[{"data":1,"prerenderedAt":108210},["ShallowReactive",2],{"sidebar-courses-with-stats":3,"wiki-uzitecnost":1626,"course-stats-imek":10789,"course-topics-imek":10793,"backlinks-uzitecnost":108178,"related-uzitecnost":108202},{"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":10788},{"id":1628,"title":1629,"body":1630,"course":1128,"courses":659,"created":10774,"description":641,"extension":661,"meta":10775,"navigation":664,"path":10776,"seo":10777,"sources":10778,"stem":10779,"tags":10780,"type":10786,"updated":677,"__hash__":10787},"topics\u002Ftopics\u002Fuzitecnost.md","Užitečnost, Cobb-Douglasova funkce užitečnosti a optimalizace spotřebitele",{"type":9,"value":1631,"toc":10748},[1632,1635,1639,1864,1875,1879,1882,1940,1944,1956,1960,1963,1980,2108,2115,2264,2274,2278,2314,2353,2403,2467,2527,2570,3164,3168,3256,3369,3466,3732,3736,3792,3904,3988,3992,4003,4238,4294,4301,4341,4407,4418,4611,4717,4871,4919,4924,5038,5076,5203,5249,5278,5355,5430,5511,5643,5704,5792,5796,5799,5868,5953,5962,6022,6333,6337,6343,6396,6412,6463,6602,6678,6792,7111,7115,7122,7283,7342,7346,7370,7467,7589,7704,7728,7791,7849,8109,8117,8121,8128,8393,8445,8501,8504,8673,8677,8776,8780,8812,8816,8951,9199,9385,9553,9861,9994,10182,10195,10199,10637,10641],[12,1633,1629],{"id":1634},"užitečnost-cobb-douglasova-funkce-užitečnosti-a-optimalizace-spotřebitele",[115,1636,1638],{"id":1637},"tldr","TL;DR",[724,1640,1641,1643,1644,1687,1688,1691,1692,1729,1730,1749,1750,1794,1795,1798,1799,1812,1813,1816,1817,1830,1831,1845,1846,1859,1860,1863],{},[38,1642,880],{}," ",[883,1645,1647],{"className":1646},[886],[888,1648,1649],{"xmlns":890},[892,1650,1651,1684],{},[895,1652,1653,1655,1660,1670,1674,1681],{},[898,1654,900],{},[1656,1657,1659],"mo",{"stretchy":1658},"false","(",[1661,1662,1663,1666],"msub",{},[898,1664,1665],{},"Q",[1667,1668,1669],"mn",{},"1",[1656,1671,1673],{"separator":1672},"true",",",[1661,1675,1676,1678],{},[898,1677,1665],{},[1667,1679,1680],{},"2",[1656,1682,1683],{"stretchy":1658},")",[902,1685,1686],{"encoding":904},"U(Q_1, Q_2)"," je číselné vyjádření uspokojení spotřebitele ze svazku zboží — v ordinalistickém přístupu slouží jen k ",[38,1689,1690],{},"uspořádání"," svazků (nikoli k měření v jednotkách). Klíčové nástroje jsou mezní užitečnosti ",[883,1693,1695],{"className":1694},[886],[888,1696,1697],{"xmlns":890},[892,1698,1699,1726],{},[895,1700,1701,1704,1711,1714],{},[898,1702,1703],{},"M",[1661,1705,1706,1708],{},[898,1707,900],{},[898,1709,1710],{},"i",[1656,1712,1713],{},"=",[1715,1716,1717,1719,1721],"msubsup",{},[898,1718,900],{},[898,1720,1710],{},[1656,1722,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},"normal","0em","′",[902,1727,1728],{"encoding":904},"MU_i = U'_i",", indiferenční křivky ",[883,1731,1733],{"className":1732},[886],[888,1734,1735],{"xmlns":890},[892,1736,1737,1746],{},[895,1738,1739,1741,1743],{},[898,1740,900],{},[1656,1742,1713],{},[898,1744,1745],{},"c",[902,1747,1748],{"encoding":904},"U = c"," a mezní míra komoditní substituce ",[883,1751,1753],{"className":1752},[886],[888,1754,1755],{"xmlns":890},[892,1756,1757,1791],{},[895,1758,1759,1761,1764,1767,1770,1772,1774,1780,1783,1785],{},[898,1760,1703],{},[898,1762,1763],{},"R",[898,1765,1766],{},"C",[898,1768,1769],{},"S",[1656,1771,1713],{},[898,1773,1703],{},[1661,1775,1776,1778],{},[898,1777,900],{},[1667,1779,1669],{},[898,1781,1782],{"mathvariant":1723},"\u002F",[898,1784,1703],{},[1661,1786,1787,1789],{},[898,1788,900],{},[1667,1790,1680],{},[902,1792,1793],{"encoding":904},"MRCS = MU_1\u002FMU_2",". Tato stránka pokrývá ",[38,1796,1797],{},"teorii užitečnosti"," — funkce ",[883,1800,1802],{"className":1801},[886],[888,1803,1804],{"xmlns":890},[892,1805,1806,1810],{},[895,1807,1808],{},[898,1809,900],{},[902,1811,900],{"encoding":904},", její vlastnosti, Cobb-Douglasův tvar, indiferenční křivky a MRCS. ",[38,1814,1815],{},"Optimalizaci spotřebitele"," (max ",[883,1818,1820],{"className":1819},[886],[888,1821,1822],{"xmlns":890},[892,1823,1824,1828],{},[895,1825,1826],{},[898,1827,900],{},[902,1829,900],{"encoding":904}," při rozpočtu, min ",[883,1832,1834],{"className":1833},[886],[888,1835,1836],{"xmlns":890},[892,1837,1838,1843],{},[895,1839,1840],{},[898,1841,1842],{},"E",[902,1844,1842],{"encoding":904}," při dané ",[883,1847,1849],{"className":1848},[886],[888,1850,1851],{"xmlns":890},[892,1852,1853,1857],{},[895,1854,1855],{},[898,1856,900],{},[902,1858,900],{"encoding":904},", Lagrange, funkce poptávky) viz ",[207,1861,913],{"className":1862,"dataFsResolvedFilePath":911,"href":912},[210],".",[724,1865,1866,1867,1870,1871,1863],{},"Kapitola 6 knihy ",[614,1868,1869],{},"Matematická ekonomie"," — model rozhodování spotřebitele. Zde: funkce užitečnosti, indiferenční křivky, mezní míra komoditní substituce. Navazující optimalizace je v ",[207,1872,1874],{"className":1873,"dataFsResolvedFilePath":911,"href":912},[210],"optimalizace-spotrebitele",[115,1876,1878],{"id":1877},"úvod-cílové-znalosti-kapitoly-6","Úvod — cílové znalosti kapitoly 6",[724,1880,1881],{},"Po prostudování této kapitoly byste měli umět:",[120,1883,1884,1890,1900,1907,1910,1917,1924,1927,1933],{},[123,1885,1886,1887,1673],{},"vyložit, co se rozumí termínem ",[38,1888,1889],{},"užitečnost",[123,1891,1892,1893,1896,1897,1673],{},"definovat pojmy ",[38,1894,1895],{},"svazek zboží"," a ",[38,1898,1899],{},"funkce užitečnosti",[123,1901,1902,1903,1906],{},"vypočítat ",[38,1904,1905],{},"mezní užitečnosti"," a ekonomicky je interpretovat,",[123,1908,1909],{},"vyjmenovat základní vlastnosti funkcí užitečnosti,",[123,1911,1912,1913,1916],{},"uvést tvar ",[38,1914,1915],{},"Cobb-Douglasových"," funkcí užitečnosti,",[123,1918,1919,1920,1923],{},"najít ",[38,1921,1922],{},"křivky užitečnosti"," (indiferenční křivky),",[123,1925,1926],{},"vyjmenovat jejich základní vlastnosti,",[123,1928,1902,1929,1932],{},[38,1930,1931],{},"mezní míru komoditní substituce"," a ekonomicky ji interpretovat,",[123,1934,1935,1936,1939],{},"řešit ",[38,1937,1938],{},"optimalizační úlohy"," s ohledem na užitečnost.",[115,1941,1943],{"id":1942},"_61-pojetí-užitečnosti","6.1 Pojetí užitečnosti",[724,1945,1946,1947,1951,1952,1955],{},"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 ",[207,1948,1950],{"className":1949,"dataFsResolvedFilePath":800,"href":801},[210],"poptávku",". Centrálním pojmem je ",[38,1953,1954],{},"užitečnost (utility)"," — vše, co vede spotřebitele k nákupu zboží (uspokojení, potěšení, splnění přání, pohodlí).",[198,1957,1959],{"id":1958},"kardinalistický-vs-ordinalistický-přístup","Kardinalistický vs. ordinalistický přístup",[724,1961,1962],{},"Historicky se vyvíjela dvě pojetí „měření\" užitečnosti:",[120,1964,1965,1971],{},[123,1966,1967,1970],{},[38,1968,1969],{},"Kardinalistický přístup"," (19. století — Gossen, Jevons, Walras): užitečnost měřena kvantitativně (např. peněžními jednotkami). Tento přístup se ukázal být nevýhodný.",[123,1972,1973,1976,1977,1979],{},[38,1974,1975],{},"Ordinalistický přístup"," (v současnosti preferovaný): postačuje ",[38,1978,1690],{}," svazků zboží podle preferencí; kvantitativní číselné hodnocení užitečnosti se nepožaduje.",[1981,1982,1983],"blockquote",{},[724,1984,1985,1988,1989,1992,1993,1643,2006,2009,2010,1896,2023,2043,2044,1343,2071,2099,2100,2103,2104,2107],{},[883,1986,1987],{},"!warning"," Pozor — ordinalisté užitečnost ",[38,1990,1991],{},"neměří","\nV ordinalistickém přístupu hodnoty funkce ",[883,1994,1996],{"className":1995},[886],[888,1997,1998],{"xmlns":890},[892,1999,2000,2004],{},[895,2001,2002],{},[898,2003,900],{},[902,2005,900],{"encoding":904},[38,2007,2008],{},"nemají samostatný ekonomický význam"," — slouží pouze k uspořádání svazků. Dvě funkce ",[883,2011,2013],{"className":2012},[886],[888,2014,2015],{"xmlns":890},[892,2016,2017,2021],{},[895,2018,2019],{},[898,2020,900],{},[902,2022,900],{"encoding":904},[883,2024,2026],{"className":2025},[886],[888,2027,2028],{"xmlns":890},[892,2029,2030,2040],{},[895,2031,2032],{},[2033,2034,2035,2037],"mover",{"accent":1672},[898,2036,900],{},[1656,2038,2039],{},"~",[902,2041,2042],{"encoding":904},"\\tilde U"," reprezentují tytéž preference, jsou-li navzájem monotónní transformací (např. ",[883,2045,2047],{"className":2046},[886],[888,2048,2049],{"xmlns":890},[892,2050,2051,2068],{},[895,2052,2053,2059,2061],{},[2033,2054,2055,2057],{"accent":1672},[898,2056,900],{},[1656,2058,2039],{},[1656,2060,1713],{},[2062,2063,2064,2066],"msup",{},[898,2065,900],{},[1667,2067,1680],{},[902,2069,2070],{"encoding":904},"\\tilde U = U^2",[883,2072,2074],{"className":2073},[886],[888,2075,2076],{"xmlns":890},[892,2077,2078,2096],{},[895,2079,2080,2086,2088,2091,2094],{},[2033,2081,2082,2084],{"accent":1672},[898,2083,900],{},[1656,2085,2039],{},[1656,2087,1713],{},[898,2089,2090],{},"ln",[1656,2092,2093],{},"⁡",[898,2095,900],{},[902,2097,2098],{"encoding":904},"\\tilde U = \\ln U","). Výroky typu „užitečnost je 250 jednotek\" proto samy o sobě nic neříkají — smysl mají jen ",[38,2101,2102],{},"porovnání"," mezi svazky a ",[38,2105,2106],{},"poměry"," mezních veličin.",[724,2109,2110,2111,2114],{},"Ordinalistický přístup vychází z ",[38,2112,2113],{},"pěti hlavních předpokladů",":",[152,2116,2117,2123,2129,2252,2258],{},[123,2118,2119,2122],{},[38,2120,2121],{},"Racionalita."," Spotřebitel jedná racionálně — snaží se maximalizovat své uspokojení (užitečnost) s ohledem na daný důchod a tržní ceny; disponuje všemi potřebnými informacemi.",[123,2124,2125,2128],{},[38,2126,2127],{},"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.",[123,2130,2131,2134,2135,2149,2150,2164,2165,2149,2178,2191,2192,2195,2196,1896,2215,2233,2234,1863],{},[38,2132,2133],{},"Konzistence a tranzitivita."," Preferuje-li v jisté době svazek ",[883,2136,2138],{"className":2137},[886],[888,2139,2140],{"xmlns":890},[892,2141,2142,2147],{},[895,2143,2144],{},[898,2145,2146],{},"A",[902,2148,2146],{"encoding":904}," před ",[883,2151,2153],{"className":2152},[886],[888,2154,2155],{"xmlns":890},[892,2156,2157,2162],{},[895,2158,2159],{},[898,2160,2161],{},"B",[902,2163,2161],{"encoding":904},", nebude jindy preferovat ",[883,2166,2168],{"className":2167},[886],[888,2169,2170],{"xmlns":890},[892,2171,2172,2176],{},[895,2173,2174],{},[898,2175,2161],{},[902,2177,2161],{"encoding":904},[883,2179,2181],{"className":2180},[886],[888,2182,2183],{"xmlns":890},[892,2184,2185,2189],{},[895,2186,2187],{},[898,2188,2146],{},[902,2190,2146],{"encoding":904},". ",[38,2193,2194],{},"Tranzitivita",": pokud ",[883,2197,2199],{"className":2198},[886],[888,2200,2201],{"xmlns":890},[892,2202,2203,2212],{},[895,2204,2205,2207,2210],{},[898,2206,2146],{},[1656,2208,2209],{},"≻",[898,2211,2161],{},[902,2213,2214],{"encoding":904},"A \\succ B",[883,2216,2218],{"className":2217},[886],[888,2219,2220],{"xmlns":890},[892,2221,2222,2230],{},[895,2223,2224,2226,2228],{},[898,2225,2161],{},[1656,2227,2209],{},[898,2229,1766],{},[902,2231,2232],{"encoding":904},"B \\succ C",", pak ",[883,2235,2237],{"className":2236},[886],[888,2238,2239],{"xmlns":890},[892,2240,2241,2249],{},[895,2242,2243,2245,2247],{},[898,2244,2146],{},[1656,2246,2209],{},[898,2248,1766],{},[902,2250,2251],{"encoding":904},"A \\succ C",[123,2253,2254,2257],{},[38,2255,2256],{},"Rostoucí užitečnost."," Uspokojení roste s množstvím zboží.",[123,2259,2260,2263],{},[38,2261,2262],{},"Klesající mezní užitečnost."," „Přírůstky\" uspokojení klesají s růstem množství zboží.",[724,2265,2266,2267,2270,2271,1863],{},"K naplnění předpokladů je ordinalistický přístup založen na pojmech ",[614,2268,2269],{},"preference"," a na příbuzné ",[614,2272,2273],{},"funkci užitečnosti",[115,2275,2277],{"id":2276},"_62-model-užitečnosti-svazek-zboží-a-funkce-užitečnosti","6.2 Model užitečnosti — svazek zboží a funkce užitečnosti",[724,2279,2280,2281,2295,2296,2299,2300,2313],{},"Uvažujme ",[883,2282,2284],{"className":2283},[886],[888,2285,2286],{"xmlns":890},[892,2287,2288,2293],{},[895,2289,2290],{},[898,2291,2292],{},"n",[902,2294,2292],{"encoding":904}," různých zboží. ",[38,2297,2298],{},"Svazek zboží (bundle of goods)"," je uspořádaná ",[883,2301,2303],{"className":2302},[886],[888,2304,2305],{"xmlns":890},[892,2306,2307,2311],{},[895,2308,2309],{},[898,2310,2292],{},[902,2312,2292],{"encoding":904},"-tice",[724,2315,2316],{},[883,2317,2319],{"className":2318},[886],[888,2320,2321],{"xmlns":890},[892,2322,2323,2350],{},[895,2324,2325,2327,2333,2335,2338,2340,2346,2348],{},[1656,2326,1659],{"stretchy":1658},[1661,2328,2329,2331],{},[898,2330,1665],{},[1667,2332,1669],{},[1656,2334,1673],{"separator":1672},[1656,2336,2337],{},"…",[1656,2339,1673],{"separator":1672},[1661,2341,2342,2344],{},[898,2343,1665],{},[898,2345,2292],{},[1656,2347,1683],{"stretchy":1658},[1656,2349,1673],{"separator":1672},[902,2351,2352],{"encoding":904},"(Q_1, \\dots, Q_n),",[724,2354,2355,2356,2374,2375,2388,2389,2392,2393,2396,2397,2400,2401,2114],{},"kde ",[883,2357,2359],{"className":2358},[886],[888,2360,2361],{"xmlns":890},[892,2362,2363,2371],{},[895,2364,2365],{},[1661,2366,2367,2369],{},[898,2368,1665],{},[898,2370,1710],{},[902,2372,2373],{"encoding":904},"Q_i"," značí množství ",[883,2376,2378],{"className":2377},[886],[888,2379,2380],{"xmlns":890},[892,2381,2382,2386],{},[895,2383,2384],{},[898,2385,1710],{},[902,2387,1710],{"encoding":904},"-tého zboží. Spotřebitel je schopen svazky ",[38,2390,2391],{},"uspořádat"," s rostoucí užitečností, případně je prohlásit za ",[38,2394,2395],{},"indiferentní"," (tj. stejně užitečné). Tím je definována ",[38,2398,2399],{},"relace preference",". Preferenci vyjadřujeme číselně: svazku preferovanému přiřadíme větší číslo, indiferentním svazkům stejné číslo. Dostáváme ",[38,2402,2273],{},[883,2404,2406],{"className":2405},[886],[888,2407,2409],{"xmlns":890,"display":2408},"block",[892,2410,2411,2464],{},[2412,2413,2415],"mtable",{"width":2414},"100%",[2416,2417,2418,2422,2456,2458],"mtr",{},[2419,2420],"mtd",{"width":2421},"50%",[2419,2423,2424],{},[895,2425,2426,2428,2430,2432,2434,2440,2442,2444,2446,2452,2454],{},[898,2427,900],{},[1656,2429,1713],{},[898,2431,900],{},[1656,2433,1659],{"stretchy":1658},[1661,2435,2436,2438],{},[898,2437,1665],{},[1667,2439,1669],{},[1656,2441,1673],{"separator":1672},[1656,2443,2337],{},[1656,2445,1673],{"separator":1672},[1661,2447,2448,2450],{},[898,2449,1665],{},[898,2451,2292],{},[1656,2453,1683],{"stretchy":1658},[1656,2455,1673],{"separator":1672},[2419,2457],{"width":2421},[2419,2459,2460],{},[2461,2462,2463],"mtext",{},"(6.1)",[902,2465,2466],{"encoding":904},"U = U(Q_1, \\dots, Q_n), \\tag{6.1}",[724,2468,2355,2469,2499,2500,2522,2523,2526],{},[883,2470,2472],{"className":2471},[886],[888,2473,2474],{"xmlns":890},[892,2475,2476,2496],{},[895,2477,2478,2484,2486,2488,2490],{},[1661,2479,2480,2482],{},[898,2481,1665],{},[1667,2483,1669],{},[1656,2485,1673],{"separator":1672},[1656,2487,2337],{},[1656,2489,1673],{"separator":1672},[1661,2491,2492,2494],{},[898,2493,1665],{},[898,2495,2292],{},[902,2497,2498],{"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 ",[883,2501,2503],{"className":2502},[886],[888,2504,2505],{"xmlns":890},[892,2506,2507,2519],{},[895,2508,2509,2511,2513],{},[898,2510,900],{},[1656,2512,1673],{"separator":1672},[2033,2514,2515,2517],{"accent":1672},[898,2516,900],{},[1656,2518,2039],{},[902,2520,2521],{"encoding":904},"U, \\tilde U"," reprezentují stejné preference, pokud mezi nimi existuje ",[38,2524,2525],{},"monotónní transformace"," zachovávající pořadí.",[724,2528,2529,2530,2533,2534,1863],{},"Dále se omezíme na funkce pro ",[38,2531,2532],{},"dvě zboží"," — ",[883,2535,2537],{"className":2536},[886],[888,2538,2539],{"xmlns":890},[892,2540,2541,2567],{},[895,2542,2543,2545,2547,2549,2551,2557,2559,2565],{},[898,2544,900],{},[1656,2546,1713],{},[898,2548,900],{},[1656,2550,1659],{"stretchy":1658},[1661,2552,2553,2555],{},[898,2554,1665],{},[1667,2556,1669],{},[1656,2558,1673],{"separator":1672},[1661,2560,2561,2563],{},[898,2562,1665],{},[1667,2564,1680],{},[1656,2566,1683],{"stretchy":1658},[902,2568,2569],{"encoding":904},"U = U(Q_1, Q_2)",[1981,2571,2572,2650],{},[724,2573,2574,2577,2578,2114],{},[883,2575,2576],{},"!example"," Příklad 6.1 — uspořádání a indiference\nPro ",[883,2579,2581],{"className":2580},[886],[888,2582,2583],{"xmlns":890},[892,2584,2585,2647],{},[895,2586,2587,2589,2591,2593,2595,2601,2603,2609,2611,2618,2620,2622,2624],{},[898,2588,900],{},[1656,2590,1713],{},[898,2592,900],{},[1656,2594,1659],{"stretchy":1658},[1661,2596,2597,2599],{},[898,2598,1665],{},[1667,2600,1669],{},[1656,2602,1673],{"separator":1672},[1661,2604,2605,2607],{},[898,2606,1665],{},[1667,2608,1680],{},[1656,2610,1673],{"separator":1672},[1661,2612,2613,2615],{},[898,2614,1665],{},[1667,2616,2617],{},"3",[1656,2619,1683],{"stretchy":1658},[1656,2621,1713],{},[1667,2623,1680],{},[2625,2626,2627],"msqrt",{},[895,2628,2629,2635,2641],{},[1661,2630,2631,2633],{},[898,2632,1665],{},[1667,2634,1669],{},[1661,2636,2637,2639],{},[898,2638,1665],{},[1667,2640,1680],{},[1661,2642,2643,2645],{},[898,2644,1665],{},[1667,2646,2617],{},[902,2648,2649],{"encoding":904},"U = U(Q_1, Q_2, Q_3) = 2\\sqrt{Q_1 Q_2 Q_3}",[120,2651,2652,2857],{},[123,2653,2654,2655,2684,2685,2713,2714,1896,2775,2836,2837,2856],{},"svazek ",[883,2656,2658],{"className":2657},[886],[888,2659,2660],{"xmlns":890},[892,2661,2662,2681],{},[895,2663,2664,2666,2669,2671,2674,2676,2679],{},[1656,2665,1659],{"stretchy":1658},[1667,2667,2668],{},"16",[1656,2670,1673],{"separator":1672},[1667,2672,2673],{},"4",[1656,2675,1673],{"separator":1672},[1667,2677,2678],{},"64",[1656,2680,1683],{"stretchy":1658},[902,2682,2683],{"encoding":904},"(16, 4, 64)"," je preferován před ",[883,2686,2688],{"className":2687},[886],[888,2689,2690],{"xmlns":890},[892,2691,2692,2710],{},[895,2693,2694,2696,2699,2701,2703,2705,2708],{},[1656,2695,1659],{"stretchy":1658},[1667,2697,2698],{},"9",[1656,2700,1673],{"separator":1672},[1667,2702,2698],{},[1656,2704,1673],{"separator":1672},[1667,2706,2707],{},"27",[1656,2709,1683],{"stretchy":1658},[902,2711,2712],{"encoding":904},"(9, 9, 27)",", neboť ",[883,2715,2717],{"className":2716},[886],[888,2718,2719],{"xmlns":890},[892,2720,2721,2772],{},[895,2722,2723,2725,2727,2729,2731,2733,2735,2737,2739,2741,2743,2758,2760,2762,2767,2769],{},[898,2724,900],{},[1656,2726,1659],{"stretchy":1658},[1667,2728,2668],{},[1656,2730,1673],{"separator":1672},[1667,2732,2673],{},[1656,2734,1673],{"separator":1672},[1667,2736,2678],{},[1656,2738,1683],{"stretchy":1658},[1656,2740,1713],{},[1667,2742,1680],{},[2625,2744,2745],{},[895,2746,2747,2749,2752,2754,2756],{},[1667,2748,2668],{},[1656,2750,2751],{},"⋅",[1667,2753,2673],{},[1656,2755,2751],{},[1667,2757,2678],{},[1656,2759,1713],{},[1667,2761,1680],{},[2625,2763,2764],{},[1667,2765,2766],{},"4096",[1656,2768,1713],{},[1667,2770,2771],{},"128",[902,2773,2774],{"encoding":904},"U(16,4,64) = 2\\sqrt{16 \\cdot 4 \\cdot 64} = 2\\sqrt{4096} = 128",[883,2776,2778],{"className":2777},[886],[888,2779,2780],{"xmlns":890},[892,2781,2782,2833],{},[895,2783,2784,2786,2788,2790,2792,2794,2796,2798,2800,2802,2804,2818,2820,2822,2827,2830],{},[898,2785,900],{},[1656,2787,1659],{"stretchy":1658},[1667,2789,2698],{},[1656,2791,1673],{"separator":1672},[1667,2793,2698],{},[1656,2795,1673],{"separator":1672},[1667,2797,2707],{},[1656,2799,1683],{"stretchy":1658},[1656,2801,1713],{},[1667,2803,1680],{},[2625,2805,2806],{},[895,2807,2808,2810,2812,2814,2816],{},[1667,2809,2698],{},[1656,2811,2751],{},[1667,2813,2698],{},[1656,2815,2751],{},[1667,2817,2707],{},[1656,2819,1713],{},[1667,2821,1680],{},[2625,2823,2824],{},[1667,2825,2826],{},"2187",[1656,2828,2829],{},"≐",[1667,2831,2832],{},"93,53",[902,2834,2835],{"encoding":904},"U(9,9,27) = 2\\sqrt{9 \\cdot 9 \\cdot 27} = 2\\sqrt{2187} \\doteq 93{,}53",", tedy ",[883,2838,2840],{"className":2839},[886],[888,2841,2842],{"xmlns":890},[892,2843,2844,2853],{},[895,2845,2846,2848,2851],{},[1667,2847,2771],{},[1656,2849,2850],{},">",[1667,2852,2832],{},[902,2854,2855],{"encoding":904},"128 > 93{,}53",";",[123,2858,2859,2860,1896,2887,2913,2914,1896,2954,2996,2997,3043,3044,1896,3070,3096,3097,1896,3115,3133,3134,1863],{},"svazky ",[883,2861,2863],{"className":2862},[886],[888,2864,2865],{"xmlns":890},[892,2866,2867,2884],{},[895,2868,2869,2871,2873,2875,2878,2880,2882],{},[1656,2870,1659],{"stretchy":1658},[1667,2872,2673],{},[1656,2874,1673],{"separator":1672},[1667,2876,2877],{},"8",[1656,2879,1673],{"separator":1672},[1667,2881,1680],{},[1656,2883,1683],{"stretchy":1658},[902,2885,2886],{"encoding":904},"(4, 8, 2)",[883,2888,2890],{"className":2889},[886],[888,2891,2892],{"xmlns":890},[892,2893,2894,2910],{},[895,2895,2896,2898,2900,2902,2904,2906,2908],{},[1656,2897,1659],{"stretchy":1658},[1667,2899,2678],{},[1656,2901,1673],{"separator":1672},[1667,2903,1669],{},[1656,2905,1673],{"separator":1672},[1667,2907,2673],{},[1656,2909,1683],{"stretchy":1658},[902,2911,2912],{"encoding":904},"(64, 1, 4)"," jsou indiferentní, protože ",[883,2915,2917],{"className":2916},[886],[888,2918,2919],{"xmlns":890},[892,2920,2921,2951],{},[895,2922,2923,2925,2927,2929,2931,2933,2935,2937,2939,2941,2943,2947,2949],{},[898,2924,900],{},[1656,2926,1659],{"stretchy":1658},[1667,2928,2673],{},[1656,2930,1673],{"separator":1672},[1667,2932,2877],{},[1656,2934,1673],{"separator":1672},[1667,2936,1680],{},[1656,2938,1683],{"stretchy":1658},[1656,2940,1713],{},[1667,2942,1680],{},[2625,2944,2945],{},[1667,2946,2678],{},[1656,2948,1713],{},[1667,2950,2668],{},[902,2952,2953],{"encoding":904},"U(4,8,2) = 2\\sqrt{64} = 16",[883,2955,2957],{"className":2956},[886],[888,2958,2959],{"xmlns":890},[892,2960,2961,2993],{},[895,2962,2963,2965,2967,2969,2971,2973,2975,2977,2979,2981,2983,2988,2990],{},[898,2964,900],{},[1656,2966,1659],{"stretchy":1658},[1667,2968,2678],{},[1656,2970,1673],{"separator":1672},[1667,2972,1669],{},[1656,2974,1673],{"separator":1672},[1667,2976,2673],{},[1656,2978,1683],{"stretchy":1658},[1656,2980,1713],{},[1667,2982,1680],{},[2625,2984,2985],{},[1667,2986,2987],{},"256",[1656,2989,1713],{},[1667,2991,2992],{},"32",[902,2994,2995],{"encoding":904},"U(64,1,4) = 2\\sqrt{256} = 32"," — jsou stejně užitečné mezi sebou, pokud ",[883,2998,3000],{"className":2999},[886],[888,3001,3002],{"xmlns":890},[892,3003,3004,3040],{},[895,3005,3006,3008,3010,3012,3014,3016,3018,3020,3022,3024,3026,3028,3030,3032,3034,3036,3038],{},[898,3007,900],{},[1656,3009,1659],{"stretchy":1658},[1667,3011,2673],{},[1656,3013,1673],{"separator":1672},[1667,3015,2877],{},[1656,3017,1673],{"separator":1672},[1667,3019,1680],{},[1656,3021,1683],{"stretchy":1658},[1656,3023,1713],{},[898,3025,900],{},[1656,3027,1659],{"stretchy":1658},[1667,3029,2678],{},[1656,3031,1673],{"separator":1672},[1667,3033,1669],{},[1656,3035,1673],{"separator":1672},[1667,3037,2673],{},[1656,3039,1683],{"stretchy":1658},[902,3041,3042],{"encoding":904},"U(4,8,2) = U(64,1,4)","; ověření: ",[883,3045,3047],{"className":3046},[886],[888,3048,3049],{"xmlns":890},[892,3050,3051,3067],{},[895,3052,3053,3055,3057,3059,3061,3063,3065],{},[1667,3054,2673],{},[1656,3056,2751],{},[1667,3058,2877],{},[1656,3060,2751],{},[1667,3062,1680],{},[1656,3064,1713],{},[1667,3066,2678],{},[902,3068,3069],{"encoding":904},"4 \\cdot 8 \\cdot 2 = 64",[883,3071,3073],{"className":3072},[886],[888,3074,3075],{"xmlns":890},[892,3076,3077,3093],{},[895,3078,3079,3081,3083,3085,3087,3089,3091],{},[1667,3080,2678],{},[1656,3082,2751],{},[1667,3084,1669],{},[1656,3086,2751],{},[1667,3088,2673],{},[1656,3090,1713],{},[1667,3092,2987],{},[902,3094,3095],{"encoding":904},"64 \\cdot 1 \\cdot 4 = 256",", takže ",[883,3098,3100],{"className":3099},[886],[888,3101,3102],{"xmlns":890},[892,3103,3104,3112],{},[895,3105,3106,3108,3110],{},[898,3107,900],{},[1656,3109,1713],{},[1667,3111,2668],{},[902,3113,3114],{"encoding":904},"U = 16",[883,3116,3118],{"className":3117},[886],[888,3119,3120],{"xmlns":890},[892,3121,3122,3130],{},[895,3123,3124,3126,3128],{},[898,3125,900],{},[1656,3127,1713],{},[1667,3129,2992],{},[902,3131,3132],{"encoding":904},"U = 32"," — nejsou indiferentní. Správně indiferentní jsou svazky s týmž součinem ",[883,3135,3137],{"className":3136},[886],[888,3138,3139],{"xmlns":890},[892,3140,3141,3161],{},[895,3142,3143,3149,3155],{},[1661,3144,3145,3147],{},[898,3146,1665],{},[1667,3148,1669],{},[1661,3150,3151,3153],{},[898,3152,1665],{},[1667,3154,1680],{},[1661,3156,3157,3159],{},[898,3158,1665],{},[1667,3160,2617],{},[902,3162,3163],{"encoding":904},"Q_1 Q_2 Q_3",[115,3165,3167],{"id":3166},"mezní-užitečnost-mu","Mezní užitečnost (MU)",[724,3169,3170,3171,3206,3207,1643,3210,3228,3229,3247,3248,3251,3252,3255],{},"Pro funkci užitečnosti ",[883,3172,3174],{"className":3173},[886],[888,3175,3176],{"xmlns":890},[892,3177,3178,3204],{},[895,3179,3180,3182,3184,3186,3188,3194,3196,3202],{},[898,3181,900],{},[1656,3183,1713],{},[898,3185,900],{},[1656,3187,1659],{"stretchy":1658},[1661,3189,3190,3192],{},[898,3191,1665],{},[1667,3193,1669],{},[1656,3195,1673],{"separator":1672},[1661,3197,3198,3200],{},[898,3199,1665],{},[1667,3201,1680],{},[1656,3203,1683],{"stretchy":1658},[902,3205,2569],{"encoding":904}," je ",[38,3208,3209],{},"mezní užitečnost",[883,3211,3213],{"className":3212},[886],[888,3214,3215],{"xmlns":890},[892,3216,3217,3225],{},[895,3218,3219],{},[1661,3220,3221,3223],{},[898,3222,1665],{},[1667,3224,1669],{},[902,3226,3227],{"encoding":904},"Q_1",", resp. ",[883,3230,3232],{"className":3231},[886],[888,3233,3234],{"xmlns":890},[892,3235,3236,3244],{},[895,3237,3238],{},[1661,3239,3240,3242],{},[898,3241,1665],{},[1667,3243,1680],{},[902,3245,3246],{"encoding":904},"Q_2"," (",[38,3249,3250],{},"marginal utility",") parciální ",[207,3253,1145],{"className":3254,"dataFsResolvedFilePath":764,"href":765},[210]," užitečnosti podle příslušné proměnné:",[883,3257,3259],{"className":3258},[886],[888,3260,3261],{"xmlns":890,"display":2408},[892,3262,3263,3366],{},[2412,3264,3265],{"width":2414},[2416,3266,3267,3269,3359,3361],{},[2419,3268],{"width":2421},[2419,3270,3271],{},[895,3272,3273,3275,3281,3283,3291,3293,3313,3315,3319,3321,3327,3329,3337,3339,3357],{},[898,3274,1703],{},[1661,3276,3277,3279],{},[898,3278,900],{},[1667,3280,1669],{},[1656,3282,1713],{},[1715,3284,3285,3287,3289],{},[898,3286,900],{},[1667,3288,1669],{},[1656,3290,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,3292,1713],{},[3294,3295,3296,3303],"mfrac",{},[895,3297,3298,3301],{},[898,3299,3300],{"mathvariant":1723},"∂",[898,3302,900],{},[895,3304,3305,3307],{},[898,3306,3300],{"mathvariant":1723},[1661,3308,3309,3311],{},[898,3310,1665],{},[1667,3312,1669],{},[1656,3314,1673],{"separator":1672},[3316,3317],"mspace",{"width":3318},"1em",[898,3320,1703],{},[1661,3322,3323,3325],{},[898,3324,900],{},[1667,3326,1680],{},[1656,3328,1713],{},[1715,3330,3331,3333,3335],{},[898,3332,900],{},[1667,3334,1680],{},[1656,3336,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,3338,1713],{},[3294,3340,3341,3347],{},[895,3342,3343,3345],{},[898,3344,3300],{"mathvariant":1723},[898,3346,900],{},[895,3348,3349,3351],{},[898,3350,3300],{"mathvariant":1723},[1661,3352,3353,3355],{},[898,3354,1665],{},[1667,3356,1680],{},[898,3358,1863],{"mathvariant":1723},[2419,3360],{"width":2421},[2419,3362,3363],{},[2461,3364,3365],{},"(6.2)",[902,3367,3368],{"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}",[724,3370,3371,3372,3407,3408,3438,3439,1643,3442,1863],{},"Pro pevné ",[883,3373,3375],{"className":3374},[886],[888,3376,3377],{"xmlns":890},[892,3378,3379,3404],{},[895,3380,3381,3387,3389,3391,3393,3399,3401],{},[1661,3382,3383,3385],{},[898,3384,1665],{},[1667,3386,1669],{},[1656,3388,1713],{},[898,3390,207],{},[1656,3392,1673],{"separator":1672},[1661,3394,3395,3397],{},[898,3396,1665],{},[1667,3398,1680],{},[1656,3400,1713],{},[898,3402,3403],{},"b",[902,3405,3406],{"encoding":904},"Q_1 = a, Q_2 = b"," se hodnota ",[883,3409,3411],{"className":3410},[886],[888,3412,3413],{"xmlns":890},[892,3414,3415,3435],{},[895,3416,3417,3419,3425,3427,3429,3431,3433],{},[898,3418,1703],{},[1661,3420,3421,3423],{},[898,3422,900],{},[1667,3424,1669],{},[1656,3426,1659],{"stretchy":1658},[898,3428,207],{},[1656,3430,1673],{"separator":1672},[898,3432,3403],{},[1656,3434,1683],{"stretchy":1658},[902,3436,3437],{"encoding":904},"MU_1(a, b)"," nazývá mezní užitečnost ",[38,3440,3441],{},"v bodě (na hladině)",[883,3443,3445],{"className":3444},[886],[888,3446,3447],{"xmlns":890},[892,3448,3449,3463],{},[895,3450,3451,3454,3456,3458,3460],{},[1656,3452,3453],{"stretchy":1658},"[",[898,3455,207],{},[1656,3457,1673],{"separator":1672},[898,3459,3403],{},[1656,3461,3462],{"stretchy":1658},"]",[902,3464,3465],{"encoding":904},"[a, b]",[1981,3467,3468],{},[724,3469,3470,3473,3474,3504,3533,3534,3547,3548,3565,3566,3587,3588,3605,3606,3619,3620,3639,3640,3662,3663,3692,3693,3713,3714,3731],{},[883,3471,3472],{},"!info"," Intuice — co říká ",[883,3475,3477],{"className":3476},[886],[888,3478,3479],{"xmlns":890},[892,3480,3481,3501],{},[895,3482,3483,3485,3491,3493,3495,3497,3499],{},[898,3484,1703],{},[1661,3486,3487,3489],{},[898,3488,900],{},[1667,3490,1669],{},[1656,3492,1659],{"stretchy":1658},[898,3494,207],{},[1656,3496,1673],{"separator":1672},[898,3498,3403],{},[1656,3500,1683],{"stretchy":1658},[902,3502,3503],{"encoding":904},"MU_1(a,b)",[883,3505,3507],{"className":3506},[886],[888,3508,3509],{"xmlns":890},[892,3510,3511,3531],{},[895,3512,3513,3515,3521,3523,3525,3527,3529],{},[898,3514,1703],{},[1661,3516,3517,3519],{},[898,3518,900],{},[1667,3520,1669],{},[1656,3522,1659],{"stretchy":1658},[898,3524,207],{},[1656,3526,1673],{"separator":1672},[898,3528,3403],{},[1656,3530,1683],{"stretchy":1658},[902,3532,3437],{"encoding":904}," je rychlost změny ",[883,3535,3537],{"className":3536},[886],[888,3538,3539],{"xmlns":890},[892,3540,3541,3545],{},[895,3542,3543],{},[898,3544,900],{},[902,3546,900],{"encoding":904}," vzhledem k ",[883,3549,3551],{"className":3550},[886],[888,3552,3553],{"xmlns":890},[892,3554,3555,3563],{},[895,3556,3557],{},[1661,3558,3559,3561],{},[898,3560,1665],{},[1667,3562,1669],{},[902,3564,3227],{"encoding":904}," v bodě ",[883,3567,3569],{"className":3568},[886],[888,3570,3571],{"xmlns":890},[892,3572,3573,3585],{},[895,3574,3575,3577,3579,3581,3583],{},[1656,3576,3453],{"stretchy":1658},[898,3578,207],{},[1656,3580,1673],{"separator":1672},[898,3582,3403],{},[1656,3584,3462],{"stretchy":1658},[902,3586,3465],{"encoding":904},". Přibližně: změní-li se ",[883,3589,3591],{"className":3590},[886],[888,3592,3593],{"xmlns":890},[892,3594,3595,3603],{},[895,3596,3597],{},[1661,3598,3599,3601],{},[898,3600,1665],{},[1667,3602,1669],{},[902,3604,3227],{"encoding":904}," z ",[883,3607,3609],{"className":3608},[886],[888,3610,3611],{"xmlns":890},[892,3612,3613,3617],{},[895,3614,3615],{},[898,3616,207],{},[902,3618,207],{"encoding":904}," na ",[883,3621,3623],{"className":3622},[886],[888,3624,3625],{"xmlns":890},[892,3626,3627,3636],{},[895,3628,3629,3631,3634],{},[898,3630,207],{},[1656,3632,3633],{},"+",[1667,3635,1669],{},[902,3637,3638],{"encoding":904},"a+1"," při pevném ",[883,3641,3643],{"className":3642},[886],[888,3644,3645],{"xmlns":890},[892,3646,3647,3659],{},[895,3648,3649,3655,3657],{},[1661,3650,3651,3653],{},[898,3652,1665],{},[1667,3654,1680],{},[1656,3656,1713],{},[898,3658,3403],{},[902,3660,3661],{"encoding":904},"Q_2 = b",", změní se užitečnost zhruba o ",[883,3664,3666],{"className":3665},[886],[888,3667,3668],{"xmlns":890},[892,3669,3670,3690],{},[895,3671,3672,3674,3680,3682,3684,3686,3688],{},[898,3673,1703],{},[1661,3675,3676,3678],{},[898,3677,900],{},[1667,3679,1669],{},[1656,3681,1659],{"stretchy":1658},[898,3683,207],{},[1656,3685,1673],{"separator":1672},[898,3687,3403],{},[1656,3689,1683],{"stretchy":1658},[902,3691,3437],{"encoding":904},". Stejně tak ",[883,3694,3696],{"className":3695},[886],[888,3697,3698],{"xmlns":890},[892,3699,3700,3710],{},[895,3701,3702,3704],{},[898,3703,1703],{},[1661,3705,3706,3708],{},[898,3707,900],{},[1667,3709,1680],{},[902,3711,3712],{"encoding":904},"MU_2"," pro ",[883,3715,3717],{"className":3716},[886],[888,3718,3719],{"xmlns":890},[892,3720,3721,3729],{},[895,3722,3723],{},[1661,3724,3725,3727],{},[898,3726,1665],{},[1667,3728,1680],{},[902,3730,3246],{"encoding":904},". Mezní užitečnost tedy odpovídá „užitku z další jednotky\" a podle předpokladu 5 s množstvím klesá.",[198,3733,3735],{"id":3734},"totální-diferenciál","Totální diferenciál",[724,3737,3738,3739,3756,3757,3788,3789,2114],{},"Přibližnou změnu užitečnosti ",[883,3740,3742],{"className":3741},[886],[888,3743,3744],{"xmlns":890},[892,3745,3746,3753],{},[895,3747,3748,3751],{},[898,3749,3750],{"mathvariant":1723},"Δ",[898,3752,900],{},[902,3754,3755],{"encoding":904},"\\Delta U"," odpovídající změnám ",[883,3758,3760],{"className":3759},[886],[888,3761,3762],{"xmlns":890},[892,3763,3764,3785],{},[895,3765,3766,3769,3775,3777,3779],{},[898,3767,3768],{"mathvariant":1723},"d",[1661,3770,3771,3773],{},[898,3772,1665],{},[1667,3774,1669],{},[1656,3776,1673],{"separator":1672},[898,3778,3768],{"mathvariant":1723},[1661,3780,3781,3783],{},[898,3782,1665],{},[1667,3784,1680],{},[902,3786,3787],{"encoding":904},"\\mathrm{d} Q_1, \\mathrm{d} Q_2"," stanovíme pomocí ",[38,3790,3791],{},"totálního diferenciálu",[883,3793,3795],{"className":3794},[886],[888,3796,3797],{"xmlns":890,"display":2408},[892,3798,3799,3901],{},[2412,3800,3801],{"width":2414},[2416,3802,3803,3805,3894,3896],{},[2419,3804],{"width":2421},[2419,3806,3807],{},[895,3808,3809,3811,3813,3816,3818,3820,3822,3830,3832,3838,3840,3848,3850,3856,3858,3860,3866,3868,3874,3876,3878,3884,3886,3892],{},[898,3810,3750],{"mathvariant":1723},[898,3812,900],{},[1656,3814,3815],{},"≈",[898,3817,3768],{"mathvariant":1723},[898,3819,900],{},[1656,3821,1713],{},[1715,3823,3824,3826,3828],{},[898,3825,900],{},[1667,3827,1669],{},[1656,3829,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[898,3831,3768],{"mathvariant":1723},[1661,3833,3834,3836],{},[898,3835,1665],{},[1667,3837,1669],{},[1656,3839,3633],{},[1715,3841,3842,3844,3846],{},[898,3843,900],{},[1667,3845,1680],{},[1656,3847,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[898,3849,3768],{"mathvariant":1723},[1661,3851,3852,3854],{},[898,3853,1665],{},[1667,3855,1680],{},[1656,3857,1713],{},[898,3859,1703],{},[1661,3861,3862,3864],{},[898,3863,900],{},[1667,3865,1669],{},[898,3867,3768],{"mathvariant":1723},[1661,3869,3870,3872],{},[898,3871,1665],{},[1667,3873,1669],{},[1656,3875,3633],{},[898,3877,1703],{},[1661,3879,3880,3882],{},[898,3881,900],{},[1667,3883,1680],{},[898,3885,3768],{"mathvariant":1723},[1661,3887,3888,3890],{},[898,3889,1665],{},[1667,3891,1680],{},[898,3893,1863],{"mathvariant":1723},[2419,3895],{"width":2421},[2419,3897,3898],{},[2461,3899,3900],{},"(6.3)",[902,3902,3903],{"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}",[724,3905,3906,3907,1863],{},"Skutečná změna je ",[883,3908,3910],{"className":3909},[886],[888,3911,3912],{"xmlns":890},[892,3913,3914,3985],{},[895,3915,3916,3918,3920,3922,3924,3926,3932,3934,3936,3942,3944,3950,3952,3954,3960,3962,3965,3967,3969,3975,3977,3983],{},[898,3917,3750],{"mathvariant":1723},[898,3919,900],{},[1656,3921,1713],{},[898,3923,900],{},[1656,3925,1659],{"stretchy":1658},[1661,3927,3928,3930],{},[898,3929,1665],{},[1667,3931,1669],{},[1656,3933,3633],{},[898,3935,3768],{"mathvariant":1723},[1661,3937,3938,3940],{},[898,3939,1665],{},[1667,3941,1669],{},[1656,3943,1673],{"separator":1672},[1661,3945,3946,3948],{},[898,3947,1665],{},[1667,3949,1680],{},[1656,3951,3633],{},[898,3953,3768],{"mathvariant":1723},[1661,3955,3956,3958],{},[898,3957,1665],{},[1667,3959,1680],{},[1656,3961,1683],{"stretchy":1658},[1656,3963,3964],{},"−",[898,3966,900],{},[1656,3968,1659],{"stretchy":1658},[1661,3970,3971,3973],{},[898,3972,1665],{},[1667,3974,1669],{},[1656,3976,1673],{"separator":1672},[1661,3978,3979,3981],{},[898,3980,1665],{},[1667,3982,1680],{},[1656,3984,1683],{"stretchy":1658},[902,3986,3987],{"encoding":904},"\\Delta U = U(Q_1 + \\mathrm{d} Q_1, Q_2 + \\mathrm{d} Q_2) - U(Q_1, Q_2)",[115,3989,3991],{"id":3990},"vlastnosti-funkce-užitečnosti","Vlastnosti funkce užitečnosti",[724,3993,3994,3995,3998,3999,4002],{},"Funkce užitečnosti musí vyjadřovat dva ekonomicky zásadní předpoklady — ",[38,3996,3997],{},"rostoucí užitečnost"," (předpoklad 4) a ",[38,4000,4001],{},"klesající mezní užitečnost"," (předpoklad 5).",[724,4004,4005,4008,4009,3228,4036,4062,4063,1343,4095,4127,4128,1896,4183,4237],{},[38,4006,4007],{},"Předpoklad 4"," (rostoucí užitečnost) znamená, že při pevně zadaných ",[883,4010,4012],{"className":4011},[886],[888,4013,4014],{"xmlns":890},[892,4015,4016,4033],{},[895,4017,4018,4024,4026],{},[1661,4019,4020,4022],{},[898,4021,1665],{},[1667,4023,1680],{},[1656,4025,1713],{},[1661,4027,4028,4030],{},[898,4029,207],{},[1667,4031,4032],{},"0",[902,4034,4035],{"encoding":904},"Q_2 = a_0",[883,4037,4039],{"className":4038},[886],[888,4040,4041],{"xmlns":890},[892,4042,4043,4059],{},[895,4044,4045,4051,4053],{},[1661,4046,4047,4049],{},[898,4048,1665],{},[1667,4050,1669],{},[1656,4052,1713],{},[1661,4054,4055,4057],{},[898,4056,3403],{},[1667,4058,4032],{},[902,4060,4061],{"encoding":904},"Q_1 = b_0"," jsou funkce jedné proměnné ",[883,4064,4066],{"className":4065},[886],[888,4067,4068],{"xmlns":890},[892,4069,4070,4092],{},[895,4071,4072,4074,4076,4082,4084,4090],{},[898,4073,900],{},[1656,4075,1659],{"stretchy":1658},[1661,4077,4078,4080],{},[898,4079,1665],{},[1667,4081,1669],{},[1656,4083,1673],{"separator":1672},[1661,4085,4086,4088],{},[898,4087,207],{},[1667,4089,4032],{},[1656,4091,1683],{"stretchy":1658},[902,4093,4094],{"encoding":904},"U(Q_1, a_0)",[883,4096,4098],{"className":4097},[886],[888,4099,4100],{"xmlns":890},[892,4101,4102,4124],{},[895,4103,4104,4106,4108,4114,4116,4122],{},[898,4105,900],{},[1656,4107,1659],{"stretchy":1658},[1661,4109,4110,4112],{},[898,4111,3403],{},[1667,4113,4032],{},[1656,4115,1673],{"separator":1672},[1661,4117,4118,4120],{},[898,4119,1665],{},[1667,4121,1680],{},[1656,4123,1683],{"stretchy":1658},[902,4125,4126],{"encoding":904},"U(b_0, Q_2)"," rostoucí. To platí, jestliže ",[883,4129,4131],{"className":4130},[886],[888,4132,4133],{"xmlns":890},[892,4134,4135,4180],{},[895,4136,4137,4176,4178],{},[4138,4139,4140],"mstyle",{"scriptlevel":4032,"displaystyle":1672},[3294,4141,4142,4166],{},[895,4143,4144,4146,4148,4150,4156,4158,4164],{},[898,4145,3768],{"mathvariant":1723},[898,4147,900],{},[1656,4149,1659],{"stretchy":1658},[1661,4151,4152,4154],{},[898,4153,1665],{},[1667,4155,1669],{},[1656,4157,1673],{"separator":1672},[1661,4159,4160,4162],{},[898,4161,207],{},[1667,4163,4032],{},[1656,4165,1683],{"stretchy":1658},[895,4167,4168,4170],{},[898,4169,3768],{"mathvariant":1723},[1661,4171,4172,4174],{},[898,4173,1665],{},[1667,4175,1669],{},[1656,4177,2850],{},[1667,4179,4032],{},[902,4181,4182],{"encoding":904},"\\dfrac{\\mathrm{d} U(Q_1, a_0)}{\\mathrm{d} Q_1} > 0",[883,4184,4186],{"className":4185},[886],[888,4187,4188],{"xmlns":890},[892,4189,4190,4234],{},[895,4191,4192,4230,4232],{},[4138,4193,4194],{"scriptlevel":4032,"displaystyle":1672},[3294,4195,4196,4220],{},[895,4197,4198,4200,4202,4204,4210,4212,4218],{},[898,4199,3768],{"mathvariant":1723},[898,4201,900],{},[1656,4203,1659],{"stretchy":1658},[1661,4205,4206,4208],{},[898,4207,3403],{},[1667,4209,4032],{},[1656,4211,1673],{"separator":1672},[1661,4213,4214,4216],{},[898,4215,1665],{},[1667,4217,1680],{},[1656,4219,1683],{"stretchy":1658},[895,4221,4222,4224],{},[898,4223,3768],{"mathvariant":1723},[1661,4225,4226,4228],{},[898,4227,1665],{},[1667,4229,1680],{},[1656,4231,2850],{},[1667,4233,4032],{},[902,4235,4236],{"encoding":904},"\\dfrac{\\mathrm{d} U(b_0, Q_2)}{\\mathrm{d} Q_2} > 0",", tj.",[883,4239,4241],{"className":4240},[886],[888,4242,4243],{"xmlns":890,"display":2408},[892,4244,4245,4291],{},[2412,4246,4247],{"width":2414},[2416,4248,4249,4251,4284,4286],{},[2419,4250],{"width":2421},[2419,4252,4253],{},[895,4254,4255,4263,4265,4267,4269,4271,4279,4281],{},[1715,4256,4257,4259,4261],{},[898,4258,900],{},[1667,4260,1669],{},[1656,4262,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,4264,2850],{},[1667,4266,4032],{},[1656,4268,1673],{"separator":1672},[3316,4270],{"width":3318},[1715,4272,4273,4275,4277],{},[898,4274,900],{},[1667,4276,1680],{},[1656,4278,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,4280,2850],{},[1667,4282,4283],{},"0.",[2419,4285],{"width":2421},[2419,4287,4288],{},[2461,4289,4290],{},"(6.4)",[902,4292,4293],{"encoding":904},"U'_1 > 0, \\quad U'_2 > 0. \\tag{6.4}",[724,4295,4296,4297,4300],{},"Tedy mezní užitečnosti obou zboží jsou ",[38,4298,4299],{},"kladné"," — užitečnost roste s množstvím každého zboží.",[724,4302,4303,4306,4307,4337,4338,2114],{},[38,4304,4305],{},"Předpoklad 5"," (klesající mezní užitečnost) požaduje, aby ",[883,4308,4310],{"className":4309},[886],[888,4311,4312],{"xmlns":890},[892,4313,4314,4334],{},[895,4315,4316,4324,4326],{},[1715,4317,4318,4320,4322],{},[898,4319,900],{},[1667,4321,1669],{},[1656,4323,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,4325,1673],{"separator":1672},[1715,4327,4328,4330,4332],{},[898,4329,900],{},[1667,4331,1680],{},[1656,4333,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[902,4335,4336],{"encoding":904},"U'_1, U'_2"," byly klesající funkce. To znamená, že jejich parciální derivace podle příslušné proměnné jsou ",[38,4339,4340],{},"záporné",[883,4342,4344],{"className":4343},[886],[888,4345,4346],{"xmlns":890,"display":2408},[892,4347,4348,4404],{},[2412,4349,4350],{"width":2414},[2416,4351,4352,4354,4397,4399],{},[2419,4353],{"width":2421},[2419,4355,4356],{},[895,4357,4358,4371,4374,4376,4378,4380,4393,4395],{},[1715,4359,4360,4362,4365],{},[898,4361,900],{},[1667,4363,4364],{},"11",[895,4366,4367,4369],{},[1656,4368,1725],{"mathvariant":1723},[1656,4370,1725],{"mathvariant":1723},[1656,4372,4373],{},"\u003C",[1667,4375,4032],{},[1656,4377,1673],{"separator":1672},[3316,4379],{"width":3318},[1715,4381,4382,4384,4387],{},[898,4383,900],{},[1667,4385,4386],{},"22",[895,4388,4389,4391],{},[1656,4390,1725],{"mathvariant":1723},[1656,4392,1725],{"mathvariant":1723},[1656,4394,4373],{},[1667,4396,4283],{},[2419,4398],{"width":2421},[2419,4400,4401],{},[2461,4402,4403],{},"(6.5)",[902,4405,4406],{"encoding":904},"U''_{11} \u003C 0, \\quad U''_{22} \u003C 0. \\tag{6.5}",[724,4408,4409,4410,4413,4414,1863],{},"Podmínka (6.5) je známa jako ",[38,4411,4412],{},"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 ",[207,4415,4417],{"className":4416,"dataFsResolvedFilePath":857,"href":858},[210],"produkční teorie",[724,4419,4420,4421,1896,4453,4485,4486,1896,4512,4538,4539,4567,4568,1896,4571,4574,4575,4610],{},"Podmínky (6.4), (6.5) určují tvary křivek ",[883,4422,4424],{"className":4423},[886],[888,4425,4426],{"xmlns":890},[892,4427,4428,4450],{},[895,4429,4430,4432,4434,4440,4442,4448],{},[898,4431,900],{},[1656,4433,1659],{"stretchy":1658},[1661,4435,4436,4438],{},[898,4437,1665],{},[1667,4439,1669],{},[1656,4441,1673],{"separator":1672},[1661,4443,4444,4446],{},[898,4445,3403],{},[1667,4447,4032],{},[1656,4449,1683],{"stretchy":1658},[902,4451,4452],{"encoding":904},"U(Q_1, b_0)",[883,4454,4456],{"className":4455},[886],[888,4457,4458],{"xmlns":890},[892,4459,4460,4482],{},[895,4461,4462,4464,4466,4472,4474,4480],{},[898,4463,900],{},[1656,4465,1659],{"stretchy":1658},[1661,4467,4468,4470],{},[898,4469,207],{},[1667,4471,4032],{},[1656,4473,1673],{"separator":1672},[1661,4475,4476,4478],{},[898,4477,1665],{},[1667,4479,1680],{},[1656,4481,1683],{"stretchy":1658},[902,4483,4484],{"encoding":904},"U(a_0, Q_2)"," v souřadnicových rovinách ",[883,4487,4489],{"className":4488},[886],[888,4490,4491],{"xmlns":890},[892,4492,4493,4509],{},[895,4494,4495,4497,4499,4501,4507],{},[1656,4496,1659],{"stretchy":1658},[898,4498,900],{},[1656,4500,1673],{"separator":1672},[1661,4502,4503,4505],{},[898,4504,1665],{},[1667,4506,1669],{},[1656,4508,1683],{"stretchy":1658},[902,4510,4511],{"encoding":904},"(U, Q_1)",[883,4513,4515],{"className":4514},[886],[888,4516,4517],{"xmlns":890},[892,4518,4519,4535],{},[895,4520,4521,4523,4525,4527,4533],{},[1656,4522,1659],{"stretchy":1658},[898,4524,900],{},[1656,4526,1673],{"separator":1672},[1661,4528,4529,4531],{},[898,4530,1665],{},[1667,4532,1680],{},[1656,4534,1683],{"stretchy":1658},[902,4536,4537],{"encoding":904},"(U, Q_2)"," (obrázek 6.1). Tyto křivky procházejí počátkem (neboť obvykle ",[883,4540,4542],{"className":4541},[886],[888,4543,4544],{"xmlns":890},[892,4545,4546,4564],{},[895,4547,4548,4550,4552,4554,4556,4558,4560,4562],{},[898,4549,900],{},[1656,4551,1659],{"stretchy":1658},[1667,4553,4032],{},[1656,4555,1673],{"separator":1672},[1667,4557,4032],{},[1656,4559,1683],{"stretchy":1658},[1656,4561,1713],{},[1667,4563,4032],{},[902,4565,4566],{"encoding":904},"U(0, 0) = 0","), jsou ",[38,4569,4570],{},"rostoucí",[38,4572,4573],{},"konkávní",". Typický tvar grafu ",[883,4576,4578],{"className":4577},[886],[888,4579,4580],{"xmlns":890},[892,4581,4582,4608],{},[895,4583,4584,4586,4588,4590,4592,4598,4600,4606],{},[898,4585,900],{},[1656,4587,1713],{},[898,4589,900],{},[1656,4591,1659],{"stretchy":1658},[1661,4593,4594,4596],{},[898,4595,1665],{},[1667,4597,1669],{},[1656,4599,1673],{"separator":1672},[1661,4601,4602,4604],{},[898,4603,1665],{},[1667,4605,1680],{},[1656,4607,1683],{"stretchy":1658},[902,4609,2569],{"encoding":904}," — plocha v prostoru — je na obrázku 6.2.",[724,4612,4613],{},[614,4614,4615,4616,3639,4644,4665,4666,3639,4694,4716],{},"Obrázek 6.1 — typické průběhy funkce užitečnosti ",[883,4617,4619],{"className":4618},[886],[888,4620,4621],{"xmlns":890},[892,4622,4623,4641],{},[895,4624,4625,4627,4629,4635,4637,4639],{},[898,4626,900],{},[1656,4628,1659],{"stretchy":1658},[1661,4630,4631,4633],{},[898,4632,1665],{},[1667,4634,1669],{},[1656,4636,1673],{"separator":1672},[898,4638,3403],{},[1656,4640,1683],{"stretchy":1658},[902,4642,4643],{"encoding":904},"U(Q_1, b)",[883,4645,4647],{"className":4646},[886],[888,4648,4649],{"xmlns":890},[892,4650,4651,4663],{},[895,4652,4653,4659,4661],{},[1661,4654,4655,4657],{},[898,4656,1665],{},[1667,4658,1680],{},[1656,4660,1713],{},[898,4662,3403],{},[902,4664,3661],{"encoding":904}," (vlevo) a ",[883,4667,4669],{"className":4668},[886],[888,4670,4671],{"xmlns":890},[892,4672,4673,4691],{},[895,4674,4675,4677,4679,4681,4683,4689],{},[898,4676,900],{},[1656,4678,1659],{"stretchy":1658},[898,4680,207],{},[1656,4682,1673],{"separator":1672},[1661,4684,4685,4687],{},[898,4686,1665],{},[1667,4688,1680],{},[1656,4690,1683],{"stretchy":1658},[902,4692,4693],{"encoding":904},"U(a, Q_2)",[883,4695,4697],{"className":4696},[886],[888,4698,4699],{"xmlns":890},[892,4700,4701,4713],{},[895,4702,4703,4709,4711],{},[1661,4704,4705,4707],{},[898,4706,1665],{},[1667,4708,1669],{},[1656,4710,1713],{},[898,4712,207],{},[902,4714,4715],{"encoding":904},"Q_1 = a"," (vpravo) pro různé hladiny druhé proměnné.",[724,4718,4719],{},[614,4720,4721,4722,4757,4758,4788,4789,1896,4812,4834,4835,1863],{},"Obrázek 6.2 — plocha funkce užitečnosti ",[883,4723,4725],{"className":4724},[886],[888,4726,4727],{"xmlns":890},[892,4728,4729,4755],{},[895,4730,4731,4733,4735,4737,4739,4745,4747,4753],{},[898,4732,900],{},[1656,4734,1713],{},[898,4736,900],{},[1656,4738,1659],{"stretchy":1658},[1661,4740,4741,4743],{},[898,4742,1665],{},[1667,4744,1669],{},[1656,4746,1673],{"separator":1672},[1661,4748,4749,4751],{},[898,4750,1665],{},[1667,4752,1680],{},[1656,4754,1683],{"stretchy":1658},[902,4756,2569],{"encoding":904}," nad rovinou ",[883,4759,4761],{"className":4760},[886],[888,4762,4763],{"xmlns":890},[892,4764,4765,4785],{},[895,4766,4767,4769,4775,4777,4783],{},[1656,4768,1659],{"stretchy":1658},[1661,4770,4771,4773],{},[898,4772,1665],{},[1667,4774,1669],{},[1656,4776,1673],{"separator":1672},[1661,4778,4779,4781],{},[898,4780,1665],{},[1667,4782,1680],{},[1656,4784,1683],{"stretchy":1658},[902,4786,4787],{"encoding":904},"(Q_1, Q_2)"," s řezy rovinami ",[883,4790,4792],{"className":4791},[886],[888,4793,4794],{"xmlns":890},[892,4795,4796,4809],{},[895,4797,4798,4804,4806],{},[1661,4799,4800,4802],{},[898,4801,1665],{},[1667,4803,1669],{},[1656,4805,1713],{},[2461,4807,4808],{},"const",[902,4810,4811],{"encoding":904},"Q_1 = \\text{const}",[883,4813,4815],{"className":4814},[886],[888,4816,4817],{"xmlns":890},[892,4818,4819,4831],{},[895,4820,4821,4827,4829],{},[1661,4822,4823,4825],{},[898,4824,1665],{},[1667,4826,1680],{},[1656,4828,1713],{},[2461,4830,4808],{},[902,4832,4833],{"encoding":904},"Q_2 = \\text{const}"," a s křivkou ",[883,4836,4838],{"className":4837},[886],[888,4839,4840],{"xmlns":890},[892,4841,4842,4868],{},[895,4843,4844,4846,4848,4854,4856,4862,4864,4866],{},[898,4845,900],{},[1656,4847,1659],{"stretchy":1658},[1661,4849,4850,4852],{},[898,4851,1665],{},[1667,4853,1669],{},[1656,4855,1673],{"separator":1672},[1661,4857,4858,4860],{},[898,4859,1665],{},[1667,4861,1680],{},[1656,4863,1683],{"stretchy":1658},[1656,4865,1713],{},[898,4867,1745],{},[902,4869,4870],{"encoding":904},"U(Q_1, Q_2) = c",[198,4872,4874,4875],{"id":4873},"příklad-62-ověření-vlastností-a-dopočet-pro-uq112q213u-q_112-q_213","Příklad 6.2 — ověření vlastností a dopočet pro ",[883,4876,4878],{"className":4877},[886],[888,4879,4880],{"xmlns":890},[892,4881,4882,4916],{},[895,4883,4884,4886,4888,4902],{},[898,4885,900],{},[1656,4887,1713],{},[1715,4889,4890,4892,4894],{},[898,4891,1665],{},[1667,4893,1669],{},[895,4895,4896,4898,4900],{},[1667,4897,1669],{},[898,4899,1782],{"mathvariant":1723},[1667,4901,1680],{},[1715,4903,4904,4906,4908],{},[898,4905,1665],{},[1667,4907,1680],{},[895,4909,4910,4912,4914],{},[1667,4911,1669],{},[898,4913,1782],{"mathvariant":1723},[1667,4915,2617],{},[902,4917,4918],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F3}",[724,4920,4921],{},[38,4922,4923],{},"Ověření (6.4) a (6.5).",[883,4925,4927],{"className":4926},[886],[888,4928,4929],{"xmlns":890,"display":2408},[892,4930,4931,5035],{},[895,4932,4933,4941,4943,4951,4967,4981,4983,4985,4993,4995,5003,5017,5033],{},[1715,4934,4935,4937,4939],{},[898,4936,900],{},[1667,4938,1669],{},[1656,4940,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,4942,1713],{},[4138,4944,4945],{"scriptlevel":4032,"displaystyle":1658},[3294,4946,4947,4949],{},[1667,4948,1669],{},[1667,4950,1680],{},[1715,4952,4953,4955,4957],{},[898,4954,1665],{},[1667,4956,1669],{},[895,4958,4959,4961,4963,4965],{},[1656,4960,3964],{},[1667,4962,1669],{},[898,4964,1782],{"mathvariant":1723},[1667,4966,1680],{},[1715,4968,4969,4971,4973],{},[898,4970,1665],{},[1667,4972,1680],{},[895,4974,4975,4977,4979],{},[1667,4976,1669],{},[898,4978,1782],{"mathvariant":1723},[1667,4980,2617],{},[1656,4982,1673],{"separator":1672},[3316,4984],{"width":3318},[1715,4986,4987,4989,4991],{},[898,4988,900],{},[1667,4990,1680],{},[1656,4992,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,4994,1713],{},[4138,4996,4997],{"scriptlevel":4032,"displaystyle":1658},[3294,4998,4999,5001],{},[1667,5000,1669],{},[1667,5002,2617],{},[1715,5004,5005,5007,5009],{},[898,5006,1665],{},[1667,5008,1669],{},[895,5010,5011,5013,5015],{},[1667,5012,1669],{},[898,5014,1782],{"mathvariant":1723},[1667,5016,1680],{},[1715,5018,5019,5021,5023],{},[898,5020,1665],{},[1667,5022,1680],{},[895,5024,5025,5027,5029,5031],{},[1656,5026,3964],{},[1667,5028,1680],{},[898,5030,1782],{"mathvariant":1723},[1667,5032,2617],{},[1656,5034,1673],{"separator":1672},[902,5036,5037],{"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},",[724,5039,5040,5041,5075],{},"zřejmě ",[883,5042,5044],{"className":5043},[886],[888,5045,5046],{"xmlns":890},[892,5047,5048,5072],{},[895,5049,5050,5058,5060,5068,5070],{},[1715,5051,5052,5054,5056],{},[898,5053,900],{},[1667,5055,1669],{},[1656,5057,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,5059,1673],{"separator":1672},[1715,5061,5062,5064,5066],{},[898,5063,900],{},[1667,5065,1680],{},[1656,5067,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,5069,2850],{},[1667,5071,4032],{},[902,5073,5074],{"encoding":904},"U'_1, U'_2 > 0"," a platí (6.4). Dále:",[883,5077,5079],{"className":5078},[886],[888,5080,5081],{"xmlns":890,"display":2408},[892,5082,5083,5200],{},[895,5084,5085,5097,5099,5101,5109,5125,5139,5141,5143,5155,5157,5159,5167,5181,5198],{},[1715,5086,5087,5089,5091],{},[898,5088,900],{},[1667,5090,4364],{},[895,5092,5093,5095],{},[1656,5094,1725],{"mathvariant":1723},[1656,5096,1725],{"mathvariant":1723},[1656,5098,1713],{},[1656,5100,3964],{},[4138,5102,5103],{"scriptlevel":4032,"displaystyle":1658},[3294,5104,5105,5107],{},[1667,5106,1669],{},[1667,5108,2673],{},[1715,5110,5111,5113,5115],{},[898,5112,1665],{},[1667,5114,1669],{},[895,5116,5117,5119,5121,5123],{},[1656,5118,3964],{},[1667,5120,2617],{},[898,5122,1782],{"mathvariant":1723},[1667,5124,1680],{},[1715,5126,5127,5129,5131],{},[898,5128,1665],{},[1667,5130,1680],{},[895,5132,5133,5135,5137],{},[1667,5134,1669],{},[898,5136,1782],{"mathvariant":1723},[1667,5138,2617],{},[1656,5140,1673],{"separator":1672},[3316,5142],{"width":3318},[1715,5144,5145,5147,5149],{},[898,5146,900],{},[1667,5148,4386],{},[895,5150,5151,5153],{},[1656,5152,1725],{"mathvariant":1723},[1656,5154,1725],{"mathvariant":1723},[1656,5156,1713],{},[1656,5158,3964],{},[4138,5160,5161],{"scriptlevel":4032,"displaystyle":1658},[3294,5162,5163,5165],{},[1667,5164,1680],{},[1667,5166,2698],{},[1715,5168,5169,5171,5173],{},[898,5170,1665],{},[1667,5172,1669],{},[895,5174,5175,5177,5179],{},[1667,5176,1669],{},[898,5178,1782],{"mathvariant":1723},[1667,5180,1680],{},[1715,5182,5183,5185,5187],{},[898,5184,1665],{},[1667,5186,1680],{},[895,5188,5189,5191,5194,5196],{},[1656,5190,3964],{},[1667,5192,5193],{},"5",[898,5195,1782],{"mathvariant":1723},[1667,5197,2617],{},[1656,5199,1673],{"separator":1672},[902,5201,5202],{"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},",[724,5204,5205,5206,5248],{},"opět ",[883,5207,5209],{"className":5208},[886],[888,5210,5211],{"xmlns":890},[892,5212,5213,5245],{},[895,5214,5215,5227,5229,5241,5243],{},[1715,5216,5217,5219,5221],{},[898,5218,900],{},[1667,5220,4364],{},[895,5222,5223,5225],{},[1656,5224,1725],{"mathvariant":1723},[1656,5226,1725],{"mathvariant":1723},[1656,5228,1673],{"separator":1672},[1715,5230,5231,5233,5235],{},[898,5232,900],{},[1667,5234,4386],{},[895,5236,5237,5239],{},[1656,5238,1725],{"mathvariant":1723},[1656,5240,1725],{"mathvariant":1723},[1656,5242,4373],{},[1667,5244,4032],{},[902,5246,5247],{"encoding":904},"U''_{11}, U''_{22} \u003C 0",", platí (6.5).",[724,5250,5251],{},[38,5252,5253,5254,1863],{},"(a) Mezní užitečnosti v bodě ",[883,5255,5257],{"className":5256},[886],[888,5258,5259],{"xmlns":890},[892,5260,5261,5275],{},[895,5262,5263,5265,5268,5270,5273],{},[1656,5264,3453],{"stretchy":1658},[1667,5266,5267],{},"100",[1656,5269,1673],{"separator":1672},[1667,5271,5272],{},"200",[1656,5274,3462],{"stretchy":1658},[902,5276,5277],{"encoding":904},"[100, 200]",[883,5279,5281],{"className":5280},[886],[888,5282,5283],{"xmlns":890,"display":2408},[892,5284,5285,5352],{},[895,5286,5287,5289,5295,5297,5299,5301,5303,5305,5307,5315,5317,5331,5333,5345,5347,5350],{},[898,5288,1703],{},[1661,5290,5291,5293],{},[898,5292,900],{},[1667,5294,1669],{},[1656,5296,1659],{"stretchy":1658},[1667,5298,5267],{},[1656,5300,1673],{"separator":1672},[1667,5302,5272],{},[1656,5304,1683],{"stretchy":1658},[1656,5306,1713],{},[4138,5308,5309],{"scriptlevel":4032,"displaystyle":1658},[3294,5310,5311,5313],{},[1667,5312,1669],{},[1667,5314,1680],{},[1656,5316,2751],{},[2062,5318,5319,5321],{},[1667,5320,5267],{},[895,5322,5323,5325,5327,5329],{},[1656,5324,3964],{},[1667,5326,1669],{},[898,5328,1782],{"mathvariant":1723},[1667,5330,1680],{},[1656,5332,2751],{},[2062,5334,5335,5337],{},[1667,5336,5272],{},[895,5338,5339,5341,5343],{},[1667,5340,1669],{},[898,5342,1782],{"mathvariant":1723},[1667,5344,2617],{},[1656,5346,2829],{},[1667,5348,5349],{},"0,4204",[1656,5351,1673],{"separator":1672},[902,5353,5354],{"encoding":904},"MU_1(100, 200) = \\tfrac{1}{2} \\cdot 100^{-1\u002F2} \\cdot 200^{1\u002F3} \\doteq 0{,}4204,",[883,5356,5358],{"className":5357},[886],[888,5359,5360],{"xmlns":890,"display":2408},[892,5361,5362,5427],{},[895,5363,5364,5366,5372,5374,5376,5378,5380,5382,5384,5392,5394,5406,5408,5422,5424],{},[898,5365,1703],{},[1661,5367,5368,5370],{},[898,5369,900],{},[1667,5371,1680],{},[1656,5373,1659],{"stretchy":1658},[1667,5375,5267],{},[1656,5377,1673],{"separator":1672},[1667,5379,5272],{},[1656,5381,1683],{"stretchy":1658},[1656,5383,1713],{},[4138,5385,5386],{"scriptlevel":4032,"displaystyle":1658},[3294,5387,5388,5390],{},[1667,5389,1669],{},[1667,5391,2617],{},[1656,5393,2751],{},[2062,5395,5396,5398],{},[1667,5397,5267],{},[895,5399,5400,5402,5404],{},[1667,5401,1669],{},[898,5403,1782],{"mathvariant":1723},[1667,5405,1680],{},[1656,5407,2751],{},[2062,5409,5410,5412],{},[1667,5411,5272],{},[895,5413,5414,5416,5418,5420],{},[1656,5415,3964],{},[1667,5417,1680],{},[898,5419,1782],{"mathvariant":1723},[1667,5421,2617],{},[1656,5423,2829],{},[1667,5425,5426],{},"0,63067.",[902,5428,5429],{"encoding":904},"MU_2(100, 200) = \\tfrac{1}{3} \\cdot 100^{1\u002F2} \\cdot 200^{-2\u002F3} \\doteq 0{,}63067.",[724,5431,5432,1643,5435,5470,5471,5492,5493,5510],{},[614,5433,5434],{},"Interpretace:",[883,5436,5438],{"className":5437},[886],[888,5439,5440],{"xmlns":890},[892,5441,5442,5467],{},[895,5443,5444,5446,5452,5454,5456,5458,5460,5462,5464],{},[898,5445,1703],{},[1661,5447,5448,5450],{},[898,5449,900],{},[1667,5451,1680],{},[1656,5453,1659],{"stretchy":1658},[1667,5455,5267],{},[1656,5457,1673],{"separator":1672},[1667,5459,5272],{},[1656,5461,1683],{"stretchy":1658},[1656,5463,2829],{},[1667,5465,5466],{},"0,63067",[902,5468,5469],{"encoding":904},"MU_2(100, 200) \\doteq 0{,}63067"," znamená, že na hladině ",[883,5472,5474],{"className":5473},[886],[888,5475,5476],{"xmlns":890},[892,5477,5478,5490],{},[895,5479,5480,5482,5484,5486,5488],{},[1656,5481,3453],{"stretchy":1658},[1667,5483,5267],{},[1656,5485,1673],{"separator":1672},[1667,5487,5272],{},[1656,5489,3462],{"stretchy":1658},[902,5491,5277],{"encoding":904}," roste užitečnost při jednotkové změně ",[883,5494,5496],{"className":5495},[886],[888,5497,5498],{"xmlns":890},[892,5499,5500,5508],{},[895,5501,5502],{},[1661,5503,5504,5506],{},[898,5505,1665],{},[1667,5507,1680],{},[902,5509,3246],{"encoding":904}," přibližně o 0,63067.",[724,5512,5513,5532,5533,5554,5555,5572,5573,5599,5600,5617,5618,5642],{},[38,5514,5515,5516,5531],{},"(b) Odhad změny ",[883,5517,5519],{"className":5518},[886],[888,5520,5521],{"xmlns":890},[892,5522,5523,5529],{},[895,5524,5525,5527],{},[898,5526,3750],{"mathvariant":1723},[898,5528,900],{},[902,5530,3755],{"encoding":904}," pomocí totálního diferenciálu (6.3)."," Klesne-li vzhledem k hladině ",[883,5534,5536],{"className":5535},[886],[888,5537,5538],{"xmlns":890},[892,5539,5540,5552],{},[895,5541,5542,5544,5546,5548,5550],{},[1656,5543,3453],{"stretchy":1658},[1667,5545,5267],{},[1656,5547,1673],{"separator":1672},[1667,5549,5272],{},[1656,5551,3462],{"stretchy":1658},[902,5553,5277],{"encoding":904}," množství ",[883,5556,5558],{"className":5557},[886],[888,5559,5560],{"xmlns":890},[892,5561,5562,5570],{},[895,5563,5564],{},[1661,5565,5566,5568],{},[898,5567,1665],{},[1667,5569,1669],{},[902,5571,3227],{"encoding":904}," na 98 (tj. ",[883,5574,5576],{"className":5575},[886],[888,5577,5578],{"xmlns":890},[892,5579,5580,5596],{},[895,5581,5582,5584,5590,5592,5594],{},[898,5583,3768],{"mathvariant":1723},[1661,5585,5586,5588],{},[898,5587,1665],{},[1667,5589,1669],{},[1656,5591,1713],{},[1656,5593,3964],{},[1667,5595,1680],{},[902,5597,5598],{"encoding":904},"\\mathrm{d} Q_1 = -2",") a vzroste-li ",[883,5601,5603],{"className":5602},[886],[888,5604,5605],{"xmlns":890},[892,5606,5607,5615],{},[895,5608,5609],{},[1661,5610,5611,5613],{},[898,5612,1665],{},[1667,5614,1680],{},[902,5616,3246],{"encoding":904}," o 3 (tj. ",[883,5619,5621],{"className":5620},[886],[888,5622,5623],{"xmlns":890},[892,5624,5625,5639],{},[895,5626,5627,5629,5635,5637],{},[898,5628,3768],{"mathvariant":1723},[1661,5630,5631,5633],{},[898,5632,1665],{},[1667,5634,1680],{},[1656,5636,1713],{},[1667,5638,2617],{},[902,5640,5641],{"encoding":904},"\\mathrm{d} Q_2 = 3","):",[883,5644,5646],{"className":5645},[886],[888,5647,5648],{"xmlns":890,"display":2408},[892,5649,5650,5701],{},[895,5651,5652,5654,5656,5658,5660,5662,5664,5666,5668,5670,5672,5674,5676,5678,5680,5682,5684,5686,5688,5691,5693,5696,5698],{},[898,5653,3750],{"mathvariant":1723},[898,5655,900],{},[1656,5657,3815],{},[898,5659,3768],{"mathvariant":1723},[898,5661,900],{},[1656,5663,1713],{},[1667,5665,5349],{},[1656,5667,2751],{},[1656,5669,1659],{"stretchy":1658},[1656,5671,3964],{},[1667,5673,1680],{},[1656,5675,1683],{"stretchy":1658},[1656,5677,3633],{},[1667,5679,5466],{},[1656,5681,2751],{},[1667,5683,2617],{},[1656,5685,1713],{},[1656,5687,3964],{},[1667,5689,5690],{},"0,8408",[1656,5692,3633],{},[1667,5694,5695],{},"1,89201",[1656,5697,2829],{},[1667,5699,5700],{},"1,05.",[902,5702,5703],{"encoding":904},"\\Delta U \\approx \\mathrm{d} U = 0{,}4204 \\cdot (-2) + 0{,}63067 \\cdot 3 = -0{,}8408 + 1{,}89201 \\doteq 1{,}05.",[724,5705,5706,5707,5710,5711,5762,5763,1863],{},"Užitečnost se tedy zvýší přibližně o ",[38,5708,5709],{},"1,05",". Skutečná změna je ",[883,5712,5714],{"className":5713},[886],[888,5715,5716],{"xmlns":890},[892,5717,5718,5759],{},[895,5719,5720,5722,5724,5726,5728,5730,5733,5735,5738,5740,5742,5744,5746,5748,5750,5752,5754,5756],{},[898,5721,3750],{"mathvariant":1723},[898,5723,900],{},[1656,5725,1713],{},[898,5727,900],{},[1656,5729,1659],{"stretchy":1658},[1667,5731,5732],{},"98",[1656,5734,1673],{"separator":1672},[1667,5736,5737],{},"203",[1656,5739,1683],{"stretchy":1658},[1656,5741,3964],{},[898,5743,900],{},[1656,5745,1659],{"stretchy":1658},[1667,5747,5267],{},[1656,5749,1673],{"separator":1672},[1667,5751,5272],{},[1656,5753,1683],{"stretchy":1658},[1656,5755,2829],{},[1667,5757,5758],{},"1,031",[902,5760,5761],{"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 ",[883,5764,5766],{"className":5765},[886],[888,5767,5768],{"xmlns":890},[892,5769,5770,5790],{},[895,5771,5772,5774,5780,5782,5784],{},[898,5773,3768],{"mathvariant":1723},[1661,5775,5776,5778],{},[898,5777,1665],{},[1667,5779,1669],{},[1656,5781,1673],{"separator":1672},[898,5783,3768],{"mathvariant":1723},[1661,5785,5786,5788],{},[898,5787,1665],{},[1667,5789,1680],{},[902,5791,3787],{"encoding":904},[115,5793,5795],{"id":5794},"cobb-douglasova-funkce-užitečnosti","Cobb-Douglasova funkce užitečnosti",[724,5797,5798],{},"Nejčastěji používané funkce užitečnosti mají tvar",[883,5800,5802],{"className":5801},[886],[888,5803,5804],{"xmlns":890,"display":2408},[892,5805,5806,5865],{},[2412,5807,5808],{"width":2414},[2416,5809,5810,5812,5858,5860],{},[2419,5811],{"width":2421},[2419,5813,5814],{},[895,5815,5816,5818,5820,5826,5828,5834,5836,5838,5846,5848,5856],{},[898,5817,900],{},[1656,5819,1659],{"stretchy":1658},[1661,5821,5822,5824],{},[898,5823,1665],{},[1667,5825,1669],{},[1656,5827,1673],{"separator":1672},[1661,5829,5830,5832],{},[898,5831,1665],{},[1667,5833,1680],{},[1656,5835,1683],{"stretchy":1658},[1656,5837,1713],{},[1715,5839,5840,5842,5844],{},[898,5841,1665],{},[1667,5843,1669],{},[898,5845,207],{},[1656,5847,2751],{},[1715,5849,5850,5852,5854],{},[898,5851,1665],{},[1667,5853,1680],{},[898,5855,3403],{},[1656,5857,1673],{"separator":1672},[2419,5859],{"width":2421},[2419,5861,5862],{},[2461,5863,5864],{},"(6.6)",[902,5866,5867],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^b, \\tag{6.6}",[724,5869,2355,5870,5888,5889,5892,5893,5897,5898,5929,5930,5952],{},[883,5871,5873],{"className":5872},[886],[888,5874,5875],{"xmlns":890},[892,5876,5877,5885],{},[895,5878,5879,5881,5883],{},[898,5880,207],{},[1656,5882,1673],{"separator":1672},[898,5884,3403],{},[902,5886,5887],{"encoding":904},"a, b"," jsou kladná čísla; nazývají se ",[38,5890,5891],{},"Cobb-Douglasovy"," (v příbuznosti s produkčními funkcemi — viz ",[207,5894,5896],{"className":5895,"dataFsResolvedFilePath":857,"href":858},[210],"kapitola 5","). Obvykle se volí ",[883,5899,5901],{"className":5900},[886],[888,5902,5903],{"xmlns":890},[892,5904,5905,5926],{},[895,5906,5907,5909,5911,5913,5916,5918,5920,5922,5924],{},[898,5908,207],{},[1656,5910,1673],{"separator":1672},[898,5912,3403],{},[1656,5914,5915],{},"∈",[1656,5917,1659],{"stretchy":1658},[1667,5919,4032],{},[1656,5921,1673],{"separator":1672},[1667,5923,1669],{},[1656,5925,1683],{"stretchy":1658},[902,5927,5928],{"encoding":904},"a, b \\in (0, 1)",", často se klade ",[883,5931,5933],{"className":5932},[886],[888,5934,5935],{"xmlns":890},[892,5936,5937,5949],{},[895,5938,5939,5941,5943,5945,5947],{},[898,5940,3403],{},[1656,5942,1713],{},[1667,5944,1669],{},[1656,5946,3964],{},[898,5948,207],{},[902,5950,5951],{"encoding":904},"b = 1 - a",", čímž (6.6) přejde na tvar",[724,5954,5955],{},[5956,5957],"img",{"alt":5958,"className":5959,"src":5961},"imek-cobb-douglas-3d-plus-ic",[210,5960],"wikilink-broken","\u002Fwiki-assets\u002Fimek-cobb-douglas-3d-plus-ic.jpeg",[883,5963,5965],{"className":5964},[886],[888,5966,5967],{"xmlns":890,"display":2408},[892,5968,5969,6019],{},[895,5970,5971,5973,5975,5981,5983,5989,5991,5993,6001,6003,6017],{},[898,5972,900],{},[1656,5974,1659],{"stretchy":1658},[1661,5976,5977,5979],{},[898,5978,1665],{},[1667,5980,1669],{},[1656,5982,1673],{"separator":1672},[1661,5984,5985,5987],{},[898,5986,1665],{},[1667,5988,1680],{},[1656,5990,1683],{"stretchy":1658},[1656,5992,1713],{},[1715,5994,5995,5997,5999],{},[898,5996,1665],{},[1667,5998,1669],{},[898,6000,207],{},[1656,6002,2751],{},[1715,6004,6005,6007,6009],{},[898,6006,1665],{},[1667,6008,1680],{},[895,6010,6011,6013,6015],{},[1667,6012,1669],{},[1656,6014,3964],{},[898,6016,207],{},[898,6018,1863],{"mathvariant":1723},[902,6020,6021],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^{1-a}.",[1981,6023,6024,6073,6195,6330],{},[724,6025,6026,6028,6029],{},[883,6027,2576],{}," Příklad 6.3 — ověření vlastností pro ",[883,6030,6032],{"className":6031},[886],[888,6033,6034],{"xmlns":890},[892,6035,6036,6070],{},[895,6037,6038,6040,6042,6056],{},[898,6039,900],{},[1656,6041,1713],{},[1715,6043,6044,6046,6048],{},[898,6045,1665],{},[1667,6047,1669],{},[895,6049,6050,6052,6054],{},[1667,6051,1669],{},[898,6053,1782],{"mathvariant":1723},[1667,6055,2673],{},[1715,6057,6058,6060,6062],{},[898,6059,1665],{},[1667,6061,1680],{},[895,6063,6064,6066,6068],{},[1667,6065,2617],{},[898,6067,1782],{"mathvariant":1723},[1667,6069,2673],{},[902,6071,6072],{"encoding":904},"U = Q_1^{1\u002F4} Q_2^{3\u002F4}",[883,6074,6076],{"className":6075},[886],[888,6077,6078],{"xmlns":890,"display":2408},[892,6079,6080,6192],{},[895,6081,6082,6090,6092,6100,6116,6130,6132,6134,6136,6138,6146,6148,6156,6170,6186,6188,6190],{},[1715,6083,6084,6086,6088],{},[898,6085,900],{},[1667,6087,1669],{},[1656,6089,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,6091,1713],{},[4138,6093,6094],{"scriptlevel":4032,"displaystyle":1658},[3294,6095,6096,6098],{},[1667,6097,1669],{},[1667,6099,2673],{},[1715,6101,6102,6104,6106],{},[898,6103,1665],{},[1667,6105,1669],{},[895,6107,6108,6110,6112,6114],{},[1656,6109,3964],{},[1667,6111,2617],{},[898,6113,1782],{"mathvariant":1723},[1667,6115,2673],{},[1715,6117,6118,6120,6122],{},[898,6119,1665],{},[1667,6121,1680],{},[895,6123,6124,6126,6128],{},[1667,6125,2617],{},[898,6127,1782],{"mathvariant":1723},[1667,6129,2673],{},[1656,6131,2850],{},[1667,6133,4032],{},[1656,6135,1673],{"separator":1672},[3316,6137],{"width":3318},[1715,6139,6140,6142,6144],{},[898,6141,900],{},[1667,6143,1680],{},[1656,6145,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,6147,1713],{},[4138,6149,6150],{"scriptlevel":4032,"displaystyle":1658},[3294,6151,6152,6154],{},[1667,6153,2617],{},[1667,6155,2673],{},[1715,6157,6158,6160,6162],{},[898,6159,1665],{},[1667,6161,1669],{},[895,6163,6164,6166,6168],{},[1667,6165,1669],{},[898,6167,1782],{"mathvariant":1723},[1667,6169,2673],{},[1715,6171,6172,6174,6176],{},[898,6173,1665],{},[1667,6175,1680],{},[895,6177,6178,6180,6182,6184],{},[1656,6179,3964],{},[1667,6181,1669],{},[898,6183,1782],{"mathvariant":1723},[1667,6185,2673],{},[1656,6187,2850],{},[1667,6189,4032],{},[1656,6191,1673],{"separator":1672},[902,6193,6194],{"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,",[883,6196,6198],{"className":6197},[886],[888,6199,6200],{"xmlns":890,"display":2408},[892,6201,6202,6327],{},[895,6203,6204,6216,6218,6220,6228,6245,6259,6261,6263,6265,6267,6279,6281,6283,6291,6305,6321,6323,6325],{},[1715,6205,6206,6208,6210],{},[898,6207,900],{},[1667,6209,4364],{},[895,6211,6212,6214],{},[1656,6213,1725],{"mathvariant":1723},[1656,6215,1725],{"mathvariant":1723},[1656,6217,1713],{},[1656,6219,3964],{},[4138,6221,6222],{"scriptlevel":4032,"displaystyle":1658},[3294,6223,6224,6226],{},[1667,6225,2617],{},[1667,6227,2668],{},[1715,6229,6230,6232,6234],{},[898,6231,1665],{},[1667,6233,1669],{},[895,6235,6236,6238,6241,6243],{},[1656,6237,3964],{},[1667,6239,6240],{},"7",[898,6242,1782],{"mathvariant":1723},[1667,6244,2673],{},[1715,6246,6247,6249,6251],{},[898,6248,1665],{},[1667,6250,1680],{},[895,6252,6253,6255,6257],{},[1667,6254,2617],{},[898,6256,1782],{"mathvariant":1723},[1667,6258,2673],{},[1656,6260,4373],{},[1667,6262,4032],{},[1656,6264,1673],{"separator":1672},[3316,6266],{"width":3318},[1715,6268,6269,6271,6273],{},[898,6270,900],{},[1667,6272,4386],{},[895,6274,6275,6277],{},[1656,6276,1725],{"mathvariant":1723},[1656,6278,1725],{"mathvariant":1723},[1656,6280,1713],{},[1656,6282,3964],{},[4138,6284,6285],{"scriptlevel":4032,"displaystyle":1658},[3294,6286,6287,6289],{},[1667,6288,2617],{},[1667,6290,2668],{},[1715,6292,6293,6295,6297],{},[898,6294,1665],{},[1667,6296,1669],{},[895,6298,6299,6301,6303],{},[1667,6300,1669],{},[898,6302,1782],{"mathvariant":1723},[1667,6304,2673],{},[1715,6306,6307,6309,6311],{},[898,6308,1665],{},[1667,6310,1680],{},[895,6312,6313,6315,6317,6319],{},[1656,6314,3964],{},[1667,6316,5193],{},[898,6318,1782],{"mathvariant":1723},[1667,6320,2673],{},[1656,6322,4373],{},[1667,6324,4032],{},[1656,6326,1673],{"separator":1672},[902,6328,6329],{"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,",[724,6331,6332],{},"tedy podmínky (6.4) i (6.5) jsou splněny.",[115,6334,6336],{"id":6335},"indiferenční-křivky-křivky-užitečnosti-a-jejich-vlastnosti","Indiferenční křivky (křivky užitečnosti) a jejich vlastnosti",[724,6338,6339,6342],{},[38,6340,6341],{},"Křivky užitečnosti"," (utility curves) jsou indiferenční křivky funkce užitečnosti. Jsou dány rovnicí",[883,6344,6346],{"className":6345},[886],[888,6347,6348],{"xmlns":890,"display":2408},[892,6349,6350,6393],{},[2412,6351,6352],{"width":2414},[2416,6353,6354,6356,6386,6388],{},[2419,6355],{"width":2421},[2419,6357,6358],{},[895,6359,6360,6362,6364,6370,6372,6378,6380,6382,6384],{},[898,6361,900],{},[1656,6363,1659],{"stretchy":1658},[1661,6365,6366,6368],{},[898,6367,1665],{},[1667,6369,1669],{},[1656,6371,1673],{"separator":1672},[1661,6373,6374,6376],{},[898,6375,1665],{},[1667,6377,1680],{},[1656,6379,1683],{"stretchy":1658},[1656,6381,1713],{},[898,6383,1745],{},[1656,6385,1673],{"separator":1672},[2419,6387],{"width":2421},[2419,6389,6390],{},[2461,6391,6392],{},"(6.7)",[902,6394,6395],{"encoding":904},"U(Q_1, Q_2) = c, \\tag{6.7}",[724,6397,2355,6398,6411],{},[883,6399,6401],{"className":6400},[886],[888,6402,6403],{"xmlns":890},[892,6404,6405,6409],{},[895,6406,6407],{},[898,6408,1745],{},[902,6410,1745],{"encoding":904}," je kladná konstanta. Pro Cobb-Douglasovu funkci:",[883,6413,6415],{"className":6414},[886],[888,6416,6417],{"xmlns":890,"display":2408},[892,6418,6419,6460],{},[2412,6420,6421],{"width":2414},[2416,6422,6423,6425,6453,6455],{},[2419,6424],{"width":2421},[2419,6426,6427],{},[895,6428,6429,6437,6439,6447,6449,6451],{},[1715,6430,6431,6433,6435],{},[898,6432,1665],{},[1667,6434,1669],{},[898,6436,207],{},[1656,6438,2751],{},[1715,6440,6441,6443,6445],{},[898,6442,1665],{},[1667,6444,1680],{},[898,6446,3403],{},[1656,6448,1713],{},[898,6450,1745],{},[898,6452,1863],{"mathvariant":1723},[2419,6454],{"width":2421},[2419,6456,6457],{},[2461,6458,6459],{},"(6.8)",[902,6461,6462],{"encoding":904},"Q_1^a \\cdot Q_2^b = c. \\tag{6.8}",[724,6464,6465,6466,6496,6497,1643,6500,6513,6514,6549,6550,6567,6568,6597,6598,6601],{},"Body na téže křivce užitečnosti reprezentují kombinace ",[883,6467,6469],{"className":6468},[886],[888,6470,6471],{"xmlns":890},[892,6472,6473,6493],{},[895,6474,6475,6477,6483,6485,6491],{},[1656,6476,3453],{"stretchy":1658},[1661,6478,6479,6481],{},[898,6480,1665],{},[1667,6482,1669],{},[1656,6484,1673],{"separator":1672},[1661,6486,6487,6489],{},[898,6488,1665],{},[1667,6490,1680],{},[1656,6492,3462],{"stretchy":1658},[902,6494,6495],{"encoding":904},"[Q_1, Q_2]"," se ",[38,6498,6499],{},"stejnou úrovní uspokojení",[883,6501,6503],{"className":6502},[886],[888,6504,6505],{"xmlns":890},[892,6506,6507,6511],{},[895,6508,6509],{},[898,6510,1745],{},[902,6512,1745],{"encoding":904},". Křivky užitečnosti vznikají jako průsečnice plochy ",[883,6515,6517],{"className":6516},[886],[888,6518,6519],{"xmlns":890},[892,6520,6521,6547],{},[895,6522,6523,6525,6527,6529,6531,6537,6539,6545],{},[898,6524,900],{},[1656,6526,1713],{},[898,6528,900],{},[1656,6530,1659],{"stretchy":1658},[1661,6532,6533,6535],{},[898,6534,1665],{},[1667,6536,1669],{},[1656,6538,1673],{"separator":1672},[1661,6540,6541,6543],{},[898,6542,1665],{},[1667,6544,1680],{},[1656,6546,1683],{"stretchy":1658},[902,6548,2569],{"encoding":904}," s rovinami ",[883,6551,6553],{"className":6552},[886],[888,6554,6555],{"xmlns":890},[892,6556,6557,6565],{},[895,6558,6559,6561,6563],{},[898,6560,900],{},[1656,6562,1713],{},[898,6564,1745],{},[902,6566,1748],{"encoding":904}," rovnoběžnými s rovinou ",[883,6569,6571],{"className":6570},[886],[888,6572,6573],{"xmlns":890},[892,6574,6575,6595],{},[895,6576,6577,6579,6585,6587,6593],{},[1656,6578,1659],{"stretchy":1658},[1661,6580,6581,6583],{},[898,6582,1665],{},[1667,6584,1669],{},[1656,6586,1673],{"separator":1672},[1661,6588,6589,6591],{},[898,6590,1665],{},[1667,6592,1680],{},[1656,6594,1683],{"stretchy":1658},[902,6596,4787],{"encoding":904}," (obrázek 6.2). Jsou v příbuznosti s ",[38,6599,6600],{},"izokvantami"," produkčních funkcí.",[724,6603,6604],{},[614,6605,6606,6607,4665,6625,6643,6644,1863],{},"Obrázek 6.3 — typický tvar křivek užitečnosti pro Cobb-Douglasovu funkci pro ",[883,6608,6610],{"className":6609},[886],[888,6611,6612],{"xmlns":890},[892,6613,6614,6622],{},[895,6615,6616,6618,6620],{},[898,6617,207],{},[1656,6619,4373],{},[898,6621,3403],{},[902,6623,6624],{"encoding":904},"a \u003C b",[883,6626,6628],{"className":6627},[886],[888,6629,6630],{"xmlns":890},[892,6631,6632,6640],{},[895,6633,6634,6636,6638],{},[898,6635,207],{},[1656,6637,2850],{},[898,6639,3403],{},[902,6641,6642],{"encoding":904},"a > b"," (vpravo); různé hladiny ",[883,6645,6647],{"className":6646},[886],[888,6648,6649],{"xmlns":890},[892,6650,6651,6675],{},[895,6652,6653,6659,6661,6667,6669],{},[1661,6654,6655,6657],{},[898,6656,1745],{},[1667,6658,4032],{},[1656,6660,4373],{},[1661,6662,6663,6665],{},[898,6664,1745],{},[1667,6666,1669],{},[1656,6668,4373],{},[1661,6670,6671,6673],{},[898,6672,1745],{},[1667,6674,1680],{},[902,6676,6677],{"encoding":904},"c_0 \u003C c_1 \u003C c_2",[724,6679,6680],{},[614,6681,6682,6683,6712,6713,6771,6772,6791],{},"Obrázek 6.4 — soustava křivek užitečnosti pro tři hladiny (10, 20, 30) v rovině ",[883,6684,6686],{"className":6685},[886],[888,6687,6688],{"xmlns":890},[892,6689,6690,6710],{},[895,6691,6692,6694,6700,6702,6708],{},[1656,6693,1659],{"stretchy":1658},[1661,6695,6696,6698],{},[898,6697,1665],{},[1667,6699,1669],{},[1656,6701,1673],{"separator":1672},[1661,6703,6704,6706],{},[898,6705,1665],{},[1667,6707,1680],{},[1656,6709,1683],{"stretchy":1658},[902,6711,4787],{"encoding":904},"; body ",[883,6714,6716],{"className":6715},[886],[888,6717,6718],{"xmlns":890},[892,6719,6720,6768],{},[895,6721,6722,6724,6726,6728,6734,6736,6742,6744,6746,6748,6750,6752,6758,6760,6766],{},[898,6723,2146],{},[1656,6725,1713],{},[1656,6727,3453],{"stretchy":1658},[1661,6729,6730,6732],{},[898,6731,207],{},[1667,6733,1669],{},[1656,6735,1673],{"separator":1672},[1661,6737,6738,6740],{},[898,6739,207],{},[1667,6741,1680],{},[1656,6743,3462],{"stretchy":1658},[1656,6745,1673],{"separator":1672},[898,6747,2161],{},[1656,6749,1713],{},[1656,6751,3453],{"stretchy":1658},[1661,6753,6754,6756],{},[898,6755,3403],{},[1667,6757,1669],{},[1656,6759,1673],{"separator":1672},[1661,6761,6762,6764],{},[898,6763,3403],{},[1667,6765,1680],{},[1656,6767,3462],{"stretchy":1658},[902,6769,6770],{"encoding":904},"A = [a_1, a_2], B = [b_1, b_2]"," leží na téže křivce (hladina 10), body ",[883,6773,6775],{"className":6774},[886],[888,6776,6777],{"xmlns":890},[892,6778,6779,6788],{},[895,6780,6781,6783,6785],{},[898,6782,1766],{},[1656,6784,1673],{"separator":1672},[898,6786,6787],{},"D",[902,6789,6790],{"encoding":904},"C, D"," na vyšší hladině.",[1981,6793,6794],{},[724,6795,6796,6798,6799,6861,6862,6906,6907,6941,6942,6960,6961,6941,7016,6960,7034,7110],{},[883,6797,2576],{}," Příklad 6.4 — rovnice křivek užitečnosti\nPro ",[883,6800,6802],{"className":6801},[886],[888,6803,6804],{"xmlns":890},[892,6805,6806,6858],{},[895,6807,6808,6810,6812,6818,6820,6826,6828,6830,6844],{},[898,6809,900],{},[1656,6811,1659],{"stretchy":1658},[1661,6813,6814,6816],{},[898,6815,1665],{},[1667,6817,1669],{},[1656,6819,1673],{"separator":1672},[1661,6821,6822,6824],{},[898,6823,1665],{},[1667,6825,1680],{},[1656,6827,1683],{"stretchy":1658},[1656,6829,1713],{},[1715,6831,6832,6834,6836],{},[898,6833,1665],{},[1667,6835,1669],{},[895,6837,6838,6840,6842],{},[1667,6839,1669],{},[898,6841,1782],{"mathvariant":1723},[1667,6843,2673],{},[1715,6845,6846,6848,6850],{},[898,6847,1665],{},[1667,6849,1680],{},[895,6851,6852,6854,6856],{},[1667,6853,2617],{},[898,6855,1782],{"mathvariant":1723},[1667,6857,2673],{},[902,6859,6860],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F4} Q_2^{3\u002F4}"," mají křivky užitečnosti rovnici ",[883,6863,6865],{"className":6864},[886],[888,6866,6867],{"xmlns":890},[892,6868,6869,6903],{},[895,6870,6871,6885,6899,6901],{},[1715,6872,6873,6875,6877],{},[898,6874,1665],{},[1667,6876,1669],{},[895,6878,6879,6881,6883],{},[1667,6880,1669],{},[898,6882,1782],{"mathvariant":1723},[1667,6884,2673],{},[1715,6886,6887,6889,6891],{},[898,6888,1665],{},[1667,6890,1680],{},[895,6892,6893,6895,6897],{},[1667,6894,2617],{},[898,6896,1782],{"mathvariant":1723},[1667,6898,2673],{},[1656,6900,1713],{},[898,6902,1745],{},[902,6904,6905],{"encoding":904},"Q_1^{1\u002F4} Q_2^{3\u002F4} = c",". Umocněním na čtvrtou mocninu dostáváme ",[883,6908,6910],{"className":6909},[886],[888,6911,6912],{"xmlns":890},[892,6913,6914,6938],{},[895,6915,6916,6922,6930,6932],{},[1661,6917,6918,6920],{},[898,6919,1665],{},[1667,6921,1669],{},[1715,6923,6924,6926,6928],{},[898,6925,1665],{},[1667,6927,1680],{},[1667,6929,2617],{},[1656,6931,1713],{},[2062,6933,6934,6936],{},[898,6935,1745],{},[1667,6937,2673],{},[902,6939,6940],{"encoding":904},"Q_1 Q_2^{3} = c^{4}",". Pro ",[883,6943,6945],{"className":6944},[886],[888,6946,6947],{"xmlns":890},[892,6948,6949,6957],{},[895,6950,6951,6953,6955],{},[898,6952,1745],{},[1656,6954,1713],{},[1667,6956,1669],{},[902,6958,6959],{"encoding":904},"c = 1",": ",[883,6962,6964],{"className":6963},[886],[888,6965,6966],{"xmlns":890},[892,6967,6968,7013],{},[895,6969,6970,6976,6978,6994,6996],{},[1661,6971,6972,6974],{},[898,6973,1665],{},[1667,6975,1680],{},[1656,6977,1713],{},[1715,6979,6980,6982,6984],{},[898,6981,1665],{},[1667,6983,1669],{},[895,6985,6986,6988,6990,6992],{},[1656,6987,3964],{},[1667,6989,1669],{},[898,6991,1782],{"mathvariant":1723},[1667,6993,2617],{},[1656,6995,1713],{},[4138,6997,6998],{"scriptlevel":4032,"displaystyle":1672},[3294,6999,7000,7002],{},[1667,7001,1669],{},[7003,7004,7005,7011],"mroot",{},[1661,7006,7007,7009],{},[898,7008,1665],{},[1667,7010,1669],{},[1667,7012,2617],{},[902,7014,7015],{"encoding":904},"Q_2 = Q_1^{-1\u002F3} = \\dfrac{1}{\\sqrt[3]{Q_1}}",[883,7017,7019],{"className":7018},[886],[888,7020,7021],{"xmlns":890},[892,7022,7023,7031],{},[895,7024,7025,7027,7029],{},[898,7026,1745],{},[1656,7028,1713],{},[1667,7030,1680],{},[902,7032,7033],{"encoding":904},"c = 2",[883,7035,7037],{"className":7036},[886],[888,7038,7039],{"xmlns":890},[892,7040,7041,7107],{},[895,7042,7043,7049,7051,7063,7065,7081,7083],{},[1661,7044,7045,7047],{},[898,7046,1665],{},[1667,7048,1680],{},[1656,7050,1713],{},[2062,7052,7053,7055],{},[1667,7054,1680],{},[895,7056,7057,7059,7061],{},[1667,7058,2673],{},[898,7060,1782],{"mathvariant":1723},[1667,7062,2617],{},[1656,7064,2751],{},[1715,7066,7067,7069,7071],{},[898,7068,1665],{},[1667,7070,1669],{},[895,7072,7073,7075,7077,7079],{},[1656,7074,3964],{},[1667,7076,1669],{},[898,7078,1782],{"mathvariant":1723},[1667,7080,2617],{},[1656,7082,1713],{},[4138,7084,7085],{"scriptlevel":4032,"displaystyle":1672},[3294,7086,7087,7097],{},[895,7088,7089,7091],{},[1667,7090,1680],{},[7003,7092,7093,7095],{},[1667,7094,1680],{},[1667,7096,2617],{},[7003,7098,7099,7105],{},[1661,7100,7101,7103],{},[898,7102,1665],{},[1667,7104,1669],{},[1667,7106,2617],{},[902,7108,7109],{"encoding":904},"Q_2 = 2^{4\u002F3} \\cdot Q_1^{-1\u002F3} = \\dfrac{2 \\sqrt[3]{2}}{\\sqrt[3]{Q_1}}"," (obrázek 6.5).",[198,7112,7114],{"id":7113},"čtyři-vlastnosti-křivek-užitečnosti","Čtyři vlastnosti křivek užitečnosti",[724,7116,7117],{},[5956,7118],{"alt":7119,"className":7120,"src":7121},"imek-ic-4vlastnosti-anotovane",[210,5960],"\u002Fwiki-assets\u002Fimek-ic-4vlastnosti-anotovane.jpeg",[1981,7123,7124,7133,7181,7225,7231,7237],{},[724,7125,7126,7128,7129,7132],{},[883,7127,1987],{}," Čtyři základní vlastnosti indiferenčních křivek\n",[38,7130,7131],{},"1° Klesající."," Je-li nakoupeno méně jednoho zboží, je k dosažení stejného uspokojení třeba kompenzovat větším množstvím druhého zboží. Sklon tečny je",[724,7134,7135],{},[883,7136,7138],{"className":7137},[886],[888,7139,7140],{"xmlns":890},[892,7141,7142,7178],{},[895,7143,7144,7147,7149,7152,7154,7156,7174,7176],{},[898,7145,7146],{"mathvariant":1723},"tg",[1656,7148,2093],{},[898,7150,7151],{},"α",[1656,7153,1713],{},[1656,7155,3964],{},[3294,7157,7158,7166],{},[1715,7159,7160,7162,7164],{},[898,7161,900],{},[1667,7163,1669],{},[1656,7165,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1715,7167,7168,7170,7172],{},[898,7169,900],{},[1667,7171,1680],{},[1656,7173,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,7175,4373],{},[1667,7177,4032],{},[902,7179,7180],{"encoding":904},"\\operatorname{tg} \\alpha = -\\frac{U'_1}{U'_2} \u003C 0",[724,7182,7183,7184,7224],{},"(derivace implicitně zadané funkce ",[883,7185,7187],{"className":7186},[886],[888,7188,7189],{"xmlns":890},[892,7190,7191,7221],{},[895,7192,7193,7195,7197,7203,7205,7211,7213,7215,7217,7219],{},[898,7194,900],{},[1656,7196,1659],{"stretchy":1658},[1661,7198,7199,7201],{},[898,7200,1665],{},[1667,7202,1669],{},[1656,7204,1673],{"separator":1672},[1661,7206,7207,7209],{},[898,7208,1665],{},[1667,7210,1680],{},[1656,7212,1683],{"stretchy":1658},[1656,7214,3964],{},[898,7216,1745],{},[1656,7218,1713],{},[1667,7220,4032],{},[902,7222,7223],{"encoding":904},"U(Q_1, Q_2) - c = 0","). Ze záporné derivace plyne klesající průběh.",[724,7226,7227,7230],{},[38,7228,7229],{},"2° Neprotínají se."," V průsečíku by týž svazek ležel na dvou různých hladinách užitečnosti, což je spor.",[724,7232,7233,7236],{},[38,7234,7235],{},"3° Čím vzdálenější od počátku, tím vyšší užitečnost"," (obrázek 6.4).",[724,7238,7239,7242,7243,7261,7262,7278,7279,7282],{},[38,7240,7241],{},"4° Konvexní."," Pro každé dva body ",[883,7244,7246],{"className":7245},[886],[888,7247,7248],{"xmlns":890},[892,7249,7250,7258],{},[895,7251,7252,7254,7256],{},[898,7253,2146],{},[1656,7255,1673],{"separator":1672},[898,7257,2161],{},[902,7259,7260],{"encoding":904},"A, B"," na téže křivce leží vnitřní body úsečky ",[883,7263,7265],{"className":7264},[886],[888,7266,7267],{"xmlns":890},[892,7268,7269,7275],{},[895,7270,7271,7273],{},[898,7272,2146],{},[898,7274,2161],{},[902,7276,7277],{"encoding":904},"AB"," ve ",[38,7280,7281],{},"vyšší"," hladině užitečnosti (tj. „nad\" křivkou) — vyjadřuje to preferenci smíšených svazků před krajními.",[724,7284,7285],{},[614,7286,7287,7288,7323,7324,1863],{},"Obrázek 6.6 — klesající a konvexní průběh ",[883,7289,7291],{"className":7290},[886],[888,7292,7293],{"xmlns":890},[892,7294,7295,7321],{},[895,7296,7297,7299,7301,7307,7309,7315,7317,7319],{},[898,7298,900],{},[1656,7300,1659],{"stretchy":1658},[1661,7302,7303,7305],{},[898,7304,1665],{},[1667,7306,1669],{},[1656,7308,1673],{"separator":1672},[1661,7310,7311,7313],{},[898,7312,1665],{},[1667,7314,1680],{},[1656,7316,1683],{"stretchy":1658},[1656,7318,1713],{},[898,7320,1745],{},[902,7322,4870],{"encoding":904}," s tečnou se sklonem ",[883,7325,7327],{"className":7326},[886],[888,7328,7329],{"xmlns":890},[892,7330,7331,7339],{},[895,7332,7333,7335,7337],{},[898,7334,7146],{"mathvariant":1723},[1656,7336,2093],{},[898,7338,7151],{},[902,7340,7341],{"encoding":904},"\\operatorname{tg}\\alpha",[115,7343,7345],{"id":7344},"mezní-míra-komoditní-substituce-mrcs","Mezní míra komoditní substituce (MRCS)",[724,7347,7348,1643,7351,3247,7366,7369],{},[38,7349,7350],{},"Mezní míra komoditní substituce",[883,7352,7354],{"className":7353},[886],[888,7355,7356],{"xmlns":890},[892,7357,7358,7363],{},[895,7359,7360],{},[2461,7361,7362],{},"MRCS",[902,7364,7365],{"encoding":904},"\\text{MRCS}",[38,7367,7368],{},"marginal rate of commodity substitution",") je podíl mezních užitečností:",[883,7371,7373],{"className":7372},[886],[888,7374,7375],{"xmlns":890,"display":2408},[892,7376,7377,7464],{},[2412,7378,7379],{"width":2414},[2416,7380,7381,7383,7457,7459],{},[2419,7382],{"width":2421},[2419,7384,7385],{},[895,7386,7387,7389,7391,7393,7395,7401,7403,7409,7411,7413,7435,7437,7455],{},[2461,7388,7362],{},[1656,7390,1713],{},[2461,7392,7362],{},[1656,7394,1659],{"stretchy":1658},[1661,7396,7397,7399],{},[898,7398,1665],{},[1667,7400,1669],{},[1656,7402,1673],{"separator":1672},[1661,7404,7405,7407],{},[898,7406,1665],{},[1667,7408,1680],{},[1656,7410,1683],{"stretchy":1658},[1656,7412,1713],{},[3294,7414,7415,7425],{},[895,7416,7417,7419],{},[898,7418,1703],{},[1661,7420,7421,7423],{},[898,7422,900],{},[1667,7424,1669],{},[895,7426,7427,7429],{},[898,7428,1703],{},[1661,7430,7431,7433],{},[898,7432,900],{},[1667,7434,1680],{},[1656,7436,1713],{},[3294,7438,7439,7447],{},[1715,7440,7441,7443,7445],{},[898,7442,900],{},[1667,7444,1669],{},[1656,7446,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1715,7448,7449,7451,7453],{},[898,7450,900],{},[1667,7452,1680],{},[1656,7454,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[898,7456,1863],{"mathvariant":1723},[2419,7458],{"width":2421},[2419,7460,7461],{},[2461,7462,7463],{},"(6.9)",[902,7465,7466],{"encoding":904},"\\text{MRCS} = \\text{MRCS}(Q_1, Q_2) = \\frac{MU_1}{MU_2} = \\frac{U'_1}{U'_2}. \\tag{6.9}",[724,7468,7469,7470,7504,7505,7538,7539,7574,7575,7588],{},"Geometricky: ",[883,7471,7473],{"className":7472},[886],[888,7474,7475],{"xmlns":890},[892,7476,7477,7501],{},[895,7478,7479,7481],{},[1656,7480,3964],{},[4138,7482,7483],{"scriptlevel":4032,"displaystyle":1658},[3294,7484,7485,7493],{},[1715,7486,7487,7489,7491],{},[898,7488,900],{},[1667,7490,1669],{},[1656,7492,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1715,7494,7495,7497,7499],{},[898,7496,900],{},[1667,7498,1680],{},[1656,7500,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[902,7502,7503],{"encoding":904},"-\\tfrac{U'_1}{U'_2}"," je derivace funkce ",[883,7506,7508],{"className":7507},[886],[888,7509,7510],{"xmlns":890},[892,7511,7512,7535],{},[895,7513,7514,7520,7522,7525,7527,7533],{},[1661,7515,7516,7518],{},[898,7517,1665],{},[1667,7519,1680],{},[1656,7521,1713],{},[898,7523,7524],{},"f",[1656,7526,1659],{"stretchy":1658},[1661,7528,7529,7531],{},[898,7530,1665],{},[1667,7532,1669],{},[1656,7534,1683],{"stretchy":1658},[902,7536,7537],{"encoding":904},"Q_2 = f(Q_1)"," zadané implicitně rovnicí ",[883,7540,7542],{"className":7541},[886],[888,7543,7544],{"xmlns":890},[892,7545,7546,7572],{},[895,7547,7548,7550,7552,7558,7560,7566,7568,7570],{},[898,7549,900],{},[1656,7551,1659],{"stretchy":1658},[1661,7553,7554,7556],{},[898,7555,1665],{},[1667,7557,1669],{},[1656,7559,1673],{"separator":1672},[1661,7561,7562,7564],{},[898,7563,1665],{},[1667,7565,1680],{},[1656,7567,1683],{"stretchy":1658},[1656,7569,1713],{},[898,7571,1745],{},[902,7573,4870],{"encoding":904},". Protože je vždy záporná (křivka je klesající), bereme absolutní hodnotu a kladný ",[883,7576,7578],{"className":7577},[886],[888,7579,7580],{"xmlns":890},[892,7581,7582,7586],{},[895,7583,7584],{},[2461,7585,7362],{},[902,7587,7365],{"encoding":904}," chápeme jako velikost kompenzace.",[1981,7590,7591],{},[724,7592,7593,7595,7596,3206,7628,7667,7668,7685,7686,7703],{},[883,7594,3472],{}," Intuice — MRCS jako sklon indiferenční křivky\n",[883,7597,7599],{"className":7598},[886],[888,7600,7601],{"xmlns":890},[892,7602,7603,7625],{},[895,7604,7605,7607,7609,7615,7617,7623],{},[2461,7606,7362],{},[1656,7608,1659],{"stretchy":1658},[1661,7610,7611,7613],{},[898,7612,1665],{},[1667,7614,1669],{},[1656,7616,1673],{"separator":1672},[1661,7618,7619,7621],{},[898,7620,1665],{},[1667,7622,1680],{},[1656,7624,1683],{"stretchy":1658},[902,7626,7627],{"encoding":904},"\\text{MRCS}(Q_1, Q_2)",[38,7629,7630,7631,7648,7649,7666],{},"míra, jakou je spotřebitel ochoten zaměnit ",[883,7632,7634],{"className":7633},[886],[888,7635,7636],{"xmlns":890},[892,7637,7638,7646],{},[895,7639,7640],{},[1661,7641,7642,7644],{},[898,7643,1665],{},[1667,7645,1669],{},[902,7647,3227],{"encoding":904}," za ",[883,7650,7652],{"className":7651},[886],[888,7653,7654],{"xmlns":890},[892,7655,7656,7664],{},[895,7657,7658],{},[1661,7659,7660,7662],{},[898,7661,1665],{},[1667,7663,1680],{},[902,7665,3246],{"encoding":904}," při zachování užitečnosti"," — tedy kolik jednotek ",[883,7669,7671],{"className":7670},[886],[888,7672,7673],{"xmlns":890},[892,7674,7675,7683],{},[895,7676,7677],{},[1661,7678,7679,7681],{},[898,7680,1665],{},[1667,7682,1680],{},[902,7684,3246],{"encoding":904}," „obětuje\" za jednu jednotku ",[883,7687,7689],{"className":7688},[886],[888,7690,7691],{"xmlns":890},[892,7692,7693,7701],{},[895,7694,7695],{},[1661,7696,7697,7699],{},[898,7698,1665],{},[1667,7700,1669],{},[902,7702,3227],{"encoding":904}," navíc, aby zůstal na téže indiferenční křivce. Geometricky jde o absolutní hodnotu sklonu tečny k indiferenční křivce v daném bodě.",[724,7705,7706,7707,7727],{},"Pro obecnou změnu ",[883,7708,7710],{"className":7709},[886],[888,7711,7712],{"xmlns":890},[892,7713,7714,7724],{},[895,7715,7716,7718],{},[898,7717,3768],{"mathvariant":1723},[1661,7719,7720,7722],{},[898,7721,1665],{},[1667,7723,1669],{},[902,7725,7726],{"encoding":904},"\\mathrm{d} Q_1"," platí",[883,7729,7731],{"className":7730},[886],[888,7732,7733],{"xmlns":890,"display":2408},[892,7734,7735,7788],{},[2412,7736,7737],{"width":2414},[2416,7738,7739,7741,7781,7783],{},[2419,7740],{"width":2421},[2419,7742,7743],{},[895,7744,7745,7747,7753,7755,7757,7763,7765,7767,7769,7771,7773,7779],{},[898,7746,3750],{"mathvariant":1723},[1661,7748,7749,7751],{},[898,7750,1665],{},[1667,7752,1680],{},[1656,7754,3815],{},[898,7756,3768],{"mathvariant":1723},[1661,7758,7759,7761],{},[898,7760,1665],{},[1667,7762,1680],{},[1656,7764,1713],{},[1656,7766,3964],{},[2461,7768,7362],{},[1656,7770,2751],{},[898,7772,3768],{"mathvariant":1723},[1661,7774,7775,7777],{},[898,7776,1665],{},[1667,7778,1669],{},[1656,7780,1673],{"separator":1672},[2419,7782],{"width":2421},[2419,7784,7785],{},[2461,7786,7787],{},"(6.10)",[902,7789,7790],{"encoding":904},"\\Delta Q_2 \\approx \\mathrm{d} Q_2 = -\\text{MRCS} \\cdot \\mathrm{d} Q_1, \\tag{6.10}",[883,7792,7794],{"className":7793},[886],[888,7795,7796],{"xmlns":890,"display":2408},[892,7797,7798,7846],{},[2412,7799,7800],{"width":2414},[2416,7801,7802,7804,7839,7841],{},[2419,7803],{"width":2421},[2419,7805,7806],{},[895,7807,7808,7810,7816,7818,7820,7826,7829,7831,7837],{},[898,7809,3768],{"mathvariant":1723},[1661,7811,7812,7814],{},[898,7813,1665],{},[1667,7815,1669],{},[1656,7817,1713],{},[1656,7819,3964],{},[3294,7821,7822,7824],{},[1667,7823,1669],{},[2461,7825,7362],{},[2461,7827,7828],{}," ",[898,7830,3768],{"mathvariant":1723},[1661,7832,7833,7835],{},[898,7834,1665],{},[1667,7836,1680],{},[898,7838,1863],{"mathvariant":1723},[2419,7840],{"width":2421},[2419,7842,7843],{},[2461,7844,7845],{},"(6.11)",[902,7847,7848],{"encoding":904},"\\mathrm{d} Q_1 = -\\frac{1}{\\text{MRCS}}\\, \\mathrm{d} Q_2. \\tag{6.11}",[1981,7850,7851,7918,8036],{},[724,7852,7853,7855,7856,7727],{},[883,7854,2576],{}," Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost\nPro ",[883,7857,7859],{"className":7858},[886],[888,7860,7861],{"xmlns":890},[892,7862,7863,7915],{},[895,7864,7865,7867,7869,7875,7877,7883,7885,7887,7901],{},[898,7866,900],{},[1656,7868,1659],{"stretchy":1658},[1661,7870,7871,7873],{},[898,7872,1665],{},[1667,7874,1669],{},[1656,7876,1673],{"separator":1672},[1661,7878,7879,7881],{},[898,7880,1665],{},[1667,7882,1680],{},[1656,7884,1683],{"stretchy":1658},[1656,7886,1713],{},[1715,7888,7889,7891,7893],{},[898,7890,1665],{},[1667,7892,1669],{},[895,7894,7895,7897,7899],{},[1667,7896,1669],{},[898,7898,1782],{"mathvariant":1723},[1667,7900,1680],{},[1715,7902,7903,7905,7907],{},[898,7904,1665],{},[1667,7906,1680],{},[895,7908,7909,7911,7913],{},[1667,7910,1669],{},[898,7912,1782],{"mathvariant":1723},[1667,7914,1680],{},[902,7916,7917],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F2} Q_2^{1\u002F2}",[724,7919,7920],{},[883,7921,7923],{"className":7922},[886],[888,7924,7925],{"xmlns":890},[892,7926,7927,8033],{},[895,7928,7929,7931,7933,8015,8017,8031],{},[2461,7930,7362],{},[1656,7932,1713],{},[3294,7934,7935,7975],{},[895,7936,7937,7945,7961],{},[4138,7938,7939],{"scriptlevel":4032,"displaystyle":1658},[3294,7940,7941,7943],{},[1667,7942,1669],{},[1667,7944,1680],{},[1715,7946,7947,7949,7951],{},[898,7948,1665],{},[1667,7950,1669],{},[895,7952,7953,7955,7957,7959],{},[1656,7954,3964],{},[1667,7956,1669],{},[898,7958,1782],{"mathvariant":1723},[1667,7960,1680],{},[1715,7962,7963,7965,7967],{},[898,7964,1665],{},[1667,7966,1680],{},[895,7968,7969,7971,7973],{},[1667,7970,1669],{},[898,7972,1782],{"mathvariant":1723},[1667,7974,1680],{},[895,7976,7977,7985,7999],{},[4138,7978,7979],{"scriptlevel":4032,"displaystyle":1658},[3294,7980,7981,7983],{},[1667,7982,1669],{},[1667,7984,1680],{},[1715,7986,7987,7989,7991],{},[898,7988,1665],{},[1667,7990,1669],{},[895,7992,7993,7995,7997],{},[1667,7994,1669],{},[898,7996,1782],{"mathvariant":1723},[1667,7998,1680],{},[1715,8000,8001,8003,8005],{},[898,8002,1665],{},[1667,8004,1680],{},[895,8006,8007,8009,8011,8013],{},[1656,8008,3964],{},[1667,8010,1669],{},[898,8012,1782],{"mathvariant":1723},[1667,8014,1680],{},[1656,8016,1713],{},[3294,8018,8019,8025],{},[1661,8020,8021,8023],{},[898,8022,1665],{},[1667,8024,1680],{},[1661,8026,8027,8029],{},[898,8028,1665],{},[1667,8030,1669],{},[898,8032,1863],{"mathvariant":1723},[902,8034,8035],{"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}.",[724,8037,8038,8039,2191,8085,8087,8088,8108],{},"Tedy ",[883,8040,8042],{"className":8041},[886],[888,8043,8044],{"xmlns":890},[892,8045,8046,8082],{},[895,8047,8048,8050,8052,8055,8057,8060,8062,8064,8072,8074],{},[2461,8049,7362],{},[1656,8051,1659],{"stretchy":1658},[1667,8053,8054],{},"300",[1656,8056,1673],{"separator":1672},[1667,8058,8059],{},"500",[1656,8061,1683],{"stretchy":1658},[1656,8063,1713],{},[4138,8065,8066],{"scriptlevel":4032,"displaystyle":1658},[3294,8067,8068,8070],{},[1667,8069,8059],{},[1667,8071,8054],{},[1656,8073,1713],{},[4138,8075,8076],{"scriptlevel":4032,"displaystyle":1658},[3294,8077,8078,8080],{},[1667,8079,5193],{},[1667,8081,2617],{},[902,8083,8084],{"encoding":904},"\\text{MRCS}(300, 500) = \\tfrac{500}{300} = \\tfrac{5}{3}",[614,8086,5434],{}," zvýší-li spotřebitel nákup prvního zboží o 1 jednotku, musí snížit nákup druhého zboží přibližně o ",[883,8089,8091],{"className":8090},[886],[888,8092,8093],{"xmlns":890},[892,8094,8095,8105],{},[895,8096,8097],{},[4138,8098,8099],{"scriptlevel":4032,"displaystyle":1658},[3294,8100,8101,8103],{},[1667,8102,5193],{},[1667,8104,2617],{},[902,8106,8107],{"encoding":904},"\\tfrac{5}{3}"," jednotky, aby se užitečnost zachovala.",[724,8110,8111,8112,8116],{},"(Paralelou je ",[207,8113,8115],{"className":8114,"dataFsResolvedFilePath":857,"href":858},[210],"mezní míra technické substituce MRTS"," z produkční teorie.)",[115,8118,8120],{"id":8119},"_63-64-optimalizace-spotřebitele-přehled","6.3 – 6.4 Optimalizace spotřebitele — přehled",[724,8122,8123,8124,8127],{},"Rámcově se v kapitole 6 studují ",[38,8125,8126],{},"dvě vázané optimalizační úlohy"," s užitečností:",[120,8129,8130,8273],{},[123,8131,8132,8135,8136,8167,8168,1643,8171,8224,8225,1863],{},[38,8133,8134],{},"Primární úloha"," — maximalizace ",[883,8137,8139],{"className":8138},[886],[888,8140,8141],{"xmlns":890},[892,8142,8143,8165],{},[895,8144,8145,8147,8149,8155,8157,8163],{},[898,8146,900],{},[1656,8148,1659],{"stretchy":1658},[1661,8150,8151,8153],{},[898,8152,1665],{},[1667,8154,1669],{},[1656,8156,1673],{"separator":1672},[1661,8158,8159,8161],{},[898,8160,1665],{},[1667,8162,1680],{},[1656,8164,1683],{"stretchy":1658},[902,8166,1686],{"encoding":904}," při ",[38,8169,8170],{},"rozpočtovém omezení",[883,8172,8174],{"className":8173},[886],[888,8175,8176],{"xmlns":890},[892,8177,8178,8221],{},[895,8179,8180,8188,8190,8199,8205,8207,8215],{},[2062,8181,8182,8185],{},[898,8183,8184],{},"Y",[1656,8186,8187],{},"∗",[1656,8189,1713],{},[1715,8191,8192,8195,8197],{},[898,8193,8194],{},"P",[1667,8196,1669],{},[1656,8198,8187],{},[1661,8200,8201,8203],{},[898,8202,1665],{},[1667,8204,1669],{},[1656,8206,3633],{},[1715,8208,8209,8211,8213],{},[898,8210,8194],{},[1667,8212,1680],{},[1656,8214,8187],{},[1661,8216,8217,8219],{},[898,8218,1665],{},[1667,8220,1680],{},[902,8222,8223],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2",". Výstupem je Marshallova poptávka ",[883,8226,8228],{"className":8227},[886],[888,8229,8230],{"xmlns":890},[892,8231,8232,8270],{},[895,8233,8234,8240,8242,8248,8250,8256,8258,8264,8266,8268],{},[1661,8235,8236,8238],{},[898,8237,1665],{},[898,8239,1710],{},[1656,8241,1713],{},[1661,8243,8244,8246],{},[898,8245,6787],{},[898,8247,1710],{},[1656,8249,1659],{"stretchy":1658},[1661,8251,8252,8254],{},[898,8253,8194],{},[1667,8255,1669],{},[1656,8257,1673],{"separator":1672},[1661,8259,8260,8262],{},[898,8261,8194],{},[1667,8263,1680],{},[1656,8265,1673],{"separator":1672},[898,8267,8184],{},[1656,8269,1683],{"stretchy":1658},[902,8271,8272],{"encoding":904},"Q_i = D_i(P_1, P_2, Y)",[123,8274,8275,8278,8279,8325,8326,8344,8345,1863],{},[38,8276,8277],{},"Duální úloha"," — minimalizace výdajů ",[883,8280,8282],{"className":8281},[886],[888,8283,8284],{"xmlns":890},[892,8285,8286,8322],{},[895,8287,8288,8290,8292,8300,8306,8308,8316],{},[898,8289,1842],{},[1656,8291,1713],{},[1715,8293,8294,8296,8298],{},[898,8295,8194],{},[1667,8297,1669],{},[1656,8299,8187],{},[1661,8301,8302,8304],{},[898,8303,1665],{},[1667,8305,1669],{},[1656,8307,3633],{},[1715,8309,8310,8312,8314],{},[898,8311,8194],{},[1667,8313,1680],{},[1656,8315,8187],{},[1661,8317,8318,8320],{},[898,8319,1665],{},[1667,8321,1680],{},[902,8323,8324],{"encoding":904},"E = P_1^* Q_1 + P_2^* Q_2"," při zadané hladině užitečnosti ",[883,8327,8329],{"className":8328},[886],[888,8330,8331],{"xmlns":890},[892,8332,8333,8341],{},[895,8334,8335],{},[2062,8336,8337,8339],{},[898,8338,900],{},[1656,8340,8187],{},[902,8342,8343],{"encoding":904},"U^*",". Výstupem je Hicksova poptávka ",[883,8346,8348],{"className":8347},[886],[888,8349,8350],{"xmlns":890},[892,8351,8352,8390],{},[895,8353,8354,8360,8362,8368,8370,8376,8378,8384,8386,8388],{},[1661,8355,8356,8358],{},[898,8357,1665],{},[898,8359,1710],{},[1656,8361,1713],{},[1661,8363,8364,8366],{},[898,8365,6787],{},[898,8367,1710],{},[1656,8369,1659],{"stretchy":1658},[1661,8371,8372,8374],{},[898,8373,8194],{},[1667,8375,1669],{},[1656,8377,1673],{"separator":1672},[1661,8379,8380,8382],{},[898,8381,8194],{},[1667,8383,1680],{},[1656,8385,1673],{"separator":1672},[898,8387,900],{},[1656,8389,1683],{"stretchy":1658},[902,8391,8392],{"encoding":904},"Q_i = D_i(P_1, P_2, U)",[724,8394,8395,8396,8400,8401,1643,8404,8444],{},"Obě úlohy se řeší ",[207,8397,8399],{"className":8398,"dataFsResolvedFilePath":791,"href":792},[210],"metodou Lagrangeových multiplikátorů"," a vedou na ",[38,8402,8403],{},"tentýž bod dotyku",[883,8405,8407],{"className":8406},[886],[888,8408,8409],{"xmlns":890},[892,8410,8411,8441],{},[895,8412,8413,8419,8421,8429,8431,8439],{},[2062,8414,8415,8417],{},[898,8416,1665],{},[1656,8418,8187],{},[1656,8420,3453],{"stretchy":1658},[1715,8422,8423,8425,8427],{},[898,8424,1665],{},[1667,8426,1669],{},[1656,8428,8187],{},[1656,8430,1673],{"separator":1672},[1715,8432,8433,8435,8437],{},[898,8434,1665],{},[1667,8436,1680],{},[1656,8438,8187],{},[1656,8440,3462],{"stretchy":1658},[902,8442,8443],{"encoding":904},"Q^*[Q_1^*, Q_2^*]"," indiferenční křivky a rozpočtové přímky (resp. přímky výdajů), v němž platí podmínka optimality",[883,8446,8448],{"className":8447},[886],[888,8449,8450],{"xmlns":890,"display":2408},[892,8451,8452,8498],{},[895,8453,8454,8456,8458,8476,8478,8496],{},[2461,8455,7362],{},[1656,8457,1713],{},[3294,8459,8460,8468],{},[1715,8461,8462,8464,8466],{},[898,8463,900],{},[1667,8465,1669],{},[1656,8467,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1715,8469,8470,8472,8474],{},[898,8471,900],{},[1667,8473,1680],{},[1656,8475,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,8477,1713],{},[3294,8479,8480,8488],{},[1715,8481,8482,8484,8486],{},[898,8483,8194],{},[1667,8485,1669],{},[1656,8487,8187],{},[1715,8489,8490,8492,8494],{},[898,8491,8194],{},[1667,8493,1680],{},[1656,8495,8187],{},[898,8497,1863],{"mathvariant":1723},[902,8499,8500],{"encoding":904},"\\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*}.",[724,8502,8503],{},"Poměr mezních užitečností se rovná poměru cen — sklon indiferenční křivky v optimu se rovná sklonu rozpočtové přímky.",[1981,8505,8506],{},[724,8507,8508,8510,8511,8514,8515,8518,8519,8547,8548,8584,8585,8619,8620,8664,8665,8668,8669,1863],{},[883,8509,3472],{}," Pro detailní postup viz ",[207,8512,1874],{"className":8513,"dataFsResolvedFilePath":911,"href":912},[210],"\nKompletní odvození obou úloh Lagrangeovou metodou, geometrická interpretace, řešené ",[38,8516,8517],{},"Příklady 6.5–6.8"," (MRCS pro Cobb-Douglase, maximalizace ",[883,8520,8522],{"className":8521},[886],[888,8523,8524],{"xmlns":890},[892,8525,8526,8544],{},[895,8527,8528,8530,8532,8538],{},[898,8529,900],{},[1656,8531,1713],{},[1661,8533,8534,8536],{},[898,8535,1665],{},[1667,8537,1669],{},[1661,8539,8540,8542],{},[898,8541,1665],{},[1667,8543,1680],{},[902,8545,8546],{"encoding":904},"U = Q_1 Q_2"," s výsledkem ",[883,8549,8551],{"className":8550},[886],[888,8552,8553],{"xmlns":890},[892,8554,8555,8581],{},[895,8556,8557,8563,8565,8568,8570,8576,8578],{},[1661,8558,8559,8561],{},[898,8560,1665],{},[1667,8562,1669],{},[1656,8564,1713],{},[1667,8566,8567],{},"25",[1656,8569,1673],{"separator":1672},[1661,8571,8572,8574],{},[898,8573,1665],{},[1667,8575,1680],{},[1656,8577,1713],{},[1667,8579,8580],{},"10",[902,8582,8583],{"encoding":904},"Q_1 = 25, Q_2 = 10","; minimalizace výdajů s ",[883,8586,8588],{"className":8587},[886],[888,8589,8590],{"xmlns":890},[892,8591,8592,8616],{},[895,8593,8594,8600,8602,8604,8606,8612,8614],{},[1661,8595,8596,8598],{},[898,8597,1665],{},[1667,8599,1669],{},[1656,8601,1713],{},[1667,8603,2673],{},[1656,8605,1673],{"separator":1672},[1661,8607,8608,8610],{},[898,8609,1665],{},[1667,8611,1680],{},[1656,8613,1713],{},[1667,8615,1669],{},[902,8617,8618],{"encoding":904},"Q_1 = 4, Q_2 = 1","; obecná Hicksova poptávka pro ",[883,8621,8623],{"className":8622},[886],[888,8624,8625],{"xmlns":890},[892,8626,8627,8661],{},[895,8628,8629,8631,8633,8647],{},[898,8630,900],{},[1656,8632,1713],{},[1715,8634,8635,8637,8639],{},[898,8636,1665],{},[1667,8638,1669],{},[895,8640,8641,8643,8645],{},[1667,8642,1669],{},[898,8644,1782],{"mathvariant":1723},[1667,8646,1680],{},[1715,8648,8649,8651,8653],{},[898,8650,1665],{},[1667,8652,1680],{},[895,8654,8655,8657,8659],{},[1667,8656,1669],{},[898,8658,1782],{"mathvariant":1723},[1667,8660,1680],{},[902,8662,8663],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F2}","), odvození Marshallovy i Hicksovy funkce poptávky a Engelových funkcí, vztah dualita primární ↔ duální úlohy a úlohy ",[38,8666,8667],{},"6.8–6.13"," jsou na stránce ",[207,8670,8672],{"className":8671,"dataFsResolvedFilePath":911,"href":912},[210],"Optimalizace spotřebitele — Lagrange, poptávka, minimalizace výdajů",[115,8674,8676],{"id":8675},"shrnutí-kapitoly-6","Shrnutí kapitoly 6",[724,8678,8679,8680,8693,8694,8696,8697,8699,8700,8702,8703,8705,8706,8708,8709,8711,8712,1643,8715,8750,8751,8764,8765,8768,8769,8772,8773,1863],{},"Každá ",[883,8681,8683],{"className":8682},[886],[888,8684,8685],{"xmlns":890},[892,8686,8687,8691],{},[895,8688,8689],{},[898,8690,2292],{},[902,8692,2292],{"encoding":904},"-tice množství jednotlivých zboží je ",[38,8695,1895],{},". Přiřadíme-li každému svazku kladné číslo (jeho užitečnost), můžeme svazky uspořádat podle rostoucí užitečnosti; svazky se stejnou užitečností jsou indiferentní. Tím je definována ",[38,8698,2399],{}," a současně ",[38,8701,1899],{},". Její parciální derivace (podle jednotlivých množství) jsou ",[38,8704,1905],{}," — přibližná změna užitečnosti při jednotkové změně příslušného zboží. Aby funkce mohla být funkcí užitečnosti, musejí být její první parciální derivace ",[38,8707,4299],{}," (6.4) a druhé parciální derivace ",[38,8710,4340],{}," (6.5 — zákon klesající mezní užitečnosti). ",[38,8713,8714],{},"Indiferenční křivky",[883,8716,8718],{"className":8717},[886],[888,8719,8720],{"xmlns":890},[892,8721,8722,8748],{},[895,8723,8724,8726,8728,8734,8736,8742,8744,8746],{},[898,8725,900],{},[1656,8727,1659],{"stretchy":1658},[1661,8729,8730,8732],{},[898,8731,1665],{},[1667,8733,1669],{},[1656,8735,1673],{"separator":1672},[1661,8737,8738,8740],{},[898,8739,1665],{},[1667,8741,1680],{},[1656,8743,1683],{"stretchy":1658},[1656,8745,1713],{},[898,8747,1745],{},[902,8749,4870],{"encoding":904}," jsou klesající, neprotínající se, vzdálenější od počátku mají vyšší užitečnost a jsou konvexní. ",[883,8752,8754],{"className":8753},[886],[888,8755,8756],{"xmlns":890},[892,8757,8758,8762],{},[895,8759,8760],{},[2461,8761,7362],{},[902,8763,7365],{"encoding":904}," = podíl mezních užitečností udává náhradu jednoho zboží druhým při zachování užitečnosti. Na tento teoretický základ navazují optimalizační úlohy (",[38,8766,8767],{},"maximalizace užitečnosti"," a duální ",[38,8770,8771],{},"minimalizace výdajů",") řešené Lagrangeovou metodou — viz ",[207,8774,1874],{"className":8775,"dataFsResolvedFilePath":911,"href":912},[210],[115,8777,8779],{"id":8778},"otázky-k-sebehodnocení","Otázky k sebehodnocení",[152,8781,8782,8785,8788,8791,8794,8797,8800,8803,8806,8809],{},[123,8783,8784],{},"Co se zahrnuje pod termín užitečnost?",[123,8786,8787],{},"Co se rozumí svazkem zboží? Které svazky zboží jsou indiferentní?",[123,8789,8790],{},"Jak souvisejí hodnoty funkce užitečnosti s preferencí svazků?",[123,8792,8793],{},"Jak se vypočítá mezní užitečnost?",[123,8795,8796],{},"Jak lze ekonomicky interpretovat fakt, že mezní užitečnost určitého zboží se rovná 2,5?",[123,8798,8799],{},"Jaké vlastnosti musí mít funkce více proměnných, aby mohla být funkcí užitečnosti?",[123,8801,8802],{},"Které jsou nejčastěji používané funkce užitečnosti?",[123,8804,8805],{},"Jakou rovnici mají křivky užitečnosti? Co platí v bodech ležících na téže křivce užitečnosti?",[123,8807,8808],{},"Proč mají křivky užitečnosti záporný sklon?",[123,8810,8811],{},"Jak se vypočte mezní míra komoditní substituce? Vysvětlete, co vypočtená hodnota vyjadřuje.",[115,8813,8815],{"id":8814},"úlohy-teorie-užitečnosti-61-67","Úlohy — teorie užitečnosti (6.1 – 6.7)",[724,8817,8818,8821,8822,8865,8866,1343,8894,1343,8922,8950],{},[38,8819,8820],{},"6.1"," Užitečnost pro tři zboží — hudbu, čokoládu a sýr je dána vztahem ",[883,8823,8825],{"className":8824},[886],[888,8826,8827],{"xmlns":890},[892,8828,8829,8862],{},[895,8830,8831,8833,8835,8841,8843,8846,8852,8854,8856],{},[898,8832,900],{},[1656,8834,1713],{},[1661,8836,8837,8839],{},[898,8838,1665],{},[1667,8840,1669],{},[1656,8842,3633],{},[1667,8844,8845],{},"1,5",[1661,8847,8848,8850],{},[898,8849,1665],{},[1667,8851,1680],{},[1656,8853,3633],{},[1667,8855,1680],{},[1661,8857,8858,8860],{},[898,8859,1665],{},[1667,8861,2617],{},[902,8863,8864],{"encoding":904},"U = Q_1 + 1{,}5 Q_2 + 2 Q_3",". (a) Vypočtěte ",[883,8867,8869],{"className":8868},[886],[888,8870,8871],{"xmlns":890},[892,8872,8873,8891],{},[895,8874,8875,8877,8879,8881,8883,8885,8887,8889],{},[898,8876,900],{},[1656,8878,1659],{"stretchy":1658},[1667,8880,2673],{},[1656,8882,1673],{"separator":1672},[1667,8884,1680],{},[1656,8886,1673],{"separator":1672},[1667,8888,1680],{},[1656,8890,1683],{"stretchy":1658},[902,8892,8893],{"encoding":904},"U(4, 2, 2)",[883,8895,8897],{"className":8896},[886],[888,8898,8899],{"xmlns":890},[892,8900,8901,8919],{},[895,8902,8903,8905,8907,8909,8911,8913,8915,8917],{},[898,8904,900],{},[1656,8906,1659],{"stretchy":1658},[1667,8908,1669],{},[1656,8910,1673],{"separator":1672},[1667,8912,2673],{},[1656,8914,1673],{"separator":1672},[1667,8916,1680],{},[1656,8918,1683],{"stretchy":1658},[902,8920,8921],{"encoding":904},"U(1, 4, 2)",[883,8923,8925],{"className":8924},[886],[888,8926,8927],{"xmlns":890},[892,8928,8929,8947],{},[895,8930,8931,8933,8935,8937,8939,8941,8943,8945],{},[898,8932,900],{},[1656,8934,1659],{"stretchy":1658},[1667,8936,1680],{},[1656,8938,1673],{"separator":1672},[1667,8940,2617],{},[1656,8942,1673],{"separator":1672},[1667,8944,1669],{},[1656,8946,1683],{"stretchy":1658},[902,8948,8949],{"encoding":904},"U(2, 3, 1)",". (b) Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků v (a).",[724,8952,8953,8956,8957,9009,9010,1343,9037,1343,9064,1343,9090,1343,9118,1343,9146,1343,9172,9198],{},[38,8954,8955],{},"6.2"," Je dána užitečnost ",[883,8958,8960],{"className":8959},[886],[888,8961,8962],{"xmlns":890},[892,8963,8964,9006],{},[895,8965,8966,8968,8970,8972,8986,9000],{},[898,8967,900],{},[1656,8969,1713],{},[1667,8971,1680],{},[1715,8973,8974,8976,8978],{},[898,8975,1665],{},[1667,8977,1669],{},[895,8979,8980,8982,8984],{},[1667,8981,1669],{},[898,8983,1782],{"mathvariant":1723},[1667,8985,2617],{},[1715,8987,8988,8990,8992],{},[898,8989,1665],{},[1667,8991,1680],{},[895,8993,8994,8996,8998],{},[1667,8995,1669],{},[898,8997,1782],{"mathvariant":1723},[1667,8999,1680],{},[1661,9001,9002,9004],{},[898,9003,1665],{},[1667,9005,2617],{},[902,9007,9008],{"encoding":904},"U = 2 Q_1^{1\u002F3} Q_2^{1\u002F2} Q_3"," pro tři zboží. Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků ",[883,9011,9013],{"className":9012},[886],[888,9014,9015],{"xmlns":890},[892,9016,9017,9034],{},[895,9018,9019,9021,9024,9026,9028,9030,9032],{},[1656,9020,1659],{"stretchy":1658},[1667,9022,9023],{},"36",[1656,9025,1673],{"separator":1672},[1667,9027,2707],{},[1656,9029,1673],{"separator":1672},[1667,9031,8580],{},[1656,9033,1683],{"stretchy":1658},[902,9035,9036],{"encoding":904},"(36, 27, 10)",[883,9038,9040],{"className":9039},[886],[888,9041,9042],{"xmlns":890},[892,9043,9044,9061],{},[895,9045,9046,9048,9050,9052,9054,9056,9059],{},[1656,9047,1659],{"stretchy":1658},[1667,9049,2678],{},[1656,9051,1673],{"separator":1672},[1667,9053,2877],{},[1656,9055,1673],{"separator":1672},[1667,9057,9058],{},"20",[1656,9060,1683],{"stretchy":1658},[902,9062,9063],{"encoding":904},"(64, 8, 20)",[883,9065,9067],{"className":9066},[886],[888,9068,9069],{"xmlns":890},[892,9070,9071,9087],{},[895,9072,9073,9075,9077,9079,9081,9083,9085],{},[1656,9074,1659],{"stretchy":1658},[1667,9076,8567],{},[1656,9078,1673],{"separator":1672},[1667,9080,2678],{},[1656,9082,1673],{"separator":1672},[1667,9084,2877],{},[1656,9086,1683],{"stretchy":1658},[902,9088,9089],{"encoding":904},"(25, 64, 8)",[883,9091,9093],{"className":9092},[886],[888,9094,9095],{"xmlns":890},[892,9096,9097,9115],{},[895,9098,9099,9101,9103,9105,9108,9110,9113],{},[1656,9100,1659],{"stretchy":1658},[1667,9102,2673],{},[1656,9104,1673],{"separator":1672},[1667,9106,9107],{},"125",[1656,9109,1673],{"separator":1672},[1667,9111,9112],{},"6",[1656,9114,1683],{"stretchy":1658},[902,9116,9117],{"encoding":904},"(4, 125, 6)",[883,9119,9121],{"className":9120},[886],[888,9122,9123],{"xmlns":890},[892,9124,9125,9143],{},[895,9126,9127,9129,9131,9133,9136,9138,9141],{},[1656,9128,1659],{"stretchy":1658},[1667,9130,2698],{},[1656,9132,1673],{"separator":1672},[1667,9134,9135],{},"40",[1656,9137,1673],{"separator":1672},[1667,9139,9140],{},"12",[1656,9142,1683],{"stretchy":1658},[902,9144,9145],{"encoding":904},"(9, 40, 12)",[883,9147,9149],{"className":9148},[886],[888,9150,9151],{"xmlns":890},[892,9152,9153,9169],{},[895,9154,9155,9157,9159,9161,9163,9165,9167],{},[1656,9156,1659],{"stretchy":1658},[1667,9158,2698],{},[1656,9160,1673],{"separator":1672},[1667,9162,2678],{},[1656,9164,1673],{"separator":1672},[1667,9166,5193],{},[1656,9168,1683],{"stretchy":1658},[902,9170,9171],{"encoding":904},"(9, 64, 5)",[883,9173,9175],{"className":9174},[886],[888,9176,9177],{"xmlns":890},[892,9178,9179,9195],{},[895,9180,9181,9183,9185,9187,9189,9191,9193],{},[1656,9182,1659],{"stretchy":1658},[1667,9184,2678],{},[1656,9186,1673],{"separator":1672},[1667,9188,2877],{},[1656,9190,1673],{"separator":1672},[1667,9192,8580],{},[1656,9194,1683],{"stretchy":1658},[902,9196,9197],{"encoding":904},"(64, 8, 10)"," a uspořádejte je s neklesající užitečností.",[724,9200,9201,8956,9204,9247,9248,9284,9285,3713,9315,9348,9349,9366,9367,9384],{},[38,9202,9203],{},"6.3",[883,9205,9207],{"className":9206},[886],[888,9208,9209],{"xmlns":890},[892,9210,9211,9245],{},[895,9212,9213,9215,9217,9231],{},[898,9214,900],{},[1656,9216,1713],{},[1715,9218,9219,9221,9223],{},[898,9220,1665],{},[1667,9222,1669],{},[895,9224,9225,9227,9229],{},[1667,9226,1669],{},[898,9228,1782],{"mathvariant":1723},[1667,9230,1680],{},[1715,9232,9233,9235,9237],{},[898,9234,1665],{},[1667,9236,1680],{},[895,9238,9239,9241,9243],{},[1667,9240,1669],{},[898,9242,1782],{"mathvariant":1723},[1667,9244,1680],{},[902,9246,8663],{"encoding":904},". (a) Vypočtěte užitečnost pro ",[883,9249,9251],{"className":9250},[886],[888,9252,9253],{"xmlns":890},[892,9254,9255,9281],{},[895,9256,9257,9263,9265,9268,9270,9276,9278],{},[1661,9258,9259,9261],{},[898,9260,1665],{},[1667,9262,1669],{},[1656,9264,1713],{},[1667,9266,9267],{},"50",[1656,9269,1673],{"separator":1672},[1661,9271,9272,9274],{},[898,9273,1665],{},[1667,9275,1680],{},[1656,9277,1713],{},[1667,9279,9280],{},"80",[902,9282,9283],{"encoding":904},"Q_1 = 50, Q_2 = 80",". (b) Určete mezní užitečnosti ",[883,9286,9288],{"className":9287},[886],[888,9289,9290],{"xmlns":890},[892,9291,9292,9312],{},[895,9293,9294,9296,9302,9304,9306],{},[898,9295,1703],{},[1661,9297,9298,9300],{},[898,9299,900],{},[1667,9301,1669],{},[1656,9303,1673],{"separator":1672},[898,9305,1703],{},[1661,9307,9308,9310],{},[898,9309,900],{},[1667,9311,1680],{},[902,9313,9314],{"encoding":904},"MU_1, MU_2",[883,9316,9318],{"className":9317},[886],[888,9319,9320],{"xmlns":890},[892,9321,9322,9346],{},[895,9323,9324,9330,9332,9334,9336,9342,9344],{},[1661,9325,9326,9328],{},[898,9327,1665],{},[1667,9329,1669],{},[1656,9331,1713],{},[1667,9333,9267],{},[1656,9335,1673],{"separator":1672},[1661,9337,9338,9340],{},[898,9339,1665],{},[1667,9341,1680],{},[1656,9343,1713],{},[1667,9345,9280],{},[902,9347,9283],{"encoding":904}," a výsledky ekonomicky interpretujte. (d) Odhadněte změnu užitečnosti v důsledku změny ",[883,9350,9352],{"className":9351},[886],[888,9353,9354],{"xmlns":890},[892,9355,9356,9364],{},[895,9357,9358],{},[1661,9359,9360,9362],{},[898,9361,1665],{},[1667,9363,1669],{},[902,9365,3227],{"encoding":904}," na 60 a poklesu ",[883,9368,9370],{"className":9369},[886],[888,9371,9372],{"xmlns":890},[892,9373,9374,9382],{},[895,9375,9376],{},[1661,9377,9378,9380],{},[898,9379,1665],{},[1667,9381,1680],{},[902,9383,3246],{"encoding":904}," o 5 vzhledem k hladině dle (a) a porovnejte se skutečnou změnou užitečnosti.",[724,9386,9387,9390,9391,9452,9453,1863],{},[38,9388,9389],{},"6.4"," Je dána funkce ",[883,9392,9394],{"className":9393},[886],[888,9395,9396],{"xmlns":890},[892,9397,9398,9450],{},[895,9399,9400,9402,9404,9410,9412,9418,9420,9422,9436],{},[898,9401,900],{},[1656,9403,1659],{"stretchy":1658},[1661,9405,9406,9408],{},[898,9407,1665],{},[1667,9409,1669],{},[1656,9411,1673],{"separator":1672},[1661,9413,9414,9416],{},[898,9415,1665],{},[1667,9417,1680],{},[1656,9419,1683],{"stretchy":1658},[1656,9421,1713],{},[1715,9423,9424,9426,9428],{},[898,9425,1665],{},[1667,9427,1669],{},[895,9429,9430,9432,9434],{},[1667,9431,1669],{},[898,9433,1782],{"mathvariant":1723},[1667,9435,1680],{},[1715,9437,9438,9440,9442],{},[898,9439,1665],{},[1667,9441,1680],{},[895,9443,9444,9446,9448],{},[1667,9445,1669],{},[898,9447,1782],{"mathvariant":1723},[1667,9449,1680],{},[902,9451,7917],{"encoding":904},". (a) Ověřte, že tato funkce vykazuje vlastnosti funkce užitečnosti. (b) Najděte a načrtněte křivky ",[883,9454,9456],{"className":9455},[886],[888,9457,9458],{"xmlns":890},[892,9459,9460,9550],{},[895,9461,9462,9464,9466,9472,9474,9476,9478,9480,9482,9484,9490,9492,9494,9496,9498,9500,9502,9504,9506,9512,9514,9516,9518,9520,9522,9524,9530,9532,9534,9536,9538,9540,9542,9548],{},[898,9463,900],{},[1656,9465,1659],{"stretchy":1658},[1661,9467,9468,9470],{},[898,9469,1665],{},[1667,9471,1669],{},[1656,9473,1673],{"separator":1672},[1667,9475,1669],{},[1656,9477,1683],{"stretchy":1658},[1656,9479,1673],{"separator":1672},[898,9481,900],{},[1656,9483,1659],{"stretchy":1658},[1661,9485,9486,9488],{},[898,9487,1665],{},[1667,9489,1669],{},[1656,9491,1673],{"separator":1672},[1667,9493,1680],{},[1656,9495,1683],{"stretchy":1658},[1656,9497,1673],{"separator":1672},[898,9499,900],{},[1656,9501,1659],{"stretchy":1658},[1667,9503,1669],{},[1656,9505,1673],{"separator":1672},[1661,9507,9508,9510],{},[898,9509,1665],{},[1667,9511,1680],{},[1656,9513,1683],{"stretchy":1658},[1656,9515,1673],{"separator":1672},[898,9517,900],{},[1656,9519,1659],{"stretchy":1658},[1667,9521,1680],{},[1656,9523,1673],{"separator":1672},[1661,9525,9526,9528],{},[898,9527,1665],{},[1667,9529,1680],{},[1656,9531,1683],{"stretchy":1658},[1656,9533,1673],{"separator":1672},[898,9535,900],{},[1656,9537,1659],{"stretchy":1658},[1667,9539,2617],{},[1656,9541,1673],{"separator":1672},[1661,9543,9544,9546],{},[898,9545,1665],{},[1667,9547,1680],{},[1656,9549,1683],{"stretchy":1658},[902,9551,9552],{"encoding":904},"U(Q_1, 1), U(Q_1, 2), U(1, Q_2), U(2, Q_2), U(3, Q_2)",[724,9554,9555,8956,9558,9602,9603,9711,9712,1343,9737,1343,9763,9805,9806,1343,9835,9860],{},[38,9556,9557],{},"6.5",[883,9559,9561],{"className":9560},[886],[888,9562,9563],{"xmlns":890},[892,9564,9565,9599],{},[895,9566,9567,9569,9571,9585],{},[898,9568,900],{},[1656,9570,1713],{},[1715,9572,9573,9575,9577],{},[898,9574,1665],{},[1667,9576,1669],{},[895,9578,9579,9581,9583],{},[1667,9580,1680],{},[898,9582,1782],{"mathvariant":1723},[1667,9584,2617],{},[1715,9586,9587,9589,9591],{},[898,9588,1665],{},[1667,9590,1680],{},[895,9592,9593,9595,9597],{},[1667,9594,1669],{},[898,9596,1782],{"mathvariant":1723},[1667,9598,2617],{},[902,9600,9601],{"encoding":904},"U = Q_1^{2\u002F3} Q_2^{1\u002F3}",". (a) Najděte rovnici křivek užitečnosti. (b) Určete a načrtněte křivky ",[883,9604,9606],{"className":9605},[886],[888,9607,9608],{"xmlns":890},[892,9609,9610,9708],{},[895,9611,9612,9614,9616,9622,9624,9630,9632,9634,9636,9638,9640,9642,9648,9650,9652,9654,9656,9658,9660,9666,9668,9670,9672,9674,9676,9678,9680,9682,9688,9690,9692,9694,9696,9698,9700,9706],{},[898,9613,900],{},[1656,9615,1659],{"stretchy":1658},[1661,9617,9618,9620],{},[898,9619,1665],{},[1667,9621,1669],{},[1656,9623,1673],{"separator":1672},[1661,9625,9626,9628],{},[898,9627,1665],{},[1667,9629,1680],{},[1656,9631,1683],{"stretchy":1658},[1656,9633,1713],{},[1667,9635,1680],{},[1656,9637,1673],{"separator":1672},[898,9639,900],{},[1656,9641,1659],{"stretchy":1658},[1661,9643,9644,9646],{},[898,9645,1665],{},[1667,9647,1669],{},[1656,9649,1673],{"separator":1672},[1667,9651,2617],{},[1656,9653,1683],{"stretchy":1658},[1656,9655,1673],{"separator":1672},[898,9657,900],{},[1656,9659,1659],{"stretchy":1658},[1661,9661,9662,9664],{},[898,9663,1665],{},[1667,9665,1669],{},[1656,9667,1673],{"separator":1672},[1667,9669,1680],{},[1656,9671,1683],{"stretchy":1658},[1656,9673,1673],{"separator":1672},[898,9675,900],{},[1656,9677,1659],{"stretchy":1658},[1667,9679,1680],{},[1656,9681,1673],{"separator":1672},[1661,9683,9684,9686],{},[898,9685,1665],{},[1667,9687,1680],{},[1656,9689,1683],{"stretchy":1658},[1656,9691,1673],{"separator":1672},[898,9693,900],{},[1656,9695,1659],{"stretchy":1658},[1667,9697,2617],{},[1656,9699,1673],{"separator":1672},[1661,9701,9702,9704],{},[898,9703,1665],{},[1667,9705,1680],{},[1656,9707,1683],{"stretchy":1658},[902,9709,9710],{"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 ",[883,9713,9715],{"className":9714},[886],[888,9716,9717],{"xmlns":890},[892,9718,9719,9734],{},[895,9720,9721,9723,9725,9727,9729,9732],{},[898,9722,2146],{},[1656,9724,3453],{"stretchy":1658},[1667,9726,8845],{},[1656,9728,2856],{"separator":1672},[1667,9730,9731],{},"3,555",[1656,9733,3462],{"stretchy":1658},[902,9735,9736],{"encoding":904},"A[1{,}5; 3{,}555]",[883,9738,9740],{"className":9739},[886],[888,9741,9742],{"xmlns":890},[892,9743,9744,9760],{},[895,9745,9746,9748,9750,9753,9755,9758],{},[898,9747,2161],{},[1656,9749,3453],{"stretchy":1658},[1667,9751,9752],{},"2,5",[1656,9754,2856],{"separator":1672},[1667,9756,9757],{},"1,28",[1656,9759,3462],{"stretchy":1658},[902,9761,9762],{"encoding":904},"B[2{,}5; 1{,}28]",[883,9764,9766],{"className":9765},[886],[888,9767,9768],{"xmlns":890},[892,9769,9770,9802],{},[895,9771,9772,9774,9776,9778,9780,9782,9784,9790,9792,9794,9796,9798,9800],{},[898,9773,1766],{},[1656,9775,3453],{"stretchy":1658},[1667,9777,1680],{},[1656,9779,2856],{"separator":1672},[898,9781,900],{},[1656,9783,1659],{"stretchy":1658},[1661,9785,9786,9788],{},[898,9787,1665],{},[1667,9789,1669],{},[1656,9791,1673],{"separator":1672},[1667,9793,2617],{},[1656,9795,1683],{"stretchy":1658},[1656,9797,1713],{},[1667,9799,2617],{},[1656,9801,3462],{"stretchy":1658},[902,9803,9804],{"encoding":904},"C[2; U(Q_1, 3) = 3]"," (c) Leží některé z bodů ",[883,9807,9809],{"className":9808},[886],[888,9810,9811],{"xmlns":890},[892,9812,9813,9832],{},[895,9814,9815,9817,9819,9821,9823,9825,9827,9830],{},[898,9816,6787],{},[1656,9818,3453],{"stretchy":1658},[1667,9820,2617],{},[1656,9822,2856],{"separator":1672},[1667,9824,1669],{},[1656,9826,2856],{"separator":1672},[1667,9828,9829],{},"0,832",[1656,9831,3462],{"stretchy":1658},[902,9833,9834],{"encoding":904},"D[3; 1; 0{,}832]",[883,9836,9838],{"className":9837},[886],[888,9839,9840],{"xmlns":890},[892,9841,9842,9857],{},[895,9843,9844,9846,9848,9850,9852,9855],{},[898,9845,1842],{},[1656,9847,3453],{"stretchy":1658},[1667,9849,9752],{},[1656,9851,2856],{"separator":1672},[1667,9853,9854],{},"4,32",[1656,9856,3462],{"stretchy":1658},[902,9858,9859],{"encoding":904},"E[2{,}5; 4{,}32]"," na téže křivce užitečnosti? Když ano, určete ji.",[724,9862,9863,8956,9866,9909,9910,3713,9923,9957,9958,9975,9976,9993],{},[38,9864,9865],{},"6.6",[883,9867,9869],{"className":9868},[886],[888,9870,9871],{"xmlns":890},[892,9872,9873,9907],{},[895,9874,9875,9877,9879,9893],{},[898,9876,900],{},[1656,9878,1713],{},[1715,9880,9881,9883,9885],{},[898,9882,1665],{},[1667,9884,1669],{},[895,9886,9887,9889,9891],{},[1667,9888,1680],{},[898,9890,1782],{"mathvariant":1723},[1667,9892,2617],{},[1715,9894,9895,9897,9899],{},[898,9896,1665],{},[1667,9898,1680],{},[895,9900,9901,9903,9905],{},[1667,9902,1669],{},[898,9904,1782],{"mathvariant":1723},[1667,9906,2617],{},[902,9908,9601],{"encoding":904},". (a) Najděte mezní míru komoditní substituce ",[883,9911,9913],{"className":9912},[886],[888,9914,9915],{"xmlns":890},[892,9916,9917,9921],{},[895,9918,9919],{},[2461,9920,7362],{},[902,9922,7365],{"encoding":904},[883,9924,9926],{"className":9925},[886],[888,9927,9928],{"xmlns":890},[892,9929,9930,9954],{},[895,9931,9932,9938,9940,9942,9944,9950,9952],{},[1661,9933,9934,9936],{},[898,9935,1665],{},[1667,9937,1669],{},[1656,9939,1713],{},[1667,9941,5267],{},[1656,9943,1673],{"separator":1672},[1661,9945,9946,9948],{},[898,9947,1665],{},[1667,9949,1680],{},[1656,9951,1713],{},[1667,9953,5272],{},[902,9955,9956],{"encoding":904},"Q_1 = 100, Q_2 = 200"," a výsledek ekonomicky interpretujte. (c) Odhadněte, o kolik je třeba změnit ",[883,9959,9961],{"className":9960},[886],[888,9962,9963],{"xmlns":890},[892,9964,9965,9973],{},[895,9966,9967],{},[1661,9968,9969,9971],{},[898,9970,1665],{},[1667,9972,1669],{},[902,9974,3227],{"encoding":904},", poklesne-li ",[883,9977,9979],{"className":9978},[886],[888,9980,9981],{"xmlns":890},[892,9982,9983,9991],{},[895,9984,9985],{},[1661,9986,9987,9989],{},[898,9988,1665],{},[1667,9990,1680],{},[902,9992,3246],{"encoding":904}," o 5 vzhledem k hladině dle (b).",[724,9995,9996,9999,10000,10017,10018,10035,10036,10068,10069,10095,10096,10109,10110,1343,10134,1343,10158,1863],{},[38,9997,9998],{},"6.7"," Míra uspokojení z nákupu množství ",[883,10001,10003],{"className":10002},[886],[888,10004,10005],{"xmlns":890},[892,10006,10007,10015],{},[895,10008,10009],{},[1661,10010,10011,10013],{},[898,10012,1665],{},[1667,10014,1669],{},[902,10016,3227],{"encoding":904}," nealko nápojů a množství ",[883,10019,10021],{"className":10020},[886],[888,10022,10023],{"xmlns":890},[892,10024,10025,10033],{},[895,10026,10027],{},[1661,10028,10029,10031],{},[898,10030,1665],{},[1667,10032,1680],{},[902,10034,3246],{"encoding":904}," hamburgerů za týden je dána funkcí užitečnosti ",[883,10037,10039],{"className":10038},[886],[888,10040,10041],{"xmlns":890},[892,10042,10043,10065],{},[895,10044,10045,10047,10049],{},[898,10046,900],{},[1656,10048,1713],{},[2625,10050,10051],{},[895,10052,10053,10059],{},[1661,10054,10055,10057],{},[898,10056,1665],{},[1667,10058,1669],{},[1661,10060,10061,10063],{},[898,10062,1665],{},[1667,10064,1680],{},[902,10066,10067],{"encoding":904},"U = \\sqrt{Q_1 Q_2}",". (a) Najděte vztah pro hodnoty ",[883,10070,10072],{"className":10071},[886],[888,10073,10074],{"xmlns":890},[892,10075,10076,10092],{},[895,10077,10078,10084,10086],{},[1661,10079,10080,10082],{},[898,10081,1665],{},[1667,10083,1669],{},[1656,10085,1673],{"separator":1672},[1661,10087,10088,10090],{},[898,10089,1665],{},[1667,10091,1680],{},[902,10093,10094],{"encoding":904},"Q_1, Q_2",", pro něž je dosaženo užitečnosti 10 a uveďte několik takových dvojic hodnot. (b) Najděte ",[883,10097,10099],{"className":10098},[886],[888,10100,10101],{"xmlns":890},[892,10102,10103,10107],{},[895,10104,10105],{},[2461,10106,7362],{},[902,10108,7365],{"encoding":904}," na křivce nalezené v (a). (c) Ekonomicky interpretujte smysl ",[883,10111,10113],{"className":10112},[886],[888,10114,10115],{"xmlns":890},[892,10116,10117,10131],{},[895,10118,10119,10121,10123,10125,10127,10129],{},[2461,10120,7362],{},[1656,10122,1659],{"stretchy":1658},[1667,10124,5193],{},[1656,10126,1673],{"separator":1672},[1667,10128,9058],{},[1656,10130,1683],{"stretchy":1658},[902,10132,10133],{"encoding":904},"\\text{MRCS}(5, 20)",[883,10135,10137],{"className":10136},[886],[888,10138,10139],{"xmlns":890},[892,10140,10141,10155],{},[895,10142,10143,10145,10147,10149,10151,10153],{},[2461,10144,7362],{},[1656,10146,1659],{"stretchy":1658},[1667,10148,9058],{},[1656,10150,1673],{"separator":1672},[1667,10152,5193],{},[1656,10154,1683],{"stretchy":1658},[902,10156,10157],{"encoding":904},"\\text{MRCS}(20, 5)",[883,10159,10161],{"className":10160},[886],[888,10162,10163],{"xmlns":890},[892,10164,10165,10179],{},[895,10166,10167,10169,10171,10173,10175,10177],{},[2461,10168,7362],{},[1656,10170,1659],{"stretchy":1658},[1667,10172,1680],{},[1656,10174,1673],{"separator":1672},[1667,10176,9267],{},[1656,10178,1683],{"stretchy":1658},[902,10180,10181],{"encoding":904},"\\text{MRCS}(2, 50)",[1981,10183,10184],{},[724,10185,10186,10189,10190,1863],{},[883,10187,10188],{},"!tip"," Úlohy 6.8 – 6.13 (optimalizace, Lagrange, poptávka)\nÚlohy navázané na maximalizaci užitečnosti, minimalizaci výdajů a odvození Marshallových\u002FHicksových funkcí poptávky jsou na stránce ",[207,10191,10194],{"className":10192,"dataFsResolvedFilePath":911,"href":10193},[210],"\u002Fwiki\u002Foptimalizace-spotrebitele#Úlohy k optimalizaci","Optimalizace spotřebitele — Úlohy",[115,10196,10198],{"id":10197},"klíčové-pojmy","Klíčové pojmy",[120,10200,10201,10207,10212,10218,10271,10281,10327,10382,10445,10503,10558,10597],{},[123,10202,10203,10206],{},[38,10204,10205],{},"Užitečnost (utility)"," — ordinálně měřený ukazatel uspokojení spotřebitele ze svazku zboží.",[123,10208,10209,10211],{},[38,10210,1959],{}," — historická pojetí užitečnosti; v současnosti se preferuje ordinalistický.",[123,10213,10214,10217],{},[38,10215,10216],{},"Pět předpokladů chování spotřebitele"," — racionalita, ordinalita, konzistence a tranzitivita, rostoucí užitečnost, klesající mezní užitečnost.",[123,10219,10220,10222,10223,10236,10237,1863],{},[38,10221,2298],{}," — uspořádaná ",[883,10224,10226],{"className":10225},[886],[888,10227,10228],{"xmlns":890},[892,10229,10230,10234],{},[895,10231,10232],{},[898,10233,2292],{},[902,10235,2292],{"encoding":904},"-tice ",[883,10238,10240],{"className":10239},[886],[888,10241,10242],{"xmlns":890},[892,10243,10244,10268],{},[895,10245,10246,10248,10254,10256,10258,10260,10266],{},[1656,10247,1659],{"stretchy":1658},[1661,10249,10250,10252],{},[898,10251,1665],{},[1667,10253,1669],{},[1656,10255,1673],{"separator":1672},[1656,10257,2337],{},[1656,10259,1673],{"separator":1672},[1661,10261,10262,10264],{},[898,10263,1665],{},[898,10265,2292],{},[1656,10267,1683],{"stretchy":1658},[902,10269,10270],{"encoding":904},"(Q_1, \\dots, Q_n)",[123,10272,10273,10276,10277,10280],{},[38,10274,10275],{},"Relace preference"," — uspořádání svazků podle užitečnosti; ",[38,10278,10279],{},"indiferentní svazky"," mají stejnou užitečnost.",[123,10282,10283,1643,10286,10326],{},[38,10284,10285],{},"Funkce užitečnosti",[883,10287,10289],{"className":10288},[886],[888,10290,10291],{"xmlns":890},[892,10292,10293,10323],{},[895,10294,10295,10297,10299,10301,10303,10309,10311,10313,10315,10321],{},[898,10296,900],{},[1656,10298,1713],{},[898,10300,900],{},[1656,10302,1659],{"stretchy":1658},[1661,10304,10305,10307],{},[898,10306,1665],{},[1667,10308,1669],{},[1656,10310,1673],{"separator":1672},[1656,10312,2337],{},[1656,10314,1673],{"separator":1672},[1661,10316,10317,10319],{},[898,10318,1665],{},[898,10320,2292],{},[1656,10322,1683],{"stretchy":1658},[902,10324,10325],{"encoding":904},"U = U(Q_1, \\dots, Q_n)"," — vzorec (6.1); ekvivalentní až na monotónní transformaci.",[123,10328,10329,1643,10332,10361,10362,1643,10365,10381],{},[38,10330,10331],{},"Mezní užitečnost",[883,10333,10335],{"className":10334},[886],[888,10336,10337],{"xmlns":890},[892,10338,10339,10359],{},[895,10340,10341,10343,10349,10351],{},[898,10342,1703],{},[1661,10344,10345,10347],{},[898,10346,900],{},[898,10348,1710],{},[1656,10350,1713],{},[1715,10352,10353,10355,10357],{},[898,10354,900],{},[898,10356,1710],{},[1656,10358,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[902,10360,1728],{"encoding":904}," — vzorec (6.2); ",[38,10363,10364],{},"totální diferenciál",[883,10366,10368],{"className":10367},[886],[888,10369,10370],{"xmlns":890},[892,10371,10372,10378],{},[895,10373,10374,10376],{},[898,10375,3768],{"mathvariant":1723},[898,10377,900],{},[902,10379,10380],{"encoding":904},"\\mathrm{d} U"," — (6.3).",[123,10383,10384,10386,10387,10411,10412,10444],{},[38,10385,3991],{}," — (6.4) ",[883,10388,10390],{"className":10389},[886],[888,10391,10392],{"xmlns":890},[892,10393,10394,10408],{},[895,10395,10396,10404,10406],{},[1715,10397,10398,10400,10402],{},[898,10399,900],{},[898,10401,1710],{},[1656,10403,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,10405,2850],{},[1667,10407,4032],{},[902,10409,10410],{"encoding":904},"U'_i > 0",", (6.5) ",[883,10413,10415],{"className":10414},[886],[888,10416,10417],{"xmlns":890},[892,10418,10419,10441],{},[895,10420,10421,10437,10439],{},[1715,10422,10423,10425,10431],{},[898,10424,900],{},[895,10426,10427,10429],{},[898,10428,1710],{},[898,10430,1710],{},[895,10432,10433,10435],{},[1656,10434,1725],{"mathvariant":1723},[1656,10436,1725],{"mathvariant":1723},[1656,10438,4373],{},[1667,10440,4032],{},[902,10442,10443],{"encoding":904},"U''_{ii} \u003C 0"," (zákon klesající mezní užitečnosti).",[123,10446,10447,1643,10449,10481,10482,1863],{},[38,10448,5795],{},[883,10450,10452],{"className":10451},[886],[888,10453,10454],{"xmlns":890},[892,10455,10456,10478],{},[895,10457,10458,10460,10462,10470],{},[898,10459,900],{},[1656,10461,1713],{},[1715,10463,10464,10466,10468],{},[898,10465,1665],{},[1667,10467,1669],{},[898,10469,207],{},[1715,10471,10472,10474,10476],{},[898,10473,1665],{},[1667,10475,1680],{},[898,10477,3403],{},[902,10479,10480],{"encoding":904},"U = Q_1^a Q_2^b"," — (6.6), speciálně ",[883,10483,10485],{"className":10484},[886],[888,10486,10487],{"xmlns":890},[892,10488,10489,10501],{},[895,10490,10491,10493,10495,10497,10499],{},[898,10492,3403],{},[1656,10494,1713],{},[1667,10496,1669],{},[1656,10498,3964],{},[898,10500,207],{},[902,10502,5951],{"encoding":904},[123,10504,10505,1643,10508,10543,10544,10557],{},[38,10506,10507],{},"Křivky užitečnosti (indiferenční)",[883,10509,10511],{"className":10510},[886],[888,10512,10513],{"xmlns":890},[892,10514,10515,10541],{},[895,10516,10517,10519,10521,10527,10529,10535,10537,10539],{},[898,10518,900],{},[1656,10520,1659],{"stretchy":1658},[1661,10522,10523,10525],{},[898,10524,1665],{},[1667,10526,1669],{},[1656,10528,1673],{"separator":1672},[1661,10530,10531,10533],{},[898,10532,1665],{},[1667,10534,1680],{},[1656,10536,1683],{"stretchy":1658},[1656,10538,1713],{},[898,10540,1745],{},[902,10542,4870],{"encoding":904}," — (6.7), (6.8); čtyři vlastnosti: klesající, neprotínající se, vzdálenější od počátku = vyšší ",[883,10545,10547],{"className":10546},[886],[888,10548,10549],{"xmlns":890},[892,10550,10551,10555],{},[895,10552,10553],{},[898,10554,900],{},[902,10556,900],{"encoding":904},", konvexní.",[123,10559,10560,1643,10562,10596],{},[38,10561,7350],{},[883,10563,10565],{"className":10564},[886],[888,10566,10567],{"xmlns":890},[892,10568,10569,10593],{},[895,10570,10571,10573,10575,10577,10583,10585,10587],{},[2461,10572,7362],{},[1656,10574,1713],{},[898,10576,1703],{},[1661,10578,10579,10581],{},[898,10580,900],{},[1667,10582,1669],{},[898,10584,1782],{"mathvariant":1723},[898,10586,1703],{},[1661,10588,10589,10591],{},[898,10590,900],{},[1667,10592,1680],{},[902,10594,10595],{"encoding":904},"\\text{MRCS} = MU_1 \u002F MU_2"," — (6.9); vztahy (6.10), (6.11).",[123,10598,10599,1643,10602,10632,10633,10636],{},[38,10600,10601],{},"Podmínka optimality",[883,10603,10605],{"className":10604},[886],[888,10606,10607],{"xmlns":890},[892,10608,10609,10629],{},[895,10610,10611,10613,10615,10621,10623],{},[2461,10612,7362],{},[1656,10614,1713],{},[1661,10616,10617,10619],{},[898,10618,8194],{},[1667,10620,1669],{},[898,10622,1782],{"mathvariant":1723},[1661,10624,10625,10627],{},[898,10626,8194],{},[1667,10628,1680],{},[902,10630,10631],{"encoding":904},"\\text{MRCS} = P_1\u002FP_2"," — viz ",[207,10634,1874],{"className":10635,"dataFsResolvedFilePath":911,"href":912},[210]," pro plné odvození.",[115,10638,10640],{"id":10639},"navigace","Navigace",[120,10642,10643,10680,10727,10738],{},[123,10644,10645,1643,10648,10651,10652,10665,10666,10679],{},[38,10646,10647],{},"Navazující téma:",[207,10649,913],{"className":10650,"dataFsResolvedFilePath":911,"href":912},[210]," (Lagrange, max ",[883,10653,10655],{"className":10654},[886],[888,10656,10657],{"xmlns":890},[892,10658,10659,10663],{},[895,10660,10661],{},[898,10662,900],{},[902,10664,900],{"encoding":904},", min ",[883,10667,10669],{"className":10668},[886],[888,10670,10671],{"xmlns":890},[892,10672,10673,10677],{},[895,10674,10675],{},[898,10676,1842],{},[902,10678,1842],{"encoding":904},", funkce poptávky, Příklady 6.5–6.8, úlohy 6.8–6.13).",[123,10681,10682,1643,10685,10688,10689,10693,10694,10698,10699,10703,10704,10722,10723,10726],{},[38,10683,10684],{},"Související pojmy:",[207,10686,784],{"className":10687,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace = mezní užitečnost), ",[207,10690,10692],{"className":10691,"dataFsResolvedFilePath":764,"href":765},[210],"Derivace"," (parciální derivace, totální diferenciál), ",[207,10695,10697],{"className":10696,"dataFsResolvedFilePath":857,"href":858},[210],"Produkce"," (paralela: MRCS ↔ MRTS, izokvanty ↔ indiferenční křivky, Cobb-Douglas), ",[207,10700,10702],{"className":10701,"dataFsResolvedFilePath":800,"href":801},[210],"Poptávka a nabídka"," (Marshallovy poptávkové funkce ",[883,10705,10707],{"className":10706},[886],[888,10708,10709],{"xmlns":890},[892,10710,10711,10719],{},[895,10712,10713],{},[1661,10714,10715,10717],{},[898,10716,6787],{},[898,10718,1710],{},[902,10720,10721],{"encoding":904},"D_i","), ",[207,10724,793],{"className":10725,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace — nástroj pro navazující téma).",[123,10728,10729,1643,10732,1343,10735],{},[38,10730,10731],{},"Přednášky:",[207,10733,1094],{"className":10734,"dataFsResolvedFilePath":838,"href":839},[210],[207,10736,1101],{"className":10737,"dataFsResolvedFilePath":868,"href":869},[210],[123,10739,10740,1643,10743],{},[38,10741,10742],{},"Kurz:",[207,10744,1869],{"className":10745,"dataFsResolvedFilePath":10746,"href":10747},[210],"courses\u002Fimek.md","\u002Fwiki\u002Fimek",{"title":641,"searchDepth":642,"depth":642,"links":10749},[10750,10751,10752,10755,10756,10759,10763,10764,10767,10768,10769,10770,10771,10772,10773],{"id":1637,"depth":642,"text":1638},{"id":1877,"depth":642,"text":1878},{"id":1942,"depth":642,"text":1943,"children":10753},[10754],{"id":1958,"depth":649,"text":1959},{"id":2276,"depth":642,"text":2277},{"id":3166,"depth":642,"text":3167,"children":10757},[10758],{"id":3734,"depth":649,"text":3735},{"id":3990,"depth":642,"text":3991,"children":10760},[10761],{"id":4873,"depth":649,"text":10762},"Příklad 6.2 — ověření vlastností a dopočet pro U=Q11\u002F2Q21\u002F3U = Q_1^{1\u002F2} Q_2^{1\u002F3}",{"id":5794,"depth":642,"text":5795},{"id":6335,"depth":642,"text":6336,"children":10765},[10766],{"id":7113,"depth":649,"text":7114},{"id":7344,"depth":642,"text":7345},{"id":8119,"depth":642,"text":8120},{"id":8675,"depth":642,"text":8676},{"id":8778,"depth":642,"text":8779},{"id":8814,"depth":642,"text":8815},{"id":10197,"depth":642,"text":10198},{"id":10639,"depth":642,"text":10640},"2026-04-22",{},"\u002Ftopics\u002Fuzitecnost",{"title":1629,"description":641},[1138,1137],"topics\u002Fuzitecnost",[1128,10781,10782,10783,10784,10785],"uzitecnost","mezni-uzitecnost","cobb-douglas","indiferencni-krivky","mrcs","topic","xXggD9rfV5faUAk1b2B3YYbozpQLu-pObiMaZX5f7yI","topics",{"zapisku":1625,"topics":10790,"summaries":10791,"outputs":10792},15,5,1,[10794,12643,18317,19861,20732,25005,26608,36480,45442,59498,63787,83124,95225,103605,103893],{"id":10795,"title":10796,"body":10797,"course":1128,"courses":659,"created":1129,"description":12632,"extension":661,"meta":12633,"navigation":664,"path":12634,"seo":12635,"sources":12636,"stem":12637,"tags":12638,"type":10786,"updated":677,"__hash__":12642},"topics\u002Ftopics\u002Fderivace.md","Derivace, diferenciál a extrémy funkcí jedné proměnné",{"type":9,"value":10798,"toc":12615},[10799,10802,10821,10825,10903,10906,11029,11173,11175,11255,11259,11318,11368,11375,11379,11509,11559,11563,11605,11671,11739,11747,11751,11789,11861,11865,11943,11991,12035,12039,12043,12113,12117,12167,12244,12251,12254,12306,12576,12578],[12,10800,10796],{"id":10801},"derivace-diferenciál-a-extrémy-funkcí-jedné-proměnné",[724,10803,10804,10805,10809,10810,10813,10814,10817,10818,1863],{},"Matematický aparát kurzu ",[207,10806,10808],{"className":10807,"dataFsResolvedFilePath":10746,"href":10747},[210],"ImeK",". Bez derivace se neobejdou ",[38,10811,10812],{},"mezní veličiny"," (mezní náklady, mezní příjem, mezní užitečnost), bez extrémů se neobejde ",[38,10815,10816],{},"maximalizace zisku"," ani ",[38,10819,10820],{},"minimalizace nákladů",[115,10822,10824],{"id":10823},"funkce-a-polynomy","Funkce a polynomy",[724,10826,10827,10828,10854,10855,10868,10869,10882,10883,1863],{},"Funkce jedné proměnné ",[883,10829,10831],{"className":10830},[886],[888,10832,10833],{"xmlns":890},[892,10834,10835,10851],{},[895,10836,10837,10840,10842,10844,10846,10849],{},[898,10838,10839],{},"y",[1656,10841,1713],{},[898,10843,7524],{},[1656,10845,1659],{"stretchy":1658},[898,10847,10848],{},"x",[1656,10850,1683],{"stretchy":1658},[902,10852,10853],{"encoding":904},"y = f(x)"," — předpis závislosti ",[883,10856,10858],{"className":10857},[886],[888,10859,10860],{"xmlns":890},[892,10861,10862,10866],{},[895,10863,10864],{},[898,10865,10848],{},[902,10867,10848],{"encoding":904}," (nezávislá) → ",[883,10870,10872],{"className":10871},[886],[888,10873,10874],{"xmlns":890},[892,10875,10876,10880],{},[895,10877,10878],{},[898,10879,10839],{},[902,10881,10839],{"encoding":904}," (závislá). Hodnota v bodě: ",[883,10884,10886],{"className":10885},[886],[888,10887,10888],{"xmlns":890},[892,10889,10890,10900],{},[895,10891,10892,10894,10896,10898],{},[898,10893,7524],{},[1656,10895,1659],{"stretchy":1658},[898,10897,207],{},[1656,10899,1683],{"stretchy":1658},[902,10901,10902],{"encoding":904},"f(a)",[724,10904,10905],{},"Polynomy:",[120,10907,10908,10939,10979],{},[123,10909,10910],{},[152,10911,10912],{},[123,10913,10914,10915],{},"stupně: ",[883,10916,10918],{"className":10917},[886],[888,10919,10920],{"xmlns":890},[892,10921,10922,10936],{},[895,10923,10924,10926,10928,10930,10932,10934],{},[898,10925,10839],{},[1656,10927,1713],{},[898,10929,207],{},[898,10931,10848],{},[1656,10933,3633],{},[898,10935,3403],{},[902,10937,10938],{"encoding":904},"y = ax + b",[123,10940,10941],{},[152,10942,10943],{"start":642},[123,10944,10914,10945],{},[883,10946,10948],{"className":10947},[886],[888,10949,10950],{"xmlns":890},[892,10951,10952,10976],{},[895,10953,10954,10956,10958,10960,10966,10968,10970,10972,10974],{},[898,10955,10839],{},[1656,10957,1713],{},[898,10959,207],{},[2062,10961,10962,10964],{},[898,10963,10848],{},[1667,10965,1680],{},[1656,10967,3633],{},[898,10969,3403],{},[898,10971,10848],{},[1656,10973,3633],{},[898,10975,1745],{},[902,10977,10978],{"encoding":904},"y = ax^2 + bx + c",[123,10980,10981],{},[152,10982,10983],{"start":649},[123,10984,10914,10985],{},[883,10986,10988],{"className":10987},[886],[888,10989,10990],{"xmlns":890},[892,10991,10992,11026],{},[895,10993,10994,10996,10998,11000,11006,11008,11010,11016,11018,11020,11022,11024],{},[898,10995,10839],{},[1656,10997,1713],{},[898,10999,207],{},[2062,11001,11002,11004],{},[898,11003,10848],{},[1667,11005,2617],{},[1656,11007,3633],{},[898,11009,3403],{},[2062,11011,11012,11014],{},[898,11013,10848],{},[1667,11015,1680],{},[1656,11017,3633],{},[898,11019,1745],{},[898,11021,10848],{},[1656,11023,3633],{},[898,11025,3768],{},[902,11027,11028],{"encoding":904},"y = ax^3 + bx^2 + cx + d",[724,11030,11031,1643,11034,11088,11089,11126,11127,1863],{},[38,11032,11033],{},"Příklad rozkladu:",[883,11035,11037],{"className":11036},[886],[888,11038,11039],{"xmlns":890},[892,11040,11041,11085],{},[895,11042,11043,11045,11047,11053,11055,11057,11059,11061,11063,11065,11067,11069,11071,11073,11075,11077,11079,11081,11083],{},[898,11044,10839],{},[1656,11046,1713],{},[2062,11048,11049,11051],{},[898,11050,10848],{},[1667,11052,1680],{},[1656,11054,3964],{},[1667,11056,5193],{},[898,11058,10848],{},[1656,11060,3633],{},[1667,11062,9112],{},[1656,11064,1713],{},[1656,11066,1659],{"stretchy":1658},[898,11068,10848],{},[1656,11070,3964],{},[1667,11072,1680],{},[1656,11074,1683],{"stretchy":1658},[1656,11076,1659],{"stretchy":1658},[898,11078,10848],{},[1656,11080,3964],{},[1667,11082,2617],{},[1656,11084,1683],{"stretchy":1658},[902,11086,11087],{"encoding":904},"y = x^2 - 5x + 6 = (x-2)(x-3)",", kořeny ",[883,11090,11092],{"className":11091},[886],[888,11093,11094],{"xmlns":890},[892,11095,11096,11123],{},[895,11097,11098,11104,11106,11108,11110,11113,11119,11121],{},[1661,11099,11100,11102],{},[898,11101,10848],{},[1667,11103,1669],{},[1656,11105,1713],{},[1667,11107,1680],{},[1656,11109,1673],{"separator":1672},[2461,11111,11112],{}," ",[1661,11114,11115,11117],{},[898,11116,10848],{},[1667,11118,1680],{},[1656,11120,1713],{},[1667,11122,2617],{},[902,11124,11125],{"encoding":904},"x_1 = 2,\\ x_2 = 3",". Vrcholový tvar ",[883,11128,11130],{"className":11129},[886],[888,11131,11132],{"xmlns":890},[892,11133,11134,11170],{},[895,11135,11136,11138,11140,11142,11144,11146,11154,11160,11162],{},[898,11137,10839],{},[1656,11139,1713],{},[1656,11141,1659],{"stretchy":1658},[898,11143,10848],{},[1656,11145,3964],{},[4138,11147,11148],{"scriptlevel":4032,"displaystyle":1658},[3294,11149,11150,11152],{},[1667,11151,5193],{},[1667,11153,1680],{},[2062,11155,11156,11158],{},[1656,11157,1683],{"stretchy":1658},[1667,11159,1680],{},[1656,11161,3964],{},[4138,11163,11164],{"scriptlevel":4032,"displaystyle":1658},[3294,11165,11166,11168],{},[1667,11167,1669],{},[1667,11169,2673],{},[902,11171,11172],{"encoding":904},"y = (x - \\tfrac{5}{2})^2 - \\tfrac{1}{4}",[115,11174,10692],{"id":1145},[724,11176,11177,11178,1348,11202,11230,11231,1863],{},"Označení ",[883,11179,11181],{"className":11180},[886],[888,11182,11183],{"xmlns":890},[892,11184,11185,11199],{},[895,11186,11187,11193,11195,11197],{},[2062,11188,11189,11191],{},[898,11190,7524],{},[1656,11192,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,11194,1659],{"stretchy":1658},[898,11196,10848],{},[1656,11198,1683],{"stretchy":1658},[902,11200,11201],{"encoding":904},"f'(x)",[883,11203,11205],{"className":11204},[886],[888,11206,11207],{"xmlns":890},[892,11208,11209,11227],{},[895,11210,11211],{},[4138,11212,11213],{"scriptlevel":4032,"displaystyle":1672},[3294,11214,11215,11221],{},[895,11216,11217,11219],{},[898,11218,3768],{},[898,11220,10839],{},[895,11222,11223,11225],{},[898,11224,3768],{},[898,11226,10848],{},[902,11228,11229],{"encoding":904},"\\dfrac{dy}{dx}",". Hodnota v bodě: ",[883,11232,11234],{"className":11233},[886],[888,11235,11236],{"xmlns":890},[892,11237,11238,11252],{},[895,11239,11240,11246,11248,11250],{},[2062,11241,11242,11244],{},[898,11243,7524],{},[1656,11245,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,11247,1659],{"stretchy":1658},[898,11249,207],{},[1656,11251,1683],{"stretchy":1658},[902,11253,11254],{"encoding":904},"f'(a)",[198,11256,11258],{"id":11257},"geometrická-interpretace","Geometrická interpretace",[724,11260,11261,11284,11285,11288,11289,11317],{},[883,11262,11264],{"className":11263},[886],[888,11265,11266],{"xmlns":890},[892,11267,11268,11282],{},[895,11269,11270,11276,11278,11280],{},[2062,11271,11272,11274],{},[898,11273,7524],{},[1656,11275,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,11277,1659],{"stretchy":1658},[898,11279,207],{},[1656,11281,1683],{"stretchy":1658},[902,11283,11254],{"encoding":904}," = ",[38,11286,11287],{},"sklon tečny"," ke grafu funkce v bodě ",[883,11290,11292],{"className":11291},[886],[888,11293,11294],{"xmlns":890},[892,11295,11296,11314],{},[895,11297,11298,11300,11302,11304,11306,11308,11310,11312],{},[1656,11299,3453],{"stretchy":1658},[898,11301,207],{},[1656,11303,1673],{"separator":1672},[898,11305,7524],{},[1656,11307,1659],{"stretchy":1658},[898,11309,207],{},[1656,11311,1683],{"stretchy":1658},[1656,11313,3462],{"stretchy":1658},[902,11315,11316],{"encoding":904},"[a, f(a)]",". Rovnice tečny:",[724,11319,11320],{},[883,11321,11323],{"className":11322},[886],[888,11324,11325],{"xmlns":890},[892,11326,11327,11365],{},[895,11328,11329,11331,11333,11335,11337,11339,11341,11343,11349,11351,11353,11355,11357,11359,11361,11363],{},[898,11330,10839],{},[1656,11332,3964],{},[898,11334,7524],{},[1656,11336,1659],{"stretchy":1658},[898,11338,207],{},[1656,11340,1683],{"stretchy":1658},[1656,11342,1713],{},[2062,11344,11345,11347],{},[898,11346,7524],{},[1656,11348,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,11350,1659],{"stretchy":1658},[898,11352,207],{},[1656,11354,1683],{"stretchy":1658},[1656,11356,1659],{"stretchy":1658},[898,11358,10848],{},[1656,11360,3964],{},[898,11362,207],{},[1656,11364,1683],{"stretchy":1658},[902,11366,11367],{"encoding":904},"y - f(a) = f'(a)(x - a)",[724,11369,11370],{},[5956,11371],{"alt":11372,"className":11373,"src":11374},"imek-derivace-tecna",[210,5960],"\u002Fwiki-assets\u002Fimek-derivace-tecna.jpeg",[198,11376,11378],{"id":11377},"inženýrská-interpretace","Inženýrská interpretace",[724,11380,11381,11284,11404,1643,11407,3547,11420,3565,11433,11451,11452,11465,11466,3605,11479,3619,11492,2114],{},[883,11382,11384],{"className":11383},[886],[888,11385,11386],{"xmlns":890},[892,11387,11388,11402],{},[895,11389,11390,11396,11398,11400],{},[2062,11391,11392,11394],{},[898,11393,7524],{},[1656,11395,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,11397,1659],{"stretchy":1658},[898,11399,207],{},[1656,11401,1683],{"stretchy":1658},[902,11403,11254],{"encoding":904},[38,11405,11406],{},"rychlost změny",[883,11408,11410],{"className":11409},[886],[888,11411,11412],{"xmlns":890},[892,11413,11414,11418],{},[895,11415,11416],{},[898,11417,10839],{},[902,11419,10839],{"encoding":904},[883,11421,11423],{"className":11422},[886],[888,11424,11425],{"xmlns":890},[892,11426,11427,11431],{},[895,11428,11429],{},[898,11430,10848],{},[902,11432,10848],{"encoding":904},[883,11434,11436],{"className":11435},[886],[888,11437,11438],{"xmlns":890},[892,11439,11440,11448],{},[895,11441,11442,11444,11446],{},[898,11443,10848],{},[1656,11445,1713],{},[898,11447,207],{},[902,11449,11450],{"encoding":904},"x = a","; přibližná změna ",[883,11453,11455],{"className":11454},[886],[888,11456,11457],{"xmlns":890},[892,11458,11459,11463],{},[895,11460,11461],{},[898,11462,10839],{},[902,11464,10839],{"encoding":904}," při změně ",[883,11467,11469],{"className":11468},[886],[888,11470,11471],{"xmlns":890},[892,11472,11473,11477],{},[895,11474,11475],{},[898,11476,10848],{},[902,11478,10848],{"encoding":904},[883,11480,11482],{"className":11481},[886],[888,11483,11484],{"xmlns":890},[892,11485,11486,11490],{},[895,11487,11488],{},[898,11489,207],{},[902,11491,207],{"encoding":904},[883,11493,11495],{"className":11494},[886],[888,11496,11497],{"xmlns":890},[892,11498,11499,11507],{},[895,11500,11501,11503,11505],{},[898,11502,207],{},[1656,11504,3633],{},[1667,11506,1669],{},[902,11508,3638],{"encoding":904},[724,11510,11511],{},[883,11512,11514],{"className":11513},[886],[888,11515,11516],{"xmlns":890},[892,11517,11518,11556],{},[895,11519,11520,11522,11524,11526,11528,11530,11532,11534,11536,11538,11540,11542,11544,11550,11552,11554],{},[898,11521,7524],{},[1656,11523,1659],{"stretchy":1658},[898,11525,207],{},[1656,11527,3633],{},[1667,11529,1669],{},[1656,11531,1683],{"stretchy":1658},[1656,11533,3815],{},[898,11535,7524],{},[1656,11537,1659],{"stretchy":1658},[898,11539,207],{},[1656,11541,1683],{"stretchy":1658},[1656,11543,3633],{},[2062,11545,11546,11548],{},[898,11547,7524],{},[1656,11549,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,11551,1659],{"stretchy":1658},[898,11553,207],{},[1656,11555,1683],{"stretchy":1658},[902,11557,11558],{"encoding":904},"f(a+1) \\approx f(a) + f'(a)",[198,11560,11562],{"id":11561},"příklad-mezní-náklady","Příklad — mezní náklady",[724,11564,11565,11566,1863],{},"Celkové náklady ",[883,11567,11569],{"className":11568},[886],[888,11570,11571],{"xmlns":890},[892,11572,11573,11602],{},[895,11574,11575,11578,11580,11582,11585,11587,11589,11591,11593,11596],{},[898,11576,11577],{},"T",[898,11579,1766],{},[1656,11581,1713],{},[1667,11583,11584],{},"1000",[1656,11586,3633],{},[1667,11588,1680],{},[898,11590,1665],{},[1656,11592,3633],{},[1667,11594,11595],{},"0,1",[2062,11597,11598,11600],{},[898,11599,1665],{},[1667,11601,1680],{},[902,11603,11604],{"encoding":904},"TC = 1000 + 2Q + 0{,}1 Q^2",[724,11606,11607,11608,3096,11645,1863],{},"Mezní náklady: ",[883,11609,11611],{"className":11610},[886],[888,11612,11613],{"xmlns":890},[892,11614,11615,11642],{},[895,11616,11617,11619,11621,11623,11625,11631,11633,11635,11637,11640],{},[898,11618,1703],{},[898,11620,1766],{},[1656,11622,1713],{},[898,11624,11577],{},[2062,11626,11627,11629],{},[898,11628,1766],{},[1656,11630,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,11632,1713],{},[1667,11634,1680],{},[1656,11636,3633],{},[1667,11638,11639],{},"0,2",[898,11641,1665],{},[902,11643,11644],{"encoding":904},"MC = TC' = 2 + 0{,}2 Q",[883,11646,11648],{"className":11647},[886],[888,11649,11650],{"xmlns":890},[892,11651,11652,11668],{},[895,11653,11654,11656,11658,11660,11662,11664,11666],{},[898,11655,1703],{},[898,11657,1766],{},[1656,11659,1659],{"stretchy":1658},[1667,11661,8580],{},[1656,11663,1683],{"stretchy":1658},[1656,11665,1713],{},[1667,11667,2673],{},[902,11669,11670],{"encoding":904},"MC(10) = 4",[724,11672,11673,1643,11676,2191,11723,1643,11726,1863],{},[38,11674,11675],{},"Skutečný přírůstek:",[883,11677,11679],{"className":11678},[886],[888,11680,11681],{"xmlns":890},[892,11682,11683,11720],{},[895,11684,11685,11687,11689,11691,11693,11695,11697,11699,11701,11703,11705,11707,11709,11711,11713,11715,11717],{},[898,11686,3750],{"mathvariant":1723},[898,11688,11577],{},[898,11690,1766],{},[1656,11692,1713],{},[898,11694,11577],{},[898,11696,1766],{},[1656,11698,1659],{"stretchy":1658},[1667,11700,4364],{},[1656,11702,1683],{"stretchy":1658},[1656,11704,3964],{},[898,11706,11577],{},[898,11708,1766],{},[1656,11710,1659],{"stretchy":1658},[1667,11712,8580],{},[1656,11714,1683],{"stretchy":1658},[1656,11716,1713],{},[1667,11718,11719],{},"4,2",[902,11721,11722],{"encoding":904},"\\Delta TC = TC(11) - TC(10) = 4{,}2",[38,11724,11725],{},"Přibližný (lineární):",[883,11727,11729],{"className":11728},[886],[888,11730,11731],{"xmlns":890},[892,11732,11733,11737],{},[895,11734,11735],{},[1667,11736,2673],{},[902,11738,2673],{"encoding":904},[724,11740,11741,11742,11746],{},"(Viz aplikace v ",[207,11743,11745],{"className":11744,"dataFsResolvedFilePath":827,"href":828},[210],"prijem-naklady-zisk",".)",[115,11748,11750],{"id":11749},"diferenciál","Diferenciál",[724,11752,11753],{},[883,11754,11756],{"className":11755},[886],[888,11757,11758],{"xmlns":890},[892,11759,11760,11786],{},[895,11761,11762,11764,11766,11768,11774,11776,11778,11780,11782,11784],{},[898,11763,3768],{},[898,11765,7524],{},[1656,11767,1713],{},[2062,11769,11770,11772],{},[898,11771,7524],{},[1656,11773,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,11775,1659],{"stretchy":1658},[898,11777,10848],{},[1656,11779,1683],{"stretchy":1658},[2461,11781,7828],{},[898,11783,3768],{},[898,11785,10848],{},[902,11787,11788],{"encoding":904},"df = f'(x)\\, dx",[724,11790,11791,11792,11808,11809,11857,11858,1863],{},"Pro malá ",[883,11793,11795],{"className":11794},[886],[888,11796,11797],{"xmlns":890},[892,11798,11799,11805],{},[895,11800,11801,11803],{},[898,11802,3768],{},[898,11804,10848],{},[902,11806,11807],{"encoding":904},"dx"," platí: ",[883,11810,11812],{"className":11811},[886],[888,11813,11814],{"xmlns":890},[892,11815,11816,11854],{},[895,11817,11818,11820,11822,11824,11826,11828,11830,11832,11834,11836,11838,11840,11842,11844,11846,11848,11850,11852],{},[898,11819,3750],{"mathvariant":1723},[898,11821,7524],{},[1656,11823,1713],{},[898,11825,7524],{},[1656,11827,1659],{"stretchy":1658},[898,11829,10848],{},[1656,11831,3633],{},[898,11833,3768],{},[898,11835,10848],{},[1656,11837,1683],{"stretchy":1658},[1656,11839,3964],{},[898,11841,7524],{},[1656,11843,1659],{"stretchy":1658},[898,11845,10848],{},[1656,11847,1683],{"stretchy":1658},[1656,11849,3815],{},[898,11851,3768],{},[898,11853,7524],{},[902,11855,11856],{"encoding":904},"\\Delta f = f(x + dx) - f(x) \\approx df",". Diferenciál je ",[38,11859,11860],{},"lineární odhad přírůstku",[198,11862,11864],{"id":11863},"příklad","Příklad",[724,11866,11867,11897,11898,11922,11923,5642],{},[883,11868,11870],{"className":11869},[886],[888,11871,11872],{"xmlns":890},[892,11873,11874,11894],{},[895,11875,11876,11878,11880,11882,11884,11886,11888],{},[898,11877,11577],{},[898,11879,1766],{},[1656,11881,1713],{},[1667,11883,5267],{},[1656,11885,3633],{},[1667,11887,11595],{},[2062,11889,11890,11892],{},[898,11891,1665],{},[1667,11893,1680],{},[902,11895,11896],{"encoding":904},"TC = 100 + 0{,}1 Q^2",", odhad změny při ",[883,11899,11901],{"className":11900},[886],[888,11902,11903],{"xmlns":890},[892,11904,11905,11919],{},[895,11906,11907,11909,11911,11913,11916],{},[898,11908,1665],{},[1656,11910,2114],{},[1667,11912,9267],{},[1656,11914,11915],{},"→",[1667,11917,11918],{},"60",[902,11920,11921],{"encoding":904},"Q: 50 \\to 60"," (tj. ",[883,11924,11926],{"className":11925},[886],[888,11927,11928],{"xmlns":890},[892,11929,11930,11940],{},[895,11931,11932,11934,11936,11938],{},[898,11933,3768],{},[898,11935,1665],{},[1656,11937,1713],{},[1667,11939,8580],{},[902,11941,11942],{"encoding":904},"dQ = 10",[724,11944,11945],{},[883,11946,11948],{"className":11947},[886],[888,11949,11950],{"xmlns":890},[892,11951,11952,11988],{},[895,11953,11954,11956,11958,11960,11962,11964,11966,11968,11970,11972,11974,11976,11978,11980,11982,11984,11986],{},[898,11955,3768],{},[898,11957,11577],{},[898,11959,1766],{},[1656,11961,1713],{},[1667,11963,11639],{},[898,11965,1665],{},[1656,11967,2751],{},[898,11969,3768],{},[898,11971,1665],{},[1656,11973,1713],{},[1667,11975,11639],{},[1656,11977,2751],{},[1667,11979,9267],{},[1656,11981,2751],{},[1667,11983,8580],{},[1656,11985,1713],{},[1667,11987,5267],{},[902,11989,11990],{"encoding":904},"dTC = 0{,}2 Q \\cdot dQ = 0{,}2 \\cdot 50 \\cdot 10 = 100",[724,11992,11993,11994,12017,12018,12034],{},"Přesná změna: ",[883,11995,11997],{"className":11996},[886],[888,11998,11999],{"xmlns":890},[892,12000,12001,12014],{},[895,12002,12003,12005,12007,12009,12011],{},[898,12004,3750],{"mathvariant":1723},[898,12006,11577],{},[898,12008,1766],{},[1656,12010,1713],{},[1667,12012,12013],{},"110",[902,12015,12016],{"encoding":904},"\\Delta TC = 110",". Lineární odhad mírně podstřeluje, protože ",[883,12019,12021],{"className":12020},[886],[888,12022,12023],{"xmlns":890},[892,12024,12025,12031],{},[895,12026,12027,12029],{},[898,12028,11577],{},[898,12030,1766],{},[902,12032,12033],{"encoding":904},"TC"," je konvexní.",[115,12036,12038],{"id":12037},"extrémy-funkce-jedné-proměnné","Extrémy funkce jedné proměnné",[198,12040,12042],{"id":12041},"nutná-podmínka","Nutná podmínka",[724,12044,12045,12046,3565,12066,12079,12080,12108,12109,12112],{},"Má-li ",[883,12047,12049],{"className":12048},[886],[888,12050,12051],{"xmlns":890},[892,12052,12053,12063],{},[895,12054,12055,12057,12059,12061],{},[898,12056,7524],{},[1656,12058,1659],{"stretchy":1658},[898,12060,10848],{},[1656,12062,1683],{"stretchy":1658},[902,12064,12065],{"encoding":904},"f(x)",[883,12067,12069],{"className":12068},[886],[888,12070,12071],{"xmlns":890},[892,12072,12073,12077],{},[895,12074,12075],{},[898,12076,207],{},[902,12078,207],{"encoding":904}," extrém, pak ",[883,12081,12083],{"className":12082},[886],[888,12084,12085],{"xmlns":890},[892,12086,12087,12105],{},[895,12088,12089,12095,12097,12099,12101,12103],{},[2062,12090,12091,12093],{},[898,12092,7524],{},[1656,12094,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,12096,1659],{"stretchy":1658},[898,12098,207],{},[1656,12100,1683],{"stretchy":1658},[1656,12102,1713],{},[1667,12104,4032],{},[902,12106,12107],{"encoding":904},"f'(a) = 0",". Body splňující tuto podmínku se nazývají ",[38,12110,12111],{},"stacionární"," (podezřelé) body.",[198,12114,12116],{"id":12115},"postačující-podmínka","Postačující podmínka",[724,12118,12119,12120,12133,12134,2114],{},"Pro stacionární bod ",[883,12121,12123],{"className":12122},[886],[888,12124,12125],{"xmlns":890},[892,12126,12127,12131],{},[895,12128,12129],{},[898,12130,207],{},[902,12132,207],{"encoding":904},", je-li ",[883,12135,12137],{"className":12136},[886],[888,12138,12139],{"xmlns":890},[892,12140,12141,12164],{},[895,12142,12143,12153,12155,12157,12159,12162],{},[2062,12144,12145,12147],{},[898,12146,7524],{},[895,12148,12149,12151],{},[1656,12150,1725],{"mathvariant":1723},[1656,12152,1725],{"mathvariant":1723},[1656,12154,1659],{"stretchy":1658},[898,12156,207],{},[1656,12158,1683],{"stretchy":1658},[1656,12160,12161],{"mathvariant":1723},"≠",[1667,12163,4032],{},[902,12165,12166],{"encoding":904},"f''(a) \\neq 0",[120,12168,12169,12207],{},[123,12170,12171,12203,12204],{},[883,12172,12174],{"className":12173},[886],[888,12175,12176],{"xmlns":890},[892,12177,12178,12200],{},[895,12179,12180,12190,12192,12194,12196,12198],{},[2062,12181,12182,12184],{},[898,12183,7524],{},[895,12185,12186,12188],{},[1656,12187,1725],{"mathvariant":1723},[1656,12189,1725],{"mathvariant":1723},[1656,12191,1659],{"stretchy":1658},[898,12193,207],{},[1656,12195,1683],{"stretchy":1658},[1656,12197,2850],{},[1667,12199,4032],{},[902,12201,12202],{"encoding":904},"f''(a) > 0"," ⇒ ",[38,12205,12206],{},"lokální minimum",[123,12208,12209,12203,12241],{},[883,12210,12212],{"className":12211},[886],[888,12213,12214],{"xmlns":890},[892,12215,12216,12238],{},[895,12217,12218,12228,12230,12232,12234,12236],{},[2062,12219,12220,12222],{},[898,12221,7524],{},[895,12223,12224,12226],{},[1656,12225,1725],{"mathvariant":1723},[1656,12227,1725],{"mathvariant":1723},[1656,12229,1659],{"stretchy":1658},[898,12231,207],{},[1656,12233,1683],{"stretchy":1658},[1656,12235,4373],{},[1667,12237,4032],{},[902,12239,12240],{"encoding":904},"f''(a) \u003C 0",[38,12242,12243],{},"lokální maximum",[724,12245,12246],{},[5956,12247],{"alt":12248,"className":12249,"src":12250},"imek-extremy-1d",[210,5960],"\u002Fwiki-assets\u002Fimek-extremy-1d.jpeg",[198,12252,11864],{"id":12253},"příklad-1",[724,12255,12256],{},[883,12257,12259],{"className":12258},[886],[888,12260,12261],{"xmlns":890},[892,12262,12263,12303],{},[895,12264,12265,12267,12269,12271,12273,12275,12277,12283,12285,12287,12293,12295,12297,12299,12301],{},[898,12266,7524],{},[1656,12268,1659],{"stretchy":1658},[898,12270,10848],{},[1656,12272,1683],{"stretchy":1658},[1656,12274,1713],{},[1667,12276,1680],{},[2062,12278,12279,12281],{},[898,12280,10848],{},[1667,12282,2617],{},[1656,12284,3964],{},[1667,12286,2617],{},[2062,12288,12289,12291],{},[898,12290,10848],{},[1667,12292,1680],{},[1656,12294,3964],{},[1667,12296,9140],{},[898,12298,10848],{},[1656,12300,3633],{},[1667,12302,2617],{},[902,12304,12305],{"encoding":904},"f(x) = 2x^3 - 3x^2 - 12x + 3",[120,12307,12308,12419,12459,12522],{},[123,12309,12310,12382,12383],{},[883,12311,12313],{"className":12312},[886],[888,12314,12315],{"xmlns":890},[892,12316,12317,12379],{},[895,12318,12319,12325,12327,12329,12331,12333,12335,12341,12343,12345,12347,12349,12351,12353,12355,12357,12359,12361,12363,12365,12367,12369,12371,12373,12375,12377],{},[2062,12320,12321,12323],{},[898,12322,7524],{},[1656,12324,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,12326,1659],{"stretchy":1658},[898,12328,10848],{},[1656,12330,1683],{"stretchy":1658},[1656,12332,1713],{},[1667,12334,9112],{},[2062,12336,12337,12339],{},[898,12338,10848],{},[1667,12340,1680],{},[1656,12342,3964],{},[1667,12344,9112],{},[898,12346,10848],{},[1656,12348,3964],{},[1667,12350,9140],{},[1656,12352,1713],{},[1667,12354,9112],{},[1656,12356,1659],{"stretchy":1658},[898,12358,10848],{},[1656,12360,3633],{},[1667,12362,1669],{},[1656,12364,1683],{"stretchy":1658},[1656,12366,1659],{"stretchy":1658},[898,12368,10848],{},[1656,12370,3964],{},[1667,12372,1680],{},[1656,12374,1683],{"stretchy":1658},[1656,12376,1713],{},[1667,12378,4032],{},[902,12380,12381],{"encoding":904},"f'(x) = 6x^2 - 6x - 12 = 6(x+1)(x-2) = 0"," ⇒ S.B. ",[883,12384,12386],{"className":12385},[886],[888,12387,12388],{"xmlns":890},[892,12389,12390,12416],{},[895,12391,12392,12398,12400,12402,12404,12406,12412,12414],{},[1661,12393,12394,12396],{},[898,12395,10848],{},[1667,12397,1669],{},[1656,12399,1713],{},[1656,12401,3964],{},[1667,12403,1669],{},[1656,12405,1673],{"separator":1672},[1661,12407,12408,12410],{},[898,12409,10848],{},[1667,12411,1680],{},[1656,12413,1713],{},[1667,12415,1680],{},[902,12417,12418],{"encoding":904},"x_1 = -1, x_2 = 2",[123,12420,12421],{},[883,12422,12424],{"className":12423},[886],[888,12425,12426],{"xmlns":890},[892,12427,12428,12456],{},[895,12429,12430,12440,12442,12444,12446,12448,12450,12452,12454],{},[2062,12431,12432,12434],{},[898,12433,7524],{},[895,12435,12436,12438],{},[1656,12437,1725],{"mathvariant":1723},[1656,12439,1725],{"mathvariant":1723},[1656,12441,1659],{"stretchy":1658},[898,12443,10848],{},[1656,12445,1683],{"stretchy":1658},[1656,12447,1713],{},[1667,12449,9140],{},[898,12451,10848],{},[1656,12453,3964],{},[1667,12455,9112],{},[902,12457,12458],{"encoding":904},"f''(x) = 12x - 6",[123,12460,12461,12203,12502,12505,12506],{},[883,12462,12464],{"className":12463},[886],[888,12465,12466],{"xmlns":890},[892,12467,12468,12499],{},[895,12469,12470,12480,12482,12484,12486,12488,12490,12492,12495,12497],{},[2062,12471,12472,12474],{},[898,12473,7524],{},[895,12475,12476,12478],{},[1656,12477,1725],{"mathvariant":1723},[1656,12479,1725],{"mathvariant":1723},[1656,12481,1659],{"stretchy":1658},[1656,12483,3964],{},[1667,12485,1669],{},[1656,12487,1683],{"stretchy":1658},[1656,12489,1713],{},[1656,12491,3964],{},[1667,12493,12494],{},"18",[1656,12496,4373],{},[1667,12498,4032],{},[902,12500,12501],{"encoding":904},"f''(-1) = -18 \u003C 0",[38,12503,12504],{},"maximum"," v ",[883,12507,12509],{"className":12508},[886],[888,12510,12511],{"xmlns":890},[892,12512,12513,12519],{},[895,12514,12515,12517],{},[1656,12516,3964],{},[1667,12518,1669],{},[902,12520,12521],{"encoding":904},"-1",[123,12523,12524,12203,12560,12505,12563],{},[883,12525,12527],{"className":12526},[886],[888,12528,12529],{"xmlns":890},[892,12530,12531,12557],{},[895,12532,12533,12543,12545,12547,12549,12551,12553,12555],{},[2062,12534,12535,12537],{},[898,12536,7524],{},[895,12538,12539,12541],{},[1656,12540,1725],{"mathvariant":1723},[1656,12542,1725],{"mathvariant":1723},[1656,12544,1659],{"stretchy":1658},[1667,12546,1680],{},[1656,12548,1683],{"stretchy":1658},[1656,12550,1713],{},[1667,12552,12494],{},[1656,12554,2850],{},[1667,12556,4032],{},[902,12558,12559],{"encoding":904},"f''(2) = 18 > 0",[38,12561,12562],{},"minimum",[883,12564,12566],{"className":12565},[886],[888,12567,12568],{"xmlns":890},[892,12569,12570,12574],{},[895,12571,12572],{},[1667,12573,1680],{},[902,12575,1680],{"encoding":904},[115,12577,10640],{"id":10639},[120,12579,12580,12588,12596],{},[123,12581,12582,1643,12585],{},[38,12583,12584],{},"Předchozí:",[207,12586,757],{"className":12587,"dataFsResolvedFilePath":755,"href":756},[210],[123,12589,12590,1643,12593],{},[38,12591,12592],{},"Navazující:",[207,12594,775],{"className":12595,"dataFsResolvedFilePath":773,"href":774},[210],[123,12597,12598,1643,12601,12604,12605,12609,12610,12614],{},[38,12599,12600],{},"Souvislosti:",[207,12602,784],{"className":12603,"dataFsResolvedFilePath":782,"href":783},[210]," (rozšíření na 2D), ",[207,12606,12608],{"className":12607,"dataFsResolvedFilePath":827,"href":828},[210],"Příjem, náklady, zisk"," (aplikace mezních veličin), ",[207,12611,12613],{"className":12612,"dataFsResolvedFilePath":848,"href":849},[210],"Elasticita"," (procentní citlivost přes derivaci)",{"title":641,"searchDepth":642,"depth":642,"links":12616},[12617,12618,12623,12626,12631],{"id":10823,"depth":642,"text":10824},{"id":1145,"depth":642,"text":10692,"children":12619},[12620,12621,12622],{"id":11257,"depth":649,"text":11258},{"id":11377,"depth":649,"text":11378},{"id":11561,"depth":649,"text":11562},{"id":11749,"depth":642,"text":11750,"children":12624},[12625],{"id":11863,"depth":649,"text":11864},{"id":12037,"depth":642,"text":12038,"children":12627},[12628,12629,12630],{"id":12041,"depth":649,"text":12042},{"id":12115,"depth":649,"text":12116},{"id":12253,"depth":649,"text":11864},{"id":10639,"depth":642,"text":10640},"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":10796,"description":12632},[1135],"topics\u002Fderivace",[1128,1145,12639,12640,12641],"diferencial","extremy","mezni-naklady","U4vqwJqO65hVzq9khEr5sxPHpHJLXAz_kTaaHdKCCIw",{"id":12644,"title":12645,"body":12646,"course":1128,"courses":659,"created":10774,"description":641,"extension":661,"meta":18306,"navigation":664,"path":18307,"seo":18308,"sources":18309,"stem":18310,"tags":18311,"type":10786,"updated":677,"__hash__":18316},"topics\u002Ftopics\u002Felasticita.md","Elasticita poptávky a nabídky",{"type":9,"value":12647,"toc":18279},[12648,12651,12672,12676,12703,12707,12748,12837,12881,12885,12909,12916,12920,12930,12941,12945,12973,12982,13037,13043,13046,13052,13079,13085,13180,13339,13628,13632,13712,13718,13722,13819,13885,14052,14056,14134,14165,14192,14198,14230,14308,14391,14395,14458,14464,14467,14473,14587,14670,14714,14718,14764,14771,15088,15093,15117,15146,15213,15308,15312,15319,15326,15397,15517,15601,15604,15610,15936,15940,16103,16111,16247,16255,16493,16501,16504,16509,16765,16769,16941,17075,17112,17154,17157,17286,17376,17394,17398,17405,17411,17471,17474,17498,17501,17507,17510,17516,17519,17523,17561,17619,17807,17811,17883,17889,17896,17900,17906,18046,18050,18056,18092,18097,18274],[12,12649,12645],{"id":12650},"elasticita-poptávky-a-nabídky",[1981,12652,12653],{},[724,12654,12655,12658,12659,12661,12662,12665,12666,1896,12669,1863],{},[883,12656,12657],{},"!abstract"," TL;DR\n",[38,12660,12613],{}," 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: ",[38,12663,12664],{},"cenovou elasticitu poptávky"," (a nabídky), ",[38,12667,12668],{},"křížově-cenovou elasticitu",[38,12670,12671],{},"důchodovou elasticitu",[115,12673,12675],{"id":12674},"úvod-motivace","Úvod — motivace",[724,12677,12678,12679,12682,12683,12686,12687,12690,12691,12694,12695,12698,12699,12702],{},"Termín ",[614,12680,12681],{},"elasticita"," (alternativně ",[614,12684,12685],{},"pružnost",") patří ke klíčovým pojmům ekonomické teorie. Slouží ke ",[38,12688,12689],{},"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 ",[614,12692,12693],{},"cenové elasticity poptávky"," (resp. ",[614,12696,12697],{},"nabídky","). Matematickým modelem míry citlivosti je elasticita funkce (viz ",[207,12700,10692],{"className":12701,"dataFsResolvedFilePath":764,"href":765},[210],").",[198,12704,12706],{"id":12705},"srovnání-trh-1-vs-trh-2","Srovnání Trh 1 vs Trh 2",[724,12708,12709,12710,12728,12729,12747],{},"Uvažujme dvě různá tržní prostředí. Zboží má na obou trzích stejnou cenu ",[883,12711,12713],{"className":12712},[886],[888,12714,12715],{"xmlns":890},[892,12716,12717,12725],{},[895,12718,12719,12721,12723],{},[898,12720,8194],{},[1656,12722,1713],{},[1667,12724,8580],{},[902,12726,12727],{"encoding":904},"P=10"," a při této ceně se prodá ",[883,12730,12732],{"className":12731},[886],[888,12733,12734],{"xmlns":890},[892,12735,12736,12744],{},[895,12737,12738,12740,12742],{},[898,12739,1665],{},[1656,12741,1713],{},[1667,12743,5267],{},[902,12745,12746],{"encoding":904},"Q=100"," jednotek. Prodejce sníží cenu z 10 na 9:",[120,12749,12750,12794],{},[123,12751,12752,12755,12756,12793],{},[38,12753,12754],{},"Trh 1"," zareaguje zvýšením množství na 110 ",[883,12757,12759],{"className":12758},[886],[888,12760,12761],{"xmlns":890},[892,12762,12763,12790],{},[895,12764,12765,12768,12771,12773,12775,12777,12779,12781,12783,12785,12787],{},[2461,12766,12767],{},"  ",[1656,12769,12770],{},"⇒",[2461,12772,12767],{},[898,12774,11577],{},[898,12776,1763],{},[1656,12778,1713],{},[1667,12780,2698],{},[1656,12782,2751],{},[1667,12784,12013],{},[1656,12786,1713],{},[1667,12788,12789],{},"990",[902,12791,12792],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 110 = 990"," (pokles z 1000).",[123,12795,12796,12799,12800,12836],{},[38,12797,12798],{},"Trh 2"," zareaguje zvýšením množství na 120 ",[883,12801,12803],{"className":12802},[886],[888,12804,12805],{"xmlns":890},[892,12806,12807,12833],{},[895,12808,12809,12811,12813,12815,12817,12819,12821,12823,12825,12828,12830],{},[2461,12810,12767],{},[1656,12812,12770],{},[2461,12814,12767],{},[898,12816,11577],{},[898,12818,1763],{},[1656,12820,1713],{},[1667,12822,2698],{},[1656,12824,2751],{},[1667,12826,12827],{},"120",[1656,12829,1713],{},[1667,12831,12832],{},"1080",[902,12834,12835],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 120 = 1080"," (růst z 1000).",[724,12838,12839,12840,12843,12844,12847,12848,12851,12852,12855,12856,12859,12860,12876,12877,12880],{},"Závěr: snížení ceny bylo na Trhu 1 ",[38,12841,12842],{},"nerozumné",", na Trhu 2 ",[38,12845,12846],{},"rozumné",". Trh 2 je ",[38,12849,12850],{},"relativně citlivý"," na změnu ceny — říkáme, že poptávka je ",[614,12853,12854],{},"elastická"," a snížení ceny je „překompenzováno\" zvýšením poptávaného množství. Na Trhu 1 je poptávka ",[614,12857,12858],{},"neelastická"," a vyššího ",[883,12861,12863],{"className":12862},[886],[888,12864,12865],{"xmlns":890},[892,12866,12867,12873],{},[895,12868,12869,12871],{},[898,12870,11577],{},[898,12872,1763],{},[902,12874,12875],{"encoding":904},"TR"," lze naopak dosáhnout ",[614,12878,12879],{},"zvýšením"," ceny.",[198,12882,12884],{"id":12883},"hypotéza-41","Hypotéza 4.1",[1981,12886,12887],{},[724,12888,12889,12890],{},"Aby nedošlo k poklesu celkového příjmu, musí být procentní růst poptávaného množství alespoň takový, jaký je procentní pokles jeho ceny. ",[883,12891,12893],{"className":12892},[886],[888,12894,12895],{"xmlns":890},[892,12896,12897,12906],{},[895,12898,12899,12901,12904],{},[1656,12900,1659],{"stretchy":1658},[1667,12902,12903],{},"4.1",[1656,12905,1683],{"stretchy":1658},[902,12907,12908],{"encoding":904},"(4.1)",[724,12910,12911,12912,12915],{},"Rozhodující nejsou nominální změny (jsou měřeny v různých jednotkách), nýbrž ",[38,12913,12914],{},"procentní změny"," obou faktorů.",[115,12917,12919],{"id":12918},"pojem-elasticity","Pojem elasticity",[724,12921,12922,12923,12925,12926,12929],{},"Obecně ",[38,12924,12681],{}," jedné veličiny vzhledem k druhé kvantifikuje, o kolik procent se první veličina přibližně změní, když se druhá veličina změní o 1 %. Jde o ",[38,12927,12928],{},"bezrozměrnou veličinu"," — nezávislou na jednotkách, ve kterých jsou proměnné měřeny (viz čl. 1.5.1).",[1981,12931,12932],{},[724,12933,12934,12936,12937,12940],{},[883,12935,3472],{}," Intuice\nElasticitu lze číst jako ",[38,12938,12939],{},"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.",[115,12942,12944],{"id":12943},"cenová-elasticita-poptávky-jednofaktorový-model","Cenová elasticita poptávky — jednofaktorový model",[724,12946,12947,12948,12972],{},"Nechť ",[883,12949,12951],{"className":12950},[886],[888,12952,12953],{"xmlns":890},[892,12954,12955,12969],{},[895,12956,12957,12959,12961,12963,12965,12967],{},[898,12958,1665],{},[1656,12960,1713],{},[898,12962,6787],{},[1656,12964,1659],{"stretchy":1658},[898,12966,8194],{},[1656,12968,1683],{"stretchy":1658},[902,12970,12971],{"encoding":904},"Q = D(P)"," je funkce poptávky (ceteris paribus). Zkoumáme podíl procentních změn",[724,12974,12975],{},[883,12976,12981],{"className":12977,"title":12979,"style":12980},[12978],"katex-error","ParseError: KaTeX parse error: \\tag works only in display equations","color:#cc0000","E^A = -\\frac{\\Delta Q\\%}{\\Delta P\\%}. \\tag{4.2}",[724,12983,12984,12985,1896,13001,13017,13018,13036],{},"Znaménko minus je korekce: změny ",[883,12986,12988],{"className":12987},[886],[888,12989,12990],{"xmlns":890},[892,12991,12992,12998],{},[895,12993,12994,12996],{},[898,12995,3750],{"mathvariant":1723},[898,12997,1665],{},[902,12999,13000],{"encoding":904},"\\Delta Q",[883,13002,13004],{"className":13003},[886],[888,13005,13006],{"xmlns":890},[892,13007,13008,13014],{},[895,13009,13010,13012],{},[898,13011,3750],{"mathvariant":1723},[898,13013,8194],{},[902,13015,13016],{"encoding":904},"\\Delta P"," mají vždy opačná znaménka, takže bez korekce by ",[883,13019,13021],{"className":13020},[886],[888,13022,13023],{"xmlns":890},[892,13024,13025,13033],{},[895,13026,13027],{},[2062,13028,13029,13031],{},[898,13030,1842],{},[898,13032,2146],{},[902,13034,13035],{"encoding":904},"E^A"," bylo záporné; pro pohodlí pracujeme s nezápornými hodnotami. Pro procentní změny