24229,24231,24233,24235,24237],{},[895,24228],{},[898,24230,3035],{},[1688,24232,1690],{},[1793,24234,24030],{},[898,24236,1854],{},[1688,24238,1733],{"separator":1732},[21000,24240,24241,24257],{},[21003,24242,24243],{},[1777,24244,24245],{"scriptlevel":1779,"displaystyle":1732},[895,24246,24247,24249,24251,24253,24255],{},[1688,24248,2066],{"stretchy":2065},[898,24250,2046],{},[1793,24252,2616],{},[1688,24254,2076],{"stretchy":2065},[2041,24256,2558],{},[21003,24258,24259],{},[1777,24260,24261],{"scriptlevel":1779,"displaystyle":1732},[895,24262,24263,24265,24267,24269,24271,24273,24279],{},[895,24264],{},[898,24266,1661],{},[1688,24268,1690],{},[1793,24270,24003],{},[2041,24272,2043],{},[1788,24274,24275,24277],{},[898,24276,1854],{},[898,24278,4440],{},[1688,24280,1733],{"separator":1732},[21000,24282,24283,24299],{},[21003,24284,24285],{},[1777,24286,24287],{"scriptlevel":1779,"displaystyle":1732},[895,24288,24289,24291,24293,24295,24297],{},[1688,24290,2066],{"stretchy":2065},[898,24292,2046],{},[1793,24294,2501],{},[1688,24296,2076],{"stretchy":2065},[2041,24298,2558],{},[21003,24300,24301],{},[1777,24302,24303],{"scriptlevel":1779,"displaystyle":1732},[895,24304,24305,24307,24309,24311,24313,24315,24317,24319,24321,24323,24325,24327,24329],{},[895,24306],{},[898,24308,1854],{},[1688,24310,1690],{},[898,24312,1693],{},[1688,24314,1696],{},[1793,24316,15357],{},[1688,24318,1696],{},[1793,24320,9058],{},[1688,24322,1696],{},[1793,24324,24099],{},[1688,24326,1954],{},[898,24328,1661],{},[898,24330,2263],{"mathvariant":1822},[902,24332,24333],{"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}",[724,24335,24336,24337,24371],{},"Postupná substituce — z (r3) do (r2): ",[883,24338,24340],{"className":24339},[886],[888,24341,24342],{"xmlns":890},[892,24343,24344,24368],{},[895,24345,24346,24352,24354,24356,24358,24360,24362,24364,24366],{},[1788,24347,24348,24350],{},[898,24349,1854],{},[898,24351,4440],{},[1688,24353,1690],{},[898,24355,1854],{},[1688,24357,1954],{},[1793,24359,24030],{},[898,24361,1854],{},[1688,24363,1690],{},[1793,24365,23971],{},[898,24367,1854],{},[902,24369,24370],{"encoding":904},"Y_D = Y - 0{,}25Y = 0{,}75Y",". Dosazením do (r1) a (r4):",[724,24373,24374],{},[883,24375,24377],{"className":24376},[886],[888,24378,24379],{"xmlns":890},[892,24380,24381,24422],{},[895,24382,24383,24385,24387,24389,24391,24393,24395,24397,24399,24401,24403,24405,24407,24409,24411,24414,24416,24418,24420],{},[1688,24384,2066],{"stretchy":2065},[898,24386,2046],{},[1793,24388,2508],{},[1688,24390,2076],{"stretchy":2065},[2041,24392,2558],{},[898,24394,1693],{},[1688,24396,1690],{},[1793,24398,23971],{},[1688,24400,3434],{},[1793,24402,23971],{},[898,24404,1854],{},[1688,24406,1696],{},[1793,24408,23984],{},[1688,24410,1690],{},[1793,24412,24413],{},"0,5625",[898,24415,1854],{},[1688,24417,1696],{},[1793,24419,23984],{},[1688,24421,1733],{"separator":1732},[902,24423,24424],{"encoding":904},"(r6)\\ C = 0{,}75 \\cdot 0{,}75Y + 750 = 0{,}5625Y + 750,",[724,24426,24427],{},[883,24428,24430],{"className":24429},[886],[888,24431,24432],{"xmlns":890},[892,24433,24434,24468],{},[895,24435,24436,24438,24440,24443,24445,24447,24449,24451,24453,24455,24457,24459,24461,24464,24466],{},[1688,24437,2066],{"stretchy":2065},[898,24439,2046],{},[1793,24441,24442],{},"7",[1688,24444,2076],{"stretchy":2065},[2041,24446,2558],{},[898,24448,1661],{},[1688,24450,1690],{},[1793,24452,24003],{},[1688,24454,3434],{},[1793,24456,23971],{},[898,24458,1854],{},[1688,24460,1690],{},[1793,24462,24463],{},"0,1125",[898,24465,1854],{},[898,24467,2263],{"mathvariant":1822},[902,24469,24470],{"encoding":904},"(r7)\\ M = 0{,}15 \\cdot 0{,}75Y = 0{,}1125Y.",[724,24472,24473],{},"Dosazením do (r5):",[724,24475,24476],{},[883,24477,24479],{"className":24478},[886],[888,24480,24481],{"xmlns":890},[892,24482,24483,24527],{},[895,24484,24485,24487,24489,24491,24493,24495,24497,24499,24501,24503,24505,24507,24509,24511,24513,24515,24517,24520,24522,24524],{},[898,24486,1854],{},[1688,24488,1690],{},[1793,24490,24413],{},[898,24492,1854],{},[1688,24494,1696],{},[1793,24496,23984],{},[1688,24498,1696],{},[1793,24500,15357],{},[1688,24502,1696],{},[1793,24504,9058],{},[1688,24506,1696],{},[1793,24508,24099],{},[1688,24510,1954],{},[1793,24512,24463],{},[898,24514,1854],{},[1688,24516,1690],{},[1793,24518,24519],{},"0,45",[898,24521,1854],{},[1688,24523,1696],{},[1793,24525,24526],{},"2200.",[902,24528,24529],{"encoding":904},"Y = 0{,}5625Y + 750 + 500 + 150 + 800 - 0{,}1125Y = 0{,}45Y + 2200.",[724,24531,24532,24533,5845,24555,24578],{},"Odtud ",[883,24534,24536],{"className":24535},[886],[888,24537,24538],{"xmlns":890},[892,24539,24540,24552],{},[895,24541,24542,24545,24547,24549],{},[1793,24543,24544],{},"0,55",[898,24546,1854],{},[1688,24548,1690],{},[1793,24550,24551],{},"2200",[902,24553,24554],{"encoding":904},"0{,}55Y = 2200",[883,24556,24558],{"className":24557},[886],[888,24559,24560],{"xmlns":890},[892,24561,24562,24575],{},[895,24563,24564,24570,24572],{},[1850,24565,24566,24568],{},[898,24567,1854],{},[898,24569,4509],{},[1688,24571,1690],{},[1793,24573,24574],{},"4000",[902,24576,24577],{"encoding":904},"Y^E = 4000",". Rovnovážné veličiny:",[120,24580,24581,24604,24636,24671,24704,24740],{},[123,24582,24583,1733],{},[883,24584,24586],{"className":24585},[886],[888,24587,24588],{"xmlns":890},[892,24589,24590,24602],{},[895,24591,24592,24598,24600],{},[1850,24593,24594,24596],{},[898,24595,1854],{},[898,24597,4509],{},[1688,24599,1690],{},[1793,24601,24574],{},[902,24603,24577],{"encoding":904},[123,24605,24606,1733],{},[883,24607,24609],{"className":24608},[886],[888,24610,24611],{"xmlns":890},[892,24612,24613,24633],{},[895,24614,24615,24621,24623,24625,24627,24629,24631],{},[1850,24616,24617,24619],{},[898,24618,3035],{},[898,24620,4509],{},[1688,24622,1690],{},[1793,24624,24030],{},[1688,24626,3434],{},[1793,24628,24574],{},[1688,24630,1690],{},[1793,24632,3042],{},[902,24634,24635],{"encoding":904},"T^E = 0{,}25 \\cdot 4000 = 1000",[123,24637,24638,1733],{},[883,24639,24641],{"className":24640},[886],[888,24642,24643],{"xmlns":890},[892,24644,24645,24668],{},[895,24646,24647,24655,24657,24659,24661,24663,24665],{},[1814,24648,24649,24651,24653],{},[898,24650,1854],{},[898,24652,4440],{},[898,24654,4509],{},[1688,24656,1690],{},[1793,24658,23971],{},[1688,24660,3434],{},[1793,24662,24574],{},[1688,24664,1690],{},[1793,24666,24667],{},"3000",[902,24669,24670],{"encoding":904},"Y_D^E = 0{,}75 \\cdot 4000 = 3000",[123,24672,24673,1733],{},[883,24674,24676],{"className":24675},[886],[888,24677,24678],{"xmlns":890},[892,24679,24680,24701],{},[895,24681,24682,24688,24690,24692,24694,24696,24698],{},[1850,24683,24684,24686],{},[898,24685,1661],{},[898,24687,4509],{},[1688,24689,1690],{},[1793,24691,24003],{},[1688,24693,3434],{},[1793,24695,24667],{},[1688,24697,1690],{},[1793,24699,24700],{},"450",[902,24702,24703],{"encoding":904},"M^E = 0{,}15 \\cdot 3000 = 450",[123,24705,24706,1733],{},[883,24707,24709],{"className":24708},[886],[888,24710,24711],{"xmlns":890},[892,24712,24713,24737],{},[895,24714,24715,24721,24723,24725,24727,24729,24731,24733,24735],{},[1850,24716,24717,24719],{},[898,24718,1693],{},[898,24720,4509],{},[1688,24722,1690],{},[1793,24724,23971],{},[1688,24726,3434],{},[1793,24728,24667],{},[1688,24730,1696],{},[1793,24732,23984],{},[1688,24734,1690],{},[1793,24736,24667],{},[902,24738,24739],{"encoding":904},"C^E = 0{,}75 \\cdot 3000 + 750 = 3000",[123,24741,24742,24782],{},[883,24743,24745],{"className":24744},[886],[888,24746,24747],{"xmlns":890},[892,24748,24749,24779],{},[895,24750,24751,24757,24759,24767,24769,24775,24777],{},[1850,24752,24753,24755],{},[898,24754,1740],{},[898,24756,4509],{},[1688,24758,1690],{},[1814,24760,24761,24763,24765],{},[898,24762,1854],{},[898,24764,4440],{},[898,24766,4509],{},[1688,24768,1954],{},[1850,24770,24771,24773],{},[898,24772,1693],{},[898,24774,4509],{},[1688,24776,1690],{},[1793,24778,1779],{},[902,24780,24781],{"encoding":904},"S^E = Y_D^E - C^E = 0"," (při této kalibraci domácnosti celý disponibilní důchod spotřebují).",[724,24784,24785,24787,24788,1343,24805,4142,24826,24851,24852,24855,24856,24869,24870,2263],{},[38,24786,21590],{}," Modely ",[883,24789,24791],{"className":24790},[886],[888,24792,24793],{"xmlns":890},[892,24794,24795,24803],{},[895,24796,24797,24799,24801],{},[898,24798,1693],{},[2041,24800,12539],{},[898,24802,1699],{},[902,24804,12544],{"encoding":904},[883,24806,24808],{"className":24807},[886],[888,24809,24810],{"xmlns":890},[892,24811,24812,24824],{},[895,24813,24814,24816,24818,24820,24822],{},[898,24815,1693],{},[2041,24817,12539],{},[898,24819,1699],{},[2041,24821,12539],{},[898,24823,1704],{},[902,24825,18462],{"encoding":904},[883,24827,24829],{"className":24828},[886],[888,24830,24831],{"xmlns":890},[892,24832,24833,24849],{},[895,24834,24835,24837,24839,24841,24843,24845,24847],{},[898,24836,1693],{},[2041,24838,12539],{},[898,24840,1699],{},[2041,24842,12539],{},[898,24844,1704],{},[2041,24846,12539],{},[898,24848,1709],{},[902,24850,12571],{"encoding":904}," pokládají investice za ",[38,24853,24854],{},"konstantní",". To není realistické — investice závisejí na úrokové míře ",[883,24857,24859],{"className":24858},[886],[888,24860,24861],{"xmlns":890},[892,24862,24863,24867],{},[895,24864,24865],{},[898,24866,2046],{},[902,24868,2046],{"encoding":904},". Přidáním trhu peněz a úrokové míry vzniká ",[38,24871,24872],{},"model IS-LM",[115,24874,24876],{"id":24875},"_74-multiplikátory-pro-makroekonomické-proměnné","7.4 Multiplikátory pro makroekonomické proměnné",[724,24878,24879,24880,24884,24885,24888,24889,24892],{},"V článku ",[207,24881,24883],{"className":24882,"dataFsResolvedFilePath":827,"href":828},[210],"2.4"," (mikroekonomie) byly zavedeny multiplikátory pro mikroekonomické proměnné. ",[38,24886,24887],{},"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 ",[38,24890,24891],{},"výraznější"," než v mikroekonomických modelech.",[724,24894,24895],{},[2821,24896],{"alt":24897,"className":24898,"src":24899},"imek-multiplikatorovy-efekt-chain",[210,2825],"\u002Fwiki-assets\u002Fimek-multiplikatorovy-efekt-chain.jpeg",[724,24901,12414,24902,1343,24919,1343,24940,24965,24966,24969,24970,24988,24989,25007,25008,25026,25027,25030,25031,1343,25048,25065,25066,25068],{},[883,24903,24905],{"className":24904},[886],[888,24906,24907],{"xmlns":890},[892,24908,24909,24917],{},[895,24910,24911,24913,24915],{},[898,24912,1693],{},[2041,24914,12539],{},[898,24916,1699],{},[902,24918,12544],{"encoding":904},[883,24920,24922],{"className":24921},[886],[888,24923,24924],{"xmlns":890},[892,24925,24926,24938],{},[895,24927,24928,24930,24932,24934,24936],{},[898,24929,1693],{},[2041,24931,12539],{},[898,24933,1699],{},[2041,24935,12539],{},[898,24937,1704],{},[902,24939,18462],{"encoding":904},[883,24941,24943],{"className":24942},[886],[888,24944,24945],{"xmlns":890},[892,24946,24947,24963],{},[895,24948,24949,24951,24953,24955,24957,24959,24961],{},[898,24950,1693],{},[2041,24952,12539],{},[898,24954,1699],{},[2041,24956,12539],{},[898,24958,1704],{},[2041,24960,12539],{},[898,24962,1709],{},[902,24964,12571],{"encoding":904}," se vyšetřuje vliv změn ",[38,24967,24968],{},"exogenních"," veličin (plánovaných investic ",[883,24971,24973],{"className":24972},[886],[888,24974,24975],{"xmlns":890},[892,24976,24977,24985],{},[895,24978,24979],{},[1850,24980,24981,24983],{},[898,24982,1699],{},[1688,24984,1857],{},[902,24986,24987],{"encoding":904},"I^*",", vládních výdajů ",[883,24990,24992],{"className":24991},[886],[888,24993,24994],{"xmlns":890},[892,24995,24996,25004],{},[895,24997,24998],{},[1850,24999,25000,25002],{},[898,25001,1704],{},[1688,25003,1857],{},[902,25005,25006],{"encoding":904},"G^*",", exportu ",[883,25009,25011],{"className":25010},[886],[888,25012,25013],{"xmlns":890},[892,25014,25015,25023],{},[895,25016,25017],{},[1850,25018,25019,25021],{},[898,25020,23494],{},[1688,25022,1857],{},[902,25024,25025],{"encoding":904},"B^*",") na změny ",[38,25028,25029],{},"endogenních"," rovnovážných veličin (",[883,25032,25034],{"className":25033},[886],[888,25035,25036],{"xmlns":890},[892,25037,25038,25046],{},[895,25039,25040],{},[1850,25041,25042,25044],{},[898,25043,1854],{},[898,25045,4509],{},[902,25047,14150],{"encoding":904},[883,25049,25051],{"className":25050},[886],[888,25052,25053],{"xmlns":890},[892,25054,25055,25063],{},[895,25056,25057],{},[1850,25058,25059,25061],{},[898,25060,1693],{},[898,25062,4509],{},[902,25064,14209],{"encoding":904}," atd.). Tyto citlivosti se vyjadřují ",[38,25067,18219],{}," — parciálními derivacemi rovnovážných veličin podle exogenních veličin.",[198,25070,25072],{"id":25071},"multiplikátory-v-modelu-c-i","Multiplikátory v modelu C-I",[724,25074,21136,25075,25098,25099,25143],{},[883,25076,25078],{"className":25077},[886],[888,25079,25080],{"xmlns":890},[892,25081,25082,25096],{},[895,25083,25084,25086,25088,25090,25092,25094],{},[898,25085,1693],{},[1688,25087,1690],{},[898,25089,207],{},[898,25091,1854],{},[1688,25093,1696],{},[898,25095,1918],{},[902,25097,1921],{"encoding":904}," dává (7.7) redukovaný tvar ",[883,25100,25102],{"className":25101},[886],[888,25103,25104],{"xmlns":890},[892,25105,25106,25140],{},[895,25107,25108,25114,25116],{},[1850,25109,25110,25112],{},[898,25111,1854],{},[898,25113,4509],{},[1688,25115,1690],{},[1777,25117,25118],{"scriptlevel":1779,"displaystyle":1732},[1781,25119,25120,25132],{},[895,25121,25122,25124,25126],{},[898,25123,1918],{},[1688,25125,1696],{},[1850,25127,25128,25130],{},[898,25129,1699],{},[1688,25131,1857],{},[895,25133,25134,25136,25138],{},[1793,25135,1795],{},[1688,25137,1954],{},[898,25139,207],{},[902,25141,25142],{"encoding":904},"Y^E = \\dfrac{b + I^*}{1 - a}",". Parciální derivace:",[724,25145,25146],{},[883,25147,25149],{"className":25148},[886],[888,25150,25151],{"xmlns":890},[892,25152,25153,25222],{},[895,25154,25155,25173,25175,25205,25207],{},[1781,25156,25157,25167],{},[895,25158,25159,25161],{},[898,25160,10124],{"mathvariant":1822},[1850,25162,25163,25165],{},[898,25164,1854],{},[898,25166,4509],{},[895,25168,25169,25171],{},[898,25170,10124],{"mathvariant":1822},[898,25172,207],{},[1688,25174,1690],{},[1781,25176,25177,25189],{},[895,25178,25179,25181,25183],{},[898,25180,1918],{},[1688,25182,1696],{},[1850,25184,25185,25187],{},[898,25186,1699],{},[1688,25188,1857],{},[895,25190,25191,25193,25195,25197,25199],{},[1688,25192,2066],{"stretchy":2065},[1793,25194,1795],{},[1688,25196,1954],{},[898,25198,207],{},[1850,25200,25201,25203],{},[1688,25202,2076],{"stretchy":2065},[1793,25204,1806],{},[6134,25206],{"width":6136},[895,25208,25209,25212,25219],{},[2041,25210,25211],{},"(multiplik",[8642,25213,25214,25216],{"accent":1732},[2041,25215,207],{},[1688,25217,25218],{},"ˊ",[2041,25220,25221],{},"tor MPC)",[902,25223,25224],{"encoding":904},"\\frac{\\partial Y^E}{\\partial a} = \\frac{b + I^*}{(1 - a)^2} \\qquad \\text{(multiplikátor MPC)}",[724,25226,25227],{},[883,25228,25230],{"className":25229},[886],[888,25231,25232],{"xmlns":890},[892,25233,25234,25303],{},[895,25235,25236,25254,25256,25268,25270],{},[1781,25237,25238,25248],{},[895,25239,25240,25242],{},[898,25241,10124],{"mathvariant":1822},[1850,25243,25244,25246],{},[898,25245,1854],{},[898,25247,4509],{},[895,25249,25250,25252],{},[898,25251,10124],{"mathvariant":1822},[898,25253,1918],{},[1688,25255,1690],{},[1781,25257,25258,25260],{},[1793,25259,1795],{},[895,25261,25262,25264,25266],{},[1793,25263,1795],{},[1688,25265,1954],{},[898,25267,207],{},[6134,25269],{"width":6136},[895,25271,25272,25274,25280,25283,25290,25293,25300],{},[2041,25273,25211],{},[8642,25275,25276,25278],{"accent":1732},[2041,25277,207],{},[1688,25279,25218],{},[2041,25281,25282],{},"tor autonomn",[8642,25284,25285,25288],{"accent":1732},[2041,25286,25287],{},"ı",[1688,25289,25218],{},[2041,25291,25292],{}," spot",[8642,25294,25295,25297],{"accent":1732},[2041,25296,2046],{},[1688,25298,25299],{},"ˇ",[2041,25301,25302],{},"eby)",[902,25304,25305],{"encoding":904},"\\frac{\\partial Y^E}{\\partial b} = \\frac{1}{1 - a} \\qquad \\text{(multiplikátor autonomní spotřeby)}",[724,25307,25308],{},[883,25309,25311],{"className":25310},[886],[888,25312,25313],{"xmlns":890},[892,25314,25315,25382],{},[895,25316,25317,25339,25341,25353,25355,25367,25369],{},[1781,25318,25319,25329],{},[895,25320,25321,25323],{},[898,25322,10124],{"mathvariant":1822},[1850,25324,25325,25327],{},[898,25326,1854],{},[898,25328,4509],{},[895,25330,25331,25333],{},[898,25332,10124],{"mathvariant":1822},[1850,25334,25335,25337],{},[898,25336,1699],{},[1688,25338,1857],{},[1688,25340,1690],{},[1781,25342,25343,25345],{},[1793,25344,1795],{},[895,25346,25347,25349,25351],{},[1793,25348,1795],{},[1688,25350,1954],{},[898,25352,207],{},[1688,25354,1690],{},[1781,25356,25357,25359],{},[1793,25358,1795],{},[895,25360,25361,25363,25365],{},[898,25362,1661],{},[898,25364,1727],{},[898,25366,1740],{},[6134,25368],{"width":6136},[895,25370,25371,25373,25379],{},[2041,25372,25211],{},[8642,25374,25375,25377],{"accent":1732},[2041,25376,207],{},[1688,25378,25218],{},[2041,25380,25381],{},"tor investic)",[902,25383,25384],{"encoding":904},"\\frac{\\partial Y^E}{\\partial I^*} = \\frac{1}{1 - a} = \\frac{1}{MPS} \\qquad \\text{(multiplikátor investic)}",[4124,25386,25387],{},[724,25388,25389,25391,25392,25395,25396,25409,25410,25427,25428,25446,25447,25491,25492,21661,25509,25512,25513,25530],{},[883,25390,4412],{}," Intuice — proč Keynesův multiplikátor funguje\nInvestice o 1 Kč se stanou něčím ",[38,25393,25394],{},"důchodem","; z něj se utratí ",[883,25397,25399],{"className":25398},[886],[888,25400,25401],{"xmlns":890},[892,25402,25403,25407],{},[895,25404,25405],{},[898,25406,207],{},[902,25408,207],{"encoding":904}," Kč (= ",[883,25411,25413],{"className":25412},[886],[888,25414,25415],{"xmlns":890},[892,25416,25417,25425],{},[895,25418,25419,25421,25423],{},[898,25420,1661],{},[898,25422,1727],{},[898,25424,1693],{},[902,25426,18287],{"encoding":904},"), to je zase něčí důchod, z něj ",[883,25429,25431],{"className":25430},[886],[888,25432,25433],{"xmlns":890},[892,25434,25435,25443],{},[895,25436,25437],{},[1850,25438,25439,25441],{},[898,25440,207],{},[1793,25442,1806],{},[902,25444,25445],{"encoding":904},"a^2"," Kč… Součet geometrické řady ",[883,25448,25450],{"className":25449},[886],[888,25451,25452],{"xmlns":890},[892,25453,25454,25488],{},[895,25455,25456,25458,25460,25462,25464,25470,25472,25474,25476],{},[1793,25457,1795],{},[1688,25459,1696],{},[898,25461,207],{},[1688,25463,1696],{},[1850,25465,25466,25468],{},[898,25467,207],{},[1793,25469,1806],{},[1688,25471,1696],{},[1688,25473,18347],{},[1688,25475,1690],{},[1781,25477,25478,25480],{},[1793,25479,1795],{},[895,25481,25482,25484,25486],{},[1793,25483,1795],{},[1688,25485,1954],{},[898,25487,207],{},[902,25489,25490],{"encoding":904},"1 + a + a^2 + \\dots = \\frac{1}{1-a}",". Proto jedna koruna investic navíc zvedne ",[883,25493,25495],{"className":25494},[886],[888,25496,25497],{"xmlns":890},[892,25498,25499,25507],{},[895,25500,25501],{},[1850,25502,25503,25505],{},[898,25504,1854],{},[898,25506,4509],{},[902,25508,14150],{"encoding":904},[38,25510,25511],{},"více"," než korunu — čím vyšší ",[883,25514,25516],{"className":25515},[886],[888,25517,25518],{"xmlns":890},[892,25519,25520,25528],{},[895,25521,25522,25524,25526],{},[898,25523,1661],{},[898,25525,1727],{},[898,25527,1693],{},[902,25529,18287],{"encoding":904},", tím silnější multiplikační efekt.",[724,25532,25533,25536,25537,25563,25564,25567,25568,4142,25589,25614,25615,2263],{},[38,25534,25535],{},"Multiplikátor autonomní spotřeby se rovná multiplikátoru investic"," — oba činí ",[883,25538,25540],{"className":25539},[886],[888,25541,25542],{"xmlns":890},[892,25543,25544,25560],{},[895,25545,25546],{},[1777,25547,25548],{"scriptlevel":1779,"displaystyle":2065},[1781,25549,25550,25552],{},[1793,25551,1795],{},[895,25553,25554,25556,25558],{},[1793,25555,1795],{},[1688,25557,1954],{},[898,25559,207],{},[902,25561,25562],{"encoding":904},"\\tfrac{1}{1-a}",", což je standardní ",[38,25565,25566],{},"Keynesův multiplikátor",". Analogicky se v modelech ",[883,25569,25571],{"className":25570},[886],[888,25572,25573],{"xmlns":890},[892,25574,25575,25587],{},[895,25576,25577,25579,25581,25583,25585],{},[898,25578,1693],{},[2041,25580,12539],{},[898,25582,1699],{},[2041,25584,12539],{},[898,25586,1704],{},[902,25588,18462],{"encoding":904},[883,25590,25592],{"className":25591},[886],[888,25593,25594],{"xmlns":890},[892,25595,25596,25612],{},[895,25597,25598,25600,25602,25604,25606,25608,25610],{},[898,25599,1693],{},[2041,25601,12539],{},[898,25603,1699],{},[2041,25605,12539],{},[898,25607,1704],{},[2041,25609,12539],{},[898,25611,1709],{},[902,25613,12571],{"encoding":904}," zavádějí multiplikátory vládních výdajů, zdanění a exportu. Paralela k mikroekonomickým multiplikátorům viz ",[207,25616,25618],{"className":25617,"dataFsResolvedFilePath":800,"href":801},[210],"poptávka a nabídka",[115,25620,25622],{"id":25621},"is-lm-analýza-stručný-přehled","IS-LM analýza (stručný přehled)",[724,25624,12414,25625,1343,25642,4142,25663,12419,25688,10277,25691,25712,25713,2170,25716,25729,25730,5925,25759,25776,25777,25780,25781,25783,25784,25805],{},[883,25626,25628],{"className":25627},[886],[888,25629,25630],{"xmlns":890},[892,25631,25632,25640],{},[895,25633,25634,25636,25638],{},[898,25635,1693],{},[2041,25637,12539],{},[898,25639,1699],{},[902,25641,12544],{"encoding":904},[883,25643,25645],{"className":25644},[886],[888,25646,25647],{"xmlns":890},[892,25648,25649,25661],{},[895,25650,25651,25653,25655,25657,25659],{},[898,25652,1693],{},[2041,25654,12539],{},[898,25656,1699],{},[2041,25658,12539],{},[898,25660,1704],{},[902,25662,18462],{"encoding":904},[883,25664,25666],{"className":25665},[886],[888,25667,25668],{"xmlns":890},[892,25669,25670,25686],{},[895,25671,25672,25674,25676,25678,25680,25682,25684],{},[898,25673,1693],{},[2041,25675,12539],{},[898,25677,1699],{},[2041,25679,12539],{},[898,25681,1704],{},[2041,25683,12539],{},[898,25685,1709],{},[902,25687,12571],{"encoding":904},[38,25689,25690],{},"investice konstantní",[883,25692,25694],{"className":25693},[886],[888,25695,25696],{"xmlns":890},[892,25697,25698,25710],{},[895,25699,25700,25702,25704],{},[898,25701,1699],{},[1688,25703,1690],{},[1850,25705,25706,25708],{},[898,25707,1699],{},[1688,25709,1857],{},[902,25711,12444],{"encoding":904},"). Reálnější je předpoklad, že ",[38,25714,25715],{},"investice závisejí na úrokové míře",[883,25717,25719],{"className":25718},[886],[888,25720,25721],{"xmlns":890},[892,25722,25723,25727],{},[895,25724,25725],{},[898,25726,2046],{},[902,25728,2046],{"encoding":904}," — klesající funkce ",[883,25731,25733],{"className":25732},[886],[888,25734,25735],{"xmlns":890},[892,25736,25737,25757],{},[895,25738,25739,25741,25743,25745,25747,25749,25751,25753,25755],{},[898,25740,1699],{},[1688,25742,2066],{"stretchy":2065},[898,25744,2046],{},[1688,25746,2076],{"stretchy":2065},[1688,25748,1690],{},[898,25750,2031],{},[898,25752,2046],{},[1688,25754,1696],{},[898,25756,2073],{},[902,25758,16004],{"encoding":904},[883,25760,25762],{"className":25761},[886],[888,25763,25764],{"xmlns":890},[892,25765,25766,25774],{},[895,25767,25768,25770,25772],{},[898,25769,2031],{},[1688,25771,3704],{},[1793,25773,1779],{},[902,25775,12763],{"encoding":904},". Přidáním ",[38,25778,25779],{},"trhu peněz"," k trhu zboží vzniká model ",[38,25782,1756],{}," se dvěma neznámými ",[883,25785,25787],{"className":25786},[886],[888,25788,25789],{"xmlns":890},[892,25790,25791,25803],{},[895,25792,25793,25795,25797,25799,25801],{},[1688,25794,2066],{"stretchy":2065},[898,25796,1854],{},[1688,25798,1733],{"separator":1732},[898,25800,2046],{},[1688,25802,2076],{"stretchy":2065},[902,25804,18392],{"encoding":904}," a dvěma rovnicemi:",[120,25807,25808,25858],{},[123,25809,25810,10277,25812,25814,25815,25836,25837,2263],{},[38,25811,16093],{},[614,25813,12305],{},") — klesající přímka v rovině ",[883,25816,25818],{"className":25817},[886],[888,25819,25820],{"xmlns":890},[892,25821,25822,25834],{},[895,25823,25824,25826,25828,25830,25832],{},[1688,25825,2066],{"stretchy":2065},[898,25827,2046],{},[1688,25829,1733],{"separator":1732},[898,25831,1854],{},[1688,25833,2076],{"stretchy":2065},[902,25835,13185],{"encoding":904},", odvozená z rovnováhy trhu zboží ",[883,25838,25840],{"className":25839},[886],[888,25841,25842],{"xmlns":890},[892,25843,25844,25856],{},[895,25845,25846,25848,25850,25852,25854],{},[898,25847,1854],{},[1688,25849,1690],{},[898,25851,1693],{},[1688,25853,1696],{},[898,25855,1699],{},[902,25857,14991],{"encoding":904},[123,25859,25860,10277,25862,25864,25865,21835,25890,25936],{},[38,25861,16292],{},[614,25863,12312],{},") — rostoucí přímka, odvozená z rovnováhy trhu peněz ",[883,25866,25868],{"className":25867},[886],[888,25869,25870],{"xmlns":890},[892,25871,25872,25888],{},[895,25873,25874,25880,25882],{},[1850,25875,25876,25878],{},[898,25877,1661],{},[898,25879,4440],{},[1688,25881,1690],{},[1850,25883,25884,25886],{},[898,25885,1661],{},[1688,25887,1857],{},[902,25889,13727],{"encoding":904},[883,25891,25893],{"className":25892},[886],[888,25894,25895],{"xmlns":890},[892,25896,25897,25933],{},[895,25898,25899,25905,25907,25913,25915,25917,25923,25925,25927],{},[1850,25900,25901,25903],{},[898,25902,1661],{},[898,25904,4440],{},[1688,25906,1690],{},[1788,25908,25909,25911],{},[898,25910,2106],{},[1793,25912,1795],{},[898,25914,1854],{},[1688,25916,1696],{},[1788,25918,25919,25921],{},[898,25920,2106],{},[1793,25922,1806],{},[898,25924,2046],{},[1688,25926,1696],{},[1788,25928,25929,25931],{},[898,25930,2106],{},[1793,25932,2131],{},[902,25934,25935],{"encoding":904},"M^D = k_1 Y + k_2 r + k_3"," (transakční, opatrnostní a spekulační poptávka).",[724,25938,25939,2170,25942,25975,25976,25978,25979,25981],{},[38,25940,25941],{},"Simultánní rovnovážný bod",[883,25943,25945],{"className":25944},[886],[888,25946,25947],{"xmlns":890},[892,25948,25949,25973],{},[895,25950,25951,25953,25955,25957,25963,25965,25971],{},[898,25952,4509],{},[1688,25954,1690],{},[1688,25956,2066],{"stretchy":2065},[1850,25958,25959,25961],{},[898,25960,2046],{},[898,25962,4509],{},[1688,25964,1733],{"separator":1732},[1850,25966,25967,25969],{},[898,25968,1854],{},[898,25970,4509],{},[1688,25972,2076],{"stretchy":2065},[902,25974,16384],{"encoding":904}," je průsečík křivek IS a LM; určuje současně rovnovážný důchod a rovnovážnou úrokovou míru. Model slouží jako rámec pro analýzu ",[38,25977,12350],{}," (posun IS) a ",[38,25980,12381],{}," (posun LM).",[724,25983,25984],{},[38,25985,25986,25987,1343,26009,1343,26031,1343,26053,26075,26076,2263],{},"Pro detailní odvození obou křivek, řešení Příkladu 7.6 (",[883,25988,25990],{"className":25989},[886],[888,25991,25992],{"xmlns":890},[892,25993,25994,26006],{},[895,25995,25996,26002,26004],{},[1850,25997,25998,26000],{},[898,25999,1854],{},[898,26001,4509],{},[1688,26003,1690],{},[1793,26005,15362],{},[902,26007,26008],{"encoding":904},"Y^E = 5000",[883,26010,26012],{"className":26011},[886],[888,26013,26014],{"xmlns":890},[892,26015,26016,26028],{},[895,26017,26018,26024,26026],{},[1850,26019,26020,26022],{},[898,26021,2046],{},[898,26023,4509],{},[1688,26025,1690],{},[1793,26027,2501],{},[902,26029,26030],{"encoding":904},"r^E = 5",[883,26032,26034],{"className":26033},[886],[888,26035,26036],{"xmlns":890},[892,26037,26038,26050],{},[895,26039,26040,26046,26048],{},[1850,26041,26042,26044],{},[898,26043,1693],{},[898,26045,4509],{},[1688,26047,1690],{},[1793,26049,15399],{},[902,26051,26052],{"encoding":904},"C^E = 4100",[883,26054,26056],{"className":26055},[886],[888,26057,26058],{"xmlns":890},[892,26059,26060,26072],{},[895,26061,26062,26068,26070],{},[1850,26063,26064,26066],{},[898,26065,1699],{},[898,26067,4509],{},[1688,26069,1690],{},[1793,26071,15438],{},[902,26073,26074],{"encoding":904},"I^E = 900",") a ekonomickou interpretaci posunů viz ",[207,26077,945],{"className":26078,"dataFsResolvedFilePath":943,"href":944},[210],[115,26080,26082],{"id":26081},"shrnutí-kapitoly-7","Shrnutí kapitoly 7",[152,26084,26085,26149,26260,26403,26645,26713],{},[123,26086,26087,26090,26091,26113,26114,26148],{},[38,26088,26089],{},"Zjednodušený makroekonomický model"," ztotožňuje ",[883,26092,26094],{"className":26093},[886],[888,26095,26096],{"xmlns":890},[892,26097,26098,26110],{},[895,26099,26100,26102,26104,26106,26108],{},[898,26101,1704],{},[898,26103,18536],{},[898,26105,1727],{},[1688,26107,2991],{},[898,26109,1854],{},[902,26111,26112],{"encoding":904},"GNP \\approx Y"," (národní důchod). Základ: ",[883,26115,26117],{"className":26116},[886],[888,26118,26119],{"xmlns":890},[892,26120,26121,26145],{},[895,26122,26123,26125,26127,26129,26131,26133,26135,26137,26139,26141,26143],{},[898,26124,1704],{},[898,26126,18536],{},[898,26128,1727],{},[1688,26130,1690],{},[898,26132,1693],{},[1688,26134,1696],{},[898,26136,1699],{},[1688,26138,1696],{},[898,26140,1704],{},[1688,26142,1696],{},[898,26144,1709],{},[902,26146,26147],{"encoding":904},"GNP = C + I + G + X"," (7.1).",[123,26150,26151,26153,26154,26175,26176,1343,26199,26230,26231,26244,26245,2263],{},[38,26152,18770],{}," splňují ",[883,26155,26157],{"className":26156},[886],[888,26158,26159],{"xmlns":890},[892,26160,26161,26173],{},[895,26162,26163,26165,26167,26169,26171],{},[898,26164,1854],{},[1688,26166,1690],{},[898,26168,1693],{},[1688,26170,1696],{},[898,26172,1740],{},[902,26174,12942],{"encoding":904}," (7.2); lineární model ",[883,26177,26179],{"className":26178},[886],[888,26180,26181],{"xmlns":890},[892,26182,26183,26197],{},[895,26184,26185,26187,26189,26191,26193,26195],{},[898,26186,1693],{},[1688,26188,1690],{},[898,26190,207],{},[898,26192,1854],{},[1688,26194,1696],{},[898,26196,1918],{},[902,26198,1921],{"encoding":904},[883,26200,26202],{"className":26201},[886],[888,26203,26204],{"xmlns":890},[892,26205,26206,26228],{},[895,26207,26208,26210,26212,26214,26216,26218,26220,26222,26224,26226],{},[898,26209,1740],{},[1688,26211,1690],{},[1688,26213,2066],{"stretchy":2065},[1793,26215,1795],{},[1688,26217,1954],{},[898,26219,207],{},[1688,26221,2076],{"stretchy":2065},[898,26223,1854],{},[1688,26225,1954],{},[898,26227,1918],{},[902,26229,19410],{"encoding":904}," s autonomní spotřebou ",[883,26232,26234],{"className":26233},[886],[888,26235,26236],{"xmlns":890},[892,26237,26238,26242],{},[895,26239,26240],{},[898,26241,1918],{},[902,26243,1918],{"encoding":904}," a autonomními úsporami ",[883,26246,26248],{"className":26247},[886],[888,26249,26250],{"xmlns":890},[892,26251,26252,26258],{},[895,26253,26254,26256],{},[1688,26255,1954],{},[898,26257,1918],{},[902,26259,19489],{"encoding":904},[123,26261,26262,2170,26265,1343,26295,26325,26326,26356,26357,1343,26378,2263],{},[38,26263,26264],{},"Mezní sklony",[883,26266,26268],{"className":26267},[886],[888,26269,26270],{"xmlns":890},[892,26271,26272,26292],{},[895,26273,26274,26276,26278,26280,26282,26284,26286,26288,26290],{},[898,26275,1661],{},[898,26277,1727],{},[898,26279,1693],{},[1688,26281,1690],{},[898,26283,2073],{"mathvariant":1822},[898,26285,1693],{},[898,26287,4930],{"mathvariant":1822},[898,26289,2073],{"mathvariant":1822},[898,26291,1854],{},[902,26293,26294],{"encoding":904},"MPC = \\mathrm{d}C\u002F\\mathrm{d}Y",[883,26296,26298],{"className":26297},[886],[888,26299,26300],{"xmlns":890},[892,26301,26302,26322],{},[895,26303,26304,26306,26308,26310,26312,26314,26316,26318,26320],{},[898,26305,1661],{},[898,26307,1727],{},[898,26309,1740],{},[1688,26311,1690],{},[898,26313,2073],{"mathvariant":1822},[898,26315,1740],{},[898,26317,4930],{"mathvariant":1822},[898,26319,2073],{"mathvariant":1822},[898,26321,1854],{},[902,26323,26324],{"encoding":904},"MPS = \\mathrm{d}S\u002F\\mathrm{d}Y",", vazba ",[883,26327,26329],{"className":26328},[886],[888,26330,26331],{"xmlns":890},[892,26332,26333,26353],{},[895,26334,26335,26337,26339,26341,26343,26345,26347,26349,26351],{},[898,26336,1661],{},[898,26338,1727],{},[898,26340,1693],{},[1688,26342,1696],{},[898,26344,1661],{},[898,26346,1727],{},[898,26348,1740],{},[1688,26350,1690],{},[1793,26352,1795],{},[902,26354,26355],{"encoding":904},"MPC + MPS = 1"," (7.5). V lineárním modelu ",[883,26358,26360],{"className":26359},[886],[888,26361,26362],{"xmlns":890},[892,26363,26364,26376],{},[895,26365,26366,26368,26370,26372,26374],{},[898,26367,1661],{},[898,26369,1727],{},[898,26371,1693],{},[1688,26373,1690],{},[898,26375,207],{},[902,26377,20130],{"encoding":904},[883,26379,26381],{"className":26380},[886],[888,26382,26383],{"xmlns":890},[892,26384,26385,26401],{},[895,26386,26387,26389,26391,26393,26395,26397,26399],{},[898,26388,1661],{},[898,26390,1727],{},[898,26392,1740],{},[1688,26394,1690],{},[1793,26396,1795],{},[1688,26398,1954],{},[898,26400,207],{},[902,26402,20156],{"encoding":904},[123,26404,26405,26408,26409],{},[38,26406,26407],{},"Modely národní ekonomiky"," postupně bohatnou:\n",[120,26410,26411,26499,26568],{},[123,26412,26413,26430,26431,26452,26453,1733],{},[883,26414,26416],{"className":26415},[886],[888,26417,26418],{"xmlns":890},[892,26419,26420,26428],{},[895,26421,26422,26424,26426],{},[898,26423,1693],{},[2041,26425,12539],{},[898,26427,1699],{},[902,26429,12544],{"encoding":904},": ",[883,26432,26434],{"className":26433},[886],[888,26435,26436],{"xmlns":890},[892,26437,26438,26450],{},[895,26439,26440,26442,26444,26446,26448],{},[898,26441,1854],{},[1688,26443,1690],{},[898,26445,1693],{},[1688,26447,1696],{},[898,26449,1699],{},[902,26451,14991],{"encoding":904}," (uzavřená ekonomika bez vlády), ",[883,26454,26456],{"className":26455},[886],[888,26457,26458],{"xmlns":890},[892,26459,26460,26496],{},[895,26461,26462,26468,26470,26472,26474,26476,26482,26484,26486,26488,26490,26492,26494],{},[1850,26463,26464,26466],{},[898,26465,1854],{},[898,26467,4509],{},[1688,26469,1690],{},[1688,26471,2066],{"stretchy":2065},[898,26473,1918],{},[1688,26475,1696],{},[1850,26477,26478,26480],{},[898,26479,1699],{},[1688,26481,1857],{},[1688,26483,2076],{"stretchy":2065},[898,26485,4930],{"mathvariant":1822},[1688,26487,2066],{"stretchy":2065},[1793,26489,1795],{},[1688,26491,1954],{},[898,26493,207],{},[1688,26495,2076],{"stretchy":2065},[902,26497,26498],{"encoding":904},"Y^E = (b + I^*)\u002F(1-a)",[123,26500,26501,26522,26523,26542,26543,1733],{},[883,26502,26504],{"className":26503},[886],[888,26505,26506],{"xmlns":890},[892,26507,26508,26520],{},[895,26509,26510,26512,26514,26516,26518],{},[898,26511,1693],{},[2041,26513,12539],{},[898,26515,1699],{},[2041,26517,12539],{},[898,26519,1704],{},[902,26521,18462],{"encoding":904},": přidává vládu, zdanění ",[883,26524,26526],{"className":26525},[886],[888,26527,26528],{"xmlns":890},[892,26529,26530,26540],{},[895,26531,26532,26534,26536,26538],{},[898,26533,3035],{},[1688,26535,2066],{"stretchy":2065},[898,26537,1854],{},[1688,26539,2076],{"stretchy":2065},[902,26541,22460],{"encoding":904}," a disponibilní důchod ",[883,26544,26546],{"className":26545},[886],[888,26547,26548],{"xmlns":890},[892,26549,26550,26566],{},[895,26551,26552,26558,26560,26562,26564],{},[1788,26553,26554,26556],{},[898,26555,1854],{},[898,26557,4440],{},[1688,26559,1690],{},[898,26561,1854],{},[1688,26563,1954],{},[898,26565,3035],{},[902,26567,21959],{"encoding":904},[123,26569,26570,26595,26596,21835,26617,2263],{},[883,26571,26573],{"className":26572},[886],[888,26574,26575],{"xmlns":890},[892,26576,26577,26593],{},[895,26578,26579,26581,26583,26585,26587,26589,26591],{},[898,26580,1693],{},[2041,26582,12539],{},[898,26584,1699],{},[2041,26586,12539],{},[898,26588,1704],{},[2041,26590,12539],{},[898,26592,1709],{},[902,26594,12571],{"encoding":904},": otevírá ekonomiku čistým exportem ",[883,26597,26599],{"className":26598},[886],[888,26600,26601],{"xmlns":890},[892,26602,26603,26615],{},[895,26604,26605,26607,26609,26611,26613],{},[898,26606,1709],{},[1688,26608,1690],{},[898,26610,23494],{},[1688,26612,1954],{},[898,26614,1661],{},[902,26616,23501],{"encoding":904},[883,26618,26620],{"className":26619},[886],[888,26621,26622],{"xmlns":890},[892,26623,26624,26642],{},[895,26625,26626,26628,26630,26632,26634,26640],{},[898,26627,1661],{},[1688,26629,1690],{},[898,26631,1661],{},[1688,26633,2066],{"stretchy":2065},[1788,26635,26636,26638],{},[898,26637,1854],{},[898,26639,4440],{},[1688,26641,2076],{"stretchy":2065},[902,26643,26644],{"encoding":904},"M = M(Y_D)",[123,26646,26647,26650,26651,2170,26654,26712],{},[38,26648,26649],{},"Multiplikátory"," (parciální derivace rovnovážných veličin podle exogenních) — klíčový ",[38,26652,26653],{},"multiplikátor investic",[883,26655,26657],{"className":26656},[886],[888,26658,26659],{"xmlns":890},[892,26660,26661,26709],{},[895,26662,26663,26665,26671,26673,26675,26681,26683,26685,26687,26689,26691,26693,26695,26697,26699,26701,26703,26705,26707],{},[898,26664,10124],{"mathvariant":1822},[1850,26666,26667,26669],{},[898,26668,1854],{},[898,26670,4509],{},[898,26672,4930],{"mathvariant":1822},[898,26674,10124],{"mathvariant":1822},[1850,26676,26677,26679],{},[898,26678,1699],{},[1688,26680,1857],{},[1688,26682,1690],{},[1793,26684,1795],{},[898,26686,4930],{"mathvariant":1822},[1688,26688,2066],{"stretchy":2065},[1793,26690,1795],{},[1688,26692,1954],{},[898,26694,207],{},[1688,26696,2076],{"stretchy":2065},[1688,26698,1690],{},[1793,26700,1795],{},[898,26702,4930],{"mathvariant":1822},[898,26704,1661],{},[898,26706,1727],{},[898,26708,1740],{},[902,26710,26711],{"encoding":904},"\\partial Y^E\u002F\\partial I^* = 1\u002F(1-a) = 1\u002FMPS"," (Keynesův multiplikátor).",[123,26714,26715,26717,26718,26733,26734,18890,26751,26766,26767,26792,26793,2263],{},[38,26716,945],{}," doplňuje obraz o trh peněz: investice závisejí na úrokové míře, ",[883,26719,26721],{"className":26720},[886],[888,26722,26723],{"xmlns":890},[892,26724,26725,26731],{},[895,26726,26727,26729],{},[898,26728,1699],{},[898,26730,1740],{},[902,26732,12302],{"encoding":904}," popisuje rovnováhu trhu zboží (",[883,26735,26737],{"className":26736},[886],[888,26738,26739],{"xmlns":890},[892,26740,26741,26749],{},[895,26742,26743,26745,26747],{},[898,26744,1699],{},[1688,26746,1690],{},[898,26748,1740],{},[902,26750,12960],{"encoding":904},[883,26752,26754],{"className":26753},[886],[888,26755,26756],{"xmlns":890},[892,26757,26758,26764],{},[895,26759,26760,26762],{},[898,26761,10047],{},[898,26763,1661],{},[902,26765,12309],{"encoding":904}," rovnováhu trhu peněz (",[883,26768,26770],{"className":26769},[886],[888,26771,26772],{"xmlns":890},[892,26773,26774,26790],{},[895,26775,26776,26782,26784],{},[1850,26777,26778,26780],{},[898,26779,1661],{},[898,26781,4440],{},[1688,26783,1690],{},[1850,26785,26786,26788],{},[898,26787,1661],{},[1688,26789,1857],{},[902,26791,13727],{"encoding":904},"); průsečík dává ",[883,26794,26796],{"className":26795},[886],[888,26797,26798],{"xmlns":890},[892,26799,26800,26820],{},[895,26801,26802,26804,26810,26812,26818],{},[1688,26803,2066],{"stretchy":2065},[1850,26805,26806,26808],{},[898,26807,1854],{},[898,26809,4509],{},[1688,26811,1733],{"separator":1732},[1850,26813,26814,26816],{},[898,26815,2046],{},[898,26817,4509],{},[1688,26819,2076],{"stretchy":2065},[902,26821,12346],{"encoding":904},[115,26823,15967],{"id":15966},[120,26825,26826,26864,26904,26994,27076,27130,27186,27245,27280,27285,27357,27432,27518,27580,27648,27706,27759,27798],{},[123,26827,26828,7271,26831,26148],{},[38,26829,26830],{},"Hrubý národní produkt (GNP)",[883,26832,26834],{"className":26833},[886],[888,26835,26836],{"xmlns":890},[892,26837,26838,26862],{},[895,26839,26840,26842,26844,26846,26848,26850,26852,26854,26856,26858,26860],{},[898,26841,1704],{},[898,26843,18536],{},[898,26845,1727],{},[1688,26847,1690],{},[898,26849,1693],{},[1688,26851,1696],{},[898,26853,1699],{},[1688,26855,1696],{},[898,26857,1704],{},[1688,26859,1696],{},[898,26861,1709],{},[902,26863,26147],{"encoding":904},[123,26865,26866,26882,26883,2263],{},[38,26867,26868,26869],{},"Národní důchod ",[883,26870,26872],{"className":26871},[886],[888,26873,26874],{"xmlns":890},[892,26875,26876,26880],{},[895,26877,26878],{},[898,26879,1854],{},[902,26881,1854],{"encoding":904}," — součet důchodů domácností; v modelech ",[883,26884,26886],{"className":26885},[886],[888,26887,26888],{"xmlns":890},[892,26889,26890,26902],{},[895,26891,26892,26894,26896,26898,26900],{},[898,26893,1704],{},[898,26895,18536],{},[898,26897,1727],{},[1688,26899,2991],{},[898,26901,1854],{},[902,26903,26112],{"encoding":904},[123,26905,26906,26932,26933,1343,26956,1343,26977,2263],{},[38,26907,26908,26909],{},"Funkce spotřeby ",[883,26910,26912],{"className":26911},[886],[888,26913,26914],{"xmlns":890},[892,26915,26916,26930],{},[895,26917,26918,26920,26922,26924,26926,26928],{},[898,26919,1693],{},[1688,26921,1690],{},[898,26923,1693],{},[1688,26925,2066],{"stretchy":2065},[898,26927,1854],{},[1688,26929,2076],{"stretchy":2065},[902,26931,20981],{"encoding":904}," — lineární model ",[883,26934,26936],{"className":26935},[886],[888,26937,26938],{"xmlns":890},[892,26939,26940,26954],{},[895,26941,26942,26944,26946,26948,26950,26952],{},[898,26943,1693],{},[1688,26945,1690],{},[898,26947,207],{},[898,26949,1854],{},[1688,26951,1696],{},[898,26953,1918],{},[902,26955,1921],{"encoding":904},[883,26957,26959],{"className":26958},[886],[888,26960,26961],{"xmlns":890},[892,26962,26963,26975],{},[895,26964,26965,26967,26969,26971,26973],{},[1793,26966,1779],{},[1688,26968,3704],{},[898,26970,207],{},[1688,26972,3704],{},[1793,26974,1795],{},[902,26976,19078],{"encoding":904},[883,26978,26980],{"className":26979},[886],[888,26981,26982],{"xmlns":890},[892,26983,26984,26992],{},[895,26985,26986,26988,26990],{},[898,26987,1918],{},[1688,26989,3665],{},[1793,26991,1779],{},[902,26993,19056],{"encoding":904},[123,26995,26996,7271,27023,27044,27045,2263],{},[38,26997,26998,26999],{},"Funkce úspor ",[883,27000,27002],{"className":27001},[886],[888,27003,27004],{"xmlns":890},[892,27005,27006,27020],{},[895,27007,27008,27010,27012,27014,27016,27018],{},[898,27009,1740],{},[1688,27011,1690],{},[898,27013,1740],{},[1688,27015,2066],{"stretchy":2065},[898,27017,1854],{},[1688,27019,2076],{"stretchy":2065},[902,27021,27022],{"encoding":904},"S = S(Y)",[883,27024,27026],{"className":27025},[886],[888,27027,27028],{"xmlns":890},[892,27029,27030,27042],{},[895,27031,27032,27034,27036,27038,27040],{},[898,27033,1854],{},[1688,27035,1690],{},[898,27037,1693],{},[1688,27039,1696],{},[898,27041,1740],{},[902,27043,12942],{"encoding":904},"; lineární ",[883,27046,27048],{"className":27047},[886],[888,27049,27050],{"xmlns":890},[892,27051,27052,27074],{},[895,27053,27054,27056,27058,27060,27062,27064,27066,27068,27070,27072],{},[898,27055,1740],{},[1688,27057,1690],{},[1688,27059,2066],{"stretchy":2065},[1793,27061,1795],{},[1688,27063,1954],{},[898,27065,207],{},[1688,27067,2076],{"stretchy":2065},[898,27069,1854],{},[1688,27071,1954],{},[898,27073,1918],{},[902,27075,19410],{"encoding":904},[123,27077,27078,7271,27081,1343,27104,2263],{},[38,27079,27080],{},"Autonomní spotřeba\u002Fúspory",[883,27082,27084],{"className":27083},[886],[888,27085,27086],{"xmlns":890},[892,27087,27088,27102],{},[895,27089,27090,27092,27094,27096,27098,27100],{},[898,27091,1693],{},[1688,27093,2066],{"stretchy":2065},[1793,27095,1779],{},[1688,27097,2076],{"stretchy":2065},[1688,27099,1690],{},[898,27101,1918],{},[902,27103,19802],{"encoding":904},[883,27105,27107],{"className":27106},[886],[888,27108,27109],{"xmlns":890},[892,27110,27111,27127],{},[895,27112,27113,27115,27117,27119,27121,27123,27125],{},[898,27114,1740],{},[1688,27116,2066],{"stretchy":2065},[1793,27118,1779],{},[1688,27120,2076],{"stretchy":2065},[1688,27122,1690],{},[1688,27124,1954],{},[898,27126,1918],{},[902,27128,27129],{"encoding":904},"S(0) = -b",[123,27131,27132,27164,27165,4176],{},[38,27133,27134,27135],{},"Mezní sklon ke spotřebě ",[883,27136,27138],{"className":27137},[886],[888,27139,27140],{"xmlns":890},[892,27141,27142,27162],{},[895,27143,27144,27146,27148,27150,27152,27154,27156,27158,27160],{},[898,27145,1661],{},[898,27147,1727],{},[898,27149,1693],{},[1688,27151,1690],{},[898,27153,2073],{"mathvariant":1822},[898,27155,1693],{},[898,27157,4930],{"mathvariant":1822},[898,27159,2073],{"mathvariant":1822},[898,27161,1854],{},[902,27163,26294],{"encoding":904}," (v lineárním modelu ",[883,27166,27168],{"className":27167},[886],[888,27169,27170],{"xmlns":890},[892,27171,27172,27184],{},[895,27173,27174,27176,27178,27180,27182],{},[898,27175,1661],{},[898,27177,1727],{},[898,27179,1693],{},[1688,27181,1690],{},[898,27183,207],{},[902,27185,20130],{"encoding":904},[123,27187,27188,27164,27220,4176],{},[38,27189,27190,27191],{},"Mezní sklon k úsporám ",[883,27192,27194],{"className":27193},[886],[888,27195,27196],{"xmlns":890},[892,27197,27198,27218],{},[895,27199,27200,27202,27204,27206,27208,27210,27212,27214,27216],{},[898,27201,1661],{},[898,27203,1727],{},[898,27205,1740],{},[1688,27207,1690],{},[898,27209,2073],{"mathvariant":1822},[898,27211,1740],{},[898,27213,4930],{"mathvariant":1822},[898,27215,2073],{"mathvariant":1822},[898,27217,1854],{},[902,27219,26324],{"encoding":904},[883,27221,27223],{"className":27222},[886],[888,27224,27225],{"xmlns":890},[892,27226,27227,27243],{},[895,27228,27229,27231,27233,27235,27237,27239,27241],{},[898,27230,1661],{},[898,27232,1727],{},[898,27234,1740],{},[1688,27236,1690],{},[1793,27238,1795],{},[1688,27240,1954],{},[898,27242,207],{},[902,27244,20156],{"encoding":904},[123,27246,27247,2170,27250,27279],{},[38,27248,27249],{},"Vztah",[883,27251,27253],{"className":27252},[886],[888,27254,27255],{"xmlns":890},[892,27256,27257,27277],{},[895,27258,27259,27261,27263,27265,27267,27269,27271,27273,27275],{},[898,27260,1661],{},[898,27262,1727],{},[898,27264,1693],{},[1688,27266,1696],{},[898,27268,1661],{},[898,27270,1727],{},[898,27272,1740],{},[1688,27274,1690],{},[1793,27276,1795],{},[902,27278,26355],{"encoding":904}," (7.5).",[123,27281,27282,27284],{},[38,27283,20824],{}," — rovnováha agregátní poptávky a nabídky.",[123,27286,27287,27290,27291,16039,27312,2263],{},[38,27288,27289],{},"Model C-I"," — uzavřená ekonomika bez vlády; ",[883,27292,27294],{"className":27293},[886],[888,27295,27296],{"xmlns":890},[892,27297,27298,27310],{},[895,27299,27300,27302,27304,27306,27308],{},[898,27301,1854],{},[1688,27303,1690],{},[898,27305,1693],{},[1688,27307,1696],{},[898,27309,1699],{},[902,27311,14991],{"encoding":904},[883,27313,27315],{"className":27314},[886],[888,27316,27317],{"xmlns":890},[892,27318,27319,27355],{},[895,27320,27321,27327,27329,27331,27333,27335,27341,27343,27345,27347,27349,27351,27353],{},[1850,27322,27323,27325],{},[898,27324,1854],{},[898,27326,4509],{},[1688,27328,1690],{},[1688,27330,2066],{"stretchy":2065},[898,27332,1918],{},[1688,27334,1696],{},[1850,27336,27337,27339],{},[898,27338,1699],{},[1688,27340,1857],{},[1688,27342,2076],{"stretchy":2065},[898,27344,4930],{"mathvariant":1822},[1688,27346,2066],{"stretchy":2065},[1793,27348,1795],{},[1688,27350,1954],{},[898,27352,207],{},[1688,27354,2076],{"stretchy":2065},[902,27356,26498],{"encoding":904},[123,27358,27359,27362,27363,1343,27382,16039,27407,2263],{},[38,27360,27361],{},"Model C-I-G"," — ekonomika s vládou, zdaněním ",[883,27364,27366],{"className":27365},[886],[888,27367,27368],{"xmlns":890},[892,27369,27370,27380],{},[895,27371,27372,27374,27376,27378],{},[898,27373,3035],{},[1688,27375,2066],{"stretchy":2065},[898,27377,1854],{},[1688,27379,2076],{"stretchy":2065},[902,27381,22460],{"encoding":904},[883,27383,27385],{"className":27384},[886],[888,27386,27387],{"xmlns":890},[892,27388,27389,27405],{},[895,27390,27391,27397,27399,27401,27403],{},[1788,27392,27393,27395],{},[898,27394,1854],{},[898,27396,4440],{},[1688,27398,1690],{},[898,27400,1854],{},[1688,27402,1954],{},[898,27404,3035],{},[902,27406,21959],{"encoding":904},[883,27408,27410],{"className":27409},[886],[888,27411,27412],{"xmlns":890},[892,27413,27414,27430],{},[895,27415,27416,27418,27420,27422,27424,27426,27428],{},[898,27417,1854],{},[1688,27419,1690],{},[898,27421,1693],{},[1688,27423,1696],{},[898,27425,1699],{},[1688,27427,1696],{},[898,27429,1704],{},[902,27431,21930],{"encoding":904},[123,27433,27434,27437,27438,27459,27460,16039,27484,2263],{},[38,27435,27436],{},"Model C-I-G-X"," — otevřená ekonomika s čistým exportem ",[883,27439,27441],{"className":27440},[886],[888,27442,27443],{"xmlns":890},[892,27444,27445,27457],{},[895,27446,27447,27449,27451,27453,27455],{},[898,27448,1709],{},[1688,27450,1690],{},[898,27452,23494],{},[1688,27454,1954],{},[898,27456,1661],{},[902,27458,23501],{"encoding":904},", importem ",[883,27461,27463],{"className":27462},[886],[888,27464,27465],{"xmlns":890},[892,27466,27467,27481],{},[895,27468,27469,27471,27473,27479],{},[898,27470,1661],{},[1688,27472,2066],{"stretchy":2065},[1788,27474,27475,27477],{},[898,27476,1854],{},[898,27478,4440],{},[1688,27480,2076],{"stretchy":2065},[902,27482,27483],{"encoding":904},"M(Y_D)",[883,27485,27487],{"className":27486},[886],[888,27488,27489],{"xmlns":890},[892,27490,27491,27515],{},[895,27492,27493,27495,27497,27499,27501,27503,27505,27507,27509,27511,27513],{},[898,27494,1854],{},[1688,27496,1690],{},[898,27498,1693],{},[1688,27500,1696],{},[898,27502,1699],{},[1688,27504,1696],{},[898,27506,1704],{},[1688,27508,1696],{},[898,27510,23494],{},[1688,27512,1954],{},[898,27514,1661],{},[902,27516,27517],{"encoding":904},"Y = C + I + G + B - M",[123,27519,27520,7271,27523,26712],{},[38,27521,27522],{},"Multiplikátor investic",[883,27524,27526],{"className":27525},[886],[888,27527,27528],{"xmlns":890},[892,27529,27530,27578],{},[895,27531,27532,27534,27540,27542,27544,27550,27552,27554,27556,27558,27560,27562,27564,27566,27568,27570,27572,27574,27576],{},[898,27533,10124],{"mathvariant":1822},[1850,27535,27536,27538],{},[898,27537,1854],{},[898,27539,4509],{},[898,27541,4930],{"mathvariant":1822},[898,27543,10124],{"mathvariant":1822},[1850,27545,27546,27548],{},[898,27547,1699],{},[1688,27549,1857],{},[1688,27551,1690],{},[1793,27553,1795],{},[898,27555,4930],{"mathvariant":1822},[1688,27557,2066],{"stretchy":2065},[1793,27559,1795],{},[1688,27561,1954],{},[898,27563,207],{},[1688,27565,2076],{"stretchy":2065},[1688,27567,1690],{},[1793,27569,1795],{},[898,27571,4930],{"mathvariant":1822},[898,27573,1661],{},[898,27575,1727],{},[898,27577,1740],{},[902,27579,26711],{"encoding":904},[123,27581,27582,7271,27613,1343,27630,27647],{},[38,27583,15974,27584],{},[883,27585,27587],{"className":27586},[886],[888,27588,27589],{"xmlns":890},[892,27590,27591,27611],{},[895,27592,27593,27595,27597,27599,27601,27603,27605,27607,27609],{},[898,27594,1699],{},[1688,27596,2066],{"stretchy":2065},[898,27598,2046],{},[1688,27600,2076],{"stretchy":2065},[1688,27602,1690],{},[898,27604,2031],{},[898,27606,2046],{},[1688,27608,1696],{},[898,27610,2073],{},[902,27612,16004],{"encoding":904},[883,27614,27616],{"className":27615},[886],[888,27617,27618],{"xmlns":890},[892,27619,27620,27628],{},[895,27621,27622,27624,27626],{},[898,27623,2031],{},[1688,27625,3704],{},[1793,27627,1779],{},[902,27629,12763],{"encoding":904},[883,27631,27633],{"className":27632},[886],[888,27634,27635],{"xmlns":890},[892,27636,27637,27645],{},[895,27638,27639,27641,27643],{},[898,27640,2073],{},[1688,27642,3665],{},[1793,27644,1779],{},[902,27646,12742],{"encoding":904},"; klesající.",[123,27649,27650,27652,27653,27655,27656,27705],{},[38,27651,16093],{}," — rovnováha na trhu zboží (",[614,27654,12305],{},"); ",[883,27657,27659],{"className":27658},[886],[888,27660,27661],{"xmlns":890},[892,27662,27663,27703],{},[895,27664,27665,27667,27669,27681,27683,27685],{},[898,27666,1854],{},[1688,27668,1690],{},[1781,27670,27671,27673],{},[898,27672,2031],{},[895,27674,27675,27677,27679],{},[1793,27676,1795],{},[1688,27678,1954],{},[898,27680,207],{},[898,27682,2046],{},[1688,27684,1696],{},[1781,27686,27687,27695],{},[895,27688,27689,27691,27693],{},[898,27690,1918],{},[1688,27692,1696],{},[898,27694,2073],{},[895,27696,27697,27699,27701],{},[1793,27698,1795],{},[1688,27700,1954],{},[898,27702,207],{},[902,27704,16146],{"encoding":904}," (7.14); klesající.",[123,27707,27708,27710,27711,27655,27713,27758],{},[38,27709,16292],{}," — rovnováha na trhu peněz (",[614,27712,12312],{},[883,27714,27716],{"className":27715},[886],[888,27717,27718],{"xmlns":890},[892,27719,27720,27756],{},[895,27721,27722,27728,27730,27736,27738,27740,27746,27748,27750],{},[1850,27723,27724,27726],{},[898,27725,1661],{},[1688,27727,1857],{},[1688,27729,1690],{},[1788,27731,27732,27734],{},[898,27733,2106],{},[1793,27735,1795],{},[898,27737,1854],{},[1688,27739,1696],{},[1788,27741,27742,27744],{},[898,27743,2106],{},[1793,27745,1806],{},[898,27747,2046],{},[1688,27749,1696],{},[1788,27751,27752,27754],{},[898,27753,2106],{},[1793,27755,2131],{},[902,27757,16340],{"encoding":904}," (7.15); rostoucí.",[123,27760,27761,7271,27764,2263],{},[38,27762,27763],{},"Transakční, opatrnostní a spekulační poptávka po penězích",[883,27765,27767],{"className":27766},[886],[888,27768,27769],{"xmlns":890},[892,27770,27771,27795],{},[895,27772,27773,27779,27781,27787,27789],{},[1850,27774,27775,27777],{},[898,27776,1661],{},[898,27778,4440],{},[1688,27780,1690],{},[1788,27782,27783,27785],{},[898,27784,10047],{},[1793,27786,1795],{},[1688,27788,1696],{},[1788,27790,27791,27793],{},[898,27792,10047],{},[1793,27794,1806],{},[902,27796,27797],{"encoding":904},"M^D = L_1 + L_2",[123,27799,27800,16350,27802,14227,27815,4142,27830,27845,27846,2263],{},[38,27801,945],{},[883,27803,27805],{"className":27804},[886],[888,27806,27807],{"xmlns":890},[892,27808,27809,27813],{},[895,27810,27811],{},[898,27812,4509],{},[902,27814,4509],{"encoding":904},[883,27816,27818],{"className":27817},[886],[888,27819,27820],{"xmlns":890},[892,27821,27822,27828],{},[895,27823,27824,27826],{},[898,27825,1699],{},[898,27827,1740],{},[902,27829,12302],{"encoding":904},[883,27831,27833],{"className":27832},[886],[888,27834,27835],{"xmlns":890},[892,27836,27837,27843],{},[895,27838,27839,27841],{},[898,27840,10047],{},[898,27842,1661],{},[902,27844,12309],{"encoding":904}," určuje ",[883,27847,27849],{"className":27848},[886],[888,27850,27851],{"xmlns":890},[892,27852,27853,27873],{},[895,27854,27855,27857,27863,27865,27871],{},[1688,27856,2066],{"stretchy":2065},[1850,27858,27859,27861],{},[898,27860,1854],{},[898,27862,4509],{},[1688,27864,1733],{"separator":1732},[1850,27866,27867,27869],{},[898,27868,2046],{},[898,27870,4509],{},[1688,27872,2076],{"stretchy":2065},[902,27874,12346],{"encoding":904},[115,27876,4049],{"id":4048},[120,27878,27879,27886,27893],{},[123,27880,27881,2170,27883],{},[38,27882,16451],{},[207,27884,16455],{"className":27885,"dataFsResolvedFilePath":2210,"href":2211},[210],[123,27887,27888,2170,27890],{},[38,27889,16460],{},[207,27891,16464],{"className":27892,"dataFsResolvedFilePath":868,"href":869},[210],[123,27894,27895,27897],{},[38,27896,16479],{},[120,27898,27899,27905,27911,27917],{},[123,27900,27901,27904],{},[207,27902,2226],{"className":27903,"dataFsResolvedFilePath":943,"href":944},[210]," — detailní IS-LM analýza (odvození křivek, Příklad 7.6, fiskální vs monetární politika)",[123,27906,27907,27910],{},[207,27908,16487],{"className":27909,"dataFsResolvedFilePath":800,"href":801},[210]," — paralela mikroekonomických multiplikátorů (multiplikátory rovnovážné ceny a množství)",[123,27912,27913,27916],{},[207,27914,3208],{"className":27915,"dataFsResolvedFilePath":827,"href":828},[210]," — mikroekonomické analogie, článek 2.4 o multiplikátorech",[123,27918,27919,27922,27923,1343,27940,27957],{},[207,27920,1145],{"className":27921,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro ",[883,27924,27926],{"className":27925},[886],[888,27927,27928],{"xmlns":890},[892,27929,27930,27938],{},[895,27931,27932,27934,27936],{},[898,27933,1661],{},[898,27935,1727],{},[898,27937,1693],{},[902,27939,18287],{"encoding":904},[883,27941,27943],{"className":27942},[886],[888,27944,27945],{"xmlns":890},[892,27946,27947,27955],{},[895,27948,27949,27951,27953],{},[898,27950,1661],{},[898,27952,1727],{},[898,27954,1740],{},[902,27956,19900],{"encoding":904}," a interpretaci změn diferenciálem",{"title":641,"searchDepth":642,"depth":642,"links":27959},[27960,27961,27962,27963,27968,27971,27972,27979,27984,27989,27992,27993,27994,27995],{"id":12258,"depth":642,"text":12259},{"id":18396,"depth":642,"text":18397},{"id":18516,"depth":642,"text":18517},{"id":18769,"depth":642,"text":18770,"children":27964},[27965,27966,27967],{"id":18773,"depth":649,"text":18774},{"id":18985,"depth":649,"text":18986},{"id":19492,"depth":649,"text":19493},{"id":19812,"depth":642,"text":19813,"children":27969},[27970],{"id":20328,"depth":649,"text":20329},{"id":20823,"depth":642,"text":20824},{"id":20850,"depth":642,"text":20851,"children":27973},[27974,27975,27976,27978],{"id":20861,"depth":649,"text":20862},{"id":20931,"depth":649,"text":20932},{"id":21115,"depth":649,"text":27977},"Výpočet YEY^E",{"id":21258,"depth":649,"text":21259},{"id":21636,"depth":642,"text":21637,"children":27980},[27981,27982,27983],{"id":21640,"depth":649,"text":20862},{"id":22089,"depth":649,"text":20932},{"id":22745,"depth":649,"text":22746},{"id":23532,"depth":642,"text":23533,"children":27985},[27986,27987,27988],{"id":23536,"depth":649,"text":20862},{"id":23681,"depth":649,"text":20932},{"id":23951,"depth":649,"text":23952},{"id":24875,"depth":642,"text":24876,"children":27990},[27991],{"id":25071,"depth":649,"text":25072},{"id":25621,"depth":642,"text":25622},{"id":26081,"depth":642,"text":26082},{"id":15966,"depth":642,"text":15967},{"id":4048,"depth":642,"text":4049},{},"\u002Ftopics\u002Fnarodni-duchod",{"title":936,"description":641},[1138,1137],"topics\u002Fnarodni-duchod",[1128,16473,1143,2227,28002,28003,2226,18128],"mpc","mps","BMicmr68yKQbb8qpoE9KfzU5NFshq3Inq6w0tL8-GjU",{"id":28006,"title":28007,"body":28008,"course":1128,"courses":659,"created":9809,"description":641,"extension":661,"meta":36988,"navigation":664,"path":36989,"seo":36990,"sources":36991,"stem":36992,"tags":36993,"type":4113,"updated":677,"__hash__":36998},"topics\u002Ftopics\u002Foptimalizace-spotrebitele.md","Optimalizace spotřebitele — Lagrange, poptávka, minimalizace výdajů",{"type":9,"value":28009,"toc":36957},[28010,28013,28015,28244,28248,28301,28371,28483,28642,28646,28762,28766,28769,28891,28894,29087,29111,29179,29343,29361,29427,29805,29809,29816,30060,30116,30120,30185,30303,30435,30467,30587,30669,30672,30794,30987,31208,31212,31252,31357,31414,31514,31691,31821,31874,31877,31964,31968,32144,32148,32151,32236,32239,32296,32401,32405,32526,32529,32712,32715,32823,33032,33352,33400,33473,33547,33549,33773,34008,34276,34280,34283,34388,34445,34479,34526,34559,34643,34645,34877,35010,35087,35209,35364,35368,35509,35516,35740,35751,35755,35759,35864,36006,36116,36215,36219,36378,36488,36490,36883,36885],[12,28011,28007],{"id":28012},"optimalizace-spotřebitele-lagrange-poptávka-minimalizace-výdajů",[115,28014,12259],{"id":12258},[724,28016,28017,28019,28020,28054,28055,28058,28059,28090,28091,28137,28138,28141,28142,28184,28185,28203,28204,28208,28209,28239,28240,28243],{},[38,28018,913],{}," řeší, jaký svazek zboží ",[883,28021,28023],{"className":28022},[886],[888,28024,28025],{"xmlns":890},[892,28026,28027,28051],{},[895,28028,28029,28031,28039,28041,28049],{},[1688,28030,2748],{"stretchy":2065},[1814,28032,28033,28035,28037],{},[898,28034,1872],{},[1793,28036,1795],{},[1688,28038,1857],{},[1688,28040,1733],{"separator":1732},[1814,28042,28043,28045,28047],{},[898,28044,1872],{},[1793,28046,1806],{},[1688,28048,1857],{},[1688,28050,2763],{"stretchy":2065},[902,28052,28053],{"encoding":904},"[Q_1^*, Q_2^*]"," zvolit při známých cenách a důchodu. Existují dvě ekvivalentní formulace: ",[38,28056,28057],{},"primární úloha"," — maximalizace užitečnosti ",[883,28060,28062],{"className":28061},[886],[888,28063,28064],{"xmlns":890},[892,28065,28066,28088],{},[895,28067,28068,28070,28072,28078,28080,28086],{},[898,28069,900],{},[1688,28071,2066],{"stretchy":2065},[1788,28073,28074,28076],{},[898,28075,1872],{},[1793,28077,1795],{},[1688,28079,1733],{"separator":1732},[1788,28081,28082,28084],{},[898,28083,1872],{},[1793,28085,1806],{},[1688,28087,2076],{"stretchy":2065},[902,28089,16590],{"encoding":904}," při rozpočtovém omezení ",[883,28092,28094],{"className":28093},[886],[888,28095,28096],{"xmlns":890},[892,28097,28098,28134],{},[895,28099,28100,28106,28108,28114,28120,28122,28128],{},[1850,28101,28102,28104],{},[898,28103,1854],{},[1688,28105,1857],{},[1688,28107,1690],{},[1788,28109,28110,28112],{},[898,28111,1727],{},[1793,28113,1795],{},[1788,28115,28116,28118],{},[898,28117,1872],{},[1793,28119,1795],{},[1688,28121,1696],{},[1788,28123,28124,28126],{},[898,28125,1727],{},[1793,28127,1806],{},[1788,28129,28130,28132],{},[898,28131,1872],{},[1793,28133,1806],{},[902,28135,28136],{"encoding":904},"Y^* = P_1 Q_1 + P_2 Q_2",", a ",[38,28139,28140],{},"duální úloha"," — minimalizace výdajů ",[883,28143,28145],{"className":28144},[886],[888,28146,28147],{"xmlns":890},[892,28148,28149,28181],{},[895,28150,28151,28153,28155,28161,28167,28169,28175],{},[898,28152,4509],{},[1688,28154,1690],{},[1788,28156,28157,28159],{},[898,28158,1727],{},[1793,28160,1795],{},[1788,28162,28163,28165],{},[898,28164,1872],{},[1793,28166,1795],{},[1688,28168,1696],{},[1788,28170,28171,28173],{},[898,28172,1727],{},[1793,28174,1806],{},[1788,28176,28177,28179],{},[898,28178,1872],{},[1793,28180,1806],{},[902,28182,28183],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2"," při zadané hladině užitečnosti ",[883,28186,28188],{"className":28187},[886],[888,28189,28190],{"xmlns":890},[892,28191,28192,28200],{},[895,28193,28194],{},[1850,28195,28196,28198],{},[898,28197,900],{},[1688,28199,1857],{},[902,28201,28202],{"encoding":904},"U^*",". Obě úlohy se řeší ",[207,28205,28207],{"className":28206,"dataFsResolvedFilePath":791,"href":792},[210],"metodou Lagrangeových multiplikátorů"," a vedou na tentýž bod dotyku indiferenční křivky a rozpočtové přímky, v němž platí ",[883,28210,28212],{"className":28211},[886],[888,28213,28214],{"xmlns":890},[892,28215,28216,28236],{},[895,28217,28218,28220,28222,28228,28230],{},[2041,28219,1670],{},[1688,28221,1690],{},[1788,28223,28224,28226],{},[898,28225,1727],{},[1793,28227,1795],{},[898,28229,4930],{"mathvariant":1822},[1788,28231,28232,28234],{},[898,28233,1727],{},[1793,28235,1806],{},[902,28237,28238],{"encoding":904},"\\text{MRCS} = P_1\u002FP_2",". Výstupem jsou ",[38,28241,28242],{},"funkce poptávky"," — Marshallova (závislá na důchodu) a Hicksova (závislá na hladině užitečnosti).",[115,28245,28247],{"id":28246},"úvod-proč-optimalizovat","Úvod — proč optimalizovat",[724,28249,28250,28251,28269,28270,28300],{},"Racionální spotřebitel má omezený důchod a musí se rozhodnout, jak jej rozdělit mezi spotřebovávané zboží. V modelu pro dvě zboží je k dispozici částka ",[883,28252,28254],{"className":28253},[886],[888,28255,28256],{"xmlns":890},[892,28257,28258,28266],{},[895,28259,28260],{},[1850,28261,28262,28264],{},[898,28263,1854],{},[1688,28265,1857],{},[902,28267,28268],{"encoding":904},"Y^*"," a ceny ",[883,28271,28273],{"className":28272},[886],[888,28274,28275],{"xmlns":890},[892,28276,28277,28297],{},[895,28278,28279,28287,28289],{},[1814,28280,28281,28283,28285],{},[898,28282,1727],{},[1793,28284,1795],{},[1688,28286,1857],{},[1688,28288,1733],{"separator":1732},[1814,28290,28291,28293,28295],{},[898,28292,1727],{},[1793,28294,1806],{},[1688,28296,1857],{},[902,28298,28299],{"encoding":904},"P_1^*, P_2^*",", rozpočtové omezení má tvar",[883,28302,28304],{"className":28303},[886],[888,28305,28307],{"xmlns":890,"display":28306},"block",[892,28308,28309,28368],{},[20995,28310,28312],{"width":28311},"100%",[21000,28313,28314,28317,28361,28363],{},[21003,28315],{"width":28316},"50%",[21003,28318,28319],{},[895,28320,28321,28327,28329,28337,28343,28345,28353,28359],{},[1850,28322,28323,28325],{},[898,28324,1854],{},[1688,28326,1857],{},[1688,28328,1690],{},[1814,28330,28331,28333,28335],{},[898,28332,1727],{},[1793,28334,1795],{},[1688,28336,1857],{},[1788,28338,28339,28341],{},[898,28340,1872],{},[1793,28342,1795],{},[1688,28344,1696],{},[1814,28346,28347,28349,28351],{},[898,28348,1727],{},[1793,28350,1806],{},[1688,28352,1857],{},[1788,28354,28355,28357],{},[898,28356,1872],{},[1793,28358,1806],{},[1688,28360,1733],{"separator":1732},[21003,28362],{"width":28316},[21003,28364,28365],{},[2041,28366,28367],{},"(6.12)",[902,28369,28370],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2, \\tag{6.12}",[724,28372,28373,28374,28377,28378,4142,28414,28450,28451,28464,28465,28479,28480,2263],{},"geometricky ",[38,28375,28376],{},"rozpočtová přímka (budget line)"," procházející body ",[883,28379,28381],{"className":28380},[886],[888,28382,28383],{"xmlns":890},[892,28384,28385,28411],{},[895,28386,28387,28389,28395,28397,28405,28407,28409],{},[1688,28388,2748],{"stretchy":2065},[1850,28390,28391,28393],{},[898,28392,1854],{},[1688,28394,1857],{},[898,28396,4930],{"mathvariant":1822},[1814,28398,28399,28401,28403],{},[898,28400,1727],{},[1793,28402,1795],{},[1688,28404,1857],{},[1688,28406,1733],{"separator":1732},[1793,28408,1779],{},[1688,28410,2763],{"stretchy":2065},[902,28412,28413],{"encoding":904},"[Y^*\u002FP_1^*, 0]",[883,28415,28417],{"className":28416},[886],[888,28418,28419],{"xmlns":890},[892,28420,28421,28447],{},[895,28422,28423,28425,28427,28429,28435,28437,28445],{},[1688,28424,2748],{"stretchy":2065},[1793,28426,1779],{},[1688,28428,1733],{"separator":1732},[1850,28430,28431,28433],{},[898,28432,1854],{},[1688,28434,1857],{},[898,28436,4930],{"mathvariant":1822},[1814,28438,28439,28441,28443],{},[898,28440,1727],{},[1793,28442,1806],{},[1688,28444,1857],{},[1688,28446,2763],{"stretchy":2065},[902,28448,28449],{"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 ",[883,28452,28454],{"className":28453},[886],[888,28455,28456],{"xmlns":890},[892,28457,28458,28462],{},[895,28459,28460],{},[898,28461,900],{},[902,28463,900],{"encoding":904},", indiferenční křivky a ",[883,28466,28468],{"className":28467},[886],[888,28469,28470],{"xmlns":890},[892,28471,28472,28476],{},[895,28473,28474],{},[2041,28475,1670],{},[902,28477,28478],{"encoding":904},"\\text{MRCS}"," — je shrnuta v ",[207,28481,880],{"className":28482,"dataFsResolvedFilePath":878,"href":879},[210],[4124,28484,28485],{},[724,28486,28487,28489,28490,28493,28494,28507,28508,28510,28511,28524,28525,2170,28528,28568,28569,28586,28587,28604,28605,28622,28623,28641],{},[883,28488,4668],{}," Pozor — dvě úlohy, totéž řešení\n",[38,28491,28492],{},"Primární úloha"," (max ",[883,28495,28497],{"className":28496},[886],[888,28498,28499],{"xmlns":890},[892,28500,28501,28505],{},[895,28502,28503],{},[898,28504,900],{},[902,28506,900],{"encoding":904}," při pevném rozpočtu) a ",[38,28509,28140],{}," (min ",[883,28512,28514],{"className":28513},[886],[888,28515,28516],{"xmlns":890},[892,28517,28518,28522],{},[895,28519,28520],{},[898,28521,4509],{},[902,28523,4509],{"encoding":904}," při pevné užitečnosti) vedou na ",[38,28526,28527],{},"tentýž bod",[883,28529,28531],{"className":28530},[886],[888,28532,28533],{"xmlns":890},[892,28534,28535,28565],{},[895,28536,28537,28543,28545,28553,28555,28563],{},[1850,28538,28539,28541],{},[898,28540,1872],{},[1688,28542,1857],{},[1688,28544,2748],{"stretchy":2065},[1814,28546,28547,28549,28551],{},[898,28548,1872],{},[1793,28550,1795],{},[1688,28552,1857],{},[1688,28554,1733],{"separator":1732},[1814,28556,28557,28559,28561],{},[898,28558,1872],{},[1793,28560,1806],{},[1688,28562,1857],{},[1688,28564,2763],{"stretchy":2065},[902,28566,28567],{"encoding":904},"Q^*[Q_1^*, Q_2^*]",". Rozdíl je v tom, co je „vstup\" a co „výstup\": u primární úlohy je zadán důchod ",[883,28570,28572],{"className":28571},[886],[888,28573,28574],{"xmlns":890},[892,28575,28576,28584],{},[895,28577,28578],{},[1850,28579,28580,28582],{},[898,28581,1854],{},[1688,28583,1857],{},[902,28585,28268],{"encoding":904}," a hledáme maximální ",[883,28588,28590],{"className":28589},[886],[888,28591,28592],{"xmlns":890},[892,28593,28594,28602],{},[895,28595,28596],{},[1850,28597,28598,28600],{},[898,28599,900],{},[1688,28601,1857],{},[902,28603,28202],{"encoding":904},"; u duální úlohy je zadána hladina ",[883,28606,28608],{"className":28607},[886],[888,28609,28610],{"xmlns":890},[892,28611,28612,28620],{},[895,28613,28614],{},[1850,28615,28616,28618],{},[898,28617,900],{},[1688,28619,1857],{},[902,28621,28202],{"encoding":904}," a hledáme minimální ",[883,28624,28626],{"className":28625},[886],[888,28627,28628],{"xmlns":890},[892,28629,28630,28638],{},[895,28631,28632],{},[1850,28633,28634,28636],{},[898,28635,4509],{},[1688,28637,1857],{},[902,28639,28640],{"encoding":904},"E^*",". Z pozorování je přirozenější minimalizace výdajů (výdaje lze měřit).",[115,28643,28645],{"id":28644},"maximalizace-užitečnosti-za-rozpočtového-omezení","Maximalizace užitečnosti za rozpočtového omezení",[724,28647,28648,28649,28680,28681,28757,28758,2263],{},"Úlohou je najít maximum ",[883,28650,28652],{"className":28651},[886],[888,28653,28654],{"xmlns":890},[892,28655,28656,28678],{},[895,28657,28658,28660,28662,28668,28670,28676],{},[898,28659,900],{},[1688,28661,2066],{"stretchy":2065},[1788,28663,28664,28666],{},[898,28665,1872],{},[1793,28667,1795],{},[1688,28669,1733],{"separator":1732},[1788,28671,28672,28674],{},[898,28673,1872],{},[1793,28675,1806],{},[1688,28677,2076],{"stretchy":2065},[902,28679,16590],{"encoding":904}," vázané podmínkou (6.12) ve tvaru ",[883,28682,28684],{"className":28683},[886],[888,28685,28686],{"xmlns":890},[892,28687,28688,28754],{},[895,28689,28690,28692,28694,28700,28702,28708,28710,28712,28718,28720,28728,28734,28736,28744,28750,28752],{},[898,28691,11292],{},[1688,28693,2066],{"stretchy":2065},[1788,28695,28696,28698],{},[898,28697,1872],{},[1793,28699,1795],{},[1688,28701,1733],{"separator":1732},[1788,28703,28704,28706],{},[898,28705,1872],{},[1793,28707,1806],{},[1688,28709,2076],{"stretchy":2065},[1688,28711,1690],{},[1850,28713,28714,28716],{},[898,28715,1854],{},[1688,28717,1857],{},[1688,28719,1954],{},[1814,28721,28722,28724,28726],{},[898,28723,1727],{},[1793,28725,1795],{},[1688,28727,1857],{},[1788,28729,28730,28732],{},[898,28731,1872],{},[1793,28733,1795],{},[1688,28735,1954],{},[1814,28737,28738,28740,28742],{},[898,28739,1727],{},[1793,28741,1806],{},[1688,28743,1857],{},[1788,28745,28746,28748],{},[898,28747,1872],{},[1793,28749,1806],{},[1688,28751,1690],{},[1793,28753,1779],{},[902,28755,28756],{"encoding":904},"g(Q_1, Q_2) = Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",". Použijeme ",[207,28759,28761],{"className":28760,"dataFsResolvedFilePath":791,"href":792},[210],"metodu Lagrangeových multiplikátorů",[198,28763,28765],{"id":28764},"lagrangeova-funkce-a-podmínky-optimality","Lagrangeova funkce a podmínky optimality",[724,28767,28768],{},"Sestavíme",[883,28770,28772],{"className":28771},[886],[888,28773,28774],{"xmlns":890,"display":28306},[892,28775,28776,28888],{},[20995,28777,28778],{"width":28311},[21000,28779,28780,28782,28881,28883],{},[21003,28781],{"width":28316},[21003,28783,28784],{},[895,28785,28786,28789,28791,28797,28799,28805,28807,28809,28811,28813,28815,28817,28823,28825,28831,28833,28835,28837,28839,28845,28847,28855,28861,28863,28871,28877,28879],{},[898,28787,10047],{"mathvariant":28788},"script",[1688,28790,2066],{"stretchy":2065},[1788,28792,28793,28795],{},[898,28794,1872],{},[1793,28796,1795],{},[1688,28798,1733],{"separator":1732},[1788,28800,28801,28803],{},[898,28802,1872],{},[1793,28804,1806],{},[1688,28806,1733],{"separator":1732},[898,28808,16690],{},[1688,28810,2076],{"stretchy":2065},[1688,28812,1690],{},[898,28814,900],{},[1688,28816,2066],{"stretchy":2065},[1788,28818,28819,28821],{},[898,28820,1872],{},[1793,28822,1795],{},[1688,28824,1733],{"separator":1732},[1788,28826,28827,28829],{},[898,28828,1872],{},[1793,28830,1806],{},[1688,28832,2076],{"stretchy":2065},[1688,28834,1696],{},[898,28836,16690],{},[1688,28838,2066],{"stretchy":2065},[1850,28840,28841,28843],{},[898,28842,1854],{},[1688,28844,1857],{},[1688,28846,1954],{},[1814,28848,28849,28851,28853],{},[898,28850,1727],{},[1793,28852,1795],{},[1688,28854,1857],{},[1788,28856,28857,28859],{},[898,28858,1872],{},[1793,28860,1795],{},[1688,28862,1954],{},[1814,28864,28865,28867,28869],{},[898,28866,1727],{},[1793,28868,1806],{},[1688,28870,1857],{},[1788,28872,28873,28875],{},[898,28874,1872],{},[1793,28876,1806],{},[1688,28878,2076],{"stretchy":2065},[898,28880,2263],{"mathvariant":1822},[21003,28882],{"width":28316},[21003,28884,28885],{},[2041,28886,28887],{},"(6.13)",[902,28889,28890],{"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}",[724,28892,28893],{},"Soustava prvního řádu:",[883,28895,28897],{"className":28896},[886],[888,28898,28899],{"xmlns":890,"display":28306},[892,28900,28901,29084],{},[20995,28902,28903],{"width":28311},[21000,28904,28905,28907,29077,29079],{},[21003,28906],{"width":28316},[21003,28908,28909],{},[20995,28910,28911,28961,29011],{"rowspacing":20997,"columnalign":20998,"columnspacing":1823},[21000,28912,28913,28925],{},[21003,28914,28915],{},[1777,28916,28917],{"scriptlevel":1779,"displaystyle":1732},[1814,28918,28919,28921,28923],{},[898,28920,10047],{"mathvariant":28788},[1793,28922,1795],{},[1688,28924,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[21003,28926,28927],{},[1777,28928,28929],{"scriptlevel":1779,"displaystyle":1732},[895,28930,28931,28933,28935,28943,28945,28947,28955,28957,28959],{},[895,28932],{},[1688,28934,1690],{},[1814,28936,28937,28939,28941],{},[898,28938,900],{},[1793,28940,1795],{},[1688,28942,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,28944,1954],{},[898,28946,16690],{},[1814,28948,28949,28951,28953],{},[898,28950,1727],{},[1793,28952,1795],{},[1688,28954,1857],{},[1688,28956,1690],{},[1793,28958,1779],{},[1688,28960,1733],{"separator":1732},[21000,28962,28963,28975],{},[21003,28964,28965],{},[1777,28966,28967],{"scriptlevel":1779,"displaystyle":1732},[1814,28968,28969,28971,28973],{},[898,28970,10047],{"mathvariant":28788},[1793,28972,1806],{},[1688,28974,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[21003,28976,28977],{},[1777,28978,28979],{"scriptlevel":1779,"displaystyle":1732},[895,28980,28981,28983,28985,28993,28995,28997,29005,29007,29009],{},[895,28982],{},[1688,28984,1690],{},[1814,28986,28987,28989,28991],{},[898,28988,900],{},[1793,28990,1806],{},[1688,28992,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,28994,1954],{},[898,28996,16690],{},[1814,28998,28999,29001,29003],{},[898,29000,1727],{},[1793,29002,1806],{},[1688,29004,1857],{},[1688,29006,1690],{},[1793,29008,1779],{},[1688,29010,1733],{"separator":1732},[21000,29012,29013,29025],{},[21003,29014,29015],{},[1777,29016,29017],{"scriptlevel":1779,"displaystyle":1732},[1814,29018,29019,29021,29023],{},[898,29020,10047],{"mathvariant":28788},[898,29022,16690],{},[1688,29024,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[21003,29026,29027],{},[1777,29028,29029],{"scriptlevel":1779,"displaystyle":1732},[895,29030,29031,29033,29035,29041,29043,29051,29057,29059,29067,29073,29075],{},[895,29032],{},[1688,29034,1690],{},[1850,29036,29037,29039],{},[898,29038,1854],{},[1688,29040,1857],{},[1688,29042,1954],{},[1814,29044,29045,29047,29049],{},[898,29046,1727],{},[1793,29048,1795],{},[1688,29050,1857],{},[1788,29052,29053,29055],{},[898,29054,1872],{},[1793,29056,1795],{},[1688,29058,1954],{},[1814,29060,29061,29063,29065],{},[898,29062,1727],{},[1793,29064,1806],{},[1688,29066,1857],{},[1788,29068,29069,29071],{},[898,29070,1872],{},[1793,29072,1806],{},[1688,29074,1690],{},[1793,29076,12708],{},[21003,29078],{"width":28316},[21003,29080,29081],{},[2041,29082,29083],{},"(6.14)",[902,29085,29086],{"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}",[724,29088,29089,29090,29093,29094,29107,29108,2965],{},"Díky konvexitě indiferenčních křivek je řešení ",[38,29091,29092],{},"vázaným maximem",". Z prvních dvou rovnic po vyloučení ",[883,29095,29097],{"className":29096},[886],[888,29098,29099],{"xmlns":890},[892,29100,29101,29105],{},[895,29102,29103],{},[898,29104,16690],{},[902,29106,16743],{"encoding":904}," dostáváme ",[38,29109,29110],{},"podmínku optimality",[883,29112,29114],{"className":29113},[886],[888,29115,29116],{"xmlns":890,"display":28306},[892,29117,29118,29176],{},[895,29119,29120],{},[13080,29121,29122],{"notation":13082},[1777,29123,29124],{"scriptlevel":1779,"displaystyle":2065},[1777,29125,29126],{"scriptlevel":1779,"displaystyle":2065},[1777,29127,29128],{"scriptlevel":1779,"displaystyle":1732},[895,29129,29130,29132,29134,29136,29154,29156,29174],{},[2041,29131,4241],{},[2041,29133,1670],{},[1688,29135,1690],{},[1781,29137,29138,29146],{},[1814,29139,29140,29142,29144],{},[898,29141,900],{},[1793,29143,1795],{},[1688,29145,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1814,29147,29148,29150,29152],{},[898,29149,900],{},[1793,29151,1806],{},[1688,29153,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,29155,1690],{},[1781,29157,29158,29166],{},[1814,29159,29160,29162,29164],{},[898,29161,1727],{},[1793,29163,1795],{},[1688,29165,1857],{},[1814,29167,29168,29170,29172],{},[898,29169,1727],{},[1793,29171,1806],{},[1688,29173,1857],{},[2041,29175,4241],{},[902,29177,29178],{"encoding":904},"\\boxed{\\; \\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*} \\;}",[4124,29180,29181],{},[724,29182,29183,29185,29186,29220,29221,29224,29225,29243,29244,29262,29263,29293,29294,29311,29312,29342],{},[883,29184,4412],{}," Intuice — mezní poměr užitečnosti = mezní poměr cen\nPodmínka ",[883,29187,29189],{"className":29188},[886],[888,29190,29191],{"xmlns":890},[892,29192,29193,29217],{},[895,29194,29195,29197,29199,29207,29209],{},[2041,29196,1670],{},[1688,29198,1690],{},[1814,29200,29201,29203,29205],{},[898,29202,1727],{},[1793,29204,1795],{},[1688,29206,1857],{},[898,29208,4930],{"mathvariant":1822},[1814,29210,29211,29213,29215],{},[898,29212,1727],{},[1793,29214,1806],{},[1688,29216,1857],{},[902,29218,29219],{"encoding":904},"\\text{MRCS} = P_1^*\u002FP_2^*"," říká, že v optimu je ",[38,29222,29223],{},"sklon indiferenční křivky roven sklonu rozpočtové přímky",". Ekonomicky: spotřebitel je ochoten vyměnit ",[883,29226,29228],{"className":29227},[886],[888,29229,29230],{"xmlns":890},[892,29231,29232,29240],{},[895,29233,29234],{},[1788,29235,29236,29238],{},[898,29237,1872],{},[1793,29239,1795],{},[902,29241,29242],{"encoding":904},"Q_1"," za ",[883,29245,29247],{"className":29246},[886],[888,29248,29249],{"xmlns":890},[892,29250,29251,29259],{},[895,29252,29253],{},[1788,29254,29255,29257],{},[898,29256,1872],{},[1793,29258,1806],{},[902,29260,29261],{"encoding":904},"Q_2"," v přesně tom poměru, v jakém je trh (ceny) umožňuje vyměňovat. Kdyby ",[883,29264,29266],{"className":29265},[886],[888,29267,29268],{"xmlns":890},[892,29269,29270,29290],{},[895,29271,29272,29274,29276,29282,29284],{},[2041,29273,1670],{},[1688,29275,3665],{},[1788,29277,29278,29280],{},[898,29279,1727],{},[1793,29281,1795],{},[898,29283,4930],{"mathvariant":1822},[1788,29285,29286,29288],{},[898,29287,1727],{},[1793,29289,1806],{},[902,29291,29292],{"encoding":904},"\\text{MRCS} > P_1\u002FP_2",", vyplatilo by se nakupovat více ",[883,29295,29297],{"className":29296},[886],[888,29298,29299],{"xmlns":890},[892,29300,29301,29309],{},[895,29302,29303],{},[1788,29304,29305,29307],{},[898,29306,1872],{},[1793,29308,1795],{},[902,29310,29242],{"encoding":904}," (subjektivní ocenění převažuje nad tržním); kdyby ",[883,29313,29315],{"className":29314},[886],[888,29316,29317],{"xmlns":890},[892,29318,29319,29339],{},[895,29320,29321,29323,29325,29331,29333],{},[2041,29322,1670],{},[1688,29324,3704],{},[1788,29326,29327,29329],{},[898,29328,1727],{},[1793,29330,1795],{},[898,29332,4930],{"mathvariant":1822},[1788,29334,29335,29337],{},[898,29336,1727],{},[1793,29338,1806],{},[902,29340,29341],{"encoding":904},"\\text{MRCS} \u003C P_1\u002FP_2",", vyplatil by se opak.",[198,29344,29346,29347,29360],{"id":29345},"interpretace-λlambda-mezní-užitečnost-důchodu","Interpretace ",[883,29348,29350],{"className":29349},[886],[888,29351,29352],{"xmlns":890},[892,29353,29354,29358],{},[895,29355,29356],{},[898,29357,16690],{},[902,29359,16743],{"encoding":904}," — mezní užitečnost důchodu",[724,29362,29363,29364,29382,29383,29386,29387,29404,29405,29422,29423,29426],{},"Lagrangeův multiplikátor ",[883,29365,29367],{"className":29366},[886],[888,29368,29369],{"xmlns":890},[892,29370,29371,29379],{},[895,29372,29373],{},[1850,29374,29375,29377],{},[898,29376,16690],{},[1688,29378,1857],{},[902,29380,29381],{"encoding":904},"\\lambda^*"," představuje ",[38,29384,29385],{},"mezní užitečnost důchodu"," — přibližnou změnu maximální užitečnosti ",[883,29388,29390],{"className":29389},[886],[888,29391,29392],{"xmlns":890},[892,29393,29394,29402],{},[895,29395,29396],{},[1850,29397,29398,29400],{},[898,29399,900],{},[1688,29401,1857],{},[902,29403,28202],{"encoding":904}," při jednotkové změně důchodu ",[883,29406,29408],{"className":29407},[886],[888,29409,29410],{"xmlns":890},[892,29411,29412,29420],{},[895,29413,29414],{},[1850,29415,29416,29418],{},[898,29417,1854],{},[1688,29419,1857],{},[902,29421,28268],{"encoding":904},". Je to ",[38,29424,29425],{},"stínová cena"," rozpočtového omezení.",[4124,29428,29429,29434],{},[724,29430,29431,29433],{},[883,29432,4828],{}," Postup — maximalizace užitečnosti Lagrangeovou metodou",[152,29435,29436,29496,29583,29619,29706],{},[123,29437,29438,29441,29442,2263],{},[38,29439,29440],{},"Zapiš rozpočtové omezení"," ve tvaru ",[883,29443,29445],{"className":29444},[886],[888,29446,29447],{"xmlns":890},[892,29448,29449,29493],{},[895,29450,29451,29457,29459,29467,29473,29475,29483,29489,29491],{},[1850,29452,29453,29455],{},[898,29454,1854],{},[1688,29456,1857],{},[1688,29458,1954],{},[1814,29460,29461,29463,29465],{},[898,29462,1727],{},[1793,29464,1795],{},[1688,29466,1857],{},[1788,29468,29469,29471],{},[898,29470,1872],{},[1793,29472,1795],{},[1688,29474,1954],{},[1814,29476,29477,29479,29481],{},[898,29478,1727],{},[1793,29480,1806],{},[1688,29482,1857],{},[1788,29484,29485,29487],{},[898,29486,1872],{},[1793,29488,1806],{},[1688,29490,1690],{},[1793,29492,1779],{},[902,29494,29495],{"encoding":904},"Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",[123,29497,29498,2170,29501,2263],{},[38,29499,29500],{},"Sestav Lagrangeovu funkci",[883,29502,29504],{"className":29503},[886],[888,29505,29506],{"xmlns":890},[892,29507,29508,29580],{},[895,29509,29510,29512,29514,29516,29518,29524,29526,29532,29534,29536,29538,29540,29546,29548,29556,29562,29564,29572,29578],{},[898,29511,10047],{"mathvariant":28788},[1688,29513,1690],{},[898,29515,900],{},[1688,29517,2066],{"stretchy":2065},[1788,29519,29520,29522],{},[898,29521,1872],{},[1793,29523,1795],{},[1688,29525,1733],{"separator":1732},[1788,29527,29528,29530],{},[898,29529,1872],{},[1793,29531,1806],{},[1688,29533,2076],{"stretchy":2065},[1688,29535,1696],{},[898,29537,16690],{},[1688,29539,2066],{"stretchy":2065},[1850,29541,29542,29544],{},[898,29543,1854],{},[1688,29545,1857],{},[1688,29547,1954],{},[1814,29549,29550,29552,29554],{},[898,29551,1727],{},[1793,29553,1795],{},[1688,29555,1857],{},[1788,29557,29558,29560],{},[898,29559,1872],{},[1793,29561,1795],{},[1688,29563,1954],{},[1814,29565,29566,29568,29570],{},[898,29567,1727],{},[1793,29569,1806],{},[1688,29571,1857],{},[1788,29573,29574,29576],{},[898,29575,1872],{},[1793,29577,1806],{},[1688,29579,2076],{"stretchy":2065},[902,29581,29582],{"encoding":904},"\\mathcal{L} = U(Q_1, Q_2) + \\lambda(Y^* - P_1^* Q_1 - P_2^* Q_2)",[123,29584,29585,10720,29588,29618],{},[38,29586,29587],{},"Spočítej parciální derivace",[883,29589,29591],{"className":29590},[886],[888,29592,29593],{"xmlns":890},[892,29594,29595,29615],{},[895,29596,29597,29603,29605,29611,29613],{},[1788,29598,29599,29601],{},[898,29600,1872],{},[1793,29602,1795],{},[1688,29604,1733],{"separator":1732},[1788,29606,29607,29609],{},[898,29608,1872],{},[1793,29610,1806],{},[1688,29612,1733],{"separator":1732},[898,29614,16690],{},[902,29616,29617],{"encoding":904},"Q_1, Q_2, \\lambda"," a polož je rovny nule.",[123,29620,29621,29637,29638,29671,29672,4142,29689,2263],{},[38,29622,29623,29624],{},"Vyluč ",[883,29625,29627],{"className":29626},[886],[888,29628,29629],{"xmlns":890},[892,29630,29631,29635],{},[895,29632,29633],{},[898,29634,16690],{},[902,29636,16743],{"encoding":904}," dělením prvních dvou rovnic — dostaneš podmínku ",[883,29639,29641],{"className":29640},[886],[888,29642,29643],{"xmlns":890},[892,29644,29645,29669],{},[895,29646,29647,29649,29651,29659,29661],{},[2041,29648,1670],{},[1688,29650,1690],{},[1814,29652,29653,29655,29657],{},[898,29654,1727],{},[1793,29656,1795],{},[1688,29658,1857],{},[898,29660,4930],{"mathvariant":1822},[1814,29662,29663,29665,29667],{},[898,29664,1727],{},[1793,29666,1806],{},[1688,29668,1857],{},[902,29670,29219],{"encoding":904},", která dá vztah mezi ",[883,29673,29675],{"className":29674},[886],[888,29676,29677],{"xmlns":890},[892,29678,29679,29687],{},[895,29680,29681],{},[1788,29682,29683,29685],{},[898,29684,1872],{},[1793,29686,1795],{},[902,29688,29242],{"encoding":904},[883,29690,29692],{"className":29691},[886],[888,29693,29694],{"xmlns":890},[892,29695,29696,29704],{},[895,29697,29698],{},[1788,29699,29700,29702],{},[898,29701,1872],{},[1793,29703,1806],{},[902,29705,29261],{"encoding":904},[123,29707,29708,29711,29712,29742,29743,29760,29761,2263],{},[38,29709,29710],{},"Dosaď do rozpočtového omezení"," a vypočítej ",[883,29713,29715],{"className":29714},[886],[888,29716,29717],{"xmlns":890},[892,29718,29719,29739],{},[895,29720,29721,29729,29731],{},[1814,29722,29723,29725,29727],{},[898,29724,1872],{},[1793,29726,1795],{},[1688,29728,1857],{},[1688,29730,1733],{"separator":1732},[1814,29732,29733,29735,29737],{},[898,29734,1872],{},[1793,29736,1806],{},[1688,29738,1857],{},[902,29740,29741],{"encoding":904},"Q_1^*, Q_2^*",", případně ",[883,29744,29746],{"className":29745},[886],[888,29747,29748],{"xmlns":890},[892,29749,29750,29758],{},[895,29751,29752],{},[1850,29753,29754,29756],{},[898,29755,16690],{},[1688,29757,1857],{},[902,29759,29381],{"encoding":904}," a maximální užitečnost ",[883,29762,29764],{"className":29763},[886],[888,29765,29766],{"xmlns":890},[892,29767,29768,29802],{},[895,29769,29770,29776,29778,29780,29782,29790,29792,29800],{},[1850,29771,29772,29774],{},[898,29773,900],{},[1688,29775,1857],{},[1688,29777,1690],{},[898,29779,900],{},[1688,29781,2066],{"stretchy":2065},[1814,29783,29784,29786,29788],{},[898,29785,1872],{},[1793,29787,1795],{},[1688,29789,1857],{},[1688,29791,1733],{"separator":1732},[1814,29793,29794,29796,29798],{},[898,29795,1872],{},[1793,29797,1806],{},[1688,29799,1857],{},[1688,29801,2076],{"stretchy":2065},[902,29803,29804],{"encoding":904},"U^* = U(Q_1^*, Q_2^*)",[115,29806,29808],{"id":29807},"geometrie-optima-tečnost-ic-a-rozpočtové-přímky","Geometrie optima — tečnost IC a rozpočtové přímky",[724,29810,29811],{},[2821,29812],{"alt":29813,"className":29814,"src":29815},"imek-uzitecnost-optimum",[210,2825],"\u002Fwiki-assets\u002Fimek-uzitecnost-optimum.jpeg",[724,29817,29818],{},[614,29819,29820,29821,29870,29871,4142,29899,29927,29928,29962,29963,30002,30003,30021,30022,30040,30041,30059],{},"Obrázek 6.7 — Rozpočtová přímka ",[883,29822,29824],{"className":29823},[886],[888,29825,29826],{"xmlns":890},[892,29827,29828,29868],{},[895,29829,29830,29836,29838,29846,29852,29854,29862],{},[1850,29831,29832,29834],{},[898,29833,1854],{},[1688,29835,1857],{},[1688,29837,1690],{},[1814,29839,29840,29842,29844],{},[898,29841,1727],{},[1793,29843,1795],{},[1688,29845,1857],{},[1788,29847,29848,29850],{},[898,29849,1872],{},[1793,29851,1795],{},[1688,29853,1696],{},[1814,29855,29856,29858,29860],{},[898,29857,1727],{},[1793,29859,1806],{},[1688,29861,1857],{},[1788,29863,29864,29866],{},[898,29865,1872],{},[1793,29867,1806],{},[902,29869,1893],{"encoding":904}," protíná osy v ",[883,29872,29874],{"className":29873},[886],[888,29875,29876],{"xmlns":890},[892,29877,29878,29896],{},[895,29879,29880,29886,29888],{},[1850,29881,29882,29884],{},[898,29883,1854],{},[1688,29885,1857],{},[898,29887,4930],{"mathvariant":1822},[1814,29889,29890,29892,29894],{},[898,29891,1727],{},[1793,29893,1795],{},[1688,29895,1857],{},[902,29897,29898],{"encoding":904},"Y^*\u002FP_1^*",[883,29900,29902],{"className":29901},[886],[888,29903,29904],{"xmlns":890},[892,29905,29906,29924],{},[895,29907,29908,29914,29916],{},[1850,29909,29910,29912],{},[898,29911,1854],{},[1688,29913,1857],{},[898,29915,4930],{"mathvariant":1822},[1814,29917,29918,29920,29922],{},[898,29919,1727],{},[1793,29921,1806],{},[1688,29923,1857],{},[902,29925,29926],{"encoding":904},"Y^*\u002FP_2^*",". Tři indiferenční křivky ",[883,29929,29931],{"className":29930},[886],[888,29932,29933],{"xmlns":890},[892,29934,29935,29959],{},[895,29936,29937,29943,29945,29951,29953],{},[1788,29938,29939,29941],{},[898,29940,2031],{},[1793,29942,1795],{},[1688,29944,3704],{},[1850,29946,29947,29949],{},[898,29948,2031],{},[1688,29950,1857],{},[1688,29952,3704],{},[1788,29954,29955,29957],{},[898,29956,2031],{},[1793,29958,1806],{},[902,29960,29961],{"encoding":904},"c_1 \u003C c^* \u003C c_2",". Optimum ",[883,29964,29966],{"className":29965},[886],[888,29967,29968],{"xmlns":890},[892,29969,29970,30000],{},[895,29971,29972,29978,29980,29988,29990,29998],{},[1850,29973,29974,29976],{},[898,29975,1872],{},[1688,29977,1857],{},[1688,29979,2748],{"stretchy":2065},[1814,29981,29982,29984,29986],{},[898,29983,1872],{},[1793,29985,1795],{},[1688,29987,1857],{},[1688,29989,1733],{"separator":1732},[1814,29991,29992,29994,29996],{},[898,29993,1872],{},[1793,29995,1806],{},[1688,29997,1857],{},[1688,29999,2763],{"stretchy":2065},[902,30001,28567],{"encoding":904}," je bod dotyku rozpočtové přímky s křivkou ",[883,30004,30006],{"className":30005},[886],[888,30007,30008],{"xmlns":890},[892,30009,30010,30018],{},[895,30011,30012],{},[1850,30013,30014,30016],{},[898,30015,2031],{},[1688,30017,1857],{},[902,30019,30020],{"encoding":904},"c^*",". Křivka ",[883,30023,30025],{"className":30024},[886],[888,30026,30027],{"xmlns":890},[892,30028,30029,30037],{},[895,30030,30031],{},[1788,30032,30033,30035],{},[898,30034,2031],{},[1793,30036,1795],{},[902,30038,30039],{"encoding":904},"c_1"," je dosažitelná, ale nemaximalizuje užitečnost; křivka ",[883,30042,30044],{"className":30043},[886],[888,30045,30046],{"xmlns":890},[892,30047,30048,30056],{},[895,30049,30050],{},[1788,30051,30052,30054],{},[898,30053,2031],{},[1793,30055,1806],{},[902,30057,30058],{"encoding":904},"c_2"," není při daném důchodu dosažitelná.",[724,30061,30062,30063,30066,30067,30085,30086,30115],{},"Geometrie je jádrem intuice: přímka (rozpočet) a křivka (užitečnost) se v optimu ",[38,30064,30065],{},"dotýkají",", tj. mají v bodě ",[883,30068,30070],{"className":30069},[886],[888,30071,30072],{"xmlns":890},[892,30073,30074,30082],{},[895,30075,30076],{},[1850,30077,30078,30080],{},[898,30079,1872],{},[1688,30081,1857],{},[902,30083,30084],{"encoding":904},"Q^*"," společnou tečnu. To přímo převádí podmínku ",[883,30087,30089],{"className":30088},[886],[888,30090,30091],{"xmlns":890},[892,30092,30093,30113],{},[895,30094,30095,30097,30099,30105,30107],{},[2041,30096,1670],{},[1688,30098,1690],{},[1788,30100,30101,30103],{},[898,30102,1727],{},[1793,30104,1795],{},[898,30106,4930],{"mathvariant":1822},[1788,30108,30109,30111],{},[898,30110,1727],{},[1793,30112,1806],{},[902,30114,28238],{"encoding":904}," — poměr mezních užitečností (sklon IC) = poměr cen (sklon přímky).",[115,30117,30119],{"id":30118},"příklad-65-mrcs-pro-cobb-douglasovu-užitečnost","Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost",[724,30121,9916,30122,30184],{},[883,30123,30125],{"className":30124},[886],[888,30126,30127],{"xmlns":890},[892,30128,30129,30181],{},[895,30130,30131,30133,30135,30141,30143,30149,30151,30153,30167],{},[898,30132,900],{},[1688,30134,2066],{"stretchy":2065},[1788,30136,30137,30139],{},[898,30138,1872],{},[1793,30140,1795],{},[1688,30142,1733],{"separator":1732},[1788,30144,30145,30147],{},[898,30146,1872],{},[1793,30148,1806],{},[1688,30150,2076],{"stretchy":2065},[1688,30152,1690],{},[1814,30154,30155,30157,30159],{},[898,30156,1872],{},[1793,30158,1795],{},[895,30160,30161,30163,30165],{},[1793,30162,1795],{},[898,30164,4930],{"mathvariant":1822},[1793,30166,1806],{},[1814,30168,30169,30171,30173],{},[898,30170,1872],{},[1793,30172,1806],{},[895,30174,30175,30177,30179],{},[1793,30176,1795],{},[898,30178,4930],{"mathvariant":1822},[1793,30180,1806],{},[902,30182,30183],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F2} Q_2^{1\u002F2}"," platí",[724,30186,30187],{},[883,30188,30190],{"className":30189},[886],[888,30191,30192],{"xmlns":890},[892,30193,30194,30300],{},[895,30195,30196,30198,30200,30282,30284,30298],{},[2041,30197,1670],{},[1688,30199,1690],{},[1781,30201,30202,30242],{},[895,30203,30204,30212,30228],{},[1777,30205,30206],{"scriptlevel":1779,"displaystyle":2065},[1781,30207,30208,30210],{},[1793,30209,1795],{},[1793,30211,1806],{},[1814,30213,30214,30216,30218],{},[898,30215,1872],{},[1793,30217,1795],{},[895,30219,30220,30222,30224,30226],{},[1688,30221,1954],{},[1793,30223,1795],{},[898,30225,4930],{"mathvariant":1822},[1793,30227,1806],{},[1814,30229,30230,30232,30234],{},[898,30231,1872],{},[1793,30233,1806],{},[895,30235,30236,30238,30240],{},[1793,30237,1795],{},[898,30239,4930],{"mathvariant":1822},[1793,30241,1806],{},[895,30243,30244,30252,30266],{},[1777,30245,30246],{"scriptlevel":1779,"displaystyle":2065},[1781,30247,30248,30250],{},[1793,30249,1795],{},[1793,30251,1806],{},[1814,30253,30254,30256,30258],{},[898,30255,1872],{},[1793,30257,1795],{},[895,30259,30260,30262,30264],{},[1793,30261,1795],{},[898,30263,4930],{"mathvariant":1822},[1793,30265,1806],{},[1814,30267,30268,30270,30272],{},[898,30269,1872],{},[1793,30271,1806],{},[895,30273,30274,30276,30278,30280],{},[1688,30275,1954],{},[1793,30277,1795],{},[898,30279,4930],{"mathvariant":1822},[1793,30281,1806],{},[1688,30283,1690],{},[1781,30285,30286,30292],{},[1788,30287,30288,30290],{},[898,30289,1872],{},[1793,30291,1806],{},[1788,30293,30294,30296],{},[898,30295,1872],{},[1793,30297,1795],{},[898,30299,2263],{"mathvariant":1822},[902,30301,30302],{"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}.",[724,30304,30305,30306,3185,30351,30353,30354,30374,30375,30405,30406,2263],{},"Tedy ",[883,30307,30309],{"className":30308},[886],[888,30310,30311],{"xmlns":890},[892,30312,30313,30348],{},[895,30314,30315,30317,30319,30322,30324,30326,30328,30330,30338,30340],{},[2041,30316,1670],{},[1688,30318,2066],{"stretchy":2065},[1793,30320,30321],{},"300",[1688,30323,1733],{"separator":1732},[1793,30325,15357],{},[1688,30327,2076],{"stretchy":2065},[1688,30329,1690],{},[1777,30331,30332],{"scriptlevel":1779,"displaystyle":2065},[1781,30333,30334,30336],{},[1793,30335,15357],{},[1793,30337,30321],{},[1688,30339,1690],{},[1777,30341,30342],{"scriptlevel":1779,"displaystyle":2065},[1781,30343,30344,30346],{},[1793,30345,2501],{},[1793,30347,2131],{},[902,30349,30350],{"encoding":904},"\\text{MRCS}(300, 500) = \\tfrac{500}{300} = \\tfrac{5}{3}",[614,30352,9469],{}," zvýší-li spotřebitel nákup prvního zboží o 1 jednotku, musí snížit nákup druhého zboží přibližně o ",[883,30355,30357],{"className":30356},[886],[888,30358,30359],{"xmlns":890},[892,30360,30361,30371],{},[895,30362,30363],{},[1777,30364,30365],{"scriptlevel":1779,"displaystyle":2065},[1781,30366,30367,30369],{},[1793,30368,2501],{},[1793,30370,2131],{},[902,30372,30373],{"encoding":904},"\\tfrac{5}{3}"," jednotky, aby se užitečnost zachovala. Tato forma ",[883,30376,30378],{"className":30377},[886],[888,30379,30380],{"xmlns":890},[892,30381,30382,30402],{},[895,30383,30384,30386,30388,30394,30396],{},[2041,30385,1670],{},[1688,30387,1690],{},[1788,30389,30390,30392],{},[898,30391,1872],{},[1793,30393,1806],{},[898,30395,4930],{"mathvariant":1822},[1788,30397,30398,30400],{},[898,30399,1872],{},[1793,30401,1795],{},[902,30403,30404],{"encoding":904},"\\text{MRCS} = Q_2\u002FQ_1"," je typická pro symetrické Cobb-Douglasovy preference a vstupuje do optimalizace skrze podmínku ",[883,30407,30409],{"className":30408},[886],[888,30410,30411],{"xmlns":890},[892,30412,30413,30433],{},[895,30414,30415,30417,30419,30425,30427],{},[2041,30416,1670],{},[1688,30418,1690],{},[1788,30420,30421,30423],{},[898,30422,1727],{},[1793,30424,1795],{},[898,30426,4930],{"mathvariant":1822},[1788,30428,30429,30431],{},[898,30430,1727],{},[1793,30432,1806],{},[902,30434,28238],{"encoding":904},[115,30436,30438,30439],{"id":30437},"příklad-66-maximalizace-užitečnosti-pro-uq1q2u-q_1-q_2","Příklad 6.6 — maximalizace užitečnosti pro ",[883,30440,30442],{"className":30441},[886],[888,30443,30444],{"xmlns":890},[892,30445,30446,30464],{},[895,30447,30448,30450,30452,30458],{},[898,30449,900],{},[1688,30451,1690],{},[1788,30453,30454,30456],{},[898,30455,1872],{},[1793,30457,1795],{},[1788,30459,30460,30462],{},[898,30461,1872],{},[1793,30463,1806],{},[902,30465,30466],{"encoding":904},"U = Q_1 Q_2",[724,30468,30469,30470,1343,30516,1343,30540,1343,30564,30586],{},"Je dána ",[883,30471,30473],{"className":30472},[886],[888,30474,30475],{"xmlns":890},[892,30476,30477,30513],{},[895,30478,30479,30481,30483,30489,30491,30497,30499,30501,30507],{},[898,30480,900],{},[1688,30482,2066],{"stretchy":2065},[1788,30484,30485,30487],{},[898,30486,1872],{},[1793,30488,1795],{},[1688,30490,1733],{"separator":1732},[1788,30492,30493,30495],{},[898,30494,1872],{},[1793,30496,1806],{},[1688,30498,2076],{"stretchy":2065},[1688,30500,1690],{},[1788,30502,30503,30505],{},[898,30504,1872],{},[1793,30506,1795],{},[1788,30508,30509,30511],{},[898,30510,1872],{},[1793,30512,1806],{},[902,30514,30515],{"encoding":904},"U(Q_1, Q_2) = Q_1 Q_2",[883,30517,30519],{"className":30518},[886],[888,30520,30521],{"xmlns":890},[892,30522,30523,30537],{},[895,30524,30525,30533,30535],{},[1814,30526,30527,30529,30531],{},[898,30528,1727],{},[1793,30530,1795],{},[1688,30532,1857],{},[1688,30534,1690],{},[1793,30536,1806],{},[902,30538,30539],{"encoding":904},"P_1^* = 2",[883,30541,30543],{"className":30542},[886],[888,30544,30545],{"xmlns":890},[892,30546,30547,30561],{},[895,30548,30549,30557,30559],{},[1814,30550,30551,30553,30555],{},[898,30552,1727],{},[1793,30554,1806],{},[1688,30556,1857],{},[1688,30558,1690],{},[1793,30560,2501],{},[902,30562,30563],{"encoding":904},"P_2^* = 5",[883,30565,30567],{"className":30566},[886],[888,30568,30569],{"xmlns":890},[892,30570,30571,30583],{},[895,30572,30573,30579,30581],{},[1850,30574,30575,30577],{},[898,30576,1854],{},[1688,30578,1857],{},[1688,30580,1690],{},[1793,30582,3347],{},[902,30584,30585],{"encoding":904},"Y^* = 100",". Lagrangeova funkce:",[883,30588,30590],{"className":30589},[886],[888,30591,30592],{"xmlns":890,"display":28306},[892,30593,30594,30666],{},[895,30595,30596,30598,30600,30606,30608,30614,30616,30618,30620,30622,30628,30634,30636,30638,30640,30642,30644,30646,30652,30654,30656,30662,30664],{},[898,30597,10047],{"mathvariant":28788},[1688,30599,2066],{"stretchy":2065},[1788,30601,30602,30604],{},[898,30603,1872],{},[1793,30605,1795],{},[1688,30607,1733],{"separator":1732},[1788,30609,30610,30612],{},[898,30611,1872],{},[1793,30613,1806],{},[1688,30615,1733],{"separator":1732},[898,30617,16690],{},[1688,30619,2076],{"stretchy":2065},[1688,30621,1690],{},[1788,30623,30624,30626],{},[898,30625,1872],{},[1793,30627,1795],{},[1788,30629,30630,30632],{},[898,30631,1872],{},[1793,30633,1806],{},[1688,30635,1696],{},[898,30637,16690],{},[1688,30639,2066],{"stretchy":2065},[1793,30641,3347],{},[1688,30643,1954],{},[1793,30645,1806],{},[1788,30647,30648,30650],{},[898,30649,1872],{},[1793,30651,1795],{},[1688,30653,1954],{},[1793,30655,2501],{},[1788,30657,30658,30660],{},[898,30659,1872],{},[1793,30661,1806],{},[1688,30663,2076],{"stretchy":2065},[898,30665,2263],{"mathvariant":1822},[902,30667,30668],{"encoding":904},"\\mathcal{L}(Q_1, Q_2, \\lambda) = Q_1 Q_2 + \\lambda(100 - 2 Q_1 - 5 Q_2).",[724,30670,30671],{},"Soustava:",[883,30673,30675],{"className":30674},[886],[888,30676,30677],{"xmlns":890,"display":28306},[892,30678,30679,30791],{},[20995,30680,30681,30715,30749],{"rowspacing":20997,"columnalign":20998,"columnspacing":1823},[21000,30682,30683,30701],{},[21003,30684,30685],{},[1777,30686,30687],{"scriptlevel":1779,"displaystyle":1732},[895,30688,30689,30695,30697,30699],{},[1788,30690,30691,30693],{},[898,30692,1872],{},[1793,30694,1806],{},[1688,30696,1954],{},[1793,30698,1806],{},[898,30700,16690],{},[21003,30702,30703],{},[1777,30704,30705],{"scriptlevel":1779,"displaystyle":1732},[895,30706,30707,30709,30711,30713],{},[895,30708],{},[1688,30710,1690],{},[1793,30712,1779],{},[1688,30714,1733],{"separator":1732},[21000,30716,30717,30735],{},[21003,30718,30719],{},[1777,30720,30721],{"scriptlevel":1779,"displaystyle":1732},[895,30722,30723,30729,30731,30733],{},[1788,30724,30725,30727],{},[898,30726,1872],{},[1793,30728,1795],{},[1688,30730,1954],{},[1793,30732,2501],{},[898,30734,16690],{},[21003,30736,30737],{},[1777,30738,30739],{"scriptlevel":1779,"displaystyle":1732},[895,30740,30741,30743,30745,30747],{},[895,30742],{},[1688,30744,1690],{},[1793,30746,1779],{},[1688,30748,1733],{"separator":1732},[21000,30750,30751,30779],{},[21003,30752,30753],{},[1777,30754,30755],{"scriptlevel":1779,"displaystyle":1732},[895,30756,30757,30759,30761,30763,30769,30771,30773],{},[1793,30758,3347],{},[1688,30760,1954],{},[1793,30762,1806],{},[1788,30764,30765,30767],{},[898,30766,1872],{},[1793,30768,1795],{},[1688,30770,1954],{},[1793,30772,2501],{},[1788,30774,30775,30777],{},[898,30776,1872],{},[1793,30778,1806],{},[21003,30780,30781],{},[1777,30782,30783],{"scriptlevel":1779,"displaystyle":1732},[895,30784,30785,30787,30789],{},[895,30786],{},[1688,30788,1690],{},[1793,30790,12708],{},[902,30792,30793],{"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}",[724,30795,30796,30797,1343,30821,30845,30846,5845,30886,30904,30905,30955,30956,2263],{},"Z prvních dvou rovnic ",[883,30798,30800],{"className":30799},[886],[888,30801,30802],{"xmlns":890},[892,30803,30804,30818],{},[895,30805,30806,30812,30814,30816],{},[1788,30807,30808,30810],{},[898,30809,1872],{},[1793,30811,1806],{},[1688,30813,1690],{},[1793,30815,1806],{},[898,30817,16690],{},[902,30819,30820],{"encoding":904},"Q_2 = 2\\lambda",[883,30822,30824],{"className":30823},[886],[888,30825,30826],{"xmlns":890},[892,30827,30828,30842],{},[895,30829,30830,30836,30838,30840],{},[1788,30831,30832,30834],{},[898,30833,1872],{},[1793,30835,1795],{},[1688,30837,1690],{},[1793,30839,2501],{},[898,30841,16690],{},[902,30843,30844],{"encoding":904},"Q_1 = 5\\lambda","; dosazením do třetí ",[883,30847,30849],{"className":30848},[886],[888,30850,30851],{"xmlns":890},[892,30852,30853,30883],{},[895,30854,30855,30857,30859,30861,30863,30865,30867,30869,30871,30873,30875,30877,30879,30881],{},[1793,30856,3347],{},[1688,30858,1690],{},[1793,30860,1806],{},[1688,30862,3434],{},[1793,30864,2501],{},[898,30866,16690],{},[1688,30868,1696],{},[1793,30870,2501],{},[1688,30872,3434],{},[1793,30874,1806],{},[898,30876,16690],{},[1688,30878,1690],{},[1793,30880,9290],{},[898,30882,16690],{},[902,30884,30885],{"encoding":904},"100 = 2 \\cdot 5\\lambda + 5 \\cdot 2\\lambda = 20\\lambda",[883,30887,30889],{"className":30888},[886],[888,30890,30891],{"xmlns":890},[892,30892,30893,30901],{},[895,30894,30895,30897,30899],{},[898,30896,16690],{},[1688,30898,1690],{},[1793,30900,2501],{},[902,30902,30903],{"encoding":904},"\\lambda = 5",". Odtud ",[38,30906,30907,1343,30931],{},[883,30908,30910],{"className":30909},[886],[888,30911,30912],{"xmlns":890},[892,30913,30914,30928],{},[895,30915,30916,30924,30926],{},[1814,30917,30918,30920,30922],{},[898,30919,1872],{},[1793,30921,1795],{},[1688,30923,1857],{},[1688,30925,1690],{},[1793,30927,5260],{},[902,30929,30930],{"encoding":904},"Q_1^* = 25",[883,30932,30934],{"className":30933},[886],[888,30935,30936],{"xmlns":890},[892,30937,30938,30952],{},[895,30939,30940,30948,30950],{},[1814,30941,30942,30944,30946],{},[898,30943,1872],{},[1793,30945,1806],{},[1688,30947,1857],{},[1688,30949,1690],{},[1793,30951,3121],{},[902,30953,30954],{"encoding":904},"Q_2^* = 10",", maximální užitečnost ",[883,30957,30959],{"className":30958},[886],[888,30960,30961],{"xmlns":890},[892,30962,30963,30984],{},[895,30964,30965,30971,30973,30975,30977,30979,30981],{},[1850,30966,30967,30969],{},[898,30968,900],{},[1688,30970,1857],{},[1688,30972,1690],{},[1793,30974,5260],{},[1688,30976,3434],{},[1793,30978,3121],{},[1688,30980,1690],{},[1793,30982,30983],{},"250",[902,30985,30986],{"encoding":904},"U^* = 25 \\cdot 10 = 250",[724,30988,30989],{},[614,30990,30991,30992,28377,31030,4142,31054,31078,31079,31109,31110,31134,31135,31157,31158,2263],{},"Obrázek 6.8 — Rozpočtová přímka ",[883,30993,30995],{"className":30994},[886],[888,30996,30997],{"xmlns":890},[892,30998,30999,31027],{},[895,31000,31001,31003,31005,31007,31013,31015,31017,31023,31025],{},[1793,31002,3347],{},[1688,31004,1954],{},[1793,31006,1806],{},[1788,31008,31009,31011],{},[898,31010,1872],{},[1793,31012,1795],{},[1688,31014,1954],{},[1793,31016,2501],{},[1788,31018,31019,31021],{},[898,31020,1872],{},[1793,31022,1806],{},[1688,31024,1690],{},[1793,31026,1779],{},[902,31028,31029],{"encoding":904},"100 - 2 Q_1 - 5 Q_2 = 0",[883,31031,31033],{"className":31032},[886],[888,31034,31035],{"xmlns":890},[892,31036,31037,31051],{},[895,31038,31039,31041,31043,31045,31047,31049],{},[898,31040,4512],{},[1688,31042,2748],{"stretchy":2065},[1793,31044,1779],{},[1688,31046,1733],{"separator":1732},[1793,31048,9290],{},[1688,31050,2763],{"stretchy":2065},[902,31052,31053],{"encoding":904},"A[0, 20]",[883,31055,31057],{"className":31056},[886],[888,31058,31059],{"xmlns":890},[892,31060,31061,31075],{},[895,31062,31063,31065,31067,31069,31071,31073],{},[898,31064,23494],{},[1688,31066,2748],{"stretchy":2065},[1793,31068,3377],{},[1688,31070,1733],{"separator":1732},[1793,31072,1779],{},[1688,31074,2763],{"stretchy":2065},[902,31076,31077],{"encoding":904},"B[50, 0]","; hyperbolická indiferenční křivka ",[883,31080,31082],{"className":31081},[886],[888,31083,31084],{"xmlns":890},[892,31085,31086,31106],{},[895,31087,31088,31094,31096,31098,31100],{},[1788,31089,31090,31092],{},[898,31091,1872],{},[1793,31093,1806],{},[1688,31095,1690],{},[1793,31097,30983],{},[898,31099,4930],{"mathvariant":1822},[1788,31101,31102,31104],{},[898,31103,1872],{},[1793,31105,1795],{},[902,31107,31108],{"encoding":904},"Q_2 = 250\u002FQ_1"," se dotýká rozpočtové přímky v bodě ",[883,31111,31113],{"className":31112},[886],[888,31114,31115],{"xmlns":890},[892,31116,31117,31131],{},[895,31118,31119,31121,31123,31125,31127,31129],{},[898,31120,4509],{},[1688,31122,2748],{"stretchy":2065},[1793,31124,5260],{},[1688,31126,1733],{"separator":1732},[1793,31128,3121],{},[1688,31130,2763],{"stretchy":2065},[902,31132,31133],{"encoding":904},"E[25, 10]",". Sklon přímky ",[883,31136,31138],{"className":31137},[886],[888,31139,31140],{"xmlns":890},[892,31141,31142,31154],{},[895,31143,31144,31146],{},[1688,31145,1954],{},[1777,31147,31148],{"scriptlevel":1779,"displaystyle":2065},[1781,31149,31150,31152],{},[1793,31151,1806],{},[1793,31153,2501],{},[902,31155,31156],{"encoding":904},"-\\tfrac{2}{5}"," odpovídá ",[883,31159,31161],{"className":31160},[886],[888,31162,31163],{"xmlns":890},[892,31164,31165,31205],{},[895,31166,31167,31169,31171,31173,31175,31177,31179,31181,31183,31185,31193,31195,31197],{},[1688,31168,1954],{},[2041,31170,1670],{},[1688,31172,2066],{"stretchy":2065},[1793,31174,5260],{},[1688,31176,1733],{"separator":1732},[1793,31178,3121],{},[1688,31180,2076],{"stretchy":2065},[1688,31182,1690],{},[1688,31184,1954],{},[1777,31186,31187],{"scriptlevel":1779,"displaystyle":2065},[1781,31188,31189,31191],{},[1793,31190,3121],{},[1793,31192,5260],{},[1688,31194,1690],{},[1688,31196,1954],{},[1777,31198,31199],{"scriptlevel":1779,"displaystyle":2065},[1781,31200,31201,31203],{},[1793,31202,1806],{},[1793,31204,2501],{},[902,31206,31207],{"encoding":904},"-\\text{MRCS}(25, 10) = -\\tfrac{10}{25} = -\\tfrac{2}{5}",[115,31209,31211],{"id":31210},"funkce-poptávky-spotřebitele-marshallova","Funkce poptávky spotřebitele (Marshallova)",[724,31213,31214,31215,29243,31245,31248,31249,2965],{},"Považujeme-li v úloze ",[883,31216,31218],{"className":31217},[886],[888,31219,31220],{"xmlns":890},[892,31221,31222,31242],{},[895,31223,31224,31230,31232,31238,31240],{},[1788,31225,31226,31228],{},[898,31227,1727],{},[1793,31229,1795],{},[1688,31231,1733],{"separator":1732},[1788,31233,31234,31236],{},[898,31235,1727],{},[1793,31237,1806],{},[1688,31239,1733],{"separator":1732},[898,31241,1854],{},[902,31243,31244],{"encoding":904},"P_1, P_2, Y",[38,31246,31247],{},"parametry"," (nikoli čísla), dostáváme z první řádové podmínky ",[38,31250,31251],{},"Marshallovy poptávkové funkce",[883,31253,31255],{"className":31254},[886],[888,31256,31257],{"xmlns":890,"display":28306},[892,31258,31259,31354],{},[20995,31260,31261],{"width":28311},[21000,31262,31263,31265,31347,31349],{},[21003,31264],{"width":28316},[21003,31266,31267],{},[895,31268,31269,31275,31277,31283,31285,31291,31293,31299,31301,31303,31305,31307,31309,31315,31317,31323,31325,31331,31333,31339,31341,31343,31345],{},[1788,31270,31271,31273],{},[898,31272,1872],{},[1793,31274,1795],{},[1688,31276,1690],{},[1788,31278,31279,31281],{},[898,31280,4440],{},[1793,31282,1795],{},[1688,31284,2066],{"stretchy":2065},[1788,31286,31287,31289],{},[898,31288,1727],{},[1793,31290,1795],{},[1688,31292,1733],{"separator":1732},[1788,31294,31295,31297],{},[898,31296,1727],{},[1793,31298,1806],{},[1688,31300,1733],{"separator":1732},[898,31302,1854],{},[1688,31304,2076],{"stretchy":2065},[1688,31306,1733],{"separator":1732},[6134,31308],{"width":15531},[1788,31310,31311,31313],{},[898,31312,1872],{},[1793,31314,1806],{},[1688,31316,1690],{},[1788,31318,31319,31321],{},[898,31320,4440],{},[1793,31322,1806],{},[1688,31324,2066],{"stretchy":2065},[1788,31326,31327,31329],{},[898,31328,1727],{},[1793,31330,1795],{},[1688,31332,1733],{"separator":1732},[1788,31334,31335,31337],{},[898,31336,1727],{},[1793,31338,1806],{},[1688,31340,1733],{"separator":1732},[898,31342,1854],{},[1688,31344,2076],{"stretchy":2065},[1688,31346,1733],{"separator":1732},[21003,31348],{"width":28316},[21003,31350,31351],{},[2041,31352,31353],{},"(6.15)",[902,31355,31356],{"encoding":904},"Q_1 = D_1(P_1, P_2, Y), \\quad Q_2 = D_2(P_1, P_2, Y), \\tag{6.15}",[883,31358,31360],{"className":31359},[886],[888,31361,31362],{"xmlns":890,"display":28306},[892,31363,31364,31411],{},[20995,31365,31366],{"width":28311},[21000,31367,31368,31370,31404,31406],{},[21003,31369],{"width":28316},[21003,31371,31372],{},[895,31373,31374,31376,31378,31380,31382,31388,31390,31396,31398,31400,31402],{},[898,31375,16690],{},[1688,31377,1690],{},[898,31379,16690],{},[1688,31381,2066],{"stretchy":2065},[1788,31383,31384,31386],{},[898,31385,1727],{},[1793,31387,1795],{},[1688,31389,1733],{"separator":1732},[1788,31391,31392,31394],{},[898,31393,1727],{},[1793,31395,1806],{},[1688,31397,1733],{"separator":1732},[898,31399,1854],{},[1688,31401,2076],{"stretchy":2065},[898,31403,2263],{"mathvariant":1822},[21003,31405],{"width":28316},[21003,31407,31408],{},[2041,31409,31410],{},"(6.16)",[902,31412,31413],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, Y). \\tag{6.16}",[724,31415,31416,31446,31447,31513],{},[38,31417,31418,31419,2263],{},"Odvození pro ",[883,31420,31422],{"className":31421},[886],[888,31423,31424],{"xmlns":890},[892,31425,31426,31444],{},[895,31427,31428,31430,31432,31438],{},[898,31429,900],{},[1688,31431,1690],{},[1788,31433,31434,31436],{},[898,31435,1872],{},[1793,31437,1795],{},[1788,31439,31440,31442],{},[898,31441,1872],{},[1793,31443,1806],{},[902,31445,30466],{"encoding":904}," Lagrangeova funkce ",[883,31448,31450],{"className":31449},[886],[888,31451,31452],{"xmlns":890},[892,31453,31454,31510],{},[895,31455,31456,31458,31460,31466,31472,31474,31476,31478,31480,31482,31488,31494,31496,31502,31508],{},[898,31457,10047],{"mathvariant":28788},[1688,31459,1690],{},[1788,31461,31462,31464],{},[898,31463,1872],{},[1793,31465,1795],{},[1788,31467,31468,31470],{},[898,31469,1872],{},[1793,31471,1806],{},[1688,31473,1696],{},[898,31475,16690],{},[1688,31477,2066],{"stretchy":2065},[898,31479,1854],{},[1688,31481,1954],{},[1788,31483,31484,31486],{},[898,31485,1727],{},[1793,31487,1795],{},[1788,31489,31490,31492],{},[898,31491,1872],{},[1793,31493,1795],{},[1688,31495,1954],{},[1788,31497,31498,31500],{},[898,31499,1727],{},[1793,31501,1806],{},[1788,31503,31504,31506],{},[898,31505,1872],{},[1793,31507,1806],{},[1688,31509,2076],{"stretchy":2065},[902,31511,31512],{"encoding":904},"\\mathcal{L} = Q_1 Q_2 + \\lambda(Y - P_1 Q_1 - P_2 Q_2)"," dává soustavu",[883,31515,31517],{"className":31516},[886],[888,31518,31519],{"xmlns":890,"display":28306},[892,31520,31521,31688],{},[20995,31522,31523],{"width":28311},[21000,31524,31525,31527,31681,31683],{},[21003,31526],{"width":28316},[21003,31528,31529],{},[20995,31530,31531,31577,31623],{"rowspacing":20997,"columnalign":20998,"columnspacing":1823},[21000,31532,31533,31545],{},[21003,31534,31535],{},[1777,31536,31537],{"scriptlevel":1779,"displaystyle":1732},[1814,31538,31539,31541,31543],{},[898,31540,10047],{"mathvariant":28788},[1793,31542,1795],{},[1688,31544,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[21003,31546,31547],{},[1777,31548,31549],{"scriptlevel":1779,"displaystyle":1732},[895,31550,31551,31553,31555,31561,31563,31565,31571,31573,31575],{},[895,31552],{},[1688,31554,1690],{},[1788,31556,31557,31559],{},[898,31558,1872],{},[1793,31560,1806],{},[1688,31562,1954],{},[898,31564,16690],{},[1788,31566,31567,31569],{},[898,31568,1727],{},[1793,31570,1795],{},[1688,31572,1690],{},[1793,31574,1779],{},[1688,31576,1733],{"separator":1732},[21000,31578,31579,31591],{},[21003,31580,31581],{},[1777,31582,31583],{"scriptlevel":1779,"displaystyle":1732},[1814,31584,31585,31587,31589],{},[898,31586,10047],{"mathvariant":28788},[1793,31588,1806],{},[1688,31590,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[21003,31592,31593],{},[1777,31594,31595],{"scriptlevel":1779,"displaystyle":1732},[895,31596,31597,31599,31601,31607,31609,31611,31617,31619,31621],{},[895,31598],{},[1688,31600,1690],{},[1788,31602,31603,31605],{},[898,31604,1872],{},[1793,31606,1795],{},[1688,31608,1954],{},[898,31610,16690],{},[1788,31612,31613,31615],{},[898,31614,1727],{},[1793,31616,1806],{},[1688,31618,1690],{},[1793,31620,1779],{},[1688,31622,1733],{"separator":1732},[21000,31624,31625,31637],{},[21003,31626,31627],{},[1777,31628,31629],{"scriptlevel":1779,"displaystyle":1732},[1814,31630,31631,31633,31635],{},[898,31632,10047],{"mathvariant":28788},[898,31634,16690],{},[1688,31636,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[21003,31638,31639],{},[1777,31640,31641],{"scriptlevel":1779,"displaystyle":1732},[895,31642,31643,31645,31647,31649,31651,31657,31663,31665,31671,31677,31679],{},[895,31644],{},[1688,31646,1690],{},[898,31648,1854],{},[1688,31650,1954],{},[1788,31652,31653,31655],{},[898,31654,1727],{},[1793,31656,1795],{},[1788,31658,31659,31661],{},[898,31660,1872],{},[1793,31662,1795],{},[1688,31664,1954],{},[1788,31666,31667,31669],{},[898,31668,1727],{},[1793,31670,1806],{},[1788,31672,31673,31675],{},[898,31674,1872],{},[1793,31676,1806],{},[1688,31678,1690],{},[1793,31680,12708],{},[21003,31682],{"width":28316},[21003,31684,31685],{},[2041,31686,31687],{},"(6.17)",[902,31689,31690],{"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}",[724,31692,31693,31694,31722,31723,31751,31752,31820],{},"Z prvních dvou: ",[883,31695,31697],{"className":31696},[886],[888,31698,31699],{"xmlns":890},[892,31700,31701,31719],{},[895,31702,31703,31709,31711,31717],{},[1788,31704,31705,31707],{},[898,31706,1872],{},[1793,31708,1806],{},[1688,31710,1690],{},[1788,31712,31713,31715],{},[898,31714,1727],{},[1793,31716,1795],{},[898,31718,16690],{},[902,31720,31721],{"encoding":904},"Q_2 = P_1 \\lambda"," (6.18), ",[883,31724,31726],{"className":31725},[886],[888,31727,31728],{"xmlns":890},[892,31729,31730,31748],{},[895,31731,31732,31738,31740,31746],{},[1788,31733,31734,31736],{},[898,31735,1872],{},[1793,31737,1795],{},[1688,31739,1690],{},[1788,31741,31742,31744],{},[898,31743,1727],{},[1793,31745,1806],{},[898,31747,16690],{},[902,31749,31750],{"encoding":904},"Q_1 = P_2 \\lambda"," (6.19). Dosazením do třetí ",[883,31753,31755],{"className":31754},[886],[888,31756,31757],{"xmlns":890},[892,31758,31759,31817],{},[895,31760,31761,31763,31765,31771,31773,31779,31781,31783,31789,31791,31797,31799,31801,31803,31809,31815],{},[898,31762,1854],{},[1688,31764,1690],{},[1788,31766,31767,31769],{},[898,31768,1727],{},[1793,31770,1795],{},[1688,31772,3434],{},[1788,31774,31775,31777],{},[898,31776,1727],{},[1793,31778,1806],{},[898,31780,16690],{},[1688,31782,1696],{},[1788,31784,31785,31787],{},[898,31786,1727],{},[1793,31788,1806],{},[1688,31790,3434],{},[1788,31792,31793,31795],{},[898,31794,1727],{},[1793,31796,1795],{},[898,31798,16690],{},[1688,31800,1690],{},[1793,31802,1806],{},[1788,31804,31805,31807],{},[898,31806,1727],{},[1793,31808,1795],{},[1788,31810,31811,31813],{},[898,31812,1727],{},[1793,31814,1806],{},[898,31816,16690],{},[902,31818,31819],{"encoding":904},"Y = P_1 \\cdot P_2 \\lambda + P_2 \\cdot P_1 \\lambda = 2 P_1 P_2 \\lambda",", odtud",[883,31822,31824],{"className":31823},[886],[888,31825,31826],{"xmlns":890,"display":28306},[892,31827,31828,31871],{},[20995,31829,31830],{"width":28311},[21000,31831,31832,31834,31864,31866],{},[21003,31833],{"width":28316},[21003,31835,31836],{},[895,31837,31838,31840,31842,31862],{},[898,31839,16690],{},[1688,31841,1690],{},[1781,31843,31844,31846],{},[898,31845,1854],{},[895,31847,31848,31850,31856],{},[1793,31849,1806],{},[1788,31851,31852,31854],{},[898,31853,1727],{},[1793,31855,1795],{},[1788,31857,31858,31860],{},[898,31859,1727],{},[1793,31861,1806],{},[898,31863,2263],{"mathvariant":1822},[21003,31865],{"width":28316},[21003,31867,31868],{},[2041,31869,31870],{},"(6.20)",[902,31872,31873],{"encoding":904},"\\lambda = \\frac{Y}{2 P_1 P_2}. \\tag{6.20}",[724,31875,31876],{},"Zpětně:",[883,31878,31880],{"className":31879},[886],[888,31881,31882],{"xmlns":890,"display":28306},[892,31883,31884,31961],{},[20995,31885,31886],{"width":28311},[21000,31887,31888,31890,31954,31956],{},[21003,31889],{"width":28316},[21003,31891,31892],{},[13080,31893,31894],{"notation":13082},[1777,31895,31896],{"scriptlevel":1779,"displaystyle":2065},[1777,31897,31898],{"scriptlevel":1779,"displaystyle":2065},[1777,31899,31900],{"scriptlevel":1779,"displaystyle":1732},[895,31901,31902,31904,31910,31912,31926,31928,31930,31936,31938,31952],{},[2041,31903,4241],{},[1788,31905,31906,31908],{},[898,31907,1872],{},[1793,31909,1795],{},[1688,31911,1690],{},[1781,31913,31914,31916],{},[898,31915,1854],{},[895,31917,31918,31920],{},[1793,31919,1806],{},[1788,31921,31922,31924],{},[898,31923,1727],{},[1793,31925,1795],{},[1688,31927,1733],{"separator":1732},[6134,31929],{"width":15531},[1788,31931,31932,31934],{},[898,31933,1872],{},[1793,31935,1806],{},[1688,31937,1690],{},[1781,31939,31940,31942],{},[898,31941,1854],{},[895,31943,31944,31946],{},[1793,31945,1806],{},[1788,31947,31948,31950],{},[898,31949,1727],{},[1793,31951,1806],{},[2041,31953,4241],{},[21003,31955],{"width":28316},[21003,31957,31958],{},[2041,31959,31960],{},"(6.21)",[902,31962,31963],{"encoding":904},"\\boxed{\\; Q_1 = \\frac{Y}{2 P_1}, \\quad Q_2 = \\frac{Y}{2 P_2} \\;} \\tag{6.21}",[198,31965,31967],{"id":31966},"engelova-funkce","Engelova funkce",[724,31969,9916,31970,31973,31974,31977,31978,20108,31995,1343,32025,32055,32056,32090,32091,1343,32117,32143],{},[38,31971,31972],{},"pevné ceny"," a proměnný důchod se Marshallova poptávka stává ",[38,31975,31976],{},"Engelovou funkcí",": pro ",[883,31979,31981],{"className":31980},[886],[888,31982,31983],{"xmlns":890},[892,31984,31985,31993],{},[895,31986,31987,31989,31991],{},[898,31988,1854],{},[1688,31990,1690],{},[1793,31992,3347],{},[902,31994,20560],{"encoding":904},[883,31996,31998],{"className":31997},[886],[888,31999,32000],{"xmlns":890},[892,32001,32002,32022],{},[895,32003,32004,32010,32012,32014,32016],{},[1788,32005,32006,32008],{},[898,32007,1872],{},[1793,32009,1795],{},[1688,32011,1690],{},[1793,32013,3377],{},[898,32015,4930],{"mathvariant":1822},[1788,32017,32018,32020],{},[898,32019,1727],{},[1793,32021,1795],{},[902,32023,32024],{"encoding":904},"Q_1 = 50\u002FP_1",[883,32026,32028],{"className":32027},[886],[888,32029,32030],{"xmlns":890},[892,32031,32032,32052],{},[895,32033,32034,32040,32042,32044,32046],{},[1788,32035,32036,32038],{},[898,32037,1872],{},[1793,32039,1806],{},[1688,32041,1690],{},[1793,32043,3377],{},[898,32045,4930],{"mathvariant":1822},[1788,32047,32048,32050],{},[898,32049,1727],{},[1793,32051,1806],{},[902,32053,32054],{"encoding":904},"Q_2 = 50\u002FP_2",". Pro pevné ceny ",[883,32057,32059],{"className":32058},[886],[888,32060,32061],{"xmlns":890},[892,32062,32063,32087],{},[895,32064,32065,32071,32073,32075,32077,32083,32085],{},[1788,32066,32067,32069],{},[898,32068,1727],{},[1793,32070,1795],{},[1688,32072,1690],{},[1793,32074,3121],{},[1688,32076,1733],{"separator":1732},[1788,32078,32079,32081],{},[898,32080,1727],{},[1793,32082,1806],{},[1688,32084,1690],{},[1793,32086,9290],{},[902,32088,32089],{"encoding":904},"P_1 = 10, P_2 = 20"," dostáváme Engelovy funkce ",[883,32092,32094],{"className":32093},[886],[888,32095,32096],{"xmlns":890},[892,32097,32098,32114],{},[895,32099,32100,32106,32108,32110,32112],{},[1788,32101,32102,32104],{},[898,32103,1872],{},[1793,32105,1795],{},[1688,32107,1690],{},[898,32109,1854],{},[898,32111,4930],{"mathvariant":1822},[1793,32113,9290],{},[902,32115,32116],{"encoding":904},"Q_1 = Y\u002F20",[883,32118,32120],{"className":32119},[886],[888,32121,32122],{"xmlns":890},[892,32123,32124,32140],{},[895,32125,32126,32132,32134,32136,32138],{},[1788,32127,32128,32130],{},[898,32129,1872],{},[1793,32131,1806],{},[1688,32133,1690],{},[898,32135,1854],{},[898,32137,4930],{"mathvariant":1822},[1793,32139,5467],{},[902,32141,32142],{"encoding":904},"Q_2 = Y\u002F40"," — lineární závislost spotřebovaného množství na důchodu.",[115,32145,32147],{"id":32146},"duální-úloha-minimalizace-výdajů","Duální úloha — minimalizace výdajů",[724,32149,32150],{},"Výdaje spotřebitele jsou",[883,32152,32154],{"className":32153},[886],[888,32155,32156],{"xmlns":890,"display":28306},[892,32157,32158,32233],{},[20995,32159,32160],{"width":28311},[21000,32161,32162,32164,32226,32228],{},[21003,32163],{"width":28316},[21003,32165,32166],{},[895,32167,32168,32170,32172,32174,32176,32182,32184,32190,32192,32194,32202,32208,32210,32218,32224],{},[898,32169,4509],{},[1688,32171,1690],{},[898,32173,4509],{},[1688,32175,2066],{"stretchy":2065},[1788,32177,32178,32180],{},[898,32179,1872],{},[1793,32181,1795],{},[1688,32183,1733],{"separator":1732},[1788,32185,32186,32188],{},[898,32187,1872],{},[1793,32189,1806],{},[1688,32191,2076],{"stretchy":2065},[1688,32193,1690],{},[1814,32195,32196,32198,32200],{},[898,32197,1727],{},[1793,32199,1795],{},[1688,32201,1857],{},[1788,32203,32204,32206],{},[898,32205,1872],{},[1793,32207,1795],{},[1688,32209,1696],{},[1814,32211,32212,32214,32216],{},[898,32213,1727],{},[1793,32215,1806],{},[1688,32217,1857],{},[1788,32219,32220,32222],{},[898,32221,1872],{},[1793,32223,1806],{},[1688,32225,1733],{"separator":1732},[21003,32227],{"width":28316},[21003,32229,32230],{},[2041,32231,32232],{},"(6.22)",[902,32234,32235],{"encoding":904},"E = E(Q_1, Q_2) = P_1^* Q_1 + P_2^* Q_2, \\tag{6.22}",[724,32237,32238],{},"a je pevně zadána hladina užitečnosti",[883,32240,32242],{"className":32241},[886],[888,32243,32244],{"xmlns":890,"display":28306},[892,32245,32246,32293],{},[20995,32247,32248],{"width":28311},[21000,32249,32250,32252,32286,32288],{},[21003,32251],{"width":28316},[21003,32253,32254],{},[895,32255,32256,32262,32264,32266,32268,32274,32276,32282,32284],{},[1850,32257,32258,32260],{},[898,32259,900],{},[1688,32261,1857],{},[1688,32263,1690],{},[898,32265,900],{},[1688,32267,2066],{"stretchy":2065},[1788,32269,32270,32272],{},[898,32271,1872],{},[1793,32273,1795],{},[1688,32275,1733],{"separator":1732},[1788,32277,32278,32280],{},[898,32279,1872],{},[1793,32281,1806],{},[1688,32283,2076],{"stretchy":2065},[898,32285,2263],{"mathvariant":1822},[21003,32287],{"width":28316},[21003,32289,32290],{},[2041,32291,32292],{},"(6.23)",[902,32294,32295],{"encoding":904},"U^* = U(Q_1, Q_2). \\tag{6.23}",[724,32297,32298,32301,32302,32334,32335,2263],{},[38,32299,32300],{},"Úlohou o minimalizaci výdajů"," je najít minimum ",[883,32303,32305],{"className":32304},[886],[888,32306,32307],{"xmlns":890},[892,32308,32309,32331],{},[895,32310,32311,32313,32315,32321,32323,32329],{},[898,32312,4509],{},[1688,32314,2066],{"stretchy":2065},[1788,32316,32317,32319],{},[898,32318,1872],{},[1793,32320,1795],{},[1688,32322,1733],{"separator":1732},[1788,32324,32325,32327],{},[898,32326,1872],{},[1793,32328,1806],{},[1688,32330,2076],{"stretchy":2065},[902,32332,32333],{"encoding":904},"E(Q_1, Q_2)"," vázané podmínkou (6.23) ve tvaru ",[883,32336,32338],{"className":32337},[886],[888,32339,32340],{"xmlns":890},[892,32341,32342,32398],{},[895,32343,32344,32346,32348,32354,32356,32362,32364,32366,32372,32374,32376,32378,32384,32386,32392,32394,32396],{},[898,32345,11292],{},[1688,32347,2066],{"stretchy":2065},[1788,32349,32350,32352],{},[898,32351,1872],{},[1793,32353,1795],{},[1688,32355,1733],{"separator":1732},[1788,32357,32358,32360],{},[898,32359,1872],{},[1793,32361,1806],{},[1688,32363,2076],{"stretchy":2065},[1688,32365,1690],{},[1850,32367,32368,32370],{},[898,32369,900],{},[1688,32371,1857],{},[1688,32373,1954],{},[898,32375,900],{},[1688,32377,2066],{"stretchy":2065},[1788,32379,32380,32382],{},[898,32381,1872],{},[1793,32383,1795],{},[1688,32385,1733],{"separator":1732},[1788,32387,32388,32390],{},[898,32389,1872],{},[1793,32391,1806],{},[1688,32393,2076],{"stretchy":2065},[1688,32395,1690],{},[1793,32397,1779],{},[902,32399,32400],{"encoding":904},"g(Q_1, Q_2) = U^* - U(Q_1, Q_2) = 0",[198,32402,32404],{"id":32403},"lagrangeova-funkce","Lagrangeova funkce",[883,32406,32408],{"className":32407},[886],[888,32409,32410],{"xmlns":890,"display":28306},[892,32411,32412,32523],{},[20995,32413,32414],{"width":28311},[21000,32415,32416,32418,32516,32518],{},[21003,32417],{"width":28316},[21003,32419,32420],{},[895,32421,32422,32424,32426,32432,32434,32440,32442,32444,32446,32448,32456,32462,32464,32472,32478,32480,32482,32484,32490,32492,32494,32496,32502,32504,32510,32512,32514],{},[898,32423,10047],{"mathvariant":28788},[1688,32425,2066],{"stretchy":2065},[1788,32427,32428,32430],{},[898,32429,1872],{},[1793,32431,1795],{},[1688,32433,1733],{"separator":1732},[1788,32435,32436,32438],{},[898,32437,1872],{},[1793,32439,1806],{},[1688,32441,1733],{"separator":1732},[898,32443,16690],{},[1688,32445,2076],{"stretchy":2065},[1688,32447,1690],{},[1814,32449,32450,32452,32454],{},[898,32451,1727],{},[1793,32453,1795],{},[1688,32455,1857],{},[1788,32457,32458,32460],{},[898,32459,1872],{},[1793,32461,1795],{},[1688,32463,1696],{},[1814,32465,32466,32468,32470],{},[898,32467,1727],{},[1793,32469,1806],{},[1688,32471,1857],{},[1788,32473,32474,32476],{},[898,32475,1872],{},[1793,32477,1806],{},[1688,32479,1696],{},[898,32481,16690],{},[1688,32483,2066],{"stretchy":2065},[1850,32485,32486,32488],{},[898,32487,900],{},[1688,32489,1857],{},[1688,32491,1954],{},[898,32493,900],{},[1688,32495,2066],{"stretchy":2065},[1788,32497,32498,32500],{},[898,32499,1872],{},[1793,32501,1795],{},[1688,32503,1733],{"separator":1732},[1788,32505,32506,32508],{},[898,32507,1872],{},[1793,32509,1806],{},[1688,32511,2076],{"stretchy":2065},[1688,32513,2076],{"stretchy":2065},[898,32515,2263],{"mathvariant":1822},[21003,32517],{"width":28316},[21003,32519,32520],{},[2041,32521,32522],{},"(6.24)",[902,32524,32525],{"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}",[724,32527,32528],{},"Soustava podmínek prvního řádu:",[883,32530,32532],{"className":32531},[886],[888,32533,32534],{"xmlns":890,"display":28306},[892,32535,32536,32709],{},[20995,32537,32538],{"width":28311},[21000,32539,32540,32542,32702,32704],{},[21003,32541],{"width":28316},[21003,32543,32544],{},[20995,32545,32546,32596,32646],{"rowspacing":20997,"columnalign":20998,"columnspacing":1823},[21000,32547,32548,32560],{},[21003,32549,32550],{},[1777,32551,32552],{"scriptlevel":1779,"displaystyle":1732},[1814,32553,32554,32556,32558],{},[898,32555,10047],{"mathvariant":28788},[1793,32557,1795],{},[1688,32559,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[21003,32561,32562],{},[1777,32563,32564],{"scriptlevel":1779,"displaystyle":1732},[895,32565,32566,32568,32570,32578,32580,32582,32590,32592,32594],{},[895,32567],{},[1688,32569,1690],{},[1814,32571,32572,32574,32576],{},[898,32573,1727],{},[1793,32575,1795],{},[1688,32577,1857],{},[1688,32579,1954],{},[898,32581,16690],{},[1814,32583,32584,32586,32588],{},[898,32585,900],{},[1793,32587,1795],{},[1688,32589,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,32591,1690],{},[1793,32593,1779],{},[1688,32595,1733],{"separator":1732},[21000,32597,32598,32610],{},[21003,32599,32600],{},[1777,32601,32602],{"scriptlevel":1779,"displaystyle":1732},[1814,32603,32604,32606,32608],{},[898,32605,10047],{"mathvariant":28788},[1793,32607,1806],{},[1688,32609,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[21003,32611,32612],{},[1777,32613,32614],{"scriptlevel":1779,"displaystyle":1732},[895,32615,32616,32618,32620,32628,32630,32632,32640,32642,32644],{},[895,32617],{},[1688,32619,1690],{},[1814,32621,32622,32624,32626],{},[898,32623,1727],{},[1793,32625,1806],{},[1688,32627,1857],{},[1688,32629,1954],{},[898,32631,16690],{},[1814,32633,32634,32636,32638],{},[898,32635,900],{},[1793,32637,1806],{},[1688,32639,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,32641,1690],{},[1793,32643,1779],{},[1688,32645,1733],{"separator":1732},[21000,32647,32648,32660],{},[21003,32649,32650],{},[1777,32651,32652],{"scriptlevel":1779,"displaystyle":1732},[1814,32653,32654,32656,32658],{},[898,32655,10047],{"mathvariant":28788},[898,32657,16690],{},[1688,32659,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[21003,32661,32662],{},[1777,32663,32664],{"scriptlevel":1779,"displaystyle":1732},[895,32665,32666,32668,32670,32676,32678,32680,32682,32688,32690,32696,32698,32700],{},[895,32667],{},[1688,32669,1690],{},[1850,32671,32672,32674],{},[898,32673,900],{},[1688,32675,1857],{},[1688,32677,1954],{},[898,32679,900],{},[1688,32681,2066],{"stretchy":2065},[1788,32683,32684,32686],{},[898,32685,1872],{},[1793,32687,1795],{},[1688,32689,1733],{"separator":1732},[1788,32691,32692,32694],{},[898,32693,1872],{},[1793,32695,1806],{},[1688,32697,2076],{"stretchy":2065},[1688,32699,1690],{},[1793,32701,12708],{},[21003,32703],{"width":28316},[21003,32705,32706],{},[2041,32707,32708],{},"(6.25)",[902,32710,32711],{"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}",[724,32713,32714],{},"Postačující podmínka pro minimum (vzhledem k linearitě funkce výdajů) má tvar",[883,32716,32718],{"className":32717},[886],[888,32719,32720],{"xmlns":890,"display":28306},[892,32721,32722,32820],{},[20995,32723,32724],{"width":28311},[21000,32725,32726,32728,32813,32815],{},[21003,32727],{"width":28316},[21003,32729,32730],{},[895,32731,32732,32734,32736,32742,32744,32750,32752,32754,32756,32758,32760,32762,32811],{},[898,32733,4440],{},[1688,32735,2066],{"stretchy":2065},[1788,32737,32738,32740],{},[898,32739,1872],{},[1793,32741,1795],{},[1688,32743,1733],{"separator":1732},[1788,32745,32746,32748],{},[898,32747,1872],{},[1793,32749,1806],{},[1688,32751,1733],{"separator":1732},[898,32753,16690],{},[1688,32755,2076],{"stretchy":2065},[1688,32757,1690],{},[1688,32759,1954],{},[898,32761,16690],{},[895,32763,32764,32766,32778,32780,32793,32795,32797,32809],{},[1688,32765,2066],{"fence":1732},[1814,32767,32768,32770,32772],{},[898,32769,900],{},[1793,32771,3162],{},[895,32773,32774,32776],{},[1688,32775,1824],{"mathvariant":1822},[1688,32777,1824],{"mathvariant":1822},[1688,32779,1696],{},[1814,32781,32782,32784,32787],{},[898,32783,900],{},[1793,32785,32786],{},"22",[895,32788,32789,32791],{},[1688,32790,1824],{"mathvariant":1822},[1688,32792,1824],{"mathvariant":1822},[1688,32794,1696],{},[1793,32796,1806],{},[1814,32798,32799,32801,32803],{},[898,32800,900],{},[1793,32802,3766],{},[895,32804,32805,32807],{},[1688,32806,1824],{"mathvariant":1822},[1688,32808,1824],{"mathvariant":1822},[1688,32810,2076],{"fence":1732},[898,32812,2263],{"mathvariant":1822},[21003,32814],{"width":28316},[21003,32816,32817],{},[2041,32818,32819],{},"(6.26)",[902,32821,32822],{"encoding":904},"D(Q_1, Q_2, \\lambda) = -\\lambda \\left(U''_{11} + U''_{22} + 2 U''_{12}\\right). \\tag{6.26}",[724,32824,32825,32828,32829,32868,32869,32908,32909,32959,32960,32986,32987,33004,33005,33031],{},[38,32826,32827],{},"Geometrie (obrázek 6.9)."," Řešením je bod ",[883,32830,32832],{"className":32831},[886],[888,32833,32834],{"xmlns":890},[892,32835,32836,32866],{},[895,32837,32838,32844,32846,32854,32856,32864],{},[1850,32839,32840,32842],{},[898,32841,1872],{},[1688,32843,1857],{},[1688,32845,2748],{"stretchy":2065},[1814,32847,32848,32850,32852],{},[898,32849,1872],{},[1793,32851,1795],{},[1688,32853,1857],{},[1688,32855,1733],{"separator":1732},[1814,32857,32858,32860,32862],{},[898,32859,1872],{},[1793,32861,1806],{},[1688,32863,1857],{},[1688,32865,2763],{"stretchy":2065},[902,32867,28567],{"encoding":904}," dotyku křivky užitečnosti ",[883,32870,32872],{"className":32871},[886],[888,32873,32874],{"xmlns":890},[892,32875,32876,32906],{},[895,32877,32878,32884,32886,32888,32890,32896,32898,32904],{},[1850,32879,32880,32882],{},[898,32881,900],{},[1688,32883,1857],{},[1688,32885,1690],{},[898,32887,900],{},[1688,32889,2066],{"stretchy":2065},[1788,32891,32892,32894],{},[898,32893,1872],{},[1793,32895,1795],{},[1688,32897,1733],{"separator":1732},[1788,32899,32900,32902],{},[898,32901,1872],{},[1793,32903,1806],{},[1688,32905,2076],{"stretchy":2065},[902,32907,17910],{"encoding":904}," s přímkou výdajů ",[883,32910,32912],{"className":32911},[886],[888,32913,32914],{"xmlns":890},[892,32915,32916,32956],{},[895,32917,32918,32924,32926,32934,32940,32942,32950],{},[1850,32919,32920,32922],{},[898,32921,4509],{},[1688,32923,1857],{},[1688,32925,1690],{},[1814,32927,32928,32930,32932],{},[898,32929,1727],{},[1793,32931,1795],{},[1688,32933,1857],{},[1788,32935,32936,32938],{},[898,32937,1872],{},[1793,32939,1795],{},[1688,32941,1696],{},[1814,32943,32944,32946,32948],{},[898,32945,1727],{},[1793,32947,1806],{},[1688,32949,1857],{},[1788,32951,32952,32954],{},[898,32953,1872],{},[1793,32955,1806],{},[902,32957,32958],{"encoding":904},"E^* = P_1^* Q_1 + P_2^* Q_2",". Hladina ",[883,32961,32963],{"className":32962},[886],[888,32964,32965],{"xmlns":890},[892,32966,32967,32983],{},[895,32968,32969,32975,32977],{},[1788,32970,32971,32973],{},[898,32972,4509],{},[1793,32974,1779],{},[1688,32976,3704],{},[1850,32978,32979,32981],{},[898,32980,4509],{},[1688,32982,1857],{},[902,32984,32985],{"encoding":904},"E_0 \u003C E^*"," nestačí k dosažení ",[883,32988,32990],{"className":32989},[886],[888,32991,32992],{"xmlns":890},[892,32993,32994,33002],{},[895,32995,32996],{},[1850,32997,32998,33000],{},[898,32999,900],{},[1688,33001,1857],{},[902,33003,28202],{"encoding":904},", hladina ",[883,33006,33008],{"className":33007},[886],[888,33009,33010],{"xmlns":890},[892,33011,33012,33028],{},[895,33013,33014,33020,33022],{},[1788,33015,33016,33018],{},[898,33017,4509],{},[1793,33019,1795],{},[1688,33021,3665],{},[1850,33023,33024,33026],{},[898,33025,4509],{},[1688,33027,1857],{},[902,33029,33030],{"encoding":904},"E_1 > E^*"," je nadbytečná.",[4124,33033,33034,33039],{},[724,33035,33036,33038],{},[883,33037,4828],{}," Postup — duální úloha (minimalizace výdajů)",[152,33040,33041,33091,33177,33217,33292],{},[123,33042,33043,2170,33046,33090],{},[38,33044,33045],{},"Zapiš vazbu",[883,33047,33049],{"className":33048},[886],[888,33050,33051],{"xmlns":890},[892,33052,33053,33087],{},[895,33054,33055,33061,33063,33065,33067,33073,33075,33081,33083,33085],{},[1850,33056,33057,33059],{},[898,33058,900],{},[1688,33060,1857],{},[1688,33062,1954],{},[898,33064,900],{},[1688,33066,2066],{"stretchy":2065},[1788,33068,33069,33071],{},[898,33070,1872],{},[1793,33072,1795],{},[1688,33074,1733],{"separator":1732},[1788,33076,33077,33079],{},[898,33078,1872],{},[1793,33080,1806],{},[1688,33082,2076],{"stretchy":2065},[1688,33084,1690],{},[1793,33086,1779],{},[902,33088,33089],{"encoding":904},"U^* - U(Q_1, Q_2) = 0"," (zadaná hladina užitečnosti).",[123,33092,33093,2170,33095,2263],{},[38,33094,29500],{},[883,33096,33098],{"className":33097},[886],[888,33099,33100],{"xmlns":890},[892,33101,33102,33174],{},[895,33103,33104,33106,33108,33116,33122,33124,33132,33138,33140,33142,33144,33150,33152,33154,33156,33162,33164,33170,33172],{},[898,33105,10047],{"mathvariant":28788},[1688,33107,1690],{},[1814,33109,33110,33112,33114],{},[898,33111,1727],{},[1793,33113,1795],{},[1688,33115,1857],{},[1788,33117,33118,33120],{},[898,33119,1872],{},[1793,33121,1795],{},[1688,33123,1696],{},[1814,33125,33126,33128,33130],{},[898,33127,1727],{},[1793,33129,1806],{},[1688,33131,1857],{},[1788,33133,33134,33136],{},[898,33135,1872],{},[1793,33137,1806],{},[1688,33139,1696],{},[898,33141,16690],{},[1688,33143,2066],{"stretchy":2065},[1850,33145,33146,33148],{},[898,33147,900],{},[1688,33149,1857],{},[1688,33151,1954],{},[898,33153,900],{},[1688,33155,2066],{"stretchy":2065},[1788,33157,33158,33160],{},[898,33159,1872],{},[1793,33161,1795],{},[1688,33163,1733],{"separator":1732},[1788,33165,33166,33168],{},[898,33167,1872],{},[1793,33169,1806],{},[1688,33171,2076],{"stretchy":2065},[1688,33173,2076],{"stretchy":2065},[902,33175,33176],{"encoding":904},"\\mathcal{L} = P_1^* Q_1 + P_2^* Q_2 + \\lambda(U^* - U(Q_1, Q_2))",[123,33178,33179,33182,33183,33216],{},[38,33180,33181],{},"Derivace rovny nule",", z prvních dvou rovnic podílem dostaneš podmínku ",[883,33184,33186],{"className":33185},[886],[888,33187,33188],{"xmlns":890},[892,33189,33190,33214],{},[895,33191,33192,33194,33196,33204,33206],{},[2041,33193,1670],{},[1688,33195,1690],{},[1814,33197,33198,33200,33202],{},[898,33199,1727],{},[1793,33201,1795],{},[1688,33203,1857],{},[898,33205,4930],{"mathvariant":1822},[1814,33207,33208,33210,33212],{},[898,33209,1727],{},[1793,33211,1806],{},[1688,33213,1857],{},[902,33215,29219],{"encoding":904}," (stejná jako u maximalizace!).",[123,33218,33219,2170,33222,33262,33263,2263],{},[38,33220,33221],{},"Dosaď do vazby",[883,33223,33225],{"className":33224},[886],[888,33226,33227],{"xmlns":890},[892,33228,33229,33259],{},[895,33230,33231,33233,33235,33241,33243,33249,33251,33253],{},[898,33232,900],{},[1688,33234,2066],{"stretchy":2065},[1788,33236,33237,33239],{},[898,33238,1872],{},[1793,33240,1795],{},[1688,33242,1733],{"separator":1732},[1788,33244,33245,33247],{},[898,33246,1872],{},[1793,33248,1806],{},[1688,33250,2076],{"stretchy":2065},[1688,33252,1690],{},[1850,33254,33255,33257],{},[898,33256,900],{},[1688,33258,1857],{},[902,33260,33261],{"encoding":904},"U(Q_1, Q_2) = U^*"," a vyřeš pro ",[883,33264,33266],{"className":33265},[886],[888,33267,33268],{"xmlns":890},[892,33269,33270,33290],{},[895,33271,33272,33280,33282],{},[1814,33273,33274,33276,33278],{},[898,33275,1872],{},[1793,33277,1795],{},[1688,33279,1857],{},[1688,33281,1733],{"separator":1732},[1814,33283,33284,33286,33288],{},[898,33285,1872],{},[1793,33287,1806],{},[1688,33289,1857],{},[902,33291,29741],{"encoding":904},[123,33293,33294,2170,33297,33351],{},[38,33295,33296],{},"Vypočítej minimální výdaje",[883,33298,33300],{"className":33299},[886],[888,33301,33302],{"xmlns":890},[892,33303,33304,33348],{},[895,33305,33306,33312,33314,33322,33330,33332,33340],{},[1850,33307,33308,33310],{},[898,33309,4509],{},[1688,33311,1857],{},[1688,33313,1690],{},[1814,33315,33316,33318,33320],{},[898,33317,1727],{},[1793,33319,1795],{},[1688,33321,1857],{},[1814,33323,33324,33326,33328],{},[898,33325,1872],{},[1793,33327,1795],{},[1688,33329,1857],{},[1688,33331,1696],{},[1814,33333,33334,33336,33338],{},[898,33335,1727],{},[1793,33337,1806],{},[1688,33339,1857],{},[1814,33341,33342,33344,33346],{},[898,33343,1872],{},[1793,33345,1806],{},[1688,33347,1857],{},[902,33349,33350],{"encoding":904},"E^* = P_1^* Q_1^* + P_2^* Q_2^*"," a případně ověř druhou podmínku (6.26).",[115,33353,33355,33356],{"id":33354},"příklad-67-minimalizace-výdajů-pro-uq112q212u-q_112-q_212","Příklad 6.7 — minimalizace výdajů pro ",[883,33357,33359],{"className":33358},[886],[888,33360,33361],{"xmlns":890},[892,33362,33363,33397],{},[895,33364,33365,33367,33369,33383],{},[898,33366,900],{},[1688,33368,1690],{},[1814,33370,33371,33373,33375],{},[898,33372,1872],{},[1793,33374,1795],{},[895,33376,33377,33379,33381],{},[1793,33378,1795],{},[898,33380,4930],{"mathvariant":1822},[1793,33382,1806],{},[1814,33384,33385,33387,33389],{},[898,33386,1872],{},[1793,33388,1806],{},[895,33390,33391,33393,33395],{},[1793,33392,1795],{},[898,33394,4930],{"mathvariant":1822},[1793,33396,1806],{},[902,33398,33399],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F2}",[724,33401,33402,33403,1343,33425,1343,33449,30586],{},"Dáno ",[883,33404,33406],{"className":33405},[886],[888,33407,33408],{"xmlns":890},[892,33409,33410,33422],{},[895,33411,33412,33418,33420],{},[1850,33413,33414,33416],{},[898,33415,900],{},[1688,33417,1857],{},[1688,33419,1690],{},[1793,33421,1806],{},[902,33423,33424],{"encoding":904},"U^* = 2",[883,33426,33428],{"className":33427},[886],[888,33429,33430],{"xmlns":890},[892,33431,33432,33446],{},[895,33433,33434,33442,33444],{},[1814,33435,33436,33438,33440],{},[898,33437,1727],{},[1793,33439,1795],{},[1688,33441,1857],{},[1688,33443,1690],{},[1793,33445,24030],{},[902,33447,33448],{"encoding":904},"P_1^* = 0{,}25",[883,33450,33452],{"className":33451},[886],[888,33453,33454],{"xmlns":890},[892,33455,33456,33470],{},[895,33457,33458,33466,33468],{},[1814,33459,33460,33462,33464],{},[898,33461,1727],{},[1793,33463,1806],{},[1688,33465,1857],{},[1688,33467,1690],{},[1793,33469,1795],{},[902,33471,33472],{"encoding":904},"P_2^* = 1",[883,33474,33476],{"className":33475},[886],[888,33477,33478],{"xmlns":890,"display":28306},[892,33479,33480,33544],{},[895,33481,33482,33484,33486,33488,33494,33496,33502,33504,33506,33508,33510,33512,33526,33540,33542],{},[898,33483,10047],{"mathvariant":28788},[1688,33485,1690],{},[1793,33487,24030],{},[1788,33489,33490,33492],{},[898,33491,1872],{},[1793,33493,1795],{},[1688,33495,1696],{},[1788,33497,33498,33500],{},[898,33499,1872],{},[1793,33501,1806],{},[1688,33503,1696],{},[898,33505,16690],{},[1688,33507,2066],{"stretchy":2065},[1793,33509,1806],{},[1688,33511,1954],{},[1814,33513,33514,33516,33518],{},[898,33515,1872],{},[1793,33517,1795],{},[895,33519,33520,33522,33524],{},[1793,33521,1795],{},[898,33523,4930],{"mathvariant":1822},[1793,33525,1806],{},[1814,33527,33528,33530,33532],{},[898,33529,1872],{},[1793,33531,1806],{},[895,33533,33534,33536,33538],{},[1793,33535,1795],{},[898,33537,4930],{"mathvariant":1822},[1793,33539,1806],{},[1688,33541,2076],{"stretchy":2065},[898,33543,2263],{"mathvariant":1822},[902,33545,33546],{"encoding":904},"\\mathcal{L} = 0{,}25 Q_1 + Q_2 + \\lambda(2 - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,33548,30671],{},[883,33550,33552],{"className":33551},[886],[888,33553,33554],{"xmlns":890,"display":28306},[892,33555,33556,33770],{},[20995,33557,33558,33634,33710],{"rowspacing":20997,"columnalign":20998,"columnspacing":1823},[21000,33559,33560,33572],{},[21003,33561,33562],{},[1777,33563,33564],{"scriptlevel":1779,"displaystyle":1732},[1814,33565,33566,33568,33570],{},[898,33567,10047],{"mathvariant":28788},[1793,33569,1795],{},[1688,33571,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[21003,33573,33574],{},[1777,33575,33576],{"scriptlevel":1779,"displaystyle":1732},[895,33577,33578,33580,33582,33584,33586,33588,33590,33598,33614,33628,33630,33632],{},[895,33579],{},[1688,33581,1690],{},[1793,33583,24030],{},[1688,33585,1954],{},[898,33587,16690],{},[1688,33589,3434],{},[1777,33591,33592],{"scriptlevel":1779,"displaystyle":2065},[1781,33593,33594,33596],{},[1793,33595,1795],{},[1793,33597,1806],{},[1814,33599,33600,33602,33604],{},[898,33601,1872],{},[1793,33603,1795],{},[895,33605,33606,33608,33610,33612],{},[1688,33607,1954],{},[1793,33609,1795],{},[898,33611,4930],{"mathvariant":1822},[1793,33613,1806],{},[1814,33615,33616,33618,33620],{},[898,33617,1872],{},[1793,33619,1806],{},[895,33621,33622,33624,33626],{},[1793,33623,1795],{},[898,33625,4930],{"mathvariant":1822},[1793,33627,1806],{},[1688,33629,1690],{},[1793,33631,1779],{},[1688,33633,1733],{"separator":1732},[21000,33635,33636,33648],{},[21003,33637,33638],{},[1777,33639,33640],{"scriptlevel":1779,"displaystyle":1732},[1814,33641,33642,33644,33646],{},[898,33643,10047],{"mathvariant":28788},[1793,33645,1806],{},[1688,33647,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[21003,33649,33650],{},[1777,33651,33652],{"scriptlevel":1779,"displaystyle":1732},[895,33653,33654,33656,33658,33660,33662,33664,33666,33674,33688,33704,33706,33708],{},[895,33655],{},[1688,33657,1690],{},[1793,33659,1795],{},[1688,33661,1954],{},[898,33663,16690],{},[1688,33665,3434],{},[1777,33667,33668],{"scriptlevel":1779,"displaystyle":2065},[1781,33669,33670,33672],{},[1793,33671,1795],{},[1793,33673,1806],{},[1814,33675,33676,33678,33680],{},[898,33677,1872],{},[1793,33679,1795],{},[895,33681,33682,33684,33686],{},[1793,33683,1795],{},[898,33685,4930],{"mathvariant":1822},[1793,33687,1806],{},[1814,33689,33690,33692,33694],{},[898,33691,1872],{},[1793,33693,1806],{},[895,33695,33696,33698,33700,33702],{},[1688,33697,1954],{},[1793,33699,1795],{},[898,33701,4930],{"mathvariant":1822},[1793,33703,1806],{},[1688,33705,1690],{},[1793,33707,1779],{},[1688,33709,1733],{"separator":1732},[21000,33711,33712,33724],{},[21003,33713,33714],{},[1777,33715,33716],{"scriptlevel":1779,"displaystyle":1732},[1814,33717,33718,33720,33722],{},[898,33719,10047],{"mathvariant":28788},[898,33721,16690],{},[1688,33723,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[21003,33725,33726],{},[1777,33727,33728],{"scriptlevel":1779,"displaystyle":1732},[895,33729,33730,33732,33734,33736,33738,33752,33766,33768],{},[895,33731],{},[1688,33733,1690],{},[1793,33735,1806],{},[1688,33737,1954],{},[1814,33739,33740,33742,33744],{},[898,33741,1872],{},[1793,33743,1795],{},[895,33745,33746,33748,33750],{},[1793,33747,1795],{},[898,33749,4930],{"mathvariant":1822},[1793,33751,1806],{},[1814,33753,33754,33756,33758],{},[898,33755,1872],{},[1793,33757,1806],{},[895,33759,33760,33762,33764],{},[1793,33761,1795],{},[898,33763,4930],{"mathvariant":1822},[1793,33765,1806],{},[1688,33767,1690],{},[1793,33769,12708],{},[902,33771,33772],{"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}",[724,33774,33775,33776,17821,33806,33834,33835,5845,33897,1343,33947,33969,33970,2263],{},"Podílem