platí",[724,13038,13039],{},[883,13040,13042],{"className":13041,"title":12979,"style":12980},[12978],"\\Delta Q\\% = \\frac{\\Delta Q}{Q}\\cdot 100, \\qquad \\Delta P\\% = \\frac{\\Delta P}{P}\\cdot 100. \\tag{4.3}",[724,13044,13045],{},"Po dosazení:",[724,13047,13048],{},[883,13049,13051],{"className":13050,"title":12979,"style":12980},[12978],"E^A = -\\frac{\\frac{\\Delta Q}{Q}}{\\frac{\\Delta P}{P}} = -\\frac{P}{Q}\\cdot \\frac{\\Delta Q}{\\Delta P}. \\tag{4.4}",[724,13053,13054,13055,13075,13076,13078],{},"Limitním přechodem ",[883,13056,13058],{"className":13057},[886],[888,13059,13060],{"xmlns":890},[892,13061,13062,13072],{},[895,13063,13064,13066,13068,13070],{},[898,13065,3750],{"mathvariant":1723},[898,13067,8194],{},[1656,13069,11915],{},[1667,13071,4032],{},[902,13073,13074],{"encoding":904},"\\Delta P \\to 0"," získáme definici ",[38,13077,12693],{}," (price elasticity of demand):",[724,13080,13081],{},[883,13082,13084],{"className":13083,"title":12979,"style":12980},[12978],"\\boxed{\\;E = E(P) = -\\frac{P}{Q}\\cdot \\frac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\frac{P}{Q}\\,Q'(P)\\;} \\tag{4.5}",[724,13086,2355,13087,13110,13111,6496,13133,13157,13158,13179],{},[883,13088,13090],{"className":13089},[886],[888,13091,13092],{"xmlns":890},[892,13093,13094,13108],{},[895,13095,13096,13098,13100,13102,13104,13106],{},[898,13097,1665],{},[1656,13099,1713],{},[898,13101,6787],{},[1656,13103,1659],{"stretchy":1658},[898,13105,8194],{},[1656,13107,1683],{"stretchy":1658},[902,13109,12971],{"encoding":904},". Pro pevnou cenu ",[883,13112,13114],{"className":13113},[886],[888,13115,13116],{"xmlns":890},[892,13117,13118,13130],{},[895,13119,13120,13122,13124],{},[898,13121,8194],{},[1656,13123,1713],{},[2062,13125,13126,13128],{},[898,13127,8194],{},[1656,13129,8187],{},[902,13131,13132],{"encoding":904},"P = P^*",[883,13134,13136],{"className":13135},[886],[888,13137,13138],{"xmlns":890},[892,13139,13140,13154],{},[895,13141,13142,13144,13146,13152],{},[898,13143,1842],{},[1656,13145,1659],{"stretchy":1658},[2062,13147,13148,13150],{},[898,13149,8194],{},[1656,13151,8187],{},[1656,13153,1683],{"stretchy":1658},[902,13155,13156],{"encoding":904},"E(P^*)"," nazývá ",[614,13159,13160,13161],{},"elasticita poptávky při ceně ",[883,13162,13164],{"className":13163},[886],[888,13165,13166],{"xmlns":890},[892,13167,13168,13176],{},[895,13169,13170],{},[2062,13171,13172,13174],{},[898,13173,8194],{},[1656,13175,8187],{},[902,13177,13178],{"encoding":904},"P^*"," a je to vždy nezáporné číslo.",[1981,13181,13182],{},[724,13183,13184,13186,13187,13205,13206,13234,13235,13264,13265,1343,13283,1343,13301,13319,13320,13335,13336,1863],{},[883,13185,1987],{}," Pozor na znaménko\nV (4.5) je ",[38,13188,13189,13190],{},"explicitní ",[883,13191,13193],{"className":13192},[886],[888,13194,13195],{"xmlns":890},[892,13196,13197,13203],{},[895,13198,13199,13201],{},[1656,13200,3964],{},[1667,13202,1669],{},[902,13204,12521],{"encoding":904}," právě proto, že ",[883,13207,13209],{"className":13208},[886],[888,13210,13211],{"xmlns":890},[892,13212,13213,13231],{},[895,13214,13215,13221,13223,13225,13227,13229],{},[2062,13216,13217,13219],{},[898,13218,1665],{},[1656,13220,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,13222,1659],{"stretchy":1658},[898,13224,8194],{},[1656,13226,1683],{"stretchy":1658},[1656,13228,4373],{},[1667,13230,4032],{},[902,13232,13233],{"encoding":904},"Q'(P) \u003C 0"," (poptávka klesá s cenou). Díky korekčnímu znaménku je výsledné ",[883,13236,13238],{"className":13237},[886],[888,13239,13240],{"xmlns":890},[892,13241,13242,13261],{},[895,13243,13244,13246,13248,13254,13256,13259],{},[898,13245,1842],{},[1656,13247,1659],{"stretchy":1658},[2062,13249,13250,13252],{},[898,13251,8194],{},[1656,13253,8187],{},[1656,13255,1683],{"stretchy":1658},[1656,13257,13258],{},"≥",[1667,13260,4032],{},[902,13262,13263],{"encoding":904},"E(P^*) \\ge 0"," a s touto nezápornou konvencí pracuje celá klasifikace ",[883,13266,13268],{"className":13267},[886],[888,13269,13270],{"xmlns":890},[892,13271,13272,13280],{},[895,13273,13274,13276,13278],{},[898,13275,1842],{},[1656,13277,2850],{},[1667,13279,1669],{},[902,13281,13282],{"encoding":904},"E > 1",[883,13284,13286],{"className":13285},[886],[888,13287,13288],{"xmlns":890},[892,13289,13290,13298],{},[895,13291,13292,13294,13296],{},[898,13293,1842],{},[1656,13295,4373],{},[1667,13297,1669],{},[902,13299,13300],{"encoding":904},"E \u003C 1",[883,13302,13304],{"className":13303},[886],[888,13305,13306],{"xmlns":890},[892,13307,13308,13316],{},[895,13309,13310,13312,13314],{},[898,13311,1842],{},[1656,13313,1713],{},[1667,13315,1669],{},[902,13317,13318],{"encoding":904},"E = 1",". V některých starších pramenech se ",[883,13321,13323],{"className":13322},[886],[888,13324,13325],{"xmlns":890},[892,13326,13327,13333],{},[895,13328,13329,13331],{},[1656,13330,3964],{},[1667,13332,1669],{},[902,13334,12521],{"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 ",[38,13337,13338],{},"absolutní hodnotou",[1981,13340,13341,13360],{},[724,13342,13343,13345,13346,13359],{},[883,13344,10188],{}," Postup: jak spočítat ",[883,13347,13349],{"className":13348},[886],[888,13350,13351],{"xmlns":890},[892,13352,13353,13357],{},[895,13354,13355],{},[898,13356,1842],{},[902,13358,1842],{"encoding":904}," v bodě",[152,13361,13362,13414,13453,13506,13571],{},[123,13363,13364,13365,13388,13389,13413],{},"Zapište ",[883,13366,13368],{"className":13367},[886],[888,13369,13370],{"xmlns":890},[892,13371,13372,13386],{},[895,13373,13374,13376,13378,13380,13382,13384],{},[898,13375,1665],{},[1656,13377,1713],{},[898,13379,6787],{},[1656,13381,1659],{"stretchy":1658},[898,13383,8194],{},[1656,13385,1683],{"stretchy":1658},[902,13387,12971],{"encoding":904},". Pokud je poptávka zadaná jako ",[883,13390,13392],{"className":13391},[886],[888,13393,13394],{"xmlns":890},[892,13395,13396,13410],{},[895,13397,13398,13400,13402,13404,13406,13408],{},[898,13399,8194],{},[1656,13401,1713],{},[898,13403,6787],{},[1656,13405,1659],{"stretchy":1658},[898,13407,1665],{},[1656,13409,1683],{"stretchy":1658},[902,13411,13412],{"encoding":904},"P = D(Q)",", použijte vztah (4.9).",[123,13415,13416,13417,1863],{},"Spočítejte derivaci ",[883,13418,13420],{"className":13419},[886],[888,13421,13422],{"xmlns":890},[892,13423,13424,13450],{},[895,13425,13426,13432,13434,13436,13438,13440,13442,13444,13446,13448],{},[2062,13427,13428,13430],{},[898,13429,1665],{},[1656,13431,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,13433,1659],{"stretchy":1658},[898,13435,8194],{},[1656,13437,1683],{"stretchy":1658},[1656,13439,1713],{},[898,13441,3768],{"mathvariant":1723},[898,13443,1665],{},[898,13445,1782],{"mathvariant":1723},[898,13447,3768],{"mathvariant":1723},[898,13449,8194],{},[902,13451,13452],{"encoding":904},"Q'(P) = \\mathrm{d}Q\u002F\\mathrm{d}P",[123,13454,13455,13456,13473,13474,1863],{},"Dosaďte zadanou cenu ",[883,13457,13459],{"className":13458},[886],[888,13460,13461],{"xmlns":890},[892,13462,13463,13471],{},[895,13464,13465],{},[2062,13466,13467,13469],{},[898,13468,8194],{},[1656,13470,8187],{},[902,13472,13178],{"encoding":904}," a dopočítejte odpovídající ",[883,13475,13477],{"className":13476},[886],[888,13478,13479],{"xmlns":890},[892,13480,13481,13503],{},[895,13482,13483,13489,13491,13493,13495,13501],{},[2062,13484,13485,13487],{},[898,13486,1665],{},[1656,13488,8187],{},[1656,13490,1713],{},[898,13492,6787],{},[1656,13494,1659],{"stretchy":1658},[2062,13496,13497,13499],{},[898,13498,8194],{},[1656,13500,8187],{},[1656,13502,1683],{"stretchy":1658},[902,13504,13505],{"encoding":904},"Q^* = D(P^*)",[123,13507,13508,13509,1863],{},"Dosaďte do (4.5): ",[883,13510,13512],{"className":13511},[886],[888,13513,13514],{"xmlns":890},[892,13515,13516,13568],{},[895,13517,13518,13520,13522,13528,13530,13532,13534,13550,13552,13558,13560,13566],{},[898,13519,1842],{},[1656,13521,1659],{"stretchy":1658},[2062,13523,13524,13526],{},[898,13525,8194],{},[1656,13527,8187],{},[1656,13529,1683],{"stretchy":1658},[1656,13531,1713],{},[1656,13533,3964],{},[4138,13535,13536],{"scriptlevel":4032,"displaystyle":1672},[3294,13537,13538,13544],{},[2062,13539,13540,13542],{},[898,13541,8194],{},[1656,13543,8187],{},[2062,13545,13546,13548],{},[898,13547,1665],{},[1656,13549,8187],{},[2461,13551,7828],{},[2062,13553,13554,13556],{},[898,13555,1665],{},[1656,13557,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,13559,1659],{"stretchy":1658},[2062,13561,13562,13564],{},[898,13563,8194],{},[1656,13565,8187],{},[1656,13567,1683],{"stretchy":1658},[902,13569,13570],{"encoding":904},"E(P^*) = -\\dfrac{P^*}{Q^*}\\,Q'(P^*)",[123,13572,13573,13574,13591,13592,13609,13610,13627],{},"Klasifikujte: ",[883,13575,13577],{"className":13576},[886],[888,13578,13579],{"xmlns":890},[892,13580,13581,13589],{},[895,13582,13583,13585,13587],{},[898,13584,1842],{},[1656,13586,2850],{},[1667,13588,1669],{},[902,13590,13282],{"encoding":904}," elastická, ",[883,13593,13595],{"className":13594},[886],[888,13596,13597],{"xmlns":890},[892,13598,13599,13607],{},[895,13600,13601,13603,13605],{},[898,13602,1842],{},[1656,13604,1713],{},[1667,13606,1669],{},[902,13608,13318],{"encoding":904}," jednotková, ",[883,13611,13613],{"className":13612},[886],[888,13614,13615],{"xmlns":890},[892,13616,13617,13625],{},[895,13618,13619,13621,13623],{},[898,13620,1842],{},[1656,13622,4373],{},[1667,13624,1669],{},[902,13626,13300],{"encoding":904}," neelastická.",[198,13629,13631],{"id":13630},"interpretace-46","Interpretace (4.6)",[1981,13633,13634],{},[724,13635,13636,13637,13660,13661,13674,13675,13692,13693],{},"Číslo ",[883,13638,13640],{"className":13639},[886],[888,13641,13642],{"xmlns":890},[892,13643,13644,13658],{},[895,13645,13646,13648,13650,13656],{},[898,13647,1842],{},[1656,13649,1659],{"stretchy":1658},[2062,13651,13652,13654],{},[898,13653,8194],{},[1656,13655,8187],{},[1656,13657,1683],{"stretchy":1658},[902,13659,13156],{"encoding":904}," udává, o kolik % se přibližně změní poptávané množství ",[883,13662,13664],{"className":13663},[886],[888,13665,13666],{"xmlns":890},[892,13667,13668,13672],{},[895,13669,13670],{},[898,13671,1665],{},[902,13673,1665],{"encoding":904},", jestliže se cena ",[883,13676,13678],{"className":13677},[886],[888,13679,13680],{"xmlns":890},[892,13681,13682,13690],{},[895,13683,13684],{},[2062,13685,13686,13688],{},[898,13687,8194],{},[1656,13689,8187],{},[902,13691,13178],{"encoding":904}," změní o 1 %. ",[883,13694,13696],{"className":13695},[886],[888,13697,13698],{"xmlns":890},[892,13699,13700,13709],{},[895,13701,13702,13704,13707],{},[1656,13703,1659],{"stretchy":1658},[1667,13705,13706],{},"4.6",[1656,13708,1683],{"stretchy":1658},[902,13710,13711],{"encoding":904},"(4.6)",[724,13713,13714,13717],{},[38,13715,13716],{},"Historicky:"," úvahy vedoucí k hypotéze (4.1) formuloval již Cournot (1838), dnešní vymezení se připisuje Marshallovi (1881).",[198,13719,13721],{"id":13720},"příklad-41","Příklad 4.1",[724,13723,13724,13725,13759,13760,1343,13785,2114],{},"Poptávka ",[883,13726,13728],{"className":13727},[886],[888,13729,13730],{"xmlns":890},[892,13731,13732,13756],{},[895,13733,13734,13736,13738,13740,13742,13744,13746,13748,13750,13752,13754],{},[898,13735,8194],{},[1656,13737,1713],{},[898,13739,6787],{},[1656,13741,1659],{"stretchy":1658},[898,13743,1665],{},[1656,13745,1683],{"stretchy":1658},[1656,13747,1713],{},[1667,13749,9267],{},[1656,13751,3964],{},[1667,13753,1680],{},[898,13755,1665],{},[902,13757,13758],{"encoding":904},"P = D(Q) = 50 - 2Q",". Vyjádříme ",[883,13761,13763],{"className":13762},[886],[888,13764,13765],{"xmlns":890},[892,13766,13767,13782],{},[895,13768,13769,13771,13773,13775,13777,13780],{},[898,13770,1665],{},[1656,13772,1713],{},[1667,13774,8567],{},[1656,13776,3964],{},[1667,13778,13779],{},"0,5",[898,13781,8194],{},[902,13783,13784],{"encoding":904},"Q = 25 - 0{,}5P",[883,13786,13788],{"className":13787},[886],[888,13789,13790],{"xmlns":890},[892,13791,13792,13816],{},[895,13793,13794,13810,13812,13814],{},[4138,13795,13796],{"scriptlevel":4032,"displaystyle":1672},[3294,13797,13798,13804],{},[895,13799,13800,13802],{},[898,13801,3768],{"mathvariant":1723},[898,13803,1665],{},[895,13805,13806,13808],{},[898,13807,3768],{"mathvariant":1723},[898,13809,8194],{},[1656,13811,1713],{},[1656,13813,3964],{},[1667,13815,13779],{},[902,13817,13818],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -0{,}5",[724,13820,13821],{},[883,13822,13824],{"className":13823},[886],[888,13825,13826],{"xmlns":890},[892,13827,13828,13882],{},[895,13829,13830,13832,13834,13836,13850,13852,13854,13856,13858,13860,13862,13880],{},[898,13831,1842],{},[1656,13833,1713],{},[1656,13835,3964],{},[3294,13837,13838,13840],{},[898,13839,8194],{},[895,13841,13842,13844,13846,13848],{},[1667,13843,8567],{},[1656,13845,3964],{},[1667,13847,13779],{},[898,13849,8194],{},[1656,13851,2751],{},[1656,13853,1659],{"stretchy":1658},[1656,13855,3964],{},[1667,13857,13779],{},[1656,13859,1683],{"stretchy":1658},[1656,13861,1713],{},[3294,13863,13864,13870],{},[895,13865,13866,13868],{},[1667,13867,13779],{},[898,13869,8194],{},[895,13871,13872,13874,13876,13878],{},[1667,13873,8567],{},[1656,13875,3964],{},[1667,13877,13779],{},[898,13879,8194],{},[898,13881,1863],{"mathvariant":1723},[902,13883,13884],{"encoding":904},"E = -\\frac{P}{25-0{,}5P}\\cdot(-0{,}5) = \\frac{0{,}5P}{25-0{,}5P}.",[724,13886,13887,13888,1343,13912,1343,13942,1343,13966,13990,13991,14014,14015,3619,14033,12702],{},"Potom ",[883,13889,13891],{"className":13890},[886],[888,13892,13893],{"xmlns":890},[892,13894,13895,13909],{},[895,13896,13897,13899,13901,13903,13905,13907],{},[898,13898,1842],{},[1656,13900,1659],{"stretchy":1658},[1667,13902,4032],{},[1656,13904,1683],{"stretchy":1658},[1656,13906,1713],{},[1667,13908,4032],{},[902,13910,13911],{"encoding":904},"E(0)=0",[883,13913,13915],{"className":13914},[886],[888,13916,13917],{"xmlns":890},[892,13918,13919,13939],{},[895,13920,13921,13923,13925,13927,13929,13931],{},[898,13922,1842],{},[1656,13924,1659],{"stretchy":1658},[1667,13926,8580],{},[1656,13928,1683],{"stretchy":1658},[1656,13930,1713],{},[4138,13932,13933],{"scriptlevel":4032,"displaystyle":1658},[3294,13934,13935,13937],{},[1667,13936,1669],{},[1667,13938,2673],{},[902,13940,13941],{"encoding":904},"E(10)=\\tfrac{1}{4}",[883,13943,13945],{"className":13944},[886],[888,13946,13947],{"xmlns":890},[892,13948,13949,13963],{},[895,13950,13951,13953,13955,13957,13959,13961],{},[898,13952,1842],{},[1656,13954,1659],{"stretchy":1658},[1667,13956,8567],{},[1656,13958,1683],{"stretchy":1658},[1656,13960,1713],{},[1667,13962,1669],{},[902,13964,13965],{"encoding":904},"E(25)=1",[883,13967,13969],{"className":13968},[886],[888,13970,13971],{"xmlns":890},[892,13972,13973,13987],{},[895,13974,13975,13977,13979,13981,13983,13985],{},[898,13976,1842],{},[1656,13978,1659],{"stretchy":1658},[1667,13980,9135],{},[1656,13982,1683],{"stretchy":1658},[1656,13984,1713],{},[1667,13986,2673],{},[902,13988,13989],{"encoding":904},"E(40)=4",". Např. ",[883,13992,13994],{"className":13993},[886],[888,13995,13996],{"xmlns":890},[892,13997,13998,14012],{},[895,13999,14000,14002,14004,14006,14008,14010],{},[898,14001,1842],{},[1656,14003,1659],{"stretchy":1658},[1667,14005,9135],{},[1656,14007,1683],{"stretchy":1658},[1656,14009,1713],{},[1667,14011,2673],{},[902,14013,13989],{"encoding":904}," znamená, že zvýšení ceny o 1 % (z 40 na 40,4) způsobí pokles množství o 4 % (z ",[883,14016,14018],{"className":14017},[886],[888,14019,14020],{"xmlns":890},[892,14021,14022,14030],{},[895,14023,14024,14026,14028],{},[898,14025,1665],{},[1656,14027,1713],{},[1667,14029,5193],{},[902,14031,14032],{"encoding":904},"Q=5",[883,14034,14036],{"className":14035},[886],[888,14037,14038],{"xmlns":890},[892,14039,14040,14049],{},[895,14041,14042,14044,14046],{},[898,14043,1665],{},[1656,14045,1713],{},[1667,14047,14048],{},"4,8",[902,14050,14051],{"encoding":904},"Q=4{,}8",[198,14053,14055],{"id":14054},"oblouková-průměrná-vs-bodová-okamžitá-elasticita","Oblouková (průměrná) vs. bodová (okamžitá) elasticita",[120,14057,14058,14114],{},[123,14059,14060,14063,14064,14081,14082,1863],{},[38,14061,14062],{},"Oblouková"," (průměrná) elasticita: výraz ",[883,14065,14067],{"className":14066},[886],[888,14068,14069],{"xmlns":890},[892,14070,14071,14079],{},[895,14072,14073],{},[2062,14074,14075,14077],{},[898,14076,1842],{},[898,14078,2146],{},[902,14080,13035],{"encoding":904}," ze (4.4) vztažený k intervalu ",[883,14083,14085],{"className":14084},[886],[888,14086,14087],{"xmlns":890},[892,14088,14089,14111],{},[895,14090,14091,14094,14096,14098,14100,14102,14104,14106,14108],{},[1656,14092,14093],{"stretchy":1658},"⟨",[898,14095,8194],{},[1656,14097,1673],{"separator":1672},[2461,14099,7828],{},[898,14101,8194],{},[1656,14103,3633],{},[898,14105,3750],{"mathvariant":1723},[898,14107,8194],{},[1656,14109,14110],{"stretchy":1658},"⟩",[902,14112,14113],{"encoding":904},"\\langle P,\\, P+\\Delta P\\rangle",[123,14115,14116,14119,14120,14133],{},[38,14117,14118],{},"Bodová"," (okamžitá) elasticita: ",[883,14121,14123],{"className":14122},[886],[888,14124,14125],{"xmlns":890},[892,14126,14127,14131],{},[895,14128,14129],{},[898,14130,1842],{},[902,14132,1842],{"encoding":904}," dle (4.5) — výchozí pojem dále v textu.",[198,14135,14137,14138,14151,14152],{"id":14136},"výpočet-je-li-dáno-pp-jako-funkce-qq","Výpočet, je-li dáno ",[883,14139,14141],{"className":14140},[886],[888,14142,14143],{"xmlns":890},[892,14144,14145,14149],{},[895,14146,14147],{},[898,14148,8194],{},[902,14150,8194],{"encoding":904}," jako funkce ",[883,14153,14155],{"className":14154},[886],[888,14156,14157],{"xmlns":890},[892,14158,14159,14163],{},[895,14160,14161],{},[898,14162,1665],{},[902,14164,1665],{"encoding":904},[724,14166,14167,14168,14191],{},"Pokud je poptávka zadaná ve tvaru ",[883,14169,14171],{"className":14170},[886],[888,14172,14173],{"xmlns":890},[892,14174,14175,14189],{},[895,14176,14177,14179,14181,14183,14185,14187],{},[898,14178,8194],{},[1656,14180,1713],{},[898,14182,6787],{},[1656,14184,1659],{"stretchy":1658},[898,14186,1665],{},[1656,14188,1683],{"stretchy":1658},[902,14190,13412],{"encoding":904},", využijeme vztah pro derivaci inverzní funkce",[724,14193,14194],{},[883,14195,14197],{"className":14196,"title":12979,"style":12980},[12978],"\\frac{\\mathrm{d}Q}{\\mathrm{d}P} = \\frac{1}{\\frac{\\mathrm{d}P}{\\mathrm{d}Q}}. \\tag{4.9}",[724,14199,14200,1643,14203,14229],{},[38,14201,14202],{},"Příklad 4.3.",[883,14204,14206],{"className":14205},[886],[888,14207,14208],{"xmlns":890},[892,14209,14210,14226],{},[895,14211,14212,14214,14216,14218,14220],{},[898,14213,8194],{},[1656,14215,1713],{},[1667,14217,5267],{},[1656,14219,3964],{},[2062,14221,14222,14224],{},[898,14223,1665],{},[1667,14225,1680],{},[902,14227,14228],{"encoding":904},"P = 100 - Q^2",", ptáme se na elasticitu při ceně 36. Dostáváme",[724,14231,14232],{},[883,14233,14235],{"className":14234},[886],[888,14236,14237],{"xmlns":890},[892,14238,14239,14305],{},[895,14240,14241,14243,14245,14247,14263,14265,14277,14279,14303],{},[898,14242,1842],{},[1656,14244,1713],{},[1656,14246,3964],{},[3294,14248,14249,14261],{},[895,14250,14251,14253,14255],{},[1667,14252,5267],{},[1656,14254,3964],{},[2062,14256,14257,14259],{},[898,14258,1665],{},[1667,14260,1680],{},[898,14262,1665],{},[1656,14264,2751],{},[3294,14266,14267,14269],{},[1667,14268,1669],{},[895,14270,14271,14273,14275],{},[1656,14272,3964],{},[1667,14274,1680],{},[898,14276,1665],{},[1656,14278,1713],{},[3294,14280,14281,14293],{},[895,14282,14283,14285,14287],{},[1667,14284,5267],{},[1656,14286,3964],{},[2062,14288,14289,14291],{},[898,14290,1665],{},[1667,14292,1680],{},[895,14294,14295,14297],{},[1667,14296,1680],{},[2062,14298,14299,14301],{},[898,14300,1665],{},[1667,14302,1680],{},[898,14304,1863],{"mathvariant":1723},[902,14306,14307],{"encoding":904},"E = -\\frac{100-Q^2}{Q}\\cdot \\frac{1}{-2Q} = \\frac{100-Q^2}{2Q^2}.",[724,14309,14310,14311,14337,14338,2836,14356,1863],{},"Z rovnice ",[883,14312,14314],{"className":14313},[886],[888,14315,14316],{"xmlns":890},[892,14317,14318,14334],{},[895,14319,14320,14322,14324,14330,14332],{},[1667,14321,5267],{},[1656,14323,3964],{},[2062,14325,14326,14328],{},[898,14327,1665],{},[1667,14329,1680],{},[1656,14331,1713],{},[1667,14333,9023],{},[902,14335,14336],{"encoding":904},"100 - Q^2 = 36"," plyne ",[883,14339,14341],{"className":14340},[886],[888,14342,14343],{"xmlns":890},[892,14344,14345,14353],{},[895,14346,14347,14349,14351],{},[898,14348,1665],{},[1656,14350,1713],{},[1667,14352,2877],{},[902,14354,14355],{"encoding":904},"Q = 8",[883,14357,14359],{"className":14358},[886],[888,14360,14361],{"xmlns":890},[892,14362,14363,14388],{},[895,14364,14365,14367,14369,14371,14373,14375,14383,14385],{},[898,14366,1842],{},[1656,14368,1659],{"stretchy":1658},[1667,14370,2877],{},[1656,14372,1683],{"stretchy":1658},[1656,14374,1713],{},[4138,14376,14377],{"scriptlevel":4032,"displaystyle":1658},[3294,14378,14379,14381],{},[1667,14380,9023],{},[1667,14382,2771],{},[1656,14384,1713],{},[1667,14386,14387],{},"0,281",[902,14389,14390],{"encoding":904},"E(8) = \\tfrac{36}{128} = 0{,}281",[198,14392,14394],{"id":14393},"přibližné-změny","Přibližné změny",[724,14396,14397,14398,14434,14435,14457],{},"Diferenciál ",[883,14399,14401],{"className":14400},[886],[888,14402,14403],{"xmlns":890},[892,14404,14405,14431],{},[895,14406,14407,14409,14411,14413,14419,14421,14423,14425,14427,14429],{},[898,14408,3768],{"mathvariant":1723},[898,14410,1665],{},[1656,14412,1713],{},[2062,14414,14415,14417],{},[898,14416,1665],{},[1656,14418,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,14420,1659],{"stretchy":1658},[898,14422,8194],{},[1656,14424,1683],{"stretchy":1658},[2461,14426,7828],{},[898,14428,3768],{"mathvariant":1723},[898,14430,8194],{},[902,14432,14433],{"encoding":904},"\\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P"," s ",[883,14436,14438],{"className":14437},[886],[888,14439,14440],{"xmlns":890},[892,14441,14442,14454],{},[895,14443,14444,14446,14448,14450,14452],{},[898,14445,3768],{"mathvariant":1723},[898,14447,8194],{},[1656,14449,1713],{},[898,14451,3750],{"mathvariant":1723},[898,14453,8194],{},[902,14455,14456],{"encoding":904},"\\mathrm{d}P = \\Delta P"," dává nominální odhad",[724,14459,14460],{},[883,14461,14463],{"className":14462,"title":12979,"style":12980},[12978],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P. \\tag{4.10}",[724,14465,14466],{},"Po přechodu na procentní změny (vztah (4.3)):",[724,14468,14469],{},[883,14470,14472],{"className":14471,"title":12979,"style":12980},[12978],"\\boxed{\\;\\Delta Q\\% \\approx -E(P)\\,\\Delta P\\%\\;} \\tag{4.11}",[724,14474,14475,1643,14478,14513,14514,14533,14534,14568,14569,14586],{},[38,14476,14477],{},"Příklad 4.5.",[883,14479,14481],{"className":14480},[886],[888,14482,14483],{"xmlns":890},[892,14484,14485,14510],{},[895,14486,14487,14489,14491,14493,14499,14501,14503,14505,14507],{},[898,14488,8194],{},[1656,14490,1713],{},[1656,14492,3964],{},[2062,14494,14495,14497],{},[898,14496,1665],{},[1667,14498,1680],{},[1656,14500,3964],{},[1667,14502,2673],{},[898,14504,1665],{},[1656,14506,3633],{},[1667,14508,14509],{},"96",[902,14511,14512],{"encoding":904},"P = -Q^2 - 4Q + 96",", cena ",[883,14515,14517],{"className":14516},[886],[888,14518,14519],{"xmlns":890},[892,14520,14521,14530],{},[895,14522,14523,14525,14527],{},[898,14524,8194],{},[1656,14526,1713],{},[1667,14528,14529],{},"51",[902,14531,14532],{"encoding":904},"P=51",". Z rovnice ",[883,14535,14537],{"className":14536},[886],[888,14538,14539],{"xmlns":890},[892,14540,14541,14565],{},[895,14542,14543,14545,14547,14549,14555,14557,14559,14561,14563],{},[1667,14544,14529],{},[1656,14546,1713],{},[1656,14548,3964],{},[2062,14550,14551,14553],{},[898,14552,1665],{},[1667,14554,1680],{},[1656,14556,3964],{},[1667,14558,2673],{},[898,14560,1665],{},[1656,14562,3633],{},[1667,14564,14509],{},[902,14566,14567],{"encoding":904},"51 = -Q^2-4Q+96"," volíme (kladný kořen) ",[883,14570,14572],{"className":14571},[886],[888,14573,14574],{"xmlns":890},[892,14575,14576,14584],{},[895,14577,14578,14580,14582],{},[898,14579,1665],{},[1656,14581,1713],{},[1667,14583,5193],{},[902,14585,14032],{"encoding":904},". Elasticita:",[724,14588,14589],{},[883,14590,14592],{"className":14591},[886],[888,14593,14594],{"xmlns":890},[892,14595,14596,14667],{},[895,14597,14598,14600,14602,14640,14642,14645,14647,14649,14651,14653,14655,14662,14664],{},[898,14599,1842],{},[1656,14601,1713],{},[3294,14603,14604,14624],{},[895,14605,14606,14608,14614,14616,14618,14620,14622],{},[1656,14607,3964],{},[2062,14609,14610,14612],{},[898,14611,1665],{},[1667,14613,1680],{},[1656,14615,3964],{},[1667,14617,2673],{},[898,14619,1665],{},[1656,14621,3633],{},[1667,14623,14509],{},[895,14625,14626,14628,14630,14632,14634,14636,14638],{},[898,14627,1665],{},[1656,14629,1659],{"stretchy":1658},[1667,14631,1680],{},[898,14633,1665],{},[1656,14635,3633],{},[1667,14637,2673],{},[1656,14639,1683],{"stretchy":1658},[1656,14641,1673],{"separator":1672},[3316,14643],{"width":14644},"2em",[898,14646,1842],{},[1656,14648,1659],{"stretchy":1658},[1667,14650,5193],{},[1656,14652,1683],{"stretchy":1658},[1656,14654,1713],{},[3294,14656,14657,14659],{},[1667,14658,14529],{},[1667,14660,14661],{},"70",[1656,14663,2829],{},[1667,14665,14666],{},"0,728.",[902,14668,14669],{"encoding":904},"E = \\frac{-Q^2-4Q+96}{Q(2Q+4)}, \\qquad E(5) = \\frac{51}{70} \\doteq 0{,}728.",[724,14671,14672,14673,1863],{},"Jde o neelastickou poptávku. Zvýší-li se cena o 2 %, pak ",[883,14674,14676],{"className":14675},[886],[888,14677,14678],{"xmlns":890},[892,14679,14680,14711],{},[895,14681,14682,14684,14686,14689,14691,14693,14696,14698,14700,14702,14704,14707,14709],{},[898,14683,3750],{"mathvariant":1723},[898,14685,1665],{},[898,14687,14688],{"mathvariant":1723},"%",[1656,14690,3815],{},[1656,14692,3964],{},[1667,14694,14695],{},"0,728",[1656,14697,2751],{},[1667,14699,1680],{},[1656,14701,1713],{},[1656,14703,3964],{},[1667,14705,14706],{},"1,456",[2461,14708,7828],{},[898,14710,14688],{"mathvariant":1723},[902,14712,14713],{"encoding":904},"\\Delta Q\\% \\approx -0{,}728\\cdot 2 = -1{,}456\\,\\%",[115,14715,14717],{"id":14716},"klasifikace-elasticit-poptávky","Klasifikace elasticit poptávky",[724,14719,14720,14721,14744,14745,2114],{},"V závislosti na hodnotě ",[883,14722,14724],{"className":14723},[886],[888,14725,14726],{"xmlns":890},[892,14727,14728,14742],{},[895,14729,14730,14732,14734,14740],{},[898,14731,1842],{},[1656,14733,1659],{"stretchy":1658},[2062,14735,14736,14738],{},[898,14737,8194],{},[1656,14739,8187],{},[1656,14741,1683],{"stretchy":1658},[902,14743,13156],{"encoding":904}," mluvíme o poptávce podle následující tabulky ",[883,14746,14748],{"className":14747},[886],[888,14749,14750],{"xmlns":890},[892,14751,14752,14761],{},[895,14753,14754,14756,14759],{},[1656,14755,1659],{"stretchy":1658},[1667,14757,14758],{},"4.7",[1656,14760,1683],{"stretchy":1658},[902,14762,14763],{"encoding":904},"(4.7)",[724,14765,14766],{},[5956,14767],{"alt":14768,"className":14769,"src":14770},"imek-typy-elasticity-5panelu",[210,5960],"\u002Fwiki-assets\u002Fimek-typy-elasticity-5panelu.jpeg",[16,14772,14773,14812],{},[19,14774,14775],{},[22,14776,14777,14803,14806,14809],{},[25,14778,14779,14780],{},"Hodnota ",[883,14781,14783],{"className":14782},[886],[888,14784,14785],{"xmlns":890},[892,14786,14787,14801],{},[895,14788,14789,14791,14793,14799],{},[898,14790,1842],{},[1656,14792,1659],{"stretchy":1658},[2062,14794,14795,14797],{},[898,14796,8194],{},[1656,14798,8187],{},[1656,14800,1683],{"stretchy":1658},[902,14802,13156],{"encoding":904},[25,14804,14805],{},"Typ poptávky",[25,14807,14808],{},"Termín",[25,14810,14811],{},"Význam",[30,14813,14814,14847,14909,14984,15041],{},[22,14815,14816,14836,14841,14844],{},[35,14817,14818],{},[883,14819,14821],{"className":14820},[886],[888,14822,14823],{"xmlns":890},[892,14824,14825,14833],{},[895,14826,14827,14829,14831],{},[898,14828,1842],{},[1656,14830,1713],{},[1667,14832,4032],{},[902,14834,14835],{"encoding":904},"E = 0",[35,14837,14838],{},[38,14839,14840],{},"dokonale neelastická",[35,14842,14843],{},"perfectly inelastic",[35,14845,14846],{},"množství se nemění bez ohledu na cenu",[22,14848,14849,14873,14877,14880],{},[35,14850,14851],{},[883,14852,14854],{"className":14853},[886],[888,14855,14856],{"xmlns":890},[892,14857,14858,14870],{},[895,14859,14860,14862,14864,14866,14868],{},[1667,14861,4032],{},[1656,14863,4373],{},[898,14865,1842],{},[1656,14867,4373],{},[1667,14869,1669],{},[902,14871,14872],{"encoding":904},"0 \u003C E \u003C 1",[35,14874,14875],{},[38,14876,12858],{},[35,14878,14879],{},"inelastic",[35,14881,14882,14895,14896],{},[883,14883,14885],{"className":14884},[886],[888,14886,14887],{"xmlns":890},[892,14888,14889,14893],{},[895,14890,14891],{},[898,14892,1665],{},[902,14894,1665],{"encoding":904}," se mění pomaleji než ",[883,14897,14899],{"className":14898},[886],[888,14900,14901],{"xmlns":890},[892,14902,14903,14907],{},[895,14904,14905],{},[898,14906,8194],{},[902,14908,8194],{"encoding":904},[22,14910,14911,14930,14935,14938],{},[35,14912,14913],{},[883,14914,14916],{"className":14915},[886],[888,14917,14918],{"xmlns":890},[892,14919,14920,14928],{},[895,14921,14922,14924,14926],{},[898,14923,1842],{},[1656,14925,1713],{},[1667,14927,1669],{},[902,14929,13318],{"encoding":904},[35,14931,14932],{},[38,14933,14934],{},"jednotkově elastická",[35,14936,14937],{},"unit elastic",[35,14939,14940,14953,14954,14967,14968,14983],{},[883,14941,14943],{"className":14942},[886],[888,14944,14945],{"xmlns":890},[892,14946,14947,14951],{},[895,14948,14949],{},[898,14950,1665],{},[902,14952,1665],{"encoding":904}," i ",[883,14955,14957],{"className":14956},[886],[888,14958,14959],{"xmlns":890},[892,14960,14961,14965],{},[895,14962,14963],{},[898,14964,8194],{},[902,14966,8194],{"encoding":904}," se mění stejně rychle; ",[883,14969,14971],{"className":14970},[886],[888,14972,14973],{"xmlns":890},[892,14974,14975,14981],{},[895,14976,14977,14979],{},[898,14978,11577],{},[898,14980,1763],{},[902,14982,12875],{"encoding":904}," má maximum",[22,14985,14986,15005,15009,15012],{},[35,14987,14988],{},[883,14989,14991],{"className":14990},[886],[888,14992,14993],{"xmlns":890},[892,14994,14995,15003],{},[895,14996,14997,14999,15001],{},[898,14998,1842],{},[1656,15000,2850],{},[1667,15002,1669],{},[902,15004,13282],{"encoding":904},[35,15006,15007],{},[38,15008,12854],{},[35,15010,15011],{},"elastic",[35,15013,15014,15027,15028],{},[883,15015,15017],{"className":15016},[886],[888,15018,15019],{"xmlns":890},[892,15020,15021,15025],{},[895,15022,15023],{},[898,15024,1665],{},[902,15026,1665],{"encoding":904}," se mění rychleji než ",[883,15029,15031],{"className":15030},[886],[888,15032,15033],{"xmlns":890},[892,15034,15035,15039],{},[895,15036,15037],{},[898,15038,8194],{},[902,15040,8194],{"encoding":904},[22,15042,15043,15064,15069,15072],{},[35,15044,15045],{},[883,15046,15048],{"className":15047},[886],[888,15049,15050],{"xmlns":890},[892,15051,15052,15061],{},[895,15053,15054,15056,15058],{},[898,15055,1842],{},[1656,15057,11915],{},[898,15059,15060],{"mathvariant":1723},"∞",[902,15062,15063],{"encoding":904},"E \\to \\infty",[35,15065,15066],{},[38,15067,15068],{},"dokonale elastická",[35,15070,15071],{},"perfectly elastic",[35,15073,15074,15075],{},"sebemenší změna ceny úplně mění ",[883,15076,15078],{"className":15077},[886],[888,15079,15080],{"xmlns":890},[892,15081,15082,15086],{},[895,15083,15084],{},[898,15085,1665],{},[902,15087,1665],{"encoding":904},[724,15089,15090],{},[38,15091,15092],{},"Pravidlo růstu elasticity s cenou:",[1981,15094,15095],{},[724,15096,15097,15098],{},"S rostoucí cenou elasticita poptávky roste. ",[883,15099,15101],{"className":15100},[886],[888,15102,15103],{"xmlns":890},[892,15104,15105,15114],{},[895,15106,15107,15109,15112],{},[1656,15108,1659],{"stretchy":1658},[1667,15110,15111],{},"4.8",[1656,15113,1683],{"stretchy":1658},[902,15115,15116],{"encoding":904},"(4.8)",[724,15118,15119,15120,15123,15124,15127,15128,15145],{},"Z toho plyne, že při ",[614,15121,15122],{},"dostatečně nízkých"," cenách je poptávka neelastická a při ",[614,15125,15126],{},"dostatečně vysokých"," elastická. Existuje tedy cena ",[883,15129,15131],{"className":15130},[886],[888,15132,15133],{"xmlns":890},[892,15134,15135,15143],{},[895,15136,15137],{},[2062,15138,15139,15141],{},[898,15140,8194],{},[1656,15142,8187],{},[902,15144,13178],{"encoding":904},", při které je poptávka jednotkově elastická, a ta rozděluje reálné cenové rozpětí na obě zóny.",[1981,15147,15148,15153],{},[724,15149,15150,15152],{},[883,15151,10188],{}," Postup: jak klasifikovat poptávku",[152,15154,15155,15182,15185],{},[123,15156,15157,15158,15181],{},"Spočítejte ",[883,15159,15161],{"className":15160},[886],[888,15162,15163],{"xmlns":890},[892,15164,15165,15179],{},[895,15166,15167,15169,15171,15177],{},[898,15168,1842],{},[1656,15170,1659],{"stretchy":1658},[2062,15172,15173,15175],{},[898,15174,8194],{},[1656,15176,8187],{},[1656,15178,1683],{"stretchy":1658},[902,15180,13156],{"encoding":904}," dle (4.5).",[123,15183,15184],{},"Porovnejte s jedničkou (viz tabulka výše).",[123,15186,15187,15188,15212],{},"Chcete-li najít hranici mezi elastickou a neelastickou zónou, řešte rovnici ",[883,15189,15191],{"className":15190},[886],[888,15192,15193],{"xmlns":890},[892,15194,15195,15209],{},[895,15196,15197,15199,15201,15203,15205,15207],{},[898,15198,1842],{},[1656,15200,1659],{"stretchy":1658},[898,15202,8194],{},[1656,15204,1683],{"stretchy":1658},[1656,15206,1713],{},[1667,15208,1669],{},[902,15210,15211],{"encoding":904},"E(P) = 1"," a výsledek porovnejte s reálným cenovým rozpětím.",[724,15214,15215,15218,15219,3713,15236,15254,15255,15281,15282,1863],{},[38,15216,15217],{},"Příklad 4.2."," Pro poptávku z Příkladu 4.1: ",[883,15220,15222],{"className":15221},[886],[888,15223,15224],{"xmlns":890},[892,15225,15226,15234],{},[895,15227,15228,15230,15232],{},[898,15229,1842],{},[1656,15231,1713],{},[1667,15233,1669],{},[902,15235,13318],{"encoding":904},[883,15237,15239],{"className":15238},[886],[888,15240,15241],{"xmlns":890},[892,15242,15243,15251],{},[895,15244,15245,15247,15249],{},[898,15246,8194],{},[1656,15248,1713],{},[1667,15250,8567],{},[902,15252,15253],{"encoding":904},"P = 25",". Podle (4.8) je poptávka neelastická pro ",[883,15256,15258],{"className":15257},[886],[888,15259,15260],{"xmlns":890},[892,15261,15262,15278],{},[895,15263,15264,15266,15268,15270,15272,15274,15276],{},[898,15265,8194],{},[1656,15267,5915],{},[1656,15269,14093],{"stretchy":1658},[1667,15271,4032],{},[1656,15273,1673],{"separator":1672},[1667,15275,8567],{},[1656,15277,1683],{"stretchy":1658},[902,15279,15280],{"encoding":904},"P \\in \\langle 0, 25)"," a elastická pro ",[883,15283,15285],{"className":15284},[886],[888,15286,15287],{"xmlns":890},[892,15288,15289,15305],{},[895,15290,15291,15293,15295,15297,15299,15301,15303],{},[898,15292,8194],{},[1656,15294,5915],{},[1656,15296,1659],{"stretchy":1658},[1667,15298,8567],{},[1656,15300,1673],{"separator":1672},[1667,15302,9267],{},[1656,15304,14110],{"stretchy":1658},[902,15306,15307],{"encoding":904},"P \\in (25, 50\\rangle",[115,15309,15311],{"id":15310},"elasticita-a-celkový-příjem","Elasticita a celkový příjem",[724,15313,15314],{},[5956,15315],{"alt":15316,"className":15317,"src":15318},"imek-elasticita-tr",[210,5960],"\u002Fwiki-assets\u002Fimek-elasticita-tr.jpeg",[724,15320,15321],{},[5956,15322],{"alt":15323,"className":15324,"src":15325},"imek-elasticita-podel-linearni-poptavky",[210,5960],"\u002Fwiki-assets\u002Fimek-elasticita-podel-linearni-poptavky.jpeg",[724,15327,15328,15329,15379,15380,15396],{},"Pro celkový příjem platí ",[883,15330,15332],{"className":15331},[886],[888,15333,15334],{"xmlns":890},[892,15335,15336,15376],{},[895,15337,15338,15340,15342,15344,15346,15348,15350,15352,15354,15356,15358,15360,15362,15364,15366,15368,15370,15372,15374],{},[898,15339,11577],{},[898,15341,1763],{},[1656,15343,1713],{},[898,15345,11577],{},[898,15347,1763],{},[1656,15349,1659],{"stretchy":1658},[898,15351,1665],{},[1656,15353,1683],{"stretchy":1658},[1656,15355,1713],{},[898,15357,8194],{},[1656,15359,2751],{},[898,15361,1665],{},[1656,15363,1713],{},[898,15365,1665],{},[1656,15367,2751],{},[898,15369,6787],{},[1656,15371,1659],{"stretchy":1658},[898,15373,1665],{},[1656,15375,1683],{"stretchy":1658},[902,15377,15378],{"encoding":904},"TR = TR(Q) = P\\cdot Q = Q\\cdot D(Q)",". Pro mezní příjem ",[883,15381,15383],{"className":15382},[886],[888,15384,15385],{"xmlns":890},[892,15386,15387,15393],{},[895,15388,15389,15391],{},[898,15390,1703],{},[898,15392,1763],{},[902,15394,15395],{"encoding":904},"MR"," odvodíme:",[724,15398,15399],{},[883,15400,15402],{"className":15401},[886],[888,15403,15404],{"xmlns":890},[892,15405,15406,15514],{},[895,15407,15408,15410,15412,15414,15416,15422,15424,15426,15428,15430,15432,15434,15436,15438,15440,15442,15444,15450,15452,15454,15456,15458,15460,15462,15464,15478,15480,15482],{},[898,15409,1703],{},[898,15411,1763],{},[1656,15413,1713],{},[898,15415,11577],{},[2062,15417,15418,15420],{},[898,15419,1763],{},[1656,15421,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,15423,1659],{"stretchy":1658},[898,15425,1665],{},[1656,15427,1683],{"stretchy":1658},[1656,15429,1713],{},[898,15431,6787],{},[1656,15433,1659],{"stretchy":1658},[898,15435,1665],{},[1656,15437,1683],{"stretchy":1658},[1656,15439,3633],{},[898,15441,1665],{},[2461,15443,7828],{},[2062,15445,15446,15448],{},[898,15447,6787],{},[1656,15449,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,15451,1659],{"stretchy":1658},[898,15453,1665],{},[1656,15455,1683],{"stretchy":1658},[1656,15457,1713],{},[898,15459,8194],{},[1656,15461,3633],{},[898,15463,1665],{},[3294,15465,15466,15472],{},[895,15467,15468,15470],{},[898,15469,3768],{"mathvariant":1723},[898,15471,8194],{},[895,15473,15474,15476],{},[898,15475,3768],{"mathvariant":1723},[898,15477,1665],{},[1656,15479,1713],{},[898,15481,8194],{},[895,15483,15484,15486,15488,15490,15496,15498,15512],{},[1656,15485,1659],{"fence":1672},[1667,15487,1669],{},[1656,15489,3633],{},[3294,15491,15492,15494],{},[898,15493,1665],{},[898,15495,8194],{},[1656,15497,2751],{},[3294,15499,15500,15506],{},[895,15501,15502,15504],{},[898,15503,3768],{"mathvariant":1723},[898,15505,8194],{},[895,15507,15508,15510],{},[898,15509,3768],{"mathvariant":1723},[898,15511,1665],{},[1656,15513,1683],{"fence":1672},[902,15515,15516],{"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)",[724,15518,15519],{},[883,15520,15522],{"className":15521},[886],[888,15523,15524],{"xmlns":890},[892,15525,15526,15598],{},[895,15527,15528,15530,15532,15574,15576,15578],{},[1656,15529,1713],{},[898,15531,8194],{},[895,15533,15534,15536,15538,15540,15572],{},[1656,15535,1659],{"fence":1672},[1667,15537,1669],{},[1656,15539,3633],{},[3294,15541,15542,15544],{},[1667,15543,1669],{},[895,15545,15546,15554,15556],{},[4138,15547,15548],{"scriptlevel":4032,"displaystyle":1658},[3294,15549,15550,15552],{},[898,15551,8194],{},[898,15553,1665],{},[1656,15555,2751],{},[4138,15557,15558],{"scriptlevel":4032,"displaystyle":1658},[3294,15559,15560,15566],{},[895,15561,15562,15564],{},[898,15563,3768],{"mathvariant":1723},[898,15565,1665],{},[895,15567,15568,15570],{},[898,15569,3768],{"mathvariant":1723},[898,15571,8194],{},[1656,15573,1683],{"fence":1672},[1656,15575,1713],{},[898,15577,8194],{},[895,15579,15580,15582,15584,15586,15596],{},[1656,15581,1659],{"fence":1672},[1667,15583,1669],{},[1656,15585,3633],{},[3294,15587,15588,15590],{},[1667,15589,1669],{},[895,15591,15592,15594],{},[1656,15593,3964],{},[898,15595,1842],{},[1656,15597,1683],{"fence":1672},[902,15599,15600],{"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)",[724,15602,15603],{},"a tedy",[724,15605,15606],{},[883,15607,15609],{"className":15608,"title":12979,"style":12980},[12978],"\\boxed{\\;MR = P\\left(1 - \\frac{1}{E}\\right) = D(Q)\\left(1 - \\frac{1}{E}\\right)\\;} \\tag{4.12}",[1981,15611,15612,15681,15930],{},[724,15613,15614,15616,15617,15651,15652,15667,15668,2114],{},[883,15615,3472],{}," Intuice: vztah ",[883,15618,15620],{"className":15619},[886],[888,15621,15622],{"xmlns":890},[892,15623,15624,15648],{},[895,15625,15626,15628,15630,15632,15634,15636,15638,15640,15642,15644,15646],{},[898,15627,1703],{},[898,15629,1763],{},[1656,15631,1713],{},[898,15633,8194],{},[1656,15635,1659],{"stretchy":1658},[1667,15637,1669],{},[1656,15639,3964],{},[1667,15641,1669],{},[898,15643,1782],{"mathvariant":1723},[898,15645,1842],{},[1656,15647,1683],{"stretchy":1658},[902,15649,15650],{"encoding":904},"MR = P(1 - 1\u002FE)","\nVztah (4.12) je „most\" mezi elasticitou a mezním příjmem — znaménko ",[883,15653,15655],{"className":15654},[886],[888,15656,15657],{"xmlns":890},[892,15658,15659,15665],{},[895,15660,15661,15663],{},[898,15662,1703],{},[898,15664,1763],{},[902,15666,15395],{"encoding":904}," jednoznačně určuje hodnota ",[883,15669,15671],{"className":15670},[886],[888,15672,15673],{"xmlns":890},[892,15674,15675,15679],{},[895,15676,15677],{},[898,15678,1842],{},[902,15680,1842],{"encoding":904},[120,15682,15683,15792,15861],{},[123,15684,15685,15702,15703,1643,15717,1643,15743,1643,15756,2533,15776,15791],{},[883,15686,15688],{"className":15687},[886],[888,15689,15690],{"xmlns":890},[892,15691,15692,15700],{},[895,15693,15694,15696,15698],{},[898,15695,1842],{},[1656,15697,2850],{},[1667,15699,1669],{},[902,15701,13282],{"encoding":904}," (elastická) ",[883,15704,15706],{"className":15705},[886],[888,15707,15708],{"xmlns":890},[892,15709,15710,15714],{},[895,15711,15712],{},[1656,15713,12770],{},[902,15715,15716],{"encoding":904},"\\Rightarrow",[883,15718,15720],{"className":15719},[886],[888,15721,15722],{"xmlns":890},[892,15723,15724,15740],{},[895,15725,15726,15728,15730,15732,15734,15736,15738],{},[1667,15727,1669],{},[1656,15729,3964],{},[1667,15731,1669],{},[898,15733,1782],{"mathvariant":1723},[898,15735,1842],{},[1656,15737,2850],{},[1667,15739,4032],{},[902,15741,15742],{"encoding":904},"1 - 1\u002FE > 0",[883,15744,15746],{"className":15745},[886],[888,15747,15748],{"xmlns":890},[892,15749,15750,15754],{},[895,15751,15752],{},[1656,15753,12770],{},[902,15755,15716],{"encoding":904},[883,15757,15759],{"className":15758},[886],[888,15760,15761],{"xmlns":890},[892,15762,15763,15773],{},[895,15764,15765,15767,15769,15771],{},[898,15766,1703],{},[898,15768,1763],{},[1656,15770,2850],{},[1667,15772,4032],{},[902,15774,15775],{"encoding":904},"MR > 0",[883,15777,15779],{"className":15778},[886],[888,15780,15781],{"xmlns":890},[892,15782,15783,15789],{},[895,15784,15785,15787],{},[898,15786,11577],{},[898,15788,1763],{},[902,15790,12875],{"encoding":904}," roste s množstvím, tj. klesá s cenou.",[123,15793,15794,15811,15812,1643,15825,2533,15845,15860],{},[883,15795,15797],{"className":15796},[886],[888,15798,15799],{"xmlns":890},[892,15800,15801,15809],{},[895,15802,15803,15805,15807],{},[898,15804,1842],{},[1656,15806,1713],{},[1667,15808,1669],{},[902,15810,13318],{"encoding":904}," (jednotková) ",[883,15813,15815],{"className":15814},[886],[888,15816,15817],{"xmlns":890},[892,15818,15819,15823],{},[895,15820,15821],{},[1656,15822,12770],{},[902,15824,15716],{"encoding":904},[883,15826,15828],{"className":15827},[886],[888,15829,15830],{"xmlns":890},[892,15831,15832,15842],{},[895,15833,15834,15836,15838,15840],{},[898,15835,1703],{},[898,15837,1763],{},[1656,15839,1713],{},[1667,15841,4032],{},[902,15843,15844],{"encoding":904},"MR = 0",[883,15846,15848],{"className":15847},[886],[888,15849,15850],{"xmlns":890},[892,15851,15852,15858],{},[895,15853,15854,15856],{},[898,15855,11577],{},[898,15857,1763],{},[902,15859,12875],{"encoding":904}," je extrém (maximum).",[123,15862,15863,15880,15881,1643,15894,2533,15914,15929],{},[883,15864,15866],{"className":15865},[886],[888,15867,15868],{"xmlns":890},[892,15869,15870,15878],{},[895,15871,15872,15874,15876],{},[898,15873,1842],{},[1656,15875,4373],{},[1667,15877,1669],{},[902,15879,13300],{"encoding":904}," (neelastická) ",[883,15882,15884],{"className":15883},[886],[888,15885,15886],{"xmlns":890},[892,15887,15888,15892],{},[895,15889,15890],{},[1656,15891,12770],{},[902,15893,15716],{"encoding":904},[883,15895,15897],{"className":15896},[886],[888,15898,15899],{"xmlns":890},[892,15900,15901,15911],{},[895,15902,15903,15905,15907,15909],{},[898,15904,1703],{},[898,15906,1763],{},[1656,15908,4373],{},[1667,15910,4032],{},[902,15912,15913],{"encoding":904},"MR \u003C 0",[883,15915,15917],{"className":15916},[886],[888,15918,15919],{"xmlns":890},[892,15920,15921,15927],{},[895,15922,15923,15925],{},[898,15924,11577],{},[898,15926,1763],{},[902,15928,12875],{"encoding":904}," klesá s množstvím, tj. roste s cenou.",[724,15931,15932,15933,1863],{},"Viz také ",[207,15934,12608],{"className":15935,"dataFsResolvedFilePath":827,"href":828},[210],[198,15937,15939],{"id":15938},"pravidla-13-odvození-z-412","Pravidla 1–3 (odvození z (4.12))",[724,15941,15942,15962,15963,15989,15990,16005,16006,16019,16020,16033,16034,16047,16048,16064,16065,1643,16080,16083,16084,16064,16100,1863],{},[38,15943,15944,15945,12702],{},"(a) Poptávka elastická (",[883,15946,15948],{"className":15947},[886],[888,15949,15950],{"xmlns":890},[892,15951,15952,15960],{},[895,15953,15954,15956,15958],{},[898,15955,1842],{},[1656,15957,2850],{},[1667,15959,1669],{},[902,15961,13282],{"encoding":904}," Z (4.12) plyne ",[883,15964,15966],{"className":15965},[886],[888,15967,15968],{"xmlns":890},[892,15969,15970,15986],{},[895,15971,15972,15974,15976,15978,15980,15982,15984],{},[898,15973,1703],{},[898,15975,1763],{},[1656,15977,1659],{"stretchy":1658},[898,15979,1665],{},[1656,15981,1683],{"stretchy":1658},[1656,15983,2850],{},[1667,15985,4032],{},[902,15987,15988],{"encoding":904},"MR(Q) > 0",", a tedy celkový příjem ",[883,15991,15993],{"className":15992},[886],[888,15994,15995],{"xmlns":890},[892,15996,15997,16003],{},[895,15998,15999,16001],{},[898,16000,11577],{},[898,16002,1763],{},[902,16004,12875],{"encoding":904}," je rostoucí funkcí ",[883,16007,16009],{"className":16008},[886],[888,16010,16011],{"xmlns":890},[892,16012,16013,16017],{},[895,16014,16015],{},[898,16016,1665],{},[902,16018,1665],{"encoding":904},". Avšak růst ",[883,16021,16023],{"className":16022},[886],[888,16024,16025],{"xmlns":890},[892,16026,16027,16031],{},[895,16028,16029],{},[898,16030,1665],{},[902,16032,1665],{"encoding":904}," je odezvou na pokles ceny ",[883,16035,16037],{"className":16036},[886],[888,16038,16039],{"xmlns":890},[892,16040,16041,16045],{},[895,16042,16043],{},[898,16044,8194],{},[902,16046,8194],{"encoding":904},". Tudíž s ",[614,16049,16050,16051],{},"poklesem ceny ",[883,16052,16054],{"className":16053},[886],[888,16055,16056],{"xmlns":890},[892,16057,16058,16062],{},[895,16059,16060],{},[898,16061,8194],{},[902,16063,8194],{"encoding":904}," celkový příjem ",[883,16066,16068],{"className":16067},[886],[888,16069,16070],{"xmlns":890},[892,16071,16072,16078],{},[895,16073,16074,16076],{},[898,16075,11577],{},[898,16077,1763],{},[902,16079,12875],{"encoding":904},[614,16081,16082],{},"roste"," a s ",[614,16085,16086,16087],{},"růstem ceny ",[883,16088,16090],{"className":16089},[886],[888,16091,16092],{"xmlns":890},[892,16093,16094,16098],{},[895,16095,16096],{},[898,16097,8194],{},[902,16099,8194],{"encoding":904},[614,16101,16102],{},"klesá",[1981,16104,16105],{},[724,16106,16107,16110],{},[38,16108,16109],{},"Pravidlo 1."," Je-li poptávka elastická, pak s poklesem ceny celkový příjem roste a s růstem ceny celkový příjem klesá.",[724,16112,16113,15962,16133,1343,16159,16174,16175,16188,16189,16202,16203,16216,16217,16064,16230,1643,16245,1863],{},[38,16114,16115,16116,12702],{},"(b) Poptávka neelastická (",[883,16117,16119],{"className":16118},[886],[888,16120,16121],{"xmlns":890},[892,16122,16123,16131],{},[895,16124,16125,16127,16129],{},[898,16126,1842],{},[1656,16128,4373],{},[1667,16130,1669],{},[902,16132,13300],{"encoding":904},[883,16134,16136],{"className":16135},[886],[888,16137,16138],{"xmlns":890},[892,16139,16140,16156],{},[895,16141,16142,16144,16146,16148,16150,16152,16154],{},[898,16143,1703],{},[898,16145,1763],{},[1656,16147,1659],{"stretchy":1658},[898,16149,1665],{},[1656,16151,1683],{"stretchy":1658},[1656,16153,4373],{},[1667,16155,4032],{},[902,16157,16158],{"encoding":904},"MR(Q) \u003C 0",[883,16160,16162],{"className":16161},[886],[888,16163,16164],{"xmlns":890},[892,16165,16166,16172],{},[895,16167,16168,16170],{},[898,16169,11577],{},[898,16171,1763],{},[902,16173,12875],{"encoding":904}," je klesající funkce ",[883,16176,16178],{"className":16177},[886],[888,16179,16180],{"xmlns":890},[892,16181,16182,16186],{},[895,16183,16184],{},[898,16185,1665],{},[902,16187,1665],{"encoding":904},", tj. s růstem ",[883,16190,16192],{"className":16191},[886],[888,16193,16194],{"xmlns":890},[892,16195,16196,16200],{},[895,16197,16198],{},[898,16199,1665],{},[902,16201,1665],{"encoding":904}," (s poklesem ceny ",[883,16204,16206],{"className":16205},[886],[888,16207,16208],{"xmlns":890},[892,16209,16210,16214],{},[895,16211,16212],{},[898,16213,8194],{},[902,16215,8194],{"encoding":904},") celkový příjem klesá. S růstem ceny ",[883,16218,16220],{"className":16219},[886],[888,16221,16222],{"xmlns":890},[892,16223,16224,16228],{},[895,16225,16226],{},[898,16227,8194],{},[902,16229,8194],{"encoding":904},[883,16231,16233],{"className":16232},[886],[888,16234,16235],{"xmlns":890},[892,16236,16237,16243],{},[895,16238,16239,16241],{},[898,16240,11577],{},[898,16242,1763],{},[902,16244,12875],{"encoding":904},[614,16246,16082],{},[1981,16248,16249],{},[724,16250,16251,16254],{},[38,16252,16253],{},"Pravidlo 2."," Je-li poptávka neelastická, pak s poklesem ceny celkový příjem klesá a s růstem ceny celkový příjem roste.",[724,16256,16257,15962,16277,16296,16297,16312,16313,16383,16384,1896,16412,16445,16446,2836,16474,16489,16490,1863],{},[38,16258,16259,16260,12702],{},"(c) Jednotková elasticita (",[883,16261,16263],{"className":16262},[886],[888,16264,16265],{"xmlns":890},[892,16266,16267,16275],{},[895,16268,16269,16271,16273],{},[898,16270,1842],{},[1656,16272,1713],{},[1667,16274,1669],{},[902,16276,13318],{"encoding":904},[883,16278,16280],{"className":16279},[886],[888,16281,16282],{"xmlns":890},[892,16283,16284,16294],{},[895,16285,16286,16288,16290,16292],{},[898,16287,1703],{},[898,16289,1763],{},[1656,16291,1713],{},[1667,16293,4032],{},[902,16295,15844],{"encoding":904}," — nutná podmínka extrému ",[883,16298,16300],{"className":16299},[886],[888,16301,16302],{"xmlns":890},[892,16303,16304,16310],{},[895,16305,16306,16308],{},[898,16307,11577],{},[898,16309,1763],{},[902,16311,12875],{"encoding":904},". Dále ",[883,16314,16316],{"className":16315},[886],[888,16317,16318],{"xmlns":890},[892,16319,16320,16380],{},[895,16321,16322,16324,16334,16336,16338,16344,16346,16352,16354,16356,16358,16360,16362,16364,16374,16376,16378],{},[898,16323,11577],{},[2062,16325,16326,16328],{},[898,16327,1763],{},[895,16329,16330,16332],{},[1656,16331,1725],{"mathvariant":1723},[1656,16333,1725],{"mathvariant":1723},[1656,16335,1713],{},[898,16337,1703],{},[2062,16339,16340,16342],{},[898,16341,1763],{},[1656,16343,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,16345,1713],{},[2062,16347,16348,16350],{},[898,16349,6787],{},[1656,16351,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,16353,1659],{"stretchy":1658},[898,16355,1665],{},[1656,16357,1683],{"stretchy":1658},[1656,16359,3633],{},[898,16361,1665],{},[2461,16363,7828],{},[2062,16365,16366,16368],{},[898,16367,6787],{},[895,16369,16370,16372],{},[1656,16371,1725],{"mathvariant":1723},[1656,16373,1725],{"mathvariant":1723},[1656,16375,1659],{"stretchy":1658},[898,16377,1665],{},[1656,16379,1683],{"stretchy":1658},[902,16381,16382],{"encoding":904},"TR'' = MR' = D'(Q) + Q\\,D''(Q)","; za normálních podmínek ",[883,16385,16387],{"className":16386},[886],[888,16388,16389],{"xmlns":890},[892,16390,16391,16409],{},[895,16392,16393,16399,16401,16403,16405,16407],{},[2062,16394,16395,16397],{},[898,16396,6787],{},[1656,16398,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,16400,1659],{"stretchy":1658},[898,16402,1665],{},[1656,16404,1683],{"stretchy":1658},[1656,16406,4373],{},[1667,16408,4032],{},[902,16410,16411],{"encoding":904},"D'(Q) \u003C 0",[883,16413,16415],{"className":16414},[886],[888,16416,16417],{"xmlns":890},[892,16418,16419,16442],{},[895,16420,16421,16431,16433,16435,16437,16440],{},[2062,16422,16423,16425],{},[898,16424,6787],{},[895,16426,16427,16429],{},[1656,16428,1725],{"mathvariant":1723},[1656,16430,1725],{"mathvariant":1723},[1656,16432,1659],{"stretchy":1658},[898,16434,1665],{},[1656,16436,1683],{"stretchy":1658},[1656,16438,16439],{},"≤",[1667,16441,4032],{},[902,16443,16444],{"encoding":904},"D''(Q) \\le 0",", odkud ",[883,16447,16449],{"className":16448},[886],[888,16450,16451],{"xmlns":890},[892,16452,16453,16471],{},[895,16454,16455,16457,16467,16469],{},[898,16456,11577],{},[2062,16458,16459,16461],{},[898,16460,1763],{},[895,16462,16463,16465],{},[1656,16464,1725],{"mathvariant":1723},[1656,16466,1725],{"mathvariant":1723},[1656,16468,4373],{},[1667,16470,4032],{},[902,16472,16473],{"encoding":904},"TR'' \u003C 0",[883,16475,16477],{"className":16476},[886],[888,16478,16479],{"xmlns":890},[892,16480,16481,16487],{},[895,16482,16483,16485],{},[898,16484,11577],{},[898,16486,1763],{},[902,16488,12875],{"encoding":904}," nabývá ",[38,16491,16492],{},"maxima",[1981,16494,16495],{},[724,16496,16497,16500],{},[38,16498,16499],{},"Pravidlo 3."," Celkový příjem nabývá maxima při ceně, pro kterou je poptávka jednotkově elastická.",[724,16502,16503],{},"Tato tři pravidla potvrzují hypotézu (4.1) a jsou klíčem k regulaci ceny za účelem zvýšení (maximalizace) celkového příjmu.",[724,16505,16506],{},[38,16507,16508],{},"Souhrnná tabulka Pravidel 1–3:",[16,16510,16511,16615],{},[19,16512,16513],{},[22,16514,16515,16518,16533,16550,16581,16612],{},[25,16516,16517],{},"Charakter poptávky",[25,16519,16520],{},[883,16521,16523],{"className":16522},[886],[888,16524,16525],{"xmlns":890},[892,16526,16527,16531],{},[895,16528,16529],{},[898,16530,1842],{},[902,16532,1842],{"encoding":904},[25,16534,16535],{},[883,16536,16538],{"className":16537},[886],[888,16539,16540],{"xmlns":890},[892,16541,16542,16548],{},[895,16543,16544,16546],{},[898,16545,1703],{},[898,16547,1763],{},[902,16549,15395],{"encoding":904},[25,16551,16552,16553,1643,16566],{},"Pokles ceny ",[883,16554,16556],{"className":16555},[886],[888,16557,16558],{"xmlns":890},[892,16559,16560,16564],{},[895,16561,16562],{},[1656,16563,12770],{},[902,16565,15716],{"encoding":904},[883,16567,16569],{"className":16568},[886],[888,16570,16571],{"xmlns":890},[892,16572,16573,16579],{},[895,16574,16575,16577],{},[898,16576,11577],{},[898,16578,1763],{},[902,16580,12875],{"encoding":904},[25,16582,16583,16584,1643,16597],{},"Růst ceny ",[883,16585,16587],{"className":16586},[886],[888,16588,16589],{"xmlns":890},[892,16590,16591,16595],{},[895,16592,16593],{},[1656,16594,12770],{},[902,16596,15716],{"encoding":904},[883,16598,16600],{"className":16599},[886],[888,16601,16602],{"xmlns":890},[892,16603,16604,16610],{},[895,16605,16606,16608],{},[898,16607,11577],{},[898,16609,1763],{},[902,16611,12875],{"encoding":904},[25,16613,16614],{},"Doporučení",[30,16616,16617,16666,16716],{},[22,16618,16619,16621,16639,16657,16659,16661],{},[35,16620,12854],{},[35,16622,16623],{},[883,16624,16626],{"className":16625},[886],[888,16627,16628],{"xmlns":890},[892,16629,16630,16636],{},[895,16631,16632,16634],{},[1656,16633,2850],{},[1667,16635,1669],{},[902,16637,16638],{"encoding":904},"> 1",[35,16640,16641],{},[883,16642,16644],{"className":16643},[886],[888,16645,16646],{"xmlns":890},[892,16647,16648,16654],{},[895,16649,16650,16652],{},[1656,16651,2850],{},[1667,16653,4032],{},[902,16655,16656],{"encoding":904},"> 0",[35,16658,16082],{},[35,16660,16102],{},[35,16662,16663],{},[38,16664,16665],{},"snížit cenu",[22,16667,16668,16671,16689,16707,16709,16711],{},[35,16669,16670],{},"jednotková",[35,16672,16673],{},[883,16674,16676],{"className":16675},[886],[888,16677,16678],{"xmlns":890},[892,16679,16680,16686],{},[895,16681,16682,16684],{},[1656,16683,1713],{},[1667,16685,1669],{},[902,16687,16688],{"encoding":904},"= 1",[35,16690,16691],{},[883,16692,16694],{"className":16693},[886],[888,16695,16696],{"xmlns":890},[892,16697,16698,16704],{},[895,16699,16700,16702],{},[1656,16701,1713],{},[1667,16703,4032],{},[902,16705,16706],{"encoding":904},"= 0",[35,16708,12504],{},[35,16710,12504],{},[35,16712,16713],{},[38,16714,16715],{},"držet cenu",[22,16717,16718,16720,16738,16756,16758,16760],{},[35,16719,12858],{},[35,16721,16722],{},[883,16723,16725],{"className":16724},[886],[888,16726,16727],{"xmlns":890},[892,16728,16729,16735],{},[895,16730,16731,16733],{},[1656,16732,4373],{},[1667,16734,1669],{},[902,16736,16737],{"encoding":904},"\u003C 1",[35,16739,16740],{},[883,16741,16743],{"className":16742},[886],[888,16744,16745],{"xmlns":890},[892,16746,16747,16753],{},[895,16748,16749,16751],{},[1656,16750,4373],{},[1667,16752,4032],{},[902,16754,16755],{"encoding":904},"\u003C 0",[35,16757,16102],{},[35,16759,16082],{},[35,16761,16762],{},[38,16763,16764],{},"zvýšit cenu",[198,16766,16768],{"id":16767},"příklad-46-aplikace-pravidel-13","Příklad 4.6 — aplikace Pravidel 1–3",[724,16770,16771,16772,16797,16798,16820,16821,16834,16835,16848,16849,3206,16862,2836,16888,16940],{},"Aplikujme pravidla 1–3 pro poptávku ",[883,16773,16775],{"className":16774},[886],[888,16776,16777],{"xmlns":890},[892,16778,16779,16795],{},[895,16780,16781,16783,16785,16787,16789],{},[898,16782,8194],{},[1656,16784,1713],{},[1667,16786,5267],{},[1656,16788,3964],{},[2062,16790,16791,16793],{},[898,16792,1665],{},[1667,16794,1680],{},[902,16796,14228],{"encoding":904},". Reálné cenové rozpětí je ",[883,16799,16801],{"className":16800},[886],[888,16802,16803],{"xmlns":890},[892,16804,16805,16817],{},[895,16806,16807,16809,16811,16813,16815],{},[1656,16808,14093],{"stretchy":1658},[1667,16810,1669],{},[1656,16812,1673],{"separator":1672},[1667,16814,5267],{},[1656,16816,14110],{"stretchy":1658},[902,16818,16819],{"encoding":904},"\\langle 1, 100\\rangle",". Pro výpočet elasticity vyjádříme ",[883,16822,16824],{"className":16823},[886],[888,16825,16826],{"xmlns":890},[892,16827,16828,16832],{},[895,16829,16830],{},[898,16831,1665],{},[902,16833,1665],{"encoding":904}," jako funkci ",[883,16836,16838],{"className":16837},[886],[888,16839,16840],{"xmlns":890},[892,16841,16842,16846],{},[895,16843,16844],{},[898,16845,8194],{},[902,16847,8194],{"encoding":904},"; pro nezáporné ",[883,16850,16852],{"className":16851},[886],[888,16853,16854],{"xmlns":890},[892,16855,16856,16860],{},[895,16857,16858],{},[898,16859,1665],{},[902,16861,1665],{"encoding":904},[883,16863,16865],{"className":16864},[886],[888,16866,16867],{"xmlns":890},[892,16868,16869,16885],{},[895,16870,16871,16873,16875],{},[898,16872,1665],{},[1656,16874,1713],{},[2625,16876,16877],{},[895,16878,16879,16881,16883],{},[1667,16880,5267],{},[1656,16882,3964],{},[898,16884,8194],{},[902,16886,16887],{"encoding":904},"Q = \\sqrt{100 - P}",[883,16889,16891],{"className":16890},[886],[888,16892,16893],{"xmlns":890},[892,16894,16895,16937],{},[895,16896,16897,16913,16915,16917],{},[4138,16898,16899],{"scriptlevel":4032,"displaystyle":1672},[3294,16900,16901,16907],{},[895,16902,16903,16905],{},[898,16904,3768],{"mathvariant":1723},[898,16906,1665],{},[895,16908,16909,16911],{},[898,16910,3768],{"mathvariant":1723},[898,16912,8194],{},[1656,16914,1713],{},[1656,16916,3964],{},[4138,16918,16919],{"scriptlevel":4032,"displaystyle":1672},[3294,16920,16921,16923],{},[1667,16922,1669],{},[895,16924,16925,16927],{},[1667,16926,1680],{},[2625,16928,16929],{},[895,16930,16931,16933,16935],{},[1667,16932,5267],{},[1656,16934,3964],{},[898,16936,8194],{},[902,16938,16939],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\dfrac{1}{2\\sqrt{100-P}}",". Podle (4.5):",[724,16942,16943],{},[883,16944,16946],{"className":16945},[886],[888,16947,16948],{"xmlns":890},[892,16949,16950,17072],{},[895,16951,16952,16954,16956,16958,16960,16962,16964,16970,16972,16986,16988,16990,17004,17006,17032,17034,17052,17054,17070],{},[898,16953,1842],{},[1656,16955,1659],{"stretchy":1658},[898,16957,8194],{},[1656,16959,1683],{"stretchy":1658},[1656,16961,1713],{},[1656,16963,3964],{},[3294,16965,16966,16968],{},[898,16967,8194],{},[898,16969,1665],{},[1656,16971,2751],{},[3294,16973,16974,16980],{},[895,16975,16976,16978],{},[898,16977,3768],{"mathvariant":1723},[898,16979,1665],{},[895,16981,16982,16984],{},[898,16983,3768],{"mathvariant":1723},[898,16985,8194],{},[1656,16987,1713],{},[1656,16989,3964],{},[3294,16991,16992,16994],{},[898,16993,8194],{},[2625,16995,16996],{},[895,16997,16998,17000,17002],{},[1667,16999,5267],{},[1656,17001,3964],{},[898,17003,8194],{},[1656,17005,2751],{},[895,17007,17008,17010,17012,17030],{},[1656,17009,1659],{"fence":1672},[1656,17011,3964],{},[3294,17013,17014,17016],{},[1667,17015,1669],{},[895,17017,17018,17020],{},[1667,17019,1680],{},[2625,17021,17022],{},[895,17023,17024,17026,17028],{},[1667,17025,5267],{},[1656,17027,3964],{},[898,17029,8194],{},[1656,17031,1683],{"fence":1672},[1656,17033,1713],{},[3294,17035,17036,17038],{},[898,17037,8194],{},[895,17039,17040,17042,17044,17046,17048,17050],{},[1667,17041,1680],{},[1656,17043,1659],{"stretchy":1658},[1667,17045,5267],{},[1656,17047,3964],{},[898,17049,8194],{},[1656,17051,1683],{"stretchy":1658},[1656,17053,1713],{},[3294,17055,17056,17062],{},[895,17057,17058,17060],{},[1667,17059,13779],{},[898,17061,8194],{},[895,17063,17064,17066,17068],{},[1667,17065,5267],{},[1656,17067,3964],{},[898,17069,8194],{},[898,17071,1863],{"mathvariant":1723},[902,17073,17074],{"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}.",[724,17076,17077,17078,2114],{},"Stanovíme cenu, při které je poptávka jednotkově elastická. Řešíme ",[883,17079,17081],{"className":17080},[886],[888,17082,17083],{"xmlns":890},[892,17084,17085,17109],{},[895,17086,17087,17105,17107],{},[4138,17088,17089],{"scriptlevel":4032,"displaystyle":1672},[3294,17090,17091,17097],{},[895,17092,17093,17095],{},[1667,17094,13779],{},[898,17096,8194],{},[895,17098,17099,17101,17103],{},[1667,17100,5267],{},[1656,17102,3964],{},[898,17104,8194],{},[1656,17106,1713],{},[1667,17108,1669],{},[902,17110,17111],{"encoding":904},"\\dfrac{0{,}5P}{100-P} = 1",[724,17113,17114],{},[883,17115,17117],{"className":17116},[886],[888,17118,17119],{"xmlns":890},[892,17120,17121,17151],{},[895,17122,17123,17129,17131,17137,17139,17142,17149],{},[2062,17124,17125,17127],{},[898,17126,8194],{},[1656,17128,8187],{},[1656,17130,1713],{},[3294,17132,17133,17135],{},[1667,17134,5272],{},[1667,17136,2617],{},[1656,17138,2829],{},[1667,17140,17141],{},"66,",[2033,17143,17144,17146],{"accent":1672},[1667,17145,9112],{},[1656,17147,17148],{"stretchy":1672},"‾",[898,17150,1863],{"mathvariant":1723},[902,17152,17153],{"encoding":904},"P^* = \\frac{200}{3} \\doteq 66{,}\\overline{6}.",[724,17155,17156],{},"S využitím vlastnosti (4.8):",[120,17158,17159,17204,17246],{},[123,17160,17161,17162,17196,17197,17199,17200,17203],{},"Při cenách ",[883,17163,17165],{"className":17164},[886],[888,17166,17167],{"xmlns":890},[892,17168,17169,17193],{},[895,17170,17171,17173,17175,17177,17179,17181,17183,17185,17191],{},[898,17172,8194],{},[1656,17174,5915],{},[1656,17176,14093],{"stretchy":1658},[1667,17178,1669],{},[1656,17180,2856],{"separator":1672},[2461,17182,7828],{},[1667,17184,17141],{},[2033,17186,17187,17189],{"accent":1672},[1667,17188,9112],{},[1656,17190,17148],{"stretchy":1672},[1656,17192,1683],{"stretchy":1658},[902,17194,17195],{"encoding":904},"P \\in \\langle 1;\\, 66{,}\\overline{6})"," je poptávka ",[38,17198,12858],{}," — dle ",[614,17201,17202],{},"Pravidla 2"," přiměřené zvýšení ceny zvýší celkový příjem.",[123,17205,17161,17206,17196,17240,17199,17242,17245],{},[883,17207,17209],{"className":17208},[886],[888,17210,17211],{"xmlns":890},[892,17212,17213,17237],{},[895,17214,17215,17217,17219,17221,17223,17229,17231,17233,17235],{},[898,17216,8194],{},[1656,17218,5915],{},[1656,17220,1659],{"stretchy":1658},[1667,17222,17141],{},[2033,17224,17225,17227],{"accent":1672},[1667,17226,9112],{},[1656,17228,17148],{"stretchy":1672},[1656,17230,2856],{"separator":1672},[2461,17232,7828],{},[1667,17234,5267],{},[1656,17236,14110],{"stretchy":1658},[902,17238,17239],{"encoding":904},"P \\in (66{,}\\overline{6};\\, 100\\rangle",[38,17241,12854],{},[614,17243,17244],{},"Pravidla 1"," přiměřené snížení ceny povede ke zvýšení celkového příjmu.",[123,17247,17248,17249,17252,17253,17281,17282,17285],{},"Dle ",[614,17250,17251],{},"Pravidla 3"," je při ceně ",[883,17254,17256],{"className":17255},[886],[888,17257,17258],{"xmlns":890},[892,17259,17260,17278],{},[895,17261,17262,17268,17270,17272],{},[2062,17263,17264,17266],{},[898,17265,8194],{},[1656,17267,8187],{},[1656,17269,1713],{},[1667,17271,17141],{},[2033,17273,17274,17276],{"accent":1672},[1667,17275,9112],{},[1656,17277,17148],{"stretchy":1672},[902,17279,17280],{"encoding":904},"P^* = 66{,}\\overline{6}"," dosaženo ",[38,17283,17284],{},"maxima celkového příjmu"," ve výši",[724,17287,17288],{},[883,17289,17291],{"className":17290},[886],[888,17292,17293],{"xmlns":890},[892,17294,17295,17373],{},[895,17296,17297,17299,17301,17303,17309,17311,17313,17319,17321,17335,17337,17343,17345,17353,17355,17368,17370],{},[898,17298,11577],{},[898,17300,1763],{},[1656,17302,1659],{"stretchy":1658},[2062,17304,17305,17307],{},[898,17306,8194],{},[1656,17308,8187],{},[1656,17310,1683],{"stretchy":1658},[1656,17312,1713],{},[2062,17314,17315,17317],{},[898,17316,8194],{},[1656,17318,8187],{},[1656,17320,2751],{},[2625,17322,17323],{},[895,17324,17325,17327,17329],{},[1667,17326,5267],{},[1656,17328,3964],{},[2062,17330,17331,17333],{},[898,17332,8194],{},[1656,17334,8187],{},[1656,17336,1713],{},[3294,17338,17339,17341],{},[1667,17340,5272],{},[1667,17342,2617],{},[1656,17344,2751],{},[2625,17346,17347],{},[3294,17348,17349,17351],{},[1667,17350,5267],{},[1667,17352,2617],{},[1656,17354,1713],{},[3294,17356,17357,17360],{},[1667,17358,17359],{},"2000",[895,17361,17362,17364],{},[1667,17363,2617],{},[2625,17365,17366],{},[1667,17367,2617],{},[1656,17369,2829],{},[1667,17371,17372],{},"384,9.",[902,17374,17375],{"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.",[724,17377,17378,17379,1863],{},"Ke stejnému výsledku bychom dospěli přímým hledáním maxima funkce ",[883,17380,17382],{"className":17381},[886],[888,17383,17384],{"xmlns":890},[892,17385,17386,17392],{},[895,17387,17388,17390],{},[898,17389,11577],{},[898,17391,1763],{},[902,17393,12875],{"encoding":904},[115,17395,17397],{"id":17396},"cenová-elasticita-nabídky","Cenová elasticita nabídky",[724,17399,17400,17401,17404],{},"Analogicky se definuje ",[38,17402,17403],{},"cenová elasticita nabídky"," (price elasticity of supply):",[724,17406,17407],{},[883,17408,17410],{"className":17409,"title":12979,"style":12980},[12978],"\\boxed{\\;E = E(P) = \\frac{P}{Q}\\cdot\\frac{\\mathrm{d}Q}{\\mathrm{d}P}\\;} \\tag{4.13}",[724,17412,2355,17413,17437,17438,17470],{},[883,17414,17416],{"className":17415},[886],[888,17417,17418],{"xmlns":890},[892,17419,17420,17434],{},[895,17421,17422,17424,17426,17428,17430,17432],{},[898,17423,1665],{},[1656,17425,1713],{},[898,17427,1769],{},[1656,17429,1659],{"stretchy":1658},[898,17431,8194],{},[1656,17433,1683],{"stretchy":1658},[902,17435,17436],{"encoding":904},"Q = S(P)"," je funkce nabídky. Protože nabídka je rostoucí, ",[883,17439,17441],{"className":17440},[886],[888,17442,17443],{"xmlns":890},[892,17444,17445,17467],{},[895,17446,17447,17463,17465],{},[4138,17448,17449],{"scriptlevel":4032,"displaystyle":1672},[3294,17450,17451,17457],{},[895,17452,17453,17455],{},[898,17454,3768],{"mathvariant":1723},[898,17456,1665],{},[895,17458,17459,17461],{},[898,17460,3768],{"mathvariant":1723},[898,17462,8194],{},[1656,17464,2850],{},[1667,17466,4032],{},[902,17468,17469],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} > 0",", a elasticita nabídky je vždy nezáporná — proto zde není znaménková korekce jako u poptávky.",[724,17472,17473],{},"Klasifikace na elastickou \u002F jednotkově elastickou \u002F neelastickou je analogická jako u poptávky (tabulka (4.7)). Platí paralela k (4.8):",[1981,17475,17476],{},[724,17477,17478,17479],{},"S rostoucí cenou elasticita nabídky roste. ",[883,17480,17482],{"className":17481},[886],[888,17483,17484],{"xmlns":890},[892,17485,17486,17495],{},[895,17487,17488,17490,17493],{},[1656,17489,1659],{"stretchy":1658},[1667,17491,17492],{},"4.14",[1656,17494,1683],{"stretchy":1658},[902,17496,17497],{"encoding":904},"(4.14)",[724,17499,17500],{},"Pro nominální změny platí",[724,17502,17503],{},[883,17504,17506],{"className":17505,"title":12979,"style":12980},[12978],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P, \\qquad \\mathrm{d}P = \\Delta P, \\tag{4.15}",[724,17508,17509],{},"a pro procentní změny",[724,17511,17512],{},[883,17513,17515],{"className":17514,"title":12979,"style":12980},[12978],"\\boxed{\\;\\Delta Q\\% \\approx E(P)\\,\\Delta P\\%\\;} \\tag{4.16}",[724,17517,17518],{},"(bez znaménka minus).",[198,17520,17522],{"id":17521},"příklad-47","Příklad 4.7",[724,17524,17525,17526,2114],{},"Nabídka ",[883,17527,17529],{"className":17528},[886],[888,17530,17531],{"xmlns":890},[892,17532,17533,17558],{},[895,17534,17535,17537,17539,17541,17547,17549,17551,17553,17555],{},[898,17536,1665],{},[1656,17538,1713],{},[1667,17540,11595],{},[2062,17542,17543,17545],{},[898,17544,8194],{},[1667,17546,1680],{},[1656,17548,3633],{},[1667,17550,5193],{},[898,17552,8194],{},[1656,17554,3633],{},[1667,17556,17557],{},"150",[902,17559,17560],{"encoding":904},"Q = 0{,}1P^2 + 5P + 150",[724,17562,17563],{},[883,17564,17566],{"className":17565},[886],[888,17567,17568],{"xmlns":890},[892,17569,17570,17616],{},[895,17571,17572,17574,17576,17600,17602,17604,17606,17608,17610,17612,17614],{},[898,17573,1842],{},[1656,17575,1713],{},[3294,17577,17578,17580],{},[898,17579,8194],{},[895,17581,17582,17584,17590,17592,17594,17596,17598],{},[1667,17583,11595],{},[2062,17585,17586,17588],{},[898,17587,8194],{},[1667,17589,1680],{},[1656,17591,3633],{},[1667,17593,5193],{},[898,17595,8194],{},[1656,17597,3633],{},[1667,17599,17557],{},[2461,17601,7828],{},[1656,17603,1659],{"stretchy":1658},[1667,17605,11639],{},[898,17607,8194],{},[1656,17609,3633],{},[1667,17611,5193],{},[1656,17613,1683],{"stretchy":1658},[898,17615,1863],{"mathvariant":1723},[902,17617,17618],{"encoding":904},"E = \\frac{P}{0{,}1P^2 + 5P + 150}\\,(0{,}2P + 5).",[724,17620,13887,17621,1343,17651,1343,17678,17714,17715,17740,17741,17759,17760,1863],{},[883,17622,17624],{"className":17623},[886],[888,17625,17626],{"xmlns":890},[892,17627,17628,17648],{},[895,17629,17630,17632,17634,17636,17638,17640],{},[898,17631,1842],{},[1656,17633,1659],{"stretchy":1658},[1667,17635,8580],{},[1656,17637,1683],{"stretchy":1658},[1656,17639,1713],{},[4138,17641,17642],{"scriptlevel":4032,"displaystyle":1658},[3294,17643,17644,17646],{},[1667,17645,1669],{},[1667,17647,2617],{},[902,17649,17650],{"encoding":904},"E(10) = \\tfrac{1}{3}",[883,17652,17654],{"className":17653},[886],[888,17655,17656],{"xmlns":890},[892,17657,17658,17675],{},[895,17659,17660,17662,17664,17669,17671,17673],{},[898,17661,1842],{},[1656,17663,1659],{"stretchy":1658},[2625,17665,17666],{},[1667,17667,17668],{},"1500",[1656,17670,1683],{"stretchy":1658},[1656,17672,1713],{},[1667,17674,1669],{},[902,17676,17677],{"encoding":904},"E(\\sqrt{1500}) = 1",[883,17679,17681],{"className":17680},[886],[888,17682,17683],{"xmlns":890},[892,17684,17685,17711],{},[895,17686,17687,17689,17691,17693,17695,17697,17706,17708],{},[898,17688,1842],{},[1656,17690,1659],{"stretchy":1658},[1667,17692,5267],{},[1656,17694,1683],{"stretchy":1658},[1656,17696,1713],{},[4138,17698,17699],{"scriptlevel":4032,"displaystyle":1658},[3294,17700,17701,17703],{},[1667,17702,9267],{},[1667,17704,17705],{},"33",[1656,17707,2829],{},[1667,17709,17710],{},"1,515",[902,17712,17713],{"encoding":904},"E(100) = \\tfrac{50}{33} \\doteq 1{,}515",". Dle (4.14): pro ",[883,17716,17718],{"className":17717},[886],[888,17719,17720],{"xmlns":890},[892,17721,17722,17737],{},[895,17723,17724,17726,17728,17732,17734],{},[898,17725,8194],{},[1656,17727,2850],{},[2625,17729,17730],{},[1667,17731,17668],{},[1656,17733,3815],{},[1667,17735,17736],{},"38,7",[902,17738,17739],{"encoding":904},"P > \\sqrt{1500} \\approx 38{,}7"," je nabídka elastická, pro ",[883,17742,17744],{"className":17743},[886],[888,17745,17746],{"xmlns":890},[892,17747,17748,17756],{},[895,17749,17750,17752,17754],{},[898,17751,8194],{},[1656,17753,4373],{},[1667,17755,17736],{},[902,17757,17758],{"encoding":904},"P \u003C 38{,}7"," neelastická. Zvýší-li se cena z 10 o 20 %, pak ",[883,17761,17763],{"className":17762},[886],[888,17764,17765],{"xmlns":890},[892,17766,17767,17804],{},[895,17768,17769,17771,17773,17775,17777,17785,17787,17789,17791,17794,17800,17802],{},[898,17770,3750],{"mathvariant":1723},[898,17772,1665],{},[898,17774,14688],{"mathvariant":1723},[1656,17776,3815],{},[4138,17778,17779],{"scriptlevel":4032,"displaystyle":1658},[3294,17780,17781,17783],{},[1667,17782,1669],{},[1667,17784,2617],{},[1656,17786,2751],{},[1667,17788,9058],{},[1656,17790,1713],{},[1667,17792,17793],{},"6,",[2033,17795,17796,17798],{"accent":1672},[1667,17797,9112],{},[1656,17799,17148],{"stretchy":1672},[2461,17801,7828],{},[898,17803,14688],{"mathvariant":1723},[902,17805,17806],{"encoding":904},"\\Delta Q\\% \\approx \\tfrac{1}{3}\\cdot 20 = 6{,}\\overline{6}\\,\\%",[115,17808,17810],{"id":17809},"vícefaktorový-model","Vícefaktorový model",[724,17812,17813,17814,17827,17828,1643,17831,17844,17845,1643,17848,17866,17867,1643,17870,2114],{},"Předpokládejme, že poptávané množství ",[883,17815,17817],{"className":17816},[886],[888,17818,17819],{"xmlns":890},[892,17820,17821,17825],{},[895,17822,17823],{},[898,17824,1665],{},[902,17826,1665],{"encoding":904}," závisí na ",[38,17829,17830],{},"ceně základního zboží",[883,17832,17834],{"className":17833},[886],[888,17835,17836],{"xmlns":890},[892,17837,17838,17842],{},[895,17839,17840],{},[898,17841,8194],{},[902,17843,8194],{"encoding":904},", na ",[38,17846,17847],{},"ceně alternativního zboží",[883,17849,17851],{"className":17850},[886],[888,17852,17853],{"xmlns":890},[892,17854,17855,17863],{},[895,17856,17857],{},[1661,17858,17859,17861],{},[898,17860,8194],{},[898,17862,2146],{},[902,17864,17865],{"encoding":904},"P_A"," a na ",[38,17868,17869],{},"důchodu",[883,17871,17873],{"className":17872},[886],[888,17874,17875],{"xmlns":890},[892,17876,17877,17881],{},[895,17878,17879],{},[898,17880,8184],{},[902,17882,8184],{"encoding":904},[724,17884,17885],{},[883,17886,17888],{"className":17887,"title":12979,"style":12980},[12978],"Q = D(P, P_A, Y). \\tag{4.17}",[724,17890,17891,17892,17895],{},"V analogii jednofaktorového modelu pracujeme s ",[38,17893,17894],{},"parciálními derivacemi"," funkce poptávky.",[198,17897,17899],{"id":17898},"cenová-elasticita-poptávky-vícefaktorová","Cenová elasticita poptávky (vícefaktorová)",[724,17901,17902],{},[883,17903,17905],{"className":17904,"title":12979,"style":12980},[12978],"\\boxed{\\;E_P = -\\frac{P}{Q}\\,Q'_P\\;} \\tag{4.18}",[724,17907,2355,17908,17928,17929,17942,17943,2191,17965,1643,17967,18013,18014,18027,18028,18045],{},[883,17909,17911],{"className":17910},[886],[888,17912,17913],{"xmlns":890},[892,17914,17915,17925],{},[895,17916,17917],{},[1715,17918,17919,17921,17923],{},[898,17920,1665],{},[898,17922,8194],{},[1656,17924,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[902,17926,17927],{"encoding":904},"Q'_P"," je parciální derivace (4.17) podle ",[883,17930,17932],{"className":17931},[886],[888,17933,17934],{"xmlns":890},[892,17935,17936,17940],{},[895,17937,17938],{},[898,17939,8194],{},[902,17941,8194],{"encoding":904},". Vždy ",[883,17944,17946],{"className":17945},[886],[888,17947,17948],{"xmlns":890},[892,17949,17950,17962],{},[895,17951,17952,17958,17960],{},[1661,17953,17954,17956],{},[898,17955,1842],{},[898,17957,8194],{},[1656,17959,13258],{},[1667,17961,4032],{},[902,17963,17964],{"encoding":904},"E_P \\ge 0",[614,17966,5434],{},[883,17968,17970],{"className":17969},[886],[888,17971,17972],{"xmlns":890},[892,17973,17974,18010],{},[895,17975,17976,17982,17984,17990,17992,18000,18002,18008],{},[1661,17977,17978,17980],{},[898,17979,1842],{},[898,17981,8194],{},[1656,17983,1659],{"stretchy":1658},[2062,17985,17986,17988],{},[898,17987,8194],{},[1656,17989,8187],{},[1656,17991,1673],{"separator":1672},[1715,17993,17994,17996,17998],{},[898,17995,8194],{},[898,17997,2146],{},[1656,17999,8187],{},[1656,18001,1673],{"separator":1672},[2062,18003,18004,18006],{},[898,18005,8184],{},[1656,18007,8187],{},[1656,18009,1683],{"stretchy":1658},[902,18011,18012],{"encoding":904},"E_P(P^*, P_A^*, Y^*)"," udává přibližnou procentní změnu ",[883,18015,18017],{"className":18016},[886],[888,18018,18019],{"xmlns":890},[892,18020,18021,18025],{},[895,18022,18023],{},[898,18024,1665],{},[902,18026,1665],{"encoding":904}," při 1% změně ",[883,18029,18031],{"className":18030},[886],[888,18032,18033],{"xmlns":890},[892,18034,18035,18043],{},[895,18036,18037],{},[2062,18038,18039,18041],{},[898,18040,8194],{},[1656,18042,8187],{},[902,18044,13178],{"encoding":904},", ceteris paribus.",[198,18047,18049],{"id":18048},"křížová-křížově-cenová-elasticita-poptávky","Křížová (křížově-cenová) elasticita poptávky",[724,18051,18052],{},[883,18053,18055],{"className":18054,"title":12979,"style":12980},[12978],"\\boxed{\\;E_{P_A} = \\frac{P_A}{Q}\\,Q'_{P_A}\\;} \\tag{4.19}",[724,18057,18058,18013,18060,18073,18074,18091],{},[614,18059,5434],{},[883,18061,18063],{"className":18062},[886],[888,18064,18065],{"xmlns":890},[892,18066,18067,18071],{},[895,18068,18069],{},[898,18070,1665],{},[902,18072,1665],{"encoding":904}," základního zboží při 1% změně ceny ",[883,18075,18077],{"className":18076},[886],[888,18078,18079],{"xmlns":890},[892,18080,18081,18089],{},[895,18082,18083],{},[1661,18084,18085,18087],{},[898,18086,8194],{},[898,18088,2146],{},[902,18090,17865],{"encoding":904}," alternativního zboží (ceteris paribus).",[724,18093,18094],{},[38,18095,18096],{},"Znaménko závisí na povaze alternativního zboží:",[120,18098,18099,18187],{},[123,18100,18101,18102,18105,18106,18123,18124,1643,18137,1863],{},"Je-li alternativní zboží ",[38,18103,18104],{},"komplement",", růst ",[883,18107,18109],{"className":18108},[886],[888,18110,18111],{"xmlns":890},[892,18112,18113,18121],{},[895,18114,18115],{},[1661,18116,18117,18119],{},[898,18118,8194],{},[898,18120,2146],{},[902,18122,17865],{"encoding":904}," způsobí zdražení dvojice, pokles ",[883,18125,18127],{"className":18126},[886],[888,18128,18129],{"xmlns":890},[892,18130,18131,18135],{},[895,18132,18133],{},[898,18134,1665],{},[902,18136,1665],{"encoding":904},[883,18138,18140],{"className":18139},[886],[888,18141,18142],{"xmlns":890},[892,18143,18144,18184],{},[895,18145,18146,18148,18150,18162,18164,18166,18168,18170,18180,18182],{},[1656,18147,12770],{},[2461,18149,12767],{},[1715,18151,18152,18154,18160],{},[898,18153,1665],{},[1661,18155,18156,18158],{},[898,18157,8194],{},[898,18159,2146],{},[1656,18161,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,18163,4373],{},[1667,18165,4032],{},[1656,18167,1673],{"separator":1672},[2461,18169,12767],{},[1661,18171,18172,18174],{},[898,18173,1842],{},[1661,18175,18176,18178],{},[898,18177,8194],{},[898,18179,2146],{},[1656,18181,4373],{},[1667,18183,4032],{},[902,18185,18186],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} \u003C 0,\\; E_{P_A} \u003C 0",[123,18188,18101,18189,18105,18192,18209,18210,18223,18224,1863],{},[38,18190,18191],{},"substitut",[883,18193,18195],{"className":18194},[886],[888,18196,18197],{"xmlns":890},[892,18198,18199,18207],{},[895,18200,18201],{},[1661,18202,18203,18205],{},[898,18204,8194],{},[898,18206,2146],{},[902,18208,17865],{"encoding":904}," učiní základní zboží relativně levnější, zájem se přesune, ",[883,18211,18213],{"className":18212},[886],[888,18214,18215],{"xmlns":890},[892,18216,18217,18221],{},[895,18218,18219],{},[898,18220,1665],{},[902,18222,1665],{"encoding":904}," roste ",[883,18225,18227],{"className":18226},[886],[888,18228,18229],{"xmlns":890},[892,18230,18231,18271],{},[895,18232,18233,18235,18237,18249,18251,18253,18255,18257,18267,18269],{},[1656,18234,12770],{},[2461,18236,12767],{},[1715,18238,18239,18241,18247],{},[898,18240,1665],{},[1661,18242,18243,18245],{},[898,18244,8194],{},[898,18246,2146],{},[1656,18248,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,18250,2850],{},[1667,18252,4032],{},[1656,18254,1673],{"separator":1672},[2461,18256,12767],{},[1661,18258,18259,18261],{},[898,18260,1842],{},[1661,18262,18263,18265],{},[898,18264,8194],{},[898,18266,2146],{},[1656,18268,2850],{},[1667,18270,4032],{},[902,18272,18273],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} > 0,\\; E_{P_A} > 0",[883,18275,18278],{"className":18276,"title":18277,"style":12980},[12978],"ParseError: KaTeX parse error: Expected 'EOF', got '&' at position 9: E_{P_A} &̲> 0 \\;\\;\\Leftri…","undefined",{"title":641,"searchDepth":642,"depth":642,"links":18280},[18281,18285,18286,18294,18295,18299,18302],{"id":12674,"depth":642,"text":12675,"children":18282},[18283,18284],{"id":12705,"depth":649,"text":12706},{"id":12883,"depth":649,"text":12884},{"id":12918,"depth":642,"text":12919},{"id":12943,"depth":642,"text":12944,"children":18287},[18288,18289,18290,18291,18293],{"id":13630,"depth":649,"text":13631},{"id":13720,"depth":649,"text":13721},{"id":14054,"depth":649,"text":14055},{"id":14136,"depth":649,"text":18292},"Výpočet, je-li dáno PP jako funkce QQ",{"id":14393,"depth":649,"text":14394},{"id":14716,"depth":642,"text":14717},{"id":15310,"depth":642,"text":15311,"children":18296},[18297,18298],{"id":15938,"depth":649,"text":15939},{"id":16767,"depth":649,"text":16768},{"id":17396,"depth":642,"text":17397,"children":18300},[18301],{"id":17521,"depth":649,"text":17522},{"id":17809,"depth":642,"text":17810,"children":18303},[18304,18305],{"id":17898,"depth":649,"text":17899},{"id":18048,"depth":649,"text":18049},{},"\u002Ftopics\u002Felasticita",{"title":12645,"description":641},[1138,1136],"topics\u002Felasticita",[1128,12681,18312,18313,18314,18315],"cenova-elasticita","krizova-elasticita","duchodova-elasticita","mr-tr","c_Ilj6dK9Ey4kbyp6EKogVl_p8zmryyIur0pCOtxlhM",{"id":18318,"title":18319,"body":18320,"course":1128,"courses":659,"created":1129,"description":19850,"extension":661,"meta":19851,"navigation":664,"path":19852,"seo":19853,"sources":19854,"stem":19855,"tags":19856,"type":10786,"updated":677,"__hash__":19860},"topics\u002Ftopics\u002Ffunkce-vice-promennych.md","Kalkul funkcí více proměnných",{"type":9,"value":18321,"toc":19835},[18322,18325,18398,18405,18409,18473,18558,18562,18589,18655,18710,18714,18741,18833,18835,18867,19037,19041,19111,19159,19163,19224,19330,19344,19348,19350,19378,19443,19445,19452,19540,19564,19762,19766,19802,19804],[12,18323,18319],{"id":18324},"kalkul-funkcí-více-proměnných",[724,18326,18327,18328,18331,18332,1343,18361,1863],{},"Většina ekonomických veličin závisí na ",[38,18329,18330],{},"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 ",[883,18333,18335],{"className":18334},[886],[888,18336,18337],{"xmlns":890},[892,18338,18339,18358],{},[895,18340,18341,18344,18346,18348,18350,18352,18354,18356],{},[898,18342,18343],{},"z",[1656,18345,1713],{},[898,18347,7524],{},[1656,18349,1659],{"stretchy":1658},[898,18351,10848],{},[1656,18353,1673],{"separator":1672},[898,18355,10839],{},[1656,18357,1683],{"stretchy":1658},[902,18359,18360],{"encoding":904},"z = f(x, y)",[883,18362,18364],{"className":18363},[886],[888,18365,18366],{"xmlns":890},[892,18367,18368,18395],{},[895,18369,18370,18373,18375,18377,18379,18381,18383,18385,18387,18389,18391,18393],{},[898,18371,18372],{},"w",[1656,18374,1713],{},[898,18376,7524],{},[1656,18378,1659],{"stretchy":1658},[898,18380,10848],{},[1656,18382,1673],{"separator":1672},[898,18384,10839],{},[1656,18386,1673],{"separator":1672},[898,18388,18343],{},[1656,18390,1683],{"stretchy":1658},[1656,18392,1673],{"separator":1672},[1656,18394,2337],{},[902,18396,18397],{"encoding":904},"w = f(x, y, z), \\ldots",[724,18399,18400],{},[5956,18401],{"alt":18402,"className":18403,"src":18404},"imek-funkce-2d-vrstevnice",[210,5960],"\u002Fwiki-assets\u002Fimek-funkce-2d-vrstevnice.jpeg",[115,18406,18408],{"id":18407},"indiferenční-izokvantové-křivky","Indiferenční \u002F izokvantové křivky",[724,18410,18411,18412,18439,18440,18468,18469,18472],{},"Pro ",[883,18413,18415],{"className":18414},[886],[888,18416,18417],{"xmlns":890},[892,18418,18419,18437],{},[895,18420,18421,18423,18425,18427,18429,18431,18433,18435],{},[898,18422,18343],{},[1656,18424,1713],{},[898,18426,7524],{},[1656,18428,1659],{"stretchy":1658},[898,18430,10848],{},[1656,18432,1673],{"separator":1672},[898,18434,10839],{},[1656,18436,1683],{"stretchy":1658},[902,18438,18360],{"encoding":904}," se křivkou s předpisem ",[883,18441,18443],{"className":18442},[886],[888,18444,18445],{"xmlns":890},[892,18446,18447,18465],{},[895,18448,18449,18451,18453,18455,18457,18459,18461,18463],{},[898,18450,7524],{},[1656,18452,1659],{"stretchy":1658},[898,18454,10848],{},[1656,18456,1673],{"separator":1672},[898,18458,10839],{},[1656,18460,1683],{"stretchy":1658},[1656,18462,1713],{},[898,18464,1745],{},[902,18466,18467],{"encoding":904},"f(x, y) = c"," (konstanta) rozumí ",[38,18470,18471],{},"vrstevnice"," funkce. V ekonomii:",[120,18474,18475,18518],{},[123,18476,18477,18479,18480,10632,18515,1863],{},[38,18478,8714],{}," užitečnosti ",[883,18481,18483],{"className":18482},[886],[888,18484,18485],{"xmlns":890},[892,18486,18487,18513],{},[895,18488,18489,18491,18493,18499,18501,18507,18509,18511],{},[898,18490,900],{},[1656,18492,1659],{"stretchy":1658},[1661,18494,18495,18497],{},[898,18496,1665],{},[1667,18498,1669],{},[1656,18500,1673],{"separator":1672},[1661,18502,18503,18505],{},[898,18504,1665],{},[1667,18506,1680],{},[1656,18508,1683],{"stretchy":1658},[1656,18510,1713],{},[898,18512,1745],{},[902,18514,4870],{"encoding":904},[207,18516,10781],{"className":18517,"dataFsResolvedFilePath":878,"href":879},[210],[123,18519,18520,18523,18524,10632,18554,1863],{},[38,18521,18522],{},"Izokvanty"," produkce ",[883,18525,18527],{"className":18526},[886],[888,18528,18529],{"xmlns":890},[892,18530,18531,18551],{},[895,18532,18533,18535,18537,18540,18542,18545,18547,18549],{},[898,18534,1665],{},[1656,18536,1659],{"stretchy":1658},[898,18538,18539],{},"L",[1656,18541,1673],{"separator":1672},[898,18543,18544],{},"K",[1656,18546,1683],{"stretchy":1658},[1656,18548,1713],{},[898,18550,1745],{},[902,18552,18553],{"encoding":904},"Q(L, K) = c",[207,18555,18557],{"className":18556,"dataFsResolvedFilePath":857,"href":858},[210],"produkce",[115,18559,18561],{"id":18560},"parciální-derivace","Parciální derivace",[724,18563,18411,18564,18588],{},[883,18565,18567],{"className":18566},[886],[888,18568,18569],{"xmlns":890},[892,18570,18571,18585],{},[895,18572,18573,18575,18577,18579,18581,18583],{},[898,18574,7524],{},[1656,18576,1659],{"stretchy":1658},[898,18578,10848],{},[1656,18580,1673],{"separator":1672},[898,18582,10839],{},[1656,18584,1683],{"stretchy":1658},[902,18586,18587],{"encoding":904},"f(x, y)"," derivujeme jako kdyby druhá proměnná byla konstanta:",[724,18590,18591],{},[883,18592,18594],{"className":18593},[886],[888,18595,18596],{"xmlns":890},[892,18597,18598,18652],{},[895,18599,18600,18608,18610,18624,18626,18628,18636,18638],{},[1715,18601,18602,18604,18606],{},[898,18603,7524],{},[898,18605,10848],{},[1656,18607,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,18609,1713],{},[3294,18611,18612,18618],{},[895,18613,18614,18616],{},[898,18615,3300],{"mathvariant":1723},[898,18617,7524],{},[895,18619,18620,18622],{},[898,18621,3300],{"mathvariant":1723},[898,18623,10848],{},[1656,18625,1673],{"separator":1672},[3316,18627],{"width":14644},[1715,18629,18630,18632,18634],{},[898,18631,7524],{},[898,18633,10839],{},[1656,18635,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,18637,1713],{},[3294,18639,18640,18646],{},[895,18641,18642,18644],{},[898,18643,3300],{"mathvariant":1723},[898,18645,7524],{},[895,18647,18648,18650],{},[898,18649,3300],{"mathvariant":1723},[898,18651,10839],{},[902,18653,18654],{"encoding":904},"f'_x = \\frac{\\partial f}{\\partial x}, \\qquad f'_y = \\frac{\\partial f}{\\partial y}",[724,18656,18657,18658,1863],{},"Hodnoty v bodě: ",[883,18659,18661],{"className":18660},[886],[888,18662,18663],{"xmlns":890},[892,18664,18665,18707],{},[895,18666,18667,18675,18677,18679,18681,18683,18685,18687,18689,18697,18699,18701,18703,18705],{},[1715,18668,18669,18671,18673],{},[898,18670,7524],{},[898,18672,10848],{},[1656,18674,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,18676,1659],{"stretchy":1658},[898,18678,207],{},[1656,18680,1673],{"separator":1672},[898,18682,3403],{},[1656,18684,1683],{"stretchy":1658},[1656,18686,1673],{"separator":1672},[2461,18688,11112],{},[1715,18690,18691,18693,18695],{},[898,18692,7524],{},[898,18694,10839],{},[1656,18696,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,18698,1659],{"stretchy":1658},[898,18700,207],{},[1656,18702,1673],{"separator":1672},[898,18704,3403],{},[1656,18706,1683],{"stretchy":1658},[902,18708,18709],{"encoding":904},"f'_x(a, b),\\ f'_y(a, b)",[198,18711,18713],{"id":18712},"ekonomické-značení","Ekonomické značení",[724,18715,18716,18717,2114],{},"Pro produkční funkci ",[883,18718,18720],{"className":18719},[886],[888,18721,18722],{"xmlns":890},[892,18723,18724,18738],{},[895,18725,18726,18728,18730,18732,18734,18736],{},[898,18727,1665],{},[1656,18729,1659],{"stretchy":1658},[898,18731,18539],{},[1656,18733,1673],{"separator":1672},[898,18735,18544],{},[1656,18737,1683],{"stretchy":1658},[902,18739,18740],{"encoding":904},"Q(L, K)",[120,18742,18743,18788],{},[123,18744,18745,11284,18765,3247,18768,1683],{},[883,18746,18748],{"className":18747},[886],[888,18749,18750],{"xmlns":890},[892,18751,18752,18762],{},[895,18753,18754],{},[1715,18755,18756,18758,18760],{},[898,18757,1665],{},[898,18759,18539],{},[1656,18761,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[902,18763,18764],{"encoding":904},"Q'_L",[38,18766,18767],{},"mezní produkt práce",[883,18769,18771],{"className":18770},[886],[888,18772,18773],{"xmlns":890},[892,18774,18775,18785],{},[895,18776,18777,18779],{},[898,18778,1703],{},[1661,18780,18781,18783],{},[898,18782,8194],{},[898,18784,18539],{},[902,18786,18787],{"encoding":904},"MP_L",[123,18789,18790,11284,18810,3247,18813,1683],{},[883,18791,18793],{"className":18792},[886],[888,18794,18795],{"xmlns":890},[892,18796,18797,18807],{},[895,18798,18799],{},[1715,18800,18801,18803,18805],{},[898,18802,1665],{},[898,18804,18544],{},[1656,18806,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[902,18808,18809],{"encoding":904},"Q'_K",[38,18811,18812],{},"mezní produkt kapitálu",[883,18814,18816],{"className":18815},[886],[888,18817,18818],{"xmlns":890},[892,18819,18820,18830],{},[895,18821,18822,18824],{},[898,18823,1703],{},[1661,18825,18826,18828],{},[898,18827,8194],{},[898,18829,18544],{},[902,18831,18832],{"encoding":904},"MP_K",[198,18834,11378],{"id":11377},[724,18836,18837,2114],{},[883,18838,18840],{"className":18839},[886],[888,18841,18842],{"xmlns":890},[892,18843,18844,18864],{},[895,18845,18846,18854,18856,18858,18860,18862],{},[1715,18847,18848,18850,18852],{},[898,18849,7524],{},[898,18851,10848],{},[1656,18853,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,18855,1659],{"stretchy":1658},[898,18857,207],{},[1656,18859,1673],{"separator":1672},[898,18861,3403],{},[1656,18863,1683],{"stretchy":1658},[902,18865,18866],{"encoding":904},"f'_x(a, b)",[120,18868,18869,18926],{},[123,18870,18871,18872,18885,18886,8167,18899,18925],{},"rychlost změny ",[883,18873,18875],{"className":18874},[886],[888,18876,18877],{"xmlns":890},[892,18878,18879,18883],{},[895,18880,18881],{},[898,18882,7524],{},[902,18884,7524],{"encoding":904}," vůči ",[883,18887,18889],{"className":18888},[886],[888,18890,18891],{"xmlns":890},[892,18892,18893,18897],{},[895,18894,18895],{},[898,18896,10848],{},[902,18898,10848],{"encoding":904},[883,18900,18902],{"className":18901},[886],[888,18903,18904],{"xmlns":890},[892,18905,18906,18922],{},[895,18907,18908,18910,18912,18914,18916,18918,18920],{},[898,18909,10848],{},[1656,18911,1713],{},[898,18913,207],{},[1656,18915,1673],{"separator":1672},[898,18917,10839],{},[1656,18919,1713],{},[898,18921,3403],{},[902,18923,18924],{"encoding":904},"x = a, y = b"," (kapitál fixní),",[123,18927,18928,18929,11465,18942,18955,18956,18974,18975,1863],{},"přibližná změna ",[883,18930,18932],{"className":18931},[886],[888,18933,18934],{"xmlns":890},[892,18935,18936,18940],{},[895,18937,18938],{},[898,18939,7524],{},[902,18941,7524],{"encoding":904},[883,18943,18945],{"className":18944},[886],[888,18946,18947],{"xmlns":890},[892,18948,18949,18953],{},[895,18950,18951],{},[898,18952,10848],{},[902,18954,10848],{"encoding":904}," o 1 (a pevném ",[883,18957,18959],{"className":18958},[886],[888,18960,18961],{"xmlns":890},[892,18962,18963,18971],{},[895,18964,18965,18967,18969],{},[898,18966,10839],{},[1656,18968,1713],{},[898,18970,3403],{},[902,18972,18973],{"encoding":904},"y = b","): ",[883,18976,18978],{"className":18977},[886],[888,18979,18980],{"xmlns":890},[892,18981,18982,19034],{},[895,18983,18984,18986,18988,18990,18992,18994,18996,18998,19000,19002,19004,19006,19008,19010,19012,19014,19016,19024,19026,19028,19030,19032],{},[898,18985,7524],{},[1656,18987,1659],{"stretchy":1658},[898,18989,207],{},[1656,18991,3633],{},[1667,18993,1669],{},[1656,18995,1673],{"separator":1672},[898,18997,3403],{},[1656,18999,1683],{"stretchy":1658},[1656,19001,3815],{},[898,19003,7524],{},[1656,19005,1659],{"stretchy":1658},[898,19007,207],{},[1656,19009,1673],{"separator":1672},[898,19011,3403],{},[1656,19013,1683],{"stretchy":1658},[1656,19015,3633],{},[1715,19017,19018,19020,19022],{},[898,19019,7524],{},[898,19021,10848],{},[1656,19023,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,19025,1659],{"stretchy":1658},[898,19027,207],{},[1656,19029,1673],{"separator":1672},[898,19031,3403],{},[1656,19033,1683],{"stretchy":1658},[902,19035,19036],{"encoding":904},"f(a+1, b) \\approx f(a, b) + f'_x(a, b)",[115,19038,19040],{"id":19039},"diferenciál-funkce-dvou-proměnných","Diferenciál funkce dvou proměnných",[724,19042,19043],{},[883,19044,19046],{"className":19045},[886],[888,19047,19048],{"xmlns":890},[892,19049,19050,19108],{},[895,19051,19052,19054,19056,19058,19066,19068,19070,19072,19074,19076,19078,19080,19082,19084,19092,19094,19096,19098,19100,19102,19104,19106],{},[898,19053,3768],{},[898,19055,7524],{},[1656,19057,1713],{},[1715,19059,19060,19062,19064],{},[898,19061,7524],{},[898,19063,10848],{},[1656,19065,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,19067,1659],{"stretchy":1658},[898,19069,10848],{},[1656,19071,1673],{"separator":1672},[898,19073,10839],{},[1656,19075,1683],{"stretchy":1658},[2461,19077,7828],{},[898,19079,3768],{},[898,19081,10848],{},[1656,19083,3633],{},[1715,19085,19086,19088,19090],{},[898,19087,7524],{},[898,19089,10839],{},[1656,19091,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,19093,1659],{"stretchy":1658},[898,19095,10848],{},[1656,19097,1673],{"separator":1672},[898,19099,10839],{},[1656,19101,1683],{"stretchy":1658},[2461,19103,7828],{},[898,19105,3768],{},[898,19107,10839],{},[902,19109,19110],{"encoding":904},"df = f'_x(x, y)\\, dx + f'_y(x, y)\\, dy",[724,19112,11791,19113,19135,19136,19158],{},[883,19114,19116],{"className":19115},[886],[888,19117,19118],{"xmlns":890},[892,19119,19120,19132],{},[895,19121,19122,19124,19126,19128,19130],{},[898,19123,3768],{},[898,19125,10848],{},[1656,19127,1673],{"separator":1672},[898,19129,3768],{},[898,19131,10839],{},[902,19133,19134],{"encoding":904},"dx, dy"," platí ",[883,19137,19139],{"className":19138},[886],[888,19140,19141],{"xmlns":890},[892,19142,19143,19155],{},[895,19144,19145,19147,19149,19151,19153],{},[898,19146,3750],{"mathvariant":1723},[898,19148,7524],{},[1656,19150,3815],{},[898,19152,3768],{},[898,19154,7524],{},[902,19156,19157],{"encoding":904},"\\Delta f \\approx df",". Linearizace přírůstku ve dvou směrech současně.",[115,19160,19162],{"id":19161},"implicitní-funkce","Implicitní funkce",[724,19164,19165,19166,19195,19196,19209,19210,19223],{},"Je-li vztah dán rovnicí ",[883,19167,19169],{"className":19168},[886],[888,19170,19171],{"xmlns":890},[892,19172,19173,19192],{},[895,19174,19175,19178,19180,19182,19184,19186,19188,19190],{},[898,19176,19177],{},"F",[1656,19179,1659],{"stretchy":1658},[898,19181,10848],{},[1656,19183,1673],{"separator":1672},[898,19185,10839],{},[1656,19187,1683],{"stretchy":1658},[1656,19189,1713],{},[1667,19191,4032],{},[902,19193,19194],{"encoding":904},"F(x, y) = 0"," a chceme derivaci ",[883,19197,19199],{"className":19198},[886],[888,19200,19201],{"xmlns":890},[892,19202,19203,19207],{},[895,19204,19205],{},[898,19206,10839],{},[902,19208,10839],{"encoding":904}," podle ",[883,19211,19213],{"className":19212},[886],[888,19214,19215],{"xmlns":890},[892,19216,19217,19221],{},[895,19218,19219],{},[898,19220,10848],{},[902,19222,10848],{"encoding":904}," (nebo naopak):",[724,19225,19226],{},[883,19227,19229],{"className":19228},[886],[888,19230,19231],{"xmlns":890},[892,19232,19233,19327],{},[895,19234,19235,19241,19243,19257,19259,19261,19279,19281,19283,19289,19291,19305,19307,19309],{},[2062,19236,19237,19239],{},[898,19238,10839],{},[1656,19240,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,19242,1713],{},[3294,19244,19245,19251],{},[895,19246,19247,19249],{},[898,19248,3768],{},[898,19250,10839],{},[895,19252,19253,19255],{},[898,19254,3768],{},[898,19256,10848],{},[1656,19258,1713],{},[1656,19260,3964],{},[3294,19262,19263,19271],{},[1715,19264,19265,19267,19269],{},[898,19266,19177],{},[898,19268,10848],{},[1656,19270,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1715,19272,19273,19275,19277],{},[898,19274,19177],{},[898,19276,10839],{},[1656,19278,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,19280,1673],{"separator":1672},[3316,19282],{"width":14644},[2062,19284,19285,19287],{},[898,19286,10848],{},[1656,19288,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,19290,1713],{},[3294,19292,19293,19299],{},[895,19294,19295,19297],{},[898,19296,3768],{},[898,19298,10848],{},[895,19300,19301,19303],{},[898,19302,3768],{},[898,19304,10839],{},[1656,19306,1713],{},[1656,19308,3964],{},[3294,19310,19311,19319],{},[1715,19312,19313,19315,19317],{},[898,19314,19177],{},[898,19316,10839],{},[1656,19318,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1715,19320,19321,19323,19325],{},[898,19322,19177],{},[898,19324,10848],{},[1656,19326,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[902,19328,19329],{"encoding":904},"y' = \\frac{dy}{dx} = -\\frac{F'_x}{F'_y}, \\qquad x' = \\frac{dx}{dy} = -\\frac{F'_y}{F'_x}",[724,19331,19332,19333,19336,19337,1896,19341,1863],{},"Tato vzorec dává ",[38,19334,19335],{},"sklon vrstevnice"," — používá se mj. pro výpočet ",[207,19338,19340],{"className":19339,"dataFsResolvedFilePath":857,"href":858},[210],"MRTS",[207,19342,7362],{"className":19343,"dataFsResolvedFilePath":878,"href":879},[210],[115,19345,19347],{"id":19346},"volné-extrémy-funkce-dvou-proměnných","Volné extrémy funkce dvou proměnných",[198,19349,12042],{"id":12041},[724,19351,19352,19353,19377],{},"V bodě extrému ",[883,19354,19356],{"className":19355},[886],[888,19357,19358],{"xmlns":890},[892,19359,19360,19374],{},[895,19361,19362,19364,19366,19368,19370,19372],{},[898,19363,2146],{},[1656,19365,3453],{"stretchy":1658},[898,19367,207],{},[1656,19369,1673],{"separator":1672},[898,19371,3403],{},[1656,19373,3462],{"stretchy":1658},[902,19375,19376],{"encoding":904},"A[a, b]"," musí platit současně:",[724,19379,19380],{},[883,19381,19383],{"className":19382},[886],[888,19384,19385],{"xmlns":890},[892,19386,19387,19440],{},[895,19388,19389,19397,19399,19401,19403,19405,19407,19409,19411,19413,19416,19418,19426,19428,19430,19432,19434,19436,19438],{},[1715,19390,19391,19393,19395],{},[898,19392,7524],{},[898,19394,10848],{},[1656,19396,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,19398,1659],{"stretchy":1658},[898,19400,207],{},[1656,19402,1673],{"separator":1672},[898,19404,3403],{},[1656,19406,1683],{"stretchy":1658},[1656,19408,1713],{},[1667,19410,4032],{},[2461,19412,12767],{},[1656,19414,19415],{},"∧",[2461,19417,12767],{},[1715,19419,19420,19422,19424],{},[898,19421,7524],{},[898,19423,10839],{},[1656,19425,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,19427,1659],{"stretchy":1658},[898,19429,207],{},[1656,19431,1673],{"separator":1672},[898,19433,3403],{},[1656,19435,1683],{"stretchy":1658},[1656,19437,1713],{},[1667,19439,4032],{},[902,19441,19442],{"encoding":904},"f'_x(a, b) = 0 \\;\\wedge\\; f'_y(a, b) = 0",[198,19444,12116],{"id":12115},[724,19446,19447,19448,19451],{},"Definujeme ",[38,19449,19450],{},"diskriminant"," (Hessián zjednodušeně):",[724,19453,19454],{},[883,19455,19457],{"className":19456},[886],[888,19458,19459],{"xmlns":890},[892,19460,19461,19537],{},[895,19462,19463,19465,19467,19469,19471,19473,19475,19477,19493,19495,19511,19513,19515,19531],{},[898,19464,6787],{},[1656,19466,1659],{"stretchy":1658},[898,19468,10848],{},[1656,19470,1673],{"separator":1672},[898,19472,10839],{},[1656,19474,1683],{"stretchy":1658},[1656,19476,1713],{},[1715,19478,19479,19481,19487],{},[898,19480,7524],{},[895,19482,19483,19485],{},[898,19484,10848],{},[898,19486,10848],{},[895,19488,19489,19491],{},[1656,19490,1725],{"mathvariant":1723},[1656,19492,1725],{"mathvariant":1723},[1656,19494,2751],{},[1715,19496,19497,19499,19505],{},[898,19498,7524],{},[895,19500,19501,19503],{},[898,19502,10839],{},[898,19504,10839],{},[895,19506,19507,19509],{},[1656,19508,1725],{"mathvariant":1723},[1656,19510,1725],{"mathvariant":1723},[1656,19512,3964],{},[1656,19514,1659],{"stretchy":1658},[1715,19516,19517,19519,19525],{},[898,19518,7524],{},[895,19520,19521,19523],{},[898,19522,10848],{},[898,19524,10839],{},[895,19526,19527,19529],{},[1656,19528,1725],{"mathvariant":1723},[1656,19530,1725],{"mathvariant":1723},[2062,19532,19533,19535],{},[1656,19534,1683],{"stretchy":1658},[1667,19536,1680],{},[902,19538,19539],{"encoding":904},"D(x, y) = f''_{xx} \\cdot f''_{yy} - (f''_{xy})^2",[724,19541,19542,19543,2114],{},"V podezřelém bodě ",[883,19544,19546],{"className":19545},[886],[888,19547,19548],{"xmlns":890},[892,19549,19550,19562],{},[895,19551,19552,19554,19556,19558,19560],{},[1656,19553,3453],{"stretchy":1658},[898,19555,207],{},[1656,19557,1673],{"separator":1672},[898,19559,3403],{},[1656,19561,3462],{"stretchy":1658},[902,19563,3465],{"encoding":904},[152,19565,19566,19693,19729],{},[123,19567,19568,19598,19599],{},[38,19569,19570,2114],{},[883,19571,19573],{"className":19572},[886],[888,19574,19575],{"xmlns":890},[892,19576,19577,19595],{},[895,19578,19579,19581,19583,19585,19587,19589,19591,19593],{},[898,19580,6787],{},[1656,19582,1659],{"stretchy":1658},[898,19584,207],{},[1656,19586,1673],{"separator":1672},[898,19588,3403],{},[1656,19590,1683],{"stretchy":1658},[1656,19592,2850],{},[1667,19594,4032],{},[902,19596,19597],{"encoding":904},"D(a, b) > 0"," je to extrém.\n",[120,19600,19601,19647],{},[123,19602,19603,12203,19645],{},[883,19604,19606],{"className":19605},[886],[888,19607,19608],{"xmlns":890},[892,19609,19610,19642],{},[895,19611,19612,19628,19630,19632,19634,19636,19638,19640],{},[1715,19613,19614,19616,19622],{},[898,19615,7524],{},[895,19617,19618,19620],{},[898,19619,10848],{},[898,19621,10848],{},[895,19623,19624,19626],{},[1656,19625,1725],{"mathvariant":1723},[1656,19627,1725],{"mathvariant":1723},[1656,19629,1659],{"stretchy":1658},[898,19631,207],{},[1656,19633,1673],{"separator":1672},[898,19635,3403],{},[1656,19637,1683],{"stretchy":1658},[1656,19639,2850],{},[1667,19641,4032],{},[902,19643,19644],{"encoding":904},"f''_{xx}(a, b) > 0",[38,19646,12562],{},[123,19648,19649,12203,19691],{},[883,19650,19652],{"className":19651},[886],[888,19653,19654],{"xmlns":890},[892,19655,19656,19688],{},[895,19657,19658,19674,19676,19678,19680,19682,19684,19686],{},[1715,19659,19660,19662,19668],{},[898,19661,7524],{},[895,19663,19664,19666],{},[898,19665,10848],{},[898,19667,10848],{},[895,19669,19670,19672],{},[1656,19671,1725],{"mathvariant":1723},[1656,19673,1725],{"mathvariant":1723},[1656,19675,1659],{"stretchy":1658},[898,19677,207],{},[1656,19679,1673],{"separator":1672},[898,19681,3403],{},[1656,19683,1683],{"stretchy":1658},[1656,19685,4373],{},[1667,19687,4032],{},[902,19689,19690],{"encoding":904},"f''_{xx}(a, b) \u003C 0",[38,19692,12504],{},[123,19694,19695,1643,19725,19728],{},[38,19696,19697,2114],{},[883,19698,19700],{"className":19699},[886],[888,19701,19702],{"xmlns":890},[892,19703,19704,19722],{},[895,19705,19706,19708,19710,19712,19714,19716,19718,19720],{},[898,19707,6787],{},[1656,19709,1659],{"stretchy":1658},[898,19711,207],{},[1656,19713,1673],{"separator":1672},[898,19715,3403],{},[1656,19717,1683],{"stretchy":1658},[1656,19719,4373],{},[1667,19721,4032],{},[902,19723,19724],{"encoding":904},"D(a, b) \u003C 0",[38,19726,19727],{},"sedlo"," (v daném bodě extrém není).",[123,19730,19731,19761],{},[38,19732,19733,2114],{},[883,19734,19736],{"className":19735},[886],[888,19737,19738],{"xmlns":890},[892,19739,19740,19758],{},[895,19741,19742,19744,19746,19748,19750,19752,19754,19756],{},[898,19743,6787],{},[1656,19745,1659],{"stretchy":1658},[898,19747,207],{},[1656,19749,1673],{"separator":1672},[898,19751,3403],{},[1656,19753,1683],{"stretchy":1658},[1656,19755,1713],{},[1667,19757,4032],{},[902,19759,19760],{"encoding":904},"D(a, b) = 0"," podmínka nerozhoduje.",[115,19763,19765],{"id":19764},"vázané-extrémy","Vázané extrémy",[724,19767,19768,19769,19798,19799,1863],{},"Pro extrémy s omezující podmínkou ",[883,19770,19772],{"className":19771},[886],[888,19773,19774],{"xmlns":890},[892,19775,19776,19795],{},[895,19777,19778,19781,19783,19785,19787,19789,19791,19793],{},[898,19779,19780],{},"g",[1656,19782,1659],{"stretchy":1658},[898,19784,10848],{},[1656,19786,1673],{"separator":1672},[898,19788,10839],{},[1656,19790,1683],{"stretchy":1658},[1656,19792,1713],{},[1667,19794,4032],{},[902,19796,19797],{"encoding":904},"g(x, y) = 0"," se používá ",[207,19800,793],{"className":19801,"dataFsResolvedFilePath":791,"href":792},[210],[115,19803,10640],{"id":10639},[120,19805,19806,19813,19820],{},[123,19807,19808,1643,19810],{},[38,19809,12584],{},[207,19811,775],{"className":19812,"dataFsResolvedFilePath":773,"href":774},[210],[123,19814,19815,1643,19817],{},[38,19816,12592],{},[207,19818,793],{"className":19819,"dataFsResolvedFilePath":791,"href":792},[210],[123,19821,19822,1643,19824,19827,19828,10688,19831,19834],{},[38,19823,12600],{},[207,19825,10697],{"className":19826,"dataFsResolvedFilePath":857,"href":858},[210]," (parciální derivace = mezní produkty), ",[207,19829,880],{"className":19830,"dataFsResolvedFilePath":878,"href":879},[210],[207,19832,12613],{"className":19833,"dataFsResolvedFilePath":848,"href":849},[210]," (vícefaktorový model)",{"title":641,"searchDepth":642,"depth":642,"links":19836},[19837,19838,19842,19843,19844,19848,19849],{"id":18407,"depth":642,"text":18408},{"id":18560,"depth":642,"text":18561,"children":19839},[19840,19841],{"id":18712,"depth":649,"text":18713},{"id":11377,"depth":649,"text":11378},{"id":19039,"depth":642,"text":19040},{"id":19161,"depth":642,"text":19162},{"id":19346,"depth":642,"text":19347,"children":19845},[19846,19847],{"id":12041,"depth":649,"text":12042},{"id":12115,"depth":649,"text":12116},{"id":19764,"depth":642,"text":19765},{"id":10639,"depth":642,"text":10640},"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":18319,"description":19850},[1135],"topics\u002Ffunkce-vice-promennych",[1128,19857,12639,19858,19859,10784],"parcialni-derivace","implicitni-funkce","volne-extremy","iuWLbpl-7gHnuMDZKTa3RcRM2uCyFhGx9GhXHIN1R_A",{"id":19862,"title":775,"body":19863,"course":1128,"courses":659,"created":1129,"description":20718,"extension":661,"meta":20719,"navigation":664,"path":20720,"seo":20721,"sources":20722,"stem":20723,"tags":20724,"type":10786,"updated":677,"__hash__":20731},"topics\u002Ftopics\u002Fintegral.md",{"type":9,"value":19864,"toc":20708},[19865,19868,19879,19883,19928,20008,20012,20088,20130,20137,20141,20145,20174,20232,20279,20317,20321,20371,20423,20475,20519,20522,20525,20597,20600,20672,20678,20680],[12,19866,775],{"id":19867},"integrál",[724,19869,19870,19871,19874,19875,19878],{},"Druhá polovina kalkulu jedné proměnné. Slouží k ",[38,19872,19873],{},"rekonstrukci totální veličiny z mezní"," (TR z MR, TC z MC) a k výpočtu ",[38,19876,19877],{},"přebytků"," (consumer\u002Fproducer surplus).",[115,19880,19882],{"id":19881},"neurčitý-integrál","Neurčitý integrál",[724,19884,19885],{},[883,19886,19888],{"className":19887},[886],[888,19889,19890],{"xmlns":890},[892,19891,19892,19925],{},[895,19893,19894,19896,19898,19900,19902,19904,19907,19909,19911,19913,19915,19917,19919,19921,19923],{},[898,19895,19177],{},[1656,19897,1659],{"stretchy":1658},[898,19899,10848],{},[1656,19901,1683],{"stretchy":1658},[1656,19903,1713],{},[1656,19905,19906],{},"∫",[898,19908,7524],{},[1656,19910,1659],{"stretchy":1658},[898,19912,10848],{},[1656,19914,1683],{"stretchy":1658},[2461,19916,7828],{},[898,19918,3768],{},[898,19920,10848],{},[1656,19922,3633],{},[898,19924,1766],{},[902,19926,19927],{"encoding":904},"F(x) = \\int f(x)\\, dx + C",[724,19929,2355,19930,2191,19964,3206,19977,19980,19981,1343,19994,20007],{},[883,19931,19933],{"className":19932},[886],[888,19934,19935],{"xmlns":890},[892,19936,19937,19961],{},[895,19938,19939,19945,19947,19949,19951,19953,19955,19957,19959],{},[2062,19940,19941,19943],{},[898,19942,19177],{},[1656,19944,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,19946,1659],{"stretchy":1658},[898,19948,10848],{},[1656,19950,1683],{"stretchy":1658},[1656,19952,1713],{},[898,19954,7524],{},[1656,19956,1659],{"stretchy":1658},[898,19958,10848],{},[1656,19960,1683],{"stretchy":1658},[902,19962,19963],{"encoding":904},"F'(x) = f(x)",[883,19965,19967],{"className":19966},[886],[888,19968,19969],{"xmlns":890},[892,19970,19971,19975],{},[895,19972,19973],{},[898,19974,19177],{},[902,19976,19177],{"encoding":904},[38,19978,19979],{},"primitivní funkce"," k ",[883,19982,19984],{"className":19983},[886],[888,19985,19986],{"xmlns":890},[892,19987,19988,19992],{},[895,19989,19990],{},[898,19991,7524],{},[902,19993,7524],{"encoding":904},[883,19995,19997],{"className":19996},[886],[888,19998,19999],{"xmlns":890},[892,20000,20001,20005],{},[895,20002,20003],{},[898,20004,1766],{},[902,20006,1766],{"encoding":904}," konstanta.",[115,20009,20011],{"id":20010},"určitý-integrál","Určitý integrál",[724,20013,20014],{},[883,20015,20017],{"className":20016},[886],[888,20018,20019],{"xmlns":890},[892,20020,20021,20085],{},[895,20022,20023,20031,20033,20035,20037,20039,20041,20043,20045,20047,20049,20051,20053,20055,20057,20065,20067,20069,20071,20073,20075,20077,20079,20081,20083],{},[1715,20024,20025,20027,20029],{},[1656,20026,19906],{},[898,20028,207],{},[898,20030,3403],{},[898,20032,7524],{},[1656,20034,1659],{"stretchy":1658},[898,20036,10848],{},[1656,20038,1683],{"stretchy":1658},[2461,20040,7828],{},[898,20042,3768],{},[898,20044,10848],{},[1656,20046,1713],{},[1656,20048,3453],{"stretchy":1658},[898,20050,19177],{},[1656,20052,1659],{"stretchy":1658},[898,20054,10848],{},[1656,20056,1683],{"stretchy":1658},[1715,20058,20059,20061,20063],{},[1656,20060,3462],{"stretchy":1658},[898,20062,207],{},[898,20064,3403],{},[1656,20066,1713],{},[898,20068,19177],{},[1656,20070,1659],{"stretchy":1658},[898,20072,3403],{},[1656,20074,1683],{"stretchy":1658},[1656,20076,3964],{},[898,20078,19177],{},[1656,20080,1659],{"stretchy":1658},[898,20082,207],{},[1656,20084,1683],{"stretchy":1658},[902,20086,20087],{"encoding":904},"\\int_a^b f(x)\\, dx = [F(x)]_a^b = F(b) - F(a)",[724,20089,20090,20091,1643,20094,20107,20108,20129],{},"Geometricky ",[38,20092,20093],{},"plocha pod grafem",[883,20095,20097],{"className":20096},[886],[888,20098,20099],{"xmlns":890},[892,20100,20101,20105],{},[895,20102,20103],{},[898,20104,7524],{},[902,20106,7524],{"encoding":904}," na intervalu ",[883,20109,20111],{"className":20110},[886],[888,20112,20113],{"xmlns":890},[892,20114,20115,20127],{},[895,20116,20117,20119,20121,20123,20125],{},[1656,20118,3453],{"stretchy":1658},[898,20120,207],{},[1656,20122,1673],{"separator":1672},[898,20124,3403],{},[1656,20126,3462],{"stretchy":1658},[902,20128,3465],{"encoding":904}," (orientovaná).",[724,20131,20132],{},[5956,20133],{"alt":20134,"className":20135,"src":20136},"imek-integral-plocha",[210,5960],"\u002Fwiki-assets\u002Fimek-integral-plocha.jpeg",[115,20138,20140],{"id":20139},"aplikace-v-ekonomii","Aplikace v ekonomii",[198,20142,20144],{"id":20143},"příklad-tr-z-mr","Příklad — TR z MR",[724,20146,20147,20148,1863],{},"Mezní příjem ",[883,20149,20151],{"className":20150},[886],[888,20152,20153],{"xmlns":890},[892,20154,20155,20171],{},[895,20156,20157,20159,20161,20163,20165,20167,20169],{},[898,20158,1703],{},[898,20160,1763],{},[1656,20162,1713],{},[1667,20164,5267],{},[1656,20166,3964],{},[1667,20168,1680],{},[898,20170,1665],{},[902,20172,20173],{"encoding":904},"MR = 100 - 2Q",[724,20175,20176],{},[883,20177,20179],{"className":20178},[886],[888,20180,20181],{"xmlns":890},[892,20182,20183,20229],{},[895,20184,20185,20187,20189,20191,20193,20195,20197,20199,20201,20203,20205,20207,20209,20211,20213,20215,20217,20219,20225,20227],{},[898,20186,11577],{},[898,20188,1763],{},[1656,20190,1713],{},[1656,20192,19906],{},[1656,20194,1659],{"stretchy":1658},[1667,20196,5267],{},[1656,20198,3964],{},[1667,20200,1680],{},[898,20202,1665],{},[1656,20204,1683],{"stretchy":1658},[2461,20206,7828],{},[898,20208,3768],{},[898,20210,1665],{},[1656,20212,1713],{},[1667,20214,5267],{},[898,20216,1665],{},[1656,20218,3964],{},[2062,20220,20221,20223],{},[898,20222,1665],{},[1667,20224,1680],{},[1656,20226,3633],{},[898,20228,1745],{},[902,20230,20231],{"encoding":904},"TR = \\int (100 - 2Q)\\, dQ = 100Q - Q^2 + c",[724,20233,20234,20235,12203,20261,2114],{},"Okrajová podmínka ",[883,20236,20238],{"className":20237},[886],[888,20239,20240],{"xmlns":890},[892,20241,20242,20258],{},[895,20243,20244,20246,20248,20250,20252,20254,20256],{},[898,20245,11577],{},[898,20247,1763],{},[1656,20249,1659],{"stretchy":1658},[1667,20251,4032],{},[1656,20253,1683],{"stretchy":1658},[1656,20255,1713],{},[1667,20257,4032],{},[902,20259,20260],{"encoding":904},"TR(0) = 0",[883,20262,20264],{"className":20263},[886],[888,20265,20266],{"xmlns":890},[892,20267,20268,20276],{},[895,20269,20270,20272,20274],{},[898,20271,1745],{},[1656,20273,1713],{},[1667,20275,4032],{},[902,20277,20278],{"encoding":904},"c = 0",[724,20280,20281],{},[883,20282,20284],{"className":20283},[886],[888,20285,20286],{"xmlns":890},[892,20287,20288,20314],{},[895,20289,20290,20292,20294,20296,20298,20300,20302,20304,20306,20308],{},[898,20291,11577],{},[898,20293,1763],{},[1656,20295,1659],{"stretchy":1658},[898,20297,1665],{},[1656,20299,1683],{"stretchy":1658},[1656,20301,1713],{},[1667,20303,5267],{},[898,20305,1665],{},[1656,20307,3964],{},[2062,20309,20310,20312],{},[898,20311,1665],{},[1667,20313,1680],{},[902,20315,20316],{"encoding":904},"TR(Q) = 100Q - Q^2",[198,20318,20320],{"id":20319},"příklad-tc-z-mc","Příklad — TC z MC",[724,20322,20323,20324,20350,20351,1863],{},"Mezní náklady ",[883,20325,20327],{"className":20326},[886],[888,20328,20329],{"xmlns":890},[892,20330,20331,20347],{},[895,20332,20333,20335,20337,20339,20341,20343,20345],{},[898,20334,1703],{},[898,20336,1766],{},[1656,20338,1713],{},[1667,20340,1680],{},[1656,20342,3633],{},[1667,20344,11639],{},[898,20346,1665],{},[902,20348,20349],{"encoding":904},"MC = 2 + 0{,}2 Q",", fixní náklady ",[883,20352,20354],{"className":20353},[886],[888,20355,20356],{"xmlns":890},[892,20357,20358,20368],{},[895,20359,20360,20362,20364,20366],{},[898,20361,19177],{},[898,20363,1766],{},[1656,20365,1713],{},[1667,20367,5267],{},[902,20369,20370],{"encoding":904},"FC = 100",[724,20372,20373],{},[883,20374,20376],{"className":20375},[886],[888,20377,20378],{"xmlns":890},[892,20379,20380,20420],{},[895,20381,20382,20384,20386,20388,20390,20392,20394,20396,20398,20400,20402,20404,20406,20408,20410,20416,20418],{},[898,20383,11577],{},[898,20385,1766],{},[1656,20387,1713],{},[1656,20389,19906],{},[898,20391,1703],{},[898,20393,1766],{},[2461,20395,7828],{},[898,20397,3768],{},[898,20399,1665],{},[1656,20401,1713],{},[1667,20403,1680],{},[898,20405,1665],{},[1656,20407,3633],{},[1667,20409,11595],{},[2062,20411,20412,20414],{},[898,20413,1665],{},[1667,20415,1680],{},[1656,20417,3633],{},[898,20419,1745],{},[902,20421,20422],{"encoding":904},"TC = \\int MC\\, dQ = 2Q + 0{,}1 Q^2 + c",[724,20424,20234,20425,12203,20457,2114],{},[883,20426,20428],{"className":20427},[886],[888,20429,20430],{"xmlns":890},[892,20431,20432,20454],{},[895,20433,20434,20436,20438,20440,20442,20444,20446,20448,20450,20452],{},[898,20435,11577],{},[898,20437,1766],{},[1656,20439,1659],{"stretchy":1658},[1667,20441,4032],{},[1656,20443,1683],{"stretchy":1658},[1656,20445,1713],{},[898,20447,19177],{},[898,20449,1766],{},[1656,20451,1713],{},[1667,20453,5267],{},[902,20455,20456],{"encoding":904},"TC(0) = FC = 100",[883,20458,20460],{"className":20459},[886],[888,20461,20462],{"xmlns":890},[892,20463,20464,20472],{},[895,20465,20466,20468,20470],{},[898,20467,1745],{},[1656,20469,1713],{},[1667,20471,5267],{},[902,20473,20474],{"encoding":904},"c = 100",[724,20476,20477],{},[883,20478,20480],{"className":20479},[886],[888,20481,20482],{"xmlns":890},[892,20483,20484,20516],{},[895,20485,20486,20488,20490,20492,20494,20496,20498,20500,20502,20504,20506,20508,20510],{},[898,20487,11577],{},[898,20489,1766],{},[1656,20491,1659],{"stretchy":1658},[898,20493,1665],{},[1656,20495,1683],{"stretchy":1658},[1656,20497,1713],{},[1667,20499,5267],{},[1656,20501,3633],{},[1667,20503,1680],{},[898,20505,1665],{},[1656,20507,3633],{},[1667,20509,11595],{},[2062,20511,20512,20514],{},[898,20513,1665],{},[1667,20515,1680],{},[902,20517,20518],{"encoding":904},"TC(Q) = 100 + 2Q + 0{,}1 Q^2",[198,20520,820],{"id":20521},"přebytek-spotřebitele-a-výrobce",[724,20523,20524],{},"Přebytek spotřebitele:",[724,20526,20527],{},[883,20528,20530],{"className":20529},[886],[888,20531,20532],{"xmlns":890},[892,20533,20534,20594],{},[895,20535,20536,20538,20540,20542,20548,20550,20552,20564,20566,20568,20570,20572,20574,20576,20578,20580,20586,20588],{},[898,20537,1766],{},[898,20539,1769],{},[1656,20541,1659],{"stretchy":1658},[1661,20543,20544,20546],{},[898,20545,1665],{},[1667,20547,4032],{},[1656,20549,1683],{"stretchy":1658},[1656,20551,1713],{},[1715,20553,20554,20556,20558],{},[1656,20555,19906],{},[1667,20557,4032],{},[1661,20559,20560,20562],{},[898,20561,1665],{},[1667,20563,4032],{},[898,20565,6787],{},[1656,20567,1659],{"stretchy":1658},[898,20569,1665],{},[1656,20571,1683],{"stretchy":1658},[2461,20573,7828],{},[898,20575,3768],{},[898,20577,1665],{},[1656,20579,3964],{},[1661,20581,20582,20584],{},[898,20583,8194],{},[1667,20585,4032],{},[2461,20587,7828],{},[1661,20589,20590,20592],{},[898,20591,1665],{},[1667,20593,4032],{},[902,20595,20596],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\, dQ - P_0\\, Q_0",[724,20598,20599],{},"Přebytek výrobce:",[724,20601,20602],{},[883,20603,20605],{"className":20604},[886],[888,20606,20607],{"xmlns":890},[892,20608,20609,20669],{},[895,20610,20611,20613,20615,20617,20623,20625,20627,20633,20635,20641,20643,20655,20657,20659,20661,20663,20665,20667],{},[898,20612,8194],{},[898,20614,1769],{},[1656,20616,1659],{"stretchy":1658},[1661,20618,20619,20621],{},[898,20620,1665],{},[1667,20622,4032],{},[1656,20624,1683],{"stretchy":1658},[1656,20626,1713],{},[1661,20628,20629,20631],{},[898,20630,8194],{},[1667,20632,4032],{},[2461,20634,7828],{},[1661,20636,20637,20639],{},[898,20638,1665],{},[1667,20640,4032],{},[1656,20642,3964],{},[1715,20644,20645,20647,20649],{},[1656,20646,19906],{},[1667,20648,4032],{},[1661,20650,20651,20653],{},[898,20652,1665],{},[1667,20654,4032],{},[898,20656,1769],{},[1656,20658,1659],{"stretchy":1658},[898,20660,1665],{},[1656,20662,1683],{"stretchy":1658},[2461,20664,7828],{},[898,20666,3768],{},[898,20668,1665],{},[902,20670,20671],{"encoding":904},"PS(Q_0) = P_0\\, Q_0 - \\int_0^{Q_0} S(Q)\\, dQ",[724,20673,20674,20675,1863],{},"Detailně viz ",[207,20676,10702],{"className":20677,"dataFsResolvedFilePath":800,"href":801},[210],[115,20679,10640],{"id":10639},[120,20681,20682,20689,20696],{},[123,20683,20684,1643,20686],{},[38,20685,12584],{},[207,20687,766],{"className":20688,"dataFsResolvedFilePath":764,"href":765},[210],[123,20690,20691,1643,20693],{},[38,20692,12592],{},[207,20694,784],{"className":20695,"dataFsResolvedFilePath":782,"href":783},[210],[123,20697,20698,1643,20700,20703,20704,20707],{},[38,20699,12600],{},[207,20701,12608],{"className":20702,"dataFsResolvedFilePath":827,"href":828},[210]," (TR\u002FTC), ",[207,20705,10702],{"className":20706,"dataFsResolvedFilePath":800,"href":801},[210]," (přebytky CS\u002FPS)",{"title":641,"searchDepth":642,"depth":642,"links":20709},[20710,20711,20712,20717],{"id":19881,"depth":642,"text":19882},{"id":20010,"depth":642,"text":20011},{"id":20139,"depth":642,"text":20140,"children":20713},[20714,20715,20716],{"id":20143,"depth":649,"text":20144},{"id":20319,"depth":649,"text":20320},{"id":20521,"depth":649,"text":820},{"id":10639,"depth":642,"text":10640},"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":20718},[1135],"topics\u002Fintegral",[1128,20725,20726,20727,20728,20729,20730],"integral","neurcity","urcity","primitivni-funkce","tr-z-mr","tc-z-mc","H1oOmn3Z5yZ_KZm1LLzfN_DVUhYSxx7eveFc7CASwZY",{"id":20733,"title":20734,"body":20735,"course":1128,"courses":659,"created":10774,"description":641,"extension":661,"meta":24993,"navigation":664,"path":24994,"seo":24995,"sources":24996,"stem":24997,"tags":24998,"type":10786,"updated":677,"__hash__":25004},"topics\u002Ftopics\u002Fis-lm.md","IS-LM analýza — simultánní rovnováha trhu zboží a peněz",{"type":9,"value":20736,"toc":24981},[20737,20740,20742,20886,20893,20897,20967,21005,21108,21112,21142,21207,21254,21257,21326,21329,21364,21400,21404,21452,21459,21505,21551,21554,21633,21729,21812,21816,21860,21890,21896,21925,21947,21997,22050,22116,22119,22185,22214,22273,22289,22376,22473,22604,22608,22765,22914,23294,23298,23301,23360,23363,23449,23477,23515,23518,23555,23595,23629,23631,23668,23700,23798,23803,23926,23978,24059,24198,24202,24322,24329,24440,24447,24449,24924,24926],[12,20738,20734],{"id":20739},"is-lm-analýza-simultánní-rovnováha-trhu-zboží-a-peněz",[115,20741,1638],{"id":1637},[724,20743,20744,20747,20748,3247,20751,20764,20765,20779,20780,20783,20784,1343,20787,20790,20791,1343,20794,20797,20798,1643,20801,20831,20832,20835,20836,1343,20850,20863,20864,20867,20868,12702],{},[38,20745,20746],{},"IS-LM"," je makroekonomický model se ",[38,20749,20750],{},"dvěma neznámými",[883,20752,20754],{"className":20753},[886],[888,20755,20756],{"xmlns":890},[892,20757,20758,20762],{},[895,20759,20760],{},[898,20761,8184],{},[902,20763,8184],{"encoding":904}," — národní důchod a ",[883,20766,20768],{"className":20767},[886],[888,20769,20770],{"xmlns":890},[892,20771,20772,20777],{},[895,20773,20774],{},[898,20775,20776],{},"r",[902,20778,20776],{"encoding":904}," — úroková míra) a ",[38,20781,20782],{},"dvěma trhy",": trhem zboží (křivka ",[38,20785,20786],{},"IS",[614,20788,20789],{},"Investment = Savings",") a trhem peněz (křivka ",[38,20792,20793],{},"LM",[614,20795,20796],{},"Liquidity of Money","). Průsečík obou křivek určuje ",[38,20799,20800],{},"simultánní rovnováhu",[883,20802,20804],{"className":20803},[886],[888,20805,20806],{"xmlns":890},[892,20807,20808,20828],{},[895,20809,20810,20812,20818,20820,20826],{},[1656,20811,1659],{"stretchy":1658},[2062,20813,20814,20816],{},[898,20815,8184],{},[898,20817,1842],{},[1656,20819,1673],{"separator":1672},[2062,20821,20822,20824],{},[898,20823,20776],{},[898,20825,1842],{},[1656,20827,1683],{"stretchy":1658},[902,20829,20830],{"encoding":904},"(Y^E, r^E)",", v níž jsou oba trhy vyvážené zároveň. Model je klíčovým nástrojem pro analýzu ",[38,20833,20834],{},"fiskální politiky"," (posun IS změnou ",[883,20837,20839],{"className":20838},[886],[888,20840,20841],{"xmlns":890},[892,20842,20843,20848],{},[895,20844,20845],{},[898,20846,20847],{},"G",[902,20849,20847],{"encoding":904},[883,20851,20853],{"className":20852},[886],[888,20854,20855],{"xmlns":890},[892,20856,20857,20861],{},[895,20858,20859],{},[898,20860,11577],{},[902,20862,11577],{"encoding":904},") a ",[38,20865,20866],{},"monetární politiky"," (posun LM změnou nabídky peněz ",[883,20869,20871],{"className":20870},[886],[888,20872,20873],{"xmlns":890},[892,20874,20875,20883],{},[895,20876,20877],{},[2062,20878,20879,20881],{},[898,20880,1703],{},[1656,20882,8187],{},[902,20884,20885],{"encoding":904},"M^*",[724,20887,20888],{},[5956,20889],{"alt":20890,"className":20891,"src":20892},"imek-is-lm-model",[210,5960],"\u002Fwiki-assets\u002Fimek-is-lm-model.jpeg",[115,20894,20896],{"id":20895},"motivace-proč-přejít-od-c-i-g-x-k-is-lm","Motivace — proč přejít od C-I-G-X k IS-LM",[724,20898,20899,20900,20904,20905,3247,20908,20931,20932,20935,20936,20952,20953,20966],{},"V modelech ",[207,20901,20903],{"className":20902,"dataFsResolvedFilePath":934,"href":935},[210],"C-I, C-I-G a C-I-G-X"," byly ",[38,20906,20907],{},"investice pokládány za konstantní",[883,20909,20911],{"className":20910},[886],[888,20912,20913],{"xmlns":890},[892,20914,20915,20928],{},[895,20916,20917,20920,20922],{},[898,20918,20919],{},"I",[1656,20921,1713],{},[2062,20923,20924,20926],{},[898,20925,20919],{},[1656,20927,8187],{},[902,20929,20930],{"encoding":904},"I = I^*","). To není realistické — investice firem závisejí na ",[38,20933,20934],{},"ceně peněz",", tedy na ",[38,20937,20938,20939],{},"úrokové míře ",[883,20940,20942],{"className":20941},[886],[888,20943,20944],{"xmlns":890},[892,20945,20946,20950],{},[895,20947,20948],{},[898,20949,20776],{},[902,20951,20776],{"encoding":904},": čím vyšší ",[883,20954,20956],{"className":20955},[886],[888,20957,20958],{"xmlns":890},[892,20959,20960,20964],{},[895,20961,20962],{},[898,20963,20776],{},[902,20965,20776],{"encoding":904},", tím dražší úvěr a tím méně investic. IS-LM analýza proto zavádí:",[120,20968,20969,20999],{},[123,20970,20971,1643,20974,20998],{},[38,20972,20973],{},"funkci investic",[883,20975,20977],{"className":20976},[886],[888,20978,20979],{"xmlns":890},[892,20980,20981,20995],{},[895,20982,20983,20985,20987,20989,20991,20993],{},[898,20984,20919],{},[1656,20986,1713],{},[898,20988,20919],{},[1656,20990,1659],{"stretchy":1658},[898,20992,20776],{},[1656,20994,1683],{"stretchy":1658},[902,20996,20997],{"encoding":904},"I = I(r)"," jako klesající funkci úrokové míry,",[123,21000,21001,21004],{},[38,21002,21003],{},"trh peněz",", jehož rovnováha (poptávka = nabídka peněz) doplňuje druhou rovnici potřebnou pro určení obou neznámých.",[1981,21006,21007],{},[724,21008,21009,21011,21012,21031,21032,21059,21060,21073,21074,21103,21104,21107],{},[883,21010,1987],{}," Pozor — dvě neznámé vyžadují dvě rovnice\nV modelech ",[883,21013,21015],{"className":21014},[886],[888,21016,21017],{"xmlns":890},[892,21018,21019,21028],{},[895,21020,21021,21023,21026],{},[898,21022,1766],{},[2461,21024,21025],{},"-",[898,21027,20919],{},[902,21029,21030],{"encoding":904},"C\\text{-}I"," až ",[883,21033,21035],{"className":21034},[886],[888,21036,21037],{"xmlns":890},[892,21038,21039,21056],{},[895,21040,21041,21043,21045,21047,21049,21051,21053],{},[898,21042,1766],{},[2461,21044,21025],{},[898,21046,20919],{},[2461,21048,21025],{},[898,21050,20847],{},[2461,21052,21025],{},[898,21054,21055],{},"X",[902,21057,21058],{"encoding":904},"C\\text{-}I\\text{-}G\\text{-}X"," byla hlavní neznámou jen ",[883,21061,21063],{"className":21062},[886],[888,21064,21065],{"xmlns":890},[892,21066,21067,21071],{},[895,21068,21069],{},[898,21070,8184],{},[902,21072,8184],{"encoding":904},". V IS-LM jsou ",[38,21075,21076,21077,1896,21090],{},"dvě neznámé ",[883,21078,21080],{"className":21079},[886],[888,21081,21082],{"xmlns":890},[892,21083,21084,21088],{},[895,21085,21086],{},[898,21087,8184],{},[902,21089,8184],{"encoding":904},[883,21091,21093],{"className":21092},[886],[888,21094,21095],{"xmlns":890},[892,21096,21097,21101],{},[895,21098,21099],{},[898,21100,20776],{},[902,21102,20776],{"encoding":904},", a proto potřebujeme ",[38,21105,21106],{},"dvě rovnice",": jednu z trhu zboží (křivka IS) a jednu z trhu peněz (křivka LM).",[115,21109,21111],{"id":21110},"funkce-investic-a-funkce-spotřeby","Funkce investic a funkce spotřeby",[724,21113,21114,21115,21128,21129,2114],{},"Lineární závislost investic ",[883,21116,21118],{"className":21117},[886],[888,21119,21120],{"xmlns":890},[892,21121,21122,21126],{},[895,21123,21124],{},[898,21125,20919],{},[902,21127,20919],{"encoding":904}," na úrokové míře ",[883,21130,21132],{"className":21131},[886],[888,21133,21134],{"xmlns":890},[892,21135,21136,21140],{},[895,21137,21138],{},[898,21139,20776],{},[902,21141,20776],{"encoding":904},[724,21143,21144],{},[883,21145,21147],{"className":21146},[886],[888,21148,21149],{"xmlns":890},[892,21150,21151,21204],{},[895,21152,21153,21155,21157,21159,21161,21163,21165,21167,21169,21171,21173,21175,21177,21179,21181,21183,21185,21187,21189,21191,21193,21195,21197,21199,21202],{},[898,21154,20919],{},[1656,21156,1713],{},[898,21158,20919],{},[1656,21160,1659],{"stretchy":1658},[898,21162,20776],{},[1656,21164,1683],{"stretchy":1658},[1656,21166,1713],{},[898,21168,1745],{},[898,21170,20776],{},[1656,21172,3633],{},[898,21174,3768],{},[1656,21176,1673],{"separator":1672},[3316,21178],{"width":14644},[898,21180,1745],{},[1656,21182,4373],{},[1667,21184,4032],{},[1656,21186,1673],{"separator":1672},[2461,21188,11112],{},[898,21190,3768],{},[1656,21192,2850],{},[1667,21194,4283],{},[3316,21196],{"width":14644},[1656,21198,1659],{"stretchy":1658},[1667,21200,21201],{},"7.11",[1656,21203,1683],{"stretchy":1658},[902,21205,21206],{"encoding":904},"I = I(r) = cr + d, \\qquad c \u003C 0,\\ d > 0. \\qquad (7.11)",[120,21208,21209,21230],{},[123,21210,21211,21229],{},[883,21212,21214],{"className":21213},[886],[888,21215,21216],{"xmlns":890},[892,21217,21218,21226],{},[895,21219,21220,21222,21224],{},[898,21221,3768],{},[1656,21223,2850],{},[1667,21225,4032],{},[902,21227,21228],{"encoding":904},"d > 0"," zřejmé,",[123,21231,21232,21250,21251,1863],{},[883,21233,21235],{"className":21234},[886],[888,21236,21237],{"xmlns":890},[892,21238,21239,21247],{},[895,21240,21241,21243,21245],{},[898,21242,1745],{},[1656,21244,4373],{},[1667,21246,4032],{},[902,21248,21249],{"encoding":904},"c \u003C 0",", protože růst úrokové míry tlumí investice — funkce investic je ",[38,21252,21253],{},"klesající",[724,21255,21256],{},"Spotřeba zůstává lineární funkcí důchodu:",[724,21258,21259],{},[883,21260,21262],{"className":21261},[886],[888,21263,21264],{"xmlns":890},[892,21265,21266,21323],{},[895,21267,21268,21270,21272,21274,21276,21278,21280,21282,21284,21286,21288,21290,21292,21294,21296,21298,21300,21302,21304,21306,21308,21310,21312,21314,21316,21318,21321],{},[898,21269,1766],{},[1656,21271,1713],{},[898,21273,1766],{},[1656,21275,1659],{"stretchy":1658},[898,21277,8184],{},[1656,21279,1683],{"stretchy":1658},[1656,21281,1713],{},[898,21283,207],{},[898,21285,8184],{},[1656,21287,3633],{},[898,21289,3403],{},[1656,21291,1673],{"separator":1672},[3316,21293],{"width":14644},[1667,21295,4032],{},[1656,21297,4373],{},[898,21299,207],{},[1656,21301,4373],{},[1667,21303,1669],{},[1656,21305,1673],{"separator":1672},[2461,21307,11112],{},[898,21309,3403],{},[1656,21311,2850],{},[1667,21313,4283],{},[3316,21315],{"width":14644},[1656,21317,1659],{"stretchy":1658},[1667,21319,21320],{},"7.12",[1656,21322,1683],{"stretchy":1658},[902,21324,21325],{"encoding":904},"C = C(Y) = aY + b, \\qquad 0 \u003C a \u003C 1,\\ b > 0. \\qquad (7.12)",[724,21327,21328],{},"Podmínka rovnováhy na trhu zboží:",[724,21330,21331],{},[883,21332,21334],{"className":21333},[886],[888,21335,21336],{"xmlns":890},[892,21337,21338,21361],{},[895,21339,21340,21342,21344,21346,21348,21350,21352,21354,21356,21359],{},[898,21341,8184],{},[1656,21343,1713],{},[898,21345,1766],{},[1656,21347,3633],{},[898,21349,20919],{},[898,21351,1863],{"mathvariant":1723},[3316,21353],{"width":14644},[1656,21355,1659],{"stretchy":1658},[1667,21357,21358],{},"7.13",[1656,21360,1683],{"stretchy":1658},[902,21362,21363],{"encoding":904},"Y = C + I. \\qquad (7.13)",[724,21365,21366,21367,1643,21370,21396,21397,1863],{},"To dává ",[38,21368,21369],{},"tři rovnice o čtyřech neznámých",[883,21371,21373],{"className":21372},[886],[888,21374,21375],{"xmlns":890},[892,21376,21377,21393],{},[895,21378,21379,21381,21383,21385,21387,21389,21391],{},[898,21380,8184],{},[1656,21382,1673],{"separator":1672},[898,21384,1766],{},[1656,21386,1673],{"separator":1672},[898,21388,20919],{},[1656,21390,1673],{"separator":1672},[898,21392,20776],{},[902,21394,21395],{"encoding":904},"Y, C, I, r",". Pro jednoznačné určení rovnováhy potřebujeme čtvrtou rovnici — odvodí se z ",[38,21398,21399],{},"rovnováhy na trhu peněz",[115,21401,21403],{"id":21402},"křivka-is-rovnováha-na-trhu-zboží","Křivka IS — rovnováha na trhu zboží",[724,21405,21406,21407,14337,21429,21447,21448,21451],{},"Podmínka (7.13) reprezentuje rovnováhu na trhu zboží, protože s ohledem na ",[883,21408,21410],{"className":21409},[886],[888,21411,21412],{"xmlns":890},[892,21413,21414,21426],{},[895,21415,21416,21418,21420,21422,21424],{},[898,21417,8184],{},[1656,21419,1713],{},[898,21421,1766],{},[1656,21423,3633],{},[898,21425,1769],{},[902,21427,21428],{"encoding":904},"Y = C + S",[883,21430,21432],{"className":21431},[886],[888,21433,21434],{"xmlns":890},[892,21435,21436,21444],{},[895,21437,21438,21440,21442],{},[898,21439,20919],{},[1656,21441,1713],{},[898,21443,1769],{},[902,21445,21446],{"encoding":904},"I = S"," (plánované ",[38,21449,21450],{},"investice = úspory","). Dosazením (7.11) a (7.12) do (7.13):",[724,21453,21454],{},[5956,21455],{"alt":21456,"className":21457,"src":21458},"imek-odvozeni-is-4panelu",[210,5960],"\u002Fwiki-assets\u002Fimek-odvozeni-is-4panelu.jpeg",[724,21460,21461],{},[883,21462,21464],{"className":21463},[886],[888,21465,21466],{"xmlns":890},[892,21467,21468,21502],{},[895,21469,21470,21472,21474,21476,21478,21480,21482,21484,21486,21488,21490,21492,21494,21496,21498,21500],{},[898,21471,8184],{},[1656,21473,1713],{},[1656,21475,1659],{"stretchy":1658},[898,21477,207],{},[898,21479,8184],{},[1656,21481,3633],{},[898,21483,3403],{},[1656,21485,1683],{"stretchy":1658},[1656,21487,3633],{},[1656,21489,1659],{"stretchy":1658},[898,21491,1745],{},[898,21493,20776],{},[1656,21495,3633],{},[898,21497,3768],{},[1656,21499,1683],{"stretchy":1658},[1656,21501,1673],{"separator":1672},[902,21503,21504],{"encoding":904},"Y = (aY + b) + (cr + d),",[724,21506,21507],{},[883,21508,21510],{"className":21509},[886],[888,21511,21512],{"xmlns":890},[892,21513,21514,21548],{},[895,21515,21516,21518,21520,21522,21524,21526,21528,21530,21532,21534,21536,21538,21540,21542,21544,21546],{},[1656,21517,1659],{"stretchy":1658},[1667,21519,1669],{},[1656,21521,3964],{},[898,21523,207],{},[1656,21525,1683],{"stretchy":1658},[898,21527,8184],{},[1656,21529,3964],{},[898,21531,1745],{},[898,21533,20776],{},[1656,21535,3964],{},[898,21537,3403],{},[1656,21539,3964],{},[898,21541,3768],{},[1656,21543,1713],{},[1667,21545,4032],{},[1656,21547,1673],{"separator":1672},[902,21549,21550],{"encoding":904},"(1 - a)Y - cr - b - d = 0,",[724,21552,21553],{},"odkud",[724,21555,21556],{},[883,21557,21559],{"className":21558},[886],[888,21560,21561],{"xmlns":890},[892,21562,21563,21630],{},[895,21564,21565,21621,21623,21625,21628],{},[21566,21567,21569],"menclose",{"notation":21568},"box",[4138,21570,21571],{"scriptlevel":4032,"displaystyle":1658},[4138,21572,21573],{"scriptlevel":4032,"displaystyle":1658},[4138,21574,21575],{"scriptlevel":4032,"displaystyle":1672},[895,21576,21577,21579,21581,21583,21595,21597,21599,21601,21619],{},[2461,21578,7828],{},[898,21580,8184],{},[1656,21582,1713],{},[3294,21584,21585,21587],{},[898,21586,1745],{},[895,21588,21589,21591,21593],{},[1667,21590,1669],{},[1656,21592,3964],{},[898,21594,207],{},[2461,21596,7828],{},[898,21598,20776],{},[1656,21600,3633],{},[3294,21602,21603,21611],{},[895,21604,21605,21607,21609],{},[898,21606,3403],{},[1656,21608,3633],{},[898,21610,3768],{},[895,21612,21613,21615,21617],{},[1667,21614,1669],{},[1656,21616,3964],{},[898,21618,207],{},[2461,21620,7828],{},[3316,21622],{"width":14644},[1656,21624,1659],{"stretchy":1658},[1667,21626,21627],{},"7.14",[1656,21629,1683],{"stretchy":1658},[902,21631,21632],{"encoding":904},"\\boxed{\\,Y = \\frac{c}{1 - a}\\,r + \\frac{b + d}{1 - a}\\,} \\qquad (7.14)",[724,21634,21635,21636,3247,21639,21642,21643,21646,21647,21649,21650,2713,21672,21700,21701,21722,21723,21725,21726,21728],{},"Tento vztah se nazývá ",[38,21637,21638],{},"funkce IS",[614,21640,21641],{},"IS schedule",") a její graf ",[38,21644,21645],{},"křivka IS",". Křivka je ",[38,21648,21253],{}," přímka v rovině ",[883,21651,21653],{"className":21652},[886],[888,21654,21655],{"xmlns":890},[892,21656,21657,21669],{},[895,21658,21659,21661,21663,21665,21667],{},[1656,21660,1659],{"stretchy":1658},[898,21662,20776],{},[1656,21664,1673],{"separator":1672},[898,21666,8184],{},[1656,21668,1683],{"stretchy":1658},[902,21670,21671],{"encoding":904},"(r, Y)",[883,21673,21675],{"className":21674},[886],[888,21676,21677],{"xmlns":890},[892,21678,21679,21697],{},[895,21680,21681,21693,21695],{},[3294,21682,21683,21685],{},[898,21684,1745],{},[895,21686,21687,21689,21691],{},[1667,21688,1669],{},[1656,21690,3964],{},[898,21692,207],{},[1656,21694,4373],{},[1667,21696,4032],{},[902,21698,21699],{"encoding":904},"\\frac{c}{1-a} \u003C 0"," (čitatel záporný, jmenovatel kladný). Název vyjadřuje, že křivka popisuje ty kombinace ",[883,21702,21704],{"className":21703},[886],[888,21705,21706],{"xmlns":890},[892,21707,21708,21720],{},[895,21709,21710,21712,21714,21716,21718],{},[1656,21711,1659],{"stretchy":1658},[898,21713,20776],{},[1656,21715,1673],{"separator":1672},[898,21717,8184],{},[1656,21719,1683],{"stretchy":1658},[902,21721,21671],{"encoding":904},", pro které plánované ",[38,21724,20919],{},"nvestment = ",[38,21727,1769],{},"avings.",[1981,21730,21731],{},[724,21732,21733,21735,21736,21749,21750,1643,21753,21766,21767,21780,21781,1896,21794,21807,21808,21811],{},[883,21734,3472],{}," Intuice — proč IS klesá\nNižší úroková míra ",[883,21737,21739],{"className":21738},[886],[888,21740,21741],{"xmlns":890},[892,21742,21743,21747],{},[895,21744,21745],{},[898,21746,20776],{},[902,21748,20776],{"encoding":904}," → levnější úvěr → ",[38,21751,21752],{},"více investic",[883,21754,21756],{"className":21755},[886],[888,21757,21758],{"xmlns":890},[892,21759,21760,21764],{},[895,21761,21762],{},[898,21763,20919],{},[902,21765,20919],{"encoding":904}," → vyšší agregátní poptávka → vyšší rovnovážný důchod ",[883,21768,21770],{"className":21769},[886],[888,21771,21772],{"xmlns":890},[892,21773,21774,21778],{},[895,21775,21776],{},[898,21777,8184],{},[902,21779,8184],{"encoding":904},". Vztah mezi ",[883,21782,21784],{"className":21783},[886],[888,21785,21786],{"xmlns":890},[892,21787,21788,21792],{},[895,21789,21790],{},[898,21791,20776],{},[902,21793,20776],{"encoding":904},[883,21795,21797],{"className":21796},[886],[888,21798,21799],{"xmlns":890},[892,21800,21801,21805],{},[895,21802,21803],{},[898,21804,8184],{},[902,21806,8184],{"encoding":904}," na trhu zboží je proto ",[38,21809,21810],{},"nepřímý"," (klesající křivka).",[115,21813,21815],{"id":21814},"křivka-lm-rovnováha-na-trhu-peněz","Křivka LM — rovnováha na trhu peněz",[724,21817,21818,21819,21837,21838,2191,21856,21859],{},"Rovnováha na trhu peněz: poptávka po penězích ",[883,21820,21822],{"className":21821},[886],[888,21823,21824],{"xmlns":890},[892,21825,21826,21834],{},[895,21827,21828],{},[2062,21829,21830,21832],{},[898,21831,1703],{},[898,21833,6787],{},[902,21835,21836],{"encoding":904},"M^D"," se rovná nabídce peněz ",[883,21839,21841],{"className":21840},[886],[888,21842,21843],{"xmlns":890},[892,21844,21845,21853],{},[895,21846,21847],{},[2062,21848,21849,21851],{},[898,21850,1703],{},[898,21852,1769],{},[902,21854,21855],{"encoding":904},"M^S",[38,21857,21858],{},"Nabídka"," je pod kontrolou národní banky a je pevně zadána:",[724,21861,21862],{},[883,21863,21865],{"className":21864},[886],[888,21866,21867],{"xmlns":890},[892,21868,21869,21887],{},[895,21870,21871,21877,21879,21885],{},[2062,21872,21873,21875],{},[898,21874,1703],{},[898,21876,1769],{},[1656,21878,1713],{},[2062,21880,21881,21883],{},[898,21882,1703],{},[1656,21884,8187],{},[898,21886,1863],{"mathvariant":1723},[902,21888,21889],{"encoding":904},"M^S = M^*.",[724,21891,21892,21895],{},[38,21893,21894],{},"Poptávka"," po penězích má tři zdroje:",[120,21897,21898,21907,21916],{},[123,21899,21900,3247,21903,21906],{},[38,21901,21902],{},"transakční poptávka",[614,21904,21905],{},"transactions demand",") — peníze pro nákup zboží,",[123,21908,21909,3247,21912,21915],{},[38,21910,21911],{},"opatrnostní poptávka",[614,21913,21914],{},"precautionary demand",") — peníze pro nenadálé výdaje,",[123,21917,21918,3247,21921,21924],{},[38,21919,21920],{},"spekulační poptávka",[614,21922,21923],{},"speculative demand",") — peníze pro zhodnocení (akcie, obligace).",[724,21926,21927,21928,21946],{},"Součet transakční a opatrnostní poptávky ",[883,21929,21931],{"className":21930},[886],[888,21932,21933],{"xmlns":890},[892,21934,21935,21943],{},[895,21936,21937],{},[1661,21938,21939,21941],{},[898,21940,18539],{},[1667,21942,1669],{},[902,21944,21945],{"encoding":904},"L_1"," je úměrný důchodu:",[724,21948,21949],{},[883,21950,21952],{"className":21951},[886],[888,21953,21954],{"xmlns":890},[892,21955,21956,21994],{},[895,21957,21958,21964,21966,21973,21975,21977,21979,21981,21983,21989,21991],{},[1661,21959,21960,21962],{},[898,21961,18539],{},[1667,21963,1669],{},[1656,21965,1713],{},[1661,21967,21968,21971],{},[898,21969,21970],{},"k",[1667,21972,1669],{},[898,21974,8184],{},[1656,21976,1673],{"separator":1672},[3316,21978],{"width":14644},[1667,21980,4032],{},[1656,21982,4373],{},[1661,21984,21985,21987],{},[898,21986,21970],{},[1667,21988,1669],{},[1656,21990,4373],{},[1667,21992,21993],{},"1.",[902,21995,21996],{"encoding":904},"L_1 = k_1 Y, \\qquad 0 \u003C k_1 \u003C 1.",[724,21998,21999,22000,22018,22019,1343,22032,22049],{},"Spekulační poptávka ",[883,22001,22003],{"className":22002},[886],[888,22004,22005],{"xmlns":890},[892,22006,22007,22015],{},[895,22008,22009],{},[1661,22010,22011,22013],{},[898,22012,18539],{},[1667,22014,1680],{},[902,22016,22017],{"encoding":904},"L_2"," závisí na úrokové míře (roste-li ",[883,22020,22022],{"className":22021},[886],[888,22023,22024],{"xmlns":890},[892,22025,22026,22030],{},[895,22027,22028],{},[898,22029,20776],{},[902,22031,20776],{"encoding":904},[883,22033,22035],{"className":22034},[886],[888,22036,22037],{"xmlns":890},[892,22038,22039,22047],{},[895,22040,22041],{},[1661,22042,22043,22045],{},[898,22044,18539],{},[1667,22046,1680],{},[902,22048,22017],{"encoding":904}," klesá, protože vyšší výnos obligací snižuje atraktivitu držby peněz):",[724,22051,22052],{},[883,22053,22055],{"className":22054},[886],[888,22056,22057],{"xmlns":890},[892,22058,22059,22113],{},[895,22060,22061,22067,22069,22075,22077,22079,22085,22087,22089,22095,22097,22099,22101,22103,22109,22111],{},[1661,22062,22063,22065],{},[898,22064,18539],{},[1667,22066,1680],{},[1656,22068,1713],{},[1661,22070,22071,22073],{},[898,22072,21970],{},[1667,22074,1680],{},[898,22076,20776],{},[1656,22078,3633],{},[1661,22080,22081,22083],{},[898,22082,21970],{},[1667,22084,2617],{},[1656,22086,1673],{"separator":1672},[3316,22088],{"width":14644},[1661,22090,22091,22093],{},[898,22092,21970],{},[1667,22094,1680],{},[1656,22096,4373],{},[1667,22098,4032],{},[1656,22100,1673],{"separator":1672},[2461,22102,11112],{},[1661,22104,22105,22107],{},[898,22106,21970],{},[1667,22108,2617],{},[1656,22110,2850],{},[1667,22112,4283],{},[902,22114,22115],{"encoding":904},"L_2 = k_2 r + k_3, \\qquad k_2 \u003C 0,\\ k_3 > 0.",[724,22117,22118],{},"Celková poptávka po penězích:",[724,22120,22121],{},[883,22122,22124],{"className":22123},[886],[888,22125,22126],{"xmlns":890},[892,22127,22128,22182],{},[895,22129,22130,22136,22138,22144,22146,22152,22154,22160,22162,22164,22170,22172,22174,22180],{},[2062,22131,22132,22134],{},[898,22133,1703],{},[898,22135,6787],{},[1656,22137,1713],{},[1661,22139,22140,22142],{},[898,22141,18539],{},[1667,22143,1669],{},[1656,22145,3633],{},[1661,22147,22148,22150],{},[898,22149,18539],{},[1667,22151,1680],{},[1656,22153,1713],{},[1661,22155,22156,22158],{},[898,22157,21970],{},[1667,22159,1669],{},[898,22161,8184],{},[1656,22163,3633],{},[1661,22165,22166,22168],{},[898,22167,21970],{},[1667,22169,1680],{},[898,22171,20776],{},[1656,22173,3633],{},[1661,22175,22176,22178],{},[898,22177,21970],{},[1667,22179,2617],{},[898,22181,1863],{"mathvariant":1723},[902,22183,22184],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3.",[724,22186,22187,22188,2114],{},"Podmínka rovnováhy na trhu peněz ",[883,22189,22191],{"className":22190},[886],[888,22192,22193],{"xmlns":890},[892,22194,22195,22211],{},[895,22196,22197,22203,22205],{},[2062,22198,22199,22201],{},[898,22200,1703],{},[898,22202,6787],{},[1656,22204,1713],{},[2062,22206,22207,22209],{},[898,22208,1703],{},[1656,22210,8187],{},[902,22212,22213],{"encoding":904},"M^D = M^*",[724,22215,22216],{},[883,22217,22219],{"className":22218},[886],[888,22220,22221],{"xmlns":890},[892,22222,22223,22270],{},[895,22224,22225,22231,22233,22239,22241,22243,22249,22251,22253,22259,22261,22263,22265,22268],{},[2062,22226,22227,22229],{},[898,22228,1703],{},[1656,22230,8187],{},[1656,22232,1713],{},[1661,22234,22235,22237],{},[898,22236,21970],{},[1667,22238,1669],{},[898,22240,8184],{},[1656,22242,3633],{},[1661,22244,22245,22247],{},[898,22246,21970],{},[1667,22248,1680],{},[898,22250,20776],{},[1656,22252,3633],{},[1661,22254,22255,22257],{},[898,22256,21970],{},[1667,22258,2617],{},[1656,22260,1673],{"separator":1672},[3316,22262],{"width":14644},[1656,22264,1659],{"stretchy":1658},[1667,22266,22267],{},"7.15",[1656,22269,1683],{"stretchy":1658},[902,22271,22272],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3, \\qquad (7.15)",[724,22274,22275,22276,5642],{},"po úpravě (vyjádření ",[883,22277,22279],{"className":22278},[886],[888,22280,22281],{"xmlns":890},[892,22282,22283,22287],{},[895,22284,22285],{},[898,22286,8184],{},[902,22288,8184],{"encoding":904},[724,22290,22291],{},[883,22292,22294],{"className":22293},[886],[888,22295,22296],{"xmlns":890},[892,22297,22298,22373],{},[895,22299,22300,22364,22366,22368,22371],{},[21566,22301,22302],{"notation":21568},[4138,22303,22304],{"scriptlevel":4032,"displaystyle":1658},[4138,22305,22306],{"scriptlevel":4032,"displaystyle":1658},[4138,22307,22308],{"scriptlevel":4032,"displaystyle":1672},[895,22309,22310,22312,22314,22316,22318,22332,22334,22336,22338,22362],{},[2461,22311,7828],{},[898,22313,8184],{},[1656,22315,1713],{},[1656,22317,3964],{},[3294,22319,22320,22326],{},[1661,22321,22322,22324],{},[898,22323,21970],{},[1667,22325,1680],{},[1661,22327,22328,22330],{},[898,22329,21970],{},[1667,22331,1669],{},[2461,22333,7828],{},[898,22335,20776],{},[1656,22337,3633],{},[3294,22339,22340,22356],{},[895,22341,22342,22348,22350],{},[2062,22343,22344,22346],{},[898,22345,1703],{},[1656,22347,8187],{},[1656,22349,3964],{},[1661,22351,22352,22354],{},[898,22353,21970],{},[1667,22355,2617],{},[1661,22357,22358,22360],{},[898,22359,21970],{},[1667,22361,1669],{},[2461,22363,7828],{},[3316,22365],{"width":14644},[1656,22367,1659],{"stretchy":1658},[1667,22369,22370],{},"7.16",[1656,22372,1683],{"stretchy":1658},[902,22374,22375],{"encoding":904},"\\boxed{\\,Y = -\\frac{k_2}{k_1}\\,r + \\frac{M^* - k_3}{k_1}\\,} \\qquad (7.16)",[724,22377,21635,22378,3247,22381,22384,22385,21646,22388,21649,22390,2713,22411,22443,22444,22466,22467,22469,22470,22472],{},[38,22379,22380],{},"funkce LM",[614,22382,22383],{},"LM schedule","), její graf ",[38,22386,22387],{},"křivka LM",[38,22389,4570],{},[883,22391,22393],{"className":22392},[886],[888,22394,22395],{"xmlns":890},[892,22396,22397,22409],{},[895,22398,22399,22401,22403,22405,22407],{},[1656,22400,1659],{"stretchy":1658},[898,22402,20776],{},[1656,22404,1673],{"separator":1672},[898,22406,8184],{},[1656,22408,1683],{"stretchy":1658},[902,22410,21671],{"encoding":904},[883,22412,22414],{"className":22413},[886],[888,22415,22416],{"xmlns":890},[892,22417,22418,22440],{},[895,22419,22420,22422,22436,22438],{},[1656,22421,3964],{},[3294,22423,22424,22430],{},[1661,22425,22426,22428],{},[898,22427,21970],{},[1667,22429,1680],{},[1661,22431,22432,22434],{},[898,22433,21970],{},[1667,22435,1669],{},[1656,22437,2850],{},[1667,22439,4032],{},[902,22441,22442],{"encoding":904},"-\\frac{k_2}{k_1} > 0"," (čitatel kladný, protože ",[883,22445,22447],{"className":22446},[886],[888,22448,22449],{"xmlns":890},[892,22450,22451,22463],{},[895,22452,22453,22459,22461],{},[1661,22454,22455,22457],{},[898,22456,21970],{},[1667,22458,1680],{},[1656,22460,4373],{},[1667,22462,4032],{},[902,22464,22465],{"encoding":904},"k_2 \u003C 0",", jmenovatel kladný). Název: ",[38,22468,18539],{},"iquidity of ",[38,22471,1703],{},"oney.",[1981,22474,22475],{},[724,22476,22477,22479,22480,22493,22494,22522,22523,22540,22541,22554,22555,22572,22573,1896,22586,22599,22600,22603],{},[883,22478,3472],{}," Intuice — proč LM roste\nVyšší důchod ",[883,22481,22483],{"className":22482},[886],[888,22484,22485],{"xmlns":890},[892,22486,22487,22491],{},[895,22488,22489],{},[898,22490,8184],{},[902,22492,8184],{"encoding":904}," → větší transakční poptávka po penězích ",[883,22495,22497],{"className":22496},[886],[888,22498,22499],{"xmlns":890},[892,22500,22501,22519],{},[895,22502,22503,22509,22511,22517],{},[1661,22504,22505,22507],{},[898,22506,18539],{},[1667,22508,1669],{},[1656,22510,1713],{},[1661,22512,22513,22515],{},[898,22514,21970],{},[1667,22516,1669],{},[898,22518,8184],{},[902,22520,22521],{"encoding":904},"L_1 = k_1 Y"," → při pevné nabídce ",[883,22524,22526],{"className":22525},[886],[888,22527,22528],{"xmlns":890},[892,22529,22530,22538],{},[895,22531,22532],{},[2062,22533,22534,22536],{},[898,22535,1703],{},[1656,22537,8187],{},[902,22539,20885],{"encoding":904}," vzniká na trhu peněz přebytek poptávky → úroková míra ",[883,22542,22544],{"className":22543},[886],[888,22545,22546],{"xmlns":890},[892,22547,22548,22552],{},[895,22549,22550],{},[898,22551,20776],{},[902,22553,20776],{"encoding":904}," musí vzrůst, aby se spekulační poptávka ",[883,22556,22558],{"className":22557},[886],[888,22559,22560],{"xmlns":890},[892,22561,22562,22570],{},[895,22563,22564],{},[1661,22565,22566,22568],{},[898,22567,18539],{},[1667,22569,1680],{},[902,22571,22017],{"encoding":904}," stlačila a trh se vyrovnal. Vztah mezi ",[883,22574,22576],{"className":22575},[886],[888,22577,22578],{"xmlns":890},[892,22579,22580,22584],{},[895,22581,22582],{},[898,22583,8184],{},[902,22585,8184],{"encoding":904},[883,22587,22589],{"className":22588},[886],[888,22590,22591],{"xmlns":890},[892,22592,22593,22597],{},[895,22594,22595],{},[898,22596,20776],{},[902,22598,20776],{"encoding":904}," na trhu peněz je proto ",[38,22601,22602],{},"přímý"," (rostoucí křivka).",[115,22605,22607],{"id":22606},"simultánní-rovnováha-is-lm","Simultánní rovnováha IS-LM",[724,22609,22610,22611,22614,22615,1643,22618,1896,22636,1643,22639,22657,22658,22676,22677,22695,22696,22712,22713,1896,22728,22743,22744,1863],{},"Řešením ",[38,22612,22613],{},"soustavy dvou lineárních rovnic"," (7.14) a (7.15) určíme ",[38,22616,22617],{},"rovnovážný důchod",[883,22619,22621],{"className":22620},[886],[888,22622,22623],{"xmlns":890},[892,22624,22625,22633],{},[895,22626,22627],{},[2062,22628,22629,22631],{},[898,22630,8184],{},[898,22632,1842],{},[902,22634,22635],{"encoding":904},"Y^E",[38,22637,22638],{},"rovnovážnou úrokovou míru",[883,22640,22642],{"className":22641},[886],[888,22643,22644],{"xmlns":890},[892,22645,22646,22654],{},[895,22647,22648],{},[2062,22649,22650,22652],{},[898,22651,20776],{},[898,22653,1842],{},[902,22655,22656],{"encoding":904},"r^E","; zpětným dosazením do (7.11) a (7.12) pak rovnovážné investice ",[883,22659,22661],{"className":22660},[886],[888,22662,22663],{"xmlns":890},[892,22664,22665,22673],{},[895,22666,22667],{},[2062,22668,22669,22671],{},[898,22670,20919],{},[898,22672,1842],{},[902,22674,22675],{"encoding":904},"I^E"," a rovnovážnou spotřebu ",[883,22678,22680],{"className":22679},[886],[888,22681,22682],{"xmlns":890},[892,22683,22684,22692],{},[895,22685,22686],{},[2062,22687,22688,22690],{},[898,22689,1766],{},[898,22691,1842],{},[902,22693,22694],{"encoding":904},"C^E",". Graficky jde o ",[38,22697,22698,22699],{},"průsečík ",[883,22700,22702],{"className":22701},[886],[888,22703,22704],{"xmlns":890},[892,22705,22706,22710],{},[895,22707,22708],{},[898,22709,1842],{},[902,22711,1842],{"encoding":904}," křivek ",[883,22714,22716],{"className":22715},[886],[888,22717,22718],{"xmlns":890},[892,22719,22720,22726],{},[895,22721,22722,22724],{},[898,22723,20919],{},[898,22725,1769],{},[902,22727,20786],{"encoding":904},[883,22729,22731],{"className":22730},[886],[888,22732,22733],{"xmlns":890},[892,22734,22735,22741],{},[895,22736,22737,22739],{},[898,22738,18539],{},[898,22740,1703],{},[902,22742,20793],{"encoding":904}," v rovině ",[883,22745,22747],{"className":22746},[886],[888,22748,22749],{"xmlns":890},[892,22750,22751,22763],{},[895,22752,22753,22755,22757,22759,22761],{},[1656,22754,1659],{"stretchy":1658},[898,22756,20776],{},[1656,22758,1673],{"separator":1672},[898,22760,8184],{},[1656,22762,1683],{"stretchy":1658},[902,22764,21671],{"encoding":904},[724,22766,22767],{},[614,22768,22769,22770,22791,22792,22807,22808,22823,22824,22837,22838,22855,22856,20863,22869,22855,22886,22899,22900,22913],{},"Obrázek 7.6 — Schematický graf v rovině ",[883,22771,22773],{"className":22772},[886],[888,22774,22775],{"xmlns":890},[892,22776,22777,22789],{},[895,22778,22779,22781,22783,22785,22787],{},[1656,22780,1659],{"stretchy":1658},[898,22782,20776],{},[1656,22784,1673],{"separator":1672},[898,22786,8184],{},[1656,22788,1683],{"stretchy":1658},[902,22790,21671],{"encoding":904},". Rostoucí přímka ",[883,22793,22795],{"className":22794},[886],[888,22796,22797],{"xmlns":890},[892,22798,22799,22805],{},[895,22800,22801,22803],{},[898,22802,18539],{},[898,22804,1703],{},[902,22806,20793],{"encoding":904}," a klesající přímka ",[883,22809,22811],{"className":22810},[886],[888,22812,22813],{"xmlns":890},[892,22814,22815,22821],{},[895,22816,22817,22819],{},[898,22818,20919],{},[898,22820,1769],{},[902,22822,20786],{"encoding":904}," se protínají v bodě ",[883,22825,22827],{"className":22826},[886],[888,22828,22829],{"xmlns":890},[892,22830,22831,22835],{},[895,22832,22833],{},[898,22834,1842],{},[902,22836,1842],{"encoding":904}," se souřadnicemi ",[883,22839,22841],{"className":22840},[886],[888,22842,22843],{"xmlns":890},[892,22844,22845,22853],{},[895,22846,22847],{},[2062,22848,22849,22851],{},[898,22850,20776],{},[898,22852,1842],{},[902,22854,22656],{"encoding":904}," (na ose ",[883,22857,22859],{"className":22858},[886],[888,22860,22861],{"xmlns":890},[892,22862,22863,22867],{},[895,22864,22865],{},[898,22866,20776],{},[902,22868,20776],{"encoding":904},[883,22870,22872],{"className":22871},[886],[888,22873,22874],{"xmlns":890},[892,22875,22876,22884],{},[895,22877,22878],{},[2062,22879,22880,22882],{},[898,22881,8184],{},[898,22883,1842],{},[902,22885,22635],{"encoding":904},[883,22887,22889],{"className":22888},[886],[888,22890,22891],{"xmlns":890},[892,22892,22893,22897],{},[895,22894,22895],{},[898,22896,8184],{},[902,22898,8184],{"encoding":904},"); tečkované čáry z ",[883,22901,22903],{"className":22902},[886],[888,22904,22905],{"xmlns":890},[892,22906,22907,22911],{},[895,22908,22909],{},[898,22910,1842],{},[902,22912,1842],{"encoding":904}," kolmé k osám vyznačují polohu rovnovážné úrokové míry a rovnovážného národního důchodu.",[1981,22915,22916,22921],{},[724,22917,22918,22920],{},[883,22919,10188],{}," Postup — jak najít IS-LM rovnováhu",[152,22922,22923,22999,23067,23125,23198],{},[123,22924,22925,22928,22929,1896,22949,22969,22970,1896,22983,22996,22997,1863],{},[38,22926,22927],{},"Z trhu zboží (7.13)"," dosaď funkce ",[883,22930,22932],{"className":22931},[886],[888,22933,22934],{"xmlns":890},[892,22935,22936,22946],{},[895,22937,22938,22940,22942,22944],{},[898,22939,1766],{},[1656,22941,1659],{"stretchy":1658},[898,22943,8184],{},[1656,22945,1683],{"stretchy":1658},[902,22947,22948],{"encoding":904},"C(Y)",[883,22950,22952],{"className":22951},[886],[888,22953,22954],{"xmlns":890},[892,22955,22956,22966],{},[895,22957,22958,22960,22962,22964],{},[898,22959,20919],{},[1656,22961,1659],{"stretchy":1658},[898,22963,20776],{},[1656,22965,1683],{"stretchy":1658},[902,22967,22968],{"encoding":904},"I(r)"," a vyjádři vztah mezi ",[883,22971,22973],{"className":22972},[886],[888,22974,22975],{"xmlns":890},[892,22976,22977,22981],{},[895,22978,22979],{},[898,22980,8184],{},[902,22982,8184],{"encoding":904},[883,22984,22986],{"className":22985},[886],[888,22987,22988],{"xmlns":890},[892,22989,22990,22994],{},[895,22991,22992],{},[898,22993,20776],{},[902,22995,20776],{"encoding":904}," — dostaneš rovnici ",[38,22998,20786],{},[123,23000,23001,23004,23005,1896,23022,23039,23040,22996,23065,1863],{},[38,23002,23003],{},"Z trhu peněz (7.15)"," dosaď ",[883,23006,23008],{"className":23007},[886],[888,23009,23010],{"xmlns":890},[892,23011,23012,23020],{},[895,23013,23014],{},[1661,23015,23016,23018],{},[898,23017,18539],{},[1667,23019,1669],{},[902,23021,21945],{"encoding":904},[883,23023,23025],{"className":23024},[886],[888,23026,23027],{"xmlns":890},[892,23028,23029,23037],{},[895,23030,23031],{},[1661,23032,23033,23035],{},[898,23034,18539],{},[1667,23036,1680],{},[902,23038,22017],{"encoding":904}," a vztah ",[883,23041,23043],{"className":23042},[886],[888,23044,23045],{"xmlns":890},[892,23046,23047,23063],{},[895,23048,23049,23055,23057],{},[2062,23050,23051,23053],{},[898,23052,1703],{},[898,23054,6787],{},[1656,23056,1713],{},[2062,23058,23059,23061],{},[898,23060,1703],{},[1656,23062,8187],{},[902,23064,22213],{"encoding":904},[38,23066,20793],{},[123,23068,23069,23072,23073,1896,23086,23099,23100,23124],{},[38,23070,23071],{},"Vyřeš soustavu"," dvou lineárních rovnic o dvou neznámých ",[883,23074,23076],{"className":23075},[886],[888,23077,23078],{"xmlns":890},[892,23079,23080,23084],{},[895,23081,23082],{},[898,23083,8184],{},[902,23085,8184],{"encoding":904},[883,23087,23089],{"className":23088},[886],[888,23090,23091],{"xmlns":890},[892,23092,23093,23097],{},[895,23094,23095],{},[898,23096,20776],{},[902,23098,20776],{"encoding":904}," — nejsnáze substituční metodou (vyjádři z IS ",[883,23101,23103],{"className":23102},[886],[888,23104,23105],{"xmlns":890},[892,23106,23107,23121],{},[895,23108,23109,23111,23113,23115,23117,23119],{},[898,23110,8184],{},[1656,23112,1713],{},[898,23114,7524],{},[1656,23116,1659],{"stretchy":1658},[898,23118,20776],{},[1656,23120,1683],{"stretchy":1658},[902,23122,23123],{"encoding":904},"Y = f(r)"," a dosaď do LM).",[123,23126,23127,1643,23130,1896,23164,1863],{},[38,23128,23129],{},"Zpětně dopočítej",[883,23131,23133],{"className":23132},[886],[888,23134,23135],{"xmlns":890},[892,23136,23137,23161],{},[895,23138,23139,23145,23147,23149,23151,23157,23159],{},[2062,23140,23141,23143],{},[898,23142,1766],{},[898,23144,1842],{},[1656,23146,1713],{},[898,23148,207],{},[2461,23150,7828],{},[2062,23152,23153,23155],{},[898,23154,8184],{},[898,23156,1842],{},[1656,23158,3633],{},[898,23160,3403],{},[902,23162,23163],{"encoding":904},"C^E = a\\,Y^E + b",[883,23165,23167],{"className":23166},[886],[888,23168,23169],{"xmlns":890},[892,23170,23171,23195],{},[895,23172,23173,23179,23181,23183,23185,23191,23193],{},[2062,23174,23175,23177],{},[898,23176,20919],{},[898,23178,1842],{},[1656,23180,1713],{},[898,23182,1745],{},[2461,23184,7828],{},[2062,23186,23187,23189],{},[898,23188,20776],{},[898,23190,1842],{},[1656,23192,3633],{},[898,23194,3768],{},[902,23196,23197],{"encoding":904},"I^E = c\\,r^E + d",[123,23199,23200,23203,23204,23238,23239,23293],{},[38,23201,23202],{},"Ověř:"," musí platit ",[883,23205,23207],{"className":23206},[886],[888,23208,23209],{"xmlns":890},[892,23210,23211,23235],{},[895,23212,23213,23219,23221,23227,23229],{},[2062,23214,23215,23217],{},[898,23216,8184],{},[898,23218,1842],{},[1656,23220,1713],{},[2062,23222,23223,23225],{},[898,23224,1766],{},[898,23226,1842],{},[1656,23228,3633],{},[2062,23230,23231,23233],{},[898,23232,20919],{},[898,23234,1842],{},[902,23236,23237],{"encoding":904},"Y^E = C^E + I^E"," (rovnováha trhu zboží) i ",[883,23240,23242],{"className":23241},[886],[888,23243,23244],{"xmlns":890},[892,23245,23246,23290],{},[895,23247,23248,23254,23256,23262,23268,23270,23276,23282,23284],{},[2062,23249,23250,23252],{},[898,23251,1703],{},[1656,23253,8187],{},[1656,23255,1713],{},[1661,23257,23258,23260],{},[898,23259,21970],{},[1667,23261,1669],{},[2062,23263,23264,23266],{},[898,23265,8184],{},[898,23267,1842],{},[1656,23269,3633],{},[1661,23271,23272,23274],{},[898,23273,21970],{},[1667,23275,1680],{},[2062,23277,23278,23280],{},[898,23279,20776],{},[898,23281,1842],{},[1656,23283,3633],{},[1661,23285,23286,23288],{},[898,23287,21970],{},[1667,23289,2617],{},[902,23291,23292],{"encoding":904},"M^* = k_1 Y^E + k_2 r^E + k_3"," (rovnováha trhu peněz).",[115,23295,23297],{"id":23296},"příklad-76-is-lm","Příklad 7.6 (IS-LM)",[724,23299,23300],{},"Pro trh zboží jsou dány:",[120,23302,23303,23331],{},[123,23304,23305,23306,1673],{},"spotřeba ",[883,23307,23309],{"className":23308},[886],[888,23310,23311],{"xmlns":890},[892,23312,23313,23328],{},[895,23314,23315,23317,23319,23322,23324,23326],{},[898,23316,1766],{},[1656,23318,1713],{},[1667,23320,23321],{},"0,8",[898,23323,8184],{},[1656,23325,3633],{},[1667,23327,5267],{},[902,23329,23330],{"encoding":904},"C = 0{,}8Y + 100",[123,23332,23333,23334,1863],{},"investice ",[883,23335,23337],{"className":23336},[886],[888,23338,23339],{"xmlns":890},[892,23340,23341,23357],{},[895,23342,23343,23345,23347,23349,23351,23353,23355],{},[898,23344,20919],{},[1656,23346,1713],{},[1656,23348,3964],{},[1667,23350,9058],{},[898,23352,20776],{},[1656,23354,3633],{},[1667,23356,11584],{},[902,23358,23359],{"encoding":904},"I = -20r + 1000",[724,23361,23362],{},"Pro trh peněz:",[120,23364,23365,23391,23423],{},[123,23366,23367,1673],{},[883,23368,23370],{"className":23369},[886],[888,23371,23372],{"xmlns":890},[892,23373,23374,23388],{},[895,23375,23376,23382,23384,23386],{},[1661,23377,23378,23380],{},[898,23379,18539],{},[1667,23381,1669],{},[1656,23383,1713],{},[1667,23385,11595],{},[898,23387,8184],{},[902,23389,23390],{"encoding":904},"L_1 = 0{,}1Y",[123,23392,23393,1673],{},[883,23394,23396],{"className":23395},[886],[888,23397,23398],{"xmlns":890},[892,23399,23400,23420],{},[895,23401,23402,23408,23410,23412,23414,23416,23418],{},[1661,23403,23404,23406],{},[898,23405,18539],{},[1667,23407,1680],{},[1656,23409,1713],{},[1656,23411,3964],{},[1667,23413,8567],{},[898,23415,20776],{},[1656,23417,3633],{},[1667,23419,17359],{},[902,23421,23422],{"encoding":904},"L_2 = -25r + 2000",[123,23424,23425,23426,1863],{},"nabídka peněz ",[883,23427,23429],{"className":23428},[886],[888,23430,23431],{"xmlns":890},[892,23432,23433,23446],{},[895,23434,23435,23441,23443],{},[2062,23436,23437,23439],{},[898,23438,1703],{},[1656,23440,8187],{},[1656,23442,1713],{},[1667,23444,23445],{},"2375",[902,23447,23448],{"encoding":904},"M^* = 2375",[724,23450,23451,23454,23455,2114],{},[38,23452,23453],{},"Funkce IS"," — dosazením do (7.13) ",[883,23456,23458],{"className":23457},[886],[888,23459,23460],{"xmlns":890},[892,23461,23462,23474],{},[895,23463,23464,23466,23468,23470,23472],{},[898,23465,8184],{},[1656,23467,1713],{},[898,23469,1766],{},[1656,23471,3633],{},[898,23473,20919],{},[902,23475,23476],{"encoding":904},"Y = C + I",[724,23478,23479],{},[883,23480,23482],{"className":23481},[886],[888,23483,23484],{"xmlns":890},[892,23485,23486,23512],{},[895,23487,23488,23490,23492,23494,23496,23498,23500,23502,23504,23506,23508,23510],{},[898,23489,8184],{},[1656,23491,1713],{},[1667,23493,23321],{},[898,23495,8184],{},[1656,23497,3633],{},[1667,23499,5267],{},[1656,23501,3964],{},[1667,23503,9058],{},[898,23505,20776],{},[1656,23507,3633],{},[1667,23509,11584],{},[1656,23511,1673],{"separator":1672},[902,23513,23514],{"encoding":904},"Y = 0{,}8Y + 100 - 20r + 1000,",[724,23516,23517],{},"tj.",[724,23519,23520],{},[883,23521,23523],{"className":23522},[886],[888,23524,23525],{"xmlns":890},[892,23526,23527,23552],{},[895,23528,23529,23531,23533,23535,23537,23539,23541,23544,23546,23548,23550],{},[1667,23530,11639],{},[898,23532,8184],{},[1656,23534,3633],{},[1667,23536,9058],{},[898,23538,20776],{},[1656,23540,1713],{},[1667,23542,23543],{},"1100.",[3316,23545],{"width":14644},[1656,23547,1659],{"stretchy":1658},[2461,23549,20786],{},[1656,23551,1683],{"stretchy":1658},[902,23553,23554],{"encoding":904},"0{,}2Y + 20r = 1100. \\qquad (\\text{IS})",[724,23556,23557,23560,23561,2114],{},[38,23558,23559],{},"Funkce LM"," — dosazením do (7.15) ",[883,23562,23564],{"className":23563},[886],[888,23565,23566],{"xmlns":890},[892,23567,23568,23592],{},[895,23569,23570,23576,23578,23584,23586],{},[2062,23571,23572,23574],{},[898,23573,1703],{},[1656,23575,8187],{},[1656,23577,1713],{},[1661,23579,23580,23582],{},[898,23581,18539],{},[1667,23583,1669],{},[1656,23585,3633],{},[1661,23587,23588,23590],{},[898,23589,18539],{},[1667,23591,1680],{},[902,23593,23594],{"encoding":904},"M^* = L_1 + L_2",[724,23596,23597],{},[883,23598,23600],{"className":23599},[886],[888,23601,23602],{"xmlns":890},[892,23603,23604,23626],{},[895,23605,23606,23608,23610,23612,23614,23616,23618,23620,23622,23624],{},[1667,23607,23445],{},[1656,23609,1713],{},[1667,23611,11595],{},[898,23613,8184],{},[1656,23615,3964],{},[1667,23617,8567],{},[898,23619,20776],{},[1656,23621,3633],{},[1667,23623,17359],{},[1656,23625,1673],{"separator":1672},[902,23627,23628],{"encoding":904},"2375 = 0{,}1Y - 25r + 2000,",[724,23630,23517],{},[724,23632,23633],{},[883,23634,23636],{"className":23635},[886],[888,23637,23638],{"xmlns":890},[892,23639,23640,23665],{},[895,23641,23642,23644,23646,23648,23650,23652,23654,23657,23659,23661,23663],{},[1667,23643,11595],{},[898,23645,8184],{},[1656,23647,3964],{},[1667,23649,8567],{},[898,23651,20776],{},[1656,23653,1713],{},[1667,23655,23656],{},"375.",[3316,23658],{"width":14644},[1656,23660,1659],{"stretchy":1658},[2461,23662,20793],{},[1656,23664,1683],{"stretchy":1658},[902,23666,23667],{"encoding":904},"0{,}1Y - 25r = 375. \\qquad (\\text{LM})",[724,23669,23670,23673,23674,23699],{},[38,23671,23672],{},"Řešení soustavy."," Z (IS) vyjádříme ",[883,23675,23677],{"className":23676},[886],[888,23678,23679],{"xmlns":890},[892,23680,23681,23696],{},[895,23682,23683,23685,23687,23690,23692,23694],{},[898,23684,8184],{},[1656,23686,1713],{},[1667,23688,23689],{},"5500",[1656,23691,3964],{},[1667,23693,5267],{},[898,23695,20776],{},[902,23697,23698],{"encoding":904},"Y = 5500 - 100r"," a dosadíme do (LM):",[724,23701,23702],{},[883,23703,23705],{"className":23704},[886],[888,23706,23707],{"xmlns":890},[892,23708,23709,23795],{},[895,23710,23711,23713,23715,23717,23719,23721,23723,23725,23727,23729,23731,23733,23736,23738,23741,23743,23746,23748,23750,23752,23754,23756,23758,23760,23762,23764,23766,23768,23771,23773,23775,23778,23780,23782,23784,23790,23792],{},[1667,23712,11595],{},[1656,23714,1659],{"stretchy":1658},[1667,23716,23689],{},[1656,23718,3964],{},[1667,23720,5267],{},[898,23722,20776],{},[1656,23724,1683],{"stretchy":1658},[1656,23726,3964],{},[1667,23728,8567],{},[898,23730,20776],{},[1656,23732,1713],{},[1667,23734,23735],{},"375",[2461,23737,12767],{},[1656,23739,23740],{},"⟹",[2461,23742,12767],{},[1667,23744,23745],{},"550",[1656,23747,3964],{},[1667,23749,8580],{},[898,23751,20776],{},[1656,23753,3964],{},[1667,23755,8567],{},[898,23757,20776],{},[1656,23759,1713],{},[1667,23761,23735],{},[2461,23763,12767],{},[1656,23765,23740],{},[2461,23767,12767],{},[1667,23769,23770],{},"35",[898,23772,20776],{},[1656,23774,1713],{},[1667,23776,23777],{},"175",[2461,23779,12767],{},[1656,23781,23740],{},[2461,23783,12767],{},[2062,23785,23786,23788],{},[898,23787,20776],{},[898,23789,1842],{},[1656,23791,1713],{},[1667,23793,23794],{},"5.",[902,23796,23797],{"encoding":904},"0{,}1(5500 - 100r) - 25r = 375 \\;\\Longrightarrow\\; 550 - 10r - 25r = 375 \\;\\Longrightarrow\\; 35r = 175 \\;\\Longrightarrow\\; r^E = 5.",[724,23799,23800],{},[38,23801,23802],{},"Zpětné dosazení:",[120,23804,23805,23850,23887],{},[123,23806,23807,1673],{},[883,23808,23810],{"className":23809},[886],[888,23811,23812],{"xmlns":890},[892,23813,23814,23847],{},[895,23815,23816,23822,23824,23826,23828,23830,23832,23834,23836,23838,23840,23842,23844],{},[2062,23817,23818,23820],{},[898,23819,8184],{},[898,23821,1842],{},[1656,23823,1713],{},[1667,23825,23689],{},[1656,23827,3964],{},[1667,23829,5267],{},[1656,23831,2751],{},[1667,23833,5193],{},[1656,23835,1713],{},[1667,23837,23689],{},[1656,23839,3964],{},[1667,23841,8059],{},[1656,23843,1713],{},[1667,23845,23846],{},"5000",[902,23848,23849],{"encoding":904},"Y^E = 5500 - 100 \\cdot 5 = 5500 - 500 = 5000",[123,23851,23852,1673],{},[883,23853,23855],{"className":23854},[886],[888,23856,23857],{"xmlns":890},[892,23858,23859,23884],{},[895,23860,23861,23867,23869,23871,23873,23875,23877,23879,23881],{},[2062,23862,23863,23865],{},[898,23864,1766],{},[898,23866,1842],{},[1656,23868,1713],{},[1667,23870,23321],{},[1656,23872,2751],{},[1667,23874,23846],{},[1656,23876,3633],{},[1667,23878,5267],{},[1656,23880,1713],{},[1667,23882,23883],{},"4100",[902,23885,23886],{"encoding":904},"C^E = 0{,}8 \\cdot 5000 + 100 = 4100",[123,23888,23889,1863],{},[883,23890,23892],{"className":23891},[886],[888,23893,23894],{"xmlns":890},[892,23895,23896,23923],{},[895,23897,23898,23904,23906,23908,23910,23912,23914,23916,23918,23920],{},[2062,23899,23900,23902],{},[898,23901,20919],{},[898,23903,1842],{},[1656,23905,1713],{},[1656,23907,3964],{},[1667,23909,9058],{},[1656,23911,2751],{},[1667,23913,5193],{},[1656,23915,3633],{},[1667,23917,11584],{},[1656,23919,1713],{},[1667,23921,23922],{},"900",[902,23924,23925],{"encoding":904},"I^E = -20 \\cdot 5 + 1000 = 900",[724,23927,23928,1643,23931,23977],{},[38,23929,23930],{},"Ověření:",[883,23932,23934],{"className":23933},[886],[888,23935,23936],{"xmlns":890},[892,23937,23938,23974],{},[895,23939,23940,23946,23948,23954,23956,23958,23960,23962,23964,23966,23968],{},[2062,23941,23942,23944],{},[898,23943,1766],{},[898,23945,1842],{},[1656,23947,3633],{},[2062,23949,23950,23952],{},[898,23951,20919],{},[898,23953,1842],{},[1656,23955,1713],{},[1667,23957,23883],{},[1656,23959,3633],{},[1667,23961,23922],{},[1656,23963,1713],{},[1667,23965,23846],{},[1656,23967,1713],{},[2062,23969,23970,23972],{},[898,23971,8184],{},[898,23973,1842],{},[902,23975,23976],{"encoding":904},"C^E + I^E = 4100 + 900 = 5000 = Y^E",". ✓",[724,23979,23980],{},[883,23981,23983],{"className":23982},[886],[888,23984,23985],{"xmlns":890},[892,23986,23987,24056],{},[895,23988,23989],{},[21566,23990,23991],{"notation":21568},[4138,23992,23993],{"scriptlevel":4032,"displaystyle":1658},[4138,23994,23995],{"scriptlevel":4032,"displaystyle":1658},[4138,23996,23997],{"scriptlevel":4032,"displaystyle":1672},[895,23998,23999,24001,24007,24009,24011,24013,24015,24021,24023,24025,24027,24029,24035,24037,24039,24041,24043,24049,24051,24054],{},[2461,24000,7828],{},[2062,24002,24003,24005],{},[898,24004,8184],{},[898,24006,1842],{},[1656,24008,1713],{},[1667,24010,23846],{},[1656,24012,1673],{"separator":1672},[3316,24014],{"width":3318},[2062,24016,24017,24019],{},[898,24018,20776],{},[898,24020,1842],{},[1656,24022,1713],{},[1667,24024,5193],{},[1656,24026,1673],{"separator":1672},[3316,24028],{"width":3318},[2062,24030,24031,24033],{},[898,24032,1766],{},[898,24034,1842],{},[1656,24036,1713],{},[1667,24038,23883],{},[1656,24040,1673],{"separator":1672},[3316,24042],{"width":3318},[2062,24044,24045,24047],{},[898,24046,20919],{},[898,24048,1842],{},[1656,24050,1713],{},[1667,24052,24053],{},"900.",[2461,24055,7828],{},[902,24057,24058],{"encoding":904},"\\boxed{\\,Y^E = 5000, \\quad r^E = 5, \\quad C^E = 4100, \\quad I^E = 900.\\,}",[724,24060,24061],{},[614,24062,24063,24064,24077,24078,24091,24092,24107,24108,24121,24122,24137,24138,24151,24152,24165,24166,1863],{},"Obrázek 7.7 — Konkrétní numerický příklad IS-LM rovnováhy. Na ose ",[883,24065,24067],{"className":24066},[886],[888,24068,24069],{"xmlns":890},[892,24070,24071,24075],{},[895,24072,24073],{},[898,24074,8184],{},[902,24076,8184],{"encoding":904}," jsou vyznačeny hodnoty 3750, 5000, 5500; na ose ",[883,24079,24081],{"className":24080},[886],[888,24082,24083],{"xmlns":890},[892,24084,24085,24089],{},[895,24086,24087],{},[898,24088,20776],{},[902,24090,20776],{"encoding":904}," hodnoty 5 a 55. Přímka ",[883,24093,24095],{"className":24094},[886],[888,24096,24097],{"xmlns":890},[892,24098,24099,24105],{},[895,24100,24101,24103],{},[898,24102,18539],{},[898,24104,1703],{},[902,24106,20793],{"encoding":904}," stoupá z oblasti nízkých ",[883,24109,24111],{"className":24110},[886],[888,24112,24113],{"xmlns":890},[892,24114,24115,24119],{},[895,24116,24117],{},[898,24118,20776],{},[902,24120,20776],{"encoding":904},", přímka ",[883,24123,24125],{"className":24124},[886],[888,24126,24127],{"xmlns":890},[892,24128,24129,24135],{},[895,24130,24131,24133],{},[898,24132,20919],{},[898,24134,1769],{},[902,24136,20786],{"encoding":904}," klesá a protíná osu ",[883,24139,24141],{"className":24140},[886],[888,24142,24143],{"xmlns":890},[892,24144,24145,24149],{},[895,24146,24147],{},[898,24148,20776],{},[902,24150,20776],{"encoding":904}," kolem hodnoty 55. Průsečík ",[883,24153,24155],{"className":24154},[886],[888,24156,24157],{"xmlns":890},[892,24158,24159,24163],{},[895,24160,24161],{},[898,24162,1842],{},[902,24164,1842],{"encoding":904}," leží v bodě ",[883,24167,24169],{"className":24168},[886],[888,24170,24171],{"xmlns":890},[892,24172,24173,24195],{},[895,24174,24175,24177,24179,24181,24183,24185,24187,24189,24191,24193],{},[1656,24176,3453],{"stretchy":1658},[898,24178,20776],{},[1656,24180,1713],{},[1667,24182,5193],{},[1656,24184,1673],{"separator":1672},[2461,24186,11112],{},[898,24188,8184],{},[1656,24190,1713],{},[1667,24192,23846],{},[1656,24194,3462],{"stretchy":1658},[902,24196,24197],{"encoding":904},"[r = 5,\\ Y = 5000]",[115,24199,24201],{"id":24200},"ekonomická-interpretace-fiskální-a-monetární-politika","Ekonomická interpretace — fiskální a monetární politika",[724,24203,24204,24207,24208,24221,24222,2533,24235,24238,24239,24257,24258,24275,24276,24293,24294,24307,24308,24321],{},[38,24205,24206],{},"Posun křivky IS (fiskální politika)."," Expanzivní fiskální politika — zvýšení vládních výdajů ",[883,24209,24211],{"className":24210},[886],[888,24212,24213],{"xmlns":890},[892,24214,24215,24219],{},[895,24216,24217],{},[898,24218,20847],{},[902,24220,20847],{"encoding":904}," nebo snížení daní ",[883,24223,24225],{"className":24224},[886],[888,24226,24227],{"xmlns":890},[892,24228,24229,24233],{},[895,24230,24231],{},[898,24232,11577],{},[902,24234,11577],{"encoding":904},[38,24236,24237],{},"posouvá IS doprava",": při dané úrokové míře vzroste rovnovážný důchod trhu zboží. Nová rovnováha ",[883,24240,24242],{"className":24241},[886],[888,24243,24244],{"xmlns":890},[892,24245,24246,24254],{},[895,24247,24248],{},[2062,24249,24250,24252],{},[898,24251,1842],{},[1656,24253,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[902,24255,24256],{"encoding":904},"E'"," má vyšší ",[883,24259,24261],{"className":24260},[886],[888,24262,24263],{"xmlns":890},[892,24264,24265,24273],{},[895,24266,24267],{},[2062,24268,24269,24271],{},[898,24270,8184],{},[898,24272,1842],{},[902,24274,22635],{"encoding":904}," i vyšší ",[883,24277,24279],{"className":24278},[886],[888,24280,24281],{"xmlns":890},[892,24282,24283,24291],{},[895,24284,24285],{},[2062,24286,24287,24289],{},[898,24288,20776],{},[898,24290,1842],{},[902,24292,22656],{"encoding":904}," (vyšší ",[883,24295,24297],{"className":24296},[886],[888,24298,24299],{"xmlns":890},[892,24300,24301,24305],{},[895,24302,24303],{},[898,24304,8184],{},[902,24306,8184],{"encoding":904}," zvedá poptávku po penězích, což tlačí ",[883,24309,24311],{"className":24310},[886],[888,24312,24313],{"xmlns":890},[892,24314,24315,24319],{},[895,24316,24317],{},[898,24318,20776],{},[902,24320,20776],{"encoding":904}," nahoru).",[724,24323,24324],{},[5956,24325],{"alt":24326,"className":24327,"src":24328},"imek-posun-is-lm-politiky",[210,5960],"\u002Fwiki-assets\u002Fimek-posun-is-lm-politiky.jpeg",[724,24330,24331,24334,24335,24352,24353,24356,24357,24374,24375,24392,24393,24406,24407,24426,24427,12702],{},[38,24332,24333],{},"Posun křivky LM (monetární politika)."," Expanzivní monetární politika — zvýšení nabídky peněz ",[883,24336,24338],{"className":24337},[886],[888,24339,24340],{"xmlns":890},[892,24341,24342,24350],{},[895,24343,24344],{},[2062,24345,24346,24348],{},[898,24347,1703],{},[1656,24349,8187],{},[902,24351,20885],{"encoding":904}," národní bankou — ",[38,24354,24355],{},"posouvá LM doprava\u002Fdolů",": při daném důchodu je trh peněz v rovnováze při nižší úrokové míře. Nová rovnováha má nižší ",[883,24358,24360],{"className":24359},[886],[888,24361,24362],{"xmlns":890},[892,24363,24364,24372],{},[895,24365,24366],{},[2062,24367,24368,24370],{},[898,24369,20776],{},[898,24371,1842],{},[902,24373,22656],{"encoding":904}," a vyšší ",[883,24376,24378],{"className":24377},[886],[888,24379,24380],{"xmlns":890},[892,24381,24382,24390],{},[895,24383,24384],{},[2062,24385,24386,24388],{},[898,24387,8184],{},[898,24389,1842],{},[902,24391,22635],{"encoding":904}," (nižší ",[883,24394,24396],{"className":24395},[886],[888,24397,24398],{"xmlns":890},[892,24399,24400,24404],{},[895,24401,24402],{},[898,24403,20776],{},[902,24405,20776],{"encoding":904}," povzbuzuje investice ",[883,24408,24410],{"className":24409},[886],[888,24411,24412],{"xmlns":890},[892,24413,24414,24424],{},[895,24415,24416,24418,24420,24422],{},[898,24417,20919],{},[1656,24419,1659],{"stretchy":1658},[898,24421,20776],{},[1656,24423,1683],{"stretchy":1658},[902,24425,22968],{"encoding":904},", ty zvedají ",[883,24428,24430],{"className":24429},[886],[888,24431,24432],{"xmlns":890},[892,24433,24434,24438],{},[895,24435,24436],{},[898,24437,8184],{},[902,24439,8184],{"encoding":904},[724,24441,24442,24443,24446],{},"IS-LM tak dává jednotný rámec pro diskusi ",[38,24444,24445],{},"dopadu obou typů politik"," na důchod a úrokovou míru současně.",[115,24448,10198],{"id":10197},[120,24450,24451,24524,24570,24652,24702,24769,24826,24867,24900],{},[123,24452,24453,2533,24486,1343,24503,24520,24521,24523],{},[38,24454,24455,24456],{},"Funkce investic ",[883,24457,24459],{"className":24458},[886],[888,24460,24461],{"xmlns":890},[892,24462,24463,24483],{},[895,24464,24465,24467,24469,24471,24473,24475,24477,24479,24481],{},[898,24466,20919],{},[1656,24468,1659],{"stretchy":1658},[898,24470,20776],{},[1656,24472,1683],{"stretchy":1658},[1656,24474,1713],{},[898,24476,1745],{},[898,24478,20776],{},[1656,24480,3633],{},[898,24482,3768],{},[902,24484,24485],{"encoding":904},"I(r) = cr + d",[883,24487,24489],{"className":24488},[886],[888,24490,24491],{"xmlns":890},[892,24492,24493,24501],{},[895,24494,24495,24497,24499],{},[898,24496,1745],{},[1656,24498,4373],{},[1667,24500,4032],{},[902,24502,21249],{"encoding":904},[883,24504,24506],{"className":24505},[886],[888,24507,24508],{"xmlns":890},[892,24509,24510,24518],{},[895,24511,24512,24514,24516],{},[898,24513,3768],{},[1656,24515,2850],{},[1667,24517,4032],{},[902,24519,21228],{"encoding":904},"; ",[38,24522,21253],{}," funkce úrokové míry.",[123,24525,24526,24529,24530,24551,24552,24569],{},[38,24527,24528],{},"Trh zboží"," — rovnováha ",[883,24531,24533],{"className":24532},[886],[888,24534,24535],{"xmlns":890},[892,24536,24537,24549],{},[895,24538,24539,24541,24543,24545,24547],{},[898,24540,8184],{},[1656,24542,1713],{},[898,24544,1766],{},[1656,24546,3633],{},[898,24548,20919],{},[902,24550,23476],{"encoding":904},", ekvivalentně ",[883,24553,24555],{"className":24554},[886],[888,24556,24557],{"xmlns":890},[892,24558,24559,24567],{},[895,24560,24561,24563,24565],{},[898,24562,20919],{},[1656,24564,1713],{},[898,24566,1769],{},[902,24568,21446],{"encoding":904}," (investice = úspory).",[123,24571,24572,3247,24575,24577,24578,24628,24629,21649,24631,1863],{},[38,24573,24574],{},"Křivka IS",[614,24576,20789],{},") — ",[883,24579,24581],{"className":24580},[886],[888,24582,24583],{"xmlns":890},[892,24584,24585,24625],{},[895,24586,24587,24589,24591,24603,24605,24607],{},[898,24588,8184],{},[1656,24590,1713],{},[3294,24592,24593,24595],{},[898,24594,1745],{},[895,24596,24597,24599,24601],{},[1667,24598,1669],{},[1656,24600,3964],{},[898,24602,207],{},[898,24604,20776],{},[1656,24606,3633],{},[3294,24608,24609,24617],{},[895,24610,24611,24613,24615],{},[898,24612,3403],{},[1656,24614,3633],{},[898,24616,3768],{},[895,24618,24619,24621,24623],{},[1667,24620,1669],{},[1656,24622,3964],{},[898,24624,207],{},[902,24626,24627],{"encoding":904},"Y = \\frac{c}{1-a}r + \\frac{b+d}{1-a}"," (7.14); ",[38,24630,21253],{},[883,24632,24634],{"className":24633},[886],[888,24635,24636],{"xmlns":890},[892,24637,24638,24650],{},[895,24639,24640,24642,24644,24646,24648],{},[1656,24641,1659],{"stretchy":1658},[898,24643,20776],{},[1656,24645,1673],{"separator":1672},[898,24647,8184],{},[1656,24649,1683],{"stretchy":1658},[902,24651,21671],{"encoding":904},[123,24653,24654,24529,24657,24683,24684,1863],{},[38,24655,24656],{},"Trh peněz",[883,24658,24660],{"className":24659},[886],[888,24661,24662],{"xmlns":890},[892,24663,24664,24680],{},[895,24665,24666,24672,24674],{},[2062,24667,24668,24670],{},[898,24669,1703],{},[898,24671,6787],{},[1656,24673,1713],{},[2062,24675,24676,24678],{},[898,24677,1703],{},[898,24679,1769],{},[902,24681,24682],{"encoding":904},"M^D = M^S"," při pevné nabídce ",[883,24685,24687],{"className":24686},[886],[888,24688,24689],{"xmlns":890},[892,24690,24691,24699],{},[895,24692,24693],{},[2062,24694,24695,24697],{},[898,24696,1703],{},[1656,24698,8187],{},[902,24700,24701],{"encoding":904},"M^* ",[123,24703,24704,2533,24707,1863],{},[38,24705,24706],{},"Transakční, opatrnostní, spekulační poptávka",[883,24708,24710],{"className":24709},[886],[888,24711,24712],{"xmlns":890},[892,24713,24714,24766],{},[895,24715,24716,24722,24724,24730,24732,24738,24740,24746,24748,24750,24756,24758,24760],{},[2062,24717,24718,24720],{},[898,24719,1703],{},[898,24721,6787],{},[1656,24723,1713],{},[1661,24725,24726,24728],{},[898,24727,18539],{},[1667,24729,1669],{},[1656,24731,3633],{},[1661,24733,24734,24736],{},[898,24735,18539],{},[1667,24737,1680],{},[1656,24739,1713],{},[1661,24741,24742,24744],{},[898,24743,21970],{},[1667,24745,1669],{},[898,24747,8184],{},[1656,24749,3633],{},[1661,24751,24752,24754],{},[898,24753,21970],{},[1667,24755,1680],{},[898,24757,20776],{},[1656,24759,3633],{},[1661,24761,24762,24764],{},[898,24763,21970],{},[1667,24765,2617],{},[902,24767,24768],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3",[123,24770,24771,3247,24774,24577,24776,24822,24823,24825],{},[38,24772,24773],{},"Křivka LM",[614,24775,20796],{},[883,24777,24779],{"className":24778},[886],[888,24780,24781],{"xmlns":890},[892,24782,24783,24819],{},[895,24784,24785,24791,24793,24799,24801,24803,24809,24811,24813],{},[2062,24786,24787,24789],{},[898,24788,1703],{},[1656,24790,8187],{},[1656,24792,1713],{},[1661,24794,24795,24797],{},[898,24796,21970],{},[1667,24798,1669],{},[898,24800,8184],{},[1656,24802,3633],{},[1661,24804,24805,24807],{},[898,24806,21970],{},[1667,24808,1680],{},[898,24810,20776],{},[1656,24812,3633],{},[1661,24814,24815,24817],{},[898,24816,21970],{},[1667,24818,2617],{},[902,24820,24821],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3"," (7.15); ",[38,24824,4570],{}," přímka.",[123,24827,24828,24831,24832,24866],{},[38,24829,24830],{},"Simultánní rovnováha"," — průsečík ",[883,24833,24835],{"className":24834},[886],[888,24836,24837],{"xmlns":890},[892,24838,24839,24863],{},[895,24840,24841,24843,24845,24847,24853,24855,24861],{},[898,24842,1842],{},[1656,24844,1713],{},[1656,24846,1659],{"stretchy":1658},[2062,24848,24849,24851],{},[898,24850,20776],{},[898,24852,1842],{},[1656,24854,1673],{"separator":1672},[2062,24856,24857,24859],{},[898,24858,8184],{},[898,24860,1842],{},[1656,24862,1683],{"stretchy":1658},[902,24864,24865],{"encoding":904},"E = (r^E, Y^E)"," křivek IS a LM.",[123,24868,24869,24872,24873,1343,24886,24899],{},[38,24870,24871],{},"Fiskální politika"," — nástroje ",[883,24874,24876],{"className":24875},[886],[888,24877,24878],{"xmlns":890},[892,24879,24880,24884],{},[895,24881,24882],{},[898,24883,20847],{},[902,24885,20847],{"encoding":904},[883,24887,24889],{"className":24888},[886],[888,24890,24891],{"xmlns":890},[892,24892,24893,24897],{},[895,24894,24895],{},[898,24896,11577],{},[902,24898,11577],{"encoding":904}," posouvající křivku IS.",[123,24901,24902,24905,24906,24923],{},[38,24903,24904],{},"Monetární politika"," — nástroj ",[883,24907,24909],{"className":24908},[886],[888,24910,24911],{"xmlns":890},[892,24912,24913,24921],{},[895,24914,24915],{},[2062,24916,24917,24919],{},[898,24918,1703],{},[1656,24920,8187],{},[902,24922,20885],{"encoding":904}," posouvající křivku LM.",[115,24925,10640],{"id":10639},[120,24927,24928,24935,24944,24954],{},[123,24929,24930,1643,24932],{},[38,24931,10742],{},[207,24933,1869],{"className":24934,"dataFsResolvedFilePath":10746,"href":10747},[210],[123,24936,24937,1643,24940],{},[38,24938,24939],{},"Přednáška:",[207,24941,24943],{"className":24942,"dataFsResolvedFilePath":868,"href":869},[210],"imek-blok-03",[123,24945,24946,1643,24949,24953],{},[38,24947,24948],{},"Nadřazené téma:",[207,24950,24952],{"className":24951,"dataFsResolvedFilePath":934,"href":935},[210],"narodni-duchod"," — makroekonomické modely C-I, C-I-G, C-I-G-X a úvod do IS-LM",[123,24955,24956,24959],{},[38,24957,24958],{},"Související:",[120,24960,24961,24968,24974],{},[123,24962,24963,24967],{},[207,24964,24966],{"className":24965,"dataFsResolvedFilePath":800,"href":801},[210],"poptavka-nabidka"," — paralela rovnovážného bodu (průsečík dvou křivek) v mikroekonomii",[123,24969,24970,24973],{},[207,24971,1145],{"className":24972,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro směrnice IS a LM",[123,24975,24976,24980],{},[207,24977,24979],{"className":24978,"dataFsResolvedFilePath":782,"href":783},[210],"funkce-vice-promennych"," — dvě neznámé a řešení lineárních soustav",{"title":641,"searchDepth":642,"depth":642,"links":24982},[24983,24984,24985,24986,24987,24988,24989,24990,24991,24992],{"id":1637,"depth":642,"text":1638},{"id":20895,"depth":642,"text":20896},{"id":21110,"depth":642,"text":21111},{"id":21402,"depth":642,"text":21403},{"id":21814,"depth":642,"text":21815},{"id":22606,"depth":642,"text":22607},{"id":23296,"depth":642,"text":23297},{"id":24200,"depth":642,"text":24201},{"id":10197,"depth":642,"text":10198},{"id":10639,"depth":642,"text":10640},{},"\u002Ftopics\u002Fis-lm",{"title":20734,"description":641},[1138,1137],"topics\u002Fis-lm",[1128,24999,1143,25000,25001,25002,25003,24952],"is-lm","trh-zbozi","trh-penez","urokova-mira","investice","OcXqlUxNqiCsj643lVoQEu_ZWU2vH0D_lWZ_-SxoyHk",{"id":25006,"title":25007,"body":25008,"course":659,"courses":26597,"created":1129,"description":26598,"extension":661,"meta":26599,"navigation":664,"path":26600,"seo":26601,"sources":26602,"stem":26603,"tags":26604,"type":10786,"updated":677,"__hash__":26607},"topics\u002Ftopics\u002Flagrangeova-metoda.md","Lagrangeova metoda (vázané extrémy)",{"type":9,"value":25009,"toc":26585},[25010,25013,25108,25115,25135,25139,25144,25207,25226,25228,25231,25367,25369,25579,25613,25750,25754,25818,25834,25862,25866,25964,25968,25972,26024,26130,26344,26348,26391,26497,26547,26549],[12,25011,25007],{"id":25012},"lagrangeova-metoda-vázané-extrémy",[724,25014,25015,25016,12694,25039,25070,25071,25074,25075,25102,25103,25107],{},"Hledáme extrém funkce ",[883,25017,25019],{"className":25018},[886],[888,25020,25021],{"xmlns":890},[892,25022,25023,25037],{},[895,25024,25025,25027,25029,25031,25033,25035],{},[898,25026,7524],{},[1656,25028,1659],{"stretchy":1658},[898,25030,10848],{},[1656,25032,1673],{"separator":1672},[898,25034,10839],{},[1656,25036,1683],{"stretchy":1658},[902,25038,18587],{"encoding":904},[883,25040,25042],{"className":25041},[886],[888,25043,25044],{"xmlns":890},[892,25045,25046,25068],{},[895,25047,25048,25050,25052,25058,25060,25066],{},[898,25049,900],{},[1656,25051,1659],{"stretchy":1658},[1661,25053,25054,25056],{},[898,25055,1665],{},[1667,25057,1669],{},[1656,25059,1673],{"separator":1672},[1661,25061,25062,25064],{},[898,25063,1665],{},[1667,25065,1680],{},[1656,25067,1683],{"stretchy":1658},[902,25069,1686],{"encoding":904}," apod.) ",[38,25072,25073],{},"podmíněný"," rovnicí ",[883,25076,25078],{"className":25077},[886],[888,25079,25080],{"xmlns":890},[892,25081,25082,25100],{},[895,25083,25084,25086,25088,25090,25092,25094,25096,25098],{},[898,25085,19780],{},[1656,25087,1659],{"stretchy":1658},[898,25089,10848],{},[1656,25091,1673],{"separator":1672},[898,25093,10839],{},[1656,25095,1683],{"stretchy":1658},[1656,25097,1713],{},[1667,25099,4032],{},[902,25101,19797],{"encoding":904},". V ",[207,25104,25106],{"className":25105,"dataFsResolvedFilePath":10746,"href":10747},[210],"matematické ekonomii"," se používá pro:",[724,25109,25110],{},[5956,25111],{"alt":25112,"className":25113,"src":25114},"imek-lagrange-tecnost",[210,5960],"\u002Fwiki-assets\u002Fimek-lagrange-tecnost.jpeg",[120,25116,25117,25126,25132],{},[123,25118,25119,25122,25123,1683],{},[38,25120,25121],{},"Maximalizaci užitečnosti"," při rozpočtovém omezení (viz ",[207,25124,10781],{"className":25125,"dataFsResolvedFilePath":878,"href":879},[210],[123,25127,25128,25131],{},[38,25129,25130],{},"Minimalizaci výdajů"," při dané úrovni užitečnosti (duální úloha)",[123,25133,25134],{},"Optimalizaci produkce \u002F nákladů za omezení",[115,25136,25138],{"id":25137},"princip","Princip",[724,25140,19447,25141,2114],{},[38,25142,25143],{},"Lagrangeovu funkci",[724,25145,25146],{},[883,25147,25149],{"className":25148},[886],[888,25150,25151],{"xmlns":890},[892,25152,25153,25204],{},[895,25154,25155,25157,25159,25161,25163,25165,25167,25170,25172,25174,25176,25178,25180,25182,25184,25186,25188,25190,25192,25194,25196,25198,25200,25202],{},[898,25156,18539],{},[1656,25158,1659],{"stretchy":1658},[898,25160,10848],{},[1656,25162,1673],{"separator":1672},[898,25164,10839],{},[1656,25166,1673],{"separator":1672},[898,25168,25169],{},"λ",[1656,25171,1683],{"stretchy":1658},[1656,25173,1713],{},[898,25175,7524],{},[1656,25177,1659],{"stretchy":1658},[898,25179,10848],{},[1656,25181,1673],{"separator":1672},[898,25183,10839],{},[1656,25185,1683],{"stretchy":1658},[1656,25187,3633],{},[898,25189,25169],{},[2461,25191,7828],{},[898,25193,19780],{},[1656,25195,1659],{"stretchy":1658},[898,25197,10848],{},[1656,25199,1673],{"separator":1672},[898,25201,10839],{},[1656,25203,1683],{"stretchy":1658},[902,25205,25206],{"encoding":904},"L(x, y, \\lambda) = f(x, y) + \\lambda\\, g(x, y)",[724,25208,2355,25209,3206,25223,1863],{},[883,25210,25212],{"className":25211},[886],[888,25213,25214],{"xmlns":890},[892,25215,25216,25220],{},[895,25217,25218],{},[898,25219,25169],{},[902,25221,25222],{"encoding":904},"\\lambda",[38,25224,25225],{},"Lagrangeův multiplikátor",[115,25227,12042],{"id":12041},[724,25229,25230],{},"Řešíme soustavu:",[724,25232,25233,25281,25329],{},[883,25234,25236],{"className":25235},[886],[888,25237,25238],{"xmlns":890},[892,25239,25240,25278],{},[895,25241,25242,25250,25252,25260,25262,25264,25266,25274,25276],{},[1715,25243,25244,25246,25248],{},[898,25245,18539],{},[898,25247,10848],{},[1656,25249,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,25251,1713],{},[1715,25253,25254,25256,25258],{},[898,25255,7524],{},[898,25257,10848],{},[1656,25259,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,25261,3633],{},[898,25263,25169],{},[2461,25265,7828],{},[1715,25267,25268,25270,25272],{},[898,25269,19780],{},[898,25271,10848],{},[1656,25273,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,25275,1713],{},[1667,25277,4032],{},[902,25279,25280],{"encoding":904},"L'_x = f'_x + \\lambda\\, g'_x = 0",[883,25282,25284],{"className":25283},[886],[888,25285,25286],{"xmlns":890},[892,25287,25288,25326],{},[895,25289,25290,25298,25300,25308,25310,25312,25314,25322,25324],{},[1715,25291,25292,25294,25296],{},[898,25293,18539],{},[898,25295,10839],{},[1656,25297,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,25299,1713],{},[1715,25301,25302,25304,25306],{},[898,25303,7524],{},[898,25305,10839],{},[1656,25307,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,25309,3633],{},[898,25311,25169],{},[2461,25313,7828],{},[1715,25315,25316,25318,25320],{},[898,25317,19780],{},[898,25319,10839],{},[1656,25321,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,25323,1713],{},[1667,25325,4032],{},[902,25327,25328],{"encoding":904},"L'_y = f'_y + \\lambda\\, g'_y = 0",[883,25330,25332],{"className":25331},[886],[888,25333,25334],{"xmlns":890},[892,25335,25336,25364],{},[895,25337,25338,25346,25348,25350,25352,25354,25356,25358,25360,25362],{},[1715,25339,25340,25342,25344],{},[898,25341,18539],{},[898,25343,25169],{},[1656,25345,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,25347,1713],{},[898,25349,19780],{},[1656,25351,1659],{"stretchy":1658},[898,25353,10848],{},[1656,25355,1673],{"separator":1672},[898,25357,10839],{},[1656,25359,1683],{"stretchy":1658},[1656,25361,1713],{},[1667,25363,4032],{},[902,25365,25366],{"encoding":904},"L'_\\lambda = g(x, y) = 0",[115,25368,12116],{"id":12115},[724,25370,25371],{},[883,25372,25374],{"className":25373},[886],[888,25375,25376],{"xmlns":890},[892,25377,25378,25576],{},[895,25379,25380,25382,25384,25386,25388,25390,25392,25394,25396,25398,25400,25416,25418,25420,25436,25438,25440,25448,25454,25456,25458,25474,25476,25478,25494,25496,25498,25506,25512,25514,25516,25518,25534,25536,25538,25554,25556,25558,25566,25568],{},[898,25381,6787],{},[1656,25383,1659],{"stretchy":1658},[898,25385,10848],{},[1656,25387,1673],{"separator":1672},[898,25389,10839],{},[1656,25391,1673],{"separator":1672},[898,25393,25169],{},[1656,25395,1683],{"stretchy":1658},[1656,25397,1713],{},[1656,25399,1659],{"stretchy":1658},[1715,25401,25402,25404,25410],{},[898,25403,7524],{},[895,25405,25406,25408],{},[898,25407,10848],{},[898,25409,10848],{},[895,25411,25412,25414],{},[1656,25413,1725],{"mathvariant":1723},[1656,25415,1725],{"mathvariant":1723},[1656,25417,3633],{},[898,25419,25169],{},[1715,25421,25422,25424,25430],{},[898,25423,19780],{},[895,25425,25426,25428],{},[898,25427,10848],{},[898,25429,10848],{},[895,25431,25432,25434],{},[1656,25433,1725],{"mathvariant":1723},[1656,25435,1725],{"mathvariant":1723},[1656,25437,1683],{"stretchy":1658},[1656,25439,1659],{"stretchy":1658},[1715,25441,25442,25444,25446],{},[898,25443,19780],{},[898,25445,10839],{},[1656,25447,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[2062,25449,25450,25452],{},[1656,25451,1683],{"stretchy":1658},[1667,25453,1680],{},[1656,25455,3633],{},[1656,25457,1659],{"stretchy":1658},[1715,25459,25460,25462,25468],{},[898,25461,7524],{},[895,25463,25464,25466],{},[898,25465,10839],{},[898,25467,10839],{},[895,25469,25470,25472],{},[1656,25471,1725],{"mathvariant":1723},[1656,25473,1725],{"mathvariant":1723},[1656,25475,3633],{},[898,25477,25169],{},[1715,25479,25480,25482,25488],{},[898,25481,19780],{},[895,25483,25484,25486],{},[898,25485,10839],{},[898,25487,10839],{},[895,25489,25490,25492],{},[1656,25491,1725],{"mathvariant":1723},[1656,25493,1725],{"mathvariant":1723},[1656,25495,1683],{"stretchy":1658},[1656,25497,1659],{"stretchy":1658},[1715,25499,25500,25502,25504],{},[898,25501,19780],{},[898,25503,10848],{},[1656,25505,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[2062,25507,25508,25510],{},[1656,25509,1683],{"stretchy":1658},[1667,25511,1680],{},[1656,25513,3964],{},[1667,25515,1680],{},[1656,25517,1659],{"stretchy":1658},[1715,25519,25520,25522,25528],{},[898,25521,7524],{},[895,25523,25524,25526],{},[898,25525,10848],{},[898,25527,10839],{},[895,25529,25530,25532],{},[1656,25531,1725],{"mathvariant":1723},[1656,25533,1725],{"mathvariant":1723},[1656,25535,3633],{},[898,25537,25169],{},[1715,25539,25540,25542,25548],{},[898,25541,19780],{},[895,25543,25544,25546],{},[898,25545,10848],{},[898,25547,10839],{},[895,25549,25550,25552],{},[1656,25551,1725],{"mathvariant":1723},[1656,25553,1725],{"mathvariant":1723},[1656,25555,1683],{"stretchy":1658},[2461,25557,7828],{},[1715,25559,25560,25562,25564],{},[898,25561,19780],{},[898,25563,10848],{},[1656,25565,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[2461,25567,7828],{},[1715,25569,25570,25572,25574],{},[898,25571,19780],{},[898,25573,10839],{},[1656,25575,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[902,25577,25578],{"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",[724,25580,25581,25582,25612],{},"Je-li ",[883,25583,25585],{"className":25584},[886],[888,25586,25587],{"xmlns":890},[892,25588,25589,25609],{},[895,25590,25591,25593,25595,25597,25599,25601,25607],{},[1656,25592,3453],{"stretchy":1658},[898,25594,207],{},[1656,25596,1673],{"separator":1672},[898,25598,3403],{},[1656,25600,1673],{"separator":1672},[1661,25602,25603,25605],{},[898,25604,25169],{},[1667,25606,4032],{},[1656,25608,3462],{"stretchy":1658},[902,25610,25611],{"encoding":904},"[a, b, \\lambda_0]"," podezřelý bod:",[120,25614,25615,25683],{},[123,25616,25617,12203,25653,25655,25656],{},[883,25618,25620],{"className":25619},[886],[888,25621,25622],{"xmlns":890},[892,25623,25624,25650],{},[895,25625,25626,25628,25630,25632,25634,25636,25638,25644,25646,25648],{},[898,25627,6787],{},[1656,25629,1659],{"stretchy":1658},[898,25631,207],{},[1656,25633,1673],{"separator":1672},[898,25635,3403],{},[1656,25637,1673],{"separator":1672},[1661,25639,25640,25642],{},[898,25641,25169],{},[1667,25643,4032],{},[1656,25645,1683],{"stretchy":1658},[1656,25647,4373],{},[1667,25649,4032],{},[902,25651,25652],{"encoding":904},"D(a, b, \\lambda_0) \u003C 0",[38,25654,12504],{}," vázané podmínkou ",[883,25657,25659],{"className":25658},[886],[888,25660,25661],{"xmlns":890},[892,25662,25663,25681],{},[895,25664,25665,25667,25669,25671,25673,25675,25677,25679],{},[898,25666,19780],{},[1656,25668,1659],{"stretchy":1658},[898,25670,10848],{},[1656,25672,1673],{"separator":1672},[898,25674,10839],{},[1656,25676,1683],{"stretchy":1658},[1656,25678,1713],{},[1667,25680,4032],{},[902,25682,19797],{"encoding":904},[123,25684,25685,12203,25721,25655,25723],{},[883,25686,25688],{"className":25687},[886],[888,25689,25690],{"xmlns":890},[892,25691,25692,25718],{},[895,25693,25694,25696,25698,25700,25702,25704,25706,25712,25714,25716],{},[898,25695,6787],{},[1656,25697,1659],{"stretchy":1658},[898,25699,207],{},[1656,25701,1673],{"separator":1672},[898,25703,3403],{},[1656,25705,1673],{"separator":1672},[1661,25707,25708,25710],{},[898,25709,25169],{},[1667,25711,4032],{},[1656,25713,1683],{"stretchy":1658},[1656,25715,2850],{},[1667,25717,4032],{},[902,25719,25720],{"encoding":904},"D(a, b, \\lambda_0) > 0",[38,25722,12562],{},[883,25724,25726],{"className":25725},[886],[888,25727,25728],{"xmlns":890},[892,25729,25730,25748],{},[895,25731,25732,25734,25736,25738,25740,25742,25744,25746],{},[898,25733,19780],{},[1656,25735,1659],{"stretchy":1658},[898,25737,10848],{},[1656,25739,1673],{"separator":1672},[898,25741,10839],{},[1656,25743,1683],{"stretchy":1658},[1656,25745,1713],{},[1667,25747,4032],{},[902,25749,19797],{"encoding":904},[115,25751,25753],{"id":25752},"význam-multiplikátoru","Význam multiplikátoru",[724,25755,25756],{},[883,25757,25759],{"className":25758},[886],[888,25760,25761],{"xmlns":890},[892,25762,25763,25815],{},[895,25764,25765,25767,25769,25791,25793],{},[898,25766,25169],{},[1656,25768,1713],{},[3294,25770,25771,25779],{},[1715,25772,25773,25775,25777],{},[898,25774,7524],{},[898,25776,10848],{},[1656,25778,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[895,25780,25781,25783],{},[1656,25782,3964],{},[1715,25784,25785,25787,25789],{},[898,25786,19780],{},[898,25788,10848],{},[1656,25790,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,25792,1713],{},[3294,25794,25795,25803],{},[1715,25796,25797,25799,25801],{},[898,25798,7524],{},[898,25800,10839],{},[1656,25802,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[895,25804,25805,25807],{},[1656,25806,3964],{},[1715,25808,25809,25811,25813],{},[898,25810,19780],{},[898,25812,10839],{},[1656,25814,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[902,25816,25817],{"encoding":904},"\\lambda = \\frac{f'_x}{-g'_x} = \\frac{f'_y}{-g'_y}",[724,25819,25820,25833],{},[883,25821,25823],{"className":25822},[886],[888,25824,25825],{"xmlns":890},[892,25826,25827,25831],{},[895,25828,25829],{},[898,25830,25169],{},[902,25832,25222],{"encoding":904}," udává:",[120,25835,25836,25842],{},[123,25837,25838,25839],{},"konstantní ",[38,25840,25841],{},"poměr mezi mezním prospěchem a mezním nákladem",[123,25843,25844,25847,25848,25861],{},[38,25845,25846],{},"náklady příležitosti"," (opportunity cost) — o kolik vzroste optimální hodnota ",[883,25849,25851],{"className":25850},[886],[888,25852,25853],{"xmlns":890},[892,25854,25855,25859],{},[895,25856,25857],{},[898,25858,7524],{},[902,25860,7524],{"encoding":904},", uvolní-li se omezení o jednotku",[115,25863,25865],{"id":25864},"alternativní-postup","Alternativní postup",[724,25867,25868,25869,25896,25897,25921,25922,25946,25947,25960,25961,1863],{},"Lze-li z ",[883,25870,25872],{"className":25871},[886],[888,25873,25874],{"xmlns":890},[892,25875,25876,25894],{},[895,25877,25878,25880,25882,25884,25886,25888,25890,25892],{},[898,25879,19780],{},[1656,25881,1659],{"stretchy":1658},[898,25883,10848],{},[1656,25885,1673],{"separator":1672},[898,25887,10839],{},[1656,25889,1683],{"stretchy":1658},[1656,25891,1713],{},[1667,25893,4032],{},[902,25895,19797],{"encoding":904}," vyjádřit ",[883,25898,25900],{"className":25899},[886],[888,25901,25902],{"xmlns":890},[892,25903,25904,25918],{},[895,25905,25906,25908,25910,25912,25914,25916],{},[898,25907,10839],{},[1656,25909,1713],{},[898,25911,10839],{},[1656,25913,1659],{"stretchy":1658},[898,25915,10848],{},[1656,25917,1683],{"stretchy":1658},[902,25919,25920],{"encoding":904},"y = y(x)"," (nebo ",[883,25923,25925],{"className":25924},[886],[888,25926,25927],{"xmlns":890},[892,25928,25929,25943],{},[895,25930,25931,25933,25935,25937,25939,25941],{},[898,25932,10848],{},[1656,25934,1713],{},[898,25936,10848],{},[1656,25938,1659],{"stretchy":1658},[898,25940,10839],{},[1656,25942,1683],{"stretchy":1658},[902,25944,25945],{"encoding":904},"x = x(y)","), dosadíme do ",[883,25948,25950],{"className":25949},[886],[888,25951,25952],{"xmlns":890},[892,25953,25954,25958],{},[895,25955,25956],{},[898,25957,7524],{},[902,25959,7524],{"encoding":904}," a převedeme na ",[38,25962,25963],{},"extrém funkce jedné proměnné",[115,25965,25967],{"id":25966},"použití-v-imek","Použití v ImeK",[198,25969,25971],{"id":25970},"maximalizace-užitečnosti","Maximalizace užitečnosti",[724,25973,25974,25975,1863],{},"Rozpočtové omezení: ",[883,25976,25978],{"className":25977},[886],[888,25979,25980],{"xmlns":890},[892,25981,25982,26022],{},[895,25983,25984,25990,25992,26000,26006,26008,26016],{},[2062,25985,25986,25988],{},[898,25987,8184],{},[1656,25989,8187],{},[1656,25991,1713],{},[1715,25993,25994,25996,25998],{},[898,25995,8194],{},[1667,25997,1669],{},[1656,25999,8187],{},[1661,26001,26002,26004],{},[898,26003,1665],{},[1667,26005,1669],{},[1656,26007,3633],{},[1715,26009,26010,26012,26014],{},[898,26011,8194],{},[1667,26013,1680],{},[1656,26015,8187],{},[1661,26017,26018,26020],{},[898,26019,1665],{},[1667,26021,1680],{},[902,26023,8223],{"encoding":904},[724,26025,26026],{},[883,26027,26029],{"className":26028},[886],[888,26030,26031],{"xmlns":890},[892,26032,26033,26127],{},[895,26034,26035,26037,26039,26045,26047,26053,26055,26057,26059,26061,26063,26065,26071,26073,26079,26081,26083,26085,26087,26093,26095,26103,26109,26111,26119,26125],{},[898,26036,18539],{},[1656,26038,1659],{"stretchy":1658},[1661,26040,26041,26043],{},[898,26042,1665],{},[1667,26044,1669],{},[1656,26046,1673],{"separator":1672},[1661,26048,26049,26051],{},[898,26050,1665],{},[1667,26052,1680],{},[1656,26054,1673],{"separator":1672},[898,26056,25169],{},[1656,26058,1683],{"stretchy":1658},[1656,26060,1713],{},[898,26062,900],{},[1656,26064,1659],{"stretchy":1658},[1661,26066,26067,26069],{},[898,26068,1665],{},[1667,26070,1669],{},[1656,26072,1673],{"separator":1672},[1661,26074,26075,26077],{},[898,26076,1665],{},[1667,26078,1680],{},[1656,26080,1683],{"stretchy":1658},[1656,26082,3633],{},[898,26084,25169],{},[1656,26086,1659],{"stretchy":1658},[2062,26088,26089,26091],{},[898,26090,8184],{},[1656,26092,8187],{},[1656,26094,3964],{},[1715,26096,26097,26099,26101],{},[898,26098,8194],{},[1667,26100,1669],{},[1656,26102,8187],{},[1661,26104,26105,26107],{},[898,26106,1665],{},[1667,26108,1669],{},[1656,26110,3964],{},[1715,26112,26113,26115,26117],{},[898,26114,8194],{},[1667,26116,1680],{},[1656,26118,8187],{},[1661,26120,26121,26123],{},[898,26122,1665],{},[1667,26124,1680],{},[1656,26126,1683],{"stretchy":1658},[902,26128,26129],{"encoding":904},"L(Q_1, Q_2, \\lambda) = U(Q_1, Q_2) + \\lambda (Y^* - P_1^* Q_1 - P_2^* Q_2)",[724,26131,26132,26133,1343,26165,1343,26197,26246,26247,26301,26302,1863],{},"Soustava: ",[883,26134,26136],{"className":26135},[886],[888,26137,26138],{"xmlns":890},[892,26139,26140,26162],{},[895,26141,26142,26150,26152,26154],{},[1715,26143,26144,26146,26148],{},[898,26145,900],{},[1667,26147,1669],{},[1656,26149,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,26151,1713],{},[898,26153,25169],{},[1715,26155,26156,26158,26160],{},[898,26157,8194],{},[1667,26159,1669],{},[1656,26161,8187],{},[902,26163,26164],{"encoding":904},"U'_1 = \\lambda P_1^*",[883,26166,26168],{"className":26167},[886],[888,26169,26170],{"xmlns":890},[892,26171,26172,26194],{},[895,26173,26174,26182,26184,26186],{},[1715,26175,26176,26178,26180],{},[898,26177,900],{},[1667,26179,1680],{},[1656,26181,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,26183,1713],{},[898,26185,25169],{},[1715,26187,26188,26190,26192],{},[898,26189,8194],{},[1667,26191,1680],{},[1656,26193,8187],{},[902,26195,26196],{"encoding":904},"U'_2 = \\lambda P_2^*",[883,26198,26200],{"className":26199},[886],[888,26201,26202],{"xmlns":890},[892,26203,26204,26244],{},[895,26205,26206,26212,26214,26222,26228,26230,26238],{},[2062,26207,26208,26210],{},[898,26209,8184],{},[1656,26211,8187],{},[1656,26213,1713],{},[1715,26215,26216,26218,26220],{},[898,26217,8194],{},[1667,26219,1669],{},[1656,26221,8187],{},[1661,26223,26224,26226],{},[898,26225,1665],{},[1667,26227,1669],{},[1656,26229,3633],{},[1715,26231,26232,26234,26236],{},[898,26233,8194],{},[1667,26235,1680],{},[1656,26237,8187],{},[1661,26239,26240,26242],{},[898,26241,1665],{},[1667,26243,1680],{},[902,26245,8223],{"encoding":904},". Z prvních dvou: ",[883,26248,26250],{"className":26249},[886],[888,26251,26252],{"xmlns":890},[892,26253,26254,26298],{},[895,26255,26256,26276,26278],{},[4138,26257,26258],{"scriptlevel":4032,"displaystyle":1658},[3294,26259,26260,26268],{},[1715,26261,26262,26264,26266],{},[898,26263,900],{},[1667,26265,1669],{},[1656,26267,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1715,26269,26270,26272,26274],{},[898,26271,900],{},[1667,26273,1680],{},[1656,26275,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,26277,1713],{},[4138,26279,26280],{"scriptlevel":4032,"displaystyle":1658},[3294,26281,26282,26290],{},[1715,26283,26284,26286,26288],{},[898,26285,8194],{},[1667,26287,1669],{},[1656,26289,8187],{},[1715,26291,26292,26294,26296],{},[898,26293,8194],{},[1667,26295,1680],{},[1656,26297,8187],{},[902,26299,26300],{"encoding":904},"\\tfrac{U'_1}{U'_2} = \\tfrac{P_1^*}{P_2^*}",", tj. ",[883,26303,26305],{"className":26304},[886],[888,26306,26307],{"xmlns":890},[892,26308,26309,26341],{},[895,26310,26311,26313,26315,26317,26319,26321],{},[898,26312,1703],{},[898,26314,1763],{},[898,26316,1766],{},[898,26318,1769],{},[1656,26320,1713],{},[4138,26322,26323],{"scriptlevel":4032,"displaystyle":1658},[3294,26324,26325,26333],{},[1715,26326,26327,26329,26331],{},[898,26328,8194],{},[1667,26330,1669],{},[1656,26332,8187],{},[1715,26334,26335,26337,26339],{},[898,26336,8194],{},[1667,26338,1680],{},[1656,26340,8187],{},[902,26342,26343],{"encoding":904},"MRCS = \\tfrac{P_1^*}{P_2^*}",[198,26345,26347],{"id":26346},"minimalizace-výdajů","Minimalizace výdajů",[724,26349,26350,26351,1863],{},"Podmínka dané užitečnosti ",[883,26352,26354],{"className":26353},[886],[888,26355,26356],{"xmlns":890},[892,26357,26358,26388],{},[895,26359,26360,26366,26368,26370,26372,26378,26380,26386],{},[2062,26361,26362,26364],{},[898,26363,900],{},[1656,26365,8187],{},[1656,26367,1713],{},[898,26369,900],{},[1656,26371,1659],{"stretchy":1658},[1661,26373,26374,26376],{},[898,26375,1665],{},[1667,26377,1669],{},[1656,26379,1673],{"separator":1672},[1661,26381,26382,26384],{},[898,26383,1665],{},[1667,26385,1680],{},[1656,26387,1683],{"stretchy":1658},[902,26389,26390],{"encoding":904},"U^* = U(Q_1, Q_2)",[724,26392,26393],{},[883,26394,26396],{"className":26395},[886],[888,26397,26398],{"xmlns":890},[892,26399,26400,26494],{},[895,26401,26402,26404,26406,26412,26414,26420,26422,26424,26426,26428,26436,26442,26444,26452,26458,26460,26462,26464,26470,26472,26474,26476,26482,26484,26490,26492],{},[898,26403,18539],{},[1656,26405,1659],{"stretchy":1658},[1661,26407,26408,26410],{},[898,26409,1665],{},[1667,26411,1669],{},[1656,26413,1673],{"separator":1672},[1661,26415,26416,26418],{},[898,26417,1665],{},[1667,26419,1680],{},[1656,26421,1673],{"separator":1672},[898,26423,25169],{},[1656,26425,1683],{"stretchy":1658},[1656,26427,1713],{},[1715,26429,26430,26432,26434],{},[898,26431,8194],{},[1667,26433,1669],{},[1656,26435,8187],{},[1661,26437,26438,26440],{},[898,26439,1665],{},[1667,26441,1669],{},[1656,26443,3633],{},[1715,26445,26446,26448,26450],{},[898,26447,8194],{},[1667,26449,1680],{},[1656,26451,8187],{},[1661,26453,26454,26456],{},[898,26455,1665],{},[1667,26457,1680],{},[1656,26459,3633],{},[898,26461,25169],{},[1656,26463,1659],{"stretchy":1658},[2062,26465,26466,26468],{},[898,26467,900],{},[1656,26469,8187],{},[1656,26471,3964],{},[898,26473,900],{},[1656,26475,1659],{"stretchy":1658},[1661,26477,26478,26480],{},[898,26479,1665],{},[1667,26481,1669],{},[1656,26483,1673],{"separator":1672},[1661,26485,26486,26488],{},[898,26487,1665],{},[1667,26489,1680],{},[1656,26491,1683],{"stretchy":1658},[1656,26493,1683],{"stretchy":1658},[902,26495,26496],{"encoding":904},"L(Q_1, Q_2, \\lambda) = P_1^* Q_1 + P_2^* Q_2 + \\lambda (U^* - U(Q_1, Q_2))",[724,26498,26499,26500,1863],{},"Duálně dostaneme Hicksovy poptávkové funkce ",[883,26501,26503],{"className":26502},[886],[888,26504,26505],{"xmlns":890},[892,26506,26507,26545],{},[895,26508,26509,26515,26517,26523,26525,26531,26533,26539,26541,26543],{},[1661,26510,26511,26513],{},[898,26512,1665],{},[898,26514,1710],{},[1656,26516,1713],{},[1661,26518,26519,26521],{},[898,26520,6787],{},[898,26522,1710],{},[1656,26524,1659],{"stretchy":1658},[1661,26526,26527,26529],{},[898,26528,8194],{},[1667,26530,1669],{},[1656,26532,1673],{"separator":1672},[1661,26534,26535,26537],{},[898,26536,8194],{},[1667,26538,1680],{},[1656,26540,1673],{"separator":1672},[898,26542,900],{},[1656,26544,1683],{"stretchy":1658},[902,26546,8392],{"encoding":904},[115,26548,10640],{"id":10639},[120,26550,26551,26558,26565,26574],{},[123,26552,26553,1643,26555],{},[38,26554,12584],{},[207,26556,784],{"className":26557,"dataFsResolvedFilePath":782,"href":783},[210],[123,26559,26560,1643,26562],{},[38,26561,12592],{},[207,26563,10702],{"className":26564,"dataFsResolvedFilePath":800,"href":801},[210],[123,26566,26567,1643,26570,26573],{},[38,26568,26569],{},"Aplikace v kurzu:",[207,26571,880],{"className":26572,"dataFsResolvedFilePath":878,"href":879},[210]," (maximalizace užitečnosti při rozpočtovém omezení), minimalizace výdajů (duální úloha), optimalizace produkce",[123,26575,26576,1643,26578,1343,26581,26584],{},[38,26577,12600],{},[207,26579,936],{"className":26580,"dataFsResolvedFilePath":934,"href":935},[210],[207,26582,1400],{"className":26583,"dataFsResolvedFilePath":1398,"href":1399},[210]," (IpmrK)",{"title":641,"searchDepth":642,"depth":642,"links":26586},[26587,26588,26589,26590,26591,26592,26596],{"id":25137,"depth":642,"text":25138},{"id":12041,"depth":642,"text":12042},{"id":12115,"depth":642,"text":12116},{"id":25752,"depth":642,"text":25753},{"id":25864,"depth":642,"text":25865},{"id":25966,"depth":642,"text":25967,"children":26593},[26594,26595],{"id":25970,"depth":649,"text":25971},{"id":26346,"depth":649,"text":26347},{"id":10639,"depth":642,"text":10640},[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":25007,"description":26598},[1135,1137],"topics\u002Flagrangeova-metoda",[1128,1619,26605,26606],"vazane-extremy","multiplikator","PRnK6wpMGySFp-C47ico7wAs4MDBp47Titm-Obyzgow",{"id":26609,"title":936,"body":26610,"course":1128,"courses":659,"created":10774,"description":641,"extension":661,"meta":36470,"navigation":664,"path":36471,"seo":36472,"sources":36473,"stem":36474,"tags":36475,"type":10786,"updated":677,"__hash__":36479},"topics\u002Ftopics\u002Fnarodni-duchod.md",{"type":9,"value":26611,"toc":36432},[26612,26615,26617,26740,26875,26879,26882,26995,26999,27027,27074,27077,27143,27188,27191,27217,27248,27252,27256,27300,27344,27405,27460,27463,27467,27470,27517,27613,27719,27725,27802,27831,27970,27974,28003,28053,28200,28290,28294,28320,28358,28385,28423,28485,28560,28638,28696,28762,28806,28810,28868,28917,28962,29175,29295,29301,29305,29328,29332,29339,29343,29374,29409,29413,29463,29548,29590,29611,29673,29733,29737,29808,29876,29948,30063,30111,30115,30118,30159,30198,30221,30335,30499,30507,30534,30564,30567,30644,30797,30881,31220,31224,31348,31484,31620,31673,31676,31926,32006,32010,32013,32071,32103,32106,32155,32158,32229,32425,32429,32580,32810,32848,32901,32946,32949,33005,33054,33258,33348,33352,33368,33375,33544,33548,33619,33700,33781,33860,34006,34094,34098,34281,34412,34457,34554,34558,35296,35298,36349,36351],[12,26613,936],{"id":26614},"národní-důchod",[115,26616,1638],{"id":1637},[724,26618,26619,26620,1643,26624,26627,26628,1643,26631,26644,26645,26648,26649,26652,26653,26656,26657,26659,26660,1643,26662,26679,26680,26697,26698,26701,26702,12702],{},"Kapitola 7 ",[207,26621,26623],{"className":26622,"dataFsResolvedFilePath":10746,"href":10747},[210],"Matematické ekonomie",[38,26625,26626],{},"přechází z mikroekonomie do makroekonomie",": předmětem zkoumání už není jedna firma, ale celá národní ekonomika popsaná ",[38,26629,26630],{},"národním důchodem",[883,26632,26634],{"className":26633},[886],[888,26635,26636],{"xmlns":890},[892,26637,26638,26642],{},[895,26639,26640],{},[898,26641,8184],{},[902,26643,8184],{"encoding":904},". Budují se postupně bohatší modely — ",[38,26646,26647],{},"C-I"," (jen spotřeba a investice) → ",[38,26650,26651],{},"C-I-G"," (přidá vládu a zdanění) → ",[38,26654,26655],{},"C-I-G-X"," (otevře ekonomiku o čistý export) → ",[38,26658,20746],{}," (propojí trh zboží s trhem peněz přes úrokovou míru). V každém modelu hledáme ",[38,26661,22617],{},[883,26663,26665],{"className":26664},[886],[888,26666,26667],{"xmlns":890},[892,26668,26669,26677],{},[895,26670,26671],{},[2062,26672,26673,26675],{},[898,26674,8184],{},[898,26676,1842],{},[902,26678,22635],{"encoding":904}," jako řešení soustavy lineárních rovnic; citlivost ",[883,26681,26683],{"className":26682},[886],[888,26684,26685],{"xmlns":890},[892,26686,26687,26695],{},[895,26688,26689],{},[2062,26690,26691,26693],{},[898,26692,8184],{},[898,26694,1842],{},[902,26696,22635],{"encoding":904}," na exogenní veličiny popisují ",[38,26699,26700],{},"multiplikátory"," (zejména Keynesův multiplikátor investic ",[883,26703,26705],{"className":26704},[886],[888,26706,26707],{"xmlns":890},[892,26708,26709,26737],{},[895,26710,26711,26713,26715,26717,26719,26721,26723,26725,26727,26729,26731,26733,26735],{},[1667,26712,1669],{},[898,26714,1782],{"mathvariant":1723},[1656,26716,1659],{"stretchy":1658},[1667,26718,1669],{},[1656,26720,3964],{},[898,26722,207],{},[1656,26724,1683],{"stretchy":1658},[1656,26726,1713],{},[1667,26728,1669],{},[898,26730,1782],{"mathvariant":1723},[898,26732,1703],{},[898,26734,8194],{},[898,26736,1769],{},[902,26738,26739],{"encoding":904},"1\u002F(1-a) = 1\u002FMPS",[1981,26741,26742],{},[724,26743,26744,26746,26747,26750,26751,26769,26770,26800,26801,26848,26849,26851,26852,26874],{},[883,26745,3472],{}," Intuice\n",[38,26748,26749],{},"Makroekonomie je zrcadlovým obrazem mikroekonomie"," na úrovni celé ekonomiky. Mezní sklon ke spotřebě ",[883,26752,26754],{"className":26753},[886],[888,26755,26756],{"xmlns":890},[892,26757,26758,26766],{},[895,26759,26760,26762,26764],{},[898,26761,1703],{},[898,26763,8194],{},[898,26765,1766],{},[902,26767,26768],{"encoding":904},"MPC"," je „ta část dodatečné korunky důchodu, kterou domácnost utratí“; zbytek ",[883,26771,26773],{"className":26772},[886],[888,26774,26775],{"xmlns":890},[892,26776,26777,26797],{},[895,26778,26779,26781,26783,26785,26787,26789,26791,26793,26795],{},[898,26780,1703],{},[898,26782,8194],{},[898,26784,1769],{},[1656,26786,1713],{},[1667,26788,1669],{},[1656,26790,3964],{},[898,26792,1703],{},[898,26794,8194],{},[898,26796,1766],{},[902,26798,26799],{"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 ",[883,26802,26804],{"className":26803},[886],[888,26805,26806],{"xmlns":890},[892,26807,26808,26845],{},[895,26809,26810,26812,26814,26816,26818,26824,26826,26829,26831,26833,26835,26837,26839,26841,26843],{},[1667,26811,1669],{},[1656,26813,3633],{},[898,26815,207],{},[1656,26817,3633],{},[2062,26819,26820,26822],{},[898,26821,207],{},[1667,26823,1680],{},[1656,26825,3633],{},[1656,26827,26828],{},"⋯",[1656,26830,1713],{},[1667,26832,1669],{},[898,26834,1782],{"mathvariant":1723},[1656,26836,1659],{"stretchy":1658},[1667,26838,1669],{},[1656,26840,3964],{},[898,26842,207],{},[1656,26844,1683],{"stretchy":1658},[902,26846,26847],{"encoding":904},"1 + a + a^2 + \\dots = 1\u002F(1-a)","). ",[38,26850,20746],{}," 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 ",[883,26853,26855],{"className":26854},[886],[888,26856,26857],{"xmlns":890},[892,26858,26859,26871],{},[895,26860,26861,26863,26865,26867,26869],{},[1656,26862,1659],{"stretchy":1658},[898,26864,8184],{},[1656,26866,1673],{"separator":1672},[898,26868,20776],{},[1656,26870,1683],{"stretchy":1658},[902,26872,26873],{"encoding":904},"(Y, r)"," jsou oba trhy v rovnováze současně.",[115,26876,26878],{"id":26877},"úvod-cílové-znalosti-kapitoly-7","Úvod — cílové znalosti kapitoly 7",[724,26880,26881],{},"Po prostudování kapitoly by čtenář měl umět:",[120,26883,26884,26887,26890,26893,26896,26899,26902,26992],{},[123,26885,26886],{},"popsat zjednodušený model národní ekonomiky,",[123,26888,26889],{},"formulovat pojmy funkcí spotřeby a úspor spolu s jejich základními vlastnostmi,",[123,26891,26892],{},"popsat lineární model spotřeby a úspor,",[123,26894,26895],{},"stanovit mezní sklony ke spotřebě a úsporám,",[123,26897,26898],{},"vymezit pojem makroekonomické rovnováhy ve vztahu k agregátní poptávce a nabídce,",[123,26900,26901],{},"vyložit pojmy křivek agregátní poptávky, agregátní nabídky a rovnovážného bodu,",[123,26903,26904,26905,1343,26922,1343,26944,1896,26969,26991],{},"popsat modely ",[883,26906,26908],{"className":26907},[886],[888,26909,26910],{"xmlns":890},[892,26911,26912,26920],{},[895,26913,26914,26916,26918],{},[898,26915,1766],{},[2461,26917,21025],{},[898,26919,20919],{},[902,26921,21030],{"encoding":904},[883,26923,26925],{"className":26924},[886],[888,26926,26927],{"xmlns":890},[892,26928,26929,26941],{},[895,26930,26931,26933,26935,26937,26939],{},[898,26932,1766],{},[2461,26934,21025],{},[898,26936,20919],{},[2461,26938,21025],{},[898,26940,20847],{},[902,26942,26943],{"encoding":904},"C\\text{-}I\\text{-}G",[883,26945,26947],{"className":26946},[886],[888,26948,26949],{"xmlns":890},[892,26950,26951,26967],{},[895,26952,26953,26955,26957,26959,26961,26963,26965],{},[898,26954,1766],{},[2461,26956,21025],{},[898,26958,20919],{},[2461,26960,21025],{},[898,26962,20847],{},[2461,26964,21025],{},[898,26966,21055],{},[902,26968,21058],{"encoding":904},[883,26970,26972],{"className":26971},[886],[888,26973,26974],{"xmlns":890},[892,26975,26976,26988],{},[895,26977,26978,26980,26982,26984,26986],{},[898,26979,20919],{},[898,26981,1769],{},[2461,26983,21025],{},[898,26985,18539],{},[898,26987,1703],{},[902,26989,26990],{"encoding":904},"IS\\text{-}LM"," národních ekonomik a vypočítat rovnovážné veličiny,",[123,26993,26994],{},"formulovat a stanovit základní makroekonomické multiplikátory.",[115,26996,26998],{"id":26997},"gnp-a-národní-důchod","GNP a národní důchod",[724,27000,27001,1643,27004,3247,27023,27026],{},[38,27002,27003],{},"Hrubý národní produkt",[883,27005,27007],{"className":27006},[886],[888,27008,27009],{"xmlns":890},[892,27010,27011,27020],{},[895,27012,27013,27015,27018],{},[898,27014,20847],{},[898,27016,27017],{},"N",[898,27019,8194],{},[902,27021,27022],{"encoding":904},"GNP",[614,27024,27025],{},"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:",[724,27028,27029],{},[883,27030,27032],{"className":27031},[886],[888,27033,27034],{"xmlns":890},[892,27035,27036,27071],{},[895,27037,27038,27040,27042,27044,27046,27048,27050,27052,27054,27056,27058,27060,27062,27064,27066,27069],{},[898,27039,20847],{},[898,27041,27017],{},[898,27043,8194],{},[1656,27045,1713],{},[898,27047,1766],{},[1656,27049,3633],{},[898,27051,20919],{},[1656,27053,3633],{},[898,27055,20847],{},[1656,27057,3633],{},[898,27059,21055],{},[1656,27061,1673],{"separator":1672},[3316,27063],{"width":14644},[1656,27065,1659],{"stretchy":1658},[1667,27067,27068],{},"7.1",[1656,27070,1683],{"stretchy":1658},[902,27072,27073],{"encoding":904},"GNP = C + I + G + X, \\qquad (7.1)",[724,27075,27076],{},"kde",[120,27078,27079,27095,27111,27127],{},[123,27080,27081,27094],{},[883,27082,27084],{"className":27083},[886],[888,27085,27086],{"xmlns":890},[892,27087,27088,27092],{},[895,27089,27090],{},[898,27091,1766],{},[902,27093,1766],{"encoding":904}," — výdaje domácností na spotřebu,",[123,27096,27097,27110],{},[883,27098,27100],{"className":27099},[886],[888,27101,27102],{"xmlns":890},[892,27103,27104,27108],{},[895,27105,27106],{},[898,27107,20919],{},[902,27109,20919],{"encoding":904}," — hrubé domácí investice,",[123,27112,27113,27126],{},[883,27114,27116],{"className":27115},[886],[888,27117,27118],{"xmlns":890},[892,27119,27120,27124],{},[895,27121,27122],{},[898,27123,20847],{},[902,27125,20847],{"encoding":904}," — vládní výdaje,",[123,27128,27129,27142],{},[883,27130,27132],{"className":27131},[886],[888,27133,27134],{"xmlns":890},[892,27135,27136,27140],{},[895,27137,27138],{},[898,27139,21055],{},[902,27141,21055],{"encoding":904}," — čistý export.",[724,27144,27145,27146,27163,27164,27167,27168,1643,27171,3247,27184,27187],{},"K měření ",[883,27147,27149],{"className":27148},[886],[888,27150,27151],{"xmlns":890},[892,27152,27153,27161],{},[895,27154,27155,27157,27159],{},[898,27156,20847],{},[898,27158,27017],{},[898,27160,8194],{},[902,27162,27022],{"encoding":904}," se užívá ",[38,27165,27166],{},"důchodová metoda",". Jejím hlavním konstrukčním prvkem je ",[38,27169,27170],{},"národní důchod",[883,27172,27174],{"className":27173},[886],[888,27175,27176],{"xmlns":890},[892,27177,27178,27182],{},[895,27179,27180],{},[898,27181,8184],{},[902,27183,8184],{"encoding":904},[614,27185,27186],{},"national income",") — součet důchodů všech vrstev domácností, tj. tok důchodů od firem k domácnostem jako platba za pronájem výrobních faktorů.",[724,27189,27190],{},"Pro tvorbu základních makroekonomických modelů se zjednodušeně ztotožňuje hrubý národní produkt s národním důchodem (rovněž s agregátní poptávkou):",[724,27192,27193],{},[883,27194,27196],{"className":27195},[886],[888,27197,27198],{"xmlns":890},[892,27199,27200,27214],{},[895,27201,27202,27204,27206,27208,27210,27212],{},[898,27203,20847],{},[898,27205,27017],{},[898,27207,8194],{},[1656,27209,3815],{},[898,27211,8184],{},[1656,27213,1673],{"separator":1672},[902,27215,27216],{"encoding":904},"GNP \\approx Y,",[724,27218,27219,27220,3247,27223,27226,27227,27240,27241,27244,27245,1863],{},"a užívá se společného názvu ",[38,27221,27222],{},"důchod",[614,27224,27225],{},"income",") s označením ",[883,27228,27230],{"className":27229},[886],[888,27231,27232],{"xmlns":890},[892,27233,27234,27238],{},[895,27235,27236],{},[898,27237,8184],{},[902,27239,8184],{"encoding":904},". Domácnosti důchod použijí ke ",[38,27242,27243],{},"spotřebě"," zboží a služeb nebo ke tvorbě ",[38,27246,27247],{},"úspor",[115,27249,27251],{"id":27250},"spotřeba-a-úspory","Spotřeba a úspory",[198,27253,27255],{"id":27254},"funkce-spotřeby-a-úspor","Funkce spotřeby a úspor",[724,27257,27258,27259,27272,27273,27286,27287,2114],{},"Jak spotřeba ",[883,27260,27262],{"className":27261},[886],[888,27263,27264],{"xmlns":890},[892,27265,27266,27270],{},[895,27267,27268],{},[898,27269,1766],{},[902,27271,1766],{"encoding":904},", tak úspory ",[883,27274,27276],{"className":27275},[886],[888,27277,27278],{"xmlns":890},[892,27279,27280,27284],{},[895,27281,27282],{},[898,27283,1769],{},[902,27285,1769],{"encoding":904}," závisejí na důchodu ",[883,27288,27290],{"className":27289},[886],[888,27291,27292],{"xmlns":890},[892,27293,27294,27298],{},[895,27295,27296],{},[898,27297,8184],{},[902,27299,8184],{"encoding":904},[724,27301,27302],{},[883,27303,27305],{"className":27304},[886],[888,27306,27307],{"xmlns":890},[892,27308,27309,27341],{},[895,27310,27311,27313,27315,27317,27319,27321,27323,27325,27327,27329,27331,27333,27335,27337,27339],{},[898,27312,1766],{},[1656,27314,1713],{},[898,27316,1766],{},[1656,27318,1659],{"stretchy":1658},[898,27320,8184],{},[1656,27322,1683],{"stretchy":1658},[1656,27324,1673],{"separator":1672},[3316,27326],{"width":14644},[898,27328,1769],{},[1656,27330,1713],{},[898,27332,1769],{},[1656,27334,1659],{"stretchy":1658},[898,27336,8184],{},[1656,27338,1683],{"stretchy":1658},[898,27340,1863],{"mathvariant":1723},[902,27342,27343],{"encoding":904},"C = C(Y), \\qquad S = S(Y).",[724,27345,27346,3206,27365,3247,27368,10722,27371,3206,27391,3247,27394,27397,27398,1896,27401,27404],{},[883,27347,27349],{"className":27348},[886],[888,27350,27351],{"xmlns":890},[892,27352,27353,27363],{},[895,27354,27355,27357,27359,27361],{},[898,27356,1766],{},[1656,27358,1659],{"stretchy":1658},[898,27360,8184],{},[1656,27362,1683],{"stretchy":1658},[902,27364,22948],{"encoding":904},[38,27366,27367],{},"funkce spotřeby",[614,27369,27370],{},"consumption function",[883,27372,27374],{"className":27373},[886],[888,27375,27376],{"xmlns":890},[892,27377,27378,27388],{},[895,27379,27380,27382,27384,27386],{},[898,27381,1769],{},[1656,27383,1659],{"stretchy":1658},[898,27385,8184],{},[1656,27387,1683],{"stretchy":1658},[902,27389,27390],{"encoding":904},"S(Y)",[38,27392,27393],{},"funkce úspor",[614,27395,27396],{},"savings function","); jejich grafy se nazývají ",[38,27399,27400],{},"křivka spotřeby",[38,27402,27403],{},"křivka úspor",". Platí základní identita",[724,27406,27407],{},[883,27408,27410],{"className":27409},[886],[888,27411,27412],{"xmlns":890},[892,27413,27414,27457],{},[895,27415,27416,27418,27420,27422,27424,27426,27428,27430,27432,27434,27436,27438,27440,27442,27444,27446,27448,27450,27452,27455],{},[898,27417,8184],{},[1656,27419,1713],{},[898,27421,1766],{},[1656,27423,3633],{},[898,27425,1769],{},[1656,27427,1713],{},[898,27429,1766],{},[1656,27431,1659],{"stretchy":1658},[898,27433,8184],{},[1656,27435,1683],{"stretchy":1658},[1656,27437,3633],{},[898,27439,1769],{},[1656,27441,1659],{"stretchy":1658},[898,27443,8184],{},[1656,27445,1683],{"stretchy":1658},[898,27447,1863],{"mathvariant":1723},[3316,27449],{"width":14644},[1656,27451,1659],{"stretchy":1658},[1667,27453,27454],{},"7.2",[1656,27456,1683],{"stretchy":1658},[902,27458,27459],{"encoding":904},"Y = C + S = C(Y) + S(Y). \\qquad (7.2)",[724,27461,27462],{},"Známe-li jednu z funkcí, je tím určena i druhá. Obě funkce jsou rostoucí (s růstem důchodu roste spotřeba i úspory).",[198,27464,27466],{"id":27465},"lineární-model-spotřeby-a-úspor","Lineární model spotřeby a úspor",[724,27468,27469],{},"Nejjednodušší model předpokládá lineární tvar",[724,27471,27472],{},[883,27473,27475],{"className":27474},[886],[888,27476,27477],{"xmlns":890},[892,27478,27479,27514],{},[895,27480,27481,27483,27485,27487,27489,27491,27493,27495,27497,27499,27501,27503,27505,27507,27509,27512],{},[898,27482,1766],{},[1656,27484,1713],{},[898,27486,1766],{},[1656,27488,1659],{"stretchy":1658},[898,27490,8184],{},[1656,27492,1683],{"stretchy":1658},[1656,27494,1713],{},[898,27496,207],{},[898,27498,8184],{},[1656,27500,3633],{},[898,27502,3403],{},[1656,27504,1673],{"separator":1672},[3316,27506],{"width":14644},[1656,27508,1659],{"stretchy":1658},[1667,27510,27511],{},"7.3",[1656,27513,1683],{"stretchy":1658},[902,27515,27516],{"encoding":904},"C = C(Y) = aY + b, \\qquad (7.3)",[724,27518,2355,27519,1896,27537,27559,27560,27599,27600,1863],{},[883,27520,27522],{"className":27521},[886],[888,27523,27524],{"xmlns":890},[892,27525,27526,27534],{},[895,27527,27528,27530,27532],{},[898,27529,3403],{},[1656,27531,2850],{},[1667,27533,4032],{},[902,27535,27536],{"encoding":904},"b > 0",[883,27538,27540],{"className":27539},[886],[888,27541,27542],{"xmlns":890},[892,27543,27544,27556],{},[895,27545,27546,27548,27550,27552,27554],{},[1667,27547,4032],{},[1656,27549,4373],{},[898,27551,207],{},[1656,27553,4373],{},[1667,27555,1669],{},[902,27557,27558],{"encoding":904},"0 \u003C a \u003C 1",". Směrnice ",[883,27561,27563],{"className":27562},[886],[888,27564,27565],{"xmlns":890},[892,27566,27567,27596],{},[895,27568,27569,27571,27573,27580,27582,27584,27586,27588,27590,27592,27594],{},[898,27570,207],{},[1656,27572,1713],{},[895,27574,27575,27578],{},[898,27576,27577],{"mathvariant":1723},"t",[898,27579,19780],{"mathvariant":1723},[2461,27581,7828],{},[898,27583,7151],{},[1656,27585,1713],{},[898,27587,3750],{"mathvariant":1723},[898,27589,1766],{},[898,27591,1782],{"mathvariant":1723},[898,27593,3750],{"mathvariant":1723},[898,27595,8184],{},[902,27597,27598],{"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 ",[883,27601,27603],{"className":27602},[886],[888,27604,27605],{"xmlns":890},[892,27606,27607,27611],{},[895,27608,27609],{},[898,27610,8184],{},[902,27612,8184],{"encoding":904},[724,27614,27615],{},[614,27616,27617,27618,27642,27643,27681,27682,27698,27699,1863],{},"Obrázek 7.1 — Přímka spotřeby ",[883,27619,27621],{"className":27620},[886],[888,27622,27623],{"xmlns":890},[892,27624,27625,27639],{},[895,27626,27627,27629,27631,27633,27635,27637],{},[898,27628,1766],{},[1656,27630,1713],{},[898,27632,207],{},[898,27634,8184],{},[1656,27636,3633],{},[898,27638,3403],{},[902,27640,27641],{"encoding":904},"C = aY + b"," se směrnicí ",[883,27644,27646],{"className":27645},[886],[888,27647,27648],{"xmlns":890},[892,27649,27650,27678],{},[895,27651,27652,27654,27656,27662,27664,27666,27668,27670,27672,27674,27676],{},[898,27653,207],{},[1656,27655,1713],{},[895,27657,27658,27660],{},[898,27659,27577],{"mathvariant":1723},[898,27661,19780],{"mathvariant":1723},[2461,27663,7828],{},[898,27665,7151],{},[1656,27667,1713],{},[898,27669,3750],{"mathvariant":1723},[898,27671,1766],{},[898,27673,1782],{"mathvariant":1723},[898,27675,3750],{"mathvariant":1723},[898,27677,8184],{},[902,27679,27680],{"encoding":904},"a = \\mathrm{tg}\\,\\alpha = \\Delta C\u002F\\Delta Y","; znázornění ",[883,27683,27685],{"className":27684},[886],[888,27686,27687],{"xmlns":890},[892,27688,27689,27695],{},[895,27690,27691,27693],{},[898,27692,3750],{"mathvariant":1723},[898,27694,1766],{},[902,27696,27697],{"encoding":904},"\\Delta C"," při jednotkovém přírůstku ",[883,27700,27702],{"className":27701},[886],[888,27703,27704],{"xmlns":890},[892,27705,27706,27716],{},[895,27707,27708,27710,27712,27714],{},[898,27709,3750],{"mathvariant":1723},[898,27711,8184],{},[1656,27713,1713],{},[1667,27715,1669],{},[902,27717,27718],{"encoding":904},"\\Delta Y = 1",[724,27720,27721,27722,2114],{},"Dosazením do (7.2) plyne ",[38,27723,27724],{},"lineární model úspor",[724,27726,27727],{},[883,27728,27730],{"className":27729},[886],[888,27731,27732],{"xmlns":890},[892,27733,27734,27799],{},[895,27735,27736,27738,27740,27742,27744,27746,27748,27750,27752,27754,27756,27758,27760,27762,27764,27766,27768,27770,27772,27774,27776,27778,27780,27782,27784,27786,27788,27790,27792,27794,27797],{},[898,27737,1769],{},[1656,27739,1713],{},[898,27741,8184],{},[1656,27743,3964],{},[898,27745,1766],{},[1656,27747,1659],{"stretchy":1658},[898,27749,8184],{},[1656,27751,1683],{"stretchy":1658},[1656,27753,1713],{},[898,27755,8184],{},[1656,27757,3964],{},[1656,27759,1659],{"stretchy":1658},[898,27761,207],{},[898,27763,8184],{},[1656,27765,3633],{},[898,27767,3403],{},[1656,27769,1683],{"stretchy":1658},[1656,27771,1713],{},[1656,27773,1659],{"stretchy":1658},[1667,27775,1669],{},[1656,27777,3964],{},[898,27779,207],{},[1656,27781,1683],{"stretchy":1658},[898,27783,8184],{},[1656,27785,3964],{},[898,27787,3403],{},[898,27789,1863],{"mathvariant":1723},[3316,27791],{"width":14644},[1656,27793,1659],{"stretchy":1658},[1667,27795,27796],{},"7.4",[1656,27798,1683],{"stretchy":1658},[902,27800,27801],{"encoding":904},"S = Y - C(Y) = Y - (aY + b) = (1 - a)Y - b. \\qquad (7.4)",[724,27803,27804,27805,12702],{},"Úspory jsou také lineární a „pomalu rostoucí“ (protože ",[883,27806,27808],{"className":27807},[886],[888,27809,27810],{"xmlns":890},[892,27811,27812,27828],{},[895,27813,27814,27816,27818,27820,27822,27824,27826],{},[1667,27815,4032],{},[1656,27817,4373],{},[1667,27819,1669],{},[1656,27821,3964],{},[898,27823,207],{},[1656,27825,4373],{},[1667,27827,1669],{},[902,27829,27830],{"encoding":904},"0 \u003C 1 - a \u003C 1",[724,27832,27833],{},[614,27834,27835,27836,1896,27859,27891,27892,3565,27905,27935,27936,3565,27954,1863],{},"Obrázek 7.2 — Přímky ",[883,27837,27839],{"className":27838},[886],[888,27840,27841],{"xmlns":890},[892,27842,27843,27857],{},[895,27844,27845,27847,27849,27851,27853,27855],{},[898,27846,1766],{},[1656,27848,1713],{},[898,27850,207],{},[898,27852,8184],{},[1656,27854,3633],{},[898,27856,3403],{},[902,27858,27641],{"encoding":904},[883,27860,27862],{"className":27861},[886],[888,27863,27864],{"xmlns":890},[892,27865,27866,27888],{},[895,27867,27868,27870,27872,27874,27876,27878,27880,27882,27884,27886],{},[898,27869,1769],{},[1656,27871,1713],{},[1656,27873,1659],{"stretchy":1658},[1667,27875,1669],{},[1656,27877,3964],{},[898,27879,207],{},[1656,27881,1683],{"stretchy":1658},[898,27883,8184],{},[1656,27885,3964],{},[898,27887,3403],{},[902,27889,27890],{"encoding":904},"S = (1-a)Y - b",". Přímka úspor protíná osu ",[883,27893,27895],{"className":27894},[886],[888,27896,27897],{"xmlns":890},[892,27898,27899,27903],{},[895,27900,27901],{},[898,27902,8184],{},[902,27904,8184],{"encoding":904},[883,27906,27908],{"className":27907},[886],[888,27909,27910],{"xmlns":890},[892,27911,27912,27932],{},[895,27913,27914,27916,27918,27920,27922,27924,27926,27928,27930],{},[898,27915,8184],{},[1656,27917,1713],{},[898,27919,3403],{},[898,27921,1782],{"mathvariant":1723},[1656,27923,1659],{"stretchy":1658},[1667,27925,1669],{},[1656,27927,3964],{},[898,27929,207],{},[1656,27931,1683],{"stretchy":1658},[902,27933,27934],{"encoding":904},"Y = b\u002F(1-a)"," a osu ",[883,27937,27939],{"className":27938},[886],[888,27940,27941],{"xmlns":890},[892,27942,27943,27951],{},[895,27944,27945,27947,27949],{},[898,27946,1766],{},[1656,27948,1673],{"separator":1672},[898,27950,1769],{},[902,27952,27953],{"encoding":904},"C, S",[883,27955,27957],{"className":27956},[886],[888,27958,27959],{"xmlns":890},[892,27960,27961,27967],{},[895,27962,27963,27965],{},[1656,27964,3964],{},[898,27966,3403],{},[902,27968,27969],{"encoding":904},"-b",[198,27971,27973],{"id":27972},"příklad-71","Příklad 7.1",[724,27975,27976,27977,28002],{},"Pro spotřebu ",[883,27978,27980],{"className":27979},[886],[888,27981,27982],{"xmlns":890},[892,27983,27984,27999],{},[895,27985,27986,27988,27990,27993,27995,27997],{},[898,27987,1766],{},[1656,27989,1713],{},[1667,27991,27992],{},"0,4",[898,27994,8184],{},[1656,27996,3633],{},[1667,27998,8580],{},[902,28000,28001],{"encoding":904},"C = 0{,}4Y + 10"," jsou úspory",[724,28004,28005],{},[883,28006,28008],{"className":28007},[886],[888,28009,28010],{"xmlns":890},[892,28011,28012,28050],{},[895,28013,28014,28016,28018,28020,28022,28024,28026,28028,28030,28032,28034,28036,28038,28040,28043,28045,28047],{},[898,28015,1769],{},[1656,28017,1713],{},[898,28019,8184],{},[1656,28021,3964],{},[898,28023,1766],{},[1656,28025,1713],{},[898,28027,8184],{},[1656,28029,3964],{},[1667,28031,27992],{},[898,28033,8184],{},[1656,28035,3964],{},[1667,28037,8580],{},[1656,28039,1713],{},[1667,28041,28042],{},"0,6",[898,28044,8184],{},[1656,28046,3964],{},[1667,28048,28049],{},"10.",[902,28051,28052],{"encoding":904},"S = Y - C = Y - 0{,}4Y - 10 = 0{,}6Y - 10.",[724,28054,28055],{},[614,28056,28057,28058,1896,28081,28105,28106,3206,28119,28143,28144,3206,28161,28177,28178,1863],{},"Obrázek 7.3 — Přímky ",[883,28059,28061],{"className":28060},[886],[888,28062,28063],{"xmlns":890},[892,28064,28065,28079],{},[895,28066,28067,28069,28071,28073,28075,28077],{},[898,28068,1766],{},[1656,28070,1713],{},[1667,28072,27992],{},[898,28074,8184],{},[1656,28076,3633],{},[1667,28078,8580],{},[902,28080,28001],{"encoding":904},[883,28082,28084],{"className":28083},[886],[888,28085,28086],{"xmlns":890},[892,28087,28088,28102],{},[895,28089,28090,28092,28094,28096,28098,28100],{},[898,28091,1769],{},[1656,28093,1713],{},[1667,28095,28042],{},[898,28097,8184],{},[1656,28099,3964],{},[1667,28101,8580],{},[902,28103,28104],{"encoding":904},"S = 0{,}6Y - 10","; průsečík přímky úspor s osou ",[883,28107,28109],{"className":28108},[886],[888,28110,28111],{"xmlns":890},[892,28112,28113,28117],{},[895,28114,28115],{},[898,28116,8184],{},[902,28118,8184],{"encoding":904},[883,28120,28122],{"className":28121},[886],[888,28123,28124],{"xmlns":890},[892,28125,28126,28140],{},[895,28127,28128,28130,28133],{},[1656,28129,3815],{},[1667,28131,28132],{},"16,",[2033,28134,28135,28137],{"accent":1672},[1667,28136,9112],{},[1656,28138,28139],{},"ˉ",[902,28141,28142],{"encoding":904},"\\approx 16{,}\\bar{6}",", s osou ",[883,28145,28147],{"className":28146},[886],[888,28148,28149],{"xmlns":890},[892,28150,28151,28159],{},[895,28152,28153,28155,28157],{},[898,28154,1766],{},[1656,28156,1673],{"separator":1672},[898,28158,1769],{},[902,28160,27953],{"encoding":904},[883,28162,28164],{"className":28163},[886],[888,28165,28166],{"xmlns":890},[892,28167,28168,28174],{},[895,28169,28170,28172],{},[1656,28171,3964],{},[1667,28173,8580],{},[902,28175,28176],{"encoding":904},"-10","; přímka spotřeby prochází bodem ",[883,28179,28181],{"className":28180},[886],[888,28182,28183],{"xmlns":890},[892,28184,28185,28197],{},[895,28186,28187,28189,28191,28193,28195],{},[1656,28188,1659],{"stretchy":1658},[1667,28190,4032],{},[1656,28192,1673],{"separator":1672},[1667,28194,8580],{},[1656,28196,1683],{"stretchy":1658},[902,28198,28199],{"encoding":904},"(0, 10)",[724,28201,28202,28203,3206,28221,28251,28252,3247,28255,28258,28259,3206,28283,3247,28286,28289],{},"Funkce úspor může nabývat záporných hodnot — pro ",[883,28204,28206],{"className":28205},[886],[888,28207,28208],{"xmlns":890},[892,28209,28210,28218],{},[895,28211,28212,28214,28216],{},[898,28213,8184],{},[1656,28215,1713],{},[1667,28217,4032],{},[902,28219,28220],{"encoding":904},"Y = 0",[883,28222,28224],{"className":28223},[886],[888,28225,28226],{"xmlns":890},[892,28227,28228,28248],{},[895,28229,28230,28232,28234,28236,28238,28240,28242,28244,28246],{},[898,28231,1769],{},[1656,28233,1659],{"stretchy":1658},[1667,28235,4032],{},[1656,28237,1683],{"stretchy":1658},[1656,28239,1713],{},[1656,28241,3964],{},[898,28243,3403],{},[1656,28245,4373],{},[1667,28247,4032],{},[902,28249,28250],{"encoding":904},"S(0) = -b \u003C 0","; hovoří se o ",[38,28253,28254],{},"autonomních úsporách",[614,28256,28257],{},"autonomous savings","). Analogicky ",[883,28260,28262],{"className":28261},[886],[888,28263,28264],{"xmlns":890},[892,28265,28266,28280],{},[895,28267,28268,28270,28272,28274,28276,28278],{},[898,28269,1766],{},[1656,28271,1659],{"stretchy":1658},[1667,28273,4032],{},[1656,28275,1683],{"stretchy":1658},[1656,28277,1713],{},[898,28279,3403],{},[902,28281,28282],{"encoding":904},"C(0) = b",[38,28284,28285],{},"autonomní spotřeba",[614,28287,28288],{},"autonomous consumption",") — spotřeba při nulovém důchodu krytá dřívějšími úsporami.",[115,28291,28293],{"id":28292},"mezní-sklon-ke-spotřebě-mpc-a-k-úsporám-mps","Mezní sklon ke spotřebě (MPC) a k úsporám (MPS)",[724,28295,28296,1643,28299,3247,28316,28319],{},[38,28297,28298],{},"Mezní sklon ke spotřebě",[883,28300,28302],{"className":28301},[886],[888,28303,28304],{"xmlns":890},[892,28305,28306,28314],{},[895,28307,28308,28310,28312],{},[898,28309,1703],{},[898,28311,8194],{},[898,28313,1766],{},[902,28315,26768],{"encoding":904},[614,28317,28318],{},"marginal propensity to consume",") je derivace spotřeby podle důchodu:",[724,28321,28322],{},[883,28323,28325],{"className":28324},[886],[888,28326,28327],{"xmlns":890},[892,28328,28329,28355],{},[895,28330,28331,28333,28335,28337,28339,28353],{},[898,28332,1703],{},[898,28334,8194],{},[898,28336,1766],{},[1656,28338,1713],{},[3294,28340,28341,28347],{},[895,28342,28343,28345],{},[898,28344,3768],{"mathvariant":1723},[898,28346,1766],{},[895,28348,28349,28351],{},[898,28350,3768],{"mathvariant":1723},[898,28352,8184],{},[898,28354,1863],{"mathvariant":1723},[902,28356,28357],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y}.",[724,28359,28360,1643,28363,3247,28381,28384],{},[38,28361,28362],{},"Mezní sklon k úsporám",[883,28364,28366],{"className":28365},[886],[888,28367,28368],{"xmlns":890},[892,28369,28370,28378],{},[895,28371,28372,28374,28376],{},[898,28373,1703],{},[898,28375,8194],{},[898,28377,1769],{},[902,28379,28380],{"encoding":904},"MPS",[614,28382,28383],{},"marginal propensity to save",") je derivace úspor podle důchodu:",[724,28386,28387],{},[883,28388,28390],{"className":28389},[886],[888,28391,28392],{"xmlns":890},[892,28393,28394,28420],{},[895,28395,28396,28398,28400,28402,28404,28418],{},[898,28397,1703],{},[898,28399,8194],{},[898,28401,1769],{},[1656,28403,1713],{},[3294,28405,28406,28412],{},[895,28407,28408,28410],{},[898,28409,3768],{"mathvariant":1723},[898,28411,1769],{},[895,28413,28414,28416],{},[898,28415,3768],{"mathvariant":1723},[898,28417,8184],{},[898,28419,1863],{"mathvariant":1723},[902,28421,28422],{"encoding":904},"MPS = \\frac{\\mathrm{d}S}{\\mathrm{d}Y}.",[724,28424,28425,28426,28484],{},"Z (7.2) plyne ",[883,28427,28429],{"className":28428},[886],[888,28430,28431],{"xmlns":890},[892,28432,28433,28481],{},[895,28434,28435,28449,28451,28465,28467],{},[3294,28436,28437,28443],{},[895,28438,28439,28441],{},[898,28440,3768],{"mathvariant":1723},[898,28442,8184],{},[895,28444,28445,28447],{},[898,28446,3768],{"mathvariant":1723},[898,28448,8184],{},[1656,28450,1713],{},[3294,28452,28453,28459],{},[895,28454,28455,28457],{},[898,28456,3768],{"mathvariant":1723},[898,28458,1766],{},[895,28460,28461,28463],{},[898,28462,3768],{"mathvariant":1723},[898,28464,8184],{},[1656,28466,3633],{},[3294,28468,28469,28475],{},[895,28470,28471,28473],{},[898,28472,3768],{"mathvariant":1723},[898,28474,1769],{},[895,28476,28477,28479],{},[898,28478,3768],{"mathvariant":1723},[898,28480,8184],{},[902,28482,28483],{"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",[724,28486,28487],{},[883,28488,28490],{"className":28489},[886],[888,28491,28492],{"xmlns":890},[892,28493,28494,28557],{},[895,28495,28496,28548,28550,28552,28555],{},[21566,28497,28498],{"notation":21568},[4138,28499,28500],{"scriptlevel":4032,"displaystyle":1658},[4138,28501,28502],{"scriptlevel":4032,"displaystyle":1658},[4138,28503,28504],{"scriptlevel":4032,"displaystyle":1672},[895,28505,28506,28508,28510,28512,28514,28516,28518,28520,28522,28524,28526,28528,28530,28532,28534,28536,28538,28540,28542,28544,28546],{},[898,28507,1703],{},[898,28509,8194],{},[898,28511,1766],{},[1656,28513,3633],{},[898,28515,1703],{},[898,28517,8194],{},[898,28519,1769],{},[1656,28521,1713],{},[1667,28523,1669],{},[1656,28525,1673],{"separator":1672},[3316,28527],{"width":14644},[898,28529,1703],{},[898,28531,8194],{},[898,28533,1769],{},[1656,28535,1713],{},[1667,28537,1669],{},[1656,28539,3964],{},[898,28541,1703],{},[898,28543,8194],{},[898,28545,1766],{},[898,28547,1863],{"mathvariant":1723},[3316,28549],{"width":14644},[1656,28551,1659],{"stretchy":1658},[1667,28553,28554],{},"7.5",[1656,28556,1683],{"stretchy":1658},[902,28558,28559],{"encoding":904},"\\boxed{MPC + MPS = 1, \\qquad MPS = 1 - MPC.} \\qquad (7.5)",[724,28561,28562,1643,28565,28588,28589,1896,28611,28637],{},[38,28563,28564],{},"Pro lineární model",[883,28566,28568],{"className":28567},[886],[888,28569,28570],{"xmlns":890},[892,28571,28572,28586],{},[895,28573,28574,28576,28578,28580,28582,28584],{},[898,28575,1766],{},[1656,28577,1713],{},[898,28579,207],{},[898,28581,8184],{},[1656,28583,3633],{},[898,28585,3403],{},[902,28587,27641],{"encoding":904}," vychází ",[883,28590,28592],{"className":28591},[886],[888,28593,28594],{"xmlns":890},[892,28595,28596,28608],{},[895,28597,28598,28600,28602,28604,28606],{},[898,28599,1703],{},[898,28601,8194],{},[898,28603,1766],{},[1656,28605,1713],{},[898,28607,207],{},[902,28609,28610],{"encoding":904},"MPC = a",[883,28612,28614],{"className":28613},[886],[888,28615,28616],{"xmlns":890},[892,28617,28618,28634],{},[895,28619,28620,28622,28624,28626,28628,28630,28632],{},[898,28621,1703],{},[898,28623,8194],{},[898,28625,1769],{},[1656,28627,1713],{},[1667,28629,1669],{},[1656,28631,3964],{},[898,28633,207],{},[902,28635,28636],{"encoding":904},"MPS = 1 - a"," — tedy směrnice přímek spotřeby a úspor.",[724,28639,28640,28643,28644,28666,28667,28695],{},[38,28641,28642],{},"Interpretace diferenciálem."," Pro pevné ",[883,28645,28647],{"className":28646},[886],[888,28648,28649],{"xmlns":890},[892,28650,28651,28663],{},[895,28652,28653,28655,28657],{},[898,28654,8184],{},[1656,28656,1713],{},[2062,28658,28659,28661],{},[898,28660,8184],{},[1656,28662,8187],{},[902,28664,28665],{"encoding":904},"Y = Y^*"," udává ",[883,28668,28670],{"className":28669},[886],[888,28671,28672],{"xmlns":890},[892,28673,28674,28692],{},[895,28675,28676,28678,28680,28682,28684,28690],{},[898,28677,1703],{},[898,28679,8194],{},[898,28681,1766],{},[1656,28683,1659],{"stretchy":1658},[2062,28685,28686,28688],{},[898,28687,8184],{},[1656,28689,8187],{},[1656,28691,1683],{"stretchy":1658},[902,28693,28694],{"encoding":904},"MPC(Y^*)"," přibližnou změnu spotřeby při jednotkovém přírůstku důchodu:",[724,28697,28698],{},[883,28699,28701],{"className":28700},[886],[888,28702,28703],{"xmlns":890},[892,28704,28705,28759],{},[895,28706,28707,28709,28711,28713,28715,28717,28719,28725,28727,28729,28731,28733,28735,28737,28739,28741,28743,28745,28747,28749,28751,28753,28755,28757],{},[898,28708,3750],{"mathvariant":1723},[898,28710,1766],{},[1656,28712,3815],{},[898,28714,3768],{"mathvariant":1723},[898,28716,1766],{},[1656,28718,1713],{},[2062,28720,28721,28723],{},[898,28722,1766],{},[1656,28724,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,28726,1659],{"stretchy":1658},[898,28728,8184],{},[1656,28730,1683],{"stretchy":1658},[2461,28732,7828],{},[898,28734,3768],{"mathvariant":1723},[898,28736,8184],{},[1656,28738,1713],{},[898,28740,1703],{},[898,28742,8194],{},[898,28744,1766],{},[1656,28746,1659],{"stretchy":1658},[898,28748,8184],{},[1656,28750,1683],{"stretchy":1658},[2461,28752,7828],{},[898,28754,3768],{"mathvariant":1723},[898,28756,8184],{},[898,28758,1863],{"mathvariant":1723},[902,28760,28761],{"encoding":904},"\\Delta C \\approx \\mathrm{d}C = C'(Y)\\,\\mathrm{d}Y = MPC(Y)\\,\\mathrm{d}Y.",[724,28763,28764,28765,28801,28802,28805],{},"Analogicky ",[883,28766,28768],{"className":28767},[886],[888,28769,28770],{"xmlns":890},[892,28771,28772,28798],{},[895,28773,28774,28776,28778,28780,28782,28784,28786,28788,28790,28792,28794,28796],{},[898,28775,3750],{"mathvariant":1723},[898,28777,1769],{},[1656,28779,3815],{},[898,28781,1703],{},[898,28783,8194],{},[898,28785,1769],{},[1656,28787,1659],{"stretchy":1658},[898,28789,8184],{},[1656,28791,1683],{"stretchy":1658},[2461,28793,7828],{},[898,28795,3768],{"mathvariant":1723},[898,28797,8184],{},[902,28799,28800],{"encoding":904},"\\Delta S \\approx MPS(Y)\\,\\mathrm{d}Y",". Viz ",[207,28803,1145],{"className":28804,"dataFsResolvedFilePath":764,"href":765},[210]," a její ekonomická interpretace.",[198,28807,28809],{"id":28808},"příklad-72","Příklad 7.2",[724,28811,27976,28812,28847,28848,28867],{},[883,28813,28815],{"className":28814},[886],[888,28816,28817],{"xmlns":890},[892,28818,28819,28844],{},[895,28820,28821,28823,28825,28828,28834,28836,28838,28840,28842],{},[898,28822,1766],{},[1656,28824,1713],{},[1667,28826,28827],{},"0,001",[2062,28829,28830,28832],{},[898,28831,8184],{},[1667,28833,1680],{},[1656,28835,3633],{},[1667,28837,11639],{},[898,28839,8184],{},[1656,28841,3633],{},[1667,28843,9267],{},[902,28845,28846],{"encoding":904},"C = 0{,}001Y^2 + 0{,}2Y + 50"," (pro ",[883,28849,28851],{"className":28850},[886],[888,28852,28853],{"xmlns":890},[892,28854,28855,28864],{},[895,28856,28857,28859,28861],{},[898,28858,8184],{},[1656,28860,4373],{},[1667,28862,28863],{},"400",[902,28865,28866],{"encoding":904},"Y \u003C 400",") platí",[724,28869,28870],{},[883,28871,28873],{"className":28872},[886],[888,28874,28875],{"xmlns":890},[892,28876,28877,28914],{},[895,28878,28879,28881,28883,28885,28887,28901,28903,28906,28908,28910,28912],{},[898,28880,1703],{},[898,28882,8194],{},[898,28884,1766],{},[1656,28886,1713],{},[3294,28888,28889,28895],{},[895,28890,28891,28893],{},[898,28892,3768],{"mathvariant":1723},[898,28894,1766],{},[895,28896,28897,28899],{},[898,28898,3768],{"mathvariant":1723},[898,28900,8184],{},[1656,28902,1713],{},[1667,28904,28905],{},"0,002",[898,28907,8184],{},[1656,28909,3633],{},[1667,28911,11639],{},[1656,28913,1673],{"separator":1672},[902,28915,28916],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y} = 0{,}002Y + 0{,}2,",[724,28918,28919],{},[883,28920,28922],{"className":28921},[886],[888,28923,28924],{"xmlns":890},[892,28925,28926,28959],{},[895,28927,28928,28930,28932,28934,28936,28938,28940,28942,28944,28946,28948,28950,28952,28954,28956],{},[898,28929,1703],{},[898,28931,8194],{},[898,28933,1769],{},[1656,28935,1713],{},[1667,28937,1669],{},[1656,28939,3964],{},[898,28941,1703],{},[898,28943,8194],{},[898,28945,1766],{},[1656,28947,1713],{},[1656,28949,3964],{},[1667,28951,28905],{},[898,28953,8184],{},[1656,28955,3633],{},[1667,28957,28958],{},"0,8.",[902,28960,28961],{"encoding":904},"MPS = 1 - MPC = -0{,}002Y + 0{,}8.",[120,28963,28964,29044,29123],{},[123,28965,28966,1343,28994,29022,29023,3206,29041,1863],{},[883,28967,28969],{"className":28968},[886],[888,28970,28971],{"xmlns":890},[892,28972,28973,28991],{},[895,28974,28975,28977,28979,28981,28983,28985,28987,28989],{},[898,28976,1703],{},[898,28978,8194],{},[898,28980,1766],{},[1656,28982,1659],{"stretchy":1658},[1667,28984,5267],{},[1656,28986,1683],{"stretchy":1658},[1656,28988,1713],{},[1667,28990,27992],{},[902,28992,28993],{"encoding":904},"MPC(100) = 0{,}4",[883,28995,28997],{"className":28996},[886],[888,28998,28999],{"xmlns":890},[892,29000,29001,29019],{},[895,29002,29003,29005,29007,29009,29011,29013,29015,29017],{},[898,29004,1703],{},[898,29006,8194],{},[898,29008,1769],{},[1656,29010,1659],{"stretchy":1658},[1667,29012,5267],{},[1656,29014,1683],{"stretchy":1658},[1656,29016,1713],{},[1667,29018,28042],{},[902,29020,29021],{"encoding":904},"MPS(100) = 0{,}6"," — při ",[883,29024,29026],{"className":29025},[886],[888,29027,29028],{"xmlns":890},[892,29029,29030,29038],{},[895,29031,29032,29034,29036],{},[898,29033,8184],{},[1656,29035,1713],{},[1667,29037,5267],{},[902,29039,29040],{"encoding":904},"Y = 100",[38,29042,29043],{},"větší sklon k úsporám",[123,29045,29046,1343,29074,29022,29102,3206,29120,1863],{},[883,29047,29049],{"className":29048},[886],[888,29050,29051],{"xmlns":890},[892,29052,29053,29071],{},[895,29054,29055,29057,29059,29061,29063,29065,29067,29069],{},[898,29056,1703],{},[898,29058,8194],{},[898,29060,1766],{},[1656,29062,1659],{"stretchy":1658},[1667,29064,5272],{},[1656,29066,1683],{"stretchy":1658},[1656,29068,1713],{},[1667,29070,28042],{},[902,29072,29073],{"encoding":904},"MPC(200) = 0{,}6",[883,29075,29077],{"className":29076},[886],[888,29078,29079],{"xmlns":890},[892,29080,29081,29099],{},[895,29082,29083,29085,29087,29089,29091,29093,29095,29097],{},[898,29084,1703],{},[898,29086,8194],{},[898,29088,1769],{},[1656,29090,1659],{"stretchy":1658},[1667,29092,5272],{},[1656,29094,1683],{"stretchy":1658},[1656,29096,1713],{},[1667,29098,27992],{},[902,29100,29101],{"encoding":904},"MPS(200) = 0{,}4",[883,29103,29105],{"className":29104},[886],[888,29106,29107],{"xmlns":890},[892,29108,29109,29117],{},[895,29110,29111,29113,29115],{},[898,29112,8184],{},[1656,29114,1713],{},[1667,29116,5272],{},[902,29118,29119],{"encoding":904},"Y = 200",[38,29121,29122],{},"větší sklon ke spotřebě",[123,29124,29125,29126,29144,29145,12702],{},"Přesně při ",[883,29127,29129],{"className":29128},[886],[888,29130,29131],{"xmlns":890},[892,29132,29133,29141],{},[895,29134,29135,29137,29139],{},[898,29136,8184],{},[1656,29138,1713],{},[1667,29140,17557],{},[902,29142,29143],{"encoding":904},"Y = 150"," se oba sklony rovnají (",[883,29146,29148],{"className":29147},[886],[888,29149,29150],{"xmlns":890},[892,29151,29152,29172],{},[895,29153,29154,29156,29158,29160,29162,29164,29166,29168,29170],{},[898,29155,1703],{},[898,29157,8194],{},[898,29159,1766],{},[1656,29161,1713],{},[898,29163,1703],{},[898,29165,8194],{},[898,29167,1769],{},[1656,29169,1713],{},[1667,29171,13779],{},[902,29173,29174],{"encoding":904},"MPC = MPS = 0{,}5",[724,29176,29177,29178,29195,29196,29210,29211,3619,29224,29238,29239,29252,29253,29294],{},"Interpretace: při ",[883,29179,29181],{"className":29180},[886],[888,29182,29183],{"xmlns":890},[892,29184,29185,29193],{},[895,29186,29187,29189,29191],{},[898,29188,8184],{},[1656,29190,1713],{},[1667,29192,5267],{},[902,29194,29040],{"encoding":904}," se spotřeba mění ",[883,29197,29199],{"className":29198},[886],[888,29200,29201],{"xmlns":890},[892,29202,29203,29207],{},[895,29204,29205],{},[1667,29206,27992],{},[902,29208,29209],{"encoding":904},"0{,}4","-krát rychleji než důchod; změní-li se důchod ze ",[883,29212,29214],{"className":29213},[886],[888,29215,29216],{"xmlns":890},[892,29217,29218,29222],{},[895,29219,29220],{},[1667,29221,5267],{},[902,29223,5267],{"encoding":904},[883,29225,29227],{"className":29226},[886],[888,29228,29229],{"xmlns":890},[892,29230,29231,29236],{},[895,29232,29233],{},[1667,29234,29235],{},"101",[902,29237,29235],{"encoding":904},", změní se spotřeba přibližně o ",[883,29240,29242],{"className":29241},[886],[888,29243,29244],{"xmlns":890},[892,29245,29246,29250],{},[895,29247,29248],{},[1667,29249,27992],{},[902,29251,29209],{"encoding":904},". Skutečná změna ",[883,29254,29256],{"className":29255},[886],[888,29257,29258],{"xmlns":890},[892,29259,29260,29291],{},[895,29261,29262,29264,29266,29268,29270,29272,29274,29276,29278,29280,29282,29284,29286,29288],{},[898,29263,3750],{"mathvariant":1723},[898,29265,1766],{},[1656,29267,1713],{},[898,29269,1766],{},[1656,29271,1659],{"stretchy":1658},[1667,29273,29235],{},[1656,29275,1683],{"stretchy":1658},[1656,29277,3964],{},[898,29279,1766],{},[1656,29281,1659],{"stretchy":1658},[1667,29283,5267],{},[1656,29285,1683],{"stretchy":1658},[1656,29287,1713],{},[1667,29289,29290],{},"0,401",[902,29292,29293],{"encoding":904},"\\Delta C = C(101) - C(100) = 0{,}401"," — aproximace diferenciálem je přesná na setiny.",[724,29296,29297,29298],{},"Obecný trend: ",[38,29299,29300],{},"s růstem důchodu se sklon ke spotřebě zvětšuje.",[115,29302,29304],{"id":29303},"makroekonomická-rovnováha","Makroekonomická rovnováha",[724,29306,29307,29308,3247,29311,29314,29315,3247,29318,20863,29321,3247,29324,29327],{},"Při modelování národní ekonomiky hraje klíčovou roli ",[38,29309,29310],{},"makroekonomická rovnováha",[614,29312,29313],{},"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 ",[38,29316,29317],{},"agregátní poptávky",[614,29319,29320],{},"aggregate demand",[38,29322,29323],{},"agregátní nabídky",[614,29325,29326],{},"aggregate supply",") — obě popisují závislost mezi cenovou hladinou a množstvím, které jsou spotřebitelé ochotni koupit (agregátními výdaji).",[115,29329,29331],{"id":29330},"model-c-i-uzavřená-ekonomika-bez-vlády","Model C-I — uzavřená ekonomika bez vlády",[724,29333,29334],{},[5956,29335],{"alt":29336,"className":29337,"src":29338},"imek-keynesian-kriz",[210,5960],"\u002Fwiki-assets\u002Fimek-keynesian-kriz.jpeg",[198,29340,29342],{"id":29341},"zadání-modelu","Zadání modelu",[724,29344,29345,29346,29359,29360,29373],{},"Nejjednodušší model uzavřené ekonomiky bez vlády obsahuje jen spotřebu ",[883,29347,29349],{"className":29348},[886],[888,29350,29351],{"xmlns":890},[892,29352,29353,29357],{},[895,29354,29355],{},[898,29356,1766],{},[902,29358,1766],{"encoding":904}," a investice ",[883,29361,29363],{"className":29362},[886],[888,29364,29365],{"xmlns":890},[892,29366,29367,29371],{},[895,29368,29369],{},[898,29370,20919],{},[902,29372,20919],{"encoding":904},". Podmínka rovnováhy:",[724,29375,29376],{},[883,29377,29379],{"className":29378},[886],[888,29380,29381],{"xmlns":890},[892,29382,29383,29406],{},[895,29384,29385,29387,29389,29391,29393,29395,29397,29399,29401,29404],{},[898,29386,8184],{},[1656,29388,1713],{},[898,29390,1766],{},[1656,29392,3633],{},[898,29394,20919],{},[898,29396,1863],{"mathvariant":1723},[3316,29398],{"width":14644},[1656,29400,1659],{"stretchy":1658},[1667,29402,29403],{},"7.6",[1656,29405,1683],{"stretchy":1658},[902,29407,29408],{"encoding":904},"Y = C + I. \\qquad (7.6)",[198,29410,29412],{"id":29411},"soustava-rovnic","Soustava rovnic",[724,29414,29415,29416,29437,29438,29462],{},"Pro pevně zadané (plánované) investice ",[883,29417,29419],{"className":29418},[886],[888,29420,29421],{"xmlns":890},[892,29422,29423,29435],{},[895,29424,29425,29427,29429],{},[898,29426,20919],{},[1656,29428,1713],{},[2062,29430,29431,29433],{},[898,29432,20919],{},[1656,29434,8187],{},[902,29436,20930],{"encoding":904}," a funkci spotřeby ",[883,29439,29441],{"className":29440},[886],[888,29442,29443],{"xmlns":890},[892,29444,29445,29459],{},[895,29446,29447,29449,29451,29453,29455,29457],{},[898,29448,1766],{},[1656,29450,1713],{},[898,29452,1766],{},[1656,29454,1659],{"stretchy":1658},[898,29456,8184],{},[1656,29458,1683],{"stretchy":1658},[902,29460,29461],{"encoding":904},"C = C(Y)"," dostáváme soustavu",[724,29464,29465],{},[883,29466,29468],{"className":29467},[886],[888,29469,29470],{"xmlns":890},[892,29471,29472,29545],{},[895,29473,29474,29536,29538,29540,29543],{},[2412,29475,29478,29508],{"rowspacing":29476,"columnalign":29477,"columnspacing":1724},"0.25em","right left",[2416,29479,29480,29486],{},[2419,29481,29482],{},[4138,29483,29484],{"scriptlevel":4032,"displaystyle":1672},[898,29485,8184],{},[2419,29487,29488],{},[4138,29489,29490],{"scriptlevel":4032,"displaystyle":1672},[895,29491,29492,29494,29496,29498,29500,29506],{},[895,29493],{},[1656,29495,1713],{},[898,29497,1766],{},[1656,29499,3633],{},[2062,29501,29502,29504],{},[898,29503,20919],{},[1656,29505,8187],{},[1656,29507,1673],{"separator":1672},[2416,29509,29510,29516],{},[2419,29511,29512],{},[4138,29513,29514],{"scriptlevel":4032,"displaystyle":1672},[898,29515,1766],{},[2419,29517,29518],{},[4138,29519,29520],{"scriptlevel":4032,"displaystyle":1672},[895,29521,29522,29524,29526,29528,29530,29532,29534],{},[895,29523],{},[1656,29525,1713],{},[898,29527,1766],{},[1656,29529,1659],{"stretchy":1658},[898,29531,8184],{},[1656,29533,1683],{"stretchy":1658},[1656,29535,1673],{"separator":1672},[3316,29537],{"width":14644},[1656,29539,1659],{"stretchy":1658},[1667,29541,29542],{},"7.7",[1656,29544,1683],{"stretchy":1658},[902,29546,29547],{"encoding":904},"\\begin{aligned} Y &= C + I^*, \\\\ C &= C(Y), \\end{aligned} \\qquad (7.7)",[724,29549,29550,29551,1643,29553,1896,29570,1643,29573,1863],{},"jejímž řešením jsou ",[38,29552,22617],{},[883,29554,29556],{"className":29555},[886],[888,29557,29558],{"xmlns":890},[892,29559,29560,29568],{},[895,29561,29562],{},[2062,29563,29564,29566],{},[898,29565,8184],{},[898,29567,1842],{},[902,29569,22635],{"encoding":904},[38,29571,29572],{},"rovnovážná spotřeba",[883,29574,29576],{"className":29575},[886],[888,29577,29578],{"xmlns":890},[892,29579,29580,29588],{},[895,29581,29582],{},[2062,29583,29584,29586],{},[898,29585,1766],{},[898,29587,1842],{},[902,29589,22694],{"encoding":904},[198,29591,29593,29594],{"id":29592},"výpočet-yeye","Výpočet ",[883,29595,29597],{"className":29596},[886],[888,29598,29599],{"xmlns":890},[892,29600,29601,29609],{},[895,29602,29603],{},[2062,29604,29605,29607],{},[898,29606,8184],{},[898,29608,1842],{},[902,29610,22635],{"encoding":904},[724,29612,29613,29614,29637,29638,16445,29670],{},"Pro lineární spotřebu ",[883,29615,29617],{"className":29616},[886],[888,29618,29619],{"xmlns":890},[892,29620,29621,29635],{},[895,29622,29623,29625,29627,29629,29631,29633],{},[898,29624,1766],{},[1656,29626,1713],{},[898,29628,207],{},[898,29630,8184],{},[1656,29632,3633],{},[898,29634,3403],{},[902,29636,27641],{"encoding":904}," plyne z (7.7) rovnice ",[883,29639,29641],{"className":29640},[886],[888,29642,29643],{"xmlns":890},[892,29644,29645,29667],{},[895,29646,29647,29649,29651,29653,29655,29657,29659,29661],{},[898,29648,8184],{},[1656,29650,1713],{},[898,29652,207],{},[898,29654,8184],{},[1656,29656,3633],{},[898,29658,3403],{},[1656,29660,3633],{},[2062,29662,29663,29665],{},[898,29664,20919],{},[1656,29666,8187],{},[902,29668,29669],{"encoding":904},"Y = aY + b + I^*",[38,29671,29672],{},"redukovaný tvar",[724,29674,29675],{},[883,29676,29678],{"className":29677},[886],[888,29679,29680],{"xmlns":890},[892,29681,29682,29730],{},[895,29683,29684],{},[21566,29685,29686],{"notation":21568},[4138,29687,29688],{"scriptlevel":4032,"displaystyle":1658},[4138,29689,29690],{"scriptlevel":4032,"displaystyle":1658},[4138,29691,29692],{"scriptlevel":4032,"displaystyle":1672},[895,29693,29694,29696,29702,29704,29726,29728],{},[2461,29695,7828],{},[2062,29697,29698,29700],{},[898,29699,8184],{},[898,29701,1842],{},[1656,29703,1713],{},[3294,29705,29706,29718],{},[895,29707,29708,29710,29712],{},[898,29709,3403],{},[1656,29711,3633],{},[2062,29713,29714,29716],{},[898,29715,20919],{},[1656,29717,8187],{},[895,29719,29720,29722,29724],{},[1667,29721,1669],{},[1656,29723,3964],{},[898,29725,207],{},[898,29727,1863],{"mathvariant":1723},[2461,29729,7828],{},[902,29731,29732],{"encoding":904},"\\boxed{\\,Y^E = \\frac{b + I^*}{1 - a}.\\,}",[198,29734,29736],{"id":29735},"příklad-73","Příklad 7.3",[724,29738,29739,29740,3206,29757,1896,29781,29807],{},"V modelu ",[883,29741,29743],{"className":29742},[886],[888,29744,29745],{"xmlns":890},[892,29746,29747,29755],{},[895,29748,29749,29751,29753],{},[898,29750,1766],{},[2461,29752,21025],{},[898,29754,20919],{},[902,29756,21030],{"encoding":904},[883,29758,29760],{"className":29759},[886],[888,29761,29762],{"xmlns":890},[892,29763,29764,29778],{},[895,29765,29766,29768,29770,29772,29774,29776],{},[898,29767,1766],{},[1656,29769,1713],{},[1667,29771,28042],{},[898,29773,8184],{},[1656,29775,3633],{},[1667,29777,8580],{},[902,29779,29780],{"encoding":904},"C = 0{,}6Y + 10",[883,29782,29784],{"className":29783},[886],[888,29785,29786],{"xmlns":890},[892,29787,29788,29804],{},[895,29789,29790,29792,29794,29796,29798],{},[898,29791,20919],{},[1656,29793,1713],{},[1667,29795,9140],{},[1656,29797,1713],{},[2062,29799,29800,29802],{},[898,29801,20919],{},[1656,29803,8187],{},[902,29805,29806],{"encoding":904},"I = 12 = I^*",". Soustava",[724,29809,29810],{},[883,29811,29813],{"className":29812},[886],[888,29814,29815],{"xmlns":890},[892,29816,29817,29873],{},[2412,29818,29819,29845],{"rowspacing":29476,"columnalign":29477,"columnspacing":1724},[2416,29820,29821,29827],{},[2419,29822,29823],{},[4138,29824,29825],{"scriptlevel":4032,"displaystyle":1672},[898,29826,8184],{},[2419,29828,29829],{},[4138,29830,29831],{"scriptlevel":4032,"displaystyle":1672},[895,29832,29833,29835,29837,29839,29841,29843],{},[895,29834],{},[1656,29836,1713],{},[898,29838,1766],{},[1656,29840,3633],{},[1667,29842,9140],{},[1656,29844,1673],{"separator":1672},[2416,29846,29847,29853],{},[2419,29848,29849],{},[4138,29850,29851],{"scriptlevel":4032,"displaystyle":1672},[898,29852,1766],{},[2419,29854,29855],{},[4138,29856,29857],{"scriptlevel":4032,"displaystyle":1672},[895,29858,29859,29861,29863,29865,29867,29869,29871],{},[895,29860],{},[1656,29862,1713],{},[1667,29864,28042],{},[898,29866,8184],{},[1656,29868,3633],{},[1667,29870,8580],{},[1656,29872,1673],{"separator":1672},[902,29874,29875],{"encoding":904},"\\begin{aligned} Y &= C + 12, \\\\ C &= 0{,}6Y + 10, \\end{aligned}",[724,29877,29878,29879,1343,29902,29925,29926,12702],{},"má řešení ",[883,29880,29882],{"className":29881},[886],[888,29883,29884],{"xmlns":890},[892,29885,29886,29899],{},[895,29887,29888,29894,29896],{},[2062,29889,29890,29892],{},[898,29891,8184],{},[898,29893,1842],{},[1656,29895,1713],{},[1667,29897,29898],{},"55",[902,29900,29901],{"encoding":904},"Y^E = 55",[883,29903,29905],{"className":29904},[886],[888,29906,29907],{"xmlns":890},[892,29908,29909,29922],{},[895,29910,29911,29917,29919],{},[2062,29912,29913,29915],{},[898,29914,1766],{},[898,29916,1842],{},[1656,29918,1713],{},[1667,29920,29921],{},"43",[902,29923,29924],{"encoding":904},"C^E = 43"," (a ",[883,29927,29929],{"className":29928},[886],[888,29930,29931],{"xmlns":890},[892,29932,29933,29945],{},[895,29934,29935,29941,29943],{},[2062,29936,29937,29939],{},[898,29938,1769],{},[898,29940,1842],{},[1656,29942,1713],{},[1667,29944,9140],{},[902,29946,29947],{"encoding":904},"S^E = 12",[724,29949,29950],{},[614,29951,29952,29953,29975,29976,20863,29997,30020,30021,1863],{},"Obrázek 7.5 — Přímky ",[883,29954,29956],{"className":29955},[886],[888,29957,29958],{"xmlns":890},[892,29959,29960,29972],{},[895,29961,29962,29964,29966,29968,29970],{},[898,29963,1766],{},[1656,29965,1713],{},[898,29967,8184],{},[1656,29969,3964],{},[1667,29971,9140],{},[902,29973,29974],{"encoding":904},"C = Y - 12"," (rovnováha ",[883,29977,29979],{"className":29978},[886],[888,29980,29981],{"xmlns":890},[892,29982,29983,29995],{},[895,29984,29985,29987,29989,29991,29993],{},[898,29986,8184],{},[1656,29988,1713],{},[898,29990,1766],{},[1656,29992,3633],{},[898,29994,20919],{},[902,29996,23476],{"encoding":904},[883,29998,30000],{"className":29999},[886],[888,30001,30002],{"xmlns":890},[892,30003,30004,30018],{},[895,30005,30006,30008,30010,30012,30014,30016],{},[898,30007,1766],{},[1656,30009,1713],{},[1667,30011,28042],{},[898,30013,8184],{},[1656,30015,3633],{},[1667,30017,8580],{},[902,30019,29780],{"encoding":904}," (funkce spotřeby) se protínají v bodě ",[883,30022,30024],{"className":30023},[886],[888,30025,30026],{"xmlns":890},[892,30027,30028,30060],{},[895,30029,30030,30032,30038,30040,30046,30048,30050,30052,30054,30056,30058],{},[1656,30031,3453],{"stretchy":1658},[2062,30033,30034,30036],{},[898,30035,8184],{},[898,30037,1842],{},[1656,30039,1673],{"separator":1672},[2062,30041,30042,30044],{},[898,30043,1766],{},[898,30045,1842],{},[1656,30047,3462],{"stretchy":1658},[1656,30049,1713],{},[1656,30051,3453],{"stretchy":1658},[1667,30053,29898],{},[1656,30055,1673],{"separator":1672},[1667,30057,29921],{},[1656,30059,3462],{"stretchy":1658},[902,30061,30062],{"encoding":904},"[Y^E, C^E] = [55, 43]",[724,30064,30065,30068,30069,30086,30087,1863],{},[38,30066,30067],{},"Komentář k přechodu."," Model ",[883,30070,30072],{"className":30071},[886],[888,30073,30074],{"xmlns":890},[892,30075,30076,30084],{},[895,30077,30078,30080,30082],{},[898,30079,1766],{},[2461,30081,21025],{},[898,30083,20919],{},[902,30085,21030],{"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 ",[38,30088,30089,30090],{},"model ",[883,30091,30093],{"className":30092},[886],[888,30094,30095],{"xmlns":890},[892,30096,30097,30109],{},[895,30098,30099,30101,30103,30105,30107],{},[898,30100,1766],{},[2461,30102,21025],{},[898,30104,20919],{},[2461,30106,21025],{},[898,30108,20847],{},[902,30110,26943],{"encoding":904},[115,30112,30114],{"id":30113},"model-c-i-g-s-vládním-sektorem","Model C-I-G — s vládním sektorem",[198,30116,29342],{"id":30117},"zadání-modelu-1",[724,30119,30120,30121,30138,30139,1643,30142,3247,30155,30158],{},"Rozšíření modelu ",[883,30122,30124],{"className":30123},[886],[888,30125,30126],{"xmlns":890},[892,30127,30128,30136],{},[895,30129,30130,30132,30134],{},[898,30131,1766],{},[2461,30133,21025],{},[898,30135,20919],{},[902,30137,21030],{"encoding":904}," o ",[38,30140,30141],{},"vládní výdaje",[883,30143,30145],{"className":30144},[886],[888,30146,30147],{"xmlns":890},[892,30148,30149,30153],{},[895,30150,30151],{},[898,30152,20847],{},[902,30154,20847],{"encoding":904},[614,30156,30157],{},"government expenditure","). Podmínka rovnováhy:",[724,30160,30161],{},[883,30162,30164],{"className":30163},[886],[888,30165,30166],{"xmlns":890},[892,30167,30168,30195],{},[895,30169,30170,30172,30174,30176,30178,30180,30182,30184,30186,30188,30190,30193],{},[898,30171,8184],{},[1656,30173,1713],{},[898,30175,1766],{},[1656,30177,3633],{},[898,30179,20919],{},[1656,30181,3633],{},[898,30183,20847],{},[898,30185,1863],{"mathvariant":1723},[3316,30187],{"width":14644},[1656,30189,1659],{"stretchy":1658},[1667,30191,30192],{},"7.8",[1656,30194,1683],{"stretchy":1658},[902,30196,30197],{"encoding":904},"Y = C + I + G. \\qquad (7.8)",[724,30199,30200,30201,1643,30204,3247,30217,30220],{},"Stát se stává spotřebitelem, jehož „důchod“ získává ",[38,30202,30203],{},"zdaněním domácností",[883,30205,30207],{"className":30206},[886],[888,30208,30209],{"xmlns":890},[892,30210,30211,30215],{},[895,30212,30213],{},[898,30214,11577],{},[902,30216,11577],{"encoding":904},[614,30218,30219],{},"taxation","). Zdanění bývá:",[120,30222,30223,30256,30281],{},[123,30224,30225,30226,1673],{},"úměrné důchodu: ",[883,30227,30229],{"className":30228},[886],[888,30230,30231],{"xmlns":890},[892,30232,30233,30253],{},[895,30234,30235,30237,30239,30241,30243,30245,30247,30249,30251],{},[898,30236,11577],{},[1656,30238,1713],{},[898,30240,11577],{},[1656,30242,1659],{"stretchy":1658},[898,30244,8184],{},[1656,30246,1683],{"stretchy":1658},[1656,30248,1713],{},[898,30250,27577],{},[898,30252,8184],{},[902,30254,30255],{"encoding":904},"T = T(Y) = tY",[123,30257,30258,30259,1673],{},"fixní: ",[883,30260,30262],{"className":30261},[886],[888,30263,30264],{"xmlns":890},[892,30265,30266,30278],{},[895,30267,30268,30270,30272],{},[898,30269,11577],{},[1656,30271,1713],{},[2062,30273,30274,30276],{},[898,30275,11577],{},[1656,30277,8187],{},[902,30279,30280],{"encoding":904},"T = T^*",[123,30282,30283,30284,30312,30313,1863],{},"kombinované: ",[883,30285,30287],{"className":30286},[886],[888,30288,30289],{"xmlns":890},[892,30290,30291,30309],{},[895,30292,30293,30295,30297,30303,30305,30307],{},[898,30294,11577],{},[1656,30296,1713],{},[2062,30298,30299,30301],{},[898,30300,11577],{},[1656,30302,8187],{},[1656,30304,3633],{},[898,30306,27577],{},[898,30308,8184],{},[902,30310,30311],{"encoding":904},"T = T^* + tY",", kde ",[883,30314,30316],{"className":30315},[886],[888,30317,30318],{"xmlns":890},[892,30319,30320,30332],{},[895,30321,30322,30324,30326,30328,30330],{},[1667,30323,4032],{},[1656,30325,16439],{},[898,30327,27577],{},[1656,30329,4373],{},[1667,30331,1669],{},[902,30333,30334],{"encoding":904},"0 \\le t \u003C 1",[1981,30336,30337],{},[724,30338,30339,30341,30342,30363,30364,30367,30368,30381,30382,20863,30408,1643,30411,30437,30438,30466,30467,1896,30480,30498],{},[883,30340,1987],{}," Pozor na disponibilní důchod\nV modelu ",[883,30343,30345],{"className":30344},[886],[888,30346,30347],{"xmlns":890},[892,30348,30349,30361],{},[895,30350,30351,30353,30355,30357,30359],{},[898,30352,1766],{},[2461,30354,21025],{},[898,30356,20919],{},[2461,30358,21025],{},[898,30360,20847],{},[902,30362,26943],{"encoding":904}," je nutné ",[38,30365,30366],{},"důsledně rozlišovat dva důchody",": celkový národní důchod ",[883,30369,30371],{"className":30370},[886],[888,30372,30373],{"xmlns":890},[892,30374,30375,30379],{},[895,30376,30377],{},[898,30378,8184],{},[902,30380,8184],{"encoding":904}," (vstupuje do podmínky rovnováhy ",[883,30383,30385],{"className":30384},[886],[888,30386,30387],{"xmlns":890},[892,30388,30389,30405],{},[895,30390,30391,30393,30395,30397,30399,30401,30403],{},[898,30392,8184],{},[1656,30394,1713],{},[898,30396,1766],{},[1656,30398,3633],{},[898,30400,20919],{},[1656,30402,3633],{},[898,30404,20847],{},[902,30406,30407],{"encoding":904},"Y = C + I + G",[38,30409,30410],{},"disponibilní důchod",[883,30412,30414],{"className":30413},[886],[888,30415,30416],{"xmlns":890},[892,30417,30418,30434],{},[895,30419,30420,30426,30428,30430,30432],{},[1661,30421,30422,30424],{},[898,30423,8184],{},[898,30425,6787],{},[1656,30427,1713],{},[898,30429,8184],{},[1656,30431,3964],{},[898,30433,11577],{},[902,30435,30436],{"encoding":904},"Y_D = Y - T"," (na něm závisí spotřeba domácností, ",[883,30439,30441],{"className":30440},[886],[888,30442,30443],{"xmlns":890},[892,30444,30445,30463],{},[895,30446,30447,30449,30451,30453,30455,30461],{},[898,30448,1766],{},[1656,30450,1713],{},[898,30452,1766],{},[1656,30454,1659],{"stretchy":1658},[1661,30456,30457,30459],{},[898,30458,8184],{},[898,30460,6787],{},[1656,30462,1683],{"stretchy":1658},[902,30464,30465],{"encoding":904},"C = C(Y_D)","). Záměna ",[883,30468,30470],{"className":30469},[886],[888,30471,30472],{"xmlns":890},[892,30473,30474,30478],{},[895,30475,30476],{},[898,30477,8184],{},[902,30479,8184],{"encoding":904},[883,30481,30483],{"className":30482},[886],[888,30484,30485],{"xmlns":890},[892,30486,30487,30495],{},[895,30488,30489],{},[1661,30490,30491,30493],{},[898,30492,8184],{},[898,30494,6787],{},[902,30496,30497],{"encoding":904},"Y_D"," ve funkci spotřeby je nejčastější zdroj chyb.",[724,30500,30501,3247,30504,1683],{},[38,30502,30503],{},"Disponibilní důchod",[614,30505,30506],{},"disposable income",[724,30508,30509],{},[883,30510,30512],{"className":30511},[886],[888,30513,30514],{"xmlns":890},[892,30515,30516,30532],{},[895,30517,30518,30524,30526,30528,30530],{},[1661,30519,30520,30522],{},[898,30521,8184],{},[898,30523,6787],{},[1656,30525,1713],{},[898,30527,8184],{},[1656,30529,3964],{},[898,30531,11577],{},[902,30533,30436],{"encoding":904},[724,30535,30536,30537,1863],{},"je to, co zbývá domácnostem po zdanění. Spotřeba je pak funkcí disponibilního důchodu: ",[883,30538,30540],{"className":30539},[886],[888,30541,30542],{"xmlns":890},[892,30543,30544,30562],{},[895,30545,30546,30548,30550,30552,30554,30560],{},[898,30547,1766],{},[1656,30549,1713],{},[898,30551,1766],{},[1656,30553,1659],{"stretchy":1658},[1661,30555,30556,30558],{},[898,30557,8184],{},[898,30559,6787],{},[1656,30561,1683],{"stretchy":1658},[902,30563,30465],{"encoding":904},[198,30565,29412],{"id":30566},"soustava-rovnic-1",[724,30568,30569,30570,1343,30591,30613,30614,2114],{},"Pro pevně zadané ",[883,30571,30573],{"className":30572},[886],[888,30574,30575],{"xmlns":890},[892,30576,30577,30589],{},[895,30578,30579,30581,30583],{},[898,30580,20919],{},[1656,30582,1713],{},[2062,30584,30585,30587],{},[898,30586,20919],{},[1656,30588,8187],{},[902,30590,20930],{"encoding":904},[883,30592,30594],{"className":30593},[886],[888,30595,30596],{"xmlns":890},[892,30597,30598,30610],{},[895,30599,30600,30602,30604],{},[898,30601,20847],{},[1656,30603,1713],{},[2062,30605,30606,30608],{},[898,30607,20847],{},[1656,30609,8187],{},[902,30611,30612],{"encoding":904},"G = G^*"," dostáváme soustavu 4 rovnic o 4 neznámých ",[883,30615,30617],{"className":30616},[886],[888,30618,30619],{"xmlns":890},[892,30620,30621,30641],{},[895,30622,30623,30625,30627,30629,30631,30637,30639],{},[898,30624,8184],{},[1656,30626,1673],{"separator":1672},[898,30628,1766],{},[1656,30630,1673],{"separator":1672},[1661,30632,30633,30635],{},[898,30634,8184],{},[898,30636,6787],{},[1656,30638,1673],{"separator":1672},[898,30640,11577],{},[902,30642,30643],{"encoding":904},"Y, C, Y_D, T",[724,30645,30646],{},[883,30647,30649],{"className":30648},[886],[888,30650,30651],{"xmlns":890},[892,30652,30653,30794],{},[895,30654,30655,30785,30787,30789,30792],{},[2412,30656,30657,30695,30723,30755],{"rowspacing":29476,"columnalign":29477,"columnspacing":1724},[2416,30658,30659,30665],{},[2419,30660,30661],{},[4138,30662,30663],{"scriptlevel":4032,"displaystyle":1672},[898,30664,8184],{},[2419,30666,30667],{},[4138,30668,30669],{"scriptlevel":4032,"displaystyle":1672},[895,30670,30671,30673,30675,30677,30679,30685,30687,30693],{},[895,30672],{},[1656,30674,1713],{},[898,30676,1766],{},[1656,30678,3633],{},[2062,30680,30681,30683],{},[898,30682,20919],{},[1656,30684,8187],{},[1656,30686,3633],{},[2062,30688,30689,30691],{},[898,30690,20847],{},[1656,30692,8187],{},[1656,30694,1673],{"separator":1672},[2416,30696,30697,30703],{},[2419,30698,30699],{},[4138,30700,30701],{"scriptlevel":4032,"displaystyle":1672},[898,30702,11577],{},[2419,30704,30705],{},[4138,30706,30707],{"scriptlevel":4032,"displaystyle":1672},[895,30708,30709,30711,30713,30715,30717,30719,30721],{},[895,30710],{},[1656,30712,1713],{},[898,30714,11577],{},[1656,30716,1659],{"stretchy":1658},[898,30718,8184],{},[1656,30720,1683],{"stretchy":1658},[1656,30722,1673],{"separator":1672},[2416,30724,30725,30731],{},[2419,30726,30727],{},[4138,30728,30729],{"scriptlevel":4032,"displaystyle":1672},[898,30730,1766],{},[2419,30732,30733],{},[4138,30734,30735],{"scriptlevel":4032,"displaystyle":1672},[895,30736,30737,30739,30741,30743,30745,30751,30753],{},[895,30738],{},[1656,30740,1713],{},[898,30742,1766],{},[1656,30744,1659],{"stretchy":1658},[1661,30746,30747,30749],{},[898,30748,8184],{},[898,30750,6787],{},[1656,30752,1683],{"stretchy":1658},[1656,30754,1673],{"separator":1672},[2416,30756,30757,30767],{},[2419,30758,30759],{},[4138,30760,30761],{"scriptlevel":4032,"displaystyle":1672},[1661,30762,30763,30765],{},[898,30764,8184],{},[898,30766,6787],{},[2419,30768,30769],{},[4138,30770,30771],{"scriptlevel":4032,"displaystyle":1672},[895,30772,30773,30775,30777,30779,30781,30783],{},[895,30774],{},[1656,30776,1713],{},[898,30778,8184],{},[1656,30780,3964],{},[898,30782,11577],{},[1656,30784,1673],{"separator":1672},[3316,30786],{"width":14644},[1656,30788,1659],{"stretchy":1658},[1667,30790,30791],{},"7.9",[1656,30793,1683],{"stretchy":1658},[902,30795,30796],{"encoding":904},"\\begin{aligned} Y &= C + I^* + G^*, \\\\ T &= T(Y), \\\\ C &= C(Y_D), \\\\ Y_D &= Y - T, \\end{aligned} \\qquad (7.9)",[724,30798,30799,30800,30844,30845,1863],{},"s řešeními ",[883,30801,30803],{"className":30802},[886],[888,30804,30805],{"xmlns":890},[892,30806,30807,30841],{},[895,30808,30809,30815,30817,30823,30825,30831,30833],{},[2062,30810,30811,30813],{},[898,30812,8184],{},[898,30814,1842],{},[1656,30816,1673],{"separator":1672},[2062,30818,30819,30821],{},[898,30820,1766],{},[898,30822,1842],{},[1656,30824,1673],{"separator":1672},[2062,30826,30827,30829],{},[898,30828,11577],{},[898,30830,1842],{},[1656,30832,1673],{"separator":1672},[1715,30834,30835,30837,30839],{},[898,30836,8184],{},[898,30838,6787],{},[898,30840,1842],{},[902,30842,30843],{"encoding":904},"Y^E, C^E, T^E, Y_D^E",", případně rovnovážnými úsporami domácností ",[883,30846,30848],{"className":30847},[886],[888,30849,30850],{"xmlns":890},[892,30851,30852,30878],{},[895,30853,30854,30860,30862,30870,30872],{},[2062,30855,30856,30858],{},[898,30857,1769],{},[898,30859,1842],{},[1656,30861,1713],{},[1715,30863,30864,30866,30868],{},[898,30865,8184],{},[898,30867,6787],{},[898,30869,1842],{},[1656,30871,3964],{},[2062,30873,30874,30876],{},[898,30875,1766],{},[898,30877,1842],{},[902,30879,30880],{"encoding":904},"S^E = Y_D^E - C^E",[1981,30882,30883,30888],{},[724,30884,30885,30887],{},[883,30886,10188],{}," Postup — jak sestavit a vyřešit soustavu C-I-G",[152,30889,30890,30913,30996,31051,31141],{},[123,30891,30892,30895,30896,1863],{},[38,30893,30894],{},"Zapiš všechny 4 rovnice"," ze zadání: podmínku rovnováhy, daňovou funkci, funkci spotřeby, definici ",[883,30897,30899],{"className":30898},[886],[888,30900,30901],{"xmlns":890},[892,30902,30903,30911],{},[895,30904,30905],{},[1661,30906,30907,30909],{},[898,30908,8184],{},[898,30910,6787],{},[902,30912,30497],{"encoding":904},[123,30914,30915,30964,30965,30982,30983,1863],{},[38,30916,30917,30918,30938,30939],{},"Dosaď ",[883,30919,30921],{"className":30920},[886],[888,30922,30923],{"xmlns":890},[892,30924,30925,30935],{},[895,30926,30927,30929,30931,30933],{},[898,30928,11577],{},[1656,30930,1659],{"stretchy":1658},[898,30932,8184],{},[1656,30934,1683],{"stretchy":1658},[902,30936,30937],{"encoding":904},"T(Y)"," do ",[883,30940,30942],{"className":30941},[886],[888,30943,30944],{"xmlns":890},[892,30945,30946,30962],{},[895,30947,30948,30954,30956,30958,30960],{},[1661,30949,30950,30952],{},[898,30951,8184],{},[898,30953,6787],{},[1656,30955,1713],{},[898,30957,8184],{},[1656,30959,3964],{},[898,30961,11577],{},[902,30963,30436],{"encoding":904}," — dostaneš ",[883,30966,30968],{"className":30967},[886],[888,30969,30970],{"xmlns":890},[892,30971,30972,30980],{},[895,30973,30974],{},[1661,30975,30976,30978],{},[898,30977,8184],{},[898,30979,6787],{},[902,30981,30497],{"encoding":904}," jako lineární funkci ",[883,30984,30986],{"className":30985},[886],[888,30987,30988],{"xmlns":890},[892,30989,30990,30994],{},[895,30991,30992],{},[898,30993,8184],{},[902,30995,8184],{"encoding":904},[123,30997,30998,30964,31025,30982,31038,1863],{},[38,30999,30917,31000,31024],{},[883,31001,31003],{"className":31002},[886],[888,31004,31005],{"xmlns":890},[892,31006,31007,31021],{},[895,31008,31009,31015,31017,31019],{},[1661,31010,31011,31013],{},[898,31012,8184],{},[898,31014,6787],{},[1656,31016,1659],{"stretchy":1658},[898,31018,8184],{},[1656,31020,1683],{"stretchy":1658},[902,31022,31023],{"encoding":904},"Y_D(Y)"," do funkce spotřeby",[883,31026,31028],{"className":31027},[886],[888,31029,31030],{"xmlns":890},[892,31031,31032,31036],{},[895,31033,31034],{},[898,31035,1766],{},[902,31037,1766],{"encoding":904},[883,31039,31041],{"className":31040},[886],[888,31042,31043],{"xmlns":890},[892,31044,31045,31049],{},[895,31046,31047],{},[898,31048,8184],{},[902,31050,8184],{"encoding":904},[123,31052,31053,1643,31075,31109,31110,31123,31124,1863],{},[38,31054,30917,31055,31074],{},[883,31056,31058],{"className":31057},[886],[888,31059,31060],{"xmlns":890},[892,31061,31062,31072],{},[895,31063,31064,31066,31068,31070],{},[898,31065,1766],{},[1656,31067,1659],{"stretchy":1658},[898,31069,8184],{},[1656,31071,1683],{"stretchy":1658},[902,31073,22948],{"encoding":904}," do podmínky rovnováhy",[883,31076,31078],{"className":31077},[886],[888,31079,31080],{"xmlns":890},[892,31081,31082,31106],{},[895,31083,31084,31086,31088,31090,31092,31098,31100],{},[898,31085,8184],{},[1656,31087,1713],{},[898,31089,1766],{},[1656,31091,3633],{},[2062,31093,31094,31096],{},[898,31095,20919],{},[1656,31097,8187],{},[1656,31099,3633],{},[2062,31101,31102,31104],{},[898,31103,20847],{},[1656,31105,8187],{},[902,31107,31108],{"encoding":904},"Y = C + I^* + G^*"," — zbývá jediná rovnice o jedné neznámé ",[883,31111,31113],{"className":31112},[886],[888,31114,31115],{"xmlns":890},[892,31116,31117,31121],{},[895,31118,31119],{},[898,31120,8184],{},[902,31122,8184],{"encoding":904},", odtud ",[883,31125,31127],{"className":31126},[886],[888,31128,31129],{"xmlns":890},[892,31130,31131,31139],{},[895,31132,31133],{},[2062,31134,31135,31137],{},[898,31136,8184],{},[898,31138,1842],{},[902,31140,22635],{"encoding":904},[123,31142,31143,31146,31147,1343,31165,1343,31185,1343,31202,1863],{},[38,31144,31145],{},"Zpětným dosazením"," dopočítej ",[883,31148,31150],{"className":31149},[886],[888,31151,31152],{"xmlns":890},[892,31153,31154,31162],{},[895,31155,31156],{},[2062,31157,31158,31160],{},[898,31159,11577],{},[898,31161,1842],{},[902,31163,31164],{"encoding":904},"T^E",[883,31166,31168],{"className":31167},[886],[888,31169,31170],{"xmlns":890},[892,31171,31172,31182],{},[895,31173,31174],{},[1715,31175,31176,31178,31180],{},[898,31177,8184],{},[898,31179,6787],{},[898,31181,1842],{},[902,31183,31184],{"encoding":904},"Y_D^E",[883,31186,31188],{"className":31187},[886],[888,31189,31190],{"xmlns":890},[892,31191,31192,31200],{},[895,31193,31194],{},[2062,31195,31196,31198],{},[898,31197,1766],{},[898,31199,1842],{},[902,31201,22694],{"encoding":904},[883,31203,31205],{"className":31204},[886],[888,31206,31207],{"xmlns":890},[892,31208,31209,31217],{},[895,31210,31211],{},[2062,31212,31213,31215],{},[898,31214,1769],{},[898,31216,1842],{},[902,31218,31219],{"encoding":904},"S^E",[198,31221,31223],{"id":31222},"příklad-74","Příklad 7.4",[724,31225,29739,31226,31247,31248,1343,31279,1343,31303,1343,31325,31347],{},[883,31227,31229],{"className":31228},[886],[888,31230,31231],{"xmlns":890},[892,31232,31233,31245],{},[895,31234,31235,31237,31239,31241,31243],{},[898,31236,1766],{},[2461,31238,21025],{},[898,31240,20919],{},[2461,31242,21025],{},[898,31244,20847],{},[902,31246,26943],{"encoding":904}," jsou dány ",[883,31249,31251],{"className":31250},[886],[888,31252,31253],{"xmlns":890},[892,31254,31255,31276],{},[895,31256,31257,31259,31261,31264,31266,31272,31274],{},[898,31258,1766],{},[1656,31260,1713],{},[1667,31262,31263],{},"0,9",[2461,31265,7828],{},[1661,31267,31268,31270],{},[898,31269,8184],{},[898,31271,6787],{},[1656,31273,3633],{},[1667,31275,14661],{},[902,31277,31278],{"encoding":904},"C = 0{,}9\\,Y_D + 70",[883,31280,31282],{"className":31281},[886],[888,31283,31284],{"xmlns":890},[892,31285,31286,31300],{},[895,31287,31288,31290,31292,31294,31296,31298],{},[898,31289,11577],{},[1656,31291,1713],{},[1667,31293,11639],{},[898,31295,8184],{},[1656,31297,3633],{},[1667,31299,8567],{},[902,31301,31302],{"encoding":904},"T = 0{,}2Y + 25",[883,31304,31306],{"className":31305},[886],[888,31307,31308],{"xmlns":890},[892,31309,31310,31322],{},[895,31311,31312,31318,31320],{},[2062,31313,31314,31316],{},[898,31315,20919],{},[1656,31317,8187],{},[1656,31319,1713],{},[1667,31321,23770],{},[902,31323,31324],{"encoding":904},"I^* = 35",[883,31326,31328],{"className":31327},[886],[888,31329,31330],{"xmlns":890},[892,31331,31332,31344],{},[895,31333,31334,31340,31342],{},[2062,31335,31336,31338],{},[898,31337,20847],{},[1656,31339,8187],{},[1656,31341,1713],{},[1667,31343,9058],{},[902,31345,31346],{"encoding":904},"G^* = 20",". Soustava (7.9):",[724,31349,31350],{},[883,31351,31353],{"className":31352},[886],[888,31354,31355],{"xmlns":890},[892,31356,31357,31481],{},[2412,31358,31359,31389,31417,31451],{"rowspacing":29476,"columnalign":29477,"columnspacing":1724},[2416,31360,31361,31367],{},[2419,31362,31363],{},[4138,31364,31365],{"scriptlevel":4032,"displaystyle":1672},[898,31366,8184],{},[2419,31368,31369],{},[4138,31370,31371],{"scriptlevel":4032,"displaystyle":1672},[895,31372,31373,31375,31377,31379,31381,31383,31385,31387],{},[895,31374],{},[1656,31376,1713],{},[898,31378,1766],{},[1656,31380,3633],{},[1667,31382,23770],{},[1656,31384,3633],{},[1667,31386,9058],{},[1656,31388,1673],{"separator":1672},[2416,31390,31391,31397],{},[2419,31392,31393],{},[4138,31394,31395],{"scriptlevel":4032,"displaystyle":1672},[898,31396,11577],{},[2419,31398,31399],{},[4138,31400,31401],{"scriptlevel":4032,"displaystyle":1672},[895,31402,31403,31405,31407,31409,31411,31413,31415],{},[895,31404],{},[1656,31406,1713],{},[1667,31408,11639],{},[898,31410,8184],{},[1656,31412,3633],{},[1667,31414,8567],{},[1656,31416,1673],{"separator":1672},[2416,31418,31419,31425],{},[2419,31420,31421],{},[4138,31422,31423],{"scriptlevel":4032,"displaystyle":1672},[898,31424,1766],{},[2419,31426,31427],{},[4138,31428,31429],{"scriptlevel":4032,"displaystyle":1672},[895,31430,31431,31433,31435,31437,31439,31445,31447,31449],{},[895,31432],{},[1656,31434,1713],{},[1667,31436,31263],{},[2461,31438,7828],{},[1661,31440,31441,31443],{},[898,31442,8184],{},[898,31444,6787],{},[1656,31446,3633],{},[1667,31448,14661],{},[1656,31450,1673],{"separator":1672},[2416,31452,31453,31463],{},[2419,31454,31455],{},[4138,31456,31457],{"scriptlevel":4032,"displaystyle":1672},[1661,31458,31459,31461],{},[898,31460,8184],{},[898,31462,6787],{},[2419,31464,31465],{},[4138,31466,31467],{"scriptlevel":4032,"displaystyle":1672},[895,31468,31469,31471,31473,31475,31477,31479],{},[895,31470],{},[1656,31472,1713],{},[898,31474,8184],{},[1656,31476,3964],{},[898,31478,11577],{},[898,31480,1863],{"mathvariant":1723},[902,31482,31483],{"encoding":904},"\\begin{aligned} Y &= C + 35 + 20, \\\\ T &= 0{,}2Y + 25, \\\\ C &= 0{,}9\\,Y_D + 70, \\\\ Y_D &= Y - T. \\end{aligned}",[724,31485,31486,31489,31490,31544,31545,31591,31592,2114],{},[38,31487,31488],{},"Řešení."," Z definice ",[883,31491,31493],{"className":31492},[886],[888,31494,31495],{"xmlns":890},[892,31496,31497,31541],{},[895,31498,31499,31505,31507,31509,31511,31513,31515,31517,31519,31521,31523,31525,31527,31529,31531,31533,31535,31537,31539],{},[1661,31500,31501,31503],{},[898,31502,8184],{},[898,31504,6787],{},[1656,31506,1713],{},[898,31508,8184],{},[1656,31510,3964],{},[898,31512,11577],{},[1656,31514,1713],{},[898,31516,8184],{},[1656,31518,3964],{},[1656,31520,1659],{"stretchy":1658},[1667,31522,11639],{},[898,31524,8184],{},[1656,31526,3633],{},[1667,31528,8567],{},[1656,31530,1683],{"stretchy":1658},[1656,31532,1713],{},[1667,31534,23321],{},[898,31536,8184],{},[1656,31538,3964],{},[1667,31540,8567],{},[902,31542,31543],{"encoding":904},"Y_D = Y - T = Y - (0{,}2Y + 25) = 0{,}8Y - 25",". Dosazením do spotřeby: ",[883,31546,31548],{"className":31547},[886],[888,31549,31550],{"xmlns":890},[892,31551,31552,31588],{},[895,31553,31554,31556,31558,31560,31562,31564,31566,31568,31570,31572,31574,31576,31578,31581,31583,31585],{},[898,31555,1766],{},[1656,31557,1713],{},[1667,31559,31263],{},[1656,31561,1659],{"stretchy":1658},[1667,31563,23321],{},[898,31565,8184],{},[1656,31567,3964],{},[1667,31569,8567],{},[1656,31571,1683],{"stretchy":1658},[1656,31573,3633],{},[1667,31575,14661],{},[1656,31577,1713],{},[1667,31579,31580],{},"0,72",[898,31582,8184],{},[1656,31584,3633],{},[1667,31586,31587],{},"47,5",[902,31589,31590],{"encoding":904},"C = 0{,}9(0{,}8Y - 25) + 70 = 0{,}72Y + 47{,}5",". Dosazením do rovnovážné rovnice ",[883,31593,31595],{"className":31594},[886],[888,31596,31597],{"xmlns":890},[892,31598,31599,31617],{},[895,31600,31601,31603,31605,31607,31609,31611,31613,31615],{},[898,31602,8184],{},[1656,31604,1713],{},[1667,31606,31580],{},[898,31608,8184],{},[1656,31610,3633],{},[1667,31612,31587],{},[1656,31614,3633],{},[1667,31616,29898],{},[902,31618,31619],{"encoding":904},"Y = 0{,}72Y + 47{,}5 + 55",[724,31621,31622],{},[883,31623,31625],{"className":31624},[886],[888,31626,31627],{"xmlns":890},[892,31628,31629,31670],{},[895,31630,31631,31634,31636,31638,31641,31643,31645,31647,31653,31655,31665,31667],{},[1667,31632,31633],{},"0,28",[898,31635,8184],{},[1656,31637,1713],{},[1667,31639,31640],{},"102,5",[2461,31642,12767],{},[1656,31644,23740],{},[2461,31646,12767],{},[2062,31648,31649,31651],{},[898,31650,8184],{},[898,31652,1842],{},[1656,31654,1713],{},[4138,31656,31657],{"scriptlevel":4032,"displaystyle":1658},[3294,31658,31659,31662],{},[1667,31660,31661],{},"5125",[1667,31663,31664],{},"14",[1656,31666,2829],{},[1667,31668,31669],{},"366,071.",[902,31671,31672],{"encoding":904},"0{,}28Y = 102{,}5 \\;\\Longrightarrow\\; Y^E = \\tfrac{5125}{14} \\doteq 366{,}071.",[724,31674,31675],{},"Rovnovážné veličiny:",[120,31677,31678,31713,31765,31819,31867],{},[123,31679,31680,1673],{},[883,31681,31683],{"className":31682},[886],[888,31684,31685],{"xmlns":890},[892,31686,31687,31710],{},[895,31688,31689,31695,31697,31705,31707],{},[2062,31690,31691,31693],{},[898,31692,8184],{},[898,31694,1842],{},[1656,31696,1713],{},[4138,31698,31699],{"scriptlevel":4032,"displaystyle":1658},[3294,31700,31701,31703],{},[1667,31702,31661],{},[1667,31704,31664],{},[1656,31706,2829],{},[1667,31708,31709],{},"366,071",[902,31711,31712],{"encoding":904},"Y^E = \\tfrac{5125}{14} \\doteq 366{,}071",[123,31714,31715,1673],{},[883,31716,31718],{"className":31717},[886],[888,31719,31720],{"xmlns":890},[892,31721,31722,31762],{},[895,31723,31724,31730,31732,31734,31736,31742,31744,31746,31748,31757,31759],{},[2062,31725,31726,31728],{},[898,31727,11577],{},[898,31729,1842],{},[1656,31731,1713],{},[1667,31733,11639],{},[2461,31735,7828],{},[2062,31737,31738,31740],{},[898,31739,8184],{},[898,31741,1842],{},[1656,31743,3633],{},[1667,31745,8567],{},[1656,31747,1713],{},[4138,31749,31750],{"scriptlevel":4032,"displaystyle":1658},[3294,31751,31752,31755],{},[1667,31753,31754],{},"1375",[1667,31756,31664],{},[1656,31758,2829],{},[1667,31760,31761],{},"98,214",[902,31763,31764],{"encoding":904},"T^E = 0{,}2\\,Y^E + 25 = \\tfrac{1375}{14} \\doteq 98{,}214",[123,31766,31767,1673],{},[883,31768,31770],{"className":31769},[886],[888,31771,31772],{"xmlns":890},[892,31773,31774,31816],{},[895,31775,31776,31784,31786,31792,31794,31800,31802,31811,31813],{},[1715,31777,31778,31780,31782],{},[898,31779,8184],{},[898,31781,6787],{},[898,31783,1842],{},[1656,31785,1713],{},[2062,31787,31788,31790],{},[898,31789,8184],{},[898,31791,1842],{},[1656,31793,3964],{},[2062,31795,31796,31798],{},[898,31797,11577],{},[898,31799,1842],{},[1656,31801,1713],{},[4138,31803,31804],{"scriptlevel":4032,"displaystyle":1658},[3294,31805,31806,31809],{},[1667,31807,31808],{},"3750",[1667,31810,31664],{},[1656,31812,2829],{},[1667,31814,31815],{},"267,857",[902,31817,31818],{"encoding":904},"Y_D^E = Y^E - T^E = \\tfrac{3750}{14} \\doteq 267{,}857",[123,31820,31821,1673],{},[883,31822,31824],{"className":31823},[886],[888,31825,31826],{"xmlns":890},[892,31827,31828,31864],{},[895,31829,31830,31836,31838,31844,31846,31848,31850,31859,31861],{},[2062,31831,31832,31834],{},[898,31833,1766],{},[898,31835,1842],{},[1656,31837,1713],{},[2062,31839,31840,31842],{},[898,31841,8184],{},[898,31843,1842],{},[1656,31845,3964],{},[1667,31847,29898],{},[1656,31849,1713],{},[4138,31851,31852],{"scriptlevel":4032,"displaystyle":1658},[3294,31853,31854,31857],{},[1667,31855,31856],{},"4355",[1667,31858,31664],{},[1656,31860,2829],{},[1667,31862,31863],{},"311,071",[902,31865,31866],{"encoding":904},"C^E = Y^E - 55 = \\tfrac{4355}{14} \\doteq 311{,}071",[123,31868,31869,31925],{},[883,31870,31872],{"className":31871},[886],[888,31873,31874],{"xmlns":890},[892,31875,31876,31922],{},[895,31877,31878,31884,31886,31894,31896,31902,31904,31906,31915,31917,31919],{},[2062,31879,31880,31882],{},[898,31881,1769],{},[898,31883,1842],{},[1656,31885,1713],{},[1715,31887,31888,31890,31892],{},[898,31889,8184],{},[898,31891,6787],{},[898,31893,1842],{},[1656,31895,3964],{},[2062,31897,31898,31900],{},[898,31899,1766],{},[898,31901,1842],{},[1656,31903,1713],{},[1656,31905,3964],{},[4138,31907,31908],{"scriptlevel":4032,"displaystyle":1658},[3294,31909,31910,31913],{},[1667,31911,31912],{},"605",[1667,31914,31664],{},[1656,31916,2829],{},[1656,31918,3964],{},[1667,31920,31921],{},"43,214",[902,31923,31924],{"encoding":904},"S^E = Y_D^E - C^E = -\\tfrac{605}{14} \\doteq -43{,}214"," (záporné — domácnosti při této kalibraci čerpají úspory).",[724,31927,31928,30068,31930,31951,31952,31955,31956,31978,31979,1863],{},[38,31929,30067],{},[883,31931,31933],{"className":31932},[886],[888,31934,31935],{"xmlns":890},[892,31936,31937,31949],{},[895,31938,31939,31941,31943,31945,31947],{},[898,31940,1766],{},[2461,31942,21025],{},[898,31944,20919],{},[2461,31946,21025],{},[898,31948,20847],{},[902,31950,26943],{"encoding":904}," stále uvažuje ",[38,31953,31954],{},"uzavřenou"," ekonomiku. Reálné ekonomiky dovážejí a vyvážejí zboží — otevření ekonomiky o čistý export ",[883,31957,31959],{"className":31958},[886],[888,31960,31961],{"xmlns":890},[892,31962,31963,31975],{},[895,31964,31965,31967,31969,31971,31973],{},[898,31966,21055],{},[1656,31968,1713],{},[898,31970,2161],{},[1656,31972,3964],{},[898,31974,1703],{},[902,31976,31977],{"encoding":904},"X = B - M"," dává ",[38,31980,30089,31981],{},[883,31982,31984],{"className":31983},[886],[888,31985,31986],{"xmlns":890},[892,31987,31988,32004],{},[895,31989,31990,31992,31994,31996,31998,32000,32002],{},[898,31991,1766],{},[2461,31993,21025],{},[898,31995,20919],{},[2461,31997,21025],{},[898,31999,20847],{},[2461,32001,21025],{},[898,32003,21055],{},[902,32005,21058],{"encoding":904},[115,32007,32009],{"id":32008},"model-c-i-g-x-otevřená-ekonomika","Model C-I-G-X — otevřená ekonomika",[198,32011,29342],{"id":32012},"zadání-modelu-2",[724,32014,32015,32016,1643,32019,30312,32040,32053,32054,20863,32057,32070],{},"Rozšíření o ",[38,32017,32018],{},"čistý export",[883,32020,32022],{"className":32021},[886],[888,32023,32024],{"xmlns":890},[892,32025,32026,32038],{},[895,32027,32028,32030,32032,32034,32036],{},[898,32029,21055],{},[1656,32031,1713],{},[898,32033,2161],{},[1656,32035,3964],{},[898,32037,1703],{},[902,32039,31977],{"encoding":904},[883,32041,32043],{"className":32042},[886],[888,32044,32045],{"xmlns":890},[892,32046,32047,32051],{},[895,32048,32049],{},[898,32050,2161],{},[902,32052,2161],{"encoding":904}," je hrubý export (",[614,32055,32056],{},"brutto export",[883,32058,32060],{"className":32059},[886],[888,32061,32062],{"xmlns":890},[892,32063,32064,32068],{},[895,32065,32066],{},[898,32067,1703],{},[902,32069,1703],{"encoding":904}," import. Obvyklá konstrukce: import závisí (nejčastěji je úměrný) disponibilnímu důchodu:",[724,32072,32073],{},[883,32074,32076],{"className":32075},[886],[888,32077,32078],{"xmlns":890},[892,32079,32080,32100],{},[895,32081,32082,32084,32086,32088,32090,32096,32098],{},[898,32083,1703],{},[1656,32085,1713],{},[898,32087,1703],{},[1656,32089,1659],{"stretchy":1658},[1661,32091,32092,32094],{},[898,32093,8184],{},[898,32095,6787],{},[1656,32097,1683],{"stretchy":1658},[898,32099,1863],{"mathvariant":1723},[902,32101,32102],{"encoding":904},"M = M(Y_D).",[724,32104,32105],{},"Podmínka rovnováhy:",[724,32107,32108],{},[883,32109,32111],{"className":32110},[886],[888,32112,32113],{"xmlns":890},[892,32114,32115,32152],{},[895,32116,32117,32119,32121,32123,32125,32127,32129,32131,32133,32135,32137,32139,32141,32143,32145,32148,32150],{},[898,32118,8184],{},[1656,32120,1713],{},[898,32122,1766],{},[1656,32124,3633],{},[898,32126,20919],{},[1656,32128,3633],{},[898,32130,20847],{},[1656,32132,3633],{},[898,32134,2161],{},[1656,32136,3964],{},[898,32138,1703],{},[898,32140,1863],{"mathvariant":1723},[3316,32142],{"width":14644},[1656,32144,1659],{"stretchy":1658},[1667,32146,32147],{},"7.10",[2461,32149,207],{},[1656,32151,1683],{"stretchy":1658},[902,32153,32154],{"encoding":904},"Y = C + I + G + B - M. \\qquad (7.10\\text{a})",[198,32156,29412],{"id":32157},"soustava-rovnic-2",[724,32159,30569,32160,32194,32195,2114],{},[883,32161,32163],{"className":32162},[886],[888,32164,32165],{"xmlns":890},[892,32166,32167,32191],{},[895,32168,32169,32175,32177,32183,32185],{},[2062,32170,32171,32173],{},[898,32172,20919],{},[1656,32174,8187],{},[1656,32176,1673],{"separator":1672},[2062,32178,32179,32181],{},[898,32180,20847],{},[1656,32182,8187],{},[1656,32184,1673],{"separator":1672},[2062,32186,32187,32189],{},[898,32188,2161],{},[1656,32190,8187],{},[902,32192,32193],{"encoding":904},"I^*, G^*, B^*"," dostáváme soustavu 5 rovnic o 5 neznámých ",[883,32196,32198],{"className":32197},[886],[888,32199,32200],{"xmlns":890},[892,32201,32202,32226],{},[895,32203,32204,32206,32208,32210,32212,32214,32216,32222,32224],{},[898,32205,8184],{},[1656,32207,1673],{"separator":1672},[898,32209,1766],{},[1656,32211,1673],{"separator":1672},[898,32213,11577],{},[1656,32215,1673],{"separator":1672},[1661,32217,32218,32220],{},[898,32219,8184],{},[898,32221,6787],{},[1656,32223,1673],{"separator":1672},[898,32225,1703],{},[902,32227,32228],{"encoding":904},"Y, C, T, Y_D, M",[724,32230,32231],{},[883,32232,32234],{"className":32233},[886],[888,32235,32236],{"xmlns":890},[892,32237,32238,32422],{},[895,32239,32240,32414,32416,32418,32420],{},[2412,32241,32242,32274,32304,32332,32364],{"rowspacing":29476,"columnalign":29477,"columnspacing":1724},[2416,32243,32244,32250],{},[2419,32245,32246],{},[4138,32247,32248],{"scriptlevel":4032,"displaystyle":1672},[898,32249,1766],{},[2419,32251,32252],{},[4138,32253,32254],{"scriptlevel":4032,"displaystyle":1672},[895,32255,32256,32258,32260,32262,32264,32270,32272],{},[895,32257],{},[1656,32259,1713],{},[898,32261,1766],{},[1656,32263,1659],{"stretchy":1658},[1661,32265,32266,32268],{},[898,32267,8184],{},[898,32269,6787],{},[1656,32271,1683],{"stretchy":1658},[1656,32273,1673],{"separator":1672},[2416,32275,32276,32286],{},[2419,32277,32278],{},[4138,32279,32280],{"scriptlevel":4032,"displaystyle":1672},[1661,32281,32282,32284],{},[898,32283,8184],{},[898,32285,6787],{},[2419,32287,32288],{},[4138,32289,32290],{"scriptlevel":4032,"displaystyle":1672},[895,32291,32292,32294,32296,32298,32300,32302],{},[895,32293],{},[1656,32295,1713],{},[898,32297,8184],{},[1656,32299,3964],{},[898,32301,11577],{},[1656,32303,1673],{"separator":1672},[2416,32305,32306,32312],{},[2419,32307,32308],{},[4138,32309,32310],{"scriptlevel":4032,"displaystyle":1672},[898,32311,11577],{},[2419,32313,32314],{},[4138,32315,32316],{"scriptlevel":4032,"displaystyle":1672},[895,32317,32318,32320,32322,32324,32326,32328,32330],{},[895,32319],{},[1656,32321,1713],{},[898,32323,11577],{},[1656,32325,1659],{"stretchy":1658},[898,32327,8184],{},[1656,32329,1683],{"stretchy":1658},[1656,32331,1673],{"separator":1672},[2416,32333,32334,32340],{},[2419,32335,32336],{},[4138,32337,32338],{"scriptlevel":4032,"displaystyle":1672},[898,32339,1703],{},[2419,32341,32342],{},[4138,32343,32344],{"scriptlevel":4032,"displaystyle":1672},[895,32345,32346,32348,32350,32352,32354,32360,32362],{},[895,32347],{},[1656,32349,1713],{},[898,32351,1703],{},[1656,32353,1659],{"stretchy":1658},[1661,32355,32356,32358],{},[898,32357,8184],{},[898,32359,6787],{},[1656,32361,1683],{"stretchy":1658},[1656,32363,1673],{"separator":1672},[2416,32365,32366,32372],{},[2419,32367,32368],{},[4138,32369,32370],{"scriptlevel":4032,"displaystyle":1672},[898,32371,8184],{},[2419,32373,32374],{},[4138,32375,32376],{"scriptlevel":4032,"displaystyle":1672},[895,32377,32378,32380,32382,32384,32386,32392,32394,32400,32402,32408,32410,32412],{},[895,32379],{},[1656,32381,1713],{},[898,32383,1766],{},[1656,32385,3633],{},[2062,32387,32388,32390],{},[898,32389,20919],{},[1656,32391,8187],{},[1656,32393,3633],{},[2062,32395,32396,32398],{},[898,32397,20847],{},[1656,32399,8187],{},[1656,32401,3633],{},[2062,32403,32404,32406],{},[898,32405,2161],{},[1656,32407,8187],{},[1656,32409,3964],{},[898,32411,1703],{},[898,32413,1863],{"mathvariant":1723},[3316,32415],{"width":14644},[1656,32417,1659],{"stretchy":1658},[1667,32419,32147],{},[1656,32421,1683],{"stretchy":1658},[902,32423,32424],{"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)",[198,32426,32428],{"id":32427},"příklad-75","Příklad 7.5",[724,32430,32431,32432,1343,32464,1343,32491,1343,32512,1343,32534,1343,32556,32579],{},"Dáno: ",[883,32433,32435],{"className":32434},[886],[888,32436,32437],{"xmlns":890},[892,32438,32439,32461],{},[895,32440,32441,32443,32445,32448,32450,32456,32458],{},[898,32442,1766],{},[1656,32444,1713],{},[1667,32446,32447],{},"0,75",[2461,32449,7828],{},[1661,32451,32452,32454],{},[898,32453,8184],{},[898,32455,6787],{},[1656,32457,3633],{},[1667,32459,32460],{},"750",[902,32462,32463],{"encoding":904},"C = 0{,}75\\,Y_D + 750",[883,32465,32467],{"className":32466},[886],[888,32468,32469],{"xmlns":890},[892,32470,32471,32488],{},[895,32472,32473,32475,32477,32480,32482],{},[898,32474,1703],{},[1656,32476,1713],{},[1667,32478,32479],{},"0,15",[2461,32481,7828],{},[1661,32483,32484,32486],{},[898,32485,8184],{},[898,32487,6787],{},[902,32489,32490],{"encoding":904},"M = 0{,}15\\,Y_D",[883,32492,32494],{"className":32493},[886],[888,32495,32496],{"xmlns":890},[892,32497,32498,32509],{},[895,32499,32500,32502,32504,32507],{},[898,32501,11577],{},[1656,32503,1713],{},[1667,32505,32506],{},"0,25",[898,32508,8184],{},[902,32510,32511],{"encoding":904},"T = 0{,}25Y",[883,32513,32515],{"className":32514},[886],[888,32516,32517],{"xmlns":890},[892,32518,32519,32531],{},[895,32520,32521,32527,32529],{},[2062,32522,32523,32525],{},[898,32524,20919],{},[1656,32526,8187],{},[1656,32528,1713],{},[1667,32530,8059],{},[902,32532,32533],{"encoding":904},"I^* = 500",[883,32535,32537],{"className":32536},[886],[888,32538,32539],{"xmlns":890},[892,32540,32541,32553],{},[895,32542,32543,32549,32551],{},[2062,32544,32545,32547],{},[898,32546,20847],{},[1656,32548,8187],{},[1656,32550,1713],{},[1667,32552,17557],{},[902,32554,32555],{"encoding":904},"G^* = 150",[883,32557,32559],{"className":32558},[886],[888,32560,32561],{"xmlns":890},[892,32562,32563,32576],{},[895,32564,32565,32571,32573],{},[2062,32566,32567,32569],{},[898,32568,2161],{},[1656,32570,8187],{},[1656,32572,1713],{},[1667,32574,32575],{},"800",[902,32577,32578],{"encoding":904},"B^* = 800",". Soustava:",[724,32581,32582],{},[883,32583,32585],{"className":32584},[886],[888,32586,32587],{"xmlns":890},[892,32588,32589,32807],{},[2412,32590,32591,32637,32679,32715,32757],{"rowspacing":29476,"columnalign":29477,"columnspacing":1724},[2416,32592,32593,32609],{},[2419,32594,32595],{},[4138,32596,32597],{"scriptlevel":4032,"displaystyle":1672},[895,32598,32599,32601,32603,32605,32607],{},[1656,32600,1659],{"stretchy":1658},[898,32602,20776],{},[1667,32604,1669],{},[1656,32606,1683],{"stretchy":1658},[2461,32608,11112],{},[2419,32610,32611],{},[4138,32612,32613],{"scriptlevel":4032,"displaystyle":1672},[895,32614,32615,32617,32619,32621,32623,32625,32631,32633,32635],{},[895,32616],{},[898,32618,1766],{},[1656,32620,1713],{},[1667,32622,32447],{},[2461,32624,7828],{},[1661,32626,32627,32629],{},[898,32628,8184],{},[898,32630,6787],{},[1656,32632,3633],{},[1667,32634,32460],{},[1656,32636,1673],{"separator":1672},[2416,32638,32639,32655],{},[2419,32640,32641],{},[4138,32642,32643],{"scriptlevel":4032,"displaystyle":1672},[895,32644,32645,32647,32649,32651,32653],{},[1656,32646,1659],{"stretchy":1658},[898,32648,20776],{},[1667,32650,1680],{},[1656,32652,1683],{"stretchy":1658},[2461,32654,11112],{},[2419,32656,32657],{},[4138,32658,32659],{"scriptlevel":4032,"displaystyle":1672},[895,32660,32661,32663,32669,32671,32673,32675,32677],{},[895,32662],{},[1661,32664,32665,32667],{},[898,32666,8184],{},[898,32668,6787],{},[1656,32670,1713],{},[898,32672,8184],{},[1656,32674,3964],{},[898,32676,11577],{},[1656,32678,1673],{"separator":1672},[2416,32680,32681,32697],{},[2419,32682,32683],{},[4138,32684,32685],{"scriptlevel":4032,"displaystyle":1672},[895,32686,32687,32689,32691,32693,32695],{},[1656,32688,1659],{"stretchy":1658},[898,32690,20776],{},[1667,32692,2617],{},[1656,32694,1683],{"stretchy":1658},[2461,32696,11112],{},[2419,32698,32699],{},[4138,32700,32701],{"scriptlevel":4032,"displaystyle":1672},[895,32702,32703,32705,32707,32709,32711,32713],{},[895,32704],{},[898,32706,11577],{},[1656,32708,1713],{},[1667,32710,32506],{},[898,32712,8184],{},[1656,32714,1673],{"separator":1672},[2416,32716,32717,32733],{},[2419,32718,32719],{},[4138,32720,32721],{"scriptlevel":4032,"displaystyle":1672},[895,32722,32723,32725,32727,32729,32731],{},[1656,32724,1659],{"stretchy":1658},[898,32726,20776],{},[1667,32728,2673],{},[1656,32730,1683],{"stretchy":1658},[2461,32732,11112],{},[2419,32734,32735],{},[4138,32736,32737],{"scriptlevel":4032,"displaystyle":1672},[895,32738,32739,32741,32743,32745,32747,32749,32755],{},[895,32740],{},[898,32742,1703],{},[1656,32744,1713],{},[1667,32746,32479],{},[2461,32748,7828],{},[1661,32750,32751,32753],{},[898,32752,8184],{},[898,32754,6787],{},[1656,32756,1673],{"separator":1672},[2416,32758,32759,32775],{},[2419,32760,32761],{},[4138,32762,32763],{"scriptlevel":4032,"displaystyle":1672},[895,32764,32765,32767,32769,32771,32773],{},[1656,32766,1659],{"stretchy":1658},[898,32768,20776],{},[1667,32770,5193],{},[1656,32772,1683],{"stretchy":1658},[2461,32774,11112],{},[2419,32776,32777],{},[4138,32778,32779],{"scriptlevel":4032,"displaystyle":1672},[895,32780,32781,32783,32785,32787,32789,32791,32793,32795,32797,32799,32801,32803,32805],{},[895,32782],{},[898,32784,8184],{},[1656,32786,1713],{},[898,32788,1766],{},[1656,32790,3633],{},[1667,32792,8059],{},[1656,32794,3633],{},[1667,32796,17557],{},[1656,32798,3633],{},[1667,32800,32575],{},[1656,32802,3964],{},[898,32804,1703],{},[898,32806,1863],{"mathvariant":1723},[902,32808,32809],{"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}",[724,32811,32812,32813,32847],{},"Postupná substituce — z (r3) do (r2): ",[883,32814,32816],{"className":32815},[886],[888,32817,32818],{"xmlns":890},[892,32819,32820,32844],{},[895,32821,32822,32828,32830,32832,32834,32836,32838,32840,32842],{},[1661,32823,32824,32826],{},[898,32825,8184],{},[898,32827,6787],{},[1656,32829,1713],{},[898,32831,8184],{},[1656,32833,3964],{},[1667,32835,32506],{},[898,32837,8184],{},[1656,32839,1713],{},[1667,32841,32447],{},[898,32843,8184],{},[902,32845,32846],{"encoding":904},"Y_D = Y - 0{,}25Y = 0{,}75Y",". Dosazením do (r1) a (r4):",[724,32849,32850],{},[883,32851,32853],{"className":32852},[886],[888,32854,32855],{"xmlns":890},[892,32856,32857,32898],{},[895,32858,32859,32861,32863,32865,32867,32869,32871,32873,32875,32877,32879,32881,32883,32885,32887,32890,32892,32894,32896],{},[1656,32860,1659],{"stretchy":1658},[898,32862,20776],{},[1667,32864,9112],{},[1656,32866,1683],{"stretchy":1658},[2461,32868,11112],{},[898,32870,1766],{},[1656,32872,1713],{},[1667,32874,32447],{},[1656,32876,2751],{},[1667,32878,32447],{},[898,32880,8184],{},[1656,32882,3633],{},[1667,32884,32460],{},[1656,32886,1713],{},[1667,32888,32889],{},"0,5625",[898,32891,8184],{},[1656,32893,3633],{},[1667,32895,32460],{},[1656,32897,1673],{"separator":1672},[902,32899,32900],{"encoding":904},"(r6)\\ C = 0{,}75 \\cdot 0{,}75Y + 750 = 0{,}5625Y + 750,",[724,32902,32903],{},[883,32904,32906],{"className":32905},[886],[888,32907,32908],{"xmlns":890},[892,32909,32910,32943],{},[895,32911,32912,32914,32916,32918,32920,32922,32924,32926,32928,32930,32932,32934,32936,32939,32941],{},[1656,32913,1659],{"stretchy":1658},[898,32915,20776],{},[1667,32917,6240],{},[1656,32919,1683],{"stretchy":1658},[2461,32921,11112],{},[898,32923,1703],{},[1656,32925,1713],{},[1667,32927,32479],{},[1656,32929,2751],{},[1667,32931,32447],{},[898,32933,8184],{},[1656,32935,1713],{},[1667,32937,32938],{},"0,1125",[898,32940,8184],{},[898,32942,1863],{"mathvariant":1723},[902,32944,32945],{"encoding":904},"(r7)\\ M = 0{,}15 \\cdot 0{,}75Y = 0{,}1125Y.",[724,32947,32948],{},"Dosazením do (r5):",[724,32950,32951],{},[883,32952,32954],{"className":32953},[886],[888,32955,32956],{"xmlns":890},[892,32957,32958,33002],{},[895,32959,32960,32962,32964,32966,32968,32970,32972,32974,32976,32978,32980,32982,32984,32986,32988,32990,32992,32995,32997,32999],{},[898,32961,8184],{},[1656,32963,1713],{},[1667,32965,32889],{},[898,32967,8184],{},[1656,32969,3633],{},[1667,32971,32460],{},[1656,32973,3633],{},[1667,32975,8059],{},[1656,32977,3633],{},[1667,32979,17557],{},[1656,32981,3633],{},[1667,32983,32575],{},[1656,32985,3964],{},[1667,32987,32938],{},[898,32989,8184],{},[1656,32991,1713],{},[1667,32993,32994],{},"0,45",[898,32996,8184],{},[1656,32998,3633],{},[1667,33000,33001],{},"2200.",[902,33003,33004],{"encoding":904},"Y = 0{,}5625Y + 750 + 500 + 150 + 800 - 0{,}1125Y = 0{,}45Y + 2200.",[724,33006,33007,33008,2836,33030,33053],{},"Odtud ",[883,33009,33011],{"className":33010},[886],[888,33012,33013],{"xmlns":890},[892,33014,33015,33027],{},[895,33016,33017,33020,33022,33024],{},[1667,33018,33019],{},"0,55",[898,33021,8184],{},[1656,33023,1713],{},[1667,33025,33026],{},"2200",[902,33028,33029],{"encoding":904},"0{,}55Y = 2200",[883,33031,33033],{"className":33032},[886],[888,33034,33035],{"xmlns":890},[892,33036,33037,33050],{},[895,33038,33039,33045,33047],{},[2062,33040,33041,33043],{},[898,33042,8184],{},[898,33044,1842],{},[1656,33046,1713],{},[1667,33048,33049],{},"4000",[902,33051,33052],{"encoding":904},"Y^E = 4000",". Rovnovážné veličiny:",[120,33055,33056,33079,33111,33146,33179,33215],{},[123,33057,33058,1673],{},[883,33059,33061],{"className":33060},[886],[888,33062,33063],{"xmlns":890},[892,33064,33065,33077],{},[895,33066,33067,33073,33075],{},[2062,33068,33069,33071],{},[898,33070,8184],{},[898,33072,1842],{},[1656,33074,1713],{},[1667,33076,33049],{},[902,33078,33052],{"encoding":904},[123,33080,33081,1673],{},[883,33082,33084],{"className":33083},[886],[888,33085,33086],{"xmlns":890},[892,33087,33088,33108],{},[895,33089,33090,33096,33098,33100,33102,33104,33106],{},[2062,33091,33092,33094],{},[898,33093,11577],{},[898,33095,1842],{},[1656,33097,1713],{},[1667,33099,32506],{},[1656,33101,2751],{},[1667,33103,33049],{},[1656,33105,1713],{},[1667,33107,11584],{},[902,33109,33110],{"encoding":904},"T^E = 0{,}25 \\cdot 4000 = 1000",[123,33112,33113,1673],{},[883,33114,33116],{"className":33115},[886],[888,33117,33118],{"xmlns":890},[892,33119,33120,33143],{},[895,33121,33122,33130,33132,33134,33136,33138,33140],{},[1715,33123,33124,33126,33128],{},[898,33125,8184],{},[898,33127,6787],{},[898,33129,1842],{},[1656,33131,1713],{},[1667,33133,32447],{},[1656,33135,2751],{},[1667,33137,33049],{},[1656,33139,1713],{},[1667,33141,33142],{},"3000",[902,33144,33145],{"encoding":904},"Y_D^E = 0{,}75 \\cdot 4000 = 3000",[123,33147,33148,1673],{},[883,33149,33151],{"className":33150},[886],[888,33152,33153],{"xmlns":890},[892,33154,33155,33176],{},[895,33156,33157,33163,33165,33167,33169,33171,33173],{},[2062,33158,33159,33161],{},[898,33160,1703],{},[898,33162,1842],{},[1656,33164,1713],{},[1667,33166,32479],{},[1656,33168,2751],{},[1667,33170,33142],{},[1656,33172,1713],{},[1667,33174,33175],{},"450",[902,33177,33178],{"encoding":904},"M^E = 0{,}15 \\cdot 3000 = 450",[123,33180,33181,1673],{},[883,33182,33184],{"className":33183},[886],[888,33185,33186],{"xmlns":890},[892,33187,33188,33212],{},[895,33189,33190,33196,33198,33200,33202,33204,33206,33208,33210],{},[2062,33191,33192,33194],{},[898,33193,1766],{},[898,33195,1842],{},[1656,33197,1713],{},[1667,33199,32447],{},[1656,33201,2751],{},[1667,33203,33142],{},[1656,33205,3633],{},[1667,33207,32460],{},[1656,33209,1713],{},[1667,33211,33142],{},[902,33213,33214],{"encoding":904},"C^E = 0{,}75 \\cdot 3000 + 750 = 3000",[123,33216,33217,33257],{},[883,33218,33220],{"className":33219},[886],[888,33221,33222],{"xmlns":890},[892,33223,33224,33254],{},[895,33225,33226,33232,33234,33242,33244,33250,33252],{},[2062,33227,33228,33230],{},[898,33229,1769],{},[898,33231,1842],{},[1656,33233,1713],{},[1715,33235,33236,33238,33240],{},[898,33237,8184],{},[898,33239,6787],{},[898,33241,1842],{},[1656,33243,3964],{},[2062,33245,33246,33248],{},[898,33247,1766],{},[898,33249,1842],{},[1656,33251,1713],{},[1667,33253,4032],{},[902,33255,33256],{"encoding":904},"S^E = Y_D^E - C^E = 0"," (při této kalibraci domácnosti celý disponibilní důchod spotřebují).",[724,33259,33260,33262,33263,1343,33280,1896,33301,33326,33327,33330,33331,33344,33345,1863],{},[38,33261,30067],{}," Modely ",[883,33264,33266],{"className":33265},[886],[888,33267,33268],{"xmlns":890},[892,33269,33270,33278],{},[895,33271,33272,33274,33276],{},[898,33273,1766],{},[2461,33275,21025],{},[898,33277,20919],{},[902,33279,21030],{"encoding":904},[883,33281,33283],{"className":33282},[886],[888,33284,33285],{"xmlns":890},[892,33286,33287,33299],{},[895,33288,33289,33291,33293,33295,33297],{},[898,33290,1766],{},[2461,33292,21025],{},[898,33294,20919],{},[2461,33296,21025],{},[898,33298,20847],{},[902,33300,26943],{"encoding":904},[883,33302,33304],{"className":33303},[886],[888,33305,33306],{"xmlns":890},[892,33307,33308,33324],{},[895,33309,33310,33312,33314,33316,33318,33320,33322],{},[898,33311,1766],{},[2461,33313,21025],{},[898,33315,20919],{},[2461,33317,21025],{},[898,33319,20847],{},[2461,33321,21025],{},[898,33323,21055],{},[902,33325,21058],{"encoding":904}," pokládají investice za ",[38,33328,33329],{},"konstantní",". To není realistické — investice závisejí na úrokové míře ",[883,33332,33334],{"className":33333},[886],[888,33335,33336],{"xmlns":890},[892,33337,33338,33342],{},[895,33339,33340],{},[898,33341,20776],{},[902,33343,20776],{"encoding":904},". Přidáním trhu peněz a úrokové míry vzniká ",[38,33346,33347],{},"model IS-LM",[115,33349,33351],{"id":33350},"_74-multiplikátory-pro-makroekonomické-proměnné","7.4 Multiplikátory pro makroekonomické proměnné",[724,33353,33354,33355,33359,33360,33363,33364,33367],{},"V článku ",[207,33356,33358],{"className":33357,"dataFsResolvedFilePath":827,"href":828},[210],"2.4"," (mikroekonomie) byly zavedeny multiplikátory pro mikroekonomické proměnné. ",[38,33361,33362],{},"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 ",[38,33365,33366],{},"výraznější"," než v mikroekonomických modelech.",[724,33369,33370],{},[5956,33371],{"alt":33372,"className":33373,"src":33374},"imek-multiplikatorovy-efekt-chain",[210,5960],"\u002Fwiki-assets\u002Fimek-multiplikatorovy-efekt-chain.jpeg",[724,33376,20899,33377,1343,33394,1343,33415,33440,33441,33444,33445,33463,33464,33482,33483,33501,33502,33505,33506,1343,33523,33540,33541,33543],{},[883,33378,33380],{"className":33379},[886],[888,33381,33382],{"xmlns":890},[892,33383,33384,33392],{},[895,33385,33386,33388,33390],{},[898,33387,1766],{},[2461,33389,21025],{},[898,33391,20919],{},[902,33393,21030],{"encoding":904},[883,33395,33397],{"className":33396},[886],[888,33398,33399],{"xmlns":890},[892,33400,33401,33413],{},[895,33402,33403,33405,33407,33409,33411],{},[898,33404,1766],{},[2461,33406,21025],{},[898,33408,20919],{},[2461,33410,21025],{},[898,33412,20847],{},[902,33414,26943],{"encoding":904},[883,33416,33418],{"className":33417},[886],[888,33419,33420],{"xmlns":890},[892,33421,33422,33438],{},[895,33423,33424,33426,33428,33430,33432,33434,33436],{},[898,33425,1766],{},[2461,33427,21025],{},[898,33429,20919],{},[2461,33431,21025],{},[898,33433,20847],{},[2461,33435,21025],{},[898,33437,21055],{},[902,33439,21058],{"encoding":904}," se vyšetřuje vliv změn ",[38,33442,33443],{},"exogenních"," veličin (plánovaných investic ",[883,33446,33448],{"className":33447},[886],[888,33449,33450],{"xmlns":890},[892,33451,33452,33460],{},[895,33453,33454],{},[2062,33455,33456,33458],{},[898,33457,20919],{},[1656,33459,8187],{},[902,33461,33462],{"encoding":904},"I^*",", vládních výdajů ",[883,33465,33467],{"className":33466},[886],[888,33468,33469],{"xmlns":890},[892,33470,33471,33479],{},[895,33472,33473],{},[2062,33474,33475,33477],{},[898,33476,20847],{},[1656,33478,8187],{},[902,33480,33481],{"encoding":904},"G^*",", exportu ",[883,33484,33486],{"className":33485},[886],[888,33487,33488],{"xmlns":890},[892,33489,33490,33498],{},[895,33491,33492],{},[2062,33493,33494,33496],{},[898,33495,2161],{},[1656,33497,8187],{},[902,33499,33500],{"encoding":904},"B^*",") na změny ",[38,33503,33504],{},"endogenních"," rovnovážných veličin (",[883,33507,33509],{"className":33508},[886],[888,33510,33511],{"xmlns":890},[892,33512,33513,33521],{},[895,33514,33515],{},[2062,33516,33517,33519],{},[898,33518,8184],{},[898,33520,1842],{},[902,33522,22635],{"encoding":904},[883,33524,33526],{"className":33525},[886],[888,33527,33528],{"xmlns":890},[892,33529,33530,33538],{},[895,33531,33532],{},[2062,33533,33534,33536],{},[898,33535,1766],{},[898,33537,1842],{},[902,33539,22694],{"encoding":904}," atd.). Tyto citlivosti se vyjadřují ",[38,33542,26700],{}," — parciálními derivacemi rovnovážných veličin podle exogenních veličin.",[198,33545,33547],{"id":33546},"multiplikátory-v-modelu-c-i","Multiplikátory v modelu C-I",[724,33549,29613,33550,33573,33574,33618],{},[883,33551,33553],{"className":33552},[886],[888,33554,33555],{"xmlns":890},[892,33556,33557,33571],{},[895,33558,33559,33561,33563,33565,33567,33569],{},[898,33560,1766],{},[1656,33562,1713],{},[898,33564,207],{},[898,33566,8184],{},[1656,33568,3633],{},[898,33570,3403],{},[902,33572,27641],{"encoding":904}," dává (7.7) redukovaný tvar ",[883,33575,33577],{"className":33576},[886],[888,33578,33579],{"xmlns":890},[892,33580,33581,33615],{},[895,33582,33583,33589,33591],{},[2062,33584,33585,33587],{},[898,33586,8184],{},[898,33588,1842],{},[1656,33590,1713],{},[4138,33592,33593],{"scriptlevel":4032,"displaystyle":1672},[3294,33594,33595,33607],{},[895,33596,33597,33599,33601],{},[898,33598,3403],{},[1656,33600,3633],{},[2062,33602,33603,33605],{},[898,33604,20919],{},[1656,33606,8187],{},[895,33608,33609,33611,33613],{},[1667,33610,1669],{},[1656,33612,3964],{},[898,33614,207],{},[902,33616,33617],{"encoding":904},"Y^E = \\dfrac{b + I^*}{1 - a}",". Parciální derivace:",[724,33620,33621],{},[883,33622,33624],{"className":33623},[886],[888,33625,33626],{"xmlns":890},[892,33627,33628,33697],{},[895,33629,33630,33648,33650,33680,33682],{},[3294,33631,33632,33642],{},[895,33633,33634,33636],{},[898,33635,3300],{"mathvariant":1723},[2062,33637,33638,33640],{},[898,33639,8184],{},[898,33641,1842],{},[895,33643,33644,33646],{},[898,33645,3300],{"mathvariant":1723},[898,33647,207],{},[1656,33649,1713],{},[3294,33651,33652,33664],{},[895,33653,33654,33656,33658],{},[898,33655,3403],{},[1656,33657,3633],{},[2062,33659,33660,33662],{},[898,33661,20919],{},[1656,33663,8187],{},[895,33665,33666,33668,33670,33672,33674],{},[1656,33667,1659],{"stretchy":1658},[1667,33669,1669],{},[1656,33671,3964],{},[898,33673,207],{},[2062,33675,33676,33678],{},[1656,33677,1683],{"stretchy":1658},[1667,33679,1680],{},[3316,33681],{"width":14644},[895,33683,33684,33687,33694],{},[2461,33685,33686],{},"(multiplik",[2033,33688,33689,33691],{"accent":1672},[2461,33690,207],{},[1656,33692,33693],{},"ˊ",[2461,33695,33696],{},"tor MPC)",[902,33698,33699],{"encoding":904},"\\frac{\\partial Y^E}{\\partial a} = \\frac{b + I^*}{(1 - a)^2} \\qquad \\text{(multiplikátor MPC)}",[724,33701,33702],{},[883,33703,33705],{"className":33704},[886],[888,33706,33707],{"xmlns":890},[892,33708,33709,33778],{},[895,33710,33711,33729,33731,33743,33745],{},[3294,33712,33713,33723],{},[895,33714,33715,33717],{},[898,33716,3300],{"mathvariant":1723},[2062,33718,33719,33721],{},[898,33720,8184],{},[898,33722,1842],{},[895,33724,33725,33727],{},[898,33726,3300],{"mathvariant":1723},[898,33728,3403],{},[1656,33730,1713],{},[3294,33732,33733,33735],{},[1667,33734,1669],{},[895,33736,33737,33739,33741],{},[1667,33738,1669],{},[1656,33740,3964],{},[898,33742,207],{},[3316,33744],{"width":14644},[895,33746,33747,33749,33755,33758,33765,33768,33775],{},[2461,33748,33686],{},[2033,33750,33751,33753],{"accent":1672},[2461,33752,207],{},[1656,33754,33693],{},[2461,33756,33757],{},"tor autonomn",[2033,33759,33760,33763],{"accent":1672},[2461,33761,33762],{},"ı",[1656,33764,33693],{},[2461,33766,33767],{}," spot",[2033,33769,33770,33772],{"accent":1672},[2461,33771,20776],{},[1656,33773,33774],{},"ˇ",[2461,33776,33777],{},"eby)",[902,33779,33780],{"encoding":904},"\\frac{\\partial Y^E}{\\partial b} = \\frac{1}{1 - a} \\qquad \\text{(multiplikátor autonomní spotřeby)}",[724,33782,33783],{},[883,33784,33786],{"className":33785},[886],[888,33787,33788],{"xmlns":890},[892,33789,33790,33857],{},[895,33791,33792,33814,33816,33828,33830,33842,33844],{},[3294,33793,33794,33804],{},[895,33795,33796,33798],{},[898,33797,3300],{"mathvariant":1723},[2062,33799,33800,33802],{},[898,33801,8184],{},[898,33803,1842],{},[895,33805,33806,33808],{},[898,33807,3300],{"mathvariant":1723},[2062,33809,33810,33812],{},[898,33811,20919],{},[1656,33813,8187],{},[1656,33815,1713],{},[3294,33817,33818,33820],{},[1667,33819,1669],{},[895,33821,33822,33824,33826],{},[1667,33823,1669],{},[1656,33825,3964],{},[898,33827,207],{},[1656,33829,1713],{},[3294,33831,33832,33834],{},[1667,33833,1669],{},[895,33835,33836,33838,33840],{},[898,33837,1703],{},[898,33839,8194],{},[898,33841,1769],{},[3316,33843],{"width":14644},[895,33845,33846,33848,33854],{},[2461,33847,33686],{},[2033,33849,33850,33852],{"accent":1672},[2461,33851,207],{},[1656,33853,33693],{},[2461,33855,33856],{},"tor investic)",[902,33858,33859],{"encoding":904},"\\frac{\\partial Y^E}{\\partial I^*} = \\frac{1}{1 - a} = \\frac{1}{MPS} \\qquad \\text{(multiplikátor investic)}",[1981,33861,33862],{},[724,33863,33864,33866,33867,33870,33871,33884,33885,33902,33903,33921,33922,33966,33967,30138,33984,33987,33988,34005],{},[883,33865,3472],{}," Intuice — proč Keynesův multiplikátor funguje\nInvestice o 1 Kč se stanou něčím ",[38,33868,33869],{},"důchodem","; z něj se utratí ",[883,33872,33874],{"className":33873},[886],[888,33875,33876],{"xmlns":890},[892,33877,33878,33882],{},[895,33879,33880],{},[898,33881,207],{},[902,33883,207],{"encoding":904}," Kč (= ",[883,33886,33888],{"className":33887},[886],[888,33889,33890],{"xmlns":890},[892,33891,33892,33900],{},[895,33893,33894,33896,33898],{},[898,33895,1703],{},[898,33897,8194],{},[898,33899,1766],{},[902,33901,26768],{"encoding":904},"), to je zase něčí důchod, z něj ",[883,33904,33906],{"className":33905},[886],[888,33907,33908],{"xmlns":890},[892,33909,33910,33918],{},[895,33911,33912],{},[2062,33913,33914,33916],{},[898,33915,207],{},[1667,33917,1680],{},[902,33919,33920],{"encoding":904},"a^2"," Kč… Součet geometrické řady ",[883,33923,33925],{"className":33924},[886],[888,33926,33927],{"xmlns":890},[892,33928,33929,33963],{},[895,33930,33931,33933,33935,33937,33939,33945,33947,33949,33951],{},[1667,33932,1669],{},[1656,33934,3633],{},[898,33936,207],{},[1656,33938,3633],{},[2062,33940,33941,33943],{},[898,33942,207],{},[1667,33944,1680],{},[1656,33946,3633],{},[1656,33948,26828],{},[1656,33950,1713],{},[3294,33952,33953,33955],{},[1667,33954,1669],{},[895,33956,33957,33959,33961],{},[1667,33958,1669],{},[1656,33960,3964],{},[898,33962,207],{},[902,33964,33965],{"encoding":904},"1 + a + a^2 + \\dots = \\frac{1}{1-a}",". Proto jedna koruna investic navíc zvedne ",[883,33968,33970],{"className":33969},[886],[888,33971,33972],{"xmlns":890},[892,33973,33974,33982],{},[895,33975,33976],{},[2062,33977,33978,33980],{},[898,33979,8184],{},[898,33981,1842],{},[902,33983,22635],{"encoding":904},[38,33985,33986],{},"více"," než korunu — čím vyšší ",[883,33989,33991],{"className":33990},[886],[888,33992,33993],{"xmlns":890},[892,33994,33995,34003],{},[895,33996,33997,33999,34001],{},[898,33998,1703],{},[898,34000,8194],{},[898,34002,1766],{},[902,34004,26768],{"encoding":904},", tím silnější multiplikační efekt.",[724,34007,34008,34011,34012,34038,34039,34042,34043,1896,34064,34089,34090,1863],{},[38,34009,34010],{},"Multiplikátor autonomní spotřeby se rovná multiplikátoru investic"," — oba činí ",[883,34013,34015],{"className":34014},[886],[888,34016,34017],{"xmlns":890},[892,34018,34019,34035],{},[895,34020,34021],{},[4138,34022,34023],{"scriptlevel":4032,"displaystyle":1658},[3294,34024,34025,34027],{},[1667,34026,1669],{},[895,34028,34029,34031,34033],{},[1667,34030,1669],{},[1656,34032,3964],{},[898,34034,207],{},[902,34036,34037],{"encoding":904},"\\tfrac{1}{1-a}",", což je standardní ",[38,34040,34041],{},"Keynesův multiplikátor",". Analogicky se v modelech ",[883,34044,34046],{"className":34045},[886],[888,34047,34048],{"xmlns":890},[892,34049,34050,34062],{},[895,34051,34052,34054,34056,34058,34060],{},[898,34053,1766],{},[2461,34055,21025],{},[898,34057,20919],{},[2461,34059,21025],{},[898,34061,20847],{},[902,34063,26943],{"encoding":904},[883,34065,34067],{"className":34066},[886],[888,34068,34069],{"xmlns":890},[892,34070,34071,34087],{},[895,34072,34073,34075,34077,34079,34081,34083,34085],{},[898,34074,1766],{},[2461,34076,21025],{},[898,34078,20919],{},[2461,34080,21025],{},[898,34082,20847],{},[2461,34084,21025],{},[898,34086,21055],{},[902,34088,21058],{"encoding":904}," zavádějí multiplikátory vládních výdajů, zdanění a exportu. Paralela k mikroekonomickým multiplikátorům viz ",[207,34091,34093],{"className":34092,"dataFsResolvedFilePath":800,"href":801},[210],"poptávka a nabídka",[115,34095,34097],{"id":34096},"is-lm-analýza-stručný-přehled","IS-LM analýza (stručný přehled)",[724,34099,20899,34100,1343,34117,1896,34138,20904,34163,3247,34166,34187,34188,1643,34191,34204,34205,14434,34234,34251,34252,34255,34256,34258,34259,34280],{},[883,34101,34103],{"className":34102},[886],[888,34104,34105],{"xmlns":890},[892,34106,34107,34115],{},[895,34108,34109,34111,34113],{},[898,34110,1766],{},[2461,34112,21025],{},[898,34114,20919],{},[902,34116,21030],{"encoding":904},[883,34118,34120],{"className":34119},[886],[888,34121,34122],{"xmlns":890},[892,34123,34124,34136],{},[895,34125,34126,34128,34130,34132,34134],{},[898,34127,1766],{},[2461,34129,21025],{},[898,34131,20919],{},[2461,34133,21025],{},[898,34135,20847],{},[902,34137,26943],{"encoding":904},[883,34139,34141],{"className":34140},[886],[888,34142,34143],{"xmlns":890},[892,34144,34145,34161],{},[895,34146,34147,34149,34151,34153,34155,34157,34159],{},[898,34148,1766],{},[2461,34150,21025],{},[898,34152,20919],{},[2461,34154,21025],{},[898,34156,20847],{},[2461,34158,21025],{},[898,34160,21055],{},[902,34162,21058],{"encoding":904},[38,34164,34165],{},"investice konstantní",[883,34167,34169],{"className":34168},[886],[888,34170,34171],{"xmlns":890},[892,34172,34173,34185],{},[895,34174,34175,34177,34179],{},[898,34176,20919],{},[1656,34178,1713],{},[2062,34180,34181,34183],{},[898,34182,20919],{},[1656,34184,8187],{},[902,34186,20930],{"encoding":904},"). Reálnější je předpoklad, že ",[38,34189,34190],{},"investice závisejí na úrokové míře",[883,34192,34194],{"className":34193},[886],[888,34195,34196],{"xmlns":890},[892,34197,34198,34202],{},[895,34199,34200],{},[898,34201,20776],{},[902,34203,20776],{"encoding":904}," — klesající funkce ",[883,34206,34208],{"className":34207},[886],[888,34209,34210],{"xmlns":890},[892,34211,34212,34232],{},[895,34213,34214,34216,34218,34220,34222,34224,34226,34228,34230],{},[898,34215,20919],{},[1656,34217,1659],{"stretchy":1658},[898,34219,20776],{},[1656,34221,1683],{"stretchy":1658},[1656,34223,1713],{},[898,34225,1745],{},[898,34227,20776],{},[1656,34229,3633],{},[898,34231,3768],{},[902,34233,24485],{"encoding":904},[883,34235,34237],{"className":34236},[886],[888,34238,34239],{"xmlns":890},[892,34240,34241,34249],{},[895,34242,34243,34245,34247],{},[898,34244,1745],{},[1656,34246,4373],{},[1667,34248,4032],{},[902,34250,21249],{"encoding":904},". Přidáním ",[38,34253,34254],{},"trhu peněz"," k trhu zboží vzniká model ",[38,34257,20746],{}," se dvěma neznámými ",[883,34260,34262],{"className":34261},[886],[888,34263,34264],{"xmlns":890},[892,34265,34266,34278],{},[895,34267,34268,34270,34272,34274,34276],{},[1656,34269,1659],{"stretchy":1658},[898,34271,8184],{},[1656,34273,1673],{"separator":1672},[898,34275,20776],{},[1656,34277,1683],{"stretchy":1658},[902,34279,26873],{"encoding":904}," a dvěma rovnicemi:",[120,34282,34283,34333],{},[123,34284,34285,3247,34287,34289,34290,34311,34312,1863],{},[38,34286,24574],{},[614,34288,20789],{},") — klesající přímka v rovině ",[883,34291,34293],{"className":34292},[886],[888,34294,34295],{"xmlns":890},[892,34296,34297,34309],{},[895,34298,34299,34301,34303,34305,34307],{},[1656,34300,1659],{"stretchy":1658},[898,34302,20776],{},[1656,34304,1673],{"separator":1672},[898,34306,8184],{},[1656,34308,1683],{"stretchy":1658},[902,34310,21671],{"encoding":904},", odvozená z rovnováhy trhu zboží ",[883,34313,34315],{"className":34314},[886],[888,34316,34317],{"xmlns":890},[892,34318,34319,34331],{},[895,34320,34321,34323,34325,34327,34329],{},[898,34322,8184],{},[1656,34324,1713],{},[898,34326,1766],{},[1656,34328,3633],{},[898,34330,20919],{},[902,34332,23476],{"encoding":904},[123,34334,34335,3247,34337,34339,34340,30312,34365,34411],{},[38,34336,24773],{},[614,34338,20796],{},") — rostoucí přímka, odvozená z rovnováhy trhu peněz ",[883,34341,34343],{"className":34342},[886],[888,34344,34345],{"xmlns":890},[892,34346,34347,34363],{},[895,34348,34349,34355,34357],{},[2062,34350,34351,34353],{},[898,34352,1703],{},[898,34354,6787],{},[1656,34356,1713],{},[2062,34358,34359,34361],{},[898,34360,1703],{},[1656,34362,8187],{},[902,34364,22213],{"encoding":904},[883,34366,34368],{"className":34367},[886],[888,34369,34370],{"xmlns":890},[892,34371,34372,34408],{},[895,34373,34374,34380,34382,34388,34390,34392,34398,34400,34402],{},[2062,34375,34376,34378],{},[898,34377,1703],{},[898,34379,6787],{},[1656,34381,1713],{},[1661,34383,34384,34386],{},[898,34385,21970],{},[1667,34387,1669],{},[898,34389,8184],{},[1656,34391,3633],{},[1661,34393,34394,34396],{},[898,34395,21970],{},[1667,34397,1680],{},[898,34399,20776],{},[1656,34401,3633],{},[1661,34403,34404,34406],{},[898,34405,21970],{},[1667,34407,2617],{},[902,34409,34410],{"encoding":904},"M^D = k_1 Y + k_2 r + k_3"," (transakční, opatrnostní a spekulační poptávka).",[724,34413,34414,1643,34417,34450,34451,34453,34454,34456],{},[38,34415,34416],{},"Simultánní rovnovážný bod",[883,34418,34420],{"className":34419},[886],[888,34421,34422],{"xmlns":890},[892,34423,34424,34448],{},[895,34425,34426,34428,34430,34432,34438,34440,34446],{},[898,34427,1842],{},[1656,34429,1713],{},[1656,34431,1659],{"stretchy":1658},[2062,34433,34434,34436],{},[898,34435,20776],{},[898,34437,1842],{},[1656,34439,1673],{"separator":1672},[2062,34441,34442,34444],{},[898,34443,8184],{},[898,34445,1842],{},[1656,34447,1683],{"stretchy":1658},[902,34449,24865],{"encoding":904}," je průsečík křivek IS a LM; určuje současně rovnovážný důchod a rovnovážnou úrokovou míru. Model slouží jako rámec pro analýzu ",[38,34452,20834],{}," (posun IS) a ",[38,34455,20866],{}," (posun LM).",[724,34458,34459],{},[38,34460,34461,34462,1343,34484,1343,34506,1343,34528,34550,34551,1863],{},"Pro detailní odvození obou křivek, řešení Příkladu 7.6 (",[883,34463,34465],{"className":34464},[886],[888,34466,34467],{"xmlns":890},[892,34468,34469,34481],{},[895,34470,34471,34477,34479],{},[2062,34472,34473,34475],{},[898,34474,8184],{},[898,34476,1842],{},[1656,34478,1713],{},[1667,34480,23846],{},[902,34482,34483],{"encoding":904},"Y^E = 5000",[883,34485,34487],{"className":34486},[886],[888,34488,34489],{"xmlns":890},[892,34490,34491,34503],{},[895,34492,34493,34499,34501],{},[2062,34494,34495,34497],{},[898,34496,20776],{},[898,34498,1842],{},[1656,34500,1713],{},[1667,34502,5193],{},[902,34504,34505],{"encoding":904},"r^E = 5",[883,34507,34509],{"className":34508},[886],[888,34510,34511],{"xmlns":890},[892,34512,34513,34525],{},[895,34514,34515,34521,34523],{},[2062,34516,34517,34519],{},[898,34518,1766],{},[898,34520,1842],{},[1656,34522,1713],{},[1667,34524,23883],{},[902,34526,34527],{"encoding":904},"C^E = 4100",[883,34529,34531],{"className":34530},[886],[888,34532,34533],{"xmlns":890},[892,34534,34535,34547],{},[895,34536,34537,34543,34545],{},[2062,34538,34539,34541],{},[898,34540,20919],{},[898,34542,1842],{},[1656,34544,1713],{},[1667,34546,23922],{},[902,34548,34549],{"encoding":904},"I^E = 900",") a ekonomickou interpretaci posunů viz ",[207,34552,945],{"className":34553,"dataFsResolvedFilePath":943,"href":944},[210],[115,34555,34557],{"id":34556},"shrnutí-kapitoly-7","Shrnutí kapitoly 7",[152,34559,34560,34624,34735,34878,35119,35187],{},[123,34561,34562,34565,34566,34588,34589,34623],{},[38,34563,34564],{},"Zjednodušený makroekonomický model"," ztotožňuje ",[883,34567,34569],{"className":34568},[886],[888,34570,34571],{"xmlns":890},[892,34572,34573,34585],{},[895,34574,34575,34577,34579,34581,34583],{},[898,34576,20847],{},[898,34578,27017],{},[898,34580,8194],{},[1656,34582,3815],{},[898,34584,8184],{},[902,34586,34587],{"encoding":904},"GNP \\approx Y"," (národní důchod). Základ: ",[883,34590,34592],{"className":34591},[886],[888,34593,34594],{"xmlns":890},[892,34595,34596,34620],{},[895,34597,34598,34600,34602,34604,34606,34608,34610,34612,34614,34616,34618],{},[898,34599,20847],{},[898,34601,27017],{},[898,34603,8194],{},[1656,34605,1713],{},[898,34607,1766],{},[1656,34609,3633],{},[898,34611,20919],{},[1656,34613,3633],{},[898,34615,20847],{},[1656,34617,3633],{},[898,34619,21055],{},[902,34621,34622],{"encoding":904},"GNP = C + I + G + X"," (7.1).",[123,34625,34626,34628,34629,34650,34651,1343,34674,34705,34706,34719,34720,1863],{},[38,34627,27251],{}," splňují ",[883,34630,34632],{"className":34631},[886],[888,34633,34634],{"xmlns":890},[892,34635,34636,34648],{},[895,34637,34638,34640,34642,34644,34646],{},[898,34639,8184],{},[1656,34641,1713],{},[898,34643,1766],{},[1656,34645,3633],{},[898,34647,1769],{},[902,34649,21428],{"encoding":904}," (7.2); lineární model ",[883,34652,34654],{"className":34653},[886],[888,34655,34656],{"xmlns":890},[892,34657,34658,34672],{},[895,34659,34660,34662,34664,34666,34668,34670],{},[898,34661,1766],{},[1656,34663,1713],{},[898,34665,207],{},[898,34667,8184],{},[1656,34669,3633],{},[898,34671,3403],{},[902,34673,27641],{"encoding":904},[883,34675,34677],{"className":34676},[886],[888,34678,34679],{"xmlns":890},[892,34680,34681,34703],{},[895,34682,34683,34685,34687,34689,34691,34693,34695,34697,34699,34701],{},[898,34684,1769],{},[1656,34686,1713],{},[1656,34688,1659],{"stretchy":1658},[1667,34690,1669],{},[1656,34692,3964],{},[898,34694,207],{},[1656,34696,1683],{"stretchy":1658},[898,34698,8184],{},[1656,34700,3964],{},[898,34702,3403],{},[902,34704,27890],{"encoding":904}," s autonomní spotřebou ",[883,34707,34709],{"className":34708},[886],[888,34710,34711],{"xmlns":890},[892,34712,34713,34717],{},[895,34714,34715],{},[898,34716,3403],{},[902,34718,3403],{"encoding":904}," a autonomními úsporami ",[883,34721,34723],{"className":34722},[886],[888,34724,34725],{"xmlns":890},[892,34726,34727,34733],{},[895,34728,34729,34731],{},[1656,34730,3964],{},[898,34732,3403],{},[902,34734,27969],{"encoding":904},[123,34736,34737,1643,34740,1343,34770,34800,34801,34831,34832,1343,34853,1863],{},[38,34738,34739],{},"Mezní sklony",[883,34741,34743],{"className":34742},[886],[888,34744,34745],{"xmlns":890},[892,34746,34747,34767],{},[895,34748,34749,34751,34753,34755,34757,34759,34761,34763,34765],{},[898,34750,1703],{},[898,34752,8194],{},[898,34754,1766],{},[1656,34756,1713],{},[898,34758,3768],{"mathvariant":1723},[898,34760,1766],{},[898,34762,1782],{"mathvariant":1723},[898,34764,3768],{"mathvariant":1723},[898,34766,8184],{},[902,34768,34769],{"encoding":904},"MPC = \\mathrm{d}C\u002F\\mathrm{d}Y",[883,34771,34773],{"className":34772},[886],[888,34774,34775],{"xmlns":890},[892,34776,34777,34797],{},[895,34778,34779,34781,34783,34785,34787,34789,34791,34793,34795],{},[898,34780,1703],{},[898,34782,8194],{},[898,34784,1769],{},[1656,34786,1713],{},[898,34788,3768],{"mathvariant":1723},[898,34790,1769],{},[898,34792,1782],{"mathvariant":1723},[898,34794,3768],{"mathvariant":1723},[898,34796,8184],{},[902,34798,34799],{"encoding":904},"MPS = \\mathrm{d}S\u002F\\mathrm{d}Y",", vazba ",[883,34802,34804],{"className":34803},[886],[888,34805,34806],{"xmlns":890},[892,34807,34808,34828],{},[895,34809,34810,34812,34814,34816,34818,34820,34822,34824,34826],{},[898,34811,1703],{},[898,34813,8194],{},[898,34815,1766],{},[1656,34817,3633],{},[898,34819,1703],{},[898,34821,8194],{},[898,34823,1769],{},[1656,34825,1713],{},[1667,34827,1669],{},[902,34829,34830],{"encoding":904},"MPC + MPS = 1"," (7.5). V lineárním modelu ",[883,34833,34835],{"className":34834},[886],[888,34836,34837],{"xmlns":890},[892,34838,34839,34851],{},[895,34840,34841,34843,34845,34847,34849],{},[898,34842,1703],{},[898,34844,8194],{},[898,34846,1766],{},[1656,34848,1713],{},[898,34850,207],{},[902,34852,28610],{"encoding":904},[883,34854,34856],{"className":34855},[886],[888,34857,34858],{"xmlns":890},[892,34859,34860,34876],{},[895,34861,34862,34864,34866,34868,34870,34872,34874],{},[898,34863,1703],{},[898,34865,8194],{},[898,34867,1769],{},[1656,34869,1713],{},[1667,34871,1669],{},[1656,34873,3964],{},[898,34875,207],{},[902,34877,28636],{"encoding":904},[123,34879,34880,34883,34884],{},[38,34881,34882],{},"Modely národní ekonomiky"," postupně bohatnou:\n",[120,34885,34886,34973,35042],{},[123,34887,34888,6960,34905,34926,34927,1673],{},[883,34889,34891],{"className":34890},[886],[888,34892,34893],{"xmlns":890},[892,34894,34895,34903],{},[895,34896,34897,34899,34901],{},[898,34898,1766],{},[2461,34900,21025],{},[898,34902,20919],{},[902,34904,21030],{"encoding":904},[883,34906,34908],{"className":34907},[886],[888,34909,34910],{"xmlns":890},[892,34911,34912,34924],{},[895,34913,34914,34916,34918,34920,34922],{},[898,34915,8184],{},[1656,34917,1713],{},[898,34919,1766],{},[1656,34921,3633],{},[898,34923,20919],{},[902,34925,23476],{"encoding":904}," (uzavřená ekonomika bez vlády), ",[883,34928,34930],{"className":34929},[886],[888,34931,34932],{"xmlns":890},[892,34933,34934,34970],{},[895,34935,34936,34942,34944,34946,34948,34950,34956,34958,34960,34962,34964,34966,34968],{},[2062,34937,34938,34940],{},[898,34939,8184],{},[898,34941,1842],{},[1656,34943,1713],{},[1656,34945,1659],{"stretchy":1658},[898,34947,3403],{},[1656,34949,3633],{},[2062,34951,34952,34954],{},[898,34953,20919],{},[1656,34955,8187],{},[1656,34957,1683],{"stretchy":1658},[898,34959,1782],{"mathvariant":1723},[1656,34961,1659],{"stretchy":1658},[1667,34963,1669],{},[1656,34965,3964],{},[898,34967,207],{},[1656,34969,1683],{"stretchy":1658},[902,34971,34972],{"encoding":904},"Y^E = (b + I^*)\u002F(1-a)",[123,34974,34975,34996,34997,35016,35017,1673],{},[883,34976,34978],{"className":34977},[886],[888,34979,34980],{"xmlns":890},[892,34981,34982,34994],{},[895,34983,34984,34986,34988,34990,34992],{},[898,34985,1766],{},[2461,34987,21025],{},[898,34989,20919],{},[2461,34991,21025],{},[898,34993,20847],{},[902,34995,26943],{"encoding":904},": přidává vládu, zdanění ",[883,34998,35000],{"className":34999},[886],[888,35001,35002],{"xmlns":890},[892,35003,35004,35014],{},[895,35005,35006,35008,35010,35012],{},[898,35007,11577],{},[1656,35009,1659],{"stretchy":1658},[898,35011,8184],{},[1656,35013,1683],{"stretchy":1658},[902,35015,30937],{"encoding":904}," a disponibilní důchod ",[883,35018,35020],{"className":35019},[886],[888,35021,35022],{"xmlns":890},[892,35023,35024,35040],{},[895,35025,35026,35032,35034,35036,35038],{},[1661,35027,35028,35030],{},[898,35029,8184],{},[898,35031,6787],{},[1656,35033,1713],{},[898,35035,8184],{},[1656,35037,3964],{},[898,35039,11577],{},[902,35041,30436],{"encoding":904},[123,35043,35044,35069,35070,30312,35091,1863],{},[883,35045,35047],{"className":35046},[886],[888,35048,35049],{"xmlns":890},[892,35050,35051,35067],{},[895,35052,35053,35055,35057,35059,35061,35063,35065],{},[898,35054,1766],{},[2461,35056,21025],{},[898,35058,20919],{},[2461,35060,21025],{},[898,35062,20847],{},[2461,35064,21025],{},[898,35066,21055],{},[902,35068,21058],{"encoding":904},": otevírá ekonomiku čistým exportem ",[883,35071,35073],{"className":35072},[886],[888,35074,35075],{"xmlns":890},[892,35076,35077,35089],{},[895,35078,35079,35081,35083,35085,35087],{},[898,35080,21055],{},[1656,35082,1713],{},[898,35084,2161],{},[1656,35086,3964],{},[898,35088,1703],{},[902,35090,31977],{"encoding":904},[883,35092,35094],{"className":35093},[886],[888,35095,35096],{"xmlns":890},[892,35097,35098,35116],{},[895,35099,35100,35102,35104,35106,35108,35114],{},[898,35101,1703],{},[1656,35103,1713],{},[898,35105,1703],{},[1656,35107,1659],{"stretchy":1658},[1661,35109,35110,35112],{},[898,35111,8184],{},[898,35113,6787],{},[1656,35115,1683],{"stretchy":1658},[902,35117,35118],{"encoding":904},"M = M(Y_D)",[123,35120,35121,35124,35125,1643,35128,35186],{},[38,35122,35123],{},"Multiplikátory"," (parciální derivace rovnovážných veličin podle exogenních) — klíčový ",[38,35126,35127],{},"multiplikátor investic",[883,35129,35131],{"className":35130},[886],[888,35132,35133],{"xmlns":890},[892,35134,35135,35183],{},[895,35136,35137,35139,35145,35147,35149,35155,35157,35159,35161,35163,35165,35167,35169,35171,35173,35175,35177,35179,35181],{},[898,35138,3300],{"mathvariant":1723},[2062,35140,35141,35143],{},[898,35142,8184],{},[898,35144,1842],{},[898,35146,1782],{"mathvariant":1723},[898,35148,3300],{"mathvariant":1723},[2062,35150,35151,35153],{},[898,35152,20919],{},[1656,35154,8187],{},[1656,35156,1713],{},[1667,35158,1669],{},[898,35160,1782],{"mathvariant":1723},[1656,35162,1659],{"stretchy":1658},[1667,35164,1669],{},[1656,35166,3964],{},[898,35168,207],{},[1656,35170,1683],{"stretchy":1658},[1656,35172,1713],{},[1667,35174,1669],{},[898,35176,1782],{"mathvariant":1723},[898,35178,1703],{},[898,35180,8194],{},[898,35182,1769],{},[902,35184,35185],{"encoding":904},"\\partial Y^E\u002F\\partial I^* = 1\u002F(1-a) = 1\u002FMPS"," (Keynesův multiplikátor).",[123,35188,35189,35191,35192,35207,35208,10722,35225,35240,35241,35266,35267,1863],{},[38,35190,945],{}," doplňuje obraz o trh peněz: investice závisejí na úrokové míře, ",[883,35193,35195],{"className":35194},[886],[888,35196,35197],{"xmlns":890},[892,35198,35199,35205],{},[895,35200,35201,35203],{},[898,35202,20919],{},[898,35204,1769],{},[902,35206,20786],{"encoding":904}," popisuje rovnováhu trhu zboží (",[883,35209,35211],{"className":35210},[886],[888,35212,35213],{"xmlns":890},[892,35214,35215,35223],{},[895,35216,35217,35219,35221],{},[898,35218,20919],{},[1656,35220,1713],{},[898,35222,1769],{},[902,35224,21446],{"encoding":904},[883,35226,35228],{"className":35227},[886],[888,35229,35230],{"xmlns":890},[892,35231,35232,35238],{},[895,35233,35234,35236],{},[898,35235,18539],{},[898,35237,1703],{},[902,35239,20793],{"encoding":904}," rovnováhu trhu peněz (",[883,35242,35244],{"className":35243},[886],[888,35245,35246],{"xmlns":890},[892,35247,35248,35264],{},[895,35249,35250,35256,35258],{},[2062,35251,35252,35254],{},[898,35253,1703],{},[898,35255,6787],{},[1656,35257,1713],{},[2062,35259,35260,35262],{},[898,35261,1703],{},[1656,35263,8187],{},[902,35265,22213],{"encoding":904},"); průsečík dává ",[883,35268,35270],{"className":35269},[886],[888,35271,35272],{"xmlns":890},[892,35273,35274,35294],{},[895,35275,35276,35278,35284,35286,35292],{},[1656,35277,1659],{"stretchy":1658},[2062,35279,35280,35282],{},[898,35281,8184],{},[898,35283,1842],{},[1656,35285,1673],{"separator":1672},[2062,35287,35288,35290],{},[898,35289,20776],{},[898,35291,1842],{},[1656,35293,1683],{"stretchy":1658},[902,35295,20830],{"encoding":904},[115,35297,10198],{"id":10197},[120,35299,35300,35338,35378,35468,35550,35604,35660,35719,35754,35759,35831,35906,35992,36054,36122,36180,36233,36272],{},[123,35301,35302,2533,35305,34623],{},[38,35303,35304],{},"Hrubý národní produkt (GNP)",[883,35306,35308],{"className":35307},[886],[888,35309,35310],{"xmlns":890},[892,35311,35312,35336],{},[895,35313,35314,35316,35318,35320,35322,35324,35326,35328,35330,35332,35334],{},[898,35315,20847],{},[898,35317,27017],{},[898,35319,8194],{},[1656,35321,1713],{},[898,35323,1766],{},[1656,35325,3633],{},[898,35327,20919],{},[1656,35329,3633],{},[898,35331,20847],{},[1656,35333,3633],{},[898,35335,21055],{},[902,35337,34622],{"encoding":904},[123,35339,35340,35356,35357,1863],{},[38,35341,35342,35343],{},"Národní důchod ",[883,35344,35346],{"className":35345},[886],[888,35347,35348],{"xmlns":890},[892,35349,35350,35354],{},[895,35351,35352],{},[898,35353,8184],{},[902,35355,8184],{"encoding":904}," — součet důchodů domácností; v modelech ",[883,35358,35360],{"className":35359},[886],[888,35361,35362],{"xmlns":890},[892,35363,35364,35376],{},[895,35365,35366,35368,35370,35372,35374],{},[898,35367,20847],{},[898,35369,27017],{},[898,35371,8194],{},[1656,35373,3815],{},[898,35375,8184],{},[902,35377,34587],{"encoding":904},[123,35379,35380,35406,35407,1343,35430,1343,35451,1863],{},[38,35381,35382,35383],{},"Funkce spotřeby ",[883,35384,35386],{"className":35385},[886],[888,35387,35388],{"xmlns":890},[892,35389,35390,35404],{},[895,35391,35392,35394,35396,35398,35400,35402],{},[898,35393,1766],{},[1656,35395,1713],{},[898,35397,1766],{},[1656,35399,1659],{"stretchy":1658},[898,35401,8184],{},[1656,35403,1683],{"stretchy":1658},[902,35405,29461],{"encoding":904}," — lineární model ",[883,35408,35410],{"className":35409},[886],[888,35411,35412],{"xmlns":890},[892,35413,35414,35428],{},[895,35415,35416,35418,35420,35422,35424,35426],{},[898,35417,1766],{},[1656,35419,1713],{},[898,35421,207],{},[898,35423,8184],{},[1656,35425,3633],{},[898,35427,3403],{},[902,35429,27641],{"encoding":904},[883,35431,35433],{"className":35432},[886],[888,35434,35435],{"xmlns":890},[892,35436,35437,35449],{},[895,35438,35439,35441,35443,35445,35447],{},[1667,35440,4032],{},[1656,35442,4373],{},[898,35444,207],{},[1656,35446,4373],{},[1667,35448,1669],{},[902,35450,27558],{"encoding":904},[883,35452,35454],{"className":35453},[886],[888,35455,35456],{"xmlns":890},[892,35457,35458,35466],{},[895,35459,35460,35462,35464],{},[898,35461,3403],{},[1656,35463,2850],{},[1667,35465,4032],{},[902,35467,27536],{"encoding":904},[123,35469,35470,2533,35497,35518,35519,1863],{},[38,35471,35472,35473],{},"Funkce úspor ",[883,35474,35476],{"className":35475},[886],[888,35477,35478],{"xmlns":890},[892,35479,35480,35494],{},[895,35481,35482,35484,35486,35488,35490,35492],{},[898,35483,1769],{},[1656,35485,1713],{},[898,35487,1769],{},[1656,35489,1659],{"stretchy":1658},[898,35491,8184],{},[1656,35493,1683],{"stretchy":1658},[902,35495,35496],{"encoding":904},"S = S(Y)",[883,35498,35500],{"className":35499},[886],[888,35501,35502],{"xmlns":890},[892,35503,35504,35516],{},[895,35505,35506,35508,35510,35512,35514],{},[898,35507,8184],{},[1656,35509,1713],{},[898,35511,1766],{},[1656,35513,3633],{},[898,35515,1769],{},[902,35517,21428],{"encoding":904},"; lineární ",[883,35520,35522],{"className":35521},[886],[888,35523,35524],{"xmlns":890},[892,35525,35526,35548],{},[895,35527,35528,35530,35532,35534,35536,35538,35540,35542,35544,35546],{},[898,35529,1769],{},[1656,35531,1713],{},[1656,35533,1659],{"stretchy":1658},[1667,35535,1669],{},[1656,35537,3964],{},[898,35539,207],{},[1656,35541,1683],{"stretchy":1658},[898,35543,8184],{},[1656,35545,3964],{},[898,35547,3403],{},[902,35549,27890],{"encoding":904},[123,35551,35552,2533,35555,1343,35578,1863],{},[38,35553,35554],{},"Autonomní spotřeba\u002Fúspory",[883,35556,35558],{"className":35557},[886],[888,35559,35560],{"xmlns":890},[892,35561,35562,35576],{},[895,35563,35564,35566,35568,35570,35572,35574],{},[898,35565,1766],{},[1656,35567,1659],{"stretchy":1658},[1667,35569,4032],{},[1656,35571,1683],{"stretchy":1658},[1656,35573,1713],{},[898,35575,3403],{},[902,35577,28282],{"encoding":904},[883,35579,35581],{"className":35580},[886],[888,35582,35583],{"xmlns":890},[892,35584,35585,35601],{},[895,35586,35587,35589,35591,35593,35595,35597,35599],{},[898,35588,1769],{},[1656,35590,1659],{"stretchy":1658},[1667,35592,4032],{},[1656,35594,1683],{"stretchy":1658},[1656,35596,1713],{},[1656,35598,3964],{},[898,35600,3403],{},[902,35602,35603],{"encoding":904},"S(0) = -b",[123,35605,35606,35638,35639,12702],{},[38,35607,35608,35609],{},"Mezní sklon ke spotřebě ",[883,35610,35612],{"className":35611},[886],[888,35613,35614],{"xmlns":890},[892,35615,35616,35636],{},[895,35617,35618,35620,35622,35624,35626,35628,35630,35632,35634],{},[898,35619,1703],{},[898,35621,8194],{},[898,35623,1766],{},[1656,35625,1713],{},[898,35627,3768],{"mathvariant":1723},[898,35629,1766],{},[898,35631,1782],{"mathvariant":1723},[898,35633,3768],{"mathvariant":1723},[898,35635,8184],{},[902,35637,34769],{"encoding":904}," (v lineárním modelu ",[883,35640,35642],{"className":35641},[886],[888,35643,35644],{"xmlns":890},[892,35645,35646,35658],{},[895,35647,35648,35650,35652,35654,35656],{},[898,35649,1703],{},[898,35651,8194],{},[898,35653,1766],{},[1656,35655,1713],{},[898,35657,207],{},[902,35659,28610],{"encoding":904},[123,35661,35662,35638,35694,12702],{},[38,35663,35664,35665],{},"Mezní sklon k úsporám ",[883,35666,35668],{"className":35667},[886],[888,35669,35670],{"xmlns":890},[892,35671,35672,35692],{},[895,35673,35674,35676,35678,35680,35682,35684,35686,35688,35690],{},[898,35675,1703],{},[898,35677,8194],{},[898,35679,1769],{},[1656,35681,1713],{},[898,35683,3768],{"mathvariant":1723},[898,35685,1769],{},[898,35687,1782],{"mathvariant":1723},[898,35689,3768],{"mathvariant":1723},[898,35691,8184],{},[902,35693,34799],{"encoding":904},[883,35695,35697],{"className":35696},[886],[888,35698,35699],{"xmlns":890},[892,35700,35701,35717],{},[895,35702,35703,35705,35707,35709,35711,35713,35715],{},[898,35704,1703],{},[898,35706,8194],{},[898,35708,1769],{},[1656,35710,1713],{},[1667,35712,1669],{},[1656,35714,3964],{},[898,35716,207],{},[902,35718,28636],{"encoding":904},[123,35720,35721,1643,35724,35753],{},[38,35722,35723],{},"Vztah",[883,35725,35727],{"className":35726},[886],[888,35728,35729],{"xmlns":890},[892,35730,35731,35751],{},[895,35732,35733,35735,35737,35739,35741,35743,35745,35747,35749],{},[898,35734,1703],{},[898,35736,8194],{},[898,35738,1766],{},[1656,35740,3633],{},[898,35742,1703],{},[898,35744,8194],{},[898,35746,1769],{},[1656,35748,1713],{},[1667,35750,1669],{},[902,35752,34830],{"encoding":904}," (7.5).",[123,35755,35756,35758],{},[38,35757,29304],{}," — rovnováha agregátní poptávky a nabídky.",[123,35760,35761,35764,35765,24520,35786,1863],{},[38,35762,35763],{},"Model C-I"," — uzavřená ekonomika bez vlády; ",[883,35766,35768],{"className":35767},[886],[888,35769,35770],{"xmlns":890},[892,35771,35772,35784],{},[895,35773,35774,35776,35778,35780,35782],{},[898,35775,8184],{},[1656,35777,1713],{},[898,35779,1766],{},[1656,35781,3633],{},[898,35783,20919],{},[902,35785,23476],{"encoding":904},[883,35787,35789],{"className":35788},[886],[888,35790,35791],{"xmlns":890},[892,35792,35793,35829],{},[895,35794,35795,35801,35803,35805,35807,35809,35815,35817,35819,35821,35823,35825,35827],{},[2062,35796,35797,35799],{},[898,35798,8184],{},[898,35800,1842],{},[1656,35802,1713],{},[1656,35804,1659],{"stretchy":1658},[898,35806,3403],{},[1656,35808,3633],{},[2062,35810,35811,35813],{},[898,35812,20919],{},[1656,35814,8187],{},[1656,35816,1683],{"stretchy":1658},[898,35818,1782],{"mathvariant":1723},[1656,35820,1659],{"stretchy":1658},[1667,35822,1669],{},[1656,35824,3964],{},[898,35826,207],{},[1656,35828,1683],{"stretchy":1658},[902,35830,34972],{"encoding":904},[123,35832,35833,35836,35837,1343,35856,24520,35881,1863],{},[38,35834,35835],{},"Model C-I-G"," — ekonomika s vládou, zdaněním ",[883,35838,35840],{"className":35839},[886],[888,35841,35842],{"xmlns":890},[892,35843,35844,35854],{},[895,35845,35846,35848,35850,35852],{},[898,35847,11577],{},[1656,35849,1659],{"stretchy":1658},[898,35851,8184],{},[1656,35853,1683],{"stretchy":1658},[902,35855,30937],{"encoding":904},[883,35857,35859],{"className":35858},[886],[888,35860,35861],{"xmlns":890},[892,35862,35863,35879],{},[895,35864,35865,35871,35873,35875,35877],{},[1661,35866,35867,35869],{},[898,35868,8184],{},[898,35870,6787],{},[1656,35872,1713],{},[898,35874,8184],{},[1656,35876,3964],{},[898,35878,11577],{},[902,35880,30436],{"encoding":904},[883,35882,35884],{"className":35883},[886],[888,35885,35886],{"xmlns":890},[892,35887,35888,35904],{},[895,35889,35890,35892,35894,35896,35898,35900,35902],{},[898,35891,8184],{},[1656,35893,1713],{},[898,35895,1766],{},[1656,35897,3633],{},[898,35899,20919],{},[1656,35901,3633],{},[898,35903,20847],{},[902,35905,30407],{"encoding":904},[123,35907,35908,35911,35912,35933,35934,24520,35958,1863],{},[38,35909,35910],{},"Model C-I-G-X"," — otevřená ekonomika s čistým exportem ",[883,35913,35915],{"className":35914},[886],[888,35916,35917],{"xmlns":890},[892,35918,35919,35931],{},[895,35920,35921,35923,35925,35927,35929],{},[898,35922,21055],{},[1656,35924,1713],{},[898,35926,2161],{},[1656,35928,3964],{},[898,35930,1703],{},[902,35932,31977],{"encoding":904},", importem ",[883,35935,35937],{"className":35936},[886],[888,35938,35939],{"xmlns":890},[892,35940,35941,35955],{},[895,35942,35943,35945,35947,35953],{},[898,35944,1703],{},[1656,35946,1659],{"stretchy":1658},[1661,35948,35949,35951],{},[898,35950,8184],{},[898,35952,6787],{},[1656,35954,1683],{"stretchy":1658},[902,35956,35957],{"encoding":904},"M(Y_D)",[883,35959,35961],{"className":35960},[886],[888,35962,35963],{"xmlns":890},[892,35964,35965,35989],{},[895,35966,35967,35969,35971,35973,35975,35977,35979,35981,35983,35985,35987],{},[898,35968,8184],{},[1656,35970,1713],{},[898,35972,1766],{},[1656,35974,3633],{},[898,35976,20919],{},[1656,35978,3633],{},[898,35980,20847],{},[1656,35982,3633],{},[898,35984,2161],{},[1656,35986,3964],{},[898,35988,1703],{},[902,35990,35991],{"encoding":904},"Y = C + I + G + B - M",[123,35993,35994,2533,35997,35186],{},[38,35995,35996],{},"Multiplikátor investic",[883,35998,36000],{"className":35999},[886],[888,36001,36002],{"xmlns":890},[892,36003,36004,36052],{},[895,36005,36006,36008,36014,36016,36018,36024,36026,36028,36030,36032,36034,36036,36038,36040,36042,36044,36046,36048,36050],{},[898,36007,3300],{"mathvariant":1723},[2062,36009,36010,36012],{},[898,36011,8184],{},[898,36013,1842],{},[898,36015,1782],{"mathvariant":1723},[898,36017,3300],{"mathvariant":1723},[2062,36019,36020,36022],{},[898,36021,20919],{},[1656,36023,8187],{},[1656,36025,1713],{},[1667,36027,1669],{},[898,36029,1782],{"mathvariant":1723},[1656,36031,1659],{"stretchy":1658},[1667,36033,1669],{},[1656,36035,3964],{},[898,36037,207],{},[1656,36039,1683],{"stretchy":1658},[1656,36041,1713],{},[1667,36043,1669],{},[898,36045,1782],{"mathvariant":1723},[898,36047,1703],{},[898,36049,8194],{},[898,36051,1769],{},[902,36053,35185],{"encoding":904},[123,36055,36056,2533,36087,1343,36104,36121],{},[38,36057,24455,36058],{},[883,36059,36061],{"className":36060},[886],[888,36062,36063],{"xmlns":890},[892,36064,36065,36085],{},[895,36066,36067,36069,36071,36073,36075,36077,36079,36081,36083],{},[898,36068,20919],{},[1656,36070,1659],{"stretchy":1658},[898,36072,20776],{},[1656,36074,1683],{"stretchy":1658},[1656,36076,1713],{},[898,36078,1745],{},[898,36080,20776],{},[1656,36082,3633],{},[898,36084,3768],{},[902,36086,24485],{"encoding":904},[883,36088,36090],{"className":36089},[886],[888,36091,36092],{"xmlns":890},[892,36093,36094,36102],{},[895,36095,36096,36098,36100],{},[898,36097,1745],{},[1656,36099,4373],{},[1667,36101,4032],{},[902,36103,21249],{"encoding":904},[883,36105,36107],{"className":36106},[886],[888,36108,36109],{"xmlns":890},[892,36110,36111,36119],{},[895,36112,36113,36115,36117],{},[898,36114,3768],{},[1656,36116,2850],{},[1667,36118,4032],{},[902,36120,21228],{"encoding":904},"; klesající.",[123,36123,36124,36126,36127,36129,36130,36179],{},[38,36125,24574],{}," — rovnováha na trhu zboží (",[614,36128,20789],{},"); ",[883,36131,36133],{"className":36132},[886],[888,36134,36135],{"xmlns":890},[892,36136,36137,36177],{},[895,36138,36139,36141,36143,36155,36157,36159],{},[898,36140,8184],{},[1656,36142,1713],{},[3294,36144,36145,36147],{},[898,36146,1745],{},[895,36148,36149,36151,36153],{},[1667,36150,1669],{},[1656,36152,3964],{},[898,36154,207],{},[898,36156,20776],{},[1656,36158,3633],{},[3294,36160,36161,36169],{},[895,36162,36163,36165,36167],{},[898,36164,3403],{},[1656,36166,3633],{},[898,36168,3768],{},[895,36170,36171,36173,36175],{},[1667,36172,1669],{},[1656,36174,3964],{},[898,36176,207],{},[902,36178,24627],{"encoding":904}," (7.14); klesající.",[123,36181,36182,36184,36185,36129,36187,36232],{},[38,36183,24773],{}," — rovnováha na trhu peněz (",[614,36186,20796],{},[883,36188,36190],{"className":36189},[886],[888,36191,36192],{"xmlns":890},[892,36193,36194,36230],{},[895,36195,36196,36202,36204,36210,36212,36214,36220,36222,36224],{},[2062,36197,36198,36200],{},[898,36199,1703],{},[1656,36201,8187],{},[1656,36203,1713],{},[1661,36205,36206,36208],{},[898,36207,21970],{},[1667,36209,1669],{},[898,36211,8184],{},[1656,36213,3633],{},[1661,36215,36216,36218],{},[898,36217,21970],{},[1667,36219,1680],{},[898,36221,20776],{},[1656,36223,3633],{},[1661,36225,36226,36228],{},[898,36227,21970],{},[1667,36229,2617],{},[902,36231,24821],{"encoding":904}," (7.15); rostoucí.",[123,36234,36235,2533,36238,1863],{},[38,36236,36237],{},"Transakční, opatrnostní a spekulační poptávka po penězích",[883,36239,36241],{"className":36240},[886],[888,36242,36243],{"xmlns":890},[892,36244,36245,36269],{},[895,36246,36247,36253,36255,36261,36263],{},[2062,36248,36249,36251],{},[898,36250,1703],{},[898,36252,6787],{},[1656,36254,1713],{},[1661,36256,36257,36259],{},[898,36258,18539],{},[1667,36260,1669],{},[1656,36262,3633],{},[1661,36264,36265,36267],{},[898,36266,18539],{},[1667,36268,1680],{},[902,36270,36271],{"encoding":904},"M^D = L_1 + L_2",[123,36273,36274,24831,36276,22712,36289,1896,36304,36319,36320,1863],{},[38,36275,945],{},[883,36277,36279],{"className":36278},[886],[888,36280,36281],{"xmlns":890},[892,36282,36283,36287],{},[895,36284,36285],{},[898,36286,1842],{},[902,36288,1842],{"encoding":904},[883,36290,36292],{"className":36291},[886],[888,36293,36294],{"xmlns":890},[892,36295,36296,36302],{},[895,36297,36298,36300],{},[898,36299,20919],{},[898,36301,1769],{},[902,36303,20786],{"encoding":904},[883,36305,36307],{"className":36306},[886],[888,36308,36309],{"xmlns":890},[892,36310,36311,36317],{},[895,36312,36313,36315],{},[898,36314,18539],{},[898,36316,1703],{},[902,36318,20793],{"encoding":904}," určuje ",[883,36321,36323],{"className":36322},[886],[888,36324,36325],{"xmlns":890},[892,36326,36327,36347],{},[895,36328,36329,36331,36337,36339,36345],{},[1656,36330,1659],{"stretchy":1658},[2062,36332,36333,36335],{},[898,36334,8184],{},[898,36336,1842],{},[1656,36338,1673],{"separator":1672},[2062,36340,36341,36343],{},[898,36342,20776],{},[898,36344,1842],{},[1656,36346,1683],{"stretchy":1658},[902,36348,20830],{"encoding":904},[115,36350,10640],{"id":10639},[120,36352,36353,36360,36367],{},[123,36354,36355,1643,36357],{},[38,36356,10742],{},[207,36358,1869],{"className":36359,"dataFsResolvedFilePath":10746,"href":10747},[210],[123,36361,36362,1643,36364],{},[38,36363,24939],{},[207,36365,24943],{"className":36366,"dataFsResolvedFilePath":868,"href":869},[210],[123,36368,36369,36371],{},[38,36370,24958],{},[120,36372,36373,36379,36385,36391],{},[123,36374,36375,36378],{},[207,36376,24999],{"className":36377,"dataFsResolvedFilePath":943,"href":944},[210]," — detailní IS-LM analýza (odvození křivek, Příklad 7.6, fiskální vs monetární politika)",[123,36380,36381,36384],{},[207,36382,24966],{"className":36383,"dataFsResolvedFilePath":800,"href":801},[210]," — paralela mikroekonomických multiplikátorů (multiplikátory rovnovážné ceny a množství)",[123,36386,36387,36390],{},[207,36388,11745],{"className":36389,"dataFsResolvedFilePath":827,"href":828},[210]," — mikroekonomické analogie, článek 2.4 o multiplikátorech",[123,36392,36393,36396,36397,1343,36414,36431],{},[207,36394,1145],{"className":36395,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro ",[883,36398,36400],{"className":36399},[886],[888,36401,36402],{"xmlns":890},[892,36403,36404,36412],{},[895,36405,36406,36408,36410],{},[898,36407,1703],{},[898,36409,8194],{},[898,36411,1766],{},[902,36413,26768],{"encoding":904},[883,36415,36417],{"className":36416},[886],[888,36418,36419],{"xmlns":890},[892,36420,36421,36429],{},[895,36422,36423,36425,36427],{},[898,36424,1703],{},[898,36426,8194],{},[898,36428,1769],{},[902,36430,28380],{"encoding":904}," a interpretaci změn diferenciálem",{"title":641,"searchDepth":642,"depth":642,"links":36433},[36434,36435,36436,36437,36442,36445,36446,36453,36458,36463,36466,36467,36468,36469],{"id":1637,"depth":642,"text":1638},{"id":26877,"depth":642,"text":26878},{"id":26997,"depth":642,"text":26998},{"id":27250,"depth":642,"text":27251,"children":36438},[36439,36440,36441],{"id":27254,"depth":649,"text":27255},{"id":27465,"depth":649,"text":27466},{"id":27972,"depth":649,"text":27973},{"id":28292,"depth":642,"text":28293,"children":36443},[36444],{"id":28808,"depth":649,"text":28809},{"id":29303,"depth":642,"text":29304},{"id":29330,"depth":642,"text":29331,"children":36447},[36448,36449,36450,36452],{"id":29341,"depth":649,"text":29342},{"id":29411,"depth":649,"text":29412},{"id":29592,"depth":649,"text":36451},"Výpočet YEY^E",{"id":29735,"depth":649,"text":29736},{"id":30113,"depth":642,"text":30114,"children":36454},[36455,36456,36457],{"id":30117,"depth":649,"text":29342},{"id":30566,"depth":649,"text":29412},{"id":31222,"depth":649,"text":31223},{"id":32008,"depth":642,"text":32009,"children":36459},[36460,36461,36462],{"id":32012,"depth":649,"text":29342},{"id":32157,"depth":649,"text":29412},{"id":32427,"depth":649,"text":32428},{"id":33350,"depth":642,"text":33351,"children":36464},[36465],{"id":33546,"depth":649,"text":33547},{"id":34096,"depth":642,"text":34097},{"id":34556,"depth":642,"text":34557},{"id":10197,"depth":642,"text":10198},{"id":10639,"depth":642,"text":10640},{},"\u002Ftopics\u002Fnarodni-duchod",{"title":936,"description":641},[1138,1137],"topics\u002Fnarodni-duchod",[1128,24952,1143,36476,36477,36478,24999,26606],"gnp","mpc","mps","BMicmr68yKQbb8qpoE9KfzU5NFshq3Inq6w0tL8-GjU",{"id":36481,"title":8672,"body":36482,"course":1128,"courses":659,"created":10774,"description":641,"extension":661,"meta":45432,"navigation":664,"path":45433,"seo":45434,"sources":45435,"stem":45436,"tags":45437,"type":10786,"updated":677,"__hash__":45441},"topics\u002Ftopics\u002Foptimalizace-spotrebitele.md",{"type":9,"value":36483,"toc":45401},[36484,36487,36489,36713,36717,36770,36837,36948,37104,37108,37224,37228,37231,37353,37356,37549,37573,37641,37802,37820,37886,38264,38268,38275,38519,38575,38579,38642,38759,38886,38917,39037,39119,39122,39244,39437,39658,39662,39702,39807,39864,39964,40141,40271,40324,40327,40414,40418,40594,40598,40601,40686,40689,40746,40851,40855,40976,40979,41162,41165,41272,41481,41801,41848,41921,41995,41997,42221,42456,42724,42728,42731,42836,42893,42927,42974,43007,43091,43093,43325,43458,43535,43657,43812,43816,43957,43964,44188,44199,44203,44207,44311,44453,44562,44661,44665,44824,44934,44936,45328,45330],[12,36485,8672],{"id":36486},"optimalizace-spotřebitele-lagrange-poptávka-minimalizace-výdajů",[115,36488,1638],{"id":1637},[724,36490,36491,36493,36494,36528,36529,36532,36533,36564,36565,36611,36612,8278,36615,8325,36657,36674,36675,36678,36679,36708,36709,36712],{},[38,36492,913],{}," řeší, jaký svazek zboží ",[883,36495,36497],{"className":36496},[886],[888,36498,36499],{"xmlns":890},[892,36500,36501,36525],{},[895,36502,36503,36505,36513,36515,36523],{},[1656,36504,3453],{"stretchy":1658},[1715,36506,36507,36509,36511],{},[898,36508,1665],{},[1667,36510,1669],{},[1656,36512,8187],{},[1656,36514,1673],{"separator":1672},[1715,36516,36517,36519,36521],{},[898,36518,1665],{},[1667,36520,1680],{},[1656,36522,8187],{},[1656,36524,3462],{"stretchy":1658},[902,36526,36527],{"encoding":904},"[Q_1^*, Q_2^*]"," zvolit při známých cenách a důchodu. Existují dvě ekvivalentní formulace: ",[38,36530,36531],{},"primární úloha"," — maximalizace užitečnosti ",[883,36534,36536],{"className":36535},[886],[888,36537,36538],{"xmlns":890},[892,36539,36540,36562],{},[895,36541,36542,36544,36546,36552,36554,36560],{},[898,36543,900],{},[1656,36545,1659],{"stretchy":1658},[1661,36547,36548,36550],{},[898,36549,1665],{},[1667,36551,1669],{},[1656,36553,1673],{"separator":1672},[1661,36555,36556,36558],{},[898,36557,1665],{},[1667,36559,1680],{},[1656,36561,1683],{"stretchy":1658},[902,36563,1686],{"encoding":904}," při rozpočtovém omezení ",[883,36566,36568],{"className":36567},[886],[888,36569,36570],{"xmlns":890},[892,36571,36572,36608],{},[895,36573,36574,36580,36582,36588,36594,36596,36602],{},[2062,36575,36576,36578],{},[898,36577,8184],{},[1656,36579,8187],{},[1656,36581,1713],{},[1661,36583,36584,36586],{},[898,36585,8194],{},[1667,36587,1669],{},[1661,36589,36590,36592],{},[898,36591,1665],{},[1667,36593,1669],{},[1656,36595,3633],{},[1661,36597,36598,36600],{},[898,36599,8194],{},[1667,36601,1680],{},[1661,36603,36604,36606],{},[898,36605,1665],{},[1667,36607,1680],{},[902,36609,36610],{"encoding":904},"Y^* = P_1 Q_1 + P_2 Q_2",", a ",[38,36613,36614],{},"duální úloha",[883,36616,36618],{"className":36617},[886],[888,36619,36620],{"xmlns":890},[892,36621,36622,36654],{},[895,36623,36624,36626,36628,36634,36640,36642,36648],{},[898,36625,1842],{},[1656,36627,1713],{},[1661,36629,36630,36632],{},[898,36631,8194],{},[1667,36633,1669],{},[1661,36635,36636,36638],{},[898,36637,1665],{},[1667,36639,1669],{},[1656,36641,3633],{},[1661,36643,36644,36646],{},[898,36645,8194],{},[1667,36647,1680],{},[1661,36649,36650,36652],{},[898,36651,1665],{},[1667,36653,1680],{},[902,36655,36656],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2",[883,36658,36660],{"className":36659},[886],[888,36661,36662],{"xmlns":890},[892,36663,36664,36672],{},[895,36665,36666],{},[2062,36667,36668,36670],{},[898,36669,900],{},[1656,36671,8187],{},[902,36673,8343],{"encoding":904},". Obě úlohy se řeší ",[207,36676,8399],{"className":36677,"dataFsResolvedFilePath":791,"href":792},[210]," a vedou na tentýž bod dotyku indiferenční křivky a rozpočtové přímky, v němž platí ",[883,36680,36682],{"className":36681},[886],[888,36683,36684],{"xmlns":890},[892,36685,36686,36706],{},[895,36687,36688,36690,36692,36698,36700],{},[2461,36689,7362],{},[1656,36691,1713],{},[1661,36693,36694,36696],{},[898,36695,8194],{},[1667,36697,1669],{},[898,36699,1782],{"mathvariant":1723},[1661,36701,36702,36704],{},[898,36703,8194],{},[1667,36705,1680],{},[902,36707,10631],{"encoding":904},". Výstupem jsou ",[38,36710,36711],{},"funkce poptávky"," — Marshallova (závislá na důchodu) a Hicksova (závislá na hladině užitečnosti).",[115,36714,36716],{"id":36715},"úvod-proč-optimalizovat","Úvod — proč optimalizovat",[724,36718,36719,36720,36738,36739,36769],{},"Racionální spotřebitel má omezený důchod a musí se rozhodnout, jak jej rozdělit mezi spotřebovávané zboží. V modelu pro dvě zboží je k dispozici částka ",[883,36721,36723],{"className":36722},[886],[888,36724,36725],{"xmlns":890},[892,36726,36727,36735],{},[895,36728,36729],{},[2062,36730,36731,36733],{},[898,36732,8184],{},[1656,36734,8187],{},[902,36736,36737],{"encoding":904},"Y^*"," a ceny ",[883,36740,36742],{"className":36741},[886],[888,36743,36744],{"xmlns":890},[892,36745,36746,36766],{},[895,36747,36748,36756,36758],{},[1715,36749,36750,36752,36754],{},[898,36751,8194],{},[1667,36753,1669],{},[1656,36755,8187],{},[1656,36757,1673],{"separator":1672},[1715,36759,36760,36762,36764],{},[898,36761,8194],{},[1667,36763,1680],{},[1656,36765,8187],{},[902,36767,36768],{"encoding":904},"P_1^*, P_2^*",", rozpočtové omezení má tvar",[883,36771,36773],{"className":36772},[886],[888,36774,36775],{"xmlns":890,"display":2408},[892,36776,36777,36834],{},[2412,36778,36779],{"width":2414},[2416,36780,36781,36783,36827,36829],{},[2419,36782],{"width":2421},[2419,36784,36785],{},[895,36786,36787,36793,36795,36803,36809,36811,36819,36825],{},[2062,36788,36789,36791],{},[898,36790,8184],{},[1656,36792,8187],{},[1656,36794,1713],{},[1715,36796,36797,36799,36801],{},[898,36798,8194],{},[1667,36800,1669],{},[1656,36802,8187],{},[1661,36804,36805,36807],{},[898,36806,1665],{},[1667,36808,1669],{},[1656,36810,3633],{},[1715,36812,36813,36815,36817],{},[898,36814,8194],{},[1667,36816,1680],{},[1656,36818,8187],{},[1661,36820,36821,36823],{},[898,36822,1665],{},[1667,36824,1680],{},[1656,36826,1673],{"separator":1672},[2419,36828],{"width":2421},[2419,36830,36831],{},[2461,36832,36833],{},"(6.12)",[902,36835,36836],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2, \\tag{6.12}",[724,36838,36839,36840,36843,36844,1896,36880,36916,36917,36930,36931,36944,36945,1863],{},"geometricky ",[38,36841,36842],{},"rozpočtová přímka (budget line)"," procházející body ",[883,36845,36847],{"className":36846},[886],[888,36848,36849],{"xmlns":890},[892,36850,36851,36877],{},[895,36852,36853,36855,36861,36863,36871,36873,36875],{},[1656,36854,3453],{"stretchy":1658},[2062,36856,36857,36859],{},[898,36858,8184],{},[1656,36860,8187],{},[898,36862,1782],{"mathvariant":1723},[1715,36864,36865,36867,36869],{},[898,36866,8194],{},[1667,36868,1669],{},[1656,36870,8187],{},[1656,36872,1673],{"separator":1672},[1667,36874,4032],{},[1656,36876,3462],{"stretchy":1658},[902,36878,36879],{"encoding":904},"[Y^*\u002FP_1^*, 0]",[883,36881,36883],{"className":36882},[886],[888,36884,36885],{"xmlns":890},[892,36886,36887,36913],{},[895,36888,36889,36891,36893,36895,36901,36903,36911],{},[1656,36890,3453],{"stretchy":1658},[1667,36892,4032],{},[1656,36894,1673],{"separator":1672},[2062,36896,36897,36899],{},[898,36898,8184],{},[1656,36900,8187],{},[898,36902,1782],{"mathvariant":1723},[1715,36904,36905,36907,36909],{},[898,36906,8194],{},[1667,36908,1680],{},[1656,36910,8187],{},[1656,36912,3462],{"stretchy":1658},[902,36914,36915],{"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 ",[883,36918,36920],{"className":36919},[886],[888,36921,36922],{"xmlns":890},[892,36923,36924,36928],{},[895,36925,36926],{},[898,36927,900],{},[902,36929,900],{"encoding":904},", indiferenční křivky a ",[883,36932,36934],{"className":36933},[886],[888,36935,36936],{"xmlns":890},[892,36937,36938,36942],{},[895,36939,36940],{},[2461,36941,7362],{},[902,36943,7365],{"encoding":904}," — je shrnuta v ",[207,36946,880],{"className":36947,"dataFsResolvedFilePath":878,"href":879},[210],[1981,36949,36950],{},[724,36951,36952,36954,36955,1816,36957,36970,36971,36973,36974,36987,36988,1643,36991,37030,37031,37048,37049,37066,37067,37084,37085,37103],{},[883,36953,1987],{}," Pozor — dvě úlohy, totéž řešení\n",[38,36956,8134],{},[883,36958,36960],{"className":36959},[886],[888,36961,36962],{"xmlns":890},[892,36963,36964,36968],{},[895,36965,36966],{},[898,36967,900],{},[902,36969,900],{"encoding":904}," při pevném rozpočtu) a ",[38,36972,36614],{}," (min ",[883,36975,36977],{"className":36976},[886],[888,36978,36979],{"xmlns":890},[892,36980,36981,36985],{},[895,36982,36983],{},[898,36984,1842],{},[902,36986,1842],{"encoding":904}," při pevné užitečnosti) vedou na ",[38,36989,36990],{},"tentýž bod",[883,36992,36994],{"className":36993},[886],[888,36995,36996],{"xmlns":890},[892,36997,36998,37028],{},[895,36999,37000,37006,37008,37016,37018,37026],{},[2062,37001,37002,37004],{},[898,37003,1665],{},[1656,37005,8187],{},[1656,37007,3453],{"stretchy":1658},[1715,37009,37010,37012,37014],{},[898,37011,1665],{},[1667,37013,1669],{},[1656,37015,8187],{},[1656,37017,1673],{"separator":1672},[1715,37019,37020,37022,37024],{},[898,37021,1665],{},[1667,37023,1680],{},[1656,37025,8187],{},[1656,37027,3462],{"stretchy":1658},[902,37029,8443],{"encoding":904},". Rozdíl je v tom, co je „vstup\" a co „výstup\": u primární úlohy je zadán důchod ",[883,37032,37034],{"className":37033},[886],[888,37035,37036],{"xmlns":890},[892,37037,37038,37046],{},[895,37039,37040],{},[2062,37041,37042,37044],{},[898,37043,8184],{},[1656,37045,8187],{},[902,37047,36737],{"encoding":904}," a hledáme maximální ",[883,37050,37052],{"className":37051},[886],[888,37053,37054],{"xmlns":890},[892,37055,37056,37064],{},[895,37057,37058],{},[2062,37059,37060,37062],{},[898,37061,900],{},[1656,37063,8187],{},[902,37065,8343],{"encoding":904},"; u duální úlohy je zadána hladina ",[883,37068,37070],{"className":37069},[886],[888,37071,37072],{"xmlns":890},[892,37073,37074,37082],{},[895,37075,37076],{},[2062,37077,37078,37080],{},[898,37079,900],{},[1656,37081,8187],{},[902,37083,8343],{"encoding":904}," a hledáme minimální ",[883,37086,37088],{"className":37087},[886],[888,37089,37090],{"xmlns":890},[892,37091,37092,37100],{},[895,37093,37094],{},[2062,37095,37096,37098],{},[898,37097,1842],{},[1656,37099,8187],{},[902,37101,37102],{"encoding":904},"E^*",". Z pozorování je přirozenější minimalizace výdajů (výdaje lze měřit).",[115,37105,37107],{"id":37106},"maximalizace-užitečnosti-za-rozpočtového-omezení","Maximalizace užitečnosti za rozpočtového omezení",[724,37109,37110,37111,37142,37143,37219,37220,1863],{},"Úlohou je najít maximum ",[883,37112,37114],{"className":37113},[886],[888,37115,37116],{"xmlns":890},[892,37117,37118,37140],{},[895,37119,37120,37122,37124,37130,37132,37138],{},[898,37121,900],{},[1656,37123,1659],{"stretchy":1658},[1661,37125,37126,37128],{},[898,37127,1665],{},[1667,37129,1669],{},[1656,37131,1673],{"separator":1672},[1661,37133,37134,37136],{},[898,37135,1665],{},[1667,37137,1680],{},[1656,37139,1683],{"stretchy":1658},[902,37141,1686],{"encoding":904}," vázané podmínkou (6.12) ve tvaru ",[883,37144,37146],{"className":37145},[886],[888,37147,37148],{"xmlns":890},[892,37149,37150,37216],{},[895,37151,37152,37154,37156,37162,37164,37170,37172,37174,37180,37182,37190,37196,37198,37206,37212,37214],{},[898,37153,19780],{},[1656,37155,1659],{"stretchy":1658},[1661,37157,37158,37160],{},[898,37159,1665],{},[1667,37161,1669],{},[1656,37163,1673],{"separator":1672},[1661,37165,37166,37168],{},[898,37167,1665],{},[1667,37169,1680],{},[1656,37171,1683],{"stretchy":1658},[1656,37173,1713],{},[2062,37175,37176,37178],{},[898,37177,8184],{},[1656,37179,8187],{},[1656,37181,3964],{},[1715,37183,37184,37186,37188],{},[898,37185,8194],{},[1667,37187,1669],{},[1656,37189,8187],{},[1661,37191,37192,37194],{},[898,37193,1665],{},[1667,37195,1669],{},[1656,37197,3964],{},[1715,37199,37200,37202,37204],{},[898,37201,8194],{},[1667,37203,1680],{},[1656,37205,8187],{},[1661,37207,37208,37210],{},[898,37209,1665],{},[1667,37211,1680],{},[1656,37213,1713],{},[1667,37215,4032],{},[902,37217,37218],{"encoding":904},"g(Q_1, Q_2) = Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",". Použijeme ",[207,37221,37223],{"className":37222,"dataFsResolvedFilePath":791,"href":792},[210],"metodu Lagrangeových multiplikátorů",[198,37225,37227],{"id":37226},"lagrangeova-funkce-a-podmínky-optimality","Lagrangeova funkce a podmínky optimality",[724,37229,37230],{},"Sestavíme",[883,37232,37234],{"className":37233},[886],[888,37235,37236],{"xmlns":890,"display":2408},[892,37237,37238,37350],{},[2412,37239,37240],{"width":2414},[2416,37241,37242,37244,37343,37345],{},[2419,37243],{"width":2421},[2419,37245,37246],{},[895,37247,37248,37251,37253,37259,37261,37267,37269,37271,37273,37275,37277,37279,37285,37287,37293,37295,37297,37299,37301,37307,37309,37317,37323,37325,37333,37339,37341],{},[898,37249,18539],{"mathvariant":37250},"script",[1656,37252,1659],{"stretchy":1658},[1661,37254,37255,37257],{},[898,37256,1665],{},[1667,37258,1669],{},[1656,37260,1673],{"separator":1672},[1661,37262,37263,37265],{},[898,37264,1665],{},[1667,37266,1680],{},[1656,37268,1673],{"separator":1672},[898,37270,25169],{},[1656,37272,1683],{"stretchy":1658},[1656,37274,1713],{},[898,37276,900],{},[1656,37278,1659],{"stretchy":1658},[1661,37280,37281,37283],{},[898,37282,1665],{},[1667,37284,1669],{},[1656,37286,1673],{"separator":1672},[1661,37288,37289,37291],{},[898,37290,1665],{},[1667,37292,1680],{},[1656,37294,1683],{"stretchy":1658},[1656,37296,3633],{},[898,37298,25169],{},[1656,37300,1659],{"stretchy":1658},[2062,37302,37303,37305],{},[898,37304,8184],{},[1656,37306,8187],{},[1656,37308,3964],{},[1715,37310,37311,37313,37315],{},[898,37312,8194],{},[1667,37314,1669],{},[1656,37316,8187],{},[1661,37318,37319,37321],{},[898,37320,1665],{},[1667,37322,1669],{},[1656,37324,3964],{},[1715,37326,37327,37329,37331],{},[898,37328,8194],{},[1667,37330,1680],{},[1656,37332,8187],{},[1661,37334,37335,37337],{},[898,37336,1665],{},[1667,37338,1680],{},[1656,37340,1683],{"stretchy":1658},[898,37342,1863],{"mathvariant":1723},[2419,37344],{"width":2421},[2419,37346,37347],{},[2461,37348,37349],{},"(6.13)",[902,37351,37352],{"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}",[724,37354,37355],{},"Soustava prvního řádu:",[883,37357,37359],{"className":37358},[886],[888,37360,37361],{"xmlns":890,"display":2408},[892,37362,37363,37546],{},[2412,37364,37365],{"width":2414},[2416,37366,37367,37369,37539,37541],{},[2419,37368],{"width":2421},[2419,37370,37371],{},[2412,37372,37373,37423,37473],{"rowspacing":29476,"columnalign":29477,"columnspacing":1724},[2416,37374,37375,37387],{},[2419,37376,37377],{},[4138,37378,37379],{"scriptlevel":4032,"displaystyle":1672},[1715,37380,37381,37383,37385],{},[898,37382,18539],{"mathvariant":37250},[1667,37384,1669],{},[1656,37386,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[2419,37388,37389],{},[4138,37390,37391],{"scriptlevel":4032,"displaystyle":1672},[895,37392,37393,37395,37397,37405,37407,37409,37417,37419,37421],{},[895,37394],{},[1656,37396,1713],{},[1715,37398,37399,37401,37403],{},[898,37400,900],{},[1667,37402,1669],{},[1656,37404,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,37406,3964],{},[898,37408,25169],{},[1715,37410,37411,37413,37415],{},[898,37412,8194],{},[1667,37414,1669],{},[1656,37416,8187],{},[1656,37418,1713],{},[1667,37420,4032],{},[1656,37422,1673],{"separator":1672},[2416,37424,37425,37437],{},[2419,37426,37427],{},[4138,37428,37429],{"scriptlevel":4032,"displaystyle":1672},[1715,37430,37431,37433,37435],{},[898,37432,18539],{"mathvariant":37250},[1667,37434,1680],{},[1656,37436,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[2419,37438,37439],{},[4138,37440,37441],{"scriptlevel":4032,"displaystyle":1672},[895,37442,37443,37445,37447,37455,37457,37459,37467,37469,37471],{},[895,37444],{},[1656,37446,1713],{},[1715,37448,37449,37451,37453],{},[898,37450,900],{},[1667,37452,1680],{},[1656,37454,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,37456,3964],{},[898,37458,25169],{},[1715,37460,37461,37463,37465],{},[898,37462,8194],{},[1667,37464,1680],{},[1656,37466,8187],{},[1656,37468,1713],{},[1667,37470,4032],{},[1656,37472,1673],{"separator":1672},[2416,37474,37475,37487],{},[2419,37476,37477],{},[4138,37478,37479],{"scriptlevel":4032,"displaystyle":1672},[1715,37480,37481,37483,37485],{},[898,37482,18539],{"mathvariant":37250},[898,37484,25169],{},[1656,37486,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[2419,37488,37489],{},[4138,37490,37491],{"scriptlevel":4032,"displaystyle":1672},[895,37492,37493,37495,37497,37503,37505,37513,37519,37521,37529,37535,37537],{},[895,37494],{},[1656,37496,1713],{},[2062,37498,37499,37501],{},[898,37500,8184],{},[1656,37502,8187],{},[1656,37504,3964],{},[1715,37506,37507,37509,37511],{},[898,37508,8194],{},[1667,37510,1669],{},[1656,37512,8187],{},[1661,37514,37515,37517],{},[898,37516,1665],{},[1667,37518,1669],{},[1656,37520,3964],{},[1715,37522,37523,37525,37527],{},[898,37524,8194],{},[1667,37526,1680],{},[1656,37528,8187],{},[1661,37530,37531,37533],{},[898,37532,1665],{},[1667,37534,1680],{},[1656,37536,1713],{},[1667,37538,4283],{},[2419,37540],{"width":2421},[2419,37542,37543],{},[2461,37544,37545],{},"(6.14)",[902,37547,37548],{"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}",[724,37550,37551,37552,37555,37556,37569,37570,2114],{},"Díky konvexitě indiferenčních křivek je řešení ",[38,37553,37554],{},"vázaným maximem",". Z prvních dvou rovnic po vyloučení ",[883,37557,37559],{"className":37558},[886],[888,37560,37561],{"xmlns":890},[892,37562,37563,37567],{},[895,37564,37565],{},[898,37566,25169],{},[902,37568,25222],{"encoding":904}," dostáváme ",[38,37571,37572],{},"podmínku optimality",[883,37574,37576],{"className":37575},[886],[888,37577,37578],{"xmlns":890,"display":2408},[892,37579,37580,37638],{},[895,37581,37582],{},[21566,37583,37584],{"notation":21568},[4138,37585,37586],{"scriptlevel":4032,"displaystyle":1658},[4138,37587,37588],{"scriptlevel":4032,"displaystyle":1658},[4138,37589,37590],{"scriptlevel":4032,"displaystyle":1672},[895,37591,37592,37594,37596,37598,37616,37618,37636],{},[2461,37593,12767],{},[2461,37595,7362],{},[1656,37597,1713],{},[3294,37599,37600,37608],{},[1715,37601,37602,37604,37606],{},[898,37603,900],{},[1667,37605,1669],{},[1656,37607,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1715,37609,37610,37612,37614],{},[898,37611,900],{},[1667,37613,1680],{},[1656,37615,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,37617,1713],{},[3294,37619,37620,37628],{},[1715,37621,37622,37624,37626],{},[898,37623,8194],{},[1667,37625,1669],{},[1656,37627,8187],{},[1715,37629,37630,37632,37634],{},[898,37631,8194],{},[1667,37633,1680],{},[1656,37635,8187],{},[2461,37637,12767],{},[902,37639,37640],{"encoding":904},"\\boxed{\\; \\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*} \\;}",[1981,37642,37643],{},[724,37644,37645,37647,37648,37682,37683,37686,37687,7648,37704,37721,37722,37752,37753,37770,37771,37801],{},[883,37646,3472],{}," Intuice — mezní poměr užitečnosti = mezní poměr cen\nPodmínka ",[883,37649,37651],{"className":37650},[886],[888,37652,37653],{"xmlns":890},[892,37654,37655,37679],{},[895,37656,37657,37659,37661,37669,37671],{},[2461,37658,7362],{},[1656,37660,1713],{},[1715,37662,37663,37665,37667],{},[898,37664,8194],{},[1667,37666,1669],{},[1656,37668,8187],{},[898,37670,1782],{"mathvariant":1723},[1715,37672,37673,37675,37677],{},[898,37674,8194],{},[1667,37676,1680],{},[1656,37678,8187],{},[902,37680,37681],{"encoding":904},"\\text{MRCS} = P_1^*\u002FP_2^*"," říká, že v optimu je ",[38,37684,37685],{},"sklon indiferenční křivky roven sklonu rozpočtové přímky",". Ekonomicky: spotřebitel je ochoten vyměnit ",[883,37688,37690],{"className":37689},[886],[888,37691,37692],{"xmlns":890},[892,37693,37694,37702],{},[895,37695,37696],{},[1661,37697,37698,37700],{},[898,37699,1665],{},[1667,37701,1669],{},[902,37703,3227],{"encoding":904},[883,37705,37707],{"className":37706},[886],[888,37708,37709],{"xmlns":890},[892,37710,37711,37719],{},[895,37712,37713],{},[1661,37714,37715,37717],{},[898,37716,1665],{},[1667,37718,1680],{},[902,37720,3246],{"encoding":904}," v přesně tom poměru, v jakém je trh (ceny) umožňuje vyměňovat. Kdyby ",[883,37723,37725],{"className":37724},[886],[888,37726,37727],{"xmlns":890},[892,37728,37729,37749],{},[895,37730,37731,37733,37735,37741,37743],{},[2461,37732,7362],{},[1656,37734,2850],{},[1661,37736,37737,37739],{},[898,37738,8194],{},[1667,37740,1669],{},[898,37742,1782],{"mathvariant":1723},[1661,37744,37745,37747],{},[898,37746,8194],{},[1667,37748,1680],{},[902,37750,37751],{"encoding":904},"\\text{MRCS} > P_1\u002FP_2",", vyplatilo by se nakupovat více ",[883,37754,37756],{"className":37755},[886],[888,37757,37758],{"xmlns":890},[892,37759,37760,37768],{},[895,37761,37762],{},[1661,37763,37764,37766],{},[898,37765,1665],{},[1667,37767,1669],{},[902,37769,3227],{"encoding":904}," (subjektivní ocenění převažuje nad tržním); kdyby ",[883,37772,37774],{"className":37773},[886],[888,37775,37776],{"xmlns":890},[892,37777,37778,37798],{},[895,37779,37780,37782,37784,37790,37792],{},[2461,37781,7362],{},[1656,37783,4373],{},[1661,37785,37786,37788],{},[898,37787,8194],{},[1667,37789,1669],{},[898,37791,1782],{"mathvariant":1723},[1661,37793,37794,37796],{},[898,37795,8194],{},[1667,37797,1680],{},[902,37799,37800],{"encoding":904},"\\text{MRCS} \u003C P_1\u002FP_2",", vyplatil by se opak.",[198,37803,37805,37806,37819],{"id":37804},"interpretace-λlambda-mezní-užitečnost-důchodu","Interpretace ",[883,37807,37809],{"className":37808},[886],[888,37810,37811],{"xmlns":890},[892,37812,37813,37817],{},[895,37814,37815],{},[898,37816,25169],{},[902,37818,25222],{"encoding":904}," — mezní užitečnost důchodu",[724,37821,37822,37823,37841,37842,37845,37846,37863,37864,37881,37882,37885],{},"Lagrangeův multiplikátor ",[883,37824,37826],{"className":37825},[886],[888,37827,37828],{"xmlns":890},[892,37829,37830,37838],{},[895,37831,37832],{},[2062,37833,37834,37836],{},[898,37835,25169],{},[1656,37837,8187],{},[902,37839,37840],{"encoding":904},"\\lambda^*"," představuje ",[38,37843,37844],{},"mezní užitečnost důchodu"," — přibližnou změnu maximální užitečnosti ",[883,37847,37849],{"className":37848},[886],[888,37850,37851],{"xmlns":890},[892,37852,37853,37861],{},[895,37854,37855],{},[2062,37856,37857,37859],{},[898,37858,900],{},[1656,37860,8187],{},[902,37862,8343],{"encoding":904}," při jednotkové změně důchodu ",[883,37865,37867],{"className":37866},[886],[888,37868,37869],{"xmlns":890},[892,37870,37871,37879],{},[895,37872,37873],{},[2062,37874,37875,37877],{},[898,37876,8184],{},[1656,37878,8187],{},[902,37880,36737],{"encoding":904},". Je to ",[38,37883,37884],{},"stínová cena"," rozpočtového omezení.",[1981,37887,37888,37893],{},[724,37889,37890,37892],{},[883,37891,10188],{}," Postup — maximalizace užitečnosti Lagrangeovou metodou",[152,37894,37895,37955,38042,38078,38165],{},[123,37896,37897,37900,37901,1863],{},[38,37898,37899],{},"Zapiš rozpočtové omezení"," ve tvaru ",[883,37902,37904],{"className":37903},[886],[888,37905,37906],{"xmlns":890},[892,37907,37908,37952],{},[895,37909,37910,37916,37918,37926,37932,37934,37942,37948,37950],{},[2062,37911,37912,37914],{},[898,37913,8184],{},[1656,37915,8187],{},[1656,37917,3964],{},[1715,37919,37920,37922,37924],{},[898,37921,8194],{},[1667,37923,1669],{},[1656,37925,8187],{},[1661,37927,37928,37930],{},[898,37929,1665],{},[1667,37931,1669],{},[1656,37933,3964],{},[1715,37935,37936,37938,37940],{},[898,37937,8194],{},[1667,37939,1680],{},[1656,37941,8187],{},[1661,37943,37944,37946],{},[898,37945,1665],{},[1667,37947,1680],{},[1656,37949,1713],{},[1667,37951,4032],{},[902,37953,37954],{"encoding":904},"Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",[123,37956,37957,1643,37960,1863],{},[38,37958,37959],{},"Sestav Lagrangeovu funkci",[883,37961,37963],{"className":37962},[886],[888,37964,37965],{"xmlns":890},[892,37966,37967,38039],{},[895,37968,37969,37971,37973,37975,37977,37983,37985,37991,37993,37995,37997,37999,38005,38007,38015,38021,38023,38031,38037],{},[898,37970,18539],{"mathvariant":37250},[1656,37972,1713],{},[898,37974,900],{},[1656,37976,1659],{"stretchy":1658},[1661,37978,37979,37981],{},[898,37980,1665],{},[1667,37982,1669],{},[1656,37984,1673],{"separator":1672},[1661,37986,37987,37989],{},[898,37988,1665],{},[1667,37990,1680],{},[1656,37992,1683],{"stretchy":1658},[1656,37994,3633],{},[898,37996,25169],{},[1656,37998,1659],{"stretchy":1658},[2062,38000,38001,38003],{},[898,38002,8184],{},[1656,38004,8187],{},[1656,38006,3964],{},[1715,38008,38009,38011,38013],{},[898,38010,8194],{},[1667,38012,1669],{},[1656,38014,8187],{},[1661,38016,38017,38019],{},[898,38018,1665],{},[1667,38020,1669],{},[1656,38022,3964],{},[1715,38024,38025,38027,38029],{},[898,38026,8194],{},[1667,38028,1680],{},[1656,38030,8187],{},[1661,38032,38033,38035],{},[898,38034,1665],{},[1667,38036,1680],{},[1656,38038,1683],{"stretchy":1658},[902,38040,38041],{"encoding":904},"\\mathcal{L} = U(Q_1, Q_2) + \\lambda(Y^* - P_1^* Q_1 - P_2^* Q_2)",[123,38043,38044,19209,38047,38077],{},[38,38045,38046],{},"Spočítej parciální derivace",[883,38048,38050],{"className":38049},[886],[888,38051,38052],{"xmlns":890},[892,38053,38054,38074],{},[895,38055,38056,38062,38064,38070,38072],{},[1661,38057,38058,38060],{},[898,38059,1665],{},[1667,38061,1669],{},[1656,38063,1673],{"separator":1672},[1661,38065,38066,38068],{},[898,38067,1665],{},[1667,38069,1680],{},[1656,38071,1673],{"separator":1672},[898,38073,25169],{},[902,38075,38076],{"encoding":904},"Q_1, Q_2, \\lambda"," a polož je rovny nule.",[123,38079,38080,38096,38097,38130,38131,1896,38148,1863],{},[38,38081,38082,38083],{},"Vyluč ",[883,38084,38086],{"className":38085},[886],[888,38087,38088],{"xmlns":890},[892,38089,38090,38094],{},[895,38091,38092],{},[898,38093,25169],{},[902,38095,25222],{"encoding":904}," dělením prvních dvou rovnic — dostaneš podmínku ",[883,38098,38100],{"className":38099},[886],[888,38101,38102],{"xmlns":890},[892,38103,38104,38128],{},[895,38105,38106,38108,38110,38118,38120],{},[2461,38107,7362],{},[1656,38109,1713],{},[1715,38111,38112,38114,38116],{},[898,38113,8194],{},[1667,38115,1669],{},[1656,38117,8187],{},[898,38119,1782],{"mathvariant":1723},[1715,38121,38122,38124,38126],{},[898,38123,8194],{},[1667,38125,1680],{},[1656,38127,8187],{},[902,38129,37681],{"encoding":904},", která dá vztah mezi ",[883,38132,38134],{"className":38133},[886],[888,38135,38136],{"xmlns":890},[892,38137,38138,38146],{},[895,38139,38140],{},[1661,38141,38142,38144],{},[898,38143,1665],{},[1667,38145,1669],{},[902,38147,3227],{"encoding":904},[883,38149,38151],{"className":38150},[886],[888,38152,38153],{"xmlns":890},[892,38154,38155,38163],{},[895,38156,38157],{},[1661,38158,38159,38161],{},[898,38160,1665],{},[1667,38162,1680],{},[902,38164,3246],{"encoding":904},[123,38166,38167,38170,38171,38201,38202,38219,38220,1863],{},[38,38168,38169],{},"Dosaď do rozpočtového omezení"," a vypočítej ",[883,38172,38174],{"className":38173},[886],[888,38175,38176],{"xmlns":890},[892,38177,38178,38198],{},[895,38179,38180,38188,38190],{},[1715,38181,38182,38184,38186],{},[898,38183,1665],{},[1667,38185,1669],{},[1656,38187,8187],{},[1656,38189,1673],{"separator":1672},[1715,38191,38192,38194,38196],{},[898,38193,1665],{},[1667,38195,1680],{},[1656,38197,8187],{},[902,38199,38200],{"encoding":904},"Q_1^*, Q_2^*",", případně ",[883,38203,38205],{"className":38204},[886],[888,38206,38207],{"xmlns":890},[892,38208,38209,38217],{},[895,38210,38211],{},[2062,38212,38213,38215],{},[898,38214,25169],{},[1656,38216,8187],{},[902,38218,37840],{"encoding":904}," a maximální užitečnost ",[883,38221,38223],{"className":38222},[886],[888,38224,38225],{"xmlns":890},[892,38226,38227,38261],{},[895,38228,38229,38235,38237,38239,38241,38249,38251,38259],{},[2062,38230,38231,38233],{},[898,38232,900],{},[1656,38234,8187],{},[1656,38236,1713],{},[898,38238,900],{},[1656,38240,1659],{"stretchy":1658},[1715,38242,38243,38245,38247],{},[898,38244,1665],{},[1667,38246,1669],{},[1656,38248,8187],{},[1656,38250,1673],{"separator":1672},[1715,38252,38253,38255,38257],{},[898,38254,1665],{},[1667,38256,1680],{},[1656,38258,8187],{},[1656,38260,1683],{"stretchy":1658},[902,38262,38263],{"encoding":904},"U^* = U(Q_1^*, Q_2^*)",[115,38265,38267],{"id":38266},"geometrie-optima-tečnost-ic-a-rozpočtové-přímky","Geometrie optima — tečnost IC a rozpočtové přímky",[724,38269,38270],{},[5956,38271],{"alt":38272,"className":38273,"src":38274},"imek-uzitecnost-optimum",[210,5960],"\u002Fwiki-assets\u002Fimek-uzitecnost-optimum.jpeg",[724,38276,38277],{},[614,38278,38279,38280,38329,38330,1896,38358,38386,38387,38421,38422,38461,38462,38480,38481,38499,38500,38518],{},"Obrázek 6.7 — Rozpočtová přímka ",[883,38281,38283],{"className":38282},[886],[888,38284,38285],{"xmlns":890},[892,38286,38287,38327],{},[895,38288,38289,38295,38297,38305,38311,38313,38321],{},[2062,38290,38291,38293],{},[898,38292,8184],{},[1656,38294,8187],{},[1656,38296,1713],{},[1715,38298,38299,38301,38303],{},[898,38300,8194],{},[1667,38302,1669],{},[1656,38304,8187],{},[1661,38306,38307,38309],{},[898,38308,1665],{},[1667,38310,1669],{},[1656,38312,3633],{},[1715,38314,38315,38317,38319],{},[898,38316,8194],{},[1667,38318,1680],{},[1656,38320,8187],{},[1661,38322,38323,38325],{},[898,38324,1665],{},[1667,38326,1680],{},[902,38328,8223],{"encoding":904}," protíná osy v ",[883,38331,38333],{"className":38332},[886],[888,38334,38335],{"xmlns":890},[892,38336,38337,38355],{},[895,38338,38339,38345,38347],{},[2062,38340,38341,38343],{},[898,38342,8184],{},[1656,38344,8187],{},[898,38346,1782],{"mathvariant":1723},[1715,38348,38349,38351,38353],{},[898,38350,8194],{},[1667,38352,1669],{},[1656,38354,8187],{},[902,38356,38357],{"encoding":904},"Y^*\u002FP_1^*",[883,38359,38361],{"className":38360},[886],[888,38362,38363],{"xmlns":890},[892,38364,38365,38383],{},[895,38366,38367,38373,38375],{},[2062,38368,38369,38371],{},[898,38370,8184],{},[1656,38372,8187],{},[898,38374,1782],{"mathvariant":1723},[1715,38376,38377,38379,38381],{},[898,38378,8194],{},[1667,38380,1680],{},[1656,38382,8187],{},[902,38384,38385],{"encoding":904},"Y^*\u002FP_2^*",". Tři indiferenční křivky ",[883,38388,38390],{"className":38389},[886],[888,38391,38392],{"xmlns":890},[892,38393,38394,38418],{},[895,38395,38396,38402,38404,38410,38412],{},[1661,38397,38398,38400],{},[898,38399,1745],{},[1667,38401,1669],{},[1656,38403,4373],{},[2062,38405,38406,38408],{},[898,38407,1745],{},[1656,38409,8187],{},[1656,38411,4373],{},[1661,38413,38414,38416],{},[898,38415,1745],{},[1667,38417,1680],{},[902,38419,38420],{"encoding":904},"c_1 \u003C c^* \u003C c_2",". Optimum ",[883,38423,38425],{"className":38424},[886],[888,38426,38427],{"xmlns":890},[892,38428,38429,38459],{},[895,38430,38431,38437,38439,38447,38449,38457],{},[2062,38432,38433,38435],{},[898,38434,1665],{},[1656,38436,8187],{},[1656,38438,3453],{"stretchy":1658},[1715,38440,38441,38443,38445],{},[898,38442,1665],{},[1667,38444,1669],{},[1656,38446,8187],{},[1656,38448,1673],{"separator":1672},[1715,38450,38451,38453,38455],{},[898,38452,1665],{},[1667,38454,1680],{},[1656,38456,8187],{},[1656,38458,3462],{"stretchy":1658},[902,38460,8443],{"encoding":904}," je bod dotyku rozpočtové přímky s křivkou ",[883,38463,38465],{"className":38464},[886],[888,38466,38467],{"xmlns":890},[892,38468,38469,38477],{},[895,38470,38471],{},[2062,38472,38473,38475],{},[898,38474,1745],{},[1656,38476,8187],{},[902,38478,38479],{"encoding":904},"c^*",". Křivka ",[883,38482,38484],{"className":38483},[886],[888,38485,38486],{"xmlns":890},[892,38487,38488,38496],{},[895,38489,38490],{},[1661,38491,38492,38494],{},[898,38493,1745],{},[1667,38495,1669],{},[902,38497,38498],{"encoding":904},"c_1"," je dosažitelná, ale nemaximalizuje užitečnost; křivka ",[883,38501,38503],{"className":38502},[886],[888,38504,38505],{"xmlns":890},[892,38506,38507,38515],{},[895,38508,38509],{},[1661,38510,38511,38513],{},[898,38512,1745],{},[1667,38514,1680],{},[902,38516,38517],{"encoding":904},"c_2"," není při daném důchodu dosažitelná.",[724,38520,38521,38522,38525,38526,38544,38545,38574],{},"Geometrie je jádrem intuice: přímka (rozpočet) a křivka (užitečnost) se v optimu ",[38,38523,38524],{},"dotýkají",", tj. mají v bodě ",[883,38527,38529],{"className":38528},[886],[888,38530,38531],{"xmlns":890},[892,38532,38533,38541],{},[895,38534,38535],{},[2062,38536,38537,38539],{},[898,38538,1665],{},[1656,38540,8187],{},[902,38542,38543],{"encoding":904},"Q^*"," společnou tečnu. To přímo převádí podmínku ",[883,38546,38548],{"className":38547},[886],[888,38549,38550],{"xmlns":890},[892,38551,38552,38572],{},[895,38553,38554,38556,38558,38564,38566],{},[2461,38555,7362],{},[1656,38557,1713],{},[1661,38559,38560,38562],{},[898,38561,8194],{},[1667,38563,1669],{},[898,38565,1782],{"mathvariant":1723},[1661,38567,38568,38570],{},[898,38569,8194],{},[1667,38571,1680],{},[902,38573,10631],{"encoding":904}," — poměr mezních užitečností (sklon IC) = poměr cen (sklon přímky).",[115,38576,38578],{"id":38577},"příklad-65-mrcs-pro-cobb-douglasovu-užitečnost","Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost",[724,38580,18411,38581,7727],{},[883,38582,38584],{"className":38583},[886],[888,38585,38586],{"xmlns":890},[892,38587,38588,38640],{},[895,38589,38590,38592,38594,38600,38602,38608,38610,38612,38626],{},[898,38591,900],{},[1656,38593,1659],{"stretchy":1658},[1661,38595,38596,38598],{},[898,38597,1665],{},[1667,38599,1669],{},[1656,38601,1673],{"separator":1672},[1661,38603,38604,38606],{},[898,38605,1665],{},[1667,38607,1680],{},[1656,38609,1683],{"stretchy":1658},[1656,38611,1713],{},[1715,38613,38614,38616,38618],{},[898,38615,1665],{},[1667,38617,1669],{},[895,38619,38620,38622,38624],{},[1667,38621,1669],{},[898,38623,1782],{"mathvariant":1723},[1667,38625,1680],{},[1715,38627,38628,38630,38632],{},[898,38629,1665],{},[1667,38631,1680],{},[895,38633,38634,38636,38638],{},[1667,38635,1669],{},[898,38637,1782],{"mathvariant":1723},[1667,38639,1680],{},[902,38641,7917],{"encoding":904},[724,38643,38644],{},[883,38645,38647],{"className":38646},[886],[888,38648,38649],{"xmlns":890},[892,38650,38651,38757],{},[895,38652,38653,38655,38657,38739,38741,38755],{},[2461,38654,7362],{},[1656,38656,1713],{},[3294,38658,38659,38699],{},[895,38660,38661,38669,38685],{},[4138,38662,38663],{"scriptlevel":4032,"displaystyle":1658},[3294,38664,38665,38667],{},[1667,38666,1669],{},[1667,38668,1680],{},[1715,38670,38671,38673,38675],{},[898,38672,1665],{},[1667,38674,1669],{},[895,38676,38677,38679,38681,38683],{},[1656,38678,3964],{},[1667,38680,1669],{},[898,38682,1782],{"mathvariant":1723},[1667,38684,1680],{},[1715,38686,38687,38689,38691],{},[898,38688,1665],{},[1667,38690,1680],{},[895,38692,38693,38695,38697],{},[1667,38694,1669],{},[898,38696,1782],{"mathvariant":1723},[1667,38698,1680],{},[895,38700,38701,38709,38723],{},[4138,38702,38703],{"scriptlevel":4032,"displaystyle":1658},[3294,38704,38705,38707],{},[1667,38706,1669],{},[1667,38708,1680],{},[1715,38710,38711,38713,38715],{},[898,38712,1665],{},[1667,38714,1669],{},[895,38716,38717,38719,38721],{},[1667,38718,1669],{},[898,38720,1782],{"mathvariant":1723},[1667,38722,1680],{},[1715,38724,38725,38727,38729],{},[898,38726,1665],{},[1667,38728,1680],{},[895,38730,38731,38733,38735,38737],{},[1656,38732,3964],{},[1667,38734,1669],{},[898,38736,1782],{"mathvariant":1723},[1667,38738,1680],{},[1656,38740,1713],{},[3294,38742,38743,38749],{},[1661,38744,38745,38747],{},[898,38746,1665],{},[1667,38748,1680],{},[1661,38750,38751,38753],{},[898,38752,1665],{},[1667,38754,1669],{},[898,38756,1863],{"mathvariant":1723},[902,38758,8035],{"encoding":904},[724,38760,8038,38761,2191,38804,8087,38806,38825,38826,38856,38857,1863],{},[883,38762,38764],{"className":38763},[886],[888,38765,38766],{"xmlns":890},[892,38767,38768,38802],{},[895,38769,38770,38772,38774,38776,38778,38780,38782,38784,38792,38794],{},[2461,38771,7362],{},[1656,38773,1659],{"stretchy":1658},[1667,38775,8054],{},[1656,38777,1673],{"separator":1672},[1667,38779,8059],{},[1656,38781,1683],{"stretchy":1658},[1656,38783,1713],{},[4138,38785,38786],{"scriptlevel":4032,"displaystyle":1658},[3294,38787,38788,38790],{},[1667,38789,8059],{},[1667,38791,8054],{},[1656,38793,1713],{},[4138,38795,38796],{"scriptlevel":4032,"displaystyle":1658},[3294,38797,38798,38800],{},[1667,38799,5193],{},[1667,38801,2617],{},[902,38803,8084],{"encoding":904},[614,38805,5434],{},[883,38807,38809],{"className":38808},[886],[888,38810,38811],{"xmlns":890},[892,38812,38813,38823],{},[895,38814,38815],{},[4138,38816,38817],{"scriptlevel":4032,"displaystyle":1658},[3294,38818,38819,38821],{},[1667,38820,5193],{},[1667,38822,2617],{},[902,38824,8107],{"encoding":904}," jednotky, aby se užitečnost zachovala. Tato forma ",[883,38827,38829],{"className":38828},[886],[888,38830,38831],{"xmlns":890},[892,38832,38833,38853],{},[895,38834,38835,38837,38839,38845,38847],{},[2461,38836,7362],{},[1656,38838,1713],{},[1661,38840,38841,38843],{},[898,38842,1665],{},[1667,38844,1680],{},[898,38846,1782],{"mathvariant":1723},[1661,38848,38849,38851],{},[898,38850,1665],{},[1667,38852,1669],{},[902,38854,38855],{"encoding":904},"\\text{MRCS} = Q_2\u002FQ_1"," je typická pro symetrické Cobb-Douglasovy preference a vstupuje do optimalizace skrze podmínku ",[883,38858,38860],{"className":38859},[886],[888,38861,38862],{"xmlns":890},[892,38863,38864,38884],{},[895,38865,38866,38868,38870,38876,38878],{},[2461,38867,7362],{},[1656,38869,1713],{},[1661,38871,38872,38874],{},[898,38873,8194],{},[1667,38875,1669],{},[898,38877,1782],{"mathvariant":1723},[1661,38879,38880,38882],{},[898,38881,8194],{},[1667,38883,1680],{},[902,38885,10631],{"encoding":904},[115,38887,38889,38890],{"id":38888},"příklad-66-maximalizace-užitečnosti-pro-uq1q2u-q_1-q_2","Příklad 6.6 — maximalizace užitečnosti pro ",[883,38891,38893],{"className":38892},[886],[888,38894,38895],{"xmlns":890},[892,38896,38897,38915],{},[895,38898,38899,38901,38903,38909],{},[898,38900,900],{},[1656,38902,1713],{},[1661,38904,38905,38907],{},[898,38906,1665],{},[1667,38908,1669],{},[1661,38910,38911,38913],{},[898,38912,1665],{},[1667,38914,1680],{},[902,38916,8546],{"encoding":904},[724,38918,38919,38920,1343,38966,1343,38990,1343,39014,39036],{},"Je dána ",[883,38921,38923],{"className":38922},[886],[888,38924,38925],{"xmlns":890},[892,38926,38927,38963],{},[895,38928,38929,38931,38933,38939,38941,38947,38949,38951,38957],{},[898,38930,900],{},[1656,38932,1659],{"stretchy":1658},[1661,38934,38935,38937],{},[898,38936,1665],{},[1667,38938,1669],{},[1656,38940,1673],{"separator":1672},[1661,38942,38943,38945],{},[898,38944,1665],{},[1667,38946,1680],{},[1656,38948,1683],{"stretchy":1658},[1656,38950,1713],{},[1661,38952,38953,38955],{},[898,38954,1665],{},[1667,38956,1669],{},[1661,38958,38959,38961],{},[898,38960,1665],{},[1667,38962,1680],{},[902,38964,38965],{"encoding":904},"U(Q_1, Q_2) = Q_1 Q_2",[883,38967,38969],{"className":38968},[886],[888,38970,38971],{"xmlns":890},[892,38972,38973,38987],{},[895,38974,38975,38983,38985],{},[1715,38976,38977,38979,38981],{},[898,38978,8194],{},[1667,38980,1669],{},[1656,38982,8187],{},[1656,38984,1713],{},[1667,38986,1680],{},[902,38988,38989],{"encoding":904},"P_1^* = 2",[883,38991,38993],{"className":38992},[886],[888,38994,38995],{"xmlns":890},[892,38996,38997,39011],{},[895,38998,38999,39007,39009],{},[1715,39000,39001,39003,39005],{},[898,39002,8194],{},[1667,39004,1680],{},[1656,39006,8187],{},[1656,39008,1713],{},[1667,39010,5193],{},[902,39012,39013],{"encoding":904},"P_2^* = 5",[883,39015,39017],{"className":39016},[886],[888,39018,39019],{"xmlns":890},[892,39020,39021,39033],{},[895,39022,39023,39029,39031],{},[2062,39024,39025,39027],{},[898,39026,8184],{},[1656,39028,8187],{},[1656,39030,1713],{},[1667,39032,5267],{},[902,39034,39035],{"encoding":904},"Y^* = 100",". Lagrangeova funkce:",[883,39038,39040],{"className":39039},[886],[888,39041,39042],{"xmlns":890,"display":2408},[892,39043,39044,39116],{},[895,39045,39046,39048,39050,39056,39058,39064,39066,39068,39070,39072,39078,39084,39086,39088,39090,39092,39094,39096,39102,39104,39106,39112,39114],{},[898,39047,18539],{"mathvariant":37250},[1656,39049,1659],{"stretchy":1658},[1661,39051,39052,39054],{},[898,39053,1665],{},[1667,39055,1669],{},[1656,39057,1673],{"separator":1672},[1661,39059,39060,39062],{},[898,39061,1665],{},[1667,39063,1680],{},[1656,39065,1673],{"separator":1672},[898,39067,25169],{},[1656,39069,1683],{"stretchy":1658},[1656,39071,1713],{},[1661,39073,39074,39076],{},[898,39075,1665],{},[1667,39077,1669],{},[1661,39079,39080,39082],{},[898,39081,1665],{},[1667,39083,1680],{},[1656,39085,3633],{},[898,39087,25169],{},[1656,39089,1659],{"stretchy":1658},[1667,39091,5267],{},[1656,39093,3964],{},[1667,39095,1680],{},[1661,39097,39098,39100],{},[898,39099,1665],{},[1667,39101,1669],{},[1656,39103,3964],{},[1667,39105,5193],{},[1661,39107,39108,39110],{},[898,39109,1665],{},[1667,39111,1680],{},[1656,39113,1683],{"stretchy":1658},[898,39115,1863],{"mathvariant":1723},[902,39117,39118],{"encoding":904},"\\mathcal{L}(Q_1, Q_2, \\lambda) = Q_1 Q_2 + \\lambda(100 - 2 Q_1 - 5 Q_2).",[724,39120,39121],{},"Soustava:",[883,39123,39125],{"className":39124},[886],[888,39126,39127],{"xmlns":890,"display":2408},[892,39128,39129,39241],{},[2412,39130,39131,39165,39199],{"rowspacing":29476,"columnalign":29477,"columnspacing":1724},[2416,39132,39133,39151],{},[2419,39134,39135],{},[4138,39136,39137],{"scriptlevel":4032,"displaystyle":1672},[895,39138,39139,39145,39147,39149],{},[1661,39140,39141,39143],{},[898,39142,1665],{},[1667,39144,1680],{},[1656,39146,3964],{},[1667,39148,1680],{},[898,39150,25169],{},[2419,39152,39153],{},[4138,39154,39155],{"scriptlevel":4032,"displaystyle":1672},[895,39156,39157,39159,39161,39163],{},[895,39158],{},[1656,39160,1713],{},[1667,39162,4032],{},[1656,39164,1673],{"separator":1672},[2416,39166,39167,39185],{},[2419,39168,39169],{},[4138,39170,39171],{"scriptlevel":4032,"displaystyle":1672},[895,39172,39173,39179,39181,39183],{},[1661,39174,39175,39177],{},[898,39176,1665],{},[1667,39178,1669],{},[1656,39180,3964],{},[1667,39182,5193],{},[898,39184,25169],{},[2419,39186,39187],{},[4138,39188,39189],{"scriptlevel":4032,"displaystyle":1672},[895,39190,39191,39193,39195,39197],{},[895,39192],{},[1656,39194,1713],{},[1667,39196,4032],{},[1656,39198,1673],{"separator":1672},[2416,39200,39201,39229],{},[2419,39202,39203],{},[4138,39204,39205],{"scriptlevel":4032,"displaystyle":1672},[895,39206,39207,39209,39211,39213,39219,39221,39223],{},[1667,39208,5267],{},[1656,39210,3964],{},[1667,39212,1680],{},[1661,39214,39215,39217],{},[898,39216,1665],{},[1667,39218,1669],{},[1656,39220,3964],{},[1667,39222,5193],{},[1661,39224,39225,39227],{},[898,39226,1665],{},[1667,39228,1680],{},[2419,39230,39231],{},[4138,39232,39233],{"scriptlevel":4032,"displaystyle":1672},[895,39234,39235,39237,39239],{},[895,39236],{},[1656,39238,1713],{},[1667,39240,4283],{},[902,39242,39243],{"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}",[724,39245,39246,39247,1343,39271,39295,39296,2836,39336,39354,39355,39405,39406,1863],{},"Z prvních dvou rovnic ",[883,39248,39250],{"className":39249},[886],[888,39251,39252],{"xmlns":890},[892,39253,39254,39268],{},[895,39255,39256,39262,39264,39266],{},[1661,39257,39258,39260],{},[898,39259,1665],{},[1667,39261,1680],{},[1656,39263,1713],{},[1667,39265,1680],{},[898,39267,25169],{},[902,39269,39270],{"encoding":904},"Q_2 = 2\\lambda",[883,39272,39274],{"className":39273},[886],[888,39275,39276],{"xmlns":890},[892,39277,39278,39292],{},[895,39279,39280,39286,39288,39290],{},[1661,39281,39282,39284],{},[898,39283,1665],{},[1667,39285,1669],{},[1656,39287,1713],{},[1667,39289,5193],{},[898,39291,25169],{},[902,39293,39294],{"encoding":904},"Q_1 = 5\\lambda","; dosazením do třetí ",[883,39297,39299],{"className":39298},[886],[888,39300,39301],{"xmlns":890},[892,39302,39303,39333],{},[895,39304,39305,39307,39309,39311,39313,39315,39317,39319,39321,39323,39325,39327,39329,39331],{},[1667,39306,5267],{},[1656,39308,1713],{},[1667,39310,1680],{},[1656,39312,2751],{},[1667,39314,5193],{},[898,39316,25169],{},[1656,39318,3633],{},[1667,39320,5193],{},[1656,39322,2751],{},[1667,39324,1680],{},[898,39326,25169],{},[1656,39328,1713],{},[1667,39330,9058],{},[898,39332,25169],{},[902,39334,39335],{"encoding":904},"100 = 2 \\cdot 5\\lambda + 5 \\cdot 2\\lambda = 20\\lambda",[883,39337,39339],{"className":39338},[886],[888,39340,39341],{"xmlns":890},[892,39342,39343,39351],{},[895,39344,39345,39347,39349],{},[898,39346,25169],{},[1656,39348,1713],{},[1667,39350,5193],{},[902,39352,39353],{"encoding":904},"\\lambda = 5",". Odtud ",[38,39356,39357,1343,39381],{},[883,39358,39360],{"className":39359},[886],[888,39361,39362],{"xmlns":890},[892,39363,39364,39378],{},[895,39365,39366,39374,39376],{},[1715,39367,39368,39370,39372],{},[898,39369,1665],{},[1667,39371,1669],{},[1656,39373,8187],{},[1656,39375,1713],{},[1667,39377,8567],{},[902,39379,39380],{"encoding":904},"Q_1^* = 25",[883,39382,39384],{"className":39383},[886],[888,39385,39386],{"xmlns":890},[892,39387,39388,39402],{},[895,39389,39390,39398,39400],{},[1715,39391,39392,39394,39396],{},[898,39393,1665],{},[1667,39395,1680],{},[1656,39397,8187],{},[1656,39399,1713],{},[1667,39401,8580],{},[902,39403,39404],{"encoding":904},"Q_2^* = 10",", maximální užitečnost ",[883,39407,39409],{"className":39408},[886],[888,39410,39411],{"xmlns":890},[892,39412,39413,39434],{},[895,39414,39415,39421,39423,39425,39427,39429,39431],{},[2062,39416,39417,39419],{},[898,39418,900],{},[1656,39420,8187],{},[1656,39422,1713],{},[1667,39424,8567],{},[1656,39426,2751],{},[1667,39428,8580],{},[1656,39430,1713],{},[1667,39432,39433],{},"250",[902,39435,39436],{"encoding":904},"U^* = 25 \\cdot 10 = 250",[724,39438,39439],{},[614,39440,39441,39442,36843,39480,1896,39504,39528,39529,39559,39560,39584,39585,39607,39608,1863],{},"Obrázek 6.8 — Rozpočtová přímka ",[883,39443,39445],{"className":39444},[886],[888,39446,39447],{"xmlns":890},[892,39448,39449,39477],{},[895,39450,39451,39453,39455,39457,39463,39465,39467,39473,39475],{},[1667,39452,5267],{},[1656,39454,3964],{},[1667,39456,1680],{},[1661,39458,39459,39461],{},[898,39460,1665],{},[1667,39462,1669],{},[1656,39464,3964],{},[1667,39466,5193],{},[1661,39468,39469,39471],{},[898,39470,1665],{},[1667,39472,1680],{},[1656,39474,1713],{},[1667,39476,4032],{},[902,39478,39479],{"encoding":904},"100 - 2 Q_1 - 5 Q_2 = 0",[883,39481,39483],{"className":39482},[886],[888,39484,39485],{"xmlns":890},[892,39486,39487,39501],{},[895,39488,39489,39491,39493,39495,39497,39499],{},[898,39490,2146],{},[1656,39492,3453],{"stretchy":1658},[1667,39494,4032],{},[1656,39496,1673],{"separator":1672},[1667,39498,9058],{},[1656,39500,3462],{"stretchy":1658},[902,39502,39503],{"encoding":904},"A[0, 20]",[883,39505,39507],{"className":39506},[886],[888,39508,39509],{"xmlns":890},[892,39510,39511,39525],{},[895,39512,39513,39515,39517,39519,39521,39523],{},[898,39514,2161],{},[1656,39516,3453],{"stretchy":1658},[1667,39518,9267],{},[1656,39520,1673],{"separator":1672},[1667,39522,4032],{},[1656,39524,3462],{"stretchy":1658},[902,39526,39527],{"encoding":904},"B[50, 0]","; hyperbolická indiferenční křivka ",[883,39530,39532],{"className":39531},[886],[888,39533,39534],{"xmlns":890},[892,39535,39536,39556],{},[895,39537,39538,39544,39546,39548,39550],{},[1661,39539,39540,39542],{},[898,39541,1665],{},[1667,39543,1680],{},[1656,39545,1713],{},[1667,39547,39433],{},[898,39549,1782],{"mathvariant":1723},[1661,39551,39552,39554],{},[898,39553,1665],{},[1667,39555,1669],{},[902,39557,39558],{"encoding":904},"Q_2 = 250\u002FQ_1"," se dotýká rozpočtové přímky v bodě ",[883,39561,39563],{"className":39562},[886],[888,39564,39565],{"xmlns":890},[892,39566,39567,39581],{},[895,39568,39569,39571,39573,39575,39577,39579],{},[898,39570,1842],{},[1656,39572,3453],{"stretchy":1658},[1667,39574,8567],{},[1656,39576,1673],{"separator":1672},[1667,39578,8580],{},[1656,39580,3462],{"stretchy":1658},[902,39582,39583],{"encoding":904},"E[25, 10]",". Sklon přímky ",[883,39586,39588],{"className":39587},[886],[888,39589,39590],{"xmlns":890},[892,39591,39592,39604],{},[895,39593,39594,39596],{},[1656,39595,3964],{},[4138,39597,39598],{"scriptlevel":4032,"displaystyle":1658},[3294,39599,39600,39602],{},[1667,39601,1680],{},[1667,39603,5193],{},[902,39605,39606],{"encoding":904},"-\\tfrac{2}{5}"," odpovídá ",[883,39609,39611],{"className":39610},[886],[888,39612,39613],{"xmlns":890},[892,39614,39615,39655],{},[895,39616,39617,39619,39621,39623,39625,39627,39629,39631,39633,39635,39643,39645,39647],{},[1656,39618,3964],{},[2461,39620,7362],{},[1656,39622,1659],{"stretchy":1658},[1667,39624,8567],{},[1656,39626,1673],{"separator":1672},[1667,39628,8580],{},[1656,39630,1683],{"stretchy":1658},[1656,39632,1713],{},[1656,39634,3964],{},[4138,39636,39637],{"scriptlevel":4032,"displaystyle":1658},[3294,39638,39639,39641],{},[1667,39640,8580],{},[1667,39642,8567],{},[1656,39644,1713],{},[1656,39646,3964],{},[4138,39648,39649],{"scriptlevel":4032,"displaystyle":1658},[3294,39650,39651,39653],{},[1667,39652,1680],{},[1667,39654,5193],{},[902,39656,39657],{"encoding":904},"-\\text{MRCS}(25, 10) = -\\tfrac{10}{25} = -\\tfrac{2}{5}",[115,39659,39661],{"id":39660},"funkce-poptávky-spotřebitele-marshallova","Funkce poptávky spotřebitele (Marshallova)",[724,39663,39664,39665,7648,39695,39698,39699,2114],{},"Považujeme-li v úloze ",[883,39666,39668],{"className":39667},[886],[888,39669,39670],{"xmlns":890},[892,39671,39672,39692],{},[895,39673,39674,39680,39682,39688,39690],{},[1661,39675,39676,39678],{},[898,39677,8194],{},[1667,39679,1669],{},[1656,39681,1673],{"separator":1672},[1661,39683,39684,39686],{},[898,39685,8194],{},[1667,39687,1680],{},[1656,39689,1673],{"separator":1672},[898,39691,8184],{},[902,39693,39694],{"encoding":904},"P_1, P_2, Y",[38,39696,39697],{},"parametry"," (nikoli čísla), dostáváme z první řádové podmínky ",[38,39700,39701],{},"Marshallovy poptávkové funkce",[883,39703,39705],{"className":39704},[886],[888,39706,39707],{"xmlns":890,"display":2408},[892,39708,39709,39804],{},[2412,39710,39711],{"width":2414},[2416,39712,39713,39715,39797,39799],{},[2419,39714],{"width":2421},[2419,39716,39717],{},[895,39718,39719,39725,39727,39733,39735,39741,39743,39749,39751,39753,39755,39757,39759,39765,39767,39773,39775,39781,39783,39789,39791,39793,39795],{},[1661,39720,39721,39723],{},[898,39722,1665],{},[1667,39724,1669],{},[1656,39726,1713],{},[1661,39728,39729,39731],{},[898,39730,6787],{},[1667,39732,1669],{},[1656,39734,1659],{"stretchy":1658},[1661,39736,39737,39739],{},[898,39738,8194],{},[1667,39740,1669],{},[1656,39742,1673],{"separator":1672},[1661,39744,39745,39747],{},[898,39746,8194],{},[1667,39748,1680],{},[1656,39750,1673],{"separator":1672},[898,39752,8184],{},[1656,39754,1683],{"stretchy":1658},[1656,39756,1673],{"separator":1672},[3316,39758],{"width":3318},[1661,39760,39761,39763],{},[898,39762,1665],{},[1667,39764,1680],{},[1656,39766,1713],{},[1661,39768,39769,39771],{},[898,39770,6787],{},[1667,39772,1680],{},[1656,39774,1659],{"stretchy":1658},[1661,39776,39777,39779],{},[898,39778,8194],{},[1667,39780,1669],{},[1656,39782,1673],{"separator":1672},[1661,39784,39785,39787],{},[898,39786,8194],{},[1667,39788,1680],{},[1656,39790,1673],{"separator":1672},[898,39792,8184],{},[1656,39794,1683],{"stretchy":1658},[1656,39796,1673],{"separator":1672},[2419,39798],{"width":2421},[2419,39800,39801],{},[2461,39802,39803],{},"(6.15)",[902,39805,39806],{"encoding":904},"Q_1 = D_1(P_1, P_2, Y), \\quad Q_2 = D_2(P_1, P_2, Y), \\tag{6.15}",[883,39808,39810],{"className":39809},[886],[888,39811,39812],{"xmlns":890,"display":2408},[892,39813,39814,39861],{},[2412,39815,39816],{"width":2414},[2416,39817,39818,39820,39854,39856],{},[2419,39819],{"width":2421},[2419,39821,39822],{},[895,39823,39824,39826,39828,39830,39832,39838,39840,39846,39848,39850,39852],{},[898,39825,25169],{},[1656,39827,1713],{},[898,39829,25169],{},[1656,39831,1659],{"stretchy":1658},[1661,39833,39834,39836],{},[898,39835,8194],{},[1667,39837,1669],{},[1656,39839,1673],{"separator":1672},[1661,39841,39842,39844],{},[898,39843,8194],{},[1667,39845,1680],{},[1656,39847,1673],{"separator":1672},[898,39849,8184],{},[1656,39851,1683],{"stretchy":1658},[898,39853,1863],{"mathvariant":1723},[2419,39855],{"width":2421},[2419,39857,39858],{},[2461,39859,39860],{},"(6.16)",[902,39862,39863],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, Y). \\tag{6.16}",[724,39865,39866,39896,39897,39963],{},[38,39867,39868,39869,1863],{},"Odvození pro ",[883,39870,39872],{"className":39871},[886],[888,39873,39874],{"xmlns":890},[892,39875,39876,39894],{},[895,39877,39878,39880,39882,39888],{},[898,39879,900],{},[1656,39881,1713],{},[1661,39883,39884,39886],{},[898,39885,1665],{},[1667,39887,1669],{},[1661,39889,39890,39892],{},[898,39891,1665],{},[1667,39893,1680],{},[902,39895,8546],{"encoding":904}," Lagrangeova funkce ",[883,39898,39900],{"className":39899},[886],[888,39901,39902],{"xmlns":890},[892,39903,39904,39960],{},[895,39905,39906,39908,39910,39916,39922,39924,39926,39928,39930,39932,39938,39944,39946,39952,39958],{},[898,39907,18539],{"mathvariant":37250},[1656,39909,1713],{},[1661,39911,39912,39914],{},[898,39913,1665],{},[1667,39915,1669],{},[1661,39917,39918,39920],{},[898,39919,1665],{},[1667,39921,1680],{},[1656,39923,3633],{},[898,39925,25169],{},[1656,39927,1659],{"stretchy":1658},[898,39929,8184],{},[1656,39931,3964],{},[1661,39933,39934,39936],{},[898,39935,8194],{},[1667,39937,1669],{},[1661,39939,39940,39942],{},[898,39941,1665],{},[1667,39943,1669],{},[1656,39945,3964],{},[1661,39947,39948,39950],{},[898,39949,8194],{},[1667,39951,1680],{},[1661,39953,39954,39956],{},[898,39955,1665],{},[1667,39957,1680],{},[1656,39959,1683],{"stretchy":1658},[902,39961,39962],{"encoding":904},"\\mathcal{L} = Q_1 Q_2 + \\lambda(Y - P_1 Q_1 - P_2 Q_2)"," dává soustavu",[883,39965,39967],{"className":39966},[886],[888,39968,39969],{"xmlns":890,"display":2408},[892,39970,39971,40138],{},[2412,39972,39973],{"width":2414},[2416,39974,39975,39977,40131,40133],{},[2419,39976],{"width":2421},[2419,39978,39979],{},[2412,39980,39981,40027,40073],{"rowspacing":29476,"columnalign":29477,"columnspacing":1724},[2416,39982,39983,39995],{},[2419,39984,39985],{},[4138,39986,39987],{"scriptlevel":4032,"displaystyle":1672},[1715,39988,39989,39991,39993],{},[898,39990,18539],{"mathvariant":37250},[1667,39992,1669],{},[1656,39994,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[2419,39996,39997],{},[4138,39998,39999],{"scriptlevel":4032,"displaystyle":1672},[895,40000,40001,40003,40005,40011,40013,40015,40021,40023,40025],{},[895,40002],{},[1656,40004,1713],{},[1661,40006,40007,40009],{},[898,40008,1665],{},[1667,40010,1680],{},[1656,40012,3964],{},[898,40014,25169],{},[1661,40016,40017,40019],{},[898,40018,8194],{},[1667,40020,1669],{},[1656,40022,1713],{},[1667,40024,4032],{},[1656,40026,1673],{"separator":1672},[2416,40028,40029,40041],{},[2419,40030,40031],{},[4138,40032,40033],{"scriptlevel":4032,"displaystyle":1672},[1715,40034,40035,40037,40039],{},[898,40036,18539],{"mathvariant":37250},[1667,40038,1680],{},[1656,40040,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[2419,40042,40043],{},[4138,40044,40045],{"scriptlevel":4032,"displaystyle":1672},[895,40046,40047,40049,40051,40057,40059,40061,40067,40069,40071],{},[895,40048],{},[1656,40050,1713],{},[1661,40052,40053,40055],{},[898,40054,1665],{},[1667,40056,1669],{},[1656,40058,3964],{},[898,40060,25169],{},[1661,40062,40063,40065],{},[898,40064,8194],{},[1667,40066,1680],{},[1656,40068,1713],{},[1667,40070,4032],{},[1656,40072,1673],{"separator":1672},[2416,40074,40075,40087],{},[2419,40076,40077],{},[4138,40078,40079],{"scriptlevel":4032,"displaystyle":1672},[1715,40080,40081,40083,40085],{},[898,40082,18539],{"mathvariant":37250},[898,40084,25169],{},[1656,40086,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[2419,40088,40089],{},[4138,40090,40091],{"scriptlevel":4032,"displaystyle":1672},[895,40092,40093,40095,40097,40099,40101,40107,40113,40115,40121,40127,40129],{},[895,40094],{},[1656,40096,1713],{},[898,40098,8184],{},[1656,40100,3964],{},[1661,40102,40103,40105],{},[898,40104,8194],{},[1667,40106,1669],{},[1661,40108,40109,40111],{},[898,40110,1665],{},[1667,40112,1669],{},[1656,40114,3964],{},[1661,40116,40117,40119],{},[898,40118,8194],{},[1667,40120,1680],{},[1661,40122,40123,40125],{},[898,40124,1665],{},[1667,40126,1680],{},[1656,40128,1713],{},[1667,40130,4283],{},[2419,40132],{"width":2421},[2419,40134,40135],{},[2461,40136,40137],{},"(6.17)",[902,40139,40140],{"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}",[724,40142,40143,40144,40172,40173,40201,40202,40270],{},"Z prvních dvou: ",[883,40145,40147],{"className":40146},[886],[888,40148,40149],{"xmlns":890},[892,40150,40151,40169],{},[895,40152,40153,40159,40161,40167],{},[1661,40154,40155,40157],{},[898,40156,1665],{},[1667,40158,1680],{},[1656,40160,1713],{},[1661,40162,40163,40165],{},[898,40164,8194],{},[1667,40166,1669],{},[898,40168,25169],{},[902,40170,40171],{"encoding":904},"Q_2 = P_1 \\lambda"," (6.18), ",[883,40174,40176],{"className":40175},[886],[888,40177,40178],{"xmlns":890},[892,40179,40180,40198],{},[895,40181,40182,40188,40190,40196],{},[1661,40183,40184,40186],{},[898,40185,1665],{},[1667,40187,1669],{},[1656,40189,1713],{},[1661,40191,40192,40194],{},[898,40193,8194],{},[1667,40195,1680],{},[898,40197,25169],{},[902,40199,40200],{"encoding":904},"Q_1 = P_2 \\lambda"," (6.19). Dosazením do třetí ",[883,40203,40205],{"className":40204},[886],[888,40206,40207],{"xmlns":890},[892,40208,40209,40267],{},[895,40210,40211,40213,40215,40221,40223,40229,40231,40233,40239,40241,40247,40249,40251,40253,40259,40265],{},[898,40212,8184],{},[1656,40214,1713],{},[1661,40216,40217,40219],{},[898,40218,8194],{},[1667,40220,1669],{},[1656,40222,2751],{},[1661,40224,40225,40227],{},[898,40226,8194],{},[1667,40228,1680],{},[898,40230,25169],{},[1656,40232,3633],{},[1661,40234,40235,40237],{},[898,40236,8194],{},[1667,40238,1680],{},[1656,40240,2751],{},[1661,40242,40243,40245],{},[898,40244,8194],{},[1667,40246,1669],{},[898,40248,25169],{},[1656,40250,1713],{},[1667,40252,1680],{},[1661,40254,40255,40257],{},[898,40256,8194],{},[1667,40258,1669],{},[1661,40260,40261,40263],{},[898,40262,8194],{},[1667,40264,1680],{},[898,40266,25169],{},[902,40268,40269],{"encoding":904},"Y = P_1 \\cdot P_2 \\lambda + P_2 \\cdot P_1 \\lambda = 2 P_1 P_2 \\lambda",", odtud",[883,40272,40274],{"className":40273},[886],[888,40275,40276],{"xmlns":890,"display":2408},[892,40277,40278,40321],{},[2412,40279,40280],{"width":2414},[2416,40281,40282,40284,40314,40316],{},[2419,40283],{"width":2421},[2419,40285,40286],{},[895,40287,40288,40290,40292,40312],{},[898,40289,25169],{},[1656,40291,1713],{},[3294,40293,40294,40296],{},[898,40295,8184],{},[895,40297,40298,40300,40306],{},[1667,40299,1680],{},[1661,40301,40302,40304],{},[898,40303,8194],{},[1667,40305,1669],{},[1661,40307,40308,40310],{},[898,40309,8194],{},[1667,40311,1680],{},[898,40313,1863],{"mathvariant":1723},[2419,40315],{"width":2421},[2419,40317,40318],{},[2461,40319,40320],{},"(6.20)",[902,40322,40323],{"encoding":904},"\\lambda = \\frac{Y}{2 P_1 P_2}. \\tag{6.20}",[724,40325,40326],{},"Zpětně:",[883,40328,40330],{"className":40329},[886],[888,40331,40332],{"xmlns":890,"display":2408},[892,40333,40334,40411],{},[2412,40335,40336],{"width":2414},[2416,40337,40338,40340,40404,40406],{},[2419,40339],{"width":2421},[2419,40341,40342],{},[21566,40343,40344],{"notation":21568},[4138,40345,40346],{"scriptlevel":4032,"displaystyle":1658},[4138,40347,40348],{"scriptlevel":4032,"displaystyle":1658},[4138,40349,40350],{"scriptlevel":4032,"displaystyle":1672},[895,40351,40352,40354,40360,40362,40376,40378,40380,40386,40388,40402],{},[2461,40353,12767],{},[1661,40355,40356,40358],{},[898,40357,1665],{},[1667,40359,1669],{},[1656,40361,1713],{},[3294,40363,40364,40366],{},[898,40365,8184],{},[895,40367,40368,40370],{},[1667,40369,1680],{},[1661,40371,40372,40374],{},[898,40373,8194],{},[1667,40375,1669],{},[1656,40377,1673],{"separator":1672},[3316,40379],{"width":3318},[1661,40381,40382,40384],{},[898,40383,1665],{},[1667,40385,1680],{},[1656,40387,1713],{},[3294,40389,40390,40392],{},[898,40391,8184],{},[895,40393,40394,40396],{},[1667,40395,1680],{},[1661,40397,40398,40400],{},[898,40399,8194],{},[1667,40401,1680],{},[2461,40403,12767],{},[2419,40405],{"width":2421},[2419,40407,40408],{},[2461,40409,40410],{},"(6.21)",[902,40412,40413],{"encoding":904},"\\boxed{\\; Q_1 = \\frac{Y}{2 P_1}, \\quad Q_2 = \\frac{Y}{2 P_2} \\;} \\tag{6.21}",[198,40415,40417],{"id":40416},"engelova-funkce","Engelova funkce",[724,40419,18411,40420,40423,40424,40427,40428,28588,40445,1343,40475,40505,40506,40540,40541,1343,40567,40593],{},[38,40421,40422],{},"pevné ceny"," a proměnný důchod se Marshallova poptávka stává ",[38,40425,40426],{},"Engelovou funkcí",": pro ",[883,40429,40431],{"className":40430},[886],[888,40432,40433],{"xmlns":890},[892,40434,40435,40443],{},[895,40436,40437,40439,40441],{},[898,40438,8184],{},[1656,40440,1713],{},[1667,40442,5267],{},[902,40444,29040],{"encoding":904},[883,40446,40448],{"className":40447},[886],[888,40449,40450],{"xmlns":890},[892,40451,40452,40472],{},[895,40453,40454,40460,40462,40464,40466],{},[1661,40455,40456,40458],{},[898,40457,1665],{},[1667,40459,1669],{},[1656,40461,1713],{},[1667,40463,9267],{},[898,40465,1782],{"mathvariant":1723},[1661,40467,40468,40470],{},[898,40469,8194],{},[1667,40471,1669],{},[902,40473,40474],{"encoding":904},"Q_1 = 50\u002FP_1",[883,40476,40478],{"className":40477},[886],[888,40479,40480],{"xmlns":890},[892,40481,40482,40502],{},[895,40483,40484,40490,40492,40494,40496],{},[1661,40485,40486,40488],{},[898,40487,1665],{},[1667,40489,1680],{},[1656,40491,1713],{},[1667,40493,9267],{},[898,40495,1782],{"mathvariant":1723},[1661,40497,40498,40500],{},[898,40499,8194],{},[1667,40501,1680],{},[902,40503,40504],{"encoding":904},"Q_2 = 50\u002FP_2",". Pro pevné ceny ",[883,40507,40509],{"className":40508},[886],[888,40510,40511],{"xmlns":890},[892,40512,40513,40537],{},[895,40514,40515,40521,40523,40525,40527,40533,40535],{},[1661,40516,40517,40519],{},[898,40518,8194],{},[1667,40520,1669],{},[1656,40522,1713],{},[1667,40524,8580],{},[1656,40526,1673],{"separator":1672},[1661,40528,40529,40531],{},[898,40530,8194],{},[1667,40532,1680],{},[1656,40534,1713],{},[1667,40536,9058],{},[902,40538,40539],{"encoding":904},"P_1 = 10, P_2 = 20"," dostáváme Engelovy funkce ",[883,40542,40544],{"className":40543},[886],[888,40545,40546],{"xmlns":890},[892,40547,40548,40564],{},[895,40549,40550,40556,40558,40560,40562],{},[1661,40551,40552,40554],{},[898,40553,1665],{},[1667,40555,1669],{},[1656,40557,1713],{},[898,40559,8184],{},[898,40561,1782],{"mathvariant":1723},[1667,40563,9058],{},[902,40565,40566],{"encoding":904},"Q_1 = Y\u002F20",[883,40568,40570],{"className":40569},[886],[888,40571,40572],{"xmlns":890},[892,40573,40574,40590],{},[895,40575,40576,40582,40584,40586,40588],{},[1661,40577,40578,40580],{},[898,40579,1665],{},[1667,40581,1680],{},[1656,40583,1713],{},[898,40585,8184],{},[898,40587,1782],{"mathvariant":1723},[1667,40589,9135],{},[902,40591,40592],{"encoding":904},"Q_2 = Y\u002F40"," — lineární závislost spotřebovaného množství na důchodu.",[115,40595,40597],{"id":40596},"duální-úloha-minimalizace-výdajů","Duální úloha — minimalizace výdajů",[724,40599,40600],{},"Výdaje spotřebitele jsou",[883,40602,40604],{"className":40603},[886],[888,40605,40606],{"xmlns":890,"display":2408},[892,40607,40608,40683],{},[2412,40609,40610],{"width":2414},[2416,40611,40612,40614,40676,40678],{},[2419,40613],{"width":2421},[2419,40615,40616],{},[895,40617,40618,40620,40622,40624,40626,40632,40634,40640,40642,40644,40652,40658,40660,40668,40674],{},[898,40619,1842],{},[1656,40621,1713],{},[898,40623,1842],{},[1656,40625,1659],{"stretchy":1658},[1661,40627,40628,40630],{},[898,40629,1665],{},[1667,40631,1669],{},[1656,40633,1673],{"separator":1672},[1661,40635,40636,40638],{},[898,40637,1665],{},[1667,40639,1680],{},[1656,40641,1683],{"stretchy":1658},[1656,40643,1713],{},[1715,40645,40646,40648,40650],{},[898,40647,8194],{},[1667,40649,1669],{},[1656,40651,8187],{},[1661,40653,40654,40656],{},[898,40655,1665],{},[1667,40657,1669],{},[1656,40659,3633],{},[1715,40661,40662,40664,40666],{},[898,40663,8194],{},[1667,40665,1680],{},[1656,40667,8187],{},[1661,40669,40670,40672],{},[898,40671,1665],{},[1667,40673,1680],{},[1656,40675,1673],{"separator":1672},[2419,40677],{"width":2421},[2419,40679,40680],{},[2461,40681,40682],{},"(6.22)",[902,40684,40685],{"encoding":904},"E = E(Q_1, Q_2) = P_1^* Q_1 + P_2^* Q_2, \\tag{6.22}",[724,40687,40688],{},"a je pevně zadána hladina užitečnosti",[883,40690,40692],{"className":40691},[886],[888,40693,40694],{"xmlns":890,"display":2408},[892,40695,40696,40743],{},[2412,40697,40698],{"width":2414},[2416,40699,40700,40702,40736,40738],{},[2419,40701],{"width":2421},[2419,40703,40704],{},[895,40705,40706,40712,40714,40716,40718,40724,40726,40732,40734],{},[2062,40707,40708,40710],{},[898,40709,900],{},[1656,40711,8187],{},[1656,40713,1713],{},[898,40715,900],{},[1656,40717,1659],{"stretchy":1658},[1661,40719,40720,40722],{},[898,40721,1665],{},[1667,40723,1669],{},[1656,40725,1673],{"separator":1672},[1661,40727,40728,40730],{},[898,40729,1665],{},[1667,40731,1680],{},[1656,40733,1683],{"stretchy":1658},[898,40735,1863],{"mathvariant":1723},[2419,40737],{"width":2421},[2419,40739,40740],{},[2461,40741,40742],{},"(6.23)",[902,40744,40745],{"encoding":904},"U^* = U(Q_1, Q_2). \\tag{6.23}",[724,40747,40748,40751,40752,40784,40785,1863],{},[38,40749,40750],{},"Úlohou o minimalizaci výdajů"," je najít minimum ",[883,40753,40755],{"className":40754},[886],[888,40756,40757],{"xmlns":890},[892,40758,40759,40781],{},[895,40760,40761,40763,40765,40771,40773,40779],{},[898,40762,1842],{},[1656,40764,1659],{"stretchy":1658},[1661,40766,40767,40769],{},[898,40768,1665],{},[1667,40770,1669],{},[1656,40772,1673],{"separator":1672},[1661,40774,40775,40777],{},[898,40776,1665],{},[1667,40778,1680],{},[1656,40780,1683],{"stretchy":1658},[902,40782,40783],{"encoding":904},"E(Q_1, Q_2)"," vázané podmínkou (6.23) ve tvaru ",[883,40786,40788],{"className":40787},[886],[888,40789,40790],{"xmlns":890},[892,40791,40792,40848],{},[895,40793,40794,40796,40798,40804,40806,40812,40814,40816,40822,40824,40826,40828,40834,40836,40842,40844,40846],{},[898,40795,19780],{},[1656,40797,1659],{"stretchy":1658},[1661,40799,40800,40802],{},[898,40801,1665],{},[1667,40803,1669],{},[1656,40805,1673],{"separator":1672},[1661,40807,40808,40810],{},[898,40809,1665],{},[1667,40811,1680],{},[1656,40813,1683],{"stretchy":1658},[1656,40815,1713],{},[2062,40817,40818,40820],{},[898,40819,900],{},[1656,40821,8187],{},[1656,40823,3964],{},[898,40825,900],{},[1656,40827,1659],{"stretchy":1658},[1661,40829,40830,40832],{},[898,40831,1665],{},[1667,40833,1669],{},[1656,40835,1673],{"separator":1672},[1661,40837,40838,40840],{},[898,40839,1665],{},[1667,40841,1680],{},[1656,40843,1683],{"stretchy":1658},[1656,40845,1713],{},[1667,40847,4032],{},[902,40849,40850],{"encoding":904},"g(Q_1, Q_2) = U^* - U(Q_1, Q_2) = 0",[198,40852,40854],{"id":40853},"lagrangeova-funkce","Lagrangeova funkce",[883,40856,40858],{"className":40857},[886],[888,40859,40860],{"xmlns":890,"display":2408},[892,40861,40862,40973],{},[2412,40863,40864],{"width":2414},[2416,40865,40866,40868,40966,40968],{},[2419,40867],{"width":2421},[2419,40869,40870],{},[895,40871,40872,40874,40876,40882,40884,40890,40892,40894,40896,40898,40906,40912,40914,40922,40928,40930,40932,40934,40940,40942,40944,40946,40952,40954,40960,40962,40964],{},[898,40873,18539],{"mathvariant":37250},[1656,40875,1659],{"stretchy":1658},[1661,40877,40878,40880],{},[898,40879,1665],{},[1667,40881,1669],{},[1656,40883,1673],{"separator":1672},[1661,40885,40886,40888],{},[898,40887,1665],{},[1667,40889,1680],{},[1656,40891,1673],{"separator":1672},[898,40893,25169],{},[1656,40895,1683],{"stretchy":1658},[1656,40897,1713],{},[1715,40899,40900,40902,40904],{},[898,40901,8194],{},[1667,40903,1669],{},[1656,40905,8187],{},[1661,40907,40908,40910],{},[898,40909,1665],{},[1667,40911,1669],{},[1656,40913,3633],{},[1715,40915,40916,40918,40920],{},[898,40917,8194],{},[1667,40919,1680],{},[1656,40921,8187],{},[1661,40923,40924,40926],{},[898,40925,1665],{},[1667,40927,1680],{},[1656,40929,3633],{},[898,40931,25169],{},[1656,40933,1659],{"stretchy":1658},[2062,40935,40936,40938],{},[898,40937,900],{},[1656,40939,8187],{},[1656,40941,3964],{},[898,40943,900],{},[1656,40945,1659],{"stretchy":1658},[1661,40947,40948,40950],{},[898,40949,1665],{},[1667,40951,1669],{},[1656,40953,1673],{"separator":1672},[1661,40955,40956,40958],{},[898,40957,1665],{},[1667,40959,1680],{},[1656,40961,1683],{"stretchy":1658},[1656,40963,1683],{"stretchy":1658},[898,40965,1863],{"mathvariant":1723},[2419,40967],{"width":2421},[2419,40969,40970],{},[2461,40971,40972],{},"(6.24)",[902,40974,40975],{"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}",[724,40977,40978],{},"Soustava podmínek prvního řádu:",[883,40980,40982],{"className":40981},[886],[888,40983,40984],{"xmlns":890,"display":2408},[892,40985,40986,41159],{},[2412,40987,40988],{"width":2414},[2416,40989,40990,40992,41152,41154],{},[2419,40991],{"width":2421},[2419,40993,40994],{},[2412,40995,40996,41046,41096],{"rowspacing":29476,"columnalign":29477,"columnspacing":1724},[2416,40997,40998,41010],{},[2419,40999,41000],{},[4138,41001,41002],{"scriptlevel":4032,"displaystyle":1672},[1715,41003,41004,41006,41008],{},[898,41005,18539],{"mathvariant":37250},[1667,41007,1669],{},[1656,41009,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[2419,41011,41012],{},[4138,41013,41014],{"scriptlevel":4032,"displaystyle":1672},[895,41015,41016,41018,41020,41028,41030,41032,41040,41042,41044],{},[895,41017],{},[1656,41019,1713],{},[1715,41021,41022,41024,41026],{},[898,41023,8194],{},[1667,41025,1669],{},[1656,41027,8187],{},[1656,41029,3964],{},[898,41031,25169],{},[1715,41033,41034,41036,41038],{},[898,41035,900],{},[1667,41037,1669],{},[1656,41039,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,41041,1713],{},[1667,41043,4032],{},[1656,41045,1673],{"separator":1672},[2416,41047,41048,41060],{},[2419,41049,41050],{},[4138,41051,41052],{"scriptlevel":4032,"displaystyle":1672},[1715,41053,41054,41056,41058],{},[898,41055,18539],{"mathvariant":37250},[1667,41057,1680],{},[1656,41059,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[2419,41061,41062],{},[4138,41063,41064],{"scriptlevel":4032,"displaystyle":1672},[895,41065,41066,41068,41070,41078,41080,41082,41090,41092,41094],{},[895,41067],{},[1656,41069,1713],{},[1715,41071,41072,41074,41076],{},[898,41073,8194],{},[1667,41075,1680],{},[1656,41077,8187],{},[1656,41079,3964],{},[898,41081,25169],{},[1715,41083,41084,41086,41088],{},[898,41085,900],{},[1667,41087,1680],{},[1656,41089,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,41091,1713],{},[1667,41093,4032],{},[1656,41095,1673],{"separator":1672},[2416,41097,41098,41110],{},[2419,41099,41100],{},[4138,41101,41102],{"scriptlevel":4032,"displaystyle":1672},[1715,41103,41104,41106,41108],{},[898,41105,18539],{"mathvariant":37250},[898,41107,25169],{},[1656,41109,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[2419,41111,41112],{},[4138,41113,41114],{"scriptlevel":4032,"displaystyle":1672},[895,41115,41116,41118,41120,41126,41128,41130,41132,41138,41140,41146,41148,41150],{},[895,41117],{},[1656,41119,1713],{},[2062,41121,41122,41124],{},[898,41123,900],{},[1656,41125,8187],{},[1656,41127,3964],{},[898,41129,900],{},[1656,41131,1659],{"stretchy":1658},[1661,41133,41134,41136],{},[898,41135,1665],{},[1667,41137,1669],{},[1656,41139,1673],{"separator":1672},[1661,41141,41142,41144],{},[898,41143,1665],{},[1667,41145,1680],{},[1656,41147,1683],{"stretchy":1658},[1656,41149,1713],{},[1667,41151,4283],{},[2419,41153],{"width":2421},[2419,41155,41156],{},[2461,41157,41158],{},"(6.25)",[902,41160,41161],{"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}",[724,41163,41164],{},"Postačující podmínka pro minimum (vzhledem k linearitě funkce výdajů) má tvar",[883,41166,41168],{"className":41167},[886],[888,41169,41170],{"xmlns":890,"display":2408},[892,41171,41172,41269],{},[2412,41173,41174],{"width":2414},[2416,41175,41176,41178,41262,41264],{},[2419,41177],{"width":2421},[2419,41179,41180],{},[895,41181,41182,41184,41186,41192,41194,41200,41202,41204,41206,41208,41210,41212,41260],{},[898,41183,6787],{},[1656,41185,1659],{"stretchy":1658},[1661,41187,41188,41190],{},[898,41189,1665],{},[1667,41191,1669],{},[1656,41193,1673],{"separator":1672},[1661,41195,41196,41198],{},[898,41197,1665],{},[1667,41199,1680],{},[1656,41201,1673],{"separator":1672},[898,41203,25169],{},[1656,41205,1683],{"stretchy":1658},[1656,41207,1713],{},[1656,41209,3964],{},[898,41211,25169],{},[895,41213,41214,41216,41228,41230,41242,41244,41246,41258],{},[1656,41215,1659],{"fence":1672},[1715,41217,41218,41220,41222],{},[898,41219,900],{},[1667,41221,4364],{},[895,41223,41224,41226],{},[1656,41225,1725],{"mathvariant":1723},[1656,41227,1725],{"mathvariant":1723},[1656,41229,3633],{},[1715,41231,41232,41234,41236],{},[898,41233,900],{},[1667,41235,4386],{},[895,41237,41238,41240],{},[1656,41239,1725],{"mathvariant":1723},[1656,41241,1725],{"mathvariant":1723},[1656,41243,3633],{},[1667,41245,1680],{},[1715,41247,41248,41250,41252],{},[898,41249,900],{},[1667,41251,9140],{},[895,41253,41254,41256],{},[1656,41255,1725],{"mathvariant":1723},[1656,41257,1725],{"mathvariant":1723},[1656,41259,1683],{"fence":1672},[898,41261,1863],{"mathvariant":1723},[2419,41263],{"width":2421},[2419,41265,41266],{},[2461,41267,41268],{},"(6.26)",[902,41270,41271],{"encoding":904},"D(Q_1, Q_2, \\lambda) = -\\lambda \\left(U''_{11} + U''_{22} + 2 U''_{12}\\right). \\tag{6.26}",[724,41273,41274,41277,41278,41317,41318,41357,41358,41408,41409,41435,41436,41453,41454,41480],{},[38,41275,41276],{},"Geometrie (obrázek 6.9)."," Řešením je bod ",[883,41279,41281],{"className":41280},[886],[888,41282,41283],{"xmlns":890},[892,41284,41285,41315],{},[895,41286,41287,41293,41295,41303,41305,41313],{},[2062,41288,41289,41291],{},[898,41290,1665],{},[1656,41292,8187],{},[1656,41294,3453],{"stretchy":1658},[1715,41296,41297,41299,41301],{},[898,41298,1665],{},[1667,41300,1669],{},[1656,41302,8187],{},[1656,41304,1673],{"separator":1672},[1715,41306,41307,41309,41311],{},[898,41308,1665],{},[1667,41310,1680],{},[1656,41312,8187],{},[1656,41314,3462],{"stretchy":1658},[902,41316,8443],{"encoding":904}," dotyku křivky užitečnosti ",[883,41319,41321],{"className":41320},[886],[888,41322,41323],{"xmlns":890},[892,41324,41325,41355],{},[895,41326,41327,41333,41335,41337,41339,41345,41347,41353],{},[2062,41328,41329,41331],{},[898,41330,900],{},[1656,41332,8187],{},[1656,41334,1713],{},[898,41336,900],{},[1656,41338,1659],{"stretchy":1658},[1661,41340,41341,41343],{},[898,41342,1665],{},[1667,41344,1669],{},[1656,41346,1673],{"separator":1672},[1661,41348,41349,41351],{},[898,41350,1665],{},[1667,41352,1680],{},[1656,41354,1683],{"stretchy":1658},[902,41356,26390],{"encoding":904}," s přímkou výdajů ",[883,41359,41361],{"className":41360},[886],[888,41362,41363],{"xmlns":890},[892,41364,41365,41405],{},[895,41366,41367,41373,41375,41383,41389,41391,41399],{},[2062,41368,41369,41371],{},[898,41370,1842],{},[1656,41372,8187],{},[1656,41374,1713],{},[1715,41376,41377,41379,41381],{},[898,41378,8194],{},[1667,41380,1669],{},[1656,41382,8187],{},[1661,41384,41385,41387],{},[898,41386,1665],{},[1667,41388,1669],{},[1656,41390,3633],{},[1715,41392,41393,41395,41397],{},[898,41394,8194],{},[1667,41396,1680],{},[1656,41398,8187],{},[1661,41400,41401,41403],{},[898,41402,1665],{},[1667,41404,1680],{},[902,41406,41407],{"encoding":904},"E^* = P_1^* Q_1 + P_2^* Q_2",". Hladina ",[883,41410,41412],{"className":41411},[886],[888,41413,41414],{"xmlns":890},[892,41415,41416,41432],{},[895,41417,41418,41424,41426],{},[1661,41419,41420,41422],{},[898,41421,1842],{},[1667,41423,4032],{},[1656,41425,4373],{},[2062,41427,41428,41430],{},[898,41429,1842],{},[1656,41431,8187],{},[902,41433,41434],{"encoding":904},"E_0 \u003C E^*"," nestačí k dosažení ",[883,41437,41439],{"className":41438},[886],[888,41440,41441],{"xmlns":890},[892,41442,41443,41451],{},[895,41444,41445],{},[2062,41446,41447,41449],{},[898,41448,900],{},[1656,41450,8187],{},[902,41452,8343],{"encoding":904},", hladina ",[883,41455,41457],{"className":41456},[886],[888,41458,41459],{"xmlns":890},[892,41460,41461,41477],{},[895,41462,41463,41469,41471],{},[1661,41464,41465,41467],{},[898,41466,1842],{},[1667,41468,1669],{},[1656,41470,2850],{},[2062,41472,41473,41475],{},[898,41474,1842],{},[1656,41476,8187],{},[902,41478,41479],{"encoding":904},"E_1 > E^*"," je nadbytečná.",[1981,41482,41483,41488],{},[724,41484,41485,41487],{},[883,41486,10188],{}," Postup — duální úloha (minimalizace výdajů)",[152,41489,41490,41540,41626,41666,41741],{},[123,41491,41492,1643,41495,41539],{},[38,41493,41494],{},"Zapiš vazbu",[883,41496,41498],{"className":41497},[886],[888,41499,41500],{"xmlns":890},[892,41501,41502,41536],{},[895,41503,41504,41510,41512,41514,41516,41522,41524,41530,41532,41534],{},[2062,41505,41506,41508],{},[898,41507,900],{},[1656,41509,8187],{},[1656,41511,3964],{},[898,41513,900],{},[1656,41515,1659],{"stretchy":1658},[1661,41517,41518,41520],{},[898,41519,1665],{},[1667,41521,1669],{},[1656,41523,1673],{"separator":1672},[1661,41525,41526,41528],{},[898,41527,1665],{},[1667,41529,1680],{},[1656,41531,1683],{"stretchy":1658},[1656,41533,1713],{},[1667,41535,4032],{},[902,41537,41538],{"encoding":904},"U^* - U(Q_1, Q_2) = 0"," (zadaná hladina užitečnosti).",[123,41541,41542,1643,41544,1863],{},[38,41543,37959],{},[883,41545,41547],{"className":41546},[886],[888,41548,41549],{"xmlns":890},[892,41550,41551,41623],{},[895,41552,41553,41555,41557,41565,41571,41573,41581,41587,41589,41591,41593,41599,41601,41603,41605,41611,41613,41619,41621],{},[898,41554,18539],{"mathvariant":37250},[1656,41556,1713],{},[1715,41558,41559,41561,41563],{},[898,41560,8194],{},[1667,41562,1669],{},[1656,41564,8187],{},[1661,41566,41567,41569],{},[898,41568,1665],{},[1667,41570,1669],{},[1656,41572,3633],{},[1715,41574,41575,41577,41579],{},[898,41576,8194],{},[1667,41578,1680],{},[1656,41580,8187],{},[1661,41582,41583,41585],{},[898,41584,1665],{},[1667,41586,1680],{},[1656,41588,3633],{},[898,41590,25169],{},[1656,41592,1659],{"stretchy":1658},[2062,41594,41595,41597],{},[898,41596,900],{},[1656,41598,8187],{},[1656,41600,3964],{},[898,41602,900],{},[1656,41604,1659],{"stretchy":1658},[1661,41606,41607,41609],{},[898,41608,1665],{},[1667,41610,1669],{},[1656,41612,1673],{"separator":1672},[1661,41614,41615,41617],{},[898,41616,1665],{},[1667,41618,1680],{},[1656,41620,1683],{"stretchy":1658},[1656,41622,1683],{"stretchy":1658},[902,41624,41625],{"encoding":904},"\\mathcal{L} = P_1^* Q_1 + P_2^* Q_2 + \\lambda(U^* - U(Q_1, Q_2))",[123,41627,41628,41631,41632,41665],{},[38,41629,41630],{},"Derivace rovny nule",", z prvních dvou rovnic podílem dostaneš podmínku ",[883,41633,41635],{"className":41634},[886],[888,41636,41637],{"xmlns":890},[892,41638,41639,41663],{},[895,41640,41641,41643,41645,41653,41655],{},[2461,41642,7362],{},[1656,41644,1713],{},[1715,41646,41647,41649,41651],{},[898,41648,8194],{},[1667,41650,1669],{},[1656,41652,8187],{},[898,41654,1782],{"mathvariant":1723},[1715,41656,41657,41659,41661],{},[898,41658,8194],{},[1667,41660,1680],{},[1656,41662,8187],{},[902,41664,37681],{"encoding":904}," (stejná jako u maximalizace!).",[123,41667,41668,1643,41671,41711,41712,1863],{},[38,41669,41670],{},"Dosaď do vazby",[883,41672,41674],{"className":41673},[886],[888,41675,41676],{"xmlns":890},[892,41677,41678,41708],{},[895,41679,41680,41682,41684,41690,41692,41698,41700,41702],{},[898,41681,900],{},[1656,41683,1659],{"stretchy":1658},[1661,41685,41686,41688],{},[898,41687,1665],{},[1667,41689,1669],{},[1656,41691,1673],{"separator":1672},[1661,41693,41694,41696],{},[898,41695,1665],{},[1667,41697,1680],{},[1656,41699,1683],{"stretchy":1658},[1656,41701,1713],{},[2062,41703,41704,41706],{},[898,41705,900],{},[1656,41707,8187],{},[902,41709,41710],{"encoding":904},"U(Q_1, Q_2) = U^*"," a vyřeš pro ",[883,41713,41715],{"className":41714},[886],[888,41716,41717],{"xmlns":890},[892,41718,41719,41739],{},[895,41720,41721,41729,41731],{},[1715,41722,41723,41725,41727],{},[898,41724,1665],{},[1667,41726,1669],{},[1656,41728,8187],{},[1656,41730,1673],{"separator":1672},[1715,41732,41733,41735,41737],{},[898,41734,1665],{},[1667,41736,1680],{},[1656,41738,8187],{},[902,41740,38200],{"encoding":904},[123,41742,41743,1643,41746,41800],{},[38,41744,41745],{},"Vypočítej minimální výdaje",[883,41747,41749],{"className":41748},[886],[888,41750,41751],{"xmlns":890},[892,41752,41753,41797],{},[895,41754,41755,41761,41763,41771,41779,41781,41789],{},[2062,41756,41757,41759],{},[898,41758,1842],{},[1656,41760,8187],{},[1656,41762,1713],{},[1715,41764,41765,41767,41769],{},[898,41766,8194],{},[1667,41768,1669],{},[1656,41770,8187],{},[1715,41772,41773,41775,41777],{},[898,41774,1665],{},[1667,41776,1669],{},[1656,41778,8187],{},[1656,41780,3633],{},[1715,41782,41783,41785,41787],{},[898,41784,8194],{},[1667,41786,1680],{},[1656,41788,8187],{},[1715,41790,41791,41793,41795],{},[898,41792,1665],{},[1667,41794,1680],{},[1656,41796,8187],{},[902,41798,41799],{"encoding":904},"E^* = P_1^* Q_1^* + P_2^* Q_2^*"," a případně ověř druhou podmínku (6.26).",[115,41802,41804,41805],{"id":41803},"příklad-67-minimalizace-výdajů-pro-uq112q212u-q_112-q_212","Příklad 6.7 — minimalizace výdajů pro ",[883,41806,41808],{"className":41807},[886],[888,41809,41810],{"xmlns":890},[892,41811,41812,41846],{},[895,41813,41814,41816,41818,41832],{},[898,41815,900],{},[1656,41817,1713],{},[1715,41819,41820,41822,41824],{},[898,41821,1665],{},[1667,41823,1669],{},[895,41825,41826,41828,41830],{},[1667,41827,1669],{},[898,41829,1782],{"mathvariant":1723},[1667,41831,1680],{},[1715,41833,41834,41836,41838],{},[898,41835,1665],{},[1667,41837,1680],{},[895,41839,41840,41842,41844],{},[1667,41841,1669],{},[898,41843,1782],{"mathvariant":1723},[1667,41845,1680],{},[902,41847,8663],{"encoding":904},[724,41849,41850,41851,1343,41873,1343,41897,39036],{},"Dáno ",[883,41852,41854],{"className":41853},[886],[888,41855,41856],{"xmlns":890},[892,41857,41858,41870],{},[895,41859,41860,41866,41868],{},[2062,41861,41862,41864],{},[898,41863,900],{},[1656,41865,8187],{},[1656,41867,1713],{},[1667,41869,1680],{},[902,41871,41872],{"encoding":904},"U^* = 2",[883,41874,41876],{"className":41875},[886],[888,41877,41878],{"xmlns":890},[892,41879,41880,41894],{},[895,41881,41882,41890,41892],{},[1715,41883,41884,41886,41888],{},[898,41885,8194],{},[1667,41887,1669],{},[1656,41889,8187],{},[1656,41891,1713],{},[1667,41893,32506],{},[902,41895,41896],{"encoding":904},"P_1^* = 0{,}25",[883,41898,41900],{"className":41899},[886],[888,41901,41902],{"xmlns":890},[892,41903,41904,41918],{},[895,41905,41906,41914,41916],{},[1715,41907,41908,41910,41912],{},[898,41909,8194],{},[1667,41911,1680],{},[1656,41913,8187],{},[1656,41915,1713],{},[1667,41917,1669],{},[902,41919,41920],{"encoding":904},"P_2^* = 1",[883,41922,41924],{"className":41923},[886],[888,41925,41926],{"xmlns":890,"display":2408},[892,41927,41928,41992],{},[895,41929,41930,41932,41934,41936,41942,41944,41950,41952,41954,41956,41958,41960,41974,41988,41990],{},[898,41931,18539],{"mathvariant":37250},[1656,41933,1713],{},[1667,41935,32506],{},[1661,41937,41938,41940],{},[898,41939,1665],{},[1667,41941,1669],{},[1656,41943,3633],{},[1661,41945,41946,41948],{},[898,41947,1665],{},[1667,41949,1680],{},[1656,41951,3633],{},[898,41953,25169],{},[1656,41955,1659],{"stretchy":1658},[1667,41957,1680],{},[1656,41959,3964],{},[1715,41961,41962,41964,41966],{},[898,41963,1665],{},[1667,41965,1669],{},[895,41967,41968,41970,41972],{},[1667,41969,1669],{},[898,41971,1782],{"mathvariant":1723},[1667,41973,1680],{},[1715,41975,41976,41978,41980],{},[898,41977,1665],{},[1667,41979,1680],{},[895,41981,41982,41984,41986],{},[1667,41983,1669],{},[898,41985,1782],{"mathvariant":1723},[1667,41987,1680],{},[1656,41989,1683],{"stretchy":1658},[898,41991,1863],{"mathvariant":1723},[902,41993,41994],{"encoding":904},"\\mathcal{L} = 0{,}25 Q_1 + Q_2 + \\lambda(2 - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,41996,39121],{},[883,41998,42000],{"className":41999},[886],[888,42001,42002],{"xmlns":890,"display":2408},[892,42003,42004,42218],{},[2412,42005,42006,42082,42158],{"rowspacing":29476,"columnalign":29477,"columnspacing":1724},[2416,42007,42008,42020],{},[2419,42009,42010],{},[4138,42011,42012],{"scriptlevel":4032,"displaystyle":1672},[1715,42013,42014,42016,42018],{},[898,42015,18539],{"mathvariant":37250},[1667,42017,1669],{},[1656,42019,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[2419,42021,42022],{},[4138,42023,42024],{"scriptlevel":4032,"displaystyle":1672},[895,42025,42026,42028,42030,42032,42034,42036,42038,42046,42062,42076,42078,42080],{},[895,42027],{},[1656,42029,1713],{},[1667,42031,32506],{},[1656,42033,3964],{},[898,42035,25169],{},[1656,42037,2751],{},[4138,42039,42040],{"scriptlevel":4032,"displaystyle":1658},[3294,42041,42042,42044],{},[1667,42043,1669],{},[1667,42045,1680],{},[1715,42047,42048,42050,42052],{},[898,42049,1665],{},[1667,42051,1669],{},[895,42053,42054,42056,42058,42060],{},[1656,42055,3964],{},[1667,42057,1669],{},[898,42059,1782],{"mathvariant":1723},[1667,42061,1680],{},[1715,42063,42064,42066,42068],{},[898,42065,1665],{},[1667,42067,1680],{},[895,42069,42070,42072,42074],{},[1667,42071,1669],{},[898,42073,1782],{"mathvariant":1723},[1667,42075,1680],{},[1656,42077,1713],{},[1667,42079,4032],{},[1656,42081,1673],{"separator":1672},[2416,42083,42084,42096],{},[2419,42085,42086],{},[4138,42087,42088],{"scriptlevel":4032,"displaystyle":1672},[1715,42089,42090,42092,42094],{},[898,42091,18539],{"mathvariant":37250},[1667,42093,1680],{},[1656,42095,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[2419,42097,42098],{},[4138,42099,42100],{"scriptlevel":4032,"displaystyle":1672},[895,42101,42102,42104,42106,42108,42110,42112,42114,42122,42136,42152,42154,42156],{},[895,42103],{},[1656,42105,1713],{},[1667,42107,1669],{},[1656,42109,3964],{},[898,42111,25169],{},[1656,42113,2751],{},[4138,42115,42116],{"scriptlevel":4032,"displaystyle":1658},[3294,42117,42118,42120],{},[1667,42119,1669],{},[1667,42121,1680],{},[1715,42123,42124,42126,42128],{},[898,42125,1665],{},[1667,42127,1669],{},[895,42129,42130,42132,42134],{},[1667,42131,1669],{},[898,42133,1782],{"mathvariant":1723},[1667,42135,1680],{},[1715,42137,42138,42140,42142],{},[898,42139,1665],{},[1667,42141,1680],{},[895,42143,42144,42146,42148,42150],{},[1656,42145,3964],{},[1667,42147,1669],{},[898,42149,1782],{"mathvariant":1723},[1667,42151,1680],{},[1656,42153,1713],{},[1667,42155,4032],{},[1656,42157,1673],{"separator":1672},[2416,42159,42160,42172],{},[2419,42161,42162],{},[4138,42163,42164],{"scriptlevel":4032,"displaystyle":1672},[1715,42165,42166,42168,42170],{},[898,42167,18539],{"mathvariant":37250},[898,42169,25169],{},[1656,42171,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[2419,42173,42174],{},[4138,42175,42176],{"scriptlevel":4032,"displaystyle":1672},[895,42177,42178,42180,42182,42184,42186,42200,42214,42216],{},[895,42179],{},[1656,42181,1713],{},[1667,42183,1680],{},[1656,42185,3964],{},[1715,42187,42188,42190,42192],{},[898,42189,1665],{},[1667,42191,1669],{},[895,42193,42194,42196,42198],{},[1667,42195,1669],{},[898,42197,1782],{"mathvariant":1723},[1667,42199,1680],{},[1715,42201,42202,42204,42206],{},[898,42203,1665],{},[1667,42205,1680],{},[895,42207,42208,42210,42212],{},[1667,42209,1669],{},[898,42211,1782],{"mathvariant":1723},[1667,42213,1680],{},[1656,42215,1713],{},[1667,42217,4283],{},[902,42219,42220],{"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}",[724,42222,42223,42224,26301,42254,42282,42283,2836,42345,1343,42395,42417,42418,1863],{},"Podílem prvních dvou rovnic: ",[883,42225,42227],{"className":42226},[886],[888,42228,42229],{"xmlns":890},[892,42230,42231,42251],{},[895,42232,42233,42235,42237,42243,42245],{},[1667,42234,32506],{},[1656,42236,1713],{},[1661,42238,42239,42241],{},[898,42240,1665],{},[1667,42242,1680],{},[898,42244,1782],{"mathvariant":1723},[1661,42246,42247,42249],{},[898,42248,1665],{},[1667,42250,1669],{},[902,42252,42253],{"encoding":904},"0{,}25 = Q_2 \u002F Q_1",[883,42255,42257],{"className":42256},[886],[888,42258,42259],{"xmlns":890},[892,42260,42261,42279],{},[895,42262,42263,42269,42271,42273],{},[1661,42264,42265,42267],{},[898,42266,1665],{},[1667,42268,1680],{},[1656,42270,1713],{},[1667,42272,32506],{},[1661,42274,42275,42277],{},[898,42276,1665],{},[1667,42278,1669],{},[902,42280,42281],{"encoding":904},"Q_2 = 0{,}25 Q_1",". Dosazením do třetí: ",[883,42284,42286],{"className":42285},[886],[888,42287,42288],{"xmlns":890},[892,42289,42290,42342],{},[895,42291,42292,42306,42308,42310,42316,42328,42330,42332,42338,42340],{},[1715,42293,42294,42296,42298],{},[898,42295,1665],{},[1667,42297,1669],{},[895,42299,42300,42302,42304],{},[1667,42301,1669],{},[898,42303,1782],{"mathvariant":1723},[1667,42305,1680],{},[1656,42307,1659],{"stretchy":1658},[1667,42309,32506],{},[1661,42311,42312,42314],{},[898,42313,1665],{},[1667,42315,1669],{},[2062,42317,42318,42320],{},[1656,42319,1683],{"stretchy":1658},[895,42321,42322,42324,42326],{},[1667,42323,1669],{},[898,42325,1782],{"mathvariant":1723},[1667,42327,1680],{},[1656,42329,1713],{},[1667,42331,13779],{},[1661,42333,42334,42336],{},[898,42335,1665],{},[1667,42337,1669],{},[1656,42339,1713],{},[1667,42341,1680],{},[902,42343,42344],{"encoding":904},"Q_1^{1\u002F2} (0{,}25 Q_1)^{1\u002F2} = 0{,}5 Q_1 = 2",[38,42346,42347,1343,42371],{},[883,42348,42350],{"className":42349},[886],[888,42351,42352],{"xmlns":890},[892,42353,42354,42368],{},[895,42355,42356,42364,42366],{},[1715,42357,42358,42360,42362],{},[898,42359,1665],{},[1667,42361,1669],{},[1656,42363,8187],{},[1656,42365,1713],{},[1667,42367,2673],{},[902,42369,42370],{"encoding":904},"Q_1^* = 4",[883,42372,42374],{"className":42373},[886],[888,42375,42376],{"xmlns":890},[892,42377,42378,42392],{},[895,42379,42380,42388,42390],{},[1715,42381,42382,42384,42386],{},[898,42383,1665],{},[1667,42385,1680],{},[1656,42387,8187],{},[1656,42389,1713],{},[1667,42391,1669],{},[902,42393,42394],{"encoding":904},"Q_2^* = 1",[883,42396,42398],{"className":42397},[886],[888,42399,42400],{"xmlns":890},[892,42401,42402,42414],{},[895,42403,42404,42410,42412],{},[2062,42405,42406,42408],{},[898,42407,25169],{},[1656,42409,8187],{},[1656,42411,1713],{},[1667,42413,1669],{},[902,42415,42416],{"encoding":904},"\\lambda^* = 1",". Minimální výdaje: ",[883,42419,42421],{"className":42420},[886],[888,42422,42423],{"xmlns":890},[892,42424,42425,42453],{},[895,42426,42427,42433,42435,42437,42439,42441,42443,42445,42447,42449,42451],{},[2062,42428,42429,42431],{},[898,42430,1842],{},[1656,42432,8187],{},[1656,42434,1713],{},[1667,42436,32506],{},[1656,42438,2751],{},[1667,42440,2673],{},[1656,42442,3633],{},[1667,42444,1669],{},[1656,42446,2751],{},[1667,42448,1669],{},[1656,42450,1713],{},[1667,42452,1680],{},[902,42454,42455],{"encoding":904},"E^* = 0{,}25 \\cdot 4 + 1 \\cdot 1 = 2",[724,42457,42458,42461,42462,1343,42528,1343,42594,42660,42661,42698,42699,42721,42722,1863],{},[614,42459,42460],{},"Ověření postačující podmínky"," (6.26): ",[883,42463,42465],{"className":42464},[886],[888,42466,42467],{"xmlns":890},[892,42468,42469,42525],{},[895,42470,42471,42483,42485,42487,42495,42511],{},[1715,42472,42473,42475,42477],{},[898,42474,900],{},[1667,42476,4364],{},[895,42478,42479,42481],{},[1656,42480,1725],{"mathvariant":1723},[1656,42482,1725],{"mathvariant":1723},[1656,42484,1713],{},[1656,42486,3964],{},[4138,42488,42489],{"scriptlevel":4032,"displaystyle":1658},[3294,42490,42491,42493],{},[1667,42492,1669],{},[1667,42494,2673],{},[1715,42496,42497,42499,42501],{},[898,42498,1665],{},[1667,42500,1669],{},[895,42502,42503,42505,42507,42509],{},[1656,42504,3964],{},[1667,42506,2617],{},[898,42508,1782],{"mathvariant":1723},[1667,42510,1680],{},[1715,42512,42513,42515,42517],{},[898,42514,1665],{},[1667,42516,1680],{},[895,42518,42519,42521,42523],{},[1667,42520,1669],{},[898,42522,1782],{"mathvariant":1723},[1667,42524,1680],{},[902,42526,42527],{"encoding":904},"U''_{11} = -\\tfrac{1}{4} Q_1^{-3\u002F2} Q_2^{1\u002F2}",[883,42529,42531],{"className":42530},[886],[888,42532,42533],{"xmlns":890},[892,42534,42535,42591],{},[895,42536,42537,42549,42551,42553,42561,42575],{},[1715,42538,42539,42541,42543],{},[898,42540,900],{},[1667,42542,4386],{},[895,42544,42545,42547],{},[1656,42546,1725],{"mathvariant":1723},[1656,42548,1725],{"mathvariant":1723},[1656,42550,1713],{},[1656,42552,3964],{},[4138,42554,42555],{"scriptlevel":4032,"displaystyle":1658},[3294,42556,42557,42559],{},[1667,42558,1669],{},[1667,42560,2673],{},[1715,42562,42563,42565,42567],{},[898,42564,1665],{},[1667,42566,1669],{},[895,42568,42569,42571,42573],{},[1667,42570,1669],{},[898,42572,1782],{"mathvariant":1723},[1667,42574,1680],{},[1715,42576,42577,42579,42581],{},[898,42578,1665],{},[1667,42580,1680],{},[895,42582,42583,42585,42587,42589],{},[1656,42584,3964],{},[1667,42586,2617],{},[898,42588,1782],{"mathvariant":1723},[1667,42590,1680],{},[902,42592,42593],{"encoding":904},"U''_{22} = -\\tfrac{1}{4} Q_1^{1\u002F2} Q_2^{-3\u002F2}",[883,42595,42597],{"className":42596},[886],[888,42598,42599],{"xmlns":890},[892,42600,42601,42657],{},[895,42602,42603,42615,42617,42625,42641],{},[1715,42604,42605,42607,42609],{},[898,42606,900],{},[1667,42608,9140],{},[895,42610,42611,42613],{},[1656,42612,1725],{"mathvariant":1723},[1656,42614,1725],{"mathvariant":1723},[1656,42616,1713],{},[4138,42618,42619],{"scriptlevel":4032,"displaystyle":1658},[3294,42620,42621,42623],{},[1667,42622,1669],{},[1667,42624,2673],{},[1715,42626,42627,42629,42631],{},[898,42628,1665],{},[1667,42630,1669],{},[895,42632,42633,42635,42637,42639],{},[1656,42634,3964],{},[1667,42636,1669],{},[898,42638,1782],{"mathvariant":1723},[1667,42640,1680],{},[1715,42642,42643,42645,42647],{},[898,42644,1665],{},[1667,42646,1680],{},[895,42648,42649,42651,42653,42655],{},[1656,42650,3964],{},[1667,42652,1669],{},[898,42654,1782],{"mathvariant":1723},[1667,42656,1680],{},[902,42658,42659],{"encoding":904},"U''_{12} = \\tfrac{1}{4} Q_1^{-1\u002F2} Q_2^{-1\u002F2}",". Po dosazení ",[883,42662,42664],{"className":42663},[886],[888,42665,42666],{"xmlns":890},[892,42667,42668,42695],{},[895,42669,42670,42672,42674,42676,42678,42680,42682,42684,42686,42688,42691,42693],{},[898,42671,6787],{},[1656,42673,1659],{"stretchy":1658},[1667,42675,2673],{},[1656,42677,1673],{"separator":1672},[1667,42679,1669],{},[1656,42681,1673],{"separator":1672},[1667,42683,1669],{},[1656,42685,1683],{"stretchy":1658},[1656,42687,1713],{},[1667,42689,42690],{},"0,28125",[1656,42692,2850],{},[1667,42694,4032],{},[902,42696,42697],{"encoding":904},"D(4, 1, 1) = 0{,}28125 > 0"," — v bodě ",[883,42700,42702],{"className":42701},[886],[888,42703,42704],{"xmlns":890},[892,42705,42706,42718],{},[895,42707,42708,42710,42712,42714,42716],{},[1656,42709,3453],{"stretchy":1658},[1667,42711,2673],{},[1656,42713,1673],{"separator":1672},[1667,42715,1669],{},[1656,42717,3462],{"stretchy":1658},[902,42719,42720],{"encoding":904},"[4, 1]"," je vázané ",[38,42723,12562],{},[115,42725,42727],{"id":42726},"poptávka-minimalizující-výdaje-hicksova","Poptávka minimalizující výdaje (Hicksova)",[724,42729,42730],{},"Obecně:",[883,42732,42734],{"className":42733},[886],[888,42735,42736],{"xmlns":890,"display":2408},[892,42737,42738,42833],{},[2412,42739,42740],{"width":2414},[2416,42741,42742,42744,42826,42828],{},[2419,42743],{"width":2421},[2419,42745,42746],{},[895,42747,42748,42754,42756,42762,42764,42770,42772,42778,42780,42782,42784,42786,42788,42794,42796,42802,42804,42810,42812,42818,42820,42822,42824],{},[1661,42749,42750,42752],{},[898,42751,1665],{},[1667,42753,1669],{},[1656,42755,1713],{},[1661,42757,42758,42760],{},[898,42759,6787],{},[1667,42761,1669],{},[1656,42763,1659],{"stretchy":1658},[1661,42765,42766,42768],{},[898,42767,8194],{},[1667,42769,1669],{},[1656,42771,1673],{"separator":1672},[1661,42773,42774,42776],{},[898,42775,8194],{},[1667,42777,1680],{},[1656,42779,1673],{"separator":1672},[898,42781,900],{},[1656,42783,1683],{"stretchy":1658},[1656,42785,1673],{"separator":1672},[3316,42787],{"width":3318},[1661,42789,42790,42792],{},[898,42791,1665],{},[1667,42793,1680],{},[1656,42795,1713],{},[1661,42797,42798,42800],{},[898,42799,6787],{},[1667,42801,1680],{},[1656,42803,1659],{"stretchy":1658},[1661,42805,42806,42808],{},[898,42807,8194],{},[1667,42809,1669],{},[1656,42811,1673],{"separator":1672},[1661,42813,42814,42816],{},[898,42815,8194],{},[1667,42817,1680],{},[1656,42819,1673],{"separator":1672},[898,42821,900],{},[1656,42823,1683],{"stretchy":1658},[1656,42825,1673],{"separator":1672},[2419,42827],{"width":2421},[2419,42829,42830],{},[2461,42831,42832],{},"(6.27)",[902,42834,42835],{"encoding":904},"Q_1 = D_1(P_1, P_2, U), \\quad Q_2 = D_2(P_1, P_2, U), \\tag{6.27}",[883,42837,42839],{"className":42838},[886],[888,42840,42841],{"xmlns":890,"display":2408},[892,42842,42843,42890],{},[2412,42844,42845],{"width":2414},[2416,42846,42847,42849,42883,42885],{},[2419,42848],{"width":2421},[2419,42850,42851],{},[895,42852,42853,42855,42857,42859,42861,42867,42869,42875,42877,42879,42881],{},[898,42854,25169],{},[1656,42856,1713],{},[898,42858,25169],{},[1656,42860,1659],{"stretchy":1658},[1661,42862,42863,42865],{},[898,42864,8194],{},[1667,42866,1669],{},[1656,42868,1673],{"separator":1672},[1661,42870,42871,42873],{},[898,42872,8194],{},[1667,42874,1680],{},[1656,42876,1673],{"separator":1672},[898,42878,900],{},[1656,42880,1683],{"stretchy":1658},[898,42882,1863],{"mathvariant":1723},[2419,42884],{"width":2421},[2419,42886,42887],{},[2461,42888,42889],{},"(6.28)",[902,42891,42892],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, U). \\tag{6.28}",[724,42894,42895,42896,1643,42899,42912,42913,42926],{},"Hicksova poptávka závisí na ",[38,42897,42898],{},"hladině užitečnosti",[883,42900,42902],{"className":42901},[886],[888,42903,42904],{"xmlns":890},[892,42905,42906,42910],{},[895,42907,42908],{},[898,42909,900],{},[902,42911,900],{"encoding":904}," (nikoli na důchodu ",[883,42914,42916],{"className":42915},[886],[888,42917,42918],{"xmlns":890},[892,42919,42920,42924],{},[895,42921,42922],{},[898,42923,8184],{},[902,42925,8184],{"encoding":904}," jako u Marshallovy). Fyzická interpretace: jaké množství zboží koupit při daných cenách, abych dosáhl předem stanovené úrovně uspokojení s minimálními výdaji.",[115,42928,42930,42931],{"id":42929},"příklad-68-obecné-odvození-pro-uq112q212u-q_112-q_212","Příklad 6.8 — obecné odvození pro ",[883,42932,42934],{"className":42933},[886],[888,42935,42936],{"xmlns":890},[892,42937,42938,42972],{},[895,42939,42940,42942,42944,42958],{},[898,42941,900],{},[1656,42943,1713],{},[1715,42945,42946,42948,42950],{},[898,42947,1665],{},[1667,42949,1669],{},[895,42951,42952,42954,42956],{},[1667,42953,1669],{},[898,42955,1782],{"mathvariant":1723},[1667,42957,1680],{},[1715,42959,42960,42962,42964],{},[898,42961,1665],{},[1667,42963,1680],{},[895,42965,42966,42968,42970],{},[1667,42967,1669],{},[898,42969,1782],{"mathvariant":1723},[1667,42971,1680],{},[902,42973,8663],{"encoding":904},[724,42975,42976,43006],{},[883,42977,42979],{"className":42978},[886],[888,42980,42981],{"xmlns":890},[892,42982,42983,43003],{},[895,42984,42985,42991,42993,42999,43001],{},[1661,42986,42987,42989],{},[898,42988,8194],{},[1667,42990,1669],{},[1656,42992,1673],{"separator":1672},[1661,42994,42995,42997],{},[898,42996,8194],{},[1667,42998,1680],{},[1656,43000,1673],{"separator":1672},[898,43002,900],{},[902,43004,43005],{"encoding":904},"P_1, P_2, U"," jsou parametry. Lagrangeova funkce:",[883,43008,43010],{"className":43009},[886],[888,43011,43012],{"xmlns":890,"display":2408},[892,43013,43014,43088],{},[895,43015,43016,43018,43020,43026,43032,43034,43040,43046,43048,43050,43052,43054,43056,43070,43084,43086],{},[898,43017,18539],{"mathvariant":37250},[1656,43019,1713],{},[1661,43021,43022,43024],{},[898,43023,8194],{},[1667,43025,1669],{},[1661,43027,43028,43030],{},[898,43029,1665],{},[1667,43031,1669],{},[1656,43033,3633],{},[1661,43035,43036,43038],{},[898,43037,8194],{},[1667,43039,1680],{},[1661,43041,43042,43044],{},[898,43043,1665],{},[1667,43045,1680],{},[1656,43047,3633],{},[898,43049,25169],{},[1656,43051,1659],{"stretchy":1658},[898,43053,900],{},[1656,43055,3964],{},[1715,43057,43058,43060,43062],{},[898,43059,1665],{},[1667,43061,1669],{},[895,43063,43064,43066,43068],{},[1667,43065,1669],{},[898,43067,1782],{"mathvariant":1723},[1667,43069,1680],{},[1715,43071,43072,43074,43076],{},[898,43073,1665],{},[1667,43075,1680],{},[895,43077,43078,43080,43082],{},[1667,43079,1669],{},[898,43081,1782],{"mathvariant":1723},[1667,43083,1680],{},[1656,43085,1683],{"stretchy":1658},[898,43087,1863],{"mathvariant":1723},[902,43089,43090],{"encoding":904},"\\mathcal{L} = P_1 Q_1 + P_2 Q_2 + \\lambda(U - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,43092,39121],{},[883,43094,43096],{"className":43095},[886],[888,43097,43098],{"xmlns":890,"display":2408},[892,43099,43100,43322],{},[2412,43101,43102,43182,43262],{"rowspacing":29476,"columnalign":29477,"columnspacing":1724},[2416,43103,43104,43116],{},[2419,43105,43106],{},[4138,43107,43108],{"scriptlevel":4032,"displaystyle":1672},[1715,43109,43110,43112,43114],{},[898,43111,18539],{"mathvariant":37250},[1667,43113,1669],{},[1656,43115,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[2419,43117,43118],{},[4138,43119,43120],{"scriptlevel":4032,"displaystyle":1672},[895,43121,43122,43124,43126,43132,43134,43136,43138,43146,43162,43176,43178,43180],{},[895,43123],{},[1656,43125,1713],{},[1661,43127,43128,43130],{},[898,43129,8194],{},[1667,43131,1669],{},[1656,43133,3964],{},[898,43135,25169],{},[1656,43137,2751],{},[4138,43139,43140],{"scriptlevel":4032,"displaystyle":1658},[3294,43141,43142,43144],{},[1667,43143,1669],{},[1667,43145,1680],{},[1715,43147,43148,43150,43152],{},[898,43149,1665],{},[1667,43151,1669],{},[895,43153,43154,43156,43158,43160],{},[1656,43155,3964],{},[1667,43157,1669],{},[898,43159,1782],{"mathvariant":1723},[1667,43161,1680],{},[1715,43163,43164,43166,43168],{},[898,43165,1665],{},[1667,43167,1680],{},[895,43169,43170,43172,43174],{},[1667,43171,1669],{},[898,43173,1782],{"mathvariant":1723},[1667,43175,1680],{},[1656,43177,1713],{},[1667,43179,4032],{},[1656,43181,1673],{"separator":1672},[2416,43183,43184,43196],{},[2419,43185,43186],{},[4138,43187,43188],{"scriptlevel":4032,"displaystyle":1672},[1715,43189,43190,43192,43194],{},[898,43191,18539],{"mathvariant":37250},[1667,43193,1680],{},[1656,43195,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[2419,43197,43198],{},[4138,43199,43200],{"scriptlevel":4032,"displaystyle":1672},[895,43201,43202,43204,43206,43212,43214,43216,43218,43226,43240,43256,43258,43260],{},[895,43203],{},[1656,43205,1713],{},[1661,43207,43208,43210],{},[898,43209,8194],{},[1667,43211,1680],{},[1656,43213,3964],{},[898,43215,25169],{},[1656,43217,2751],{},[4138,43219,43220],{"scriptlevel":4032,"displaystyle":1658},[3294,43221,43222,43224],{},[1667,43223,1669],{},[1667,43225,1680],{},[1715,43227,43228,43230,43232],{},[898,43229,1665],{},[1667,43231,1669],{},[895,43233,43234,43236,43238],{},[1667,43235,1669],{},[898,43237,1782],{"mathvariant":1723},[1667,43239,1680],{},[1715,43241,43242,43244,43246],{},[898,43243,1665],{},[1667,43245,1680],{},[895,43247,43248,43250,43252,43254],{},[1656,43249,3964],{},[1667,43251,1669],{},[898,43253,1782],{"mathvariant":1723},[1667,43255,1680],{},[1656,43257,1713],{},[1667,43259,4032],{},[1656,43261,1673],{"separator":1672},[2416,43263,43264,43276],{},[2419,43265,43266],{},[4138,43267,43268],{"scriptlevel":4032,"displaystyle":1672},[1715,43269,43270,43272,43274],{},[898,43271,18539],{"mathvariant":37250},[898,43273,25169],{},[1656,43275,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[2419,43277,43278],{},[4138,43279,43280],{"scriptlevel":4032,"displaystyle":1672},[895,43281,43282,43284,43286,43288,43290,43304,43318,43320],{},[895,43283],{},[1656,43285,1713],{},[898,43287,900],{},[1656,43289,3964],{},[1715,43291,43292,43294,43296],{},[898,43293,1665],{},[1667,43295,1669],{},[895,43297,43298,43300,43302],{},[1667,43299,1669],{},[898,43301,1782],{"mathvariant":1723},[1667,43303,1680],{},[1715,43305,43306,43308,43310],{},[898,43307,1665],{},[1667,43309,1680],{},[895,43311,43312,43314,43316],{},[1667,43313,1669],{},[898,43315,1782],{"mathvariant":1723},[1667,43317,1680],{},[1656,43319,1713],{},[1667,43321,4283],{},[902,43323,43324],{"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}",[724,43326,43327,43328,43398,43399,43457],{},"Podílem rovnic: ",[883,43329,43331],{"className":43330},[886],[888,43332,43333],{"xmlns":890},[892,43334,43335,43395],{},[895,43336,43337,43343,43345,43351,43353,43359,43361,43367,43369,43375,43381,43383,43389],{},[1661,43338,43339,43341],{},[898,43340,8194],{},[1667,43342,1669],{},[898,43344,1782],{"mathvariant":1723},[1661,43346,43347,43349],{},[898,43348,8194],{},[1667,43350,1680],{},[1656,43352,1713],{},[1661,43354,43355,43357],{},[898,43356,1665],{},[1667,43358,1680],{},[898,43360,1782],{"mathvariant":1723},[1661,43362,43363,43365],{},[898,43364,1665],{},[1667,43366,1669],{},[1656,43368,12770],{},[1661,43370,43371,43373],{},[898,43372,8194],{},[1667,43374,1669],{},[1661,43376,43377,43379],{},[898,43378,1665],{},[1667,43380,1669],{},[1656,43382,1713],{},[1661,43384,43385,43387],{},[898,43386,8194],{},[1667,43388,1680],{},[1661,43390,43391,43393],{},[898,43392,1665],{},[1667,43394,1680],{},[902,43396,43397],{"encoding":904},"P_1\u002FP_2 = Q_2\u002FQ_1 \\Rightarrow P_1 Q_1 = P_2 Q_2",", tedy celkové výdaje ",[883,43400,43402],{"className":43401},[886],[888,43403,43404],{"xmlns":890},[892,43405,43406,43454],{},[895,43407,43408,43410,43412,43418,43424,43426,43432,43438,43440,43442,43448],{},[898,43409,1842],{},[1656,43411,1713],{},[1661,43413,43414,43416],{},[898,43415,8194],{},[1667,43417,1669],{},[1661,43419,43420,43422],{},[898,43421,1665],{},[1667,43423,1669],{},[1656,43425,3633],{},[1661,43427,43428,43430],{},[898,43429,8194],{},[1667,43431,1680],{},[1661,43433,43434,43436],{},[898,43435,1665],{},[1667,43437,1680],{},[1656,43439,1713],{},[1667,43441,1680],{},[1661,43443,43444,43446],{},[898,43445,8194],{},[1667,43447,1669],{},[1661,43449,43450,43452],{},[898,43451,1665],{},[1667,43453,1669],{},[902,43455,43456],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2 = 2 P_1 Q_1",". Odtud",[883,43459,43461],{"className":43460},[886],[888,43462,43463],{"xmlns":890,"display":2408},[892,43464,43465,43532],{},[2412,43466,43467],{"width":2414},[2416,43468,43469,43471,43525,43527],{},[2419,43470],{"width":2421},[2419,43472,43473],{},[895,43474,43475,43481,43483,43497,43499,43501,43507,43509,43523],{},[1661,43476,43477,43479],{},[898,43478,1665],{},[1667,43480,1669],{},[1656,43482,1713],{},[3294,43484,43485,43487],{},[898,43486,1842],{},[895,43488,43489,43491],{},[1667,43490,1680],{},[1661,43492,43493,43495],{},[898,43494,8194],{},[1667,43496,1669],{},[1656,43498,1673],{"separator":1672},[3316,43500],{"width":3318},[1661,43502,43503,43505],{},[898,43504,1665],{},[1667,43506,1680],{},[1656,43508,1713],{},[3294,43510,43511,43513],{},[898,43512,1842],{},[895,43514,43515,43517],{},[1667,43516,1680],{},[1661,43518,43519,43521],{},[898,43520,8194],{},[1667,43522,1680],{},[898,43524,1863],{"mathvariant":1723},[2419,43526],{"width":2421},[2419,43528,43529],{},[2461,43530,43531],{},"(6.29)",[902,43533,43534],{"encoding":904},"Q_1 = \\frac{E}{2 P_1}, \\quad Q_2 = \\frac{E}{2 P_2}. \\tag{6.29}",[724,43536,43537,43538,26301,43620,43656],{},"Ze třetí rovnice ",[883,43539,43541],{"className":43540},[886],[888,43542,43543],{"xmlns":890},[892,43544,43545,43617],{},[895,43546,43547,43549,43551,43589,43591],{},[898,43548,900],{},[1656,43550,1713],{},[2625,43552,43553],{},[895,43554,43555,43571,43573],{},[4138,43556,43557],{"scriptlevel":4032,"displaystyle":1658},[3294,43558,43559,43561],{},[898,43560,1842],{},[895,43562,43563,43565],{},[1667,43564,1680],{},[1661,43566,43567,43569],{},[898,43568,8194],{},[1667,43570,1669],{},[1656,43572,2751],{},[4138,43574,43575],{"scriptlevel":4032,"displaystyle":1658},[3294,43576,43577,43579],{},[898,43578,1842],{},[895,43580,43581,43583],{},[1667,43582,1680],{},[1661,43584,43585,43587],{},[898,43586,8194],{},[1667,43588,1680],{},[1656,43590,1713],{},[4138,43592,43593],{"scriptlevel":4032,"displaystyle":1658},[3294,43594,43595,43597],{},[898,43596,1842],{},[895,43598,43599,43601],{},[1667,43600,1680],{},[2625,43602,43603],{},[895,43604,43605,43611],{},[1661,43606,43607,43609],{},[898,43608,8194],{},[1667,43610,1669],{},[1661,43612,43613,43615],{},[898,43614,8194],{},[1667,43616,1680],{},[902,43618,43619],{"encoding":904},"U = \\sqrt{\\tfrac{E}{2 P_1} \\cdot \\tfrac{E}{2 P_2}} = \\tfrac{E}{2\\sqrt{P_1 P_2}}",[883,43621,43623],{"className":43622},[886],[888,43624,43625],{"xmlns":890},[892,43626,43627,43653],{},[895,43628,43629,43631,43633,43635,43637],{},[898,43630,1842],{},[1656,43632,1713],{},[1667,43634,1680],{},[898,43636,900],{},[2625,43638,43639],{},[895,43640,43641,43647],{},[1661,43642,43643,43645],{},[898,43644,8194],{},[1667,43646,1669],{},[1661,43648,43649,43651],{},[898,43650,8194],{},[1667,43652,1680],{},[902,43654,43655],{"encoding":904},"E = 2 U \\sqrt{P_1 P_2}",". Dosazením:",[883,43658,43660],{"className":43659},[886],[888,43661,43662],{"xmlns":890,"display":2408},[892,43663,43664,43809],{},[2412,43665,43666],{"width":2414},[2416,43667,43668,43670,43802,43804],{},[2419,43669],{"width":2421},[2419,43671,43672],{},[21566,43673,43674],{"notation":21568},[4138,43675,43676],{"scriptlevel":4032,"displaystyle":1658},[4138,43677,43678],{"scriptlevel":4032,"displaystyle":1658},[4138,43679,43680],{"scriptlevel":4032,"displaystyle":1672},[895,43681,43682,43684,43690,43692,43694,43710,43712,43718,43720,43726,43728,43734,43736,43738,43740,43742,43744,43750,43752,43754,43770,43772,43778,43780,43786,43788,43794,43796,43798,43800],{},[2461,43683,12767],{},[1661,43685,43686,43688],{},[898,43687,1665],{},[1667,43689,1669],{},[1656,43691,1713],{},[898,43693,900],{},[2625,43695,43696],{},[3294,43697,43698,43704],{},[1661,43699,43700,43702],{},[898,43701,8194],{},[1667,43703,1680],{},[1661,43705,43706,43708],{},[898,43707,8194],{},[1667,43709,1669],{},[1656,43711,1713],{},[1661,43713,43714,43716],{},[898,43715,6787],{},[1667,43717,1669],{},[1656,43719,1659],{"stretchy":1658},[1661,43721,43722,43724],{},[898,43723,8194],{},[1667,43725,1669],{},[1656,43727,1673],{"separator":1672},[1661,43729,43730,43732],{},[898,43731,8194],{},[1667,43733,1680],{},[1656,43735,1673],{"separator":1672},[898,43737,900],{},[1656,43739,1683],{"stretchy":1658},[1656,43741,1673],{"separator":1672},[3316,43743],{"width":3318},[1661,43745,43746,43748],{},[898,43747,1665],{},[1667,43749,1680],{},[1656,43751,1713],{},[898,43753,900],{},[2625,43755,43756],{},[3294,43757,43758,43764],{},[1661,43759,43760,43762],{},[898,43761,8194],{},[1667,43763,1669],{},[1661,43765,43766,43768],{},[898,43767,8194],{},[1667,43769,1680],{},[1656,43771,1713],{},[1661,43773,43774,43776],{},[898,43775,6787],{},[1667,43777,1680],{},[1656,43779,1659],{"stretchy":1658},[1661,43781,43782,43784],{},[898,43783,8194],{},[1667,43785,1669],{},[1656,43787,1673],{"separator":1672},[1661,43789,43790,43792],{},[898,43791,8194],{},[1667,43793,1680],{},[1656,43795,1673],{"separator":1672},[898,43797,900],{},[1656,43799,1683],{"stretchy":1658},[2461,43801,12767],{},[2419,43803],{"width":2421},[2419,43805,43806],{},[2461,43807,43808],{},"(6.30)",[902,43810,43811],{"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}",[115,43813,43815],{"id":43814},"vztah-primární-a-duální-úlohy","Vztah primární a duální úlohy",[724,43817,43818,43819,43832,43833,43850,43851,43864,43865,43882,43883,43886,43887,43926,43927,43956],{},"Primární (max ",[883,43820,43822],{"className":43821},[886],[888,43823,43824],{"xmlns":890},[892,43825,43826,43830],{},[895,43827,43828],{},[898,43829,900],{},[902,43831,900],{"encoding":904}," při rozpočtu ",[883,43834,43836],{"className":43835},[886],[888,43837,43838],{"xmlns":890},[892,43839,43840,43848],{},[895,43841,43842],{},[2062,43843,43844,43846],{},[898,43845,8184],{},[1656,43847,8187],{},[902,43849,36737],{"encoding":904},") a duální (min ",[883,43852,43854],{"className":43853},[886],[888,43855,43856],{"xmlns":890},[892,43857,43858,43862],{},[895,43859,43860],{},[898,43861,1842],{},[902,43863,1842],{"encoding":904}," při užitečnosti ",[883,43866,43868],{"className":43867},[886],[888,43869,43870],{"xmlns":890},[892,43871,43872,43880],{},[895,43873,43874],{},[2062,43875,43876,43878],{},[898,43877,900],{},[1656,43879,8187],{},[902,43881,8343],{"encoding":904},") úloha jsou ",[38,43884,43885],{},"ekvivalentní",": mají tentýž bod optima ",[883,43888,43890],{"className":43889},[886],[888,43891,43892],{"xmlns":890},[892,43893,43894,43924],{},[895,43895,43896,43902,43904,43912,43914,43922],{},[2062,43897,43898,43900],{},[898,43899,1665],{},[1656,43901,8187],{},[1656,43903,3453],{"stretchy":1658},[1715,43905,43906,43908,43910],{},[898,43907,1665],{},[1667,43909,1669],{},[1656,43911,8187],{},[1656,43913,1673],{"separator":1672},[1715,43915,43916,43918,43920],{},[898,43917,1665],{},[1667,43919,1680],{},[1656,43921,8187],{},[1656,43923,3462],{"stretchy":1658},[902,43925,8443],{"encoding":904}," a v obou platí ",[883,43928,43930],{"className":43929},[886],[888,43931,43932],{"xmlns":890},[892,43933,43934,43954],{},[895,43935,43936,43938,43940,43946,43948],{},[2461,43937,7362],{},[1656,43939,1713],{},[1661,43941,43942,43944],{},[898,43943,8194],{},[1667,43945,1669],{},[898,43947,1782],{"mathvariant":1723},[1661,43949,43950,43952],{},[898,43951,8194],{},[1667,43953,1680],{},[902,43955,10631],{"encoding":904},". Rozdíl je v tom, která veličina je zadána a která se optimalizuje:",[724,43958,43959],{},[5956,43960],{"alt":43961,"className":43962,"src":43963},"imek-primarni-vs-dualni",[210,5960],"\u002Fwiki-assets\u002Fimek-primarni-vs-dualni.jpeg",[120,43965,43966,44077],{},[123,43967,43968,43971,43972,43985,43986,44026,44027,1863],{},[38,43969,43970],{},"Primární"," (Marshall): zadáno ",[883,43973,43975],{"className":43974},[886],[888,43976,43977],{"xmlns":890},[892,43978,43979,43983],{},[895,43980,43981],{},[898,43982,8184],{},[902,43984,8184],{"encoding":904},", hledáme maximální ",[883,43987,43989],{"className":43988},[886],[888,43990,43991],{"xmlns":890},[892,43992,43993,44023],{},[895,43994,43995,44001,44003,44009,44011,44017,44019,44021],{},[2062,43996,43997,43999],{},[898,43998,900],{},[1656,44000,8187],{},[1656,44002,1659],{"stretchy":1658},[1661,44004,44005,44007],{},[898,44006,8194],{},[1667,44008,1669],{},[1656,44010,1673],{"separator":1672},[1661,44012,44013,44015],{},[898,44014,8194],{},[1667,44016,1680],{},[1656,44018,1673],{"separator":1672},[898,44020,8184],{},[1656,44022,1683],{"stretchy":1658},[902,44024,44025],{"encoding":904},"U^*(P_1, P_2, Y)"," a poptávku ",[883,44028,44030],{"className":44029},[886],[888,44031,44032],{"xmlns":890},[892,44033,44034,44074],{},[895,44035,44036,44042,44044,44052,44054,44060,44062,44068,44070,44072],{},[1661,44037,44038,44040],{},[898,44039,1665],{},[898,44041,1710],{},[1656,44043,1713],{},[1715,44045,44046,44048,44050],{},[898,44047,6787],{},[898,44049,1710],{},[898,44051,1703],{},[1656,44053,1659],{"stretchy":1658},[1661,44055,44056,44058],{},[898,44057,8194],{},[1667,44059,1669],{},[1656,44061,1673],{"separator":1672},[1661,44063,44064,44066],{},[898,44065,8194],{},[1667,44067,1680],{},[1656,44069,1673],{"separator":1672},[898,44071,8184],{},[1656,44073,1683],{"stretchy":1658},[902,44075,44076],{"encoding":904},"Q_i = D_i^M(P_1, P_2, Y)",[123,44078,44079,44082,44083,44096,44097,44026,44137,1863],{},[38,44080,44081],{},"Duální"," (Hicks): zadáno ",[883,44084,44086],{"className":44085},[886],[888,44087,44088],{"xmlns":890},[892,44089,44090,44094],{},[895,44091,44092],{},[898,44093,900],{},[902,44095,900],{"encoding":904},", hledáme minimální ",[883,44098,44100],{"className":44099},[886],[888,44101,44102],{"xmlns":890},[892,44103,44104,44134],{},[895,44105,44106,44112,44114,44120,44122,44128,44130,44132],{},[2062,44107,44108,44110],{},[898,44109,1842],{},[1656,44111,8187],{},[1656,44113,1659],{"stretchy":1658},[1661,44115,44116,44118],{},[898,44117,8194],{},[1667,44119,1669],{},[1656,44121,1673],{"separator":1672},[1661,44123,44124,44126],{},[898,44125,8194],{},[1667,44127,1680],{},[1656,44129,1673],{"separator":1672},[898,44131,900],{},[1656,44133,1683],{"stretchy":1658},[902,44135,44136],{"encoding":904},"E^*(P_1, P_2, U)",[883,44138,44140],{"className":44139},[886],[888,44141,44142],{"xmlns":890},[892,44143,44144,44185],{},[895,44145,44146,44152,44154,44163,44165,44171,44173,44179,44181,44183],{},[1661,44147,44148,44150],{},[898,44149,1665],{},[898,44151,1710],{},[1656,44153,1713],{},[1715,44155,44156,44158,44160],{},[898,44157,6787],{},[898,44159,1710],{},[898,44161,44162],{},"H",[1656,44164,1659],{"stretchy":1658},[1661,44166,44167,44169],{},[898,44168,8194],{},[1667,44170,1669],{},[1656,44172,1673],{"separator":1672},[1661,44174,44175,44177],{},[898,44176,8194],{},[1667,44178,1680],{},[1656,44180,1673],{"separator":1672},[898,44182,900],{},[1656,44184,1683],{"stretchy":1658},[902,44186,44187],{"encoding":904},"Q_i = D_i^H(P_1, P_2, U)",[724,44189,44190,44191,44194,44195,44198],{},"Proč se studují obě? Marshallova poptávka je ",[38,44192,44193],{},"pozorovatelná"," (lze odhadnout z dat o spotřebě a důchodech), zatímco Hicksova umožňuje čistě oddělit ",[38,44196,44197],{},"substituční efekt"," změny ceny od efektu důchodového — je klíčová pro teorii blahobytu a cenové indexy.",[115,44200,44202],{"id":44201},"úlohy-k-optimalizaci","Úlohy k optimalizaci",[198,44204,44206],{"id":44205},"maximalizace-užitečnosti-a-marshallova-poptávka","Maximalizace užitečnosti a Marshallova poptávka",[724,44208,44209,44212,44213,44245,44246,44284,44285,44310],{},[38,44210,44211],{},"6.8"," Jsou dány užitečnost ",[883,44214,44216],{"className":44215},[886],[888,44217,44218],{"xmlns":890},[892,44219,44220,44242],{},[895,44221,44222,44224,44226,44234],{},[898,44223,900],{},[1656,44225,1713],{},[1715,44227,44228,44230,44232],{},[898,44229,1665],{},[1667,44231,1669],{},[1667,44233,13779],{},[1715,44235,44236,44238,44240],{},[898,44237,1665],{},[1667,44239,1680],{},[1667,44241,13779],{},[902,44243,44244],{"encoding":904},"U = Q_1^{0{,}5} Q_2^{0{,}5}",", ceny ",[883,44247,44249],{"className":44248},[886],[888,44250,44251],{"xmlns":890},[892,44252,44253,44281],{},[895,44254,44255,44263,44265,44267,44269,44277,44279],{},[1715,44256,44257,44259,44261],{},[898,44258,8194],{},[1667,44260,1669],{},[1656,44262,8187],{},[1656,44264,1713],{},[1667,44266,2673],{},[1656,44268,1673],{"separator":1672},[1715,44270,44271,44273,44275],{},[898,44272,8194],{},[1667,44274,1680],{},[1656,44276,8187],{},[1656,44278,1713],{},[1667,44280,8580],{},[902,44282,44283],{"encoding":904},"P_1^* = 4, P_2^* = 10"," za jednotku zboží a důchod spotřebitele 200. Určete množství ",[883,44286,44288],{"className":44287},[886],[888,44289,44290],{"xmlns":890},[892,44291,44292,44308],{},[895,44293,44294,44300,44302],{},[1661,44295,44296,44298],{},[898,44297,1665],{},[1667,44299,1669],{},[1656,44301,1673],{"separator":1672},[1661,44303,44304,44306],{},[898,44305,1665],{},[1667,44307,1680],{},[902,44309,10094],{"encoding":904}," maximalizující užitečnost.",[724,44312,44313,44316,44317,44359,44360,44391,44392,44414,44415,1863],{},[38,44314,44315],{},"6.9"," Jsou dány rozpočtové omezení ",[883,44318,44320],{"className":44319},[886],[888,44321,44322],{"xmlns":890},[892,44323,44324,44356],{},[895,44325,44326,44328,44330,44336,44342,44344,44350],{},[898,44327,8184],{},[1656,44329,1713],{},[1661,44331,44332,44334],{},[898,44333,8194],{},[1667,44335,1669],{},[1661,44337,44338,44340],{},[898,44339,1665],{},[1667,44341,1669],{},[1656,44343,3633],{},[1661,44345,44346,44348],{},[898,44347,8194],{},[1667,44349,1680],{},[1661,44351,44352,44354],{},[898,44353,1665],{},[1667,44355,1680],{},[902,44357,44358],{"encoding":904},"Y = P_1 Q_1 + P_2 Q_2"," a užitečnost ",[883,44361,44363],{"className":44362},[886],[888,44364,44365],{"xmlns":890},[892,44366,44367,44389],{},[895,44368,44369,44371,44373,44381],{},[898,44370,900],{},[1656,44372,1713],{},[1715,44374,44375,44377,44379],{},[898,44376,1665],{},[1667,44378,1669],{},[1667,44380,13779],{},[1715,44382,44383,44385,44387],{},[898,44384,1665],{},[1667,44386,1680],{},[1667,44388,13779],{},[902,44390,44244],{"encoding":904},". (a) Odvoďte funkce poptávky maximalizující užitečnost. (b) Najděte funkce poptávky pro důchod ",[883,44393,44395],{"className":44394},[886],[888,44396,44397],{"xmlns":890},[892,44398,44399,44411],{},[895,44400,44401,44407,44409],{},[2062,44402,44403,44405],{},[898,44404,8184],{},[1656,44406,8187],{},[1656,44408,1713],{},[1667,44410,8059],{},[902,44412,44413],{"encoding":904},"Y^* = 500",". (c) Najděte Engelovy funkce pro ceny ",[883,44416,44418],{"className":44417},[886],[888,44419,44420],{"xmlns":890},[892,44421,44422,44450],{},[895,44423,44424,44432,44434,44436,44438,44446,44448],{},[1715,44425,44426,44428,44430],{},[898,44427,8194],{},[1667,44429,1669],{},[1656,44431,8187],{},[1656,44433,1713],{},[1667,44435,5193],{},[1656,44437,1673],{"separator":1672},[1715,44439,44440,44442,44444],{},[898,44441,8194],{},[1667,44443,1680],{},[1656,44445,8187],{},[1656,44447,1713],{},[1667,44449,8580],{},[902,44451,44452],{"encoding":904},"P_1^* = 5, P_2^* = 10",[724,44454,44455,44458,44459,30312,44490,44520,44521,1863],{},[38,44456,44457],{},"6.10"," Odvoďte funkce poptávky pro Cobb-Douglasovy funkce užitečnosti ",[883,44460,44462],{"className":44461},[886],[888,44463,44464],{"xmlns":890},[892,44465,44466,44488],{},[895,44467,44468,44470,44472,44480],{},[898,44469,900],{},[1656,44471,1713],{},[1715,44473,44474,44476,44478],{},[898,44475,1665],{},[1667,44477,1669],{},[898,44479,207],{},[1715,44481,44482,44484,44486],{},[898,44483,1665],{},[1667,44485,1680],{},[898,44487,3403],{},[902,44489,10480],{"encoding":904},[883,44491,44493],{"className":44492},[886],[888,44494,44495],{"xmlns":890},[892,44496,44497,44517],{},[895,44498,44499,44501,44503,44505,44507,44509,44511,44513,44515],{},[898,44500,207],{},[1656,44502,1673],{"separator":1672},[898,44504,3403],{},[1656,44506,5915],{},[1656,44508,14093],{"stretchy":1658},[1667,44510,4032],{},[1656,44512,1673],{"separator":1672},[1667,44514,1669],{},[1656,44516,14110],{"stretchy":1658},[902,44518,44519],{"encoding":904},"a, b \\in \\langle 0, 1 \\rangle"," a rozpočtové omezení ",[883,44522,44524],{"className":44523},[886],[888,44525,44526],{"xmlns":890},[892,44527,44528,44560],{},[895,44529,44530,44532,44534,44540,44546,44548,44554],{},[898,44531,8184],{},[1656,44533,1713],{},[1661,44535,44536,44538],{},[898,44537,8194],{},[1667,44539,1669],{},[1661,44541,44542,44544],{},[898,44543,1665],{},[1667,44545,1669],{},[1656,44547,3633],{},[1661,44549,44550,44552],{},[898,44551,8194],{},[1667,44553,1680],{},[1661,44555,44556,44558],{},[898,44557,1665],{},[1667,44559,1680],{},[902,44561,44358],{"encoding":904},[724,44563,44564,44567,44568,30312,44602,44520,44620,1863],{},[38,44565,44566],{},"6.11"," Odvoďte funkce poptávky pro funkce užitečnosti CES typu ",[883,44569,44571],{"className":44570},[886],[888,44572,44573],{"xmlns":890},[892,44574,44575,44599],{},[895,44576,44577,44579,44581,44589,44591],{},[898,44578,900],{},[1656,44580,1713],{},[1715,44582,44583,44585,44587],{},[898,44584,1665],{},[1667,44586,1669],{},[898,44588,207],{},[1656,44590,3633],{},[1715,44592,44593,44595,44597],{},[898,44594,1665],{},[1667,44596,1680],{},[898,44598,207],{},[902,44600,44601],{"encoding":904},"U = Q_1^a + Q_2^a",[883,44603,44605],{"className":44604},[886],[888,44606,44607],{"xmlns":890},[892,44608,44609,44617],{},[895,44610,44611,44613,44615],{},[898,44612,207],{},[1656,44614,12161],{"mathvariant":1723},[1667,44616,4032],{},[902,44618,44619],{"encoding":904},"a \\neq 0",[883,44621,44623],{"className":44622},[886],[888,44624,44625],{"xmlns":890},[892,44626,44627,44659],{},[895,44628,44629,44631,44633,44639,44645,44647,44653],{},[898,44630,8184],{},[1656,44632,1713],{},[1661,44634,44635,44637],{},[898,44636,8194],{},[1667,44638,1669],{},[1661,44640,44641,44643],{},[898,44642,1665],{},[1667,44644,1669],{},[1656,44646,3633],{},[1661,44648,44649,44651],{},[898,44650,8194],{},[1667,44652,1680],{},[1661,44654,44655,44657],{},[898,44656,1665],{},[1667,44658,1680],{},[902,44660,44358],{"encoding":904},[198,44662,44664],{"id":44663},"minimalizace-výdajů-a-hicksova-poptávka","Minimalizace výdajů a Hicksova poptávka",[724,44666,44667,44212,44670,1343,44697,44719,44720,1343,44743,44767,44768,44793,44794,1863],{},[38,44668,44669],{},"6.12",[883,44671,44673],{"className":44672},[886],[888,44674,44675],{"xmlns":890},[892,44676,44677,44695],{},[895,44678,44679,44681,44683,44689],{},[898,44680,900],{},[1656,44682,1713],{},[1661,44684,44685,44687],{},[898,44686,1665],{},[1667,44688,1669],{},[1661,44690,44691,44693],{},[898,44692,1665],{},[1667,44694,1680],{},[902,44696,8546],{"encoding":904},[883,44698,44700],{"className":44699},[886],[888,44701,44702],{"xmlns":890},[892,44703,44704,44716],{},[895,44705,44706,44712,44714],{},[2062,44707,44708,44710],{},[898,44709,900],{},[1656,44711,8187],{},[1656,44713,1713],{},[1667,44715,8580],{},[902,44717,44718],{"encoding":904},"U^* = 10"," hladina užitečnosti a ceny ",[883,44721,44723],{"className":44722},[886],[888,44724,44725],{"xmlns":890},[892,44726,44727,44741],{},[895,44728,44729,44737,44739],{},[1715,44730,44731,44733,44735],{},[898,44732,8194],{},[1667,44734,1669],{},[1656,44736,8187],{},[1656,44738,1713],{},[1667,44740,1680],{},[902,44742,38989],{"encoding":904},[883,44744,44746],{"className":44745},[886],[888,44747,44748],{"xmlns":890},[892,44749,44750,44764],{},[895,44751,44752,44760,44762],{},[1715,44753,44754,44756,44758],{},[898,44755,8194],{},[1667,44757,1680],{},[1656,44759,8187],{},[1656,44761,1713],{},[1667,44763,2673],{},[902,44765,44766],{"encoding":904},"P_2^* = 4",". Určete množství ",[883,44769,44771],{"className":44770},[886],[888,44772,44773],{"xmlns":890},[892,44774,44775,44791],{},[895,44776,44777,44783,44785],{},[1661,44778,44779,44781],{},[898,44780,1665],{},[1667,44782,1669],{},[1656,44784,1673],{"separator":1672},[1661,44786,44787,44789],{},[898,44788,1665],{},[1667,44790,1680],{},[902,44792,10094],{"encoding":904}," minimalizující výdaje spotřebitele ",[883,44795,44797],{"className":44796},[886],[888,44798,44799],{"xmlns":890},[892,44800,44801,44821],{},[895,44802,44803,44805,44807,44813,44815],{},[898,44804,900],{},[1656,44806,1713],{},[1661,44808,44809,44811],{},[898,44810,1665],{},[1667,44812,1669],{},[1656,44814,2751],{},[1661,44816,44817,44819],{},[898,44818,1665],{},[1667,44820,1680],{},[902,44822,44823],{"encoding":904},"U = Q_1 \\cdot Q_2",[724,44825,44826,44829,44830,44871,44872,44894,44895,1863],{},[38,44827,44828],{},"6.13"," Jsou dány výdaje spotřebitele ",[883,44831,44833],{"className":44832},[886],[888,44834,44835],{"xmlns":890},[892,44836,44837,44869],{},[895,44838,44839,44841,44843,44849,44855,44857,44863],{},[898,44840,1842],{},[1656,44842,1713],{},[1661,44844,44845,44847],{},[898,44846,8194],{},[1667,44848,1669],{},[1661,44850,44851,44853],{},[898,44852,1665],{},[1667,44854,1669],{},[1656,44856,3633],{},[1661,44858,44859,44861],{},[898,44860,8194],{},[1667,44862,1680],{},[1661,44864,44865,44867],{},[898,44866,1665],{},[1667,44868,1680],{},[902,44870,36656],{"encoding":904}," a užitečnost. (a) Najděte funkce poptávky minimalizující výdaje spotřebitele. (b) Určete funkce poptávky pro užitečnost ",[883,44873,44875],{"className":44874},[886],[888,44876,44877],{"xmlns":890},[892,44878,44879,44891],{},[895,44880,44881,44887,44889],{},[2062,44882,44883,44885],{},[898,44884,900],{},[1656,44886,8187],{},[1656,44888,1713],{},[1667,44890,8567],{},[902,44892,44893],{"encoding":904},"U^* = 25"," a stanovte příslušné výdaje spotřebitele při cenách ",[883,44896,44898],{"className":44897},[886],[888,44899,44900],{"xmlns":890},[892,44901,44902,44931],{},[895,44903,44904,44912,44914,44916,44918,44926,44928],{},[1715,44905,44906,44908,44910],{},[898,44907,8194],{},[1667,44909,1669],{},[1656,44911,8187],{},[1656,44913,1713],{},[1667,44915,9058],{},[1656,44917,1673],{"separator":1672},[1715,44919,44920,44922,44924],{},[898,44921,8194],{},[1667,44923,1680],{},[1656,44925,8187],{},[1656,44927,1713],{},[1667,44929,44930],{},"15",[902,44932,44933],{"encoding":904},"P_1^* = 20, P_2^* = 15",[115,44935,10198],{"id":10197},[120,44937,44938,44995,45034,45054,45089,45142,45147,45153,45249,45294],{},[123,44939,44940,1643,44943,44992,44993,1863],{},[38,44941,44942],{},"Rozpočtové omezení (budget constraint)",[883,44944,44946],{"className":44945},[886],[888,44947,44948],{"xmlns":890},[892,44949,44950,44990],{},[895,44951,44952,44958,44960,44968,44974,44976,44984],{},[2062,44953,44954,44956],{},[898,44955,8184],{},[1656,44957,8187],{},[1656,44959,1713],{},[1715,44961,44962,44964,44966],{},[898,44963,8194],{},[1667,44965,1669],{},[1656,44967,8187],{},[1661,44969,44970,44972],{},[898,44971,1665],{},[1667,44973,1669],{},[1656,44975,3633],{},[1715,44977,44978,44980,44982],{},[898,44979,8194],{},[1667,44981,1680],{},[1656,44983,8187],{},[1661,44985,44986,44988],{},[898,44987,1665],{},[1667,44989,1680],{},[902,44991,8223],{"encoding":904}," — (6.12); ",[38,44994,36842],{},[123,44996,44997,45000,45001,1863],{},[38,44998,44999],{},"Úloha o maximalizaci užitečnosti"," (primární) — Lagrangeova funkce (6.13), soustava (6.14), podmínka optimality ",[883,45002,45004],{"className":45003},[886],[888,45005,45006],{"xmlns":890},[892,45007,45008,45032],{},[895,45009,45010,45012,45014,45022,45024],{},[2461,45011,7362],{},[1656,45013,1713],{},[1715,45015,45016,45018,45020],{},[898,45017,8194],{},[1667,45019,1669],{},[1656,45021,8187],{},[898,45023,1782],{"mathvariant":1723},[1715,45025,45026,45028,45030],{},[898,45027,8194],{},[1667,45029,1680],{},[1656,45031,8187],{},[902,45033,37681],{"encoding":904},[123,45035,45036,45051,45052,1863],{},[38,45037,37822,45038],{},[883,45039,45041],{"className":45040},[886],[888,45042,45043],{"xmlns":890},[892,45044,45045,45049],{},[895,45046,45047],{},[898,45048,25169],{},[902,45050,25222],{"encoding":904}," — stínová cena uvolnění omezení; u maximalizace ",[38,45053,37844],{},[123,45055,45056,45059,45060,1863],{},[38,45057,45058],{},"Podmínka tečnosti"," — sklon indiferenční křivky = sklon rozpočtové přímky; ",[883,45061,45063],{"className":45062},[886],[888,45064,45065],{"xmlns":890},[892,45066,45067,45087],{},[895,45068,45069,45071,45073,45079,45081],{},[2461,45070,7362],{},[1656,45072,1713],{},[1661,45074,45075,45077],{},[898,45076,8194],{},[1667,45078,1669],{},[898,45080,1782],{"mathvariant":1723},[1661,45082,45083,45085],{},[898,45084,8194],{},[1667,45086,1680],{},[902,45088,10631],{"encoding":904},[123,45090,45091,2533,45094,45141],{},[38,45092,45093],{},"Poptávka maximalizující užitečnost (Marshallova)",[883,45095,45097],{"className":45096},[886],[888,45098,45099],{"xmlns":890},[892,45100,45101,45139],{},[895,45102,45103,45109,45111,45117,45119,45125,45127,45133,45135,45137],{},[1661,45104,45105,45107],{},[898,45106,1665],{},[898,45108,1710],{},[1656,45110,1713],{},[1661,45112,45113,45115],{},[898,45114,6787],{},[898,45116,1710],{},[1656,45118,1659],{"stretchy":1658},[1661,45120,45121,45123],{},[898,45122,8194],{},[1667,45124,1669],{},[1656,45126,1673],{"separator":1672},[1661,45128,45129,45131],{},[898,45130,8194],{},[1667,45132,1680],{},[1656,45134,1673],{"separator":1672},[898,45136,8184],{},[1656,45138,1683],{"stretchy":1658},[902,45140,8272],{"encoding":904}," — (6.15).",[123,45143,45144,45146],{},[38,45145,40417],{}," — poptávka jako funkce důchodu při pevných cenách.",[123,45148,45149,45152],{},[38,45150,45151],{},"Úloha o minimalizaci výdajů"," (duální) — Lagrangeova funkce (6.24), soustava (6.25), postačující podmínka (6.26).",[123,45154,45155,2533,45157,45204,45205,45248],{},[38,45156,42727],{},[883,45158,45160],{"className":45159},[886],[888,45161,45162],{"xmlns":890},[892,45163,45164,45202],{},[895,45165,45166,45172,45174,45180,45182,45188,45190,45196,45198,45200],{},[1661,45167,45168,45170],{},[898,45169,1665],{},[898,45171,1710],{},[1656,45173,1713],{},[1661,45175,45176,45178],{},[898,45177,6787],{},[898,45179,1710],{},[1656,45181,1659],{"stretchy":1658},[1661,45183,45184,45186],{},[898,45185,8194],{},[1667,45187,1669],{},[1656,45189,1673],{"separator":1672},[1661,45191,45192,45194],{},[898,45193,8194],{},[1667,45195,1680],{},[1656,45197,1673],{"separator":1672},[898,45199,900],{},[1656,45201,1683],{"stretchy":1658},[902,45203,8392],{"encoding":904}," — (6.27); obecný výsledek pro ",[883,45206,45208],{"className":45207},[886],[888,45209,45210],{"xmlns":890},[892,45211,45212,45246],{},[895,45213,45214,45216,45218,45232],{},[898,45215,900],{},[1656,45217,1713],{},[1715,45219,45220,45222,45224],{},[898,45221,1665],{},[1667,45223,1669],{},[895,45225,45226,45228,45230],{},[1667,45227,1669],{},[898,45229,1782],{"mathvariant":1723},[1667,45231,1680],{},[1715,45233,45234,45236,45238],{},[898,45235,1665],{},[1667,45237,1680],{},[895,45239,45240,45242,45244],{},[1667,45241,1669],{},[898,45243,1782],{"mathvariant":1723},[1667,45245,1680],{},[902,45247,8663],{"encoding":904},": (6.30).",[123,45250,45251,45293],{},[38,45252,45253,45254],{},"Bod dotyku ",[883,45255,45257],{"className":45256},[886],[888,45258,45259],{"xmlns":890},[892,45260,45261,45291],{},[895,45262,45263,45269,45271,45279,45281,45289],{},[2062,45264,45265,45267],{},[898,45266,1665],{},[1656,45268,8187],{},[1656,45270,3453],{"stretchy":1658},[1715,45272,45273,45275,45277],{},[898,45274,1665],{},[1667,45276,1669],{},[1656,45278,8187],{},[1656,45280,1673],{"separator":1672},[1715,45282,45283,45285,45287],{},[898,45284,1665],{},[1667,45286,1680],{},[1656,45288,8187],{},[1656,45290,3462],{"stretchy":1658},[902,45292,8443],{"encoding":904}," — řešení obou úloh; totožný pro primární i duální formulaci.",[123,45295,45296,45299,45300,45313,45314,45327],{},[38,45297,45298],{},"Dualita"," — ekvivalence max ",[883,45301,45303],{"className":45302},[886],[888,45304,45305],{"xmlns":890},[892,45306,45307,45311],{},[895,45308,45309],{},[898,45310,900],{},[902,45312,900],{"encoding":904}," a min ",[883,45315,45317],{"className":45316},[886],[888,45318,45319],{"xmlns":890},[892,45320,45321,45325],{},[895,45322,45323],{},[898,45324,1842],{},[902,45326,1842],{"encoding":904},"; Marshallova a Hicksova poptávka.",[115,45329,10640],{"id":10639},[120,45331,45332,45355,45371,45384,45394],{},[123,45333,45334,1643,45337,45340,45341,45354],{},[38,45335,45336],{},"Teorie před optimalizací:",[207,45338,880],{"className":45339,"dataFsResolvedFilePath":878,"href":879},[210]," (funkce ",[883,45342,45344],{"className":45343},[886],[888,45345,45346],{"xmlns":890},[892,45347,45348,45352],{},[895,45349,45350],{},[898,45351,900],{},[902,45353,900],{"encoding":904},", indiferenční křivky, MRCS).",[123,45356,45357,1643,45360,45363,45364,45367,45368,1863],{},[38,45358,45359],{},"Matematický aparát:",[207,45361,793],{"className":45362,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace), ",[207,45365,784],{"className":45366,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace), ",[207,45369,10692],{"className":45370,"dataFsResolvedFilePath":764,"href":765},[210],[123,45372,45373,1643,45376,45379,45380,45383],{},[38,45374,45375],{},"Paralely:",[207,45377,10697],{"className":45378,"dataFsResolvedFilePath":857,"href":858},[210]," (MRTS ↔ MRCS, izokvanty ↔ IC, Eulerova věta pro CD), ",[207,45381,10702],{"className":45382,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallova poptávka jako vstup tržního modelu).",[123,45385,45386,1643,45388,1343,45391],{},[38,45387,10731],{},[207,45389,1094],{"className":45390,"dataFsResolvedFilePath":838,"href":839},[210],[207,45392,1101],{"className":45393,"dataFsResolvedFilePath":868,"href":869},[210],[123,45395,45396,1643,45398],{},[38,45397,10742],{},[207,45399,1869],{"className":45400,"dataFsResolvedFilePath":10746,"href":10747},[210],{"title":641,"searchDepth":642,"depth":642,"links":45402},[45403,45404,45405,45410,45411,45412,45414,45417,45420,45422,45423,45425,45426,45430,45431],{"id":1637,"depth":642,"text":1638},{"id":36715,"depth":642,"text":36716},{"id":37106,"depth":642,"text":37107,"children":45406},[45407,45408],{"id":37226,"depth":649,"text":37227},{"id":37804,"depth":649,"text":45409},"Interpretace λ\\lambda — mezní užitečnost důchodu",{"id":38266,"depth":642,"text":38267},{"id":38577,"depth":642,"text":38578},{"id":38888,"depth":642,"text":45413},"Příklad 6.6 — maximalizace užitečnosti pro U=Q1Q2U = Q_1 Q_2",{"id":39660,"depth":642,"text":39661,"children":45415},[45416],{"id":40416,"depth":649,"text":40417},{"id":40596,"depth":642,"text":40597,"children":45418},[45419],{"id":40853,"depth":649,"text":40854},{"id":41803,"depth":642,"text":45421},"Příklad 6.7 — minimalizace výdajů pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":42726,"depth":642,"text":42727},{"id":42929,"depth":642,"text":45424},"Příklad 6.8 — obecné odvození pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":43814,"depth":642,"text":43815},{"id":44201,"depth":642,"text":44202,"children":45427},[45428,45429],{"id":44205,"depth":649,"text":44206},{"id":44663,"depth":649,"text":44664},{"id":10197,"depth":642,"text":10198},{"id":10639,"depth":642,"text":10640},{},"\u002Ftopics\u002Foptimalizace-spotrebitele",{"title":8672,"description":641},[1138,1137],"topics\u002Foptimalizace-spotrebitele",[1128,1874,1144,10781,45438,45439,45440],"poptavka-spotrebitele","minimalizace-vydaju","dualita","jxXhWsWsCIcDvEqLkcWTWs-jk9CvI-eFUi2Afo7U40o",{"id":45443,"title":802,"body":45444,"course":1128,"courses":659,"created":10774,"description":641,"extension":661,"meta":59486,"navigation":664,"path":59487,"seo":59488,"sources":59489,"stem":59490,"tags":59491,"type":10786,"updated":677,"__hash__":59497},"topics\u002Ftopics\u002Fpoptavka-nabidka.md",{"type":9,"value":45445,"toc":59442},[45446,45449,45475,45479,45486,45637,45651,45654,45656,45743,45747,45783,45856,45877,46002,46012,46025,46029,46034,46064,46126,46135,46139,46201,46208,46229,46347,46425,46429,46432,46491,46606,46611,46643,46705,46753,46808,46812,46833,46857,46905,46909,46921,46925,47035,47039,47055,47096,47107,47265,47275,47280,47284,47406,47416,47423,47427,47505,47516,47596,47602,47609,47748,47755,47758,47815,47819,47896,47942,47986,47992,48105,48109,48112,48307,48311,48548,48551,48705,48858,48860,48862,48942,48945,49050,49119,49128,49132,49135,49196,49205,49209,49242,49320,49359,49363,49412,49466,49470,49499,49528,49580,49587,49641,49719,49723,49766,49833,49877,49981,50000,50002,50006,50114,50118,50186,50235,50242,50327,50331,50403,50408,50456,50642,50646,50651,50827,50832,50891,50996,51000,51027,51031,51038,51202,51289,51294,51296,51299,51399,51549,51621,51695,51697,51701,51715,51719,51852,51907,52019,52096,52100,52157,52260,52319,52480,52484,52559,52631,52729,52787,52881,52934,52955,53009,53014,53092,53140,53227,53265,53353,53506,53542,53596,53599,53601,53603,53652,53659,53667,53754,53763,53850,53857,53859,53863,54088,54090,54094,54098,54167,54218,54421,54427,54438,54506,54512,54934,54938,55002,55026,55222,55228,55242,55310,55313,55353,55576,55644,55946,56354,56431,56597,56603,56606,56681,57133,57184,57590,57695,58358,58361,58438,58446,58520,58551,58553,58555,58599,58601,58603,58607,58837,58841,58932,58937,59031,59036,59209,59213,59331,59336,59385,59387,59389],[12,45447,802],{"id":45448},"poptávka-nabídka-a-tržní-rovnováha",[1981,45450,45451],{},[724,45452,45453,45455,45456,45459,45460,45463,45464,45467,45468,45470,45471,45474],{},[883,45454,3472],{}," TL;DR\nKapitola buduje základní mikroekonomický model trhu: chování spotřebitele (",[38,45457,45458],{},"poptávka",") a výrobce (",[38,45461,45462],{},"nabídka","), jejich interakci v ",[38,45465,45466],{},"tržní rovnováze"," a kvantitativní analýzu reakce modelu na změnu exogenních proměnných (posuny, zdanění, ",[38,45469,26700],{},"). Uzavírá ji pojem ",[38,45472,45473],{},"přebytku spotřebitele a výrobce"," jako míry čistého prospěchu obou stran trhu.",[115,45476,45478],{"id":45477},"úvod-model-a-proměnné","Úvod — model a proměnné",[724,45480,45481,45482,45485],{},"Cílem je popsat chování spotřebitele a výrobce za předpokladu racionality jedince (",[614,45483,45484],{},"homo economicus","). Mezi hlavní proměnné patří:",[120,45487,45488,45505,45546,45562],{},[123,45489,45490,45491,45504],{},"cena ",[883,45492,45494],{"className":45493},[886],[888,45495,45496],{"xmlns":890},[892,45497,45498,45502],{},[895,45499,45500],{},[898,45501,8194],{},[902,45503,8194],{"encoding":904}," zkoumaného zboží,",[123,45506,45507,45508,1673],{},"ceny alternativních zboží ",[883,45509,45511],{"className":45510},[886],[888,45512,45513],{"xmlns":890},[892,45514,45515,45543],{},[895,45516,45517,45523,45525,45531,45533,45535,45537],{},[1661,45518,45519,45521],{},[898,45520,8194],{},[1667,45522,1669],{},[1656,45524,1673],{"separator":1672},[1661,45526,45527,45529],{},[898,45528,8194],{},[1667,45530,1680],{},[1656,45532,1673],{"separator":1672},[1656,45534,2337],{},[1656,45536,1673],{"separator":1672},[1661,45538,45539,45541],{},[898,45540,8194],{},[898,45542,2292],{},[902,45544,45545],{"encoding":904},"P_1, P_2, \\dots, P_n",[123,45547,45548,45549,1673],{},"důchod ",[883,45550,45552],{"className":45551},[886],[888,45553,45554],{"xmlns":890},[892,45555,45556,45560],{},[895,45557,45558],{},[898,45559,8184],{},[902,45561,8184],{"encoding":904},[123,45563,45564,45565,45578,45579,45592,45593,45606,45607,45621,45622,45636],{},"preference, očekávání, populace, výrobní faktory (práce ",[883,45566,45568],{"className":45567},[886],[888,45569,45570],{"xmlns":890},[892,45571,45572,45576],{},[895,45573,45574],{},[898,45575,18539],{},[902,45577,18539],{"encoding":904},", kapitál ",[883,45580,45582],{"className":45581},[886],[888,45583,45584],{"xmlns":890},[892,45585,45586,45590],{},[895,45587,45588],{},[898,45589,18544],{},[902,45591,18544],{"encoding":904},", půda ",[883,45594,45596],{"className":45595},[886],[888,45597,45598],{"xmlns":890},[892,45599,45600,45604],{},[895,45601,45602],{},[898,45603,1842],{},[902,45605,1842],{"encoding":904},"), technologie, počet výrobců ",[883,45608,45610],{"className":45609},[886],[888,45611,45612],{"xmlns":890},[892,45613,45614,45619],{},[895,45615,45616],{},[898,45617,45618],{},"O",[902,45620,45618],{"encoding":904},", počasí ",[883,45623,45625],{"className":45624},[886],[888,45626,45627],{"xmlns":890},[892,45628,45629,45634],{},[895,45630,45631],{},[898,45632,45633],{},"W",[902,45635,45633],{"encoding":904}," atd.",[724,45638,45639,45640,45643,45644,45647,45648,1863],{},"Vybereme-li právě jeden z faktorů jako endogenní (",[614,45641,45642],{},"ceteris paribus","), hovoříme o ",[38,45645,45646],{},"jednofaktorovém modelu","; jinak jde o model ",[38,45649,45650],{},"vícefaktorový",[45652,45653],"hr",{},[115,45655,21894],{"id":45458},[1981,45657,45658],{},[724,45659,45660,45662,45663,45676,45677,45690,45691,45694,45695,45718,45719,1863],{},[883,45661,3472],{}," TL;DR\nPoptávka vyjadřuje závislost nakupovaného množství ",[883,45664,45666],{"className":45665},[886],[888,45667,45668],{"xmlns":890},[892,45669,45670,45674],{},[895,45671,45672],{},[898,45673,1665],{},[902,45675,1665],{"encoding":904}," na ceně ",[883,45678,45680],{"className":45679},[886],[888,45681,45682],{"xmlns":890},[892,45683,45684,45688],{},[895,45685,45686],{},[898,45687,8194],{},[902,45689,8194],{"encoding":904}," (případně dalších proměnných). Základní vlastností je ",[38,45692,45693],{},"zákon klesající poptávky",": při růstu ceny množství klesá. Z důvodu přehlednosti se pracuje s jednofaktorovým modelem ",[883,45696,45698],{"className":45697},[886],[888,45699,45700],{"xmlns":890},[892,45701,45702,45716],{},[895,45703,45704,45706,45708,45710,45712,45714],{},[898,45705,1665],{},[1656,45707,1713],{},[898,45709,6787],{},[1656,45711,1659],{"stretchy":1658},[898,45713,8194],{},[1656,45715,1683],{"stretchy":1658},[902,45717,12971],{"encoding":904}," a jeho lineární verzí ",[883,45720,45722],{"className":45721},[886],[888,45723,45724],{"xmlns":890},[892,45725,45726,45740],{},[895,45727,45728,45730,45732,45734,45736,45738],{},[898,45729,8194],{},[1656,45731,1713],{},[898,45733,207],{},[898,45735,1665],{},[1656,45737,3633],{},[898,45739,3403],{},[902,45741,45742],{"encoding":904},"P = aQ + b",[198,45744,45746],{"id":45745},"obecný-vícefaktorový-model","Obecný vícefaktorový model",[724,45748,45749,45750,45763,45764,45777,45778,3247,45780,5642],{},"Ve vícefaktorovém modelu uvažujeme, že poptávané množství ",[883,45751,45753],{"className":45752},[886],[888,45754,45755],{"xmlns":890},[892,45756,45757,45761],{},[895,45758,45759],{},[898,45760,1665],{},[902,45762,1665],{"encoding":904}," závisí na ceně ",[883,45765,45767],{"className":45766},[886],[888,45768,45769],{"xmlns":890},[892,45770,45771,45775],{},[895,45772,45773],{},[898,45774,8194],{},[902,45776,8194],{"encoding":904},", na cenách alternativních zboží a důchodu. Závislost vyjadřuje ",[38,45779,36711],{},[614,45781,45782],{},"demand function",[883,45784,45786],{"className":45785},[886],[888,45787,45788],{"xmlns":890,"display":2408},[892,45789,45790,45853],{},[2412,45791,45792],{"width":2414},[2416,45793,45794,45796,45846,45848],{},[2419,45795],{"width":2421},[2419,45797,45798],{},[895,45799,45800,45802,45804,45806,45808,45810,45812,45818,45820,45826,45828,45830,45832,45838,45840,45842,45844],{},[898,45801,1665],{},[1656,45803,1713],{},[898,45805,6787],{},[1656,45807,1659],{"stretchy":1658},[898,45809,8194],{},[1656,45811,1673],{"separator":1672},[1661,45813,45814,45816],{},[898,45815,8194],{},[1667,45817,1669],{},[1656,45819,1673],{"separator":1672},[1661,45821,45822,45824],{},[898,45823,8194],{},[1667,45825,1680],{},[1656,45827,1673],{"separator":1672},[1656,45829,2337],{},[1656,45831,1673],{"separator":1672},[1661,45833,45834,45836],{},[898,45835,8194],{},[898,45837,2292],{},[1656,45839,1673],{"separator":1672},[898,45841,8184],{},[1656,45843,1683],{"stretchy":1658},[898,45845,1863],{"mathvariant":1723},[2419,45847],{"width":2421},[2419,45849,45850],{},[2461,45851,45852],{},"(2.1)",[902,45854,45855],{"encoding":904},"Q = D(P, P_1, P_2, \\dots, P_n, Y). \\tag{2.1}",[724,45857,45858,45859,45862,45863,45876],{},"Důležitou vlastností je ",[38,45860,45861],{},"homogenita",": změní-li se všechny nezávisle proměnné ",[883,45864,45866],{"className":45865},[886],[888,45867,45868],{"xmlns":890},[892,45869,45870,45874],{},[895,45871,45872],{},[898,45873,20776],{},[902,45875,20776],{"encoding":904},"-krát, poptávané množství se nezmění,",[883,45878,45880],{"className":45879},[886],[888,45881,45882],{"xmlns":890,"display":2408},[892,45883,45884,45999],{},[2412,45885,45886],{"width":2414},[2416,45887,45888,45890,45992,45994],{},[2419,45889],{"width":2421},[2419,45891,45892],{},[895,45893,45894,45896,45898,45900,45902,45904,45906,45908,45910,45916,45918,45920,45926,45928,45930,45932,45934,45940,45942,45944,45946,45948,45950,45952,45954,45956,45958,45964,45966,45972,45974,45976,45978,45984,45986,45988,45990],{},[898,45895,1665],{},[1656,45897,1713],{},[898,45899,6787],{},[1656,45901,1659],{"stretchy":1658},[898,45903,20776],{},[898,45905,8194],{},[1656,45907,1673],{"separator":1672},[898,45909,20776],{},[1661,45911,45912,45914],{},[898,45913,8194],{},[1667,45915,1669],{},[1656,45917,1673],{"separator":1672},[898,45919,20776],{},[1661,45921,45922,45924],{},[898,45923,8194],{},[1667,45925,1680],{},[1656,45927,1673],{"separator":1672},[1656,45929,2337],{},[1656,45931,1673],{"separator":1672},[898,45933,20776],{},[1661,45935,45936,45938],{},[898,45937,8194],{},[898,45939,2292],{},[1656,45941,1673],{"separator":1672},[898,45943,20776],{},[898,45945,8184],{},[1656,45947,1683],{"stretchy":1658},[1656,45949,1713],{},[898,45951,6787],{},[1656,45953,1659],{"stretchy":1658},[898,45955,8194],{},[1656,45957,1673],{"separator":1672},[1661,45959,45960,45962],{},[898,45961,8194],{},[1667,45963,1669],{},[1656,45965,1673],{"separator":1672},[1661,45967,45968,45970],{},[898,45969,8194],{},[1667,45971,1680],{},[1656,45973,1673],{"separator":1672},[1656,45975,2337],{},[1656,45977,1673],{"separator":1672},[1661,45979,45980,45982],{},[898,45981,8194],{},[898,45983,2292],{},[1656,45985,1673],{"separator":1672},[898,45987,8184],{},[1656,45989,1683],{"stretchy":1658},[898,45991,1863],{"mathvariant":1723},[2419,45993],{"width":2421},[2419,45995,45996],{},[2461,45997,45998],{},"(2.2)",[902,46000,46001],{"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}",[1981,46003,46004],{},[724,46005,46006,46008,46009,1863],{},[883,46007,1987],{}," Pozor\nHomogenita platí pouze v zidealizovaném vícefaktorovém modelu; ",[38,46010,46011],{},"v jednofaktorových modelech neplatí",[724,46013,46014,46015,1343,46018,1896,46021,46024],{},"Rozlišuje se poptávka ",[38,46016,46017],{},"individuální",[38,46019,46020],{},"tržní",[38,46022,46023],{},"agregátní"," (není-li specifikováno, rozumí se tržní).",[198,46026,46028],{"id":46027},"jednofaktorové-modely","Jednofaktorové modely",[46030,46031,46033],"h4",{"id":46032},"funkce-poptávky-v-užším-slova-smyslu","Funkce poptávky v užším slova smyslu",[724,46035,46036,46037,46050,46051,2114],{},"Poptávané množství ",[883,46038,46040],{"className":46039},[886],[888,46041,46042],{"xmlns":890},[892,46043,46044,46048],{},[895,46045,46046],{},[898,46047,1665],{},[902,46049,1665],{"encoding":904}," závisí pouze na ceně ",[883,46052,46054],{"className":46053},[886],[888,46055,46056],{"xmlns":890},[892,46057,46058,46062],{},[895,46059,46060],{},[898,46061,8194],{},[902,46063,8194],{"encoding":904},[883,46065,46067],{"className":46066},[886],[888,46068,46069],{"xmlns":890,"display":2408},[892,46070,46071,46123],{},[2412,46072,46073],{"width":2414},[2416,46074,46075,46077,46116,46118],{},[2419,46076],{"width":2421},[2419,46078,46079],{},[895,46080,46081,46083,46085,46087,46089,46091,46093,46095,46097,46100,46102,46104,46106,46108,46110,46112,46114],{},[898,46082,1665],{},[1656,46084,1713],{},[898,46086,6787],{},[1656,46088,1659],{"stretchy":1658},[898,46090,8194],{},[1656,46092,1683],{"stretchy":1658},[1656,46094,1673],{"separator":1672},[3316,46096],{"width":14644},[2461,46098,46099],{},"resp.",[3316,46101],{"width":14644},[898,46103,8194],{},[1656,46105,1713],{},[898,46107,6787],{},[1656,46109,1659],{"stretchy":1658},[898,46111,1665],{},[1656,46113,1683],{"stretchy":1658},[898,46115,1863],{"mathvariant":1723},[2419,46117],{"width":2421},[2419,46119,46120],{},[2461,46121,46122],{},"(2.3)",[902,46124,46125],{"encoding":904},"Q = D(P), \\qquad \\text{resp.