prvních dvou rovnic: ",[883,33777,33779],{"className":33778},[886],[888,33780,33781],{"xmlns":890},[892,33782,33783,33803],{},[895,33784,33785,33787,33789,33795,33797],{},[1793,33786,24030],{},[1688,33788,1690],{},[1788,33790,33791,33793],{},[898,33792,1872],{},[1793,33794,1806],{},[898,33796,4930],{"mathvariant":1822},[1788,33798,33799,33801],{},[898,33800,1872],{},[1793,33802,1795],{},[902,33804,33805],{"encoding":904},"0{,}25 = Q_2 \u002F Q_1",[883,33807,33809],{"className":33808},[886],[888,33810,33811],{"xmlns":890},[892,33812,33813,33831],{},[895,33814,33815,33821,33823,33825],{},[1788,33816,33817,33819],{},[898,33818,1872],{},[1793,33820,1806],{},[1688,33822,1690],{},[1793,33824,24030],{},[1788,33826,33827,33829],{},[898,33828,1872],{},[1793,33830,1795],{},[902,33832,33833],{"encoding":904},"Q_2 = 0{,}25 Q_1",". Dosazením do třetí: ",[883,33836,33838],{"className":33837},[886],[888,33839,33840],{"xmlns":890},[892,33841,33842,33894],{},[895,33843,33844,33858,33860,33862,33868,33880,33882,33884,33890,33892],{},[1814,33845,33846,33848,33850],{},[898,33847,1872],{},[1793,33849,1795],{},[895,33851,33852,33854,33856],{},[1793,33853,1795],{},[898,33855,4930],{"mathvariant":1822},[1793,33857,1806],{},[1688,33859,2066],{"stretchy":2065},[1793,33861,24030],{},[1788,33863,33864,33866],{},[898,33865,1872],{},[1793,33867,1795],{},[1850,33869,33870,33872],{},[1688,33871,2076],{"stretchy":2065},[895,33873,33874,33876,33878],{},[1793,33875,1795],{},[898,33877,4930],{"mathvariant":1822},[1793,33879,1806],{},[1688,33881,1690],{},[1793,33883,5265],{},[1788,33885,33886,33888],{},[898,33887,1872],{},[1793,33889,1795],{},[1688,33891,1690],{},[1793,33893,1806],{},[902,33895,33896],{"encoding":904},"Q_1^{1\u002F2} (0{,}25 Q_1)^{1\u002F2} = 0{,}5 Q_1 = 2",[38,33898,33899,1343,33923],{},[883,33900,33902],{"className":33901},[886],[888,33903,33904],{"xmlns":890},[892,33905,33906,33920],{},[895,33907,33908,33916,33918],{},[1814,33909,33910,33912,33914],{},[898,33911,1872],{},[1793,33913,1795],{},[1688,33915,1857],{},[1688,33917,1690],{},[1793,33919,2616],{},[902,33921,33922],{"encoding":904},"Q_1^* = 4",[883,33924,33926],{"className":33925},[886],[888,33927,33928],{"xmlns":890},[892,33929,33930,33944],{},[895,33931,33932,33940,33942],{},[1814,33933,33934,33936,33938],{},[898,33935,1872],{},[1793,33937,1806],{},[1688,33939,1857],{},[1688,33941,1690],{},[1793,33943,1795],{},[902,33945,33946],{"encoding":904},"Q_2^* = 1",[883,33948,33950],{"className":33949},[886],[888,33951,33952],{"xmlns":890},[892,33953,33954,33966],{},[895,33955,33956,33962,33964],{},[1850,33957,33958,33960],{},[898,33959,16690],{},[1688,33961,1857],{},[1688,33963,1690],{},[1793,33965,1795],{},[902,33967,33968],{"encoding":904},"\\lambda^* = 1",". Minimální výdaje: ",[883,33971,33973],{"className":33972},[886],[888,33974,33975],{"xmlns":890},[892,33976,33977,34005],{},[895,33978,33979,33985,33987,33989,33991,33993,33995,33997,33999,34001,34003],{},[1850,33980,33981,33983],{},[898,33982,4509],{},[1688,33984,1857],{},[1688,33986,1690],{},[1793,33988,24030],{},[1688,33990,3434],{},[1793,33992,2616],{},[1688,33994,1696],{},[1793,33996,1795],{},[1688,33998,3434],{},[1793,34000,1795],{},[1688,34002,1690],{},[1793,34004,1806],{},[902,34006,34007],{"encoding":904},"E^* = 0{,}25 \\cdot 4 + 1 \\cdot 1 = 2",[724,34009,34010,34013,34014,1343,34080,1343,34146,34212,34213,34250,34251,34273,34274,2263],{},[614,34011,34012],{},"Ověření postačující podmínky"," (6.26): ",[883,34015,34017],{"className":34016},[886],[888,34018,34019],{"xmlns":890},[892,34020,34021,34077],{},[895,34022,34023,34035,34037,34039,34047,34063],{},[1814,34024,34025,34027,34029],{},[898,34026,900],{},[1793,34028,3162],{},[895,34030,34031,34033],{},[1688,34032,1824],{"mathvariant":1822},[1688,34034,1824],{"mathvariant":1822},[1688,34036,1690],{},[1688,34038,1954],{},[1777,34040,34041],{"scriptlevel":1779,"displaystyle":2065},[1781,34042,34043,34045],{},[1793,34044,1795],{},[1793,34046,2616],{},[1814,34048,34049,34051,34053],{},[898,34050,1872],{},[1793,34052,1795],{},[895,34054,34055,34057,34059,34061],{},[1688,34056,1954],{},[1793,34058,2131],{},[898,34060,4930],{"mathvariant":1822},[1793,34062,1806],{},[1814,34064,34065,34067,34069],{},[898,34066,1872],{},[1793,34068,1806],{},[895,34070,34071,34073,34075],{},[1793,34072,1795],{},[898,34074,4930],{"mathvariant":1822},[1793,34076,1806],{},[902,34078,34079],{"encoding":904},"U''_{11} = -\\tfrac{1}{4} Q_1^{-3\u002F2} Q_2^{1\u002F2}",[883,34081,34083],{"className":34082},[886],[888,34084,34085],{"xmlns":890},[892,34086,34087,34143],{},[895,34088,34089,34101,34103,34105,34113,34127],{},[1814,34090,34091,34093,34095],{},[898,34092,900],{},[1793,34094,32786],{},[895,34096,34097,34099],{},[1688,34098,1824],{"mathvariant":1822},[1688,34100,1824],{"mathvariant":1822},[1688,34102,1690],{},[1688,34104,1954],{},[1777,34106,34107],{"scriptlevel":1779,"displaystyle":2065},[1781,34108,34109,34111],{},[1793,34110,1795],{},[1793,34112,2616],{},[1814,34114,34115,34117,34119],{},[898,34116,1872],{},[1793,34118,1795],{},[895,34120,34121,34123,34125],{},[1793,34122,1795],{},[898,34124,4930],{"mathvariant":1822},[1793,34126,1806],{},[1814,34128,34129,34131,34133],{},[898,34130,1872],{},[1793,34132,1806],{},[895,34134,34135,34137,34139,34141],{},[1688,34136,1954],{},[1793,34138,2131],{},[898,34140,4930],{"mathvariant":1822},[1793,34142,1806],{},[902,34144,34145],{"encoding":904},"U''_{22} = -\\tfrac{1}{4} Q_1^{1\u002F2} Q_2^{-3\u002F2}",[883,34147,34149],{"className":34148},[886],[888,34150,34151],{"xmlns":890},[892,34152,34153,34209],{},[895,34154,34155,34167,34169,34177,34193],{},[1814,34156,34157,34159,34161],{},[898,34158,900],{},[1793,34160,3766],{},[895,34162,34163,34165],{},[1688,34164,1824],{"mathvariant":1822},[1688,34166,1824],{"mathvariant":1822},[1688,34168,1690],{},[1777,34170,34171],{"scriptlevel":1779,"displaystyle":2065},[1781,34172,34173,34175],{},[1793,34174,1795],{},[1793,34176,2616],{},[1814,34178,34179,34181,34183],{},[898,34180,1872],{},[1793,34182,1795],{},[895,34184,34185,34187,34189,34191],{},[1688,34186,1954],{},[1793,34188,1795],{},[898,34190,4930],{"mathvariant":1822},[1793,34192,1806],{},[1814,34194,34195,34197,34199],{},[898,34196,1872],{},[1793,34198,1806],{},[895,34200,34201,34203,34205,34207],{},[1688,34202,1954],{},[1793,34204,1795],{},[898,34206,4930],{"mathvariant":1822},[1793,34208,1806],{},[902,34210,34211],{"encoding":904},"U''_{12} = \\tfrac{1}{4} Q_1^{-1\u002F2} Q_2^{-1\u002F2}",". Po dosazení ",[883,34214,34216],{"className":34215},[886],[888,34217,34218],{"xmlns":890},[892,34219,34220,34247],{},[895,34221,34222,34224,34226,34228,34230,34232,34234,34236,34238,34240,34243,34245],{},[898,34223,4440],{},[1688,34225,2066],{"stretchy":2065},[1793,34227,2616],{},[1688,34229,1733],{"separator":1732},[1793,34231,1795],{},[1688,34233,1733],{"separator":1732},[1793,34235,1795],{},[1688,34237,2076],{"stretchy":2065},[1688,34239,1690],{},[1793,34241,34242],{},"0,28125",[1688,34244,3665],{},[1793,34246,1779],{},[902,34248,34249],{"encoding":904},"D(4, 1, 1) = 0{,}28125 > 0"," — v bodě ",[883,34252,34254],{"className":34253},[886],[888,34255,34256],{"xmlns":890},[892,34257,34258,34270],{},[895,34259,34260,34262,34264,34266,34268],{},[1688,34261,2748],{"stretchy":2065},[1793,34263,2616],{},[1688,34265,1733],{"separator":1732},[1793,34267,1795],{},[1688,34269,2763],{"stretchy":2065},[902,34271,34272],{"encoding":904},"[4, 1]"," je vázané ",[38,34275,4032],{},[115,34277,34279],{"id":34278},"poptávka-minimalizující-výdaje-hicksova","Poptávka minimalizující výdaje (Hicksova)",[724,34281,34282],{},"Obecně:",[883,34284,34286],{"className":34285},[886],[888,34287,34288],{"xmlns":890,"display":28306},[892,34289,34290,34385],{},[20995,34291,34292],{"width":28311},[21000,34293,34294,34296,34378,34380],{},[21003,34295],{"width":28316},[21003,34297,34298],{},[895,34299,34300,34306,34308,34314,34316,34322,34324,34330,34332,34334,34336,34338,34340,34346,34348,34354,34356,34362,34364,34370,34372,34374,34376],{},[1788,34301,34302,34304],{},[898,34303,1872],{},[1793,34305,1795],{},[1688,34307,1690],{},[1788,34309,34310,34312],{},[898,34311,4440],{},[1793,34313,1795],{},[1688,34315,2066],{"stretchy":2065},[1788,34317,34318,34320],{},[898,34319,1727],{},[1793,34321,1795],{},[1688,34323,1733],{"separator":1732},[1788,34325,34326,34328],{},[898,34327,1727],{},[1793,34329,1806],{},[1688,34331,1733],{"separator":1732},[898,34333,900],{},[1688,34335,2076],{"stretchy":2065},[1688,34337,1733],{"separator":1732},[6134,34339],{"width":15531},[1788,34341,34342,34344],{},[898,34343,1872],{},[1793,34345,1806],{},[1688,34347,1690],{},[1788,34349,34350,34352],{},[898,34351,4440],{},[1793,34353,1806],{},[1688,34355,2066],{"stretchy":2065},[1788,34357,34358,34360],{},[898,34359,1727],{},[1793,34361,1795],{},[1688,34363,1733],{"separator":1732},[1788,34365,34366,34368],{},[898,34367,1727],{},[1793,34369,1806],{},[1688,34371,1733],{"separator":1732},[898,34373,900],{},[1688,34375,2076],{"stretchy":2065},[1688,34377,1733],{"separator":1732},[21003,34379],{"width":28316},[21003,34381,34382],{},[2041,34383,34384],{},"(6.27)",[902,34386,34387],{"encoding":904},"Q_1 = D_1(P_1, P_2, U), \\quad Q_2 = D_2(P_1, P_2, U), \\tag{6.27}",[883,34389,34391],{"className":34390},[886],[888,34392,34393],{"xmlns":890,"display":28306},[892,34394,34395,34442],{},[20995,34396,34397],{"width":28311},[21000,34398,34399,34401,34435,34437],{},[21003,34400],{"width":28316},[21003,34402,34403],{},[895,34404,34405,34407,34409,34411,34413,34419,34421,34427,34429,34431,34433],{},[898,34406,16690],{},[1688,34408,1690],{},[898,34410,16690],{},[1688,34412,2066],{"stretchy":2065},[1788,34414,34415,34417],{},[898,34416,1727],{},[1793,34418,1795],{},[1688,34420,1733],{"separator":1732},[1788,34422,34423,34425],{},[898,34424,1727],{},[1793,34426,1806],{},[1688,34428,1733],{"separator":1732},[898,34430,900],{},[1688,34432,2076],{"stretchy":2065},[898,34434,2263],{"mathvariant":1822},[21003,34436],{"width":28316},[21003,34438,34439],{},[2041,34440,34441],{},"(6.28)",[902,34443,34444],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, U). \\tag{6.28}",[724,34446,34447,34448,2170,34451,34464,34465,34478],{},"Hicksova poptávka závisí na ",[38,34449,34450],{},"hladině užitečnosti",[883,34452,34454],{"className":34453},[886],[888,34455,34456],{"xmlns":890},[892,34457,34458,34462],{},[895,34459,34460],{},[898,34461,900],{},[902,34463,900],{"encoding":904}," (nikoli na důchodu ",[883,34466,34468],{"className":34467},[886],[888,34469,34470],{"xmlns":890},[892,34471,34472,34476],{},[895,34473,34474],{},[898,34475,1854],{},[902,34477,1854],{"encoding":904}," jako u Marshallovy). Fyzická interpretace: jaké množství zboží koupit při daných cenách, abych dosáhl předem stanovené úrovně uspokojení s minimálními výdaji.",[115,34480,34482,34483],{"id":34481},"příklad-68-obecné-odvození-pro-uq112q212u-q_112-q_212","Příklad 6.8 — obecné odvození pro ",[883,34484,34486],{"className":34485},[886],[888,34487,34488],{"xmlns":890},[892,34489,34490,34524],{},[895,34491,34492,34494,34496,34510],{},[898,34493,900],{},[1688,34495,1690],{},[1814,34497,34498,34500,34502],{},[898,34499,1872],{},[1793,34501,1795],{},[895,34503,34504,34506,34508],{},[1793,34505,1795],{},[898,34507,4930],{"mathvariant":1822},[1793,34509,1806],{},[1814,34511,34512,34514,34516],{},[898,34513,1872],{},[1793,34515,1806],{},[895,34517,34518,34520,34522],{},[1793,34519,1795],{},[898,34521,4930],{"mathvariant":1822},[1793,34523,1806],{},[902,34525,33399],{"encoding":904},[724,34527,34528,34558],{},[883,34529,34531],{"className":34530},[886],[888,34532,34533],{"xmlns":890},[892,34534,34535,34555],{},[895,34536,34537,34543,34545,34551,34553],{},[1788,34538,34539,34541],{},[898,34540,1727],{},[1793,34542,1795],{},[1688,34544,1733],{"separator":1732},[1788,34546,34547,34549],{},[898,34548,1727],{},[1793,34550,1806],{},[1688,34552,1733],{"separator":1732},[898,34554,900],{},[902,34556,34557],{"encoding":904},"P_1, P_2, U"," jsou parametry. Lagrangeova funkce:",[883,34560,34562],{"className":34561},[886],[888,34563,34564],{"xmlns":890,"display":28306},[892,34565,34566,34640],{},[895,34567,34568,34570,34572,34578,34584,34586,34592,34598,34600,34602,34604,34606,34608,34622,34636,34638],{},[898,34569,10047],{"mathvariant":28788},[1688,34571,1690],{},[1788,34573,34574,34576],{},[898,34575,1727],{},[1793,34577,1795],{},[1788,34579,34580,34582],{},[898,34581,1872],{},[1793,34583,1795],{},[1688,34585,1696],{},[1788,34587,34588,34590],{},[898,34589,1727],{},[1793,34591,1806],{},[1788,34593,34594,34596],{},[898,34595,1872],{},[1793,34597,1806],{},[1688,34599,1696],{},[898,34601,16690],{},[1688,34603,2066],{"stretchy":2065},[898,34605,900],{},[1688,34607,1954],{},[1814,34609,34610,34612,34614],{},[898,34611,1872],{},[1793,34613,1795],{},[895,34615,34616,34618,34620],{},[1793,34617,1795],{},[898,34619,4930],{"mathvariant":1822},[1793,34621,1806],{},[1814,34623,34624,34626,34628],{},[898,34625,1872],{},[1793,34627,1806],{},[895,34629,34630,34632,34634],{},[1793,34631,1795],{},[898,34633,4930],{"mathvariant":1822},[1793,34635,1806],{},[1688,34637,2076],{"stretchy":2065},[898,34639,2263],{"mathvariant":1822},[902,34641,34642],{"encoding":904},"\\mathcal{L} = P_1 Q_1 + P_2 Q_2 + \\lambda(U - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,34644,30671],{},[883,34646,34648],{"className":34647},[886],[888,34649,34650],{"xmlns":890,"display":28306},[892,34651,34652,34874],{},[20995,34653,34654,34734,34814],{"rowspacing":20997,"columnalign":20998,"columnspacing":1823},[21000,34655,34656,34668],{},[21003,34657,34658],{},[1777,34659,34660],{"scriptlevel":1779,"displaystyle":1732},[1814,34661,34662,34664,34666],{},[898,34663,10047],{"mathvariant":28788},[1793,34665,1795],{},[1688,34667,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[21003,34669,34670],{},[1777,34671,34672],{"scriptlevel":1779,"displaystyle":1732},[895,34673,34674,34676,34678,34684,34686,34688,34690,34698,34714,34728,34730,34732],{},[895,34675],{},[1688,34677,1690],{},[1788,34679,34680,34682],{},[898,34681,1727],{},[1793,34683,1795],{},[1688,34685,1954],{},[898,34687,16690],{},[1688,34689,3434],{},[1777,34691,34692],{"scriptlevel":1779,"displaystyle":2065},[1781,34693,34694,34696],{},[1793,34695,1795],{},[1793,34697,1806],{},[1814,34699,34700,34702,34704],{},[898,34701,1872],{},[1793,34703,1795],{},[895,34705,34706,34708,34710,34712],{},[1688,34707,1954],{},[1793,34709,1795],{},[898,34711,4930],{"mathvariant":1822},[1793,34713,1806],{},[1814,34715,34716,34718,34720],{},[898,34717,1872],{},[1793,34719,1806],{},[895,34721,34722,34724,34726],{},[1793,34723,1795],{},[898,34725,4930],{"mathvariant":1822},[1793,34727,1806],{},[1688,34729,1690],{},[1793,34731,1779],{},[1688,34733,1733],{"separator":1732},[21000,34735,34736,34748],{},[21003,34737,34738],{},[1777,34739,34740],{"scriptlevel":1779,"displaystyle":1732},[1814,34741,34742,34744,34746],{},[898,34743,10047],{"mathvariant":28788},[1793,34745,1806],{},[1688,34747,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[21003,34749,34750],{},[1777,34751,34752],{"scriptlevel":1779,"displaystyle":1732},[895,34753,34754,34756,34758,34764,34766,34768,34770,34778,34792,34808,34810,34812],{},[895,34755],{},[1688,34757,1690],{},[1788,34759,34760,34762],{},[898,34761,1727],{},[1793,34763,1806],{},[1688,34765,1954],{},[898,34767,16690],{},[1688,34769,3434],{},[1777,34771,34772],{"scriptlevel":1779,"displaystyle":2065},[1781,34773,34774,34776],{},[1793,34775,1795],{},[1793,34777,1806],{},[1814,34779,34780,34782,34784],{},[898,34781,1872],{},[1793,34783,1795],{},[895,34785,34786,34788,34790],{},[1793,34787,1795],{},[898,34789,4930],{"mathvariant":1822},[1793,34791,1806],{},[1814,34793,34794,34796,34798],{},[898,34795,1872],{},[1793,34797,1806],{},[895,34799,34800,34802,34804,34806],{},[1688,34801,1954],{},[1793,34803,1795],{},[898,34805,4930],{"mathvariant":1822},[1793,34807,1806],{},[1688,34809,1690],{},[1793,34811,1779],{},[1688,34813,1733],{"separator":1732},[21000,34815,34816,34828],{},[21003,34817,34818],{},[1777,34819,34820],{"scriptlevel":1779,"displaystyle":1732},[1814,34821,34822,34824,34826],{},[898,34823,10047],{"mathvariant":28788},[898,34825,16690],{},[1688,34827,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[21003,34829,34830],{},[1777,34831,34832],{"scriptlevel":1779,"displaystyle":1732},[895,34833,34834,34836,34838,34840,34842,34856,34870,34872],{},[895,34835],{},[1688,34837,1690],{},[898,34839,900],{},[1688,34841,1954],{},[1814,34843,34844,34846,34848],{},[898,34845,1872],{},[1793,34847,1795],{},[895,34849,34850,34852,34854],{},[1793,34851,1795],{},[898,34853,4930],{"mathvariant":1822},[1793,34855,1806],{},[1814,34857,34858,34860,34862],{},[898,34859,1872],{},[1793,34861,1806],{},[895,34863,34864,34866,34868],{},[1793,34865,1795],{},[898,34867,4930],{"mathvariant":1822},[1793,34869,1806],{},[1688,34871,1690],{},[1793,34873,12708],{},[902,34875,34876],{"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}",[724,34878,34879,34880,34950,34951,35009],{},"Podílem rovnic: ",[883,34881,34883],{"className":34882},[886],[888,34884,34885],{"xmlns":890},[892,34886,34887,34947],{},[895,34888,34889,34895,34897,34903,34905,34911,34913,34919,34921,34927,34933,34935,34941],{},[1788,34890,34891,34893],{},[898,34892,1727],{},[1793,34894,1795],{},[898,34896,4930],{"mathvariant":1822},[1788,34898,34899,34901],{},[898,34900,1727],{},[1793,34902,1806],{},[1688,34904,1690],{},[1788,34906,34907,34909],{},[898,34908,1872],{},[1793,34910,1806],{},[898,34912,4930],{"mathvariant":1822},[1788,34914,34915,34917],{},[898,34916,1872],{},[1793,34918,1795],{},[1688,34920,4244],{},[1788,34922,34923,34925],{},[898,34924,1727],{},[1793,34926,1795],{},[1788,34928,34929,34931],{},[898,34930,1872],{},[1793,34932,1795],{},[1688,34934,1690],{},[1788,34936,34937,34939],{},[898,34938,1727],{},[1793,34940,1806],{},[1788,34942,34943,34945],{},[898,34944,1872],{},[1793,34946,1806],{},[902,34948,34949],{"encoding":904},"P_1\u002FP_2 = Q_2\u002FQ_1 \\Rightarrow P_1 Q_1 = P_2 Q_2",", tedy celkové výdaje ",[883,34952,34954],{"className":34953},[886],[888,34955,34956],{"xmlns":890},[892,34957,34958,35006],{},[895,34959,34960,34962,34964,34970,34976,34978,34984,34990,34992,34994,35000],{},[898,34961,4509],{},[1688,34963,1690],{},[1788,34965,34966,34968],{},[898,34967,1727],{},[1793,34969,1795],{},[1788,34971,34972,34974],{},[898,34973,1872],{},[1793,34975,1795],{},[1688,34977,1696],{},[1788,34979,34980,34982],{},[898,34981,1727],{},[1793,34983,1806],{},[1788,34985,34986,34988],{},[898,34987,1872],{},[1793,34989,1806],{},[1688,34991,1690],{},[1793,34993,1806],{},[1788,34995,34996,34998],{},[898,34997,1727],{},[1793,34999,1795],{},[1788,35001,35002,35004],{},[898,35003,1872],{},[1793,35005,1795],{},[902,35007,35008],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2 = 2 P_1 Q_1",". Odtud",[883,35011,35013],{"className":35012},[886],[888,35014,35015],{"xmlns":890,"display":28306},[892,35016,35017,35084],{},[20995,35018,35019],{"width":28311},[21000,35020,35021,35023,35077,35079],{},[21003,35022],{"width":28316},[21003,35024,35025],{},[895,35026,35027,35033,35035,35049,35051,35053,35059,35061,35075],{},[1788,35028,35029,35031],{},[898,35030,1872],{},[1793,35032,1795],{},[1688,35034,1690],{},[1781,35036,35037,35039],{},[898,35038,4509],{},[895,35040,35041,35043],{},[1793,35042,1806],{},[1788,35044,35045,35047],{},[898,35046,1727],{},[1793,35048,1795],{},[1688,35050,1733],{"separator":1732},[6134,35052],{"width":15531},[1788,35054,35055,35057],{},[898,35056,1872],{},[1793,35058,1806],{},[1688,35060,1690],{},[1781,35062,35063,35065],{},[898,35064,4509],{},[895,35066,35067,35069],{},[1793,35068,1806],{},[1788,35070,35071,35073],{},[898,35072,1727],{},[1793,35074,1806],{},[898,35076,2263],{"mathvariant":1822},[21003,35078],{"width":28316},[21003,35080,35081],{},[2041,35082,35083],{},"(6.29)",[902,35085,35086],{"encoding":904},"Q_1 = \\frac{E}{2 P_1}, \\quad Q_2 = \\frac{E}{2 P_2}. \\tag{6.29}",[724,35088,35089,35090,17821,35172,35208],{},"Ze třetí rovnice ",[883,35091,35093],{"className":35092},[886],[888,35094,35095],{"xmlns":890},[892,35096,35097,35169],{},[895,35098,35099,35101,35103,35141,35143],{},[898,35100,900],{},[1688,35102,1690],{},[8373,35104,35105],{},[895,35106,35107,35123,35125],{},[1777,35108,35109],{"scriptlevel":1779,"displaystyle":2065},[1781,35110,35111,35113],{},[898,35112,4509],{},[895,35114,35115,35117],{},[1793,35116,1806],{},[1788,35118,35119,35121],{},[898,35120,1727],{},[1793,35122,1795],{},[1688,35124,3434],{},[1777,35126,35127],{"scriptlevel":1779,"displaystyle":2065},[1781,35128,35129,35131],{},[898,35130,4509],{},[895,35132,35133,35135],{},[1793,35134,1806],{},[1788,35136,35137,35139],{},[898,35138,1727],{},[1793,35140,1806],{},[1688,35142,1690],{},[1777,35144,35145],{"scriptlevel":1779,"displaystyle":2065},[1781,35146,35147,35149],{},[898,35148,4509],{},[895,35150,35151,35153],{},[1793,35152,1806],{},[8373,35154,35155],{},[895,35156,35157,35163],{},[1788,35158,35159,35161],{},[898,35160,1727],{},[1793,35162,1795],{},[1788,35164,35165,35167],{},[898,35166,1727],{},[1793,35168,1806],{},[902,35170,35171],{"encoding":904},"U = \\sqrt{\\tfrac{E}{2 P_1} \\cdot \\tfrac{E}{2 P_2}} = \\tfrac{E}{2\\sqrt{P_1 P_2}}",[883,35173,35175],{"className":35174},[886],[888,35176,35177],{"xmlns":890},[892,35178,35179,35205],{},[895,35180,35181,35183,35185,35187,35189],{},[898,35182,4509],{},[1688,35184,1690],{},[1793,35186,1806],{},[898,35188,900],{},[8373,35190,35191],{},[895,35192,35193,35199],{},[1788,35194,35195,35197],{},[898,35196,1727],{},[1793,35198,1795],{},[1788,35200,35201,35203],{},[898,35202,1727],{},[1793,35204,1806],{},[902,35206,35207],{"encoding":904},"E = 2 U \\sqrt{P_1 P_2}",". Dosazením:",[883,35210,35212],{"className":35211},[886],[888,35213,35214],{"xmlns":890,"display":28306},[892,35215,35216,35361],{},[20995,35217,35218],{"width":28311},[21000,35219,35220,35222,35354,35356],{},[21003,35221],{"width":28316},[21003,35223,35224],{},[13080,35225,35226],{"notation":13082},[1777,35227,35228],{"scriptlevel":1779,"displaystyle":2065},[1777,35229,35230],{"scriptlevel":1779,"displaystyle":2065},[1777,35231,35232],{"scriptlevel":1779,"displaystyle":1732},[895,35233,35234,35236,35242,35244,35246,35262,35264,35270,35272,35278,35280,35286,35288,35290,35292,35294,35296,35302,35304,35306,35322,35324,35330,35332,35338,35340,35346,35348,35350,35352],{},[2041,35235,4241],{},[1788,35237,35238,35240],{},[898,35239,1872],{},[1793,35241,1795],{},[1688,35243,1690],{},[898,35245,900],{},[8373,35247,35248],{},[1781,35249,35250,35256],{},[1788,35251,35252,35254],{},[898,35253,1727],{},[1793,35255,1806],{},[1788,35257,35258,35260],{},[898,35259,1727],{},[1793,35261,1795],{},[1688,35263,1690],{},[1788,35265,35266,35268],{},[898,35267,4440],{},[1793,35269,1795],{},[1688,35271,2066],{"stretchy":2065},[1788,35273,35274,35276],{},[898,35275,1727],{},[1793,35277,1795],{},[1688,35279,1733],{"separator":1732},[1788,35281,35282,35284],{},[898,35283,1727],{},[1793,35285,1806],{},[1688,35287,1733],{"separator":1732},[898,35289,900],{},[1688,35291,2076],{"stretchy":2065},[1688,35293,1733],{"separator":1732},[6134,35295],{"width":15531},[1788,35297,35298,35300],{},[898,35299,1872],{},[1793,35301,1806],{},[1688,35303,1690],{},[898,35305,900],{},[8373,35307,35308],{},[1781,35309,35310,35316],{},[1788,35311,35312,35314],{},[898,35313,1727],{},[1793,35315,1795],{},[1788,35317,35318,35320],{},[898,35319,1727],{},[1793,35321,1806],{},[1688,35323,1690],{},[1788,35325,35326,35328],{},[898,35327,4440],{},[1793,35329,1806],{},[1688,35331,2066],{"stretchy":2065},[1788,35333,35334,35336],{},[898,35335,1727],{},[1793,35337,1795],{},[1688,35339,1733],{"separator":1732},[1788,35341,35342,35344],{},[898,35343,1727],{},[1793,35345,1806],{},[1688,35347,1733],{"separator":1732},[898,35349,900],{},[1688,35351,2076],{"stretchy":2065},[2041,35353,4241],{},[21003,35355],{"width":28316},[21003,35357,35358],{},[2041,35359,35360],{},"(6.30)",[902,35362,35363],{"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}",[115,35365,35367],{"id":35366},"vztah-primární-a-duální-úlohy","Vztah primární a duální úlohy",[724,35369,35370,35371,35384,35385,35402,35403,35416,35417,35434,35435,35438,35439,35478,35479,35508],{},"Primární (max ",[883,35372,35374],{"className":35373},[886],[888,35375,35376],{"xmlns":890},[892,35377,35378,35382],{},[895,35379,35380],{},[898,35381,900],{},[902,35383,900],{"encoding":904}," při rozpočtu ",[883,35386,35388],{"className":35387},[886],[888,35389,35390],{"xmlns":890},[892,35391,35392,35400],{},[895,35393,35394],{},[1850,35395,35396,35398],{},[898,35397,1854],{},[1688,35399,1857],{},[902,35401,28268],{"encoding":904},") a duální (min ",[883,35404,35406],{"className":35405},[886],[888,35407,35408],{"xmlns":890},[892,35409,35410,35414],{},[895,35411,35412],{},[898,35413,4509],{},[902,35415,4509],{"encoding":904}," při užitečnosti ",[883,35418,35420],{"className":35419},[886],[888,35421,35422],{"xmlns":890},[892,35423,35424,35432],{},[895,35425,35426],{},[1850,35427,35428,35430],{},[898,35429,900],{},[1688,35431,1857],{},[902,35433,28202],{"encoding":904},") úloha jsou ",[38,35436,35437],{},"ekvivalentní",": mají tentýž bod optima ",[883,35440,35442],{"className":35441},[886],[888,35443,35444],{"xmlns":890},[892,35445,35446,35476],{},[895,35447,35448,35454,35456,35464,35466,35474],{},[1850,35449,35450,35452],{},[898,35451,1872],{},[1688,35453,1857],{},[1688,35455,2748],{"stretchy":2065},[1814,35457,35458,35460,35462],{},[898,35459,1872],{},[1793,35461,1795],{},[1688,35463,1857],{},[1688,35465,1733],{"separator":1732},[1814,35467,35468,35470,35472],{},[898,35469,1872],{},[1793,35471,1806],{},[1688,35473,1857],{},[1688,35475,2763],{"stretchy":2065},[902,35477,28567],{"encoding":904}," a v obou platí ",[883,35480,35482],{"className":35481},[886],[888,35483,35484],{"xmlns":890},[892,35485,35486,35506],{},[895,35487,35488,35490,35492,35498,35500],{},[2041,35489,1670],{},[1688,35491,1690],{},[1788,35493,35494,35496],{},[898,35495,1727],{},[1793,35497,1795],{},[898,35499,4930],{"mathvariant":1822},[1788,35501,35502,35504],{},[898,35503,1727],{},[1793,35505,1806],{},[902,35507,28238],{"encoding":904},". Rozdíl je v tom, která veličina je zadána a která se optimalizuje:",[724,35510,35511],{},[2821,35512],{"alt":35513,"className":35514,"src":35515},"imek-primarni-vs-dualni",[210,2825],"\u002Fwiki-assets\u002Fimek-primarni-vs-dualni.jpeg",[120,35517,35518,35629],{},[123,35519,35520,35523,35524,35537,35538,35578,35579,2263],{},[38,35521,35522],{},"Primární"," (Marshall): zadáno ",[883,35525,35527],{"className":35526},[886],[888,35528,35529],{"xmlns":890},[892,35530,35531,35535],{},[895,35532,35533],{},[898,35534,1854],{},[902,35536,1854],{"encoding":904},", hledáme maximální ",[883,35539,35541],{"className":35540},[886],[888,35542,35543],{"xmlns":890},[892,35544,35545,35575],{},[895,35546,35547,35553,35555,35561,35563,35569,35571,35573],{},[1850,35548,35549,35551],{},[898,35550,900],{},[1688,35552,1857],{},[1688,35554,2066],{"stretchy":2065},[1788,35556,35557,35559],{},[898,35558,1727],{},[1793,35560,1795],{},[1688,35562,1733],{"separator":1732},[1788,35564,35565,35567],{},[898,35566,1727],{},[1793,35568,1806],{},[1688,35570,1733],{"separator":1732},[898,35572,1854],{},[1688,35574,2076],{"stretchy":2065},[902,35576,35577],{"encoding":904},"U^*(P_1, P_2, Y)"," a poptávku ",[883,35580,35582],{"className":35581},[886],[888,35583,35584],{"xmlns":890},[892,35585,35586,35626],{},[895,35587,35588,35594,35596,35604,35606,35612,35614,35620,35622,35624],{},[1788,35589,35590,35592],{},[898,35591,1872],{},[898,35593,18035],{},[1688,35595,1690],{},[1814,35597,35598,35600,35602],{},[898,35599,4440],{},[898,35601,18035],{},[898,35603,1661],{},[1688,35605,2066],{"stretchy":2065},[1788,35607,35608,35610],{},[898,35609,1727],{},[1793,35611,1795],{},[1688,35613,1733],{"separator":1732},[1788,35615,35616,35618],{},[898,35617,1727],{},[1793,35619,1806],{},[1688,35621,1733],{"separator":1732},[898,35623,1854],{},[1688,35625,2076],{"stretchy":2065},[902,35627,35628],{"encoding":904},"Q_i = D_i^M(P_1, P_2, Y)",[123,35630,35631,35634,35635,35648,35649,35578,35689,2263],{},[38,35632,35633],{},"Duální"," (Hicks): zadáno ",[883,35636,35638],{"className":35637},[886],[888,35639,35640],{"xmlns":890},[892,35641,35642,35646],{},[895,35643,35644],{},[898,35645,900],{},[902,35647,900],{"encoding":904},", hledáme minimální ",[883,35650,35652],{"className":35651},[886],[888,35653,35654],{"xmlns":890},[892,35655,35656,35686],{},[895,35657,35658,35664,35666,35672,35674,35680,35682,35684],{},[1850,35659,35660,35662],{},[898,35661,4509],{},[1688,35663,1857],{},[1688,35665,2066],{"stretchy":2065},[1788,35667,35668,35670],{},[898,35669,1727],{},[1793,35671,1795],{},[1688,35673,1733],{"separator":1732},[1788,35675,35676,35678],{},[898,35677,1727],{},[1793,35679,1806],{},[1688,35681,1733],{"separator":1732},[898,35683,900],{},[1688,35685,2076],{"stretchy":2065},[902,35687,35688],{"encoding":904},"E^*(P_1, P_2, U)",[883,35690,35692],{"className":35691},[886],[888,35693,35694],{"xmlns":890},[892,35695,35696,35737],{},[895,35697,35698,35704,35706,35715,35717,35723,35725,35731,35733,35735],{},[1788,35699,35700,35702],{},[898,35701,1872],{},[898,35703,18035],{},[1688,35705,1690],{},[1814,35707,35708,35710,35712],{},[898,35709,4440],{},[898,35711,18035],{},[898,35713,35714],{},"H",[1688,35716,2066],{"stretchy":2065},[1788,35718,35719,35721],{},[898,35720,1727],{},[1793,35722,1795],{},[1688,35724,1733],{"separator":1732},[1788,35726,35727,35729],{},[898,35728,1727],{},[1793,35730,1806],{},[1688,35732,1733],{"separator":1732},[898,35734,900],{},[1688,35736,2076],{"stretchy":2065},[902,35738,35739],{"encoding":904},"Q_i = D_i^H(P_1, P_2, U)",[724,35741,35742,35743,35746,35747,35750],{},"Proč se studují obě? Marshallova poptávka je ",[38,35744,35745],{},"pozorovatelná"," (lze odhadnout z dat o spotřebě a důchodech), zatímco Hicksova umožňuje čistě oddělit ",[38,35748,35749],{},"substituční efekt"," změny ceny od efektu důchodového — je klíčová pro teorii blahobytu a cenové indexy.",[115,35752,35754],{"id":35753},"úlohy-k-optimalizaci","Úlohy k optimalizaci",[198,35756,35758],{"id":35757},"maximalizace-užitečnosti-a-marshallova-poptávka","Maximalizace užitečnosti a Marshallova poptávka",[724,35760,35761,35764,35765,35797,35798,35836,35837,35863],{},[38,35762,35763],{},"6.8"," Jsou dány užitečnost ",[883,35766,35768],{"className":35767},[886],[888,35769,35770],{"xmlns":890},[892,35771,35772,35794],{},[895,35773,35774,35776,35778,35786],{},[898,35775,900],{},[1688,35777,1690],{},[1814,35779,35780,35782,35784],{},[898,35781,1872],{},[1793,35783,1795],{},[1793,35785,5265],{},[1814,35787,35788,35790,35792],{},[898,35789,1872],{},[1793,35791,1806],{},[1793,35793,5265],{},[902,35795,35796],{"encoding":904},"U = Q_1^{0{,}5} Q_2^{0{,}5}",", ceny ",[883,35799,35801],{"className":35800},[886],[888,35802,35803],{"xmlns":890},[892,35804,35805,35833],{},[895,35806,35807,35815,35817,35819,35821,35829,35831],{},[1814,35808,35809,35811,35813],{},[898,35810,1727],{},[1793,35812,1795],{},[1688,35814,1857],{},[1688,35816,1690],{},[1793,35818,2616],{},[1688,35820,1733],{"separator":1732},[1814,35822,35823,35825,35827],{},[898,35824,1727],{},[1793,35826,1806],{},[1688,35828,1857],{},[1688,35830,1690],{},[1793,35832,3121],{},[902,35834,35835],{"encoding":904},"P_1^* = 4, P_2^* = 10"," za jednotku zboží a důchod spotřebitele 200. Určete množství ",[883,35838,35840],{"className":35839},[886],[888,35841,35842],{"xmlns":890},[892,35843,35844,35860],{},[895,35845,35846,35852,35854],{},[1788,35847,35848,35850],{},[898,35849,1872],{},[1793,35851,1795],{},[1688,35853,1733],{"separator":1732},[1788,35855,35856,35858],{},[898,35857,1872],{},[1793,35859,1806],{},[902,35861,35862],{"encoding":904},"Q_1, Q_2"," maximalizující užitečnost.",[724,35865,35866,35869,35870,35912,35913,35944,35945,35967,35968,2263],{},[38,35867,35868],{},"6.9"," Jsou dány rozpočtové omezení ",[883,35871,35873],{"className":35872},[886],[888,35874,35875],{"xmlns":890},[892,35876,35877,35909],{},[895,35878,35879,35881,35883,35889,35895,35897,35903],{},[898,35880,1854],{},[1688,35882,1690],{},[1788,35884,35885,35887],{},[898,35886,1727],{},[1793,35888,1795],{},[1788,35890,35891,35893],{},[898,35892,1872],{},[1793,35894,1795],{},[1688,35896,1696],{},[1788,35898,35899,35901],{},[898,35900,1727],{},[1793,35902,1806],{},[1788,35904,35905,35907],{},[898,35906,1872],{},[1793,35908,1806],{},[902,35910,35911],{"encoding":904},"Y = P_1 Q_1 + P_2 Q_2"," a užitečnost ",[883,35914,35916],{"className":35915},[886],[888,35917,35918],{"xmlns":890},[892,35919,35920,35942],{},[895,35921,35922,35924,35926,35934],{},[898,35923,900],{},[1688,35925,1690],{},[1814,35927,35928,35930,35932],{},[898,35929,1872],{},[1793,35931,1795],{},[1793,35933,5265],{},[1814,35935,35936,35938,35940],{},[898,35937,1872],{},[1793,35939,1806],{},[1793,35941,5265],{},[902,35943,35796],{"encoding":904},". (a) Odvoďte funkce poptávky maximalizující užitečnost. (b) Najděte funkce poptávky pro důchod ",[883,35946,35948],{"className":35947},[886],[888,35949,35950],{"xmlns":890},[892,35951,35952,35964],{},[895,35953,35954,35960,35962],{},[1850,35955,35956,35958],{},[898,35957,1854],{},[1688,35959,1857],{},[1688,35961,1690],{},[1793,35963,15357],{},[902,35965,35966],{"encoding":904},"Y^* = 500",". (c) Najděte Engelovy funkce pro ceny ",[883,35969,35971],{"className":35970},[886],[888,35972,35973],{"xmlns":890},[892,35974,35975,36003],{},[895,35976,35977,35985,35987,35989,35991,35999,36001],{},[1814,35978,35979,35981,35983],{},[898,35980,1727],{},[1793,35982,1795],{},[1688,35984,1857],{},[1688,35986,1690],{},[1793,35988,2501],{},[1688,35990,1733],{"separator":1732},[1814,35992,35993,35995,35997],{},[898,35994,1727],{},[1793,35996,1806],{},[1688,35998,1857],{},[1688,36000,1690],{},[1793,36002,3121],{},[902,36004,36005],{"encoding":904},"P_1^* = 5, P_2^* = 10",[724,36007,36008,36011,36012,21835,36044,36074,36075,2263],{},[38,36009,36010],{},"6.10"," Odvoďte funkce poptávky pro Cobb-Douglasovy funkce užitečnosti ",[883,36013,36015],{"className":36014},[886],[888,36016,36017],{"xmlns":890},[892,36018,36019,36041],{},[895,36020,36021,36023,36025,36033],{},[898,36022,900],{},[1688,36024,1690],{},[1814,36026,36027,36029,36031],{},[898,36028,1872],{},[1793,36030,1795],{},[898,36032,207],{},[1814,36034,36035,36037,36039],{},[898,36036,1872],{},[1793,36038,1806],{},[898,36040,1918],{},[902,36042,36043],{"encoding":904},"U = Q_1^a Q_2^b",[883,36045,36047],{"className":36046},[886],[888,36048,36049],{"xmlns":890},[892,36050,36051,36071],{},[895,36052,36053,36055,36057,36059,36061,36063,36065,36067,36069],{},[898,36054,207],{},[1688,36056,1733],{"separator":1732},[898,36058,1918],{},[1688,36060,6762],{},[1688,36062,5580],{"stretchy":2065},[1793,36064,1779],{},[1688,36066,1733],{"separator":1732},[1793,36068,1795],{},[1688,36070,5597],{"stretchy":2065},[902,36072,36073],{"encoding":904},"a, b \\in \\langle 0, 1 \\rangle"," a rozpočtové omezení ",[883,36076,36078],{"className":36077},[886],[888,36079,36080],{"xmlns":890},[892,36081,36082,36114],{},[895,36083,36084,36086,36088,36094,36100,36102,36108],{},[898,36085,1854],{},[1688,36087,1690],{},[1788,36089,36090,36092],{},[898,36091,1727],{},[1793,36093,1795],{},[1788,36095,36096,36098],{},[898,36097,1872],{},[1793,36099,1795],{},[1688,36101,1696],{},[1788,36103,36104,36106],{},[898,36105,1727],{},[1793,36107,1806],{},[1788,36109,36110,36112],{},[898,36111,1872],{},[1793,36113,1806],{},[902,36115,35911],{"encoding":904},[724,36117,36118,36121,36122,21835,36156,36074,36174,2263],{},[38,36119,36120],{},"6.11"," Odvoďte funkce poptávky pro funkce užitečnosti CES typu ",[883,36123,36125],{"className":36124},[886],[888,36126,36127],{"xmlns":890},[892,36128,36129,36153],{},[895,36130,36131,36133,36135,36143,36145],{},[898,36132,900],{},[1688,36134,1690],{},[1814,36136,36137,36139,36141],{},[898,36138,1872],{},[1793,36140,1795],{},[898,36142,207],{},[1688,36144,1696],{},[1814,36146,36147,36149,36151],{},[898,36148,1872],{},[1793,36150,1806],{},[898,36152,207],{},[902,36154,36155],{"encoding":904},"U = Q_1^a + Q_2^a",[883,36157,36159],{"className":36158},[886],[888,36160,36161],{"xmlns":890},[892,36162,36163,36171],{},[895,36164,36165,36167,36169],{},[898,36166,207],{},[1688,36168,3628],{"mathvariant":1822},[1793,36170,1779],{},[902,36172,36173],{"encoding":904},"a \\neq 0",[883,36175,36177],{"className":36176},[886],[888,36178,36179],{"xmlns":890},[892,36180,36181,36213],{},[895,36182,36183,36185,36187,36193,36199,36201,36207],{},[898,36184,1854],{},[1688,36186,1690],{},[1788,36188,36189,36191],{},[898,36190,1727],{},[1793,36192,1795],{},[1788,36194,36195,36197],{},[898,36196,1872],{},[1793,36198,1795],{},[1688,36200,1696],{},[1788,36202,36203,36205],{},[898,36204,1727],{},[1793,36206,1806],{},[1788,36208,36209,36211],{},[898,36210,1872],{},[1793,36212,1806],{},[902,36214,35911],{"encoding":904},[198,36216,36218],{"id":36217},"minimalizace-výdajů-a-hicksova-poptávka","Minimalizace výdajů a Hicksova poptávka",[724,36220,36221,35764,36224,1343,36251,36273,36274,1343,36297,36321,36322,36347,36348,2263],{},[38,36222,36223],{},"6.12",[883,36225,36227],{"className":36226},[886],[888,36228,36229],{"xmlns":890},[892,36230,36231,36249],{},[895,36232,36233,36235,36237,36243],{},[898,36234,900],{},[1688,36236,1690],{},[1788,36238,36239,36241],{},[898,36240,1872],{},[1793,36242,1795],{},[1788,36244,36245,36247],{},[898,36246,1872],{},[1793,36248,1806],{},[902,36250,30466],{"encoding":904},[883,36252,36254],{"className":36253},[886],[888,36255,36256],{"xmlns":890},[892,36257,36258,36270],{},[895,36259,36260,36266,36268],{},[1850,36261,36262,36264],{},[898,36263,900],{},[1688,36265,1857],{},[1688,36267,1690],{},[1793,36269,3121],{},[902,36271,36272],{"encoding":904},"U^* = 10"," hladina užitečnosti a ceny ",[883,36275,36277],{"className":36276},[886],[888,36278,36279],{"xmlns":890},[892,36280,36281,36295],{},[895,36282,36283,36291,36293],{},[1814,36284,36285,36287,36289],{},[898,36286,1727],{},[1793,36288,1795],{},[1688,36290,1857],{},[1688,36292,1690],{},[1793,36294,1806],{},[902,36296,30539],{"encoding":904},[883,36298,36300],{"className":36299},[886],[888,36301,36302],{"xmlns":890},[892,36303,36304,36318],{},[895,36305,36306,36314,36316],{},[1814,36307,36308,36310,36312],{},[898,36309,1727],{},[1793,36311,1806],{},[1688,36313,1857],{},[1688,36315,1690],{},[1793,36317,2616],{},[902,36319,36320],{"encoding":904},"P_2^* = 4",". Určete množství ",[883,36323,36325],{"className":36324},[886],[888,36326,36327],{"xmlns":890},[892,36328,36329,36345],{},[895,36330,36331,36337,36339],{},[1788,36332,36333,36335],{},[898,36334,1872],{},[1793,36336,1795],{},[1688,36338,1733],{"separator":1732},[1788,36340,36341,36343],{},[898,36342,1872],{},[1793,36344,1806],{},[902,36346,35862],{"encoding":904}," minimalizující výdaje spotřebitele ",[883,36349,36351],{"className":36350},[886],[888,36352,36353],{"xmlns":890},[892,36354,36355,36375],{},[895,36356,36357,36359,36361,36367,36369],{},[898,36358,900],{},[1688,36360,1690],{},[1788,36362,36363,36365],{},[898,36364,1872],{},[1793,36366,1795],{},[1688,36368,3434],{},[1788,36370,36371,36373],{},[898,36372,1872],{},[1793,36374,1806],{},[902,36376,36377],{"encoding":904},"U = Q_1 \\cdot Q_2",[724,36379,36380,36383,36384,36425,36426,36448,36449,2263],{},[38,36381,36382],{},"6.13"," Jsou dány výdaje spotřebitele ",[883,36385,36387],{"className":36386},[886],[888,36388,36389],{"xmlns":890},[892,36390,36391,36423],{},[895,36392,36393,36395,36397,36403,36409,36411,36417],{},[898,36394,4509],{},[1688,36396,1690],{},[1788,36398,36399,36401],{},[898,36400,1727],{},[1793,36402,1795],{},[1788,36404,36405,36407],{},[898,36406,1872],{},[1793,36408,1795],{},[1688,36410,1696],{},[1788,36412,36413,36415],{},[898,36414,1727],{},[1793,36416,1806],{},[1788,36418,36419,36421],{},[898,36420,1872],{},[1793,36422,1806],{},[902,36424,28183],{"encoding":904}," a užitečnost. (a) Najděte funkce poptávky minimalizující výdaje spotřebitele. (b) Určete funkce poptávky pro užitečnost ",[883,36427,36429],{"className":36428},[886],[888,36430,36431],{"xmlns":890},[892,36432,36433,36445],{},[895,36434,36435,36441,36443],{},[1850,36436,36437,36439],{},[898,36438,900],{},[1688,36440,1857],{},[1688,36442,1690],{},[1793,36444,5260],{},[902,36446,36447],{"encoding":904},"U^* = 25"," a stanovte příslušné výdaje spotřebitele při cenách ",[883,36450,36452],{"className":36451},[886],[888,36453,36454],{"xmlns":890},[892,36455,36456,36485],{},[895,36457,36458,36466,36468,36470,36472,36480,36482],{},[1814,36459,36460,36462,36464],{},[898,36461,1727],{},[1793,36463,1795],{},[1688,36465,1857],{},[1688,36467,1690],{},[1793,36469,9290],{},[1688,36471,1733],{"separator":1732},[1814,36473,36474,36476,36478],{},[898,36475,1727],{},[1793,36477,1806],{},[1688,36479,1857],{},[1688,36481,1690],{},[1793,36483,36484],{},"15",[902,36486,36487],{"encoding":904},"P_1^* = 20, P_2^* = 15",[115,36489,15967],{"id":15966},[120,36491,36492,36549,36588,36608,36643,36697,36702,36708,36804,36849],{},[123,36493,36494,2170,36497,36546,36547,2263],{},[38,36495,36496],{},"Rozpočtové omezení (budget constraint)",[883,36498,36500],{"className":36499},[886],[888,36501,36502],{"xmlns":890},[892,36503,36504,36544],{},[895,36505,36506,36512,36514,36522,36528,36530,36538],{},[1850,36507,36508,36510],{},[898,36509,1854],{},[1688,36511,1857],{},[1688,36513,1690],{},[1814,36515,36516,36518,36520],{},[898,36517,1727],{},[1793,36519,1795],{},[1688,36521,1857],{},[1788,36523,36524,36526],{},[898,36525,1872],{},[1793,36527,1795],{},[1688,36529,1696],{},[1814,36531,36532,36534,36536],{},[898,36533,1727],{},[1793,36535,1806],{},[1688,36537,1857],{},[1788,36539,36540,36542],{},[898,36541,1872],{},[1793,36543,1806],{},[902,36545,1893],{"encoding":904}," — (6.12); ",[38,36548,28376],{},[123,36550,36551,36554,36555,2263],{},[38,36552,36553],{},"Úloha o maximalizaci užitečnosti"," (primární) — Lagrangeova funkce (6.13), soustava (6.14), podmínka optimality ",[883,36556,36558],{"className":36557},[886],[888,36559,36560],{"xmlns":890},[892,36561,36562,36586],{},[895,36563,36564,36566,36568,36576,36578],{},[2041,36565,1670],{},[1688,36567,1690],{},[1814,36569,36570,36572,36574],{},[898,36571,1727],{},[1793,36573,1795],{},[1688,36575,1857],{},[898,36577,4930],{"mathvariant":1822},[1814,36579,36580,36582,36584],{},[898,36581,1727],{},[1793,36583,1806],{},[1688,36585,1857],{},[902,36587,29219],{"encoding":904},[123,36589,36590,36605,36606,2263],{},[38,36591,29363,36592],{},[883,36593,36595],{"className":36594},[886],[888,36596,36597],{"xmlns":890},[892,36598,36599,36603],{},[895,36600,36601],{},[898,36602,16690],{},[902,36604,16743],{"encoding":904}," — stínová cena uvolnění omezení; u maximalizace ",[38,36607,29385],{},[123,36609,36610,36613,36614,2263],{},[38,36611,36612],{},"Podmínka tečnosti"," — sklon indiferenční křivky = sklon rozpočtové přímky; ",[883,36615,36617],{"className":36616},[886],[888,36618,36619],{"xmlns":890},[892,36620,36621,36641],{},[895,36622,36623,36625,36627,36633,36635],{},[2041,36624,1670],{},[1688,36626,1690],{},[1788,36628,36629,36631],{},[898,36630,1727],{},[1793,36632,1795],{},[898,36634,4930],{"mathvariant":1822},[1788,36636,36637,36639],{},[898,36638,1727],{},[1793,36640,1806],{},[902,36642,28238],{"encoding":904},[123,36644,36645,7271,36648,36696],{},[38,36646,36647],{},"Poptávka maximalizující užitečnost (Marshallova)",[883,36649,36651],{"className":36650},[886],[888,36652,36653],{"xmlns":890},[892,36654,36655,36693],{},[895,36656,36657,36663,36665,36671,36673,36679,36681,36687,36689,36691],{},[1788,36658,36659,36661],{},[898,36660,1872],{},[898,36662,18035],{},[1688,36664,1690],{},[1788,36666,36667,36669],{},[898,36668,4440],{},[898,36670,18035],{},[1688,36672,2066],{"stretchy":2065},[1788,36674,36675,36677],{},[898,36676,1727],{},[1793,36678,1795],{},[1688,36680,1733],{"separator":1732},[1788,36682,36683,36685],{},[898,36684,1727],{},[1793,36686,1806],{},[1688,36688,1733],{"separator":1732},[898,36690,1854],{},[1688,36692,2076],{"stretchy":2065},[902,36694,36695],{"encoding":904},"Q_i = D_i(P_1, P_2, Y)"," — (6.15).",[123,36698,36699,36701],{},[38,36700,31967],{}," — poptávka jako funkce důchodu při pevných cenách.",[123,36703,36704,36707],{},[38,36705,36706],{},"Úloha o minimalizaci výdajů"," (duální) — Lagrangeova funkce (6.24), soustava (6.25), postačující podmínka (6.26).",[123,36709,36710,7271,36712,36759,36760,36803],{},[38,36711,34279],{},[883,36713,36715],{"className":36714},[886],[888,36716,36717],{"xmlns":890},[892,36718,36719,36757],{},[895,36720,36721,36727,36729,36735,36737,36743,36745,36751,36753,36755],{},[1788,36722,36723,36725],{},[898,36724,1872],{},[898,36726,18035],{},[1688,36728,1690],{},[1788,36730,36731,36733],{},[898,36732,4440],{},[898,36734,18035],{},[1688,36736,2066],{"stretchy":2065},[1788,36738,36739,36741],{},[898,36740,1727],{},[1793,36742,1795],{},[1688,36744,1733],{"separator":1732},[1788,36746,36747,36749],{},[898,36748,1727],{},[1793,36750,1806],{},[1688,36752,1733],{"separator":1732},[898,36754,900],{},[1688,36756,2076],{"stretchy":2065},[902,36758,18068],{"encoding":904}," — (6.27); obecný výsledek pro ",[883,36761,36763],{"className":36762},[886],[888,36764,36765],{"xmlns":890},[892,36766,36767,36801],{},[895,36768,36769,36771,36773,36787],{},[898,36770,900],{},[1688,36772,1690],{},[1814,36774,36775,36777,36779],{},[898,36776,1872],{},[1793,36778,1795],{},[895,36780,36781,36783,36785],{},[1793,36782,1795],{},[898,36784,4930],{"mathvariant":1822},[1793,36786,1806],{},[1814,36788,36789,36791,36793],{},[898,36790,1872],{},[1793,36792,1806],{},[895,36794,36795,36797,36799],{},[1793,36796,1795],{},[898,36798,4930],{"mathvariant":1822},[1793,36800,1806],{},[902,36802,33399],{"encoding":904},": (6.30).",[123,36805,36806,36848],{},[38,36807,36808,36809],{},"Bod dotyku ",[883,36810,36812],{"className":36811},[886],[888,36813,36814],{"xmlns":890},[892,36815,36816,36846],{},[895,36817,36818,36824,36826,36834,36836,36844],{},[1850,36819,36820,36822],{},[898,36821,1872],{},[1688,36823,1857],{},[1688,36825,2748],{"stretchy":2065},[1814,36827,36828,36830,36832],{},[898,36829,1872],{},[1793,36831,1795],{},[1688,36833,1857],{},[1688,36835,1733],{"separator":1732},[1814,36837,36838,36840,36842],{},[898,36839,1872],{},[1793,36841,1806],{},[1688,36843,1857],{},[1688,36845,2763],{"stretchy":2065},[902,36847,28567],{"encoding":904}," — řešení obou úloh; totožný pro primární i duální formulaci.",[123,36850,36851,36854,36855,36868,36869,36882],{},[38,36852,36853],{},"Dualita"," — ekvivalence max ",[883,36856,36858],{"className":36857},[886],[888,36859,36860],{"xmlns":890},[892,36861,36862,36866],{},[895,36863,36864],{},[898,36865,900],{},[902,36867,900],{"encoding":904}," a min ",[883,36870,36872],{"className":36871},[886],[888,36873,36874],{"xmlns":890},[892,36875,36876,36880],{},[895,36877,36878],{},[898,36879,4509],{},[902,36881,4509],{"encoding":904},"; Marshallova a Hicksova poptávka.",[115,36884,4049],{"id":4048},[120,36886,36887,36910,36926,36939,36950],{},[123,36888,36889,2170,36892,36895,36896,36909],{},[38,36890,36891],{},"Teorie před optimalizací:",[207,36893,880],{"className":36894,"dataFsResolvedFilePath":878,"href":879},[210]," (funkce ",[883,36897,36899],{"className":36898},[886],[888,36900,36901],{"xmlns":890},[892,36902,36903,36907],{},[895,36904,36905],{},[898,36906,900],{},[902,36908,900],{"encoding":904},", indiferenční křivky, MRCS).",[123,36911,36912,2170,36915,36918,36919,36922,36923,2263],{},[38,36913,36914],{},"Matematický aparát:",[207,36916,793],{"className":36917,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace), ",[207,36920,784],{"className":36921,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace), ",[207,36924,2622],{"className":36925,"dataFsResolvedFilePath":764,"href":765},[210],[123,36927,36928,2170,36931,36934,36935,36938],{},[38,36929,36930],{},"Paralely:",[207,36932,11339],{"className":36933,"dataFsResolvedFilePath":857,"href":858},[210]," (MRTS ↔ MRCS, izokvanty ↔ IC, Eulerova věta pro CD), ",[207,36936,12193],{"className":36937,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallova poptávka jako vstup tržního modelu).",[123,36940,36941,2170,36944,1343,36947],{},[38,36942,36943],{},"Přednášky:",[207,36945,1094],{"className":36946,"dataFsResolvedFilePath":838,"href":839},[210],[207,36948,1101],{"className":36949,"dataFsResolvedFilePath":868,"href":869},[210],[123,36951,36952,2170,36954],{},[38,36953,16451],{},[207,36955,16455],{"className":36956,"dataFsResolvedFilePath":2210,"href":2211},[210],{"title":641,"searchDepth":642,"depth":642,"links":36958},[36959,36960,36961,36966,36967,36968,36970,36973,36976,36978,36979,36981,36982,36986,36987],{"id":12258,"depth":642,"text":12259},{"id":28246,"depth":642,"text":28247},{"id":28644,"depth":642,"text":28645,"children":36962},[36963,36964],{"id":28764,"depth":649,"text":28765},{"id":29345,"depth":649,"text":36965},"Interpretace λ\\lambda — mezní užitečnost důchodu",{"id":29807,"depth":642,"text":29808},{"id":30118,"depth":642,"text":30119},{"id":30437,"depth":642,"text":36969},"Příklad 6.6 — maximalizace užitečnosti pro U=Q1Q2U = Q_1 Q_2",{"id":31210,"depth":642,"text":31211,"children":36971},[36972],{"id":31966,"depth":649,"text":31967},{"id":32146,"depth":642,"text":32147,"children":36974},[36975],{"id":32403,"depth":649,"text":32404},{"id":33354,"depth":642,"text":36977},"Příklad 6.7 — minimalizace výdajů pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":34278,"depth":642,"text":34279},{"id":34481,"depth":642,"text":36980},"Příklad 6.8 — obecné odvození pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":35366,"depth":642,"text":35367},{"id":35753,"depth":642,"text":35754,"children":36983},[36984,36985],{"id":35757,"depth":649,"text":35758},{"id":36217,"depth":649,"text":36218},{"id":15966,"depth":642,"text":15967},{"id":4048,"depth":642,"text":4049},{},"\u002Ftopics\u002Foptimalizace-spotrebitele",{"title":28007,"description":641},[1138,1137],"topics\u002Foptimalizace-spotrebitele",[1128,36994,1144,2225,36995,36996,36997],"optimalizace-spotrebitele","poptavka-spotrebitele","minimalizace-vydaju","dualita","jxXhWsWsCIcDvEqLkcWTWs-jk9CvI-eFUi2Afo7U40o",{"id":37000,"title":802,"body":37001,"course":1128,"courses":659,"created":9809,"description":641,"extension":661,"meta":51054,"navigation":664,"path":51055,"seo":51056,"sources":51057,"stem":51058,"tags":51059,"type":4113,"updated":677,"__hash__":51065},"topics\u002Ftopics\u002Fpoptavka-nabidka.md",{"type":9,"value":37002,"toc":51010},[37003,37006,37032,37036,37043,37195,37209,37212,37214,37301,37305,37341,37414,37435,37560,37570,37583,37587,37592,37622,37684,37693,37697,37759,37766,37787,37905,37983,37987,37990,38049,38164,38169,38201,38263,38311,38366,38370,38391,38415,38463,38467,38479,38483,38593,38597,38613,38654,38665,38824,38834,38839,38843,38965,38975,38982,38986,39064,39075,39155,39161,39168,39307,39314,39317,39374,39378,39456,39502,39546,39552,39665,39669,39672,39867,39871,40108,40111,40265,40418,40420,40422,40502,40505,40610,40679,40688,40692,40695,40756,40765,40769,40802,40880,40919,40923,40972,41026,41030,41059,41088,41140,41147,41201,41279,41283,41326,41393,41437,41541,41560,41562,41566,41674,41678,41746,41795,41802,41887,41891,41963,41968,42016,42205,42209,42214,42390,42395,42454,42559,42563,42590,42594,42601,42765,42852,42857,42859,42862,42962,43112,43184,43258,43260,43264,43278,43282,43415,43470,43582,43659,43663,43720,43823,43882,44043,44047,44122,44194,44292,44350,44444,44497,44518,44572,44577,44655,44703,44790,44828,44916,45069,45105,45159,45162,45164,45166,45215,45222,45230,45317,45326,45413,45420,45422,45426,45651,45653,45657,45661,45730,45781,45984,45990,46001,46069,46075,46497,46501,46565,46589,46785,46791,46805,46873,46876,46916,47140,47208,47510,47919,47996,48162,48168,48171,48246,48699,48750,49156,49261,49924,49927,50004,50012,50086,50117,50119,50123,50167,50169,50171,50175,50405,50409,50500,50505,50599,50604,50777,50781,50899,50904,50953,50955,50957],[12,37004,802],{"id":37005},"poptávka-nabídka-a-tržní-rovnováha",[4124,37007,37008],{},[724,37009,37010,37012,37013,37016,37017,37020,37021,37024,37025,37027,37028,37031],{},[883,37011,4412],{}," TL;DR\nKapitola buduje základní mikroekonomický model trhu: chování spotřebitele (",[38,37014,37015],{},"poptávka",") a výrobce (",[38,37018,37019],{},"nabídka","), jejich interakci v ",[38,37022,37023],{},"tržní rovnováze"," a kvantitativní analýzu reakce modelu na změnu exogenních proměnných (posuny, zdanění, ",[38,37026,18219],{},"). Uzavírá ji pojem ",[38,37029,37030],{},"přebytku spotřebitele a výrobce"," jako míry čistého prospěchu obou stran trhu.",[115,37033,37035],{"id":37034},"úvod-model-a-proměnné","Úvod — model a proměnné",[724,37037,37038,37039,37042],{},"Cílem je popsat chování spotřebitele a výrobce za předpokladu racionality jedince (",[614,37040,37041],{},"homo economicus","). Mezi hlavní proměnné patří:",[120,37044,37045,37062,37104,37120],{},[123,37046,37047,37048,37061],{},"cena ",[883,37049,37051],{"className":37050},[886],[888,37052,37053],{"xmlns":890},[892,37054,37055,37059],{},[895,37056,37057],{},[898,37058,1727],{},[902,37060,1727],{"encoding":904}," zkoumaného zboží,",[123,37063,37064,37065,1733],{},"ceny alternativních zboží ",[883,37066,37068],{"className":37067},[886],[888,37069,37070],{"xmlns":890},[892,37071,37072,37101],{},[895,37073,37074,37080,37082,37088,37090,37092,37094],{},[1788,37075,37076,37078],{},[898,37077,1727],{},[1793,37079,1795],{},[1688,37081,1733],{"separator":1732},[1788,37083,37084,37086],{},[898,37085,1727],{},[1793,37087,1806],{},[1688,37089,1733],{"separator":1732},[1688,37091,9899],{},[1688,37093,1733],{"separator":1732},[1788,37095,37096,37098],{},[898,37097,1727],{},[898,37099,37100],{},"n",[902,37102,37103],{"encoding":904},"P_1, P_2, \\dots, P_n",[123,37105,37106,37107,1733],{},"důchod ",[883,37108,37110],{"className":37109},[886],[888,37111,37112],{"xmlns":890},[892,37113,37114,37118],{},[895,37115,37116],{},[898,37117,1854],{},[902,37119,1854],{"encoding":904},[123,37121,37122,37123,37136,37137,37150,37151,37164,37165,37179,37180,37194],{},"preference, očekávání, populace, výrobní faktory (práce ",[883,37124,37126],{"className":37125},[886],[888,37127,37128],{"xmlns":890},[892,37129,37130,37134],{},[895,37131,37132],{},[898,37133,10047],{},[902,37135,10047],{"encoding":904},", kapitál ",[883,37138,37140],{"className":37139},[886],[888,37141,37142],{"xmlns":890},[892,37143,37144,37148],{},[895,37145,37146],{},[898,37147,10052],{},[902,37149,10052],{"encoding":904},", půda ",[883,37152,37154],{"className":37153},[886],[888,37155,37156],{"xmlns":890},[892,37157,37158,37162],{},[895,37159,37160],{},[898,37161,4509],{},[902,37163,4509],{"encoding":904},"), technologie, počet výrobců ",[883,37166,37168],{"className":37167},[886],[888,37169,37170],{"xmlns":890},[892,37171,37172,37177],{},[895,37173,37174],{},[898,37175,37176],{},"O",[902,37178,37176],{"encoding":904},", počasí ",[883,37181,37183],{"className":37182},[886],[888,37184,37185],{"xmlns":890},[892,37186,37187,37192],{},[895,37188,37189],{},[898,37190,37191],{},"W",[902,37193,37191],{"encoding":904}," atd.",[724,37196,37197,37198,37201,37202,37205,37206,2263],{},"Vybereme-li právě jeden z faktorů jako endogenní (",[614,37199,37200],{},"ceteris paribus","), hovoříme o ",[38,37203,37204],{},"jednofaktorovém modelu","; jinak jde o model ",[38,37207,37208],{},"vícefaktorový",[37210,37211],"hr",{},[115,37213,13409],{"id":37015},[4124,37215,37216],{},[724,37217,37218,37220,37221,37234,37235,37248,37249,37252,37253,37276,37277,2263],{},[883,37219,4412],{}," TL;DR\nPoptávka vyjadřuje závislost nakupovaného množství ",[883,37222,37224],{"className":37223},[886],[888,37225,37226],{"xmlns":890},[892,37227,37228,37232],{},[895,37229,37230],{},[898,37231,1872],{},[902,37233,1872],{"encoding":904}," na ceně ",[883,37236,37238],{"className":37237},[886],[888,37239,37240],{"xmlns":890},[892,37241,37242,37246],{},[895,37243,37244],{},[898,37245,1727],{},[902,37247,1727],{"encoding":904}," (případně dalších proměnných). Základní vlastností je ",[38,37250,37251],{},"zákon klesající poptávky",": při růstu ceny množství klesá. Z důvodu přehlednosti se pracuje s jednofaktorovým modelem ",[883,37254,37256],{"className":37255},[886],[888,37257,37258],{"xmlns":890},[892,37259,37260,37274],{},[895,37261,37262,37264,37266,37268,37270,37272],{},[898,37263,1872],{},[1688,37265,1690],{},[898,37267,4440],{},[1688,37269,2066],{"stretchy":2065},[898,37271,1727],{},[1688,37273,2076],{"stretchy":2065},[902,37275,4449],{"encoding":904}," a jeho lineární verzí ",[883,37278,37280],{"className":37279},[886],[888,37281,37282],{"xmlns":890},[892,37283,37284,37298],{},[895,37285,37286,37288,37290,37292,37294,37296],{},[898,37287,1727],{},[1688,37289,1690],{},[898,37291,207],{},[898,37293,1872],{},[1688,37295,1696],{},[898,37297,1918],{},[902,37299,37300],{"encoding":904},"P = aQ + b",[198,37302,37304],{"id":37303},"obecný-vícefaktorový-model","Obecný vícefaktorový model",[724,37306,37307,37308,37321,37322,37335,37336,10277,37338,3408],{},"Ve vícefaktorovém modelu uvažujeme, že poptávané množství ",[883,37309,37311],{"className":37310},[886],[888,37312,37313],{"xmlns":890},[892,37314,37315,37319],{},[895,37316,37317],{},[898,37318,1872],{},[902,37320,1872],{"encoding":904}," závisí na ceně ",[883,37323,37325],{"className":37324},[886],[888,37326,37327],{"xmlns":890},[892,37328,37329,37333],{},[895,37330,37331],{},[898,37332,1727],{},[902,37334,1727],{"encoding":904},", na cenách alternativních zboží a důchodu. Závislost vyjadřuje ",[38,37337,28242],{},[614,37339,37340],{},"demand function",[883,37342,37344],{"className":37343},[886],[888,37345,37346],{"xmlns":890,"display":28306},[892,37347,37348,37411],{},[20995,37349,37350],{"width":28311},[21000,37351,37352,37354,37404,37406],{},[21003,37353],{"width":28316},[21003,37355,37356],{},[895,37357,37358,37360,37362,37364,37366,37368,37370,37376,37378,37384,37386,37388,37390,37396,37398,37400,37402],{},[898,37359,1872],{},[1688,37361,1690],{},[898,37363,4440],{},[1688,37365,2066],{"stretchy":2065},[898,37367,1727],{},[1688,37369,1733],{"separator":1732},[1788,37371,37372,37374],{},[898,37373,1727],{},[1793,37375,1795],{},[1688,37377,1733],{"separator":1732},[1788,37379,37380,37382],{},[898,37381,1727],{},[1793,37383,1806],{},[1688,37385,1733],{"separator":1732},[1688,37387,9899],{},[1688,37389,1733],{"separator":1732},[1788,37391,37392,37394],{},[898,37393,1727],{},[898,37395,37100],{},[1688,37397,1733],{"separator":1732},[898,37399,1854],{},[1688,37401,2076],{"stretchy":2065},[898,37403,2263],{"mathvariant":1822},[21003,37405],{"width":28316},[21003,37407,37408],{},[2041,37409,37410],{},"(2.1)",[902,37412,37413],{"encoding":904},"Q = D(P, P_1, P_2, \\dots, P_n, Y). \\tag{2.1}",[724,37415,37416,37417,37420,37421,37434],{},"Důležitou vlastností je ",[38,37418,37419],{},"homogenita",": změní-li se všechny nezávisle proměnné ",[883,37422,37424],{"className":37423},[886],[888,37425,37426],{"xmlns":890},[892,37427,37428,37432],{},[895,37429,37430],{},[898,37431,2046],{},[902,37433,2046],{"encoding":904},"-krát, poptávané množství se nezmění,",[883,37436,37438],{"className":37437},[886],[888,37439,37440],{"xmlns":890,"display":28306},[892,37441,37442,37557],{},[20995,37443,37444],{"width":28311},[21000,37445,37446,37448,37550,37552],{},[21003,37447],{"width":28316},[21003,37449,37450],{},[895,37451,37452,37454,37456,37458,37460,37462,37464,37466,37468,37474,37476,37478,37484,37486,37488,37490,37492,37498,37500,37502,37504,37506,37508,37510,37512,37514,37516,37522,37524,37530,37532,37534,37536,37542,37544,37546,37548],{},[898,37453,1872],{},[1688,37455,1690],{},[898,37457,4440],{},[1688,37459,2066],{"stretchy":2065},[898,37461,2046],{},[898,37463,1727],{},[1688,37465,1733],{"separator":1732},[898,37467,2046],{},[1788,37469,37470,37472],{},[898,37471,1727],{},[1793,37473,1795],{},[1688,37475,1733],{"separator":1732},[898,37477,2046],{},[1788,37479,37480,37482],{},[898,37481,1727],{},[1793,37483,1806],{},[1688,37485,1733],{"separator":1732},[1688,37487,9899],{},[1688,37489,1733],{"separator":1732},[898,37491,2046],{},[1788,37493,37494,37496],{},[898,37495,1727],{},[898,37497,37100],{},[1688,37499,1733],{"separator":1732},[898,37501,2046],{},[898,37503,1854],{},[1688,37505,2076],{"stretchy":2065},[1688,37507,1690],{},[898,37509,4440],{},[1688,37511,2066],{"stretchy":2065},[898,37513,1727],{},[1688,37515,1733],{"separator":1732},[1788,37517,37518,37520],{},[898,37519,1727],{},[1793,37521,1795],{},[1688,37523,1733],{"separator":1732},[1788,37525,37526,37528],{},[898,37527,1727],{},[1793,37529,1806],{},[1688,37531,1733],{"separator":1732},[1688,37533,9899],{},[1688,37535,1733],{"separator":1732},[1788,37537,37538,37540],{},[898,37539,1727],{},[898,37541,37100],{},[1688,37543,1733],{"separator":1732},[898,37545,1854],{},[1688,37547,2076],{"stretchy":2065},[898,37549,2263],{"mathvariant":1822},[21003,37551],{"width":28316},[21003,37553,37554],{},[2041,37555,37556],{},"(2.2)",[902,37558,37559],{"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}",[4124,37561,37562],{},[724,37563,37564,37566,37567,2263],{},[883,37565,4668],{}," Pozor\nHomogenita platí pouze v zidealizovaném vícefaktorovém modelu; ",[38,37568,37569],{},"v jednofaktorových modelech neplatí",[724,37571,37572,37573,1343,37576,4142,37579,37582],{},"Rozlišuje se poptávka ",[38,37574,37575],{},"individuální",[38,37577,37578],{},"tržní",[38,37580,37581],{},"agregátní"," (není-li specifikováno, rozumí se tržní).",[198,37584,37586],{"id":37585},"jednofaktorové-modely","Jednofaktorové modely",[37588,37589,37591],"h4",{"id":37590},"funkce-poptávky-v-užším-slova-smyslu","Funkce poptávky v užším slova smyslu",[724,37593,37594,37595,37608,37609,2965],{},"Poptávané množství ",[883,37596,37598],{"className":37597},[886],[888,37599,37600],{"xmlns":890},[892,37601,37602,37606],{},[895,37603,37604],{},[898,37605,1872],{},[902,37607,1872],{"encoding":904}," závisí pouze na ceně ",[883,37610,37612],{"className":37611},[886],[888,37613,37614],{"xmlns":890},[892,37615,37616,37620],{},[895,37617,37618],{},[898,37619,1727],{},[902,37621,1727],{"encoding":904},[883,37623,37625],{"className":37624},[886],[888,37626,37627],{"xmlns":890,"display":28306},[892,37628,37629,37681],{},[20995,37630,37631],{"width":28311},[21000,37632,37633,37635,37674,37676],{},[21003,37634],{"width":28316},[21003,37636,37637],{},[895,37638,37639,37641,37643,37645,37647,37649,37651,37653,37655,37658,37660,37662,37664,37666,37668,37670,37672],{},[898,37640,1872],{},[1688,37642,1690],{},[898,37644,4440],{},[1688,37646,2066],{"stretchy":2065},[898,37648,1727],{},[1688,37650,2076],{"stretchy":2065},[1688,37652,1733],{"separator":1732},[6134,37654],{"width":6136},[2041,37656,37657],{},"resp.",[6134,37659],{"width":6136},[898,37661,1727],{},[1688,37663,1690],{},[898,37665,4440],{},[1688,37667,2066],{"stretchy":2065},[898,37669,1872],{},[1688,37671,2076],{"stretchy":2065},[898,37673,2263],{"mathvariant":1822},[21003,37675],{"width":28316},[21003,37677,37678],{},[2041,37679,37680],{},"(2.3)",[902,37682,37683],{"encoding":904},"Q = D(P), \\qquad \\text{resp.} \\qquad P = D(Q). \\tag{2.3}",[724,37685,37686,37687,10277,37690,4176],{},"Graf této funkce se nazývá ",[38,37688,37689],{},"křivka poptávky",[614,37691,37692],{},"demand curve",[37588,37694,37696],{"id":37695},"zákon-klesající-poptávky","Zákon klesající poptávky",[4124,37698,37699],{},[724,37700,37701],{},[38,37702,37703,37704,37717,37718,37731,37732,37717,37745,37758],{},"Roste-li cena ",[883,37705,37707],{"className":37706},[886],[888,37708,37709],{"xmlns":890},[892,37710,37711,37715],{},[895,37712,37713],{},[898,37714,1727],{},[902,37716,1727],{"encoding":904},", pak množství ",[883,37719,37721],{"className":37720},[886],[888,37722,37723],{"xmlns":890},[892,37724,37725,37729],{},[895,37726,37727],{},[898,37728,1872],{},[902,37730,1872],{"encoding":904}," klesá; klesá-li cena ",[883,37733,37735],{"className":37734},[886],[888,37736,37737],{"xmlns":890},[892,37738,37739,37743],{},[895,37740,37741],{},[898,37742,1727],{},[902,37744,1727],{"encoding":904},[883,37746,37748],{"className":37747},[886],[888,37749,37750],{"xmlns":890},[892,37751,37752,37756],{},[895,37753,37754],{},[898,37755,1872],{},[902,37757,1872],{"encoding":904}," roste.",[724,37760,37761,37762,37765],{},"Spotřebitelé jsou ochotni nakoupit větší množství za nižší cenu (mezní užitečnost — viz kap. 6). Zákon platí za ",[38,37763,37764],{},"normálních podmínek","; první kvantitativní formulaci podal Marshall (1890).",[4124,37767,37768,37773],{},[724,37769,37770,37772],{},[883,37771,4412],{}," Intuice — proč zákon platí",[120,37774,37775,37781],{},[123,37776,37777,37780],{},[38,37778,37779],{},"Substituční efekt"," — růst ceny vede ke snaze nahradit zboží jiným.",[123,37782,37783,37786],{},[38,37784,37785],{},"Důchodový efekt"," — růst ceny způsobí nevítaný úbytek reálného důchodu.",[724,37788,37789,37790,37803,37804,37817,37818,37844,37845,37871,37872,8358,37898,37901,37902,2263],{},"Každá funkce poptávky je tedy klesající. Cena ",[883,37791,37793],{"className":37792},[886],[888,37794,37795],{"xmlns":890},[892,37796,37797,37801],{},[895,37798,37799],{},[898,37800,1727],{},[902,37802,1727],{"encoding":904}," se vynáší na svislou osu, množství ",[883,37805,37807],{"className":37806},[886],[888,37808,37809],{"xmlns":890},[892,37810,37811,37815],{},[895,37812,37813],{},[898,37814,1872],{},[902,37816,1872],{"encoding":904}," na vodorovnou. Hypotetická křivka prochází body ",[883,37819,37821],{"className":37820},[886],[888,37822,37823],{"xmlns":890},[892,37824,37825,37841],{},[895,37826,37827,37829,37831,37833,37839],{},[1688,37828,2748],{"stretchy":2065},[1793,37830,1779],{},[1688,37832,1733],{"separator":1732},[1788,37834,37835,37837],{},[898,37836,1727],{},[1793,37838,1779],{},[1688,37840,2763],{"stretchy":2065},[902,37842,37843],{"encoding":904},"[0, P_0]"," (cena, při níž je zboží neprodejné) a ",[883,37846,37848],{"className":37847},[886],[888,37849,37850],{"xmlns":890},[892,37851,37852,37868],{},[895,37853,37854,37856,37862,37864,37866],{},[1688,37855,2748],{"stretchy":2065},[1788,37857,37858,37860],{},[898,37859,1872],{},[1793,37861,1779],{},[1688,37863,1733],{"separator":1732},[1793,37865,1779],{},[1688,37867,2763],{"stretchy":2065},[902,37869,37870],{"encoding":904},"[Q_0, 0]"," (teoretický objem při nulové ceně). Interval ",[883,37873,37875],{"className":37874},[886],[888,37876,37877],{"xmlns":890},[892,37878,37879,37895],{},[895,37880,37881,37883,37885,37887,37893],{},[1688,37882,2066],{"stretchy":2065},[1793,37884,1779],{},[1688,37886,1733],{"separator":1732},[1788,37888,37889,37891],{},[898,37890,1727],{},[1793,37892,1779],{},[1688,37894,2076],{"stretchy":2065},[902,37896,37897],{"encoding":904},"(0, P_0)",[38,37899,37900],{},"reálné cenové rozpětí",". Za teoretických předpokladů je křivka ",[38,37903,37904],{},"konvexní",[724,37906,37907],{},[614,37908,37909,37910,37932,37933,4142,37958,2263],{},"Obrázek 2.1: Hypotetická křivka poptávky v rovině ",[883,37911,37913],{"className":37912},[886],[888,37914,37915],{"xmlns":890},[892,37916,37917,37929],{},[895,37918,37919,37921,37923,37925,37927],{},[1688,37920,2066],{"stretchy":2065},[898,37922,1872],{},[1688,37924,1733],{"separator":1732},[898,37926,1727],{},[1688,37928,2076],{"stretchy":2065},[902,37930,37931],{"encoding":904},"(Q, P)"," — klesající, konvexní, procházející body ",[883,37934,37936],{"className":37935},[886],[888,37937,37938],{"xmlns":890},[892,37939,37940,37956],{},[895,37941,37942,37944,37946,37948,37954],{},[1688,37943,2748],{"stretchy":2065},[1793,37945,1779],{},[1688,37947,1733],{"separator":1732},[1788,37949,37950,37952],{},[898,37951,1727],{},[1793,37953,1779],{},[1688,37955,2763],{"stretchy":2065},[902,37957,37843],{"encoding":904},[883,37959,37961],{"className":37960},[886],[888,37962,37963],{"xmlns":890},[892,37964,37965,37981],{},[895,37966,37967,37969,37975,37977,37979],{},[1688,37968,2748],{"stretchy":2065},[1788,37970,37971,37973],{},[898,37972,1872],{},[1793,37974,1779],{},[1688,37976,1733],{"separator":1732},[1793,37978,1779],{},[1688,37980,2763],{"stretchy":2065},[902,37982,37870],{"encoding":904},[37588,37984,37986],{"id":37985},"lineární-model-poptávky","Lineární model poptávky",[724,37988,37989],{},"Nejjednodušší závislostí je",[883,37991,37993],{"className":37992},[886],[888,37994,37995],{"xmlns":890,"display":28306},[892,37996,37997,38046],{},[20995,37998,37999],{"width":28311},[21000,38000,38001,38003,38039,38041],{},[21003,38002],{"width":28316},[21003,38004,38005],{},[895,38006,38007,38009,38011,38013,38015,38017,38019,38021,38023,38025,38027,38029,38031,38033,38035,38037],{},[898,38008,1727],{},[1688,38010,1690],{},[898,38012,207],{},[898,38014,1872],{},[1688,38016,1696],{},[898,38018,1918],{},[1688,38020,1733],{"separator":1732},[6134,38022],{"width":6136},[898,38024,207],{},[1688,38026,3704],{},[1793,38028,1779],{},[1688,38030,1733],{"separator":1732},[2041,38032,2558],{},[898,38034,1918],{},[1688,38036,3665],{},[1793,38038,12708],{},[21003,38040],{"width":28316},[21003,38042,38043],{},[2041,38044,38045],{},"(2.4)",[902,38047,38048],{"encoding":904},"P = aQ + b, \\qquad a \u003C 0,\\ b > 0. \\tag{2.4}",[724,38050,38051,38052,21835,38088,4142,38112,8293,38138,38160,38161,2263],{},"Křivka poptávky je přímka se záporným sklonem. Alternativně ",[883,38053,38055],{"className":38054},[886],[888,38056,38057],{"xmlns":890},[892,38058,38059,38085],{},[895,38060,38061,38063,38065,38073,38075,38077],{},[898,38062,1872],{},[1688,38064,1690],{},[1777,38066,38067],{"scriptlevel":1779,"displaystyle":2065},[1781,38068,38069,38071],{},[1793,38070,1795],{},[898,38072,207],{},[898,38074,1727],{},[1688,38076,1954],{},[1777,38078,38079],{"scriptlevel":1779,"displaystyle":2065},[1781,38080,38081,38083],{},[898,38082,1918],{},[898,38084,207],{},[902,38086,38087],{"encoding":904},"Q = \\tfrac{1}{a}P - \\tfrac{b}{a}",[883,38089,38091],{"className":38090},[886],[888,38092,38093],{"xmlns":890},[892,38094,38095,38109],{},[895,38096,38097,38105,38107],{},[1777,38098,38099],{"scriptlevel":1779,"displaystyle":2065},[1781,38100,38101,38103],{},[1793,38102,1795],{},[898,38104,207],{},[1688,38106,3704],{},[1793,38108,1779],{},[902,38110,38111],{"encoding":904},"\\tfrac{1}{a} \u003C 0",[883,38113,38115],{"className":38114},[886],[888,38116,38117],{"xmlns":890},[892,38118,38119,38135],{},[895,38120,38121,38123,38131,38133],{},[1688,38122,1954],{},[1777,38124,38125],{"scriptlevel":1779,"displaystyle":2065},[1781,38126,38127,38129],{},[898,38128,1918],{},[898,38130,207],{},[1688,38132,3665],{},[1793,38134,1779],{},[902,38136,38137],{"encoding":904},"-\\tfrac{b}{a} > 0",[883,38139,38141],{"className":38140},[886],[888,38142,38143],{"xmlns":890},[892,38144,38145,38157],{},[895,38146,38147,38149,38151,38153,38155],{},[1688,38148,2066],{"stretchy":2065},[1793,38150,1779],{},[1688,38152,1733],{"separator":1732},[898,38154,1918],{},[1688,38156,2076],{"stretchy":2065},[902,38158,38159],{"encoding":904},"(0, b)",". Tento model odpovídá ",[38,38162,38163],{},"nedokonalé konkurenci",[38165,38166,38168],"h5",{"id":38167},"příklad-21","Příklad 2.1",[724,38170,38171,38174,38175,2263],{},[38,38172,38173],{},"Zadání:"," Lineární poptávka ",[883,38176,38178],{"className":38177},[886],[888,38179,38180],{"xmlns":890},[892,38181,38182,38198],{},[895,38183,38184,38186,38188,38190,38192,38194,38196],{},[898,38185,1727],{},[1688,38187,1690],{},[1688,38189,1954],{},[1793,38191,1806],{},[898,38193,1872],{},[1688,38195,1696],{},[1793,38197,3383],{},[902,38199,38200],{"encoding":904},"P = -2Q + 60",[724,38202,38203,38206,38207,38229,38230,2263],{},[38,38204,38205],{},"Řešení:"," Reálné cenové rozpětí je ",[883,38208,38210],{"className":38209},[886],[888,38211,38212],{"xmlns":890},[892,38213,38214,38226],{},[895,38215,38216,38218,38220,38222,38224],{},[1688,38217,2066],{"stretchy":2065},[1793,38219,1779],{},[1688,38221,1733],{"separator":1732},[1793,38223,3383],{},[1688,38225,2076],{"stretchy":2065},[902,38227,38228],{"encoding":904},"(0, 60)","; alternativní tvar je ",[883,38231,38233],{"className":38232},[886],[888,38234,38235],{"xmlns":890},[892,38236,38237,38260],{},[895,38238,38239,38241,38243,38245,38253,38255,38257],{},[898,38240,1872],{},[1688,38242,1690],{},[1688,38244,1954],{},[1777,38246,38247],{"scriptlevel":1779,"displaystyle":2065},[1781,38248,38249,38251],{},[1793,38250,1795],{},[1793,38252,1806],{},[898,38254,1727],{},[1688,38256,1696],{},[1793,38258,38259],{},"30",[902,38261,38262],{"encoding":904},"Q = -\\tfrac{1}{2}P + 30",[16,38264,38265,38288],{},[19,38266,38267],{},[22,38268,38269,38284,38286],{},[25,38270,38271],{},[883,38272,38274],{"className":38273},[886],[888,38275,38276],{"xmlns":890},[892,38277,38278,38282],{},[895,38279,38280],{},[898,38281,1727],{},[902,38283,1727],{"encoding":904},[25,38285,5467],{},[25,38287,9290],{},[30,38289,38290],{},[22,38291,38292,38307,38309],{},[35,38293,38294],{},[883,38295,38297],{"className":38296},[886],[888,38298,38299],{"xmlns":890},[892,38300,38301,38305],{},[895,38302,38303],{},[898,38304,1872],{},[902,38306,1872],{"encoding":904},[35,38308,3121],{},[35,38310,9290],{},[724,38312,38313],{},[614,38314,38315,38316,4142,38338,2263],{},"Obrázek 2.2 \u002F 2.3: Lineární poptávka — přímka s průsečíky ",[883,38317,38319],{"className":38318},[886],[888,38320,38321],{"xmlns":890},[892,38322,38323,38335],{},[895,38324,38325,38327,38329,38331,38333],{},[1688,38326,2748],{"stretchy":2065},[1793,38328,1779],{},[1688,38330,1733],{"separator":1732},[898,38332,1918],{},[1688,38334,2763],{"stretchy":2065},[902,38336,38337],{"encoding":904},"[0, b]",[883,38339,38341],{"className":38340},[886],[888,38342,38343],{"xmlns":890},[892,38344,38345,38363],{},[895,38346,38347,38349,38351,38353,38355,38357,38359,38361],{},[1688,38348,2748],{"stretchy":2065},[1688,38350,1954],{},[898,38352,1918],{},[898,38354,4930],{"mathvariant":1822},[898,38356,207],{},[1688,38358,1733],{"separator":1732},[1793,38360,1779],{},[1688,38362,2763],{"stretchy":2065},[902,38364,38365],{"encoding":904},"[-b\u002Fa, 0]",[37588,38367,38369],{"id":38368},"poptávka-při-dokonalé-konkurenci","Poptávka při dokonalé konkurenci",[724,38371,38372,38373,38390],{},"Přebírá-li každý účastník trhu pevnou tržní cenu ",[883,38374,38376],{"className":38375},[886],[888,38377,38378],{"xmlns":890},[892,38379,38380,38388],{},[895,38381,38382],{},[1850,38383,38384,38386],{},[898,38385,1727],{},[1688,38387,1857],{},[902,38389,4660],{"encoding":904},", je funkce poptávky konstantní:",[883,38392,38394],{"className":38393},[886],[888,38395,38396],{"xmlns":890,"display":28306},[892,38397,38398,38412],{},[895,38399,38400,38402,38404,38410],{},[898,38401,1727],{},[1688,38403,1690],{},[1850,38405,38406,38408],{},[898,38407,1727],{},[1688,38409,1857],{},[898,38411,2263],{"mathvariant":1822},[902,38413,38414],{"encoding":904},"P = P^*.",[724,38416,38417],{},[614,38418,38419,38420,38441,38442,2263],{},"Obrázek 2.4: Vodorovná přímka v rovině ",[883,38421,38423],{"className":38422},[886],[888,38424,38425],{"xmlns":890},[892,38426,38427,38439],{},[895,38428,38429,38431,38433,38435,38437],{},[1688,38430,2066],{"stretchy":2065},[898,38432,1872],{},[1688,38434,1733],{"separator":1732},[898,38436,1727],{},[1688,38438,2076],{"stretchy":2065},[902,38440,37931],{"encoding":904}," na úrovni ",[883,38443,38445],{"className":38444},[886],[888,38446,38447],{"xmlns":890},[892,38448,38449,38461],{},[895,38450,38451,38453,38455],{},[898,38452,1727],{},[1688,38454,1690],{},[1850,38456,38457,38459],{},[898,38458,1727],{},[1688,38460,1857],{},[902,38462,4613],{"encoding":904},[37588,38464,38466],{"id":38465},"giffenův-statek","Giffenův statek",[724,38468,38469,38470,38472,38473,38475,38476,2263],{},"Existují zboží, u nichž je křivka poptávky ",[38,38471,13904],{}," — tzv. ",[38,38474,38466],{},". Jde o případy, kdy důchodový efekt převáží substituční (klasický příklad: rýže u chudých asijských spotřebitelů). Giffenův statek patří k ",[38,38477,38478],{},"podřadnému zboží",[38165,38480,38482],{"id":38481},"příklad-22","Příklad 2.2",[724,38484,38485,38488,38489,38507,38508,38530,38531,38549,38550,38568,38569,38592],{},[38,38486,38487],{},"Zadání a popis:"," Křivka ",[883,38490,38492],{"className":38491},[886],[888,38493,38494],{"xmlns":890},[892,38495,38496,38504],{},[895,38497,38498],{},[1788,38499,38500,38502],{},[898,38501,4440],{},[1793,38503,1795],{},[902,38505,38506],{"encoding":904},"D_1"," reprezentuje poptávku rodiny po cukru s reálným cenovým rozpětím ",[883,38509,38511],{"className":38510},[886],[888,38512,38513],{"xmlns":890},[892,38514,38515,38527],{},[895,38516,38517,38519,38521,38523,38525],{},[1688,38518,2066],{"stretchy":2065},[1793,38520,1779],{},[1688,38522,1733],{"separator":1732},[1793,38524,36484],{},[1688,38526,2076],{"stretchy":2065},[902,38528,38529],{"encoding":904},"(0, 15)"," pencí za libru; je nejprve konvexní, od inflexního bodu ",[883,38532,38534],{"className":38533},[886],[888,38535,38536],{"xmlns":890},[892,38537,38538,38546],{},[895,38539,38540],{},[1788,38541,38542,38544],{},[898,38543,1872],{},[1793,38545,1779],{},[902,38547,38548],{"encoding":904},"Q_0"," konkávní, se saturací kolem 17 liber. Křivka ",[883,38551,38553],{"className":38552},[886],[888,38554,38555],{"xmlns":890},[892,38556,38557,38565],{},[895,38558,38559],{},[1788,38560,38561,38563],{},[898,38562,4440],{},[1793,38564,1806],{},[902,38566,38567],{"encoding":904},"D_2"," na širším trhu je konvexní klesající z bodu ",[883,38570,38572],{"className":38571},[886],[888,38573,38574],{"xmlns":890},[892,38575,38576,38589],{},[895,38577,38578,38580,38582,38584,38587],{},[1688,38579,2748],{"stretchy":2065},[1793,38581,1779],{},[1688,38583,1733],{"separator":1732},[1793,38585,38586],{},"21",[1688,38588,2763],{"stretchy":2065},[902,38590,38591],{"encoding":904},"[0, 21]"," centů.",[198,38594,38596],{"id":38595},"engelova-funkce-závislost-na-důchodu","Engelova funkce (závislost na důchodu)",[724,38598,38599,38600,2965],{},"Druhý jednofaktorový model předpokládá závislost množství pouze na důchodu ",[883,38601,38603],{"className":38602},[886],[888,38604,38605],{"xmlns":890},[892,38606,38607,38611],{},[895,38608,38609],{},[898,38610,1854],{},[902,38612,1854],{"encoding":904},[883,38614,38616],{"className":38615},[886],[888,38617,38618],{"xmlns":890,"display":28306},[892,38619,38620,38651],{},[20995,38621,38622],{"width":28311},[21000,38623,38624,38626,38644,38646],{},[21003,38625],{"width":28316},[21003,38627,38628],{},[895,38629,38630,38632,38634,38636,38638,38640,38642],{},[898,38631,1872],{},[1688,38633,1690],{},[898,38635,4509],{},[1688,38637,2066],{"stretchy":2065},[898,38639,1854],{},[1688,38641,2076],{"stretchy":2065},[898,38643,2263],{"mathvariant":1822},[21003,38645],{"width":28316},[21003,38647,38648],{},[2041,38649,38650],{},"(2.5)",[902,38652,38653],{"encoding":904},"Q = E(Y). \\tag{2.5}",[724,38655,38656,38657,38660,38661,38664],{},"Funkce se nazývá ",[38,38658,38659],{},"Engelova",", její graf ",[38,38662,38663],{},"Engelova křivka",". Tvar závisí na typu zboží:",[120,38666,38667,38799],{},[123,38668,38669,7271,38672,38685,38686,38699,38700,38717,38718],{},[38,38670,38671],{},"Normální (superior) zboží",[883,38673,38675],{"className":38674},[886],[888,38676,38677],{"xmlns":890},[892,38678,38679,38683],{},[895,38680,38681],{},[898,38682,1872],{},[902,38684,1872],{"encoding":904}," roste s ",[883,38687,38689],{"className":38688},[886],[888,38690,38691],{"xmlns":890},[892,38692,38693,38697],{},[895,38694,38695],{},[898,38696,1854],{},[902,38698,1854],{"encoding":904},", nepřesáhne hodnotu ",[883,38701,38703],{"className":38702},[886],[888,38704,38705],{"xmlns":890},[892,38706,38707,38715],{},[895,38708,38709],{},[1788,38710,38711,38713],{},[898,38712,1872],{},[1793,38714,1779],{},[902,38716,38548],{"encoding":904},":\n",[120,38719,38720,38752],{},[123,38721,38722,38725,38726,38729,38730,2263],{},[38,38723,38724],{},"Nezbytné zboží"," (potraviny, léky) — malá citlivost, ",[38,38727,38728],{},"konkávní"," křivka, autonomní spotřeba ",[883,38731,38733],{"className":38732},[886],[888,38734,38735],{"xmlns":890},[892,38736,38737,38749],{},[895,38738,38739,38745,38747],{},[1788,38740,38741,38743],{},[898,38742,1872],{},[1793,38744,1795],{},[1688,38746,3665],{},[1793,38748,1779],{},[902,38750,38751],{"encoding":904},"Q_1 > 0",[123,38753,38754,38757,38758,38776,38777,38779,38780,2170,38797,2263],{},[38,38755,38756],{},"Luxusní zboží"," — velká citlivost až od hladiny ",[883,38759,38761],{"className":38760},[886],[888,38762,38763],{"xmlns":890},[892,38764,38765,38773],{},[895,38766,38767],{},[1788,38768,38769,38771],{},[898,38770,1854],{},[1793,38772,1795],{},[902,38774,38775],{"encoding":904},"Y_1",", křivka je nejprve ",[38,38778,37904],{}," a od ",[883,38781,38783],{"className":38782},[886],[888,38784,38785],{"xmlns":890},[892,38786,38787,38795],{},[895,38788,38789],{},[1788,38790,38791,38793],{},[898,38792,1854],{},[1793,38794,1795],{},[902,38796,38775],{"encoding":904},[38,38798,38728],{},[123,38800,38801,38804,38805,38823],{},[38,38802,38803],{},"Podřadné (inferior) zboží"," — od hladiny ",[883,38806,38808],{"className":38807},[886],[888,38809,38810],{"xmlns":890},[892,38811,38812,38820],{},[895,38813,38814],{},[1788,38815,38816,38818],{},[898,38817,1854],{},[1793,38819,1779],{},[902,38821,38822],{"encoding":904},"Y_0"," množství s růstem důchodu klesá.",[724,38825,38826,38827,38830,38831,4176],{},"Mírou citlivosti je ",[614,38828,38829],{},"důchodová elasticita"," (viz ",[207,38832,4155],{"className":38833,"dataFsResolvedFilePath":848,"href":849},[210],[724,38835,38836],{},[614,38837,38838],{},"Obrázek 2.6: Tři panely Engelových křivek — (a) nezbytné, (b) luxusní, (c) podřadné zboží.",[37588,38840,38842],{"id":38841},"intuice-co-vlastně-znamená-podřadné","Intuice — co vlastně znamená „podřadné\"?",[4124,38844,38845,38916,38959],{},[724,38846,38847,38849,38850,2170,38853,2170,38866,5925,38868,38881,38882,38885,38886,2263],{},[883,38848,4668],{}," Pozor — nezbytné ≠ podřadné\n",[38,38851,38852],{},"Nezbytné zboží:",[883,38854,38856],{"className":38855},[886],[888,38857,38858],{"xmlns":890},[892,38859,38860,38864],{},[895,38861,38862],{},[898,38863,1872],{},[902,38865,1872],{"encoding":904},[38,38867,7578],{},[883,38869,38871],{"className":38870},[886],[888,38872,38873],{"xmlns":890},[892,38874,38875,38879],{},[895,38876,38877],{},[898,38878,1854],{},[902,38880,1854],{"encoding":904},", ale ",[38,38883,38884],{},"pomaleji"," než důchod (2× plat → třeba 1,3× spotřeba). ",[883,38887,38889],{"className":38888},[886],[888,38890,38891],{"xmlns":890},[892,38892,38893,38913],{},[895,38894,38895,38901,38903,38905,38907,38909,38911],{},[1788,38896,38897,38899],{},[898,38898,4509],{},[898,38900,1854],{},[1688,38902,6762],{},[1688,38904,2066],{"stretchy":2065},[1793,38906,1779],{},[1688,38908,1733],{"separator":1732},[1793,38910,1795],{},[1688,38912,2076],{"stretchy":2065},[902,38914,38915],{"encoding":904},"E_Y \\in (0, 1)",[724,38917,38918,2170,38921,2170,38934,38936,38937,2263],{},[38,38919,38920],{},"Podřadné zboží:",[883,38922,38924],{"className":38923},[886],[888,38925,38926],{"xmlns":890},[892,38927,38928,38932],{},[895,38929,38930],{},[898,38931,1872],{},[902,38933,1872],{"encoding":904},[38,38935,7598],{}," v absolutních číslech (2× plat → třeba 0,7× spotřeba). ",[883,38938,38940],{"className":38939},[886],[888,38941,38942],{"xmlns":890},[892,38943,38944,38956],{},[895,38945,38946,38952,38954],{},[1788,38947,38948,38950],{},[898,38949,4509],{},[898,38951,1854],{},[1688,38953,3704],{},[1793,38955,1779],{},[902,38957,38958],{"encoding":904},"E_Y \u003C 0",[724,38960,38961,38962,2263],{},"Klíčový rozdíl: u podřadného zboží si při vyšším důchodu kupuješ ",[38,38963,38964],{},"méně kusů, ne jen proporčně méně",[724,38966,38967,38970,38971,38974],{},[38,38968,38969],{},"Mechanismus — substituce „nahoru\"."," Samotné zboží se nezhoršilo, jen si teď můžeš dovolit ",[38,38972,38973],{},"kvalitnější alternativu",". Růst důchodu → přesun k prémiovému substitutu → absolutní pokles nákupu „levnější verze\".",[724,38976,38977],{},[2821,38978],{"alt":38979,"className":38980,"src":38981},"imek-engelovy-krivky-3typy",[210,2825],"\u002Fwiki-assets\u002Fimek-engelovy-krivky-3typy.jpeg",[38165,38983,38985],{"id":38984},"české-příklady","České příklady",[16,38987,38988,38998],{},[19,38989,38990],{},[22,38991,38992,38995],{},[25,38993,38994],{},"Podřadné",[25,38996,38997],{},"Nahradí se za",[30,38999,39000,39008,39016,39024,39032,39040,39048,39056],{},[22,39001,39002,39005],{},[35,39003,39004],{},"Instantní polévky, ramen",[35,39006,39007],{},"Čerstvé jídlo, restaurace",[22,39009,39010,39013],{},[35,39011,39012],{},"MHD (autobus, tramvaj)",[35,39014,39015],{},"Vlastní auto, Uber, taxi",[22,39017,39018,39021],{},[35,39019,39020],{},"Mražené polotovary, pizza z mrazáku",[35,39022,39023],{},"Čerstvé suroviny, hotovky",[22,39025,39026,39029],{},[35,39027,39028],{},"Privátní značky supermarketů (K-Classic, Clever)",[35,39030,39031],{},"Značkové produkty",[22,39033,39034,39037],{},[35,39035,39036],{},"Paštika Májka, obyčejný měkký salám",[35,39038,39039],{},"Kvalitní uzeniny, šunka od kosti",[22,39041,39042,39045],{},[35,39043,39044],{},"Second hand oblečení",[35,39046,39047],{},"Nové oblečení, značky",[22,39049,39050,39053],{},[35,39051,39052],{},"Krabicové víno, nejlevnější pivo",[35,39054,39055],{},"Lahvové víno, řemeslná piva",[22,39057,39058,39061],{},[35,39059,39060],{},"Ojetá auta nižších tříd",[35,39062,39063],{},"Nová auta, prémiové značky",[4124,39065,39066],{},[724,39067,39068,39070,39071,39074],{},[883,39069,4828],{}," Test 50 milionů\nPředstav si, že vyhraješ 50 milionů. ",[38,39072,39073],{},"Čeho si najednou koupíš méně"," (nebo vůbec)? To je tvoje podřadné zboží.",[724,39076,39077,39080,39081,10277,39084,39106,39107,10277,39110,39131,39132,39150,39151,39154],{},[38,39078,39079],{},"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 ",[38,39082,39083],{},"luxus",[883,39085,39087],{"className":39086},[886],[888,39088,39089],{"xmlns":890},[892,39090,39091,39103],{},[895,39092,39093,39099,39101],{},[1788,39094,39095,39097],{},[898,39096,4509],{},[898,39098,1854],{},[1688,39100,3665],{},[1793,39102,1795],{},[902,39104,39105],{"encoding":904},"E_Y > 1","), pro manažera s 200k platem ",[38,39108,39109],{},"podřadné",[883,39111,39113],{"className":39112},[886],[888,39114,39115],{"xmlns":890},[892,39116,39117,39129],{},[895,39118,39119,39125,39127],{},[1788,39120,39121,39123],{},[898,39122,4509],{},[898,39124,1854],{},[1688,39126,3704],{},[1793,39128,1779],{},[902,39130,38958],{"encoding":904},"). Proto je ",[883,39133,39135],{"className":39134},[886],[888,39136,39137],{"xmlns":890},[892,39138,39139,39147],{},[895,39140,39141],{},[1788,39142,39143,39145],{},[898,39144,4509],{},[898,39146,1854],{},[902,39148,39149],{"encoding":904},"E_Y"," vždy ",[38,39152,39153],{},"lokální veličina"," — platí pro danou úroveň důchodu, ne absolutně.",[724,39156,39157,39158,39160],{},"Extrémním případem podřadného zboží, kde substituční efekt převáží už na straně ceny, je ",[38,39159,38466],{}," (viz níže) — tam poptávková křivka dokonce roste.",[198,39162,39164,39165,2076],{"id":39163},"posun-poptávky-shift-of-demand","Posun poptávky (",[614,39166,39167],{},"shift of demand",[724,39169,39170,39171,39189,39190,39207,39208,39221,39222,2946,39235,39257,39258,39275,39276,39302,39303,39306],{},"Při změně exogenní proměnné (např. důchodu) se celá křivka poptávky posouvá. Uvažujme normální zboží. Ceně ",[883,39172,39174],{"className":39173},[886],[888,39175,39176],{"xmlns":890},[892,39177,39178,39186],{},[895,39179,39180],{},[1788,39181,39182,39184],{},[898,39183,1727],{},[1793,39185,1779],{},[902,39187,39188],{"encoding":904},"P_0"," odpovídá množství ",[883,39191,39193],{"className":39192},[886],[888,39194,39195],{"xmlns":890},[892,39196,39197,39205],{},[895,39198,39199],{},[1788,39200,39201,39203],{},[898,39202,1872],{},[1793,39204,1779],{},[902,39206,38548],{"encoding":904}," na křivce ",[883,39209,39211],{"className":39210},[886],[888,39212,39213],{"xmlns":890},[892,39214,39215,39219],{},[895,39216,39217],{},[898,39218,4440],{},[902,39220,4440],{"encoding":904},"; vzroste-li důchod z ",[883,39223,39225],{"className":39224},[886],[888,39226,39227],{"xmlns":890},[892,39228,39229,39233],{},[895,39230,39231],{},[898,39232,1854],{},[902,39234,1854],{"encoding":904},[883,39236,39238],{"className":39237},[886],[888,39239,39240],{"xmlns":890},[892,39241,39242,39254],{},[895,39243,39244,39250,39252],{},[1788,39245,39246,39248],{},[898,39247,1854],{},[1793,39249,1795],{},[1688,39251,3665],{},[898,39253,1854],{},[902,39255,39256],{"encoding":904},"Y_1 > Y",", pak stejné ceně ",[883,39259,39261],{"className":39260},[886],[888,39262,39263],{"xmlns":890},[892,39264,39265,39273],{},[895,39266,39267],{},[1788,39268,39269,39271],{},[898,39270,1727],{},[1793,39272,1779],{},[902,39274,39188],{"encoding":904}," odpovídá vyšší ",[883,39277,39279],{"className":39278},[886],[888,39280,39281],{"xmlns":890},[892,39282,39283,39299],{},[895,39284,39285,39291,39293],{},[1788,39286,39287,39289],{},[898,39288,1872],{},[1793,39290,1795],{},[1688,39292,3665],{},[1788,39294,39295,39297],{},[898,39296,1872],{},[1793,39298,1779],{},[902,39300,39301],{"encoding":904},"Q_1 > Q_0"," — křivka se ",[38,39304,39305],{},"posouvá doprava",". Pokles důchodu vede k posunu doleva.",[724,39308,39309],{},[2821,39310],{"alt":39311,"className":39312,"src":39313},"imek-posun-vs-pohyb-po-krivce",[210,2825],"\u002Fwiki-assets\u002Fimek-posun-vs-pohyb-po-krivce.jpeg",[724,39315,39316],{},"Posun může být způsoben i jinými faktory (např. zdaněním spotřebitele — viz dále).",[724,39318,39319],{},[614,39320,39321,39322,14258,39352,39373],{},"Obrázek 2.7: Posun poptávky — tři křivky ",[883,39323,39325],{"className":39324},[886],[888,39326,39327],{"xmlns":890},[892,39328,39329,39349],{},[895,39330,39331,39337,39339,39341,39343],{},[1788,39332,39333,39335],{},[898,39334,4440],{},[1793,39336,1806],{},[1688,39338,1733],{"separator":1732},[898,39340,4440],{},[1688,39342,1733],{"separator":1732},[1788,39344,39345,39347],{},[898,39346,4440],{},[1793,39348,1795],{},[902,39350,39351],{"encoding":904},"D_2, D, D_1",[883,39353,39355],{"className":39354},[886],[888,39356,39357],{"xmlns":890},[892,39358,39359,39371],{},[895,39360,39361,39363,39365,39367,39369],{},[1688,39362,2066],{"stretchy":2065},[898,39364,1872],{},[1688,39366,1733],{"separator":1732},[898,39368,1727],{},[1688,39370,2076],{"stretchy":2065},[902,39372,37931],{"encoding":904},", šipky naznačují posuny.",[38165,39375,39377],{"id":39376},"příklad-23-zdanění-kupujícího","Příklad 2.3 — zdanění kupujícího",[724,39379,39380,39382,39383,39406,39407,39424,39425,39442,39443,2263],{},[38,39381,38173],{}," Poptávce ",[883,39384,39386],{"className":39385},[886],[888,39387,39388],{"xmlns":890},[892,39389,39390,39404],{},[895,39391,39392,39394,39396,39398,39400,39402],{},[898,39393,1727],{},[1688,39395,1690],{},[898,39397,4440],{},[1688,39399,2066],{"stretchy":2065},[898,39401,1872],{},[1688,39403,2076],{"stretchy":2065},[902,39405,4896],{"encoding":904}," odpovídá ceně ",[883,39408,39410],{"className":39409},[886],[888,39411,39412],{"xmlns":890},[892,39413,39414,39422],{},[895,39415,39416],{},[1788,39417,39418,39420],{},[898,39419,1727],{},[1793,39421,1779],{},[902,39423,39188],{"encoding":904}," množství ",[883,39426,39428],{"className":39427},[886],[888,39429,39430],{"xmlns":890},[892,39431,39432,39440],{},[895,39433,39434],{},[1788,39435,39436,39438],{},[898,39437,1872],{},[1793,39439,1779],{},[902,39441,38548],{"encoding":904},". Na kupujícího je uložena jednotková daň ",[883,39444,39446],{"className":39445},[886],[888,39447,39448],{"xmlns":890},[892,39449,39450,39454],{},[895,39451,39452],{},[898,39453,3035],{},[902,39455,3035],{"encoding":904},[724,39457,39458,39460,39461,39478,39479,39501],{},[38,39459,38205],{}," Kupující nakupuje množství ",[883,39462,39464],{"className":39463},[886],[888,39465,39466],{"xmlns":890},[892,39467,39468,39476],{},[895,39469,39470],{},[1788,39471,39472,39474],{},[898,39473,1872],{},[1793,39475,1795],{},[902,39477,29242],{"encoding":904},", které odpovídá ceně ",[883,39480,39482],{"className":39481},[886],[888,39483,39484],{"xmlns":890},[892,39485,39486,39498],{},[895,39487,39488,39494,39496],{},[1788,39489,39490,39492],{},[898,39491,1727],{},[1793,39493,1779],{},[1688,39495,1696],{},[898,39497,3035],{},[902,39499,39500],{"encoding":904},"P_0 + T"," na původní křivce. Nová poptávka je",[883,39503,39505],{"className":39504},[886],[888,39506,39507],{"xmlns":890,"display":28306},[892,39508,39509,39543],{},[895,39510,39511,39513,39515,39521,39523,39525,39527,39529,39531,39533,39535,39537,39539,39541],{},[898,39512,1727],{},[1688,39514,1690],{},[1788,39516,39517,39519],{},[898,39518,4440],{},[1793,39520,1795],{},[1688,39522,2066],{"stretchy":2065},[898,39524,1872],{},[1688,39526,2076],{"stretchy":2065},[1688,39528,1690],{},[898,39530,4440],{},[1688,39532,2066],{"stretchy":2065},[898,39534,1872],{},[1688,39536,2076],{"stretchy":2065},[1688,39538,1954],{},[898,39540,3035],{},[1688,39542,1733],{"separator":1732},[902,39544,39545],{"encoding":904},"P = D_1(Q) = D(Q) - T,",[724,39547,39548,39549,2263],{},"tj. dojde k ",[38,39550,39551],{},"posunu poptávky doleva",[724,39553,39554],{},[614,39555,39556,39557,39578,39579,1343,39596,1343,39609,39630,39631,4142,39648,2263],{},"Obrázek 2.8: Dvě klesající poptávkové přímky v ",[883,39558,39560],{"className":39559},[886],[888,39561,39562],{"xmlns":890},[892,39563,39564,39576],{},[895,39565,39566,39568,39570,39572,39574],{},[1688,39567,2066],{"stretchy":2065},[898,39569,1872],{},[1688,39571,1733],{"separator":1732},[898,39573,1727],{},[1688,39575,2076],{"stretchy":2065},[902,39577,37931],{"encoding":904},"; na svislé ose jsou vyznačeny ",[883,39580,39582],{"className":39581},[886],[888,39583,39584],{"xmlns":890},[892,39585,39586,39594],{},[895,39587,39588],{},[1788,39589,39590,39592],{},[898,39591,1727],{},[1793,39593,1779],{},[902,39595,39188],{"encoding":904},[883,39597,39599],{"className":39598},[886],[888,39600,39601],{"xmlns":890},[892,39602,39603,39607],{},[895,39604,39605],{},[898,39606,3035],{},[902,39608,3035],{"encoding":904},[883,39610,39612],{"className":39611},[886],[888,39613,39614],{"xmlns":890},[892,39615,39616,39628],{},[895,39617,39618,39624,39626],{},[1788,39619,39620,39622],{},[898,39621,1727],{},[1793,39623,1779],{},[1688,39625,1696],{},[898,39627,3035],{},[902,39629,39500],{"encoding":904},"; na vodorovné ",[883,39632,39634],{"className":39633},[886],[888,39635,39636],{"xmlns":890},[892,39637,39638,39646],{},[895,39639,39640],{},[1788,39641,39642,39644],{},[898,39643,1872],{},[1793,39645,1795],{},[902,39647,29242],{"encoding":904},[883,39649,39651],{"className":39650},[886],[888,39652,39653],{"xmlns":890},[892,39654,39655,39663],{},[895,39656,39657],{},[1788,39658,39659,39661],{},[898,39660,1872],{},[1793,39662,1779],{},[902,39664,38548],{"encoding":904},[198,39666,39668],{"id":39667},"vícekomoditní-dvoukomoditní-trh","Vícekomoditní (dvoukomoditní) trh",[724,39670,39671],{},"Uvažujme dvě tržně závislá zboží s lineárními funkcemi poptávky:",[883,39673,39675],{"className":39674},[886],[888,39676,39677],{"xmlns":890,"display":28306},[892,39678,39679,39864],{},[20995,39680,39681],{"width":28311},[21000,39682,39683,39685,39857,39859],{},[21003,39684],{"width":28316},[21003,39686,39687],{},[20995,39688,39689,39773],{"rowspacing":20997,"columnalign":20998,"columnspacing":1823},[21000,39690,39691,39701],{},[21003,39692,39693],{},[1777,39694,39695],{"scriptlevel":1779,"displaystyle":1732},[1788,39696,39697,39699],{},[898,39698,1872],{},[1793,39700,1795],{},[21003,39702,39703],{},[1777,39704,39705],{"scriptlevel":1779,"displaystyle":1732},[895,39706,39707,39709,39711,39717,39719,39725,39727,39733,39735,39737,39743,39745,39751,39757,39759,39765,39771],{},[895,39708],{},[1688,39710,1690],{},[1788,39712,39713,39715],{},[898,39714,4440],{},[1793,39716,1795],{},[1688,39718,2066],{"stretchy":2065},[1788,39720,39721,39723],{},[898,39722,1727],{},[1793,39724,1795],{},[1688,39726,1733],{"separator":1732},[1788,39728,39729,39731],{},[898,39730,1727],{},[1793,39732,1806],{},[1688,39734,2076],{"stretchy":2065},[1688,39736,1690],{},[1788,39738,39739,39741],{},[898,39740,207],{},[1793,39742,1795],{},[1688,39744,1696],{},[1788,39746,39747,39749],{},[898,39748,1918],{},[1793,39750,1795],{},[1788,39752,39753,39755],{},[898,39754,1727],{},[1793,39756,1795],{},[1688,39758,1696],{},[1788,39760,39761,39763],{},[898,39762,2031],{},[1793,39764,1795],{},[1788,39766,39767,39769],{},[898,39768,1727],{},[1793,39770,1806],{},[1688,39772,1733],{"separator":1732},[21000,39774,39775,39785],{},[21003,39776,39777],{},[1777,39778,39779],{"scriptlevel":1779,"displaystyle":1732},[1788,39780,39781,39783],{},[898,39782,1872],{},[1793,39784,1806],{},[21003,39786,39787],{},[1777,39788,39789],{"scriptlevel":1779,"displaystyle":1732},[895,39790,39791,39793,39795,39801,39803,39809,39811,39817,39819,39821,39827,39829,39835,39841,39843,39849,39855],{},[895,39792],{},[1688,39794,1690],{},[1788,39796,39797,39799],{},[898,39798,4440],{},[1793,39800,1806],{},[1688,39802,2066],{"stretchy":2065},[1788,39804,39805,39807],{},[898,39806,1727],{},[1793,39808,1795],{},[1688,39810,1733],{"separator":1732},[1788,39812,39813,39815],{},[898,39814,1727],{},[1793,39816,1806],{},[1688,39818,2076],{"stretchy":2065},[1688,39820,1690],{},[1788,39822,39823,39825],{},[898,39824,207],{},[1793,39826,1806],{},[1688,39828,1696],{},[1788,39830,39831,39833],{},[898,39832,1918],{},[1793,39834,1806],{},[1788,39836,39837,39839],{},[898,39838,1727],{},[1793,39840,1795],{},[1688,39842,1696],{},[1788,39844,39845,39847],{},[898,39846,2031],{},[1793,39848,1806],{},[1788,39850,39851,39853],{},[898,39852,1727],{},[1793,39854,1806],{},[898,39856,2263],{"mathvariant":1822},[21003,39858],{"width":28316},[21003,39860,39861],{},[2041,39862,39863],{},"(2.6)",[902,39865,39866],{"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}",[37588,39868,39870],{"id":39869},"znaménková-analýza-parametrů","Znaménková analýza parametrů",[120,39872,39873,39920,39967],{},[123,39874,39875,1343,39897,39919],{},[883,39876,39878],{"className":39877},[886],[888,39879,39880],{"xmlns":890},[892,39881,39882,39894],{},[895,39883,39884,39890,39892],{},[1788,39885,39886,39888],{},[898,39887,207],{},[1793,39889,1795],{},[1688,39891,3665],{},[1793,39893,1779],{},[902,39895,39896],{"encoding":904},"a_1 > 0",[883,39898,39900],{"className":39899},[886],[888,39901,39902],{"xmlns":890},[892,39903,39904,39916],{},[895,39905,39906,39912,39914],{},[1788,39907,39908,39910],{},[898,39909,207],{},[1793,39911,1806],{},[1688,39913,3665],{},[1793,39915,1779],{},[902,39917,39918],{"encoding":904},"a_2 > 0"," (při nulových cenách je poptávané množství kladné),",[123,39921,39922,1343,39944,39966],{},[883,39923,39925],{"className":39924},[886],[888,39926,39927],{"xmlns":890},[892,39928,39929,39941],{},[895,39930,39931,39937,39939],{},[1788,39932,39933,39935],{},[898,39934,1918],{},[1793,39936,1795],{},[1688,39938,3704],{},[1793,39940,1779],{},[902,39942,39943],{"encoding":904},"b_1 \u003C 0",[883,39945,39947],{"className":39946},[886],[888,39948,39949],{"xmlns":890},[892,39950,39951,39963],{},[895,39952,39953,39959,39961],{},[1788,39954,39955,39957],{},[898,39956,2031],{},[1793,39958,1806],{},[1688,39960,3704],{},[1793,39962,1779],{},[902,39964,39965],{"encoding":904},"c_2 \u003C 0"," (vlastní koeficienty — zákon klesající poptávky),",[123,39968,39969,39970,1343,39987,40005,40006],{},"zkřížené koeficienty ",[883,39971,39973],{"className":39972},[886],[888,39974,39975],{"xmlns":890},[892,39976,39977,39985],{},[895,39978,39979],{},[1788,39980,39981,39983],{},[898,39982,2031],{},[1793,39984,1795],{},[902,39986,30039],{"encoding":904},[883,39988,39990],{"className":39989},[886],[888,39991,39992],{"xmlns":890},[892,39993,39994,40002],{},[895,39995,39996],{},[1788,39997,39998,40000],{},[898,39999,1918],{},[1793,40001,1806],{},[902,40003,40004],{"encoding":904},"b_2"," určují povahu vztahu:\n",[120,40007,40008,40058],{},[123,40009,40010,40013,40014,1343,40036,1733],{},[38,40011,40012],{},"substituty"," (máslo vs. margarín): ",[883,40015,40017],{"className":40016},[886],[888,40018,40019],{"xmlns":890},[892,40020,40021,40033],{},[895,40022,40023,40029,40031],{},[1788,40024,40025,40027],{},[898,40026,2031],{},[1793,40028,1795],{},[1688,40030,3665],{},[1793,40032,1779],{},[902,40034,40035],{"encoding":904},"c_1 > 0",[883,40037,40039],{"className":40038},[886],[888,40040,40041],{"xmlns":890},[892,40042,40043,40055],{},[895,40044,40045,40051,40053],{},[1788,40046,40047,40049],{},[898,40048,1918],{},[1793,40050,1806],{},[1688,40052,3665],{},[1793,40054,1779],{},[902,40056,40057],{"encoding":904},"b_2 > 0",[123,40059,40060,40063,40064,1343,40086,2263],{},[38,40061,40062],{},"komplementy"," (auto vs. benzín): ",[883,40065,40067],{"className":40066},[886],[888,40068,40069],{"xmlns":890},[892,40070,40071,40083],{},[895,40072,40073,40079,40081],{},[1788,40074,40075,40077],{},[898,40076,2031],{},[1793,40078,1795],{},[1688,40080,3704],{},[1793,40082,1779],{},[902,40084,40085],{"encoding":904},"c_1 \u003C 0",[883,40087,40089],{"className":40088},[886],[888,40090,40091],{"xmlns":890},[892,40092,40093,40105],{},[895,40094,40095,40101,40103],{},[1788,40096,40097,40099],{},[898,40098,1918],{},[1793,40100,1806],{},[1688,40102,3704],{},[1793,40104,1779],{},[902,40106,40107],{"encoding":904},"b_2 \u003C 0",[724,40109,40110],{},"Schematicky:",[724,40112,40113,40116],{},[38,40114,40115],{},"Substituty",[883,40117,40119],{"className":40118},[886],[888,40120,40121],{"xmlns":890},[892,40122,40123,40262],{},[895,40124,40125,40131,40133,40148,40150,40170,40172,40192,40194,40196,40202,40204,40218,40220,40240,40242],{},[1788,40126,40127,40129],{},[898,40128,1872],{},[1793,40130,1795],{},[1688,40132,1690],{},[898,40134,40135],{},[40136,40137,40138,40146],"munder",{},[1688,40139,40140],{},[1788,40141,40142,40144],{},[898,40143,207],{},[1793,40145,1795],{},[1688,40147,1696],{"lspace":1823,"rspace":1823},[1688,40149,1696],{},[898,40151,40152],{},[40136,40153,40154,40168],{},[1688,40155,40156,40162],{},[1788,40157,40158,40160],{},[898,40159,1918],{},[1793,40161,1795],{},[1788,40163,40164,40166],{},[898,40165,1727],{},[1793,40167,1795],{},[1688,40169,1954],{"lspace":1823,"rspace":1823},[1688,40171,1696],{},[898,40173,40174],{},[40136,40175,40176,40190],{},[1688,40177,40178,40184],{},[1788,40179,40180,40182],{},[898,40181,2031],{},[1793,40183,1795],{},[1788,40185,40186,40188],{},[898,40187,1727],{},[1793,40189,1806],{},[1688,40191,1696],{"lspace":1823,"rspace":1823},[1688,40193,1733],{"separator":1732},[6134,40195],{"width":6136},[1788,40197,40198,40200],{},[898,40199,1872],{},[1793,40201,1806],{},[1688,40203,1690],{},[898,40205,40206],{},[40136,40207,40208,40216],{},[1688,40209,40210],{},[1788,40211,40212,40214],{},[898,40213,207],{},[1793,40215,1806],{},[1688,40217,1696],{"lspace":1823,"rspace":1823},[1688,40219,1696],{},[898,40221,40222],{},[40136,40223,40224,40238],{},[1688,40225,40226,40232],{},[1788,40227,40228,40230],{},[898,40229,1918],{},[1793,40231,1806],{},[1788,40233,40234,40236],{},[898,40235,1727],{},[1793,40237,1795],{},[1688,40239,1696],{"lspace":1823,"rspace":1823},[1688,40241,1696],{},[898,40243,40244],{},[40136,40245,40246,40260],{},[1688,40247,40248,40254],{},[1788,40249,40250,40252],{},[898,40251,2031],{},[1793,40253,1806],{},[1788,40255,40256,40258],{},[898,40257,1727],{},[1793,40259,1806],{},[1688,40261,1954],{"lspace":1823,"rspace":1823},[902,40263,40264],{"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}",[724,40266,40267,40270],{},[38,40268,40269],{},"Komplementy",[883,40271,40273],{"className":40272},[886],[888,40274,40275],{"xmlns":890},[892,40276,40277,40415],{},[895,40278,40279,40285,40287,40301,40303,40323,40325,40345,40347,40349,40355,40357,40371,40373,40393,40395],{},[1788,40280,40281,40283],{},[898,40282,1872],{},[1793,40284,1795],{},[1688,40286,1690],{},[898,40288,40289],{},[40136,40290,40291,40299],{},[1688,40292,40293],{},[1788,40294,40295,40297],{},[898,40296,207],{},[1793,40298,1795],{},[1688,40300,1696],{"lspace":1823,"rspace":1823},[1688,40302,1696],{},[898,40304,40305],{},[40136,40306,40307,40321],{},[1688,40308,40309,40315],{},[1788,40310,40311,40313],{},[898,40312,1918],{},[1793,40314,1795],{},[1788,40316,40317,40319],{},[898,40318,1727],{},[1793,40320,1795],{},[1688,40322,1954],{"lspace":1823,"rspace":1823},[1688,40324,1696],{},[898,40326,40327],{},[40136,40328,40329,40343],{},[1688,40330,40331,40337],{},[1788,40332,40333,40335],{},[898,40334,2031],{},[1793,40336,1795],{},[1788,40338,40339,40341],{},[898,40340,1727],{},[1793,40342,1806],{},[1688,40344,1954],{"lspace":1823,"rspace":1823},[1688,40346,1733],{"separator":1732},[6134,40348],{"width":6136},[1788,40350,40351,40353],{},[898,40352,1872],{},[1793,40354,1806],{},[1688,40356,1690],{},[898,40358,40359],{},[40136,40360,40361,40369],{},[1688,40362,40363],{},[1788,40364,40365,40367],{},[898,40366,207],{},[1793,40368,1806],{},[1688,40370,1696],{"lspace":1823,"rspace":1823},[1688,40372,1696],{},[898,40374,40375],{},[40136,40376,40377,40391],{},[1688,40378,40379,40385],{},[1788,40380,40381,40383],{},[898,40382,1918],{},[1793,40384,1806],{},[1788,40386,40387,40389],{},[898,40388,1727],{},[1793,40390,1795],{},[1688,40392,1954],{"lspace":1823,"rspace":1823},[1688,40394,1696],{},[898,40396,40397],{},[40136,40398,40399,40413],{},[1688,40400,40401,40407],{},[1788,40402,40403,40405],{},[898,40404,2031],{},[1793,40406,1806],{},[1788,40408,40409,40411],{},[898,40410,1727],{},[1793,40412,1806],{},[1688,40414,1954],{"lspace":1823,"rspace":1823},[902,40416,40417],{"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}",[37210,40419],{},[115,40421,13373],{"id":37019},[4124,40423,40424],{},[724,40425,40426,40428,40429,37234,40442,37248,40455,40458,40459,5925,40483,40501],{},[883,40427,4412],{}," TL;DR\nNabídka vyjadřuje závislost nabízeného množství ",[883,40430,40432],{"className":40431},[886],[888,40433,40434],{"xmlns":890},[892,40435,40436,40440],{},[895,40437,40438],{},[898,40439,1872],{},[902,40441,1872],{"encoding":904},[883,40443,40445],{"className":40444},[886],[888,40446,40447],{"xmlns":890},[892,40448,40449,40453],{},[895,40450,40451],{},[898,40452,1727],{},[902,40454,1727],{"encoding":904},[38,40456,40457],{},"zákon rostoucí nabídky",": při vyšší ceně je výrobce ochoten nabídnout více. Lineární model ",[883,40460,40462],{"className":40461},[886],[888,40463,40464],{"xmlns":890},[892,40465,40466,40480],{},[895,40467,40468,40470,40472,40474,40476,40478],{},[898,40469,1727],{},[1688,40471,1690],{},[898,40473,2031],{},[898,40475,1872],{},[1688,40477,1696],{},[898,40479,2073],{},[902,40481,40482],{"encoding":904},"P = cQ + d",[883,40484,40486],{"className":40485},[886],[888,40487,40488],{"xmlns":890},[892,40489,40490,40498],{},[895,40491,40492,40494,40496],{},[898,40493,2031],{},[1688,40495,3665],{},[1793,40497,1779],{},[902,40499,40500],{"encoding":904},"c > 0"," je standardní aproximací.",[198,40503,37304],{"id":40504},"obecný-vícefaktorový-model-1",[724,40506,40507,10277,40510,40513,40514,40527,40528,37136,40541,37150,40554,40567,40568,40582,40583,37179,40596,40609],{},[38,40508,40509],{},"Nabízené množství",[614,40511,40512],{},"quantity supplied",") závisí na ceně ",[883,40515,40517],{"className":40516},[886],[888,40518,40519],{"xmlns":890},[892,40520,40521,40525],{},[895,40522,40523],{},[898,40524,1727],{},[902,40526,1727],{"encoding":904},", cenách výrobních faktorů (práce ",[883,40529,40531],{"className":40530},[886],[888,40532,40533],{"xmlns":890},[892,40534,40535,40539],{},[895,40536,40537],{},[898,40538,10047],{},[902,40540,10047],{"encoding":904},[883,40542,40544],{"className":40543},[886],[888,40545,40546],{"xmlns":890},[892,40547,40548,40552],{},[895,40549,40550],{},[898,40551,10052],{},[902,40553,10052],{"encoding":904},[883,40555,40557],{"className":40556},[886],[888,40558,40559],{"xmlns":890},[892,40560,40561,40565],{},[895,40562,40563],{},[898,40564,4509],{},[902,40566,4509],{"encoding":904},"), očekávání ",[883,40569,40571],{"className":40570},[886],[888,40572,40573],{"xmlns":890},[892,40574,40575,40580],{},[895,40576,40577],{},[898,40578,40579],{},"V",[902,40581,40579],{"encoding":904},", počtu výrobců ",[883,40584,40586],{"className":40585},[886],[888,40587,40588],{"xmlns":890},[892,40589,40590,40594],{},[895,40591,40592],{},[898,40593,37176],{},[902,40595,37176],{"encoding":904},[883,40597,40599],{"className":40598},[886],[888,40600,40601],{"xmlns":890},[892,40602,40603,40607],{},[895,40604,40605],{},[898,40606,37191],{},[902,40608,37191],{"encoding":904}," a dalších:",[883,40611,40613],{"className":40612},[886],[888,40614,40615],{"xmlns":890,"display":28306},[892,40616,40617,40676],{},[20995,40618,40619],{"width":28311},[21000,40620,40621,40623,40669,40671],{},[21003,40622],{"width":28316},[21003,40624,40625],{},[895,40626,40627,40629,40631,40633,40635,40637,40639,40641,40643,40645,40647,40649,40651,40653,40655,40657,40659,40661,40663,40665,40667],{},[898,40628,1872],{},[1688,40630,1690],{},[898,40632,1740],{},[1688,40634,2066],{"stretchy":2065},[898,40636,1727],{},[1688,40638,1733],{"separator":1732},[898,40640,10047],{},[1688,40642,1733],{"separator":1732},[898,40644,10052],{},[1688,40646,1733],{"separator":1732},[898,40648,4509],{},[1688,40650,1733],{"separator":1732},[898,40652,40579],{},[1688,40654,1733],{"separator":1732},[898,40656,37176],{},[1688,40658,1733],{"separator":1732},[898,40660,37191],{},[1688,40662,1733],{"separator":1732},[1688,40664,9899],{},[1688,40666,2076],{"stretchy":2065},[898,40668,2263],{"mathvariant":1822},[21003,40670],{"width":28316},[21003,40672,40673],{},[2041,40674,40675],{},"(2.7)",[902,40677,40678],{"encoding":904},"Q = S(P, L, K, E, V, O, W, \\ldots). \\tag{2.7}",[724,40680,38656,40681,10277,40684,40687],{},[38,40682,40683],{},"funkce nabídky",[614,40685,40686],{},"supply function",") v širším slova smyslu.",[198,40689,40691],{"id":40690},"jednofaktorový-model","Jednofaktorový model",[724,40693,40694],{},"V nejpřirozenějším jednofaktorovém modelu",[883,40696,40698],{"className":40697},[886],[888,40699,40700],{"xmlns":890,"display":28306},[892,40701,40702,40753],{},[20995,40703,40704],{"width":28311},[21000,40705,40706,40708,40746,40748],{},[21003,40707],{"width":28316},[21003,40709,40710],{},[895,40711,40712,40714,40716,40718,40720,40722,40724,40726,40728,40730,40732,40734,40736,40738,40740,40742,40744],{},[898,40713,1872],{},[1688,40715,1690],{},[898,40717,1740],{},[1688,40719,2066],{"stretchy":2065},[898,40721,1727],{},[1688,40723,2076],{"stretchy":2065},[1688,40725,1733],{"separator":1732},[6134,40727],{"width":6136},[2041,40729,37657],{},[6134,40731],{"width":6136},[898,40733,1727],{},[1688,40735,1690],{},[898,40737,1740],{},[1688,40739,2066],{"stretchy":2065},[898,40741,1872],{},[1688,40743,2076],{"stretchy":2065},[898,40745,2263],{"mathvariant":1822},[21003,40747],{"width":28316},[21003,40749,40750],{},[2041,40751,40752],{},"(2.8)",[902,40754,40755],{"encoding":904},"Q = S(P), \\qquad \\text{resp.} \\qquad P = S(Q). \\tag{2.8}",[724,40757,40758,40759,10277,40762,4176],{},"Graf je ",[38,40760,40761],{},"křivka nabídky",[614,40763,40764],{},"supply curve",[37588,40766,40768],{"id":40767},"zákon-rostoucí-nabídky","Zákon rostoucí nabídky",[4124,40770,40771],{},[724,40772,40773],{},[38,40774,37703,40775,40788,40789,37758],{},[883,40776,40778],{"className":40777},[886],[888,40779,40780],{"xmlns":890},[892,40781,40782,40786],{},[895,40783,40784],{},[898,40785,1727],{},[902,40787,1727],{"encoding":904},", pak nabízené množství ",[883,40790,40792],{"className":40791},[886],[888,40793,40794],{"xmlns":890},[892,40795,40796,40800],{},[895,40797,40798],{},[898,40799,1872],{},[902,40801,1872],{"encoding":904},[724,40803,40804,40805,40830,40831,40861,40862,40879],{},"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 ",[883,40806,40808],{"className":40807},[886],[888,40809,40810],{"xmlns":890},[892,40811,40812,40828],{},[895,40813,40814,40816,40818,40820,40826],{},[1688,40815,2748],{"stretchy":2065},[1793,40817,1779],{},[1688,40819,1733],{"separator":1732},[1788,40821,40822,40824],{},[898,40823,1727],{},[1793,40825,1779],{},[1688,40827,2763],{"stretchy":2065},[902,40829,37843],{"encoding":904}," na svislé ose (případně z ",[883,40832,40834],{"className":40833},[886],[888,40835,40836],{"xmlns":890},[892,40837,40838,40858],{},[895,40839,40840,40842,40848,40850,40856],{},[1688,40841,2748],{"stretchy":2065},[1788,40843,40844,40846],{},[898,40845,1872],{},[1793,40847,1795],{},[1688,40849,1733],{"separator":1732},[1788,40851,40852,40854],{},[898,40853,1727],{},[1793,40855,1795],{},[1688,40857,2763],{"stretchy":2065},[902,40859,40860],{"encoding":904},"[Q_1, P_1]","), kde ",[883,40863,40865],{"className":40864},[886],[888,40866,40867],{"xmlns":890},[892,40868,40869,40877],{},[895,40870,40871],{},[1788,40872,40873,40875],{},[898,40874,1727],{},[1793,40876,1779],{},[902,40878,39188],{"encoding":904}," je minimální cena, při které je výrobce ochoten vyrábět.",[724,40881,40882],{},[614,40883,40884,40885,3975,40898,2263],{},"Obrázek 2.9: Typická rostoucí křivka nabídky ",[883,40886,40888],{"className":40887},[886],[888,40889,40890],{"xmlns":890},[892,40891,40892,40896],{},[895,40893,40894],{},[898,40895,1740],{},[902,40897,1740],{"encoding":904},[883,40899,40901],{"className":40900},[886],[888,40902,40903],{"xmlns":890},[892,40904,40905,40917],{},[895,40906,40907,40909,40911,40913,40915],{},[1688,40908,2066],{"stretchy":2065},[898,40910,1872],{},[1688,40912,1733],{"separator":1732},[898,40914,1727],{},[1688,40916,2076],{"stretchy":2065},[902,40918,37931],{"encoding":904},[37588,40920,40922],{"id":40921},"lineární-model-nabídky","Lineární model nabídky",[883,40924,40926],{"className":40925},[886],[888,40927,40928],{"xmlns":890,"display":28306},[892,40929,40930,40969],{},[20995,40931,40932],{"width":28311},[21000,40933,40934,40936,40962,40964],{},[21003,40935],{"width":28316},[21003,40937,40938],{},[895,40939,40940,40942,40944,40946,40948,40950,40952,40954,40956,40958,40960],{},[898,40941,1727],{},[1688,40943,1690],{},[898,40945,2031],{},[898,40947,1872],{},[1688,40949,1696],{},[898,40951,2073],{},[1688,40953,1733],{"separator":1732},[6134,40955],{"width":6136},[898,40957,2031],{},[1688,40959,3665],{},[1793,40961,12708],{},[21003,40963],{"width":28316},[21003,40965,40966],{},[2041,40967,40968],{},"(2.9)",[902,40970,40971],{"encoding":904},"P = cQ + d, \\qquad c > 0. \\tag{2.9}",[724,40973,40974,40975,41011,41012,41025],{},"Alternativně ",[883,40976,40978],{"className":40977},[886],[888,40979,40980],{"xmlns":890},[892,40981,40982,41008],{},[895,40983,40984,40986,40988,40996,40998,41000],{},[898,40985,1872],{},[1688,40987,1690],{},[1777,40989,40990],{"scriptlevel":1779,"displaystyle":2065},[1781,40991,40992,40994],{},[1793,40993,1795],{},[898,40995,2031],{},[898,40997,1727],{},[1688,40999,1954],{},[1777,41001,41002],{"scriptlevel":1779,"displaystyle":2065},[1781,41003,41004,41006],{},[898,41005,2073],{},[898,41007,2031],{},[902,41009,41010],{"encoding":904},"Q = \\tfrac{1}{c}P - \\tfrac{d}{c}","; znaménko koeficientu u ",[883,41013,41015],{"className":41014},[886],[888,41016,41017],{"xmlns":890},[892,41018,41019,41023],{},[895,41020,41021],{},[898,41022,1727],{},[902,41024,1727],{"encoding":904}," zůstává, znaménko absolutního členu se mění.",[38165,41027,41029],{"id":41028},"příklad-25","Příklad 2.5",[724,41031,41032,41034,41035,2263],{},[38,41033,38173],{}," Lineární nabídka ",[883,41036,41038],{"className":41037},[886],[888,41039,41040],{"xmlns":890},[892,41041,41042,41056],{},[895,41043,41044,41046,41048,41050,41052,41054],{},[898,41045,1727],{},[1688,41047,1690],{},[1793,41049,5265],{},[898,41051,1872],{},[1688,41053,1696],{},[1793,41055,5260],{},[902,41057,41058],{"encoding":904},"P = 0{,}5Q + 25",[724,41060,41061,41063,41064,2263],{},[38,41062,38205],{}," Alternativní tvar ",[883,41065,41067],{"className":41066},[886],[888,41068,41069],{"xmlns":890},[892,41070,41071,41085],{},[895,41072,41073,41075,41077,41079,41081,41083],{},[898,41074,1872],{},[1688,41076,1690],{},[1793,41078,1806],{},[898,41080,1727],{},[1688,41082,1954],{},[1793,41084,3377],{},[902,41086,41087],{"encoding":904},"Q = 2P - 50",[16,41089,41090,41115],{},[19,41091,41092],{},[22,41093,41094,41109,41111,41113],{},[25,41095,41096],{},[883,41097,41099],{"className":41098},[886],[888,41100,41101],{"xmlns":890},[892,41102,41103,41107],{},[895,41104,41105],{},[898,41106,1727],{},[902,41108,1727],{"encoding":904},[25,41110,38259],{},[25,41112,15285],{},[25,41114,5467],{},[30,41116,41117],{},[22,41118,41119,41134,41136,41138],{},[35,41120,41121],{},[883,41122,41124],{"className":41123},[886],[888,41125,41126],{"xmlns":890},[892,41127,41128,41132],{},[895,41129,41130],{},[898,41131,1872],{},[902,41133,1872],{"encoding":904},[35,41135,3121],{},[35,41137,9290],{},[35,41139,38259],{},[198,41141,41143,41144,2076],{"id":41142},"posun-nabídky-shift-of-supply","Posun nabídky (",[614,41145,41146],{},"shift of supply",[724,41148,41149,41150,41153,41154,41171,41172,41197,41198,2263],{},"Posun nastává při změně exogenních proměnných — nová technologie snižuje náklady (posun ",[38,41151,41152],{},"doprava",": při stejné ceně ",[883,41155,41157],{"className":41156},[886],[888,41158,41159],{"xmlns":890},[892,41160,41161,41169],{},[895,41162,41163],{},[1788,41164,41165,41167],{},[898,41166,1727],{},[1793,41168,1779],{},[902,41170,39188],{"encoding":904}," vyrobí výrobce větší ",[883,41173,41175],{"className":41174},[886],[888,41176,41177],{"xmlns":890},[892,41178,41179,41195],{},[895,41180,41181,41187,41189],{},[1788,41182,41183,41185],{},[898,41184,1872],{},[1793,41186,1795],{},[1688,41188,3665],{},[1788,41190,41191,41193],{},[898,41192,1872],{},[1793,41194,1779],{},[902,41196,39301],{"encoding":904},"); zdražení vstupů posune křivku ",[38,41199,41200],{},"doleva",[724,41202,41203],{},[614,41204,41205,41206,41219,41220,41238,41239,41257,41258,2263],{},"Obrázek 2.11: Původní ",[883,41207,41209],{"className":41208},[886],[888,41210,41211],{"xmlns":890},[892,41212,41213,41217],{},[895,41214,41215],{},[898,41216,1740],{},[902,41218,1740],{"encoding":904},", posunuté ",[883,41221,41223],{"className":41222},[886],[888,41224,41225],{"xmlns":890},[892,41226,41227,41235],{},[895,41228,41229],{},[1788,41230,41231,41233],{},[898,41232,1740],{},[1793,41234,1795],{},[902,41236,41237],{"encoding":904},"S_1"," (doprava) a ",[883,41240,41242],{"className":41241},[886],[888,41243,41244],{"xmlns":890},[892,41245,41246,41254],{},[895,41247,41248],{},[1788,41249,41250,41252],{},[898,41251,1740],{},[1793,41253,1806],{},[902,41255,41256],{"encoding":904},"S_2"," (doleva) v ",[883,41259,41261],{"className":41260},[886],[888,41262,41263],{"xmlns":890},[892,41264,41265,41277],{},[895,41266,41267,41269,41271,41273,41275],{},[1688,41268,2066],{"stretchy":2065},[898,41270,1872],{},[1688,41272,1733],{"separator":1732},[898,41274,1727],{},[1688,41276,2076],{"stretchy":2065},[902,41278,37931],{"encoding":904},[38165,41280,41282],{"id":41281},"příklad-26-zdanění-výrobce","Příklad 2.6 — zdanění výrobce",[724,41284,41285,41287,41288,41312,41313,2263],{},[38,41286,38173],{}," Nabídka ",[883,41289,41291],{"className":41290},[886],[888,41292,41293],{"xmlns":890},[892,41294,41295,41309],{},[895,41296,41297,41299,41301,41303,41305,41307],{},[898,41298,1727],{},[1688,41300,1690],{},[898,41302,1740],{},[1688,41304,2066],{"stretchy":2065},[898,41306,1872],{},[1688,41308,2076],{"stretchy":2065},[902,41310,41311],{"encoding":904},"P = S(Q)","; na výrobce je uložena jednotková daň ",[883,41314,41316],{"className":41315},[886],[888,41317,41318],{"xmlns":890},[892,41319,41320,41324],{},[895,41321,41322],{},[898,41323,3035],{},[902,41325,3035],{"encoding":904},[724,41327,41328,41330,41331,41344,41345,41363,41364,41392],{},[38,41329,38205],{}," Spotřebitel zaplatí ",[883,41332,41334],{"className":41333},[886],[888,41335,41336],{"xmlns":890},[892,41337,41338,41342],{},[895,41339,41340],{},[898,41341,1727],{},[902,41343,1727],{"encoding":904},", výrobce obdrží ",[883,41346,41348],{"className":41347},[886],[888,41349,41350],{"xmlns":890},[892,41351,41352,41360],{},[895,41353,41354,41356,41358],{},[898,41355,1727],{},[1688,41357,1954],{},[898,41359,3035],{},[902,41361,41362],{"encoding":904},"P - T",". Z podmínky ",[883,41365,41367],{"className":41366},[886],[888,41368,41369],{"xmlns":890},[892,41370,41371,41389],{},[895,41372,41373,41375,41377,41379,41381,41383,41385,41387],{},[898,41374,1727],{},[1688,41376,1954],{},[898,41378,3035],{},[1688,41380,1690],{},[898,41382,1740],{},[1688,41384,2066],{"stretchy":2065},[898,41386,1872],{},[1688,41388,2076],{"stretchy":2065},[902,41390,41391],{"encoding":904},"P - T = S(Q)"," plyne",[883,41394,41396],{"className":41395},[886],[888,41397,41398],{"xmlns":890,"display":28306},[892,41399,41400,41434],{},[895,41401,41402,41404,41406,41412,41414,41416,41418,41420,41422,41424,41426,41428,41430,41432],{},[898,41403,1727],{},[1688,41405,1690],{},[1788,41407,41408,41410],{},[898,41409,1740],{},[1793,41411,1795],{},[1688,41413,2066],{"stretchy":2065},[898,41415,1872],{},[1688,41417,2076],{"stretchy":2065},[1688,41419,1690],{},[898,41421,1740],{},[1688,41423,2066],{"stretchy":2065},[898,41425,1872],{},[1688,41427,2076],{"stretchy":2065},[1688,41429,1696],{},[898,41431,3035],{},[898,41433,2263],{"mathvariant":1822},[902,41435,41436],{"encoding":904},"P = S_1(Q) = S(Q) + T.",[724,41438,41439,41440,41453,41454,2170,41467,41470,41471,4142,41491,8358,41509,2263],{},"Křivka ",[883,41441,41443],{"className":41442},[886],[888,41444,41445],{"xmlns":890},[892,41446,41447,41451],{},[895,41448,41449],{},[898,41450,1740],{},[902,41452,1740],{"encoding":904}," se tedy posune o ",[883,41455,41457],{"className":41456},[886],[888,41458,41459],{"xmlns":890},[892,41460,41461,41465],{},[895,41462,41463],{},[898,41464,3035],{},[902,41466,3035],{"encoding":904},[38,41468,41469],{},"svisle nahoru"," (tj. doleva). Např. pro ",[883,41472,41474],{"className":41473},[886],[888,41475,41476],{"xmlns":890},[892,41477,41478,41488],{},[895,41479,41480,41482,41484,41486],{},[898,41481,1727],{},[1688,41483,1690],{},[1793,41485,1806],{},[898,41487,1872],{},[902,41489,41490],{"encoding":904},"P = 2Q",[883,41492,41494],{"className":41493},[886],[888,41495,41496],{"xmlns":890},[892,41497,41498,41506],{},[895,41499,41500,41502,41504],{},[898,41501,3035],{},[1688,41503,1690],{},[1793,41505,2508],{},[902,41507,41508],{"encoding":904},"T = 6",[883,41510,41512],{"className":41511},[886],[888,41513,41514],{"xmlns":890},[892,41515,41516,41538],{},[895,41517,41518,41524,41526,41528,41530,41532,41534,41536],{},[1788,41519,41520,41522],{},[898,41521,1740],{},[1793,41523,1795],{},[1688,41525,2965],{},[898,41527,1727],{},[1688,41529,1690],{},[1793,41531,1806],{},[898,41533,1872],{},[1688,41535,1696],{},[1793,41537,2508],{},[902,41539,41540],{"encoding":904},"S_1: P = 2Q + 6",[724,41542,41543],{},[614,41544,41545,41546,41559],{},"Obrázek 2.12: Posun nabídky o ",[883,41547,41549],{"className":41548},[886],[888,41550,41551],{"xmlns":890},[892,41552,41553,41557],{},[895,41554,41555],{},[898,41556,3035],{},[902,41558,3035],{"encoding":904}," svisle nahoru.",[37210,41561],{},[115,41563,41565],{"id":41564},"tržní-rovnováha","Tržní rovnováha",[4124,41567,41568],{},[724,41569,41570,41572,41573,2170,41576,41608,41609,1343,41632,41655,41656,41659,41660,41673],{},[883,41571,4412],{}," TL;DR\nV ",[38,41574,41575],{},"rovnovážném bodě",[883,41577,41579],{"className":41578},[886],[888,41580,41581],{"xmlns":890},[892,41582,41583,41605],{},[895,41584,41585,41587,41589,41595,41597,41603],{},[898,41586,4509],{},[1688,41588,2748],{"stretchy":2065},[1850,41590,41591,41593],{},[898,41592,1872],{},[898,41594,4509],{},[1688,41596,1733],{"separator":1732},[1850,41598,41599,41601],{},[898,41600,1727],{},[898,41602,4509],{},[1688,41604,2763],{"stretchy":2065},[902,41606,41607],{"encoding":904},"E[Q^E, P^E]"," se poptávané a nabízené množství rovnají. Najde se jako řešení soustavy ",[883,41610,41612],{"className":41611},[886],[888,41613,41614],{"xmlns":890},[892,41615,41616,41630],{},[895,41617,41618,41620,41622,41624,41626,41628],{},[898,41619,1727],{},[1688,41621,1690],{},[898,41623,4440],{},[1688,41625,2066],{"stretchy":2065},[898,41627,1872],{},[1688,41629,2076],{"stretchy":2065},[902,41631,4896],{"encoding":904},[883,41633,41635],{"className":41634},[886],[888,41636,41637],{"xmlns":890},[892,41638,41639,41653],{},[895,41640,41641,41643,41645,41647,41649,41651],{},[898,41642,1727],{},[1688,41644,1690],{},[898,41646,1740],{},[1688,41648,2066],{"stretchy":2065},[898,41650,1872],{},[1688,41652,2076],{"stretchy":2065},[902,41654,41311],{"encoding":904},". Čtyři ",[38,41657,41658],{},"pravidla komparativní statiky"," popisují, jak se ",[883,41661,41663],{"className":41662},[886],[888,41664,41665],{"xmlns":890},[892,41666,41667,41671],{},[895,41668,41669],{},[898,41670,4509],{},[902,41672,4509],{"encoding":904}," posune při změně poptávky nebo nabídky.",[198,41675,41677],{"id":41676},"definice","Definice",[724,41679,41680,10277,41682,41685,41686,2170,41689,41707,41708,41739,41740,10277,41743,4176],{},[38,41681,41565],{},[614,41683,41684],{},"market equilibrium",") je stav, kdy poptávané množství = nabízené množství. Při ",[38,41687,41688],{},"rovnovážné ceně",[883,41690,41692],{"className":41691},[886],[888,41693,41694],{"xmlns":890},[892,41695,41696,41704],{},[895,41697,41698],{},[1850,41699,41700,41702],{},[898,41701,1727],{},[898,41703,4509],{},[902,41705,41706],{"encoding":904},"P^E"," není přebytek ani nedostatek zboží. Bod ",[883,41709,41711],{"className":41710},[886],[888,41712,41713],{"xmlns":890},[892,41714,41715,41737],{},[895,41716,41717,41719,41721,41727,41729,41735],{},[898,41718,4509],{},[1688,41720,2748],{"stretchy":2065},[1850,41722,41723,41725],{},[898,41724,1872],{},[898,41726,4509],{},[1688,41728,1733],{"separator":1732},[1850,41730,41731,41733],{},[898,41732,1727],{},[898,41734,4509],{},[1688,41736,2763],{"stretchy":2065},[902,41738,41607],{"encoding":904}," se nazývá ",[38,41741,41742],{},"rovnovážný bod",[614,41744,41745],{},"equilibrium point",[724,41747,41748,41749,1343,41772,2263],{},"Rovnovážný bod je průsečíkem křivek poptávky a nabídky; nalézá se jako řešení soustavy ",[883,41750,41752],{"className":41751},[886],[888,41753,41754],{"xmlns":890},[892,41755,41756,41770],{},[895,41757,41758,41760,41762,41764,41766,41768],{},[898,41759,1727],{},[1688,41761,1690],{},[898,41763,4440],{},[1688,41765,2066],{"stretchy":2065},[898,41767,1872],{},[1688,41769,2076],{"stretchy":2065},[902,41771,4896],{"encoding":904},[883,41773,41775],{"className":41774},[886],[888,41776,41777],{"xmlns":890},[892,41778,41779,41793],{},[895,41780,41781,41783,41785,41787,41789,41791],{},[898,41782,1727],{},[1688,41784,1690],{},[898,41786,1740],{},[1688,41788,2066],{"stretchy":2065},[898,41790,1872],{},[1688,41792,2076],{"stretchy":2065},[902,41794,41311],{"encoding":904},[724,41796,41797],{},[2821,41798],{"alt":41799,"className":41800,"src":41801},"imek-poptavka-nabidka-rovnovaha",[210,2825],"\u002Fwiki-assets\u002Fimek-poptavka-nabidka-rovnovaha.jpeg",[724,41803,41804],{},[614,41805,41806,41807,41820,41821,14258,41834,41855,41856,2263],{},"Obrázek 2.13: Klesající ",[883,41808,41810],{"className":41809},[886],[888,41811,41812],{"xmlns":890},[892,41813,41814,41818],{},[895,41815,41816],{},[898,41817,4440],{},[902,41819,4440],{"encoding":904}," a rostoucí ",[883,41822,41824],{"className":41823},[886],[888,41825,41826],{"xmlns":890},[892,41827,41828,41832],{},[895,41829,41830],{},[898,41831,1740],{},[902,41833,1740],{"encoding":904},[883,41835,41837],{"className":41836},[886],[888,41838,41839],{"xmlns":890},[892,41840,41841,41853],{},[895,41842,41843,41845,41847,41849,41851],{},[1688,41844,2066],{"stretchy":2065},[898,41846,1872],{},[1688,41848,1733],{"separator":1732},[898,41850,1727],{},[1688,41852,2076],{"stretchy":2065},[902,41854,37931],{"encoding":904}," protínající se v ",[883,41857,41859],{"className":41858},[886],[888,41860,41861],{"xmlns":890},[892,41862,41863,41885],{},[895,41864,41865,41867,41869,41875,41877,41883],{},[898,41866,4509],{},[1688,41868,2748],{"stretchy":2065},[1850,41870,41871,41873],{},[898,41872,1872],{},[898,41874,4509],{},[1688,41876,1733],{"separator":1732},[1850,41878,41879,41881],{},[898,41880,1727],{},[898,41882,4509],{},[1688,41884,2763],{"stretchy":2065},[902,41886,41607],{"encoding":904},[198,41888,41890],{"id":41889},"příklad-27-kvadratický-model","Příklad 2.7 (kvadratický model)",[724,41892,41893,41895,41896,41930,41931,2263],{},[38,41894,38173],{}," Poptávka ",[883,41897,41899],{"className":41898},[886],[888,41900,41901],{"xmlns":890},[892,41902,41903,41927],{},[895,41904,41905,41907,41909,41911,41917,41919,41921,41923,41925],{},[898,41906,1727],{},[1688,41908,1690],{},[1688,41910,1954],{},[1850,41912,41913,41915],{},[898,41914,1872],{},[1793,41916,1806],{},[1688,41918,1954],{},[1793,41920,3121],{},[898,41922,1872],{},[1688,41924,1696],{},[1793,41926,9058],{},[902,41928,41929],{"encoding":904},"P = -Q^2 - 10Q + 150",", nabídka ",[883,41932,41934],{"className":41933},[886],[888,41935,41936],{"xmlns":890},[892,41937,41938,41960],{},[895,41939,41940,41942,41944,41950,41952,41954,41956,41958],{},[898,41941,1727],{},[1688,41943,1690],{},[1850,41945,41946,41948],{},[898,41947,1872],{},[1793,41949,1806],{},[1688,41951,1696],{},[1793,41953,23187],{},[898,41955,1872],{},[1688,41957,1696],{},[1793,41959,32786],{},[902,41961,41962],{"encoding":904},"P = Q^2 + 14Q + 22",[724,41964,41965,41967],{},[38,41966,38205],{}," Z rovnosti",[883,41969,41971],{"className":41970},[886],[888,41972,41973],{"xmlns":890,"display":28306},[892,41974,41975,42013],{},[895,41976,41977,41979,41985,41987,41989,41991,41993,41995,41997,42003,42005,42007,42009,42011],{},[1688,41978,1954],{},[1850,41980,41981,41983],{},[898,41982,1872],{},[1793,41984,1806],{},[1688,41986,1954],{},[1793,41988,3121],{},[898,41990,1872],{},[1688,41992,1696],{},[1793,41994,9058],{},[1688,41996,1690],{},[1850,41998,41999,42001],{},[898,42000,1872],{},[1793,42002,1806],{},[1688,42004,1696],{},[1793,42006,23187],{},[898,42008,1872],{},[1688,42010,1696],{},[1793,42012,32786],{},[902,42014,42015],{"encoding":904},"-Q^2 - 10Q + 150 = Q^2 + 14Q + 22",[724,42017,42018,42019,42054,42055,42088,42089,42106,42107,42120,42121,1343,42143,42180,42181,2263],{},"dostaneme ",[883,42020,42022],{"className":42021},[886],[888,42023,42024],{"xmlns":890},[892,42025,42026,42051],{},[895,42027,42028,42030,42036,42038,42041,42043,42045,42047,42049],{},[1793,42029,1806],{},[1850,42031,42032,42034],{},[898,42033,1872],{},[1793,42035,1806],{},[1688,42037,1696],{},[1793,42039,42040],{},"24",[898,42042,1872],{},[1688,42044,1954],{},[1793,42046,5873],{},[1688,42048,1690],{},[1793,42050,1779],{},[902,42052,42053],{"encoding":904},"2Q^2 + 24Q - 128 = 0",", resp. ",[883,42056,42058],{"className":42057},[886],[888,42059,42060],{"xmlns":890},[892,42061,42062,42085],{},[895,42063,42064,42070,42072,42074,42076,42078,42081,42083],{},[1850,42065,42066,42068],{},[898,42067,1872],{},[1793,42069,1806],{},[1688,42071,1696],{},[1793,42073,3766],{},[898,42075,1872],{},[1688,42077,1954],{},[1793,42079,42080],{},"64",[1688,42082,1690],{},[1793,42084,1779],{},[902,42086,42087],{"encoding":904},"Q^2 + 12Q - 64 = 0",". Kořeny jsou ",[883,42090,42092],{"className":42091},[886],[888,42093,42094],{"xmlns":890},[892,42095,42096,42103],{},[895,42097,42098,42100],{},[1688,42099,1954],{},[1793,42101,42102],{},"16",[902,42104,42105],{"encoding":904},"-16"," (nevyhovuje) a ",[883,42108,42110],{"className":42109},[886],[888,42111,42112],{"xmlns":890},[892,42113,42114,42118],{},[895,42115,42116],{},[1793,42117,2616],{},[902,42119,2616],{"encoding":904},". Tedy ",[883,42122,42124],{"className":42123},[886],[888,42125,42126],{"xmlns":890},[892,42127,42128,42140],{},[895,42129,42130,42136,42138],{},[1850,42131,42132,42134],{},[898,42133,1872],{},[898,42135,4509],{},[1688,42137,1690],{},[1793,42139,2616],{},[902,42141,42142],{"encoding":904},"Q^E = 4",[883,42144,42146],{"className":42145},[886],[888,42147,42148],{"xmlns":890},[892,42149,42150,42177],{},[895,42151,42152,42158,42160,42162,42164,42166,42168,42170,42172,42174],{},[1850,42153,42154,42156],{},[898,42155,1727],{},[898,42157,4509],{},[1688,42159,1690],{},[1688,42161,1954],{},[1793,42163,42102],{},[1688,42165,1954],{},[1793,42167,5467],{},[1688,42169,1696],{},[1793,42171,9058],{},[1688,42173,1690],{},[1793,42175,42176],{},"94",[902,42178,42179],{"encoding":904},"P^E = -16 - 40 + 150 = 94",", rovnovážný bod ",[883,42182,42184],{"className":42183},[886],[888,42185,42186],{"xmlns":890},[892,42187,42188,42202],{},[895,42189,42190,42192,42194,42196,42198,42200],{},[898,42191,4509],{},[1688,42193,2748],{"stretchy":2065},[1793,42195,2616],{},[1688,42197,1733],{"separator":1732},[1793,42199,42176],{},[1688,42201,2763],{"stretchy":2065},[902,42203,42204],{"encoding":904},"E[4, 94]",[198,42206,42208],{"id":42207},"příklad-28-dvoukomoditní-trh","Příklad 2.8 (dvoukomoditní trh)",[724,42210,42211,42213],{},[38,42212,38173],{}," Poptávky a nabídky dvou zboží",[883,42215,42217],{"className":42216},[886],[888,42218,42219],{"xmlns":890,"display":28306},[892,42220,42221,42387],{},[20995,42222,42225,42313],{"rowspacing":20997,"columnalign":42223,"columnspacing":42224},"right left right left","0em 1em 0em",[21000,42226,42227,42237,42269,42279],{},[21003,42228,42229],{},[1777,42230,42231],{"scriptlevel":1779,"displaystyle":1732},[1788,42232,42233,42235],{},[898,42234,1872],{},[1793,42236,1795],{},[21003,42238,42239],{},[1777,42240,42241],{"scriptlevel":1779,"displaystyle":1732},[895,42242,42243,42245,42247,42249,42251,42253,42259,42261,42267],{},[895,42244],{},[1688,42246,1690],{},[1793,42248,5467],{},[1688,42250,1954],{},[1793,42252,2501],{},[1788,42254,42255,42257],{},[898,42256,1727],{},[1793,42258,1795],{},[1688,42260,1954],{},[1788,42262,42263,42265],{},[898,42264,1727],{},[1793,42266,1806],{},[1688,42268,1733],{"separator":1732},[21003,42270,42271],{},[1777,42272,42273],{"scriptlevel":1779,"displaystyle":1732},[1788,42274,42275,42277],{},[898,42276,1872],{},[1793,42278,1806],{},[21003,42280,42281],{},[1777,42282,42283],{"scriptlevel":1779,"displaystyle":1732},[895,42284,42285,42287,42289,42291,42293,42295,42301,42303,42305,42311],{},[895,42286],{},[1688,42288,1690],{},[1793,42290,3377],{},[1688,42292,1954],{},[1793,42294,1806],{},[1788,42296,42297,42299],{},[898,42298,1727],{},[1793,42300,1795],{},[1688,42302,1954],{},[1793,42304,2616],{},[1788,42306,42307,42309],{},[898,42308,1727],{},[1793,42310,1806],{},[1688,42312,1733],{"separator":1732},[21000,42314,42315,42325,42351,42361],{},[21003,42316,42317],{},[1777,42318,42319],{"scriptlevel":1779,"displaystyle":1732},[1788,42320,42321,42323],{},[898,42322,1872],{},[1793,42324,1795],{},[21003,42326,42327],{},[1777,42328,42329],{"scriptlevel":1779,"displaystyle":1732},[895,42330,42331,42333,42335,42337,42339,42341,42343,42349],{},[895,42332],{},[1688,42334,1690],{},[1688,42336,1954],{},[1793,42338,2131],{},[1688,42340,1696],{},[1793,42342,2616],{},[1788,42344,42345,42347],{},[898,42346,1727],{},[1793,42348,1795],{},[1688,42350,1733],{"separator":1732},[21003,42352,42353],{},[1777,42354,42355],{"scriptlevel":1779,"displaystyle":1732},[1788,42356,42357,42359],{},[898,42358,1872],{},[1793,42360,1806],{},[21003,42362,42363],{},[1777,42364,42365],{"scriptlevel":1779,"displaystyle":1732},[895,42366,42367,42369,42371,42373,42375,42377,42379,42385],{},[895,42368],{},[1688,42370,1690],{},[1688,42372,1954],{},[1793,42374,24442],{},[1688,42376,1696],{},[1793,42378,2131],{},[1788,42380,42381,42383],{},[898,42382,1727],{},[1793,42384,1806],{},[898,42386,2263],{"mathvariant":1822},[902,42388,42389],{"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}",[724,42391,42392,42394],{},[38,42393,38205],{}," Z rovností poptávek a nabídek dostaneme",[883,42396,42398],{"className":42397},[886],[888,42399,42400],{"xmlns":890,"display":28306},[892,42401,42402,42451],{},[895,42403,42404,42406,42412,42414,42420,42422,42424,42426,42428,42430,42436,42438,42440,42446,42448],{},[1793,42405,4256],{},[1788,42407,42408,42410],{},[898,42409,1727],{},[1793,42411,1795],{},[1688,42413,1696],{},[1788,42415,42416,42418],{},[898,42417,1727],{},[1793,42419,1806],{},[1688,42421,1690],{},[1793,42423,21444],{},[1688,42425,1733],{"separator":1732},[6134,42427],{"width":6136},[1793,42429,1806],{},[1788,42431,42432,42434],{},[898,42433,1727],{},[1793,42435,1795],{},[1688,42437,1696],{},[1793,42439,24442],{},[1788,42441,42442,42444],{},[898,42443,1727],{},[1793,42445,1806],{},[1688,42447,1690],{},[1793,42449,42450],{},"57.",[902,42452,42453],{"encoding":904},"9P_1 + P_2 = 43, \\qquad 2P_1 + 7P_2 = 57.",[724,42455,42456,42457,1343,42481,42505,42506,1343,42531,42555,42556,42558],{},"Řešením je ",[883,42458,42460],{"className":42459},[886],[888,42461,42462],{"xmlns":890},[892,42463,42464,42478],{},[895,42465,42466,42474,42476],{},[1814,42467,42468,42470,42472],{},[898,42469,1727],{},[1793,42471,1795],{},[898,42473,4509],{},[1688,42475,1690],{},[1793,42477,2616],{},[902,42479,42480],{"encoding":904},"P_1^E = 4",[883,42482,42484],{"className":42483},[886],[888,42485,42486],{"xmlns":890},[892,42487,42488,42502],{},[895,42489,42490,42498,42500],{},[1814,42491,42492,42494,42496],{},[898,42493,1727],{},[1793,42495,1806],{},[898,42497,4509],{},[1688,42499,1690],{},[1793,42501,24442],{},[902,42503,42504],{"encoding":904},"P_2^E = 7","; zpětným dosazením ",[883,42507,42509],{"className":42508},[886],[888,42510,42511],{"xmlns":890},[892,42512,42513,42528],{},[895,42514,42515,42523,42525],{},[1814,42516,42517,42519,42521],{},[898,42518,1872],{},[1793,42520,1795],{},[898,42522,4509],{},[1688,42524,1690],{},[1793,42526,42527],{},"13",[902,42529,42530],{"encoding":904},"Q_1^E = 13",[883,42532,42534],{"className":42533},[886],[888,42535,42536],{"xmlns":890},[892,42537,42538,42552],{},[895,42539,42540,42548,42550],{},[1814,42541,42542,42544,42546],{},[898,42543,1872],{},[1793,42545,1806],{},[898,42547,4509],{},[1688,42549,1690],{},[1793,42551,23187],{},[902,42553,42554],{"encoding":904},"Q_2^E = 14",". Zboží jsou ",[38,42557,40062],{}," (zkřížené koeficienty v poptávce jsou záporné).",[198,42560,42562],{"id":42561},"dynamický-model-pavučinový-teorém","Dynamický model — pavučinový teorém",[724,42564,42565,42566,42583,42584,10277,42587,4176],{},"Rovnovážná cena se obecně liší od tržní ceny, která vzniká působením tržních sil v čase. Za podmínky stability se tržní cena přibližuje k ",[883,42567,42569],{"className":42568},[886],[888,42570,42571],{"xmlns":890},[892,42572,42573,42581],{},[895,42574,42575],{},[1850,42576,42577,42579],{},[898,42578,1727],{},[898,42580,4509],{},[902,42582,41706],{"encoding":904},"; mechanismus popisuje ",[38,42585,42586],{},"teorém pavučiny",[614,42588,42589],{},"cobweb model",[198,42591,42593],{"id":42592},"pravidla-komparativní-statiky-14","Pravidla komparativní statiky (1–4)",[724,42595,42596],{},[2821,42597],{"alt":42598,"className":42599,"src":42600},"imek-komparativni-statika-4pripady",[210,2825],"\u002Fwiki-assets\u002Fimek-komparativni-statika-4pripady.jpeg",[4124,42602,42603,42644,42684,42724],{},[724,42604,42605,42608,42609,6446,42626,2263],{},[38,42606,42607],{},"Pravidlo 1:"," Růst poptávky ⟹ růst ",[883,42610,42612],{"className":42611},[886],[888,42613,42614],{"xmlns":890},[892,42615,42616,42624],{},[895,42617,42618],{},[1850,42619,42620,42622],{},[898,42621,1727],{},[898,42623,4509],{},[902,42625,41706],{"encoding":904},[883,42627,42629],{"className":42628},[886],[888,42630,42631],{"xmlns":890},[892,42632,42633,42641],{},[895,42634,42635],{},[1850,42636,42637,42639],{},[898,42638,1872],{},[898,42640,4509],{},[902,42642,42643],{"encoding":904},"Q^E",[724,42645,42646,42649,42650,6446,42667,2263],{},[38,42647,42648],{},"Pravidlo 2:"," Pokles poptávky ⟹ pokles ",[883,42651,42653],{"className":42652},[886],[888,42654,42655],{"xmlns":890},[892,42656,42657,42665],{},[895,42658,42659],{},[1850,42660,42661,42663],{},[898,42662,1727],{},[898,42664,4509],{},[902,42666,41706],{"encoding":904},[883,42668,42670],{"className":42669},[886],[888,42671,42672],{"xmlns":890},[892,42673,42674,42682],{},[895,42675,42676],{},[1850,42677,42678,42680],{},[898,42679,1872],{},[898,42681,4509],{},[902,42683,42643],{"encoding":904},[724,42685,42686,42689,42690,9608,42707,2263],{},[38,42687,42688],{},"Pravidlo 3:"," Růst nabídky ⟹ pokles ",[883,42691,42693],{"className":42692},[886],[888,42694,42695],{"xmlns":890},[892,42696,42697,42705],{},[895,42698,42699],{},[1850,42700,42701,42703],{},[898,42702,1727],{},[898,42704,4509],{},[902,42706,41706],{"encoding":904},[883,42708,42710],{"className":42709},[886],[888,42711,42712],{"xmlns":890},[892,42713,42714,42722],{},[895,42715,42716],{},[1850,42717,42718,42720],{},[898,42719,1872],{},[898,42721,4509],{},[902,42723,42643],{"encoding":904},[724,42725,42726,42729,42730,42747,42748,2263],{},[38,42727,42728],{},"Pravidlo 4:"," Pokles nabídky ⟹ růst ",[883,42731,42733],{"className":42732},[886],[888,42734,42735],{"xmlns":890},[892,42736,42737,42745],{},[895,42738,42739],{},[1850,42740,42741,42743],{},[898,42742,1727],{},[898,42744,4509],{},[902,42746,41706],{"encoding":904},", pokles ",[883,42749,42751],{"className":42750},[886],[888,42752,42753],{"xmlns":890},[892,42754,42755,42763],{},[895,42756,42757],{},[1850,42758,42759,42761],{},[898,42760,1872],{},[898,42762,4509],{},[902,42764,42643],{"encoding":904},[16,42766,42767,42812],{},[19,42768,42769],{},[22,42770,42771,42774,42793],{},[25,42772,42773],{},"Změna",[25,42775,42776],{},[883,42777,42779],{"className":42778},[886],[888,42780,42781],{"xmlns":890},[892,42782,42783,42791],{},[895,42784,42785],{},[1850,42786,42787,42789],{},[898,42788,1727],{},[898,42790,4509],{},[902,42792,41706],{"encoding":904},[25,42794,42795],{},[883,42796,42798],{"className":42797},[886],[888,42799,42800],{"xmlns":890},[892,42801,42802,42810],{},[895,42803,42804],{},[1850,42805,42806,42808],{},[898,42807,1872],{},[898,42809,4509],{},[902,42811,42643],{"encoding":904},[30,42813,42814,42824,42834,42843],{},[22,42815,42816,42819,42822],{},[35,42817,42818],{},"Růst poptávky",[35,42820,42821],{},"↑",[35,42823,42821],{},[22,42825,42826,42829,42832],{},[35,42827,42828],{},"Pokles poptávky",[35,42830,42831],{},"↓",[35,42833,42831],{},[22,42835,42836,42839,42841],{},[35,42837,42838],{},"Růst nabídky",[35,42840,42831],{},[35,42842,42821],{},[22,42844,42845,42848,42850],{},[35,42846,42847],{},"Pokles nabídky",[35,42849,42821],{},[35,42851,42831],{},[724,42853,42854],{},[614,42855,42856],{},"Obrázky 2.15–2.18 ilustrují všechny čtyři situace pomocí posunu jedné z křivek.",[37210,42858],{},[115,42860,811],{"id":42861},"zdanění-trhu",[4124,42863,42864,42953],{},[724,42865,42866,42868,42869,42882,42883,3185,42896,42899,42900,37016,42923,42948,42949,42952],{},[883,42867,4412],{}," TL;DR\nJednotková daň ",[883,42870,42872],{"className":42871},[886],[888,42873,42874],{"xmlns":890},[892,42875,42876,42880],{},[895,42877,42878],{},[898,42879,3035],{},[902,42881,3035],{"encoding":904}," uložená na každou prodanou jednotku způsobí posun jedné z křivek o ",[883,42884,42886],{"className":42885},[886],[888,42887,42888],{"xmlns":890},[892,42889,42890,42894],{},[895,42891,42892],{},[898,42893,3035],{},[902,42895,3035],{"encoding":904},[38,42897,42898],{},"Daňové břemeno"," se dělí mezi spotřebitele (",[883,42901,42903],{"className":42902},[886],[888,42904,42905],{"xmlns":890},[892,42906,42907,42920],{},[895,42908,42909],{},[1788,42910,42911,42913],{},[898,42912,3035],{},[895,42914,42915,42918],{},[898,42916,42917],{},"s",[898,42919,724],{},[902,42921,42922],{"encoding":904},"T_{sp}",[883,42924,42926],{"className":42925},[886],[888,42927,42928],{"xmlns":890},[892,42929,42930,42945],{},[895,42931,42932],{},[1788,42933,42934,42936],{},[898,42935,3035],{},[895,42937,42938,42941,42943],{},[898,42939,42940],{},"v",[898,42942,2282],{},[898,42944,2046],{},[902,42946,42947],{"encoding":904},"T_{vyr}","). Klíčová vlastnost — ",[38,42950,42951],{},"ekvivalence zdanění",": výsledné rovnovážné množství i čistá cena pro výrobce jsou stejné bez ohledu na to, zda je daň uložena výrobci, či spotřebiteli.",[724,42954,42955],{},[614,42956,42957,42958,2263],{},"Pro detail, úplné odvození, Příklady 2.9 a 2.10 a geometrickou interpretaci viz ",[207,42959,42961],{"className":42960,"dataFsResolvedFilePath":809,"href":810},[210],"zdaneni-trhu",[724,42963,42964,42965,42968,42969,42995,42996,42999,43000,43026,43027,43044,43045,43085,43086,4142,43099,2263],{},"Existují dvě formy zdanění — daň uložená ",[38,42966,42967],{},"výrobci"," (posun nabídky ",[883,42970,42972],{"className":42971},[886],[888,42973,42974],{"xmlns":890},[892,42975,42976,42992],{},[895,42977,42978,42984,42986,42988,42990],{},[1788,42979,42980,42982],{},[898,42981,1740],{},[1793,42983,1795],{},[1688,42985,1690],{},[898,42987,1740],{},[1688,42989,1696],{},[898,42991,3035],{},[902,42993,42994],{"encoding":904},"S_1 = S + T"," svisle nahoru) a daň uložená ",[38,42997,42998],{},"spotřebiteli"," (posun poptávky ",[883,43001,43003],{"className":43002},[886],[888,43004,43005],{"xmlns":890},[892,43006,43007,43023],{},[895,43008,43009,43015,43017,43019,43021],{},[1788,43010,43011,43013],{},[898,43012,4440],{},[1793,43014,1806],{},[1688,43016,1690],{},[898,43018,4440],{},[1688,43020,1954],{},[898,43022,3035],{},[902,43024,43025],{"encoding":904},"D_2 = D - T"," svisle dolů). V obou případech nové rovnovážné množství ",[883,43028,43030],{"className":43029},[886],[888,43031,43032],{"xmlns":890},[892,43033,43034,43042],{},[895,43035,43036],{},[1850,43037,43038,43040],{},[898,43039,1872],{},[898,43041,4509],{},[902,43043,42643],{"encoding":904}," klesá a vzniká rozklad daně ",[883,43046,43048],{"className":43047},[886],[888,43049,43050],{"xmlns":890},[892,43051,43052,43082],{},[895,43053,43054,43056,43058,43068,43070],{},[898,43055,3035],{},[1688,43057,1690],{},[1788,43059,43060,43062],{},[898,43061,3035],{},[895,43063,43064,43066],{},[898,43065,42917],{},[898,43067,724],{},[1688,43069,1696],{},[1788,43071,43072,43074],{},[898,43073,3035],{},[895,43075,43076,43078,43080],{},[898,43077,42940],{},[898,43079,2282],{},[898,43081,2046],{},[902,43083,43084],{"encoding":904},"T = T_{sp} + T_{vyr}"," mezi obě strany trhu, určený relativními sklony křivek ",[883,43087,43089],{"className":43088},[886],[888,43090,43091],{"xmlns":890},[892,43092,43093,43097],{},[895,43094,43095],{},[898,43096,4440],{},[902,43098,4440],{"encoding":904},[883,43100,43102],{"className":43101},[886],[888,43103,43104],{"xmlns":890},[892,43105,43106,43110],{},[895,43107,43108],{},[898,43109,1740],{},[902,43111,1740],{"encoding":904},[724,43113,43114,43115,43118,43119,4142,43149,43183],{},"Zásadním výsledkem kapitoly je ",[38,43116,43117],{},"věta o ekvivalenci zdanění",": ať je daň uvalena formálně na kohokoli, rovnovážné množství i reálné rozdělení břemene jsou identické — ",[883,43120,43122],{"className":43121},[886],[888,43123,43124],{"xmlns":890},[892,43125,43126,43146],{},[895,43127,43128,43136,43138],{},[1814,43129,43130,43132,43134],{},[898,43131,1872],{},[1793,43133,1795],{},[898,43135,4509],{},[1688,43137,1690],{},[1814,43139,43140,43142,43144],{},[898,43141,1872],{},[1793,43143,1806],{},[898,43145,4509],{},[902,43147,43148],{"encoding":904},"Q_1^E = Q_2^E",[883,43150,43152],{"className":43151},[886],[888,43153,43154],{"xmlns":890},[892,43155,43156,43180],{},[895,43157,43158,43166,43168,43170,43172],{},[1814,43159,43160,43162,43164],{},[898,43161,1727],{},[1793,43163,1795],{},[898,43165,4509],{},[1688,43167,1954],{},[898,43169,3035],{},[1688,43171,1690],{},[1814,43173,43174,43176,43178],{},[898,43175,1727],{},[1793,43177,1806],{},[898,43179,4509],{},[902,43181,43182],{"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.",[724,43185,43186,43187,43190,43191,43217,43218,43246,43247,43250,43251,43254,43255,2263],{},"Podrobný