} \\qquad P = D(Q). \\tag{2.3}",[724,46127,46128,46129,3247,46132,12702],{},"Graf této funkce se nazývá ",[38,46130,46131],{},"křivka poptávky",[614,46133,46134],{},"demand curve",[46030,46136,46138],{"id":46137},"zákon-klesající-poptávky","Zákon klesající poptávky",[1981,46140,46141],{},[724,46142,46143],{},[38,46144,46145,46146,46159,46160,46173,46174,46159,46187,46200],{},"Roste-li cena ",[883,46147,46149],{"className":46148},[886],[888,46150,46151],{"xmlns":890},[892,46152,46153,46157],{},[895,46154,46155],{},[898,46156,8194],{},[902,46158,8194],{"encoding":904},", pak množství ",[883,46161,46163],{"className":46162},[886],[888,46164,46165],{"xmlns":890},[892,46166,46167,46171],{},[895,46168,46169],{},[898,46170,1665],{},[902,46172,1665],{"encoding":904}," klesá; klesá-li cena ",[883,46175,46177],{"className":46176},[886],[888,46178,46179],{"xmlns":890},[892,46180,46181,46185],{},[895,46182,46183],{},[898,46184,8194],{},[902,46186,8194],{"encoding":904},[883,46188,46190],{"className":46189},[886],[888,46191,46192],{"xmlns":890},[892,46193,46194,46198],{},[895,46195,46196],{},[898,46197,1665],{},[902,46199,1665],{"encoding":904}," roste.",[724,46202,46203,46204,46207],{},"Spotřebitelé jsou ochotni nakoupit větší množství za nižší cenu (mezní užitečnost — viz kap. 6). Zákon platí za ",[38,46205,46206],{},"normálních podmínek","; první kvantitativní formulaci podal Marshall (1890).",[1981,46209,46210,46215],{},[724,46211,46212,46214],{},[883,46213,3472],{}," Intuice — proč zákon platí",[120,46216,46217,46223],{},[123,46218,46219,46222],{},[38,46220,46221],{},"Substituční efekt"," — růst ceny vede ke snaze nahradit zboží jiným.",[123,46224,46225,46228],{},[38,46226,46227],{},"Důchodový efekt"," — růst ceny způsobí nevítaný úbytek reálného důchodu.",[724,46230,46231,46232,46245,46246,46259,46260,46286,46287,46313,46314,3206,46340,46343,46344,1863],{},"Každá funkce poptávky je tedy klesající. Cena ",[883,46233,46235],{"className":46234},[886],[888,46236,46237],{"xmlns":890},[892,46238,46239,46243],{},[895,46240,46241],{},[898,46242,8194],{},[902,46244,8194],{"encoding":904}," se vynáší na svislou osu, množství ",[883,46247,46249],{"className":46248},[886],[888,46250,46251],{"xmlns":890},[892,46252,46253,46257],{},[895,46254,46255],{},[898,46256,1665],{},[902,46258,1665],{"encoding":904}," na vodorovnou. Hypotetická křivka prochází body ",[883,46261,46263],{"className":46262},[886],[888,46264,46265],{"xmlns":890},[892,46266,46267,46283],{},[895,46268,46269,46271,46273,46275,46281],{},[1656,46270,3453],{"stretchy":1658},[1667,46272,4032],{},[1656,46274,1673],{"separator":1672},[1661,46276,46277,46279],{},[898,46278,8194],{},[1667,46280,4032],{},[1656,46282,3462],{"stretchy":1658},[902,46284,46285],{"encoding":904},"[0, P_0]"," (cena, při níž je zboží neprodejné) a ",[883,46288,46290],{"className":46289},[886],[888,46291,46292],{"xmlns":890},[892,46293,46294,46310],{},[895,46295,46296,46298,46304,46306,46308],{},[1656,46297,3453],{"stretchy":1658},[1661,46299,46300,46302],{},[898,46301,1665],{},[1667,46303,4032],{},[1656,46305,1673],{"separator":1672},[1667,46307,4032],{},[1656,46309,3462],{"stretchy":1658},[902,46311,46312],{"encoding":904},"[Q_0, 0]"," (teoretický objem při nulové ceně). Interval ",[883,46315,46317],{"className":46316},[886],[888,46318,46319],{"xmlns":890},[892,46320,46321,46337],{},[895,46322,46323,46325,46327,46329,46335],{},[1656,46324,1659],{"stretchy":1658},[1667,46326,4032],{},[1656,46328,1673],{"separator":1672},[1661,46330,46331,46333],{},[898,46332,8194],{},[1667,46334,4032],{},[1656,46336,1683],{"stretchy":1658},[902,46338,46339],{"encoding":904},"(0, P_0)",[38,46341,46342],{},"reálné cenové rozpětí",". Za teoretických předpokladů je křivka ",[38,46345,46346],{},"konvexní",[724,46348,46349],{},[614,46350,46351,46352,46374,46375,1896,46400,1863],{},"Obrázek 2.1: Hypotetická křivka poptávky v rovině ",[883,46353,46355],{"className":46354},[886],[888,46356,46357],{"xmlns":890},[892,46358,46359,46371],{},[895,46360,46361,46363,46365,46367,46369],{},[1656,46362,1659],{"stretchy":1658},[898,46364,1665],{},[1656,46366,1673],{"separator":1672},[898,46368,8194],{},[1656,46370,1683],{"stretchy":1658},[902,46372,46373],{"encoding":904},"(Q, P)"," — klesající, konvexní, procházející body ",[883,46376,46378],{"className":46377},[886],[888,46379,46380],{"xmlns":890},[892,46381,46382,46398],{},[895,46383,46384,46386,46388,46390,46396],{},[1656,46385,3453],{"stretchy":1658},[1667,46387,4032],{},[1656,46389,1673],{"separator":1672},[1661,46391,46392,46394],{},[898,46393,8194],{},[1667,46395,4032],{},[1656,46397,3462],{"stretchy":1658},[902,46399,46285],{"encoding":904},[883,46401,46403],{"className":46402},[886],[888,46404,46405],{"xmlns":890},[892,46406,46407,46423],{},[895,46408,46409,46411,46417,46419,46421],{},[1656,46410,3453],{"stretchy":1658},[1661,46412,46413,46415],{},[898,46414,1665],{},[1667,46416,4032],{},[1656,46418,1673],{"separator":1672},[1667,46420,4032],{},[1656,46422,3462],{"stretchy":1658},[902,46424,46312],{"encoding":904},[46030,46426,46428],{"id":46427},"lineární-model-poptávky","Lineární model poptávky",[724,46430,46431],{},"Nejjednodušší závislostí je",[883,46433,46435],{"className":46434},[886],[888,46436,46437],{"xmlns":890,"display":2408},[892,46438,46439,46488],{},[2412,46440,46441],{"width":2414},[2416,46442,46443,46445,46481,46483],{},[2419,46444],{"width":2421},[2419,46446,46447],{},[895,46448,46449,46451,46453,46455,46457,46459,46461,46463,46465,46467,46469,46471,46473,46475,46477,46479],{},[898,46450,8194],{},[1656,46452,1713],{},[898,46454,207],{},[898,46456,1665],{},[1656,46458,3633],{},[898,46460,3403],{},[1656,46462,1673],{"separator":1672},[3316,46464],{"width":14644},[898,46466,207],{},[1656,46468,4373],{},[1667,46470,4032],{},[1656,46472,1673],{"separator":1672},[2461,46474,11112],{},[898,46476,3403],{},[1656,46478,2850],{},[1667,46480,4283],{},[2419,46482],{"width":2421},[2419,46484,46485],{},[2461,46486,46487],{},"(2.4)",[902,46489,46490],{"encoding":904},"P = aQ + b, \\qquad a \u003C 0,\\ b > 0. \\tag{2.4}",[724,46492,46493,46494,30312,46530,1896,46554,16797,46580,46602,46603,1863],{},"Křivka poptávky je přímka se záporným sklonem. Alternativně ",[883,46495,46497],{"className":46496},[886],[888,46498,46499],{"xmlns":890},[892,46500,46501,46527],{},[895,46502,46503,46505,46507,46515,46517,46519],{},[898,46504,1665],{},[1656,46506,1713],{},[4138,46508,46509],{"scriptlevel":4032,"displaystyle":1658},[3294,46510,46511,46513],{},[1667,46512,1669],{},[898,46514,207],{},[898,46516,8194],{},[1656,46518,3964],{},[4138,46520,46521],{"scriptlevel":4032,"displaystyle":1658},[3294,46522,46523,46525],{},[898,46524,3403],{},[898,46526,207],{},[902,46528,46529],{"encoding":904},"Q = \\tfrac{1}{a}P - \\tfrac{b}{a}",[883,46531,46533],{"className":46532},[886],[888,46534,46535],{"xmlns":890},[892,46536,46537,46551],{},[895,46538,46539,46547,46549],{},[4138,46540,46541],{"scriptlevel":4032,"displaystyle":1658},[3294,46542,46543,46545],{},[1667,46544,1669],{},[898,46546,207],{},[1656,46548,4373],{},[1667,46550,4032],{},[902,46552,46553],{"encoding":904},"\\tfrac{1}{a} \u003C 0",[883,46555,46557],{"className":46556},[886],[888,46558,46559],{"xmlns":890},[892,46560,46561,46577],{},[895,46562,46563,46565,46573,46575],{},[1656,46564,3964],{},[4138,46566,46567],{"scriptlevel":4032,"displaystyle":1658},[3294,46568,46569,46571],{},[898,46570,3403],{},[898,46572,207],{},[1656,46574,2850],{},[1667,46576,4032],{},[902,46578,46579],{"encoding":904},"-\\tfrac{b}{a} > 0",[883,46581,46583],{"className":46582},[886],[888,46584,46585],{"xmlns":890},[892,46586,46587,46599],{},[895,46588,46589,46591,46593,46595,46597],{},[1656,46590,1659],{"stretchy":1658},[1667,46592,4032],{},[1656,46594,1673],{"separator":1672},[898,46596,3403],{},[1656,46598,1683],{"stretchy":1658},[902,46600,46601],{"encoding":904},"(0, b)",". Tento model odpovídá ",[38,46604,46605],{},"nedokonalé konkurenci",[46607,46608,46610],"h5",{"id":46609},"příklad-21","Příklad 2.1",[724,46612,46613,46616,46617,1863],{},[38,46614,46615],{},"Zadání:"," Lineární poptávka ",[883,46618,46620],{"className":46619},[886],[888,46621,46622],{"xmlns":890},[892,46623,46624,46640],{},[895,46625,46626,46628,46630,46632,46634,46636,46638],{},[898,46627,8194],{},[1656,46629,1713],{},[1656,46631,3964],{},[1667,46633,1680],{},[898,46635,1665],{},[1656,46637,3633],{},[1667,46639,11918],{},[902,46641,46642],{"encoding":904},"P = -2Q + 60",[724,46644,46645,46648,46649,46671,46672,1863],{},[38,46646,46647],{},"Řešení:"," Reálné cenové rozpětí je ",[883,46650,46652],{"className":46651},[886],[888,46653,46654],{"xmlns":890},[892,46655,46656,46668],{},[895,46657,46658,46660,46662,46664,46666],{},[1656,46659,1659],{"stretchy":1658},[1667,46661,4032],{},[1656,46663,1673],{"separator":1672},[1667,46665,11918],{},[1656,46667,1683],{"stretchy":1658},[902,46669,46670],{"encoding":904},"(0, 60)","; alternativní tvar je ",[883,46673,46675],{"className":46674},[886],[888,46676,46677],{"xmlns":890},[892,46678,46679,46702],{},[895,46680,46681,46683,46685,46687,46695,46697,46699],{},[898,46682,1665],{},[1656,46684,1713],{},[1656,46686,3964],{},[4138,46688,46689],{"scriptlevel":4032,"displaystyle":1658},[3294,46690,46691,46693],{},[1667,46692,1669],{},[1667,46694,1680],{},[898,46696,8194],{},[1656,46698,3633],{},[1667,46700,46701],{},"30",[902,46703,46704],{"encoding":904},"Q = -\\tfrac{1}{2}P + 30",[16,46706,46707,46730],{},[19,46708,46709],{},[22,46710,46711,46726,46728],{},[25,46712,46713],{},[883,46714,46716],{"className":46715},[886],[888,46717,46718],{"xmlns":890},[892,46719,46720,46724],{},[895,46721,46722],{},[898,46723,8194],{},[902,46725,8194],{"encoding":904},[25,46727,9135],{},[25,46729,9058],{},[30,46731,46732],{},[22,46733,46734,46749,46751],{},[35,46735,46736],{},[883,46737,46739],{"className":46738},[886],[888,46740,46741],{"xmlns":890},[892,46742,46743,46747],{},[895,46744,46745],{},[898,46746,1665],{},[902,46748,1665],{"encoding":904},[35,46750,8580],{},[35,46752,9058],{},[724,46754,46755],{},[614,46756,46757,46758,1896,46780,1863],{},"Obrázek 2.2 \u002F 2.3: Lineární poptávka — přímka s průsečíky ",[883,46759,46761],{"className":46760},[886],[888,46762,46763],{"xmlns":890},[892,46764,46765,46777],{},[895,46766,46767,46769,46771,46773,46775],{},[1656,46768,3453],{"stretchy":1658},[1667,46770,4032],{},[1656,46772,1673],{"separator":1672},[898,46774,3403],{},[1656,46776,3462],{"stretchy":1658},[902,46778,46779],{"encoding":904},"[0, b]",[883,46781,46783],{"className":46782},[886],[888,46784,46785],{"xmlns":890},[892,46786,46787,46805],{},[895,46788,46789,46791,46793,46795,46797,46799,46801,46803],{},[1656,46790,3453],{"stretchy":1658},[1656,46792,3964],{},[898,46794,3403],{},[898,46796,1782],{"mathvariant":1723},[898,46798,207],{},[1656,46800,1673],{"separator":1672},[1667,46802,4032],{},[1656,46804,3462],{"stretchy":1658},[902,46806,46807],{"encoding":904},"[-b\u002Fa, 0]",[46030,46809,46811],{"id":46810},"poptávka-při-dokonalé-konkurenci","Poptávka při dokonalé konkurenci",[724,46813,46814,46815,46832],{},"Přebírá-li každý účastník trhu pevnou tržní cenu ",[883,46816,46818],{"className":46817},[886],[888,46819,46820],{"xmlns":890},[892,46821,46822,46830],{},[895,46823,46824],{},[2062,46825,46826,46828],{},[898,46827,8194],{},[1656,46829,8187],{},[902,46831,13178],{"encoding":904},", je funkce poptávky konstantní:",[883,46834,46836],{"className":46835},[886],[888,46837,46838],{"xmlns":890,"display":2408},[892,46839,46840,46854],{},[895,46841,46842,46844,46846,46852],{},[898,46843,8194],{},[1656,46845,1713],{},[2062,46847,46848,46850],{},[898,46849,8194],{},[1656,46851,8187],{},[898,46853,1863],{"mathvariant":1723},[902,46855,46856],{"encoding":904},"P = P^*.",[724,46858,46859],{},[614,46860,46861,46862,46883,46884,1863],{},"Obrázek 2.4: Vodorovná přímka v rovině ",[883,46863,46865],{"className":46864},[886],[888,46866,46867],{"xmlns":890},[892,46868,46869,46881],{},[895,46870,46871,46873,46875,46877,46879],{},[1656,46872,1659],{"stretchy":1658},[898,46874,1665],{},[1656,46876,1673],{"separator":1672},[898,46878,8194],{},[1656,46880,1683],{"stretchy":1658},[902,46882,46373],{"encoding":904}," na úrovni ",[883,46885,46887],{"className":46886},[886],[888,46888,46889],{"xmlns":890},[892,46890,46891,46903],{},[895,46892,46893,46895,46897],{},[898,46894,8194],{},[1656,46896,1713],{},[2062,46898,46899,46901],{},[898,46900,8194],{},[1656,46902,8187],{},[902,46904,13132],{"encoding":904},[46030,46906,46908],{"id":46907},"giffenův-statek","Giffenův statek",[724,46910,46911,46912,46914,46915,46917,46918,1863],{},"Existují zboží, u nichž je křivka poptávky ",[38,46913,4570],{}," — tzv. ",[38,46916,46908],{},". Jde o případy, kdy důchodový efekt převáží substituční (klasický příklad: rýže u chudých asijských spotřebitelů). Giffenův statek patří k ",[38,46919,46920],{},"podřadnému zboží",[46607,46922,46924],{"id":46923},"příklad-22","Příklad 2.2",[724,46926,46927,46930,46931,46949,46950,46972,46973,46991,46992,47010,47011,47034],{},[38,46928,46929],{},"Zadání a popis:"," Křivka ",[883,46932,46934],{"className":46933},[886],[888,46935,46936],{"xmlns":890},[892,46937,46938,46946],{},[895,46939,46940],{},[1661,46941,46942,46944],{},[898,46943,6787],{},[1667,46945,1669],{},[902,46947,46948],{"encoding":904},"D_1"," reprezentuje poptávku rodiny po cukru s reálným cenovým rozpětím ",[883,46951,46953],{"className":46952},[886],[888,46954,46955],{"xmlns":890},[892,46956,46957,46969],{},[895,46958,46959,46961,46963,46965,46967],{},[1656,46960,1659],{"stretchy":1658},[1667,46962,4032],{},[1656,46964,1673],{"separator":1672},[1667,46966,44930],{},[1656,46968,1683],{"stretchy":1658},[902,46970,46971],{"encoding":904},"(0, 15)"," pencí za libru; je nejprve konvexní, od inflexního bodu ",[883,46974,46976],{"className":46975},[886],[888,46977,46978],{"xmlns":890},[892,46979,46980,46988],{},[895,46981,46982],{},[1661,46983,46984,46986],{},[898,46985,1665],{},[1667,46987,4032],{},[902,46989,46990],{"encoding":904},"Q_0"," konkávní, se saturací kolem 17 liber. Křivka ",[883,46993,46995],{"className":46994},[886],[888,46996,46997],{"xmlns":890},[892,46998,46999,47007],{},[895,47000,47001],{},[1661,47002,47003,47005],{},[898,47004,6787],{},[1667,47006,1680],{},[902,47008,47009],{"encoding":904},"D_2"," na širším trhu je konvexní klesající z bodu ",[883,47012,47014],{"className":47013},[886],[888,47015,47016],{"xmlns":890},[892,47017,47018,47031],{},[895,47019,47020,47022,47024,47026,47029],{},[1656,47021,3453],{"stretchy":1658},[1667,47023,4032],{},[1656,47025,1673],{"separator":1672},[1667,47027,47028],{},"21",[1656,47030,3462],{"stretchy":1658},[902,47032,47033],{"encoding":904},"[0, 21]"," centů.",[198,47036,47038],{"id":47037},"engelova-funkce-závislost-na-důchodu","Engelova funkce (závislost na důchodu)",[724,47040,47041,47042,2114],{},"Druhý jednofaktorový model předpokládá závislost množství pouze na důchodu ",[883,47043,47045],{"className":47044},[886],[888,47046,47047],{"xmlns":890},[892,47048,47049,47053],{},[895,47050,47051],{},[898,47052,8184],{},[902,47054,8184],{"encoding":904},[883,47056,47058],{"className":47057},[886],[888,47059,47060],{"xmlns":890,"display":2408},[892,47061,47062,47093],{},[2412,47063,47064],{"width":2414},[2416,47065,47066,47068,47086,47088],{},[2419,47067],{"width":2421},[2419,47069,47070],{},[895,47071,47072,47074,47076,47078,47080,47082,47084],{},[898,47073,1665],{},[1656,47075,1713],{},[898,47077,1842],{},[1656,47079,1659],{"stretchy":1658},[898,47081,8184],{},[1656,47083,1683],{"stretchy":1658},[898,47085,1863],{"mathvariant":1723},[2419,47087],{"width":2421},[2419,47089,47090],{},[2461,47091,47092],{},"(2.5)",[902,47094,47095],{"encoding":904},"Q = E(Y). \\tag{2.5}",[724,47097,47098,47099,47102,47103,47106],{},"Funkce se nazývá ",[38,47100,47101],{},"Engelova",", její graf ",[38,47104,47105],{},"Engelova křivka",". Tvar závisí na typu zboží:",[120,47108,47109,47240],{},[123,47110,47111,2533,47114,47127,47128,47141,47142,47159,47160],{},[38,47112,47113],{},"Normální (superior) zboží",[883,47115,47117],{"className":47116},[886],[888,47118,47119],{"xmlns":890},[892,47120,47121,47125],{},[895,47122,47123],{},[898,47124,1665],{},[902,47126,1665],{"encoding":904}," roste s ",[883,47129,47131],{"className":47130},[886],[888,47132,47133],{"xmlns":890},[892,47134,47135,47139],{},[895,47136,47137],{},[898,47138,8184],{},[902,47140,8184],{"encoding":904},", nepřesáhne hodnotu ",[883,47143,47145],{"className":47144},[886],[888,47146,47147],{"xmlns":890},[892,47148,47149,47157],{},[895,47150,47151],{},[1661,47152,47153,47155],{},[898,47154,1665],{},[1667,47156,4032],{},[902,47158,46990],{"encoding":904},":\n",[120,47161,47162,47193],{},[123,47163,47164,47167,47168,47170,47171,1863],{},[38,47165,47166],{},"Nezbytné zboží"," (potraviny, léky) — malá citlivost, ",[38,47169,4573],{}," křivka, autonomní spotřeba ",[883,47172,47174],{"className":47173},[886],[888,47175,47176],{"xmlns":890},[892,47177,47178,47190],{},[895,47179,47180,47186,47188],{},[1661,47181,47182,47184],{},[898,47183,1665],{},[1667,47185,1669],{},[1656,47187,2850],{},[1667,47189,4032],{},[902,47191,47192],{"encoding":904},"Q_1 > 0",[123,47194,47195,47198,47199,47217,47218,47220,47221,1643,47238,1863],{},[38,47196,47197],{},"Luxusní zboží"," — velká citlivost až od hladiny ",[883,47200,47202],{"className":47201},[886],[888,47203,47204],{"xmlns":890},[892,47205,47206,47214],{},[895,47207,47208],{},[1661,47209,47210,47212],{},[898,47211,8184],{},[1667,47213,1669],{},[902,47215,47216],{"encoding":904},"Y_1",", křivka je nejprve ",[38,47219,46346],{}," a od ",[883,47222,47224],{"className":47223},[886],[888,47225,47226],{"xmlns":890},[892,47227,47228,47236],{},[895,47229,47230],{},[1661,47231,47232,47234],{},[898,47233,8184],{},[1667,47235,1669],{},[902,47237,47216],{"encoding":904},[38,47239,4573],{},[123,47241,47242,47245,47246,47264],{},[38,47243,47244],{},"Podřadné (inferior) zboží"," — od hladiny ",[883,47247,47249],{"className":47248},[886],[888,47250,47251],{"xmlns":890},[892,47252,47253,47261],{},[895,47254,47255],{},[1661,47256,47257,47259],{},[898,47258,8184],{},[1667,47260,4032],{},[902,47262,47263],{"encoding":904},"Y_0"," množství s růstem důchodu klesá.",[724,47266,47267,47268,47271,47272,12702],{},"Mírou citlivosti je ",[614,47269,47270],{},"důchodová elasticita"," (viz ",[207,47273,12681],{"className":47274,"dataFsResolvedFilePath":848,"href":849},[210],[724,47276,47277],{},[614,47278,47279],{},"Obrázek 2.6: Tři panely Engelových křivek — (a) nezbytné, (b) luxusní, (c) podřadné zboží.",[46030,47281,47283],{"id":47282},"intuice-co-vlastně-znamená-podřadné","Intuice — co vlastně znamená „podřadné\"?",[1981,47285,47286,47357,47400],{},[724,47287,47288,47290,47291,1643,47294,1643,47307,14434,47309,47322,47323,47326,47327,1863],{},[883,47289,1987],{}," Pozor — nezbytné ≠ podřadné\n",[38,47292,47293],{},"Nezbytné zboží:",[883,47295,47297],{"className":47296},[886],[888,47298,47299],{"xmlns":890},[892,47300,47301,47305],{},[895,47302,47303],{},[898,47304,1665],{},[902,47306,1665],{"encoding":904},[38,47308,16082],{},[883,47310,47312],{"className":47311},[886],[888,47313,47314],{"xmlns":890},[892,47315,47316,47320],{},[895,47317,47318],{},[898,47319,8184],{},[902,47321,8184],{"encoding":904},", ale ",[38,47324,47325],{},"pomaleji"," než důchod (2× plat → třeba 1,3× spotřeba). ",[883,47328,47330],{"className":47329},[886],[888,47331,47332],{"xmlns":890},[892,47333,47334,47354],{},[895,47335,47336,47342,47344,47346,47348,47350,47352],{},[1661,47337,47338,47340],{},[898,47339,1842],{},[898,47341,8184],{},[1656,47343,5915],{},[1656,47345,1659],{"stretchy":1658},[1667,47347,4032],{},[1656,47349,1673],{"separator":1672},[1667,47351,1669],{},[1656,47353,1683],{"stretchy":1658},[902,47355,47356],{"encoding":904},"E_Y \\in (0, 1)",[724,47358,47359,1643,47362,1643,47375,47377,47378,1863],{},[38,47360,47361],{},"Podřadné zboží:",[883,47363,47365],{"className":47364},[886],[888,47366,47367],{"xmlns":890},[892,47368,47369,47373],{},[895,47370,47371],{},[898,47372,1665],{},[902,47374,1665],{"encoding":904},[38,47376,16102],{}," v absolutních číslech (2× plat → třeba 0,7× spotřeba). ",[883,47379,47381],{"className":47380},[886],[888,47382,47383],{"xmlns":890},[892,47384,47385,47397],{},[895,47386,47387,47393,47395],{},[1661,47388,47389,47391],{},[898,47390,1842],{},[898,47392,8184],{},[1656,47394,4373],{},[1667,47396,4032],{},[902,47398,47399],{"encoding":904},"E_Y \u003C 0",[724,47401,47402,47403,1863],{},"Klíčový rozdíl: u podřadného zboží si při vyšším důchodu kupuješ ",[38,47404,47405],{},"méně kusů, ne jen proporčně méně",[724,47407,47408,47411,47412,47415],{},[38,47409,47410],{},"Mechanismus — substituce „nahoru\"."," Samotné zboží se nezhoršilo, jen si teď můžeš dovolit ",[38,47413,47414],{},"kvalitnější alternativu",". Růst důchodu → přesun k prémiovému substitutu → absolutní pokles nákupu „levnější verze\".",[724,47417,47418],{},[5956,47419],{"alt":47420,"className":47421,"src":47422},"imek-engelovy-krivky-3typy",[210,5960],"\u002Fwiki-assets\u002Fimek-engelovy-krivky-3typy.jpeg",[46607,47424,47426],{"id":47425},"české-příklady","České příklady",[16,47428,47429,47439],{},[19,47430,47431],{},[22,47432,47433,47436],{},[25,47434,47435],{},"Podřadné",[25,47437,47438],{},"Nahradí se za",[30,47440,47441,47449,47457,47465,47473,47481,47489,47497],{},[22,47442,47443,47446],{},[35,47444,47445],{},"Instantní polévky, ramen",[35,47447,47448],{},"Čerstvé jídlo, restaurace",[22,47450,47451,47454],{},[35,47452,47453],{},"MHD (autobus, tramvaj)",[35,47455,47456],{},"Vlastní auto, Uber, taxi",[22,47458,47459,47462],{},[35,47460,47461],{},"Mražené polotovary, pizza z mrazáku",[35,47463,47464],{},"Čerstvé suroviny, hotovky",[22,47466,47467,47470],{},[35,47468,47469],{},"Privátní značky supermarketů (K-Classic, Clever)",[35,47471,47472],{},"Značkové produkty",[22,47474,47475,47478],{},[35,47476,47477],{},"Paštika Májka, obyčejný měkký salám",[35,47479,47480],{},"Kvalitní uzeniny, šunka od kosti",[22,47482,47483,47486],{},[35,47484,47485],{},"Second hand oblečení",[35,47487,47488],{},"Nové oblečení, značky",[22,47490,47491,47494],{},[35,47492,47493],{},"Krabicové víno, nejlevnější pivo",[35,47495,47496],{},"Lahvové víno, řemeslná piva",[22,47498,47499,47502],{},[35,47500,47501],{},"Ojetá auta nižších tříd",[35,47503,47504],{},"Nová auta, prémiové značky",[1981,47506,47507],{},[724,47508,47509,47511,47512,47515],{},[883,47510,10188],{}," Test 50 milionů\nPředstav si, že vyhraješ 50 milionů. ",[38,47513,47514],{},"Čeho si najednou koupíš méně"," (nebo vůbec)? To je tvoje podřadné zboží.",[724,47517,47518,47521,47522,3247,47525,47547,47548,3247,47551,47572,47573,47591,47592,47595],{},[38,47519,47520],{},"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 ",[38,47523,47524],{},"luxus",[883,47526,47528],{"className":47527},[886],[888,47529,47530],{"xmlns":890},[892,47531,47532,47544],{},[895,47533,47534,47540,47542],{},[1661,47535,47536,47538],{},[898,47537,1842],{},[898,47539,8184],{},[1656,47541,2850],{},[1667,47543,1669],{},[902,47545,47546],{"encoding":904},"E_Y > 1","), pro manažera s 200k platem ",[38,47549,47550],{},"podřadné",[883,47552,47554],{"className":47553},[886],[888,47555,47556],{"xmlns":890},[892,47557,47558,47570],{},[895,47559,47560,47566,47568],{},[1661,47561,47562,47564],{},[898,47563,1842],{},[898,47565,8184],{},[1656,47567,4373],{},[1667,47569,4032],{},[902,47571,47399],{"encoding":904},"). Proto je ",[883,47574,47576],{"className":47575},[886],[888,47577,47578],{"xmlns":890},[892,47579,47580,47588],{},[895,47581,47582],{},[1661,47583,47584,47586],{},[898,47585,1842],{},[898,47587,8184],{},[902,47589,47590],{"encoding":904},"E_Y"," vždy ",[38,47593,47594],{},"lokální veličina"," — platí pro danou úroveň důchodu, ne absolutně.",[724,47597,47598,47599,47601],{},"Extrémním případem podřadného zboží, kde substituční efekt převáží už na straně ceny, je ",[38,47600,46908],{}," (viz níže) — tam poptávková křivka dokonce roste.",[198,47603,47605,47606,1683],{"id":47604},"posun-poptávky-shift-of-demand","Posun poptávky (",[614,47607,47608],{},"shift of demand",[724,47610,47611,47612,47630,47631,47648,47649,47662,47663,3619,47676,47698,47699,47716,47717,47743,47744,47747],{},"Při změně exogenní proměnné (např. důchodu) se celá křivka poptávky posouvá. Uvažujme normální zboží. Ceně ",[883,47613,47615],{"className":47614},[886],[888,47616,47617],{"xmlns":890},[892,47618,47619,47627],{},[895,47620,47621],{},[1661,47622,47623,47625],{},[898,47624,8194],{},[1667,47626,4032],{},[902,47628,47629],{"encoding":904},"P_0"," odpovídá množství ",[883,47632,47634],{"className":47633},[886],[888,47635,47636],{"xmlns":890},[892,47637,47638,47646],{},[895,47639,47640],{},[1661,47641,47642,47644],{},[898,47643,1665],{},[1667,47645,4032],{},[902,47647,46990],{"encoding":904}," na křivce ",[883,47650,47652],{"className":47651},[886],[888,47653,47654],{"xmlns":890},[892,47655,47656,47660],{},[895,47657,47658],{},[898,47659,6787],{},[902,47661,6787],{"encoding":904},"; vzroste-li důchod z ",[883,47664,47666],{"className":47665},[886],[888,47667,47668],{"xmlns":890},[892,47669,47670,47674],{},[895,47671,47672],{},[898,47673,8184],{},[902,47675,8184],{"encoding":904},[883,47677,47679],{"className":47678},[886],[888,47680,47681],{"xmlns":890},[892,47682,47683,47695],{},[895,47684,47685,47691,47693],{},[1661,47686,47687,47689],{},[898,47688,8184],{},[1667,47690,1669],{},[1656,47692,2850],{},[898,47694,8184],{},[902,47696,47697],{"encoding":904},"Y_1 > Y",", pak stejné ceně ",[883,47700,47702],{"className":47701},[886],[888,47703,47704],{"xmlns":890},[892,47705,47706,47714],{},[895,47707,47708],{},[1661,47709,47710,47712],{},[898,47711,8194],{},[1667,47713,4032],{},[902,47715,47629],{"encoding":904}," odpovídá vyšší ",[883,47718,47720],{"className":47719},[886],[888,47721,47722],{"xmlns":890},[892,47723,47724,47740],{},[895,47725,47726,47732,47734],{},[1661,47727,47728,47730],{},[898,47729,1665],{},[1667,47731,1669],{},[1656,47733,2850],{},[1661,47735,47736,47738],{},[898,47737,1665],{},[1667,47739,4032],{},[902,47741,47742],{"encoding":904},"Q_1 > Q_0"," — křivka se ",[38,47745,47746],{},"posouvá doprava",". Pokles důchodu vede k posunu doleva.",[724,47749,47750],{},[5956,47751],{"alt":47752,"className":47753,"src":47754},"imek-posun-vs-pohyb-po-krivce",[210,5960],"\u002Fwiki-assets\u002Fimek-posun-vs-pohyb-po-krivce.jpeg",[724,47756,47757],{},"Posun může být způsoben i jinými faktory (např. zdaněním spotřebitele — viz dále).",[724,47759,47760],{},[614,47761,47762,47763,22743,47793,47814],{},"Obrázek 2.7: Posun poptávky — tři křivky ",[883,47764,47766],{"className":47765},[886],[888,47767,47768],{"xmlns":890},[892,47769,47770,47790],{},[895,47771,47772,47778,47780,47782,47784],{},[1661,47773,47774,47776],{},[898,47775,6787],{},[1667,47777,1680],{},[1656,47779,1673],{"separator":1672},[898,47781,6787],{},[1656,47783,1673],{"separator":1672},[1661,47785,47786,47788],{},[898,47787,6787],{},[1667,47789,1669],{},[902,47791,47792],{"encoding":904},"D_2, D, D_1",[883,47794,47796],{"className":47795},[886],[888,47797,47798],{"xmlns":890},[892,47799,47800,47812],{},[895,47801,47802,47804,47806,47808,47810],{},[1656,47803,1659],{"stretchy":1658},[898,47805,1665],{},[1656,47807,1673],{"separator":1672},[898,47809,8194],{},[1656,47811,1683],{"stretchy":1658},[902,47813,46373],{"encoding":904},", šipky naznačují posuny.",[46607,47816,47818],{"id":47817},"příklad-23-zdanění-kupujícího","Příklad 2.3 — zdanění kupujícího",[724,47820,47821,47823,47824,47847,47848,5554,47865,47882,47883,1863],{},[38,47822,46615],{}," Poptávce ",[883,47825,47827],{"className":47826},[886],[888,47828,47829],{"xmlns":890},[892,47830,47831,47845],{},[895,47832,47833,47835,47837,47839,47841,47843],{},[898,47834,8194],{},[1656,47836,1713],{},[898,47838,6787],{},[1656,47840,1659],{"stretchy":1658},[898,47842,1665],{},[1656,47844,1683],{"stretchy":1658},[902,47846,13412],{"encoding":904}," odpovídá ceně ",[883,47849,47851],{"className":47850},[886],[888,47852,47853],{"xmlns":890},[892,47854,47855,47863],{},[895,47856,47857],{},[1661,47858,47859,47861],{},[898,47860,8194],{},[1667,47862,4032],{},[902,47864,47629],{"encoding":904},[883,47866,47868],{"className":47867},[886],[888,47869,47870],{"xmlns":890},[892,47871,47872,47880],{},[895,47873,47874],{},[1661,47875,47876,47878],{},[898,47877,1665],{},[1667,47879,4032],{},[902,47881,46990],{"encoding":904},". Na kupujícího je uložena jednotková daň ",[883,47884,47886],{"className":47885},[886],[888,47887,47888],{"xmlns":890},[892,47889,47890,47894],{},[895,47891,47892],{},[898,47893,11577],{},[902,47895,11577],{"encoding":904},[724,47897,47898,47900,47901,47918,47919,47941],{},[38,47899,46647],{}," Kupující nakupuje množství ",[883,47902,47904],{"className":47903},[886],[888,47905,47906],{"xmlns":890},[892,47907,47908,47916],{},[895,47909,47910],{},[1661,47911,47912,47914],{},[898,47913,1665],{},[1667,47915,1669],{},[902,47917,3227],{"encoding":904},", které odpovídá ceně ",[883,47920,47922],{"className":47921},[886],[888,47923,47924],{"xmlns":890},[892,47925,47926,47938],{},[895,47927,47928,47934,47936],{},[1661,47929,47930,47932],{},[898,47931,8194],{},[1667,47933,4032],{},[1656,47935,3633],{},[898,47937,11577],{},[902,47939,47940],{"encoding":904},"P_0 + T"," na původní křivce. Nová poptávka je",[883,47943,47945],{"className":47944},[886],[888,47946,47947],{"xmlns":890,"display":2408},[892,47948,47949,47983],{},[895,47950,47951,47953,47955,47961,47963,47965,47967,47969,47971,47973,47975,47977,47979,47981],{},[898,47952,8194],{},[1656,47954,1713],{},[1661,47956,47957,47959],{},[898,47958,6787],{},[1667,47960,1669],{},[1656,47962,1659],{"stretchy":1658},[898,47964,1665],{},[1656,47966,1683],{"stretchy":1658},[1656,47968,1713],{},[898,47970,6787],{},[1656,47972,1659],{"stretchy":1658},[898,47974,1665],{},[1656,47976,1683],{"stretchy":1658},[1656,47978,3964],{},[898,47980,11577],{},[1656,47982,1673],{"separator":1672},[902,47984,47985],{"encoding":904},"P = D_1(Q) = D(Q) - T,",[724,47987,47988,47989,1863],{},"tj. dojde k ",[38,47990,47991],{},"posunu poptávky doleva",[724,47993,47994],{},[614,47995,47996,47997,48018,48019,1343,48036,1343,48049,48070,48071,1896,48088,1863],{},"Obrázek 2.8: Dvě klesající poptávkové přímky v ",[883,47998,48000],{"className":47999},[886],[888,48001,48002],{"xmlns":890},[892,48003,48004,48016],{},[895,48005,48006,48008,48010,48012,48014],{},[1656,48007,1659],{"stretchy":1658},[898,48009,1665],{},[1656,48011,1673],{"separator":1672},[898,48013,8194],{},[1656,48015,1683],{"stretchy":1658},[902,48017,46373],{"encoding":904},"; na svislé ose jsou vyznačeny ",[883,48020,48022],{"className":48021},[886],[888,48023,48024],{"xmlns":890},[892,48025,48026,48034],{},[895,48027,48028],{},[1661,48029,48030,48032],{},[898,48031,8194],{},[1667,48033,4032],{},[902,48035,47629],{"encoding":904},[883,48037,48039],{"className":48038},[886],[888,48040,48041],{"xmlns":890},[892,48042,48043,48047],{},[895,48044,48045],{},[898,48046,11577],{},[902,48048,11577],{"encoding":904},[883,48050,48052],{"className":48051},[886],[888,48053,48054],{"xmlns":890},[892,48055,48056,48068],{},[895,48057,48058,48064,48066],{},[1661,48059,48060,48062],{},[898,48061,8194],{},[1667,48063,4032],{},[1656,48065,3633],{},[898,48067,11577],{},[902,48069,47940],{"encoding":904},"; na vodorovné ",[883,48072,48074],{"className":48073},[886],[888,48075,48076],{"xmlns":890},[892,48077,48078,48086],{},[895,48079,48080],{},[1661,48081,48082,48084],{},[898,48083,1665],{},[1667,48085,1669],{},[902,48087,3227],{"encoding":904},[883,48089,48091],{"className":48090},[886],[888,48092,48093],{"xmlns":890},[892,48094,48095,48103],{},[895,48096,48097],{},[1661,48098,48099,48101],{},[898,48100,1665],{},[1667,48102,4032],{},[902,48104,46990],{"encoding":904},[198,48106,48108],{"id":48107},"vícekomoditní-dvoukomoditní-trh","Vícekomoditní (dvoukomoditní) trh",[724,48110,48111],{},"Uvažujme dvě tržně závislá zboží s lineárními funkcemi poptávky:",[883,48113,48115],{"className":48114},[886],[888,48116,48117],{"xmlns":890,"display":2408},[892,48118,48119,48304],{},[2412,48120,48121],{"width":2414},[2416,48122,48123,48125,48297,48299],{},[2419,48124],{"width":2421},[2419,48126,48127],{},[2412,48128,48129,48213],{"rowspacing":29476,"columnalign":29477,"columnspacing":1724},[2416,48130,48131,48141],{},[2419,48132,48133],{},[4138,48134,48135],{"scriptlevel":4032,"displaystyle":1672},[1661,48136,48137,48139],{},[898,48138,1665],{},[1667,48140,1669],{},[2419,48142,48143],{},[4138,48144,48145],{"scriptlevel":4032,"displaystyle":1672},[895,48146,48147,48149,48151,48157,48159,48165,48167,48173,48175,48177,48183,48185,48191,48197,48199,48205,48211],{},[895,48148],{},[1656,48150,1713],{},[1661,48152,48153,48155],{},[898,48154,6787],{},[1667,48156,1669],{},[1656,48158,1659],{"stretchy":1658},[1661,48160,48161,48163],{},[898,48162,8194],{},[1667,48164,1669],{},[1656,48166,1673],{"separator":1672},[1661,48168,48169,48171],{},[898,48170,8194],{},[1667,48172,1680],{},[1656,48174,1683],{"stretchy":1658},[1656,48176,1713],{},[1661,48178,48179,48181],{},[898,48180,207],{},[1667,48182,1669],{},[1656,48184,3633],{},[1661,48186,48187,48189],{},[898,48188,3403],{},[1667,48190,1669],{},[1661,48192,48193,48195],{},[898,48194,8194],{},[1667,48196,1669],{},[1656,48198,3633],{},[1661,48200,48201,48203],{},[898,48202,1745],{},[1667,48204,1669],{},[1661,48206,48207,48209],{},[898,48208,8194],{},[1667,48210,1680],{},[1656,48212,1673],{"separator":1672},[2416,48214,48215,48225],{},[2419,48216,48217],{},[4138,48218,48219],{"scriptlevel":4032,"displaystyle":1672},[1661,48220,48221,48223],{},[898,48222,1665],{},[1667,48224,1680],{},[2419,48226,48227],{},[4138,48228,48229],{"scriptlevel":4032,"displaystyle":1672},[895,48230,48231,48233,48235,48241,48243,48249,48251,48257,48259,48261,48267,48269,48275,48281,48283,48289,48295],{},[895,48232],{},[1656,48234,1713],{},[1661,48236,48237,48239],{},[898,48238,6787],{},[1667,48240,1680],{},[1656,48242,1659],{"stretchy":1658},[1661,48244,48245,48247],{},[898,48246,8194],{},[1667,48248,1669],{},[1656,48250,1673],{"separator":1672},[1661,48252,48253,48255],{},[898,48254,8194],{},[1667,48256,1680],{},[1656,48258,1683],{"stretchy":1658},[1656,48260,1713],{},[1661,48262,48263,48265],{},[898,48264,207],{},[1667,48266,1680],{},[1656,48268,3633],{},[1661,48270,48271,48273],{},[898,48272,3403],{},[1667,48274,1680],{},[1661,48276,48277,48279],{},[898,48278,8194],{},[1667,48280,1669],{},[1656,48282,3633],{},[1661,48284,48285,48287],{},[898,48286,1745],{},[1667,48288,1680],{},[1661,48290,48291,48293],{},[898,48292,8194],{},[1667,48294,1680],{},[898,48296,1863],{"mathvariant":1723},[2419,48298],{"width":2421},[2419,48300,48301],{},[2461,48302,48303],{},"(2.6)",[902,48305,48306],{"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}",[46030,48308,48310],{"id":48309},"znaménková-analýza-parametrů","Znaménková analýza parametrů",[120,48312,48313,48360,48407],{},[123,48314,48315,1343,48337,48359],{},[883,48316,48318],{"className":48317},[886],[888,48319,48320],{"xmlns":890},[892,48321,48322,48334],{},[895,48323,48324,48330,48332],{},[1661,48325,48326,48328],{},[898,48327,207],{},[1667,48329,1669],{},[1656,48331,2850],{},[1667,48333,4032],{},[902,48335,48336],{"encoding":904},"a_1 > 0",[883,48338,48340],{"className":48339},[886],[888,48341,48342],{"xmlns":890},[892,48343,48344,48356],{},[895,48345,48346,48352,48354],{},[1661,48347,48348,48350],{},[898,48349,207],{},[1667,48351,1680],{},[1656,48353,2850],{},[1667,48355,4032],{},[902,48357,48358],{"encoding":904},"a_2 > 0"," (při nulových cenách je poptávané množství kladné),",[123,48361,48362,1343,48384,48406],{},[883,48363,48365],{"className":48364},[886],[888,48366,48367],{"xmlns":890},[892,48368,48369,48381],{},[895,48370,48371,48377,48379],{},[1661,48372,48373,48375],{},[898,48374,3403],{},[1667,48376,1669],{},[1656,48378,4373],{},[1667,48380,4032],{},[902,48382,48383],{"encoding":904},"b_1 \u003C 0",[883,48385,48387],{"className":48386},[886],[888,48388,48389],{"xmlns":890},[892,48390,48391,48403],{},[895,48392,48393,48399,48401],{},[1661,48394,48395,48397],{},[898,48396,1745],{},[1667,48398,1680],{},[1656,48400,4373],{},[1667,48402,4032],{},[902,48404,48405],{"encoding":904},"c_2 \u003C 0"," (vlastní koeficienty — zákon klesající poptávky),",[123,48408,48409,48410,1343,48427,48445,48446],{},"zkřížené koeficienty ",[883,48411,48413],{"className":48412},[886],[888,48414,48415],{"xmlns":890},[892,48416,48417,48425],{},[895,48418,48419],{},[1661,48420,48421,48423],{},[898,48422,1745],{},[1667,48424,1669],{},[902,48426,38498],{"encoding":904},[883,48428,48430],{"className":48429},[886],[888,48431,48432],{"xmlns":890},[892,48433,48434,48442],{},[895,48435,48436],{},[1661,48437,48438,48440],{},[898,48439,3403],{},[1667,48441,1680],{},[902,48443,48444],{"encoding":904},"b_2"," určují povahu vztahu:\n",[120,48447,48448,48498],{},[123,48449,48450,48453,48454,1343,48476,1673],{},[38,48451,48452],{},"substituty"," (máslo vs. margarín): ",[883,48455,48457],{"className":48456},[886],[888,48458,48459],{"xmlns":890},[892,48460,48461,48473],{},[895,48462,48463,48469,48471],{},[1661,48464,48465,48467],{},[898,48466,1745],{},[1667,48468,1669],{},[1656,48470,2850],{},[1667,48472,4032],{},[902,48474,48475],{"encoding":904},"c_1 > 0",[883,48477,48479],{"className":48478},[886],[888,48480,48481],{"xmlns":890},[892,48482,48483,48495],{},[895,48484,48485,48491,48493],{},[1661,48486,48487,48489],{},[898,48488,3403],{},[1667,48490,1680],{},[1656,48492,2850],{},[1667,48494,4032],{},[902,48496,48497],{"encoding":904},"b_2 > 0",[123,48499,48500,48503,48504,1343,48526,1863],{},[38,48501,48502],{},"komplementy"," (auto vs. benzín): ",[883,48505,48507],{"className":48506},[886],[888,48508,48509],{"xmlns":890},[892,48510,48511,48523],{},[895,48512,48513,48519,48521],{},[1661,48514,48515,48517],{},[898,48516,1745],{},[1667,48518,1669],{},[1656,48520,4373],{},[1667,48522,4032],{},[902,48524,48525],{"encoding":904},"c_1 \u003C 0",[883,48527,48529],{"className":48528},[886],[888,48530,48531],{"xmlns":890},[892,48532,48533,48545],{},[895,48534,48535,48541,48543],{},[1661,48536,48537,48539],{},[898,48538,3403],{},[1667,48540,1680],{},[1656,48542,4373],{},[1667,48544,4032],{},[902,48546,48547],{"encoding":904},"b_2 \u003C 0",[724,48549,48550],{},"Schematicky:",[724,48552,48553,48556],{},[38,48554,48555],{},"Substituty",[883,48557,48559],{"className":48558},[886],[888,48560,48561],{"xmlns":890},[892,48562,48563,48702],{},[895,48564,48565,48571,48573,48588,48590,48610,48612,48632,48634,48636,48642,48644,48658,48660,48680,48682],{},[1661,48566,48567,48569],{},[898,48568,1665],{},[1667,48570,1669],{},[1656,48572,1713],{},[898,48574,48575],{},[48576,48577,48578,48586],"munder",{},[1656,48579,48580],{},[1661,48581,48582,48584],{},[898,48583,207],{},[1667,48585,1669],{},[1656,48587,3633],{"lspace":1724,"rspace":1724},[1656,48589,3633],{},[898,48591,48592],{},[48576,48593,48594,48608],{},[1656,48595,48596,48602],{},[1661,48597,48598,48600],{},[898,48599,3403],{},[1667,48601,1669],{},[1661,48603,48604,48606],{},[898,48605,8194],{},[1667,48607,1669],{},[1656,48609,3964],{"lspace":1724,"rspace":1724},[1656,48611,3633],{},[898,48613,48614],{},[48576,48615,48616,48630],{},[1656,48617,48618,48624],{},[1661,48619,48620,48622],{},[898,48621,1745],{},[1667,48623,1669],{},[1661,48625,48626,48628],{},[898,48627,8194],{},[1667,48629,1680],{},[1656,48631,3633],{"lspace":1724,"rspace":1724},[1656,48633,1673],{"separator":1672},[3316,48635],{"width":14644},[1661,48637,48638,48640],{},[898,48639,1665],{},[1667,48641,1680],{},[1656,48643,1713],{},[898,48645,48646],{},[48576,48647,48648,48656],{},[1656,48649,48650],{},[1661,48651,48652,48654],{},[898,48653,207],{},[1667,48655,1680],{},[1656,48657,3633],{"lspace":1724,"rspace":1724},[1656,48659,3633],{},[898,48661,48662],{},[48576,48663,48664,48678],{},[1656,48665,48666,48672],{},[1661,48667,48668,48670],{},[898,48669,3403],{},[1667,48671,1680],{},[1661,48673,48674,48676],{},[898,48675,8194],{},[1667,48677,1669],{},[1656,48679,3633],{"lspace":1724,"rspace":1724},[1656,48681,3633],{},[898,48683,48684],{},[48576,48685,48686,48700],{},[1656,48687,48688,48694],{},[1661,48689,48690,48692],{},[898,48691,1745],{},[1667,48693,1680],{},[1661,48695,48696,48698],{},[898,48697,8194],{},[1667,48699,1680],{},[1656,48701,3964],{"lspace":1724,"rspace":1724},[902,48703,48704],{"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}",[724,48706,48707,48710],{},[38,48708,48709],{},"Komplementy",[883,48711,48713],{"className":48712},[886],[888,48714,48715],{"xmlns":890},[892,48716,48717,48855],{},[895,48718,48719,48725,48727,48741,48743,48763,48765,48785,48787,48789,48795,48797,48811,48813,48833,48835],{},[1661,48720,48721,48723],{},[898,48722,1665],{},[1667,48724,1669],{},[1656,48726,1713],{},[898,48728,48729],{},[48576,48730,48731,48739],{},[1656,48732,48733],{},[1661,48734,48735,48737],{},[898,48736,207],{},[1667,48738,1669],{},[1656,48740,3633],{"lspace":1724,"rspace":1724},[1656,48742,3633],{},[898,48744,48745],{},[48576,48746,48747,48761],{},[1656,48748,48749,48755],{},[1661,48750,48751,48753],{},[898,48752,3403],{},[1667,48754,1669],{},[1661,48756,48757,48759],{},[898,48758,8194],{},[1667,48760,1669],{},[1656,48762,3964],{"lspace":1724,"rspace":1724},[1656,48764,3633],{},[898,48766,48767],{},[48576,48768,48769,48783],{},[1656,48770,48771,48777],{},[1661,48772,48773,48775],{},[898,48774,1745],{},[1667,48776,1669],{},[1661,48778,48779,48781],{},[898,48780,8194],{},[1667,48782,1680],{},[1656,48784,3964],{"lspace":1724,"rspace":1724},[1656,48786,1673],{"separator":1672},[3316,48788],{"width":14644},[1661,48790,48791,48793],{},[898,48792,1665],{},[1667,48794,1680],{},[1656,48796,1713],{},[898,48798,48799],{},[48576,48800,48801,48809],{},[1656,48802,48803],{},[1661,48804,48805,48807],{},[898,48806,207],{},[1667,48808,1680],{},[1656,48810,3633],{"lspace":1724,"rspace":1724},[1656,48812,3633],{},[898,48814,48815],{},[48576,48816,48817,48831],{},[1656,48818,48819,48825],{},[1661,48820,48821,48823],{},[898,48822,3403],{},[1667,48824,1680],{},[1661,48826,48827,48829],{},[898,48828,8194],{},[1667,48830,1669],{},[1656,48832,3964],{"lspace":1724,"rspace":1724},[1656,48834,3633],{},[898,48836,48837],{},[48576,48838,48839,48853],{},[1656,48840,48841,48847],{},[1661,48842,48843,48845],{},[898,48844,1745],{},[1667,48846,1680],{},[1661,48848,48849,48851],{},[898,48850,8194],{},[1667,48852,1680],{},[1656,48854,3964],{"lspace":1724,"rspace":1724},[902,48856,48857],{"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}",[45652,48859],{},[115,48861,21858],{"id":45462},[1981,48863,48864],{},[724,48865,48866,48868,48869,45676,48882,45690,48895,48898,48899,14434,48923,48941],{},[883,48867,3472],{}," TL;DR\nNabídka vyjadřuje závislost nabízeného množství ",[883,48870,48872],{"className":48871},[886],[888,48873,48874],{"xmlns":890},[892,48875,48876,48880],{},[895,48877,48878],{},[898,48879,1665],{},[902,48881,1665],{"encoding":904},[883,48883,48885],{"className":48884},[886],[888,48886,48887],{"xmlns":890},[892,48888,48889,48893],{},[895,48890,48891],{},[898,48892,8194],{},[902,48894,8194],{"encoding":904},[38,48896,48897],{},"zákon rostoucí nabídky",": při vyšší ceně je výrobce ochoten nabídnout více. Lineární model ",[883,48900,48902],{"className":48901},[886],[888,48903,48904],{"xmlns":890},[892,48905,48906,48920],{},[895,48907,48908,48910,48912,48914,48916,48918],{},[898,48909,8194],{},[1656,48911,1713],{},[898,48913,1745],{},[898,48915,1665],{},[1656,48917,3633],{},[898,48919,3768],{},[902,48921,48922],{"encoding":904},"P = cQ + d",[883,48924,48926],{"className":48925},[886],[888,48927,48928],{"xmlns":890},[892,48929,48930,48938],{},[895,48931,48932,48934,48936],{},[898,48933,1745],{},[1656,48935,2850],{},[1667,48937,4032],{},[902,48939,48940],{"encoding":904},"c > 0"," je standardní aproximací.",[198,48943,45746],{"id":48944},"obecný-vícefaktorový-model-1",[724,48946,48947,3247,48950,48953,48954,48967,48968,45578,48981,45592,48994,49007,49008,49022,49023,45621,49036,49049],{},[38,48948,48949],{},"Nabízené množství",[614,48951,48952],{},"quantity supplied",") závisí na ceně ",[883,48955,48957],{"className":48956},[886],[888,48958,48959],{"xmlns":890},[892,48960,48961,48965],{},[895,48962,48963],{},[898,48964,8194],{},[902,48966,8194],{"encoding":904},", cenách výrobních faktorů (práce ",[883,48969,48971],{"className":48970},[886],[888,48972,48973],{"xmlns":890},[892,48974,48975,48979],{},[895,48976,48977],{},[898,48978,18539],{},[902,48980,18539],{"encoding":904},[883,48982,48984],{"className":48983},[886],[888,48985,48986],{"xmlns":890},[892,48987,48988,48992],{},[895,48989,48990],{},[898,48991,18544],{},[902,48993,18544],{"encoding":904},[883,48995,48997],{"className":48996},[886],[888,48998,48999],{"xmlns":890},[892,49000,49001,49005],{},[895,49002,49003],{},[898,49004,1842],{},[902,49006,1842],{"encoding":904},"), očekávání ",[883,49009,49011],{"className":49010},[886],[888,49012,49013],{"xmlns":890},[892,49014,49015,49020],{},[895,49016,49017],{},[898,49018,49019],{},"V",[902,49021,49019],{"encoding":904},", počtu výrobců ",[883,49024,49026],{"className":49025},[886],[888,49027,49028],{"xmlns":890},[892,49029,49030,49034],{},[895,49031,49032],{},[898,49033,45618],{},[902,49035,45618],{"encoding":904},[883,49037,49039],{"className":49038},[886],[888,49040,49041],{"xmlns":890},[892,49042,49043,49047],{},[895,49044,49045],{},[898,49046,45633],{},[902,49048,45633],{"encoding":904}," a dalších:",[883,49051,49053],{"className":49052},[886],[888,49054,49055],{"xmlns":890,"display":2408},[892,49056,49057,49116],{},[2412,49058,49059],{"width":2414},[2416,49060,49061,49063,49109,49111],{},[2419,49062],{"width":2421},[2419,49064,49065],{},[895,49066,49067,49069,49071,49073,49075,49077,49079,49081,49083,49085,49087,49089,49091,49093,49095,49097,49099,49101,49103,49105,49107],{},[898,49068,1665],{},[1656,49070,1713],{},[898,49072,1769],{},[1656,49074,1659],{"stretchy":1658},[898,49076,8194],{},[1656,49078,1673],{"separator":1672},[898,49080,18539],{},[1656,49082,1673],{"separator":1672},[898,49084,18544],{},[1656,49086,1673],{"separator":1672},[898,49088,1842],{},[1656,49090,1673],{"separator":1672},[898,49092,49019],{},[1656,49094,1673],{"separator":1672},[898,49096,45618],{},[1656,49098,1673],{"separator":1672},[898,49100,45633],{},[1656,49102,1673],{"separator":1672},[1656,49104,2337],{},[1656,49106,1683],{"stretchy":1658},[898,49108,1863],{"mathvariant":1723},[2419,49110],{"width":2421},[2419,49112,49113],{},[2461,49114,49115],{},"(2.7)",[902,49117,49118],{"encoding":904},"Q = S(P, L, K, E, V, O, W, \\ldots). \\tag{2.7}",[724,49120,47098,49121,3247,49124,49127],{},[38,49122,49123],{},"funkce nabídky",[614,49125,49126],{},"supply function",") v širším slova smyslu.",[198,49129,49131],{"id":49130},"jednofaktorový-model","Jednofaktorový model",[724,49133,49134],{},"V nejpřirozenějším jednofaktorovém modelu",[883,49136,49138],{"className":49137},[886],[888,49139,49140],{"xmlns":890,"display":2408},[892,49141,49142,49193],{},[2412,49143,49144],{"width":2414},[2416,49145,49146,49148,49186,49188],{},[2419,49147],{"width":2421},[2419,49149,49150],{},[895,49151,49152,49154,49156,49158,49160,49162,49164,49166,49168,49170,49172,49174,49176,49178,49180,49182,49184],{},[898,49153,1665],{},[1656,49155,1713],{},[898,49157,1769],{},[1656,49159,1659],{"stretchy":1658},[898,49161,8194],{},[1656,49163,1683],{"stretchy":1658},[1656,49165,1673],{"separator":1672},[3316,49167],{"width":14644},[2461,49169,46099],{},[3316,49171],{"width":14644},[898,49173,8194],{},[1656,49175,1713],{},[898,49177,1769],{},[1656,49179,1659],{"stretchy":1658},[898,49181,1665],{},[1656,49183,1683],{"stretchy":1658},[898,49185,1863],{"mathvariant":1723},[2419,49187],{"width":2421},[2419,49189,49190],{},[2461,49191,49192],{},"(2.8)",[902,49194,49195],{"encoding":904},"Q = S(P), \\qquad \\text{resp.} \\qquad P = S(Q). \\tag{2.8}",[724,49197,49198,49199,3247,49202,12702],{},"Graf je ",[38,49200,49201],{},"křivka nabídky",[614,49203,49204],{},"supply curve",[46030,49206,49208],{"id":49207},"zákon-rostoucí-nabídky","Zákon rostoucí nabídky",[1981,49210,49211],{},[724,49212,49213],{},[38,49214,46145,49215,49228,49229,46200],{},[883,49216,49218],{"className":49217},[886],[888,49219,49220],{"xmlns":890},[892,49221,49222,49226],{},[895,49223,49224],{},[898,49225,8194],{},[902,49227,8194],{"encoding":904},", pak nabízené množství ",[883,49230,49232],{"className":49231},[886],[888,49233,49234],{"xmlns":890},[892,49235,49236,49240],{},[895,49237,49238],{},[898,49239,1665],{},[902,49241,1665],{"encoding":904},[724,49243,49244,49245,49270,49271,49301,49302,49319],{},"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 ",[883,49246,49248],{"className":49247},[886],[888,49249,49250],{"xmlns":890},[892,49251,49252,49268],{},[895,49253,49254,49256,49258,49260,49266],{},[1656,49255,3453],{"stretchy":1658},[1667,49257,4032],{},[1656,49259,1673],{"separator":1672},[1661,49261,49262,49264],{},[898,49263,8194],{},[1667,49265,4032],{},[1656,49267,3462],{"stretchy":1658},[902,49269,46285],{"encoding":904}," na svislé ose (případně z ",[883,49272,49274],{"className":49273},[886],[888,49275,49276],{"xmlns":890},[892,49277,49278,49298],{},[895,49279,49280,49282,49288,49290,49296],{},[1656,49281,3453],{"stretchy":1658},[1661,49283,49284,49286],{},[898,49285,1665],{},[1667,49287,1669],{},[1656,49289,1673],{"separator":1672},[1661,49291,49292,49294],{},[898,49293,8194],{},[1667,49295,1669],{},[1656,49297,3462],{"stretchy":1658},[902,49299,49300],{"encoding":904},"[Q_1, P_1]","), kde ",[883,49303,49305],{"className":49304},[886],[888,49306,49307],{"xmlns":890},[892,49308,49309,49317],{},[895,49310,49311],{},[1661,49312,49313,49315],{},[898,49314,8194],{},[1667,49316,4032],{},[902,49318,47629],{"encoding":904}," je minimální cena, při které je výrobce ochoten vyrábět.",[724,49321,49322],{},[614,49323,49324,49325,12505,49338,1863],{},"Obrázek 2.9: Typická rostoucí křivka nabídky ",[883,49326,49328],{"className":49327},[886],[888,49329,49330],{"xmlns":890},[892,49331,49332,49336],{},[895,49333,49334],{},[898,49335,1769],{},[902,49337,1769],{"encoding":904},[883,49339,49341],{"className":49340},[886],[888,49342,49343],{"xmlns":890},[892,49344,49345,49357],{},[895,49346,49347,49349,49351,49353,49355],{},[1656,49348,1659],{"stretchy":1658},[898,49350,1665],{},[1656,49352,1673],{"separator":1672},[898,49354,8194],{},[1656,49356,1683],{"stretchy":1658},[902,49358,46373],{"encoding":904},[46030,49360,49362],{"id":49361},"lineární-model-nabídky","Lineární model nabídky",[883,49364,49366],{"className":49365},[886],[888,49367,49368],{"xmlns":890,"display":2408},[892,49369,49370,49409],{},[2412,49371,49372],{"width":2414},[2416,49373,49374,49376,49402,49404],{},[2419,49375],{"width":2421},[2419,49377,49378],{},[895,49379,49380,49382,49384,49386,49388,49390,49392,49394,49396,49398,49400],{},[898,49381,8194],{},[1656,49383,1713],{},[898,49385,1745],{},[898,49387,1665],{},[1656,49389,3633],{},[898,49391,3768],{},[1656,49393,1673],{"separator":1672},[3316,49395],{"width":14644},[898,49397,1745],{},[1656,49399,2850],{},[1667,49401,4283],{},[2419,49403],{"width":2421},[2419,49405,49406],{},[2461,49407,49408],{},"(2.9)",[902,49410,49411],{"encoding":904},"P = cQ + d, \\qquad c > 0. \\tag{2.9}",[724,49413,49414,49415,49451,49452,49465],{},"Alternativně ",[883,49416,49418],{"className":49417},[886],[888,49419,49420],{"xmlns":890},[892,49421,49422,49448],{},[895,49423,49424,49426,49428,49436,49438,49440],{},[898,49425,1665],{},[1656,49427,1713],{},[4138,49429,49430],{"scriptlevel":4032,"displaystyle":1658},[3294,49431,49432,49434],{},[1667,49433,1669],{},[898,49435,1745],{},[898,49437,8194],{},[1656,49439,3964],{},[4138,49441,49442],{"scriptlevel":4032,"displaystyle":1658},[3294,49443,49444,49446],{},[898,49445,3768],{},[898,49447,1745],{},[902,49449,49450],{"encoding":904},"Q = \\tfrac{1}{c}P - \\tfrac{d}{c}","; znaménko koeficientu u ",[883,49453,49455],{"className":49454},[886],[888,49456,49457],{"xmlns":890},[892,49458,49459,49463],{},[895,49460,49461],{},[898,49462,8194],{},[902,49464,8194],{"encoding":904}," zůstává, znaménko absolutního členu se mění.",[46607,49467,49469],{"id":49468},"příklad-25","Příklad 2.5",[724,49471,49472,49474,49475,1863],{},[38,49473,46615],{}," Lineární nabídka ",[883,49476,49478],{"className":49477},[886],[888,49479,49480],{"xmlns":890},[892,49481,49482,49496],{},[895,49483,49484,49486,49488,49490,49492,49494],{},[898,49485,8194],{},[1656,49487,1713],{},[1667,49489,13779],{},[898,49491,1665],{},[1656,49493,3633],{},[1667,49495,8567],{},[902,49497,49498],{"encoding":904},"P = 0{,}5Q + 25",[724,49500,49501,49503,49504,1863],{},[38,49502,46647],{}," Alternativní tvar ",[883,49505,49507],{"className":49506},[886],[888,49508,49509],{"xmlns":890},[892,49510,49511,49525],{},[895,49512,49513,49515,49517,49519,49521,49523],{},[898,49514,1665],{},[1656,49516,1713],{},[1667,49518,1680],{},[898,49520,8194],{},[1656,49522,3964],{},[1667,49524,9267],{},[902,49526,49527],{"encoding":904},"Q = 2P - 50",[16,49529,49530,49555],{},[19,49531,49532],{},[22,49533,49534,49549,49551,49553],{},[25,49535,49536],{},[883,49537,49539],{"className":49538},[886],[888,49540,49541],{"xmlns":890},[892,49542,49543,49547],{},[895,49544,49545],{},[898,49546,8194],{},[902,49548,8194],{"encoding":904},[25,49550,46701],{},[25,49552,23770],{},[25,49554,9135],{},[30,49556,49557],{},[22,49558,49559,49574,49576,49578],{},[35,49560,49561],{},[883,49562,49564],{"className":49563},[886],[888,49565,49566],{"xmlns":890},[892,49567,49568,49572],{},[895,49569,49570],{},[898,49571,1665],{},[902,49573,1665],{"encoding":904},[35,49575,8580],{},[35,49577,9058],{},[35,49579,46701],{},[198,49581,49583,49584,1683],{"id":49582},"posun-nabídky-shift-of-supply","Posun nabídky (",[614,49585,49586],{},"shift of supply",[724,49588,49589,49590,49593,49594,49611,49612,49637,49638,1863],{},"Posun nastává při změně exogenních proměnných — nová technologie snižuje náklady (posun ",[38,49591,49592],{},"doprava",": při stejné ceně ",[883,49595,49597],{"className":49596},[886],[888,49598,49599],{"xmlns":890},[892,49600,49601,49609],{},[895,49602,49603],{},[1661,49604,49605,49607],{},[898,49606,8194],{},[1667,49608,4032],{},[902,49610,47629],{"encoding":904}," vyrobí výrobce větší ",[883,49613,49615],{"className":49614},[886],[888,49616,49617],{"xmlns":890},[892,49618,49619,49635],{},[895,49620,49621,49627,49629],{},[1661,49622,49623,49625],{},[898,49624,1665],{},[1667,49626,1669],{},[1656,49628,2850],{},[1661,49630,49631,49633],{},[898,49632,1665],{},[1667,49634,4032],{},[902,49636,47742],{"encoding":904},"); zdražení vstupů posune křivku ",[38,49639,49640],{},"doleva",[724,49642,49643],{},[614,49644,49645,49646,49659,49660,49678,49679,49697,49698,1863],{},"Obrázek 2.11: Původní ",[883,49647,49649],{"className":49648},[886],[888,49650,49651],{"xmlns":890},[892,49652,49653,49657],{},[895,49654,49655],{},[898,49656,1769],{},[902,49658,1769],{"encoding":904},", posunuté ",[883,49661,49663],{"className":49662},[886],[888,49664,49665],{"xmlns":890},[892,49666,49667,49675],{},[895,49668,49669],{},[1661,49670,49671,49673],{},[898,49672,1769],{},[1667,49674,1669],{},[902,49676,49677],{"encoding":904},"S_1"," (doprava) a ",[883,49680,49682],{"className":49681},[886],[888,49683,49684],{"xmlns":890},[892,49685,49686,49694],{},[895,49687,49688],{},[1661,49689,49690,49692],{},[898,49691,1769],{},[1667,49693,1680],{},[902,49695,49696],{"encoding":904},"S_2"," (doleva) v ",[883,49699,49701],{"className":49700},[886],[888,49702,49703],{"xmlns":890},[892,49704,49705,49717],{},[895,49706,49707,49709,49711,49713,49715],{},[1656,49708,1659],{"stretchy":1658},[898,49710,1665],{},[1656,49712,1673],{"separator":1672},[898,49714,8194],{},[1656,49716,1683],{"stretchy":1658},[902,49718,46373],{"encoding":904},[46607,49720,49722],{"id":49721},"příklad-26-zdanění-výrobce","Příklad 2.6 — zdanění výrobce",[724,49724,49725,49727,49728,49752,49753,1863],{},[38,49726,46615],{}," Nabídka ",[883,49729,49731],{"className":49730},[886],[888,49732,49733],{"xmlns":890},[892,49734,49735,49749],{},[895,49736,49737,49739,49741,49743,49745,49747],{},[898,49738,8194],{},[1656,49740,1713],{},[898,49742,1769],{},[1656,49744,1659],{"stretchy":1658},[898,49746,1665],{},[1656,49748,1683],{"stretchy":1658},[902,49750,49751],{"encoding":904},"P = S(Q)","; na výrobce je uložena jednotková daň ",[883,49754,49756],{"className":49755},[886],[888,49757,49758],{"xmlns":890},[892,49759,49760,49764],{},[895,49761,49762],{},[898,49763,11577],{},[902,49765,11577],{"encoding":904},[724,49767,49768,49770,49771,49784,49785,49803,49804,49832],{},[38,49769,46647],{}," Spotřebitel zaplatí ",[883,49772,49774],{"className":49773},[886],[888,49775,49776],{"xmlns":890},[892,49777,49778,49782],{},[895,49779,49780],{},[898,49781,8194],{},[902,49783,8194],{"encoding":904},", výrobce obdrží ",[883,49786,49788],{"className":49787},[886],[888,49789,49790],{"xmlns":890},[892,49791,49792,49800],{},[895,49793,49794,49796,49798],{},[898,49795,8194],{},[1656,49797,3964],{},[898,49799,11577],{},[902,49801,49802],{"encoding":904},"P - T",". Z podmínky ",[883,49805,49807],{"className":49806},[886],[888,49808,49809],{"xmlns":890},[892,49810,49811,49829],{},[895,49812,49813,49815,49817,49819,49821,49823,49825,49827],{},[898,49814,8194],{},[1656,49816,3964],{},[898,49818,11577],{},[1656,49820,1713],{},[898,49822,1769],{},[1656,49824,1659],{"stretchy":1658},[898,49826,1665],{},[1656,49828,1683],{"stretchy":1658},[902,49830,49831],{"encoding":904},"P - T = S(Q)"," plyne",[883,49834,49836],{"className":49835},[886],[888,49837,49838],{"xmlns":890,"display":2408},[892,49839,49840,49874],{},[895,49841,49842,49844,49846,49852,49854,49856,49858,49860,49862,49864,49866,49868,49870,49872],{},[898,49843,8194],{},[1656,49845,1713],{},[1661,49847,49848,49850],{},[898,49849,1769],{},[1667,49851,1669],{},[1656,49853,1659],{"stretchy":1658},[898,49855,1665],{},[1656,49857,1683],{"stretchy":1658},[1656,49859,1713],{},[898,49861,1769],{},[1656,49863,1659],{"stretchy":1658},[898,49865,1665],{},[1656,49867,1683],{"stretchy":1658},[1656,49869,3633],{},[898,49871,11577],{},[898,49873,1863],{"mathvariant":1723},[902,49875,49876],{"encoding":904},"P = S_1(Q) = S(Q) + T.",[724,49878,49879,49880,49893,49894,1643,49907,49910,49911,1896,49931,3206,49949,1863],{},"Křivka ",[883,49881,49883],{"className":49882},[886],[888,49884,49885],{"xmlns":890},[892,49886,49887,49891],{},[895,49888,49889],{},[898,49890,1769],{},[902,49892,1769],{"encoding":904}," se tedy posune o ",[883,49895,49897],{"className":49896},[886],[888,49898,49899],{"xmlns":890},[892,49900,49901,49905],{},[895,49902,49903],{},[898,49904,11577],{},[902,49906,11577],{"encoding":904},[38,49908,49909],{},"svisle nahoru"," (tj. doleva). Např. pro ",[883,49912,49914],{"className":49913},[886],[888,49915,49916],{"xmlns":890},[892,49917,49918,49928],{},[895,49919,49920,49922,49924,49926],{},[898,49921,8194],{},[1656,49923,1713],{},[1667,49925,1680],{},[898,49927,1665],{},[902,49929,49930],{"encoding":904},"P = 2Q",[883,49932,49934],{"className":49933},[886],[888,49935,49936],{"xmlns":890},[892,49937,49938,49946],{},[895,49939,49940,49942,49944],{},[898,49941,11577],{},[1656,49943,1713],{},[1667,49945,9112],{},[902,49947,49948],{"encoding":904},"T = 6",[883,49950,49952],{"className":49951},[886],[888,49953,49954],{"xmlns":890},[892,49955,49956,49978],{},[895,49957,49958,49964,49966,49968,49970,49972,49974,49976],{},[1661,49959,49960,49962],{},[898,49961,1769],{},[1667,49963,1669],{},[1656,49965,2114],{},[898,49967,8194],{},[1656,49969,1713],{},[1667,49971,1680],{},[898,49973,1665],{},[1656,49975,3633],{},[1667,49977,9112],{},[902,49979,49980],{"encoding":904},"S_1: P = 2Q + 6",[724,49982,49983],{},[614,49984,49985,49986,49999],{},"Obrázek 2.12: Posun nabídky o ",[883,49987,49989],{"className":49988},[886],[888,49990,49991],{"xmlns":890},[892,49992,49993,49997],{},[895,49994,49995],{},[898,49996,11577],{},[902,49998,11577],{"encoding":904}," svisle nahoru.",[45652,50001],{},[115,50003,50005],{"id":50004},"tržní-rovnováha","Tržní rovnováha",[1981,50007,50008],{},[724,50009,50010,50012,50013,1643,50016,50048,50049,1343,50072,50095,50096,50099,50100,50113],{},[883,50011,3472],{}," TL;DR\nV ",[38,50014,50015],{},"rovnovážném bodě",[883,50017,50019],{"className":50018},[886],[888,50020,50021],{"xmlns":890},[892,50022,50023,50045],{},[895,50024,50025,50027,50029,50035,50037,50043],{},[898,50026,1842],{},[1656,50028,3453],{"stretchy":1658},[2062,50030,50031,50033],{},[898,50032,1665],{},[898,50034,1842],{},[1656,50036,1673],{"separator":1672},[2062,50038,50039,50041],{},[898,50040,8194],{},[898,50042,1842],{},[1656,50044,3462],{"stretchy":1658},[902,50046,50047],{"encoding":904},"E[Q^E, P^E]"," se poptávané a nabízené množství rovnají. Najde se jako řešení soustavy ",[883,50050,50052],{"className":50051},[886],[888,50053,50054],{"xmlns":890},[892,50055,50056,50070],{},[895,50057,50058,50060,50062,50064,50066,50068],{},[898,50059,8194],{},[1656,50061,1713],{},[898,50063,6787],{},[1656,50065,1659],{"stretchy":1658},[898,50067,1665],{},[1656,50069,1683],{"stretchy":1658},[902,50071,13412],{"encoding":904},[883,50073,50075],{"className":50074},[886],[888,50076,50077],{"xmlns":890},[892,50078,50079,50093],{},[895,50080,50081,50083,50085,50087,50089,50091],{},[898,50082,8194],{},[1656,50084,1713],{},[898,50086,1769],{},[1656,50088,1659],{"stretchy":1658},[898,50090,1665],{},[1656,50092,1683],{"stretchy":1658},[902,50094,49751],{"encoding":904},". Čtyři ",[38,50097,50098],{},"pravidla komparativní statiky"," popisují, jak se ",[883,50101,50103],{"className":50102},[886],[888,50104,50105],{"xmlns":890},[892,50106,50107,50111],{},[895,50108,50109],{},[898,50110,1842],{},[902,50112,1842],{"encoding":904}," posune při změně poptávky nebo nabídky.",[198,50115,50117],{"id":50116},"definice","Definice",[724,50119,50120,3247,50122,50125,50126,1643,50129,50147,50148,50179,50180,3247,50183,12702],{},[38,50121,50005],{},[614,50123,50124],{},"market equilibrium",") je stav, kdy poptávané množství = nabízené množství. Při ",[38,50127,50128],{},"rovnovážné ceně",[883,50130,50132],{"className":50131},[886],[888,50133,50134],{"xmlns":890},[892,50135,50136,50144],{},[895,50137,50138],{},[2062,50139,50140,50142],{},[898,50141,8194],{},[898,50143,1842],{},[902,50145,50146],{"encoding":904},"P^E"," není přebytek ani nedostatek zboží. Bod ",[883,50149,50151],{"className":50150},[886],[888,50152,50153],{"xmlns":890},[892,50154,50155,50177],{},[895,50156,50157,50159,50161,50167,50169,50175],{},[898,50158,1842],{},[1656,50160,3453],{"stretchy":1658},[2062,50162,50163,50165],{},[898,50164,1665],{},[898,50166,1842],{},[1656,50168,1673],{"separator":1672},[2062,50170,50171,50173],{},[898,50172,8194],{},[898,50174,1842],{},[1656,50176,3462],{"stretchy":1658},[902,50178,50047],{"encoding":904}," se nazývá ",[38,50181,50182],{},"rovnovážný bod",[614,50184,50185],{},"equilibrium point",[724,50187,50188,50189,1343,50212,1863],{},"Rovnovážný bod je průsečíkem křivek poptávky a nabídky; nalézá se jako řešení soustavy ",[883,50190,50192],{"className":50191},[886],[888,50193,50194],{"xmlns":890},[892,50195,50196,50210],{},[895,50197,50198,50200,50202,50204,50206,50208],{},[898,50199,8194],{},[1656,50201,1713],{},[898,50203,6787],{},[1656,50205,1659],{"stretchy":1658},[898,50207,1665],{},[1656,50209,1683],{"stretchy":1658},[902,50211,13412],{"encoding":904},[883,50213,50215],{"className":50214},[886],[888,50216,50217],{"xmlns":890},[892,50218,50219,50233],{},[895,50220,50221,50223,50225,50227,50229,50231],{},[898,50222,8194],{},[1656,50224,1713],{},[898,50226,1769],{},[1656,50228,1659],{"stretchy":1658},[898,50230,1665],{},[1656,50232,1683],{"stretchy":1658},[902,50234,49751],{"encoding":904},[724,50236,50237],{},[5956,50238],{"alt":50239,"className":50240,"src":50241},"imek-poptavka-nabidka-rovnovaha",[210,5960],"\u002Fwiki-assets\u002Fimek-poptavka-nabidka-rovnovaha.jpeg",[724,50243,50244],{},[614,50245,50246,50247,50260,50261,22743,50274,50295,50296,1863],{},"Obrázek 2.13: Klesající ",[883,50248,50250],{"className":50249},[886],[888,50251,50252],{"xmlns":890},[892,50253,50254,50258],{},[895,50255,50256],{},[898,50257,6787],{},[902,50259,6787],{"encoding":904}," a rostoucí ",[883,50262,50264],{"className":50263},[886],[888,50265,50266],{"xmlns":890},[892,50267,50268,50272],{},[895,50269,50270],{},[898,50271,1769],{},[902,50273,1769],{"encoding":904},[883,50275,50277],{"className":50276},[886],[888,50278,50279],{"xmlns":890},[892,50280,50281,50293],{},[895,50282,50283,50285,50287,50289,50291],{},[1656,50284,1659],{"stretchy":1658},[898,50286,1665],{},[1656,50288,1673],{"separator":1672},[898,50290,8194],{},[1656,50292,1683],{"stretchy":1658},[902,50294,46373],{"encoding":904}," protínající se v ",[883,50297,50299],{"className":50298},[886],[888,50300,50301],{"xmlns":890},[892,50302,50303,50325],{},[895,50304,50305,50307,50309,50315,50317,50323],{},[898,50306,1842],{},[1656,50308,3453],{"stretchy":1658},[2062,50310,50311,50313],{},[898,50312,1665],{},[898,50314,1842],{},[1656,50316,1673],{"separator":1672},[2062,50318,50319,50321],{},[898,50320,8194],{},[898,50322,1842],{},[1656,50324,3462],{"stretchy":1658},[902,50326,50047],{"encoding":904},[198,50328,50330],{"id":50329},"příklad-27-kvadratický-model","Příklad 2.7 (kvadratický model)",[724,50332,50333,50335,50336,50370,50371,1863],{},[38,50334,46615],{}," Poptávka ",[883,50337,50339],{"className":50338},[886],[888,50340,50341],{"xmlns":890},[892,50342,50343,50367],{},[895,50344,50345,50347,50349,50351,50357,50359,50361,50363,50365],{},[898,50346,8194],{},[1656,50348,1713],{},[1656,50350,3964],{},[2062,50352,50353,50355],{},[898,50354,1665],{},[1667,50356,1680],{},[1656,50358,3964],{},[1667,50360,8580],{},[898,50362,1665],{},[1656,50364,3633],{},[1667,50366,17557],{},[902,50368,50369],{"encoding":904},"P = -Q^2 - 10Q + 150",", nabídka ",[883,50372,50374],{"className":50373},[886],[888,50375,50376],{"xmlns":890},[892,50377,50378,50400],{},[895,50379,50380,50382,50384,50390,50392,50394,50396,50398],{},[898,50381,8194],{},[1656,50383,1713],{},[2062,50385,50386,50388],{},[898,50387,1665],{},[1667,50389,1680],{},[1656,50391,3633],{},[1667,50393,31664],{},[898,50395,1665],{},[1656,50397,3633],{},[1667,50399,4386],{},[902,50401,50402],{"encoding":904},"P = Q^2 + 14Q + 22",[724,50404,50405,50407],{},[38,50406,46647],{}," Z rovnosti",[883,50409,50411],{"className":50410},[886],[888,50412,50413],{"xmlns":890,"display":2408},[892,50414,50415,50453],{},[895,50416,50417,50419,50425,50427,50429,50431,50433,50435,50437,50443,50445,50447,50449,50451],{},[1656,50418,3964],{},[2062,50420,50421,50423],{},[898,50422,1665],{},[1667,50424,1680],{},[1656,50426,3964],{},[1667,50428,8580],{},[898,50430,1665],{},[1656,50432,3633],{},[1667,50434,17557],{},[1656,50436,1713],{},[2062,50438,50439,50441],{},[898,50440,1665],{},[1667,50442,1680],{},[1656,50444,3633],{},[1667,50446,31664],{},[898,50448,1665],{},[1656,50450,3633],{},[1667,50452,4386],{},[902,50454,50455],{"encoding":904},"-Q^2 - 10Q + 150 = Q^2 + 14Q + 22",[724,50457,50458,50459,3228,50494,50526,50527,50543,50544,50557,50558,1343,50580,50617,50618,1863],{},"dostaneme ",[883,50460,50462],{"className":50461},[886],[888,50463,50464],{"xmlns":890},[892,50465,50466,50491],{},[895,50467,50468,50470,50476,50478,50481,50483,50485,50487,50489],{},[1667,50469,1680],{},[2062,50471,50472,50474],{},[898,50473,1665],{},[1667,50475,1680],{},[1656,50477,3633],{},[1667,50479,50480],{},"24",[898,50482,1665],{},[1656,50484,3964],{},[1667,50486,2771],{},[1656,50488,1713],{},[1667,50490,4032],{},[902,50492,50493],{"encoding":904},"2Q^2 + 24Q - 128 = 0",[883,50495,50497],{"className":50496},[886],[888,50498,50499],{"xmlns":890},[892,50500,50501,50523],{},[895,50502,50503,50509,50511,50513,50515,50517,50519,50521],{},[2062,50504,50505,50507],{},[898,50506,1665],{},[1667,50508,1680],{},[1656,50510,3633],{},[1667,50512,9140],{},[898,50514,1665],{},[1656,50516,3964],{},[1667,50518,2678],{},[1656,50520,1713],{},[1667,50522,4032],{},[902,50524,50525],{"encoding":904},"Q^2 + 12Q - 64 = 0",". Kořeny jsou ",[883,50528,50530],{"className":50529},[886],[888,50531,50532],{"xmlns":890},[892,50533,50534,50540],{},[895,50535,50536,50538],{},[1656,50537,3964],{},[1667,50539,2668],{},[902,50541,50542],{"encoding":904},"-16"," (nevyhovuje) a ",[883,50545,50547],{"className":50546},[886],[888,50548,50549],{"xmlns":890},[892,50550,50551,50555],{},[895,50552,50553],{},[1667,50554,2673],{},[902,50556,2673],{"encoding":904},". Tedy ",[883,50559,50561],{"className":50560},[886],[888,50562,50563],{"xmlns":890},[892,50564,50565,50577],{},[895,50566,50567,50573,50575],{},[2062,50568,50569,50571],{},[898,50570,1665],{},[898,50572,1842],{},[1656,50574,1713],{},[1667,50576,2673],{},[902,50578,50579],{"encoding":904},"Q^E = 4",[883,50581,50583],{"className":50582},[886],[888,50584,50585],{"xmlns":890},[892,50586,50587,50614],{},[895,50588,50589,50595,50597,50599,50601,50603,50605,50607,50609,50611],{},[2062,50590,50591,50593],{},[898,50592,8194],{},[898,50594,1842],{},[1656,50596,1713],{},[1656,50598,3964],{},[1667,50600,2668],{},[1656,50602,3964],{},[1667,50604,9135],{},[1656,50606,3633],{},[1667,50608,17557],{},[1656,50610,1713],{},[1667,50612,50613],{},"94",[902,50615,50616],{"encoding":904},"P^E = -16 - 40 + 150 = 94",", rovnovážný bod ",[883,50619,50621],{"className":50620},[886],[888,50622,50623],{"xmlns":890},[892,50624,50625,50639],{},[895,50626,50627,50629,50631,50633,50635,50637],{},[898,50628,1842],{},[1656,50630,3453],{"stretchy":1658},[1667,50632,2673],{},[1656,50634,1673],{"separator":1672},[1667,50636,50613],{},[1656,50638,3462],{"stretchy":1658},[902,50640,50641],{"encoding":904},"E[4, 94]",[198,50643,50645],{"id":50644},"příklad-28-dvoukomoditní-trh","Příklad 2.8 (dvoukomoditní trh)",[724,50647,50648,50650],{},[38,50649,46615],{}," Poptávky a nabídky dvou zboží",[883,50652,50654],{"className":50653},[886],[888,50655,50656],{"xmlns":890,"display":2408},[892,50657,50658,50824],{},[2412,50659,50662,50750],{"rowspacing":29476,"columnalign":50660,"columnspacing":50661},"right left right left","0em 1em 0em",[2416,50663,50664,50674,50706,50716],{},[2419,50665,50666],{},[4138,50667,50668],{"scriptlevel":4032,"displaystyle":1672},[1661,50669,50670,50672],{},[898,50671,1665],{},[1667,50673,1669],{},[2419,50675,50676],{},[4138,50677,50678],{"scriptlevel":4032,"displaystyle":1672},[895,50679,50680,50682,50684,50686,50688,50690,50696,50698,50704],{},[895,50681],{},[1656,50683,1713],{},[1667,50685,9135],{},[1656,50687,3964],{},[1667,50689,5193],{},[1661,50691,50692,50694],{},[898,50693,8194],{},[1667,50695,1669],{},[1656,50697,3964],{},[1661,50699,50700,50702],{},[898,50701,8194],{},[1667,50703,1680],{},[1656,50705,1673],{"separator":1672},[2419,50707,50708],{},[4138,50709,50710],{"scriptlevel":4032,"displaystyle":1672},[1661,50711,50712,50714],{},[898,50713,1665],{},[1667,50715,1680],{},[2419,50717,50718],{},[4138,50719,50720],{"scriptlevel":4032,"displaystyle":1672},[895,50721,50722,50724,50726,50728,50730,50732,50738,50740,50742,50748],{},[895,50723],{},[1656,50725,1713],{},[1667,50727,9267],{},[1656,50729,3964],{},[1667,50731,1680],{},[1661,50733,50734,50736],{},[898,50735,8194],{},[1667,50737,1669],{},[1656,50739,3964],{},[1667,50741,2673],{},[1661,50743,50744,50746],{},[898,50745,8194],{},[1667,50747,1680],{},[1656,50749,1673],{"separator":1672},[2416,50751,50752,50762,50788,50798],{},[2419,50753,50754],{},[4138,50755,50756],{"scriptlevel":4032,"displaystyle":1672},[1661,50757,50758,50760],{},[898,50759,1665],{},[1667,50761,1669],{},[2419,50763,50764],{},[4138,50765,50766],{"scriptlevel":4032,"displaystyle":1672},[895,50767,50768,50770,50772,50774,50776,50778,50780,50786],{},[895,50769],{},[1656,50771,1713],{},[1656,50773,3964],{},[1667,50775,2617],{},[1656,50777,3633],{},[1667,50779,2673],{},[1661,50781,50782,50784],{},[898,50783,8194],{},[1667,50785,1669],{},[1656,50787,1673],{"separator":1672},[2419,50789,50790],{},[4138,50791,50792],{"scriptlevel":4032,"displaystyle":1672},[1661,50793,50794,50796],{},[898,50795,1665],{},[1667,50797,1680],{},[2419,50799,50800],{},[4138,50801,50802],{"scriptlevel":4032,"displaystyle":1672},[895,50803,50804,50806,50808,50810,50812,50814,50816,50822],{},[895,50805],{},[1656,50807,1713],{},[1656,50809,3964],{},[1667,50811,6240],{},[1656,50813,3633],{},[1667,50815,2617],{},[1661,50817,50818,50820],{},[898,50819,8194],{},[1667,50821,1680],{},[898,50823,1863],{"mathvariant":1723},[902,50825,50826],{"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}",[724,50828,50829,50831],{},[38,50830,46647],{}," Z rovností poptávek a nabídek dostaneme",[883,50833,50835],{"className":50834},[886],[888,50836,50837],{"xmlns":890,"display":2408},[892,50838,50839,50888],{},[895,50840,50841,50843,50849,50851,50857,50859,50861,50863,50865,50867,50873,50875,50877,50883,50885],{},[1667,50842,2698],{},[1661,50844,50845,50847],{},[898,50846,8194],{},[1667,50848,1669],{},[1656,50850,3633],{},[1661,50852,50853,50855],{},[898,50854,8194],{},[1667,50856,1680],{},[1656,50858,1713],{},[1667,50860,29921],{},[1656,50862,1673],{"separator":1672},[3316,50864],{"width":14644},[1667,50866,1680],{},[1661,50868,50869,50871],{},[898,50870,8194],{},[1667,50872,1669],{},[1656,50874,3633],{},[1667,50876,6240],{},[1661,50878,50879,50881],{},[898,50880,8194],{},[1667,50882,1680],{},[1656,50884,1713],{},[1667,50886,50887],{},"57.",[902,50889,50890],{"encoding":904},"9P_1 + P_2 = 43, \\qquad 2P_1 + 7P_2 = 57.",[724,50892,50893,50894,1343,50918,50942,50943,1343,50968,50992,50993,50995],{},"Řešením je ",[883,50895,50897],{"className":50896},[886],[888,50898,50899],{"xmlns":890},[892,50900,50901,50915],{},[895,50902,50903,50911,50913],{},[1715,50904,50905,50907,50909],{},[898,50906,8194],{},[1667,50908,1669],{},[898,50910,1842],{},[1656,50912,1713],{},[1667,50914,2673],{},[902,50916,50917],{"encoding":904},"P_1^E = 4",[883,50919,50921],{"className":50920},[886],[888,50922,50923],{"xmlns":890},[892,50924,50925,50939],{},[895,50926,50927,50935,50937],{},[1715,50928,50929,50931,50933],{},[898,50930,8194],{},[1667,50932,1680],{},[898,50934,1842],{},[1656,50936,1713],{},[1667,50938,6240],{},[902,50940,50941],{"encoding":904},"P_2^E = 7","; zpětným dosazením ",[883,50944,50946],{"className":50945},[886],[888,50947,50948],{"xmlns":890},[892,50949,50950,50965],{},[895,50951,50952,50960,50962],{},[1715,50953,50954,50956,50958],{},[898,50955,1665],{},[1667,50957,1669],{},[898,50959,1842],{},[1656,50961,1713],{},[1667,50963,50964],{},"13",[902,50966,50967],{"encoding":904},"Q_1^E = 13",[883,50969,50971],{"className":50970},[886],[888,50972,50973],{"xmlns":890},[892,50974,50975,50989],{},[895,50976,50977,50985,50987],{},[1715,50978,50979,50981,50983],{},[898,50980,1665],{},[1667,50982,1680],{},[898,50984,1842],{},[1656,50986,1713],{},[1667,50988,31664],{},[902,50990,50991],{"encoding":904},"Q_2^E = 14",". Zboží jsou ",[38,50994,48502],{}," (zkřížené koeficienty v poptávce jsou záporné).",[198,50997,50999],{"id":50998},"dynamický-model-pavučinový-teorém","Dynamický model — pavučinový teorém",[724,51001,51002,51003,51020,51021,3247,51024,12702],{},"Rovnovážná cena se obecně liší od tržní ceny, která vzniká působením tržních sil v čase. Za podmínky stability se tržní cena přibližuje k ",[883,51004,51006],{"className":51005},[886],[888,51007,51008],{"xmlns":890},[892,51009,51010,51018],{},[895,51011,51012],{},[2062,51013,51014,51016],{},[898,51015,8194],{},[898,51017,1842],{},[902,51019,50146],{"encoding":904},"; mechanismus popisuje ",[38,51022,51023],{},"teorém pavučiny",[614,51025,51026],{},"cobweb model",[198,51028,51030],{"id":51029},"pravidla-komparativní-statiky-14","Pravidla komparativní statiky (1–4)",[724,51032,51033],{},[5956,51034],{"alt":51035,"className":51036,"src":51037},"imek-komparativni-statika-4pripady",[210,5960],"\u002Fwiki-assets\u002Fimek-komparativni-statika-4pripady.jpeg",[1981,51039,51040,51081,51121,51161],{},[724,51041,51042,51045,51046,14953,51063,1863],{},[38,51043,51044],{},"Pravidlo 1:"," Růst poptávky ⟹ růst ",[883,51047,51049],{"className":51048},[886],[888,51050,51051],{"xmlns":890},[892,51052,51053,51061],{},[895,51054,51055],{},[2062,51056,51057,51059],{},[898,51058,8194],{},[898,51060,1842],{},[902,51062,50146],{"encoding":904},[883,51064,51066],{"className":51065},[886],[888,51067,51068],{"xmlns":890},[892,51069,51070,51078],{},[895,51071,51072],{},[2062,51073,51074,51076],{},[898,51075,1665],{},[898,51077,1842],{},[902,51079,51080],{"encoding":904},"Q^E",[724,51082,51083,51086,51087,14953,51104,1863],{},[38,51084,51085],{},"Pravidlo 2:"," Pokles poptávky ⟹ pokles ",[883,51088,51090],{"className":51089},[886],[888,51091,51092],{"xmlns":890},[892,51093,51094,51102],{},[895,51095,51096],{},[2062,51097,51098,51100],{},[898,51099,8194],{},[898,51101,1842],{},[902,51103,50146],{"encoding":904},[883,51105,51107],{"className":51106},[886],[888,51108,51109],{"xmlns":890},[892,51110,51111,51119],{},[895,51112,51113],{},[2062,51114,51115,51117],{},[898,51116,1665],{},[898,51118,1842],{},[902,51120,51080],{"encoding":904},[724,51122,51123,51126,51127,18105,51144,1863],{},[38,51124,51125],{},"Pravidlo 3:"," Růst nabídky ⟹ pokles ",[883,51128,51130],{"className":51129},[886],[888,51131,51132],{"xmlns":890},[892,51133,51134,51142],{},[895,51135,51136],{},[2062,51137,51138,51140],{},[898,51139,8194],{},[898,51141,1842],{},[902,51143,50146],{"encoding":904},[883,51145,51147],{"className":51146},[886],[888,51148,51149],{"xmlns":890},[892,51150,51151,51159],{},[895,51152,51153],{},[2062,51154,51155,51157],{},[898,51156,1665],{},[898,51158,1842],{},[902,51160,51080],{"encoding":904},[724,51162,51163,51166,51167,51184,51185,1863],{},[38,51164,51165],{},"Pravidlo 4:"," Pokles nabídky ⟹ růst ",[883,51168,51170],{"className":51169},[886],[888,51171,51172],{"xmlns":890},[892,51173,51174,51182],{},[895,51175,51176],{},[2062,51177,51178,51180],{},[898,51179,8194],{},[898,51181,1842],{},[902,51183,50146],{"encoding":904},", pokles ",[883,51186,51188],{"className":51187},[886],[888,51189,51190],{"xmlns":890},[892,51191,51192,51200],{},[895,51193,51194],{},[2062,51195,51196,51198],{},[898,51197,1665],{},[898,51199,1842],{},[902,51201,51080],{"encoding":904},[16,51203,51204,51249],{},[19,51205,51206],{},[22,51207,51208,51211,51230],{},[25,51209,51210],{},"Změna",[25,51212,51213],{},[883,51214,51216],{"className":51215},[886],[888,51217,51218],{"xmlns":890},[892,51219,51220,51228],{},[895,51221,51222],{},[2062,51223,51224,51226],{},[898,51225,8194],{},[898,51227,1842],{},[902,51229,50146],{"encoding":904},[25,51231,51232],{},[883,51233,51235],{"className":51234},[886],[888,51236,51237],{"xmlns":890},[892,51238,51239,51247],{},[895,51240,51241],{},[2062,51242,51243,51245],{},[898,51244,1665],{},[898,51246,1842],{},[902,51248,51080],{"encoding":904},[30,51250,51251,51261,51271,51280],{},[22,51252,51253,51256,51259],{},[35,51254,51255],{},"Růst poptávky",[35,51257,51258],{},"↑",[35,51260,51258],{},[22,51262,51263,51266,51269],{},[35,51264,51265],{},"Pokles poptávky",[35,51267,51268],{},"↓",[35,51270,51268],{},[22,51272,51273,51276,51278],{},[35,51274,51275],{},"Růst nabídky",[35,51277,51268],{},[35,51279,51258],{},[22,51281,51282,51285,51287],{},[35,51283,51284],{},"Pokles nabídky",[35,51286,51258],{},[35,51288,51268],{},[724,51290,51291],{},[614,51292,51293],{},"Obrázky 2.15–2.18 ilustrují všechny čtyři situace pomocí posunu jedné z křivek.",[45652,51295],{},[115,51297,811],{"id":51298},"zdanění-trhu",[1981,51300,51301,51390],{},[724,51302,51303,51305,51306,51319,51320,2191,51333,51336,51337,45459,51360,51385,51386,51389],{},[883,51304,3472],{}," TL;DR\nJednotková daň ",[883,51307,51309],{"className":51308},[886],[888,51310,51311],{"xmlns":890},[892,51312,51313,51317],{},[895,51314,51315],{},[898,51316,11577],{},[902,51318,11577],{"encoding":904}," uložená na každou prodanou jednotku způsobí posun jedné z křivek o ",[883,51321,51323],{"className":51322},[886],[888,51324,51325],{"xmlns":890},[892,51326,51327,51331],{},[895,51328,51329],{},[898,51330,11577],{},[902,51332,11577],{"encoding":904},[38,51334,51335],{},"Daňové břemeno"," se dělí mezi spotřebitele (",[883,51338,51340],{"className":51339},[886],[888,51341,51342],{"xmlns":890},[892,51343,51344,51357],{},[895,51345,51346],{},[1661,51347,51348,51350],{},[898,51349,11577],{},[895,51351,51352,51355],{},[898,51353,51354],{},"s",[898,51356,724],{},[902,51358,51359],{"encoding":904},"T_{sp}",[883,51361,51363],{"className":51362},[886],[888,51364,51365],{"xmlns":890},[892,51366,51367,51382],{},[895,51368,51369],{},[1661,51370,51371,51373],{},[898,51372,11577],{},[895,51374,51375,51378,51380],{},[898,51376,51377],{},"v",[898,51379,10839],{},[898,51381,20776],{},[902,51383,51384],{"encoding":904},"T_{vyr}","). Klíčová vlastnost — ",[38,51387,51388],{},"ekvivalence zdanění",": výsledné rovnovážné množství i čistá cena pro výrobce jsou stejné bez ohledu na to, zda je daň uložena výrobci, či spotřebiteli.",[724,51391,51392],{},[614,51393,51394,51395,1863],{},"Pro detail, úplné odvození, Příklady 2.9 a 2.10 a geometrickou interpretaci viz ",[207,51396,51398],{"className":51397,"dataFsResolvedFilePath":809,"href":810},[210],"zdaneni-trhu",[724,51400,51401,51402,51405,51406,51432,51433,51436,51437,51463,51464,51481,51482,51522,51523,1896,51536,1863],{},"Existují dvě formy zdanění — daň uložená ",[38,51403,51404],{},"výrobci"," (posun nabídky ",[883,51407,51409],{"className":51408},[886],[888,51410,51411],{"xmlns":890},[892,51412,51413,51429],{},[895,51414,51415,51421,51423,51425,51427],{},[1661,51416,51417,51419],{},[898,51418,1769],{},[1667,51420,1669],{},[1656,51422,1713],{},[898,51424,1769],{},[1656,51426,3633],{},[898,51428,11577],{},[902,51430,51431],{"encoding":904},"S_1 = S + T"," svisle nahoru) a daň uložená ",[38,51434,51435],{},"spotřebiteli"," (posun poptávky ",[883,51438,51440],{"className":51439},[886],[888,51441,51442],{"xmlns":890},[892,51443,51444,51460],{},[895,51445,51446,51452,51454,51456,51458],{},[1661,51447,51448,51450],{},[898,51449,6787],{},[1667,51451,1680],{},[1656,51453,1713],{},[898,51455,6787],{},[1656,51457,3964],{},[898,51459,11577],{},[902,51461,51462],{"encoding":904},"D_2 = D - T"," svisle dolů). V obou případech nové rovnovážné množství ",[883,51465,51467],{"className":51466},[886],[888,51468,51469],{"xmlns":890},[892,51470,51471,51479],{},[895,51472,51473],{},[2062,51474,51475,51477],{},[898,51476,1665],{},[898,51478,1842],{},[902,51480,51080],{"encoding":904}," klesá a vzniká rozklad daně ",[883,51483,51485],{"className":51484},[886],[888,51486,51487],{"xmlns":890},[892,51488,51489,51519],{},[895,51490,51491,51493,51495,51505,51507],{},[898,51492,11577],{},[1656,51494,1713],{},[1661,51496,51497,51499],{},[898,51498,11577],{},[895,51500,51501,51503],{},[898,51502,51354],{},[898,51504,724],{},[1656,51506,3633],{},[1661,51508,51509,51511],{},[898,51510,11577],{},[895,51512,51513,51515,51517],{},[898,51514,51377],{},[898,51516,10839],{},[898,51518,20776],{},[902,51520,51521],{"encoding":904},"T = T_{sp} + T_{vyr}"," mezi obě strany trhu, určený relativními sklony křivek ",[883,51524,51526],{"className":51525},[886],[888,51527,51528],{"xmlns":890},[892,51529,51530,51534],{},[895,51531,51532],{},[898,51533,6787],{},[902,51535,6787],{"encoding":904},[883,51537,51539],{"className":51538},[886],[888,51540,51541],{"xmlns":890},[892,51542,51543,51547],{},[895,51544,51545],{},[898,51546,1769],{},[902,51548,1769],{"encoding":904},[724,51550,51551,51552,51555,51556,1896,51586,51620],{},"Zásadním výsledkem kapitoly je ",[38,51553,51554],{},"věta o ekvivalenci zdanění",": ať je daň uvalena formálně na kohokoli, rovnovážné množství i reálné rozdělení břemene jsou identické — ",[883,51557,51559],{"className":51558},[886],[888,51560,51561],{"xmlns":890},[892,51562,51563,51583],{},[895,51564,51565,51573,51575],{},[1715,51566,51567,51569,51571],{},[898,51568,1665],{},[1667,51570,1669],{},[898,51572,1842],{},[1656,51574,1713],{},[1715,51576,51577,51579,51581],{},[898,51578,1665],{},[1667,51580,1680],{},[898,51582,1842],{},[902,51584,51585],{"encoding":904},"Q_1^E = Q_2^E",[883,51587,51589],{"className":51588},[886],[888,51590,51591],{"xmlns":890},[892,51592,51593,51617],{},[895,51594,51595,51603,51605,51607,51609],{},[1715,51596,51597,51599,51601],{},[898,51598,8194],{},[1667,51600,1669],{},[898,51602,1842],{},[1656,51604,3964],{},[898,51606,11577],{},[1656,51608,1713],{},[1715,51610,51611,51613,51615],{},[898,51612,8194],{},[1667,51614,1680],{},[898,51616,1842],{},[902,51618,51619],{"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.",[724,51622,51623,51624,51627,51628,51654,51655,51683,51684,51687,51688,51691,51692,1863],{},"Podrobný výklad, Příklady ",[38,51625,51626],{},"2.9"," (daň výrobci, ",[883,51629,51631],{"className":51630},[886],[888,51632,51633],{"xmlns":890},[892,51634,51635,51651],{},[895,51636,51637,51647,51649],{},[1661,51638,51639,51641],{},[898,51640,11577],{},[895,51642,51643,51645],{},[898,51644,51354],{},[898,51646,724],{},[1656,51648,1713],{},[1667,51650,1680],{},[902,51652,51653],{"encoding":904},"T_{sp} = 2"," Kč, ",[883,51656,51658],{"className":51657},[886],[888,51659,51660],{"xmlns":890},[892,51661,51662,51680],{},[895,51663,51664,51676,51678],{},[1661,51665,51666,51668],{},[898,51667,11577],{},[895,51669,51670,51672,51674],{},[898,51671,51377],{},[898,51673,10839],{},[898,51675,20776],{},[1656,51677,1713],{},[1667,51679,2673],{},[902,51681,51682],{"encoding":904},"T_{vyr} = 4"," Kč) a ",[38,51685,51686],{},"2.10"," (táž daň, ale na spotřebitele), postup výpočtu rozkladu břemene a ",[38,51689,51690],{},"Obrázky 2.17–2.21"," jsou na samostatné stránce ",[207,51693,51398],{"className":51694,"dataFsResolvedFilePath":809,"href":810},[210],[45652,51696],{},[115,51698,51700],{"id":51699},"multiplikátory-pro-mikroekonomické-proměnné","Multiplikátory pro mikroekonomické proměnné",[1981,51702,51703],{},[724,51704,51705,51707,51708,51711,51712,51714],{},[883,51706,3472],{}," TL;DR\nMultiplikátory jsou ",[38,51709,51710],{},"parciální derivace redukovaného tvaru"," endogenní proměnné podle exogenních parametrů. Udávají přibližnou odezvu rovnovážného bodu na jednotkovou změnu parametru (",[614,51713,45642],{},"). Kvalitativní smysl (znaménko) je invariantní, kvantitativní závisí na konkrétních hodnotách.",[198,51716,51718],{"id":51717},"redukovaný-tvar","Redukovaný tvar",[724,51720,51721,51722,3247,51745,1343,51763,20863,51780,3247,51803,51820,51821,51851],{},"Pro lineární model ",[883,51723,51725],{"className":51724},[886],[888,51726,51727],{"xmlns":890},[892,51728,51729,51743],{},[895,51730,51731,51733,51735,51737,51739,51741],{},[898,51732,8194],{},[1656,51734,1713],{},[898,51736,207],{},[898,51738,1665],{},[1656,51740,3633],{},[898,51742,3403],{},[902,51744,45742],{"encoding":904},[883,51746,51748],{"className":51747},[886],[888,51749,51750],{"xmlns":890},[892,51751,51752,51760],{},[895,51753,51754,51756,51758],{},[898,51755,207],{},[1656,51757,4373],{},[1667,51759,4032],{},[902,51761,51762],{"encoding":904},"a \u003C 0",[883,51764,51766],{"className":51765},[886],[888,51767,51768],{"xmlns":890},[892,51769,51770,51778],{},[895,51771,51772,51774,51776],{},[898,51773,3403],{},[1656,51775,2850],{},[1667,51777,4032],{},[902,51779,27536],{"encoding":904},[883,51781,51783],{"className":51782},[886],[888,51784,51785],{"xmlns":890},[892,51786,51787,51801],{},[895,51788,51789,51791,51793,51795,51797,51799],{},[898,51790,8194],{},[1656,51792,1713],{},[898,51794,1745],{},[898,51796,1665],{},[1656,51798,3633],{},[898,51800,3768],{},[902,51802,48922],{"encoding":904},[883,51804,51806],{"className":51805},[886],[888,51807,51808],{"xmlns":890},[892,51809,51810,51818],{},[895,51811,51812,51814,51816],{},[898,51813,1745],{},[1656,51815,2850],{},[1667,51817,4032],{},[902,51819,48940],{"encoding":904},") dává podmínka rovnováhy ",[883,51822,51824],{"className":51823},[886],[888,51825,51826],{"xmlns":890},[892,51827,51828,51848],{},[895,51829,51830,51832,51834,51836,51838,51840,51842,51844,51846],{},[898,51831,207],{},[898,51833,1665],{},[1656,51835,3633],{},[898,51837,3403],{},[1656,51839,1713],{},[898,51841,1745],{},[898,51843,1665],{},[1656,51845,3633],{},[898,51847,3768],{},[902,51849,51850],{"encoding":904},"aQ + b = cQ + d",", odkud",[883,51853,51855],{"className":51854},[886],[888,51856,51857],{"xmlns":890,"display":2408},[892,51858,51859,51904],{},[2412,51860,51861],{"width":2414},[2416,51862,51863,51865,51897,51899],{},[2419,51864],{"width":2421},[2419,51866,51867],{},[895,51868,51869,51875,51877,51895],{},[2062,51870,51871,51873],{},[898,51872,1665],{},[898,51874,1842],{},[1656,51876,1713],{},[3294,51878,51879,51887],{},[895,51880,51881,51883,51885],{},[898,51882,3403],{},[1656,51884,3964],{},[898,51886,3768],{},[895,51888,51889,51891,51893],{},[898,51890,1745],{},[1656,51892,3964],{},[898,51894,207],{},[898,51896,1863],{"mathvariant":1723},[2419,51898],{"width":2421},[2419,51900,51901],{},[2461,51902,51903],{},"(2.10)",[902,51905,51906],{"encoding":904},"Q^E = \\frac{b - d}{c - a}. \\tag{2.10}",[724,51908,51909,51910,3247,51912,51915,51916,51933,51934,1643,51937,51963,51964,51977,51978,51996,51997,12702],{},"Vztah (2.10) je ",[38,51911,29672],{},[614,51913,51914],{},"reduced form",") pro ",[883,51917,51919],{"className":51918},[886],[888,51920,51921],{"xmlns":890},[892,51922,51923,51931],{},[895,51924,51925],{},[2062,51926,51927,51929],{},[898,51928,1665],{},[898,51930,1842],{},[902,51932,51080],{"encoding":904},": endogenní proměnná je vyjádřena pomocí exogenních ",[38,51935,51936],{},"parametrů",[883,51938,51940],{"className":51939},[886],[888,51941,51942],{"xmlns":890},[892,51943,51944,51960],{},[895,51945,51946,51948,51950,51952,51954,51956,51958],{},[898,51947,207],{},[1656,51949,1673],{"separator":1672},[898,51951,3403],{},[1656,51953,1673],{"separator":1672},[898,51955,1745],{},[1656,51957,1673],{"separator":1672},[898,51959,3768],{},[902,51961,51962],{"encoding":904},"a, b, c, d",". Aby ",[883,51965,51967],{"className":51966},[886],[888,51968,51969],{"xmlns":890},[892,51970,51971,51975],{},[895,51972,51973],{},[898,51974,1842],{},[902,51976,1842],{"encoding":904}," ležel v 1. kvadrantu, musí platit ",[883,51979,51981],{"className":51980},[886],[888,51982,51983],{"xmlns":890},[892,51984,51985,51993],{},[895,51986,51987,51989,51991],{},[898,51988,3403],{},[1656,51990,2850],{},[898,51992,3768],{},[902,51994,51995],{"encoding":904},"b > d"," (neboť ",[883,51998,52000],{"className":51999},[886],[888,52001,52002],{"xmlns":890},[892,52003,52004,52016],{},[895,52005,52006,52008,52010,52012,52014],{},[898,52007,1745],{},[1656,52009,3964],{},[898,52011,207],{},[1656,52013,2850],{},[1667,52015,4032],{},[902,52017,52018],{"encoding":904},"c - a > 0",[724,52020,52021],{},[614,52022,52023,52024,52037,52038,52051,52052,10722,52065,50617,52082,52095],{},"Obrázek 2.22: Lineární poptávka (úsek ",[883,52025,52027],{"className":52026},[886],[888,52028,52029],{"xmlns":890},[892,52030,52031,52035],{},[895,52032,52033],{},[898,52034,3403],{},[902,52036,3403],{"encoding":904}," na ose ",[883,52039,52041],{"className":52040},[886],[888,52042,52043],{"xmlns":890},[892,52044,52045,52049],{},[895,52046,52047],{},[898,52048,8194],{},[902,52050,8194],{"encoding":904},") a nabídka (úsek ",[883,52053,52055],{"className":52054},[886],[888,52056,52057],{"xmlns":890},[892,52058,52059,52063],{},[895,52060,52061],{},[898,52062,3768],{},[902,52064,3768],{"encoding":904},[883,52066,52068],{"className":52067},[886],[888,52069,52070],{"xmlns":890},[892,52071,52072,52080],{},[895,52073,52074,52076,52078],{},[898,52075,3403],{},[1656,52077,2850],{},[898,52079,3768],{},[902,52081,51995],{"encoding":904},[883,52083,52085],{"className":52084},[886],[888,52086,52087],{"xmlns":890},[892,52088,52089,52093],{},[895,52090,52091],{},[898,52092,1842],{},[902,52094,1842],{"encoding":904}," v 1. kvadrantu.",[198,52097,52099],{"id":52098},"definice-multiplikátorů","Definice multiplikátorů",[724,52101,52102,52103,52128,52129,52142,52143,52156],{},"V komparativní statice jsou ",[883,52104,52106],{"className":52105},[886],[888,52107,52108],{"xmlns":890},[892,52109,52110,52126],{},[895,52111,52112,52114,52116,52118,52120,52122,52124],{},[898,52113,207],{},[1656,52115,1673],{"separator":1672},[898,52117,3403],{},[1656,52119,1673],{"separator":1672},[898,52121,1745],{},[1656,52123,1673],{"separator":1672},[898,52125,3768],{},[902,52127,51962],{"encoding":904}," exogenní proměnné a ",[883,52130,52132],{"className":52131},[886],[888,52133,52134],{"xmlns":890},[892,52135,52136,52140],{},[895,52137,52138],{},[898,52139,1665],{},[902,52141,1665],{"encoding":904}," endogenní. Přibližná změna ",[883,52144,52146],{"className":52145},[886],[888,52147,52148],{"xmlns":890},[892,52149,52150,52154],{},[895,52151,52152],{},[898,52153,1665],{},[902,52155,1665],{"encoding":904}," se rovná totálnímu diferenciálu:",[883,52158,52160],{"className":52159},[886],[888,52161,52162],{"xmlns":890,"display":2408},[892,52163,52164,52257],{},[2412,52165,52166],{"width":2414},[2416,52167,52168,52170,52250,52252],{},[2419,52169],{"width":2421},[2419,52171,52172],{},[895,52173,52174,52176,52178,52180,52182,52184,52186,52194,52196,52198,52200,52202,52210,52212,52214,52216,52218,52226,52228,52230,52232,52234,52242,52244,52246,52248],{},[898,52175,3750],{"mathvariant":1723},[898,52177,1665],{},[1656,52179,3815],{},[898,52181,3768],{},[898,52183,1665],{},[1656,52185,1713],{},[1715,52187,52188,52190,52192],{},[898,52189,1665],{},[898,52191,207],{},[1656,52193,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[2461,52195,7828],{},[898,52197,3768],{},[898,52199,207],{},[1656,52201,3633],{},[1715,52203,52204,52206,52208],{},[898,52205,1665],{},[898,52207,3403],{},[1656,52209,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[2461,52211,7828],{},[898,52213,3768],{},[898,52215,3403],{},[1656,52217,3633],{},[1715,52219,52220,52222,52224],{},[898,52221,1665],{},[898,52223,1745],{},[1656,52225,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[2461,52227,7828],{},[898,52229,3768],{},[898,52231,1745],{},[1656,52233,3633],{},[1715,52235,52236,52238,52240],{},[898,52237,1665],{},[898,52239,3768],{},[1656,52241,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[2461,52243,7828],{},[898,52245,3768],{},[898,52247,3768],{},[898,52249,1863],{"mathvariant":1723},[2419,52251],{"width":2421},[2419,52253,52254],{},[2461,52255,52256],{},"(2.11)",[902,52258,52259],{"encoding":904},"\\Delta Q \\approx dQ = Q'_a\\,da + Q'_b\\,db + Q'_c\\,dc + Q'_d\\,dd. \\tag{2.11}",[724,52261,52262,52263,52313,52314,3247,52316,5642],{},"Parciální derivace ",[883,52264,52266],{"className":52265},[886],[888,52267,52268],{"xmlns":890},[892,52269,52270,52310],{},[895,52271,52272,52280,52282,52290,52292,52300,52302],{},[1715,52273,52274,52276,52278],{},[898,52275,1665],{},[898,52277,207],{},[1656,52279,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,52281,1673],{"separator":1672},[1715,52283,52284,52286,52288],{},[898,52285,1665],{},[898,52287,3403],{},[1656,52289,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,52291,1673],{"separator":1672},[1715,52293,52294,52296,52298],{},[898,52295,1665],{},[898,52297,1745],{},[1656,52299,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,52301,1673],{"separator":1672},[1715,52303,52304,52306,52308],{},[898,52305,1665],{},[898,52307,3768],{},[1656,52309,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[902,52311,52312],{"encoding":904},"Q'_a, Q'_b, Q'_c, Q'_d"," se nazývají ",[38,52315,26700],{},[614,52317,52318],{},"multipliers",[883,52320,52322],{"className":52321},[886],[888,52323,52324],{"xmlns":890,"display":2408},[892,52325,52326,52477],{},[2412,52327,52328],{"width":2414},[2416,52329,52330,52332,52470,52472],{},[2419,52331],{"width":2421},[2419,52333,52334],{},[895,52335,52336,52344,52346,52372,52374,52376,52384,52386,52398,52400,52402,52410,52412,52414,52440,52442,52444,52452,52454,52456,52468],{},[1715,52337,52338,52340,52342],{},[898,52339,1665],{},[898,52341,207],{},[1656,52343,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,52345,1713],{},[3294,52347,52348,52356],{},[895,52349,52350,52352,52354],{},[898,52351,3403],{},[1656,52353,3964],{},[898,52355,3768],{},[895,52357,52358,52360,52362,52364,52366],{},[1656,52359,1659],{"stretchy":1658},[898,52361,1745],{},[1656,52363,3964],{},[898,52365,207],{},[2062,52367,52368,52370],{},[1656,52369,1683],{"stretchy":1658},[1667,52371,1680],{},[1656,52373,1673],{"separator":1672},[3316,52375],{"width":3318},[1715,52377,52378,52380,52382],{},[898,52379,1665],{},[898,52381,3403],{},[1656,52383,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,52385,1713],{},[3294,52387,52388,52390],{},[1667,52389,1669],{},[895,52391,52392,52394,52396],{},[898,52393,1745],{},[1656,52395,3964],{},[898,52397,207],{},[1656,52399,1673],{"separator":1672},[3316,52401],{"width":3318},[1715,52403,52404,52406,52408],{},[898,52405,1665],{},[898,52407,1745],{},[1656,52409,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,52411,1713],{},[1656,52413,3964],{},[3294,52415,52416,52424],{},[895,52417,52418,52420,52422],{},[898,52419,3403],{},[1656,52421,3964],{},[898,52423,3768],{},[895,52425,52426,52428,52430,52432,52434],{},[1656,52427,1659],{"stretchy":1658},[898,52429,1745],{},[1656,52431,3964],{},[898,52433,207],{},[2062,52435,52436,52438],{},[1656,52437,1683],{"stretchy":1658},[1667,52439,1680],{},[1656,52441,1673],{"separator":1672},[3316,52443],{"width":3318},[1715,52445,52446,52448,52450],{},[898,52447,1665],{},[898,52449,3768],{},[1656,52451,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,52453,1713],{},[1656,52455,3964],{},[3294,52457,52458,52460],{},[1667,52459,1669],{},[895,52461,52462,52464,52466],{},[898,52463,1745],{},[1656,52465,3964],{},[898,52467,207],{},[898,52469,1863],{"mathvariant":1723},[2419,52471],{"width":2421},[2419,52473,52474],{},[2461,52475,52476],{},"(2.12)",[902,52478,52479],{"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}",[198,52481,52483],{"id":52482},"znaménka-a-interpretace","Znaménka a interpretace",[724,52485,52486,52487,1343,52504,1343,52521,1343,52538,52555,52556,5642],{},"Za podmínek ",[883,52488,52490],{"className":52489},[886],[888,52491,52492],{"xmlns":890},[892,52493,52494,52502],{},[895,52495,52496,52498,52500],{},[898,52497,207],{},[1656,52499,4373],{},[1667,52501,4032],{},[902,52503,51762],{"encoding":904},[883,52505,52507],{"className":52506},[886],[888,52508,52509],{"xmlns":890},[892,52510,52511,52519],{},[895,52512,52513,52515,52517],{},[898,52514,3403],{},[1656,52516,2850],{},[1667,52518,4032],{},[902,52520,27536],{"encoding":904},[883,52522,52524],{"className":52523},[886],[888,52525,52526],{"xmlns":890},[892,52527,52528,52536],{},[895,52529,52530,52532,52534],{},[898,52531,1745],{},[1656,52533,2850],{},[1667,52535,4032],{},[902,52537,48940],{"encoding":904},[883,52539,52541],{"className":52540},[886],[888,52542,52543],{"xmlns":890},[892,52544,52545,52553],{},[895,52546,52547,52549,52551],{},[898,52548,3403],{},[1656,52550,2850],{},[898,52552,3768],{},[902,52554,51995],{"encoding":904}," platí (znaménka se ",[38,52557,52558],{},"nemění",[883,52560,52562],{"className":52561},[886],[888,52563,52564],{"xmlns":890,"display":2408},[892,52565,52566,52628],{},[895,52567,52568,52576,52578,52580,52582,52584,52592,52594,52596,52598,52600,52608,52610,52612,52614,52616,52624,52626],{},[1715,52569,52570,52572,52574],{},[898,52571,1665],{},[898,52573,207],{},[1656,52575,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,52577,2850],{},[1667,52579,4032],{},[1656,52581,1673],{"separator":1672},[3316,52583],{"width":14644},[1715,52585,52586,52588,52590],{},[898,52587,1665],{},[898,52589,3403],{},[1656,52591,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,52593,2850],{},[1667,52595,4032],{},[1656,52597,1673],{"separator":1672},[3316,52599],{"width":14644},[1715,52601,52602,52604,52606],{},[898,52603,1665],{},[898,52605,1745],{},[1656,52607,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,52609,4373],{},[1667,52611,4032],{},[1656,52613,1673],{"separator":1672},[3316,52615],{"width":14644},[1715,52617,52618,52620,52622],{},[898,52619,1665],{},[898,52621,3768],{},[1656,52623,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,52625,4373],{},[1667,52627,4283],{},[902,52629,52630],{"encoding":904},"Q'_a > 0, \\qquad Q'_b > 0, \\qquad Q'_c \u003C 0, \\qquad Q'_d \u003C 0.",[120,52632,52633,52692],{},[123,52634,52635,1643,52638,52658,52659,52676,52677,1343,52690,1863],{},[38,52636,52637],{},"Kvantitativní smysl:",[883,52639,52641],{"className":52640},[886],[888,52642,52643],{"xmlns":890},[892,52644,52645,52655],{},[895,52646,52647],{},[1715,52648,52649,52651,52653],{},[898,52650,1665],{},[898,52652,10848],{},[1656,52654,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[902,52656,52657],{"encoding":904},"Q'_x"," udává, o kolik přibližně vzroste ",[883,52660,52662],{"className":52661},[886],[888,52663,52664],{"xmlns":890},[892,52665,52666,52674],{},[895,52667,52668],{},[2062,52669,52670,52672],{},[898,52671,1665],{},[898,52673,1842],{},[902,52675,51080],{"encoding":904}," při jednotkové změně parametru ",[883,52678,52680],{"className":52679},[886],[888,52681,52682],{"xmlns":890},[892,52683,52684,52688],{},[895,52685,52686],{},[898,52687,10848],{},[902,52689,10848],{"encoding":904},[614,52691,45642],{},[123,52693,52694,52697,52698,52715,52716,1863],{},[38,52695,52696],{},"Kvalitativní smysl:"," znaménko určuje směr reakce ",[883,52699,52701],{"className":52700},[886],[888,52702,52703],{"xmlns":890},[892,52704,52705,52713],{},[895,52706,52707],{},[2062,52708,52709,52711],{},[898,52710,1665],{},[898,52712,1842],{},[902,52714,51080],{"encoding":904}," na růst ",[883,52717,52719],{"className":52718},[886],[888,52720,52721],{"xmlns":890},[892,52722,52723,52727],{},[895,52724,52725],{},[898,52726,10848],{},[902,52728,10848],{"encoding":904},[724,52730,52731,52732,52745,52746,51996,52763,12702],{},"Např. růst ",[883,52733,52735],{"className":52734},[886],[888,52736,52737],{"xmlns":890},[892,52738,52739,52743],{},[895,52740,52741],{},[898,52742,1745],{},[902,52744,1745],{"encoding":904}," (strmější nabídka) ⟹ pokles ",[883,52747,52749],{"className":52748},[886],[888,52750,52751],{"xmlns":890},[892,52752,52753,52761],{},[895,52754,52755],{},[2062,52756,52757,52759],{},[898,52758,1665],{},[898,52760,1842],{},[902,52762,51080],{"encoding":904},[883,52764,52766],{"className":52765},[886],[888,52767,52768],{"xmlns":890},[892,52769,52770,52784],{},[895,52771,52772,52780,52782],{},[1715,52773,52774,52776,52778],{},[898,52775,1665],{},[898,52777,1745],{},[1656,52779,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,52781,4373],{},[1667,52783,4032],{},[902,52785,52786],{"encoding":904},"Q'_c \u003C 0",[724,52788,52789],{},[614,52790,52791,52792,52812,52813,52837,52838,52860,52861,1863],{},"Obrázek 2.23: Pootočení přímky nabídky z ",[883,52793,52795],{"className":52794},[886],[888,52796,52797],{"xmlns":890},[892,52798,52799,52809],{},[895,52800,52801,52803,52805,52807],{},[898,52802,1745],{},[898,52804,1665],{},[1656,52806,3633],{},[898,52808,3768],{},[902,52810,52811],{"encoding":904},"cQ + d"," na strmější ",[883,52814,52816],{"className":52815},[886],[888,52817,52818],{"xmlns":890},[892,52819,52820,52834],{},[895,52821,52822,52828,52830,52832],{},[1661,52823,52824,52826],{},[898,52825,1745],{},[1667,52827,1669],{},[898,52829,1665],{},[1656,52831,3633],{},[898,52833,3768],{},[902,52835,52836],{"encoding":904},"c_1 Q + d"," (při ",[883,52839,52841],{"className":52840},[886],[888,52842,52843],{"xmlns":890},[892,52844,52845,52857],{},[895,52846,52847,52853,52855],{},[1661,52848,52849,52851],{},[898,52850,1745],{},[1667,52852,1669],{},[1656,52854,2850],{},[898,52856,1745],{},[902,52858,52859],{"encoding":904},"c_1 > c",") — rovnovážný bod se posouvá vlevo, ",[883,52862,52864],{"className":52863},[886],[888,52865,52866],{"xmlns":890},[892,52867,52868,52878],{},[895,52869,52870,52876],{},[2062,52871,52872,52874],{},[898,52873,1665],{},[898,52875,1842],{},[1656,52877,51268],{},[902,52879,52880],{"encoding":904},"Q^E \\downarrow",[724,52882,52883,52884,52916,52917,1863],{},"Při změně jediné proměnné se (2.11) redukuje např. na ",[883,52885,52887],{"className":52886},[886],[888,52888,52889],{"xmlns":890},[892,52890,52891,52913],{},[895,52892,52893,52895,52897,52899,52907,52909,52911],{},[898,52894,3750],{"mathvariant":1723},[898,52896,1665],{},[1656,52898,3815],{},[1715,52900,52901,52903,52905],{},[898,52902,1665],{},[898,52904,3403],{},[1656,52906,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[2461,52908,7828],{},[898,52910,3768],{},[898,52912,3403],{},[902,52914,52915],{"encoding":904},"\\Delta Q \\approx Q'_b\\,db",". Analogicky lze odvodit multiplikátory pro ",[883,52918,52920],{"className":52919},[886],[888,52921,52922],{"xmlns":890},[892,52923,52924,52932],{},[895,52925,52926],{},[2062,52927,52928,52930],{},[898,52929,8194],{},[898,52931,1842],{},[902,52933,50146],{"encoding":904},[198,52935,52937,52938],{"id":52936},"příklad-211-komparativní-statika-pro-qeqe","Příklad 2.11 — komparativní statika pro ",[883,52939,52941],{"className":52940},[886],[888,52942,52943],{"xmlns":890},[892,52944,52945,52953],{},[895,52946,52947],{},[2062,52948,52949,52951],{},[898,52950,1665],{},[898,52952,1842],{},[902,52954,51080],{"encoding":904},[724,52956,52957,50335,52959,50370,52985,1863],{},[38,52958,46615],{},[883,52960,52962],{"className":52961},[886],[888,52963,52964],{"xmlns":890},[892,52965,52966,52982],{},[895,52967,52968,52970,52972,52974,52976,52978,52980],{},[898,52969,8194],{},[1656,52971,1713],{},[1656,52973,3964],{},[1667,52975,2617],{},[898,52977,1665],{},[1656,52979,3633],{},[1667,52981,9135],{},[902,52983,52984],{"encoding":904},"P = -3Q + 40",[883,52986,52988],{"className":52987},[886],[888,52989,52990],{"xmlns":890},[892,52991,52992,53006],{},[895,52993,52994,52996,52998,53000,53002,53004],{},[898,52995,8194],{},[1656,52997,1713],{},[1667,52999,13779],{},[898,53001,1665],{},[1656,53003,3633],{},[1667,53005,8580],{},[902,53007,53008],{"encoding":904},"P = 0{,}5Q + 10",[724,53010,53011,53013],{},[38,53012,46647],{}," Rovnovážné množství",[883,53015,53017],{"className":53016},[886],[888,53018,53019],{"xmlns":890,"display":2408},[892,53020,53021,53089],{},[895,53022,53023,53029,53031,53049,53051,53075,53077,53084,53086],{},[2062,53024,53025,53027],{},[898,53026,1665],{},[898,53028,1842],{},[1656,53030,1713],{},[3294,53032,53033,53041],{},[895,53034,53035,53037,53039],{},[898,53036,3403],{},[1656,53038,3964],{},[898,53040,3768],{},[895,53042,53043,53045,53047],{},[898,53044,1745],{},[1656,53046,3964],{},[898,53048,207],{},[1656,53050,1713],{},[3294,53052,53053,53061],{},[895,53054,53055,53057,53059],{},[1667,53056,9135],{},[1656,53058,3964],{},[1667,53060,8580],{},[895,53062,53063,53065,53067,53069,53071,53073],{},[1667,53064,13779],{},[1656,53066,3964],{},[1656,53068,1659],{"stretchy":1658},[1656,53070,3964],{},[1667,53072,2617],{},[1656,53074,1683],{"stretchy":1658},[1656,53076,1713],{},[3294,53078,53079,53081],{},[1667,53080,46701],{},[1667,53082,53083],{},"3,5",[1656,53085,3815],{},[1667,53087,53088],{},"8,571.",[902,53090,53091],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\approx 8{,}571.",[724,53093,53094,53139],{},[38,53095,53096,53097,3605,53110,3619,53124,53138],{},"(a) Změna ",[883,53098,53100],{"className":53099},[886],[888,53101,53102],{"xmlns":890},[892,53103,53104,53108],{},[895,53105,53106],{},[898,53107,1745],{},[902,53109,1745],{"encoding":904},[883,53111,53113],{"className":53112},[886],[888,53114,53115],{"xmlns":890},[892,53116,53117,53121],{},[895,53118,53119],{},[1667,53120,13779],{},[902,53122,53123],{"encoding":904},"0{,}5",[883,53125,53127],{"className":53126},[886],[888,53128,53129],{"xmlns":890},[892,53130,53131,53135],{},[895,53132,53133],{},[1667,53134,28042],{},[902,53136,53137],{"encoding":904},"0{,}6"," (ceteris paribus)."," Dle (2.12):",[883,53141,53143],{"className":53142},[886],[888,53144,53145],{"xmlns":890,"display":2408},[892,53146,53147,53224],{},[895,53148,53149,53157,53159,53161,53163,53165,53167,53193,53195,53197,53199,53201,53203,53213,53215,53217,53219,53221],{},[1715,53150,53151,53153,53155],{},[898,53152,1665],{},[898,53154,1745],{},[1656,53156,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[2461,53158,7828],{},[898,53160,3768],{},[898,53162,1745],{},[1656,53164,1713],{},[1656,53166,3964],{},[3294,53168,53169,53177],{},[895,53170,53171,53173,53175],{},[898,53172,3403],{},[1656,53174,3964],{},[898,53176,3768],{},[895,53178,53179,53181,53183,53185,53187],{},[1656,53180,1659],{"stretchy":1658},[898,53182,1745],{},[1656,53184,3964],{},[898,53186,207],{},[2062,53188,53189,53191],{},[1656,53190,1683],{"stretchy":1658},[1667,53192,1680],{},[2461,53194,7828],{},[898,53196,3768],{},[898,53198,1745],{},[1656,53200,1713],{},[1656,53202,3964],{},[3294,53204,53205,53207],{},[1667,53206,46701],{},[2062,53208,53209,53211],{},[1667,53210,53083],{},[1667,53212,1680],{},[1656,53214,2751],{},[1667,53216,11595],{},[1656,53218,3815],{},[1656,53220,3964],{},[1667,53222,53223],{},"0,245.",[902,53225,53226],{"encoding":904},"Q'_c\\,dc = -\\frac{b - d}{(c - a)^2}\\,dc = -\\frac{30}{3{,}5^2}\\cdot 0{,}1 \\approx -0{,}245.",[724,53228,53229,53230,1863],{},"Nové rovnovážné množství ",[883,53231,53233],{"className":53232},[886],[888,53234,53235],{"xmlns":890},[892,53236,53237,53262],{},[895,53238,53239,53247,53249,53252,53254,53257,53259],{},[1715,53240,53241,53243,53245],{},[898,53242,1665],{},[1667,53244,1669],{},[898,53246,1842],{},[1656,53248,3815],{},[1667,53250,53251],{},"8,571",[1656,53253,3964],{},[1667,53255,53256],{},"0,245",[1656,53258,1713],{},[1667,53260,53261],{},"8,326",[902,53263,53264],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326",[724,53266,53267,53352],{},[38,53268,53269,53270,1343,53290,1343,53312,1343,53332,1863],{},"(b) Současné změny ",[883,53271,53273],{"className":53272},[886],[888,53274,53275],{"xmlns":890},[892,53276,53277,53287],{},[895,53278,53279,53281,53283,53285],{},[898,53280,3768],{},[898,53282,207],{},[1656,53284,1713],{},[1667,53286,13779],{},[902,53288,53289],{"encoding":904},"da = 0{,}5",[883,53291,53293],{"className":53292},[886],[888,53294,53295],{"xmlns":890},[892,53296,53297,53309],{},[895,53298,53299,53301,53303,53305,53307],{},[898,53300,3768],{},[898,53302,3403],{},[1656,53304,1713],{},[1656,53306,3964],{},[1667,53308,5193],{},[902,53310,53311],{"encoding":904},"db = -5",[883,53313,53315],{"className":53314},[886],[888,53316,53317],{"xmlns":890},[892,53318,53319,53329],{},[895,53320,53321,53323,53325,53327],{},[898,53322,3768],{},[898,53324,1745],{},[1656,53326,1713],{},[1667,53328,11595],{},[902,53330,53331],{"encoding":904},"dc = 0{,}1",[883,53333,53335],{"className":53334},[886],[888,53336,53337],{"xmlns":890},[892,53338,53339,53349],{},[895,53340,53341,53343,53345,53347],{},[898,53342,3768],{},[898,53344,3768],{},[1656,53346,1713],{},[1667,53348,1669],{},[902,53350,53351],{"encoding":904},"dd = 1"," Dosazením do (2.11):",[883,53354,53356],{"className":53355},[886],[888,53357,53358],{"xmlns":890,"display":2408},[892,53359,53360,53503],{},[2412,53361,53362,53444,53480],{"rowspacing":29476,"columnalign":29477,"columnspacing":1724},[2416,53363,53364,53374],{},[2419,53365,53366],{},[4138,53367,53368],{"scriptlevel":4032,"displaystyle":1672},[895,53369,53370,53372],{},[898,53371,3750],{"mathvariant":1723},[898,53373,1665],{},[2419,53375,53376],{},[4138,53377,53378],{"scriptlevel":4032,"displaystyle":1672},[895,53379,53380,53382,53384,53394,53396,53398,53400,53406,53408,53410,53412,53414,53416,53418,53428,53430,53432,53434,53440,53442],{},[895,53381],{},[1656,53383,3815],{},[3294,53385,53386,53388],{},[1667,53387,46701],{},[2062,53389,53390,53392],{},[1667,53391,53083],{},[1667,53393,1680],{},[1656,53395,2751],{},[1667,53397,13779],{},[1656,53399,3633],{},[3294,53401,53402,53404],{},[1667,53403,1669],{},[1667,53405,53083],{},[1656,53407,2751],{},[1656,53409,1659],{"stretchy":1658},[1656,53411,3964],{},[1667,53413,5193],{},[1656,53415,1683],{"stretchy":1658},[1656,53417,3964],{},[3294,53419,53420,53422],{},[1667,53421,46701],{},[2062,53423,53424,53426],{},[1667,53425,53083],{},[1667,53427,1680],{},[1656,53429,2751],{},[1667,53431,11595],{},[1656,53433,3964],{},[3294,53435,53436,53438],{},[1667,53437,1669],{},[1667,53439,53083],{},[1656,53441,2751],{},[1667,53443,1669],{},[2416,53445,53446,53452],{},[2419,53447,53448],{},[4138,53449,53450],{"scriptlevel":4032,"displaystyle":1672},[895,53451],{},[2419,53453,53454],{},[4138,53455,53456],{"scriptlevel":4032,"displaystyle":1672},[895,53457,53458,53460,53462,53465,53467,53470,53472,53475,53477],{},[895,53459],{},[1656,53461,1713],{},[1667,53463,53464],{},"1,2245",[1656,53466,3964],{},[1667,53468,53469],{},"1,4286",[1656,53471,3964],{},[1667,53473,53474],{},"0,2449",[1656,53476,3964],{},[1667,53478,53479],{},"0,2857",[2416,53481,53482,53488],{},[2419,53483,53484],{},[4138,53485,53486],{"scriptlevel":4032,"displaystyle":1672},[895,53487],{},[2419,53489,53490],{},[4138,53491,53492],{"scriptlevel":4032,"displaystyle":1672},[895,53493,53494,53496,53498,53500],{},[895,53495],{},[1656,53497,3815],{},[1656,53499,3964],{},[1667,53501,53502],{},"0,735.",[902,53504,53505],{"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}",[724,53507,8038,53508,1863],{},[883,53509,53511],{"className":53510},[886],[888,53512,53513],{"xmlns":890},[892,53514,53515,53539],{},[895,53516,53517,53525,53527,53529,53531,53534,53536],{},[1715,53518,53519,53521,53523],{},[898,53520,1665],{},[1667,53522,1669],{},[898,53524,1842],{},[1656,53526,3815],{},[1667,53528,53251],{},[1656,53530,3964],{},[1667,53532,53533],{},"0,735",[1656,53535,1713],{},[1667,53537,53538],{},"7,836",[902,53540,53541],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 = 7{,}836",[1981,53543,53544],{},[724,53545,53546,53548,53549,53572,53573,53595],{},[883,53547,1987],{}," Pozn. — oprava\nV knize je u této dílčí úlohy uvedena hodnota ",[883,53550,53552],{"className":53551},[886],[888,53553,53554],{"xmlns":890},[892,53555,53556,53569],{},[895,53557,53558,53560,53562,53564,53566],{},[898,53559,3750],{"mathvariant":1723},[898,53561,1665],{},[1656,53563,3815],{},[1656,53565,3964],{},[1667,53567,53568],{},"2,69",[902,53570,53571],{"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 ",[883,53574,53576],{"className":53575},[886],[888,53577,53578],{"xmlns":890},[892,53579,53580,53592],{},[895,53581,53582,53584,53586,53588,53590],{},[898,53583,3750],{"mathvariant":1723},[898,53585,1665],{},[1656,53587,3815],{},[1656,53589,3964],{},[1667,53591,53533],{},[902,53593,53594],{"encoding":904},"\\Delta Q \\approx -0{,}735",". Výsledek byl v této wiki opraven.",[724,53597,53598],{},"Princip multiplikátorů lze uplatnit na libovolné ekonomické proměnné — analogicky v makroekonomii (kap. 7).",[45652,53600],{},[115,53602,820],{"id":20521},[1981,53604,53605],{},[724,53606,53607,12658,53609,3247,53612,20863,53628,3247,53631,53647,53648,1863],{},[883,53608,3472],{},[38,53610,53611],{},"Přebytek spotřebitele",[883,53613,53615],{"className":53614},[886],[888,53616,53617],{"xmlns":890},[892,53618,53619,53625],{},[895,53620,53621,53623],{},[898,53622,1766],{},[898,53624,1769],{},[902,53626,53627],{"encoding":904},"CS",[38,53629,53630],{},"přebytek výrobce",[883,53632,53634],{"className":53633},[886],[888,53635,53636],{"xmlns":890},[892,53637,53638,53644],{},[895,53639,53640,53642],{},[898,53641,8194],{},[898,53643,1769],{},[902,53645,53646],{"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 ",[207,53649,53651],{"className":53650,"dataFsResolvedFilePath":818,"href":819},[210],"prebytek-spotrebitele-vyrobce",[724,53653,53654],{},[5956,53655],{"alt":53656,"className":53657,"src":53658},"imek-prebytky-cs-ps",[210,5960],"\u002Fwiki-assets\u002Fimek-prebytky-cs-ps.jpeg",[724,53660,53661,3247,53663,53666],{},[38,53662,53611],{},[614,53664,53665],{},"consumer surplus",") — rozdíl mezi ochotou platit a skutečnou platbou:",[883,53668,53670],{"className":53669},[886],[888,53671,53672],{"xmlns":890,"display":2408},[892,53673,53674,53751],{},[2412,53675,53676],{"width":2414},[2416,53677,53678,53680,53744,53746],{},[2419,53679],{"width":2421},[2419,53681,53682],{},[895,53683,53684,53686,53688,53690,53696,53698,53700,53712,53714,53716,53718,53720,53722,53724,53726,53728,53734,53736,53742],{},[898,53685,1766],{},[898,53687,1769],{},[1656,53689,1659],{"stretchy":1658},[1661,53691,53692,53694],{},[898,53693,1665],{},[1667,53695,4032],{},[1656,53697,1683],{"stretchy":1658},[1656,53699,1713],{},[1715,53701,53702,53704,53706],{},[1656,53703,19906],{},[1667,53705,4032],{},[1661,53707,53708,53710],{},[898,53709,1665],{},[1667,53711,4032],{},[898,53713,6787],{},[1656,53715,1659],{"stretchy":1658},[898,53717,1665],{},[1656,53719,1683],{"stretchy":1658},[2461,53721,7828],{},[898,53723,3768],{},[898,53725,1665],{},[1656,53727,3964],{},[1661,53729,53730,53732],{},[898,53731,8194],{},[1667,53733,4032],{},[2461,53735,7828],{},[1661,53737,53738,53740],{},[898,53739,1665],{},[1667,53741,4032],{},[898,53743,1863],{"mathvariant":1723},[2419,53745],{"width":2421},[2419,53747,53748],{},[2461,53749,53750],{},"(2.14)",[902,53752,53753],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\,dQ - P_0\\,Q_0. \\tag{2.14}",[724,53755,53756,3247,53759,53762],{},[38,53757,53758],{},"Přebytek výrobce",[614,53760,53761],{},"producer surplus",") — rozdíl mezi tržbou a minimální cenou:",[883,53764,53766],{"className":53765},[886],[888,53767,53768],{"xmlns":890,"display":2408},[892,53769,53770,53847],{},[2412,53771,53772],{"width":2414},[2416,53773,53774,53776,53840,53842],{},[2419,53775],{"width":2421},[2419,53777,53778],{},[895,53779,53780,53782,53784,53786,53792,53794,53796,53802,53804,53810,53812,53824,53826,53828,53830,53832,53834,53836,53838],{},[898,53781,8194],{},[898,53783,1769],{},[1656,53785,1659],{"stretchy":1658},[1661,53787,53788,53790],{},[898,53789,1665],{},[1667,53791,4032],{},[1656,53793,1683],{"stretchy":1658},[1656,53795,1713],{},[1661,53797,53798,53800],{},[898,53799,8194],{},[1667,53801,4032],{},[2461,53803,7828],{},[1661,53805,53806,53808],{},[898,53807,1665],{},[1667,53809,4032],{},[1656,53811,3964],{},[1715,53813,53814,53816,53818],{},[1656,53815,19906],{},[1667,53817,4032],{},[1661,53819,53820,53822],{},[898,53821,1665],{},[1667,53823,4032],{},[898,53825,1769],{},[1656,53827,1659],{"stretchy":1658},[898,53829,1665],{},[1656,53831,1683],{"stretchy":1658},[2461,53833,7828],{},[898,53835,3768],{},[898,53837,1665],{},[898,53839,1863],{"mathvariant":1723},[2419,53841],{"width":2421},[2419,53843,53844],{},[2461,53845,53846],{},"(2.15)",[902,53848,53849],{"encoding":904},"PS(Q_0) = P_0\\,Q_0 - \\int_0^{Q_0} S(Q)\\,dQ. \\tag{2.15}",[724,53851,53852,53853,1863],{},"Geometricky jde o plochy mezi rovnovážnou cenou a příslušnou křivkou; výpočet využívá aparát ",[207,53854,53856],{"className":53855,"dataFsResolvedFilePath":773,"href":774},[210],"určitého integrálu",[45652,53858],{},[115,53860,53862],{"id":53861},"příklady-z-knihy-přehled","Příklady z knihy — přehled",[120,53864,53865,53896,53901,53907,53935,53941,53970,53976,54056,54082],{},[123,53866,53867,53869,53870,53895],{},[38,53868,46610],{}," — lineární poptávka ",[883,53871,53873],{"className":53872},[886],[888,53874,53875],{"xmlns":890},[892,53876,53877,53893],{},[895,53878,53879,53881,53883,53885,53887,53889,53891],{},[898,53880,8194],{},[1656,53882,1713],{},[1656,53884,3964],{},[1667,53886,1680],{},[898,53888,1665],{},[1656,53890,3633],{},[1667,53892,11918],{},[902,53894,46642],{"encoding":904},", alternativní tvar, cenové rozpětí.",[123,53897,53898,53900],{},[38,53899,46924],{}," — empirické křivky poptávky po cukru (rodina vs. trh).",[123,53902,53903,53906],{},[38,53904,53905],{},"Příklad 2.3"," — posun poptávky při zdanění kupujícího.",[123,53908,53909,53911,53912,1863],{},[38,53910,49469],{}," — lineární nabídka ",[883,53913,53915],{"className":53914},[886],[888,53916,53917],{"xmlns":890},[892,53918,53919,53933],{},[895,53920,53921,53923,53925,53927,53929,53931],{},[898,53922,8194],{},[1656,53924,1713],{},[1667,53926,13779],{},[898,53928,1665],{},[1656,53930,3633],{},[1667,53932,8567],{},[902,53934,49498],{"encoding":904},[123,53936,53937,53940],{},[38,53938,53939],{},"Příklad 2.6"," — posun nabídky při zdanění výrobce.",[123,53942,53943,53946,53947,1863],{},[38,53944,53945],{},"Příklad 2.7"," — kvadratická rovnováha, ",[883,53948,53950],{"className":53949},[886],[888,53951,53952],{"xmlns":890},[892,53953,53954,53968],{},[895,53955,53956,53958,53960,53962,53964,53966],{},[898,53957,1842],{},[1656,53959,3453],{"stretchy":1658},[1667,53961,2673],{},[1656,53963,1673],{"separator":1672},[1667,53965,50613],{},[1656,53967,3462],{"stretchy":1658},[902,53969,50641],{"encoding":904},[123,53971,53972,53975],{},[38,53973,53974],{},"Příklad 2.8"," — dvoukomoditní trh, soustava rovnic, komplementy.",[123,53977,53978,53981,53982,53999,54000,1343,54025,54052,54053,11746],{},[38,53979,53980],{},"Příklad 2.9"," — daň ",[883,53983,53985],{"className":53984},[886],[888,53986,53987],{"xmlns":890},[892,53988,53989,53997],{},[895,53990,53991,53993,53995],{},[898,53992,11577],{},[1656,53994,1713],{},[1667,53996,9112],{},[902,53998,49948],{"encoding":904}," na výrobce; rozklad ",[883,54001,54003],{"className":54002},[886],[888,54004,54005],{"xmlns":890},[892,54006,54007,54023],{},[895,54008,54009,54019,54021],{},[1661,54010,54011,54013],{},[898,54012,11577],{},[895,54014,54015,54017],{},[898,54016,51354],{},[898,54018,724],{},[1656,54020,1713],{},[1667,54022,1680],{},[902,54024,51653],{"encoding":904},[883,54026,54028],{"className":54027},[886],[888,54029,54030],{"xmlns":890},[892,54031,54032,54050],{},[895,54033,54034,54046,54048],{},[1661,54035,54036,54038],{},[898,54037,11577],{},[895,54039,54040,54042,54044],{},[898,54041,51377],{},[898,54043,10839],{},[898,54045,20776],{},[1656,54047,1713],{},[1667,54049,2673],{},[902,54051,51682],{"encoding":904},". (Viz ",[207,54054,51398],{"className":54055,"dataFsResolvedFilePath":809,"href":810},[210],[123,54057,54058,53981,54061,54078,54079,11746],{},[38,54059,54060],{},"Příklad 2.10",[883,54062,54064],{"className":54063},[886],[888,54065,54066],{"xmlns":890},[892,54067,54068,54076],{},[895,54069,54070,54072,54074],{},[898,54071,11577],{},[1656,54073,1713],{},[1667,54075,9112],{},[902,54077,49948],{"encoding":904}," na spotřebitele; stejné čisté ceny i množství. (Viz ",[207,54080,51398],{"className":54081,"dataFsResolvedFilePath":809,"href":810},[210],[123,54083,54084,54087],{},[38,54085,54086],{},"Příklad 2.11"," — komparativní statika, multiplikátory, změny parametrů.",[45652,54089],{},[115,54091,54093],{"id":54092},"úlohy-k-samostatnému-řešení","Úlohy k samostatnému řešení",[198,54095,54097],{"id":54096},"základní-analýza-poptávky","Základní analýza poptávky",[724,54099,54100,54103,54104,54139,54140,54166],{},[38,54101,54102],{},"2.1"," Je dána poptávka ",[883,54105,54107],{"className":54106},[886],[888,54108,54109],{"xmlns":890},[892,54110,54111,54136],{},[895,54112,54113,54115,54117,54119,54121,54123,54125,54127,54130,54132,54134],{},[898,54114,1665],{},[1656,54116,1713],{},[898,54118,6787],{},[1656,54120,1659],{"stretchy":1658},[898,54122,8194],{},[1656,54124,1683],{"stretchy":1658},[1656,54126,1713],{},[1667,54128,54129],{},"75",[1656,54131,3964],{},[1667,54133,5193],{},[898,54135,8194],{},[902,54137,54138],{"encoding":904},"Q = D(P) = 75 - 5P",". (a) Načrtněte křivku poptávky. (b) Stanovte reálné cenové rozpětí. (c) Vypočtěte množství při cenách ",[883,54141,54143],{"className":54142},[886],[888,54144,54145],{"xmlns":890},[892,54146,54147,54163],{},[895,54148,54149,54151,54153,54155,54157,54159,54161],{},[1667,54150,4032],{},[1656,54152,1673],{"separator":1672},[1667,54154,5193],{},[1656,54156,1673],{"separator":1672},[1667,54158,8580],{},[1656,54160,1673],{"separator":1672},[1667,54162,44930],{},[902,54164,54165],{"encoding":904},"0, 5, 10, 15"," a výsledky vyznačte na křivku poptávky.",[724,54168,54169,54172,54173,54191,54192,5642],{},[38,54170,54171],{},"2.2"," Ověřte, že uvedené funkce vyjadřují (s případným omezením pro ",[883,54174,54176],{"className":54175},[886],[888,54177,54178],{"xmlns":890},[892,54179,54180,54188],{},[895,54181,54182,54184,54186],{},[898,54183,8194],{},[1656,54185,1673],{"separator":1672},[898,54187,1665],{},[902,54189,54190],{"encoding":904},"P, Q",") poptávku (využijte testu na zápornost derivace), charakterizujte tvar křivky poptávky a vyjádřete ve tvaru poptávky v alternativním tvaru (",[883,54193,54195],{"className":54194},[886],[888,54196,54197],{"xmlns":890},[892,54198,54199,54215],{},[895,54200,54201,54203,54205,54207,54209,54211,54213],{},[898,54202,207],{},[1656,54204,1673],{"separator":1672},[898,54206,3403],{},[1656,54208,1673],{"separator":1672},[898,54210,1745],{},[1656,54212,2850],{},[1667,54214,4032],{},[902,54216,54217],{"encoding":904},"a, b, c > 0",[120,54219,54220,54253,54284,54319,54350,54385],{},[123,54221,54222,54223],{},"(a) ",[883,54224,54226],{"className":54225},[886],[888,54227,54228],{"xmlns":890},[892,54229,54230,54250],{},[895,54231,54232,54234,54236],{},[898,54233,1665],{},[1656,54235,1713],{},[4138,54237,54238],{"scriptlevel":4032,"displaystyle":1672},[3294,54239,54240,54242],{},[898,54241,207],{},[895,54243,54244,54246,54248],{},[898,54245,8194],{},[1656,54247,3633],{},[898,54249,1745],{},[902,54251,54252],{"encoding":904},"Q = \\dfrac{a}{P + c}",[123,54254,54255,54256],{},"(b) ",[883,54257,54259],{"className":54258},[886],[888,54260,54261],{"xmlns":890},[892,54262,54263,54281],{},[895,54264,54265,54267,54269],{},[898,54266,1665],{},[1656,54268,1713],{},[2625,54270,54271],{},[895,54272,54273,54275,54277,54279],{},[898,54274,207],{},[1656,54276,3964],{},[898,54278,3403],{},[898,54280,1665],{},[902,54282,54283],{"encoding":904},"Q = \\sqrt{a - bQ}",[123,54285,54286,54287],{},"(c) ",[883,54288,54290],{"className":54289},[886],[888,54291,54292],{"xmlns":890},[892,54293,54294,54316],{},[895,54295,54296,54298,54300],{},[898,54297,1665],{},[1656,54299,1713],{},[4138,54301,54302],{"scriptlevel":4032,"displaystyle":1672},[3294,54303,54304,54314],{},[895,54305,54306,54308,54310],{},[898,54307,207],{},[1656,54309,3964],{},[2625,54311,54312],{},[898,54313,8194],{},[898,54315,3403],{},[902,54317,54318],{"encoding":904},"Q = \\dfrac{a - \\sqrt{P}}{b}",[123,54320,54321,54322],{},"(d) ",[883,54323,54325],{"className":54324},[886],[888,54326,54327],{"xmlns":890},[892,54328,54329,54347],{},[895,54330,54331,54333,54335,54337,54339,54341],{},[898,54332,8194],{},[1656,54334,1713],{},[898,54336,207],{},[1656,54338,3964],{},[898,54340,3403],{},[2062,54342,54343,54345],{},[898,54344,1665],{},[1667,54346,1680],{},[902,54348,54349],{"encoding":904},"P = a - bQ^2",[123,54351,54352,54353],{},"(e) ",[883,54354,54356],{"className":54355},[886],[888,54357,54358],{"xmlns":890},[892,54359,54360,54382],{},[895,54361,54362,54364,54366,54368,54378,54380],{},[898,54363,1665],{},[1656,54365,1713],{},[898,54367,3403],{},[2062,54369,54370,54372],{},[898,54371,8194],{},[895,54373,54374,54376],{},[1656,54375,3964],{},[898,54377,207],{},[1656,54379,3633],{},[898,54381,1745],{},[902,54383,54384],{"encoding":904},"Q = bP^{-a} + c",[123,54386,54387,54388],{},"(f) ",[883,54389,54391],{"className":54390},[886],[888,54392,54393],{"xmlns":890},[892,54394,54395,54418],{},[895,54396,54397,54399,54401,54403,54405],{},[898,54398,1665],{},[1656,54400,1713],{},[898,54402,207],{},[1656,54404,2751],{},[2062,54406,54407,54410],{},[898,54408,54409],{},"e",[895,54411,54412,54414,54416],{},[1656,54413,3964],{},[898,54415,3403],{},[898,54417,8194],{},[902,54419,54420],{"encoding":904},"Q = a \\cdot e^{-bP}",[724,54422,54423,54426],{},[38,54424,54425],{},"2.3"," Rozhodněte, jak se změní křivka poptávky, jestliže se zvýší (ceteris paribus):",[120,54428,54429,54432,54435],{},[123,54430,54431],{},"(a) Cena substitutu.",[123,54433,54434],{},"(b) Cena komplementu.",[123,54436,54437],{},"(c) Výdaje na reklamu.",[724,54439,54440,54103,54442,54476,54477,54505],{},[38,54441,33358],{},[883,54443,54445],{"className":54444},[886],[888,54446,54447],{"xmlns":890},[892,54448,54449,54473],{},[895,54450,54451,54453,54455,54457,54459,54461,54463,54465,54467,54469,54471],{},[898,54452,8194],{},[1656,54454,1713],{},[898,54456,6787],{},[1656,54458,1659],{"stretchy":1658},[898,54460,1665],{},[1656,54462,1683],{"stretchy":1658},[1656,54464,1713],{},[1667,54466,9140],{},[1656,54468,3964],{},[1667,54470,1680],{},[898,54472,1665],{},[902,54474,54475],{"encoding":904},"P = D(Q) = 12 - 2Q",". Najděte novou poptávku ",[883,54478,54480],{"className":54479},[886],[888,54481,54482],{"xmlns":890},[892,54483,54484,54502],{},[895,54485,54486,54488,54490,54496,54498,54500],{},[898,54487,8194],{},[1656,54489,1713],{},[2062,54491,54492,54494],{},[898,54493,6787],{},[1656,54495,8187],{},[1656,54497,1659],{"stretchy":1658},[898,54499,1665],{},[1656,54501,1683],{"stretchy":1658},[902,54503,54504],{"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.",[724,54507,54508,54511],{},[38,54509,54510],{},"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:",[120,54513,54514,54598,54674,54760,54848],{},[123,54515,54222,54516,1343,54556,1863],{},[883,54517,54519],{"className":54518},[886],[888,54520,54521],{"xmlns":890},[892,54522,54523,54553],{},[895,54524,54525,54531,54533,54535,54537,54539,54545,54547],{},[1661,54526,54527,54529],{},[898,54528,2161],{},[1667,54530,1669],{},[1656,54532,1713],{},[1667,54534,9058],{},[1656,54536,3964],{},[1667,54538,2673],{},[1661,54540,54541,54543],{},[898,54542,2146],{},[1667,54544,1669],{},[1656,54546,3633],{},[1661,54548,54549,54551],{},[898,54550,2146],{},[1667,54552,1680],{},[902,54554,54555],{"encoding":904},"B_1 = 20 - 4A_1 + A_2",[883,54557,54559],{"className":54558},[886],[888,54560,54561],{"xmlns":890},[892,54562,54563,54595],{},[895,54564,54565,54571,54573,54575,54577,54579,54585,54587,54589],{},[1661,54566,54567,54569],{},[898,54568,2161],{},[1667,54570,1680],{},[1656,54572,1713],{},[1667,54574,8580],{},[1656,54576,3633],{},[1667,54578,1680],{},[1661,54580,54581,54583],{},[898,54582,2146],{},[1667,54584,1669],{},[1656,54586,3964],{},[1667,54588,2673],{},[1661,54590,54591,54593],{},[898,54592,2146],{},[1667,54594,1680],{},[902,54596,54597],{"encoding":904},"B_2 = 10 + 2A_1 - 4A_2",[123,54599,54255,54600,1343,54642,1863],{},[883,54601,54603],{"className":54602},[886],[888,54604,54605],{"xmlns":890},[892,54606,54607,54639],{},[895,54608,54609,54615,54617,54619,54621,54623,54629,54631,54633],{},[1661,54610,54611,54613],{},[898,54612,2161],{},[1667,54614,1669],{},[1656,54616,1713],{},[1667,54618,9267],{},[1656,54620,3964],{},[1667,54622,8580],{},[1661,54624,54625,54627],{},[898,54626,2146],{},[1667,54628,1669],{},[1656,54630,3964],{},[1667,54632,9112],{},[1661,54634,54635,54637],{},[898,54636,2146],{},[1667,54638,1680],{},[902,54640,54641],{"encoding":904},"B_1 = 50 - 10A_1 - 6A_2",[883,54643,54645],{"className":54644},[886],[888,54646,54647],{"xmlns":890},[892,54648,54649,54671],{},[895,54650,54651,54657,54659,54661,54663,54665],{},[1661,54652,54653,54655],{},[898,54654,2161],{},[1667,54656,1680],{},[1656,54658,1713],{},[1667,54660,44930],{},[1656,54662,3964],{},[1667,54664,8580],{},[1661,54666,54667,54669],{},[898,54668,2146],{},[1667,54670,1680],{},[902,54672,54673],{"encoding":904},"B_2 = 15 - 10A_2",[123,54675,54286,54676,1343,54718,1863],{},[883,54677,54679],{"className":54678},[886],[888,54680,54681],{"xmlns":890},[892,54682,54683,54715],{},[895,54684,54685,54691,54693,54695,54697,54699,54705,54707,54709],{},[1661,54686,54687,54689],{},[898,54688,2161],{},[1667,54690,1669],{},[1656,54692,1713],{},[1667,54694,46701],{},[1656,54696,3964],{},[1667,54698,1680],{},[1661,54700,54701,54703],{},[898,54702,2146],{},[1667,54704,1669],{},[1656,54706,3964],{},[1667,54708,2673],{},[1661,54710,54711,54713],{},[898,54712,2146],{},[1667,54714,1680],{},[902,54716,54717],{"encoding":904},"B_1 = 30 - 2A_1 - 4A_2",[883,54719,54721],{"className":54720},[886],[888,54722,54723],{"xmlns":890},[892,54724,54725,54757],{},[895,54726,54727,54733,54735,54737,54739,54741,54747,54749,54751],{},[1661,54728,54729,54731],{},[898,54730,2161],{},[1667,54732,1680],{},[1656,54734,1713],{},[1667,54736,44930],{},[1656,54738,3633],{},[1667,54740,1680],{},[1661,54742,54743,54745],{},[898,54744,2146],{},[1667,54746,1669],{},[1656,54748,3964],{},[1667,54750,1680],{},[1661,54752,54753,54755],{},[898,54754,2146],{},[1667,54756,1680],{},[902,54758,54759],{"encoding":904},"B_2 = 15 + 2A_1 - 2A_2",[123,54761,54321,54762,1343,54806,1863],{},[883,54763,54765],{"className":54764},[886],[888,54766,54767],{"xmlns":890},[892,54768,54769,54803],{},[895,54770,54771,54777,54779,54781,54783,54785,54787,54793,54795,54797],{},[1661,54772,54773,54775],{},[898,54774,2161],{},[1667,54776,1669],{},[1656,54778,1713],{},[1656,54780,3964],{},[1667,54782,9058],{},[1656,54784,3964],{},[1667,54786,1680],{},[1661,54788,54789,54791],{},[898,54790,2146],{},[1667,54792,1669],{},[1656,54794,3633],{},[1667,54796,2617],{},[1661,54798,54799,54801],{},[898,54800,2146],{},[1667,54802,1680],{},[902,54804,54805],{"encoding":904},"B_1 = -20 - 2A_1 + 3A_2",[883,54807,54809],{"className":54808},[886],[888,54810,54811],{"xmlns":890},[892,54812,54813,54845],{},[895,54814,54815,54821,54823,54825,54827,54829,54835,54837,54839],{},[1661,54816,54817,54819],{},[898,54818,2161],{},[1667,54820,1680],{},[1656,54822,1713],{},[1667,54824,8580],{},[1656,54826,3633],{},[1667,54828,1680],{},[1661,54830,54831,54833],{},[898,54832,2146],{},[1667,54834,1669],{},[1656,54836,3964],{},[1667,54838,1680],{},[1661,54840,54841,54843],{},[898,54842,2146],{},[1667,54844,1680],{},[902,54846,54847],{"encoding":904},"B_2 = 10 + 2A_1 - 2A_2",[123,54849,54352,54850,1343,54892,1863],{},[883,54851,54853],{"className":54852},[886],[888,54854,54855],{"xmlns":890},[892,54856,54857,54889],{},[895,54858,54859,54865,54867,54869,54871,54873,54879,54881,54883],{},[1661,54860,54861,54863],{},[898,54862,2161],{},[1667,54864,1669],{},[1656,54866,1713],{},[1667,54868,9058],{},[1656,54870,3633],{},[1667,54872,1680],{},[1661,54874,54875,54877],{},[898,54876,2146],{},[1667,54878,1669],{},[1656,54880,3633],{},[1667,54882,2673],{},[1661,54884,54885,54887],{},[898,54886,2146],{},[1667,54888,1680],{},[902,54890,54891],{"encoding":904},"B_1 = 20 + 2A_1 + 4A_2",[883,54893,54895],{"className":54894},[886],[888,54896,54897],{"xmlns":890},[892,54898,54899,54931],{},[895,54900,54901,54907,54909,54911,54913,54915,54921,54923,54925],{},[1661,54902,54903,54905],{},[898,54904,2161],{},[1667,54906,1680],{},[1656,54908,1713],{},[1667,54910,9135],{},[1656,54912,3964],{},[1667,54914,2617],{},[1661,54916,54917,54919],{},[898,54918,2146],{},[1667,54920,1669],{},[1656,54922,3633],{},[1667,54924,5193],{},[1661,54926,54927,54929],{},[898,54928,2146],{},[1667,54930,1680],{},[902,54932,54933],{"encoding":904},"B_2 = 40 - 3A_1 + 5A_2",[198,54935,54937],{"id":54936},"základní-analýza-nabídky","Základní analýza nabídky",[724,54939,54940,54943,54944,54978,54979,55001],{},[38,54941,54942],{},"2.6"," Je dána nabídka ",[883,54945,54947],{"className":54946},[886],[888,54948,54949],{"xmlns":890},[892,54950,54951,54975],{},[895,54952,54953,54955,54957,54959,54961,54963,54965,54967,54969,54971,54973],{},[898,54954,8194],{},[1656,54956,1713],{},[898,54958,1769],{},[1656,54960,1659],{"stretchy":1658},[898,54962,1665],{},[1656,54964,1683],{"stretchy":1658},[1656,54966,1713],{},[1667,54968,9058],{},[1656,54970,3633],{},[1667,54972,11639],{},[898,54974,1665],{},[902,54976,54977],{"encoding":904},"P = S(Q) = 20 + 0{,}2Q",". (a) Načrtněte křivku nabídky. (b) Vypočtěte množství při cenách ",[883,54980,54982],{"className":54981},[886],[888,54983,54984],{"xmlns":890},[892,54985,54986,54998],{},[895,54987,54988,54990,54992,54994,54996],{},[1667,54989,8567],{},[1656,54991,1673],{"separator":1672},[1667,54993,46701],{},[1656,54995,1673],{"separator":1672},[1667,54997,23770],{},[902,54999,55000],{"encoding":904},"25, 30, 35"," a vyznačte výsledky na křivku nabídky.",[724,55003,55004,55007,55008,55025],{},[38,55005,55006],{},"2.7"," Ověřte, že zadané funkce vyjadřují (s případným omezením na ",[883,55009,55011],{"className":55010},[886],[888,55012,55013],{"xmlns":890},[892,55014,55015,55023],{},[895,55016,55017,55019,55021],{},[898,55018,8194],{},[1656,55020,1673],{"separator":1672},[898,55022,1665],{},[902,55024,54190],{"encoding":904},") nabídku (využijte testu na kladnost derivace), charakterizujte tvar křivky nabídky a vyjádřete nabídku v alternativním tvaru:",[120,55027,55028,55054,55082,55115,55149,55185],{},[123,55029,54222,55030],{},[883,55031,55033],{"className":55032},[886],[888,55034,55035],{"xmlns":890},[892,55036,55037,55051],{},[895,55038,55039,55041,55043,55045,55047,55049],{},[898,55040,8194],{},[1656,55042,1713],{},[1667,55044,46701],{},[1656,55046,3633],{},[1667,55048,1680],{},[898,55050,1665],{},[902,55052,55053],{"encoding":904},"P = 30 + 2Q",[123,55055,54255,55056],{},[883,55057,55059],{"className":55058},[886],[888,55060,55061],{"xmlns":890},[892,55062,55063,55079],{},[895,55064,55065,55067,55069,55071,55073,55075,55077],{},[898,55066,1665],{},[1656,55068,1713],{},[1656,55070,3964],{},[1667,55072,2617],{},[1656,55074,3633],{},[1667,55076,9140],{},[898,55078,8194],{},[902,55080,55081],{"encoding":904},"Q = -3 + 12P",[123,55083,54286,55084],{},[883,55085,55087],{"className":55086},[886],[888,55088,55089],{"xmlns":890},[892,55090,55091,55113],{},[895,55092,55093,55095,55097,55103,55105,55107,55109,55111],{},[898,55094,8194],{},[1656,55096,1713],{},[2062,55098,55099,55101],{},[898,55100,1665],{},[1667,55102,1680],{},[1656,55104,3633],{},[1667,55106,31664],{},[898,55108,1665],{},[1656,55110,3633],{},[1667,55112,4386],{},[902,55114,50402],{"encoding":904},[123,55116,54321,55117],{},[883,55118,55120],{"className":55119},[886],[888,55121,55122],{"xmlns":890},[892,55123,55124,55146],{},[895,55125,55126,55128,55130,55136,55138,55140,55142,55144],{},[898,55127,8194],{},[1656,55129,1713],{},[2062,55131,55132,55134],{},[898,55133,1665],{},[1667,55135,1680],{},[1656,55137,3633],{},[1667,55139,1680],{},[898,55141,1665],{},[1656,55143,3633],{},[1667,55145,9140],{},[902,55147,55148],{"encoding":904},"P = Q^2 + 2Q + 12",[123,55150,54352,55151],{},[883,55152,55154],{"className":55153},[886],[888,55155,55156],{"xmlns":890},[892,55157,55158,55182],{},[895,55159,55160,55162,55164,55166,55168,55170,55172,55174,55176],{},[898,55161,1665],{},[1656,55163,1713],{},[1667,55165,17557],{},[1656,55167,3633],{},[1667,55169,5193],{},[898,55171,8194],{},[1656,55173,3633],{},[1667,55175,11595],{},[2062,55177,55178,55180],{},[898,55179,8194],{},[1667,55181,1680],{},[902,55183,55184],{"encoding":904},"Q = 150 + 5P + 0{,}1P^2",[123,55186,54387,55187],{},[883,55188,55190],{"className":55189},[886],[888,55191,55192],{"xmlns":890},[892,55193,55194,55219],{},[895,55195,55196,55198,55200,55202,55204,55206,55208,55210,55213],{},[898,55197,1665],{},[1656,55199,1713],{},[1667,55201,6240],{},[1656,55203,3633],{},[1667,55205,11595],{},[898,55207,8194],{},[1656,55209,3633],{},[1667,55211,55212],{},"0,004",[2062,55214,55215,55217],{},[898,55216,8194],{},[1667,55218,1680],{},[902,55220,55221],{"encoding":904},"Q = 7 + 0{,}1P + 0{,}004P^2",[724,55223,55224,55227],{},[38,55225,55226],{},"2.8"," Rozhodněte, jak se změní křivka nabídky, jestliže se (ceteris paribus):",[120,55229,55230,55233,55236,55239],{},[123,55231,55232],{},"(a) Sníží ceny surovin — vstupů.",[123,55234,55235],{},"(b) Zavede nová ekologičtější technologie zvyšující výrobní náklady.",[123,55237,55238],{},"(c) Zvýší ceny všech energií.",[123,55240,55241],{},"(d) Sníží daňové odvody státu.",[724,55243,55244,54943,55246,55280,55281,55309],{},[38,55245,51626],{},[883,55247,55249],{"className":55248},[886],[888,55250,55251],{"xmlns":890},[892,55252,55253,55277],{},[895,55254,55255,55257,55259,55261,55263,55265,55267,55269,55271,55273,55275],{},[898,55256,8194],{},[1656,55258,1713],{},[898,55260,1769],{},[1656,55262,1659],{"stretchy":1658},[898,55264,1665],{},[1656,55266,1683],{"stretchy":1658},[1656,55268,1713],{},[1667,55270,13779],{},[898,55272,1665],{},[1656,55274,3633],{},[1667,55276,44930],{},[902,55278,55279],{"encoding":904},"P = S(Q) = 0{,}5Q + 15",". Najděte novou nabídku ",[883,55282,55284],{"className":55283},[886],[888,55285,55286],{"xmlns":890},[892,55287,55288,55306],{},[895,55289,55290,55292,55294,55300,55302,55304],{},[898,55291,8194],{},[1656,55293,1713],{},[2062,55295,55296,55298],{},[898,55297,1769],{},[1656,55299,8187],{},[1656,55301,1659],{"stretchy":1658},[898,55303,1665],{},[1656,55305,1683],{"stretchy":1658},[902,55307,55308],{"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.",[198,55311,50005],{"id":55312},"tržní-rovnováha-1",[724,55314,55315,55317,55318,55335,55336,2114],{},[38,55316,51686],{}," Pro zadanou poptávku a nabídku najděte rovnovážné množství ",[883,55319,55321],{"className":55320},[886],[888,55322,55323],{"xmlns":890},[892,55324,55325,55333],{},[895,55326,55327],{},[2062,55328,55329,55331],{},[898,55330,1665],{},[898,55332,1842],{},[902,55334,51080],{"encoding":904}," a rovnovážnou cenu ",[883,55337,55339],{"className":55338},[886],[888,55340,55341],{"xmlns":890},[892,55342,55343,55351],{},[895,55344,55345],{},[2062,55346,55347,55349],{},[898,55348,8194],{},[898,55350,1842],{},[902,55352,50146],{"encoding":904},[120,55354,55355,55407,55458,55517],{},[123,55356,54222,55357,1343,55383,1863],{},[883,55358,55360],{"className":55359},[886],[888,55361,55362],{"xmlns":890},[892,55363,55364,55380],{},[895,55365,55366,55368,55370,55372,55374,55376,55378],{},[898,55367,8194],{},[1656,55369,1713],{},[1656,55371,3964],{},[1667,55373,5193],{},[898,55375,1665],{},[1656,55377,3633],{},[1667,55379,9280],{},[902,55381,55382],{"encoding":904},"P = -5Q + 80",[883,55384,55386],{"className":55385},[886],[888,55387,55388],{"xmlns":890},[892,55389,55390,55404],{},[895,55391,55392,55394,55396,55398,55400,55402],{},[898,55393,8194],{},[1656,55395,1713],{},[1667,55397,1680],{},[898,55399,1665],{},[1656,55401,3633],{},[1667,55403,8580],{},[902,55405,55406],{"encoding":904},"P = 2Q + 10",[123,55408,54255,55409,1343,55435,1863],{},[883,55410,55412],{"className":55411},[886],[888,55413,55414],{"xmlns":890},[892,55415,55416,55432],{},[895,55417,55418,55420,55422,55424,55426,55428,55430],{},[898,55419,1665],{},[1656,55421,1713],{},[1656,55423,3964],{},[1667,55425,13779],{},[898,55427,8194],{},[1656,55429,3633],{},[1667,55431,8567],{},[902,55433,55434],{"encoding":904},"Q = -0{,}5P + 25",[883,55436,55438],{"className":55437},[886],[888,55439,55440],{"xmlns":890},[892,55441,55442,55456],{},[895,55443,55444,55446,55448,55450,55452,55454],{},[898,55445,1665],{},[1656,55447,1713],{},[1667,55449,1680],{},[898,55451,8194],{},[1656,55453,3964],{},[1667,55455,9267],{},[902,55457,49527],{"encoding":904},[123,55459,54286,55460,1343,55486,1863],{},[883,55461,55463],{"className":55462},[886],[888,55464,55465],{"xmlns":890},[892,55466,55467,55483],{},[895,55468,55469,55471,55473,55475,55477,55479,55481],{},[898,55470,8194],{},[1656,55472,1713],{},[1656,55474,3964],{},[1667,55476,2673],{},[898,55478,1665],{},[1656,55480,3633],{},[1667,55482,12827],{},[902,55484,55485],{"encoding":904},"P = -4Q + 120",[883,55487,55489],{"className":55488},[886],[888,55490,55491],{"xmlns":890},[892,55492,55493,55514],{},[895,55494,55495,55497,55499,55507,55509,55511],{},[898,55496,8194],{},[1656,55498,1713],{},[4138,55500,55501],{"scriptlevel":4032,"displaystyle":1658},[3294,55502,55503,55505],{},[1667,55504,1669],{},[1667,55506,2617],{},[898,55508,1665],{},[1656,55510,3633],{},[1667,55512,55513],{},"29",[902,55515,55516],{"encoding":904},"P = \\tfrac{1}{3}Q + 29",[123,55518,54321,55519,1343,55548,1863],{},[883,55520,55522],{"className":55521},[886],[888,55523,55524],{"xmlns":890},[892,55525,55526,55545],{},[895,55527,55528,55530,55532,55534,55540,55542],{},[898,55529,8194],{},[1656,55531,1713],{},[1656,55533,3964],{},[2062,55535,55536,55538],{},[898,55537,1665],{},[1667,55539,1680],{},[1656,55541,3633],{},[1667,55543,55544],{},"52",[902,55546,55547],{"encoding":904},"P = -Q^2 + 52",[883,55549,55551],{"className":55550},[886],[888,55552,55553],{"xmlns":890},[892,55554,55555,55573],{},[895,55556,55557,55559,55561,55563,55569,55571],{},[898,55558,8194],{},[1656,55560,1713],{},[1667,55562,1680],{},[2062,55564,55565,55567],{},[898,55566,1665],{},[1667,55568,1680],{},[1656,55570,3633],{},[1667,55572,8580],{},[902,55574,55575],{"encoding":904},"P = 2Q^2 + 10",[724,55577,55578,55581,55582,55612,55613,55643],{},[38,55579,55580],{},"2.11"," Pro zadanou poptávku a nabídku dvou závislých zboží najděte rovnovážná množství ",[883,55583,55585],{"className":55584},[886],[888,55586,55587],{"xmlns":890},[892,55588,55589,55609],{},[895,55590,55591,55599,55601],{},[1715,55592,55593,55595,55597],{},[898,55594,1665],{},[1667,55596,1669],{},[898,55598,1842],{},[1656,55600,1673],{"separator":1672},[1715,55602,55603,55605,55607],{},[898,55604,1665],{},[1667,55606,1680],{},[898,55608,1842],{},[902,55610,55611],{"encoding":904},"Q_1^E, Q_2^E"," a rovnovážné ceny ",[883,55614,55616],{"className":55615},[886],[888,55617,55618],{"xmlns":890},[892,55619,55620,55640],{},[895,55621,55622,55630,55632],{},[1715,55623,55624,55626,55628],{},[898,55625,8194],{},[1667,55627,1669],{},[898,55629,1842],{},[1656,55631,1673],{"separator":1672},[1715,55633,55634,55636,55638],{},[898,55635,8194],{},[1667,55637,1680],{},[898,55639,1842],{},[902,55641,55642],{"encoding":904},"P_1^E, P_2^E"," (index 1 přísluší prvnímu, index 2 druhému zboží):",[120,55645,55646,55798],{},[123,55647,54222,55648,1343,55688,1343,55730,1343,55764,1863],{},[883,55649,55651],{"className":55650},[886],[888,55652,55653],{"xmlns":890},[892,55654,55655,55685],{},[895,55656,55657,55663,55665,55667,55669,55671,55677,55679],{},[1661,55658,55659,55661],{},[898,55660,1665],{},[1667,55662,1669],{},[1656,55664,1713],{},[1667,55666,8580],{},[1656,55668,3964],{},[1667,55670,1680],{},[1661,55672,55673,55675],{},[898,55674,8194],{},[1667,55676,1669],{},[1656,55678,3633],{},[1661,55680,55681,55683],{},[898,55682,8194],{},[1667,55684,1680],{},[902,55686,55687],{"encoding":904},"Q_1 = 10 - 2P_1 + P_2",[883,55689,55691],{"className":55690},[886],[888,55692,55693],{"xmlns":890},[892,55694,55695,55727],{},[895,55696,55697,55703,55705,55707,55709,55711,55717,55719,55721],{},[1661,55698,55699,55701],{},[898,55700,1665],{},[1667,55702,1680],{},[1656,55704,1713],{},[1667,55706,5193],{},[1656,55708,3633],{},[1667,55710,1680],{},[1661,55712,55713,55715],{},[898,55714,8194],{},[1667,55716,1669],{},[1656,55718,3964],{},[1667,55720,1680],{},[1661,55722,55723,55725],{},[898,55724,8194],{},[1667,55726,1680],{},[902,55728,55729],{"encoding":904},"Q_2 = 5 + 2P_1 - 2P_2",[883,55731,55733],{"className":55732},[886],[888,55734,55735],{"xmlns":890},[892,55736,55737,55761],{},[895,55738,55739,55745,55747,55749,55751,55753,55755],{},[1661,55740,55741,55743],{},[898,55742,1665],{},[1667,55744,1669],{},[1656,55746,1713],{},[1656,55748,3964],{},[1667,55750,2617],{},[1656,55752,3633],{},[1667,55754,1680],{},[1661,55756,55757,55759],{},[898,55758,8194],{},[1667,55760,1669],{},[902,55762,55763],{"encoding":904},"Q_1 = -3 + 2P_1",[883,55765,55767],{"className":55766},[886],[888,55768,55769],{"xmlns":890},[892,55770,55771,55795],{},[895,55772,55773,55779,55781,55783,55785,55787,55789],{},[1661,55774,55775,55777],{},[898,55776,1665],{},[1667,55778,1680],{},[1656,55780,1713],{},[1656,55782,3964],{},[1667,55784,1680],{},[1656,55786,3633],{},[1667,55788,2617],{},[1661,55790,55791,55793],{},[898,55792,8194],{},[1667,55794,1680],{},[902,55796,55797],{"encoding":904},"Q_2 = -2 + 3P_2",[123,55799,54255,55800,1343,55840,1343,55882,1343,55914,1863],{},[883,55801,55803],{"className":55802},[886],[888,55804,55805],{"xmlns":890},[892,55806,55807,55837],{},[895,55808,55809,55815,55817,55819,55821,55823,55829,55831],{},[1661,55810,55811,55813],{},[898,55812,1665],{},[1667,55814,1669],{},[1656,55816,1713],{},[1667,55818,5267],{},[1656,55820,3964],{},[1667,55822,1680],{},[1661,55824,55825,55827],{},[898,55826,8194],{},[1667,55828,1669],{},[1656,55830,3633],{},[1661,55832,55833,55835],{},[898,55834,8194],{},[1667,55836,1680],{},[902,55838,55839],{"encoding":904},"Q_1 = 100 - 2P_1 + P_2",[883,55841,55843],{"className":55842},[886],[888,55844,55845],{"xmlns":890},[892,55846,55847,55879],{},[895,55848,55849,55855,55857,55859,55861,55863,55869,55871,55873],{},[1661,55850,55851,55853],{},[898,55852,1665],{},[1667,55854,1680],{},[1656,55856,1713],{},[1667,55858,5193],{},[1656,55860,3633],{},[1667,55862,1680],{},[1661,55864,55865,55867],{},[898,55866,8194],{},[1667,55868,1669],{},[1656,55870,3964],{},[1667,55872,2617],{},[1661,55874,55875,55877],{},[898,55876,8194],{},[1667,55878,1680],{},[902,55880,55881],{"encoding":904},"Q_2 = 5 + 2P_1 - 3P_2",[883,55883,55885],{"className":55884},[886],[888,55886,55887],{"xmlns":890},[892,55888,55889,55911],{},[895,55890,55891,55897,55899,55901,55903,55905],{},[1661,55892,55893,55895],{},[898,55894,1665],{},[1667,55896,1669],{},[1656,55898,1713],{},[1656,55900,3964],{},[1667,55902,8580],{},[1656,55904,3633],{},[1661,55906,55907,55909],{},[898,55908,8194],{},[1667,55910,1669],{},[902,55912,55913],{"encoding":904},"Q_1 = -10 + P_1",[883,55915,55917],{"className":55916},[886],[888,55918,55919],{"xmlns":890},[892,55920,55921,55943],{},[895,55922,55923,55929,55931,55933,55935,55937],{},[1661,55924,55925,55927],{},[898,55926,1665],{},[1667,55928,1680],{},[1656,55930,1713],{},[1667,55932,5193],{},[1656,55934,3633],{},[1667,55936,9112],{},[1661,55938,55939,55941],{},[898,55940,8194],{},[1667,55942,1680],{},[902,55944,55945],{"encoding":904},"Q_2 = 5 + 6P_2",[724,55947,55948,55951,55952,1343,56000,1343,56046,56096,56097,1343,56129,1343,56163,30312,56197,1896,56214,56232,56233,56246,56247,56273,56274,55612,56314,1863],{},[38,55949,55950],{},"2.12"," Pro tři závislá zboží jsou dány poptávky rovnicemi ",[883,55953,55955],{"className":55954},[886],[888,55956,55957],{"xmlns":890},[892,55958,55959,55997],{},[895,55960,55961,55967,55969,55971,55973,55979,55981,55983,55989,55991],{},[1661,55962,55963,55965],{},[898,55964,1665],{},[1667,55966,1669],{},[1656,55968,1713],{},[1667,55970,44930],{},[1656,55972,3964],{},[1661,55974,55975,55977],{},[898,55976,8194],{},[1667,55978,1669],{},[1656,55980,3633],{},[1667,55982,1680],{},[1661,55984,55985,55987],{},[898,55986,8194],{},[1667,55988,1680],{},[1656,55990,3633],{},[1661,55992,55993,55995],{},[898,55994,8194],{},[1667,55996,2617],{},[902,55998,55999],{"encoding":904},"Q_1 = 15 - P_1 + 2P_2 + P_3",[883,56001,56003],{"className":56002},[886],[888,56004,56005],{"xmlns":890},[892,56006,56007,56043],{},[895,56008,56009,56015,56017,56019,56021,56027,56029,56035,56037],{},[1661,56010,56011,56013],{},[898,56012,1665],{},[1667,56014,1680],{},[1656,56016,1713],{},[1667,56018,2698],{},[1656,56020,3633],{},[1661,56022,56023,56025],{},[898,56024,8194],{},[1667,56026,1669],{},[1656,56028,3964],{},[1661,56030,56031,56033],{},[898,56032,8194],{},[1667,56034,1680],{},[1656,56036,3964],{},[1661,56038,56039,56041],{},[898,56040,8194],{},[1667,56042,2617],{},[902,56044,56045],{"encoding":904},"Q_2 = 9 + P_1 - P_2 - P_3",[883,56047,56049],{"className":56048},[886],[888,56050,56051],{"xmlns":890},[892,56052,56053,56093],{},[895,56054,56055,56061,56063,56065,56067,56069,56075,56077,56083,56085,56087],{},[1661,56056,56057,56059],{},[898,56058,1665],{},[1667,56060,2617],{},[1656,56062,1713],{},[1667,56064,2877],{},[1656,56066,3633],{},[1667,56068,1680],{},[1661,56070,56071,56073],{},[898,56072,8194],{},[1667,56074,1669],{},[1656,56076,3964],{},[1661,56078,56079,56081],{},[898,56080,8194],{},[1667,56082,1680],{},[1656,56084,3964],{},[1667,56086,2673],{},[1661,56088,56089,56091],{},[898,56090,8194],{},[1667,56092,2617],{},[902,56094,56095],{"encoding":904},"Q_3 = 8 + 2P_1 - P_2 - 4P_3"," a nabídky rovnicemi ",[883,56098,56100],{"className":56099},[886],[888,56101,56102],{"xmlns":890},[892,56103,56104,56126],{},[895,56105,56106,56112,56114,56116,56118,56120],{},[1661,56107,56108,56110],{},[898,56109,1665],{},[1667,56111,1669],{},[1656,56113,1713],{},[1656,56115,3964],{},[1667,56117,6240],{},[1656,56119,3633],{},[1661,56121,56122,56124],{},[898,56123,8194],{},[1667,56125,1669],{},[902,56127,56128],{"encoding":904},"Q_1 = -7 + P_1",[883,56130,56132],{"className":56131},[886],[888,56133,56134],{"xmlns":890},[892,56135,56136,56160],{},[895,56137,56138,56144,56146,56148,56150,56152,56154],{},[1661,56139,56140,56142],{},[898,56141,1665],{},[1667,56143,1680],{},[1656,56145,1713],{},[1656,56147,3964],{},[1667,56149,2673],{},[1656,56151,3633],{},[1667,56153,2673],{},[1661,56155,56156,56158],{},[898,56157,8194],{},[1667,56159,1680],{},[902,56161,56162],{"encoding":904},"Q_2 = -4 + 4P_2",[883,56164,56166],{"className":56165},[886],[888,56167,56168],{"xmlns":890},[892,56169,56170,56194],{},[895,56171,56172,56178,56180,56182,56184,56186,56188],{},[1661,56173,56174,56176],{},[898,56175,1665],{},[1667,56177,2617],{},[1656,56179,1713],{},[1656,56181,3964],{},[1667,56183,5193],{},[1656,56185,3633],{},[1667,56187,1680],{},[1661,56189,56190,56192],{},[898,56191,8194],{},[1667,56193,2617],{},[902,56195,56196],{"encoding":904},"Q_3 = -5 + 2P_3",[883,56198,56200],{"className":56199},[886],[888,56201,56202],{"xmlns":890},[892,56203,56204,56212],{},[895,56205,56206],{},[1661,56207,56208,56210],{},[898,56209,1665],{},[898,56211,1710],{},[902,56213,2373],{"encoding":904},[883,56215,56217],{"className":56216},[886],[888,56218,56219],{"xmlns":890},[892,56220,56221,56229],{},[895,56222,56223],{},[1661,56224,56225,56227],{},[898,56226,8194],{},[898,56228,1710],{},[902,56230,56231],{"encoding":904},"P_i"," značí příslušné množství a ceny ",[883,56234,56236],{"className":56235},[886],[888,56237,56238],{"xmlns":890},[892,56239,56240,56244],{},[895,56241,56242],{},[898,56243,1710],{},[902,56245,1710],{"encoding":904},"-tého zboží, ",[883,56248,56250],{"className":56249},[886],[888,56251,56252],{"xmlns":890},[892,56253,56254,56270],{},[895,56255,56256,56258,56260,56262,56264,56266,56268],{},[898,56257,1710],{},[1656,56259,1713],{},[1667,56261,1669],{},[1656,56263,1673],{"separator":1672},[1667,56265,1680],{},[1656,56267,1673],{"separator":1672},[1667,56269,2617],{},[902,56271,56272],{"encoding":904},"i = 1, 2, 3",". Najděte rovnovážná množství ",[883,56275,56277],{"className":56276},[886],[888,56278,56279],{"xmlns":890},[892,56280,56281,56311],{},[895,56282,56283,56291,56293,56301,56303],{},[1715,56284,56285,56287,56289],{},[898,56286,1665],{},[1667,56288,1669],{},[898,56290,1842],{},[1656,56292,1673],{"separator":1672},[1715,56294,56295,56297,56299],{},[898,56296,1665],{},[1667,56298,1680],{},[898,56300,1842],{},[1656,56302,1673],{"separator":1672},[1715,56304,56305,56307,56309],{},[898,56306,1665],{},[1667,56308,2617],{},[898,56310,1842],{},[902,56312,56313],{"encoding":904},"Q_1^E, Q_2^E, Q_3^E",[883,56315,56317],{"className":56316},[886],[888,56318,56319],{"xmlns":890},[892,56320,56321,56351],{},[895,56322,56323,56331,56333,56341,56343],{},[1715,56324,56325,56327,56329],{},[898,56326,8194],{},[1667,56328,1669],{},[898,56330,1842],{},[1656,56332,1673],{"separator":1672},[1715,56334,56335,56337,56339],{},[898,56336,8194],{},[1667,56338,1680],{},[898,56340,1842],{},[1656,56342,1673],{"separator":1672},[1715,56344,56345,56347,56349],{},[898,56346,8194],{},[1667,56348,2617],{},[898,56350,1842],{},[902,56352,56353],{"encoding":904},"P_1^E, P_2^E, P_3^E",[724,56355,56356,56359,56360,56396,56397,1863],{},[38,56357,56358],{},"2.13"," Jsou dány poptávka ",[883,56361,56363],{"className":56362},[886],[888,56364,56365],{"xmlns":890},[892,56366,56367,56393],{},[895,56368,56369,56371,56373,56375,56377,56379,56381,56383,56385,56387,56389,56391],{},[898,56370,8194],{},[1656,56372,1713],{},[898,56374,6787],{},[1656,56376,1659],{"stretchy":1658},[898,56378,1665],{},[1656,56380,1683],{"stretchy":1658},[1656,56382,1713],{},[1656,56384,3964],{},[1667,56386,2673],{},[898,56388,1665],{},[1656,56390,3633],{},[1667,56392,9280],{},[902,56394,56395],{"encoding":904},"P = D(Q) = -4Q + 80"," a nabídka ",[883,56398,56400],{"className":56399},[886],[888,56401,56402],{"xmlns":890},[892,56403,56404,56428],{},[895,56405,56406,56408,56410,56412,56414,56416,56418,56420,56422,56424,56426],{},[898,56407,8194],{},[1656,56409,1713],{},[898,56411,1769],{},[1656,56413,1659],{"stretchy":1658},[898,56415,1665],{},[1656,56417,1683],{"stretchy":1658},[1656,56419,1713],{},[1667,56421,2617],{},[898,56423,1665],{},[1656,56425,3633],{},[1667,56427,8580],{},[902,56429,56430],{"encoding":904},"P = S(Q) = 3Q + 10",[120,56432,56433,56470,56534,56594],{},[123,56434,56435,56436,55335,56453,1863],{},"(a) Určete rovnovážné množství ",[883,56437,56439],{"className":56438},[886],[888,56440,56441],{"xmlns":890},[892,56442,56443,56451],{},[895,56444,56445],{},[2062,56446,56447,56449],{},[898,56448,1665],{},[898,56450,1842],{},[902,56452,51080],{"encoding":904},[883,56454,56456],{"className":56455},[886],[888,56457,56458],{"xmlns":890},[892,56459,56460,56468],{},[895,56461,56462],{},[2062,56463,56464,56466],{},[898,56465,8194],{},[898,56467,1842],{},[902,56469,50146],{"encoding":904},[123,56471,56472,56473,56491,56492,56512,56513,56533],{},"(b) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží výrobci daň ",[883,56474,56476],{"className":56475},[886],[888,56477,56478],{"xmlns":890},[892,56479,56480,56488],{},[895,56481,56482,56484,56486],{},[898,56483,11577],{},[1656,56485,1713],{},[1667,56487,6240],{},[902,56489,56490],{"encoding":904},"T = 7"," Kč na každou jednotku zboží, vypočtěte nové rovnovážné množství ",[883,56493,56495],{"className":56494},[886],[888,56496,56497],{"xmlns":890},[892,56498,56499,56509],{},[895,56500,56501],{},[1715,56502,56503,56505,56507],{},[898,56504,1665],{},[1667,56506,1669],{},[898,56508,1842],{},[902,56510,56511],{"encoding":904},"Q_1^E"," a novou rovnovážnou cenu ",[883,56514,56516],{"className":56515},[886],[888,56517,56518],{"xmlns":890},[892,56519,56520,56530],{},[895,56521,56522],{},[1715,56523,56524,56526,56528],{},[898,56525,8194],{},[1667,56527,1669],{},[898,56529,1842],{},[902,56531,56532],{"encoding":904},"P_1^E"," a určete, kolik z daňového zatížení zaplatí výrobce a kolik spotřebitel.",[123,56535,56536,56537,56491,56554,56512,56574,56533],{},"(c) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží spotřebiteli daň ",[883,56538,56540],{"className":56539},[886],[888,56541,56542],{"xmlns":890},[892,56543,56544,56552],{},[895,56545,56546,56548,56550],{},[898,56547,11577],{},[1656,56549,1713],{},[1667,56551,6240],{},[902,56553,56490],{"encoding":904},[883,56555,56557],{"className":56556},[886],[888,56558,56559],{"xmlns":890},[892,56560,56561,56571],{},[895,56562,56563],{},[1715,56564,56565,56567,56569],{},[898,56566,1665],{},[1667,56568,1680],{},[898,56570,1842],{},[902,56572,56573],{"encoding":904},"Q_2^E",[883,56575,56577],{"className":56576},[886],[888,56578,56579],{"xmlns":890},[892,56580,56581,56591],{},[895,56582,56583],{},[1715,56584,56585,56587,56589],{},[898,56586,8194],{},[1667,56588,1680],{},[898,56590,1842],{},[902,56592,56593],{"encoding":904},"P_2^E",[123,56595,56596],{},"(d) Proveďte analýzu dopadu daňového zatížení na spotřebitele a výrobce vyplývající z výsledků (b) a (c).",[724,56598,56599,56600,1863],{},"Viz též ",[207,56601,51398],{"className":56602,"dataFsResolvedFilePath":809,"href":810},[210],[198,56604,51700],{"id":56605},"multiplikátory-pro-mikroekonomické-proměnné-1",[724,56607,56608,56359,56611,56396,56647,1863],{},[38,56609,56610],{},"2.14",[883,56612,56614],{"className":56613},[886],[888,56615,56616],{"xmlns":890},[892,56617,56618,56644],{},[895,56619,56620,56622,56624,56626,56628,56630,56632,56634,56636,56638,56640,56642],{},[898,56621,8194],{},[1656,56623,1713],{},[898,56625,207],{},[898,56627,1665],{},[1656,56629,3633],{},[898,56631,3403],{},[1656,56633,1713],{},[1656,56635,3964],{},[1667,56637,1680],{},[898,56639,1665],{},[1656,56641,3633],{},[1667,56643,9267],{},[902,56645,56646],{"encoding":904},"P = aQ + b = -2Q + 50",[883,56648,56650],{"className":56649},[886],[888,56651,56652],{"xmlns":890},[892,56653,56654,56678],{},[895,56655,56656,56658,56660,56662,56664,56666,56668,56670,56672,56674,56676],{},[898,56657,8194],{},[1656,56659,1713],{},[898,56661,1745],{},[898,56663,1665],{},[1656,56665,3633],{},[898,56667,3768],{},[1656,56669,1713],{},[1667,56671,28042],{},[898,56673,1665],{},[1656,56675,3633],{},[1667,56677,9058],{},[902,56679,56680],{"encoding":904},"P = cQ + d = 0{,}6Q + 20",[120,56682,56683,56719,56722,56808,56861,56941,56995],{},[123,56684,56435,56685,55335,56702,1863],{},[883,56686,56688],{"className":56687},[886],[888,56689,56690],{"xmlns":890},[892,56691,56692,56700],{},[895,56693,56694],{},[2062,56695,56696,56698],{},[898,56697,1665],{},[898,56699,1842],{},[902,56701,51080],{"encoding":904},[883,56703,56705],{"className":56704},[886],[888,56706,56707],{"xmlns":890},[892,56708,56709,56717],{},[895,56710,56711],{},[2062,56712,56713,56715],{},[898,56714,8194],{},[898,56716,1842],{},[902,56718,50146],{"encoding":904},[123,56720,56721],{},"(b) Určete hodnoty multiplikátorů pro zadané parametry.",[123,56723,56724,56725,56742,56743,3605,56756,3619,56772,56788,56789,1863],{},"(c) Určete přibližnou změnu rovnovážného množství ",[883,56726,56728],{"className":56727},[886],[888,56729,56730],{"xmlns":890},[892,56731,56732,56740],{},[895,56733,56734],{},[2062,56735,56736,56738],{},[898,56737,1665],{},[898,56739,1842],{},[902,56741,51080],{"encoding":904}," odpovídající změně ",[883,56744,56746],{"className":56745},[886],[888,56747,56748],{"xmlns":890},[892,56749,56750,56754],{},[895,56751,56752],{},[898,56753,207],{},[902,56755,207],{"encoding":904},[883,56757,56759],{"className":56758},[886],[888,56760,56761],{"xmlns":890},[892,56762,56763,56769],{},[895,56764,56765,56767],{},[1656,56766,3964],{},[1667,56768,1680],{},[902,56770,56771],{"encoding":904},"-2",[883,56773,56775],{"className":56774},[886],[888,56776,56777],{"xmlns":890},[892,56778,56779,56785],{},[895,56780,56781,56783],{},[1656,56782,3964],{},[1667,56784,2617],{},[902,56786,56787],{"encoding":904},"-3"," (ceteris paribus) a stanovte nové rovnovážné množství ",[883,56790,56792],{"className":56791},[886],[888,56793,56794],{"xmlns":890},[892,56795,56796,56806],{},[895,56797,56798],{},[1715,56799,56800,56802,56804],{},[898,56801,1665],{},[1667,56803,1669],{},[898,56805,1842],{},[902,56807,56511],{"encoding":904},[123,56809,56810,56811,56742,56828,56841,56842,1863],{},"(d) Určete přibližnou změnu rovnovážného množství ",[883,56812,56814],{"className":56813},[886],[888,56815,56816],{"xmlns":890},[892,56817,56818,56826],{},[895,56819,56820],{},[2062,56821,56822,56824],{},[898,56823,1665],{},[898,56825,1842],{},[902,56827,51080],{"encoding":904},[883,56829,56831],{"className":56830},[886],[888,56832,56833],{"xmlns":890},[892,56834,56835,56839],{},[895,56836,56837],{},[898,56838,3403],{},[902,56840,3403],{"encoding":904}," z 50 na 60 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,56843,56845],{"className":56844},[886],[888,56846,56847],{"xmlns":890},[892,56848,56849,56859],{},[895,56850,56851],{},[1715,56852,56853,56855,56857],{},[898,56854,1665],{},[1667,56856,1680],{},[898,56858,1842],{},[902,56860,56573],{"encoding":904},[123,56862,56863,56864,56742,56881,3605,56894,3619,56907,56788,56921,1863],{},"(e) Určete přibližnou změnu rovnovážného množství ",[883,56865,56867],{"className":56866},[886],[888,56868,56869],{"xmlns":890},[892,56870,56871,56879],{},[895,56872,56873],{},[2062,56874,56875,56877],{},[898,56876,1665],{},[898,56878,1842],{},[902,56880,51080],{"encoding":904},[883,56882,56884],{"className":56883},[886],[888,56885,56886],{"xmlns":890},[892,56887,56888,56892],{},[895,56889,56890],{},[898,56891,1745],{},[902,56893,1745],{"encoding":904},[883,56895,56897],{"className":56896},[886],[888,56898,56899],{"xmlns":890},[892,56900,56901,56905],{},[895,56902,56903],{},[1667,56904,28042],{},[902,56906,53137],{"encoding":904},[883,56908,56910],{"className":56909},[886],[888,56911,56912],{"xmlns":890},[892,56913,56914,56918],{},[895,56915,56916],{},[1667,56917,23321],{},[902,56919,56920],{"encoding":904},"0{,}8",[883,56922,56924],{"className":56923},[886],[888,56925,56926],{"xmlns":890},[892,56927,56928,56938],{},[895,56929,56930],{},[1715,56931,56932,56934,56936],{},[898,56933,1665],{},[1667,56935,2617],{},[898,56937,1842],{},[902,56939,56940],{"encoding":904},"Q_3^E",[123,56942,56943,56944,56742,56961,56974,56975,1863],{},"(f) Určete přibližnou změnu rovnovážného množství ",[883,56945,56947],{"className":56946},[886],[888,56948,56949],{"xmlns":890},[892,56950,56951,56959],{},[895,56952,56953],{},[2062,56954,56955,56957],{},[898,56956,1665],{},[898,56958,1842],{},[902,56960,51080],{"encoding":904},[883,56962,56964],{"className":56963},[886],[888,56965,56966],{"xmlns":890},[892,56967,56968,56972],{},[895,56969,56970],{},[898,56971,3768],{},[902,56973,3768],{"encoding":904}," z 20 na 10 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,56976,56978],{"className":56977},[886],[888,56979,56980],{"xmlns":890},[892,56981,56982,56992],{},[895,56983,56984],{},[1715,56985,56986,56988,56990],{},[898,56987,1665],{},[1667,56989,2673],{},[898,56991,1842],{},[902,56993,56994],{"encoding":904},"Q_4^E",[123,56996,56997,56998,3756,57015,57028,57029,30138,57042,1343,57057,30138,57070,1896,57084,30138,57097,57112,57113,1863],{},"(g) Určete přibližnou změnu rovnovážného množství ",[883,56999,57001],{"className":57000},[886],[888,57002,57003],{"xmlns":890},[892,57004,57005,57013],{},[895,57006,57007],{},[2062,57008,57009,57011],{},[898,57010,1665],{},[898,57012,1842],{},[902,57014,51080],{"encoding":904},[883,57016,57018],{"className":57017},[886],[888,57019,57020],{"xmlns":890},[892,57021,57022,57026],{},[895,57023,57024],{},[898,57025,207],{},[902,57027,207],{"encoding":904}," o 1, ",[883,57030,57032],{"className":57031},[886],[888,57033,57034],{"xmlns":890},[892,57035,57036,57040],{},[895,57037,57038],{},[898,57039,3403],{},[902,57041,3403],{"encoding":904},[883,57043,57045],{"className":57044},[886],[888,57046,57047],{"xmlns":890},[892,57048,57049,57055],{},[895,57050,57051,57053],{},[1656,57052,3964],{},[1667,57054,8580],{},[902,57056,28176],{"encoding":904},[883,57058,57060],{"className":57059},[886],[888,57061,57062],{"xmlns":890},[892,57063,57064,57068],{},[895,57065,57066],{},[898,57067,1745],{},[902,57069,1745],{"encoding":904},[883,57071,57073],{"className":57072},[886],[888,57074,57075],{"xmlns":890},[892,57076,57077,57081],{},[895,57078,57079],{},[1667,57080,11595],{},[902,57082,57083],{"encoding":904},"0{,}1",[883,57085,57087],{"className":57086},[886],[888,57088,57089],{"xmlns":890},[892,57090,57091,57095],{},[895,57092,57093],{},[898,57094,3768],{},[902,57096,3768],{"encoding":904},[883,57098,57100],{"className":57099},[886],[888,57101,57102],{"xmlns":890},[892,57103,57104,57110],{},[895,57105,57106,57108],{},[1656,57107,3964],{},[1667,57109,8580],{},[902,57111,28176],{"encoding":904}," vzhledem k zadaným hodnotám a stanovte nové rovnovážné množství ",[883,57114,57116],{"className":57115},[886],[888,57117,57118],{"xmlns":890},[892,57119,57120,57130],{},[895,57121,57122],{},[1715,57123,57124,57126,57128],{},[898,57125,1665],{},[1667,57127,5193],{},[898,57129,1842],{},[902,57131,57132],{"encoding":904},"Q_5^E",[724,57134,57135,56359,57138,56396,57161,1863],{},[38,57136,57137],{},"2.15",[883,57139,57141],{"className":57140},[886],[888,57142,57143],{"xmlns":890},[892,57144,57145,57159],{},[895,57146,57147,57149,57151,57153,57155,57157],{},[898,57148,8194],{},[1656,57150,1713],{},[898,57152,207],{},[898,57154,1665],{},[1656,57156,3633],{},[898,57158,3403],{},[902,57160,45742],{"encoding":904},[883,57162,57164],{"className":57163},[886],[888,57165,57166],{"xmlns":890},[892,57167,57168,57182],{},[895,57169,57170,57172,57174,57176,57178,57180],{},[898,57171,8194],{},[1656,57173,1713],{},[898,57175,1745],{},[898,57177,1665],{},[1656,57179,3633],{},[898,57181,3768],{},[902,57183,48922],{"encoding":904},[120,57185,57186,57261,57278,57387,57440,57494],{},[123,57187,57188,57189,57202,57203,57228,57229,57260],{},"(a) Odvoďte redukovaný tvar pro ",[883,57190,57192],{"className":57191},[886],[888,57193,57194],{"xmlns":890},[892,57195,57196,57200],{},[895,57197,57198],{},[898,57199,8194],{},[902,57201,8194],{"encoding":904},". Stanovte podmínky pro ",[883,57204,57206],{"className":57205},[886],[888,57207,57208],{"xmlns":890},[892,57209,57210,57226],{},[895,57211,57212,57214,57216,57218,57220,57222,57224],{},[898,57213,207],{},[1656,57215,1673],{"separator":1672},[898,57217,3403],{},[1656,57219,1673],{"separator":1672},[898,57221,1745],{},[1656,57223,1673],{"separator":1672},[898,57225,3768],{},[902,57227,51962],{"encoding":904}," tak, aby rovnovážný bod ",[883,57230,57232],{"className":57231},[886],[888,57233,57234],{"xmlns":890},[892,57235,57236,57258],{},[895,57237,57238,57240,57242,57248,57250,57256],{},[898,57239,1842],{},[1656,57241,3453],{"stretchy":1658},[2062,57243,57244,57246],{},[898,57245,1665],{},[898,57247,1842],{},[1656,57249,1673],{"separator":1672},[2062,57251,57252,57254],{},[898,57253,8194],{},[898,57255,1842],{},[1656,57257,3462],{"stretchy":1658},[902,57259,50047],{"encoding":904}," patřil do 1. kvadrantu (využijte obrázku 2.22).",[123,57262,57263,57264,57277],{},"(b) Vypočtěte multiplikátory pro ",[883,57265,57267],{"className":57266},[886],[888,57268,57269],{"xmlns":890},[892,57270,57271,57275],{},[895,57272,57273],{},[898,57274,8194],{},[902,57276,8194],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků 2.22, 2.23).",[123,57279,57280,57281,1343,57301,1343,57319,1343,57337,57355,57356,57373,57374,1863],{},"(c) Pro hodnoty parametrů ",[883,57282,57284],{"className":57283},[886],[888,57285,57286],{"xmlns":890},[892,57287,57288,57298],{},[895,57289,57290,57292,57294,57296],{},[898,57291,207],{},[1656,57293,1713],{},[1656,57295,3964],{},[1667,57297,1680],{},[902,57299,57300],{"encoding":904},"a = -2",[883,57302,57304],{"className":57303},[886],[888,57305,57306],{"xmlns":890},[892,57307,57308,57316],{},[895,57309,57310,57312,57314],{},[898,57311,3403],{},[1656,57313,1713],{},[1667,57315,9135],{},[902,57317,57318],{"encoding":904},"b = 40",[883,57320,57322],{"className":57321},[886],[888,57323,57324],{"xmlns":890},[892,57325,57326,57334],{},[895,57327,57328,57330,57332],{},[898,57329,1745],{},[1656,57331,1713],{},[1667,57333,13779],{},[902,57335,57336],{"encoding":904},"c = 0{,}5",[883,57338,57340],{"className":57339},[886],[888,57341,57342],{"xmlns":890},[892,57343,57344,57352],{},[895,57345,57346,57348,57350],{},[898,57347,3768],{},[1656,57349,1713],{},[1667,57351,8580],{},[902,57353,57354],{"encoding":904},"d = 10"," určete rovnovážnou cenu ",[883,57357,57359],{"className":57358},[886],[888,57360,57361],{"xmlns":890},[892,57362,57363,57371],{},[895,57364,57365],{},[2062,57366,57367,57369],{},[898,57368,8194],{},[898,57370,1842],{},[902,57372,50146],{"encoding":904}," a hodnoty multiplikátorů pro ",[883,57375,57377],{"className":57376},[886],[888,57378,57379],{"xmlns":890},[892,57380,57381,57385],{},[895,57382,57383],{},[898,57384,8194],{},[902,57386,8194],{"encoding":904},[123,57388,57389,57390,56742,57407,57420,57421,1863],{},"(d) Určete přibližnou změnu rovnovážné ceny ",[883,57391,57393],{"className":57392},[886],[888,57394,57395],{"xmlns":890},[892,57396,57397,57405],{},[895,57398,57399],{},[2062,57400,57401,57403],{},[898,57402,8194],{},[898,57404,1842],{},[902,57406,50146],{"encoding":904},[883,57408,57410],{"className":57409},[886],[888,57411,57412],{"xmlns":890},[892,57413,57414,57418],{},[895,57415,57416],{},[898,57417,207],{},[902,57419,207],{"encoding":904}," o 5 (ceteris paribus) a stanovte novou rovnovážnou cenu ",[883,57422,57424],{"className":57423},[886],[888,57425,57426],{"xmlns":890},[892,57427,57428,57438],{},[895,57429,57430],{},[1715,57431,57432,57434,57436],{},[898,57433,8194],{},[1667,57435,1669],{},[898,57437,1842],{},[902,57439,56532],{"encoding":904},[123,57441,57442,57443,57460,57461,57474,57475,1863],{},"(e) Určete přibližnou změnu rovnovážné ceny ",[883,57444,57446],{"className":57445},[886],[888,57447,57448],{"xmlns":890},[892,57449,57450,57458],{},[895,57451,57452],{},[2062,57453,57454,57456],{},[898,57455,8194],{},[898,57457,1842],{},[902,57459,50146],{"encoding":904}," odpovídající poklesu ",[883,57462,57464],{"className":57463},[886],[888,57465,57466],{"xmlns":890},[892,57467,57468,57472],{},[895,57469,57470],{},[898,57471,207],{},[902,57473,207],{"encoding":904}," o 1 a stanovte novou rovnovážnou cenu ",[883,57476,57478],{"className":57477},[886],[888,57479,57480],{"xmlns":890},[892,57481,57482,57492],{},[895,57483,57484],{},[1715,57485,57486,57488,57490],{},[898,57487,8194],{},[1667,57489,1680],{},[898,57491,1842],{},[902,57493,56593],{"encoding":904},[123,57495,57496,57497,3756,57514,57527,57528,3619,57541,1896,57556,57569,57570,1863],{},"(f) Určete přibližnou změnu rovnovážné ceny ",[883,57498,57500],{"className":57499},[886],[888,57501,57502],{"xmlns":890},[892,57503,57504,57512],{},[895,57505,57506],{},[2062,57507,57508,57510],{},[898,57509,8194],{},[898,57511,1842],{},[902,57513,50146],{"encoding":904},[883,57515,57517],{"className":57516},[886],[888,57518,57519],{"xmlns":890},[892,57520,57521,57525],{},[895,57522,57523],{},[898,57524,207],{},[902,57526,207],{"encoding":904}," na 35, ",[883,57529,57531],{"className":57530},[886],[888,57532,57533],{"xmlns":890},[892,57534,57535,57539],{},[895,57536,57537],{},[898,57538,1745],{},[902,57540,1745],{"encoding":904},[883,57542,57544],{"className":57543},[886],[888,57545,57546],{"xmlns":890},[892,57547,57548,57553],{},[895,57549,57550],{},[1667,57551,57552],{},"0,7",[902,57554,57555],{"encoding":904},"0{,}7",[883,57557,57559],{"className":57558},[886],[888,57560,57561],{"xmlns":890},[892,57562,57563,57567],{},[895,57564,57565],{},[898,57566,3768],{},[902,57568,3768],{"encoding":904}," na 12 vzhledem k hodnotám dle (d) a stanovte novou rovnovážnou cenu ",[883,57571,57573],{"className":57572},[886],[888,57574,57575],{"xmlns":890},[892,57576,57577,57587],{},[895,57578,57579],{},[1715,57580,57581,57583,57585],{},[898,57582,8194],{},[1667,57584,2617],{},[898,57586,1842],{},[902,57588,57589],{"encoding":904},"P_3^E",[724,57591,57592,56359,57595,56396,57623,30312,57651,1896,57677,1863],{},[38,57593,57594],{},"2.16",[883,57596,57598],{"className":57597},[886],[888,57599,57600],{"xmlns":890},[892,57601,57602,57620],{},[895,57603,57604,57606,57608,57610,57612,57614],{},[898,57605,8194],{},[1656,57607,1713],{},[898,57609,207],{},[1656,57611,3633],{},[898,57613,3403],{},[2062,57615,57616,57618],{},[898,57617,1665],{},[1667,57619,1680],{},[902,57621,57622],{"encoding":904},"P = a + bQ^2",[883,57624,57626],{"className":57625},[886],[888,57627,57628],{"xmlns":890},[892,57629,57630,57648],{},[895,57631,57632,57634,57636,57638,57640,57642],{},[898,57633,8194],{},[1656,57635,1713],{},[898,57637,1745],{},[1656,57639,3633],{},[898,57641,3768],{},[2062,57643,57644,57646],{},[898,57645,1665],{},[1667,57647,1680],{},[902,57649,57650],{"encoding":904},"P = c + dQ^2",[883,57652,57654],{"className":57653},[886],[888,57655,57656],{"xmlns":890},[892,57657,57658,57674],{},[895,57659,57660,57662,57664,57666,57668,57670,57672],{},[898,57661,207],{},[1656,57663,1673],{"separator":1672},[898,57665,1745],{},[1656,57667,1673],{"separator":1672},[898,57669,3768],{},[1656,57671,2850],{},[1667,57673,4032],{},[902,57675,57676],{"encoding":904},"a, c, d > 0",[883,57678,57680],{"className":57679},[886],[888,57681,57682],{"xmlns":890},[892,57683,57684,57692],{},[895,57685,57686,57688,57690],{},[898,57687,3403],{},[1656,57689,4373],{},[1667,57691,4032],{},[902,57693,57694],{"encoding":904},"b \u003C 0",[120,57696,57697,57745,57761,57868,57920,57972,58081,58097,58196,58249],{},[123,57698,57188,57699,57712,57713,57744],{},[883,57700,57702],{"className":57701},[886],[888,57703,57704],{"xmlns":890},[892,57705,57706,57710],{},[895,57707,57708],{},[898,57709,1665],{},[902,57711,1665],{"encoding":904},". Načrtněte křivky poptávky a nabídky a stanovte podmínky, aby rovnovážný bod ",[883,57714,57716],{"className":57715},[886],[888,57717,57718],{"xmlns":890},[892,57719,57720,57742],{},[895,57721,57722,57724,57726,57732,57734,57740],{},[898,57723,1842],{},[1656,57725,3453],{"stretchy":1658},[2062,57727,57728,57730],{},[898,57729,1665],{},[898,57731,1842],{},[1656,57733,1673],{"separator":1672},[2062,57735,57736,57738],{},[898,57737,8194],{},[898,57739,1842],{},[1656,57741,3462],{"stretchy":1658},[902,57743,50047],{"encoding":904}," patřil do 1. kvadrantu.",[123,57746,57263,57747,57760],{},[883,57748,57750],{"className":57749},[886],[888,57751,57752],{"xmlns":890},[892,57753,57754,57758],{},[895,57755,57756],{},[898,57757,1665],{},[902,57759,1665],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků v (b)).",[123,57762,57280,57763,1343,57781,1343,57801,1343,57819,57837,57838,57373,57855,1863],{},[883,57764,57766],{"className":57765},[886],[888,57767,57768],{"xmlns":890},[892,57769,57770,57778],{},[895,57771,57772,57774,57776],{},[898,57773,207],{},[1656,57775,1713],{},[1667,57777,5267],{},[902,57779,57780],{"encoding":904},"a = 100",[883,57782,57784],{"className":57783},[886],[888,57785,57786],{"xmlns":890},[892,57787,57788,57798],{},[895,57789,57790,57792,57794,57796],{},[898,57791,3403],{},[1656,57793,1713],{},[1656,57795,3964],{},[1667,57797,1669],{},[902,57799,57800],{"encoding":904},"b = -1",[883,57802,57804],{"className":57803},[886],[888,57805,57806],{"xmlns":890},[892,57807,57808,57816],{},[895,57809,57810,57812,57814],{},[898,57811,1745],{},[1656,57813,1713],{},[1667,57815,9058],{},[902,57817,57818],{"encoding":904},"c = 20",[883,57820,57822],{"className":57821},[886],[888,57823,57824],{"xmlns":890},[892,57825,57826,57834],{},[895,57827,57828,57830,57832],{},[898,57829,3768],{},[1656,57831,1713],{},[1667,57833,1669],{},[902,57835,57836],{"encoding":904},"d = 1"," určete rovnovážné množství ",[883,57839,57841],{"className":57840},[886],[888,57842,57843],{"xmlns":890},[892,57844,57845,57853],{},[895,57846,57847],{},[2062,57848,57849,57851],{},[898,57850,1665],{},[898,57852,1842],{},[902,57854,51080],{"encoding":904},[883,57856,57858],{"className":57857},[886],[888,57859,57860],{"xmlns":890},[892,57861,57862,57866],{},[895,57863,57864],{},[898,57865,1665],{},[902,57867,1665],{"encoding":904},[123,57869,56810,57870,56742,57887,57900,57901,1863],{},[883,57871,57873],{"className":57872},[886],[888,57874,57875],{"xmlns":890},[892,57876,57877,57885],{},[895,57878,57879],{},[2062,57880,57881,57883],{},[898,57882,1665],{},[898,57884,1842],{},[902,57886,51080],{"encoding":904},[883,57888,57890],{"className":57889},[886],[888,57891,57892],{"xmlns":890},[892,57893,57894,57898],{},[895,57895,57896],{},[898,57897,207],{},[902,57899,207],{"encoding":904}," na 110 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,57902,57904],{"className":57903},[886],[888,57905,57906],{"xmlns":890},[892,57907,57908,57918],{},[895,57909,57910],{},[1715,57911,57912,57914,57916],{},[898,57913,1665],{},[1667,57915,1669],{},[898,57917,1842],{},[902,57919,56511],{"encoding":904},[123,57921,56863,57922,56742,57939,57952,57953,1863],{},[883,57923,57925],{"className":57924},[886],[888,57926,57927],{"xmlns":890},[892,57928,57929,57937],{},[895,57930,57931],{},[2062,57932,57933,57935],{},[898,57934,1665],{},[898,57936,1842],{},[902,57938,51080],{"encoding":904},[883,57940,57942],{"className":57941},[886],[888,57943,57944],{"xmlns":890},[892,57945,57946,57950],{},[895,57947,57948],{},[898,57949,1745],{},[902,57951,1745],{"encoding":904}," na 25 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,57954,57956],{"className":57955},[886],[888,57957,57958],{"xmlns":890},[892,57959,57960,57970],{},[895,57961,57962],{},[1715,57963,57964,57966,57968],{},[898,57965,1665],{},[1667,57967,1680],{},[898,57969,1842],{},[902,57971,56573],{"encoding":904},[123,57973,56943,57974,3756,57991,58004,58005,3619,58018,58033,58034,58047,58048,58061,58062,1863],{},[883,57975,57977],{"className":57976},[886],[888,57978,57979],{"xmlns":890},[892,57980,57981,57989],{},[895,57982,57983],{},[2062,57984,57985,57987],{},[898,57986,1665],{},[898,57988,1842],{},[902,57990,51080],{"encoding":904},[883,57992,57994],{"className":57993},[886],[888,57995,57996],{"xmlns":890},[892,57997,57998,58002],{},[895,57999,58000],{},[898,58001,207],{},[902,58003,207],{"encoding":904}," na 110, poklesu ",[883,58006,58008],{"className":58007},[886],[888,58009,58010],{"xmlns":890},[892,58011,58012,58016],{},[895,58013,58014],{},[898,58015,3403],{},[902,58017,3403],{"encoding":904},[883,58019,58021],{"className":58020},[886],[888,58022,58023],{"xmlns":890},[892,58024,58025,58031],{},[895,58026,58027,58029],{},[1656,58028,3964],{},[1667,58030,1680],{},[902,58032,56771],{"encoding":904},", růstu ",[883,58035,58037],{"className":58036},[886],[888,58038,58039],{"xmlns":890},[892,58040,58041,58045],{},[895,58042,58043],{},[898,58044,1745],{},[902,58046,1745],{"encoding":904}," na 25 a růstu ",[883,58049,58051],{"className":58050},[886],[888,58052,58053],{"xmlns":890},[892,58054,58055,58059],{},[895,58056,58057],{},[898,58058,3768],{},[902,58060,3768],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte nové rovnovážné množství ",[883,58063,58065],{"className":58064},[886],[888,58066,58067],{"xmlns":890},[892,58068,58069,58079],{},[895,58070,58071],{},[1715,58072,58073,58075,58077],{},[898,58074,1665],{},[1667,58076,2617],{},[898,58078,1842],{},[902,58080,56940],{"encoding":904},[123,58082,58083,58084,57760],{},"(i) Vypočtěte multiplikátory pro ",[883,58085,58087],{"className":58086},[886],[888,58088,58089],{"xmlns":890},[892,58090,58091,58095],{},[895,58092,58093],{},[898,58094,8194],{},[902,58096,8194],{"encoding":904},[123,58098,58099,58100,57373,58117,58130,58131,56742,58148,3619,58161,58176,58177,1863],{},"(j) Pro hodnoty parametrů dle (b) určete rovnovážnou cenu ",[883,58101,58103],{"className":58102},[886],[888,58104,58105],{"xmlns":890},[892,58106,58107,58115],{},[895,58108,58109],{},[2062,58110,58111,58113],{},[898,58112,8194],{},[898,58114,1842],{},[902,58116,50146],{"encoding":904},[883,58118,58120],{"className":58119},[886],[888,58121,58122],{"xmlns":890},[892,58123,58124,58128],{},[895,58125,58126],{},[898,58127,8194],{},[902,58129,8194],{"encoding":904},", přibližnou změnu rovnovážné ceny ",[883,58132,58134],{"className":58133},[886],[888,58135,58136],{"xmlns":890},[892,58137,58138,58146],{},[895,58139,58140],{},[2062,58141,58142,58144],{},[898,58143,8194],{},[898,58145,1842],{},[902,58147,50146],{"encoding":904},[883,58149,58151],{"className":58150},[886],[888,58152,58153],{"xmlns":890},[892,58154,58155,58159],{},[895,58156,58157],{},[898,58158,207],{},[902,58160,207],{"encoding":904},[883,58162,58164],{"className":58163},[886],[888,58165,58166],{"xmlns":890},[892,58167,58168,58174],{},[895,58169,58170,58172],{},[1656,58171,3964],{},[1667,58173,2617],{},[902,58175,56787],{"encoding":904}," (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,58178,58180],{"className":58179},[886],[888,58181,58182],{"xmlns":890},[892,58183,58184,58194],{},[895,58185,58186],{},[1715,58187,58188,58190,58192],{},[898,58189,8194],{},[1667,58191,1669],{},[898,58193,1842],{},[902,58195,56532],{"encoding":904},[123,58197,58198,58199,56742,58216,58229,58230,1863],{},"(k) Určete přibližnou změnu rovnovážné ceny ",[883,58200,58202],{"className":58201},[886],[888,58203,58204],{"xmlns":890},[892,58205,58206,58214],{},[895,58207,58208],{},[2062,58209,58210,58212],{},[898,58211,8194],{},[898,58213,1842],{},[902,58215,50146],{"encoding":904},[883,58217,58219],{"className":58218},[886],[888,58220,58221],{"xmlns":890},[892,58222,58223,58227],{},[895,58224,58225],{},[898,58226,207],{},[902,58228,207],{"encoding":904}," na 2 (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,58231,58233],{"className":58232},[886],[888,58234,58235],{"xmlns":890},[892,58236,58237,58247],{},[895,58238,58239],{},[1715,58240,58241,58243,58245],{},[898,58242,8194],{},[1667,58244,1680],{},[898,58246,1842],{},[902,58248,56593],{"encoding":904},[123,58250,58251,58252,57460,58269,58282,58283,3619,58296,58033,58311,58324,58325,58338,58339,1863],{},"(l) Určete přibližnou změnu rovnovážné ceny ",[883,58253,58255],{"className":58254},[886],[888,58256,58257],{"xmlns":890},[892,58258,58259,58267],{},[895,58260,58261],{},[2062,58262,58263,58265],{},[898,58264,8194],{},[898,58266,1842],{},[902,58268,50146],{"encoding":904},[883,58270,58272],{"className":58271},[886],[888,58273,58274],{"xmlns":890},[892,58275,58276,58280],{},[895,58277,58278],{},[898,58279,207],{},[902,58281,207],{"encoding":904}," na 90, poklesu ",[883,58284,58286],{"className":58285},[886],[888,58287,58288],{"xmlns":890},[892,58289,58290,58294],{},[895,58291,58292],{},[898,58293,3403],{},[902,58295,3403],{"encoding":904},[883,58297,58299],{"className":58298},[886],[888,58300,58301],{"xmlns":890},[892,58302,58303,58309],{},[895,58304,58305,58307],{},[1656,58306,3964],{},[1667,58308,2617],{},[902,58310,56787],{"encoding":904},[883,58312,58314],{"className":58313},[886],[888,58315,58316],{"xmlns":890},[892,58317,58318,58322],{},[895,58319,58320],{},[898,58321,1745],{},[902,58323,1745],{"encoding":904}," na 30 a růstu ",[883,58326,58328],{"className":58327},[886],[888,58329,58330],{"xmlns":890},[892,58331,58332,58336],{},[895,58333,58334],{},[898,58335,3768],{},[902,58337,3768],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,58340,58342],{"className":58341},[886],[888,58343,58344],{"xmlns":890},[892,58345,58346,58356],{},[895,58347,58348],{},[1715,58349,58350,58352,58354],{},[898,58351,8194],{},[1667,58353,2617],{},[898,58355,1842],{},[902,58357,57589],{"encoding":904},[198,58359,820],{"id":58360},"přebytek-spotřebitele-a-výrobce-1",[724,58362,58363,56359,58366,56396,58402,1863],{},[38,58364,58365],{},"2.17",[883,58367,58369],{"className":58368},[886],[888,58370,58371],{"xmlns":890},[892,58372,58373,58399],{},[895,58374,58375,58377,58379,58381,58383,58385,58387,58389,58391,58393],{},[898,58376,8194],{},[1656,58378,1713],{},[898,58380,6787],{},[1656,58382,1659],{"stretchy":1658},[898,58384,1665],{},[1656,58386,1683],{"stretchy":1658},[1656,58388,1713],{},[1667,58390,23770],{},[1656,58392,3964],{},[2062,58394,58395,58397],{},[898,58396,1665],{},[1667,58398,1680],{},[902,58400,58401],{"encoding":904},"P = D(Q) = 35 - Q^2",[883,58403,58405],{"className":58404},[886],[888,58406,58407],{"xmlns":890},[892,58408,58409,58435],{},[895,58410,58411,58413,58415,58417,58419,58421,58423,58425,58427,58429],{},[898,58412,8194],{},[1656,58414,1713],{},[898,58416,1769],{},[1656,58418,1659],{"stretchy":1658},[898,58420,1665],{},[1656,58422,1683],{"stretchy":1658},[1656,58424,1713],{},[1667,58426,2617],{},[1656,58428,3633],{},[2062,58430,58431,58433],{},[898,58432,1665],{},[1667,58434,1680],{},[902,58436,58437],{"encoding":904},"P = S(Q) = 3 + Q^2",[120,58439,58440,58443],{},[123,58441,58442],{},"(a) Vypočtěte přebytek spotřebitele při množství 4.",[123,58444,58445],{},"(b) Vypočtěte přebytek výrobce při množství 4.",[724,58447,58448,56359,58451,56396,58485,1863],{},[38,58449,58450],{},"2.18",[883,58452,58454],{"className":58453},[886],[888,58455,58456],{"xmlns":890},[892,58457,58458,58482],{},[895,58459,58460,58462,58464,58466,58468,58470,58472,58474,58476,58478,58480],{},[898,58461,8194],{},[1656,58463,1713],{},[898,58465,6787],{},[1656,58467,1659],{"stretchy":1658},[898,58469,1665],{},[1656,58471,1683],{"stretchy":1658},[1656,58473,1713],{},[1667,58475,12494],{},[1656,58477,3964],{},[1667,58479,1680],{},[898,58481,1665],{},[902,58483,58484],{"encoding":904},"P = D(Q) = 18 - 2Q",[883,58486,58488],{"className":58487},[886],[888,58489,58490],{"xmlns":890},[892,58491,58492,58518],{},[895,58493,58494,58496,58498,58500,58502,58504,58506,58508,58510,58512],{},[898,58495,8194],{},[1656,58497,1713],{},[898,58499,1769],{},[1656,58501,1659],{"stretchy":1658},[898,58503,1665],{},[1656,58505,1683],{"stretchy":1658},[1656,58507,1713],{},[1667,58509,2617],{},[1656,58511,3633],{},[2062,58513,58514,58516],{},[898,58515,1665],{},[1667,58517,1680],{},[902,58519,58437],{"encoding":904},[120,58521,58522,58542,58545,58548],{},[123,58523,58524,58525,1863],{},"(a) Vypočtěte rovnovážné množství ",[883,58526,58528],{"className":58527},[886],[888,58529,58530],{"xmlns":890},[892,58531,58532,58540],{},[895,58533,58534],{},[2062,58535,58536,58538],{},[898,58537,1665],{},[898,58539,1842],{},[902,58541,51080],{"encoding":904},[123,58543,58544],{},"(b) Vypočtěte přebytek spotřebitele při rovnovážném množství.",[123,58546,58547],{},"(b) Vypočtěte přebytek výrobce při rovnovážném množství.",[123,58549,58550],{},"(c) Graficky interpretujte.",[45652,58552],{},[115,58554,8779],{"id":8778},[152,58556,58557,58560,58563,58566,58569,58572,58575,58578,58581,58584,58587,58590,58593,58596],{},[123,58558,58559],{},"Jaký je rozdíl mezi jednofaktorovým a vícefaktorovým modelem poptávky?",[123,58561,58562],{},"Vyjádřete (vícefaktorovou) funkci poptávky. Jakou má vlastnost?",[123,58564,58565],{},"Definujte funkci poptávky (jednofaktorovou). Jaká je její základní vlastnost? Zdůvodněte.",[123,58567,58568],{},"Definujte Engelovu funkci. Na čem závisí tvar příslušné Engelovy křivky?",[123,58570,58571],{},"Jaký charakter má odezva poptávky na změnu některé z exogenních proměnných?",[123,58573,58574],{},"Definujte funkci nabídky. Jaká je její základní vlastnost? Zdůvodněte.",[123,58576,58577],{},"Co znamená tržní rovnováha? Čím je reprezentována?",[123,58579,58580],{},"Jak se určí rovnovážné množství a rovnovážná cena?",[123,58582,58583],{},"Jaká jsou pravidla pro změnu rovnovážného bodu jako odezvy na posun poptávky, resp. nabídky?",[123,58585,58586],{},"K čemu slouží multiplikátory?",[123,58588,58589],{},"Jak se najde redukovaný tvar pro vybranou rovnovážnou veličinu?",[123,58591,58592],{},"Jak se vypočtou multiplikátory? Mění se jejich znaménka?",[123,58594,58595],{},"Co se rozumí přebytkem spotřebitele? Jak se vypočte?",[123,58597,58598],{},"Co se rozumí přebytkem výrobce? Jak se vypočte?",[45652,58600],{},[115,58602,10198],{"id":10197},[724,58604,58605],{},[38,58606,21894],{},[120,58608,58609,58644,58649,58679,58684,58747,58773,58778,58808,58817,58824,58830],{},[123,58610,58611,3247,58614,10722,58617,1643,58619,1343,58642],{},[38,58612,58613],{},"Poptávané množství",[614,58615,58616],{},"quantity demanded",[38,58618,36711],{},[883,58620,58622],{"className":58621},[886],[888,58623,58624],{"xmlns":890},[892,58625,58626,58640],{},[895,58627,58628,58630,58632,58634,58636,58638],{},[898,58629,1665],{},[1656,58631,1713],{},[898,58633,6787],{},[1656,58635,1659],{"stretchy":1658},[898,58637,8194],{},[1656,58639,1683],{"stretchy":1658},[902,58641,12971],{"encoding":904},[38,58643,46131],{},[123,58645,58646,58648],{},[38,58647,46138],{}," — substituční + důchodový efekt",[123,58650,58651,1643,58654],{},[38,58652,58653],{},"Reálné cenové