výklad, Příklady ",[38,43188,43189],{},"2.9"," (daň výrobci, ",[883,43192,43194],{"className":43193},[886],[888,43195,43196],{"xmlns":890},[892,43197,43198,43214],{},[895,43199,43200,43210,43212],{},[1788,43201,43202,43204],{},[898,43203,3035],{},[895,43205,43206,43208],{},[898,43207,42917],{},[898,43209,724],{},[1688,43211,1690],{},[1793,43213,1806],{},[902,43215,43216],{"encoding":904},"T_{sp} = 2"," Kč, ",[883,43219,43221],{"className":43220},[886],[888,43222,43223],{"xmlns":890},[892,43224,43225,43243],{},[895,43226,43227,43239,43241],{},[1788,43228,43229,43231],{},[898,43230,3035],{},[895,43232,43233,43235,43237],{},[898,43234,42940],{},[898,43236,2282],{},[898,43238,2046],{},[1688,43240,1690],{},[1793,43242,2616],{},[902,43244,43245],{"encoding":904},"T_{vyr} = 4"," Kč) a ",[38,43248,43249],{},"2.10"," (táž daň, ale na spotřebitele), postup výpočtu rozkladu břemene a ",[38,43252,43253],{},"Obrázky 2.17–2.21"," jsou na samostatné stránce ",[207,43256,42961],{"className":43257,"dataFsResolvedFilePath":809,"href":810},[210],[37210,43259],{},[115,43261,43263],{"id":43262},"multiplikátory-pro-mikroekonomické-proměnné","Multiplikátory pro mikroekonomické proměnné",[4124,43265,43266],{},[724,43267,43268,43270,43271,43274,43275,43277],{},[883,43269,4412],{}," TL;DR\nMultiplikátory jsou ",[38,43272,43273],{},"parciální derivace redukovaného tvaru"," endogenní proměnné podle exogenních parametrů. Udávají přibližnou odezvu rovnovážného bodu na jednotkovou změnu parametru (",[614,43276,37200],{},"). Kvalitativní smysl (znaménko) je invariantní, kvantitativní závisí na konkrétních hodnotách.",[198,43279,43281],{"id":43280},"redukovaný-tvar","Redukovaný tvar",[724,43283,43284,43285,10277,43308,1343,43326,12378,43343,10277,43366,43383,43384,43414],{},"Pro lineární model ",[883,43286,43288],{"className":43287},[886],[888,43289,43290],{"xmlns":890},[892,43291,43292,43306],{},[895,43293,43294,43296,43298,43300,43302,43304],{},[898,43295,1727],{},[1688,43297,1690],{},[898,43299,207],{},[898,43301,1872],{},[1688,43303,1696],{},[898,43305,1918],{},[902,43307,37300],{"encoding":904},[883,43309,43311],{"className":43310},[886],[888,43312,43313],{"xmlns":890},[892,43314,43315,43323],{},[895,43316,43317,43319,43321],{},[898,43318,207],{},[1688,43320,3704],{},[1793,43322,1779],{},[902,43324,43325],{"encoding":904},"a \u003C 0",[883,43327,43329],{"className":43328},[886],[888,43330,43331],{"xmlns":890},[892,43332,43333,43341],{},[895,43334,43335,43337,43339],{},[898,43336,1918],{},[1688,43338,3665],{},[1793,43340,1779],{},[902,43342,19056],{"encoding":904},[883,43344,43346],{"className":43345},[886],[888,43347,43348],{"xmlns":890},[892,43349,43350,43364],{},[895,43351,43352,43354,43356,43358,43360,43362],{},[898,43353,1727],{},[1688,43355,1690],{},[898,43357,2031],{},[898,43359,1872],{},[1688,43361,1696],{},[898,43363,2073],{},[902,43365,40482],{"encoding":904},[883,43367,43369],{"className":43368},[886],[888,43370,43371],{"xmlns":890},[892,43372,43373,43381],{},[895,43374,43375,43377,43379],{},[898,43376,2031],{},[1688,43378,3665],{},[1793,43380,1779],{},[902,43382,40500],{"encoding":904},") dává podmínka rovnováhy ",[883,43385,43387],{"className":43386},[886],[888,43388,43389],{"xmlns":890},[892,43390,43391,43411],{},[895,43392,43393,43395,43397,43399,43401,43403,43405,43407,43409],{},[898,43394,207],{},[898,43396,1872],{},[1688,43398,1696],{},[898,43400,1918],{},[1688,43402,1690],{},[898,43404,2031],{},[898,43406,1872],{},[1688,43408,1696],{},[898,43410,2073],{},[902,43412,43413],{"encoding":904},"aQ + b = cQ + d",", odkud",[883,43416,43418],{"className":43417},[886],[888,43419,43420],{"xmlns":890,"display":28306},[892,43421,43422,43467],{},[20995,43423,43424],{"width":28311},[21000,43425,43426,43428,43460,43462],{},[21003,43427],{"width":28316},[21003,43429,43430],{},[895,43431,43432,43438,43440,43458],{},[1850,43433,43434,43436],{},[898,43435,1872],{},[898,43437,4509],{},[1688,43439,1690],{},[1781,43441,43442,43450],{},[895,43443,43444,43446,43448],{},[898,43445,1918],{},[1688,43447,1954],{},[898,43449,2073],{},[895,43451,43452,43454,43456],{},[898,43453,2031],{},[1688,43455,1954],{},[898,43457,207],{},[898,43459,2263],{"mathvariant":1822},[21003,43461],{"width":28316},[21003,43463,43464],{},[2041,43465,43466],{},"(2.10)",[902,43468,43469],{"encoding":904},"Q^E = \\frac{b - d}{c - a}. \\tag{2.10}",[724,43471,43472,43473,10277,43475,43478,43479,43496,43497,2170,43500,43526,43527,43540,43541,43559,43560,4176],{},"Vztah (2.10) je ",[38,43474,21195],{},[614,43476,43477],{},"reduced form",") pro ",[883,43480,43482],{"className":43481},[886],[888,43483,43484],{"xmlns":890},[892,43485,43486,43494],{},[895,43487,43488],{},[1850,43489,43490,43492],{},[898,43491,1872],{},[898,43493,4509],{},[902,43495,42643],{"encoding":904},": endogenní proměnná je vyjádřena pomocí exogenních ",[38,43498,43499],{},"parametrů",[883,43501,43503],{"className":43502},[886],[888,43504,43505],{"xmlns":890},[892,43506,43507,43523],{},[895,43508,43509,43511,43513,43515,43517,43519,43521],{},[898,43510,207],{},[1688,43512,1733],{"separator":1732},[898,43514,1918],{},[1688,43516,1733],{"separator":1732},[898,43518,2031],{},[1688,43520,1733],{"separator":1732},[898,43522,2073],{},[902,43524,43525],{"encoding":904},"a, b, c, d",". Aby ",[883,43528,43530],{"className":43529},[886],[888,43531,43532],{"xmlns":890},[892,43533,43534,43538],{},[895,43535,43536],{},[898,43537,4509],{},[902,43539,4509],{"encoding":904}," ležel v 1. kvadrantu, musí platit ",[883,43542,43544],{"className":43543},[886],[888,43545,43546],{"xmlns":890},[892,43547,43548,43556],{},[895,43549,43550,43552,43554],{},[898,43551,1918],{},[1688,43553,3665],{},[898,43555,2073],{},[902,43557,43558],{"encoding":904},"b > d"," (neboť ",[883,43561,43563],{"className":43562},[886],[888,43564,43565],{"xmlns":890},[892,43566,43567,43579],{},[895,43568,43569,43571,43573,43575,43577],{},[898,43570,2031],{},[1688,43572,1954],{},[898,43574,207],{},[1688,43576,3665],{},[1793,43578,1779],{},[902,43580,43581],{"encoding":904},"c - a > 0",[724,43583,43584],{},[614,43585,43586,43587,43600,43601,43614,43615,18890,43628,42180,43645,43658],{},"Obrázek 2.22: Lineární poptávka (úsek ",[883,43588,43590],{"className":43589},[886],[888,43591,43592],{"xmlns":890},[892,43593,43594,43598],{},[895,43595,43596],{},[898,43597,1918],{},[902,43599,1918],{"encoding":904}," na ose ",[883,43602,43604],{"className":43603},[886],[888,43605,43606],{"xmlns":890},[892,43607,43608,43612],{},[895,43609,43610],{},[898,43611,1727],{},[902,43613,1727],{"encoding":904},") a nabídka (úsek ",[883,43616,43618],{"className":43617},[886],[888,43619,43620],{"xmlns":890},[892,43621,43622,43626],{},[895,43623,43624],{},[898,43625,2073],{},[902,43627,2073],{"encoding":904},[883,43629,43631],{"className":43630},[886],[888,43632,43633],{"xmlns":890},[892,43634,43635,43643],{},[895,43636,43637,43639,43641],{},[898,43638,1918],{},[1688,43640,3665],{},[898,43642,2073],{},[902,43644,43558],{"encoding":904},[883,43646,43648],{"className":43647},[886],[888,43649,43650],{"xmlns":890},[892,43651,43652,43656],{},[895,43653,43654],{},[898,43655,4509],{},[902,43657,4509],{"encoding":904}," v 1. kvadrantu.",[198,43660,43662],{"id":43661},"definice-multiplikátorů","Definice multiplikátorů",[724,43664,43665,43666,43691,43692,43705,43706,43719],{},"V komparativní statice jsou ",[883,43667,43669],{"className":43668},[886],[888,43670,43671],{"xmlns":890},[892,43672,43673,43689],{},[895,43674,43675,43677,43679,43681,43683,43685,43687],{},[898,43676,207],{},[1688,43678,1733],{"separator":1732},[898,43680,1918],{},[1688,43682,1733],{"separator":1732},[898,43684,2031],{},[1688,43686,1733],{"separator":1732},[898,43688,2073],{},[902,43690,43525],{"encoding":904}," exogenní proměnné a ",[883,43693,43695],{"className":43694},[886],[888,43696,43697],{"xmlns":890},[892,43698,43699,43703],{},[895,43700,43701],{},[898,43702,1872],{},[902,43704,1872],{"encoding":904}," endogenní. Přibližná změna ",[883,43707,43709],{"className":43708},[886],[888,43710,43711],{"xmlns":890},[892,43712,43713,43717],{},[895,43714,43715],{},[898,43716,1872],{},[902,43718,1872],{"encoding":904}," se rovná totálnímu diferenciálu:",[883,43721,43723],{"className":43722},[886],[888,43724,43725],{"xmlns":890,"display":28306},[892,43726,43727,43820],{},[20995,43728,43729],{"width":28311},[21000,43730,43731,43733,43813,43815],{},[21003,43732],{"width":28316},[21003,43734,43735],{},[895,43736,43737,43739,43741,43743,43745,43747,43749,43757,43759,43761,43763,43765,43773,43775,43777,43779,43781,43789,43791,43793,43795,43797,43805,43807,43809,43811],{},[898,43738,3147],{"mathvariant":1822},[898,43740,1872],{},[1688,43742,2991],{},[898,43744,2073],{},[898,43746,1872],{},[1688,43748,1690],{},[1814,43750,43751,43753,43755],{},[898,43752,1872],{},[898,43754,207],{},[1688,43756,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[2041,43758,2043],{},[898,43760,2073],{},[898,43762,207],{},[1688,43764,1696],{},[1814,43766,43767,43769,43771],{},[898,43768,1872],{},[898,43770,1918],{},[1688,43772,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[2041,43774,2043],{},[898,43776,2073],{},[898,43778,1918],{},[1688,43780,1696],{},[1814,43782,43783,43785,43787],{},[898,43784,1872],{},[898,43786,2031],{},[1688,43788,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[2041,43790,2043],{},[898,43792,2073],{},[898,43794,2031],{},[1688,43796,1696],{},[1814,43798,43799,43801,43803],{},[898,43800,1872],{},[898,43802,2073],{},[1688,43804,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[2041,43806,2043],{},[898,43808,2073],{},[898,43810,2073],{},[898,43812,2263],{"mathvariant":1822},[21003,43814],{"width":28316},[21003,43816,43817],{},[2041,43818,43819],{},"(2.11)",[902,43821,43822],{"encoding":904},"\\Delta Q \\approx dQ = Q'_a\\,da + Q'_b\\,db + Q'_c\\,dc + Q'_d\\,dd. \\tag{2.11}",[724,43824,43825,43826,43876,43877,10277,43879,3408],{},"Parciální derivace ",[883,43827,43829],{"className":43828},[886],[888,43830,43831],{"xmlns":890},[892,43832,43833,43873],{},[895,43834,43835,43843,43845,43853,43855,43863,43865],{},[1814,43836,43837,43839,43841],{},[898,43838,1872],{},[898,43840,207],{},[1688,43842,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,43844,1733],{"separator":1732},[1814,43846,43847,43849,43851],{},[898,43848,1872],{},[898,43850,1918],{},[1688,43852,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,43854,1733],{"separator":1732},[1814,43856,43857,43859,43861],{},[898,43858,1872],{},[898,43860,2031],{},[1688,43862,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,43864,1733],{"separator":1732},[1814,43866,43867,43869,43871],{},[898,43868,1872],{},[898,43870,2073],{},[1688,43872,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[902,43874,43875],{"encoding":904},"Q'_a, Q'_b, Q'_c, Q'_d"," se nazývají ",[38,43878,18219],{},[614,43880,43881],{},"multipliers",[883,43883,43885],{"className":43884},[886],[888,43886,43887],{"xmlns":890,"display":28306},[892,43888,43889,44040],{},[20995,43890,43891],{"width":28311},[21000,43892,43893,43895,44033,44035],{},[21003,43894],{"width":28316},[21003,43896,43897],{},[895,43898,43899,43907,43909,43935,43937,43939,43947,43949,43961,43963,43965,43973,43975,43977,44003,44005,44007,44015,44017,44019,44031],{},[1814,43900,43901,43903,43905],{},[898,43902,1872],{},[898,43904,207],{},[1688,43906,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,43908,1690],{},[1781,43910,43911,43919],{},[895,43912,43913,43915,43917],{},[898,43914,1918],{},[1688,43916,1954],{},[898,43918,2073],{},[895,43920,43921,43923,43925,43927,43929],{},[1688,43922,2066],{"stretchy":2065},[898,43924,2031],{},[1688,43926,1954],{},[898,43928,207],{},[1850,43930,43931,43933],{},[1688,43932,2076],{"stretchy":2065},[1793,43934,1806],{},[1688,43936,1733],{"separator":1732},[6134,43938],{"width":15531},[1814,43940,43941,43943,43945],{},[898,43942,1872],{},[898,43944,1918],{},[1688,43946,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,43948,1690],{},[1781,43950,43951,43953],{},[1793,43952,1795],{},[895,43954,43955,43957,43959],{},[898,43956,2031],{},[1688,43958,1954],{},[898,43960,207],{},[1688,43962,1733],{"separator":1732},[6134,43964],{"width":15531},[1814,43966,43967,43969,43971],{},[898,43968,1872],{},[898,43970,2031],{},[1688,43972,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,43974,1690],{},[1688,43976,1954],{},[1781,43978,43979,43987],{},[895,43980,43981,43983,43985],{},[898,43982,1918],{},[1688,43984,1954],{},[898,43986,2073],{},[895,43988,43989,43991,43993,43995,43997],{},[1688,43990,2066],{"stretchy":2065},[898,43992,2031],{},[1688,43994,1954],{},[898,43996,207],{},[1850,43998,43999,44001],{},[1688,44000,2076],{"stretchy":2065},[1793,44002,1806],{},[1688,44004,1733],{"separator":1732},[6134,44006],{"width":15531},[1814,44008,44009,44011,44013],{},[898,44010,1872],{},[898,44012,2073],{},[1688,44014,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,44016,1690],{},[1688,44018,1954],{},[1781,44020,44021,44023],{},[1793,44022,1795],{},[895,44024,44025,44027,44029],{},[898,44026,2031],{},[1688,44028,1954],{},[898,44030,207],{},[898,44032,2263],{"mathvariant":1822},[21003,44034],{"width":28316},[21003,44036,44037],{},[2041,44038,44039],{},"(2.12)",[902,44041,44042],{"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}",[198,44044,44046],{"id":44045},"znaménka-a-interpretace","Znaménka a interpretace",[724,44048,44049,44050,1343,44067,1343,44084,1343,44101,44118,44119,3408],{},"Za podmínek ",[883,44051,44053],{"className":44052},[886],[888,44054,44055],{"xmlns":890},[892,44056,44057,44065],{},[895,44058,44059,44061,44063],{},[898,44060,207],{},[1688,44062,3704],{},[1793,44064,1779],{},[902,44066,43325],{"encoding":904},[883,44068,44070],{"className":44069},[886],[888,44071,44072],{"xmlns":890},[892,44073,44074,44082],{},[895,44075,44076,44078,44080],{},[898,44077,1918],{},[1688,44079,3665],{},[1793,44081,1779],{},[902,44083,19056],{"encoding":904},[883,44085,44087],{"className":44086},[886],[888,44088,44089],{"xmlns":890},[892,44090,44091,44099],{},[895,44092,44093,44095,44097],{},[898,44094,2031],{},[1688,44096,3665],{},[1793,44098,1779],{},[902,44100,40500],{"encoding":904},[883,44102,44104],{"className":44103},[886],[888,44105,44106],{"xmlns":890},[892,44107,44108,44116],{},[895,44109,44110,44112,44114],{},[898,44111,1918],{},[1688,44113,3665],{},[898,44115,2073],{},[902,44117,43558],{"encoding":904}," platí (znaménka se ",[38,44120,44121],{},"nemění",[883,44123,44125],{"className":44124},[886],[888,44126,44127],{"xmlns":890,"display":28306},[892,44128,44129,44191],{},[895,44130,44131,44139,44141,44143,44145,44147,44155,44157,44159,44161,44163,44171,44173,44175,44177,44179,44187,44189],{},[1814,44132,44133,44135,44137],{},[898,44134,1872],{},[898,44136,207],{},[1688,44138,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,44140,3665],{},[1793,44142,1779],{},[1688,44144,1733],{"separator":1732},[6134,44146],{"width":6136},[1814,44148,44149,44151,44153],{},[898,44150,1872],{},[898,44152,1918],{},[1688,44154,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,44156,3665],{},[1793,44158,1779],{},[1688,44160,1733],{"separator":1732},[6134,44162],{"width":6136},[1814,44164,44165,44167,44169],{},[898,44166,1872],{},[898,44168,2031],{},[1688,44170,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,44172,3704],{},[1793,44174,1779],{},[1688,44176,1733],{"separator":1732},[6134,44178],{"width":6136},[1814,44180,44181,44183,44185],{},[898,44182,1872],{},[898,44184,2073],{},[1688,44186,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,44188,3704],{},[1793,44190,12708],{},[902,44192,44193],{"encoding":904},"Q'_a > 0, \\qquad Q'_b > 0, \\qquad Q'_c \u003C 0, \\qquad Q'_d \u003C 0.",[120,44195,44196,44255],{},[123,44197,44198,2170,44201,44221,44222,44239,44240,1343,44253,2263],{},[38,44199,44200],{},"Kvantitativní smysl:",[883,44202,44204],{"className":44203},[886],[888,44205,44206],{"xmlns":890},[892,44207,44208,44218],{},[895,44209,44210],{},[1814,44211,44212,44214,44216],{},[898,44213,1872],{},[898,44215,2292],{},[1688,44217,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[902,44219,44220],{"encoding":904},"Q'_x"," udává, o kolik přibližně vzroste ",[883,44223,44225],{"className":44224},[886],[888,44226,44227],{"xmlns":890},[892,44228,44229,44237],{},[895,44230,44231],{},[1850,44232,44233,44235],{},[898,44234,1872],{},[898,44236,4509],{},[902,44238,42643],{"encoding":904}," při jednotkové změně parametru ",[883,44241,44243],{"className":44242},[886],[888,44244,44245],{"xmlns":890},[892,44246,44247,44251],{},[895,44248,44249],{},[898,44250,2292],{},[902,44252,2292],{"encoding":904},[614,44254,37200],{},[123,44256,44257,44260,44261,44278,44279,2263],{},[38,44258,44259],{},"Kvalitativní smysl:"," znaménko určuje směr reakce ",[883,44262,44264],{"className":44263},[886],[888,44265,44266],{"xmlns":890},[892,44267,44268,44276],{},[895,44269,44270],{},[1850,44271,44272,44274],{},[898,44273,1872],{},[898,44275,4509],{},[902,44277,42643],{"encoding":904}," na růst ",[883,44280,44282],{"className":44281},[886],[888,44283,44284],{"xmlns":890},[892,44285,44286,44290],{},[895,44287,44288],{},[898,44289,2292],{},[902,44291,2292],{"encoding":904},[724,44293,44294,44295,44308,44309,43559,44326,4176],{},"Např. růst ",[883,44296,44298],{"className":44297},[886],[888,44299,44300],{"xmlns":890},[892,44301,44302,44306],{},[895,44303,44304],{},[898,44305,2031],{},[902,44307,2031],{"encoding":904}," (strmější nabídka) ⟹ pokles ",[883,44310,44312],{"className":44311},[886],[888,44313,44314],{"xmlns":890},[892,44315,44316,44324],{},[895,44317,44318],{},[1850,44319,44320,44322],{},[898,44321,1872],{},[898,44323,4509],{},[902,44325,42643],{"encoding":904},[883,44327,44329],{"className":44328},[886],[888,44330,44331],{"xmlns":890},[892,44332,44333,44347],{},[895,44334,44335,44343,44345],{},[1814,44336,44337,44339,44341],{},[898,44338,1872],{},[898,44340,2031],{},[1688,44342,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,44344,3704],{},[1793,44346,1779],{},[902,44348,44349],{"encoding":904},"Q'_c \u003C 0",[724,44351,44352],{},[614,44353,44354,44355,44375,44376,44400,44401,44423,44424,2263],{},"Obrázek 2.23: Pootočení přímky nabídky z ",[883,44356,44358],{"className":44357},[886],[888,44359,44360],{"xmlns":890},[892,44361,44362,44372],{},[895,44363,44364,44366,44368,44370],{},[898,44365,2031],{},[898,44367,1872],{},[1688,44369,1696],{},[898,44371,2073],{},[902,44373,44374],{"encoding":904},"cQ + d"," na strmější ",[883,44377,44379],{"className":44378},[886],[888,44380,44381],{"xmlns":890},[892,44382,44383,44397],{},[895,44384,44385,44391,44393,44395],{},[1788,44386,44387,44389],{},[898,44388,2031],{},[1793,44390,1795],{},[898,44392,1872],{},[1688,44394,1696],{},[898,44396,2073],{},[902,44398,44399],{"encoding":904},"c_1 Q + d"," (při ",[883,44402,44404],{"className":44403},[886],[888,44405,44406],{"xmlns":890},[892,44407,44408,44420],{},[895,44409,44410,44416,44418],{},[1788,44411,44412,44414],{},[898,44413,2031],{},[1793,44415,1795],{},[1688,44417,3665],{},[898,44419,2031],{},[902,44421,44422],{"encoding":904},"c_1 > c",") — rovnovážný bod se posouvá vlevo, ",[883,44425,44427],{"className":44426},[886],[888,44428,44429],{"xmlns":890},[892,44430,44431,44441],{},[895,44432,44433,44439],{},[1850,44434,44435,44437],{},[898,44436,1872],{},[898,44438,4509],{},[1688,44440,42831],{},[902,44442,44443],{"encoding":904},"Q^E \\downarrow",[724,44445,44446,44447,44479,44480,2263],{},"Při změně jediné proměnné se (2.11) redukuje např. na ",[883,44448,44450],{"className":44449},[886],[888,44451,44452],{"xmlns":890},[892,44453,44454,44476],{},[895,44455,44456,44458,44460,44462,44470,44472,44474],{},[898,44457,3147],{"mathvariant":1822},[898,44459,1872],{},[1688,44461,2991],{},[1814,44463,44464,44466,44468],{},[898,44465,1872],{},[898,44467,1918],{},[1688,44469,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[2041,44471,2043],{},[898,44473,2073],{},[898,44475,1918],{},[902,44477,44478],{"encoding":904},"\\Delta Q \\approx Q'_b\\,db",". Analogicky lze odvodit multiplikátory pro ",[883,44481,44483],{"className":44482},[886],[888,44484,44485],{"xmlns":890},[892,44486,44487,44495],{},[895,44488,44489],{},[1850,44490,44491,44493],{},[898,44492,1727],{},[898,44494,4509],{},[902,44496,41706],{"encoding":904},[198,44498,44500,44501],{"id":44499},"příklad-211-komparativní-statika-pro-qeqe","Příklad 2.11 — komparativní statika pro ",[883,44502,44504],{"className":44503},[886],[888,44505,44506],{"xmlns":890},[892,44507,44508,44516],{},[895,44509,44510],{},[1850,44511,44512,44514],{},[898,44513,1872],{},[898,44515,4509],{},[902,44517,42643],{"encoding":904},[724,44519,44520,41895,44522,41930,44548,2263],{},[38,44521,38173],{},[883,44523,44525],{"className":44524},[886],[888,44526,44527],{"xmlns":890},[892,44528,44529,44545],{},[895,44530,44531,44533,44535,44537,44539,44541,44543],{},[898,44532,1727],{},[1688,44534,1690],{},[1688,44536,1954],{},[1793,44538,2131],{},[898,44540,1872],{},[1688,44542,1696],{},[1793,44544,5467],{},[902,44546,44547],{"encoding":904},"P = -3Q + 40",[883,44549,44551],{"className":44550},[886],[888,44552,44553],{"xmlns":890},[892,44554,44555,44569],{},[895,44556,44557,44559,44561,44563,44565,44567],{},[898,44558,1727],{},[1688,44560,1690],{},[1793,44562,5265],{},[898,44564,1872],{},[1688,44566,1696],{},[1793,44568,3121],{},[902,44570,44571],{"encoding":904},"P = 0{,}5Q + 10",[724,44573,44574,44576],{},[38,44575,38205],{}," Rovnovážné množství",[883,44578,44580],{"className":44579},[886],[888,44581,44582],{"xmlns":890,"display":28306},[892,44583,44584,44652],{},[895,44585,44586,44592,44594,44612,44614,44638,44640,44647,44649],{},[1850,44587,44588,44590],{},[898,44589,1872],{},[898,44591,4509],{},[1688,44593,1690],{},[1781,44595,44596,44604],{},[895,44597,44598,44600,44602],{},[898,44599,1918],{},[1688,44601,1954],{},[898,44603,2073],{},[895,44605,44606,44608,44610],{},[898,44607,2031],{},[1688,44609,1954],{},[898,44611,207],{},[1688,44613,1690],{},[1781,44615,44616,44624],{},[895,44617,44618,44620,44622],{},[1793,44619,5467],{},[1688,44621,1954],{},[1793,44623,3121],{},[895,44625,44626,44628,44630,44632,44634,44636],{},[1793,44627,5265],{},[1688,44629,1954],{},[1688,44631,2066],{"stretchy":2065},[1688,44633,1954],{},[1793,44635,2131],{},[1688,44637,2076],{"stretchy":2065},[1688,44639,1690],{},[1781,44641,44642,44644],{},[1793,44643,38259],{},[1793,44645,44646],{},"3,5",[1688,44648,2991],{},[1793,44650,44651],{},"8,571.",[902,44653,44654],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\approx 8{,}571.",[724,44656,44657,44702],{},[38,44658,44659,44660,2194,44673,2946,44687,44701],{},"(a) Změna ",[883,44661,44663],{"className":44662},[886],[888,44664,44665],{"xmlns":890},[892,44666,44667,44671],{},[895,44668,44669],{},[898,44670,2031],{},[902,44672,2031],{"encoding":904},[883,44674,44676],{"className":44675},[886],[888,44677,44678],{"xmlns":890},[892,44679,44680,44684],{},[895,44681,44682],{},[1793,44683,5265],{},[902,44685,44686],{"encoding":904},"0{,}5",[883,44688,44690],{"className":44689},[886],[888,44691,44692],{"xmlns":890},[892,44693,44694,44698],{},[895,44695,44696],{},[1793,44697,19562],{},[902,44699,44700],{"encoding":904},"0{,}6"," (ceteris paribus)."," Dle (2.12):",[883,44704,44706],{"className":44705},[886],[888,44707,44708],{"xmlns":890,"display":28306},[892,44709,44710,44787],{},[895,44711,44712,44720,44722,44724,44726,44728,44730,44756,44758,44760,44762,44764,44766,44776,44778,44780,44782,44784],{},[1814,44713,44714,44716,44718],{},[898,44715,1872],{},[898,44717,2031],{},[1688,44719,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[2041,44721,2043],{},[898,44723,2073],{},[898,44725,2031],{},[1688,44727,1690],{},[1688,44729,1954],{},[1781,44731,44732,44740],{},[895,44733,44734,44736,44738],{},[898,44735,1918],{},[1688,44737,1954],{},[898,44739,2073],{},[895,44741,44742,44744,44746,44748,44750],{},[1688,44743,2066],{"stretchy":2065},[898,44745,2031],{},[1688,44747,1954],{},[898,44749,207],{},[1850,44751,44752,44754],{},[1688,44753,2076],{"stretchy":2065},[1793,44755,1806],{},[2041,44757,2043],{},[898,44759,2073],{},[898,44761,2031],{},[1688,44763,1690],{},[1688,44765,1954],{},[1781,44767,44768,44770],{},[1793,44769,38259],{},[1850,44771,44772,44774],{},[1793,44773,44646],{},[1793,44775,1806],{},[1688,44777,3434],{},[1793,44779,3053],{},[1688,44781,2991],{},[1688,44783,1954],{},[1793,44785,44786],{},"0,245.",[902,44788,44789],{"encoding":904},"Q'_c\\,dc = -\\frac{b - d}{(c - a)^2}\\,dc = -\\frac{30}{3{,}5^2}\\cdot 0{,}1 \\approx -0{,}245.",[724,44791,44792,44793,2263],{},"Nové rovnovážné množství ",[883,44794,44796],{"className":44795},[886],[888,44797,44798],{"xmlns":890},[892,44799,44800,44825],{},[895,44801,44802,44810,44812,44815,44817,44820,44822],{},[1814,44803,44804,44806,44808],{},[898,44805,1872],{},[1793,44807,1795],{},[898,44809,4509],{},[1688,44811,2991],{},[1793,44813,44814],{},"8,571",[1688,44816,1954],{},[1793,44818,44819],{},"0,245",[1688,44821,1690],{},[1793,44823,44824],{},"8,326",[902,44826,44827],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326",[724,44829,44830,44915],{},[38,44831,44832,44833,1343,44853,1343,44875,1343,44895,2263],{},"(b) Současné změny ",[883,44834,44836],{"className":44835},[886],[888,44837,44838],{"xmlns":890},[892,44839,44840,44850],{},[895,44841,44842,44844,44846,44848],{},[898,44843,2073],{},[898,44845,207],{},[1688,44847,1690],{},[1793,44849,5265],{},[902,44851,44852],{"encoding":904},"da = 0{,}5",[883,44854,44856],{"className":44855},[886],[888,44857,44858],{"xmlns":890},[892,44859,44860,44872],{},[895,44861,44862,44864,44866,44868,44870],{},[898,44863,2073],{},[898,44865,1918],{},[1688,44867,1690],{},[1688,44869,1954],{},[1793,44871,2501],{},[902,44873,44874],{"encoding":904},"db = -5",[883,44876,44878],{"className":44877},[886],[888,44879,44880],{"xmlns":890},[892,44881,44882,44892],{},[895,44883,44884,44886,44888,44890],{},[898,44885,2073],{},[898,44887,2031],{},[1688,44889,1690],{},[1793,44891,3053],{},[902,44893,44894],{"encoding":904},"dc = 0{,}1",[883,44896,44898],{"className":44897},[886],[888,44899,44900],{"xmlns":890},[892,44901,44902,44912],{},[895,44903,44904,44906,44908,44910],{},[898,44905,2073],{},[898,44907,2073],{},[1688,44909,1690],{},[1793,44911,1795],{},[902,44913,44914],{"encoding":904},"dd = 1"," Dosazením do (2.11):",[883,44917,44919],{"className":44918},[886],[888,44920,44921],{"xmlns":890,"display":28306},[892,44922,44923,45066],{},[20995,44924,44925,45007,45043],{"rowspacing":20997,"columnalign":20998,"columnspacing":1823},[21000,44926,44927,44937],{},[21003,44928,44929],{},[1777,44930,44931],{"scriptlevel":1779,"displaystyle":1732},[895,44932,44933,44935],{},[898,44934,3147],{"mathvariant":1822},[898,44936,1872],{},[21003,44938,44939],{},[1777,44940,44941],{"scriptlevel":1779,"displaystyle":1732},[895,44942,44943,44945,44947,44957,44959,44961,44963,44969,44971,44973,44975,44977,44979,44981,44991,44993,44995,44997,45003,45005],{},[895,44944],{},[1688,44946,2991],{},[1781,44948,44949,44951],{},[1793,44950,38259],{},[1850,44952,44953,44955],{},[1793,44954,44646],{},[1793,44956,1806],{},[1688,44958,3434],{},[1793,44960,5265],{},[1688,44962,1696],{},[1781,44964,44965,44967],{},[1793,44966,1795],{},[1793,44968,44646],{},[1688,44970,3434],{},[1688,44972,2066],{"stretchy":2065},[1688,44974,1954],{},[1793,44976,2501],{},[1688,44978,2076],{"stretchy":2065},[1688,44980,1954],{},[1781,44982,44983,44985],{},[1793,44984,38259],{},[1850,44986,44987,44989],{},[1793,44988,44646],{},[1793,44990,1806],{},[1688,44992,3434],{},[1793,44994,3053],{},[1688,44996,1954],{},[1781,44998,44999,45001],{},[1793,45000,1795],{},[1793,45002,44646],{},[1688,45004,3434],{},[1793,45006,1795],{},[21000,45008,45009,45015],{},[21003,45010,45011],{},[1777,45012,45013],{"scriptlevel":1779,"displaystyle":1732},[895,45014],{},[21003,45016,45017],{},[1777,45018,45019],{"scriptlevel":1779,"displaystyle":1732},[895,45020,45021,45023,45025,45028,45030,45033,45035,45038,45040],{},[895,45022],{},[1688,45024,1690],{},[1793,45026,45027],{},"1,2245",[1688,45029,1954],{},[1793,45031,45032],{},"1,4286",[1688,45034,1954],{},[1793,45036,45037],{},"0,2449",[1688,45039,1954],{},[1793,45041,45042],{},"0,2857",[21000,45044,45045,45051],{},[21003,45046,45047],{},[1777,45048,45049],{"scriptlevel":1779,"displaystyle":1732},[895,45050],{},[21003,45052,45053],{},[1777,45054,45055],{"scriptlevel":1779,"displaystyle":1732},[895,45056,45057,45059,45061,45063],{},[895,45058],{},[1688,45060,2991],{},[1688,45062,1954],{},[1793,45064,45065],{},"0,735.",[902,45067,45068],{"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}",[724,45070,30305,45071,2263],{},[883,45072,45074],{"className":45073},[886],[888,45075,45076],{"xmlns":890},[892,45077,45078,45102],{},[895,45079,45080,45088,45090,45092,45094,45097,45099],{},[1814,45081,45082,45084,45086],{},[898,45083,1872],{},[1793,45085,1795],{},[898,45087,4509],{},[1688,45089,2991],{},[1793,45091,44814],{},[1688,45093,1954],{},[1793,45095,45096],{},"0,735",[1688,45098,1690],{},[1793,45100,45101],{},"7,836",[902,45103,45104],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 = 7{,}836",[4124,45106,45107],{},[724,45108,45109,45111,45112,45135,45136,45158],{},[883,45110,4668],{}," Pozn. — oprava\nV knize je u této dílčí úlohy uvedena hodnota ",[883,45113,45115],{"className":45114},[886],[888,45116,45117],{"xmlns":890},[892,45118,45119,45132],{},[895,45120,45121,45123,45125,45127,45129],{},[898,45122,3147],{"mathvariant":1822},[898,45124,1872],{},[1688,45126,2991],{},[1688,45128,1954],{},[1793,45130,45131],{},"2,69",[902,45133,45134],{"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 ",[883,45137,45139],{"className":45138},[886],[888,45140,45141],{"xmlns":890},[892,45142,45143,45155],{},[895,45144,45145,45147,45149,45151,45153],{},[898,45146,3147],{"mathvariant":1822},[898,45148,1872],{},[1688,45150,2991],{},[1688,45152,1954],{},[1793,45154,45096],{},[902,45156,45157],{"encoding":904},"\\Delta Q \\approx -0{,}735",". Výsledek byl v této wiki opraven.",[724,45160,45161],{},"Princip multiplikátorů lze uplatnit na libovolné ekonomické proměnné — analogicky v makroekonomii (kap. 7).",[37210,45163],{},[115,45165,820],{"id":12036},[4124,45167,45168],{},[724,45169,45170,4131,45172,10277,45175,12378,45191,10277,45194,45210,45211,2263],{},[883,45171,4412],{},[38,45173,45174],{},"Přebytek spotřebitele",[883,45176,45178],{"className":45177},[886],[888,45179,45180],{"xmlns":890},[892,45181,45182,45188],{},[895,45183,45184,45186],{},[898,45185,1693],{},[898,45187,1740],{},[902,45189,45190],{"encoding":904},"CS",[38,45192,45193],{},"přebytek výrobce",[883,45195,45197],{"className":45196},[886],[888,45198,45199],{"xmlns":890},[892,45200,45201,45207],{},[895,45202,45203,45205],{},[898,45204,1727],{},[898,45206,1740],{},[902,45208,45209],{"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 ",[207,45212,45214],{"className":45213,"dataFsResolvedFilePath":818,"href":819},[210],"prebytek-spotrebitele-vyrobce",[724,45216,45217],{},[2821,45218],{"alt":45219,"className":45220,"src":45221},"imek-prebytky-cs-ps",[210,2825],"\u002Fwiki-assets\u002Fimek-prebytky-cs-ps.jpeg",[724,45223,45224,10277,45226,45229],{},[38,45225,45174],{},[614,45227,45228],{},"consumer surplus",") — rozdíl mezi ochotou platit a skutečnou platbou:",[883,45231,45233],{"className":45232},[886],[888,45234,45235],{"xmlns":890,"display":28306},[892,45236,45237,45314],{},[20995,45238,45239],{"width":28311},[21000,45240,45241,45243,45307,45309],{},[21003,45242],{"width":28316},[21003,45244,45245],{},[895,45246,45247,45249,45251,45253,45259,45261,45263,45275,45277,45279,45281,45283,45285,45287,45289,45291,45297,45299,45305],{},[898,45248,1693],{},[898,45250,1740],{},[1688,45252,2066],{"stretchy":2065},[1788,45254,45255,45257],{},[898,45256,1872],{},[1793,45258,1779],{},[1688,45260,2076],{"stretchy":2065},[1688,45262,1690],{},[1814,45264,45265,45267,45269],{},[1688,45266,11421],{},[1793,45268,1779],{},[1788,45270,45271,45273],{},[898,45272,1872],{},[1793,45274,1779],{},[898,45276,4440],{},[1688,45278,2066],{"stretchy":2065},[898,45280,1872],{},[1688,45282,2076],{"stretchy":2065},[2041,45284,2043],{},[898,45286,2073],{},[898,45288,1872],{},[1688,45290,1954],{},[1788,45292,45293,45295],{},[898,45294,1727],{},[1793,45296,1779],{},[2041,45298,2043],{},[1788,45300,45301,45303],{},[898,45302,1872],{},[1793,45304,1779],{},[898,45306,2263],{"mathvariant":1822},[21003,45308],{"width":28316},[21003,45310,45311],{},[2041,45312,45313],{},"(2.14)",[902,45315,45316],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\,dQ - P_0\\,Q_0. \\tag{2.14}",[724,45318,45319,10277,45322,45325],{},[38,45320,45321],{},"Přebytek výrobce",[614,45323,45324],{},"producer surplus",") — rozdíl mezi tržbou a minimální cenou:",[883,45327,45329],{"className":45328},[886],[888,45330,45331],{"xmlns":890,"display":28306},[892,45332,45333,45410],{},[20995,45334,45335],{"width":28311},[21000,45336,45337,45339,45403,45405],{},[21003,45338],{"width":28316},[21003,45340,45341],{},[895,45342,45343,45345,45347,45349,45355,45357,45359,45365,45367,45373,45375,45387,45389,45391,45393,45395,45397,45399,45401],{},[898,45344,1727],{},[898,45346,1740],{},[1688,45348,2066],{"stretchy":2065},[1788,45350,45351,45353],{},[898,45352,1872],{},[1793,45354,1779],{},[1688,45356,2076],{"stretchy":2065},[1688,45358,1690],{},[1788,45360,45361,45363],{},[898,45362,1727],{},[1793,45364,1779],{},[2041,45366,2043],{},[1788,45368,45369,45371],{},[898,45370,1872],{},[1793,45372,1779],{},[1688,45374,1954],{},[1814,45376,45377,45379,45381],{},[1688,45378,11421],{},[1793,45380,1779],{},[1788,45382,45383,45385],{},[898,45384,1872],{},[1793,45386,1779],{},[898,45388,1740],{},[1688,45390,2066],{"stretchy":2065},[898,45392,1872],{},[1688,45394,2076],{"stretchy":2065},[2041,45396,2043],{},[898,45398,2073],{},[898,45400,1872],{},[898,45402,2263],{"mathvariant":1822},[21003,45404],{"width":28316},[21003,45406,45407],{},[2041,45408,45409],{},"(2.15)",[902,45411,45412],{"encoding":904},"PS(Q_0) = P_0\\,Q_0 - \\int_0^{Q_0} S(Q)\\,dQ. \\tag{2.15}",[724,45414,45415,45416,2263],{},"Geometricky jde o plochy mezi rovnovážnou cenou a příslušnou křivkou; výpočet využívá aparát ",[207,45417,45419],{"className":45418,"dataFsResolvedFilePath":773,"href":774},[210],"určitého integrálu",[37210,45421],{},[115,45423,45425],{"id":45424},"příklady-z-knihy-přehled","Příklady z knihy — přehled",[120,45427,45428,45459,45464,45470,45498,45504,45533,45539,45619,45645],{},[123,45429,45430,45432,45433,45458],{},[38,45431,38168],{}," — lineární poptávka ",[883,45434,45436],{"className":45435},[886],[888,45437,45438],{"xmlns":890},[892,45439,45440,45456],{},[895,45441,45442,45444,45446,45448,45450,45452,45454],{},[898,45443,1727],{},[1688,45445,1690],{},[1688,45447,1954],{},[1793,45449,1806],{},[898,45451,1872],{},[1688,45453,1696],{},[1793,45455,3383],{},[902,45457,38200],{"encoding":904},", alternativní tvar, cenové rozpětí.",[123,45460,45461,45463],{},[38,45462,38482],{}," — empirické křivky poptávky po cukru (rodina vs. trh).",[123,45465,45466,45469],{},[38,45467,45468],{},"Příklad 2.3"," — posun poptávky při zdanění kupujícího.",[123,45471,45472,45474,45475,2263],{},[38,45473,41029],{}," — lineární nabídka ",[883,45476,45478],{"className":45477},[886],[888,45479,45480],{"xmlns":890},[892,45481,45482,45496],{},[895,45483,45484,45486,45488,45490,45492,45494],{},[898,45485,1727],{},[1688,45487,1690],{},[1793,45489,5265],{},[898,45491,1872],{},[1688,45493,1696],{},[1793,45495,5260],{},[902,45497,41058],{"encoding":904},[123,45499,45500,45503],{},[38,45501,45502],{},"Příklad 2.6"," — posun nabídky při zdanění výrobce.",[123,45505,45506,45509,45510,2263],{},[38,45507,45508],{},"Příklad 2.7"," — kvadratická rovnováha, ",[883,45511,45513],{"className":45512},[886],[888,45514,45515],{"xmlns":890},[892,45516,45517,45531],{},[895,45518,45519,45521,45523,45525,45527,45529],{},[898,45520,4509],{},[1688,45522,2748],{"stretchy":2065},[1793,45524,2616],{},[1688,45526,1733],{"separator":1732},[1793,45528,42176],{},[1688,45530,2763],{"stretchy":2065},[902,45532,42204],{"encoding":904},[123,45534,45535,45538],{},[38,45536,45537],{},"Příklad 2.8"," — dvoukomoditní trh, soustava rovnic, komplementy.",[123,45540,45541,45544,45545,45562,45563,1343,45588,45615,45616,3209],{},[38,45542,45543],{},"Příklad 2.9"," — daň ",[883,45546,45548],{"className":45547},[886],[888,45549,45550],{"xmlns":890},[892,45551,45552,45560],{},[895,45553,45554,45556,45558],{},[898,45555,3035],{},[1688,45557,1690],{},[1793,45559,2508],{},[902,45561,41508],{"encoding":904}," na výrobce; rozklad ",[883,45564,45566],{"className":45565},[886],[888,45567,45568],{"xmlns":890},[892,45569,45570,45586],{},[895,45571,45572,45582,45584],{},[1788,45573,45574,45576],{},[898,45575,3035],{},[895,45577,45578,45580],{},[898,45579,42917],{},[898,45581,724],{},[1688,45583,1690],{},[1793,45585,1806],{},[902,45587,43216],{"encoding":904},[883,45589,45591],{"className":45590},[886],[888,45592,45593],{"xmlns":890},[892,45594,45595,45613],{},[895,45596,45597,45609,45611],{},[1788,45598,45599,45601],{},[898,45600,3035],{},[895,45602,45603,45605,45607],{},[898,45604,42940],{},[898,45606,2282],{},[898,45608,2046],{},[1688,45610,1690],{},[1793,45612,2616],{},[902,45614,43245],{"encoding":904},". (Viz ",[207,45617,42961],{"className":45618,"dataFsResolvedFilePath":809,"href":810},[210],[123,45620,45621,45544,45624,45641,45642,3209],{},[38,45622,45623],{},"Příklad 2.10",[883,45625,45627],{"className":45626},[886],[888,45628,45629],{"xmlns":890},[892,45630,45631,45639],{},[895,45632,45633,45635,45637],{},[898,45634,3035],{},[1688,45636,1690],{},[1793,45638,2508],{},[902,45640,41508],{"encoding":904}," na spotřebitele; stejné čisté ceny i množství. (Viz ",[207,45643,42961],{"className":45644,"dataFsResolvedFilePath":809,"href":810},[210],[123,45646,45647,45650],{},[38,45648,45649],{},"Příklad 2.11"," — komparativní statika, multiplikátory, změny parametrů.",[37210,45652],{},[115,45654,45656],{"id":45655},"úlohy-k-samostatnému-řešení","Úlohy k samostatnému řešení",[198,45658,45660],{"id":45659},"základní-analýza-poptávky","Základní analýza poptávky",[724,45662,45663,45666,45667,45702,45703,45729],{},[38,45664,45665],{},"2.1"," Je dána poptávka ",[883,45668,45670],{"className":45669},[886],[888,45671,45672],{"xmlns":890},[892,45673,45674,45699],{},[895,45675,45676,45678,45680,45682,45684,45686,45688,45690,45693,45695,45697],{},[898,45677,1872],{},[1688,45679,1690],{},[898,45681,4440],{},[1688,45683,2066],{"stretchy":2065},[898,45685,1727],{},[1688,45687,2076],{"stretchy":2065},[1688,45689,1690],{},[1793,45691,45692],{},"75",[1688,45694,1954],{},[1793,45696,2501],{},[898,45698,1727],{},[902,45700,45701],{"encoding":904},"Q = D(P) = 75 - 5P",". (a) Načrtněte křivku poptávky. (b) Stanovte reálné cenové rozpětí. (c) Vypočtěte množství při cenách ",[883,45704,45706],{"className":45705},[886],[888,45707,45708],{"xmlns":890},[892,45709,45710,45726],{},[895,45711,45712,45714,45716,45718,45720,45722,45724],{},[1793,45713,1779],{},[1688,45715,1733],{"separator":1732},[1793,45717,2501],{},[1688,45719,1733],{"separator":1732},[1793,45721,3121],{},[1688,45723,1733],{"separator":1732},[1793,45725,36484],{},[902,45727,45728],{"encoding":904},"0, 5, 10, 15"," a výsledky vyznačte na křivku poptávky.",[724,45731,45732,45735,45736,45754,45755,3408],{},[38,45733,45734],{},"2.2"," Ověřte, že uvedené funkce vyjadřují (s případným omezením pro ",[883,45737,45739],{"className":45738},[886],[888,45740,45741],{"xmlns":890},[892,45742,45743,45751],{},[895,45744,45745,45747,45749],{},[898,45746,1727],{},[1688,45748,1733],{"separator":1732},[898,45750,1872],{},[902,45752,45753],{"encoding":904},"P, Q",") poptávku (využijte testu na zápornost derivace), charakterizujte tvar křivky poptávky a vyjádřete ve tvaru poptávky v alternativním tvaru (",[883,45756,45758],{"className":45757},[886],[888,45759,45760],{"xmlns":890},[892,45761,45762,45778],{},[895,45763,45764,45766,45768,45770,45772,45774,45776],{},[898,45765,207],{},[1688,45767,1733],{"separator":1732},[898,45769,1918],{},[1688,45771,1733],{"separator":1732},[898,45773,2031],{},[1688,45775,3665],{},[1793,45777,1779],{},[902,45779,45780],{"encoding":904},"a, b, c > 0",[120,45782,45783,45816,45847,45882,45913,45948],{},[123,45784,45785,45786],{},"(a) ",[883,45787,45789],{"className":45788},[886],[888,45790,45791],{"xmlns":890},[892,45792,45793,45813],{},[895,45794,45795,45797,45799],{},[898,45796,1872],{},[1688,45798,1690],{},[1777,45800,45801],{"scriptlevel":1779,"displaystyle":1732},[1781,45802,45803,45805],{},[898,45804,207],{},[895,45806,45807,45809,45811],{},[898,45808,1727],{},[1688,45810,1696],{},[898,45812,2031],{},[902,45814,45815],{"encoding":904},"Q = \\dfrac{a}{P + c}",[123,45817,45818,45819],{},"(b) ",[883,45820,45822],{"className":45821},[886],[888,45823,45824],{"xmlns":890},[892,45825,45826,45844],{},[895,45827,45828,45830,45832],{},[898,45829,1872],{},[1688,45831,1690],{},[8373,45833,45834],{},[895,45835,45836,45838,45840,45842],{},[898,45837,207],{},[1688,45839,1954],{},[898,45841,1918],{},[898,45843,1872],{},[902,45845,45846],{"encoding":904},"Q = \\sqrt{a - bQ}",[123,45848,45849,45850],{},"(c) ",[883,45851,45853],{"className":45852},[886],[888,45854,45855],{"xmlns":890},[892,45856,45857,45879],{},[895,45858,45859,45861,45863],{},[898,45860,1872],{},[1688,45862,1690],{},[1777,45864,45865],{"scriptlevel":1779,"displaystyle":1732},[1781,45866,45867,45877],{},[895,45868,45869,45871,45873],{},[898,45870,207],{},[1688,45872,1954],{},[8373,45874,45875],{},[898,45876,1727],{},[898,45878,1918],{},[902,45880,45881],{"encoding":904},"Q = \\dfrac{a - \\sqrt{P}}{b}",[123,45883,45884,45885],{},"(d) ",[883,45886,45888],{"className":45887},[886],[888,45889,45890],{"xmlns":890},[892,45891,45892,45910],{},[895,45893,45894,45896,45898,45900,45902,45904],{},[898,45895,1727],{},[1688,45897,1690],{},[898,45899,207],{},[1688,45901,1954],{},[898,45903,1918],{},[1850,45905,45906,45908],{},[898,45907,1872],{},[1793,45909,1806],{},[902,45911,45912],{"encoding":904},"P = a - bQ^2",[123,45914,45915,45916],{},"(e) ",[883,45917,45919],{"className":45918},[886],[888,45920,45921],{"xmlns":890},[892,45922,45923,45945],{},[895,45924,45925,45927,45929,45931,45941,45943],{},[898,45926,1872],{},[1688,45928,1690],{},[898,45930,1918],{},[1850,45932,45933,45935],{},[898,45934,1727],{},[895,45936,45937,45939],{},[1688,45938,1954],{},[898,45940,207],{},[1688,45942,1696],{},[898,45944,2031],{},[902,45946,45947],{"encoding":904},"Q = bP^{-a} + c",[123,45949,45950,45951],{},"(f) ",[883,45952,45954],{"className":45953},[886],[888,45955,45956],{"xmlns":890},[892,45957,45958,45981],{},[895,45959,45960,45962,45964,45966,45968],{},[898,45961,1872],{},[1688,45963,1690],{},[898,45965,207],{},[1688,45967,3434],{},[1850,45969,45970,45973],{},[898,45971,45972],{},"e",[895,45974,45975,45977,45979],{},[1688,45976,1954],{},[898,45978,1918],{},[898,45980,1727],{},[902,45982,45983],{"encoding":904},"Q = a \\cdot e^{-bP}",[724,45985,45986,45989],{},[38,45987,45988],{},"2.3"," Rozhodněte, jak se změní křivka poptávky, jestliže se zvýší (ceteris paribus):",[120,45991,45992,45995,45998],{},[123,45993,45994],{},"(a) Cena substitutu.",[123,45996,45997],{},"(b) Cena komplementu.",[123,45999,46000],{},"(c) Výdaje na reklamu.",[724,46002,46003,45666,46005,46039,46040,46068],{},[38,46004,24883],{},[883,46006,46008],{"className":46007},[886],[888,46009,46010],{"xmlns":890},[892,46011,46012,46036],{},[895,46013,46014,46016,46018,46020,46022,46024,46026,46028,46030,46032,46034],{},[898,46015,1727],{},[1688,46017,1690],{},[898,46019,4440],{},[1688,46021,2066],{"stretchy":2065},[898,46023,1872],{},[1688,46025,2076],{"stretchy":2065},[1688,46027,1690],{},[1793,46029,3766],{},[1688,46031,1954],{},[1793,46033,1806],{},[898,46035,1872],{},[902,46037,46038],{"encoding":904},"P = D(Q) = 12 - 2Q",". Najděte novou poptávku ",[883,46041,46043],{"className":46042},[886],[888,46044,46045],{"xmlns":890},[892,46046,46047,46065],{},[895,46048,46049,46051,46053,46059,46061,46063],{},[898,46050,1727],{},[1688,46052,1690],{},[1850,46054,46055,46057],{},[898,46056,4440],{},[1688,46058,1857],{},[1688,46060,2066],{"stretchy":2065},[898,46062,1872],{},[1688,46064,2076],{"stretchy":2065},[902,46066,46067],{"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.",[724,46070,46071,46074],{},[38,46072,46073],{},"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:",[120,46076,46077,46161,46237,46323,46411],{},[123,46078,45785,46079,1343,46119,2263],{},[883,46080,46082],{"className":46081},[886],[888,46083,46084],{"xmlns":890},[892,46085,46086,46116],{},[895,46087,46088,46094,46096,46098,46100,46102,46108,46110],{},[1788,46089,46090,46092],{},[898,46091,23494],{},[1793,46093,1795],{},[1688,46095,1690],{},[1793,46097,9290],{},[1688,46099,1954],{},[1793,46101,2616],{},[1788,46103,46104,46106],{},[898,46105,4512],{},[1793,46107,1795],{},[1688,46109,1696],{},[1788,46111,46112,46114],{},[898,46113,4512],{},[1793,46115,1806],{},[902,46117,46118],{"encoding":904},"B_1 = 20 - 4A_1 + A_2",[883,46120,46122],{"className":46121},[886],[888,46123,46124],{"xmlns":890},[892,46125,46126,46158],{},[895,46127,46128,46134,46136,46138,46140,46142,46148,46150,46152],{},[1788,46129,46130,46132],{},[898,46131,23494],{},[1793,46133,1806],{},[1688,46135,1690],{},[1793,46137,3121],{},[1688,46139,1696],{},[1793,46141,1806],{},[1788,46143,46144,46146],{},[898,46145,4512],{},[1793,46147,1795],{},[1688,46149,1954],{},[1793,46151,2616],{},[1788,46153,46154,46156],{},[898,46155,4512],{},[1793,46157,1806],{},[902,46159,46160],{"encoding":904},"B_2 = 10 + 2A_1 - 4A_2",[123,46162,45818,46163,1343,46205,2263],{},[883,46164,46166],{"className":46165},[886],[888,46167,46168],{"xmlns":890},[892,46169,46170,46202],{},[895,46171,46172,46178,46180,46182,46184,46186,46192,46194,46196],{},[1788,46173,46174,46176],{},[898,46175,23494],{},[1793,46177,1795],{},[1688,46179,1690],{},[1793,46181,3377],{},[1688,46183,1954],{},[1793,46185,3121],{},[1788,46187,46188,46190],{},[898,46189,4512],{},[1793,46191,1795],{},[1688,46193,1954],{},[1793,46195,2508],{},[1788,46197,46198,46200],{},[898,46199,4512],{},[1793,46201,1806],{},[902,46203,46204],{"encoding":904},"B_1 = 50 - 10A_1 - 6A_2",[883,46206,46208],{"className":46207},[886],[888,46209,46210],{"xmlns":890},[892,46211,46212,46234],{},[895,46213,46214,46220,46222,46224,46226,46228],{},[1788,46215,46216,46218],{},[898,46217,23494],{},[1793,46219,1806],{},[1688,46221,1690],{},[1793,46223,36484],{},[1688,46225,1954],{},[1793,46227,3121],{},[1788,46229,46230,46232],{},[898,46231,4512],{},[1793,46233,1806],{},[902,46235,46236],{"encoding":904},"B_2 = 15 - 10A_2",[123,46238,45849,46239,1343,46281,2263],{},[883,46240,46242],{"className":46241},[886],[888,46243,46244],{"xmlns":890},[892,46245,46246,46278],{},[895,46247,46248,46254,46256,46258,46260,46262,46268,46270,46272],{},[1788,46249,46250,46252],{},[898,46251,23494],{},[1793,46253,1795],{},[1688,46255,1690],{},[1793,46257,38259],{},[1688,46259,1954],{},[1793,46261,1806],{},[1788,46263,46264,46266],{},[898,46265,4512],{},[1793,46267,1795],{},[1688,46269,1954],{},[1793,46271,2616],{},[1788,46273,46274,46276],{},[898,46275,4512],{},[1793,46277,1806],{},[902,46279,46280],{"encoding":904},"B_1 = 30 - 2A_1 - 4A_2",[883,46282,46284],{"className":46283},[886],[888,46285,46286],{"xmlns":890},[892,46287,46288,46320],{},[895,46289,46290,46296,46298,46300,46302,46304,46310,46312,46314],{},[1788,46291,46292,46294],{},[898,46293,23494],{},[1793,46295,1806],{},[1688,46297,1690],{},[1793,46299,36484],{},[1688,46301,1696],{},[1793,46303,1806],{},[1788,46305,46306,46308],{},[898,46307,4512],{},[1793,46309,1795],{},[1688,46311,1954],{},[1793,46313,1806],{},[1788,46315,46316,46318],{},[898,46317,4512],{},[1793,46319,1806],{},[902,46321,46322],{"encoding":904},"B_2 = 15 + 2A_1 - 2A_2",[123,46324,45884,46325,1343,46369,2263],{},[883,46326,46328],{"className":46327},[886],[888,46329,46330],{"xmlns":890},[892,46331,46332,46366],{},[895,46333,46334,46340,46342,46344,46346,46348,46350,46356,46358,46360],{},[1788,46335,46336,46338],{},[898,46337,23494],{},[1793,46339,1795],{},[1688,46341,1690],{},[1688,46343,1954],{},[1793,46345,9290],{},[1688,46347,1954],{},[1793,46349,1806],{},[1788,46351,46352,46354],{},[898,46353,4512],{},[1793,46355,1795],{},[1688,46357,1696],{},[1793,46359,2131],{},[1788,46361,46362,46364],{},[898,46363,4512],{},[1793,46365,1806],{},[902,46367,46368],{"encoding":904},"B_1 = -20 - 2A_1 + 3A_2",[883,46370,46372],{"className":46371},[886],[888,46373,46374],{"xmlns":890},[892,46375,46376,46408],{},[895,46377,46378,46384,46386,46388,46390,46392,46398,46400,46402],{},[1788,46379,46380,46382],{},[898,46381,23494],{},[1793,46383,1806],{},[1688,46385,1690],{},[1793,46387,3121],{},[1688,46389,1696],{},[1793,46391,1806],{},[1788,46393,46394,46396],{},[898,46395,4512],{},[1793,46397,1795],{},[1688,46399,1954],{},[1793,46401,1806],{},[1788,46403,46404,46406],{},[898,46405,4512],{},[1793,46407,1806],{},[902,46409,46410],{"encoding":904},"B_2 = 10 + 2A_1 - 2A_2",[123,46412,45915,46413,1343,46455,2263],{},[883,46414,46416],{"className":46415},[886],[888,46417,46418],{"xmlns":890},[892,46419,46420,46452],{},[895,46421,46422,46428,46430,46432,46434,46436,46442,46444,46446],{},[1788,46423,46424,46426],{},[898,46425,23494],{},[1793,46427,1795],{},[1688,46429,1690],{},[1793,46431,9290],{},[1688,46433,1696],{},[1793,46435,1806],{},[1788,46437,46438,46440],{},[898,46439,4512],{},[1793,46441,1795],{},[1688,46443,1696],{},[1793,46445,2616],{},[1788,46447,46448,46450],{},[898,46449,4512],{},[1793,46451,1806],{},[902,46453,46454],{"encoding":904},"B_1 = 20 + 2A_1 + 4A_2",[883,46456,46458],{"className":46457},[886],[888,46459,46460],{"xmlns":890},[892,46461,46462,46494],{},[895,46463,46464,46470,46472,46474,46476,46478,46484,46486,46488],{},[1788,46465,46466,46468],{},[898,46467,23494],{},[1793,46469,1806],{},[1688,46471,1690],{},[1793,46473,5467],{},[1688,46475,1954],{},[1793,46477,2131],{},[1788,46479,46480,46482],{},[898,46481,4512],{},[1793,46483,1795],{},[1688,46485,1696],{},[1793,46487,2501],{},[1788,46489,46490,46492],{},[898,46491,4512],{},[1793,46493,1806],{},[902,46495,46496],{"encoding":904},"B_2 = 40 - 3A_1 + 5A_2",[198,46498,46500],{"id":46499},"základní-analýza-nabídky","Základní analýza nabídky",[724,46502,46503,46506,46507,46541,46542,46564],{},[38,46504,46505],{},"2.6"," Je dána nabídka ",[883,46508,46510],{"className":46509},[886],[888,46511,46512],{"xmlns":890},[892,46513,46514,46538],{},[895,46515,46516,46518,46520,46522,46524,46526,46528,46530,46532,46534,46536],{},[898,46517,1727],{},[1688,46519,1690],{},[898,46521,1740],{},[1688,46523,2066],{"stretchy":2065},[898,46525,1872],{},[1688,46527,2076],{"stretchy":2065},[1688,46529,1690],{},[1793,46531,9290],{},[1688,46533,1696],{},[1793,46535,3097],{},[898,46537,1872],{},[902,46539,46540],{"encoding":904},"P = S(Q) = 20 + 0{,}2Q",". (a) Načrtněte křivku nabídky. (b) Vypočtěte množství při cenách ",[883,46543,46545],{"className":46544},[886],[888,46546,46547],{"xmlns":890},[892,46548,46549,46561],{},[895,46550,46551,46553,46555,46557,46559],{},[1793,46552,5260],{},[1688,46554,1733],{"separator":1732},[1793,46556,38259],{},[1688,46558,1733],{"separator":1732},[1793,46560,15285],{},[902,46562,46563],{"encoding":904},"25, 30, 35"," a vyznačte výsledky na křivku nabídky.",[724,46566,46567,46570,46571,46588],{},[38,46568,46569],{},"2.7"," Ověřte, že zadané funkce vyjadřují (s případným omezením na ",[883,46572,46574],{"className":46573},[886],[888,46575,46576],{"xmlns":890},[892,46577,46578,46586],{},[895,46579,46580,46582,46584],{},[898,46581,1727],{},[1688,46583,1733],{"separator":1732},[898,46585,1872],{},[902,46587,45753],{"encoding":904},") nabídku (využijte testu na kladnost derivace), charakterizujte tvar křivky nabídky a vyjádřete nabídku v alternativním tvaru:",[120,46590,46591,46617,46645,46678,46712,46748],{},[123,46592,45785,46593],{},[883,46594,46596],{"className":46595},[886],[888,46597,46598],{"xmlns":890},[892,46599,46600,46614],{},[895,46601,46602,46604,46606,46608,46610,46612],{},[898,46603,1727],{},[1688,46605,1690],{},[1793,46607,38259],{},[1688,46609,1696],{},[1793,46611,1806],{},[898,46613,1872],{},[902,46615,46616],{"encoding":904},"P = 30 + 2Q",[123,46618,45818,46619],{},[883,46620,46622],{"className":46621},[886],[888,46623,46624],{"xmlns":890},[892,46625,46626,46642],{},[895,46627,46628,46630,46632,46634,46636,46638,46640],{},[898,46629,1872],{},[1688,46631,1690],{},[1688,46633,1954],{},[1793,46635,2131],{},[1688,46637,1696],{},[1793,46639,3766],{},[898,46641,1727],{},[902,46643,46644],{"encoding":904},"Q = -3 + 12P",[123,46646,45849,46647],{},[883,46648,46650],{"className":46649},[886],[888,46651,46652],{"xmlns":890},[892,46653,46654,46676],{},[895,46655,46656,46658,46660,46666,46668,46670,46672,46674],{},[898,46657,1727],{},[1688,46659,1690],{},[1850,46661,46662,46664],{},[898,46663,1872],{},[1793,46665,1806],{},[1688,46667,1696],{},[1793,46669,23187],{},[898,46671,1872],{},[1688,46673,1696],{},[1793,46675,32786],{},[902,46677,41962],{"encoding":904},[123,46679,45884,46680],{},[883,46681,46683],{"className":46682},[886],[888,46684,46685],{"xmlns":890},[892,46686,46687,46709],{},[895,46688,46689,46691,46693,46699,46701,46703,46705,46707],{},[898,46690,1727],{},[1688,46692,1690],{},[1850,46694,46695,46697],{},[898,46696,1872],{},[1793,46698,1806],{},[1688,46700,1696],{},[1793,46702,1806],{},[898,46704,1872],{},[1688,46706,1696],{},[1793,46708,3766],{},[902,46710,46711],{"encoding":904},"P = Q^2 + 2Q + 12",[123,46713,45915,46714],{},[883,46715,46717],{"className":46716},[886],[888,46718,46719],{"xmlns":890},[892,46720,46721,46745],{},[895,46722,46723,46725,46727,46729,46731,46733,46735,46737,46739],{},[898,46724,1872],{},[1688,46726,1690],{},[1793,46728,9058],{},[1688,46730,1696],{},[1793,46732,2501],{},[898,46734,1727],{},[1688,46736,1696],{},[1793,46738,3053],{},[1850,46740,46741,46743],{},[898,46742,1727],{},[1793,46744,1806],{},[902,46746,46747],{"encoding":904},"Q = 150 + 5P + 0{,}1P^2",[123,46749,45950,46750],{},[883,46751,46753],{"className":46752},[886],[888,46754,46755],{"xmlns":890},[892,46756,46757,46782],{},[895,46758,46759,46761,46763,46765,46767,46769,46771,46773,46776],{},[898,46760,1872],{},[1688,46762,1690],{},[1793,46764,24442],{},[1688,46766,1696],{},[1793,46768,3053],{},[898,46770,1727],{},[1688,46772,1696],{},[1793,46774,46775],{},"0,004",[1850,46777,46778,46780],{},[898,46779,1727],{},[1793,46781,1806],{},[902,46783,46784],{"encoding":904},"Q = 7 + 0{,}1P + 0{,}004P^2",[724,46786,46787,46790],{},[38,46788,46789],{},"2.8"," Rozhodněte, jak se změní křivka nabídky, jestliže se (ceteris paribus):",[120,46792,46793,46796,46799,46802],{},[123,46794,46795],{},"(a) Sníží ceny surovin — vstupů.",[123,46797,46798],{},"(b) Zavede nová ekologičtější technologie zvyšující výrobní náklady.",[123,46800,46801],{},"(c) Zvýší ceny všech energií.",[123,46803,46804],{},"(d) Sníží daňové odvody státu.",[724,46806,46807,46506,46809,46843,46844,46872],{},[38,46808,43189],{},[883,46810,46812],{"className":46811},[886],[888,46813,46814],{"xmlns":890},[892,46815,46816,46840],{},[895,46817,46818,46820,46822,46824,46826,46828,46830,46832,46834,46836,46838],{},[898,46819,1727],{},[1688,46821,1690],{},[898,46823,1740],{},[1688,46825,2066],{"stretchy":2065},[898,46827,1872],{},[1688,46829,2076],{"stretchy":2065},[1688,46831,1690],{},[1793,46833,5265],{},[898,46835,1872],{},[1688,46837,1696],{},[1793,46839,36484],{},[902,46841,46842],{"encoding":904},"P = S(Q) = 0{,}5Q + 15",". Najděte novou nabídku ",[883,46845,46847],{"className":46846},[886],[888,46848,46849],{"xmlns":890},[892,46850,46851,46869],{},[895,46852,46853,46855,46857,46863,46865,46867],{},[898,46854,1727],{},[1688,46856,1690],{},[1850,46858,46859,46861],{},[898,46860,1740],{},[1688,46862,1857],{},[1688,46864,2066],{"stretchy":2065},[898,46866,1872],{},[1688,46868,2076],{"stretchy":2065},[902,46870,46871],{"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.",[198,46874,41565],{"id":46875},"tržní-rovnováha-1",[724,46877,46878,46880,46881,46898,46899,2965],{},[38,46879,43249],{}," Pro zadanou poptávku a nabídku najděte rovnovážné množství ",[883,46882,46884],{"className":46883},[886],[888,46885,46886],{"xmlns":890},[892,46887,46888,46896],{},[895,46889,46890],{},[1850,46891,46892,46894],{},[898,46893,1872],{},[898,46895,4509],{},[902,46897,42643],{"encoding":904}," a rovnovážnou cenu ",[883,46900,46902],{"className":46901},[886],[888,46903,46904],{"xmlns":890},[892,46905,46906,46914],{},[895,46907,46908],{},[1850,46909,46910,46912],{},[898,46911,1727],{},[898,46913,4509],{},[902,46915,41706],{"encoding":904},[120,46917,46918,46971,47022,47081],{},[123,46919,45785,46920,1343,46947,2263],{},[883,46921,46923],{"className":46922},[886],[888,46924,46925],{"xmlns":890},[892,46926,46927,46944],{},[895,46928,46929,46931,46933,46935,46937,46939,46941],{},[898,46930,1727],{},[1688,46932,1690],{},[1688,46934,1954],{},[1793,46936,2501],{},[898,46938,1872],{},[1688,46940,1696],{},[1793,46942,46943],{},"80",[902,46945,46946],{"encoding":904},"P = -5Q + 80",[883,46948,46950],{"className":46949},[886],[888,46951,46952],{"xmlns":890},[892,46953,46954,46968],{},[895,46955,46956,46958,46960,46962,46964,46966],{},[898,46957,1727],{},[1688,46959,1690],{},[1793,46961,1806],{},[898,46963,1872],{},[1688,46965,1696],{},[1793,46967,3121],{},[902,46969,46970],{"encoding":904},"P = 2Q + 10",[123,46972,45818,46973,1343,46999,2263],{},[883,46974,46976],{"className":46975},[886],[888,46977,46978],{"xmlns":890},[892,46979,46980,46996],{},[895,46981,46982,46984,46986,46988,46990,46992,46994],{},[898,46983,1872],{},[1688,46985,1690],{},[1688,46987,1954],{},[1793,46989,5265],{},[898,46991,1727],{},[1688,46993,1696],{},[1793,46995,5260],{},[902,46997,46998],{"encoding":904},"Q = -0{,}5P + 25",[883,47000,47002],{"className":47001},[886],[888,47003,47004],{"xmlns":890},[892,47005,47006,47020],{},[895,47007,47008,47010,47012,47014,47016,47018],{},[898,47009,1872],{},[1688,47011,1690],{},[1793,47013,1806],{},[898,47015,1727],{},[1688,47017,1954],{},[1793,47019,3377],{},[902,47021,41087],{"encoding":904},[123,47023,45849,47024,1343,47050,2263],{},[883,47025,47027],{"className":47026},[886],[888,47028,47029],{"xmlns":890},[892,47030,47031,47047],{},[895,47032,47033,47035,47037,47039,47041,47043,47045],{},[898,47034,1727],{},[1688,47036,1690],{},[1688,47038,1954],{},[1793,47040,2616],{},[898,47042,1872],{},[1688,47044,1696],{},[1793,47046,4303],{},[902,47048,47049],{"encoding":904},"P = -4Q + 120",[883,47051,47053],{"className":47052},[886],[888,47054,47055],{"xmlns":890},[892,47056,47057,47078],{},[895,47058,47059,47061,47063,47071,47073,47075],{},[898,47060,1727],{},[1688,47062,1690],{},[1777,47064,47065],{"scriptlevel":1779,"displaystyle":2065},[1781,47066,47067,47069],{},[1793,47068,1795],{},[1793,47070,2131],{},[898,47072,1872],{},[1688,47074,1696],{},[1793,47076,47077],{},"29",[902,47079,47080],{"encoding":904},"P = \\tfrac{1}{3}Q + 29",[123,47082,45884,47083,1343,47112,2263],{},[883,47084,47086],{"className":47085},[886],[888,47087,47088],{"xmlns":890},[892,47089,47090,47109],{},[895,47091,47092,47094,47096,47098,47104,47106],{},[898,47093,1727],{},[1688,47095,1690],{},[1688,47097,1954],{},[1850,47099,47100,47102],{},[898,47101,1872],{},[1793,47103,1806],{},[1688,47105,1696],{},[1793,47107,47108],{},"52",[902,47110,47111],{"encoding":904},"P = -Q^2 + 52",[883,47113,47115],{"className":47114},[886],[888,47116,47117],{"xmlns":890},[892,47118,47119,47137],{},[895,47120,47121,47123,47125,47127,47133,47135],{},[898,47122,1727],{},[1688,47124,1690],{},[1793,47126,1806],{},[1850,47128,47129,47131],{},[898,47130,1872],{},[1793,47132,1806],{},[1688,47134,1696],{},[1793,47136,3121],{},[902,47138,47139],{"encoding":904},"P = 2Q^2 + 10",[724,47141,47142,47145,47146,47176,47177,47207],{},[38,47143,47144],{},"2.11"," Pro zadanou poptávku a nabídku dvou závislých zboží najděte rovnovážná množství ",[883,47147,47149],{"className":47148},[886],[888,47150,47151],{"xmlns":890},[892,47152,47153,47173],{},[895,47154,47155,47163,47165],{},[1814,47156,47157,47159,47161],{},[898,47158,1872],{},[1793,47160,1795],{},[898,47162,4509],{},[1688,47164,1733],{"separator":1732},[1814,47166,47167,47169,47171],{},[898,47168,1872],{},[1793,47170,1806],{},[898,47172,4509],{},[902,47174,47175],{"encoding":904},"Q_1^E, Q_2^E"," a rovnovážné ceny ",[883,47178,47180],{"className":47179},[886],[888,47181,47182],{"xmlns":890},[892,47183,47184,47204],{},[895,47185,47186,47194,47196],{},[1814,47187,47188,47190,47192],{},[898,47189,1727],{},[1793,47191,1795],{},[898,47193,4509],{},[1688,47195,1733],{"separator":1732},[1814,47197,47198,47200,47202],{},[898,47199,1727],{},[1793,47201,1806],{},[898,47203,4509],{},[902,47205,47206],{"encoding":904},"P_1^E, P_2^E"," (index 1 přísluší prvnímu, index 2 druhému zboží):",[120,47209,47210,47362],{},[123,47211,45785,47212,1343,47252,1343,47294,1343,47328,2263],{},[883,47213,47215],{"className":47214},[886],[888,47216,47217],{"xmlns":890},[892,47218,47219,47249],{},[895,47220,47221,47227,47229,47231,47233,47235,47241,47243],{},[1788,47222,47223,47225],{},[898,47224,1872],{},[1793,47226,1795],{},[1688,47228,1690],{},[1793,47230,3121],{},[1688,47232,1954],{},[1793,47234,1806],{},[1788,47236,47237,47239],{},[898,47238,1727],{},[1793,47240,1795],{},[1688,47242,1696],{},[1788,47244,47245,47247],{},[898,47246,1727],{},[1793,47248,1806],{},[902,47250,47251],{"encoding":904},"Q_1 = 10 - 2P_1 + P_2",[883,47253,47255],{"className":47254},[886],[888,47256,47257],{"xmlns":890},[892,47258,47259,47291],{},[895,47260,47261,47267,47269,47271,47273,47275,47281,47283,47285],{},[1788,47262,47263,47265],{},[898,47264,1872],{},[1793,47266,1806],{},[1688,47268,1690],{},[1793,47270,2501],{},[1688,47272,1696],{},[1793,47274,1806],{},[1788,47276,47277,47279],{},[898,47278,1727],{},[1793,47280,1795],{},[1688,47282,1954],{},[1793,47284,1806],{},[1788,47286,47287,47289],{},[898,47288,1727],{},[1793,47290,1806],{},[902,47292,47293],{"encoding":904},"Q_2 = 5 + 2P_1 - 2P_2",[883,47295,47297],{"className":47296},[886],[888,47298,47299],{"xmlns":890},[892,47300,47301,47325],{},[895,47302,47303,47309,47311,47313,47315,47317,47319],{},[1788,47304,47305,47307],{},[898,47306,1872],{},[1793,47308,1795],{},[1688,47310,1690],{},[1688,47312,1954],{},[1793,47314,2131],{},[1688,47316,1696],{},[1793,47318,1806],{},[1788,47320,47321,47323],{},[898,47322,1727],{},[1793,47324,1795],{},[902,47326,47327],{"encoding":904},"Q_1 = -3 + 2P_1",[883,47329,47331],{"className":47330},[886],[888,47332,47333],{"xmlns":890},[892,47334,47335,47359],{},[895,47336,47337,47343,47345,47347,47349,47351,47353],{},[1788,47338,47339,47341],{},[898,47340,1872],{},[1793,47342,1806],{},[1688,47344,1690],{},[1688,47346,1954],{},[1793,47348,1806],{},[1688,47350,1696],{},[1793,47352,2131],{},[1788,47354,47355,47357],{},[898,47356,1727],{},[1793,47358,1806],{},[902,47360,47361],{"encoding":904},"Q_2 = -2 + 3P_2",[123,47363,45818,47364,1343,47404,1343,47446,1343,47478,2263],{},[883,47365,47367],{"className":47366},[886],[888,47368,47369],{"xmlns":890},[892,47370,47371,47401],{},[895,47372,47373,47379,47381,47383,47385,47387,47393,47395],{},[1788,47374,47375,47377],{},[898,47376,1872],{},[1793,47378,1795],{},[1688,47380,1690],{},[1793,47382,3347],{},[1688,47384,1954],{},[1793,47386,1806],{},[1788,47388,47389,47391],{},[898,47390,1727],{},[1793,47392,1795],{},[1688,47394,1696],{},[1788,47396,47397,47399],{},[898,47398,1727],{},[1793,47400,1806],{},[902,47402,47403],{"encoding":904},"Q_1 = 100 - 2P_1 + P_2",[883,47405,47407],{"className":47406},[886],[888,47408,47409],{"xmlns":890},[892,47410,47411,47443],{},[895,47412,47413,47419,47421,47423,47425,47427,47433,47435,47437],{},[1788,47414,47415,47417],{},[898,47416,1872],{},[1793,47418,1806],{},[1688,47420,1690],{},[1793,47422,2501],{},[1688,47424,1696],{},[1793,47426,1806],{},[1788,47428,47429,47431],{},[898,47430,1727],{},[1793,47432,1795],{},[1688,47434,1954],{},[1793,47436,2131],{},[1788,47438,47439,47441],{},[898,47440,1727],{},[1793,47442,1806],{},[902,47444,47445],{"encoding":904},"Q_2 = 5 + 2P_1 - 3P_2",[883,47447,47449],{"className":47448},[886],[888,47450,47451],{"xmlns":890},[892,47452,47453,47475],{},[895,47454,47455,47461,47463,47465,47467,47469],{},[1788,47456,47457,47459],{},[898,47458,1872],{},[1793,47460,1795],{},[1688,47462,1690],{},[1688,47464,1954],{},[1793,47466,3121],{},[1688,47468,1696],{},[1788,47470,47471,47473],{},[898,47472,1727],{},[1793,47474,1795],{},[902,47476,47477],{"encoding":904},"Q_1 = -10 + P_1",[883,47479,47481],{"className":47480},[886],[888,47482,47483],{"xmlns":890},[892,47484,47485,47507],{},[895,47486,47487,47493,47495,47497,47499,47501],{},[1788,47488,47489,47491],{},[898,47490,1872],{},[1793,47492,1806],{},[1688,47494,1690],{},[1793,47496,2501],{},[1688,47498,1696],{},[1793,47500,2508],{},[1788,47502,47503,47505],{},[898,47504,1727],{},[1793,47506,1806],{},[902,47508,47509],{"encoding":904},"Q_2 = 5 + 6P_2",[724,47511,47512,47515,47516,1343,47564,1343,47610,47660,47661,1343,47693,1343,47727,21835,47761,4142,47779,47797,47798,47811,47812,47838,47839,47176,47879,2263],{},[38,47513,47514],{},"2.12"," Pro tři závislá zboží jsou dány poptávky rovnicemi ",[883,47517,47519],{"className":47518},[886],[888,47520,47521],{"xmlns":890},[892,47522,47523,47561],{},[895,47524,47525,47531,47533,47535,47537,47543,47545,47547,47553,47555],{},[1788,47526,47527,47529],{},[898,47528,1872],{},[1793,47530,1795],{},[1688,47532,1690],{},[1793,47534,36484],{},[1688,47536,1954],{},[1788,47538,47539,47541],{},[898,47540,1727],{},[1793,47542,1795],{},[1688,47544,1696],{},[1793,47546,1806],{},[1788,47548,47549,47551],{},[898,47550,1727],{},[1793,47552,1806],{},[1688,47554,1696],{},[1788,47556,47557,47559],{},[898,47558,1727],{},[1793,47560,2131],{},[902,47562,47563],{"encoding":904},"Q_1 = 15 - P_1 + 2P_2 + P_3",[883,47565,47567],{"className":47566},[886],[888,47568,47569],{"xmlns":890},[892,47570,47571,47607],{},[895,47572,47573,47579,47581,47583,47585,47591,47593,47599,47601],{},[1788,47574,47575,47577],{},[898,47576,1872],{},[1793,47578,1806],{},[1688,47580,1690],{},[1793,47582,4256],{},[1688,47584,1696],{},[1788,47586,47587,47589],{},[898,47588,1727],{},[1793,47590,1795],{},[1688,47592,1954],{},[1788,47594,47595,47597],{},[898,47596,1727],{},[1793,47598,1806],{},[1688,47600,1954],{},[1788,47602,47603,47605],{},[898,47604,1727],{},[1793,47606,2131],{},[902,47608,47609],{"encoding":904},"Q_2 = 9 + P_1 - P_2 - P_3",[883,47611,47613],{"className":47612},[886],[888,47614,47615],{"xmlns":890},[892,47616,47617,47657],{},[895,47618,47619,47625,47627,47629,47631,47633,47639,47641,47647,47649,47651],{},[1788,47620,47621,47623],{},[898,47622,1872],{},[1793,47624,2131],{},[1688,47626,1690],{},[1793,47628,5841],{},[1688,47630,1696],{},[1793,47632,1806],{},[1788,47634,47635,47637],{},[898,47636,1727],{},[1793,47638,1795],{},[1688,47640,1954],{},[1788,47642,47643,47645],{},[898,47644,1727],{},[1793,47646,1806],{},[1688,47648,1954],{},[1793,47650,2616],{},[1788,47652,47653,47655],{},[898,47654,1727],{},[1793,47656,2131],{},[902,47658,47659],{"encoding":904},"Q_3 = 8 + 2P_1 - P_2 - 4P_3"," a nabídky rovnicemi ",[883,47662,47664],{"className":47663},[886],[888,47665,47666],{"xmlns":890},[892,47667,47668,47690],{},[895,47669,47670,47676,47678,47680,47682,47684],{},[1788,47671,47672,47674],{},[898,47673,1872],{},[1793,47675,1795],{},[1688,47677,1690],{},[1688,47679,1954],{},[1793,47681,24442],{},[1688,47683,1696],{},[1788,47685,47686,47688],{},[898,47687,1727],{},[1793,47689,1795],{},[902,47691,47692],{"encoding":904},"Q_1 = -7 + P_1",[883,47694,47696],{"className":47695},[886],[888,47697,47698],{"xmlns":890},[892,47699,47700,47724],{},[895,47701,47702,47708,47710,47712,47714,47716,47718],{},[1788,47703,47704,47706],{},[898,47705,1872],{},[1793,47707,1806],{},[1688,47709,1690],{},[1688,47711,1954],{},[1793,47713,2616],{},[1688,47715,1696],{},[1793,47717,2616],{},[1788,47719,47720,47722],{},[898,47721,1727],{},[1793,47723,1806],{},[902,47725,47726],{"encoding":904},"Q_2 = -4 + 4P_2",[883,47728,47730],{"className":47729},[886],[888,47731,47732],{"xmlns":890},[892,47733,47734,47758],{},[895,47735,47736,47742,47744,47746,47748,47750,47752],{},[1788,47737,47738,47740],{},[898,47739,1872],{},[1793,47741,2131],{},[1688,47743,1690],{},[1688,47745,1954],{},[1793,47747,2501],{},[1688,47749,1696],{},[1793,47751,1806],{},[1788,47753,47754,47756],{},[898,47755,1727],{},[1793,47757,2131],{},[902,47759,47760],{"encoding":904},"Q_3 = -5 + 2P_3",[883,47762,47764],{"className":47763},[886],[888,47765,47766],{"xmlns":890},[892,47767,47768,47776],{},[895,47769,47770],{},[1788,47771,47772,47774],{},[898,47773,1872],{},[898,47775,18035],{},[902,47777,47778],{"encoding":904},"Q_i",[883,47780,47782],{"className":47781},[886],[888,47783,47784],{"xmlns":890},[892,47785,47786,47794],{},[895,47787,47788],{},[1788,47789,47790,47792],{},[898,47791,1727],{},[898,47793,18035],{},[902,47795,47796],{"encoding":904},"P_i"," značí příslušné množství a ceny ",[883,47799,47801],{"className":47800},[886],[888,47802,47803],{"xmlns":890},[892,47804,47805,47809],{},[895,47806,47807],{},[898,47808,18035],{},[902,47810,18035],{"encoding":904},"-tého zboží, ",[883,47813,47815],{"className":47814},[886],[888,47816,47817],{"xmlns":890},[892,47818,47819,47835],{},[895,47820,47821,47823,47825,47827,47829,47831,47833],{},[898,47822,18035],{},[1688,47824,1690],{},[1793,47826,1795],{},[1688,47828,1733],{"separator":1732},[1793,47830,1806],{},[1688,47832,1733],{"separator":1732},[1793,47834,2131],{},[902,47836,47837],{"encoding":904},"i = 1, 2, 3",". Najděte rovnovážná množství ",[883,47840,47842],{"className":47841},[886],[888,47843,47844],{"xmlns":890},[892,47845,47846,47876],{},[895,47847,47848,47856,47858,47866,47868],{},[1814,47849,47850,47852,47854],{},[898,47851,1872],{},[1793,47853,1795],{},[898,47855,4509],{},[1688,47857,1733],{"separator":1732},[1814,47859,47860,47862,47864],{},[898,47861,1872],{},[1793,47863,1806],{},[898,47865,4509],{},[1688,47867,1733],{"separator":1732},[1814,47869,47870,47872,47874],{},[898,47871,1872],{},[1793,47873,2131],{},[898,47875,4509],{},[902,47877,47878],{"encoding":904},"Q_1^E, Q_2^E, Q_3^E",[883,47880,47882],{"className":47881},[886],[888,47883,47884],{"xmlns":890},[892,47885,47886,47916],{},[895,47887,47888,47896,47898,47906,47908],{},[1814,47889,47890,47892,47894],{},[898,47891,1727],{},[1793,47893,1795],{},[898,47895,4509],{},[1688,47897,1733],{"separator":1732},[1814,47899,47900,47902,47904],{},[898,47901,1727],{},[1793,47903,1806],{},[898,47905,4509],{},[1688,47907,1733],{"separator":1732},[1814,47909,47910,47912,47914],{},[898,47911,1727],{},[1793,47913,2131],{},[898,47915,4509],{},[902,47917,47918],{"encoding":904},"P_1^E, P_2^E, P_3^E",[724,47920,47921,47924,47925,47961,47962,2263],{},[38,47922,47923],{},"2.13"," Jsou dány poptávka ",[883,47926,47928],{"className":47927},[886],[888,47929,47930],{"xmlns":890},[892,47931,47932,47958],{},[895,47933,47934,47936,47938,47940,47942,47944,47946,47948,47950,47952,47954,47956],{},[898,47935,1727],{},[1688,47937,1690],{},[898,47939,4440],{},[1688,47941,2066],{"stretchy":2065},[898,47943,1872],{},[1688,47945,2076],{"stretchy":2065},[1688,47947,1690],{},[1688,47949,1954],{},[1793,47951,2616],{},[898,47953,1872],{},[1688,47955,1696],{},[1793,47957,46943],{},[902,47959,47960],{"encoding":904},"P = D(Q) = -4Q + 80"," a nabídka ",[883,47963,47965],{"className":47964},[886],[888,47966,47967],{"xmlns":890},[892,47968,47969,47993],{},[895,47970,47971,47973,47975,47977,47979,47981,47983,47985,47987,47989,47991],{},[898,47972,1727],{},[1688,47974,1690],{},[898,47976,1740],{},[1688,47978,2066],{"stretchy":2065},[898,47980,1872],{},[1688,47982,2076],{"stretchy":2065},[1688,47984,1690],{},[1793,47986,2131],{},[898,47988,1872],{},[1688,47990,1696],{},[1793,47992,3121],{},[902,47994,47995],{"encoding":904},"P = S(Q) = 3Q + 10",[120,47997,47998,48035,48099,48159],{},[123,47999,48000,48001,46898,48018,2263],{},"(a) Určete rovnovážné množství ",[883,48002,48004],{"className":48003},[886],[888,48005,48006],{"xmlns":890},[892,48007,48008,48016],{},[895,48009,48010],{},[1850,48011,48012,48014],{},[898,48013,1872],{},[898,48015,4509],{},[902,48017,42643],{"encoding":904},[883,48019,48021],{"className":48020},[886],[888,48022,48023],{"xmlns":890},[892,48024,48025,48033],{},[895,48026,48027],{},[1850,48028,48029,48031],{},[898,48030,1727],{},[898,48032,4509],{},[902,48034,41706],{"encoding":904},[123,48036,48037,48038,48056,48057,48077,48078,48098],{},"(b) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží výrobci daň ",[883,48039,48041],{"className":48040},[886],[888,48042,48043],{"xmlns":890},[892,48044,48045,48053],{},[895,48046,48047,48049,48051],{},[898,48048,3035],{},[1688,48050,1690],{},[1793,48052,24442],{},[902,48054,48055],{"encoding":904},"T = 7"," Kč na každou jednotku zboží, vypočtěte nové rovnovážné množství ",[883,48058,48060],{"className":48059},[886],[888,48061,48062],{"xmlns":890},[892,48063,48064,48074],{},[895,48065,48066],{},[1814,48067,48068,48070,48072],{},[898,48069,1872],{},[1793,48071,1795],{},[898,48073,4509],{},[902,48075,48076],{"encoding":904},"Q_1^E"," a novou rovnovážnou cenu ",[883,48079,48081],{"className":48080},[886],[888,48082,48083],{"xmlns":890},[892,48084,48085,48095],{},[895,48086,48087],{},[1814,48088,48089,48091,48093],{},[898,48090,1727],{},[1793,48092,1795],{},[898,48094,4509],{},[902,48096,48097],{"encoding":904},"P_1^E"," a určete, kolik z daňového zatížení zaplatí výrobce a kolik spotřebitel.",[123,48100,48101,48102,48056,48119,48077,48139,48098],{},"(c) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží spotřebiteli daň ",[883,48103,48105],{"className":48104},[886],[888,48106,48107],{"xmlns":890},[892,48108,48109,48117],{},[895,48110,48111,48113,48115],{},[898,48112,3035],{},[1688,48114,1690],{},[1793,48116,24442],{},[902,48118,48055],{"encoding":904},[883,48120,48122],{"className":48121},[886],[888,48123,48124],{"xmlns":890},[892,48125,48126,48136],{},[895,48127,48128],{},[1814,48129,48130,48132,48134],{},[898,48131,1872],{},[1793,48133,1806],{},[898,48135,4509],{},[902,48137,48138],{"encoding":904},"Q_2^E",[883,48140,48142],{"className":48141},[886],[888,48143,48144],{"xmlns":890},[892,48145,48146,48156],{},[895,48147,48148],{},[1814,48149,48150,48152,48154],{},[898,48151,1727],{},[1793,48153,1806],{},[898,48155,4509],{},[902,48157,48158],{"encoding":904},"P_2^E",[123,48160,48161],{},"(d) Proveďte analýzu dopadu daňového zatížení na spotřebitele a výrobce vyplývající z výsledků (b) a (c).",[724,48163,48164,48165,2263],{},"Viz též ",[207,48166,42961],{"className":48167,"dataFsResolvedFilePath":809,"href":810},[210],[198,48169,43263],{"id":48170},"multiplikátory-pro-mikroekonomické-proměnné-1",[724,48172,48173,47924,48176,47961,48212,2263],{},[38,48174,48175],{},"2.14",[883,48177,48179],{"className":48178},[886],[888,48180,48181],{"xmlns":890},[892,48182,48183,48209],{},[895,48184,48185,48187,48189,48191,48193,48195,48197,48199,48201,48203,48205,48207],{},[898,48186,1727],{},[1688,48188,1690],{},[898,48190,207],{},[898,48192,1872],{},[1688,48194,1696],{},[898,48196,1918],{},[1688,48198,1690],{},[1688,48200,1954],{},[1793,48202,1806],{},[898,48204,1872],{},[1688,48206,1696],{},[1793,48208,3377],{},[902,48210,48211],{"encoding":904},"P = aQ + b = -2Q + 50",[883,48213,48215],{"className":48214},[886],[888,48216,48217],{"xmlns":890},[892,48218,48219,48243],{},[895,48220,48221,48223,48225,48227,48229,48231,48233,48235,48237,48239,48241],{},[898,48222,1727],{},[1688,48224,1690],{},[898,48226,2031],{},[898,48228,1872],{},[1688,48230,1696],{},[898,48232,2073],{},[1688,48234,1690],{},[1793,48236,19562],{},[898,48238,1872],{},[1688,48240,1696],{},[1793,48242,9290],{},[902,48244,48245],{"encoding":904},"P = cQ + d = 0{,}6Q + 20",[120,48247,48248,48284,48287,48373,48426,48506,48560],{},[123,48249,48000,48250,46898,48267,2263],{},[883,48251,48253],{"className":48252},[886],[888,48254,48255],{"xmlns":890},[892,48256,48257,48265],{},[895,48258,48259],{},[1850,48260,48261,48263],{},[898,48262,1872],{},[898,48264,4509],{},[902,48266,42643],{"encoding":904},[883,48268,48270],{"className":48269},[886],[888,48271,48272],{"xmlns":890},[892,48273,48274,48282],{},[895,48275,48276],{},[1850,48277,48278,48280],{},[898,48279,1727],{},[898,48281,4509],{},[902,48283,41706],{"encoding":904},[123,48285,48286],{},"(b) Určete hodnoty multiplikátorů pro zadané parametry.",[123,48288,48289,48290,48307,48308,2194,48321,2946,48337,48353,48354,2263],{},"(c) Určete přibližnou změnu rovnovážného množství ",[883,48291,48293],{"className":48292},[886],[888,48294,48295],{"xmlns":890},[892,48296,48297,48305],{},[895,48298,48299],{},[1850,48300,48301,48303],{},[898,48302,1872],{},[898,48304,4509],{},[902,48306,42643],{"encoding":904}," odpovídající změně ",[883,48309,48311],{"className":48310},[886],[888,48312,48313],{"xmlns":890},[892,48314,48315,48319],{},[895,48316,48317],{},[898,48318,207],{},[902,48320,207],{"encoding":904},[883,48322,48324],{"className":48323},[886],[888,48325,48326],{"xmlns":890},[892,48327,48328,48334],{},[895,48329,48330,48332],{},[1688,48331,1954],{},[1793,48333,1806],{},[902,48335,48336],{"encoding":904},"-2",[883,48338,48340],{"className":48339},[886],[888,48341,48342],{"xmlns":890},[892,48343,48344,48350],{},[895,48345,48346,48348],{},[1688,48347,1954],{},[1793,48349,2131],{},[902,48351,48352],{"encoding":904},"-3"," (ceteris paribus) a stanovte nové rovnovážné množství ",[883,48355,48357],{"className":48356},[886],[888,48358,48359],{"xmlns":890},[892,48360,48361,48371],{},[895,48362,48363],{},[1814,48364,48365,48367,48369],{},[898,48366,1872],{},[1793,48368,1795],{},[898,48370,4509],{},[902,48372,48076],{"encoding":904},[123,48374,48375,48376,48307,48393,48406,48407,2263],{},"(d) Určete přibližnou změnu rovnovážného množství ",[883,48377,48379],{"className":48378},[886],[888,48380,48381],{"xmlns":890},[892,48382,48383,48391],{},[895,48384,48385],{},[1850,48386,48387,48389],{},[898,48388,1872],{},[898,48390,4509],{},[902,48392,42643],{"encoding":904},[883,48394,48396],{"className":48395},[886],[888,48397,48398],{"xmlns":890},[892,48399,48400,48404],{},[895,48401,48402],{},[898,48403,1918],{},[902,48405,1918],{"encoding":904}," z 50 na 60 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,48408,48410],{"className":48409},[886],[888,48411,48412],{"xmlns":890},[892,48413,48414,48424],{},[895,48415,48416],{},[1814,48417,48418,48420,48422],{},[898,48419,1872],{},[1793,48421,1806],{},[898,48423,4509],{},[902,48425,48138],{"encoding":904},[123,48427,48428,48429,48307,48446,2194,48459,2946,48472,48353,48486,2263],{},"(e) Určete přibližnou změnu rovnovážného množství ",[883,48430,48432],{"className":48431},[886],[888,48433,48434],{"xmlns":890},[892,48435,48436,48444],{},[895,48437,48438],{},[1850,48439,48440,48442],{},[898,48441,1872],{},[898,48443,4509],{},[902,48445,42643],{"encoding":904},[883,48447,48449],{"className":48448},[886],[888,48450,48451],{"xmlns":890},[892,48452,48453,48457],{},[895,48454,48455],{},[898,48456,2031],{},[902,48458,2031],{"encoding":904},[883,48460,48462],{"className":48461},[886],[888,48463,48464],{"xmlns":890},[892,48465,48466,48470],{},[895,48467,48468],{},[1793,48469,19562],{},[902,48471,44700],{"encoding":904},[883,48473,48475],{"className":48474},[886],[888,48476,48477],{"xmlns":890},[892,48478,48479,48483],{},[895,48480,48481],{},[1793,48482,14836],{},[902,48484,48485],{"encoding":904},"0{,}8",[883,48487,48489],{"className":48488},[886],[888,48490,48491],{"xmlns":890},[892,48492,48493,48503],{},[895,48494,48495],{},[1814,48496,48497,48499,48501],{},[898,48498,1872],{},[1793,48500,2131],{},[898,48502,4509],{},[902,48504,48505],{"encoding":904},"Q_3^E",[123,48507,48508,48509,48307,48526,48539,48540,2263],{},"(f) Určete přibližnou změnu rovnovážného množství ",[883,48510,48512],{"className":48511},[886],[888,48513,48514],{"xmlns":890},[892,48515,48516,48524],{},[895,48517,48518],{},[1850,48519,48520,48522],{},[898,48521,1872],{},[898,48523,4509],{},[902,48525,42643],{"encoding":904},[883,48527,48529],{"className":48528},[886],[888,48530,48531],{"xmlns":890},[892,48532,48533,48537],{},[895,48534,48535],{},[898,48536,2073],{},[902,48538,2073],{"encoding":904}," z 20 na 10 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,48541,48543],{"className":48542},[886],[888,48544,48545],{"xmlns":890},[892,48546,48547,48557],{},[895,48548,48549],{},[1814,48550,48551,48553,48555],{},[898,48552,1872],{},[1793,48554,2616],{},[898,48556,4509],{},[902,48558,48559],{"encoding":904},"Q_4^E",[123,48561,48562,48563,48580,48581,48594,48595,21661,48608,1343,48623,21661,48636,4142,48650,21661,48663,48678,48679,2263],{},"(g) Určete přibližnou změnu rovnovážného množství ",[883,48564,48566],{"className":48565},[886],[888,48567,48568],{"xmlns":890},[892,48569,48570,48578],{},[895,48571,48572],{},[1850,48573,48574,48576],{},[898,48575,1872],{},[898,48577,4509],{},[902,48579,42643],{"encoding":904}," odpovídající změnám ",[883,48582,48584],{"className":48583},[886],[888,48585,48586],{"xmlns":890},[892,48587,48588,48592],{},[895,48589,48590],{},[898,48591,207],{},[902,48593,207],{"encoding":904}," o 1, ",[883,48596,48598],{"className":48597},[886],[888,48599,48600],{"xmlns":890},[892,48601,48602,48606],{},[895,48603,48604],{},[898,48605,1918],{},[902,48607,1918],{"encoding":904},[883,48609,48611],{"className":48610},[886],[888,48612,48613],{"xmlns":890},[892,48614,48615,48621],{},[895,48616,48617,48619],{},[1688,48618,1954],{},[1793,48620,3121],{},[902,48622,19696],{"encoding":904},[883,48624,48626],{"className":48625},[886],[888,48627,48628],{"xmlns":890},[892,48629,48630,48634],{},[895,48631,48632],{},[898,48633,2031],{},[902,48635,2031],{"encoding":904},[883,48637,48639],{"className":48638},[886],[888,48640,48641],{"xmlns":890},[892,48642,48643,48647],{},[895,48644,48645],{},[1793,48646,3053],{},[902,48648,48649],{"encoding":904},"0{,}1",[883,48651,48653],{"className":48652},[886],[888,48654,48655],{"xmlns":890},[892,48656,48657,48661],{},[895,48658,48659],{},[898,48660,2073],{},[902,48662,2073],{"encoding":904},[883,48664,48666],{"className":48665},[886],[888,48667,48668],{"xmlns":890},[892,48669,48670,48676],{},[895,48671,48672,48674],{},[1688,48673,1954],{},[1793,48675,3121],{},[902,48677,19696],{"encoding":904}," vzhledem k zadaným hodnotám a stanovte nové rovnovážné množství ",[883,48680,48682],{"className":48681},[886],[888,48683,48684],{"xmlns":890},[892,48685,48686,48696],{},[895,48687,48688],{},[1814,48689,48690,48692,48694],{},[898,48691,1872],{},[1793,48693,2501],{},[898,48695,4509],{},[902,48697,48698],{"encoding":904},"Q_5^E",[724,48700,48701,47924,48704,47961,48727,2263],{},[38,48702,48703],{},"2.15",[883,48705,48707],{"className":48706},[886],[888,48708,48709],{"xmlns":890},[892,48710,48711,48725],{},[895,48712,48713,48715,48717,48719,48721,48723],{},[898,48714,1727],{},[1688,48716,1690],{},[898,48718,207],{},[898,48720,1872],{},[1688,48722,1696],{},[898,48724,1918],{},[902,48726,37300],{"encoding":904},[883,48728,48730],{"className":48729},[886],[888,48731,48732],{"xmlns":890},[892,48733,48734,48748],{},[895,48735,48736,48738,48740,48742,48744,48746],{},[898,48737,1727],{},[1688,48739,1690],{},[898,48741,2031],{},[898,48743,1872],{},[1688,48745,1696],{},[898,48747,2073],{},[902,48749,40482],{"encoding":904},[120,48751,48752,48827,48844,48953,49006,49060],{},[123,48753,48754,48755,48768,48769,48794,48795,48826],{},"(a) Odvoďte redukovaný tvar pro ",[883,48756,48758],{"className":48757},[886],[888,48759,48760],{"xmlns":890},[892,48761,48762,48766],{},[895,48763,48764],{},[898,48765,1727],{},[902,48767,1727],{"encoding":904},". Stanovte podmínky pro ",[883,48770,48772],{"className":48771},[886],[888,48773,48774],{"xmlns":890},[892,48775,48776,48792],{},[895,48777,48778,48780,48782,48784,48786,48788,48790],{},[898,48779,207],{},[1688,48781,1733],{"separator":1732},[898,48783,1918],{},[1688,48785,1733],{"separator":1732},[898,48787,2031],{},[1688,48789,1733],{"separator":1732},[898,48791,2073],{},[902,48793,43525],{"encoding":904}," tak, aby rovnovážný bod ",[883,48796,48798],{"className":48797},[886],[888,48799,48800],{"xmlns":890},[892,48801,48802,48824],{},[895,48803,48804,48806,48808,48814,48816,48822],{},[898,48805,4509],{},[1688,48807,2748],{"stretchy":2065},[1850,48809,48810,48812],{},[898,48811,1872],{},[898,48813,4509],{},[1688,48815,1733],{"separator":1732},[1850,48817,48818,48820],{},[898,48819,1727],{},[898,48821,4509],{},[1688,48823,2763],{"stretchy":2065},[902,48825,41607],{"encoding":904}," patřil do 1. kvadrantu (využijte obrázku 2.22).",[123,48828,48829,48830,48843],{},"(b) Vypočtěte multiplikátory pro ",[883,48831,48833],{"className":48832},[886],[888,48834,48835],{"xmlns":890},[892,48836,48837,48841],{},[895,48838,48839],{},[898,48840,1727],{},[902,48842,1727],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků 2.22, 2.23).",[123,48845,48846,48847,1343,48867,1343,48885,1343,48903,48921,48922,48939,48940,2263],{},"(c) Pro hodnoty parametrů ",[883,48848,48850],{"className":48849},[886],[888,48851,48852],{"xmlns":890},[892,48853,48854,48864],{},[895,48855,48856,48858,48860,48862],{},[898,48857,207],{},[1688,48859,1690],{},[1688,48861,1954],{},[1793,48863,1806],{},[902,48865,48866],{"encoding":904},"a = -2",[883,48868,48870],{"className":48869},[886],[888,48871,48872],{"xmlns":890},[892,48873,48874,48882],{},[895,48875,48876,48878,48880],{},[898,48877,1918],{},[1688,48879,1690],{},[1793,48881,5467],{},[902,48883,48884],{"encoding":904},"b = 40",[883,48886,48888],{"className":48887},[886],[888,48889,48890],{"xmlns":890},[892,48891,48892,48900],{},[895,48893,48894,48896,48898],{},[898,48895,2031],{},[1688,48897,1690],{},[1793,48899,5265],{},[902,48901,48902],{"encoding":904},"c = 0{,}5",[883,48904,48906],{"className":48905},[886],[888,48907,48908],{"xmlns":890},[892,48909,48910,48918],{},[895,48911,48912,48914,48916],{},[898,48913,2073],{},[1688,48915,1690],{},[1793,48917,3121],{},[902,48919,48920],{"encoding":904},"d = 10"," určete rovnovážnou cenu ",[883,48923,48925],{"className":48924},[886],[888,48926,48927],{"xmlns":890},[892,48928,48929,48937],{},[895,48930,48931],{},[1850,48932,48933,48935],{},[898,48934,1727],{},[898,48936,4509],{},[902,48938,41706],{"encoding":904}," a hodnoty multiplikátorů pro ",[883,48941,48943],{"className":48942},[886],[888,48944,48945],{"xmlns":890},[892,48946,48947,48951],{},[895,48948,48949],{},[898,48950,1727],{},[902,48952,1727],{"encoding":904},[123,48954,48955,48956,48307,48973,48986,48987,2263],{},"(d) Určete přibližnou změnu rovnovážné ceny ",[883,48957,48959],{"className":48958},[886],[888,48960,48961],{"xmlns":890},[892,48962,48963,48971],{},[895,48964,48965],{},[1850,48966,48967,48969],{},[898,48968,1727],{},[898,48970,4509],{},[902,48972,41706],{"encoding":904},[883,48974,48976],{"className":48975},[886],[888,48977,48978],{"xmlns":890},[892,48979,48980,48984],{},[895,48981,48982],{},[898,48983,207],{},[902,48985,207],{"encoding":904}," o 5 (ceteris paribus) a stanovte novou rovnovážnou cenu ",[883,48988,48990],{"className":48989},[886],[888,48991,48992],{"xmlns":890},[892,48993,48994,49004],{},[895,48995,48996],{},[1814,48997,48998,49000,49002],{},[898,48999,1727],{},[1793,49001,1795],{},[898,49003,4509],{},[902,49005,48097],{"encoding":904},[123,49007,49008,49009,49026,49027,49040,49041,2263],{},"(e) Určete přibližnou změnu rovnovážné ceny ",[883,49010,49012],{"className":49011},[886],[888,49013,49014],{"xmlns":890},[892,49015,49016,49024],{},[895,49017,49018],{},[1850,49019,49020,49022],{},[898,49021,1727],{},[898,49023,4509],{},[902,49025,41706],{"encoding":904}," odpovídající poklesu ",[883,49028,49030],{"className":49029},[886],[888,49031,49032],{"xmlns":890},[892,49033,49034,49038],{},[895,49035,49036],{},[898,49037,207],{},[902,49039,207],{"encoding":904}," o 1 a stanovte novou rovnovážnou cenu ",[883,49042,49044],{"className":49043},[886],[888,49045,49046],{"xmlns":890},[892,49047,49048,49058],{},[895,49049,49050],{},[1814,49051,49052,49054,49056],{},[898,49053,1727],{},[1793,49055,1806],{},[898,49057,4509],{},[902,49059,48158],{"encoding":904},[123,49061,49062,49063,48580,49080,49093,49094,2946,49107,4142,49122,49135,49136,2263],{},"(f) Určete přibližnou změnu rovnovážné ceny ",[883,49064,49066],{"className":49065},[886],[888,49067,49068],{"xmlns":890},[892,49069,49070,49078],{},[895,49071,49072],{},[1850,49073,49074,49076],{},[898,49075,1727],{},[898,49077,4509],{},[902,49079,41706],{"encoding":904},[883,49081,49083],{"className":49082},[886],[888,49084,49085],{"xmlns":890},[892,49086,49087,49091],{},[895,49088,49089],{},[898,49090,207],{},[902,49092,207],{"encoding":904}," na 35, ",[883,49095,49097],{"className":49096},[886],[888,49098,49099],{"xmlns":890},[892,49100,49101,49105],{},[895,49102,49103],{},[898,49104,2031],{},[902,49106,2031],{"encoding":904},[883,49108,49110],{"className":49109},[886],[888,49111,49112],{"xmlns":890},[892,49113,49114,49119],{},[895,49115,49116],{},[1793,49117,49118],{},"0,7",[902,49120,49121],{"encoding":904},"0{,}7",[883,49123,49125],{"className":49124},[886],[888,49126,49127],{"xmlns":890},[892,49128,49129,49133],{},[895,49130,49131],{},[898,49132,2073],{},[902,49134,2073],{"encoding":904}," na 12 vzhledem k hodnotám dle (d) a stanovte novou rovnovážnou cenu ",[883,49137,49139],{"className":49138},[886],[888,49140,49141],{"xmlns":890},[892,49142,49143,49153],{},[895,49144,49145],{},[1814,49146,49147,49149,49151],{},[898,49148,1727],{},[1793,49150,2131],{},[898,49152,4509],{},[902,49154,49155],{"encoding":904},"P_3^E",[724,49157,49158,47924,49161,47961,49189,21835,49217,4142,49243,2263],{},[38,49159,49160],{},"2.16",[883,49162,49164],{"className":49163},[886],[888,49165,49166],{"xmlns":890},[892,49167,49168,49186],{},[895,49169,49170,49172,49174,49176,49178,49180],{},[898,49171,1727],{},[1688,49173,1690],{},[898,49175,207],{},[1688,49177,1696],{},[898,49179,1918],{},[1850,49181,49182,49184],{},[898,49183,1872],{},[1793,49185,1806],{},[902,49187,49188],{"encoding":904},"P = a + bQ^2",[883,49190,49192],{"className":49191},[886],[888,49193,49194],{"xmlns":890},[892,49195,49196,49214],{},[895,49197,49198,49200,49202,49204,49206,49208],{},[898,49199,1727],{},[1688,49201,1690],{},[898,49203,2031],{},[1688,49205,1696],{},[898,49207,2073],{},[1850,49209,49210,49212],{},[898,49211,1872],{},[1793,49213,1806],{},[902,49215,49216],{"encoding":904},"P = c + dQ^2",[883,49218,49220],{"className":49219},[886],[888,49221,49222],{"xmlns":890},[892,49223,49224,49240],{},[895,49225,49226,49228,49230,49232,49234,49236,49238],{},[898,49227,207],{},[1688,49229,1733],{"separator":1732},[898,49231,2031],{},[1688,49233,1733],{"separator":1732},[898,49235,2073],{},[1688,49237,3665],{},[1793,49239,1779],{},[902,49241,49242],{"encoding":904},"a, c, d > 0",[883,49244,49246],{"className":49245},[886],[888,49247,49248],{"xmlns":890},[892,49249,49250,49258],{},[895,49251,49252,49254,49256],{},[898,49253,1918],{},[1688,49255,3704],{},[1793,49257,1779],{},[902,49259,49260],{"encoding":904},"b \u003C 0",[120,49262,49263,49311,49327,49434,49486,49538,49647,49663,49762,49815],{},[123,49264,48754,49265,49278,49279,49310],{},[883,49266,49268],{"className":49267},[886],[888,49269,49270],{"xmlns":890},[892,49271,49272,49276],{},[895,49273,49274],{},[898,49275,1872],{},[902,49277,1872],{"encoding":904},". Načrtněte křivky poptávky a nabídky a stanovte podmínky, aby rovnovážný bod ",[883,49280,49282],{"className":49281},[886],[888,49283,49284],{"xmlns":890},[892,49285,49286,49308],{},[895,49287,49288,49290,49292,49298,49300,49306],{},[898,49289,4509],{},[1688,49291,2748],{"stretchy":2065},[1850,49293,49294,49296],{},[898,49295,1872],{},[898,49297,4509],{},[1688,49299,1733],{"separator":1732},[1850,49301,49302,49304],{},[898,49303,1727],{},[898,49305,4509],{},[1688,49307,2763],{"stretchy":2065},[902,49309,41607],{"encoding":904}," patřil do 1. kvadrantu.",[123,49312,48829,49313,49326],{},[883,49314,49316],{"className":49315},[886],[888,49317,49318],{"xmlns":890},[892,49319,49320,49324],{},[895,49321,49322],{},[898,49323,1872],{},[902,49325,1872],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků v (b)).",[123,49328,48846,49329,1343,49347,1343,49367,1343,49385,49403,49404,48939,49421,2263],{},[883,49330,49332],{"className":49331},[886],[888,49333,49334],{"xmlns":890},[892,49335,49336,49344],{},[895,49337,49338,49340,49342],{},[898,49339,207],{},[1688,49341,1690],{},[1793,49343,3347],{},[902,49345,49346],{"encoding":904},"a = 100",[883,49348,49350],{"className":49349},[886],[888,49351,49352],{"xmlns":890},[892,49353,49354,49364],{},[895,49355,49356,49358,49360,49362],{},[898,49357,1918],{},[1688,49359,1690],{},[1688,49361,1954],{},[1793,49363,1795],{},[902,49365,49366],{"encoding":904},"b = -1",[883,49368,49370],{"className":49369},[886],[888,49371,49372],{"xmlns":890},[892,49373,49374,49382],{},[895,49375,49376,49378,49380],{},[898,49377,2031],{},[1688,49379,1690],{},[1793,49381,9290],{},[902,49383,49384],{"encoding":904},"c = 20",[883,49386,49388],{"className":49387},[886],[888,49389,49390],{"xmlns":890},[892,49391,49392,49400],{},[895,49393,49394,49396,49398],{},[898,49395,2073],{},[1688,49397,1690],{},[1793,49399,1795],{},[902,49401,49402],{"encoding":904},"d = 1"," určete rovnovážné množství ",[883,49405,49407],{"className":49406},[886],[888,49408,49409],{"xmlns":890},[892,49410,49411,49419],{},[895,49412,49413],{},[1850,49414,49415,49417],{},[898,49416,1872],{},[898,49418,4509],{},[902,49420,42643],{"encoding":904},[883,49422,49424],{"className":49423},[886],[888,49425,49426],{"xmlns":890},[892,49427,49428,49432],{},[895,49429,49430],{},[898,49431,1872],{},[902,49433,1872],{"encoding":904},[123,49435,48375,49436,48307,49453,49466,49467,2263],{},[883,49437,49439],{"className":49438},[886],[888,49440,49441],{"xmlns":890},[892,49442,49443,49451],{},[895,49444,49445],{},[1850,49446,49447,49449],{},[898,49448,1872],{},[898,49450,4509],{},[902,49452,42643],{"encoding":904},[883,49454,49456],{"className":49455},[886],[888,49457,49458],{"xmlns":890},[892,49459,49460,49464],{},[895,49461,49462],{},[898,49463,207],{},[902,49465,207],{"encoding":904}," na 110 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,49468,49470],{"className":49469},[886],[888,49471,49472],{"xmlns":890},[892,49473,49474,49484],{},[895,49475,49476],{},[1814,49477,49478,49480,49482],{},[898,49479,1872],{},[1793,49481,1795],{},[898,49483,4509],{},[902,49485,48076],{"encoding":904},[123,49487,48428,49488,48307,49505,49518,49519,2263],{},[883,49489,49491],{"className":49490},[886],[888,49492,49493],{"xmlns":890},[892,49494,49495,49503],{},[895,49496,49497],{},[1850,49498,49499,49501],{},[898,49500,1872],{},[898,49502,4509],{},[902,49504,42643],{"encoding":904},[883,49506,49508],{"className":49507},[886],[888,49509,49510],{"xmlns":890},[892,49511,49512,49516],{},[895,49513,49514],{},[898,49515,2031],{},[902,49517,2031],{"encoding":904}," na 25 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,49520,49522],{"className":49521},[886],[888,49523,49524],{"xmlns":890},[892,49525,49526,49536],{},[895,49527,49528],{},[1814,49529,49530,49532,49534],{},[898,49531,1872],{},[1793,49533,1806],{},[898,49535,4509],{},[902,49537,48138],{"encoding":904},[123,49539,48508,49540,48580,49557,49570,49571,2946,49584,49599,49600,49613,49614,49627,49628,2263],{},[883,49541,49543],{"className":49542},[886],[888,49544,49545],{"xmlns":890},[892,49546,49547,49555],{},[895,49548,49549],{},[1850,49550,49551,49553],{},[898,49552,1872],{},[898,49554,4509],{},[902,49556,42643],{"encoding":904},[883,49558,49560],{"className":49559},[886],[888,49561,49562],{"xmlns":890},[892,49563,49564,49568],{},[895,49565,49566],{},[898,49567,207],{},[902,49569,207],{"encoding":904}," na 110, poklesu ",[883,49572,49574],{"className":49573},[886],[888,49575,49576],{"xmlns":890},[892,49577,49578,49582],{},[895,49579,49580],{},[898,49581,1918],{},[902,49583,1918],{"encoding":904},[883,49585,49587],{"className":49586},[886],[888,49588,49589],{"xmlns":890},[892,49590,49591,49597],{},[895,49592,49593,49595],{},[1688,49594,1954],{},[1793,49596,1806],{},[902,49598,48336],{"encoding":904},", růstu ",[883,49601,49603],{"className":49602},[886],[888,49604,49605],{"xmlns":890},[892,49606,49607,49611],{},[895,49608,49609],{},[898,49610,2031],{},[902,49612,2031],{"encoding":904}," na 25 a růstu ",[883,49615,49617],{"className":49616},[886],[888,49618,49619],{"xmlns":890},[892,49620,49621,49625],{},[895,49622,49623],{},[898,49624,2073],{},[902,49626,2073],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte nové rovnovážné množství ",[883,49629,49631],{"className":49630},[886],[888,49632,49633],{"xmlns":890},[892,49634,49635,49645],{},[895,49636,49637],{},[1814,49638,49639,49641,49643],{},[898,49640,1872],{},[1793,49642,2131],{},[898,49644,4509],{},[902,49646,48505],{"encoding":904},[123,49648,49649,49650,49326],{},"(i) Vypočtěte multiplikátory pro ",[883,49651,49653],{"className":49652},[886],[888,49654,49655],{"xmlns":890},[892,49656,49657,49661],{},[895,49658,49659],{},[898,49660,1727],{},[902,49662,1727],{"encoding":904},[123,49664,49665,49666,48939,49683,49696,49697,48307,49714,2946,49727,49742,49743,2263],{},"(j) Pro hodnoty parametrů dle (b) určete rovnovážnou cenu ",[883,49667,49669],{"className":49668},[886],[888,49670,49671],{"xmlns":890},[892,49672,49673,49681],{},[895,49674,49675],{},[1850,49676,49677,49679],{},[898,49678,1727],{},[898,49680,4509],{},[902,49682,41706],{"encoding":904},[883,49684,49686],{"className":49685},[886],[888,49687,49688],{"xmlns":890},[892,49689,49690,49694],{},[895,49691,49692],{},[898,49693,1727],{},[902,49695,1727],{"encoding":904},", přibližnou změnu rovnovážné ceny ",[883,49698,49700],{"className":49699},[886],[888,49701,49702],{"xmlns":890},[892,49703,49704,49712],{},[895,49705,49706],{},[1850,49707,49708,49710],{},[898,49709,1727],{},[898,49711,4509],{},[902,49713,41706],{"encoding":904},[883,49715,49717],{"className":49716},[886],[888,49718,49719],{"xmlns":890},[892,49720,49721,49725],{},[895,49722,49723],{},[898,49724,207],{},[902,49726,207],{"encoding":904},[883,49728,49730],{"className":49729},[886],[888,49731,49732],{"xmlns":890},[892,49733,49734,49740],{},[895,49735,49736,49738],{},[1688,49737,1954],{},[1793,49739,2131],{},[902,49741,48352],{"encoding":904}," (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,49744,49746],{"className":49745},[886],[888,49747,49748],{"xmlns":890},[892,49749,49750,49760],{},[895,49751,49752],{},[1814,49753,49754,49756,49758],{},[898,49755,1727],{},[1793,49757,1795],{},[898,49759,4509],{},[902,49761,48097],{"encoding":904},[123,49763,49764,49765,48307,49782,49795,49796,2263],{},"(k) Určete přibližnou změnu rovnovážné ceny ",[883,49766,49768],{"className":49767},[886],[888,49769,49770],{"xmlns":890},[892,49771,49772,49780],{},[895,49773,49774],{},[1850,49775,49776,49778],{},[898,49777,1727],{},[898,49779,4509],{},[902,49781,41706],{"encoding":904},[883,49783,49785],{"className":49784},[886],[888,49786,49787],{"xmlns":890},[892,49788,49789,49793],{},[895,49790,49791],{},[898,49792,207],{},[902,49794,207],{"encoding":904}," na 2 (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,49797,49799],{"className":49798},[886],[888,49800,49801],{"xmlns":890},[892,49802,49803,49813],{},[895,49804,49805],{},[1814,49806,49807,49809,49811],{},[898,49808,1727],{},[1793,49810,1806],{},[898,49812,4509],{},[902,49814,48158],{"encoding":904},[123,49816,49817,49818,49026,49835,49848,49849,2946,49862,49599,49877,49890,49891,49904,49905,2263],{},"(l) Určete přibližnou změnu rovnovážné ceny ",[883,49819,49821],{"className":49820},[886],[888,49822,49823],{"xmlns":890},[892,49824,49825,49833],{},[895,49826,49827],{},[1850,49828,49829,49831],{},[898,49830,1727],{},[898,49832,4509],{},[902,49834,41706],{"encoding":904},[883,49836,49838],{"className":49837},[886],[888,49839,49840],{"xmlns":890},[892,49841,49842,49846],{},[895,49843,49844],{},[898,49845,207],{},[902,49847,207],{"encoding":904}," na 90, poklesu ",[883,49850,49852],{"className":49851},[886],[888,49853,49854],{"xmlns":890},[892,49855,49856,49860],{},[895,49857,49858],{},[898,49859,1918],{},[902,49861,1918],{"encoding":904},[883,49863,49865],{"className":49864},[886],[888,49866,49867],{"xmlns":890},[892,49868,49869,49875],{},[895,49870,49871,49873],{},[1688,49872,1954],{},[1793,49874,2131],{},[902,49876,48352],{"encoding":904},[883,49878,49880],{"className":49879},[886],[888,49881,49882],{"xmlns":890},[892,49883,49884,49888],{},[895,49885,49886],{},[898,49887,2031],{},[902,49889,2031],{"encoding":904}," na 30 a růstu ",[883,49892,49894],{"className":49893},[886],[888,49895,49896],{"xmlns":890},[892,49897,49898,49902],{},[895,49899,49900],{},[898,49901,2073],{},[902,49903,2073],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,49906,49908],{"className":49907},[886],[888,49909,49910],{"xmlns":890},[892,49911,49912,49922],{},[895,49913,49914],{},[1814,49915,49916,49918,49920],{},[898,49917,1727],{},[1793,49919,2131],{},[898,49921,4509],{},[902,49923,49155],{"encoding":904},[198,49925,820],{"id":49926},"přebytek-spotřebitele-a-výrobce-1",[724,49928,49929,47924,49932,47961,49968,2263],{},[38,49930,49931],{},"2.17",[883,49933,49935],{"className":49934},[886],[888,49936,49937],{"xmlns":890},[892,49938,49939,49965],{},[895,49940,49941,49943,49945,49947,49949,49951,49953,49955,49957,49959],{},[898,49942,1727],{},[1688,49944,1690],{},[898,49946,4440],{},[1688,49948,2066],{"stretchy":2065},[898,49950,1872],{},[1688,49952,2076],{"stretchy":2065},[1688,49954,1690],{},[1793,49956,15285],{},[1688,49958,1954],{},[1850,49960,49961,49963],{},[898,49962,1872],{},[1793,49964,1806],{},[902,49966,49967],{"encoding":904},"P = D(Q) = 35 - Q^2",[883,49969,49971],{"className":49970},[886],[888,49972,49973],{"xmlns":890},[892,49974,49975,50001],{},[895,49976,49977,49979,49981,49983,49985,49987,49989,49991,49993,49995],{},[898,49978,1727],{},[1688,49980,1690],{},[898,49982,1740],{},[1688,49984,2066],{"stretchy":2065},[898,49986,1872],{},[1688,49988,2076],{"stretchy":2065},[1688,49990,1690],{},[1793,49992,2131],{},[1688,49994,1696],{},[1850,49996,49997,49999],{},[898,49998,1872],{},[1793,50000,1806],{},[902,50002,50003],{"encoding":904},"P = S(Q) = 3 + Q^2",[120,50005,50006,50009],{},[123,50007,50008],{},"(a) Vypočtěte přebytek spotřebitele při množství 4.",[123,50010,50011],{},"(b) Vypočtěte přebytek výrobce při množství 4.",[724,50013,50014,47924,50017,47961,50051,2263],{},[38,50015,50016],{},"2.18",[883,50018,50020],{"className":50019},[886],[888,50021,50022],{"xmlns":890},[892,50023,50024,50048],{},[895,50025,50026,50028,50030,50032,50034,50036,50038,50040,50042,50044,50046],{},[898,50027,1727],{},[1688,50029,1690],{},[898,50031,4440],{},[1688,50033,2066],{"stretchy":2065},[898,50035,1872],{},[1688,50037,2076],{"stretchy":2065},[1688,50039,1690],{},[1793,50041,3964],{},[1688,50043,1954],{},[1793,50045,1806],{},[898,50047,1872],{},[902,50049,50050],{"encoding":904},"P = D(Q) = 18 - 2Q",[883,50052,50054],{"className":50053},[886],[888,50055,50056],{"xmlns":890},[892,50057,50058,50084],{},[895,50059,50060,50062,50064,50066,50068,50070,50072,50074,50076,50078],{},[898,50061,1727],{},[1688,50063,1690],{},[898,50065,1740],{},[1688,50067,2066],{"stretchy":2065},[898,50069,1872],{},[1688,50071,2076],{"stretchy":2065},[1688,50073,1690],{},[1793,50075,2131],{},[1688,50077,1696],{},[1850,50079,50080,50082],{},[898,50081,1872],{},[1793,50083,1806],{},[902,50085,50003],{"encoding":904},[120,50087,50088,50108,50111,50114],{},[123,50089,50090,50091,2263],{},"(a) Vypočtěte rovnovážné množství ",[883,50092,50094],{"className":50093},[886],[888,50095,50096],{"xmlns":890},[892,50097,50098,50106],{},[895,50099,50100],{},[1850,50101,50102,50104],{},[898,50103,1872],{},[898,50105,4509],{},[902,50107,42643],{"encoding":904},[123,50109,50110],{},"(b) Vypočtěte přebytek spotřebitele při rovnovážném množství.",[123,50112,50113],{},"(b) Vypočtěte přebytek výrobce při rovnovážném množství.",[123,50115,50116],{},"(c) Graficky interpretujte.",[37210,50118],{},[115,50120,50122],{"id":50121},"otázky-k-sebehodnocení","Otázky k sebehodnocení",[152,50124,50125,50128,50131,50134,50137,50140,50143,50146,50149,50152,50155,50158,50161,50164],{},[123,50126,50127],{},"Jaký je rozdíl mezi jednofaktorovým a vícefaktorovým modelem poptávky?",[123,50129,50130],{},"Vyjádřete (vícefaktorovou) funkci poptávky. Jakou má vlastnost?",[123,50132,50133],{},"Definujte funkci poptávky (jednofaktorovou). Jaká je její základní vlastnost? Zdůvodněte.",[123,50135,50136],{},"Definujte Engelovu funkci. Na čem závisí tvar příslušné Engelovy křivky?",[123,50138,50139],{},"Jaký charakter má odezva poptávky na změnu některé z exogenních proměnných?",[123,50141,50142],{},"Definujte funkci nabídky. Jaká je její základní vlastnost? Zdůvodněte.",[123,50144,50145],{},"Co znamená tržní rovnováha? Čím je reprezentována?",[123,50147,50148],{},"Jak se určí rovnovážné množství a rovnovážná cena?",[123,50150,50151],{},"Jaká jsou pravidla pro změnu rovnovážného bodu jako odezvy na posun poptávky, resp. nabídky?",[123,50153,50154],{},"K čemu slouží multiplikátory?",[123,50156,50157],{},"Jak se najde redukovaný tvar pro vybranou rovnovážnou veličinu?",[123,50159,50160],{},"Jak se vypočtou multiplikátory? Mění se jejich znaménka?",[123,50162,50163],{},"Co se rozumí přebytkem spotřebitele? Jak se vypočte?",[123,50165,50166],{},"Co se rozumí přebytkem výrobce? Jak se vypočte?",[37210,50168],{},[115,50170,15967],{"id":15966},[724,50172,50173],{},[38,50174,13409],{},[120,50176,50177,50212,50217,50247,50252,50315,50341,50346,50376,50385,50392,50398],{},[123,50178,50179,10277,50182,18890,50185,2170,50187,1343,50210],{},[38,50180,50181],{},"Poptávané množství",[614,50183,50184],{},"quantity demanded",[38,50186,28242],{},[883,50188,50190],{"className":50189},[886],[888,50191,50192],{"xmlns":890},[892,50193,50194,50208],{},[895,50195,50196,50198,50200,50202,50204,50206],{},[898,50197,1872],{},[1688,50199,1690],{},[898,50201,4440],{},[1688,50203,2066],{"stretchy":2065},[898,50205,1727],{},[1688,50207,2076],{"stretchy":2065},[902,50209,4449],{"encoding":904},[38,50211,37689],{},[123,50213,50214,50216],{},[38,50215,37696],{}," — substituční + důchodový efekt",[123,50218,50219,2170,50222],{},[38,50220,50221],{},"Reálné cenové rozpětí",[883,50223,50225],{"className":50224},[886],[888,50226,50227],{"xmlns":890},[892,50228,50229,50245],{},[895,50230,50231,50233,50235,50237,50243],{},[1688,50232,2066],{"stretchy":2065},[1793,50234,1779],{},[1688,50236,1733],{"separator":1732},[1788,50238,50239,50241],{},[898,50240,1727],{},[1793,50242,1779],{},[1688,50244,2076],{"stretchy":2065},[902,50246,37897],{"encoding":904},[123,50248,50249,11348],{},[38,50250,50251],{},"Homogenita poptávky",[123,50253,50254,2170,50257,1343,50280,1343,50297,50314],{},[38,50255,50256],{},"Lineární poptávka",[883,50258,50260],{"className":50259},[886],[888,50261,50262],{"xmlns":890},[892,50263,50264,50278],{},[895,50265,50266,50268,50270,50272,50274,50276],{},[898,50267,1727],{},[1688,50269,1690],{},[898,50271,207],{},[898,50273,1872],{},[1688,50275,1696],{},[898,50277,1918],{},[902,50279,37300],{"encoding":904},[883,50281,50283],{"className":50282},[886],[888,50284,50285],{"xmlns":890},[892,50286,50287,50295],{},[895,50288,50289,50291,50293],{},[898,50290,207],{},[1688,50292,3704],{},[1793,50294,1779],{},[902,50296,43325],{"encoding":904},[883,50298,50300],{"className":50299},[886],[888,50301,50302],{"xmlns":890},[892,50303,50304,50312],{},[895,50305,50306,50308,50310],{},[898,50307,1918],{},[1688,50309,3665],{},[1793,50311,1779],{},[902,50313,19056],{"encoding":904}," — nedokonalá konkurence",[123,50316,50317,7271,50320],{},[38,50318,50319],{},"Dokonalá konkurence",[883,50321,50323],{"className":50322},[886],[888,50324,50325],{"xmlns":890},[892,50326,50327,50339],{},[895,50328,50329,50331,50333],{},[898,50330,1727],{},[1688,50332,1690],{},[1850,50334,50335,50337],{},[898,50336,1727],{},[1688,50338,1857],{},[902,50340,4613],{"encoding":904},[123,50342,50343,50345],{},[38,50344,38466],{}," — rostoucí křivka poptávky (důchodový efekt > substituční)",[123,50347,50348,2170,50350,1343,50374],{},[38,50349,31967],{},[883,50351,50353],{"className":50352},[886],[888,50354,50355],{"xmlns":890},[892,50356,50357,50371],{},[895,50358,50359,50361,50363,50365,50367,50369],{},[898,50360,1872],{},[1688,50362,1690],{},[898,50364,4509],{},[1688,50366,2066],{"stretchy":2065},[898,50368,1854],{},[1688,50370,2076],{"stretchy":2065},[902,50372,50373],{"encoding":904},"Q = E(Y)",[38,50375,38663],{},[123,50377,50378,50381,50382,50384],{},[38,50379,50380],{},"Normální"," (nezbytné \u002F luxusní) vs. ",[38,50383,39109],{}," zboží",[123,50386,50387,4142,50389,50391],{},[38,50388,40115],{},[38,50390,40062],{}," — znaménka zkřížených koeficientů",[123,50393,50394,50397],{},[38,50395,50396],{},"Dvoukomoditní trh"," (2.6)",[123,50399,50400,10277,50403,2076],{},[38,50401,50402],{},"Posun poptávky",[614,50404,39167],{},[724,50406,50407],{},[38,50408,13373],{},[120,50410,50411,50444,50448,50493],{},[123,50412,50413,10277,50415,18890,50417,2170,50419,1343,50442],{},[38,50414,40509],{},[614,50416,40512],{},[38,50418,40683],{},[883,50420,50422],{"className":50421},[886],[888,50423,50424],{"xmlns":890},[892,50425,50426,50440],{},[895,50427,50428,50430,50432,50434,50436,50438],{},[898,50429,1872],{},[1688,50431,1690],{},[898,50433,1740],{},[1688,50435,2066],{"stretchy":2065},[898,50437,1727],{},[1688,50439,2076],{"stretchy":2065},[902,50441,8937],{"encoding":904},[38,50443,40761],{},[123,50445,50446],{},[38,50447,40768],{},[123,50449,50450,2170,50453,1343,50476],{},[38,50451,50452],{},"Lineární nabídka",[883,50454,50456],{"className":50455},[886],[888,50457,50458],{"xmlns":890},[892,50459,50460,50474],{},[895,50461,50462,50464,50466,50468,50470,50472],{},[898,50463,1727],{},[1688,50465,1690],{},[898,50467,2031],{},[898,50469,1872],{},[1688,50471,1696],{},[898,50473,2073],{},[902,50475,40482],{"encoding":904},[883,50477,50479],{"className":50478},[886],[888,50480,50481],{"xmlns":890},[892,50482,50483,50491],{},[895,50484,50485,50487,50489],{},[898,50486,2031],{},[1688,50488,3665],{},[1793,50490,1779],{},[902,50492,40500],{"encoding":904},[123,50494,50495,10277,50498,2076],{},[38,50496,50497],{},"Posun nabídky",[614,50499,41146],{},[724,50501,50502],{},[38,50503,50504],{},"Rovnováha a komparativní statika",[120,50506,50507,50586,50592],{},[123,50508,50509,10277,50511,18890,50513,2170,50516,1343,50533,2170,50536,1343,50553,2170,50555],{},[38,50510,41565],{},[614,50512,41684],{},[38,50514,50515],{},"rovnovážná cena",[883,50517,50519],{"className":50518},[886],[888,50520,50521],{"xmlns":890},[892,50522,50523,50531],{},[895,50524,50525],{},[1850,50526,50527,50529],{},[898,50528,1727],{},[898,50530,4509],{},[902,50532,41706],{"encoding":904},[38,50534,50535],{},"rovnovážné množství",[883,50537,50539],{"className":50538},[886],[888,50540,50541],{"xmlns":890},[892,50542,50543,50551],{},[895,50544,50545],{},[1850,50546,50547,50549],{},[898,50548,1872],{},[898,50550,4509],{},[902,50552,42643],{"encoding":904},[38,50554,41742],{},[883,50556,50558],{"className":50557},[886],[888,50559,50560],{"xmlns":890},[892,50561,50562,50584],{},[895,50563,50564,50566,50568,50574,50576,50582],{},[898,50565,4509],{},[1688,50567,2748],{"stretchy":2065},[1850,50569,50570,50572],{},[898,50571,1872],{},[898,50573,4509],{},[1688,50575,1733],{"separator":1732},[1850,50577,50578,50580],{},[898,50579,1727],{},[898,50581,4509],{},[1688,50583,2763],{"stretchy":2065},[902,50585,41607],{"encoding":904},[123,50587,50588,50591],{},[38,50589,50590],{},"Pravidla 1–4"," komparativní statiky",[123,50593,50594,10277,50597,2076],{},[38,50595,50596],{},"Teorém pavučiny",[614,50598,42589],{},[724,50600,50601],{},[38,50602,50603],{},"Zdanění",[120,50605,50606,50662,50710],{},[123,50607,50608,50610,50611,50636,50637,2076],{},[38,50609,50603],{}," — daň výrobci (",[883,50612,50614],{"className":50613},[886],[888,50615,50616],{"xmlns":890},[892,50617,50618,50634],{},[895,50619,50620,50626,50628,50630,50632],{},[1788,50621,50622,50624],{},[898,50623,1740],{},[1793,50625,1795],{},[1688,50627,1690],{},[898,50629,1740],{},[1688,50631,1696],{},[898,50633,3035],{},[902,50635,42994],{"encoding":904},") vs. daň spotřebiteli (",[883,50638,50640],{"className":50639},[886],[888,50641,50642],{"xmlns":890},[892,50643,50644,50660],{},[895,50645,50646,50652,50654,50656,50658],{},[1788,50647,50648,50650],{},[898,50649,4440],{},[1793,50651,1806],{},[1688,50653,1690],{},[898,50655,4440],{},[1688,50657,1954],{},[898,50659,3035],{},[902,50661,43025],{"encoding":904},[123,50663,50664,2170,50666,1343,50687],{},[38,50665,42898],{},[883,50667,50669],{"className":50668},[886],[888,50670,50671],{"xmlns":890},[892,50672,50673,50685],{},[895,50674,50675],{},[1788,50676,50677,50679],{},[898,50678,3035],{},[895,50680,50681,50683],{},[898,50682,42917],{},[898,50684,724],{},[902,50686,42922],{"encoding":904},[883,50688,50690],{"className":50689},[886],[888,50691,50692],{"xmlns":890},[892,50693,50694,50708],{},[895,50695,50696],{},[1788,50697,50698,50700],{},[898,50699,3035],{},[895,50701,50702,50704,50706],{},[898,50703,42940],{},[898,50705,2282],{},[898,50707,2046],{},[902,50709,42947],{"encoding":904},[123,50711,50712,2170,50715,1343,50744],{},[38,50713,50714],{},"Ekvivalence zdanění",[883,50716,50718],{"className":50717},[886],[888,50719,50720],{"xmlns":890},[892,50721,50722,50742],{},[895,50723,50724,50732,50734],{},[1814,50725,50726,50728,50730],{},[898,50727,1872],{},[1793,50729,1795],{},[898,50731,4509],{},[1688,50733,1690],{},[1814,50735,50736,50738,50740],{},[898,50737,1872],{},[1793,50739,1806],{},[898,50741,4509],{},[902,50743,43148],{"encoding":904},[883,50745,50747],{"className":50746},[886],[888,50748,50749],{"xmlns":890},[892,50750,50751,50775],{},[895,50752,50753,50761,50763,50765,50767],{},[1814,50754,50755,50757,50759],{},[898,50756,1727],{},[1793,50758,1795],{},[898,50760,4509],{},[1688,50762,1954],{},[898,50764,3035],{},[1688,50766,1690],{},[1814,50768,50769,50771,50773],{},[898,50770,1727],{},[1793,50772,1806],{},[898,50774,4509],{},[902,50776,43182],{"encoding":904},[724,50778,50779],{},[38,50780,26649],{},[120,50782,50783,50829,50860,50865,50871,50878],{},[123,50784,50785,2170,50787],{},[38,50786,43281],{},[883,50788,50790],{"className":50789},[886],[888,50791,50792],{"xmlns":890},[892,50793,50794,50826],{},[895,50795,50796,50802,50804,50806,50808,50810,50812,50814,50816,50818,50820,50822,50824],{},[1850,50797,50798,50800],{},[898,50799,1872],{},[898,50801,4509],{},[1688,50803,1690],{},[1688,50805,2066],{"stretchy":2065},[898,50807,1918],{},[1688,50809,1954],{},[898,50811,2073],{},[1688,50813,2076],{"stretchy":2065},[898,50815,4930],{"mathvariant":1822},[1688,50817,2066],{"stretchy":2065},[898,50819,2031],{},[1688,50821,1954],{},[898,50823,207],{},[1688,50825,2076],{"stretchy":2065},[902,50827,50828],{"encoding":904},"Q^E = (b - d)\u002F(c - a)",[123,50830,50831,2170,50834,50859],{},[38,50832,50833],{},"Parametry",[883,50835,50837],{"className":50836},[886],[888,50838,50839],{"xmlns":890},[892,50840,50841,50857],{},[895,50842,50843,50845,50847,50849,50851,50853,50855],{},[898,50844,207],{},[1688,50846,1733],{"separator":1732},[898,50848,1918],{},[1688,50850,1733],{"separator":1732},[898,50852,2031],{},[1688,50854,1733],{"separator":1732},[898,50856,2073],{},[902,50858,43525],{"encoding":904}," — exogenní proměnné",[123,50861,50862],{},[38,50863,50864],{},"Endogenní \u002F exogenní proměnná",[123,50866,50867,50870],{},[38,50868,50869],{},"Multiplikátor"," — parciální derivace redukovaného tvaru",[123,50872,50873,1343,50876],{},[38,50874,50875],{},"Komparativní statika",[38,50877,37200],{},[123,50879,50880,2170,50882,50898],{},[38,50881,3213],{},[883,50883,50885],{"className":50884},[886],[888,50886,50887],{"xmlns":890},[892,50888,50889,50895],{},[895,50890,50891,50893],{},[898,50892,2073],{},[898,50894,1872],{},[902,50896,50897],{"encoding":904},"dQ"," (2.11)",[724,50900,50901],{},[38,50902,50903],{},"Přebytky a ostatní",[120,50905,50906,50944],{},[123,50907,50908,2170,50910,50925,50926,2170,50928,50943],{},[38,50909,45174],{},[883,50911,50913],{"className":50912},[886],[888,50914,50915],{"xmlns":890},[892,50916,50917,50923],{},[895,50918,50919,50921],{},[898,50920,1693],{},[898,50922,1740],{},[902,50924,45190],{"encoding":904}," (2.14), ",[38,50927,45193],{},[883,50929,50931],{"className":50930},[886],[888,50932,50933],{"xmlns":890},[892,50934,50935,50941],{},[895,50936,50937,50939],{},[898,50938,1727],{},[898,50940,1740],{},[902,50942,45209],{"encoding":904}," (2.15)",[123,50945,50946,1343,50949,50952],{},[38,50947,50948],{},"Homo economicus",[38,50950,50951],{},"Marshallova formulace"," (1890)",[37210,50954],{},[115,50956,4049],{"id":4048},[120,50958,50959,50994,51003],{},[123,50960,50961,2170,50964,50967,50968,1343,50971,50974,50975,50978,50979,50982,50983,50986,50987,50990,50991],{},[38,50962,50963],{},"Související témata:",[207,50965,811],{"className":50966,"dataFsResolvedFilePath":809,"href":810},[210]," (dopady daně, daňové břemeno, ekvivalence), ",[207,50969,820],{"className":50970,"dataFsResolvedFilePath":818,"href":819},[210],[207,50972,2622],{"className":50973,"dataFsResolvedFilePath":764,"href":765},[210]," (zákon klesající\u002Frostoucí, monotonie), ",[207,50976,775],{"className":50977,"dataFsResolvedFilePath":773,"href":774},[210]," (CS a PS), ",[207,50980,784],{"className":50981,"dataFsResolvedFilePath":782,"href":783},[210]," (vícefaktorové modely, multiplikátory), ",[207,50984,793],{"className":50985,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace spotřebitele), ",[207,50988,4084],{"className":50989,"dataFsResolvedFilePath":848,"href":849},[210]," (důchodová a cenová citlivost), ",[207,50992,4079],{"className":50993,"dataFsResolvedFilePath":827,"href":828},[210],[123,50995,50996,2170,50999],{},[38,50997,50998],{},"Shrnutí přednášek:",[207,51000,51002],{"className":51001,"dataFsResolvedFilePath":745,"href":746},[210],"KS — 1. blok",[123,51004,51005,2170,51007],{},[38,51006,16451],{},[207,51008,16455],{"className":51009,"dataFsResolvedFilePath":2210,"href":2211},[210],{"title":641,"searchDepth":642,"depth":642,"links":51011},[51012,51013,51021,51027,51034,51035,51042,51043,51044,51051,51052,51053],{"id":37034,"depth":642,"text":37035},{"id":37015,"depth":642,"text":13409,"children":51014},[51015,51016,51017,51018,51020],{"id":37303,"depth":649,"text":37304},{"id":37585,"depth":649,"text":37586},{"id":38595,"depth":649,"text":38596},{"id":39163,"depth":649,"text":51019},"Posun poptávky (shift of demand)",{"id":39667,"depth":649,"text":39668},{"id":37019,"depth":642,"text":13373,"children":51022},[51023,51024,51025],{"id":40504,"depth":649,"text":37304},{"id":40690,"depth":649,"text":40691},{"id":41142,"depth":649,"text":51026},"Posun nabídky (shift of supply)",{"id":41564,"depth":642,"text":41565,"children":51028},[51029,51030,51031,51032,51033],{"id":41676,"depth":649,"text":41677},{"id":41889,"depth":649,"text":41890},{"id":42207,"depth":649,"text":42208},{"id":42561,"depth":649,"text":42562},{"id":42592,"depth":649,"text":42593},{"id":42861,"depth":642,"text":811},{"id":43262,"depth":642,"text":43263,"children":51036},[51037,51038,51039,51040],{"id":43280,"depth":649,"text":43281},{"id":43661,"depth":649,"text":43662},{"id":44045,"depth":649,"text":44046},{"id":44499,"depth":649,"text":51041},"Příklad 2.11 — komparativní statika pro QEQ^E",{"id":12036,"depth":642,"text":820},{"id":45424,"depth":642,"text":45425},{"id":45655,"depth":642,"text":45656,"children":51045},[51046,51047,51048,51049,51050],{"id":45659,"depth":649,"text":45660},{"id":46499,"depth":649,"text":46500},{"id":46875,"depth":649,"text":41565},{"id":48170,"depth":649,"text":43263},{"id":49926,"depth":649,"text":820},{"id":50121,"depth":642,"text":50122},{"id":15966,"depth":642,"text":15967},{"id":4048,"depth":642,"text":4049},{},"\u002Ftopics\u002Fpoptavka-nabidka",{"title":802,"description":641},[1138,1135],"topics\u002Fpoptavka-nabidka",[1128,51060,51061,51062,18128,51063,51064],"poptavka","nabidka","rovnovaha","zdaneni","prebytek","VHXMOe03Z24g0HTNlL2geCMzNcnJ3vQ8m2Org-s9n8Q",{"id":51067,"title":820,"body":51068,"course":1128,"courses":659,"created":9809,"description":641,"extension":661,"meta":55347,"navigation":664,"path":55348,"seo":55349,"sources":55350,"stem":55351,"tags":55352,"type":4113,"updated":677,"__hash__":55357},"topics\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce.md",{"type":9,"value":51069,"toc":55325},[51070,51072,51140,51190,51192,51195,51453,51529,51534,51536,51555,51559,51635,51720,51722,52036,52129,52131,52150,52154,52228,52313,52316,52492,52497,52499,52919,52921,52925,52929,53165,53209,53309,53375,53378,53411,53587,53649,53779,53857,53968,54002,54200,54219,54238,54303,54307,54310,54355,54358,54476,54522,54524,54528,54876,54878,54880,55158,55160,55164,55199,55206,55279,55281,55283],[12,51071,820],{"id":12036},[4124,51073,51074],{},[724,51075,51076,4131,51078,10277,51080,51095,51096,10277,51098,51113,51114,51136,51137,2263],{},[883,51077,4130],{},[38,51079,45174],{},[883,51081,51083],{"className":51082},[886],[888,51084,51085],{"xmlns":890},[892,51086,51087,51093],{},[895,51088,51089,51091],{},[898,51090,1693],{},[898,51092,1740],{},[902,51094,45190],{"encoding":904},") je rozdíl mezi tím, co byl spotřebitel ochoten zaplatit, a tím, co skutečně zaplatil. ",[38,51097,45321],{},[883,51099,51101],{"className":51100},[886],[888,51102,51103],{"xmlns":890},[892,51104,51105,51111],{},[895,51106,51107,51109],{},[898,51108,1727],{},[898,51110,1740],{},[902,51112,45209],{"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 ",[883,51115,51117],{"className":51116},[886],[888,51118,51119],{"xmlns":890},[892,51120,51121,51133],{},[895,51122,51123,51125,51127,51129,51131],{},[898,51124,1693],{},[898,51126,1740],{},[1688,51128,1696],{},[898,51130,1727],{},[898,51132,1740],{},[902,51134,51135],{"encoding":904},"CS + PS"," měří ",[38,51138,51139],{},"celkový blahobyt trhu",[724,51141,51142,10277,51144,1343,51146,12378,51161,10277,51163,1343,51165,51180,51181,51185,51186,2263],{},[38,51143,45174],{},[614,51145,45228],{},[883,51147,51149],{"className":51148},[886],[888,51150,51151],{"xmlns":890},[892,51152,51153,51159],{},[895,51154,51155,51157],{},[898,51156,1693],{},[898,51158,1740],{},[902,51160,45190],{"encoding":904},[38,51162,45193],{},[614,51164,45324],{},[883,51166,51168],{"className":51167},[886],[888,51169,51170],{"xmlns":890},[892,51171,51172,51178],{},[895,51173,51174,51176],{},[898,51175,1727],{},[898,51177,1740],{},[902,51179,45209],{"encoding":904},") kvantifikují čistý prospěch jednotlivých stran trhu. Navazují na pojmy ",[207,51182,51184],{"className":51183,"dataFsResolvedFilePath":800,"href":801},[210],"tržní rovnováhy"," a využívají aparát ",[207,51187,51189],{"className":51188,"dataFsResolvedFilePath":773,"href":774},[210],"integrálního počtu",[37210,51191],{},[115,51193,1241],{"id":51194},"úvod",[724,51196,51197,51198,51221,51222,51245,51246,51263,51264,4168,51296,51328,51329,51355,51356,51359,51360,51363,51364,14258,51398,21835,51419,2263],{},"Je dána funkce poptávky ",[883,51199,51201],{"className":51200},[886],[888,51202,51203],{"xmlns":890},[892,51204,51205,51219],{},[895,51206,51207,51209,51211,51213,51215,51217],{},[898,51208,1727],{},[1688,51210,1690],{},[898,51212,4440],{},[1688,51214,2066],{"stretchy":2065},[898,51216,1872],{},[1688,51218,2076],{"stretchy":2065},[902,51220,4896],{"encoding":904},", resp. funkce nabídky ",[883,51223,51225],{"className":51224},[886],[888,51226,51227],{"xmlns":890},[892,51228,51229,51243],{},[895,51230,51231,51233,51235,51237,51239,51241],{},[898,51232,1727],{},[1688,51234,1690],{},[898,51236,1740],{},[1688,51238,2066],{"stretchy":2065},[898,51240,1872],{},[1688,51242,2076],{"stretchy":2065},[902,51244,41311],{"encoding":904},". Pro pevně zadané množství ",[883,51247,51249],{"className":51248},[886],[888,51250,51251],{"xmlns":890},[892,51252,51253,51261],{},[895,51254,51255],{},[1788,51256,51257,51259],{},[898,51258,1872],{},[1793,51260,1779],{},[902,51262,38548],{"encoding":904}," je odpovídající cena ",[883,51265,51267],{"className":51266},[886],[888,51268,51269],{"xmlns":890},[892,51270,51271,51293],{},[895,51272,51273,51279,51281,51283,51285,51291],{},[1788,51274,51275,51277],{},[898,51276,1727],{},[1793,51278,1779],{},[1688,51280,1690],{},[898,51282,4440],{},[1688,51284,2066],{"stretchy":2065},[1788,51286,51287,51289],{},[898,51288,1872],{},[1793,51290,1779],{},[1688,51292,2076],{"stretchy":2065},[902,51294,51295],{"encoding":904},"P_0 = D(Q_0)",[883,51297,51299],{"className":51298},[886],[888,51300,51301],{"xmlns":890},[892,51302,51303,51325],{},[895,51304,51305,51311,51313,51315,51317,51323],{},[1788,51306,51307,51309],{},[898,51308,1727],{},[1793,51310,1779],{},[1688,51312,1690],{},[898,51314,1740],{},[1688,51316,2066],{"stretchy":2065},[1788,51318,51319,51321],{},[898,51320,1872],{},[1793,51322,1779],{},[1688,51324,2076],{"stretchy":2065},[902,51326,51327],{"encoding":904},"P_0 = S(Q_0)","). Součin ",[883,51330,51332],{"className":51331},[886],[888,51333,51334],{"xmlns":890},[892,51335,51336,51352],{},[895,51337,51338,51344,51346],{},[1788,51339,51340,51342],{},[898,51341,1727],{},[1793,51343,1779],{},[2041,51345,2043],{},[1788,51347,51348,51350],{},[898,51349,1872],{},[1793,51351,1779],{},[902,51353,51354],{"encoding":904},"P_0 \\, Q_0"," reprezentuje buď ",[38,51357,51358],{},"výdaje spotřebitele",", nebo ",[38,51361,51362],{},"tržby výrobce"," a geometricky odpovídá obsahu obdélníka ",[883,51365,51367],{"className":51366},[886],[888,51368,51369],{"xmlns":890},[892,51370,51371,51395],{},[895,51372,51373,51375,51377,51383,51385,51387,51389],{},[1793,51374,1779],{},[2041,51376,2043],{},[1788,51378,51379,51381],{},[898,51380,1872],{},[1793,51382,1779],{},[2041,51384,2043],{},[898,51386,4512],{},[2041,51388,2043],{},[1788,51390,51391,51393],{},[898,51392,1727],{},[1793,51394,1779],{},[902,51396,51397],{"encoding":904},"0\\,Q_0\\,A\\,P_0",[883,51399,51401],{"className":51400},[886],[888,51402,51403],{"xmlns":890},[892,51404,51405,51417],{},[895,51406,51407,51409,51411,51413,51415],{},[1688,51408,2066],{"stretchy":2065},[898,51410,1872],{},[1688,51412,1733],{"separator":1732},[898,51414,1727],{},[1688,51416,2076],{"stretchy":2065},[902,51418,37931],{"encoding":904},[883,51420,51422],{"className":51421},[886],[888,51423,51424],{"xmlns":890},[892,51425,51426,51450],{},[895,51427,51428,51430,51432,51434,51440,51442,51448],{},[898,51429,4512],{},[1688,51431,1690],{},[1688,51433,2748],{"stretchy":2065},[1788,51435,51436,51438],{},[898,51437,1872],{},[1793,51439,1779],{},[1688,51441,1733],{"separator":1732},[1788,51443,51444,51446],{},[898,51445,1727],{},[1793,51447,1779],{},[1688,51449,2763],{"stretchy":2065},[902,51451,51452],{"encoding":904},"A = [Q_0, P_0]",[4124,51454,51455,51460,51518],{},[724,51456,51457,51459],{},[883,51458,4412],{}," Intuice",[120,51461,51462,51490],{},[123,51463,51464,51465,51468,51469,51471,51472,51489],{},"Za jednotky zboží nakoupené ",[38,51466,51467],{},"před"," posledním kusem je spotřebitel podle funkce poptávky ochoten platit ",[614,51470,25511],{}," než ",[883,51473,51475],{"className":51474},[886],[888,51476,51477],{"xmlns":890},[892,51478,51479,51487],{},[895,51480,51481],{},[1788,51482,51483,51485],{},[898,51484,1727],{},[1793,51486,1779],{},[902,51488,39188],{"encoding":904}," — rozdíl si „šetří do kapsy\" jako přebytek.",[123,51491,51492,51493,51495,51496,51499,51500,51517],{},"Za jednotky zboží prodané ",[38,51494,51467],{}," posledním kusem by výrobce podle funkce nabídky byl ochoten prodávat i za ",[614,51497,51498],{},"nižší"," cenu než ",[883,51501,51503],{"className":51502},[886],[888,51504,51505],{"xmlns":890},[892,51506,51507,51515],{},[895,51508,51509],{},[1788,51510,51511,51513],{},[898,51512,1727],{},[1793,51514,1779],{},[902,51516,39188],{"encoding":904}," — rozdíl je jeho přebytek.",[724,51519,51520,51521,51524,51525,51528],{},"Přebytek je tedy rozdíl mezi ",[614,51522,51523],{},"ochotou"," (platit \u002F prodávat) a ",[614,51526,51527],{},"skutečností"," (zaplaceno \u002F obdrženo).",[724,51530,51531],{},[2821,51532],{"alt":45219,"className":51533,"src":45221},[210,2825],[37210,51535],{},[115,51537,51539,51540,2076],{"id":51538},"přebytek-spotřebitele-cscs","Přebytek spotřebitele (",[883,51541,51543],{"className":51542},[886],[888,51544,51545],{"xmlns":890},[892,51546,51547,51553],{},[895,51548,51549,51551],{},[898,51550,1693],{},[898,51552,1740],{},[902,51554,45190],{"encoding":904},[198,51556,51558],{"id":51557},"definice-vzorec-214","Definice (vzorec 2.14)",[724,51560,51561,51562,51585,51586,51603,51604,2965],{},"Pro poptávku ",[883,51563,51565],{"className":51564},[886],[888,51566,51567],{"xmlns":890},[892,51568,51569,51583],{},[895,51570,51571,51573,51575,51577,51579,51581],{},[898,51572,1727],{},[1688,51574,1690],{},[898,51576,4440],{},[1688,51578,2066],{"stretchy":2065},[898,51580,1872],{},[1688,51582,2076],{"stretchy":2065},[902,51584,4896],{"encoding":904}," a pevně zadané ",[883,51587,51589],{"className":51588},[886],[888,51590,51591],{"xmlns":890},[892,51592,51593,51601],{},[895,51594,51595],{},[1788,51596,51597,51599],{},[898,51598,1872],{},[1793,51600,1779],{},[902,51602,38548],{"encoding":904}," s cenou ",[883,51605,51607],{"className":51606},[886],[888,51608,51609],{"xmlns":890},[892,51610,51611,51633],{},[895,51612,51613,51619,51621,51623,51625,51631],{},[1788,51614,51615,51617],{},[898,51616,1727],{},[1793,51618,1779],{},[1688,51620,1690],{},[898,51622,4440],{},[1688,51624,2066],{"stretchy":2065},[1788,51626,51627,51629],{},[898,51628,1872],{},[1793,51630,1779],{},[1688,51632,2076],{"stretchy":2065},[902,51634,51295],{"encoding":904},[883,51636,51638],{"className":51637},[886],[888,51639,51640],{"xmlns":890,"display":28306},[892,51641,51642,51718],{},[20995,51643,51644],{"width":28311},[21000,51645,51646,51648,51712,51714],{},[21003,51647],{"width":28316},[21003,51649,51650],{},[895,51651,51652,51654,51656,51658,51664,51666,51668,51680,51682,51684,51686,51688,51690,51692,51694,51696,51702,51704,51710],{},[898,51653,1693],{},[898,51655,1740],{},[1688,51657,2066],{"stretchy":2065},[1788,51659,51660,51662],{},[898,51661,1872],{},[1793,51663,1779],{},[1688,51665,2076],{"stretchy":2065},[1688,51667,1690],{},[1814,51669,51670,51672,51674],{},[1688,51671,11421],{},[1793,51673,1779],{},[1788,51675,51676,51678],{},[898,51677,1872],{},[1793,51679,1779],{},[898,51681,4440],{},[1688,51683,2066],{"stretchy":2065},[898,51685,1872],{},[1688,51687,2076],{"stretchy":2065},[2041,51689,2043],{},[898,51691,2073],{},[898,51693,1872],{},[1688,51695,1954],{},[1788,51697,51698,51700],{},[898,51699,1727],{},[1793,51701,1779],{},[2041,51703,2043],{},[1788,51705,51706,51708],{},[898,51707,1872],{},[1793,51709,1779],{},[898,51711,2263],{"mathvariant":1822},[21003,51713],{"width":28316},[21003,51715,51716],{},[2041,51717,45313],{},[902,51719,45316],{"encoding":904},[198,51721,2706],{"id":2705},[120,51723,51724,51816,51878],{},[123,51725,51726,51766,51767,51793,51794,51797,51798,51815],{},[883,51727,51729],{"className":51728},[886],[888,51730,51731],{"xmlns":890},[892,51732,51733,51763],{},[895,51734,51735],{},[1777,51736,51737,51749,51751,51753,51755,51757,51759,51761],{"scriptlevel":1779,"displaystyle":1732},[1814,51738,51739,51741,51743],{},[1688,51740,11421],{},[1793,51742,1779],{},[1788,51744,51745,51747],{},[898,51746,1872],{},[1793,51748,1779],{},[898,51750,4440],{},[1688,51752,2066],{"stretchy":2065},[898,51754,1872],{},[1688,51756,2076],{"stretchy":2065},[2041,51758,2043],{},[898,51760,2073],{},[898,51762,1872],{},[902,51764,51765],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ"," — plocha pod křivkou poptávky v intervalu ",[883,51768,51770],{"className":51769},[886],[888,51771,51772],{"xmlns":890},[892,51773,51774,51790],{},[895,51775,51776,51778,51780,51782,51788],{},[1688,51777,2748],{"stretchy":2065},[1793,51779,1779],{},[1688,51781,1733],{"separator":1732},[1788,51783,51784,51786],{},[898,51785,1872],{},[1793,51787,1779],{},[1688,51789,2763],{"stretchy":2065},[902,51791,51792],{"encoding":904},"[0, Q_0]","; představuje celkovou ",[38,51795,51796],{},"ochotu platit"," (maximální částku, kterou by spotřebitel za ",[883,51799,51801],{"className":51800},[886],[888,51802,51803],{"xmlns":890},[892,51804,51805,51813],{},[895,51806,51807],{},[1788,51808,51809,51811],{},[898,51810,1872],{},[1793,51812,1779],{},[902,51814,38548],{"encoding":904}," jednotek byl ochoten zaplatit).",[123,51817,51818,51844,51845,4176],{},[883,51819,51821],{"className":51820},[886],[888,51822,51823],{"xmlns":890},[892,51824,51825,51841],{},[895,51826,51827,51833,51835],{},[1788,51828,51829,51831],{},[898,51830,1727],{},[1793,51832,1779],{},[2041,51834,2043],{},[1788,51836,51837,51839],{},[898,51838,1872],{},[1793,51840,1779],{},[902,51842,51843],{"encoding":904},"P_0\\,Q_0"," — skutečně zaplacená částka (obdélník ",[883,51846,51848],{"className":51847},[886],[888,51849,51850],{"xmlns":890},[892,51851,51852,51876],{},[895,51853,51854,51856,51858,51864,51866,51868,51870],{},[1793,51855,1779],{},[2041,51857,2043],{},[1788,51859,51860,51862],{},[898,51861,1872],{},[1793,51863,1779],{},[2041,51865,2043],{},[898,51867,4512],{},[2041,51869,2043],{},[1788,51871,51872,51874],{},[898,51873,1727],{},[1793,51875,1779],{},[902,51877,51397],{"encoding":904},[123,51879,51880,51895,51896,51918,51919,51944,51945,21835,51971,4142,52003,2263],{},[883,51881,51883],{"className":51882},[886],[888,51884,51885],{"xmlns":890},[892,51886,51887,51893],{},[895,51888,51889,51891],{},[898,51890,1693],{},[898,51892,1740],{},[902,51894,45190],{"encoding":904}," je plocha mezi křivkou poptávky a vodorovnou přímkou ",[883,51897,51899],{"className":51898},[886],[888,51900,51901],{"xmlns":890},[892,51902,51903,51915],{},[895,51904,51905,51907,51909],{},[898,51906,1727],{},[1688,51908,1690],{},[1788,51910,51911,51913],{},[898,51912,1727],{},[1793,51914,1779],{},[902,51916,51917],{"encoding":904},"P = P_0"," v pásu ",[883,51920,51922],{"className":51921},[886],[888,51923,51924],{"xmlns":890},[892,51925,51926,51942],{},[895,51927,51928,51930,51932,51934,51940],{},[1688,51929,2748],{"stretchy":2065},[1793,51931,1779],{},[1688,51933,1733],{"separator":1732},[1788,51935,51936,51938],{},[898,51937,1872],{},[1793,51939,1779],{},[1688,51941,2763],{"stretchy":2065},[902,51943,51792],{"encoding":904}," — „křivočarý trojúhelník\" ",[883,51946,51948],{"className":51947},[886],[888,51949,51950],{"xmlns":890},[892,51951,51952,51968],{},[895,51953,51954,51960,51962,51964,51966],{},[1788,51955,51956,51958],{},[898,51957,1727],{},[1793,51959,1779],{},[2041,51961,2043],{},[898,51963,23494],{},[2041,51965,2043],{},[898,51967,4512],{},[902,51969,51970],{"encoding":904},"P_0\\,B\\,A",[883,51972,51974],{"className":51973},[886],[888,51975,51976],{"xmlns":890},[892,51977,51978,52000],{},[895,51979,51980,51982,51984,51986,51988,51990,51992,51994,51996,51998],{},[898,51981,23494],{},[1688,51983,1690],{},[1688,51985,2748],{"stretchy":2065},[1793,51987,1779],{},[1688,51989,1733],{"separator":1732},[898,51991,4440],{},[1688,51993,2066],{"stretchy":2065},[1793,51995,1779],{},[1688,51997,2076],{"stretchy":2065},[1688,51999,2763],{"stretchy":2065},[902,52001,52002],{"encoding":904},"B = [0, D(0)]",[883,52004,52006],{"className":52005},[886],[888,52007,52008],{"xmlns":890},[892,52009,52010,52034],{},[895,52011,52012,52014,52016,52018,52024,52026,52032],{},[898,52013,4512],{},[1688,52015,1690],{},[1688,52017,2748],{"stretchy":2065},[1788,52019,52020,52022],{},[898,52021,1872],{},[1793,52023,1779],{},[1688,52025,1733],{"separator":1732},[1788,52027,52028,52030],{},[898,52029,1727],{},[1793,52031,1779],{},[1688,52033,2763],{"stretchy":2065},[902,52035,51452],{"encoding":904},[724,52037,52038],{},[614,52039,52040,52041,52054,52055,52088,52089,29382,52114,2263],{},"Obrázek 2.24: Křivka poptávky ",[883,52042,52044],{"className":52043},[886],[888,52045,52046],{"xmlns":890},[892,52047,52048,52052],{},[895,52049,52050],{},[898,52051,4440],{},[902,52053,4440],{"encoding":904},", bod ",[883,52056,52058],{"className":52057},[886],[888,52059,52060],{"xmlns":890},[892,52061,52062,52086],{},[895,52063,52064,52066,52068,52070,52076,52078,52084],{},[898,52065,4512],{},[1688,52067,1690],{},[1688,52069,2748],{"stretchy":2065},[1788,52071,52072,52074],{},[898,52073,1872],{},[1793,52075,1779],{},[1688,52077,1733],{"separator":1732},[1788,52079,52080,52082],{},[898,52081,1727],{},[1793,52083,1779],{},[1688,52085,2763],{"stretchy":2065},[902,52087,51452],{"encoding":904},", vyšrafovaná plocha trojúhelníku ",[883,52090,52092],{"className":52091},[886],[888,52093,52094],{"xmlns":890},[892,52095,52096,52112],{},[895,52097,52098,52104,52106,52108,52110],{},[1788,52099,52100,52102],{},[898,52101,1727],{},[1793,52103,1779],{},[2041,52105,2043],{},[898,52107,23494],{},[2041,52109,2043],{},[898,52111,4512],{},[902,52113,51970],{"encoding":904},[883,52115,52117],{"className":52116},[886],[888,52118,52119],{"xmlns":890},[892,52120,52121,52127],{},[895,52122,52123,52125],{},[898,52124,1693],{},[898,52126,1740],{},[902,52128,45190],{"encoding":904},[37210,52130],{},[115,52132,52134,52135,2076],{"id":52133},"přebytek-výrobce-psps","Přebytek výrobce (",[883,52136,52138],{"className":52137},[886],[888,52139,52140],{"xmlns":890},[892,52141,52142,52148],{},[895,52143,52144,52146],{},[898,52145,1727],{},[898,52147,1740],{},[902,52149,45209],{"encoding":904},[198,52151,52153],{"id":52152},"definice-vzorec-215","Definice (vzorec 2.15)",[724,52155,52156,52157,51585,52180,51603,52197,2965],{},"Analogicky — pro nabídku ",[883,52158,52160],{"className":52159},[886],[888,52161,52162],{"xmlns":890},[892,52163,52164,52178],{},[895,52165,52166,52168,52170,52172,52174,52176],{},[898,52167,1727],{},[1688,52169,1690],{},[898,52171,1740],{},[1688,52173,2066],{"stretchy":2065},[898,52175,1872],{},[1688,52177,2076],{"stretchy":2065},[902,52179,41311],{"encoding":904},[883,52181,52183],{"className":52182},[886],[888,52184,52185],{"xmlns":890},[892,52186,52187,52195],{},[895,52188,52189],{},[1788,52190,52191,52193],{},[898,52192,1872],{},[1793,52194,1779],{},[902,52196,38548],{"encoding":904},[883,52198,52200],{"className":52199},[886],[888,52201,52202],{"xmlns":890},[892,52203,52204,52226],{},[895,52205,52206,52212,52214,52216,52218,52224],{},[1788,52207,52208,52210],{},[898,52209,1727],{},[1793,52211,1779],{},[1688,52213,1690],{},[898,52215,1740],{},[1688,52217,2066],{"stretchy":2065},[1788,52219,52220,52222],{},[898,52221,1872],{},[1793,52223,1779],{},[1688,52225,2076],{"stretchy":2065},[902,52227,51327],{"encoding":904},[883,52229,52231],{"className":52230},[886],[888,52232,52233],{"xmlns":890,"display":28306},[892,52234,52235,52311],{},[20995,52236,52237],{"width":28311},[21000,52238,52239,52241,52305,52307],{},[21003,52240],{"width":28316},[21003,52242,52243],{},[895,52244,52245,52247,52249,52251,52257,52259,52261,52267,52269,52275,52277,52289,52291,52293,52295,52297,52299,52301,52303],{},[898,52246,1727],{},[898,52248,1740],{},[1688,52250,2066],{"stretchy":2065},[1788,52252,52253,52255],{},[898,52254,1872],{},[1793,52256,1779],{},[1688,52258,2076],{"stretchy":2065},[1688,52260,1690],{},[1788,52262,52263,52265],{},[898,52264,1727],{},[1793,52266,1779],{},[2041,52268,2043],{},[1788,52270,52271,52273],{},[898,52272,1872],{},[1793,52274,1779],{},[1688,52276,1954],{},[1814,52278,52279,52281,52283],{},[1688,52280,11421],{},[1793,52282,1779],{},[1788,52284,52285,52287],{},[898,52286,1872],{},[1793,52288,1779],{},[898,52290,1740],{},[1688,52292,2066],{"stretchy":2065},[898,52294,1872],{},[1688,52296,2076],{"stretchy":2065},[2041,52298,2043],{},[898,52300,2073],{},[898,52302,1872],{},[898,52304,2263],{"mathvariant":1822},[21003,52306],{"width":28316},[21003,52308,52309],{},[2041,52310,45409],{},[902,52312,45412],{"encoding":904},[198,52314,2706],{"id":52315},"geometrická-interpretace-1",[120,52317,52318,52366,52427],{},[123,52319,52320,7271,52345,52348,52349,2263],{},[883,52321,52323],{"className":52322},[886],[888,52324,52325],{"xmlns":890},[892,52326,52327,52343],{},[895,52328,52329,52335,52337],{},[1788,52330,52331,52333],{},[898,52332,1727],{},[1793,52334,1779],{},[2041,52336,2043],{},[1788,52338,52339,52341],{},[898,52340,1872],{},[1793,52342,1779],{},[902,52344,51843],{"encoding":904},[38,52346,52347],{},"tržba"," výrobce za prodané množství ",[883,52350,52352],{"className":52351},[886],[888,52353,52354],{"xmlns":890},[892,52355,52356,52364],{},[895,52357,52358],{},[1788,52359,52360,52362],{},[898,52361,1872],{},[1793,52363,1779],{},[902,52365,38548],{"encoding":904},[123,52367,52368,52408,52409,52426],{},[883,52369,52371],{"className":52370},[886],[888,52372,52373],{"xmlns":890},[892,52374,52375,52405],{},[895,52376,52377],{},[1777,52378,52379,52391,52393,52395,52397,52399,52401,52403],{"scriptlevel":1779,"displaystyle":1732},[1814,52380,52381,52383,52385],{},[1688,52382,11421],{},[1793,52384,1779],{},[1788,52386,52387,52389],{},[898,52388,1872],{},[1793,52390,1779],{},[898,52392,1740],{},[1688,52394,2066],{"stretchy":2065},[898,52396,1872],{},[1688,52398,2076],{"stretchy":2065},[2041,52400,2043],{},[898,52402,2073],{},[898,52404,1872],{},[902,52406,52407],{"encoding":904},"\\displaystyle \\int_0^{Q_0} S(Q)\\,dQ"," — plocha pod křivkou nabídky; minimální částka, za kterou by byl výrobce ochoten ",[883,52410,52412],{"className":52411},[886],[888,52413,52414],{"xmlns":890},[892,52415,52416,52424],{},[895,52417,52418],{},[1788,52419,52420,52422],{},[898,52421,1872],{},[1793,52423,1779],{},[902,52425,38548],{"encoding":904}," jednotek dodat (souvisí s mezními náklady).",[123,52428,52429,52444,52445,52466,52467,2263],{},[883,52430,52432],{"className":52431},[886],[888,52433,52434],{"xmlns":890},[892,52435,52436,52442],{},[895,52437,52438,52440],{},[898,52439,1727],{},[898,52441,1740],{},[902,52443,45209],{"encoding":904}," je plocha mezi vodorovnou přímkou ",[883,52446,52448],{"className":52447},[886],[888,52449,52450],{"xmlns":890},[892,52451,52452,52464],{},[895,52453,52454,52456,52458],{},[898,52455,1727],{},[1688,52457,1690],{},[1788,52459,52460,52462],{},[898,52461,1727],{},[1793,52463,1779],{},[902,52465,51917],{"encoding":904}," a křivkou nabídky v pásu ",[883,52468,52470],{"className":52469},[886],[888,52471,52472],{"xmlns":890},[892,52473,52474,52490],{},[895,52475,52476,52478,52480,52482,52488],{},[1688,52477,2748],{"stretchy":2065},[1793,52479,1779],{},[1688,52481,1733],{"separator":1732},[1788,52483,52484,52486],{},[898,52485,1872],{},[1793,52487,1779],{},[1688,52489,2763],{"stretchy":2065},[902,52491,51792],{"encoding":904},[724,52493,52494],{},[614,52495,52496],{},"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.",[37210,52498],{},[4124,52500,52501,52506],{},[724,52502,52503,52505],{},[883,52504,4828],{}," Postup výpočtu CS a PS",[152,52507,52508,52639,52749,52778,52912],{},[123,52509,52510,52511,52528,52529,52560,52561,52592,52593,2263],{},"Zjisti (nebo si zvol) množství ",[883,52512,52514],{"className":52513},[886],[888,52515,52516],{"xmlns":890},[892,52517,52518,52526],{},[895,52519,52520],{},[1788,52521,52522,52524],{},[898,52523,1872],{},[1793,52525,1779],{},[902,52527,38548],{"encoding":904}," a odpovídající cenu ",[883,52530,52532],{"className":52531},[886],[888,52533,52534],{"xmlns":890},[892,52535,52536,52558],{},[895,52537,52538,52544,52546,52548,52550,52556],{},[1788,52539,52540,52542],{},[898,52541,1727],{},[1793,52543,1779],{},[1688,52545,1690],{},[898,52547,4440],{},[1688,52549,2066],{"stretchy":2065},[1788,52551,52552,52554],{},[898,52553,1872],{},[1793,52555,1779],{},[1688,52557,2076],{"stretchy":2065},[902,52559,51295],{"encoding":904}," resp. ",[883,52562,52564],{"className":52563},[886],[888,52565,52566],{"xmlns":890},[892,52567,52568,52590],{},[895,52569,52570,52576,52578,52580,52582,52588],{},[1788,52571,52572,52574],{},[898,52573,1727],{},[1793,52575,1779],{},[1688,52577,1690],{},[898,52579,1740],{},[1688,52581,2066],{"stretchy":2065},[1788,52583,52584,52586],{},[898,52585,1872],{},[1793,52587,1779],{},[1688,52589,2076],{"stretchy":2065},[902,52591,51327],{"encoding":904},". V rovnováze platí ",[883,52594,52596],{"className":52595},[886],[888,52597,52598],{"xmlns":890},[892,52599,52600,52636],{},[895,52601,52602,52604,52606,52612,52614,52616,52618,52620,52626,52628,52630],{},[898,52603,4440],{},[1688,52605,2066],{"stretchy":2065},[1850,52607,52608,52610],{},[898,52609,1872],{},[898,52611,4509],{},[1688,52613,2076],{"stretchy":2065},[1688,52615,1690],{},[898,52617,1740],{},[1688,52619,2066],{"stretchy":2065},[1850,52621,52622,52624],{},[898,52623,1872],{},[898,52625,4509],{},[1688,52627,2076],{"stretchy":2065},[1688,52629,1690],{},[1850,52631,52632,52634],{},[898,52633,1727],{},[898,52635,4509],{},[902,52637,52638],{"encoding":904},"D(Q^E) = S(Q^E) = P^E",[123,52640,52641,52642,20367,52680,52695,52696,20367,52734,4176],{},"Spočti určitý integrál ",[883,52643,52645],{"className":52644},[886],[888,52646,52647],{"xmlns":890},[892,52648,52649,52677],{},[895,52650,52651,52663,52665,52667,52669,52671,52673,52675],{},[1814,52652,52653,52655,52657],{},[1688,52654,11421],{},[1793,52656,1779],{},[1788,52658,52659,52661],{},[898,52660,1872],{},[1793,52662,1779],{},[898,52664,4440],{},[1688,52666,2066],{"stretchy":2065},[898,52668,1872],{},[1688,52670,2076],{"stretchy":2065},[2041,52672,2043],{},[898,52674,2073],{},[898,52676,1872],{},[902,52678,52679],{"encoding":904},"\\int_0^{Q_0} D(Q)\\,dQ",[883,52681,52683],{"className":52682},[886],[888,52684,52685],{"xmlns":890},[892,52686,52687,52693],{},[895,52688,52689,52691],{},[898,52690,1693],{},[898,52692,1740],{},[902,52694,45190],{"encoding":904},") nebo ",[883,52697,52699],{"className":52698},[886],[888,52700,52701],{"xmlns":890},[892,52702,52703,52731],{},[895,52704,52705,52717,52719,52721,52723,52725,52727,52729],{},[1814,52706,52707,52709,52711],{},[1688,52708,11421],{},[1793,52710,1779],{},[1788,52712,52713,52715],{},[898,52714,1872],{},[1793,52716,1779],{},[898,52718,1740],{},[1688,52720,2066],{"stretchy":2065},[898,52722,1872],{},[1688,52724,2076],{"stretchy":2065},[2041,52726,2043],{},[898,52728,2073],{},[898,52730,1872],{},[902,52732,52733],{"encoding":904},"\\int_0^{Q_0} S(Q)\\,dQ",[883,52735,52737],{"className":52736},[886],[888,52738,52739],{"xmlns":890},[892,52740,52741,52747],{},[895,52742,52743,52745],{},[898,52744,1727],{},[898,52746,1740],{},[902,52748,45209],{"encoding":904},[123,52750,52751,52752,2263],{},"Sestav obdélník ",[883,52753,52755],{"className":52754},[886],[888,52756,52757],{"xmlns":890},[892,52758,52759,52775],{},[895,52760,52761,52767,52769],{},[1788,52762,52763,52765],{},[898,52764,1727],{},[1793,52766,1779],{},[1688,52768,3434],{},[1788,52770,52771,52773],{},[898,52772,1872],{},[1793,52774,1779],{},[902,52776,52777],{"encoding":904},"P_0 \\cdot Q_0",[123,52779,52780,52781],{},"Dosaď:\n",[120,52782,52783,52848],{},[123,52784,52785,52843,52844,52847],{},[883,52786,52788],{"className":52787},[886],[888,52789,52790],{"xmlns":890},[892,52791,52792,52840],{},[895,52793,52794,52796,52798,52800,52812,52814,52816,52818,52820,52822,52824,52826,52828,52834],{},[898,52795,1693],{},[898,52797,1740],{},[1688,52799,1690],{},[1814,52801,52802,52804,52806],{},[1688,52803,11421],{},[1793,52805,1779],{},[1788,52807,52808,52810],{},[898,52809,1872],{},[1793,52811,1779],{},[898,52813,4440],{},[1688,52815,2066],{"stretchy":2065},[898,52817,1872],{},[1688,52819,2076],{"stretchy":2065},[2041,52821,2043],{},[898,52823,2073],{},[898,52825,1872],{},[1688,52827,1954],{},[1788,52829,52830,52832],{},[898,52831,1727],{},[1793,52833,1779],{},[1788,52835,52836,52838],{},[898,52837,1872],{},[1793,52839,1779],{},[902,52841,52842],{"encoding":904},"CS = \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0"," (integrál ",[38,52845,52846],{},"mínus"," obdélník)",[123,52849,52850,52908,52909,52911],{},[883,52851,52853],{"className":52852},[886],[888,52854,52855],{"xmlns":890},[892,52856,52857,52905],{},[895,52858,52859,52861,52863,52865,52871,52877,52879,52891,52893,52895,52897,52899,52901,52903],{},[898,52860,1727],{},[898,52862,1740],{},[1688,52864,1690],{},[1788,52866,52867,52869],{},[898,52868,1727],{},[1793,52870,1779],{},[1788,52872,52873,52875],{},[898,52874,1872],{},[1793,52876,1779],{},[1688,52878,1954],{},[1814,52880,52881,52883,52885],{},[1688,52882,11421],{},[1793,52884,1779],{},[1788,52886,52887,52889],{},[898,52888,1872],{},[1793,52890,1779],{},[898,52892,1740],{},[1688,52894,2066],{"stretchy":2065},[898,52896,1872],{},[1688,52898,2076],{"stretchy":2065},[2041,52900,2043],{},[898,52902,2073],{},[898,52904,1872],{},[902,52906,52907],{"encoding":904},"PS = P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ"," (obdélník ",[38,52910,52846],{}," integrál)",[123,52913,52914,52915,52918],{},"Kontrola znaménka: obě hodnoty musí být ",[38,52916,52917],{},"kladné",". Pokud vyjde záporná, máš prohozené pořadí.",[37210,52920],{},[115,52922,52924],{"id":52923},"příklady","Příklady",[198,52926,52928],{"id":52927},"příklad-211-komparativní-statika-pro-rovnovážné-množství","Příklad 2.11 — komparativní statika pro rovnovážné množství",[4124,52930,52931],{},[724,52932,52933,52936,52937,47961,52960,52983,52984,1343,53004,1343,53021,1343,53038,53055,53056,53132,53133,53150,53151,53164],{},[883,52934,52935],{},"!example"," Zadání\nJsou dány poptávka ",[883,52938,52940],{"className":52939},[886],[888,52941,52942],{"xmlns":890},[892,52943,52944,52958],{},[895,52945,52946,52948,52950,52952,52954,52956],{},[898,52947,1727],{},[1688,52949,1690],{},[898,52951,207],{},[898,52953,1872],{},[1688,52955,1696],{},[898,52957,1918],{},[902,52959,37300],{"encoding":904},[883,52961,52963],{"className":52962},[886],[888,52964,52965],{"xmlns":890},[892,52966,52967,52981],{},[895,52968,52969,52971,52973,52975,52977,52979],{},[898,52970,1727],{},[1688,52972,1690],{},[898,52974,2031],{},[898,52976,1872],{},[1688,52978,1696],{},[898,52980,2073],{},[902,52982,40482],{"encoding":904}," s hodnotami ",[883,52985,52987],{"className":52986},[886],[888,52988,52989],{"xmlns":890},[892,52990,52991,53001],{},[895,52992,52993,52995,52997,52999],{},[898,52994,207],{},[1688,52996,1690],{},[1688,52998,1954],{},[1793,53000,2131],{},[902,53002,53003],{"encoding":904},"a = -3",[883,53005,53007],{"className":53006},[886],[888,53008,53009],{"xmlns":890},[892,53010,53011,53019],{},[895,53012,53013,53015,53017],{},[898,53014,1918],{},[1688,53016,1690],{},[1793,53018,5467],{},[902,53020,48884],{"encoding":904},[883,53022,53024],{"className":53023},[886],[888,53025,53026],{"xmlns":890},[892,53027,53028,53036],{},[895,53029,53030,53032,53034],{},[898,53031,2031],{},[1688,53033,1690],{},[1793,53035,5265],{},[902,53037,48902],{"encoding":904},[883,53039,53041],{"className":53040},[886],[888,53042,53043],{"xmlns":890},[892,53044,53045,53053],{},[895,53046,53047,53049,53051],{},[898,53048,2073],{},[1688,53050,1690],{},[1793,53052,3121],{},[902,53054,48920],{"encoding":904},".\nRovnovážné množství:\n",[883,53057,53059],{"className":53058},[886],[888,53060,53061],{"xmlns":890},[892,53062,53063,53129],{},[895,53064,53065,53071,53073,53091,53093,53117,53119,53125,53127],{},[1850,53066,53067,53069],{},[898,53068,1872],{},[898,53070,4509],{},[1688,53072,1690],{},[1781,53074,53075,53083],{},[895,53076,53077,53079,53081],{},[898,53078,1918],{},[1688,53080,1954],{},[898,53082,2073],{},[895,53084,53085,53087,53089],{},[898,53086,2031],{},[1688,53088,1954],{},[898,53090,207],{},[1688,53092,1690],{},[1781,53094,53095,53103],{},[895,53096,53097,53099,53101],{},[1793,53098,5467],{},[1688,53100,1954],{},[1793,53102,3121],{},[895,53104,53105,53107,53109,53111,53113,53115],{},[1793,53106,5265],{},[1688,53108,1954],{},[1688,53110,2066],{"stretchy":2065},[1688,53112,1954],{},[1793,53114,2131],{},[1688,53116,2076],{"stretchy":2065},[1688,53118,1690],{},[1781,53120,53121,53123],{},[1793,53122,38259],{},[1793,53124,44646],{},[1688,53126,6156],{},[1793,53128,44651],{},[902,53130,53131],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\doteq 8{,}571.","\nZjistěte změnu ",[883,53134,53136],{"className":53135},[886],[888,53137,53138],{"xmlns":890},[892,53139,53140,53148],{},[895,53141,53142],{},[1850,53143,53144,53146],{},[898,53145,1872],{},[898,53147,4509],{},[902,53149,42643],{"encoding":904}," (a) při změně samotného parametru ",[883,53152,53154],{"className":53153},[886],[888,53155,53156],{"xmlns":890},[892,53157,53158,53162],{},[895,53159,53160],{},[898,53161,2031],{},[902,53163,2031],{"encoding":904},", (b) při současné změně všech čtyř parametrů.",[724,53166,53167],{},[38,53168,53169,53170,2194,53183,2946,53196,9548],{},"Řešení (a) — změna ",[883,53171,53173],{"className":53172},[886],[888,53174,53175],{"xmlns":890},[892,53176,53177,53181],{},[895,53178,53179],{},[898,53180,2031],{},[902,53182,2031],{"encoding":904},[883,53184,53186],{"className":53185},[886],[888,53187,53188],{"xmlns":890},[892,53189,53190,53194],{},[895,53191,53192],{},[1793,53193,5265],{},[902,53195,44686],{"encoding":904},[883,53197,53199],{"className":53198},[886],[888,53200,53201],{"xmlns":890},[892,53202,53203,53207],{},[895,53204,53205],{},[1793,53206,19562],{},[902,53208,44700],{"encoding":904},[724,53210,53211,53212,53276,53277,2965],{},"Pomocí vzorce (2.13) pro ",[883,53213,53215],{"className":53214},[886],[888,53216,53217],{"xmlns":890},[892,53218,53219,53273],{},[895,53220,53221,53241,53243,53245],{},[1777,53222,53223],{"scriptlevel":1779,"displaystyle":1732},[1781,53224,53225,53235],{},[895,53226,53227,53229],{},[898,53228,10124],{"mathvariant":1822},[1850,53230,53231,53233],{},[898,53232,1872],{},[898,53234,4509],{},[895,53236,53237,53239],{},[898,53238,10124],{"mathvariant":1822},[898,53240,2031],{},[1688,53242,1690],{},[1688,53244,1954],{},[1777,53246,53247],{"scriptlevel":1779,"displaystyle":1732},[1781,53248,53249,53257],{},[895,53250,53251,53253,53255],{},[898,53252,1918],{},[1688,53254,1954],{},[898,53256,2073],{},[895,53258,53259,53261,53263,53265,53267],{},[1688,53260,2066],{"stretchy":2065},[898,53262,2031],{},[1688,53264,1954],{},[898,53266,207],{},[1850,53268,53269,53271],{},[1688,53270,2076],{"stretchy":2065},[1793,53272,1806],{},[902,53274,53275],{"encoding":904},"\\dfrac{\\partial Q^E}{\\partial c} = -\\dfrac{b-d}{(c-a)^2}",", resp. ekvivalentně ",[883,53278,53280],{"className":53279},[886],[888,53281,53282],{"xmlns":890},[892,53283,53284,53306],{},[895,53285,53286,53288],{},[1688,53287,1954],{},[1777,53289,53290],{"scriptlevel":1779,"displaystyle":1732},[1781,53291,53292,53298],{},[1850,53293,53294,53296],{},[898,53295,1872],{},[898,53297,4509],{},[895,53299,53300,53302,53304],{},[898,53301,2031],{},[1688,53303,1954],{},[898,53305,207],{},[902,53307,53308],{"encoding":904},"-\\dfrac{Q^E}{c-a}",[883,53310,53312],{"className":53311},[886],[888,53313,53314],{"xmlns":890,"display":28306},[892,53315,53316,53372],{},[895,53317,53318,53320,53326,53328,53330,53346,53348,53350,53352,53354,53356,53362,53364,53366,53368,53370],{},[898,53319,2073],{},[1850,53321,53322,53324],{},[898,53323,1872],{},[898,53325,4509],{},[1688,53327,1690],{},[1688,53329,1954],{},[1781,53331,53332,53338],{},[1850,53333,53334,53336],{},[898,53335,1872],{},[898,53337,4509],{},[895,53339,53340,53342,53344],{},[898,53341,2031],{},[1688,53343,1954],{},[898,53345,207],{},[2041,53347,2043],{},[898,53349,2073],{},[898,53351,2031],{},[1688,53353,1690],{},[1688,53355,1954],{},[1781,53357,53358,53360],{},[1793,53359,44814],{},[1793,53361,44646],{},[1688,53363,3434],{},[1793,53365,3053],{},[1688,53367,6156],{},[1688,53369,1954],{},[1793,53371,44786],{},[902,53373,53374],{"encoding":904},"dQ^E = -\\frac{Q^E}{c - a}\\,dc = -\\frac{8{,}571}{3{,}5}\\cdot 0{,}1 \\doteq -0{,}245.",[724,53376,53377],{},"Nové rovnovážné množství:",[883,53379,53381],{"className":53380},[886],[888,53382,53383],{"xmlns":890,"display":28306},[892,53384,53385,53408],{},[895,53386,53387,53395,53397,53399,53401,53403,53405],{},[1814,53388,53389,53391,53393],{},[898,53390,1872],{},[1793,53392,1795],{},[898,53394,4509],{},[1688,53396,2991],{},[1793,53398,44814],{},[1688,53400,1954],{},[1793,53402,44819],{},[1688,53404,1690],{},[1793,53406,53407],{},"8,326.",[902,53409,53410],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326.",[724,53412,53413,2170,53416,1343,53443,1343,53465,1343,53487,5845,53509,1343,53528,1343,53549,1343,53568,2263],{},[38,53414,53415],{},"Řešení (b) — současná změna všech parametrů:",[883,53417,53419],{"className":53418},[886],[888,53420,53421],{"xmlns":890},[892,53422,53423,53440],{},[895,53424,53425,53427,53429,53431,53433,53435,53437],{},[898,53426,207],{},[1688,53428,2965],{},[1688,53430,1954],{},[1793,53432,2131],{},[1688,53434,3380],{},[1688,53436,1954],{},[1793,53438,53439],{},"2,5",[902,53441,53442],{"encoding":904},"a: -3 \\to -2{,}5",[883,53444,53446],{"className":53445},[886],[888,53447,53448],{"xmlns":890},[892,53449,53450,53462],{},[895,53451,53452,53454,53456,53458,53460],{},[898,53453,1918],{},[1688,53455,2965],{},[1793,53457,5467],{},[1688,53459,3380],{},[1793,53461,15285],{},[902,53463,53464],{"encoding":904},"b: 40 \\to 35",[883,53466,53468],{"className":53467},[886],[888,53469,53470],{"xmlns":890},[892,53471,53472,53484],{},[895,53473,53474,53476,53478,53480,53482],{},[898,53475,2031],{},[1688,53477,2965],{},[1793,53479,5265],{},[1688,53481,3380],{},[1793,53483,19562],{},[902,53485,53486],{"encoding":904},"c: 0{,}5 \\to 0{,}6",[883,53488,53490],{"className":53489},[886],[888,53491,53492],{"xmlns":890},[892,53493,53494,53506],{},[895,53495,53496,53498,53500,53502,53504],{},[898,53497,2073],{},[1688,53499,2965],{},[1793,53501,3121],{},[1688,53503,3380],{},[1793,53505,3162],{},[902,53507,53508],{"encoding":904},"d: 10 \\to 11",[883,53510,53512],{"className":53511},[886],[888,53513,53514],{"xmlns":890},[892,53515,53516,53526],{},[895,53517,53518,53520,53522,53524],{},[898,53519,2073],{},[898,53521,207],{},[1688,53523,1690],{},[1793,53525,5265],{},[902,53527,44852],{"encoding":904},[883,53529,53531],{"className":53530},[886],[888,53532,53533],{"xmlns":890},[892,53534,53535,53547],{},[895,53536,53537,53539,53541,53543,53545],{},[898,53538,2073],{},[898,53540,1918],{},[1688,53542,1690],{},[1688,53544,1954],{},[1793,53546,2501],{},[902,53548,44874],{"encoding":904},[883,53550,53552],{"className":53551},[886],[888,53553,53554],{"xmlns":890},[892,53555,53556,53566],{},[895,53557,53558,53560,53562,53564],{},[898,53559,2073],{},[898,53561,2031],{},[1688,53563,1690],{},[1793,53565,3053],{},[902,53567,44894],{"encoding":904},[883,53569,53571],{"className":53570},[886],[888,53572,53573],{"xmlns":890},[892,53574,53575,53585],{},[895,53576,53577,53579,53581,53583],{},[898,53578,2073],{},[898,53580,2073],{},[1688,53582,1690],{},[1793,53584,1795],{},[902,53586,44914],{"encoding":904},[724,53588,53589,53590,53648],{},"Totální diferenciál ",[883,53591,53593],{"className":53592},[886],[888,53594,53595],{"xmlns":890},[892,53596,53597,53645],{},[895,53598,53599,53605,53607,53609,53611,53613,53615,53617,53619,53621,53623,53625],{},[1850,53600,53601,53603],{},[898,53602,1872],{},[898,53604,4509],{},[1688,53606,2066],{"stretchy":2065},[898,53608,207],{},[1688,53610,1733],{"separator":1732},[898,53612,1918],{},[1688,53614,1733],{"separator":1732},[898,53616,2031],{},[1688,53618,1733],{"separator":1732},[898,53620,2073],{},[1688,53622,2076],{"stretchy":2065},[1688,53624,1690],{},[1777,53626,53627],{"scriptlevel":1779,"displaystyle":1732},[1781,53628,53629,53637],{},[895,53630,53631,53633,53635],{},[898,53632,1918],{},[1688,53634,1954],{},[898,53636,2073],{},[895,53638,53639,53641,53643],{},[898,53640,2031],{},[1688,53642,1954],{},[898,53644,207],{},[902,53646,53647],{"encoding":904},"Q^E(a, b, c, d) = \\dfrac{b - d}{c - a}"," podle (2.11) a (2.12):",[883,53650,53652],{"className":53651},[886],[888,53653,53654],{"xmlns":890,"display":28306},[892,53655,53656,53776],{},[895,53657,53658,53660,53666,53668,53694,53696,53698,53700,53702,53714,53716,53718,53720,53722,53748,53750,53752,53754,53756,53768,53770,53772,53774],{},[898,53659,2073],{},[1850,53661,53662,53664],{},[898,53663,1872],{},[898,53665,4509],{},[1688,53667,1690],{},[1781,53669,53670,53678],{},[895,53671,53672,53674,53676],{},[898,53673,1918],{},[1688,53675,1954],{},[898,53677,2073],{},[895,53679,53680,53682,53684,53686,53688],{},[1688,53681,2066],{"stretchy":2065},[898,53683,2031],{},[1688,53685,1954],{},[898,53687,207],{},[1850,53689,53690,53692],{},[1688,53691,2076],{"stretchy":2065},[1793,53693,1806],{},[2041,53695,2043],{},[898,53697,2073],{},[898,53699,207],{},[1688,53701,1696],{},[1781,53703,53704,53706],{},[1793,53705,1795],{},[895,53707,53708,53710,53712],{},[898,53709,2031],{},[1688,53711,1954],{},[898,53713,207],{},[2041,53715,2043],{},[898,53717,2073],{},[898,53719,1918],{},[1688,53721,1954],{},[1781,53723,53724,53732],{},[895,53725,53726,53728,53730],{},[898,53727,1918],{},[1688,53729,1954],{},[898,53731,2073],{},[895,53733,53734,53736,53738,53740,53742],{},[1688,53735,2066],{"stretchy":2065},[898,53737,2031],{},[1688,53739,1954],{},[898,53741,207],{},[1850,53743,53744,53746],{},[1688,53745,2076],{"stretchy":2065},[1793,53747,1806],{},[2041,53749,2043],{},[898,53751,2073],{},[898,53753,2031],{},[1688,53755,1954],{},[1781,53757,53758,53760],{},[1793,53759,1795],{},[895,53761,53762,53764,53766],{},[898,53763,2031],{},[1688,53765,1954],{},[898,53767,207],{},[2041,53769,2043],{},[898,53771,2073],{},[898,53773,2073],{},[898,53775,2263],{"mathvariant":1822},[902,53777,53778],{"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.",[724,53780,53781,53782,1343,53804,1343,53835,3408],{},"Dosazením číselných hodnot (",[883,53783,53785],{"className":53784},[886],[888,53786,53787],{"xmlns":890},[892,53788,53789,53801],{},[895,53790,53791,53793,53795,53797,53799],{},[898,53792,2031],{},[1688,53794,1954],{},[898,53796,207],{},[1688,53798,1690],{},[1793,53800,44646],{},[902,53802,53803],{"encoding":904},"c - a = 3{,}5",[883,53805,53807],{"className":53806},[886],[888,53808,53809],{"xmlns":890},[892,53810,53811,53832],{},[895,53812,53813,53815,53817,53819,53821,53827,53829],{},[1688,53814,2066],{"stretchy":2065},[898,53816,2031],{},[1688,53818,1954],{},[898,53820,207],{},[1850,53822,53823,53825],{},[1688,53824,2076],{"stretchy":2065},[1793,53826,1806],{},[1688,53828,1690],{},[1793,53830,53831],{},"12,25",[902,53833,53834],{"encoding":904},"(c-a)^2 = 12{,}25",[883,53836,53838],{"className":53837},[886],[888,53839,53840],{"xmlns":890},[892,53841,53842,53854],{},[895,53843,53844,53846,53848,53850,53852],{},[898,53845,1918],{},[1688,53847,1954],{},[898,53849,2073],{},[1688,53851,1690],{},[1793,53853,38259],{},[902,53855,53856],{"encoding":904},"b - d = 30",[883,53858,53860],{"className":53859},[886],[888,53861,53862],{"xmlns":890,"display":28306},[892,53863,53864,53965],{},[895,53865,53866,53868,53874,53876,53884,53886,53888,53890,53892,53900,53902,53904,53906,53908,53910,53918,53920,53922,53924,53926,53934,53936,53938,53940,53942,53945,53947,53950,53952,53954,53956,53959,53961,53963],{},[898,53867,2073],{},[1850,53869,53870,53872],{},[898,53871,1872],{},[898,53873,4509],{},[1688,53875,2991],{},[1777,53877,53878],{"scriptlevel":1779,"displaystyle":2065},[1781,53879,53880,53882],{},[1793,53881,38259],{},[1793,53883,53831],{},[1688,53885,2066],{"stretchy":2065},[1793,53887,5265],{},[1688,53889,2076],{"stretchy":2065},[1688,53891,1696],{},[1777,53893,53894],{"scriptlevel":1779,"displaystyle":2065},[1781,53895,53896,53898],{},[1793,53897,1795],{},[1793,53899,44646],{},[1688,53901,2066],{"stretchy":2065},[1688,53903,1954],{},[1793,53905,2501],{},[1688,53907,2076],{"stretchy":2065},[1688,53909,1954],{},[1777,53911,53912],{"scriptlevel":1779,"displaystyle":2065},[1781,53913,53914,53916],{},[1793,53915,38259],{},[1793,53917,53831],{},[1688,53919,2066],{"stretchy":2065},[1793,53921,3053],{},[1688,53923,2076],{"stretchy":2065},[1688,53925,1954],{},[1777,53927,53928],{"scriptlevel":1779,"displaystyle":2065},[1781,53929,53930,53932],{},[1793,53931,1795],{},[1793,53933,44646],{},[1688,53935,2066],{"stretchy":2065},[1793,53937,1795],{},[1688,53939,2076],{"stretchy":2065},[1688,53941,6156],{},[1793,53943,53944],{},"1,224",[1688,53946,1954],{},[1793,53948,53949],{},"1,429",[1688,53951,1954],{},[1793,53953,44819],{},[1688,53955,1954],{},[1793,53957,53958],{},"0,286",[1688,53960,6156],{},[1688,53962,1954],{},[1793,53964,45065],{},[902,53966,53967],{"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.",[724,53969,30305,53970,2263],{},[883,53971,53973],{"className":53972},[886],[888,53974,53975],{"xmlns":890},[892,53976,53977,53999],{},[895,53978,53979,53987,53989,53991,53993,53995,53997],{},[1814,53980,53981,53983,53985],{},[898,53982,1872],{},[1793,53984,1795],{},[898,53986,4509],{},[1688,53988,2991],{},[1793,53990,44814],{},[1688,53992,1954],{},[1793,53994,45096],{},[1688,53996,6156],{},[1793,53998,45101],{},[902,54000,54001],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 \\doteq 7{,}836",[4124,54003,54004],{},[724,54005,54006,54008,54009,54030,54031,54057,54058,54061,54062,54158,54159,54182,54183,54199],{},[883,54007,4668],{}," Pozn. k přepisu učebnice\nV původním skenu přednášky byla u části (b) uvedena hodnota ",[883,54010,54012],{"className":54011},[886],[888,54013,54014],{"xmlns":890},[892,54015,54016,54028],{},[895,54017,54018,54020,54022,54024,54026],{},[898,54019,3147],{"mathvariant":1822},[898,54021,1872],{},[1688,54023,2991],{},[1688,54025,1954],{},[1793,54027,45131],{},[902,54029,45134],{"encoding":904},", což neodpovídá součtu dílčích derivací při daných přírůstcích. Podle vlastního přepočtu vychází ",[883,54032,54034],{"className":54033},[886],[888,54035,54036],{"xmlns":890},[892,54037,54038,54054],{},[895,54039,54040,54042,54048,54050,54052],{},[898,54041,2073],{},[1850,54043,54044,54046],{},[898,54045,1872],{},[898,54047,4509],{},[1688,54049,6156],{},[1688,54051,1954],{},[1793,54053,45096],{},[902,54055,54056],{"encoding":904},"dQ^E \\doteq -0{,}735",". Totální diferenciál je navíc pouze ",[38,54059,54060],{},"lineární aproximací","; přesná změna zjištěná ze změněného vzorce\n",[883,54063,54065],{"className":54064},[886],[888,54066,54067],{"xmlns":890},[892,54068,54069,54155],{},[895,54070,54071,54079,54081,54115,54117,54141,54143,54150,54152],{},[1814,54072,54073,54075,54077],{},[898,54074,1872],{},[1793,54076,1795],{},[898,54078,4509],{},[1688,54080,1690],{},[1781,54082,54083,54099],{},[895,54084,54085,54091,54093],{},[1850,54086,54087,54089],{},[898,54088,1918],{},[1688,54090,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,54092,1954],{},[1850,54094,54095,54097],{},[898,54096,2073],{},[1688,54098,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[895,54100,54101,54107,54109],{},[1850,54102,54103,54105],{},[898,54104,2031],{},[1688,54106,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,54108,1954],{},[1850,54110,54111,54113],{},[898,54112,207],{},[1688,54114,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,54116,1690],{},[1781,54118,54119,54127],{},[895,54120,54121,54123,54125],{},[1793,54122,15285],{},[1688,54124,1954],{},[1793,54126,3162],{},[895,54128,54129,54131,54133,54135,54137,54139],{},[1793,54130,19562],{},[1688,54132,1954],{},[1688,54134,2066],{"stretchy":2065},[1688,54136,1954],{},[1793,54138,53439],{},[1688,54140,2076],{"stretchy":2065},[1688,54142,1690],{},[1781,54144,54145,54147],{},[1793,54146,42040],{},[1793,54148,54149],{},"3,1",[1688,54151,6156],{},[1793,54153,54154],{},"7,742",[902,54156,54157],{"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 ",[883,54160,54162],{"className":54161},[886],[888,54163,54164],{"xmlns":890},[892,54165,54166,54179],{},[895,54167,54168,54170,54172,54174,54176],{},[898,54169,3147],{"mathvariant":1822},[898,54171,1872],{},[1688,54173,6156],{},[1688,54175,1954],{},[1793,54177,54178],{},"0,829",[902,54180,54181],{"encoding":904},"\\Delta Q \\doteq -0{,}829"," — dobře konzistentní s diferenciálem. Hodnota ",[883,54184,54186],{"className":54185},[886],[888,54187,54188],{"xmlns":890},[892,54189,54190,54196],{},[895,54191,54192,54194],{},[1688,54193,1954],{},[1793,54195,45131],{},[902,54197,54198],{"encoding":904},"-2{,}69"," je tedy pravděpodobně chyba v zápisu.",[724,54201,54202],{},[614,54203,54204,54205,54218],{},"Příklad 2.11 je primárně o multiplikátorech pro ",[883,54206,54208],{"className":54207},[886],[888,54209,54210],{"xmlns":890},[892,54211,54212,54216],{},[895,54213,54214],{},[898,54215,1872],{},[902,54217,1872],{"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.",[198,54220,54222,54223],{"id":54221},"příklad-213-numerický-výpočet-psps","Příklad 2.13 — numerický výpočet ",[883,54224,54226],{"className":54225},[886],[888,54227,54228],{"xmlns":890},[892,54229,54230,54236],{},[895,54231,54232,54234],{},[898,54233,1727],{},[898,54235,1740],{},[902,54237,45209],{"encoding":904},[4124,54239,54240],{},[724,54241,54242,54244,54245,54279,54280,54302],{},[883,54243,52935],{}," Zadání\nPro nabídku ",[883,54246,54248],{"className":54247},[886],[888,54249,54250],{"xmlns":890},[892,54251,54252,54276],{},[895,54253,54254,54256,54258,54260,54262,54264,54266,54268,54270,54272,54274],{},[898,54255,1727],{},[1688,54257,1690],{},[898,54259,1740],{},[1688,54261,2066],{"stretchy":2065},[898,54263,1872],{},[1688,54265,2076],{"stretchy":2065},[1688,54267,1690],{},[1793,54269,3121],{},[1688,54271,1696],{},[1793,54273,1806],{},[898,54275,1872],{},[902,54277,54278],{"encoding":904},"P = S(Q) = 10 + 2Q"," a množství ",[883,54281,54283],{"className":54282},[886],[888,54284,54285],{"xmlns":890},[892,54286,54287,54299],{},[895,54288,54289,54295,54297],{},[1788,54290,54291,54293],{},[898,54292,1872],{},[1793,54294,1779],{},[1688,54296,1690],{},[1793,54298,3121],{},[902,54300,54301],{"encoding":904},"Q_0 = 10"," vypočítejte přebytek výrobce.",[724,54304,54305],{},[38,54306,23011],{},[724,54308,54309],{},"Odpovídající cena:",[883,54311,54313],{"className":54312},[886],[888,54314,54315],{"xmlns":890,"display":28306},[892,54316,54317,54352],{},[895,54318,54319,54325,54327,54329,54331,54333,54335,54337,54339,54341,54343,54345,54347,54349],{},[1788,54320,54321,54323],{},[898,54322,1727],{},[1793,54324,1779],{},[1688,54326,1690],{},[898,54328,1740],{},[1688,54330,2066],{"stretchy":2065},[1793,54332,3121],{},[1688,54334,2076],{"stretchy":2065},[1688,54336,1690],{},[1793,54338,3121],{},[1688,54340,1696],{},[1793,54342,1806],{},[1688,54344,3434],{},[1793,54346,3121],{},[1688,54348,1690],{},[1793,54350,54351],{},"30.",[902,54353,54354],{"encoding":904},"P_0 = S(10) = 10 + 2\\cdot 10 = 30.",[724,54356,54357],{},"Dle vzorce (2.15):",[883,54359,54361],{"className":54360},[886],[888,54362,54363],{"xmlns":890,"display":28306},[892,54364,54365,54473],{},[895,54366,54367,54369,54371,54373,54375,54377,54379,54385,54391,54393,54401,54403,54405,54407,54409,54411,54413,54415,54417,54419,54421,54423,54425,54427,54429,54432,54434,54436,54438,54444,54452,54454,54456,54458,54460,54462,54464,54466,54468,54470],{},[898,54368,1727],{},[898,54370,1740],{},[1688,54372,2066],{"stretchy":2065},[1793,54374,3121],{},[1688,54376,2076],{"stretchy":2065},[1688,54378,1690],{},[1788,54380,54381,54383],{},[898,54382,1727],{},[1793,54384,1779],{},[1788,54386,54387,54389],{},[898,54388,1872],{},[1793,54390,1779],{},[1688,54392,1954],{},[1814,54394,54395,54397,54399],{},[1688,54396,11421],{},[1793,54398,1779],{},[1793,54400,3121],{},[1688,54402,2066],{"stretchy":2065},[1793,54404,3121],{},[1688,54406,1696],{},[1793,54408,1806],{},[898,54410,1872],{},[1688,54412,2076],{"stretchy":2065},[2041,54414,2043],{},[898,54416,2073],{},[898,54418,1872],{},[1688,54420,1690],{},[1793,54422,3121],{},[1688,54424,3434],{},[1793,54426,38259],{},[1688,54428,1954],{},[1688,54430,2748],{"fence":2065,"stretchy":1732,"minsize":54431,"maxsize":54431},"1.8em",[1793,54433,3121],{},[898,54435,1872],{},[1688,54437,1696],{},[1850,54439,54440,54442],{},[898,54441,1872],{},[1793,54443,1806],{},[1814,54445,54446,54448,54450],{},[1688,54447,2763],{"fence":2065,"stretchy":1732,"minsize":54431,"maxsize":54431},[1793,54449,1779],{},[1793,54451,3121],{},[1688,54453,1690],{},[1793,54455,30321],{},[1688,54457,1954],{},[1688,54459,2066],{"stretchy":2065},[1793,54461,3347],{},[1688,54463,1696],{},[1793,54465,3347],{},[1688,54467,2076],{"stretchy":2065},[1688,54469,1690],{},[1793,54471,54472],{},"100.",[902,54474,54475],{"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.",[724,54477,54478,54479,54500,54501,54521],{},"Přebytek výrobce při množství ",[883,54480,54482],{"className":54481},[886],[888,54483,54484],{"xmlns":890},[892,54485,54486,54498],{},[895,54487,54488,54494,54496],{},[1788,54489,54490,54492],{},[898,54491,1872],{},[1793,54493,1779],{},[1688,54495,1690],{},[1793,54497,3121],{},[902,54499,54301],{"encoding":904}," je tedy ",[883,54502,54504],{"className":54503},[886],[888,54505,54506],{"xmlns":890},[892,54507,54508,54518],{},[895,54509,54510,54512,54514,54516],{},[898,54511,1727],{},[898,54513,1740],{},[1688,54515,1690],{},[1793,54517,3347],{},[902,54519,54520],{"encoding":904},"PS = 100"," (peněžních jednotek).",[37210,54523],{},[115,54525,54527],{"id":54526},"cheat-sheet","Cheat sheet",[16,54529,54530,54543],{},[19,54531,54532],{},[22,54533,54534,54537,54540],{},[25,54535,54536],{},"Veličina",[25,54538,54539],{},"Vzorec",[25,54541,54542],{},"Geometrie",[30,54544,54545,54663,54777,54845],{},[22,54546,54547,54575,54631],{},[35,54548,54549],{},[883,54550,54552],{"className":54551},[886],[888,54553,54554],{"xmlns":890},[892,54555,54556,54572],{},[895,54557,54558,54560,54562,54564,54570],{},[898,54559,1693],{},[898,54561,1740],{},[1688,54563,2066],{"stretchy":2065},[1788,54565,54566,54568],{},[898,54567,1872],{},[1793,54569,1779],{},[1688,54571,2076],{"stretchy":2065},[902,54573,54574],{"encoding":904},"CS(Q_0)",[35,54576,54577],{},[883,54578,54580],{"className":54579},[886],[888,54581,54582],{"xmlns":890},[892,54583,54584,54628],{},[895,54585,54586],{},[1777,54587,54588,54600,54602,54604,54606,54608,54610,54612,54614,54616,54622],{"scriptlevel":1779,"displaystyle":1732},[1814,54589,54590,54592,54594],{},[1688,54591,11421],{},[1793,54593,1779],{},[1788,54595,54596,54598],{},[898,54597,1872],{},[1793,54599,1779],{},[898,54601,4440],{},[1688,54603,2066],{"stretchy":2065},[898,54605,1872],{},[1688,54607,2076],{"stretchy":2065},[2041,54609,2043],{},[898,54611,2073],{},[898,54613,1872],{},[1688,54615,1954],{},[1788,54617,54618,54620],{},[898,54619,1727],{},[1793,54621,1779],{},[1788,54623,54624,54626],{},[898,54625,1872],{},[1793,54627,1779],{},[902,54629,54630],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0",[35,54632,54633,54634,54637,54638,54641,54642],{},"plocha ",[38,54635,54636],{},"pod"," křivkou poptávky, ",[38,54639,54640],{},"nad"," čárou ",[883,54643,54645],{"className":54644},[886],[888,54646,54647],{"xmlns":890},[892,54648,54649,54661],{},[895,54650,54651,54653,54655],{},[898,54652,1727],{},[1688,54654,1690],{},[1788,54656,54657,54659],{},[898,54658,1727],{},[1793,54660,1779],{},[902,54662,51917],{"encoding":904},[22,54664,54665,54693,54749],{},[35,54666,54667],{},[883,54668,54670],{"className":54669},[886],[888,54671,54672],{"xmlns":890},[892,54673,54674,54690],{},[895,54675,54676,54678,54680,54682,54688],{},[898,54677,1727],{},[898,54679,1740],{},[1688,54681,2066],{"stretchy":2065},[1788,54683,54684,54686],{},[898,54685,1872],{},[1793,54687,1779],{},[1688,54689,2076],{"stretchy":2065},[902,54691,54692],{"encoding":904},"PS(Q_0)",[35,54694,54695],{},[883,54696,54698],{"className":54697},[886],[888,54699,54700],{"xmlns":890},[892,54701,54702,54746],{},[895,54703,54704],{},[1777,54705,54706,54712,54718,54720,54732,54734,54736,54738,54740,54742,54744],{"scriptlevel":1779,"displaystyle":1732},[1788,54707,54708,54710],{},[898,54709,1727],{},[1793,54711,1779],{},[1788,54713,54714,54716],{},[898,54715,1872],{},[1793,54717,1779],{},[1688,54719,1954],{},[1814,54721,54722,54724,54726],{},[1688,54723,11421],{},[1793,54725,1779],{},[1788,54727,54728,54730],{},[898,54729,1872],{},[1793,54731,1779],{},[898,54733,1740],{},[1688,54735,2066],{"stretchy":2065},[898,54737,1872],{},[1688,54739,2076],{"stretchy":2065},[2041,54741,2043],{},[898,54743,2073],{},[898,54745,1872],{},[902,54747,54748],{"encoding":904},"\\displaystyle P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ",[35,54750,54633,54751,54753,54754,54641,54756],{},[38,54752,54640],{}," křivkou nabídky, ",[38,54755,54636],{},[883,54757,54759],{"className":54758},[886],[888,54760,54761],{"xmlns":890},[892,54762,54763,54775],{},[895,54764,54765,54767,54769],{},[898,54766,1727],{},[1688,54768,1690],{},[1788,54770,54771,54773],{},[898,54772,1727],{},[1793,54774,1779],{},[902,54776,51917],{"encoding":904},[22,54778,54779,54782,54809],{},[35,54780,54781],{},"Výdaje \u002F tržby",[35,54783,54784],{},[883,54785,54787],{"className":54786},[886],[888,54788,54789],{"xmlns":890},[892,54790,54791,54807],{},[895,54792,54793,54799,54801],{},[1788,54794,54795,54797],{},[898,54796,1727],{},[1793,54798,1779],{},[1688,54800,3434],{},[1788,54802,54803,54805],{},[898,54804,1872],{},[1793,54806,1779],{},[902,54808,52777],{"encoding":904},[35,54810,54811,54812],{},"obdélník ",[883,54813,54815],{"className":54814},[886],[888,54816,54817],{"xmlns":890},[892,54818,54819,54843],{},[895,54820,54821,54823,54825,54831,54833,54835,54837],{},[1793,54822,1779],{},[2041,54824,2043],{},[1788,54826,54827,54829],{},[898,54828,1872],{},[1793,54830,1779],{},[2041,54832,2043],{},[898,54834,4512],{},[2041,54836,2043],{},[1788,54838,54839,54841],{},[898,54840,1727],{},[1793,54842,1779],{},[902,54844,51397],{"encoding":904},[22,54846,54847,54850,54873],{},[35,54848,54849],{},"Celkový přebytek",[35,54851,54852],{},[883,54853,54855],{"className":54854},[886],[888,54856,54857],{"xmlns":890},[892,54858,54859,54871],{},[895,54860,54861,54863,54865,54867,54869],{},[898,54862,1693],{},[898,54864,1740],{},[1688,54866,1696],{},[898,54868,1727],{},[898,54870,1740],{},[902,54872,51135],{"encoding":904},[35,54874,54875],{},"součet obou ploch v rovnováze",[37210,54877],{},[115,54879,15967],{"id":15966},[120,54881,54882,54904,54926,54970,55014,55077,55105],{},[123,54883,54884,10277,54886,1343,54901,54903],{},[38,54885,45174],{},[883,54887,54889],{"className":54888},[886],[888,54890,54891],{"xmlns":890},[892,54892,54893,54899],{},[895,54894,54895,54897],{},[898,54896,1693],{},[898,54898,1740],{},[902,54900,45190],{"encoding":904},[614,54902,45228],{},") — rozdíl mezi ochotou platit a skutečnou platbou, vzorec (2.14).",[123,54905,54906,10277,54908,1343,54923,54925],{},[38,54907,45321],{},[883,54909,54911],{"className":54910},[886],[888,54912,54913],{"xmlns":890},[892,54914,54915,54921],{},[895,54916,54917,54919],{},[898,54918,1727],{},[898,54920,1740],{},[902,54922,45209],{"encoding":904},[614,54924,45324],{},") — rozdíl mezi tržbou a minimální cenou dle nabídky, vzorec (2.15).",[123,54927,54928,7271,54931,2263],{},[38,54929,54930],{},"Ochota platit",[883,54932,54934],{"className":54933},[886],[888,54935,54936],{"xmlns":890},[892,54937,54938,54968],{},[895,54939,54940],{},[1777,54941,54942,54954,54956,54958,54960,54962,54964,54966],{"scriptlevel":1779,"displaystyle":1732},[1814,54943,54944,54946,54948],{},[1688,54945,11421],{},[1793,54947,1779],{},[1788,54949,54950,54952],{},[898,54951,1872],{},[1793,54953,1779],{},[898,54955,4440],{},[1688,54957,2066],{"stretchy":2065},[898,54959,1872],{},[1688,54961,2076],{"stretchy":2065},[2041,54963,2043],{},[898,54965,2073],{},[898,54967,1872],{},[902,54969,51765],{"encoding":904},[123,54971,54972,7271,54975,2263],{},[38,54973,54974],{},"Minimální cena výrobce",[883,54976,54978],{"className":54977},[886],[888,54979,54980],{"xmlns":890},[892,54981,54982,55012],{},[895,54983,54984],{},[1777,54985,54986,54998,55000,55002,55004,55006,55008,55010],{"scriptlevel":1779,"displaystyle":1732},[1814,54987,54988,54990,54992],{},[1688,54989,11421],{},[1793,54991,1779],{},[1788,54993,54994,54996],{},[898,54995,1872],{},[1793,54997,1779],{},[898,54999,1740],{},[1688,55001,2066],{"stretchy":2065},[898,55003,1872],{},[1688,55005,2076],{"stretchy":2065},[2041,55007,2043],{},[898,55009,2073],{},[898,55011,1872],{},[902,55013,52407],{"encoding":904},[123,55015,55016,7271,55019,52908,55044,4176],{},[38,55017,55018],{},"Výdaje spotřebitele \u002F tržby výrobce",[883,55020,55022],{"className":55021},[886],[888,55023,55024],{"xmlns":890},[892,55025,55026,55042],{},[895,55027,55028,55034,55036],{},[1788,55029,55030,55032],{},[898,55031,1727],{},[1793,55033,1779],{},[2041,55035,2043],{},[1788,55037,55038,55040],{},[898,55039,1872],{},[1793,55041,1779],{},[902,55043,51843],{"encoding":904},[883,55045,55047],{"className":55046},[886],[888,55048,55049],{"xmlns":890},[892,55050,55051,55075],{},[895,55052,55053,55055,55057,55063,55065,55067,55069],{},[1793,55054,1779],{},[2041,55056,2043],{},[1788,55058,55059,55061],{},[898,55060,1872],{},[1793,55062,1779],{},[2041,55064,2043],{},[898,55066,4512],{},[2041,55068,2043],{},[1788,55070,55071,55073],{},[898,55072,1727],{},[1793,55074,1779],{},[902,55076,51397],{"encoding":904},[123,55078,55079,55082,55083,55104],{},[38,55080,55081],{},"Celkový přebytek trhu"," — součet ",[883,55084,55086],{"className":55085},[886],[888,55087,55088],{"xmlns":890},[892,55089,55090,55102],{},[895,55091,55092,55094,55096,55098,55100],{},[898,55093,1693],{},[898,55095,1740],{},[1688,55097,1696],{},[898,55099,1727],{},[898,55101,1740],{},[902,55103,51135],{"encoding":904}," v rovnovážném bodě.",[123,55106,55107,55109,55110,1343,55123,55136,55137,2263],{},[38,55108,2706],{}," — plochy ohraničené křivkami ",[883,55111,55113],{"className":55112},[886],[888,55114,55115],{"xmlns":890},[892,55116,55117,55121],{},[895,55118,55119],{},[898,55120,4440],{},[902,55122,4440],{"encoding":904},[883,55124,55126],{"className":55125},[886],[888,55127,55128],{"xmlns":890},[892,55129,55130,55134],{},[895,55131,55132],{},[898,55133,1740],{},[902,55135,1740],{"encoding":904}," a přímkou ",[883,55138,55140],{"className":55139},[886],[888,55141,55142],{"xmlns":890},[892,55143,55144,55156],{},[895,55145,55146,55148,55150],{},[898,55147,1727],{},[1688,55149,1690],{},[1788,55151,55152,55154],{},[898,55153,1727],{},[1793,55155,1779],{},[902,55157,51917],{"encoding":904},[37210,55159],{},[115,55161,55163],{"id":55162},"dopad-daně-na-přebytky-a-mrtvá-ztráta","Dopad daně na přebytky a mrtvá ztráta",[724,55165,55166,55167,55180,55181,55198],{},"Uvalení jednotkové daně ",[883,55168,55170],{"className":55169},[886],[888,55171,55172],{"xmlns":890},[892,55173,55174,55178],{},[895,55175,55176],{},[898,55177,3035],{},[902,55179,3035],{"encoding":904}," na trh posouvá rovnovážné množství pod ",[883,55182,55184],{"className":55183},[886],[888,55185,55186],{"xmlns":890},[892,55187,55188,55196],{},[895,55189,55190],{},[1850,55191,55192,55194],{},[898,55193,1872],{},[898,55195,4509],{},[902,55197,42643],{"encoding":904}," a rozkládá původní plochu přebytků na nové části.",[724,55200,55201],{},[2821,55202],{"alt":55203,"className":55204,"src":55205},"imek-prebytky-s-dani-deadweight",[210,2825],"\u002Fwiki-assets\u002Fimek-prebytky-s-dani-deadweight.jpeg",[724,55207,55208,55209,55224,55225,55240,55241,52908,55244,55268,55269,10277,55272,55275,55276,2263],{},"Přebytek spotřebitele ",[883,55210,55212],{"className":55211},[886],[888,55213,55214],{"xmlns":890},[892,55215,55216,55222],{},[895,55217,55218,55220],{},[898,55219,1693],{},[898,55221,1740],{},[902,55223,45190],{"encoding":904}," se zmenší (spotřebitelé platí víc a nakupují méně), přebytek výrobce ",[883,55226,55228],{"className":55227},[886],[888,55229,55230],{"xmlns":890},[892,55231,55232,55238],{},[895,55233,55234,55236],{},[898,55235,1727],{},[898,55237,1740],{},[902,55239,45209],{"encoding":904}," se rovněž zmenší (výrobci obdrží po odvodu méně). Stát získává ",[38,55242,55243],{},"daňový příjem",[883,55245,55247],{"className":55246},[886],[888,55248,55249],{"xmlns":890},[892,55250,55251,55265],{},[895,55252,55253,55255,55257],{},[898,55254,3035],{},[1688,55256,3434],{},[1814,55258,55259,55261,55263],{},[898,55260,1872],{},[1793,55262,1795],{},[898,55264,4509],{},[902,55266,55267],{"encoding":904},"T \\cdot Q_1^E","). Zbývající část původních přebytků — ",[38,55270,55271],{},"mrtvá ztráta",[614,55273,55274],{},"deadweight loss",", DWL) — je čistým úbytkem blahobytu, který nikdo neinkasuje, a je důsledkem transakcí, které se kvůli dani vůbec neuskuteční. Detailní rozbor viz ",[207,55277,811],{"className":55278,"dataFsResolvedFilePath":809,"href":810},[210],[37210,55280],{},[115,55282,4049],{"id":4048},[120,55284,55285,55292,55304,55311,55318],{},[123,55286,55287,2170,55289],{},[38,55288,16469],{},[207,55290,802],{"className":55291,"dataFsResolvedFilePath":800,"href":801},[210],[123,55293,55294,2170,55296,55299,55300,55303],{},[38,55295,36914],{},[207,55297,775],{"className":55298,"dataFsResolvedFilePath":773,"href":774},[210]," (určitý integrál, plocha pod křivkou), ",[207,55301,2622],{"className":55302,"dataFsResolvedFilePath":764,"href":765},[210]," (monotonie křivek)",[123,55305,55306,2170,55308],{},[38,55307,16479],{},[207,55309,4079],{"className":55310,"dataFsResolvedFilePath":827,"href":828},[210],[123,55312,55313,2170,55315],{},[38,55314,50998],{},[207,55316,51002],{"className":55317,"dataFsResolvedFilePath":745,"href":746},[210],[123,55319,55320,2170,55322],{},[38,55321,16451],{},[207,55323,16455],{"className":55324,"dataFsResolvedFilePath":2210,"href":2211},[210],{"title":641,"searchDepth":642,"depth":642,"links":55326},[55327,55328,55333,55338,55343,55344,55345,55346],{"id":51194,"depth":642,"text":1241},{"id":51538,"depth":642,"text":55329,"children":55330},"Přebytek spotřebitele (CSCS)",[55331,55332],{"id":51557,"depth":649,"text":51558},{"id":2705,"depth":649,"text":2706},{"id":52133,"depth":642,"text":55334,"children":55335},"Přebytek výrobce (PSPS)",[55336,55337],{"id":52152,"depth":649,"text":52153},{"id":52315,"depth":649,"text":2706},{"id":52923,"depth":642,"text":52924,"children":55339},[55340,55341],{"id":52927,"depth":649,"text":52928},{"id":54221,"depth":649,"text":55342},"Příklad 2.13 — numerický výpočet PSPS",{"id":54526,"depth":642,"text":54527},{"id":15966,"depth":642,"text":15967},{"id":55162,"depth":642,"text":55163},{"id":4048,"depth":642,"text":4049},{},"\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce",{"title":820,"description":641},[1138,1135],"topics\u002Fprebytek-spotrebitele-vyrobce",[1128,51064,55353,55354,12241,16487,55355,55356],"cs","ps","spotrebitel","vyrobce","FhK0gkf2tjMxSgO0-74OuedOn6U35QtJczf-f255pZs",{"id":55359,"title":55360,"body":55361,"course":1128,"courses":659,"created":9809,"description":641,"extension":661,"meta":74690,"navigation":664,"path":74691,"seo":74692,"sources":74693,"stem":74694,"tags":74695,"type":4113,"updated":677,"__hash__":74701},"topics\u002Ftopics\u002Fprijem-naklady-zisk.md","Příjem, náklady, zisk a nabídka firmy",{"type":9,"value":55362,"toc":74654},[55363,55366,55552,55554,55645,55650,55976,55980,55987,55991,56036,56103,56134,56184,56219,56223,56282,56287,56353,56471,56573,56577,56600,56678,56721,56725,56754,56821,56827,56941,56945,57025,57062,57114,57312,57376,57463,57467,57470,57549,57552,57670,57689,57754,57758,57850,57918,57959,58013,58081,58118,58122,58180,58210,58421,58493,58545,58711,58804,58839,58843,58847,58884,58949,59004,59008,59031,59120,59224,59293,59297,59394,59507,59563,59617,59675,59736,59739,59775,59840,59870,60099,60157,60191,60195,60222,60301,60415,60436,60515,60517,60625,60629,60767,61089,61093,61096,61100,61149,61153,61407,61559,61566,61639,61823,61828,62171,62175,62198,62200,62221,62280,62290,62339,62481,62555,62650,62765,62863,62981,62985,63054,63059,63171,63316,63367,63479,63521,63525,63545,63606,63633,63695,63699,63721,63790,64070,64077,64107,64114,64307,64311,64389,64394,64470,64473,64561,64637,64704,64753,64856,64929,65050,65401,65514,65616,65620,65623,65630,65633,65669,65728,65737,65886,66110,66114,66177,66356,66448,66503,66507,66563,66633,66685,66706,66787,66790,66865,66909,66913,66954,66997,67023,67027,67098,67194,67256,67308,67411,67489,67512,67541,67545,67711,67828,67900,68215,68375,68379,68430,68492,68527,68557,68657,68699,68868,68873,68969,69007,69011,69130,69431,69433,69468,69472,69476,69604,69736,70058,70246,70324,70328,70633,70746,70892,71077,71183,71415,71530,71612,71731,71829,71870,71874,71929,72073,72227,72387,72480,72674,72986,73117,73246,73250,73322,73364,73415,73417,74612,74614],[12,55364,55360],{"id":55365},"příjem-náklady-zisk-a-nabídka-firmy",[4124,55367,55368],{},[724,55369,55370,4131,55372,2170,55375,55390,55391,2170,55394,55409,55410,2170,55413,55441,55442,55464,55465,55489,55490,55512,55513,55516,55517,55533,55534,2263],{},[883,55371,4130],{},[38,55373,55374],{},"Příjem",[883,55376,55378],{"className":55377},[886],[888,55379,55380],{"xmlns":890},[892,55381,55382,55388],{},[895,55383,55384,55386],{},[898,55385,3035],{},[898,55387,4251],{},[902,55389,4351],{"encoding":904}," je to, co firma inkasuje (cena krát množství), ",[38,55392,55393],{},"náklady",[883,55395,55397],{"className":55396},[886],[888,55398,55399],{"xmlns":890},[892,55400,55401,55407],{},[895,55402,55403,55405],{},[898,55404,3035],{},[898,55406,1693],{},[902,55408,3500],{"encoding":904}," to, co vynaloží (fixní plus variabilní), a ",[38,55411,55412],{},"zisk",[883,55414,55416],{"className":55415},[886],[888,55417,55418],{"xmlns":890},[892,55419,55420,55438],{},[895,55421,55422,55424,55426,55428,55430,55432,55434,55436],{},[898,55423,1727],{},[898,55425,4251],{},[1688,55427,1690],{},[898,55429,3035],{},[898,55431,4251],{},[1688,55433,1954],{},[898,55435,3035],{},[898,55437,1693],{},[902,55439,55440],{"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: ",[883,55443,55445],{"className":55444},[886],[888,55446,55447],{"xmlns":890},[892,55448,55449,55461],{},[895,55450,55451,55453,55455,55457,55459],{},[898,55452,4512],{},[898,55454,1693],{},[1688,55456,1690],{},[898,55458,1661],{},[898,55460,1693],{},[902,55462,55463],{"encoding":904},"AC = MC"," v minimu průměrných nákladů, ",[883,55466,55468],{"className":55467},[886],[888,55469,55470],{"xmlns":890},[892,55471,55472,55486],{},[895,55473,55474,55476,55478,55480,55482,55484],{},[898,55475,4512],{},[898,55477,40579],{},[898,55479,1693],{},[1688,55481,1690],{},[898,55483,1661],{},[898,55485,1693],{},[902,55487,55488],{"encoding":904},"AVC = MC"," v minimu průměrných variabilních nákladů a ",[883,55491,55493],{"className":55492},[886],[888,55494,55495],{"xmlns":890},[892,55496,55497,55509],{},[895,55498,55499,55501,55503,55505,55507],{},[898,55500,1661],{},[898,55502,4251],{},[1688,55504,1690],{},[898,55506,1661],{},[898,55508,1693],{},[902,55510,55511],{"encoding":904},"MR = MC"," v maximu zisku. Na závěr se sestaví ",[38,55514,55515],{},"funkce nabídky firmy"," jako rostoucí část křivky ",[883,55518,55520],{"className":55519},[886],[888,55521,55522],{"xmlns":890},[892,55523,55524,55530],{},[895,55525,55526,55528],{},[898,55527,1661],{},[898,55529,1693],{},[902,55531,55532],{"encoding":904},"MC"," nad bodem minima ",[883,55535,55537],{"className":55536},[886],[888,55538,55539],{"xmlns":890},[892,55540,55541,55549],{},[895,55542,55543,55545,55547],{},[898,55544,4512],{},[898,55546,40579],{},[898,55548,1693],{},[902,55550,55551],{"encoding":904},"AVC",[115,55553,1241],{"id":51194},[724,55555,55556,55557,55560,55561,55563,55564,1343,55567,1343,55570,55572,55573,55576,55577,55580,55581,55584,55585,2194,55600,1348,55615,2194,55630,4176],{},"Kapitola 3 se zabývá dvěma základními veličinami popisujícími ekonomickou aktivitu firmy — ",[38,55558,55559],{},"příjmem"," (revenue) a ",[38,55562,55393],{}," (cost) — v jejich třech standardních podobách: celkové, průměrné a mezní. Navazuje analýzou ",[38,55565,55566],{},"zisku",[38,55568,55569],{},"bodů zvratu",[38,55571,2258],{}," a konstrukcí ",[38,55574,55575],{},"nabídkové křivky firmy",". Klíčovými matematickými nástroji jsou ",[207,55578,1145],{"className":55579,"dataFsResolvedFilePath":764,"href":765},[210]," (pro mezní veličiny) a diferenciál (pro odhad přírůstků); v několika úlohách se využívá také ",[207,55582,11382],{"className":55583,"dataFsResolvedFilePath":773,"href":774},[210]," (pro zpětnou rekonstrukci ",[883,55586,55588],{"className":55587},[886],[888,55589,55590],{"xmlns":890},[892,55591,55592,55598],{},[895,55593,55594,55596],{},[898,55595,3035],{},[898,55597,4251],{},[902,55599,4351],{"encoding":904},[883,55601,55603],{"className":55602},[886],[888,55604,55605],{"xmlns":890},[892,55606,55607,55613],{},[895,55608,55609,55611],{},[898,55610,1661],{},[898,55612,4251],{},[902,55614,6890],{"encoding":904},[883,55616,55618],{"className":55617},[886],[888,55619,55620],{"xmlns":890},[892,55621,55622,55628],{},[895,55623,55624,55626],{},[898,55625,3035],{},[898,55627,1693],{},[902,55629,3500],{"encoding":904},[883,55631,55633],{"className":55632},[886],[888,55634,55635],{"xmlns":890},[892,55636,55637,55643],{},[895,55638,55639,55641],{},[898,55640,1661],{},[898,55642,1693],{},[902,55644,55532],{"encoding":904},[724,55646,55647],{},[38,55648,55649],{},"Cílové znalosti:",[120,55651,55652,55816,55819,55822,55915,55962,55969],{},[123,55653,55654,55655,1343,55670,1343,55686,4142,55701,1343,55716,1343,55732,1343,55750,1343,55768,1343,55785,1343,55801,8681],{},"odvodit a interpretovat funkce ",[883,55656,55658],{"className":55657},[886],[888,55659,55660],{"xmlns":890},[892,55661,55662,55668],{},[895,55663,55664,55666],{},[898,55665,3035],{},[898,55667,4251],{},[902,55669,4351],{"encoding":904},[883,55671,55673],{"className":55672},[886],[888,55674,55675],{"xmlns":890},[892,55676,55677,55683],{},[895,55678,55679,55681],{},[898,55680,4512],{},[898,55682,4251],{},[902,55684,55685],{"encoding":904},"AR",[883,55687,55689],{"className":55688},[886],[888,55690,55691],{"xmlns":890},[892,55692,55693,55699],{},[895,55694,55695,55697],{},[898,55696,1661],{},[898,55698,4251],{},[902,55700,6890],{"encoding":904},[883,55702,55704],{"className":55703},[886],[888,55705,55706],{"xmlns":890},[892,55707,55708,55714],{},[895,55709,55710,55712],{},[898,55711,3035],{},[898,55713,1693],{},[902,55715,3500],{"encoding":904},[883,55717,55719],{"className":55718},[886],[888,55720,55721],{"xmlns":890},[892,55722,55723,55729],{},[895,55724,55725,55727],{},[898,55726,10688],{},[898,55728,1693],{},[902,55730,55731],{"encoding":904},"FC",[883,55733,55735],{"className":55734},[886],[888,55736,55737],{"xmlns":890},[892,55738,55739,55747],{},[895,55740,55741,55743,55745],{},[898,55742,3035],{},[898,55744,40579],{},[898,55746,1693],{},[902,55748,55749],{"encoding":904},"TVC",[883,55751,55753],{"className":55752},[886],[888,55754,55755],{"xmlns":890},[892,55756,55757,55765],{},[895,55758,55759,55761,55763],{},[898,55760,4512],{},[898,55762,10688],{},[898,55764,1693],{},[902,55766,55767],{"encoding":904},"AFC",[883,55769,55771],{"className":55770},[886],[888,55772,55773],{"xmlns":890},[892,55774,55775,55783],{},[895,55776,55777,55779,55781],{},[898,55778,4512],{},[898,55780,40579],{},[898,55782,1693],{},[902,55784,55551],{"encoding":904},[883,55786,55788],{"className":55787},[886],[888,55789,55790],{"xmlns":890},[892,55791,55792,55798],{},[895,55793,55794,55796],{},[898,55795,4512],{},[898,55797,1693],{},[902,55799,55800],{"encoding":904},"AC",[883,55802,55804],{"className":55803},[886],[888,55805,55806],{"xmlns":890},[892,55807,55808,55814],{},[895,55809,55810,55812],{},[898,55811,1661],{},[898,55813,1693],{},[902,55815,55532],{"encoding":904},[123,55817,55818],{},"porozumět vzájemným vztahům mezi průměrnou a mezní veličinou, zvláště pro lineární poptávku;",[123,55820,55821],{},"pomocí diferenciálu odhadovat změny celkových veličin;",[123,55823,55824,55825,55828,55829,42054,55871,8681],{},"osvojit si ",[38,55826,55827],{},"princip minimalizace průměrných (variabilních) nákladů"," — podmínku ",[883,55830,55832],{"className":55831},[886],[888,55833,55834],{"xmlns":890},[892,55835,55836,55868],{},[895,55837,55838,55840,55842,55844,55850,55852,55854,55856,55858,55860,55866],{},[898,55839,4512],{},[898,55841,1693],{},[1688,55843,2066],{"stretchy":2065},[1788,55845,55846,55848],{},[898,55847,1872],{},[1793,55849,1779],{},[1688,55851,2076],{"stretchy":2065},[1688,55853,1690],{},[898,55855,1661],{},[898,55857,1693],{},[1688,55859,2066],{"stretchy":2065},[1788,55861,55862,55864],{},[898,55863,1872],{},[1793,55865,1779],{},[1688,55867,2076],{"stretchy":2065},[902,55869,55870],{"encoding":904},"AC(Q_0)=MC(Q_0)",[883,55872,55874],{"className":55873},[886],[888,55875,55876],{"xmlns":890},[892,55877,55878,55912],{},[895,55879,55880,55882,55884,55886,55888,55894,55896,55898,55900,55902,55904,55910],{},[898,55881,4512],{},[898,55883,40579],{},[898,55885,1693],{},[1688,55887,2066],{"stretchy":2065},[1788,55889,55890,55892],{},[898,55891,1872],{},[1793,55893,1779],{},[1688,55895,2076],{"stretchy":2065},[1688,55897,1690],{},[898,55899,1661],{},[898,55901,1693],{},[1688,55903,2066],{"stretchy":2065},[1788,55905,55906,55908],{},[898,55907,1872],{},[1793,55909,1779],{},[1688,55911,2076],{"stretchy":2065},[902,55913,55914],{"encoding":904},"AVC(Q_0)=MC(Q_0)",[123,55916,55824,55917,55828,55920,8681],{},[38,55918,55919],{},"princip maximalizace zisku",[883,55921,55923],{"className":55922},[886],[888,55924,55925],{"xmlns":890},[892,55926,55927,55959],{},[895,55928,55929,55931,55933,55935,55941,55943,55945,55947,55949,55951,55957],{},[898,55930,1661],{},[898,55932,4251],{},[1688,55934,2066],{"stretchy":2065},[1788,55936,55937,55939],{},[898,55938,1872],{},[1793,55940,1779],{},[1688,55942,2076],{"stretchy":2065},[1688,55944,1690],{},[898,55946,1661],{},[898,55948,1693],{},[1688,55950,2066],{"stretchy":2065},[1788,55952,55953,55955],{},[898,55954,1872],{},[1793,55956,1779],{},[1688,55958,2076],{"stretchy":2065},[902,55960,55961],{"encoding":904},"MR(Q_0)=MC(Q_0)",[123,55963,55964,55965,55968],{},"stanovit ",[38,55966,55967],{},"body zvratu"," a interval zisku;",[123,55970,55971,55972,55975],{},"zkonstruovat ",[38,55973,55974],{},"funkci nabídky firmy"," na základě nákladových charakteristik.",[115,55977,55979],{"id":55978},"příjem-firmy","Příjem firmy",[724,55981,55982],{},[2821,55983],{"alt":55984,"className":55985,"src":55986},"imek-ar-mr-dvojnasobny-sklon",[210,2825],"\u002Fwiki-assets\u002Fimek-ar-mr-dvojnasobny-sklon.jpeg",[198,55988,55990],{"id":55989},"celkový-příjem","Celkový příjem",[724,55992,55993,55994,10277,56009,56012,56013,30184],{},"Celkový příjem ",[883,55995,55997],{"className":55996},[886],[888,55998,55999],{"xmlns":890},[892,56000,56001,56007],{},[895,56002,56003,56005],{},[898,56004,3035],{},[898,56006,4251],{},[902,56008,4351],{"encoding":904},[38,56010,56011],{},"total revenue",") je součin ceny a prodaného množství. Při poptávce ",[883,56014,56016],{"className":56015},[886],[888,56017,56018],{"xmlns":890},[892,56019,56020,56034],{},[895,56021,56022,56024,56026,56028,56030,56032],{},[898,56023,1727],{},[1688,56025,1690],{},[898,56027,4440],{},[1688,56029,2066],{"stretchy":2065},[898,56031,1872],{},[1688,56033,2076],{"stretchy":2065},[902,56035,4896],{"encoding":904},[883,56037,56039],{"className":56038},[886],[888,56040,56041],{"xmlns":890,"display":28306},[892,56042,56043,56100],{},[20995,56044,56045],{"width":28311},[21000,56046,56047,56049,56093,56095],{},[21003,56048],{"width":28316},[21003,56050,56051],{},[895,56052,56053,56055,56057,56059,56061,56063,56065,56067,56069,56071,56073,56075,56077,56079,56081,56083,56085,56087,56089,56091],{},[898,56054,3035],{},[898,56056,4251],{},[1688,56058,1690],{},[898,56060,3035],{},[898,56062,4251],{},[1688,56064,2066],{"stretchy":2065},[898,56066,1872],{},[1688,56068,2076],{"stretchy":2065},[1688,56070,1690],{},[898,56072,1727],{},[1688,56074,3434],{},[898,56076,1872],{},[1688,56078,1690],{},[898,56080,4440],{},[1688,56082,2066],{"stretchy":2065},[898,56084,1872],{},[1688,56086,2076],{"stretchy":2065},[1688,56088,3434],{},[898,56090,1872],{},[898,56092,2263],{"mathvariant":1822},[21003,56094],{"width":28316},[21003,56096,56097],{},[2041,56098,56099],{},"(3.1)",[902,56101,56102],{"encoding":904},"TR = TR(Q) = P \\cdot Q = D(Q) \\cdot Q.\n\\tag{3.1}",[724,56104,56105,56106,56109,56110,56133],{},"Graf funkce se nazývá ",[38,56107,56108],{},"křivka celkového příjmu"," (total revenue curve). Za předpokladu linearity poptávky, tj. ",[883,56111,56113],{"className":56112},[886],[888,56114,56115],{"xmlns":890},[892,56116,56117,56131],{},[895,56118,56119,56121,56123,56125,56127,56129],{},[898,56120,1727],{},[1688,56122,1690],{},[898,56124,207],{},[898,56126,1872],{},[1688,56128,1696],{},[898,56130,1918],{},[902,56132,37300],{"encoding":904},", je celkový příjem kvadratickou funkcí, neboť",[883,56135,56137],{"className":56136},[886],[888,56138,56139],{"xmlns":890,"display":28306},[892,56140,56141,56181],{},[895,56142,56143,56145,56147,56149,56151,56153,56155,56157,56159,56161,56163,56165,56167,56173,56175,56177,56179],{},[898,56144,3035],{},[898,56146,4251],{},[1688,56148,1690],{},[898,56150,1872],{},[1688,56152,2066],{"stretchy":2065},[898,56154,207],{},[898,56156,1872],{},[1688,56158,1696],{},[898,56160,1918],{},[1688,56162,2076],{"stretchy":2065},[1688,56164,1690],{},[898,56166,207],{},[1850,56168,56169,56171],{},[898,56170,1872],{},[1793,56172,1806],{},[1688,56174,1696],{},[898,56176,1918],{},[898,56178,1872],{},[1688,56180,1733],{"separator":1732},[902,56182,56183],{"encoding":904},"TR = Q(aQ + b) = aQ^2 + bQ,",[724,56185,56186,56187,56200,56201,56218],{},"a křivka celkového příjmu je parabola tvaru obráceného ",[883,56188,56190],{"className":56189},[886],[888,56191,56192],{"xmlns":890},[892,56193,56194,56198],{},[895,56195,56196],{},[898,56197,900],{},[902,56199,900],{"encoding":904}," (jelikož ",[883,56202,56204],{"className":56203},[886],[888,56205,56206],{"xmlns":890},[892,56207,56208,56216],{},[895,56209,56210,56212,56214],{},[898,56211,207],{},[1688,56213,3704],{},[1793,56215,1779],{},[902,56217,43325],{"encoding":904},") procházející počátkem.",[37588,56220,56222],{"id":56221},"příklad-31","Příklad 3.1",[724,56224,56225,56228,56229,56265,56266,56281],{},[38,56226,56227],{},"Zadání."," Pro poptávku ",[883,56230,56232],{"className":56231},[886],[888,56233,56234],{"xmlns":890},[892,56235,56236,56262],{},[895,56237,56238,56240,56242,56244,56246,56248,56250,56252,56254,56256,56258,56260],{},[898,56239,1727],{},[1688,56241,1690],{},[898,56243,4440],{},[1688,56245,2066],{"stretchy":2065},[898,56247,1872],{},[1688,56249,2076],{"stretchy":2065},[1688,56251,1690],{},[1688,56253,1954],{},[1793,56255,1806],{},[898,56257,1872],{},[1688,56259,1696],{},[1793,56261,3347],{},[902,56263,56264],{"encoding":904},"P = D(Q) = -2Q + 100"," určete ",[883,56267,56269],{"className":56268},[886],[888,56270,56271],{"xmlns":890},[892,56272,56273,56279],{},[895,56274,56275,56277],{},[898,56276,3035],{},[898,56278,4251],{},[902,56280,4351],{"encoding":904}," a charakterizujte jeho křivku.",[724,56283,56284,56286],{},[38,56285,23011],{}," Celkový příjem je",[883,56288,56290],{"className":56289},[886],[888,56291,56292],{"xmlns":890,"display":28306},[892,56293,56294,56350],{},[895,56295,56296,56298,56300,56302,56304,56306,56308,56310,56312,56314,56316,56318,56320,56322,56324,56326,56328,56330,56332,56334,56336,56342,56344,56346,56348],{},[898,56297,3035],{},[898,56299,4251],{},[1688,56301,1690],{},[898,56303,3035],{},[898,56305,4251],{},[1688,56307,2066],{"stretchy":2065},[898,56309,1872],{},[1688,56311,2076],{"stretchy":2065},[1688,56313,1690],{},[898,56315,1872],{},[1688,56317,2066],{"stretchy":2065},[1688,56319,1954],{},[1793,56321,1806],{},[898,56323,1872],{},[1688,56325,1696],{},[1793,56327,3347],{},[1688,56329,2076],{"stretchy":2065},[1688,56331,1690],{},[1688,56333,1954],{},[1793,56335,1806],{},[1850,56337,56338,56340],{},[898,56339,1872],{},[1793,56341,1806],{},[1688,56343,1696],{},[1793,56345,3347],{},[898,56347,1872],{},[898,56349,2263],{"mathvariant":1822},[902,56351,56352],{"encoding":904},"TR = TR(Q) = Q(-2Q + 100) = -2Q^2 + 100Q.",[724,56354,56355,56356,4142,56378,56400,56401,56419,56420,2263],{},"Křivkou je parabola (obrázek 3.1) s nulami v ",[883,56357,56359],{"className":56358},[886],[888,56360,56361],{"xmlns":890},[892,56362,56363,56375],{},[895,56364,56365,56371,56373],{},[1788,56366,56367,56369],{},[898,56368,1872],{},[1793,56370,1795],{},[1688,56372,1690],{},[1793,56374,1779],{},[902,56376,56377],{"encoding":904},"Q_1 = 0",[883,56379,56381],{"className":56380},[886],[888,56382,56383],{"xmlns":890},[892,56384,56385,56397],{},[895,56386,56387,56393,56395],{},[1788,56388,56389,56391],{},[898,56390,1872],{},[1793,56392,1806],{},[1688,56394,1690],{},[1793,56396,3377],{},[902,56398,56399],{"encoding":904},"Q_2 = 50",". Maxima dosahuje při ",[883,56402,56404],{"className":56403},[886],[888,56405,56406],{"xmlns":890},[892,56407,56408,56416],{},[895,56409,56410,56412,56414],{},[898,56411,1872],{},[1688,56413,1690],{},[1793,56415,5260],{},[902,56417,56418],{"encoding":904},"Q = 25"," ve výši ",[883,56421,56423],{"className":56422},[886],[888,56424,56425],{"xmlns":890},[892,56426,56427,56468],{},[895,56428,56429,56431,56441,56443,56445,56447,56449,56452,56454,56456,56458,56460,56462,56464,56466],{},[898,56430,3035],{},[1788,56432,56433,56435,56438],{},[898,56434,4251],{},[898,56436,56437],{},"max",[1688,56439,56440],{},"⁡",[1688,56442,1690],{},[1688,56444,1954],{},[1793,56446,1806],{},[1688,56448,3434],{},[1793,56450,56451],{},"625",[1688,56453,1696],{},[1793,56455,3347],{},[1688,56457,3434],{},[1793,56459,5260],{},[1688,56461,1690],{},[1793,56463,1795],{},[2041,56465,2043],{},[1793,56467,30983],{},[902,56469,56470],{"encoding":904},"TR_{\\max} = -2 \\cdot 625 + 100 \\cdot 25 = 1\\,250",[724,56472,56473],{},[614,56474,56475,56476,56510,56511,4142,56524,56537,56538,2886,56556,2263],{},"Obrázek 3.1: Parabola ",[883,56477,56479],{"className":56478},[886],[888,56480,56481],{"xmlns":890},[892,56482,56483,56507],{},[895,56484,56485,56487,56489,56491,56493,56495,56501,56503,56505],{},[898,56486,3035],{},[898,56488,4251],{},[1688,56490,1690],{},[1688,56492,1954],{},[1793,56494,1806],{},[1850,56496,56497,56499],{},[898,56498,1872],{},[1793,56500,1806],{},[1688,56502,1696],{},[1793,56504,3347],{},[898,56506,1872],{},[902,56508,56509],{"encoding":904},"TR = -2Q^2 + 100Q"," s nulami v ",[883,56512,56514],{"className":56513},[886],[888,56515,56516],{"xmlns":890},[892,56517,56518,56522],{},[895,56519,56520],{},[1793,56521,1779],{},[902,56523,1779],{"encoding":904},[883,56525,56527],{"className":56526},[886],[888,56528,56529],{"xmlns":890},[892,56530,56531,56535],{},[895,56532,56533],{},[1793,56534,3377],{},[902,56536,3377],{"encoding":904}," a maximem ",[883,56539,56541],{"className":56540},[886],[888,56542,56543],{"xmlns":890},[892,56544,56545,56553],{},[895,56546,56547,56549,56551],{},[1793,56548,1795],{},[2041,56550,2043],{},[1793,56552,30983],{},[902,56554,56555],{"encoding":904},"1\\,250",[883,56557,56559],{"className":56558},[886],[888,56560,56561],{"xmlns":890},[892,56562,56563,56571],{},[895,56564,56565,56567,56569],{},[898,56566,1872],{},[1688,56568,1690],{},[1793,56570,5260],{},[902,56572,56418],{"encoding":904},[198,56574,56576],{"id":56575},"průměrný-příjem","Průměrný příjem",[724,56578,56579,2170,56581,10277,56596,56599],{},[38,56580,56576],{},[883,56582,56584],{"className":56583},[886],[888,56585,56586],{"xmlns":890},[892,56587,56588,56594],{},[895,56589,56590,56592],{},[898,56591,4512],{},[898,56593,4251],{},[902,56595,55685],{"encoding":904},[38,56597,56598],{},"average revenue",") je podíl celkového příjmu a množství. Z (3.1) plyne",[883,56601,56603],{"className":56602},[886],[888,56604,56605],{"xmlns":890,"display":28306},[892,56606,56607,56675],{},[895,56608,56609,56611,56613,56615,56617,56619,56621,56623,56625,56627,56643,56645,56663,56665,56667,56669,56671,56673],{},[898,56610,4512],{},[898,56612,4251],{},[1688,56614,1690],{},[898,56616,4512],{},[898,56618,4251],{},[1688,56620,2066],{"stretchy":2065},[898,56622,1872],{},[1688,56624,2076],{"stretchy":2065},[1688,56626,1690],{},[1781,56628,56629,56641],{},[895,56630,56631,56633,56635,56637,56639],{},[898,56632,3035],{},[898,56634,4251],{},[1688,56636,2066],{"stretchy":2065},[898,56638,1872],{},[1688,56640,2076],{"stretchy":2065},[898,56642,1872],{},[1688,56644,1690],{},[1781,56646,56647,56661],{},[895,56648,56649,56651,56653,56655,56657,56659],{},[898,56650,1872],{},[2041,56652,2043],{},[898,56654,4440],{},[1688,56656,2066],{"stretchy":2065},[898,56658,1872],{},[1688,56660,2076],{"stretchy":2065},[898,56662,1872],{},[1688,56664,1690],{},[898,56666,4440],{},[1688,56668,2066],{"stretchy":2065},[898,56670,1872],{},[1688,56672,2076],{"stretchy":2065},[898,56674,2263],{"mathvariant":1822},[902,56676,56677],{"encoding":904},"AR = AR(Q) = \\frac{TR(Q)}{Q} = \\frac{Q \\, D(Q)}{Q} = D(Q).",[4124,56679,56680],{},[724,56681,56682,56685,56686,1343,56689,2263],{},[883,56683,56684],{},"!note"," Klíčové pozorování\n",[38,56687,56688],{},"Průměrný příjem se vždy rovná poptávkové funkci",[883,56690,56692],{"className":56691},[886],[888,56693,56694],{"xmlns":890},[892,56695,56696,56718],{},[895,56697,56698,56700,56702,56704,56706,56708,56710,56712,56714,56716],{},[898,56699,4512],{},[898,56701,4251],{},[1688,56703,2066],{"stretchy":2065},[898,56705,1872],{},[1688,56707,2076],{"stretchy":2065},[1688,56709,1690],{},[898,56711,4440],{},[1688,56713,2066],{"stretchy":2065},[898,56715,1872],{},[1688,56717,2076],{"stretchy":2065},[902,56719,56720],{"encoding":904},"AR(Q) = D(Q)",[198,56722,56724],{"id":56723},"mezní-příjem","Mezní příjem",[724,56726,56727,56728,2170,56731,10277,56746,56749,56750,56753],{},"Pro zkoumání dynamiky změn celkového příjmu zavádíme ",[38,56729,56730],{},"mezní příjem",[883,56732,56734],{"className":56733},[886],[888,56735,56736],{"xmlns":890},[892,56737,56738,56744],{},[895,56739,56740,56742],{},[898,56741,1661],{},[898,56743,4251],{},[902,56745,6890],{"encoding":904},[38,56747,56748],{},"marginal revenue","), definovaný jako ",[207,56751,1145],{"className":56752,"dataFsResolvedFilePath":764,"href":765},[210]," celkového příjmu podle množství:",[883,56755,56757],{"className":56756},[886],[888,56758,56759],{"xmlns":890,"display":28306},[892,56760,56761,56818],{},[20995,56762,56763],{"width":28311},[21000,56764,56765,56767,56811,56813],{},[21003,56766],{"width":28316},[21003,56768,56769],{},[895,56770,56771,56773,56775,56777,56793,56795,56797,56803,56805,56807,56809],{},[898,56772,1661],{},[898,56774,4251],{},[1688,56776,1690],{},[1781,56778,56779,56787],{},[895,56780,56781,56783,56785],{},[898,56782,2073],{"mathvariant":1822},[898,56784,3035],{},[898,56786,4251],{},[895,56788,56789,56791],{},[898,56790,2073],{"mathvariant":1822},[898,56792,1872],{},[1688,56794,1690],{},[898,56796,3035],{},[1850,56798,56799,56801],{},[898,56800,4251],{},[1688,56802,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,56804,2066],{"stretchy":2065},[898,56806,1872],{},[1688,56808,2076],{"stretchy":2065},[898,56810,2263],{"mathvariant":1822},[21003,56812],{"width":28316},[21003,56814,56815],{},[2041,56816,56817],{},"(3.2)",[902,56819,56820],{"encoding":904},"MR = \\frac{\\mathrm{d}TR}{\\mathrm{d}Q} = TR'(Q).\n\\tag{3.2}",[724,56822,56823,56824,56826],{},"Mezní příjem udává ",[38,56825,2858],{}," celkového příjmu vzhledem k množství.",[4124,56828,56829],{},[724,56830,56831,56833,56834,56860,56861,56878,56879,2263],{},[883,56832,4412],{}," Intuice — „kolik vyděláš za další kus\"\nHodnota ",[883,56835,56837],{"className":56836},[886],[888,56838,56839],{"xmlns":890},[892,56840,56841,56857],{},[895,56842,56843,56845,56847,56849,56855],{},[898,56844,1661],{},[898,56846,4251],{},[1688,56848,2066],{"stretchy":2065},[1850,56850,56851,56853],{},[898,56852,1872],{},[1688,56854,1857],{},[1688,56856,2076],{"stretchy":2065},[902,56858,56859],{"encoding":904},"MR(Q^*)"," je přibližně to, o kolik se zvýší celkový příjem, prodá-li firma jednu další jednotku nad aktuální úroveň ",[883,56862,56864],{"className":56863},[886],[888,56865,56866],{"xmlns":890},[892,56867,56868,56876],{},[895,56869,56870],{},[1850,56871,56872,56874],{},[898,56873,1872],{},[1688,56875,1857],{},[902,56877,30084],{"encoding":904},". Jinak řečeno: ",[883,56880,56882],{"className":56881},[886],[888,56883,56884],{"xmlns":890},[892,56885,56886,56938],{},[895,56887,56888,56890,56892,56894,56900,56902,56904,56906,56908,56910,56916,56918,56920,56922,56924,56926,56928,56930,56936],{},[898,56889,1661],{},[898,56891,4251],{},[1688,56893,2066],{"stretchy":2065},[1850,56895,56896,56898],{},[898,56897,1872],{},[1688,56899,1857],{},[1688,56901,2076],{"stretchy":2065},[1688,56903,2991],{},[898,56905,3035],{},[898,56907,4251],{},[1688,56909,2066],{"stretchy":2065},[1850,56911,56912,56914],{},[898,56913,1872],{},[1688,56915,1857],{},[1688,56917,1696],{},[1793,56919,1795],{},[1688,56921,2076],{"stretchy":2065},[1688,56923,1954],{},[898,56925,3035],{},[898,56927,4251],{},[1688,56929,2066],{"stretchy":2065},[1850,56931,56932,56934],{},[898,56933,1872],{},[1688,56935,1857],{},[1688,56937,2076],{"stretchy":2065},[902,56939,56940],{"encoding":904},"MR(Q^*) \\approx TR(Q^* + 1) - TR(Q^*)",[37588,56942,56944],{"id":56943},"příklad-32","Příklad 3.2",[724,56946,56947,56228,56949,56265,56983,56998,56999,2263],{},[38,56948,56227],{},[883,56950,56952],{"className":56951},[886],[888,56953,56954],{"xmlns":890},[892,56955,56956,56980],{},[895,56957,56958,56960,56962,56964,56966,56968,56970,56972,56974,56976,56978],{},[898,56959,1727],{},[1688,56961,1690],{},[898,56963,4440],{},[1688,56965,2066],{"stretchy":2065},[898,56967,1872],{},[1688,56969,2076],{"stretchy":2065},[1688,56971,1690],{},[1793,56973,3347],{},[1688,56975,1954],{},[1793,56977,1806],{},[898,56979,1872],{},[902,56981,56982],{"encoding":904},"P = D(Q) = 100 - 2Q",[883,56984,56986],{"className":56985},[886],[888,56987,56988],{"xmlns":890},[892,56989,56990,56996],{},[895,56991,56992,56994],{},[898,56993,1661],{},[898,56995,4251],{},[902,56997,6890],{"encoding":904}," a interpretujte jeho hodnoty pro ",[883,57000,57002],{"className":57001},[886],[888,57003,57004],{"xmlns":890},[892,57005,57006,57022],{},[895,57007,57008,57010,57012,57014,57016,57018,57020],{},[898,57009,1872],{},[1688,57011,1690],{},[1793,57013,36484],{},[1688,57015,1733],{"separator":1732},[1793,57017,42102],{},[1688,57019,1733],{"separator":1732},[1793,57021,9290],{},[902,57023,57024],{"encoding":904},"Q = 15, 16, 20",[724,57026,57027,2170,57029,57061],{},[38,57028,23011],{},[883,57030,57032],{"className":57031},[886],[888,57033,57034],{"xmlns":890},[892,57035,57036,57058],{},[895,57037,57038,57040,57042,57044,57046,57048,57050,57052],{},[898,57039,3035],{},[898,57041,4251],{},[1688,57043,1690],{},[1793,57045,3347],{},[898,57047,1872],{},[1688,57049,1954],{},[1793,57051,1806],{},[1850,57053,57054,57056],{},[898,57055,1872],{},[1793,57057,1806],{},[902,57059,57060],{"encoding":904},"TR = 100Q - 2Q^2",", tedy",[883,57063,57065],{"className":57064},[886],[888,57066,57067],{"xmlns":890,"display":28306},[892,57068,57069,57111],{},[895,57070,57071,57073,57075,57077,57079,57081,57083,57085,57087,57093,57099,57101,57103,57105,57107,57109],{},[898,57072,1661],{},[898,57074,4251],{},[1688,57076,1690],{},[1688,57078,2066],{"stretchy":2065},[1793,57080,3347],{},[898,57082,1872],{},[1688,57084,1954],{},[1793,57086,1806],{},[1850,57088,57089,57091],{},[898,57090,1872],{},[1793,57092,1806],{},[1850,57094,57095,57097],{},[1688,57096,2076],{"stretchy":2065},[1688,57098,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,57100,1690],{},[1793,57102,3347],{},[1688,57104,1954],{},[1793,57106,2616],{},[898,57108,1872],{},[898,57110,2263],{"mathvariant":1822},[902,57112,57113],{"encoding":904},"MR = (100Q - 2Q^2)' = 100 - 4Q.",[724,57115,9916,57116,8358,57134,57160,57161,4614,57174,57189,57190,57203,57204,21661,57217,4614,57230,57245,57246,57259,57260,57291,57292,57311],{},[883,57117,57119],{"className":57118},[886],[888,57120,57121],{"xmlns":890},[892,57122,57123,57131],{},[895,57124,57125,57127,57129],{},[898,57126,1872],{},[1688,57128,1690],{},[1793,57130,36484],{},[902,57132,57133],{"encoding":904},"Q = 15",[883,57135,57137],{"className":57136},[886],[888,57138,57139],{"xmlns":890},[892,57140,57141,57157],{},[895,57142,57143,57145,57147,57149,57151,57153,57155],{},[898,57144,1661],{},[898,57146,4251],{},[1688,57148,2066],{"stretchy":2065},[1793,57150,36484],{},[1688,57152,2076],{"stretchy":2065},[1688,57154,1690],{},[1793,57156,5467],{},[902,57158,57159],{"encoding":904},"MR(15) = 40",": při množství ",[883,57162,57164],{"className":57163},[886],[888,57165,57166],{"xmlns":890},[892,57167,57168,57172],{},[895,57169,57170],{},[1793,57171,36484],{},[902,57173,36484],{"encoding":904},[883,57175,57177],{"className":57176},[886],[888,57178,57179],{"xmlns":890},[892,57180,57181,57187],{},[895,57182,57183,57185],{},[898,57184,3035],{},[898,57186,4251],{},[902,57188,4351],{"encoding":904}," mění asi ",[883,57191,57193],{"className":57192},[886],[888,57194,57195],{"xmlns":890},[892,57196,57197,57201],{},[895,57198,57199],{},[1793,57200,5467],{},[902,57202,5467],{"encoding":904},"-krát rychleji než množství; s růstem ",[883,57205,57207],{"className":57206},[886],[888,57208,57209],{"xmlns":890},[892,57210,57211,57215],{},[895,57212,57213],{},[898,57214,1872],{},[902,57216,1872],{"encoding":904},[883,57218,57220],{"className":57219},[886],[888,57221,57222],{"xmlns":890},[892,57223,57224,57228],{},[895,57225,57226],{},[1793,57227,1795],{},[902,57229,1795],{"encoding":904},[883,57231,57233],{"className":57232},[886],[888,57234,57235],{"xmlns":890},[892,57236,57237,57243],{},[895,57238,57239,57241],{},[898,57240,3035],{},[898,57242,4251],{},[902,57244,4351],{"encoding":904}," zvýší přibližně o ",[883,57247,57249],{"className":57248},[886],[888,57250,57251],{"xmlns":890},[892,57252,57253,57257],{},[895,57254,57255],{},[1793,57256,5467],{},[902,57258,5467],{"encoding":904},", tj. ze skutečné hodnoty ",[883,57261,57263],{"className":57262},[886],[888,57264,57265],{"xmlns":890},[892,57266,57267,57288],{},[895,57268,57269,57271,57273,57275,57277,57279,57281,57283,57285],{},[898,57270,3035],{},[898,57272,4251],{},[1688,57274,2066],{"stretchy":2065},[1793,57276,36484],{},[1688,57278,2076],{"stretchy":2065},[1688,57280,1690],{},[1793,57282,1795],{},[2041,57284,2043],{},[1793,57286,57287],{},"050",[902,57289,57290],{"encoding":904},"TR(15) = 1\\,050"," na přibližně ",[883,57293,57295],{"className":57294},[886],[888,57296,57297],{"xmlns":890},[892,57298,57299,57308],{},[895,57300,57301,57303,57305],{},[1793,57302,1795],{},[2041,57304,2043],{},[1793,57306,57307],{},"090",[902,57309,57310],{"encoding":904},"1\\,090",". Skutečná změna je",[883,57313,57315],{"className":57314},[886],[888,57316,57317],{"xmlns":890,"display":28306},[892,57318,57319,57373],{},[895,57320,57321,57323,57325,57327,57329,57331,57333,57335,57337,57339,57341,57343,57345,57347,57349,57351,57353,57355,57357,57360,57362,57364,57366,57368,57370],{},[898,57322,3147],{"mathvariant":1822},[898,57324,3035],{},[898,57326,4251],{},[1688,57328,1690],{},[898,57330,3035],{},[898,57332,4251],{},[1688,57334,2066],{"stretchy":2065},[1793,57336,42102],{},[1688,57338,2076],{"stretchy":2065},[1688,57340,1954],{},[898,57342,3035],{},[898,57344,4251],{},[1688,57346,2066],{"stretchy":2065},[1793,57348,36484],{},[1688,57350,2076],{"stretchy":2065},[1688,57352,1690],{},[1793,57354,1795],{},[2041,57356,2043],{},[1793,57358,57359],{},"088",[1688,57361,1954],{},[1793,57363,1795],{},[2041,57365,2043],{},[1793,57367,57287],{},[1688,57369,1690],{},[1793,57371,57372],{},"38.",[902,57374,57375],{"encoding":904},"\\Delta TR = TR(16) - TR(15) = 1\\,088 - 1\\,050 = 38.",[724,57377,57378,57379,1343,57405,3185,57431,57446,57447,57462],{},"Podobně ",[883,57380,57382],{"className":57381},[886],[888,57383,57384],{"xmlns":890},[892,57385,57386,57402],{},[895,57387,57388,57390,57392,57394,57396,57398,57400],{},[898,57389,1661],{},[898,57391,4251],{},[1688,57393,2066],{"stretchy":2065},[1793,57395,42102],{},[1688,57397,2076],{"stretchy":2065},[1688,57399,1690],{},[1793,57401,5821],{},[902,57403,57404],{"encoding":904},"MR(16) = 36",[883,57406,57408],{"className":57407},[886],[888,57409,57410],{"xmlns":890},[892,57411,57412,57428],{},[895,57413,57414,57416,57418,57420,57422,57424,57426],{},[898,57415,1661],{},[898,57417,4251],{},[1688,57419,2066],{"stretchy":2065},[1793,57421,9290],{},[1688,57423,2076],{"stretchy":2065},[1688,57425,1690],{},[1793,57427,9290],{},[902,57429,57430],{"encoding":904},"MR(20) = 20",[883,57432,57434],{"className":57433},[886],[888,57435,57436],{"xmlns":890},[892,57437,57438,57444],{},[895,57439,57440,57442],{},[898,57441,1661],{},[898,57443,4251],{},[902,57445,6890],{"encoding":904}," je klesající funkce — rychlost změny ",[883,57448,57450],{"className":57449},[886],[888,57451,57452],{"xmlns":890},[892,57453,57454,57460],{},[895,57455,57456,57458],{},[898,57457,3035],{},[898,57459,4251],{},[902,57461,4351],{"encoding":904}," s růstem množství klesá.",[198,57464,57466],{"id":57465},"odhad-změny-tr-pomocí-diferenciálu","Odhad změny TR pomocí diferenciálu",[724,57468,57469],{},"Užitím mezního příjmu lze odhadnout změnu celkového příjmu jako odezvu na změnu množství:",[883,57471,57473],{"className":57472},[886],[888,57474,57475],{"xmlns":890,"display":28306},[892,57476,57477,57546],{},[20995,57478,57479],{"width":28311},[21000,57480,57481,57483,57539,57541],{},[21003,57482],{"width":28316},[21003,57484,57485],{},[895,57486,57487,57489,57491,57493,57495,57497,57499,57501,57503,57505,57507,57509,57511,57513,57519,57521,57523,57525,57527,57529,57531,57533,57535,57537],{},[898,57488,3147],{"mathvariant":1822},[898,57490,3035],{},[898,57492,4251],{},[2041,57494,4241],{},[1688,57496,2991],{},[2041,57498,4241],{},[898,57500,2073],{"mathvariant":1822},[898,57502,3035],{},[898,57504,4251],{},[1688,57506,1690],{},[1688,57508,2066],{"stretchy":2065},[898,57510,3035],{},[898,57512,4251],{},[1850,57514,57515,57517],{},[1688,57516,2076],{"stretchy":2065},[1688,57518,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[2041,57520,2043],{},[898,57522,2073],{"mathvariant":1822},[898,57524,1872],{},[1688,57526,1690],{},[898,57528,1661],{},[898,57530,4251],{},[2041,57532,2043],{},[898,57534,2073],{"mathvariant":1822},[898,57536,1872],{},[1688,57538,1733],{"separator":1732},[21003,57540],{"width":28316},[21003,57542,57543],{},[2041,57544,57545],{},"(3.3)",[902,57547,57548],{"encoding":904},"\\Delta TR \\;\\approx\\; \\mathrm{d}TR = (TR)' \\, \\mathrm{d}Q = MR \\, \\mathrm{d}Q,\n\\tag{3.3}",[724,57550,57551],{},"schematicky:",[883,57553,57555],{"className":57554},[886],[888,57556,57557],{"xmlns":890,"display":28306},[892,57558,57559,57667],{},[895,57560,57561,57599,57601,57603,57605,57634,57637,57665],{},[895,57562,57563,57566,57572,57575,57581,57584,57590,57596],{},[2041,57564,57565],{},"zm",[8642,57567,57568,57570],{"accent":1732},[2041,57569,45972],{},[1688,57571,25299],{},[2041,57573,57574],{},"na celkov",[8642,57576,57577,57579],{"accent":1732},[2041,57578,45972],{},[1688,57580,25218],{},[2041,57582,57583],{},"ho p",[8642,57585,57586,57588],{"accent":1732},[2041,57587,2046],{},[1688,57589,25299],{},[8642,57591,57592,57594],{"accent":1732},[2041,57593,25287],{},[1688,57595,25218],{},[2041,57597,57598],{},"jmu",[2041,57600,4241],{},[1688,57602,2991],{},[2041,57604,4241],{},[895,57606,57607,57610,57616,57619,57625,57631],{},[2041,57608,57609],{},"mezn",[8642,57611,57612,57614],{"accent":1732},[2041,57613,25287],{},[1688,57615,25218],{},[2041,57617,57618],{}," p",[8642,57620,57621,57623],{"accent":1732},[2041,57622,2046],{},[1688,57624,25299],{},[8642,57626,57627,57629],{"accent":1732},[2041,57628,25287],{},[1688,57630,25218],{},[2041,57632,57633],{},"jem",[1688,57635,57636],{},"×",[895,57638,57639,57641,57647,57650,57656,57659],{},[2041,57640,57565],{},[8642,57642,57643,57645],{"accent":1732},[2041,57644,45972],{},[1688,57646,25299],{},[2041,57648,57649],{},"na mno",[8642,57651,57652,57654],{"accent":1732},[2041,57653,9847],{},[1688,57655,25299],{},[2041,57657,57658],{},"stv",[8642,57660,57661,57663],{"accent":1732},[2041,57662,25287],{},[1688,57664,25218],{},[898,57666,2263],{"mathvariant":1822},[902,57668,57669],{"encoding":904},"\\text{změna celkového příjmu} \\;\\approx\\; \\text{mezní příjem} \\times \\text{změna množství}.",[724,57671,57672,57673,57688],{},"Pro porovnání skutečná změna ",[883,57674,57676],{"className":57675},[886],[888,57677,57678],{"xmlns":890},[892,57679,57680,57686],{},[895,57681,57682,57684],{},[898,57683,3035],{},[898,57685,4251],{},[902,57687,4351],{"encoding":904}," je",[883,57690,57692],{"className":57691},[886],[888,57693,57694],{"xmlns":890,"display":28306},[892,57695,57696,57751],{},[20995,57697,57698],{"width":28311},[21000,57699,57700,57702,57744,57746],{},[21003,57701],{"width":28316},[21003,57703,57704],{},[895,57705,57706,57708,57710,57712,57714,57716,57718,57720,57722,57724,57726,57728,57730,57732,57734,57736,57738,57740,57742],{},[898,57707,3147],{"mathvariant":1822},[898,57709,3035],{},[898,57711,4251],{},[1688,57713,1690],{},[898,57715,3035],{},[898,57717,4251],{},[1688,57719,2066],{"stretchy":2065},[898,57721,1872],{},[1688,57723,1696],{},[898,57725,2073],{"mathvariant":1822},[898,57727,1872],{},[1688,57729,2076],{"stretchy":2065},[1688,57731,1954],{},[898,57733,3035],{},[898,57735,4251],{},[1688,57737,2066],{"stretchy":2065},[898,57739,1872],{},[1688,57741,2076],{"stretchy":2065},[898,57743,2263],{"mathvariant":1822},[21003,57745],{"width":28316},[21003,57747,57748],{},[2041,57749,57750],{},"(3.4)",[902,57752,57753],{"encoding":904},"\\Delta TR = TR(Q + \\mathrm{d}Q) - TR(Q).\n\\tag{3.4}",[37588,57755,57757],{"id":57756},"příklad-33","Příklad 3.3",[724,57759,57760,57762,57763,57793,57794,2919,57809,2194,57822,2946,57835,57849],{},[38,57761,56227],{}," Pro ",[883,57764,57766],{"className":57765},[886],[888,57767,57768],{"xmlns":890},[892,57769,57770,57790],{},[895,57771,57772,57774,57776,57778,57780,57782,57784],{},[898,57773,3035],{},[898,57775,4251],{},[1688,57777,1690],{},[1793,57779,3347],{},[898,57781,1872],{},[1688,57783,1954],{},[1850,57785,57786,57788],{},[898,57787,1872],{},[1793,57789,1806],{},[902,57791,57792],{"encoding":904},"TR = 100Q - Q^2"," odhadněte změnu ",[883,57795,57797],{"className":57796},[886],[888,57798,57799],{"xmlns":890},[892,57800,57801,57807],{},[895,57802,57803,57805],{},[898,57804,3035],{},[898,57806,4251],{},[902,57808,4351],{"encoding":904},[883,57810,57812],{"className":57811},[886],[888,57813,57814],{"xmlns":890},[892,57815,57816,57820],{},[895,57817,57818],{},[898,57819,1872],{},[902,57821,1872],{"encoding":904},[883,57823,57825],{"className":57824},[886],[888,57826,57827],{"xmlns":890},[892,57828,57829,57833],{},[895,57830,57831],{},[1793,57832,3383],{},[902,57834,3383],{"encoding":904},[883,57836,57838],{"className":57837},[886],[888,57839,57840],{"xmlns":890},[892,57841,57842,57847],{},[895,57843,57844],{},[1793,57845,57846],{},"63",[902,57848,57846],{"encoding":904}," a porovnejte se skutečnou změnou.",[724,57851,57852,2170,57854,57879,57880,1343,57898,2965],{},[38,57853,23011],{},[883,57855,57857],{"className":57856},[886],[888,57858,57859],{"xmlns":890},[892,57860,57861,57877],{},[895,57862,57863,57865,57867,57869,57871,57873,57875],{},[898,57864,1661],{},[898,57866,4251],{},[1688,57868,1690],{},[1793,57870,3347],{},[1688,57872,1954],{},[1793,57874,1806],{},[898,57876,1872],{},[902,57878,11688],{"encoding":904},", tedy při ",[883,57881,57883],{"className":57882},[886],[888,57884,57885],{"xmlns":890},[892,57886,57887,57895],{},[895,57888,57889,57891,57893],{},[898,57890,1872],{},[1688,57892,1690],{},[1793,57894,3383],{},[902,57896,57897],{"encoding":904},"Q = 60",[883,57899,57901],{"className":57900},[886],[888,57902,57903],{"xmlns":890},[892,57904,57905,57915],{},[895,57906,57907,57909,57911,57913],{},[898,57908,2073],{"mathvariant":1822},[898,57910,1872],{},[1688,57912,1690],{},[1793,57914,2131],{},[902,57916,57917],{"encoding":904},"\\mathrm{d}Q = 3",[883,57919,57921],{"className":57920},[886],[888,57922,57923],{"xmlns":890,"display":28306},[892,57924,57925,57956],{},[895,57926,57927,57929,57931,57933,57935,57937,57939,57941,57943,57945,57947,57949,57951,57953],{},[898,57928,2073],{"mathvariant":1822},[898,57930,3035],{},[898,57932,4251],{},[1688,57934,1690],{},[1688,57936,2066],{"stretchy":2065},[1793,57938,3347],{},[1688,57940,1954],{},[1793,57942,4303],{},[1688,57944,2076],{"stretchy":2065},[1688,57946,3434],{},[1793,57948,2131],{},[1688,57950,1690],{},[1688,57952,1954],{},[1793,57954,57955],{},"60.",[902,57957,57958],{"encoding":904},"\\mathrm{d}TR = (100 - 120) \\cdot 3 = -60.",[724,57960,57961,57962,57992,57993,58012],{},"Celkový příjem klesne z ",[883,57963,57965],{"className":57964},[886],[888,57966,57967],{"xmlns":890},[892,57968,57969,57989],{},[895,57970,57971,57973,57975,57977,57979,57981,57983,57985,57987],{},[898,57972,3035],{},[898,57974,4251],{},[1688,57976,2066],{"stretchy":2065},[1793,57978,3383],{},[1688,57980,2076],{"stretchy":2065},[1688,57982,1690],{},[1793,57984,1806],{},[2041,57986,2043],{},[1793,57988,20383],{},[902,57990,57991],{"encoding":904},"TR(60) = 2\\,400"," přibližně na ",[883,57994,57996],{"className":57995},[886],[888,57997,57998],{"xmlns":890},[892,57999,58000,58009],{},[895,58001,58002,58004,58006],{},[1793,58003,1806],{},[2041,58005,2043],{},[1793,58007,58008],{},"340",[902,58010,58011],{"encoding":904},"2\\,340",". Skutečná změna dle (3.4):",[883,58014,58016],{"className":58015},[886],[888,58017,58018],{"xmlns":890,"display":28306},[892,58019,58020,58078],{},[895,58021,58022,58024,58026,58028,58030,58032,58034,58036,58038,58040,58042,58044,58046,58048,58050,58052,58054,58056,58058,58061,58063,58065,58067,58069,58071,58073,58076],{},[898,58023,3147],{"mathvariant":1822},[898,58025,3035],{},[898,58027,4251],{},[1688,58029,1690],{},[898,58031,3035],{},[898,58033,4251],{},[1688,58035,2066],{"stretchy":2065},[1793,58037,57846],{},[1688,58039,2076],{"stretchy":2065},[1688,58041,1954],{},[898,58043,3035],{},[898,58045,4251],{},[1688,58047,2066],{"stretchy":2065},[1793,58049,3383],{},[1688,58051,2076],{"stretchy":2065},[1688,58053,1690],{},[1793,58055,1806],{},[2041,58057,2043],{},[1793,58059,58060],{},"331",[1688,58062,1954],{},[1793,58064,1806],{},[2041,58066,2043],{},[1793,58068,20383],{},[1688,58070,1690],{},[1688,58072,1954],{},[1793,58074,58075],{},"69",[1688,58077,1733],{"separator":1732},[902,58079,58080],{"encoding":904},"\\Delta TR = TR(63) - TR(60) = 2\\,331 - 2\\,400 = -69,",[724,58082,58083,58084,58099,58100,2263],{},"tj. ",[883,58085,58087],{"className":58086},[886],[888,58088,58089],{"xmlns":890},[892,58090,58091,58097],{},[895,58092,58093,58095],{},[898,58094,3035],{},[898,58096,4251],{},[902,58098,4351],{"encoding":904}," klesne na ",[883,58101,58103],{"className":58102},[886],[888,58104,58105],{"xmlns":890},[892,58106,58107,58115],{},[895,58108,58109,58111,58113],{},[1793,58110,1806],{},[2041,58112,2043],{},[1793,58114,58060],{},[902,58116,58117],{"encoding":904},"2\\,331",[198,58119,58121],{"id":58120},"vztah-ar-a-mr-pro-lineární-poptávku","Vztah AR a MR pro lineární poptávku",[724,58123,58124,58125,10646,58148,31820],{},"Obecně pro lineární poptávku ",[883,58126,58128],{"className":58127},[886],[888,58129,58130],{"xmlns":890},[892,58131,58132,58146],{},[895,58133,58134,58136,58138,58140,58142,58144],{},[898,58135,1727],{},[1688,58137,1690],{},[898,58139,207],{},[898,58141,1872],{},[1688,58143,1696],{},[898,58145,1918],{},[902,58147,37300],{"encoding":904},[883,58149,58151],{"className":58150},[886],[888,58152,58153],{"xmlns":890},[892,58154,58155,58177],{},[895,58156,58157,58159,58161,58163,58165,58171,58173,58175],{},[898,58158,3035],{},[898,58160,4251],{},[1688,58162,1690],{},[898,58164,207],{},[1850,58166,58167,58169],{},[898,58168,1872],{},[1793,58170,1806],{},[1688,58172,1696],{},[898,58174,1918],{},[898,58176,1872],{},[902,58178,58179],{"encoding":904},"TR = aQ^2 + bQ",[883,58181,58183],{"className":58182},[886],[888,58184,58185],{"xmlns":890,"display":28306},[892,58186,58187,58207],{},[895,58188,58189,58191,58193,58195,58197,58199,58201,58203,58205],{},[898,58190,1661],{},[898,58192,4251],{},[1688,58194,1690],{},[1793,58196,1806],{},[898,58198,207],{},[898,58200,1872],{},[1688,58202,1696],{},[898,58204,1918],{},[898,58206,2263],{"mathvariant":1822},[902,58208,58209],{"encoding":904},"MR = 2aQ + b.",[724,58211,58212,58213,58228,58229,58244,58245,58258,58259,10277,58262,58278,58279,58292,58293,58308,58309,58324,58325,58340,58341,2886,58354,58384,58385,58404,58405,58420],{},"Křivky ",[883,58214,58216],{"className":58215},[886],[888,58217,58218],{"xmlns":890},[892,58219,58220,58226],{},[895,58221,58222,58224],{},[898,58223,1661],{},[898,58225,4251],{},[902,58227,6890],{"encoding":904}," a poptávky (resp. ",[883,58230,58232],{"className":58231},[886],[888,58233,58234],{"xmlns":890},[892,58235,58236,58242],{},[895,58237,58238,58240],{},[898,58239,4512],{},[898,58241,4251],{},[902,58243,55685],{"encoding":904},") jsou přímky protínající svislou osu v témže bodě ",[883,58246,58248],{"className":58247},[886],[888,58249,58250],{"xmlns":890},[892,58251,58252,58256],{},[895,58253,58254],{},[898,58255,1918],{},[902,58257,1918],{"encoding":904},", přičemž ",[38,58260,58261],{},"přímka mezního příjmu má sklon rovný dvojnásobku sklonu přímky poptávky",[883,58263,58265],{"className":58264},[886],[888,58266,58267],{"xmlns":890},[892,58268,58269,58275],{},[895,58270,58271,58273],{},[1793,58272,1806],{},[898,58274,207],{},[902,58276,58277],{"encoding":904},"2a"," vs. ",[883,58280,58282],{"className":58281},[886],[888,58283,58284],{"xmlns":890},[892,58285,58286,58290],{},[895,58287,58288],{},[898,58289,207],{},[902,58291,207],{"encoding":904},", obrázek 3.2). ",[883,58294,58296],{"className":58295},[886],[888,58297,58298],{"xmlns":890},[892,58299,58300,58306],{},[895,58301,58302,58304],{},[898,58303,1661],{},[898,58305,4251],{},[902,58307,6890],{"encoding":904}," nabývá jak kladných, tak záporných hodnot; křivka ",[883,58310,58312],{"className":58311},[886],[888,58313,58314],{"xmlns":890},[892,58315,58316,58322],{},[895,58317,58318,58320],{},[898,58319,3035],{},[898,58321,4251],{},[902,58323,4351],{"encoding":904}," nejprve roste, v bodě maxima protíná ",[883,58326,58328],{"className":58327},[886],[888,58329,58330],{"xmlns":890},[892,58331,58332,58338],{},[895,58333,58334,58336],{},[898,58335,1661],{},[898,58337,4251],{},[902,58339,6890],{"encoding":904}," osu ",[883,58342,58344],{"className":58343},[886],[888,58345,58346],{"xmlns":890},[892,58347,58348,58352],{},[895,58349,58350],{},[898,58351,1872],{},[902,58353,1872],{"encoding":904},[883,58355,58357],{"className":58356},[886],[888,58358,58359],{"xmlns":890},[892,58360,58361,58381],{},[895,58362,58363,58365,58367,58369],{},[898,58364,1872],{},[1688,58366,1690],{},[1688,58368,1954],{},[1777,58370,58371],{"scriptlevel":1779,"displaystyle":2065},[1781,58372,58373,58375],{},[898,58374,1918],{},[895,58376,58377,58379],{},[1793,58378,1806],{},[898,58380,207],{},[902,58382,58383],{"encoding":904},"Q = -\\tfrac{b}{2a}"," hodnotou ",[883,58386,58388],{"className":58387},[886],[888,58389,58390],{"xmlns":890},[892,58391,58392,58402],{},[895,58393,58394,58396,58398,58400],{},[898,58395,1661],{},[898,58397,4251],{},[1688,58399,1690],{},[1793,58401,1779],{},[902,58403,7340],{"encoding":904},", a dále ",[883,58406,58408],{"className":58407},[886],[888,58409,58410],{"xmlns":890},[892,58411,58412,58418],{},[895,58413,58414,58416],{},[898,58415,3035],{},[898,58417,4251],{},[902,58419,4351],{"encoding":904}," klesá.",[724,58422,58423,58424,58430,58431,58463,58464,58492],{},"V případě ",[38,58425,58426],{},[207,58427,58429],{"className":58428,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurence",", kdy poptávka ",[883,58432,58434],{"className":58433},[886],[888,58435,58436],{"xmlns":890},[892,58437,58438,58460],{},[895,58439,58440,58442,58444,58446,58448,58450,58452,58454],{},[898,58441,1727],{},[1688,58443,1690],{},[898,58445,4440],{},[1688,58447,2066],{"stretchy":2065},[898,58449,1872],{},[1688,58451,2076],{"stretchy":2065},[1688,58453,1690],{},[1850,58455,58456,58458],{},[898,58457,1727],{},[1688,58459,1857],{},[902,58461,58462],{"encoding":904},"P = D(Q) = P^*"," je pevná tržní cena, platí ",[883,58465,58467],{"className":58466},[886],[888,58468,58469],{"xmlns":890},[892,58470,58471,58489],{},[895,58472,58473,58475,58477,58479,58481,58483],{},[898,58474,3035],{},[898,58476,4251],{},[1688,58478,1690],{},[898,58480,1872],{},[1688,58482,3434],{},[1850,58484,58485,58487],{},[898,58486,1727],{},[1688,58488,1857],{},[902,58490,58491],{"encoding":904},"TR = Q \\cdot P^*"," a tedy",[883,58494,58496],{"className":58495},[886],[888,58497,58498],{"xmlns":890,"display":28306},[892,58499,58500,58542],{},[895,58501,58502,58504,58506,58508,58510,58512,58514,58520,58522,58524,58538,58540],{},[898,58503,1661],{},[898,58505,4251],{},[1688,58507,1690],{},[898,58509,4512],{},[898,58511,4251],{},[1688,58513,1690],{},[1850,58515,58516,58518],{},[898,58517,1727],{},[1688,58519,1857],{},[6134,58521],{"width":15531},[1688,58523,2066],{"stretchy":2065},[895,58525,58526,58529,58535],{},[2041,58527,58528],{},"obr",[8642,58530,58531,58533],{"accent":1732},[2041,58532,207],{},[1688,58534,25218],{},[2041,58536,58537],{},"zek 3.4",[1688,58539,2076],{"stretchy":2065},[898,58541,2263],{"mathvariant":1822},[902,58543,58544],{"encoding":904},"MR = AR = P^* \\quad (\\text{obrázek 3.4}).",[724,58546,58547],{},[614,58548,58549,58550,4142,58576,58604,58605,58618,58619,58634,58635,3975,58648,1343,58674,3975,58689,2263],{},"Obrázek 3.2: Přímky ",[883,58551,58553],{"className":58552},[886],[888,58554,58555],{"xmlns":890},[892,58556,58557,58573],{},[895,58558,58559,58561,58563,58565,58567,58569,58571],{},[898,58560,4512],{},[898,58562,4251],{},[1688,58564,1690],{},[898,58566,207],{},[898,58568,1872],{},[1688,58570,1696],{},[898,58572,1918],{},[902,58574,58575],{"encoding":904},"AR = aQ + b",[883,58577,58579],{"className":58578},[886],[888,58580,58581],{"xmlns":890},[892,58582,58583,58601],{},[895,58584,58585,58587,58589,58591,58593,58595,58597,58599],{},[898,58586,1661],{},[898,58588,4251],{},[1688,58590,1690],{},[1793,58592,1806],{},[898,58594,207],{},[898,58596,1872],{},[1688,58598,1696],{},[898,58600,1918],{},[902,58602,58603],{"encoding":904},"MR = 2aQ + b"," v jednom grafu; společný průsečík ",[883,58606,58608],{"className":58607},[886],[888,58609,58610],{"xmlns":890},[892,58611,58612,58616],{},[895,58613,58614],{},[898,58615,1918],{},[902,58617,1918],{"encoding":904}," se svislou osou, ",[883,58620,58622],{"className":58621},[886],[888,58623,58624],{"xmlns":890},[892,58625,58626,58632],{},[895,58627,58628,58630],{},[898,58629,1661],{},[898,58631,4251],{},[902,58633,6890],{"encoding":904}," protíná osu ",[883,58636,58638],{"className":58637},[886],[888,58639,58640],{"xmlns":890},[892,58641,58642,58646],{},[895,58643,58644],{},[898,58645,1872],{},[902,58647,1872],{"encoding":904},[883,58649,58651],{"className":58650},[886],[888,58652,58653],{"xmlns":890},[892,58654,58655,58671],{},[895,58656,58657,58659],{},[1688,58658,1954],{},[1777,58660,58661],{"scriptlevel":1779,"displaystyle":2065},[1781,58662,58663,58665],{},[898,58664,1918],{},[895,58666,58667,58669],{},[1793,58668,1806],{},[898,58670,207],{},[902,58672,58673],{"encoding":904},"-\\tfrac{b}{2a}",[883,58675,58677],{"className":58676},[886],[888,58678,58679],{"xmlns":890},[892,58680,58681,58687],{},[895,58682,58683,58685],{},[898,58684,4512],{},[898,58686,4251],{},[902,58688,55685],{"encoding":904},[883,58690,58692],{"className":58691},[886],[888,58693,58694],{"xmlns":890},[892,58695,58696,58708],{},[895,58697,58698,58700],{},[1688,58699,1954],{},[1777,58701,58702],{"scriptlevel":1779,"displaystyle":2065},[1781,58703,58704,58706],{},[898,58705,1918],{},[898,58707,207],{},[902,58709,58710],{"encoding":904},"-\\tfrac{b}{a}",[724,58712,58713],{},[614,58714,58715,58716,58747,58748,58777,58778,2263],{},"Obrázek 3.3: Parabola ",[883,58717,58719],{"className":58718},[886],[888,58720,58721],{"xmlns":890},[892,58722,58723,58745],{},[895,58724,58725,58727,58729,58731,58733,58739,58741,58743],{},[898,58726,3035],{},[898,58728,4251],{},[1688,58730,1690],{},[898,58732,207],{},[1850,58734,58735,58737],{},[898,58736,1872],{},[1793,58738,1806],{},[1688,58740,1696],{},[898,58742,1918],{},[898,58744,1872],{},[902,58746,58179],{"encoding":904}," s maximem v ",[883,58749,58751],{"className":58750},[886],[888,58752,58753],{"xmlns":890},[892,58754,58755,58775],{},[895,58756,58757,58759,58761,58763],{},[898,58758,1872],{},[1688,58760,1690],{},[1688,58762,1954],{},[1777,58764,58765],{"scriptlevel":1779,"displaystyle":2065},[1781,58766,58767,58769],{},[898,58768,1918],{},[895,58770,58771,58773],{},[1793,58772,1806],{},[898,58774,207],{},[902,58776,58383],{"encoding":904}," a nulou v ",[883,58779,58781],{"className":58780},[886],[888,58782,58783],{"xmlns":890},[892,58784,58785,58801],{},[895,58786,58787,58789,58791,58793],{},[898,58788,1872],{},[1688,58790,1690],{},[1688,58792,1954],{},[1777,58794,58795],{"scriptlevel":1779,"displaystyle":2065},[1781,58796,58797,58799],{},[898,58798,1918],{},[898,58800,207],{},[902,58802,58803],{"encoding":904},"Q = -\\tfrac{b}{a}",[724,58805,58806],{},[614,58807,58808,58809,2263],{},"Obrázek 3.4: Dokonalá konkurence — vodorovná přímka ",[883,58810,58812],{"className":58811},[886],[888,58813,58814],{"xmlns":890},[892,58815,58816,58836],{},[895,58817,58818,58820,58822,58824,58826,58828,58830],{},[898,58819,4512],{},[898,58821,4251],{},[1688,58823,1690],{},[898,58825,1661],{},[898,58827,4251],{},[1688,58829,1690],{},[1850,58831,58832,58834],{},[898,58833,1727],{},[1688,58835,1857],{},[902,58837,58838],{"encoding":904},"AR = MR = P^*",[115,58840,58842],{"id":58841},"náklady-firmy","Náklady firmy",[198,58844,58846],{"id":58845},"celkové-náklady","Celkové náklady",[724,58848,58849,2170,58851,10277,58866,58869,58870,58883],{},[38,58850,58846],{},[883,58852,58854],{"className":58853},[886],[888,58855,58856],{"xmlns":890},[892,58857,58858,58864],{},[895,58859,58860,58862],{},[898,58861,3035],{},[898,58863,1693],{},[902,58865,3500],{"encoding":904},[38,58867,58868],{},"total cost",") jsou veškeré náklady na realizaci ",[883,58871,58873],{"className":58872},[886],[888,58874,58875],{"xmlns":890},[892,58876,58877,58881],{},[895,58878,58879],{},[898,58880,1872],{},[902,58882,1872],{"encoding":904}," jednotek produkce:",[883,58885,58887],{"className":58886},[886],[888,58888,58889],{"xmlns":890,"display":28306},[892,58890,58891,58946],{},[20995,58892,58893],{"width":28311},[21000,58894,58895,58897,58939,58941],{},[21003,58896],{"width":28316},[21003,58898,58899],{},[895,58900,58901,58903,58905,58907,58909,58911,58913,58915,58917,58919,58921,58923,58925,58927,58929,58931,58933,58935,58937],{},[898,58902,3035],{},[898,58904,1693],{},[1688,58906,1690],{},[898,58908,3035],{},[898,58910,1693],{},[1688,58912,2066],{"stretchy":2065},[898,58914,1872],{},[1688,58916,2076],{"stretchy":2065},[1688,58918,1690],{},[898,58920,10688],{},[898,58922,1693],{},[1688,58924,1696],{},[898,58926,3035],{},[898,58928,40579],{},[898,58930,1693],{},[1688,58932,2066],{"stretchy":2065},[898,58934,1872],{},[1688,58936,2076],{"stretchy":2065},[1688,58938,1733],{"separator":1732},[21003,58940],{"width":28316},[21003,58942,58943],{},[2041,58944,58945],{},"(3.5)",[902,58947,58948],{"encoding":904},"TC = TC(Q) = FC + TVC(Q),\n\\tag{3.5}",[724,58950,4567,58951,58966,58967,10277,58970,12378,58973,58966,58997,10277,59000,59003],{},[883,58952,58954],{"className":58953},[886],[888,58955,58956],{"xmlns":890},[892,58957,58958,58964],{},[895,58959,58960,58962],{},[898,58961,10688],{},[898,58963,1693],{},[902,58965,55731],{"encoding":904}," jsou ",[38,58968,58969],{},"fixní náklady",[38,58971,58972],{},"fixed cost",[883,58974,58976],{"className":58975},[886],[888,58977,58978],{"xmlns":890},[892,58979,58980,58994],{},[895,58981,58982,58984,58986,58988,58990,58992],{},[898,58983,3035],{},[898,58985,40579],{},[898,58987,1693],{},[1688,58989,2066],{"stretchy":2065},[898,58991,1872],{},[1688,58993,2076],{"stretchy":2065},[902,58995,58996],{"encoding":904},"TVC(Q)",[38,58998,58999],{},"celkové variabilní náklady",[38,59001,59002],{},"total variable cost","). Celkové náklady jsou rostoucí, neboť růst množství objektivně vynutí jejich růst.",[198,59005,59007],{"id":59006},"průměrné-náklady","Průměrné náklady",[724,59009,59010,2170,59012,10277,59027,59030],{},[38,59011,59007],{},[883,59013,59015],{"className":59014},[886],[888,59016,59017],{"xmlns":890},[892,59018,59019,59025],{},[895,59020,59021,59023],{},[898,59022,4512],{},[898,59024,1693],{},[902,59026,55800],{"encoding":904},[38,59028,59029],{},"average cost",") jsou podíl celkových nákladů a množství. Z (3.5):",[883,59032,59034],{"className":59033},[886],[888,59035,59036],{"xmlns":890,"display":28306},[892,59037,59038,59117],{},[20995,59039,59040],{"width":28311},[21000,59041,59042,59044,59110,59112],{},[21003,59043],{"width":28316},[21003,59045,59046],{},[895,59047,59048,59050,59052,59054,59056,59058,59060,59062,59064,59066,59076,59078,59088,59090,59108],{},[898,59049,4512],{},[898,59051,1693],{},[1688,59053,1690],{},[898,59055,4512],{},[898,59057,1693],{},[1688,59059,2066],{"stretchy":2065},[898,59061,1872],{},[1688,59063,2076],{"stretchy":2065},[1688,59065,1690],{},[1781,59067,59068,59074],{},[895,59069,59070,59072],{},[898,59071,3035],{},[898,59073,1693],{},[898,59075,1872],{},[1688,59077,1690],{},[1781,59079,59080,59086],{},[895,59081,59082,59084],{},[898,59083,10688],{},[898,59085,1693],{},[898,59087,1872],{},[1688,59089,1696],{},[1781,59091,59092,59106],{},[895,59093,59094,59096,59098,59100,59102,59104],{},[898,59095,3035],{},[898,59097,40579],{},[898,59099,1693],{},[1688,59101,2066],{"stretchy":2065},[898,59103,1872],{},[1688,59105,2076],{"stretchy":2065},[898,59107,1872],{},[1688,59109,1733],{"separator":1732},[21003,59111],{"width":28316},[21003,59113,59114],{},[2041,59115,59116],{},"(3.6)",[902,59118,59119],{"encoding":904},"AC = AC(Q) = \\frac{TC}{Q} = \\frac{FC}{Q} + \\frac{TVC(Q)}{Q},\n\\tag{3.6}",[724,59121,4567,59122,58966,59146,2170,59149,10277,59166,12378,59169,58966,59201,2170,59204,10277,59221,3408],{},[883,59123,59125],{"className":59124},[886],[888,59126,59127],{"xmlns":890},[892,59128,59129,59143],{},[895,59130,59131],{},[1777,59132,59133],{"scriptlevel":1779,"displaystyle":2065},[1781,59134,59135,59141],{},[895,59136,59137,59139],{},[898,59138,10688],{},[898,59140,1693],{},[898,59142,1872],{},[902,59144,59145],{"encoding":904},"\\tfrac{FC}{Q}",[38,59147,59148],{},"průměrné fixní náklady",[883,59150,59152],{"className":59151},[886],[888,59153,59154],{"xmlns":890},[892,59155,59156,59164],{},[895,59157,59158,59160,59162],{},[898,59159,4512],{},[898,59161,10688],{},[898,59163,1693],{},[902,59165,55767],{"encoding":904},[38,59167,59168],{},"average fixed cost",[883,59170,59172],{"className":59171},[886],[888,59173,59174],{"xmlns":890},[892,59175,59176,59198],{},[895,59177,59178],{},[1777,59179,59180],{"scriptlevel":1779,"displaystyle":2065},[1781,59181,59182,59196],{},[895,59183,59184,59186,59188,59190,59192,59194],{},[898,59185,3035],{},[898,59187,40579],{},[898,59189,1693],{},[1688,59191,2066],{"stretchy":2065},[898,59193,1872],{},[1688,59195,2076],{"stretchy":2065},[898,59197,1872],{},[902,59199,59200],{"encoding":904},"\\tfrac{TVC(Q)}{Q}",[38,59202,59203],{},"průměrné variabilní náklady",[883,59205,59207],{"className":59206},[886],[888,59208,59209],{"xmlns":890},[892,59210,59211,59219],{},[895,59212,59213,59215,59217],{},[898,59214,4512],{},[898,59216,40579],{},[898,59218,1693],{},[902,59220,55551],{"encoding":904},[38,59222,59223],{},"average variable cost",[883,59225,59227],{"className":59226},[886],[888,59228,59229],{"xmlns":890,"display":28306},[892,59230,59231,59290],{},[20995,59232,59233],{"width":28311},[21000,59234,59235,59237,59283,59285],{},[21003,59236],{"width":28316},[21003,59238,59239],{},[895,59240,59241,59243,59245,59247,59249,59251,59253,59255,59257,59259,59261,59263,59281],{},[898,59242,4512],{},[898,59244,40579],{},[898,59246,1693],{},[1688,59248,1690],{},[898,59250,4512],{},[898,59252,40579],{},[898,59254,1693],{},[1688,59256,2066],{"stretchy":2065},[898,59258,1872],{},[1688,59260,2076],{"stretchy":2065},[1688,59262,1690],{},[1781,59264,59265,59279],{},[895,59266,59267,59269,59271,59273,59275,59277],{},[898,59268,3035],{},[898,59270,40579],{},[898,59272,1693],{},[1688,59274,2066],{"stretchy":2065},[898,59276,1872],{},[1688,59278,2076],{"stretchy":2065},[898,59280,1872],{},[898,59282,2263],{"mathvariant":1822},[21003,59284],{"width":28316},[21003,59286,59287],{},[2041,59288,59289],{},"(3.7)",[902,59291,59292],{"encoding":904},"AVC = AVC(Q) = \\frac{TVC(Q)}{Q}.\n\\tag{3.7}",[37588,59294,59296],{"id":59295},"příklad-34","Příklad 3.4",[724,59298,59299,57762,59301,4142,59326,56265,59350,4142,59365,59380,59381,2263],{},[38,59300,56227],{},[883,59302,59304],{"className":59303},[886],[888,59305,59306],{"xmlns":890},[892,59307,59308,59323],{},[895,59309,59310,59312,59314,59316,59318,59320],{},[898,59311,10688],{},[898,59313,1693],{},[1688,59315,1690],{},[1793,59317,1795],{},[2041,59319,2043],{},[1793,59321,59322],{},"000",[902,59324,59325],{"encoding":904},"FC = 1\\,000",[883,59327,59329],{"className":59328},[886],[888,59330,59331],{"xmlns":890},[892,59332,59333,59347],{},[895,59334,59335,59337,59339,59341,59343,59345],{},[898,59336,3035],{},[898,59338,40579],{},[898,59340,1693],{},[1688,59342,1690],{},[1793,59344,2616],{},[898,59346,1872],{},[902,59348,59349],{"encoding":904},"TVC = 4Q",[883,59351,59353],{"className":59352},[886],[888,59354,59355],{"xmlns":890},[892,59356,59357,59363],{},[895,59358,59359,59361],{},[898,59360,3035],{},[898,59362,1693],{},[902,59364,3500],{"encoding":904},[883,59366,59368],{"className":59367},[886],[888,59369,59370],{"xmlns":890},[892,59371,59372,59378],{},[895,59373,59374,59376],{},[898,59375,4512],{},[898,59377,1693],{},[902,59379,55800],{"encoding":904}," a jejich chování s rostoucím ",[883,59382,59384],{"className":59383},[886],[888,59385,59386],{"xmlns":890},[892,59387,59388,59392],{},[895,59389,59390],{},[898,59391,1872],{},[902,59393,1872],{"encoding":904},[724,59395,59396,2170,59398,4142,59428,59464,59465,4614,59478,59493,59494,2965],{},[38,59397,23011],{},[883,59399,59401],{"className":59400},[886],[888,59402,59403],{"xmlns":890},[892,59404,59405,59425],{},[895,59406,59407,59409,59411,59413,59415,59417,59419,59421,59423],{},[898,59408,3035],{},[898,59410,1693],{},[1688,59412,1690],{},[1793,59414,1795],{},[2041,59416,2043],{},[1793,59418,59322],{},[1688,59420,1696],{},[1793,59422,2616],{},[898,59424,1872],{},[902,59426,59427],{"encoding":904},"TC = 1\\,000 + 4Q",[883,59429,59431],{"className":59430},[886],[888,59432,59433],{"xmlns":890},[892,59434,59435,59461],{},[895,59436,59437,59439,59441,59443,59457,59459],{},[898,59438,4512],{},[898,59440,1693],{},[1688,59442,1690],{},[1777,59444,59445],{"scriptlevel":1779,"displaystyle":2065},[1781,59446,59447,59455],{},[895,59448,59449,59451,59453],{},[1793,59450,1795],{},[2041,59452,2043],{},[1793,59454,59322],{},[898,59456,1872],{},[1688,59458,1696],{},[1793,59460,2616],{},[902,59462,59463],{"encoding":904},"AC = \\tfrac{1\\,000}{Q} + 4",". S rostoucím ",[883,59466,59468],{"className":59467},[886],[888,59469,59470],{"xmlns":890},[892,59471,59472,59476],{},[895,59473,59474],{},[898,59475,1872],{},[902,59477,1872],{"encoding":904},[883,59479,59481],{"className":59480},[886],[888,59482,59483],{"xmlns":890},[892,59484,59485,59491],{},[895,59486,59487,59489],{},[898,59488,4512],{},[898,59490,1693],{},[902,59492,55800],{"encoding":904}," blíží ",[883,59495,59497],{"className":59496},[886],[888,59498,59499],{"xmlns":890},[892,59500,59501,59505],{},[895,59502,59503],{},[1793,59504,2616],{},[902,59506,2616],{"encoding":904},[883,59508,59510],{"className":59509},[886],[888,59511,59512],{"xmlns":890,"display":28306},[892,59513,59514,59560],{},[895,59515,59516,59533,59555,59557],{},[40136,59517,59518,59525],{},[895,59519,59520,59523],{},[898,59521,59522],{},"lim",[1688,59524,56440],{},[895,59526,59527,59529,59531],{},[898,59528,1872],{},[1688,59530,3380],{},[898,59532,6553],{"mathvariant":1822},[895,59534,59535,59537,59549,59551,59553],{},[1688,59536,2066],{"fence":1732},[1781,59538,59539,59547],{},[895,59540,59541,59543,59545],{},[1793,59542,1795],{},[2041,59544,2043],{},[1793,59546,59322],{},[898,59548,1872],{},[1688,59550,1696],{},[1793,59552,2616],{},[1688,59554,2076],{"fence":1732},[1688,59556,1690],{},[1793,59558,59559],{},"4.",[902,59561,59562],{"encoding":904},"\\lim_{Q \\to \\infty} \\left( \\frac{1\\,000}{Q} + 4 \\right) = 4.",[724,59564,59565,59603,59604,2263],{},[883,59566,59568],{"className":59567},[886],[888,59569,59570],{"xmlns":890},[892,59571,59572,59600],{},[895,59573,59574,59576,59578,59580,59582,59596,59598],{},[898,59575,4512],{},[898,59577,10688],{},[898,59579,1693],{},[1688,59581,1690],{},[1777,59583,59584],{"scriptlevel":1779,"displaystyle":2065},[1781,59585,59586,59594],{},[895,59587,59588,59590,59592],{},[1793,59589,1795],{},[2041,59591,2043],{},[1793,59593,59322],{},[898,59595,1872],{},[1688,59597,3380],{},[1793,59599,1779],{},[902,59601,59602],{"encoding":904},"AFC = \\tfrac{1\\,000}{Q} \\to 0"," s rostoucím ",[883,59605,59607],{"className":59606},[886],[888,59608,59609],{"xmlns":890},[892,59610,59611,59615],{},[895,59612,59613],{},[898,59614,1872],{},[902,59616,1872],{"encoding":904},[724,59618,59619],{},[614,59620,59621,59622,59651,59652,2263],{},"Obrázek 3.5: Přímka ",[883,59623,59625],{"className":59624},[886],[888,59626,59627],{"xmlns":890},[892,59628,59629,59649],{},[895,59630,59631,59633,59635,59637,59639,59641,59643,59645,59647],{},[898,59632,3035],{},[898,59634,1693],{},[1688,59636,1690],{},[1793,59638,1795],{},[2041,59640,2043],{},[1793,59642,59322],{},[1688,59644,1696],{},[1793,59646,2616],{},[898,59648,1872],{},[902,59650,59427],{"encoding":904}," protínající svislou osu ve výši ",[883,59653,59655],{"className":59654},[886],[888,59656,59657],{"xmlns":890},[892,59658,59659,59673],{},[895,59660,59661,59663,59665,59667,59669,59671],{},[898,59662,10688],{},[898,59664,1693],{},[1688,59666,1690],{},[1793,59668,1795],{},[2041,59670,2043],{},[1793,59672,59322],{},[902,59674,59325],{"encoding":904},[724,59676,59677],{},[614,59678,59679,59680,59715,59716,2263],{},"Obrázek 3.6: Hyperbola ",[883,59681,59683],{"className":59682},[886],[888,59684,59685],{"xmlns":890},[892,59686,59687,59713],{},[895,59688,59689,59691,59693,59695,59709,59711],{},[898,59690,4512],{},[898,59692,1693],{},[1688,59694,1690],{},[1777,59696,59697],{"scriptlevel":1779,"displaystyle":2065},[1781,59698,59699,59707],{},[895,59700,59701,59703,59705],{},[1793,59702,1795],{},[2041,59704,2043],{},[1793,59706,59322],{},[898,59708,1872],{},[1688,59710,1696],{},[1793,59712,2616],{},[902,59714,59463],{"encoding":904}," s vodorovnou asymptotou ",[883,59717,59719],{"className":59718},[886],[888,59720,59721],{"xmlns":890},[892,59722,59723,59733],{},[895,59724,59725,59727,59729,59731],{},[898,59726,4512],{},[898,59728,1693],{},[1688,59730,1690],{},[1793,59732,2616],{},[902,59734,59735],{"encoding":904},"AC = 4",[724,59737,59738],{},"Celkové variabilní náklady lze často vyjádřit ve tvaru",[883,59740,59742],{"className":59741},[886],[888,59743,59744],{"xmlns":890,"display":28306},[892,59745,59746,59772],{},[895,59747,59748,59750,59752,59754,59756,59758,59760,59762,59764,59766,59768,59770],{},[898,59749,3035],{},[898,59751,40579],{},[898,59753,1693],{},[1688,59755,1690],{},[898,59757,1872],{},[1688,59759,3434],{},[898,59761,40579],{},[898,59763,1693],{},[1688,59765,2066],{"stretchy":2065},[898,59767,1872],{},[1688,59769,2076],{"stretchy":2065},[1688,59771,1733],{"separator":1732},[902,59773,59774],{"encoding":904},"TVC = Q \\cdot VC(Q),",[724,59776,4567,59777,58966,59805,59808,59809,59839],{},[883,59778,59780],{"className":59779},[886],[888,59781,59782],{"xmlns":890},[892,59783,59784,59802],{},[895,59785,59786,59788,59790,59792,59794,59796,59798,59800],{},[898,59787,40579],{},[898,59789,1693],{},[1688,59791,1690],{},[898,59793,40579],{},[898,59795,1693],{},[1688,59797,2066],{"stretchy":2065},[898,59799,1872],{},[1688,59801,2076],{"stretchy":2065},[902,59803,59804],{"encoding":904},"VC = VC(Q)",[38,59806,59807],{},"variabilní náklady na jednotku množství",". Jsou-li konstantní, ",[883,59810,59812],{"className":59811},[886],[888,59813,59814],{"xmlns":890},[892,59815,59816,59836],{},[895,59817,59818,59820,59822,59824,59826,59828,59830,59832,59834],{},[898,59819,3035],{},[898,59821,40579],{},[898,59823,1693],{},[1688,59825,2066],{"stretchy":2065},[898,59827,1872],{},[1688,59829,2076],{"stretchy":2065},[1688,59831,1690],{},[898,59833,207],{},[898,59835,1872],{},[902,59837,59838],{"encoding":904},"TVC(Q) = aQ"," a nejjednodušší model nákladů má tvar",[883,59841,59843],{"className":59842},[886],[888,59844,59845],{"xmlns":890,"display":28306},[892,59846,59847,59867],{},[895,59848,59849,59851,59853,59855,59857,59859,59861,59863,59865],{},[898,59850,3035],{},[898,59852,1693],{},[1688,59854,1690],{},[898,59856,10688],{},[898,59858,1693],{},[1688,59860,1696],{},[898,59862,207],{},[898,59864,1872],{},[898,59866,2263],{"mathvariant":1822},[902,59868,59869],{"encoding":904},"TC = FC + aQ.",[724,59871,59872,59873,59888,59889,59904,59905,59928,59929,59963,59964,59715,59977,59990,59991,4142,60039,60083,60084,2263],{},"Křivkou ",[883,59874,59876],{"className":59875},[886],[888,59877,59878],{"xmlns":890},[892,59879,59880,59886],{},[895,59881,59882,59884],{},[898,59883,3035],{},[898,59885,1693],{},[902,59887,3500],{"encoding":904}," je přímka se svislým průsečíkem ",[883,59890,59892],{"className":59891},[886],[888,59893,59894],{"xmlns":890},[892,59895,59896,59902],{},[895,59897,59898,59900],{},[898,59899,10688],{},[898,59901,1693],{},[902,59903,55731],{"encoding":904}," a sklonem ",[883,59906,59908],{"className":59907},[886],[888,59909,59910],{"xmlns":890},[892,59911,59912,59925],{},[895,59913,59914,59917,59919,59921,59923],{},[898,59915,59916],{},"tan",[1688,59918,56440],{},[898,59920,19104],{},[1688,59922,1690],{},[898,59924,207],{},[902,59926,59927],{"encoding":904},"\\tan\\alpha = a"," (obrázek 3.7). Průměrné náklady tvoří hyperbolu ",[883,59930,59932],{"className":59931},[886],[888,59933,59934],{"xmlns":890},[892,59935,59936,59960],{},[895,59937,59938,59940,59942,59944,59956,59958],{},[898,59939,4512],{},[898,59941,1693],{},[1688,59943,1690],{},[1777,59945,59946],{"scriptlevel":1779,"displaystyle":2065},[1781,59947,59948,59954],{},[895,59949,59950,59952],{},[898,59951,10688],{},[898,59953,1693],{},[898,59955,1872],{},[1688,59957,1696],{},[898,59959,207],{},[902,59961,59962],{"encoding":904},"AC = \\tfrac{FC}{Q} + a"," tvaru ",[883,59965,59967],{"className":59966},[886],[888,59968,59969],{"xmlns":890},[892,59970,59971,59975],{},[895,59972,59973],{},[898,59974,10047],{},[902,59976,10047],{"encoding":904},[883,59978,59980],{"className":59979},[886],[888,59981,59982],{"xmlns":890},[892,59983,59984,59988],{},[895,59985,59986],{},[898,59987,207],{},[902,59989,207],{"encoding":904}," (obrázek 3.8). Limity ",[883,59992,59994],{"className":59993},[886],[888,59995,59996],{"xmlns":890},[892,59997,59998,60036],{},[895,59999,60000,60020,60032,60034],{},[1788,60001,60002,60008],{},[895,60003,60004,60006],{},[898,60005,59522],{},[1688,60007,56440],{},[895,60009,60010,60012,60014],{},[898,60011,1872],{},[1688,60013,3380],{},[1850,60015,60016,60018],{},[1793,60017,1779],{},[1688,60019,1696],{},[1777,60021,60022],{"scriptlevel":1779,"displaystyle":2065},[1781,60023,60024,60030],{},[895,60025,60026,60028],{},[898,60027,10688],{},[898,60029,1693],{},[898,60031,1872],{},[1688,60033,1690],{},[898,60035,6553],{"mathvariant":1822},[902,60037,60038],{"encoding":904},"\\lim_{Q \\to 0^+} \\tfrac{FC}{Q} = \\infty",[883,60040,60042],{"className":60041},[886],[888,60043,60044],{"xmlns":890},[892,60045,60046,60080],{},[895,60047,60048,60064,60076,60078],{},[1788,60049,60050,60056],{},[895,60051,60052,60054],{},[898,60053,59522],{},[1688,60055,56440],{},[895,60057,60058,60060,60062],{},[898,60059,1872],{},[1688,60061,3380],{},[898,60063,6553],{"mathvariant":1822},[1777,60065,60066],{"scriptlevel":1779,"displaystyle":2065},[1781,60067,60068,60074],{},[895,60069,60070,60072],{},[898,60071,10688],{},[898,60073,1693],{},[898,60075,1872],{},[1688,60077,1690],{},[1793,60079,1779],{},[902,60081,60082],{"encoding":904},"\\lim_{Q \\to \\infty} \\tfrac{FC}{Q} = 0"," vysvětlují, proč s rostoucí produkcí fixní náklady stále méně ovlivňují ",[883,60085,60087],{"className":60086},[886],[888,60088,60089],{"xmlns":890},[892,60090,60091,60097],{},[895,60092,60093,60095],{},[898,60094,4512],{},[898,60096,1693],{},[902,60098,55800],{"encoding":904},[724,60100,60101],{},[614,60102,60103,60104,60119,60120,60135,60136,2263],{},"Obrázek 3.7: Přímka ",[883,60105,60107],{"className":60106},[886],[888,60108,60109],{"xmlns":890},[892,60110,60111,60117],{},[895,60112,60113,60115],{},[898,60114,3035],{},[898,60116,1693],{},[902,60118,3500],{"encoding":904}," s osovým průsečíkem ve výši ",[883,60121,60123],{"className":60122},[886],[888,60124,60125],{"xmlns":890},[892,60126,60127,60133],{},[895,60128,60129,60131],{},[898,60130,10688],{},[898,60132,1693],{},[902,60134,55731],{"encoding":904}," a se sklonem ",[883,60137,60139],{"className":60138},[886],[888,60140,60141],{"xmlns":890},[892,60142,60143,60155],{},[895,60144,60145,60147,60149,60151,60153],{},[898,60146,59916],{},[1688,60148,56440],{},[898,60150,19104],{},[1688,60152,1690],{},[898,60154,207],{},[902,60156,59927],{"encoding":904},[724,60158,60159],{},[614,60160,60161,60162,60177,60178,2263],{},"Obrázek 3.8: Klesající hyperbola ",[883,60163,60165],{"className":60164},[886],[888,60166,60167],{"xmlns":890},[892,60168,60169,60175],{},[895,60170,60171,60173],{},[898,60172,4512],{},[898,60174,1693],{},[902,60176,55800],{"encoding":904}," s vodorovnou asymptotou ve výši ",[883,60179,60181],{"className":60180},[886],[888,60182,60183],{"xmlns":890},[892,60184,60185,60189],{},[895,60186,60187],{},[898,60188,207],{},[902,60190,207],{"encoding":904},[198,60192,60194],{"id":60193},"mezní-náklady","Mezní náklady",[724,60196,60197,2170,60199,10277,60214,60217,60218,60221],{},[38,60198,60194],{},[883,60200,60202],{"className":60201},[886],[888,60203,60204],{"xmlns":890},[892,60205,60206,60212],{},[895,60207,60208,60210],{},[898,60209,1661],{},[898,60211,1693],{},[902,60213,55532],{"encoding":904},[38,60215,60216],{},"marginal cost",") jsou ",[207,60219,1145],{"className":60220,"dataFsResolvedFilePath":764,"href":765},[210]," celkových nákladů podle množství:",[883,60223,60225],{"className":60224},[886],[888,60226,60227],{"xmlns":890,"display":28306},[892,60228,60229,60298],{},[20995,60230,60231],{"width":28311},[21000,60232,60233,60235,60291,60293],{},[21003,60234],{"width":28316},[21003,60236,60237],{},[895,60238,60239,60241,60243,60245,60247,60249,60251,60253,60255,60257,60273,60275,60277,60283,60285,60287,60289],{},[898,60240,1661],{},[898,60242,1693],{},[1688,60244,1690],{},[898,60246,1661],{},[898,60248,1693],{},[1688,60250,2066],{"stretchy":2065},[898,60252,1872],{},[1688,60254,2076],{"stretchy":2065},[1688,60256,1690],{},[1781,60258,60259,60267],{},[895,60260,60261,60263,60265],{},[898,60262,2073],{"mathvariant":1822},[898,60264,3035],{},[898,60266,1693],{},[895,60268,60269,60271],{},[898,60270,2073],{"mathvariant":1822},[898,60272,1872],{},[1688,60274,1690],{},[898,60276,3035],{},[1850,60278,60279,60281],{},[898,60280,1693],{},[1688,60282,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,60284,2066],{"stretchy":2065},[898,60286,1872],{},[1688,60288,2076],{"stretchy":2065},[898,60290,2263],{"mathvariant":1822},[21003,60292],{"width":28316},[21003,60294,60295],{},[2041,60296,60297],{},"(3.8)",[902,60299,60300],{"encoding":904},"MC = MC(Q) = \\frac{\\mathrm{d}TC}{\\mathrm{d}Q} = TC'(Q).\n\\tag{3.8}",[4124,60302,60303],{},[724,60304,60305,60307,60308,60334,60335,60352,60353,2263],{},[883,60306,4412],{}," Intuice — „kolik stojí další kus\"\n",[883,60309,60311],{"className":60310},[886],[888,60312,60313],{"xmlns":890},[892,60314,60315,60331],{},[895,60316,60317,60319,60321,60323,60329],{},[898,60318,1661],{},[898,60320,1693],{},[1688,60322,2066],{"stretchy":2065},[1850,60324,60325,60327],{},[898,60326,1872],{},[1688,60328,1857],{},[1688,60330,2076],{"stretchy":2065},[902,60332,60333],{"encoding":904},"MC(Q^*)"," udává přibližné náklady na výrobu jedné další jednotky, když firma aktuálně produkuje ",[883,60336,60338],{"className":60337},[886],[888,60339,60340],{"xmlns":890},[892,60341,60342,60350],{},[895,60343,60344],{},[1850,60345,60346,60348],{},[898,60347,1872],{},[1688,60349,1857],{},[902,60351,30084],{"encoding":904},". Formálně ",[883,60354,60356],{"className":60355},[886],[888,60357,60358],{"xmlns":890},[892,60359,60360,60412],{},[895,60361,60362,60364,60366,60368,60374,60376,60378,60380,60382,60384,60390,60392,60394,60396,60398,60400,60402,60404,60410],{},[898,60363,1661],{},[898,60365,1693],{},[1688,60367,2066],{"stretchy":2065},[1850,60369,60370,60372],{},[898,60371,1872],{},[1688,60373,1857],{},[1688,60375,2076],{"stretchy":2065},[1688,60377,2991],{},[898,60379,3035],{},[898,60381,1693],{},[1688,60383,2066],{"stretchy":2065},[1850,60385,60386,60388],{},[898,60387,1872],{},[1688,60389,1857],{},[1688,60391,1696],{},[1793,60393,1795],{},[1688,60395,2076],{"stretchy":2065},[1688,60397,1954],{},[898,60399,3035],{},[898,60401,1693],{},[1688,60403,2066],{"stretchy":2065},[1850,60405,60406,60408],{},[898,60407,1872],{},[1688,60409,1857],{},[1688,60411,2076],{"stretchy":2065},[902,60413,60414],{"encoding":904},"MC(Q^*) \\approx TC(Q^* + 1) - TC(Q^*)",[724,60416,60417,60418,2965],{},"Analogicky ke vztahu (3.3) platí pro odhad změny ",[883,60419,60421],{"className":60420},[886],[888,60422,60423],{"xmlns":890},[892,60424,60425,60433],{},[895,60426,60427,60429,60431],{},[898,60428,3147],{"mathvariant":1822},[898,60430,3035],{},[898,60432,1693],{},[902,60434,60435],{"encoding":904},"\\Delta TC",[883,60437,60439],{"className":60438},[886],[888,60440,60441],{"xmlns":890,"display":28306},[892,60442,60443,60512],{},[20995,60444,60445],{"width":28311},[21000,60446,60447,60449,60505,60507],{},[21003,60448],{"width":28316},[21003,60450,60451],{},[895,60452,60453,60455,60457,60459,60461,60463,60465,60467,60469,60471,60473,60475,60477,60479,60485,60487,60489,60491,60493,60495,60497,60499,60501,60503],{},[898,60454,3147],{"mathvariant":1822},[898,60456,3035],{},[898,60458,1693],{},[2041,60460,4241],{},[1688,60462,2991],{},[2041,60464,4241],{},[898,60466,2073],{"mathvariant":1822},[898,60468,3035],{},[898,60470,1693],{},[1688,60472,1690],{},[1688,60474,2066],{"stretchy":2065},[898,60476,3035],{},[898,60478,1693],{},[1850,60480,60481,60483],{},[1688,60482,2076],{"stretchy":2065},[1688,60484,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[2041,60486,2043],{},[898,60488,2073],{"mathvariant":1822},[898,60490,1872],{},[1688,60492,1690],{},[898,60494,1661],{},[898,60496,1693],{},[2041,60498,2043],{},[898,60500,2073],{"mathvariant":1822},[898,60502,1872],{},[1688,60504,1733],{"separator":1732},[21003,60506],{"width":28316},[21003,60508,60509],{},[2041,60510,60511],{},"(3.9)",[902,60513,60514],{"encoding":904},"\\Delta TC \\;\\approx\\; \\mathrm{d}TC = (TC)' \\, \\mathrm{d}Q = MC \\, \\mathrm{d}Q,\n\\tag{3.9}",[724,60516,57551],{},[883,60518,60520],{"className":60519},[886],[888,60521,60522],{"xmlns":890,"display":28306},[892,60523,60524,60622],{},[895,60525,60526,60564,60566,60568,60570,60592,60594,60620],{},[895,60527,60528,60530,60536,60538,60544,60547,60553,60556],{},[2041,60529,57565],{},[8642,60531,60532,60534],{"accent":1732},[2041,60533,45972],{},[1688,60535,25299],{},[2041,60537,57574],{},[8642,60539,60540,60542],{"accent":1732},[2041,60541,2282],{},[1688,60543,25218],{},[2041,60545,60546],{},"ch n",[8642,60548,60549,60551],{"accent":1732},[2041,60550,207],{},[1688,60552,25218],{},[2041,60554,60555],{},"klad",[8642,60557,60558,60561],{"accent":1732},[2041,60559,60560],{},"u",[1688,60562,60563],{},"˚",[2041,60565,4241],{},[1688,60567,2991],{},[2041,60569,4241],{},[895,60571,60572,60574,60580,60583,60589],{},[2041,60573,57609],{},[8642,60575,60576,60578],{"accent":1732},[2041,60577,25287],{},[1688,60579,25218],{},[2041,60581,60582],{}," n",[8642,60584,60585,60587],{"accent":1732},[2041,60586,207],{},[1688,60588,25218],{},[2041,60590,60591],{},"klady",[1688,60593,57636],{},[895,60595,60596,60598,60604,60606,60612,60614],{},[2041,60597,57565],{},[8642,60599,60600,60602],{"accent":1732},[2041,60601,45972],{},[1688,60603,25299],{},[2041,60605,57649],{},[8642,60607,60608,60610],{"accent":1732},[2041,60609,9847],{},[1688,60611,25299],{},[2041,60613,57658],{},[8642,60615,60616,60618],{"accent":1732},[2041,60617,25287],{},[1688,60619,25218],{},[898,60621,2263],{"mathvariant":1822},[902,60623,60624],{"encoding":904},"\\text{změna celkových nákladů} \\;\\approx\\; \\text{mezní náklady} \\times \\text{změna množství}.",[37588,60626,60628],{"id":60627},"příklad-35","Příklad 3.5",[724,60630,60631,57762,60633,56265,60669,60684,60685,60700,60701,2194,60714,2946,60727,60740,60741,2946,60754,2263],{},[38,60632,56227],{},[883,60634,60636],{"className":60635},[886],[888,60637,60638],{"xmlns":890},[892,60639,60640,60666],{},[895,60641,60642,60644,60646,60648,60650,60652,60654,60656,60658,60660],{},[898,60643,3035],{},[898,60645,1693],{},[1688,60647,1690],{},[1793,60649,8633],{},[1688,60651,1696],{},[1793,60653,2508],{},[898,60655,1872],{},[1688,60657,1696],{},[1793,60659,1806],{},[1850,60661,60662,60664],{},[898,60663,1872],{},[1793,60665,1806],{},[902,60667,60668],{"encoding":904},"TC = 200 + 6Q + 2Q^2",[883,60670,60672],{"className":60671},[886],[888,60673,60674],{"xmlns":890},[892,60675,60676,60682],{},[895,60677,60678,60680],{},[898,60679,1661],{},[898,60681,1693],{},[902,60683,55532],{"encoding":904}," a odhadněte změny ",[883,60686,60688],{"className":60687},[886],[888,60689,60690],{"xmlns":890},[892,60691,60692,60698],{},[895,60693,60694,60696],{},[898,60695,3035],{},[898,60697,1693],{},[902,60699,3500],{"encoding":904}," při změnách ",[883,60702,60704],{"className":60703},[886],[888,60705,60706],{"xmlns":890},[892,60707,60708,60712],{},[895,60709,60710],{},[898,60711,1872],{},[902,60713,1872],{"encoding":904},[883,60715,60717],{"className":60716},[886],[888,60718,60719],{"xmlns":890},[892,60720,60721,60725],{},[895,60722,60723],{},[1793,60724,36484],{},[902,60726,36484],{"encoding":904},[883,60728,60730],{"className":60729},[886],[888,60731,60732],{"xmlns":890},[892,60733,60734,60738],{},[895,60735,60736],{},[1793,60737,42102],{},[902,60739,42102],{"encoding":904}," a z ",[883,60742,60744],{"className":60743},[886],[888,60745,60746],{"xmlns":890},[892,60747,60748,60752],{},[895,60749,60750],{},[1793,60751,36484],{},[902,60753,36484],{"encoding":904},[883,60755,60757],{"className":60756},[886],[888,60758,60759],{"xmlns":890},[892,60760,60761,60765],{},[895,60762,60763],{},[1793,60764,3766],{},[902,60766,3766],{"encoding":904},[724,60768,60769,2170,60771,3185,60797,1343,60824,60851,60852,60867,60868,60883,60884,60911,60912,60932,60933,20772,60954,61010,61011,2194,61024,2946,61037,8358,61050,2263],{},[38,60770,23011],{},[883,60772,60774],{"className":60773},[886],[888,60775,60776],{"xmlns":890},[892,60777,60778,60794],{},[895,60779,60780,60782,60784,60786,60788,60790,60792],{},[898,60781,1661],{},[898,60783,1693],{},[1688,60785,1690],{},[1793,60787,2508],{},[1688,60789,1696],{},[1793,60791,2616],{},[898,60793,1872],{},[902,60795,60796],{"encoding":904},"MC = 6 + 4Q",[883,60798,60800],{"className":60799},[886],[888,60801,60802],{"xmlns":890},[892,60803,60804,60821],{},[895,60805,60806,60808,60810,60812,60814,60816,60818],{},[898,60807,1661],{},[898,60809,1693],{},[1688,60811,2066],{"stretchy":2065},[1793,60813,36484],{},[1688,60815,2076],{"stretchy":2065},[1688,60817,1690],{},[1793,60819,60820],{},"66",[902,60822,60823],{"encoding":904},"MC(15) = 66",[883,60825,60827],{"className":60826},[886],[888,60828,60829],{"xmlns":890},[892,60830,60831,60848],{},[895,60832,60833,60835,60837,60839,60841,60843,60845],{},[898,60834,1661],{},[898,60836,1693],{},[1688,60838,2066],{"stretchy":2065},[1793,60840,9290],{},[1688,60842,2076],{"stretchy":2065},[1688,60844,1690],{},[1793,60846,60847],{},"86",[902,60849,60850],{"encoding":904},"MC(20) = 86",": s růstem množství se rychlost změny ",[883,60853,60855],{"className":60854},[886],[888,60856,60857],{"xmlns":890},[892,60858,60859,60865],{},[895,60860,60861,60863],{},[898,60862,3035],{},[898,60864,1693],{},[902,60866,3500],{"encoding":904}," zvyšuje (",[883,60869,60871],{"className":60870},[886],[888,60872,60873],{"xmlns":890},[892,60874,60875,60881],{},[895,60876,60877,60879],{},[898,60878,1661],{},[898,60880,1693],{},[902,60882,55532],{"encoding":904}," je rostoucí). Z ",[883,60885,60887],{"className":60886},[886],[888,60888,60889],{"xmlns":890},[892,60890,60891,60908],{},[895,60892,60893,60895,60897,60899,60901,60903,60905],{},[898,60894,3035],{},[898,60896,1693],{},[1688,60898,2066],{"stretchy":2065},[1793,60900,36484],{},[1688,60902,2076],{"stretchy":2065},[1688,60904,1690],{},[1793,60906,60907],{},"740",[902,60909,60910],{"encoding":904},"TC(15) = 740"," se po přírůstku ",[883,60913,60915],{"className":60914},[886],[888,60916,60917],{"xmlns":890},[892,60918,60919,60929],{},[895,60920,60921,60923,60925,60927],{},[898,60922,2073],{"mathvariant":1822},[898,60924,1872],{},[1688,60926,1690],{},[1793,60928,1795],{},[902,60930,60931],{"encoding":904},"\\mathrm{d}Q = 1"," předpokládá ",[883,60934,60936],{"className":60935},[886],[888,60937,60938],{"xmlns":890},[892,60939,60940,60951],{},[895,60941,60942,60944,60946,60948],{},[898,60943,3035],{},[898,60945,1693],{},[1688,60947,2991],{},[1793,60949,60950],{},"806",[902,60952,60953],{"encoding":904},"TC \\approx 806",[883,60955,60957],{"className":60956},[886],[888,60958,60959],{"xmlns":890},[892,60960,60961,61007],{},[895,60962,60963,60965,60967,60969,60971,60973,60975,60977,60979,60981,60983,60985,60987,60989,60991,60993,60995,60998,61000,61002,61004],{},[898,60964,3147],{"mathvariant":1822},[898,60966,3035],{},[898,60968,1693],{},[1688,60970,1690],{},[898,60972,3035],{},[898,60974,1693],{},[1688,60976,2066],{"stretchy":2065},[1793,60978,42102],{},[1688,60980,2076],{"stretchy":2065},[1688,60982,1954],{},[898,60984,3035],{},[898,60986,1693],{},[1688,60988,2066],{"stretchy":2065},[1793,60990,36484],{},[1688,60992,2076],{"stretchy":2065},[1688,60994,1690],{},[1793,60996,60997],{},"808",[1688,60999,1954],{},[1793,61001,60907],{},[1688,61003,1690],{},[1793,61005,61006],{},"68",[902,61008,61009],{"encoding":904},"\\Delta TC = TC(16) - TC(15) = 808 - 740 = 68",". Při poklesu ",[883,61012,61014],{"className":61013},[886],[888,61015,61016],{"xmlns":890},[892,61017,61018,61022],{},[895,61019,61020],{},[898,61021,1872],{},[902,61023,1872],{"encoding":904},[883,61025,61027],{"className":61026},[886],[888,61028,61029],{"xmlns":890},[892,61030,61031,61035],{},[895,61032,61033],{},[1793,61034,36484],{},[902,61036,36484],{"encoding":904},[883,61038,61040],{"className":61039},[886],[888,61041,61042],{"xmlns":890},[892,61043,61044,61048],{},[895,61045,61046],{},[1793,61047,3766],{},[902,61049,3766],{"encoding":904},[883,61051,61053],{"className":61052},[886],[888,61054,61055],{"xmlns":890},[892,61056,61057,61086],{},[895,61058,61059,61061,61063,61065,61067,61069,61071,61073,61075,61077,61079,61081,61083],{},[898,61060,3147],{"mathvariant":1822},[898,61062,3035],{},[898,61064,1693],{},[1688,61066,2991],{},[1793,61068,60820],{},[1688,61070,3434],{},[1688,61072,2066],{"stretchy":2065},[1688,61074,1954],{},[1793,61076,2131],{},[1688,61078,2076],{"stretchy":2065},[1688,61080,1690],{},[1688,61082,1954],{},[1793,61084,61085],{},"198",[902,61087,61088],{"encoding":904},"\\Delta TC \\approx 66 \\cdot (-3) = -198",[198,61090,61092],{"id":61091},"kubická-nákladová-funkce","Kubická nákladová funkce",[724,61094,61095],{},"V ekonomicky reálných situacích mají křivky nákladů charakteristické vazby a tvary.",[37588,61097,61099],{"id":61098},"příklad-36","Příklad 3.6",[724,61101,61102,57762,61104,61148],{},[38,61103,56227],{},[883,61105,61107],{"className":61106},[886],[888,61108,61109],{"xmlns":890},[892,61110,61111,61145],{},[895,61112,61113,61115,61117,61119,61121,61123,61125,61127,61129,61131,61137,61139],{},[898,61114,3035],{},[898,61116,1693],{},[1688,61118,1690],{},[1793,61120,3347],{},[1688,61122,1696],{},[1793,61124,5260],{},[898,61126,1872],{},[1688,61128,1954],{},[1793,61130,2501],{},[1850,61132,61133,61135],{},[898,61134,1872],{},[1793,61136,1806],{},[1688,61138,1696],{},[1850,61140,61141,61143],{},[898,61142,1872],{},[1793,61144,2131],{},[902,61146,61147],{"encoding":904},"TC = 100 + 25Q - 5Q^2 + Q^3"," odvoďte všechny nákladové charakteristiky.",[724,61150,61151],{},[38,61152,23011],{},[883,61154,61156],{"className":61155},[886],[888,61157,61158],{"xmlns":890,"display":28306},[892,61159,61160,61404],{},[20995,61161,61162,61188,61236,61270,61312,61362],{"rowspacing":20997,"columnalign":20998,"columnspacing":1823},[21000,61163,61164,61174],{},[21003,61165,61166],{},[1777,61167,61168],{"scriptlevel":1779,"displaystyle":1732},[895,61169,61170,61172],{},[898,61171,10688],{},[898,61173,1693],{},[21003,61175,61176],{},[1777,61177,61178],{"scriptlevel":1779,"displaystyle":1732},[895,61179,61180,61182,61184,61186],{},[895,61181],{},[1688,61183,1690],{},[1793,61185,3347],{},[1688,61187,1733],{"separator":1732},[21000,61189,61190,61202],{},[21003,61191,61192],{},[1777,61193,61194],{"scriptlevel":1779,"displaystyle":1732},[895,61195,61196,61198,61200],{},[898,61197,3035],{},[898,61199,40579],{},[898,61201,1693],{},[21003,61203,61204],{},[1777,61205,61206],{"scriptlevel":1779,"displaystyle":1732},[895,61207,61208,61210,61212,61214,61216,61218,61220,61226,61228,61234],{},[895,61209],{},[1688,61211,1690],{},[1793,61213,5260],{},[898,61215,1872],{},[1688,61217,1954],{},[1793,61219,2501],{},[1850,61221,61222,61224],{},[898,61223,1872],{},[1793,61225,1806],{},[1688,61227,1696],{},[1850,61229,61230,61232],{},[898,61231,1872],{},[1793,61233,2131],{},[1688,61235,1733],{"separator":1732},[21000,61237,61238,61250],{},[21003,61239,61240],{},[1777,61241,61242],{"scriptlevel":1779,"displaystyle":1732},[895,61243,61244,61246,61248],{},[898,61245,4512],{},[898,61247,10688],{},[898,61249,1693],{},[21003,61251,61252],{},[1777,61253,61254],{"scriptlevel":1779,"displaystyle":1732},[895,61255,61256,61258,61260,61268],{},[895,61257],{},[1688,61259,1690],{},[1777,61261,61262],{"scriptlevel":1779,"displaystyle":2065},[1781,61263,61264,61266],{},[1793,61265,3347],{},[898,61267,1872],{},[1688,61269,1733],{"separator":1732},[21000,61271,61272,61284],{},[21003,61273,61274],{},[1777,61275,61276],{"scriptlevel":1779,"displaystyle":1732},[895,61277,61278,61280,61282],{},[898,61279,4512],{},[898,61281,40579],{},[898,61283,1693],{},[21003,61285,61286],{},[1777,61287,61288],{"scriptlevel":1779,"displaystyle":1732},[895,61289,61290,61292,61294,61296,61298,61300,61302,61304,61310],{},[895,61291],{},[1688,61293,1690],{},[1793,61295,5260],{},[1688,61297,1954],{},[1793,61299,2501],{},[898,61301,1872],{},[1688,61303,1696],{},[1850,61305,61306,61308],{},[898,61307,1872],{},[1793,61309,1806],{},[1688,61311,1733],{"separator":1732},[21000,61313,61314,61324],{},[21003,61315,61316],{},[1777,61317,61318],{"scriptlevel":1779,"displaystyle":1732},[895,61319,61320,61322],{},[898,61321,4512],{},[898,61323,1693],{},[21003,61325,61326],{},[1777,61327,61328],{"scriptlevel":1779,"displaystyle":1732},[895,61329,61330,61332,61334,61342,61344,61346,61348,61350,61352,61354,61360],{},[895,61331],{},[1688,61333,1690],{},[1777,61335,61336],{"scriptlevel":1779,"displaystyle":2065},[1781,61337,61338,61340],{},[1793,61339,3347],{},[898,61341,1872],{},[1688,61343,1696],{},[1793,61345,5260],{},[1688,61347,1954],{},[1793,61349,2501],{},[898,61351,1872],{},[1688,61353,1696],{},[1850,61355,61356,61358],{},[898,61357,1872],{},[1793,61359,1806],{},[1688,61361,1733],{"separator":1732},[21000,61363,61364,61374],{},[21003,61365,61366],{},[1777,61367,61368],{"scriptlevel":1779,"displaystyle":1732},[895,61369,61370,61372],{},[898,61371,1661],{},[898,61373,1693],{},[21003,61375,61376],{},[1777,61377,61378],{"scriptlevel":1779,"displaystyle":1732},[895,61379,61380,61382,61384,61386,61388,61390,61392,61394,61396,61402],{},[895,61381],{},[1688,61383,1690],{},[1793,61385,5260],{},[1688,61387,1954],{},[1793,61389,3121],{},[898,61391,1872],{},[1688,61393,1696],{},[1793,61395,2131],{},[1850,61397,61398,61400],{},[898,61399,1872],{},[1793,61401,1806],{},[898,61403,2263],{"mathvariant":1822},[902,61405,61406],{"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}",[724,61408,61409,61410,16039,61425,16039,61440,61455,61456,61471,61472,1343,61490,61471,61507,1343,61525,61471,61540,61558],{},"Význačné body ",[883,61411,61413],{"className":61412},[886],[888,61414,61415],{"xmlns":890},[892,61416,61417,61422],{},[895,61418,61419],{},[1793,61420,61421],{},"1,67",[902,61423,61424],{"encoding":904},"1{,}67",[883,61426,61428],{"className":61427},[886],[888,61429,61430],{"xmlns":890},[892,61431,61432,61437],{},[895,61433,61434],{},[1793,61435,61436],{},"2,50",[902,61438,61439],{"encoding":904},"2{,}50",[883,61441,61443],{"className":61442},[886],[888,61444,61445],{"xmlns":890},[892,61446,61447,61452],{},[895,61448,61449],{},[1793,61450,61451],{},"4,73",[902,61453,61454],{"encoding":904},"4{,}73"," odpovídají: ",[883,61457,61459],{"className":61458},[886],[888,61460,61461],{"xmlns":890},[892,61462,61463,61469],{},[895,61464,61465,61467],{},[898,61466,1661],{},[898,61468,1693],{},[902,61470,55532],{"encoding":904}," minimum v ",[883,61473,61475],{"className":61474},[886],[888,61476,61477],{"xmlns":890},[892,61478,61479,61487],{},[895,61480,61481,61483,61485],{},[898,61482,1872],{},[1688,61484,6156],{},[1793,61486,61421],{},[902,61488,61489],{"encoding":904},"Q \\doteq 1{,}67",[883,61491,61493],{"className":61492},[886],[888,61494,61495],{"xmlns":890},[892,61496,61497,61505],{},[895,61498,61499,61501,61503],{},[898,61500,4512],{},[898,61502,40579],{},[898,61504,1693],{},[902,61506,55551],{"encoding":904},[883,61508,61510],{"className":61509},[886],[888,61511,61512],{"xmlns":890},[892,61513,61514,61522],{},[895,61515,61516,61518,61520],{},[898,61517,1872],{},[1688,61519,1690],{},[1793,61521,61436],{},[902,61523,61524],{"encoding":904},"Q = 2{,}50",[883,61526,61528],{"className":61527},[886],[888,61529,61530],{"xmlns":890},[892,61531,61532,61538],{},[895,61533,61534,61536],{},[898,61535,4512],{},[898,61537,1693],{},[902,61539,55800],{"encoding":904},[883,61541,61543],{"className":61542},[886],[888,61544,61545],{"xmlns":890},[892,61546,61547,61555],{},[895,61548,61549,61551,61553],{},[898,61550,1872],{},[1688,61552,6156],{},[1793,61554,61451],{},[902,61556,61557],{"encoding":904},"Q \\doteq 4{,}73"," (téma úlohy 3.11).",[724,61560,61561],{},[2821,61562],{"alt":61563,"className":61564,"src":61565},"imek-ac-avc-mc",[210,2825],"\u002Fwiki-assets\u002Fimek-ac-avc-mc.jpeg",[724,61567,61568],{},[614,61569,61570,61571,4142,61586,61603,61604,16039,61623,61638],{},"Obrázek 3.9: Kubické křivky ",[883,61572,61574],{"className":61573},[886],[888,61575,61576],{"xmlns":890},[892,61577,61578,61584],{},[895,61579,61580,61582],{},[898,61581,3035],{},[898,61583,1693],{},[902,61585,3500],{"encoding":904},[883,61587,61589],{"className":61588},[886],[888,61590,61591],{"xmlns":890},[892,61592,61593,61601],{},[895,61594,61595,61597,61599],{},[898,61596,3035],{},[898,61598,40579],{},[898,61600,1693],{},[902,61602,55749],{"encoding":904}," rostoucí od bodu ",[883,61605,61607],{"className":61606},[886],[888,61608,61609],{"xmlns":890},[892,61610,61611,61621],{},[895,61612,61613,61615,61617,61619],{},[898,61614,10688],{},[898,61616,1693],{},[1688,61618,1690],{},[1793,61620,3347],{},[902,61622,11885],{"encoding":904},[883,61624,61626],{"className":61625},[886],[888,61627,61628],{"xmlns":890},[892,61629,61630,61636],{},[895,61631,61632,61634],{},[898,61633,10688],{},[898,61635,1693],{},[902,61637,55731],{"encoding":904}," je vodorovná přímka.",[724,61640,61641],{},[614,61642,61643,61644,1343,61659,1343,61676,29441,61691,61704,61705,3185,61722,61737,61738,6446,61755,61770,61771,26430,61784,1343,61797,1343,61810,2263],{},"Obrázek 3.10: Křivky ",[883,61645,61647],{"className":61646},[886],[888,61648,61649],{"xmlns":890},[892,61650,61651,61657],{},[895,61652,61653,61655],{},[898,61654,4512],{},[898,61656,1693],{},[902,61658,55800],{"encoding":904},[883,61660,61662],{"className":61661},[886],[888,61663,61664],{"xmlns":890},[892,61665,61666,61674],{},[895,61667,61668,61670,61672],{},[898,61669,4512],{},[898,61671,40579],{},[898,61673,1693],{},[902,61675,55551],{"encoding":904},[883,61677,61679],{"className":61678},[886],[888,61680,61681],{"xmlns":890},[892,61682,61683,61689],{},[895,61684,61685,61687],{},[898,61686,1661],{},[898,61688,1693],{},[902,61690,55532],{"encoding":904},[883,61692,61694],{"className":61693},[886],[888,61695,61696],{"xmlns":890},[892,61697,61698,61702],{},[895,61699,61700],{},[898,61701,900],{},[902,61703,900],{"encoding":904}," a klesající hyperbola ",[883,61706,61708],{"className":61707},[886],[888,61709,61710],{"xmlns":890},[892,61711,61712,61720],{},[895,61713,61714,61716,61718],{},[898,61715,4512],{},[898,61717,10688],{},[898,61719,1693],{},[902,61721,55767],{"encoding":904},[883,61723,61725],{"className":61724},[886],[888,61726,61727],{"xmlns":890},[892,61728,61729,61735],{},[895,61730,61731,61733],{},[898,61732,1661],{},[898,61734,1693],{},[902,61736,55532],{"encoding":904}," protíná ",[883,61739,61741],{"className":61740},[886],[888,61742,61743],{"xmlns":890},[892,61744,61745,61753],{},[895,61746,61747,61749,61751],{},[898,61748,4512],{},[898,61750,40579],{},[898,61752,1693],{},[902,61754,55551],{"encoding":904},[883,61756,61758],{"className":61757},[886],[888,61759,61760],{"xmlns":890},[892,61761,61762,61768],{},[895,61763,61764,61766],{},[898,61765,4512],{},[898,61767,1693],{},[902,61769,55800],{"encoding":904}," zdola v jejich minimech; význačné hodnoty na ose ",[883,61772,61774],{"className":61773},[886],[888,61775,61776],{"xmlns":890},[892,61777,61778,61782],{},[895,61779,61780],{},[898,61781,1872],{},[902,61783,1872],{"encoding":904},[883,61785,61787],{"className":61786},[886],[888,61788,61789],{"xmlns":890},[892,61790,61791,61795],{},[895,61792,61793],{},[1793,61794,61421],{},[902,61796,61424],{"encoding":904},[883,61798,61800],{"className":61799},[886],[888,61801,61802],{"xmlns":890},[892,61803,61804,61808],{},[895,61805,61806],{},[1793,61807,61436],{},[902,61809,61439],{"encoding":904},[883,61811,61813],{"className":61812},[886],[888,61814,61815],{"xmlns":890},[892,61816,61817,61821],{},[895,61818,61819],{},[1793,61820,61451],{},[902,61822,61454],{"encoding":904},[724,61824,61825],{},[38,61826,61827],{},"Standardní vlastnosti:",[120,61829,61830,61865,61929,61997,62047,62067],{},[123,61831,61832,4142,61847,61864],{},[883,61833,61835],{"className":61834},[886],[888,61836,61837],{"xmlns":890},[892,61838,61839,61845],{},[895,61840,61841,61843],{},[898,61842,3035],{},[898,61844,1693],{},[902,61846,3500],{"encoding":904},[883,61848,61850],{"className":61849},[886],[888,61851,61852],{"xmlns":890},[892,61853,61854,61862],{},[895,61855,61856,61858,61860],{},[898,61857,3035],{},[898,61859,40579],{},[898,61861,1693],{},[902,61863,55749],{"encoding":904}," jsou kubické funkce;",[123,61866,61867,1343,61882,1343,61899,61914,61915,61928],{},[883,61868,61870],{"className":61869},[886],[888,61871,61872],{"xmlns":890},[892,61873,61874,61880],{},[895,61875,61876,61878],{},[898,61877,4512],{},[898,61879,1693],{},[902,61881,55800],{"encoding":904},[883,61883,61885],{"className":61884},[886],[888,61886,61887],{"xmlns":890},[892,61888,61889,61897],{},[895,61890,61891,61893,61895],{},[898,61892,4512],{},[898,61894,40579],{},[898,61896,1693],{},[902,61898,55551],{"encoding":904},[883,61900,61902],{"className":61901},[886],[888,61903,61904],{"xmlns":890},[892,61905,61906,61912],{},[895,61907,61908,61910],{},[898,61909,1661],{},[898,61911,1693],{},[902,61913,55532],{"encoding":904}," jsou křivky tvaru ",[883,61916,61918],{"className":61917},[886],[888,61919,61920],{"xmlns":890},[892,61921,61922,61926],{},[895,61923,61924],{},[898,61925,900],{},[902,61927,900],{"encoding":904}," (nejprve klesají, po minimu rostou);",[123,61930,61931,61946,61947,1343,61964,61981,61982,8681],{},[883,61932,61934],{"className":61933},[886],[888,61935,61936],{"xmlns":890},[892,61937,61938,61944],{},[895,61939,61940,61942],{},[898,61941,1661],{},[898,61943,1693],{},[902,61945,55532],{"encoding":904}," nabývá minima před ",[883,61948,61950],{"className":61949},[886],[888,61951,61952],{"xmlns":890},[892,61953,61954,61962],{},[895,61955,61956,61958,61960],{},[898,61957,4512],{},[898,61959,40579],{},[898,61961,1693],{},[902,61963,55551],{"encoding":904},[883,61965,61967],{"className":61966},[886],[888,61968,61969],{"xmlns":890},[892,61970,61971,61979],{},[895,61972,61973,61975,61977],{},[898,61974,4512],{},[898,61976,40579],{},[898,61978,1693],{},[902,61980,55551],{"encoding":904}," před ",[883,61983,61985],{"className":61984},[886],[888,61986,61987],{"xmlns":890},[892,61988,61989,61995],{},[895,61990,61991,61993],{},[898,61992,4512],{},[898,61994,1693],{},[902,61996,55800],{"encoding":904},[123,61998,61999,61737,62014,4142,62029,62046],{},[883,62000,62002],{"className":62001},[886],[888,62003,62004],{"xmlns":890},[892,62005,62006,62012],{},[895,62007,62008,62010],{},[898,62009,1661],{},[898,62011,1693],{},[902,62013,55532],{"encoding":904},[883,62015,62017],{"className":62016},[886],[888,62018,62019],{"xmlns":890},[892,62020,62021,62027],{},[895,62022,62023,62025],{},[898,62024,4512],{},[898,62026,1693],{},[902,62028,55800],{"encoding":904},[883,62030,62032],{"className":62031},[886],[888,62033,62034],{"xmlns":890},[892,62035,62036,62044],{},[895,62037,62038,62040,62042],{},[898,62039,4512],{},[898,62041,40579],{},[898,62043,1693],{},[902,62045,55551],{"encoding":904}," zdola právě v jejich minimech;",[123,62048,62049,62066],{},[883,62050,62052],{"className":62051},[886],[888,62053,62054],{"xmlns":890},[892,62055,62056,62064],{},[895,62057,62058,62060,62062],{},[898,62059,4512],{},[898,62061,10688],{},[898,62063,1693],{},[902,62065,55767],{"encoding":904}," je hyperbola, stále klesající;",[123,62068,62069,62101,62102,4142,62117,62134,62135,62148,62149,4176],{},[883,62070,62072],{"className":62071},[886],[888,62073,62074],{"xmlns":890},[892,62075,62076,62098],{},[895,62077,62078,62080,62082,62084,62086,62088,62090,62092,62094,62096],{},[898,62079,4512],{},[898,62081,1693],{},[1688,62083,1690],{},[898,62085,4512],{},[898,62087,10688],{},[898,62089,1693],{},[1688,62091,1696],{},[898,62093,4512],{},[898,62095,40579],{},[898,62097,1693],{},[902,62099,62100],{"encoding":904},"AC = AFC + AVC","; vzdálenost mezi ",[883,62103,62105],{"className":62104},[886],[888,62106,62107],{"xmlns":890},[892,62108,62109,62115],{},[895,62110,62111,62113],{},[898,62112,4512],{},[898,62114,1693],{},[902,62116,55800],{"encoding":904},[883,62118,62120],{"className":62119},[886],[888,62121,62122],{"xmlns":890},[892,62123,62124,62132],{},[895,62125,62126,62128,62130],{},[898,62127,4512],{},[898,62129,40579],{},[898,62131,1693],{},[902,62133,55551],{"encoding":904}," klesá s rostoucím ",[883,62136,62138],{"className":62137},[886],[888,62139,62140],{"xmlns":890},[892,62141,62142,62146],{},[895,62143,62144],{},[898,62145,1872],{},[902,62147,1872],{"encoding":904}," (protože ",[883,62150,62152],{"className":62151},[886],[888,62153,62154],{"xmlns":890},[892,62155,62156,62168],{},[895,62157,62158,62160,62162,62164,62166],{},[898,62159,4512],{},[898,62161,10688],{},[898,62163,1693],{},[1688,62165,3380],{},[1793,62167,1779],{},[902,62169,62170],{"encoding":904},"AFC \\to 0",[115,62172,62174],{"id":62173},"princip-minimalizace-průměrných-nákladů","Princip minimalizace průměrných nákladů",[724,62176,62177,62178,62181,62182,62197],{},"Častou optimalizační úlohou je ",[38,62179,62180],{},"minimalizace průměrných nákladů"," — stanovení produkce, pro niž je ",[883,62183,62185],{"className":62184},[886],[888,62186,62187],{"xmlns":890},[892,62188,62189,62195],{},[895,62190,62191,62193],{},[898,62192,4512],{},[898,62194,1693],{},[902,62196,55800],{"encoding":904}," minimální.",[198,62199,16659],{"id":16658},[724,62201,62202,62203,62220],{},"Mají-li průměrné náklady minimum v bodě ",[883,62204,62206],{"className":62205},[886],[888,62207,62208],{"xmlns":890},[892,62209,62210,62218],{},[895,62211,62212],{},[1788,62213,62214,62216],{},[898,62215,1872],{},[1793,62217,1779],{},[902,62219,38548],{"encoding":904},", pak platí",[883,62222,62224],{"className":62223},[886],[888,62225,62226],{"xmlns":890,"display":28306},[892,62227,62228,62277],{},[20995,62229,62230],{"width":28311},[21000,62231,62232,62234,62270,62272],{},[21003,62233],{"width":28316},[21003,62235,62236],{},[895,62237,62238,62240,62242,62244,62250,62252,62254,62256,62258,62260,62266,62268],{},[898,62239,4512],{},[898,62241,1693],{},[1688,62243,2066],{"stretchy":2065},[1788,62245,62246,62248],{},[898,62247,1872],{},[1793,62249,1779],{},[1688,62251,2076],{"stretchy":2065},[1688,62253,1690],{},[898,62255,1661],{},[898,62257,1693],{},[1688,62259,2066],{"stretchy":2065},[1788,62261,62262,62264],{},[898,62263,1872],{},[1793,62265,1779],{},[1688,62267,2076],{"stretchy":2065},[898,62269,2263],{"mathvariant":1822},[21003,62271],{"width":28316},[21003,62273,62274],{},[2041,62275,62276],{},"(3.10)",[902,62278,62279],{"encoding":904},"AC(Q_0) = MC(Q_0).