rozpětí",[883,58655,58657],{"className":58656},[886],[888,58658,58659],{"xmlns":890},[892,58660,58661,58677],{},[895,58662,58663,58665,58667,58669,58675],{},[1656,58664,1659],{"stretchy":1658},[1667,58666,4032],{},[1656,58668,1673],{"separator":1672},[1661,58670,58671,58673],{},[898,58672,8194],{},[1667,58674,4032],{},[1656,58676,1683],{"stretchy":1658},[902,58678,46339],{"encoding":904},[123,58680,58681,19834],{},[38,58682,58683],{},"Homogenita poptávky",[123,58685,58686,1643,58689,1343,58712,1343,58729,58746],{},[38,58687,58688],{},"Lineární poptávka",[883,58690,58692],{"className":58691},[886],[888,58693,58694],{"xmlns":890},[892,58695,58696,58710],{},[895,58697,58698,58700,58702,58704,58706,58708],{},[898,58699,8194],{},[1656,58701,1713],{},[898,58703,207],{},[898,58705,1665],{},[1656,58707,3633],{},[898,58709,3403],{},[902,58711,45742],{"encoding":904},[883,58713,58715],{"className":58714},[886],[888,58716,58717],{"xmlns":890},[892,58718,58719,58727],{},[895,58720,58721,58723,58725],{},[898,58722,207],{},[1656,58724,4373],{},[1667,58726,4032],{},[902,58728,51762],{"encoding":904},[883,58730,58732],{"className":58731},[886],[888,58733,58734],{"xmlns":890},[892,58735,58736,58744],{},[895,58737,58738,58740,58742],{},[898,58739,3403],{},[1656,58741,2850],{},[1667,58743,4032],{},[902,58745,27536],{"encoding":904}," — nedokonalá konkurence",[123,58748,58749,2533,58752],{},[38,58750,58751],{},"Dokonalá konkurence",[883,58753,58755],{"className":58754},[886],[888,58756,58757],{"xmlns":890},[892,58758,58759,58771],{},[895,58760,58761,58763,58765],{},[898,58762,8194],{},[1656,58764,1713],{},[2062,58766,58767,58769],{},[898,58768,8194],{},[1656,58770,8187],{},[902,58772,13132],{"encoding":904},[123,58774,58775,58777],{},[38,58776,46908],{}," — rostoucí křivka poptávky (důchodový efekt > substituční)",[123,58779,58780,1643,58782,1343,58806],{},[38,58781,40417],{},[883,58783,58785],{"className":58784},[886],[888,58786,58787],{"xmlns":890},[892,58788,58789,58803],{},[895,58790,58791,58793,58795,58797,58799,58801],{},[898,58792,1665],{},[1656,58794,1713],{},[898,58796,1842],{},[1656,58798,1659],{"stretchy":1658},[898,58800,8184],{},[1656,58802,1683],{"stretchy":1658},[902,58804,58805],{"encoding":904},"Q = E(Y)",[38,58807,47105],{},[123,58809,58810,58813,58814,58816],{},[38,58811,58812],{},"Normální"," (nezbytné \u002F luxusní) vs. ",[38,58815,47550],{}," zboží",[123,58818,58819,1896,58821,58823],{},[38,58820,48555],{},[38,58822,48502],{}," — znaménka zkřížených koeficientů",[123,58825,58826,58829],{},[38,58827,58828],{},"Dvoukomoditní trh"," (2.6)",[123,58831,58832,3247,58835,1683],{},[38,58833,58834],{},"Posun poptávky",[614,58836,47608],{},[724,58838,58839],{},[38,58840,21858],{},[120,58842,58843,58876,58880,58925],{},[123,58844,58845,3247,58847,10722,58849,1643,58851,1343,58874],{},[38,58846,48949],{},[614,58848,48952],{},[38,58850,49123],{},[883,58852,58854],{"className":58853},[886],[888,58855,58856],{"xmlns":890},[892,58857,58858,58872],{},[895,58859,58860,58862,58864,58866,58868,58870],{},[898,58861,1665],{},[1656,58863,1713],{},[898,58865,1769],{},[1656,58867,1659],{"stretchy":1658},[898,58869,8194],{},[1656,58871,1683],{"stretchy":1658},[902,58873,17436],{"encoding":904},[38,58875,49201],{},[123,58877,58878],{},[38,58879,49208],{},[123,58881,58882,1643,58885,1343,58908],{},[38,58883,58884],{},"Lineární nabídka",[883,58886,58888],{"className":58887},[886],[888,58889,58890],{"xmlns":890},[892,58891,58892,58906],{},[895,58893,58894,58896,58898,58900,58902,58904],{},[898,58895,8194],{},[1656,58897,1713],{},[898,58899,1745],{},[898,58901,1665],{},[1656,58903,3633],{},[898,58905,3768],{},[902,58907,48922],{"encoding":904},[883,58909,58911],{"className":58910},[886],[888,58912,58913],{"xmlns":890},[892,58914,58915,58923],{},[895,58916,58917,58919,58921],{},[898,58918,1745],{},[1656,58920,2850],{},[1667,58922,4032],{},[902,58924,48940],{"encoding":904},[123,58926,58927,3247,58930,1683],{},[38,58928,58929],{},"Posun nabídky",[614,58931,49586],{},[724,58933,58934],{},[38,58935,58936],{},"Rovnováha a komparativní statika",[120,58938,58939,59018,59024],{},[123,58940,58941,3247,58943,10722,58945,1643,58948,1343,58965,1643,58968,1343,58985,1643,58987],{},[38,58942,50005],{},[614,58944,50124],{},[38,58946,58947],{},"rovnovážná cena",[883,58949,58951],{"className":58950},[886],[888,58952,58953],{"xmlns":890},[892,58954,58955,58963],{},[895,58956,58957],{},[2062,58958,58959,58961],{},[898,58960,8194],{},[898,58962,1842],{},[902,58964,50146],{"encoding":904},[38,58966,58967],{},"rovnovážné množství",[883,58969,58971],{"className":58970},[886],[888,58972,58973],{"xmlns":890},[892,58974,58975,58983],{},[895,58976,58977],{},[2062,58978,58979,58981],{},[898,58980,1665],{},[898,58982,1842],{},[902,58984,51080],{"encoding":904},[38,58986,50182],{},[883,58988,58990],{"className":58989},[886],[888,58991,58992],{"xmlns":890},[892,58993,58994,59016],{},[895,58995,58996,58998,59000,59006,59008,59014],{},[898,58997,1842],{},[1656,58999,3453],{"stretchy":1658},[2062,59001,59002,59004],{},[898,59003,1665],{},[898,59005,1842],{},[1656,59007,1673],{"separator":1672},[2062,59009,59010,59012],{},[898,59011,8194],{},[898,59013,1842],{},[1656,59015,3462],{"stretchy":1658},[902,59017,50047],{"encoding":904},[123,59019,59020,59023],{},[38,59021,59022],{},"Pravidla 1–4"," komparativní statiky",[123,59025,59026,3247,59029,1683],{},[38,59027,59028],{},"Teorém pavučiny",[614,59030,51026],{},[724,59032,59033],{},[38,59034,59035],{},"Zdanění",[120,59037,59038,59094,59142],{},[123,59039,59040,59042,59043,59068,59069,1683],{},[38,59041,59035],{}," — daň výrobci (",[883,59044,59046],{"className":59045},[886],[888,59047,59048],{"xmlns":890},[892,59049,59050,59066],{},[895,59051,59052,59058,59060,59062,59064],{},[1661,59053,59054,59056],{},[898,59055,1769],{},[1667,59057,1669],{},[1656,59059,1713],{},[898,59061,1769],{},[1656,59063,3633],{},[898,59065,11577],{},[902,59067,51431],{"encoding":904},") vs. daň spotřebiteli (",[883,59070,59072],{"className":59071},[886],[888,59073,59074],{"xmlns":890},[892,59075,59076,59092],{},[895,59077,59078,59084,59086,59088,59090],{},[1661,59079,59080,59082],{},[898,59081,6787],{},[1667,59083,1680],{},[1656,59085,1713],{},[898,59087,6787],{},[1656,59089,3964],{},[898,59091,11577],{},[902,59093,51462],{"encoding":904},[123,59095,59096,1643,59098,1343,59119],{},[38,59097,51335],{},[883,59099,59101],{"className":59100},[886],[888,59102,59103],{"xmlns":890},[892,59104,59105,59117],{},[895,59106,59107],{},[1661,59108,59109,59111],{},[898,59110,11577],{},[895,59112,59113,59115],{},[898,59114,51354],{},[898,59116,724],{},[902,59118,51359],{"encoding":904},[883,59120,59122],{"className":59121},[886],[888,59123,59124],{"xmlns":890},[892,59125,59126,59140],{},[895,59127,59128],{},[1661,59129,59130,59132],{},[898,59131,11577],{},[895,59133,59134,59136,59138],{},[898,59135,51377],{},[898,59137,10839],{},[898,59139,20776],{},[902,59141,51384],{"encoding":904},[123,59143,59144,1643,59147,1343,59176],{},[38,59145,59146],{},"Ekvivalence zdanění",[883,59148,59150],{"className":59149},[886],[888,59151,59152],{"xmlns":890},[892,59153,59154,59174],{},[895,59155,59156,59164,59166],{},[1715,59157,59158,59160,59162],{},[898,59159,1665],{},[1667,59161,1669],{},[898,59163,1842],{},[1656,59165,1713],{},[1715,59167,59168,59170,59172],{},[898,59169,1665],{},[1667,59171,1680],{},[898,59173,1842],{},[902,59175,51585],{"encoding":904},[883,59177,59179],{"className":59178},[886],[888,59180,59181],{"xmlns":890},[892,59182,59183,59207],{},[895,59184,59185,59193,59195,59197,59199],{},[1715,59186,59187,59189,59191],{},[898,59188,8194],{},[1667,59190,1669],{},[898,59192,1842],{},[1656,59194,3964],{},[898,59196,11577],{},[1656,59198,1713],{},[1715,59200,59201,59203,59205],{},[898,59202,8194],{},[1667,59204,1680],{},[898,59206,1842],{},[902,59208,51619],{"encoding":904},[724,59210,59211],{},[38,59212,35123],{},[120,59214,59215,59261,59292,59297,59303,59310],{},[123,59216,59217,1643,59219],{},[38,59218,51718],{},[883,59220,59222],{"className":59221},[886],[888,59223,59224],{"xmlns":890},[892,59225,59226,59258],{},[895,59227,59228,59234,59236,59238,59240,59242,59244,59246,59248,59250,59252,59254,59256],{},[2062,59229,59230,59232],{},[898,59231,1665],{},[898,59233,1842],{},[1656,59235,1713],{},[1656,59237,1659],{"stretchy":1658},[898,59239,3403],{},[1656,59241,3964],{},[898,59243,3768],{},[1656,59245,1683],{"stretchy":1658},[898,59247,1782],{"mathvariant":1723},[1656,59249,1659],{"stretchy":1658},[898,59251,1745],{},[1656,59253,3964],{},[898,59255,207],{},[1656,59257,1683],{"stretchy":1658},[902,59259,59260],{"encoding":904},"Q^E = (b - d)\u002F(c - a)",[123,59262,59263,1643,59266,59291],{},[38,59264,59265],{},"Parametry",[883,59267,59269],{"className":59268},[886],[888,59270,59271],{"xmlns":890},[892,59272,59273,59289],{},[895,59274,59275,59277,59279,59281,59283,59285,59287],{},[898,59276,207],{},[1656,59278,1673],{"separator":1672},[898,59280,3403],{},[1656,59282,1673],{"separator":1672},[898,59284,1745],{},[1656,59286,1673],{"separator":1672},[898,59288,3768],{},[902,59290,51962],{"encoding":904}," — exogenní proměnné",[123,59293,59294],{},[38,59295,59296],{},"Endogenní \u002F exogenní proměnná",[123,59298,59299,59302],{},[38,59300,59301],{},"Multiplikátor"," — parciální derivace redukovaného tvaru",[123,59304,59305,1343,59308],{},[38,59306,59307],{},"Komparativní statika",[38,59309,45642],{},[123,59311,59312,1643,59314,59330],{},[38,59313,11750],{},[883,59315,59317],{"className":59316},[886],[888,59318,59319],{"xmlns":890},[892,59320,59321,59327],{},[895,59322,59323,59325],{},[898,59324,3768],{},[898,59326,1665],{},[902,59328,59329],{"encoding":904},"dQ"," (2.11)",[724,59332,59333],{},[38,59334,59335],{},"Přebytky a ostatní",[120,59337,59338,59376],{},[123,59339,59340,1643,59342,59357,59358,1643,59360,59375],{},[38,59341,53611],{},[883,59343,59345],{"className":59344},[886],[888,59346,59347],{"xmlns":890},[892,59348,59349,59355],{},[895,59350,59351,59353],{},[898,59352,1766],{},[898,59354,1769],{},[902,59356,53627],{"encoding":904}," (2.14), ",[38,59359,53630],{},[883,59361,59363],{"className":59362},[886],[888,59364,59365],{"xmlns":890},[892,59366,59367,59373],{},[895,59368,59369,59371],{},[898,59370,8194],{},[898,59372,1769],{},[902,59374,53646],{"encoding":904}," (2.15)",[123,59377,59378,1343,59381,59384],{},[38,59379,59380],{},"Homo economicus",[38,59382,59383],{},"Marshallova formulace"," (1890)",[45652,59386],{},[115,59388,10640],{"id":10639},[120,59390,59391,59426,59435],{},[123,59392,59393,1643,59396,59399,59400,1343,59403,59406,59407,59410,59411,59414,59415,59418,59419,59422,59423],{},[38,59394,59395],{},"Související témata:",[207,59397,811],{"className":59398,"dataFsResolvedFilePath":809,"href":810},[210]," (dopady daně, daňové břemeno, ekvivalence), ",[207,59401,820],{"className":59402,"dataFsResolvedFilePath":818,"href":819},[210],[207,59404,10692],{"className":59405,"dataFsResolvedFilePath":764,"href":765},[210]," (zákon klesající\u002Frostoucí, monotonie), ",[207,59408,775],{"className":59409,"dataFsResolvedFilePath":773,"href":774},[210]," (CS a PS), ",[207,59412,784],{"className":59413,"dataFsResolvedFilePath":782,"href":783},[210]," (vícefaktorové modely, multiplikátory), ",[207,59416,793],{"className":59417,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace spotřebitele), ",[207,59420,12613],{"className":59421,"dataFsResolvedFilePath":848,"href":849},[210]," (důchodová a cenová citlivost), ",[207,59424,12608],{"className":59425,"dataFsResolvedFilePath":827,"href":828},[210],[123,59427,59428,1643,59431],{},[38,59429,59430],{},"Shrnutí přednášek:",[207,59432,59434],{"className":59433,"dataFsResolvedFilePath":745,"href":746},[210],"KS — 1. blok",[123,59436,59437,1643,59439],{},[38,59438,10742],{},[207,59440,1869],{"className":59441,"dataFsResolvedFilePath":10746,"href":10747},[210],{"title":641,"searchDepth":642,"depth":642,"links":59443},[59444,59445,59453,59459,59466,59467,59474,59475,59476,59483,59484,59485],{"id":45477,"depth":642,"text":45478},{"id":45458,"depth":642,"text":21894,"children":59446},[59447,59448,59449,59450,59452],{"id":45745,"depth":649,"text":45746},{"id":46027,"depth":649,"text":46028},{"id":47037,"depth":649,"text":47038},{"id":47604,"depth":649,"text":59451},"Posun poptávky (shift of demand)",{"id":48107,"depth":649,"text":48108},{"id":45462,"depth":642,"text":21858,"children":59454},[59455,59456,59457],{"id":48944,"depth":649,"text":45746},{"id":49130,"depth":649,"text":49131},{"id":49582,"depth":649,"text":59458},"Posun nabídky (shift of supply)",{"id":50004,"depth":642,"text":50005,"children":59460},[59461,59462,59463,59464,59465],{"id":50116,"depth":649,"text":50117},{"id":50329,"depth":649,"text":50330},{"id":50644,"depth":649,"text":50645},{"id":50998,"depth":649,"text":50999},{"id":51029,"depth":649,"text":51030},{"id":51298,"depth":642,"text":811},{"id":51699,"depth":642,"text":51700,"children":59468},[59469,59470,59471,59472],{"id":51717,"depth":649,"text":51718},{"id":52098,"depth":649,"text":52099},{"id":52482,"depth":649,"text":52483},{"id":52936,"depth":649,"text":59473},"Příklad 2.11 — komparativní statika pro QEQ^E",{"id":20521,"depth":642,"text":820},{"id":53861,"depth":642,"text":53862},{"id":54092,"depth":642,"text":54093,"children":59477},[59478,59479,59480,59481,59482],{"id":54096,"depth":649,"text":54097},{"id":54936,"depth":649,"text":54937},{"id":55312,"depth":649,"text":50005},{"id":56605,"depth":649,"text":51700},{"id":58360,"depth":649,"text":820},{"id":8778,"depth":642,"text":8779},{"id":10197,"depth":642,"text":10198},{"id":10639,"depth":642,"text":10640},{},"\u002Ftopics\u002Fpoptavka-nabidka",{"title":802,"description":641},[1138,1135],"topics\u002Fpoptavka-nabidka",[1128,59492,59493,59494,26606,59495,59496],"poptavka","nabidka","rovnovaha","zdaneni","prebytek","VHXMOe03Z24g0HTNlL2geCMzNcnJ3vQ8m2Org-s9n8Q",{"id":59499,"title":820,"body":59500,"course":1128,"courses":659,"created":10774,"description":641,"extension":661,"meta":63776,"navigation":664,"path":63777,"seo":63778,"sources":63779,"stem":63780,"tags":63781,"type":10786,"updated":677,"__hash__":63786},"topics\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce.md",{"type":9,"value":59501,"toc":63754},[59502,59504,59572,59622,59624,59627,59885,59961,59966,59968,59987,59991,60067,60152,60154,60468,60561,60563,60582,60586,60660,60745,60748,60924,60929,60931,61350,61352,61356,61360,61595,61639,61739,61805,61808,61841,62016,62078,62208,62286,62397,62431,62629,62648,62667,62732,62736,62739,62784,62787,62905,62951,62953,62957,63305,63307,63309,63587,63589,63593,63628,63635,63708,63710,63712],[12,59503,820],{"id":20521},[1981,59505,59506],{},[724,59507,59508,12658,59510,3247,59512,59527,59528,3247,59530,59545,59546,59568,59569,1863],{},[883,59509,12657],{},[38,59511,53611],{},[883,59513,59515],{"className":59514},[886],[888,59516,59517],{"xmlns":890},[892,59518,59519,59525],{},[895,59520,59521,59523],{},[898,59522,1766],{},[898,59524,1769],{},[902,59526,53627],{"encoding":904},") je rozdíl mezi tím, co byl spotřebitel ochoten zaplatit, a tím, co skutečně zaplatil. ",[38,59529,53758],{},[883,59531,59533],{"className":59532},[886],[888,59534,59535],{"xmlns":890},[892,59536,59537,59543],{},[895,59538,59539,59541],{},[898,59540,8194],{},[898,59542,1769],{},[902,59544,53646],{"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 ",[883,59547,59549],{"className":59548},[886],[888,59550,59551],{"xmlns":890},[892,59552,59553,59565],{},[895,59554,59555,59557,59559,59561,59563],{},[898,59556,1766],{},[898,59558,1769],{},[1656,59560,3633],{},[898,59562,8194],{},[898,59564,1769],{},[902,59566,59567],{"encoding":904},"CS + PS"," měří ",[38,59570,59571],{},"celkový blahobyt trhu",[724,59573,59574,3247,59576,1343,59578,20863,59593,3247,59595,1343,59597,59612,59613,59617,59618,1863],{},[38,59575,53611],{},[614,59577,53665],{},[883,59579,59581],{"className":59580},[886],[888,59582,59583],{"xmlns":890},[892,59584,59585,59591],{},[895,59586,59587,59589],{},[898,59588,1766],{},[898,59590,1769],{},[902,59592,53627],{"encoding":904},[38,59594,53630],{},[614,59596,53761],{},[883,59598,59600],{"className":59599},[886],[888,59601,59602],{"xmlns":890},[892,59603,59604,59610],{},[895,59605,59606,59608],{},[898,59607,8194],{},[898,59609,1769],{},[902,59611,53646],{"encoding":904},") kvantifikují čistý prospěch jednotlivých stran trhu. Navazují na pojmy ",[207,59614,59616],{"className":59615,"dataFsResolvedFilePath":800,"href":801},[210],"tržní rovnováhy"," a využívají aparát ",[207,59619,59621],{"className":59620,"dataFsResolvedFilePath":773,"href":774},[210],"integrálního počtu",[45652,59623],{},[115,59625,1241],{"id":59626},"úvod",[724,59628,59629,59630,59653,59654,59677,59678,59695,59696,12694,59728,59760,59761,59787,59788,59791,59792,59795,59796,22743,59830,30312,59851,1863],{},"Je dána funkce poptávky ",[883,59631,59633],{"className":59632},[886],[888,59634,59635],{"xmlns":890},[892,59636,59637,59651],{},[895,59638,59639,59641,59643,59645,59647,59649],{},[898,59640,8194],{},[1656,59642,1713],{},[898,59644,6787],{},[1656,59646,1659],{"stretchy":1658},[898,59648,1665],{},[1656,59650,1683],{"stretchy":1658},[902,59652,13412],{"encoding":904},", resp. funkce nabídky ",[883,59655,59657],{"className":59656},[886],[888,59658,59659],{"xmlns":890},[892,59660,59661,59675],{},[895,59662,59663,59665,59667,59669,59671,59673],{},[898,59664,8194],{},[1656,59666,1713],{},[898,59668,1769],{},[1656,59670,1659],{"stretchy":1658},[898,59672,1665],{},[1656,59674,1683],{"stretchy":1658},[902,59676,49751],{"encoding":904},". Pro pevně zadané množství ",[883,59679,59681],{"className":59680},[886],[888,59682,59683],{"xmlns":890},[892,59684,59685,59693],{},[895,59686,59687],{},[1661,59688,59689,59691],{},[898,59690,1665],{},[1667,59692,4032],{},[902,59694,46990],{"encoding":904}," je odpovídající cena ",[883,59697,59699],{"className":59698},[886],[888,59700,59701],{"xmlns":890},[892,59702,59703,59725],{},[895,59704,59705,59711,59713,59715,59717,59723],{},[1661,59706,59707,59709],{},[898,59708,8194],{},[1667,59710,4032],{},[1656,59712,1713],{},[898,59714,6787],{},[1656,59716,1659],{"stretchy":1658},[1661,59718,59719,59721],{},[898,59720,1665],{},[1667,59722,4032],{},[1656,59724,1683],{"stretchy":1658},[902,59726,59727],{"encoding":904},"P_0 = D(Q_0)",[883,59729,59731],{"className":59730},[886],[888,59732,59733],{"xmlns":890},[892,59734,59735,59757],{},[895,59736,59737,59743,59745,59747,59749,59755],{},[1661,59738,59739,59741],{},[898,59740,8194],{},[1667,59742,4032],{},[1656,59744,1713],{},[898,59746,1769],{},[1656,59748,1659],{"stretchy":1658},[1661,59750,59751,59753],{},[898,59752,1665],{},[1667,59754,4032],{},[1656,59756,1683],{"stretchy":1658},[902,59758,59759],{"encoding":904},"P_0 = S(Q_0)","). Součin ",[883,59762,59764],{"className":59763},[886],[888,59765,59766],{"xmlns":890},[892,59767,59768,59784],{},[895,59769,59770,59776,59778],{},[1661,59771,59772,59774],{},[898,59773,8194],{},[1667,59775,4032],{},[2461,59777,7828],{},[1661,59779,59780,59782],{},[898,59781,1665],{},[1667,59783,4032],{},[902,59785,59786],{"encoding":904},"P_0 \\, Q_0"," reprezentuje buď ",[38,59789,59790],{},"výdaje spotřebitele",", nebo ",[38,59793,59794],{},"tržby výrobce"," a geometricky odpovídá obsahu obdélníka ",[883,59797,59799],{"className":59798},[886],[888,59800,59801],{"xmlns":890},[892,59802,59803,59827],{},[895,59804,59805,59807,59809,59815,59817,59819,59821],{},[1667,59806,4032],{},[2461,59808,7828],{},[1661,59810,59811,59813],{},[898,59812,1665],{},[1667,59814,4032],{},[2461,59816,7828],{},[898,59818,2146],{},[2461,59820,7828],{},[1661,59822,59823,59825],{},[898,59824,8194],{},[1667,59826,4032],{},[902,59828,59829],{"encoding":904},"0\\,Q_0\\,A\\,P_0",[883,59831,59833],{"className":59832},[886],[888,59834,59835],{"xmlns":890},[892,59836,59837,59849],{},[895,59838,59839,59841,59843,59845,59847],{},[1656,59840,1659],{"stretchy":1658},[898,59842,1665],{},[1656,59844,1673],{"separator":1672},[898,59846,8194],{},[1656,59848,1683],{"stretchy":1658},[902,59850,46373],{"encoding":904},[883,59852,59854],{"className":59853},[886],[888,59855,59856],{"xmlns":890},[892,59857,59858,59882],{},[895,59859,59860,59862,59864,59866,59872,59874,59880],{},[898,59861,2146],{},[1656,59863,1713],{},[1656,59865,3453],{"stretchy":1658},[1661,59867,59868,59870],{},[898,59869,1665],{},[1667,59871,4032],{},[1656,59873,1673],{"separator":1672},[1661,59875,59876,59878],{},[898,59877,8194],{},[1667,59879,4032],{},[1656,59881,3462],{"stretchy":1658},[902,59883,59884],{"encoding":904},"A = [Q_0, P_0]",[1981,59886,59887,59892,59950],{},[724,59888,59889,59891],{},[883,59890,3472],{}," Intuice",[120,59893,59894,59922],{},[123,59895,59896,59897,59900,59901,59903,59904,59921],{},"Za jednotky zboží nakoupené ",[38,59898,59899],{},"před"," posledním kusem je spotřebitel podle funkce poptávky ochoten platit ",[614,59902,33986],{}," než ",[883,59905,59907],{"className":59906},[886],[888,59908,59909],{"xmlns":890},[892,59910,59911,59919],{},[895,59912,59913],{},[1661,59914,59915,59917],{},[898,59916,8194],{},[1667,59918,4032],{},[902,59920,47629],{"encoding":904}," — rozdíl si „šetří do kapsy\" jako přebytek.",[123,59923,59924,59925,59927,59928,59931,59932,59949],{},"Za jednotky zboží prodané ",[38,59926,59899],{}," posledním kusem by výrobce podle funkce nabídky byl ochoten prodávat i za ",[614,59929,59930],{},"nižší"," cenu než ",[883,59933,59935],{"className":59934},[886],[888,59936,59937],{"xmlns":890},[892,59938,59939,59947],{},[895,59940,59941],{},[1661,59942,59943,59945],{},[898,59944,8194],{},[1667,59946,4032],{},[902,59948,47629],{"encoding":904}," — rozdíl je jeho přebytek.",[724,59951,59952,59953,59956,59957,59960],{},"Přebytek je tedy rozdíl mezi ",[614,59954,59955],{},"ochotou"," (platit \u002F prodávat) a ",[614,59958,59959],{},"skutečností"," (zaplaceno \u002F obdrženo).",[724,59962,59963],{},[5956,59964],{"alt":53656,"className":59965,"src":53658},[210,5960],[45652,59967],{},[115,59969,59971,59972,1683],{"id":59970},"přebytek-spotřebitele-cscs","Přebytek spotřebitele (",[883,59973,59975],{"className":59974},[886],[888,59976,59977],{"xmlns":890},[892,59978,59979,59985],{},[895,59980,59981,59983],{},[898,59982,1766],{},[898,59984,1769],{},[902,59986,53627],{"encoding":904},[198,59988,59990],{"id":59989},"definice-vzorec-214","Definice (vzorec 2.14)",[724,59992,59993,59994,60017,60018,60035,60036,2114],{},"Pro poptávku ",[883,59995,59997],{"className":59996},[886],[888,59998,59999],{"xmlns":890},[892,60000,60001,60015],{},[895,60002,60003,60005,60007,60009,60011,60013],{},[898,60004,8194],{},[1656,60006,1713],{},[898,60008,6787],{},[1656,60010,1659],{"stretchy":1658},[898,60012,1665],{},[1656,60014,1683],{"stretchy":1658},[902,60016,13412],{"encoding":904}," a pevně zadané ",[883,60019,60021],{"className":60020},[886],[888,60022,60023],{"xmlns":890},[892,60024,60025,60033],{},[895,60026,60027],{},[1661,60028,60029,60031],{},[898,60030,1665],{},[1667,60032,4032],{},[902,60034,46990],{"encoding":904}," s cenou ",[883,60037,60039],{"className":60038},[886],[888,60040,60041],{"xmlns":890},[892,60042,60043,60065],{},[895,60044,60045,60051,60053,60055,60057,60063],{},[1661,60046,60047,60049],{},[898,60048,8194],{},[1667,60050,4032],{},[1656,60052,1713],{},[898,60054,6787],{},[1656,60056,1659],{"stretchy":1658},[1661,60058,60059,60061],{},[898,60060,1665],{},[1667,60062,4032],{},[1656,60064,1683],{"stretchy":1658},[902,60066,59727],{"encoding":904},[883,60068,60070],{"className":60069},[886],[888,60071,60072],{"xmlns":890,"display":2408},[892,60073,60074,60150],{},[2412,60075,60076],{"width":2414},[2416,60077,60078,60080,60144,60146],{},[2419,60079],{"width":2421},[2419,60081,60082],{},[895,60083,60084,60086,60088,60090,60096,60098,60100,60112,60114,60116,60118,60120,60122,60124,60126,60128,60134,60136,60142],{},[898,60085,1766],{},[898,60087,1769],{},[1656,60089,1659],{"stretchy":1658},[1661,60091,60092,60094],{},[898,60093,1665],{},[1667,60095,4032],{},[1656,60097,1683],{"stretchy":1658},[1656,60099,1713],{},[1715,60101,60102,60104,60106],{},[1656,60103,19906],{},[1667,60105,4032],{},[1661,60107,60108,60110],{},[898,60109,1665],{},[1667,60111,4032],{},[898,60113,6787],{},[1656,60115,1659],{"stretchy":1658},[898,60117,1665],{},[1656,60119,1683],{"stretchy":1658},[2461,60121,7828],{},[898,60123,3768],{},[898,60125,1665],{},[1656,60127,3964],{},[1661,60129,60130,60132],{},[898,60131,8194],{},[1667,60133,4032],{},[2461,60135,7828],{},[1661,60137,60138,60140],{},[898,60139,1665],{},[1667,60141,4032],{},[898,60143,1863],{"mathvariant":1723},[2419,60145],{"width":2421},[2419,60147,60148],{},[2461,60149,53750],{},[902,60151,53753],{"encoding":904},[198,60153,11258],{"id":11257},[120,60155,60156,60248,60310],{},[123,60157,60158,60198,60199,60225,60226,60229,60230,60247],{},[883,60159,60161],{"className":60160},[886],[888,60162,60163],{"xmlns":890},[892,60164,60165,60195],{},[895,60166,60167],{},[4138,60168,60169,60181,60183,60185,60187,60189,60191,60193],{"scriptlevel":4032,"displaystyle":1672},[1715,60170,60171,60173,60175],{},[1656,60172,19906],{},[1667,60174,4032],{},[1661,60176,60177,60179],{},[898,60178,1665],{},[1667,60180,4032],{},[898,60182,6787],{},[1656,60184,1659],{"stretchy":1658},[898,60186,1665],{},[1656,60188,1683],{"stretchy":1658},[2461,60190,7828],{},[898,60192,3768],{},[898,60194,1665],{},[902,60196,60197],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ"," — plocha pod křivkou poptávky v intervalu ",[883,60200,60202],{"className":60201},[886],[888,60203,60204],{"xmlns":890},[892,60205,60206,60222],{},[895,60207,60208,60210,60212,60214,60220],{},[1656,60209,3453],{"stretchy":1658},[1667,60211,4032],{},[1656,60213,1673],{"separator":1672},[1661,60215,60216,60218],{},[898,60217,1665],{},[1667,60219,4032],{},[1656,60221,3462],{"stretchy":1658},[902,60223,60224],{"encoding":904},"[0, Q_0]","; představuje celkovou ",[38,60227,60228],{},"ochotu platit"," (maximální částku, kterou by spotřebitel za ",[883,60231,60233],{"className":60232},[886],[888,60234,60235],{"xmlns":890},[892,60236,60237,60245],{},[895,60238,60239],{},[1661,60240,60241,60243],{},[898,60242,1665],{},[1667,60244,4032],{},[902,60246,46990],{"encoding":904}," jednotek byl ochoten zaplatit).",[123,60249,60250,60276,60277,12702],{},[883,60251,60253],{"className":60252},[886],[888,60254,60255],{"xmlns":890},[892,60256,60257,60273],{},[895,60258,60259,60265,60267],{},[1661,60260,60261,60263],{},[898,60262,8194],{},[1667,60264,4032],{},[2461,60266,7828],{},[1661,60268,60269,60271],{},[898,60270,1665],{},[1667,60272,4032],{},[902,60274,60275],{"encoding":904},"P_0\\,Q_0"," — skutečně zaplacená částka (obdélník ",[883,60278,60280],{"className":60279},[886],[888,60281,60282],{"xmlns":890},[892,60283,60284,60308],{},[895,60285,60286,60288,60290,60296,60298,60300,60302],{},[1667,60287,4032],{},[2461,60289,7828],{},[1661,60291,60292,60294],{},[898,60293,1665],{},[1667,60295,4032],{},[2461,60297,7828],{},[898,60299,2146],{},[2461,60301,7828],{},[1661,60303,60304,60306],{},[898,60305,8194],{},[1667,60307,4032],{},[902,60309,59829],{"encoding":904},[123,60311,60312,60327,60328,60350,60351,60376,60377,30312,60403,1896,60435,1863],{},[883,60313,60315],{"className":60314},[886],[888,60316,60317],{"xmlns":890},[892,60318,60319,60325],{},[895,60320,60321,60323],{},[898,60322,1766],{},[898,60324,1769],{},[902,60326,53627],{"encoding":904}," je plocha mezi křivkou poptávky a vodorovnou přímkou ",[883,60329,60331],{"className":60330},[886],[888,60332,60333],{"xmlns":890},[892,60334,60335,60347],{},[895,60336,60337,60339,60341],{},[898,60338,8194],{},[1656,60340,1713],{},[1661,60342,60343,60345],{},[898,60344,8194],{},[1667,60346,4032],{},[902,60348,60349],{"encoding":904},"P = P_0"," v pásu ",[883,60352,60354],{"className":60353},[886],[888,60355,60356],{"xmlns":890},[892,60357,60358,60374],{},[895,60359,60360,60362,60364,60366,60372],{},[1656,60361,3453],{"stretchy":1658},[1667,60363,4032],{},[1656,60365,1673],{"separator":1672},[1661,60367,60368,60370],{},[898,60369,1665],{},[1667,60371,4032],{},[1656,60373,3462],{"stretchy":1658},[902,60375,60224],{"encoding":904}," — „křivočarý trojúhelník\" ",[883,60378,60380],{"className":60379},[886],[888,60381,60382],{"xmlns":890},[892,60383,60384,60400],{},[895,60385,60386,60392,60394,60396,60398],{},[1661,60387,60388,60390],{},[898,60389,8194],{},[1667,60391,4032],{},[2461,60393,7828],{},[898,60395,2161],{},[2461,60397,7828],{},[898,60399,2146],{},[902,60401,60402],{"encoding":904},"P_0\\,B\\,A",[883,60404,60406],{"className":60405},[886],[888,60407,60408],{"xmlns":890},[892,60409,60410,60432],{},[895,60411,60412,60414,60416,60418,60420,60422,60424,60426,60428,60430],{},[898,60413,2161],{},[1656,60415,1713],{},[1656,60417,3453],{"stretchy":1658},[1667,60419,4032],{},[1656,60421,1673],{"separator":1672},[898,60423,6787],{},[1656,60425,1659],{"stretchy":1658},[1667,60427,4032],{},[1656,60429,1683],{"stretchy":1658},[1656,60431,3462],{"stretchy":1658},[902,60433,60434],{"encoding":904},"B = [0, D(0)]",[883,60436,60438],{"className":60437},[886],[888,60439,60440],{"xmlns":890},[892,60441,60442,60466],{},[895,60443,60444,60446,60448,60450,60456,60458,60464],{},[898,60445,2146],{},[1656,60447,1713],{},[1656,60449,3453],{"stretchy":1658},[1661,60451,60452,60454],{},[898,60453,1665],{},[1667,60455,4032],{},[1656,60457,1673],{"separator":1672},[1661,60459,60460,60462],{},[898,60461,8194],{},[1667,60463,4032],{},[1656,60465,3462],{"stretchy":1658},[902,60467,59884],{"encoding":904},[724,60469,60470],{},[614,60471,60472,60473,60486,60487,60520,60521,37841,60546,1863],{},"Obrázek 2.24: Křivka poptávky ",[883,60474,60476],{"className":60475},[886],[888,60477,60478],{"xmlns":890},[892,60479,60480,60484],{},[895,60481,60482],{},[898,60483,6787],{},[902,60485,6787],{"encoding":904},", bod ",[883,60488,60490],{"className":60489},[886],[888,60491,60492],{"xmlns":890},[892,60493,60494,60518],{},[895,60495,60496,60498,60500,60502,60508,60510,60516],{},[898,60497,2146],{},[1656,60499,1713],{},[1656,60501,3453],{"stretchy":1658},[1661,60503,60504,60506],{},[898,60505,1665],{},[1667,60507,4032],{},[1656,60509,1673],{"separator":1672},[1661,60511,60512,60514],{},[898,60513,8194],{},[1667,60515,4032],{},[1656,60517,3462],{"stretchy":1658},[902,60519,59884],{"encoding":904},", vyšrafovaná plocha trojúhelníku ",[883,60522,60524],{"className":60523},[886],[888,60525,60526],{"xmlns":890},[892,60527,60528,60544],{},[895,60529,60530,60536,60538,60540,60542],{},[1661,60531,60532,60534],{},[898,60533,8194],{},[1667,60535,4032],{},[2461,60537,7828],{},[898,60539,2161],{},[2461,60541,7828],{},[898,60543,2146],{},[902,60545,60402],{"encoding":904},[883,60547,60549],{"className":60548},[886],[888,60550,60551],{"xmlns":890},[892,60552,60553,60559],{},[895,60554,60555,60557],{},[898,60556,1766],{},[898,60558,1769],{},[902,60560,53627],{"encoding":904},[45652,60562],{},[115,60564,60566,60567,1683],{"id":60565},"přebytek-výrobce-psps","Přebytek výrobce (",[883,60568,60570],{"className":60569},[886],[888,60571,60572],{"xmlns":890},[892,60573,60574,60580],{},[895,60575,60576,60578],{},[898,60577,8194],{},[898,60579,1769],{},[902,60581,53646],{"encoding":904},[198,60583,60585],{"id":60584},"definice-vzorec-215","Definice (vzorec 2.15)",[724,60587,60588,60589,60017,60612,60035,60629,2114],{},"Analogicky — pro nabídku ",[883,60590,60592],{"className":60591},[886],[888,60593,60594],{"xmlns":890},[892,60595,60596,60610],{},[895,60597,60598,60600,60602,60604,60606,60608],{},[898,60599,8194],{},[1656,60601,1713],{},[898,60603,1769],{},[1656,60605,1659],{"stretchy":1658},[898,60607,1665],{},[1656,60609,1683],{"stretchy":1658},[902,60611,49751],{"encoding":904},[883,60613,60615],{"className":60614},[886],[888,60616,60617],{"xmlns":890},[892,60618,60619,60627],{},[895,60620,60621],{},[1661,60622,60623,60625],{},[898,60624,1665],{},[1667,60626,4032],{},[902,60628,46990],{"encoding":904},[883,60630,60632],{"className":60631},[886],[888,60633,60634],{"xmlns":890},[892,60635,60636,60658],{},[895,60637,60638,60644,60646,60648,60650,60656],{},[1661,60639,60640,60642],{},[898,60641,8194],{},[1667,60643,4032],{},[1656,60645,1713],{},[898,60647,1769],{},[1656,60649,1659],{"stretchy":1658},[1661,60651,60652,60654],{},[898,60653,1665],{},[1667,60655,4032],{},[1656,60657,1683],{"stretchy":1658},[902,60659,59759],{"encoding":904},[883,60661,60663],{"className":60662},[886],[888,60664,60665],{"xmlns":890,"display":2408},[892,60666,60667,60743],{},[2412,60668,60669],{"width":2414},[2416,60670,60671,60673,60737,60739],{},[2419,60672],{"width":2421},[2419,60674,60675],{},[895,60676,60677,60679,60681,60683,60689,60691,60693,60699,60701,60707,60709,60721,60723,60725,60727,60729,60731,60733,60735],{},[898,60678,8194],{},[898,60680,1769],{},[1656,60682,1659],{"stretchy":1658},[1661,60684,60685,60687],{},[898,60686,1665],{},[1667,60688,4032],{},[1656,60690,1683],{"stretchy":1658},[1656,60692,1713],{},[1661,60694,60695,60697],{},[898,60696,8194],{},[1667,60698,4032],{},[2461,60700,7828],{},[1661,60702,60703,60705],{},[898,60704,1665],{},[1667,60706,4032],{},[1656,60708,3964],{},[1715,60710,60711,60713,60715],{},[1656,60712,19906],{},[1667,60714,4032],{},[1661,60716,60717,60719],{},[898,60718,1665],{},[1667,60720,4032],{},[898,60722,1769],{},[1656,60724,1659],{"stretchy":1658},[898,60726,1665],{},[1656,60728,1683],{"stretchy":1658},[2461,60730,7828],{},[898,60732,3768],{},[898,60734,1665],{},[898,60736,1863],{"mathvariant":1723},[2419,60738],{"width":2421},[2419,60740,60741],{},[2461,60742,53846],{},[902,60744,53849],{"encoding":904},[198,60746,11258],{"id":60747},"geometrická-interpretace-1",[120,60749,60750,60798,60859],{},[123,60751,60752,2533,60777,60780,60781,1863],{},[883,60753,60755],{"className":60754},[886],[888,60756,60757],{"xmlns":890},[892,60758,60759,60775],{},[895,60760,60761,60767,60769],{},[1661,60762,60763,60765],{},[898,60764,8194],{},[1667,60766,4032],{},[2461,60768,7828],{},[1661,60770,60771,60773],{},[898,60772,1665],{},[1667,60774,4032],{},[902,60776,60275],{"encoding":904},[38,60778,60779],{},"tržba"," výrobce za prodané množství ",[883,60782,60784],{"className":60783},[886],[888,60785,60786],{"xmlns":890},[892,60787,60788,60796],{},[895,60789,60790],{},[1661,60791,60792,60794],{},[898,60793,1665],{},[1667,60795,4032],{},[902,60797,46990],{"encoding":904},[123,60799,60800,60840,60841,60858],{},[883,60801,60803],{"className":60802},[886],[888,60804,60805],{"xmlns":890},[892,60806,60807,60837],{},[895,60808,60809],{},[4138,60810,60811,60823,60825,60827,60829,60831,60833,60835],{"scriptlevel":4032,"displaystyle":1672},[1715,60812,60813,60815,60817],{},[1656,60814,19906],{},[1667,60816,4032],{},[1661,60818,60819,60821],{},[898,60820,1665],{},[1667,60822,4032],{},[898,60824,1769],{},[1656,60826,1659],{"stretchy":1658},[898,60828,1665],{},[1656,60830,1683],{"stretchy":1658},[2461,60832,7828],{},[898,60834,3768],{},[898,60836,1665],{},[902,60838,60839],{"encoding":904},"\\displaystyle \\int_0^{Q_0} S(Q)\\,dQ"," — plocha pod křivkou nabídky; minimální částka, za kterou by byl výrobce ochoten ",[883,60842,60844],{"className":60843},[886],[888,60845,60846],{"xmlns":890},[892,60847,60848,60856],{},[895,60849,60850],{},[1661,60851,60852,60854],{},[898,60853,1665],{},[1667,60855,4032],{},[902,60857,46990],{"encoding":904}," jednotek dodat (souvisí s mezními náklady).",[123,60860,60861,60876,60877,60898,60899,1863],{},[883,60862,60864],{"className":60863},[886],[888,60865,60866],{"xmlns":890},[892,60867,60868,60874],{},[895,60869,60870,60872],{},[898,60871,8194],{},[898,60873,1769],{},[902,60875,53646],{"encoding":904}," je plocha mezi vodorovnou přímkou ",[883,60878,60880],{"className":60879},[886],[888,60881,60882],{"xmlns":890},[892,60883,60884,60896],{},[895,60885,60886,60888,60890],{},[898,60887,8194],{},[1656,60889,1713],{},[1661,60891,60892,60894],{},[898,60893,8194],{},[1667,60895,4032],{},[902,60897,60349],{"encoding":904}," a křivkou nabídky v pásu ",[883,60900,60902],{"className":60901},[886],[888,60903,60904],{"xmlns":890},[892,60905,60906,60922],{},[895,60907,60908,60910,60912,60914,60920],{},[1656,60909,3453],{"stretchy":1658},[1667,60911,4032],{},[1656,60913,1673],{"separator":1672},[1661,60915,60916,60918],{},[898,60917,1665],{},[1667,60919,4032],{},[1656,60921,3462],{"stretchy":1658},[902,60923,60224],{"encoding":904},[724,60925,60926],{},[614,60927,60928],{},"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.",[45652,60930],{},[1981,60932,60933,60938],{},[724,60934,60935,60937],{},[883,60936,10188],{}," Postup výpočtu CS a PS",[152,60939,60940,61071,61181,61210,61344],{},[123,60941,60942,60943,60960,60961,60992,60993,61024,61025,1863],{},"Zjisti (nebo si zvol) množství ",[883,60944,60946],{"className":60945},[886],[888,60947,60948],{"xmlns":890},[892,60949,60950,60958],{},[895,60951,60952],{},[1661,60953,60954,60956],{},[898,60955,1665],{},[1667,60957,4032],{},[902,60959,46990],{"encoding":904}," a odpovídající cenu ",[883,60962,60964],{"className":60963},[886],[888,60965,60966],{"xmlns":890},[892,60967,60968,60990],{},[895,60969,60970,60976,60978,60980,60982,60988],{},[1661,60971,60972,60974],{},[898,60973,8194],{},[1667,60975,4032],{},[1656,60977,1713],{},[898,60979,6787],{},[1656,60981,1659],{"stretchy":1658},[1661,60983,60984,60986],{},[898,60985,1665],{},[1667,60987,4032],{},[1656,60989,1683],{"stretchy":1658},[902,60991,59727],{"encoding":904}," resp. ",[883,60994,60996],{"className":60995},[886],[888,60997,60998],{"xmlns":890},[892,60999,61000,61022],{},[895,61001,61002,61008,61010,61012,61014,61020],{},[1661,61003,61004,61006],{},[898,61005,8194],{},[1667,61007,4032],{},[1656,61009,1713],{},[898,61011,1769],{},[1656,61013,1659],{"stretchy":1658},[1661,61015,61016,61018],{},[898,61017,1665],{},[1667,61019,4032],{},[1656,61021,1683],{"stretchy":1658},[902,61023,59759],{"encoding":904},". V rovnováze platí ",[883,61026,61028],{"className":61027},[886],[888,61029,61030],{"xmlns":890},[892,61031,61032,61068],{},[895,61033,61034,61036,61038,61044,61046,61048,61050,61052,61058,61060,61062],{},[898,61035,6787],{},[1656,61037,1659],{"stretchy":1658},[2062,61039,61040,61042],{},[898,61041,1665],{},[898,61043,1842],{},[1656,61045,1683],{"stretchy":1658},[1656,61047,1713],{},[898,61049,1769],{},[1656,61051,1659],{"stretchy":1658},[2062,61053,61054,61056],{},[898,61055,1665],{},[898,61057,1842],{},[1656,61059,1683],{"stretchy":1658},[1656,61061,1713],{},[2062,61063,61064,61066],{},[898,61065,8194],{},[898,61067,1842],{},[902,61069,61070],{"encoding":904},"D(Q^E) = S(Q^E) = P^E",[123,61072,61073,61074,28847,61112,61127,61128,28847,61166,12702],{},"Spočti určitý integrál ",[883,61075,61077],{"className":61076},[886],[888,61078,61079],{"xmlns":890},[892,61080,61081,61109],{},[895,61082,61083,61095,61097,61099,61101,61103,61105,61107],{},[1715,61084,61085,61087,61089],{},[1656,61086,19906],{},[1667,61088,4032],{},[1661,61090,61091,61093],{},[898,61092,1665],{},[1667,61094,4032],{},[898,61096,6787],{},[1656,61098,1659],{"stretchy":1658},[898,61100,1665],{},[1656,61102,1683],{"stretchy":1658},[2461,61104,7828],{},[898,61106,3768],{},[898,61108,1665],{},[902,61110,61111],{"encoding":904},"\\int_0^{Q_0} D(Q)\\,dQ",[883,61113,61115],{"className":61114},[886],[888,61116,61117],{"xmlns":890},[892,61118,61119,61125],{},[895,61120,61121,61123],{},[898,61122,1766],{},[898,61124,1769],{},[902,61126,53627],{"encoding":904},") nebo ",[883,61129,61131],{"className":61130},[886],[888,61132,61133],{"xmlns":890},[892,61134,61135,61163],{},[895,61136,61137,61149,61151,61153,61155,61157,61159,61161],{},[1715,61138,61139,61141,61143],{},[1656,61140,19906],{},[1667,61142,4032],{},[1661,61144,61145,61147],{},[898,61146,1665],{},[1667,61148,4032],{},[898,61150,1769],{},[1656,61152,1659],{"stretchy":1658},[898,61154,1665],{},[1656,61156,1683],{"stretchy":1658},[2461,61158,7828],{},[898,61160,3768],{},[898,61162,1665],{},[902,61164,61165],{"encoding":904},"\\int_0^{Q_0} S(Q)\\,dQ",[883,61167,61169],{"className":61168},[886],[888,61170,61171],{"xmlns":890},[892,61172,61173,61179],{},[895,61174,61175,61177],{},[898,61176,8194],{},[898,61178,1769],{},[902,61180,53646],{"encoding":904},[123,61182,61183,61184,1863],{},"Sestav obdélník ",[883,61185,61187],{"className":61186},[886],[888,61188,61189],{"xmlns":890},[892,61190,61191,61207],{},[895,61192,61193,61199,61201],{},[1661,61194,61195,61197],{},[898,61196,8194],{},[1667,61198,4032],{},[1656,61200,2751],{},[1661,61202,61203,61205],{},[898,61204,1665],{},[1667,61206,4032],{},[902,61208,61209],{"encoding":904},"P_0 \\cdot Q_0",[123,61211,61212,61213],{},"Dosaď:\n",[120,61214,61215,61280],{},[123,61216,61217,61275,61276,61279],{},[883,61218,61220],{"className":61219},[886],[888,61221,61222],{"xmlns":890},[892,61223,61224,61272],{},[895,61225,61226,61228,61230,61232,61244,61246,61248,61250,61252,61254,61256,61258,61260,61266],{},[898,61227,1766],{},[898,61229,1769],{},[1656,61231,1713],{},[1715,61233,61234,61236,61238],{},[1656,61235,19906],{},[1667,61237,4032],{},[1661,61239,61240,61242],{},[898,61241,1665],{},[1667,61243,4032],{},[898,61245,6787],{},[1656,61247,1659],{"stretchy":1658},[898,61249,1665],{},[1656,61251,1683],{"stretchy":1658},[2461,61253,7828],{},[898,61255,3768],{},[898,61257,1665],{},[1656,61259,3964],{},[1661,61261,61262,61264],{},[898,61263,8194],{},[1667,61265,4032],{},[1661,61267,61268,61270],{},[898,61269,1665],{},[1667,61271,4032],{},[902,61273,61274],{"encoding":904},"CS = \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0"," (integrál ",[38,61277,61278],{},"mínus"," obdélník)",[123,61281,61282,61340,61341,61343],{},[883,61283,61285],{"className":61284},[886],[888,61286,61287],{"xmlns":890},[892,61288,61289,61337],{},[895,61290,61291,61293,61295,61297,61303,61309,61311,61323,61325,61327,61329,61331,61333,61335],{},[898,61292,8194],{},[898,61294,1769],{},[1656,61296,1713],{},[1661,61298,61299,61301],{},[898,61300,8194],{},[1667,61302,4032],{},[1661,61304,61305,61307],{},[898,61306,1665],{},[1667,61308,4032],{},[1656,61310,3964],{},[1715,61312,61313,61315,61317],{},[1656,61314,19906],{},[1667,61316,4032],{},[1661,61318,61319,61321],{},[898,61320,1665],{},[1667,61322,4032],{},[898,61324,1769],{},[1656,61326,1659],{"stretchy":1658},[898,61328,1665],{},[1656,61330,1683],{"stretchy":1658},[2461,61332,7828],{},[898,61334,3768],{},[898,61336,1665],{},[902,61338,61339],{"encoding":904},"PS = P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ"," (obdélník ",[38,61342,61278],{}," integrál)",[123,61345,61346,61347,61349],{},"Kontrola znaménka: obě hodnoty musí být ",[38,61348,4299],{},". Pokud vyjde záporná, máš prohozené pořadí.",[45652,61351],{},[115,61353,61355],{"id":61354},"příklady","Příklady",[198,61357,61359],{"id":61358},"příklad-211-komparativní-statika-pro-rovnovážné-množství","Příklad 2.11 — komparativní statika pro rovnovážné množství",[1981,61361,61362],{},[724,61363,61364,61366,61367,56396,61390,61413,61414,1343,61434,1343,61451,1343,61468,61485,61486,61562,61563,61580,61581,61594],{},[883,61365,2576],{}," Zadání\nJsou dány poptávka ",[883,61368,61370],{"className":61369},[886],[888,61371,61372],{"xmlns":890},[892,61373,61374,61388],{},[895,61375,61376,61378,61380,61382,61384,61386],{},[898,61377,8194],{},[1656,61379,1713],{},[898,61381,207],{},[898,61383,1665],{},[1656,61385,3633],{},[898,61387,3403],{},[902,61389,45742],{"encoding":904},[883,61391,61393],{"className":61392},[886],[888,61394,61395],{"xmlns":890},[892,61396,61397,61411],{},[895,61398,61399,61401,61403,61405,61407,61409],{},[898,61400,8194],{},[1656,61402,1713],{},[898,61404,1745],{},[898,61406,1665],{},[1656,61408,3633],{},[898,61410,3768],{},[902,61412,48922],{"encoding":904}," s hodnotami ",[883,61415,61417],{"className":61416},[886],[888,61418,61419],{"xmlns":890},[892,61420,61421,61431],{},[895,61422,61423,61425,61427,61429],{},[898,61424,207],{},[1656,61426,1713],{},[1656,61428,3964],{},[1667,61430,2617],{},[902,61432,61433],{"encoding":904},"a = -3",[883,61435,61437],{"className":61436},[886],[888,61438,61439],{"xmlns":890},[892,61440,61441,61449],{},[895,61442,61443,61445,61447],{},[898,61444,3403],{},[1656,61446,1713],{},[1667,61448,9135],{},[902,61450,57318],{"encoding":904},[883,61452,61454],{"className":61453},[886],[888,61455,61456],{"xmlns":890},[892,61457,61458,61466],{},[895,61459,61460,61462,61464],{},[898,61461,1745],{},[1656,61463,1713],{},[1667,61465,13779],{},[902,61467,57336],{"encoding":904},[883,61469,61471],{"className":61470},[886],[888,61472,61473],{"xmlns":890},[892,61474,61475,61483],{},[895,61476,61477,61479,61481],{},[898,61478,3768],{},[1656,61480,1713],{},[1667,61482,8580],{},[902,61484,57354],{"encoding":904},".\nRovnovážné množství:\n",[883,61487,61489],{"className":61488},[886],[888,61490,61491],{"xmlns":890},[892,61492,61493,61559],{},[895,61494,61495,61501,61503,61521,61523,61547,61549,61555,61557],{},[2062,61496,61497,61499],{},[898,61498,1665],{},[898,61500,1842],{},[1656,61502,1713],{},[3294,61504,61505,61513],{},[895,61506,61507,61509,61511],{},[898,61508,3403],{},[1656,61510,3964],{},[898,61512,3768],{},[895,61514,61515,61517,61519],{},[898,61516,1745],{},[1656,61518,3964],{},[898,61520,207],{},[1656,61522,1713],{},[3294,61524,61525,61533],{},[895,61526,61527,61529,61531],{},[1667,61528,9135],{},[1656,61530,3964],{},[1667,61532,8580],{},[895,61534,61535,61537,61539,61541,61543,61545],{},[1667,61536,13779],{},[1656,61538,3964],{},[1656,61540,1659],{"stretchy":1658},[1656,61542,3964],{},[1667,61544,2617],{},[1656,61546,1683],{"stretchy":1658},[1656,61548,1713],{},[3294,61550,61551,61553],{},[1667,61552,46701],{},[1667,61554,53083],{},[1656,61556,2829],{},[1667,61558,53088],{},[902,61560,61561],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\doteq 8{,}571.","\nZjistěte změnu ",[883,61564,61566],{"className":61565},[886],[888,61567,61568],{"xmlns":890},[892,61569,61570,61578],{},[895,61571,61572],{},[2062,61573,61574,61576],{},[898,61575,1665],{},[898,61577,1842],{},[902,61579,51080],{"encoding":904}," (a) při změně samotného parametru ",[883,61582,61584],{"className":61583},[886],[888,61585,61586],{"xmlns":890},[892,61587,61588,61592],{},[895,61589,61590],{},[898,61591,1745],{},[902,61593,1745],{"encoding":904},", (b) při současné změně všech čtyř parametrů.",[724,61596,61597],{},[38,61598,61599,61600,3605,61613,3619,61626,18045],{},"Řešení (a) — změna ",[883,61601,61603],{"className":61602},[886],[888,61604,61605],{"xmlns":890},[892,61606,61607,61611],{},[895,61608,61609],{},[898,61610,1745],{},[902,61612,1745],{"encoding":904},[883,61614,61616],{"className":61615},[886],[888,61617,61618],{"xmlns":890},[892,61619,61620,61624],{},[895,61621,61622],{},[1667,61623,13779],{},[902,61625,53123],{"encoding":904},[883,61627,61629],{"className":61628},[886],[888,61630,61631],{"xmlns":890},[892,61632,61633,61637],{},[895,61634,61635],{},[1667,61636,28042],{},[902,61638,53137],{"encoding":904},[724,61640,61641,61642,61706,61707,2114],{},"Pomocí vzorce (2.13) pro ",[883,61643,61645],{"className":61644},[886],[888,61646,61647],{"xmlns":890},[892,61648,61649,61703],{},[895,61650,61651,61671,61673,61675],{},[4138,61652,61653],{"scriptlevel":4032,"displaystyle":1672},[3294,61654,61655,61665],{},[895,61656,61657,61659],{},[898,61658,3300],{"mathvariant":1723},[2062,61660,61661,61663],{},[898,61662,1665],{},[898,61664,1842],{},[895,61666,61667,61669],{},[898,61668,3300],{"mathvariant":1723},[898,61670,1745],{},[1656,61672,1713],{},[1656,61674,3964],{},[4138,61676,61677],{"scriptlevel":4032,"displaystyle":1672},[3294,61678,61679,61687],{},[895,61680,61681,61683,61685],{},[898,61682,3403],{},[1656,61684,3964],{},[898,61686,3768],{},[895,61688,61689,61691,61693,61695,61697],{},[1656,61690,1659],{"stretchy":1658},[898,61692,1745],{},[1656,61694,3964],{},[898,61696,207],{},[2062,61698,61699,61701],{},[1656,61700,1683],{"stretchy":1658},[1667,61702,1680],{},[902,61704,61705],{"encoding":904},"\\dfrac{\\partial Q^E}{\\partial c} = -\\dfrac{b-d}{(c-a)^2}",", resp. ekvivalentně ",[883,61708,61710],{"className":61709},[886],[888,61711,61712],{"xmlns":890},[892,61713,61714,61736],{},[895,61715,61716,61718],{},[1656,61717,3964],{},[4138,61719,61720],{"scriptlevel":4032,"displaystyle":1672},[3294,61721,61722,61728],{},[2062,61723,61724,61726],{},[898,61725,1665],{},[898,61727,1842],{},[895,61729,61730,61732,61734],{},[898,61731,1745],{},[1656,61733,3964],{},[898,61735,207],{},[902,61737,61738],{"encoding":904},"-\\dfrac{Q^E}{c-a}",[883,61740,61742],{"className":61741},[886],[888,61743,61744],{"xmlns":890,"display":2408},[892,61745,61746,61802],{},[895,61747,61748,61750,61756,61758,61760,61776,61778,61780,61782,61784,61786,61792,61794,61796,61798,61800],{},[898,61749,3768],{},[2062,61751,61752,61754],{},[898,61753,1665],{},[898,61755,1842],{},[1656,61757,1713],{},[1656,61759,3964],{},[3294,61761,61762,61768],{},[2062,61763,61764,61766],{},[898,61765,1665],{},[898,61767,1842],{},[895,61769,61770,61772,61774],{},[898,61771,1745],{},[1656,61773,3964],{},[898,61775,207],{},[2461,61777,7828],{},[898,61779,3768],{},[898,61781,1745],{},[1656,61783,1713],{},[1656,61785,3964],{},[3294,61787,61788,61790],{},[1667,61789,53251],{},[1667,61791,53083],{},[1656,61793,2751],{},[1667,61795,11595],{},[1656,61797,2829],{},[1656,61799,3964],{},[1667,61801,53223],{},[902,61803,61804],{"encoding":904},"dQ^E = -\\frac{Q^E}{c - a}\\,dc = -\\frac{8{,}571}{3{,}5}\\cdot 0{,}1 \\doteq -0{,}245.",[724,61806,61807],{},"Nové rovnovážné množství:",[883,61809,61811],{"className":61810},[886],[888,61812,61813],{"xmlns":890,"display":2408},[892,61814,61815,61838],{},[895,61816,61817,61825,61827,61829,61831,61833,61835],{},[1715,61818,61819,61821,61823],{},[898,61820,1665],{},[1667,61822,1669],{},[898,61824,1842],{},[1656,61826,3815],{},[1667,61828,53251],{},[1656,61830,3964],{},[1667,61832,53256],{},[1656,61834,1713],{},[1667,61836,61837],{},"8,326.",[902,61839,61840],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326.",[724,61842,61843,1643,61846,1343,61872,1343,61894,1343,61916,2836,61938,1343,61957,1343,61978,1343,61997,1863],{},[38,61844,61845],{},"Řešení (b) — současná změna všech parametrů:",[883,61847,61849],{"className":61848},[886],[888,61850,61851],{"xmlns":890},[892,61852,61853,61869],{},[895,61854,61855,61857,61859,61861,61863,61865,61867],{},[898,61856,207],{},[1656,61858,2114],{},[1656,61860,3964],{},[1667,61862,2617],{},[1656,61864,11915],{},[1656,61866,3964],{},[1667,61868,9752],{},[902,61870,61871],{"encoding":904},"a: -3 \\to -2{,}5",[883,61873,61875],{"className":61874},[886],[888,61876,61877],{"xmlns":890},[892,61878,61879,61891],{},[895,61880,61881,61883,61885,61887,61889],{},[898,61882,3403],{},[1656,61884,2114],{},[1667,61886,9135],{},[1656,61888,11915],{},[1667,61890,23770],{},[902,61892,61893],{"encoding":904},"b: 40 \\to 35",[883,61895,61897],{"className":61896},[886],[888,61898,61899],{"xmlns":890},[892,61900,61901,61913],{},[895,61902,61903,61905,61907,61909,61911],{},[898,61904,1745],{},[1656,61906,2114],{},[1667,61908,13779],{},[1656,61910,11915],{},[1667,61912,28042],{},[902,61914,61915],{"encoding":904},"c: 0{,}5 \\to 0{,}6",[883,61917,61919],{"className":61918},[886],[888,61920,61921],{"xmlns":890},[892,61922,61923,61935],{},[895,61924,61925,61927,61929,61931,61933],{},[898,61926,3768],{},[1656,61928,2114],{},[1667,61930,8580],{},[1656,61932,11915],{},[1667,61934,4364],{},[902,61936,61937],{"encoding":904},"d: 10 \\to 11",[883,61939,61941],{"className":61940},[886],[888,61942,61943],{"xmlns":890},[892,61944,61945,61955],{},[895,61946,61947,61949,61951,61953],{},[898,61948,3768],{},[898,61950,207],{},[1656,61952,1713],{},[1667,61954,13779],{},[902,61956,53289],{"encoding":904},[883,61958,61960],{"className":61959},[886],[888,61961,61962],{"xmlns":890},[892,61963,61964,61976],{},[895,61965,61966,61968,61970,61972,61974],{},[898,61967,3768],{},[898,61969,3403],{},[1656,61971,1713],{},[1656,61973,3964],{},[1667,61975,5193],{},[902,61977,53311],{"encoding":904},[883,61979,61981],{"className":61980},[886],[888,61982,61983],{"xmlns":890},[892,61984,61985,61995],{},[895,61986,61987,61989,61991,61993],{},[898,61988,3768],{},[898,61990,1745],{},[1656,61992,1713],{},[1667,61994,11595],{},[902,61996,53331],{"encoding":904},[883,61998,62000],{"className":61999},[886],[888,62001,62002],{"xmlns":890},[892,62003,62004,62014],{},[895,62005,62006,62008,62010,62012],{},[898,62007,3768],{},[898,62009,3768],{},[1656,62011,1713],{},[1667,62013,1669],{},[902,62015,53351],{"encoding":904},[724,62017,62018,62019,62077],{},"Totální diferenciál ",[883,62020,62022],{"className":62021},[886],[888,62023,62024],{"xmlns":890},[892,62025,62026,62074],{},[895,62027,62028,62034,62036,62038,62040,62042,62044,62046,62048,62050,62052,62054],{},[2062,62029,62030,62032],{},[898,62031,1665],{},[898,62033,1842],{},[1656,62035,1659],{"stretchy":1658},[898,62037,207],{},[1656,62039,1673],{"separator":1672},[898,62041,3403],{},[1656,62043,1673],{"separator":1672},[898,62045,1745],{},[1656,62047,1673],{"separator":1672},[898,62049,3768],{},[1656,62051,1683],{"stretchy":1658},[1656,62053,1713],{},[4138,62055,62056],{"scriptlevel":4032,"displaystyle":1672},[3294,62057,62058,62066],{},[895,62059,62060,62062,62064],{},[898,62061,3403],{},[1656,62063,3964],{},[898,62065,3768],{},[895,62067,62068,62070,62072],{},[898,62069,1745],{},[1656,62071,3964],{},[898,62073,207],{},[902,62075,62076],{"encoding":904},"Q^E(a, b, c, d) = \\dfrac{b - d}{c - a}"," podle (2.11) a (2.12):",[883,62079,62081],{"className":62080},[886],[888,62082,62083],{"xmlns":890,"display":2408},[892,62084,62085,62205],{},[895,62086,62087,62089,62095,62097,62123,62125,62127,62129,62131,62143,62145,62147,62149,62151,62177,62179,62181,62183,62185,62197,62199,62201,62203],{},[898,62088,3768],{},[2062,62090,62091,62093],{},[898,62092,1665],{},[898,62094,1842],{},[1656,62096,1713],{},[3294,62098,62099,62107],{},[895,62100,62101,62103,62105],{},[898,62102,3403],{},[1656,62104,3964],{},[898,62106,3768],{},[895,62108,62109,62111,62113,62115,62117],{},[1656,62110,1659],{"stretchy":1658},[898,62112,1745],{},[1656,62114,3964],{},[898,62116,207],{},[2062,62118,62119,62121],{},[1656,62120,1683],{"stretchy":1658},[1667,62122,1680],{},[2461,62124,7828],{},[898,62126,3768],{},[898,62128,207],{},[1656,62130,3633],{},[3294,62132,62133,62135],{},[1667,62134,1669],{},[895,62136,62137,62139,62141],{},[898,62138,1745],{},[1656,62140,3964],{},[898,62142,207],{},[2461,62144,7828],{},[898,62146,3768],{},[898,62148,3403],{},[1656,62150,3964],{},[3294,62152,62153,62161],{},[895,62154,62155,62157,62159],{},[898,62156,3403],{},[1656,62158,3964],{},[898,62160,3768],{},[895,62162,62163,62165,62167,62169,62171],{},[1656,62164,1659],{"stretchy":1658},[898,62166,1745],{},[1656,62168,3964],{},[898,62170,207],{},[2062,62172,62173,62175],{},[1656,62174,1683],{"stretchy":1658},[1667,62176,1680],{},[2461,62178,7828],{},[898,62180,3768],{},[898,62182,1745],{},[1656,62184,3964],{},[3294,62186,62187,62189],{},[1667,62188,1669],{},[895,62190,62191,62193,62195],{},[898,62192,1745],{},[1656,62194,3964],{},[898,62196,207],{},[2461,62198,7828],{},[898,62200,3768],{},[898,62202,3768],{},[898,62204,1863],{"mathvariant":1723},[902,62206,62207],{"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.",[724,62209,62210,62211,1343,62233,1343,62264,5642],{},"Dosazením číselných hodnot (",[883,62212,62214],{"className":62213},[886],[888,62215,62216],{"xmlns":890},[892,62217,62218,62230],{},[895,62219,62220,62222,62224,62226,62228],{},[898,62221,1745],{},[1656,62223,3964],{},[898,62225,207],{},[1656,62227,1713],{},[1667,62229,53083],{},[902,62231,62232],{"encoding":904},"c - a = 3{,}5",[883,62234,62236],{"className":62235},[886],[888,62237,62238],{"xmlns":890},[892,62239,62240,62261],{},[895,62241,62242,62244,62246,62248,62250,62256,62258],{},[1656,62243,1659],{"stretchy":1658},[898,62245,1745],{},[1656,62247,3964],{},[898,62249,207],{},[2062,62251,62252,62254],{},[1656,62253,1683],{"stretchy":1658},[1667,62255,1680],{},[1656,62257,1713],{},[1667,62259,62260],{},"12,25",[902,62262,62263],{"encoding":904},"(c-a)^2 = 12{,}25",[883,62265,62267],{"className":62266},[886],[888,62268,62269],{"xmlns":890},[892,62270,62271,62283],{},[895,62272,62273,62275,62277,62279,62281],{},[898,62274,3403],{},[1656,62276,3964],{},[898,62278,3768],{},[1656,62280,1713],{},[1667,62282,46701],{},[902,62284,62285],{"encoding":904},"b - d = 30",[883,62287,62289],{"className":62288},[886],[888,62290,62291],{"xmlns":890,"display":2408},[892,62292,62293,62394],{},[895,62294,62295,62297,62303,62305,62313,62315,62317,62319,62321,62329,62331,62333,62335,62337,62339,62347,62349,62351,62353,62355,62363,62365,62367,62369,62371,62374,62376,62379,62381,62383,62385,62388,62390,62392],{},[898,62296,3768],{},[2062,62298,62299,62301],{},[898,62300,1665],{},[898,62302,1842],{},[1656,62304,3815],{},[4138,62306,62307],{"scriptlevel":4032,"displaystyle":1658},[3294,62308,62309,62311],{},[1667,62310,46701],{},[1667,62312,62260],{},[1656,62314,1659],{"stretchy":1658},[1667,62316,13779],{},[1656,62318,1683],{"stretchy":1658},[1656,62320,3633],{},[4138,62322,62323],{"scriptlevel":4032,"displaystyle":1658},[3294,62324,62325,62327],{},[1667,62326,1669],{},[1667,62328,53083],{},[1656,62330,1659],{"stretchy":1658},[1656,62332,3964],{},[1667,62334,5193],{},[1656,62336,1683],{"stretchy":1658},[1656,62338,3964],{},[4138,62340,62341],{"scriptlevel":4032,"displaystyle":1658},[3294,62342,62343,62345],{},[1667,62344,46701],{},[1667,62346,62260],{},[1656,62348,1659],{"stretchy":1658},[1667,62350,11595],{},[1656,62352,1683],{"stretchy":1658},[1656,62354,3964],{},[4138,62356,62357],{"scriptlevel":4032,"displaystyle":1658},[3294,62358,62359,62361],{},[1667,62360,1669],{},[1667,62362,53083],{},[1656,62364,1659],{"stretchy":1658},[1667,62366,1669],{},[1656,62368,1683],{"stretchy":1658},[1656,62370,2829],{},[1667,62372,62373],{},"1,224",[1656,62375,3964],{},[1667,62377,62378],{},"1,429",[1656,62380,3964],{},[1667,62382,53256],{},[1656,62384,3964],{},[1667,62386,62387],{},"0,286",[1656,62389,2829],{},[1656,62391,3964],{},[1667,62393,53502],{},[902,62395,62396],{"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.",[724,62398,8038,62399,1863],{},[883,62400,62402],{"className":62401},[886],[888,62403,62404],{"xmlns":890},[892,62405,62406,62428],{},[895,62407,62408,62416,62418,62420,62422,62424,62426],{},[1715,62409,62410,62412,62414],{},[898,62411,1665],{},[1667,62413,1669],{},[898,62415,1842],{},[1656,62417,3815],{},[1667,62419,53251],{},[1656,62421,3964],{},[1667,62423,53533],{},[1656,62425,2829],{},[1667,62427,53538],{},[902,62429,62430],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 \\doteq 7{,}836",[1981,62432,62433],{},[724,62434,62435,62437,62438,62459,62460,62486,62487,62490,62491,62587,62588,62611,62612,62628],{},[883,62436,1987],{}," Pozn. k přepisu učebnice\nV původním skenu přednášky byla u části (b) uvedena hodnota ",[883,62439,62441],{"className":62440},[886],[888,62442,62443],{"xmlns":890},[892,62444,62445,62457],{},[895,62446,62447,62449,62451,62453,62455],{},[898,62448,3750],{"mathvariant":1723},[898,62450,1665],{},[1656,62452,3815],{},[1656,62454,3964],{},[1667,62456,53568],{},[902,62458,53571],{"encoding":904},", což neodpovídá součtu dílčích derivací při daných přírůstcích. Podle vlastního přepočtu vychází ",[883,62461,62463],{"className":62462},[886],[888,62464,62465],{"xmlns":890},[892,62466,62467,62483],{},[895,62468,62469,62471,62477,62479,62481],{},[898,62470,3768],{},[2062,62472,62473,62475],{},[898,62474,1665],{},[898,62476,1842],{},[1656,62478,2829],{},[1656,62480,3964],{},[1667,62482,53533],{},[902,62484,62485],{"encoding":904},"dQ^E \\doteq -0{,}735",". Totální diferenciál je navíc pouze ",[38,62488,62489],{},"lineární aproximací","; přesná změna zjištěná ze změněného vzorce\n",[883,62492,62494],{"className":62493},[886],[888,62495,62496],{"xmlns":890},[892,62497,62498,62584],{},[895,62499,62500,62508,62510,62544,62546,62570,62572,62579,62581],{},[1715,62501,62502,62504,62506],{},[898,62503,1665],{},[1667,62505,1669],{},[898,62507,1842],{},[1656,62509,1713],{},[3294,62511,62512,62528],{},[895,62513,62514,62520,62522],{},[2062,62515,62516,62518],{},[898,62517,3403],{},[1656,62519,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,62521,3964],{},[2062,62523,62524,62526],{},[898,62525,3768],{},[1656,62527,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[895,62529,62530,62536,62538],{},[2062,62531,62532,62534],{},[898,62533,1745],{},[1656,62535,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,62537,3964],{},[2062,62539,62540,62542],{},[898,62541,207],{},[1656,62543,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,62545,1713],{},[3294,62547,62548,62556],{},[895,62549,62550,62552,62554],{},[1667,62551,23770],{},[1656,62553,3964],{},[1667,62555,4364],{},[895,62557,62558,62560,62562,62564,62566,62568],{},[1667,62559,28042],{},[1656,62561,3964],{},[1656,62563,1659],{"stretchy":1658},[1656,62565,3964],{},[1667,62567,9752],{},[1656,62569,1683],{"stretchy":1658},[1656,62571,1713],{},[3294,62573,62574,62576],{},[1667,62575,50480],{},[1667,62577,62578],{},"3,1",[1656,62580,2829],{},[1667,62582,62583],{},"7,742",[902,62585,62586],{"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 ",[883,62589,62591],{"className":62590},[886],[888,62592,62593],{"xmlns":890},[892,62594,62595,62608],{},[895,62596,62597,62599,62601,62603,62605],{},[898,62598,3750],{"mathvariant":1723},[898,62600,1665],{},[1656,62602,2829],{},[1656,62604,3964],{},[1667,62606,62607],{},"0,829",[902,62609,62610],{"encoding":904},"\\Delta Q \\doteq -0{,}829"," — dobře konzistentní s diferenciálem. Hodnota ",[883,62613,62615],{"className":62614},[886],[888,62616,62617],{"xmlns":890},[892,62618,62619,62625],{},[895,62620,62621,62623],{},[1656,62622,3964],{},[1667,62624,53568],{},[902,62626,62627],{"encoding":904},"-2{,}69"," je tedy pravděpodobně chyba v zápisu.",[724,62630,62631],{},[614,62632,62633,62634,62647],{},"Příklad 2.11 je primárně o multiplikátorech pro ",[883,62635,62637],{"className":62636},[886],[888,62638,62639],{"xmlns":890},[892,62640,62641,62645],{},[895,62642,62643],{},[898,62644,1665],{},[902,62646,1665],{"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.",[198,62649,62651,62652],{"id":62650},"příklad-213-numerický-výpočet-psps","Příklad 2.13 — numerický výpočet ",[883,62653,62655],{"className":62654},[886],[888,62656,62657],{"xmlns":890},[892,62658,62659,62665],{},[895,62660,62661,62663],{},[898,62662,8194],{},[898,62664,1769],{},[902,62666,53646],{"encoding":904},[1981,62668,62669],{},[724,62670,62671,62673,62674,62708,62709,62731],{},[883,62672,2576],{}," Zadání\nPro nabídku ",[883,62675,62677],{"className":62676},[886],[888,62678,62679],{"xmlns":890},[892,62680,62681,62705],{},[895,62682,62683,62685,62687,62689,62691,62693,62695,62697,62699,62701,62703],{},[898,62684,8194],{},[1656,62686,1713],{},[898,62688,1769],{},[1656,62690,1659],{"stretchy":1658},[898,62692,1665],{},[1656,62694,1683],{"stretchy":1658},[1656,62696,1713],{},[1667,62698,8580],{},[1656,62700,3633],{},[1667,62702,1680],{},[898,62704,1665],{},[902,62706,62707],{"encoding":904},"P = S(Q) = 10 + 2Q"," a množství ",[883,62710,62712],{"className":62711},[886],[888,62713,62714],{"xmlns":890},[892,62715,62716,62728],{},[895,62717,62718,62724,62726],{},[1661,62719,62720,62722],{},[898,62721,1665],{},[1667,62723,4032],{},[1656,62725,1713],{},[1667,62727,8580],{},[902,62729,62730],{"encoding":904},"Q_0 = 10"," vypočítejte přebytek výrobce.",[724,62733,62734],{},[38,62735,31488],{},[724,62737,62738],{},"Odpovídající cena:",[883,62740,62742],{"className":62741},[886],[888,62743,62744],{"xmlns":890,"display":2408},[892,62745,62746,62781],{},[895,62747,62748,62754,62756,62758,62760,62762,62764,62766,62768,62770,62772,62774,62776,62778],{},[1661,62749,62750,62752],{},[898,62751,8194],{},[1667,62753,4032],{},[1656,62755,1713],{},[898,62757,1769],{},[1656,62759,1659],{"stretchy":1658},[1667,62761,8580],{},[1656,62763,1683],{"stretchy":1658},[1656,62765,1713],{},[1667,62767,8580],{},[1656,62769,3633],{},[1667,62771,1680],{},[1656,62773,2751],{},[1667,62775,8580],{},[1656,62777,1713],{},[1667,62779,62780],{},"30.",[902,62782,62783],{"encoding":904},"P_0 = S(10) = 10 + 2\\cdot 10 = 30.",[724,62785,62786],{},"Dle vzorce (2.15):",[883,62788,62790],{"className":62789},[886],[888,62791,62792],{"xmlns":890,"display":2408},[892,62793,62794,62902],{},[895,62795,62796,62798,62800,62802,62804,62806,62808,62814,62820,62822,62830,62832,62834,62836,62838,62840,62842,62844,62846,62848,62850,62852,62854,62856,62858,62861,62863,62865,62867,62873,62881,62883,62885,62887,62889,62891,62893,62895,62897,62899],{},[898,62797,8194],{},[898,62799,1769],{},[1656,62801,1659],{"stretchy":1658},[1667,62803,8580],{},[1656,62805,1683],{"stretchy":1658},[1656,62807,1713],{},[1661,62809,62810,62812],{},[898,62811,8194],{},[1667,62813,4032],{},[1661,62815,62816,62818],{},[898,62817,1665],{},[1667,62819,4032],{},[1656,62821,3964],{},[1715,62823,62824,62826,62828],{},[1656,62825,19906],{},[1667,62827,4032],{},[1667,62829,8580],{},[1656,62831,1659],{"stretchy":1658},[1667,62833,8580],{},[1656,62835,3633],{},[1667,62837,1680],{},[898,62839,1665],{},[1656,62841,1683],{"stretchy":1658},[2461,62843,7828],{},[898,62845,3768],{},[898,62847,1665],{},[1656,62849,1713],{},[1667,62851,8580],{},[1656,62853,2751],{},[1667,62855,46701],{},[1656,62857,3964],{},[1656,62859,3453],{"fence":1658,"stretchy":1672,"minsize":62860,"maxsize":62860},"1.8em",[1667,62862,8580],{},[898,62864,1665],{},[1656,62866,3633],{},[2062,62868,62869,62871],{},[898,62870,1665],{},[1667,62872,1680],{},[1715,62874,62875,62877,62879],{},[1656,62876,3462],{"fence":1658,"stretchy":1672,"minsize":62860,"maxsize":62860},[1667,62878,4032],{},[1667,62880,8580],{},[1656,62882,1713],{},[1667,62884,8054],{},[1656,62886,3964],{},[1656,62888,1659],{"stretchy":1658},[1667,62890,5267],{},[1656,62892,3633],{},[1667,62894,5267],{},[1656,62896,1683],{"stretchy":1658},[1656,62898,1713],{},[1667,62900,62901],{},"100.",[902,62903,62904],{"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.",[724,62906,62907,62908,62929,62930,62950],{},"Přebytek výrobce při množství ",[883,62909,62911],{"className":62910},[886],[888,62912,62913],{"xmlns":890},[892,62914,62915,62927],{},[895,62916,62917,62923,62925],{},[1661,62918,62919,62921],{},[898,62920,1665],{},[1667,62922,4032],{},[1656,62924,1713],{},[1667,62926,8580],{},[902,62928,62730],{"encoding":904}," je tedy ",[883,62931,62933],{"className":62932},[886],[888,62934,62935],{"xmlns":890},[892,62936,62937,62947],{},[895,62938,62939,62941,62943,62945],{},[898,62940,8194],{},[898,62942,1769],{},[1656,62944,1713],{},[1667,62946,5267],{},[902,62948,62949],{"encoding":904},"PS = 100"," (peněžních jednotek).",[45652,62952],{},[115,62954,62956],{"id":62955},"cheat-sheet","Cheat sheet",[16,62958,62959,62972],{},[19,62960,62961],{},[22,62962,62963,62966,62969],{},[25,62964,62965],{},"Veličina",[25,62967,62968],{},"Vzorec",[25,62970,62971],{},"Geometrie",[30,62973,62974,63092,63206,63274],{},[22,62975,62976,63004,63060],{},[35,62977,62978],{},[883,62979,62981],{"className":62980},[886],[888,62982,62983],{"xmlns":890},[892,62984,62985,63001],{},[895,62986,62987,62989,62991,62993,62999],{},[898,62988,1766],{},[898,62990,1769],{},[1656,62992,1659],{"stretchy":1658},[1661,62994,62995,62997],{},[898,62996,1665],{},[1667,62998,4032],{},[1656,63000,1683],{"stretchy":1658},[902,63002,63003],{"encoding":904},"CS(Q_0)",[35,63005,63006],{},[883,63007,63009],{"className":63008},[886],[888,63010,63011],{"xmlns":890},[892,63012,63013,63057],{},[895,63014,63015],{},[4138,63016,63017,63029,63031,63033,63035,63037,63039,63041,63043,63045,63051],{"scriptlevel":4032,"displaystyle":1672},[1715,63018,63019,63021,63023],{},[1656,63020,19906],{},[1667,63022,4032],{},[1661,63024,63025,63027],{},[898,63026,1665],{},[1667,63028,4032],{},[898,63030,6787],{},[1656,63032,1659],{"stretchy":1658},[898,63034,1665],{},[1656,63036,1683],{"stretchy":1658},[2461,63038,7828],{},[898,63040,3768],{},[898,63042,1665],{},[1656,63044,3964],{},[1661,63046,63047,63049],{},[898,63048,8194],{},[1667,63050,4032],{},[1661,63052,63053,63055],{},[898,63054,1665],{},[1667,63056,4032],{},[902,63058,63059],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0",[35,63061,63062,63063,63066,63067,63070,63071],{},"plocha ",[38,63064,63065],{},"pod"," křivkou poptávky, ",[38,63068,63069],{},"nad"," čárou ",[883,63072,63074],{"className":63073},[886],[888,63075,63076],{"xmlns":890},[892,63077,63078,63090],{},[895,63079,63080,63082,63084],{},[898,63081,8194],{},[1656,63083,1713],{},[1661,63085,63086,63088],{},[898,63087,8194],{},[1667,63089,4032],{},[902,63091,60349],{"encoding":904},[22,63093,63094,63122,63178],{},[35,63095,63096],{},[883,63097,63099],{"className":63098},[886],[888,63100,63101],{"xmlns":890},[892,63102,63103,63119],{},[895,63104,63105,63107,63109,63111,63117],{},[898,63106,8194],{},[898,63108,1769],{},[1656,63110,1659],{"stretchy":1658},[1661,63112,63113,63115],{},[898,63114,1665],{},[1667,63116,4032],{},[1656,63118,1683],{"stretchy":1658},[902,63120,63121],{"encoding":904},"PS(Q_0)",[35,63123,63124],{},[883,63125,63127],{"className":63126},[886],[888,63128,63129],{"xmlns":890},[892,63130,63131,63175],{},[895,63132,63133],{},[4138,63134,63135,63141,63147,63149,63161,63163,63165,63167,63169,63171,63173],{"scriptlevel":4032,"displaystyle":1672},[1661,63136,63137,63139],{},[898,63138,8194],{},[1667,63140,4032],{},[1661,63142,63143,63145],{},[898,63144,1665],{},[1667,63146,4032],{},[1656,63148,3964],{},[1715,63150,63151,63153,63155],{},[1656,63152,19906],{},[1667,63154,4032],{},[1661,63156,63157,63159],{},[898,63158,1665],{},[1667,63160,4032],{},[898,63162,1769],{},[1656,63164,1659],{"stretchy":1658},[898,63166,1665],{},[1656,63168,1683],{"stretchy":1658},[2461,63170,7828],{},[898,63172,3768],{},[898,63174,1665],{},[902,63176,63177],{"encoding":904},"\\displaystyle P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ",[35,63179,63062,63180,63182,63183,63070,63185],{},[38,63181,63069],{}," křivkou nabídky, ",[38,63184,63065],{},[883,63186,63188],{"className":63187},[886],[888,63189,63190],{"xmlns":890},[892,63191,63192,63204],{},[895,63193,63194,63196,63198],{},[898,63195,8194],{},[1656,63197,1713],{},[1661,63199,63200,63202],{},[898,63201,8194],{},[1667,63203,4032],{},[902,63205,60349],{"encoding":904},[22,63207,63208,63211,63238],{},[35,63209,63210],{},"Výdaje \u002F tržby",[35,63212,63213],{},[883,63214,63216],{"className":63215},[886],[888,63217,63218],{"xmlns":890},[892,63219,63220,63236],{},[895,63221,63222,63228,63230],{},[1661,63223,63224,63226],{},[898,63225,8194],{},[1667,63227,4032],{},[1656,63229,2751],{},[1661,63231,63232,63234],{},[898,63233,1665],{},[1667,63235,4032],{},[902,63237,61209],{"encoding":904},[35,63239,63240,63241],{},"obdélník ",[883,63242,63244],{"className":63243},[886],[888,63245,63246],{"xmlns":890},[892,63247,63248,63272],{},[895,63249,63250,63252,63254,63260,63262,63264,63266],{},[1667,63251,4032],{},[2461,63253,7828],{},[1661,63255,63256,63258],{},[898,63257,1665],{},[1667,63259,4032],{},[2461,63261,7828],{},[898,63263,2146],{},[2461,63265,7828],{},[1661,63267,63268,63270],{},[898,63269,8194],{},[1667,63271,4032],{},[902,63273,59829],{"encoding":904},[22,63275,63276,63279,63302],{},[35,63277,63278],{},"Celkový přebytek",[35,63280,63281],{},[883,63282,63284],{"className":63283},[886],[888,63285,63286],{"xmlns":890},[892,63287,63288,63300],{},[895,63289,63290,63292,63294,63296,63298],{},[898,63291,1766],{},[898,63293,1769],{},[1656,63295,3633],{},[898,63297,8194],{},[898,63299,1769],{},[902,63301,59567],{"encoding":904},[35,63303,63304],{},"součet obou ploch v rovnováze",[45652,63306],{},[115,63308,10198],{"id":10197},[120,63310,63311,63333,63355,63399,63443,63506,63534],{},[123,63312,63313,3247,63315,1343,63330,63332],{},[38,63314,53611],{},[883,63316,63318],{"className":63317},[886],[888,63319,63320],{"xmlns":890},[892,63321,63322,63328],{},[895,63323,63324,63326],{},[898,63325,1766],{},[898,63327,1769],{},[902,63329,53627],{"encoding":904},[614,63331,53665],{},") — rozdíl mezi ochotou platit a skutečnou platbou, vzorec (2.14).",[123,63334,63335,3247,63337,1343,63352,63354],{},[38,63336,53758],{},[883,63338,63340],{"className":63339},[886],[888,63341,63342],{"xmlns":890},[892,63343,63344,63350],{},[895,63345,63346,63348],{},[898,63347,8194],{},[898,63349,1769],{},[902,63351,53646],{"encoding":904},[614,63353,53761],{},") — rozdíl mezi tržbou a minimální cenou dle nabídky, vzorec (2.15).",[123,63356,63357,2533,63360,1863],{},[38,63358,63359],{},"Ochota platit",[883,63361,63363],{"className":63362},[886],[888,63364,63365],{"xmlns":890},[892,63366,63367,63397],{},[895,63368,63369],{},[4138,63370,63371,63383,63385,63387,63389,63391,63393,63395],{"scriptlevel":4032,"displaystyle":1672},[1715,63372,63373,63375,63377],{},[1656,63374,19906],{},[1667,63376,4032],{},[1661,63378,63379,63381],{},[898,63380,1665],{},[1667,63382,4032],{},[898,63384,6787],{},[1656,63386,1659],{"stretchy":1658},[898,63388,1665],{},[1656,63390,1683],{"stretchy":1658},[2461,63392,7828],{},[898,63394,3768],{},[898,63396,1665],{},[902,63398,60197],{"encoding":904},[123,63400,63401,2533,63404,1863],{},[38,63402,63403],{},"Minimální cena výrobce",[883,63405,63407],{"className":63406},[886],[888,63408,63409],{"xmlns":890},[892,63410,63411,63441],{},[895,63412,63413],{},[4138,63414,63415,63427,63429,63431,63433,63435,63437,63439],{"scriptlevel":4032,"displaystyle":1672},[1715,63416,63417,63419,63421],{},[1656,63418,19906],{},[1667,63420,4032],{},[1661,63422,63423,63425],{},[898,63424,1665],{},[1667,63426,4032],{},[898,63428,1769],{},[1656,63430,1659],{"stretchy":1658},[898,63432,1665],{},[1656,63434,1683],{"stretchy":1658},[2461,63436,7828],{},[898,63438,3768],{},[898,63440,1665],{},[902,63442,60839],{"encoding":904},[123,63444,63445,2533,63448,61340,63473,12702],{},[38,63446,63447],{},"Výdaje spotřebitele \u002F tržby výrobce",[883,63449,63451],{"className":63450},[886],[888,63452,63453],{"xmlns":890},[892,63454,63455,63471],{},[895,63456,63457,63463,63465],{},[1661,63458,63459,63461],{},[898,63460,8194],{},[1667,63462,4032],{},[2461,63464,7828],{},[1661,63466,63467,63469],{},[898,63468,1665],{},[1667,63470,4032],{},[902,63472,60275],{"encoding":904},[883,63474,63476],{"className":63475},[886],[888,63477,63478],{"xmlns":890},[892,63479,63480,63504],{},[895,63481,63482,63484,63486,63492,63494,63496,63498],{},[1667,63483,4032],{},[2461,63485,7828],{},[1661,63487,63488,63490],{},[898,63489,1665],{},[1667,63491,4032],{},[2461,63493,7828],{},[898,63495,2146],{},[2461,63497,7828],{},[1661,63499,63500,63502],{},[898,63501,8194],{},[1667,63503,4032],{},[902,63505,59829],{"encoding":904},[123,63507,63508,63511,63512,63533],{},[38,63509,63510],{},"Celkový přebytek trhu"," — součet ",[883,63513,63515],{"className":63514},[886],[888,63516,63517],{"xmlns":890},[892,63518,63519,63531],{},[895,63520,63521,63523,63525,63527,63529],{},[898,63522,1766],{},[898,63524,1769],{},[1656,63526,3633],{},[898,63528,8194],{},[898,63530,1769],{},[902,63532,59567],{"encoding":904}," v rovnovážném bodě.",[123,63535,63536,63538,63539,1343,63552,63565,63566,1863],{},[38,63537,11258],{}," — plochy ohraničené křivkami ",[883,63540,63542],{"className":63541},[886],[888,63543,63544],{"xmlns":890},[892,63545,63546,63550],{},[895,63547,63548],{},[898,63549,6787],{},[902,63551,6787],{"encoding":904},[883,63553,63555],{"className":63554},[886],[888,63556,63557],{"xmlns":890},[892,63558,63559,63563],{},[895,63560,63561],{},[898,63562,1769],{},[902,63564,1769],{"encoding":904}," a přímkou ",[883,63567,63569],{"className":63568},[886],[888,63570,63571],{"xmlns":890},[892,63572,63573,63585],{},[895,63574,63575,63577,63579],{},[898,63576,8194],{},[1656,63578,1713],{},[1661,63580,63581,63583],{},[898,63582,8194],{},[1667,63584,4032],{},[902,63586,60349],{"encoding":904},[45652,63588],{},[115,63590,63592],{"id":63591},"dopad-daně-na-přebytky-a-mrtvá-ztráta","Dopad daně na přebytky a mrtvá ztráta",[724,63594,63595,63596,63609,63610,63627],{},"Uvalení jednotkové daně ",[883,63597,63599],{"className":63598},[886],[888,63600,63601],{"xmlns":890},[892,63602,63603,63607],{},[895,63604,63605],{},[898,63606,11577],{},[902,63608,11577],{"encoding":904}," na trh posouvá rovnovážné množství pod ",[883,63611,63613],{"className":63612},[886],[888,63614,63615],{"xmlns":890},[892,63616,63617,63625],{},[895,63618,63619],{},[2062,63620,63621,63623],{},[898,63622,1665],{},[898,63624,1842],{},[902,63626,51080],{"encoding":904}," a rozkládá původní plochu přebytků na nové části.",[724,63629,63630],{},[5956,63631],{"alt":63632,"className":63633,"src":63634},"imek-prebytky-s-dani-deadweight",[210,5960],"\u002Fwiki-assets\u002Fimek-prebytky-s-dani-deadweight.jpeg",[724,63636,63637,63638,63653,63654,63669,63670,61340,63673,63697,63698,3247,63701,63704,63705,1863],{},"Přebytek spotřebitele ",[883,63639,63641],{"className":63640},[886],[888,63642,63643],{"xmlns":890},[892,63644,63645,63651],{},[895,63646,63647,63649],{},[898,63648,1766],{},[898,63650,1769],{},[902,63652,53627],{"encoding":904}," se zmenší (spotřebitelé platí víc a nakupují méně), přebytek výrobce ",[883,63655,63657],{"className":63656},[886],[888,63658,63659],{"xmlns":890},[892,63660,63661,63667],{},[895,63662,63663,63665],{},[898,63664,8194],{},[898,63666,1769],{},[902,63668,53646],{"encoding":904}," se rovněž zmenší (výrobci obdrží po odvodu méně). Stát získává ",[38,63671,63672],{},"daňový příjem",[883,63674,63676],{"className":63675},[886],[888,63677,63678],{"xmlns":890},[892,63679,63680,63694],{},[895,63681,63682,63684,63686],{},[898,63683,11577],{},[1656,63685,2751],{},[1715,63687,63688,63690,63692],{},[898,63689,1665],{},[1667,63691,1669],{},[898,63693,1842],{},[902,63695,63696],{"encoding":904},"T \\cdot Q_1^E","). Zbývající část původních přebytků — ",[38,63699,63700],{},"mrtvá ztráta",[614,63702,63703],{},"deadweight loss",", DWL) — je čistým úbytkem blahobytu, který nikdo neinkasuje, a je důsledkem transakcí, které se kvůli dani vůbec neuskuteční. Detailní rozbor viz ",[207,63706,811],{"className":63707,"dataFsResolvedFilePath":809,"href":810},[210],[45652,63709],{},[115,63711,10640],{"id":10639},[120,63713,63714,63721,63733,63740,63747],{},[123,63715,63716,1643,63718],{},[38,63717,24948],{},[207,63719,802],{"className":63720,"dataFsResolvedFilePath":800,"href":801},[210],[123,63722,63723,1643,63725,63728,63729,63732],{},[38,63724,45359],{},[207,63726,775],{"className":63727,"dataFsResolvedFilePath":773,"href":774},[210]," (určitý integrál, plocha pod křivkou), ",[207,63730,10692],{"className":63731,"dataFsResolvedFilePath":764,"href":765},[210]," (monotonie křivek)",[123,63734,63735,1643,63737],{},[38,63736,24958],{},[207,63738,12608],{"className":63739,"dataFsResolvedFilePath":827,"href":828},[210],[123,63741,63742,1643,63744],{},[38,63743,59430],{},[207,63745,59434],{"className":63746,"dataFsResolvedFilePath":745,"href":746},[210],[123,63748,63749,1643,63751],{},[38,63750,10742],{},[207,63752,1869],{"className":63753,"dataFsResolvedFilePath":10746,"href":10747},[210],{"title":641,"searchDepth":642,"depth":642,"links":63755},[63756,63757,63762,63767,63772,63773,63774,63775],{"id":59626,"depth":642,"text":1241},{"id":59970,"depth":642,"text":63758,"children":63759},"Přebytek spotřebitele (CSCS)",[63760,63761],{"id":59989,"depth":649,"text":59990},{"id":11257,"depth":649,"text":11258},{"id":60565,"depth":642,"text":63763,"children":63764},"Přebytek výrobce (PSPS)",[63765,63766],{"id":60584,"depth":649,"text":60585},{"id":60747,"depth":649,"text":11258},{"id":61354,"depth":642,"text":61355,"children":63768},[63769,63770],{"id":61358,"depth":649,"text":61359},{"id":62650,"depth":649,"text":63771},"Příklad 2.13 — numerický výpočet PSPS",{"id":62955,"depth":642,"text":62956},{"id":10197,"depth":642,"text":10198},{"id":63591,"depth":642,"text":63592},{"id":10639,"depth":642,"text":10640},{},"\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce",{"title":820,"description":641},[1138,1135],"topics\u002Fprebytek-spotrebitele-vyrobce",[1128,59496,63782,63783,20725,24966,63784,63785],"cs","ps","spotrebitel","vyrobce","FhK0gkf2tjMxSgO0-74OuedOn6U35QtJczf-f255pZs",{"id":63788,"title":63789,"body":63790,"course":1128,"courses":659,"created":10774,"description":641,"extension":661,"meta":83112,"navigation":664,"path":83113,"seo":83114,"sources":83115,"stem":83116,"tags":83117,"type":10786,"updated":677,"__hash__":83123},"topics\u002Ftopics\u002Fprijem-naklady-zisk.md","Příjem, náklady, zisk a nabídka firmy",{"type":9,"value":63791,"toc":83076},[63792,63795,63981,63983,64074,64079,64405,64409,64416,64420,64465,64532,64563,64613,64648,64652,64711,64716,64782,64899,65001,65005,65028,65106,65149,65153,65182,65249,65255,65369,65373,65453,65490,65542,65740,65804,65891,65895,65898,65977,65980,66098,66117,66182,66186,66278,66346,66387,66441,66509,66546,66550,66608,66638,66849,66921,66973,67139,67232,67267,67271,67275,67312,67377,67432,67436,67459,67548,67652,67721,67725,67822,67935,67991,68045,68103,68164,68167,68203,68268,68298,68527,68585,68619,68623,68650,68729,68843,68864,68943,68945,69053,69057,69195,69517,69521,69524,69528,69577,69581,69835,69987,69994,70067,70251,70256,70598,70602,70625,70627,70648,70707,70717,70766,70908,70982,71077,71192,71289,71407,71411,71480,71485,71597,71742,71793,71905,71947,71951,71971,72032,72059,72121,72125,72147,72216,72496,72503,72533,72540,72733,72737,72815,72820,72896,72899,72987,73063,73130,73179,73281,73354,73475,73826,73939,74041,74045,74048,74055,74058,74094,74153,74162,74311,74535,74539,74602,74781,74873,74928,74932,74988,75058,75110,75131,75212,75215,75289,75333,75337,75378,75421,75447,75451,75522,75618,75680,75732,75835,75913,75936,75965,75969,76135,76252,76324,76639,76799,76803,76854,76916,76951,76981,77081,77123,77292,77297,77393,77431,77435,77554,77855,77857,77892,77896,77900,78028,78160,78482,78670,78748,78752,79057,79170,79316,79501,79607,79839,79954,80036,80155,80253,80294,80298,80353,80497,80651,80811,80904,81097,81408,81539,81668,81672,81744,81786,81837,81839,83034,83036],[12,63793,63789],{"id":63794},"příjem-náklady-zisk-a-nabídka-firmy",[1981,63796,63797],{},[724,63798,63799,12658,63801,1643,63804,63819,63820,1643,63823,63838,63839,1643,63842,63870,63871,63893,63894,63918,63919,63941,63942,63945,63946,63962,63963,1863],{},[883,63800,12657],{},[38,63802,63803],{},"Příjem",[883,63805,63807],{"className":63806},[886],[888,63808,63809],{"xmlns":890},[892,63810,63811,63817],{},[895,63812,63813,63815],{},[898,63814,11577],{},[898,63816,1763],{},[902,63818,12875],{"encoding":904}," je to, co firma inkasuje (cena krát množství), ",[38,63821,63822],{},"náklady",[883,63824,63826],{"className":63825},[886],[888,63827,63828],{"xmlns":890},[892,63829,63830,63836],{},[895,63831,63832,63834],{},[898,63833,11577],{},[898,63835,1766],{},[902,63837,12033],{"encoding":904}," to, co vynaloží (fixní plus variabilní), a ",[38,63840,63841],{},"zisk",[883,63843,63845],{"className":63844},[886],[888,63846,63847],{"xmlns":890},[892,63848,63849,63867],{},[895,63850,63851,63853,63855,63857,63859,63861,63863,63865],{},[898,63852,8194],{},[898,63854,1763],{},[1656,63856,1713],{},[898,63858,11577],{},[898,63860,1763],{},[1656,63862,3964],{},[898,63864,11577],{},[898,63866,1766],{},[902,63868,63869],{"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: ",[883,63872,63874],{"className":63873},[886],[888,63875,63876],{"xmlns":890},[892,63877,63878,63890],{},[895,63879,63880,63882,63884,63886,63888],{},[898,63881,2146],{},[898,63883,1766],{},[1656,63885,1713],{},[898,63887,1703],{},[898,63889,1766],{},[902,63891,63892],{"encoding":904},"AC = MC"," v minimu průměrných nákladů, ",[883,63895,63897],{"className":63896},[886],[888,63898,63899],{"xmlns":890},[892,63900,63901,63915],{},[895,63902,63903,63905,63907,63909,63911,63913],{},[898,63904,2146],{},[898,63906,49019],{},[898,63908,1766],{},[1656,63910,1713],{},[898,63912,1703],{},[898,63914,1766],{},[902,63916,63917],{"encoding":904},"AVC = MC"," v minimu průměrných variabilních nákladů a ",[883,63920,63922],{"className":63921},[886],[888,63923,63924],{"xmlns":890},[892,63925,63926,63938],{},[895,63927,63928,63930,63932,63934,63936],{},[898,63929,1703],{},[898,63931,1763],{},[1656,63933,1713],{},[898,63935,1703],{},[898,63937,1766],{},[902,63939,63940],{"encoding":904},"MR = MC"," v maximu zisku. Na závěr se sestaví ",[38,63943,63944],{},"funkce nabídky firmy"," jako rostoucí část křivky ",[883,63947,63949],{"className":63948},[886],[888,63950,63951],{"xmlns":890},[892,63952,63953,63959],{},[895,63954,63955,63957],{},[898,63956,1703],{},[898,63958,1766],{},[902,63960,63961],{"encoding":904},"MC"," nad bodem minima ",[883,63964,63966],{"className":63965},[886],[888,63967,63968],{"xmlns":890},[892,63969,63970,63978],{},[895,63971,63972,63974,63976],{},[898,63973,2146],{},[898,63975,49019],{},[898,63977,1766],{},[902,63979,63980],{"encoding":904},"AVC",[115,63982,1241],{"id":59626},[724,63984,63985,63986,63989,63990,63992,63993,1343,63996,1343,63999,64001,64002,64005,64006,64009,64010,64013,64014,3605,64029,1348,64044,3605,64059,12702],{},"Kapitola 3 se zabývá dvěma základními veličinami popisujícími ekonomickou aktivitu firmy — ",[38,63987,63988],{},"příjmem"," (revenue) a ",[38,63991,63822],{}," (cost) — v jejich třech standardních podobách: celkové, průměrné a mezní. Navazuje analýzou ",[38,63994,63995],{},"zisku",[38,63997,63998],{},"bodů zvratu",[38,64000,10816],{}," a konstrukcí ",[38,64003,64004],{},"nabídkové křivky firmy",". Klíčovými matematickými nástroji jsou ",[207,64007,1145],{"className":64008,"dataFsResolvedFilePath":764,"href":765},[210]," (pro mezní veličiny) a diferenciál (pro odhad přírůstků); v několika úlohách se využívá také ",[207,64011,19867],{"className":64012,"dataFsResolvedFilePath":773,"href":774},[210]," (pro zpětnou rekonstrukci ",[883,64015,64017],{"className":64016},[886],[888,64018,64019],{"xmlns":890},[892,64020,64021,64027],{},[895,64022,64023,64025],{},[898,64024,11577],{},[898,64026,1763],{},[902,64028,12875],{"encoding":904},[883,64030,64032],{"className":64031},[886],[888,64033,64034],{"xmlns":890},[892,64035,64036,64042],{},[895,64037,64038,64040],{},[898,64039,1703],{},[898,64041,1763],{},[902,64043,15395],{"encoding":904},[883,64045,64047],{"className":64046},[886],[888,64048,64049],{"xmlns":890},[892,64050,64051,64057],{},[895,64052,64053,64055],{},[898,64054,11577],{},[898,64056,1766],{},[902,64058,12033],{"encoding":904},[883,64060,64062],{"className":64061},[886],[888,64063,64064],{"xmlns":890},[892,64065,64066,64072],{},[895,64067,64068,64070],{},[898,64069,1703],{},[898,64071,1766],{},[902,64073,63961],{"encoding":904},[724,64075,64076],{},[38,64077,64078],{},"Cílové znalosti:",[120,64080,64081,64245,64248,64251,64344,64391,64398],{},[123,64082,64083,64084,1343,64099,1343,64115,1896,64130,1343,64145,1343,64161,1343,64179,1343,64197,1343,64214,1343,64230,2856],{},"odvodit a interpretovat funkce ",[883,64085,64087],{"className":64086},[886],[888,64088,64089],{"xmlns":890},[892,64090,64091,64097],{},[895,64092,64093,64095],{},[898,64094,11577],{},[898,64096,1763],{},[902,64098,12875],{"encoding":904},[883,64100,64102],{"className":64101},[886],[888,64103,64104],{"xmlns":890},[892,64105,64106,64112],{},[895,64107,64108,64110],{},[898,64109,2146],{},[898,64111,1763],{},[902,64113,64114],{"encoding":904},"AR",[883,64116,64118],{"className":64117},[886],[888,64119,64120],{"xmlns":890},[892,64121,64122,64128],{},[895,64123,64124,64126],{},[898,64125,1703],{},[898,64127,1763],{},[902,64129,15395],{"encoding":904},[883,64131,64133],{"className":64132},[886],[888,64134,64135],{"xmlns":890},[892,64136,64137,64143],{},[895,64138,64139,64141],{},[898,64140,11577],{},[898,64142,1766],{},[902,64144,12033],{"encoding":904},[883,64146,64148],{"className":64147},[886],[888,64149,64150],{"xmlns":890},[892,64151,64152,64158],{},[895,64153,64154,64156],{},[898,64155,19177],{},[898,64157,1766],{},[902,64159,64160],{"encoding":904},"FC",[883,64162,64164],{"className":64163},[886],[888,64165,64166],{"xmlns":890},[892,64167,64168,64176],{},[895,64169,64170,64172,64174],{},[898,64171,11577],{},[898,64173,49019],{},[898,64175,1766],{},[902,64177,64178],{"encoding":904},"TVC",[883,64180,64182],{"className":64181},[886],[888,64183,64184],{"xmlns":890},[892,64185,64186,64194],{},[895,64187,64188,64190,64192],{},[898,64189,2146],{},[898,64191,19177],{},[898,64193,1766],{},[902,64195,64196],{"encoding":904},"AFC",[883,64198,64200],{"className":64199},[886],[888,64201,64202],{"xmlns":890},[892,64203,64204,64212],{},[895,64205,64206,64208,64210],{},[898,64207,2146],{},[898,64209,49019],{},[898,64211,1766],{},[902,64213,63980],{"encoding":904},[883,64215,64217],{"className":64216},[886],[888,64218,64219],{"xmlns":890},[892,64220,64221,64227],{},[895,64222,64223,64225],{},[898,64224,2146],{},[898,64226,1766],{},[902,64228,64229],{"encoding":904},"AC",[883,64231,64233],{"className":64232},[886],[888,64234,64235],{"xmlns":890},[892,64236,64237,64243],{},[895,64238,64239,64241],{},[898,64240,1703],{},[898,64242,1766],{},[902,64244,63961],{"encoding":904},[123,64246,64247],{},"porozumět vzájemným vztahům mezi průměrnou a mezní veličinou, zvláště pro lineární poptávku;",[123,64249,64250],{},"pomocí diferenciálu odhadovat změny celkových veličin;",[123,64252,64253,64254,64257,64258,3228,64300,2856],{},"osvojit si ",[38,64255,64256],{},"princip minimalizace průměrných (variabilních) nákladů"," — podmínku ",[883,64259,64261],{"className":64260},[886],[888,64262,64263],{"xmlns":890},[892,64264,64265,64297],{},[895,64266,64267,64269,64271,64273,64279,64281,64283,64285,64287,64289,64295],{},[898,64268,2146],{},[898,64270,1766],{},[1656,64272,1659],{"stretchy":1658},[1661,64274,64275,64277],{},[898,64276,1665],{},[1667,64278,4032],{},[1656,64280,1683],{"stretchy":1658},[1656,64282,1713],{},[898,64284,1703],{},[898,64286,1766],{},[1656,64288,1659],{"stretchy":1658},[1661,64290,64291,64293],{},[898,64292,1665],{},[1667,64294,4032],{},[1656,64296,1683],{"stretchy":1658},[902,64298,64299],{"encoding":904},"AC(Q_0)=MC(Q_0)",[883,64301,64303],{"className":64302},[886],[888,64304,64305],{"xmlns":890},[892,64306,64307,64341],{},[895,64308,64309,64311,64313,64315,64317,64323,64325,64327,64329,64331,64333,64339],{},[898,64310,2146],{},[898,64312,49019],{},[898,64314,1766],{},[1656,64316,1659],{"stretchy":1658},[1661,64318,64319,64321],{},[898,64320,1665],{},[1667,64322,4032],{},[1656,64324,1683],{"stretchy":1658},[1656,64326,1713],{},[898,64328,1703],{},[898,64330,1766],{},[1656,64332,1659],{"stretchy":1658},[1661,64334,64335,64337],{},[898,64336,1665],{},[1667,64338,4032],{},[1656,64340,1683],{"stretchy":1658},[902,64342,64343],{"encoding":904},"AVC(Q_0)=MC(Q_0)",[123,64345,64253,64346,64257,64349,2856],{},[38,64347,64348],{},"princip maximalizace zisku",[883,64350,64352],{"className":64351},[886],[888,64353,64354],{"xmlns":890},[892,64355,64356,64388],{},[895,64357,64358,64360,64362,64364,64370,64372,64374,64376,64378,64380,64386],{},[898,64359,1703],{},[898,64361,1763],{},[1656,64363,1659],{"stretchy":1658},[1661,64365,64366,64368],{},[898,64367,1665],{},[1667,64369,4032],{},[1656,64371,1683],{"stretchy":1658},[1656,64373,1713],{},[898,64375,1703],{},[898,64377,1766],{},[1656,64379,1659],{"stretchy":1658},[1661,64381,64382,64384],{},[898,64383,1665],{},[1667,64385,4032],{},[1656,64387,1683],{"stretchy":1658},[902,64389,64390],{"encoding":904},"MR(Q_0)=MC(Q_0)",[123,64392,64393,64394,64397],{},"stanovit ",[38,64395,64396],{},"body zvratu"," a interval zisku;",[123,64399,64400,64401,64404],{},"zkonstruovat ",[38,64402,64403],{},"funkci nabídky firmy"," na základě nákladových charakteristik.",[115,64406,64408],{"id":64407},"příjem-firmy","Příjem firmy",[724,64410,64411],{},[5956,64412],{"alt":64413,"className":64414,"src":64415},"imek-ar-mr-dvojnasobny-sklon",[210,5960],"\u002Fwiki-assets\u002Fimek-ar-mr-dvojnasobny-sklon.jpeg",[198,64417,64419],{"id":64418},"celkový-příjem","Celkový příjem",[724,64421,64422,64423,3247,64438,64441,64442,7727],{},"Celkový příjem ",[883,64424,64426],{"className":64425},[886],[888,64427,64428],{"xmlns":890},[892,64429,64430,64436],{},[895,64431,64432,64434],{},[898,64433,11577],{},[898,64435,1763],{},[902,64437,12875],{"encoding":904},[38,64439,64440],{},"total revenue",") je součin ceny a prodaného množství. Při poptávce ",[883,64443,64445],{"className":64444},[886],[888,64446,64447],{"xmlns":890},[892,64448,64449,64463],{},[895,64450,64451,64453,64455,64457,64459,64461],{},[898,64452,8194],{},[1656,64454,1713],{},[898,64456,6787],{},[1656,64458,1659],{"stretchy":1658},[898,64460,1665],{},[1656,64462,1683],{"stretchy":1658},[902,64464,13412],{"encoding":904},[883,64466,64468],{"className":64467},[886],[888,64469,64470],{"xmlns":890,"display":2408},[892,64471,64472,64529],{},[2412,64473,64474],{"width":2414},[2416,64475,64476,64478,64522,64524],{},[2419,64477],{"width":2421},[2419,64479,64480],{},[895,64481,64482,64484,64486,64488,64490,64492,64494,64496,64498,64500,64502,64504,64506,64508,64510,64512,64514,64516,64518,64520],{},[898,64483,11577],{},[898,64485,1763],{},[1656,64487,1713],{},[898,64489,11577],{},[898,64491,1763],{},[1656,64493,1659],{"stretchy":1658},[898,64495,1665],{},[1656,64497,1683],{"stretchy":1658},[1656,64499,1713],{},[898,64501,8194],{},[1656,64503,2751],{},[898,64505,1665],{},[1656,64507,1713],{},[898,64509,6787],{},[1656,64511,1659],{"stretchy":1658},[898,64513,1665],{},[1656,64515,1683],{"stretchy":1658},[1656,64517,2751],{},[898,64519,1665],{},[898,64521,1863],{"mathvariant":1723},[2419,64523],{"width":2421},[2419,64525,64526],{},[2461,64527,64528],{},"(3.1)",[902,64530,64531],{"encoding":904},"TR = TR(Q) = P \\cdot Q = D(Q) \\cdot Q.\n\\tag{3.1}",[724,64533,64534,64535,64538,64539,64562],{},"Graf funkce se nazývá ",[38,64536,64537],{},"křivka celkového příjmu"," (total revenue curve). Za předpokladu linearity poptávky, tj. ",[883,64540,64542],{"className":64541},[886],[888,64543,64544],{"xmlns":890},[892,64545,64546,64560],{},[895,64547,64548,64550,64552,64554,64556,64558],{},[898,64549,8194],{},[1656,64551,1713],{},[898,64553,207],{},[898,64555,1665],{},[1656,64557,3633],{},[898,64559,3403],{},[902,64561,45742],{"encoding":904},", je celkový příjem kvadratickou funkcí, neboť",[883,64564,64566],{"className":64565},[886],[888,64567,64568],{"xmlns":890,"display":2408},[892,64569,64570,64610],{},[895,64571,64572,64574,64576,64578,64580,64582,64584,64586,64588,64590,64592,64594,64596,64602,64604,64606,64608],{},[898,64573,11577],{},[898,64575,1763],{},[1656,64577,1713],{},[898,64579,1665],{},[1656,64581,1659],{"stretchy":1658},[898,64583,207],{},[898,64585,1665],{},[1656,64587,3633],{},[898,64589,3403],{},[1656,64591,1683],{"stretchy":1658},[1656,64593,1713],{},[898,64595,207],{},[2062,64597,64598,64600],{},[898,64599,1665],{},[1667,64601,1680],{},[1656,64603,3633],{},[898,64605,3403],{},[898,64607,1665],{},[1656,64609,1673],{"separator":1672},[902,64611,64612],{"encoding":904},"TR = Q(aQ + b) = aQ^2 + bQ,",[724,64614,64615,64616,64629,64630,64647],{},"a křivka celkového příjmu je parabola tvaru obráceného ",[883,64617,64619],{"className":64618},[886],[888,64620,64621],{"xmlns":890},[892,64622,64623,64627],{},[895,64624,64625],{},[898,64626,900],{},[902,64628,900],{"encoding":904}," (jelikož ",[883,64631,64633],{"className":64632},[886],[888,64634,64635],{"xmlns":890},[892,64636,64637,64645],{},[895,64638,64639,64641,64643],{},[898,64640,207],{},[1656,64642,4373],{},[1667,64644,4032],{},[902,64646,51762],{"encoding":904},") procházející počátkem.",[46030,64649,64651],{"id":64650},"příklad-31","Příklad 3.1",[724,64653,64654,64657,64658,64694,64695,64710],{},[38,64655,64656],{},"Zadání."," Pro poptávku ",[883,64659,64661],{"className":64660},[886],[888,64662,64663],{"xmlns":890},[892,64664,64665,64691],{},[895,64666,64667,64669,64671,64673,64675,64677,64679,64681,64683,64685,64687,64689],{},[898,64668,8194],{},[1656,64670,1713],{},[898,64672,6787],{},[1656,64674,1659],{"stretchy":1658},[898,64676,1665],{},[1656,64678,1683],{"stretchy":1658},[1656,64680,1713],{},[1656,64682,3964],{},[1667,64684,1680],{},[898,64686,1665],{},[1656,64688,3633],{},[1667,64690,5267],{},[902,64692,64693],{"encoding":904},"P = D(Q) = -2Q + 100"," určete ",[883,64696,64698],{"className":64697},[886],[888,64699,64700],{"xmlns":890},[892,64701,64702,64708],{},[895,64703,64704,64706],{},[898,64705,11577],{},[898,64707,1763],{},[902,64709,12875],{"encoding":904}," a charakterizujte jeho křivku.",[724,64712,64713,64715],{},[38,64714,31488],{}," Celkový příjem je",[883,64717,64719],{"className":64718},[886],[888,64720,64721],{"xmlns":890,"display":2408},[892,64722,64723,64779],{},[895,64724,64725,64727,64729,64731,64733,64735,64737,64739,64741,64743,64745,64747,64749,64751,64753,64755,64757,64759,64761,64763,64765,64771,64773,64775,64777],{},[898,64726,11577],{},[898,64728,1763],{},[1656,64730,1713],{},[898,64732,11577],{},[898,64734,1763],{},[1656,64736,1659],{"stretchy":1658},[898,64738,1665],{},[1656,64740,1683],{"stretchy":1658},[1656,64742,1713],{},[898,64744,1665],{},[1656,64746,1659],{"stretchy":1658},[1656,64748,3964],{},[1667,64750,1680],{},[898,64752,1665],{},[1656,64754,3633],{},[1667,64756,5267],{},[1656,64758,1683],{"stretchy":1658},[1656,64760,1713],{},[1656,64762,3964],{},[1667,64764,1680],{},[2062,64766,64767,64769],{},[898,64768,1665],{},[1667,64770,1680],{},[1656,64772,3633],{},[1667,64774,5267],{},[898,64776,1665],{},[898,64778,1863],{"mathvariant":1723},[902,64780,64781],{"encoding":904},"TR = TR(Q) = Q(-2Q + 100) = -2Q^2 + 100Q.",[724,64783,64784,64785,1896,64807,64829,64830,64848,64849,1863],{},"Křivkou je parabola (obrázek 3.1) s nulami v ",[883,64786,64788],{"className":64787},[886],[888,64789,64790],{"xmlns":890},[892,64791,64792,64804],{},[895,64793,64794,64800,64802],{},[1661,64795,64796,64798],{},[898,64797,1665],{},[1667,64799,1669],{},[1656,64801,1713],{},[1667,64803,4032],{},[902,64805,64806],{"encoding":904},"Q_1 = 0",[883,64808,64810],{"className":64809},[886],[888,64811,64812],{"xmlns":890},[892,64813,64814,64826],{},[895,64815,64816,64822,64824],{},[1661,64817,64818,64820],{},[898,64819,1665],{},[1667,64821,1680],{},[1656,64823,1713],{},[1667,64825,9267],{},[902,64827,64828],{"encoding":904},"Q_2 = 50",". Maxima dosahuje při ",[883,64831,64833],{"className":64832},[886],[888,64834,64835],{"xmlns":890},[892,64836,64837,64845],{},[895,64838,64839,64841,64843],{},[898,64840,1665],{},[1656,64842,1713],{},[1667,64844,8567],{},[902,64846,64847],{"encoding":904},"Q = 25"," ve výši ",[883,64850,64852],{"className":64851},[886],[888,64853,64854],{"xmlns":890},[892,64855,64856,64896],{},[895,64857,64858,64860,64869,64871,64873,64875,64877,64880,64882,64884,64886,64888,64890,64892,64894],{},[898,64859,11577],{},[1661,64861,64862,64864,64867],{},[898,64863,1763],{},[898,64865,64866],{},"max",[1656,64868,2093],{},[1656,64870,1713],{},[1656,64872,3964],{},[1667,64874,1680],{},[1656,64876,2751],{},[1667,64878,64879],{},"625",[1656,64881,3633],{},[1667,64883,5267],{},[1656,64885,2751],{},[1667,64887,8567],{},[1656,64889,1713],{},[1667,64891,1669],{},[2461,64893,7828],{},[1667,64895,39433],{},[902,64897,64898],{"encoding":904},"TR_{\\max} = -2 \\cdot 625 + 100 \\cdot 25 = 1\\,250",[724,64900,64901],{},[614,64902,64903,64904,64938,64939,1896,64952,64965,64966,3565,64984,1863],{},"Obrázek 3.1: Parabola ",[883,64905,64907],{"className":64906},[886],[888,64908,64909],{"xmlns":890},[892,64910,64911,64935],{},[895,64912,64913,64915,64917,64919,64921,64923,64929,64931,64933],{},[898,64914,11577],{},[898,64916,1763],{},[1656,64918,1713],{},[1656,64920,3964],{},[1667,64922,1680],{},[2062,64924,64925,64927],{},[898,64926,1665],{},[1667,64928,1680],{},[1656,64930,3633],{},[1667,64932,5267],{},[898,64934,1665],{},[902,64936,64937],{"encoding":904},"TR = -2Q^2 + 100Q"," s nulami v ",[883,64940,64942],{"className":64941},[886],[888,64943,64944],{"xmlns":890},[892,64945,64946,64950],{},[895,64947,64948],{},[1667,64949,4032],{},[902,64951,4032],{"encoding":904},[883,64953,64955],{"className":64954},[886],[888,64956,64957],{"xmlns":890},[892,64958,64959,64963],{},[895,64960,64961],{},[1667,64962,9267],{},[902,64964,9267],{"encoding":904}," a maximem ",[883,64967,64969],{"className":64968},[886],[888,64970,64971],{"xmlns":890},[892,64972,64973,64981],{},[895,64974,64975,64977,64979],{},[1667,64976,1669],{},[2461,64978,7828],{},[1667,64980,39433],{},[902,64982,64983],{"encoding":904},"1\\,250",[883,64985,64987],{"className":64986},[886],[888,64988,64989],{"xmlns":890},[892,64990,64991,64999],{},[895,64992,64993,64995,64997],{},[898,64994,1665],{},[1656,64996,1713],{},[1667,64998,8567],{},[902,65000,64847],{"encoding":904},[198,65002,65004],{"id":65003},"průměrný-příjem","Průměrný příjem",[724,65006,65007,1643,65009,3247,65024,65027],{},[38,65008,65004],{},[883,65010,65012],{"className":65011},[886],[888,65013,65014],{"xmlns":890},[892,65015,65016,65022],{},[895,65017,65018,65020],{},[898,65019,2146],{},[898,65021,1763],{},[902,65023,64114],{"encoding":904},[38,65025,65026],{},"average revenue",") je podíl celkového příjmu a množství. Z (3.1) plyne",[883,65029,65031],{"className":65030},[886],[888,65032,65033],{"xmlns":890,"display":2408},[892,65034,65035,65103],{},[895,65036,65037,65039,65041,65043,65045,65047,65049,65051,65053,65055,65071,65073,65091,65093,65095,65097,65099,65101],{},[898,65038,2146],{},[898,65040,1763],{},[1656,65042,1713],{},[898,65044,2146],{},[898,65046,1763],{},[1656,65048,1659],{"stretchy":1658},[898,65050,1665],{},[1656,65052,1683],{"stretchy":1658},[1656,65054,1713],{},[3294,65056,65057,65069],{},[895,65058,65059,65061,65063,65065,65067],{},[898,65060,11577],{},[898,65062,1763],{},[1656,65064,1659],{"stretchy":1658},[898,65066,1665],{},[1656,65068,1683],{"stretchy":1658},[898,65070,1665],{},[1656,65072,1713],{},[3294,65074,65075,65089],{},[895,65076,65077,65079,65081,65083,65085,65087],{},[898,65078,1665],{},[2461,65080,7828],{},[898,65082,6787],{},[1656,65084,1659],{"stretchy":1658},[898,65086,1665],{},[1656,65088,1683],{"stretchy":1658},[898,65090,1665],{},[1656,65092,1713],{},[898,65094,6787],{},[1656,65096,1659],{"stretchy":1658},[898,65098,1665],{},[1656,65100,1683],{"stretchy":1658},[898,65102,1863],{"mathvariant":1723},[902,65104,65105],{"encoding":904},"AR = AR(Q) = \\frac{TR(Q)}{Q} = \\frac{Q \\, D(Q)}{Q} = D(Q).",[1981,65107,65108],{},[724,65109,65110,65113,65114,1343,65117,1863],{},[883,65111,65112],{},"!note"," Klíčové pozorování\n",[38,65115,65116],{},"Průměrný příjem se vždy rovná poptávkové funkci",[883,65118,65120],{"className":65119},[886],[888,65121,65122],{"xmlns":890},[892,65123,65124,65146],{},[895,65125,65126,65128,65130,65132,65134,65136,65138,65140,65142,65144],{},[898,65127,2146],{},[898,65129,1763],{},[1656,65131,1659],{"stretchy":1658},[898,65133,1665],{},[1656,65135,1683],{"stretchy":1658},[1656,65137,1713],{},[898,65139,6787],{},[1656,65141,1659],{"stretchy":1658},[898,65143,1665],{},[1656,65145,1683],{"stretchy":1658},[902,65147,65148],{"encoding":904},"AR(Q) = D(Q)",[198,65150,65152],{"id":65151},"mezní-příjem","Mezní příjem",[724,65154,65155,65156,1643,65159,3247,65174,65177,65178,65181],{},"Pro zkoumání dynamiky změn celkového příjmu zavádíme ",[38,65157,65158],{},"mezní příjem",[883,65160,65162],{"className":65161},[886],[888,65163,65164],{"xmlns":890},[892,65165,65166,65172],{},[895,65167,65168,65170],{},[898,65169,1703],{},[898,65171,1763],{},[902,65173,15395],{"encoding":904},[38,65175,65176],{},"marginal revenue","), definovaný jako ",[207,65179,1145],{"className":65180,"dataFsResolvedFilePath":764,"href":765},[210]," celkového příjmu podle množství:",[883,65183,65185],{"className":65184},[886],[888,65186,65187],{"xmlns":890,"display":2408},[892,65188,65189,65246],{},[2412,65190,65191],{"width":2414},[2416,65192,65193,65195,65239,65241],{},[2419,65194],{"width":2421},[2419,65196,65197],{},[895,65198,65199,65201,65203,65205,65221,65223,65225,65231,65233,65235,65237],{},[898,65200,1703],{},[898,65202,1763],{},[1656,65204,1713],{},[3294,65206,65207,65215],{},[895,65208,65209,65211,65213],{},[898,65210,3768],{"mathvariant":1723},[898,65212,11577],{},[898,65214,1763],{},[895,65216,65217,65219],{},[898,65218,3768],{"mathvariant":1723},[898,65220,1665],{},[1656,65222,1713],{},[898,65224,11577],{},[2062,65226,65227,65229],{},[898,65228,1763],{},[1656,65230,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,65232,1659],{"stretchy":1658},[898,65234,1665],{},[1656,65236,1683],{"stretchy":1658},[898,65238,1863],{"mathvariant":1723},[2419,65240],{"width":2421},[2419,65242,65243],{},[2461,65244,65245],{},"(3.2)",[902,65247,65248],{"encoding":904},"MR = \\frac{\\mathrm{d}TR}{\\mathrm{d}Q} = TR'(Q).\n\\tag{3.2}",[724,65250,65251,65252,65254],{},"Mezní příjem udává ",[38,65253,11406],{}," celkového příjmu vzhledem k množství.",[1981,65256,65257],{},[724,65258,65259,65261,65262,65288,65289,65306,65307,1863],{},[883,65260,3472],{}," Intuice — „kolik vyděláš za další kus\"\nHodnota ",[883,65263,65265],{"className":65264},[886],[888,65266,65267],{"xmlns":890},[892,65268,65269,65285],{},[895,65270,65271,65273,65275,65277,65283],{},[898,65272,1703],{},[898,65274,1763],{},[1656,65276,1659],{"stretchy":1658},[2062,65278,65279,65281],{},[898,65280,1665],{},[1656,65282,8187],{},[1656,65284,1683],{"stretchy":1658},[902,65286,65287],{"encoding":904},"MR(Q^*)"," je přibližně to, o kolik se zvýší celkový příjem, prodá-li firma jednu další jednotku nad aktuální úroveň ",[883,65290,65292],{"className":65291},[886],[888,65293,65294],{"xmlns":890},[892,65295,65296,65304],{},[895,65297,65298],{},[2062,65299,65300,65302],{},[898,65301,1665],{},[1656,65303,8187],{},[902,65305,38543],{"encoding":904},". Jinak řečeno: ",[883,65308,65310],{"className":65309},[886],[888,65311,65312],{"xmlns":890},[892,65313,65314,65366],{},[895,65315,65316,65318,65320,65322,65328,65330,65332,65334,65336,65338,65344,65346,65348,65350,65352,65354,65356,65358,65364],{},[898,65317,1703],{},[898,65319,1763],{},[1656,65321,1659],{"stretchy":1658},[2062,65323,65324,65326],{},[898,65325,1665],{},[1656,65327,8187],{},[1656,65329,1683],{"stretchy":1658},[1656,65331,3815],{},[898,65333,11577],{},[898,65335,1763],{},[1656,65337,1659],{"stretchy":1658},[2062,65339,65340,65342],{},[898,65341,1665],{},[1656,65343,8187],{},[1656,65345,3633],{},[1667,65347,1669],{},[1656,65349,1683],{"stretchy":1658},[1656,65351,3964],{},[898,65353,11577],{},[898,65355,1763],{},[1656,65357,1659],{"stretchy":1658},[2062,65359,65360,65362],{},[898,65361,1665],{},[1656,65363,8187],{},[1656,65365,1683],{"stretchy":1658},[902,65367,65368],{"encoding":904},"MR(Q^*) \\approx TR(Q^* + 1) - TR(Q^*)",[46030,65370,65372],{"id":65371},"příklad-32","Příklad 3.2",[724,65374,65375,64657,65377,64694,65411,65426,65427,1863],{},[38,65376,64656],{},[883,65378,65380],{"className":65379},[886],[888,65381,65382],{"xmlns":890},[892,65383,65384,65408],{},[895,65385,65386,65388,65390,65392,65394,65396,65398,65400,65402,65404,65406],{},[898,65387,8194],{},[1656,65389,1713],{},[898,65391,6787],{},[1656,65393,1659],{"stretchy":1658},[898,65395,1665],{},[1656,65397,1683],{"stretchy":1658},[1656,65399,1713],{},[1667,65401,5267],{},[1656,65403,3964],{},[1667,65405,1680],{},[898,65407,1665],{},[902,65409,65410],{"encoding":904},"P = D(Q) = 100 - 2Q",[883,65412,65414],{"className":65413},[886],[888,65415,65416],{"xmlns":890},[892,65417,65418,65424],{},[895,65419,65420,65422],{},[898,65421,1703],{},[898,65423,1763],{},[902,65425,15395],{"encoding":904}," a interpretujte jeho hodnoty pro ",[883,65428,65430],{"className":65429},[886],[888,65431,65432],{"xmlns":890},[892,65433,65434,65450],{},[895,65435,65436,65438,65440,65442,65444,65446,65448],{},[898,65437,1665],{},[1656,65439,1713],{},[1667,65441,44930],{},[1656,65443,1673],{"separator":1672},[1667,65445,2668],{},[1656,65447,1673],{"separator":1672},[1667,65449,9058],{},[902,65451,65452],{"encoding":904},"Q = 15, 16, 20",[724,65454,65455,1643,65457,65489],{},[38,65456,31488],{},[883,65458,65460],{"className":65459},[886],[888,65461,65462],{"xmlns":890},[892,65463,65464,65486],{},[895,65465,65466,65468,65470,65472,65474,65476,65478,65480],{},[898,65467,11577],{},[898,65469,1763],{},[1656,65471,1713],{},[1667,65473,5267],{},[898,65475,1665],{},[1656,65477,3964],{},[1667,65479,1680],{},[2062,65481,65482,65484],{},[898,65483,1665],{},[1667,65485,1680],{},[902,65487,65488],{"encoding":904},"TR = 100Q - 2Q^2",", tedy",[883,65491,65493],{"className":65492},[886],[888,65494,65495],{"xmlns":890,"display":2408},[892,65496,65497,65539],{},[895,65498,65499,65501,65503,65505,65507,65509,65511,65513,65515,65521,65527,65529,65531,65533,65535,65537],{},[898,65500,1703],{},[898,65502,1763],{},[1656,65504,1713],{},[1656,65506,1659],{"stretchy":1658},[1667,65508,5267],{},[898,65510,1665],{},[1656,65512,3964],{},[1667,65514,1680],{},[2062,65516,65517,65519],{},[898,65518,1665],{},[1667,65520,1680],{},[2062,65522,65523,65525],{},[1656,65524,1683],{"stretchy":1658},[1656,65526,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,65528,1713],{},[1667,65530,5267],{},[1656,65532,3964],{},[1667,65534,2673],{},[898,65536,1665],{},[898,65538,1863],{"mathvariant":1723},[902,65540,65541],{"encoding":904},"MR = (100Q - 2Q^2)' = 100 - 4Q.",[724,65543,18411,65544,3206,65562,65588,65589,6496,65602,65617,65618,65631,65632,30138,65645,6496,65658,65673,65674,65687,65688,65719,65720,65739],{},[883,65545,65547],{"className":65546},[886],[888,65548,65549],{"xmlns":890},[892,65550,65551,65559],{},[895,65552,65553,65555,65557],{},[898,65554,1665],{},[1656,65556,1713],{},[1667,65558,44930],{},[902,65560,65561],{"encoding":904},"Q = 15",[883,65563,65565],{"className":65564},[886],[888,65566,65567],{"xmlns":890},[892,65568,65569,65585],{},[895,65570,65571,65573,65575,65577,65579,65581,65583],{},[898,65572,1703],{},[898,65574,1763],{},[1656,65576,1659],{"stretchy":1658},[1667,65578,44930],{},[1656,65580,1683],{"stretchy":1658},[1656,65582,1713],{},[1667,65584,9135],{},[902,65586,65587],{"encoding":904},"MR(15) = 40",": při množství ",[883,65590,65592],{"className":65591},[886],[888,65593,65594],{"xmlns":890},[892,65595,65596,65600],{},[895,65597,65598],{},[1667,65599,44930],{},[902,65601,44930],{"encoding":904},[883,65603,65605],{"className":65604},[886],[888,65606,65607],{"xmlns":890},[892,65608,65609,65615],{},[895,65610,65611,65613],{},[898,65612,11577],{},[898,65614,1763],{},[902,65616,12875],{"encoding":904}," mění asi ",[883,65619,65621],{"className":65620},[886],[888,65622,65623],{"xmlns":890},[892,65624,65625,65629],{},[895,65626,65627],{},[1667,65628,9135],{},[902,65630,9135],{"encoding":904},"-krát rychleji než množství; s růstem ",[883,65633,65635],{"className":65634},[886],[888,65636,65637],{"xmlns":890},[892,65638,65639,65643],{},[895,65640,65641],{},[898,65642,1665],{},[902,65644,1665],{"encoding":904},[883,65646,65648],{"className":65647},[886],[888,65649,65650],{"xmlns":890},[892,65651,65652,65656],{},[895,65653,65654],{},[1667,65655,1669],{},[902,65657,1669],{"encoding":904},[883,65659,65661],{"className":65660},[886],[888,65662,65663],{"xmlns":890},[892,65664,65665,65671],{},[895,65666,65667,65669],{},[898,65668,11577],{},[898,65670,1763],{},[902,65672,12875],{"encoding":904}," zvýší přibližně o ",[883,65675,65677],{"className":65676},[886],[888,65678,65679],{"xmlns":890},[892,65680,65681,65685],{},[895,65682,65683],{},[1667,65684,9135],{},[902,65686,9135],{"encoding":904},", tj. ze skutečné hodnoty ",[883,65689,65691],{"className":65690},[886],[888,65692,65693],{"xmlns":890},[892,65694,65695,65716],{},[895,65696,65697,65699,65701,65703,65705,65707,65709,65711,65713],{},[898,65698,11577],{},[898,65700,1763],{},[1656,65702,1659],{"stretchy":1658},[1667,65704,44930],{},[1656,65706,1683],{"stretchy":1658},[1656,65708,1713],{},[1667,65710,1669],{},[2461,65712,7828],{},[1667,65714,65715],{},"050",[902,65717,65718],{"encoding":904},"TR(15) = 1\\,050"," na přibližně ",[883,65721,65723],{"className":65722},[886],[888,65724,65725],{"xmlns":890},[892,65726,65727,65736],{},[895,65728,65729,65731,65733],{},[1667,65730,1669],{},[2461,65732,7828],{},[1667,65734,65735],{},"090",[902,65737,65738],{"encoding":904},"1\\,090",". Skutečná změna je",[883,65741,65743],{"className":65742},[886],[888,65744,65745],{"xmlns":890,"display":2408},[892,65746,65747,65801],{},[895,65748,65749,65751,65753,65755,65757,65759,65761,65763,65765,65767,65769,65771,65773,65775,65777,65779,65781,65783,65785,65788,65790,65792,65794,65796,65798],{},[898,65750,3750],{"mathvariant":1723},[898,65752,11577],{},[898,65754,1763],{},[1656,65756,1713],{},[898,65758,11577],{},[898,65760,1763],{},[1656,65762,1659],{"stretchy":1658},[1667,65764,2668],{},[1656,65766,1683],{"stretchy":1658},[1656,65768,3964],{},[898,65770,11577],{},[898,65772,1763],{},[1656,65774,1659],{"stretchy":1658},[1667,65776,44930],{},[1656,65778,1683],{"stretchy":1658},[1656,65780,1713],{},[1667,65782,1669],{},[2461,65784,7828],{},[1667,65786,65787],{},"088",[1656,65789,3964],{},[1667,65791,1669],{},[2461,65793,7828],{},[1667,65795,65715],{},[1656,65797,1713],{},[1667,65799,65800],{},"38.",[902,65802,65803],{"encoding":904},"\\Delta TR = TR(16) - TR(15) = 1\\,088 - 1\\,050 = 38.",[724,65805,65806,65807,1343,65833,2191,65859,65874,65875,65890],{},"Podobně ",[883,65808,65810],{"className":65809},[886],[888,65811,65812],{"xmlns":890},[892,65813,65814,65830],{},[895,65815,65816,65818,65820,65822,65824,65826,65828],{},[898,65817,1703],{},[898,65819,1763],{},[1656,65821,1659],{"stretchy":1658},[1667,65823,2668],{},[1656,65825,1683],{"stretchy":1658},[1656,65827,1713],{},[1667,65829,9023],{},[902,65831,65832],{"encoding":904},"MR(16) = 36",[883,65834,65836],{"className":65835},[886],[888,65837,65838],{"xmlns":890},[892,65839,65840,65856],{},[895,65841,65842,65844,65846,65848,65850,65852,65854],{},[898,65843,1703],{},[898,65845,1763],{},[1656,65847,1659],{"stretchy":1658},[1667,65849,9058],{},[1656,65851,1683],{"stretchy":1658},[1656,65853,1713],{},[1667,65855,9058],{},[902,65857,65858],{"encoding":904},"MR(20) = 20",[883,65860,65862],{"className":65861},[886],[888,65863,65864],{"xmlns":890},[892,65865,65866,65872],{},[895,65867,65868,65870],{},[898,65869,1703],{},[898,65871,1763],{},[902,65873,15395],{"encoding":904}," je klesající funkce — rychlost změny ",[883,65876,65878],{"className":65877},[886],[888,65879,65880],{"xmlns":890},[892,65881,65882,65888],{},[895,65883,65884,65886],{},[898,65885,11577],{},[898,65887,1763],{},[902,65889,12875],{"encoding":904}," s růstem množství klesá.",[198,65892,65894],{"id":65893},"odhad-změny-tr-pomocí-diferenciálu","Odhad změny TR pomocí diferenciálu",[724,65896,65897],{},"Užitím mezního příjmu lze odhadnout změnu celkového příjmu jako odezvu na změnu množství:",[883,65899,65901],{"className":65900},[886],[888,65902,65903],{"xmlns":890,"display":2408},[892,65904,65905,65974],{},[2412,65906,65907],{"width":2414},[2416,65908,65909,65911,65967,65969],{},[2419,65910],{"width":2421},[2419,65912,65913],{},[895,65914,65915,65917,65919,65921,65923,65925,65927,65929,65931,65933,65935,65937,65939,65941,65947,65949,65951,65953,65955,65957,65959,65961,65963,65965],{},[898,65916,3750],{"mathvariant":1723},[898,65918,11577],{},[898,65920,1763],{},[2461,65922,12767],{},[1656,65924,3815],{},[2461,65926,12767],{},[898,65928,3768],{"mathvariant":1723},[898,65930,11577],{},[898,65932,1763],{},[1656,65934,1713],{},[1656,65936,1659],{"stretchy":1658},[898,65938,11577],{},[898,65940,1763],{},[2062,65942,65943,65945],{},[1656,65944,1683],{"stretchy":1658},[1656,65946,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[2461,65948,7828],{},[898,65950,3768],{"mathvariant":1723},[898,65952,1665],{},[1656,65954,1713],{},[898,65956,1703],{},[898,65958,1763],{},[2461,65960,7828],{},[898,65962,3768],{"mathvariant":1723},[898,65964,1665],{},[1656,65966,1673],{"separator":1672},[2419,65968],{"width":2421},[2419,65970,65971],{},[2461,65972,65973],{},"(3.3)",[902,65975,65976],{"encoding":904},"\\Delta TR \\;\\approx\\; \\mathrm{d}TR = (TR)' \\, \\mathrm{d}Q = MR \\, \\mathrm{d}Q,\n\\tag{3.3}",[724,65978,65979],{},"schematicky:",[883,65981,65983],{"className":65982},[886],[888,65984,65985],{"xmlns":890,"display":2408},[892,65986,65987,66095],{},[895,65988,65989,66027,66029,66031,66033,66062,66065,66093],{},[895,65990,65991,65994,66000,66003,66009,66012,66018,66024],{},[2461,65992,65993],{},"zm",[2033,65995,65996,65998],{"accent":1672},[2461,65997,54409],{},[1656,65999,33774],{},[2461,66001,66002],{},"na celkov",[2033,66004,66005,66007],{"accent":1672},[2461,66006,54409],{},[1656,66008,33693],{},[2461,66010,66011],{},"ho p",[2033,66013,66014,66016],{"accent":1672},[2461,66015,20776],{},[1656,66017,33774],{},[2033,66019,66020,66022],{"accent":1672},[2461,66021,33762],{},[1656,66023,33693],{},[2461,66025,66026],{},"jmu",[2461,66028,12767],{},[1656,66030,3815],{},[2461,66032,12767],{},[895,66034,66035,66038,66044,66047,66053,66059],{},[2461,66036,66037],{},"mezn",[2033,66039,66040,66042],{"accent":1672},[2461,66041,33762],{},[1656,66043,33693],{},[2461,66045,66046],{}," p",[2033,66048,66049,66051],{"accent":1672},[2461,66050,20776],{},[1656,66052,33774],{},[2033,66054,66055,66057],{"accent":1672},[2461,66056,33762],{},[1656,66058,33693],{},[2461,66060,66061],{},"jem",[1656,66063,66064],{},"×",[895,66066,66067,66069,66075,66078,66084,66087],{},[2461,66068,65993],{},[2033,66070,66071,66073],{"accent":1672},[2461,66072,54409],{},[1656,66074,33774],{},[2461,66076,66077],{},"na mno",[2033,66079,66080,66082],{"accent":1672},[2461,66081,18343],{},[1656,66083,33774],{},[2461,66085,66086],{},"stv",[2033,66088,66089,66091],{"accent":1672},[2461,66090,33762],{},[1656,66092,33693],{},[898,66094,1863],{"mathvariant":1723},[902,66096,66097],{"encoding":904},"\\text{změna celkového příjmu} \\;\\approx\\; \\text{mezní příjem} \\times \\text{změna množství}.",[724,66099,66100,66101,66116],{},"Pro porovnání skutečná změna ",[883,66102,66104],{"className":66103},[886],[888,66105,66106],{"xmlns":890},[892,66107,66108,66114],{},[895,66109,66110,66112],{},[898,66111,11577],{},[898,66113,1763],{},[902,66115,12875],{"encoding":904}," je",[883,66118,66120],{"className":66119},[886],[888,66121,66122],{"xmlns":890,"display":2408},[892,66123,66124,66179],{},[2412,66125,66126],{"width":2414},[2416,66127,66128,66130,66172,66174],{},[2419,66129],{"width":2421},[2419,66131,66132],{},[895,66133,66134,66136,66138,66140,66142,66144,66146,66148,66150,66152,66154,66156,66158,66160,66162,66164,66166,66168,66170],{},[898,66135,3750],{"mathvariant":1723},[898,66137,11577],{},[898,66139,1763],{},[1656,66141,1713],{},[898,66143,11577],{},[898,66145,1763],{},[1656,66147,1659],{"stretchy":1658},[898,66149,1665],{},[1656,66151,3633],{},[898,66153,3768],{"mathvariant":1723},[898,66155,1665],{},[1656,66157,1683],{"stretchy":1658},[1656,66159,3964],{},[898,66161,11577],{},[898,66163,1763],{},[1656,66165,1659],{"stretchy":1658},[898,66167,1665],{},[1656,66169,1683],{"stretchy":1658},[898,66171,1863],{"mathvariant":1723},[2419,66173],{"width":2421},[2419,66175,66176],{},[2461,66177,66178],{},"(3.4)",[902,66180,66181],{"encoding":904},"\\Delta TR = TR(Q + \\mathrm{d}Q) - TR(Q).\n\\tag{3.4}",[46030,66183,66185],{"id":66184},"příklad-33","Příklad 3.3",[724,66187,66188,66190,66191,66221,66222,11465,66237,3605,66250,3619,66263,66277],{},[38,66189,64656],{}," Pro ",[883,66192,66194],{"className":66193},[886],[888,66195,66196],{"xmlns":890},[892,66197,66198,66218],{},[895,66199,66200,66202,66204,66206,66208,66210,66212],{},[898,66201,11577],{},[898,66203,1763],{},[1656,66205,1713],{},[1667,66207,5267],{},[898,66209,1665],{},[1656,66211,3964],{},[2062,66213,66214,66216],{},[898,66215,1665],{},[1667,66217,1680],{},[902,66219,66220],{"encoding":904},"TR = 100Q - Q^2"," odhadněte změnu ",[883,66223,66225],{"className":66224},[886],[888,66226,66227],{"xmlns":890},[892,66228,66229,66235],{},[895,66230,66231,66233],{},[898,66232,11577],{},[898,66234,1763],{},[902,66236,12875],{"encoding":904},[883,66238,66240],{"className":66239},[886],[888,66241,66242],{"xmlns":890},[892,66243,66244,66248],{},[895,66245,66246],{},[898,66247,1665],{},[902,66249,1665],{"encoding":904},[883,66251,66253],{"className":66252},[886],[888,66254,66255],{"xmlns":890},[892,66256,66257,66261],{},[895,66258,66259],{},[1667,66260,11918],{},[902,66262,11918],{"encoding":904},[883,66264,66266],{"className":66265},[886],[888,66267,66268],{"xmlns":890},[892,66269,66270,66275],{},[895,66271,66272],{},[1667,66273,66274],{},"63",[902,66276,66274],{"encoding":904}," a porovnejte se skutečnou změnou.",[724,66279,66280,1643,66282,66307,66308,1343,66326,2114],{},[38,66281,31488],{},[883,66283,66285],{"className":66284},[886],[888,66286,66287],{"xmlns":890},[892,66288,66289,66305],{},[895,66290,66291,66293,66295,66297,66299,66301,66303],{},[898,66292,1703],{},[898,66294,1763],{},[1656,66296,1713],{},[1667,66298,5267],{},[1656,66300,3964],{},[1667,66302,1680],{},[898,66304,1665],{},[902,66306,20173],{"encoding":904},", tedy při ",[883,66309,66311],{"className":66310},[886],[888,66312,66313],{"xmlns":890},[892,66314,66315,66323],{},[895,66316,66317,66319,66321],{},[898,66318,1665],{},[1656,66320,1713],{},[1667,66322,11918],{},[902,66324,66325],{"encoding":904},"Q = 60",[883,66327,66329],{"className":66328},[886],[888,66330,66331],{"xmlns":890},[892,66332,66333,66343],{},[895,66334,66335,66337,66339,66341],{},[898,66336,3768],{"mathvariant":1723},[898,66338,1665],{},[1656,66340,1713],{},[1667,66342,2617],{},[902,66344,66345],{"encoding":904},"\\mathrm{d}Q = 3",[883,66347,66349],{"className":66348},[886],[888,66350,66351],{"xmlns":890,"display":2408},[892,66352,66353,66384],{},[895,66354,66355,66357,66359,66361,66363,66365,66367,66369,66371,66373,66375,66377,66379,66381],{},[898,66356,3768],{"mathvariant":1723},[898,66358,11577],{},[898,66360,1763],{},[1656,66362,1713],{},[1656,66364,1659],{"stretchy":1658},[1667,66366,5267],{},[1656,66368,3964],{},[1667,66370,12827],{},[1656,66372,1683],{"stretchy":1658},[1656,66374,2751],{},[1667,66376,2617],{},[1656,66378,1713],{},[1656,66380,3964],{},[1667,66382,66383],{},"60.",[902,66385,66386],{"encoding":904},"\\mathrm{d}TR = (100 - 120) \\cdot 3 = -60.",[724,66388,66389,66390,66420,66421,66440],{},"Celkový příjem klesne z ",[883,66391,66393],{"className":66392},[886],[888,66394,66395],{"xmlns":890},[892,66396,66397,66417],{},[895,66398,66399,66401,66403,66405,66407,66409,66411,66413,66415],{},[898,66400,11577],{},[898,66402,1763],{},[1656,66404,1659],{"stretchy":1658},[1667,66406,11918],{},[1656,66408,1683],{"stretchy":1658},[1656,66410,1713],{},[1667,66412,1680],{},[2461,66414,7828],{},[1667,66416,28863],{},[902,66418,66419],{"encoding":904},"TR(60) = 2\\,400"," přibližně na ",[883,66422,66424],{"className":66423},[886],[888,66425,66426],{"xmlns":890},[892,66427,66428,66437],{},[895,66429,66430,66432,66434],{},[1667,66431,1680],{},[2461,66433,7828],{},[1667,66435,66436],{},"340",[902,66438,66439],{"encoding":904},"2\\,340",". Skutečná změna dle (3.4):",[883,66442,66444],{"className":66443},[886],[888,66445,66446],{"xmlns":890,"display":2408},[892,66447,66448,66506],{},[895,66449,66450,66452,66454,66456,66458,66460,66462,66464,66466,66468,66470,66472,66474,66476,66478,66480,66482,66484,66486,66489,66491,66493,66495,66497,66499,66501,66504],{},[898,66451,3750],{"mathvariant":1723},[898,66453,11577],{},[898,66455,1763],{},[1656,66457,1713],{},[898,66459,11577],{},[898,66461,1763],{},[1656,66463,1659],{"stretchy":1658},[1667,66465,66274],{},[1656,66467,1683],{"stretchy":1658},[1656,66469,3964],{},[898,66471,11577],{},[898,66473,1763],{},[1656,66475,1659],{"stretchy":1658},[1667,66477,11918],{},[1656,66479,1683],{"stretchy":1658},[1656,66481,1713],{},[1667,66483,1680],{},[2461,66485,7828],{},[1667,66487,66488],{},"331",[1656,66490,3964],{},[1667,66492,1680],{},[2461,66494,7828],{},[1667,66496,28863],{},[1656,66498,1713],{},[1656,66500,3964],{},[1667,66502,66503],{},"69",[1656,66505,1673],{"separator":1672},[902,66507,66508],{"encoding":904},"\\Delta TR = TR(63) - TR(60) = 2\\,331 - 2\\,400 = -69,",[724,66510,66511,66512,66527,66528,1863],{},"tj. ",[883,66513,66515],{"className":66514},[886],[888,66516,66517],{"xmlns":890},[892,66518,66519,66525],{},[895,66520,66521,66523],{},[898,66522,11577],{},[898,66524,1763],{},[902,66526,12875],{"encoding":904}," klesne na ",[883,66529,66531],{"className":66530},[886],[888,66532,66533],{"xmlns":890},[892,66534,66535,66543],{},[895,66536,66537,66539,66541],{},[1667,66538,1680],{},[2461,66540,7828],{},[1667,66542,66488],{},[902,66544,66545],{"encoding":904},"2\\,331",[198,66547,66549],{"id":66548},"vztah-ar-a-mr-pro-lineární-poptávku","Vztah AR a MR pro lineární poptávku",[724,66551,66552,66553,19135,66576,40270],{},"Obecně pro lineární poptávku ",[883,66554,66556],{"className":66555},[886],[888,66557,66558],{"xmlns":890},[892,66559,66560,66574],{},[895,66561,66562,66564,66566,66568,66570,66572],{},[898,66563,8194],{},[1656,66565,1713],{},[898,66567,207],{},[898,66569,1665],{},[1656,66571,3633],{},[898,66573,3403],{},[902,66575,45742],{"encoding":904},[883,66577,66579],{"className":66578},[886],[888,66580,66581],{"xmlns":890},[892,66582,66583,66605],{},[895,66584,66585,66587,66589,66591,66593,66599,66601,66603],{},[898,66586,11577],{},[898,66588,1763],{},[1656,66590,1713],{},[898,66592,207],{},[2062,66594,66595,66597],{},[898,66596,1665],{},[1667,66598,1680],{},[1656,66600,3633],{},[898,66602,3403],{},[898,66604,1665],{},[902,66606,66607],{"encoding":904},"TR = aQ^2 + bQ",[883,66609,66611],{"className":66610},[886],[888,66612,66613],{"xmlns":890,"display":2408},[892,66614,66615,66635],{},[895,66616,66617,66619,66621,66623,66625,66627,66629,66631,66633],{},[898,66618,1703],{},[898,66620,1763],{},[1656,66622,1713],{},[1667,66624,1680],{},[898,66626,207],{},[898,66628,1665],{},[1656,66630,3633],{},[898,66632,3403],{},[898,66634,1863],{"mathvariant":1723},[902,66636,66637],{"encoding":904},"MR = 2aQ + b.",[724,66639,66640,66641,66656,66657,66672,66673,66686,66687,3247,66690,66706,66707,66720,66721,66736,66737,66752,66753,66768,66769,3565,66782,66812,66813,66832,66833,66848],{},"Křivky ",[883,66642,66644],{"className":66643},[886],[888,66645,66646],{"xmlns":890},[892,66647,66648,66654],{},[895,66649,66650,66652],{},[898,66651,1703],{},[898,66653,1763],{},[902,66655,15395],{"encoding":904}," a poptávky (resp. ",[883,66658,66660],{"className":66659},[886],[888,66661,66662],{"xmlns":890},[892,66663,66664,66670],{},[895,66665,66666,66668],{},[898,66667,2146],{},[898,66669,1763],{},[902,66671,64114],{"encoding":904},") jsou přímky protínající svislou osu v témže bodě ",[883,66674,66676],{"className":66675},[886],[888,66677,66678],{"xmlns":890},[892,66679,66680,66684],{},[895,66681,66682],{},[898,66683,3403],{},[902,66685,3403],{"encoding":904},", přičemž ",[38,66688,66689],{},"přímka mezního příjmu má sklon rovný dvojnásobku sklonu přímky poptávky",[883,66691,66693],{"className":66692},[886],[888,66694,66695],{"xmlns":890},[892,66696,66697,66703],{},[895,66698,66699,66701],{},[1667,66700,1680],{},[898,66702,207],{},[902,66704,66705],{"encoding":904},"2a"," vs. ",[883,66708,66710],{"className":66709},[886],[888,66711,66712],{"xmlns":890},[892,66713,66714,66718],{},[895,66715,66716],{},[898,66717,207],{},[902,66719,207],{"encoding":904},", obrázek 3.2). ",[883,66722,66724],{"className":66723},[886],[888,66725,66726],{"xmlns":890},[892,66727,66728,66734],{},[895,66729,66730,66732],{},[898,66731,1703],{},[898,66733,1763],{},[902,66735,15395],{"encoding":904}," nabývá jak kladných, tak záporných hodnot; křivka ",[883,66738,66740],{"className":66739},[886],[888,66741,66742],{"xmlns":890},[892,66743,66744,66750],{},[895,66745,66746,66748],{},[898,66747,11577],{},[898,66749,1763],{},[902,66751,12875],{"encoding":904}," nejprve roste, v bodě maxima protíná ",[883,66754,66756],{"className":66755},[886],[888,66757,66758],{"xmlns":890},[892,66759,66760,66766],{},[895,66761,66762,66764],{},[898,66763,1703],{},[898,66765,1763],{},[902,66767,15395],{"encoding":904}," osu ",[883,66770,66772],{"className":66771},[886],[888,66773,66774],{"xmlns":890},[892,66775,66776,66780],{},[895,66777,66778],{},[898,66779,1665],{},[902,66781,1665],{"encoding":904},[883,66783,66785],{"className":66784},[886],[888,66786,66787],{"xmlns":890},[892,66788,66789,66809],{},[895,66790,66791,66793,66795,66797],{},[898,66792,1665],{},[1656,66794,1713],{},[1656,66796,3964],{},[4138,66798,66799],{"scriptlevel":4032,"displaystyle":1658},[3294,66800,66801,66803],{},[898,66802,3403],{},[895,66804,66805,66807],{},[1667,66806,1680],{},[898,66808,207],{},[902,66810,66811],{"encoding":904},"Q = -\\tfrac{b}{2a}"," hodnotou ",[883,66814,66816],{"className":66815},[886],[888,66817,66818],{"xmlns":890},[892,66819,66820,66830],{},[895,66821,66822,66824,66826,66828],{},[898,66823,1703],{},[898,66825,1763],{},[1656,66827,1713],{},[1667,66829,4032],{},[902,66831,15844],{"encoding":904},", a dále ",[883,66834,66836],{"className":66835},[886],[888,66837,66838],{"xmlns":890},[892,66839,66840,66846],{},[895,66841,66842,66844],{},[898,66843,11577],{},[898,66845,1763],{},[902,66847,12875],{"encoding":904}," klesá.",[724,66850,66851,66852,66858,66859,66891,66892,66920],{},"V případě ",[38,66853,66854],{},[207,66855,66857],{"className":66856,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurence",", kdy poptávka ",[883,66860,66862],{"className":66861},[886],[888,66863,66864],{"xmlns":890},[892,66865,66866,66888],{},[895,66867,66868,66870,66872,66874,66876,66878,66880,66882],{},[898,66869,8194],{},[1656,66871,1713],{},[898,66873,6787],{},[1656,66875,1659],{"stretchy":1658},[898,66877,1665],{},[1656,66879,1683],{"stretchy":1658},[1656,66881,1713],{},[2062,66883,66884,66886],{},[898,66885,8194],{},[1656,66887,8187],{},[902,66889,66890],{"encoding":904},"P = D(Q) = P^*"," je pevná tržní cena, platí ",[883,66893,66895],{"className":66894},[886],[888,66896,66897],{"xmlns":890},[892,66898,66899,66917],{},[895,66900,66901,66903,66905,66907,66909,66911],{},[898,66902,11577],{},[898,66904,1763],{},[1656,66906,1713],{},[898,66908,1665],{},[1656,66910,2751],{},[2062,66912,66913,66915],{},[898,66914,8194],{},[1656,66916,8187],{},[902,66918,66919],{"encoding":904},"TR = Q \\cdot P^*"," a tedy",[883,66922,66924],{"className":66923},[886],[888,66925,66926],{"xmlns":890,"display":2408},[892,66927,66928,66970],{},[895,66929,66930,66932,66934,66936,66938,66940,66942,66948,66950,66952,66966,66968],{},[898,66931,1703],{},[898,66933,1763],{},[1656,66935,1713],{},[898,66937,2146],{},[898,66939,1763],{},[1656,66941,1713],{},[2062,66943,66944,66946],{},[898,66945,8194],{},[1656,66947,8187],{},[3316,66949],{"width":3318},[1656,66951,1659],{"stretchy":1658},[895,66953,66954,66957,66963],{},[2461,66955,66956],{},"obr",[2033,66958,66959,66961],{"accent":1672},[2461,66960,207],{},[1656,66962,33693],{},[2461,66964,66965],{},"zek 3.4",[1656,66967,1683],{"stretchy":1658},[898,66969,1863],{"mathvariant":1723},[902,66971,66972],{"encoding":904},"MR = AR = P^* \\quad (\\text{obrázek 3.4}).",[724,66974,66975],{},[614,66976,66977,66978,1896,67004,67032,67033,67046,67047,67062,67063,12505,67076,1343,67102,12505,67117,1863],{},"Obrázek 3.2: Přímky ",[883,66979,66981],{"className":66980},[886],[888,66982,66983],{"xmlns":890},[892,66984,66985,67001],{},[895,66986,66987,66989,66991,66993,66995,66997,66999],{},[898,66988,2146],{},[898,66990,1763],{},[1656,66992,1713],{},[898,66994,207],{},[898,66996,1665],{},[1656,66998,3633],{},[898,67000,3403],{},[902,67002,67003],{"encoding":904},"AR = aQ + b",[883,67005,67007],{"className":67006},[886],[888,67008,67009],{"xmlns":890},[892,67010,67011,67029],{},[895,67012,67013,67015,67017,67019,67021,67023,67025,67027],{},[898,67014,1703],{},[898,67016,1763],{},[1656,67018,1713],{},[1667,67020,1680],{},[898,67022,207],{},[898,67024,1665],{},[1656,67026,3633],{},[898,67028,3403],{},[902,67030,67031],{"encoding":904},"MR = 2aQ + b"," v jednom grafu; společný průsečík ",[883,67034,67036],{"className":67035},[886],[888,67037,67038],{"xmlns":890},[892,67039,67040,67044],{},[895,67041,67042],{},[898,67043,3403],{},[902,67045,3403],{"encoding":904}," se svislou osou, ",[883,67048,67050],{"className":67049},[886],[888,67051,67052],{"xmlns":890},[892,67053,67054,67060],{},[895,67055,67056,67058],{},[898,67057,1703],{},[898,67059,1763],{},[902,67061,15395],{"encoding":904}," protíná osu ",[883,67064,67066],{"className":67065},[886],[888,67067,67068],{"xmlns":890},[892,67069,67070,67074],{},[895,67071,67072],{},[898,67073,1665],{},[902,67075,1665],{"encoding":904},[883,67077,67079],{"className":67078},[886],[888,67080,67081],{"xmlns":890},[892,67082,67083,67099],{},[895,67084,67085,67087],{},[1656,67086,3964],{},[4138,67088,67089],{"scriptlevel":4032,"displaystyle":1658},[3294,67090,67091,67093],{},[898,67092,3403],{},[895,67094,67095,67097],{},[1667,67096,1680],{},[898,67098,207],{},[902,67100,67101],{"encoding":904},"-\\tfrac{b}{2a}",[883,67103,67105],{"className":67104},[886],[888,67106,67107],{"xmlns":890},[892,67108,67109,67115],{},[895,67110,67111,67113],{},[898,67112,2146],{},[898,67114,1763],{},[902,67116,64114],{"encoding":904},[883,67118,67120],{"className":67119},[886],[888,67121,67122],{"xmlns":890},[892,67123,67124,67136],{},[895,67125,67126,67128],{},[1656,67127,3964],{},[4138,67129,67130],{"scriptlevel":4032,"displaystyle":1658},[3294,67131,67132,67134],{},[898,67133,3403],{},[898,67135,207],{},[902,67137,67138],{"encoding":904},"-\\tfrac{b}{a}",[724,67140,67141],{},[614,67142,67143,67144,67175,67176,67205,67206,1863],{},"Obrázek 3.3: Parabola ",[883,67145,67147],{"className":67146},[886],[888,67148,67149],{"xmlns":890},[892,67150,67151,67173],{},[895,67152,67153,67155,67157,67159,67161,67167,67169,67171],{},[898,67154,11577],{},[898,67156,1763],{},[1656,67158,1713],{},[898,67160,207],{},[2062,67162,67163,67165],{},[898,67164,1665],{},[1667,67166,1680],{},[1656,67168,3633],{},[898,67170,3403],{},[898,67172,1665],{},[902,67174,66607],{"encoding":904}," s maximem v ",[883,67177,67179],{"className":67178},[886],[888,67180,67181],{"xmlns":890},[892,67182,67183,67203],{},[895,67184,67185,67187,67189,67191],{},[898,67186,1665],{},[1656,67188,1713],{},[1656,67190,3964],{},[4138,67192,67193],{"scriptlevel":4032,"displaystyle":1658},[3294,67194,67195,67197],{},[898,67196,3403],{},[895,67198,67199,67201],{},[1667,67200,1680],{},[898,67202,207],{},[902,67204,66811],{"encoding":904}," a nulou v ",[883,67207,67209],{"className":67208},[886],[888,67210,67211],{"xmlns":890},[892,67212,67213,67229],{},[895,67214,67215,67217,67219,67221],{},[898,67216,1665],{},[1656,67218,1713],{},[1656,67220,3964],{},[4138,67222,67223],{"scriptlevel":4032,"displaystyle":1658},[3294,67224,67225,67227],{},[898,67226,3403],{},[898,67228,207],{},[902,67230,67231],{"encoding":904},"Q = -\\tfrac{b}{a}",[724,67233,67234],{},[614,67235,67236,67237,1863],{},"Obrázek 3.4: Dokonalá konkurence — vodorovná přímka ",[883,67238,67240],{"className":67239},[886],[888,67241,67242],{"xmlns":890},[892,67243,67244,67264],{},[895,67245,67246,67248,67250,67252,67254,67256,67258],{},[898,67247,2146],{},[898,67249,1763],{},[1656,67251,1713],{},[898,67253,1703],{},[898,67255,1763],{},[1656,67257,1713],{},[2062,67259,67260,67262],{},[898,67261,8194],{},[1656,67263,8187],{},[902,67265,67266],{"encoding":904},"AR = MR = P^*",[115,67268,67270],{"id":67269},"náklady-firmy","Náklady firmy",[198,67272,67274],{"id":67273},"celkové-náklady","Celkové náklady",[724,67276,67277,1643,67279,3247,67294,67297,67298,67311],{},[38,67278,67274],{},[883,67280,67282],{"className":67281},[886],[888,67283,67284],{"xmlns":890},[892,67285,67286,67292],{},[895,67287,67288,67290],{},[898,67289,11577],{},[898,67291,1766],{},[902,67293,12033],{"encoding":904},[38,67295,67296],{},"total cost",") jsou veškeré náklady na realizaci ",[883,67299,67301],{"className":67300},[886],[888,67302,67303],{"xmlns":890},[892,67304,67305,67309],{},[895,67306,67307],{},[898,67308,1665],{},[902,67310,1665],{"encoding":904}," jednotek produkce:",[883,67313,67315],{"className":67314},[886],[888,67316,67317],{"xmlns":890,"display":2408},[892,67318,67319,67374],{},[2412,67320,67321],{"width":2414},[2416,67322,67323,67325,67367,67369],{},[2419,67324],{"width":2421},[2419,67326,67327],{},[895,67328,67329,67331,67333,67335,67337,67339,67341,67343,67345,67347,67349,67351,67353,67355,67357,67359,67361,67363,67365],{},[898,67330,11577],{},[898,67332,1766],{},[1656,67334,1713],{},[898,67336,11577],{},[898,67338,1766],{},[1656,67340,1659],{"stretchy":1658},[898,67342,1665],{},[1656,67344,1683],{"stretchy":1658},[1656,67346,1713],{},[898,67348,19177],{},[898,67350,1766],{},[1656,67352,3633],{},[898,67354,11577],{},[898,67356,49019],{},[898,67358,1766],{},[1656,67360,1659],{"stretchy":1658},[898,67362,1665],{},[1656,67364,1683],{"stretchy":1658},[1656,67366,1673],{"separator":1672},[2419,67368],{"width":2421},[2419,67370,67371],{},[2461,67372,67373],{},"(3.5)",[902,67375,67376],{"encoding":904},"TC = TC(Q) = FC + TVC(Q),\n\\tag{3.5}",[724,67378,2355,67379,67394,67395,3247,67398,20863,67401,67394,67425,3247,67428,67431],{},[883,67380,67382],{"className":67381},[886],[888,67383,67384],{"xmlns":890},[892,67385,67386,67392],{},[895,67387,67388,67390],{},[898,67389,19177],{},[898,67391,1766],{},[902,67393,64160],{"encoding":904}," jsou ",[38,67396,67397],{},"fixní náklady",[38,67399,67400],{},"fixed cost",[883,67402,67404],{"className":67403},[886],[888,67405,67406],{"xmlns":890},[892,67407,67408,67422],{},[895,67409,67410,67412,67414,67416,67418,67420],{},[898,67411,11577],{},[898,67413,49019],{},[898,67415,1766],{},[1656,67417,1659],{"stretchy":1658},[898,67419,1665],{},[1656,67421,1683],{"stretchy":1658},[902,67423,67424],{"encoding":904},"TVC(Q)",[38,67426,67427],{},"celkové variabilní náklady",[38,67429,67430],{},"total variable cost","). Celkové náklady jsou rostoucí, neboť růst množství objektivně vynutí jejich růst.",[198,67433,67435],{"id":67434},"průměrné-náklady","Průměrné náklady",[724,67437,67438,1643,67440,3247,67455,67458],{},[38,67439,67435],{},[883,67441,67443],{"className":67442},[886],[888,67444,67445],{"xmlns":890},[892,67446,67447,67453],{},[895,67448,67449,67451],{},[898,67450,2146],{},[898,67452,1766],{},[902,67454,64229],{"encoding":904},[38,67456,67457],{},"average cost",") jsou podíl celkových nákladů a množství. Z (3.5):",[883,67460,67462],{"className":67461},[886],[888,67463,67464],{"xmlns":890,"display":2408},[892,67465,67466,67545],{},[2412,67467,67468],{"width":2414},[2416,67469,67470,67472,67538,67540],{},[2419,67471],{"width":2421},[2419,67473,67474],{},[895,67475,67476,67478,67480,67482,67484,67486,67488,67490,67492,67494,67504,67506,67516,67518,67536],{},[898,67477,2146],{},[898,67479,1766],{},[1656,67481,1713],{},[898,67483,2146],{},[898,67485,1766],{},[1656,67487,1659],{"stretchy":1658},[898,67489,1665],{},[1656,67491,1683],{"stretchy":1658},[1656,67493,1713],{},[3294,67495,67496,67502],{},[895,67497,67498,67500],{},[898,67499,11577],{},[898,67501,1766],{},[898,67503,1665],{},[1656,67505,1713],{},[3294,67507,67508,67514],{},[895,67509,67510,67512],{},[898,67511,19177],{},[898,67513,1766],{},[898,67515,1665],{},[1656,67517,3633],{},[3294,67519,67520,67534],{},[895,67521,67522,67524,67526,67528,67530,67532],{},[898,67523,11577],{},[898,67525,49019],{},[898,67527,1766],{},[1656,67529,1659],{"stretchy":1658},[898,67531,1665],{},[1656,67533,1683],{"stretchy":1658},[898,67535,1665],{},[1656,67537,1673],{"separator":1672},[2419,67539],{"width":2421},[2419,67541,67542],{},[2461,67543,67544],{},"(3.6)",[902,67546,67547],{"encoding":904},"AC = AC(Q) = \\frac{TC}{Q} = \\frac{FC}{Q} + \\frac{TVC(Q)}{Q},\n\\tag{3.6}",[724,67549,2355,67550,67394,67574,1643,67577,3247,67594,20863,67597,67394,67629,1643,67632,3247,67649,5642],{},[883,67551,67553],{"className":67552},[886],[888,67554,67555],{"xmlns":890},[892,67556,67557,67571],{},[895,67558,67559],{},[4138,67560,67561],{"scriptlevel":4032,"displaystyle":1658},[3294,67562,67563,67569],{},[895,67564,67565,67567],{},[898,67566,19177],{},[898,67568,1766],{},[898,67570,1665],{},[902,67572,67573],{"encoding":904},"\\tfrac{FC}{Q}",[38,67575,67576],{},"průměrné fixní náklady",[883,67578,67580],{"className":67579},[886],[888,67581,67582],{"xmlns":890},[892,67583,67584,67592],{},[895,67585,67586,67588,67590],{},[898,67587,2146],{},[898,67589,19177],{},[898,67591,1766],{},[902,67593,64196],{"encoding":904},[38,67595,67596],{},"average fixed cost",[883,67598,67600],{"className":67599},[886],[888,67601,67602],{"xmlns":890},[892,67603,67604,67626],{},[895,67605,67606],{},[4138,67607,67608],{"scriptlevel":4032,"displaystyle":1658},[3294,67609,67610,67624],{},[895,67611,67612,67614,67616,67618,67620,67622],{},[898,67613,11577],{},[898,67615,49019],{},[898,67617,1766],{},[1656,67619,1659],{"stretchy":1658},[898,67621,1665],{},[1656,67623,1683],{"stretchy":1658},[898,67625,1665],{},[902,67627,67628],{"encoding":904},"\\tfrac{TVC(Q)}{Q}",[38,67630,67631],{},"průměrné variabilní náklady",[883,67633,67635],{"className":67634},[886],[888,67636,67637],{"xmlns":890},[892,67638,67639,67647],{},[895,67640,67641,67643,67645],{},[898,67642,2146],{},[898,67644,49019],{},[898,67646,1766],{},[902,67648,63980],{"encoding":904},[38,67650,67651],{},"average variable cost",[883,67653,67655],{"className":67654},[886],[888,67656,67657],{"xmlns":890,"display":2408},[892,67658,67659,67718],{},[2412,67660,67661],{"width":2414},[2416,67662,67663,67665,67711,67713],{},[2419,67664],{"width":2421},[2419,67666,67667],{},[895,67668,67669,67671,67673,67675,67677,67679,67681,67683,67685,67687,67689,67691,67709],{},[898,67670,2146],{},[898,67672,49019],{},[898,67674,1766],{},[1656,67676,1713],{},[898,67678,2146],{},[898,67680,49019],{},[898,67682,1766],{},[1656,67684,1659],{"stretchy":1658},[898,67686,1665],{},[1656,67688,1683],{"stretchy":1658},[1656,67690,1713],{},[3294,67692,67693,67707],{},[895,67694,67695,67697,67699,67701,67703,67705],{},[898,67696,11577],{},[898,67698,49019],{},[898,67700,1766],{},[1656,67702,1659],{"stretchy":1658},[898,67704,1665],{},[1656,67706,1683],{"stretchy":1658},[898,67708,1665],{},[898,67710,1863],{"mathvariant":1723},[2419,67712],{"width":2421},[2419,67714,67715],{},[2461,67716,67717],{},"(3.7)",[902,67719,67720],{"encoding":904},"AVC = AVC(Q) = \\frac{TVC(Q)}{Q}.\n\\tag{3.7}",[46030,67722,67724],{"id":67723},"příklad-34","Příklad 3.4",[724,67726,67727,66190,67729,1896,67754,64694,67778,1896,67793,67808,67809,1863],{},[38,67728,64656],{},[883,67730,67732],{"className":67731},[886],[888,67733,67734],{"xmlns":890},[892,67735,67736,67751],{},[895,67737,67738,67740,67742,67744,67746,67748],{},[898,67739,19177],{},[898,67741,1766],{},[1656,67743,1713],{},[1667,67745,1669],{},[2461,67747,7828],{},[1667,67749,67750],{},"000",[902,67752,67753],{"encoding":904},"FC = 1\\,000",[883,67755,67757],{"className":67756},[886],[888,67758,67759],{"xmlns":890},[892,67760,67761,67775],{},[895,67762,67763,67765,67767,67769,67771,67773],{},[898,67764,11577],{},[898,67766,49019],{},[898,67768,1766],{},[1656,67770,1713],{},[1667,67772,2673],{},[898,67774,1665],{},[902,67776,67777],{"encoding":904},"TVC = 4Q",[883,67779,67781],{"className":67780},[886],[888,67782,67783],{"xmlns":890},[892,67784,67785,67791],{},[895,67786,67787,67789],{},[898,67788,11577],{},[898,67790,1766],{},[902,67792,12033],{"encoding":904},[883,67794,67796],{"className":67795},[886],[888,67797,67798],{"xmlns":890},[892,67799,67800,67806],{},[895,67801,67802,67804],{},[898,67803,2146],{},[898,67805,1766],{},[902,67807,64229],{"encoding":904}," a jejich chování s rostoucím ",[883,67810,67812],{"className":67811},[886],[888,67813,67814],{"xmlns":890},[892,67815,67816,67820],{},[895,67817,67818],{},[898,67819,1665],{},[902,67821,1665],{"encoding":904},[724,67823,67824,1643,67826,1896,67856,67892,67893,6496,67906,67921,67922,2114],{},[38,67825,31488],{},[883,67827,67829],{"className":67828},[886],[888,67830,67831],{"xmlns":890},[892,67832,67833,67853],{},[895,67834,67835,67837,67839,67841,67843,67845,67847,67849,67851],{},[898,67836,11577],{},[898,67838,1766],{},[1656,67840,1713],{},[1667,67842,1669],{},[2461,67844,7828],{},[1667,67846,67750],{},[1656,67848,3633],{},[1667,67850,2673],{},[898,67852,1665],{},[902,67854,67855],{"encoding":904},"TC = 1\\,000 + 4Q",[883,67857,67859],{"className":67858},[886],[888,67860,67861],{"xmlns":890},[892,67862,67863,67889],{},[895,67864,67865,67867,67869,67871,67885,67887],{},[898,67866,2146],{},[898,67868,1766],{},[1656,67870,1713],{},[4138,67872,67873],{"scriptlevel":4032,"displaystyle":1658},[3294,67874,67875,67883],{},[895,67876,67877,67879,67881],{},[1667,67878,1669],{},[2461,67880,7828],{},[1667,67882,67750],{},[898,67884,1665],{},[1656,67886,3633],{},[1667,67888,2673],{},[902,67890,67891],{"encoding":904},"AC = \\tfrac{1\\,000}{Q} + 4",". S rostoucím ",[883,67894,67896],{"className":67895},[886],[888,67897,67898],{"xmlns":890},[892,67899,67900,67904],{},[895,67901,67902],{},[898,67903,1665],{},[902,67905,1665],{"encoding":904},[883,67907,67909],{"className":67908},[886],[888,67910,67911],{"xmlns":890},[892,67912,67913,67919],{},[895,67914,67915,67917],{},[898,67916,2146],{},[898,67918,1766],{},[902,67920,64229],{"encoding":904}," blíží ",[883,67923,67925],{"className":67924},[886],[888,67926,67927],{"xmlns":890},[892,67928,67929,67933],{},[895,67930,67931],{},[1667,67932,2673],{},[902,67934,2673],{"encoding":904},[883,67936,67938],{"className":67937},[886],[888,67939,67940],{"xmlns":890,"display":2408},[892,67941,67942,67988],{},[895,67943,67944,67961,67983,67985],{},[48576,67945,67946,67953],{},[895,67947,67948,67951],{},[898,67949,67950],{},"lim",[1656,67952,2093],{},[895,67954,67955,67957,67959],{},[898,67956,1665],{},[1656,67958,11915],{},[898,67960,15060],{"mathvariant":1723},[895,67962,67963,67965,67977,67979,67981],{},[1656,67964,1659],{"fence":1672},[3294,67966,67967,67975],{},[895,67968,67969,67971,67973],{},[1667,67970,1669],{},[2461,67972,7828],{},[1667,67974,67750],{},[898,67976,1665],{},[1656,67978,3633],{},[1667,67980,2673],{},[1656,67982,1683],{"fence":1672},[1656,67984,1713],{},[1667,67986,67987],{},"4.",[902,67989,67990],{"encoding":904},"\\lim_{Q \\to \\infty} \\left( \\frac{1\\,000}{Q} + 4 \\right) = 4.",[724,67992,67993,68031,68032,1863],{},[883,67994,67996],{"className":67995},[886],[888,67997,67998],{"xmlns":890},[892,67999,68000,68028],{},[895,68001,68002,68004,68006,68008,68010,68024,68026],{},[898,68003,2146],{},[898,68005,19177],{},[898,68007,1766],{},[1656,68009,1713],{},[4138,68011,68012],{"scriptlevel":4032,"displaystyle":1658},[3294,68013,68014,68022],{},[895,68015,68016,68018,68020],{},[1667,68017,1669],{},[2461,68019,7828],{},[1667,68021,67750],{},[898,68023,1665],{},[1656,68025,11915],{},[1667,68027,4032],{},[902,68029,68030],{"encoding":904},"AFC = \\tfrac{1\\,000}{Q} \\to 0"," s rostoucím ",[883,68033,68035],{"className":68034},[886],[888,68036,68037],{"xmlns":890},[892,68038,68039,68043],{},[895,68040,68041],{},[898,68042,1665],{},[902,68044,1665],{"encoding":904},[724,68046,68047],{},[614,68048,68049,68050,68079,68080,1863],{},"Obrázek 3.5: Přímka ",[883,68051,68053],{"className":68052},[886],[888,68054,68055],{"xmlns":890},[892,68056,68057,68077],{},[895,68058,68059,68061,68063,68065,68067,68069,68071,68073,68075],{},[898,68060,11577],{},[898,68062,1766],{},[1656,68064,1713],{},[1667,68066,1669],{},[2461,68068,7828],{},[1667,68070,67750],{},[1656,68072,3633],{},[1667,68074,2673],{},[898,68076,1665],{},[902,68078,67855],{"encoding":904}," protínající svislou osu ve výši ",[883,68081,68083],{"className":68082},[886],[888,68084,68085],{"xmlns":890},[892,68086,68087,68101],{},[895,68088,68089,68091,68093,68095,68097,68099],{},[898,68090,19177],{},[898,68092,1766],{},[1656,68094,1713],{},[1667,68096,1669],{},[2461,68098,7828],{},[1667,68100,67750],{},[902,68102,67753],{"encoding":904},[724,68104,68105],{},[614,68106,68107,68108,68143,68144,1863],{},"Obrázek 3.6: Hyperbola ",[883,68109,68111],{"className":68110},[886],[888,68112,68113],{"xmlns":890},[892,68114,68115,68141],{},[895,68116,68117,68119,68121,68123,68137,68139],{},[898,68118,2146],{},[898,68120,1766],{},[1656,68122,1713],{},[4138,68124,68125],{"scriptlevel":4032,"displaystyle":1658},[3294,68126,68127,68135],{},[895,68128,68129,68131,68133],{},[1667,68130,1669],{},[2461,68132,7828],{},[1667,68134,67750],{},[898,68136,1665],{},[1656,68138,3633],{},[1667,68140,2673],{},[902,68142,67891],{"encoding":904}," s vodorovnou asymptotou ",[883,68145,68147],{"className":68146},[886],[888,68148,68149],{"xmlns":890},[892,68150,68151,68161],{},[895,68152,68153,68155,68157,68159],{},[898,68154,2146],{},[898,68156,1766],{},[1656,68158,1713],{},[1667,68160,2673],{},[902,68162,68163],{"encoding":904},"AC = 4",[724,68165,68166],{},"Celkové variabilní náklady lze často vyjádřit ve tvaru",[883,68168,68170],{"className":68169},[886],[888,68171,68172],{"xmlns":890,"display":2408},[892,68173,68174,68200],{},[895,68175,68176,68178,68180,68182,68184,68186,68188,68190,68192,68194,68196,68198],{},[898,68177,11577],{},[898,68179,49019],{},[898,68181,1766],{},[1656,68183,1713],{},[898,68185,1665],{},[1656,68187,2751],{},[898,68189,49019],{},[898,68191,1766],{},[1656,68193,1659],{"stretchy":1658},[898,68195,1665],{},[1656,68197,1683],{"stretchy":1658},[1656,68199,1673],{"separator":1672},[902,68201,68202],{"encoding":904},"TVC = Q \\cdot VC(Q),",[724,68204,2355,68205,67394,68233,68236,68237,68267],{},[883,68206,68208],{"className":68207},[886],[888,68209,68210],{"xmlns":890},[892,68211,68212,68230],{},[895,68213,68214,68216,68218,68220,68222,68224,68226,68228],{},[898,68215,49019],{},[898,68217,1766],{},[1656,68219,1713],{},[898,68221,49019],{},[898,68223,1766],{},[1656,68225,1659],{"stretchy":1658},[898,68227,1665],{},[1656,68229,1683],{"stretchy":1658},[902,68231,68232],{"encoding":904},"VC = VC(Q)",[38,68234,68235],{},"variabilní náklady na jednotku množství",". Jsou-li konstantní, ",[883,68238,68240],{"className":68239},[886],[888,68241,68242],{"xmlns":890},[892,68243,68244,68264],{},[895,68245,68246,68248,68250,68252,68254,68256,68258,68260,68262],{},[898,68247,11577],{},[898,68249,49019],{},[898,68251,1766],{},[1656,68253,1659],{"stretchy":1658},[898,68255,1665],{},[1656,68257,1683],{"stretchy":1658},[1656,68259,1713],{},[898,68261,207],{},[898,68263,1665],{},[902,68265,68266],{"encoding":904},"TVC(Q) = aQ"," a nejjednodušší model nákladů má tvar",[883,68269,68271],{"className":68270},[886],[888,68272,68273],{"xmlns":890,"display":2408},[892,68274,68275,68295],{},[895,68276,68277,68279,68281,68283,68285,68287,68289,68291,68293],{},[898,68278,11577],{},[898,68280,1766],{},[1656,68282,1713],{},[898,68284,19177],{},[898,68286,1766],{},[1656,68288,3633],{},[898,68290,207],{},[898,68292,1665],{},[898,68294,1863],{"mathvariant":1723},[902,68296,68297],{"encoding":904},"TC = FC + aQ.",[724,68299,68300,68301,68316,68317,68332,68333,68356,68357,68391,68392,68143,68405,68418,68419,1896,68467,68511,68512,1863],{},"Křivkou ",[883,68302,68304],{"className":68303},[886],[888,68305,68306],{"xmlns":890},[892,68307,68308,68314],{},[895,68309,68310,68312],{},[898,68311,11577],{},[898,68313,1766],{},[902,68315,12033],{"encoding":904}," je přímka se svislým průsečíkem ",[883,68318,68320],{"className":68319},[886],[888,68321,68322],{"xmlns":890},[892,68323,68324,68330],{},[895,68325,68326,68328],{},[898,68327,19177],{},[898,68329,1766],{},[902,68331,64160],{"encoding":904}," a sklonem ",[883,68334,68336],{"className":68335},[886],[888,68337,68338],{"xmlns":890},[892,68339,68340,68353],{},[895,68341,68342,68345,68347,68349,68351],{},[898,68343,68344],{},"tan",[1656,68346,2093],{},[898,68348,7151],{},[1656,68350,1713],{},[898,68352,207],{},[902,68354,68355],{"encoding":904},"\\tan\\alpha = a"," (obrázek 3.7). Průměrné náklady tvoří hyperbolu ",[883,68358,68360],{"className":68359},[886],[888,68361,68362],{"xmlns":890},[892,68363,68364,68388],{},[895,68365,68366,68368,68370,68372,68384,68386],{},[898,68367,2146],{},[898,68369,1766],{},[1656,68371,1713],{},[4138,68373,68374],{"scriptlevel":4032,"displaystyle":1658},[3294,68375,68376,68382],{},[895,68377,68378,68380],{},[898,68379,19177],{},[898,68381,1766],{},[898,68383,1665],{},[1656,68385,3633],{},[898,68387,207],{},[902,68389,68390],{"encoding":904},"AC = \\tfrac{FC}{Q} + a"," tvaru ",[883,68393,68395],{"className":68394},[886],[888,68396,68397],{"xmlns":890},[892,68398,68399,68403],{},[895,68400,68401],{},[898,68402,18539],{},[902,68404,18539],{"encoding":904},[883,68406,68408],{"className":68407},[886],[888,68409,68410],{"xmlns":890},[892,68411,68412,68416],{},[895,68413,68414],{},[898,68415,207],{},[902,68417,207],{"encoding":904}," (obrázek 3.8). Limity ",[883,68420,68422],{"className":68421},[886],[888,68423,68424],{"xmlns":890},[892,68425,68426,68464],{},[895,68427,68428,68448,68460,68462],{},[1661,68429,68430,68436],{},[895,68431,68432,68434],{},[898,68433,67950],{},[1656,68435,2093],{},[895,68437,68438,68440,68442],{},[898,68439,1665],{},[1656,68441,11915],{},[2062,68443,68444,68446],{},[1667,68445,4032],{},[1656,68447,3633],{},[4138,68449,68450],{"scriptlevel":4032,"displaystyle":1658},[3294,68451,68452,68458],{},[895,68453,68454,68456],{},[898,68455,19177],{},[898,68457,1766],{},[898,68459,1665],{},[1656,68461,1713],{},[898,68463,15060],{"mathvariant":1723},[902,68465,68466],{"encoding":904},"\\lim_{Q \\to 0^+} \\tfrac{FC}{Q} = \\infty",[883,68468,68470],{"className":68469},[886],[888,68471,68472],{"xmlns":890},[892,68473,68474,68508],{},[895,68475,68476,68492,68504,68506],{},[1661,68477,68478,68484],{},[895,68479,68480,68482],{},[898,68481,67950],{},[1656,68483,2093],{},[895,68485,68486,68488,68490],{},[898,68487,1665],{},[1656,68489,11915],{},[898,68491,15060],{"mathvariant":1723},[4138,68493,68494],{"scriptlevel":4032,"displaystyle":1658},[3294,68495,68496,68502],{},[895,68497,68498,68500],{},[898,68499,19177],{},[898,68501,1766],{},[898,68503,1665],{},[1656,68505,1713],{},[1667,68507,4032],{},[902,68509,68510],{"encoding":904},"\\lim_{Q \\to \\infty} \\tfrac{FC}{Q} = 0"," vysvětlují, proč s rostoucí produkcí fixní náklady stále méně ovlivňují ",[883,68513,68515],{"className":68514},[886],[888,68516,68517],{"xmlns":890},[892,68518,68519,68525],{},[895,68520,68521,68523],{},[898,68522,2146],{},[898,68524,1766],{},[902,68526,64229],{"encoding":904},[724,68528,68529],{},[614,68530,68531,68532,68547,68548,68563,68564,1863],{},"Obrázek 3.7: Přímka ",[883,68533,68535],{"className":68534},[886],[888,68536,68537],{"xmlns":890},[892,68538,68539,68545],{},[895,68540,68541,68543],{},[898,68542,11577],{},[898,68544,1766],{},[902,68546,12033],{"encoding":904}," s osovým průsečíkem ve výši ",[883,68549,68551],{"className":68550},[886],[888,68552,68553],{"xmlns":890},[892,68554,68555,68561],{},[895,68556,68557,68559],{},[898,68558,19177],{},[898,68560,1766],{},[902,68562,64160],{"encoding":904}," a se sklonem ",[883,68565,68567],{"className":68566},[886],[888,68568,68569],{"xmlns":890},[892,68570,68571,68583],{},[895,68572,68573,68575,68577,68579,68581],{},[898,68574,68344],{},[1656,68576,2093],{},[898,68578,7151],{},[1656,68580,1713],{},[898,68582,207],{},[902,68584,68355],{"encoding":904},[724,68586,68587],{},[614,68588,68589,68590,68605,68606,1863],{},"Obrázek 3.8: Klesající hyperbola ",[883,68591,68593],{"className":68592},[886],[888,68594,68595],{"xmlns":890},[892,68596,68597,68603],{},[895,68598,68599,68601],{},[898,68600,2146],{},[898,68602,1766],{},[902,68604,64229],{"encoding":904}," s vodorovnou asymptotou ve výši ",[883,68607,68609],{"className":68608},[886],[888,68610,68611],{"xmlns":890},[892,68612,68613,68617],{},[895,68614,68615],{},[898,68616,207],{},[902,68618,207],{"encoding":904},[198,68620,68622],{"id":68621},"mezní-náklady","Mezní náklady",[724,68624,68625,1643,68627,3247,68642,68645,68646,68649],{},[38,68626,68622],{},[883,68628,68630],{"className":68629},[886],[888,68631,68632],{"xmlns":890},[892,68633,68634,68640],{},[895,68635,68636,68638],{},[898,68637,1703],{},[898,68639,1766],{},[902,68641,63961],{"encoding":904},[38,68643,68644],{},"marginal cost",") jsou ",[207,68647,1145],{"className":68648,"dataFsResolvedFilePath":764,"href":765},[210]," celkových nákladů podle množství:",[883,68651,68653],{"className":68652},[886],[888,68654,68655],{"xmlns":890,"display":2408},[892,68656,68657,68726],{},[2412,68658,68659],{"width":2414},[2416,68660,68661,68663,68719,68721],{},[2419,68662],{"width":2421},[2419,68664,68665],{},[895,68666,68667,68669,68671,68673,68675,68677,68679,68681,68683,68685,68701,68703,68705,68711,68713,68715,68717],{},[898,68668,1703],{},[898,68670,1766],{},[1656,68672,1713],{},[898,68674,1703],{},[898,68676,1766],{},[1656,68678,1659],{"stretchy":1658},[898,68680,1665],{},[1656,68682,1683],{"stretchy":1658},[1656,68684,1713],{},[3294,68686,68687,68695],{},[895,68688,68689,68691,68693],{},[898,68690,3768],{"mathvariant":1723},[898,68692,11577],{},[898,68694,1766],{},[895,68696,68697,68699],{},[898,68698,3768],{"mathvariant":1723},[898,68700,1665],{},[1656,68702,1713],{},[898,68704,11577],{},[2062,68706,68707,68709],{},[898,68708,1766],{},[1656,68710,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,68712,1659],{"stretchy":1658},[898,68714,1665],{},[1656,68716,1683],{"stretchy":1658},[898,68718,1863],{"mathvariant":1723},[2419,68720],{"width":2421},[2419,68722,68723],{},[2461,68724,68725],{},"(3.8)",[902,68727,68728],{"encoding":904},"MC = MC(Q) = \\frac{\\mathrm{d}TC}{\\mathrm{d}Q} = TC'(Q).\n\\tag{3.8}",[1981,68730,68731],{},[724,68732,68733,68735,68736,68762,68763,68780,68781,1863],{},[883,68734,3472],{}," Intuice — „kolik stojí další kus\"\n",[883,68737,68739],{"className":68738},[886],[888,68740,68741],{"xmlns":890},[892,68742,68743,68759],{},[895,68744,68745,68747,68749,68751,68757],{},[898,68746,1703],{},[898,68748,1766],{},[1656,68750,1659],{"stretchy":1658},[2062,68752,68753,68755],{},[898,68754,1665],{},[1656,68756,8187],{},[1656,68758,1683],{"stretchy":1658},[902,68760,68761],{"encoding":904},"MC(Q^*)"," udává přibližné náklady na výrobu jedné další jednotky, když firma aktuálně produkuje ",[883,68764,68766],{"className":68765},[886],[888,68767,68768],{"xmlns":890},[892,68769,68770,68778],{},[895,68771,68772],{},[2062,68773,68774,68776],{},[898,68775,1665],{},[1656,68777,8187],{},[902,68779,38543],{"encoding":904},". Formálně ",[883,68782,68784],{"className":68783},[886],[888,68785,68786],{"xmlns":890},[892,68787,68788,68840],{},[895,68789,68790,68792,68794,68796,68802,68804,68806,68808,68810,68812,68818,68820,68822,68824,68826,68828,68830,68832,68838],{},[898,68791,1703],{},[898,68793,1766],{},[1656,68795,1659],{"stretchy":1658},[2062,68797,68798,68800],{},[898,68799,1665],{},[1656,68801,8187],{},[1656,68803,1683],{"stretchy":1658},[1656,68805,3815],{},[898,68807,11577],{},[898,68809,1766],{},[1656,68811,1659],{"stretchy":1658},[2062,68813,68814,68816],{},[898,68815,1665],{},[1656,68817,8187],{},[1656,68819,3633],{},[1667,68821,1669],{},[1656,68823,1683],{"stretchy":1658},[1656,68825,3964],{},[898,68827,11577],{},[898,68829,1766],{},[1656,68831,1659],{"stretchy":1658},[2062,68833,68834,68836],{},[898,68835,1665],{},[1656,68837,8187],{},[1656,68839,1683],{"stretchy":1658},[902,68841,68842],{"encoding":904},"MC(Q^*) \\approx TC(Q^* + 1) - TC(Q^*)",[724,68844,68845,68846,2114],{},"Analogicky ke vztahu (3.3) platí pro odhad změny ",[883,68847,68849],{"className":68848},[886],[888,68850,68851],{"xmlns":890},[892,68852,68853,68861],{},[895,68854,68855,68857,68859],{},[898,68856,3750],{"mathvariant":1723},[898,68858,11577],{},[898,68860,1766],{},[902,68862,68863],{"encoding":904},"\\Delta TC",[883,68865,68867],{"className":68866},[886],[888,68868,68869],{"xmlns":890,"display":2408},[892,68870,68871,68940],{},[2412,68872,68873],{"width":2414},[2416,68874,68875,68877,68933,68935],{},[2419,68876],{"width":2421},[2419,68878,68879],{},[895,68880,68881,68883,68885,68887,68889,68891,68893,68895,68897,68899,68901,68903,68905,68907,68913,68915,68917,68919,68921,68923,68925,68927,68929,68931],{},[898,68882,3750],{"mathvariant":1723},[898,68884,11577],{},[898,68886,1766],{},[2461,68888,12767],{},[1656,68890,3815],{},[2461,68892,12767],{},[898,68894,3768],{"mathvariant":1723},[898,68896,11577],{},[898,68898,1766],{},[1656,68900,1713],{},[1656,68902,1659],{"stretchy":1658},[898,68904,11577],{},[898,68906,1766],{},[2062,68908,68909,68911],{},[1656,68910,1683],{"stretchy":1658},[1656,68912,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[2461,68914,7828],{},[898,68916,3768],{"mathvariant":1723},[898,68918,1665],{},[1656,68920,1713],{},[898,68922,1703],{},[898,68924,1766],{},[2461,68926,7828],{},[898,68928,3768],{"mathvariant":1723},[898,68930,1665],{},[1656,68932,1673],{"separator":1672},[2419,68934],{"width":2421},[2419,68936,68937],{},[2461,68938,68939],{},"(3.9)",[902,68941,68942],{"encoding":904},"\\Delta TC \\;\\approx\\; \\mathrm{d}TC = (TC)' \\, \\mathrm{d}Q = MC \\, \\mathrm{d}Q,\n\\tag{3.9}",[724,68944,65979],{},[883,68946,68948],{"className":68947},[886],[888,68949,68950],{"xmlns":890,"display":2408},[892,68951,68952,69050],{},[895,68953,68954,68992,68994,68996,68998,69020,69022,69048],{},[895,68955,68956,68958,68964,68966,68972,68975,68981,68984],{},[2461,68957,65993],{},[2033,68959,68960,68962],{"accent":1672},[2461,68961,54409],{},[1656,68963,33774],{},[2461,68965,66002],{},[2033,68967,68968,68970],{"accent":1672},[2461,68969,10839],{},[1656,68971,33693],{},[2461,68973,68974],{},"ch n",[2033,68976,68977,68979],{"accent":1672},[2461,68978,207],{},[1656,68980,33693],{},[2461,68982,68983],{},"klad",[2033,68985,68986,68989],{"accent":1672},[2461,68987,68988],{},"u",[1656,68990,68991],{},"˚",[2461,68993,12767],{},[1656,68995,3815],{},[2461,68997,12767],{},[895,68999,69000,69002,69008,69011,69017],{},[2461,69001,66037],{},[2033,69003,69004,69006],{"accent":1672},[2461,69005,33762],{},[1656,69007,33693],{},[2461,69009,69010],{}," n",[2033,69012,69013,69015],{"accent":1672},[2461,69014,207],{},[1656,69016,33693],{},[2461,69018,69019],{},"klady",[1656,69021,66064],{},[895,69023,69024,69026,69032,69034,69040,69042],{},[2461,69025,65993],{},[2033,69027,69028,69030],{"accent":1672},[2461,69029,54409],{},[1656,69031,33774],{},[2461,69033,66077],{},[2033,69035,69036,69038],{"accent":1672},[2461,69037,18343],{},[1656,69039,33774],{},[2461,69041,66086],{},[2033,69043,69044,69046],{"accent":1672},[2461,69045,33762],{},[1656,69047,33693],{},[898,69049,1863],{"mathvariant":1723},[902,69051,69052],{"encoding":904},"\\text{změna celkových nákladů} \\;\\approx\\; \\text{mezní náklady} \\times \\text{změna množství}.",[46030,69054,69056],{"id":69055},"příklad-35","Příklad 3.5",[724,69058,69059,66190,69061,64694,69097,69112,69113,69128,69129,3605,69142,3619,69155,69168,69169,3619,69182,1863],{},[38,69060,64656],{},[883,69062,69064],{"className":69063},[886],[888,69065,69066],{"xmlns":890},[892,69067,69068,69094],{},[895,69069,69070,69072,69074,69076,69078,69080,69082,69084,69086,69088],{},[898,69071,11577],{},[898,69073,1766],{},[1656,69075,1713],{},[1667,69077,5272],{},[1656,69079,3633],{},[1667,69081,9112],{},[898,69083,1665],{},[1656,69085,3633],{},[1667,69087,1680],{},[2062,69089,69090,69092],{},[898,69091,1665],{},[1667,69093,1680],{},[902,69095,69096],{"encoding":904},"TC = 200 + 6Q + 2Q^2",[883,69098,69100],{"className":69099},[886],[888,69101,69102],{"xmlns":890},[892,69103,69104,69110],{},[895,69105,69106,69108],{},[898,69107,1703],{},[898,69109,1766],{},[902,69111,63961],{"encoding":904}," a odhadněte změny ",[883,69114,69116],{"className":69115},[886],[888,69117,69118],{"xmlns":890},[892,69119,69120,69126],{},[895,69121,69122,69124],{},[898,69123,11577],{},[898,69125,1766],{},[902,69127,12033],{"encoding":904}," při změnách ",[883,69130,69132],{"className":69131},[886],[888,69133,69134],{"xmlns":890},[892,69135,69136,69140],{},[895,69137,69138],{},[898,69139,1665],{},[902,69141,1665],{"encoding":904},[883,69143,69145],{"className":69144},[886],[888,69146,69147],{"xmlns":890},[892,69148,69149,69153],{},[895,69150,69151],{},[1667,69152,44930],{},[902,69154,44930],{"encoding":904},[883,69156,69158],{"className":69157},[886],[888,69159,69160],{"xmlns":890},[892,69161,69162,69166],{},[895,69163,69164],{},[1667,69165,2668],{},[902,69167,2668],{"encoding":904}," a z ",[883,69170,69172],{"className":69171},[886],[888,69173,69174],{"xmlns":890},[892,69175,69176,69180],{},[895,69177,69178],{},[1667,69179,44930],{},[902,69181,44930],{"encoding":904},[883,69183,69185],{"className":69184},[886],[888,69186,69187],{"xmlns":890},[892,69188,69189,69193],{},[895,69190,69191],{},[1667,69192,9140],{},[902,69194,9140],{"encoding":904},[724,69196,69197,1643,69199,2191,69225,1343,69252,69279,69280,69295,69296,69311,69312,69339,69340,69360,69361,29252,69382,69438,69439,3605,69452,3619,69465,3206,69478,1863],{},[38,69198,31488],{},[883,69200,69202],{"className":69201},[886],[888,69203,69204],{"xmlns":890},[892,69205,69206,69222],{},[895,69207,69208,69210,69212,69214,69216,69218,69220],{},[898,69209,1703],{},[898,69211,1766],{},[1656,69213,1713],{},[1667,69215,9112],{},[1656,69217,3633],{},[1667,69219,2673],{},[898,69221,1665],{},[902,69223,69224],{"encoding":904},"MC = 6 + 4Q",[883,69226,69228],{"className":69227},[886],[888,69229,69230],{"xmlns":890},[892,69231,69232,69249],{},[895,69233,69234,69236,69238,69240,69242,69244,69246],{},[898,69235,1703],{},[898,69237,1766],{},[1656,69239,1659],{"stretchy":1658},[1667,69241,44930],{},[1656,69243,1683],{"stretchy":1658},[1656,69245,1713],{},[1667,69247,69248],{},"66",[902,69250,69251],{"encoding":904},"MC(15) = 66",[883,69253,69255],{"className":69254},[886],[888,69256,69257],{"xmlns":890},[892,69258,69259,69276],{},[895,69260,69261,69263,69265,69267,69269,69271,69273],{},[898,69262,1703],{},[898,69264,1766],{},[1656,69266,1659],{"stretchy":1658},[1667,69268,9058],{},[1656,69270,1683],{"stretchy":1658},[1656,69272,1713],{},[1667,69274,69275],{},"86",[902,69277,69278],{"encoding":904},"MC(20) = 86",": s růstem množství se rychlost změny ",[883,69281,69283],{"className":69282},[886],[888,69284,69285],{"xmlns":890},[892,69286,69287,69293],{},[895,69288,69289,69291],{},[898,69290,11577],{},[898,69292,1766],{},[902,69294,12033],{"encoding":904}," zvyšuje (",[883,69297,69299],{"className":69298},[886],[888,69300,69301],{"xmlns":890},[892,69302,69303,69309],{},[895,69304,69305,69307],{},[898,69306,1703],{},[898,69308,1766],{},[902,69310,63961],{"encoding":904}," je rostoucí). Z ",[883,69313,69315],{"className":69314},[886],[888,69316,69317],{"xmlns":890},[892,69318,69319,69336],{},[895,69320,69321,69323,69325,69327,69329,69331,69333],{},[898,69322,11577],{},[898,69324,1766],{},[1656,69326,1659],{"stretchy":1658},[1667,69328,44930],{},[1656,69330,1683],{"stretchy":1658},[1656,69332,1713],{},[1667,69334,69335],{},"740",[902,69337,69338],{"encoding":904},"TC(15) = 740"," se po přírůstku ",[883,69341,69343],{"className":69342},[886],[888,69344,69345],{"xmlns":890},[892,69346,69347,69357],{},[895,69348,69349,69351,69353,69355],{},[898,69350,3768],{"mathvariant":1723},[898,69352,1665],{},[1656,69354,1713],{},[1667,69356,1669],{},[902,69358,69359],{"encoding":904},"\\mathrm{d}Q = 1"," předpokládá ",[883,69362,69364],{"className":69363},[886],[888,69365,69366],{"xmlns":890},[892,69367,69368,69379],{},[895,69369,69370,69372,69374,69376],{},[898,69371,11577],{},[898,69373,1766],{},[1656,69375,3815],{},[1667,69377,69378],{},"806",[902,69380,69381],{"encoding":904},"TC \\approx 806",[883,69383,69385],{"className":69384},[886],[888,69386,69387],{"xmlns":890},[892,69388,69389,69435],{},[895,69390,69391,69393,69395,69397,69399,69401,69403,69405,69407,69409,69411,69413,69415,69417,69419,69421,69423,69426,69428,69430,69432],{},[898,69392,3750],{"mathvariant":1723},[898,69394,11577],{},[898,69396,1766],{},[1656,69398,1713],{},[898,69400,11577],{},[898,69402,1766],{},[1656,69404,1659],{"stretchy":1658},[1667,69406,2668],{},[1656,69408,1683],{"stretchy":1658},[1656,69410,3964],{},[898,69412,11577],{},[898,69414,1766],{},[1656,69416,1659],{"stretchy":1658},[1667,69418,44930],{},[1656,69420,1683],{"stretchy":1658},[1656,69422,1713],{},[1667,69424,69425],{},"808",[1656,69427,3964],{},[1667,69429,69335],{},[1656,69431,1713],{},[1667,69433,69434],{},"68",[902,69436,69437],{"encoding":904},"\\Delta TC = TC(16) - TC(15) = 808 - 740 = 68",". Při poklesu ",[883,69440,69442],{"className":69441},[886],[888,69443,69444],{"xmlns":890},[892,69445,69446,69450],{},[895,69447,69448],{},[898,69449,1665],{},[902,69451,1665],{"encoding":904},[883,69453,69455],{"className":69454},[886],[888,69456,69457],{"xmlns":890},[892,69458,69459,69463],{},[895,69460,69461],{},[1667,69462,44930],{},[902,69464,44930],{"encoding":904},[883,69466,69468],{"className":69467},[886],[888,69469,69470],{"xmlns":890},[892,69471,69472,69476],{},[895,69473,69474],{},[1667,69475,9140],{},[902,69477,9140],{"encoding":904},[883,69479,69481],{"className":69480},[886],[888,69482,69483],{"xmlns":890},[892,69484,69485,69514],{},[895,69486,69487,69489,69491,69493,69495,69497,69499,69501,69503,69505,69507,69509,69511],{},[898,69488,3750],{"mathvariant":1723},[898,69490,11577],{},[898,69492,1766],{},[1656,69494,3815],{},[1667,69496,69248],{},[1656,69498,2751],{},[1656,69500,1659],{"stretchy":1658},[1656,69502,3964],{},[1667,69504,2617],{},[1656,69506,1683],{"stretchy":1658},[1656,69508,1713],{},[1656,69510,3964],{},[1667,69512,69513],{},"198",[902,69515,69516],{"encoding":904},"\\Delta TC \\approx 66 \\cdot (-3) = -198",[198,69518,69520],{"id":69519},"kubická-nákladová-funkce","Kubická nákladová funkce",[724,69522,69523],{},"V ekonomicky reálných situacích mají křivky nákladů charakteristické vazby a tvary.",[46030,69525,69527],{"id":69526},"příklad-36","Příklad 3.6",[724,69529,69530,66190,69532,69576],{},[38,69531,64656],{},[883,69533,69535],{"className":69534},[886],[888,69536,69537],{"xmlns":890},[892,69538,69539,69573],{},[895,69540,69541,69543,69545,69547,69549,69551,69553,69555,69557,69559,69565,69567],{},[898,69542,11577],{},[898,69544,1766],{},[1656,69546,1713],{},[1667,69548,5267],{},[1656,69550,3633],{},[1667,69552,8567],{},[898,69554,1665],{},[1656,69556,3964],{},[1667,69558,5193],{},[2062,69560,69561,69563],{},[898,69562,1665],{},[1667,69564,1680],{},[1656,69566,3633],{},[2062,69568,69569,69571],{},[898,69570,1665],{},[1667,69572,2617],{},[902,69574,69575],{"encoding":904},"TC = 100 + 25Q - 5Q^2 + Q^3"," odvoďte všechny nákladové charakteristiky.",[724,69578,69579],{},[38,69580,31488],{},[883,69582,69584],{"className":69583},[886],[888,69585,69586],{"xmlns":890,"display":2408},[892,69587,69588,69832],{},[2412,69589,69590,69616,69664,69698,69740,69790],{"rowspacing":29476,"columnalign":29477,"columnspacing":1724},[2416,69591,69592,69602],{},[2419,69593,69594],{},[4138,69595,69596],{"scriptlevel":4032,"displaystyle":1672},[895,69597,69598,69600],{},[898,69599,19177],{},[898,69601,1766],{},[2419,69603,69604],{},[4138,69605,69606],{"scriptlevel":4032,"displaystyle":1672},[895,69607,69608,69610,69612,69614],{},[895,69609],{},[1656,69611,1713],{},[1667,69613,5267],{},[1656,69615,1673],{"separator":1672},[2416,69617,69618,69630],{},[2419,69619,69620],{},[4138,69621,69622],{"scriptlevel":4032,"displaystyle":1672},[895,69623,69624,69626,69628],{},[898,69625,11577],{},[898,69627,49019],{},[898,69629,1766],{},[2419,69631,69632],{},[4138,69633,69634],{"scriptlevel":4032,"displaystyle":1672},[895,69635,69636,69638,69640,69642,69644,69646,69648,69654,69656,69662],{},[895,69637],{},[1656,69639,1713],{},[1667,69641,8567],{},[898,69643,1665],{},[1656,69645,3964],{},[1667,69647,5193],{},[2062,69649,69650,69652],{},[898,69651,1665],{},[1667,69653,1680],{},[1656,69655,3633],{},[2062,69657,69658,69660],{},[898,69659,1665],{},[1667,69661,2617],{},[1656,69663,1673],{"separator":1672},[2416,69665,69666,69678],{},[2419,69667,69668],{},[4138,69669,69670],{"scriptlevel":4032,"displaystyle":1672},[895,69671,69672,69674,69676],{},[898,69673,2146],{},[898,69675,19177],{},[898,69677,1766],{},[2419,69679,69680],{},[4138,69681,69682],{"scriptlevel":4032,"displaystyle":1672},[895,69683,69684,69686,69688,69696],{},[895,69685],{},[1656,69687,1713],{},[4138,69689,69690],{"scriptlevel":4032,"displaystyle":1658},[3294,69691,69692,69694],{},[1667,69693,5267],{},[898,69695,1665],{},[1656,69697,1673],{"separator":1672},[2416,69699,69700,69712],{},[2419,69701,69702],{},[4138,69703,69704],{"scriptlevel":4032,"displaystyle":1672},[895,69705,69706,69708,69710],{},[898,69707,2146],{},[898,69709,49019],{},[898,69711,1766],{},[2419,69713,69714],{},[4138,69715,69716],{"scriptlevel":4032,"displaystyle":1672},[895,69717,69718,69720,69722,69724,69726,69728,69730,69732,69738],{},[895,69719],{},[1656,69721,1713],{},[1667,69723,8567],{},[1656,69725,3964],{},[1667,69727,5193],{},[898,69729,1665],{},[1656,69731,3633],{},[2062,69733,69734,69736],{},[898,69735,1665],{},[1667,69737,1680],{},[1656,69739,1673],{"separator":1672},[2416,69741,69742,69752],{},[2419,69743,69744],{},[4138,69745,69746],{"scriptlevel":4032,"displaystyle":1672},[895,69747,69748,69750],{},[898,69749,2146],{},[898,69751,1766],{},[2419,69753,69754],{},[4138,69755,69756],{"scriptlevel":4032,"displaystyle":1672},[895,69757,69758,69760,69762,69770,69772,69774,69776,69778,69780,69782,69788],{},[895,69759],{},[1656,69761,1713],{},[4138,69763,69764],{"scriptlevel":4032,"displaystyle":1658},[3294,69765,69766,69768],{},[1667,69767,5267],{},[898,69769,1665],{},[1656,69771,3633],{},[1667,69773,8567],{},[1656,69775,3964],{},[1667,69777,5193],{},[898,69779,1665],{},[1656,69781,3633],{},[2062,69783,69784,69786],{},[898,69785,1665],{},[1667,69787,1680],{},[1656,69789,1673],{"separator":1672},[2416,69791,69792,69802],{},[2419,69793,69794],{},[4138,69795,69796],{"scriptlevel":4032,"displaystyle":1672},[895,69797,69798,69800],{},[898,69799,1703],{},[898,69801,1766],{},[2419,69803,69804],{},[4138,69805,69806],{"scriptlevel":4032,"displaystyle":1672},[895,69807,69808,69810,69812,69814,69816,69818,69820,69822,69824,69830],{},[895,69809],{},[1656,69811,1713],{},[1667,69813,8567],{},[1656,69815,3964],{},[1667,69817,8580],{},[898,69819,1665],{},[1656,69821,3633],{},[1667,69823,2617],{},[2062,69825,69826,69828],{},[898,69827,1665],{},[1667,69829,1680],{},[898,69831,1863],{"mathvariant":1723},[902,69833,69834],{"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}",[724,69836,69837,69838,24520,69853,24520,69868,69883,69884,69899,69900,1343,69918,69899,69935,1343,69953,69899,69968,69986],{},"Význačné body ",[883,69839,69841],{"className":69840},[886],[888,69842,69843],{"xmlns":890},[892,69844,69845,69850],{},[895,69846,69847],{},[1667,69848,69849],{},"1,67",[902,69851,69852],{"encoding":904},"1{,}67",[883,69854,69856],{"className":69855},[886],[888,69857,69858],{"xmlns":890},[892,69859,69860,69865],{},[895,69861,69862],{},[1667,69863,69864],{},"2,50",[902,69866,69867],{"encoding":904},"2{,}50",[883,69869,69871],{"className":69870},[886],[888,69872,69873],{"xmlns":890},[892,69874,69875,69880],{},[895,69876,69877],{},[1667,69878,69879],{},"4,73",[902,69881,69882],{"encoding":904},"4{,}73"," odpovídají: ",[883,69885,69887],{"className":69886},[886],[888,69888,69889],{"xmlns":890},[892,69890,69891,69897],{},[895,69892,69893,69895],{},[898,69894,1703],{},[898,69896,1766],{},[902,69898,63961],{"encoding":904}," minimum v ",[883,69901,69903],{"className":69902},[886],[888,69904,69905],{"xmlns":890},[892,69906,69907,69915],{},[895,69908,69909,69911,69913],{},[898,69910,1665],{},[1656,69912,2829],{},[1667,69914,69849],{},[902,69916,69917],{"encoding":904},"Q \\doteq 1{,}67",[883,69919,69921],{"className":69920},[886],[888,69922,69923],{"xmlns":890},[892,69924,69925,69933],{},[895,69926,69927,69929,69931],{},[898,69928,2146],{},[898,69930,49019],{},[898,69932,1766],{},[902,69934,63980],{"encoding":904},[883,69936,69938],{"className":69937},[886],[888,69939,69940],{"xmlns":890},[892,69941,69942,69950],{},[895,69943,69944,69946,69948],{},[898,69945,1665],{},[1656,69947,1713],{},[1667,69949,69864],{},[902,69951,69952],{"encoding":904},"Q = 2{,}50",[883,69954,69956],{"className":69955},[886],[888,69957,69958],{"xmlns":890},[892,69959,69960,69966],{},[895,69961,69962,69964],{},[898,69963,2146],{},[898,69965,1766],{},[902,69967,64229],{"encoding":904},[883,69969,69971],{"className":69970},[886],[888,69972,69973],{"xmlns":890},[892,69974,69975,69983],{},[895,69976,69977,69979,69981],{},[898,69978,1665],{},[1656,69980,2829],{},[1667,69982,69879],{},[902,69984,69985],{"encoding":904},"Q \\doteq 4{,}73"," (téma úlohy 3.11).",[724,69988,69989],{},[5956,69990],{"alt":69991,"className":69992,"src":69993},"imek-ac-avc-mc",[210,5960],"\u002Fwiki-assets\u002Fimek-ac-avc-mc.jpeg",[724,69995,69996],{},[614,69997,69998,69999,1896,70014,70031,70032,24520,70051,70066],{},"Obrázek 3.9: Kubické křivky ",[883,70000,70002],{"className":70001},[886],[888,70003,70004],{"xmlns":890},[892,70005,70006,70012],{},[895,70007,70008,70010],{},[898,70009,11577],{},[898,70011,1766],{},[902,70013,12033],{"encoding":904},[883,70015,70017],{"className":70016},[886],[888,70018,70019],{"xmlns":890},[892,70020,70021,70029],{},[895,70022,70023,70025,70027],{},[898,70024,11577],{},[898,70026,49019],{},[898,70028,1766],{},[902,70030,64178],{"encoding":904}," rostoucí od bodu ",[883,70033,70035],{"className":70034},[886],[888,70036,70037],{"xmlns":890},[892,70038,70039,70049],{},[895,70040,70041,70043,70045,70047],{},[898,70042,19177],{},[898,70044,1766],{},[1656,70046,1713],{},[1667,70048,5267],{},[902,70050,20370],{"encoding":904},[883,70052,70054],{"className":70053},[886],[888,70055,70056],{"xmlns":890},[892,70057,70058,70064],{},[895,70059,70060,70062],{},[898,70061,19177],{},[898,70063,1766],{},[902,70065,64160],{"encoding":904}," je vodorovná přímka.",[724,70068,70069],{},[614,70070,70071,70072,1343,70087,1343,70104,37900,70119,70132,70133,2191,70150,70165,70166,14953,70183,70198,70199,6960,70212,1343,70225,1343,70238,1863],{},"Obrázek 3.10: Křivky ",[883,70073,70075],{"className":70074},[886],[888,70076,70077],{"xmlns":890},[892,70078,70079,70085],{},[895,70080,70081,70083],{},[898,70082,2146],{},[898,70084,1766],{},[902,70086,64229],{"encoding":904},[883,70088,70090],{"className":70089},[886],[888,70091,70092],{"xmlns":890},[892,70093,70094,70102],{},[895,70095,70096,70098,70100],{},[898,70097,2146],{},[898,70099,49019],{},[898,70101,1766],{},[902,70103,63980],{"encoding":904},[883,70105,70107],{"className":70106},[886],[888,70108,70109],{"xmlns":890},[892,70110,70111,70117],{},[895,70112,70113,70115],{},[898,70114,1703],{},[898,70116,1766],{},[902,70118,63961],{"encoding":904},[883,70120,70122],{"className":70121},[886],[888,70123,70124],{"xmlns":890},[892,70125,70126,70130],{},[895,70127,70128],{},[898,70129,900],{},[902,70131,900],{"encoding":904}," a klesající hyperbola ",[883,70134,70136],{"className":70135},[886],[888,70137,70138],{"xmlns":890},[892,70139,70140,70148],{},[895,70141,70142,70144,70146],{},[898,70143,2146],{},[898,70145,19177],{},[898,70147,1766],{},[902,70149,64196],{"encoding":904},[883,70151,70153],{"className":70152},[886],[888,70154,70155],{"xmlns":890},[892,70156,70157,70163],{},[895,70158,70159,70161],{},[898,70160,1703],{},[898,70162,1766],{},[902,70164,63961],{"encoding":904}," protíná ",[883,70167,70169],{"className":70168},[886],[888,70170,70171],{"xmlns":890},[892,70172,70173,70181],{},[895,70174,70175,70177,70179],{},[898,70176,2146],{},[898,70178,49019],{},[898,70180,1766],{},[902,70182,63980],{"encoding":904},[883,70184,70186],{"className":70185},[886],[888,70187,70188],{"xmlns":890},[892,70189,70190,70196],{},[895,70191,70192,70194],{},[898,70193,2146],{},[898,70195,1766],{},[902,70197,64229],{"encoding":904}," zdola v jejich minimech; význačné hodnoty na ose ",[883,70200,70202],{"className":70201},[886],[888,70203,70204],{"xmlns":890},[892,70205,70206,70210],{},[895,70207,70208],{},[898,70209,1665],{},[902,70211,1665],{"encoding":904},[883,70213,70215],{"className":70214},[886],[888,70216,70217],{"xmlns":890},[892,70218,70219,70223],{},[895,70220,70221],{},[1667,70222,69849],{},[902,70224,69852],{"encoding":904},[883,70226,70228],{"className":70227},[886],[888,70229,70230],{"xmlns":890},[892,70231,70232,70236],{},[895,70233,70234],{},[1667,70235,69864],{},[902,70237,69867],{"encoding":904},[883,70239,70241],{"className":70240},[886],[888,70242,70243],{"xmlns":890},[892,70244,70245,70249],{},[895,70246,70247],{},[1667,70248,69879],{},[902,70250,69882],{"encoding":904},[724,70252,70253],{},[38,70254,70255],{},"Standardní vlastnosti:",[120,70257,70258,70293,70357,70424,70474,70494],{},[123,70259,70260,1896,70275,70292],{},[883,70261,70263],{"className":70262},[886],[888,70264,70265],{"xmlns":890},[892,70266,70267,70273],{},[895,70268,70269,70271],{},[898,70270,11577],{},[898,70272,1766],{},[902,70274,12033],{"encoding":904},[883,70276,70278],{"className":70277},[886],[888,70279,70280],{"xmlns":890},[892,70281,70282,70290],{},[895,70283,70284,70286,70288],{},[898,70285,11577],{},[898,70287,49019],{},[898,70289,1766],{},[902,70291,64178],{"encoding":904}," jsou kubické funkce;",[123,70294,70295,1343,70310,1343,70327,70342,70343,70356],{},[883,70296,70298],{"className":70297},[886],[888,70299,70300],{"xmlns":890},[892,70301,70302,70308],{},[895,70303,70304,70306],{},[898,70305,2146],{},[898,70307,1766],{},[902,70309,64229],{"encoding":904},[883,70311,70313],{"className":70312},[886],[888,70314,70315],{"xmlns":890},[892,70316,70317,70325],{},[895,70318,70319,70321,70323],{},[898,70320,2146],{},[898,70322,49019],{},[898,70324,1766],{},[902,70326,63980],{"encoding":904},[883,70328,70330],{"className":70329},[886],[888,70331,70332],{"xmlns":890},[892,70333,70334,70340],{},[895,70335,70336,70338],{},[898,70337,1703],{},[898,70339,1766],{},[902,70341,63961],{"encoding":904}," jsou křivky tvaru ",[883,70344,70346],{"className":70345},[886],[888,70347,70348],{"xmlns":890},[892,70349,70350,70354],{},[895,70351,70352],{},[898,70353,900],{},[902,70355,900],{"encoding":904}," (nejprve klesají, po minimu rostou);",[123,70358,70359,70374,70375,1343,70392,2149,70409,2856],{},[883,70360,70362],{"className":70361},[886],[888,70363,70364],{"xmlns":890},[892,70365,70366,70372],{},[895,70367,70368,70370],{},[898,70369,1703],{},[898,70371,1766],{},[902,70373,63961],{"encoding":904}," nabývá minima před ",[883,70376,70378],{"className":70377},[886],[888,70379,70380],{"xmlns":890},[892,70381,70382,70390],{},[895,70383,70384,70386,70388],{},[898,70385,2146],{},[898,70387,49019],{},[898,70389,1766],{},[902,70391,63980],{"encoding":904},[883,70393,70395],{"className":70394},[886],[888,70396,70397],{"xmlns":890},[892,70398,70399,70407],{},[895,70400,70401,70403,70405],{},[898,70402,2146],{},[898,70404,49019],{},[898,70406,1766],{},[902,70408,63980],{"encoding":904},[883,70410,70412],{"className":70411},[886],[888,70413,70414],{"xmlns":890},[892,70415,70416,70422],{},[895,70417,70418,70420],{},[898,70419,2146],{},[898,70421,1766],{},[902,70423,64229],{"encoding":904},[123,70425,70426,70165,70441,1896,70456,70473],{},[883,70427,70429],{"className":70428},[886],[888,70430,70431],{"xmlns":890},[892,70432,70433,70439],{},[895,70434,70435,70437],{},[898,70436,1703],{},[898,70438,1766],{},[902,70440,63961],{"encoding":904},[883,70442,70444],{"className":70443},[886],[888,70445,70446],{"xmlns":890},[892,70447,70448,70454],{},[895,70449,70450,70452],{},[898,70451,2146],{},[898,70453,1766],{},[902,70455,64229],{"encoding":904},[883,70457,70459],{"className":70458},[886],[888,70460,70461],{"xmlns":890},[892,70462,70463,70471],{},[895,70464,70465,70467,70469],{},[898,70466,2146],{},[898,70468,49019],{},[898,70470,1766],{},[902,70472,63980],{"encoding":904}," zdola právě v jejich minimech;",[123,70475,70476,70493],{},[883,70477,70479],{"className":70478},[886],[888,70480,70481],{"xmlns":890},[892,70482,70483,70491],{},[895,70484,70485,70487,70489],{},[898,70486,2146],{},[898,70488,19177],{},[898,70490,1766],{},[902,70492,64196],{"encoding":904}," je hyperbola, stále klesající;",[123,70495,70496,70528,70529,1896,70544,70561,70562,70575,70576,12702],{},[883,70497,70499],{"className":70498},[886],[888,70500,70501],{"xmlns":890},[892,70502,70503,70525],{},[895,70504,70505,70507,70509,70511,70513,70515,70517,70519,70521,70523],{},[898,70506,2146],{},[898,70508,1766],{},[1656,70510,1713],{},[898,70512,2146],{},[898,70514,19177],{},[898,70516,1766],{},[1656,70518,3633],{},[898,70520,2146],{},[898,70522,49019],{},[898,70524,1766],{},[902,70526,70527],{"encoding":904},"AC = AFC + AVC","; vzdálenost mezi ",[883,70530,70532],{"className":70531},[886],[888,70533,70534],{"xmlns":890},[892,70535,70536,70542],{},[895,70537,70538,70540],{},[898,70539,2146],{},[898,70541,1766],{},[902,70543,64229],{"encoding":904},[883,70545,70547],{"className":70546},[886],[888,70548,70549],{"xmlns":890},[892,70550,70551,70559],{},[895,70552,70553,70555,70557],{},[898,70554,2146],{},[898,70556,49019],{},[898,70558,1766],{},[902,70560,63980],{"encoding":904}," klesá s rostoucím ",[883,70563,70565],{"className":70564},[886],[888,70566,70567],{"xmlns":890},[892,70568,70569,70573],{},[895,70570,70571],{},[898,70572,1665],{},[902,70574,1665],{"encoding":904}," (protože ",[883,70577,70579],{"className":70578},[886],[888,70580,70581],{"xmlns":890},[892,70582,70583,70595],{},[895,70584,70585,70587,70589,70591,70593],{},[898,70586,2146],{},[898,70588,19177],{},[898,70590,1766],{},[1656,70592,11915],{},[1667,70594,4032],{},[902,70596,70597],{"encoding":904},"AFC \\to 0",[115,70599,70601],{"id":70600},"princip-minimalizace-průměrných-nákladů","Princip minimalizace průměrných nákladů",[724,70603,70604,70605,70608,70609,70624],{},"Častou optimalizační úlohou je ",[38,70606,70607],{},"minimalizace průměrných nákladů"," — stanovení produkce, pro niž je ",[883,70610,70612],{"className":70611},[886],[888,70613,70614],{"xmlns":890},[892,70615,70616,70622],{},[895,70617,70618,70620],{},[898,70619,2146],{},[898,70621,1766],{},[902,70623,64229],{"encoding":904}," minimální.",[198,70626,25138],{"id":25137},[724,70628,70629,70630,70647],{},"Mají-li průměrné náklady minimum v bodě ",[883,70631,70633],{"className":70632},[886],[888,70634,70635],{"xmlns":890},[892,70636,70637,70645],{},[895,70638,70639],{},[1661,70640,70641,70643],{},[898,70642,1665],{},[1667,70644,4032],{},[902,70646,46990],{"encoding":904},", pak platí",[883,70649,70651],{"className":70650},[886],[888,70652,70653],{"xmlns":890,"display":2408},[892,70654,70655,70704],{},[2412,70656,70657],{"width":2414},[2416,70658,70659,70661,70697,70699],{},[2419,70660],{"width":2421},[2419,70662,70663],{},[895,70664,70665,70667,70669,70671,70677,70679,70681,70683,70685,70687,70693,70695],{},[898,70666,2146],{},[898,70668,1766],{},[1656,70670,1659],{"stretchy":1658},[1661,70672,70673,70675],{},[898,70674,1665],{},[1667,70676,4032],{},[1656,70678,1683],{"stretchy":1658},[1656,70680,1713],{},[898,70682,1703],{},[898,70684,1766],{},[1656,70686,1659],{"stretchy":1658},[1661,70688,70689,70691],{},[898,70690,1665],{},[1667,70692,4032],{},[1656,70694,1683],{"stretchy":1658},[898,70696,1863],{"mathvariant":1723},[2419,70698],{"width":2421},[2419,70700,70701],{},[2461,70702,70703],{},"(3.10)",[902,70705,70706],{"encoding":904},"AC(Q_0) = MC(Q_0).