\n\\tag{3.10}",[4124,62281,62282],{},[724,62283,62284,62286,62287],{},[883,62285,56684],{}," Princip\n",[38,62288,62289],{},"V bodě minima průměrných nákladů se průměrné náklady rovnají mezním nákladům.",[724,62291,62292,62295,62296,62338],{},[38,62293,62294],{},"Odvození."," Z ",[883,62297,62299],{"className":62298},[886],[888,62300,62301],{"xmlns":890},[892,62302,62303,62335],{},[895,62304,62305,62307,62309,62311,62313,62315,62317],{},[898,62306,4512],{},[898,62308,1693],{},[1688,62310,2066],{"stretchy":2065},[898,62312,1872],{},[1688,62314,2076],{"stretchy":2065},[1688,62316,1690],{},[1777,62318,62319],{"scriptlevel":1779,"displaystyle":2065},[1781,62320,62321,62333],{},[895,62322,62323,62325,62327,62329,62331],{},[898,62324,3035],{},[898,62326,1693],{},[1688,62328,2066],{"stretchy":2065},[898,62330,1872],{},[1688,62332,2076],{"stretchy":2065},[898,62334,1872],{},[902,62336,62337],{"encoding":904},"AC(Q) = \\tfrac{TC(Q)}{Q}"," derivací podílu plyne",[883,62340,62342],{"className":62341},[886],[888,62343,62344],{"xmlns":890,"display":28306},[892,62345,62346,62478],{},[895,62347,62348,62350,62356,62358,62360,62362,62364,62404,62406,62446,62448,62476],{},[898,62349,4512],{},[1850,62351,62352,62354],{},[898,62353,1693],{},[1688,62355,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,62357,2066],{"stretchy":2065},[898,62359,1872],{},[1688,62361,2076],{"stretchy":2065},[1688,62363,1690],{},[1781,62365,62366,62398],{},[895,62367,62368,62370,62376,62378,62380,62382,62384,62386,62388,62390,62392,62394,62396],{},[898,62369,3035],{},[1850,62371,62372,62374],{},[898,62373,1693],{},[1688,62375,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,62377,2066],{"stretchy":2065},[898,62379,1872],{},[1688,62381,2076],{"stretchy":2065},[1688,62383,3434],{},[898,62385,1872],{},[1688,62387,1954],{},[898,62389,3035],{},[898,62391,1693],{},[1688,62393,2066],{"stretchy":2065},[898,62395,1872],{},[1688,62397,2076],{"stretchy":2065},[1850,62399,62400,62402],{},[898,62401,1872],{},[1793,62403,1806],{},[1688,62405,1690],{},[1781,62407,62408,62440],{},[895,62409,62410,62412,62414,62416,62418,62420,62422,62424,62426,62428,62430,62432,62434,62436,62438],{},[898,62411,1661],{},[898,62413,1693],{},[1688,62415,2066],{"stretchy":2065},[898,62417,1872],{},[1688,62419,2076],{"stretchy":2065},[1688,62421,3434],{},[898,62423,1872],{},[1688,62425,1954],{},[898,62427,4512],{},[898,62429,1693],{},[1688,62431,2066],{"stretchy":2065},[898,62433,1872],{},[1688,62435,2076],{"stretchy":2065},[1688,62437,3434],{},[898,62439,1872],{},[1850,62441,62442,62444],{},[898,62443,1872],{},[1793,62445,1806],{},[1688,62447,1690],{},[1781,62449,62450,62474],{},[895,62451,62452,62454,62456,62458,62460,62462,62464,62466,62468,62470,62472],{},[898,62453,1661],{},[898,62455,1693],{},[1688,62457,2066],{"stretchy":2065},[898,62459,1872],{},[1688,62461,2076],{"stretchy":2065},[1688,62463,1954],{},[898,62465,4512],{},[898,62467,1693],{},[1688,62469,2066],{"stretchy":2065},[898,62471,1872],{},[1688,62473,2076],{"stretchy":2065},[898,62475,1872],{},[898,62477,2263],{"mathvariant":1822},[902,62479,62480],{"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}.",[724,62482,62483,62484,2886,62499,8358,62521,57061],{},"Nutnou podmínkou minima ",[883,62485,62487],{"className":62486},[886],[888,62488,62489],{"xmlns":890},[892,62490,62491,62497],{},[895,62492,62493,62495],{},[898,62494,4512],{},[898,62496,1693],{},[902,62498,55800],{"encoding":904},[883,62500,62502],{"className":62501},[886],[888,62503,62504],{"xmlns":890},[892,62505,62506,62518],{},[895,62507,62508,62514,62516],{},[1788,62509,62510,62512],{},[898,62511,1872],{},[1793,62513,1779],{},[1688,62515,3665],{},[1793,62517,1779],{},[902,62519,62520],{"encoding":904},"Q_0 > 0",[883,62522,62524],{"className":62523},[886],[888,62525,62526],{"xmlns":890},[892,62527,62528,62552],{},[895,62529,62530,62532,62538,62540,62546,62548,62550],{},[898,62531,4512],{},[1850,62533,62534,62536],{},[898,62535,1693],{},[1688,62537,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,62539,2066],{"stretchy":2065},[1788,62541,62542,62544],{},[898,62543,1872],{},[1793,62545,1779],{},[1688,62547,2076],{"stretchy":2065},[1688,62549,1690],{},[1793,62551,1779],{},[902,62553,62554],{"encoding":904},"AC'(Q_0) = 0",[883,62556,62558],{"className":62557},[886],[888,62559,62560],{"xmlns":890,"display":28306},[892,62561,62562,62647],{},[895,62563,62564,62604,62606,62608,62610,62613,62615,62617,62619,62621,62627,62629,62631,62633,62635,62637,62643,62645],{},[1781,62565,62566,62598],{},[895,62567,62568,62570,62572,62574,62580,62582,62584,62586,62588,62590,62596],{},[898,62569,1661],{},[898,62571,1693],{},[1688,62573,2066],{"stretchy":2065},[1788,62575,62576,62578],{},[898,62577,1872],{},[1793,62579,1779],{},[1688,62581,2076],{"stretchy":2065},[1688,62583,1954],{},[898,62585,4512],{},[898,62587,1693],{},[1688,62589,2066],{"stretchy":2065},[1788,62591,62592,62594],{},[898,62593,1872],{},[1793,62595,1779],{},[1688,62597,2076],{"stretchy":2065},[1788,62599,62600,62602],{},[898,62601,1872],{},[1793,62603,1779],{},[1688,62605,1690],{},[1793,62607,1779],{},[6134,62609],{"width":15531},[1688,62611,62612],{},"⟺",[6134,62614],{"width":15531},[898,62616,1661],{},[898,62618,1693],{},[1688,62620,2066],{"stretchy":2065},[1788,62622,62623,62625],{},[898,62624,1872],{},[1793,62626,1779],{},[1688,62628,2076],{"stretchy":2065},[1688,62630,1690],{},[898,62632,4512],{},[898,62634,1693],{},[1688,62636,2066],{"stretchy":2065},[1788,62638,62639,62641],{},[898,62640,1872],{},[1793,62642,1779],{},[1688,62644,2076],{"stretchy":2065},[898,62646,2263],{"mathvariant":1822},[902,62648,62649],{"encoding":904},"\\frac{MC(Q_0) - AC(Q_0)}{Q_0} = 0 \\quad\\Longleftrightarrow\\quad MC(Q_0) = AC(Q_0).",[724,62651,62652,2170,62655,61737,62670,62685,62686,62701,62702,8358,62719,62741,62742,62764],{},[38,62653,62654],{},"Geometrická interpretace.",[883,62656,62658],{"className":62657},[886],[888,62659,62660],{"xmlns":890},[892,62661,62662,62668],{},[895,62663,62664,62666],{},[898,62665,1661],{},[898,62667,1693],{},[902,62669,55532],{"encoding":904},[883,62671,62673],{"className":62672},[886],[888,62674,62675],{"xmlns":890},[892,62676,62677,62683],{},[895,62678,62679,62681],{},[898,62680,4512],{},[898,62682,1693],{},[902,62684,55800],{"encoding":904}," právě v bodě minima ",[883,62687,62689],{"className":62688},[886],[888,62690,62691],{"xmlns":890},[892,62692,62693,62699],{},[895,62694,62695,62697],{},[898,62696,4512],{},[898,62698,1693],{},[902,62700,55800],{"encoding":904}," (obrázek 3.10); nalevo od ",[883,62703,62705],{"className":62704},[886],[888,62706,62707],{"xmlns":890},[892,62708,62709,62717],{},[895,62710,62711],{},[1788,62712,62713,62715],{},[898,62714,1872],{},[1793,62716,1779],{},[902,62718,38548],{"encoding":904},[883,62720,62722],{"className":62721},[886],[888,62723,62724],{"xmlns":890},[892,62725,62726,62738],{},[895,62727,62728,62730,62732,62734,62736],{},[898,62729,1661],{},[898,62731,1693],{},[1688,62733,3704],{},[898,62735,4512],{},[898,62737,1693],{},[902,62739,62740],{"encoding":904},"MC \u003C AC"," (průměrné náklady klesají), napravo ",[883,62743,62745],{"className":62744},[886],[888,62746,62747],{"xmlns":890},[892,62748,62749,62761],{},[895,62750,62751,62753,62755,62757,62759],{},[898,62752,1661],{},[898,62754,1693],{},[1688,62756,3665],{},[898,62758,4512],{},[898,62760,1693],{},[902,62762,62763],{"encoding":904},"MC > AC"," (průměrné náklady rostou).",[724,62766,62767,62768,62810,62811,62828,62829,2263],{},"Za obvyklých ekonomických podmínek platí i obrácené tvrzení — jestliže ",[883,62769,62771],{"className":62770},[886],[888,62772,62773],{"xmlns":890},[892,62774,62775,62807],{},[895,62776,62777,62779,62781,62783,62789,62791,62793,62795,62797,62799,62805],{},[898,62778,4512],{},[898,62780,1693],{},[1688,62782,2066],{"stretchy":2065},[1788,62784,62785,62787],{},[898,62786,1872],{},[1793,62788,1779],{},[1688,62790,2076],{"stretchy":2065},[1688,62792,1690],{},[898,62794,1661],{},[898,62796,1693],{},[1688,62798,2066],{"stretchy":2065},[1788,62800,62801,62803],{},[898,62802,1872],{},[1793,62804,1779],{},[1688,62806,2076],{"stretchy":2065},[902,62808,62809],{"encoding":904},"AC(Q_0) = MC(Q_0)",", pak ",[883,62812,62814],{"className":62813},[886],[888,62815,62816],{"xmlns":890},[892,62817,62818,62826],{},[895,62819,62820],{},[1788,62821,62822,62824],{},[898,62823,1872],{},[1793,62825,1779],{},[902,62827,38548],{"encoding":904}," je bod minima. V praktických úlohách tedy postačí řešit rovnici ",[883,62830,62832],{"className":62831},[886],[888,62833,62834],{"xmlns":890},[892,62835,62836,62860],{},[895,62837,62838,62840,62842,62844,62846,62848,62850,62852,62854,62856,62858],{},[898,62839,4512],{},[898,62841,1693],{},[1688,62843,2066],{"stretchy":2065},[898,62845,1872],{},[1688,62847,2076],{"stretchy":2065},[1688,62849,1690],{},[898,62851,1661],{},[898,62853,1693],{},[1688,62855,2066],{"stretchy":2065},[898,62857,1872],{},[1688,62859,2076],{"stretchy":2065},[902,62861,62862],{"encoding":904},"AC(Q) = MC(Q)",[4124,62864,62865],{},[724,62866,62867,62869,62870,10646,62888,62909,62910,10646,62913,62934,62935,62950,62951,58278,62966,4176],{},[883,62868,4668],{}," Pozor — neplést s principem maxima zisku\nPro ",[38,62871,62872,62873],{},"minimum ",[883,62874,62876],{"className":62875},[886],[888,62877,62878],{"xmlns":890},[892,62879,62880,62886],{},[895,62881,62882,62884],{},[898,62883,4512],{},[898,62885,1693],{},[902,62887,55800],{"encoding":904},[883,62889,62891],{"className":62890},[886],[888,62892,62893],{"xmlns":890},[892,62894,62895,62907],{},[895,62896,62897,62899,62901,62903,62905],{},[898,62898,4512],{},[898,62900,1693],{},[1688,62902,1690],{},[898,62904,1661],{},[898,62906,1693],{},[902,62908,55463],{"encoding":904},", pro ",[38,62911,62912],{},"maximum zisku",[883,62914,62916],{"className":62915},[886],[888,62917,62918],{"xmlns":890},[892,62919,62920,62932],{},[895,62921,62922,62924,62926,62928,62930],{},[898,62923,1661],{},[898,62925,4251],{},[1688,62927,1690],{},[898,62929,1661],{},[898,62931,1693],{},[902,62933,55511],{"encoding":904},". Obě podmínky využívají ",[883,62936,62938],{"className":62937},[886],[888,62939,62940],{"xmlns":890},[892,62941,62942,62948],{},[895,62943,62944,62946],{},[898,62945,1661],{},[898,62947,1693],{},[902,62949,55532],{"encoding":904},", ale rovnají ho rozdílným veličinám (",[883,62952,62954],{"className":62953},[886],[888,62955,62956],{"xmlns":890},[892,62957,62958,62964],{},[895,62959,62960,62962],{},[898,62961,4512],{},[898,62963,1693],{},[902,62965,55800],{"encoding":904},[883,62967,62969],{"className":62968},[886],[888,62970,62971],{"xmlns":890},[892,62972,62973,62979],{},[895,62974,62975,62977],{},[898,62976,1661],{},[898,62978,4251],{},[902,62980,6890],{"encoding":904},[37588,62982,62984],{"id":62983},"příklad-37","Příklad 3.7",[724,62986,62987,57762,62989,63023,63024,63037,63038,63053],{},[38,62988,56227],{},[883,62990,62992],{"className":62991},[886],[888,62993,62994],{"xmlns":890},[892,62995,62996,63020],{},[895,62997,62998,63000,63002,63004,63010,63012,63014,63016,63018],{},[898,62999,3035],{},[898,63001,1693],{},[1688,63003,1690],{},[1850,63005,63006,63008],{},[898,63007,1872],{},[1793,63009,1806],{},[1688,63011,1696],{},[1793,63013,2131],{},[898,63015,1872],{},[1688,63017,1696],{},[1793,63019,5821],{},[902,63021,63022],{"encoding":904},"TC = Q^2 + 3Q + 36"," najděte ",[883,63025,63027],{"className":63026},[886],[888,63028,63029],{"xmlns":890},[892,63030,63031,63035],{},[895,63032,63033],{},[898,63034,1872],{},[902,63036,1872],{"encoding":904}," minimalizující ",[883,63039,63041],{"className":63040},[886],[888,63042,63043],{"xmlns":890},[892,63044,63045,63051],{},[895,63046,63047,63049],{},[898,63048,4512],{},[898,63050,1693],{},[902,63052,55800],{"encoding":904}," a ověřte princip (3.10).",[724,63055,63056,63058],{},[38,63057,23011],{}," Přímý výpočet:",[883,63060,63062],{"className":63061},[886],[888,63063,63064],{"xmlns":890,"display":28306},[892,63065,63066,63168],{},[895,63067,63068,63070,63072,63074,63096,63098,63100,63102,63104,63106,63112,63114,63116,63118,63120,63122,63128,63130,63132,63134,63144,63146,63166],{},[898,63069,4512],{},[898,63071,1693],{},[1688,63073,1690],{},[1781,63075,63076,63094],{},[895,63077,63078,63084,63086,63088,63090,63092],{},[1850,63079,63080,63082],{},[898,63081,1872],{},[1793,63083,1806],{},[1688,63085,1696],{},[1793,63087,2131],{},[898,63089,1872],{},[1688,63091,1696],{},[1793,63093,5821],{},[898,63095,1872],{},[1688,63097,1690],{},[898,63099,1872],{},[1688,63101,1696],{},[1793,63103,2131],{},[1688,63105,1696],{},[1781,63107,63108,63110],{},[1793,63109,5821],{},[898,63111,1872],{},[1688,63113,1733],{"separator":1732},[6134,63115],{"width":6136},[1688,63117,2066],{"stretchy":2065},[898,63119,4512],{},[898,63121,1693],{},[1850,63123,63124,63126],{},[1688,63125,2076],{"stretchy":2065},[1688,63127,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,63129,1690],{},[1793,63131,1795],{},[1688,63133,1954],{},[1781,63135,63136,63138],{},[1793,63137,5821],{},[1850,63139,63140,63142],{},[898,63141,1872],{},[1793,63143,1806],{},[1688,63145,1690],{},[1781,63147,63148,63160],{},[895,63149,63150,63156,63158],{},[1850,63151,63152,63154],{},[898,63153,1872],{},[1793,63155,1806],{},[1688,63157,1954],{},[1793,63159,5821],{},[1850,63161,63162,63164],{},[898,63163,1872],{},[1793,63165,1806],{},[898,63167,2263],{"mathvariant":1822},[902,63169,63170],{"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}.",[724,63172,63173,63213,63214,63238,63239,63289,63290,2263],{},[883,63174,63176],{"className":63175},[886],[888,63177,63178],{"xmlns":890},[892,63179,63180,63210],{},[895,63181,63182,63184,63186,63188,63194,63196,63198,63200,63206,63208],{},[1688,63183,2066],{"stretchy":2065},[898,63185,4512],{},[898,63187,1693],{},[1850,63189,63190,63192],{},[1688,63191,2076],{"stretchy":2065},[1688,63193,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,63195,1690],{},[1793,63197,1779],{},[1688,63199,4244],{},[1788,63201,63202,63204],{},[898,63203,1872],{},[1793,63205,1795],{},[1688,63207,1690],{},[1793,63209,2508],{},[902,63211,63212],{"encoding":904},"(AC)' = 0 \\Rightarrow Q_1 = 6"," (smysluplné), ",[883,63215,63217],{"className":63216},[886],[888,63218,63219],{"xmlns":890},[892,63220,63221,63235],{},[895,63222,63223,63229,63231,63233],{},[1788,63224,63225,63227],{},[898,63226,1872],{},[1793,63228,1806],{},[1688,63230,1690],{},[1688,63232,1954],{},[1793,63234,2508],{},[902,63236,63237],{"encoding":904},"Q_2 = -6"," (vyloučeno). ",[883,63240,63242],{"className":63241},[886],[888,63243,63244],{"xmlns":890},[892,63245,63246,63286],{},[895,63247,63248,63250,63252,63254,63264,63266,63268,63270,63272,63280,63282,63284],{},[1688,63249,2066],{"stretchy":2065},[898,63251,4512],{},[898,63253,1693],{},[1850,63255,63256,63258],{},[1688,63257,2076],{"stretchy":2065},[895,63259,63260,63262],{},[1688,63261,1824],{"mathvariant":1822},[1688,63263,1824],{"mathvariant":1822},[1688,63265,2066],{"stretchy":2065},[1793,63267,2508],{},[1688,63269,2076],{"stretchy":2065},[1688,63271,1690],{},[1777,63273,63274],{"scriptlevel":1779,"displaystyle":2065},[1781,63275,63276,63278],{},[1793,63277,1795],{},[1793,63279,2131],{},[1688,63281,3665],{},[1793,63283,1779],{},[1688,63285,4244],{},[902,63287,63288],{"encoding":904},"(AC)''(6) = \\tfrac{1}{3} > 0 \\Rightarrow"," minimum. ",[883,63291,63293],{"className":63292},[886],[888,63294,63295],{"xmlns":890},[892,63296,63297,63313],{},[895,63298,63299,63301,63303,63305,63307,63309,63311],{},[898,63300,4512],{},[898,63302,1693],{},[1688,63304,2066],{"stretchy":2065},[1793,63306,2508],{},[1688,63308,2076],{"stretchy":2065},[1688,63310,1690],{},[1793,63312,36484],{},[902,63314,63315],{"encoding":904},"AC(6) = 15",[724,63317,63318,63319,63345,63346,2965],{},"Pomocí principu: ",[883,63320,63322],{"className":63321},[886],[888,63323,63324],{"xmlns":890},[892,63325,63326,63342],{},[895,63327,63328,63330,63332,63334,63336,63338,63340],{},[898,63329,1661],{},[898,63331,1693],{},[1688,63333,1690],{},[1793,63335,1806],{},[898,63337,1872],{},[1688,63339,1696],{},[1793,63341,2131],{},[902,63343,63344],{"encoding":904},"MC = 2Q + 3",", rovnice ",[883,63347,63349],{"className":63348},[886],[888,63350,63351],{"xmlns":890},[892,63352,63353,63365],{},[895,63354,63355,63357,63359,63361,63363],{},[898,63356,4512],{},[898,63358,1693],{},[1688,63360,1690],{},[898,63362,1661],{},[898,63364,1693],{},[902,63366,55463],{"encoding":904},[883,63368,63370],{"className":63369},[886],[888,63371,63372],{"xmlns":890,"display":28306},[892,63373,63374,63476],{},[895,63375,63376,63398,63400,63402,63404,63406,63408,63410,63412,63414,63420,63422,63424,63426,63428,63430,63432,63434,63440,63442,63444,63446,63448,63450,63452,63458,63460,63462,63464,63466,63468,63470,63472,63474],{},[1781,63377,63378,63396],{},[895,63379,63380,63386,63388,63390,63392,63394],{},[1850,63381,63382,63384],{},[898,63383,1872],{},[1793,63385,1806],{},[1688,63387,1696],{},[1793,63389,2131],{},[898,63391,1872],{},[1688,63393,1696],{},[1793,63395,5821],{},[898,63397,1872],{},[1688,63399,1690],{},[1793,63401,1806],{},[898,63403,1872],{},[1688,63405,1696],{},[1793,63407,2131],{},[2041,63409,4241],{},[1688,63411,4244],{},[2041,63413,4241],{},[1850,63415,63416,63418],{},[898,63417,1872],{},[1793,63419,1806],{},[1688,63421,1696],{},[1793,63423,2131],{},[898,63425,1872],{},[1688,63427,1696],{},[1793,63429,5821],{},[1688,63431,1690],{},[1793,63433,1806],{},[1850,63435,63436,63438],{},[898,63437,1872],{},[1793,63439,1806],{},[1688,63441,1696],{},[1793,63443,2131],{},[898,63445,1872],{},[2041,63447,4241],{},[1688,63449,4244],{},[2041,63451,4241],{},[1850,63453,63454,63456],{},[898,63455,1872],{},[1793,63457,1806],{},[1688,63459,1690],{},[1793,63461,5821],{},[2041,63463,4241],{},[1688,63465,4244],{},[2041,63467,4241],{},[898,63469,1872],{},[1688,63471,1690],{},[1793,63473,2508],{},[1688,63475,1733],{"separator":1732},[902,63477,63478],{"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,",[724,63480,63481,63482,63520],{},"a ",[883,63483,63485],{"className":63484},[886],[888,63486,63487],{"xmlns":890},[892,63488,63489,63517],{},[895,63490,63491,63493,63495,63497,63499,63501,63503,63505,63507,63509,63511,63513,63515],{},[898,63492,4512],{},[898,63494,1693],{},[1688,63496,2066],{"stretchy":2065},[1793,63498,2508],{},[1688,63500,2076],{"stretchy":2065},[1688,63502,1690],{},[898,63504,1661],{},[898,63506,1693],{},[1688,63508,2066],{"stretchy":2065},[1793,63510,2508],{},[1688,63512,2076],{"stretchy":2065},[1688,63514,1690],{},[1793,63516,36484],{},[902,63518,63519],{"encoding":904},"AC(6) = MC(6) = 15",". Oba postupy dávají stejný výsledek.",[198,63522,63524],{"id":63523},"princip-minimalizace-průměrných-variabilních-nákladů","Princip minimalizace průměrných variabilních nákladů",[724,63526,63527,63528,2965],{},"Analogicky pro ",[883,63529,63531],{"className":63530},[886],[888,63532,63533],{"xmlns":890},[892,63534,63535,63543],{},[895,63536,63537,63539,63541],{},[898,63538,4512],{},[898,63540,40579],{},[898,63542,1693],{},[902,63544,55551],{"encoding":904},[883,63546,63548],{"className":63547},[886],[888,63549,63550],{"xmlns":890,"display":28306},[892,63551,63552,63603],{},[20995,63553,63554],{"width":28311},[21000,63555,63556,63558,63596,63598],{},[21003,63557],{"width":28316},[21003,63559,63560],{},[895,63561,63562,63564,63566,63568,63570,63576,63578,63580,63582,63584,63586,63592,63594],{},[898,63563,4512],{},[898,63565,40579],{},[898,63567,1693],{},[1688,63569,2066],{"stretchy":2065},[1788,63571,63572,63574],{},[898,63573,1872],{},[1793,63575,1779],{},[1688,63577,2076],{"stretchy":2065},[1688,63579,1690],{},[898,63581,1661],{},[898,63583,1693],{},[1688,63585,2066],{"stretchy":2065},[1788,63587,63588,63590],{},[898,63589,1872],{},[1793,63591,1779],{},[1688,63593,2076],{"stretchy":2065},[898,63595,2263],{"mathvariant":1822},[21003,63597],{"width":28316},[21003,63599,63600],{},[2041,63601,63602],{},"(3.11)",[902,63604,63605],{"encoding":904},"AVC(Q_0) = MC(Q_0).\n\\tag{3.11}",[4124,63607,63608],{},[724,63609,63610,62286,63612],{},[883,63611,56684],{},[38,63613,63614,63615,63632],{},"V bodě minima průměrných variabilních nákladů se ",[883,63616,63618],{"className":63617},[886],[888,63619,63620],{"xmlns":890},[892,63621,63622,63630],{},[895,63623,63624,63626,63628],{},[898,63625,4512],{},[898,63627,40579],{},[898,63629,1693],{},[902,63631,55551],{"encoding":904}," rovnají mezním nákladům.",[724,63634,63635,63636,63658,63659,2263],{},"Odvození je analogické (úloha 3.14). V obrázku 3.10 odpovídá ",[883,63637,63639],{"className":63638},[886],[888,63640,63641],{"xmlns":890},[892,63642,63643,63655],{},[895,63644,63645,63651,63653],{},[1788,63646,63647,63649],{},[898,63648,1872],{},[1793,63650,1779],{},[1688,63652,1690],{},[1793,63654,53439],{},[902,63656,63657],{"encoding":904},"Q_0 = 2{,}5",". Za obvyklých podmínek platí i obrácené tvrzení — postačí řešit rovnici ",[883,63660,63662],{"className":63661},[886],[888,63663,63664],{"xmlns":890},[892,63665,63666,63692],{},[895,63667,63668,63670,63672,63674,63676,63678,63680,63682,63684,63686,63688,63690],{},[898,63669,4512],{},[898,63671,40579],{},[898,63673,1693],{},[1688,63675,2066],{"stretchy":2065},[898,63677,1872],{},[1688,63679,2076],{"stretchy":2065},[1688,63681,1690],{},[898,63683,1661],{},[898,63685,1693],{},[1688,63687,2066],{"stretchy":2065},[898,63689,1872],{},[1688,63691,2076],{"stretchy":2065},[902,63693,63694],{"encoding":904},"AVC(Q) = MC(Q)",[115,63696,63698],{"id":63697},"zisk-a-body-zvratu","Zisk a body zvratu",[724,63700,63701,2170,63704,63720],{},[38,63702,63703],{},"Zisk",[883,63705,63707],{"className":63706},[886],[888,63708,63709],{"xmlns":890},[892,63710,63711,63717],{},[895,63712,63713,63715],{},[898,63714,1727],{},[898,63716,4251],{},[902,63718,63719],{"encoding":904},"PR"," (profit) je rozdíl celkového příjmu a celkových nákladů:",[883,63722,63724],{"className":63723},[886],[888,63725,63726],{"xmlns":890,"display":28306},[892,63727,63728,63787],{},[20995,63729,63730],{"width":28311},[21000,63731,63732,63734,63780,63782],{},[21003,63733],{"width":28316},[21003,63735,63736],{},[895,63737,63738,63740,63742,63744,63746,63748,63750,63752,63754,63756,63758,63760,63762,63764,63766,63768,63770,63772,63774,63776,63778],{},[898,63739,1727],{},[898,63741,4251],{},[1688,63743,1690],{},[898,63745,1727],{},[898,63747,4251],{},[1688,63749,2066],{"stretchy":2065},[898,63751,1872],{},[1688,63753,2076],{"stretchy":2065},[1688,63755,1690],{},[898,63757,3035],{},[898,63759,4251],{},[1688,63761,2066],{"stretchy":2065},[898,63763,1872],{},[1688,63765,2076],{"stretchy":2065},[1688,63767,1954],{},[898,63769,3035],{},[898,63771,1693],{},[1688,63773,2066],{"stretchy":2065},[898,63775,1872],{},[1688,63777,2076],{"stretchy":2065},[898,63779,2263],{"mathvariant":1822},[21003,63781],{"width":28316},[21003,63783,63784],{},[2041,63785,63786],{},"(3.12)",[902,63788,63789],{"encoding":904},"PR = PR(Q) = TR(Q) - TC(Q).\n\\tag{3.12}",[724,63791,63792,63793,4142,63808,43876,63823,63825,63826,63829,63830,63846,63847,63862,63863,63878,63879,1343,63892,63905,63906,1343,63924,63942,63943,10277,63946,63949,63950,1348,63972,8358,63994,64016,64017,8358,64047,64069],{},"Body rovnosti ",[883,63794,63796],{"className":63795},[886],[888,63797,63798],{"xmlns":890},[892,63799,63800,63806],{},[895,63801,63802,63804],{},[898,63803,3035],{},[898,63805,4251],{},[902,63807,4351],{"encoding":904},[883,63809,63811],{"className":63810},[886],[888,63812,63813],{"xmlns":890},[892,63814,63815,63821],{},[895,63816,63817,63819],{},[898,63818,3035],{},[898,63820,1693],{},[902,63822,3500],{"encoding":904},[38,63824,55967],{}," (též vyrovnání, ",[614,63827,63828],{},"break-even points","). V nejjednodušším modelu (lineární poptávka, konstantní ",[883,63831,63833],{"className":63832},[886],[888,63834,63835],{"xmlns":890},[892,63836,63837,63843],{},[895,63838,63839,63841],{},[898,63840,40579],{},[898,63842,1693],{},[902,63844,63845],{"encoding":904},"VC",") je ",[883,63848,63850],{"className":63849},[886],[888,63851,63852],{"xmlns":890},[892,63853,63854,63860],{},[895,63855,63856,63858],{},[898,63857,3035],{},[898,63859,4251],{},[902,63861,4351],{"encoding":904}," kvadratická a ",[883,63864,63866],{"className":63865},[886],[888,63867,63868],{"xmlns":890},[892,63869,63870,63876],{},[895,63871,63872,63874],{},[898,63873,3035],{},[898,63875,1693],{},[902,63877,3500],{"encoding":904}," lineární (obrázek 3.11). Křivky se protínají v bodech ",[883,63880,63882],{"className":63881},[886],[888,63883,63884],{"xmlns":890},[892,63885,63886,63890],{},[895,63887,63888],{},[898,63889,4512],{},[902,63891,4512],{"encoding":904},[883,63893,63895],{"className":63894},[886],[888,63896,63897],{"xmlns":890},[892,63898,63899,63903],{},[895,63900,63901],{},[898,63902,23494],{},[902,63904,23494],{"encoding":904}," odpovídajících množstvím ",[883,63907,63909],{"className":63908},[886],[888,63910,63911],{"xmlns":890},[892,63912,63913,63921],{},[895,63914,63915],{},[1788,63916,63917,63919],{},[898,63918,1872],{},[898,63920,4512],{},[902,63922,63923],{"encoding":904},"Q_A",[883,63925,63927],{"className":63926},[886],[888,63928,63929],{"xmlns":890},[892,63930,63931,63939],{},[895,63932,63933],{},[1788,63934,63935,63937],{},[898,63936,1872],{},[898,63938,23494],{},[902,63940,63941],{"encoding":904},"Q_B"," — firma je na ",[38,63944,63945],{},"prahu rentability",[614,63947,63948],{},"break even","). Pro ",[883,63951,63953],{"className":63952},[886],[888,63954,63955],{"xmlns":890},[892,63956,63957,63969],{},[895,63958,63959,63961,63963],{},[898,63960,1872],{},[1688,63962,3704],{},[1788,63964,63965,63967],{},[898,63966,1872],{},[898,63968,4512],{},[902,63970,63971],{"encoding":904},"Q \u003C Q_A",[883,63973,63975],{"className":63974},[886],[888,63976,63977],{"xmlns":890},[892,63978,63979,63991],{},[895,63980,63981,63983,63985],{},[898,63982,1872],{},[1688,63984,3665],{},[1788,63986,63987,63989],{},[898,63988,1872],{},[898,63990,23494],{},[902,63992,63993],{"encoding":904},"Q > Q_B",[883,63995,63997],{"className":63996},[886],[888,63998,63999],{"xmlns":890},[892,64000,64001,64013],{},[895,64002,64003,64005,64007,64009,64011],{},[898,64004,3035],{},[898,64006,1693],{},[1688,64008,3665],{},[898,64010,3035],{},[898,64012,4251],{},[902,64014,64015],{"encoding":904},"TC > TR"," (ztráta); pro ",[883,64018,64020],{"className":64019},[886],[888,64021,64022],{"xmlns":890},[892,64023,64024,64044],{},[895,64025,64026,64032,64034,64036,64038],{},[1788,64027,64028,64030],{},[898,64029,1872],{},[898,64031,4512],{},[1688,64033,3704],{},[898,64035,1872],{},[1688,64037,3704],{},[1788,64039,64040,64042],{},[898,64041,1872],{},[898,64043,23494],{},[902,64045,64046],{"encoding":904},"Q_A \u003C Q \u003C Q_B",[883,64048,64050],{"className":64049},[886],[888,64051,64052],{"xmlns":890},[892,64053,64054,64066],{},[895,64055,64056,64058,64060,64062,64064],{},[898,64057,3035],{},[898,64059,4251],{},[1688,64061,3665],{},[898,64063,3035],{},[898,64065,1693],{},[902,64067,64068],{"encoding":904},"TR > TC"," (zisk).",[4124,64071,64072],{},[724,64073,64074,64076],{},[883,64075,4412],{}," 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.",[724,64078,64079,64080,64106],{},"Body zvratu jsou řešení rovnice ",[883,64081,64083],{"className":64082},[886],[888,64084,64085],{"xmlns":890},[892,64086,64087,64103],{},[895,64088,64089,64091,64093,64095,64097,64099,64101],{},[898,64090,1727],{},[898,64092,4251],{},[1688,64094,2066],{"stretchy":2065},[898,64096,1872],{},[1688,64098,2076],{"stretchy":2065},[1688,64100,1690],{},[1793,64102,1779],{},[902,64104,64105],{"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.",[724,64108,64109],{},[2821,64110],{"alt":64111,"className":64112,"src":64113},"imek-tr-tc-body-zvratu",[210,2825],"\u002Fwiki-assets\u002Fimek-tr-tc-body-zvratu.jpeg",[724,64115,64116],{},[614,64117,64118,64119,64134,64135,64150,64151,4142,64164,43600,64177,64190,64191,4142,64208,64225,64226,64246,64247,4142,64262,6729,64277,64306],{},"Obrázek 3.11: Body zvratu — křivky ",[883,64120,64122],{"className":64121},[886],[888,64123,64124],{"xmlns":890},[892,64125,64126,64132],{},[895,64127,64128,64130],{},[898,64129,3035],{},[898,64131,4251],{},[902,64133,4351],{"encoding":904}," (obrácená parabola) a ",[883,64136,64138],{"className":64137},[886],[888,64139,64140],{"xmlns":890},[892,64141,64142,64148],{},[895,64143,64144,64146],{},[898,64145,3035],{},[898,64147,1693],{},[902,64149,3500],{"encoding":904}," (přímka) se protínají v bodech ",[883,64152,64154],{"className":64153},[886],[888,64155,64156],{"xmlns":890},[892,64157,64158,64162],{},[895,64159,64160],{},[898,64161,4512],{},[902,64163,4512],{"encoding":904},[883,64165,64167],{"className":64166},[886],[888,64168,64169],{"xmlns":890},[892,64170,64171,64175],{},[895,64172,64173],{},[898,64174,23494],{},[902,64176,23494],{"encoding":904},[883,64178,64180],{"className":64179},[886],[888,64181,64182],{"xmlns":890},[892,64183,64184,64188],{},[895,64185,64186],{},[898,64187,1872],{},[902,64189,1872],{"encoding":904}," v hodnotách ",[883,64192,64194],{"className":64193},[886],[888,64195,64196],{"xmlns":890},[892,64197,64198,64206],{},[895,64199,64200],{},[1788,64201,64202,64204],{},[898,64203,1872],{},[898,64205,4512],{},[902,64207,63923],{"encoding":904},[883,64209,64211],{"className":64210},[886],[888,64212,64213],{"xmlns":890},[892,64214,64215,64223],{},[895,64216,64217],{},[1788,64218,64219,64221],{},[898,64220,1872],{},[898,64222,23494],{},[902,64224,63941],{"encoding":904},"; maximum zisku leží mezi nimi v bodě ",[883,64227,64229],{"className":64228},[886],[888,64230,64231],{"xmlns":890},[892,64232,64233,64243],{},[895,64234,64235],{},[1788,64236,64237,64239,64241],{},[898,64238,1872],{},[898,64240,56437],{},[1688,64242,56440],{},[902,64244,64245],{"encoding":904},"Q_{\\max}","; svislá vzdálenost mezi ",[883,64248,64250],{"className":64249},[886],[888,64251,64252],{"xmlns":890},[892,64253,64254,64260],{},[895,64255,64256,64258],{},[898,64257,3035],{},[898,64259,4251],{},[902,64261,4351],{"encoding":904},[883,64263,64265],{"className":64264},[886],[888,64266,64267],{"xmlns":890},[892,64268,64269,64275],{},[895,64270,64271,64273],{},[898,64272,3035],{},[898,64274,1693],{},[902,64276,3500],{"encoding":904},[883,64278,64280],{"className":64279},[886],[888,64281,64282],{"xmlns":890},[892,64283,64284,64304],{},[895,64285,64286,64292,64294,64296,64298],{},[1788,64287,64288,64290],{},[898,64289,1872],{},[898,64291,4512],{},[1688,64293,3704],{},[898,64295,1872],{},[1688,64297,3704],{},[1788,64299,64300,64302],{},[898,64301,1872],{},[898,64303,23494],{},[902,64305,64046],{"encoding":904}," vyznačuje zisk.",[37588,64308,64310],{"id":64309},"příklad-38","Příklad 3.8",[724,64312,64313,64315,64316,1343,64336,1343,64362,64388],{},[38,64314,56227],{}," Dáno ",[883,64317,64319],{"className":64318},[886],[888,64320,64321],{"xmlns":890},[892,64322,64323,64333],{},[895,64324,64325,64327,64329,64331],{},[898,64326,10688],{},[898,64328,1693],{},[1688,64330,1690],{},[1793,64332,2616],{},[902,64334,64335],{"encoding":904},"FC = 4",[883,64337,64339],{"className":64338},[886],[888,64340,64341],{"xmlns":890},[892,64342,64343,64359],{},[895,64344,64345,64347,64349,64351,64353],{},[898,64346,3035],{},[898,64348,40579],{},[898,64350,1693],{},[1688,64352,1690],{},[1850,64354,64355,64357],{},[898,64356,1872],{},[1793,64358,1806],{},[902,64360,64361],{"encoding":904},"TVC = Q^2",[883,64363,64365],{"className":64364},[886],[888,64366,64367],{"xmlns":890},[892,64368,64369,64385],{},[895,64370,64371,64373,64375,64377,64379,64381,64383],{},[898,64372,1727],{},[1688,64374,1690],{},[1688,64376,1954],{},[1793,64378,1806],{},[898,64380,1872],{},[1688,64382,1696],{},[1793,64384,4256],{},[902,64386,64387],{"encoding":904},"P = -2Q + 9",". Určete zisk, body zvratu a bod maxima zisku.",[724,64390,64391,64393],{},[38,64392,23011],{}," Celkové náklady a příjem:",[883,64395,64397],{"className":64396},[886],[888,64398,64399],{"xmlns":890,"display":28306},[892,64400,64401,64467],{},[895,64402,64403,64405,64407,64409,64411,64413,64419,64421,64423,64425,64427,64429,64431,64433,64435,64437,64439,64441,64443,64445,64447,64449,64451,64453,64459,64461,64463,64465],{},[898,64404,3035],{},[898,64406,1693],{},[1688,64408,1690],{},[1793,64410,2616],{},[1688,64412,1696],{},[1850,64414,64415,64417],{},[898,64416,1872],{},[1793,64418,1806],{},[1688,64420,1733],{"separator":1732},[6134,64422],{"width":6136},[898,64424,3035],{},[898,64426,4251],{},[1688,64428,1690],{},[898,64430,1872],{},[1688,64432,3434],{},[1688,64434,2066],{"stretchy":2065},[1688,64436,1954],{},[1793,64438,1806],{},[898,64440,1872],{},[1688,64442,1696],{},[1793,64444,4256],{},[1688,64446,2076],{"stretchy":2065},[1688,64448,1690],{},[1688,64450,1954],{},[1793,64452,1806],{},[1850,64454,64455,64457],{},[898,64456,1872],{},[1793,64458,1806],{},[1688,64460,1696],{},[1793,64462,4256],{},[898,64464,1872],{},[898,64466,2263],{"mathvariant":1822},[902,64468,64469],{"encoding":904},"TC = 4 + Q^2, \\qquad TR = Q \\cdot (-2Q + 9) = -2Q^2 + 9Q.",[724,64471,64472],{},"Zisk dle (3.12):",[883,64474,64476],{"className":64475},[886],[888,64477,64478],{"xmlns":890,"display":28306},[892,64479,64480,64558],{},[895,64481,64482,64484,64486,64488,64490,64492,64494,64496,64498,64500,64502,64504,64506,64512,64514,64516,64518,64520,64522,64524,64526,64528,64534,64536,64538,64540,64542,64548,64550,64552,64554,64556],{},[898,64483,1727],{},[898,64485,4251],{},[1688,64487,1690],{},[898,64489,3035],{},[898,64491,4251],{},[1688,64493,1954],{},[898,64495,3035],{},[898,64497,1693],{},[1688,64499,1690],{},[1688,64501,2066],{"stretchy":2065},[1688,64503,1954],{},[1793,64505,1806],{},[1850,64507,64508,64510],{},[898,64509,1872],{},[1793,64511,1806],{},[1688,64513,1696],{},[1793,64515,4256],{},[898,64517,1872],{},[1688,64519,2076],{"stretchy":2065},[1688,64521,1954],{},[1688,64523,2066],{"stretchy":2065},[1793,64525,2616],{},[1688,64527,1696],{},[1850,64529,64530,64532],{},[898,64531,1872],{},[1793,64533,1806],{},[1688,64535,2076],{"stretchy":2065},[1688,64537,1690],{},[1688,64539,1954],{},[1793,64541,2131],{},[1850,64543,64544,64546],{},[898,64545,1872],{},[1793,64547,1806],{},[1688,64549,1696],{},[1793,64551,4256],{},[898,64553,1872],{},[1688,64555,1954],{},[1793,64557,59559],{},[902,64559,64560],{"encoding":904},"PR = TR - TC = (-2Q^2 + 9Q) - (4 + Q^2) = -3Q^2 + 9Q - 4.",[724,64562,64563,64566,64567,17821,64603,2965],{},[38,64564,64565],{},"Body zvratu"," jsou kořeny rovnice ",[883,64568,64570],{"className":64569},[886],[888,64571,64572],{"xmlns":890},[892,64573,64574,64600],{},[895,64575,64576,64578,64580,64586,64588,64590,64592,64594,64596,64598],{},[1688,64577,1954],{},[1793,64579,2131],{},[1850,64581,64582,64584],{},[898,64583,1872],{},[1793,64585,1806],{},[1688,64587,1696],{},[1793,64589,4256],{},[898,64591,1872],{},[1688,64593,1954],{},[1793,64595,2616],{},[1688,64597,1690],{},[1793,64599,1779],{},[902,64601,64602],{"encoding":904},"-3Q^2 + 9Q - 4 = 0",[883,64604,64606],{"className":64605},[886],[888,64607,64608],{"xmlns":890},[892,64609,64610,64634],{},[895,64611,64612,64614,64620,64622,64624,64626,64628,64630,64632],{},[1793,64613,2131],{},[1850,64615,64616,64618],{},[898,64617,1872],{},[1793,64619,1806],{},[1688,64621,1954],{},[1793,64623,4256],{},[898,64625,1872],{},[1688,64627,1696],{},[1793,64629,2616],{},[1688,64631,1690],{},[1793,64633,1779],{},[902,64635,64636],{"encoding":904},"3Q^2 - 9Q + 4 = 0",[883,64638,64640],{"className":64639},[886],[888,64641,64642],{"xmlns":890,"display":28306},[892,64643,64644,64701],{},[895,64645,64646,64658,64660,64683,64685,64699],{},[1788,64647,64648,64650],{},[898,64649,1872],{},[895,64651,64652,64654,64656],{},[1793,64653,1795],{},[1688,64655,1733],{"separator":1732},[1793,64657,1806],{},[1688,64659,1690],{},[1781,64661,64662,64681],{},[895,64663,64664,64666,64669],{},[1793,64665,4256],{},[1688,64667,64668],{},"±",[8373,64670,64671],{},[895,64672,64673,64676,64678],{},[1793,64674,64675],{},"81",[1688,64677,1954],{},[1793,64679,64680],{},"48",[1793,64682,2508],{},[1688,64684,1690],{},[1781,64686,64687,64697],{},[895,64688,64689,64691,64693],{},[1793,64690,4256],{},[1688,64692,64668],{},[8373,64694,64695],{},[1793,64696,9206],{},[1793,64698,2508],{},[1688,64700,1733],{"separator":1732},[902,64702,64703],{"encoding":904},"Q_{1,2} = \\frac{9 \\pm \\sqrt{81 - 48}}{6} = \\frac{9 \\pm \\sqrt{33}}{6},",[724,64705,64706,64707,4142,64730,2263],{},"numericky ",[883,64708,64710],{"className":64709},[886],[888,64711,64712],{"xmlns":890},[892,64713,64714,64727],{},[895,64715,64716,64722,64724],{},[1788,64717,64718,64720],{},[898,64719,1872],{},[1793,64721,1795],{},[1688,64723,6156],{},[1793,64725,64726],{},"0,543",[902,64728,64729],{"encoding":904},"Q_1 \\doteq 0{,}543",[883,64731,64733],{"className":64732},[886],[888,64734,64735],{"xmlns":890},[892,64736,64737,64750],{},[895,64738,64739,64745,64747],{},[1788,64740,64741,64743],{},[898,64742,1872],{},[1793,64744,1806],{},[1688,64746,6156],{},[1793,64748,64749],{},"2,457",[902,64751,64752],{"encoding":904},"Q_2 \\doteq 2{,}457",[724,64754,64755,2170,64758,7808,64803,17821,64837,64855],{},[38,64756,64757],{},"Maximum zisku.",[883,64759,64761],{"className":64760},[886],[888,64762,64763],{"xmlns":890},[892,64764,64765,64800],{},[895,64766,64767,64769,64775,64777,64779,64781,64783,64785,64787,64789,64791,64793,64795,64797],{},[898,64768,1727],{},[1850,64770,64771,64773],{},[898,64772,4251],{},[1688,64774,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,64776,1690],{},[1688,64778,1954],{},[1793,64780,2508],{},[898,64782,1872],{},[1688,64784,1696],{},[1793,64786,4256],{},[1688,64788,1690],{},[1793,64790,1779],{},[1688,64792,4244],{},[898,64794,1872],{},[1688,64796,1690],{},[1793,64798,64799],{},"1,5",[902,64801,64802],{"encoding":904},"PR' = -6Q + 9 = 0 \\Rightarrow Q = 1{,}5",[883,64804,64806],{"className":64805},[886],[888,64807,64808],{"xmlns":890},[892,64809,64810,64834],{},[895,64811,64812,64814,64824,64826,64828,64830,64832],{},[898,64813,1727],{},[1850,64815,64816,64818],{},[898,64817,4251],{},[895,64819,64820,64822],{},[1688,64821,1824],{"mathvariant":1822},[1688,64823,1824],{"mathvariant":1822},[1688,64825,1690],{},[1688,64827,1954],{},[1793,64829,2508],{},[1688,64831,3704],{},[1793,64833,1779],{},[902,64835,64836],{"encoding":904},"PR'' = -6 \u003C 0",[883,64838,64840],{"className":64839},[886],[888,64841,64842],{"xmlns":890},[892,64843,64844,64852],{},[895,64845,64846,64848,64850],{},[898,64847,1872],{},[1688,64849,1690],{},[1793,64851,64799],{},[902,64853,64854],{"encoding":904},"Q = 1{,}5"," je bod maxima s hodnotou",[883,64857,64859],{"className":64858},[886],[888,64860,64861],{"xmlns":890,"display":28306},[892,64862,64863,64926],{},[895,64864,64865,64867,64869,64871,64873,64875,64877,64879,64881,64883,64885,64887,64893,64895,64897,64899,64901,64903,64905,64907,64909,64912,64914,64917,64919,64921,64923],{},[898,64866,1727],{},[898,64868,4251],{},[1688,64870,2066],{"stretchy":2065},[1793,64872,64799],{},[1688,64874,2076],{"stretchy":2065},[1688,64876,1690],{},[1688,64878,1954],{},[1793,64880,2131],{},[1688,64882,3434],{},[1688,64884,2066],{"stretchy":2065},[1793,64886,64799],{},[1850,64888,64889,64891],{},[1688,64890,2076],{"stretchy":2065},[1793,64892,1806],{},[1688,64894,1696],{},[1793,64896,4256],{},[1688,64898,3434],{},[1793,64900,64799],{},[1688,64902,1954],{},[1793,64904,2616],{},[1688,64906,1690],{},[1688,64908,1954],{},[1793,64910,64911],{},"6,75",[1688,64913,1696],{},[1793,64915,64916],{},"13,5",[1688,64918,1954],{},[1793,64920,2616],{},[1688,64922,1690],{},[1793,64924,64925],{},"2,75.",[902,64927,64928],{"encoding":904},"PR(1{,}5) = -3 \\cdot (1{,}5)^2 + 9 \\cdot 1{,}5 - 4 = -6{,}75 + 13{,}5 - 4 = 2{,}75.",[724,64930,64931,64932,1343,64977,65030,65031,65049],{},"Pro srovnání maximum celkového příjmu (bez ohledu na náklady): ",[883,64933,64935],{"className":64934},[886],[888,64936,64937],{"xmlns":890},[892,64938,64939,64974],{},[895,64940,64941,64943,64949,64951,64953,64955,64957,64959,64961,64963,64965,64967,64969,64971],{},[898,64942,3035],{},[1850,64944,64945,64947],{},[898,64946,4251],{},[1688,64948,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,64950,1690],{},[1688,64952,1954],{},[1793,64954,2616],{},[898,64956,1872],{},[1688,64958,1696],{},[1793,64960,4256],{},[1688,64962,1690],{},[1793,64964,1779],{},[1688,64966,4244],{},[898,64968,1872],{},[1688,64970,1690],{},[1793,64972,64973],{},"2,25",[902,64975,64976],{"encoding":904},"TR' = -4Q + 9 = 0 \\Rightarrow Q = 2{,}25",[883,64978,64980],{"className":64979},[886],[888,64981,64982],{"xmlns":890},[892,64983,64984,65027],{},[895,64985,64986,64988,64996,64998,65000,65002,65004,65006,65008,65014,65016,65018,65020,65022,65024],{},[898,64987,3035],{},[1788,64989,64990,64992,64994],{},[898,64991,4251],{},[898,64993,56437],{},[1688,64995,56440],{},[1688,64997,1690],{},[1688,64999,1954],{},[1793,65001,1806],{},[1688,65003,3434],{},[1688,65005,2066],{"stretchy":2065},[1793,65007,64973],{},[1850,65009,65010,65012],{},[1688,65011,2076],{"stretchy":2065},[1793,65013,1806],{},[1688,65015,1696],{},[1793,65017,4256],{},[1688,65019,3434],{},[1793,65021,64973],{},[1688,65023,1690],{},[1793,65025,65026],{},"10,125",[902,65028,65029],{"encoding":904},"TR_{\\max} = -2 \\cdot (2{,}25)^2 + 9 \\cdot 2{,}25 = 10{,}125",". Leží vpravo od bodu maxima zisku, protože při ",[883,65032,65034],{"className":65033},[886],[888,65035,65036],{"xmlns":890},[892,65037,65038,65046],{},[895,65039,65040,65042,65044],{},[898,65041,1872],{},[1688,65043,1690],{},[1793,65045,64973],{},[902,65047,65048],{"encoding":904},"Q = 2{,}25"," rostou už náklady rychleji než příjem.",[4124,65051,65052],{},[724,65053,65054,65056,65057,1343,65079,65101,65102,1343,65119,65140,65141,65173,65174,65212,65213,2194,65231,65248,65249,4142,65277,65311,65312,7941,65350,4142,65374,2263],{},[883,65055,4668],{}," Nekonzistence v původním zdroji\nSkenovaný knižní text obsahoval v tomto příkladu dvě nesourodé hodnoty: uváděl body zvratu ",[883,65058,65060],{"className":65059},[886],[888,65061,65062],{"xmlns":890},[892,65063,65064,65076],{},[895,65065,65066,65072,65074],{},[1788,65067,65068,65070],{},[898,65069,1872],{},[1793,65071,1795],{},[1688,65073,1690],{},[1793,65075,5265],{},[902,65077,65078],{"encoding":904},"Q_1 = 0{,}5",[883,65080,65082],{"className":65081},[886],[888,65083,65084],{"xmlns":890},[892,65085,65086,65098],{},[895,65087,65088,65094,65096],{},[1788,65089,65090,65092],{},[898,65091,1872],{},[1793,65093,1806],{},[1688,65095,1690],{},[1793,65097,2616],{},[902,65099,65100],{"encoding":904},"Q_2 = 4"," (odpovídající starší verzi zadání) a zároveň maximum v ",[883,65103,65105],{"className":65104},[886],[888,65106,65107],{"xmlns":890},[892,65108,65109,65117],{},[895,65110,65111,65113,65115],{},[898,65112,1872],{},[1688,65114,1690],{},[1793,65116,64973],{},[902,65118,65048],{"encoding":904},[883,65120,65122],{"className":65121},[886],[888,65123,65124],{"xmlns":890},[892,65125,65126,65137],{},[895,65127,65128,65130,65132,65134],{},[898,65129,1727],{},[898,65131,4251],{},[1688,65133,1690],{},[1793,65135,65136],{},"6,125",[902,65138,65139],{"encoding":904},"PR = 6{,}125"," (odpovídající derivaci ",[883,65142,65144],{"className":65143},[886],[888,65145,65146],{"xmlns":890},[892,65147,65148,65170],{},[895,65149,65150,65152,65158,65160,65162,65164,65166,65168],{},[898,65151,1727],{},[1850,65153,65154,65156],{},[898,65155,4251],{},[1688,65157,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,65159,1690],{},[1688,65161,1954],{},[1793,65163,2616],{},[898,65165,1872],{},[1688,65167,1696],{},[1793,65169,4256],{},[902,65171,65172],{"encoding":904},"PR' = -4Q + 9",", tj. zisku ",[883,65175,65177],{"className":65176},[886],[888,65178,65179],{"xmlns":890},[892,65180,65181,65209],{},[895,65182,65183,65185,65187,65189,65191,65193,65199,65201,65203,65205,65207],{},[898,65184,1727],{},[898,65186,4251],{},[1688,65188,1690],{},[1688,65190,1954],{},[1793,65192,1806],{},[1850,65194,65195,65197],{},[898,65196,1872],{},[1793,65198,1806],{},[1688,65200,1696],{},[1793,65202,4256],{},[898,65204,1872],{},[1688,65206,1954],{},[1793,65208,2616],{},[902,65210,65211],{"encoding":904},"PR = -2Q^2 + 9Q - 4"," bez odčtení kvadratického členu ",[883,65214,65216],{"className":65215},[886],[888,65217,65218],{"xmlns":890},[892,65219,65220,65228],{},[895,65221,65222],{},[1850,65223,65224,65226],{},[898,65225,1872],{},[1793,65227,1806],{},[902,65229,65230],{"encoding":904},"Q^2",[883,65232,65234],{"className":65233},[886],[888,65235,65236],{"xmlns":890},[892,65237,65238,65246],{},[895,65239,65240,65242,65244],{},[898,65241,3035],{},[898,65243,40579],{},[898,65245,1693],{},[902,65247,55749],{"encoding":904},"). Zde je uvedena matematicky konzistentní verze: zadané ",[883,65250,65252],{"className":65251},[886],[888,65253,65254],{"xmlns":890},[892,65255,65256,65274],{},[895,65257,65258,65260,65262,65264,65266,65268],{},[898,65259,3035],{},[898,65261,1693],{},[1688,65263,1690],{},[1793,65265,2616],{},[1688,65267,1696],{},[1850,65269,65270,65272],{},[898,65271,1872],{},[1793,65273,1806],{},[902,65275,65276],{"encoding":904},"TC = 4 + Q^2",[883,65278,65280],{"className":65279},[886],[888,65281,65282],{"xmlns":890},[892,65283,65284,65308],{},[895,65285,65286,65288,65290,65292,65294,65296,65302,65304,65306],{},[898,65287,3035],{},[898,65289,4251],{},[1688,65291,1690],{},[1688,65293,1954],{},[1793,65295,1806],{},[1850,65297,65298,65300],{},[898,65299,1872],{},[1793,65301,1806],{},[1688,65303,1696],{},[1793,65305,4256],{},[898,65307,1872],{},[902,65309,65310],{"encoding":904},"TR = -2Q^2 + 9Q"," vedou na ",[883,65313,65315],{"className":65314},[886],[888,65316,65317],{"xmlns":890},[892,65318,65319,65347],{},[895,65320,65321,65323,65325,65327,65329,65331,65337,65339,65341,65343,65345],{},[898,65322,1727],{},[898,65324,4251],{},[1688,65326,1690],{},[1688,65328,1954],{},[1793,65330,2131],{},[1850,65332,65333,65335],{},[898,65334,1872],{},[1793,65336,1806],{},[1688,65338,1696],{},[1793,65340,4256],{},[898,65342,1872],{},[1688,65344,1954],{},[1793,65346,2616],{},[902,65348,65349],{"encoding":904},"PR = -3Q^2 + 9Q - 4",[883,65351,65353],{"className":65352},[886],[888,65354,65355],{"xmlns":890},[892,65356,65357,65371],{},[895,65358,65359,65367,65369],{},[1788,65360,65361,65363,65365],{},[898,65362,1872],{},[898,65364,56437],{},[1688,65366,56440],{},[1688,65368,1690],{},[1793,65370,64799],{},[902,65372,65373],{"encoding":904},"Q_{\\max} = 1{,}5",[883,65375,65377],{"className":65376},[886],[888,65378,65379],{"xmlns":890},[892,65380,65381,65398],{},[895,65382,65383,65385,65393,65395],{},[898,65384,1727],{},[1788,65386,65387,65389,65391],{},[898,65388,4251],{},[898,65390,56437],{},[1688,65392,56440],{},[1688,65394,1690],{},[1793,65396,65397],{},"2,75",[902,65399,65400],{"encoding":904},"PR_{\\max} = 2{,}75",[724,65402,65403],{},[614,65404,65405,65406,65433,65434,65467,65468,1343,65491,2263],{},"Obrázek 3.12: Graf ",[883,65407,65409],{"className":65408},[886],[888,65410,65411],{"xmlns":890},[892,65412,65413,65431],{},[895,65414,65415,65417,65419,65421,65423,65425],{},[898,65416,3035],{},[898,65418,1693],{},[1688,65420,1690],{},[1793,65422,2616],{},[1688,65424,1696],{},[1850,65426,65427,65429],{},[898,65428,1872],{},[1793,65430,1806],{},[902,65432,65276],{"encoding":904}," (parabola) a ",[883,65435,65437],{"className":65436},[886],[888,65438,65439],{"xmlns":890},[892,65440,65441,65465],{},[895,65442,65443,65445,65447,65449,65451,65453,65459,65461,65463],{},[898,65444,3035],{},[898,65446,4251],{},[1688,65448,1690],{},[1688,65450,1954],{},[1793,65452,1806],{},[1850,65454,65455,65457],{},[898,65456,1872],{},[1793,65458,1806],{},[1688,65460,1696],{},[1793,65462,4256],{},[898,65464,1872],{},[902,65466,65310],{"encoding":904}," (parabola); průsečíky vyznačují body zvratu ",[883,65469,65471],{"className":65470},[886],[888,65472,65473],{"xmlns":890},[892,65474,65475,65488],{},[895,65476,65477,65483,65485],{},[1788,65478,65479,65481],{},[898,65480,1872],{},[1793,65482,1795],{},[1688,65484,6156],{},[1793,65486,65487],{},"0,54",[902,65489,65490],{"encoding":904},"Q_1 \\doteq 0{,}54",[883,65492,65494],{"className":65493},[886],[888,65495,65496],{"xmlns":890},[892,65497,65498,65511],{},[895,65499,65500,65506,65508],{},[1788,65501,65502,65504],{},[898,65503,1872],{},[1793,65505,1806],{},[1688,65507,6156],{},[1793,65509,65510],{},"2,46",[902,65512,65513],{"encoding":904},"Q_2 \\doteq 2{,}46",[724,65515,65516],{},[614,65517,65518,65519,58747,65556,65573,65574,1343,65595,2263],{},"Obrázek 3.13: Graf zisku ",[883,65520,65522],{"className":65521},[886],[888,65523,65524],{"xmlns":890},[892,65525,65526,65554],{},[895,65527,65528,65530,65532,65534,65536,65538,65544,65546,65548,65550,65552],{},[898,65529,1727],{},[898,65531,4251],{},[1688,65533,1690],{},[1688,65535,1954],{},[1793,65537,2131],{},[1850,65539,65540,65542],{},[898,65541,1872],{},[1793,65543,1806],{},[1688,65545,1696],{},[1793,65547,4256],{},[898,65549,1872],{},[1688,65551,1954],{},[1793,65553,2616],{},[902,65555,65349],{"encoding":904},[883,65557,65559],{"className":65558},[886],[888,65560,65561],{"xmlns":890},[892,65562,65563,65571],{},[895,65564,65565,65567,65569],{},[898,65566,1872],{},[1688,65568,1690],{},[1793,65570,64799],{},[902,65572,64854],{"encoding":904}," a nulami ",[883,65575,65577],{"className":65576},[886],[888,65578,65579],{"xmlns":890},[892,65580,65581,65593],{},[895,65582,65583,65589,65591],{},[1788,65584,65585,65587],{},[898,65586,1872],{},[1793,65588,1795],{},[1688,65590,6156],{},[1793,65592,65487],{},[902,65594,65490],{"encoding":904},[883,65596,65598],{"className":65597},[886],[888,65599,65600],{"xmlns":890},[892,65601,65602,65614],{},[895,65603,65604,65610,65612],{},[1788,65605,65606,65608],{},[898,65607,1872],{},[1793,65609,1806],{},[1688,65611,6156],{},[1793,65613,65510],{},[902,65615,65513],{"encoding":904},[115,65617,65619],{"id":65618},"princip-maximalizace-zisku","Princip maximalizace zisku",[724,65621,65622],{},"Kromě standardního hledání extrému lze využít následující princip.",[724,65624,65625],{},[2821,65626],{"alt":65627,"className":65628,"src":65629},"imek-max-zisku-dva-pohledy",[210,2825],"\u002Fwiki-assets\u002Fimek-max-zisku-dva-pohledy.jpeg",[198,65631,16659],{"id":65632},"princip-1",[724,65634,65635,65636,2886,65651,65668],{},"Má-li zisk ",[883,65637,65639],{"className":65638},[886],[888,65640,65641],{"xmlns":890},[892,65642,65643,65649],{},[895,65644,65645,65647],{},[898,65646,1727],{},[898,65648,4251],{},[902,65650,63719],{"encoding":904},[883,65652,65654],{"className":65653},[886],[888,65655,65656],{"xmlns":890},[892,65657,65658,65666],{},[895,65659,65660],{},[1788,65661,65662,65664],{},[898,65663,1872],{},[1793,65665,1779],{},[902,65667,38548],{"encoding":904}," maximum, pak platí",[883,65670,65672],{"className":65671},[886],[888,65673,65674],{"xmlns":890,"display":28306},[892,65675,65676,65725],{},[20995,65677,65678],{"width":28311},[21000,65679,65680,65682,65718,65720],{},[21003,65681],{"width":28316},[21003,65683,65684],{},[895,65685,65686,65688,65690,65692,65698,65700,65702,65704,65706,65708,65714,65716],{},[898,65687,1661],{},[898,65689,4251],{},[1688,65691,2066],{"stretchy":2065},[1788,65693,65694,65696],{},[898,65695,1872],{},[1793,65697,1779],{},[1688,65699,2076],{"stretchy":2065},[1688,65701,1690],{},[898,65703,1661],{},[898,65705,1693],{},[1688,65707,2066],{"stretchy":2065},[1788,65709,65710,65712],{},[898,65711,1872],{},[1793,65713,1779],{},[1688,65715,2076],{"stretchy":2065},[898,65717,2263],{"mathvariant":1822},[21003,65719],{"width":28316},[21003,65721,65722],{},[2041,65723,65724],{},"(3.13)",[902,65726,65727],{"encoding":904},"MR(Q_0) = MC(Q_0).\n\\tag{3.13}",[4124,65729,65730],{},[724,65731,65732,62286,65734],{},[883,65733,56684],{},[38,65735,65736],{},"V bodě maxima zisku se mezní příjem rovná mezním nákladům.",[724,65738,65739,65742,65743,8358,65770,17821,65844,2263],{},[38,65740,65741],{},"Odvození"," (úloha 3.21): nutnou podmínkou maxima ",[883,65744,65746],{"className":65745},[886],[888,65747,65748],{"xmlns":890},[892,65749,65750,65768],{},[895,65751,65752,65754,65756,65758,65760,65762,65764,65766],{},[898,65753,1727],{},[898,65755,4251],{},[1688,65757,1690],{},[898,65759,3035],{},[898,65761,4251],{},[1688,65763,1954],{},[898,65765,3035],{},[898,65767,1693],{},[902,65769,55440],{"encoding":904},[883,65771,65773],{"className":65772},[886],[888,65774,65775],{"xmlns":890},[892,65776,65777,65841],{},[895,65778,65779,65781,65787,65789,65795,65797,65799,65801,65807,65809,65815,65817,65819,65821,65827,65829,65835,65837,65839],{},[898,65780,1727],{},[1850,65782,65783,65785],{},[898,65784,4251],{},[1688,65786,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,65788,2066],{"stretchy":2065},[1788,65790,65791,65793],{},[898,65792,1872],{},[1793,65794,1779],{},[1688,65796,2076],{"stretchy":2065},[1688,65798,1690],{},[898,65800,3035],{},[1850,65802,65803,65805],{},[898,65804,4251],{},[1688,65806,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,65808,2066],{"stretchy":2065},[1788,65810,65811,65813],{},[898,65812,1872],{},[1793,65814,1779],{},[1688,65816,2076],{"stretchy":2065},[1688,65818,1954],{},[898,65820,3035],{},[1850,65822,65823,65825],{},[898,65824,1693],{},[1688,65826,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,65828,2066],{"stretchy":2065},[1788,65830,65831,65833],{},[898,65832,1872],{},[1793,65834,1779],{},[1688,65836,2076],{"stretchy":2065},[1688,65838,1690],{},[1793,65840,1779],{},[902,65842,65843],{"encoding":904},"PR'(Q_0) = TR'(Q_0) - TC'(Q_0) = 0",[883,65845,65847],{"className":65846},[886],[888,65848,65849],{"xmlns":890},[892,65850,65851,65883],{},[895,65852,65853,65855,65857,65859,65865,65867,65869,65871,65873,65875,65881],{},[898,65854,1661],{},[898,65856,4251],{},[1688,65858,2066],{"stretchy":2065},[1788,65860,65861,65863],{},[898,65862,1872],{},[1793,65864,1779],{},[1688,65866,2076],{"stretchy":2065},[1688,65868,1690],{},[898,65870,1661],{},[898,65872,1693],{},[1688,65874,2066],{"stretchy":2065},[1788,65876,65877,65879],{},[898,65878,1872],{},[1793,65880,1779],{},[1688,65882,2076],{"stretchy":2065},[902,65884,65885],{"encoding":904},"MR(Q_0) = MC(Q_0)",[4124,65887,65888,65893],{},[724,65889,65890,65892],{},[883,65891,4828],{}," Postup — jak najít maximum zisku",[152,65894,65895,65959,66014,66051,66079],{},[123,65896,65897,65898,4142,65913,65928,65929,4176],{},"Sestavte ",[883,65899,65901],{"className":65900},[886],[888,65902,65903],{"xmlns":890},[892,65904,65905,65911],{},[895,65906,65907,65909],{},[898,65908,3035],{},[898,65910,4251],{},[902,65912,4351],{"encoding":904},[883,65914,65916],{"className":65915},[886],[888,65917,65918],{"xmlns":890},[892,65919,65920,65926],{},[895,65921,65922,65924],{},[898,65923,3035],{},[898,65925,1693],{},[902,65927,3500],{"encoding":904}," ze zadání (typicky ",[883,65930,65932],{"className":65931},[886],[888,65933,65934],{"xmlns":890},[892,65935,65936,65956],{},[895,65937,65938,65940,65942,65944,65946,65948,65950,65952,65954],{},[898,65939,3035],{},[898,65941,4251],{},[1688,65943,1690],{},[898,65945,1727],{},[1688,65947,2066],{"stretchy":2065},[898,65949,1872],{},[1688,65951,2076],{"stretchy":2065},[1688,65953,3434],{},[898,65955,1872],{},[902,65957,65958],{"encoding":904},"TR = P(Q) \\cdot Q",[123,65960,65961,65962,4142,65988,2263],{},"Vypočtěte ",[883,65963,65965],{"className":65964},[886],[888,65966,65967],{"xmlns":890},[892,65968,65969,65985],{},[895,65970,65971,65973,65975,65977,65979],{},[898,65972,1661],{},[898,65974,4251],{},[1688,65976,1690],{},[898,65978,3035],{},[1850,65980,65981,65983],{},[898,65982,4251],{},[1688,65984,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[902,65986,65987],{"encoding":904},"MR = TR'",[883,65989,65991],{"className":65990},[886],[888,65992,65993],{"xmlns":890},[892,65994,65995,66011],{},[895,65996,65997,65999,66001,66003,66005],{},[898,65998,1661],{},[898,66000,1693],{},[1688,66002,1690],{},[898,66004,3035],{},[1850,66006,66007,66009],{},[898,66008,1693],{},[1688,66010,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[902,66012,66013],{"encoding":904},"MC = TC'",[123,66015,66016,66017,2263],{},"Řešte rovnici ",[883,66018,66020],{"className":66019},[886],[888,66021,66022],{"xmlns":890},[892,66023,66024,66048],{},[895,66025,66026,66028,66030,66032,66034,66036,66038,66040,66042,66044,66046],{},[898,66027,1661],{},[898,66029,4251],{},[1688,66031,2066],{"stretchy":2065},[898,66033,1872],{},[1688,66035,2076],{"stretchy":2065},[1688,66037,1690],{},[898,66039,1661],{},[898,66041,1693],{},[1688,66043,2066],{"stretchy":2065},[898,66045,1872],{},[1688,66047,2076],{"stretchy":2065},[902,66049,66050],{"encoding":904},"MR(Q) = MC(Q)",[123,66052,66053,66054,66078],{},"Ověřte druhou derivaci ",[883,66055,66057],{"className":66056},[886],[888,66058,66059],{"xmlns":890},[892,66060,66061,66075],{},[895,66062,66063,66065],{},[898,66064,1727],{},[1850,66066,66067,66069],{},[898,66068,4251],{},[895,66070,66071,66073],{},[1688,66072,1824],{"mathvariant":1822},[1688,66074,1824],{"mathvariant":1822},[902,66076,66077],{"encoding":904},"PR''"," (nebo že má rovnice jediný ekonomicky smysluplný kořen).",[123,66080,66081,66082,66109],{},"Dosaďte do ",[883,66083,66085],{"className":66084},[886],[888,66086,66087],{"xmlns":890},[892,66088,66089,66107],{},[895,66090,66091,66093,66095,66097,66099,66101,66103,66105],{},[898,66092,1727],{},[898,66094,4251],{},[1688,66096,1690],{},[898,66098,3035],{},[898,66100,4251],{},[1688,66102,1954],{},[898,66104,3035],{},[898,66106,1693],{},[902,66108,55440],{"encoding":904}," pro hodnotu maxima.",[37588,66111,66113],{"id":66112},"příklad-39","Příklad 3.9",[724,66115,66116,56228,66118,4142,66140,66176],{},[38,66117,56227],{},[883,66119,66121],{"className":66120},[886],[888,66122,66123],{"xmlns":890},[892,66124,66125,66137],{},[895,66126,66127,66129,66131,66133,66135],{},[898,66128,1727],{},[1688,66130,1690],{},[1793,66132,38259],{},[1688,66134,1954],{},[898,66136,1872],{},[902,66138,66139],{"encoding":904},"P = 30 - Q",[883,66141,66143],{"className":66142},[886],[888,66144,66145],{"xmlns":890},[892,66146,66147,66173],{},[895,66148,66149,66151,66153,66155,66157,66163,66165,66167,66169,66171],{},[898,66150,3035],{},[898,66152,1693],{},[1688,66154,1690],{},[1793,66156,5265],{},[1850,66158,66159,66161],{},[898,66160,1872],{},[1793,66162,1806],{},[1688,66164,1696],{},[1793,66166,2508],{},[898,66168,1872],{},[1688,66170,1696],{},[1793,66172,24442],{},[902,66174,66175],{"encoding":904},"TC = 0{,}5Q^2 + 6Q + 7"," stanovte produkci maximalizující zisk.",[724,66178,66179,2170,66181,1343,66211,66249,66250,16039,66294,66328,66329,2263],{},[38,66180,23011],{},[883,66182,66184],{"className":66183},[886],[888,66185,66186],{"xmlns":890},[892,66187,66188,66208],{},[895,66189,66190,66192,66194,66196,66198,66200,66202],{},[898,66191,3035],{},[898,66193,4251],{},[1688,66195,1690],{},[1793,66197,38259],{},[898,66199,1872],{},[1688,66201,1954],{},[1850,66203,66204,66206],{},[898,66205,1872],{},[1793,66207,1806],{},[902,66209,66210],{"encoding":904},"TR = 30Q - Q^2",[883,66212,66214],{"className":66213},[886],[888,66215,66216],{"xmlns":890},[892,66217,66218,66246],{},[895,66219,66220,66222,66224,66226,66228,66230,66236,66238,66240,66242,66244],{},[898,66221,1727],{},[898,66223,4251],{},[1688,66225,1690],{},[1688,66227,1954],{},[1793,66229,64799],{},[1850,66231,66232,66234],{},[898,66233,1872],{},[1793,66235,1806],{},[1688,66237,1696],{},[1793,66239,42040],{},[898,66241,1872],{},[1688,66243,1954],{},[1793,66245,24442],{},[902,66247,66248],{"encoding":904},"PR = -1{,}5Q^2 + 24Q - 7",". Extrém: ",[883,66251,66253],{"className":66252},[886],[888,66254,66255],{"xmlns":890},[892,66256,66257,66291],{},[895,66258,66259,66261,66267,66269,66271,66273,66275,66277,66279,66281,66283,66285,66287,66289],{},[898,66260,1727],{},[1850,66262,66263,66265],{},[898,66264,4251],{},[1688,66266,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,66268,1690],{},[1688,66270,1954],{},[1793,66272,2131],{},[898,66274,1872],{},[1688,66276,1696],{},[1793,66278,42040],{},[1688,66280,1690],{},[1793,66282,1779],{},[1688,66284,4244],{},[898,66286,1872],{},[1688,66288,1690],{},[1793,66290,5841],{},[902,66292,66293],{"encoding":904},"PR' = -3Q + 24 = 0 \\Rightarrow Q = 8",[883,66295,66297],{"className":66296},[886],[888,66298,66299],{"xmlns":890},[892,66300,66301,66325],{},[895,66302,66303,66305,66315,66317,66319,66321,66323],{},[898,66304,1727],{},[1850,66306,66307,66309],{},[898,66308,4251],{},[895,66310,66311,66313],{},[1688,66312,1824],{"mathvariant":1822},[1688,66314,1824],{"mathvariant":1822},[1688,66316,1690],{},[1688,66318,1954],{},[1793,66320,2131],{},[1688,66322,3704],{},[1793,66324,1779],{},[902,66326,66327],{"encoding":904},"PR'' = -3 \u003C 0"," (maximum); ",[883,66330,66332],{"className":66331},[886],[888,66333,66334],{"xmlns":890},[892,66335,66336,66353],{},[895,66337,66338,66340,66342,66344,66346,66348,66350],{},[898,66339,1727],{},[898,66341,4251],{},[1688,66343,2066],{"stretchy":2065},[1793,66345,5841],{},[1688,66347,2076],{"stretchy":2065},[1688,66349,1690],{},[1793,66351,66352],{},"89",[902,66354,66355],{"encoding":904},"PR(8) = 89",[724,66357,66358,66359,1343,66385,16039,66409,66447],{},"Ověření principu: ",[883,66360,66362],{"className":66361},[886],[888,66363,66364],{"xmlns":890},[892,66365,66366,66382],{},[895,66367,66368,66370,66372,66374,66376,66378,66380],{},[898,66369,1661],{},[898,66371,4251],{},[1688,66373,1690],{},[1793,66375,38259],{},[1688,66377,1954],{},[1793,66379,1806],{},[898,66381,1872],{},[902,66383,66384],{"encoding":904},"MR = 30 - 2Q",[883,66386,66388],{"className":66387},[886],[888,66389,66390],{"xmlns":890},[892,66391,66392,66406],{},[895,66393,66394,66396,66398,66400,66402,66404],{},[898,66395,1661],{},[898,66397,1693],{},[1688,66399,1690],{},[898,66401,1872],{},[1688,66403,1696],{},[1793,66405,2508],{},[902,66407,66408],{"encoding":904},"MC = Q + 6",[883,66410,66412],{"className":66411},[886],[888,66413,66414],{"xmlns":890},[892,66415,66416,66444],{},[895,66417,66418,66420,66422,66424,66426,66428,66430,66432,66434,66436,66438,66440,66442],{},[898,66419,1661],{},[898,66421,4251],{},[1688,66423,2066],{"stretchy":2065},[1793,66425,5841],{},[1688,66427,2076],{"stretchy":2065},[1688,66429,1690],{},[1793,66431,23187],{},[1688,66433,1690],{},[898,66435,1661],{},[898,66437,1693],{},[1688,66439,2066],{"stretchy":2065},[1793,66441,5841],{},[1688,66443,2076],{"stretchy":2065},[902,66445,66446],{"encoding":904},"MR(8) = 14 = MC(8)",", tj. platí (3.13).",[724,66449,66450,66451,66484,66485,66502],{},"V řadě případů — má-li rovnice ",[883,66452,66454],{"className":66453},[886],[888,66455,66456],{"xmlns":890},[892,66457,66458,66482],{},[895,66459,66460,66462,66464,66466,66468,66470,66472,66474,66476,66478,66480],{},[898,66461,1661],{},[898,66463,4251],{},[1688,66465,2066],{"stretchy":2065},[898,66467,1872],{},[1688,66469,2076],{"stretchy":2065},[1688,66471,1690],{},[898,66473,1661],{},[898,66475,1693],{},[1688,66477,2066],{"stretchy":2065},[898,66479,1872],{},[1688,66481,2076],{"stretchy":2065},[902,66483,66050],{"encoding":904}," jediné ekonomicky smysluplné řešení ",[883,66486,66488],{"className":66487},[886],[888,66489,66490],{"xmlns":890},[892,66491,66492,66500],{},[895,66493,66494],{},[1788,66495,66496,66498],{},[898,66497,1872],{},[1793,66499,1779],{},[902,66501,38548],{"encoding":904}," — není třeba provádět test druhé derivace.",[37588,66504,66506],{"id":66505},"příklad-310","Příklad 3.10",[724,66508,66509,66511,66512,66516,66517,66530,66531,66562],{},[38,66510,56227],{}," Firma vyrábí minipočítače v ",[207,66513,66515],{"className":66514,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurenci",", produkuje 30 výrobků denně za ",[883,66518,66520],{"className":66519},[886],[888,66521,66522],{"xmlns":890},[892,66523,66524,66528],{},[895,66525,66526],{},[1793,66527,15438],{},[902,66529,15438],{"encoding":904}," EUR\u002Fks. ",[883,66532,66534],{"className":66533},[886],[888,66535,66536],{"xmlns":890},[892,66537,66538,66559],{},[895,66539,66540,66542,66544,66546,66548,66550,66553],{},[898,66541,3035],{},[898,66543,1693],{},[1688,66545,1690],{},[1793,66547,3377],{},[1688,66549,1696],{},[1793,66551,66552],{},"28",[1850,66554,66555,66557],{},[898,66556,1872],{},[1793,66558,1806],{},[902,66560,66561],{"encoding":904},"TC = 50 + 28Q^2",". Určete optimální denní produkci a zisk.",[724,66564,66565,2170,66567,1343,66589,1343,66609,66632],{},[38,66566,23011],{},[883,66568,66570],{"className":66569},[886],[888,66571,66572],{"xmlns":890},[892,66573,66574,66586],{},[895,66575,66576,66578,66580,66582,66584],{},[898,66577,3035],{},[898,66579,4251],{},[1688,66581,1690],{},[1793,66583,15438],{},[898,66585,1872],{},[902,66587,66588],{"encoding":904},"TR = 900Q",[883,66590,66592],{"className":66591},[886],[888,66593,66594],{"xmlns":890},[892,66595,66596,66606],{},[895,66597,66598,66600,66602,66604],{},[898,66599,1661],{},[898,66601,4251],{},[1688,66603,1690],{},[1793,66605,15438],{},[902,66607,66608],{"encoding":904},"MR = 900",[883,66610,66612],{"className":66611},[886],[888,66613,66614],{"xmlns":890},[892,66615,66616,66629],{},[895,66617,66618,66620,66622,66624,66627],{},[898,66619,1661],{},[898,66621,1693],{},[1688,66623,1690],{},[1793,66625,66626],{},"56",[898,66628,1872],{},[902,66630,66631],{"encoding":904},"MC = 56Q",". Z principu:",[883,66634,66636],{"className":66635},[886],[888,66637,66638],{"xmlns":890,"display":28306},[892,66639,66640,66682],{},[895,66641,66642,66644,66646,66648,66650,66652,66654,66656,66658,66660,66668,66670,66673,66675,66677,66679],{},[1793,66643,15438],{},[1688,66645,1690],{},[1793,66647,66626],{},[898,66649,1872],{},[2041,66651,4241],{},[1688,66653,4244],{},[2041,66655,4241],{},[898,66657,1872],{},[1688,66659,1690],{},[1777,66661,66662],{"scriptlevel":1779,"displaystyle":2065},[1781,66663,66664,66666],{},[1793,66665,15438],{},[1793,66667,66626],{},[1688,66669,6156],{},[1793,66671,66672],{},"16,07",[2041,66674,4241],{},[1688,66676,2991],{},[2041,66678,4241],{},[1793,66680,66681],{},"16.",[902,66683,66684],{"encoding":904},"900 = 56Q \\;\\Rightarrow\\; Q = \\tfrac{900}{56} \\doteq 16{,}07 \\;\\approx\\; 16.",[724,66686,66687,66688,2965],{},"Zisk při ",[883,66689,66691],{"className":66690},[886],[888,66692,66693],{"xmlns":890},[892,66694,66695,66703],{},[895,66696,66697,66699,66701],{},[898,66698,1872],{},[1688,66700,1690],{},[1793,66702,42102],{},[902,66704,66705],{"encoding":904},"Q = 16",[883,66707,66709],{"className":66708},[886],[888,66710,66711],{"xmlns":890,"display":28306},[892,66712,66713,66784],{},[895,66714,66715,66717,66719,66721,66723,66725,66727,66729,66731,66733,66735,66737,66739,66741,66743,66745,66751,66753,66755,66757,66759,66761,66763,66765,66767,66770,66772,66774,66776,66779,66782],{},[898,66716,1727],{},[898,66718,4251],{},[1688,66720,2066],{"stretchy":2065},[1793,66722,42102],{},[1688,66724,2076],{"stretchy":2065},[1688,66726,1690],{},[1793,66728,15438],{},[1688,66730,3434],{},[1793,66732,42102],{},[1688,66734,1954],{},[1688,66736,2066],{"stretchy":2065},[1793,66738,3377],{},[1688,66740,1696],{},[1793,66742,66552],{},[1688,66744,3434],{},[1850,66746,66747,66749],{},[1793,66748,42102],{},[1793,66750,1806],{},[1688,66752,2076],{"stretchy":2065},[1688,66754,1690],{},[1793,66756,23187],{},[2041,66758,2043],{},[1793,66760,20383],{},[1688,66762,1954],{},[1793,66764,24442],{},[2041,66766,2043],{},[1793,66768,66769],{},"218",[1688,66771,1690],{},[1793,66773,24442],{},[2041,66775,2043],{},[1793,66777,66778],{},"182",[2041,66780,66781],{}," EUR",[898,66783,2263],{"mathvariant":1822},[902,66785,66786],{"encoding":904},"PR(16) = 900 \\cdot 16 - (50 + 28 \\cdot 16^2) = 14\\,400 - 7\\,218 = 7\\,182 \\text{ EUR}.",[724,66788,66789],{},"Pro srovnání při původních 30 ks:",[883,66791,66793],{"className":66792},[886],[888,66794,66795],{"xmlns":890,"display":28306},[892,66796,66797,66862],{},[895,66798,66799,66801,66803,66805,66807,66809,66811,66813,66815,66817,66819,66821,66823,66825,66827,66829,66831,66833,66835,66838,66840,66842,66844,66846,66848,66850,66852,66854,66856,66858,66860],{},[898,66800,1727],{},[898,66802,4251],{},[1688,66804,2066],{"stretchy":2065},[1793,66806,38259],{},[1688,66808,2076],{"stretchy":2065},[1688,66810,1690],{},[1793,66812,15438],{},[1688,66814,3434],{},[1793,66816,38259],{},[1688,66818,1954],{},[1688,66820,2066],{"stretchy":2065},[1793,66822,3377],{},[1688,66824,1696],{},[1793,66826,66552],{},[1688,66828,3434],{},[1793,66830,15438],{},[1688,66832,2076],{"stretchy":2065},[1688,66834,1690],{},[1793,66836,66837],{},"27",[2041,66839,2043],{},[1793,66841,59322],{},[1688,66843,1954],{},[1793,66845,5260],{},[2041,66847,2043],{},[1793,66849,30983],{},[1688,66851,1690],{},[1793,66853,1795],{},[2041,66855,2043],{},[1793,66857,23984],{},[2041,66859,66781],{},[898,66861,2263],{"mathvariant":1822},[902,66863,66864],{"encoding":904},"PR(30) = 900 \\cdot 30 - (50 + 28 \\cdot 900) = 27\\,000 - 25\\,250 = 1\\,750 \\text{ EUR}.",[724,66866,66867,66870,66871,66889,66890,66908],{},[38,66868,66869],{},"Doporučení:"," vyrábět 16 ks\u002Fden se ziskem ",[883,66872,66874],{"className":66873},[886],[888,66875,66876],{"xmlns":890},[892,66877,66878,66886],{},[895,66879,66880,66882,66884],{},[1793,66881,24442],{},[2041,66883,2043],{},[1793,66885,66778],{},[902,66887,66888],{"encoding":904},"7\\,182"," EUR namísto původních ",[883,66891,66893],{"className":66892},[886],[888,66894,66895],{"xmlns":890},[892,66896,66897,66905],{},[895,66898,66899,66901,66903],{},[1793,66900,1795],{},[2041,66902,2043],{},[1793,66904,23984],{},[902,66906,66907],{"encoding":904},"1\\,750"," EUR.",[198,66910,66912],{"id":66911},"speciální-tvar-pro-pevnou-cenu","Speciální tvar pro pevnou cenu",[724,66914,66915,66916,62810,66929,66953],{},"Předpokládáme-li, že výrobce prodává za pevnou cenu ",[883,66917,66919],{"className":66918},[886],[888,66920,66921],{"xmlns":890},[892,66922,66923,66927],{},[895,66924,66925],{},[898,66926,1727],{},[902,66928,1727],{"encoding":904},[883,66930,66932],{"className":66931},[886],[888,66933,66934],{"xmlns":890},[892,66935,66936,66950],{},[895,66937,66938,66940,66942,66944,66946,66948],{},[898,66939,3035],{},[898,66941,4251],{},[1688,66943,1690],{},[898,66945,1727],{},[1688,66947,3434],{},[898,66949,1872],{},[902,66951,66952],{"encoding":904},"TR = P \\cdot Q"," a z (3.13) speciálně:",[883,66955,66957],{"className":66956},[886],[888,66958,66959],{"xmlns":890,"display":28306},[892,66960,66961,66994],{},[20995,66962,66963],{"width":28311},[21000,66964,66965,66967,66987,66989],{},[21003,66966],{"width":28316},[21003,66968,66969],{},[895,66970,66971,66973,66975,66977,66979,66981,66983,66985],{},[898,66972,1727],{},[1688,66974,1690],{},[898,66976,1661],{},[898,66978,1693],{},[1688,66980,2066],{"stretchy":2065},[898,66982,1872],{},[1688,66984,2076],{"stretchy":2065},[898,66986,2263],{"mathvariant":1822},[21003,66988],{"width":28316},[21003,66990,66991],{},[2041,66992,66993],{},"(3.14)",[902,66995,66996],{"encoding":904},"P = MC(Q).\n\\tag{3.14}",[724,66998,66999,67000,2263],{},"Výrobce musí nastavit nabízené množství tak, aby se mezní náklady rovnaly ceně. Má-li rovnice (3.14) více řešení, rozhoduje znaménko ",[883,67001,67003],{"className":67002},[886],[888,67004,67005],{"xmlns":890},[892,67006,67007,67021],{},[895,67008,67009,67011],{},[898,67010,1727],{},[1850,67012,67013,67015],{},[898,67014,4251],{},[895,67016,67017,67019],{},[1688,67018,1824],{"mathvariant":1822},[1688,67020,1824],{"mathvariant":1822},[902,67022,66077],{"encoding":904},[37588,67024,67026],{"id":67025},"příklad-311","Příklad 3.11",[724,67028,67029,57762,67031,67078,67079,67097],{},[38,67030,56227],{},[883,67032,67034],{"className":67033},[886],[888,67035,67036],{"xmlns":890},[892,67037,67038,67075],{},[895,67039,67040,67042,67044,67046,67049,67055,67057,67059,67065,67067,67069,67071,67073],{},[898,67041,3035],{},[898,67043,1693],{},[1688,67045,1690],{},[1793,67047,67048],{},"0,04",[1850,67050,67051,67053],{},[898,67052,1872],{},[1793,67054,2131],{},[1688,67056,1954],{},[1793,67058,22786],{},[1850,67060,67061,67063],{},[898,67062,1872],{},[1793,67064,1806],{},[1688,67066,1696],{},[1793,67068,3121],{},[898,67070,1872],{},[1688,67072,1696],{},[1793,67074,2501],{},[902,67076,67077],{"encoding":904},"TC = 0{,}04Q^3 - 0{,}9Q^2 + 10Q + 5"," a pevnou cenu ",[883,67080,67082],{"className":67081},[886],[888,67083,67084],{"xmlns":890},[892,67085,67086,67094],{},[895,67087,67088,67090,67092],{},[898,67089,1727],{},[1688,67091,1690],{},[1793,67093,2616],{},[902,67095,67096],{"encoding":904},"P = 4"," stanovte optimální produkci.",[724,67099,67100,67102,67103,17821,67145,67179,67180,2965],{},[38,67101,23011],{}," Z (3.14): ",[883,67104,67106],{"className":67105},[886],[888,67107,67108],{"xmlns":890},[892,67109,67110,67142],{},[895,67111,67112,67114,67116,67118,67121,67127,67129,67132,67134,67136,67138,67140],{},[898,67113,1661],{},[898,67115,1693],{},[1688,67117,1690],{},[1793,67119,67120],{},"0,12",[1850,67122,67123,67125],{},[898,67124,1872],{},[1793,67126,1806],{},[1688,67128,1954],{},[1793,67130,67131],{},"1,8",[898,67133,1872],{},[1688,67135,1696],{},[1793,67137,3121],{},[1688,67139,1690],{},[1793,67141,2616],{},[902,67143,67144],{"encoding":904},"MC = 0{,}12Q^2 - 1{,}8Q + 10 = 4",[883,67146,67148],{"className":67147},[886],[888,67149,67150],{"xmlns":890},[892,67151,67152,67176],{},[895,67153,67154,67156,67162,67164,67166,67168,67170,67172,67174],{},[1793,67155,67120],{},[1850,67157,67158,67160],{},[898,67159,1872],{},[1793,67161,1806],{},[1688,67163,1954],{},[1793,67165,67131],{},[898,67167,1872],{},[1688,67169,1696],{},[1793,67171,2508],{},[1688,67173,1690],{},[1793,67175,1779],{},[902,67177,67178],{"encoding":904},"0{,}12Q^2 - 1{,}8Q + 6 = 0",", po vydělení ",[883,67181,67183],{"className":67182},[886],[888,67184,67185],{"xmlns":890},[892,67186,67187,67191],{},[895,67188,67189],{},[1793,67190,67120],{},[902,67192,67193],{"encoding":904},"0{,}12",[883,67195,67197],{"className":67196},[886],[888,67198,67199],{"xmlns":890,"display":28306},[892,67200,67201,67253],{},[895,67202,67203,67209,67211,67213,67215,67217,67219,67221,67223,67225,67227,67229,67235,67237,67239,67241,67243,67249,67251],{},[1850,67204,67205,67207],{},[898,67206,1872],{},[1793,67208,1806],{},[1688,67210,1954],{},[1793,67212,36484],{},[898,67214,1872],{},[1688,67216,1696],{},[1793,67218,3377],{},[1688,67220,1690],{},[1793,67222,1779],{},[2041,67224,4241],{},[1688,67226,4244],{},[2041,67228,4241],{},[1788,67230,67231,67233],{},[898,67232,1872],{},[1793,67234,1795],{},[1688,67236,1690],{},[1793,67238,2501],{},[1688,67240,1733],{"separator":1732},[2041,67242,4241],{},[1788,67244,67245,67247],{},[898,67246,1872],{},[1793,67248,1806],{},[1688,67250,1690],{},[1793,67252,19569],{},[902,67254,67255],{"encoding":904},"Q^2 - 15Q + 50 = 0 \\;\\Rightarrow\\; Q_1 = 5, \\; Q_2 = 10.",[724,67257,67258,67259,2965],{},"Dále ",[883,67260,67262],{"className":67261},[886],[888,67263,67264],{"xmlns":890},[892,67265,67266,67305],{},[895,67267,67268,67270,67280,67282,67284,67286,67292,67294,67296,67299,67301,67303],{},[898,67269,1727],{},[1850,67271,67272,67274],{},[898,67273,4251],{},[895,67275,67276,67278],{},[1688,67277,1824],{"mathvariant":1822},[1688,67279,1824],{"mathvariant":1822},[1688,67281,1690],{},[1688,67283,1954],{},[898,67285,1661],{},[1850,67287,67288,67290],{},[898,67289,1693],{},[1688,67291,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,67293,1690],{},[1688,67295,1954],{},[1793,67297,67298],{},"0,24",[898,67300,1872],{},[1688,67302,1696],{},[1793,67304,67131],{},[902,67306,67307],{"encoding":904},"PR'' = -MC' = -0{,}24Q + 1{,}8",[120,67309,67310,67360],{},[123,67311,67312,67356,67357,67359],{},[883,67313,67315],{"className":67314},[886],[888,67316,67317],{"xmlns":890},[892,67318,67319,67353],{},[895,67320,67321,67323,67333,67335,67337,67339,67341,67343,67345,67347,67349,67351],{},[898,67322,1727],{},[1850,67324,67325,67327],{},[898,67326,4251],{},[895,67328,67329,67331],{},[1688,67330,1824],{"mathvariant":1822},[1688,67332,1824],{"mathvariant":1822},[1688,67334,2066],{"stretchy":2065},[1793,67336,2501],{},[1688,67338,2076],{"stretchy":2065},[1688,67340,1690],{},[1793,67342,19562],{},[1688,67344,3665],{},[1793,67346,1779],{},[2041,67348,4241],{},[1688,67350,4244],{},[2041,67352,4241],{},[902,67354,67355],{"encoding":904},"PR''(5) = 0{,}6 > 0 \\;\\Rightarrow\\;"," lokální ",[38,67358,4032],{}," zisku (minimalizace ztráty);",[123,67361,67362,67356,67408,67410],{},[883,67363,67365],{"className":67364},[886],[888,67366,67367],{"xmlns":890},[892,67368,67369,67405],{},[895,67370,67371,67373,67383,67385,67387,67389,67391,67393,67395,67397,67399,67401,67403],{},[898,67372,1727],{},[1850,67374,67375,67377],{},[898,67376,4251],{},[895,67378,67379,67381],{},[1688,67380,1824],{"mathvariant":1822},[1688,67382,1824],{"mathvariant":1822},[1688,67384,2066],{"stretchy":2065},[1793,67386,3121],{},[1688,67388,2076],{"stretchy":2065},[1688,67390,1690],{},[1688,67392,1954],{},[1793,67394,19562],{},[1688,67396,3704],{},[1793,67398,1779],{},[2041,67400,4241],{},[1688,67402,4244],{},[2041,67404,4241],{},[902,67406,67407],{"encoding":904},"PR''(10) = -0{,}6 \u003C 0 \\;\\Rightarrow\\;",[38,67409,3974],{}," zisku, avšak",[883,67412,67414],{"className":67413},[886],[888,67415,67416],{"xmlns":890,"display":28306},[892,67417,67418,67486],{},[895,67419,67420,67422,67424,67426,67428,67430,67432,67434,67436,67438,67440,67442,67444,67446,67448,67450,67452,67454,67456,67458,67460,67462,67464,67466,67468,67470,67472,67474,67476,67478,67480,67482,67484],{},[898,67421,1727],{},[898,67423,4251],{},[1688,67425,2066],{"stretchy":2065},[1793,67427,3121],{},[1688,67429,2076],{"stretchy":2065},[1688,67431,1690],{},[1793,67433,2616],{},[1688,67435,3434],{},[1793,67437,3121],{},[1688,67439,1954],{},[1688,67441,2066],{"stretchy":2065},[1793,67443,67048],{},[1688,67445,3434],{},[1793,67447,1795],{},[2041,67449,2043],{},[1793,67451,59322],{},[1688,67453,1954],{},[1793,67455,22786],{},[1688,67457,3434],{},[1793,67459,3347],{},[1688,67461,1696],{},[1793,67463,3347],{},[1688,67465,1696],{},[1793,67467,2501],{},[1688,67469,2076],{"stretchy":2065},[1688,67471,1690],{},[1793,67473,5467],{},[1688,67475,1954],{},[1793,67477,21421],{},[1688,67479,1690],{},[1688,67481,1954],{},[1793,67483,36484],{},[1688,67485,1733],{"separator":1732},[902,67487,67488],{"encoding":904},"PR(10) = 4 \\cdot 10 - (0{,}04 \\cdot 1\\,000 - 0{,}9 \\cdot 100 + 100 + 5) = 40 - 55 = -15,",[724,67490,67491,67492,2263],{},"tj. ztráta větší než ",[883,67493,67495],{"className":67494},[886],[888,67496,67497],{"xmlns":890},[892,67498,67499,67509],{},[895,67500,67501,67503,67505,67507],{},[898,67502,10688],{},[898,67504,1693],{},[1688,67506,1690],{},[1793,67508,2501],{},[902,67510,67511],{"encoding":904},"FC = 5",[724,67513,67514,67517,67518,67521,67522,2263],{},[38,67515,67516],{},"Závěr:"," firma by měla ",[38,67519,67520],{},"zastavit výrobu"," — i vypnutí provozu způsobí menší ztrátu, a to pouze ve výši ",[883,67523,67525],{"className":67524},[886],[888,67526,67527],{"xmlns":890},[892,67528,67529,67539],{},[895,67530,67531,67533,67535,67537],{},[898,67532,10688],{},[898,67534,1693],{},[1688,67536,1690],{},[1793,67538,2501],{},[902,67540,67511],{"encoding":904},[115,67542,67544],{"id":67543},"konstrukce-křivky-nabídky-firmy","Konstrukce křivky nabídky firmy",[724,67546,67547,67548,67550,67551,67566,67567,67580,67581,67607,67608,67621,67622,67639,67640,2886,67657,67660,67661,67681,67682,67697,67698,2965],{},"Důležitým završením analýzy je konstrukce ",[38,67549,55515],{},". S nabízeným množstvím rostou mezní náklady ",[883,67552,67554],{"className":67553},[886],[888,67555,67556],{"xmlns":890},[892,67557,67558,67564],{},[895,67559,67560,67562],{},[898,67561,1661],{},[898,67563,1693],{},[902,67565,55532],{"encoding":904}," a tyto určují cenu ",[883,67568,67570],{"className":67569},[886],[888,67571,67572],{"xmlns":890},[892,67573,67574,67578],{},[895,67575,67576],{},[898,67577,1727],{},[902,67579,1727],{"encoding":904},", za kterou je firma ochotna toto množství realizovat. Proto platí ",[883,67582,67584],{"className":67583},[886],[888,67585,67586],{"xmlns":890},[892,67587,67588,67604],{},[895,67589,67590,67592,67594,67596,67598,67600,67602],{},[898,67591,1727],{},[1688,67593,1690],{},[898,67595,1661],{},[898,67597,1693],{},[1688,67599,2066],{"stretchy":2065},[898,67601,1872],{},[1688,67603,2076],{"stretchy":2065},[902,67605,67606],{"encoding":904},"P = MC(Q)"," (obrázek 3.14). Cena ",[883,67609,67611],{"className":67610},[886],[888,67612,67613],{"xmlns":890},[892,67614,67615,67619],{},[895,67616,67617],{},[898,67618,1727],{},[902,67620,1727],{"encoding":904}," však nemůže být nižší než ",[883,67623,67625],{"className":67624},[886],[888,67626,67627],{"xmlns":890},[892,67628,67629,67637],{},[895,67630,67631],{},[1850,67632,67633,67635],{},[898,67634,1727],{},[1688,67636,1857],{},[902,67638,4660],{"encoding":904}," odpovídající množství ",[883,67641,67643],{"className":67642},[886],[888,67644,67645],{"xmlns":890},[892,67646,67647,67655],{},[895,67648,67649],{},[1850,67650,67651,67653],{},[898,67652,1872],{},[1688,67654,1857],{},[902,67656,30084],{"encoding":904},[38,67658,67659],{},"minima průměrných variabilních nákladů"," (fixní náklady nelze při optimalizaci zahrnout — jsou konstantní součástí nákladů i zisku). Křivka nabídky se tedy skládá z úsečky ",[883,67662,67664],{"className":67663},[886],[888,67665,67666],{"xmlns":890},[892,67667,67668,67678],{},[895,67669,67670,67672],{},[1793,67671,1779],{},[1850,67673,67674,67676],{},[898,67675,1872],{},[1688,67677,1857],{},[902,67679,67680],{"encoding":904},"0Q^*"," (kde firma nenabízí nic) a rostoucí části ",[883,67683,67685],{"className":67684},[886],[888,67686,67687],{"xmlns":890},[892,67688,67689,67695],{},[895,67690,67691,67693],{},[898,67692,1661],{},[898,67694,1693],{},[902,67696,55532],{"encoding":904}," nad bodem ",[883,67699,67701],{"className":67700},[886],[888,67702,67703],{"xmlns":890},[892,67704,67705,67709],{},[895,67706,67707],{},[898,67708,4512],{},[902,67710,4512],{"encoding":904},[883,67712,67714],{"className":67713},[886],[888,67715,67716],{"xmlns":890,"display":28306},[892,67717,67718,67825],{},[20995,67719,67720],{"width":28311},[21000,67721,67722,67724,67818,67820],{},[21003,67723],{"width":28316},[21003,67725,67726],{},[895,67727,67728,67730,67732,67734,67736,67738,67740,67742],{},[898,67729,1727],{},[1688,67731,1690],{},[898,67733,1740],{},[1688,67735,2066],{"stretchy":2065},[898,67737,1872],{},[1688,67739,2076],{"stretchy":2065},[1688,67741,1690],{},[895,67743,67744,67747],{},[1688,67745,67746],{"fence":1732},"{",[20995,67748,67751,67790],{"rowspacing":67749,"columnalign":67750,"columnspacing":15531},"0.36em","left left",[21000,67752,67753,67769],{},[21003,67754,67755],{},[1777,67756,67757],{"scriptlevel":1779,"displaystyle":2065},[895,67758,67759,67761,67763,67765,67767],{},[898,67760,1661],{},[898,67762,1693],{},[1688,67764,2066],{"stretchy":2065},[898,67766,1872],{},[1688,67768,2076],{"stretchy":2065},[21003,67770,67771],{},[1777,67772,67773],{"scriptlevel":1779,"displaystyle":2065},[895,67774,67775,67778,67780,67782,67788],{},[2041,67776,67777],{},"pro ",[898,67779,1872],{},[1688,67781,4741],{},[1850,67783,67784,67786],{},[898,67785,1872],{},[1688,67787,1857],{},[1688,67789,1733],{"separator":1732},[21000,67791,67792,67798],{},[21003,67793,67794],{},[1777,67795,67796],{"scriptlevel":1779,"displaystyle":2065},[1793,67797,1779],{},[21003,67799,67800],{},[1777,67801,67802],{"scriptlevel":1779,"displaystyle":2065},[895,67803,67804,67806,67808,67810,67816],{},[2041,67805,67777],{},[898,67807,1872],{},[1688,67809,3704],{},[1850,67811,67812,67814],{},[898,67813,1872],{},[1688,67815,1857],{},[1688,67817,1733],{"separator":1732},[21003,67819],{"width":28316},[21003,67821,67822],{},[2041,67823,67824],{},"(3.15)",[902,67826,67827],{"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}",[724,67829,4567,67830,67847,67848,67865,67866,41739,67896,67899],{},[883,67831,67833],{"className":67832},[886],[888,67834,67835],{"xmlns":890},[892,67836,67837,67845],{},[895,67838,67839],{},[1850,67840,67841,67843],{},[898,67842,1872],{},[1688,67844,1857],{},[902,67846,30084],{"encoding":904}," je bod minima ",[883,67849,67851],{"className":67850},[886],[888,67852,67853],{"xmlns":890},[892,67854,67855,67863],{},[895,67856,67857,67859,67861],{},[898,67858,4512],{},[898,67860,40579],{},[898,67862,1693],{},[902,67864,55551],{"encoding":904},". Bod ",[883,67867,67869],{"className":67868},[886],[888,67870,67871],{"xmlns":890},[892,67872,67873,67893],{},[895,67874,67875,67877,67883,67885,67891],{},[1688,67876,2066],{"stretchy":2065},[1850,67878,67879,67881],{},[898,67880,1872],{},[1688,67882,1857],{},[1688,67884,1733],{"separator":1732},[1850,67886,67887,67889],{},[898,67888,1727],{},[1688,67890,1857],{},[1688,67892,2076],{"stretchy":2065},[902,67894,67895],{"encoding":904},"(Q^*, P^*)",[38,67897,67898],{},"shutdown point"," — pod ním se firmě nevyplatí produkovat.",[4124,67901,67902,67907],{},[724,67903,67904,67906],{},[883,67905,4828],{}," Postup — jak odvodit nabídku firmy",[152,67908,67909,67958,68053,68108,68179],{},[123,67910,67911,67912,4142,67934,2263],{},"Ze zadaných nákladů určete ",[883,67913,67915],{"className":67914},[886],[888,67916,67917],{"xmlns":890},[892,67918,67919,67931],{},[895,67920,67921,67923,67925,67927,67929],{},[898,67922,1661],{},[898,67924,1693],{},[1688,67926,2066],{"stretchy":2065},[898,67928,1872],{},[1688,67930,2076],{"stretchy":2065},[902,67932,67933],{"encoding":904},"MC(Q)",[883,67935,67937],{"className":67936},[886],[888,67938,67939],{"xmlns":890},[892,67940,67941,67955],{},[895,67942,67943,67945,67947,67949,67951,67953],{},[898,67944,4512],{},[898,67946,40579],{},[898,67948,1693],{},[1688,67950,2066],{"stretchy":2065},[898,67952,1872],{},[1688,67954,2076],{"stretchy":2065},[902,67956,67957],{"encoding":904},"AVC(Q)",[123,67959,67960,67961,67978,67979,67996,67997,68029,68030,4176],{},"Najděte ",[883,67962,67964],{"className":67963},[886],[888,67965,67966],{"xmlns":890},[892,67967,67968,67976],{},[895,67969,67970],{},[1850,67971,67972,67974],{},[898,67973,1872],{},[1688,67975,1857],{},[902,67977,30084],{"encoding":904}," jako bod minima ",[883,67980,67982],{"className":67981},[886],[888,67983,67984],{"xmlns":890},[892,67985,67986,67994],{},[895,67987,67988,67990,67992],{},[898,67989,4512],{},[898,67991,40579],{},[898,67993,1693],{},[902,67995,55551],{"encoding":904}," (řešením ",[883,67998,68000],{"className":67999},[886],[888,68001,68002],{"xmlns":890},[892,68003,68004,68026],{},[895,68005,68006,68008,68010,68016,68018,68020,68022,68024],{},[898,68007,4512],{},[898,68009,40579],{},[1850,68011,68012,68014],{},[898,68013,1693],{},[1688,68015,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,68017,2066],{"stretchy":2065},[898,68019,1872],{},[1688,68021,2076],{"stretchy":2065},[1688,68023,1690],{},[1793,68025,1779],{},[902,68027,68028],{"encoding":904},"AVC'(Q) = 0",", případně rovnice ",[883,68031,68033],{"className":68032},[886],[888,68034,68035],{"xmlns":890},[892,68036,68037,68051],{},[895,68038,68039,68041,68043,68045,68047,68049],{},[898,68040,4512],{},[898,68042,40579],{},[898,68044,1693],{},[1688,68046,1690],{},[898,68048,1661],{},[898,68050,1693],{},[902,68052,55488],{"encoding":904},[123,68054,65961,68055,68107],{},[883,68056,68058],{"className":68057},[886],[888,68059,68060],{"xmlns":890},[892,68061,68062,68104],{},[895,68063,68064,68070,68072,68074,68076,68078,68084,68086,68088,68090,68092,68094,68096,68102],{},[1850,68065,68066,68068],{},[898,68067,1727],{},[1688,68069,1857],{},[1688,68071,1690],{},[898,68073,1661],{},[898,68075,1693],{},[1688,68077,2066],{"stretchy":2065},[1850,68079,68080,68082],{},[898,68081,1872],{},[1688,68083,1857],{},[1688,68085,2076],{"stretchy":2065},[1688,68087,1690],{},[898,68089,4512],{},[898,68091,40579],{},[898,68093,1693],{},[1688,68095,2066],{"stretchy":2065},[1850,68097,68098,68100],{},[898,68099,1872],{},[1688,68101,1857],{},[1688,68103,2076],{"stretchy":2065},[902,68105,68106],{"encoding":904},"P^* = MC(Q^*) = AVC(Q^*)"," — minimální cenu nabídky.",[123,68109,68110,68111,6729,68143,68165,68166,2263],{},"Zapište nabídku: ",[883,68112,68114],{"className":68113},[886],[888,68115,68116],{"xmlns":890},[892,68117,68118,68140],{},[895,68119,68120,68122,68124,68126,68128,68130,68132,68134,68136,68138],{},[898,68121,1740],{},[1688,68123,2066],{"stretchy":2065},[898,68125,1872],{},[1688,68127,2076],{"stretchy":2065},[1688,68129,1690],{},[898,68131,1661],{},[898,68133,1693],{},[1688,68135,2066],{"stretchy":2065},[898,68137,1872],{},[1688,68139,2076],{"stretchy":2065},[902,68141,68142],{"encoding":904},"S(Q) = MC(Q)",[883,68144,68146],{"className":68145},[886],[888,68147,68148],{"xmlns":890},[892,68149,68150,68162],{},[895,68151,68152,68154,68156],{},[898,68153,1872],{},[1688,68155,4741],{},[1850,68157,68158,68160],{},[898,68159,1872],{},[1688,68161,1857],{},[902,68163,68164],{"encoding":904},"Q \\geq Q^*",", jinak ",[883,68167,68169],{"className":68168},[886],[888,68170,68171],{"xmlns":890},[892,68172,68173,68177],{},[895,68174,68175],{},[1793,68176,1779],{},[902,68178,1779],{"encoding":904},[123,68180,68181,68182,68214],{},"V případě potřeby vyjádřete inverzi ",[883,68183,68185],{"className":68184},[886],[888,68186,68187],{"xmlns":890},[892,68188,68189,68211],{},[895,68190,68191,68193,68195,68205,68207,68209],{},[898,68192,1872],{},[1688,68194,1690],{},[1850,68196,68197,68199],{},[898,68198,1740],{},[895,68200,68201,68203],{},[1688,68202,1954],{},[1793,68204,1795],{},[1688,68206,2066],{"stretchy":2065},[898,68208,1727],{},[1688,68210,2076],{"stretchy":2065},[902,68212,68213],{"encoding":904},"Q = S^{-1}(P)"," doplněním na čtverec.",[724,68216,68217],{},[614,68218,68219,68220,1343,68235,4142,68252,29441,68267,68280,68281,68306,68307,68320,68321,68338,68339,68356,68357,68374],{},"Obrázek 3.14: Křivky ",[883,68221,68223],{"className":68222},[886],[888,68224,68225],{"xmlns":890},[892,68226,68227,68233],{},[895,68228,68229,68231],{},[898,68230,4512],{},[898,68232,1693],{},[902,68234,55800],{"encoding":904},[883,68236,68238],{"className":68237},[886],[888,68239,68240],{"xmlns":890},[892,68241,68242,68250],{},[895,68243,68244,68246,68248],{},[898,68245,4512],{},[898,68247,40579],{},[898,68249,1693],{},[902,68251,55551],{"encoding":904},[883,68253,68255],{"className":68254},[886],[888,68256,68257],{"xmlns":890},[892,68258,68259,68265],{},[895,68260,68261,68263],{},[898,68262,1661],{},[898,68264,1693],{},[902,68266,55532],{"encoding":904},[883,68268,68270],{"className":68269},[886],[888,68271,68272],{"xmlns":890},[892,68273,68274,68278],{},[895,68275,68276],{},[898,68277,900],{},[902,68279,900],{"encoding":904},"; křivka nabídky ",[883,68282,68284],{"className":68283},[886],[888,68285,68286],{"xmlns":890},[892,68287,68288,68304],{},[895,68289,68290,68292,68294,68296,68298,68300,68302],{},[898,68291,1727],{},[1688,68293,1690],{},[898,68295,1661],{},[898,68297,1693],{},[1688,68299,2066],{"stretchy":2065},[898,68301,1872],{},[1688,68303,2076],{"stretchy":2065},[902,68305,67606],{"encoding":904}," začíná v bodě ",[883,68308,68310],{"className":68309},[886],[888,68311,68312],{"xmlns":890},[892,68313,68314,68318],{},[895,68315,68316],{},[898,68317,4512],{},[902,68319,4512],{"encoding":904}," odpovídajícím minimu ",[883,68322,68324],{"className":68323},[886],[888,68325,68326],{"xmlns":890},[892,68327,68328,68336],{},[895,68329,68330,68332,68334],{},[898,68331,4512],{},[898,68333,40579],{},[898,68335,1693],{},[902,68337,55551],{"encoding":904}," při ceně ",[883,68340,68342],{"className":68341},[886],[888,68343,68344],{"xmlns":890},[892,68345,68346,68354],{},[895,68347,68348],{},[1850,68349,68350,68352],{},[898,68351,1727],{},[1688,68353,1857],{},[902,68355,4660],{"encoding":904}," (minimální cena nabídky); pod ",[883,68358,68360],{"className":68359},[886],[888,68361,68362],{"xmlns":890},[892,68363,68364,68372],{},[895,68365,68366],{},[1850,68367,68368,68370],{},[898,68369,1872],{},[1688,68371,1857],{},[902,68373,30084],{"encoding":904}," je nabídka nulová.",[37588,68376,68378],{"id":68377},"příklad-312","Příklad 3.12",[724,68380,68381,57762,68383,68429],{},[38,68382,56227],{},[883,68384,68386],{"className":68385},[886],[888,68387,68388],{"xmlns":890},[892,68389,68390,68426],{},[895,68391,68392,68394,68396,68398,68400,68406,68408,68410,68416,68418,68420,68422,68424],{},[898,68393,3035],{},[898,68395,1693],{},[1688,68397,1690],{},[1793,68399,3053],{},[1850,68401,68402,68404],{},[898,68403,1872],{},[1793,68405,2131],{},[1688,68407,1954],{},[1793,68409,1806],{},[1850,68411,68412,68414],{},[898,68413,1872],{},[1793,68415,1806],{},[1688,68417,1696],{},[1793,68419,36484],{},[898,68421,1872],{},[1688,68423,1696],{},[1793,68425,3121],{},[902,68427,68428],{"encoding":904},"TC = 0{,}1Q^3 - 2Q^2 + 15Q + 10"," odvoďte funkci nabídky firmy.",[724,68431,68432,2170,68434,68471,68472,2965],{},[38,68433,23011],{},[883,68435,68437],{"className":68436},[886],[888,68438,68439],{"xmlns":890},[892,68440,68441,68468],{},[895,68442,68443,68445,68447,68449,68452,68458,68460,68462,68464,68466],{},[898,68444,1661],{},[898,68446,1693],{},[1688,68448,1690],{},[1793,68450,68451],{},"0,3",[1850,68453,68454,68456],{},[898,68455,1872],{},[1793,68457,1806],{},[1688,68459,1954],{},[1793,68461,2616],{},[898,68463,1872],{},[1688,68465,1696],{},[1793,68467,36484],{},[902,68469,68470],{"encoding":904},"MC = 0{,}3Q^2 - 4Q + 15",", takže z ",[883,68473,68475],{"className":68474},[886],[888,68476,68477],{"xmlns":890},[892,68478,68479,68489],{},[895,68480,68481,68483,68485,68487],{},[898,68482,1727],{},[1688,68484,1690],{},[898,68486,1661],{},[898,68488,1693],{},[902,68490,68491],{"encoding":904},"P = MC",[883,68493,68495],{"className":68494},[886],[888,68496,68497],{"xmlns":890,"display":28306},[892,68498,68499,68524],{},[895,68500,68501,68503,68505,68507,68513,68515,68517,68519,68521],{},[898,68502,1727],{},[1688,68504,1690],{},[1793,68506,68451],{},[1850,68508,68509,68511],{},[898,68510,1872],{},[1793,68512,1806],{},[1688,68514,1954],{},[1793,68516,2616],{},[898,68518,1872],{},[1688,68520,1696],{},[1793,68522,68523],{},"15.",[902,68525,68526],{"encoding":904},"P = 0{,}3Q^2 - 4Q + 15.",[724,68528,68529,68530,5638,68543,68556],{},"Vyjádření ",[883,68531,68533],{"className":68532},[886],[888,68534,68535],{"xmlns":890},[892,68536,68537,68541],{},[895,68538,68539],{},[898,68540,1872],{},[902,68542,1872],{"encoding":904},[883,68544,68546],{"className":68545},[886],[888,68547,68548],{"xmlns":890},[892,68549,68550,68554],{},[895,68551,68552],{},[898,68553,1727],{},[902,68555,1727],{"encoding":904}," doplněním na čtverec:",[883,68558,68560],{"className":68559},[886],[888,68561,68562],{"xmlns":890,"display":28306},[892,68563,68564,68654],{},[895,68565,68566,68568,68570,68572,68610,68612,68614,68636,68638,68652],{},[898,68567,1727],{},[1688,68569,1690],{},[1793,68571,68451],{},[895,68573,68574,68576,68598,68600,68608],{},[1688,68575,2066],{"fence":1732},[1850,68577,68578,68596],{},[895,68579,68580,68582,68584,68586,68594],{},[1688,68581,2066],{"fence":1732},[898,68583,1872],{},[1688,68585,1954],{},[1777,68587,68588],{"scriptlevel":1779,"displaystyle":2065},[1781,68589,68590,68592],{},[1793,68591,9290],{},[1793,68593,2131],{},[1688,68595,2076],{"fence":1732},[1793,68597,1806],{},[1688,68599,1696],{},[1777,68601,68602],{"scriptlevel":1779,"displaystyle":2065},[1781,68603,68604,68606],{},[1793,68605,3377],{},[1793,68607,4256],{},[1688,68609,2076],{"fence":1732},[1688,68611,1733],{"separator":1732},[6134,68613],{"width":6136},[1850,68615,68616,68634],{},[895,68617,68618,68620,68622,68624,68632],{},[1688,68619,2066],{"fence":1732},[898,68621,1872],{},[1688,68623,1954],{},[1777,68625,68626],{"scriptlevel":1779,"displaystyle":2065},[1781,68627,68628,68630],{},[1793,68629,9290],{},[1793,68631,2131],{},[1688,68633,2076],{"fence":1732},[1793,68635,1806],{},[1688,68637,1690],{},[1781,68639,68640,68650],{},[895,68641,68642,68644,68646,68648],{},[1793,68643,38259],{},[898,68645,1727],{},[1688,68647,1954],{},[1793,68649,3377],{},[1793,68651,4256],{},[1688,68653,1733],{"separator":1732},[902,68655,68656],{"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},",[883,68658,68660],{"className":68659},[886],[888,68661,68662],{"xmlns":890,"display":28306},[892,68663,68664,68696],{},[895,68665,68666,68668,68670,68676,68678,68694],{},[898,68667,1872],{},[1688,68669,1690],{},[1781,68671,68672,68674],{},[1793,68673,9290],{},[1793,68675,2131],{},[1688,68677,1696],{},[1781,68679,68680,68692],{},[8373,68681,68682],{},[895,68683,68684,68686,68688,68690],{},[1793,68685,38259],{},[898,68687,1727],{},[1688,68689,1954],{},[1793,68691,3377],{},[1793,68693,2131],{},[898,68695,2263],{"mathvariant":1822},[902,68697,68698],{"encoding":904},"Q = \\frac{20}{3} + \\frac{\\sqrt{30P - 50}}{3}.",[724,68700,67258,68701,1343,68739,1343,68787,68821,68822,2263],{},[883,68702,68704],{"className":68703},[886],[888,68705,68706],{"xmlns":890},[892,68707,68708,68736],{},[895,68709,68710,68712,68714,68716,68718,68720,68726,68728,68730,68732,68734],{},[898,68711,4512],{},[898,68713,40579],{},[898,68715,1693],{},[1688,68717,1690],{},[1793,68719,3053],{},[1850,68721,68722,68724],{},[898,68723,1872],{},[1793,68725,1806],{},[1688,68727,1954],{},[1793,68729,1806],{},[898,68731,1872],{},[1688,68733,1696],{},[1793,68735,36484],{},[902,68737,68738],{"encoding":904},"AVC = 0{,}1Q^2 - 2Q + 15",[883,68740,68742],{"className":68741},[886],[888,68743,68744],{"xmlns":890},[892,68745,68746,68784],{},[895,68747,68748,68750,68752,68758,68760,68762,68764,68766,68768,68770,68772,68774,68780,68782],{},[898,68749,4512],{},[898,68751,40579],{},[1850,68753,68754,68756],{},[898,68755,1693],{},[1688,68757,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,68759,1690],{},[1793,68761,3097],{},[898,68763,1872],{},[1688,68765,1954],{},[1793,68767,1806],{},[1688,68769,1690],{},[1793,68771,1779],{},[1688,68773,4244],{},[1850,68775,68776,68778],{},[898,68777,1872],{},[1688,68779,1857],{},[1688,68781,1690],{},[1793,68783,3121],{},[902,68785,68786],{"encoding":904},"AVC' = 0{,}2Q - 2 = 0 \\Rightarrow Q^* = 10",[883,68788,68790],{"className":68789},[886],[888,68791,68792],{"xmlns":890},[892,68793,68794,68818],{},[895,68795,68796,68798,68800,68810,68812,68814,68816],{},[898,68797,4512],{},[898,68799,40579],{},[1850,68801,68802,68804],{},[898,68803,1693],{},[895,68805,68806,68808],{},[1688,68807,1824],{"mathvariant":1822},[1688,68809,1824],{"mathvariant":1822},[1688,68811,1690],{},[1793,68813,3097],{},[1688,68815,3665],{},[1793,68817,1779],{},[902,68819,68820],{"encoding":904},"AVC'' = 0{,}2 > 0"," (minimum). Minimální cena nabídky ",[883,68823,68825],{"className":68824},[886],[888,68826,68827],{"xmlns":890},[892,68828,68829,68865],{},[895,68830,68831,68837,68839,68841,68843,68845,68847,68849,68851,68853,68855,68857,68859,68861,68863],{},[1850,68832,68833,68835],{},[898,68834,1727],{},[1688,68836,1857],{},[1688,68838,1690],{},[898,68840,1661],{},[898,68842,1693],{},[1688,68844,2066],{"stretchy":2065},[1793,68846,3121],{},[1688,68848,2076],{"stretchy":2065},[1688,68850,1690],{},[1793,68852,38259],{},[1688,68854,1954],{},[1793,68856,5467],{},[1688,68858,1696],{},[1793,68860,36484],{},[1688,68862,1690],{},[1793,68864,2501],{},[902,68866,68867],{"encoding":904},"P^* = MC(10) = 30 - 40 + 15 = 5",[724,68869,68870],{},[38,68871,68872],{},"Závěr.",[883,68874,68876],{"className":68875},[886],[888,68877,68878],{"xmlns":890,"display":28306},[892,68879,68880,68966],{},[895,68881,68882,68884,68886,68888,68890,68892,68894,68896],{},[898,68883,1727],{},[1688,68885,1690],{},[898,68887,1740],{},[1688,68889,2066],{"stretchy":2065},[898,68891,1872],{},[1688,68893,2076],{"stretchy":2065},[1688,68895,1690],{},[895,68897,68898,68900],{},[1688,68899,67746],{"fence":1732},[20995,68901,68902,68944],{"rowspacing":67749,"columnalign":67750,"columnspacing":15531},[21000,68903,68904,68928],{},[21003,68905,68906],{},[1777,68907,68908],{"scriptlevel":1779,"displaystyle":2065},[895,68909,68910,68912,68918,68920,68922,68924,68926],{},[1793,68911,68451],{},[1850,68913,68914,68916],{},[898,68915,1872],{},[1793,68917,1806],{},[1688,68919,1954],{},[1793,68921,2616],{},[898,68923,1872],{},[1688,68925,1696],{},[1793,68927,36484],{},[21003,68929,68930],{},[1777,68931,68932],{"scriptlevel":1779,"displaystyle":2065},[895,68933,68934,68936,68938,68940,68942],{},[2041,68935,67777],{},[898,68937,1872],{},[1688,68939,4741],{},[1793,68941,3121],{},[1688,68943,1733],{"separator":1732},[21000,68945,68946,68952],{},[21003,68947,68948],{},[1777,68949,68950],{"scriptlevel":1779,"displaystyle":2065},[1793,68951,1779],{},[21003,68953,68954],{},[1777,68955,68956],{"scriptlevel":1779,"displaystyle":2065},[895,68957,68958,68960,68962,68964],{},[2041,68959,67777],{},[898,68961,1872],{},[1688,68963,3704],{},[1793,68965,19569],{},[902,68967,68968],{"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}",[724,68970,68971],{},[614,68972,68973,68974,68989,68990,2263],{},"Obrázek 3.15: Grafická ilustrace nabídky firmy odvozené z části křivky ",[883,68975,68977],{"className":68976},[886],[888,68978,68979],{"xmlns":890},[892,68980,68981,68987],{},[895,68982,68983,68985],{},[898,68984,1661],{},[898,68986,1693],{},[902,68988,55532],{"encoding":904}," ležící nad minimem ",[883,68991,68993],{"className":68992},[886],[888,68994,68995],{"xmlns":890},[892,68996,68997,69005],{},[895,68998,68999,69001,69003],{},[898,69000,4512],{},[898,69002,40579],{},[898,69004,1693],{},[902,69006,55551],{"encoding":904},[115,69008,69010],{"id":69009},"shrnutí-kapitoly-3","Shrnutí kapitoly 3",[724,69012,69013,69014,69018,69019,69034,69035,69055,69056,4142,69059,69062,69063,69065,69066,20186,69088,69090,69091,4142,69093,58966,69096,2170,69099,42054,69114,69129],{},"Celkový příjem je součin ceny a množství, kde cena je dána funkcí ",[207,69015,69017],{"className":69016,"dataFsResolvedFilePath":800,"href":801},[210],"poptávky",". Pro lineární poptávku je ",[883,69020,69022],{"className":69021},[886],[888,69023,69024],{"xmlns":890},[892,69025,69026,69032],{},[895,69027,69028,69030],{},[898,69029,3035],{},[898,69031,4251],{},[902,69033,4351],{"encoding":904}," kvadratická. Průměrný příjem je podíl ",[883,69036,69038],{"className":69037},[886],[888,69039,69040],{"xmlns":890},[892,69041,69042,69052],{},[895,69043,69044,69046,69048,69050],{},[898,69045,3035],{},[898,69047,4251],{},[898,69049,4930],{"mathvariant":1822},[898,69051,1872],{},[902,69053,69054],{"encoding":904},"TR\u002FQ"," a rovná se poptávkové funkci. Celkové náklady se skládají z ",[38,69057,69058],{},"fixních",[38,69060,69061],{},"celkových variabilních"," nákladů. Průměrné veličiny jsou jejich podíly s množstvím. ",[38,69064,64565],{}," identifikují, kdy se firma nachází na prahu rentability. Rozdíl ",[883,69067,69069],{"className":69068},[886],[888,69070,69071],{"xmlns":890},[892,69072,69073,69085],{},[895,69074,69075,69077,69079,69081,69083],{},[898,69076,3035],{},[898,69078,4251],{},[1688,69080,1954],{},[898,69082,3035],{},[898,69084,1693],{},[902,69086,69087],{"encoding":904},"TR - TC",[38,69089,55412],{},"; klíčový je výpočet produkce, která zisk maximalizuje. ",[38,69092,56724],{},[38,69094,69095],{},"mezní náklady",[207,69097,1145],{"className":69098,"dataFsResolvedFilePath":764,"href":765},[210],[883,69100,69102],{"className":69101},[886],[888,69103,69104],{"xmlns":890},[892,69105,69106,69112],{},[895,69107,69108,69110],{},[898,69109,3035],{},[898,69111,4251],{},[902,69113,4351],{"encoding":904},[883,69115,69117],{"className":69116},[886],[888,69118,69119],{"xmlns":890},[892,69120,69121,69127],{},[895,69122,69123,69125],{},[898,69124,3035],{},[898,69126,1693],{},[902,69128,3500],{"encoding":904}," podle produkce; udávají rychlosti změn, resp. přibližné změny odpovídající jednotkové změně produkce.",[120,69131,69132,69194,69260,69322],{},[123,69133,69134,69137,69138,10646,69153,2263],{},[38,69135,69136],{},"Princip minimalizace průměrných nákladů:"," v bodě minima ",[883,69139,69141],{"className":69140},[886],[888,69142,69143],{"xmlns":890},[892,69144,69145,69151],{},[895,69146,69147,69149],{},[898,69148,4512],{},[898,69150,1693],{},[902,69152,55800],{"encoding":904},[883,69154,69156],{"className":69155},[886],[888,69157,69158],{"xmlns":890},[892,69159,69160,69192],{},[895,69161,69162,69164,69166,69168,69174,69176,69178,69180,69182,69184,69190],{},[898,69163,4512],{},[898,69165,1693],{},[1688,69167,2066],{"stretchy":2065},[1788,69169,69170,69172],{},[898,69171,1872],{},[1793,69173,1779],{},[1688,69175,2076],{"stretchy":2065},[1688,69177,1690],{},[898,69179,1661],{},[898,69181,1693],{},[1688,69183,2066],{"stretchy":2065},[1788,69185,69186,69188],{},[898,69187,1872],{},[1793,69189,1779],{},[1688,69191,2076],{"stretchy":2065},[902,69193,62809],{"encoding":904},[123,69195,69196,69137,69199,10646,69216,2263],{},[38,69197,69198],{},"Princip minimalizace průměrných variabilních nákladů:",[883,69200,69202],{"className":69201},[886],[888,69203,69204],{"xmlns":890},[892,69205,69206,69214],{},[895,69207,69208,69210,69212],{},[898,69209,4512],{},[898,69211,40579],{},[898,69213,1693],{},[902,69215,55551],{"encoding":904},[883,69217,69219],{"className":69218},[886],[888,69220,69221],{"xmlns":890},[892,69222,69223,69257],{},[895,69224,69225,69227,69229,69231,69233,69239,69241,69243,69245,69247,69249,69255],{},[898,69226,4512],{},[898,69228,40579],{},[898,69230,1693],{},[1688,69232,2066],{"stretchy":2065},[1788,69234,69235,69237],{},[898,69236,1872],{},[1793,69238,1779],{},[1688,69240,2076],{"stretchy":2065},[1688,69242,1690],{},[898,69244,1661],{},[898,69246,1693],{},[1688,69248,2066],{"stretchy":2065},[1788,69250,69251,69253],{},[898,69252,1872],{},[1793,69254,1779],{},[1688,69256,2076],{"stretchy":2065},[902,69258,69259],{"encoding":904},"AVC(Q_0) = MC(Q_0)",[123,69261,69262,69265,69266,10646,69281,2263],{},[38,69263,69264],{},"Princip maximalizace zisku:"," v bodě maxima ",[883,69267,69269],{"className":69268},[886],[888,69270,69271],{"xmlns":890},[892,69272,69273,69279],{},[895,69274,69275,69277],{},[898,69276,1727],{},[898,69278,4251],{},[902,69280,63719],{"encoding":904},[883,69282,69284],{"className":69283},[886],[888,69285,69286],{"xmlns":890},[892,69287,69288,69320],{},[895,69289,69290,69292,69294,69296,69302,69304,69306,69308,69310,69312,69318],{},[898,69291,1661],{},[898,69293,4251],{},[1688,69295,2066],{"stretchy":2065},[1788,69297,69298,69300],{},[898,69299,1872],{},[1793,69301,1779],{},[1688,69303,2076],{"stretchy":2065},[1688,69305,1690],{},[898,69307,1661],{},[898,69309,1693],{},[1688,69311,2066],{"stretchy":2065},[1788,69313,69314,69316],{},[898,69315,1872],{},[1793,69317,1779],{},[1688,69319,2076],{"stretchy":2065},[902,69321,65885],{"encoding":904},[123,69323,69324,2170,69327,6729,69363,68165,69384,21835,69397,67847,69414,2263],{},[38,69325,69326],{},"Funkce nabídky firmy:",[883,69328,69330],{"className":69329},[886],[888,69331,69332],{"xmlns":890},[892,69333,69334,69360],{},[895,69335,69336,69338,69340,69342,69344,69346,69348,69350,69352,69354,69356,69358],{},[898,69337,1727],{},[1688,69339,1690],{},[898,69341,1740],{},[1688,69343,2066],{"stretchy":2065},[898,69345,1872],{},[1688,69347,2076],{"stretchy":2065},[1688,69349,1690],{},[898,69351,1661],{},[898,69353,1693],{},[1688,69355,2066],{"stretchy":2065},[898,69357,1872],{},[1688,69359,2076],{"stretchy":2065},[902,69361,69362],{"encoding":904},"P = S(Q) = MC(Q)",[883,69364,69366],{"className":69365},[886],[888,69367,69368],{"xmlns":890},[892,69369,69370,69382],{},[895,69371,69372,69374,69376],{},[898,69373,1872],{},[1688,69375,4741],{},[1850,69377,69378,69380],{},[898,69379,1872],{},[1688,69381,1857],{},[902,69383,68164],{"encoding":904},[883,69385,69387],{"className":69386},[886],[888,69388,69389],{"xmlns":890},[892,69390,69391,69395],{},[895,69392,69393],{},[1793,69394,1779],{},[902,69396,1779],{"encoding":904},[883,69398,69400],{"className":69399},[886],[888,69401,69402],{"xmlns":890},[892,69403,69404,69412],{},[895,69405,69406],{},[1850,69407,69408,69410],{},[898,69409,1872],{},[1688,69411,1857],{},[902,69413,30084],{"encoding":904},[883,69415,69417],{"className":69416},[886],[888,69418,69419],{"xmlns":890},[892,69420,69421,69429],{},[895,69422,69423,69425,69427],{},[898,69424,4512],{},[898,69426,40579],{},[898,69428,1693],{},[902,69430,55551],{"encoding":904},[115,69432,50122],{"id":50121},[152,69434,69435,69438,69441,69444,69447,69450,69453,69456,69459,69462,69465],{},[123,69436,69437],{},"Jaký je vztah pro celkový příjem v podmínkách dokonalé konkurence?",[123,69439,69440],{},"Jaký tvar má křivka celkového příjmu pro lineární poptávku?",[123,69442,69443],{},"Jak se vypočte mezní příjem a co udává?",[123,69445,69446],{},"Z jakých složek se skládají celkové náklady?",[123,69448,69449],{},"Jak se stanoví celkové náklady, známe-li náklady mezní?",[123,69451,69452],{},"Jaký je trend průměrných fixních nákladů a průměrných nákladů, roste-li produkce?",[123,69454,69455],{},"Jak se stanoví přibližně změna celkových nákladů?",[123,69457,69458],{},"Jak se vypočte zisk?",[123,69460,69461],{},"Jaká vlastnost platí v bodě maxima zisku?",[123,69463,69464],{},"Co jsou body zvratu? Jak se najdou?",[123,69466,69467],{},"Z jakých nákladových charakteristik se vychází při konstrukci nabídky?",[115,69469,69471],{"id":69470},"úlohy-31328","Úlohy 3.1–3.28",[198,69473,69475],{"id":69474},"příjem-3135","Příjem (3.1–3.5)",[724,69477,69478,45666,69481,69509,69510,69525,69526,69541,69542,69557,69558,1343,69573,1343,69588,69603],{},[38,69479,69480],{},"3.1",[883,69482,69484],{"className":69483},[886],[888,69485,69486],{"xmlns":890},[892,69487,69488,69506],{},[895,69489,69490,69492,69494,69496,69498,69500,69502,69504],{},[898,69491,1727],{},[1688,69493,1690],{},[898,69495,4440],{},[1688,69497,2066],{"stretchy":2065},[898,69499,1872],{},[1688,69501,2076],{"stretchy":2065},[1688,69503,1690],{},[1793,69505,3347],{},[902,69507,69508],{"encoding":904},"P = D(Q) = 100",". (a) Rozhodněte, v jakých podmínkách konkurence zadaná poptávka platí. (b) Najděte celkový příjem ",[883,69511,69513],{"className":69512},[886],[888,69514,69515],{"xmlns":890},[892,69516,69517,69523],{},[895,69518,69519,69521],{},[898,69520,3035],{},[898,69522,4251],{},[902,69524,4351],{"encoding":904},", průměrný příjem ",[883,69527,69529],{"className":69528},[886],[888,69530,69531],{"xmlns":890},[892,69532,69533,69539],{},[895,69534,69535,69537],{},[898,69536,4512],{},[898,69538,4251],{},[902,69540,55685],{"encoding":904}," a mezní příjem ",[883,69543,69545],{"className":69544},[886],[888,69546,69547],{"xmlns":890},[892,69548,69549,69555],{},[895,69550,69551,69553],{},[898,69552,1661],{},[898,69554,4251],{},[902,69556,6890],{"encoding":904},". (c) Vypočtěte ",[883,69559,69561],{"className":69560},[886],[888,69562,69563],{"xmlns":890},[892,69564,69565,69571],{},[895,69566,69567,69569],{},[898,69568,3035],{},[898,69570,4251],{},[902,69572,4351],{"encoding":904},[883,69574,69576],{"className":69575},[886],[888,69577,69578],{"xmlns":890},[892,69579,69580,69586],{},[895,69581,69582,69584],{},[898,69583,4512],{},[898,69585,4251],{},[902,69587,55685],{"encoding":904},[883,69589,69591],{"className":69590},[886],[888,69592,69593],{"xmlns":890},[892,69594,69595,69601],{},[895,69596,69597,69599],{},[898,69598,1661],{},[898,69600,4251],{},[902,69602,6890],{"encoding":904}," při množství 20. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,69605,69606,45666,69609,69509,69645,69525,69660,69541,69675,69557,69690,1343,69705,1343,69720,69735],{},[38,69607,69608],{},"3.2",[883,69610,69612],{"className":69611},[886],[888,69613,69614],{"xmlns":890},[892,69615,69616,69642],{},[895,69617,69618,69620,69622,69624,69626,69628,69630,69632,69634,69636,69638,69640],{},[898,69619,1727],{},[1688,69621,1690],{},[898,69623,4440],{},[1688,69625,2066],{"stretchy":2065},[898,69627,1872],{},[1688,69629,2076],{"stretchy":2065},[1688,69631,1690],{},[1688,69633,1954],{},[1793,69635,5265],{},[898,69637,1872],{},[1688,69639,1696],{},[1793,69641,9290],{},[902,69643,69644],{"encoding":904},"P = D(Q) = -0{,}5Q + 20",[883,69646,69648],{"className":69647},[886],[888,69649,69650],{"xmlns":890},[892,69651,69652,69658],{},[895,69653,69654,69656],{},[898,69655,3035],{},[898,69657,4251],{},[902,69659,4351],{"encoding":904},[883,69661,69663],{"className":69662},[886],[888,69664,69665],{"xmlns":890},[892,69666,69667,69673],{},[895,69668,69669,69671],{},[898,69670,4512],{},[898,69672,4251],{},[902,69674,55685],{"encoding":904},[883,69676,69678],{"className":69677},[886],[888,69679,69680],{"xmlns":890},[892,69681,69682,69688],{},[895,69683,69684,69686],{},[898,69685,1661],{},[898,69687,4251],{},[902,69689,6890],{"encoding":904},[883,69691,69693],{"className":69692},[886],[888,69694,69695],{"xmlns":890},[892,69696,69697,69703],{},[895,69698,69699,69701],{},[898,69700,3035],{},[898,69702,4251],{},[902,69704,4351],{"encoding":904},[883,69706,69708],{"className":69707},[886],[888,69709,69710],{"xmlns":890},[892,69711,69712,69718],{},[895,69713,69714,69716],{},[898,69715,4512],{},[898,69717,4251],{},[902,69719,55685],{"encoding":904},[883,69721,69723],{"className":69722},[886],[888,69724,69725],{"xmlns":890},[892,69726,69727,69733],{},[895,69728,69729,69731],{},[898,69730,1661],{},[898,69732,4251],{},[902,69734,6890],{"encoding":904}," při množství 10. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,69737,69738,45666,69741,69778,69779,69525,69794,69541,69809,69824,69825,6729,69840,69866,69867,69882,69883,1343,69898,6729,69913,69866,69938,69953,69954,69967,69968,69983,69984,69999,70000,1343,70013,1343,70028,1343,70043,2263],{},[38,69739,69740],{},"3.3",[883,69742,69744],{"className":69743},[886],[888,69745,69746],{"xmlns":890},[892,69747,69748,69775],{},[895,69749,69750,69752,69754,69756,69758,69760,69762,69764,69767,69769],{},[898,69751,1727],{},[1688,69753,1690],{},[898,69755,4440],{},[1688,69757,2066],{"stretchy":2065},[898,69759,1872],{},[1688,69761,2076],{"stretchy":2065},[1688,69763,1690],{},[1793,69765,69766],{},"1200",[1688,69768,1954],{},[1850,69770,69771,69773],{},[898,69772,1872],{},[1793,69774,1806],{},[902,69776,69777],{"encoding":904},"P = D(Q) = 1200 - Q^2",". (a) Najděte celkový příjem ",[883,69780,69782],{"className":69781},[886],[888,69783,69784],{"xmlns":890},[892,69785,69786,69792],{},[895,69787,69788,69790],{},[898,69789,3035],{},[898,69791,4251],{},[902,69793,4351],{"encoding":904},[883,69795,69797],{"className":69796},[886],[888,69798,69799],{"xmlns":890},[892,69800,69801,69807],{},[895,69802,69803,69805],{},[898,69804,4512],{},[898,69806,4251],{},[902,69808,55685],{"encoding":904},[883,69810,69812],{"className":69811},[886],[888,69813,69814],{"xmlns":890},[892,69815,69816,69822],{},[895,69817,69818,69820],{},[898,69819,1661],{},[898,69821,4251],{},[902,69823,6890],{"encoding":904},". (b) Vypočtěte ",[883,69826,69828],{"className":69827},[886],[888,69829,69830],{"xmlns":890},[892,69831,69832,69838],{},[895,69833,69834,69836],{},[898,69835,3035],{},[898,69837,4251],{},[902,69839,4351],{"encoding":904},[883,69841,69843],{"className":69842},[886],[888,69844,69845],{"xmlns":890},[892,69846,69847,69863],{},[895,69848,69849,69851,69853,69855,69857,69859,69861],{},[898,69850,1872],{},[1688,69852,1690],{},[1793,69854,3121],{},[1688,69856,1733],{"separator":1732},[1793,69858,9290],{},[1688,69860,1733],{"separator":1732},[1793,69862,38259],{},[902,69864,69865],{"encoding":904},"Q = 10, 20, 30"," a rozhodněte, kdy ",[883,69868,69870],{"className":69869},[886],[888,69871,69872],{"xmlns":890},[892,69873,69874,69880],{},[895,69875,69876,69878],{},[898,69877,3035],{},[898,69879,4251],{},[902,69881,4351],{"encoding":904}," roste, resp. klesá. (c) Vypočtěte ",[883,69884,69886],{"className":69885},[886],[888,69887,69888],{"xmlns":890},[892,69889,69890,69896],{},[895,69891,69892,69894],{},[898,69893,4512],{},[898,69895,4251],{},[902,69897,55685],{"encoding":904},[883,69899,69901],{"className":69900},[886],[888,69902,69903],{"xmlns":890},[892,69904,69905,69911],{},[895,69906,69907,69909],{},[898,69908,1661],{},[898,69910,4251],{},[902,69912,6890],{"encoding":904},[883,69914,69916],{"className":69915},[886],[888,69917,69918],{"xmlns":890},[892,69919,69920,69936],{},[895,69921,69922,69924,69926,69928,69930,69932,69934],{},[898,69923,1872],{},[1688,69925,1690],{},[1793,69927,3121],{},[1688,69929,1733],{"separator":1732},[1793,69931,9290],{},[1688,69933,1733],{"separator":1732},[1793,69935,38259],{},[902,69937,69865],{"encoding":904},[883,69939,69941],{"className":69940},[886],[888,69942,69943],{"xmlns":890},[892,69944,69945,69951],{},[895,69946,69947,69949],{},[898,69948,1661],{},[898,69950,4251],{},[902,69952,6890],{"encoding":904}," roste, resp. klesá. (d) Vypočtěte ",[883,69955,69957],{"className":69956},[886],[888,69958,69959],{"xmlns":890},[892,69960,69961,69965],{},[895,69962,69963],{},[898,69964,1872],{},[902,69966,1872],{"encoding":904},", které maximalizuje ",[883,69969,69971],{"className":69970},[886],[888,69972,69973],{"xmlns":890},[892,69974,69975,69981],{},[895,69976,69977,69979],{},[898,69978,3035],{},[898,69980,4251],{},[902,69982,4351],{"encoding":904}," a stanovte příslušnou hodnotu maxima ",[883,69985,69987],{"className":69986},[886],[888,69988,69989],{"xmlns":890},[892,69990,69991,69997],{},[895,69992,69993,69995],{},[898,69994,3035],{},[898,69996,4251],{},[902,69998,4351],{"encoding":904},". (e) Určete (je užitečné vyšetřit i jejich průběhy). (f) Charakterizujte geometricky křivky ",[883,70001,70003],{"className":70002},[886],[888,70004,70005],{"xmlns":890},[892,70006,70007,70011],{},[895,70008,70009],{},[898,70010,4440],{},[902,70012,4440],{"encoding":904},[883,70014,70016],{"className":70015},[886],[888,70017,70018],{"xmlns":890},[892,70019,70020,70026],{},[895,70021,70022,70024],{},[898,70023,3035],{},[898,70025,4251],{},[902,70027,4351],{"encoding":904},[883,70029,70031],{"className":70030},[886],[888,70032,70033],{"xmlns":890},[892,70034,70035,70041],{},[895,70036,70037,70039],{},[898,70038,4512],{},[898,70040,4251],{},[902,70042,55685],{"encoding":904},[883,70044,70046],{"className":70045},[886],[888,70047,70048],{"xmlns":890},[892,70049,70050,70056],{},[895,70051,70052,70054],{},[898,70053,1661],{},[898,70055,4251],{},[902,70057,6890],{"encoding":904},[724,70059,70060,70063,70064,70094,70095,70110,70111,10409,70124,1343,70142,1343,70159,70177,70178,70200,70201,70216,70217,70230,70231,2263],{},[38,70061,70062],{},"3.4"," Je dán celkový příjem ",[883,70065,70067],{"className":70066},[886],[888,70068,70069],{"xmlns":890},[892,70070,70071,70091],{},[895,70072,70073,70075,70077,70079,70081,70083,70085],{},[898,70074,3035],{},[898,70076,4251],{},[1688,70078,1690],{},[1793,70080,69766],{},[898,70082,1872],{},[1688,70084,1954],{},[1850,70086,70087,70089],{},[898,70088,1872],{},[1793,70090,2131],{},[902,70092,70093],{"encoding":904},"TR = 1200Q - Q^3",". (a) Určete, jak rychle se (přibližně) mění ",[883,70096,70098],{"className":70097},[886],[888,70099,70100],{"xmlns":890},[892,70101,70102,70108],{},[895,70103,70104,70106],{},[898,70105,3035],{},[898,70107,4251],{},[902,70109,4351],{"encoding":904}," vzhledem ke ",[883,70112,70114],{"className":70113},[886],[888,70115,70116],{"xmlns":890},[892,70117,70118,70122],{},[895,70119,70120],{},[898,70121,1872],{},[902,70123,1872],{"encoding":904},[883,70125,70127],{"className":70126},[886],[888,70128,70129],{"xmlns":890},[892,70130,70131,70139],{},[895,70132,70133,70135,70137],{},[898,70134,1872],{},[1688,70136,1690],{},[1793,70138,2501],{},[902,70140,70141],{"encoding":904},"Q = 5",[883,70143,70145],{"className":70144},[886],[888,70146,70147],{"xmlns":890},[892,70148,70149,70157],{},[895,70150,70151,70153,70155],{},[898,70152,1872],{},[1688,70154,1690],{},[1793,70156,5841],{},[902,70158,5844],{"encoding":904},[883,70160,70162],{"className":70161},[886],[888,70163,70164],{"xmlns":890},[892,70165,70166,70174],{},[895,70167,70168,70170,70172],{},[898,70169,1872],{},[1688,70171,1690],{},[1793,70173,3766],{},[902,70175,70176],{"encoding":904},"Q = 12"," a charakterizujte dynamiku změn. (b) Vypočtěte a ekonomicky interpretujte ",[883,70179,70181],{"className":70180},[886],[888,70182,70183],{"xmlns":890},[892,70184,70185,70197],{},[895,70186,70187,70189,70191,70193,70195],{},[898,70188,1661],{},[898,70190,4251],{},[1688,70192,2066],{"stretchy":2065},[1793,70194,3121],{},[1688,70196,2076],{"stretchy":2065},[902,70198,70199],{"encoding":904},"MR(10)",". (c) Odhadněte, o kolik se přibližně změní ",[883,70202,70204],{"className":70203},[886],[888,70205,70206],{"xmlns":890},[892,70207,70208,70214],{},[895,70209,70210,70212],{},[898,70211,3035],{},[898,70213,4251],{},[902,70215,4351],{"encoding":904},", jestliže se ",[883,70218,70220],{"className":70219},[886],[888,70221,70222],{"xmlns":890},[892,70223,70224,70228],{},[895,70225,70226],{},[898,70227,1872],{},[902,70229,1872],{"encoding":904}," změní z 10 na 12 a porovnejte se skutečnou změnou ",[883,70232,70234],{"className":70233},[886],[888,70235,70236],{"xmlns":890},[892,70237,70238,70244],{},[895,70239,70240,70242],{},[898,70241,3035],{},[898,70243,4251],{},[902,70245,4351],{"encoding":904},[724,70247,70248,70251,70252,70278,70279,70294,70295,70216,70310,70323],{},[38,70249,70250],{},"3.5"," Je dán mezní příjem ",[883,70253,70255],{"className":70254},[886],[888,70256,70257],{"xmlns":890},[892,70258,70259,70275],{},[895,70260,70261,70263,70265,70267,70269,70271,70273],{},[898,70262,1661],{},[898,70264,4251],{},[1688,70266,1690],{},[1688,70268,1954],{},[898,70270,1872],{},[1688,70272,1696],{},[1793,70274,9290],{},[902,70276,70277],{"encoding":904},"MR = -Q + 20",". (a) Určete celkový příjem ",[883,70280,70282],{"className":70281},[886],[888,70283,70284],{"xmlns":890},[892,70285,70286,70292],{},[895,70287,70288,70290],{},[898,70289,3035],{},[898,70291,4251],{},[902,70293,4351],{"encoding":904},". (b) Vypočtěte změnu ",[883,70296,70298],{"className":70297},[886],[888,70299,70300],{"xmlns":890},[892,70301,70302,70308],{},[895,70303,70304,70306],{},[898,70305,3035],{},[898,70307,4251],{},[902,70309,4351],{"encoding":904},[883,70311,70313],{"className":70312},[886],[888,70314,70315],{"xmlns":890},[892,70316,70317,70321],{},[895,70318,70319],{},[898,70320,1872],{},[902,70322,1872],{"encoding":904}," změní z 8 na 12.",[198,70325,70327],{"id":70326},"náklady-36316","Náklady (3.6–3.16)",[724,70329,70330,70333,70334,70374,70375,70390,70391,70408,70409,70426,70427,70442,70443,70458,70459,69824,70474,1343,70489,1343,70506,1343,70523,1343,70538,1343,70553,6729,70568,70586,70587,1343,70602,1343,70617,70632],{},[38,70331,70332],{},"3.6"," Jsou dány celkové náklady ",[883,70335,70337],{"className":70336},[886],[888,70338,70339],{"xmlns":890},[892,70340,70341,70371],{},[895,70342,70343,70345,70347,70349,70351,70353,70355,70357,70359],{},[898,70344,3035],{},[898,70346,1693],{},[1688,70348,1690],{},[1793,70350,3347],{},[1688,70352,1696],{},[1793,70354,1806],{},[898,70356,1872],{},[1688,70358,1696],{},[1777,70360,70361],{"scriptlevel":1779,"displaystyle":2065},[1781,70362,70363,70369],{},[1850,70364,70365,70367],{},[898,70366,1872],{},[1793,70368,1806],{},[1793,70370,3121],{},[902,70372,70373],{"encoding":904},"TC = 100 + 2Q + \\tfrac{Q^2}{10}",". (a) Určete fixní náklady ",[883,70376,70378],{"className":70377},[886],[888,70379,70380],{"xmlns":890},[892,70381,70382,70388],{},[895,70383,70384,70386],{},[898,70385,10688],{},[898,70387,1693],{},[902,70389,55731],{"encoding":904},", celkové variabilní náklady ",[883,70392,70394],{"className":70393},[886],[888,70395,70396],{"xmlns":890},[892,70397,70398,70406],{},[895,70399,70400,70402,70404],{},[898,70401,3035],{},[898,70403,40579],{},[898,70405,1693],{},[902,70407,55749],{"encoding":904},", průměrné variabilní náklady ",[883,70410,70412],{"className":70411},[886],[888,70413,70414],{"xmlns":890},[892,70415,70416,70424],{},[895,70417,70418,70420,70422],{},[898,70419,4512],{},[898,70421,40579],{},[898,70423,1693],{},[902,70425,55551],{"encoding":904},", variabilní náklady na jednotku ",[883,70428,70430],{"className":70429},[886],[888,70431,70432],{"xmlns":890},[892,70433,70434,70440],{},[895,70435,70436,70438],{},[898,70437,40579],{},[898,70439,1693],{},[902,70441,63845],{"encoding":904},", průměrné náklady ",[883,70444,70446],{"className":70445},[886],[888,70447,70448],{"xmlns":890},[892,70449,70450,70456],{},[895,70451,70452,70454],{},[898,70453,4512],{},[898,70455,1693],{},[902,70457,55800],{"encoding":904}," a mezní náklady ",[883,70460,70462],{"className":70461},[886],[888,70463,70464],{"xmlns":890},[892,70465,70466,70472],{},[895,70467,70468,70470],{},[898,70469,1661],{},[898,70471,1693],{},[902,70473,55532],{"encoding":904},[883,70475,70477],{"className":70476},[886],[888,70478,70479],{"xmlns":890},[892,70480,70481,70487],{},[895,70482,70483,70485],{},[898,70484,3035],{},[898,70486,1693],{},[902,70488,3500],{"encoding":904},[883,70490,70492],{"className":70491},[886],[888,70493,70494],{"xmlns":890},[892,70495,70496,70504],{},[895,70497,70498,70500,70502],{},[898,70499,3035],{},[898,70501,40579],{},[898,70503,1693],{},[902,70505,55749],{"encoding":904},[883,70507,70509],{"className":70508},[886],[888,70510,70511],{"xmlns":890},[892,70512,70513,70521],{},[895,70514,70515,70517,70519],{},[898,70516,4512],{},[898,70518,40579],{},[898,70520,1693],{},[902,70522,55551],{"encoding":904},[883,70524,70526],{"className":70525},[886],[888,70527,70528],{"xmlns":890},[892,70529,70530,70536],{},[895,70531,70532,70534],{},[898,70533,40579],{},[898,70535,1693],{},[902,70537,63845],{"encoding":904},[883,70539,70541],{"className":70540},[886],[888,70542,70543],{"xmlns":890},[892,70544,70545,70551],{},[895,70546,70547,70549],{},[898,70548,4512],{},[898,70550,1693],{},[902,70552,55800],{"encoding":904},[883,70554,70556],{"className":70555},[886],[888,70557,70558],{"xmlns":890},[892,70559,70560,70566],{},[895,70561,70562,70564],{},[898,70563,1661],{},[898,70565,1693],{},[902,70567,55532],{"encoding":904},[883,70569,70571],{"className":70570},[886],[888,70572,70573],{"xmlns":890},[892,70574,70575,70583],{},[895,70576,70577,70579,70581],{},[898,70578,1872],{},[1688,70580,1690],{},[1793,70582,3377],{},[902,70584,70585],{"encoding":904},"Q = 50",". (c) Rozhodněte, kdy ",[883,70588,70590],{"className":70589},[886],[888,70591,70592],{"xmlns":890},[892,70593,70594,70600],{},[895,70595,70596,70598],{},[898,70597,3035],{},[898,70599,1693],{},[902,70601,3500],{"encoding":904},[883,70603,70605],{"className":70604},[886],[888,70606,70607],{"xmlns":890},[892,70608,70609,70615],{},[895,70610,70611,70613],{},[898,70612,4512],{},[898,70614,1693],{},[902,70616,55800],{"encoding":904},[883,70618,70620],{"className":70619},[886],[888,70621,70622],{"xmlns":890},[892,70623,70624,70630],{},[895,70625,70626,70628],{},[898,70627,1661],{},[898,70629,1693],{},[902,70631,55532],{"encoding":904}," rostou, resp. klesají.",[724,70634,70635,70638,70639,70458,70669,70684,70685,70700,70701,1343,70716,1343,70731,2263],{},[38,70636,70637],{},"3.7"," Jsou dány průměrné náklady ",[883,70640,70642],{"className":70641},[886],[888,70643,70644],{"xmlns":890},[892,70645,70646,70666],{},[895,70647,70648,70650,70652,70654,70662,70664],{},[898,70649,4512],{},[898,70651,1693],{},[1688,70653,1690],{},[1777,70655,70656],{"scriptlevel":1779,"displaystyle":2065},[1781,70657,70658,70660],{},[1793,70659,3347],{},[898,70661,1872],{},[1688,70663,1696],{},[1793,70665,9290],{},[902,70667,70668],{"encoding":904},"AC = \\tfrac{100}{Q} + 20",[883,70670,70672],{"className":70671},[886],[888,70673,70674],{"xmlns":890},[892,70675,70676,70682],{},[895,70677,70678,70680],{},[898,70679,1661],{},[898,70681,1693],{},[902,70683,55532],{"encoding":904},". (a) Určete celkové náklady ",[883,70686,70688],{"className":70687},[886],[888,70689,70690],{"xmlns":890},[892,70691,70692,70698],{},[895,70693,70694,70696],{},[898,70695,3035],{},[898,70697,1693],{},[902,70699,3500],{"encoding":904},". (b) Načrtněte a geometricky charakterizujte křivky ",[883,70702,70704],{"className":70703},[886],[888,70705,70706],{"xmlns":890},[892,70707,70708,70714],{},[895,70709,70710,70712],{},[898,70711,4512],{},[898,70713,1693],{},[902,70715,55800],{"encoding":904},[883,70717,70719],{"className":70718},[886],[888,70720,70721],{"xmlns":890},[892,70722,70723,70729],{},[895,70724,70725,70727],{},[898,70726,3035],{},[898,70728,1693],{},[902,70730,3500],{"encoding":904},[883,70732,70734],{"className":70733},[886],[888,70735,70736],{"xmlns":890},[892,70737,70738,70744],{},[895,70739,70740,70742],{},[898,70741,1661],{},[898,70743,1693],{},[902,70745,55532],{"encoding":904},[724,70747,70748,70333,70751,70795,70796,1343,70813,1343,70828,1343,70845,1343,70860,1343,70877,2263],{},[38,70749,70750],{},"3.8",[883,70752,70754],{"className":70753},[886],[888,70755,70756],{"xmlns":890},[892,70757,70758,70792],{},[895,70759,70760,70762,70764,70766,70768,70770,70772,70774,70776,70778,70784,70786],{},[898,70761,3035],{},[898,70763,1693],{},[1688,70765,1690],{},[1793,70767,46943],{},[1688,70769,1696],{},[1793,70771,38259],{},[898,70773,1872],{},[1688,70775,1954],{},[1793,70777,2508],{},[1850,70779,70780,70782],{},[898,70781,1872],{},[1793,70783,1806],{},[1688,70785,1696],{},[1850,70787,70788,70790],{},[898,70789,1872],{},[1793,70791,2131],{},[902,70793,70794],{"encoding":904},"TC = 80 + 30Q - 6Q^2 + Q^3",". Určete ",[883,70797,70799],{"className":70798},[886],[888,70800,70801],{"xmlns":890},[892,70802,70803,70811],{},[895,70804,70805,70807,70809],{},[898,70806,3035],{},[898,70808,40579],{},[898,70810,1693],{},[902,70812,55749],{"encoding":904},[883,70814,70816],{"className":70815},[886],[888,70817,70818],{"xmlns":890},[892,70819,70820,70826],{},[895,70821,70822,70824],{},[898,70823,10688],{},[898,70825,1693],{},[902,70827,55731],{"encoding":904},[883,70829,70831],{"className":70830},[886],[888,70832,70833],{"xmlns":890},[892,70834,70835,70843],{},[895,70836,70837,70839,70841],{},[898,70838,4512],{},[898,70840,40579],{},[898,70842,1693],{},[902,70844,55551],{"encoding":904},[883,70846,70848],{"className":70847},[886],[888,70849,70850],{"xmlns":890},[892,70851,70852,70858],{},[895,70853,70854,70856],{},[898,70855,4512],{},[898,70857,1693],{},[902,70859,55800],{"encoding":904},[883,70861,70863],{"className":70862},[886],[888,70864,70865],{"xmlns":890},[892,70866,70867,70875],{},[895,70868,70869,70871,70873],{},[898,70870,4512],{},[898,70872,10688],{},[898,70874,1693],{},[902,70876,55767],{"encoding":904},[883,70878,70880],{"className":70879},[886],[888,70881,70882],{"xmlns":890},[892,70883,70884,70890],{},[895,70885,70886,70888],{},[898,70887,1661],{},[898,70889,1693],{},[902,70891,55532],{"encoding":904},[724,70893,70894,70333,70897,70927,70928,70110,70943,6729,70956,1343,70974,1343,70992,70177,71010,70200,71032,71047,71048,71061,71062,2263],{},[38,70895,70896],{},"3.9",[883,70898,70900],{"className":70899},[886],[888,70901,70902],{"xmlns":890},[892,70903,70904,70924],{},[895,70905,70906,70908,70910,70912,70914,70916,70918],{},[898,70907,3035],{},[898,70909,1693],{},[1688,70911,1690],{},[1793,70913,15357],{},[1688,70915,1696],{},[1793,70917,19562],{},[1850,70919,70920,70922],{},[898,70921,1872],{},[1793,70923,1806],{},[902,70925,70926],{"encoding":904},"TC = 500 + 0{,}6Q^2",". (a) Určete, jak rychle se přibližně mění ",[883,70929,70931],{"className":70930},[886],[888,70932,70933],{"xmlns":890},[892,70934,70935,70941],{},[895,70936,70937,70939],{},[898,70938,3035],{},[898,70940,1693],{},[902,70942,3500],{"encoding":904},[883,70944,70946],{"className":70945},[886],[888,70947,70948],{"xmlns":890},[892,70949,70950,70954],{},[895,70951,70952],{},[898,70953,1872],{},[902,70955,1872],{"encoding":904},[883,70957,70959],{"className":70958},[886],[888,70960,70961],{"xmlns":890},[892,70962,70963,70971],{},[895,70964,70965,70967,70969],{},[898,70966,1872],{},[1688,70968,1690],{},[1793,70970,3121],{},[902,70972,70973],{"encoding":904},"Q = 10",[883,70975,70977],{"className":70976},[886],[888,70978,70979],{"xmlns":890},[892,70980,70981,70989],{},[895,70982,70983,70985,70987],{},[898,70984,1872],{},[1688,70986,1690],{},[1793,70988,9290],{},[902,70990,70991],{"encoding":904},"Q = 20",[883,70993,70995],{"className":70994},[886],[888,70996,70997],{"xmlns":890},[892,70998,70999,71007],{},[895,71000,71001,71003,71005],{},[898,71002,1872],{},[1688,71004,1690],{},[1793,71006,38259],{},[902,71008,71009],{"encoding":904},"Q = 30",[883,71011,71013],{"className":71012},[886],[888,71014,71015],{"xmlns":890},[892,71016,71017,71029],{},[895,71018,71019,71021,71023,71025,71027],{},[898,71020,1661],{},[898,71022,1693],{},[1688,71024,2066],{"stretchy":2065},[1793,71026,36484],{},[1688,71028,2076],{"stretchy":2065},[902,71030,71031],{"encoding":904},"MC(15)",[883,71033,71035],{"className":71034},[886],[888,71036,71037],{"xmlns":890},[892,71038,71039,71045],{},[895,71040,71041,71043],{},[898,71042,3035],{},[898,71044,1693],{},[902,71046,3500],{"encoding":904}," v důsledku změny ",[883,71049,71051],{"className":71050},[886],[888,71052,71053],{"xmlns":890},[892,71054,71055,71059],{},[895,71056,71057],{},[898,71058,1872],{},[902,71060,1872],{"encoding":904}," z 15 na 20 a porovnejte se skutečnou změnou ",[883,71063,71065],{"className":71064},[886],[888,71066,71067],{"xmlns":890},[892,71068,71069,71075],{},[895,71070,71071,71073],{},[898,71072,3035],{},[898,71074,1693],{},[902,71076,3500],{"encoding":904},[724,71078,71079,71082,71083,70684,71119,71134,71135,70294,71154,71047,71169,71182],{},[38,71080,71081],{},"3.10"," Jsou dány mezní náklady ",[883,71084,71086],{"className":71085},[886],[888,71087,71088],{"xmlns":890},[892,71089,71090,71116],{},[895,71091,71092,71094,71096,71098,71100,71102,71104,71106,71108,71110],{},[898,71093,1661],{},[898,71095,1693],{},[1688,71097,1690],{},[1793,71099,3383],{},[1688,71101,1954],{},[1793,71103,42102],{},[898,71105,1872],{},[1688,71107,1696],{},[1793,71109,64799],{},[1850,71111,71112,71114],{},[898,71113,1872],{},[1793,71115,1806],{},[902,71117,71118],{"encoding":904},"MC = 60 - 16Q + 1{,}5Q^2",[883,71120,71122],{"className":71121},[886],[888,71123,71124],{"xmlns":890},[892,71125,71126,71132],{},[895,71127,71128,71130],{},[898,71129,3035],{},[898,71131,1693],{},[902,71133,3500],{"encoding":904},", jestliže fixní náklady ",[883,71136,71138],{"className":71137},[886],[888,71139,71140],{"xmlns":890},[892,71141,71142,71152],{},[895,71143,71144,71146,71148,71150],{},[898,71145,10688],{},[898,71147,1693],{},[1688,71149,1690],{},[1793,71151,3347],{},[902,71153,11885],{"encoding":904},[883,71155,71157],{"className":71156},[886],[888,71158,71159],{"xmlns":890},[892,71160,71161,71167],{},[895,71162,71163,71165],{},[898,71164,3035],{},[898,71166,1693],{},[902,71168,3500],{"encoding":904},[883,71170,71172],{"className":71171},[886],[888,71173,71174],{"xmlns":890},[892,71175,71176,71180],{},[895,71177,71178],{},[898,71179,1872],{},[902,71181,1872],{"encoding":904}," z 15 na 20.",[724,71184,71185,70333,71188,71231,71232,71245,71246,71261,71262,71277,71278,71245,71291,71261,71308,71325,71326,71245,71339,71261,71354,71369,71370,71390,71391,71414],{},[38,71186,71187],{},"3.11",[883,71189,71191],{"className":71190},[886],[888,71192,71193],{"xmlns":890},[892,71194,71195,71229],{},[895,71196,71197,71199,71201,71203,71205,71207,71209,71211,71213,71215,71221,71223],{},[898,71198,3035],{},[898,71200,1693],{},[1688,71202,1690],{},[1793,71204,3347],{},[1688,71206,1696],{},[1793,71208,5260],{},[898,71210,1872],{},[1688,71212,1954],{},[1793,71214,2501],{},[1850,71216,71217,71219],{},[898,71218,1872],{},[1793,71220,1806],{},[1688,71222,1696],{},[1850,71224,71225,71227],{},[898,71226,1872],{},[1793,71228,2131],{},[902,71230,61147],{"encoding":904},". (a) Určete ",[883,71233,71235],{"className":71234},[886],[888,71236,71237],{"xmlns":890},[892,71238,71239,71243],{},[895,71240,71241],{},[898,71242,1872],{},[902,71244,1872],{"encoding":904},", které minimalizuje ",[883,71247,71249],{"className":71248},[886],[888,71250,71251],{"xmlns":890},[892,71252,71253,71259],{},[895,71254,71255,71257],{},[898,71256,1661],{},[898,71258,1693],{},[902,71260,55532],{"encoding":904}," a stanovte příslušnou hodnotu minima ",[883,71263,71265],{"className":71264},[886],[888,71266,71267],{"xmlns":890},[892,71268,71269,71275],{},[895,71270,71271,71273],{},[898,71272,1661],{},[898,71274,1693],{},[902,71276,55532],{"encoding":904},". (b) Určete ",[883,71279,71281],{"className":71280},[886],[888,71282,71283],{"xmlns":890},[892,71284,71285,71289],{},[895,71286,71287],{},[898,71288,1872],{},[902,71290,1872],{"encoding":904},[883,71292,71294],{"className":71293},[886],[888,71295,71296],{"xmlns":890},[892,71297,71298,71306],{},[895,71299,71300,71302,71304],{},[898,71301,4512],{},[898,71303,40579],{},[898,71305,1693],{},[902,71307,55551],{"encoding":904},[883,71309,71311],{"className":71310},[886],[888,71312,71313],{"xmlns":890},[892,71314,71315,71323],{},[895,71316,71317,71319,71321],{},[898,71318,4512],{},[898,71320,40579],{},[898,71322,1693],{},[902,71324,55551],{"encoding":904},". (c) Určete ",[883,71327,71329],{"className":71328},[886],[888,71330,71331],{"xmlns":890},[892,71332,71333,71337],{},[895,71334,71335],{},[898,71336,1872],{},[902,71338,1872],{"encoding":904},[883,71340,71342],{"className":71341},[886],[888,71343,71344],{"xmlns":890},[892,71345,71346,71352],{},[895,71347,71348,71350],{},[898,71349,4512],{},[898,71351,1693],{},[902,71353,55800],{"encoding":904},[883,71355,71357],{"className":71356},[886],[888,71358,71359],{"xmlns":890},[892,71360,71361,71367],{},[895,71362,71363,71365],{},[898,71364,4512],{},[898,71366,1693],{},[902,71368,55800],{"encoding":904}," (rada: hledaný kořen ",[883,71371,71373],{"className":71372},[886],[888,71374,71375],{"xmlns":890},[892,71376,71377,71387],{},[895,71378,71379,71381],{},[898,71380,4512],{},[1850,71382,71383,71385],{},[898,71384,1693],{},[1688,71386,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[902,71388,71389],{"encoding":904},"AC'"," určete přibližně, patří do ",[883,71392,71394],{"className":71393},[886],[888,71395,71396],{"xmlns":890},[892,71397,71398,71411],{},[895,71399,71400,71402,71405,71407,71409],{},[1688,71401,2066],{"stretchy":2065},[1793,71403,71404],{},"4,7",[1688,71406,8681],{"separator":1732},[1793,71408,5535],{},[1688,71410,2076],{"stretchy":2065},[902,71412,71413],{"encoding":904},"(4{,}7; 4{,}8)",", zpřesněte).",[724,71416,71417,71420,71421,2886,71449,71466,71467,21835,71508,71529],{},[38,71418,71419],{},"3.12"," Dokažte, že mají-li průměrné náklady ",[883,71422,71424],{"className":71423},[886],[888,71425,71426],{"xmlns":890},[892,71427,71428,71446],{},[895,71429,71430,71432,71434,71436,71438,71440,71442,71444],{},[898,71431,4512],{},[898,71433,1693],{},[1688,71435,1690],{},[898,71437,4512],{},[898,71439,1693],{},[1688,71441,2066],{"stretchy":2065},[898,71443,1872],{},[1688,71445,2076],{"stretchy":2065},[902,71447,71448],{"encoding":904},"AC = AC(Q)",[883,71450,71452],{"className":71451},[886],[888,71453,71454],{"xmlns":890},[892,71455,71456,71464],{},[895,71457,71458],{},[1788,71459,71460,71462],{},[898,71461,1872],{},[1793,71463,1779],{},[902,71465,38548],{"encoding":904}," minimum, pak platí ",[883,71468,71470],{"className":71469},[886],[888,71471,71472],{"xmlns":890},[892,71473,71474,71506],{},[895,71475,71476,71478,71480,71482,71488,71490,71492,71494,71496,71498,71504],{},[898,71477,4512],{},[898,71479,1693],{},[1688,71481,2066],{"stretchy":2065},[1788,71483,71484,71486],{},[898,71485,1872],{},[1793,71487,1779],{},[1688,71489,2076],{"stretchy":2065},[1688,71491,1690],{},[898,71493,1661],{},[898,71495,1693],{},[1688,71497,2066],{"stretchy":2065},[1788,71499,71500,71502],{},[898,71501,1872],{},[1793,71503,1779],{},[1688,71505,2076],{"stretchy":2065},[902,71507,62809],{"encoding":904},[883,71509,71511],{"className":71510},[886],[888,71512,71513],{"xmlns":890},[892,71514,71515,71527],{},[895,71516,71517,71519,71521,71523,71525],{},[898,71518,1661],{},[898,71520,1693],{},[1688,71522,2066],{"stretchy":2065},[898,71524,1872],{},[1688,71526,2076],{"stretchy":2065},[902,71528,67933],{"encoding":904}," jsou mezní náklady.",[724,71531,71532,70333,71535,70795,71569,71245,71582,71261,71597,2263],{},[38,71533,71534],{},"3.13",[883,71536,71538],{"className":71537},[886],[888,71539,71540],{"xmlns":890},[892,71541,71542,71566],{},[895,71543,71544,71546,71548,71550,71556,71558,71560,71562,71564],{},[898,71545,3035],{},[898,71547,1693],{},[1688,71549,1690],{},[1850,71551,71552,71554],{},[898,71553,1872],{},[1793,71555,1806],{},[1688,71557,1696],{},[1793,71559,1806],{},[898,71561,1872],{},[1688,71563,1696],{},[1793,71565,5260],{},[902,71567,71568],{"encoding":904},"TC = Q^2 + 2Q + 25",[883,71570,71572],{"className":71571},[886],[888,71573,71574],{"xmlns":890},[892,71575,71576,71580],{},[895,71577,71578],{},[898,71579,1872],{},[902,71581,1872],{"encoding":904},[883,71583,71585],{"className":71584},[886],[888,71586,71587],{"xmlns":890},[892,71588,71589,71595],{},[895,71590,71591,71593],{},[898,71592,4512],{},[898,71594,1693],{},[902,71596,55800],{"encoding":904},[883,71598,71600],{"className":71599},[886],[888,71601,71602],{"xmlns":890},[892,71603,71604,71610],{},[895,71605,71606,71608],{},[898,71607,4512],{},[898,71609,1693],{},[902,71611,55800],{"encoding":904},[724,71613,71614,71617,71618,2886,71650,71466,71667,21835,71710,71529],{},[38,71615,71616],{},"3.14"," Dokažte, že mají-li průměrné variabilní náklady ",[883,71619,71621],{"className":71620},[886],[888,71622,71623],{"xmlns":890},[892,71624,71625,71647],{},[895,71626,71627,71629,71631,71633,71635,71637,71639,71641,71643,71645],{},[898,71628,4512],{},[898,71630,40579],{},[898,71632,1693],{},[1688,71634,1690],{},[898,71636,4512],{},[898,71638,40579],{},[898,71640,1693],{},[1688,71642,2066],{"stretchy":2065},[898,71644,1872],{},[1688,71646,2076],{"stretchy":2065},[902,71648,71649],{"encoding":904},"AVC = AVC(Q)",[883,71651,71653],{"className":71652},[886],[888,71654,71655],{"xmlns":890},[892,71656,71657,71665],{},[895,71658,71659],{},[1788,71660,71661,71663],{},[898,71662,1872],{},[1793,71664,1779],{},[902,71666,38548],{"encoding":904},[883,71668,71670],{"className":71669},[886],[888,71671,71672],{"xmlns":890},[892,71673,71674,71708],{},[895,71675,71676,71678,71680,71682,71684,71690,71692,71694,71696,71698,71700,71706],{},[898,71677,4512],{},[898,71679,40579],{},[898,71681,1693],{},[1688,71683,2066],{"stretchy":2065},[1788,71685,71686,71688],{},[898,71687,1872],{},[1793,71689,1779],{},[1688,71691,2076],{"stretchy":2065},[1688,71693,1690],{},[898,71695,1661],{},[898,71697,1693],{},[1688,71699,2066],{"stretchy":2065},[1788,71701,71702,71704],{},[898,71703,1872],{},[1793,71705,1779],{},[1688,71707,2076],{"stretchy":2065},[902,71709,69259],{"encoding":904},[883,71711,71713],{"className":71712},[886],[888,71714,71715],{"xmlns":890},[892,71716,71717,71729],{},[895,71718,71719,71721,71723,71725,71727],{},[898,71720,1661],{},[898,71722,1693],{},[1688,71724,2066],{"stretchy":2065},[898,71726,1872],{},[1688,71728,2076],{"stretchy":2065},[902,71730,67933],{"encoding":904},[724,71732,71733,70333,71736,70795,71782,71245,71795,71261,71812,2263],{},[38,71734,71735],{},"3.15",[883,71737,71739],{"className":71738},[886],[888,71740,71741],{"xmlns":890},[892,71742,71743,71779],{},[895,71744,71745,71747,71749,71751,71753,71755,71757,71759,71761,71763,71769,71771,71773],{},[898,71746,3035],{},[898,71748,1693],{},[1688,71750,1690],{},[1793,71752,3377],{},[1688,71754,1696],{},[1793,71756,36484],{},[898,71758,1872],{},[1688,71760,1954],{},[1793,71762,1806],{},[1850,71764,71765,71767],{},[898,71766,1872],{},[1793,71768,1806],{},[1688,71770,1696],{},[1793,71772,3097],{},[1850,71774,71775,71777],{},[898,71776,1872],{},[1793,71778,2131],{},[902,71780,71781],{"encoding":904},"TC = 50 + 15Q - 2Q^2 + 0{,}2Q^3",[883,71783,71785],{"className":71784},[886],[888,71786,71787],{"xmlns":890},[892,71788,71789,71793],{},[895,71790,71791],{},[898,71792,1872],{},[902,71794,1872],{"encoding":904},[883,71796,71798],{"className":71797},[886],[888,71799,71800],{"xmlns":890},[892,71801,71802,71810],{},[895,71803,71804,71806,71808],{},[898,71805,4512],{},[898,71807,40579],{},[898,71809,1693],{},[902,71811,55551],{"encoding":904},[883,71813,71815],{"className":71814},[886],[888,71816,71817],{"xmlns":890},[892,71818,71819,71827],{},[895,71820,71821,71823,71825],{},[898,71822,4512],{},[898,71824,40579],{},[898,71826,1693],{},[902,71828,55551],{"encoding":904},[724,71830,71831,71834,71835,71848,71849,71869],{},[38,71832,71833],{},"3.16"," Celkové náklady na výstavbu domu o ",[883,71836,71838],{"className":71837},[886],[888,71839,71840],{"xmlns":890},[892,71841,71842,71846],{},[895,71843,71844],{},[898,71845,2292],{},[902,71847,2292],{"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 ",[883,71850,71852],{"className":71851},[886],[888,71853,71854],{"xmlns":890},[892,71855,71856,71866],{},[895,71857,71858,71860,71862,71864],{},[1793,71859,3121],{},[2041,71861,2043],{},[1793,71863,59322],{},[898,71865,2292],{},[902,71867,71868],{"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.",[198,71871,71873],{"id":71872},"zisk-body-zvratu-317325","Zisk, body zvratu (3.17–3.25)",[724,71875,71876,71879,71880,4142,71902,71928],{},[38,71877,71878],{},"3.17"," Jsou dány ",[883,71881,71883],{"className":71882},[886],[888,71884,71885],{"xmlns":890},[892,71886,71887,71899],{},[895,71888,71889,71891,71893,71895,71897],{},[898,71890,3035],{},[898,71892,4251],{},[1688,71894,1690],{},[1793,71896,3121],{},[898,71898,1872],{},[902,71900,71901],{"encoding":904},"TR = 10Q",[883,71903,71905],{"className":71904},[886],[888,71906,71907],{"xmlns":890},[892,71908,71909,71925],{},[895,71910,71911,71913,71915,71917,71919,71921,71923],{},[898,71912,3035],{},[898,71914,1693],{},[1688,71916,1690],{},[1793,71918,3347],{},[1688,71920,1696],{},[1793,71922,2501],{},[898,71924,1872],{},[902,71926,71927],{"encoding":904},"TC = 100 + 5Q",". Určete body zvratu a geometricky výsledek interpretujte.",[724,71930,71931,71934,71935,6446,71950,71965,71966,1343,71988,21835,72015,72037,72038,72072],{},[38,71932,71933],{},"3.18"," Odvoďte, že jestliže ",[883,71936,71938],{"className":71937},[886],[888,71939,71940],{"xmlns":890},[892,71941,71942,71948],{},[895,71943,71944,71946],{},[898,71945,3035],{},[898,71947,4251],{},[902,71949,4351],{"encoding":904},[883,71951,71953],{"className":71952},[886],[888,71954,71955],{"xmlns":890},[892,71956,71957,71963],{},[895,71958,71959,71961],{},[898,71960,3035],{},[898,71962,1693],{},[902,71964,3500],{"encoding":904}," jsou lineární tvaru ",[883,71967,71969],{"className":71968},[886],[888,71970,71971],{"xmlns":890},[892,71972,71973,71985],{},[895,71974,71975,71977,71979,71981,71983],{},[898,71976,3035],{},[898,71978,4251],{},[1688,71980,1690],{},[898,71982,724],{},[898,71984,1872],{},[902,71986,71987],{"encoding":904},"TR = pQ",[883,71989,71991],{"className":71990},[886],[888,71992,71993],{"xmlns":890},[892,71994,71995,72012],{},[895,71996,71997,71999,72001,72003,72006,72008,72010],{},[898,71998,3035],{},[898,72000,1693],{},[1688,72002,1690],{},[898,72004,72005],{},"m",[1688,72007,1696],{},[898,72009,37100],{},[898,72011,1872],{},[902,72013,72014],{"encoding":904},"TC = m + nQ",[883,72016,72018],{"className":72017},[886],[888,72019,72020],{"xmlns":890},[892,72021,72022,72034],{},[895,72023,72024,72026,72028,72030,72032],{},[898,72025,72005],{},[1688,72027,1733],{"separator":1732},[898,72029,37100],{},[1688,72031,1733],{"separator":1732},[898,72033,724],{},[902,72035,72036],{"encoding":904},"m, n, p"," jsou pevně zadány, pak existuje jediný bod zvratu ",[883,72039,72041],{"className":72040},[886],[888,72042,72043],{"xmlns":890},[892,72044,72045,72069],{},[895,72046,72047,72053,72055],{},[1850,72048,72049,72051],{},[898,72050,1872],{},[1688,72052,1857],{},[1688,72054,1690],{},[1777,72056,72057],{"scriptlevel":1779,"displaystyle":2065},[1781,72058,72059,72061],{},[898,72060,72005],{},[895,72062,72063,72065,72067],{},[898,72064,724],{},[1688,72066,1954],{},[898,72068,37100],{},[902,72070,72071],{"encoding":904},"Q^* = \\tfrac{m}{p - n}"," a proveďte diskusi podmínek. Načrtněte obrázek.",[724,72074,72075,71879,72078,4142,72112,71231,72138,72151,72152,69983,72167,72182,72183,69967,72196,69983,72211,72226],{},[38,72076,72077],{},"3.19",[883,72079,72081],{"className":72080},[886],[888,72082,72083],{"xmlns":890},[892,72084,72085,72109],{},[895,72086,72087,72089,72091,72093,72095,72097,72103,72105,72107],{},[898,72088,3035],{},[898,72090,4251],{},[1688,72092,1690],{},[1688,72094,1954],{},[1793,72096,1806],{},[1850,72098,72099,72101],{},[898,72100,1872],{},[1793,72102,1806],{},[1688,72104,1696],{},[1793,72106,23187],{},[898,72108,1872],{},[902,72110,72111],{"encoding":904},"TR = -2Q^2 + 14Q",[883,72113,72115],{"className":72114},[886],[888,72116,72117],{"xmlns":890},[892,72118,72119,72135],{},[895,72120,72121,72123,72125,72127,72129,72131,72133],{},[898,72122,3035],{},[898,72124,1693],{},[1688,72126,1690],{},[1793,72128,1806],{},[898,72130,1872],{},[1688,72132,1696],{},[1793,72134,3121],{},[902,72136,72137],{"encoding":904},"TC = 2Q + 10",[883,72139,72141],{"className":72140},[886],[888,72142,72143],{"xmlns":890},[892,72144,72145,72149],{},[895,72146,72147],{},[898,72148,1872],{},[902,72150,1872],{"encoding":904},", které maximalizuje zisk ",[883,72153,72155],{"className":72154},[886],[888,72156,72157],{"xmlns":890},[892,72158,72159,72165],{},[895,72160,72161,72163],{},[898,72162,1727],{},[898,72164,4251],{},[902,72166,63719],{"encoding":904},[883,72168,72170],{"className":72169},[886],[888,72171,72172],{"xmlns":890},[892,72173,72174,72180],{},[895,72175,72176,72178],{},[898,72177,1727],{},[898,72179,4251],{},[902,72181,63719],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku. (c) Určete ",[883,72184,72186],{"className":72185},[886],[888,72187,72188],{"xmlns":890},[892,72189,72190,72194],{},[895,72191,72192],{},[898,72193,1872],{},[902,72195,1872],{"encoding":904},[883,72197,72199],{"className":72198},[886],[888,72200,72201],{"xmlns":890},[892,72202,72203,72209],{},[895,72204,72205,72207],{},[898,72206,3035],{},[898,72208,4251],{},[902,72210,4351],{"encoding":904},[883,72212,72214],{"className":72213},[886],[888,72215,72216],{"xmlns":890},[892,72217,72218,72224],{},[895,72219,72220,72222],{},[898,72221,3035],{},[898,72223,4251],{},[902,72225,4351],{"encoding":904},". (d) Graficky interpretujte.",[724,72228,72229,47924,72232,1343,72258,1343,72277,71231,72297,72151,72310,69983,72325,72340,72341,72363,72364,71414],{},[38,72230,72231],{},"3.20",[883,72233,72235],{"className":72234},[886],[888,72236,72237],{"xmlns":890},[892,72238,72239,72255],{},[895,72240,72241,72243,72245,72247,72249],{},[898,72242,1727],{},[1688,72244,1690],{},[1793,72246,20383],{},[1688,72248,1954],{},[1850,72250,72251,72253],{},[898,72252,1872],{},[1793,72254,1806],{},[902,72256,72257],{"encoding":904},"P = 400 - Q^2",[883,72259,72261],{"className":72260},[886],[888,72262,72263],{"xmlns":890},[892,72264,72265,72275],{},[895,72266,72267,72269,72271,72273],{},[898,72268,10688],{},[898,72270,1693],{},[1688,72272,1690],{},[1793,72274,3347],{},[902,72276,11885],{"encoding":904},[883,72278,72280],{"className":72279},[886],[888,72281,72282],{"xmlns":890},[892,72283,72284,72294],{},[895,72285,72286,72288,72290,72292],{},[898,72287,1661],{},[898,72289,1693],{},[1688,72291,1690],{},[1793,72293,9290],{},[902,72295,72296],{"encoding":904},"MC = 20",[883,72298,72300],{"className":72299},[886],[888,72301,72302],{"xmlns":890},[892,72303,72304,72308],{},[895,72305,72306],{},[898,72307,1872],{},[902,72309,1872],{"encoding":904},[883,72311,72313],{"className":72312},[886],[888,72314,72315],{"xmlns":890},[892,72316,72317,72323],{},[895,72318,72319,72321],{},[898,72320,1727],{},[898,72322,4251],{},[902,72324,63719],{"encoding":904},[883,72326,72328],{"className":72327},[886],[888,72329,72330],{"xmlns":890},[892,72331,72332,72338],{},[895,72333,72334,72336],{},[898,72335,1727],{},[898,72337,4251],{},[902,72339,63719],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku (rada: jeden z bodů zvratu patří do ",[883,72342,72344],{"className":72343},[886],[888,72345,72346],{"xmlns":890},[892,72347,72348,72360],{},[895,72349,72350,72352,72354,72356,72358],{},[1688,72351,2066],{"stretchy":2065},[1793,72353,1779],{},[1688,72355,1733],{"separator":1732},[1793,72357,1795],{},[1688,72359,2076],{"stretchy":2065},[902,72361,72362],{"encoding":904},"(0, 1)",", druhý do ",[883,72365,72367],{"className":72366},[886],[888,72368,72369],{"xmlns":890},[892,72370,72371,72384],{},[895,72372,72373,72375,72378,72380,72382],{},[1688,72374,2066],{"stretchy":2065},[1793,72376,72377],{},"19",[1688,72379,1733],{"separator":1732},[1793,72381,9290],{},[1688,72383,2076],{"stretchy":2065},[902,72385,72386],{"encoding":904},"(19, 20)",[724,72388,72389,72392,72393,2886,72421,72438,72439,2263],{},[38,72390,72391],{},"3.21"," Dokažte, že má-li zisk ",[883,72394,72396],{"className":72395},[886],[888,72397,72398],{"xmlns":890},[892,72399,72400,72418],{},[895,72401,72402,72404,72406,72408,72410,72412,72414,72416],{},[898,72403,1727],{},[898,72405,4251],{},[1688,72407,1690],{},[898,72409,1727],{},[898,72411,4251],{},[1688,72413,2066],{"stretchy":2065},[898,72415,1872],{},[1688,72417,2076],{"stretchy":2065},[902,72419,72420],{"encoding":904},"PR = PR(Q)",[883,72422,72424],{"className":72423},[886],[888,72425,72426],{"xmlns":890},[892,72427,72428,72436],{},[895,72429,72430],{},[1788,72431,72432,72434],{},[898,72433,1872],{},[1793,72435,1779],{},[902,72437,38548],{"encoding":904}," maximum, pak platí ",[883,72440,72442],{"className":72441},[886],[888,72443,72444],{"xmlns":890},[892,72445,72446,72478],{},[895,72447,72448,72450,72452,72454,72460,72462,72464,72466,72468,72470,72476],{},[898,72449,1661],{},[898,72451,4251],{},[1688,72453,2066],{"stretchy":2065},[1788,72455,72456,72458],{},[898,72457,1872],{},[1793,72459,1779],{},[1688,72461,2076],{"stretchy":2065},[1688,72463,1690],{},[898,72465,1661],{},[898,72467,1693],{},[1688,72469,2066],{"stretchy":2065},[1788,72471,72472,72474],{},[898,72473,1872],{},[1793,72475,1779],{},[1688,72477,2076],{"stretchy":2065},[902,72479,65885],{"encoding":904},[724,72481,72482,72485,72486,4142,72501,56265,72516,72151,72529,72544,72545,1343,72572,72609,72610,1343,72637,2263],{},[38,72483,72484],{},"3.22"," Pro zadané ",[883,72487,72489],{"className":72488},[886],[888,72490,72491],{"xmlns":890},[892,72492,72493,72499],{},[895,72494,72495,72497],{},[898,72496,1661],{},[898,72498,4251],{},[902,72500,6890],{"encoding":904},[883,72502,72504],{"className":72503},[886],[888,72505,72506],{"xmlns":890},[892,72507,72508,72514],{},[895,72509,72510,72512],{},[898,72511,1661],{},[898,72513,1693],{},[902,72515,55532],{"encoding":904},[883,72517,72519],{"className":72518},[886],[888,72520,72521],{"xmlns":890},[892,72522,72523,72527],{},[895,72524,72525],{},[898,72526,1872],{},[902,72528,1872],{"encoding":904},[883,72530,72532],{"className":72531},[886],[888,72533,72534],{"xmlns":890},[892,72535,72536,72542],{},[895,72537,72538,72540],{},[898,72539,1727],{},[898,72541,4251],{},[902,72543,63719],{"encoding":904},". (a) ",[883,72546,72548],{"className":72547},[886],[888,72549,72550],{"xmlns":890},[892,72551,72552,72569],{},[895,72553,72554,72556,72558,72560,72563,72565,72567],{},[898,72555,1661],{},[898,72557,4251],{},[1688,72559,1690],{},[1793,72561,72562],{},"236",[1688,72564,1954],{},[1793,72566,42102],{},[898,72568,1872],{},[902,72570,72571],{"encoding":904},"MR = 236 - 16Q",[883,72573,72575],{"className":72574},[886],[888,72576,72577],{"xmlns":890},[892,72578,72579,72606],{},[895,72580,72581,72583,72585,72587,72589,72595,72597,72600,72602,72604],{},[898,72582,1661],{},[898,72584,1693],{},[1688,72586,1690],{},[1793,72588,2131],{},[1850,72590,72591,72593],{},[898,72592,1872],{},[1793,72594,1806],{},[1688,72596,1954],{},[1793,72598,72599],{},"32",[898,72601,1872],{},[1688,72603,1696],{},[1793,72605,6000],{},[902,72607,72608],{"encoding":904},"MC = 3Q^2 - 32Q + 96",". (b) ",[883,72611,72613],{"className":72612},[886],[888,72614,72615],{"xmlns":890},[892,72616,72617,72634],{},[895,72618,72619,72621,72623,72625,72628,72630,72632],{},[898,72620,1661],{},[898,72622,4251],{},[1688,72624,1690],{},[1793,72626,72627],{},"280",[1688,72629,1954],{},[1793,72631,9290],{},[898,72633,1872],{},[902,72635,72636],{"encoding":904},"MR = 280 - 20Q",[883,72638,72640],{"className":72639},[886],[888,72641,72642],{"xmlns":890},[892,72643,72644,72671],{},[895,72645,72646,72648,72650,72652,72655,72661,72663,72665,72667,72669],{},[898,72647,1661],{},[898,72649,1693],{},[1688,72651,1690],{},[1793,72653,72654],{},"1,6",[1850,72656,72657,72659],{},[898,72658,1872],{},[1793,72660,1806],{},[1688,72662,1954],{},[1793,72664,36484],{},[898,72666,1872],{},[1688,72668,1696],{},[1793,72670,3383],{},[902,72672,72673],{"encoding":904},"MC = 1{,}6Q^2 - 15Q + 60",[724,72675,72676,72485,72679,4142,72694,56265,72709,69967,72722,69983,72737,72544,72752,1343,72783,72609,72819,1343,72851,72895,72896,1343,72928,2263],{},[38,72677,72678],{},"3.23",[883,72680,72682],{"className":72681},[886],[888,72683,72684],{"xmlns":890},[892,72685,72686,72692],{},[895,72687,72688,72690],{},[898,72689,3035],{},[898,72691,4251],{},[902,72693,4351],{"encoding":904},[883,72695,72697],{"className":72696},[886],[888,72698,72699],{"xmlns":890},[892,72700,72701,72707],{},[895,72702,72703,72705],{},[898,72704,3035],{},[898,72706,1693],{},[902,72708,3500],{"encoding":904},[883,72710,72712],{"className":72711},[886],[888,72713,72714],{"xmlns":890},[892,72715,72716,72720],{},[895,72717,72718],{},[898,72719,1872],{},[902,72721,1872],{"encoding":904},[883,72723,72725],{"className":72724},[886],[888,72726,72727],{"xmlns":890},[892,72728,72729,72735],{},[895,72730,72731,72733],{},[898,72732,1727],{},[898,72734,4251],{},[902,72736,63719],{"encoding":904},[883,72738,72740],{"className":72739},[886],[888,72741,72742],{"xmlns":890},[892,72743,72744,72750],{},[895,72745,72746,72748],{},[898,72747,1727],{},[898,72749,4251],{},[902,72751,63719],{"encoding":904},[883,72753,72755],{"className":72754},[886],[888,72756,72757],{"xmlns":890},[892,72758,72759,72780],{},[895,72760,72761,72763,72765,72767,72770,72772,72774],{},[898,72762,3035],{},[898,72764,4251],{},[1688,72766,1690],{},[1793,72768,72769],{},"125",[898,72771,1872],{},[1688,72773,1954],{},[1850,72775,72776,72778],{},[898,72777,1872],{},[1793,72779,1806],{},[902,72781,72782],{"encoding":904},"TR = 125Q - Q^2",[883,72784,72786],{"className":72785},[886],[888,72787,72788],{"xmlns":890},[892,72789,72790,72816],{},[895,72791,72792,72794,72796,72798,72800,72802,72804,72806,72808,72810],{},[898,72793,3035],{},[898,72795,1693],{},[1688,72797,1690],{},[1793,72799,15357],{},[1688,72801,1696],{},[1793,72803,2501],{},[898,72805,1872],{},[1688,72807,1696],{},[1793,72809,5265],{},[1850,72811,72812,72814],{},[898,72813,1872],{},[1793,72815,1806],{},[902,72817,72818],{"encoding":904},"TC = 500 + 5Q + 0{,}5Q^2",[883,72820,72822],{"className":72821},[886],[888,72823,72824],{"xmlns":890},[892,72825,72826,72848],{},[895,72827,72828,72830,72832,72834,72836,72838,72840,72842],{},[898,72829,3035],{},[898,72831,4251],{},[1688,72833,1690],{},[1793,72835,9290],{},[898,72837,1872],{},[1688,72839,1954],{},[1793,72841,1806],{},[1850,72843,72844,72846],{},[898,72845,1872],{},[1793,72847,1806],{},[902,72849,72850],{"encoding":904},"TR = 20Q - 2Q^2",[883,72852,72854],{"className":72853},[886],[888,72855,72856],{"xmlns":890},[892,72857,72858,72892],{},[895,72859,72860,72862,72864,72866,72868,72870,72872,72874,72876,72878,72884,72886],{},[898,72861,3035],{},[898,72863,1693],{},[1688,72865,1690],{},[1793,72867,1806],{},[1688,72869,1696],{},[1793,72871,9290],{},[898,72873,1872],{},[1688,72875,1954],{},[1793,72877,5841],{},[1850,72879,72880,72882],{},[898,72881,1872],{},[1793,72883,1806],{},[1688,72885,1696],{},[1850,72887,72888,72890],{},[898,72889,1872],{},[1793,72891,2131],{},[902,72893,72894],{"encoding":904},"TC = 2 + 20Q - 8Q^2 + Q^3",". (c) ",[883,72897,72899],{"className":72898},[886],[888,72900,72901],{"xmlns":890},[892,72902,72903,72925],{},[895,72904,72905,72907,72909,72911,72913,72915,72917,72919],{},[898,72906,3035],{},[898,72908,4251],{},[1688,72910,1690],{},[1793,72912,2616],{},[898,72914,1872],{},[1688,72916,1954],{},[1793,72918,24030],{},[1850,72920,72921,72923],{},[898,72922,1872],{},[1793,72924,1806],{},[902,72926,72927],{"encoding":904},"TR = 4Q - 0{,}25Q^2",[883,72929,72931],{"className":72930},[886],[888,72932,72933],{"xmlns":890},[892,72934,72935,72983],{},[895,72936,72937,72939,72941,72943,72945,72947,72949,72951,72953,72969,72971],{},[898,72938,3035],{},[898,72940,1693],{},[1688,72942,1690],{},[1793,72944,2616],{},[1688,72946,1696],{},[1793,72948,1806],{},[898,72950,1872],{},[1688,72952,1954],{},[1777,72954,72955],{"scriptlevel":1779,"displaystyle":2065},[1781,72956,72957,72967],{},[895,72958,72959,72961],{},[1793,72960,2131],{},[1850,72962,72963,72965],{},[898,72964,1872],{},[1793,72966,1806],{},[1793,72968,3121],{},[1688,72970,1696],{},[1777,72972,72973],{"scriptlevel":1779,"displaystyle":2065},[1781,72974,72975,72981],{},[1850,72976,72977,72979],{},[898,72978,1872],{},[1793,72980,2131],{},[1793,72982,9290],{},[902,72984,72985],{"encoding":904},"TC = 4 + 2Q - \\tfrac{3Q^2}{10} + \\tfrac{Q^3}{20}",[724,72987,72988,72991,72992,73022,73023,73055,73056,21835,73086,73116],{},[38,72989,72990],{},"3.24"," Firma řeší problém stanovení cen pro malé a velké odběratele za účelem maximalizace zisku. Poptávka pro maloodběratele je ",[883,72993,72995],{"className":72994},[886],[888,72996,72997],{"xmlns":890},[892,72998,72999,73019],{},[895,73000,73001,73007,73009,73011,73013],{},[1788,73002,73003,73005],{},[898,73004,1727],{},[1793,73006,1795],{},[1688,73008,1690],{},[1793,73010,15357],{},[1688,73012,1954],{},[1788,73014,73015,73017],{},[898,73016,1872],{},[1793,73018,1795],{},[902,73020,73021],{"encoding":904},"P_1 = 500 - Q_1",", pro velkoodběratele ",[883,73024,73026],{"className":73025},[886],[888,73027,73028],{"xmlns":890},[892,73029,73030,73052],{},[895,73031,73032,73038,73040,73042,73044,73046],{},[1788,73033,73034,73036],{},[898,73035,1727],{},[1793,73037,1806],{},[1688,73039,1690],{},[1793,73041,30321],{},[1688,73043,1954],{},[1793,73045,64799],{},[1788,73047,73048,73050],{},[898,73049,1872],{},[1793,73051,1806],{},[902,73053,73054],{"encoding":904},"P_2 = 300 - 1{,}5Q_2",". Celkové náklady firmy jsou ",[883,73057,73059],{"className":73058},[886],[888,73060,73061],{"xmlns":890},[892,73062,73063,73083],{},[895,73064,73065,73067,73069,73071,73073,73075,73077,73079,73081],{},[898,73066,3035],{},[898,73068,1693],{},[1688,73070,1690],{},[1793,73072,3377],{},[2041,73074,2043],{},[1793,73076,59322],{},[1688,73078,1696],{},[1793,73080,9290],{},[898,73082,1872],{},[902,73084,73085],{"encoding":904},"TC = 50\\,000 + 20Q",[883,73087,73089],{"className":73088},[886],[888,73090,73091],{"xmlns":890},[892,73092,73093,73113],{},[895,73094,73095,73097,73099,73105,73107],{},[898,73096,1872],{},[1688,73098,1690],{},[1788,73100,73101,73103],{},[898,73102,1872],{},[1793,73104,1795],{},[1688,73106,1696],{},[1788,73108,73109,73111],{},[898,73110,1872],{},[1793,73112,1806],{},[902,73114,73115],{"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.",[724,73118,73119,73122,73123,73153,73154,73055,73186,21835,73216,73245],{},[38,73120,73121],{},"3.25"," Firma řeší problém stanovení cen pro domácí a zahraniční trh za účelem maximalizace zisku. Poptávka pro domácí trh je ",[883,73124,73126],{"className":73125},[886],[888,73127,73128],{"xmlns":890},[892,73129,73130,73150],{},[895,73131,73132,73138,73140,73142,73144],{},[1788,73133,73134,73136],{},[898,73135,1727],{},[1793,73137,1795],{},[1688,73139,1690],{},[1793,73141,30321],{},[1688,73143,1954],{},[1788,73145,73146,73148],{},[898,73147,1872],{},[1793,73149,1795],{},[902,73151,73152],{"encoding":904},"P_1 = 300 - Q_1",", pro zahraniční trh ",[883,73155,73157],{"className":73156},[886],[888,73158,73159],{"xmlns":890},[892,73160,73161,73183],{},[895,73162,73163,73169,73171,73173,73175,73177],{},[1788,73164,73165,73167],{},[898,73166,1727],{},[1793,73168,1806],{},[1688,73170,1690],{},[1793,73172,8633],{},[1688,73174,1954],{},[1793,73176,5265],{},[1788,73178,73179,73181],{},[898,73180,1872],{},[1793,73182,1806],{},[902,73184,73185],{"encoding":904},"P_2 = 200 - 0{,}5Q_2",[883,73187,73189],{"className":73188},[886],[888,73190,73191],{"xmlns":890},[892,73192,73193,73213],{},[895,73194,73195,73197,73199,73201,73203,73205,73207,73209,73211],{},[898,73196,3035],{},[898,73198,1693],{},[1688,73200,1690],{},[1793,73202,2501],{},[2041,73204,2043],{},[1793,73206,59322],{},[1688,73208,1696],{},[1793,73210,3347],{},[898,73212,1872],{},[902,73214,73215],{"encoding":904},"TC = 5\\,000 + 100Q",[883,73217,73219],{"className":73218},[886],[888,73220,73221],{"xmlns":890},[892,73222,73223,73243],{},[895,73224,73225,73227,73229,73235,73237],{},[898,73226,1872],{},[1688,73228,1690],{},[1788,73230,73231,73233],{},[898,73232,1872],{},[1793,73234,1795],{},[1688,73236,1696],{},[1788,73238,73239,73241],{},[898,73240,1872],{},[1793,73242,1806],{},[902,73244,73115],{"encoding":904},". Stanovte ceny, při kterých firma maximalizuje zisk: (a) s cenovou diskriminací, (b) bez cenové diskriminace. Porovnejte zisk firmy v obou případech.",[198,73247,73249],{"id":73248},"konstrukce-nabídky-326328","Konstrukce nabídky (3.26–3.28)",[724,73251,73252,73255,73256,73303,73304,73321],{},[38,73253,73254],{},"3.26"," Jsou dány celkové variabilní náklady ",[883,73257,73259],{"className":73258},[886],[888,73260,73261],{"xmlns":890},[892,73262,73263,73300],{},[895,73264,73265,73267,73269,73271,73273,73276,73282,73284,73287,73293,73295,73298],{},[898,73266,3035],{},[898,73268,40579],{},[898,73270,1693],{},[1688,73272,1690],{},[1793,73274,73275],{},"0,85",[1850,73277,73278,73280],{},[898,73279,1872],{},[1793,73281,2131],{},[1688,73283,1954],{},[1793,73285,73286],{},"11,9",[1850,73288,73289,73291],{},[898,73290,1872],{},[1793,73292,1806],{},[1688,73294,1696],{},[1793,73296,73297],{},"102",[898,73299,1872],{},[902,73301,73302],{"encoding":904},"TVC = 0{,}85Q^3 - 11{,}9Q^2 + 102Q",". Určete minimální cenu ",[883,73305,73307],{"className":73306},[886],[888,73308,73309],{"xmlns":890},[892,73310,73311,73319],{},[895,73312,73313],{},[1850,73314,73315,73317],{},[898,73316,1727],{},[1688,73318,1857],{},[902,73320,4660],{"encoding":904}," nabídky a konstruujte nabídku. Graficky interpretujte.",[724,73323,73324,71082,73327,73363],{},[38,73325,73326],{},"3.27",[883,73328,73330],{"className":73329},[886],[888,73331,73332],{"xmlns":890},[892,73333,73334,73360],{},[895,73335,73336,73338,73340,73342,73344,73350,73352,73354,73356,73358],{},[898,73337,1661],{},[898,73339,1693],{},[1688,73341,1690],{},[1793,73343,3181],{},[1850,73345,73346,73348],{},[898,73347,1872],{},[1793,73349,1806],{},[1688,73351,1954],{},[1793,73353,64680],{},[898,73355,1872],{},[1688,73357,1696],{},[1793,73359,30983],{},[902,73361,73362],{"encoding":904},"MC = 4{,}2Q^2 - 48Q + 250",". Konstruujte nabídku.",[724,73365,73366,70333,73369,73363],{},[38,73367,73368],{},"3.28",[883,73370,73372],{"className":73371},[886],[888,73373,73374],{"xmlns":890},[892,73375,73376,73412],{},[895,73377,73378,73380,73382,73384,73386,73392,73394,73396,73402,73404,73406,73408,73410],{},[898,73379,3035],{},[898,73381,1693],{},[1688,73383,1690],{},[1793,73385,5265],{},[1850,73387,73388,73390],{},[898,73389,1872],{},[1793,73391,2131],{},[1688,73393,1954],{},[1793,73395,24442],{},[1850,73397,73398,73400],{},[898,73399,1872],{},[1793,73401,1806],{},[1688,73403,1696],{},[1793,73405,3383],{},[898,73407,1872],{},[1688,73409,1696],{},[1793,73411,15357],{},[902,73413,73414],{"encoding":904},"TC = 0{,}5Q^3 - 7Q^2 + 60Q + 500",[115,73416,15967],{"id":15966},[120,73418,73419,73447,73492,73564,73629,73669,73761,73867,73907,74021,74114,74178,74210,74270,74276,74340,74389,74443,74551,74606],{},[123,73420,73421,2170,73423,73446],{},[38,73422,55990],{},[883,73424,73426],{"className":73425},[886],[888,73427,73428],{"xmlns":890},[892,73429,73430,73444],{},[895,73431,73432,73434,73436,73438,73440,73442],{},[898,73433,3035],{},[898,73435,4251],{},[1688,73437,1690],{},[898,73439,1727],{},[1688,73441,3434],{},[898,73443,1872],{},[902,73445,66952],{"encoding":904}," — křivka celkového příjmu (total revenue curve).",[123,73448,73449,2170,73451,73491],{},[38,73450,56576],{},[883,73452,73454],{"className":73453},[886],[888,73455,73456],{"xmlns":890},[892,73457,73458,73488],{},[895,73459,73460,73462,73464,73466,73478,73480,73482,73484,73486],{},[898,73461,4512],{},[898,73463,4251],{},[1688,73465,1690],{},[1777,73467,73468],{"scriptlevel":1779,"displaystyle":2065},[1781,73469,73470,73476],{},[895,73471,73472,73474],{},[898,73473,3035],{},[898,73475,4251],{},[898,73477,1872],{},[1688,73479,1690],{},[898,73481,4440],{},[1688,73483,2066],{"stretchy":2065},[898,73485,1872],{},[1688,73487,2076],{"stretchy":2065},[902,73489,73490],{"encoding":904},"AR = \\tfrac{TR}{Q} = D(Q)"," — shoduje se s poptávkovou funkcí.",[123,73493,73494,2170,73496,73532,73533,73548,73549,2263],{},[38,73495,56724],{},[883,73497,73499],{"className":73498},[886],[888,73500,73501],{"xmlns":890},[892,73502,73503,73529],{},[895,73504,73505,73507,73509,73511],{},[898,73506,1661],{},[898,73508,4251],{},[1688,73510,1690],{},[1777,73512,73513],{"scriptlevel":1779,"displaystyle":2065},[1781,73514,73515,73523],{},[895,73516,73517,73519,73521],{},[898,73518,2073],{"mathvariant":1822},[898,73520,3035],{},[898,73522,4251],{},[895,73524,73525,73527],{},[898,73526,2073],{"mathvariant":1822},[898,73528,1872],{},[902,73530,73531],{"encoding":904},"MR = \\tfrac{\\mathrm{d}TR}{\\mathrm{d}Q}"," — rychlost změny ",[883,73534,73536],{"className":73535},[886],[888,73537,73538],{"xmlns":890},[892,73539,73540,73546],{},[895,73541,73542,73544],{},[898,73543,3035],{},[898,73545,4251],{},[902,73547,4351],{"encoding":904},"; pro lineární poptávku má sklon dvojnásobný vůči ",[883,73550,73552],{"className":73551},[886],[888,73553,73554],{"xmlns":890},[892,73555,73556,73562],{},[895,73557,73558,73560],{},[898,73559,4512],{},[898,73561,4251],{},[902,73563,55685],{"encoding":904},[123,73565,73566,2170,73569,1343,73599,2263],{},[38,73567,73568],{},"Diferenciál příjmu\u002Fnákladů",[883,73570,73572],{"className":73571},[886],[888,73573,73574],{"xmlns":890},[892,73575,73576,73596],{},[895,73577,73578,73580,73582,73584,73586,73588,73590,73592,73594],{},[898,73579,3147],{"mathvariant":1822},[898,73581,3035],{},[898,73583,4251],{},[1688,73585,2991],{},[898,73587,1661],{},[898,73589,4251],{},[2041,73591,2043],{},[898,73593,2073],{"mathvariant":1822},[898,73595,1872],{},[902,73597,73598],{"encoding":904},"\\Delta TR \\approx MR \\, \\mathrm{d}Q",[883,73600,73602],{"className":73601},[886],[888,73603,73604],{"xmlns":890},[892,73605,73606,73626],{},[895,73607,73608,73610,73612,73614,73616,73618,73620,73622,73624],{},[898,73609,3147],{"mathvariant":1822},[898,73611,3035],{},[898,73613,1693],{},[1688,73615,2991],{},[898,73617,1661],{},[898,73619,1693],{},[2041,73621,2043],{},[898,73623,2073],{"mathvariant":1822},[898,73625,1872],{},[902,73627,73628],{"encoding":904},"\\Delta TC \\approx MC \\, \\mathrm{d}Q",[123,73630,73631,2170,73633,2263],{},[38,73632,58846],{},[883,73634,73636],{"className":73635},[886],[888,73637,73638],{"xmlns":890},[892,73639,73640,73666],{},[895,73641,73642,73644,73646,73648,73650,73652,73654,73656,73658,73660,73662,73664],{},[898,73643,3035],{},[898,73645,1693],{},[1688,73647,1690],{},[898,73649,10688],{},[898,73651,1693],{},[1688,73653,1696],{},[898,73655,3035],{},[898,73657,40579],{},[898,73659,1693],{},[1688,73661,2066],{"stretchy":2065},[898,73663,1872],{},[1688,73665,2076],{"stretchy":2065},[902,73667,73668],{"encoding":904},"TC = FC + TVC(Q)",[123,73670,73671,2170,73674,1343,73689,2170,73691,1343,73714,2170,73717,2263],{},[38,73672,73673],{},"Fixní náklady",[883,73675,73677],{"className":73676},[886],[888,73678,73679],{"xmlns":890},[892,73680,73681,73687],{},[895,73682,73683,73685],{},[898,73684,10688],{},[898,73686,1693],{},[902,73688,55731],{"encoding":904},[38,73690,58999],{},[883,73692,73694],{"className":73693},[886],[888,73695,73696],{"xmlns":890},[892,73697,73698,73712],{},[895,73699,73700,73702,73704,73706,73708,73710],{},[898,73701,3035],{},[898,73703,40579],{},[898,73705,1693],{},[1688,73707,2066],{"stretchy":2065},[898,73709,1872],{},[1688,73711,2076],{"stretchy":2065},[902,73713,58996],{"encoding":904},[38,73715,73716],{},"variabilní náklady na jednotku",[883,73718,73720],{"className":73719},[886],[888,73721,73722],{"xmlns":890},[892,73723,73724,73758],{},[895,73725,73726,73728,73730,73732,73734,73736,73738],{},[898,73727,40579],{},[898,73729,1693],{},[1688,73731,2066],{"stretchy":2065},[898,73733,1872],{},[1688,73735,2076],{"stretchy":2065},[1688,73737,1690],{},[1777,73739,73740],{"scriptlevel":1779,"displaystyle":2065},[1781,73741,73742,73756],{},[895,73743,73744,73746,73748,73750,73752,73754],{},[898,73745,3035],{},[898,73747,40579],{},[898,73749,1693],{},[1688,73751,2066],{"stretchy":2065},[898,73753,1872],{},[1688,73755,2076],{"stretchy":2065},[898,73757,1872],{},[902,73759,73760],{"encoding":904},"VC(Q) = \\tfrac{TVC(Q)}{Q}",[123,73762,73763,2170,73765,1343,73795,2170,73798,1343,73830,2170,73833,2263],{},[38,73764,59007],{},[883,73766,73768],{"className":73767},[886],[888,73769,73770],{"xmlns":890},[892,73771,73772,73792],{},[895,73773,73774,73776,73778,73780],{},[898,73775,4512],{},[898,73777,1693],{},[1688,73779,1690],{},[1777,73781,73782],{"scriptlevel":1779,"displaystyle":2065},[1781,73783,73784,73790],{},[895,73785,73786,73788],{},[898,73787,3035],{},[898,73789,1693],{},[898,73791,1872],{},[902,73793,73794],{"encoding":904},"AC = \\tfrac{TC}{Q}",[38,73796,73797],{},"průměrné fixní",[883,73799,73801],{"className":73800},[886],[888,73802,73803],{"xmlns":890},[892,73804,73805,73827],{},[895,73806,73807,73809,73811,73813,73815],{},[898,73808,4512],{},[898,73810,10688],{},[898,73812,1693],{},[1688,73814,1690],{},[1777,73816,73817],{"scriptlevel":1779,"displaystyle":2065},[1781,73818,73819,73825],{},[895,73820,73821,73823],{},[898,73822,10688],{},[898,73824,1693],{},[898,73826,1872],{},[902,73828,73829],{"encoding":904},"AFC = \\tfrac{FC}{Q}",[38,73831,73832],{},"průměrné variabilní",[883,73834,73836],{"className":73835},[886],[888,73837,73838],{"xmlns":890},[892,73839,73840,73864],{},[895,73841,73842,73844,73846,73848,73850],{},[898,73843,4512],{},[898,73845,40579],{},[898,73847,1693],{},[1688,73849,1690],{},[1777,73851,73852],{"scriptlevel":1779,"displaystyle":2065},[1781,73853,73854,73862],{},[895,73855,73856,73858,73860],{},[898,73857,3035],{},[898,73859,40579],{},[898,73861,1693],{},[898,73863,1872],{},[902,73865,73866],{"encoding":904},"AVC = \\tfrac{TVC}{Q}",[123,73868,73869,2170,73871,2263],{},[38,73870,60194],{},[883,73872,73874],{"className":73873},[886],[888,73875,73876],{"xmlns":890},[892,73877,73878,73904],{},[895,73879,73880,73882,73884,73886],{},[898,73881,1661],{},[898,73883,1693],{},[1688,73885,1690],{},[1777,73887,73888],{"scriptlevel":1779,"displaystyle":2065},[1781,73889,73890,73898],{},[895,73891,73892,73894,73896],{},[898,73893,2073],{"mathvariant":1822},[898,73895,3035],{},[898,73897,1693],{},[895,73899,73900,73902],{},[898,73901,2073],{"mathvariant":1822},[898,73903,1872],{},[902,73905,73906],{"encoding":904},"MC = \\tfrac{\\mathrm{d}TC}{\\mathrm{d}Q}",[123,73908,73909,2170,73911,73959,73960,73973,73974,1343,73989,1343,74006,2263],{},[38,73910,61092],{},[883,73912,73914],{"className":73913},[886],[888,73915,73916],{"xmlns":890},[892,73917,73918,73956],{},[895,73919,73920,73922,73924,73926,73928,73930,73932,73934,73936,73938,73940,73946,73948,73950],{},[898,73921,3035],{},[898,73923,1693],{},[1688,73925,1690],{},[898,73927,10688],{},[898,73929,1693],{},[1688,73931,1696],{},[898,73933,207],{},[898,73935,1872],{},[1688,73937,1696],{},[898,73939,1918],{},[1850,73941,73942,73944],{},[898,73943,1872],{},[1793,73945,1806],{},[1688,73947,1696],{},[898,73949,2031],{},[1850,73951,73952,73954],{},[898,73953,1872],{},[1793,73955,2131],{},[902,73957,73958],{"encoding":904},"TC = FC + aQ + bQ^2 + cQ^3"," — „standardní\" tvar s ",[883,73961,73963],{"className":73962},[886],[888,73964,73965],{"xmlns":890},[892,73966,73967,73971],{},[895,73968,73969],{},[898,73970,900],{},[902,73972,900],{"encoding":904},"-průběhem ",[883,73975,73977],{"className":73976},[886],[888,73978,73979],{"xmlns":890},[892,73980,73981,73987],{},[895,73982,73983,73985],{},[898,73984,4512],{},[898,73986,1693],{},[902,73988,55800],{"encoding":904},[883,73990,73992],{"className":73991},[886],[888,73993,73994],{"xmlns":890},[892,73995,73996,74004],{},[895,73997,73998,74000,74002],{},[898,73999,4512],{},[898,74001,40579],{},[898,74003,1693],{},[902,74005,55551],{"encoding":904},[883,74007,74009],{"className":74008},[886],[888,74010,74011],{"xmlns":890},[892,74012,74013,74019],{},[895,74014,74015,74017],{},[898,74016,1661],{},[898,74018,1693],{},[902,74020,55532],{"encoding":904},[123,74022,74023,74025,74026,10646,74041,74082,74083,61737,74098,74113],{},[38,74024,62174],{},": v bodě minima ",[883,74027,74029],{"className":74028},[886],[888,74030,74031],{"xmlns":890},[892,74032,74033,74039],{},[895,74034,74035,74037],{},[898,74036,4512],{},[898,74038,1693],{},[902,74040,55800],{"encoding":904},[883,74042,74044],{"className":74043},[886],[888,74045,74046],{"xmlns":890},[892,74047,74048,74080],{},[895,74049,74050,74052,74054,74056,74062,74064,74066,74068,74070,74072,74078],{},[898,74051,4512],{},[898,74053,1693],{},[1688,74055,2066],{"stretchy":2065},[1788,74057,74058,74060],{},[898,74059,1872],{},[1793,74061,1779],{},[1688,74063,2076],{"stretchy":2065},[1688,74065,1690],{},[898,74067,1661],{},[898,74069,1693],{},[1688,74071,2066],{"stretchy":2065},[1788,74073,74074,74076],{},[898,74075,1872],{},[1793,74077,1779],{},[1688,74079,2076],{"stretchy":2065},[902,74081,62809],{"encoding":904},"; geometricky ",[883,74084,74086],{"className":74085},[886],[888,74087,74088],{"xmlns":890},[892,74089,74090,74096],{},[895,74091,74092,74094],{},[898,74093,1661],{},[898,74095,1693],{},[902,74097,55532],{"encoding":904},[883,74099,74101],{"className":74100},[886],[888,74102,74103],{"xmlns":890},[892,74104,74105,74111],{},[895,74106,74107,74109],{},[898,74108,4512],{},[898,74110,1693],{},[902,74112,55800],{"encoding":904}," v jejím minimu.",[123,74115,74116,74025,74118,10646,74135,2263],{},[38,74117,63524],{},[883,74119,74121],{"className":74120},[886],[888,74122,74123],{"xmlns":890},[892,74124,74125,74133],{},[895,74126,74127,74129,74131],{},[898,74128,4512],{},[898,74130,40579],{},[898,74132,1693],{},[902,74134,55551],{"encoding":904},[883,74136,74138],{"className":74137},[886],[888,74139,74140],{"xmlns":890},[892,74141,74142,74176],{},[895,74143,74144,74146,74148,74150,74152,74158,74160,74162,74164,74166,74168,74174],{},[898,74145,4512],{},[898,74147,40579],{},[898,74149,1693],{},[1688,74151,2066],{"stretchy":2065},[1788,74153,74154,74156],{},[898,74155,1872],{},[1793,74157,1779],{},[1688,74159,2076],{"stretchy":2065},[1688,74161,1690],{},[898,74163,1661],{},[898,74165,1693],{},[1688,74167,2066],{"stretchy":2065},[1788,74169,74170,74172],{},[898,74171,1872],{},[1793,74173,1779],{},[1688,74175,2076],{"stretchy":2065},[902,74177,69259],{"encoding":904},[123,74179,74180,2170,74182,74209],{},[38,74181,63703],{},[883,74183,74185],{"className":74184},[886],[888,74186,74187],{"xmlns":890},[892,74188,74189,74207],{},[895,74190,74191,74193,74195,74197,74199,74201,74203,74205],{},[898,74192,1727],{},[898,74194,4251],{},[1688,74196,1690],{},[898,74198,3035],{},[898,74200,4251],{},[1688,74202,1954],{},[898,74204,3035],{},[898,74206,1693],{},[902,74208,55440],{"encoding":904}," — rozdíl mezi celkovým příjmem a celkovými náklady.",[123,74211,74212,10277,74214,74216,74217,74243,74244,74269],{},[38,74213,64565],{},[614,74215,63828],{},") — hodnoty ",[883,74218,74220],{"className":74219},[886],[888,74221,74222],{"xmlns":890},[892,74223,74224,74240],{},[895,74225,74226,74232,74234],{},[1788,74227,74228,74230],{},[898,74229,1872],{},[898,74231,4512],{},[1688,74233,1733],{"separator":1732},[1788,74235,74236,74238],{},[898,74237,1872],{},[898,74239,23494],{},[902,74241,74242],{"encoding":904},"Q_A, Q_B"," splňující ",[883,74245,74247],{"className":74246},[886],[888,74248,74249],{"xmlns":890},[892,74250,74251,74267],{},[895,74252,74253,74255,74257,74259,74261,74263,74265],{},[898,74254,1727],{},[898,74256,4251],{},[1688,74258,2066],{"stretchy":2065},[898,74260,1872],{},[1688,74262,2076],{"stretchy":2065},[1688,74264,1690],{},[1793,74266,1779],{},[902,74268,64105],{"encoding":904},"; oddělují pásma ztráty a zisku.",[123,74271,74272,74275],{},[38,74273,74274],{},"Práh rentability"," — stav firmy v bodě zvratu.",[123,74277,74278,74280,74281,10646,74298,74339],{},[38,74279,65619],{}," — v bodě maxima zisku ",[883,74282,74284],{"className":74283},[886],[888,74285,74286],{"xmlns":890},[892,74287,74288,74296],{},[895,74289,74290],{},[1788,74291,74292,74294],{},[898,74293,1872],{},[1793,74295,1779],{},[902,74297,38548],{"encoding":904},[883,74299,74301],{"className":74300},[886],[888,74302,74303],{"xmlns":890},[892,74304,74305,74337],{},[895,74306,74307,74309,74311,74313,74319,74321,74323,74325,74327,74329,74335],{},[898,74308,1661],{},[898,74310,4251],{},[1688,74312,2066],{"stretchy":2065},[1788,74314,74315,74317],{},[898,74316,1872],{},[1793,74318,1779],{},[1688,74320,2076],{"stretchy":2065},[1688,74322,1690],{},[898,74324,1661],{},[898,74326,1693],{},[1688,74328,2066],{"stretchy":2065},[1788,74330,74331,74333],{},[898,74332,1872],{},[1793,74334,1779],{},[1688,74336,2076],{"stretchy":2065},[902,74338,65885],{"encoding":904}," (3.13).",[123,74341,74342,20542,74344,10646,74363,74388],{},[38,74343,66912],{},[883,74345,74347],{"className":74346},[886],[888,74348,74349],{"xmlns":890},[892,74350,74351,74360],{},[895,74352,74353,74355,74357],{},[898,74354,1727],{},[1688,74356,1690],{},[2041,74358,74359],{},"konst",[902,74361,74362],{"encoding":904},"P = \\text{konst}",[883,74364,74366],{"className":74365},[886],[888,74367,74368],{"xmlns":890},[892,74369,74370,74386],{},[895,74371,74372,74374,74376,74378,74380,74382,74384],{},[898,74373,1727],{},[1688,74375,1690],{},[898,74377,1661],{},[898,74379,1693],{},[1688,74381,2066],{"stretchy":2065},[898,74383,1872],{},[1688,74385,2076],{"stretchy":2065},[902,74387,67606],{"encoding":904}," (3.14).",[123,74390,74391,74394,74395,74424,74425,74442],{},[38,74392,74393],{},"Shutdown point"," — bod ",[883,74396,74398],{"className":74397},[886],[888,74399,74400],{"xmlns":890},[892,74401,74402,74422],{},[895,74403,74404,74406,74412,74414,74420],{},[1688,74405,2066],{"stretchy":2065},[1850,74407,74408,74410],{},[898,74409,1872],{},[1688,74411,1857],{},[1688,74413,1733],{"separator":1732},[1850,74415,74416,74418],{},[898,74417,1727],{},[1688,74419,1857],{},[1688,74421,2076],{"stretchy":2065},[902,74423,67895],{"encoding":904}," v minimu ",[883,74426,74428],{"className":74427},[886],[888,74429,74430],{"xmlns":890},[892,74431,74432,74440],{},[895,74433,74434,74436,74438],{},[898,74435,4512],{},[898,74437,40579],{},[898,74439,1693],{},[902,74441,55551],{"encoding":904},"; pod ním se firmě nevyplatí produkovat.",[123,74444,74445,2170,74448,6729,74483,68165,74504,74517,74518,74533,74534,2263],{},[38,74446,74447],{},"Funkce nabídky firmy",[883,74449,74451],{"className":74450},[886],[888,74452,74453],{"xmlns":890},[892,74454,74455,74481],{},[895,74456,74457,74459,74461,74463,74465,74467,74469,74471,74473,74475,74477,74479],{},[898,74458,1727],{},[1688,74460,1690],{},[898,74462,1740],{},[1688,74464,2066],{"stretchy":2065},[898,74466,1872],{},[1688,74468,2076],{"stretchy":2065},[1688,74470,1690],{},[898,74472,1661],{},[898,74474,1693],{},[1688,74476,2066],{"stretchy":2065},[898,74478,1872],{},[1688,74480,2076],{"stretchy":2065},[902,74482,69362],{"encoding":904},[883,74484,74486],{"className":74485},[886],[888,74487,74488],{"xmlns":890},[892,74489,74490,74502],{},[895,74491,74492,74494,74496],{},[898,74493,1872],{},[1688,74495,4741],{},[1850,74497,74498,74500],{},[898,74499,1872],{},[1688,74501,1857],{},[902,74503,68164],{"encoding":904},[883,74505,74507],{"className":74506},[886],[888,74508,74509],{"xmlns":890},[892,74510,74511,74515],{},[895,74512,74513],{},[1793,74514,1779],{},[902,74516,1779],{"encoding":904}," (3.15); vychází z rostoucí části ",[883,74519,74521],{"className":74520},[886],[888,74522,74523],{"xmlns":890},[892,74524,74525,74531],{},[895,74526,74527,74529],{},[898,74528,1661],{},[898,74530,1693],{},[902,74532,55532],{"encoding":904}," nad minimem ",[883,74535,74537],{"className":74536},[886],[888,74538,74539],{"xmlns":890},[892,74540,74541,74549],{},[895,74542,74543,74545,74547],{},[898,74544,4512],{},[898,74546,40579],{},[898,74548,1693],{},[902,74550,55551],{"encoding":904},[123,74552,74553,7271,74555,74576,74577,2263],{},[38,74554,50319],{},[883,74556,74558],{"className":74557},[886],[888,74559,74560],{"xmlns":890},[892,74561,74562,74574],{},[895,74563,74564,74566,74568],{},[898,74565,1727],{},[1688,74567,1690],{},[1850,74569,74570,74572],{},[898,74571,1727],{},[1688,74573,1857],{},[902,74575,4613],{"encoding":904}," konstantní ⇒ ",[883,74578,74580],{"className":74579},[886],[888,74581,74582],{"xmlns":890},[892,74583,74584,74604],{},[895,74585,74586,74588,74590,74592,74594,74596,74598],{},[898,74587,4512],{},[898,74589,4251],{},[1688,74591,1690],{},[898,74593,1661],{},[898,74595,4251],{},[1688,74597,1690],{},[1850,74599,74600,74602],{},[898,74601,1727],{},[1688,74603,1857],{},[902,74605,58838],{"encoding":904},[123,74607,74608,74611],{},[38,74609,74610],{},"Cenová diskriminace"," — stanovení odlišných cen pro různé segmenty trhu za účelem maximalizace zisku (úlohy 3.24–3.25).",[115,74613,4049],{"id":4048},[120,74615,74616,74635,74647],{},[123,74617,74618,2170,74620,1343,74623,1343,74626,1343,74629,1343,74632],{},[38,74619,50963],{},[207,74621,12193],{"className":74622,"dataFsResolvedFilePath":800,"href":801},[210],[207,74624,4084],{"className":74625,"dataFsResolvedFilePath":848,"href":849},[210],[207,74627,2622],{"className":74628,"dataFsResolvedFilePath":764,"href":765},[210],[207,74630,775],{"className":74631,"dataFsResolvedFilePath":773,"href":774},[210],[207,74633,859],{"className":74634,"dataFsResolvedFilePath":857,"href":858},[210],[123,74636,74637,2170,74639,1343,74643],{},[38,74638,36943],{},[207,74640,74642],{"className":74641,"dataFsResolvedFilePath":745,"href":746},[210],"KS 1. blok — souhrn",[207,74644,74646],{"className":74645,"dataFsResolvedFilePath":838,"href":839},[210],"KS 2. blok — souhrn",[123,74648,74649,2170,74651],{},[38,74650,16451],{},[207,74652,16455],{"className":74653,"dataFsResolvedFilePath":2210,"href":2211},[210],{"title":641,"searchDepth":642,"depth":642,"links":74655},[74656,74657,74664,74670,74674,74675,74679,74680,74681,74682,74688,74689],{"id":51194,"depth":642,"text":1241},{"id":55978,"depth":642,"text":55979,"children":74658},[74659,74660,74661,74662,74663],{"id":55989,"depth":649,"text":55990},{"id":56575,"depth":649,"text":56576},{"id":56723,"depth":649,"text":56724},{"id":57465,"depth":649,"text":57466},{"id":58120,"depth":649,"text":58121},{"id":58841,"depth":642,"text":58842,"children":74665},[74666,74667,74668,74669],{"id":58845,"depth":649,"text":58846},{"id":59006,"depth":649,"text":59007},{"id":60193,"depth":649,"text":60194},{"id":61091,"depth":649,"text":61092},{"id":62173,"depth":642,"text":62174,"children":74671},[74672,74673],{"id":16658,"depth":649,"text":16659},{"id":63523,"depth":649,"text":63524},{"id":63697,"depth":642,"text":63698},{"id":65618,"depth":642,"text":65619,"children":74676},[74677,74678],{"id":65632,"depth":649,"text":16659},{"id":66911,"depth":649,"text":66912},{"id":67543,"depth":642,"text":67544},{"id":69009,"depth":642,"text":69010},{"id":50121,"depth":642,"text":50122},{"id":69470,"depth":642,"text":69471,"children":74683},[74684,74685,74686,74687],{"id":69474,"depth":649,"text":69475},{"id":70326,"depth":649,"text":70327},{"id":71872,"depth":649,"text":71873},{"id":73248,"depth":649,"text":73249},{"id":15966,"depth":642,"text":15967},{"id":4048,"depth":642,"text":4049},{},"\u002Ftopics\u002Fprijem-naklady-zisk",{"title":55360,"description":641},[1138,1135],"topics\u002Fprijem-naklady-zisk",[1128,74696,74697,55412,74698,74699,74700],"prijem","naklady","body-zvratu","maximalizace-zisku","nabidka-firmy","0d2CjMGyTT-GeTvSE65iXk5mUJ-650ilVskfuGcRAwI",{"id":74703,"title":74704,"body":74705,"course":1128,"courses":659,"created":9809,"description":641,"extension":661,"meta":86802,"navigation":664,"path":86803,"seo":86804,"sources":86805,"stem":86806,"tags":86807,"type":4113,"updated":677,"__hash__":86813},"topics\u002Ftopics\u002Fprodukce.md","Produkce — produkční funkce, Cobb-Douglas, MRTS",{"type":9,"value":74706,"toc":86759},[74707,74710,75066,75070,75073,75141,75193,75203,75207,75241,75282,75306,75329,75358,75425,75532,75575,75632,75707,75752,75756,75764,75772,75775,76040,76091,76171,76241,76264,76292,76337,76359,76363,76370,76419,76445,76596,76599,76636,76799,76907,76911,76948,77023,77092,77211,77333,77414,77420,77461,77534,77627,77631,77667,77755,77869,77974,78059,78199,78203,78251,78296,78302,78306,78309,78360,78410,78417,78483,78616,78661,78665,78686,79065,79160,79177,79231,79235,79317,79401,79571,79574,79617,79684,79758,79762,79767,79836,79844,79853,79931,79997,80002,80097,80140,80145,80193,80198,80246,80364,80447,80485,80588,80647,80788,80792,80835,80908,80932,80986,80993,80995,81040,81085,81096,81101,81137,81199,81222,81231,81332,81399,81472,81479,81570,81632,81668,81725,81784,81969,82065,82069,82073,82152,82157,82281,82367,82373,82483,82520,82611,82709,82712,82716,82782,82819,82941,82993,82997,83025,83077,83151,83256,83280,83339,83343,83361,83504,83652,83654,83689,83693,83695,83785,83915,84041,84133,84208,84212,84328,84432,84622,84658,84752,84758,84871,85174,85180,85298,85397,85473,85475,86637,86639],[12,74708,74704],{"id":74709},"produkce-produkční-funkce-cobb-douglas-mrts",[4124,74711,74712],{},[724,74713,74714,4131,74716,74718,74719,37136,74732,74745,74746,16623,74759,10277,74761,74785,74786,2170,74788,4142,74822,2170,74825,74853,74854,10646,74874,74904,74905,10277,74908,74936,74937,74940,74941,74971,74972,75002,75003,2170,75006,75046,75047,75065],{},[883,74715,4130],{},[38,74717,859],{}," popisuje vztah mezi vstupy (práce ",[883,74720,74722],{"className":74721},[886],[888,74723,74724],{"xmlns":890},[892,74725,74726,74730],{},[895,74727,74728],{},[898,74729,10047],{},[902,74731,10047],{"encoding":904},[883,74733,74735],{"className":74734},[886],[888,74736,74737],{"xmlns":890},[892,74738,74739,74743],{},[895,74740,74741],{},[898,74742,10052],{},[902,74744,10052],{"encoding":904},") a výstupem ",[883,74747,74749],{"className":74748},[886],[888,74750,74751],{"xmlns":890},[892,74752,74753,74757],{},[895,74754,74755],{},[898,74756,1872],{},[902,74758,1872],{"encoding":904},[38,74760,37204],{},[883,74762,74764],{"className":74763},[886],[888,74765,74766],{"xmlns":890},[892,74767,74768,74782],{},[895,74769,74770,74772,74774,74776,74778,74780],{},[898,74771,1872],{},[1688,74773,1690],{},[898,74775,1872],{},[1688,74777,2066],{"stretchy":2065},[898,74779,10047],{},[1688,74781,2076],{"stretchy":2065},[902,74783,74784],{"encoding":904},"Q = Q(L)",") studujeme ",[614,74787,10276],{},[883,74789,74791],{"className":74790},[886],[888,74792,74793],{"xmlns":890},[892,74794,74795,74819],{},[895,74796,74797,74799,74805,74807,74813,74815,74817],{},[898,74798,1661],{},[1788,74800,74801,74803],{},[898,74802,1727],{},[898,74804,10047],{},[1688,74806,1690],{},[1850,74808,74809,74811],{},[898,74810,1872],{},[1688,74812,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,74814,2066],{"stretchy":2065},[898,74816,10047],{},[1688,74818,2076],{"stretchy":2065},[902,74820,74821],{"encoding":904},"MP_L = Q'(L)",[614,74823,74824],{},"průměrný produkt",[883,74826,74828],{"className":74827},[886],[888,74829,74830],{"xmlns":890},[892,74831,74832,74850],{},[895,74833,74834,74836,74842,74844,74846,74848],{},[898,74835,4512],{},[1788,74837,74838,74840],{},[898,74839,1727],{},[898,74841,10047],{},[1688,74843,1690],{},[898,74845,1872],{},[898,74847,4930],{"mathvariant":1822},[898,74849,10047],{},[902,74851,74852],{"encoding":904},"AP_L = Q\u002FL","; v maximu ",[883,74855,74857],{"className":74856},[886],[888,74858,74859],{"xmlns":890},[892,74860,74861,74871],{},[895,74862,74863,74865],{},[898,74864,4512],{},[1788,74866,74867,74869],{},[898,74868,1727],{},[898,74870,10047],{},[902,74872,74873],{"encoding":904},"AP_L",[883,74875,74877],{"className":74876},[886],[888,74878,74879],{"xmlns":890},[892,74880,74881,74901],{},[895,74882,74883,74885,74891,74893,74895],{},[898,74884,1661],{},[1788,74886,74887,74889],{},[898,74888,1727],{},[898,74890,10047],{},[1688,74892,1690],{},[898,74894,4512],{},[1788,74896,74897,74899],{},[898,74898,1727],{},[898,74900,10047],{},[902,74902,74903],{"encoding":904},"MP_L = AP_L",". Ve ",[38,74906,74907],{},"dvoufaktorovém modelu",[883,74909,74911],{"className":74910},[886],[888,74912,74913],{"xmlns":890},[892,74914,74915,74933],{},[895,74916,74917,74919,74921,74923,74925,74927,74929,74931],{},[898,74918,1872],{},[1688,74920,1690],{},[898,74922,1872],{},[1688,74924,2066],{"stretchy":2065},[898,74926,10047],{},[1688,74928,1733],{"separator":1732},[898,74930,10052],{},[1688,74932,2076],{"stretchy":2065},[902,74934,74935],{"encoding":904},"Q = Q(L,K)",") dominují ",[38,74938,74939],{},"Cobb-Douglasovy"," funkce ",[883,74942,74944],{"className":74943},[886],[888,74945,74946],{"xmlns":890},[892,74947,74948,74968],{},[895,74949,74950,74952,74954,74956,74962],{},[898,74951,1872],{},[1688,74953,1690],{},[898,74955,4512],{},[1850,74957,74958,74960],{},[898,74959,10047],{},[898,74961,207],{},[1850,74963,74964,74966],{},[898,74965,10052],{},[898,74967,1918],{},[902,74969,74970],{"encoding":904},"Q = AL^a K^b","; mezní produkty ",[883,74973,74975],{"className":74974},[886],[888,74976,74977],{"xmlns":890},[892,74978,74979,74999],{},[895,74980,74981,74983,74989,74991,74993],{},[898,74982,1661],{},[1788,74984,74985,74987],{},[898,74986,1727],{},[898,74988,10047],{},[1688,74990,1733],{"separator":1732},[898,74992,1661],{},[1788,74994,74995,74997],{},[898,74996,1727],{},[898,74998,10052],{},[902,75000,75001],{"encoding":904},"MP_L, MP_K"," jsou parciální derivace a jejich podíl dává ",[38,75004,75005],{},"mezní míru technické substituce",[883,75007,75009],{"className":75008},[886],[888,75010,75011],{"xmlns":890},[892,75012,75013,75043],{},[895,75014,75015,75017,75019,75021,75023,75025,75027,75033,75035,75037],{},[898,75016,1661],{},[898,75018,4251],{},[898,75020,3035],{},[898,75022,1740],{},[1688,75024,1690],{},[898,75026,1661],{},[1788,75028,75029,75031],{},[898,75030,1727],{},[898,75032,10047],{},[898,75034,4930],{"mathvariant":1822},[898,75036,1661],{},[1788,75038,75039,75041],{},[898,75040,1727],{},[898,75042,10052],{},[902,75044,75045],{"encoding":904},"MRTS = MP_L\u002FMP_K"," — sklon izokvanty. Součet exponentů ",[883,75048,75050],{"className":75049},[886],[888,75051,75052],{"xmlns":890},[892,75053,75054,75062],{},[895,75055,75056,75058,75060],{},[898,75057,207],{},[1688,75059,1696],{},[898,75061,1918],{},[902,75063,75064],{"encoding":904},"a+b"," určuje typ výnosů z rozsahu.",[115,75067,75069],{"id":75068},"úvod-cílové-znalosti-kapitoly-5","Úvod — cílové znalosti kapitoly 5",[724,75071,75072],{},"Po prostudování kapitoly 5 student umí:",[120,75074,75075,75081,75091,75097,75103,75108,75114,75124,75129,75135],{},[123,75076,75077,75078,1733],{},"popsat ",[38,75079,75080],{},"jednofaktorový model produkce",[123,75082,75083,75084,4142,75087,75090],{},"vypočítat ",[38,75085,75086],{},"mezní",[38,75088,75089],{},"průměrný produkt práce"," a ekonomicky je interpretovat,",[123,75092,75093,75094,1733],{},"charakterizovat průběh ",[38,75095,75096],{},"křivky produkce",[123,75098,75099,75100,1733],{},"formulovat ",[38,75101,75102],{},"princip maximalizace průměrného produktu práce",[123,75104,75077,75105,1733],{},[38,75106,75107],{},"dvoufaktorový model produkce",[123,75109,75110,75111,1733],{},"uvést tvar ",[38,75112,75113],{},"Cobb–Douglasových produkčních funkcí",[123,75115,75116,75117,1343,75119,1343,75121,1733],{},"vyložit, co jsou ",[38,75118,24854],{},[38,75120,13904],{},[38,75122,75123],{},"klesající výnosy z rozsahu",[123,75125,75083,75126,75090],{},[38,75127,75128],{},"mezní produkty práce a kapitálu",[123,75130,75131,75132,1733],{},"najít ",[38,75133,75134],{},"izokvanty",[123,75136,75083,75137,75140],{},[38,75138,75139],{},"mezní míru technické substituce (MRTS)"," a ekonomicky ji interpretovat.",[724,75142,75143,75144,75147,75148,75151,75152,2170,75155,1343,75168,2170,75171,4142,75184,75187,75188,75190,75191,2263],{},"Každý proces produkce je určován ",[38,75145,75146],{},"faktory"," (též ",[38,75149,75150],{},"vstupy",") produkce. K hlavním patří ",[38,75153,75154],{},"práce",[883,75156,75158],{"className":75157},[886],[888,75159,75160],{"xmlns":890},[892,75161,75162,75166],{},[895,75163,75164],{},[898,75165,10047],{},[902,75167,10047],{"encoding":904},[38,75169,75170],{},"kapitál",[883,75172,75174],{"className":75173},[886],[888,75175,75176],{"xmlns":890},[892,75177,75178,75182],{},[895,75179,75180],{},[898,75181,10052],{},[902,75183,10052],{"encoding":904},[38,75185,75186],{},"půda",". Při modelování se půda obvykle považuje za dlouhodobě konstantní, takže endogenními faktory zůstávají práce a kapitál. Je-li kapitál neměnný, hovoříme o ",[38,75189,37204],{}," (produkce závisí jen na práci); v opačném případě o ",[38,75192,74907],{},[724,75194,75195,75196,1343,75199,75202],{},"Související matematický aparát: ",[207,75197,2622],{"className":75198,"dataFsResolvedFilePath":764,"href":765},[210],[207,75200,784],{"className":75201,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace a totální diferenciál).",[115,75204,75206],{"id":75205},"jednofaktorový-model-produkce","Jednofaktorový model produkce",[724,75208,75209,75210,75223,75224,75237,75238],{},"Uvažujeme proces v krátkém období, kdy kapitál lze považovat za konstantní. Závislost produkce ",[883,75211,75213],{"className":75212},[886],[888,75214,75215],{"xmlns":890},[892,75216,75217,75221],{},[895,75218,75219],{},[898,75220,1872],{},[902,75222,1872],{"encoding":904}," na práci ",[883,75225,75227],{"className":75226},[886],[888,75228,75229],{"xmlns":890},[892,75230,75231,75235],{},[895,75232,75233],{},[898,75234,10047],{},[902,75236,10047],{"encoding":904}," vyjadřuje ",[38,75239,75240],{},"produkční funkce",[883,75242,75244],{"className":75243},[886],[888,75245,75246],{"xmlns":890,"display":28306},[892,75247,75248,75279],{},[20995,75249,75250],{"width":28311},[21000,75251,75252,75254,75272,75274],{},[21003,75253],{"width":28316},[21003,75255,75256],{},[895,75257,75258,75260,75262,75264,75266,75268,75270],{},[898,75259,1872],{},[1688,75261,1690],{},[898,75263,1872],{},[1688,75265,2066],{"stretchy":2065},[898,75267,10047],{},[1688,75269,2076],{"stretchy":2065},[1688,75271,1733],{"separator":1732},[21003,75273],{"width":28316},[21003,75275,75276],{},[2041,75277,75278],{},"(5.1)",[902,75280,75281],{"encoding":904},"Q = Q(L), \\tag{5.1}",[724,75283,75284,75285,10277,75288,75291,75292,75305],{},"jejíž graf se nazývá ",[38,75286,75287],{},"křivka produkce",[614,75289,75290],{},"production curve","). Práce ",[883,75293,75295],{"className":75294},[886],[888,75296,75297],{"xmlns":890},[892,75298,75299,75303],{},[895,75300,75301],{},[898,75302,10047],{},[902,75304,10047],{"encoding":904}," se měří počtem pracovníků, případně počtem pracovních hodin.",[115,75307,75309,75310,2076],{"id":75308},"mezní-produkt-práce-mplmp_l","Mezní produkt práce (",[883,75311,75313],{"className":75312},[886],[888,75314,75315],{"xmlns":890},[892,75316,75317,75327],{},[895,75318,75319,75321],{},[898,75320,1661],{},[1788,75322,75323,75325],{},[898,75324,1727],{},[898,75326,10047],{},[902,75328,10297],{"encoding":904},[724,75330,75331,10277,75334,75337,75338,75357],{},[38,75332,75333],{},"Mezní produkt práce",[614,75335,75336],{},"marginal product of labour",") ",[883,75339,75341],{"className":75340},[886],[888,75342,75343],{"xmlns":890},[892,75344,75345,75355],{},[895,75346,75347,75349],{},[898,75348,1661],{},[1788,75350,75351,75353],{},[898,75352,1727],{},[898,75354,10047],{},[902,75356,10297],{"encoding":904}," je derivace produkce podle práce:",[883,75359,75361],{"className":75360},[886],[888,75362,75363],{"xmlns":890,"display":28306},[892,75364,75365,75422],{},[20995,75366,75367],{"width":28311},[21000,75368,75369,75371,75415,75417],{},[21003,75370],{"width":28316},[21003,75372,75373],{},[895,75374,75375,75377,75383,75385,75399,75401,75407,75409,75411,75413],{},[898,75376,1661],{},[1788,75378,75379,75381],{},[898,75380,1727],{},[898,75382,10047],{},[1688,75384,1690],{},[1781,75386,75387,75393],{},[895,75388,75389,75391],{},[898,75390,2073],{},[898,75392,1872],{},[895,75394,75395,75397],{},[898,75396,2073],{},[898,75398,10047],{},[1688,75400,1690],{},[1850,75402,75403,75405],{},[898,75404,1872],{},[1688,75406,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,75408,2066],{"stretchy":2065},[898,75410,10047],{},[1688,75412,2076],{"stretchy":2065},[898,75414,2263],{"mathvariant":1822},[21003,75416],{"width":28316},[21003,75418,75419],{},[2041,75420,75421],{},"(5.2)",[902,75423,75424],{"encoding":904},"MP_L = \\frac{dQ}{dL} = Q'(L). \\tag{5.2}",[724,75426,75427,75428,20186,75446,75474,75475,75492,75493,2946,75510,4176],{},"Pro pevnou hodnotu ",[883,75429,75431],{"className":75430},[886],[888,75432,75433],{"xmlns":890},[892,75434,75435,75443],{},[895,75436,75437],{},[1850,75438,75439,75441],{},[898,75440,10047],{},[1688,75442,1857],{},[902,75444,75445],{"encoding":904},"L^*",[883,75447,75449],{"className":75448},[886],[888,75450,75451],{"xmlns":890},[892,75452,75453,75471],{},[895,75454,75455,75461,75463,75469],{},[1850,75456,75457,75459],{},[898,75458,1872],{},[1688,75460,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,75462,2066],{"stretchy":2065},[1850,75464,75465,75467],{},[898,75466,10047],{},[1688,75468,1857],{},[1688,75470,2076],{"stretchy":2065},[902,75472,75473],{"encoding":904},"Q'(L^*)"," rychlost změny produkce vzhledem k práci v bodě ",[883,75476,75478],{"className":75477},[886],[888,75479,75480],{"xmlns":890},[892,75481,75482,75490],{},[895,75483,75484],{},[1850,75485,75486,75488],{},[898,75487,10047],{},[1688,75489,1857],{},[902,75491,75445],{"encoding":904},", resp. přibližnou změnu produkce odpovídající jednotkové změně práce (z ",[883,75494,75496],{"className":75495},[886],[888,75497,75498],{"xmlns":890},[892,75499,75500,75508],{},[895,75501,75502],{},[1850,75503,75504,75506],{},[898,75505,10047],{},[1688,75507,1857],{},[902,75509,75445],{"encoding":904},[883,75511,75513],{"className":75512},[886],[888,75514,75515],{"xmlns":890},[892,75516,75517,75529],{},[895,75518,75519,75525,75527],{},[1850,75520,75521,75523],{},[898,75522,10047],{},[1688,75524,1857],{},[1688,75526,1696],{},[1793,75528,1795],{},[902,75530,75531],{"encoding":904},"L^*+1",[4124,75533,75534],{},[724,75535,75536,18265,75538,75557,75558,75561,75562,2263],{},[883,75537,4412],{},[883,75539,75541],{"className":75540},[886],[888,75542,75543],{"xmlns":890},[892,75544,75545,75555],{},[895,75546,75547,75549],{},[898,75548,1661],{},[1788,75550,75551,75553],{},[898,75552,1727],{},[898,75554,10047],{},[902,75556,10297],{"encoding":904}," odpovídá na otázku „",[38,75559,75560],{},"kolik produkce přibude, když přidám jednoho dalšího pracovníka"," (při neměnném kapitálu)?\". Je to sklon křivky produkce v bodě ",[883,75563,75565],{"className":75564},[886],[888,75566,75567],{"xmlns":890},[892,75568,75569,75573],{},[895,75570,75571],{},[898,75572,10047],{},[902,75574,10047],{"encoding":904},[724,75576,75577,75580,75581,75597,75598,2946,75611,75631],{},[38,75578,75579],{},"Přibližná změna produkce"," pro změnu práce o ",[883,75582,75584],{"className":75583},[886],[888,75585,75586],{"xmlns":890},[892,75587,75588,75594],{},[895,75589,75590,75592],{},[898,75591,2073],{},[898,75593,10047],{},[902,75595,75596],{"encoding":904},"dL"," (z ",[883,75599,75601],{"className":75600},[886],[888,75602,75603],{"xmlns":890},[892,75604,75605,75609],{},[895,75606,75607],{},[898,75608,10047],{},[902,75610,10047],{"encoding":904},[883,75612,75614],{"className":75613},[886],[888,75615,75616],{"xmlns":890},[892,75617,75618,75628],{},[895,75619,75620,75622,75624,75626],{},[898,75621,10047],{},[1688,75623,1696],{},[898,75625,2073],{},[898,75627,10047],{},[902,75629,75630],{"encoding":904},"L+dL",") pomocí diferenciálu:",[883,75633,75635],{"className":75634},[886],[888,75636,75637],{"xmlns":890,"display":28306},[892,75638,75639,75704],{},[20995,75640,75641],{"width":28311},[21000,75642,75643,75645,75697,75699],{},[21003,75644],{"width":28316},[21003,75646,75647],{},[895,75648,75649,75651,75653,75655,75657,75659,75661,75667,75669,75671,75673,75675,75677,75679,75681,75683,75689,75691,75693,75695],{},[898,75650,3147],{"mathvariant":1822},[898,75652,1872],{},[1688,75654,2991],{},[898,75656,2073],{},[898,75658,1872],{},[1688,75660,1690],{},[1850,75662,75663,75665],{},[898,75664,1872],{},[1688,75666,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,75668,2066],{"stretchy":2065},[898,75670,10047],{},[1688,75672,2076],{"stretchy":2065},[2041,75674,2043],{},[898,75676,2073],{},[898,75678,10047],{},[1688,75680,1690],{},[898,75682,1661],{},[1788,75684,75685,75687],{},[898,75686,1727],{},[898,75688,10047],{},[2041,75690,2043],{},[898,75692,2073],{},[898,75694,10047],{},[898,75696,2263],{"mathvariant":1822},[21003,75698],{"width":28316},[21003,75700,75701],{},[2041,75702,75703],{},"(5.3)",[902,75705,75706],{"encoding":904},"\\Delta Q \\approx dQ = Q'(L)\\,dL = MP_L\\,dL. \\tag{5.3}",[724,75708,75709,75710,2263],{},"Skutečná změna je ",[883,75711,75713],{"className":75712},[886],[888,75714,75715],{"xmlns":890},[892,75716,75717,75749],{},[895,75718,75719,75721,75723,75725,75727,75729,75731,75733,75735,75737,75739,75741,75743,75745,75747],{},[898,75720,3147],{"mathvariant":1822},[898,75722,1872],{},[1688,75724,1690],{},[898,75726,1872],{},[1688,75728,2066],{"stretchy":2065},[898,75730,10047],{},[1688,75732,1696],{},[898,75734,2073],{},[898,75736,10047],{},[1688,75738,2076],{"stretchy":2065},[1688,75740,1954],{},[898,75742,1872],{},[1688,75744,2066],{"stretchy":2065},[898,75746,10047],{},[1688,75748,2076],{"stretchy":2065},[902,75750,75751],{"encoding":904},"\\Delta Q = Q(L+dL) - Q(L)",[198,75753,75755],{"id":75754},"zákon-klesajících-mezních-výnosů","Zákon klesajících mezních výnosů",[724,75757,75758,10277,75761,3408],{},[38,75759,75760],{},"Zákon klesajících výnosů",[614,75762,75763],{},"law of diminishing marginal productivity",[4124,75765,75766],{},[724,75767,75768,75769,75771],{},"Roste-li postupně některý ze vstupů (",[614,75770,37200],{},"), budou přírůstky výstupu od jistého bodu klesat.",[724,75773,75774],{},"Typická křivka produkce (Obrázek 5.2) má dvě fáze:",[724,75776,75777,75778,2170,75799,75818,75819,75869,75870,75872,75873,2170,75893,75912,75913,75869,75945,3185,75947,75966,75967,21835,75984,76018,76019,8358,76036,76039],{},"1° ",[38,75779,75780,75781,2965],{},"Do bodu ",[883,75782,75784],{"className":75783},[886],[888,75785,75786],{"xmlns":890},[892,75787,75788,75796],{},[895,75789,75790],{},[1788,75791,75792,75794],{},[898,75793,10047],{},[1793,75795,1779],{},[902,75797,75798],{"encoding":904},"L_0",[883,75800,75802],{"className":75801},[886],[888,75803,75804],{"xmlns":890},[892,75805,75806,75816],{},[895,75807,75808,75810],{},[898,75809,1661],{},[1788,75811,75812,75814],{},[898,75813,1727],{},[898,75815,10047],{},[902,75817,10297],{"encoding":904}," roste, tj. ",[883,75820,75822],{"className":75821},[886],[888,75823,75824],{"xmlns":890},[892,75825,75826,75866],{},[895,75827,75828,75830,75832,75838,75844,75846,75856,75858,75860,75862,75864],{},[1688,75829,2066],{"stretchy":2065},[898,75831,1661],{},[1788,75833,75834,75836],{},[898,75835,1727],{},[898,75837,10047],{},[1850,75839,75840,75842],{},[1688,75841,2076],{"stretchy":2065},[1688,75843,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,75845,1690],{},[1850,75847,75848,75850],{},[898,75849,1872],{},[895,75851,75852,75854],{},[1688,75853,1824],{"mathvariant":1822},[1688,75855,1824],{"mathvariant":1822},[1688,75857,2066],{"stretchy":2065},[898,75859,10047],{},[1688,75861,2076],{"stretchy":2065},[1688,75863,3665],{},[1793,75865,1779],{},[902,75867,75868],{"encoding":904},"(MP_L)' = Q''(L) > 0"," — křivka produkce je ",[38,75871,37904],{},".\n2° ",[38,75874,75875,75876,2965],{},"Od bodu ",[883,75877,75879],{"className":75878},[886],[888,75880,75881],{"xmlns":890},[892,75882,75883,75891],{},[895,75884,75885],{},[1788,75886,75887,75889],{},[898,75888,10047],{},[1793,75890,1779],{},[902,75892,75798],{"encoding":904},[883,75894,75896],{"className":75895},[886],[888,75897,75898],{"xmlns":890},[892,75899,75900,75910],{},[895,75901,75902,75904],{},[898,75903,1661],{},[1788,75905,75906,75908],{},[898,75907,1727],{},[898,75909,10047],{},[902,75911,10297],{"encoding":904}," klesá, ",[883,75914,75916],{"className":75915},[886],[888,75917,75918],{"xmlns":890},[892,75919,75920,75942],{},[895,75921,75922,75932,75934,75936,75938,75940],{},[1850,75923,75924,75926],{},[898,75925,1872],{},[895,75927,75928,75930],{},[1688,75929,1824],{"mathvariant":1822},[1688,75931,1824],{"mathvariant":1822},[1688,75933,2066],{"stretchy":2065},[898,75935,10047],{},[1688,75937,2076],{"stretchy":2065},[1688,75939,3704],{},[1793,75941,1779],{},[902,75943,75944],{"encoding":904},"Q''(L) \u003C 0",[38,75946,38728],{},[883,75948,75950],{"className":75949},[886],[888,75951,75952],{"xmlns":890},[892,75953,75954,75964],{},[895,75955,75956,75958],{},[898,75957,1661],{},[1788,75959,75960,75962],{},[898,75961,1727],{},[898,75963,10047],{},[902,75965,10297],{"encoding":904}," v kladných hodnotách klesá do bodu ",[883,75968,75970],{"className":75969},[886],[888,75971,75972],{"xmlns":890},[892,75973,75974,75982],{},[895,75975,75976],{},[1788,75977,75978,75980],{},[898,75979,10047],{},[1793,75981,1795],{},[902,75983,13460],{"encoding":904},[883,75985,75987],{"className":75986},[886],[888,75988,75989],{"xmlns":890},[892,75990,75991,76015],{},[895,75992,75993,75995,76001,76003,76009,76011,76013],{},[898,75994,1661],{},[1788,75996,75997,75999],{},[898,75998,1727],{},[898,76000,10047],{},[1688,76002,2066],{"stretchy":2065},[1788,76004,76005,76007],{},[898,76006,10047],{},[1793,76008,1795],{},[1688,76010,2076],{"stretchy":2065},[1688,76012,1690],{},[1793,76014,1779],{},[902,76016,76017],{"encoding":904},"MP_L(L_1) = 0"," (maximum produkce), a dále pokračuje v záporných hodnotách. Bod ",[883,76020,76022],{"className":76021},[886],[888,76023,76024],{"xmlns":890},[892,76025,76026,76034],{},[895,76027,76028],{},[1788,76029,76030,76032],{},[898,76031,10047],{},[1793,76033,1779],{},[902,76035,75798],{"encoding":904},[38,76037,76038],{},"inflexním bodem"," produkční funkce.",[724,76041,76042,76043,10646,76060,2263],{},"Matematicky: zákon klesajících výnosů znamená, že od určitého ",[883,76044,76046],{"className":76045},[886],[888,76047,76048],{"xmlns":890},[892,76049,76050,76058],{},[895,76051,76052],{},[1788,76053,76054,76056],{},[898,76055,10047],{},[1793,76057,1779],{},[902,76059,75798],{"encoding":904},[883,76061,76063],{"className":76062},[886],[888,76064,76065],{"xmlns":890},[892,76066,76067,76089],{},[895,76068,76069,76079,76081,76083,76085,76087],{},[1850,76070,76071,76073],{},[898,76072,1872],{},[895,76074,76075,76077],{},[1688,76076,1824],{"mathvariant":1822},[1688,76078,1824],{"mathvariant":1822},[1688,76080,2066],{"stretchy":2065},[898,76082,10047],{},[1688,76084,2076],{"stretchy":2065},[1688,76086,3704],{},[1793,76088,1779],{},[902,76090,75944],{"encoding":904},[724,76092,76093,2170,76096,5925,76136,1343,76153,76170],{},[38,76094,76095],{},"Typický polynom třetího stupně:",[883,76097,76099],{"className":76098},[886],[888,76100,76101],{"xmlns":890},[892,76102,76103,76133],{},[895,76104,76105,76107,76109,76111,76113,76115,76117,76123,76125,76127],{},[898,76106,1872],{},[1688,76108,2066],{"stretchy":2065},[898,76110,10047],{},[1688,76112,2076],{"stretchy":2065},[1688,76114,1690],{},[898,76116,207],{},[1850,76118,76119,76121],{},[898,76120,10047],{},[1793,76122,2131],{},[1688,76124,1696],{},[898,76126,1918],{},[1850,76128,76129,76131],{},[898,76130,10047],{},[1793,76132,1806],{},[902,76134,76135],{"encoding":904},"Q(L) = aL^3 + bL^2",[883,76137,76139],{"className":76138},[886],[888,76140,76141],{"xmlns":890},[892,76142,76143,76151],{},[895,76144,76145,76147,76149],{},[898,76146,207],{},[1688,76148,3704],{},[1793,76150,1779],{},[902,76152,43325],{"encoding":904},[883,76154,76156],{"className":76155},[886],[888,76157,76158],{"xmlns":890},[892,76159,76160,76168],{},[895,76161,76162,76164,76166],{},[898,76163,1918],{},[1688,76165,3665],{},[1793,76167,1779],{},[902,76169,19056],{"encoding":904},". Pak",[883,76172,76174],{"className":76173},[886],[888,76175,76176],{"xmlns":890,"display":28306},[892,76177,76178,76238],{},[895,76179,76180,76186,76188,76190,76198,76206,76208,76210,76216,76218,76220,76228,76236],{},[1788,76181,76182,76184],{},[898,76183,10047],{},[1793,76185,1779],{},[1688,76187,1690],{},[1688,76189,1954],{},[1777,76191,76192],{"scriptlevel":1779,"displaystyle":2065},[1781,76193,76194,76196],{},[1793,76195,1795],{},[1793,76197,2131],{},[1777,76199,76200],{"scriptlevel":1779,"displaystyle":2065},[1781,76201,76202,76204],{},[898,76203,1918],{},[898,76205,207],{},[1688,76207,1733],{"separator":1732},[6134,76209],{"width":6136},[1788,76211,76212,76214],{},[898,76213,10047],{},[1793,76215,1795],{},[1688,76217,1690],{},[1688,76219,1954],{},[1777,76221,76222],{"scriptlevel":1779,"displaystyle":2065},[1781,76223,76224,76226],{},[1793,76225,1806],{},[1793,76227,2131],{},[1777,76229,76230],{"scriptlevel":1779,"displaystyle":2065},[1781,76231,76232,76234],{},[898,76233,1918],{},[898,76235,207],{},[898,76237,2263],{"mathvariant":1822},[902,76239,76240],{"encoding":904},"L_0 = -\\tfrac{1}{3}\\tfrac{b}{a}, \\qquad L_1 = -\\tfrac{2}{3}\\tfrac{b}{a}.",[115,76242,76244,76245,2076],{"id":76243},"průměrný-produkt-práce-aplap_l","Průměrný produkt práce (",[883,76246,76248],{"className":76247},[886],[888,76249,76250],{"xmlns":890},[892,76251,76252,76262],{},[895,76253,76254,76256],{},[898,76255,4512],{},[1788,76257,76258,76260],{},[898,76259,1727],{},[898,76261,10047],{},[902,76263,74873],{"encoding":904},[724,76265,76266,10277,76269,75337,76272,76291],{},[38,76267,76268],{},"Průměrný produkt práce",[614,76270,76271],{},"average product of labour",[883,76273,76275],{"className":76274},[886],[888,76276,76277],{"xmlns":890},[892,76278,76279,76289],{},[895,76280,76281,76283],{},[898,76282,4512],{},[1788,76284,76285,76287],{},[898,76286,1727],{},[898,76288,10047],{},[902,76290,74873],{"encoding":904}," je podíl produkce a práce:",[883,76293,76295],{"className":76294},[886],[888,76296,76297],{"xmlns":890,"display":28306},[892,76298,76299,76334],{},[20995,76300,76301],{"width":28311},[21000,76302,76303,76305,76327,76329],{},[21003,76304],{"width":28316},[21003,76306,76307],{},[895,76308,76309,76311,76317,76319,76325],{},[898,76310,4512],{},[1788,76312,76313,76315],{},[898,76314,1727],{},[898,76316,10047],{},[1688,76318,1690],{},[1781,76320,76321,76323],{},[898,76322,1872],{},[898,76324,10047],{},[898,76326,2263],{"mathvariant":1822},[21003,76328],{"width":28316},[21003,76330,76331],{},[2041,76332,76333],{},"(5.4)",[902,76335,76336],{"encoding":904},"AP_L = \\frac{Q}{L}. \\tag{5.4}",[724,76338,76339,76340,2263],{},"Je to nejjednodušší míra produktivity práce. Cílem optimalizace je maximalizace ",[883,76341,76343],{"className":76342},[886],[888,76344,76345],{"xmlns":890},[892,76346,76347,76357],{},[895,76348,76349,76351],{},[898,76350,4512],{},[1788,76352,76353,76355],{},[898,76354,1727],{},[898,76356,10047],{},[902,76358,74873],{"encoding":904},[115,76360,76362],{"id":76361},"princip-maximalizace-průměrného-produktu-práce","Princip maximalizace průměrného produktu práce",[724,76364,76365],{},[2821,76366],{"alt":76367,"className":76368,"src":76369},"imek-q-mpl-apl-tripanel",[210,2825],"\u002Fwiki-assets\u002Fimek-q-mpl-apl-tripanel.jpeg",[4124,76371,76372],{},[724,76373,76374,76377,76378,2886,76397,76414,76415],{},[38,76375,76376],{},"Princip:"," Má-li ",[883,76379,76381],{"className":76380},[886],[888,76382,76383],{"xmlns":890},[892,76384,76385,76395],{},[895,76386,76387,76389],{},[898,76388,4512],{},[1788,76390,76391,76393],{},[898,76392,1727],{},[898,76394,10047],{},[902,76396,74873],{"encoding":904},[883,76398,76400],{"className":76399},[886],[888,76401,76402],{"xmlns":890},[892,76403,76404,76412],{},[895,76405,76406],{},[1788,76407,76408,76410],{},[898,76409,10047],{},[1793,76411,1779],{},[902,76413,75798],{"encoding":904}," maximum, pak platí\n",[883,76416,76418],{"className":76417,"title":4457,"style":4458},[4456],"MP_L(L_0) = AP_L(L_0). \\tag{5.5}",[724,76420,76421,76422,76425,76426,2170,76430,2263],{},"Slovně: ",[38,76423,76424],{},"v bodě maxima průměrného produktu práce se mezní produkt práce rovná průměrnému produktu práce."," Jde o analogii ",[207,76427,76429],{"className":76428,"dataFsResolvedFilePath":827,"href":828},[210],"principu minimalizace průměrných nákladů",[883,76431,76433],{"className":76432},[886],[888,76434,76435],{"xmlns":890},[892,76436,76437,76443],{},[895,76438,76439,76441],{},[898,76440,4512],{},[898,76442,1693],{},[902,76444,55800],{"encoding":904},[4124,76446,76447,76471],{},[724,76448,76449,76451,76452],{},[883,76450,4828],{}," Postup — jak najít max ",[883,76453,76455],{"className":76454},[886],[888,76456,76457],{"xmlns":890},[892,76458,76459,76469],{},[895,76460,76461,76463],{},[898,76462,4512],{},[1788,76464,76465,76467],{},[898,76466,1727],{},[898,76468,10047],{},[902,76470,74873],{"encoding":904},[152,76472,76473,76511,76593],{},[123,76474,76475,76476,76510],{},"Napište ",[883,76477,76479],{"className":76478},[886],[888,76480,76481],{"xmlns":890},[892,76482,76483,76507],{},[895,76484,76485,76487,76493,76495,76497,76499,76501,76503,76505],{},[898,76486,4512],{},[1788,76488,76489,76491],{},[898,76490,1727],{},[898,76492,10047],{},[1688,76494,1690],{},[898,76496,1872],{},[1688,76498,2066],{"stretchy":2065},[898,76500,10047],{},[1688,76502,2076],{"stretchy":2065},[898,76504,4930],{"mathvariant":1822},[898,76506,10047],{},[902,76508,76509],{"encoding":904},"AP_L = Q(L)\u002FL"," a zderivujte.",[123,76512,76513,76514,76546,76547,76550,76551,2263],{},"Položte ",[883,76515,76517],{"className":76516},[886],[888,76518,76519],{"xmlns":890},[892,76520,76521,76543],{},[895,76522,76523,76525,76527,76533,76539,76541],{},[1688,76524,2066],{"stretchy":2065},[898,76526,4512],{},[1788,76528,76529,76531],{},[898,76530,1727],{},[898,76532,10047],{},[1850,76534,76535,76537],{},[1688,76536,2076],{"stretchy":2065},[1688,76538,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,76540,1690],{},[1793,76542,1779],{},[902,76544,76545],{"encoding":904},"(AP_L)' = 0"," a vyřešte. ",[614,76548,76549],{},"Zkratka:"," můžete rovnou řešit ",[883,76552,76554],{"className":76553},[886],[888,76555,76556],{"xmlns":890},[892,76557,76558,76590],{},[895,76559,76560,76562,76568,76570,76572,76574,76576,76578,76584,76586,76588],{},[898,76561,1661],{},[1788,76563,76564,76566],{},[898,76565,1727],{},[898,76567,10047],{},[1688,76569,2066],{"stretchy":2065},[898,76571,10047],{},[1688,76573,2076],{"stretchy":2065},[1688,76575,1690],{},[898,76577,4512],{},[1788,76579,76580,76582],{},[898,76581,1727],{},[898,76583,10047],{},[1688,76585,2066],{"stretchy":2065},[898,76587,10047],{},[1688,76589,2076],{"stretchy":2065},[902,76591,76592],{"encoding":904},"MP_L(L) = AP_L(L)",[123,76594,76595],{},"Ověřte 2. derivací (či grafem), že jde o maximum.",[198,76597,65741],{"id":76598},"odvození",[724,76600,76601,76602,76635],{},"Z ",[883,76603,76605],{"className":76604},[886],[888,76606,76607],{"xmlns":890},[892,76608,76609,76633],{},[895,76610,76611,76613,76619,76621,76623,76625,76627,76629,76631],{},[898,76612,4512],{},[1788,76614,76615,76617],{},[898,76616,1727],{},[898,76618,10047],{},[1688,76620,1690],{},[898,76622,1872],{},[1688,76624,2066],{"stretchy":2065},[898,76626,10047],{},[1688,76628,2076],{"stretchy":2065},[898,76630,4930],{"mathvariant":1822},[898,76632,10047],{},[902,76634,76509],{"encoding":904}," a derivace podílu:",[883,76637,76639],{"className":76638},[886],[888,76640,76641],{"xmlns":890,"display":28306},[892,76642,76643,76796],{},[895,76644,76645,76647,76649,76655,76661,76663,76665,76667,76669,76709,76711,76717,76751,76753,76759,76762,76764,76770,76772,76774,76776,76778,76780,76786,76788,76790,76792,76794],{},[1688,76646,2066],{"stretchy":2065},[898,76648,4512],{},[1788,76650,76651,76653],{},[898,76652,1727],{},[898,76654,10047],{},[1850,76656,76657,76659],{},[1688,76658,2076],{"stretchy":2065},[1688,76660,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,76662,2066],{"stretchy":2065},[898,76664,10047],{},[1688,76666,2076],{"stretchy":2065},[1688,76668,1690],{},[1781,76670,76671,76703],{},[895,76672,76673,76679,76681,76683,76685,76687,76689,76691,76693,76695,76697,76699,76701],{},[1850,76674,76675,76677],{},[898,76676,1872],{},[1688,76678,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,76680,2066],{"stretchy":2065},[898,76682,10047],{},[1688,76684,2076],{"stretchy":2065},[1688,76686,3434],{},[898,76688,10047],{},[1688,76690,1954],{},[898,76692,1872],{},[1688,76694,2066],{"stretchy":2065},[898,76696,10047],{},[1688,76698,2076],{"stretchy":2065},[1688,76700,3434],{},[1793,76702,1795],{},[1850,76704,76705,76707],{},[898,76706,10047],{},[1793,76708,1806],{},[1688,76710,1690],{},[1781,76712,76713,76715],{},[1793,76714,1795],{},[898,76716,10047],{},[895,76718,76719,76721,76727,76729,76731,76733,76735,76749],{},[1688,76720,2066],{"fence":1732},[1850,76722,76723,76725],{},[898,76724,1872],{},[1688,76726,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,76728,2066],{"stretchy":2065},[898,76730,10047],{},[1688,76732,2076],{"stretchy":2065},[1688,76734,1954],{},[1781,76736,76737,76747],{},[895,76738,76739,76741,76743,76745],{},[898,76740,1872],{},[1688,76742,2066],{"stretchy":2065},[898,76744,10047],{},[1688,76746,2076],{"stretchy":2065},[898,76748,10047],{},[1688,76750,2076],{"fence":1732},[1688,76752,1690],{},[1781,76754,76755,76757],{},[1793,76756,1795],{},[898,76758,10047],{},[1688,76760,2066],{"fence":1732,"stretchy":1732,"minsize":76761,"maxsize":76761},"1.2em",[898,76763,1661],{},[1788,76765,76766,76768],{},[898,76767,1727],{},[898,76769,10047],{},[1688,76771,2066],{"stretchy":2065},[898,76773,10047],{},[1688,76775,2076],{"stretchy":2065},[1688,76777,1954],{},[898,76779,4512],{},[1788,76781,76782,76784],{},[898,76783,1727],{},[898,76785,10047],{},[1688,76787,2066],{"stretchy":2065},[898,76789,10047],{},[1688,76791,2076],{"stretchy":2065},[1688,76793,2076],{"fence":1732,"stretchy":1732,"minsize":76761,"maxsize":76761},[898,76795,2263],{"mathvariant":1822},[902,76797,76798],{"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).",[724,76800,9916,76801,8358,76823,76906],{},[883,76802,76804],{"className":76803},[886],[888,76805,76806],{"xmlns":890},[892,76807,76808,76820],{},[895,76809,76810,76816,76818],{},[1788,76811,76812,76814],{},[898,76813,10047],{},[1793,76815,1779],{},[1688,76817,3665],{},[1793,76819,1779],{},[902,76821,76822],{"encoding":904},"L_0 > 0",[883,76824,76826],{"className":76825},[886],[888,76827,76828],{"xmlns":890},[892,76829,76830,76903],{},[895,76831,76832,76834,76836,76842,76848,76850,76856,76858,76860,76862,76865,76867,76873,76875,76881,76883,76885,76887,76893,76895,76901],{},[1688,76833,2066],{"stretchy":2065},[898,76835,4512],{},[1788,76837,76838,76840],{},[898,76839,1727],{},[898,76841,10047],{},[1850,76843,76844,76846],{},[1688,76845,2076],{"stretchy":2065},[1688,76847,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,76849,2066],{"stretchy":2065},[1788,76851,76852,76854],{},[898,76853,10047],{},[1793,76855,1779],{},[1688,76857,2076],{"stretchy":2065},[1688,76859,1690],{},[1793,76861,1779],{},[1688,76863,76864],{},"⇔",[898,76866,1661],{},[1788,76868,76869,76871],{},[898,76870,1727],{},[898,76872,10047],{},[1688,76874,2066],{"stretchy":2065},[1788,76876,76877,76879],{},[898,76878,10047],{},[1793,76880,1779],{},[1688,76882,2076],{"stretchy":2065},[1688,76884,1690],{},[898,76886,4512],{},[1788,76888,76889,76891],{},[898,76890,1727],{},[898,76892,10047],{},[1688,76894,2066],{"stretchy":2065},[1788,76896,76897,76899],{},[898,76898,10047],{},[1793,76900,1779],{},[1688,76902,2076],{"stretchy":2065},[902,76904,76905],{"encoding":904},"(AP_L)'(L_0) = 0 \\Leftrightarrow MP_L(L_0) = AP_L(L_0)",", čímž je (5.5) dokázáno.",[198,76908,76910],{"id":76909},"příklad-51","Příklad 5.1",[724,76912,76913,76914,2263],{},"Je dána produkce ",[883,76915,76917],{"className":76916},[886],[888,76918,76919],{"xmlns":890},[892,76920,76921,76945],{},[895,76922,76923,76925,76927,76929,76935,76937,76939],{},[898,76924,1872],{},[1688,76926,1690],{},[1793,76928,2508],{},[1850,76930,76931,76933],{},[898,76932,10047],{},[1793,76934,1806],{},[1688,76936,1954],{},[1793,76938,3097],{},[1850,76940,76941,76943],{},[898,76942,10047],{},[1793,76944,2131],{},[902,76946,76947],{"encoding":904},"Q = 6L^2 - 0{,}2L^3",[724,76949,76950,57762,76953,77003,77004,2263],{},[38,76951,76952],{},"(a)",[883,76954,76956],{"className":76955},[886],[888,76957,76958],{"xmlns":890},[892,76959,76960,77000],{},[895,76961,76962,76964,76966,76968,76970,76972,76974,76976,76978,76980,76982,76984,76986,76988,76990,76992,76994,76996,76998],{},[898,76963,10047],{},[1688,76965,1690],{},[1793,76967,1806],{},[1688,76969,1733],{"separator":1732},[1793,76971,2501],{},[1688,76973,1733],{"separator":1732},[1793,76975,5841],{},[1688,76977,1733],{"separator":1732},[1793,76979,3121],{},[1688,76981,1733],{"separator":1732},[1793,76983,23187],{},[1688,76985,1733],{"separator":1732},[1793,76987,3964],{},[1688,76989,1733],{"separator":1732},[1793,76991,9290],{},[1688,76993,1733],{"separator":1732},[1793,76995,38586],{},[1688,76997,1733],{"separator":1732},[1793,76999,5260],{},[902,77001,77002],{"encoding":904},"L = 2, 5, 8, 10, 14, 18, 20, 21, 25"," určíme ",[883,77005,77007],{"className":77006},[886],[888,77008,77009],{"xmlns":890},[892,77010,77011,77021],{},[895,77012,77013,77015],{},[898,77014,1661],{},[1788,77016,77017,77019],{},[898,77018,1727],{},[898,77020,10047],{},[902,77022,10297],{"encoding":904},[724,77024,77025,77026,35208],{},"Podle (5.2): ",[883,77027,77029],{"className":77028},[886],[888,77030,77031],{"xmlns":890},[892,77032,77033,77089],{},[895,77034,77035,77037,77043,77045,77051,77053,77055,77057,77059,77061,77063,77065,77067,77073,77075,77077,77079,77081,77083,77085,77087],{},[898,77036,1661],{},[1788,77038,77039,77041],{},[898,77040,1727],{},[898,77042,10047],{},[1688,77044,1690],{},[1850,77046,77047,77049],{},[898,77048,1872],{},[1688,77050,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,77052,2066],{"stretchy":2065},[898,77054,10047],{},[1688,77056,2076],{"stretchy":2065},[1688,77058,1690],{},[1793,77060,3766],{},[898,77062,10047],{},[1688,77064,1954],{},[1793,77066,19562],{},[1850,77068,77069,77071],{},[898,77070,10047],{},[1793,77072,1806],{},[1688,77074,1690],{},[898,77076,10047],{},[1688,77078,2066],{"stretchy":2065},[1793,77080,3766],{},[1688,77082,1954],{},[1793,77084,19562],{},[898,77086,10047],{},[1688,77088,2076],{"stretchy":2065},[902,77090,77091],{"encoding":904},"MP_L = Q'(L) = 12L - 0{,}6L^2 = L(12 - 0{,}6L)",[16,77093,77094,77131],{},[19,77095,77096],{},[22,77097,77098,77113,77115,77117,77119,77121,77123,77125,77127,77129],{},[25,77099,77100],{},[883,77101,77103],{"className":77102},[886],[888,77104,77105],{"xmlns":890},[892,77106,77107,77111],{},[895,77108,77109],{},[898,77110,10047],{},[902,77112,10047],{"encoding":904},[25,77114,1806],{},[25,77116,2501],{},[25,77118,5841],{},[25,77120,3121],{},[25,77122,23187],{},[25,77124,3964],{},[25,77126,9290],{},[25,77128,38586],{},[25,77130,5260],{},[30,77132,77133],{},[22,77134,77135,77156,77159,77162,77165,77167,77170,77172,77174,77193],{},[35,77136,77137],{},[883,77138,77140],{"className":77139},[886],[888,77141,77142],{"xmlns":890},[892,77143,77144,77154],{},[895,77145,77146,77148],{},[898,77147,1661],{},[1788,77149,77150,77152],{},[898,77151,1727],{},[898,77153,10047],{},[902,77155,10297],{"encoding":904},[35,77157,77158],{},"21,6",[35,77160,77161],{},"45",[35,77163,77164],{},"57,6",[35,77166,3383],{},[35,77168,77169],{},"50,4",[35,77171,77158],{},[35,77173,1779],{},[35,77175,77176],{},[883,77177,77179],{"className":77178},[886],[888,77180,77181],{"xmlns":890},[892,77182,77183,77190],{},[895,77184,77185,77187],{},[1688,77186,1954],{},[1793,77188,77189],{},"12,6",[902,77191,77192],{"encoding":904},"-12{,}6",[35,77194,77195],{},[883,77196,77198],{"className":77197},[886],[888,77199,77200],{"xmlns":890},[892,77201,77202,77208],{},[895,77203,77204,77206],{},[1688,77205,1954],{},[1793,77207,45692],{},[902,77209,77210],{"encoding":904},"-75",[724,77212,77213,77232,77233,77251,77252,77269,77270,77288,77289,77313,77314,77332],{},[883,77214,77216],{"className":77215},[886],[888,77217,77218],{"xmlns":890},[892,77219,77220,77230],{},[895,77221,77222,77224],{},[898,77223,1661],{},[1788,77225,77226,77228],{},[898,77227,1727],{},[898,77229,10047],{},[902,77231,10297],{"encoding":904}," nabývá maxima pro ",[883,77234,77236],{"className":77235},[886],[888,77237,77238],{"xmlns":890},[892,77239,77240,77248],{},[895,77241,77242,77244,77246],{},[898,77243,10047],{},[1688,77245,1690],{},[1793,77247,3121],{},[902,77249,77250],{"encoding":904},"L = 10"," (60 jednotek\u002Fprac.). Od ",[883,77253,77255],{"className":77254},[886],[888,77256,77257],{"xmlns":890},[892,77258,77259,77267],{},[895,77260,77261,77263,77265],{},[898,77262,10047],{},[1688,77264,1690],{},[1793,77266,3121],{},[902,77268,77250],{"encoding":904}," přírůstky klesají, v ",[883,77271,77273],{"className":77272},[886],[888,77274,77275],{"xmlns":890},[892,77276,77277,77285],{},[895,77278,77279,77281,77283],{},[898,77280,10047],{},[1688,77282,1690],{},[1793,77284,9290],{},[902,77286,77287],{"encoding":904},"L = 20"," produkce přestává růst (maximum ",[883,77290,77292],{"className":77291},[886],[888,77293,77294],{"xmlns":890},[892,77295,77296,77310],{},[895,77297,77298,77300,77302,77304,77306,77308],{},[898,77299,1872],{},[1688,77301,2066],{"stretchy":2065},[1793,77303,9290],{},[1688,77305,2076],{"stretchy":2065},[1688,77307,1690],{},[1793,77309,24099],{},[902,77311,77312],{"encoding":904},"Q(20) = 800","), od ",[883,77315,77317],{"className":77316},[886],[888,77318,77319],{"xmlns":890},[892,77320,77321,77329],{},[895,77322,77323,77325,77327],{},[898,77324,10047],{},[1688,77326,3665],{},[1793,77328,9290],{},[902,77330,77331],{"encoding":904},"L > 20"," produkce klesá (fyzické přeplnění pracoviště při neměnném kapitálu).",[724,77334,77335],{},[614,77336,77337,77338,77378,77379,2886,77397,2263],{},"Obrázek 5.1 — graf produkce ",[883,77339,77341],{"className":77340},[886],[888,77342,77343],{"xmlns":890},[892,77344,77345,77375],{},[895,77346,77347,77349,77351,77353,77355,77357,77359,77365,77367,77369],{},[898,77348,1872],{},[1688,77350,2066],{"stretchy":2065},[898,77352,10047],{},[1688,77354,2076],{"stretchy":2065},[1688,77356,1690],{},[1793,77358,2508],{},[1850,77360,77361,77363],{},[898,77362,10047],{},[1793,77364,1806],{},[1688,77366,1954],{},[1793,77368,3097],{},[1850,77370,77371,77373],{},[898,77372,10047],{},[1793,77374,2131],{},[902,77376,77377],{"encoding":904},"Q(L) = 6L^2 - 0{,}2L^3"," s maximem ",[883,77380,77382],{"className":77381},[886],[888,77383,77384],{"xmlns":890},[892,77385,77386,77394],{},[895,77387,77388,77390,77392],{},[898,77389,1872],{},[1688,77391,1690],{},[1793,77393,24099],{},[902,77395,77396],{"encoding":904},"Q = 800",[883,77398,77400],{"className":77399},[886],[888,77401,77402],{"xmlns":890},[892,77403,77404,77412],{},[895,77405,77406,77408,77410],{},[898,77407,10047],{},[1688,77409,1690],{},[1793,77411,9290],{},[902,77413,77287],{"encoding":904},[724,77415,77416,77419],{},[38,77417,77418],{},"(b)"," Přibližná změna produkce při růstu pracovníků z 6 na 9.",[724,77421,77422,77423,1343,77441,2965],{},"Podle (5.3) s ",[883,77424,77426],{"className":77425},[886],[888,77427,77428],{"xmlns":890},[892,77429,77430,77438],{},[895,77431,77432,77434,77436],{},[898,77433,10047],{},[1688,77435,1690],{},[1793,77437,2508],{},[902,77439,77440],{"encoding":904},"L = 6",[883,77442,77444],{"className":77443},[886],[888,77445,77446],{"xmlns":890},[892,77447,77448,77458],{},[895,77449,77450,77452,77454,77456],{},[898,77451,2073],{},[898,77453,10047],{},[1688,77455,1690],{},[1793,77457,2131],{},[902,77459,77460],{"encoding":904},"dL = 3",[883,77462,77464],{"className":77463},[886],[888,77465,77466],{"xmlns":890,"display":28306},[892,77467,77468,77531],{},[895,77469,77470,77472,77474,77476,77478,77484,77486,77488,77490,77492,77494,77496,77498,77500,77502,77504,77506,77508,77510,77512,77514,77516,77518,77520,77522,77524,77526,77528],{},[898,77471,2073],{},[898,77473,1872],{},[1688,77475,1690],{},[898,77477,1661],{},[1788,77479,77480,77482],{},[898,77481,1727],{},[898,77483,10047],{},[1688,77485,2066],{"stretchy":2065},[1793,77487,2508],{},[1688,77489,2076],{"stretchy":2065},[1688,77491,3434],{},[1793,77493,2131],{},[1688,77495,1690],{},[1688,77497,2066],{"stretchy":2065},[1793,77499,3766],{},[1688,77501,3434],{},[1793,77503,2508],{},[1688,77505,1954],{},[1793,77507,19562],{},[1688,77509,3434],{},[1793,77511,5821],{},[1688,77513,2076],{"stretchy":2065},[1688,77515,3434],{},[1793,77517,2131],{},[1688,77519,1690],{},[1793,77521,77169],{},[1688,77523,3434],{},[1793,77525,2131],{},[1688,77527,1690],{},[1793,77529,77530],{},"151,2.",[902,77532,77533],{"encoding":904},"dQ = MP_L(6)\\cdot 3 = (12\\cdot 6 - 0{,}6\\cdot 36)\\cdot 3 = 50{,}4 \\cdot 3 = 151{,}2.",[724,77535,77536,77537,57992,77562,77576,77577,2263],{},"Produkce vzroste z ",[883,77538,77540],{"className":77539},[886],[888,77541,77542],{"xmlns":890},[892,77543,77544,77559],{},[895,77545,77546,77548,77550,77552,77554,77556],{},[898,77547,1872],{},[1688,77549,2066],{"stretchy":2065},[1793,77551,2508],{},[1688,77553,2076],{"stretchy":2065},[1688,77555,1690],{},[1793,77557,77558],{},"172,8",[902,77560,77561],{"encoding":904},"Q(6) = 172{,}8",[883,77563,77565],{"className":77564},[886],[888,77566,77567],{"xmlns":890},[892,77568,77569,77574],{},[895,77570,77571],{},[1793,77572,77573],{},"324",[902,77575,77573],{"encoding":904},". Skutečná hodnota: ",[883,77578,77580],{"className":77579},[886],[888,77581,77582],{"xmlns":890},[892,77583,77584,77624],{},[895,77585,77586,77588,77590,77592,77594,77596,77598,77600,77602,77604,77606,77608,77610,77612,77615,77617,77619,77621],{},[898,77587,3147],{"mathvariant":1822},[898,77589,1872],{},[1688,77591,1690],{},[898,77593,1872],{},[1688,77595,2066],{"stretchy":2065},[1793,77597,4256],{},[1688,77599,2076],{"stretchy":2065},[1688,77601,1954],{},[898,77603,1872],{},[1688,77605,2066],{"stretchy":2065},[1793,77607,2508],{},[1688,77609,2076],{"stretchy":2065},[1688,77611,1690],{},[1793,77613,77614],{},"340,2",[1688,77616,1954],{},[1793,77618,77558],{},[1688,77620,1690],{},[1793,77622,77623],{},"167,4",[902,77625,77626],{"encoding":904},"\\Delta Q = Q(9) - Q(6) = 340{,}2 - 172{,}8 = 167{,}4",[198,77628,77630],{"id":77629},"příklad-52","Příklad 5.2",[724,77632,77633,77634,2263],{},"Ověříme princip (5.5) pro ",[883,77635,77637],{"className":77636},[886],[888,77638,77639],{"xmlns":890},[892,77640,77641,77665],{},[895,77642,77643,77645,77647,77649,77655,77657,77659],{},[898,77644,1872],{},[1688,77646,1690],{},[1793,77648,2508],{},[1850,77650,77651,77653],{},[898,77652,10047],{},[1793,77654,1806],{},[1688,77656,1954],{},[1793,77658,3097],{},[1850,77660,77661,77663],{},[898,77662,10047],{},[1793,77664,2131],{},[902,77666,76947],{"encoding":904},[883,77668,77670],{"className":77669},[886],[888,77671,77672],{"xmlns":890,"display":28306},[892,77673,77674,77752],{},[895,77675,77676,77678,77684,77686,77692,77694,77696,77698,77700,77702,77708,77710,77712,77714,77722,77724,77726,77728,77730,77732,77734,77736,77738,77740,77742,77748,77750],{},[898,77677,4512],{},[1788,77679,77680,77682],{},[898,77681,1727],{},[898,77683,10047],{},[1688,77685,1690],{},[1781,77687,77688,77690],{},[898,77689,1872],{},[898,77691,10047],{},[1688,77693,1690],{},[1793,77695,2508],{},[898,77697,10047],{},[1688,77699,1954],{},[1793,77701,3097],{},[1850,77703,77704,77706],{},[898,77705,10047],{},[1793,77707,1806],{},[1688,77709,1733],{"separator":1732},[6134,77711],{"width":15531},[898,77713,4512],{},[1814,77715,77716,77718,77720],{},[898,77717,1727],{},[898,77719,10047],{},[1688,77721,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,77723,1690],{},[1793,77725,2508],{},[1688,77727,1954],{},[1793,77729,19512],{},[898,77731,10047],{},[1688,77733,1690],{},[1793,77735,1779],{},[2041,77737,4241],{},[1688,77739,4244],{},[2041,77741,4241],{},[1788,77743,77744,77746],{},[898,77745,10047],{},[1793,77747,1779],{},[1688,77749,1690],{},[1793,77751,68523],{},[902,77753,77754],{"encoding":904},"AP_L = \\frac{Q}{L} = 6L - 0{,}2L^2, \\quad AP_L' = 6 - 0{,}4L = 0 \\;\\Rightarrow\\; L_0 = 15.",[724,77756,77757,77793,77794,77812,77813,2263],{},[883,77758,77760],{"className":77759},[886],[888,77761,77762],{"xmlns":890},[892,77763,77764,77790],{},[895,77765,77766,77768,77780,77782,77784,77786,77788],{},[898,77767,4512],{},[1814,77769,77770,77772,77774],{},[898,77771,1727],{},[898,77773,10047],{},[895,77775,77776,77778],{},[1688,77777,1824],{"mathvariant":1822},[1688,77779,1824],{"mathvariant":1822},[1688,77781,1690],{},[1688,77783,1954],{},[1793,77785,19512],{},[1688,77787,3704],{},[1793,77789,1779],{},[902,77791,77792],{"encoding":904},"AP_L'' = -0{,}4 \u003C 0",", takže v ",[883,77795,77797],{"className":77796},[886],[888,77798,77799],{"xmlns":890},[892,77800,77801,77809],{},[895,77802,77803,77805,77807],{},[898,77804,10047],{},[1688,77806,1690],{},[1793,77808,36484],{},[902,77810,77811],{"encoding":904},"L = 15"," je maximum, ",[883,77814,77816],{"className":77815},[886],[888,77817,77818],{"xmlns":890},[892,77819,77820,77866],{},[895,77821,77822,77824,77830,77832,77834,77836,77838,77840,77842,77844,77846,77848,77850,77853,77855,77858,77860,77862,77864],{},[898,77823,4512],{},[1788,77825,77826,77828],{},[898,77827,1727],{},[898,77829,10047],{},[1688,77831,2066],{"stretchy":2065},[1793,77833,36484],{},[1688,77835,2076],{"stretchy":2065},[1688,77837,1690],{},[1793,77839,2508],{},[1688,77841,3434],{},[1793,77843,36484],{},[1688,77845,1954],{},[1793,77847,3097],{},[1688,77849,3434],{},[1793,77851,77852],{},"225",[1688,77854,1690],{},[1793,77856,77857],{},"90",[1688,77859,1954],{},[1793,77861,77161],{},[1688,77863,1690],{},[1793,77865,77161],{},[902,77867,77868],{"encoding":904},"AP_L(15) = 6\\cdot 15 - 0{,}2\\cdot 225 = 90 - 45 = 45",[724,77870,77871,42120,77927,77973],{},[883,77872,77874],{"className":77873},[886],[888,77875,77876],{"xmlns":890},[892,77877,77878,77924],{},[895,77879,77880,77882,77888,77890,77892,77894,77896,77898,77900,77902,77904,77906,77908,77910,77912,77915,77917,77920,77922],{},[898,77881,1661],{},[1788,77883,77884,77886],{},[898,77885,1727],{},[898,77887,10047],{},[1688,77889,2066],{"stretchy":2065},[1793,77891,36484],{},[1688,77893,2076],{"stretchy":2065},[1688,77895,1690],{},[1793,77897,3766],{},[1688,77899,3434],{},[1793,77901,36484],{},[1688,77903,1954],{},[1793,77905,19562],{},[1688,77907,3434],{},[1793,77909,77852],{},[1688,77911,1690],{},[1793,77913,77914],{},"180",[1688,77916,1954],{},[1793,77918,77919],{},"135",[1688,77921,1690],{},[1793,77923,77161],{},[902,77925,77926],{"encoding":904},"MP_L(15) = 12\\cdot 15 - 0{,}6\\cdot 225 = 180 - 135 = 45",[883,77928,77930],{"className":77929},[886],[888,77931,77932],{"xmlns":890},[892,77933,77934,77970],{},[895,77935,77936,77938,77944,77946,77948,77950,77952,77954,77960,77962,77964,77966,77968],{},[898,77937,1661],{},[1788,77939,77940,77942],{},[898,77941,1727],{},[898,77943,10047],{},[1688,77945,2066],{"stretchy":2065},[1793,77947,36484],{},[1688,77949,2076],{"stretchy":2065},[1688,77951,1690],{},[898,77953,4512],{},[1788,77955,77956,77958],{},[898,77957,1727],{},[898,77959,10047],{},[1688,77961,2066],{"stretchy":2065},[1793,77963,36484],{},[1688,77965,2076],{"stretchy":2065},[1688,77967,1690],{},[1793,77969,77161],{},[902,77971,77972],{"encoding":904},"MP_L(15) = AP_L(15) = 45",", jak požaduje (5.5).",[724,77975,77976,77979,77980,17821,78009,2263],{},[38,77977,77978],{},"Zkratka bez hledání extrému:"," stačí řešit ",[883,77981,77983],{"className":77982},[886],[888,77984,77985],{"xmlns":890},[892,77986,77987,78007],{},[895,77988,77989,77991,77997,77999,78001],{},[898,77990,1661],{},[1788,77992,77993,77995],{},[898,77994,1727],{},[898,77996,10047],{},[1688,77998,1690],{},[898,78000,4512],{},[1788,78002,78003,78005],{},[898,78004,1727],{},[898,78006,10047],{},[902,78008,74903],{"encoding":904},[883,78010,78012],{"className":78011},[886],[888,78013,78014],{"xmlns":890},[892,78015,78016,78056],{},[895,78017,78018,78020,78022,78024,78026,78032,78034,78036,78038,78040,78042,78048,78050,78052,78054],{},[1793,78019,3766],{},[898,78021,10047],{},[1688,78023,1954],{},[1793,78025,19562],{},[1850,78027,78028,78030],{},[898,78029,10047],{},[1793,78031,1806],{},[1688,78033,1690],{},[1793,78035,2508],{},[898,78037,10047],{},[1688,78039,1954],{},[1793,78041,3097],{},[1850,78043,78044,78046],{},[898,78045,10047],{},[1793,78047,1806],{},[1688,78049,4244],{},[898,78051,10047],{},[1688,78053,1690],{},[1793,78055,36484],{},[902,78057,78058],{"encoding":904},"12L - 0{,}6L^2 = 6L - 0{,}2L^2 \\Rightarrow L = 15",[724,78060,78061],{},[614,78062,78063,78064,78083,78084,12378,78102,78121,78122,78140,78141,78158,78159,78178,78179,78198],{},"Obrázek 5.3 — křivky ",[883,78065,78067],{"className":78066},[886],[888,78068,78069],{"xmlns":890},[892,78070,78071,78081],{},[895,78072,78073,78075],{},[898,78074,1661],{},[1788,78076,78077,78079],{},[898,78078,1727],{},[898,78080,10047],{},[902,78082,10297],{"encoding":904}," (max 60 při ",[883,78085,78087],{"className":78086},[886],[888,78088,78089],{"xmlns":890},[892,78090,78091,78099],{},[895,78092,78093,78095,78097],{},[898,78094,10047],{},[1688,78096,1690],{},[1793,78098,3121],{},[902,78100,78101],{"encoding":904},"L=10",[883,78103,78105],{"className":78104},[886],[888,78106,78107],{"xmlns":890},[892,78108,78109,78119],{},[895,78110,78111,78113],{},[898,78112,4512],{},[1788,78114,78115,78117],{},[898,78116,1727],{},[898,78118,10047],{},[902,78120,74873],{"encoding":904}," (max 45 při ",[883,78123,78125],{"className":78124},[886],[888,78126,78127],{"xmlns":890},[892,78128,78129,78137],{},[895,78130,78131,78133,78135],{},[898,78132,10047],{},[1688,78134,1690],{},[1793,78136,36484],{},[902,78138,78139],{"encoding":904},"L=15","), průsečík v ",[883,78142,78144],{"className":78143},[886],[888,78145,78146],{"xmlns":890},[892,78147,78148,78156],{},[895,78149,78150,78152,78154],{},[898,78151,10047],{},[1688,78153,1690],{},[1793,78155,36484],{},[902,78157,77811],{"encoding":904},". Nalevo od 15 leží ",[883,78160,78162],{"className":78161},[886],[888,78163,78164],{"xmlns":890},[892,78165,78166,78176],{},[895,78167,78168,78170],{},[898,78169,1661],{},[1788,78171,78172,78174],{},[898,78173,1727],{},[898,78175,10047],{},[902,78177,10297],{"encoding":904}," nad ",[883,78180,78182],{"className":78181},[886],[888,78183,78184],{"xmlns":890},[892,78185,78186,78196],{},[895,78187,78188,78190],{},[898,78189,4512],{},[1788,78191,78192,78194],{},[898,78193,1727],{},[898,78195,10047],{},[902,78197,74873],{"encoding":904},", napravo pod ní.",[115,78200,78202],{"id":78201},"dvoufaktorový-model-produkce","Dvoufaktorový model produkce",[724,78204,78205,78206,2946,78219,2170,78222,6446,78235,2170,78238,2965],{},"V dvoufaktorovém modelu závisí produkce ",[883,78207,78209],{"className":78208},[886],[888,78210,78211],{"xmlns":890},[892,78212,78213,78217],{},[895,78214,78215],{},[898,78216,1872],{},[902,78218,1872],{"encoding":904},[38,78220,78221],{},"práci",[883,78223,78225],{"className":78224},[886],[888,78226,78227],{"xmlns":890},[892,78228,78229,78233],{},[895,78230,78231],{},[898,78232,10047],{},[902,78234,10047],{"encoding":904},[38,78236,78237],{},"kapitálu",[883,78239,78241],{"className":78240},[886],[888,78242,78243],{"xmlns":890},[892,78244,78245,78249],{},[895,78246,78247],{},[898,78248,10052],{},[902,78250,10052],{"encoding":904},[883,78252,78254],{"className":78253},[886],[888,78255,78256],{"xmlns":890,"display":28306},[892,78257,78258,78293],{},[20995,78259,78260],{"width":28311},[21000,78261,78262,78264,78286,78288],{},[21003,78263],{"width":28316},[21003,78265,78266],{},[895,78267,78268,78270,78272,78274,78276,78278,78280,78282,78284],{},[898,78269,1872],{},[1688,78271,1690],{},[898,78273,1872],{},[1688,78275,2066],{"stretchy":2065},[898,78277,10047],{},[1688,78279,1733],{"separator":1732},[898,78281,10052],{},[1688,78283,2076],{"stretchy":2065},[898,78285,2263],{"mathvariant":1822},[21003,78287],{"width":28316},[21003,78289,78290],{},[2041,78291,78292],{},"(5.6)",[902,78294,78295],{"encoding":904},"Q = Q(L, K). \\tag{5.6}",[724,78297,78298,78299,78301],{},"Půda je nadále standardní exogenní proměnnou. Vztah (5.6) se nazývá ",[38,78300,75240],{}," (v širším smyslu oproti jednofaktorovému modelu).",[115,78303,78305],{"id":78304},"cobb-douglasova-produkční-funkce","Cobb-Douglasova produkční funkce",[724,78307,78308],{},"Široce používané produkční funkce mají tvar",[883,78310,78312],{"className":78311},[886],[888,78313,78314],{"xmlns":890,"display":28306},[892,78315,78316,78357],{},[20995,78317,78318],{"width":28311},[21000,78319,78320,78322,78350,78352],{},[21003,78321],{"width":28316},[21003,78323,78324],{},[895,78325,78326,78328,78330,78332,78334,78340,78342,78348],{},[898,78327,1872],{},[1688,78329,1690],{},[898,78331,4512],{},[2041,78333,2043],{},[1850,78335,78336,78338],{},[898,78337,10047],{},[898,78339,207],{},[2041,78341,2043],{},[1850,78343,78344,78346],{},[898,78345,10052],{},[898,78347,1918],{},[1688,78349,1733],{"separator":1732},[21003,78351],{"width":28316},[21003,78353,78354],{},[2041,78355,78356],{},"(5.7)",[902,78358,78359],{"encoding":904},"Q = A\\,L^a\\,K^b, \\tag{5.7}",[724,78361,4567,78362,78384,78385,78387,78388,2263],{},[883,78363,78365],{"className":78364},[886],[888,78366,78367],{"xmlns":890},[892,78368,78369,78381],{},[895,78370,78371,78373,78375,78377,78379],{},[898,78372,4512],{},[1688,78374,1733],{"separator":1732},[898,78376,207],{},[1688,78378,1733],{"separator":1732},[898,78380,1918],{},[902,78382,78383],{"encoding":904},"A, a, b"," jsou kladné konstanty. Nazývají se ",[38,78386,74939],{}," (poprvé publikovány v roce 1939). V ekonomických analýzách zpravidla ",[883,78389,78391],{"className":78390},[886],[888,78392,78393],{"xmlns":890},[892,78394,78395,78407],{},[895,78396,78397,78399,78401,78403,78405],{},[898,78398,207],{},[1688,78400,1733],{"separator":1732},[898,78402,1918],{},[1688,78404,3704],{},[1793,78406,1795],{},[902,78408,78409],{"encoding":904},"a, b \u003C 1",[724,78411,78412],{},[2821,78413],{"alt":78414,"className":78415,"src":78416},"imek-vynosy-z-rozsahu-3typy",[210,2825],"\u002Fwiki-assets\u002Fimek-vynosy-z-rozsahu-3typy.jpeg",[724,78418,78419,78420,78423,78424,2946,78437,78453,78454,2946,78467,2965],{},"Reflektují ekonomickou zákonitost, že ",[38,78421,78422],{},"proporcionální změny vstupů mají odezvu v proporcionální změně výstupu",". Změní-li se práce z ",[883,78425,78427],{"className":78426},[886],[888,78428,78429],{"xmlns":890},[892,78430,78431,78435],{},[895,78432,78433],{},[898,78434,10047],{},[902,78436,10047],{"encoding":904},[883,78438,78440],{"className":78439},[886],[888,78441,78442],{"xmlns":890},[892,78443,78444,78450],{},[895,78445,78446,78448],{},[898,78447,2046],{},[898,78449,10047],{},[902,78451,78452],{"encoding":904},"rL"," a kapitál z ",[883,78455,78457],{"className":78456},[886],[888,78458,78459],{"xmlns":890},[892,78460,78461,78465],{},[895,78462,78463],{},[898,78464,10052],{},[902,78466,10052],{"encoding":904},[883,78468,78470],{"className":78469},[886],[888,78471,78472],{"xmlns":890},[892,78473,78474,78480],{},[895,78475,78476,78478],{},[898,78477,2046],{},[898,78479,10052],{},[902,78481,78482],{"encoding":904},"rK",[883,78484,78486],{"className":78485},[886],[888,78487,78488],{"xmlns":890,"display":28306},[892,78489,78490,78613],{},[20995,78491,78492],{"width":28311},[21000,78493,78494,78496,78606,78608],{},[21003,78495],{"width":28316},[21003,78497,78498],{},[895,78499,78500,78502,78504,78506,78508,78510,78512,78514,78516,78518,78520,78522,78524,78526,78532,78534,78536,78538,78544,78546,78548,78550,78562,78564,78570,78576,78578,78590,78592,78594,78596,78598,78600,78602,78604],{},[898,78501,1872],{},[1688,78503,2066],{"stretchy":2065},[898,78505,2046],{},[898,78507,10047],{},[1688,78509,1733],{"separator":1732},[898,78511,2046],{},[898,78513,10052],{},[1688,78515,2076],{"stretchy":2065},[1688,78517,1690],{},[898,78519,4512],{},[1688,78521,2066],{"stretchy":2065},[898,78523,2046],{},[898,78525,10047],{},[1850,78527,78528,78530],{},[1688,78529,2076],{"stretchy":2065},[898,78531,207],{},[1688,78533,2066],{"stretchy":2065},[898,78535,2046],{},[898,78537,10052],{},[1850,78539,78540,78542],{},[1688,78541,2076],{"stretchy":2065},[898,78543,1918],{},[1688,78545,1690],{},[898,78547,4512],{},[2041,78549,2043],{},[1850,78551,78552,78554],{},[898,78553,2046],{},[895,78555,78556,78558,78560],{},[898,78557,207],{},[1688,78559,1696],{},[898,78561,1918],{},[2041,78563,2043],{},[1850,78565,78566,78568],{},[898,78567,10047],{},[898,78569,207],{},[1850,78571,78572,78574],{},[898,78573,10052],{},[898,78575,1918],{},[1688,78577,1690],{},[1850,78579,78580,78582],{},[898,78581,2046],{},[895,78583,78584,78586,78588],{},[898,78585,207],{},[1688,78587,1696],{},[898,78589,1918],{},[2041,78591,2043],{},[898,78593,1872],{},[1688,78595,2066],{"stretchy":2065},[898,78597,10047],{},[1688,78599,1733],{"separator":1732},[898,78601,10052],{},[1688,78603,2076],{"stretchy":2065},[898,78605,2263],{"mathvariant":1822},[21003,78607],{"width":28316},[21003,78609,78610],{},[2041,78611,78612],{},"(5.8)",[902,78614,78615],{"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}",[724,78617,78618,78619],{},"Volně: ",[38,78620,78621,78622,78635,78636,78660],{},"změní-li se vstupy ",[883,78623,78625],{"className":78624},[886],[888,78626,78627],{"xmlns":890},[892,78628,78629,78633],{},[895,78630,78631],{},[898,78632,2046],{},[902,78634,2046],{"encoding":904},"-krát, změní se výstup ",[883,78637,78639],{"className":78638},[886],[888,78640,78641],{"xmlns":890},[892,78642,78643,78657],{},[895,78644,78645],{},[1850,78646,78647,78649],{},[898,78648,2046],{},[895,78650,78651,78653,78655],{},[898,78652,207],{},[1688,78654,1696],{},[898,78656,1918],{},[902,78658,78659],{"encoding":904},"r^{a+b}","-krát.",[198,78662,78664],{"id":78663},"výnosy-z-rozsahu","Výnosy z rozsahu",[724,78666,78667,78668,78685],{},"Součet exponentů ",[883,78669,78671],{"className":78670},[886],[888,78672,78673],{"xmlns":890},[892,78674,78675,78683],{},[895,78676,78677,78679,78681],{},[898,78678,207],{},[1688,78680,1696],{},[898,78682,1918],{},[902,78684,75064],{"encoding":904}," určuje typ výnosů z rozsahu:",[16,78687,78688,78717],{},[19,78689,78690],{},[22,78691,78692,78695,78698,78715],{},[25,78693,78694],{},"Typ",[25,78696,78697],{},"Podmínka",[25,78699,78700,78701,78714],{},"Chování produkce při ",[883,78702,78704],{"className":78703},[886],[888,78705,78706],{"xmlns":890},[892,78707,78708,78712],{},[895,78709,78710],{},[898,78711,2046],{},[902,78713,2046],{"encoding":904},"-násobném zvýšení vstupů",[25,78716,3327],{},[30,78718,78719,78830,78945],{},[22,78720,78721,78729,78753,78786],{},[35,78722,75777,78723,10277,78726,2076],{},[38,78724,78725],{},"Konstantní",[614,78727,78728],{},"constant returns",[35,78730,78731],{},[883,78732,78734],{"className":78733},[886],[888,78735,78736],{"xmlns":890},[892,78737,78738,78750],{},[895,78739,78740,78742,78744,78746,78748],{},[898,78741,207],{},[1688,78743,1696],{},[898,78745,1918],{},[1688,78747,1690],{},[1793,78749,1795],{},[902,78751,78752],{"encoding":904},"a+b = 1",[35,78754,78755,78768,78769,2170,78772,78785],{},[883,78756,78758],{"className":78757},[886],[888,78759,78760],{"xmlns":890},[892,78761,78762,78766],{},[895,78763,78764],{},[898,78765,1872],{},[902,78767,1872],{"encoding":904}," vzroste ",[38,78770,78771],{},"přesně",[883,78773,78775],{"className":78774},[886],[888,78776,78777],{"xmlns":890},[892,78778,78779,78783],{},[895,78780,78781],{},[898,78782,2046],{},[902,78784,2046],{"encoding":904},"-krát",[35,78787,78788],{},[883,78789,78791],{"className":78790},[886],[888,78792,78793],{"xmlns":890},[892,78794,78795,78827],{},[895,78796,78797,78799,78801,78803,78815],{},[898,78798,1872],{},[1688,78800,1690],{},[1793,78802,1806],{},[1850,78804,78805,78807],{},[898,78806,10047],{},[895,78808,78809,78811,78813],{},[1793,78810,1795],{},[898,78812,4930],{"mathvariant":1822},[1793,78814,2616],{},[1850,78816,78817,78819],{},[898,78818,10052],{},[895,78820,78821,78823,78825],{},[1793,78822,2131],{},[898,78824,4930],{"mathvariant":1822},[1793,78826,2616],{},[902,78828,78829],{"encoding":904},"Q = 2L^{1\u002F4}K^{3\u002F4}",[22,78831,78832,78841,78865,78895],{},[35,78833,78834,78835,10277,78838,2076],{},"2° ",[38,78836,78837],{},"Rostoucí",[614,78839,78840],{},"increasing returns",[35,78842,78843],{},[883,78844,78846],{"className":78845},[886],[888,78847,78848],{"xmlns":890},[892,78849,78850,78862],{},[895,78851,78852,78854,78856,78858,78860],{},[898,78853,207],{},[1688,78855,1696],{},[898,78857,1918],{},[1688,78859,3665],{},[1793,78861,1795],{},[902,78863,78864],{"encoding":904},"a+b > 1",[35,78866,78867,78768,78880,51471,78882,78785],{},[883,78868,78870],{"className":78869},[886],[888,78871,78872],{"xmlns":890},[892,78873,78874,78878],{},[895,78875,78876],{},[898,78877,1872],{},[902,78879,1872],{"encoding":904},[38,78881,25511],{},[883,78883,78885],{"className":78884},[886],[888,78886,78887],{"xmlns":890},[892,78888,78889,78893],{},[895,78890,78891],{},[898,78892,2046],{},[902,78894,2046],{"encoding":904},[35,78896,78897,10277,78923,2076],{},[883,78898,78900],{"className":78899},[886],[888,78901,78902],{"xmlns":890},[892,78903,78904,78920],{},[895,78905,78906,78908,78910,78912,78914],{},[898,78907,1872],{},[1688,78909,1690],{},[1793,78911,24442],{},[898,78913,10047],{},[1850,78915,78916,78918],{},[898,78917,10052],{},[1793,78919,1806],{},[902,78921,78922],{"encoding":904},"Q = 7LK^2",[883,78924,78926],{"className":78925},[886],[888,78927,78928],{"xmlns":890},[892,78929,78930,78942],{},[895,78931,78932,78934,78936,78938,78940],{},[898,78933,207],{},[1688,78935,1696],{},[898,78937,1918],{},[1688,78939,1690],{},[1793,78941,2131],{},[902,78943,78944],{"encoding":904},"a+b = 3",[22,78946,78947,78956,78980,79011],{},[35,78948,78949,78950,10277,78953,2076],{},"3° ",[38,78951,78952],{},"Klesající",[614,78954,78955],{},"decreasing returns",[35,78957,78958],{},[883,78959,78961],{"className":78960},[886],[888,78962,78963],{"xmlns":890},[892,78964,78965,78977],{},[895,78966,78967,78969,78971,78973,78975],{},[898,78968,207],{},[1688,78970,1696],{},[898,78972,1918],{},[1688,78974,3704],{},[1793,78976,1795],{},[902,78978,78979],{"encoding":904},"a+b \u003C 1",[35,78981,78982,78768,78995,51471,78998,78785],{},[883,78983,78985],{"className":78984},[886],[888,78986,78987],{"xmlns":890},[892,78988,78989,78993],{},[895,78990,78991],{},[898,78992,1872],{},[902,78994,1872],{"encoding":904},[38,78996,78997],{},"méně",[883,78999,79001],{"className":79000},[886],[888,79002,79003],{"xmlns":890},[892,79004,79005,79009],{},[895,79006,79007],{},[898,79008,2046],{},[902,79010,2046],{"encoding":904},[35,79012,79013,10277,79043,2076],{},[883,79014,79016],{"className":79015},[886],[888,79017,79018],{"xmlns":890},[892,79019,79020,79040],{},[895,79021,79022,79024,79026,79028,79034],{},[898,79023,1872],{},[1688,79025,1690],{},[1793,79027,3121],{},[1850,79029,79030,79032],{},[898,79031,10047],{},[1793,79033,68451],{},[1850,79035,79036,79038],{},[898,79037,10052],{},[1793,79039,5265],{},[902,79041,79042],{"encoding":904},"Q = 10L^{0{,}3}K^{0{,}5}",[883,79044,79046],{"className":79045},[886],[888,79047,79048],{"xmlns":890},[892,79049,79050,79062],{},[895,79051,79052,79054,79056,79058,79060],{},[898,79053,207],{},[1688,79055,1696],{},[898,79057,1918],{},[1688,79059,1690],{},[1793,79061,14836],{},[902,79063,79064],{"encoding":904},"a+b = 0{,}8",[4124,79066,79067],{},[724,79068,79069,79071,79072,79089,79090,79093,79094,2170,79097,79133,79134,79156,79157,2263],{},[883,79070,4668],{}," Pozor\nSoučet ",[883,79073,79075],{"className":79074},[886],[888,79076,79077],{"xmlns":890},[892,79078,79079,79087],{},[895,79080,79081,79083,79085],{},[898,79082,207],{},[1688,79084,1696],{},[898,79086,1918],{},[902,79088,75064],{"encoding":904}," neudává velikost produkce, ale ",[38,79091,79092],{},"elasticitu vůči škálování vstupů",". Speciálně ",[38,79095,79096],{},"ryzí Cobb-Douglas",[883,79098,79100],{"className":79099},[886],[888,79101,79102],{"xmlns":890},[892,79103,79104,79130],{},[895,79105,79106,79108,79110,79112,79118],{},[898,79107,1872],{},[1688,79109,1690],{},[898,79111,4512],{},[1850,79113,79114,79116],{},[898,79115,10047],{},[898,79117,207],{},[1850,79119,79120,79122],{},[898,79121,10052],{},[895,79123,79124,79126,79128],{},[1793,79125,1795],{},[1688,79127,1954],{},[898,79129,207],{},[902,79131,79132],{"encoding":904},"Q = AL^a K^{1-a}"," má ",[883,79135,79137],{"className":79136},[886],[888,79138,79139],{"xmlns":890},[892,79140,79141,79153],{},[895,79142,79143,79145,79147,79149,79151],{},[898,79144,1918],{},[1688,79146,1690],{},[1793,79148,1795],{},[1688,79150,1954],{},[898,79152,207],{},[902,79154,79155],{"encoding":904},"b = 1-a",", tedy vždy ",[38,79158,79159],{},"konstantní výnosy z rozsahu",[198,79161,79163,79164],{"id":79162},"parametr-efektivity-aa","Parametr efektivity ",[883,79165,79167],{"className":79166},[886],[888,79168,79169],{"xmlns":890},[892,79170,79171,79175],{},[895,79172,79173],{},[898,79174,4512],{},[902,79176,4512],{"encoding":904},[724,79178,79179,79180,79193,79194,79207,79208,79226,79227,79230],{},"Konstanta ",[883,79181,79183],{"className":79182},[886],[888,79184,79185],{"xmlns":890},[892,79186,79187,79191],{},[895,79188,79189],{},[898,79190,4512],{},[902,79192,4512],{"encoding":904}," v (5.7) proporcionálně ovlivňuje úroveň produkce ",[883,79195,79197],{"className":79196},[886],[888,79198,79199],{"xmlns":890},[892,79200,79201,79205],{},[895,79202,79203],{},[898,79204,1872],{},[902,79206,1872],{"encoding":904}," při pevně zadaných ",[883,79209,79211],{"className":79210},[886],[888,79212,79213],{"xmlns":890},[892,79214,79215,79223],{},[895,79216,79217,79219,79221],{},[898,79218,10047],{},[1688,79220,1733],{"separator":1732},[898,79222,10052],{},[902,79224,79225],{"encoding":904},"L, K",", a lze ji proto chápat jako ",[38,79228,79229],{},"parametr efektivity"," — indikátor stavu technologie.",[198,79232,79234],{"id":79233},"příklad-53","Příklad 5.3",[724,79236,79237,79238,79133,79280,79282,79283,2263],{},"Produkční funkce ",[883,79239,79241],{"className":79240},[886],[888,79242,79243],{"xmlns":890},[892,79244,79245,79277],{},[895,79246,79247,79249,79251,79253,79265],{},[898,79248,1872],{},[1688,79250,1690],{},[1793,79252,1806],{},[1850,79254,79255,79257],{},[898,79256,10047],{},[895,79258,79259,79261,79263],{},[1793,79260,1795],{},[898,79262,4930],{"mathvariant":1822},[1793,79264,2616],{},[1850,79266,79267,79269],{},[898,79268,10052],{},[895,79270,79271,79273,79275],{},[1793,79272,2131],{},[898,79274,4930],{"mathvariant":1822},[1793,79276,2616],{},[902,79278,79279],{"encoding":904},"Q = 2L^{1\u002F4} K^{3\u002F4}",[38,79281,24854],{}," výnosy z rozsahu, neboť ",[883,79284,79286],{"className":79285},[886],[888,79287,79288],{"xmlns":890},[892,79289,79290,79314],{},[895,79291,79292,79300,79302,79310,79312],{},[1777,79293,79294],{"scriptlevel":1779,"displaystyle":2065},[1781,79295,79296,79298],{},[1793,79297,1795],{},[1793,79299,2616],{},[1688,79301,1696],{},[1777,79303,79304],{"scriptlevel":1779,"displaystyle":2065},[1781,79305,79306,79308],{},[1793,79307,2131],{},[1793,79309,2616],{},[1688,79311,1690],{},[1793,79313,1795],{},[902,79315,79316],{"encoding":904},"\\tfrac{1}{4} + \\tfrac{3}{4} = 1",[724,79318,79319,79320,6446,79333,79346,79347,2170,79360,79400],{},"Změní-li se ",[883,79321,79323],{"className":79322},[886],[888,79324,79325],{"xmlns":890},[892,79326,79327,79331],{},[895,79328,79329],{},[898,79330,10047],{},[902,79332,10047],{"encoding":904},[883,79334,79336],{"className":79335},[886],[888,79337,79338],{"xmlns":890},[892,79339,79340,79344],{},[895,79341,79342],{},[898,79343,10052],{},[902,79345,10052],{"encoding":904}," čtyřnásobně, změní se ",[883,79348,79350],{"className":79349},[886],[888,79351,79352],{"xmlns":890},[892,79353,79354,79358],{},[895,79355,79356],{},[898,79357,1872],{},[902,79359,1872],{"encoding":904},[883,79361,79363],{"className":79362},[886],[888,79364,79365],{"xmlns":890},[892,79366,79367,79397],{},[895,79368,79369,79389,79391],{},[1850,79370,79371,79373],{},[1793,79372,2616],{},[895,79374,79375,79377,79379,79381,79383,79385,79387],{},[1793,79376,1795],{},[898,79378,4930],{"mathvariant":1822},[1793,79380,2616],{},[1688,79382,1696],{},[1793,79384,2131],{},[898,79386,4930],{"mathvariant":1822},[1793,79388,2616],{},[1688,79390,1690],{},[1850,79392,79393,79395],{},[1793,79394,2616],{},[1793,79396,1795],{},[902,79398,79399],{"encoding":904},"4^{1\u002F4 + 3\u002F4} = 4^1","-krát:",[883,79402,79404],{"className":79403},[886],[888,79405,79406],{"xmlns":890,"display":28306},[892,79407,79408,79568],{},[895,79409,79410,79412,79414,79416,79418,79420,79422,79424,79426,79428,79430,79432,79434,79436,79448,79450,79452,79454,79466,79468,79470,79472,79492,79504,79516,79518,79520,79522,79524,79536,79548,79550,79552,79554,79556,79558,79560,79562,79564,79566],{},[898,79411,1872],{},[1688,79413,2066],{"stretchy":2065},[1793,79415,2616],{},[898,79417,10047],{},[1688,79419,1733],{"separator":1732},[1793,79421,2616],{},[898,79423,10052],{},[1688,79425,2076],{"stretchy":2065},[1688,79427,1690],{},[1793,79429,1806],{},[1688,79431,2066],{"stretchy":2065},[1793,79433,2616],{},[898,79435,10047],{},[1850,79437,79438,79440],{},[1688,79439,2076],{"stretchy":2065},[895,79441,79442,79444,79446],{},[1793,79443,1795],{},[898,79445,4930],{"mathvariant":1822},[1793,79447,2616],{},[1688,79449,2066],{"stretchy":2065},[1793,79451,2616],{},[898,79453,10052],{},[1850,79455,79456,79458],{},[1688,79457,2076],{"stretchy":2065},[895,79459,79460,79462,79464],{},[1793,79461,2131],{},[898,79463,4930],{"mathvariant":1822},[1793,79465,2616],{},[1688,79467,1690],{},[1793,79469,1806],{},[1688,79471,3434],{},[1850,79473,79474,79476],{},[1793,79475,2616],{},[895,79477,79478,79480,79482,79484,79486,79488,79490],{},[1793,79479,1795],{},[898,79481,4930],{"mathvariant":1822},[1793,79483,2616],{},[1688,79485,1696],{},[1793,79487,2131],{},[898,79489,4930],{"mathvariant":1822},[1793,79491,2616],{},[1850,79493,79494,79496],{},[898,79495,10047],{},[895,79497,79498,79500,79502],{},[1793,79499,1795],{},[898,79501,4930],{"mathvariant":1822},[1793,79503,2616],{},[1850,79505,79506,79508],{},[898,79507,10052],{},[895,79509,79510,79512,79514],{},[1793,79511,2131],{},[898,79513,4930],{"mathvariant":1822},[1793,79515,2616],{},[1688,79517,1690],{},[1793,79519,2616],{},[1688,79521,3434],{},[1793,79523,1806],{},[1850,79525,79526,79528],{},[898,79527,10047],{},[895,79529,79530,79532,79534],{},[1793,79531,1795],{},[898,79533,4930],{"mathvariant":1822},[1793,79535,2616],{},[1850,79537,79538,79540],{},[898,79539,10052],{},[895,79541,79542,79544,79546],{},[1793,79543,2131],{},[898,79545,4930],{"mathvariant":1822},[1793,79547,2616],{},[1688,79549,1690],{},[1793,79551,2616],{},[2041,79553,2043],{},[898,79555,1872],{},[1688,79557,2066],{"stretchy":2065},[898,79559,10047],{},[1688,79561,1733],{"separator":1732},[898,79563,10052],{},[1688,79565,2076],{"stretchy":2065},[898,79567,2263],{"mathvariant":1822},[902,79569,79570],{"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).",[198,79572,79573],{"id":37419},"Homogenita",[724,79575,79576,79577,8358,79600,79616],{},"Funkce ",[883,79578,79580],{"className":79579},[886],[888,79581,79582],{"xmlns":890},[892,79583,79584,79598],{},[895,79585,79586,79588,79590,79592,79594,79596],{},[898,79587,1872],{},[1688,79589,2066],{"stretchy":2065},[898,79591,10047],{},[1688,79593,1733],{"separator":1732},[898,79595,10052],{},[1688,79597,2076],{"stretchy":2065},[902,79599,10249],{"encoding":904},[38,79601,79602,79603],{},"homogenní stupně ",[883,79604,79606],{"className":79605},[886],[888,79607,79608],{"xmlns":890},[892,79609,79610,79614],{},[895,79611,79612],{},[898,79613,37100],{},[902,79615,37100],{"encoding":904},", jestliže",[883,79618,79620],{"className":79619},[886],[888,79621,79622],{"xmlns":890,"display":28306},[892,79623,79624,79681],{},[20995,79625,79626],{"width":28311},[21000,79627,79628,79630,79674,79676],{},[21003,79629],{"width":28316},[21003,79631,79632],{},[895,79633,79634,79636,79638,79640,79642,79644,79646,79648,79650,79652,79658,79660,79662,79664,79666,79668,79670,79672],{},[898,79635,1872],{},[1688,79637,2066],{"stretchy":2065},[898,79639,2046],{},[898,79641,10047],{},[1688,79643,1733],{"separator":1732},[898,79645,2046],{},[898,79647,10052],{},[1688,79649,2076],{"stretchy":2065},[1688,79651,1690],{},[1850,79653,79654,79656],{},[898,79655,2046],{},[898,79657,37100],{},[2041,79659,2043],{},[898,79661,1872],{},[1688,79663,2066],{"stretchy":2065},[898,79665,10047],{},[1688,79667,1733],{"separator":1732},[898,79669,10052],{},[1688,79671,2076],{"stretchy":2065},[1688,79673,1733],{"separator":1732},[21003,79675],{"width":28316},[21003,79677,79678],{},[2041,79679,79680],{},"(5.10)",[902,79682,79683],{"encoding":904},"Q(rL, rK) = r^n\\,Q(L, K), \\tag{5.10}",[724,79685,4567,79686,79704,79705,79723,79724,43876,79737,79740,79741,2263],{},[883,79687,79689],{"className":79688},[886],[888,79690,79691],{"xmlns":890},[892,79692,79693,79701],{},[895,79694,79695,79697,79699],{},[898,79696,37100],{},[1688,79698,4741],{},[1793,79700,1779],{},[902,79702,79703],{"encoding":904},"n \\geq 0"," je celé číslo a ",[883,79706,79708],{"className":79707},[886],[888,79709,79710],{"xmlns":890},[892,79711,79712,79720],{},[895,79713,79714,79716,79718],{},[898,79715,2046],{},[1688,79717,3665],{},[1793,79719,1779],{},[902,79721,79722],{"encoding":904},"r > 0",". Homogenní funkce stupně ",[883,79725,79727],{"className":79726},[886],[888,79728,79729],{"xmlns":890},[892,79730,79731,79735],{},[895,79732,79733],{},[1793,79734,1795],{},[902,79736,1795],{"encoding":904},[38,79738,79739],{},"lineárně homogenní",". Cobb-Douglasovy funkce jsou homogenní stupně ",[883,79742,79744],{"className":79743},[886],[888,79745,79746],{"xmlns":890},[892,79747,79748,79756],{},[895,79749,79750,79752,79754],{},[898,79751,207],{},[1688,79753,1696],{},[898,79755,1918],{},[902,79757,75064],{"encoding":904},[115,79759,79761],{"id":79760},"ryzí-cobb-douglas-a-ces","Ryzí Cobb-Douglas a CES",[724,79763,79764],{},[38,79765,79766],{},"Ryzí Cobb-Douglasovy funkce:",[883,79768,79770],{"className":79769},[886],[888,79771,79772],{"xmlns":890,"display":28306},[892,79773,79774,79833],{},[20995,79775,79776],{"width":28311},[21000,79777,79778,79780,79826,79828],{},[21003,79779],{"width":28316},[21003,79781,79782],{},[895,79783,79784,79786,79788,79790,79792,79798,79800,79812,79814,79816,79818,79820,79822,79824],{},[898,79785,1872],{},[1688,79787,1690],{},[898,79789,4512],{},[2041,79791,2043],{},[1850,79793,79794,79796],{},[898,79795,10047],{},[898,79797,207],{},[2041,79799,2043],{},[1850,79801,79802,79804],{},[898,79803,10052],{},[895,79805,79806,79808,79810],{},[1793,79807,1795],{},[1688,79809,1954],{},[898,79811,207],{},[1688,79813,1733],{"separator":1732},[6134,79815],{"width":15531},[1793,79817,1779],{},[1688,79819,3704],{},[898,79821,207],{},[1688,79823,3704],{},[1793,79825,13507],{},[21003,79827],{"width":28316},[21003,79829,79830],{},[2041,79831,79832],{},"(5.9)",[902,79834,79835],{"encoding":904},"Q = A\\,L^a\\,K^{1-a}, \\quad 0 \u003C a \u003C 1. \\tag{5.9}",[724,79837,79838,79839,79841,79842,2263],{},"Mají vždy ",[38,79840,79159],{}," a jsou ",[38,79843,79739],{},[724,79845,79846,10277,79849,79852],{},[38,79847,79848],{},"CES produkční funkce",[614,79850,79851],{},"Constant Elasticity of Substitution",", 1961):",[883,79854,79856],{"className":79855},[886],[888,79857,79858],{"xmlns":890,"display":28306},[892,79859,79860,79928],{},[895,79861,79862,79864,79866,79868,79926],{},[898,79863,1872],{},[1688,79865,1690],{},[898,79867,4512],{},[1850,79869,79870,79914],{},[895,79871,79872,79874,79876,79878,79880,79882,79884,79886,79896,79898,79900,79902,79912],{},[1688,79873,2748],{"fence":1732},[1688,79875,2066],{"stretchy":2065},[1793,79877,1795],{},[1688,79879,1954],{},[898,79881,207],{},[1688,79883,2076],{"stretchy":2065},[2041,79885,2043],{},[1850,79887,79888,79890],{},[898,79889,10047],{},[895,79891,79892,79894],{},[1688,79893,1954],{},[898,79895,1918],{},[1688,79897,1696],{},[898,79899,207],{},[2041,79901,2043],{},[1850,79903,79904,79906],{},[898,79905,10052],{},[895,79907,79908,79910],{},[1688,79909,1954],{},[898,79911,1918],{},[1688,79913,2763],{"fence":1732},[895,79915,79916,79918],{},[1688,79917,1954],{},[1777,79919,79920],{"scriptlevel":1779,"displaystyle":2065},[1781,79921,79922,79924],{},[1793,79923,1795],{},[898,79925,1918],{},[1688,79927,1733],{"separator":1732},[902,79929,79930],{"encoding":904},"Q = A\\left[(1-a)\\,L^{-b} + a\\,K^{-b}\\right]^{-\\tfrac{1}{b}},",[724,79932,4567,79933,1343,79951,1343,79972,79996],{},[883,79934,79936],{"className":79935},[886],[888,79937,79938],{"xmlns":890},[892,79939,79940,79948],{},[895,79941,79942,79944,79946],{},[898,79943,4512],{},[1688,79945,3665],{},[1793,79947,1779],{},[902,79949,79950],{"encoding":904},"A > 0",[883,79952,79954],{"className":79953},[886],[888,79955,79956],{"xmlns":890},[892,79957,79958,79970],{},[895,79959,79960,79962,79964,79966,79968],{},[1793,79961,1779],{},[1688,79963,3704],{},[898,79965,207],{},[1688,79967,3704],{},[1793,79969,1795],{},[902,79971,19078],{"encoding":904},[883,79973,79975],{"className":79974},[886],[888,79976,79977],{"xmlns":890},[892,79978,79979,79993],{},[895,79980,79981,79983,79985,79987,79989,79991],{},[1688,79982,1954],{},[1793,79984,1795],{},[1688,79986,3704],{},[898,79988,1918],{},[1688,79990,3628],{"mathvariant":1822},[1793,79992,1779],{},[902,79994,79995],{"encoding":904},"-1 \u003C b \\neq 0",". Cobb-Douglasovy funkce jsou jejich zvláštním případem.",[724,79998,79999],{},[38,80000,80001],{},"Další typy:",[120,80003,80004,80046],{},[123,80005,80006,2170,80009,80045],{},[38,80007,80008],{},"Lineární:",[883,80010,80012],{"className":80011},[886],[888,80013,80014],{"xmlns":890},[892,80015,80016,80042],{},[895,80017,80018,80020,80022,80024,80026,80028,80030,80032,80034,80036,80038,80040],{},[898,80019,1872],{},[1688,80021,2066],{"stretchy":2065},[898,80023,10047],{},[1688,80025,1733],{"separator":1732},[898,80027,10052],{},[1688,80029,2076],{"stretchy":2065},[1688,80031,1690],{},[898,80033,207],{},[898,80035,10047],{},[1688,80037,1696],{},[898,80039,1918],{},[898,80041,10052],{},[902,80043,80044],{"encoding":904},"Q(L, K) = aL + bK"," — dokonalé substituty.",[123,80047,80048,2170,80051,80096],{},[38,80049,80050],{},"Leontiefova:",[883,80052,80054],{"className":80053},[886],[888,80055,80056],{"xmlns":890},[892,80057,80058,80093],{},[895,80059,80060,80062,80064,80066,80068,80070,80072,80074,80077,80079,80081,80083,80085,80087,80089,80091],{},[898,80061,1872],{},[1688,80063,2066],{"stretchy":2065},[898,80065,10047],{},[1688,80067,1733],{"separator":1732},[898,80069,10052],{},[1688,80071,2076],{"stretchy":2065},[1688,80073,1690],{},[898,80075,80076],{},"min",[1688,80078,56440],{},[1688,80080,2066],{"stretchy":2065},[898,80082,207],{},[898,80084,10047],{},[1688,80086,1733],{"separator":1732},[898,80088,1918],{},[898,80090,10052],{},[1688,80092,2076],{"stretchy":2065},[902,80094,80095],{"encoding":904},"Q(L, K) = \\min(aL, bK)"," — dokonalé komplementy (fixní proporce).",[115,80098,80100,80101,1343,80120,80139],{"id":80099},"mezní-produkty-mplmp_l-mpkmp_k-a-totální-diferenciál","Mezní produkty ",[883,80102,80104],{"className":80103},[886],[888,80105,80106],{"xmlns":890},[892,80107,80108,80118],{},[895,80109,80110,80112],{},[898,80111,1661],{},[1788,80113,80114,80116],{},[898,80115,1727],{},[898,80117,10047],{},[902,80119,10297],{"encoding":904},[883,80121,80123],{"className":80122},[886],[888,80124,80125],{"xmlns":890},[892,80126,80127,80137],{},[895,80128,80129,80131],{},[898,80130,1661],{},[1788,80132,80133,80135],{},[898,80134,1727],{},[898,80136,10052],{},[902,80138,10342],{"encoding":904}," a totální diferenciál",[724,80141,80142],{},[38,80143,80144],{},"Mezní produkt práce:",[883,80146,80148],{"className":80147},[886],[888,80149,80150],{"xmlns":890,"display":28306},[892,80151,80152,80190],{},[895,80153,80154,80156,80162,80164,80172,80174,80188],{},[898,80155,1661],{},[1788,80157,80158,80160],{},[898,80159,1727],{},[898,80161,10047],{},[1688,80163,1690],{},[1814,80165,80166,80168,80170],{},[898,80167,1872],{},[898,80169,10047],{},[1688,80171,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,80173,1690],{},[1781,80175,80176,80182],{},[895,80177,80178,80180],{},[898,80179,10124],{"mathvariant":1822},[898,80181,1872],{},[895,80183,80184,80186],{},[898,80185,10124],{"mathvariant":1822},[898,80187,10047],{},[898,80189,2263],{"mathvariant":1822},[902,80191,80192],{"encoding":904},"MP_L = Q'_L = \\frac{\\partial Q}{\\partial L}.",[724,80194,80195],{},[38,80196,80197],{},"Mezní produkt kapitálu:",[883,80199,80201],{"className":80200},[886],[888,80202,80203],{"xmlns":890,"display":28306},[892,80204,80205,80243],{},[895,80206,80207,80209,80215,80217,80225,80227,80241],{},[898,80208,1661],{},[1788,80210,80211,80213],{},[898,80212,1727],{},[898,80214,10052],{},[1688,80216,1690],{},[1814,80218,80219,80221,80223],{},[898,80220,1872],{},[898,80222,10052],{},[1688,80224,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,80226,1690],{},[1781,80228,80229,80235],{},[895,80230,80231,80233],{},[898,80232,10124],{"mathvariant":1822},[898,80234,1872],{},[895,80236,80237,80239],{},[898,80238,10124],{"mathvariant":1822},[898,80240,10052],{},[898,80242,2263],{"mathvariant":1822},[902,80244,80245],{"encoding":904},"MP_K = Q'_K = \\frac{\\partial Q}{\\partial K}.",[724,80247,80248,80278,80279,80300,80301,80319,80320,80333,80334,2263],{},[883,80249,80251],{"className":80250},[886],[888,80252,80253],{"xmlns":890},[892,80254,80255,80275],{},[895,80256,80257,80259,80265,80267,80269,80271,80273],{},[898,80258,1661],{},[1788,80260,80261,80263],{},[898,80262,1727],{},[898,80264,10047],{},[1688,80266,2066],{"stretchy":2065},[898,80268,207],{},[1688,80270,1733],{"separator":1732},[898,80272,1918],{},[1688,80274,2076],{"stretchy":2065},[902,80276,80277],{"encoding":904},"MP_L(a, b)"," udává rychlost změny produkce vzhledem k práci v bodě ",[883,80280,80282],{"className":80281},[886],[888,80283,80284],{"xmlns":890},[892,80285,80286,80298],{},[895,80287,80288,80290,80292,80294,80296],{},[1688,80289,2748],{"stretchy":2065},[898,80291,207],{},[1688,80293,1733],{"separator":1732},[898,80295,1918],{},[1688,80297,2763],{"stretchy":2065},[902,80299,11075],{"encoding":904}," (na hladině ",[883,80302,80304],{"className":80303},[886],[888,80305,80306],{"xmlns":890},[892,80307,80308,80316],{},[895,80309,80310,80312,80314],{},[898,80311,10052],{},[1688,80313,1690],{},[898,80315,1918],{},[902,80317,80318],{"encoding":904},"K = b","), resp. přibližnou změnu produkce při jednotkové změně ",[883,80321,80323],{"className":80322},[886],[888,80324,80325],{"xmlns":890},[892,80326,80327,80331],{},[895,80328,80329],{},[898,80330,10047],{},[902,80332,10047],{"encoding":904},". Analogicky ",[883,80335,80337],{"className":80336},[886],[888,80338,80339],{"xmlns":890},[892,80340,80341,80361],{},[895,80342,80343,80345,80351,80353,80355,80357,80359],{},[898,80344,1661],{},[1788,80346,80347,80349],{},[898,80348,1727],{},[898,80350,10052],{},[1688,80352,2066],{"stretchy":2065},[898,80354,207],{},[1688,80356,1733],{"separator":1732},[898,80358,1918],{},[1688,80360,2076],{"stretchy":2065},[902,80362,80363],{"encoding":904},"MP_K(a, b)",[4124,80365,80366,80370],{},[724,80367,80368,51459],{},[883,80369,4412],{},[120,80371,80372,80410],{},[123,80373,80374,26430,80393],{},[883,80375,80377],{"className":80376},[886],[888,80378,80379],{"xmlns":890},[892,80380,80381,80391],{},[895,80382,80383,80385],{},[898,80384,1661],{},[1788,80386,80387,80389],{},[898,80388,1727],{},[898,80390,10047],{},[902,80392,10297],{"encoding":904},[614,80394,80395,80396,80409],{},"„o kolik vzroste ",[883,80397,80399],{"className":80398},[886],[888,80400,80401],{"xmlns":890},[892,80402,80403,80407],{},[895,80404,80405],{},[898,80406,1872],{},[902,80408,1872],{"encoding":904},", když přidám jednu jednotku práce (a kapitál držím pevně)?\"",[123,80411,80412,26430,80431],{},[883,80413,80415],{"className":80414},[886],[888,80416,80417],{"xmlns":890},[892,80418,80419,80429],{},[895,80420,80421,80423],{},[898,80422,1661],{},[1788,80424,80425,80427],{},[898,80426,1727],{},[898,80428,10052],{},[902,80430,10342],{"encoding":904},[614,80432,80395,80433,80446],{},[883,80434,80436],{"className":80435},[886],[888,80437,80438],{"xmlns":890},[892,80439,80440,80444],{},[895,80441,80442],{},[898,80443,1872],{},[902,80445,1872],{"encoding":904},", když přidám jednu jednotku kapitálu (a práci držím pevně)?\"",[724,80448,80449,80452,80453,80468,80469,2965],{},[38,80450,80451],{},"Totální diferenciál"," — přibližná změna produkce při změně práce o ",[883,80454,80456],{"className":80455},[886],[888,80457,80458],{"xmlns":890},[892,80459,80460,80466],{},[895,80461,80462,80464],{},[898,80463,2073],{},[898,80465,10047],{},[902,80467,75596],{"encoding":904}," a kapitálu o ",[883,80470,80472],{"className":80471},[886],[888,80473,80474],{"xmlns":890},[892,80475,80476,80482],{},[895,80477,80478,80480],{},[898,80479,2073],{},[898,80481,10052],{},[902,80483,80484],{"encoding":904},"dK",[883,80486,80488],{"className":80487},[886],[888,80489,80490],{"xmlns":890,"display":28306},[892,80491,80492,80585],{},[20995,80493,80494],{"width":28311},[21000,80495,80496,80498,80578,80580],{},[21003,80497],{"width":28316},[21003,80499,80500],{},[895,80501,80502,80504,80506,80508,80510,80512,80514,80522,80524,80526,80528,80530,80538,80540,80542,80544,80546,80548,80554,80556,80558,80560,80562,80564,80570,80572,80574,80576],{},[898,80503,3147],{"mathvariant":1822},[898,80505,1872],{},[1688,80507,2991],{},[898,80509,2073],{},[898,80511,1872],{},[1688,80513,1690],{},[1814,80515,80516,80518,80520],{},[898,80517,1872],{},[898,80519,10047],{},[1688,80521,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[2041,80523,2043],{},[898,80525,2073],{},[898,80527,10047],{},[1688,80529,1696],{},[1814,80531,80532,80534,80536],{},[898,80533,1872],{},[898,80535,10052],{},[1688,80537,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[2041,80539,2043],{},[898,80541,2073],{},[898,80543,10052],{},[1688,80545,1690],{},[898,80547,1661],{},[1788,80549,80550,80552],{},[898,80551,1727],{},[898,80553,10047],{},[2041,80555,2043],{},[898,80557,2073],{},[898,80559,10047],{},[1688,80561,1696],{},[898,80563,1661],{},[1788,80565,80566,80568],{},[898,80567,1727],{},[898,80569,10052],{},[2041,80571,2043],{},[898,80573,2073],{},[898,80575,10052],{},[898,80577,2263],{"mathvariant":1822},[21003,80579],{"width":28316},[21003,80581,80582],{},[2041,80583,80584],{},"(5.11)",[902,80586,80587],{"encoding":904},"\\Delta Q \\approx dQ = Q'_L\\,dL + Q'_K\\,dK = MP_L\\,dL + MP_K\\,dK. \\tag{5.11}",[724,80589,80590,80591,2263],{},"Skutečná změna: ",[883,80592,80594],{"className":80593},[886],[888,80595,80596],{"xmlns":890},[892,80597,80598,80644],{},[895,80599,80600,80602,80604,80606,80608,80610,80612,80614,80616,80618,80620,80622,80624,80626,80628,80630,80632,80634,80636,80638,80640,80642],{},[898,80601,3147],{"mathvariant":1822},[898,80603,1872],{},[1688,80605,1690],{},[898,80607,1872],{},[1688,80609,2066],{"stretchy":2065},[898,80611,10047],{},[1688,80613,1696],{},[898,80615,2073],{},[898,80617,10047],{},[1688,80619,1733],{"separator":1732},[898,80621,10052],{},[1688,80623,1696],{},[898,80625,2073],{},[898,80627,10052],{},[1688,80629,2076],{"stretchy":2065},[1688,80631,1954],{},[898,80633,1872],{},[1688,80635,2066],{"stretchy":2065},[898,80637,10047],{},[1688,80639,1733],{"separator":1732},[898,80641,10052],{},[1688,80643,2076],{"stretchy":2065},[902,80645,80646],{"encoding":904},"\\Delta Q = Q(L+dL, K+dK) - Q(L, K)",[724,80648,80649,80651,80652,80670,80671,80684,80685,80704,80705,80737,80738,80770,80771,2263],{},[38,80650,75760],{}," platí ve 2F modelu pro oba vstupy: pro pevné ",[883,80653,80655],{"className":80654},[886],[888,80656,80657],{"xmlns":890},[892,80658,80659,80667],{},[895,80660,80661],{},[1788,80662,80663,80665],{},[898,80664,10052],{},[1793,80666,1779],{},[902,80668,80669],{"encoding":904},"K_0"," se od jistého ",[883,80672,80674],{"className":80673},[886],[888,80675,80676],{"xmlns":890},[892,80677,80678,80682],{},[895,80679,80680],{},[898,80681,10047],{},[902,80683,10047],{"encoding":904}," stane ",[883,80686,80688],{"className":80687},[886],[888,80689,80690],{"xmlns":890},[892,80691,80692,80702],{},[895,80693,80694,80696],{},[898,80695,1661],{},[1788,80697,80698,80700],{},[898,80699,1727],{},[898,80701,10047],{},[902,80703,10297],{"encoding":904}," klesající (",[883,80706,80708],{"className":80707},[886],[888,80709,80710],{"xmlns":890},[892,80711,80712,80734],{},[895,80713,80714,80730,80732],{},[1814,80715,80716,80718,80724],{},[898,80717,1872],{},[895,80719,80720,80722],{},[898,80721,10047],{},[898,80723,10047],{},[895,80725,80726,80728],{},[1688,80727,1824],{"mathvariant":1822},[1688,80729,1824],{"mathvariant":1822},[1688,80731,3704],{},[1793,80733,1779],{},[902,80735,80736],{"encoding":904},"Q''_{LL} \u003C 0","); analogicky ",[883,80739,80741],{"className":80740},[886],[888,80742,80743],{"xmlns":890},[892,80744,80745,80767],{},[895,80746,80747,80763,80765],{},[1814,80748,80749,80751,80757],{},[898,80750,1872],{},[895,80752,80753,80755],{},[898,80754,10052],{},[898,80756,10052],{},[895,80758,80759,80761],{},[1688,80760,1824],{"mathvariant":1822},[1688,80762,1824],{"mathvariant":1822},[1688,80764,3704],{},[1793,80766,1779],{},[902,80768,80769],{"encoding":904},"Q''_{KK} \u003C 0"," pro pevné ",[883,80772,80774],{"className":80773},[886],[888,80775,80776],{"xmlns":890},[892,80777,80778,80786],{},[895,80779,80780],{},[1788,80781,80782,80784],{},[898,80783,10047],{},[1793,80785,1779],{},[902,80787,75798],{"encoding":904},[115,80789,80791],{"id":80790},"eulerova-věta-pro-homogenní-funkce","Eulerova věta pro homogenní funkce",[724,80793,80794,80797,80798,80821,80822,30184],{},[38,80795,80796],{},"Eulerova věta"," (úloha 5.10): pro homogenní funkci ",[883,80799,80801],{"className":80800},[886],[888,80802,80803],{"xmlns":890},[892,80804,80805,80819],{},[895,80806,80807,80809,80811,80813,80815,80817],{},[898,80808,1872],{},[1688,80810,2066],{"stretchy":2065},[898,80812,10047],{},[1688,80814,1733],{"separator":1732},[898,80816,10052],{},[1688,80818,2076],{"stretchy":2065},[902,80820,10249],{"encoding":904}," stupně ",[883,80823,80825],{"className":80824},[886],[888,80826,80827],{"xmlns":890},[892,80828,80829,80833],{},[895,80830,80831],{},[898,80832,37100],{},[902,80834,37100],{"encoding":904},[883,80836,80838],{"className":80837},[886],[888,80839,80840],{"xmlns":890,"display":28306},[892,80841,80842,80905],{},[20995,80843,80844],{"width":28311},[21000,80845,80846,80848,80898,80900],{},[21003,80847],{"width":28316},[21003,80849,80850],{},[895,80851,80852,80854,80856,80864,80866,80868,80870,80878,80880,80882,80884,80886,80888,80890,80892,80894,80896],{},[898,80853,10047],{},[2041,80855,2043],{},[1814,80857,80858,80860,80862],{},[898,80859,1872],{},[898,80861,10047],{},[1688,80863,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,80865,1696],{},[898,80867,10052],{},[2041,80869,2043],{},[1814,80871,80872,80874,80876],{},[898,80873,1872],{},[898,80875,10052],{},[1688,80877,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,80879,1690],{},[898,80881,37100],{},[2041,80883,2043],{},[898,80885,1872],{},[1688,80887,2066],{"stretchy":2065},[898,80889,10047],{},[1688,80891,1733],{"separator":1732},[898,80893,10052],{},[1688,80895,2076],{"stretchy":2065},[898,80897,2263],{"mathvariant":1822},[21003,80899],{"width":28316},[21003,80901,80902],{},[2041,80903,80904],{},"(5.12)",[902,80906,80907],{"encoding":904},"L\\,Q'_L + K\\,Q'_K = n\\,Q(L, K). \\tag{5.12}",[724,80909,80910,80931],{},[38,80911,80912,80913],{},"Speciální případ ",[883,80914,80916],{"className":80915},[886],[888,80917,80918],{"xmlns":890},[892,80919,80920,80928],{},[895,80921,80922,80924,80926],{},[898,80923,37100],{},[1688,80925,1690],{},[1793,80927,1795],{},[902,80929,80930],{"encoding":904},"n = 1"," (konstantní výnosy z rozsahu):",[883,80933,80935],{"className":80934},[886],[888,80936,80937],{"xmlns":890,"display":28306},[892,80938,80939,80983],{},[895,80940,80941,80943,80945,80947,80953,80955,80957,80959,80961,80967,80969,80971,80973,80975,80977,80979,80981],{},[898,80942,10047],{},[1688,80944,3434],{},[898,80946,1661],{},[1788,80948,80949,80951],{},[898,80950,1727],{},[898,80952,10047],{},[1688,80954,1696],{},[898,80956,10052],{},[1688,80958,3434],{},[898,80960,1661],{},[1788,80962,80963,80965],{},[898,80964,1727],{},[898,80966,10052],{},[1688,80968,1690],{},[898,80970,1872],{},[1688,80972,2066],{"stretchy":2065},[898,80974,10047],{},[1688,80976,1733],{"separator":1732},[898,80978,10052],{},[1688,80980,2076],{"stretchy":2065},[898,80982,2263],{"mathvariant":1822},[902,80984,80985],{"encoding":904},"L\\cdot MP_L + K\\cdot MP_K = Q(L, K).",[724,80987,80988,80989,80992],{},"Slovně — ",[38,80990,80991],{},"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).",[115,80994,10030],{"id":75134},[724,80996,80997,10277,80999,81002,81003,81025,81026,2965],{},[38,80998,10030],{},[614,81000,81001],{},"isoquants",") jsou křivky stejné produkce — množina dvojic ",[883,81004,81006],{"className":81005},[886],[888,81007,81008],{"xmlns":890},[892,81009,81010,81022],{},[895,81011,81012,81014,81016,81018,81020],{},[1688,81013,2748],{"stretchy":2065},[898,81015,10047],{},[1688,81017,1733],{"separator":1732},[898,81019,10052],{},[1688,81021,2763],{"stretchy":2065},[902,81023,81024],{"encoding":904},"[L, K]",", pro něž produkční funkce nabývá pevně zvolené hodnoty ",[883,81027,81029],{"className":81028},[886],[888,81030,81031],{"xmlns":890},[892,81032,81033,81038],{},[895,81034,81035],{},[898,81036,81037],{},"q",[902,81039,81037],{"encoding":904},[883,81041,81043],{"className":81042},[886],[888,81044,81045],{"xmlns":890,"display":28306},[892,81046,81047,81082],{},[20995,81048,81049],{"width":28311},[21000,81050,81051,81053,81075,81077],{},[21003,81052],{"width":28316},[21003,81054,81055],{},[895,81056,81057,81059,81061,81063,81065,81067,81069,81071,81073],{},[898,81058,1872],{},[1688,81060,2066],{"stretchy":2065},[898,81062,10047],{},[1688,81064,1733],{"separator":1732},[898,81066,10052],{},[1688,81068,2076],{"stretchy":2065},[1688,81070,1690],{},[898,81072,81037],{},[898,81074,2263],{"mathvariant":1822},[21003,81076],{"width":28316},[21003,81078,81079],{},[2041,81080,81081],{},"(5.13)",[902,81083,81084],{"encoding":904},"Q(L, K) = q. \\tag{5.13}",[724,81086,81087,81088,81091,81092,4176],{},"Jsou to ",[38,81089,81090],{},"indiferenční křivky"," produkční funkce (analogie s indiferenčními křivkami u ",[207,81093,81095],{"className":81094,"dataFsResolvedFilePath":878,"href":879},[210],"užitečnosti",[724,81097,81098],{},[38,81099,81100],{},"Vlastnosti izokvant Cobb-Douglasových funkcí:",[120,81102,81103,81108,81113,81118],{},[123,81104,81105,81107],{},[38,81106,12767],{}," — pokles kapitálu vyžaduje kompenzující růst práce k udržení produkce;",[123,81109,81110,81112],{},[38,81111,37904],{}," (úloha 5.14);",[123,81114,81115,8681],{},[38,81116,81117],{},"neprotínají se",[123,81119,81120,81121,4614,81134,2263],{},"s rostoucím ",[883,81122,81124],{"className":81123},[886],[888,81125,81126],{"xmlns":890},[892,81127,81128,81132],{},[895,81129,81130],{},[898,81131,81037],{},[902,81133,81037],{"encoding":904},[38,81135,81136],{},"vzdalují od počátku",[724,81138,81139],{},[614,81140,81141,81142,81164,81165,2263],{},"Obrázek 5.4 — izokvanty Cobb-Douglasovy funkce v rovině ",[883,81143,81145],{"className":81144},[886],[888,81146,81147],{"xmlns":890},[892,81148,81149,81161],{},[895,81150,81151,81153,81155,81157,81159],{},[1688,81152,2066],{"stretchy":2065},[898,81154,10047],{},[1688,81156,1733],{"separator":1732},[898,81158,10052],{},[1688,81160,2076],{"stretchy":2065},[902,81162,81163],{"encoding":904},"(L, K)",": tři klesající konvexní křivky pro ",[883,81166,81168],{"className":81167},[886],[888,81169,81170],{"xmlns":890},[892,81171,81172,81196],{},[895,81173,81174,81180,81182,81188,81190],{},[1788,81175,81176,81178],{},[898,81177,81037],{},[1793,81179,1795],{},[1688,81181,3704],{},[1788,81183,81184,81186],{},[898,81185,81037],{},[1793,81187,1779],{},[1688,81189,3704],{},[1788,81191,81192,81194],{},[898,81193,81037],{},[1793,81195,1806],{},[902,81197,81198],{"encoding":904},"q_1 \u003C q_0 \u003C q_2",[115,81200,81202,81203,2076],{"id":81201},"mezní-míra-technické-substituce-mrtsmrts","Mezní míra technické substituce (",[883,81204,81206],{"className":81205},[886],[888,81207,81208],{"xmlns":890},[892,81209,81210,81220],{},[895,81211,81212,81214,81216,81218],{},[898,81213,1661],{},[898,81215,4251],{},[898,81217,3035],{},[898,81219,1740],{},[902,81221,10851],{"encoding":904},[724,81223,81224,10277,81227,81230],{},[38,81225,81226],{},"Mezní míra technické substituce",[614,81228,81229],{},"marginal rate of technical substitution",") je podíl mezních produktů:",[883,81232,81234],{"className":81233},[886],[888,81235,81236],{"xmlns":890,"display":28306},[892,81237,81238,81329],{},[20995,81239,81240],{"width":28311},[21000,81241,81242,81244,81322,81324],{},[21003,81243],{"width":28316},[21003,81245,81246],{},[895,81247,81248,81250,81252,81254,81256,81258,81260,81262,81264,81266,81268,81270,81272,81274,81276,81278,81300,81302,81320],{},[898,81249,1661],{},[898,81251,4251],{},[898,81253,3035],{},[898,81255,1740],{},[1688,81257,1690],{},[898,81259,1661],{},[898,81261,4251],{},[898,81263,3035],{},[898,81265,1740],{},[1688,81267,2066],{"stretchy":2065},[898,81269,10047],{},[1688,81271,1733],{"separator":1732},[898,81273,10052],{},[1688,81275,2076],{"stretchy":2065},[1688,81277,1690],{},[1781,81279,81280,81290],{},[895,81281,81282,81284],{},[898,81283,1661],{},[1788,81285,81286,81288],{},[898,81287,1727],{},[898,81289,10047],{},[895,81291,81292,81294],{},[898,81293,1661],{},[1788,81295,81296,81298],{},[898,81297,1727],{},[898,81299,10052],{},[1688,81301,1690],{},[1781,81303,81304,81312],{},[1814,81305,81306,81308,81310],{},[898,81307,1872],{},[898,81309,10047],{},[1688,81311,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1814,81313,81314,81316,81318],{},[898,81315,1872],{},[898,81317,10052],{},[1688,81319,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[898,81321,2263],{"mathvariant":1822},[21003,81323],{"width":28316},[21003,81325,81326],{},[2041,81327,81328],{},"(5.14)",[902,81330,81331],{"encoding":904},"MRTS = MRTS(L, K) = \\frac{MP_L}{MP_K} = \\frac{Q'_L}{Q'_K}. \\tag{5.14}",[724,81333,81334,2170,81336,81366,81367,81398],{},[38,81335,9469],{},[883,81337,81339],{"className":81338},[886],[888,81340,81341],{"xmlns":890},[892,81342,81343,81363],{},[895,81344,81345,81347,81349,81351,81353,81355,81357,81359,81361],{},[898,81346,1661],{},[898,81348,4251],{},[898,81350,3035],{},[898,81352,1740],{},[1688,81354,2066],{"stretchy":2065},[898,81356,10047],{},[1688,81358,1733],{"separator":1732},[898,81360,10052],{},[1688,81362,2076],{"stretchy":2065},[902,81364,81365],{"encoding":904},"MRTS(L, K)"," udává, ",[38,81368,81369,81370,81383,81384,81397],{},"o kolik se musí přibližně změnit kapitál ",[883,81371,81373],{"className":81372},[886],[888,81374,81375],{"xmlns":890},[892,81376,81377,81381],{},[895,81378,81379],{},[898,81380,10052],{},[902,81382,10052],{"encoding":904},", jestliže se práce ",[883,81385,81387],{"className":81386},[886],[888,81388,81389],{"xmlns":890},[892,81390,81391,81395],{},[895,81392,81393],{},[898,81394,10047],{},[902,81396,10047],{"encoding":904}," změní o jednotku, aby byla zachována produkce"," (pohyb po izokvantě).",[4124,81400,81401],{},[724,81402,81403,18265,81405,81424,81425,81462,81463,81466,81467,81471],{},[883,81404,4412],{},[883,81406,81408],{"className":81407},[886],[888,81409,81410],{"xmlns":890},[892,81411,81412,81422],{},[895,81413,81414,81416,81418,81420],{},[898,81415,1661],{},[898,81417,4251],{},[898,81419,3035],{},[898,81421,1740],{},[902,81423,10851],{"encoding":904}," říká: ",[614,81426,81427,81428,81447,81448,81461],{},"„jednu jednotku práce musím nahradit přibližně ",[883,81429,81431],{"className":81430},[886],[888,81432,81433],{"xmlns":890},[892,81434,81435,81445],{},[895,81436,81437,81439,81441,81443],{},[898,81438,1661],{},[898,81440,4251],{},[898,81442,3035],{},[898,81444,1740],{},[902,81446,10851],{"encoding":904}," jednotkami kapitálu, aby produkce ",[883,81449,81451],{"className":81450},[886],[888,81452,81453],{"xmlns":890},[892,81454,81455,81459],{},[895,81456,81457],{},[898,81458,1872],{},[902,81460,1872],{"encoding":904}," zůstala stejná.\""," Je to ",[38,81464,81465],{},"směnný kurz mezi vstupy"," při zachování produkce — přesná analogie ",[207,81468,81470],{"className":81469,"dataFsResolvedFilePath":878,"href":879},[210],"MRCS z teorie užitečnosti",", kde nahrazujeme spotřební statky při zachování užitku.",[724,81473,81474],{},[2821,81475],{"alt":81476,"className":81477,"src":81478},"imek-izokvanty-mrts",[210,2825],"\u002Fwiki-assets\u002Fimek-izokvanty-mrts.jpeg",[724,81480,81481,81484,81485,8358,81515,81537,81538,3408],{},[38,81482,81483],{},"Geometrická interpretace:"," sklon tečny k izokvantě v bodě ",[883,81486,81488],{"className":81487},[886],[888,81489,81490],{"xmlns":890},[892,81491,81492,81512],{},[895,81493,81494,81496,81502,81504,81510],{},[1688,81495,2748],{"stretchy":2065},[1788,81497,81498,81500],{},[898,81499,10047],{},[1793,81501,1779],{},[1688,81503,1733],{"separator":1732},[1788,81505,81506,81508],{},[898,81507,10052],{},[1793,81509,1779],{},[1688,81511,2763],{"stretchy":2065},[902,81513,81514],{"encoding":904},"[L_0, K_0]",[883,81516,81518],{"className":81517},[886],[888,81519,81520],{"xmlns":890},[892,81521,81522,81534],{},[895,81523,81524,81526,81528,81530,81532],{},[1688,81525,1954],{},[898,81527,1661],{},[898,81529,4251],{},[898,81531,3035],{},[898,81533,1740],{},[902,81535,81536],{"encoding":904},"-MRTS",". Z derivace implicitní funkce (při ",[883,81539,81541],{"className":81540},[886],[888,81542,81543],{"xmlns":890},[892,81544,81545,81567],{},[895,81546,81547,81549,81551,81553,81555,81557,81559,81561],{},[898,81548,1872],{},[1688,81550,2066],{"stretchy":2065},[898,81552,10047],{},[1688,81554,1733],{"separator":1732},[898,81556,10052],{},[1688,81558,2076],{"stretchy":2065},[1688,81560,1690],{},[1788,81562,81563,81565],{},[898,81564,81037],{},[1793,81566,1779],{},[902,81568,81569],{"encoding":904},"Q(L,K) = q_0",[883,81571,81573],{"className":81572},[886],[888,81574,81575],{"xmlns":890,"display":28306},[892,81576,81577,81629],{},[895,81578,81579,81593,81595,81597,81615,81617,81619,81621,81623,81625,81627],{},[1781,81580,81581,81587],{},[895,81582,81583,81585],{},[898,81584,2073],{},[898,81586,10052],{},[895,81588,81589,81591],{},[898,81590,2073],{},[898,81592,10047],{},[1688,81594,1690],{},[1688,81596,1954],{},[1781,81598,81599,81607],{},[1814,81600,81601,81603,81605],{},[898,81602,1872],{},[898,81604,10047],{},[1688,81606,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1814,81608,81609,81611,81613],{},[898,81610,1872],{},[898,81612,10052],{},[1688,81614,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,81616,1690],{},[1688,81618,1954],{},[898,81620,1661],{},[898,81622,4251],{},[898,81624,3035],{},[898,81626,1740],{},[898,81628,2263],{"mathvariant":1822},[902,81630,81631],{"encoding":904},"\\frac{dK}{dL} = -\\frac{Q'_L}{Q'_K} = -MRTS.",[724,81633,81634,81635,81650,81651,81667],{},"Změní-li se práce o ",[883,81636,81638],{"className":81637},[886],[888,81639,81640],{"xmlns":890},[892,81641,81642,81648],{},[895,81643,81644,81646],{},[898,81645,2073],{},[898,81647,10047],{},[902,81649,75596],{"encoding":904},", lze pro odhad změny kapitálu ",[883,81652,81654],{"className":81653},[886],[888,81655,81656],{"xmlns":890},[892,81657,81658,81664],{},[895,81659,81660,81662],{},[898,81661,3147],{"mathvariant":1822},[898,81663,10052],{},[902,81665,81666],{"encoding":904},"\\Delta K"," k udržení produkce použít diferenciál:",[883,81669,81671],{"className":81670},[886],[888,81672,81673],{"xmlns":890,"display":28306},[892,81674,81675,81722],{},[20995,81676,81677],{"width":28311},[21000,81678,81679,81681,81715,81717],{},[21003,81680],{"width":28316},[21003,81682,81683],{},[895,81684,81685,81687,81689,81691,81693,81695,81697,81699,81701,81703,81705,81707,81709,81711,81713],{},[898,81686,3147],{"mathvariant":1822},[898,81688,10052],{},[1688,81690,2991],{},[898,81692,2073],{},[898,81694,10052],{},[1688,81696,1690],{},[1688,81698,1954],{},[898,81700,1661],{},[898,81702,4251],{},[898,81704,3035],{},[898,81706,1740],{},[2041,81708,2043],{},[898,81710,2073],{},[898,81712,10047],{},[1688,81714,1733],{"separator":1732},[21003,81716],{"width":28316},[21003,81718,81719],{},[2041,81720,81721],{},"(5.15)",[902,81723,81724],{"encoding":904},"\\Delta K \\approx dK = -MRTS\\,dL, \\tag{5.15}",[883,81726,81728],{"className":81727},[886],[888,81729,81730],{"xmlns":890,"display":28306},[892,81731,81732,81781],{},[20995,81733,81734],{"width":28311},[21000,81735,81736,81738,81774,81776],{},[21003,81737],{"width":28316},[21003,81739,81740],{},[895,81741,81742,81744,81746,81748,81766,81768,81770,81772],{},[898,81743,2073],{},[898,81745,10047],{},[1688,81747,1690],{},[1781,81749,81750,81756],{},[895,81751,81752,81754],{},[1688,81753,1954],{},[1793,81755,1795],{},[895,81757,81758,81760,81762,81764],{},[898,81759,1661],{},[898,81761,4251],{},[898,81763,3035],{},[898,81765,1740],{},[2041,81767,2043],{},[898,81769,2073],{},[898,81771,10052],{},[898,81773,2263],{"mathvariant":1822},[21003,81775],{"width":28316},[21003,81777,81778],{},[2041,81779,81780],{},"(5.16)",[902,81782,81783],{"encoding":904},"dL = \\frac{-1}{MRTS}\\,dK. \\tag{5.16}",[4124,81785,81786,81810],{},[724,81787,81788,81790,81791],{},[883,81789,4828],{}," Postup — jak spočítat ",[883,81792,81794],{"className":81793},[886],[888,81795,81796],{"xmlns":890},[892,81797,81798,81808],{},[895,81799,81800,81802,81804,81806],{},[898,81801,1661],{},[898,81803,4251],{},[898,81805,3035],{},[898,81807,1740],{},[902,81809,10851],{"encoding":904},[152,81811,81812,81853,81896,81928],{},[123,81813,81814,81815,4142,81834,2263],{},"Vypočtěte parciální derivace ",[883,81816,81818],{"className":81817},[886],[888,81819,81820],{"xmlns":890},[892,81821,81822,81832],{},[895,81823,81824],{},[1814,81825,81826,81828,81830],{},[898,81827,1872],{},[898,81829,10047],{},[1688,81831,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[902,81833,10273],{"encoding":904},[883,81835,81837],{"className":81836},[886],[888,81838,81839],{"xmlns":890},[892,81840,81841,81851],{},[895,81842,81843],{},[1814,81844,81845,81847,81849],{},[898,81846,1872],{},[898,81848,10052],{},[1688,81850,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[902,81852,10319],{"encoding":904},[123,81854,66081,81855,81895],{},[883,81856,81858],{"className":81857},[886],[888,81859,81860],{"xmlns":890},[892,81861,81862,81892],{},[895,81863,81864,81866,81868,81870,81872,81874,81882,81884],{},[898,81865,1661],{},[898,81867,4251],{},[898,81869,3035],{},[898,81871,1740],{},[1688,81873,1690],{},[1814,81875,81876,81878,81880],{},[898,81877,1872],{},[898,81879,10047],{},[1688,81881,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[898,81883,4930],{"mathvariant":1822},[1814,81885,81886,81888,81890],{},[898,81887,1872],{},[898,81889,10052],{},[1688,81891,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[902,81893,81894],{"encoding":904},"MRTS = Q'_L \u002F Q'_K"," (zlomek zjednodušte).",[123,81897,81898,81899,2263],{},"Případně dosaďte konkrétní ",[883,81900,81902],{"className":81901},[886],[888,81903,81904],{"xmlns":890},[892,81905,81906,81926],{},[895,81907,81908,81910,81916,81918,81924],{},[1688,81909,2748],{"stretchy":2065},[1788,81911,81912,81914],{},[898,81913,10047],{},[1793,81915,1779],{},[1688,81917,1733],{"separator":1732},[1788,81919,81920,81922],{},[898,81921,10052],{},[1793,81923,1779],{},[1688,81925,2763],{"stretchy":2065},[902,81927,81514],{"encoding":904},[123,81929,81930,81931,81965,81966,81968],{},"Pro odhad substituce použijte ",[883,81932,81934],{"className":81933},[886],[888,81935,81936],{"xmlns":890},[892,81937,81938,81962],{},[895,81939,81940,81942,81944,81946,81948,81950,81952,81954,81956,81958,81960],{},[898,81941,3147],{"mathvariant":1822},[898,81943,10052],{},[1688,81945,2991],{},[1688,81947,1954],{},[898,81949,1661],{},[898,81951,4251],{},[898,81953,3035],{},[898,81955,1740],{},[1688,81957,3434],{},[898,81959,3147],{"mathvariant":1822},[898,81961,10047],{},[902,81963,81964],{"encoding":904},"\\Delta K \\approx -MRTS \\cdot \\Delta L"," (znaménko ",[38,81967,52846],{}," — substituce, ne doplnění).",[724,81970,81971],{},[614,81972,81973,81974,82006,82007,2886,82020,16039,82049,82064],{},"Obrázek 5.7 — izokvanta ",[883,81975,81977],{"className":81976},[886],[888,81978,81979],{"xmlns":890},[892,81980,81981,82003],{},[895,81982,81983,81989,81991,81993,81995,81997,81999,82001],{},[1788,81984,81985,81987],{},[898,81986,81037],{},[1793,81988,1779],{},[1688,81990,1690],{},[898,81992,1872],{},[1688,81994,2066],{"stretchy":2065},[898,81996,10047],{},[1688,81998,1733],{"separator":1732},[898,82000,10052],{},[1688,82002,2076],{"stretchy":2065},[902,82004,82005],{"encoding":904},"q_0 = Q(L,K)"," s tečnou ",[883,82008,82010],{"className":82009},[886],[888,82011,82012],{"xmlns":890},[892,82013,82014,82018],{},[895,82015,82016],{},[898,82017,19097],{},[902,82019,19097],{"encoding":904},[883,82021,82023],{"className":82022},[886],[888,82024,82025],{"xmlns":890},[892,82026,82027,82047],{},[895,82028,82029,82031,82037,82039,82045],{},[1688,82030,2748],{"stretchy":2065},[1788,82032,82033,82035],{},[898,82034,10047],{},[1793,82036,1779],{},[1688,82038,1733],{"separator":1732},[1788,82040,82041,82043],{},[898,82042,10052],{},[1793,82044,1779],{},[1688,82046,2763],{"stretchy":2065},[902,82048,81514],{"encoding":904},[883,82050,82052],{"className":82051},[886],[888,82053,82054],{"xmlns":890},[892,82055,82056,82062],{},[895,82057,82058,82060],{},[898,82059,3147],{"mathvariant":1822},[898,82061,10052],{},[902,82063,81666],{"encoding":904}," odhadnut diferenciálem (záporně vzatý sklon tečny).",[115,82066,82068],{"id":82067},"příklady-dvoufaktorový-model","Příklady (dvoufaktorový model)",[198,82070,82072],{"id":82071},"příklad-54","Příklad 5.4",[724,82074,76913,82075,1343,82117,1343,82134,2263],{},[883,82076,82078],{"className":82077},[886],[888,82079,82080],{"xmlns":890},[892,82081,82082,82114],{},[895,82083,82084,82086,82088,82090,82102],{},[898,82085,1872],{},[1688,82087,1690],{},[1793,82089,36484],{},[1850,82091,82092,82094],{},[898,82093,10047],{},[895,82095,82096,82098,82100],{},[1793,82097,1795],{},[898,82099,4930],{"mathvariant":1822},[1793,82101,1806],{},[1850,82103,82104,82106],{},[898,82105,10052],{},[895,82107,82108,82110,82112],{},[1793,82109,1795],{},[898,82111,4930],{"mathvariant":1822},[1793,82113,2131],{},[902,82115,82116],{"encoding":904},"Q = 15 L^{1\u002F2} K^{1\u002F3}",[883,82118,82120],{"className":82119},[886],[888,82121,82122],{"xmlns":890},[892,82123,82124,82132],{},[895,82125,82126,82128,82130],{},[898,82127,10047],{},[1688,82129,1690],{},[1793,82131,9290],{},[902,82133,77287],{"encoding":904},[883,82135,82137],{"className":82136},[886],[888,82138,82139],{"xmlns":890},[892,82140,82141,82149],{},[895,82142,82143,82145,82147],{},[898,82144,10052],{},[1688,82146,1690],{},[1793,82148,3347],{},[902,82150,82151],{"encoding":904},"K = 100",[724,82153,82154],{},[38,82155,82156],{},"(a) Rychlost změny produkce vzhledem k práci.",[883,82158,82160],{"className":82159},[886],[888,82161,82162],{"xmlns":890,"display":28306},[892,82163,82164,82278],{},[895,82165,82166,82168,82174,82176,82184,82186,82194,82208,82220,82222,82224,82226,82232,82234,82236,82238,82240,82242,82244,82252,82254,82264,82266,82273,82275],{},[898,82167,1661],{},[1788,82169,82170,82172],{},[898,82171,1727],{},[898,82173,10047],{},[1688,82175,1690],{},[1814,82177,82178,82180,82182],{},[898,82179,1872],{},[898,82181,10047],{},[1688,82183,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,82185,1690],{},[1777,82187,82188],{"scriptlevel":1779,"displaystyle":2065},[1781,82189,82190,82192],{},[1793,82191,36484],{},[1793,82193,1806],{},[1850,82195,82196,82198],{},[898,82197,10047],{},[895,82199,82200,82202,82204,82206],{},[1688,82201,1954],{},[1793,82203,1795],{},[898,82205,4930],{"mathvariant":1822},[1793,82207,1806],{},[1850,82209,82210,82212],{},[898,82211,10052],{},[895,82213,82214,82216,82218],{},[1793,82215,1795],{},[898,82217,4930],{"mathvariant":1822},[1793,82219,2131],{},[1688,82221,1733],{"separator":1732},[6134,82223],{"width":15531},[898,82225,1661],{},[1788,82227,82228,82230],{},[898,82229,1727],{},[898,82231,10047],{},[1688,82233,2066],{"stretchy":2065},[1793,82235,9290],{},[1688,82237,1733],{"separator":1732},[1793,82239,3347],{},[1688,82241,2076],{"stretchy":2065},[1688,82243,1690],{},[1777,82245,82246],{"scriptlevel":1779,"displaystyle":2065},[1781,82247,82248,82250],{},[1793,82249,36484],{},[1793,82251,1806],{},[1688,82253,3434],{},[1777,82255,82256],{"scriptlevel":1779,"displaystyle":2065},[1781,82257,82258,82260],{},[1793,82259,1795],{},[8373,82261,82262],{},[1793,82263,9290],{},[1688,82265,3434],{},[82267,82268,82269,82271],"mroot",{},[1793,82270,3347],{},[1793,82272,2131],{},[1688,82274,2991],{},[1793,82276,82277],{},"7,153.",[902,82279,82280],{"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.",[724,82282,82283,82284,44400,82306,10485,82323,82344,82345,82366],{},"Přibližná změna při ",[883,82285,82287],{"className":82286},[886],[888,82288,82289],{"xmlns":890},[892,82290,82291,82303],{},[895,82292,82293,82295,82297,82299,82301],{},[898,82294,10047],{},[1688,82296,2965],{},[1793,82298,9290],{},[1688,82300,3380],{},[1793,82302,38586],{},[902,82304,82305],{"encoding":904},"L: 20 \\to 21",[883,82307,82309],{"className":82308},[886],[888,82310,82311],{"xmlns":890},[892,82312,82313,82321],{},[895,82314,82315,82317,82319],{},[898,82316,10052],{},[1688,82318,1690],{},[1793,82320,3347],{},[902,82322,82151],{"encoding":904},[883,82324,82326],{"className":82325},[886],[888,82327,82328],{"xmlns":890},[892,82329,82330,82341],{},[895,82331,82332,82334,82336,82338],{},[898,82333,3147],{"mathvariant":1822},[898,82335,1872],{},[1688,82337,2991],{},[1793,82339,82340],{},"7,153",[902,82342,82343],{"encoding":904},"\\Delta Q \\approx 7{,}153",". Skutečně ",[883,82346,82348],{"className":82347},[886],[888,82349,82350],{"xmlns":890},[892,82351,82352,82363],{},[895,82353,82354,82356,82358,82360],{},[898,82355,3147],{"mathvariant":1822},[898,82357,1872],{},[1688,82359,2991],{},[1793,82361,82362],{},"26,888",[902,82364,82365],{"encoding":904},"\\Delta Q \\approx 26{,}888"," (dle knihy; zaokrouhlení v konkrétním výpočtu).",[724,82368,82369,82372],{},[38,82370,82371],{},"(b) Pokles kapitálu o 1"," (z 100 na 99).",[883,82374,82376],{"className":82375},[886],[888,82377,82378],{"xmlns":890,"display":28306},[892,82379,82380,82480],{},[895,82381,82382,82384,82390,82392,82400,82402,82404,82416,82430,82432,82434,82436,82442,82444,82446,82448,82450,82452,82454,82456,82460,82462,82475,82477],{},[898,82383,1661],{},[1788,82385,82386,82388],{},[898,82387,1727],{},[898,82389,10052],{},[1688,82391,1690],{},[1814,82393,82394,82396,82398],{},[898,82395,1872],{},[898,82397,10052],{},[1688,82399,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,82401,1690],{},[1793,82403,2501],{},[1850,82405,82406,82408],{},[898,82407,10047],{},[895,82409,82410,82412,82414],{},[1793,82411,1795],{},[898,82413,4930],{"mathvariant":1822},[1793,82415,1806],{},[1850,82417,82418,82420],{},[898,82419,10052],{},[895,82421,82422,82424,82426,82428],{},[1688,82423,1954],{},[1793,82425,1806],{},[898,82427,4930],{"mathvariant":1822},[1793,82429,2131],{},[1688,82431,1733],{"separator":1732},[6134,82433],{"width":15531},[898,82435,1661],{},[1788,82437,82438,82440],{},[898,82439,1727],{},[898,82441,10052],{},[1688,82443,2066],{"stretchy":2065},[1793,82445,9290],{},[1688,82447,1733],{"separator":1732},[1793,82449,3347],{},[1688,82451,2076],{"stretchy":2065},[1688,82453,1690],{},[1793,82455,2501],{},[8373,82457,82458],{},[1793,82459,9290],{},[1688,82461,3434],{},[1777,82463,82464],{"scriptlevel":1779,"displaystyle":2065},[1781,82465,82466,82468],{},[1793,82467,1795],{},[82267,82469,82470,82473],{},[1793,82471,82472],{},"10000",[1793,82474,2131],{},[1688,82476,2991],{},[1793,82478,82479],{},"4,525.",[902,82481,82482],{"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.",[724,82484,82485,82486,2946,82503,4176],{},"Produkce poklesne přibližně o 4,525 (z ",[883,82487,82489],{"className":82488},[886],[888,82490,82491],{"xmlns":890},[892,82492,82493,82500],{},[895,82494,82495,82497],{},[1688,82496,2991],{},[1793,82498,82499],{},"905,126",[902,82501,82502],{"encoding":904},"\\approx 905{,}126",[883,82504,82506],{"className":82505},[886],[888,82507,82508],{"xmlns":890},[892,82509,82510,82517],{},[895,82511,82512,82514],{},[1688,82513,2991],{},[1793,82515,82516],{},"900,601",[902,82518,82519],{"encoding":904},"\\approx 900{,}601",[724,82521,82522,3387,82569,1343,82591,4176],{},[38,82523,82524,82525,4142,82547],{},"(c) Změna ",[883,82526,82528],{"className":82527},[886],[888,82529,82530],{"xmlns":890},[892,82531,82532,82544],{},[895,82533,82534,82536,82538,82540,82542],{},[898,82535,10047],{},[1688,82537,2965],{},[1793,82539,9290],{},[1688,82541,3380],{},[1793,82543,36484],{},[902,82545,82546],{"encoding":904},"L: 20 \\to 15",[883,82548,82550],{"className":82549},[886],[888,82551,82552],{"xmlns":890},[892,82553,82554,82566],{},[895,82555,82556,82558,82560,82562,82564],{},[898,82557,10052],{},[1688,82559,2965],{},[1793,82561,3347],{},[1688,82563,3380],{},[1793,82565,9058],{},[902,82567,82568],{"encoding":904},"K: 100 \\to 150",[883,82570,82572],{"className":82571},[886],[888,82573,82574],{"xmlns":890},[892,82575,82576,82588],{},[895,82577,82578,82580,82582,82584,82586],{},[898,82579,2073],{},[898,82581,10047],{},[1688,82583,1690],{},[1688,82585,1954],{},[1793,82587,2501],{},[902,82589,82590],{"encoding":904},"dL = -5",[883,82592,82594],{"className":82593},[886],[888,82595,82596],{"xmlns":890},[892,82597,82598,82608],{},[895,82599,82600,82602,82604,82606],{},[898,82601,2073],{},[898,82603,10052],{},[1688,82605,1690],{},[1793,82607,3377],{},[902,82609,82610],{"encoding":904},"dK = 50",[883,82612,82614],{"className":82613},[886],[888,82615,82616],{"xmlns":890,"display":28306},[892,82617,82618,82706],{},[895,82619,82620,82622,82624,82626,82628,82634,82636,82638,82640,82642,82644,82646,82648,82650,82652,82654,82656,82658,82664,82666,82668,82670,82672,82674,82676,82678,82680,82682,82684,82686,82688,82690,82692,82694,82697,82699,82701,82703],{},[898,82621,2073],{},[898,82623,1872],{},[1688,82625,1690],{},[898,82627,1661],{},[1788,82629,82630,82632],{},[898,82631,1727],{},[898,82633,10047],{},[1688,82635,2066],{"stretchy":2065},[1793,82637,9290],{},[1688,82639,1733],{"separator":1732},[1793,82641,3347],{},[1688,82643,2076],{"stretchy":2065},[1688,82645,3434],{},[1688,82647,2066],{"stretchy":2065},[1688,82649,1954],{},[1793,82651,2501],{},[1688,82653,2076],{"stretchy":2065},[1688,82655,1696],{},[898,82657,1661],{},[1788,82659,82660,82662],{},[898,82661,1727],{},[898,82663,10052],{},[1688,82665,2066],{"stretchy":2065},[1793,82667,9290],{},[1688,82669,1733],{"separator":1732},[1793,82671,3347],{},[1688,82673,2076],{"stretchy":2065},[1688,82675,3434],{},[1793,82677,3377],{},[1688,82679,1690],{},[1793,82681,82340],{},[1688,82683,3434],{},[1688,82685,2066],{"stretchy":2065},[1688,82687,1954],{},[1793,82689,2501],{},[1688,82691,2076],{"stretchy":2065},[1688,82693,1696],{},[1793,82695,82696],{},"4,525",[1688,82698,3434],{},[1793,82700,3377],{},[1688,82702,2991],{},[1793,82704,82705],{},"190,485.",[902,82707,82708],{"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.",[724,82710,82711],{},"Produkce vzroste přibližně z 905,126 na 995,611.",[198,82713,82715],{"id":82714},"příklad-55","Příklad 5.5",[724,82717,82718,82719,82755,82756,2263],{},"Pro produkci ",[883,82720,82722],{"className":82721},[886],[888,82723,82724],{"xmlns":890},[892,82725,82726,82752],{},[895,82727,82728,82730,82732,82734,82736,82738,82740,82742,82748],{},[898,82729,1872],{},[1688,82731,2066],{"stretchy":2065},[898,82733,10047],{},[1688,82735,1733],{"separator":1732},[898,82737,10052],{},[1688,82739,2076],{"stretchy":2065},[1688,82741,1690],{},[82267,82743,82744,82746],{},[898,82745,10047],{},[1793,82747,2131],{},[8373,82749,82750],{},[898,82751,10052],{},[902,82753,82754],{"encoding":904},"Q(L, K) = \\sqrt[3]{L}\\sqrt{K}"," mají izokvanty rovnici ",[883,82757,82759],{"className":82758},[886],[888,82760,82761],{"xmlns":890},[892,82762,82763,82779],{},[895,82764,82765,82771,82775,82777],{},[82267,82766,82767,82769],{},[898,82768,10047],{},[1793,82770,2131],{},[8373,82772,82773],{},[898,82774,10052],{},[1688,82776,1690],{},[898,82778,81037],{},[902,82780,82781],{"encoding":904},"\\sqrt[3]{L}\\sqrt{K} = q",[724,82783,82784,82785,2263],{},"Umocněním na druhou: ",[883,82786,82788],{"className":82787},[886],[888,82789,82790],{"xmlns":890},[892,82791,82792,82816],{},[895,82793,82794,82796,82798,82804,82806],{},[898,82795,10052],{},[1688,82797,1690],{},[1850,82799,82800,82802],{},[898,82801,81037],{},[1793,82803,1806],{},[898,82805,4930],{"mathvariant":1822},[82267,82807,82808,82814],{},[1850,82809,82810,82812],{},[898,82811,10047],{},[1793,82813,1806],{},[1793,82815,2131],{},[902,82817,82818],{"encoding":904},"K = q^2 \u002F \\sqrt[3]{L^2}",[120,82820,82821,82861,82901],{},[123,82822,82823],{},[883,82824,82826],{"className":82825},[886],[888,82827,82828],{"xmlns":890},[892,82829,82830,82858],{},[895,82831,82832,82834,82836,82838,82840,82842,82844,82846,82848],{},[898,82833,81037],{},[1688,82835,1690],{},[1793,82837,1795],{},[1688,82839,4244],{},[898,82841,10052],{},[1688,82843,1690],{},[1793,82845,1795],{},[898,82847,4930],{"mathvariant":1822},[82267,82849,82850,82856],{},[1850,82851,82852,82854],{},[898,82853,10047],{},[1793,82855,1806],{},[1793,82857,2131],{},[902,82859,82860],{"encoding":904},"q = 1 \\Rightarrow K = 1\u002F\\sqrt[3]{L^2}",[123,82862,82863],{},[883,82864,82866],{"className":82865},[886],[888,82867,82868],{"xmlns":890},[892,82869,82870,82898],{},[895,82871,82872,82874,82876,82878,82880,82882,82884,82886,82888],{},[898,82873,81037],{},[1688,82875,1690],{},[1793,82877,1806],{},[1688,82879,4244],{},[898,82881,10052],{},[1688,82883,1690],{},[1793,82885,2616],{},[898,82887,4930],{"mathvariant":1822},[82267,82889,82890,82896],{},[1850,82891,82892,82894],{},[898,82893,10047],{},[1793,82895,1806],{},[1793,82897,2131],{},[902,82899,82900],{"encoding":904},"q = 2 \\Rightarrow K = 4\u002F\\sqrt[3]{L^2}",[123,82902,82903],{},[883,82904,82906],{"className":82905},[886],[888,82907,82908],{"xmlns":890},[892,82909,82910,82938],{},[895,82911,82912,82914,82916,82918,82920,82922,82924,82926,82928],{},[898,82913,81037],{},[1688,82915,1690],{},[1793,82917,2131],{},[1688,82919,4244],{},[898,82921,10052],{},[1688,82923,1690],{},[1793,82925,4256],{},[898,82927,4930],{"mathvariant":1822},[82267,82929,82930,82936],{},[1850,82931,82932,82934],{},[898,82933,10047],{},[1793,82935,1806],{},[1793,82937,2131],{},[902,82939,82940],{"encoding":904},"q = 3 \\Rightarrow K = 9\u002F\\sqrt[3]{L^2}",[724,82942,82943],{},[614,82944,82945,82946,6729,82967,2263],{},"Obrázek 5.5 — tři klesající konvexní izokvanty v rovině ",[883,82947,82949],{"className":82948},[886],[888,82950,82951],{"xmlns":890},[892,82952,82953,82965],{},[895,82954,82955,82957,82959,82961,82963],{},[1688,82956,2066],{"stretchy":2065},[898,82958,10047],{},[1688,82960,1733],{"separator":1732},[898,82962,10052],{},[1688,82964,2076],{"stretchy":2065},[902,82966,81163],{"encoding":904},[883,82968,82970],{"className":82969},[886],[888,82971,82972],{"xmlns":890},[892,82973,82974,82990],{},[895,82975,82976,82978,82980,82982,82984,82986,82988],{},[898,82977,81037],{},[1688,82979,1690],{},[1793,82981,1795],{},[1688,82983,1733],{"separator":1732},[1793,82985,1806],{},[1688,82987,1733],{"separator":1732},[1793,82989,2131],{},[902,82991,82992],{"encoding":904},"q = 1, 2, 3",[198,82994,82996],{"id":82995},"příklad-56","Příklad 5.6",[724,82998,76913,82999,2263],{},[883,83000,83002],{"className":83001},[886],[888,83003,83004],{"xmlns":890},[892,83005,83006,83022],{},[895,83007,83008,83010,83012,83014,83016,83018],{},[898,83009,1872],{},[1688,83011,1690],{},[1793,83013,1806],{},[898,83015,10047],{},[1688,83017,1696],{},[8373,83019,83020],{},[898,83021,10052],{},[902,83023,83024],{"encoding":904},"Q = 2L + \\sqrt{K}",[883,83026,83028],{"className":83027},[886],[888,83029,83030],{"xmlns":890,"display":28306},[892,83031,83032,83074],{},[895,83033,83034,83036,83042,83044,83046,83048,83050,83052,83058,83060,83072],{},[898,83035,1661],{},[1788,83037,83038,83040],{},[898,83039,1727],{},[898,83041,10047],{},[1688,83043,1690],{},[1793,83045,1806],{},[1688,83047,1733],{"separator":1732},[6134,83049],{"width":6136},[898,83051,1661],{},[1788,83053,83054,83056],{},[898,83055,1727],{},[898,83057,10052],{},[1688,83059,1690],{},[1781,83061,83062,83064],{},[1793,83063,1795],{},[895,83065,83066,83068],{},[1793,83067,1806],{},[8373,83069,83070],{},[898,83071,10052],{},[898,83073,2263],{"mathvariant":1822},[902,83075,83076],{"encoding":904},"MP_L = 2, \\qquad MP_K = \\frac{1}{2\\sqrt{K}}.",[883,83078,83080],{"className":83079},[886],[888,83081,83082],{"xmlns":890,"display":28306},[892,83083,83084,83148],{},[895,83085,83086,83088,83090,83092,83094,83096,83118,83120,83138,83140,83142,83146],{},[898,83087,1661],{},[898,83089,4251],{},[898,83091,3035],{},[898,83093,1740],{},[1688,83095,1690],{},[1781,83097,83098,83108],{},[895,83099,83100,83102],{},[898,83101,1661],{},[1788,83103,83104,83106],{},[898,83105,1727],{},[898,83107,10047],{},[895,83109,83110,83112],{},[898,83111,1661],{},[1788,83113,83114,83116],{},[898,83115,1727],{},[898,83117,10052],{},[1688,83119,1690],{},[1781,83121,83122,83124],{},[1793,83123,1806],{},[1777,83125,83126],{"scriptlevel":1779,"displaystyle":2065},[1781,83127,83128,83130],{},[1793,83129,1795],{},[895,83131,83132,83134],{},[1793,83133,1806],{},[8373,83135,83136],{},[898,83137,10052],{},[1688,83139,1690],{},[1793,83141,2616],{},[8373,83143,83144],{},[898,83145,10052],{},[898,83147,2263],{"mathvariant":1822},[902,83149,83150],{"encoding":904},"MRTS = \\frac{MP_L}{MP_K} = \\frac{2}{\\tfrac{1}{2\\sqrt{K}}} = 4\\sqrt{K}.",[724,83152,83153,83154,83197,83198,83237,83238,2263],{},"Například ",[883,83155,83157],{"className":83156},[886],[888,83158,83159],{"xmlns":890},[892,83160,83161,83194],{},[895,83162,83163,83165,83167,83169,83171,83173,83175,83177,83179,83181,83183,83185,83189,83191],{},[898,83164,1661],{},[898,83166,4251],{},[898,83168,3035],{},[898,83170,1740],{},[1688,83172,2066],{"stretchy":2065},[1793,83174,2616],{},[1688,83176,1733],{"separator":1732},[1793,83178,24442],{},[1688,83180,2076],{"stretchy":2065},[1688,83182,1690],{},[1793,83184,2616],{},[8373,83186,83187],{},[1793,83188,24442],{},[1688,83190,2991],{},[1793,83192,83193],{},"10,58",[902,83195,83196],{"encoding":904},"MRTS(4, 7) = 4\\sqrt{7} \\approx 10{,}58",". Klesne-li práce z 4 na 3, je k udržení produkce ",[883,83199,83201],{"className":83200},[886],[888,83202,83203],{"xmlns":890},[892,83204,83205,83234],{},[895,83206,83207,83209,83211,83213,83215,83217,83219,83221,83223,83225,83229,83231],{},[898,83208,1872],{},[1688,83210,2066],{"stretchy":2065},[1793,83212,2616],{},[1688,83214,1733],{"separator":1732},[1793,83216,24442],{},[1688,83218,2076],{"stretchy":2065},[1688,83220,1690],{},[1793,83222,5841],{},[1688,83224,1696],{},[8373,83226,83227],{},[1793,83228,24442],{},[1688,83230,2991],{},[1793,83232,83233],{},"10,646",[902,83235,83236],{"encoding":904},"Q(4,7) = 8 + \\sqrt{7} \\approx 10{,}646"," třeba zvýšit kapitál přibližně o ",[883,83239,83241],{"className":83240},[886],[888,83242,83243],{"xmlns":890},[892,83244,83245,83253],{},[895,83246,83247,83249],{},[1793,83248,2616],{},[8373,83250,83251],{},[1793,83252,24442],{},[902,83254,83255],{"encoding":904},"4\\sqrt{7}",[724,83257,83258,83259,83279],{},"Pokud se práce naopak zvýší ze 4 na 6 (",[883,83260,83262],{"className":83261},[886],[888,83263,83264],{"xmlns":890},[892,83265,83266,83276],{},[895,83267,83268,83270,83272,83274],{},[898,83269,2073],{},[898,83271,10047],{},[1688,83273,1690],{},[1793,83275,1806],{},[902,83277,83278],{"encoding":904},"dL = 2","), k udržení produkce stačí snížit kapitál o",[883,83281,83283],{"className":83282},[886],[888,83284,83285],{"xmlns":890,"display":28306},[892,83286,83287,83336],{},[895,83288,83289,83291,83293,83295,83297,83299,83301,83303,83305,83307,83309,83311,83313,83315,83317,83319,83321,83323,83325,83329,83331,83333],{},[898,83290,2073],{},[898,83292,10052],{},[1688,83294,1690],{},[1688,83296,1954],{},[898,83298,1661],{},[898,83300,4251],{},[898,83302,3035],{},[898,83304,1740],{},[1688,83306,2066],{"stretchy":2065},[1793,83308,2616],{},[1688,83310,1733],{"separator":1732},[1793,83312,24442],{},[1688,83314,2076],{"stretchy":2065},[1688,83316,3434],{},[1793,83318,1806],{},[1688,83320,1690],{},[1688,83322,1954],{},[1793,83324,5841],{},[8373,83326,83327],{},[1793,83328,24442],{},[1688,83330,2991],{},[1688,83332,1954],{},[1793,83334,83335],{},"21,17.",[902,83337,83338],{"encoding":904},"dK = -MRTS(4,7)\\cdot 2 = -8\\sqrt{7} \\approx -21{,}17.",[115,83340,83342],{"id":83341},"shrnutí-kapitoly-5","Shrnutí kapitoly 5",[724,83344,83345,83346,1343,83348,4142,83350,83352,83353,83356,83357,83360],{},"Hlavními faktory produkce jsou ",[38,83347,75154],{},[38,83349,75170],{},[38,83351,75186],{},"; půda je standardní exogenní proměnná. Přicházejí proto v úvahu ",[38,83354,83355],{},"jednofaktorový"," (pouze práce) a ",[38,83358,83359],{},"dvoufaktorový"," (práce + kapitál) model.",[724,83362,83363,83364,83367,83368,83370,83371,83373,83374,26430,83377,83396,83397,83414,83415,83432,83433,83455,83456,4614,83475,2263],{},"V ",[38,83365,83366],{},"1F modelu"," se definuje ",[38,83369,10276],{}," (derivace produkce podle práce) a ",[38,83372,75089],{}," (podíl produkce a práce). Produkční funkce má typický tvar díky ",[38,83375,83376],{},"zákonu klesajících výnosů",[883,83378,83380],{"className":83379},[886],[888,83381,83382],{"xmlns":890},[892,83383,83384,83394],{},[895,83385,83386,83388],{},[898,83387,1661],{},[1788,83389,83390,83392],{},[898,83391,1727],{},[898,83393,10047],{},[902,83395,10297],{"encoding":904}," nejprve roste, od inflexního bodu ",[883,83398,83400],{"className":83399},[886],[888,83401,83402],{"xmlns":890},[892,83403,83404,83412],{},[895,83405,83406],{},[1788,83407,83408,83410],{},[898,83409,10047],{},[1793,83411,1779],{},[902,83413,75798],{"encoding":904}," klesá a v bodě ",[883,83416,83418],{"className":83417},[886],[888,83419,83420],{"xmlns":890},[892,83421,83422,83430],{},[895,83423,83424],{},[1788,83425,83426,83428],{},[898,83427,10047],{},[1793,83429,1795],{},[902,83431,13460],{"encoding":904}," dosahuje nuly (maximum produkce). Platí ",[38,83434,83435,83436],{},"princip maximalizace ",[883,83437,83439],{"className":83438},[886],[888,83440,83441],{"xmlns":890},[892,83442,83443,83453],{},[895,83444,83445,83447],{},[898,83446,4512],{},[1788,83448,83449,83451],{},[898,83450,1727],{},[898,83452,10047],{},[902,83454,74873],{"encoding":904},": v bodě maxima ",[883,83457,83459],{"className":83458},[886],[888,83460,83461],{"xmlns":890},[892,83462,83463,83473],{},[895,83464,83465,83467],{},[898,83466,4512],{},[1788,83468,83469,83471],{},[898,83470,1727],{},[898,83472,10047],{},[902,83474,74873],{"encoding":904},[883,83476,83478],{"className":83477},[886],[888,83479,83480],{"xmlns":890},[892,83481,83482,83502],{},[895,83483,83484,83486,83492,83494,83496],{},[898,83485,1661],{},[1788,83487,83488,83490],{},[898,83489,1727],{},[898,83491,10047],{},[1688,83493,1690],{},[898,83495,4512],{},[1788,83497,83498,83500],{},[898,83499,1727],{},[898,83501,10047],{},[902,83503,74903],{"encoding":904},[724,83505,83506,83507,83510,83511,2170,83514,83543,83544,83561,83562,83565,83566,83595,83596,83598,83599,8358,83629,83651],{},"Ve ",[38,83508,83509],{},"2F modelu"," se obvykle používají ",[38,83512,83513],{},"Cobb-Douglasovy funkce",[883,83515,83517],{"className":83516},[886],[888,83518,83519],{"xmlns":890},[892,83520,83521,83541],{},[895,83522,83523,83525,83527,83529,83535],{},[898,83524,1872],{},[1688,83526,1690],{},[898,83528,4512],{},[1850,83530,83531,83533],{},[898,83532,10047],{},[898,83534,207],{},[1850,83536,83537,83539],{},[898,83538,10052],{},[898,83540,1918],{},[902,83542,74970],{"encoding":904},", které reflektují proporcionalitu změn vstupů a výstupu. Podle ",[883,83545,83547],{"className":83546},[886],[888,83548,83549],{"xmlns":890},[892,83550,83551,83559],{},[895,83552,83553,83555,83557],{},[898,83554,207],{},[1688,83556,1696],{},[898,83558,1918],{},[902,83560,75064],{"encoding":904}," rozlišujeme ",[38,83563,83564],{},"konstantní, rostoucí, klesající výnosy z rozsahu",". Mezní produkty ",[883,83567,83569],{"className":83568},[886],[888,83570,83571],{"xmlns":890},[892,83572,83573,83593],{},[895,83574,83575,83577,83583,83585,83587],{},[898,83576,1661],{},[1788,83578,83579,83581],{},[898,83580,1727],{},[898,83582,10047],{},[1688,83584,1733],{"separator":1732},[898,83586,1661],{},[1788,83588,83589,83591],{},[898,83590,1727],{},[898,83592,10052],{},[902,83594,75001],{"encoding":904}," jsou parciální derivace, totální diferenciál dává přibližnou změnu produkce. ",[38,83597,10030],{}," jsou indiferenční křivky produkční funkce. Podíl ",[883,83600,83602],{"className":83601},[886],[888,83603,83604],{"xmlns":890},[892,83605,83606,83626],{},[895,83607,83608,83610,83616,83618,83620],{},[898,83609,1661],{},[1788,83611,83612,83614],{},[898,83613,1727],{},[898,83615,10047],{},[898,83617,4930],{"mathvariant":1822},[898,83619,1661],{},[1788,83621,83622,83624],{},[898,83623,1727],{},[898,83625,10052],{},[902,83627,83628],{"encoding":904},"MP_L\u002FMP_K",[38,83630,83631,83632,2076],{},"mezní míra technické substituce (",[883,83633,83635],{"className":83634},[886],[888,83636,83637],{"xmlns":890},[892,83638,83639,83649],{},[895,83640,83641,83643,83645,83647],{},[898,83642,1661],{},[898,83644,4251],{},[898,83646,3035],{},[898,83648,1740],{},[902,83650,10851],{"encoding":904}," — udává, o kolik se musí změnit kapitál při jednotkové změně práce pro zachování produkce.",[115,83653,50122],{"id":50121},[152,83655,83656,83659,83662,83665,83668,83671,83674,83677,83680,83683,83686],{},[123,83657,83658],{},"Jaké jsou faktory produkce?",[123,83660,83661],{},"Jak se dospěje k jednofaktorovému a dvoufaktorovému modelu produkce?",[123,83663,83664],{},"Jak je zadána produkční funkce u jednofaktorového modelu?",[123,83666,83667],{},"Co udává mezní produkt práce?",[123,83669,83670],{},"Co musí respektovat průběh křivky produkce?",[123,83672,83673],{},"Jak lze matematicky vyjádřit zákon klesajících výnosů?",[123,83675,83676],{},"Jaký základní ekonomický požadavek respektují Cobb-Douglasovy funkce?",[123,83678,83679],{},"Jak se vypočtou mezní produkty práce a kapitálu?",[123,83681,83682],{},"Jak se stanoví přibližná změna produkce v závislosti na změnách práce a kapitálu?",[123,83684,83685],{},"Co vyjadřují izokvanty? Jaké jsou jejich typické vlastnosti?",[123,83687,83688],{},"Jak se vypočte mezní míra technické substituce a co vyjadřuje?",[115,83690,83692],{"id":83691},"úlohy-51517","Úlohy 5.1–5.17",[198,83694,40691],{"id":40690},[724,83696,83697,83700,83701,83723,83724,1343,83744,1343,83764,83784],{},[38,83698,83699],{},"5.1"," Je dána produkce ",[883,83702,83704],{"className":83703},[886],[888,83705,83706],{"xmlns":890},[892,83707,83708,83720],{},[895,83709,83710,83712,83714,83716],{},[898,83711,1872],{},[1688,83713,1690],{},[1793,83715,3121],{},[8373,83717,83718],{},[898,83719,10047],{},[902,83721,83722],{"encoding":904},"Q = 10\\sqrt{L}",". (a) Vypočtěte ",[883,83725,83727],{"className":83726},[886],[888,83728,83729],{"xmlns":890},[892,83730,83731,83741],{},[895,83732,83733,83735,83737,83739],{},[898,83734,1872],{},[1688,83736,2066],{"stretchy":2065},[1793,83738,1795],{},[1688,83740,2076],{"stretchy":2065},[902,83742,83743],{"encoding":904},"Q(1)",[883,83745,83747],{"className":83746},[886],[888,83748,83749],{"xmlns":890},[892,83750,83751,83761],{},[895,83752,83753,83755,83757,83759],{},[898,83754,1872],{},[1688,83756,2066],{"stretchy":2065},[1793,83758,2616],{},[1688,83760,2076],{"stretchy":2065},[902,83762,83763],{"encoding":904},"Q(4)",[883,83765,83767],{"className":83766},[886],[888,83768,83769],{"xmlns":890},[892,83770,83771,83781],{},[895,83772,83773,83775,83777,83779],{},[898,83774,1872],{},[1688,83776,2066],{"stretchy":2065},[1793,83778,4256],{},[1688,83780,2076],{"stretchy":2065},[902,83782,83783],{"encoding":904},"Q(9)",". (b) Rozhodněte, kdy produkce roste, resp. klesá. (c) Rozhodněte, kdy je křivka produkce konvexní, resp. konkávní. (d) Načrtněte křivku produkce.",[724,83786,83787,83700,83790,83826,83827,83840,83841,83860,83861,83887,83888,2946,83901,83914],{},[38,83788,83789],{},"5.2",[883,83791,83793],{"className":83792},[886],[888,83794,83795],{"xmlns":890},[892,83796,83797,83823],{},[895,83798,83799,83801,83803,83805,83807,83813,83815,83817],{},[898,83800,1872],{},[1688,83802,1690],{},[1688,83804,1954],{},[1793,83806,3053],{},[1850,83808,83809,83811],{},[898,83810,10047],{},[1793,83812,2131],{},[1688,83814,1696],{},[1793,83816,4256],{},[1850,83818,83819,83821],{},[898,83820,10047],{},[1793,83822,1806],{},[902,83824,83825],{"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 ",[883,83828,83830],{"className":83829},[886],[888,83831,83832],{"xmlns":890},[892,83833,83834,83838],{},[895,83835,83836],{},[898,83837,10047],{},[902,83839,10047],{"encoding":904}," (počet pracovníků), které maximalizuje produkci a stanovte příslušné maximum produkce. (d) Načrtněte křivku produkce. (e) Najděte mezní produkt práce ",[883,83842,83844],{"className":83843},[886],[888,83845,83846],{"xmlns":890},[892,83847,83848,83858],{},[895,83849,83850,83852],{},[898,83851,1661],{},[1788,83853,83854,83856],{},[898,83855,1727],{},[898,83857,10047],{},[902,83859,10297],{"encoding":904},". (f) Vypočtěte ",[883,83862,83864],{"className":83863},[886],[888,83865,83866],{"xmlns":890},[892,83867,83868,83884],{},[895,83869,83870,83872,83878,83880,83882],{},[898,83871,1661],{},[1788,83873,83874,83876],{},[898,83875,1727],{},[898,83877,10047],{},[1688,83879,2066],{"stretchy":2065},[1793,83881,3121],{},[1688,83883,2076],{"stretchy":2065},[902,83885,83886],{"encoding":904},"MP_L(10)"," a ekonomicky interpretujte. (g) Určete přibližnou změnu produkce v důsledku zvýšení počtu pracovníků z ",[883,83889,83891],{"className":83890},[886],[888,83892,83893],{"xmlns":890},[892,83894,83895,83899],{},[895,83896,83897],{},[1793,83898,3121],{},[902,83900,3121],{"encoding":904},[883,83902,83904],{"className":83903},[886],[888,83905,83906],{"xmlns":890},[892,83907,83908,83912],{},[895,83909,83910],{},[1793,83911,42527],{},[902,83913,42527],{"encoding":904}," a porovnejte se skutečnou změnou produkce.",[724,83916,83917,83920,83921,83943,83944,83972,83973,84004,84005,2263],{},[38,83918,83919],{},"5.3"," Pro zadanou produkci ověřte platnost zákona klesajících výnosů a charakterizujte vlastnosti mezního produktu práce:\n(a) ",[883,83922,83924],{"className":83923},[886],[888,83925,83926],{"xmlns":890},[892,83927,83928,83940],{},[895,83929,83930,83932,83934,83936],{},[898,83931,1872],{},[1688,83933,1690],{},[1793,83935,15357],{},[8373,83937,83938],{},[898,83939,10047],{},[902,83941,83942],{"encoding":904},"Q = 500\\sqrt{L}",".\n(b) ",[883,83945,83947],{"className":83946},[886],[888,83948,83949],{"xmlns":890},[892,83950,83951,83969],{},[895,83952,83953,83955,83957,83959,83963,83965,83967],{},[898,83954,1872],{},[1688,83956,1690],{},[1793,83958,30321],{},[8373,83960,83961],{},[898,83962,10047],{},[1688,83964,1954],{},[1793,83966,2616],{},[898,83968,10047],{},[902,83970,83971],{"encoding":904},"Q = 300\\sqrt{L} - 4L",".\n(c) ",[883,83974,83976],{"className":83975},[886],[888,83977,83978],{"xmlns":890},[892,83979,83980,84001],{},[895,83981,83982,83984,83986,83988,83990,83992,83995],{},[898,83983,1872],{},[1688,83985,1690],{},[1793,83987,3377],{},[898,83989,10047],{},[1688,83991,1954],{},[1793,83993,83994],{},"0,01",[1850,83996,83997,83999],{},[898,83998,10047],{},[1793,84000,1806],{},[902,84002,84003],{"encoding":904},"Q = 50L - 0{,}01 L^{2}",".\n(d) ",[883,84006,84008],{"className":84007},[886],[888,84009,84010],{"xmlns":890},[892,84011,84012,84038],{},[895,84013,84014,84016,84018,84020,84022,84028,84030,84032],{},[898,84015,1872],{},[1688,84017,1690],{},[1688,84019,1954],{},[1793,84021,68451],{},[1850,84023,84024,84026],{},[898,84025,10047],{},[1793,84027,2131],{},[1688,84029,1696],{},[1793,84031,4256],{},[1850,84033,84034,84036],{},[898,84035,10047],{},[1793,84037,1806],{},[902,84039,84040],{"encoding":904},"Q = -0{,}3 L^{3} + 9 L^{2}",[724,84042,84043,84046,84047,2886,84066,72438,84083,2263],{},[38,84044,84045],{},"5.4"," Dokažte, že má-li průměrný produkt práce ",[883,84048,84050],{"className":84049},[886],[888,84051,84052],{"xmlns":890},[892,84053,84054,84064],{},[895,84055,84056,84058],{},[898,84057,4512],{},[1788,84059,84060,84062],{},[898,84061,1727],{},[898,84063,10047],{},[902,84065,74873],{"encoding":904},[883,84067,84069],{"className":84068},[886],[888,84070,84071],{"xmlns":890},[892,84072,84073,84081],{},[895,84074,84075],{},[1788,84076,84077,84079],{},[898,84078,10047],{},[1793,84080,1779],{},[902,84082,75798],{"encoding":904},[883,84084,84086],{"className":84085},[886],[888,84087,84088],{"xmlns":890},[892,84089,84090,84130],{},[895,84091,84092,84094,84100,84102,84108,84110,84112,84114,84120,84122,84128],{},[898,84093,4512],{},[1788,84095,84096,84098],{},[898,84097,1727],{},[898,84099,10047],{},[1688,84101,2066],{"stretchy":2065},[1788,84103,84104,84106],{},[898,84105,10047],{},[1793,84107,1779],{},[1688,84109,2076],{"stretchy":2065},[1688,84111,1690],{},[898,84113,1661],{},[1788,84115,84116,84118],{},[898,84117,1727],{},[898,84119,10047],{},[1688,84121,2066],{"stretchy":2065},[1788,84123,84124,84126],{},[898,84125,10047],{},[1793,84127,1779],{},[1688,84129,2076],{"stretchy":2065},[902,84131,84132],{"encoding":904},"AP_L(L_0) = MP_L(L_0)",[724,84134,84135,83700,84138,21835,84174,84187,84188,84207],{},[38,84136,84137],{},"5.5",[883,84139,84141],{"className":84140},[886],[888,84142,84143],{"xmlns":890},[892,84144,84145,84171],{},[895,84146,84147,84149,84151,84153,84155,84161,84163,84165],{},[898,84148,1872],{},[1688,84150,1690],{},[1688,84152,1954],{},[1793,84154,3097],{},[1850,84156,84157,84159],{},[898,84158,10047],{},[1793,84160,2131],{},[1688,84162,1696],{},[1793,84164,3766],{},[1850,84166,84167,84169],{},[898,84168,10047],{},[1793,84170,1806],{},[902,84172,84173],{"encoding":904},"Q = -0{,}2 L^{3} + 12 L^{2}",[883,84175,84177],{"className":84176},[886],[888,84178,84179],{"xmlns":890},[892,84180,84181,84185],{},[895,84182,84183],{},[898,84184,10047],{},[902,84186,10047],{"encoding":904}," je počet pracovníků. (a) Určete počet pracovníků, při kterém je dosaženo nejvyšší produktivity práce (= maximálního průměrného produktu práce ",[883,84189,84191],{"className":84190},[886],[888,84192,84193],{"xmlns":890},[892,84194,84195,84205],{},[895,84196,84197,84199],{},[898,84198,4512],{},[1788,84200,84201,84203],{},[898,84202,1727],{},[898,84204,10047],{},[902,84206,74873],{"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.",[198,84209,84211],{"id":84210},"dvoufaktorový-model","Dvoufaktorový model",[724,84213,84214,84217,84218,83943,84244,83972,84286,2263],{},[38,84215,84216],{},"5.6"," Pro zadanou produkci rozhodněte, jaké výnosy z rozsahu představují:\n(a) ",[883,84219,84221],{"className":84220},[886],[888,84222,84223],{"xmlns":890},[892,84224,84225,84241],{},[895,84226,84227,84229,84231,84233,84235],{},[898,84228,1872],{},[1688,84230,1690],{},[1793,84232,24442],{},[898,84234,10047],{},[1850,84236,84237,84239],{},[898,84238,10052],{},[1793,84240,1806],{},[902,84242,84243],{"encoding":904},"Q = 7 L K^{2}",[883,84245,84247],{"className":84246},[886],[888,84248,84249],{"xmlns":890},[892,84250,84251,84283],{},[895,84252,84253,84255,84257,84259,84271],{},[898,84254,1872],{},[1688,84256,1690],{},[1793,84258,3377],{},[1850,84260,84261,84263],{},[898,84262,10047],{},[895,84264,84265,84267,84269],{},[1793,84266,1806],{},[898,84268,4930],{"mathvariant":1822},[1793,84270,2131],{},[1850,84272,84273,84275],{},[898,84274,10052],{},[895,84276,84277,84279,84281],{},[1793,84278,1795],{},[898,84280,4930],{"mathvariant":1822},[1793,84282,2131],{},[902,84284,84285],{"encoding":904},"Q = 50 L^{2\u002F3} K^{1\u002F3}",[883,84287,84289],{"className":84288},[886],[888,84290,84291],{"xmlns":890},[892,84292,84293,84325],{},[895,84294,84295,84297,84299,84301,84313],{},[898,84296,1872],{},[1688,84298,1690],{},[1793,84300,3964],{},[1850,84302,84303,84305],{},[898,84304,10047],{},[895,84306,84307,84309,84311],{},[1793,84308,2131],{},[898,84310,4930],{"mathvariant":1822},[1793,84312,2501],{},[1850,84314,84315,84317],{},[898,84316,10052],{},[895,84318,84319,84321,84323],{},[1793,84320,1806],{},[898,84322,4930],{"mathvariant":1822},[1793,84324,2501],{},[902,84326,84327],{"encoding":904},"Q = 18 L^{3\u002F5} K^{2\u002F5}",[724,84329,84330,83700,84333,84375,84376,1343,84394,84413,84414,84431],{},[38,84331,84332],{},"5.7",[883,84334,84336],{"className":84335},[886],[888,84337,84338],{"xmlns":890},[892,84339,84340,84372],{},[895,84341,84342,84344,84346,84348,84360],{},[898,84343,1872],{},[1688,84345,1690],{},[1793,84347,3121],{},[1850,84349,84350,84352],{},[898,84351,10047],{},[895,84353,84354,84356,84358],{},[1793,84355,1795],{},[898,84357,4930],{"mathvariant":1822},[1793,84359,1806],{},[1850,84361,84362,84364],{},[898,84363,10052],{},[895,84365,84366,84368,84370],{},[1793,84367,1795],{},[898,84369,4930],{"mathvariant":1822},[1793,84371,1806],{},[902,84373,84374],{"encoding":904},"Q = 10 L^{1\u002F2} K^{1\u002F2}",". (a) Vypočtěte produkci pro ",[883,84377,84379],{"className":84378},[886],[888,84380,84381],{"xmlns":890},[892,84382,84383,84391],{},[895,84384,84385,84387,84389],{},[898,84386,10047],{},[1688,84388,1690],{},[1793,84390,20383],{},[902,84392,84393],{"encoding":904},"L = 400",[883,84395,84397],{"className":84396},[886],[888,84398,84399],{"xmlns":890},[892,84400,84401,84410],{},[895,84402,84403,84405,84407],{},[898,84404,10052],{},[1688,84406,1690],{},[1793,84408,84409],{},"17576",[902,84411,84412],{"encoding":904},"K = 17576",". (b) Rozhodněte o tom, jaké výnosy z rozsahu představuje a vyložte, jak se změní produkce, jestliže se vstupy ",[883,84415,84417],{"className":84416},[886],[888,84418,84419],{"xmlns":890},[892,84420,84421,84429],{},[895,84422,84423,84425,84427],{},[898,84424,10047],{},[1688,84426,1733],{"separator":1732},[898,84428,10052],{},[902,84430,79225],{"encoding":904}," zdvojnásobí.",[724,84433,84434,84437,84438,84375,84469,1343,84487,69824,84505,84535,84536,84566,84567,2946,84580,84594,84595,2946,84608,84621],{},[38,84435,84436],{},"5.8"," V jedné empirické studii (40. léta 20. století) ze sektoru manufaktur odhadli Cobb a Douglas produkci ze zjištěných údajů ve tvaru ",[883,84439,84441],{"className":84440},[886],[888,84442,84443],{"xmlns":890},[892,84444,84445,84466],{},[895,84446,84447,84449,84451,84454,84460],{},[898,84448,1872],{},[1688,84450,1690],{},[1793,84452,84453],{},"1,01",[1850,84455,84456,84458],{},[898,84457,10047],{},[1793,84459,23971],{},[1850,84461,84462,84464],{},[898,84463,10052],{},[1793,84465,24030],{},[902,84467,84468],{"encoding":904},"Q = 1{,}01 L^{0{,}75} K^{0{,}25}",[883,84470,84472],{"className":84471},[886],[888,84473,84474],{"xmlns":890},[892,84475,84476,84484],{},[895,84477,84478,84480,84482],{},[898,84479,10047],{},[1688,84481,1690],{},[1793,84483,30983],{},[902,84485,84486],{"encoding":904},"L = 250",[883,84488,84490],{"className":84489},[886],[888,84491,84492],{"xmlns":890},[892,84493,84494,84502],{},[895,84495,84496,84498,84500],{},[898,84497,10052],{},[1688,84499,1690],{},[1793,84501,3042],{},[902,84503,84504],{"encoding":904},"K = 1000",[883,84506,84508],{"className":84507},[886],[888,84509,84510],{"xmlns":890},[892,84511,84512,84532],{},[895,84513,84514,84516,84522,84524,84526,84528,84530],{},[898,84515,1661],{},[1788,84517,84518,84520],{},[898,84519,1727],{},[898,84521,10047],{},[1688,84523,2066],{"stretchy":2065},[1793,84525,30983],{},[1688,84527,1733],{"separator":1732},[1793,84529,3042],{},[1688,84531,2076],{"stretchy":2065},[902,84533,84534],{"encoding":904},"MP_L(250, 1000)"," a výsledek ekonomicky interpretujte. (c) Vypočtěte ",[883,84537,84539],{"className":84538},[886],[888,84540,84541],{"xmlns":890},[892,84542,84543,84563],{},[895,84544,84545,84547,84553,84555,84557,84559,84561],{},[898,84546,1661],{},[1788,84548,84549,84551],{},[898,84550,1727],{},[898,84552,10052],{},[1688,84554,2066],{"stretchy":2065},[1793,84556,30983],{},[1688,84558,1733],{"separator":1732},[1793,84560,3042],{},[1688,84562,2076],{"stretchy":2065},[902,84564,84565],{"encoding":904},"MP_K(250, 1000)"," a výsledek ekonomicky interpretujte. (d) Odhadněte změnu produkce v důsledku zvýšení ",[883,84568,84570],{"className":84569},[886],[888,84571,84572],{"xmlns":890},[892,84573,84574,84578],{},[895,84575,84576],{},[898,84577,10047],{},[902,84579,10047],{"encoding":904},[883,84581,84583],{"className":84582},[886],[888,84584,84585],{"xmlns":890},[892,84586,84587,84592],{},[895,84588,84589],{},[1793,84590,84591],{},"260",[902,84593,84591],{"encoding":904}," a současném poklesu ",[883,84596,84598],{"className":84597},[886],[888,84599,84600],{"xmlns":890},[892,84601,84602,84606],{},[895,84603,84604],{},[898,84605,10052],{},[902,84607,10052],{"encoding":904},[883,84609,84611],{"className":84610},[886],[888,84612,84613],{"xmlns":890},[892,84614,84615,84619],{},[895,84616,84617],{},[1793,84618,15438],{},[902,84620,15438],{"encoding":904}," vzhledem k hladině dle (a) a porovnejte se skutečnou změnou produkce.",[724,84623,84624,84627,84628,2263],{},[38,84625,84626],{},"5.9"," Ověřte platnost zákona klesajících výnosů pro produkci ",[883,84629,84631],{"className":84630},[886],[888,84632,84633],{"xmlns":890},[892,84634,84635,84655],{},[895,84636,84637,84639,84641,84643,84649],{},[898,84638,1872],{},[1688,84640,1690],{},[1793,84642,3121],{},[1850,84644,84645,84647],{},[898,84646,10047],{},[1793,84648,68451],{},[1850,84650,84651,84653],{},[898,84652,10052],{},[1793,84654,5265],{},[902,84656,84657],{"encoding":904},"Q = 10 L^{0{,}3} K^{0{,}5}",[724,84659,84660,84663,84664,80821,84687,10646,84700,10277,84750,4176],{},[38,84661,84662],{},"5.10"," Dokažte, že pro homogenní funkci ",[883,84665,84667],{"className":84666},[886],[888,84668,84669],{"xmlns":890},[892,84670,84671,84685],{},[895,84672,84673,84675,84677,84679,84681,84683],{},[898,84674,1872],{},[1688,84676,2066],{"stretchy":2065},[898,84678,10047],{},[1688,84680,1733],{"separator":1732},[898,84682,10052],{},[1688,84684,2076],{"stretchy":2065},[902,84686,10249],{"encoding":904},[883,84688,84690],{"className":84689},[886],[888,84691,84692],{"xmlns":890},[892,84693,84694,84698],{},[895,84695,84696],{},[898,84697,37100],{},[902,84699,37100],{"encoding":904},[883,84701,84703],{"className":84702},[886],[888,84704,84705],{"xmlns":890},[892,84706,84707,84747],{},[895,84708,84709,84711,84719,84721,84723,84731,84733,84735,84737,84739,84741,84743,84745],{},[898,84710,10047],{},[1814,84712,84713,84715,84717],{},[898,84714,1872],{},[898,84716,10047],{},[1688,84718,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,84720,1696],{},[898,84722,10052],{},[1814,84724,84725,84727,84729],{},[898,84726,1872],{},[898,84728,10052],{},[1688,84730,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,84732,1690],{},[898,84734,37100],{},[898,84736,1872],{},[1688,84738,2066],{"stretchy":2065},[898,84740,10047],{},[1688,84742,1733],{"separator":1732},[898,84744,10052],{},[1688,84746,2076],{"stretchy":2065},[902,84748,84749],{"encoding":904},"L Q'_L + K Q'_K = n Q(L, K)",[614,84751,80796],{},[724,84753,84754,84757],{},[38,84755,84756],{},"5.11"," Ověřte platnost Eulerovy věty (úloha 5.10) pro Cobb-Douglasovu produkční funkci.",[724,84759,84760,83700,84763,84803,84804,1343,84826,1343,84848,84870],{},[38,84761,84762],{},"5.12",[883,84764,84766],{"className":84765},[886],[888,84767,84768],{"xmlns":890},[892,84769,84770,84800],{},[895,84771,84772,84774,84776,84788],{},[898,84773,1872],{},[1688,84775,1690],{},[1850,84777,84778,84780],{},[898,84779,10047],{},[895,84781,84782,84784,84786],{},[1793,84783,1795],{},[898,84785,4930],{"mathvariant":1822},[1793,84787,2131],{},[1850,84789,84790,84792],{},[898,84791,10052],{},[895,84793,84794,84796,84798],{},[1793,84795,1795],{},[898,84797,4930],{"mathvariant":1822},[1793,84799,2616],{},[902,84801,84802],{"encoding":904},"Q = L^{1\u002F3} K^{1\u002F4}",". (a) Najděte rovnici izokvant. (b) Najděte rovnici izokvant pro produkci ",[883,84805,84807],{"className":84806},[886],[888,84808,84809],{"xmlns":890},[892,84810,84811,84823],{},[895,84812,84813,84819,84821],{},[1788,84814,84815,84817],{},[898,84816,81037],{},[1793,84818,1779],{},[1688,84820,1690],{},[1793,84822,1795],{},[902,84824,84825],{"encoding":904},"q_0 = 1",[883,84827,84829],{"className":84828},[886],[888,84830,84831],{"xmlns":890},[892,84832,84833,84845],{},[895,84834,84835,84841,84843],{},[1788,84836,84837,84839],{},[898,84838,81037],{},[1793,84840,1795],{},[1688,84842,1690],{},[1793,84844,1806],{},[902,84846,84847],{"encoding":904},"q_1 = 2",[883,84849,84851],{"className":84850},[886],[888,84852,84853],{"xmlns":890},[892,84854,84855,84867],{},[895,84856,84857,84863,84865],{},[1788,84858,84859,84861],{},[898,84860,81037],{},[1793,84862,1806],{},[1688,84864,1690],{},[1793,84866,2131],{},[902,84868,84869],{"encoding":904},"q_2 = 3",". (c) Načrtněte izokvanty.",[724,84872,84873,83700,84876,84916,84917,1343,84945,1343,84973,1343,85001,1343,85030,1343,85059,1343,85088,1343,85117,1343,85146,2263],{},[38,84874,84875],{},"5.13",[883,84877,84879],{"className":84878},[886],[888,84880,84881],{"xmlns":890},[892,84882,84883,84913],{},[895,84884,84885,84887,84889,84901],{},[898,84886,1872],{},[1688,84888,1690],{},[1850,84890,84891,84893],{},[898,84892,10047],{},[895,84894,84895,84897,84899],{},[1793,84896,1795],{},[898,84898,4930],{"mathvariant":1822},[1793,84900,2131],{},[1850,84902,84903,84905],{},[898,84904,10052],{},[895,84906,84907,84909,84911],{},[1793,84908,1795],{},[898,84910,4930],{"mathvariant":1822},[1793,84912,1806],{},[902,84914,84915],{"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): ",[883,84918,84920],{"className":84919},[886],[888,84921,84922],{"xmlns":890},[892,84923,84924,84942],{},[895,84925,84926,84932,84934,84936,84938,84940],{},[1788,84927,84928,84930],{},[898,84929,4512],{},[1793,84931,1795],{},[1688,84933,2748],{"stretchy":2065},[1793,84935,1795],{},[1688,84937,8681],{"separator":1732},[1793,84939,1795],{},[1688,84941,2763],{"stretchy":2065},[902,84943,84944],{"encoding":904},"A_1[1; 1]",[883,84946,84948],{"className":84947},[886],[888,84949,84950],{"xmlns":890},[892,84951,84952,84970],{},[895,84953,84954,84960,84962,84964,84966,84968],{},[1788,84955,84956,84958],{},[898,84957,4512],{},[1793,84959,1806],{},[1688,84961,2748],{"stretchy":2065},[1793,84963,1795],{},[1688,84965,8681],{"separator":1732},[1793,84967,5841],{},[1688,84969,2763],{"stretchy":2065},[902,84971,84972],{"encoding":904},"A_2[1; 8]",[883,84974,84976],{"className":84975},[886],[888,84977,84978],{"xmlns":890},[892,84979,84980,84998],{},[895,84981,84982,84988,84990,84992,84994,84996],{},[1788,84983,84984,84986],{},[898,84985,4512],{},[1793,84987,2131],{},[1688,84989,2748],{"stretchy":2065},[1793,84991,1795],{},[1688,84993,8681],{"separator":1732},[1793,84995,66837],{},[1688,84997,2763],{"stretchy":2065},[902,84999,85000],{"encoding":904},"A_3[1; 27]",[883,85002,85004],{"className":85003},[886],[888,85005,85006],{"xmlns":890},[892,85007,85008,85027],{},[895,85009,85010,85016,85018,85020,85022,85025],{},[1788,85011,85012,85014],{},[898,85013,4512],{},[1793,85015,2616],{},[1688,85017,2748],{"stretchy":2065},[1793,85019,1806],{},[1688,85021,8681],{"separator":1732},[1793,85023,85024],{},"0,353",[1688,85026,2763],{"stretchy":2065},[902,85028,85029],{"encoding":904},"A_4[2; 0{,}353]",[883,85031,85033],{"className":85032},[886],[888,85034,85035],{"xmlns":890},[892,85036,85037,85056],{},[895,85038,85039,85045,85047,85049,85051,85054],{},[1788,85040,85041,85043],{},[898,85042,4512],{},[1793,85044,2501],{},[1688,85046,2748],{"stretchy":2065},[1793,85048,1806],{},[1688,85050,8681],{"separator":1732},[1793,85052,85053],{},"2,828",[1688,85055,2763],{"stretchy":2065},[902,85057,85058],{"encoding":904},"A_5[2; 2{,}828]",[883,85060,85062],{"className":85061},[886],[888,85063,85064],{"xmlns":890},[892,85065,85066,85085],{},[895,85067,85068,85074,85076,85078,85080,85083],{},[1788,85069,85070,85072],{},[898,85071,4512],{},[1793,85073,2508],{},[1688,85075,2748],{"stretchy":2065},[1793,85077,1806],{},[1688,85079,8681],{"separator":1732},[1793,85081,85082],{},"9,545",[1688,85084,2763],{"stretchy":2065},[902,85086,85087],{"encoding":904},"A_6[2; 9{,}545]",[883,85089,85091],{"className":85090},[886],[888,85092,85093],{"xmlns":890},[892,85094,85095,85114],{},[895,85096,85097,85103,85105,85107,85109,85112],{},[1788,85098,85099,85101],{},[898,85100,4512],{},[1793,85102,24442],{},[1688,85104,2748],{"stretchy":2065},[1793,85106,64799],{},[1688,85108,8681],{"separator":1732},[1793,85110,85111],{},"0,544",[1688,85113,2763],{"stretchy":2065},[902,85115,85116],{"encoding":904},"A_7[1{,}5; 0{,}544]",[883,85118,85120],{"className":85119},[886],[888,85121,85122],{"xmlns":890},[892,85123,85124,85143],{},[895,85125,85126,85132,85134,85136,85138,85141],{},[1788,85127,85128,85130],{},[898,85129,4512],{},[1793,85131,5841],{},[1688,85133,2748],{"stretchy":2065},[1793,85135,64799],{},[1688,85137,8681],{"separator":1732},[1793,85139,85140],{},"14,696",[1688,85142,2763],{"stretchy":2065},[902,85144,85145],{"encoding":904},"A_8[1{,}5; 14{,}696]",[883,85147,85149],{"className":85148},[886],[888,85150,85151],{"xmlns":890},[892,85152,85153,85171],{},[895,85154,85155,85161,85163,85165,85167,85169],{},[1788,85156,85157,85159],{},[898,85158,4512],{},[1793,85160,4256],{},[1688,85162,2748],{"stretchy":2065},[1793,85164,1806],{},[1688,85166,8681],{"separator":1732},[1793,85168,2501],{},[1688,85170,2763],{"stretchy":2065},[902,85172,85173],{"encoding":904},"A_9[2; 5]",[724,85175,85176,85179],{},[38,85177,85178],{},"5.14"," Dokažte, že izokvanty Cobb-Douglasovy produkční funkce jsou klesající a konvexní.",[724,85181,85182,85185,85186,85216,85217,85230,85231,85244,85245,69557,85264,85283,85284,2263],{},[38,85183,85184],{},"5.15"," Produkce firmy je dána vztahem ",[883,85187,85189],{"className":85188},[886],[888,85190,85191],{"xmlns":890},[892,85192,85193,85213],{},[895,85194,85195,85197,85199,85201,85207],{},[898,85196,1872],{},[1688,85198,1690],{},[1793,85200,1806],{},[1850,85202,85203,85205],{},[898,85204,10047],{},[1793,85206,5265],{},[1850,85208,85209,85211],{},[898,85210,10052],{},[1793,85212,24030],{},[902,85214,85215],{"encoding":904},"Q = 2 L^{0{,}5} K^{0{,}25}",". (a) Vypočtěte produkci, mezní produkt práce a mezní produkt kapitálu, zaměstnává-li firma ",[883,85218,85220],{"className":85219},[886],[888,85221,85222],{"xmlns":890},[892,85223,85224,85228],{},[895,85225,85226],{},[1793,85227,3347],{},[902,85229,3347],{"encoding":904}," pracovníků a disponuje-li ",[883,85232,85234],{"className":85233},[886],[888,85235,85236],{"xmlns":890},[892,85237,85238,85242],{},[895,85239,85240],{},[1793,85241,64675],{},[902,85243,64675],{"encoding":904}," jednotkami kapitálu. (b) Určete mezní míru technické substituce ",[883,85246,85248],{"className":85247},[886],[888,85249,85250],{"xmlns":890},[892,85251,85252,85262],{},[895,85253,85254,85256,85258,85260],{},[898,85255,1661],{},[898,85257,4251],{},[898,85259,3035],{},[898,85261,1740],{},[902,85263,10851],{"encoding":904},[883,85265,85267],{"className":85266},[886],[888,85268,85269],{"xmlns":890},[892,85270,85271,85281],{},[895,85272,85273,85275,85277,85279],{},[898,85274,1661],{},[898,85276,4251],{},[898,85278,3035],{},[898,85280,1740],{},[902,85282,10851],{"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 ",[883,85285,85287],{"className":85286},[886],[888,85288,85289],{"xmlns":890},[892,85290,85291,85296],{},[895,85292,85293],{},[1793,85294,85295],{},"95",[902,85297,85295],{"encoding":904},[724,85299,85300,83700,85303,71231,85335,85354,85355,85368,85369,85382,85383,85396],{},[38,85301,85302],{},"5.16",[883,85304,85306],{"className":85305},[886],[888,85307,85308],{"xmlns":890},[892,85309,85310,85332],{},[895,85311,85312,85314,85316,85322,85324,85326],{},[898,85313,1872],{},[1688,85315,1690],{},[1850,85317,85318,85320],{},[898,85319,10052],{},[1793,85321,1806],{},[1688,85323,1696],{},[1793,85325,1806],{},[1850,85327,85328,85330],{},[898,85329,10047],{},[1793,85331,1806],{},[902,85333,85334],{"encoding":904},"Q = K^{2} + 2 L^{2}",[883,85336,85338],{"className":85337},[886],[888,85339,85340],{"xmlns":890},[892,85341,85342,85352],{},[895,85343,85344,85346,85348,85350],{},[898,85345,1661],{},[898,85347,4251],{},[898,85349,3035],{},[898,85351,1740],{},[902,85353,10851],{"encoding":904},". (b) Odhadněte změnu práce potřebné k udržení produkce, která je realizována ",[883,85356,85358],{"className":85357},[886],[888,85359,85360],{"xmlns":890},[892,85361,85362,85366],{},[895,85363,85364],{},[1793,85365,3377],{},[902,85367,3377],{"encoding":904}," pracovníky a ",[883,85370,85372],{"className":85371},[886],[888,85373,85374],{"xmlns":890},[892,85375,85376,85380],{},[895,85377,85378],{},[1793,85379,77857],{},[902,85381,77857],{"encoding":904}," jednotkami kapitálu, jestliže se kapitál sníží na ",[883,85384,85386],{"className":85385},[886],[888,85387,85388],{"xmlns":890},[892,85389,85390,85394],{},[895,85391,85392],{},[1793,85393,46943],{},[902,85395,46943],{"encoding":904}," jednotek.",[724,85398,85399,85402,85403,10646,85433,2263],{},[38,85400,85401],{},"5.17"," Odvoďte, že pro Cobb-Douglasovu produkční funkci ",[883,85404,85406],{"className":85405},[886],[888,85407,85408],{"xmlns":890},[892,85409,85410,85430],{},[895,85411,85412,85414,85416,85418,85424],{},[898,85413,1872],{},[1688,85415,1690],{},[898,85417,4512],{},[1850,85419,85420,85422],{},[898,85421,10047],{},[898,85423,207],{},[1850,85425,85426,85428],{},[898,85427,10052],{},[898,85429,1918],{},[902,85431,85432],{"encoding":904},"Q = A L^{a} K^{b}",[883,85434,85436],{"className":85435},[886],[888,85437,85438],{"xmlns":890},[892,85439,85440,85470],{},[895,85441,85442,85444,85446,85448,85450,85452,85460,85462],{},[898,85443,1661],{},[898,85445,4251],{},[898,85447,3035],{},[898,85449,1740],{},[1688,85451,1690],{},[1777,85453,85454],{"scriptlevel":1779,"displaystyle":2065},[1781,85455,85456,85458],{},[898,85457,207],{},[898,85459,1918],{},[1688,85461,3434],{},[1777,85463,85464],{"scriptlevel":1779,"displaystyle":2065},[1781,85465,85466,85468],{},[898,85467,10052],{},[898,85469,10047],{},[902,85471,85472],{"encoding":904},"MRTS = \\tfrac{a}{b}\\cdot \\tfrac{K}{L}",[115,85474,15967],{"id":15966},[120,85476,85477,85510,85537,85546,85596,85627,85680,85703,85758,85831,85909,85952,85984,86017,86058,86130,86191,86257,86274,86347,86413,86465,86521,86555,86598],{},[123,85478,85479,85482,85483,37136,85496,85509],{},[38,85480,85481],{},"Faktory (vstupy) produkce:"," práce ",[883,85484,85486],{"className":85485},[886],[888,85487,85488],{"xmlns":890},[892,85489,85490,85494],{},[895,85491,85492],{},[898,85493,10047],{},[902,85495,10047],{"encoding":904},[883,85497,85499],{"className":85498},[886],[888,85500,85501],{"xmlns":890},[892,85502,85503,85507],{},[895,85504,85505],{},[898,85506,10052],{},[902,85508,10052],{"encoding":904},", půda.",[123,85511,85512,7271,85514,2263],{},[38,85513,40691],{},[883,85515,85517],{"className":85516},[886],[888,85518,85519],{"xmlns":890},[892,85520,85521,85535],{},[895,85522,85523,85525,85527,85529,85531,85533],{},[898,85524,1872],{},[1688,85526,1690],{},[898,85528,1872],{},[1688,85530,2066],{"stretchy":2065},[898,85532,10047],{},[1688,85534,2076],{"stretchy":2065},[902,85536,74784],{"encoding":904},[123,85538,85539,10277,85541,12378,85544,2263],{},[38,85540,859],{},[614,85542,85543],{},"production function",[38,85545,75287],{},[123,85547,85548,2170,85550,2263],{},[38,85549,75333],{},[883,85551,85553],{"className":85552},[886],[888,85554,85555],{"xmlns":890},[892,85556,85557,85593],{},[895,85558,85559,85561,85567,85569,85571,85573,85575,85577,85579,85581,85587,85589,85591],{},[898,85560,1661],{},[1788,85562,85563,85565],{},[898,85564,1727],{},[898,85566,10047],{},[1688,85568,1690],{},[898,85570,2073],{},[898,85572,1872],{},[898,85574,4930],{"mathvariant":1822},[898,85576,2073],{},[898,85578,10047],{},[1688,85580,1690],{},[1850,85582,85583,85585],{},[898,85584,1872],{},[1688,85586,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,85588,2066],{"stretchy":2065},[898,85590,10047],{},[1688,85592,2076],{"stretchy":2065},[902,85594,85595],{"encoding":904},"MP_L = dQ\u002FdL = Q'(L)",[123,85597,85598,2170,85600,2263],{},[38,85599,76268],{},[883,85601,85603],{"className":85602},[886],[888,85604,85605],{"xmlns":890},[892,85606,85607,85625],{},[895,85608,85609,85611,85617,85619,85621,85623],{},[898,85610,4512],{},[1788,85612,85613,85615],{},[898,85614,1727],{},[898,85616,10047],{},[1688,85618,1690],{},[898,85620,1872],{},[898,85622,4930],{"mathvariant":1822},[898,85624,10047],{},[902,85626,74852],{"encoding":904},[123,85628,85629,85631,85632,10646,85649,2263],{},[38,85630,75755],{}," — od určitého ",[883,85633,85635],{"className":85634},[886],[888,85636,85637],{"xmlns":890},[892,85638,85639,85647],{},[895,85640,85641],{},[1788,85642,85643,85645],{},[898,85644,10047],{},[1793,85646,1779],{},[902,85648,75798],{"encoding":904},[883,85650,85652],{"className":85651},[886],[888,85653,85654],{"xmlns":890},[892,85655,85656,85678],{},[895,85657,85658,85668,85670,85672,85674,85676],{},[1850,85659,85660,85662],{},[898,85661,1872],{},[895,85663,85664,85666],{},[1688,85665,1824],{"mathvariant":1822},[1688,85667,1824],{"mathvariant":1822},[1688,85669,2066],{"stretchy":2065},[898,85671,10047],{},[1688,85673,2076],{"stretchy":2065},[1688,85675,3704],{},[1793,85677,1779],{},[902,85679,75944],{"encoding":904},[123,85681,85682,2170,85685,85702],{},[38,85683,85684],{},"Inflexní bod",[883,85686,85688],{"className":85687},[886],[888,85689,85690],{"xmlns":890},[892,85691,85692,85700],{},[895,85693,85694],{},[1788,85695,85696,85698],{},[898,85697,10047],{},[1793,85699,1779],{},[902,85701,75798],{"encoding":904}," — přechod z konvexity do konkavity.",[123,85704,85705,2170,85708,7271,85725,2263],{},[38,85706,85707],{},"Bod maxima produkce",[883,85709,85711],{"className":85710},[886],[888,85712,85713],{"xmlns":890},[892,85714,85715,85723],{},[895,85716,85717],{},[1788,85718,85719,85721],{},[898,85720,10047],{},[1793,85722,1795],{},[902,85724,13460],{"encoding":904},[883,85726,85728],{"className":85727},[886],[888,85729,85730],{"xmlns":890},[892,85731,85732,85756],{},[895,85733,85734,85736,85742,85744,85750,85752,85754],{},[898,85735,1661],{},[1788,85737,85738,85740],{},[898,85739,1727],{},[898,85741,10047],{},[1688,85743,2066],{"stretchy":2065},[1788,85745,85746,85748],{},[898,85747,10047],{},[1793,85749,1795],{},[1688,85751,2076],{"stretchy":2065},[1688,85753,1690],{},[1793,85755,1779],{},[902,85757,76017],{"encoding":904},[123,85759,85760,85782,85783,10646,85802,2263],{},[38,85761,85762,85763],{},"Princip maximalizace ",[883,85764,85766],{"className":85765},[886],[888,85767,85768],{"xmlns":890},[892,85769,85770,85780],{},[895,85771,85772,85774],{},[898,85773,4512],{},[1788,85775,85776,85778],{},[898,85777,1727],{},[898,85779,10047],{},[902,85781,74873],{"encoding":904}," — v bodě maxima ",[883,85784,85786],{"className":85785},[886],[888,85787,85788],{"xmlns":890},[892,85789,85790,85800],{},[895,85791,85792,85794],{},[898,85793,4512],{},[1788,85795,85796,85798],{},[898,85797,1727],{},[898,85799,10047],{},[902,85801,74873],{"encoding":904},[883,85803,85805],{"className":85804},[886],[888,85806,85807],{"xmlns":890},[892,85808,85809,85829],{},[895,85810,85811,85813,85819,85821,85823],{},[898,85812,1661],{},[1788,85814,85815,85817],{},[898,85816,1727],{},[898,85818,10047],{},[1688,85820,1690],{},[898,85822,4512],{},[1788,85824,85825,85827],{},[898,85826,1727],{},[898,85828,10047],{},[902,85830,74903],{"encoding":904},[123,85832,85833,2170,85836,1343,85875,1343,85892,2263],{},[38,85834,85835],{},"Polynomiální produkční funkce",[883,85837,85839],{"className":85838},[886],[888,85840,85841],{"xmlns":890},[892,85842,85843,85873],{},[895,85844,85845,85847,85849,85851,85853,85855,85857,85863,85865,85867],{},[898,85846,1872],{},[1688,85848,2066],{"stretchy":2065},[898,85850,10047],{},[1688,85852,2076],{"stretchy":2065},[1688,85854,1690],{},[898,85856,207],{},[1850,85858,85859,85861],{},[898,85860,10047],{},[1793,85862,2131],{},[1688,85864,1696],{},[898,85866,1918],{},[1850,85868,85869,85871],{},[898,85870,10047],{},[1793,85872,1806],{},[902,85874,76135],{"encoding":904},[883,85876,85878],{"className":85877},[886],[888,85879,85880],{"xmlns":890},[892,85881,85882,85890],{},[895,85883,85884,85886,85888],{},[898,85885,207],{},[1688,85887,3704],{},[1793,85889,1779],{},[902,85891,43325],{"encoding":904},[883,85893,85895],{"className":85894},[886],[888,85896,85897],{"xmlns":890},[892,85898,85899,85907],{},[895,85900,85901,85903,85905],{},[898,85902,1918],{},[1688,85904,3665],{},[1793,85906,1779],{},[902,85908,19056],{"encoding":904},[123,85910,85911,2170,85914,2263],{},[38,85912,85913],{},"Diferenciál produkce",[883,85915,85917],{"className":85916},[886],[888,85918,85919],{"xmlns":890},[892,85920,85921,85949],{},[895,85922,85923,85925,85927,85929,85931,85933,85935,85937,85943,85945,85947],{},[898,85924,3147],{"mathvariant":1822},[898,85926,1872],{},[1688,85928,2991],{},[898,85930,2073],{},[898,85932,1872],{},[1688,85934,1690],{},[898,85936,1661],{},[1788,85938,85939,85941],{},[898,85940,1727],{},[898,85942,10047],{},[2041,85944,2043],{},[898,85946,2073],{},[898,85948,10047],{},[902,85950,85951],{"encoding":904},"\\Delta Q \\approx dQ = MP_L\\,dL",[123,85953,85954,7271,85956,2263],{},[38,85955,84211],{},[883,85957,85959],{"className":85958},[886],[888,85960,85961],{"xmlns":890},[892,85962,85963,85981],{},[895,85964,85965,85967,85969,85971,85973,85975,85977,85979],{},[898,85966,1872],{},[1688,85968,1690],{},[898,85970,1872],{},[1688,85972,2066],{"stretchy":2065},[898,85974,10047],{},[1688,85976,1733],{"separator":1732},[898,85978,10052],{},[1688,85980,2076],{"stretchy":2065},[902,85982,85983],{"encoding":904},"Q = Q(L, K)",[123,85985,85986,7271,85988,2263],{},[38,85987,78305],{},[883,85989,85991],{"className":85990},[886],[888,85992,85993],{"xmlns":890},[892,85994,85995,86015],{},[895,85996,85997,85999,86001,86003,86009],{},[898,85998,1872],{},[1688,86000,1690],{},[898,86002,4512],{},[1850,86004,86005,86007],{},[898,86006,10047],{},[898,86008,207],{},[1850,86010,86011,86013],{},[898,86012,10052],{},[898,86014,1918],{},[902,86016,74970],{"encoding":904},[123,86018,86019,7271,86022,86057],{},[38,86020,86021],{},"Ryzí Cobb-Douglas",[883,86023,86025],{"className":86024},[886],[888,86026,86027],{"xmlns":890},[892,86028,86029,86055],{},[895,86030,86031,86033,86035,86037,86043],{},[898,86032,1872],{},[1688,86034,1690],{},[898,86036,4512],{},[1850,86038,86039,86041],{},[898,86040,10047],{},[898,86042,207],{},[1850,86044,86045,86047],{},[898,86046,10052],{},[895,86048,86049,86051,86053],{},[1793,86050,1795],{},[1688,86052,1954],{},[898,86054,207],{},[902,86056,79132],{"encoding":904}," (konstantní výnosy).",[123,86059,86060,7271,86062,2263],{},[38,86061,79848],{},[883,86063,86065],{"className":86064},[886],[888,86066,86067],{"xmlns":890},[892,86068,86069,86127],{},[895,86070,86071,86073,86075,86077,86079,86081,86083,86085,86087,86089,86099,86101,86103,86113],{},[898,86072,1872],{},[1688,86074,1690],{},[898,86076,4512],{},[1688,86078,2748],{"stretchy":2065},[1688,86080,2066],{"stretchy":2065},[1793,86082,1795],{},[1688,86084,1954],{},[898,86086,207],{},[1688,86088,2076],{"stretchy":2065},[1850,86090,86091,86093],{},[898,86092,10047],{},[895,86094,86095,86097],{},[1688,86096,1954],{},[898,86098,1918],{},[1688,86100,1696],{},[898,86102,207],{},[1850,86104,86105,86107],{},[898,86106,10052],{},[895,86108,86109,86111],{},[1688,86110,1954],{},[898,86112,1918],{},[1850,86114,86115,86117],{},[1688,86116,2763],{"stretchy":2065},[895,86118,86119,86121,86123,86125],{},[1688,86120,1954],{},[1793,86122,1795],{},[898,86124,4930],{"mathvariant":1822},[898,86126,1918],{},[902,86128,86129],{"encoding":904},"Q = A[(1-a)L^{-b} + aK^{-b}]^{-1\u002Fb}",[123,86131,86132,10277,86135,12378,86157,10277,86160,86190],{},[38,86133,86134],{},"Lineární",[883,86136,86138],{"className":86137},[886],[888,86139,86140],{"xmlns":890},[892,86141,86142,86154],{},[895,86143,86144,86146,86148,86150,86152],{},[898,86145,207],{},[898,86147,10047],{},[1688,86149,1696],{},[898,86151,1918],{},[898,86153,10052],{},[902,86155,86156],{"encoding":904},"aL + bK",[38,86158,86159],{},"Leontiefova",[883,86161,86163],{"className":86162},[886],[888,86164,86165],{"xmlns":890},[892,86166,86167,86187],{},[895,86168,86169,86171,86173,86175,86177,86179,86181,86183,86185],{},[898,86170,80076],{},[1688,86172,56440],{},[1688,86174,2066],{"stretchy":2065},[898,86176,207],{},[898,86178,10047],{},[1688,86180,1733],{"separator":1732},[898,86182,1918],{},[898,86184,10052],{},[1688,86186,2076],{"stretchy":2065},[902,86188,86189],{"encoding":904},"\\min(aL, bK)",") produkční funkce.",[123,86192,86193,7271,86209,2263],{},[38,86194,86195,86196],{},"Homogenita stupně ",[883,86197,86199],{"className":86198},[886],[888,86200,86201],{"xmlns":890},[892,86202,86203,86207],{},[895,86204,86205],{},[898,86206,37100],{},[902,86208,37100],{"encoding":904},[883,86210,86212],{"className":86211},[886],[888,86213,86214],{"xmlns":890},[892,86215,86216,86254],{},[895,86217,86218,86220,86222,86224,86226,86228,86230,86232,86234,86236,86242,86244,86246,86248,86250,86252],{},[898,86219,1872],{},[1688,86221,2066],{"stretchy":2065},[898,86223,2046],{},[898,86225,10047],{},[1688,86227,1733],{"separator":1732},[898,86229,2046],{},[898,86231,10052],{},[1688,86233,2076],{"stretchy":2065},[1688,86235,1690],{},[1850,86237,86238,86240],{},[898,86239,2046],{},[898,86241,37100],{},[898,86243,1872],{},[1688,86245,2066],{"stretchy":2065},[898,86247,10047],{},[1688,86249,1733],{"separator":1732},[898,86251,10052],{},[1688,86253,2076],{"stretchy":2065},[902,86255,86256],{"encoding":904},"Q(rL, rK) = r^n Q(L, K)",[123,86258,86259,79230],{},[38,86260,79163,86261],{},[883,86262,86264],{"className":86263},[886],[888,86265,86266],{"xmlns":890},[892,86267,86268,86272],{},[895,86269,86270],{},[898,86271,4512],{},[902,86273,4512],{"encoding":904},[123,86275,86276,86278,86279,86301,86302,86324,86325,4176],{},[38,86277,78664],{}," — konstantní (",[883,86280,86282],{"className":86281},[886],[888,86283,86284],{"xmlns":890},[892,86285,86286,86298],{},[895,86287,86288,86290,86292,86294,86296],{},[898,86289,207],{},[1688,86291,1696],{},[898,86293,1918],{},[1688,86295,1690],{},[1793,86297,1795],{},[902,86299,86300],{"encoding":904},"a+b=1","), rostoucí (",[883,86303,86305],{"className":86304},[886],[888,86306,86307],{"xmlns":890},[892,86308,86309,86321],{},[895,86310,86311,86313,86315,86317,86319],{},[898,86312,207],{},[1688,86314,1696],{},[898,86316,1918],{},[1688,86318,3665],{},[1793,86320,1795],{},[902,86322,86323],{"encoding":904},"a+b>1","), klesající (",[883,86326,86328],{"className":86327},[886],[888,86329,86330],{"xmlns":890},[892,86331,86332,86344],{},[895,86333,86334,86336,86338,86340,86342],{},[898,86335,207],{},[1688,86337,1696],{},[898,86339,1918],{},[1688,86341,3704],{},[1793,86343,1795],{},[902,86345,86346],{"encoding":904},"a+b\u003C1",[123,86348,86349,2170,86351,1343,86381,2170,86383,2263],{},[38,86350,75333],{},[883,86352,86354],{"className":86353},[886],[888,86355,86356],{"xmlns":890},[892,86357,86358,86378],{},[895,86359,86360,86362,86368,86370],{},[898,86361,1661],{},[1788,86363,86364,86366],{},[898,86365,1727],{},[898,86367,10047],{},[1688,86369,1690],{},[1814,86371,86372,86374,86376],{},[898,86373,1872],{},[898,86375,10047],{},[1688,86377,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[902,86379,86380],{"encoding":904},"MP_L = Q'_L",[38,86382,78237],{},[883,86384,86386],{"className":86385},[886],[888,86387,86388],{"xmlns":890},[892,86389,86390,86410],{},[895,86391,86392,86394,86400,86402],{},[898,86393,1661],{},[1788,86395,86396,86398],{},[898,86397,1727],{},[898,86399,10052],{},[1688,86401,1690],{},[1814,86403,86404,86406,86408],{},[898,86405,1872],{},[898,86407,10052],{},[1688,86409,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[902,86411,86412],{"encoding":904},"MP_K = Q'_K",[123,86414,86415,2170,86417,2263],{},[38,86416,80451],{},[883,86418,86420],{"className":86419},[886],[888,86421,86422],{"xmlns":890},[892,86423,86424,86462],{},[895,86425,86426,86428,86430,86432,86434,86440,86442,86444,86446,86448,86450,86456,86458,86460],{},[898,86427,2073],{},[898,86429,1872],{},[1688,86431,1690],{},[898,86433,1661],{},[1788,86435,86436,86438],{},[898,86437,1727],{},[898,86439,10047],{},[2041,86441,2043],{},[898,86443,2073],{},[898,86445,10047],{},[1688,86447,1696],{},[898,86449,1661],{},[1788,86451,86452,86454],{},[898,86453,1727],{},[898,86455,10052],{},[2041,86457,2043],{},[898,86459,2073],{},[898,86461,10052],{},[902,86463,86464],{"encoding":904},"dQ = MP_L\\,dL + MP_K\\,dK",[123,86466,86467,7271,86469,2263],{},[38,86468,80796],{},[883,86470,86472],{"className":86471},[886],[888,86473,86474],{"xmlns":890},[892,86475,86476,86518],{},[895,86477,86478,86480,86488,86490,86492,86500,86502,86504,86506,86508,86510,86512,86514,86516],{},[898,86479,10047],{},[1814,86481,86482,86484,86486],{},[898,86483,1872],{},[898,86485,10047],{},[1688,86487,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,86489,1696],{},[898,86491,10052],{},[1814,86493,86494,86496,86498],{},[898,86495,1872],{},[898,86497,10052],{},[1688,86499,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,86501,1690],{},[898,86503,37100],{},[2041,86505,2043],{},[898,86507,1872],{},[1688,86509,2066],{"stretchy":2065},[898,86511,10047],{},[1688,86513,1733],{"separator":1732},[898,86515,10052],{},[1688,86517,2076],{"stretchy":2065},[902,86519,86520],{"encoding":904},"L Q'_L + K Q'_K = n\\,Q(L,K)",[123,86522,86523,86526,86527,2263],{},[38,86524,86525],{},"Izokvanta"," — křivka ",[883,86528,86530],{"className":86529},[886],[888,86531,86532],{"xmlns":890},[892,86533,86534,86552],{},[895,86535,86536,86538,86540,86542,86544,86546,86548,86550],{},[898,86537,1872],{},[1688,86539,2066],{"stretchy":2065},[898,86541,10047],{},[1688,86543,1733],{"separator":1732},[898,86545,10052],{},[1688,86547,2076],{"stretchy":2065},[1688,86549,1690],{},[898,86551,81037],{},[902,86553,86554],{"encoding":904},"Q(L, K) = q",[123,86556,86557,2170,86559,2263],{},[38,86558,81226],{},[883,86560,86562],{"className":86561},[886],[888,86563,86564],{"xmlns":890},[892,86565,86566,86596],{},[895,86567,86568,86570,86572,86574,86576,86578,86580,86586,86588,86590],{},[898,86569,1661],{},[898,86571,4251],{},[898,86573,3035],{},[898,86575,1740],{},[1688,86577,1690],{},[898,86579,1661],{},[1788,86581,86582,86584],{},[898,86583,1727],{},[898,86585,10047],{},[898,86587,4930],{"mathvariant":1822},[898,86589,1661],{},[1788,86591,86592,86594],{},[898,86593,1727],{},[898,86595,10052],{},[902,86597,75045],{"encoding":904},[123,86599,86600,2170,86603,2263],{},[38,86601,86602],{},"Substituční vztah",[883,86604,86606],{"className":86605},[886],[888,86607,86608],{"xmlns":890},[892,86609,86610,86634],{},[895,86611,86612,86614,86616,86618,86620,86622,86624,86626,86628,86630,86632],{},[898,86613,3147],{"mathvariant":1822},[898,86615,10052],{},[1688,86617,2991],{},[1688,86619,1954],{},[898,86621,1661],{},[898,86623,4251],{},[898,86625,3035],{},[898,86627,1740],{},[2041,86629,2043],{},[898,86631,2073],{},[898,86633,10047],{},[902,86635,86636],{"encoding":904},"\\Delta K \\approx -MRTS\\,dL",[115,86638,4049],{"id":4048},[120,86640,86641,86738,86745,86752],{},[123,86642,86643,2170,86645,86648,86649,1343,86652,86655,86656,86659,86660,86679,86680,18890,86699,86702,86703,86722,86723,4176],{},[38,86644,50963],{},[207,86646,784],{"className":86647,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace, totální diferenciál), ",[207,86650,2622],{"className":86651,"dataFsResolvedFilePath":764,"href":765},[210],[207,86653,793],{"className":86654,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace produkce s rozpočtovým omezením), ",[207,86657,880],{"className":86658,"dataFsResolvedFilePath":878,"href":879},[210]," (paralela: izokvanty ↔ indiferenční křivky, ",[883,86661,86663],{"className":86662},[886],[888,86664,86665],{"xmlns":890},[892,86666,86667,86677],{},[895,86668,86669,86671,86673,86675],{},[898,86670,1661],{},[898,86672,4251],{},[898,86674,3035],{},[898,86676,1740],{},[902,86678,10851],{"encoding":904}," ↔ ",[883,86681,86683],{"className":86682},[886],[888,86684,86685],{"xmlns":890},[892,86686,86687,86697],{},[895,86688,86689,86691,86693,86695],{},[898,86690,1661],{},[898,86692,4251],{},[898,86694,1693],{},[898,86696,1740],{},[902,86698,1670],{"encoding":904},[207,86700,4079],{"className":86701,"dataFsResolvedFilePath":827,"href":828},[210]," (analogie principu max ",[883,86704,86706],{"className":86705},[886],[888,86707,86708],{"xmlns":890},[892,86709,86710,86720],{},[895,86711,86712,86714],{},[898,86713,4512],{},[1788,86715,86716,86718],{},[898,86717,1727],{},[898,86719,10047],{},[902,86721,74873],{"encoding":904}," ↔ min ",[883,86724,86726],{"className":86725},[886],[888,86727,86728],{"xmlns":890},[892,86729,86730,86736],{},[895,86731,86732,86734],{},[898,86733,4512],{},[898,86735,1693],{},[902,86737,55800],{"encoding":904},[123,86739,86740,2170,86742,2263],{},[38,86741,4056],{},[207,86743,4084],{"className":86744,"dataFsResolvedFilePath":848,"href":849},[210],[123,86746,86747,2170,86749,2263],{},[38,86748,16460],{},[207,86750,1094],{"className":86751,"dataFsResolvedFilePath":838,"href":839},[210],[123,86753,86754,2170,86756,2263],{},[38,86755,16451],{},[207,86757,16455],{"className":86758,"dataFsResolvedFilePath":2210,"href":2211},[210],{"title":641,"searchDepth":642,"depth":642,"links":86760},[86761,86762,86763,86767,86769,86774,86775,86782,86783,86785,86786,86787,86789,86794,86795,86796,86800,86801],{"id":75068,"depth":642,"text":75069},{"id":75205,"depth":642,"text":75206},{"id":75308,"depth":642,"text":86764,"children":86765},"Mezní produkt práce (MPLMP_L)",[86766],{"id":75754,"depth":649,"text":75755},{"id":76243,"depth":642,"text":86768},"Průměrný produkt práce (APLAP_L)",{"id":76361,"depth":642,"text":76362,"children":86770},[86771,86772,86773],{"id":76598,"depth":649,"text":65741},{"id":76909,"depth":649,"text":76910},{"id":77629,"depth":649,"text":77630},{"id":78201,"depth":642,"text":78202},{"id":78304,"depth":642,"text":78305,"children":86776},[86777,86778,86780,86781],{"id":78663,"depth":649,"text":78664},{"id":79162,"depth":649,"text":86779},"Parametr efektivity AA",{"id":79233,"depth":649,"text":79234},{"id":37419,"depth":649,"text":79573},{"id":79760,"depth":642,"text":79761},{"id":80099,"depth":642,"text":86784},"Mezní produkty MPLMP_L, MPKMP_K a totální diferenciál",{"id":80790,"depth":642,"text":80791},{"id":75134,"depth":642,"text":10030},{"id":81201,"depth":642,"text":86788},"Mezní míra technické substituce (MRTSMRTS)",{"id":82067,"depth":642,"text":82068,"children":86790},[86791,86792,86793],{"id":82071,"depth":649,"text":82072},{"id":82714,"depth":649,"text":82715},{"id":82995,"depth":649,"text":82996},{"id":83341,"depth":642,"text":83342},{"id":50121,"depth":642,"text":50122},{"id":83691,"depth":642,"text":83692,"children":86797},[86798,86799],{"id":40690,"depth":649,"text":40691},{"id":84210,"depth":649,"text":84211},{"id":15966,"depth":642,"text":15967},{"id":4048,"depth":642,"text":4049},{},"\u002Ftopics\u002Fprodukce",{"title":74704,"description":641},[1138,1136],"topics\u002Fprodukce",[1128,10065,86808,86809,86810,75134,86811,86812],"produkcni-funkce","mpl-apl","cobb-douglas","mrts","euler","ZO2oG_qVOhQee90SJRry02Lau2bGvK2gaOFbwchTg1Y",{"id":86815,"title":86816,"body":86817,"course":1128,"courses":659,"created":9809,"description":641,"extension":661,"meta":95764,"navigation":664,"path":95765,"seo":95766,"sources":95767,"stem":95768,"tags":95769,"type":4113,"updated":677,"__hash__":95772},"topics\u002Ftopics\u002Fuzitecnost.md","Užitečnost, Cobb-Douglasova funkce užitečnosti a optimalizace spotřebitele",{"type":9,"value":86818,"toc":95738},[86819,86822,86824,87021,87030,87034,87037,87090,87094,87106,87110,87113,87130,87253,87259,87403,87413,87417,87452,87490,87538,87595,87655,87697,88273,88277,88360,88469,88562,88820,88823,88876,88987,89069,89073,89084,89317,89372,89378,89418,89481,89492,89683,89789,89942,89990,89995,90109,90147,90273,90319,90346,90423,90498,90578,90708,90769,90857,90861,90864,90933,91016,91023,91083,91393,91397,91403,91456,91472,91523,91661,91737,91850,92167,92171,92178,92338,92397,92401,92423,92520,92641,92755,92778,92841,92898,93150,93158,93162,93169,93423,93473,93529,93532,93696,93700,93798,93800,93832,93836,93969,94211,94395,94563,94870,95003,95190,95202,95204,95639,95641],[12,86820,86816],{"id":86821},"užitečnost-cobb-douglasova-funkce-užitečnosti-a-optimalizace-spotřebitele",[115,86823,12259],{"id":12258},[724,86825,86826,2170,86828,86859,86860,86863,86864,86894,86895,86913,86914,86954,86955,86958,86959,86972,86973,28493,86976,86989,86990,87003,87004,87017,87018,2263],{},[38,86827,880],{},[883,86829,86831],{"className":86830},[886],[888,86832,86833],{"xmlns":890},[892,86834,86835,86857],{},[895,86836,86837,86839,86841,86847,86849,86855],{},[898,86838,900],{},[1688,86840,2066],{"stretchy":2065},[1788,86842,86843,86845],{},[898,86844,1872],{},[1793,86846,1795],{},[1688,86848,1733],{"separator":1732},[1788,86850,86851,86853],{},[898,86852,1872],{},[1793,86854,1806],{},[1688,86856,2076],{"stretchy":2065},[902,86858,16590],{"encoding":904}," je číselné vyjádření uspokojení spotřebitele ze svazku zboží — v ordinalistickém přístupu slouží jen k ",[38,86861,86862],{},"uspořádání"," svazků (nikoli k měření v jednotkách). Klíčové nástroje jsou mezní užitečnosti ",[883,86865,86867],{"className":86866},[886],[888,86868,86869],{"xmlns":890},[892,86870,86871,86891],{},[895,86872,86873,86875,86881,86883],{},[898,86874,1661],{},[1788,86876,86877,86879],{},[898,86878,900],{},[898,86880,18035],{},[1688,86882,1690],{},[1814,86884,86885,86887,86889],{},[898,86886,900],{},[898,86888,18035],{},[1688,86890,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[902,86892,86893],{"encoding":904},"MU_i = U'_i",", indiferenční křivky ",[883,86896,86898],{"className":86897},[886],[888,86899,86900],{"xmlns":890},[892,86901,86902,86910],{},[895,86903,86904,86906,86908],{},[898,86905,900],{},[1688,86907,1690],{},[898,86909,2031],{},[902,86911,86912],{"encoding":904},"U = c"," a mezní míra komoditní substituce ",[883,86915,86917],{"className":86916},[886],[888,86918,86919],{"xmlns":890},[892,86920,86921,86951],{},[895,86922,86923,86925,86927,86929,86931,86933,86935,86941,86943,86945],{},[898,86924,1661],{},[898,86926,4251],{},[898,86928,1693],{},[898,86930,1740],{},[1688,86932,1690],{},[898,86934,1661],{},[1788,86936,86937,86939],{},[898,86938,900],{},[1793,86940,1795],{},[898,86942,4930],{"mathvariant":1822},[898,86944,1661],{},[1788,86946,86947,86949],{},[898,86948,900],{},[1793,86950,1806],{},[902,86952,86953],{"encoding":904},"MRCS = MU_1\u002FMU_2",". Tato stránka pokrývá ",[38,86956,86957],{},"teorii užitečnosti"," — funkce ",[883,86960,86962],{"className":86961},[886],[888,86963,86964],{"xmlns":890},[892,86965,86966,86970],{},[895,86967,86968],{},[898,86969,900],{},[902,86971,900],{"encoding":904},", její vlastnosti, Cobb-Douglasův tvar, indiferenční křivky a MRCS. ",[38,86974,86975],{},"Optimalizaci spotřebitele",[883,86977,86979],{"className":86978},[886],[888,86980,86981],{"xmlns":890},[892,86982,86983,86987],{},[895,86984,86985],{},[898,86986,900],{},[902,86988,900],{"encoding":904}," při rozpočtu, min ",[883,86991,86993],{"className":86992},[886],[888,86994,86995],{"xmlns":890},[892,86996,86997,87001],{},[895,86998,86999],{},[898,87000,4509],{},[902,87002,4509],{"encoding":904}," při dané ",[883,87005,87007],{"className":87006},[886],[888,87008,87009],{"xmlns":890},[892,87010,87011,87015],{},[895,87012,87013],{},[898,87014,900],{},[902,87016,900],{"encoding":904},", Lagrange, funkce poptávky) viz ",[207,87019,913],{"className":87020,"dataFsResolvedFilePath":911,"href":912},[210],[724,87022,87023,87024,87026,87027,2263],{},"Kapitola 6 knihy ",[614,87025,16455],{}," — model rozhodování spotřebitele. Zde: funkce užitečnosti, indiferenční křivky, mezní míra komoditní substituce. Navazující optimalizace je v ",[207,87028,36994],{"className":87029,"dataFsResolvedFilePath":911,"href":912},[210],[115,87031,87033],{"id":87032},"úvod-cílové-znalosti-kapitoly-6","Úvod — cílové znalosti kapitoly 6",[724,87035,87036],{},"Po prostudování této kapitoly byste měli umět:",[120,87038,87039,87045,87054,87059,87062,87068,87074,87077,87083],{},[123,87040,87041,87042,1733],{},"vyložit, co se rozumí termínem ",[38,87043,87044],{},"užitečnost",[123,87046,87047,87048,4142,87051,1733],{},"definovat pojmy ",[38,87049,87050],{},"svazek zboží",[38,87052,87053],{},"funkce užitečnosti",[123,87055,75083,87056,75090],{},[38,87057,87058],{},"mezní užitečnosti",[123,87060,87061],{},"vyjmenovat základní vlastnosti funkcí užitečnosti,",[123,87063,75110,87064,87067],{},[38,87065,87066],{},"Cobb-Douglasových"," funkcí užitečnosti,",[123,87069,75131,87070,87073],{},[38,87071,87072],{},"křivky užitečnosti"," (indiferenční křivky),",[123,87075,87076],{},"vyjmenovat jejich základní vlastnosti,",[123,87078,75083,87079,87082],{},[38,87080,87081],{},"mezní míru komoditní substituce"," a ekonomicky ji interpretovat,",[123,87084,87085,87086,87089],{},"řešit ",[38,87087,87088],{},"optimalizační úlohy"," s ohledem na užitečnost.",[115,87091,87093],{"id":87092},"_61-pojetí-užitečnosti","6.1 Pojetí užitečnosti",[724,87095,87096,87097,87101,87102,87105],{},"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 ",[207,87098,87100],{"className":87099,"dataFsResolvedFilePath":800,"href":801},[210],"poptávku",". Centrálním pojmem je ",[38,87103,87104],{},"užitečnost (utility)"," — vše, co vede spotřebitele k nákupu zboží (uspokojení, potěšení, splnění přání, pohodlí).",[198,87107,87109],{"id":87108},"kardinalistický-vs-ordinalistický-přístup","Kardinalistický vs. ordinalistický přístup",[724,87111,87112],{},"Historicky se vyvíjela dvě pojetí „měření\" užitečnosti:",[120,87114,87115,87121],{},[123,87116,87117,87120],{},[38,87118,87119],{},"Kardinalistický přístup"," (19. století — Gossen, Jevons, Walras): užitečnost měřena kvantitativně (např. peněžními jednotkami). Tento přístup se ukázal být nevýhodný.",[123,87122,87123,87126,87127,87129],{},[38,87124,87125],{},"Ordinalistický přístup"," (v současnosti preferovaný): postačuje ",[38,87128,86862],{}," svazků zboží podle preferencí; kvantitativní číselné hodnocení užitečnosti se nepožaduje.",[4124,87131,87132],{},[724,87133,87134,87136,87137,87140,87141,2170,87154,87157,87158,4142,87171,87190,87191,1343,87217,87244,87245,87248,87249,87252],{},[883,87135,4668],{}," Pozor — ordinalisté užitečnost ",[38,87138,87139],{},"neměří","\nV ordinalistickém přístupu hodnoty funkce ",[883,87142,87144],{"className":87143},[886],[888,87145,87146],{"xmlns":890},[892,87147,87148,87152],{},[895,87149,87150],{},[898,87151,900],{},[902,87153,900],{"encoding":904},[38,87155,87156],{},"nemají samostatný ekonomický význam"," — slouží pouze k uspořádání svazků. Dvě funkce ",[883,87159,87161],{"className":87160},[886],[888,87162,87163],{"xmlns":890},[892,87164,87165,87169],{},[895,87166,87167],{},[898,87168,900],{},[902,87170,900],{"encoding":904},[883,87172,87174],{"className":87173},[886],[888,87175,87176],{"xmlns":890},[892,87177,87178,87187],{},[895,87179,87180],{},[8642,87181,87182,87184],{"accent":1732},[898,87183,900],{},[1688,87185,87186],{},"~",[902,87188,87189],{"encoding":904},"\\tilde U"," reprezentují tytéž preference, jsou-li navzájem monotónní transformací (např. ",[883,87192,87194],{"className":87193},[886],[888,87195,87196],{"xmlns":890},[892,87197,87198,87214],{},[895,87199,87200,87206,87208],{},[8642,87201,87202,87204],{"accent":1732},[898,87203,900],{},[1688,87205,87186],{},[1688,87207,1690],{},[1850,87209,87210,87212],{},[898,87211,900],{},[1793,87213,1806],{},[902,87215,87216],{"encoding":904},"\\tilde U = U^2",[883,87218,87220],{"className":87219},[886],[888,87221,87222],{"xmlns":890},[892,87223,87224,87241],{},[895,87225,87226,87232,87234,87237,87239],{},[8642,87227,87228,87230],{"accent":1732},[898,87229,900],{},[1688,87231,87186],{},[1688,87233,1690],{},[898,87235,87236],{},"ln",[1688,87238,56440],{},[898,87240,900],{},[902,87242,87243],{"encoding":904},"\\tilde U = \\ln U","). Výroky typu „užitečnost je 250 jednotek\" proto samy o sobě nic neříkají — smysl mají jen ",[38,87246,87247],{},"porovnání"," mezi svazky a ",[38,87250,87251],{},"poměry"," mezních veličin.",[724,87254,87255,87256,2965],{},"Ordinalistický přístup vychází z ",[38,87257,87258],{},"pěti hlavních předpokladů",[152,87260,87261,87267,87273,87391,87397],{},[123,87262,87263,87266],{},[38,87264,87265],{},"Racionalita."," Spotřebitel jedná racionálně — snaží se maximalizovat své uspokojení (užitečnost) s ohledem na daný důchod a tržní ceny; disponuje všemi potřebnými informacemi.",[123,87268,87269,87272],{},[38,87270,87271],{},"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.",[123,87274,87275,87278,87279,61981,87292,87305,87306,61981,87319,3185,87332,87335,87336,4142,87355,62810,87373,2263],{},[38,87276,87277],{},"Konzistence a tranzitivita."," Preferuje-li v jisté době svazek ",[883,87280,87282],{"className":87281},[886],[888,87283,87284],{"xmlns":890},[892,87285,87286,87290],{},[895,87287,87288],{},[898,87289,4512],{},[902,87291,4512],{"encoding":904},[883,87293,87295],{"className":87294},[886],[888,87296,87297],{"xmlns":890},[892,87298,87299,87303],{},[895,87300,87301],{},[898,87302,23494],{},[902,87304,23494],{"encoding":904},", nebude jindy preferovat ",[883,87307,87309],{"className":87308},[886],[888,87310,87311],{"xmlns":890},[892,87312,87313,87317],{},[895,87314,87315],{},[898,87316,23494],{},[902,87318,23494],{"encoding":904},[883,87320,87322],{"className":87321},[886],[888,87323,87324],{"xmlns":890},[892,87325,87326,87330],{},[895,87327,87328],{},[898,87329,4512],{},[902,87331,4512],{"encoding":904},[38,87333,87334],{},"Tranzitivita",": pokud ",[883,87337,87339],{"className":87338},[886],[888,87340,87341],{"xmlns":890},[892,87342,87343,87352],{},[895,87344,87345,87347,87350],{},[898,87346,4512],{},[1688,87348,87349],{},"≻",[898,87351,23494],{},[902,87353,87354],{"encoding":904},"A \\succ B",[883,87356,87358],{"className":87357},[886],[888,87359,87360],{"xmlns":890},[892,87361,87362,87370],{},[895,87363,87364,87366,87368],{},[898,87365,23494],{},[1688,87367,87349],{},[898,87369,1693],{},[902,87371,87372],{"encoding":904},"B \\succ C",[883,87374,87376],{"className":87375},[886],[888,87377,87378],{"xmlns":890},[892,87379,87380,87388],{},[895,87381,87382,87384,87386],{},[898,87383,4512],{},[1688,87385,87349],{},[898,87387,1693],{},[902,87389,87390],{"encoding":904},"A \\succ C",[123,87392,87393,87396],{},[38,87394,87395],{},"Rostoucí užitečnost."," Uspokojení roste s množstvím zboží.",[123,87398,87399,87402],{},[38,87400,87401],{},"Klesající mezní užitečnost."," „Přírůstky\" uspokojení klesají s růstem množství zboží.",[724,87404,87405,87406,87409,87410,2263],{},"K naplnění předpokladů je ordinalistický přístup založen na pojmech ",[614,87407,87408],{},"preference"," a na příbuzné ",[614,87411,87412],{},"funkci užitečnosti",[115,87414,87416],{"id":87415},"_62-model-užitečnosti-svazek-zboží-a-funkce-užitečnosti","6.2 Model užitečnosti — svazek zboží a funkce užitečnosti",[724,87418,87419,87420,87433,87434,87437,87438,87451],{},"Uvažujme ",[883,87421,87423],{"className":87422},[886],[888,87424,87425],{"xmlns":890},[892,87426,87427,87431],{},[895,87428,87429],{},[898,87430,37100],{},[902,87432,37100],{"encoding":904}," různých zboží. ",[38,87435,87436],{},"Svazek zboží (bundle of goods)"," je uspořádaná ",[883,87439,87441],{"className":87440},[886],[888,87442,87443],{"xmlns":890},[892,87444,87445,87449],{},[895,87446,87447],{},[898,87448,37100],{},[902,87450,37100],{"encoding":904},"-tice",[724,87453,87454],{},[883,87455,87457],{"className":87456},[886],[888,87458,87459],{"xmlns":890},[892,87460,87461,87487],{},[895,87462,87463,87465,87471,87473,87475,87477,87483,87485],{},[1688,87464,2066],{"stretchy":2065},[1788,87466,87467,87469],{},[898,87468,1872],{},[1793,87470,1795],{},[1688,87472,1733],{"separator":1732},[1688,87474,9899],{},[1688,87476,1733],{"separator":1732},[1788,87478,87479,87481],{},[898,87480,1872],{},[898,87482,37100],{},[1688,87484,2076],{"stretchy":2065},[1688,87486,1733],{"separator":1732},[902,87488,87489],{"encoding":904},"(Q_1, \\dots, Q_n),",[724,87491,4567,87492,87509,87510,87523,87524,87527,87528,87531,87532,87535,87536,2965],{},[883,87493,87495],{"className":87494},[886],[888,87496,87497],{"xmlns":890},[892,87498,87499,87507],{},[895,87500,87501],{},[1788,87502,87503,87505],{},[898,87504,1872],{},[898,87506,18035],{},[902,87508,47778],{"encoding":904}," značí množství ",[883,87511,87513],{"className":87512},[886],[888,87514,87515],{"xmlns":890},[892,87516,87517,87521],{},[895,87518,87519],{},[898,87520,18035],{},[902,87522,18035],{"encoding":904},"-tého zboží. Spotřebitel je schopen svazky ",[38,87525,87526],{},"uspořádat"," s rostoucí užitečností, případně je prohlásit za ",[38,87529,87530],{},"indiferentní"," (tj. stejně užitečné). Tím je definována ",[38,87533,87534],{},"relace preference",". Preferenci vyjadřujeme číselně: svazku preferovanému přiřadíme větší číslo, indiferentním svazkům stejné číslo. Dostáváme ",[38,87537,87412],{},[883,87539,87541],{"className":87540},[886],[888,87542,87543],{"xmlns":890,"display":28306},[892,87544,87545,87592],{},[20995,87546,87547],{"width":28311},[21000,87548,87549,87551,87585,87587],{},[21003,87550],{"width":28316},[21003,87552,87553],{},[895,87554,87555,87557,87559,87561,87563,87569,87571,87573,87575,87581,87583],{},[898,87556,900],{},[1688,87558,1690],{},[898,87560,900],{},[1688,87562,2066],{"stretchy":2065},[1788,87564,87565,87567],{},[898,87566,1872],{},[1793,87568,1795],{},[1688,87570,1733],{"separator":1732},[1688,87572,9899],{},[1688,87574,1733],{"separator":1732},[1788,87576,87577,87579],{},[898,87578,1872],{},[898,87580,37100],{},[1688,87582,2076],{"stretchy":2065},[1688,87584,1733],{"separator":1732},[21003,87586],{"width":28316},[21003,87588,87589],{},[2041,87590,87591],{},"(6.1)",[902,87593,87594],{"encoding":904},"U = U(Q_1, \\dots, Q_n), \\tag{6.1}",[724,87596,4567,87597,87627,87628,87650,87651,87654],{},[883,87598,87600],{"className":87599},[886],[888,87601,87602],{"xmlns":890},[892,87603,87604,87624],{},[895,87605,87606,87612,87614,87616,87618],{},[1788,87607,87608,87610],{},[898,87609,1872],{},[1793,87611,1795],{},[1688,87613,1733],{"separator":1732},[1688,87615,9899],{},[1688,87617,1733],{"separator":1732},[1788,87619,87620,87622],{},[898,87621,1872],{},[898,87623,37100],{},[902,87625,87626],{"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 ",[883,87629,87631],{"className":87630},[886],[888,87632,87633],{"xmlns":890},[892,87634,87635,87647],{},[895,87636,87637,87639,87641],{},[898,87638,900],{},[1688,87640,1733],{"separator":1732},[8642,87642,87643,87645],{"accent":1732},[898,87644,900],{},[1688,87646,87186],{},[902,87648,87649],{"encoding":904},"U, \\tilde U"," reprezentují stejné preference, pokud mezi nimi existuje ",[38,87652,87653],{},"monotónní transformace"," zachovávající pořadí.",[724,87656,87657,87658,7271,87661,2263],{},"Dále se omezíme na funkce pro ",[38,87659,87660],{},"dvě zboží",[883,87662,87664],{"className":87663},[886],[888,87665,87666],{"xmlns":890},[892,87667,87668,87694],{},[895,87669,87670,87672,87674,87676,87678,87684,87686,87692],{},[898,87671,900],{},[1688,87673,1690],{},[898,87675,900],{},[1688,87677,2066],{"stretchy":2065},[1788,87679,87680,87682],{},[898,87681,1872],{},[1793,87683,1795],{},[1688,87685,1733],{"separator":1732},[1788,87687,87688,87690],{},[898,87689,1872],{},[1793,87691,1806],{},[1688,87693,2076],{"stretchy":2065},[902,87695,87696],{"encoding":904},"U = U(Q_1, Q_2)",[4124,87698,87699,87774],{},[724,87700,87701,87703,87704,2965],{},[883,87702,52935],{}," Příklad 6.1 — uspořádání a indiference\nPro ",[883,87705,87707],{"className":87706},[886],[888,87708,87709],{"xmlns":890},[892,87710,87711,87771],{},[895,87712,87713,87715,87717,87719,87721,87727,87729,87735,87737,87743,87745,87747,87749],{},[898,87714,900],{},[1688,87716,1690],{},[898,87718,900],{},[1688,87720,2066],{"stretchy":2065},[1788,87722,87723,87725],{},[898,87724,1872],{},[1793,87726,1795],{},[1688,87728,1733],{"separator":1732},[1788,87730,87731,87733],{},[898,87732,1872],{},[1793,87734,1806],{},[1688,87736,1733],{"separator":1732},[1788,87738,87739,87741],{},[898,87740,1872],{},[1793,87742,2131],{},[1688,87744,2076],{"stretchy":2065},[1688,87746,1690],{},[1793,87748,1806],{},[8373,87750,87751],{},[895,87752,87753,87759,87765],{},[1788,87754,87755,87757],{},[898,87756,1872],{},[1793,87758,1795],{},[1788,87760,87761,87763],{},[898,87762,1872],{},[1793,87764,1806],{},[1788,87766,87767,87769],{},[898,87768,1872],{},[1793,87770,2131],{},[902,87772,87773],{"encoding":904},"U = U(Q_1, Q_2, Q_3) = 2\\sqrt{Q_1 Q_2 Q_3}",[120,87775,87776,87969],{},[123,87777,87778,87779,87805,87806,13186,87832,4142,87891,5845,87951,8681],{},"svazek ",[883,87780,87782],{"className":87781},[886],[888,87783,87784],{"xmlns":890},[892,87785,87786,87802],{},[895,87787,87788,87790,87792,87794,87796,87798,87800],{},[1688,87789,2066],{"stretchy":2065},[1793,87791,42102],{},[1688,87793,1733],{"separator":1732},[1793,87795,2616],{},[1688,87797,1733],{"separator":1732},[1793,87799,42080],{},[1688,87801,2076],{"stretchy":2065},[902,87803,87804],{"encoding":904},"(16, 4, 64)"," je preferován před ",[883,87807,87809],{"className":87808},[886],[888,87810,87811],{"xmlns":890},[892,87812,87813,87829],{},[895,87814,87815,87817,87819,87821,87823,87825,87827],{},[1688,87816,2066],{"stretchy":2065},[1793,87818,4256],{},[1688,87820,1733],{"separator":1732},[1793,87822,4256],{},[1688,87824,1733],{"separator":1732},[1793,87826,66837],{},[1688,87828,2076],{"stretchy":2065},[902,87830,87831],{"encoding":904},"(9, 9, 27)",[883,87833,87835],{"className":87834},[886],[888,87836,87837],{"xmlns":890},[892,87838,87839,87888],{},[895,87840,87841,87843,87845,87847,87849,87851,87853,87855,87857,87859,87861,87875,87877,87879,87884,87886],{},[898,87842,900],{},[1688,87844,2066],{"stretchy":2065},[1793,87846,42102],{},[1688,87848,1733],{"separator":1732},[1793,87850,2616],{},[1688,87852,1733],{"separator":1732},[1793,87854,42080],{},[1688,87856,2076],{"stretchy":2065},[1688,87858,1690],{},[1793,87860,1806],{},[8373,87862,87863],{},[895,87864,87865,87867,87869,87871,87873],{},[1793,87866,42102],{},[1688,87868,3434],{},[1793,87870,2616],{},[1688,87872,3434],{},[1793,87874,42080],{},[1688,87876,1690],{},[1793,87878,1806],{},[8373,87880,87881],{},[1793,87882,87883],{},"4096",[1688,87885,1690],{},[1793,87887,5873],{},[902,87889,87890],{"encoding":904},"U(16,4,64) = 2\\sqrt{16 \\cdot 4 \\cdot 64} = 2\\sqrt{4096} = 128",[883,87892,87894],{"className":87893},[886],[888,87895,87896],{"xmlns":890},[892,87897,87898,87948],{},[895,87899,87900,87902,87904,87906,87908,87910,87912,87914,87916,87918,87920,87934,87936,87938,87943,87945],{},[898,87901,900],{},[1688,87903,2066],{"stretchy":2065},[1793,87905,4256],{},[1688,87907,1733],{"separator":1732},[1793,87909,4256],{},[1688,87911,1733],{"separator":1732},[1793,87913,66837],{},[1688,87915,2076],{"stretchy":2065},[1688,87917,1690],{},[1793,87919,1806],{},[8373,87921,87922],{},[895,87923,87924,87926,87928,87930,87932],{},[1793,87925,4256],{},[1688,87927,3434],{},[1793,87929,4256],{},[1688,87931,3434],{},[1793,87933,66837],{},[1688,87935,1690],{},[1793,87937,1806],{},[8373,87939,87940],{},[1793,87941,87942],{},"2187",[1688,87944,6156],{},[1793,87946,87947],{},"93,53",[902,87949,87950],{"encoding":904},"U(9,9,27) = 2\\sqrt{9 \\cdot 9 \\cdot 27} = 2\\sqrt{2187} \\doteq 93{,}53",[883,87952,87954],{"className":87953},[886],[888,87955,87956],{"xmlns":890},[892,87957,87958,87966],{},[895,87959,87960,87962,87964],{},[1793,87961,5873],{},[1688,87963,3665],{},[1793,87965,87947],{},[902,87967,87968],{"encoding":904},"128 > 93{,}53",[123,87970,87971,87972,4142,87998,88024,88025,4142,88065,88106,88107,88153,88154,4142,88180,3103,88206,4142,88224,88242,88243,2263],{},"svazky ",[883,87973,87975],{"className":87974},[886],[888,87976,87977],{"xmlns":890},[892,87978,87979,87995],{},[895,87980,87981,87983,87985,87987,87989,87991,87993],{},[1688,87982,2066],{"stretchy":2065},[1793,87984,2616],{},[1688,87986,1733],{"separator":1732},[1793,87988,5841],{},[1688,87990,1733],{"separator":1732},[1793,87992,1806],{},[1688,87994,2076],{"stretchy":2065},[902,87996,87997],{"encoding":904},"(4, 8, 2)",[883,87999,88001],{"className":88000},[886],[888,88002,88003],{"xmlns":890},[892,88004,88005,88021],{},[895,88006,88007,88009,88011,88013,88015,88017,88019],{},[1688,88008,2066],{"stretchy":2065},[1793,88010,42080],{},[1688,88012,1733],{"separator":1732},[1793,88014,1795],{},[1688,88016,1733],{"separator":1732},[1793,88018,2616],{},[1688,88020,2076],{"stretchy":2065},[902,88022,88023],{"encoding":904},"(64, 1, 4)"," jsou indiferentní, protože ",[883,88026,88028],{"className":88027},[886],[888,88029,88030],{"xmlns":890},[892,88031,88032,88062],{},[895,88033,88034,88036,88038,88040,88042,88044,88046,88048,88050,88052,88054,88058,88060],{},[898,88035,900],{},[1688,88037,2066],{"stretchy":2065},[1793,88039,2616],{},[1688,88041,1733],{"separator":1732},[1793,88043,5841],{},[1688,88045,1733],{"separator":1732},[1793,88047,1806],{},[1688,88049,2076],{"stretchy":2065},[1688,88051,1690],{},[1793,88053,1806],{},[8373,88055,88056],{},[1793,88057,42080],{},[1688,88059,1690],{},[1793,88061,42102],{},[902,88063,88064],{"encoding":904},"U(4,8,2) = 2\\sqrt{64} = 16",[883,88066,88068],{"className":88067},[886],[888,88069,88070],{"xmlns":890},[892,88071,88072,88103],{},[895,88073,88074,88076,88078,88080,88082,88084,88086,88088,88090,88092,88094,88099,88101],{},[898,88075,900],{},[1688,88077,2066],{"stretchy":2065},[1793,88079,42080],{},[1688,88081,1733],{"separator":1732},[1793,88083,1795],{},[1688,88085,1733],{"separator":1732},[1793,88087,2616],{},[1688,88089,2076],{"stretchy":2065},[1688,88091,1690],{},[1793,88093,1806],{},[8373,88095,88096],{},[1793,88097,88098],{},"256",[1688,88100,1690],{},[1793,88102,72599],{},[902,88104,88105],{"encoding":904},"U(64,1,4) = 2\\sqrt{256} = 32"," — jsou stejně užitečné mezi sebou, pokud ",[883,88108,88110],{"className":88109},[886],[888,88111,88112],{"xmlns":890},[892,88113,88114,88150],{},[895,88115,88116,88118,88120,88122,88124,88126,88128,88130,88132,88134,88136,88138,88140,88142,88144,88146,88148],{},[898,88117,900],{},[1688,88119,2066],{"stretchy":2065},[1793,88121,2616],{},[1688,88123,1733],{"separator":1732},[1793,88125,5841],{},[1688,88127,1733],{"separator":1732},[1793,88129,1806],{},[1688,88131,2076],{"stretchy":2065},[1688,88133,1690],{},[898,88135,900],{},[1688,88137,2066],{"stretchy":2065},[1793,88139,42080],{},[1688,88141,1733],{"separator":1732},[1793,88143,1795],{},[1688,88145,1733],{"separator":1732},[1793,88147,2616],{},[1688,88149,2076],{"stretchy":2065},[902,88151,88152],{"encoding":904},"U(4,8,2) = U(64,1,4)","; ověření: ",[883,88155,88157],{"className":88156},[886],[888,88158,88159],{"xmlns":890},[892,88160,88161,88177],{},[895,88162,88163,88165,88167,88169,88171,88173,88175],{},[1793,88164,2616],{},[1688,88166,3434],{},[1793,88168,5841],{},[1688,88170,3434],{},[1793,88172,1806],{},[1688,88174,1690],{},[1793,88176,42080],{},[902,88178,88179],{"encoding":904},"4 \\cdot 8 \\cdot 2 = 64",[883,88181,88183],{"className":88182},[886],[888,88184,88185],{"xmlns":890},[892,88186,88187,88203],{},[895,88188,88189,88191,88193,88195,88197,88199,88201],{},[1793,88190,42080],{},[1688,88192,3434],{},[1793,88194,1795],{},[1688,88196,3434],{},[1793,88198,2616],{},[1688,88200,1690],{},[1793,88202,88098],{},[902,88204,88205],{"encoding":904},"64 \\cdot 1 \\cdot 4 = 256",[883,88207,88209],{"className":88208},[886],[888,88210,88211],{"xmlns":890},[892,88212,88213,88221],{},[895,88214,88215,88217,88219],{},[898,88216,900],{},[1688,88218,1690],{},[1793,88220,42102],{},[902,88222,88223],{"encoding":904},"U = 16",[883,88225,88227],{"className":88226},[886],[888,88228,88229],{"xmlns":890},[892,88230,88231,88239],{},[895,88232,88233,88235,88237],{},[898,88234,900],{},[1688,88236,1690],{},[1793,88238,72599],{},[902,88240,88241],{"encoding":904},"U = 32"," — nejsou indiferentní. Správně indiferentní jsou svazky s týmž součinem ",[883,88244,88246],{"className":88245},[886],[888,88247,88248],{"xmlns":890},[892,88249,88250,88270],{},[895,88251,88252,88258,88264],{},[1788,88253,88254,88256],{},[898,88255,1872],{},[1793,88257,1795],{},[1788,88259,88260,88262],{},[898,88261,1872],{},[1793,88263,1806],{},[1788,88265,88266,88268],{},[898,88267,1872],{},[1793,88269,2131],{},[902,88271,88272],{"encoding":904},"Q_1 Q_2 Q_3",[115,88274,88276],{"id":88275},"mezní-užitečnost-mu","Mezní užitečnost (MU)",[724,88278,88279,88280,8358,88315,2170,88318,42054,88335,10277,88352,88355,88356,88359],{},"Pro funkci užitečnosti ",[883,88281,88283],{"className":88282},[886],[888,88284,88285],{"xmlns":890},[892,88286,88287,88313],{},[895,88288,88289,88291,88293,88295,88297,88303,88305,88311],{},[898,88290,900],{},[1688,88292,1690],{},[898,88294,900],{},[1688,88296,2066],{"stretchy":2065},[1788,88298,88299,88301],{},[898,88300,1872],{},[1793,88302,1795],{},[1688,88304,1733],{"separator":1732},[1788,88306,88307,88309],{},[898,88308,1872],{},[1793,88310,1806],{},[1688,88312,2076],{"stretchy":2065},[902,88314,87696],{"encoding":904},[38,88316,88317],{},"mezní užitečnost",[883,88319,88321],{"className":88320},[886],[888,88322,88323],{"xmlns":890},[892,88324,88325,88333],{},[895,88326,88327],{},[1788,88328,88329,88331],{},[898,88330,1872],{},[1793,88332,1795],{},[902,88334,29242],{"encoding":904},[883,88336,88338],{"className":88337},[886],[888,88339,88340],{"xmlns":890},[892,88341,88342,88350],{},[895,88343,88344],{},[1788,88345,88346,88348],{},[898,88347,1872],{},[1793,88349,1806],{},[902,88351,29261],{"encoding":904},[38,88353,88354],{},"marginal utility",") parciální ",[207,88357,1145],{"className":88358,"dataFsResolvedFilePath":764,"href":765},[210]," užitečnosti podle příslušné proměnné:",[883,88361,88363],{"className":88362},[886],[888,88364,88365],{"xmlns":890,"display":28306},[892,88366,88367,88466],{},[20995,88368,88369],{"width":28311},[21000,88370,88371,88373,88459,88461],{},[21003,88372],{"width":28316},[21003,88374,88375],{},[895,88376,88377,88379,88385,88387,88395,88397,88415,88417,88419,88421,88427,88429,88437,88439,88457],{},[898,88378,1661],{},[1788,88380,88381,88383],{},[898,88382,900],{},[1793,88384,1795],{},[1688,88386,1690],{},[1814,88388,88389,88391,88393],{},[898,88390,900],{},[1793,88392,1795],{},[1688,88394,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,88396,1690],{},[1781,88398,88399,88405],{},[895,88400,88401,88403],{},[898,88402,10124],{"mathvariant":1822},[898,88404,900],{},[895,88406,88407,88409],{},[898,88408,10124],{"mathvariant":1822},[1788,88410,88411,88413],{},[898,88412,1872],{},[1793,88414,1795],{},[1688,88416,1733],{"separator":1732},[6134,88418],{"width":15531},[898,88420,1661],{},[1788,88422,88423,88425],{},[898,88424,900],{},[1793,88426,1806],{},[1688,88428,1690],{},[1814,88430,88431,88433,88435],{},[898,88432,900],{},[1793,88434,1806],{},[1688,88436,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,88438,1690],{},[1781,88440,88441,88447],{},[895,88442,88443,88445],{},[898,88444,10124],{"mathvariant":1822},[898,88446,900],{},[895,88448,88449,88451],{},[898,88450,10124],{"mathvariant":1822},[1788,88452,88453,88455],{},[898,88454,1872],{},[1793,88456,1806],{},[898,88458,2263],{"mathvariant":1822},[21003,88460],{"width":28316},[21003,88462,88463],{},[2041,88464,88465],{},"(6.2)",[902,88467,88468],{"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}",[724,88470,88471,88472,88506,88507,88537,88538,2170,88541,2263],{},"Pro pevné ",[883,88473,88475],{"className":88474},[886],[888,88476,88477],{"xmlns":890},[892,88478,88479,88503],{},[895,88480,88481,88487,88489,88491,88493,88499,88501],{},[1788,88482,88483,88485],{},[898,88484,1872],{},[1793,88486,1795],{},[1688,88488,1690],{},[898,88490,207],{},[1688,88492,1733],{"separator":1732},[1788,88494,88495,88497],{},[898,88496,1872],{},[1793,88498,1806],{},[1688,88500,1690],{},[898,88502,1918],{},[902,88504,88505],{"encoding":904},"Q_1 = a, Q_2 = b"," se hodnota ",[883,88508,88510],{"className":88509},[886],[888,88511,88512],{"xmlns":890},[892,88513,88514,88534],{},[895,88515,88516,88518,88524,88526,88528,88530,88532],{},[898,88517,1661],{},[1788,88519,88520,88522],{},[898,88521,900],{},[1793,88523,1795],{},[1688,88525,2066],{"stretchy":2065},[898,88527,207],{},[1688,88529,1733],{"separator":1732},[898,88531,1918],{},[1688,88533,2076],{"stretchy":2065},[902,88535,88536],{"encoding":904},"MU_1(a, b)"," nazývá mezní užitečnost ",[38,88539,88540],{},"v bodě (na hladině)",[883,88542,88544],{"className":88543},[886],[888,88545,88546],{"xmlns":890},[892,88547,88548,88560],{},[895,88549,88550,88552,88554,88556,88558],{},[1688,88551,2748],{"stretchy":2065},[898,88553,207],{},[1688,88555,1733],{"separator":1732},[898,88557,1918],{},[1688,88559,2763],{"stretchy":2065},[902,88561,11075],{"encoding":904},[4124,88563,88564],{},[724,88565,88566,88568,88569,88599,88628,88629,2872,88642,2886,88659,88680,88681,2194,88698,2946,88711,88728,88729,88751,88752,88781,88782,6729,88802,88819],{},[883,88567,4412],{}," Intuice — co říká ",[883,88570,88572],{"className":88571},[886],[888,88573,88574],{"xmlns":890},[892,88575,88576,88596],{},[895,88577,88578,88580,88586,88588,88590,88592,88594],{},[898,88579,1661],{},[1788,88581,88582,88584],{},[898,88583,900],{},[1793,88585,1795],{},[1688,88587,2066],{"stretchy":2065},[898,88589,207],{},[1688,88591,1733],{"separator":1732},[898,88593,1918],{},[1688,88595,2076],{"stretchy":2065},[902,88597,88598],{"encoding":904},"MU_1(a,b)",[883,88600,88602],{"className":88601},[886],[888,88603,88604],{"xmlns":890},[892,88605,88606,88626],{},[895,88607,88608,88610,88616,88618,88620,88622,88624],{},[898,88609,1661],{},[1788,88611,88612,88614],{},[898,88613,900],{},[1793,88615,1795],{},[1688,88617,2066],{"stretchy":2065},[898,88619,207],{},[1688,88621,1733],{"separator":1732},[898,88623,1918],{},[1688,88625,2076],{"stretchy":2065},[902,88627,88536],{"encoding":904}," je rychlost změny ",[883,88630,88632],{"className":88631},[886],[888,88633,88634],{"xmlns":890},[892,88635,88636,88640],{},[895,88637,88638],{},[898,88639,900],{},[902,88641,900],{"encoding":904},[883,88643,88645],{"className":88644},[886],[888,88646,88647],{"xmlns":890},[892,88648,88649,88657],{},[895,88650,88651],{},[1788,88652,88653,88655],{},[898,88654,1872],{},[1793,88656,1795],{},[902,88658,29242],{"encoding":904},[883,88660,88662],{"className":88661},[886],[888,88663,88664],{"xmlns":890},[892,88665,88666,88678],{},[895,88667,88668,88670,88672,88674,88676],{},[1688,88669,2748],{"stretchy":2065},[898,88671,207],{},[1688,88673,1733],{"separator":1732},[898,88675,1918],{},[1688,88677,2763],{"stretchy":2065},[902,88679,11075],{"encoding":904},". Přibližně: změní-li se ",[883,88682,88684],{"className":88683},[886],[888,88685,88686],{"xmlns":890},[892,88687,88688,88696],{},[895,88689,88690],{},[1788,88691,88692,88694],{},[898,88693,1872],{},[1793,88695,1795],{},[902,88697,29242],{"encoding":904},[883,88699,88701],{"className":88700},[886],[888,88702,88703],{"xmlns":890},[892,88704,88705,88709],{},[895,88706,88707],{},[898,88708,207],{},[902,88710,207],{"encoding":904},[883,88712,88714],{"className":88713},[886],[888,88715,88716],{"xmlns":890},[892,88717,88718,88726],{},[895,88719,88720,88722,88724],{},[898,88721,207],{},[1688,88723,1696],{},[1793,88725,1795],{},[902,88727,2964],{"encoding":904}," při pevném ",[883,88730,88732],{"className":88731},[886],[888,88733,88734],{"xmlns":890},[892,88735,88736,88748],{},[895,88737,88738,88744,88746],{},[1788,88739,88740,88742],{},[898,88741,1872],{},[1793,88743,1806],{},[1688,88745,1690],{},[898,88747,1918],{},[902,88749,88750],{"encoding":904},"Q_2 = b",", změní se užitečnost zhruba o ",[883,88753,88755],{"className":88754},[886],[888,88756,88757],{"xmlns":890},[892,88758,88759,88779],{},[895,88760,88761,88763,88769,88771,88773,88775,88777],{},[898,88762,1661],{},[1788,88764,88765,88767],{},[898,88766,900],{},[1793,88768,1795],{},[1688,88770,2066],{"stretchy":2065},[898,88772,207],{},[1688,88774,1733],{"separator":1732},[898,88776,1918],{},[1688,88778,2076],{"stretchy":2065},[902,88780,88536],{"encoding":904},". Stejně tak ",[883,88783,88785],{"className":88784},[886],[888,88786,88787],{"xmlns":890},[892,88788,88789,88799],{},[895,88790,88791,88793],{},[898,88792,1661],{},[1788,88794,88795,88797],{},[898,88796,900],{},[1793,88798,1806],{},[902,88800,88801],{"encoding":904},"MU_2",[883,88803,88805],{"className":88804},[886],[888,88806,88807],{"xmlns":890},[892,88808,88809,88817],{},[895,88810,88811],{},[1788,88812,88813,88815],{},[898,88814,1872],{},[1793,88816,1806],{},[902,88818,29261],{"encoding":904},". Mezní užitečnost tedy odpovídá „užitku z další jednotky\" a podle předpokladu 5 s množstvím klesá.",[198,88821,80451],{"id":88822},"totální-diferenciál",[724,88824,88825,88826,48580,88842,88872,88873,2965],{},"Přibližnou změnu užitečnosti ",[883,88827,88829],{"className":88828},[886],[888,88830,88831],{"xmlns":890},[892,88832,88833,88839],{},[895,88834,88835,88837],{},[898,88836,3147],{"mathvariant":1822},[898,88838,900],{},[902,88840,88841],{"encoding":904},"\\Delta U",[883,88843,88845],{"className":88844},[886],[888,88846,88847],{"xmlns":890},[892,88848,88849,88869],{},[895,88850,88851,88853,88859,88861,88863],{},[898,88852,2073],{"mathvariant":1822},[1788,88854,88855,88857],{},[898,88856,1872],{},[1793,88858,1795],{},[1688,88860,1733],{"separator":1732},[898,88862,2073],{"mathvariant":1822},[1788,88864,88865,88867],{},[898,88866,1872],{},[1793,88868,1806],{},[902,88870,88871],{"encoding":904},"\\mathrm{d} Q_1, \\mathrm{d} Q_2"," stanovíme pomocí ",[38,88874,88875],{},"totálního diferenciálu",[883,88877,88879],{"className":88878},[886],[888,88880,88881],{"xmlns":890,"display":28306},[892,88882,88883,88984],{},[20995,88884,88885],{"width":28311},[21000,88886,88887,88889,88977,88979],{},[21003,88888],{"width":28316},[21003,88890,88891],{},[895,88892,88893,88895,88897,88899,88901,88903,88905,88913,88915,88921,88923,88931,88933,88939,88941,88943,88949,88951,88957,88959,88961,88967,88969,88975],{},[898,88894,3147],{"mathvariant":1822},[898,88896,900],{},[1688,88898,2991],{},[898,88900,2073],{"mathvariant":1822},[898,88902,900],{},[1688,88904,1690],{},[1814,88906,88907,88909,88911],{},[898,88908,900],{},[1793,88910,1795],{},[1688,88912,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[898,88914,2073],{"mathvariant":1822},[1788,88916,88917,88919],{},[898,88918,1872],{},[1793,88920,1795],{},[1688,88922,1696],{},[1814,88924,88925,88927,88929],{},[898,88926,900],{},[1793,88928,1806],{},[1688,88930,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[898,88932,2073],{"mathvariant":1822},[1788,88934,88935,88937],{},[898,88936,1872],{},[1793,88938,1806],{},[1688,88940,1690],{},[898,88942,1661],{},[1788,88944,88945,88947],{},[898,88946,900],{},[1793,88948,1795],{},[898,88950,2073],{"mathvariant":1822},[1788,88952,88953,88955],{},[898,88954,1872],{},[1793,88956,1795],{},[1688,88958,1696],{},[898,88960,1661],{},[1788,88962,88963,88965],{},[898,88964,900],{},[1793,88966,1806],{},[898,88968,2073],{"mathvariant":1822},[1788,88970,88971,88973],{},[898,88972,1872],{},[1793,88974,1806],{},[898,88976,2263],{"mathvariant":1822},[21003,88978],{"width":28316},[21003,88980,88981],{},[2041,88982,88983],{},"(6.3)",[902,88985,88986],{"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}",[724,88988,75709,88989,2263],{},[883,88990,88992],{"className":88991},[886],[888,88993,88994],{"xmlns":890},[892,88995,88996,89066],{},[895,88997,88998,89000,89002,89004,89006,89008,89014,89016,89018,89024,89026,89032,89034,89036,89042,89044,89046,89048,89050,89056,89058,89064],{},[898,88999,3147],{"mathvariant":1822},[898,89001,900],{},[1688,89003,1690],{},[898,89005,900],{},[1688,89007,2066],{"stretchy":2065},[1788,89009,89010,89012],{},[898,89011,1872],{},[1793,89013,1795],{},[1688,89015,1696],{},[898,89017,2073],{"mathvariant":1822},[1788,89019,89020,89022],{},[898,89021,1872],{},[1793,89023,1795],{},[1688,89025,1733],{"separator":1732},[1788,89027,89028,89030],{},[898,89029,1872],{},[1793,89031,1806],{},[1688,89033,1696],{},[898,89035,2073],{"mathvariant":1822},[1788,89037,89038,89040],{},[898,89039,1872],{},[1793,89041,1806],{},[1688,89043,2076],{"stretchy":2065},[1688,89045,1954],{},[898,89047,900],{},[1688,89049,2066],{"stretchy":2065},[1788,89051,89052,89054],{},[898,89053,1872],{},[1793,89055,1795],{},[1688,89057,1733],{"separator":1732},[1788,89059,89060,89062],{},[898,89061,1872],{},[1793,89063,1806],{},[1688,89065,2076],{"stretchy":2065},[902,89067,89068],{"encoding":904},"\\Delta U = U(Q_1 + \\mathrm{d} Q_1, Q_2 + \\mathrm{d} Q_2) - U(Q_1, Q_2)",[115,89070,89072],{"id":89071},"vlastnosti-funkce-užitečnosti","Vlastnosti funkce užitečnosti",[724,89074,89075,89076,89079,89080,89083],{},"Funkce užitečnosti musí vyjadřovat dva ekonomicky zásadní předpoklady — ",[38,89077,89078],{},"rostoucí užitečnost"," (předpoklad 4) a ",[38,89081,89082],{},"klesající mezní užitečnost"," (předpoklad 5).",[724,89085,89086,89089,89090,42054,89116,89142,89143,1343,89175,89207,89208,4142,89262,89316],{},[38,89087,89088],{},"Předpoklad 4"," (rostoucí užitečnost) znamená, že při pevně zadaných ",[883,89091,89093],{"className":89092},[886],[888,89094,89095],{"xmlns":890},[892,89096,89097,89113],{},[895,89098,89099,89105,89107],{},[1788,89100,89101,89103],{},[898,89102,1872],{},[1793,89104,1806],{},[1688,89106,1690],{},[1788,89108,89109,89111],{},[898,89110,207],{},[1793,89112,1779],{},[902,89114,89115],{"encoding":904},"Q_2 = a_0",[883,89117,89119],{"className":89118},[886],[888,89120,89121],{"xmlns":890},[892,89122,89123,89139],{},[895,89124,89125,89131,89133],{},[1788,89126,89127,89129],{},[898,89128,1872],{},[1793,89130,1795],{},[1688,89132,1690],{},[1788,89134,89135,89137],{},[898,89136,1918],{},[1793,89138,1779],{},[902,89140,89141],{"encoding":904},"Q_1 = b_0"," jsou funkce jedné proměnné ",[883,89144,89146],{"className":89145},[886],[888,89147,89148],{"xmlns":890},[892,89149,89150,89172],{},[895,89151,89152,89154,89156,89162,89164,89170],{},[898,89153,900],{},[1688,89155,2066],{"stretchy":2065},[1788,89157,89158,89160],{},[898,89159,1872],{},[1793,89161,1795],{},[1688,89163,1733],{"separator":1732},[1788,89165,89166,89168],{},[898,89167,207],{},[1793,89169,1779],{},[1688,89171,2076],{"stretchy":2065},[902,89173,89174],{"encoding":904},"U(Q_1, a_0)",[883,89176,89178],{"className":89177},[886],[888,89179,89180],{"xmlns":890},[892,89181,89182,89204],{},[895,89183,89184,89186,89188,89194,89196,89202],{},[898,89185,900],{},[1688,89187,2066],{"stretchy":2065},[1788,89189,89190,89192],{},[898,89191,1918],{},[1793,89193,1779],{},[1688,89195,1733],{"separator":1732},[1788,89197,89198,89200],{},[898,89199,1872],{},[1793,89201,1806],{},[1688,89203,2076],{"stretchy":2065},[902,89205,89206],{"encoding":904},"U(b_0, Q_2)"," rostoucí. To platí, jestliže ",[883,89209,89211],{"className":89210},[886],[888,89212,89213],{"xmlns":890},[892,89214,89215,89259],{},[895,89216,89217,89255,89257],{},[1777,89218,89219],{"scriptlevel":1779,"displaystyle":1732},[1781,89220,89221,89245],{},[895,89222,89223,89225,89227,89229,89235,89237,89243],{},[898,89224,2073],{"mathvariant":1822},[898,89226,900],{},[1688,89228,2066],{"stretchy":2065},[1788,89230,89231,89233],{},[898,89232,1872],{},[1793,89234,1795],{},[1688,89236,1733],{"separator":1732},[1788,89238,89239,89241],{},[898,89240,207],{},[1793,89242,1779],{},[1688,89244,2076],{"stretchy":2065},[895,89246,89247,89249],{},[898,89248,2073],{"mathvariant":1822},[1788,89250,89251,89253],{},[898,89252,1872],{},[1793,89254,1795],{},[1688,89256,3665],{},[1793,89258,1779],{},[902,89260,89261],{"encoding":904},"\\dfrac{\\mathrm{d} U(Q_1, a_0)}{\\mathrm{d} Q_1} > 0",[883,89263,89265],{"className":89264},[886],[888,89266,89267],{"xmlns":890},[892,89268,89269,89313],{},[895,89270,89271,89309,89311],{},[1777,89272,89273],{"scriptlevel":1779,"displaystyle":1732},[1781,89274,89275,89299],{},[895,89276,89277,89279,89281,89283,89289,89291,89297],{},[898,89278,2073],{"mathvariant":1822},[898,89280,900],{},[1688,89282,2066],{"stretchy":2065},[1788,89284,89285,89287],{},[898,89286,1918],{},[1793,89288,1779],{},[1688,89290,1733],{"separator":1732},[1788,89292,89293,89295],{},[898,89294,1872],{},[1793,89296,1806],{},[1688,89298,2076],{"stretchy":2065},[895,89300,89301,89303],{},[898,89302,2073],{"mathvariant":1822},[1788,89304,89305,89307],{},[898,89306,1872],{},[1793,89308,1806],{},[1688,89310,3665],{},[1793,89312,1779],{},[902,89314,89315],{"encoding":904},"\\dfrac{\\mathrm{d} U(b_0, Q_2)}{\\mathrm{d} Q_2} > 0",", tj.",[883,89318,89320],{"className":89319},[886],[888,89321,89322],{"xmlns":890,"display":28306},[892,89323,89324,89369],{},[20995,89325,89326],{"width":28311},[21000,89327,89328,89330,89362,89364],{},[21003,89329],{"width":28316},[21003,89331,89332],{},[895,89333,89334,89342,89344,89346,89348,89350,89358,89360],{},[1814,89335,89336,89338,89340],{},[898,89337,900],{},[1793,89339,1795],{},[1688,89341,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,89343,3665],{},[1793,89345,1779],{},[1688,89347,1733],{"separator":1732},[6134,89349],{"width":15531},[1814,89351,89352,89354,89356],{},[898,89353,900],{},[1793,89355,1806],{},[1688,89357,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,89359,3665],{},[1793,89361,12708],{},[21003,89363],{"width":28316},[21003,89365,89366],{},[2041,89367,89368],{},"(6.4)",[902,89370,89371],{"encoding":904},"U'_1 > 0, \\quad U'_2 > 0. \\tag{6.4}",[724,89373,89374,89375,89377],{},"Tedy mezní užitečnosti obou zboží jsou ",[38,89376,52917],{}," — užitečnost roste s množstvím každého zboží.",[724,89379,89380,89383,89384,89414,89415,2965],{},[38,89381,89382],{},"Předpoklad 5"," (klesající mezní užitečnost) požaduje, aby ",[883,89385,89387],{"className":89386},[886],[888,89388,89389],{"xmlns":890},[892,89390,89391,89411],{},[895,89392,89393,89401,89403],{},[1814,89394,89395,89397,89399],{},[898,89396,900],{},[1793,89398,1795],{},[1688,89400,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,89402,1733],{"separator":1732},[1814,89404,89405,89407,89409],{},[898,89406,900],{},[1793,89408,1806],{},[1688,89410,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[902,89412,89413],{"encoding":904},"U'_1, U'_2"," byly klesající funkce. To znamená, že jejich parciální derivace podle příslušné proměnné jsou ",[38,89416,89417],{},"záporné",[883,89419,89421],{"className":89420},[886],[888,89422,89423],{"xmlns":890,"display":28306},[892,89424,89425,89478],{},[20995,89426,89427],{"width":28311},[21000,89428,89429,89431,89471,89473],{},[21003,89430],{"width":28316},[21003,89432,89433],{},[895,89434,89435,89447,89449,89451,89453,89455,89467,89469],{},[1814,89436,89437,89439,89441],{},[898,89438,900],{},[1793,89440,3162],{},[895,89442,89443,89445],{},[1688,89444,1824],{"mathvariant":1822},[1688,89446,1824],{"mathvariant":1822},[1688,89448,3704],{},[1793,89450,1779],{},[1688,89452,1733],{"separator":1732},[6134,89454],{"width":15531},[1814,89456,89457,89459,89461],{},[898,89458,900],{},[1793,89460,32786],{},[895,89462,89463,89465],{},[1688,89464,1824],{"mathvariant":1822},[1688,89466,1824],{"mathvariant":1822},[1688,89468,3704],{},[1793,89470,12708],{},[21003,89472],{"width":28316},[21003,89474,89475],{},[2041,89476,89477],{},"(6.5)",[902,89479,89480],{"encoding":904},"U''_{11} \u003C 0, \\quad U''_{22} \u003C 0. \\tag{6.5}",[724,89482,89483,89484,89487,89488,2263],{},"Podmínka (6.5) je známa jako ",[38,89485,89486],{},"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 ",[207,89489,89491],{"className":89490,"dataFsResolvedFilePath":857,"href":858},[210],"produkční teorie",[724,89493,89494,89495,4142,89527,89559,89560,4142,89586,89612,89613,89641,89642,4142,89644,89646,89647,89682],{},"Podmínky (6.4), (6.5) určují tvary křivek ",[883,89496,89498],{"className":89497},[886],[888,89499,89500],{"xmlns":890},[892,89501,89502,89524],{},[895,89503,89504,89506,89508,89514,89516,89522],{},[898,89505,900],{},[1688,89507,2066],{"stretchy":2065},[1788,89509,89510,89512],{},[898,89511,1872],{},[1793,89513,1795],{},[1688,89515,1733],{"separator":1732},[1788,89517,89518,89520],{},[898,89519,1918],{},[1793,89521,1779],{},[1688,89523,2076],{"stretchy":2065},[902,89525,89526],{"encoding":904},"U(Q_1, b_0)",[883,89528,89530],{"className":89529},[886],[888,89531,89532],{"xmlns":890},[892,89533,89534,89556],{},[895,89535,89536,89538,89540,89546,89548,89554],{},[898,89537,900],{},[1688,89539,2066],{"stretchy":2065},[1788,89541,89542,89544],{},[898,89543,207],{},[1793,89545,1779],{},[1688,89547,1733],{"separator":1732},[1788,89549,89550,89552],{},[898,89551,1872],{},[1793,89553,1806],{},[1688,89555,2076],{"stretchy":2065},[902,89557,89558],{"encoding":904},"U(a_0, Q_2)"," v souřadnicových rovinách ",[883,89561,89563],{"className":89562},[886],[888,89564,89565],{"xmlns":890},[892,89566,89567,89583],{},[895,89568,89569,89571,89573,89575,89581],{},[1688,89570,2066],{"stretchy":2065},[898,89572,900],{},[1688,89574,1733],{"separator":1732},[1788,89576,89577,89579],{},[898,89578,1872],{},[1793,89580,1795],{},[1688,89582,2076],{"stretchy":2065},[902,89584,89585],{"encoding":904},"(U, Q_1)",[883,89587,89589],{"className":89588},[886],[888,89590,89591],{"xmlns":890},[892,89592,89593,89609],{},[895,89594,89595,89597,89599,89601,89607],{},[1688,89596,2066],{"stretchy":2065},[898,89598,900],{},[1688,89600,1733],{"separator":1732},[1788,89602,89603,89605],{},[898,89604,1872],{},[1793,89606,1806],{},[1688,89608,2076],{"stretchy":2065},[902,89610,89611],{"encoding":904},"(U, Q_2)"," (obrázek 6.1). Tyto křivky procházejí počátkem (neboť obvykle ",[883,89614,89616],{"className":89615},[886],[888,89617,89618],{"xmlns":890},[892,89619,89620,89638],{},[895,89621,89622,89624,89626,89628,89630,89632,89634,89636],{},[898,89623,900],{},[1688,89625,2066],{"stretchy":2065},[1793,89627,1779],{},[1688,89629,1733],{"separator":1732},[1793,89631,1779],{},[1688,89633,2076],{"stretchy":2065},[1688,89635,1690],{},[1793,89637,1779],{},[902,89639,89640],{"encoding":904},"U(0, 0) = 0","), jsou ",[38,89643,13904],{},[38,89645,38728],{},". Typický tvar grafu ",[883,89648,89650],{"className":89649},[886],[888,89651,89652],{"xmlns":890},[892,89653,89654,89680],{},[895,89655,89656,89658,89660,89662,89664,89670,89672,89678],{},[898,89657,900],{},[1688,89659,1690],{},[898,89661,900],{},[1688,89663,2066],{"stretchy":2065},[1788,89665,89666,89668],{},[898,89667,1872],{},[1793,89669,1795],{},[1688,89671,1733],{"separator":1732},[1788,89673,89674,89676],{},[898,89675,1872],{},[1793,89677,1806],{},[1688,89679,2076],{"stretchy":2065},[902,89681,87696],{"encoding":904}," — plocha v prostoru — je na obrázku 6.2.",[724,89684,89685],{},[614,89686,89687,89688,88728,89716,89737,89738,88728,89766,89788],{},"Obrázek 6.1 — typické průběhy funkce užitečnosti ",[883,89689,89691],{"className":89690},[886],[888,89692,89693],{"xmlns":890},[892,89694,89695,89713],{},[895,89696,89697,89699,89701,89707,89709,89711],{},[898,89698,900],{},[1688,89700,2066],{"stretchy":2065},[1788,89702,89703,89705],{},[898,89704,1872],{},[1793,89706,1795],{},[1688,89708,1733],{"separator":1732},[898,89710,1918],{},[1688,89712,2076],{"stretchy":2065},[902,89714,89715],{"encoding":904},"U(Q_1, b)",[883,89717,89719],{"className":89718},[886],[888,89720,89721],{"xmlns":890},[892,89722,89723,89735],{},[895,89724,89725,89731,89733],{},[1788,89726,89727,89729],{},[898,89728,1872],{},[1793,89730,1806],{},[1688,89732,1690],{},[898,89734,1918],{},[902,89736,88750],{"encoding":904}," (vlevo) a ",[883,89739,89741],{"className":89740},[886],[888,89742,89743],{"xmlns":890},[892,89744,89745,89763],{},[895,89746,89747,89749,89751,89753,89755,89761],{},[898,89748,900],{},[1688,89750,2066],{"stretchy":2065},[898,89752,207],{},[1688,89754,1733],{"separator":1732},[1788,89756,89757,89759],{},[898,89758,1872],{},[1793,89760,1806],{},[1688,89762,2076],{"stretchy":2065},[902,89764,89765],{"encoding":904},"U(a, Q_2)",[883,89767,89769],{"className":89768},[886],[888,89770,89771],{"xmlns":890},[892,89772,89773,89785],{},[895,89774,89775,89781,89783],{},[1788,89776,89777,89779],{},[898,89778,1872],{},[1793,89780,1795],{},[1688,89782,1690],{},[898,89784,207],{},[902,89786,89787],{"encoding":904},"Q_1 = a"," (vpravo) pro různé hladiny druhé proměnné.",[724,89790,89791],{},[614,89792,89793,89794,89829,89830,89860,89861,4142,89884,89906,89907,2263],{},"Obrázek 6.2 — plocha funkce užitečnosti ",[883,89795,89797],{"className":89796},[886],[888,89798,89799],{"xmlns":890},[892,89800,89801,89827],{},[895,89802,89803,89805,89807,89809,89811,89817,89819,89825],{},[898,89804,900],{},[1688,89806,1690],{},[898,89808,900],{},[1688,89810,2066],{"stretchy":2065},[1788,89812,89813,89815],{},[898,89814,1872],{},[1793,89816,1795],{},[1688,89818,1733],{"separator":1732},[1788,89820,89821,89823],{},[898,89822,1872],{},[1793,89824,1806],{},[1688,89826,2076],{"stretchy":2065},[902,89828,87696],{"encoding":904}," nad rovinou ",[883,89831,89833],{"className":89832},[886],[888,89834,89835],{"xmlns":890},[892,89836,89837,89857],{},[895,89838,89839,89841,89847,89849,89855],{},[1688,89840,2066],{"stretchy":2065},[1788,89842,89843,89845],{},[898,89844,1872],{},[1793,89846,1795],{},[1688,89848,1733],{"separator":1732},[1788,89850,89851,89853],{},[898,89852,1872],{},[1793,89854,1806],{},[1688,89856,2076],{"stretchy":2065},[902,89858,89859],{"encoding":904},"(Q_1, Q_2)"," s řezy rovinami ",[883,89862,89864],{"className":89863},[886],[888,89865,89866],{"xmlns":890},[892,89867,89868,89881],{},[895,89869,89870,89876,89878],{},[1788,89871,89872,89874],{},[898,89873,1872],{},[1793,89875,1795],{},[1688,89877,1690],{},[2041,89879,89880],{},"const",[902,89882,89883],{"encoding":904},"Q_1 = \\text{const}",[883,89885,89887],{"className":89886},[886],[888,89888,89889],{"xmlns":890},[892,89890,89891,89903],{},[895,89892,89893,89899,89901],{},[1788,89894,89895,89897],{},[898,89896,1872],{},[1793,89898,1806],{},[1688,89900,1690],{},[2041,89902,89880],{},[902,89904,89905],{"encoding":904},"Q_2 = \\text{const}"," a s křivkou ",[883,89908,89910],{"className":89909},[886],[888,89911,89912],{"xmlns":890},[892,89913,89914,89940],{},[895,89915,89916,89918,89920,89926,89928,89934,89936,89938],{},[898,89917,900],{},[1688,89919,2066],{"stretchy":2065},[1788,89921,89922,89924],{},[898,89923,1872],{},[1793,89925,1795],{},[1688,89927,1733],{"separator":1732},[1788,89929,89930,89932],{},[898,89931,1872],{},[1793,89933,1806],{},[1688,89935,2076],{"stretchy":2065},[1688,89937,1690],{},[898,89939,2031],{},[902,89941,10021],{"encoding":904},[198,89943,89945,89946],{"id":89944},"příklad-62-ověření-vlastností-a-dopočet-pro-uq112q213u-q_112-q_213","Příklad 6.2 — ověření vlastností a dopočet pro ",[883,89947,89949],{"className":89948},[886],[888,89950,89951],{"xmlns":890},[892,89952,89953,89987],{},[895,89954,89955,89957,89959,89973],{},[898,89956,900],{},[1688,89958,1690],{},[1814,89960,89961,89963,89965],{},[898,89962,1872],{},[1793,89964,1795],{},[895,89966,89967,89969,89971],{},[1793,89968,1795],{},[898,89970,4930],{"mathvariant":1822},[1793,89972,1806],{},[1814,89974,89975,89977,89979],{},[898,89976,1872],{},[1793,89978,1806],{},[895,89980,89981,89983,89985],{},[1793,89982,1795],{},[898,89984,4930],{"mathvariant":1822},[1793,89986,2131],{},[902,89988,89989],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F3}",[724,89991,89992],{},[38,89993,89994],{},"Ověření (6.4) a (6.5).",[883,89996,89998],{"className":89997},[886],[888,89999,90000],{"xmlns":890,"display":28306},[892,90001,90002,90106],{},[895,90003,90004,90012,90014,90022,90038,90052,90054,90056,90064,90066,90074,90088,90104],{},[1814,90005,90006,90008,90010],{},[898,90007,900],{},[1793,90009,1795],{},[1688,90011,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,90013,1690],{},[1777,90015,90016],{"scriptlevel":1779,"displaystyle":2065},[1781,90017,90018,90020],{},[1793,90019,1795],{},[1793,90021,1806],{},[1814,90023,90024,90026,90028],{},[898,90025,1872],{},[1793,90027,1795],{},[895,90029,90030,90032,90034,90036],{},[1688,90031,1954],{},[1793,90033,1795],{},[898,90035,4930],{"mathvariant":1822},[1793,90037,1806],{},[1814,90039,90040,90042,90044],{},[898,90041,1872],{},[1793,90043,1806],{},[895,90045,90046,90048,90050],{},[1793,90047,1795],{},[898,90049,4930],{"mathvariant":1822},[1793,90051,2131],{},[1688,90053,1733],{"separator":1732},[6134,90055],{"width":15531},[1814,90057,90058,90060,90062],{},[898,90059,900],{},[1793,90061,1806],{},[1688,90063,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,90065,1690],{},[1777,90067,90068],{"scriptlevel":1779,"displaystyle":2065},[1781,90069,90070,90072],{},[1793,90071,1795],{},[1793,90073,2131],{},[1814,90075,90076,90078,90080],{},[898,90077,1872],{},[1793,90079,1795],{},[895,90081,90082,90084,90086],{},[1793,90083,1795],{},[898,90085,4930],{"mathvariant":1822},[1793,90087,1806],{},[1814,90089,90090,90092,90094],{},[898,90091,1872],{},[1793,90093,1806],{},[895,90095,90096,90098,90100,90102],{},[1688,90097,1954],{},[1793,90099,1806],{},[898,90101,4930],{"mathvariant":1822},[1793,90103,2131],{},[1688,90105,1733],{"separator":1732},[902,90107,90108],{"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},",[724,90110,90111,90112,90146],{},"zřejmě ",[883,90113,90115],{"className":90114},[886],[888,90116,90117],{"xmlns":890},[892,90118,90119,90143],{},[895,90120,90121,90129,90131,90139,90141],{},[1814,90122,90123,90125,90127],{},[898,90124,900],{},[1793,90126,1795],{},[1688,90128,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,90130,1733],{"separator":1732},[1814,90132,90133,90135,90137],{},[898,90134,900],{},[1793,90136,1806],{},[1688,90138,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,90140,3665],{},[1793,90142,1779],{},[902,90144,90145],{"encoding":904},"U'_1, U'_2 > 0"," a platí (6.4). Dále:",[883,90148,90150],{"className":90149},[886],[888,90151,90152],{"xmlns":890,"display":28306},[892,90153,90154,90270],{},[895,90155,90156,90168,90170,90172,90180,90196,90210,90212,90214,90226,90228,90230,90238,90252,90268],{},[1814,90157,90158,90160,90162],{},[898,90159,900],{},[1793,90161,3162],{},[895,90163,90164,90166],{},[1688,90165,1824],{"mathvariant":1822},[1688,90167,1824],{"mathvariant":1822},[1688,90169,1690],{},[1688,90171,1954],{},[1777,90173,90174],{"scriptlevel":1779,"displaystyle":2065},[1781,90175,90176,90178],{},[1793,90177,1795],{},[1793,90179,2616],{},[1814,90181,90182,90184,90186],{},[898,90183,1872],{},[1793,90185,1795],{},[895,90187,90188,90190,90192,90194],{},[1688,90189,1954],{},[1793,90191,2131],{},[898,90193,4930],{"mathvariant":1822},[1793,90195,1806],{},[1814,90197,90198,90200,90202],{},[898,90199,1872],{},[1793,90201,1806],{},[895,90203,90204,90206,90208],{},[1793,90205,1795],{},[898,90207,4930],{"mathvariant":1822},[1793,90209,2131],{},[1688,90211,1733],{"separator":1732},[6134,90213],{"width":15531},[1814,90215,90216,90218,90220],{},[898,90217,900],{},[1793,90219,32786],{},[895,90221,90222,90224],{},[1688,90223,1824],{"mathvariant":1822},[1688,90225,1824],{"mathvariant":1822},[1688,90227,1690],{},[1688,90229,1954],{},[1777,90231,90232],{"scriptlevel":1779,"displaystyle":2065},[1781,90233,90234,90236],{},[1793,90235,1806],{},[1793,90237,4256],{},[1814,90239,90240,90242,90244],{},[898,90241,1872],{},[1793,90243,1795],{},[895,90245,90246,90248,90250],{},[1793,90247,1795],{},[898,90249,4930],{"mathvariant":1822},[1793,90251,1806],{},[1814,90253,90254,90256,90258],{},[898,90255,1872],{},[1793,90257,1806],{},[895,90259,90260,90262,90264,90266],{},[1688,90261,1954],{},[1793,90263,2501],{},[898,90265,4930],{"mathvariant":1822},[1793,90267,2131],{},[1688,90269,1733],{"separator":1732},[902,90271,90272],{"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},",[724,90274,90275,90276,90318],{},"opět ",[883,90277,90279],{"className":90278},[886],[888,90280,90281],{"xmlns":890},[892,90282,90283,90315],{},[895,90284,90285,90297,90299,90311,90313],{},[1814,90286,90287,90289,90291],{},[898,90288,900],{},[1793,90290,3162],{},[895,90292,90293,90295],{},[1688,90294,1824],{"mathvariant":1822},[1688,90296,1824],{"mathvariant":1822},[1688,90298,1733],{"separator":1732},[1814,90300,90301,90303,90305],{},[898,90302,900],{},[1793,90304,32786],{},[895,90306,90307,90309],{},[1688,90308,1824],{"mathvariant":1822},[1688,90310,1824],{"mathvariant":1822},[1688,90312,3704],{},[1793,90314,1779],{},[902,90316,90317],{"encoding":904},"U''_{11}, U''_{22} \u003C 0",", platí (6.5).",[724,90320,90321],{},[38,90322,90323,90324,2263],{},"(a) Mezní užitečnosti v bodě ",[883,90325,90327],{"className":90326},[886],[888,90328,90329],{"xmlns":890},[892,90330,90331,90343],{},[895,90332,90333,90335,90337,90339,90341],{},[1688,90334,2748],{"stretchy":2065},[1793,90336,3347],{},[1688,90338,1733],{"separator":1732},[1793,90340,8633],{},[1688,90342,2763],{"stretchy":2065},[902,90344,90345],{"encoding":904},"[100, 200]",[883,90347,90349],{"className":90348},[886],[888,90350,90351],{"xmlns":890,"display":28306},[892,90352,90353,90420],{},[895,90354,90355,90357,90363,90365,90367,90369,90371,90373,90375,90383,90385,90399,90401,90413,90415,90418],{},[898,90356,1661],{},[1788,90358,90359,90361],{},[898,90360,900],{},[1793,90362,1795],{},[1688,90364,2066],{"stretchy":2065},[1793,90366,3347],{},[1688,90368,1733],{"separator":1732},[1793,90370,8633],{},[1688,90372,2076],{"stretchy":2065},[1688,90374,1690],{},[1777,90376,90377],{"scriptlevel":1779,"displaystyle":2065},[1781,90378,90379,90381],{},[1793,90380,1795],{},[1793,90382,1806],{},[1688,90384,3434],{},[1850,90386,90387,90389],{},[1793,90388,3347],{},[895,90390,90391,90393,90395,90397],{},[1688,90392,1954],{},[1793,90394,1795],{},[898,90396,4930],{"mathvariant":1822},[1793,90398,1806],{},[1688,90400,3434],{},[1850,90402,90403,90405],{},[1793,90404,8633],{},[895,90406,90407,90409,90411],{},[1793,90408,1795],{},[898,90410,4930],{"mathvariant":1822},[1793,90412,2131],{},[1688,90414,6156],{},[1793,90416,90417],{},"0,4204",[1688,90419,1733],{"separator":1732},[902,90421,90422],{"encoding":904},"MU_1(100, 200) = \\tfrac{1}{2} \\cdot 100^{-1\u002F2} \\cdot 200^{1\u002F3} \\doteq 0{,}4204,",[883,90424,90426],{"className":90425},[886],[888,90427,90428],{"xmlns":890,"display":28306},[892,90429,90430,90495],{},[895,90431,90432,90434,90440,90442,90444,90446,90448,90450,90452,90460,90462,90474,90476,90490,90492],{},[898,90433,1661],{},[1788,90435,90436,90438],{},[898,90437,900],{},[1793,90439,1806],{},[1688,90441,2066],{"stretchy":2065},[1793,90443,3347],{},[1688,90445,1733],{"separator":1732},[1793,90447,8633],{},[1688,90449,2076],{"stretchy":2065},[1688,90451,1690],{},[1777,90453,90454],{"scriptlevel":1779,"displaystyle":2065},[1781,90455,90456,90458],{},[1793,90457,1795],{},[1793,90459,2131],{},[1688,90461,3434],{},[1850,90463,90464,90466],{},[1793,90465,3347],{},[895,90467,90468,90470,90472],{},[1793,90469,1795],{},[898,90471,4930],{"mathvariant":1822},[1793,90473,1806],{},[1688,90475,3434],{},[1850,90477,90478,90480],{},[1793,90479,8633],{},[895,90481,90482,90484,90486,90488],{},[1688,90483,1954],{},[1793,90485,1806],{},[898,90487,4930],{"mathvariant":1822},[1793,90489,2131],{},[1688,90491,6156],{},[1793,90493,90494],{},"0,63067.",[902,90496,90497],{"encoding":904},"MU_2(100, 200) = \\tfrac{1}{3} \\cdot 100^{1\u002F2} \\cdot 200^{-2\u002F3} \\doteq 0{,}63067.",[724,90499,90500,2170,90502,90537,90538,90559,90560,90577],{},[614,90501,9469],{},[883,90503,90505],{"className":90504},[886],[888,90506,90507],{"xmlns":890},[892,90508,90509,90534],{},[895,90510,90511,90513,90519,90521,90523,90525,90527,90529,90531],{},[898,90512,1661],{},[1788,90514,90515,90517],{},[898,90516,900],{},[1793,90518,1806],{},[1688,90520,2066],{"stretchy":2065},[1793,90522,3347],{},[1688,90524,1733],{"separator":1732},[1793,90526,8633],{},[1688,90528,2076],{"stretchy":2065},[1688,90530,6156],{},[1793,90532,90533],{},"0,63067",[902,90535,90536],{"encoding":904},"MU_2(100, 200) \\doteq 0{,}63067"," znamená, že na hladině ",[883,90539,90541],{"className":90540},[886],[888,90542,90543],{"xmlns":890},[892,90544,90545,90557],{},[895,90546,90547,90549,90551,90553,90555],{},[1688,90548,2748],{"stretchy":2065},[1793,90550,3347],{},[1688,90552,1733],{"separator":1732},[1793,90554,8633],{},[1688,90556,2763],{"stretchy":2065},[902,90558,90345],{"encoding":904}," roste užitečnost při jednotkové změně ",[883,90561,90563],{"className":90562},[886],[888,90564,90565],{"xmlns":890},[892,90566,90567,90575],{},[895,90568,90569],{},[1788,90570,90571,90573],{},[898,90572,1872],{},[1793,90574,1806],{},[902,90576,29261],{"encoding":904}," přibližně o 0,63067.",[724,90579,90580,90599,90600,39424,90621,90638,90639,90665,90666,90683,90684,3408],{},[38,90581,90582,90583,90598],{},"(b) Odhad změny ",[883,90584,90586],{"className":90585},[886],[888,90587,90588],{"xmlns":890},[892,90589,90590,90596],{},[895,90591,90592,90594],{},[898,90593,3147],{"mathvariant":1822},[898,90595,900],{},[902,90597,88841],{"encoding":904}," pomocí totálního diferenciálu (6.3)."," Klesne-li vzhledem k hladině ",[883,90601,90603],{"className":90602},[886],[888,90604,90605],{"xmlns":890},[892,90606,90607,90619],{},[895,90608,90609,90611,90613,90615,90617],{},[1688,90610,2748],{"stretchy":2065},[1793,90612,3347],{},[1688,90614,1733],{"separator":1732},[1793,90616,8633],{},[1688,90618,2763],{"stretchy":2065},[902,90620,90345],{"encoding":904},[883,90622,90624],{"className":90623},[886],[888,90625,90626],{"xmlns":890},[892,90627,90628,90636],{},[895,90629,90630],{},[1788,90631,90632,90634],{},[898,90633,1872],{},[1793,90635,1795],{},[902,90637,29242],{"encoding":904}," na 98 (tj. ",[883,90640,90642],{"className":90641},[886],[888,90643,90644],{"xmlns":890},[892,90645,90646,90662],{},[895,90647,90648,90650,90656,90658,90660],{},[898,90649,2073],{"mathvariant":1822},[1788,90651,90652,90654],{},[898,90653,1872],{},[1793,90655,1795],{},[1688,90657,1690],{},[1688,90659,1954],{},[1793,90661,1806],{},[902,90663,90664],{"encoding":904},"\\mathrm{d} Q_1 = -2",") a vzroste-li ",[883,90667,90669],{"className":90668},[886],[888,90670,90671],{"xmlns":890},[892,90672,90673,90681],{},[895,90674,90675],{},[1788,90676,90677,90679],{},[898,90678,1872],{},[1793,90680,1806],{},[902,90682,29261],{"encoding":904}," o 3 (tj. ",[883,90685,90687],{"className":90686},[886],[888,90688,90689],{"xmlns":890},[892,90690,90691,90705],{},[895,90692,90693,90695,90701,90703],{},[898,90694,2073],{"mathvariant":1822},[1788,90696,90697,90699],{},[898,90698,1872],{},[1793,90700,1806],{},[1688,90702,1690],{},[1793,90704,2131],{},[902,90706,90707],{"encoding":904},"\\mathrm{d} Q_2 = 3",[883,90709,90711],{"className":90710},[886],[888,90712,90713],{"xmlns":890,"display":28306},[892,90714,90715,90766],{},[895,90716,90717,90719,90721,90723,90725,90727,90729,90731,90733,90735,90737,90739,90741,90743,90745,90747,90749,90751,90753,90756,90758,90761,90763],{},[898,90718,3147],{"mathvariant":1822},[898,90720,900],{},[1688,90722,2991],{},[898,90724,2073],{"mathvariant":1822},[898,90726,900],{},[1688,90728,1690],{},[1793,90730,90417],{},[1688,90732,3434],{},[1688,90734,2066],{"stretchy":2065},[1688,90736,1954],{},[1793,90738,1806],{},[1688,90740,2076],{"stretchy":2065},[1688,90742,1696],{},[1793,90744,90533],{},[1688,90746,3434],{},[1793,90748,2131],{},[1688,90750,1690],{},[1688,90752,1954],{},[1793,90754,90755],{},"0,8408",[1688,90757,1696],{},[1793,90759,90760],{},"1,89201",[1688,90762,6156],{},[1793,90764,90765],{},"1,05.",[902,90767,90768],{"encoding":904},"\\Delta U \\approx \\mathrm{d} U = 0{,}4204 \\cdot (-2) + 0{,}63067 \\cdot 3 = -0{,}8408 + 1{,}89201 \\doteq 1{,}05.",[724,90770,90771,90772,90775,90776,90827,90828,2263],{},"Užitečnost se tedy zvýší přibližně o ",[38,90773,90774],{},"1,05",". Skutečná změna je ",[883,90777,90779],{"className":90778},[886],[888,90780,90781],{"xmlns":890},[892,90782,90783,90824],{},[895,90784,90785,90787,90789,90791,90793,90795,90798,90800,90803,90805,90807,90809,90811,90813,90815,90817,90819,90821],{},[898,90786,3147],{"mathvariant":1822},[898,90788,900],{},[1688,90790,1690],{},[898,90792,900],{},[1688,90794,2066],{"stretchy":2065},[1793,90796,90797],{},"98",[1688,90799,1733],{"separator":1732},[1793,90801,90802],{},"203",[1688,90804,2076],{"stretchy":2065},[1688,90806,1954],{},[898,90808,900],{},[1688,90810,2066],{"stretchy":2065},[1793,90812,3347],{},[1688,90814,1733],{"separator":1732},[1793,90816,8633],{},[1688,90818,2076],{"stretchy":2065},[1688,90820,6156],{},[1793,90822,90823],{},"1,031",[902,90825,90826],{"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 ",[883,90829,90831],{"className":90830},[886],[888,90832,90833],{"xmlns":890},[892,90834,90835,90855],{},[895,90836,90837,90839,90845,90847,90849],{},[898,90838,2073],{"mathvariant":1822},[1788,90840,90841,90843],{},[898,90842,1872],{},[1793,90844,1795],{},[1688,90846,1733],{"separator":1732},[898,90848,2073],{"mathvariant":1822},[1788,90850,90851,90853],{},[898,90852,1872],{},[1793,90854,1806],{},[902,90856,88871],{"encoding":904},[115,90858,90860],{"id":90859},"cobb-douglasova-funkce-užitečnosti","Cobb-Douglasova funkce užitečnosti",[724,90862,90863],{},"Nejčastěji používané funkce užitečnosti mají tvar",[883,90865,90867],{"className":90866},[886],[888,90868,90869],{"xmlns":890,"display":28306},[892,90870,90871,90930],{},[20995,90872,90873],{"width":28311},[21000,90874,90875,90877,90923,90925],{},[21003,90876],{"width":28316},[21003,90878,90879],{},[895,90880,90881,90883,90885,90891,90893,90899,90901,90903,90911,90913,90921],{},[898,90882,900],{},[1688,90884,2066],{"stretchy":2065},[1788,90886,90887,90889],{},[898,90888,1872],{},[1793,90890,1795],{},[1688,90892,1733],{"separator":1732},[1788,90894,90895,90897],{},[898,90896,1872],{},[1793,90898,1806],{},[1688,90900,2076],{"stretchy":2065},[1688,90902,1690],{},[1814,90904,90905,90907,90909],{},[898,90906,1872],{},[1793,90908,1795],{},[898,90910,207],{},[1688,90912,3434],{},[1814,90914,90915,90917,90919],{},[898,90916,1872],{},[1793,90918,1806],{},[898,90920,1918],{},[1688,90922,1733],{"separator":1732},[21003,90924],{"width":28316},[21003,90926,90927],{},[2041,90928,90929],{},"(6.6)",[902,90931,90932],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^b, \\tag{6.6}",[724,90934,4567,90935,90953,90954,90956,90957,90961,90962,90992,90993,91015],{},[883,90936,90938],{"className":90937},[886],[888,90939,90940],{"xmlns":890},[892,90941,90942,90950],{},[895,90943,90944,90946,90948],{},[898,90945,207],{},[1688,90947,1733],{"separator":1732},[898,90949,1918],{},[902,90951,90952],{"encoding":904},"a, b"," jsou kladná čísla; nazývají se ",[38,90955,74939],{}," (v příbuznosti s produkčními funkcemi — viz ",[207,90958,90960],{"className":90959,"dataFsResolvedFilePath":857,"href":858},[210],"kapitola 5","). Obvykle se volí ",[883,90963,90965],{"className":90964},[886],[888,90966,90967],{"xmlns":890},[892,90968,90969,90989],{},[895,90970,90971,90973,90975,90977,90979,90981,90983,90985,90987],{},[898,90972,207],{},[1688,90974,1733],{"separator":1732},[898,90976,1918],{},[1688,90978,6762],{},[1688,90980,2066],{"stretchy":2065},[1793,90982,1779],{},[1688,90984,1733],{"separator":1732},[1793,90986,1795],{},[1688,90988,2076],{"stretchy":2065},[902,90990,90991],{"encoding":904},"a, b \\in (0, 1)",", často se klade ",[883,90994,90996],{"className":90995},[886],[888,90997,90998],{"xmlns":890},[892,90999,91000,91012],{},[895,91001,91002,91004,91006,91008,91010],{},[898,91003,1918],{},[1688,91005,1690],{},[1793,91007,1795],{},[1688,91009,1954],{},[898,91011,207],{},[902,91013,91014],{"encoding":904},"b = 1 - a",", čímž (6.6) přejde na tvar",[724,91017,91018],{},[2821,91019],{"alt":91020,"className":91021,"src":91022},"imek-cobb-douglas-3d-plus-ic",[210,2825],"\u002Fwiki-assets\u002Fimek-cobb-douglas-3d-plus-ic.jpeg",[883,91024,91026],{"className":91025},[886],[888,91027,91028],{"xmlns":890,"display":28306},[892,91029,91030,91080],{},[895,91031,91032,91034,91036,91042,91044,91050,91052,91054,91062,91064,91078],{},[898,91033,900],{},[1688,91035,2066],{"stretchy":2065},[1788,91037,91038,91040],{},[898,91039,1872],{},[1793,91041,1795],{},[1688,91043,1733],{"separator":1732},[1788,91045,91046,91048],{},[898,91047,1872],{},[1793,91049,1806],{},[1688,91051,2076],{"stretchy":2065},[1688,91053,1690],{},[1814,91055,91056,91058,91060],{},[898,91057,1872],{},[1793,91059,1795],{},[898,91061,207],{},[1688,91063,3434],{},[1814,91065,91066,91068,91070],{},[898,91067,1872],{},[1793,91069,1806],{},[895,91071,91072,91074,91076],{},[1793,91073,1795],{},[1688,91075,1954],{},[898,91077,207],{},[898,91079,2263],{"mathvariant":1822},[902,91081,91082],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^{1-a}.",[4124,91084,91085,91134,91256,91390],{},[724,91086,91087,91089,91090],{},[883,91088,52935],{}," Příklad 