\n\\tag{3.10}",[1981,70708,70709],{},[724,70710,70711,70713,70714],{},[883,70712,65112],{}," Princip\n",[38,70715,70716],{},"V bodě minima průměrných nákladů se průměrné náklady rovnají mezním nákladům.",[724,70718,70719,70722,70723,70765],{},[38,70720,70721],{},"Odvození."," Z ",[883,70724,70726],{"className":70725},[886],[888,70727,70728],{"xmlns":890},[892,70729,70730,70762],{},[895,70731,70732,70734,70736,70738,70740,70742,70744],{},[898,70733,2146],{},[898,70735,1766],{},[1656,70737,1659],{"stretchy":1658},[898,70739,1665],{},[1656,70741,1683],{"stretchy":1658},[1656,70743,1713],{},[4138,70745,70746],{"scriptlevel":4032,"displaystyle":1658},[3294,70747,70748,70760],{},[895,70749,70750,70752,70754,70756,70758],{},[898,70751,11577],{},[898,70753,1766],{},[1656,70755,1659],{"stretchy":1658},[898,70757,1665],{},[1656,70759,1683],{"stretchy":1658},[898,70761,1665],{},[902,70763,70764],{"encoding":904},"AC(Q) = \\tfrac{TC(Q)}{Q}"," derivací podílu plyne",[883,70767,70769],{"className":70768},[886],[888,70770,70771],{"xmlns":890,"display":2408},[892,70772,70773,70905],{},[895,70774,70775,70777,70783,70785,70787,70789,70791,70831,70833,70873,70875,70903],{},[898,70776,2146],{},[2062,70778,70779,70781],{},[898,70780,1766],{},[1656,70782,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,70784,1659],{"stretchy":1658},[898,70786,1665],{},[1656,70788,1683],{"stretchy":1658},[1656,70790,1713],{},[3294,70792,70793,70825],{},[895,70794,70795,70797,70803,70805,70807,70809,70811,70813,70815,70817,70819,70821,70823],{},[898,70796,11577],{},[2062,70798,70799,70801],{},[898,70800,1766],{},[1656,70802,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,70804,1659],{"stretchy":1658},[898,70806,1665],{},[1656,70808,1683],{"stretchy":1658},[1656,70810,2751],{},[898,70812,1665],{},[1656,70814,3964],{},[898,70816,11577],{},[898,70818,1766],{},[1656,70820,1659],{"stretchy":1658},[898,70822,1665],{},[1656,70824,1683],{"stretchy":1658},[2062,70826,70827,70829],{},[898,70828,1665],{},[1667,70830,1680],{},[1656,70832,1713],{},[3294,70834,70835,70867],{},[895,70836,70837,70839,70841,70843,70845,70847,70849,70851,70853,70855,70857,70859,70861,70863,70865],{},[898,70838,1703],{},[898,70840,1766],{},[1656,70842,1659],{"stretchy":1658},[898,70844,1665],{},[1656,70846,1683],{"stretchy":1658},[1656,70848,2751],{},[898,70850,1665],{},[1656,70852,3964],{},[898,70854,2146],{},[898,70856,1766],{},[1656,70858,1659],{"stretchy":1658},[898,70860,1665],{},[1656,70862,1683],{"stretchy":1658},[1656,70864,2751],{},[898,70866,1665],{},[2062,70868,70869,70871],{},[898,70870,1665],{},[1667,70872,1680],{},[1656,70874,1713],{},[3294,70876,70877,70901],{},[895,70878,70879,70881,70883,70885,70887,70889,70891,70893,70895,70897,70899],{},[898,70880,1703],{},[898,70882,1766],{},[1656,70884,1659],{"stretchy":1658},[898,70886,1665],{},[1656,70888,1683],{"stretchy":1658},[1656,70890,3964],{},[898,70892,2146],{},[898,70894,1766],{},[1656,70896,1659],{"stretchy":1658},[898,70898,1665],{},[1656,70900,1683],{"stretchy":1658},[898,70902,1665],{},[898,70904,1863],{"mathvariant":1723},[902,70906,70907],{"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}.",[724,70909,70910,70911,3565,70926,3206,70948,65489],{},"Nutnou podmínkou minima ",[883,70912,70914],{"className":70913},[886],[888,70915,70916],{"xmlns":890},[892,70917,70918,70924],{},[895,70919,70920,70922],{},[898,70921,2146],{},[898,70923,1766],{},[902,70925,64229],{"encoding":904},[883,70927,70929],{"className":70928},[886],[888,70930,70931],{"xmlns":890},[892,70932,70933,70945],{},[895,70934,70935,70941,70943],{},[1661,70936,70937,70939],{},[898,70938,1665],{},[1667,70940,4032],{},[1656,70942,2850],{},[1667,70944,4032],{},[902,70946,70947],{"encoding":904},"Q_0 > 0",[883,70949,70951],{"className":70950},[886],[888,70952,70953],{"xmlns":890},[892,70954,70955,70979],{},[895,70956,70957,70959,70965,70967,70973,70975,70977],{},[898,70958,2146],{},[2062,70960,70961,70963],{},[898,70962,1766],{},[1656,70964,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,70966,1659],{"stretchy":1658},[1661,70968,70969,70971],{},[898,70970,1665],{},[1667,70972,4032],{},[1656,70974,1683],{"stretchy":1658},[1656,70976,1713],{},[1667,70978,4032],{},[902,70980,70981],{"encoding":904},"AC'(Q_0) = 0",[883,70983,70985],{"className":70984},[886],[888,70986,70987],{"xmlns":890,"display":2408},[892,70988,70989,71074],{},[895,70990,70991,71031,71033,71035,71037,71040,71042,71044,71046,71048,71054,71056,71058,71060,71062,71064,71070,71072],{},[3294,70992,70993,71025],{},[895,70994,70995,70997,70999,71001,71007,71009,71011,71013,71015,71017,71023],{},[898,70996,1703],{},[898,70998,1766],{},[1656,71000,1659],{"stretchy":1658},[1661,71002,71003,71005],{},[898,71004,1665],{},[1667,71006,4032],{},[1656,71008,1683],{"stretchy":1658},[1656,71010,3964],{},[898,71012,2146],{},[898,71014,1766],{},[1656,71016,1659],{"stretchy":1658},[1661,71018,71019,71021],{},[898,71020,1665],{},[1667,71022,4032],{},[1656,71024,1683],{"stretchy":1658},[1661,71026,71027,71029],{},[898,71028,1665],{},[1667,71030,4032],{},[1656,71032,1713],{},[1667,71034,4032],{},[3316,71036],{"width":3318},[1656,71038,71039],{},"⟺",[3316,71041],{"width":3318},[898,71043,1703],{},[898,71045,1766],{},[1656,71047,1659],{"stretchy":1658},[1661,71049,71050,71052],{},[898,71051,1665],{},[1667,71053,4032],{},[1656,71055,1683],{"stretchy":1658},[1656,71057,1713],{},[898,71059,2146],{},[898,71061,1766],{},[1656,71063,1659],{"stretchy":1658},[1661,71065,71066,71068],{},[898,71067,1665],{},[1667,71069,4032],{},[1656,71071,1683],{"stretchy":1658},[898,71073,1863],{"mathvariant":1723},[902,71075,71076],{"encoding":904},"\\frac{MC(Q_0) - AC(Q_0)}{Q_0} = 0 \\quad\\Longleftrightarrow\\quad MC(Q_0) = AC(Q_0).",[724,71078,71079,1643,71082,70165,71097,71112,71113,71128,71129,3206,71146,71168,71169,71191],{},[38,71080,71081],{},"Geometrická interpretace.",[883,71083,71085],{"className":71084},[886],[888,71086,71087],{"xmlns":890},[892,71088,71089,71095],{},[895,71090,71091,71093],{},[898,71092,1703],{},[898,71094,1766],{},[902,71096,63961],{"encoding":904},[883,71098,71100],{"className":71099},[886],[888,71101,71102],{"xmlns":890},[892,71103,71104,71110],{},[895,71105,71106,71108],{},[898,71107,2146],{},[898,71109,1766],{},[902,71111,64229],{"encoding":904}," právě v bodě minima ",[883,71114,71116],{"className":71115},[886],[888,71117,71118],{"xmlns":890},[892,71119,71120,71126],{},[895,71121,71122,71124],{},[898,71123,2146],{},[898,71125,1766],{},[902,71127,64229],{"encoding":904}," (obrázek 3.10); nalevo od ",[883,71130,71132],{"className":71131},[886],[888,71133,71134],{"xmlns":890},[892,71135,71136,71144],{},[895,71137,71138],{},[1661,71139,71140,71142],{},[898,71141,1665],{},[1667,71143,4032],{},[902,71145,46990],{"encoding":904},[883,71147,71149],{"className":71148},[886],[888,71150,71151],{"xmlns":890},[892,71152,71153,71165],{},[895,71154,71155,71157,71159,71161,71163],{},[898,71156,1703],{},[898,71158,1766],{},[1656,71160,4373],{},[898,71162,2146],{},[898,71164,1766],{},[902,71166,71167],{"encoding":904},"MC \u003C AC"," (průměrné náklady klesají), napravo ",[883,71170,71172],{"className":71171},[886],[888,71173,71174],{"xmlns":890},[892,71175,71176,71188],{},[895,71177,71178,71180,71182,71184,71186],{},[898,71179,1703],{},[898,71181,1766],{},[1656,71183,2850],{},[898,71185,2146],{},[898,71187,1766],{},[902,71189,71190],{"encoding":904},"MC > AC"," (průměrné náklady rostou).",[724,71193,71194,71195,2233,71237,71254,71255,1863],{},"Za obvyklých ekonomických podmínek platí i obrácené tvrzení — jestliže ",[883,71196,71198],{"className":71197},[886],[888,71199,71200],{"xmlns":890},[892,71201,71202,71234],{},[895,71203,71204,71206,71208,71210,71216,71218,71220,71222,71224,71226,71232],{},[898,71205,2146],{},[898,71207,1766],{},[1656,71209,1659],{"stretchy":1658},[1661,71211,71212,71214],{},[898,71213,1665],{},[1667,71215,4032],{},[1656,71217,1683],{"stretchy":1658},[1656,71219,1713],{},[898,71221,1703],{},[898,71223,1766],{},[1656,71225,1659],{"stretchy":1658},[1661,71227,71228,71230],{},[898,71229,1665],{},[1667,71231,4032],{},[1656,71233,1683],{"stretchy":1658},[902,71235,71236],{"encoding":904},"AC(Q_0) = MC(Q_0)",[883,71238,71240],{"className":71239},[886],[888,71241,71242],{"xmlns":890},[892,71243,71244,71252],{},[895,71245,71246],{},[1661,71247,71248,71250],{},[898,71249,1665],{},[1667,71251,4032],{},[902,71253,46990],{"encoding":904}," je bod minima. V praktických úlohách tedy postačí řešit rovnici ",[883,71256,71258],{"className":71257},[886],[888,71259,71260],{"xmlns":890},[892,71261,71262,71286],{},[895,71263,71264,71266,71268,71270,71272,71274,71276,71278,71280,71282,71284],{},[898,71265,2146],{},[898,71267,1766],{},[1656,71269,1659],{"stretchy":1658},[898,71271,1665],{},[1656,71273,1683],{"stretchy":1658},[1656,71275,1713],{},[898,71277,1703],{},[898,71279,1766],{},[1656,71281,1659],{"stretchy":1658},[898,71283,1665],{},[1656,71285,1683],{"stretchy":1658},[902,71287,71288],{"encoding":904},"AC(Q) = MC(Q)",[1981,71290,71291],{},[724,71292,71293,71295,71296,19135,71314,71335,71336,19135,71339,71360,71361,71376,71377,66706,71392,12702],{},[883,71294,1987],{}," Pozor — neplést s principem maxima zisku\nPro ",[38,71297,71298,71299],{},"minimum ",[883,71300,71302],{"className":71301},[886],[888,71303,71304],{"xmlns":890},[892,71305,71306,71312],{},[895,71307,71308,71310],{},[898,71309,2146],{},[898,71311,1766],{},[902,71313,64229],{"encoding":904},[883,71315,71317],{"className":71316},[886],[888,71318,71319],{"xmlns":890},[892,71320,71321,71333],{},[895,71322,71323,71325,71327,71329,71331],{},[898,71324,2146],{},[898,71326,1766],{},[1656,71328,1713],{},[898,71330,1703],{},[898,71332,1766],{},[902,71334,63892],{"encoding":904},", pro ",[38,71337,71338],{},"maximum zisku",[883,71340,71342],{"className":71341},[886],[888,71343,71344],{"xmlns":890},[892,71345,71346,71358],{},[895,71347,71348,71350,71352,71354,71356],{},[898,71349,1703],{},[898,71351,1763],{},[1656,71353,1713],{},[898,71355,1703],{},[898,71357,1766],{},[902,71359,63940],{"encoding":904},". Obě podmínky využívají ",[883,71362,71364],{"className":71363},[886],[888,71365,71366],{"xmlns":890},[892,71367,71368,71374],{},[895,71369,71370,71372],{},[898,71371,1703],{},[898,71373,1766],{},[902,71375,63961],{"encoding":904},", ale rovnají ho rozdílným veličinám (",[883,71378,71380],{"className":71379},[886],[888,71381,71382],{"xmlns":890},[892,71383,71384,71390],{},[895,71385,71386,71388],{},[898,71387,2146],{},[898,71389,1766],{},[902,71391,64229],{"encoding":904},[883,71393,71395],{"className":71394},[886],[888,71396,71397],{"xmlns":890},[892,71398,71399,71405],{},[895,71400,71401,71403],{},[898,71402,1703],{},[898,71404,1763],{},[902,71406,15395],{"encoding":904},[46030,71408,71410],{"id":71409},"příklad-37","Příklad 3.7",[724,71412,71413,66190,71415,71449,71450,71463,71464,71479],{},[38,71414,64656],{},[883,71416,71418],{"className":71417},[886],[888,71419,71420],{"xmlns":890},[892,71421,71422,71446],{},[895,71423,71424,71426,71428,71430,71436,71438,71440,71442,71444],{},[898,71425,11577],{},[898,71427,1766],{},[1656,71429,1713],{},[2062,71431,71432,71434],{},[898,71433,1665],{},[1667,71435,1680],{},[1656,71437,3633],{},[1667,71439,2617],{},[898,71441,1665],{},[1656,71443,3633],{},[1667,71445,9023],{},[902,71447,71448],{"encoding":904},"TC = Q^2 + 3Q + 36"," najděte ",[883,71451,71453],{"className":71452},[886],[888,71454,71455],{"xmlns":890},[892,71456,71457,71461],{},[895,71458,71459],{},[898,71460,1665],{},[902,71462,1665],{"encoding":904}," minimalizující ",[883,71465,71467],{"className":71466},[886],[888,71468,71469],{"xmlns":890},[892,71470,71471,71477],{},[895,71472,71473,71475],{},[898,71474,2146],{},[898,71476,1766],{},[902,71478,64229],{"encoding":904}," a ověřte princip (3.10).",[724,71481,71482,71484],{},[38,71483,31488],{}," Přímý výpočet:",[883,71486,71488],{"className":71487},[886],[888,71489,71490],{"xmlns":890,"display":2408},[892,71491,71492,71594],{},[895,71493,71494,71496,71498,71500,71522,71524,71526,71528,71530,71532,71538,71540,71542,71544,71546,71548,71554,71556,71558,71560,71570,71572,71592],{},[898,71495,2146],{},[898,71497,1766],{},[1656,71499,1713],{},[3294,71501,71502,71520],{},[895,71503,71504,71510,71512,71514,71516,71518],{},[2062,71505,71506,71508],{},[898,71507,1665],{},[1667,71509,1680],{},[1656,71511,3633],{},[1667,71513,2617],{},[898,71515,1665],{},[1656,71517,3633],{},[1667,71519,9023],{},[898,71521,1665],{},[1656,71523,1713],{},[898,71525,1665],{},[1656,71527,3633],{},[1667,71529,2617],{},[1656,71531,3633],{},[3294,71533,71534,71536],{},[1667,71535,9023],{},[898,71537,1665],{},[1656,71539,1673],{"separator":1672},[3316,71541],{"width":14644},[1656,71543,1659],{"stretchy":1658},[898,71545,2146],{},[898,71547,1766],{},[2062,71549,71550,71552],{},[1656,71551,1683],{"stretchy":1658},[1656,71553,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,71555,1713],{},[1667,71557,1669],{},[1656,71559,3964],{},[3294,71561,71562,71564],{},[1667,71563,9023],{},[2062,71565,71566,71568],{},[898,71567,1665],{},[1667,71569,1680],{},[1656,71571,1713],{},[3294,71573,71574,71586],{},[895,71575,71576,71582,71584],{},[2062,71577,71578,71580],{},[898,71579,1665],{},[1667,71581,1680],{},[1656,71583,3964],{},[1667,71585,9023],{},[2062,71587,71588,71590],{},[898,71589,1665],{},[1667,71591,1680],{},[898,71593,1863],{"mathvariant":1723},[902,71595,71596],{"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}.",[724,71598,71599,71639,71640,71664,71665,71715,71716,1863],{},[883,71600,71602],{"className":71601},[886],[888,71603,71604],{"xmlns":890},[892,71605,71606,71636],{},[895,71607,71608,71610,71612,71614,71620,71622,71624,71626,71632,71634],{},[1656,71609,1659],{"stretchy":1658},[898,71611,2146],{},[898,71613,1766],{},[2062,71615,71616,71618],{},[1656,71617,1683],{"stretchy":1658},[1656,71619,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,71621,1713],{},[1667,71623,4032],{},[1656,71625,12770],{},[1661,71627,71628,71630],{},[898,71629,1665],{},[1667,71631,1669],{},[1656,71633,1713],{},[1667,71635,9112],{},[902,71637,71638],{"encoding":904},"(AC)' = 0 \\Rightarrow Q_1 = 6"," (smysluplné), ",[883,71641,71643],{"className":71642},[886],[888,71644,71645],{"xmlns":890},[892,71646,71647,71661],{},[895,71648,71649,71655,71657,71659],{},[1661,71650,71651,71653],{},[898,71652,1665],{},[1667,71654,1680],{},[1656,71656,1713],{},[1656,71658,3964],{},[1667,71660,9112],{},[902,71662,71663],{"encoding":904},"Q_2 = -6"," (vyloučeno). ",[883,71666,71668],{"className":71667},[886],[888,71669,71670],{"xmlns":890},[892,71671,71672,71712],{},[895,71673,71674,71676,71678,71680,71690,71692,71694,71696,71698,71706,71708,71710],{},[1656,71675,1659],{"stretchy":1658},[898,71677,2146],{},[898,71679,1766],{},[2062,71681,71682,71684],{},[1656,71683,1683],{"stretchy":1658},[895,71685,71686,71688],{},[1656,71687,1725],{"mathvariant":1723},[1656,71689,1725],{"mathvariant":1723},[1656,71691,1659],{"stretchy":1658},[1667,71693,9112],{},[1656,71695,1683],{"stretchy":1658},[1656,71697,1713],{},[4138,71699,71700],{"scriptlevel":4032,"displaystyle":1658},[3294,71701,71702,71704],{},[1667,71703,1669],{},[1667,71705,2617],{},[1656,71707,2850],{},[1667,71709,4032],{},[1656,71711,12770],{},[902,71713,71714],{"encoding":904},"(AC)''(6) = \\tfrac{1}{3} > 0 \\Rightarrow"," minimum. ",[883,71717,71719],{"className":71718},[886],[888,71720,71721],{"xmlns":890},[892,71722,71723,71739],{},[895,71724,71725,71727,71729,71731,71733,71735,71737],{},[898,71726,2146],{},[898,71728,1766],{},[1656,71730,1659],{"stretchy":1658},[1667,71732,9112],{},[1656,71734,1683],{"stretchy":1658},[1656,71736,1713],{},[1667,71738,44930],{},[902,71740,71741],{"encoding":904},"AC(6) = 15",[724,71743,71744,71745,71771,71772,2114],{},"Pomocí principu: ",[883,71746,71748],{"className":71747},[886],[888,71749,71750],{"xmlns":890},[892,71751,71752,71768],{},[895,71753,71754,71756,71758,71760,71762,71764,71766],{},[898,71755,1703],{},[898,71757,1766],{},[1656,71759,1713],{},[1667,71761,1680],{},[898,71763,1665],{},[1656,71765,3633],{},[1667,71767,2617],{},[902,71769,71770],{"encoding":904},"MC = 2Q + 3",", rovnice ",[883,71773,71775],{"className":71774},[886],[888,71776,71777],{"xmlns":890},[892,71778,71779,71791],{},[895,71780,71781,71783,71785,71787,71789],{},[898,71782,2146],{},[898,71784,1766],{},[1656,71786,1713],{},[898,71788,1703],{},[898,71790,1766],{},[902,71792,63892],{"encoding":904},[883,71794,71796],{"className":71795},[886],[888,71797,71798],{"xmlns":890,"display":2408},[892,71799,71800,71902],{},[895,71801,71802,71824,71826,71828,71830,71832,71834,71836,71838,71840,71846,71848,71850,71852,71854,71856,71858,71860,71866,71868,71870,71872,71874,71876,71878,71884,71886,71888,71890,71892,71894,71896,71898,71900],{},[3294,71803,71804,71822],{},[895,71805,71806,71812,71814,71816,71818,71820],{},[2062,71807,71808,71810],{},[898,71809,1665],{},[1667,71811,1680],{},[1656,71813,3633],{},[1667,71815,2617],{},[898,71817,1665],{},[1656,71819,3633],{},[1667,71821,9023],{},[898,71823,1665],{},[1656,71825,1713],{},[1667,71827,1680],{},[898,71829,1665],{},[1656,71831,3633],{},[1667,71833,2617],{},[2461,71835,12767],{},[1656,71837,12770],{},[2461,71839,12767],{},[2062,71841,71842,71844],{},[898,71843,1665],{},[1667,71845,1680],{},[1656,71847,3633],{},[1667,71849,2617],{},[898,71851,1665],{},[1656,71853,3633],{},[1667,71855,9023],{},[1656,71857,1713],{},[1667,71859,1680],{},[2062,71861,71862,71864],{},[898,71863,1665],{},[1667,71865,1680],{},[1656,71867,3633],{},[1667,71869,2617],{},[898,71871,1665],{},[2461,71873,12767],{},[1656,71875,12770],{},[2461,71877,12767],{},[2062,71879,71880,71882],{},[898,71881,1665],{},[1667,71883,1680],{},[1656,71885,1713],{},[1667,71887,9023],{},[2461,71889,12767],{},[1656,71891,12770],{},[2461,71893,12767],{},[898,71895,1665],{},[1656,71897,1713],{},[1667,71899,9112],{},[1656,71901,1673],{"separator":1672},[902,71903,71904],{"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,",[724,71906,71907,71908,71946],{},"a ",[883,71909,71911],{"className":71910},[886],[888,71912,71913],{"xmlns":890},[892,71914,71915,71943],{},[895,71916,71917,71919,71921,71923,71925,71927,71929,71931,71933,71935,71937,71939,71941],{},[898,71918,2146],{},[898,71920,1766],{},[1656,71922,1659],{"stretchy":1658},[1667,71924,9112],{},[1656,71926,1683],{"stretchy":1658},[1656,71928,1713],{},[898,71930,1703],{},[898,71932,1766],{},[1656,71934,1659],{"stretchy":1658},[1667,71936,9112],{},[1656,71938,1683],{"stretchy":1658},[1656,71940,1713],{},[1667,71942,44930],{},[902,71944,71945],{"encoding":904},"AC(6) = MC(6) = 15",". Oba postupy dávají stejný výsledek.",[198,71948,71950],{"id":71949},"princip-minimalizace-průměrných-variabilních-nákladů","Princip minimalizace průměrných variabilních nákladů",[724,71952,71953,71954,2114],{},"Analogicky pro ",[883,71955,71957],{"className":71956},[886],[888,71958,71959],{"xmlns":890},[892,71960,71961,71969],{},[895,71962,71963,71965,71967],{},[898,71964,2146],{},[898,71966,49019],{},[898,71968,1766],{},[902,71970,63980],{"encoding":904},[883,71972,71974],{"className":71973},[886],[888,71975,71976],{"xmlns":890,"display":2408},[892,71977,71978,72029],{},[2412,71979,71980],{"width":2414},[2416,71981,71982,71984,72022,72024],{},[2419,71983],{"width":2421},[2419,71985,71986],{},[895,71987,71988,71990,71992,71994,71996,72002,72004,72006,72008,72010,72012,72018,72020],{},[898,71989,2146],{},[898,71991,49019],{},[898,71993,1766],{},[1656,71995,1659],{"stretchy":1658},[1661,71997,71998,72000],{},[898,71999,1665],{},[1667,72001,4032],{},[1656,72003,1683],{"stretchy":1658},[1656,72005,1713],{},[898,72007,1703],{},[898,72009,1766],{},[1656,72011,1659],{"stretchy":1658},[1661,72013,72014,72016],{},[898,72015,1665],{},[1667,72017,4032],{},[1656,72019,1683],{"stretchy":1658},[898,72021,1863],{"mathvariant":1723},[2419,72023],{"width":2421},[2419,72025,72026],{},[2461,72027,72028],{},"(3.11)",[902,72030,72031],{"encoding":904},"AVC(Q_0) = MC(Q_0).\n\\tag{3.11}",[1981,72033,72034],{},[724,72035,72036,70713,72038],{},[883,72037,65112],{},[38,72039,72040,72041,72058],{},"V bodě minima průměrných variabilních nákladů se ",[883,72042,72044],{"className":72043},[886],[888,72045,72046],{"xmlns":890},[892,72047,72048,72056],{},[895,72049,72050,72052,72054],{},[898,72051,2146],{},[898,72053,49019],{},[898,72055,1766],{},[902,72057,63980],{"encoding":904}," rovnají mezním nákladům.",[724,72060,72061,72062,72084,72085,1863],{},"Odvození je analogické (úloha 3.14). V obrázku 3.10 odpovídá ",[883,72063,72065],{"className":72064},[886],[888,72066,72067],{"xmlns":890},[892,72068,72069,72081],{},[895,72070,72071,72077,72079],{},[1661,72072,72073,72075],{},[898,72074,1665],{},[1667,72076,4032],{},[1656,72078,1713],{},[1667,72080,9752],{},[902,72082,72083],{"encoding":904},"Q_0 = 2{,}5",". Za obvyklých podmínek platí i obrácené tvrzení — postačí řešit rovnici ",[883,72086,72088],{"className":72087},[886],[888,72089,72090],{"xmlns":890},[892,72091,72092,72118],{},[895,72093,72094,72096,72098,72100,72102,72104,72106,72108,72110,72112,72114,72116],{},[898,72095,2146],{},[898,72097,49019],{},[898,72099,1766],{},[1656,72101,1659],{"stretchy":1658},[898,72103,1665],{},[1656,72105,1683],{"stretchy":1658},[1656,72107,1713],{},[898,72109,1703],{},[898,72111,1766],{},[1656,72113,1659],{"stretchy":1658},[898,72115,1665],{},[1656,72117,1683],{"stretchy":1658},[902,72119,72120],{"encoding":904},"AVC(Q) = MC(Q)",[115,72122,72124],{"id":72123},"zisk-a-body-zvratu","Zisk a body zvratu",[724,72126,72127,1643,72130,72146],{},[38,72128,72129],{},"Zisk",[883,72131,72133],{"className":72132},[886],[888,72134,72135],{"xmlns":890},[892,72136,72137,72143],{},[895,72138,72139,72141],{},[898,72140,8194],{},[898,72142,1763],{},[902,72144,72145],{"encoding":904},"PR"," (profit) je rozdíl celkového příjmu a celkových nákladů:",[883,72148,72150],{"className":72149},[886],[888,72151,72152],{"xmlns":890,"display":2408},[892,72153,72154,72213],{},[2412,72155,72156],{"width":2414},[2416,72157,72158,72160,72206,72208],{},[2419,72159],{"width":2421},[2419,72161,72162],{},[895,72163,72164,72166,72168,72170,72172,72174,72176,72178,72180,72182,72184,72186,72188,72190,72192,72194,72196,72198,72200,72202,72204],{},[898,72165,8194],{},[898,72167,1763],{},[1656,72169,1713],{},[898,72171,8194],{},[898,72173,1763],{},[1656,72175,1659],{"stretchy":1658},[898,72177,1665],{},[1656,72179,1683],{"stretchy":1658},[1656,72181,1713],{},[898,72183,11577],{},[898,72185,1763],{},[1656,72187,1659],{"stretchy":1658},[898,72189,1665],{},[1656,72191,1683],{"stretchy":1658},[1656,72193,3964],{},[898,72195,11577],{},[898,72197,1766],{},[1656,72199,1659],{"stretchy":1658},[898,72201,1665],{},[1656,72203,1683],{"stretchy":1658},[898,72205,1863],{"mathvariant":1723},[2419,72207],{"width":2421},[2419,72209,72210],{},[2461,72211,72212],{},"(3.12)",[902,72214,72215],{"encoding":904},"PR = PR(Q) = TR(Q) - TC(Q).\n\\tag{3.12}",[724,72217,72218,72219,1896,72234,52313,72249,72251,72252,72255,72256,72272,72273,72288,72289,72304,72305,1343,72318,72331,72332,1343,72350,72368,72369,3247,72372,72375,72376,1348,72398,3206,72420,72442,72443,3206,72473,72495],{},"Body rovnosti ",[883,72220,72222],{"className":72221},[886],[888,72223,72224],{"xmlns":890},[892,72225,72226,72232],{},[895,72227,72228,72230],{},[898,72229,11577],{},[898,72231,1763],{},[902,72233,12875],{"encoding":904},[883,72235,72237],{"className":72236},[886],[888,72238,72239],{"xmlns":890},[892,72240,72241,72247],{},[895,72242,72243,72245],{},[898,72244,11577],{},[898,72246,1766],{},[902,72248,12033],{"encoding":904},[38,72250,64396],{}," (též vyrovnání, ",[614,72253,72254],{},"break-even points","). V nejjednodušším modelu (lineární poptávka, konstantní ",[883,72257,72259],{"className":72258},[886],[888,72260,72261],{"xmlns":890},[892,72262,72263,72269],{},[895,72264,72265,72267],{},[898,72266,49019],{},[898,72268,1766],{},[902,72270,72271],{"encoding":904},"VC",") je ",[883,72274,72276],{"className":72275},[886],[888,72277,72278],{"xmlns":890},[892,72279,72280,72286],{},[895,72281,72282,72284],{},[898,72283,11577],{},[898,72285,1763],{},[902,72287,12875],{"encoding":904}," kvadratická a ",[883,72290,72292],{"className":72291},[886],[888,72293,72294],{"xmlns":890},[892,72295,72296,72302],{},[895,72297,72298,72300],{},[898,72299,11577],{},[898,72301,1766],{},[902,72303,12033],{"encoding":904}," lineární (obrázek 3.11). Křivky se protínají v bodech ",[883,72306,72308],{"className":72307},[886],[888,72309,72310],{"xmlns":890},[892,72311,72312,72316],{},[895,72313,72314],{},[898,72315,2146],{},[902,72317,2146],{"encoding":904},[883,72319,72321],{"className":72320},[886],[888,72322,72323],{"xmlns":890},[892,72324,72325,72329],{},[895,72326,72327],{},[898,72328,2161],{},[902,72330,2161],{"encoding":904}," odpovídajících množstvím ",[883,72333,72335],{"className":72334},[886],[888,72336,72337],{"xmlns":890},[892,72338,72339,72347],{},[895,72340,72341],{},[1661,72342,72343,72345],{},[898,72344,1665],{},[898,72346,2146],{},[902,72348,72349],{"encoding":904},"Q_A",[883,72351,72353],{"className":72352},[886],[888,72354,72355],{"xmlns":890},[892,72356,72357,72365],{},[895,72358,72359],{},[1661,72360,72361,72363],{},[898,72362,1665],{},[898,72364,2161],{},[902,72366,72367],{"encoding":904},"Q_B"," — firma je na ",[38,72370,72371],{},"prahu rentability",[614,72373,72374],{},"break even","). Pro ",[883,72377,72379],{"className":72378},[886],[888,72380,72381],{"xmlns":890},[892,72382,72383,72395],{},[895,72384,72385,72387,72389],{},[898,72386,1665],{},[1656,72388,4373],{},[1661,72390,72391,72393],{},[898,72392,1665],{},[898,72394,2146],{},[902,72396,72397],{"encoding":904},"Q \u003C Q_A",[883,72399,72401],{"className":72400},[886],[888,72402,72403],{"xmlns":890},[892,72404,72405,72417],{},[895,72406,72407,72409,72411],{},[898,72408,1665],{},[1656,72410,2850],{},[1661,72412,72413,72415],{},[898,72414,1665],{},[898,72416,2161],{},[902,72418,72419],{"encoding":904},"Q > Q_B",[883,72421,72423],{"className":72422},[886],[888,72424,72425],{"xmlns":890},[892,72426,72427,72439],{},[895,72428,72429,72431,72433,72435,72437],{},[898,72430,11577],{},[898,72432,1766],{},[1656,72434,2850],{},[898,72436,11577],{},[898,72438,1763],{},[902,72440,72441],{"encoding":904},"TC > TR"," (ztráta); pro ",[883,72444,72446],{"className":72445},[886],[888,72447,72448],{"xmlns":890},[892,72449,72450,72470],{},[895,72451,72452,72458,72460,72462,72464],{},[1661,72453,72454,72456],{},[898,72455,1665],{},[898,72457,2146],{},[1656,72459,4373],{},[898,72461,1665],{},[1656,72463,4373],{},[1661,72465,72466,72468],{},[898,72467,1665],{},[898,72469,2161],{},[902,72471,72472],{"encoding":904},"Q_A \u003C Q \u003C Q_B",[883,72474,72476],{"className":72475},[886],[888,72477,72478],{"xmlns":890},[892,72479,72480,72492],{},[895,72481,72482,72484,72486,72488,72490],{},[898,72483,11577],{},[898,72485,1763],{},[1656,72487,2850],{},[898,72489,11577],{},[898,72491,1766],{},[902,72493,72494],{"encoding":904},"TR > TC"," (zisk).",[1981,72497,72498],{},[724,72499,72500,72502],{},[883,72501,3472],{}," 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.",[724,72504,72505,72506,72532],{},"Body zvratu jsou řešení rovnice ",[883,72507,72509],{"className":72508},[886],[888,72510,72511],{"xmlns":890},[892,72512,72513,72529],{},[895,72514,72515,72517,72519,72521,72523,72525,72527],{},[898,72516,8194],{},[898,72518,1763],{},[1656,72520,1659],{"stretchy":1658},[898,72522,1665],{},[1656,72524,1683],{"stretchy":1658},[1656,72526,1713],{},[1667,72528,4032],{},[902,72530,72531],{"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.",[724,72534,72535],{},[5956,72536],{"alt":72537,"className":72538,"src":72539},"imek-tr-tc-body-zvratu",[210,5960],"\u002Fwiki-assets\u002Fimek-tr-tc-body-zvratu.jpeg",[724,72541,72542],{},[614,72543,72544,72545,72560,72561,72576,72577,1896,72590,52037,72603,72616,72617,1896,72634,72651,72652,72672,72673,1896,72688,3713,72703,72732],{},"Obrázek 3.11: Body zvratu — křivky ",[883,72546,72548],{"className":72547},[886],[888,72549,72550],{"xmlns":890},[892,72551,72552,72558],{},[895,72553,72554,72556],{},[898,72555,11577],{},[898,72557,1763],{},[902,72559,12875],{"encoding":904}," (obrácená parabola) a ",[883,72562,72564],{"className":72563},[886],[888,72565,72566],{"xmlns":890},[892,72567,72568,72574],{},[895,72569,72570,72572],{},[898,72571,11577],{},[898,72573,1766],{},[902,72575,12033],{"encoding":904}," (přímka) se protínají v bodech ",[883,72578,72580],{"className":72579},[886],[888,72581,72582],{"xmlns":890},[892,72583,72584,72588],{},[895,72585,72586],{},[898,72587,2146],{},[902,72589,2146],{"encoding":904},[883,72591,72593],{"className":72592},[886],[888,72594,72595],{"xmlns":890},[892,72596,72597,72601],{},[895,72598,72599],{},[898,72600,2161],{},[902,72602,2161],{"encoding":904},[883,72604,72606],{"className":72605},[886],[888,72607,72608],{"xmlns":890},[892,72609,72610,72614],{},[895,72611,72612],{},[898,72613,1665],{},[902,72615,1665],{"encoding":904}," v hodnotách ",[883,72618,72620],{"className":72619},[886],[888,72621,72622],{"xmlns":890},[892,72623,72624,72632],{},[895,72625,72626],{},[1661,72627,72628,72630],{},[898,72629,1665],{},[898,72631,2146],{},[902,72633,72349],{"encoding":904},[883,72635,72637],{"className":72636},[886],[888,72638,72639],{"xmlns":890},[892,72640,72641,72649],{},[895,72642,72643],{},[1661,72644,72645,72647],{},[898,72646,1665],{},[898,72648,2161],{},[902,72650,72367],{"encoding":904},"; maximum zisku leží mezi nimi v bodě ",[883,72653,72655],{"className":72654},[886],[888,72656,72657],{"xmlns":890},[892,72658,72659,72669],{},[895,72660,72661],{},[1661,72662,72663,72665,72667],{},[898,72664,1665],{},[898,72666,64866],{},[1656,72668,2093],{},[902,72670,72671],{"encoding":904},"Q_{\\max}","; svislá vzdálenost mezi ",[883,72674,72676],{"className":72675},[886],[888,72677,72678],{"xmlns":890},[892,72679,72680,72686],{},[895,72681,72682,72684],{},[898,72683,11577],{},[898,72685,1763],{},[902,72687,12875],{"encoding":904},[883,72689,72691],{"className":72690},[886],[888,72692,72693],{"xmlns":890},[892,72694,72695,72701],{},[895,72696,72697,72699],{},[898,72698,11577],{},[898,72700,1766],{},[902,72702,12033],{"encoding":904},[883,72704,72706],{"className":72705},[886],[888,72707,72708],{"xmlns":890},[892,72709,72710,72730],{},[895,72711,72712,72718,72720,72722,72724],{},[1661,72713,72714,72716],{},[898,72715,1665],{},[898,72717,2146],{},[1656,72719,4373],{},[898,72721,1665],{},[1656,72723,4373],{},[1661,72725,72726,72728],{},[898,72727,1665],{},[898,72729,2161],{},[902,72731,72472],{"encoding":904}," vyznačuje zisk.",[46030,72734,72736],{"id":72735},"příklad-38","Příklad 3.8",[724,72738,72739,72741,72742,1343,72762,1343,72788,72814],{},[38,72740,64656],{}," Dáno ",[883,72743,72745],{"className":72744},[886],[888,72746,72747],{"xmlns":890},[892,72748,72749,72759],{},[895,72750,72751,72753,72755,72757],{},[898,72752,19177],{},[898,72754,1766],{},[1656,72756,1713],{},[1667,72758,2673],{},[902,72760,72761],{"encoding":904},"FC = 4",[883,72763,72765],{"className":72764},[886],[888,72766,72767],{"xmlns":890},[892,72768,72769,72785],{},[895,72770,72771,72773,72775,72777,72779],{},[898,72772,11577],{},[898,72774,49019],{},[898,72776,1766],{},[1656,72778,1713],{},[2062,72780,72781,72783],{},[898,72782,1665],{},[1667,72784,1680],{},[902,72786,72787],{"encoding":904},"TVC = Q^2",[883,72789,72791],{"className":72790},[886],[888,72792,72793],{"xmlns":890},[892,72794,72795,72811],{},[895,72796,72797,72799,72801,72803,72805,72807,72809],{},[898,72798,8194],{},[1656,72800,1713],{},[1656,72802,3964],{},[1667,72804,1680],{},[898,72806,1665],{},[1656,72808,3633],{},[1667,72810,2698],{},[902,72812,72813],{"encoding":904},"P = -2Q + 9",". Určete zisk, body zvratu a bod maxima zisku.",[724,72816,72817,72819],{},[38,72818,31488],{}," Celkové náklady a příjem:",[883,72821,72823],{"className":72822},[886],[888,72824,72825],{"xmlns":890,"display":2408},[892,72826,72827,72893],{},[895,72828,72829,72831,72833,72835,72837,72839,72845,72847,72849,72851,72853,72855,72857,72859,72861,72863,72865,72867,72869,72871,72873,72875,72877,72879,72885,72887,72889,72891],{},[898,72830,11577],{},[898,72832,1766],{},[1656,72834,1713],{},[1667,72836,2673],{},[1656,72838,3633],{},[2062,72840,72841,72843],{},[898,72842,1665],{},[1667,72844,1680],{},[1656,72846,1673],{"separator":1672},[3316,72848],{"width":14644},[898,72850,11577],{},[898,72852,1763],{},[1656,72854,1713],{},[898,72856,1665],{},[1656,72858,2751],{},[1656,72860,1659],{"stretchy":1658},[1656,72862,3964],{},[1667,72864,1680],{},[898,72866,1665],{},[1656,72868,3633],{},[1667,72870,2698],{},[1656,72872,1683],{"stretchy":1658},[1656,72874,1713],{},[1656,72876,3964],{},[1667,72878,1680],{},[2062,72880,72881,72883],{},[898,72882,1665],{},[1667,72884,1680],{},[1656,72886,3633],{},[1667,72888,2698],{},[898,72890,1665],{},[898,72892,1863],{"mathvariant":1723},[902,72894,72895],{"encoding":904},"TC = 4 + Q^2, \\qquad TR = Q \\cdot (-2Q + 9) = -2Q^2 + 9Q.",[724,72897,72898],{},"Zisk dle (3.12):",[883,72900,72902],{"className":72901},[886],[888,72903,72904],{"xmlns":890,"display":2408},[892,72905,72906,72984],{},[895,72907,72908,72910,72912,72914,72916,72918,72920,72922,72924,72926,72928,72930,72932,72938,72940,72942,72944,72946,72948,72950,72952,72954,72960,72962,72964,72966,72968,72974,72976,72978,72980,72982],{},[898,72909,8194],{},[898,72911,1763],{},[1656,72913,1713],{},[898,72915,11577],{},[898,72917,1763],{},[1656,72919,3964],{},[898,72921,11577],{},[898,72923,1766],{},[1656,72925,1713],{},[1656,72927,1659],{"stretchy":1658},[1656,72929,3964],{},[1667,72931,1680],{},[2062,72933,72934,72936],{},[898,72935,1665],{},[1667,72937,1680],{},[1656,72939,3633],{},[1667,72941,2698],{},[898,72943,1665],{},[1656,72945,1683],{"stretchy":1658},[1656,72947,3964],{},[1656,72949,1659],{"stretchy":1658},[1667,72951,2673],{},[1656,72953,3633],{},[2062,72955,72956,72958],{},[898,72957,1665],{},[1667,72959,1680],{},[1656,72961,1683],{"stretchy":1658},[1656,72963,1713],{},[1656,72965,3964],{},[1667,72967,2617],{},[2062,72969,72970,72972],{},[898,72971,1665],{},[1667,72973,1680],{},[1656,72975,3633],{},[1667,72977,2698],{},[898,72979,1665],{},[1656,72981,3964],{},[1667,72983,67987],{},[902,72985,72986],{"encoding":904},"PR = TR - TC = (-2Q^2 + 9Q) - (4 + Q^2) = -3Q^2 + 9Q - 4.",[724,72988,72989,72992,72993,26301,73029,2114],{},[38,72990,72991],{},"Body zvratu"," jsou kořeny rovnice ",[883,72994,72996],{"className":72995},[886],[888,72997,72998],{"xmlns":890},[892,72999,73000,73026],{},[895,73001,73002,73004,73006,73012,73014,73016,73018,73020,73022,73024],{},[1656,73003,3964],{},[1667,73005,2617],{},[2062,73007,73008,73010],{},[898,73009,1665],{},[1667,73011,1680],{},[1656,73013,3633],{},[1667,73015,2698],{},[898,73017,1665],{},[1656,73019,3964],{},[1667,73021,2673],{},[1656,73023,1713],{},[1667,73025,4032],{},[902,73027,73028],{"encoding":904},"-3Q^2 + 9Q - 4 = 0",[883,73030,73032],{"className":73031},[886],[888,73033,73034],{"xmlns":890},[892,73035,73036,73060],{},[895,73037,73038,73040,73046,73048,73050,73052,73054,73056,73058],{},[1667,73039,2617],{},[2062,73041,73042,73044],{},[898,73043,1665],{},[1667,73045,1680],{},[1656,73047,3964],{},[1667,73049,2698],{},[898,73051,1665],{},[1656,73053,3633],{},[1667,73055,2673],{},[1656,73057,1713],{},[1667,73059,4032],{},[902,73061,73062],{"encoding":904},"3Q^2 - 9Q + 4 = 0",[883,73064,73066],{"className":73065},[886],[888,73067,73068],{"xmlns":890,"display":2408},[892,73069,73070,73127],{},[895,73071,73072,73084,73086,73109,73111,73125],{},[1661,73073,73074,73076],{},[898,73075,1665],{},[895,73077,73078,73080,73082],{},[1667,73079,1669],{},[1656,73081,1673],{"separator":1672},[1667,73083,1680],{},[1656,73085,1713],{},[3294,73087,73088,73107],{},[895,73089,73090,73092,73095],{},[1667,73091,2698],{},[1656,73093,73094],{},"±",[2625,73096,73097],{},[895,73098,73099,73102,73104],{},[1667,73100,73101],{},"81",[1656,73103,3964],{},[1667,73105,73106],{},"48",[1667,73108,9112],{},[1656,73110,1713],{},[3294,73112,73113,73123],{},[895,73114,73115,73117,73119],{},[1667,73116,2698],{},[1656,73118,73094],{},[2625,73120,73121],{},[1667,73122,17705],{},[1667,73124,9112],{},[1656,73126,1673],{"separator":1672},[902,73128,73129],{"encoding":904},"Q_{1,2} = \\frac{9 \\pm \\sqrt{81 - 48}}{6} = \\frac{9 \\pm \\sqrt{33}}{6},",[724,73131,73132,73133,1896,73156,1863],{},"numericky ",[883,73134,73136],{"className":73135},[886],[888,73137,73138],{"xmlns":890},[892,73139,73140,73153],{},[895,73141,73142,73148,73150],{},[1661,73143,73144,73146],{},[898,73145,1665],{},[1667,73147,1669],{},[1656,73149,2829],{},[1667,73151,73152],{},"0,543",[902,73154,73155],{"encoding":904},"Q_1 \\doteq 0{,}543",[883,73157,73159],{"className":73158},[886],[888,73160,73161],{"xmlns":890},[892,73162,73163,73176],{},[895,73164,73165,73171,73173],{},[1661,73166,73167,73169],{},[898,73168,1665],{},[1667,73170,1680],{},[1656,73172,2829],{},[1667,73174,73175],{},"2,457",[902,73177,73178],{"encoding":904},"Q_2 \\doteq 2{,}457",[724,73180,73181,1643,73184,16312,73228,26301,73262,73280],{},[38,73182,73183],{},"Maximum zisku.",[883,73185,73187],{"className":73186},[886],[888,73188,73189],{"xmlns":890},[892,73190,73191,73225],{},[895,73192,73193,73195,73201,73203,73205,73207,73209,73211,73213,73215,73217,73219,73221,73223],{},[898,73194,8194],{},[2062,73196,73197,73199],{},[898,73198,1763],{},[1656,73200,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,73202,1713],{},[1656,73204,3964],{},[1667,73206,9112],{},[898,73208,1665],{},[1656,73210,3633],{},[1667,73212,2698],{},[1656,73214,1713],{},[1667,73216,4032],{},[1656,73218,12770],{},[898,73220,1665],{},[1656,73222,1713],{},[1667,73224,8845],{},[902,73226,73227],{"encoding":904},"PR' = -6Q + 9 = 0 \\Rightarrow Q = 1{,}5",[883,73229,73231],{"className":73230},[886],[888,73232,73233],{"xmlns":890},[892,73234,73235,73259],{},[895,73236,73237,73239,73249,73251,73253,73255,73257],{},[898,73238,8194],{},[2062,73240,73241,73243],{},[898,73242,1763],{},[895,73244,73245,73247],{},[1656,73246,1725],{"mathvariant":1723},[1656,73248,1725],{"mathvariant":1723},[1656,73250,1713],{},[1656,73252,3964],{},[1667,73254,9112],{},[1656,73256,4373],{},[1667,73258,4032],{},[902,73260,73261],{"encoding":904},"PR'' = -6 \u003C 0",[883,73263,73265],{"className":73264},[886],[888,73266,73267],{"xmlns":890},[892,73268,73269,73277],{},[895,73270,73271,73273,73275],{},[898,73272,1665],{},[1656,73274,1713],{},[1667,73276,8845],{},[902,73278,73279],{"encoding":904},"Q = 1{,}5"," je bod maxima s hodnotou",[883,73282,73284],{"className":73283},[886],[888,73285,73286],{"xmlns":890,"display":2408},[892,73287,73288,73351],{},[895,73289,73290,73292,73294,73296,73298,73300,73302,73304,73306,73308,73310,73312,73318,73320,73322,73324,73326,73328,73330,73332,73334,73337,73339,73342,73344,73346,73348],{},[898,73291,8194],{},[898,73293,1763],{},[1656,73295,1659],{"stretchy":1658},[1667,73297,8845],{},[1656,73299,1683],{"stretchy":1658},[1656,73301,1713],{},[1656,73303,3964],{},[1667,73305,2617],{},[1656,73307,2751],{},[1656,73309,1659],{"stretchy":1658},[1667,73311,8845],{},[2062,73313,73314,73316],{},[1656,73315,1683],{"stretchy":1658},[1667,73317,1680],{},[1656,73319,3633],{},[1667,73321,2698],{},[1656,73323,2751],{},[1667,73325,8845],{},[1656,73327,3964],{},[1667,73329,2673],{},[1656,73331,1713],{},[1656,73333,3964],{},[1667,73335,73336],{},"6,75",[1656,73338,3633],{},[1667,73340,73341],{},"13,5",[1656,73343,3964],{},[1667,73345,2673],{},[1656,73347,1713],{},[1667,73349,73350],{},"2,75.",[902,73352,73353],{"encoding":904},"PR(1{,}5) = -3 \\cdot (1{,}5)^2 + 9 \\cdot 1{,}5 - 4 = -6{,}75 + 13{,}5 - 4 = 2{,}75.",[724,73355,73356,73357,1343,73402,73455,73456,73474],{},"Pro srovnání maximum celkového příjmu (bez ohledu na náklady): ",[883,73358,73360],{"className":73359},[886],[888,73361,73362],{"xmlns":890},[892,73363,73364,73399],{},[895,73365,73366,73368,73374,73376,73378,73380,73382,73384,73386,73388,73390,73392,73394,73396],{},[898,73367,11577],{},[2062,73369,73370,73372],{},[898,73371,1763],{},[1656,73373,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,73375,1713],{},[1656,73377,3964],{},[1667,73379,2673],{},[898,73381,1665],{},[1656,73383,3633],{},[1667,73385,2698],{},[1656,73387,1713],{},[1667,73389,4032],{},[1656,73391,12770],{},[898,73393,1665],{},[1656,73395,1713],{},[1667,73397,73398],{},"2,25",[902,73400,73401],{"encoding":904},"TR' = -4Q + 9 = 0 \\Rightarrow Q = 2{,}25",[883,73403,73405],{"className":73404},[886],[888,73406,73407],{"xmlns":890},[892,73408,73409,73452],{},[895,73410,73411,73413,73421,73423,73425,73427,73429,73431,73433,73439,73441,73443,73445,73447,73449],{},[898,73412,11577],{},[1661,73414,73415,73417,73419],{},[898,73416,1763],{},[898,73418,64866],{},[1656,73420,2093],{},[1656,73422,1713],{},[1656,73424,3964],{},[1667,73426,1680],{},[1656,73428,2751],{},[1656,73430,1659],{"stretchy":1658},[1667,73432,73398],{},[2062,73434,73435,73437],{},[1656,73436,1683],{"stretchy":1658},[1667,73438,1680],{},[1656,73440,3633],{},[1667,73442,2698],{},[1656,73444,2751],{},[1667,73446,73398],{},[1656,73448,1713],{},[1667,73450,73451],{},"10,125",[902,73453,73454],{"encoding":904},"TR_{\\max} = -2 \\cdot (2{,}25)^2 + 9 \\cdot 2{,}25 = 10{,}125",". Leží vpravo od bodu maxima zisku, protože při ",[883,73457,73459],{"className":73458},[886],[888,73460,73461],{"xmlns":890},[892,73462,73463,73471],{},[895,73464,73465,73467,73469],{},[898,73466,1665],{},[1656,73468,1713],{},[1667,73470,73398],{},[902,73472,73473],{"encoding":904},"Q = 2{,}25"," rostou už náklady rychleji než příjem.",[1981,73476,73477],{},[724,73478,73479,73481,73482,1343,73504,73526,73527,1343,73544,73565,73566,73598,73599,73637,73638,3605,73656,73673,73674,1896,73702,73736,73737,16445,73775,1896,73799,1863],{},[883,73480,1987],{}," Nekonzistence v původním zdroji\nSkenovaný knižní text obsahoval v tomto příkladu dvě nesourodé hodnoty: uváděl body zvratu ",[883,73483,73485],{"className":73484},[886],[888,73486,73487],{"xmlns":890},[892,73488,73489,73501],{},[895,73490,73491,73497,73499],{},[1661,73492,73493,73495],{},[898,73494,1665],{},[1667,73496,1669],{},[1656,73498,1713],{},[1667,73500,13779],{},[902,73502,73503],{"encoding":904},"Q_1 = 0{,}5",[883,73505,73507],{"className":73506},[886],[888,73508,73509],{"xmlns":890},[892,73510,73511,73523],{},[895,73512,73513,73519,73521],{},[1661,73514,73515,73517],{},[898,73516,1665],{},[1667,73518,1680],{},[1656,73520,1713],{},[1667,73522,2673],{},[902,73524,73525],{"encoding":904},"Q_2 = 4"," (odpovídající starší verzi zadání) a zároveň maximum v ",[883,73528,73530],{"className":73529},[886],[888,73531,73532],{"xmlns":890},[892,73533,73534,73542],{},[895,73535,73536,73538,73540],{},[898,73537,1665],{},[1656,73539,1713],{},[1667,73541,73398],{},[902,73543,73473],{"encoding":904},[883,73545,73547],{"className":73546},[886],[888,73548,73549],{"xmlns":890},[892,73550,73551,73562],{},[895,73552,73553,73555,73557,73559],{},[898,73554,8194],{},[898,73556,1763],{},[1656,73558,1713],{},[1667,73560,73561],{},"6,125",[902,73563,73564],{"encoding":904},"PR = 6{,}125"," (odpovídající derivaci ",[883,73567,73569],{"className":73568},[886],[888,73570,73571],{"xmlns":890},[892,73572,73573,73595],{},[895,73574,73575,73577,73583,73585,73587,73589,73591,73593],{},[898,73576,8194],{},[2062,73578,73579,73581],{},[898,73580,1763],{},[1656,73582,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,73584,1713],{},[1656,73586,3964],{},[1667,73588,2673],{},[898,73590,1665],{},[1656,73592,3633],{},[1667,73594,2698],{},[902,73596,73597],{"encoding":904},"PR' = -4Q + 9",", tj. zisku ",[883,73600,73602],{"className":73601},[886],[888,73603,73604],{"xmlns":890},[892,73605,73606,73634],{},[895,73607,73608,73610,73612,73614,73616,73618,73624,73626,73628,73630,73632],{},[898,73609,8194],{},[898,73611,1763],{},[1656,73613,1713],{},[1656,73615,3964],{},[1667,73617,1680],{},[2062,73619,73620,73622],{},[898,73621,1665],{},[1667,73623,1680],{},[1656,73625,3633],{},[1667,73627,2698],{},[898,73629,1665],{},[1656,73631,3964],{},[1667,73633,2673],{},[902,73635,73636],{"encoding":904},"PR = -2Q^2 + 9Q - 4"," bez odčtení kvadratického členu ",[883,73639,73641],{"className":73640},[886],[888,73642,73643],{"xmlns":890},[892,73644,73645,73653],{},[895,73646,73647],{},[2062,73648,73649,73651],{},[898,73650,1665],{},[1667,73652,1680],{},[902,73654,73655],{"encoding":904},"Q^2",[883,73657,73659],{"className":73658},[886],[888,73660,73661],{"xmlns":890},[892,73662,73663,73671],{},[895,73664,73665,73667,73669],{},[898,73666,11577],{},[898,73668,49019],{},[898,73670,1766],{},[902,73672,64178],{"encoding":904},"). Zde je uvedena matematicky konzistentní verze: zadané ",[883,73675,73677],{"className":73676},[886],[888,73678,73679],{"xmlns":890},[892,73680,73681,73699],{},[895,73682,73683,73685,73687,73689,73691,73693],{},[898,73684,11577],{},[898,73686,1766],{},[1656,73688,1713],{},[1667,73690,2673],{},[1656,73692,3633],{},[2062,73694,73695,73697],{},[898,73696,1665],{},[1667,73698,1680],{},[902,73700,73701],{"encoding":904},"TC = 4 + Q^2",[883,73703,73705],{"className":73704},[886],[888,73706,73707],{"xmlns":890},[892,73708,73709,73733],{},[895,73710,73711,73713,73715,73717,73719,73721,73727,73729,73731],{},[898,73712,11577],{},[898,73714,1763],{},[1656,73716,1713],{},[1656,73718,3964],{},[1667,73720,1680],{},[2062,73722,73723,73725],{},[898,73724,1665],{},[1667,73726,1680],{},[1656,73728,3633],{},[1667,73730,2698],{},[898,73732,1665],{},[902,73734,73735],{"encoding":904},"TR = -2Q^2 + 9Q"," vedou na ",[883,73738,73740],{"className":73739},[886],[888,73741,73742],{"xmlns":890},[892,73743,73744,73772],{},[895,73745,73746,73748,73750,73752,73754,73756,73762,73764,73766,73768,73770],{},[898,73747,8194],{},[898,73749,1763],{},[1656,73751,1713],{},[1656,73753,3964],{},[1667,73755,2617],{},[2062,73757,73758,73760],{},[898,73759,1665],{},[1667,73761,1680],{},[1656,73763,3633],{},[1667,73765,2698],{},[898,73767,1665],{},[1656,73769,3964],{},[1667,73771,2673],{},[902,73773,73774],{"encoding":904},"PR = -3Q^2 + 9Q - 4",[883,73776,73778],{"className":73777},[886],[888,73779,73780],{"xmlns":890},[892,73781,73782,73796],{},[895,73783,73784,73792,73794],{},[1661,73785,73786,73788,73790],{},[898,73787,1665],{},[898,73789,64866],{},[1656,73791,2093],{},[1656,73793,1713],{},[1667,73795,8845],{},[902,73797,73798],{"encoding":904},"Q_{\\max} = 1{,}5",[883,73800,73802],{"className":73801},[886],[888,73803,73804],{"xmlns":890},[892,73805,73806,73823],{},[895,73807,73808,73810,73818,73820],{},[898,73809,8194],{},[1661,73811,73812,73814,73816],{},[898,73813,1763],{},[898,73815,64866],{},[1656,73817,2093],{},[1656,73819,1713],{},[1667,73821,73822],{},"2,75",[902,73824,73825],{"encoding":904},"PR_{\\max} = 2{,}75",[724,73827,73828],{},[614,73829,73830,73831,73858,73859,73892,73893,1343,73916,1863],{},"Obrázek 3.12: Graf ",[883,73832,73834],{"className":73833},[886],[888,73835,73836],{"xmlns":890},[892,73837,73838,73856],{},[895,73839,73840,73842,73844,73846,73848,73850],{},[898,73841,11577],{},[898,73843,1766],{},[1656,73845,1713],{},[1667,73847,2673],{},[1656,73849,3633],{},[2062,73851,73852,73854],{},[898,73853,1665],{},[1667,73855,1680],{},[902,73857,73701],{"encoding":904}," (parabola) a ",[883,73860,73862],{"className":73861},[886],[888,73863,73864],{"xmlns":890},[892,73865,73866,73890],{},[895,73867,73868,73870,73872,73874,73876,73878,73884,73886,73888],{},[898,73869,11577],{},[898,73871,1763],{},[1656,73873,1713],{},[1656,73875,3964],{},[1667,73877,1680],{},[2062,73879,73880,73882],{},[898,73881,1665],{},[1667,73883,1680],{},[1656,73885,3633],{},[1667,73887,2698],{},[898,73889,1665],{},[902,73891,73735],{"encoding":904}," (parabola); průsečíky vyznačují body zvratu ",[883,73894,73896],{"className":73895},[886],[888,73897,73898],{"xmlns":890},[892,73899,73900,73913],{},[895,73901,73902,73908,73910],{},[1661,73903,73904,73906],{},[898,73905,1665],{},[1667,73907,1669],{},[1656,73909,2829],{},[1667,73911,73912],{},"0,54",[902,73914,73915],{"encoding":904},"Q_1 \\doteq 0{,}54",[883,73917,73919],{"className":73918},[886],[888,73920,73921],{"xmlns":890},[892,73922,73923,73936],{},[895,73924,73925,73931,73933],{},[1661,73926,73927,73929],{},[898,73928,1665],{},[1667,73930,1680],{},[1656,73932,2829],{},[1667,73934,73935],{},"2,46",[902,73937,73938],{"encoding":904},"Q_2 \\doteq 2{,}46",[724,73940,73941],{},[614,73942,73943,73944,67175,73981,73998,73999,1343,74020,1863],{},"Obrázek 3.13: Graf zisku ",[883,73945,73947],{"className":73946},[886],[888,73948,73949],{"xmlns":890},[892,73950,73951,73979],{},[895,73952,73953,73955,73957,73959,73961,73963,73969,73971,73973,73975,73977],{},[898,73954,8194],{},[898,73956,1763],{},[1656,73958,1713],{},[1656,73960,3964],{},[1667,73962,2617],{},[2062,73964,73965,73967],{},[898,73966,1665],{},[1667,73968,1680],{},[1656,73970,3633],{},[1667,73972,2698],{},[898,73974,1665],{},[1656,73976,3964],{},[1667,73978,2673],{},[902,73980,73774],{"encoding":904},[883,73982,73984],{"className":73983},[886],[888,73985,73986],{"xmlns":890},[892,73987,73988,73996],{},[895,73989,73990,73992,73994],{},[898,73991,1665],{},[1656,73993,1713],{},[1667,73995,8845],{},[902,73997,73279],{"encoding":904}," a nulami ",[883,74000,74002],{"className":74001},[886],[888,74003,74004],{"xmlns":890},[892,74005,74006,74018],{},[895,74007,74008,74014,74016],{},[1661,74009,74010,74012],{},[898,74011,1665],{},[1667,74013,1669],{},[1656,74015,2829],{},[1667,74017,73912],{},[902,74019,73915],{"encoding":904},[883,74021,74023],{"className":74022},[886],[888,74024,74025],{"xmlns":890},[892,74026,74027,74039],{},[895,74028,74029,74035,74037],{},[1661,74030,74031,74033],{},[898,74032,1665],{},[1667,74034,1680],{},[1656,74036,2829],{},[1667,74038,73935],{},[902,74040,73938],{"encoding":904},[115,74042,74044],{"id":74043},"princip-maximalizace-zisku","Princip maximalizace zisku",[724,74046,74047],{},"Kromě standardního hledání extrému lze využít následující princip.",[724,74049,74050],{},[5956,74051],{"alt":74052,"className":74053,"src":74054},"imek-max-zisku-dva-pohledy",[210,5960],"\u002Fwiki-assets\u002Fimek-max-zisku-dva-pohledy.jpeg",[198,74056,25138],{"id":74057},"princip-1",[724,74059,74060,74061,3565,74076,74093],{},"Má-li zisk ",[883,74062,74064],{"className":74063},[886],[888,74065,74066],{"xmlns":890},[892,74067,74068,74074],{},[895,74069,74070,74072],{},[898,74071,8194],{},[898,74073,1763],{},[902,74075,72145],{"encoding":904},[883,74077,74079],{"className":74078},[886],[888,74080,74081],{"xmlns":890},[892,74082,74083,74091],{},[895,74084,74085],{},[1661,74086,74087,74089],{},[898,74088,1665],{},[1667,74090,4032],{},[902,74092,46990],{"encoding":904}," maximum, pak platí",[883,74095,74097],{"className":74096},[886],[888,74098,74099],{"xmlns":890,"display":2408},[892,74100,74101,74150],{},[2412,74102,74103],{"width":2414},[2416,74104,74105,74107,74143,74145],{},[2419,74106],{"width":2421},[2419,74108,74109],{},[895,74110,74111,74113,74115,74117,74123,74125,74127,74129,74131,74133,74139,74141],{},[898,74112,1703],{},[898,74114,1763],{},[1656,74116,1659],{"stretchy":1658},[1661,74118,74119,74121],{},[898,74120,1665],{},[1667,74122,4032],{},[1656,74124,1683],{"stretchy":1658},[1656,74126,1713],{},[898,74128,1703],{},[898,74130,1766],{},[1656,74132,1659],{"stretchy":1658},[1661,74134,74135,74137],{},[898,74136,1665],{},[1667,74138,4032],{},[1656,74140,1683],{"stretchy":1658},[898,74142,1863],{"mathvariant":1723},[2419,74144],{"width":2421},[2419,74146,74147],{},[2461,74148,74149],{},"(3.13)",[902,74151,74152],{"encoding":904},"MR(Q_0) = MC(Q_0).\n\\tag{3.13}",[1981,74154,74155],{},[724,74156,74157,70713,74159],{},[883,74158,65112],{},[38,74160,74161],{},"V bodě maxima zisku se mezní příjem rovná mezním nákladům.",[724,74163,74164,74167,74168,3206,74195,26301,74269,1863],{},[38,74165,74166],{},"Odvození"," (úloha 3.21): nutnou podmínkou maxima ",[883,74169,74171],{"className":74170},[886],[888,74172,74173],{"xmlns":890},[892,74174,74175,74193],{},[895,74176,74177,74179,74181,74183,74185,74187,74189,74191],{},[898,74178,8194],{},[898,74180,1763],{},[1656,74182,1713],{},[898,74184,11577],{},[898,74186,1763],{},[1656,74188,3964],{},[898,74190,11577],{},[898,74192,1766],{},[902,74194,63869],{"encoding":904},[883,74196,74198],{"className":74197},[886],[888,74199,74200],{"xmlns":890},[892,74201,74202,74266],{},[895,74203,74204,74206,74212,74214,74220,74222,74224,74226,74232,74234,74240,74242,74244,74246,74252,74254,74260,74262,74264],{},[898,74205,8194],{},[2062,74207,74208,74210],{},[898,74209,1763],{},[1656,74211,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,74213,1659],{"stretchy":1658},[1661,74215,74216,74218],{},[898,74217,1665],{},[1667,74219,4032],{},[1656,74221,1683],{"stretchy":1658},[1656,74223,1713],{},[898,74225,11577],{},[2062,74227,74228,74230],{},[898,74229,1763],{},[1656,74231,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,74233,1659],{"stretchy":1658},[1661,74235,74236,74238],{},[898,74237,1665],{},[1667,74239,4032],{},[1656,74241,1683],{"stretchy":1658},[1656,74243,3964],{},[898,74245,11577],{},[2062,74247,74248,74250],{},[898,74249,1766],{},[1656,74251,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,74253,1659],{"stretchy":1658},[1661,74255,74256,74258],{},[898,74257,1665],{},[1667,74259,4032],{},[1656,74261,1683],{"stretchy":1658},[1656,74263,1713],{},[1667,74265,4032],{},[902,74267,74268],{"encoding":904},"PR'(Q_0) = TR'(Q_0) - TC'(Q_0) = 0",[883,74270,74272],{"className":74271},[886],[888,74273,74274],{"xmlns":890},[892,74275,74276,74308],{},[895,74277,74278,74280,74282,74284,74290,74292,74294,74296,74298,74300,74306],{},[898,74279,1703],{},[898,74281,1763],{},[1656,74283,1659],{"stretchy":1658},[1661,74285,74286,74288],{},[898,74287,1665],{},[1667,74289,4032],{},[1656,74291,1683],{"stretchy":1658},[1656,74293,1713],{},[898,74295,1703],{},[898,74297,1766],{},[1656,74299,1659],{"stretchy":1658},[1661,74301,74302,74304],{},[898,74303,1665],{},[1667,74305,4032],{},[1656,74307,1683],{"stretchy":1658},[902,74309,74310],{"encoding":904},"MR(Q_0) = MC(Q_0)",[1981,74312,74313,74318],{},[724,74314,74315,74317],{},[883,74316,10188],{}," Postup — jak najít maximum zisku",[152,74319,74320,74384,74439,74476,74504],{},[123,74321,74322,74323,1896,74338,74353,74354,12702],{},"Sestavte ",[883,74324,74326],{"className":74325},[886],[888,74327,74328],{"xmlns":890},[892,74329,74330,74336],{},[895,74331,74332,74334],{},[898,74333,11577],{},[898,74335,1763],{},[902,74337,12875],{"encoding":904},[883,74339,74341],{"className":74340},[886],[888,74342,74343],{"xmlns":890},[892,74344,74345,74351],{},[895,74346,74347,74349],{},[898,74348,11577],{},[898,74350,1766],{},[902,74352,12033],{"encoding":904}," ze zadání (typicky ",[883,74355,74357],{"className":74356},[886],[888,74358,74359],{"xmlns":890},[892,74360,74361,74381],{},[895,74362,74363,74365,74367,74369,74371,74373,74375,74377,74379],{},[898,74364,11577],{},[898,74366,1763],{},[1656,74368,1713],{},[898,74370,8194],{},[1656,74372,1659],{"stretchy":1658},[898,74374,1665],{},[1656,74376,1683],{"stretchy":1658},[1656,74378,2751],{},[898,74380,1665],{},[902,74382,74383],{"encoding":904},"TR = P(Q) \\cdot Q",[123,74385,74386,74387,1896,74413,1863],{},"Vypočtěte ",[883,74388,74390],{"className":74389},[886],[888,74391,74392],{"xmlns":890},[892,74393,74394,74410],{},[895,74395,74396,74398,74400,74402,74404],{},[898,74397,1703],{},[898,74399,1763],{},[1656,74401,1713],{},[898,74403,11577],{},[2062,74405,74406,74408],{},[898,74407,1763],{},[1656,74409,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[902,74411,74412],{"encoding":904},"MR = TR'",[883,74414,74416],{"className":74415},[886],[888,74417,74418],{"xmlns":890},[892,74419,74420,74436],{},[895,74421,74422,74424,74426,74428,74430],{},[898,74423,1703],{},[898,74425,1766],{},[1656,74427,1713],{},[898,74429,11577],{},[2062,74431,74432,74434],{},[898,74433,1766],{},[1656,74435,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[902,74437,74438],{"encoding":904},"MC = TC'",[123,74440,74441,74442,1863],{},"Řešte rovnici ",[883,74443,74445],{"className":74444},[886],[888,74446,74447],{"xmlns":890},[892,74448,74449,74473],{},[895,74450,74451,74453,74455,74457,74459,74461,74463,74465,74467,74469,74471],{},[898,74452,1703],{},[898,74454,1763],{},[1656,74456,1659],{"stretchy":1658},[898,74458,1665],{},[1656,74460,1683],{"stretchy":1658},[1656,74462,1713],{},[898,74464,1703],{},[898,74466,1766],{},[1656,74468,1659],{"stretchy":1658},[898,74470,1665],{},[1656,74472,1683],{"stretchy":1658},[902,74474,74475],{"encoding":904},"MR(Q) = MC(Q)",[123,74477,74478,74479,74503],{},"Ověřte druhou derivaci ",[883,74480,74482],{"className":74481},[886],[888,74483,74484],{"xmlns":890},[892,74485,74486,74500],{},[895,74487,74488,74490],{},[898,74489,8194],{},[2062,74491,74492,74494],{},[898,74493,1763],{},[895,74495,74496,74498],{},[1656,74497,1725],{"mathvariant":1723},[1656,74499,1725],{"mathvariant":1723},[902,74501,74502],{"encoding":904},"PR''"," (nebo že má rovnice jediný ekonomicky smysluplný kořen).",[123,74505,74506,74507,74534],{},"Dosaďte do ",[883,74508,74510],{"className":74509},[886],[888,74511,74512],{"xmlns":890},[892,74513,74514,74532],{},[895,74515,74516,74518,74520,74522,74524,74526,74528,74530],{},[898,74517,8194],{},[898,74519,1763],{},[1656,74521,1713],{},[898,74523,11577],{},[898,74525,1763],{},[1656,74527,3964],{},[898,74529,11577],{},[898,74531,1766],{},[902,74533,63869],{"encoding":904}," pro hodnotu maxima.",[46030,74536,74538],{"id":74537},"příklad-39","Příklad 3.9",[724,74540,74541,64657,74543,1896,74565,74601],{},[38,74542,64656],{},[883,74544,74546],{"className":74545},[886],[888,74547,74548],{"xmlns":890},[892,74549,74550,74562],{},[895,74551,74552,74554,74556,74558,74560],{},[898,74553,8194],{},[1656,74555,1713],{},[1667,74557,46701],{},[1656,74559,3964],{},[898,74561,1665],{},[902,74563,74564],{"encoding":904},"P = 30 - Q",[883,74566,74568],{"className":74567},[886],[888,74569,74570],{"xmlns":890},[892,74571,74572,74598],{},[895,74573,74574,74576,74578,74580,74582,74588,74590,74592,74594,74596],{},[898,74575,11577],{},[898,74577,1766],{},[1656,74579,1713],{},[1667,74581,13779],{},[2062,74583,74584,74586],{},[898,74585,1665],{},[1667,74587,1680],{},[1656,74589,3633],{},[1667,74591,9112],{},[898,74593,1665],{},[1656,74595,3633],{},[1667,74597,6240],{},[902,74599,74600],{"encoding":904},"TC = 0{,}5Q^2 + 6Q + 7"," stanovte produkci maximalizující zisk.",[724,74603,74604,1643,74606,1343,74636,74674,74675,24520,74719,74753,74754,1863],{},[38,74605,31488],{},[883,74607,74609],{"className":74608},[886],[888,74610,74611],{"xmlns":890},[892,74612,74613,74633],{},[895,74614,74615,74617,74619,74621,74623,74625,74627],{},[898,74616,11577],{},[898,74618,1763],{},[1656,74620,1713],{},[1667,74622,46701],{},[898,74624,1665],{},[1656,74626,3964],{},[2062,74628,74629,74631],{},[898,74630,1665],{},[1667,74632,1680],{},[902,74634,74635],{"encoding":904},"TR = 30Q - Q^2",[883,74637,74639],{"className":74638},[886],[888,74640,74641],{"xmlns":890},[892,74642,74643,74671],{},[895,74644,74645,74647,74649,74651,74653,74655,74661,74663,74665,74667,74669],{},[898,74646,8194],{},[898,74648,1763],{},[1656,74650,1713],{},[1656,74652,3964],{},[1667,74654,8845],{},[2062,74656,74657,74659],{},[898,74658,1665],{},[1667,74660,1680],{},[1656,74662,3633],{},[1667,74664,50480],{},[898,74666,1665],{},[1656,74668,3964],{},[1667,74670,6240],{},[902,74672,74673],{"encoding":904},"PR = -1{,}5Q^2 + 24Q - 7",". Extrém: ",[883,74676,74678],{"className":74677},[886],[888,74679,74680],{"xmlns":890},[892,74681,74682,74716],{},[895,74683,74684,74686,74692,74694,74696,74698,74700,74702,74704,74706,74708,74710,74712,74714],{},[898,74685,8194],{},[2062,74687,74688,74690],{},[898,74689,1763],{},[1656,74691,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,74693,1713],{},[1656,74695,3964],{},[1667,74697,2617],{},[898,74699,1665],{},[1656,74701,3633],{},[1667,74703,50480],{},[1656,74705,1713],{},[1667,74707,4032],{},[1656,74709,12770],{},[898,74711,1665],{},[1656,74713,1713],{},[1667,74715,2877],{},[902,74717,74718],{"encoding":904},"PR' = -3Q + 24 = 0 \\Rightarrow Q = 8",[883,74720,74722],{"className":74721},[886],[888,74723,74724],{"xmlns":890},[892,74725,74726,74750],{},[895,74727,74728,74730,74740,74742,74744,74746,74748],{},[898,74729,8194],{},[2062,74731,74732,74734],{},[898,74733,1763],{},[895,74735,74736,74738],{},[1656,74737,1725],{"mathvariant":1723},[1656,74739,1725],{"mathvariant":1723},[1656,74741,1713],{},[1656,74743,3964],{},[1667,74745,2617],{},[1656,74747,4373],{},[1667,74749,4032],{},[902,74751,74752],{"encoding":904},"PR'' = -3 \u003C 0"," (maximum); ",[883,74755,74757],{"className":74756},[886],[888,74758,74759],{"xmlns":890},[892,74760,74761,74778],{},[895,74762,74763,74765,74767,74769,74771,74773,74775],{},[898,74764,8194],{},[898,74766,1763],{},[1656,74768,1659],{"stretchy":1658},[1667,74770,2877],{},[1656,74772,1683],{"stretchy":1658},[1656,74774,1713],{},[1667,74776,74777],{},"89",[902,74779,74780],{"encoding":904},"PR(8) = 89",[724,74782,74783,74784,1343,74810,24520,74834,74872],{},"Ověření principu: ",[883,74785,74787],{"className":74786},[886],[888,74788,74789],{"xmlns":890},[892,74790,74791,74807],{},[895,74792,74793,74795,74797,74799,74801,74803,74805],{},[898,74794,1703],{},[898,74796,1763],{},[1656,74798,1713],{},[1667,74800,46701],{},[1656,74802,3964],{},[1667,74804,1680],{},[898,74806,1665],{},[902,74808,74809],{"encoding":904},"MR = 30 - 2Q",[883,74811,74813],{"className":74812},[886],[888,74814,74815],{"xmlns":890},[892,74816,74817,74831],{},[895,74818,74819,74821,74823,74825,74827,74829],{},[898,74820,1703],{},[898,74822,1766],{},[1656,74824,1713],{},[898,74826,1665],{},[1656,74828,3633],{},[1667,74830,9112],{},[902,74832,74833],{"encoding":904},"MC = Q + 6",[883,74835,74837],{"className":74836},[886],[888,74838,74839],{"xmlns":890},[892,74840,74841,74869],{},[895,74842,74843,74845,74847,74849,74851,74853,74855,74857,74859,74861,74863,74865,74867],{},[898,74844,1703],{},[898,74846,1763],{},[1656,74848,1659],{"stretchy":1658},[1667,74850,2877],{},[1656,74852,1683],{"stretchy":1658},[1656,74854,1713],{},[1667,74856,31664],{},[1656,74858,1713],{},[898,74860,1703],{},[898,74862,1766],{},[1656,74864,1659],{"stretchy":1658},[1667,74866,2877],{},[1656,74868,1683],{"stretchy":1658},[902,74870,74871],{"encoding":904},"MR(8) = 14 = MC(8)",", tj. platí (3.13).",[724,74874,74875,74876,74909,74910,74927],{},"V řadě případů — má-li rovnice ",[883,74877,74879],{"className":74878},[886],[888,74880,74881],{"xmlns":890},[892,74882,74883,74907],{},[895,74884,74885,74887,74889,74891,74893,74895,74897,74899,74901,74903,74905],{},[898,74886,1703],{},[898,74888,1763],{},[1656,74890,1659],{"stretchy":1658},[898,74892,1665],{},[1656,74894,1683],{"stretchy":1658},[1656,74896,1713],{},[898,74898,1703],{},[898,74900,1766],{},[1656,74902,1659],{"stretchy":1658},[898,74904,1665],{},[1656,74906,1683],{"stretchy":1658},[902,74908,74475],{"encoding":904}," jediné ekonomicky smysluplné řešení ",[883,74911,74913],{"className":74912},[886],[888,74914,74915],{"xmlns":890},[892,74916,74917,74925],{},[895,74918,74919],{},[1661,74920,74921,74923],{},[898,74922,1665],{},[1667,74924,4032],{},[902,74926,46990],{"encoding":904}," — není třeba provádět test druhé derivace.",[46030,74929,74931],{"id":74930},"příklad-310","Příklad 3.10",[724,74933,74934,74936,74937,74941,74942,74955,74956,74987],{},[38,74935,64656],{}," Firma vyrábí minipočítače v ",[207,74938,74940],{"className":74939,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurenci",", produkuje 30 výrobků denně za ",[883,74943,74945],{"className":74944},[886],[888,74946,74947],{"xmlns":890},[892,74948,74949,74953],{},[895,74950,74951],{},[1667,74952,23922],{},[902,74954,23922],{"encoding":904}," EUR\u002Fks. ",[883,74957,74959],{"className":74958},[886],[888,74960,74961],{"xmlns":890},[892,74962,74963,74984],{},[895,74964,74965,74967,74969,74971,74973,74975,74978],{},[898,74966,11577],{},[898,74968,1766],{},[1656,74970,1713],{},[1667,74972,9267],{},[1656,74974,3633],{},[1667,74976,74977],{},"28",[2062,74979,74980,74982],{},[898,74981,1665],{},[1667,74983,1680],{},[902,74985,74986],{"encoding":904},"TC = 50 + 28Q^2",". Určete optimální denní produkci a zisk.",[724,74989,74990,1643,74992,1343,75014,1343,75034,75057],{},[38,74991,31488],{},[883,74993,74995],{"className":74994},[886],[888,74996,74997],{"xmlns":890},[892,74998,74999,75011],{},[895,75000,75001,75003,75005,75007,75009],{},[898,75002,11577],{},[898,75004,1763],{},[1656,75006,1713],{},[1667,75008,23922],{},[898,75010,1665],{},[902,75012,75013],{"encoding":904},"TR = 900Q",[883,75015,75017],{"className":75016},[886],[888,75018,75019],{"xmlns":890},[892,75020,75021,75031],{},[895,75022,75023,75025,75027,75029],{},[898,75024,1703],{},[898,75026,1763],{},[1656,75028,1713],{},[1667,75030,23922],{},[902,75032,75033],{"encoding":904},"MR = 900",[883,75035,75037],{"className":75036},[886],[888,75038,75039],{"xmlns":890},[892,75040,75041,75054],{},[895,75042,75043,75045,75047,75049,75052],{},[898,75044,1703],{},[898,75046,1766],{},[1656,75048,1713],{},[1667,75050,75051],{},"56",[898,75053,1665],{},[902,75055,75056],{"encoding":904},"MC = 56Q",". Z principu:",[883,75059,75061],{"className":75060},[886],[888,75062,75063],{"xmlns":890,"display":2408},[892,75064,75065,75107],{},[895,75066,75067,75069,75071,75073,75075,75077,75079,75081,75083,75085,75093,75095,75098,75100,75102,75104],{},[1667,75068,23922],{},[1656,75070,1713],{},[1667,75072,75051],{},[898,75074,1665],{},[2461,75076,12767],{},[1656,75078,12770],{},[2461,75080,12767],{},[898,75082,1665],{},[1656,75084,1713],{},[4138,75086,75087],{"scriptlevel":4032,"displaystyle":1658},[3294,75088,75089,75091],{},[1667,75090,23922],{},[1667,75092,75051],{},[1656,75094,2829],{},[1667,75096,75097],{},"16,07",[2461,75099,12767],{},[1656,75101,3815],{},[2461,75103,12767],{},[1667,75105,75106],{},"16.",[902,75108,75109],{"encoding":904},"900 = 56Q \\;\\Rightarrow\\; Q = \\tfrac{900}{56} \\doteq 16{,}07 \\;\\approx\\; 16.",[724,75111,75112,75113,2114],{},"Zisk při ",[883,75114,75116],{"className":75115},[886],[888,75117,75118],{"xmlns":890},[892,75119,75120,75128],{},[895,75121,75122,75124,75126],{},[898,75123,1665],{},[1656,75125,1713],{},[1667,75127,2668],{},[902,75129,75130],{"encoding":904},"Q = 16",[883,75132,75134],{"className":75133},[886],[888,75135,75136],{"xmlns":890,"display":2408},[892,75137,75138,75209],{},[895,75139,75140,75142,75144,75146,75148,75150,75152,75154,75156,75158,75160,75162,75164,75166,75168,75170,75176,75178,75180,75182,75184,75186,75188,75190,75192,75195,75197,75199,75201,75204,75207],{},[898,75141,8194],{},[898,75143,1763],{},[1656,75145,1659],{"stretchy":1658},[1667,75147,2668],{},[1656,75149,1683],{"stretchy":1658},[1656,75151,1713],{},[1667,75153,23922],{},[1656,75155,2751],{},[1667,75157,2668],{},[1656,75159,3964],{},[1656,75161,1659],{"stretchy":1658},[1667,75163,9267],{},[1656,75165,3633],{},[1667,75167,74977],{},[1656,75169,2751],{},[2062,75171,75172,75174],{},[1667,75173,2668],{},[1667,75175,1680],{},[1656,75177,1683],{"stretchy":1658},[1656,75179,1713],{},[1667,75181,31664],{},[2461,75183,7828],{},[1667,75185,28863],{},[1656,75187,3964],{},[1667,75189,6240],{},[2461,75191,7828],{},[1667,75193,75194],{},"218",[1656,75196,1713],{},[1667,75198,6240],{},[2461,75200,7828],{},[1667,75202,75203],{},"182",[2461,75205,75206],{}," EUR",[898,75208,1863],{"mathvariant":1723},[902,75210,75211],{"encoding":904},"PR(16) = 900 \\cdot 16 - (50 + 28 \\cdot 16^2) = 14\\,400 - 7\\,218 = 7\\,182 \\text{ EUR}.",[724,75213,75214],{},"Pro srovnání při původních 30 ks:",[883,75216,75218],{"className":75217},[886],[888,75219,75220],{"xmlns":890,"display":2408},[892,75221,75222,75286],{},[895,75223,75224,75226,75228,75230,75232,75234,75236,75238,75240,75242,75244,75246,75248,75250,75252,75254,75256,75258,75260,75262,75264,75266,75268,75270,75272,75274,75276,75278,75280,75282,75284],{},[898,75225,8194],{},[898,75227,1763],{},[1656,75229,1659],{"stretchy":1658},[1667,75231,46701],{},[1656,75233,1683],{"stretchy":1658},[1656,75235,1713],{},[1667,75237,23922],{},[1656,75239,2751],{},[1667,75241,46701],{},[1656,75243,3964],{},[1656,75245,1659],{"stretchy":1658},[1667,75247,9267],{},[1656,75249,3633],{},[1667,75251,74977],{},[1656,75253,2751],{},[1667,75255,23922],{},[1656,75257,1683],{"stretchy":1658},[1656,75259,1713],{},[1667,75261,2707],{},[2461,75263,7828],{},[1667,75265,67750],{},[1656,75267,3964],{},[1667,75269,8567],{},[2461,75271,7828],{},[1667,75273,39433],{},[1656,75275,1713],{},[1667,75277,1669],{},[2461,75279,7828],{},[1667,75281,32460],{},[2461,75283,75206],{},[898,75285,1863],{"mathvariant":1723},[902,75287,75288],{"encoding":904},"PR(30) = 900 \\cdot 30 - (50 + 28 \\cdot 900) = 27\\,000 - 25\\,250 = 1\\,750 \\text{ EUR}.",[724,75290,75291,75294,75295,75313,75314,75332],{},[38,75292,75293],{},"Doporučení:"," vyrábět 16 ks\u002Fden se ziskem ",[883,75296,75298],{"className":75297},[886],[888,75299,75300],{"xmlns":890},[892,75301,75302,75310],{},[895,75303,75304,75306,75308],{},[1667,75305,6240],{},[2461,75307,7828],{},[1667,75309,75203],{},[902,75311,75312],{"encoding":904},"7\\,182"," EUR namísto původních ",[883,75315,75317],{"className":75316},[886],[888,75318,75319],{"xmlns":890},[892,75320,75321,75329],{},[895,75322,75323,75325,75327],{},[1667,75324,1669],{},[2461,75326,7828],{},[1667,75328,32460],{},[902,75330,75331],{"encoding":904},"1\\,750"," EUR.",[198,75334,75336],{"id":75335},"speciální-tvar-pro-pevnou-cenu","Speciální tvar pro pevnou cenu",[724,75338,75339,75340,2233,75353,75377],{},"Předpokládáme-li, že výrobce prodává za pevnou cenu ",[883,75341,75343],{"className":75342},[886],[888,75344,75345],{"xmlns":890},[892,75346,75347,75351],{},[895,75348,75349],{},[898,75350,8194],{},[902,75352,8194],{"encoding":904},[883,75354,75356],{"className":75355},[886],[888,75357,75358],{"xmlns":890},[892,75359,75360,75374],{},[895,75361,75362,75364,75366,75368,75370,75372],{},[898,75363,11577],{},[898,75365,1763],{},[1656,75367,1713],{},[898,75369,8194],{},[1656,75371,2751],{},[898,75373,1665],{},[902,75375,75376],{"encoding":904},"TR = P \\cdot Q"," a z (3.13) speciálně:",[883,75379,75381],{"className":75380},[886],[888,75382,75383],{"xmlns":890,"display":2408},[892,75384,75385,75418],{},[2412,75386,75387],{"width":2414},[2416,75388,75389,75391,75411,75413],{},[2419,75390],{"width":2421},[2419,75392,75393],{},[895,75394,75395,75397,75399,75401,75403,75405,75407,75409],{},[898,75396,8194],{},[1656,75398,1713],{},[898,75400,1703],{},[898,75402,1766],{},[1656,75404,1659],{"stretchy":1658},[898,75406,1665],{},[1656,75408,1683],{"stretchy":1658},[898,75410,1863],{"mathvariant":1723},[2419,75412],{"width":2421},[2419,75414,75415],{},[2461,75416,75417],{},"(3.14)",[902,75419,75420],{"encoding":904},"P = MC(Q).\n\\tag{3.14}",[724,75422,75423,75424,1863],{},"Výrobce musí nastavit nabízené množství tak, aby se mezní náklady rovnaly ceně. Má-li rovnice (3.14) více řešení, rozhoduje znaménko ",[883,75425,75427],{"className":75426},[886],[888,75428,75429],{"xmlns":890},[892,75430,75431,75445],{},[895,75432,75433,75435],{},[898,75434,8194],{},[2062,75436,75437,75439],{},[898,75438,1763],{},[895,75440,75441,75443],{},[1656,75442,1725],{"mathvariant":1723},[1656,75444,1725],{"mathvariant":1723},[902,75446,74502],{"encoding":904},[46030,75448,75450],{"id":75449},"příklad-311","Příklad 3.11",[724,75452,75453,66190,75455,75502,75503,75521],{},[38,75454,64656],{},[883,75456,75458],{"className":75457},[886],[888,75459,75460],{"xmlns":890},[892,75461,75462,75499],{},[895,75463,75464,75466,75468,75470,75473,75479,75481,75483,75489,75491,75493,75495,75497],{},[898,75465,11577],{},[898,75467,1766],{},[1656,75469,1713],{},[1667,75471,75472],{},"0,04",[2062,75474,75475,75477],{},[898,75476,1665],{},[1667,75478,2617],{},[1656,75480,3964],{},[1667,75482,31263],{},[2062,75484,75485,75487],{},[898,75486,1665],{},[1667,75488,1680],{},[1656,75490,3633],{},[1667,75492,8580],{},[898,75494,1665],{},[1656,75496,3633],{},[1667,75498,5193],{},[902,75500,75501],{"encoding":904},"TC = 0{,}04Q^3 - 0{,}9Q^2 + 10Q + 5"," a pevnou cenu ",[883,75504,75506],{"className":75505},[886],[888,75507,75508],{"xmlns":890},[892,75509,75510,75518],{},[895,75511,75512,75514,75516],{},[898,75513,8194],{},[1656,75515,1713],{},[1667,75517,2673],{},[902,75519,75520],{"encoding":904},"P = 4"," stanovte optimální produkci.",[724,75523,75524,75526,75527,26301,75569,75603,75604,2114],{},[38,75525,31488],{}," Z (3.14): ",[883,75528,75530],{"className":75529},[886],[888,75531,75532],{"xmlns":890},[892,75533,75534,75566],{},[895,75535,75536,75538,75540,75542,75545,75551,75553,75556,75558,75560,75562,75564],{},[898,75537,1703],{},[898,75539,1766],{},[1656,75541,1713],{},[1667,75543,75544],{},"0,12",[2062,75546,75547,75549],{},[898,75548,1665],{},[1667,75550,1680],{},[1656,75552,3964],{},[1667,75554,75555],{},"1,8",[898,75557,1665],{},[1656,75559,3633],{},[1667,75561,8580],{},[1656,75563,1713],{},[1667,75565,2673],{},[902,75567,75568],{"encoding":904},"MC = 0{,}12Q^2 - 1{,}8Q + 10 = 4",[883,75570,75572],{"className":75571},[886],[888,75573,75574],{"xmlns":890},[892,75575,75576,75600],{},[895,75577,75578,75580,75586,75588,75590,75592,75594,75596,75598],{},[1667,75579,75544],{},[2062,75581,75582,75584],{},[898,75583,1665],{},[1667,75585,1680],{},[1656,75587,3964],{},[1667,75589,75555],{},[898,75591,1665],{},[1656,75593,3633],{},[1667,75595,9112],{},[1656,75597,1713],{},[1667,75599,4032],{},[902,75601,75602],{"encoding":904},"0{,}12Q^2 - 1{,}8Q + 6 = 0",", po vydělení ",[883,75605,75607],{"className":75606},[886],[888,75608,75609],{"xmlns":890},[892,75610,75611,75615],{},[895,75612,75613],{},[1667,75614,75544],{},[902,75616,75617],{"encoding":904},"0{,}12",[883,75619,75621],{"className":75620},[886],[888,75622,75623],{"xmlns":890,"display":2408},[892,75624,75625,75677],{},[895,75626,75627,75633,75635,75637,75639,75641,75643,75645,75647,75649,75651,75653,75659,75661,75663,75665,75667,75673,75675],{},[2062,75628,75629,75631],{},[898,75630,1665],{},[1667,75632,1680],{},[1656,75634,3964],{},[1667,75636,44930],{},[898,75638,1665],{},[1656,75640,3633],{},[1667,75642,9267],{},[1656,75644,1713],{},[1667,75646,4032],{},[2461,75648,12767],{},[1656,75650,12770],{},[2461,75652,12767],{},[1661,75654,75655,75657],{},[898,75656,1665],{},[1667,75658,1669],{},[1656,75660,1713],{},[1667,75662,5193],{},[1656,75664,1673],{"separator":1672},[2461,75666,12767],{},[1661,75668,75669,75671],{},[898,75670,1665],{},[1667,75672,1680],{},[1656,75674,1713],{},[1667,75676,28049],{},[902,75678,75679],{"encoding":904},"Q^2 - 15Q + 50 = 0 \\;\\Rightarrow\\; Q_1 = 5, \\; Q_2 = 10.",[724,75681,75682,75683,2114],{},"Dále ",[883,75684,75686],{"className":75685},[886],[888,75687,75688],{"xmlns":890},[892,75689,75690,75729],{},[895,75691,75692,75694,75704,75706,75708,75710,75716,75718,75720,75723,75725,75727],{},[898,75693,8194],{},[2062,75695,75696,75698],{},[898,75697,1763],{},[895,75699,75700,75702],{},[1656,75701,1725],{"mathvariant":1723},[1656,75703,1725],{"mathvariant":1723},[1656,75705,1713],{},[1656,75707,3964],{},[898,75709,1703],{},[2062,75711,75712,75714],{},[898,75713,1766],{},[1656,75715,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,75717,1713],{},[1656,75719,3964],{},[1667,75721,75722],{},"0,24",[898,75724,1665],{},[1656,75726,3633],{},[1667,75728,75555],{},[902,75730,75731],{"encoding":904},"PR'' = -MC' = -0{,}24Q + 1{,}8",[120,75733,75734,75784],{},[123,75735,75736,75780,75781,75783],{},[883,75737,75739],{"className":75738},[886],[888,75740,75741],{"xmlns":890},[892,75742,75743,75777],{},[895,75744,75745,75747,75757,75759,75761,75763,75765,75767,75769,75771,75773,75775],{},[898,75746,8194],{},[2062,75748,75749,75751],{},[898,75750,1763],{},[895,75752,75753,75755],{},[1656,75754,1725],{"mathvariant":1723},[1656,75756,1725],{"mathvariant":1723},[1656,75758,1659],{"stretchy":1658},[1667,75760,5193],{},[1656,75762,1683],{"stretchy":1658},[1656,75764,1713],{},[1667,75766,28042],{},[1656,75768,2850],{},[1667,75770,4032],{},[2461,75772,12767],{},[1656,75774,12770],{},[2461,75776,12767],{},[902,75778,75779],{"encoding":904},"PR''(5) = 0{,}6 > 0 \\;\\Rightarrow\\;"," lokální ",[38,75782,12562],{}," zisku (minimalizace ztráty);",[123,75785,75786,75780,75832,75834],{},[883,75787,75789],{"className":75788},[886],[888,75790,75791],{"xmlns":890},[892,75792,75793,75829],{},[895,75794,75795,75797,75807,75809,75811,75813,75815,75817,75819,75821,75823,75825,75827],{},[898,75796,8194],{},[2062,75798,75799,75801],{},[898,75800,1763],{},[895,75802,75803,75805],{},[1656,75804,1725],{"mathvariant":1723},[1656,75806,1725],{"mathvariant":1723},[1656,75808,1659],{"stretchy":1658},[1667,75810,8580],{},[1656,75812,1683],{"stretchy":1658},[1656,75814,1713],{},[1656,75816,3964],{},[1667,75818,28042],{},[1656,75820,4373],{},[1667,75822,4032],{},[2461,75824,12767],{},[1656,75826,12770],{},[2461,75828,12767],{},[902,75830,75831],{"encoding":904},"PR''(10) = -0{,}6 \u003C 0 \\;\\Rightarrow\\;",[38,75833,12504],{}," zisku, avšak",[883,75836,75838],{"className":75837},[886],[888,75839,75840],{"xmlns":890,"display":2408},[892,75841,75842,75910],{},[895,75843,75844,75846,75848,75850,75852,75854,75856,75858,75860,75862,75864,75866,75868,75870,75872,75874,75876,75878,75880,75882,75884,75886,75888,75890,75892,75894,75896,75898,75900,75902,75904,75906,75908],{},[898,75845,8194],{},[898,75847,1763],{},[1656,75849,1659],{"stretchy":1658},[1667,75851,8580],{},[1656,75853,1683],{"stretchy":1658},[1656,75855,1713],{},[1667,75857,2673],{},[1656,75859,2751],{},[1667,75861,8580],{},[1656,75863,3964],{},[1656,75865,1659],{"stretchy":1658},[1667,75867,75472],{},[1656,75869,2751],{},[1667,75871,1669],{},[2461,75873,7828],{},[1667,75875,67750],{},[1656,75877,3964],{},[1667,75879,31263],{},[1656,75881,2751],{},[1667,75883,5267],{},[1656,75885,3633],{},[1667,75887,5267],{},[1656,75889,3633],{},[1667,75891,5193],{},[1656,75893,1683],{"stretchy":1658},[1656,75895,1713],{},[1667,75897,9135],{},[1656,75899,3964],{},[1667,75901,29898],{},[1656,75903,1713],{},[1656,75905,3964],{},[1667,75907,44930],{},[1656,75909,1673],{"separator":1672},[902,75911,75912],{"encoding":904},"PR(10) = 4 \\cdot 10 - (0{,}04 \\cdot 1\\,000 - 0{,}9 \\cdot 100 + 100 + 5) = 40 - 55 = -15,",[724,75914,75915,75916,1863],{},"tj. ztráta větší než ",[883,75917,75919],{"className":75918},[886],[888,75920,75921],{"xmlns":890},[892,75922,75923,75933],{},[895,75924,75925,75927,75929,75931],{},[898,75926,19177],{},[898,75928,1766],{},[1656,75930,1713],{},[1667,75932,5193],{},[902,75934,75935],{"encoding":904},"FC = 5",[724,75937,75938,75941,75942,75945,75946,1863],{},[38,75939,75940],{},"Závěr:"," firma by měla ",[38,75943,75944],{},"zastavit výrobu"," — i vypnutí provozu způsobí menší ztrátu, a to pouze ve výši ",[883,75947,75949],{"className":75948},[886],[888,75950,75951],{"xmlns":890},[892,75952,75953,75963],{},[895,75954,75955,75957,75959,75961],{},[898,75956,19177],{},[898,75958,1766],{},[1656,75960,1713],{},[1667,75962,5193],{},[902,75964,75935],{"encoding":904},[115,75966,75968],{"id":75967},"konstrukce-křivky-nabídky-firmy","Konstrukce křivky nabídky firmy",[724,75970,75971,75972,75974,75975,75990,75991,76004,76005,76031,76032,76045,76046,76063,76064,3565,76081,76084,76085,76105,76106,76121,76122,2114],{},"Důležitým završením analýzy je konstrukce ",[38,75973,63944],{},". S nabízeným množstvím rostou mezní náklady ",[883,75976,75978],{"className":75977},[886],[888,75979,75980],{"xmlns":890},[892,75981,75982,75988],{},[895,75983,75984,75986],{},[898,75985,1703],{},[898,75987,1766],{},[902,75989,63961],{"encoding":904}," a tyto určují cenu ",[883,75992,75994],{"className":75993},[886],[888,75995,75996],{"xmlns":890},[892,75997,75998,76002],{},[895,75999,76000],{},[898,76001,8194],{},[902,76003,8194],{"encoding":904},", za kterou je firma ochotna toto množství realizovat. Proto platí ",[883,76006,76008],{"className":76007},[886],[888,76009,76010],{"xmlns":890},[892,76011,76012,76028],{},[895,76013,76014,76016,76018,76020,76022,76024,76026],{},[898,76015,8194],{},[1656,76017,1713],{},[898,76019,1703],{},[898,76021,1766],{},[1656,76023,1659],{"stretchy":1658},[898,76025,1665],{},[1656,76027,1683],{"stretchy":1658},[902,76029,76030],{"encoding":904},"P = MC(Q)"," (obrázek 3.14). Cena ",[883,76033,76035],{"className":76034},[886],[888,76036,76037],{"xmlns":890},[892,76038,76039,76043],{},[895,76040,76041],{},[898,76042,8194],{},[902,76044,8194],{"encoding":904}," však nemůže být nižší než ",[883,76047,76049],{"className":76048},[886],[888,76050,76051],{"xmlns":890},[892,76052,76053,76061],{},[895,76054,76055],{},[2062,76056,76057,76059],{},[898,76058,8194],{},[1656,76060,8187],{},[902,76062,13178],{"encoding":904}," odpovídající množství ",[883,76065,76067],{"className":76066},[886],[888,76068,76069],{"xmlns":890},[892,76070,76071,76079],{},[895,76072,76073],{},[2062,76074,76075,76077],{},[898,76076,1665],{},[1656,76078,8187],{},[902,76080,38543],{"encoding":904},[38,76082,76083],{},"minima průměrných variabilních nákladů"," (fixní náklady nelze při optimalizaci zahrnout — jsou konstantní součástí nákladů i zisku). Křivka nabídky se tedy skládá z úsečky ",[883,76086,76088],{"className":76087},[886],[888,76089,76090],{"xmlns":890},[892,76091,76092,76102],{},[895,76093,76094,76096],{},[1667,76095,4032],{},[2062,76097,76098,76100],{},[898,76099,1665],{},[1656,76101,8187],{},[902,76103,76104],{"encoding":904},"0Q^*"," (kde firma nenabízí nic) a rostoucí části ",[883,76107,76109],{"className":76108},[886],[888,76110,76111],{"xmlns":890},[892,76112,76113,76119],{},[895,76114,76115,76117],{},[898,76116,1703],{},[898,76118,1766],{},[902,76120,63961],{"encoding":904}," nad bodem ",[883,76123,76125],{"className":76124},[886],[888,76126,76127],{"xmlns":890},[892,76128,76129,76133],{},[895,76130,76131],{},[898,76132,2146],{},[902,76134,2146],{"encoding":904},[883,76136,76138],{"className":76137},[886],[888,76139,76140],{"xmlns":890,"display":2408},[892,76141,76142,76249],{},[2412,76143,76144],{"width":2414},[2416,76145,76146,76148,76242,76244],{},[2419,76147],{"width":2421},[2419,76149,76150],{},[895,76151,76152,76154,76156,76158,76160,76162,76164,76166],{},[898,76153,8194],{},[1656,76155,1713],{},[898,76157,1769],{},[1656,76159,1659],{"stretchy":1658},[898,76161,1665],{},[1656,76163,1683],{"stretchy":1658},[1656,76165,1713],{},[895,76167,76168,76171],{},[1656,76169,76170],{"fence":1672},"{",[2412,76172,76175,76214],{"rowspacing":76173,"columnalign":76174,"columnspacing":3318},"0.36em","left left",[2416,76176,76177,76193],{},[2419,76178,76179],{},[4138,76180,76181],{"scriptlevel":4032,"displaystyle":1658},[895,76182,76183,76185,76187,76189,76191],{},[898,76184,1703],{},[898,76186,1766],{},[1656,76188,1659],{"stretchy":1658},[898,76190,1665],{},[1656,76192,1683],{"stretchy":1658},[2419,76194,76195],{},[4138,76196,76197],{"scriptlevel":4032,"displaystyle":1658},[895,76198,76199,76202,76204,76206,76212],{},[2461,76200,76201],{},"pro ",[898,76203,1665],{},[1656,76205,13258],{},[2062,76207,76208,76210],{},[898,76209,1665],{},[1656,76211,8187],{},[1656,76213,1673],{"separator":1672},[2416,76215,76216,76222],{},[2419,76217,76218],{},[4138,76219,76220],{"scriptlevel":4032,"displaystyle":1658},[1667,76221,4032],{},[2419,76223,76224],{},[4138,76225,76226],{"scriptlevel":4032,"displaystyle":1658},[895,76227,76228,76230,76232,76234,76240],{},[2461,76229,76201],{},[898,76231,1665],{},[1656,76233,4373],{},[2062,76235,76236,76238],{},[898,76237,1665],{},[1656,76239,8187],{},[1656,76241,1673],{"separator":1672},[2419,76243],{"width":2421},[2419,76245,76246],{},[2461,76247,76248],{},"(3.15)",[902,76250,76251],{"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}",[724,76253,2355,76254,76271,76272,76289,76290,50179,76320,76323],{},[883,76255,76257],{"className":76256},[886],[888,76258,76259],{"xmlns":890},[892,76260,76261,76269],{},[895,76262,76263],{},[2062,76264,76265,76267],{},[898,76266,1665],{},[1656,76268,8187],{},[902,76270,38543],{"encoding":904}," je bod minima ",[883,76273,76275],{"className":76274},[886],[888,76276,76277],{"xmlns":890},[892,76278,76279,76287],{},[895,76280,76281,76283,76285],{},[898,76282,2146],{},[898,76284,49019],{},[898,76286,1766],{},[902,76288,63980],{"encoding":904},". Bod ",[883,76291,76293],{"className":76292},[886],[888,76294,76295],{"xmlns":890},[892,76296,76297,76317],{},[895,76298,76299,76301,76307,76309,76315],{},[1656,76300,1659],{"stretchy":1658},[2062,76302,76303,76305],{},[898,76304,1665],{},[1656,76306,8187],{},[1656,76308,1673],{"separator":1672},[2062,76310,76311,76313],{},[898,76312,8194],{},[1656,76314,8187],{},[1656,76316,1683],{"stretchy":1658},[902,76318,76319],{"encoding":904},"(Q^*, P^*)",[38,76321,76322],{},"shutdown point"," — pod ním se firmě nevyplatí produkovat.",[1981,76325,76326,76331],{},[724,76327,76328,76330],{},[883,76329,10188],{}," Postup — jak odvodit nabídku firmy",[152,76332,76333,76382,76477,76532,76603],{},[123,76334,76335,76336,1896,76358,1863],{},"Ze zadaných nákladů určete ",[883,76337,76339],{"className":76338},[886],[888,76340,76341],{"xmlns":890},[892,76342,76343,76355],{},[895,76344,76345,76347,76349,76351,76353],{},[898,76346,1703],{},[898,76348,1766],{},[1656,76350,1659],{"stretchy":1658},[898,76352,1665],{},[1656,76354,1683],{"stretchy":1658},[902,76356,76357],{"encoding":904},"MC(Q)",[883,76359,76361],{"className":76360},[886],[888,76362,76363],{"xmlns":890},[892,76364,76365,76379],{},[895,76366,76367,76369,76371,76373,76375,76377],{},[898,76368,2146],{},[898,76370,49019],{},[898,76372,1766],{},[1656,76374,1659],{"stretchy":1658},[898,76376,1665],{},[1656,76378,1683],{"stretchy":1658},[902,76380,76381],{"encoding":904},"AVC(Q)",[123,76383,76384,76385,76402,76403,76420,76421,76453,76454,12702],{},"Najděte ",[883,76386,76388],{"className":76387},[886],[888,76389,76390],{"xmlns":890},[892,76391,76392,76400],{},[895,76393,76394],{},[2062,76395,76396,76398],{},[898,76397,1665],{},[1656,76399,8187],{},[902,76401,38543],{"encoding":904}," jako bod minima ",[883,76404,76406],{"className":76405},[886],[888,76407,76408],{"xmlns":890},[892,76409,76410,76418],{},[895,76411,76412,76414,76416],{},[898,76413,2146],{},[898,76415,49019],{},[898,76417,1766],{},[902,76419,63980],{"encoding":904}," (řešením ",[883,76422,76424],{"className":76423},[886],[888,76425,76426],{"xmlns":890},[892,76427,76428,76450],{},[895,76429,76430,76432,76434,76440,76442,76444,76446,76448],{},[898,76431,2146],{},[898,76433,49019],{},[2062,76435,76436,76438],{},[898,76437,1766],{},[1656,76439,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,76441,1659],{"stretchy":1658},[898,76443,1665],{},[1656,76445,1683],{"stretchy":1658},[1656,76447,1713],{},[1667,76449,4032],{},[902,76451,76452],{"encoding":904},"AVC'(Q) = 0",", případně rovnice ",[883,76455,76457],{"className":76456},[886],[888,76458,76459],{"xmlns":890},[892,76460,76461,76475],{},[895,76462,76463,76465,76467,76469,76471,76473],{},[898,76464,2146],{},[898,76466,49019],{},[898,76468,1766],{},[1656,76470,1713],{},[898,76472,1703],{},[898,76474,1766],{},[902,76476,63917],{"encoding":904},[123,76478,74386,76479,76531],{},[883,76480,76482],{"className":76481},[886],[888,76483,76484],{"xmlns":890},[892,76485,76486,76528],{},[895,76487,76488,76494,76496,76498,76500,76502,76508,76510,76512,76514,76516,76518,76520,76526],{},[2062,76489,76490,76492],{},[898,76491,8194],{},[1656,76493,8187],{},[1656,76495,1713],{},[898,76497,1703],{},[898,76499,1766],{},[1656,76501,1659],{"stretchy":1658},[2062,76503,76504,76506],{},[898,76505,1665],{},[1656,76507,8187],{},[1656,76509,1683],{"stretchy":1658},[1656,76511,1713],{},[898,76513,2146],{},[898,76515,49019],{},[898,76517,1766],{},[1656,76519,1659],{"stretchy":1658},[2062,76521,76522,76524],{},[898,76523,1665],{},[1656,76525,8187],{},[1656,76527,1683],{"stretchy":1658},[902,76529,76530],{"encoding":904},"P^* = MC(Q^*) = AVC(Q^*)"," — minimální cenu nabídky.",[123,76533,76534,76535,3713,76567,76589,76590,1863],{},"Zapište nabídku: ",[883,76536,76538],{"className":76537},[886],[888,76539,76540],{"xmlns":890},[892,76541,76542,76564],{},[895,76543,76544,76546,76548,76550,76552,76554,76556,76558,76560,76562],{},[898,76545,1769],{},[1656,76547,1659],{"stretchy":1658},[898,76549,1665],{},[1656,76551,1683],{"stretchy":1658},[1656,76553,1713],{},[898,76555,1703],{},[898,76557,1766],{},[1656,76559,1659],{"stretchy":1658},[898,76561,1665],{},[1656,76563,1683],{"stretchy":1658},[902,76565,76566],{"encoding":904},"S(Q) = MC(Q)",[883,76568,76570],{"className":76569},[886],[888,76571,76572],{"xmlns":890},[892,76573,76574,76586],{},[895,76575,76576,76578,76580],{},[898,76577,1665],{},[1656,76579,13258],{},[2062,76581,76582,76584],{},[898,76583,1665],{},[1656,76585,8187],{},[902,76587,76588],{"encoding":904},"Q \\geq Q^*",", jinak ",[883,76591,76593],{"className":76592},[886],[888,76594,76595],{"xmlns":890},[892,76596,76597,76601],{},[895,76598,76599],{},[1667,76600,4032],{},[902,76602,4032],{"encoding":904},[123,76604,76605,76606,76638],{},"V případě potřeby vyjádřete inverzi ",[883,76607,76609],{"className":76608},[886],[888,76610,76611],{"xmlns":890},[892,76612,76613,76635],{},[895,76614,76615,76617,76619,76629,76631,76633],{},[898,76616,1665],{},[1656,76618,1713],{},[2062,76620,76621,76623],{},[898,76622,1769],{},[895,76624,76625,76627],{},[1656,76626,3964],{},[1667,76628,1669],{},[1656,76630,1659],{"stretchy":1658},[898,76632,8194],{},[1656,76634,1683],{"stretchy":1658},[902,76636,76637],{"encoding":904},"Q = S^{-1}(P)"," doplněním na čtverec.",[724,76640,76641],{},[614,76642,76643,76644,1343,76659,1896,76676,37900,76691,76704,76705,76730,76731,76744,76745,76762,76763,76780,76781,76798],{},"Obrázek 3.14: Křivky ",[883,76645,76647],{"className":76646},[886],[888,76648,76649],{"xmlns":890},[892,76650,76651,76657],{},[895,76652,76653,76655],{},[898,76654,2146],{},[898,76656,1766],{},[902,76658,64229],{"encoding":904},[883,76660,76662],{"className":76661},[886],[888,76663,76664],{"xmlns":890},[892,76665,76666,76674],{},[895,76667,76668,76670,76672],{},[898,76669,2146],{},[898,76671,49019],{},[898,76673,1766],{},[902,76675,63980],{"encoding":904},[883,76677,76679],{"className":76678},[886],[888,76680,76681],{"xmlns":890},[892,76682,76683,76689],{},[895,76684,76685,76687],{},[898,76686,1703],{},[898,76688,1766],{},[902,76690,63961],{"encoding":904},[883,76692,76694],{"className":76693},[886],[888,76695,76696],{"xmlns":890},[892,76697,76698,76702],{},[895,76699,76700],{},[898,76701,900],{},[902,76703,900],{"encoding":904},"; křivka nabídky ",[883,76706,76708],{"className":76707},[886],[888,76709,76710],{"xmlns":890},[892,76711,76712,76728],{},[895,76713,76714,76716,76718,76720,76722,76724,76726],{},[898,76715,8194],{},[1656,76717,1713],{},[898,76719,1703],{},[898,76721,1766],{},[1656,76723,1659],{"stretchy":1658},[898,76725,1665],{},[1656,76727,1683],{"stretchy":1658},[902,76729,76030],{"encoding":904}," začíná v bodě ",[883,76732,76734],{"className":76733},[886],[888,76735,76736],{"xmlns":890},[892,76737,76738,76742],{},[895,76739,76740],{},[898,76741,2146],{},[902,76743,2146],{"encoding":904}," odpovídajícím minimu ",[883,76746,76748],{"className":76747},[886],[888,76749,76750],{"xmlns":890},[892,76751,76752,76760],{},[895,76753,76754,76756,76758],{},[898,76755,2146],{},[898,76757,49019],{},[898,76759,1766],{},[902,76761,63980],{"encoding":904}," při ceně ",[883,76764,76766],{"className":76765},[886],[888,76767,76768],{"xmlns":890},[892,76769,76770,76778],{},[895,76771,76772],{},[2062,76773,76774,76776],{},[898,76775,8194],{},[1656,76777,8187],{},[902,76779,13178],{"encoding":904}," (minimální cena nabídky); pod ",[883,76782,76784],{"className":76783},[886],[888,76785,76786],{"xmlns":890},[892,76787,76788,76796],{},[895,76789,76790],{},[2062,76791,76792,76794],{},[898,76793,1665],{},[1656,76795,8187],{},[902,76797,38543],{"encoding":904}," je nabídka nulová.",[46030,76800,76802],{"id":76801},"příklad-312","Příklad 3.12",[724,76804,76805,66190,76807,76853],{},[38,76806,64656],{},[883,76808,76810],{"className":76809},[886],[888,76811,76812],{"xmlns":890},[892,76813,76814,76850],{},[895,76815,76816,76818,76820,76822,76824,76830,76832,76834,76840,76842,76844,76846,76848],{},[898,76817,11577],{},[898,76819,1766],{},[1656,76821,1713],{},[1667,76823,11595],{},[2062,76825,76826,76828],{},[898,76827,1665],{},[1667,76829,2617],{},[1656,76831,3964],{},[1667,76833,1680],{},[2062,76835,76836,76838],{},[898,76837,1665],{},[1667,76839,1680],{},[1656,76841,3633],{},[1667,76843,44930],{},[898,76845,1665],{},[1656,76847,3633],{},[1667,76849,8580],{},[902,76851,76852],{"encoding":904},"TC = 0{,}1Q^3 - 2Q^2 + 15Q + 10"," odvoďte funkci nabídky firmy.",[724,76855,76856,1643,76858,76895,76896,2114],{},[38,76857,31488],{},[883,76859,76861],{"className":76860},[886],[888,76862,76863],{"xmlns":890},[892,76864,76865,76892],{},[895,76866,76867,76869,76871,76873,76876,76882,76884,76886,76888,76890],{},[898,76868,1703],{},[898,76870,1766],{},[1656,76872,1713],{},[1667,76874,76875],{},"0,3",[2062,76877,76878,76880],{},[898,76879,1665],{},[1667,76881,1680],{},[1656,76883,3964],{},[1667,76885,2673],{},[898,76887,1665],{},[1656,76889,3633],{},[1667,76891,44930],{},[902,76893,76894],{"encoding":904},"MC = 0{,}3Q^2 - 4Q + 15",", takže z ",[883,76897,76899],{"className":76898},[886],[888,76900,76901],{"xmlns":890},[892,76902,76903,76913],{},[895,76904,76905,76907,76909,76911],{},[898,76906,8194],{},[1656,76908,1713],{},[898,76910,1703],{},[898,76912,1766],{},[902,76914,76915],{"encoding":904},"P = MC",[883,76917,76919],{"className":76918},[886],[888,76920,76921],{"xmlns":890,"display":2408},[892,76922,76923,76948],{},[895,76924,76925,76927,76929,76931,76937,76939,76941,76943,76945],{},[898,76926,8194],{},[1656,76928,1713],{},[1667,76930,76875],{},[2062,76932,76933,76935],{},[898,76934,1665],{},[1667,76936,1680],{},[1656,76938,3964],{},[1667,76940,2673],{},[898,76942,1665],{},[1656,76944,3633],{},[1667,76946,76947],{},"15.",[902,76949,76950],{"encoding":904},"P = 0{,}3Q^2 - 4Q + 15.",[724,76952,76953,76954,14151,76967,76980],{},"Vyjádření ",[883,76955,76957],{"className":76956},[886],[888,76958,76959],{"xmlns":890},[892,76960,76961,76965],{},[895,76962,76963],{},[898,76964,1665],{},[902,76966,1665],{"encoding":904},[883,76968,76970],{"className":76969},[886],[888,76971,76972],{"xmlns":890},[892,76973,76974,76978],{},[895,76975,76976],{},[898,76977,8194],{},[902,76979,8194],{"encoding":904}," doplněním na čtverec:",[883,76982,76984],{"className":76983},[886],[888,76985,76986],{"xmlns":890,"display":2408},[892,76987,76988,77078],{},[895,76989,76990,76992,76994,76996,77034,77036,77038,77060,77062,77076],{},[898,76991,8194],{},[1656,76993,1713],{},[1667,76995,76875],{},[895,76997,76998,77000,77022,77024,77032],{},[1656,76999,1659],{"fence":1672},[2062,77001,77002,77020],{},[895,77003,77004,77006,77008,77010,77018],{},[1656,77005,1659],{"fence":1672},[898,77007,1665],{},[1656,77009,3964],{},[4138,77011,77012],{"scriptlevel":4032,"displaystyle":1658},[3294,77013,77014,77016],{},[1667,77015,9058],{},[1667,77017,2617],{},[1656,77019,1683],{"fence":1672},[1667,77021,1680],{},[1656,77023,3633],{},[4138,77025,77026],{"scriptlevel":4032,"displaystyle":1658},[3294,77027,77028,77030],{},[1667,77029,9267],{},[1667,77031,2698],{},[1656,77033,1683],{"fence":1672},[1656,77035,1673],{"separator":1672},[3316,77037],{"width":14644},[2062,77039,77040,77058],{},[895,77041,77042,77044,77046,77048,77056],{},[1656,77043,1659],{"fence":1672},[898,77045,1665],{},[1656,77047,3964],{},[4138,77049,77050],{"scriptlevel":4032,"displaystyle":1658},[3294,77051,77052,77054],{},[1667,77053,9058],{},[1667,77055,2617],{},[1656,77057,1683],{"fence":1672},[1667,77059,1680],{},[1656,77061,1713],{},[3294,77063,77064,77074],{},[895,77065,77066,77068,77070,77072],{},[1667,77067,46701],{},[898,77069,8194],{},[1656,77071,3964],{},[1667,77073,9267],{},[1667,77075,2698],{},[1656,77077,1673],{"separator":1672},[902,77079,77080],{"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},",[883,77082,77084],{"className":77083},[886],[888,77085,77086],{"xmlns":890,"display":2408},[892,77087,77088,77120],{},[895,77089,77090,77092,77094,77100,77102,77118],{},[898,77091,1665],{},[1656,77093,1713],{},[3294,77095,77096,77098],{},[1667,77097,9058],{},[1667,77099,2617],{},[1656,77101,3633],{},[3294,77103,77104,77116],{},[2625,77105,77106],{},[895,77107,77108,77110,77112,77114],{},[1667,77109,46701],{},[898,77111,8194],{},[1656,77113,3964],{},[1667,77115,9267],{},[1667,77117,2617],{},[898,77119,1863],{"mathvariant":1723},[902,77121,77122],{"encoding":904},"Q = \\frac{20}{3} + \\frac{\\sqrt{30P - 50}}{3}.",[724,77124,75682,77125,1343,77163,1343,77211,77245,77246,1863],{},[883,77126,77128],{"className":77127},[886],[888,77129,77130],{"xmlns":890},[892,77131,77132,77160],{},[895,77133,77134,77136,77138,77140,77142,77144,77150,77152,77154,77156,77158],{},[898,77135,2146],{},[898,77137,49019],{},[898,77139,1766],{},[1656,77141,1713],{},[1667,77143,11595],{},[2062,77145,77146,77148],{},[898,77147,1665],{},[1667,77149,1680],{},[1656,77151,3964],{},[1667,77153,1680],{},[898,77155,1665],{},[1656,77157,3633],{},[1667,77159,44930],{},[902,77161,77162],{"encoding":904},"AVC = 0{,}1Q^2 - 2Q + 15",[883,77164,77166],{"className":77165},[886],[888,77167,77168],{"xmlns":890},[892,77169,77170,77208],{},[895,77171,77172,77174,77176,77182,77184,77186,77188,77190,77192,77194,77196,77198,77204,77206],{},[898,77173,2146],{},[898,77175,49019],{},[2062,77177,77178,77180],{},[898,77179,1766],{},[1656,77181,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,77183,1713],{},[1667,77185,11639],{},[898,77187,1665],{},[1656,77189,3964],{},[1667,77191,1680],{},[1656,77193,1713],{},[1667,77195,4032],{},[1656,77197,12770],{},[2062,77199,77200,77202],{},[898,77201,1665],{},[1656,77203,8187],{},[1656,77205,1713],{},[1667,77207,8580],{},[902,77209,77210],{"encoding":904},"AVC' = 0{,}2Q - 2 = 0 \\Rightarrow Q^* = 10",[883,77212,77214],{"className":77213},[886],[888,77215,77216],{"xmlns":890},[892,77217,77218,77242],{},[895,77219,77220,77222,77224,77234,77236,77238,77240],{},[898,77221,2146],{},[898,77223,49019],{},[2062,77225,77226,77228],{},[898,77227,1766],{},[895,77229,77230,77232],{},[1656,77231,1725],{"mathvariant":1723},[1656,77233,1725],{"mathvariant":1723},[1656,77235,1713],{},[1667,77237,11639],{},[1656,77239,2850],{},[1667,77241,4032],{},[902,77243,77244],{"encoding":904},"AVC'' = 0{,}2 > 0"," (minimum). Minimální cena nabídky ",[883,77247,77249],{"className":77248},[886],[888,77250,77251],{"xmlns":890},[892,77252,77253,77289],{},[895,77254,77255,77261,77263,77265,77267,77269,77271,77273,77275,77277,77279,77281,77283,77285,77287],{},[2062,77256,77257,77259],{},[898,77258,8194],{},[1656,77260,8187],{},[1656,77262,1713],{},[898,77264,1703],{},[898,77266,1766],{},[1656,77268,1659],{"stretchy":1658},[1667,77270,8580],{},[1656,77272,1683],{"stretchy":1658},[1656,77274,1713],{},[1667,77276,46701],{},[1656,77278,3964],{},[1667,77280,9135],{},[1656,77282,3633],{},[1667,77284,44930],{},[1656,77286,1713],{},[1667,77288,5193],{},[902,77290,77291],{"encoding":904},"P^* = MC(10) = 30 - 40 + 15 = 5",[724,77293,77294],{},[38,77295,77296],{},"Závěr.",[883,77298,77300],{"className":77299},[886],[888,77301,77302],{"xmlns":890,"display":2408},[892,77303,77304,77390],{},[895,77305,77306,77308,77310,77312,77314,77316,77318,77320],{},[898,77307,8194],{},[1656,77309,1713],{},[898,77311,1769],{},[1656,77313,1659],{"stretchy":1658},[898,77315,1665],{},[1656,77317,1683],{"stretchy":1658},[1656,77319,1713],{},[895,77321,77322,77324],{},[1656,77323,76170],{"fence":1672},[2412,77325,77326,77368],{"rowspacing":76173,"columnalign":76174,"columnspacing":3318},[2416,77327,77328,77352],{},[2419,77329,77330],{},[4138,77331,77332],{"scriptlevel":4032,"displaystyle":1658},[895,77333,77334,77336,77342,77344,77346,77348,77350],{},[1667,77335,76875],{},[2062,77337,77338,77340],{},[898,77339,1665],{},[1667,77341,1680],{},[1656,77343,3964],{},[1667,77345,2673],{},[898,77347,1665],{},[1656,77349,3633],{},[1667,77351,44930],{},[2419,77353,77354],{},[4138,77355,77356],{"scriptlevel":4032,"displaystyle":1658},[895,77357,77358,77360,77362,77364,77366],{},[2461,77359,76201],{},[898,77361,1665],{},[1656,77363,13258],{},[1667,77365,8580],{},[1656,77367,1673],{"separator":1672},[2416,77369,77370,77376],{},[2419,77371,77372],{},[4138,77373,77374],{"scriptlevel":4032,"displaystyle":1658},[1667,77375,4032],{},[2419,77377,77378],{},[4138,77379,77380],{"scriptlevel":4032,"displaystyle":1658},[895,77381,77382,77384,77386,77388],{},[2461,77383,76201],{},[898,77385,1665],{},[1656,77387,4373],{},[1667,77389,28049],{},[902,77391,77392],{"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}",[724,77394,77395],{},[614,77396,77397,77398,77413,77414,1863],{},"Obrázek 3.15: Grafická ilustrace nabídky firmy odvozené z části křivky ",[883,77399,77401],{"className":77400},[886],[888,77402,77403],{"xmlns":890},[892,77404,77405,77411],{},[895,77406,77407,77409],{},[898,77408,1703],{},[898,77410,1766],{},[902,77412,63961],{"encoding":904}," ležící nad minimem ",[883,77415,77417],{"className":77416},[886],[888,77418,77419],{"xmlns":890},[892,77420,77421,77429],{},[895,77422,77423,77425,77427],{},[898,77424,2146],{},[898,77426,49019],{},[898,77428,1766],{},[902,77430,63980],{"encoding":904},[115,77432,77434],{"id":77433},"shrnutí-kapitoly-3","Shrnutí kapitoly 3",[724,77436,77437,77438,77442,77443,77458,77459,77479,77480,1896,77483,77486,77487,77489,77490,28666,77512,77514,77515,1896,77517,67394,77520,1643,77523,3228,77538,77553],{},"Celkový příjem je součin ceny a množství, kde cena je dána funkcí ",[207,77439,77441],{"className":77440,"dataFsResolvedFilePath":800,"href":801},[210],"poptávky",". Pro lineární poptávku je ",[883,77444,77446],{"className":77445},[886],[888,77447,77448],{"xmlns":890},[892,77449,77450,77456],{},[895,77451,77452,77454],{},[898,77453,11577],{},[898,77455,1763],{},[902,77457,12875],{"encoding":904}," kvadratická. Průměrný příjem je podíl ",[883,77460,77462],{"className":77461},[886],[888,77463,77464],{"xmlns":890},[892,77465,77466,77476],{},[895,77467,77468,77470,77472,77474],{},[898,77469,11577],{},[898,77471,1763],{},[898,77473,1782],{"mathvariant":1723},[898,77475,1665],{},[902,77477,77478],{"encoding":904},"TR\u002FQ"," a rovná se poptávkové funkci. Celkové náklady se skládají z ",[38,77481,77482],{},"fixních",[38,77484,77485],{},"celkových variabilních"," nákladů. Průměrné veličiny jsou jejich podíly s množstvím. ",[38,77488,72991],{}," identifikují, kdy se firma nachází na prahu rentability. Rozdíl ",[883,77491,77493],{"className":77492},[886],[888,77494,77495],{"xmlns":890},[892,77496,77497,77509],{},[895,77498,77499,77501,77503,77505,77507],{},[898,77500,11577],{},[898,77502,1763],{},[1656,77504,3964],{},[898,77506,11577],{},[898,77508,1766],{},[902,77510,77511],{"encoding":904},"TR - TC",[38,77513,63841],{},"; klíčový je výpočet produkce, která zisk maximalizuje. ",[38,77516,65152],{},[38,77518,77519],{},"mezní náklady",[207,77521,1145],{"className":77522,"dataFsResolvedFilePath":764,"href":765},[210],[883,77524,77526],{"className":77525},[886],[888,77527,77528],{"xmlns":890},[892,77529,77530,77536],{},[895,77531,77532,77534],{},[898,77533,11577],{},[898,77535,1763],{},[902,77537,12875],{"encoding":904},[883,77539,77541],{"className":77540},[886],[888,77542,77543],{"xmlns":890},[892,77544,77545,77551],{},[895,77546,77547,77549],{},[898,77548,11577],{},[898,77550,1766],{},[902,77552,12033],{"encoding":904}," podle produkce; udávají rychlosti změn, resp. přibližné změny odpovídající jednotkové změně produkce.",[120,77555,77556,77618,77684,77746],{},[123,77557,77558,77561,77562,19135,77577,1863],{},[38,77559,77560],{},"Princip minimalizace průměrných nákladů:"," v bodě minima ",[883,77563,77565],{"className":77564},[886],[888,77566,77567],{"xmlns":890},[892,77568,77569,77575],{},[895,77570,77571,77573],{},[898,77572,2146],{},[898,77574,1766],{},[902,77576,64229],{"encoding":904},[883,77578,77580],{"className":77579},[886],[888,77581,77582],{"xmlns":890},[892,77583,77584,77616],{},[895,77585,77586,77588,77590,77592,77598,77600,77602,77604,77606,77608,77614],{},[898,77587,2146],{},[898,77589,1766],{},[1656,77591,1659],{"stretchy":1658},[1661,77593,77594,77596],{},[898,77595,1665],{},[1667,77597,4032],{},[1656,77599,1683],{"stretchy":1658},[1656,77601,1713],{},[898,77603,1703],{},[898,77605,1766],{},[1656,77607,1659],{"stretchy":1658},[1661,77609,77610,77612],{},[898,77611,1665],{},[1667,77613,4032],{},[1656,77615,1683],{"stretchy":1658},[902,77617,71236],{"encoding":904},[123,77619,77620,77561,77623,19135,77640,1863],{},[38,77621,77622],{},"Princip minimalizace průměrných variabilních nákladů:",[883,77624,77626],{"className":77625},[886],[888,77627,77628],{"xmlns":890},[892,77629,77630,77638],{},[895,77631,77632,77634,77636],{},[898,77633,2146],{},[898,77635,49019],{},[898,77637,1766],{},[902,77639,63980],{"encoding":904},[883,77641,77643],{"className":77642},[886],[888,77644,77645],{"xmlns":890},[892,77646,77647,77681],{},[895,77648,77649,77651,77653,77655,77657,77663,77665,77667,77669,77671,77673,77679],{},[898,77650,2146],{},[898,77652,49019],{},[898,77654,1766],{},[1656,77656,1659],{"stretchy":1658},[1661,77658,77659,77661],{},[898,77660,1665],{},[1667,77662,4032],{},[1656,77664,1683],{"stretchy":1658},[1656,77666,1713],{},[898,77668,1703],{},[898,77670,1766],{},[1656,77672,1659],{"stretchy":1658},[1661,77674,77675,77677],{},[898,77676,1665],{},[1667,77678,4032],{},[1656,77680,1683],{"stretchy":1658},[902,77682,77683],{"encoding":904},"AVC(Q_0) = MC(Q_0)",[123,77685,77686,77689,77690,19135,77705,1863],{},[38,77687,77688],{},"Princip maximalizace zisku:"," v bodě maxima ",[883,77691,77693],{"className":77692},[886],[888,77694,77695],{"xmlns":890},[892,77696,77697,77703],{},[895,77698,77699,77701],{},[898,77700,8194],{},[898,77702,1763],{},[902,77704,72145],{"encoding":904},[883,77706,77708],{"className":77707},[886],[888,77709,77710],{"xmlns":890},[892,77711,77712,77744],{},[895,77713,77714,77716,77718,77720,77726,77728,77730,77732,77734,77736,77742],{},[898,77715,1703],{},[898,77717,1763],{},[1656,77719,1659],{"stretchy":1658},[1661,77721,77722,77724],{},[898,77723,1665],{},[1667,77725,4032],{},[1656,77727,1683],{"stretchy":1658},[1656,77729,1713],{},[898,77731,1703],{},[898,77733,1766],{},[1656,77735,1659],{"stretchy":1658},[1661,77737,77738,77740],{},[898,77739,1665],{},[1667,77741,4032],{},[1656,77743,1683],{"stretchy":1658},[902,77745,74310],{"encoding":904},[123,77747,77748,1643,77751,3713,77787,76589,77808,30312,77821,76271,77838,1863],{},[38,77749,77750],{},"Funkce nabídky firmy:",[883,77752,77754],{"className":77753},[886],[888,77755,77756],{"xmlns":890},[892,77757,77758,77784],{},[895,77759,77760,77762,77764,77766,77768,77770,77772,77774,77776,77778,77780,77782],{},[898,77761,8194],{},[1656,77763,1713],{},[898,77765,1769],{},[1656,77767,1659],{"stretchy":1658},[898,77769,1665],{},[1656,77771,1683],{"stretchy":1658},[1656,77773,1713],{},[898,77775,1703],{},[898,77777,1766],{},[1656,77779,1659],{"stretchy":1658},[898,77781,1665],{},[1656,77783,1683],{"stretchy":1658},[902,77785,77786],{"encoding":904},"P = S(Q) = MC(Q)",[883,77788,77790],{"className":77789},[886],[888,77791,77792],{"xmlns":890},[892,77793,77794,77806],{},[895,77795,77796,77798,77800],{},[898,77797,1665],{},[1656,77799,13258],{},[2062,77801,77802,77804],{},[898,77803,1665],{},[1656,77805,8187],{},[902,77807,76588],{"encoding":904},[883,77809,77811],{"className":77810},[886],[888,77812,77813],{"xmlns":890},[892,77814,77815,77819],{},[895,77816,77817],{},[1667,77818,4032],{},[902,77820,4032],{"encoding":904},[883,77822,77824],{"className":77823},[886],[888,77825,77826],{"xmlns":890},[892,77827,77828,77836],{},[895,77829,77830],{},[2062,77831,77832,77834],{},[898,77833,1665],{},[1656,77835,8187],{},[902,77837,38543],{"encoding":904},[883,77839,77841],{"className":77840},[886],[888,77842,77843],{"xmlns":890},[892,77844,77845,77853],{},[895,77846,77847,77849,77851],{},[898,77848,2146],{},[898,77850,49019],{},[898,77852,1766],{},[902,77854,63980],{"encoding":904},[115,77856,8779],{"id":8778},[152,77858,77859,77862,77865,77868,77871,77874,77877,77880,77883,77886,77889],{},[123,77860,77861],{},"Jaký je vztah pro celkový příjem v podmínkách dokonalé konkurence?",[123,77863,77864],{},"Jaký tvar má křivka celkového příjmu pro lineární poptávku?",[123,77866,77867],{},"Jak se vypočte mezní příjem a co udává?",[123,77869,77870],{},"Z jakých složek se skládají celkové náklady?",[123,77872,77873],{},"Jak se stanoví celkové náklady, známe-li náklady mezní?",[123,77875,77876],{},"Jaký je trend průměrných fixních nákladů a průměrných nákladů, roste-li produkce?",[123,77878,77879],{},"Jak se stanoví přibližně změna celkových nákladů?",[123,77881,77882],{},"Jak se vypočte zisk?",[123,77884,77885],{},"Jaká vlastnost platí v bodě maxima zisku?",[123,77887,77888],{},"Co jsou body zvratu? Jak se najdou?",[123,77890,77891],{},"Z jakých nákladových charakteristik se vychází při konstrukci nabídky?",[115,77893,77895],{"id":77894},"úlohy-31328","Úlohy 3.1–3.28",[198,77897,77899],{"id":77898},"příjem-3135","Příjem (3.1–3.5)",[724,77901,77902,54103,77905,77933,77934,77949,77950,77965,77966,77981,77982,1343,77997,1343,78012,78027],{},[38,77903,77904],{},"3.1",[883,77906,77908],{"className":77907},[886],[888,77909,77910],{"xmlns":890},[892,77911,77912,77930],{},[895,77913,77914,77916,77918,77920,77922,77924,77926,77928],{},[898,77915,8194],{},[1656,77917,1713],{},[898,77919,6787],{},[1656,77921,1659],{"stretchy":1658},[898,77923,1665],{},[1656,77925,1683],{"stretchy":1658},[1656,77927,1713],{},[1667,77929,5267],{},[902,77931,77932],{"encoding":904},"P = D(Q) = 100",". (a) Rozhodněte, v jakých podmínkách konkurence zadaná poptávka platí. (b) Najděte celkový příjem ",[883,77935,77937],{"className":77936},[886],[888,77938,77939],{"xmlns":890},[892,77940,77941,77947],{},[895,77942,77943,77945],{},[898,77944,11577],{},[898,77946,1763],{},[902,77948,12875],{"encoding":904},", průměrný příjem ",[883,77951,77953],{"className":77952},[886],[888,77954,77955],{"xmlns":890},[892,77956,77957,77963],{},[895,77958,77959,77961],{},[898,77960,2146],{},[898,77962,1763],{},[902,77964,64114],{"encoding":904}," a mezní příjem ",[883,77967,77969],{"className":77968},[886],[888,77970,77971],{"xmlns":890},[892,77972,77973,77979],{},[895,77974,77975,77977],{},[898,77976,1703],{},[898,77978,1763],{},[902,77980,15395],{"encoding":904},". (c) Vypočtěte ",[883,77983,77985],{"className":77984},[886],[888,77986,77987],{"xmlns":890},[892,77988,77989,77995],{},[895,77990,77991,77993],{},[898,77992,11577],{},[898,77994,1763],{},[902,77996,12875],{"encoding":904},[883,77998,78000],{"className":77999},[886],[888,78001,78002],{"xmlns":890},[892,78003,78004,78010],{},[895,78005,78006,78008],{},[898,78007,2146],{},[898,78009,1763],{},[902,78011,64114],{"encoding":904},[883,78013,78015],{"className":78014},[886],[888,78016,78017],{"xmlns":890},[892,78018,78019,78025],{},[895,78020,78021,78023],{},[898,78022,1703],{},[898,78024,1763],{},[902,78026,15395],{"encoding":904}," při množství 20. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,78029,78030,54103,78033,77933,78069,77949,78084,77965,78099,77981,78114,1343,78129,1343,78144,78159],{},[38,78031,78032],{},"3.2",[883,78034,78036],{"className":78035},[886],[888,78037,78038],{"xmlns":890},[892,78039,78040,78066],{},[895,78041,78042,78044,78046,78048,78050,78052,78054,78056,78058,78060,78062,78064],{},[898,78043,8194],{},[1656,78045,1713],{},[898,78047,6787],{},[1656,78049,1659],{"stretchy":1658},[898,78051,1665],{},[1656,78053,1683],{"stretchy":1658},[1656,78055,1713],{},[1656,78057,3964],{},[1667,78059,13779],{},[898,78061,1665],{},[1656,78063,3633],{},[1667,78065,9058],{},[902,78067,78068],{"encoding":904},"P = D(Q) = -0{,}5Q + 20",[883,78070,78072],{"className":78071},[886],[888,78073,78074],{"xmlns":890},[892,78075,78076,78082],{},[895,78077,78078,78080],{},[898,78079,11577],{},[898,78081,1763],{},[902,78083,12875],{"encoding":904},[883,78085,78087],{"className":78086},[886],[888,78088,78089],{"xmlns":890},[892,78090,78091,78097],{},[895,78092,78093,78095],{},[898,78094,2146],{},[898,78096,1763],{},[902,78098,64114],{"encoding":904},[883,78100,78102],{"className":78101},[886],[888,78103,78104],{"xmlns":890},[892,78105,78106,78112],{},[895,78107,78108,78110],{},[898,78109,1703],{},[898,78111,1763],{},[902,78113,15395],{"encoding":904},[883,78115,78117],{"className":78116},[886],[888,78118,78119],{"xmlns":890},[892,78120,78121,78127],{},[895,78122,78123,78125],{},[898,78124,11577],{},[898,78126,1763],{},[902,78128,12875],{"encoding":904},[883,78130,78132],{"className":78131},[886],[888,78133,78134],{"xmlns":890},[892,78135,78136,78142],{},[895,78137,78138,78140],{},[898,78139,2146],{},[898,78141,1763],{},[902,78143,64114],{"encoding":904},[883,78145,78147],{"className":78146},[886],[888,78148,78149],{"xmlns":890},[892,78150,78151,78157],{},[895,78152,78153,78155],{},[898,78154,1703],{},[898,78156,1763],{},[902,78158,15395],{"encoding":904}," při množství 10. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,78161,78162,54103,78165,78202,78203,77949,78218,77965,78233,78248,78249,3713,78264,78290,78291,78306,78307,1343,78322,3713,78337,78290,78362,78377,78378,78391,78392,78407,78408,78423,78424,1343,78437,1343,78452,1343,78467,1863],{},[38,78163,78164],{},"3.3",[883,78166,78168],{"className":78167},[886],[888,78169,78170],{"xmlns":890},[892,78171,78172,78199],{},[895,78173,78174,78176,78178,78180,78182,78184,78186,78188,78191,78193],{},[898,78175,8194],{},[1656,78177,1713],{},[898,78179,6787],{},[1656,78181,1659],{"stretchy":1658},[898,78183,1665],{},[1656,78185,1683],{"stretchy":1658},[1656,78187,1713],{},[1667,78189,78190],{},"1200",[1656,78192,3964],{},[2062,78194,78195,78197],{},[898,78196,1665],{},[1667,78198,1680],{},[902,78200,78201],{"encoding":904},"P = D(Q) = 1200 - Q^2",". (a) Najděte celkový příjem ",[883,78204,78206],{"className":78205},[886],[888,78207,78208],{"xmlns":890},[892,78209,78210,78216],{},[895,78211,78212,78214],{},[898,78213,11577],{},[898,78215,1763],{},[902,78217,12875],{"encoding":904},[883,78219,78221],{"className":78220},[886],[888,78222,78223],{"xmlns":890},[892,78224,78225,78231],{},[895,78226,78227,78229],{},[898,78228,2146],{},[898,78230,1763],{},[902,78232,64114],{"encoding":904},[883,78234,78236],{"className":78235},[886],[888,78237,78238],{"xmlns":890},[892,78239,78240,78246],{},[895,78241,78242,78244],{},[898,78243,1703],{},[898,78245,1763],{},[902,78247,15395],{"encoding":904},". (b) Vypočtěte ",[883,78250,78252],{"className":78251},[886],[888,78253,78254],{"xmlns":890},[892,78255,78256,78262],{},[895,78257,78258,78260],{},[898,78259,11577],{},[898,78261,1763],{},[902,78263,12875],{"encoding":904},[883,78265,78267],{"className":78266},[886],[888,78268,78269],{"xmlns":890},[892,78270,78271,78287],{},[895,78272,78273,78275,78277,78279,78281,78283,78285],{},[898,78274,1665],{},[1656,78276,1713],{},[1667,78278,8580],{},[1656,78280,1673],{"separator":1672},[1667,78282,9058],{},[1656,78284,1673],{"separator":1672},[1667,78286,46701],{},[902,78288,78289],{"encoding":904},"Q = 10, 20, 30"," a rozhodněte, kdy ",[883,78292,78294],{"className":78293},[886],[888,78295,78296],{"xmlns":890},[892,78297,78298,78304],{},[895,78299,78300,78302],{},[898,78301,11577],{},[898,78303,1763],{},[902,78305,12875],{"encoding":904}," roste, resp. klesá. (c) Vypočtěte ",[883,78308,78310],{"className":78309},[886],[888,78311,78312],{"xmlns":890},[892,78313,78314,78320],{},[895,78315,78316,78318],{},[898,78317,2146],{},[898,78319,1763],{},[902,78321,64114],{"encoding":904},[883,78323,78325],{"className":78324},[886],[888,78326,78327],{"xmlns":890},[892,78328,78329,78335],{},[895,78330,78331,78333],{},[898,78332,1703],{},[898,78334,1763],{},[902,78336,15395],{"encoding":904},[883,78338,78340],{"className":78339},[886],[888,78341,78342],{"xmlns":890},[892,78343,78344,78360],{},[895,78345,78346,78348,78350,78352,78354,78356,78358],{},[898,78347,1665],{},[1656,78349,1713],{},[1667,78351,8580],{},[1656,78353,1673],{"separator":1672},[1667,78355,9058],{},[1656,78357,1673],{"separator":1672},[1667,78359,46701],{},[902,78361,78289],{"encoding":904},[883,78363,78365],{"className":78364},[886],[888,78366,78367],{"xmlns":890},[892,78368,78369,78375],{},[895,78370,78371,78373],{},[898,78372,1703],{},[898,78374,1763],{},[902,78376,15395],{"encoding":904}," roste, resp. klesá. (d) Vypočtěte ",[883,78379,78381],{"className":78380},[886],[888,78382,78383],{"xmlns":890},[892,78384,78385,78389],{},[895,78386,78387],{},[898,78388,1665],{},[902,78390,1665],{"encoding":904},", které maximalizuje ",[883,78393,78395],{"className":78394},[886],[888,78396,78397],{"xmlns":890},[892,78398,78399,78405],{},[895,78400,78401,78403],{},[898,78402,11577],{},[898,78404,1763],{},[902,78406,12875],{"encoding":904}," a stanovte příslušnou hodnotu maxima ",[883,78409,78411],{"className":78410},[886],[888,78412,78413],{"xmlns":890},[892,78414,78415,78421],{},[895,78416,78417,78419],{},[898,78418,11577],{},[898,78420,1763],{},[902,78422,12875],{"encoding":904},". (e) Určete (je užitečné vyšetřit i jejich průběhy). (f) Charakterizujte geometricky křivky ",[883,78425,78427],{"className":78426},[886],[888,78428,78429],{"xmlns":890},[892,78430,78431,78435],{},[895,78432,78433],{},[898,78434,6787],{},[902,78436,6787],{"encoding":904},[883,78438,78440],{"className":78439},[886],[888,78441,78442],{"xmlns":890},[892,78443,78444,78450],{},[895,78445,78446,78448],{},[898,78447,11577],{},[898,78449,1763],{},[902,78451,12875],{"encoding":904},[883,78453,78455],{"className":78454},[886],[888,78456,78457],{"xmlns":890},[892,78458,78459,78465],{},[895,78460,78461,78463],{},[898,78462,2146],{},[898,78464,1763],{},[902,78466,64114],{"encoding":904},[883,78468,78470],{"className":78469},[886],[888,78471,78472],{"xmlns":890},[892,78473,78474,78480],{},[895,78475,78476,78478],{},[898,78477,1703],{},[898,78479,1763],{},[902,78481,15395],{"encoding":904},[724,78483,78484,78487,78488,78518,78519,78534,78535,8167,78548,1343,78566,1343,78583,78601,78602,78624,78625,78640,78641,78654,78655,1863],{},[38,78485,78486],{},"3.4"," Je dán celkový příjem ",[883,78489,78491],{"className":78490},[886],[888,78492,78493],{"xmlns":890},[892,78494,78495,78515],{},[895,78496,78497,78499,78501,78503,78505,78507,78509],{},[898,78498,11577],{},[898,78500,1763],{},[1656,78502,1713],{},[1667,78504,78190],{},[898,78506,1665],{},[1656,78508,3964],{},[2062,78510,78511,78513],{},[898,78512,1665],{},[1667,78514,2617],{},[902,78516,78517],{"encoding":904},"TR = 1200Q - Q^3",". (a) Určete, jak rychle se (přibližně) mění ",[883,78520,78522],{"className":78521},[886],[888,78523,78524],{"xmlns":890},[892,78525,78526,78532],{},[895,78527,78528,78530],{},[898,78529,11577],{},[898,78531,1763],{},[902,78533,12875],{"encoding":904}," vzhledem ke ",[883,78536,78538],{"className":78537},[886],[888,78539,78540],{"xmlns":890},[892,78541,78542,78546],{},[895,78543,78544],{},[898,78545,1665],{},[902,78547,1665],{"encoding":904},[883,78549,78551],{"className":78550},[886],[888,78552,78553],{"xmlns":890},[892,78554,78555,78563],{},[895,78556,78557,78559,78561],{},[898,78558,1665],{},[1656,78560,1713],{},[1667,78562,5193],{},[902,78564,78565],{"encoding":904},"Q = 5",[883,78567,78569],{"className":78568},[886],[888,78570,78571],{"xmlns":890},[892,78572,78573,78581],{},[895,78574,78575,78577,78579],{},[898,78576,1665],{},[1656,78578,1713],{},[1667,78580,2877],{},[902,78582,14355],{"encoding":904},[883,78584,78586],{"className":78585},[886],[888,78587,78588],{"xmlns":890},[892,78589,78590,78598],{},[895,78591,78592,78594,78596],{},[898,78593,1665],{},[1656,78595,1713],{},[1667,78597,9140],{},[902,78599,78600],{"encoding":904},"Q = 12"," a charakterizujte dynamiku změn. (b) Vypočtěte a ekonomicky interpretujte ",[883,78603,78605],{"className":78604},[886],[888,78606,78607],{"xmlns":890},[892,78608,78609,78621],{},[895,78610,78611,78613,78615,78617,78619],{},[898,78612,1703],{},[898,78614,1763],{},[1656,78616,1659],{"stretchy":1658},[1667,78618,8580],{},[1656,78620,1683],{"stretchy":1658},[902,78622,78623],{"encoding":904},"MR(10)",". (c) Odhadněte, o kolik se přibližně změní ",[883,78626,78628],{"className":78627},[886],[888,78629,78630],{"xmlns":890},[892,78631,78632,78638],{},[895,78633,78634,78636],{},[898,78635,11577],{},[898,78637,1763],{},[902,78639,12875],{"encoding":904},", jestliže se ",[883,78642,78644],{"className":78643},[886],[888,78645,78646],{"xmlns":890},[892,78647,78648,78652],{},[895,78649,78650],{},[898,78651,1665],{},[902,78653,1665],{"encoding":904}," změní z 10 na 12 a porovnejte se skutečnou změnou ",[883,78656,78658],{"className":78657},[886],[888,78659,78660],{"xmlns":890},[892,78661,78662,78668],{},[895,78663,78664,78666],{},[898,78665,11577],{},[898,78667,1763],{},[902,78669,12875],{"encoding":904},[724,78671,78672,78675,78676,78702,78703,78718,78719,78640,78734,78747],{},[38,78673,78674],{},"3.5"," Je dán mezní příjem ",[883,78677,78679],{"className":78678},[886],[888,78680,78681],{"xmlns":890},[892,78682,78683,78699],{},[895,78684,78685,78687,78689,78691,78693,78695,78697],{},[898,78686,1703],{},[898,78688,1763],{},[1656,78690,1713],{},[1656,78692,3964],{},[898,78694,1665],{},[1656,78696,3633],{},[1667,78698,9058],{},[902,78700,78701],{"encoding":904},"MR = -Q + 20",". (a) Určete celkový příjem ",[883,78704,78706],{"className":78705},[886],[888,78707,78708],{"xmlns":890},[892,78709,78710,78716],{},[895,78711,78712,78714],{},[898,78713,11577],{},[898,78715,1763],{},[902,78717,12875],{"encoding":904},". (b) Vypočtěte změnu ",[883,78720,78722],{"className":78721},[886],[888,78723,78724],{"xmlns":890},[892,78725,78726,78732],{},[895,78727,78728,78730],{},[898,78729,11577],{},[898,78731,1763],{},[902,78733,12875],{"encoding":904},[883,78735,78737],{"className":78736},[886],[888,78738,78739],{"xmlns":890},[892,78740,78741,78745],{},[895,78742,78743],{},[898,78744,1665],{},[902,78746,1665],{"encoding":904}," změní z 8 na 12.",[198,78749,78751],{"id":78750},"náklady-36316","Náklady (3.6–3.16)",[724,78753,78754,78757,78758,78798,78799,78814,78815,78832,78833,78850,78851,78866,78867,78882,78883,78248,78898,1343,78913,1343,78930,1343,78947,1343,78962,1343,78977,3713,78992,79010,79011,1343,79026,1343,79041,79056],{},[38,78755,78756],{},"3.6"," Jsou dány celkové náklady ",[883,78759,78761],{"className":78760},[886],[888,78762,78763],{"xmlns":890},[892,78764,78765,78795],{},[895,78766,78767,78769,78771,78773,78775,78777,78779,78781,78783],{},[898,78768,11577],{},[898,78770,1766],{},[1656,78772,1713],{},[1667,78774,5267],{},[1656,78776,3633],{},[1667,78778,1680],{},[898,78780,1665],{},[1656,78782,3633],{},[4138,78784,78785],{"scriptlevel":4032,"displaystyle":1658},[3294,78786,78787,78793],{},[2062,78788,78789,78791],{},[898,78790,1665],{},[1667,78792,1680],{},[1667,78794,8580],{},[902,78796,78797],{"encoding":904},"TC = 100 + 2Q + \\tfrac{Q^2}{10}",". (a) Určete fixní náklady ",[883,78800,78802],{"className":78801},[886],[888,78803,78804],{"xmlns":890},[892,78805,78806,78812],{},[895,78807,78808,78810],{},[898,78809,19177],{},[898,78811,1766],{},[902,78813,64160],{"encoding":904},", celkové variabilní náklady ",[883,78816,78818],{"className":78817},[886],[888,78819,78820],{"xmlns":890},[892,78821,78822,78830],{},[895,78823,78824,78826,78828],{},[898,78825,11577],{},[898,78827,49019],{},[898,78829,1766],{},[902,78831,64178],{"encoding":904},", průměrné variabilní náklady ",[883,78834,78836],{"className":78835},[886],[888,78837,78838],{"xmlns":890},[892,78839,78840,78848],{},[895,78841,78842,78844,78846],{},[898,78843,2146],{},[898,78845,49019],{},[898,78847,1766],{},[902,78849,63980],{"encoding":904},", variabilní náklady na jednotku ",[883,78852,78854],{"className":78853},[886],[888,78855,78856],{"xmlns":890},[892,78857,78858,78864],{},[895,78859,78860,78862],{},[898,78861,49019],{},[898,78863,1766],{},[902,78865,72271],{"encoding":904},", průměrné náklady ",[883,78868,78870],{"className":78869},[886],[888,78871,78872],{"xmlns":890},[892,78873,78874,78880],{},[895,78875,78876,78878],{},[898,78877,2146],{},[898,78879,1766],{},[902,78881,64229],{"encoding":904}," a mezní náklady ",[883,78884,78886],{"className":78885},[886],[888,78887,78888],{"xmlns":890},[892,78889,78890,78896],{},[895,78891,78892,78894],{},[898,78893,1703],{},[898,78895,1766],{},[902,78897,63961],{"encoding":904},[883,78899,78901],{"className":78900},[886],[888,78902,78903],{"xmlns":890},[892,78904,78905,78911],{},[895,78906,78907,78909],{},[898,78908,11577],{},[898,78910,1766],{},[902,78912,12033],{"encoding":904},[883,78914,78916],{"className":78915},[886],[888,78917,78918],{"xmlns":890},[892,78919,78920,78928],{},[895,78921,78922,78924,78926],{},[898,78923,11577],{},[898,78925,49019],{},[898,78927,1766],{},[902,78929,64178],{"encoding":904},[883,78931,78933],{"className":78932},[886],[888,78934,78935],{"xmlns":890},[892,78936,78937,78945],{},[895,78938,78939,78941,78943],{},[898,78940,2146],{},[898,78942,49019],{},[898,78944,1766],{},[902,78946,63980],{"encoding":904},[883,78948,78950],{"className":78949},[886],[888,78951,78952],{"xmlns":890},[892,78953,78954,78960],{},[895,78955,78956,78958],{},[898,78957,49019],{},[898,78959,1766],{},[902,78961,72271],{"encoding":904},[883,78963,78965],{"className":78964},[886],[888,78966,78967],{"xmlns":890},[892,78968,78969,78975],{},[895,78970,78971,78973],{},[898,78972,2146],{},[898,78974,1766],{},[902,78976,64229],{"encoding":904},[883,78978,78980],{"className":78979},[886],[888,78981,78982],{"xmlns":890},[892,78983,78984,78990],{},[895,78985,78986,78988],{},[898,78987,1703],{},[898,78989,1766],{},[902,78991,63961],{"encoding":904},[883,78993,78995],{"className":78994},[886],[888,78996,78997],{"xmlns":890},[892,78998,78999,79007],{},[895,79000,79001,79003,79005],{},[898,79002,1665],{},[1656,79004,1713],{},[1667,79006,9267],{},[902,79008,79009],{"encoding":904},"Q = 50",". (c) Rozhodněte, kdy ",[883,79012,79014],{"className":79013},[886],[888,79015,79016],{"xmlns":890},[892,79017,79018,79024],{},[895,79019,79020,79022],{},[898,79021,11577],{},[898,79023,1766],{},[902,79025,12033],{"encoding":904},[883,79027,79029],{"className":79028},[886],[888,79030,79031],{"xmlns":890},[892,79032,79033,79039],{},[895,79034,79035,79037],{},[898,79036,2146],{},[898,79038,1766],{},[902,79040,64229],{"encoding":904},[883,79042,79044],{"className":79043},[886],[888,79045,79046],{"xmlns":890},[892,79047,79048,79054],{},[895,79049,79050,79052],{},[898,79051,1703],{},[898,79053,1766],{},[902,79055,63961],{"encoding":904}," rostou, resp. klesají.",[724,79058,79059,79062,79063,78882,79093,79108,79109,79124,79125,1343,79140,1343,79155,1863],{},[38,79060,79061],{},"3.7"," Jsou dány průměrné náklady ",[883,79064,79066],{"className":79065},[886],[888,79067,79068],{"xmlns":890},[892,79069,79070,79090],{},[895,79071,79072,79074,79076,79078,79086,79088],{},[898,79073,2146],{},[898,79075,1766],{},[1656,79077,1713],{},[4138,79079,79080],{"scriptlevel":4032,"displaystyle":1658},[3294,79081,79082,79084],{},[1667,79083,5267],{},[898,79085,1665],{},[1656,79087,3633],{},[1667,79089,9058],{},[902,79091,79092],{"encoding":904},"AC = \\tfrac{100}{Q} + 20",[883,79094,79096],{"className":79095},[886],[888,79097,79098],{"xmlns":890},[892,79099,79100,79106],{},[895,79101,79102,79104],{},[898,79103,1703],{},[898,79105,1766],{},[902,79107,63961],{"encoding":904},". (a) Určete celkové náklady ",[883,79110,79112],{"className":79111},[886],[888,79113,79114],{"xmlns":890},[892,79115,79116,79122],{},[895,79117,79118,79120],{},[898,79119,11577],{},[898,79121,1766],{},[902,79123,12033],{"encoding":904},". (b) Načrtněte a geometricky charakterizujte křivky ",[883,79126,79128],{"className":79127},[886],[888,79129,79130],{"xmlns":890},[892,79131,79132,79138],{},[895,79133,79134,79136],{},[898,79135,2146],{},[898,79137,1766],{},[902,79139,64229],{"encoding":904},[883,79141,79143],{"className":79142},[886],[888,79144,79145],{"xmlns":890},[892,79146,79147,79153],{},[895,79148,79149,79151],{},[898,79150,11577],{},[898,79152,1766],{},[902,79154,12033],{"encoding":904},[883,79156,79158],{"className":79157},[886],[888,79159,79160],{"xmlns":890},[892,79161,79162,79168],{},[895,79163,79164,79166],{},[898,79165,1703],{},[898,79167,1766],{},[902,79169,63961],{"encoding":904},[724,79171,79172,78757,79175,79219,79220,1343,79237,1343,79252,1343,79269,1343,79284,1343,79301,1863],{},[38,79173,79174],{},"3.8",[883,79176,79178],{"className":79177},[886],[888,79179,79180],{"xmlns":890},[892,79181,79182,79216],{},[895,79183,79184,79186,79188,79190,79192,79194,79196,79198,79200,79202,79208,79210],{},[898,79185,11577],{},[898,79187,1766],{},[1656,79189,1713],{},[1667,79191,9280],{},[1656,79193,3633],{},[1667,79195,46701],{},[898,79197,1665],{},[1656,79199,3964],{},[1667,79201,9112],{},[2062,79203,79204,79206],{},[898,79205,1665],{},[1667,79207,1680],{},[1656,79209,3633],{},[2062,79211,79212,79214],{},[898,79213,1665],{},[1667,79215,2617],{},[902,79217,79218],{"encoding":904},"TC = 80 + 30Q - 6Q^2 + Q^3",". Určete ",[883,79221,79223],{"className":79222},[886],[888,79224,79225],{"xmlns":890},[892,79226,79227,79235],{},[895,79228,79229,79231,79233],{},[898,79230,11577],{},[898,79232,49019],{},[898,79234,1766],{},[902,79236,64178],{"encoding":904},[883,79238,79240],{"className":79239},[886],[888,79241,79242],{"xmlns":890},[892,79243,79244,79250],{},[895,79245,79246,79248],{},[898,79247,19177],{},[898,79249,1766],{},[902,79251,64160],{"encoding":904},[883,79253,79255],{"className":79254},[886],[888,79256,79257],{"xmlns":890},[892,79258,79259,79267],{},[895,79260,79261,79263,79265],{},[898,79262,2146],{},[898,79264,49019],{},[898,79266,1766],{},[902,79268,63980],{"encoding":904},[883,79270,79272],{"className":79271},[886],[888,79273,79274],{"xmlns":890},[892,79275,79276,79282],{},[895,79277,79278,79280],{},[898,79279,2146],{},[898,79281,1766],{},[902,79283,64229],{"encoding":904},[883,79285,79287],{"className":79286},[886],[888,79288,79289],{"xmlns":890},[892,79290,79291,79299],{},[895,79292,79293,79295,79297],{},[898,79294,2146],{},[898,79296,19177],{},[898,79298,1766],{},[902,79300,64196],{"encoding":904},[883,79302,79304],{"className":79303},[886],[888,79305,79306],{"xmlns":890},[892,79307,79308,79314],{},[895,79309,79310,79312],{},[898,79311,1703],{},[898,79313,1766],{},[902,79315,63961],{"encoding":904},[724,79317,79318,78757,79321,79351,79352,78534,79367,3713,79380,1343,79398,1343,79416,78601,79434,78624,79456,79471,79472,79485,79486,1863],{},[38,79319,79320],{},"3.9",[883,79322,79324],{"className":79323},[886],[888,79325,79326],{"xmlns":890},[892,79327,79328,79348],{},[895,79329,79330,79332,79334,79336,79338,79340,79342],{},[898,79331,11577],{},[898,79333,1766],{},[1656,79335,1713],{},[1667,79337,8059],{},[1656,79339,3633],{},[1667,79341,28042],{},[2062,79343,79344,79346],{},[898,79345,1665],{},[1667,79347,1680],{},[902,79349,79350],{"encoding":904},"TC = 500 + 0{,}6Q^2",". (a) Určete, jak rychle se přibližně mění ",[883,79353,79355],{"className":79354},[886],[888,79356,79357],{"xmlns":890},[892,79358,79359,79365],{},[895,79360,79361,79363],{},[898,79362,11577],{},[898,79364,1766],{},[902,79366,12033],{"encoding":904},[883,79368,79370],{"className":79369},[886],[888,79371,79372],{"xmlns":890},[892,79373,79374,79378],{},[895,79375,79376],{},[898,79377,1665],{},[902,79379,1665],{"encoding":904},[883,79381,79383],{"className":79382},[886],[888,79384,79385],{"xmlns":890},[892,79386,79387,79395],{},[895,79388,79389,79391,79393],{},[898,79390,1665],{},[1656,79392,1713],{},[1667,79394,8580],{},[902,79396,79397],{"encoding":904},"Q = 10",[883,79399,79401],{"className":79400},[886],[888,79402,79403],{"xmlns":890},[892,79404,79405,79413],{},[895,79406,79407,79409,79411],{},[898,79408,1665],{},[1656,79410,1713],{},[1667,79412,9058],{},[902,79414,79415],{"encoding":904},"Q = 20",[883,79417,79419],{"className":79418},[886],[888,79420,79421],{"xmlns":890},[892,79422,79423,79431],{},[895,79424,79425,79427,79429],{},[898,79426,1665],{},[1656,79428,1713],{},[1667,79430,46701],{},[902,79432,79433],{"encoding":904},"Q = 30",[883,79435,79437],{"className":79436},[886],[888,79438,79439],{"xmlns":890},[892,79440,79441,79453],{},[895,79442,79443,79445,79447,79449,79451],{},[898,79444,1703],{},[898,79446,1766],{},[1656,79448,1659],{"stretchy":1658},[1667,79450,44930],{},[1656,79452,1683],{"stretchy":1658},[902,79454,79455],{"encoding":904},"MC(15)",[883,79457,79459],{"className":79458},[886],[888,79460,79461],{"xmlns":890},[892,79462,79463,79469],{},[895,79464,79465,79467],{},[898,79466,11577],{},[898,79468,1766],{},[902,79470,12033],{"encoding":904}," v důsledku změny ",[883,79473,79475],{"className":79474},[886],[888,79476,79477],{"xmlns":890},[892,79478,79479,79483],{},[895,79480,79481],{},[898,79482,1665],{},[902,79484,1665],{"encoding":904}," z 15 na 20 a porovnejte se skutečnou změnou ",[883,79487,79489],{"className":79488},[886],[888,79490,79491],{"xmlns":890},[892,79492,79493,79499],{},[895,79494,79495,79497],{},[898,79496,11577],{},[898,79498,1766],{},[902,79500,12033],{"encoding":904},[724,79502,79503,79506,79507,79108,79543,79558,79559,78718,79578,79471,79593,79606],{},[38,79504,79505],{},"3.10"," Jsou dány mezní náklady ",[883,79508,79510],{"className":79509},[886],[888,79511,79512],{"xmlns":890},[892,79513,79514,79540],{},[895,79515,79516,79518,79520,79522,79524,79526,79528,79530,79532,79534],{},[898,79517,1703],{},[898,79519,1766],{},[1656,79521,1713],{},[1667,79523,11918],{},[1656,79525,3964],{},[1667,79527,2668],{},[898,79529,1665],{},[1656,79531,3633],{},[1667,79533,8845],{},[2062,79535,79536,79538],{},[898,79537,1665],{},[1667,79539,1680],{},[902,79541,79542],{"encoding":904},"MC = 60 - 16Q + 1{,}5Q^2",[883,79544,79546],{"className":79545},[886],[888,79547,79548],{"xmlns":890},[892,79549,79550,79556],{},[895,79551,79552,79554],{},[898,79553,11577],{},[898,79555,1766],{},[902,79557,12033],{"encoding":904},", jestliže fixní náklady ",[883,79560,79562],{"className":79561},[886],[888,79563,79564],{"xmlns":890},[892,79565,79566,79576],{},[895,79567,79568,79570,79572,79574],{},[898,79569,19177],{},[898,79571,1766],{},[1656,79573,1713],{},[1667,79575,5267],{},[902,79577,20370],{"encoding":904},[883,79579,79581],{"className":79580},[886],[888,79582,79583],{"xmlns":890},[892,79584,79585,79591],{},[895,79586,79587,79589],{},[898,79588,11577],{},[898,79590,1766],{},[902,79592,12033],{"encoding":904},[883,79594,79596],{"className":79595},[886],[888,79597,79598],{"xmlns":890},[892,79599,79600,79604],{},[895,79601,79602],{},[898,79603,1665],{},[902,79605,1665],{"encoding":904}," z 15 na 20.",[724,79608,79609,78757,79612,79655,79656,79669,79670,79685,79686,79701,79702,79669,79715,79685,79732,79749,79750,79669,79763,79685,79778,79793,79794,79814,79815,79838],{},[38,79610,79611],{},"3.11",[883,79613,79615],{"className":79614},[886],[888,79616,79617],{"xmlns":890},[892,79618,79619,79653],{},[895,79620,79621,79623,79625,79627,79629,79631,79633,79635,79637,79639,79645,79647],{},[898,79622,11577],{},[898,79624,1766],{},[1656,79626,1713],{},[1667,79628,5267],{},[1656,79630,3633],{},[1667,79632,8567],{},[898,79634,1665],{},[1656,79636,3964],{},[1667,79638,5193],{},[2062,79640,79641,79643],{},[898,79642,1665],{},[1667,79644,1680],{},[1656,79646,3633],{},[2062,79648,79649,79651],{},[898,79650,1665],{},[1667,79652,2617],{},[902,79654,69575],{"encoding":904},". (a) Určete ",[883,79657,79659],{"className":79658},[886],[888,79660,79661],{"xmlns":890},[892,79662,79663,79667],{},[895,79664,79665],{},[898,79666,1665],{},[902,79668,1665],{"encoding":904},", které minimalizuje ",[883,79671,79673],{"className":79672},[886],[888,79674,79675],{"xmlns":890},[892,79676,79677,79683],{},[895,79678,79679,79681],{},[898,79680,1703],{},[898,79682,1766],{},[902,79684,63961],{"encoding":904}," a stanovte příslušnou hodnotu minima ",[883,79687,79689],{"className":79688},[886],[888,79690,79691],{"xmlns":890},[892,79692,79693,79699],{},[895,79694,79695,79697],{},[898,79696,1703],{},[898,79698,1766],{},[902,79700,63961],{"encoding":904},". (b) Určete ",[883,79703,79705],{"className":79704},[886],[888,79706,79707],{"xmlns":890},[892,79708,79709,79713],{},[895,79710,79711],{},[898,79712,1665],{},[902,79714,1665],{"encoding":904},[883,79716,79718],{"className":79717},[886],[888,79719,79720],{"xmlns":890},[892,79721,79722,79730],{},[895,79723,79724,79726,79728],{},[898,79725,2146],{},[898,79727,49019],{},[898,79729,1766],{},[902,79731,63980],{"encoding":904},[883,79733,79735],{"className":79734},[886],[888,79736,79737],{"xmlns":890},[892,79738,79739,79747],{},[895,79740,79741,79743,79745],{},[898,79742,2146],{},[898,79744,49019],{},[898,79746,1766],{},[902,79748,63980],{"encoding":904},". (c) Určete ",[883,79751,79753],{"className":79752},[886],[888,79754,79755],{"xmlns":890},[892,79756,79757,79761],{},[895,79758,79759],{},[898,79760,1665],{},[902,79762,1665],{"encoding":904},[883,79764,79766],{"className":79765},[886],[888,79767,79768],{"xmlns":890},[892,79769,79770,79776],{},[895,79771,79772,79774],{},[898,79773,2146],{},[898,79775,1766],{},[902,79777,64229],{"encoding":904},[883,79779,79781],{"className":79780},[886],[888,79782,79783],{"xmlns":890},[892,79784,79785,79791],{},[895,79786,79787,79789],{},[898,79788,2146],{},[898,79790,1766],{},[902,79792,64229],{"encoding":904}," (rada: hledaný kořen ",[883,79795,79797],{"className":79796},[886],[888,79798,79799],{"xmlns":890},[892,79800,79801,79811],{},[895,79802,79803,79805],{},[898,79804,2146],{},[2062,79806,79807,79809],{},[898,79808,1766],{},[1656,79810,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[902,79812,79813],{"encoding":904},"AC'"," určete přibližně, patří do ",[883,79816,79818],{"className":79817},[886],[888,79819,79820],{"xmlns":890},[892,79821,79822,79835],{},[895,79823,79824,79826,79829,79831,79833],{},[1656,79825,1659],{"stretchy":1658},[1667,79827,79828],{},"4,7",[1656,79830,2856],{"separator":1672},[1667,79832,14048],{},[1656,79834,1683],{"stretchy":1658},[902,79836,79837],{"encoding":904},"(4{,}7; 4{,}8)",", zpřesněte).",[724,79840,79841,79844,79845,3565,79873,79890,79891,30312,79932,79953],{},[38,79842,79843],{},"3.12"," Dokažte, že mají-li průměrné náklady ",[883,79846,79848],{"className":79847},[886],[888,79849,79850],{"xmlns":890},[892,79851,79852,79870],{},[895,79853,79854,79856,79858,79860,79862,79864,79866,79868],{},[898,79855,2146],{},[898,79857,1766],{},[1656,79859,1713],{},[898,79861,2146],{},[898,79863,1766],{},[1656,79865,1659],{"stretchy":1658},[898,79867,1665],{},[1656,79869,1683],{"stretchy":1658},[902,79871,79872],{"encoding":904},"AC = AC(Q)",[883,79874,79876],{"className":79875},[886],[888,79877,79878],{"xmlns":890},[892,79879,79880,79888],{},[895,79881,79882],{},[1661,79883,79884,79886],{},[898,79885,1665],{},[1667,79887,4032],{},[902,79889,46990],{"encoding":904}," minimum, pak platí ",[883,79892,79894],{"className":79893},[886],[888,79895,79896],{"xmlns":890},[892,79897,79898,79930],{},[895,79899,79900,79902,79904,79906,79912,79914,79916,79918,79920,79922,79928],{},[898,79901,2146],{},[898,79903,1766],{},[1656,79905,1659],{"stretchy":1658},[1661,79907,79908,79910],{},[898,79909,1665],{},[1667,79911,4032],{},[1656,79913,1683],{"stretchy":1658},[1656,79915,1713],{},[898,79917,1703],{},[898,79919,1766],{},[1656,79921,1659],{"stretchy":1658},[1661,79923,79924,79926],{},[898,79925,1665],{},[1667,79927,4032],{},[1656,79929,1683],{"stretchy":1658},[902,79931,71236],{"encoding":904},[883,79933,79935],{"className":79934},[886],[888,79936,79937],{"xmlns":890},[892,79938,79939,79951],{},[895,79940,79941,79943,79945,79947,79949],{},[898,79942,1703],{},[898,79944,1766],{},[1656,79946,1659],{"stretchy":1658},[898,79948,1665],{},[1656,79950,1683],{"stretchy":1658},[902,79952,76357],{"encoding":904}," jsou mezní náklady.",[724,79955,79956,78757,79959,79219,79993,79669,80006,79685,80021,1863],{},[38,79957,79958],{},"3.13",[883,79960,79962],{"className":79961},[886],[888,79963,79964],{"xmlns":890},[892,79965,79966,79990],{},[895,79967,79968,79970,79972,79974,79980,79982,79984,79986,79988],{},[898,79969,11577],{},[898,79971,1766],{},[1656,79973,1713],{},[2062,79975,79976,79978],{},[898,79977,1665],{},[1667,79979,1680],{},[1656,79981,3633],{},[1667,79983,1680],{},[898,79985,1665],{},[1656,79987,3633],{},[1667,79989,8567],{},[902,79991,79992],{"encoding":904},"TC = Q^2 + 2Q + 25",[883,79994,79996],{"className":79995},[886],[888,79997,79998],{"xmlns":890},[892,79999,80000,80004],{},[895,80001,80002],{},[898,80003,1665],{},[902,80005,1665],{"encoding":904},[883,80007,80009],{"className":80008},[886],[888,80010,80011],{"xmlns":890},[892,80012,80013,80019],{},[895,80014,80015,80017],{},[898,80016,2146],{},[898,80018,1766],{},[902,80020,64229],{"encoding":904},[883,80022,80024],{"className":80023},[886],[888,80025,80026],{"xmlns":890},[892,80027,80028,80034],{},[895,80029,80030,80032],{},[898,80031,2146],{},[898,80033,1766],{},[902,80035,64229],{"encoding":904},[724,80037,80038,80041,80042,3565,80074,79890,80091,30312,80134,79953],{},[38,80039,80040],{},"3.14"," Dokažte, že mají-li průměrné variabilní náklady ",[883,80043,80045],{"className":80044},[886],[888,80046,80047],{"xmlns":890},[892,80048,80049,80071],{},[895,80050,80051,80053,80055,80057,80059,80061,80063,80065,80067,80069],{},[898,80052,2146],{},[898,80054,49019],{},[898,80056,1766],{},[1656,80058,1713],{},[898,80060,2146],{},[898,80062,49019],{},[898,80064,1766],{},[1656,80066,1659],{"stretchy":1658},[898,80068,1665],{},[1656,80070,1683],{"stretchy":1658},[902,80072,80073],{"encoding":904},"AVC = AVC(Q)",[883,80075,80077],{"className":80076},[886],[888,80078,80079],{"xmlns":890},[892,80080,80081,80089],{},[895,80082,80083],{},[1661,80084,80085,80087],{},[898,80086,1665],{},[1667,80088,4032],{},[902,80090,46990],{"encoding":904},[883,80092,80094],{"className":80093},[886],[888,80095,80096],{"xmlns":890},[892,80097,80098,80132],{},[895,80099,80100,80102,80104,80106,80108,80114,80116,80118,80120,80122,80124,80130],{},[898,80101,2146],{},[898,80103,49019],{},[898,80105,1766],{},[1656,80107,1659],{"stretchy":1658},[1661,80109,80110,80112],{},[898,80111,1665],{},[1667,80113,4032],{},[1656,80115,1683],{"stretchy":1658},[1656,80117,1713],{},[898,80119,1703],{},[898,80121,1766],{},[1656,80123,1659],{"stretchy":1658},[1661,80125,80126,80128],{},[898,80127,1665],{},[1667,80129,4032],{},[1656,80131,1683],{"stretchy":1658},[902,80133,77683],{"encoding":904},[883,80135,80137],{"className":80136},[886],[888,80138,80139],{"xmlns":890},[892,80140,80141,80153],{},[895,80142,80143,80145,80147,80149,80151],{},[898,80144,1703],{},[898,80146,1766],{},[1656,80148,1659],{"stretchy":1658},[898,80150,1665],{},[1656,80152,1683],{"stretchy":1658},[902,80154,76357],{"encoding":904},[724,80156,80157,78757,80160,79219,80206,79669,80219,79685,80236,1863],{},[38,80158,80159],{},"3.15",[883,80161,80163],{"className":80162},[886],[888,80164,80165],{"xmlns":890},[892,80166,80167,80203],{},[895,80168,80169,80171,80173,80175,80177,80179,80181,80183,80185,80187,80193,80195,80197],{},[898,80170,11577],{},[898,80172,1766],{},[1656,80174,1713],{},[1667,80176,9267],{},[1656,80178,3633],{},[1667,80180,44930],{},[898,80182,1665],{},[1656,80184,3964],{},[1667,80186,1680],{},[2062,80188,80189,80191],{},[898,80190,1665],{},[1667,80192,1680],{},[1656,80194,3633],{},[1667,80196,11639],{},[2062,80198,80199,80201],{},[898,80200,1665],{},[1667,80202,2617],{},[902,80204,80205],{"encoding":904},"TC = 50 + 15Q - 2Q^2 + 0{,}2Q^3",[883,80207,80209],{"className":80208},[886],[888,80210,80211],{"xmlns":890},[892,80212,80213,80217],{},[895,80214,80215],{},[898,80216,1665],{},[902,80218,1665],{"encoding":904},[883,80220,80222],{"className":80221},[886],[888,80223,80224],{"xmlns":890},[892,80225,80226,80234],{},[895,80227,80228,80230,80232],{},[898,80229,2146],{},[898,80231,49019],{},[898,80233,1766],{},[902,80235,63980],{"encoding":904},[883,80237,80239],{"className":80238},[886],[888,80240,80241],{"xmlns":890},[892,80242,80243,80251],{},[895,80244,80245,80247,80249],{},[898,80246,2146],{},[898,80248,49019],{},[898,80250,1766],{},[902,80252,63980],{"encoding":904},[724,80254,80255,80258,80259,80272,80273,80293],{},[38,80256,80257],{},"3.16"," Celkové náklady na výstavbu domu o ",[883,80260,80262],{"className":80261},[886],[888,80263,80264],{"xmlns":890},[892,80265,80266,80270],{},[895,80267,80268],{},[898,80269,10848],{},[902,80271,10848],{"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 ",[883,80274,80276],{"className":80275},[886],[888,80277,80278],{"xmlns":890},[892,80279,80280,80290],{},[895,80281,80282,80284,80286,80288],{},[1667,80283,8580],{},[2461,80285,7828],{},[1667,80287,67750],{},[898,80289,10848],{},[902,80291,80292],{"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.",[198,80295,80297],{"id":80296},"zisk-body-zvratu-317325","Zisk, body zvratu (3.17–3.25)",[724,80299,80300,80303,80304,1896,80326,80352],{},[38,80301,80302],{},"3.17"," Jsou dány ",[883,80305,80307],{"className":80306},[886],[888,80308,80309],{"xmlns":890},[892,80310,80311,80323],{},[895,80312,80313,80315,80317,80319,80321],{},[898,80314,11577],{},[898,80316,1763],{},[1656,80318,1713],{},[1667,80320,8580],{},[898,80322,1665],{},[902,80324,80325],{"encoding":904},"TR = 10Q",[883,80327,80329],{"className":80328},[886],[888,80330,80331],{"xmlns":890},[892,80332,80333,80349],{},[895,80334,80335,80337,80339,80341,80343,80345,80347],{},[898,80336,11577],{},[898,80338,1766],{},[1656,80340,1713],{},[1667,80342,5267],{},[1656,80344,3633],{},[1667,80346,5193],{},[898,80348,1665],{},[902,80350,80351],{"encoding":904},"TC = 100 + 5Q",". Určete body zvratu a geometricky výsledek interpretujte.",[724,80354,80355,80358,80359,14953,80374,80389,80390,1343,80412,30312,80439,80461,80462,80496],{},[38,80356,80357],{},"3.18"," Odvoďte, že jestliže ",[883,80360,80362],{"className":80361},[886],[888,80363,80364],{"xmlns":890},[892,80365,80366,80372],{},[895,80367,80368,80370],{},[898,80369,11577],{},[898,80371,1763],{},[902,80373,12875],{"encoding":904},[883,80375,80377],{"className":80376},[886],[888,80378,80379],{"xmlns":890},[892,80380,80381,80387],{},[895,80382,80383,80385],{},[898,80384,11577],{},[898,80386,1766],{},[902,80388,12033],{"encoding":904}," jsou lineární tvaru ",[883,80391,80393],{"className":80392},[886],[888,80394,80395],{"xmlns":890},[892,80396,80397,80409],{},[895,80398,80399,80401,80403,80405,80407],{},[898,80400,11577],{},[898,80402,1763],{},[1656,80404,1713],{},[898,80406,724],{},[898,80408,1665],{},[902,80410,80411],{"encoding":904},"TR = pQ",[883,80413,80415],{"className":80414},[886],[888,80416,80417],{"xmlns":890},[892,80418,80419,80436],{},[895,80420,80421,80423,80425,80427,80430,80432,80434],{},[898,80422,11577],{},[898,80424,1766],{},[1656,80426,1713],{},[898,80428,80429],{},"m",[1656,80431,3633],{},[898,80433,2292],{},[898,80435,1665],{},[902,80437,80438],{"encoding":904},"TC = m + nQ",[883,80440,80442],{"className":80441},[886],[888,80443,80444],{"xmlns":890},[892,80445,80446,80458],{},[895,80447,80448,80450,80452,80454,80456],{},[898,80449,80429],{},[1656,80451,1673],{"separator":1672},[898,80453,2292],{},[1656,80455,1673],{"separator":1672},[898,80457,724],{},[902,80459,80460],{"encoding":904},"m, n, p"," jsou pevně zadány, pak existuje jediný bod zvratu ",[883,80463,80465],{"className":80464},[886],[888,80466,80467],{"xmlns":890},[892,80468,80469,80493],{},[895,80470,80471,80477,80479],{},[2062,80472,80473,80475],{},[898,80474,1665],{},[1656,80476,8187],{},[1656,80478,1713],{},[4138,80480,80481],{"scriptlevel":4032,"displaystyle":1658},[3294,80482,80483,80485],{},[898,80484,80429],{},[895,80486,80487,80489,80491],{},[898,80488,724],{},[1656,80490,3964],{},[898,80492,2292],{},[902,80494,80495],{"encoding":904},"Q^* = \\tfrac{m}{p - n}"," a proveďte diskusi podmínek. Načrtněte obrázek.",[724,80498,80499,80303,80502,1896,80536,79655,80562,80575,80576,78407,80591,80606,80607,78391,80620,78407,80635,80650],{},[38,80500,80501],{},"3.19",[883,80503,80505],{"className":80504},[886],[888,80506,80507],{"xmlns":890},[892,80508,80509,80533],{},[895,80510,80511,80513,80515,80517,80519,80521,80527,80529,80531],{},[898,80512,11577],{},[898,80514,1763],{},[1656,80516,1713],{},[1656,80518,3964],{},[1667,80520,1680],{},[2062,80522,80523,80525],{},[898,80524,1665],{},[1667,80526,1680],{},[1656,80528,3633],{},[1667,80530,31664],{},[898,80532,1665],{},[902,80534,80535],{"encoding":904},"TR = -2Q^2 + 14Q",[883,80537,80539],{"className":80538},[886],[888,80540,80541],{"xmlns":890},[892,80542,80543,80559],{},[895,80544,80545,80547,80549,80551,80553,80555,80557],{},[898,80546,11577],{},[898,80548,1766],{},[1656,80550,1713],{},[1667,80552,1680],{},[898,80554,1665],{},[1656,80556,3633],{},[1667,80558,8580],{},[902,80560,80561],{"encoding":904},"TC = 2Q + 10",[883,80563,80565],{"className":80564},[886],[888,80566,80567],{"xmlns":890},[892,80568,80569,80573],{},[895,80570,80571],{},[898,80572,1665],{},[902,80574,1665],{"encoding":904},", které maximalizuje zisk ",[883,80577,80579],{"className":80578},[886],[888,80580,80581],{"xmlns":890},[892,80582,80583,80589],{},[895,80584,80585,80587],{},[898,80586,8194],{},[898,80588,1763],{},[902,80590,72145],{"encoding":904},[883,80592,80594],{"className":80593},[886],[888,80595,80596],{"xmlns":890},[892,80597,80598,80604],{},[895,80599,80600,80602],{},[898,80601,8194],{},[898,80603,1763],{},[902,80605,72145],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku. (c) Určete ",[883,80608,80610],{"className":80609},[886],[888,80611,80612],{"xmlns":890},[892,80613,80614,80618],{},[895,80615,80616],{},[898,80617,1665],{},[902,80619,1665],{"encoding":904},[883,80621,80623],{"className":80622},[886],[888,80624,80625],{"xmlns":890},[892,80626,80627,80633],{},[895,80628,80629,80631],{},[898,80630,11577],{},[898,80632,1763],{},[902,80634,12875],{"encoding":904},[883,80636,80638],{"className":80637},[886],[888,80639,80640],{"xmlns":890},[892,80641,80642,80648],{},[895,80643,80644,80646],{},[898,80645,11577],{},[898,80647,1763],{},[902,80649,12875],{"encoding":904},". (d) Graficky interpretujte.",[724,80652,80653,56359,80656,1343,80682,1343,80701,79655,80721,80575,80734,78407,80749,80764,80765,80787,80788,79838],{},[38,80654,80655],{},"3.20",[883,80657,80659],{"className":80658},[886],[888,80660,80661],{"xmlns":890},[892,80662,80663,80679],{},[895,80664,80665,80667,80669,80671,80673],{},[898,80666,8194],{},[1656,80668,1713],{},[1667,80670,28863],{},[1656,80672,3964],{},[2062,80674,80675,80677],{},[898,80676,1665],{},[1667,80678,1680],{},[902,80680,80681],{"encoding":904},"P = 400 - Q^2",[883,80683,80685],{"className":80684},[886],[888,80686,80687],{"xmlns":890},[892,80688,80689,80699],{},[895,80690,80691,80693,80695,80697],{},[898,80692,19177],{},[898,80694,1766],{},[1656,80696,1713],{},[1667,80698,5267],{},[902,80700,20370],{"encoding":904},[883,80702,80704],{"className":80703},[886],[888,80705,80706],{"xmlns":890},[892,80707,80708,80718],{},[895,80709,80710,80712,80714,80716],{},[898,80711,1703],{},[898,80713,1766],{},[1656,80715,1713],{},[1667,80717,9058],{},[902,80719,80720],{"encoding":904},"MC = 20",[883,80722,80724],{"className":80723},[886],[888,80725,80726],{"xmlns":890},[892,80727,80728,80732],{},[895,80729,80730],{},[898,80731,1665],{},[902,80733,1665],{"encoding":904},[883,80735,80737],{"className":80736},[886],[888,80738,80739],{"xmlns":890},[892,80740,80741,80747],{},[895,80742,80743,80745],{},[898,80744,8194],{},[898,80746,1763],{},[902,80748,72145],{"encoding":904},[883,80750,80752],{"className":80751},[886],[888,80753,80754],{"xmlns":890},[892,80755,80756,80762],{},[895,80757,80758,80760],{},[898,80759,8194],{},[898,80761,1763],{},[902,80763,72145],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku (rada: jeden z bodů zvratu patří do ",[883,80766,80768],{"className":80767},[886],[888,80769,80770],{"xmlns":890},[892,80771,80772,80784],{},[895,80773,80774,80776,80778,80780,80782],{},[1656,80775,1659],{"stretchy":1658},[1667,80777,4032],{},[1656,80779,1673],{"separator":1672},[1667,80781,1669],{},[1656,80783,1683],{"stretchy":1658},[902,80785,80786],{"encoding":904},"(0, 1)",", druhý do ",[883,80789,80791],{"className":80790},[886],[888,80792,80793],{"xmlns":890},[892,80794,80795,80808],{},[895,80796,80797,80799,80802,80804,80806],{},[1656,80798,1659],{"stretchy":1658},[1667,80800,80801],{},"19",[1656,80803,1673],{"separator":1672},[1667,80805,9058],{},[1656,80807,1683],{"stretchy":1658},[902,80809,80810],{"encoding":904},"(19, 20)",[724,80812,80813,80816,80817,3565,80845,80862,80863,1863],{},[38,80814,80815],{},"3.21"," Dokažte, že má-li zisk ",[883,80818,80820],{"className":80819},[886],[888,80821,80822],{"xmlns":890},[892,80823,80824,80842],{},[895,80825,80826,80828,80830,80832,80834,80836,80838,80840],{},[898,80827,8194],{},[898,80829,1763],{},[1656,80831,1713],{},[898,80833,8194],{},[898,80835,1763],{},[1656,80837,1659],{"stretchy":1658},[898,80839,1665],{},[1656,80841,1683],{"stretchy":1658},[902,80843,80844],{"encoding":904},"PR = PR(Q)",[883,80846,80848],{"className":80847},[886],[888,80849,80850],{"xmlns":890},[892,80851,80852,80860],{},[895,80853,80854],{},[1661,80855,80856,80858],{},[898,80857,1665],{},[1667,80859,4032],{},[902,80861,46990],{"encoding":904}," maximum, pak platí ",[883,80864,80866],{"className":80865},[886],[888,80867,80868],{"xmlns":890},[892,80869,80870,80902],{},[895,80871,80872,80874,80876,80878,80884,80886,80888,80890,80892,80894,80900],{},[898,80873,1703],{},[898,80875,1763],{},[1656,80877,1659],{"stretchy":1658},[1661,80879,80880,80882],{},[898,80881,1665],{},[1667,80883,4032],{},[1656,80885,1683],{"stretchy":1658},[1656,80887,1713],{},[898,80889,1703],{},[898,80891,1766],{},[1656,80893,1659],{"stretchy":1658},[1661,80895,80896,80898],{},[898,80897,1665],{},[1667,80899,4032],{},[1656,80901,1683],{"stretchy":1658},[902,80903,74310],{"encoding":904},[724,80905,80906,80909,80910,1896,80925,64694,80940,80575,80953,80968,80969,1343,80996,81032,81033,1343,81060,1863],{},[38,80907,80908],{},"3.22"," Pro zadané ",[883,80911,80913],{"className":80912},[886],[888,80914,80915],{"xmlns":890},[892,80916,80917,80923],{},[895,80918,80919,80921],{},[898,80920,1703],{},[898,80922,1763],{},[902,80924,15395],{"encoding":904},[883,80926,80928],{"className":80927},[886],[888,80929,80930],{"xmlns":890},[892,80931,80932,80938],{},[895,80933,80934,80936],{},[898,80935,1703],{},[898,80937,1766],{},[902,80939,63961],{"encoding":904},[883,80941,80943],{"className":80942},[886],[888,80944,80945],{"xmlns":890},[892,80946,80947,80951],{},[895,80948,80949],{},[898,80950,1665],{},[902,80952,1665],{"encoding":904},[883,80954,80956],{"className":80955},[886],[888,80957,80958],{"xmlns":890},[892,80959,80960,80966],{},[895,80961,80962,80964],{},[898,80963,8194],{},[898,80965,1763],{},[902,80967,72145],{"encoding":904},". (a) ",[883,80970,80972],{"className":80971},[886],[888,80973,80974],{"xmlns":890},[892,80975,80976,80993],{},[895,80977,80978,80980,80982,80984,80987,80989,80991],{},[898,80979,1703],{},[898,80981,1763],{},[1656,80983,1713],{},[1667,80985,80986],{},"236",[1656,80988,3964],{},[1667,80990,2668],{},[898,80992,1665],{},[902,80994,80995],{"encoding":904},"MR = 236 - 16Q",[883,80997,80999],{"className":80998},[886],[888,81000,81001],{"xmlns":890},[892,81002,81003,81029],{},[895,81004,81005,81007,81009,81011,81013,81019,81021,81023,81025,81027],{},[898,81006,1703],{},[898,81008,1766],{},[1656,81010,1713],{},[1667,81012,2617],{},[2062,81014,81015,81017],{},[898,81016,1665],{},[1667,81018,1680],{},[1656,81020,3964],{},[1667,81022,2992],{},[898,81024,1665],{},[1656,81026,3633],{},[1667,81028,14509],{},[902,81030,81031],{"encoding":904},"MC = 3Q^2 - 32Q + 96",". (b) ",[883,81034,81036],{"className":81035},[886],[888,81037,81038],{"xmlns":890},[892,81039,81040,81057],{},[895,81041,81042,81044,81046,81048,81051,81053,81055],{},[898,81043,1703],{},[898,81045,1763],{},[1656,81047,1713],{},[1667,81049,81050],{},"280",[1656,81052,3964],{},[1667,81054,9058],{},[898,81056,1665],{},[902,81058,81059],{"encoding":904},"MR = 280 - 20Q",[883,81061,81063],{"className":81062},[886],[888,81064,81065],{"xmlns":890},[892,81066,81067,81094],{},[895,81068,81069,81071,81073,81075,81078,81084,81086,81088,81090,81092],{},[898,81070,1703],{},[898,81072,1766],{},[1656,81074,1713],{},[1667,81076,81077],{},"1,6",[2062,81079,81080,81082],{},[898,81081,1665],{},[1667,81083,1680],{},[1656,81085,3964],{},[1667,81087,44930],{},[898,81089,1665],{},[1656,81091,3633],{},[1667,81093,11918],{},[902,81095,81096],{"encoding":904},"MC = 1{,}6Q^2 - 15Q + 60",[724,81098,81099,80909,81102,1896,81117,64694,81132,78391,81145,78407,81160,80968,81175,1343,81205,81032,81241,1343,81273,81317,81318,1343,81350,1863],{},[38,81100,81101],{},"3.23",[883,81103,81105],{"className":81104},[886],[888,81106,81107],{"xmlns":890},[892,81108,81109,81115],{},[895,81110,81111,81113],{},[898,81112,11577],{},[898,81114,1763],{},[902,81116,12875],{"encoding":904},[883,81118,81120],{"className":81119},[886],[888,81121,81122],{"xmlns":890},[892,81123,81124,81130],{},[895,81125,81126,81128],{},[898,81127,11577],{},[898,81129,1766],{},[902,81131,12033],{"encoding":904},[883,81133,81135],{"className":81134},[886],[888,81136,81137],{"xmlns":890},[892,81138,81139,81143],{},[895,81140,81141],{},[898,81142,1665],{},[902,81144,1665],{"encoding":904},[883,81146,81148],{"className":81147},[886],[888,81149,81150],{"xmlns":890},[892,81151,81152,81158],{},[895,81153,81154,81156],{},[898,81155,8194],{},[898,81157,1763],{},[902,81159,72145],{"encoding":904},[883,81161,81163],{"className":81162},[886],[888,81164,81165],{"xmlns":890},[892,81166,81167,81173],{},[895,81168,81169,81171],{},[898,81170,8194],{},[898,81172,1763],{},[902,81174,72145],{"encoding":904},[883,81176,81178],{"className":81177},[886],[888,81179,81180],{"xmlns":890},[892,81181,81182,81202],{},[895,81183,81184,81186,81188,81190,81192,81194,81196],{},[898,81185,11577],{},[898,81187,1763],{},[1656,81189,1713],{},[1667,81191,9107],{},[898,81193,1665],{},[1656,81195,3964],{},[2062,81197,81198,81200],{},[898,81199,1665],{},[1667,81201,1680],{},[902,81203,81204],{"encoding":904},"TR = 125Q - Q^2",[883,81206,81208],{"className":81207},[886],[888,81209,81210],{"xmlns":890},[892,81211,81212,81238],{},[895,81213,81214,81216,81218,81220,81222,81224,81226,81228,81230,81232],{},[898,81215,11577],{},[898,81217,1766],{},[1656,81219,1713],{},[1667,81221,8059],{},[1656,81223,3633],{},[1667,81225,5193],{},[898,81227,1665],{},[1656,81229,3633],{},[1667,81231,13779],{},[2062,81233,81234,81236],{},[898,81235,1665],{},[1667,81237,1680],{},[902,81239,81240],{"encoding":904},"TC = 500 + 5Q + 0{,}5Q^2",[883,81242,81244],{"className":81243},[886],[888,81245,81246],{"xmlns":890},[892,81247,81248,81270],{},[895,81249,81250,81252,81254,81256,81258,81260,81262,81264],{},[898,81251,11577],{},[898,81253,1763],{},[1656,81255,1713],{},[1667,81257,9058],{},[898,81259,1665],{},[1656,81261,3964],{},[1667,81263,1680],{},[2062,81265,81266,81268],{},[898,81267,1665],{},[1667,81269,1680],{},[902,81271,81272],{"encoding":904},"TR = 20Q - 2Q^2",[883,81274,81276],{"className":81275},[886],[888,81277,81278],{"xmlns":890},[892,81279,81280,81314],{},[895,81281,81282,81284,81286,81288,81290,81292,81294,81296,81298,81300,81306,81308],{},[898,81283,11577],{},[898,81285,1766],{},[1656,81287,1713],{},[1667,81289,1680],{},[1656,81291,3633],{},[1667,81293,9058],{},[898,81295,1665],{},[1656,81297,3964],{},[1667,81299,2877],{},[2062,81301,81302,81304],{},[898,81303,1665],{},[1667,81305,1680],{},[1656,81307,3633],{},[2062,81309,81310,81312],{},[898,81311,1665],{},[1667,81313,2617],{},[902,81315,81316],{"encoding":904},"TC = 2 + 20Q - 8Q^2 + Q^3",". (c) ",[883,81319,81321],{"className":81320},[886],[888,81322,81323],{"xmlns":890},[892,81324,81325,81347],{},[895,81326,81327,81329,81331,81333,81335,81337,81339,81341],{},[898,81328,11577],{},[898,81330,1763],{},[1656,81332,1713],{},[1667,81334,2673],{},[898,81336,1665],{},[1656,81338,3964],{},[1667,81340,32506],{},[2062,81342,81343,81345],{},[898,81344,1665],{},[1667,81346,1680],{},[902,81348,81349],{"encoding":904},"TR = 4Q - 0{,}25Q^2",[883,81351,81353],{"className":81352},[886],[888,81354,81355],{"xmlns":890},[892,81356,81357,81405],{},[895,81358,81359,81361,81363,81365,81367,81369,81371,81373,81375,81391,81393],{},[898,81360,11577],{},[898,81362,1766],{},[1656,81364,1713],{},[1667,81366,2673],{},[1656,81368,3633],{},[1667,81370,1680],{},[898,81372,1665],{},[1656,81374,3964],{},[4138,81376,81377],{"scriptlevel":4032,"displaystyle":1658},[3294,81378,81379,81389],{},[895,81380,81381,81383],{},[1667,81382,2617],{},[2062,81384,81385,81387],{},[898,81386,1665],{},[1667,81388,1680],{},[1667,81390,8580],{},[1656,81392,3633],{},[4138,81394,81395],{"scriptlevel":4032,"displaystyle":1658},[3294,81396,81397,81403],{},[2062,81398,81399,81401],{},[898,81400,1665],{},[1667,81402,2617],{},[1667,81404,9058],{},[902,81406,81407],{"encoding":904},"TC = 4 + 2Q - \\tfrac{3Q^2}{10} + \\tfrac{Q^3}{20}",[724,81409,81410,81413,81414,81444,81445,81477,81478,30312,81508,81538],{},[38,81411,81412],{},"3.24"," Firma řeší problém stanovení cen pro malé a velké odběratele za účelem maximalizace zisku. Poptávka pro maloodběratele je ",[883,81415,81417],{"className":81416},[886],[888,81418,81419],{"xmlns":890},[892,81420,81421,81441],{},[895,81422,81423,81429,81431,81433,81435],{},[1661,81424,81425,81427],{},[898,81426,8194],{},[1667,81428,1669],{},[1656,81430,1713],{},[1667,81432,8059],{},[1656,81434,3964],{},[1661,81436,81437,81439],{},[898,81438,1665],{},[1667,81440,1669],{},[902,81442,81443],{"encoding":904},"P_1 = 500 - Q_1",", pro velkoodběratele ",[883,81446,81448],{"className":81447},[886],[888,81449,81450],{"xmlns":890},[892,81451,81452,81474],{},[895,81453,81454,81460,81462,81464,81466,81468],{},[1661,81455,81456,81458],{},[898,81457,8194],{},[1667,81459,1680],{},[1656,81461,1713],{},[1667,81463,8054],{},[1656,81465,3964],{},[1667,81467,8845],{},[1661,81469,81470,81472],{},[898,81471,1665],{},[1667,81473,1680],{},[902,81475,81476],{"encoding":904},"P_2 = 300 - 1{,}5Q_2",". Celkové náklady firmy jsou ",[883,81479,81481],{"className":81480},[886],[888,81482,81483],{"xmlns":890},[892,81484,81485,81505],{},[895,81486,81487,81489,81491,81493,81495,81497,81499,81501,81503],{},[898,81488,11577],{},[898,81490,1766],{},[1656,81492,1713],{},[1667,81494,9267],{},[2461,81496,7828],{},[1667,81498,67750],{},[1656,81500,3633],{},[1667,81502,9058],{},[898,81504,1665],{},[902,81506,81507],{"encoding":904},"TC = 50\\,000 + 20Q",[883,81509,81511],{"className":81510},[886],[888,81512,81513],{"xmlns":890},[892,81514,81515,81535],{},[895,81516,81517,81519,81521,81527,81529],{},[898,81518,1665],{},[1656,81520,1713],{},[1661,81522,81523,81525],{},[898,81524,1665],{},[1667,81526,1669],{},[1656,81528,3633],{},[1661,81530,81531,81533],{},[898,81532,1665],{},[1667,81534,1680],{},[902,81536,81537],{"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.",[724,81540,81541,81544,81545,81575,81576,81477,81608,30312,81638,81667],{},[38,81542,81543],{},"3.25"," Firma řeší problém stanovení cen pro domácí a zahraniční trh za účelem maximalizace zisku. Poptávka pro domácí trh je ",[883,81546,81548],{"className":81547},[886],[888,81549,81550],{"xmlns":890},[892,81551,81552,81572],{},[895,81553,81554,81560,81562,81564,81566],{},[1661,81555,81556,81558],{},[898,81557,8194],{},[1667,81559,1669],{},[1656,81561,1713],{},[1667,81563,8054],{},[1656,81565,3964],{},[1661,81567,81568,81570],{},[898,81569,1665],{},[1667,81571,1669],{},[902,81573,81574],{"encoding":904},"P_1 = 300 - Q_1",", pro zahraniční trh ",[883,81577,81579],{"className":81578},[886],[888,81580,81581],{"xmlns":890},[892,81582,81583,81605],{},[895,81584,81585,81591,81593,81595,81597,81599],{},[1661,81586,81587,81589],{},[898,81588,8194],{},[1667,81590,1680],{},[1656,81592,1713],{},[1667,81594,5272],{},[1656,81596,3964],{},[1667,81598,13779],{},[1661,81600,81601,81603],{},[898,81602,1665],{},[1667,81604,1680],{},[902,81606,81607],{"encoding":904},"P_2 = 200 - 0{,}5Q_2",[883,81609,81611],{"className":81610},[886],[888,81612,81613],{"xmlns":890},[892,81614,81615,81635],{},[895,81616,81617,81619,81621,81623,81625,81627,81629,81631,81633],{},[898,81618,11577],{},[898,81620,1766],{},[1656,81622,1713],{},[1667,81624,5193],{},[2461,81626,7828],{},[1667,81628,67750],{},[1656,81630,3633],{},[1667,81632,5267],{},[898,81634,1665],{},[902,81636,81637],{"encoding":904},"TC = 5\\,000 + 100Q",[883,81639,81641],{"className":81640},[886],[888,81642,81643],{"xmlns":890},[892,81644,81645,81665],{},[895,81646,81647,81649,81651,81657,81659],{},[898,81648,1665],{},[1656,81650,1713],{},[1661,81652,81653,81655],{},[898,81654,1665],{},[1667,81656,1669],{},[1656,81658,3633],{},[1661,81660,81661,81663],{},[898,81662,1665],{},[1667,81664,1680],{},[902,81666,81537],{"encoding":904},". Stanovte ceny, při kterých firma maximalizuje zisk: (a) s cenovou diskriminací, (b) bez cenové diskriminace. Porovnejte zisk firmy v obou případech.",[198,81669,81671],{"id":81670},"konstrukce-nabídky-326328","Konstrukce nabídky (3.26–3.28)",[724,81673,81674,81677,81678,81725,81726,81743],{},[38,81675,81676],{},"3.26"," Jsou dány celkové variabilní náklady ",[883,81679,81681],{"className":81680},[886],[888,81682,81683],{"xmlns":890},[892,81684,81685,81722],{},[895,81686,81687,81689,81691,81693,81695,81698,81704,81706,81709,81715,81717,81720],{},[898,81688,11577],{},[898,81690,49019],{},[898,81692,1766],{},[1656,81694,1713],{},[1667,81696,81697],{},"0,85",[2062,81699,81700,81702],{},[898,81701,1665],{},[1667,81703,2617],{},[1656,81705,3964],{},[1667,81707,81708],{},"11,9",[2062,81710,81711,81713],{},[898,81712,1665],{},[1667,81714,1680],{},[1656,81716,3633],{},[1667,81718,81719],{},"102",[898,81721,1665],{},[902,81723,81724],{"encoding":904},"TVC = 0{,}85Q^3 - 11{,}9Q^2 + 102Q",". Určete minimální cenu ",[883,81727,81729],{"className":81728},[886],[888,81730,81731],{"xmlns":890},[892,81732,81733,81741],{},[895,81734,81735],{},[2062,81736,81737,81739],{},[898,81738,8194],{},[1656,81740,8187],{},[902,81742,13178],{"encoding":904}," nabídky a konstruujte nabídku. Graficky interpretujte.",[724,81745,81746,79506,81749,81785],{},[38,81747,81748],{},"3.27",[883,81750,81752],{"className":81751},[886],[888,81753,81754],{"xmlns":890},[892,81755,81756,81782],{},[895,81757,81758,81760,81762,81764,81766,81772,81774,81776,81778,81780],{},[898,81759,1703],{},[898,81761,1766],{},[1656,81763,1713],{},[1667,81765,11719],{},[2062,81767,81768,81770],{},[898,81769,1665],{},[1667,81771,1680],{},[1656,81773,3964],{},[1667,81775,73106],{},[898,81777,1665],{},[1656,81779,3633],{},[1667,81781,39433],{},[902,81783,81784],{"encoding":904},"MC = 4{,}2Q^2 - 48Q + 250",". Konstruujte nabídku.",[724,81787,81788,78757,81791,81785],{},[38,81789,81790],{},"3.28",[883,81792,81794],{"className":81793},[886],[888,81795,81796],{"xmlns":890},[892,81797,81798,81834],{},[895,81799,81800,81802,81804,81806,81808,81814,81816,81818,81824,81826,81828,81830,81832],{},[898,81801,11577],{},[898,81803,1766],{},[1656,81805,1713],{},[1667,81807,13779],{},[2062,81809,81810,81812],{},[898,81811,1665],{},[1667,81813,2617],{},[1656,81815,3964],{},[1667,81817,6240],{},[2062,81819,81820,81822],{},[898,81821,1665],{},[1667,81823,1680],{},[1656,81825,3633],{},[1667,81827,11918],{},[898,81829,1665],{},[1656,81831,3633],{},[1667,81833,8059],{},[902,81835,81836],{"encoding":904},"TC = 0{,}5Q^3 - 7Q^2 + 60Q + 500",[115,81838,10198],{"id":10197},[120,81840,81841,81869,81914,81986,82051,82091,82183,82289,82329,82443,82536,82600,82632,82692,82698,82762,82811,82865,82973,83028],{},[123,81842,81843,1643,81845,81868],{},[38,81844,64419],{},[883,81846,81848],{"className":81847},[886],[888,81849,81850],{"xmlns":890},[892,81851,81852,81866],{},[895,81853,81854,81856,81858,81860,81862,81864],{},[898,81855,11577],{},[898,81857,1763],{},[1656,81859,1713],{},[898,81861,8194],{},[1656,81863,2751],{},[898,81865,1665],{},[902,81867,75376],{"encoding":904}," — křivka celkového příjmu (total revenue curve).",[123,81870,81871,1643,81873,81913],{},[38,81872,65004],{},[883,81874,81876],{"className":81875},[886],[888,81877,81878],{"xmlns":890},[892,81879,81880,81910],{},[895,81881,81882,81884,81886,81888,81900,81902,81904,81906,81908],{},[898,81883,2146],{},[898,81885,1763],{},[1656,81887,1713],{},[4138,81889,81890],{"scriptlevel":4032,"displaystyle":1658},[3294,81891,81892,81898],{},[895,81893,81894,81896],{},[898,81895,11577],{},[898,81897,1763],{},[898,81899,1665],{},[1656,81901,1713],{},[898,81903,6787],{},[1656,81905,1659],{"stretchy":1658},[898,81907,1665],{},[1656,81909,1683],{"stretchy":1658},[902,81911,81912],{"encoding":904},"AR = \\tfrac{TR}{Q} = D(Q)"," — shoduje se s poptávkovou