6.3 — ověření vlastností pro ",[883,91091,91093],{"className":91092},[886],[888,91094,91095],{"xmlns":890},[892,91096,91097,91131],{},[895,91098,91099,91101,91103,91117],{},[898,91100,900],{},[1688,91102,1690],{},[1814,91104,91105,91107,91109],{},[898,91106,1872],{},[1793,91108,1795],{},[895,91110,91111,91113,91115],{},[1793,91112,1795],{},[898,91114,4930],{"mathvariant":1822},[1793,91116,2616],{},[1814,91118,91119,91121,91123],{},[898,91120,1872],{},[1793,91122,1806],{},[895,91124,91125,91127,91129],{},[1793,91126,2131],{},[898,91128,4930],{"mathvariant":1822},[1793,91130,2616],{},[902,91132,91133],{"encoding":904},"U = Q_1^{1\u002F4} Q_2^{3\u002F4}",[883,91135,91137],{"className":91136},[886],[888,91138,91139],{"xmlns":890,"display":28306},[892,91140,91141,91253],{},[895,91142,91143,91151,91153,91161,91177,91191,91193,91195,91197,91199,91207,91209,91217,91231,91247,91249,91251],{},[1814,91144,91145,91147,91149],{},[898,91146,900],{},[1793,91148,1795],{},[1688,91150,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,91152,1690],{},[1777,91154,91155],{"scriptlevel":1779,"displaystyle":2065},[1781,91156,91157,91159],{},[1793,91158,1795],{},[1793,91160,2616],{},[1814,91162,91163,91165,91167],{},[898,91164,1872],{},[1793,91166,1795],{},[895,91168,91169,91171,91173,91175],{},[1688,91170,1954],{},[1793,91172,2131],{},[898,91174,4930],{"mathvariant":1822},[1793,91176,2616],{},[1814,91178,91179,91181,91183],{},[898,91180,1872],{},[1793,91182,1806],{},[895,91184,91185,91187,91189],{},[1793,91186,2131],{},[898,91188,4930],{"mathvariant":1822},[1793,91190,2616],{},[1688,91192,3665],{},[1793,91194,1779],{},[1688,91196,1733],{"separator":1732},[6134,91198],{"width":15531},[1814,91200,91201,91203,91205],{},[898,91202,900],{},[1793,91204,1806],{},[1688,91206,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,91208,1690],{},[1777,91210,91211],{"scriptlevel":1779,"displaystyle":2065},[1781,91212,91213,91215],{},[1793,91214,2131],{},[1793,91216,2616],{},[1814,91218,91219,91221,91223],{},[898,91220,1872],{},[1793,91222,1795],{},[895,91224,91225,91227,91229],{},[1793,91226,1795],{},[898,91228,4930],{"mathvariant":1822},[1793,91230,2616],{},[1814,91232,91233,91235,91237],{},[898,91234,1872],{},[1793,91236,1806],{},[895,91238,91239,91241,91243,91245],{},[1688,91240,1954],{},[1793,91242,1795],{},[898,91244,4930],{"mathvariant":1822},[1793,91246,2616],{},[1688,91248,3665],{},[1793,91250,1779],{},[1688,91252,1733],{"separator":1732},[902,91254,91255],{"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,",[883,91257,91259],{"className":91258},[886],[888,91260,91261],{"xmlns":890,"display":28306},[892,91262,91263,91387],{},[895,91264,91265,91277,91279,91281,91289,91305,91319,91321,91323,91325,91327,91339,91341,91343,91351,91365,91381,91383,91385],{},[1814,91266,91267,91269,91271],{},[898,91268,900],{},[1793,91270,3162],{},[895,91272,91273,91275],{},[1688,91274,1824],{"mathvariant":1822},[1688,91276,1824],{"mathvariant":1822},[1688,91278,1690],{},[1688,91280,1954],{},[1777,91282,91283],{"scriptlevel":1779,"displaystyle":2065},[1781,91284,91285,91287],{},[1793,91286,2131],{},[1793,91288,42102],{},[1814,91290,91291,91293,91295],{},[898,91292,1872],{},[1793,91294,1795],{},[895,91296,91297,91299,91301,91303],{},[1688,91298,1954],{},[1793,91300,24442],{},[898,91302,4930],{"mathvariant":1822},[1793,91304,2616],{},[1814,91306,91307,91309,91311],{},[898,91308,1872],{},[1793,91310,1806],{},[895,91312,91313,91315,91317],{},[1793,91314,2131],{},[898,91316,4930],{"mathvariant":1822},[1793,91318,2616],{},[1688,91320,3704],{},[1793,91322,1779],{},[1688,91324,1733],{"separator":1732},[6134,91326],{"width":15531},[1814,91328,91329,91331,91333],{},[898,91330,900],{},[1793,91332,32786],{},[895,91334,91335,91337],{},[1688,91336,1824],{"mathvariant":1822},[1688,91338,1824],{"mathvariant":1822},[1688,91340,1690],{},[1688,91342,1954],{},[1777,91344,91345],{"scriptlevel":1779,"displaystyle":2065},[1781,91346,91347,91349],{},[1793,91348,2131],{},[1793,91350,42102],{},[1814,91352,91353,91355,91357],{},[898,91354,1872],{},[1793,91356,1795],{},[895,91358,91359,91361,91363],{},[1793,91360,1795],{},[898,91362,4930],{"mathvariant":1822},[1793,91364,2616],{},[1814,91366,91367,91369,91371],{},[898,91368,1872],{},[1793,91370,1806],{},[895,91372,91373,91375,91377,91379],{},[1688,91374,1954],{},[1793,91376,2501],{},[898,91378,4930],{"mathvariant":1822},[1793,91380,2616],{},[1688,91382,3704],{},[1793,91384,1779],{},[1688,91386,1733],{"separator":1732},[902,91388,91389],{"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,",[724,91391,91392],{},"tedy podmínky (6.4) i (6.5) jsou splněny.",[115,91394,91396],{"id":91395},"indiferenční-křivky-křivky-užitečnosti-a-jejich-vlastnosti","Indiferenční křivky (křivky užitečnosti) a jejich vlastnosti",[724,91398,91399,91402],{},[38,91400,91401],{},"Křivky užitečnosti"," (utility curves) jsou indiferenční křivky funkce užitečnosti. Jsou dány rovnicí",[883,91404,91406],{"className":91405},[886],[888,91407,91408],{"xmlns":890,"display":28306},[892,91409,91410,91453],{},[20995,91411,91412],{"width":28311},[21000,91413,91414,91416,91446,91448],{},[21003,91415],{"width":28316},[21003,91417,91418],{},[895,91419,91420,91422,91424,91430,91432,91438,91440,91442,91444],{},[898,91421,900],{},[1688,91423,2066],{"stretchy":2065},[1788,91425,91426,91428],{},[898,91427,1872],{},[1793,91429,1795],{},[1688,91431,1733],{"separator":1732},[1788,91433,91434,91436],{},[898,91435,1872],{},[1793,91437,1806],{},[1688,91439,2076],{"stretchy":2065},[1688,91441,1690],{},[898,91443,2031],{},[1688,91445,1733],{"separator":1732},[21003,91447],{"width":28316},[21003,91449,91450],{},[2041,91451,91452],{},"(6.7)",[902,91454,91455],{"encoding":904},"U(Q_1, Q_2) = c, \\tag{6.7}",[724,91457,4567,91458,91471],{},[883,91459,91461],{"className":91460},[886],[888,91462,91463],{"xmlns":890},[892,91464,91465,91469],{},[895,91466,91467],{},[898,91468,2031],{},[902,91470,2031],{"encoding":904}," je kladná konstanta. Pro Cobb-Douglasovu funkci:",[883,91473,91475],{"className":91474},[886],[888,91476,91477],{"xmlns":890,"display":28306},[892,91478,91479,91520],{},[20995,91480,91481],{"width":28311},[21000,91482,91483,91485,91513,91515],{},[21003,91484],{"width":28316},[21003,91486,91487],{},[895,91488,91489,91497,91499,91507,91509,91511],{},[1814,91490,91491,91493,91495],{},[898,91492,1872],{},[1793,91494,1795],{},[898,91496,207],{},[1688,91498,3434],{},[1814,91500,91501,91503,91505],{},[898,91502,1872],{},[1793,91504,1806],{},[898,91506,1918],{},[1688,91508,1690],{},[898,91510,2031],{},[898,91512,2263],{"mathvariant":1822},[21003,91514],{"width":28316},[21003,91516,91517],{},[2041,91518,91519],{},"(6.8)",[902,91521,91522],{"encoding":904},"Q_1^a \\cdot Q_2^b = c. \\tag{6.8}",[724,91524,91525,91526,4614,91556,2170,91559,91572,91573,91608,91609,91626,91627,91656,91657,91660],{},"Body na téže křivce užitečnosti reprezentují kombinace ",[883,91527,91529],{"className":91528},[886],[888,91530,91531],{"xmlns":890},[892,91532,91533,91553],{},[895,91534,91535,91537,91543,91545,91551],{},[1688,91536,2748],{"stretchy":2065},[1788,91538,91539,91541],{},[898,91540,1872],{},[1793,91542,1795],{},[1688,91544,1733],{"separator":1732},[1788,91546,91547,91549],{},[898,91548,1872],{},[1793,91550,1806],{},[1688,91552,2763],{"stretchy":2065},[902,91554,91555],{"encoding":904},"[Q_1, Q_2]",[38,91557,91558],{},"stejnou úrovní uspokojení",[883,91560,91562],{"className":91561},[886],[888,91563,91564],{"xmlns":890},[892,91565,91566,91570],{},[895,91567,91568],{},[898,91569,2031],{},[902,91571,2031],{"encoding":904},". Křivky užitečnosti vznikají jako průsečnice plochy ",[883,91574,91576],{"className":91575},[886],[888,91577,91578],{"xmlns":890},[892,91579,91580,91606],{},[895,91581,91582,91584,91586,91588,91590,91596,91598,91604],{},[898,91583,900],{},[1688,91585,1690],{},[898,91587,900],{},[1688,91589,2066],{"stretchy":2065},[1788,91591,91592,91594],{},[898,91593,1872],{},[1793,91595,1795],{},[1688,91597,1733],{"separator":1732},[1788,91599,91600,91602],{},[898,91601,1872],{},[1793,91603,1806],{},[1688,91605,2076],{"stretchy":2065},[902,91607,87696],{"encoding":904}," s rovinami ",[883,91610,91612],{"className":91611},[886],[888,91613,91614],{"xmlns":890},[892,91615,91616,91624],{},[895,91617,91618,91620,91622],{},[898,91619,900],{},[1688,91621,1690],{},[898,91623,2031],{},[902,91625,86912],{"encoding":904}," rovnoběžnými s rovinou ",[883,91628,91630],{"className":91629},[886],[888,91631,91632],{"xmlns":890},[892,91633,91634,91654],{},[895,91635,91636,91638,91644,91646,91652],{},[1688,91637,2066],{"stretchy":2065},[1788,91639,91640,91642],{},[898,91641,1872],{},[1793,91643,1795],{},[1688,91645,1733],{"separator":1732},[1788,91647,91648,91650],{},[898,91649,1872],{},[1793,91651,1806],{},[1688,91653,2076],{"stretchy":2065},[902,91655,89859],{"encoding":904}," (obrázek 6.2). Jsou v příbuznosti s ",[38,91658,91659],{},"izokvantami"," produkčních funkcí.",[724,91662,91663],{},[614,91664,91665,91666,89737,91684,91702,91703,2263],{},"Obrázek 6.3 — typický tvar křivek užitečnosti pro Cobb-Douglasovu funkci pro ",[883,91667,91669],{"className":91668},[886],[888,91670,91671],{"xmlns":890},[892,91672,91673,91681],{},[895,91674,91675,91677,91679],{},[898,91676,207],{},[1688,91678,3704],{},[898,91680,1918],{},[902,91682,91683],{"encoding":904},"a \u003C b",[883,91685,91687],{"className":91686},[886],[888,91688,91689],{"xmlns":890},[892,91690,91691,91699],{},[895,91692,91693,91695,91697],{},[898,91694,207],{},[1688,91696,3665],{},[898,91698,1918],{},[902,91700,91701],{"encoding":904},"a > b"," (vpravo); různé hladiny ",[883,91704,91706],{"className":91705},[886],[888,91707,91708],{"xmlns":890},[892,91709,91710,91734],{},[895,91711,91712,91718,91720,91726,91728],{},[1788,91713,91714,91716],{},[898,91715,2031],{},[1793,91717,1779],{},[1688,91719,3704],{},[1788,91721,91722,91724],{},[898,91723,2031],{},[1793,91725,1795],{},[1688,91727,3704],{},[1788,91729,91730,91732],{},[898,91731,2031],{},[1793,91733,1806],{},[902,91735,91736],{"encoding":904},"c_0 \u003C c_1 \u003C c_2",[724,91738,91739],{},[614,91740,91741,91742,91771,91772,91830,91831,91849],{},"Obrázek 6.4 — soustava křivek užitečnosti pro tři hladiny (10, 20, 30) v rovině ",[883,91743,91745],{"className":91744},[886],[888,91746,91747],{"xmlns":890},[892,91748,91749,91769],{},[895,91750,91751,91753,91759,91761,91767],{},[1688,91752,2066],{"stretchy":2065},[1788,91754,91755,91757],{},[898,91756,1872],{},[1793,91758,1795],{},[1688,91760,1733],{"separator":1732},[1788,91762,91763,91765],{},[898,91764,1872],{},[1793,91766,1806],{},[1688,91768,2076],{"stretchy":2065},[902,91770,89859],{"encoding":904},"; body ",[883,91773,91775],{"className":91774},[886],[888,91776,91777],{"xmlns":890},[892,91778,91779,91827],{},[895,91780,91781,91783,91785,91787,91793,91795,91801,91803,91805,91807,91809,91811,91817,91819,91825],{},[898,91782,4512],{},[1688,91784,1690],{},[1688,91786,2748],{"stretchy":2065},[1788,91788,91789,91791],{},[898,91790,207],{},[1793,91792,1795],{},[1688,91794,1733],{"separator":1732},[1788,91796,91797,91799],{},[898,91798,207],{},[1793,91800,1806],{},[1688,91802,2763],{"stretchy":2065},[1688,91804,1733],{"separator":1732},[898,91806,23494],{},[1688,91808,1690],{},[1688,91810,2748],{"stretchy":2065},[1788,91812,91813,91815],{},[898,91814,1918],{},[1793,91816,1795],{},[1688,91818,1733],{"separator":1732},[1788,91820,91821,91823],{},[898,91822,1918],{},[1793,91824,1806],{},[1688,91826,2763],{"stretchy":2065},[902,91828,91829],{"encoding":904},"A = [a_1, a_2], B = [b_1, b_2]"," leží na téže křivce (hladina 10), body ",[883,91832,91834],{"className":91833},[886],[888,91835,91836],{"xmlns":890},[892,91837,91838,91846],{},[895,91839,91840,91842,91844],{},[898,91841,1693],{},[1688,91843,1733],{"separator":1732},[898,91845,4440],{},[902,91847,91848],{"encoding":904},"C, D"," na vyšší hladině.",[4124,91851,91852],{},[724,91853,91854,91856,91857,91919,91920,91964,91965,91999,92000,26430,92018,91999,92072,26430,92090,92166],{},[883,91855,52935],{}," Příklad 6.4 — rovnice křivek užitečnosti\nPro ",[883,91858,91860],{"className":91859},[886],[888,91861,91862],{"xmlns":890},[892,91863,91864,91916],{},[895,91865,91866,91868,91870,91876,91878,91884,91886,91888,91902],{},[898,91867,900],{},[1688,91869,2066],{"stretchy":2065},[1788,91871,91872,91874],{},[898,91873,1872],{},[1793,91875,1795],{},[1688,91877,1733],{"separator":1732},[1788,91879,91880,91882],{},[898,91881,1872],{},[1793,91883,1806],{},[1688,91885,2076],{"stretchy":2065},[1688,91887,1690],{},[1814,91889,91890,91892,91894],{},[898,91891,1872],{},[1793,91893,1795],{},[895,91895,91896,91898,91900],{},[1793,91897,1795],{},[898,91899,4930],{"mathvariant":1822},[1793,91901,2616],{},[1814,91903,91904,91906,91908],{},[898,91905,1872],{},[1793,91907,1806],{},[895,91909,91910,91912,91914],{},[1793,91911,2131],{},[898,91913,4930],{"mathvariant":1822},[1793,91915,2616],{},[902,91917,91918],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F4} Q_2^{3\u002F4}"," mají křivky užitečnosti rovnici ",[883,91921,91923],{"className":91922},[886],[888,91924,91925],{"xmlns":890},[892,91926,91927,91961],{},[895,91928,91929,91943,91957,91959],{},[1814,91930,91931,91933,91935],{},[898,91932,1872],{},[1793,91934,1795],{},[895,91936,91937,91939,91941],{},[1793,91938,1795],{},[898,91940,4930],{"mathvariant":1822},[1793,91942,2616],{},[1814,91944,91945,91947,91949],{},[898,91946,1872],{},[1793,91948,1806],{},[895,91950,91951,91953,91955],{},[1793,91952,2131],{},[898,91954,4930],{"mathvariant":1822},[1793,91956,2616],{},[1688,91958,1690],{},[898,91960,2031],{},[902,91962,91963],{"encoding":904},"Q_1^{1\u002F4} Q_2^{3\u002F4} = c",". Umocněním na čtvrtou mocninu dostáváme ",[883,91966,91968],{"className":91967},[886],[888,91969,91970],{"xmlns":890},[892,91971,91972,91996],{},[895,91973,91974,91980,91988,91990],{},[1788,91975,91976,91978],{},[898,91977,1872],{},[1793,91979,1795],{},[1814,91981,91982,91984,91986],{},[898,91983,1872],{},[1793,91985,1806],{},[1793,91987,2131],{},[1688,91989,1690],{},[1850,91991,91992,91994],{},[898,91993,2031],{},[1793,91995,2616],{},[902,91997,91998],{"encoding":904},"Q_1 Q_2^{3} = c^{4}",". Pro ",[883,92001,92003],{"className":92002},[886],[888,92004,92005],{"xmlns":890},[892,92006,92007,92015],{},[895,92008,92009,92011,92013],{},[898,92010,2031],{},[1688,92012,1690],{},[1793,92014,1795],{},[902,92016,92017],{"encoding":904},"c = 1",[883,92019,92021],{"className":92020},[886],[888,92022,92023],{"xmlns":890},[892,92024,92025,92069],{},[895,92026,92027,92033,92035,92051,92053],{},[1788,92028,92029,92031],{},[898,92030,1872],{},[1793,92032,1806],{},[1688,92034,1690],{},[1814,92036,92037,92039,92041],{},[898,92038,1872],{},[1793,92040,1795],{},[895,92042,92043,92045,92047,92049],{},[1688,92044,1954],{},[1793,92046,1795],{},[898,92048,4930],{"mathvariant":1822},[1793,92050,2131],{},[1688,92052,1690],{},[1777,92054,92055],{"scriptlevel":1779,"displaystyle":1732},[1781,92056,92057,92059],{},[1793,92058,1795],{},[82267,92060,92061,92067],{},[1788,92062,92063,92065],{},[898,92064,1872],{},[1793,92066,1795],{},[1793,92068,2131],{},[902,92070,92071],{"encoding":904},"Q_2 = Q_1^{-1\u002F3} = \\dfrac{1}{\\sqrt[3]{Q_1}}",[883,92073,92075],{"className":92074},[886],[888,92076,92077],{"xmlns":890},[892,92078,92079,92087],{},[895,92080,92081,92083,92085],{},[898,92082,2031],{},[1688,92084,1690],{},[1793,92086,1806],{},[902,92088,92089],{"encoding":904},"c = 2",[883,92091,92093],{"className":92092},[886],[888,92094,92095],{"xmlns":890},[892,92096,92097,92163],{},[895,92098,92099,92105,92107,92119,92121,92137,92139],{},[1788,92100,92101,92103],{},[898,92102,1872],{},[1793,92104,1806],{},[1688,92106,1690],{},[1850,92108,92109,92111],{},[1793,92110,1806],{},[895,92112,92113,92115,92117],{},[1793,92114,2616],{},[898,92116,4930],{"mathvariant":1822},[1793,92118,2131],{},[1688,92120,3434],{},[1814,92122,92123,92125,92127],{},[898,92124,1872],{},[1793,92126,1795],{},[895,92128,92129,92131,92133,92135],{},[1688,92130,1954],{},[1793,92132,1795],{},[898,92134,4930],{"mathvariant":1822},[1793,92136,2131],{},[1688,92138,1690],{},[1777,92140,92141],{"scriptlevel":1779,"displaystyle":1732},[1781,92142,92143,92153],{},[895,92144,92145,92147],{},[1793,92146,1806],{},[82267,92148,92149,92151],{},[1793,92150,1806],{},[1793,92152,2131],{},[82267,92154,92155,92161],{},[1788,92156,92157,92159],{},[898,92158,1872],{},[1793,92160,1795],{},[1793,92162,2131],{},[902,92164,92165],{"encoding":904},"Q_2 = 2^{4\u002F3} \\cdot Q_1^{-1\u002F3} = \\dfrac{2 \\sqrt[3]{2}}{\\sqrt[3]{Q_1}}"," (obrázek 6.5).",[198,92168,92170],{"id":92169},"čtyři-vlastnosti-křivek-užitečnosti","Čtyři vlastnosti křivek užitečnosti",[724,92172,92173],{},[2821,92174],{"alt":92175,"className":92176,"src":92177},"imek-ic-4vlastnosti-anotovane",[210,2825],"\u002Fwiki-assets\u002Fimek-ic-4vlastnosti-anotovane.jpeg",[4124,92179,92180,92189,92236,92280,92286,92292],{},[724,92181,92182,92184,92185,92188],{},[883,92183,4668],{}," Čtyři základní vlastnosti indiferenčních křivek\n",[38,92186,92187],{},"1° Klesající."," Je-li nakoupeno méně jednoho zboží, je k dosažení stejného uspokojení třeba kompenzovat větším množstvím druhého zboží. Sklon tečny je",[724,92190,92191],{},[883,92192,92194],{"className":92193},[886],[888,92195,92196],{"xmlns":890},[892,92197,92198,92233],{},[895,92199,92200,92203,92205,92207,92209,92211,92229,92231],{},[898,92201,92202],{"mathvariant":1822},"tg",[1688,92204,56440],{},[898,92206,19104],{},[1688,92208,1690],{},[1688,92210,1954],{},[1781,92212,92213,92221],{},[1814,92214,92215,92217,92219],{},[898,92216,900],{},[1793,92218,1795],{},[1688,92220,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1814,92222,92223,92225,92227],{},[898,92224,900],{},[1793,92226,1806],{},[1688,92228,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,92230,3704],{},[1793,92232,1779],{},[902,92234,92235],{"encoding":904},"\\operatorname{tg} \\alpha = -\\frac{U'_1}{U'_2} \u003C 0",[724,92237,92238,92239,92279],{},"(derivace implicitně zadané funkce ",[883,92240,92242],{"className":92241},[886],[888,92243,92244],{"xmlns":890},[892,92245,92246,92276],{},[895,92247,92248,92250,92252,92258,92260,92266,92268,92270,92272,92274],{},[898,92249,900],{},[1688,92251,2066],{"stretchy":2065},[1788,92253,92254,92256],{},[898,92255,1872],{},[1793,92257,1795],{},[1688,92259,1733],{"separator":1732},[1788,92261,92262,92264],{},[898,92263,1872],{},[1793,92265,1806],{},[1688,92267,2076],{"stretchy":2065},[1688,92269,1954],{},[898,92271,2031],{},[1688,92273,1690],{},[1793,92275,1779],{},[902,92277,92278],{"encoding":904},"U(Q_1, Q_2) - c = 0","). Ze záporné derivace plyne klesající průběh.",[724,92281,92282,92285],{},[38,92283,92284],{},"2° Neprotínají se."," V průsečíku by týž svazek ležel na dvou různých hladinách užitečnosti, což je spor.",[724,92287,92288,92291],{},[38,92289,92290],{},"3° Čím vzdálenější od počátku, tím vyšší užitečnost"," (obrázek 6.4).",[724,92293,92294,92297,92298,92316,92317,92333,92334,92337],{},[38,92295,92296],{},"4° Konvexní."," Pro každé dva body ",[883,92299,92301],{"className":92300},[886],[888,92302,92303],{"xmlns":890},[892,92304,92305,92313],{},[895,92306,92307,92309,92311],{},[898,92308,4512],{},[1688,92310,1733],{"separator":1732},[898,92312,23494],{},[902,92314,92315],{"encoding":904},"A, B"," na téže křivce leží vnitřní body úsečky ",[883,92318,92320],{"className":92319},[886],[888,92321,92322],{"xmlns":890},[892,92323,92324,92330],{},[895,92325,92326,92328],{},[898,92327,4512],{},[898,92329,23494],{},[902,92331,92332],{"encoding":904},"AB"," ve ",[38,92335,92336],{},"vyšší"," hladině užitečnosti (tj. „nad\" křivkou) — vyjadřuje to preferenci smíšených svazků před krajními.",[724,92339,92340],{},[614,92341,92342,92343,92378,92379,2263],{},"Obrázek 6.6 — klesající a konvexní průběh ",[883,92344,92346],{"className":92345},[886],[888,92347,92348],{"xmlns":890},[892,92349,92350,92376],{},[895,92351,92352,92354,92356,92362,92364,92370,92372,92374],{},[898,92353,900],{},[1688,92355,2066],{"stretchy":2065},[1788,92357,92358,92360],{},[898,92359,1872],{},[1793,92361,1795],{},[1688,92363,1733],{"separator":1732},[1788,92365,92366,92368],{},[898,92367,1872],{},[1793,92369,1806],{},[1688,92371,2076],{"stretchy":2065},[1688,92373,1690],{},[898,92375,2031],{},[902,92377,10021],{"encoding":904}," s tečnou se sklonem ",[883,92380,92382],{"className":92381},[886],[888,92383,92384],{"xmlns":890},[892,92385,92386,92394],{},[895,92387,92388,92390,92392],{},[898,92389,92202],{"mathvariant":1822},[1688,92391,56440],{},[898,92393,19104],{},[902,92395,92396],{"encoding":904},"\\operatorname{tg}\\alpha",[115,92398,92400],{"id":92399},"mezní-míra-komoditní-substituce-mrcs","Mezní míra komoditní substituce (MRCS)",[724,92402,92403,2170,92406,10277,92419,92422],{},[38,92404,92405],{},"Mezní míra komoditní substituce",[883,92407,92409],{"className":92408},[886],[888,92410,92411],{"xmlns":890},[892,92412,92413,92417],{},[895,92414,92415],{},[2041,92416,1670],{},[902,92418,28478],{"encoding":904},[38,92420,92421],{},"marginal rate of commodity substitution",") je podíl mezních užitečností:",[883,92424,92426],{"className":92425},[886],[888,92427,92428],{"xmlns":890,"display":28306},[892,92429,92430,92517],{},[20995,92431,92432],{"width":28311},[21000,92433,92434,92436,92510,92512],{},[21003,92435],{"width":28316},[21003,92437,92438],{},[895,92439,92440,92442,92444,92446,92448,92454,92456,92462,92464,92466,92488,92490,92508],{},[2041,92441,1670],{},[1688,92443,1690],{},[2041,92445,1670],{},[1688,92447,2066],{"stretchy":2065},[1788,92449,92450,92452],{},[898,92451,1872],{},[1793,92453,1795],{},[1688,92455,1733],{"separator":1732},[1788,92457,92458,92460],{},[898,92459,1872],{},[1793,92461,1806],{},[1688,92463,2076],{"stretchy":2065},[1688,92465,1690],{},[1781,92467,92468,92478],{},[895,92469,92470,92472],{},[898,92471,1661],{},[1788,92473,92474,92476],{},[898,92475,900],{},[1793,92477,1795],{},[895,92479,92480,92482],{},[898,92481,1661],{},[1788,92483,92484,92486],{},[898,92485,900],{},[1793,92487,1806],{},[1688,92489,1690],{},[1781,92491,92492,92500],{},[1814,92493,92494,92496,92498],{},[898,92495,900],{},[1793,92497,1795],{},[1688,92499,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1814,92501,92502,92504,92506],{},[898,92503,900],{},[1793,92505,1806],{},[1688,92507,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[898,92509,2263],{"mathvariant":1822},[21003,92511],{"width":28316},[21003,92513,92514],{},[2041,92515,92516],{},"(6.9)",[902,92518,92519],{"encoding":904},"\\text{MRCS} = \\text{MRCS}(Q_1, Q_2) = \\frac{MU_1}{MU_2} = \\frac{U'_1}{U'_2}. \\tag{6.9}",[724,92521,92522,92523,92557,92558,92590,92591,92626,92627,92640],{},"Geometricky: ",[883,92524,92526],{"className":92525},[886],[888,92527,92528],{"xmlns":890},[892,92529,92530,92554],{},[895,92531,92532,92534],{},[1688,92533,1954],{},[1777,92535,92536],{"scriptlevel":1779,"displaystyle":2065},[1781,92537,92538,92546],{},[1814,92539,92540,92542,92544],{},[898,92541,900],{},[1793,92543,1795],{},[1688,92545,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1814,92547,92548,92550,92552],{},[898,92549,900],{},[1793,92551,1806],{},[1688,92553,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[902,92555,92556],{"encoding":904},"-\\tfrac{U'_1}{U'_2}"," je derivace funkce ",[883,92559,92561],{"className":92560},[886],[888,92562,92563],{"xmlns":890},[892,92564,92565,92587],{},[895,92566,92567,92573,92575,92577,92579,92585],{},[1788,92568,92569,92571],{},[898,92570,1872],{},[1793,92572,1806],{},[1688,92574,1690],{},[898,92576,2287],{},[1688,92578,2066],{"stretchy":2065},[1788,92580,92581,92583],{},[898,92582,1872],{},[1793,92584,1795],{},[1688,92586,2076],{"stretchy":2065},[902,92588,92589],{"encoding":904},"Q_2 = f(Q_1)"," zadané implicitně rovnicí ",[883,92592,92594],{"className":92593},[886],[888,92595,92596],{"xmlns":890},[892,92597,92598,92624],{},[895,92599,92600,92602,92604,92610,92612,92618,92620,92622],{},[898,92601,900],{},[1688,92603,2066],{"stretchy":2065},[1788,92605,92606,92608],{},[898,92607,1872],{},[1793,92609,1795],{},[1688,92611,1733],{"separator":1732},[1788,92613,92614,92616],{},[898,92615,1872],{},[1793,92617,1806],{},[1688,92619,2076],{"stretchy":2065},[1688,92621,1690],{},[898,92623,2031],{},[902,92625,10021],{"encoding":904},". Protože je vždy záporná (křivka je klesající), bereme absolutní hodnotu a kladný ",[883,92628,92630],{"className":92629},[886],[888,92631,92632],{"xmlns":890},[892,92633,92634,92638],{},[895,92635,92636],{},[2041,92637,1670],{},[902,92639,28478],{"encoding":904}," chápeme jako velikost kompenzace.",[4124,92642,92643],{},[724,92644,92645,92647,92648,8358,92680,92718,92719,92736,92737,92754],{},[883,92646,4412],{}," Intuice — MRCS jako sklon indiferenční křivky\n",[883,92649,92651],{"className":92650},[886],[888,92652,92653],{"xmlns":890},[892,92654,92655,92677],{},[895,92656,92657,92659,92661,92667,92669,92675],{},[2041,92658,1670],{},[1688,92660,2066],{"stretchy":2065},[1788,92662,92663,92665],{},[898,92664,1872],{},[1793,92666,1795],{},[1688,92668,1733],{"separator":1732},[1788,92670,92671,92673],{},[898,92672,1872],{},[1793,92674,1806],{},[1688,92676,2076],{"stretchy":2065},[902,92678,92679],{"encoding":904},"\\text{MRCS}(Q_1, Q_2)",[38,92681,92682,92683,29243,92700,92717],{},"míra, jakou je spotřebitel ochoten zaměnit ",[883,92684,92686],{"className":92685},[886],[888,92687,92688],{"xmlns":890},[892,92689,92690,92698],{},[895,92691,92692],{},[1788,92693,92694,92696],{},[898,92695,1872],{},[1793,92697,1795],{},[902,92699,29242],{"encoding":904},[883,92701,92703],{"className":92702},[886],[888,92704,92705],{"xmlns":890},[892,92706,92707,92715],{},[895,92708,92709],{},[1788,92710,92711,92713],{},[898,92712,1872],{},[1793,92714,1806],{},[902,92716,29261],{"encoding":904}," při zachování užitečnosti"," — tedy kolik jednotek ",[883,92720,92722],{"className":92721},[886],[888,92723,92724],{"xmlns":890},[892,92725,92726,92734],{},[895,92727,92728],{},[1788,92729,92730,92732],{},[898,92731,1872],{},[1793,92733,1806],{},[902,92735,29261],{"encoding":904}," „obětuje\" za jednu jednotku ",[883,92738,92740],{"className":92739},[886],[888,92741,92742],{"xmlns":890},[892,92743,92744,92752],{},[895,92745,92746],{},[1788,92747,92748,92750],{},[898,92749,1872],{},[1793,92751,1795],{},[902,92753,29242],{"encoding":904}," navíc, aby zůstal na téže indiferenční křivce. Geometricky jde o absolutní hodnotu sklonu tečny k indiferenční křivce v daném bodě.",[724,92756,92757,92758,30184],{},"Pro obecnou změnu ",[883,92759,92761],{"className":92760},[886],[888,92762,92763],{"xmlns":890},[892,92764,92765,92775],{},[895,92766,92767,92769],{},[898,92768,2073],{"mathvariant":1822},[1788,92770,92771,92773],{},[898,92772,1872],{},[1793,92774,1795],{},[902,92776,92777],{"encoding":904},"\\mathrm{d} Q_1",[883,92779,92781],{"className":92780},[886],[888,92782,92783],{"xmlns":890,"display":28306},[892,92784,92785,92838],{},[20995,92786,92787],{"width":28311},[21000,92788,92789,92791,92831,92833],{},[21003,92790],{"width":28316},[21003,92792,92793],{},[895,92794,92795,92797,92803,92805,92807,92813,92815,92817,92819,92821,92823,92829],{},[898,92796,3147],{"mathvariant":1822},[1788,92798,92799,92801],{},[898,92800,1872],{},[1793,92802,1806],{},[1688,92804,2991],{},[898,92806,2073],{"mathvariant":1822},[1788,92808,92809,92811],{},[898,92810,1872],{},[1793,92812,1806],{},[1688,92814,1690],{},[1688,92816,1954],{},[2041,92818,1670],{},[1688,92820,3434],{},[898,92822,2073],{"mathvariant":1822},[1788,92824,92825,92827],{},[898,92826,1872],{},[1793,92828,1795],{},[1688,92830,1733],{"separator":1732},[21003,92832],{"width":28316},[21003,92834,92835],{},[2041,92836,92837],{},"(6.10)",[902,92839,92840],{"encoding":904},"\\Delta Q_2 \\approx \\mathrm{d} Q_2 = -\\text{MRCS} \\cdot \\mathrm{d} Q_1, \\tag{6.10}",[883,92842,92844],{"className":92843},[886],[888,92845,92846],{"xmlns":890,"display":28306},[892,92847,92848,92895],{},[20995,92849,92850],{"width":28311},[21000,92851,92852,92854,92888,92890],{},[21003,92853],{"width":28316},[21003,92855,92856],{},[895,92857,92858,92860,92866,92868,92870,92876,92878,92880,92886],{},[898,92859,2073],{"mathvariant":1822},[1788,92861,92862,92864],{},[898,92863,1872],{},[1793,92865,1795],{},[1688,92867,1690],{},[1688,92869,1954],{},[1781,92871,92872,92874],{},[1793,92873,1795],{},[2041,92875,1670],{},[2041,92877,2043],{},[898,92879,2073],{"mathvariant":1822},[1788,92881,92882,92884],{},[898,92883,1872],{},[1793,92885,1806],{},[898,92887,2263],{"mathvariant":1822},[21003,92889],{"width":28316},[21003,92891,92892],{},[2041,92893,92894],{},"(6.11)",[902,92896,92897],{"encoding":904},"\\mathrm{d} Q_1 = -\\frac{1}{\\text{MRCS}}\\, \\mathrm{d} Q_2. \\tag{6.11}",[4124,92899,92900,92966,93083],{},[724,92901,92902,92904,92905,30184],{},[883,92903,52935],{}," Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost\nPro ",[883,92906,92908],{"className":92907},[886],[888,92909,92910],{"xmlns":890},[892,92911,92912,92964],{},[895,92913,92914,92916,92918,92924,92926,92932,92934,92936,92950],{},[898,92915,900],{},[1688,92917,2066],{"stretchy":2065},[1788,92919,92920,92922],{},[898,92921,1872],{},[1793,92923,1795],{},[1688,92925,1733],{"separator":1732},[1788,92927,92928,92930],{},[898,92929,1872],{},[1793,92931,1806],{},[1688,92933,2076],{"stretchy":2065},[1688,92935,1690],{},[1814,92937,92938,92940,92942],{},[898,92939,1872],{},[1793,92941,1795],{},[895,92943,92944,92946,92948],{},[1793,92945,1795],{},[898,92947,4930],{"mathvariant":1822},[1793,92949,1806],{},[1814,92951,92952,92954,92956],{},[898,92953,1872],{},[1793,92955,1806],{},[895,92957,92958,92960,92962],{},[1793,92959,1795],{},[898,92961,4930],{"mathvariant":1822},[1793,92963,1806],{},[902,92965,30183],{"encoding":904},[724,92967,92968],{},[883,92969,92971],{"className":92970},[886],[888,92972,92973],{"xmlns":890},[892,92974,92975,93081],{},[895,92976,92977,92979,92981,93063,93065,93079],{},[2041,92978,1670],{},[1688,92980,1690],{},[1781,92982,92983,93023],{},[895,92984,92985,92993,93009],{},[1777,92986,92987],{"scriptlevel":1779,"displaystyle":2065},[1781,92988,92989,92991],{},[1793,92990,1795],{},[1793,92992,1806],{},[1814,92994,92995,92997,92999],{},[898,92996,1872],{},[1793,92998,1795],{},[895,93000,93001,93003,93005,93007],{},[1688,93002,1954],{},[1793,93004,1795],{},[898,93006,4930],{"mathvariant":1822},[1793,93008,1806],{},[1814,93010,93011,93013,93015],{},[898,93012,1872],{},[1793,93014,1806],{},[895,93016,93017,93019,93021],{},[1793,93018,1795],{},[898,93020,4930],{"mathvariant":1822},[1793,93022,1806],{},[895,93024,93025,93033,93047],{},[1777,93026,93027],{"scriptlevel":1779,"displaystyle":2065},[1781,93028,93029,93031],{},[1793,93030,1795],{},[1793,93032,1806],{},[1814,93034,93035,93037,93039],{},[898,93036,1872],{},[1793,93038,1795],{},[895,93040,93041,93043,93045],{},[1793,93042,1795],{},[898,93044,4930],{"mathvariant":1822},[1793,93046,1806],{},[1814,93048,93049,93051,93053],{},[898,93050,1872],{},[1793,93052,1806],{},[895,93054,93055,93057,93059,93061],{},[1688,93056,1954],{},[1793,93058,1795],{},[898,93060,4930],{"mathvariant":1822},[1793,93062,1806],{},[1688,93064,1690],{},[1781,93066,93067,93073],{},[1788,93068,93069,93071],{},[898,93070,1872],{},[1793,93072,1806],{},[1788,93074,93075,93077],{},[898,93076,1872],{},[1793,93078,1795],{},[898,93080,2263],{"mathvariant":1822},[902,93082,30302],{"encoding":904},[724,93084,30305,93085,3185,93128,30353,93130,93149],{},[883,93086,93088],{"className":93087},[886],[888,93089,93090],{"xmlns":890},[892,93091,93092,93126],{},[895,93093,93094,93096,93098,93100,93102,93104,93106,93108,93116,93118],{},[2041,93095,1670],{},[1688,93097,2066],{"stretchy":2065},[1793,93099,30321],{},[1688,93101,1733],{"separator":1732},[1793,93103,15357],{},[1688,93105,2076],{"stretchy":2065},[1688,93107,1690],{},[1777,93109,93110],{"scriptlevel":1779,"displaystyle":2065},[1781,93111,93112,93114],{},[1793,93113,15357],{},[1793,93115,30321],{},[1688,93117,1690],{},[1777,93119,93120],{"scriptlevel":1779,"displaystyle":2065},[1781,93121,93122,93124],{},[1793,93123,2501],{},[1793,93125,2131],{},[902,93127,30350],{"encoding":904},[614,93129,9469],{},[883,93131,93133],{"className":93132},[886],[888,93134,93135],{"xmlns":890},[892,93136,93137,93147],{},[895,93138,93139],{},[1777,93140,93141],{"scriptlevel":1779,"displaystyle":2065},[1781,93142,93143,93145],{},[1793,93144,2501],{},[1793,93146,2131],{},[902,93148,30373],{"encoding":904}," jednotky, aby se užitečnost zachovala.",[724,93151,93152,93153,93157],{},"(Paralelou je ",[207,93154,93156],{"className":93155,"dataFsResolvedFilePath":857,"href":858},[210],"mezní míra technické substituce MRTS"," z produkční teorie.)",[115,93159,93161],{"id":93160},"_63-64-optimalizace-spotřebitele-přehled","6.3 – 6.4 Optimalizace spotřebitele — přehled",[724,93163,93164,93165,93168],{},"Rámcově se v kapitole 6 studují ",[38,93166,93167],{},"dvě vázané optimalizační úlohy"," s užitečností:",[120,93170,93171,93307],{},[123,93172,93173,93175,93176,10409,93207,2170,93210,93259,93260,2263],{},[38,93174,28492],{}," — maximalizace ",[883,93177,93179],{"className":93178},[886],[888,93180,93181],{"xmlns":890},[892,93182,93183,93205],{},[895,93184,93185,93187,93189,93195,93197,93203],{},[898,93186,900],{},[1688,93188,2066],{"stretchy":2065},[1788,93190,93191,93193],{},[898,93192,1872],{},[1793,93194,1795],{},[1688,93196,1733],{"separator":1732},[1788,93198,93199,93201],{},[898,93200,1872],{},[1793,93202,1806],{},[1688,93204,2076],{"stretchy":2065},[902,93206,16590],{"encoding":904},[38,93208,93209],{},"rozpočtovém omezení",[883,93211,93213],{"className":93212},[886],[888,93214,93215],{"xmlns":890},[892,93216,93217,93257],{},[895,93218,93219,93225,93227,93235,93241,93243,93251],{},[1850,93220,93221,93223],{},[898,93222,1854],{},[1688,93224,1857],{},[1688,93226,1690],{},[1814,93228,93229,93231,93233],{},[898,93230,1727],{},[1793,93232,1795],{},[1688,93234,1857],{},[1788,93236,93237,93239],{},[898,93238,1872],{},[1793,93240,1795],{},[1688,93242,1696],{},[1814,93244,93245,93247,93249],{},[898,93246,1727],{},[1793,93248,1806],{},[1688,93250,1857],{},[1788,93252,93253,93255],{},[898,93254,1872],{},[1793,93256,1806],{},[902,93258,1893],{"encoding":904},". Výstupem je Marshallova poptávka ",[883,93261,93263],{"className":93262},[886],[888,93264,93265],{"xmlns":890},[892,93266,93267,93305],{},[895,93268,93269,93275,93277,93283,93285,93291,93293,93299,93301,93303],{},[1788,93270,93271,93273],{},[898,93272,1872],{},[898,93274,18035],{},[1688,93276,1690],{},[1788,93278,93279,93281],{},[898,93280,4440],{},[898,93282,18035],{},[1688,93284,2066],{"stretchy":2065},[1788,93286,93287,93289],{},[898,93288,1727],{},[1793,93290,1795],{},[1688,93292,1733],{"separator":1732},[1788,93294,93295,93297],{},[898,93296,1727],{},[1793,93298,1806],{},[1688,93300,1733],{"separator":1732},[898,93302,1854],{},[1688,93304,2076],{"stretchy":2065},[902,93306,36695],{"encoding":904},[123,93308,93309,28141,93312,28184,93358,93375,93376,2263],{},[38,93310,93311],{},"Duální úloha",[883,93313,93315],{"className":93314},[886],[888,93316,93317],{"xmlns":890},[892,93318,93319,93355],{},[895,93320,93321,93323,93325,93333,93339,93341,93349],{},[898,93322,4509],{},[1688,93324,1690],{},[1814,93326,93327,93329,93331],{},[898,93328,1727],{},[1793,93330,1795],{},[1688,93332,1857],{},[1788,93334,93335,93337],{},[898,93336,1872],{},[1793,93338,1795],{},[1688,93340,1696],{},[1814,93342,93343,93345,93347],{},[898,93344,1727],{},[1793,93346,1806],{},[1688,93348,1857],{},[1788,93350,93351,93353],{},[898,93352,1872],{},[1793,93354,1806],{},[902,93356,93357],{"encoding":904},"E = P_1^* Q_1 + P_2^* Q_2",[883,93359,93361],{"className":93360},[886],[888,93362,93363],{"xmlns":890},[892,93364,93365,93373],{},[895,93366,93367],{},[1850,93368,93369,93371],{},[898,93370,900],{},[1688,93372,1857],{},[902,93374,28202],{"encoding":904},". Výstupem je Hicksova poptávka ",[883,93377,93379],{"className":93378},[886],[888,93380,93381],{"xmlns":890},[892,93382,93383,93421],{},[895,93384,93385,93391,93393,93399,93401,93407,93409,93415,93417,93419],{},[1788,93386,93387,93389],{},[898,93388,1872],{},[898,93390,18035],{},[1688,93392,1690],{},[1788,93394,93395,93397],{},[898,93396,4440],{},[898,93398,18035],{},[1688,93400,2066],{"stretchy":2065},[1788,93402,93403,93405],{},[898,93404,1727],{},[1793,93406,1795],{},[1688,93408,1733],{"separator":1732},[1788,93410,93411,93413],{},[898,93412,1727],{},[1793,93414,1806],{},[1688,93416,1733],{"separator":1732},[898,93418,900],{},[1688,93420,2076],{"stretchy":2065},[902,93422,18068],{"encoding":904},[724,93424,93425,93426,93429,93430,2170,93433,93472],{},"Obě úlohy se řeší ",[207,93427,28207],{"className":93428,"dataFsResolvedFilePath":791,"href":792},[210]," a vedou na ",[38,93431,93432],{},"tentýž bod dotyku",[883,93434,93436],{"className":93435},[886],[888,93437,93438],{"xmlns":890},[892,93439,93440,93470],{},[895,93441,93442,93448,93450,93458,93460,93468],{},[1850,93443,93444,93446],{},[898,93445,1872],{},[1688,93447,1857],{},[1688,93449,2748],{"stretchy":2065},[1814,93451,93452,93454,93456],{},[898,93453,1872],{},[1793,93455,1795],{},[1688,93457,1857],{},[1688,93459,1733],{"separator":1732},[1814,93461,93462,93464,93466],{},[898,93463,1872],{},[1793,93465,1806],{},[1688,93467,1857],{},[1688,93469,2763],{"stretchy":2065},[902,93471,28567],{"encoding":904}," indiferenční křivky a rozpočtové přímky (resp. přímky výdajů), v němž platí podmínka optimality",[883,93474,93476],{"className":93475},[886],[888,93477,93478],{"xmlns":890,"display":28306},[892,93479,93480,93526],{},[895,93481,93482,93484,93486,93504,93506,93524],{},[2041,93483,1670],{},[1688,93485,1690],{},[1781,93487,93488,93496],{},[1814,93489,93490,93492,93494],{},[898,93491,900],{},[1793,93493,1795],{},[1688,93495,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1814,93497,93498,93500,93502],{},[898,93499,900],{},[1793,93501,1806],{},[1688,93503,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,93505,1690],{},[1781,93507,93508,93516],{},[1814,93509,93510,93512,93514],{},[898,93511,1727],{},[1793,93513,1795],{},[1688,93515,1857],{},[1814,93517,93518,93520,93522],{},[898,93519,1727],{},[1793,93521,1806],{},[1688,93523,1857],{},[898,93525,2263],{"mathvariant":1822},[902,93527,93528],{"encoding":904},"\\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*}.",[724,93530,93531],{},"Poměr mezních užitečností se rovná poměru cen — sklon indiferenční křivky v optimu se rovná sklonu rozpočtové přímky.",[4124,93533,93534],{},[724,93535,93536,93538,93539,93542,93543,93546,93547,93574,93575,93609,93610,93644,93645,93688,93689,93692,93693,2263],{},[883,93537,4412],{}," Pro detailní postup viz ",[207,93540,36994],{"className":93541,"dataFsResolvedFilePath":911,"href":912},[210],"\nKompletní odvození obou úloh Lagrangeovou metodou, geometrická interpretace, řešené ",[38,93544,93545],{},"Příklady 6.5–6.8"," (MRCS pro Cobb-Douglase, maximalizace ",[883,93548,93550],{"className":93549},[886],[888,93551,93552],{"xmlns":890},[892,93553,93554,93572],{},[895,93555,93556,93558,93560,93566],{},[898,93557,900],{},[1688,93559,1690],{},[1788,93561,93562,93564],{},[898,93563,1872],{},[1793,93565,1795],{},[1788,93567,93568,93570],{},[898,93569,1872],{},[1793,93571,1806],{},[902,93573,30466],{"encoding":904}," s výsledkem ",[883,93576,93578],{"className":93577},[886],[888,93579,93580],{"xmlns":890},[892,93581,93582,93606],{},[895,93583,93584,93590,93592,93594,93596,93602,93604],{},[1788,93585,93586,93588],{},[898,93587,1872],{},[1793,93589,1795],{},[1688,93591,1690],{},[1793,93593,5260],{},[1688,93595,1733],{"separator":1732},[1788,93597,93598,93600],{},[898,93599,1872],{},[1793,93601,1806],{},[1688,93603,1690],{},[1793,93605,3121],{},[902,93607,93608],{"encoding":904},"Q_1 = 25, Q_2 = 10","; minimalizace výdajů s ",[883,93611,93613],{"className":93612},[886],[888,93614,93615],{"xmlns":890},[892,93616,93617,93641],{},[895,93618,93619,93625,93627,93629,93631,93637,93639],{},[1788,93620,93621,93623],{},[898,93622,1872],{},[1793,93624,1795],{},[1688,93626,1690],{},[1793,93628,2616],{},[1688,93630,1733],{"separator":1732},[1788,93632,93633,93635],{},[898,93634,1872],{},[1793,93636,1806],{},[1688,93638,1690],{},[1793,93640,1795],{},[902,93642,93643],{"encoding":904},"Q_1 = 4, Q_2 = 1","; obecná Hicksova poptávka pro ",[883,93646,93648],{"className":93647},[886],[888,93649,93650],{"xmlns":890},[892,93651,93652,93686],{},[895,93653,93654,93656,93658,93672],{},[898,93655,900],{},[1688,93657,1690],{},[1814,93659,93660,93662,93664],{},[898,93661,1872],{},[1793,93663,1795],{},[895,93665,93666,93668,93670],{},[1793,93667,1795],{},[898,93669,4930],{"mathvariant":1822},[1793,93671,1806],{},[1814,93673,93674,93676,93678],{},[898,93675,1872],{},[1793,93677,1806],{},[895,93679,93680,93682,93684],{},[1793,93681,1795],{},[898,93683,4930],{"mathvariant":1822},[1793,93685,1806],{},[902,93687,33399],{"encoding":904},"), odvození Marshallovy i Hicksovy funkce poptávky a Engelových funkcí, vztah dualita primární ↔ duální úlohy a úlohy ",[38,93690,93691],{},"6.8–6.13"," jsou na stránce ",[207,93694,28007],{"className":93695,"dataFsResolvedFilePath":911,"href":912},[210],[115,93697,93699],{"id":93698},"shrnutí-kapitoly-6","Shrnutí kapitoly 6",[724,93701,93702,93703,93716,93717,93719,93720,93722,93723,93725,93726,93728,93729,93731,93732,93734,93735,2170,93737,93772,93773,93786,93787,93790,93791,93794,93795,2263],{},"Každá ",[883,93704,93706],{"className":93705},[886],[888,93707,93708],{"xmlns":890},[892,93709,93710,93714],{},[895,93711,93712],{},[898,93713,37100],{},[902,93715,37100],{"encoding":904},"-tice množství jednotlivých zboží je ",[38,93718,87050],{},". Přiřadíme-li každému svazku kladné číslo (jeho užitečnost), můžeme svazky uspořádat podle rostoucí užitečnosti; svazky se stejnou užitečností jsou indiferentní. Tím je definována ",[38,93721,87534],{}," a současně ",[38,93724,87053],{},". Její parciální derivace (podle jednotlivých množství) jsou ",[38,93727,87058],{}," — přibližná změna užitečnosti při jednotkové změně příslušného zboží. Aby funkce mohla být funkcí užitečnosti, musejí být její první parciální derivace ",[38,93730,52917],{}," (6.4) a druhé parciální derivace ",[38,93733,89417],{}," (6.5 — zákon klesající mezní užitečnosti). ",[38,93736,9984],{},[883,93738,93740],{"className":93739},[886],[888,93741,93742],{"xmlns":890},[892,93743,93744,93770],{},[895,93745,93746,93748,93750,93756,93758,93764,93766,93768],{},[898,93747,900],{},[1688,93749,2066],{"stretchy":2065},[1788,93751,93752,93754],{},[898,93753,1872],{},[1793,93755,1795],{},[1688,93757,1733],{"separator":1732},[1788,93759,93760,93762],{},[898,93761,1872],{},[1793,93763,1806],{},[1688,93765,2076],{"stretchy":2065},[1688,93767,1690],{},[898,93769,2031],{},[902,93771,10021],{"encoding":904}," jsou klesající, neprotínající se, vzdálenější od počátku mají vyšší užitečnost a jsou konvexní. ",[883,93774,93776],{"className":93775},[886],[888,93777,93778],{"xmlns":890},[892,93779,93780,93784],{},[895,93781,93782],{},[2041,93783,1670],{},[902,93785,28478],{"encoding":904}," = podíl mezních užitečností udává náhradu jednoho zboží druhým při zachování užitečnosti. Na tento teoretický základ navazují optimalizační úlohy (",[38,93788,93789],{},"maximalizace užitečnosti"," a duální ",[38,93792,93793],{},"minimalizace výdajů",") řešené Lagrangeovou metodou — viz ",[207,93796,36994],{"className":93797,"dataFsResolvedFilePath":911,"href":912},[210],[115,93799,50122],{"id":50121},[152,93801,93802,93805,93808,93811,93814,93817,93820,93823,93826,93829],{},[123,93803,93804],{},"Co se zahrnuje pod termín užitečnost?",[123,93806,93807],{},"Co se rozumí svazkem zboží? Které svazky zboží jsou indiferentní?",[123,93809,93810],{},"Jak souvisejí hodnoty funkce užitečnosti s preferencí svazků?",[123,93812,93813],{},"Jak se vypočítá mezní užitečnost?",[123,93815,93816],{},"Jak lze ekonomicky interpretovat fakt, že mezní užitečnost určitého zboží se rovná 2,5?",[123,93818,93819],{},"Jaké vlastnosti musí mít funkce více proměnných, aby mohla být funkcí užitečnosti?",[123,93821,93822],{},"Které jsou nejčastěji používané funkce užitečnosti?",[123,93824,93825],{},"Jakou rovnici mají křivky užitečnosti? Co platí v bodech ležících na téže křivce užitečnosti?",[123,93827,93828],{},"Proč mají křivky užitečnosti záporný sklon?",[123,93830,93831],{},"Jak se vypočte mezní míra komoditní substituce? Vysvětlete, co vypočtená hodnota vyjadřuje.",[115,93833,93835],{"id":93834},"úlohy-teorie-užitečnosti-61-67","Úlohy — teorie užitečnosti (6.1 – 6.7)",[724,93837,93838,93841,93842,83723,93884,1343,93912,1343,93940,93968],{},[38,93839,93840],{},"6.1"," Užitečnost pro tři zboží — hudbu, čokoládu a sýr je dána vztahem ",[883,93843,93845],{"className":93844},[886],[888,93846,93847],{"xmlns":890},[892,93848,93849,93881],{},[895,93850,93851,93853,93855,93861,93863,93865,93871,93873,93875],{},[898,93852,900],{},[1688,93854,1690],{},[1788,93856,93857,93859],{},[898,93858,1872],{},[1793,93860,1795],{},[1688,93862,1696],{},[1793,93864,64799],{},[1788,93866,93867,93869],{},[898,93868,1872],{},[1793,93870,1806],{},[1688,93872,1696],{},[1793,93874,1806],{},[1788,93876,93877,93879],{},[898,93878,1872],{},[1793,93880,2131],{},[902,93882,93883],{"encoding":904},"U = Q_1 + 1{,}5 Q_2 + 2 Q_3",[883,93885,93887],{"className":93886},[886],[888,93888,93889],{"xmlns":890},[892,93890,93891,93909],{},[895,93892,93893,93895,93897,93899,93901,93903,93905,93907],{},[898,93894,900],{},[1688,93896,2066],{"stretchy":2065},[1793,93898,2616],{},[1688,93900,1733],{"separator":1732},[1793,93902,1806],{},[1688,93904,1733],{"separator":1732},[1793,93906,1806],{},[1688,93908,2076],{"stretchy":2065},[902,93910,93911],{"encoding":904},"U(4, 2, 2)",[883,93913,93915],{"className":93914},[886],[888,93916,93917],{"xmlns":890},[892,93918,93919,93937],{},[895,93920,93921,93923,93925,93927,93929,93931,93933,93935],{},[898,93922,900],{},[1688,93924,2066],{"stretchy":2065},[1793,93926,1795],{},[1688,93928,1733],{"separator":1732},[1793,93930,2616],{},[1688,93932,1733],{"separator":1732},[1793,93934,1806],{},[1688,93936,2076],{"stretchy":2065},[902,93938,93939],{"encoding":904},"U(1, 4, 2)",[883,93941,93943],{"className":93942},[886],[888,93944,93945],{"xmlns":890},[892,93946,93947,93965],{},[895,93948,93949,93951,93953,93955,93957,93959,93961,93963],{},[898,93950,900],{},[1688,93952,2066],{"stretchy":2065},[1793,93954,1806],{},[1688,93956,1733],{"separator":1732},[1793,93958,2131],{},[1688,93960,1733],{"separator":1732},[1793,93962,1795],{},[1688,93964,2076],{"stretchy":2065},[902,93966,93967],{"encoding":904},"U(2, 3, 1)",". (b) Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků v (a).",[724,93970,93971,93974,93975,94027,94028,1343,94054,1343,94080,1343,94106,1343,94132,1343,94158,1343,94184,94210],{},[38,93972,93973],{},"6.2"," Je dána užitečnost ",[883,93976,93978],{"className":93977},[886],[888,93979,93980],{"xmlns":890},[892,93981,93982,94024],{},[895,93983,93984,93986,93988,93990,94004,94018],{},[898,93985,900],{},[1688,93987,1690],{},[1793,93989,1806],{},[1814,93991,93992,93994,93996],{},[898,93993,1872],{},[1793,93995,1795],{},[895,93997,93998,94000,94002],{},[1793,93999,1795],{},[898,94001,4930],{"mathvariant":1822},[1793,94003,2131],{},[1814,94005,94006,94008,94010],{},[898,94007,1872],{},[1793,94009,1806],{},[895,94011,94012,94014,94016],{},[1793,94013,1795],{},[898,94015,4930],{"mathvariant":1822},[1793,94017,1806],{},[1788,94019,94020,94022],{},[898,94021,1872],{},[1793,94023,2131],{},[902,94025,94026],{"encoding":904},"U = 2 Q_1^{1\u002F3} Q_2^{1\u002F2} Q_3"," pro tři zboží. Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků ",[883,94029,94031],{"className":94030},[886],[888,94032,94033],{"xmlns":890},[892,94034,94035,94051],{},[895,94036,94037,94039,94041,94043,94045,94047,94049],{},[1688,94038,2066],{"stretchy":2065},[1793,94040,5821],{},[1688,94042,1733],{"separator":1732},[1793,94044,66837],{},[1688,94046,1733],{"separator":1732},[1793,94048,3121],{},[1688,94050,2076],{"stretchy":2065},[902,94052,94053],{"encoding":904},"(36, 27, 10)",[883,94055,94057],{"className":94056},[886],[888,94058,94059],{"xmlns":890},[892,94060,94061,94077],{},[895,94062,94063,94065,94067,94069,94071,94073,94075],{},[1688,94064,2066],{"stretchy":2065},[1793,94066,42080],{},[1688,94068,1733],{"separator":1732},[1793,94070,5841],{},[1688,94072,1733],{"separator":1732},[1793,94074,9290],{},[1688,94076,2076],{"stretchy":2065},[902,94078,94079],{"encoding":904},"(64, 8, 20)",[883,94081,94083],{"className":94082},[886],[888,94084,94085],{"xmlns":890},[892,94086,94087,94103],{},[895,94088,94089,94091,94093,94095,94097,94099,94101],{},[1688,94090,2066],{"stretchy":2065},[1793,94092,5260],{},[1688,94094,1733],{"separator":1732},[1793,94096,42080],{},[1688,94098,1733],{"separator":1732},[1793,94100,5841],{},[1688,94102,2076],{"stretchy":2065},[902,94104,94105],{"encoding":904},"(25, 64, 8)",[883,94107,94109],{"className":94108},[886],[888,94110,94111],{"xmlns":890},[892,94112,94113,94129],{},[895,94114,94115,94117,94119,94121,94123,94125,94127],{},[1688,94116,2066],{"stretchy":2065},[1793,94118,2616],{},[1688,94120,1733],{"separator":1732},[1793,94122,72769],{},[1688,94124,1733],{"separator":1732},[1793,94126,2508],{},[1688,94128,2076],{"stretchy":2065},[902,94130,94131],{"encoding":904},"(4, 125, 6)",[883,94133,94135],{"className":94134},[886],[888,94136,94137],{"xmlns":890},[892,94138,94139,94155],{},[895,94140,94141,94143,94145,94147,94149,94151,94153],{},[1688,94142,2066],{"stretchy":2065},[1793,94144,4256],{},[1688,94146,1733],{"separator":1732},[1793,94148,5467],{},[1688,94150,1733],{"separator":1732},[1793,94152,3766],{},[1688,94154,2076],{"stretchy":2065},[902,94156,94157],{"encoding":904},"(9, 40, 12)",[883,94159,94161],{"className":94160},[886],[888,94162,94163],{"xmlns":890},[892,94164,94165,94181],{},[895,94166,94167,94169,94171,94173,94175,94177,94179],{},[1688,94168,2066],{"stretchy":2065},[1793,94170,4256],{},[1688,94172,1733],{"separator":1732},[1793,94174,42080],{},[1688,94176,1733],{"separator":1732},[1793,94178,2501],{},[1688,94180,2076],{"stretchy":2065},[902,94182,94183],{"encoding":904},"(9, 64, 5)",[883,94185,94187],{"className":94186},[886],[888,94188,94189],{"xmlns":890},[892,94190,94191,94207],{},[895,94192,94193,94195,94197,94199,94201,94203,94205],{},[1688,94194,2066],{"stretchy":2065},[1793,94196,42080],{},[1688,94198,1733],{"separator":1732},[1793,94200,5841],{},[1688,94202,1733],{"separator":1732},[1793,94204,3121],{},[1688,94206,2076],{"stretchy":2065},[902,94208,94209],{"encoding":904},"(64, 8, 10)"," a uspořádejte je s neklesající užitečností.",[724,94212,94213,93974,94216,94259,94260,94294,94295,6729,94325,94358,94359,94376,94377,94394],{},[38,94214,94215],{},"6.3",[883,94217,94219],{"className":94218},[886],[888,94220,94221],{"xmlns":890},[892,94222,94223,94257],{},[895,94224,94225,94227,94229,94243],{},[898,94226,900],{},[1688,94228,1690],{},[1814,94230,94231,94233,94235],{},[898,94232,1872],{},[1793,94234,1795],{},[895,94236,94237,94239,94241],{},[1793,94238,1795],{},[898,94240,4930],{"mathvariant":1822},[1793,94242,1806],{},[1814,94244,94245,94247,94249],{},[898,94246,1872],{},[1793,94248,1806],{},[895,94250,94251,94253,94255],{},[1793,94252,1795],{},[898,94254,4930],{"mathvariant":1822},[1793,94256,1806],{},[902,94258,33399],{"encoding":904},". (a) Vypočtěte užitečnost pro ",[883,94261,94263],{"className":94262},[886],[888,94264,94265],{"xmlns":890},[892,94266,94267,94291],{},[895,94268,94269,94275,94277,94279,94281,94287,94289],{},[1788,94270,94271,94273],{},[898,94272,1872],{},[1793,94274,1795],{},[1688,94276,1690],{},[1793,94278,3377],{},[1688,94280,1733],{"separator":1732},[1788,94282,94283,94285],{},[898,94284,1872],{},[1793,94286,1806],{},[1688,94288,1690],{},[1793,94290,46943],{},[902,94292,94293],{"encoding":904},"Q_1 = 50, Q_2 = 80",". (b) Určete mezní užitečnosti ",[883,94296,94298],{"className":94297},[886],[888,94299,94300],{"xmlns":890},[892,94301,94302,94322],{},[895,94303,94304,94306,94312,94314,94316],{},[898,94305,1661],{},[1788,94307,94308,94310],{},[898,94309,900],{},[1793,94311,1795],{},[1688,94313,1733],{"separator":1732},[898,94315,1661],{},[1788,94317,94318,94320],{},[898,94319,900],{},[1793,94321,1806],{},[902,94323,94324],{"encoding":904},"MU_1, MU_2",[883,94326,94328],{"className":94327},[886],[888,94329,94330],{"xmlns":890},[892,94331,94332,94356],{},[895,94333,94334,94340,94342,94344,94346,94352,94354],{},[1788,94335,94336,94338],{},[898,94337,1872],{},[1793,94339,1795],{},[1688,94341,1690],{},[1793,94343,3377],{},[1688,94345,1733],{"separator":1732},[1788,94347,94348,94350],{},[898,94349,1872],{},[1793,94351,1806],{},[1688,94353,1690],{},[1793,94355,46943],{},[902,94357,94293],{"encoding":904}," a výsledky ekonomicky interpretujte. (d) Odhadněte změnu užitečnosti v důsledku změny ",[883,94360,94362],{"className":94361},[886],[888,94363,94364],{"xmlns":890},[892,94365,94366,94374],{},[895,94367,94368],{},[1788,94369,94370,94372],{},[898,94371,1872],{},[1793,94373,1795],{},[902,94375,29242],{"encoding":904}," na 60 a poklesu ",[883,94378,94380],{"className":94379},[886],[888,94381,94382],{"xmlns":890},[892,94383,94384,94392],{},[895,94385,94386],{},[1788,94387,94388,94390],{},[898,94389,1872],{},[1793,94391,1806],{},[902,94393,29261],{"encoding":904}," o 5 vzhledem k hladině dle (a) a porovnejte se skutečnou změnou užitečnosti.",[724,94396,94397,94400,94401,94462,94463,2263],{},[38,94398,94399],{},"6.4"," Je dána funkce ",[883,94402,94404],{"className":94403},[886],[888,94405,94406],{"xmlns":890},[892,94407,94408,94460],{},[895,94409,94410,94412,94414,94420,94422,94428,94430,94432,94446],{},[898,94411,900],{},[1688,94413,2066],{"stretchy":2065},[1788,94415,94416,94418],{},[898,94417,1872],{},[1793,94419,1795],{},[1688,94421,1733],{"separator":1732},[1788,94423,94424,94426],{},[898,94425,1872],{},[1793,94427,1806],{},[1688,94429,2076],{"stretchy":2065},[1688,94431,1690],{},[1814,94433,94434,94436,94438],{},[898,94435,1872],{},[1793,94437,1795],{},[895,94439,94440,94442,94444],{},[1793,94441,1795],{},[898,94443,4930],{"mathvariant":1822},[1793,94445,1806],{},[1814,94447,94448,94450,94452],{},[898,94449,1872],{},[1793,94451,1806],{},[895,94453,94454,94456,94458],{},[1793,94455,1795],{},[898,94457,4930],{"mathvariant":1822},[1793,94459,1806],{},[902,94461,30183],{"encoding":904},". (a) Ověřte, že tato funkce vykazuje vlastnosti funkce užitečnosti. (b) Najděte a načrtněte křivky ",[883,94464,94466],{"className":94465},[886],[888,94467,94468],{"xmlns":890},[892,94469,94470,94560],{},[895,94471,94472,94474,94476,94482,94484,94486,94488,94490,94492,94494,94500,94502,94504,94506,94508,94510,94512,94514,94516,94522,94524,94526,94528,94530,94532,94534,94540,94542,94544,94546,94548,94550,94552,94558],{},[898,94473,900],{},[1688,94475,2066],{"stretchy":2065},[1788,94477,94478,94480],{},[898,94479,1872],{},[1793,94481,1795],{},[1688,94483,1733],{"separator":1732},[1793,94485,1795],{},[1688,94487,2076],{"stretchy":2065},[1688,94489,1733],{"separator":1732},[898,94491,900],{},[1688,94493,2066],{"stretchy":2065},[1788,94495,94496,94498],{},[898,94497,1872],{},[1793,94499,1795],{},[1688,94501,1733],{"separator":1732},[1793,94503,1806],{},[1688,94505,2076],{"stretchy":2065},[1688,94507,1733],{"separator":1732},[898,94509,900],{},[1688,94511,2066],{"stretchy":2065},[1793,94513,1795],{},[1688,94515,1733],{"separator":1732},[1788,94517,94518,94520],{},[898,94519,1872],{},[1793,94521,1806],{},[1688,94523,2076],{"stretchy":2065},[1688,94525,1733],{"separator":1732},[898,94527,900],{},[1688,94529,2066],{"stretchy":2065},[1793,94531,1806],{},[1688,94533,1733],{"separator":1732},[1788,94535,94536,94538],{},[898,94537,1872],{},[1793,94539,1806],{},[1688,94541,2076],{"stretchy":2065},[1688,94543,1733],{"separator":1732},[898,94545,900],{},[1688,94547,2066],{"stretchy":2065},[1793,94549,2131],{},[1688,94551,1733],{"separator":1732},[1788,94553,94554,94556],{},[898,94555,1872],{},[1793,94557,1806],{},[1688,94559,2076],{"stretchy":2065},[902,94561,94562],{"encoding":904},"U(Q_1, 1), U(Q_1, 2), U(1, Q_2), U(2, Q_2), U(3, Q_2)",[724,94564,94565,93974,94568,94612,94613,94721,94722,1343,94747,1343,94772,94814,94815,1343,94844,94869],{},[38,94566,94567],{},"6.5",[883,94569,94571],{"className":94570},[886],[888,94572,94573],{"xmlns":890},[892,94574,94575,94609],{},[895,94576,94577,94579,94581,94595],{},[898,94578,900],{},[1688,94580,1690],{},[1814,94582,94583,94585,94587],{},[898,94584,1872],{},[1793,94586,1795],{},[895,94588,94589,94591,94593],{},[1793,94590,1806],{},[898,94592,4930],{"mathvariant":1822},[1793,94594,2131],{},[1814,94596,94597,94599,94601],{},[898,94598,1872],{},[1793,94600,1806],{},[895,94602,94603,94605,94607],{},[1793,94604,1795],{},[898,94606,4930],{"mathvariant":1822},[1793,94608,2131],{},[902,94610,94611],{"encoding":904},"U = Q_1^{2\u002F3} Q_2^{1\u002F3}",". (a) Najděte rovnici křivek užitečnosti. (b) Určete a načrtněte křivky ",[883,94614,94616],{"className":94615},[886],[888,94617,94618],{"xmlns":890},[892,94619,94620,94718],{},[895,94621,94622,94624,94626,94632,94634,94640,94642,94644,94646,94648,94650,94652,94658,94660,94662,94664,94666,94668,94670,94676,94678,94680,94682,94684,94686,94688,94690,94692,94698,94700,94702,94704,94706,94708,94710,94716],{},[898,94623,900],{},[1688,94625,2066],{"stretchy":2065},[1788,94627,94628,94630],{},[898,94629,1872],{},[1793,94631,1795],{},[1688,94633,1733],{"separator":1732},[1788,94635,94636,94638],{},[898,94637,1872],{},[1793,94639,1806],{},[1688,94641,2076],{"stretchy":2065},[1688,94643,1690],{},[1793,94645,1806],{},[1688,94647,1733],{"separator":1732},[898,94649,900],{},[1688,94651,2066],{"stretchy":2065},[1788,94653,94654,94656],{},[898,94655,1872],{},[1793,94657,1795],{},[1688,94659,1733],{"separator":1732},[1793,94661,2131],{},[1688,94663,2076],{"stretchy":2065},[1688,94665,1733],{"separator":1732},[898,94667,900],{},[1688,94669,2066],{"stretchy":2065},[1788,94671,94672,94674],{},[898,94673,1872],{},[1793,94675,1795],{},[1688,94677,1733],{"separator":1732},[1793,94679,1806],{},[1688,94681,2076],{"stretchy":2065},[1688,94683,1733],{"separator":1732},[898,94685,900],{},[1688,94687,2066],{"stretchy":2065},[1793,94689,1806],{},[1688,94691,1733],{"separator":1732},[1788,94693,94694,94696],{},[898,94695,1872],{},[1793,94697,1806],{},[1688,94699,2076],{"stretchy":2065},[1688,94701,1733],{"separator":1732},[898,94703,900],{},[1688,94705,2066],{"stretchy":2065},[1793,94707,2131],{},[1688,94709,1733],{"separator":1732},[1788,94711,94712,94714],{},[898,94713,1872],{},[1793,94715,1806],{},[1688,94717,2076],{"stretchy":2065},[902,94719,94720],{"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 ",[883,94723,94725],{"className":94724},[886],[888,94726,94727],{"xmlns":890},[892,94728,94729,94744],{},[895,94730,94731,94733,94735,94737,94739,94742],{},[898,94732,4512],{},[1688,94734,2748],{"stretchy":2065},[1793,94736,64799],{},[1688,94738,8681],{"separator":1732},[1793,94740,94741],{},"3,555",[1688,94743,2763],{"stretchy":2065},[902,94745,94746],{"encoding":904},"A[1{,}5; 3{,}555]",[883,94748,94750],{"className":94749},[886],[888,94751,94752],{"xmlns":890},[892,94753,94754,94769],{},[895,94755,94756,94758,94760,94762,94764,94767],{},[898,94757,23494],{},[1688,94759,2748],{"stretchy":2065},[1793,94761,53439],{},[1688,94763,8681],{"separator":1732},[1793,94765,94766],{},"1,28",[1688,94768,2763],{"stretchy":2065},[902,94770,94771],{"encoding":904},"B[2{,}5; 1{,}28]",[883,94773,94775],{"className":94774},[886],[888,94776,94777],{"xmlns":890},[892,94778,94779,94811],{},[895,94780,94781,94783,94785,94787,94789,94791,94793,94799,94801,94803,94805,94807,94809],{},[898,94782,1693],{},[1688,94784,2748],{"stretchy":2065},[1793,94786,1806],{},[1688,94788,8681],{"separator":1732},[898,94790,900],{},[1688,94792,2066],{"stretchy":2065},[1788,94794,94795,94797],{},[898,94796,1872],{},[1793,94798,1795],{},[1688,94800,1733],{"separator":1732},[1793,94802,2131],{},[1688,94804,2076],{"stretchy":2065},[1688,94806,1690],{},[1793,94808,2131],{},[1688,94810,2763],{"stretchy":2065},[902,94812,94813],{"encoding":904},"C[2; U(Q_1, 3) = 3]"," (c) Leží některé z bodů ",[883,94816,94818],{"className":94817},[886],[888,94819,94820],{"xmlns":890},[892,94821,94822,94841],{},[895,94823,94824,94826,94828,94830,94832,94834,94836,94839],{},[898,94825,4440],{},[1688,94827,2748],{"stretchy":2065},[1793,94829,2131],{},[1688,94831,8681],{"separator":1732},[1793,94833,1795],{},[1688,94835,8681],{"separator":1732},[1793,94837,94838],{},"0,832",[1688,94840,2763],{"stretchy":2065},[902,94842,94843],{"encoding":904},"D[3; 1; 0{,}832]",[883,94845,94847],{"className":94846},[886],[888,94848,94849],{"xmlns":890},[892,94850,94851,94866],{},[895,94852,94853,94855,94857,94859,94861,94864],{},[898,94854,4509],{},[1688,94856,2748],{"stretchy":2065},[1793,94858,53439],{},[1688,94860,8681],{"separator":1732},[1793,94862,94863],{},"4,32",[1688,94865,2763],{"stretchy":2065},[902,94867,94868],{"encoding":904},"E[2{,}5; 4{,}32]"," na téže křivce užitečnosti? Když ano, určete ji.",[724,94871,94872,93974,94875,94918,94919,6729,94932,94966,94967,94984,94985,95002],{},[38,94873,94874],{},"6.6",[883,94876,94878],{"className":94877},[886],[888,94879,94880],{"xmlns":890},[892,94881,94882,94916],{},[895,94883,94884,94886,94888,94902],{},[898,94885,900],{},[1688,94887,1690],{},[1814,94889,94890,94892,94894],{},[898,94891,1872],{},[1793,94893,1795],{},[895,94895,94896,94898,94900],{},[1793,94897,1806],{},[898,94899,4930],{"mathvariant":1822},[1793,94901,2131],{},[1814,94903,94904,94906,94908],{},[898,94905,1872],{},[1793,94907,1806],{},[895,94909,94910,94912,94914],{},[1793,94911,1795],{},[898,94913,4930],{"mathvariant":1822},[1793,94915,2131],{},[902,94917,94611],{"encoding":904},". (a) Najděte mezní míru komoditní substituce ",[883,94920,94922],{"className":94921},[886],[888,94923,94924],{"xmlns":890},[892,94925,94926,94930],{},[895,94927,94928],{},[2041,94929,1670],{},[902,94931,28478],{"encoding":904},[883,94933,94935],{"className":94934},[886],[888,94936,94937],{"xmlns":890},[892,94938,94939,94963],{},[895,94940,94941,94947,94949,94951,94953,94959,94961],{},[1788,94942,94943,94945],{},[898,94944,1872],{},[1793,94946,1795],{},[1688,94948,1690],{},[1793,94950,3347],{},[1688,94952,1733],{"separator":1732},[1788,94954,94955,94957],{},[898,94956,1872],{},[1793,94958,1806],{},[1688,94960,1690],{},[1793,94962,8633],{},[902,94964,94965],{"encoding":904},"Q_1 = 100, Q_2 = 200"," a výsledek ekonomicky interpretujte. (c) Odhadněte, o kolik je třeba změnit ",[883,94968,94970],{"className":94969},[886],[888,94971,94972],{"xmlns":890},[892,94973,94974,94982],{},[895,94975,94976],{},[1788,94977,94978,94980],{},[898,94979,1872],{},[1793,94981,1795],{},[902,94983,29242],{"encoding":904},", poklesne-li ",[883,94986,94988],{"className":94987},[886],[888,94989,94990],{"xmlns":890},[892,94991,94992,95000],{},[895,94993,94994],{},[1788,94995,94996,94998],{},[898,94997,1872],{},[1793,94999,1806],{},[902,95001,29261],{"encoding":904}," o 5 vzhledem k hladině dle (b).",[724,95004,95005,95008,95009,95026,95027,95044,95045,95077,95078,95103,95104,95117,95118,1343,95142,1343,95166,2263],{},[38,95006,95007],{},"6.7"," Míra uspokojení z nákupu množství ",[883,95010,95012],{"className":95011},[886],[888,95013,95014],{"xmlns":890},[892,95015,95016,95024],{},[895,95017,95018],{},[1788,95019,95020,95022],{},[898,95021,1872],{},[1793,95023,1795],{},[902,95025,29242],{"encoding":904}," nealko nápojů a množství ",[883,95028,95030],{"className":95029},[886],[888,95031,95032],{"xmlns":890},[892,95033,95034,95042],{},[895,95035,95036],{},[1788,95037,95038,95040],{},[898,95039,1872],{},[1793,95041,1806],{},[902,95043,29261],{"encoding":904}," hamburgerů za týden je dána funkcí užitečnosti ",[883,95046,95048],{"className":95047},[886],[888,95049,95050],{"xmlns":890},[892,95051,95052,95074],{},[895,95053,95054,95056,95058],{},[898,95055,900],{},[1688,95057,1690],{},[8373,95059,95060],{},[895,95061,95062,95068],{},[1788,95063,95064,95066],{},[898,95065,1872],{},[1793,95067,1795],{},[1788,95069,95070,95072],{},[898,95071,1872],{},[1793,95073,1806],{},[902,95075,95076],{"encoding":904},"U = \\sqrt{Q_1 Q_2}",". (a) Najděte vztah pro hodnoty ",[883,95079,95081],{"className":95080},[886],[888,95082,95083],{"xmlns":890},[892,95084,95085,95101],{},[895,95086,95087,95093,95095],{},[1788,95088,95089,95091],{},[898,95090,1872],{},[1793,95092,1795],{},[1688,95094,1733],{"separator":1732},[1788,95096,95097,95099],{},[898,95098,1872],{},[1793,95100,1806],{},[902,95102,35862],{"encoding":904},", pro něž je dosaženo užitečnosti 10 a uveďte několik takových dvojic hodnot. (b) Najděte ",[883,95105,95107],{"className":95106},[886],[888,95108,95109],{"xmlns":890},[892,95110,95111,95115],{},[895,95112,95113],{},[2041,95114,1670],{},[902,95116,28478],{"encoding":904}," na křivce nalezené v (a). (c) Ekonomicky interpretujte smysl ",[883,95119,95121],{"className":95120},[886],[888,95122,95123],{"xmlns":890},[892,95124,95125,95139],{},[895,95126,95127,95129,95131,95133,95135,95137],{},[2041,95128,1670],{},[1688,95130,2066],{"stretchy":2065},[1793,95132,2501],{},[1688,95134,1733],{"separator":1732},[1793,95136,9290],{},[1688,95138,2076],{"stretchy":2065},[902,95140,95141],{"encoding":904},"\\text{MRCS}(5, 20)",[883,95143,95145],{"className":95144},[886],[888,95146,95147],{"xmlns":890},[892,95148,95149,95163],{},[895,95150,95151,95153,95155,95157,95159,95161],{},[2041,95152,1670],{},[1688,95154,2066],{"stretchy":2065},[1793,95156,9290],{},[1688,95158,1733],{"separator":1732},[1793,95160,2501],{},[1688,95162,2076],{"stretchy":2065},[902,95164,95165],{"encoding":904},"\\text{MRCS}(20, 5)",[883,95167,95169],{"className":95168},[886],[888,95170,95171],{"xmlns":890},[892,95172,95173,95187],{},[895,95174,95175,95177,95179,95181,95183,95185],{},[2041,95176,1670],{},[1688,95178,2066],{"stretchy":2065},[1793,95180,1806],{},[1688,95182,1733],{"separator":1732},[1793,95184,3377],{},[1688,95186,2076],{"stretchy":2065},[902,95188,95189],{"encoding":904},"\\text{MRCS}(2, 50)",[4124,95191,95192],{},[724,95193,95194,95196,95197,2263],{},[883,95195,4828],{}," Úlohy 6.8 – 6.13 (optimalizace, Lagrange, poptávka)\nÚlohy navázané na maximalizaci užitečnosti, minimalizaci výdajů a odvození Marshallových\u002FHicksových funkcí poptávky jsou na stránce ",[207,95198,95201],{"className":95199,"dataFsResolvedFilePath":911,"href":95200},[210],"\u002Fwiki\u002Foptimalizace-spotrebitele#Úlohy k optimalizaci","Optimalizace spotřebitele — Úlohy",[115,95203,15967],{"id":15966},[120,95205,95206,95212,95217,95223,95276,95286,95332,95387,95450,95507,95562,95601],{},[123,95207,95208,95211],{},[38,95209,95210],{},"Užitečnost (utility)"," — ordinálně měřený ukazatel uspokojení spotřebitele ze svazku zboží.",[123,95213,95214,95216],{},[38,95215,87109],{}," — historická pojetí užitečnosti; v současnosti se preferuje ordinalistický.",[123,95218,95219,95222],{},[38,95220,95221],{},"Pět předpokladů chování spotřebitele"," — racionalita, ordinalita, konzistence a tranzitivita, rostoucí užitečnost, klesající mezní užitečnost.",[123,95224,95225,95227,95228,95241,95242,2263],{},[38,95226,87436],{}," — uspořádaná ",[883,95229,95231],{"className":95230},[886],[888,95232,95233],{"xmlns":890},[892,95234,95235,95239],{},[895,95236,95237],{},[898,95238,37100],{},[902,95240,37100],{"encoding":904},"-tice ",[883,95243,95245],{"className":95244},[886],[888,95246,95247],{"xmlns":890},[892,95248,95249,95273],{},[895,95250,95251,95253,95259,95261,95263,95265,95271],{},[1688,95252,2066],{"stretchy":2065},[1788,95254,95255,95257],{},[898,95256,1872],{},[1793,95258,1795],{},[1688,95260,1733],{"separator":1732},[1688,95262,9899],{},[1688,95264,1733],{"separator":1732},[1788,95266,95267,95269],{},[898,95268,1872],{},[898,95270,37100],{},[1688,95272,2076],{"stretchy":2065},[902,95274,95275],{"encoding":904},"(Q_1, \\dots, Q_n)",[123,95277,95278,95281,95282,95285],{},[38,95279,95280],{},"Relace preference"," — uspořádání svazků podle užitečnosti; ",[38,95283,95284],{},"indiferentní svazky"," mají stejnou užitečnost.",[123,95287,95288,2170,95291,95331],{},[38,95289,95290],{},"Funkce užitečnosti",[883,95292,95294],{"className":95293},[886],[888,95295,95296],{"xmlns":890},[892,95297,95298,95328],{},[895,95299,95300,95302,95304,95306,95308,95314,95316,95318,95320,95326],{},[898,95301,900],{},[1688,95303,1690],{},[898,95305,900],{},[1688,95307,2066],{"stretchy":2065},[1788,95309,95310,95312],{},[898,95311,1872],{},[1793,95313,1795],{},[1688,95315,1733],{"separator":1732},[1688,95317,9899],{},[1688,95319,1733],{"separator":1732},[1788,95321,95322,95324],{},[898,95323,1872],{},[898,95325,37100],{},[1688,95327,2076],{"stretchy":2065},[902,95329,95330],{"encoding":904},"U = U(Q_1, \\dots, Q_n)"," — vzorec (6.1); ekvivalentní až na monotónní transformaci.",[123,95333,95334,2170,95337,95366,95367,2170,95370,95386],{},[38,95335,95336],{},"Mezní užitečnost",[883,95338,95340],{"className":95339},[886],[888,95341,95342],{"xmlns":890},[892,95343,95344,95364],{},[895,95345,95346,95348,95354,95356],{},[898,95347,1661],{},[1788,95349,95350,95352],{},[898,95351,900],{},[898,95353,18035],{},[1688,95355,1690],{},[1814,95357,95358,95360,95362],{},[898,95359,900],{},[898,95361,18035],{},[1688,95363,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[902,95365,86893],{"encoding":904}," — vzorec (6.2); ",[38,95368,95369],{},"totální diferenciál",[883,95371,95373],{"className":95372},[886],[888,95374,95375],{"xmlns":890},[892,95376,95377,95383],{},[895,95378,95379,95381],{},[898,95380,2073],{"mathvariant":1822},[898,95382,900],{},[902,95384,95385],{"encoding":904},"\\mathrm{d} U"," — (6.3).",[123,95388,95389,95391,95392,95416,95417,95449],{},[38,95390,89072],{}," — (6.4) ",[883,95393,95395],{"className":95394},[886],[888,95396,95397],{"xmlns":890},[892,95398,95399,95413],{},[895,95400,95401,95409,95411],{},[1814,95402,95403,95405,95407],{},[898,95404,900],{},[898,95406,18035],{},[1688,95408,1824],{"mathvariant":1822,"lspace":1823,"rspace":1823},[1688,95410,3665],{},[1793,95412,1779],{},[902,95414,95415],{"encoding":904},"U'_i > 0",", (6.5) ",[883,95418,95420],{"className":95419},[886],[888,95421,95422],{"xmlns":890},[892,95423,95424,95446],{},[895,95425,95426,95442,95444],{},[1814,95427,95428,95430,95436],{},[898,95429,900],{},[895,95431,95432,95434],{},[898,95433,18035],{},[898,95435,18035],{},[895,95437,95438,95440],{},[1688,95439,1824],{"mathvariant":1822},[1688,95441,1824],{"mathvariant":1822},[1688,95443,3704],{},[1793,95445,1779],{},[902,95447,95448],{"encoding":904},"U''_{ii} \u003C 0"," (zákon klesající mezní užitečnosti).",[123,95451,95452,2170,95454,95485,95486,2263],{},[38,95453,90860],{},[883,95455,95457],{"className":95456},[886],[888,95458,95459],{"xmlns":890},[892,95460,95461,95483],{},[895,95462,95463,95465,95467,95475],{},[898,95464,900],{},[1688,95466,1690],{},[1814,95468,95469,95471,95473],{},[898,95470,1872],{},[1793,95472,1795],{},[898,95474,207],{},[1814,95476,95477,95479,95481],{},[898,95478,1872],{},[1793,95480,1806],{},[898,95482,1918],{},[902,95484,36043],{"encoding":904}," — (6.6), speciálně ",[883,95487,95489],{"className":95488},[886],[888,95490,95491],{"xmlns":890},[892,95492,95493,95505],{},[895,95494,95495,95497,95499,95501,95503],{},[898,95496,1918],{},[1688,95498,1690],{},[1793,95500,1795],{},[1688,95502,1954],{},[898,95504,207],{},[902,95506,91014],{"encoding":904},[123,95508,95509,2170,95512,95547,95548,95561],{},[38,95510,95511],{},"Křivky užitečnosti (indiferenční)",[883,95513,95515],{"className":95514},[886],[888,95516,95517],{"xmlns":890},[892,95518,95519,95545],{},[895,95520,95521,95523,95525,95531,95533,95539,95541,95543],{},[898,95522,900],{},[1688,95524,2066],{"stretchy":2065},[1788,95526,95527,95529],{},[898,95528,1872],{},[1793,95530,1795],{},[1688,95532,1733],{"separator":1732},[1788,95534,95535,95537],{},[898,95536,1872],{},[1793,95538,1806],{},[1688,95540,2076],{"stretchy":2065},[1688,95542,1690],{},[898,95544,2031],{},[902,95546,10021],{"encoding":904}," — (6.7), (6.8); čtyři vlastnosti: klesající, neprotínající se, vzdálenější od počátku = vyšší ",[883,95549,95551],{"className":95550},[886],[888,95552,95553],{"xmlns":890},[892,95554,95555,95559],{},[895,95556,95557],{},[898,95558,900],{},[902,95560,900],{"encoding":904},", konvexní.",[123,95563,95564,2170,95566,95600],{},[38,95565,92405],{},[883,95567,95569],{"className":95568},[886],[888,95570,95571],{"xmlns":890},[892,95572,95573,95597],{},[895,95574,95575,95577,95579,95581,95587,95589,95591],{},[2041,95576,1670],{},[1688,95578,1690],{},[898,95580,1661],{},[1788,95582,95583,95585],{},[898,95584,900],{},[1793,95586,1795],{},[898,95588,4930],{"mathvariant":1822},[898,95590,1661],{},[1788,95592,95593,95595],{},[898,95594,900],{},[1793,95596,1806],{},[902,95598,95599],{"encoding":904},"\\text{MRCS} = MU_1 \u002F MU_2"," — (6.9); vztahy (6.10), (6.11).",[123,95602,95603,2170,95606,10022,95635,95638],{},[38,95604,95605],{},"Podmínka optimality",[883,95607,95609],{"className":95608},[886],[888,95610,95611],{"xmlns":890},[892,95612,95613,95633],{},[895,95614,95615,95617,95619,95625,95627],{},[2041,95616,1670],{},[1688,95618,1690],{},[1788,95620,95621,95623],{},[898,95622,1727],{},[1793,95624,1795],{},[898,95626,4930],{"mathvariant":1822},[1788,95628,95629,95631],{},[898,95630,1727],{},[1793,95632,1806],{},[902,95634,28238],{"encoding":904},[207,95636,36994],{"className":95637,"dataFsResolvedFilePath":911,"href":912},[210]," pro plné odvození.",[115,95640,4049],{"id":4048},[120,95642,95643,95680,95721,95731],{},[123,95644,95645,2170,95648,95651,95652,95665,95666,95679],{},[38,95646,95647],{},"Navazující téma:",[207,95649,913],{"className":95650,"dataFsResolvedFilePath":911,"href":912},[210]," (Lagrange, max ",[883,95653,95655],{"className":95654},[886],[888,95656,95657],{"xmlns":890},[892,95658,95659,95663],{},[895,95660,95661],{},[898,95662,900],{},[902,95664,900],{"encoding":904},", min ",[883,95667,95669],{"className":95668},[886],[888,95670,95671],{"xmlns":890},[892,95672,95673,95677],{},[895,95674,95675],{},[898,95676,4509],{},[902,95678,4509],{"encoding":904},", funkce poptávky, Příklady 6.5–6.8, úlohy 6.8–6.13).",[123,95681,95682,2170,95685,11344,95688,86648,95691,95694,95695,95698,95699,18890,95717,95720],{},[38,95683,95684],{},"Související pojmy:",[207,95686,784],{"className":95687,"dataFsResolvedFilePath":782,"href":783},[210],[207,95689,2622],{"className":95690,"dataFsResolvedFilePath":764,"href":765},[210],[207,95692,11339],{"className":95693,"dataFsResolvedFilePath":857,"href":858},[210]," (paralela: MRCS ↔ MRTS, izokvanty ↔ indiferenční křivky, Cobb-Douglas), ",[207,95696,12193],{"className":95697,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallovy poptávkové funkce ",[883,95700,95702],{"className":95701},[886],[888,95703,95704],{"xmlns":890},[892,95705,95706,95714],{},[895,95707,95708],{},[1788,95709,95710,95712],{},[898,95711,4440],{},[898,95713,18035],{},[902,95715,95716],{"encoding":904},"D_i",[207,95718,793],{"className":95719,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace — nástroj pro navazující téma).",[123,95722,95723,2170,95725,1343,95728],{},[38,95724,36943],{},[207,95726,1094],{"className":95727,"dataFsResolvedFilePath":838,"href":839},[210],[207,95729,1101],{"className":95730,"dataFsResolvedFilePath":868,"href":869},[210],[123,95732,95733,2170,95735],{},[38,95734,16451],{},[207,95736,16455],{"className":95737,"dataFsResolvedFilePath":2210,"href":2211},[210],{"title":641,"searchDepth":642,"depth":642,"links":95739},[95740,95741,95742,95745,95746,95749,95753,95754,95757,95758,95759,95760,95761,95762,95763],{"id":12258,"depth":642,"text":12259},{"id":87032,"depth":642,"text":87033},{"id":87092,"depth":642,"text":87093,"children":95743},[95744],{"id":87108,"depth":649,"text":87109},{"id":87415,"depth":642,"text":87416},{"id":88275,"depth":642,"text":88276,"children":95747},[95748],{"id":88822,"depth":649,"text":80451},{"id":89071,"depth":642,"text":89072,"children":95750},[95751],{"id":89944,"depth":649,"text":95752},"Příklad 6.2 — ověření vlastností a dopočet pro U=Q11\u002F2Q21\u002F3U = Q_1^{1\u002F2} Q_2^{1\u002F3}",{"id":90859,"depth":642,"text":90860},{"id":91395,"depth":642,"text":91396,"children":95755},[95756],{"id":92169,"depth":649,"text":92170},{"id":92399,"depth":642,"text":92400},{"id":93160,"depth":642,"text":93161},{"id":93698,"depth":642,"text":93699},{"id":50121,"depth":642,"text":50122},{"id":93834,"depth":642,"text":93835},{"id":15966,"depth":642,"text":15967},{"id":4048,"depth":642,"text":4049},{},"\u002Ftopics\u002Fuzitecnost",{"title":86816,"description":641},[1138,1137],"topics\u002Fuzitecnost",[1128,2225,95770,86810,11374,95771],"mezni-uzitecnost","mrcs","xXggD9rfV5faUAk1b2B3YYbozpQLu-pObiMaZX5f7yI",{"id":95774,"title":757,"body":95775,"course":1128,"courses":659,"created":1129,"description":96048,"extension":661,"meta":96049,"navigation":664,"path":96050,"seo":96051,"sources":96052,"stem":96053,"tags":96054,"type":4113,"updated":677,"__hash__":96060},"topics\u002Ftopics\u002Fzaklady-matematicke-ekonomie.md",{"type":9,"value":95776,"toc":96040},[95777,95780,95787,95794,95798,95808,95810,95844,95848,95891,95894,95952,95956,95986,95990,96011,96013],[12,95778,757],{"id":95779},"základy-matematické-ekonomie",[724,95781,95782,95783,95786],{},"Úvodní pojmy a princip modelování v ",[207,95784,16627],{"className":95785,"dataFsResolvedFilePath":2210,"href":2211},[210],". Slouží jako vstupní bod pro celý kurz — bez těchto pojmů nedávají další kapitoly smysl.",[724,95788,95789],{},[2821,95790],{"alt":95791,"className":95792,"src":95793},"imek-model-promenne",[210,2825],"\u002Fwiki-assets\u002Fimek-model-promenne.jpeg",[115,95795,95797],{"id":95796},"co-je-matematická-ekonomie","Co je matematická ekonomie",[724,95799,95800,95803,95804,95807],{},[38,95801,95802],{},"Vědní disciplína",", která ekonomické vztahy vyjadřuje ",[38,95805,95806],{},"exaktními (matematickými) prostředky"," a provádí jejich analýzu. Cílem není jen popis, ale i predikce a optimalizace.",[115,95809,15967],{"id":15966},[120,95811,95812,95818,95824,95830,95839],{},[123,95813,95814,95817],{},[38,95815,95816],{},"Model"," — zjednodušený obraz reálné situace nebo jevu. Vždy jde o redukci skutečnosti, ne její kopii.",[123,95819,95820,95823],{},[38,95821,95822],{},"Endogenní proměnné"," — zahrnuté do modelu, mohou se měnit (vysvětlované).",[123,95825,95826,95829],{},[38,95827,95828],{},"Exogenní proměnné"," — nejsou v modelu zahrnuté (potenciálně by mohly), berou se jako dané.",[123,95831,95832,7271,95835,95838],{},[38,95833,95834],{},"Ceteris paribus",[614,95836,95837],{},"za jinak stejných podmínek",". Sledujeme změnu jedné proměnné, ostatní fixní.",[123,95840,95841,95843],{},[38,95842,50875],{}," — odezva endogenních proměnných na změnu některé exogenní.",[115,95845,95847],{"id":95846},"ilustrace-funkce-poptávky","Ilustrace — funkce poptávky",[724,95849,95850,95890],{},[883,95851,95853],{"className":95852},[886],[888,95854,95855],{"xmlns":890},[892,95856,95857,95887],{},[895,95858,95859,95861,95863,95865,95867,95869,95871,95873,95875,95877,95879,95881,95883,95885],{},[898,95860,1872],{},[1688,95862,1690],{},[898,95864,4440],{},[1688,95866,2066],{"stretchy":2065},[898,95868,1727],{},[1688,95870,1733],{"separator":1732},[898,95872,1854],{},[1688,95874,1733],{"separator":1732},[898,95876,18536],{},[1688,95878,1733],{"separator":1732},[898,95880,900],{},[1688,95882,1733],{"separator":1732},[1688,95884,9899],{},[1688,95886,2076],{"stretchy":2065},[902,95888,95889],{"encoding":904},"Q = D(P, Y, N, U, \\ldots)"," — plná (vícefaktorová) funkce poptávky.",[724,95892,95893],{},"Zjednodušení:",[120,95895,95896,95924],{},[123,95897,95898,2170,95901],{},[38,95899,95900],{},"Jednofaktorový model:",[883,95902,95904],{"className":95903},[886],[888,95905,95906],{"xmlns":890},[892,95907,95908,95922],{},[895,95909,95910,95912,95914,95916,95918,95920],{},[898,95911,1872],{},[1688,95913,1690],{},[898,95915,4440],{},[1688,95917,2066],{"stretchy":2065},[898,95919,1727],{},[1688,95921,2076],{"stretchy":2065},[902,95923,4449],{"encoding":904},[123,95925,95926,2170,95929],{},[38,95927,95928],{},"Inverzní zápis:",[883,95930,95932],{"className":95931},[886],[888,95933,95934],{"xmlns":890},[892,95935,95936,95950],{},[895,95937,95938,95940,95942,95944,95946,95948],{},[898,95939,1727],{},[1688,95941,1690],{},[898,95943,4440],{},[1688,95945,2066],{"stretchy":2065},[898,95947,1872],{},[1688,95949,2076],{"stretchy":2065},[902,95951,4896],{"encoding":904},[115,95953,95955],{"id":95954},"principy-řešení-ekonomických-úloh","Principy řešení ekonomických úloh",[152,95957,95958,95967],{},[123,95959,95960,95963,95964,4176],{},[38,95961,95962],{},"Princip rovnováhy"," — hledáme stav, kdy se protichůdné síly vyrovnají (např. tržní rovnováha, viz ",[207,95965,16487],{"className":95966,"dataFsResolvedFilePath":800,"href":801},[210],[123,95968,95969,95972,95973,95976,95977,95980,95981,95985],{},[38,95970,95971],{},"Princip optimalizace"," — hledáme extrém účelové funkce, případně vázaný omezujícími podmínkami (viz ",[207,95974,1145],{"className":95975,"dataFsResolvedFilePath":764,"href":765},[210]," pro 1D, ",[207,95978,16500],{"className":95979,"dataFsResolvedFilePath":782,"href":783},[210]," pro 2D, ",[207,95982,95984],{"className":95983,"dataFsResolvedFilePath":791,"href":792},[210],"lagrangeova-metoda"," pro vázané extrémy).",[115,95987,95989],{"id":95988},"konvence-z-přednášek","Konvence z přednášek",[120,95991,95992,95999,96005],{},[123,95993,95994,95995,95998],{},"Symbol ",[95996,95997,2991],"code",{}," pro přibližné rovnosti (typicky linearizace přes diferenciál).",[123,96000,96001,96002,2263],{},"Numerické výsledky ",[38,96003,96004],{},"na 3 desetinná místa",[123,96006,4152,96007,96010],{},[614,96008,96009],{},"jednotková změna"," má standardní význam (změna o 1).",[115,96012,4049],{"id":4048},[120,96014,96015,96020,96028],{},[123,96016,96017,96019],{},[38,96018,4056],{}," —",[123,96021,96022,2170,96024],{},[38,96023,2179],{},[207,96025,96027],{"className":96026,"dataFsResolvedFilePath":764,"href":765},[210],"Derivace a diferenciál",[123,96029,96030,2170,96032,1343,96036],{},[38,96031,4071],{},[207,96033,96035],{"className":96034,"dataFsResolvedFilePath":745,"href":746},[210],"Souhrn KS 1. blok",[207,96037,96039],{"className":96038,"dataFsResolvedFilePath":2210,"href":2211},[210],"kurz ImeK",{"title":641,"searchDepth":642,"depth":642,"links":96041},[96042,96043,96044,96045,96046,96047],{"id":95796,"depth":642,"text":95797},{"id":15966,"depth":642,"text":15967},{"id":95846,"depth":642,"text":95847},{"id":95954,"depth":642,"text":95955},{"id":95988,"depth":642,"text":95989},{"id":4048,"depth":642,"text":4049},"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":96048},[1135],"topics\u002Fzaklady-matematicke-ekonomie",[1128,96055,96056,96057,96058,96059],"model","endogenni","exogenni","ceteris-paribus","komparativni-statika","UZ1xD3l_gK41y8KlCBmpjprMOjIWmHZR8WZt-takTSI",{"id":96062,"title":96063,"body":96064,"course":1128,"courses":659,"created":9809,"description":641,"extension":661,"meta":100336,"navigation":664,"path":100337,"seo":100338,"sources":100339,"stem":100340,"tags":100341,"type":4113,"updated":677,"__hash__":100345},"topics\u002Ftopics\u002Fzdaneni-trhu.md","Zdanění trhu — dopady daně na rovnováhu",{"type":9,"value":96065,"toc":100319},[96066,96069,96163,96167,96189,96203,96255,96257,96261,96324,96367,96386,96549,96648,96651,96718,96722,96851,96890,96920,97032,97077,97143,97196,97272,97328,97330,97334,97398,97442,97462,97623,97626,97710,97807,97810,97876,97880,97929,97955,98060,98124,98129,98225,98272,98274,98277,98299,98341,98348,98381,98383,98454,98508,98617,98621,98710,98786,99050,99088,99090,99094,99097,99104,99415,99418,99476,99656,99685,99687,99691,99697,99835,99844,99846,99848,100273,100275,100277],[12,96067,96063],{"id":96068},"zdanění-trhu-dopady-daně-na-rovnováhu",[4124,96070,96071],{},[724,96072,96073,42868,96075,96088,96089,96092,96093,96095,96096,96099,96100,96121,96122,96145,96146,96149,96150,2263],{},[883,96074,4412],{},[883,96076,96078],{"className":96077},[886],[888,96079,96080],{"xmlns":890},[892,96081,96082,96086],{},[895,96083,96084],{},[898,96085,3035],{},[902,96087,3035],{"encoding":904}," uložená na každou prodanou jednotku zboží posouvá jednu z křivek — ",[38,96090,96091],{},"nabídku"," (je-li daň uložena výrobci) nebo ",[38,96094,87100],{}," (je-li uložena spotřebiteli). Výsledné ",[38,96097,96098],{},"daňové břemeno"," se dělí mezi obě strany trhu na ",[883,96101,96103],{"className":96102},[886],[888,96104,96105],{"xmlns":890},[892,96106,96107,96119],{},[895,96108,96109],{},[1788,96110,96111,96113],{},[898,96112,3035],{},[895,96114,96115,96117],{},[898,96116,42917],{},[898,96118,724],{},[902,96120,42922],{"encoding":904}," (spotřebitel) a ",[883,96123,96125],{"className":96124},[886],[888,96126,96127],{"xmlns":890},[892,96128,96129,96143],{},[895,96130,96131],{},[1788,96132,96133,96135],{},[898,96134,3035],{},[895,96136,96137,96139,96141],{},[898,96138,42940],{},[898,96140,2282],{},[898,96142,2046],{},[902,96144,42947],{"encoding":904}," (výrobce). Klíčovým zjištěním je ",[38,96147,96148],{},"ekvivalence obou přístupů",": rovnovážné množství i čistá cena pro výrobce jsou v obou režimech totožné; liší se pouze nominální cena na trhu o ",[883,96151,96153],{"className":96152},[886],[888,96154,96155],{"xmlns":890},[892,96156,96157,96161],{},[895,96158,96159],{},[898,96160,3035],{},[902,96162,3035],{"encoding":904},[115,96164,96166],{"id":96165},"dvě-formy-zdanění","Dvě formy zdanění",[724,96168,96169,96170,96188],{},"Uvažujme jednotkovou daň ",[883,96171,96173],{"className":96172},[886],[888,96174,96175],{"xmlns":890},[892,96176,96177,96185],{},[895,96178,96179,96181,96183],{},[898,96180,3035],{},[1688,96182,3665],{},[1793,96184,1779],{},[902,96186,96187],{"encoding":904},"T > 0"," (Kč na kus), kterou stát ukládá na každou prodanou jednotku zboží. Daň může být uložena buď:",[120,96190,96191,96197],{},[123,96192,96193,96196],{},[38,96194,96195],{},"(a) výrobci"," — výrobce ji musí odvést státu z každé prodané jednotky,",[123,96198,96199,96202],{},[38,96200,96201],{},"(b) spotřebiteli"," — spotřebitel ji platí navíc k ceně, kterou si účtuje prodejce.",[724,96204,96205,96206,96219,96220,96223,96224,2263],{},"V obou případech dochází k posunu jedné z křivek o ",[883,96207,96209],{"className":96208},[886],[888,96210,96211],{"xmlns":890},[892,96212,96213,96217],{},[895,96214,96215],{},[898,96216,3035],{},[902,96218,3035],{"encoding":904}," svisle (buď nabídky nahoru, nebo poptávky dolů) a k rozdělení ",[38,96221,96222],{},"daňového břemene"," mezi spotřebitele a výrobce. Výchozí rovnovážný bod bez daně označujeme ",[883,96225,96227],{"className":96226},[886],[888,96228,96229],{"xmlns":890},[892,96230,96231,96253],{},[895,96232,96233,96235,96237,96243,96245,96251],{},[898,96234,4509],{},[1688,96236,2748],{"stretchy":2065},[1850,96238,96239,96241],{},[898,96240,1872],{},[898,96242,4509],{},[1688,96244,1733],{"separator":1732},[1850,96246,96247,96249],{},[898,96248,1727],{},[898,96250,4509],{},[1688,96252,2763],{"stretchy":2065},[902,96254,41607],{"encoding":904},[37210,96256],{},[115,96258,96260],{"id":96259},"daň-uložená-výrobci","Daň uložená výrobci",[724,96262,96263,96264,96277,96278,96295,96296,96323],{},"Je-li daň ",[883,96265,96267],{"className":96266},[886],[888,96268,96269],{"xmlns":890},[892,96270,96271,96275],{},[895,96272,96273],{},[898,96274,3035],{},[902,96276,3035],{"encoding":904}," uložena výrobci, pak z podmínky, že výrobce za každou prodanou jednotku obdrží ",[883,96279,96281],{"className":96280},[886],[888,96282,96283],{"xmlns":890},[892,96284,96285,96293],{},[895,96286,96287,96289,96291],{},[898,96288,1727],{},[1688,96290,1954],{},[898,96292,3035],{},[902,96294,41362],{"encoding":904}," (hrubá cena mínus odvod), plyne z rovnice ",[883,96297,96299],{"className":96298},[886],[888,96300,96301],{"xmlns":890},[892,96302,96303,96321],{},[895,96304,96305,96307,96309,96311,96313,96315,96317,96319],{},[898,96306,1727],{},[1688,96308,1954],{},[898,96310,3035],{},[1688,96312,1690],{},[898,96314,1740],{},[1688,96316,2066],{"stretchy":2065},[898,96318,1872],{},[1688,96320,2076],{"stretchy":2065},[902,96322,41391],{"encoding":904}," nová funkce nabídky:",[883,96325,96327],{"className":96326},[886],[888,96328,96329],{"xmlns":890,"display":28306},[892,96330,96331,96365],{},[895,96332,96333,96335,96337,96343,96345,96347,96349,96351,96353,96355,96357,96359,96361,96363],{},[898,96334,1727],{},[1688,96336,1690],{},[1788,96338,96339,96341],{},[898,96340,1740],{},[1793,96342,1795],{},[1688,96344,2066],{"stretchy":2065},[898,96346,1872],{},[1688,96348,2076],{"stretchy":2065},[1688,96350,1690],{},[898,96352,1740],{},[1688,96354,2066],{"stretchy":2065},[898,96356,1872],{},[1688,96358,2076],{"stretchy":2065},[1688,96360,1696],{},[898,96362,3035],{},[898,96364,2263],{"mathvariant":1822},[902,96366,41436],{"encoding":904},[724,96368,96369,96370,2170,96383,96385],{},"Nabídka se tedy posouvá o ",[883,96371,96373],{"className":96372},[886],[888,96374,96375],{"xmlns":890},[892,96376,96377,96381],{},[895,96378,96379],{},[898,96380,3035],{},[902,96382,3035],{"encoding":904},[38,96384,41469],{}," (ekvivalentně doleva). Poptávka se nemění.",[724,96387,96388,96389,96429,96430,4142,96458,96486,96487,96506,96507,96531,96532,4176],{},"Nový rovnovážný bod ",[883,96390,96392],{"className":96391},[886],[888,96393,96394],{"xmlns":890},[892,96395,96396,96426],{},[895,96397,96398,96404,96406,96414,96416,96424],{},[1788,96399,96400,96402],{},[898,96401,4509],{},[1793,96403,1795],{},[1688,96405,2748],{"stretchy":2065},[1814,96407,96408,96410,96412],{},[898,96409,1872],{},[1793,96411,1795],{},[898,96413,4509],{},[1688,96415,1733],{"separator":1732},[1814,96417,96418,96420,96422],{},[898,96419,1727],{},[1793,96421,1795],{},[898,96423,4509],{},[1688,96425,2763],{"stretchy":2065},[902,96427,96428],{"encoding":904},"E_1[Q_1^E, P_1^E]"," splňuje ",[883,96431,96433],{"className":96432},[886],[888,96434,96435],{"xmlns":890},[892,96436,96437,96455],{},[895,96438,96439,96447,96449],{},[1814,96440,96441,96443,96445],{},[898,96442,1872],{},[1793,96444,1795],{},[898,96446,4509],{},[1688,96448,3704],{},[1850,96450,96451,96453],{},[898,96452,1872],{},[898,96454,4509],{},[902,96456,96457],{"encoding":904},"Q_1^E \u003C Q^E",[883,96459,96461],{"className":96460},[886],[888,96462,96463],{"xmlns":890},[892,96464,96465,96483],{},[895,96466,96467,96475,96477],{},[1814,96468,96469,96471,96473],{},[898,96470,1727],{},[1793,96472,1795],{},[898,96474,4509],{},[1688,96476,3665],{},[1850,96478,96479,96481],{},[898,96480,1727],{},[898,96482,4509],{},[902,96484,96485],{"encoding":904},"P_1^E > P^E",". Spotřebitel platí ",[883,96488,96490],{"className":96489},[886],[888,96491,96492],{"xmlns":890},[892,96493,96494,96504],{},[895,96495,96496],{},[1814,96497,96498,96500,96502],{},[898,96499,1727],{},[1793,96501,1795],{},[898,96503,4509],{},[902,96505,48097],{"encoding":904},", výrobci ale zůstává pouze čistá cena ",[883,96508,96510],{"className":96509},[886],[888,96511,96512],{"xmlns":890},[892,96513,96514,96528],{},[895,96515,96516,96524,96526],{},[1814,96517,96518,96520,96522],{},[898,96519,1727],{},[1793,96521,1795],{},[898,96523,4509],{},[1688,96525,1954],{},[898,96527,3035],{},[902,96529,96530],{"encoding":904},"P_1^E - T"," (ta je nižší než původní rovnovážná ",[883,96533,96535],{"className":96534},[886],[888,96536,96537],{"xmlns":890},[892,96538,96539,96547],{},[895,96540,96541],{},[1850,96542,96543,96545],{},[898,96544,1727],{},[898,96546,4509],{},[902,96548,41706],{"encoding":904},[724,96550,96551],{},[614,96552,96553,96554,96584,96585,96598,96599,5925,96616,96629,96630,2263],{},"Obrázek 2.17 (resp. 2.18): Posun ",[883,96555,96557],{"className":96556},[886],[888,96558,96559],{"xmlns":890},[892,96560,96561,96581],{},[895,96562,96563,96565,96567,96573,96575,96577,96579],{},[898,96564,1740],{},[1688,96566,3380],{},[1788,96568,96569,96571],{},[898,96570,1740],{},[1793,96572,1795],{},[1688,96574,1690],{},[898,96576,1740],{},[1688,96578,1696],{},[898,96580,3035],{},[902,96582,96583],{"encoding":904},"S \\to S_1 = S + T","; svislá vzdálenost mezi křivkami je přesně ",[883,96586,96588],{"className":96587},[886],[888,96589,96590],{"xmlns":890},[892,96591,96592,96596],{},[895,96593,96594],{},[898,96595,3035],{},[902,96597,3035],{"encoding":904},". Průsečík ",[883,96600,96602],{"className":96601},[886],[888,96603,96604],{"xmlns":890},[892,96605,96606,96614],{},[895,96607,96608],{},[1788,96609,96610,96612],{},[898,96611,1740],{},[1793,96613,1795],{},[902,96615,41237],{"encoding":904},[883,96617,96619],{"className":96618},[886],[888,96620,96621],{"xmlns":890},[892,96622,96623,96627],{},[895,96624,96625],{},[898,96626,4440],{},[902,96628,4440],{"encoding":904}," je nový rovnovážný bod ",[883,96631,96633],{"className":96632},[886],[888,96634,96635],{"xmlns":890},[892,96636,96637,96645],{},[895,96638,96639],{},[1788,96640,96641,96643],{},[898,96642,4509],{},[1793,96644,1795],{},[902,96646,96647],{"encoding":904},"E_1",[198,96649,45543],{"id":96650},"příklad-29",[724,96652,96653,41895,96655,41930,96679,96699,96700,96717],{},[38,96654,38173],{},[883,96656,96658],{"className":96657},[886],[888,96659,96660],{"xmlns":890},[892,96661,96662,96676],{},[895,96663,96664,96666,96668,96670,96672,96674],{},[898,96665,1727],{},[1688,96667,1690],{},[1793,96669,3766],{},[1688,96671,1954],{},[1793,96673,1806],{},[898,96675,1872],{},[902,96677,96678],{"encoding":904},"P = 12 - 2Q",[883,96680,96682],{"className":96681},[886],[888,96683,96684],{"xmlns":890},[892,96685,96686,96696],{},[895,96687,96688,96690,96692,96694],{},[898,96689,1727],{},[1688,96691,1690],{},[1793,96693,2616],{},[898,96695,1872],{},[902,96697,96698],{"encoding":904},"P = 4Q",". Na výrobce je uložena jednotková daň ",[883,96701,96703],{"className":96702},[886],[888,96704,96705],{"xmlns":890},[892,96706,96707,96715],{},[895,96708,96709,96711,96713],{},[898,96710,3035],{},[1688,96712,1690],{},[1793,96714,2508],{},[902,96716,41508],{"encoding":904}," Kč.",[724,96719,96720],{},[38,96721,38205],{},[724,96723,96724,96727,96728,5825,96754,5845,96774,1343,96796,96826,96827,2263],{},[614,96725,96726],{},"Bez daně."," Z rovnosti ",[883,96729,96731],{"className":96730},[886],[888,96732,96733],{"xmlns":890},[892,96734,96735,96751],{},[895,96736,96737,96739,96741,96743,96745,96747,96749],{},[1793,96738,3766],{},[1688,96740,1954],{},[1793,96742,1806],{},[898,96744,1872],{},[1688,96746,1690],{},[1793,96748,2616],{},[898,96750,1872],{},[902,96752,96753],{"encoding":904},"12 - 2Q = 4Q",[883,96755,96757],{"className":96756},[886],[888,96758,96759],{"xmlns":890},[892,96760,96761,96771],{},[895,96762,96763,96765,96767,96769],{},[1793,96764,2508],{},[898,96766,1872],{},[1688,96768,1690],{},[1793,96770,3766],{},[902,96772,96773],{"encoding":904},"6Q = 12",[883,96775,96777],{"className":96776},[886],[888,96778,96779],{"xmlns":890},[892,96780,96781,96793],{},[895,96782,96783,96789,96791],{},[1850,96784,96785,96787],{},[898,96786,1872],{},[898,96788,4509],{},[1688,96790,1690],{},[1793,96792,1806],{},[902,96794,96795],{"encoding":904},"Q^E = 2",[883,96797,96799],{"className":96798},[886],[888,96800,96801],{"xmlns":890},[892,96802,96803,96823],{},[895,96804,96805,96811,96813,96815,96817,96819,96821],{},[1850,96806,96807,96809],{},[898,96808,1727],{},[898,96810,4509],{},[1688,96812,1690],{},[1793,96814,2616],{},[1688,96816,3434],{},[1793,96818,1806],{},[1688,96820,1690],{},[1793,96822,5841],{},[902,96824,96825],{"encoding":904},"P^E = 4 \\cdot 2 = 8",". Rovnovážný bod ",[883,96828,96830],{"className":96829},[886],[888,96831,96832],{"xmlns":890},[892,96833,96834,96848],{},[895,96835,96836,96838,96840,96842,96844,96846],{},[898,96837,4509],{},[1688,96839,2748],{"stretchy":2065},[1793,96841,1806],{},[1688,96843,1733],{"separator":1732},[1793,96845,5841],{},[1688,96847,2763],{"stretchy":2065},[902,96849,96850],{"encoding":904},"E[2, 8]",[724,96852,96853,96856,96857,96889],{},[614,96854,96855],{},"S daní uloženou výrobci."," Nová nabídka je ",[883,96858,96860],{"className":96859},[886],[888,96861,96862],{"xmlns":890},[892,96863,96864,96886],{},[895,96865,96866,96872,96874,96876,96878,96880,96882,96884],{},[1788,96867,96868,96870],{},[898,96869,1740],{},[1793,96871,1795],{},[1688,96873,2965],{},[898,96875,1727],{},[1688,96877,1690],{},[1793,96879,2616],{},[898,96881,1872],{},[1688,96883,1696],{},[1793,96885,2508],{},[902,96887,96888],{"encoding":904},"S_1: P = 4Q + 6",". Z rovnice",[883,96891,96893],{"className":96892},[886],[888,96894,96895],{"xmlns":890,"display":28306},[892,96896,96897,96917],{},[895,96898,96899,96901,96903,96905,96907,96909,96911,96913,96915],{},[1793,96900,3766],{},[1688,96902,1954],{},[1793,96904,1806],{},[898,96906,1872],{},[1688,96908,1690],{},[1793,96910,2616],{},[898,96912,1872],{},[1688,96914,1696],{},[1793,96916,2508],{},[902,96918,96919],{"encoding":904},"12 - 2Q = 4Q + 6",[724,96921,96922,96923,5845,96943,1343,96967,97003,97004,2263],{},"plyne ",[883,96924,96926],{"className":96925},[886],[888,96927,96928],{"xmlns":890},[892,96929,96930,96940],{},[895,96931,96932,96934,96936,96938],{},[1793,96933,2508],{},[898,96935,1872],{},[1688,96937,1690],{},[1793,96939,2508],{},[902,96941,96942],{"encoding":904},"6Q = 6",[883,96944,96946],{"className":96945},[886],[888,96947,96948],{"xmlns":890},[892,96949,96950,96964],{},[895,96951,96952,96960,96962],{},[1814,96953,96954,96956,96958],{},[898,96955,1872],{},[1793,96957,1795],{},[898,96959,4509],{},[1688,96961,1690],{},[1793,96963,1795],{},[902,96965,96966],{"encoding":904},"Q_1^E = 1",[883,96968,96970],{"className":96969},[886],[888,96971,96972],{"xmlns":890},[892,96973,96974,97000],{},[895,96975,96976,96984,96986,96988,96990,96992,96994,96996,96998],{},[1814,96977,96978,96980,96982],{},[898,96979,1727],{},[1793,96981,1795],{},[898,96983,4509],{},[1688,96985,1690],{},[1793,96987,2616],{},[1688,96989,3434],{},[1793,96991,1795],{},[1688,96993,1696],{},[1793,96995,2508],{},[1688,96997,1690],{},[1793,96999,3121],{},[902,97001,97002],{"encoding":904},"P_1^E = 4 \\cdot 1 + 6 = 10",". Nový rovnovážný bod ",[883,97005,97007],{"className":97006},[886],[888,97008,97009],{"xmlns":890},[892,97010,97011,97029],{},[895,97012,97013,97019,97021,97023,97025,97027],{},[1788,97014,97015,97017],{},[898,97016,4509],{},[1793,97018,1795],{},[1688,97020,2748],{"stretchy":2065},[1793,97022,1795],{},[1688,97024,1733],{"separator":1732},[1793,97026,3121],{},[1688,97028,2763],{"stretchy":2065},[902,97030,97031],{"encoding":904},"E_1[1, 10]",[724,97033,97034,97037,97038,97062,97063,97076],{},[614,97035,97036],{},"Rozklad daňového břemene."," Spotřebitel platí ",[883,97039,97041],{"className":97040},[886],[888,97042,97043],{"xmlns":890},[892,97044,97045,97059],{},[895,97046,97047,97055,97057],{},[1814,97048,97049,97051,97053],{},[898,97050,1727],{},[1793,97052,1795],{},[898,97054,4509],{},[1688,97056,1690],{},[1793,97058,3121],{},[902,97060,97061],{"encoding":904},"P_1^E = 10"," Kč namísto původních ",[883,97064,97066],{"className":97065},[886],[888,97067,97068],{"xmlns":890},[892,97069,97070,97074],{},[895,97071,97072],{},[1793,97073,5841],{},[902,97075,5841],{"encoding":904},", navýšení je",[883,97078,97080],{"className":97079},[886],[888,97081,97082],{"xmlns":890,"display":28306},[892,97083,97084,97140],{},[895,97085,97086,97096,97098,97106,97108,97114,97116,97118,97120,97122,97124,97126,97128,97138],{},[1788,97087,97088,97090],{},[898,97089,3035],{},[895,97091,97092,97094],{},[898,97093,42917],{},[898,97095,724],{},[1688,97097,1690],{},[1814,97099,97100,97102,97104],{},[898,97101,1727],{},[1793,97103,1795],{},[898,97105,4509],{},[1688,97107,1954],{},[1850,97109,97110,97112],{},[898,97111,1727],{},[898,97113,4509],{},[1688,97115,1690],{},[1793,97117,3121],{},[1688,97119,1954],{},[1793,97121,5841],{},[1688,97123,1690],{},[1793,97125,1806],{},[2041,97127,2558],{},[895,97129,97130,97132],{},[2041,97131,10052],{},[8642,97133,97134,97136],{"accent":1732},[2041,97135,2031],{},[1688,97137,25299],{},[898,97139,2263],{"mathvariant":1822},[902,97141,97142],{"encoding":904},"T_{sp} = P_1^E - P^E = 10 - 8 = 2\\ \\text{Kč}.",[724,97144,97145,97146,97062,97182,97195],{},"Výrobci zůstává čistá cena ",[883,97147,97149],{"className":97148},[886],[888,97150,97151],{"xmlns":890},[892,97152,97153,97179],{},[895,97154,97155,97163,97165,97167,97169,97171,97173,97175,97177],{},[1814,97156,97157,97159,97161],{},[898,97158,1727],{},[1793,97160,1795],{},[898,97162,4509],{},[1688,97164,1954],{},[898,97166,3035],{},[1688,97168,1690],{},[1793,97170,3121],{},[1688,97172,1954],{},[1793,97174,2508],{},[1688,97176,1690],{},[1793,97178,2616],{},[902,97180,97181],{"encoding":904},"P_1^E - T = 10 - 6 = 4",[883,97183,97185],{"className":97184},[886],[888,97186,97187],{"xmlns":890},[892,97188,97189,97193],{},[895,97190,97191],{},[1793,97192,5841],{},[902,97194,5841],{"encoding":904},", pokles je",[883,97197,97199],{"className":97198},[886],[888,97200,97201],{"xmlns":890,"display":28306},[892,97202,97203,97269],{},[895,97204,97205,97217,97219,97225,97227,97229,97237,97239,97241,97243,97245,97247,97249,97251,97253,97255,97257,97267],{},[1788,97206,97207,97209],{},[898,97208,3035],{},[895,97210,97211,97213,97215],{},[898,97212,42940],{},[898,97214,2282],{},[898,97216,2046],{},[1688,97218,1690],{},[1850,97220,97221,97223],{},[898,97222,1727],{},[898,97224,4509],{},[1688,97226,1954],{},[1688,97228,2066],{"stretchy":2065},[1814,97230,97231,97233,97235],{},[898,97232,1727],{},[1793,97234,1795],{},[898,97236,4509],{},[1688,97238,1954],{},[898,97240,3035],{},[1688,97242,2076],{"stretchy":2065},[1688,97244,1690],{},[1793,97246,5841],{},[1688,97248,1954],{},[1793,97250,2616],{},[1688,97252,1690],{},[1793,97254,2616],{},[2041,97256,2558],{},[895,97258,97259,97261],{},[2041,97260,10052],{},[8642,97262,97263,97265],{"accent":1732},[2041,97264,2031],{},[1688,97266,25299],{},[898,97268,2263],{"mathvariant":1822},[902,97270,97271],{"encoding":904},"T_{vyr} = P^E - (P_1^E - T) = 8 - 4 = 4\\ \\text{Kč}.",[724,97273,97274,97275,97327],{},"Kontrola: ",[883,97276,97278],{"className":97277},[886],[888,97279,97280],{"xmlns":890},[892,97281,97282,97324],{},[895,97283,97284,97294,97296,97308,97310,97312,97314,97316,97318,97320,97322],{},[1788,97285,97286,97288],{},[898,97287,3035],{},[895,97289,97290,97292],{},[898,97291,42917],{},[898,97293,724],{},[1688,97295,1696],{},[1788,97297,97298,97300],{},[898,97299,3035],{},[895,97301,97302,97304,97306],{},[898,97303,42940],{},[898,97305,2282],{},[898,97307,2046],{},[1688,97309,1690],{},[1793,97311,1806],{},[1688,97313,1696],{},[1793,97315,2616],{},[1688,97317,1690],{},[1793,97319,2508],{},[1688,97321,1690],{},[898,97323,3035],{},[902,97325,97326],{"encoding":904},"T_{sp} + T_{vyr} = 2 + 4 = 6 = T",". Spotřebitel nese třetinu daně, výrobce dvě třetiny.",[37210,97329],{},[115,97331,97333],{"id":97332},"daň-uložená-spotřebiteli","Daň uložená spotřebiteli",[724,97335,96263,97336,97349,97350,97368,97369,97397],{},[883,97337,97339],{"className":97338},[886],[888,97340,97341],{"xmlns":890},[892,97342,97343,97347],{},[895,97344,97345],{},[898,97346,3035],{},[902,97348,3035],{"encoding":904}," uložena spotřebiteli, pak spotřebitel platí celkem ",[883,97351,97353],{"className":97352},[886],[888,97354,97355],{"xmlns":890},[892,97356,97357,97365],{},[895,97358,97359,97361,97363],{},[898,97360,1727],{},[1688,97362,1696],{},[898,97364,3035],{},[902,97366,97367],{"encoding":904},"P + T"," (cena prodejce plus daň). Z podmínky ",[883,97370,97372],{"className":97371},[886],[888,97373,97374],{"xmlns":890},[892,97375,97376,97394],{},[895,97377,97378,97380,97382,97384,97386,97388,97390,97392],{},[898,97379,1727],{},[1688,97381,1696],{},[898,97383,3035],{},[1688,97385,1690],{},[898,97387,4440],{},[1688,97389,2066],{"stretchy":2065},[898,97391,1872],{},[1688,97393,2076],{"stretchy":2065},[902,97395,97396],{"encoding":904},"P + T = D(Q)"," plyne nová funkce poptávky:",[883,97399,97401],{"className":97400},[886],[888,97402,97403],{"xmlns":890,"display":28306},[892,97404,97405,97439],{},[895,97406,97407,97409,97411,97417,97419,97421,97423,97425,97427,97429,97431,97433,97435,97437],{},[898,97408,1727],{},[1688,97410,1690],{},[1788,97412,97413,97415],{},[898,97414,4440],{},[1793,97416,1806],{},[1688,97418,2066],{"stretchy":2065},[898,97420,1872],{},[1688,97422,2076],{"stretchy":2065},[1688,97424,1690],{},[898,97426,4440],{},[1688,97428,2066],{"stretchy":2065},[898,97430,1872],{},[1688,97432,2076],{"stretchy":2065},[1688,97434,1954],{},[898,97436,3035],{},[898,97438,2263],{"mathvariant":1822},[902,97440,97441],{"encoding":904},"P = D_2(Q) = D(Q) - T.",[724,97443,97444,97445,2170,97458,97461],{},"Poptávka se tedy posouvá o ",[883,97446,97448],{"className":97447},[886],[888,97449,97450],{"xmlns":890},[892,97451,97452,97456],{},[895,97453,97454],{},[898,97455,3035],{},[902,97457,3035],{"encoding":904},[38,97459,97460],{},"svisle dolů",". Nabídka se nemění.",[724,97463,96388,97464,96429,97504,4142,97532,97560,97561,97580,97581,97605,97606,4176],{},[883,97465,97467],{"className":97466},[886],[888,97468,97469],{"xmlns":890},[892,97470,97471,97501],{},[895,97472,97473,97479,97481,97489,97491,97499],{},[1788,97474,97475,97477],{},[898,97476,4509],{},[1793,97478,1806],{},[1688,97480,2748],{"stretchy":2065},[1814,97482,97483,97485,97487],{},[898,97484,1872],{},[1793,97486,1806],{},[898,97488,4509],{},[1688,97490,1733],{"separator":1732},[1814,97492,97493,97495,97497],{},[898,97494,1727],{},[1793,97496,1806],{},[898,97498,4509],{},[1688,97500,2763],{"stretchy":2065},[902,97502,97503],{"encoding":904},"E_2[Q_2^E, P_2^E]",[883,97505,97507],{"className":97506},[886],[888,97508,97509],{"xmlns":890},[892,97510,97511,97529],{},[895,97512,97513,97521,97523],{},[1814,97514,97515,97517,97519],{},[898,97516,1872],{},[1793,97518,1806],{},[898,97520,4509],{},[1688,97522,3704],{},[1850,97524,97525,97527],{},[898,97526,1872],{},[898,97528,4509],{},[902,97530,97531],{"encoding":904},"Q_2^E \u003C Q^E",[883,97533,97535],{"className":97534},[886],[888,97536,97537],{"xmlns":890},[892,97538,97539,97557],{},[895,97540,97541,97549,97551],{},[1814,97542,97543,97545,97547],{},[898,97544,1727],{},[1793,97546,1806],{},[898,97548,4509],{},[1688,97550,3704],{},[1850,97552,97553,97555],{},[898,97554,1727],{},[898,97556,4509],{},[902,97558,97559],{"encoding":904},"P_2^E \u003C P^E",". Výrobce obdrží ",[883,97562,97564],{"className":97563},[886],[888,97565,97566],{"xmlns":890},[892,97567,97568,97578],{},[895,97569,97570],{},[1814,97571,97572,97574,97576],{},[898,97573,1727],{},[1793,97575,1806],{},[898,97577,4509],{},[902,97579,48158],{"encoding":904},", spotřebitel platí celkem ",[883,97582,97584],{"className":97583},[886],[888,97585,97586],{"xmlns":890},[892,97587,97588,97602],{},[895,97589,97590,97598,97600],{},[1814,97591,97592,97594,97596],{},[898,97593,1727],{},[1793,97595,1806],{},[898,97597,4509],{},[1688,97599,1696],{},[898,97601,3035],{},[902,97603,97604],{"encoding":904},"P_2^E + T"," (tato částka je vyšší než původní ",[883,97607,97609],{"className":97608},[886],[888,97610,97611],{"xmlns":890},[892,97612,97613,97621],{},[895,97614,97615],{},[1850,97616,97617,97619],{},[898,97618,1727],{},[898,97620,4509],{},[902,97622,41706],{"encoding":904},[724,97624,97625],{},"Daňové břemeno:",[883,97627,97629],{"className":97628},[886],[888,97630,97631],{"xmlns":890,"display":28306},[892,97632,97633,97707],{},[895,97634,97635,97645,97647,97649,97657,97659,97661,97663,97665,97671,97673,97675,97687,97689,97695,97697,97705],{},[1788,97636,97637,97639],{},[898,97638,3035],{},[895,97640,97641,97643],{},[898,97642,42917],{},[898,97644,724],{},[1688,97646,1690],{},[1688,97648,2066],{"stretchy":2065},[1814,97650,97651,97653,97655],{},[898,97652,1727],{},[1793,97654,1806],{},[898,97656,4509],{},[1688,97658,1696],{},[898,97660,3035],{},[1688,97662,2076],{"stretchy":2065},[1688,97664,1954],{},[1850,97666,97667,97669],{},[898,97668,1727],{},[898,97670,4509],{},[1688,97672,1733],{"separator":1732},[6134,97674],{"width":6136},[1788,97676,97677,97679],{},[898,97678,3035],{},[895,97680,97681,97683,97685],{},[898,97682,42940],{},[898,97684,2282],{},[898,97686,2046],{},[1688,97688,1690],{},[1850,97690,97691,97693],{},[898,97692,1727],{},[898,97694,4509],{},[1688,97696,1954],{},[1814,97698,97699,97701,97703],{},[898,97700,1727],{},[1793,97702,1806],{},[898,97704,4509],{},[898,97706,2263],{"mathvariant":1822},[902,97708,97709],{"encoding":904},"T_{sp} = (P_2^E + T) - P^E, \\qquad T_{vyr} = P^E - P_2^E.",[724,97711,97712],{},[614,97713,97714,97715,97745,97746,96598,97759,5925,97776,96629,97789,2263],{},"Obrázek 2.19: Posun ",[883,97716,97718],{"className":97717},[886],[888,97719,97720],{"xmlns":890},[892,97721,97722,97742],{},[895,97723,97724,97726,97728,97734,97736,97738,97740],{},[898,97725,4440],{},[1688,97727,3380],{},[1788,97729,97730,97732],{},[898,97731,4440],{},[1793,97733,1806],{},[1688,97735,1690],{},[898,97737,4440],{},[1688,97739,1954],{},[898,97741,3035],{},[902,97743,97744],{"encoding":904},"D \\to D_2 = D - T","; svislá vzdálenost mezi poptávkovými křivkami je ",[883,97747,97749],{"className":97748},[886],[888,97750,97751],{"xmlns":890},[892,97752,97753,97757],{},[895,97754,97755],{},[898,97756,3035],{},[902,97758,3035],{"encoding":904},[883,97760,97762],{"className":97761},[886],[888,97763,97764],{"xmlns":890},[892,97765,97766,97774],{},[895,97767,97768],{},[1788,97769,97770,97772],{},[898,97771,4440],{},[1793,97773,1806],{},[902,97775,38567],{"encoding":904},[883,97777,97779],{"className":97778},[886],[888,97780,97781],{"xmlns":890},[892,97782,97783,97787],{},[895,97784,97785],{},[898,97786,1740],{},[902,97788,1740],{"encoding":904},[883,97790,97792],{"className":97791},[886],[888,97793,97794],{"xmlns":890},[892,97795,97796,97804],{},[895,97797,97798],{},[1788,97799,97800,97802],{},[898,97801,4509],{},[1793,97803,1806],{},[902,97805,97806],{"encoding":904},"E_2",[198,97808,45623],{"id":97809},"příklad-210",[724,97811,97812,97814,97815,41930,97838,97857,97858,97875],{},[38,97813,38173],{}," Pokračuje z Příkladu 2.9 — stejný trh, poptávka ",[883,97816,97818],{"className":97817},[886],[888,97819,97820],{"xmlns":890},[892,97821,97822,97836],{},[895,97823,97824,97826,97828,97830,97832,97834],{},[898,97825,1727],{},[1688,97827,1690],{},[1793,97829,3766],{},[1688,97831,1954],{},[1793,97833,1806],{},[898,97835,1872],{},[902,97837,96678],{"encoding":904},[883,97839,97841],{"className":97840},[886],[888,97842,97843],{"xmlns":890},[892,97844,97845,97855],{},[895,97846,97847,97849,97851,97853],{},[898,97848,1727],{},[1688,97850,1690],{},[1793,97852,2616],{},[898,97854,1872],{},[902,97856,96698],{"encoding":904},". Daň ",[883,97859,97861],{"className":97860},[886],[888,97862,97863],{"xmlns":890},[892,97864,97865,97873],{},[895,97866,97867,97869,97871],{},[898,97868,3035],{},[1688,97870,1690],{},[1793,97872,2508],{},[902,97874,41508],{"encoding":904}," Kč je tentokrát uložena na spotřebitele.",[724,97877,97878],{},[38,97879,38205],{},[724,97881,97882,97883,96889],{},"Nová poptávka je ",[883,97884,97886],{"className":97885},[886],[888,97887,97888],{"xmlns":890},[892,97889,97890,97926],{},[895,97891,97892,97898,97900,97902,97904,97906,97908,97910,97912,97914,97916,97918,97920,97922,97924],{},[1788,97893,97894,97896],{},[898,97895,4440],{},[1793,97897,1806],{},[1688,97899,2965],{},[898,97901,1727],{},[1688,97903,1690],{},[1793,97905,3766],{},[1688,97907,1954],{},[1793,97909,1806],{},[898,97911,1872],{},[1688,97913,1954],{},[1793,97915,2508],{},[1688,97917,1690],{},[1793,97919,2508],{},[1688,97921,1954],{},[1793,97923,1806],{},[898,97925,1872],{},[902,97927,97928],{"encoding":904},"D_2: P = 12 - 2Q - 6 = 6 - 2Q",[883,97930,97932],{"className":97931},[886],[888,97933,97934],{"xmlns":890,"display":28306},[892,97935,97936,97952],{},[895,97937,97938,97940,97942,97944,97946,97948,97950],{},[1793,97939,2508],{},[1688,97941,1954],{},[1793,97943,1806],{},[898,97945,1872],{},[1688,97947,1690],{},[1793,97949,2616],{},[898,97951,1872],{},[902,97953,97954],{"encoding":904},"6 - 2Q = 4Q",[724,97956,96922,97957,5845,97976,1343,98000,97003,98032,2263],{},[883,97958,97960],{"className":97959},[886],[888,97961,97962],{"xmlns":890},[892,97963,97964,97974],{},[895,97965,97966,97968,97970,97972],{},[1793,97967,2508],{},[898,97969,1872],{},[1688,97971,1690],{},[1793,97973,2508],{},[902,97975,96942],{"encoding":904},[883,97977,97979],{"className":97978},[886],[888,97980,97981],{"xmlns":890},[892,97982,97983,97997],{},[895,97984,97985,97993,97995],{},[1814,97986,97987,97989,97991],{},[898,97988,1872],{},[1793,97990,1806],{},[898,97992,4509],{},[1688,97994,1690],{},[1793,97996,1795],{},[902,97998,97999],{"encoding":904},"Q_2^E = 1",[883,98001,98003],{"className":98002},[886],[888,98004,98005],{"xmlns":890},[892,98006,98007,98029],{},[895,98008,98009,98017,98019,98021,98023,98025,98027],{},[1814,98010,98011,98013,98015],{},[898,98012,1727],{},[1793,98014,1806],{},[898,98016,4509],{},[1688,98018,1690],{},[1793,98020,2616],{},[1688,98022,3434],{},[1793,98024,1795],{},[1688,98026,1690],{},[1793,98028,2616],{},[902,98030,98031],{"encoding":904},"P_2^E = 4 \\cdot 1 = 4",[883,98033,98035],{"className":98034},[886],[888,98036,98037],{"xmlns":890},[892,98038,98039,98057],{},[895,98040,98041,98047,98049,98051,98053,98055],{},[1788,98042,98043,98045],{},[898,98044,4509],{},[1793,98046,1806],{},[1688,98048,2748],{"stretchy":2065},[1793,98050,1795],{},[1688,98052,1733],{"separator":1732},[1793,98054,2616],{},[1688,98056,2763],{"stretchy":2065},[902,98058,98059],{"encoding":904},"E_2[1, 4]",[724,98061,98062,98063,98099,98100,96717],{},"Spotřebitel platí celkem ",[883,98064,98066],{"className":98065},[886],[888,98067,98068],{"xmlns":890},[892,98069,98070,98096],{},[895,98071,98072,98080,98082,98084,98086,98088,98090,98092,98094],{},[1814,98073,98074,98076,98078],{},[898,98075,1727],{},[1793,98077,1806],{},[898,98079,4509],{},[1688,98081,1696],{},[898,98083,3035],{},[1688,98085,1690],{},[1793,98087,2616],{},[1688,98089,1696],{},[1793,98091,2508],{},[1688,98093,1690],{},[1793,98095,3121],{},[902,98097,98098],{"encoding":904},"P_2^E + T = 4 + 6 = 10"," Kč; výrobce obdrží ",[883,98101,98103],{"className":98102},[886],[888,98104,98105],{"xmlns":890},[892,98106,98107,98121],{},[895,98108,98109,98117,98119],{},[1814,98110,98111,98113,98115],{},[898,98112,1727],{},[1793,98114,1806],{},[898,98116,4509],{},[1688,98118,1690],{},[1793,98120,2616],{},[902,98122,98123],{"encoding":904},"P_2^E = 4",[724,98125,98126],{},[614,98127,98128],{},"Rozklad daňového břemene:",[883,98130,98132],{"className":98131},[886],[888,98133,98134],{"xmlns":890,"display":28306},[892,98135,98136,98222],{},[895,98137,98138,98148,98150,98152,98154,98156,98158,98160,98162,98164,98166,98168,98170,98180,98182,98184,98196,98198,98200,98202,98204,98206,98208,98210,98220],{},[1788,98139,98140,98142],{},[898,98141,3035],{},[895,98143,98144,98146],{},[898,98145,42917],{},[898,98147,724],{},[1688,98149,1690],{},[1688,98151,2066],{"stretchy":2065},[1793,98153,2616],{},[1688,98155,1696],{},[1793,98157,2508],{},[1688,98159,2076],{"stretchy":2065},[1688,98161,1954],{},[1793,98163,5841],{},[1688,98165,1690],{},[1793,98167,1806],{},[2041,98169,2558],{},[895,98171,98172,98174],{},[2041,98173,10052],{},[8642,98175,98176,98178],{"accent":1732},[2041,98177,2031],{},[1688,98179,25299],{},[1688,98181,1733],{"separator":1732},[6134,98183],{"width":6136},[1788,98185,98186,98188],{},[898,98187,3035],{},[895,98189,98190,98192,98194],{},[898,98191,42940],{},[898,98193,2282],{},[898,98195,2046],{},[1688,98197,1690],{},[1793,98199,5841],{},[1688,98201,1954],{},[1793,98203,2616],{},[1688,98205,1690],{},[1793,98207,2616],{},[2041,98209,2558],{},[895,98211,98212,98214],{},[2041,98213,10052],{},[8642,98215,98216,98218],{"accent":1732},[2041,98217,2031],{},[1688,98219,25299],{},[898,98221,2263],{"mathvariant":1822},[902,98223,98224],{"encoding":904},"T_{sp} = (4 + 6) - 8 = 2\\ \\text{Kč}, \\qquad T_{vyr} = 8 - 4 = 4\\ \\text{Kč}.",[724,98226,98227,98228,2263],{},"Opět ",[883,98229,98231],{"className":98230},[886],[888,98232,98233],{"xmlns":890},[892,98234,98235,98269],{},[895,98236,98237,98247,98249,98261,98263,98265,98267],{},[1788,98238,98239,98241],{},[898,98240,3035],{},[895,98242,98243,98245],{},[898,98244,42917],{},[898,98246,724],{},[1688,98248,1696],{},[1788,98250,98251,98253],{},[898,98252,3035],{},[895,98254,98255,98257,98259],{},[898,98256,42940],{},[898,98258,2282],{},[898,98260,2046],{},[1688,98262,1690],{},[1793,98264,2508],{},[1688,98266,1690],{},[898,98268,3035],{},[902,98270,98271],{"encoding":904},"T_{sp} + T_{vyr} = 6 = T",[37210,98273],{},[115,98275,42898],{"id":98276},"daňové-břemeno",[724,98278,98279,10277,98281,98284,98285,98298],{},[38,98280,42898],{},[614,98282,98283],{},"tax burden",") je rozdělení zaplacené daně ",[883,98286,98288],{"className":98287},[886],[888,98289,98290],{"xmlns":890},[892,98291,98292,98296],{},[895,98293,98294],{},[898,98295,3035],{},[902,98297,3035],{"encoding":904}," mezi spotřebitele a výrobce:",[883,98300,98302],{"className":98301},[886],[888,98303,98304],{"xmlns":890,"display":28306},[892,98305,98306,98338],{},[895,98307,98308,98310,98312,98322,98324,98336],{},[898,98309,3035],{},[1688,98311,1690],{},[1788,98313,98314,98316],{},[898,98315,3035],{},[895,98317,98318,98320],{},[898,98319,42917],{},[898,98321,724],{},[1688,98323,1696],{},[1788,98325,98326,98328],{},[898,98327,3035],{},[895,98329,98330,98332,98334],{},[898,98331,42940],{},[898,98333,2282],{},[898,98335,2046],{},[898,98337,2263],{"mathvariant":1822},[902,98339,98340],{"encoding":904},"T = T_{sp} + T_{vyr}.",[724,98342,98343],{},[2821,98344],{"alt":98345,"className":98346,"src":98347},"imek-dan-rozklad-bremene-sklony",[210,2825],"\u002Fwiki-assets\u002Fimek-dan-rozklad-bremene-sklony.jpeg",[4124,98349,98350],{},[724,98351,98352,98354,98355,4142,98368,2263],{},[883,98353,4412],{}," 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 ",[883,98356,98358],{"className":98357},[886],[888,98359,98360],{"xmlns":890},[892,98361,98362,98366],{},[895,98363,98364],{},[898,98365,4440],{},[902,98367,4440],{"encoding":904},[883,98369,98371],{"className":98370},[886],[888,98372,98373],{"xmlns":890},[892,98374,98375,98379],{},[895,98376,98377],{},[898,98378,1740],{},[902,98380,1740],{"encoding":904},[198,98382,2706],{"id":2705},[724,98384,98385,98386,98407,98408,98421,98422,98439,98440,98453],{},"V grafu ",[883,98387,98389],{"className":98388},[886],[888,98390,98391],{"xmlns":890},[892,98392,98393,98405],{},[895,98394,98395,98397,98399,98401,98403],{},[1688,98396,2066],{"stretchy":2065},[898,98398,1872],{},[1688,98400,1733],{"separator":1732},[898,98402,1727],{},[1688,98404,2076],{"stretchy":2065},[902,98406,37931],{"encoding":904}," je svislá vzdálenost mezi původní a posunutou křivkou právě ",[883,98409,98411],{"className":98410},[886],[888,98412,98413],{"xmlns":890},[892,98414,98415,98419],{},[895,98416,98417],{},[898,98418,3035],{},[902,98420,3035],{"encoding":904},". Vedeme-li v novém rovnovážném bodě vodorovnou přímku na úrovni původní rovnovážné ceny ",[883,98423,98425],{"className":98424},[886],[888,98426,98427],{"xmlns":890},[892,98428,98429,98437],{},[895,98430,98431],{},[1850,98432,98433,98435],{},[898,98434,1727],{},[898,98436,4509],{},[902,98438,41706],{"encoding":904},", rozdělí se úsečka ",[883,98441,98443],{"className":98442},[886],[888,98444,98445],{"xmlns":890},[892,98446,98447,98451],{},[895,98448,98449],{},[898,98450,3035],{},[902,98452,3035],{"encoding":904}," na dvě části:",[120,98455,98456,98481],{},[123,98457,98458,98459,98480],{},"horní část odpovídá ",[883,98460,98462],{"className":98461},[886],[888,98463,98464],{"xmlns":890},[892,98465,98466,98478],{},[895,98467,98468],{},[1788,98469,98470,98472],{},[898,98471,3035],{},[895,98473,98474,98476],{},[898,98475,42917],{},[898,98477,724],{},[902,98479,42922],{"encoding":904}," (o kolik vzrostla cena placená spotřebitelem),",[123,98482,98483,98484,98507],{},"dolní část odpovídá ",[883,98485,98487],{"className":98486},[886],[888,98488,98489],{"xmlns":890},[892,98490,98491,98505],{},[895,98492,98493],{},[1788,98494,98495,98497],{},[898,98496,3035],{},[895,98498,98499,98501,98503],{},[898,98500,42940],{},[898,98502,2282],{},[898,98504,2046],{},[902,98506,42947],{"encoding":904}," (o kolik klesla cena přijímaná výrobcem).",[724,98509,98510],{},[614,98511,98512,98513,2946,98526,98547,98548,98571,98572,4142,98593,98616],{},"Obrázky 2.20 a 2.21: Ilustrace rozkladu svislé vzdálenosti ",[883,98514,98516],{"className":98515},[886],[888,98517,98518],{"xmlns":890},[892,98519,98520,98524],{},[895,98521,98522],{},[898,98523,3035],{},[902,98525,3035],{"encoding":904},[883,98527,98529],{"className":98528},[886],[888,98530,98531],{"xmlns":890},[892,98532,98533,98545],{},[895,98534,98535],{},[1788,98536,98537,98539],{},[898,98538,3035],{},[895,98540,98541,98543],{},[898,98542,42917],{},[898,98544,724],{},[902,98546,42922],{"encoding":904}," (nahoře) a ",[883,98549,98551],{"className":98550},[886],[888,98552,98553],{"xmlns":890},[892,98554,98555,98569],{},[895,98556,98557],{},[1788,98558,98559,98561],{},[898,98560,3035],{},[895,98562,98563,98565,98567],{},[898,98564,42940],{},[898,98566,2282],{},[898,98568,2046],{},[902,98570,42947],{"encoding":904}," (dole). Obrázek 2.21 porovnává obě varianty — daň výrobci vs. daň spotřebiteli — a ukazuje, že velikost ",[883,98573,98575],{"className":98574},[886],[888,98576,98577],{"xmlns":890},[892,98578,98579,98591],{},[895,98580,98581],{},[1788,98582,98583,98585],{},[898,98584,3035],{},[895,98586,98587,98589],{},[898,98588,42917],{},[898,98590,724],{},[902,98592,42922],{"encoding":904},[883,98594,98596],{"className":98595},[886],[888,98597,98598],{"xmlns":890},[892,98599,98600,98614],{},[895,98601,98602],{},[1788,98603,98604,98606],{},[898,98605,3035],{},[895,98607,98608,98610,98612],{},[898,98609,42940],{},[898,98611,2282],{},[898,98613,2046],{},[902,98615,42947],{"encoding":904}," je v obou případech stejná.",[198,98618,98620],{"id":98619},"sklony-křivek-a-rozklad","Sklony křivek a rozklad",[724,98622,98623,98624,98627,98628,10277,98651,98668,98669,10277,98692,98709],{},"Platí obecně: ",[38,98625,98626],{},"čím strmější křivka (menší elasticita), tím větší část daně nese daná strana trhu."," Pro lineární poptávku ",[883,98629,98631],{"className":98630},[886],[888,98632,98633],{"xmlns":890},[892,98634,98635,98649],{},[895,98636,98637,98639,98641,98643,98645,98647],{},[898,98638,1727],{},[1688,98640,1690],{},[898,98642,207],{},[898,98644,1872],{},[1688,98646,1696],{},[898,98648,1918],{},[902,98650,37300],{"encoding":904},[883,98652,98654],{"className":98653},[886],[888,98655,98656],{"xmlns":890},[892,98657,98658,98666],{},[895,98659,98660,98662,98664],{},[898,98661,207],{},[1688,98663,3704],{},[1793,98665,1779],{},[902,98667,43325],{"encoding":904},") a lineární nabídku ",[883,98670,98672],{"className":98671},[886],[888,98673,98674],{"xmlns":890},[892,98675,98676,98690],{},[895,98677,98678,98680,98682,98684,98686,98688],{},[898,98679,1727],{},[1688,98681,1690],{},[898,98683,2031],{},[898,98685,1872],{},[1688,98687,1696],{},[898,98689,2073],{},[902,98691,40482],{"encoding":904},[883,98693,98695],{"className":98694},[886],[888,98696,98697],{"xmlns":890},[892,98698,98699,98707],{},[895,98700,98701,98703,98705],{},[898,98702,2031],{},[1688,98704,3665],{},[1793,98706,1779],{},[902,98708,40500],{"encoding":904},") lze rozklad odvodit pomocí multiplikátorů a platí",[883,98711,98713],{"className":98712},[886],[888,98714,98715],{"xmlns":890,"display":28306},[892,98716,98717,98783],{},[895,98718,98719,98743,98745,98755,98757,98781],{},[1781,98720,98721,98731],{},[1788,98722,98723,98725],{},[898,98724,3035],{},[895,98726,98727,98729],{},[898,98728,42917],{},[898,98730,724],{},[1788,98732,98733,98735],{},[898,98734,3035],{},[895,98736,98737,98739,98741],{},[898,98738,42940],{},[898,98740,2282],{},[898,98742,2046],{},[1688,98744,1690],{},[1781,98746,98747,98749],{},[898,98748,2031],{},[895,98750,98751,98753],{},[1688,98752,1954],{},[898,98754,207],{},[1688,98756,1690],{},[1781,98758,98759,98771],{},[895,98760,98761,98764,98767,98769],{},[898,98762,98763],{"mathvariant":1822},"∣",[2041,98765,98766],{},"sklon ",[898,98768,1740],{},[898,98770,98763],{"mathvariant":1822},[895,98772,98773,98775,98777,98779],{},[898,98774,98763],{"mathvariant":1822},[2041,98776,98766],{},[898,98778,4440],{},[898,98780,98763],{"mathvariant":1822},[898,98782,2263],{"mathvariant":1822},[902,98784,98785],{"encoding":904},"\\frac{T_{sp}}{T_{vyr}} = \\frac{c}{-a} = \\frac{|\\text{sklon } S|}{|\\text{sklon } D|}.",[4124,98787,98788,98793],{},[724,98789,98790,98792],{},[883,98791,4828],{}," Postup výpočtu rozkladu",[152,98794,98795,98830,98883,98962],{},[123,98796,98797,98798,98829],{},"Spočti rovnovážný bod ",[883,98799,98801],{"className":98800},[886],[888,98802,98803],{"xmlns":890},[892,98804,98805,98827],{},[895,98806,98807,98809,98811,98817,98819,98825],{},[898,98808,4509],{},[1688,98810,2748],{"stretchy":2065},[1850,98812,98813,98815],{},[898,98814,1872],{},[898,98816,4509],{},[1688,98818,1733],{"separator":1732},[1850,98820,98821,98823],{},[898,98822,1727],{},[898,98824,4509],{},[1688,98826,2763],{"stretchy":2065},[902,98828,41607],{"encoding":904}," bez daně.",[123,98831,98832,98833,1348,98858,4176],{},"Urči posunutou křivku (",[883,98834,98836],{"className":98835},[886],[888,98837,98838],{"xmlns":890},[892,98839,98840,98856],{},[895,98841,98842,98848,98850,98852,98854],{},[1788,98843,98844,98846],{},[898,98845,1740],{},[1793,98847,1795],{},[1688,98849,1690],{},[898,98851,1740],{},[1688,98853,1696],{},[898,98855,3035],{},[902,98857,42994],{"encoding":904},[883,98859,98861],{"className":98860},[886],[888,98862,98863],{"xmlns":890},[892,98864,98865,98881],{},[895,98866,98867,98873,98875,98877,98879],{},[1788,98868,98869,98871],{},[898,98870,4440],{},[1793,98872,1806],{},[1688,98874,1690],{},[898,98876,4440],{},[1688,98878,1954],{},[898,98880,3035],{},[902,98882,43025],{"encoding":904},[123,98884,98885,98886,4168,98905,12378,98924,4168,98943,4176],{},"Vyřeš novou rovnovážnou rovnici — získáš ",[883,98887,98889],{"className":98888},[886],[888,98890,98891],{"xmlns":890},[892,98892,98893,98903],{},[895,98894,98895],{},[1814,98896,98897,98899,98901],{},[898,98898,1872],{},[1793,98900,1795],{},[898,98902,4509],{},[902,98904,48076],{"encoding":904},[883,98906,98908],{"className":98907},[886],[888,98909,98910],{"xmlns":890},[892,98911,98912,98922],{},[895,98913,98914],{},[1814,98915,98916,98918,98920],{},[898,98917,1872],{},[1793,98919,1806],{},[898,98921,4509],{},[902,98923,48138],{"encoding":904},[883,98925,98927],{"className":98926},[886],[888,98928,98929],{"xmlns":890},[892,98930,98931,98941],{},[895,98932,98933],{},[1814,98934,98935,98937,98939],{},[898,98936,1727],{},[1793,98938,1795],{},[898,98940,4509],{},[902,98942,48097],{"encoding":904},[883,98944,98946],{"className":98945},[886],[888,98947,98948],{"xmlns":890},[892,98949,98950,98960],{},[895,98951,98952],{},[1814,98953,98954,98956,98958],{},[898,98955,1727],{},[1793,98957,1806],{},[898,98959,4509],{},[902,98961,48158],{"encoding":904},[123,98963,98964,98965,4142,98986,99009,99010,2263],{},"Dopočítej ",[883,98966,98968],{"className":98967},[886],[888,98969,98970],{"xmlns":890},[892,98971,98972,98984],{},[895,98973,98974],{},[1788,98975,98976,98978],{},[898,98977,3035],{},[895,98979,98980,98982],{},[898,98981,42917],{},[898,98983,724],{},[902,98985,42922],{"encoding":904},[883,98987,98989],{"className":98988},[886],[888,98990,98991],{"xmlns":890},[892,98992,98993,99007],{},[895,98994,98995],{},[1788,98996,98997,98999],{},[898,98998,3035],{},[895,99000,99001,99003,99005],{},[898,99002,42940],{},[898,99004,2282],{},[898,99006,2046],{},[902,99008,42947],{"encoding":904}," z definice, vždy ověř ",[883,99011,99013],{"className":99012},[886],[888,99014,99015],{"xmlns":890},[892,99016,99017,99047],{},[895,99018,99019,99029,99031,99043,99045],{},[1788,99020,99021,99023],{},[898,99022,3035],{},[895,99024,99025,99027],{},[898,99026,42917],{},[898,99028,724],{},[1688,99030,1696],{},[1788,99032,99033,99035],{},[898,99034,3035],{},[895,99036,99037,99039,99041],{},[898,99038,42940],{},[898,99040,2282],{},[898,99042,2046],{},[1688,99044,1690],{},[898,99046,3035],{},[902,99048,99049],{"encoding":904},"T_{sp} + T_{vyr} = T",[4124,99051,99052],{},[724,99053,99054,99056,99057,99060,99061,4142,99074,99087],{},[883,99055,4668],{}," Pozor — zákonný vs. ekonomický nositel daně\nI když zákon ukládá daň formálně pouze jedné straně (výrobci nebo spotřebiteli), ",[38,99058,99059],{},"ekonomicky ji vždy nesou obě strany",". Skutečné rozdělení určují sklony ",[883,99062,99064],{"className":99063},[886],[888,99065,99066],{"xmlns":890},[892,99067,99068,99072],{},[895,99069,99070],{},[898,99071,4440],{},[902,99073,4440],{"encoding":904},[883,99075,99077],{"className":99076},[886],[888,99078,99079],{"xmlns":890},[892,99080,99081,99085],{},[895,99082,99083],{},[898,99084,1740],{},[902,99086,1740],{"encoding":904},", nikoli paragrafové znění zákona. Kupující a prodávající tak fakticky platí daň bez ohledu na to, na koho je uvalena.",[37210,99089],{},[115,99091,99093],{"id":99092},"ekvivalence-obou-přístupů","Ekvivalence obou přístupů",[724,99095,99096],{},"Porovnáním Příkladu 2.9 (daň výrobci) a Příkladu 2.10 (daň spotřebiteli) zjistíme:",[724,99098,99099],{},[2821,99100],{"alt":99101,"className":99102,"src":99103},"imek-dan-ekvivalence-vyrobce-spotrebitel",[210,2825],"\u002Fwiki-assets\u002Fimek-dan-ekvivalence-vyrobce-spotrebitel.jpeg",[16,99105,99106,99118],{},[19,99107,99108],{},[22,99109,99110,99112,99115],{},[25,99111,54536],{},[25,99113,99114],{},"(a) daň výrobci",[25,99116,99117],{},"(b) daň spotřebiteli",[30,99119,99120,99175,99242,99302],{},[22,99121,99122,99125,99150],{},[35,99123,99124],{},"Rovnovážné množství",[35,99126,99127],{},[883,99128,99130],{"className":99129},[886],[888,99131,99132],{"xmlns":890},[892,99133,99134,99148],{},[895,99135,99136,99144,99146],{},[1814,99137,99138,99140,99142],{},[898,99139,1872],{},[1793,99141,1795],{},[898,99143,4509],{},[1688,99145,1690],{},[1793,99147,1795],{},[902,99149,96966],{"encoding":904},[35,99151,99152],{},[883,99153,99155],{"className":99154},[886],[888,99156,99157],{"xmlns":890},[892,99158,99159,99173],{},[895,99160,99161,99169,99171],{},[1814,99162,99163,99165,99167],{},[898,99164,1872],{},[1793,99166,1806],{},[898,99168,4509],{},[1688,99170,1690],{},[1793,99172,1795],{},[902,99174,97999],{"encoding":904},[22,99176,99177,99180,99205],{},[35,99178,99179],{},"Cena placená spotřebitelem",[35,99181,99182],{},[883,99183,99185],{"className":99184},[886],[888,99186,99187],{"xmlns":890},[892,99188,99189,99203],{},[895,99190,99191,99199,99201],{},[1814,99192,99193,99195,99197],{},[898,99194,1727],{},[1793,99196,1795],{},[898,99198,4509],{},[1688,99200,1690],{},[1793,99202,3121],{},[902,99204,97061],{"encoding":904},[35,99206,99207],{},[883,99208,99210],{"className":99209},[886],[888,99211,99212],{"xmlns":890},[892,99213,99214,99240],{},[895,99215,99216,99224,99226,99228,99230,99232,99234,99236,99238],{},[1814,99217,99218,99220,99222],{},[898,99219,1727],{},[1793,99221,1806],{},[898,99223,4509],{},[1688,99225,1696],{},[898,99227,3035],{},[1688,99229,1690],{},[1793,99231,2616],{},[1688,99233,1696],{},[1793,99235,2508],{},[1688,99237,1690],{},[1793,99239,3121],{},[902,99241,98098],{"encoding":904},[22,99243,99244,99247,99277],{},[35,99245,99246],{},"Cena přijímaná výrobcem",[35,99248,99249],{},[883,99250,99252],{"className":99251},[886],[888,99253,99254],{"xmlns":890},[892,99255,99256,99274],{},[895,99257,99258,99266,99268,99270,99272],{},[1814,99259,99260,99262,99264],{},[898,99261,1727],{},[1793,99263,1795],{},[898,99265,4509],{},[1688,99267,1954],{},[898,99269,3035],{},[1688,99271,1690],{},[1793,99273,2616],{},[902,99275,99276],{"encoding":904},"P_1^E - T = 4",[35,99278,99279],{},[883,99280,99282],{"className":99281},[886],[888,99283,99284],{"xmlns":890},[892,99285,99286,99300],{},[895,99287,99288,99296,99298],{},[1814,99289,99290,99292,99294],{},[898,99291,1727],{},[1793,99293,1806],{},[898,99295,4509],{},[1688,99297,1690],{},[1793,99299,2616],{},[902,99301,98123],{"encoding":904},[22,99303,99304,99307,99361],{},[35,99305,99306],{},"Rozklad břemene",[35,99308,99309,1343,99334],{},[883,99310,99312],{"className":99311},[886],[888,99313,99314],{"xmlns":890},[892,99315,99316,99332],{},[895,99317,99318,99328,99330],{},[1788,99319,99320,99322],{},[898,99321,3035],{},[895,99323,99324,99326],{},[898,99325,42917],{},[898,99327,724],{},[1688,99329,1690],{},[1793,99331,1806],{},[902,99333,43216],{"encoding":904},[883,99335,99337],{"className":99336},[886],[888,99338,99339],{"xmlns":890},[892,99340,99341,99359],{},[895,99342,99343,99355,99357],{},[1788,99344,99345,99347],{},[898,99346,3035],{},[895,99348,99349,99351,99353],{},[898,99350,42940],{},[898,99352,2282],{},[898,99354,2046],{},[1688,99356,1690],{},[1793,99358,2616],{},[902,99360,43245],{"encoding":904},[35,99362,99363,1343,99388],{},[883,99364,99366],{"className":99365},[886],[888,99367,99368],{"xmlns":890},[892,99369,99370,99386],{},[895,99371,99372,99382,99384],{},[1788,99373,99374,99376],{},[898,99375,3035],{},[895,99377,99378,99380],{},[898,99379,42917],{},[898,99381,724],{},[1688,99383,1690],{},[1793,99385,1806],{},[902,99387,43216],{"encoding":904},[883,99389,99391],{"className":99390},[886],[888,99392,99393],{"xmlns":890},[892,99394,99395,99413],{},[895,99396,99397,99409,99411],{},[1788,99398,99399,99401],{},[898,99400,3035],{},[895,99402,99403,99405,99407],{},[898,99404,42940],{},[898,99406,2282],{},[898,99408,2046],{},[1688,99410,1690],{},[1793,99412,2616],{},[902,99414,43245],{"encoding":904},[724,99416,99417],{},"Výsledek je v obou režimech reálně totožný — liší se pouze to, kterou cenu nazveme \"tržní\":",[883,99419,99421],{"className":99420},[886],[888,99422,99423],{"xmlns":890,"display":28306},[892,99424,99425,99473],{},[895,99426,99427,99435,99437,99445,99447,99449,99457,99459,99461,99463,99471],{},[1814,99428,99429,99431,99433],{},[898,99430,1872],{},[1793,99432,1795],{},[898,99434,4509],{},[1688,99436,1690],{},[1814,99438,99439,99441,99443],{},[898,99440,1872],{},[1793,99442,1806],{},[898,99444,4509],{},[1688,99446,1733],{"separator":1732},[6134,99448],{"width":6136},[1814,99450,99451,99453,99455],{},[898,99452,1727],{},[1793,99454,1795],{},[898,99456,4509],{},[1688,99458,1954],{},[898,99460,3035],{},[1688,99462,1690],{},[1814,99464,99465,99467,99469],{},[898,99466,1727],{},[1793,99468,1806],{},[898,99470,4509],{},[898,99472,2263],{"mathvariant":1822},[902,99474,99475],{"encoding":904},"Q_1^E = Q_2^E, \\qquad P_1^E - T = P_2^E.",[4124,99477,99478,99497,99651],{},[724,99479,99480,99482,99483,99496],{},[883,99481,4828],{}," Věta o ekvivalenci zdanění\nNezávisle na tom, zda je jednotková daň ",[883,99484,99486],{"className":99485},[886],[888,99487,99488],{"xmlns":890},[892,99489,99490,99494],{},[895,99491,99492],{},[898,99493,3035],{},[902,99495,3035],{"encoding":904}," uložena výrobci, nebo spotřebiteli, se po jejím uložení rovnají:",[120,99498,99499,99531,99567,99604],{},[123,99500,99501,99502,1733],{},"rovnovážná množství obou režimů, ",[883,99503,99505],{"className":99504},[886],[888,99506,99507],{"xmlns":890},[892,99508,99509,99529],{},[895,99510,99511,99519,99521],{},[1814,99512,99513,99515,99517],{},[898,99514,1872],{},[1793,99516,1795],{},[898,99518,4509],{},[1688,99520,1690],{},[1814,99522,99523,99525,99527],{},[898,99524,1872],{},[1793,99526,1806],{},[898,99528,4509],{},[902,99530,43148],{"encoding":904},[123,99532,99533,99534,1733],{},"čistá cena přijímaná výrobcem, ",[883,99535,99537],{"className":99536},[886],[888,99538,99539],{"xmlns":890},[892,99540,99541,99565],{},[895,99542,99543,99551,99553,99555,99557],{},[1814,99544,99545,99547,99549],{},[898,99546,1727],{},[1793,99548,1795],{},[898,99550,4509],{},[1688,99552,1954],{},[898,99554,3035],{},[1688,99556,1690],{},[1814,99558,99559,99561,99563],{},[898,99560,1727],{},[1793,99562,1806],{},[898,99564,4509],{},[902,99566,43182],{"encoding":904},[123,99568,99569,99570,1733],{},"celková cena placená spotřebitelem, ",[883,99571,99573],{"className":99572},[886],[888,99574,99575],{"xmlns":890},[892,99576,99577,99601],{},[895,99578,99579,99587,99589,99597,99599],{},[1814,99580,99581,99583,99585],{},[898,99582,1727],{},[1793,99584,1795],{},[898,99586,4509],{},[1688,99588,1690],{},[1814,99590,99591,99593,99595],{},[898,99592,1727],{},[1793,99594,1806],{},[898,99596,4509],{},[1688,99598,1696],{},[898,99600,3035],{},[902,99602,99603],{"encoding":904},"P_1^E = P_2^E + T",[123,99605,99606,99607,4142,99628,2263],{},"rozklad daňového břemene ",[883,99608,99610],{"className":99609},[886],[888,99611,99612],{"xmlns":890},[892,99613,99614,99626],{},[895,99615,99616],{},[1788,99617,99618,99620],{},[898,99619,3035],{},[895,99621,99622,99624],{},[898,99623,42917],{},[898,99625,724],{},[902,99627,42922],{"encoding":904},[883,99629,99631],{"className":99630},[886],[888,99632,99633],{"xmlns":890},[892,99634,99635,99649],{},[895,99636,99637],{},[1788,99638,99639,99641],{},[898,99640,3035],{},[895,99642,99643,99645,99647],{},[898,99644,42940],{},[898,99646,2282],{},[898,99648,2046],{},[902,99650,42947],{"encoding":904},[724,99652,99653,99654,2263],{},"Z hlediska reálných dopadů na trh (objem transakcí, reálné platby stran) jsou tedy obě formy zdanění ",[38,99655,35437],{},[724,99657,99658,99659,4142,99672,4176],{},"Ekvivalence má zásadní politickou implikaci: otázka, \"kdo má platit daň\", je z hlediska trhu formální — skutečné rozdělení určuje struktura trhu (sklony ",[883,99660,99662],{"className":99661},[886],[888,99663,99664],{"xmlns":890},[892,99665,99666,99670],{},[895,99667,99668],{},[898,99669,4440],{},[902,99671,4440],{"encoding":904},[883,99673,99675],{"className":99674},[886],[888,99676,99677],{"xmlns":890},[892,99678,99679,99683],{},[895,99680,99681],{},[898,99682,1740],{},[902,99684,1740],{"encoding":904},[37210,99686],{},[115,99688,99690],{"id":99689},"úlohy","Úlohy",[724,99692,99693,99694,3408],{},"Z kapitoly 2 se zdanění týkají zejména následující úlohy (zadání v hub-page ",[207,99695,16487],{"className":99696,"dataFsResolvedFilePath":800,"href":801},[210],[120,99698,99699,99729,99760],{},[123,99700,99701,99704,99705,99728],{},[38,99702,99703],{},"Úloha 2.4"," — Poptávka ",[883,99706,99708],{"className":99707},[886],[888,99709,99710],{"xmlns":890},[892,99711,99712,99726],{},[895,99713,99714,99716,99718,99720,99722,99724],{},[898,99715,1727],{},[1688,99717,1690],{},[1793,99719,3766],{},[1688,99721,1954],{},[1793,99723,1806],{},[898,99725,1872],{},[902,99727,96678],{"encoding":904},"; najděte novou poptávku po uložení daně 6 Kč na kupujícího.",[123,99730,99731,99734,99735,99759],{},[38,99732,99733],{},"Úloha 2.9"," — Nabídka ",[883,99736,99738],{"className":99737},[886],[888,99739,99740],{"xmlns":890},[892,99741,99742,99756],{},[895,99743,99744,99746,99748,99750,99752,99754],{},[898,99745,1727],{},[1688,99747,1690],{},[1793,99749,5265],{},[898,99751,1872],{},[1688,99753,1696],{},[1793,99755,36484],{},[902,99757,99758],{"encoding":904},"P = 0{,}5Q + 15","; najděte novou nabídku po uložení daně 5 Kč na výrobce.",[123,99761,99762,99765,99766,4142,99792,99816,99817,99834],{},[38,99763,99764],{},"Úloha 2.13"," — Komplexní úloha se zadáním ",[883,99767,99769],{"className":99768},[886],[888,99770,99771],{"xmlns":890},[892,99772,99773,99789],{},[895,99774,99775,99777,99779,99781,99783,99785,99787],{},[898,99776,1727],{},[1688,99778,1690],{},[1688,99780,1954],{},[1793,99782,2616],{},[898,99784,1872],{},[1688,99786,1696],{},[1793,99788,46943],{},[902,99790,99791],{"encoding":904},"P = -4Q + 80",[883,99793,99795],{"className":99794},[886],[888,99796,99797],{"xmlns":890},[892,99798,99799,99813],{},[895,99800,99801,99803,99805,99807,99809,99811],{},[898,99802,1727],{},[1688,99804,1690],{},[1793,99806,2131],{},[898,99808,1872],{},[1688,99810,1696],{},[1793,99812,3121],{},[902,99814,99815],{"encoding":904},"P = 3Q + 10",": rovnováha, daň ",[883,99818,99820],{"className":99819},[886],[888,99821,99822],{"xmlns":890},[892,99823,99824,99832],{},[895,99825,99826,99828,99830],{},[898,99827,3035],{},[1688,99829,1690],{},[1793,99831,24442],{},[902,99833,48055],{"encoding":904}," Kč uložená postupně výrobci i spotřebiteli, rozklad daňového břemene a analýza ekvivalence.",[724,99836,99837,99838,99840,99841,99843],{},"Související úvodní příklady posunu křivek při zdanění: ",[38,99839,45468],{}," (posun poptávky při zdanění kupujícího) a ",[38,99842,45502],{}," (posun nabídky při zdanění výrobce).",[37210,99845],{},[115,99847,15967],{"id":15966},[120,99849,99850,99869,99927,99984,100067,100113,100156,100201,100267],{},[123,99851,99852,2170,99855,99868],{},[38,99853,99854],{},"Jednotková daň",[883,99856,99858],{"className":99857},[886],[888,99859,99860],{"xmlns":890},[892,99861,99862,99866],{},[895,99863,99864],{},[898,99865,3035],{},[902,99867,3035],{"encoding":904}," — fixní částka na každou prodanou jednotku zboží",[123,99870,99871,99873,99874,99912,99913,99926],{},[38,99872,96260],{}," — posun nabídky ",[883,99875,99877],{"className":99876},[886],[888,99878,99879],{"xmlns":890},[892,99880,99881,99909],{},[895,99882,99883,99889,99891,99893,99895,99897,99899,99901,99903,99905,99907],{},[1788,99884,99885,99887],{},[898,99886,1740],{},[1793,99888,1795],{},[1688,99890,2066],{"stretchy":2065},[898,99892,1872],{},[1688,99894,2076],{"stretchy":2065},[1688,99896,1690],{},[898,99898,1740],{},[1688,99900,2066],{"stretchy":2065},[898,99902,1872],{},[1688,99904,2076],{"stretchy":2065},[1688,99906,1696],{},[898,99908,3035],{},[902,99910,99911],{"encoding":904},"S_1(Q) = S(Q) + T"," (o ",[883,99914,99916],{"className":99915},[886],[888,99917,99918],{"xmlns":890},[892,99919,99920,99924],{},[895,99921,99922],{},[898,99923,3035],{},[902,99925,3035],{"encoding":904}," svisle nahoru)",[123,99928,99929,99931,99932,99912,99970,99983],{},[38,99930,97333],{}," — posun poptávky ",[883,99933,99935],{"className":99934},[886],[888,99936,99937],{"xmlns":890},[892,99938,99939,99967],{},[895,99940,99941,99947,99949,99951,99953,99955,99957,99959,99961,99963,99965],{},[1788,99942,99943,99945],{},[898,99944,4440],{},[1793,99946,1806],{},[1688,99948,2066],{"stretchy":2065},[898,99950,1872],{},[1688,99952,2076],{"stretchy":2065},[1688,99954,1690],{},[898,99956,4440],{},[1688,99958,2066],{"stretchy":2065},[898,99960,1872],{},[1688,99962,2076],{"stretchy":2065},[1688,99964,1954],{},[898,99966,3035],{},[902,99968,99969],{"encoding":904},"D_2(Q) = D(Q) - T",[883,99971,99973],{"className":99972},[886],[888,99974,99975],{"xmlns":890},[892,99976,99977,99981],{},[895,99978,99979],{},[898,99980,3035],{},[902,99982,3035],{"encoding":904}," svisle dolů)",[123,99985,99986,7271,99989,42054,100028],{},[38,99987,99988],{},"Rovnovážný bod s daní",[883,99990,99992],{"className":99991},[886],[888,99993,99994],{"xmlns":890},[892,99995,99996,100026],{},[895,99997,99998,100004,100006,100014,100016,100024],{},[1788,99999,100000,100002],{},[898,100001,4509],{},[1793,100003,1795],{},[1688,100005,2748],{"stretchy":2065},[1814,100007,100008,100010,100012],{},[898,100009,1872],{},[1793,100011,1795],{},[898,100013,4509],{},[1688,100015,1733],{"separator":1732},[1814,100017,100018,100020,100022],{},[898,100019,1727],{},[1793,100021,1795],{},[898,100023,4509],{},[1688,100025,2763],{"stretchy":2065},[902,100027,96428],{"encoding":904},[883,100029,100031],{"className":100030},[886],[888,100032,100033],{"xmlns":890},[892,100034,100035,100065],{},[895,100036,100037,100043,100045,100053,100055,100063],{},[1788,100038,100039,100041],{},[898,100040,4509],{},[1793,100042,1806],{},[1688,100044,2748],{"stretchy":2065},[1814,100046,100047,100049,100051],{},[898,100048,1872],{},[1793,100050,1806],{},[898,100052,4509],{},[1688,100054,1733],{"separator":1732},[1814,100056,100057,100059,100061],{},[898,100058,1727],{},[1793,100060,1806],{},[898,100062,4509],{},[1688,100064,2763],{"stretchy":2065},[902,100066,97503],{"encoding":904},[123,100068,100069,10277,100071,100073,100074],{},[38,100070,42898],{},[614,100072,98283],{},") — rozklad ",[883,100075,100077],{"className":100076},[886],[888,100078,100079],{"xmlns":890},[892,100080,100081,100111],{},[895,100082,100083,100085,100087,100097,100099],{},[898,100084,3035],{},[1688,100086,1690],{},[1788,100088,100089,100091],{},[898,100090,3035],{},[895,100092,100093,100095],{},[898,100094,42917],{},[898,100096,724],{},[1688,100098,1696],{},[1788,100100,100101,100103],{},[898,100102,3035],{},[895,100104,100105,100107,100109],{},[898,100106,42940],{},[898,100108,2282],{},[898,100110,2046],{},[902,100112,43084],{"encoding":904},[123,100114,100115,100138,100139,2076],{},[38,100116,100117],{},[883,100118,100120],{"className":100119},[886],[888,100121,100122],{"xmlns":890},[892,100123,100124,100136],{},[895,100125,100126],{},[1788,100127,100128,100130],{},[898,100129,3035],{},[895,100131,100132,100134],{},[898,100133,42917],{},[898,100135,724],{},[902,100137,42922],{"encoding":904}," — část daně nesená spotřebitelem (navýšení ceny nad ",[883,100140,100142],{"className":100141},[886],[888,100143,100144],{"xmlns":890},[892,100145,100146,100154],{},[895,100147,100148],{},[1850,100149,100150,100152],{},[898,100151,1727],{},[898,100153,4509],{},[902,100155,41706],{"encoding":904},[123,100157,100158,100183,100184,2076],{},[38,100159,100160],{},[883,100161,100163],{"className":100162},[886],[888,100164,100165],{"xmlns":890},[892,100166,100167,100181],{},[895,100168,100169],{},[1788,100170,100171,100173],{},[898,100172,3035],{},[895,100174,100175,100177,100179],{},[898,100176,42940],{},[898,100178,2282],{},[898,100180,2046],{},[902,100182,42947],{"encoding":904}," — část daně nesená výrobcem (pokles čisté přijímané ceny pod ",[883,100185,100187],{"className":100186},[886],[888,100188,100189],{"xmlns":890},[892,100190,100191,100199],{},[895,100192,100193],{},[1850,100194,100195,100197],{},[898,100196,1727],{},[898,100198,4509],{},[902,100200,41706],{"encoding":904},[123,100202,100203,7271,100205,1343,100234],{},[38,100204,50714],{},[883,100206,100208],{"className":100207},[886],[888,100209,100210],{"xmlns":890},[892,100211,100212,100232],{},[895,100213,100214,100222,100224],{},[1814,100215,100216,100218,100220],{},[898,100217,1872],{},[1793,100219,1795],{},[898,100221,4509],{},[1688,100223,1690],{},[1814,100225,100226,100228,100230],{},[898,100227,1872],{},[1793,100229,1806],{},[898,100231,4509],{},[902,100233,43148],{"encoding":904},[883,100235,100237],{"className":100236},[886],[888,100238,100239],{"xmlns":890},[892,100240,100241,100265],{},[895,100242,100243,100251,100253,100255,100257],{},[1814,100244,100245,100247,100249],{},[898,100246,1727],{},[1793,100248,1795],{},[898,100250,4509],{},[1688,100252,1954],{},[898,100254,3035],{},[1688,100256,1690],{},[1814,100258,100259,100261,100263],{},[898,100260,1727],{},[1793,100262,1806],{},[898,100264,4509],{},[902,100266,43182],{"encoding":904},[123,100268,100269,100272],{},[38,100270,100271],{},"Zákonný vs. ekonomický nositel daně"," — rozdíl mezi formálním ustanovením zákona a skutečným rozdělením břemene",[37210,100274],{},[115,100276,4049],{"id":4048},[120,100278,100279,100287,100305,100312],{},[123,100280,100281,2170,100284],{},[38,100282,100283],{},"Kontext (hub):",[207,100285,802],{"className":100286,"dataFsResolvedFilePath":800,"href":801},[210],[123,100288,100289,2170,100291,100294,100295,18890,100297,100300,100301,100304],{},[38,100290,50963],{},[207,100292,820],{"className":100293,"dataFsResolvedFilePath":818,"href":819},[210]," (daň vyvolává ztrátu blahobytu — ",[614,100296,55274],{},[207,100298,2622],{"className":100299,"dataFsResolvedFilePath":764,"href":765},[210]," (sklony křivek, rovnovážný bod jako řešení soustavy), ",[207,100302,4084],{"className":100303,"dataFsResolvedFilePath":848,"href":849},[210]," (kvantifikace, jak se daňové břemeno dělí podle citlivosti stran 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