funkcí.",[123,81915,81916,1643,81918,81954,81955,81970,81971,1863],{},[38,81917,65152],{},[883,81919,81921],{"className":81920},[886],[888,81922,81923],{"xmlns":890},[892,81924,81925,81951],{},[895,81926,81927,81929,81931,81933],{},[898,81928,1703],{},[898,81930,1763],{},[1656,81932,1713],{},[4138,81934,81935],{"scriptlevel":4032,"displaystyle":1658},[3294,81936,81937,81945],{},[895,81938,81939,81941,81943],{},[898,81940,3768],{"mathvariant":1723},[898,81942,11577],{},[898,81944,1763],{},[895,81946,81947,81949],{},[898,81948,3768],{"mathvariant":1723},[898,81950,1665],{},[902,81952,81953],{"encoding":904},"MR = \\tfrac{\\mathrm{d}TR}{\\mathrm{d}Q}"," — rychlost změny ",[883,81956,81958],{"className":81957},[886],[888,81959,81960],{"xmlns":890},[892,81961,81962,81968],{},[895,81963,81964,81966],{},[898,81965,11577],{},[898,81967,1763],{},[902,81969,12875],{"encoding":904},"; pro lineární poptávku má sklon dvojnásobný vůči ",[883,81972,81974],{"className":81973},[886],[888,81975,81976],{"xmlns":890},[892,81977,81978,81984],{},[895,81979,81980,81982],{},[898,81981,2146],{},[898,81983,1763],{},[902,81985,64114],{"encoding":904},[123,81987,81988,1643,81991,1343,82021,1863],{},[38,81989,81990],{},"Diferenciál příjmu\u002Fnákladů",[883,81992,81994],{"className":81993},[886],[888,81995,81996],{"xmlns":890},[892,81997,81998,82018],{},[895,81999,82000,82002,82004,82006,82008,82010,82012,82014,82016],{},[898,82001,3750],{"mathvariant":1723},[898,82003,11577],{},[898,82005,1763],{},[1656,82007,3815],{},[898,82009,1703],{},[898,82011,1763],{},[2461,82013,7828],{},[898,82015,3768],{"mathvariant":1723},[898,82017,1665],{},[902,82019,82020],{"encoding":904},"\\Delta TR \\approx MR \\, \\mathrm{d}Q",[883,82022,82024],{"className":82023},[886],[888,82025,82026],{"xmlns":890},[892,82027,82028,82048],{},[895,82029,82030,82032,82034,82036,82038,82040,82042,82044,82046],{},[898,82031,3750],{"mathvariant":1723},[898,82033,11577],{},[898,82035,1766],{},[1656,82037,3815],{},[898,82039,1703],{},[898,82041,1766],{},[2461,82043,7828],{},[898,82045,3768],{"mathvariant":1723},[898,82047,1665],{},[902,82049,82050],{"encoding":904},"\\Delta TC \\approx MC \\, \\mathrm{d}Q",[123,82052,82053,1643,82055,1863],{},[38,82054,67274],{},[883,82056,82058],{"className":82057},[886],[888,82059,82060],{"xmlns":890},[892,82061,82062,82088],{},[895,82063,82064,82066,82068,82070,82072,82074,82076,82078,82080,82082,82084,82086],{},[898,82065,11577],{},[898,82067,1766],{},[1656,82069,1713],{},[898,82071,19177],{},[898,82073,1766],{},[1656,82075,3633],{},[898,82077,11577],{},[898,82079,49019],{},[898,82081,1766],{},[1656,82083,1659],{"stretchy":1658},[898,82085,1665],{},[1656,82087,1683],{"stretchy":1658},[902,82089,82090],{"encoding":904},"TC = FC + TVC(Q)",[123,82092,82093,1643,82096,1343,82111,1643,82113,1343,82136,1643,82139,1863],{},[38,82094,82095],{},"Fixní náklady",[883,82097,82099],{"className":82098},[886],[888,82100,82101],{"xmlns":890},[892,82102,82103,82109],{},[895,82104,82105,82107],{},[898,82106,19177],{},[898,82108,1766],{},[902,82110,64160],{"encoding":904},[38,82112,67427],{},[883,82114,82116],{"className":82115},[886],[888,82117,82118],{"xmlns":890},[892,82119,82120,82134],{},[895,82121,82122,82124,82126,82128,82130,82132],{},[898,82123,11577],{},[898,82125,49019],{},[898,82127,1766],{},[1656,82129,1659],{"stretchy":1658},[898,82131,1665],{},[1656,82133,1683],{"stretchy":1658},[902,82135,67424],{"encoding":904},[38,82137,82138],{},"variabilní náklady na jednotku",[883,82140,82142],{"className":82141},[886],[888,82143,82144],{"xmlns":890},[892,82145,82146,82180],{},[895,82147,82148,82150,82152,82154,82156,82158,82160],{},[898,82149,49019],{},[898,82151,1766],{},[1656,82153,1659],{"stretchy":1658},[898,82155,1665],{},[1656,82157,1683],{"stretchy":1658},[1656,82159,1713],{},[4138,82161,82162],{"scriptlevel":4032,"displaystyle":1658},[3294,82163,82164,82178],{},[895,82165,82166,82168,82170,82172,82174,82176],{},[898,82167,11577],{},[898,82169,49019],{},[898,82171,1766],{},[1656,82173,1659],{"stretchy":1658},[898,82175,1665],{},[1656,82177,1683],{"stretchy":1658},[898,82179,1665],{},[902,82181,82182],{"encoding":904},"VC(Q) = \\tfrac{TVC(Q)}{Q}",[123,82184,82185,1643,82187,1343,82217,1643,82220,1343,82252,1643,82255,1863],{},[38,82186,67435],{},[883,82188,82190],{"className":82189},[886],[888,82191,82192],{"xmlns":890},[892,82193,82194,82214],{},[895,82195,82196,82198,82200,82202],{},[898,82197,2146],{},[898,82199,1766],{},[1656,82201,1713],{},[4138,82203,82204],{"scriptlevel":4032,"displaystyle":1658},[3294,82205,82206,82212],{},[895,82207,82208,82210],{},[898,82209,11577],{},[898,82211,1766],{},[898,82213,1665],{},[902,82215,82216],{"encoding":904},"AC = \\tfrac{TC}{Q}",[38,82218,82219],{},"průměrné fixní",[883,82221,82223],{"className":82222},[886],[888,82224,82225],{"xmlns":890},[892,82226,82227,82249],{},[895,82228,82229,82231,82233,82235,82237],{},[898,82230,2146],{},[898,82232,19177],{},[898,82234,1766],{},[1656,82236,1713],{},[4138,82238,82239],{"scriptlevel":4032,"displaystyle":1658},[3294,82240,82241,82247],{},[895,82242,82243,82245],{},[898,82244,19177],{},[898,82246,1766],{},[898,82248,1665],{},[902,82250,82251],{"encoding":904},"AFC = \\tfrac{FC}{Q}",[38,82253,82254],{},"průměrné variabilní",[883,82256,82258],{"className":82257},[886],[888,82259,82260],{"xmlns":890},[892,82261,82262,82286],{},[895,82263,82264,82266,82268,82270,82272],{},[898,82265,2146],{},[898,82267,49019],{},[898,82269,1766],{},[1656,82271,1713],{},[4138,82273,82274],{"scriptlevel":4032,"displaystyle":1658},[3294,82275,82276,82284],{},[895,82277,82278,82280,82282],{},[898,82279,11577],{},[898,82281,49019],{},[898,82283,1766],{},[898,82285,1665],{},[902,82287,82288],{"encoding":904},"AVC = \\tfrac{TVC}{Q}",[123,82290,82291,1643,82293,1863],{},[38,82292,68622],{},[883,82294,82296],{"className":82295},[886],[888,82297,82298],{"xmlns":890},[892,82299,82300,82326],{},[895,82301,82302,82304,82306,82308],{},[898,82303,1703],{},[898,82305,1766],{},[1656,82307,1713],{},[4138,82309,82310],{"scriptlevel":4032,"displaystyle":1658},[3294,82311,82312,82320],{},[895,82313,82314,82316,82318],{},[898,82315,3768],{"mathvariant":1723},[898,82317,11577],{},[898,82319,1766],{},[895,82321,82322,82324],{},[898,82323,3768],{"mathvariant":1723},[898,82325,1665],{},[902,82327,82328],{"encoding":904},"MC = \\tfrac{\\mathrm{d}TC}{\\mathrm{d}Q}",[123,82330,82331,1643,82333,82381,82382,82395,82396,1343,82411,1343,82428,1863],{},[38,82332,69520],{},[883,82334,82336],{"className":82335},[886],[888,82337,82338],{"xmlns":890},[892,82339,82340,82378],{},[895,82341,82342,82344,82346,82348,82350,82352,82354,82356,82358,82360,82362,82368,82370,82372],{},[898,82343,11577],{},[898,82345,1766],{},[1656,82347,1713],{},[898,82349,19177],{},[898,82351,1766],{},[1656,82353,3633],{},[898,82355,207],{},[898,82357,1665],{},[1656,82359,3633],{},[898,82361,3403],{},[2062,82363,82364,82366],{},[898,82365,1665],{},[1667,82367,1680],{},[1656,82369,3633],{},[898,82371,1745],{},[2062,82373,82374,82376],{},[898,82375,1665],{},[1667,82377,2617],{},[902,82379,82380],{"encoding":904},"TC = FC + aQ + bQ^2 + cQ^3"," — „standardní\" tvar s ",[883,82383,82385],{"className":82384},[886],[888,82386,82387],{"xmlns":890},[892,82388,82389,82393],{},[895,82390,82391],{},[898,82392,900],{},[902,82394,900],{"encoding":904},"-průběhem ",[883,82397,82399],{"className":82398},[886],[888,82400,82401],{"xmlns":890},[892,82402,82403,82409],{},[895,82404,82405,82407],{},[898,82406,2146],{},[898,82408,1766],{},[902,82410,64229],{"encoding":904},[883,82412,82414],{"className":82413},[886],[888,82415,82416],{"xmlns":890},[892,82417,82418,82426],{},[895,82419,82420,82422,82424],{},[898,82421,2146],{},[898,82423,49019],{},[898,82425,1766],{},[902,82427,63980],{"encoding":904},[883,82429,82431],{"className":82430},[886],[888,82432,82433],{"xmlns":890},[892,82434,82435,82441],{},[895,82436,82437,82439],{},[898,82438,1703],{},[898,82440,1766],{},[902,82442,63961],{"encoding":904},[123,82444,82445,82447,82448,19135,82463,82504,82505,70165,82520,82535],{},[38,82446,70601],{},": v bodě minima ",[883,82449,82451],{"className":82450},[886],[888,82452,82453],{"xmlns":890},[892,82454,82455,82461],{},[895,82456,82457,82459],{},[898,82458,2146],{},[898,82460,1766],{},[902,82462,64229],{"encoding":904},[883,82464,82466],{"className":82465},[886],[888,82467,82468],{"xmlns":890},[892,82469,82470,82502],{},[895,82471,82472,82474,82476,82478,82484,82486,82488,82490,82492,82494,82500],{},[898,82473,2146],{},[898,82475,1766],{},[1656,82477,1659],{"stretchy":1658},[1661,82479,82480,82482],{},[898,82481,1665],{},[1667,82483,4032],{},[1656,82485,1683],{"stretchy":1658},[1656,82487,1713],{},[898,82489,1703],{},[898,82491,1766],{},[1656,82493,1659],{"stretchy":1658},[1661,82495,82496,82498],{},[898,82497,1665],{},[1667,82499,4032],{},[1656,82501,1683],{"stretchy":1658},[902,82503,71236],{"encoding":904},"; geometricky ",[883,82506,82508],{"className":82507},[886],[888,82509,82510],{"xmlns":890},[892,82511,82512,82518],{},[895,82513,82514,82516],{},[898,82515,1703],{},[898,82517,1766],{},[902,82519,63961],{"encoding":904},[883,82521,82523],{"className":82522},[886],[888,82524,82525],{"xmlns":890},[892,82526,82527,82533],{},[895,82528,82529,82531],{},[898,82530,2146],{},[898,82532,1766],{},[902,82534,64229],{"encoding":904}," v jejím minimu.",[123,82537,82538,82447,82540,19135,82557,1863],{},[38,82539,71950],{},[883,82541,82543],{"className":82542},[886],[888,82544,82545],{"xmlns":890},[892,82546,82547,82555],{},[895,82548,82549,82551,82553],{},[898,82550,2146],{},[898,82552,49019],{},[898,82554,1766],{},[902,82556,63980],{"encoding":904},[883,82558,82560],{"className":82559},[886],[888,82561,82562],{"xmlns":890},[892,82563,82564,82598],{},[895,82565,82566,82568,82570,82572,82574,82580,82582,82584,82586,82588,82590,82596],{},[898,82567,2146],{},[898,82569,49019],{},[898,82571,1766],{},[1656,82573,1659],{"stretchy":1658},[1661,82575,82576,82578],{},[898,82577,1665],{},[1667,82579,4032],{},[1656,82581,1683],{"stretchy":1658},[1656,82583,1713],{},[898,82585,1703],{},[898,82587,1766],{},[1656,82589,1659],{"stretchy":1658},[1661,82591,82592,82594],{},[898,82593,1665],{},[1667,82595,4032],{},[1656,82597,1683],{"stretchy":1658},[902,82599,77683],{"encoding":904},[123,82601,82602,1643,82604,82631],{},[38,82603,72129],{},[883,82605,82607],{"className":82606},[886],[888,82608,82609],{"xmlns":890},[892,82610,82611,82629],{},[895,82612,82613,82615,82617,82619,82621,82623,82625,82627],{},[898,82614,8194],{},[898,82616,1763],{},[1656,82618,1713],{},[898,82620,11577],{},[898,82622,1763],{},[1656,82624,3964],{},[898,82626,11577],{},[898,82628,1766],{},[902,82630,63869],{"encoding":904}," — rozdíl mezi celkovým příjmem a celkovými náklady.",[123,82633,82634,3247,82636,82638,82639,82665,82666,82691],{},[38,82635,72991],{},[614,82637,72254],{},") — hodnoty ",[883,82640,82642],{"className":82641},[886],[888,82643,82644],{"xmlns":890},[892,82645,82646,82662],{},[895,82647,82648,82654,82656],{},[1661,82649,82650,82652],{},[898,82651,1665],{},[898,82653,2146],{},[1656,82655,1673],{"separator":1672},[1661,82657,82658,82660],{},[898,82659,1665],{},[898,82661,2161],{},[902,82663,82664],{"encoding":904},"Q_A, Q_B"," splňující ",[883,82667,82669],{"className":82668},[886],[888,82670,82671],{"xmlns":890},[892,82672,82673,82689],{},[895,82674,82675,82677,82679,82681,82683,82685,82687],{},[898,82676,8194],{},[898,82678,1763],{},[1656,82680,1659],{"stretchy":1658},[898,82682,1665],{},[1656,82684,1683],{"stretchy":1658},[1656,82686,1713],{},[1667,82688,4032],{},[902,82690,72531],{"encoding":904},"; oddělují pásma ztráty a zisku.",[123,82693,82694,82697],{},[38,82695,82696],{},"Práh rentability"," — stav firmy v bodě zvratu.",[123,82699,82700,82702,82703,19135,82720,82761],{},[38,82701,74044],{}," — v bodě maxima zisku ",[883,82704,82706],{"className":82705},[886],[888,82707,82708],{"xmlns":890},[892,82709,82710,82718],{},[895,82711,82712],{},[1661,82713,82714,82716],{},[898,82715,1665],{},[1667,82717,4032],{},[902,82719,46990],{"encoding":904},[883,82721,82723],{"className":82722},[886],[888,82724,82725],{"xmlns":890},[892,82726,82727,82759],{},[895,82728,82729,82731,82733,82735,82741,82743,82745,82747,82749,82751,82757],{},[898,82730,1703],{},[898,82732,1763],{},[1656,82734,1659],{"stretchy":1658},[1661,82736,82737,82739],{},[898,82738,1665],{},[1667,82740,4032],{},[1656,82742,1683],{"stretchy":1658},[1656,82744,1713],{},[898,82746,1703],{},[898,82748,1766],{},[1656,82750,1659],{"stretchy":1658},[1661,82752,82753,82755],{},[898,82754,1665],{},[1667,82756,4032],{},[1656,82758,1683],{"stretchy":1658},[902,82760,74310],{"encoding":904}," (3.13).",[123,82763,82764,29022,82766,19135,82785,82810],{},[38,82765,75336],{},[883,82767,82769],{"className":82768},[886],[888,82770,82771],{"xmlns":890},[892,82772,82773,82782],{},[895,82774,82775,82777,82779],{},[898,82776,8194],{},[1656,82778,1713],{},[2461,82780,82781],{},"konst",[902,82783,82784],{"encoding":904},"P = \\text{konst}",[883,82786,82788],{"className":82787},[886],[888,82789,82790],{"xmlns":890},[892,82791,82792,82808],{},[895,82793,82794,82796,82798,82800,82802,82804,82806],{},[898,82795,8194],{},[1656,82797,1713],{},[898,82799,1703],{},[898,82801,1766],{},[1656,82803,1659],{"stretchy":1658},[898,82805,1665],{},[1656,82807,1683],{"stretchy":1658},[902,82809,76030],{"encoding":904}," (3.14).",[123,82812,82813,82816,82817,82846,82847,82864],{},[38,82814,82815],{},"Shutdown point"," — bod ",[883,82818,82820],{"className":82819},[886],[888,82821,82822],{"xmlns":890},[892,82823,82824,82844],{},[895,82825,82826,82828,82834,82836,82842],{},[1656,82827,1659],{"stretchy":1658},[2062,82829,82830,82832],{},[898,82831,1665],{},[1656,82833,8187],{},[1656,82835,1673],{"separator":1672},[2062,82837,82838,82840],{},[898,82839,8194],{},[1656,82841,8187],{},[1656,82843,1683],{"stretchy":1658},[902,82845,76319],{"encoding":904}," v minimu ",[883,82848,82850],{"className":82849},[886],[888,82851,82852],{"xmlns":890},[892,82853,82854,82862],{},[895,82855,82856,82858,82860],{},[898,82857,2146],{},[898,82859,49019],{},[898,82861,1766],{},[902,82863,63980],{"encoding":904},"; pod ním se firmě nevyplatí produkovat.",[123,82866,82867,1643,82870,3713,82905,76589,82926,82939,82940,82955,82956,1863],{},[38,82868,82869],{},"Funkce nabídky firmy",[883,82871,82873],{"className":82872},[886],[888,82874,82875],{"xmlns":890},[892,82876,82877,82903],{},[895,82878,82879,82881,82883,82885,82887,82889,82891,82893,82895,82897,82899,82901],{},[898,82880,8194],{},[1656,82882,1713],{},[898,82884,1769],{},[1656,82886,1659],{"stretchy":1658},[898,82888,1665],{},[1656,82890,1683],{"stretchy":1658},[1656,82892,1713],{},[898,82894,1703],{},[898,82896,1766],{},[1656,82898,1659],{"stretchy":1658},[898,82900,1665],{},[1656,82902,1683],{"stretchy":1658},[902,82904,77786],{"encoding":904},[883,82906,82908],{"className":82907},[886],[888,82909,82910],{"xmlns":890},[892,82911,82912,82924],{},[895,82913,82914,82916,82918],{},[898,82915,1665],{},[1656,82917,13258],{},[2062,82919,82920,82922],{},[898,82921,1665],{},[1656,82923,8187],{},[902,82925,76588],{"encoding":904},[883,82927,82929],{"className":82928},[886],[888,82930,82931],{"xmlns":890},[892,82932,82933,82937],{},[895,82934,82935],{},[1667,82936,4032],{},[902,82938,4032],{"encoding":904}," (3.15); vychází z rostoucí části ",[883,82941,82943],{"className":82942},[886],[888,82944,82945],{"xmlns":890},[892,82946,82947,82953],{},[895,82948,82949,82951],{},[898,82950,1703],{},[898,82952,1766],{},[902,82954,63961],{"encoding":904}," nad minimem ",[883,82957,82959],{"className":82958},[886],[888,82960,82961],{"xmlns":890},[892,82962,82963,82971],{},[895,82964,82965,82967,82969],{},[898,82966,2146],{},[898,82968,49019],{},[898,82970,1766],{},[902,82972,63980],{"encoding":904},[123,82974,82975,2533,82977,82998,82999,1863],{},[38,82976,58751],{},[883,82978,82980],{"className":82979},[886],[888,82981,82982],{"xmlns":890},[892,82983,82984,82996],{},[895,82985,82986,82988,82990],{},[898,82987,8194],{},[1656,82989,1713],{},[2062,82991,82992,82994],{},[898,82993,8194],{},[1656,82995,8187],{},[902,82997,13132],{"encoding":904}," konstantní ⇒ ",[883,83000,83002],{"className":83001},[886],[888,83003,83004],{"xmlns":890},[892,83005,83006,83026],{},[895,83007,83008,83010,83012,83014,83016,83018,83020],{},[898,83009,2146],{},[898,83011,1763],{},[1656,83013,1713],{},[898,83015,1703],{},[898,83017,1763],{},[1656,83019,1713],{},[2062,83021,83022,83024],{},[898,83023,8194],{},[1656,83025,8187],{},[902,83027,67266],{"encoding":904},[123,83029,83030,83033],{},[38,83031,83032],{},"Cenová diskriminace"," — stanovení odlišných cen pro různé segmenty trhu za účelem maximalizace zisku (úlohy 3.24–3.25).",[115,83035,10640],{"id":10639},[120,83037,83038,83057,83069],{},[123,83039,83040,1643,83042,1343,83045,1343,83048,1343,83051,1343,83054],{},[38,83041,59395],{},[207,83043,10702],{"className":83044,"dataFsResolvedFilePath":800,"href":801},[210],[207,83046,12613],{"className":83047,"dataFsResolvedFilePath":848,"href":849},[210],[207,83049,10692],{"className":83050,"dataFsResolvedFilePath":764,"href":765},[210],[207,83052,775],{"className":83053,"dataFsResolvedFilePath":773,"href":774},[210],[207,83055,859],{"className":83056,"dataFsResolvedFilePath":857,"href":858},[210],[123,83058,83059,1643,83061,1343,83065],{},[38,83060,10731],{},[207,83062,83064],{"className":83063,"dataFsResolvedFilePath":745,"href":746},[210],"KS 1. blok — souhrn",[207,83066,83068],{"className":83067,"dataFsResolvedFilePath":838,"href":839},[210],"KS 2. blok — souhrn",[123,83070,83071,1643,83073],{},[38,83072,10742],{},[207,83074,1869],{"className":83075,"dataFsResolvedFilePath":10746,"href":10747},[210],{"title":641,"searchDepth":642,"depth":642,"links":83077},[83078,83079,83086,83092,83096,83097,83101,83102,83103,83104,83110,83111],{"id":59626,"depth":642,"text":1241},{"id":64407,"depth":642,"text":64408,"children":83080},[83081,83082,83083,83084,83085],{"id":64418,"depth":649,"text":64419},{"id":65003,"depth":649,"text":65004},{"id":65151,"depth":649,"text":65152},{"id":65893,"depth":649,"text":65894},{"id":66548,"depth":649,"text":66549},{"id":67269,"depth":642,"text":67270,"children":83087},[83088,83089,83090,83091],{"id":67273,"depth":649,"text":67274},{"id":67434,"depth":649,"text":67435},{"id":68621,"depth":649,"text":68622},{"id":69519,"depth":649,"text":69520},{"id":70600,"depth":642,"text":70601,"children":83093},[83094,83095],{"id":25137,"depth":649,"text":25138},{"id":71949,"depth":649,"text":71950},{"id":72123,"depth":642,"text":72124},{"id":74043,"depth":642,"text":74044,"children":83098},[83099,83100],{"id":74057,"depth":649,"text":25138},{"id":75335,"depth":649,"text":75336},{"id":75967,"depth":642,"text":75968},{"id":77433,"depth":642,"text":77434},{"id":8778,"depth":642,"text":8779},{"id":77894,"depth":642,"text":77895,"children":83105},[83106,83107,83108,83109],{"id":77898,"depth":649,"text":77899},{"id":78750,"depth":649,"text":78751},{"id":80296,"depth":649,"text":80297},{"id":81670,"depth":649,"text":81671},{"id":10197,"depth":642,"text":10198},{"id":10639,"depth":642,"text":10640},{},"\u002Ftopics\u002Fprijem-naklady-zisk",{"title":63789,"description":641},[1138,1135],"topics\u002Fprijem-naklady-zisk",[1128,83118,83119,63841,83120,83121,83122],"prijem","naklady","body-zvratu","maximalizace-zisku","nabidka-firmy","0d2CjMGyTT-GeTvSE65iXk5mUJ-650ilVskfuGcRAwI",{"id":83125,"title":83126,"body":83127,"course":1128,"courses":659,"created":10774,"description":641,"extension":661,"meta":95214,"navigation":664,"path":95215,"seo":95216,"sources":95217,"stem":95218,"tags":95219,"type":10786,"updated":677,"__hash__":95224},"topics\u002Ftopics\u002Fprodukce.md","Produkce — produkční funkce, Cobb-Douglas, MRTS",{"type":9,"value":83128,"toc":95171},[83129,83132,83487,83491,83494,83558,83610,83620,83624,83658,83699,83723,83746,83775,83842,83949,83992,84049,84124,84168,84172,84180,84188,84191,84456,84507,84587,84657,84680,84708,84753,84775,84779,84786,84835,84861,85012,85015,85052,85215,85323,85327,85364,85439,85508,85627,85749,85830,85836,85877,85950,86043,86047,86083,86171,86285,86390,86475,86615,86619,86667,86712,86718,86722,86725,86776,86826,86833,86899,87032,87077,87081,87102,87481,87576,87593,87647,87651,87733,87817,87987,87990,88033,88100,88174,88178,88183,88252,88260,88269,88347,88413,88418,88513,88556,88561,88609,88614,88662,88780,88863,88900,89003,89062,89203,89207,89250,89323,89347,89401,89408,89410,89455,89500,89511,89516,89552,89614,89637,89646,89747,89814,89887,89894,89985,90047,90083,90140,90199,90384,90480,90484,90488,90567,90572,90695,90781,90787,90897,90934,91025,91123,91126,91130,91196,91233,91355,91407,91411,91439,91491,91565,91670,91694,91753,91757,91775,91918,92066,92068,92103,92107,92109,92198,92328,92454,92546,92621,92625,92741,92845,93035,93071,93165,93171,93284,93587,93593,93711,93810,93886,93888,95050,95052],[12,83130,83126],{"id":83131},"produkce-produkční-funkce-cobb-douglas-mrts",[1981,83133,83134],{},[724,83135,83136,12658,83138,83140,83141,45578,83154,83167,83168,25102,83181,3247,83183,83207,83208,1643,83210,1896,83244,1643,83247,83275,83276,19135,83296,83326,83327,3247,83330,83358,83359,83361,83362,83392,83393,83423,83424,1643,83427,83467,83468,83486],{},[883,83137,12657],{},[38,83139,859],{}," popisuje vztah mezi vstupy (práce ",[883,83142,83144],{"className":83143},[886],[888,83145,83146],{"xmlns":890},[892,83147,83148,83152],{},[895,83149,83150],{},[898,83151,18539],{},[902,83153,18539],{"encoding":904},[883,83155,83157],{"className":83156},[886],[888,83158,83159],{"xmlns":890},[892,83160,83161,83165],{},[895,83162,83163],{},[898,83164,18544],{},[902,83166,18544],{"encoding":904},") a výstupem ",[883,83169,83171],{"className":83170},[886],[888,83172,83173],{"xmlns":890},[892,83174,83175,83179],{},[895,83176,83177],{},[898,83178,1665],{},[902,83180,1665],{"encoding":904},[38,83182,45646],{},[883,83184,83186],{"className":83185},[886],[888,83187,83188],{"xmlns":890},[892,83189,83190,83204],{},[895,83191,83192,83194,83196,83198,83200,83202],{},[898,83193,1665],{},[1656,83195,1713],{},[898,83197,1665],{},[1656,83199,1659],{"stretchy":1658},[898,83201,18539],{},[1656,83203,1683],{"stretchy":1658},[902,83205,83206],{"encoding":904},"Q = Q(L)",") studujeme ",[614,83209,18767],{},[883,83211,83213],{"className":83212},[886],[888,83214,83215],{"xmlns":890},[892,83216,83217,83241],{},[895,83218,83219,83221,83227,83229,83235,83237,83239],{},[898,83220,1703],{},[1661,83222,83223,83225],{},[898,83224,8194],{},[898,83226,18539],{},[1656,83228,1713],{},[2062,83230,83231,83233],{},[898,83232,1665],{},[1656,83234,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,83236,1659],{"stretchy":1658},[898,83238,18539],{},[1656,83240,1683],{"stretchy":1658},[902,83242,83243],{"encoding":904},"MP_L = Q'(L)",[614,83245,83246],{},"průměrný produkt",[883,83248,83250],{"className":83249},[886],[888,83251,83252],{"xmlns":890},[892,83253,83254,83272],{},[895,83255,83256,83258,83264,83266,83268,83270],{},[898,83257,2146],{},[1661,83259,83260,83262],{},[898,83261,8194],{},[898,83263,18539],{},[1656,83265,1713],{},[898,83267,1665],{},[898,83269,1782],{"mathvariant":1723},[898,83271,18539],{},[902,83273,83274],{"encoding":904},"AP_L = Q\u002FL","; v maximu ",[883,83277,83279],{"className":83278},[886],[888,83280,83281],{"xmlns":890},[892,83282,83283,83293],{},[895,83284,83285,83287],{},[898,83286,2146],{},[1661,83288,83289,83291],{},[898,83290,8194],{},[898,83292,18539],{},[902,83294,83295],{"encoding":904},"AP_L",[883,83297,83299],{"className":83298},[886],[888,83300,83301],{"xmlns":890},[892,83302,83303,83323],{},[895,83304,83305,83307,83313,83315,83317],{},[898,83306,1703],{},[1661,83308,83309,83311],{},[898,83310,8194],{},[898,83312,18539],{},[1656,83314,1713],{},[898,83316,2146],{},[1661,83318,83319,83321],{},[898,83320,8194],{},[898,83322,18539],{},[902,83324,83325],{"encoding":904},"MP_L = AP_L",". Ve ",[38,83328,83329],{},"dvoufaktorovém modelu",[883,83331,83333],{"className":83332},[886],[888,83334,83335],{"xmlns":890},[892,83336,83337,83355],{},[895,83338,83339,83341,83343,83345,83347,83349,83351,83353],{},[898,83340,1665],{},[1656,83342,1713],{},[898,83344,1665],{},[1656,83346,1659],{"stretchy":1658},[898,83348,18539],{},[1656,83350,1673],{"separator":1672},[898,83352,18544],{},[1656,83354,1683],{"stretchy":1658},[902,83356,83357],{"encoding":904},"Q = Q(L,K)",") dominují ",[38,83360,5891],{}," funkce ",[883,83363,83365],{"className":83364},[886],[888,83366,83367],{"xmlns":890},[892,83368,83369,83389],{},[895,83370,83371,83373,83375,83377,83383],{},[898,83372,1665],{},[1656,83374,1713],{},[898,83376,2146],{},[2062,83378,83379,83381],{},[898,83380,18539],{},[898,83382,207],{},[2062,83384,83385,83387],{},[898,83386,18544],{},[898,83388,3403],{},[902,83390,83391],{"encoding":904},"Q = AL^a K^b","; mezní produkty ",[883,83394,83396],{"className":83395},[886],[888,83397,83398],{"xmlns":890},[892,83399,83400,83420],{},[895,83401,83402,83404,83410,83412,83414],{},[898,83403,1703],{},[1661,83405,83406,83408],{},[898,83407,8194],{},[898,83409,18539],{},[1656,83411,1673],{"separator":1672},[898,83413,1703],{},[1661,83415,83416,83418],{},[898,83417,8194],{},[898,83419,18544],{},[902,83421,83422],{"encoding":904},"MP_L, MP_K"," jsou parciální derivace a jejich podíl dává ",[38,83425,83426],{},"mezní míru technické substituce",[883,83428,83430],{"className":83429},[886],[888,83431,83432],{"xmlns":890},[892,83433,83434,83464],{},[895,83435,83436,83438,83440,83442,83444,83446,83448,83454,83456,83458],{},[898,83437,1703],{},[898,83439,1763],{},[898,83441,11577],{},[898,83443,1769],{},[1656,83445,1713],{},[898,83447,1703],{},[1661,83449,83450,83452],{},[898,83451,8194],{},[898,83453,18539],{},[898,83455,1782],{"mathvariant":1723},[898,83457,1703],{},[1661,83459,83460,83462],{},[898,83461,8194],{},[898,83463,18544],{},[902,83465,83466],{"encoding":904},"MRTS = MP_L\u002FMP_K"," — sklon izokvanty. Součet exponentů ",[883,83469,83471],{"className":83470},[886],[888,83472,83473],{"xmlns":890},[892,83474,83475,83483],{},[895,83476,83477,83479,83481],{},[898,83478,207],{},[1656,83480,3633],{},[898,83482,3403],{},[902,83484,83485],{"encoding":904},"a+b"," určuje typ výnosů z rozsahu.",[115,83488,83490],{"id":83489},"úvod-cílové-znalosti-kapitoly-5","Úvod — cílové znalosti kapitoly 5",[724,83492,83493],{},"Po prostudování kapitoly 5 student umí:",[120,83495,83496,83502,83510,83516,83522,83527,83532,83542,83547,83552],{},[123,83497,83498,83499,1673],{},"popsat ",[38,83500,83501],{},"jednofaktorový model produkce",[123,83503,1902,83504,1896,83507,1906],{},[38,83505,83506],{},"mezní",[38,83508,83509],{},"průměrný produkt práce",[123,83511,83512,83513,1673],{},"charakterizovat průběh ",[38,83514,83515],{},"křivky produkce",[123,83517,83518,83519,1673],{},"formulovat ",[38,83520,83521],{},"princip maximalizace průměrného produktu práce",[123,83523,83498,83524,1673],{},[38,83525,83526],{},"dvoufaktorový model produkce",[123,83528,1912,83529,1673],{},[38,83530,83531],{},"Cobb–Douglasových produkčních funkcí",[123,83533,83534,83535,1343,83537,1343,83539,1673],{},"vyložit, co jsou ",[38,83536,33329],{},[38,83538,4570],{},[38,83540,83541],{},"klesající výnosy z rozsahu",[123,83543,1902,83544,1906],{},[38,83545,83546],{},"mezní produkty práce a kapitálu",[123,83548,1919,83549,1673],{},[38,83550,83551],{},"izokvanty",[123,83553,1902,83554,83557],{},[38,83555,83556],{},"mezní míru technické substituce (MRTS)"," a ekonomicky ji interpretovat.",[724,83559,83560,83561,83564,83565,83568,83569,1643,83572,1343,83585,1643,83588,1896,83601,83604,83605,83607,83608,1863],{},"Každý proces produkce je určován ",[38,83562,83563],{},"faktory"," (též ",[38,83566,83567],{},"vstupy",") produkce. K hlavním patří ",[38,83570,83571],{},"práce",[883,83573,83575],{"className":83574},[886],[888,83576,83577],{"xmlns":890},[892,83578,83579,83583],{},[895,83580,83581],{},[898,83582,18539],{},[902,83584,18539],{"encoding":904},[38,83586,83587],{},"kapitál",[883,83589,83591],{"className":83590},[886],[888,83592,83593],{"xmlns":890},[892,83594,83595,83599],{},[895,83596,83597],{},[898,83598,18544],{},[902,83600,18544],{"encoding":904},[38,83602,83603],{},"půda",". Při modelování se půda obvykle považuje za dlouhodobě konstantní, takže endogenními faktory zůstávají práce a kapitál. Je-li kapitál neměnný, hovoříme o ",[38,83606,45646],{}," (produkce závisí jen na práci); v opačném případě o ",[38,83609,83329],{},[724,83611,83612,83613,1343,83616,83619],{},"Související matematický aparát: ",[207,83614,10692],{"className":83615,"dataFsResolvedFilePath":764,"href":765},[210],[207,83617,784],{"className":83618,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace a totální diferenciál).",[115,83621,83623],{"id":83622},"jednofaktorový-model-produkce","Jednofaktorový model produkce",[724,83625,83626,83627,83640,83641,83654,83655],{},"Uvažujeme proces v krátkém období, kdy kapitál lze považovat za konstantní. Závislost produkce ",[883,83628,83630],{"className":83629},[886],[888,83631,83632],{"xmlns":890},[892,83633,83634,83638],{},[895,83635,83636],{},[898,83637,1665],{},[902,83639,1665],{"encoding":904}," na práci ",[883,83642,83644],{"className":83643},[886],[888,83645,83646],{"xmlns":890},[892,83647,83648,83652],{},[895,83649,83650],{},[898,83651,18539],{},[902,83653,18539],{"encoding":904}," vyjadřuje ",[38,83656,83657],{},"produkční funkce",[883,83659,83661],{"className":83660},[886],[888,83662,83663],{"xmlns":890,"display":2408},[892,83664,83665,83696],{},[2412,83666,83667],{"width":2414},[2416,83668,83669,83671,83689,83691],{},[2419,83670],{"width":2421},[2419,83672,83673],{},[895,83674,83675,83677,83679,83681,83683,83685,83687],{},[898,83676,1665],{},[1656,83678,1713],{},[898,83680,1665],{},[1656,83682,1659],{"stretchy":1658},[898,83684,18539],{},[1656,83686,1683],{"stretchy":1658},[1656,83688,1673],{"separator":1672},[2419,83690],{"width":2421},[2419,83692,83693],{},[2461,83694,83695],{},"(5.1)",[902,83697,83698],{"encoding":904},"Q = Q(L), \\tag{5.1}",[724,83700,83701,83702,3247,83705,83708,83709,83722],{},"jejíž graf se nazývá ",[38,83703,83704],{},"křivka produkce",[614,83706,83707],{},"production curve","). Práce ",[883,83710,83712],{"className":83711},[886],[888,83713,83714],{"xmlns":890},[892,83715,83716,83720],{},[895,83717,83718],{},[898,83719,18539],{},[902,83721,18539],{"encoding":904}," se měří počtem pracovníků, případně počtem pracovních hodin.",[115,83724,83726,83727,1683],{"id":83725},"mezní-produkt-práce-mplmp_l","Mezní produkt práce (",[883,83728,83730],{"className":83729},[886],[888,83731,83732],{"xmlns":890},[892,83733,83734,83744],{},[895,83735,83736,83738],{},[898,83737,1703],{},[1661,83739,83740,83742],{},[898,83741,8194],{},[898,83743,18539],{},[902,83745,18787],{"encoding":904},[724,83747,83748,3247,83751,83754,83755,83774],{},[38,83749,83750],{},"Mezní produkt práce",[614,83752,83753],{},"marginal product of labour",") ",[883,83756,83758],{"className":83757},[886],[888,83759,83760],{"xmlns":890},[892,83761,83762,83772],{},[895,83763,83764,83766],{},[898,83765,1703],{},[1661,83767,83768,83770],{},[898,83769,8194],{},[898,83771,18539],{},[902,83773,18787],{"encoding":904}," je derivace produkce podle práce:",[883,83776,83778],{"className":83777},[886],[888,83779,83780],{"xmlns":890,"display":2408},[892,83781,83782,83839],{},[2412,83783,83784],{"width":2414},[2416,83785,83786,83788,83832,83834],{},[2419,83787],{"width":2421},[2419,83789,83790],{},[895,83791,83792,83794,83800,83802,83816,83818,83824,83826,83828,83830],{},[898,83793,1703],{},[1661,83795,83796,83798],{},[898,83797,8194],{},[898,83799,18539],{},[1656,83801,1713],{},[3294,83803,83804,83810],{},[895,83805,83806,83808],{},[898,83807,3768],{},[898,83809,1665],{},[895,83811,83812,83814],{},[898,83813,3768],{},[898,83815,18539],{},[1656,83817,1713],{},[2062,83819,83820,83822],{},[898,83821,1665],{},[1656,83823,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,83825,1659],{"stretchy":1658},[898,83827,18539],{},[1656,83829,1683],{"stretchy":1658},[898,83831,1863],{"mathvariant":1723},[2419,83833],{"width":2421},[2419,83835,83836],{},[2461,83837,83838],{},"(5.2)",[902,83840,83841],{"encoding":904},"MP_L = \\frac{dQ}{dL} = Q'(L). \\tag{5.2}",[724,83843,83844,83845,28666,83863,83891,83892,83909,83910,3619,83927,12702],{},"Pro pevnou hodnotu ",[883,83846,83848],{"className":83847},[886],[888,83849,83850],{"xmlns":890},[892,83851,83852,83860],{},[895,83853,83854],{},[2062,83855,83856,83858],{},[898,83857,18539],{},[1656,83859,8187],{},[902,83861,83862],{"encoding":904},"L^*",[883,83864,83866],{"className":83865},[886],[888,83867,83868],{"xmlns":890},[892,83869,83870,83888],{},[895,83871,83872,83878,83880,83886],{},[2062,83873,83874,83876],{},[898,83875,1665],{},[1656,83877,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,83879,1659],{"stretchy":1658},[2062,83881,83882,83884],{},[898,83883,18539],{},[1656,83885,8187],{},[1656,83887,1683],{"stretchy":1658},[902,83889,83890],{"encoding":904},"Q'(L^*)"," rychlost změny produkce vzhledem k práci v bodě ",[883,83893,83895],{"className":83894},[886],[888,83896,83897],{"xmlns":890},[892,83898,83899,83907],{},[895,83900,83901],{},[2062,83902,83903,83905],{},[898,83904,18539],{},[1656,83906,8187],{},[902,83908,83862],{"encoding":904},", resp. přibližnou změnu produkce odpovídající jednotkové změně práce (z ",[883,83911,83913],{"className":83912},[886],[888,83914,83915],{"xmlns":890},[892,83916,83917,83925],{},[895,83918,83919],{},[2062,83920,83921,83923],{},[898,83922,18539],{},[1656,83924,8187],{},[902,83926,83862],{"encoding":904},[883,83928,83930],{"className":83929},[886],[888,83931,83932],{"xmlns":890},[892,83933,83934,83946],{},[895,83935,83936,83942,83944],{},[2062,83937,83938,83940],{},[898,83939,18539],{},[1656,83941,8187],{},[1656,83943,3633],{},[1667,83945,1669],{},[902,83947,83948],{"encoding":904},"L^*+1",[1981,83950,83951],{},[724,83952,83953,26746,83955,83974,83975,83978,83979,1863],{},[883,83954,3472],{},[883,83956,83958],{"className":83957},[886],[888,83959,83960],{"xmlns":890},[892,83961,83962,83972],{},[895,83963,83964,83966],{},[898,83965,1703],{},[1661,83967,83968,83970],{},[898,83969,8194],{},[898,83971,18539],{},[902,83973,18787],{"encoding":904}," odpovídá na otázku „",[38,83976,83977],{},"kolik produkce přibude, když přidám jednoho dalšího pracovníka"," (při neměnném kapitálu)?\". Je to sklon křivky produkce v bodě ",[883,83980,83982],{"className":83981},[886],[888,83983,83984],{"xmlns":890},[892,83985,83986,83990],{},[895,83987,83988],{},[898,83989,18539],{},[902,83991,18539],{"encoding":904},[724,83993,83994,83997,83998,84014,84015,3619,84028,84048],{},[38,83995,83996],{},"Přibližná změna produkce"," pro změnu práce o ",[883,83999,84001],{"className":84000},[886],[888,84002,84003],{"xmlns":890},[892,84004,84005,84011],{},[895,84006,84007,84009],{},[898,84008,3768],{},[898,84010,18539],{},[902,84012,84013],{"encoding":904},"dL"," (z ",[883,84016,84018],{"className":84017},[886],[888,84019,84020],{"xmlns":890},[892,84021,84022,84026],{},[895,84023,84024],{},[898,84025,18539],{},[902,84027,18539],{"encoding":904},[883,84029,84031],{"className":84030},[886],[888,84032,84033],{"xmlns":890},[892,84034,84035,84045],{},[895,84036,84037,84039,84041,84043],{},[898,84038,18539],{},[1656,84040,3633],{},[898,84042,3768],{},[898,84044,18539],{},[902,84046,84047],{"encoding":904},"L+dL",") pomocí diferenciálu:",[883,84050,84052],{"className":84051},[886],[888,84053,84054],{"xmlns":890,"display":2408},[892,84055,84056,84121],{},[2412,84057,84058],{"width":2414},[2416,84059,84060,84062,84114,84116],{},[2419,84061],{"width":2421},[2419,84063,84064],{},[895,84065,84066,84068,84070,84072,84074,84076,84078,84084,84086,84088,84090,84092,84094,84096,84098,84100,84106,84108,84110,84112],{},[898,84067,3750],{"mathvariant":1723},[898,84069,1665],{},[1656,84071,3815],{},[898,84073,3768],{},[898,84075,1665],{},[1656,84077,1713],{},[2062,84079,84080,84082],{},[898,84081,1665],{},[1656,84083,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,84085,1659],{"stretchy":1658},[898,84087,18539],{},[1656,84089,1683],{"stretchy":1658},[2461,84091,7828],{},[898,84093,3768],{},[898,84095,18539],{},[1656,84097,1713],{},[898,84099,1703],{},[1661,84101,84102,84104],{},[898,84103,8194],{},[898,84105,18539],{},[2461,84107,7828],{},[898,84109,3768],{},[898,84111,18539],{},[898,84113,1863],{"mathvariant":1723},[2419,84115],{"width":2421},[2419,84117,84118],{},[2461,84119,84120],{},"(5.3)",[902,84122,84123],{"encoding":904},"\\Delta Q \\approx dQ = Q'(L)\\,dL = MP_L\\,dL. \\tag{5.3}",[724,84125,3906,84126,1863],{},[883,84127,84129],{"className":84128},[886],[888,84130,84131],{"xmlns":890},[892,84132,84133,84165],{},[895,84134,84135,84137,84139,84141,84143,84145,84147,84149,84151,84153,84155,84157,84159,84161,84163],{},[898,84136,3750],{"mathvariant":1723},[898,84138,1665],{},[1656,84140,1713],{},[898,84142,1665],{},[1656,84144,1659],{"stretchy":1658},[898,84146,18539],{},[1656,84148,3633],{},[898,84150,3768],{},[898,84152,18539],{},[1656,84154,1683],{"stretchy":1658},[1656,84156,3964],{},[898,84158,1665],{},[1656,84160,1659],{"stretchy":1658},[898,84162,18539],{},[1656,84164,1683],{"stretchy":1658},[902,84166,84167],{"encoding":904},"\\Delta Q = Q(L+dL) - Q(L)",[198,84169,84171],{"id":84170},"zákon-klesajících-mezních-výnosů","Zákon klesajících mezních výnosů",[724,84173,84174,3247,84177,5642],{},[38,84175,84176],{},"Zákon klesajících výnosů",[614,84178,84179],{},"law of diminishing marginal productivity",[1981,84181,84182],{},[724,84183,84184,84185,84187],{},"Roste-li postupně některý ze vstupů (",[614,84186,45642],{},"), budou přírůstky výstupu od jistého bodu klesat.",[724,84189,84190],{},"Typická křivka produkce (Obrázek 5.2) má dvě fáze:",[724,84192,84193,84194,1643,84215,84234,84235,84285,84286,84288,84289,1643,84309,84328,84329,84285,84361,2191,84363,84382,84383,30312,84400,84434,84435,3206,84452,84455],{},"1° ",[38,84195,84196,84197,2114],{},"Do bodu ",[883,84198,84200],{"className":84199},[886],[888,84201,84202],{"xmlns":890},[892,84203,84204,84212],{},[895,84205,84206],{},[1661,84207,84208,84210],{},[898,84209,18539],{},[1667,84211,4032],{},[902,84213,84214],{"encoding":904},"L_0",[883,84216,84218],{"className":84217},[886],[888,84219,84220],{"xmlns":890},[892,84221,84222,84232],{},[895,84223,84224,84226],{},[898,84225,1703],{},[1661,84227,84228,84230],{},[898,84229,8194],{},[898,84231,18539],{},[902,84233,18787],{"encoding":904}," roste, tj. ",[883,84236,84238],{"className":84237},[886],[888,84239,84240],{"xmlns":890},[892,84241,84242,84282],{},[895,84243,84244,84246,84248,84254,84260,84262,84272,84274,84276,84278,84280],{},[1656,84245,1659],{"stretchy":1658},[898,84247,1703],{},[1661,84249,84250,84252],{},[898,84251,8194],{},[898,84253,18539],{},[2062,84255,84256,84258],{},[1656,84257,1683],{"stretchy":1658},[1656,84259,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,84261,1713],{},[2062,84263,84264,84266],{},[898,84265,1665],{},[895,84267,84268,84270],{},[1656,84269,1725],{"mathvariant":1723},[1656,84271,1725],{"mathvariant":1723},[1656,84273,1659],{"stretchy":1658},[898,84275,18539],{},[1656,84277,1683],{"stretchy":1658},[1656,84279,2850],{},[1667,84281,4032],{},[902,84283,84284],{"encoding":904},"(MP_L)' = Q''(L) > 0"," — křivka produkce je ",[38,84287,46346],{},".\n2° ",[38,84290,84291,84292,2114],{},"Od bodu ",[883,84293,84295],{"className":84294},[886],[888,84296,84297],{"xmlns":890},[892,84298,84299,84307],{},[895,84300,84301],{},[1661,84302,84303,84305],{},[898,84304,18539],{},[1667,84306,4032],{},[902,84308,84214],{"encoding":904},[883,84310,84312],{"className":84311},[886],[888,84313,84314],{"xmlns":890},[892,84315,84316,84326],{},[895,84317,84318,84320],{},[898,84319,1703],{},[1661,84321,84322,84324],{},[898,84323,8194],{},[898,84325,18539],{},[902,84327,18787],{"encoding":904}," klesá, ",[883,84330,84332],{"className":84331},[886],[888,84333,84334],{"xmlns":890},[892,84335,84336,84358],{},[895,84337,84338,84348,84350,84352,84354,84356],{},[2062,84339,84340,84342],{},[898,84341,1665],{},[895,84343,84344,84346],{},[1656,84345,1725],{"mathvariant":1723},[1656,84347,1725],{"mathvariant":1723},[1656,84349,1659],{"stretchy":1658},[898,84351,18539],{},[1656,84353,1683],{"stretchy":1658},[1656,84355,4373],{},[1667,84357,4032],{},[902,84359,84360],{"encoding":904},"Q''(L) \u003C 0",[38,84362,4573],{},[883,84364,84366],{"className":84365},[886],[888,84367,84368],{"xmlns":890},[892,84369,84370,84380],{},[895,84371,84372,84374],{},[898,84373,1703],{},[1661,84375,84376,84378],{},[898,84377,8194],{},[898,84379,18539],{},[902,84381,18787],{"encoding":904}," v kladných hodnotách klesá do bodu ",[883,84384,84386],{"className":84385},[886],[888,84387,84388],{"xmlns":890},[892,84389,84390,84398],{},[895,84391,84392],{},[1661,84393,84394,84396],{},[898,84395,18539],{},[1667,84397,1669],{},[902,84399,21945],{"encoding":904},[883,84401,84403],{"className":84402},[886],[888,84404,84405],{"xmlns":890},[892,84406,84407,84431],{},[895,84408,84409,84411,84417,84419,84425,84427,84429],{},[898,84410,1703],{},[1661,84412,84413,84415],{},[898,84414,8194],{},[898,84416,18539],{},[1656,84418,1659],{"stretchy":1658},[1661,84420,84421,84423],{},[898,84422,18539],{},[1667,84424,1669],{},[1656,84426,1683],{"stretchy":1658},[1656,84428,1713],{},[1667,84430,4032],{},[902,84432,84433],{"encoding":904},"MP_L(L_1) = 0"," (maximum produkce), a dále pokračuje v záporných hodnotách. Bod ",[883,84436,84438],{"className":84437},[886],[888,84439,84440],{"xmlns":890},[892,84441,84442,84450],{},[895,84443,84444],{},[1661,84445,84446,84448],{},[898,84447,18539],{},[1667,84449,4032],{},[902,84451,84214],{"encoding":904},[38,84453,84454],{},"inflexním bodem"," produkční funkce.",[724,84457,84458,84459,19135,84476,1863],{},"Matematicky: zákon klesajících výnosů znamená, že od určitého ",[883,84460,84462],{"className":84461},[886],[888,84463,84464],{"xmlns":890},[892,84465,84466,84474],{},[895,84467,84468],{},[1661,84469,84470,84472],{},[898,84471,18539],{},[1667,84473,4032],{},[902,84475,84214],{"encoding":904},[883,84477,84479],{"className":84478},[886],[888,84480,84481],{"xmlns":890},[892,84482,84483,84505],{},[895,84484,84485,84495,84497,84499,84501,84503],{},[2062,84486,84487,84489],{},[898,84488,1665],{},[895,84490,84491,84493],{},[1656,84492,1725],{"mathvariant":1723},[1656,84494,1725],{"mathvariant":1723},[1656,84496,1659],{"stretchy":1658},[898,84498,18539],{},[1656,84500,1683],{"stretchy":1658},[1656,84502,4373],{},[1667,84504,4032],{},[902,84506,84360],{"encoding":904},[724,84508,84509,1643,84512,14434,84552,1343,84569,84586],{},[38,84510,84511],{},"Typický polynom třetího stupně:",[883,84513,84515],{"className":84514},[886],[888,84516,84517],{"xmlns":890},[892,84518,84519,84549],{},[895,84520,84521,84523,84525,84527,84529,84531,84533,84539,84541,84543],{},[898,84522,1665],{},[1656,84524,1659],{"stretchy":1658},[898,84526,18539],{},[1656,84528,1683],{"stretchy":1658},[1656,84530,1713],{},[898,84532,207],{},[2062,84534,84535,84537],{},[898,84536,18539],{},[1667,84538,2617],{},[1656,84540,3633],{},[898,84542,3403],{},[2062,84544,84545,84547],{},[898,84546,18539],{},[1667,84548,1680],{},[902,84550,84551],{"encoding":904},"Q(L) = aL^3 + bL^2",[883,84553,84555],{"className":84554},[886],[888,84556,84557],{"xmlns":890},[892,84558,84559,84567],{},[895,84560,84561,84563,84565],{},[898,84562,207],{},[1656,84564,4373],{},[1667,84566,4032],{},[902,84568,51762],{"encoding":904},[883,84570,84572],{"className":84571},[886],[888,84573,84574],{"xmlns":890},[892,84575,84576,84584],{},[895,84577,84578,84580,84582],{},[898,84579,3403],{},[1656,84581,2850],{},[1667,84583,4032],{},[902,84585,27536],{"encoding":904},". Pak",[883,84588,84590],{"className":84589},[886],[888,84591,84592],{"xmlns":890,"display":2408},[892,84593,84594,84654],{},[895,84595,84596,84602,84604,84606,84614,84622,84624,84626,84632,84634,84636,84644,84652],{},[1661,84597,84598,84600],{},[898,84599,18539],{},[1667,84601,4032],{},[1656,84603,1713],{},[1656,84605,3964],{},[4138,84607,84608],{"scriptlevel":4032,"displaystyle":1658},[3294,84609,84610,84612],{},[1667,84611,1669],{},[1667,84613,2617],{},[4138,84615,84616],{"scriptlevel":4032,"displaystyle":1658},[3294,84617,84618,84620],{},[898,84619,3403],{},[898,84621,207],{},[1656,84623,1673],{"separator":1672},[3316,84625],{"width":14644},[1661,84627,84628,84630],{},[898,84629,18539],{},[1667,84631,1669],{},[1656,84633,1713],{},[1656,84635,3964],{},[4138,84637,84638],{"scriptlevel":4032,"displaystyle":1658},[3294,84639,84640,84642],{},[1667,84641,1680],{},[1667,84643,2617],{},[4138,84645,84646],{"scriptlevel":4032,"displaystyle":1658},[3294,84647,84648,84650],{},[898,84649,3403],{},[898,84651,207],{},[898,84653,1863],{"mathvariant":1723},[902,84655,84656],{"encoding":904},"L_0 = -\\tfrac{1}{3}\\tfrac{b}{a}, \\qquad L_1 = -\\tfrac{2}{3}\\tfrac{b}{a}.",[115,84658,84660,84661,1683],{"id":84659},"průměrný-produkt-práce-aplap_l","Průměrný produkt práce (",[883,84662,84664],{"className":84663},[886],[888,84665,84666],{"xmlns":890},[892,84667,84668,84678],{},[895,84669,84670,84672],{},[898,84671,2146],{},[1661,84673,84674,84676],{},[898,84675,8194],{},[898,84677,18539],{},[902,84679,83295],{"encoding":904},[724,84681,84682,3247,84685,83754,84688,84707],{},[38,84683,84684],{},"Průměrný produkt práce",[614,84686,84687],{},"average product of labour",[883,84689,84691],{"className":84690},[886],[888,84692,84693],{"xmlns":890},[892,84694,84695,84705],{},[895,84696,84697,84699],{},[898,84698,2146],{},[1661,84700,84701,84703],{},[898,84702,8194],{},[898,84704,18539],{},[902,84706,83295],{"encoding":904}," je podíl produkce a práce:",[883,84709,84711],{"className":84710},[886],[888,84712,84713],{"xmlns":890,"display":2408},[892,84714,84715,84750],{},[2412,84716,84717],{"width":2414},[2416,84718,84719,84721,84743,84745],{},[2419,84720],{"width":2421},[2419,84722,84723],{},[895,84724,84725,84727,84733,84735,84741],{},[898,84726,2146],{},[1661,84728,84729,84731],{},[898,84730,8194],{},[898,84732,18539],{},[1656,84734,1713],{},[3294,84736,84737,84739],{},[898,84738,1665],{},[898,84740,18539],{},[898,84742,1863],{"mathvariant":1723},[2419,84744],{"width":2421},[2419,84746,84747],{},[2461,84748,84749],{},"(5.4)",[902,84751,84752],{"encoding":904},"AP_L = \\frac{Q}{L}. \\tag{5.4}",[724,84754,84755,84756,1863],{},"Je to nejjednodušší míra produktivity práce. Cílem optimalizace je maximalizace ",[883,84757,84759],{"className":84758},[886],[888,84760,84761],{"xmlns":890},[892,84762,84763,84773],{},[895,84764,84765,84767],{},[898,84766,2146],{},[1661,84768,84769,84771],{},[898,84770,8194],{},[898,84772,18539],{},[902,84774,83295],{"encoding":904},[115,84776,84778],{"id":84777},"princip-maximalizace-průměrného-produktu-práce","Princip maximalizace průměrného produktu práce",[724,84780,84781],{},[5956,84782],{"alt":84783,"className":84784,"src":84785},"imek-q-mpl-apl-tripanel",[210,5960],"\u002Fwiki-assets\u002Fimek-q-mpl-apl-tripanel.jpeg",[1981,84787,84788],{},[724,84789,84790,84793,84794,3565,84813,84830,84831],{},[38,84791,84792],{},"Princip:"," Má-li ",[883,84795,84797],{"className":84796},[886],[888,84798,84799],{"xmlns":890},[892,84800,84801,84811],{},[895,84802,84803,84805],{},[898,84804,2146],{},[1661,84806,84807,84809],{},[898,84808,8194],{},[898,84810,18539],{},[902,84812,83295],{"encoding":904},[883,84814,84816],{"className":84815},[886],[888,84817,84818],{"xmlns":890},[892,84819,84820,84828],{},[895,84821,84822],{},[1661,84823,84824,84826],{},[898,84825,18539],{},[1667,84827,4032],{},[902,84829,84214],{"encoding":904}," maximum, pak platí\n",[883,84832,84834],{"className":84833,"title":12979,"style":12980},[12978],"MP_L(L_0) = AP_L(L_0). \\tag{5.5}",[724,84836,84837,84838,84841,84842,1643,84846,1863],{},"Slovně: ",[38,84839,84840],{},"v bodě maxima průměrného produktu práce se mezní produkt práce rovná průměrnému produktu práce."," Jde o analogii ",[207,84843,84845],{"className":84844,"dataFsResolvedFilePath":827,"href":828},[210],"principu minimalizace průměrných nákladů",[883,84847,84849],{"className":84848},[886],[888,84850,84851],{"xmlns":890},[892,84852,84853,84859],{},[895,84854,84855,84857],{},[898,84856,2146],{},[898,84858,1766],{},[902,84860,64229],{"encoding":904},[1981,84862,84863,84887],{},[724,84864,84865,84867,84868],{},[883,84866,10188],{}," Postup — jak najít max ",[883,84869,84871],{"className":84870},[886],[888,84872,84873],{"xmlns":890},[892,84874,84875,84885],{},[895,84876,84877,84879],{},[898,84878,2146],{},[1661,84880,84881,84883],{},[898,84882,8194],{},[898,84884,18539],{},[902,84886,83295],{"encoding":904},[152,84888,84889,84927,85009],{},[123,84890,84891,84892,84926],{},"Napište ",[883,84893,84895],{"className":84894},[886],[888,84896,84897],{"xmlns":890},[892,84898,84899,84923],{},[895,84900,84901,84903,84909,84911,84913,84915,84917,84919,84921],{},[898,84902,2146],{},[1661,84904,84905,84907],{},[898,84906,8194],{},[898,84908,18539],{},[1656,84910,1713],{},[898,84912,1665],{},[1656,84914,1659],{"stretchy":1658},[898,84916,18539],{},[1656,84918,1683],{"stretchy":1658},[898,84920,1782],{"mathvariant":1723},[898,84922,18539],{},[902,84924,84925],{"encoding":904},"AP_L = Q(L)\u002FL"," a zderivujte.",[123,84928,84929,84930,84962,84963,84966,84967,1863],{},"Položte ",[883,84931,84933],{"className":84932},[886],[888,84934,84935],{"xmlns":890},[892,84936,84937,84959],{},[895,84938,84939,84941,84943,84949,84955,84957],{},[1656,84940,1659],{"stretchy":1658},[898,84942,2146],{},[1661,84944,84945,84947],{},[898,84946,8194],{},[898,84948,18539],{},[2062,84950,84951,84953],{},[1656,84952,1683],{"stretchy":1658},[1656,84954,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,84956,1713],{},[1667,84958,4032],{},[902,84960,84961],{"encoding":904},"(AP_L)' = 0"," a vyřešte. ",[614,84964,84965],{},"Zkratka:"," můžete rovnou řešit ",[883,84968,84970],{"className":84969},[886],[888,84971,84972],{"xmlns":890},[892,84973,84974,85006],{},[895,84975,84976,84978,84984,84986,84988,84990,84992,84994,85000,85002,85004],{},[898,84977,1703],{},[1661,84979,84980,84982],{},[898,84981,8194],{},[898,84983,18539],{},[1656,84985,1659],{"stretchy":1658},[898,84987,18539],{},[1656,84989,1683],{"stretchy":1658},[1656,84991,1713],{},[898,84993,2146],{},[1661,84995,84996,84998],{},[898,84997,8194],{},[898,84999,18539],{},[1656,85001,1659],{"stretchy":1658},[898,85003,18539],{},[1656,85005,1683],{"stretchy":1658},[902,85007,85008],{"encoding":904},"MP_L(L) = AP_L(L)",[123,85010,85011],{},"Ověřte 2. derivací (či grafem), že jde o maximum.",[198,85013,74166],{"id":85014},"odvození",[724,85016,85017,85018,85051],{},"Z ",[883,85019,85021],{"className":85020},[886],[888,85022,85023],{"xmlns":890},[892,85024,85025,85049],{},[895,85026,85027,85029,85035,85037,85039,85041,85043,85045,85047],{},[898,85028,2146],{},[1661,85030,85031,85033],{},[898,85032,8194],{},[898,85034,18539],{},[1656,85036,1713],{},[898,85038,1665],{},[1656,85040,1659],{"stretchy":1658},[898,85042,18539],{},[1656,85044,1683],{"stretchy":1658},[898,85046,1782],{"mathvariant":1723},[898,85048,18539],{},[902,85050,84925],{"encoding":904}," a derivace podílu:",[883,85053,85055],{"className":85054},[886],[888,85056,85057],{"xmlns":890,"display":2408},[892,85058,85059,85212],{},[895,85060,85061,85063,85065,85071,85077,85079,85081,85083,85085,85125,85127,85133,85167,85169,85175,85178,85180,85186,85188,85190,85192,85194,85196,85202,85204,85206,85208,85210],{},[1656,85062,1659],{"stretchy":1658},[898,85064,2146],{},[1661,85066,85067,85069],{},[898,85068,8194],{},[898,85070,18539],{},[2062,85072,85073,85075],{},[1656,85074,1683],{"stretchy":1658},[1656,85076,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,85078,1659],{"stretchy":1658},[898,85080,18539],{},[1656,85082,1683],{"stretchy":1658},[1656,85084,1713],{},[3294,85086,85087,85119],{},[895,85088,85089,85095,85097,85099,85101,85103,85105,85107,85109,85111,85113,85115,85117],{},[2062,85090,85091,85093],{},[898,85092,1665],{},[1656,85094,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,85096,1659],{"stretchy":1658},[898,85098,18539],{},[1656,85100,1683],{"stretchy":1658},[1656,85102,2751],{},[898,85104,18539],{},[1656,85106,3964],{},[898,85108,1665],{},[1656,85110,1659],{"stretchy":1658},[898,85112,18539],{},[1656,85114,1683],{"stretchy":1658},[1656,85116,2751],{},[1667,85118,1669],{},[2062,85120,85121,85123],{},[898,85122,18539],{},[1667,85124,1680],{},[1656,85126,1713],{},[3294,85128,85129,85131],{},[1667,85130,1669],{},[898,85132,18539],{},[895,85134,85135,85137,85143,85145,85147,85149,85151,85165],{},[1656,85136,1659],{"fence":1672},[2062,85138,85139,85141],{},[898,85140,1665],{},[1656,85142,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,85144,1659],{"stretchy":1658},[898,85146,18539],{},[1656,85148,1683],{"stretchy":1658},[1656,85150,3964],{},[3294,85152,85153,85163],{},[895,85154,85155,85157,85159,85161],{},[898,85156,1665],{},[1656,85158,1659],{"stretchy":1658},[898,85160,18539],{},[1656,85162,1683],{"stretchy":1658},[898,85164,18539],{},[1656,85166,1683],{"fence":1672},[1656,85168,1713],{},[3294,85170,85171,85173],{},[1667,85172,1669],{},[898,85174,18539],{},[1656,85176,1659],{"fence":1672,"stretchy":1672,"minsize":85177,"maxsize":85177},"1.2em",[898,85179,1703],{},[1661,85181,85182,85184],{},[898,85183,8194],{},[898,85185,18539],{},[1656,85187,1659],{"stretchy":1658},[898,85189,18539],{},[1656,85191,1683],{"stretchy":1658},[1656,85193,3964],{},[898,85195,2146],{},[1661,85197,85198,85200],{},[898,85199,8194],{},[898,85201,18539],{},[1656,85203,1659],{"stretchy":1658},[898,85205,18539],{},[1656,85207,1683],{"stretchy":1658},[1656,85209,1683],{"fence":1672,"stretchy":1672,"minsize":85177,"maxsize":85177},[898,85211,1863],{"mathvariant":1723},[902,85213,85214],{"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).",[724,85216,18411,85217,3206,85239,85322],{},[883,85218,85220],{"className":85219},[886],[888,85221,85222],{"xmlns":890},[892,85223,85224,85236],{},[895,85225,85226,85232,85234],{},[1661,85227,85228,85230],{},[898,85229,18539],{},[1667,85231,4032],{},[1656,85233,2850],{},[1667,85235,4032],{},[902,85237,85238],{"encoding":904},"L_0 > 0",[883,85240,85242],{"className":85241},[886],[888,85243,85244],{"xmlns":890},[892,85245,85246,85319],{},[895,85247,85248,85250,85252,85258,85264,85266,85272,85274,85276,85278,85281,85283,85289,85291,85297,85299,85301,85303,85309,85311,85317],{},[1656,85249,1659],{"stretchy":1658},[898,85251,2146],{},[1661,85253,85254,85256],{},[898,85255,8194],{},[898,85257,18539],{},[2062,85259,85260,85262],{},[1656,85261,1683],{"stretchy":1658},[1656,85263,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,85265,1659],{"stretchy":1658},[1661,85267,85268,85270],{},[898,85269,18539],{},[1667,85271,4032],{},[1656,85273,1683],{"stretchy":1658},[1656,85275,1713],{},[1667,85277,4032],{},[1656,85279,85280],{},"⇔",[898,85282,1703],{},[1661,85284,85285,85287],{},[898,85286,8194],{},[898,85288,18539],{},[1656,85290,1659],{"stretchy":1658},[1661,85292,85293,85295],{},[898,85294,18539],{},[1667,85296,4032],{},[1656,85298,1683],{"stretchy":1658},[1656,85300,1713],{},[898,85302,2146],{},[1661,85304,85305,85307],{},[898,85306,8194],{},[898,85308,18539],{},[1656,85310,1659],{"stretchy":1658},[1661,85312,85313,85315],{},[898,85314,18539],{},[1667,85316,4032],{},[1656,85318,1683],{"stretchy":1658},[902,85320,85321],{"encoding":904},"(AP_L)'(L_0) = 0 \\Leftrightarrow MP_L(L_0) = AP_L(L_0)",", čímž je (5.5) dokázáno.",[198,85324,85326],{"id":85325},"příklad-51","Příklad 5.1",[724,85328,85329,85330,1863],{},"Je dána produkce ",[883,85331,85333],{"className":85332},[886],[888,85334,85335],{"xmlns":890},[892,85336,85337,85361],{},[895,85338,85339,85341,85343,85345,85351,85353,85355],{},[898,85340,1665],{},[1656,85342,1713],{},[1667,85344,9112],{},[2062,85346,85347,85349],{},[898,85348,18539],{},[1667,85350,1680],{},[1656,85352,3964],{},[1667,85354,11639],{},[2062,85356,85357,85359],{},[898,85358,18539],{},[1667,85360,2617],{},[902,85362,85363],{"encoding":904},"Q = 6L^2 - 0{,}2L^3",[724,85365,85366,66190,85369,85419,85420,1863],{},[38,85367,85368],{},"(a)",[883,85370,85372],{"className":85371},[886],[888,85373,85374],{"xmlns":890},[892,85375,85376,85416],{},[895,85377,85378,85380,85382,85384,85386,85388,85390,85392,85394,85396,85398,85400,85402,85404,85406,85408,85410,85412,85414],{},[898,85379,18539],{},[1656,85381,1713],{},[1667,85383,1680],{},[1656,85385,1673],{"separator":1672},[1667,85387,5193],{},[1656,85389,1673],{"separator":1672},[1667,85391,2877],{},[1656,85393,1673],{"separator":1672},[1667,85395,8580],{},[1656,85397,1673],{"separator":1672},[1667,85399,31664],{},[1656,85401,1673],{"separator":1672},[1667,85403,12494],{},[1656,85405,1673],{"separator":1672},[1667,85407,9058],{},[1656,85409,1673],{"separator":1672},[1667,85411,47028],{},[1656,85413,1673],{"separator":1672},[1667,85415,8567],{},[902,85417,85418],{"encoding":904},"L = 2, 5, 8, 10, 14, 18, 20, 21, 25"," určíme ",[883,85421,85423],{"className":85422},[886],[888,85424,85425],{"xmlns":890},[892,85426,85427,85437],{},[895,85428,85429,85431],{},[898,85430,1703],{},[1661,85432,85433,85435],{},[898,85434,8194],{},[898,85436,18539],{},[902,85438,18787],{"encoding":904},[724,85440,85441,85442,43656],{},"Podle (5.2): ",[883,85443,85445],{"className":85444},[886],[888,85446,85447],{"xmlns":890},[892,85448,85449,85505],{},[895,85450,85451,85453,85459,85461,85467,85469,85471,85473,85475,85477,85479,85481,85483,85489,85491,85493,85495,85497,85499,85501,85503],{},[898,85452,1703],{},[1661,85454,85455,85457],{},[898,85456,8194],{},[898,85458,18539],{},[1656,85460,1713],{},[2062,85462,85463,85465],{},[898,85464,1665],{},[1656,85466,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,85468,1659],{"stretchy":1658},[898,85470,18539],{},[1656,85472,1683],{"stretchy":1658},[1656,85474,1713],{},[1667,85476,9140],{},[898,85478,18539],{},[1656,85480,3964],{},[1667,85482,28042],{},[2062,85484,85485,85487],{},[898,85486,18539],{},[1667,85488,1680],{},[1656,85490,1713],{},[898,85492,18539],{},[1656,85494,1659],{"stretchy":1658},[1667,85496,9140],{},[1656,85498,3964],{},[1667,85500,28042],{},[898,85502,18539],{},[1656,85504,1683],{"stretchy":1658},[902,85506,85507],{"encoding":904},"MP_L = Q'(L) = 12L - 0{,}6L^2 = L(12 - 0{,}6L)",[16,85509,85510,85547],{},[19,85511,85512],{},[22,85513,85514,85529,85531,85533,85535,85537,85539,85541,85543,85545],{},[25,85515,85516],{},[883,85517,85519],{"className":85518},[886],[888,85520,85521],{"xmlns":890},[892,85522,85523,85527],{},[895,85524,85525],{},[898,85526,18539],{},[902,85528,18539],{"encoding":904},[25,85530,1680],{},[25,85532,5193],{},[25,85534,2877],{},[25,85536,8580],{},[25,85538,31664],{},[25,85540,12494],{},[25,85542,9058],{},[25,85544,47028],{},[25,85546,8567],{},[30,85548,85549],{},[22,85550,85551,85572,85575,85578,85581,85583,85586,85588,85590,85609],{},[35,85552,85553],{},[883,85554,85556],{"className":85555},[886],[888,85557,85558],{"xmlns":890},[892,85559,85560,85570],{},[895,85561,85562,85564],{},[898,85563,1703],{},[1661,85565,85566,85568],{},[898,85567,8194],{},[898,85569,18539],{},[902,85571,18787],{"encoding":904},[35,85573,85574],{},"21,6",[35,85576,85577],{},"45",[35,85579,85580],{},"57,6",[35,85582,11918],{},[35,85584,85585],{},"50,4",[35,85587,85574],{},[35,85589,4032],{},[35,85591,85592],{},[883,85593,85595],{"className":85594},[886],[888,85596,85597],{"xmlns":890},[892,85598,85599,85606],{},[895,85600,85601,85603],{},[1656,85602,3964],{},[1667,85604,85605],{},"12,6",[902,85607,85608],{"encoding":904},"-12{,}6",[35,85610,85611],{},[883,85612,85614],{"className":85613},[886],[888,85615,85616],{"xmlns":890},[892,85617,85618,85624],{},[895,85619,85620,85622],{},[1656,85621,3964],{},[1667,85623,54129],{},[902,85625,85626],{"encoding":904},"-75",[724,85628,85629,85648,85649,85667,85668,85685,85686,85704,85705,85729,85730,85748],{},[883,85630,85632],{"className":85631},[886],[888,85633,85634],{"xmlns":890},[892,85635,85636,85646],{},[895,85637,85638,85640],{},[898,85639,1703],{},[1661,85641,85642,85644],{},[898,85643,8194],{},[898,85645,18539],{},[902,85647,18787],{"encoding":904}," nabývá maxima pro ",[883,85650,85652],{"className":85651},[886],[888,85653,85654],{"xmlns":890},[892,85655,85656,85664],{},[895,85657,85658,85660,85662],{},[898,85659,18539],{},[1656,85661,1713],{},[1667,85663,8580],{},[902,85665,85666],{"encoding":904},"L = 10"," (60 jednotek\u002Fprac.). Od ",[883,85669,85671],{"className":85670},[886],[888,85672,85673],{"xmlns":890},[892,85674,85675,85683],{},[895,85676,85677,85679,85681],{},[898,85678,18539],{},[1656,85680,1713],{},[1667,85682,8580],{},[902,85684,85666],{"encoding":904}," přírůstky klesají, v ",[883,85687,85689],{"className":85688},[886],[888,85690,85691],{"xmlns":890},[892,85692,85693,85701],{},[895,85694,85695,85697,85699],{},[898,85696,18539],{},[1656,85698,1713],{},[1667,85700,9058],{},[902,85702,85703],{"encoding":904},"L = 20"," produkce přestává růst (maximum ",[883,85706,85708],{"className":85707},[886],[888,85709,85710],{"xmlns":890},[892,85711,85712,85726],{},[895,85713,85714,85716,85718,85720,85722,85724],{},[898,85715,1665],{},[1656,85717,1659],{"stretchy":1658},[1667,85719,9058],{},[1656,85721,1683],{"stretchy":1658},[1656,85723,1713],{},[1667,85725,32575],{},[902,85727,85728],{"encoding":904},"Q(20) = 800","), od ",[883,85731,85733],{"className":85732},[886],[888,85734,85735],{"xmlns":890},[892,85736,85737,85745],{},[895,85738,85739,85741,85743],{},[898,85740,18539],{},[1656,85742,2850],{},[1667,85744,9058],{},[902,85746,85747],{"encoding":904},"L > 20"," produkce klesá (fyzické přeplnění pracoviště při neměnném kapitálu).",[724,85750,85751],{},[614,85752,85753,85754,85794,85795,3565,85813,1863],{},"Obrázek 5.1 — graf produkce ",[883,85755,85757],{"className":85756},[886],[888,85758,85759],{"xmlns":890},[892,85760,85761,85791],{},[895,85762,85763,85765,85767,85769,85771,85773,85775,85781,85783,85785],{},[898,85764,1665],{},[1656,85766,1659],{"stretchy":1658},[898,85768,18539],{},[1656,85770,1683],{"stretchy":1658},[1656,85772,1713],{},[1667,85774,9112],{},[2062,85776,85777,85779],{},[898,85778,18539],{},[1667,85780,1680],{},[1656,85782,3964],{},[1667,85784,11639],{},[2062,85786,85787,85789],{},[898,85788,18539],{},[1667,85790,2617],{},[902,85792,85793],{"encoding":904},"Q(L) = 6L^2 - 0{,}2L^3"," s maximem ",[883,85796,85798],{"className":85797},[886],[888,85799,85800],{"xmlns":890},[892,85801,85802,85810],{},[895,85803,85804,85806,85808],{},[898,85805,1665],{},[1656,85807,1713],{},[1667,85809,32575],{},[902,85811,85812],{"encoding":904},"Q = 800",[883,85814,85816],{"className":85815},[886],[888,85817,85818],{"xmlns":890},[892,85819,85820,85828],{},[895,85821,85822,85824,85826],{},[898,85823,18539],{},[1656,85825,1713],{},[1667,85827,9058],{},[902,85829,85703],{"encoding":904},[724,85831,85832,85835],{},[38,85833,85834],{},"(b)"," Přibližná změna produkce při růstu pracovníků z 6 na 9.",[724,85837,85838,85839,1343,85857,2114],{},"Podle (5.3) s ",[883,85840,85842],{"className":85841},[886],[888,85843,85844],{"xmlns":890},[892,85845,85846,85854],{},[895,85847,85848,85850,85852],{},[898,85849,18539],{},[1656,85851,1713],{},[1667,85853,9112],{},[902,85855,85856],{"encoding":904},"L = 6",[883,85858,85860],{"className":85859},[886],[888,85861,85862],{"xmlns":890},[892,85863,85864,85874],{},[895,85865,85866,85868,85870,85872],{},[898,85867,3768],{},[898,85869,18539],{},[1656,85871,1713],{},[1667,85873,2617],{},[902,85875,85876],{"encoding":904},"dL = 3",[883,85878,85880],{"className":85879},[886],[888,85881,85882],{"xmlns":890,"display":2408},[892,85883,85884,85947],{},[895,85885,85886,85888,85890,85892,85894,85900,85902,85904,85906,85908,85910,85912,85914,85916,85918,85920,85922,85924,85926,85928,85930,85932,85934,85936,85938,85940,85942,85944],{},[898,85887,3768],{},[898,85889,1665],{},[1656,85891,1713],{},[898,85893,1703],{},[1661,85895,85896,85898],{},[898,85897,8194],{},[898,85899,18539],{},[1656,85901,1659],{"stretchy":1658},[1667,85903,9112],{},[1656,85905,1683],{"stretchy":1658},[1656,85907,2751],{},[1667,85909,2617],{},[1656,85911,1713],{},[1656,85913,1659],{"stretchy":1658},[1667,85915,9140],{},[1656,85917,2751],{},[1667,85919,9112],{},[1656,85921,3964],{},[1667,85923,28042],{},[1656,85925,2751],{},[1667,85927,9023],{},[1656,85929,1683],{"stretchy":1658},[1656,85931,2751],{},[1667,85933,2617],{},[1656,85935,1713],{},[1667,85937,85585],{},[1656,85939,2751],{},[1667,85941,2617],{},[1656,85943,1713],{},[1667,85945,85946],{},"151,2.",[902,85948,85949],{"encoding":904},"dQ = MP_L(6)\\cdot 3 = (12\\cdot 6 - 0{,}6\\cdot 36)\\cdot 3 = 50{,}4 \\cdot 3 = 151{,}2.",[724,85951,85952,85953,66420,85978,85992,85993,1863],{},"Produkce vzroste z ",[883,85954,85956],{"className":85955},[886],[888,85957,85958],{"xmlns":890},[892,85959,85960,85975],{},[895,85961,85962,85964,85966,85968,85970,85972],{},[898,85963,1665],{},[1656,85965,1659],{"stretchy":1658},[1667,85967,9112],{},[1656,85969,1683],{"stretchy":1658},[1656,85971,1713],{},[1667,85973,85974],{},"172,8",[902,85976,85977],{"encoding":904},"Q(6) = 172{,}8",[883,85979,85981],{"className":85980},[886],[888,85982,85983],{"xmlns":890},[892,85984,85985,85990],{},[895,85986,85987],{},[1667,85988,85989],{},"324",[902,85991,85989],{"encoding":904},". Skutečná hodnota: ",[883,85994,85996],{"className":85995},[886],[888,85997,85998],{"xmlns":890},[892,85999,86000,86040],{},[895,86001,86002,86004,86006,86008,86010,86012,86014,86016,86018,86020,86022,86024,86026,86028,86031,86033,86035,86037],{},[898,86003,3750],{"mathvariant":1723},[898,86005,1665],{},[1656,86007,1713],{},[898,86009,1665],{},[1656,86011,1659],{"stretchy":1658},[1667,86013,2698],{},[1656,86015,1683],{"stretchy":1658},[1656,86017,3964],{},[898,86019,1665],{},[1656,86021,1659],{"stretchy":1658},[1667,86023,9112],{},[1656,86025,1683],{"stretchy":1658},[1656,86027,1713],{},[1667,86029,86030],{},"340,2",[1656,86032,3964],{},[1667,86034,85974],{},[1656,86036,1713],{},[1667,86038,86039],{},"167,4",[902,86041,86042],{"encoding":904},"\\Delta Q = Q(9) - Q(6) = 340{,}2 - 172{,}8 = 167{,}4",[198,86044,86046],{"id":86045},"příklad-52","Příklad 5.2",[724,86048,86049,86050,1863],{},"Ověříme princip (5.5) pro ",[883,86051,86053],{"className":86052},[886],[888,86054,86055],{"xmlns":890},[892,86056,86057,86081],{},[895,86058,86059,86061,86063,86065,86071,86073,86075],{},[898,86060,1665],{},[1656,86062,1713],{},[1667,86064,9112],{},[2062,86066,86067,86069],{},[898,86068,18539],{},[1667,86070,1680],{},[1656,86072,3964],{},[1667,86074,11639],{},[2062,86076,86077,86079],{},[898,86078,18539],{},[1667,86080,2617],{},[902,86082,85363],{"encoding":904},[883,86084,86086],{"className":86085},[886],[888,86087,86088],{"xmlns":890,"display":2408},[892,86089,86090,86168],{},[895,86091,86092,86094,86100,86102,86108,86110,86112,86114,86116,86118,86124,86126,86128,86130,86138,86140,86142,86144,86146,86148,86150,86152,86154,86156,86158,86164,86166],{},[898,86093,2146],{},[1661,86095,86096,86098],{},[898,86097,8194],{},[898,86099,18539],{},[1656,86101,1713],{},[3294,86103,86104,86106],{},[898,86105,1665],{},[898,86107,18539],{},[1656,86109,1713],{},[1667,86111,9112],{},[898,86113,18539],{},[1656,86115,3964],{},[1667,86117,11639],{},[2062,86119,86120,86122],{},[898,86121,18539],{},[1667,86123,1680],{},[1656,86125,1673],{"separator":1672},[3316,86127],{"width":3318},[898,86129,2146],{},[1715,86131,86132,86134,86136],{},[898,86133,8194],{},[898,86135,18539],{},[1656,86137,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,86139,1713],{},[1667,86141,9112],{},[1656,86143,3964],{},[1667,86145,27992],{},[898,86147,18539],{},[1656,86149,1713],{},[1667,86151,4032],{},[2461,86153,12767],{},[1656,86155,12770],{},[2461,86157,12767],{},[1661,86159,86160,86162],{},[898,86161,18539],{},[1667,86163,4032],{},[1656,86165,1713],{},[1667,86167,76947],{},[902,86169,86170],{"encoding":904},"AP_L = \\frac{Q}{L} = 6L - 0{,}2L^2, \\quad AP_L' = 6 - 0{,}4L = 0 \\;\\Rightarrow\\; L_0 = 15.",[724,86172,86173,86209,86210,86228,86229,1863],{},[883,86174,86176],{"className":86175},[886],[888,86177,86178],{"xmlns":890},[892,86179,86180,86206],{},[895,86181,86182,86184,86196,86198,86200,86202,86204],{},[898,86183,2146],{},[1715,86185,86186,86188,86190],{},[898,86187,8194],{},[898,86189,18539],{},[895,86191,86192,86194],{},[1656,86193,1725],{"mathvariant":1723},[1656,86195,1725],{"mathvariant":1723},[1656,86197,1713],{},[1656,86199,3964],{},[1667,86201,27992],{},[1656,86203,4373],{},[1667,86205,4032],{},[902,86207,86208],{"encoding":904},"AP_L'' = -0{,}4 \u003C 0",", takže v ",[883,86211,86213],{"className":86212},[886],[888,86214,86215],{"xmlns":890},[892,86216,86217,86225],{},[895,86218,86219,86221,86223],{},[898,86220,18539],{},[1656,86222,1713],{},[1667,86224,44930],{},[902,86226,86227],{"encoding":904},"L = 15"," je maximum, ",[883,86230,86232],{"className":86231},[886],[888,86233,86234],{"xmlns":890},[892,86235,86236,86282],{},[895,86237,86238,86240,86246,86248,86250,86252,86254,86256,86258,86260,86262,86264,86266,86269,86271,86274,86276,86278,86280],{},[898,86239,2146],{},[1661,86241,86242,86244],{},[898,86243,8194],{},[898,86245,18539],{},[1656,86247,1659],{"stretchy":1658},[1667,86249,44930],{},[1656,86251,1683],{"stretchy":1658},[1656,86253,1713],{},[1667,86255,9112],{},[1656,86257,2751],{},[1667,86259,44930],{},[1656,86261,3964],{},[1667,86263,11639],{},[1656,86265,2751],{},[1667,86267,86268],{},"225",[1656,86270,1713],{},[1667,86272,86273],{},"90",[1656,86275,3964],{},[1667,86277,85577],{},[1656,86279,1713],{},[1667,86281,85577],{},[902,86283,86284],{"encoding":904},"AP_L(15) = 6\\cdot 15 - 0{,}2\\cdot 225 = 90 - 45 = 45",[724,86286,86287,50557,86343,86389],{},[883,86288,86290],{"className":86289},[886],[888,86291,86292],{"xmlns":890},[892,86293,86294,86340],{},[895,86295,86296,86298,86304,86306,86308,86310,86312,86314,86316,86318,86320,86322,86324,86326,86328,86331,86333,86336,86338],{},[898,86297,1703],{},[1661,86299,86300,86302],{},[898,86301,8194],{},[898,86303,18539],{},[1656,86305,1659],{"stretchy":1658},[1667,86307,44930],{},[1656,86309,1683],{"stretchy":1658},[1656,86311,1713],{},[1667,86313,9140],{},[1656,86315,2751],{},[1667,86317,44930],{},[1656,86319,3964],{},[1667,86321,28042],{},[1656,86323,2751],{},[1667,86325,86268],{},[1656,86327,1713],{},[1667,86329,86330],{},"180",[1656,86332,3964],{},[1667,86334,86335],{},"135",[1656,86337,1713],{},[1667,86339,85577],{},[902,86341,86342],{"encoding":904},"MP_L(15) = 12\\cdot 15 - 0{,}6\\cdot 225 = 180 - 135 = 45",[883,86344,86346],{"className":86345},[886],[888,86347,86348],{"xmlns":890},[892,86349,86350,86386],{},[895,86351,86352,86354,86360,86362,86364,86366,86368,86370,86376,86378,86380,86382,86384],{},[898,86353,1703],{},[1661,86355,86356,86358],{},[898,86357,8194],{},[898,86359,18539],{},[1656,86361,1659],{"stretchy":1658},[1667,86363,44930],{},[1656,86365,1683],{"stretchy":1658},[1656,86367,1713],{},[898,86369,2146],{},[1661,86371,86372,86374],{},[898,86373,8194],{},[898,86375,18539],{},[1656,86377,1659],{"stretchy":1658},[1667,86379,44930],{},[1656,86381,1683],{"stretchy":1658},[1656,86383,1713],{},[1667,86385,85577],{},[902,86387,86388],{"encoding":904},"MP_L(15) = AP_L(15) = 45",", jak požaduje (5.5).",[724,86391,86392,86395,86396,26301,86425,1863],{},[38,86393,86394],{},"Zkratka bez hledání extrému:"," stačí řešit ",[883,86397,86399],{"className":86398},[886],[888,86400,86401],{"xmlns":890},[892,86402,86403,86423],{},[895,86404,86405,86407,86413,86415,86417],{},[898,86406,1703],{},[1661,86408,86409,86411],{},[898,86410,8194],{},[898,86412,18539],{},[1656,86414,1713],{},[898,86416,2146],{},[1661,86418,86419,86421],{},[898,86420,8194],{},[898,86422,18539],{},[902,86424,83325],{"encoding":904},[883,86426,86428],{"className":86427},[886],[888,86429,86430],{"xmlns":890},[892,86431,86432,86472],{},[895,86433,86434,86436,86438,86440,86442,86448,86450,86452,86454,86456,86458,86464,86466,86468,86470],{},[1667,86435,9140],{},[898,86437,18539],{},[1656,86439,3964],{},[1667,86441,28042],{},[2062,86443,86444,86446],{},[898,86445,18539],{},[1667,86447,1680],{},[1656,86449,1713],{},[1667,86451,9112],{},[898,86453,18539],{},[1656,86455,3964],{},[1667,86457,11639],{},[2062,86459,86460,86462],{},[898,86461,18539],{},[1667,86463,1680],{},[1656,86465,12770],{},[898,86467,18539],{},[1656,86469,1713],{},[1667,86471,44930],{},[902,86473,86474],{"encoding":904},"12L - 0{,}6L^2 = 6L - 0{,}2L^2 \\Rightarrow L = 15",[724,86476,86477],{},[614,86478,86479,86480,86499,86500,20863,86518,86537,86538,86556,86557,86574,86575,86594,86595,86614],{},"Obrázek 5.3 — křivky ",[883,86481,86483],{"className":86482},[886],[888,86484,86485],{"xmlns":890},[892,86486,86487,86497],{},[895,86488,86489,86491],{},[898,86490,1703],{},[1661,86492,86493,86495],{},[898,86494,8194],{},[898,86496,18539],{},[902,86498,18787],{"encoding":904}," (max 60 při ",[883,86501,86503],{"className":86502},[886],[888,86504,86505],{"xmlns":890},[892,86506,86507,86515],{},[895,86508,86509,86511,86513],{},[898,86510,18539],{},[1656,86512,1713],{},[1667,86514,8580],{},[902,86516,86517],{"encoding":904},"L=10",[883,86519,86521],{"className":86520},[886],[888,86522,86523],{"xmlns":890},[892,86524,86525,86535],{},[895,86526,86527,86529],{},[898,86528,2146],{},[1661,86530,86531,86533],{},[898,86532,8194],{},[898,86534,18539],{},[902,86536,83295],{"encoding":904}," (max 45 při ",[883,86539,86541],{"className":86540},[886],[888,86542,86543],{"xmlns":890},[892,86544,86545,86553],{},[895,86546,86547,86549,86551],{},[898,86548,18539],{},[1656,86550,1713],{},[1667,86552,44930],{},[902,86554,86555],{"encoding":904},"L=15","), průsečík v ",[883,86558,86560],{"className":86559},[886],[888,86561,86562],{"xmlns":890},[892,86563,86564,86572],{},[895,86565,86566,86568,86570],{},[898,86567,18539],{},[1656,86569,1713],{},[1667,86571,44930],{},[902,86573,86227],{"encoding":904},". Nalevo od 15 leží ",[883,86576,86578],{"className":86577},[886],[888,86579,86580],{"xmlns":890},[892,86581,86582,86592],{},[895,86583,86584,86586],{},[898,86585,1703],{},[1661,86587,86588,86590],{},[898,86589,8194],{},[898,86591,18539],{},[902,86593,18787],{"encoding":904}," nad ",[883,86596,86598],{"className":86597},[886],[888,86599,86600],{"xmlns":890},[892,86601,86602,86612],{},[895,86603,86604,86606],{},[898,86605,2146],{},[1661,86607,86608,86610],{},[898,86609,8194],{},[898,86611,18539],{},[902,86613,83295],{"encoding":904},", napravo pod ní.",[115,86616,86618],{"id":86617},"dvoufaktorový-model-produkce","Dvoufaktorový model produkce",[724,86620,86621,86622,3619,86635,1643,86638,14953,86651,1643,86654,2114],{},"V dvoufaktorovém modelu závisí produkce ",[883,86623,86625],{"className":86624},[886],[888,86626,86627],{"xmlns":890},[892,86628,86629,86633],{},[895,86630,86631],{},[898,86632,1665],{},[902,86634,1665],{"encoding":904},[38,86636,86637],{},"práci",[883,86639,86641],{"className":86640},[886],[888,86642,86643],{"xmlns":890},[892,86644,86645,86649],{},[895,86646,86647],{},[898,86648,18539],{},[902,86650,18539],{"encoding":904},[38,86652,86653],{},"kapitálu",[883,86655,86657],{"className":86656},[886],[888,86658,86659],{"xmlns":890},[892,86660,86661,86665],{},[895,86662,86663],{},[898,86664,18544],{},[902,86666,18544],{"encoding":904},[883,86668,86670],{"className":86669},[886],[888,86671,86672],{"xmlns":890,"display":2408},[892,86673,86674,86709],{},[2412,86675,86676],{"width":2414},[2416,86677,86678,86680,86702,86704],{},[2419,86679],{"width":2421},[2419,86681,86682],{},[895,86683,86684,86686,86688,86690,86692,86694,86696,86698,86700],{},[898,86685,1665],{},[1656,86687,1713],{},[898,86689,1665],{},[1656,86691,1659],{"stretchy":1658},[898,86693,18539],{},[1656,86695,1673],{"separator":1672},[898,86697,18544],{},[1656,86699,1683],{"stretchy":1658},[898,86701,1863],{"mathvariant":1723},[2419,86703],{"width":2421},[2419,86705,86706],{},[2461,86707,86708],{},"(5.6)",[902,86710,86711],{"encoding":904},"Q = Q(L, K). \\tag{5.6}",[724,86713,86714,86715,86717],{},"Půda je nadále standardní exogenní proměnnou. Vztah (5.6) se nazývá ",[38,86716,83657],{}," (v širším smyslu oproti jednofaktorovému modelu).",[115,86719,86721],{"id":86720},"cobb-douglasova-produkční-funkce","Cobb-Douglasova produkční funkce",[724,86723,86724],{},"Široce používané produkční funkce mají tvar",[883,86726,86728],{"className":86727},[886],[888,86729,86730],{"xmlns":890,"display":2408},[892,86731,86732,86773],{},[2412,86733,86734],{"width":2414},[2416,86735,86736,86738,86766,86768],{},[2419,86737],{"width":2421},[2419,86739,86740],{},[895,86741,86742,86744,86746,86748,86750,86756,86758,86764],{},[898,86743,1665],{},[1656,86745,1713],{},[898,86747,2146],{},[2461,86749,7828],{},[2062,86751,86752,86754],{},[898,86753,18539],{},[898,86755,207],{},[2461,86757,7828],{},[2062,86759,86760,86762],{},[898,86761,18544],{},[898,86763,3403],{},[1656,86765,1673],{"separator":1672},[2419,86767],{"width":2421},[2419,86769,86770],{},[2461,86771,86772],{},"(5.7)",[902,86774,86775],{"encoding":904},"Q = A\\,L^a\\,K^b, \\tag{5.7}",[724,86777,2355,86778,86800,86801,86803,86804,1863],{},[883,86779,86781],{"className":86780},[886],[888,86782,86783],{"xmlns":890},[892,86784,86785,86797],{},[895,86786,86787,86789,86791,86793,86795],{},[898,86788,2146],{},[1656,86790,1673],{"separator":1672},[898,86792,207],{},[1656,86794,1673],{"separator":1672},[898,86796,3403],{},[902,86798,86799],{"encoding":904},"A, a, b"," jsou kladné konstanty. Nazývají se ",[38,86802,5891],{}," (poprvé publikovány v roce 1939). V ekonomických analýzách zpravidla ",[883,86805,86807],{"className":86806},[886],[888,86808,86809],{"xmlns":890},[892,86810,86811,86823],{},[895,86812,86813,86815,86817,86819,86821],{},[898,86814,207],{},[1656,86816,1673],{"separator":1672},[898,86818,3403],{},[1656,86820,4373],{},[1667,86822,1669],{},[902,86824,86825],{"encoding":904},"a, b \u003C 1",[724,86827,86828],{},[5956,86829],{"alt":86830,"className":86831,"src":86832},"imek-vynosy-z-rozsahu-3typy",[210,5960],"\u002Fwiki-assets\u002Fimek-vynosy-z-rozsahu-3typy.jpeg",[724,86834,86835,86836,86839,86840,3619,86853,86869,86870,3619,86883,2114],{},"Reflektují ekonomickou zákonitost, že ",[38,86837,86838],{},"proporcionální změny vstupů mají odezvu v proporcionální změně výstupu",". Změní-li se práce z ",[883,86841,86843],{"className":86842},[886],[888,86844,86845],{"xmlns":890},[892,86846,86847,86851],{},[895,86848,86849],{},[898,86850,18539],{},[902,86852,18539],{"encoding":904},[883,86854,86856],{"className":86855},[886],[888,86857,86858],{"xmlns":890},[892,86859,86860,86866],{},[895,86861,86862,86864],{},[898,86863,20776],{},[898,86865,18539],{},[902,86867,86868],{"encoding":904},"rL"," a kapitál z ",[883,86871,86873],{"className":86872},[886],[888,86874,86875],{"xmlns":890},[892,86876,86877,86881],{},[895,86878,86879],{},[898,86880,18544],{},[902,86882,18544],{"encoding":904},[883,86884,86886],{"className":86885},[886],[888,86887,86888],{"xmlns":890},[892,86889,86890,86896],{},[895,86891,86892,86894],{},[898,86893,20776],{},[898,86895,18544],{},[902,86897,86898],{"encoding":904},"rK",[883,86900,86902],{"className":86901},[886],[888,86903,86904],{"xmlns":890,"display":2408},[892,86905,86906,87029],{},[2412,86907,86908],{"width":2414},[2416,86909,86910,86912,87022,87024],{},[2419,86911],{"width":2421},[2419,86913,86914],{},[895,86915,86916,86918,86920,86922,86924,86926,86928,86930,86932,86934,86936,86938,86940,86942,86948,86950,86952,86954,86960,86962,86964,86966,86978,86980,86986,86992,86994,87006,87008,87010,87012,87014,87016,87018,87020],{},[898,86917,1665],{},[1656,86919,1659],{"stretchy":1658},[898,86921,20776],{},[898,86923,18539],{},[1656,86925,1673],{"separator":1672},[898,86927,20776],{},[898,86929,18544],{},[1656,86931,1683],{"stretchy":1658},[1656,86933,1713],{},[898,86935,2146],{},[1656,86937,1659],{"stretchy":1658},[898,86939,20776],{},[898,86941,18539],{},[2062,86943,86944,86946],{},[1656,86945,1683],{"stretchy":1658},[898,86947,207],{},[1656,86949,1659],{"stretchy":1658},[898,86951,20776],{},[898,86953,18544],{},[2062,86955,86956,86958],{},[1656,86957,1683],{"stretchy":1658},[898,86959,3403],{},[1656,86961,1713],{},[898,86963,2146],{},[2461,86965,7828],{},[2062,86967,86968,86970],{},[898,86969,20776],{},[895,86971,86972,86974,86976],{},[898,86973,207],{},[1656,86975,3633],{},[898,86977,3403],{},[2461,86979,7828],{},[2062,86981,86982,86984],{},[898,86983,18539],{},[898,86985,207],{},[2062,86987,86988,86990],{},[898,86989,18544],{},[898,86991,3403],{},[1656,86993,1713],{},[2062,86995,86996,86998],{},[898,86997,20776],{},[895,86999,87000,87002,87004],{},[898,87001,207],{},[1656,87003,3633],{},[898,87005,3403],{},[2461,87007,7828],{},[898,87009,1665],{},[1656,87011,1659],{"stretchy":1658},[898,87013,18539],{},[1656,87015,1673],{"separator":1672},[898,87017,18544],{},[1656,87019,1683],{"stretchy":1658},[898,87021,1863],{"mathvariant":1723},[2419,87023],{"width":2421},[2419,87025,87026],{},[2461,87027,87028],{},"(5.8)",[902,87030,87031],{"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}",[724,87033,87034,87035],{},"Volně: ",[38,87036,87037,87038,87051,87052,87076],{},"změní-li se vstupy ",[883,87039,87041],{"className":87040},[886],[888,87042,87043],{"xmlns":890},[892,87044,87045,87049],{},[895,87046,87047],{},[898,87048,20776],{},[902,87050,20776],{"encoding":904},"-krát, změní se výstup ",[883,87053,87055],{"className":87054},[886],[888,87056,87057],{"xmlns":890},[892,87058,87059,87073],{},[895,87060,87061],{},[2062,87062,87063,87065],{},[898,87064,20776],{},[895,87066,87067,87069,87071],{},[898,87068,207],{},[1656,87070,3633],{},[898,87072,3403],{},[902,87074,87075],{"encoding":904},"r^{a+b}","-krát.",[198,87078,87080],{"id":87079},"výnosy-z-rozsahu","Výnosy z rozsahu",[724,87082,87083,87084,87101],{},"Součet exponentů ",[883,87085,87087],{"className":87086},[886],[888,87088,87089],{"xmlns":890},[892,87090,87091,87099],{},[895,87092,87093,87095,87097],{},[898,87094,207],{},[1656,87096,3633],{},[898,87098,3403],{},[902,87100,83485],{"encoding":904}," určuje typ výnosů z rozsahu:",[16,87103,87104,87133],{},[19,87105,87106],{},[22,87107,87108,87111,87114,87131],{},[25,87109,87110],{},"Typ",[25,87112,87113],{},"Podmínka",[25,87115,87116,87117,87130],{},"Chování produkce při ",[883,87118,87120],{"className":87119},[886],[888,87121,87122],{"xmlns":890},[892,87123,87124,87128],{},[895,87125,87126],{},[898,87127,20776],{},[902,87129,20776],{"encoding":904},"-násobném zvýšení vstupů",[25,87132,11864],{},[30,87134,87135,87246,87361],{},[22,87136,87137,87145,87169,87202],{},[35,87138,84193,87139,3247,87142,1683],{},[38,87140,87141],{},"Konstantní",[614,87143,87144],{},"constant returns",[35,87146,87147],{},[883,87148,87150],{"className":87149},[886],[888,87151,87152],{"xmlns":890},[892,87153,87154,87166],{},[895,87155,87156,87158,87160,87162,87164],{},[898,87157,207],{},[1656,87159,3633],{},[898,87161,3403],{},[1656,87163,1713],{},[1667,87165,1669],{},[902,87167,87168],{"encoding":904},"a+b = 1",[35,87170,87171,87184,87185,1643,87188,87201],{},[883,87172,87174],{"className":87173},[886],[888,87175,87176],{"xmlns":890},[892,87177,87178,87182],{},[895,87179,87180],{},[898,87181,1665],{},[902,87183,1665],{"encoding":904}," vzroste ",[38,87186,87187],{},"přesně",[883,87189,87191],{"className":87190},[886],[888,87192,87193],{"xmlns":890},[892,87194,87195,87199],{},[895,87196,87197],{},[898,87198,20776],{},[902,87200,20776],{"encoding":904},"-krát",[35,87203,87204],{},[883,87205,87207],{"className":87206},[886],[888,87208,87209],{"xmlns":890},[892,87210,87211,87243],{},[895,87212,87213,87215,87217,87219,87231],{},[898,87214,1665],{},[1656,87216,1713],{},[1667,87218,1680],{},[2062,87220,87221,87223],{},[898,87222,18539],{},[895,87224,87225,87227,87229],{},[1667,87226,1669],{},[898,87228,1782],{"mathvariant":1723},[1667,87230,2673],{},[2062,87232,87233,87235],{},[898,87234,18544],{},[895,87236,87237,87239,87241],{},[1667,87238,2617],{},[898,87240,1782],{"mathvariant":1723},[1667,87242,2673],{},[902,87244,87245],{"encoding":904},"Q = 2L^{1\u002F4}K^{3\u002F4}",[22,87247,87248,87257,87281,87311],{},[35,87249,87250,87251,3247,87254,1683],{},"2° ",[38,87252,87253],{},"Rostoucí",[614,87255,87256],{},"increasing returns",[35,87258,87259],{},[883,87260,87262],{"className":87261},[886],[888,87263,87264],{"xmlns":890},[892,87265,87266,87278],{},[895,87267,87268,87270,87272,87274,87276],{},[898,87269,207],{},[1656,87271,3633],{},[898,87273,3403],{},[1656,87275,2850],{},[1667,87277,1669],{},[902,87279,87280],{"encoding":904},"a+b > 1",[35,87282,87283,87184,87296,59903,87298,87201],{},[883,87284,87286],{"className":87285},[886],[888,87287,87288],{"xmlns":890},[892,87289,87290,87294],{},[895,87291,87292],{},[898,87293,1665],{},[902,87295,1665],{"encoding":904},[38,87297,33986],{},[883,87299,87301],{"className":87300},[886],[888,87302,87303],{"xmlns":890},[892,87304,87305,87309],{},[895,87306,87307],{},[898,87308,20776],{},[902,87310,20776],{"encoding":904},[35,87312,87313,3247,87339,1683],{},[883,87314,87316],{"className":87315},[886],[888,87317,87318],{"xmlns":890},[892,87319,87320,87336],{},[895,87321,87322,87324,87326,87328,87330],{},[898,87323,1665],{},[1656,87325,1713],{},[1667,87327,6240],{},[898,87329,18539],{},[2062,87331,87332,87334],{},[898,87333,18544],{},[1667,87335,1680],{},[902,87337,87338],{"encoding":904},"Q = 7LK^2",[883,87340,87342],{"className":87341},[886],[888,87343,87344],{"xmlns":890},[892,87345,87346,87358],{},[895,87347,87348,87350,87352,87354,87356],{},[898,87349,207],{},[1656,87351,3633],{},[898,87353,3403],{},[1656,87355,1713],{},[1667,87357,2617],{},[902,87359,87360],{"encoding":904},"a+b = 3",[22,87362,87363,87372,87396,87427],{},[35,87364,87365,87366,3247,87369,1683],{},"3° ",[38,87367,87368],{},"Klesající",[614,87370,87371],{},"decreasing returns",[35,87373,87374],{},[883,87375,87377],{"className":87376},[886],[888,87378,87379],{"xmlns":890},[892,87380,87381,87393],{},[895,87382,87383,87385,87387,87389,87391],{},[898,87384,207],{},[1656,87386,3633],{},[898,87388,3403],{},[1656,87390,4373],{},[1667,87392,1669],{},[902,87394,87395],{"encoding":904},"a+b \u003C 1",[35,87397,87398,87184,87411,59903,87414,87201],{},[883,87399,87401],{"className":87400},[886],[888,87402,87403],{"xmlns":890},[892,87404,87405,87409],{},[895,87406,87407],{},[898,87408,1665],{},[902,87410,1665],{"encoding":904},[38,87412,87413],{},"méně",[883,87415,87417],{"className":87416},[886],[888,87418,87419],{"xmlns":890},[892,87420,87421,87425],{},[895,87422,87423],{},[898,87424,20776],{},[902,87426,20776],{"encoding":904},[35,87428,87429,3247,87459,1683],{},[883,87430,87432],{"className":87431},[886],[888,87433,87434],{"xmlns":890},[892,87435,87436,87456],{},[895,87437,87438,87440,87442,87444,87450],{},[898,87439,1665],{},[1656,87441,1713],{},[1667,87443,8580],{},[2062,87445,87446,87448],{},[898,87447,18539],{},[1667,87449,76875],{},[2062,87451,87452,87454],{},[898,87453,18544],{},[1667,87455,13779],{},[902,87457,87458],{"encoding":904},"Q = 10L^{0{,}3}K^{0{,}5}",[883,87460,87462],{"className":87461},[886],[888,87463,87464],{"xmlns":890},[892,87465,87466,87478],{},[895,87467,87468,87470,87472,87474,87476],{},[898,87469,207],{},[1656,87471,3633],{},[898,87473,3403],{},[1656,87475,1713],{},[1667,87477,23321],{},[902,87479,87480],{"encoding":904},"a+b = 0{,}8",[1981,87482,87483],{},[724,87484,87485,87487,87488,87505,87506,87509,87510,1643,87513,87549,87550,87572,87573,1863],{},[883,87486,1987],{}," Pozor\nSoučet ",[883,87489,87491],{"className":87490},[886],[888,87492,87493],{"xmlns":890},[892,87494,87495,87503],{},[895,87496,87497,87499,87501],{},[898,87498,207],{},[1656,87500,3633],{},[898,87502,3403],{},[902,87504,83485],{"encoding":904}," neudává velikost produkce, ale ",[38,87507,87508],{},"elasticitu vůči škálování vstupů",". Speciálně ",[38,87511,87512],{},"ryzí Cobb-Douglas",[883,87514,87516],{"className":87515},[886],[888,87517,87518],{"xmlns":890},[892,87519,87520,87546],{},[895,87521,87522,87524,87526,87528,87534],{},[898,87523,1665],{},[1656,87525,1713],{},[898,87527,2146],{},[2062,87529,87530,87532],{},[898,87531,18539],{},[898,87533,207],{},[2062,87535,87536,87538],{},[898,87537,18544],{},[895,87539,87540,87542,87544],{},[1667,87541,1669],{},[1656,87543,3964],{},[898,87545,207],{},[902,87547,87548],{"encoding":904},"Q = AL^a K^{1-a}"," má ",[883,87551,87553],{"className":87552},[886],[888,87554,87555],{"xmlns":890},[892,87556,87557,87569],{},[895,87558,87559,87561,87563,87565,87567],{},[898,87560,3403],{},[1656,87562,1713],{},[1667,87564,1669],{},[1656,87566,3964],{},[898,87568,207],{},[902,87570,87571],{"encoding":904},"b = 1-a",", tedy vždy ",[38,87574,87575],{},"konstantní výnosy z rozsahu",[198,87577,87579,87580],{"id":87578},"parametr-efektivity-aa","Parametr efektivity ",[883,87581,87583],{"className":87582},[886],[888,87584,87585],{"xmlns":890},[892,87586,87587,87591],{},[895,87588,87589],{},[898,87590,2146],{},[902,87592,2146],{"encoding":904},[724,87594,87595,87596,87609,87610,87623,87624,87642,87643,87646],{},"Konstanta ",[883,87597,87599],{"className":87598},[886],[888,87600,87601],{"xmlns":890},[892,87602,87603,87607],{},[895,87604,87605],{},[898,87606,2146],{},[902,87608,2146],{"encoding":904}," v (5.7) proporcionálně ovlivňuje úroveň produkce ",[883,87611,87613],{"className":87612},[886],[888,87614,87615],{"xmlns":890},[892,87616,87617,87621],{},[895,87618,87619],{},[898,87620,1665],{},[902,87622,1665],{"encoding":904}," při pevně zadaných ",[883,87625,87627],{"className":87626},[886],[888,87628,87629],{"xmlns":890},[892,87630,87631,87639],{},[895,87632,87633,87635,87637],{},[898,87634,18539],{},[1656,87636,1673],{"separator":1672},[898,87638,18544],{},[902,87640,87641],{"encoding":904},"L, K",", a lze ji proto chápat jako ",[38,87644,87645],{},"parametr efektivity"," — indikátor stavu technologie.",[198,87648,87650],{"id":87649},"příklad-53","Příklad 5.3",[724,87652,87653,87654,87549,87696,87698,87699,1863],{},"Produkční funkce ",[883,87655,87657],{"className":87656},[886],[888,87658,87659],{"xmlns":890},[892,87660,87661,87693],{},[895,87662,87663,87665,87667,87669,87681],{},[898,87664,1665],{},[1656,87666,1713],{},[1667,87668,1680],{},[2062,87670,87671,87673],{},[898,87672,18539],{},[895,87674,87675,87677,87679],{},[1667,87676,1669],{},[898,87678,1782],{"mathvariant":1723},[1667,87680,2673],{},[2062,87682,87683,87685],{},[898,87684,18544],{},[895,87686,87687,87689,87691],{},[1667,87688,2617],{},[898,87690,1782],{"mathvariant":1723},[1667,87692,2673],{},[902,87694,87695],{"encoding":904},"Q = 2L^{1\u002F4} K^{3\u002F4}",[38,87697,33329],{}," výnosy z rozsahu, neboť ",[883,87700,87702],{"className":87701},[886],[888,87703,87704],{"xmlns":890},[892,87705,87706,87730],{},[895,87707,87708,87716,87718,87726,87728],{},[4138,87709,87710],{"scriptlevel":4032,"displaystyle":1658},[3294,87711,87712,87714],{},[1667,87713,1669],{},[1667,87715,2673],{},[1656,87717,3633],{},[4138,87719,87720],{"scriptlevel":4032,"displaystyle":1658},[3294,87721,87722,87724],{},[1667,87723,2617],{},[1667,87725,2673],{},[1656,87727,1713],{},[1667,87729,1669],{},[902,87731,87732],{"encoding":904},"\\tfrac{1}{4} + \\tfrac{3}{4} = 1",[724,87734,87735,87736,14953,87749,87762,87763,1643,87776,87816],{},"Změní-li se ",[883,87737,87739],{"className":87738},[886],[888,87740,87741],{"xmlns":890},[892,87742,87743,87747],{},[895,87744,87745],{},[898,87746,18539],{},[902,87748,18539],{"encoding":904},[883,87750,87752],{"className":87751},[886],[888,87753,87754],{"xmlns":890},[892,87755,87756,87760],{},[895,87757,87758],{},[898,87759,18544],{},[902,87761,18544],{"encoding":904}," čtyřnásobně, změní se ",[883,87764,87766],{"className":87765},[886],[888,87767,87768],{"xmlns":890},[892,87769,87770,87774],{},[895,87771,87772],{},[898,87773,1665],{},[902,87775,1665],{"encoding":904},[883,87777,87779],{"className":87778},[886],[888,87780,87781],{"xmlns":890},[892,87782,87783,87813],{},[895,87784,87785,87805,87807],{},[2062,87786,87787,87789],{},[1667,87788,2673],{},[895,87790,87791,87793,87795,87797,87799,87801,87803],{},[1667,87792,1669],{},[898,87794,1782],{"mathvariant":1723},[1667,87796,2673],{},[1656,87798,3633],{},[1667,87800,2617],{},[898,87802,1782],{"mathvariant":1723},[1667,87804,2673],{},[1656,87806,1713],{},[2062,87808,87809,87811],{},[1667,87810,2673],{},[1667,87812,1669],{},[902,87814,87815],{"encoding":904},"4^{1\u002F4 + 3\u002F4} = 4^1","-krát:",[883,87818,87820],{"className":87819},[886],[888,87821,87822],{"xmlns":890,"display":2408},[892,87823,87824,87984],{},[895,87825,87826,87828,87830,87832,87834,87836,87838,87840,87842,87844,87846,87848,87850,87852,87864,87866,87868,87870,87882,87884,87886,87888,87908,87920,87932,87934,87936,87938,87940,87952,87964,87966,87968,87970,87972,87974,87976,87978,87980,87982],{},[898,87827,1665],{},[1656,87829,1659],{"stretchy":1658},[1667,87831,2673],{},[898,87833,18539],{},[1656,87835,1673],{"separator":1672},[1667,87837,2673],{},[898,87839,18544],{},[1656,87841,1683],{"stretchy":1658},[1656,87843,1713],{},[1667,87845,1680],{},[1656,87847,1659],{"stretchy":1658},[1667,87849,2673],{},[898,87851,18539],{},[2062,87853,87854,87856],{},[1656,87855,1683],{"stretchy":1658},[895,87857,87858,87860,87862],{},[1667,87859,1669],{},[898,87861,1782],{"mathvariant":1723},[1667,87863,2673],{},[1656,87865,1659],{"stretchy":1658},[1667,87867,2673],{},[898,87869,18544],{},[2062,87871,87872,87874],{},[1656,87873,1683],{"stretchy":1658},[895,87875,87876,87878,87880],{},[1667,87877,2617],{},[898,87879,1782],{"mathvariant":1723},[1667,87881,2673],{},[1656,87883,1713],{},[1667,87885,1680],{},[1656,87887,2751],{},[2062,87889,87890,87892],{},[1667,87891,2673],{},[895,87893,87894,87896,87898,87900,87902,87904,87906],{},[1667,87895,1669],{},[898,87897,1782],{"mathvariant":1723},[1667,87899,2673],{},[1656,87901,3633],{},[1667,87903,2617],{},[898,87905,1782],{"mathvariant":1723},[1667,87907,2673],{},[2062,87909,87910,87912],{},[898,87911,18539],{},[895,87913,87914,87916,87918],{},[1667,87915,1669],{},[898,87917,1782],{"mathvariant":1723},[1667,87919,2673],{},[2062,87921,87922,87924],{},[898,87923,18544],{},[895,87925,87926,87928,87930],{},[1667,87927,2617],{},[898,87929,1782],{"mathvariant":1723},[1667,87931,2673],{},[1656,87933,1713],{},[1667,87935,2673],{},[1656,87937,2751],{},[1667,87939,1680],{},[2062,87941,87942,87944],{},[898,87943,18539],{},[895,87945,87946,87948,87950],{},[1667,87947,1669],{},[898,87949,1782],{"mathvariant":1723},[1667,87951,2673],{},[2062,87953,87954,87956],{},[898,87955,18544],{},[895,87957,87958,87960,87962],{},[1667,87959,2617],{},[898,87961,1782],{"mathvariant":1723},[1667,87963,2673],{},[1656,87965,1713],{},[1667,87967,2673],{},[2461,87969,7828],{},[898,87971,1665],{},[1656,87973,1659],{"stretchy":1658},[898,87975,18539],{},[1656,87977,1673],{"separator":1672},[898,87979,18544],{},[1656,87981,1683],{"stretchy":1658},[898,87983,1863],{"mathvariant":1723},[902,87985,87986],{"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).",[198,87988,87989],{"id":45861},"Homogenita",[724,87991,87992,87993,3206,88016,88032],{},"Funkce ",[883,87994,87996],{"className":87995},[886],[888,87997,87998],{"xmlns":890},[892,87999,88000,88014],{},[895,88001,88002,88004,88006,88008,88010,88012],{},[898,88003,1665],{},[1656,88005,1659],{"stretchy":1658},[898,88007,18539],{},[1656,88009,1673],{"separator":1672},[898,88011,18544],{},[1656,88013,1683],{"stretchy":1658},[902,88015,18740],{"encoding":904},[38,88017,88018,88019],{},"homogenní stupně ",[883,88020,88022],{"className":88021},[886],[888,88023,88024],{"xmlns":890},[892,88025,88026,88030],{},[895,88027,88028],{},[898,88029,2292],{},[902,88031,2292],{"encoding":904},", jestliže",[883,88034,88036],{"className":88035},[886],[888,88037,88038],{"xmlns":890,"display":2408},[892,88039,88040,88097],{},[2412,88041,88042],{"width":2414},[2416,88043,88044,88046,88090,88092],{},[2419,88045],{"width":2421},[2419,88047,88048],{},[895,88049,88050,88052,88054,88056,88058,88060,88062,88064,88066,88068,88074,88076,88078,88080,88082,88084,88086,88088],{},[898,88051,1665],{},[1656,88053,1659],{"stretchy":1658},[898,88055,20776],{},[898,88057,18539],{},[1656,88059,1673],{"separator":1672},[898,88061,20776],{},[898,88063,18544],{},[1656,88065,1683],{"stretchy":1658},[1656,88067,1713],{},[2062,88069,88070,88072],{},[898,88071,20776],{},[898,88073,2292],{},[2461,88075,7828],{},[898,88077,1665],{},[1656,88079,1659],{"stretchy":1658},[898,88081,18539],{},[1656,88083,1673],{"separator":1672},[898,88085,18544],{},[1656,88087,1683],{"stretchy":1658},[1656,88089,1673],{"separator":1672},[2419,88091],{"width":2421},[2419,88093,88094],{},[2461,88095,88096],{},"(5.10)",[902,88098,88099],{"encoding":904},"Q(rL, rK) = r^n\\,Q(L, K), \\tag{5.10}",[724,88101,2355,88102,88120,88121,88139,88140,52313,88153,88156,88157,1863],{},[883,88103,88105],{"className":88104},[886],[888,88106,88107],{"xmlns":890},[892,88108,88109,88117],{},[895,88110,88111,88113,88115],{},[898,88112,2292],{},[1656,88114,13258],{},[1667,88116,4032],{},[902,88118,88119],{"encoding":904},"n \\geq 0"," je celé číslo a ",[883,88122,88124],{"className":88123},[886],[888,88125,88126],{"xmlns":890},[892,88127,88128,88136],{},[895,88129,88130,88132,88134],{},[898,88131,20776],{},[1656,88133,2850],{},[1667,88135,4032],{},[902,88137,88138],{"encoding":904},"r > 0",". Homogenní funkce stupně ",[883,88141,88143],{"className":88142},[886],[888,88144,88145],{"xmlns":890},[892,88146,88147,88151],{},[895,88148,88149],{},[1667,88150,1669],{},[902,88152,1669],{"encoding":904},[38,88154,88155],{},"lineárně homogenní",". Cobb-Douglasovy funkce jsou homogenní stupně ",[883,88158,88160],{"className":88159},[886],[888,88161,88162],{"xmlns":890},[892,88163,88164,88172],{},[895,88165,88166,88168,88170],{},[898,88167,207],{},[1656,88169,3633],{},[898,88171,3403],{},[902,88173,83485],{"encoding":904},[115,88175,88177],{"id":88176},"ryzí-cobb-douglas-a-ces","Ryzí Cobb-Douglas a CES",[724,88179,88180],{},[38,88181,88182],{},"Ryzí Cobb-Douglasovy funkce:",[883,88184,88186],{"className":88185},[886],[888,88187,88188],{"xmlns":890,"display":2408},[892,88189,88190,88249],{},[2412,88191,88192],{"width":2414},[2416,88193,88194,88196,88242,88244],{},[2419,88195],{"width":2421},[2419,88197,88198],{},[895,88199,88200,88202,88204,88206,88208,88214,88216,88228,88230,88232,88234,88236,88238,88240],{},[898,88201,1665],{},[1656,88203,1713],{},[898,88205,2146],{},[2461,88207,7828],{},[2062,88209,88210,88212],{},[898,88211,18539],{},[898,88213,207],{},[2461,88215,7828],{},[2062,88217,88218,88220],{},[898,88219,18544],{},[895,88221,88222,88224,88226],{},[1667,88223,1669],{},[1656,88225,3964],{},[898,88227,207],{},[1656,88229,1673],{"separator":1672},[3316,88231],{"width":3318},[1667,88233,4032],{},[1656,88235,4373],{},[898,88237,207],{},[1656,88239,4373],{},[1667,88241,21993],{},[2419,88243],{"width":2421},[2419,88245,88246],{},[2461,88247,88248],{},"(5.9)",[902,88250,88251],{"encoding":904},"Q = A\\,L^a\\,K^{1-a}, \\quad 0 \u003C a \u003C 1. \\tag{5.9}",[724,88253,88254,88255,88257,88258,1863],{},"Mají vždy ",[38,88256,87575],{}," a jsou ",[38,88259,88155],{},[724,88261,88262,3247,88265,88268],{},[38,88263,88264],{},"CES produkční funkce",[614,88266,88267],{},"Constant Elasticity of Substitution",", 1961):",[883,88270,88272],{"className":88271},[886],[888,88273,88274],{"xmlns":890,"display":2408},[892,88275,88276,88344],{},[895,88277,88278,88280,88282,88284,88342],{},[898,88279,1665],{},[1656,88281,1713],{},[898,88283,2146],{},[2062,88285,88286,88330],{},[895,88287,88288,88290,88292,88294,88296,88298,88300,88302,88312,88314,88316,88318,88328],{},[1656,88289,3453],{"fence":1672},[1656,88291,1659],{"stretchy":1658},[1667,88293,1669],{},[1656,88295,3964],{},[898,88297,207],{},[1656,88299,1683],{"stretchy":1658},[2461,88301,7828],{},[2062,88303,88304,88306],{},[898,88305,18539],{},[895,88307,88308,88310],{},[1656,88309,3964],{},[898,88311,3403],{},[1656,88313,3633],{},[898,88315,207],{},[2461,88317,7828],{},[2062,88319,88320,88322],{},[898,88321,18544],{},[895,88323,88324,88326],{},[1656,88325,3964],{},[898,88327,3403],{},[1656,88329,3462],{"fence":1672},[895,88331,88332,88334],{},[1656,88333,3964],{},[4138,88335,88336],{"scriptlevel":4032,"displaystyle":1658},[3294,88337,88338,88340],{},[1667,88339,1669],{},[898,88341,3403],{},[1656,88343,1673],{"separator":1672},[902,88345,88346],{"encoding":904},"Q = A\\left[(1-a)\\,L^{-b} + a\\,K^{-b}\\right]^{-\\tfrac{1}{b}},",[724,88348,2355,88349,1343,88367,1343,88388,88412],{},[883,88350,88352],{"className":88351},[886],[888,88353,88354],{"xmlns":890},[892,88355,88356,88364],{},[895,88357,88358,88360,88362],{},[898,88359,2146],{},[1656,88361,2850],{},[1667,88363,4032],{},[902,88365,88366],{"encoding":904},"A > 0",[883,88368,88370],{"className":88369},[886],[888,88371,88372],{"xmlns":890},[892,88373,88374,88386],{},[895,88375,88376,88378,88380,88382,88384],{},[1667,88377,4032],{},[1656,88379,4373],{},[898,88381,207],{},[1656,88383,4373],{},[1667,88385,1669],{},[902,88387,27558],{"encoding":904},[883,88389,88391],{"className":88390},[886],[888,88392,88393],{"xmlns":890},[892,88394,88395,88409],{},[895,88396,88397,88399,88401,88403,88405,88407],{},[1656,88398,3964],{},[1667,88400,1669],{},[1656,88402,4373],{},[898,88404,3403],{},[1656,88406,12161],{"mathvariant":1723},[1667,88408,4032],{},[902,88410,88411],{"encoding":904},"-1 \u003C b \\neq 0",". Cobb-Douglasovy funkce jsou jejich zvláštním případem.",[724,88414,88415],{},[38,88416,88417],{},"Další typy:",[120,88419,88420,88462],{},[123,88421,88422,1643,88425,88461],{},[38,88423,88424],{},"Lineární:",[883,88426,88428],{"className":88427},[886],[888,88429,88430],{"xmlns":890},[892,88431,88432,88458],{},[895,88433,88434,88436,88438,88440,88442,88444,88446,88448,88450,88452,88454,88456],{},[898,88435,1665],{},[1656,88437,1659],{"stretchy":1658},[898,88439,18539],{},[1656,88441,1673],{"separator":1672},[898,88443,18544],{},[1656,88445,1683],{"stretchy":1658},[1656,88447,1713],{},[898,88449,207],{},[898,88451,18539],{},[1656,88453,3633],{},[898,88455,3403],{},[898,88457,18544],{},[902,88459,88460],{"encoding":904},"Q(L, K) = aL + bK"," — dokonalé substituty.",[123,88463,88464,1643,88467,88512],{},[38,88465,88466],{},"Leontiefova:",[883,88468,88470],{"className":88469},[886],[888,88471,88472],{"xmlns":890},[892,88473,88474,88509],{},[895,88475,88476,88478,88480,88482,88484,88486,88488,88490,88493,88495,88497,88499,88501,88503,88505,88507],{},[898,88477,1665],{},[1656,88479,1659],{"stretchy":1658},[898,88481,18539],{},[1656,88483,1673],{"separator":1672},[898,88485,18544],{},[1656,88487,1683],{"stretchy":1658},[1656,88489,1713],{},[898,88491,88492],{},"min",[1656,88494,2093],{},[1656,88496,1659],{"stretchy":1658},[898,88498,207],{},[898,88500,18539],{},[1656,88502,1673],{"separator":1672},[898,88504,3403],{},[898,88506,18544],{},[1656,88508,1683],{"stretchy":1658},[902,88510,88511],{"encoding":904},"Q(L, K) = \\min(aL, bK)"," — dokonalé komplementy (fixní proporce).",[115,88514,88516,88517,1343,88536,88555],{"id":88515},"mezní-produkty-mplmp_l-mpkmp_k-a-totální-diferenciál","Mezní produkty ",[883,88518,88520],{"className":88519},[886],[888,88521,88522],{"xmlns":890},[892,88523,88524,88534],{},[895,88525,88526,88528],{},[898,88527,1703],{},[1661,88529,88530,88532],{},[898,88531,8194],{},[898,88533,18539],{},[902,88535,18787],{"encoding":904},[883,88537,88539],{"className":88538},[886],[888,88540,88541],{"xmlns":890},[892,88542,88543,88553],{},[895,88544,88545,88547],{},[898,88546,1703],{},[1661,88548,88549,88551],{},[898,88550,8194],{},[898,88552,18544],{},[902,88554,18832],{"encoding":904}," a totální diferenciál",[724,88557,88558],{},[38,88559,88560],{},"Mezní produkt práce:",[883,88562,88564],{"className":88563},[886],[888,88565,88566],{"xmlns":890,"display":2408},[892,88567,88568,88606],{},[895,88569,88570,88572,88578,88580,88588,88590,88604],{},[898,88571,1703],{},[1661,88573,88574,88576],{},[898,88575,8194],{},[898,88577,18539],{},[1656,88579,1713],{},[1715,88581,88582,88584,88586],{},[898,88583,1665],{},[898,88585,18539],{},[1656,88587,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,88589,1713],{},[3294,88591,88592,88598],{},[895,88593,88594,88596],{},[898,88595,3300],{"mathvariant":1723},[898,88597,1665],{},[895,88599,88600,88602],{},[898,88601,3300],{"mathvariant":1723},[898,88603,18539],{},[898,88605,1863],{"mathvariant":1723},[902,88607,88608],{"encoding":904},"MP_L = Q'_L = \\frac{\\partial Q}{\\partial L}.",[724,88610,88611],{},[38,88612,88613],{},"Mezní produkt kapitálu:",[883,88615,88617],{"className":88616},[886],[888,88618,88619],{"xmlns":890,"display":2408},[892,88620,88621,88659],{},[895,88622,88623,88625,88631,88633,88641,88643,88657],{},[898,88624,1703],{},[1661,88626,88627,88629],{},[898,88628,8194],{},[898,88630,18544],{},[1656,88632,1713],{},[1715,88634,88635,88637,88639],{},[898,88636,1665],{},[898,88638,18544],{},[1656,88640,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,88642,1713],{},[3294,88644,88645,88651],{},[895,88646,88647,88649],{},[898,88648,3300],{"mathvariant":1723},[898,88650,1665],{},[895,88652,88653,88655],{},[898,88654,3300],{"mathvariant":1723},[898,88656,18544],{},[898,88658,1863],{"mathvariant":1723},[902,88660,88661],{"encoding":904},"MP_K = Q'_K = \\frac{\\partial Q}{\\partial K}.",[724,88663,88664,88694,88695,88716,88717,88735,88736,88749,88750,1863],{},[883,88665,88667],{"className":88666},[886],[888,88668,88669],{"xmlns":890},[892,88670,88671,88691],{},[895,88672,88673,88675,88681,88683,88685,88687,88689],{},[898,88674,1703],{},[1661,88676,88677,88679],{},[898,88678,8194],{},[898,88680,18539],{},[1656,88682,1659],{"stretchy":1658},[898,88684,207],{},[1656,88686,1673],{"separator":1672},[898,88688,3403],{},[1656,88690,1683],{"stretchy":1658},[902,88692,88693],{"encoding":904},"MP_L(a, b)"," udává rychlost změny produkce vzhledem k práci v bodě ",[883,88696,88698],{"className":88697},[886],[888,88699,88700],{"xmlns":890},[892,88701,88702,88714],{},[895,88703,88704,88706,88708,88710,88712],{},[1656,88705,3453],{"stretchy":1658},[898,88707,207],{},[1656,88709,1673],{"separator":1672},[898,88711,3403],{},[1656,88713,3462],{"stretchy":1658},[902,88715,3465],{"encoding":904}," (na hladině ",[883,88718,88720],{"className":88719},[886],[888,88721,88722],{"xmlns":890},[892,88723,88724,88732],{},[895,88725,88726,88728,88730],{},[898,88727,18544],{},[1656,88729,1713],{},[898,88731,3403],{},[902,88733,88734],{"encoding":904},"K = b","), resp. přibližnou změnu produkce při jednotkové změně ",[883,88737,88739],{"className":88738},[886],[888,88740,88741],{"xmlns":890},[892,88742,88743,88747],{},[895,88744,88745],{},[898,88746,18539],{},[902,88748,18539],{"encoding":904},". Analogicky ",[883,88751,88753],{"className":88752},[886],[888,88754,88755],{"xmlns":890},[892,88756,88757,88777],{},[895,88758,88759,88761,88767,88769,88771,88773,88775],{},[898,88760,1703],{},[1661,88762,88763,88765],{},[898,88764,8194],{},[898,88766,18544],{},[1656,88768,1659],{"stretchy":1658},[898,88770,207],{},[1656,88772,1673],{"separator":1672},[898,88774,3403],{},[1656,88776,1683],{"stretchy":1658},[902,88778,88779],{"encoding":904},"MP_K(a, b)",[1981,88781,88782,88786],{},[724,88783,88784,59891],{},[883,88785,3472],{},[120,88787,88788,88826],{},[123,88789,88790,6960,88809],{},[883,88791,88793],{"className":88792},[886],[888,88794,88795],{"xmlns":890},[892,88796,88797,88807],{},[895,88798,88799,88801],{},[898,88800,1703],{},[1661,88802,88803,88805],{},[898,88804,8194],{},[898,88806,18539],{},[902,88808,18787],{"encoding":904},[614,88810,88811,88812,88825],{},"„o kolik vzroste ",[883,88813,88815],{"className":88814},[886],[888,88816,88817],{"xmlns":890},[892,88818,88819,88823],{},[895,88820,88821],{},[898,88822,1665],{},[902,88824,1665],{"encoding":904},", když přidám jednu jednotku práce (a kapitál držím pevně)?\"",[123,88827,88828,6960,88847],{},[883,88829,88831],{"className":88830},[886],[888,88832,88833],{"xmlns":890},[892,88834,88835,88845],{},[895,88836,88837,88839],{},[898,88838,1703],{},[1661,88840,88841,88843],{},[898,88842,8194],{},[898,88844,18544],{},[902,88846,18832],{"encoding":904},[614,88848,88811,88849,88862],{},[883,88850,88852],{"className":88851},[886],[888,88853,88854],{"xmlns":890},[892,88855,88856,88860],{},[895,88857,88858],{},[898,88859,1665],{},[902,88861,1665],{"encoding":904},", když přidám jednu jednotku kapitálu (a práci držím pevně)?\"",[724,88864,88865,88867,88868,88883,88884,2114],{},[38,88866,3735],{}," — přibližná změna produkce při změně práce o ",[883,88869,88871],{"className":88870},[886],[888,88872,88873],{"xmlns":890},[892,88874,88875,88881],{},[895,88876,88877,88879],{},[898,88878,3768],{},[898,88880,18539],{},[902,88882,84013],{"encoding":904}," a kapitálu o ",[883,88885,88887],{"className":88886},[886],[888,88888,88889],{"xmlns":890},[892,88890,88891,88897],{},[895,88892,88893,88895],{},[898,88894,3768],{},[898,88896,18544],{},[902,88898,88899],{"encoding":904},"dK",[883,88901,88903],{"className":88902},[886],[888,88904,88905],{"xmlns":890,"display":2408},[892,88906,88907,89000],{},[2412,88908,88909],{"width":2414},[2416,88910,88911,88913,88993,88995],{},[2419,88912],{"width":2421},[2419,88914,88915],{},[895,88916,88917,88919,88921,88923,88925,88927,88929,88937,88939,88941,88943,88945,88953,88955,88957,88959,88961,88963,88969,88971,88973,88975,88977,88979,88985,88987,88989,88991],{},[898,88918,3750],{"mathvariant":1723},[898,88920,1665],{},[1656,88922,3815],{},[898,88924,3768],{},[898,88926,1665],{},[1656,88928,1713],{},[1715,88930,88931,88933,88935],{},[898,88932,1665],{},[898,88934,18539],{},[1656,88936,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[2461,88938,7828],{},[898,88940,3768],{},[898,88942,18539],{},[1656,88944,3633],{},[1715,88946,88947,88949,88951],{},[898,88948,1665],{},[898,88950,18544],{},[1656,88952,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[2461,88954,7828],{},[898,88956,3768],{},[898,88958,18544],{},[1656,88960,1713],{},[898,88962,1703],{},[1661,88964,88965,88967],{},[898,88966,8194],{},[898,88968,18539],{},[2461,88970,7828],{},[898,88972,3768],{},[898,88974,18539],{},[1656,88976,3633],{},[898,88978,1703],{},[1661,88980,88981,88983],{},[898,88982,8194],{},[898,88984,18544],{},[2461,88986,7828],{},[898,88988,3768],{},[898,88990,18544],{},[898,88992,1863],{"mathvariant":1723},[2419,88994],{"width":2421},[2419,88996,88997],{},[2461,88998,88999],{},"(5.11)",[902,89001,89002],{"encoding":904},"\\Delta Q \\approx dQ = Q'_L\\,dL + Q'_K\\,dK = MP_L\\,dL + MP_K\\,dK. \\tag{5.11}",[724,89004,89005,89006,1863],{},"Skutečná změna: ",[883,89007,89009],{"className":89008},[886],[888,89010,89011],{"xmlns":890},[892,89012,89013,89059],{},[895,89014,89015,89017,89019,89021,89023,89025,89027,89029,89031,89033,89035,89037,89039,89041,89043,89045,89047,89049,89051,89053,89055,89057],{},[898,89016,3750],{"mathvariant":1723},[898,89018,1665],{},[1656,89020,1713],{},[898,89022,1665],{},[1656,89024,1659],{"stretchy":1658},[898,89026,18539],{},[1656,89028,3633],{},[898,89030,3768],{},[898,89032,18539],{},[1656,89034,1673],{"separator":1672},[898,89036,18544],{},[1656,89038,3633],{},[898,89040,3768],{},[898,89042,18544],{},[1656,89044,1683],{"stretchy":1658},[1656,89046,3964],{},[898,89048,1665],{},[1656,89050,1659],{"stretchy":1658},[898,89052,18539],{},[1656,89054,1673],{"separator":1672},[898,89056,18544],{},[1656,89058,1683],{"stretchy":1658},[902,89060,89061],{"encoding":904},"\\Delta Q = Q(L+dL, K+dK) - Q(L, K)",[724,89063,89064,89066,89067,89085,89086,89099,89100,89119,89120,89152,89153,89185,89186,1863],{},[38,89065,84176],{}," platí ve 2F modelu pro oba vstupy: pro pevné ",[883,89068,89070],{"className":89069},[886],[888,89071,89072],{"xmlns":890},[892,89073,89074,89082],{},[895,89075,89076],{},[1661,89077,89078,89080],{},[898,89079,18544],{},[1667,89081,4032],{},[902,89083,89084],{"encoding":904},"K_0"," se od jistého ",[883,89087,89089],{"className":89088},[886],[888,89090,89091],{"xmlns":890},[892,89092,89093,89097],{},[895,89094,89095],{},[898,89096,18539],{},[902,89098,18539],{"encoding":904}," stane ",[883,89101,89103],{"className":89102},[886],[888,89104,89105],{"xmlns":890},[892,89106,89107,89117],{},[895,89108,89109,89111],{},[898,89110,1703],{},[1661,89112,89113,89115],{},[898,89114,8194],{},[898,89116,18539],{},[902,89118,18787],{"encoding":904}," klesající (",[883,89121,89123],{"className":89122},[886],[888,89124,89125],{"xmlns":890},[892,89126,89127,89149],{},[895,89128,89129,89145,89147],{},[1715,89130,89131,89133,89139],{},[898,89132,1665],{},[895,89134,89135,89137],{},[898,89136,18539],{},[898,89138,18539],{},[895,89140,89141,89143],{},[1656,89142,1725],{"mathvariant":1723},[1656,89144,1725],{"mathvariant":1723},[1656,89146,4373],{},[1667,89148,4032],{},[902,89150,89151],{"encoding":904},"Q''_{LL} \u003C 0","); analogicky ",[883,89154,89156],{"className":89155},[886],[888,89157,89158],{"xmlns":890},[892,89159,89160,89182],{},[895,89161,89162,89178,89180],{},[1715,89163,89164,89166,89172],{},[898,89165,1665],{},[895,89167,89168,89170],{},[898,89169,18544],{},[898,89171,18544],{},[895,89173,89174,89176],{},[1656,89175,1725],{"mathvariant":1723},[1656,89177,1725],{"mathvariant":1723},[1656,89179,4373],{},[1667,89181,4032],{},[902,89183,89184],{"encoding":904},"Q''_{KK} \u003C 0"," pro pevné ",[883,89187,89189],{"className":89188},[886],[888,89190,89191],{"xmlns":890},[892,89192,89193,89201],{},[895,89194,89195],{},[1661,89196,89197,89199],{},[898,89198,18539],{},[1667,89200,4032],{},[902,89202,84214],{"encoding":904},[115,89204,89206],{"id":89205},"eulerova-věta-pro-homogenní-funkce","Eulerova věta pro homogenní funkce",[724,89208,89209,89212,89213,89236,89237,7727],{},[38,89210,89211],{},"Eulerova věta"," (úloha 5.10): pro homogenní funkci ",[883,89214,89216],{"className":89215},[886],[888,89217,89218],{"xmlns":890},[892,89219,89220,89234],{},[895,89221,89222,89224,89226,89228,89230,89232],{},[898,89223,1665],{},[1656,89225,1659],{"stretchy":1658},[898,89227,18539],{},[1656,89229,1673],{"separator":1672},[898,89231,18544],{},[1656,89233,1683],{"stretchy":1658},[902,89235,18740],{"encoding":904}," stupně ",[883,89238,89240],{"className":89239},[886],[888,89241,89242],{"xmlns":890},[892,89243,89244,89248],{},[895,89245,89246],{},[898,89247,2292],{},[902,89249,2292],{"encoding":904},[883,89251,89253],{"className":89252},[886],[888,89254,89255],{"xmlns":890,"display":2408},[892,89256,89257,89320],{},[2412,89258,89259],{"width":2414},[2416,89260,89261,89263,89313,89315],{},[2419,89262],{"width":2421},[2419,89264,89265],{},[895,89266,89267,89269,89271,89279,89281,89283,89285,89293,89295,89297,89299,89301,89303,89305,89307,89309,89311],{},[898,89268,18539],{},[2461,89270,7828],{},[1715,89272,89273,89275,89277],{},[898,89274,1665],{},[898,89276,18539],{},[1656,89278,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,89280,3633],{},[898,89282,18544],{},[2461,89284,7828],{},[1715,89286,89287,89289,89291],{},[898,89288,1665],{},[898,89290,18544],{},[1656,89292,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,89294,1713],{},[898,89296,2292],{},[2461,89298,7828],{},[898,89300,1665],{},[1656,89302,1659],{"stretchy":1658},[898,89304,18539],{},[1656,89306,1673],{"separator":1672},[898,89308,18544],{},[1656,89310,1683],{"stretchy":1658},[898,89312,1863],{"mathvariant":1723},[2419,89314],{"width":2421},[2419,89316,89317],{},[2461,89318,89319],{},"(5.12)",[902,89321,89322],{"encoding":904},"L\\,Q'_L + K\\,Q'_K = n\\,Q(L, K). \\tag{5.12}",[724,89324,89325,89346],{},[38,89326,89327,89328],{},"Speciální případ ",[883,89329,89331],{"className":89330},[886],[888,89332,89333],{"xmlns":890},[892,89334,89335,89343],{},[895,89336,89337,89339,89341],{},[898,89338,2292],{},[1656,89340,1713],{},[1667,89342,1669],{},[902,89344,89345],{"encoding":904},"n = 1"," (konstantní výnosy z rozsahu):",[883,89348,89350],{"className":89349},[886],[888,89351,89352],{"xmlns":890,"display":2408},[892,89353,89354,89398],{},[895,89355,89356,89358,89360,89362,89368,89370,89372,89374,89376,89382,89384,89386,89388,89390,89392,89394,89396],{},[898,89357,18539],{},[1656,89359,2751],{},[898,89361,1703],{},[1661,89363,89364,89366],{},[898,89365,8194],{},[898,89367,18539],{},[1656,89369,3633],{},[898,89371,18544],{},[1656,89373,2751],{},[898,89375,1703],{},[1661,89377,89378,89380],{},[898,89379,8194],{},[898,89381,18544],{},[1656,89383,1713],{},[898,89385,1665],{},[1656,89387,1659],{"stretchy":1658},[898,89389,18539],{},[1656,89391,1673],{"separator":1672},[898,89393,18544],{},[1656,89395,1683],{"stretchy":1658},[898,89397,1863],{"mathvariant":1723},[902,89399,89400],{"encoding":904},"L\\cdot MP_L + K\\cdot MP_K = Q(L, K).",[724,89402,89403,89404,89407],{},"Slovně — ",[38,89405,89406],{},"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).",[115,89409,18522],{"id":83551},[724,89411,89412,3247,89414,89417,89418,89440,89441,2114],{},[38,89413,18522],{},[614,89415,89416],{},"isoquants",") jsou křivky stejné produkce — množina dvojic ",[883,89419,89421],{"className":89420},[886],[888,89422,89423],{"xmlns":890},[892,89424,89425,89437],{},[895,89426,89427,89429,89431,89433,89435],{},[1656,89428,3453],{"stretchy":1658},[898,89430,18539],{},[1656,89432,1673],{"separator":1672},[898,89434,18544],{},[1656,89436,3462],{"stretchy":1658},[902,89438,89439],{"encoding":904},"[L, K]",", pro něž produkční funkce nabývá pevně zvolené hodnoty ",[883,89442,89444],{"className":89443},[886],[888,89445,89446],{"xmlns":890},[892,89447,89448,89453],{},[895,89449,89450],{},[898,89451,89452],{},"q",[902,89454,89452],{"encoding":904},[883,89456,89458],{"className":89457},[886],[888,89459,89460],{"xmlns":890,"display":2408},[892,89461,89462,89497],{},[2412,89463,89464],{"width":2414},[2416,89465,89466,89468,89490,89492],{},[2419,89467],{"width":2421},[2419,89469,89470],{},[895,89471,89472,89474,89476,89478,89480,89482,89484,89486,89488],{},[898,89473,1665],{},[1656,89475,1659],{"stretchy":1658},[898,89477,18539],{},[1656,89479,1673],{"separator":1672},[898,89481,18544],{},[1656,89483,1683],{"stretchy":1658},[1656,89485,1713],{},[898,89487,89452],{},[898,89489,1863],{"mathvariant":1723},[2419,89491],{"width":2421},[2419,89493,89494],{},[2461,89495,89496],{},"(5.13)",[902,89498,89499],{"encoding":904},"Q(L, K) = q. \\tag{5.13}",[724,89501,89502,89503,89506,89507,12702],{},"Jsou to ",[38,89504,89505],{},"indiferenční křivky"," produkční funkce (analogie s indiferenčními křivkami u ",[207,89508,89510],{"className":89509,"dataFsResolvedFilePath":878,"href":879},[210],"užitečnosti",[724,89512,89513],{},[38,89514,89515],{},"Vlastnosti izokvant Cobb-Douglasových funkcí:",[120,89517,89518,89523,89528,89533],{},[123,89519,89520,89522],{},[38,89521,21253],{}," — pokles kapitálu vyžaduje kompenzující růst práce k udržení produkce;",[123,89524,89525,89527],{},[38,89526,46346],{}," (úloha 5.14);",[123,89529,89530,2856],{},[38,89531,89532],{},"neprotínají se",[123,89534,89535,89536,6496,89549,1863],{},"s rostoucím ",[883,89537,89539],{"className":89538},[886],[888,89540,89541],{"xmlns":890},[892,89542,89543,89547],{},[895,89544,89545],{},[898,89546,89452],{},[902,89548,89452],{"encoding":904},[38,89550,89551],{},"vzdalují od počátku",[724,89553,89554],{},[614,89555,89556,89557,89579,89580,1863],{},"Obrázek 5.4 — izokvanty Cobb-Douglasovy funkce v rovině ",[883,89558,89560],{"className":89559},[886],[888,89561,89562],{"xmlns":890},[892,89563,89564,89576],{},[895,89565,89566,89568,89570,89572,89574],{},[1656,89567,1659],{"stretchy":1658},[898,89569,18539],{},[1656,89571,1673],{"separator":1672},[898,89573,18544],{},[1656,89575,1683],{"stretchy":1658},[902,89577,89578],{"encoding":904},"(L, K)",": tři klesající konvexní křivky pro ",[883,89581,89583],{"className":89582},[886],[888,89584,89585],{"xmlns":890},[892,89586,89587,89611],{},[895,89588,89589,89595,89597,89603,89605],{},[1661,89590,89591,89593],{},[898,89592,89452],{},[1667,89594,1669],{},[1656,89596,4373],{},[1661,89598,89599,89601],{},[898,89600,89452],{},[1667,89602,4032],{},[1656,89604,4373],{},[1661,89606,89607,89609],{},[898,89608,89452],{},[1667,89610,1680],{},[902,89612,89613],{"encoding":904},"q_1 \u003C q_0 \u003C q_2",[115,89615,89617,89618,1683],{"id":89616},"mezní-míra-technické-substituce-mrtsmrts","Mezní míra technické substituce (",[883,89619,89621],{"className":89620},[886],[888,89622,89623],{"xmlns":890},[892,89624,89625,89635],{},[895,89626,89627,89629,89631,89633],{},[898,89628,1703],{},[898,89630,1763],{},[898,89632,11577],{},[898,89634,1769],{},[902,89636,19340],{"encoding":904},[724,89638,89639,3247,89642,89645],{},[38,89640,89641],{},"Mezní míra technické substituce",[614,89643,89644],{},"marginal rate of technical substitution",") je podíl mezních produktů:",[883,89647,89649],{"className":89648},[886],[888,89650,89651],{"xmlns":890,"display":2408},[892,89652,89653,89744],{},[2412,89654,89655],{"width":2414},[2416,89656,89657,89659,89737,89739],{},[2419,89658],{"width":2421},[2419,89660,89661],{},[895,89662,89663,89665,89667,89669,89671,89673,89675,89677,89679,89681,89683,89685,89687,89689,89691,89693,89715,89717,89735],{},[898,89664,1703],{},[898,89666,1763],{},[898,89668,11577],{},[898,89670,1769],{},[1656,89672,1713],{},[898,89674,1703],{},[898,89676,1763],{},[898,89678,11577],{},[898,89680,1769],{},[1656,89682,1659],{"stretchy":1658},[898,89684,18539],{},[1656,89686,1673],{"separator":1672},[898,89688,18544],{},[1656,89690,1683],{"stretchy":1658},[1656,89692,1713],{},[3294,89694,89695,89705],{},[895,89696,89697,89699],{},[898,89698,1703],{},[1661,89700,89701,89703],{},[898,89702,8194],{},[898,89704,18539],{},[895,89706,89707,89709],{},[898,89708,1703],{},[1661,89710,89711,89713],{},[898,89712,8194],{},[898,89714,18544],{},[1656,89716,1713],{},[3294,89718,89719,89727],{},[1715,89720,89721,89723,89725],{},[898,89722,1665],{},[898,89724,18539],{},[1656,89726,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1715,89728,89729,89731,89733],{},[898,89730,1665],{},[898,89732,18544],{},[1656,89734,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[898,89736,1863],{"mathvariant":1723},[2419,89738],{"width":2421},[2419,89740,89741],{},[2461,89742,89743],{},"(5.14)",[902,89745,89746],{"encoding":904},"MRTS = MRTS(L, K) = \\frac{MP_L}{MP_K} = \\frac{Q'_L}{Q'_K}. \\tag{5.14}",[724,89748,89749,1643,89751,89781,89782,89813],{},[38,89750,5434],{},[883,89752,89754],{"className":89753},[886],[888,89755,89756],{"xmlns":890},[892,89757,89758,89778],{},[895,89759,89760,89762,89764,89766,89768,89770,89772,89774,89776],{},[898,89761,1703],{},[898,89763,1763],{},[898,89765,11577],{},[898,89767,1769],{},[1656,89769,1659],{"stretchy":1658},[898,89771,18539],{},[1656,89773,1673],{"separator":1672},[898,89775,18544],{},[1656,89777,1683],{"stretchy":1658},[902,89779,89780],{"encoding":904},"MRTS(L, K)"," udává, ",[38,89783,89784,89785,89798,89799,89812],{},"o kolik se musí přibližně změnit kapitál ",[883,89786,89788],{"className":89787},[886],[888,89789,89790],{"xmlns":890},[892,89791,89792,89796],{},[895,89793,89794],{},[898,89795,18544],{},[902,89797,18544],{"encoding":904},", jestliže se práce ",[883,89800,89802],{"className":89801},[886],[888,89803,89804],{"xmlns":890},[892,89805,89806,89810],{},[895,89807,89808],{},[898,89809,18539],{},[902,89811,18539],{"encoding":904}," změní o jednotku, aby byla zachována produkce"," (pohyb po izokvantě).",[1981,89815,89816],{},[724,89817,89818,26746,89820,89839,89840,89877,89878,89881,89882,89886],{},[883,89819,3472],{},[883,89821,89823],{"className":89822},[886],[888,89824,89825],{"xmlns":890},[892,89826,89827,89837],{},[895,89828,89829,89831,89833,89835],{},[898,89830,1703],{},[898,89832,1763],{},[898,89834,11577],{},[898,89836,1769],{},[902,89838,19340],{"encoding":904}," říká: ",[614,89841,89842,89843,89862,89863,89876],{},"„jednu jednotku práce musím nahradit přibližně ",[883,89844,89846],{"className":89845},[886],[888,89847,89848],{"xmlns":890},[892,89849,89850,89860],{},[895,89851,89852,89854,89856,89858],{},[898,89853,1703],{},[898,89855,1763],{},[898,89857,11577],{},[898,89859,1769],{},[902,89861,19340],{"encoding":904}," jednotkami kapitálu, aby produkce ",[883,89864,89866],{"className":89865},[886],[888,89867,89868],{"xmlns":890},[892,89869,89870,89874],{},[895,89871,89872],{},[898,89873,1665],{},[902,89875,1665],{"encoding":904}," zůstala stejná.\""," Je to ",[38,89879,89880],{},"směnný kurz mezi vstupy"," při zachování produkce — přesná analogie ",[207,89883,89885],{"className":89884,"dataFsResolvedFilePath":878,"href":879},[210],"MRCS z teorie užitečnosti",", kde nahrazujeme spotřební statky při zachování užitku.",[724,89888,89889],{},[5956,89890],{"alt":89891,"className":89892,"src":89893},"imek-izokvanty-mrts",[210,5960],"\u002Fwiki-assets\u002Fimek-izokvanty-mrts.jpeg",[724,89895,89896,89899,89900,3206,89930,89952,89953,5642],{},[38,89897,89898],{},"Geometrická interpretace:"," sklon tečny k izokvantě v bodě ",[883,89901,89903],{"className":89902},[886],[888,89904,89905],{"xmlns":890},[892,89906,89907,89927],{},[895,89908,89909,89911,89917,89919,89925],{},[1656,89910,3453],{"stretchy":1658},[1661,89912,89913,89915],{},[898,89914,18539],{},[1667,89916,4032],{},[1656,89918,1673],{"separator":1672},[1661,89920,89921,89923],{},[898,89922,18544],{},[1667,89924,4032],{},[1656,89926,3462],{"stretchy":1658},[902,89928,89929],{"encoding":904},"[L_0, K_0]",[883,89931,89933],{"className":89932},[886],[888,89934,89935],{"xmlns":890},[892,89936,89937,89949],{},[895,89938,89939,89941,89943,89945,89947],{},[1656,89940,3964],{},[898,89942,1703],{},[898,89944,1763],{},[898,89946,11577],{},[898,89948,1769],{},[902,89950,89951],{"encoding":904},"-MRTS",". Z derivace implicitní funkce (při ",[883,89954,89956],{"className":89955},[886],[888,89957,89958],{"xmlns":890},[892,89959,89960,89982],{},[895,89961,89962,89964,89966,89968,89970,89972,89974,89976],{},[898,89963,1665],{},[1656,89965,1659],{"stretchy":1658},[898,89967,18539],{},[1656,89969,1673],{"separator":1672},[898,89971,18544],{},[1656,89973,1683],{"stretchy":1658},[1656,89975,1713],{},[1661,89977,89978,89980],{},[898,89979,89452],{},[1667,89981,4032],{},[902,89983,89984],{"encoding":904},"Q(L,K) = q_0",[883,89986,89988],{"className":89987},[886],[888,89989,89990],{"xmlns":890,"display":2408},[892,89991,89992,90044],{},[895,89993,89994,90008,90010,90012,90030,90032,90034,90036,90038,90040,90042],{},[3294,89995,89996,90002],{},[895,89997,89998,90000],{},[898,89999,3768],{},[898,90001,18544],{},[895,90003,90004,90006],{},[898,90005,3768],{},[898,90007,18539],{},[1656,90009,1713],{},[1656,90011,3964],{},[3294,90013,90014,90022],{},[1715,90015,90016,90018,90020],{},[898,90017,1665],{},[898,90019,18539],{},[1656,90021,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1715,90023,90024,90026,90028],{},[898,90025,1665],{},[898,90027,18544],{},[1656,90029,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,90031,1713],{},[1656,90033,3964],{},[898,90035,1703],{},[898,90037,1763],{},[898,90039,11577],{},[898,90041,1769],{},[898,90043,1863],{"mathvariant":1723},[902,90045,90046],{"encoding":904},"\\frac{dK}{dL} = -\\frac{Q'_L}{Q'_K} = -MRTS.",[724,90048,90049,90050,90065,90066,90082],{},"Změní-li se práce o ",[883,90051,90053],{"className":90052},[886],[888,90054,90055],{"xmlns":890},[892,90056,90057,90063],{},[895,90058,90059,90061],{},[898,90060,3768],{},[898,90062,18539],{},[902,90064,84013],{"encoding":904},", lze pro odhad změny kapitálu ",[883,90067,90069],{"className":90068},[886],[888,90070,90071],{"xmlns":890},[892,90072,90073,90079],{},[895,90074,90075,90077],{},[898,90076,3750],{"mathvariant":1723},[898,90078,18544],{},[902,90080,90081],{"encoding":904},"\\Delta K"," k udržení produkce použít diferenciál:",[883,90084,90086],{"className":90085},[886],[888,90087,90088],{"xmlns":890,"display":2408},[892,90089,90090,90137],{},[2412,90091,90092],{"width":2414},[2416,90093,90094,90096,90130,90132],{},[2419,90095],{"width":2421},[2419,90097,90098],{},[895,90099,90100,90102,90104,90106,90108,90110,90112,90114,90116,90118,90120,90122,90124,90126,90128],{},[898,90101,3750],{"mathvariant":1723},[898,90103,18544],{},[1656,90105,3815],{},[898,90107,3768],{},[898,90109,18544],{},[1656,90111,1713],{},[1656,90113,3964],{},[898,90115,1703],{},[898,90117,1763],{},[898,90119,11577],{},[898,90121,1769],{},[2461,90123,7828],{},[898,90125,3768],{},[898,90127,18539],{},[1656,90129,1673],{"separator":1672},[2419,90131],{"width":2421},[2419,90133,90134],{},[2461,90135,90136],{},"(5.15)",[902,90138,90139],{"encoding":904},"\\Delta K \\approx dK = -MRTS\\,dL, \\tag{5.15}",[883,90141,90143],{"className":90142},[886],[888,90144,90145],{"xmlns":890,"display":2408},[892,90146,90147,90196],{},[2412,90148,90149],{"width":2414},[2416,90150,90151,90153,90189,90191],{},[2419,90152],{"width":2421},[2419,90154,90155],{},[895,90156,90157,90159,90161,90163,90181,90183,90185,90187],{},[898,90158,3768],{},[898,90160,18539],{},[1656,90162,1713],{},[3294,90164,90165,90171],{},[895,90166,90167,90169],{},[1656,90168,3964],{},[1667,90170,1669],{},[895,90172,90173,90175,90177,90179],{},[898,90174,1703],{},[898,90176,1763],{},[898,90178,11577],{},[898,90180,1769],{},[2461,90182,7828],{},[898,90184,3768],{},[898,90186,18544],{},[898,90188,1863],{"mathvariant":1723},[2419,90190],{"width":2421},[2419,90192,90193],{},[2461,90194,90195],{},"(5.16)",[902,90197,90198],{"encoding":904},"dL = \\frac{-1}{MRTS}\\,dK. \\tag{5.16}",[1981,90200,90201,90225],{},[724,90202,90203,90205,90206],{},[883,90204,10188],{}," Postup — jak spočítat ",[883,90207,90209],{"className":90208},[886],[888,90210,90211],{"xmlns":890},[892,90212,90213,90223],{},[895,90214,90215,90217,90219,90221],{},[898,90216,1703],{},[898,90218,1763],{},[898,90220,11577],{},[898,90222,1769],{},[902,90224,19340],{"encoding":904},[152,90226,90227,90268,90311,90343],{},[123,90228,90229,90230,1896,90249,1863],{},"Vypočtěte parciální derivace ",[883,90231,90233],{"className":90232},[886],[888,90234,90235],{"xmlns":890},[892,90236,90237,90247],{},[895,90238,90239],{},[1715,90240,90241,90243,90245],{},[898,90242,1665],{},[898,90244,18539],{},[1656,90246,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[902,90248,18764],{"encoding":904},[883,90250,90252],{"className":90251},[886],[888,90253,90254],{"xmlns":890},[892,90255,90256,90266],{},[895,90257,90258],{},[1715,90259,90260,90262,90264],{},[898,90261,1665],{},[898,90263,18544],{},[1656,90265,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[902,90267,18809],{"encoding":904},[123,90269,74506,90270,90310],{},[883,90271,90273],{"className":90272},[886],[888,90274,90275],{"xmlns":890},[892,90276,90277,90307],{},[895,90278,90279,90281,90283,90285,90287,90289,90297,90299],{},[898,90280,1703],{},[898,90282,1763],{},[898,90284,11577],{},[898,90286,1769],{},[1656,90288,1713],{},[1715,90290,90291,90293,90295],{},[898,90292,1665],{},[898,90294,18539],{},[1656,90296,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[898,90298,1782],{"mathvariant":1723},[1715,90300,90301,90303,90305],{},[898,90302,1665],{},[898,90304,18544],{},[1656,90306,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[902,90308,90309],{"encoding":904},"MRTS = Q'_L \u002F Q'_K"," (zlomek zjednodušte).",[123,90312,90313,90314,1863],{},"Případně dosaďte konkrétní ",[883,90315,90317],{"className":90316},[886],[888,90318,90319],{"xmlns":890},[892,90320,90321,90341],{},[895,90322,90323,90325,90331,90333,90339],{},[1656,90324,3453],{"stretchy":1658},[1661,90326,90327,90329],{},[898,90328,18539],{},[1667,90330,4032],{},[1656,90332,1673],{"separator":1672},[1661,90334,90335,90337],{},[898,90336,18544],{},[1667,90338,4032],{},[1656,90340,3462],{"stretchy":1658},[902,90342,89929],{"encoding":904},[123,90344,90345,90346,90380,90381,90383],{},"Pro odhad substituce použijte ",[883,90347,90349],{"className":90348},[886],[888,90350,90351],{"xmlns":890},[892,90352,90353,90377],{},[895,90354,90355,90357,90359,90361,90363,90365,90367,90369,90371,90373,90375],{},[898,90356,3750],{"mathvariant":1723},[898,90358,18544],{},[1656,90360,3815],{},[1656,90362,3964],{},[898,90364,1703],{},[898,90366,1763],{},[898,90368,11577],{},[898,90370,1769],{},[1656,90372,2751],{},[898,90374,3750],{"mathvariant":1723},[898,90376,18539],{},[902,90378,90379],{"encoding":904},"\\Delta K \\approx -MRTS \\cdot \\Delta L"," (znaménko ",[38,90382,61278],{}," — substituce, ne doplnění).",[724,90385,90386],{},[614,90387,90388,90389,90421,90422,3565,90435,24520,90464,90479],{},"Obrázek 5.7 — izokvanta ",[883,90390,90392],{"className":90391},[886],[888,90393,90394],{"xmlns":890},[892,90395,90396,90418],{},[895,90397,90398,90404,90406,90408,90410,90412,90414,90416],{},[1661,90399,90400,90402],{},[898,90401,89452],{},[1667,90403,4032],{},[1656,90405,1713],{},[898,90407,1665],{},[1656,90409,1659],{"stretchy":1658},[898,90411,18539],{},[1656,90413,1673],{"separator":1672},[898,90415,18544],{},[1656,90417,1683],{"stretchy":1658},[902,90419,90420],{"encoding":904},"q_0 = Q(L,K)"," s tečnou ",[883,90423,90425],{"className":90424},[886],[888,90426,90427],{"xmlns":890},[892,90428,90429,90433],{},[895,90430,90431],{},[898,90432,27577],{},[902,90434,27577],{"encoding":904},[883,90436,90438],{"className":90437},[886],[888,90439,90440],{"xmlns":890},[892,90441,90442,90462],{},[895,90443,90444,90446,90452,90454,90460],{},[1656,90445,3453],{"stretchy":1658},[1661,90447,90448,90450],{},[898,90449,18539],{},[1667,90451,4032],{},[1656,90453,1673],{"separator":1672},[1661,90455,90456,90458],{},[898,90457,18544],{},[1667,90459,4032],{},[1656,90461,3462],{"stretchy":1658},[902,90463,89929],{"encoding":904},[883,90465,90467],{"className":90466},[886],[888,90468,90469],{"xmlns":890},[892,90470,90471,90477],{},[895,90472,90473,90475],{},[898,90474,3750],{"mathvariant":1723},[898,90476,18544],{},[902,90478,90081],{"encoding":904}," odhadnut diferenciálem (záporně vzatý sklon tečny).",[115,90481,90483],{"id":90482},"příklady-dvoufaktorový-model","Příklady (dvoufaktorový model)",[198,90485,90487],{"id":90486},"příklad-54","Příklad 5.4",[724,90489,85329,90490,1343,90532,1343,90549,1863],{},[883,90491,90493],{"className":90492},[886],[888,90494,90495],{"xmlns":890},[892,90496,90497,90529],{},[895,90498,90499,90501,90503,90505,90517],{},[898,90500,1665],{},[1656,90502,1713],{},[1667,90504,44930],{},[2062,90506,90507,90509],{},[898,90508,18539],{},[895,90510,90511,90513,90515],{},[1667,90512,1669],{},[898,90514,1782],{"mathvariant":1723},[1667,90516,1680],{},[2062,90518,90519,90521],{},[898,90520,18544],{},[895,90522,90523,90525,90527],{},[1667,90524,1669],{},[898,90526,1782],{"mathvariant":1723},[1667,90528,2617],{},[902,90530,90531],{"encoding":904},"Q = 15 L^{1\u002F2} K^{1\u002F3}",[883,90533,90535],{"className":90534},[886],[888,90536,90537],{"xmlns":890},[892,90538,90539,90547],{},[895,90540,90541,90543,90545],{},[898,90542,18539],{},[1656,90544,1713],{},[1667,90546,9058],{},[902,90548,85703],{"encoding":904},[883,90550,90552],{"className":90551},[886],[888,90553,90554],{"xmlns":890},[892,90555,90556,90564],{},[895,90557,90558,90560,90562],{},[898,90559,18544],{},[1656,90561,1713],{},[1667,90563,5267],{},[902,90565,90566],{"encoding":904},"K = 100",[724,90568,90569],{},[38,90570,90571],{},"(a) Rychlost změny produkce vzhledem k práci.",[883,90573,90575],{"className":90574},[886],[888,90576,90577],{"xmlns":890,"display":2408},[892,90578,90579,90692],{},[895,90580,90581,90583,90589,90591,90599,90601,90609,90623,90635,90637,90639,90641,90647,90649,90651,90653,90655,90657,90659,90667,90669,90679,90681,90687,90689],{},[898,90582,1703],{},[1661,90584,90585,90587],{},[898,90586,8194],{},[898,90588,18539],{},[1656,90590,1713],{},[1715,90592,90593,90595,90597],{},[898,90594,1665],{},[898,90596,18539],{},[1656,90598,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,90600,1713],{},[4138,90602,90603],{"scriptlevel":4032,"displaystyle":1658},[3294,90604,90605,90607],{},[1667,90606,44930],{},[1667,90608,1680],{},[2062,90610,90611,90613],{},[898,90612,18539],{},[895,90614,90615,90617,90619,90621],{},[1656,90616,3964],{},[1667,90618,1669],{},[898,90620,1782],{"mathvariant":1723},[1667,90622,1680],{},[2062,90624,90625,90627],{},[898,90626,18544],{},[895,90628,90629,90631,90633],{},[1667,90630,1669],{},[898,90632,1782],{"mathvariant":1723},[1667,90634,2617],{},[1656,90636,1673],{"separator":1672},[3316,90638],{"width":3318},[898,90640,1703],{},[1661,90642,90643,90645],{},[898,90644,8194],{},[898,90646,18539],{},[1656,90648,1659],{"stretchy":1658},[1667,90650,9058],{},[1656,90652,1673],{"separator":1672},[1667,90654,5267],{},[1656,90656,1683],{"stretchy":1658},[1656,90658,1713],{},[4138,90660,90661],{"scriptlevel":4032,"displaystyle":1658},[3294,90662,90663,90665],{},[1667,90664,44930],{},[1667,90666,1680],{},[1656,90668,2751],{},[4138,90670,90671],{"scriptlevel":4032,"displaystyle":1658},[3294,90672,90673,90675],{},[1667,90674,1669],{},[2625,90676,90677],{},[1667,90678,9058],{},[1656,90680,2751],{},[7003,90682,90683,90685],{},[1667,90684,5267],{},[1667,90686,2617],{},[1656,90688,3815],{},[1667,90690,90691],{},"7,153.",[902,90693,90694],{"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.",[724,90696,90697,90698,52837,90720,18974,90737,90758,90759,90780],{},"Přibližná změna při ",[883,90699,90701],{"className":90700},[886],[888,90702,90703],{"xmlns":890},[892,90704,90705,90717],{},[895,90706,90707,90709,90711,90713,90715],{},[898,90708,18539],{},[1656,90710,2114],{},[1667,90712,9058],{},[1656,90714,11915],{},[1667,90716,47028],{},[902,90718,90719],{"encoding":904},"L: 20 \\to 21",[883,90721,90723],{"className":90722},[886],[888,90724,90725],{"xmlns":890},[892,90726,90727,90735],{},[895,90728,90729,90731,90733],{},[898,90730,18544],{},[1656,90732,1713],{},[1667,90734,5267],{},[902,90736,90566],{"encoding":904},[883,90738,90740],{"className":90739},[886],[888,90741,90742],{"xmlns":890},[892,90743,90744,90755],{},[895,90745,90746,90748,90750,90752],{},[898,90747,3750],{"mathvariant":1723},[898,90749,1665],{},[1656,90751,3815],{},[1667,90753,90754],{},"7,153",[902,90756,90757],{"encoding":904},"\\Delta Q \\approx 7{,}153",". Skutečně ",[883,90760,90762],{"className":90761},[886],[888,90763,90764],{"xmlns":890},[892,90765,90766,90777],{},[895,90767,90768,90770,90772,90774],{},[898,90769,3750],{"mathvariant":1723},[898,90771,1665],{},[1656,90773,3815],{},[1667,90775,90776],{},"26,888",[902,90778,90779],{"encoding":904},"\\Delta Q \\approx 26{,}888"," (dle knihy; zaokrouhlení v konkrétním výpočtu).",[724,90782,90783,90786],{},[38,90784,90785],{},"(b) Pokles kapitálu o 1"," (z 100 na 99).",[883,90788,90790],{"className":90789},[886],[888,90791,90792],{"xmlns":890,"display":2408},[892,90793,90794,90894],{},[895,90795,90796,90798,90804,90806,90814,90816,90818,90830,90844,90846,90848,90850,90856,90858,90860,90862,90864,90866,90868,90870,90874,90876,90889,90891],{},[898,90797,1703],{},[1661,90799,90800,90802],{},[898,90801,8194],{},[898,90803,18544],{},[1656,90805,1713],{},[1715,90807,90808,90810,90812],{},[898,90809,1665],{},[898,90811,18544],{},[1656,90813,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,90815,1713],{},[1667,90817,5193],{},[2062,90819,90820,90822],{},[898,90821,18539],{},[895,90823,90824,90826,90828],{},[1667,90825,1669],{},[898,90827,1782],{"mathvariant":1723},[1667,90829,1680],{},[2062,90831,90832,90834],{},[898,90833,18544],{},[895,90835,90836,90838,90840,90842],{},[1656,90837,3964],{},[1667,90839,1680],{},[898,90841,1782],{"mathvariant":1723},[1667,90843,2617],{},[1656,90845,1673],{"separator":1672},[3316,90847],{"width":3318},[898,90849,1703],{},[1661,90851,90852,90854],{},[898,90853,8194],{},[898,90855,18544],{},[1656,90857,1659],{"stretchy":1658},[1667,90859,9058],{},[1656,90861,1673],{"separator":1672},[1667,90863,5267],{},[1656,90865,1683],{"stretchy":1658},[1656,90867,1713],{},[1667,90869,5193],{},[2625,90871,90872],{},[1667,90873,9058],{},[1656,90875,2751],{},[4138,90877,90878],{"scriptlevel":4032,"displaystyle":1658},[3294,90879,90880,90882],{},[1667,90881,1669],{},[7003,90883,90884,90887],{},[1667,90885,90886],{},"10000",[1667,90888,2617],{},[1656,90890,3815],{},[1667,90892,90893],{},"4,525.",[902,90895,90896],{"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.",[724,90898,90899,90900,3619,90917,12702],{},"Produkce poklesne přibližně o 4,525 (z ",[883,90901,90903],{"className":90902},[886],[888,90904,90905],{"xmlns":890},[892,90906,90907,90914],{},[895,90908,90909,90911],{},[1656,90910,3815],{},[1667,90912,90913],{},"905,126",[902,90915,90916],{"encoding":904},"\\approx 905{,}126",[883,90918,90920],{"className":90919},[886],[888,90921,90922],{"xmlns":890},[892,90923,90924,90931],{},[895,90925,90926,90928],{},[1656,90927,3815],{},[1667,90929,90930],{},"900,601",[902,90932,90933],{"encoding":904},"\\approx 900{,}601",[724,90935,90936,11922,90983,1343,91005,12702],{},[38,90937,90938,90939,1896,90961],{},"(c) Změna ",[883,90940,90942],{"className":90941},[886],[888,90943,90944],{"xmlns":890},[892,90945,90946,90958],{},[895,90947,90948,90950,90952,90954,90956],{},[898,90949,18539],{},[1656,90951,2114],{},[1667,90953,9058],{},[1656,90955,11915],{},[1667,90957,44930],{},[902,90959,90960],{"encoding":904},"L: 20 \\to 15",[883,90962,90964],{"className":90963},[886],[888,90965,90966],{"xmlns":890},[892,90967,90968,90980],{},[895,90969,90970,90972,90974,90976,90978],{},[898,90971,18544],{},[1656,90973,2114],{},[1667,90975,5267],{},[1656,90977,11915],{},[1667,90979,17557],{},[902,90981,90982],{"encoding":904},"K: 100 \\to 150",[883,90984,90986],{"className":90985},[886],[888,90987,90988],{"xmlns":890},[892,90989,90990,91002],{},[895,90991,90992,90994,90996,90998,91000],{},[898,90993,3768],{},[898,90995,18539],{},[1656,90997,1713],{},[1656,90999,3964],{},[1667,91001,5193],{},[902,91003,91004],{"encoding":904},"dL = -5",[883,91006,91008],{"className":91007},[886],[888,91009,91010],{"xmlns":890},[892,91011,91012,91022],{},[895,91013,91014,91016,91018,91020],{},[898,91015,3768],{},[898,91017,18544],{},[1656,91019,1713],{},[1667,91021,9267],{},[902,91023,91024],{"encoding":904},"dK = 50",[883,91026,91028],{"className":91027},[886],[888,91029,91030],{"xmlns":890,"display":2408},[892,91031,91032,91120],{},[895,91033,91034,91036,91038,91040,91042,91048,91050,91052,91054,91056,91058,91060,91062,91064,91066,91068,91070,91072,91078,91080,91082,91084,91086,91088,91090,91092,91094,91096,91098,91100,91102,91104,91106,91108,91111,91113,91115,91117],{},[898,91035,3768],{},[898,91037,1665],{},[1656,91039,1713],{},[898,91041,1703],{},[1661,91043,91044,91046],{},[898,91045,8194],{},[898,91047,18539],{},[1656,91049,1659],{"stretchy":1658},[1667,91051,9058],{},[1656,91053,1673],{"separator":1672},[1667,91055,5267],{},[1656,91057,1683],{"stretchy":1658},[1656,91059,2751],{},[1656,91061,1659],{"stretchy":1658},[1656,91063,3964],{},[1667,91065,5193],{},[1656,91067,1683],{"stretchy":1658},[1656,91069,3633],{},[898,91071,1703],{},[1661,91073,91074,91076],{},[898,91075,8194],{},[898,91077,18544],{},[1656,91079,1659],{"stretchy":1658},[1667,91081,9058],{},[1656,91083,1673],{"separator":1672},[1667,91085,5267],{},[1656,91087,1683],{"stretchy":1658},[1656,91089,2751],{},[1667,91091,9267],{},[1656,91093,1713],{},[1667,91095,90754],{},[1656,91097,2751],{},[1656,91099,1659],{"stretchy":1658},[1656,91101,3964],{},[1667,91103,5193],{},[1656,91105,1683],{"stretchy":1658},[1656,91107,3633],{},[1667,91109,91110],{},"4,525",[1656,91112,2751],{},[1667,91114,9267],{},[1656,91116,3815],{},[1667,91118,91119],{},"190,485.",[902,91121,91122],{"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.",[724,91124,91125],{},"Produkce vzroste přibližně z 905,126 na 995,611.",[198,91127,91129],{"id":91128},"příklad-55","Příklad 5.5",[724,91131,91132,91133,91169,91170,1863],{},"Pro produkci ",[883,91134,91136],{"className":91135},[886],[888,91137,91138],{"xmlns":890},[892,91139,91140,91166],{},[895,91141,91142,91144,91146,91148,91150,91152,91154,91156,91162],{},[898,91143,1665],{},[1656,91145,1659],{"stretchy":1658},[898,91147,18539],{},[1656,91149,1673],{"separator":1672},[898,91151,18544],{},[1656,91153,1683],{"stretchy":1658},[1656,91155,1713],{},[7003,91157,91158,91160],{},[898,91159,18539],{},[1667,91161,2617],{},[2625,91163,91164],{},[898,91165,18544],{},[902,91167,91168],{"encoding":904},"Q(L, K) = \\sqrt[3]{L}\\sqrt{K}"," mají izokvanty rovnici ",[883,91171,91173],{"className":91172},[886],[888,91174,91175],{"xmlns":890},[892,91176,91177,91193],{},[895,91178,91179,91185,91189,91191],{},[7003,91180,91181,91183],{},[898,91182,18539],{},[1667,91184,2617],{},[2625,91186,91187],{},[898,91188,18544],{},[1656,91190,1713],{},[898,91192,89452],{},[902,91194,91195],{"encoding":904},"\\sqrt[3]{L}\\sqrt{K} = q",[724,91197,91198,91199,1863],{},"Umocněním na druhou: ",[883,91200,91202],{"className":91201},[886],[888,91203,91204],{"xmlns":890},[892,91205,91206,91230],{},[895,91207,91208,91210,91212,91218,91220],{},[898,91209,18544],{},[1656,91211,1713],{},[2062,91213,91214,91216],{},[898,91215,89452],{},[1667,91217,1680],{},[898,91219,1782],{"mathvariant":1723},[7003,91221,91222,91228],{},[2062,91223,91224,91226],{},[898,91225,18539],{},[1667,91227,1680],{},[1667,91229,2617],{},[902,91231,91232],{"encoding":904},"K = q^2 \u002F \\sqrt[3]{L^2}",[120,91234,91235,91275,91315],{},[123,91236,91237],{},[883,91238,91240],{"className":91239},[886],[888,91241,91242],{"xmlns":890},[892,91243,91244,91272],{},[895,91245,91246,91248,91250,91252,91254,91256,91258,91260,91262],{},[898,91247,89452],{},[1656,91249,1713],{},[1667,91251,1669],{},[1656,91253,12770],{},[898,91255,18544],{},[1656,91257,1713],{},[1667,91259,1669],{},[898,91261,1782],{"mathvariant":1723},[7003,91263,91264,91270],{},[2062,91265,91266,91268],{},[898,91267,18539],{},[1667,91269,1680],{},[1667,91271,2617],{},[902,91273,91274],{"encoding":904},"q = 1 \\Rightarrow K = 1\u002F\\sqrt[3]{L^2}",[123,91276,91277],{},[883,91278,91280],{"className":91279},[886],[888,91281,91282],{"xmlns":890},[892,91283,91284,91312],{},[895,91285,91286,91288,91290,91292,91294,91296,91298,91300,91302],{},[898,91287,89452],{},[1656,91289,1713],{},[1667,91291,1680],{},[1656,91293,12770],{},[898,91295,18544],{},[1656,91297,1713],{},[1667,91299,2673],{},[898,91301,1782],{"mathvariant":1723},[7003,91303,91304,91310],{},[2062,91305,91306,91308],{},[898,91307,18539],{},[1667,91309,1680],{},[1667,91311,2617],{},[902,91313,91314],{"encoding":904},"q = 2 \\Rightarrow K = 4\u002F\\sqrt[3]{L^2}",[123,91316,91317],{},[883,91318,91320],{"className":91319},[886],[888,91321,91322],{"xmlns":890},[892,91323,91324,91352],{},[895,91325,91326,91328,91330,91332,91334,91336,91338,91340,91342],{},[898,91327,89452],{},[1656,91329,1713],{},[1667,91331,2617],{},[1656,91333,12770],{},[898,91335,18544],{},[1656,91337,1713],{},[1667,91339,2698],{},[898,91341,1782],{"mathvariant":1723},[7003,91343,91344,91350],{},[2062,91345,91346,91348],{},[898,91347,18539],{},[1667,91349,1680],{},[1667,91351,2617],{},[902,91353,91354],{"encoding":904},"q = 3 \\Rightarrow K = 9\u002F\\sqrt[3]{L^2}",[724,91356,91357],{},[614,91358,91359,91360,3713,91381,1863],{},"Obrázek 5.5 — tři klesající konvexní izokvanty v rovině ",[883,91361,91363],{"className":91362},[886],[888,91364,91365],{"xmlns":890},[892,91366,91367,91379],{},[895,91368,91369,91371,91373,91375,91377],{},[1656,91370,1659],{"stretchy":1658},[898,91372,18539],{},[1656,91374,1673],{"separator":1672},[898,91376,18544],{},[1656,91378,1683],{"stretchy":1658},[902,91380,89578],{"encoding":904},[883,91382,91384],{"className":91383},[886],[888,91385,91386],{"xmlns":890},[892,91387,91388,91404],{},[895,91389,91390,91392,91394,91396,91398,91400,91402],{},[898,91391,89452],{},[1656,91393,1713],{},[1667,91395,1669],{},[1656,91397,1673],{"separator":1672},[1667,91399,1680],{},[1656,91401,1673],{"separator":1672},[1667,91403,2617],{},[902,91405,91406],{"encoding":904},"q = 1, 2, 3",[198,91408,91410],{"id":91409},"příklad-56","Příklad 5.6",[724,91412,85329,91413,1863],{},[883,91414,91416],{"className":91415},[886],[888,91417,91418],{"xmlns":890},[892,91419,91420,91436],{},[895,91421,91422,91424,91426,91428,91430,91432],{},[898,91423,1665],{},[1656,91425,1713],{},[1667,91427,1680],{},[898,91429,18539],{},[1656,91431,3633],{},[2625,91433,91434],{},[898,91435,18544],{},[902,91437,91438],{"encoding":904},"Q = 2L + \\sqrt{K}",[883,91440,91442],{"className":91441},[886],[888,91443,91444],{"xmlns":890,"display":2408},[892,91445,91446,91488],{},[895,91447,91448,91450,91456,91458,91460,91462,91464,91466,91472,91474,91486],{},[898,91449,1703],{},[1661,91451,91452,91454],{},[898,91453,8194],{},[898,91455,18539],{},[1656,91457,1713],{},[1667,91459,1680],{},[1656,91461,1673],{"separator":1672},[3316,91463],{"width":14644},[898,91465,1703],{},[1661,91467,91468,91470],{},[898,91469,8194],{},[898,91471,18544],{},[1656,91473,1713],{},[3294,91475,91476,91478],{},[1667,91477,1669],{},[895,91479,91480,91482],{},[1667,91481,1680],{},[2625,91483,91484],{},[898,91485,18544],{},[898,91487,1863],{"mathvariant":1723},[902,91489,91490],{"encoding":904},"MP_L = 2, \\qquad MP_K = \\frac{1}{2\\sqrt{K}}.",[883,91492,91494],{"className":91493},[886],[888,91495,91496],{"xmlns":890,"display":2408},[892,91497,91498,91562],{},[895,91499,91500,91502,91504,91506,91508,91510,91532,91534,91552,91554,91556,91560],{},[898,91501,1703],{},[898,91503,1763],{},[898,91505,11577],{},[898,91507,1769],{},[1656,91509,1713],{},[3294,91511,91512,91522],{},[895,91513,91514,91516],{},[898,91515,1703],{},[1661,91517,91518,91520],{},[898,91519,8194],{},[898,91521,18539],{},[895,91523,91524,91526],{},[898,91525,1703],{},[1661,91527,91528,91530],{},[898,91529,8194],{},[898,91531,18544],{},[1656,91533,1713],{},[3294,91535,91536,91538],{},[1667,91537,1680],{},[4138,91539,91540],{"scriptlevel":4032,"displaystyle":1658},[3294,91541,91542,91544],{},[1667,91543,1669],{},[895,91545,91546,91548],{},[1667,91547,1680],{},[2625,91549,91550],{},[898,91551,18544],{},[1656,91553,1713],{},[1667,91555,2673],{},[2625,91557,91558],{},[898,91559,18544],{},[898,91561,1863],{"mathvariant":1723},[902,91563,91564],{"encoding":904},"MRTS = \\frac{MP_L}{MP_K} = \\frac{2}{\\tfrac{1}{2\\sqrt{K}}} = 4\\sqrt{K}.",[724,91566,91567,91568,91611,91612,91651,91652,1863],{},"Například ",[883,91569,91571],{"className":91570},[886],[888,91572,91573],{"xmlns":890},[892,91574,91575,91608],{},[895,91576,91577,91579,91581,91583,91585,91587,91589,91591,91593,91595,91597,91599,91603,91605],{},[898,91578,1703],{},[898,91580,1763],{},[898,91582,11577],{},[898,91584,1769],{},[1656,91586,1659],{"stretchy":1658},[1667,91588,2673],{},[1656,91590,1673],{"separator":1672},[1667,91592,6240],{},[1656,91594,1683],{"stretchy":1658},[1656,91596,1713],{},[1667,91598,2673],{},[2625,91600,91601],{},[1667,91602,6240],{},[1656,91604,3815],{},[1667,91606,91607],{},"10,58",[902,91609,91610],{"encoding":904},"MRTS(4, 7) = 4\\sqrt{7} \\approx 10{,}58",". Klesne-li práce z 4 na 3, je k udržení produkce ",[883,91613,91615],{"className":91614},[886],[888,91616,91617],{"xmlns":890},[892,91618,91619,91648],{},[895,91620,91621,91623,91625,91627,91629,91631,91633,91635,91637,91639,91643,91645],{},[898,91622,1665],{},[1656,91624,1659],{"stretchy":1658},[1667,91626,2673],{},[1656,91628,1673],{"separator":1672},[1667,91630,6240],{},[1656,91632,1683],{"stretchy":1658},[1656,91634,1713],{},[1667,91636,2877],{},[1656,91638,3633],{},[2625,91640,91641],{},[1667,91642,6240],{},[1656,91644,3815],{},[1667,91646,91647],{},"10,646",[902,91649,91650],{"encoding":904},"Q(4,7) = 8 + \\sqrt{7} \\approx 10{,}646"," třeba zvýšit kapitál přibližně o ",[883,91653,91655],{"className":91654},[886],[888,91656,91657],{"xmlns":890},[892,91658,91659,91667],{},[895,91660,91661,91663],{},[1667,91662,2673],{},[2625,91664,91665],{},[1667,91666,6240],{},[902,91668,91669],{"encoding":904},"4\\sqrt{7}",[724,91671,91672,91673,91693],{},"Pokud se práce naopak zvýší ze 4 na 6 (",[883,91674,91676],{"className":91675},[886],[888,91677,91678],{"xmlns":890},[892,91679,91680,91690],{},[895,91681,91682,91684,91686,91688],{},[898,91683,3768],{},[898,91685,18539],{},[1656,91687,1713],{},[1667,91689,1680],{},[902,91691,91692],{"encoding":904},"dL = 2","), k udržení produkce stačí snížit kapitál o",[883,91695,91697],{"className":91696},[886],[888,91698,91699],{"xmlns":890,"display":2408},[892,91700,91701,91750],{},[895,91702,91703,91705,91707,91709,91711,91713,91715,91717,91719,91721,91723,91725,91727,91729,91731,91733,91735,91737,91739,91743,91745,91747],{},[898,91704,3768],{},[898,91706,18544],{},[1656,91708,1713],{},[1656,91710,3964],{},[898,91712,1703],{},[898,91714,1763],{},[898,91716,11577],{},[898,91718,1769],{},[1656,91720,1659],{"stretchy":1658},[1667,91722,2673],{},[1656,91724,1673],{"separator":1672},[1667,91726,6240],{},[1656,91728,1683],{"stretchy":1658},[1656,91730,2751],{},[1667,91732,1680],{},[1656,91734,1713],{},[1656,91736,3964],{},[1667,91738,2877],{},[2625,91740,91741],{},[1667,91742,6240],{},[1656,91744,3815],{},[1656,91746,3964],{},[1667,91748,91749],{},"21,17.",[902,91751,91752],{"encoding":904},"dK = -MRTS(4,7)\\cdot 2 = -8\\sqrt{7} \\approx -21{,}17.",[115,91754,91756],{"id":91755},"shrnutí-kapitoly-5","Shrnutí kapitoly 5",[724,91758,91759,91760,1343,91762,1896,91764,91766,91767,91770,91771,91774],{},"Hlavními faktory produkce jsou ",[38,91761,83571],{},[38,91763,83587],{},[38,91765,83603],{},"; půda je standardní exogenní proměnná. Přicházejí proto v úvahu ",[38,91768,91769],{},"jednofaktorový"," (pouze práce) a ",[38,91772,91773],{},"dvoufaktorový"," (práce + kapitál) model.",[724,91776,91777,91778,91781,91782,91784,91785,91787,91788,6960,91791,91810,91811,91828,91829,91846,91847,91869,91870,6496,91889,1863],{},"V ",[38,91779,91780],{},"1F modelu"," se definuje ",[38,91783,18767],{}," (derivace produkce podle práce) a ",[38,91786,83509],{}," (podíl produkce a práce). Produkční funkce má typický tvar díky ",[38,91789,91790],{},"zákonu klesajících výnosů",[883,91792,91794],{"className":91793},[886],[888,91795,91796],{"xmlns":890},[892,91797,91798,91808],{},[895,91799,91800,91802],{},[898,91801,1703],{},[1661,91803,91804,91806],{},[898,91805,8194],{},[898,91807,18539],{},[902,91809,18787],{"encoding":904}," nejprve roste, od inflexního bodu ",[883,91812,91814],{"className":91813},[886],[888,91815,91816],{"xmlns":890},[892,91817,91818,91826],{},[895,91819,91820],{},[1661,91821,91822,91824],{},[898,91823,18539],{},[1667,91825,4032],{},[902,91827,84214],{"encoding":904}," klesá a v bodě ",[883,91830,91832],{"className":91831},[886],[888,91833,91834],{"xmlns":890},[892,91835,91836,91844],{},[895,91837,91838],{},[1661,91839,91840,91842],{},[898,91841,18539],{},[1667,91843,1669],{},[902,91845,21945],{"encoding":904}," dosahuje nuly (maximum produkce). Platí ",[38,91848,91849,91850],{},"princip maximalizace ",[883,91851,91853],{"className":91852},[886],[888,91854,91855],{"xmlns":890},[892,91856,91857,91867],{},[895,91858,91859,91861],{},[898,91860,2146],{},[1661,91862,91863,91865],{},[898,91864,8194],{},[898,91866,18539],{},[902,91868,83295],{"encoding":904},": v bodě maxima ",[883,91871,91873],{"className":91872},[886],[888,91874,91875],{"xmlns":890},[892,91876,91877,91887],{},[895,91878,91879,91881],{},[898,91880,2146],{},[1661,91882,91883,91885],{},[898,91884,8194],{},[898,91886,18539],{},[902,91888,83295],{"encoding":904},[883,91890,91892],{"className":91891},[886],[888,91893,91894],{"xmlns":890},[892,91895,91896,91916],{},[895,91897,91898,91900,91906,91908,91910],{},[898,91899,1703],{},[1661,91901,91902,91904],{},[898,91903,8194],{},[898,91905,18539],{},[1656,91907,1713],{},[898,91909,2146],{},[1661,91911,91912,91914],{},[898,91913,8194],{},[898,91915,18539],{},[902,91917,83325],{"encoding":904},[724,91919,91920,91921,91924,91925,1643,91928,91957,91958,91975,91976,91979,91980,92009,92010,92012,92013,3206,92043,92065],{},"Ve ",[38,91922,91923],{},"2F modelu"," se obvykle používají ",[38,91926,91927],{},"Cobb-Douglasovy funkce",[883,91929,91931],{"className":91930},[886],[888,91932,91933],{"xmlns":890},[892,91934,91935,91955],{},[895,91936,91937,91939,91941,91943,91949],{},[898,91938,1665],{},[1656,91940,1713],{},[898,91942,2146],{},[2062,91944,91945,91947],{},[898,91946,18539],{},[898,91948,207],{},[2062,91950,91951,91953],{},[898,91952,18544],{},[898,91954,3403],{},[902,91956,83391],{"encoding":904},", které reflektují proporcionalitu změn vstupů a výstupu. Podle ",[883,91959,91961],{"className":91960},[886],[888,91962,91963],{"xmlns":890},[892,91964,91965,91973],{},[895,91966,91967,91969,91971],{},[898,91968,207],{},[1656,91970,3633],{},[898,91972,3403],{},[902,91974,83485],{"encoding":904}," rozlišujeme ",[38,91977,91978],{},"konstantní, rostoucí, klesající výnosy z rozsahu",". Mezní produkty ",[883,91981,91983],{"className":91982},[886],[888,91984,91985],{"xmlns":890},[892,91986,91987,92007],{},[895,91988,91989,91991,91997,91999,92001],{},[898,91990,1703],{},[1661,91992,91993,91995],{},[898,91994,8194],{},[898,91996,18539],{},[1656,91998,1673],{"separator":1672},[898,92000,1703],{},[1661,92002,92003,92005],{},[898,92004,8194],{},[898,92006,18544],{},[902,92008,83422],{"encoding":904}," jsou parciální derivace, totální diferenciál dává přibližnou změnu produkce. ",[38,92011,18522],{}," jsou indiferenční křivky produkční funkce. Podíl ",[883,92014,92016],{"className":92015},[886],[888,92017,92018],{"xmlns":890},[892,92019,92020,92040],{},[895,92021,92022,92024,92030,92032,92034],{},[898,92023,1703],{},[1661,92025,92026,92028],{},[898,92027,8194],{},[898,92029,18539],{},[898,92031,1782],{"mathvariant":1723},[898,92033,1703],{},[1661,92035,92036,92038],{},[898,92037,8194],{},[898,92039,18544],{},[902,92041,92042],{"encoding":904},"MP_L\u002FMP_K",[38,92044,92045,92046,1683],{},"mezní míra technické substituce (",[883,92047,92049],{"className":92048},[886],[888,92050,92051],{"xmlns":890},[892,92052,92053,92063],{},[895,92054,92055,92057,92059,92061],{},[898,92056,1703],{},[898,92058,1763],{},[898,92060,11577],{},[898,92062,1769],{},[902,92064,19340],{"encoding":904}," — udává, o kolik se musí změnit kapitál při jednotkové změně práce pro zachování produkce.",[115,92067,8779],{"id":8778},[152,92069,92070,92073,92076,92079,92082,92085,92088,92091,92094,92097,92100],{},[123,92071,92072],{},"Jaké jsou faktory produkce?",[123,92074,92075],{},"Jak se dospěje k jednofaktorovému a dvoufaktorovému modelu produkce?",[123,92077,92078],{},"Jak je zadána produkční funkce u jednofaktorového modelu?",[123,92080,92081],{},"Co udává mezní produkt práce?",[123,92083,92084],{},"Co musí respektovat průběh křivky produkce?",[123,92086,92087],{},"Jak lze matematicky vyjádřit zákon klesajících výnosů?",[123,92089,92090],{},"Jaký základní ekonomický požadavek respektují Cobb-Douglasovy funkce?",[123,92092,92093],{},"Jak se vypočtou mezní produkty práce a kapitálu?",[123,92095,92096],{},"Jak se stanoví přibližná změna produkce v závislosti na změnách práce a kapitálu?",[123,92098,92099],{},"Co vyjadřují izokvanty? Jaké jsou jejich typické vlastnosti?",[123,92101,92102],{},"Jak se vypočte mezní míra technické substituce a co vyjadřuje?",[115,92104,92106],{"id":92105},"úlohy-51517","Úlohy 5.1–5.17",[198,92108,49131],{"id":49130},[724,92110,92111,92114,92115,8865,92137,1343,92157,1343,92177,92197],{},[38,92112,92113],{},"5.1"," Je dána produkce ",[883,92116,92118],{"className":92117},[886],[888,92119,92120],{"xmlns":890},[892,92121,92122,92134],{},[895,92123,92124,92126,92128,92130],{},[898,92125,1665],{},[1656,92127,1713],{},[1667,92129,8580],{},[2625,92131,92132],{},[898,92133,18539],{},[902,92135,92136],{"encoding":904},"Q = 10\\sqrt{L}",[883,92138,92140],{"className":92139},[886],[888,92141,92142],{"xmlns":890},[892,92143,92144,92154],{},[895,92145,92146,92148,92150,92152],{},[898,92147,1665],{},[1656,92149,1659],{"stretchy":1658},[1667,92151,1669],{},[1656,92153,1683],{"stretchy":1658},[902,92155,92156],{"encoding":904},"Q(1)",[883,92158,92160],{"className":92159},[886],[888,92161,92162],{"xmlns":890},[892,92163,92164,92174],{},[895,92165,92166,92168,92170,92172],{},[898,92167,1665],{},[1656,92169,1659],{"stretchy":1658},[1667,92171,2673],{},[1656,92173,1683],{"stretchy":1658},[902,92175,92176],{"encoding":904},"Q(4)",[883,92178,92180],{"className":92179},[886],[888,92181,92182],{"xmlns":890},[892,92183,92184,92194],{},[895,92185,92186,92188,92190,92192],{},[898,92187,1665],{},[1656,92189,1659],{"stretchy":1658},[1667,92191,2698],{},[1656,92193,1683],{"stretchy":1658},[902,92195,92196],{"encoding":904},"Q(9)",". (b) Rozhodněte, kdy produkce roste, resp. klesá. (c) Rozhodněte, kdy je křivka produkce konvexní, resp. konkávní. (d) Načrtněte křivku produkce.",[724,92199,92200,92114,92203,92239,92240,92253,92254,92273,92274,92300,92301,3619,92314,92327],{},[38,92201,92202],{},"5.2",[883,92204,92206],{"className":92205},[886],[888,92207,92208],{"xmlns":890},[892,92209,92210,92236],{},[895,92211,92212,92214,92216,92218,92220,92226,92228,92230],{},[898,92213,1665],{},[1656,92215,1713],{},[1656,92217,3964],{},[1667,92219,11595],{},[2062,92221,92222,92224],{},[898,92223,18539],{},[1667,92225,2617],{},[1656,92227,3633],{},[1667,92229,2698],{},[2062,92231,92232,92234],{},[898,92233,18539],{},[1667,92235,1680],{},[902,92237,92238],{"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 ",[883,92241,92243],{"className":92242},[886],[888,92244,92245],{"xmlns":890},[892,92246,92247,92251],{},[895,92248,92249],{},[898,92250,18539],{},[902,92252,18539],{"encoding":904}," (počet pracovníků), které maximalizuje produkci a stanovte příslušné maximum produkce. (d) Načrtněte křivku produkce. (e) Najděte mezní produkt práce ",[883,92255,92257],{"className":92256},[886],[888,92258,92259],{"xmlns":890},[892,92260,92261,92271],{},[895,92262,92263,92265],{},[898,92264,1703],{},[1661,92266,92267,92269],{},[898,92268,8194],{},[898,92270,18539],{},[902,92272,18787],{"encoding":904},". (f) Vypočtěte ",[883,92275,92277],{"className":92276},[886],[888,92278,92279],{"xmlns":890},[892,92280,92281,92297],{},[895,92282,92283,92285,92291,92293,92295],{},[898,92284,1703],{},[1661,92286,92287,92289],{},[898,92288,8194],{},[898,92290,18539],{},[1656,92292,1659],{"stretchy":1658},[1667,92294,8580],{},[1656,92296,1683],{"stretchy":1658},[902,92298,92299],{"encoding":904},"MP_L(10)"," a ekonomicky interpretujte. (g) Určete přibližnou změnu produkce v důsledku zvýšení počtu pracovníků z ",[883,92302,92304],{"className":92303},[886],[888,92305,92306],{"xmlns":890},[892,92307,92308,92312],{},[895,92309,92310],{},[1667,92311,8580],{},[902,92313,8580],{"encoding":904},[883,92315,92317],{"className":92316},[886],[888,92318,92319],{"xmlns":890},[892,92320,92321,92325],{},[895,92322,92323],{},[1667,92324,50964],{},[902,92326,50964],{"encoding":904}," a porovnejte se skutečnou změnou produkce.",[724,92329,92330,92333,92334,92356,92357,92385,92386,92417,92418,1863],{},[38,92331,92332],{},"5.3"," Pro zadanou produkci ověřte platnost zákona klesajících výnosů a charakterizujte vlastnosti mezního produktu práce:\n(a) ",[883,92335,92337],{"className":92336},[886],[888,92338,92339],{"xmlns":890},[892,92340,92341,92353],{},[895,92342,92343,92345,92347,92349],{},[898,92344,1665],{},[1656,92346,1713],{},[1667,92348,8059],{},[2625,92350,92351],{},[898,92352,18539],{},[902,92354,92355],{"encoding":904},"Q = 500\\sqrt{L}",".\n(b) ",[883,92358,92360],{"className":92359},[886],[888,92361,92362],{"xmlns":890},[892,92363,92364,92382],{},[895,92365,92366,92368,92370,92372,92376,92378,92380],{},[898,92367,1665],{},[1656,92369,1713],{},[1667,92371,8054],{},[2625,92373,92374],{},[898,92375,18539],{},[1656,92377,3964],{},[1667,92379,2673],{},[898,92381,18539],{},[902,92383,92384],{"encoding":904},"Q = 300\\sqrt{L} - 4L",".\n(c) ",[883,92387,92389],{"className":92388},[886],[888,92390,92391],{"xmlns":890},[892,92392,92393,92414],{},[895,92394,92395,92397,92399,92401,92403,92405,92408],{},[898,92396,1665],{},[1656,92398,1713],{},[1667,92400,9267],{},[898,92402,18539],{},[1656,92404,3964],{},[1667,92406,92407],{},"0,01",[2062,92409,92410,92412],{},[898,92411,18539],{},[1667,92413,1680],{},[902,92415,92416],{"encoding":904},"Q = 50L - 0{,}01 L^{2}",".\n(d) ",[883,92419,92421],{"className":92420},[886],[888,92422,92423],{"xmlns":890},[892,92424,92425,92451],{},[895,92426,92427,92429,92431,92433,92435,92441,92443,92445],{},[898,92428,1665],{},[1656,92430,1713],{},[1656,92432,3964],{},[1667,92434,76875],{},[2062,92436,92437,92439],{},[898,92438,18539],{},[1667,92440,2617],{},[1656,92442,3633],{},[1667,92444,2698],{},[2062,92446,92447,92449],{},[898,92448,18539],{},[1667,92450,1680],{},[902,92452,92453],{"encoding":904},"Q = -0{,}3 L^{3} + 9 L^{2}",[724,92455,92456,92459,92460,3565,92479,80862,92496,1863],{},[38,92457,92458],{},"5.4"," Dokažte, že má-li průměrný produkt práce ",[883,92461,92463],{"className":92462},[886],[888,92464,92465],{"xmlns":890},[892,92466,92467,92477],{},[895,92468,92469,92471],{},[898,92470,2146],{},[1661,92472,92473,92475],{},[898,92474,8194],{},[898,92476,18539],{},[902,92478,83295],{"encoding":904},[883,92480,92482],{"className":92481},[886],[888,92483,92484],{"xmlns":890},[892,92485,92486,92494],{},[895,92487,92488],{},[1661,92489,92490,92492],{},[898,92491,18539],{},[1667,92493,4032],{},[902,92495,84214],{"encoding":904},[883,92497,92499],{"className":92498},[886],[888,92500,92501],{"xmlns":890},[892,92502,92503,92543],{},[895,92504,92505,92507,92513,92515,92521,92523,92525,92527,92533,92535,92541],{},[898,92506,2146],{},[1661,92508,92509,92511],{},[898,92510,8194],{},[898,92512,18539],{},[1656,92514,1659],{"stretchy":1658},[1661,92516,92517,92519],{},[898,92518,18539],{},[1667,92520,4032],{},[1656,92522,1683],{"stretchy":1658},[1656,92524,1713],{},[898,92526,1703],{},[1661,92528,92529,92531],{},[898,92530,8194],{},[898,92532,18539],{},[1656,92534,1659],{"stretchy":1658},[1661,92536,92537,92539],{},[898,92538,18539],{},[1667,92540,4032],{},[1656,92542,1683],{"stretchy":1658},[902,92544,92545],{"encoding":904},"AP_L(L_0) = MP_L(L_0)",[724,92547,92548,92114,92551,30312,92587,92600,92601,92620],{},[38,92549,92550],{},"5.5",[883,92552,92554],{"className":92553},[886],[888,92555,92556],{"xmlns":890},[892,92557,92558,92584],{},[895,92559,92560,92562,92564,92566,92568,92574,92576,92578],{},[898,92561,1665],{},[1656,92563,1713],{},[1656,92565,3964],{},[1667,92567,11639],{},[2062,92569,92570,92572],{},[898,92571,18539],{},[1667,92573,2617],{},[1656,92575,3633],{},[1667,92577,9140],{},[2062,92579,92580,92582],{},[898,92581,18539],{},[1667,92583,1680],{},[902,92585,92586],{"encoding":904},"Q = -0{,}2 L^{3} + 12 L^{2}",[883,92588,92590],{"className":92589},[886],[888,92591,92592],{"xmlns":890},[892,92593,92594,92598],{},[895,92595,92596],{},[898,92597,18539],{},[902,92599,18539],{"encoding":904}," je počet pracovníků. (a) Určete počet pracovníků, při kterém je dosaženo nejvyšší produktivity práce (= maximálního průměrného produktu práce ",[883,92602,92604],{"className":92603},[886],[888,92605,92606],{"xmlns":890},[892,92607,92608,92618],{},[895,92609,92610,92612],{},[898,92611,2146],{},[1661,92613,92614,92616],{},[898,92615,8194],{},[898,92617,18539],{},[902,92619,83295],{"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.",[198,92622,92624],{"id":92623},"dvoufaktorový-model","Dvoufaktorový model",[724,92626,92627,92630,92631,92356,92657,92385,92699,1863],{},[38,92628,92629],{},"5.6"," Pro zadanou produkci rozhodněte, jaké výnosy z rozsahu představují:\n(a) ",[883,92632,92634],{"className":92633},[886],[888,92635,92636],{"xmlns":890},[892,92637,92638,92654],{},[895,92639,92640,92642,92644,92646,92648],{},[898,92641,1665],{},[1656,92643,1713],{},[1667,92645,6240],{},[898,92647,18539],{},[2062,92649,92650,92652],{},[898,92651,18544],{},[1667,92653,1680],{},[902,92655,92656],{"encoding":904},"Q = 7 L K^{2}",[883,92658,92660],{"className":92659},[886],[888,92661,92662],{"xmlns":890},[892,92663,92664,92696],{},[895,92665,92666,92668,92670,92672,92684],{},[898,92667,1665],{},[1656,92669,1713],{},[1667,92671,9267],{},[2062,92673,92674,92676],{},[898,92675,18539],{},[895,92677,92678,92680,92682],{},[1667,92679,1680],{},[898,92681,1782],{"mathvariant":1723},[1667,92683,2617],{},[2062,92685,92686,92688],{},[898,92687,18544],{},[895,92689,92690,92692,92694],{},[1667,92691,1669],{},[898,92693,1782],{"mathvariant":1723},[1667,92695,2617],{},[902,92697,92698],{"encoding":904},"Q = 50 L^{2\u002F3} K^{1\u002F3}",[883,92700,92702],{"className":92701},[886],[888,92703,92704],{"xmlns":890},[892,92705,92706,92738],{},[895,92707,92708,92710,92712,92714,92726],{},[898,92709,1665],{},[1656,92711,1713],{},[1667,92713,12494],{},[2062,92715,92716,92718],{},[898,92717,18539],{},[895,92719,92720,92722,92724],{},[1667,92721,2617],{},[898,92723,1782],{"mathvariant":1723},[1667,92725,5193],{},[2062,92727,92728,92730],{},[898,92729,18544],{},[895,92731,92732,92734,92736],{},[1667,92733,1680],{},[898,92735,1782],{"mathvariant":1723},[1667,92737,5193],{},[902,92739,92740],{"encoding":904},"Q = 18 L^{3\u002F5} K^{2\u002F5}",[724,92742,92743,92114,92746,92788,92789,1343,92807,92826,92827,92844],{},[38,92744,92745],{},"5.7",[883,92747,92749],{"className":92748},[886],[888,92750,92751],{"xmlns":890},[892,92752,92753,92785],{},[895,92754,92755,92757,92759,92761,92773],{},[898,92756,1665],{},[1656,92758,1713],{},[1667,92760,8580],{},[2062,92762,92763,92765],{},[898,92764,18539],{},[895,92766,92767,92769,92771],{},[1667,92768,1669],{},[898,92770,1782],{"mathvariant":1723},[1667,92772,1680],{},[2062,92774,92775,92777],{},[898,92776,18544],{},[895,92778,92779,92781,92783],{},[1667,92780,1669],{},[898,92782,1782],{"mathvariant":1723},[1667,92784,1680],{},[902,92786,92787],{"encoding":904},"Q = 10 L^{1\u002F2} K^{1\u002F2}",". (a) Vypočtěte produkci pro ",[883,92790,92792],{"className":92791},[886],[888,92793,92794],{"xmlns":890},[892,92795,92796,92804],{},[895,92797,92798,92800,92802],{},[898,92799,18539],{},[1656,92801,1713],{},[1667,92803,28863],{},[902,92805,92806],{"encoding":904},"L = 400",[883,92808,92810],{"className":92809},[886],[888,92811,92812],{"xmlns":890},[892,92813,92814,92823],{},[895,92815,92816,92818,92820],{},[898,92817,18544],{},[1656,92819,1713],{},[1667,92821,92822],{},"17576",[902,92824,92825],{"encoding":904},"K = 17576",". (b) Rozhodněte o tom, jaké výnosy z rozsahu představuje a vyložte, jak se změní produkce, jestliže se vstupy ",[883,92828,92830],{"className":92829},[886],[888,92831,92832],{"xmlns":890},[892,92833,92834,92842],{},[895,92835,92836,92838,92840],{},[898,92837,18539],{},[1656,92839,1673],{"separator":1672},[898,92841,18544],{},[902,92843,87641],{"encoding":904}," zdvojnásobí.",[724,92846,92847,92850,92851,92788,92882,1343,92900,78248,92918,92948,92949,92979,92980,3619,92993,93007,93008,3619,93021,93034],{},[38,92848,92849],{},"5.8"," V jedné empirické studii (40. léta 20. století) ze sektoru manufaktur odhadli Cobb a Douglas produkci ze zjištěných údajů ve tvaru ",[883,92852,92854],{"className":92853},[886],[888,92855,92856],{"xmlns":890},[892,92857,92858,92879],{},[895,92859,92860,92862,92864,92867,92873],{},[898,92861,1665],{},[1656,92863,1713],{},[1667,92865,92866],{},"1,01",[2062,92868,92869,92871],{},[898,92870,18539],{},[1667,92872,32447],{},[2062,92874,92875,92877],{},[898,92876,18544],{},[1667,92878,32506],{},[902,92880,92881],{"encoding":904},"Q = 1{,}01 L^{0{,}75} K^{0{,}25}",[883,92883,92885],{"className":92884},[886],[888,92886,92887],{"xmlns":890},[892,92888,92889,92897],{},[895,92890,92891,92893,92895],{},[898,92892,18539],{},[1656,92894,1713],{},[1667,92896,39433],{},[902,92898,92899],{"encoding":904},"L = 250",[883,92901,92903],{"className":92902},[886],[888,92904,92905],{"xmlns":890},[892,92906,92907,92915],{},[895,92908,92909,92911,92913],{},[898,92910,18544],{},[1656,92912,1713],{},[1667,92914,11584],{},[902,92916,92917],{"encoding":904},"K = 1000",[883,92919,92921],{"className":92920},[886],[888,92922,92923],{"xmlns":890},[892,92924,92925,92945],{},[895,92926,92927,92929,92935,92937,92939,92941,92943],{},[898,92928,1703],{},[1661,92930,92931,92933],{},[898,92932,8194],{},[898,92934,18539],{},[1656,92936,1659],{"stretchy":1658},[1667,92938,39433],{},[1656,92940,1673],{"separator":1672},[1667,92942,11584],{},[1656,92944,1683],{"stretchy":1658},[902,92946,92947],{"encoding":904},"MP_L(250, 1000)"," a výsledek ekonomicky interpretujte. (c) Vypočtěte ",[883,92950,92952],{"className":92951},[886],[888,92953,92954],{"xmlns":890},[892,92955,92956,92976],{},[895,92957,92958,92960,92966,92968,92970,92972,92974],{},[898,92959,1703],{},[1661,92961,92962,92964],{},[898,92963,8194],{},[898,92965,18544],{},[1656,92967,1659],{"stretchy":1658},[1667,92969,39433],{},[1656,92971,1673],{"separator":1672},[1667,92973,11584],{},[1656,92975,1683],{"stretchy":1658},[902,92977,92978],{"encoding":904},"MP_K(250, 1000)"," a výsledek ekonomicky interpretujte. (d) Odhadněte změnu produkce v důsledku zvýšení ",[883,92981,92983],{"className":92982},[886],[888,92984,92985],{"xmlns":890},[892,92986,92987,92991],{},[895,92988,92989],{},[898,92990,18539],{},[902,92992,18539],{"encoding":904},[883,92994,92996],{"className":92995},[886],[888,92997,92998],{"xmlns":890},[892,92999,93000,93005],{},[895,93001,93002],{},[1667,93003,93004],{},"260",[902,93006,93004],{"encoding":904}," a současném poklesu ",[883,93009,93011],{"className":93010},[886],[888,93012,93013],{"xmlns":890},[892,93014,93015,93019],{},[895,93016,93017],{},[898,93018,18544],{},[902,93020,18544],{"encoding":904},[883,93022,93024],{"className":93023},[886],[888,93025,93026],{"xmlns":890},[892,93027,93028,93032],{},[895,93029,93030],{},[1667,93031,23922],{},[902,93033,23922],{"encoding":904}," vzhledem k hladině dle (a) a porovnejte se skutečnou změnou produkce.",[724,93036,93037,93040,93041,1863],{},[38,93038,93039],{},"5.9"," Ověřte platnost zákona klesajících výnosů pro produkci ",[883,93042,93044],{"className":93043},[886],[888,93045,93046],{"xmlns":890},[892,93047,93048,93068],{},[895,93049,93050,93052,93054,93056,93062],{},[898,93051,1665],{},[1656,93053,1713],{},[1667,93055,8580],{},[2062,93057,93058,93060],{},[898,93059,18539],{},[1667,93061,76875],{},[2062,93063,93064,93066],{},[898,93065,18544],{},[1667,93067,13779],{},[902,93069,93070],{"encoding":904},"Q = 10 L^{0{,}3} K^{0{,}5}",[724,93072,93073,93076,93077,89236,93100,19135,93113,3247,93163,12702],{},[38,93074,93075],{},"5.10"," Dokažte, že pro homogenní funkci ",[883,93078,93080],{"className":93079},[886],[888,93081,93082],{"xmlns":890},[892,93083,93084,93098],{},[895,93085,93086,93088,93090,93092,93094,93096],{},[898,93087,1665],{},[1656,93089,1659],{"stretchy":1658},[898,93091,18539],{},[1656,93093,1673],{"separator":1672},[898,93095,18544],{},[1656,93097,1683],{"stretchy":1658},[902,93099,18740],{"encoding":904},[883,93101,93103],{"className":93102},[886],[888,93104,93105],{"xmlns":890},[892,93106,93107,93111],{},[895,93108,93109],{},[898,93110,2292],{},[902,93112,2292],{"encoding":904},[883,93114,93116],{"className":93115},[886],[888,93117,93118],{"xmlns":890},[892,93119,93120,93160],{},[895,93121,93122,93124,93132,93134,93136,93144,93146,93148,93150,93152,93154,93156,93158],{},[898,93123,18539],{},[1715,93125,93126,93128,93130],{},[898,93127,1665],{},[898,93129,18539],{},[1656,93131,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,93133,3633],{},[898,93135,18544],{},[1715,93137,93138,93140,93142],{},[898,93139,1665],{},[898,93141,18544],{},[1656,93143,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,93145,1713],{},[898,93147,2292],{},[898,93149,1665],{},[1656,93151,1659],{"stretchy":1658},[898,93153,18539],{},[1656,93155,1673],{"separator":1672},[898,93157,18544],{},[1656,93159,1683],{"stretchy":1658},[902,93161,93162],{"encoding":904},"L Q'_L + K Q'_K = n Q(L, K)",[614,93164,89211],{},[724,93166,93167,93170],{},[38,93168,93169],{},"5.11"," Ověřte platnost Eulerovy věty (úloha 5.10) pro Cobb-Douglasovu produkční funkci.",[724,93172,93173,92114,93176,93216,93217,1343,93239,1343,93261,93283],{},[38,93174,93175],{},"5.12",[883,93177,93179],{"className":93178},[886],[888,93180,93181],{"xmlns":890},[892,93182,93183,93213],{},[895,93184,93185,93187,93189,93201],{},[898,93186,1665],{},[1656,93188,1713],{},[2062,93190,93191,93193],{},[898,93192,18539],{},[895,93194,93195,93197,93199],{},[1667,93196,1669],{},[898,93198,1782],{"mathvariant":1723},[1667,93200,2617],{},[2062,93202,93203,93205],{},[898,93204,18544],{},[895,93206,93207,93209,93211],{},[1667,93208,1669],{},[898,93210,1782],{"mathvariant":1723},[1667,93212,2673],{},[902,93214,93215],{"encoding":904},"Q = L^{1\u002F3} K^{1\u002F4}",". (a) Najděte rovnici izokvant. (b) Najděte rovnici izokvant pro produkci ",[883,93218,93220],{"className":93219},[886],[888,93221,93222],{"xmlns":890},[892,93223,93224,93236],{},[895,93225,93226,93232,93234],{},[1661,93227,93228,93230],{},[898,93229,89452],{},[1667,93231,4032],{},[1656,93233,1713],{},[1667,93235,1669],{},[902,93237,93238],{"encoding":904},"q_0 = 1",[883,93240,93242],{"className":93241},[886],[888,93243,93244],{"xmlns":890},[892,93245,93246,93258],{},[895,93247,93248,93254,93256],{},[1661,93249,93250,93252],{},[898,93251,89452],{},[1667,93253,1669],{},[1656,93255,1713],{},[1667,93257,1680],{},[902,93259,93260],{"encoding":904},"q_1 = 2",[883,93262,93264],{"className":93263},[886],[888,93265,93266],{"xmlns":890},[892,93267,93268,93280],{},[895,93269,93270,93276,93278],{},[1661,93271,93272,93274],{},[898,93273,89452],{},[1667,93275,1680],{},[1656,93277,1713],{},[1667,93279,2617],{},[902,93281,93282],{"encoding":904},"q_2 = 3",". (c) Načrtněte izokvanty.",[724,93285,93286,92114,93289,93329,93330,1343,93358,1343,93386,1343,93414,1343,93443,1343,93472,1343,93501,1343,93530,1343,93559,1863],{},[38,93287,93288],{},"5.13",[883,93290,93292],{"className":93291},[886],[888,93293,93294],{"xmlns":890},[892,93295,93296,93326],{},[895,93297,93298,93300,93302,93314],{},[898,93299,1665],{},[1656,93301,1713],{},[2062,93303,93304,93306],{},[898,93305,18539],{},[895,93307,93308,93310,93312],{},[1667,93309,1669],{},[898,93311,1782],{"mathvariant":1723},[1667,93313,2617],{},[2062,93315,93316,93318],{},[898,93317,18544],{},[895,93319,93320,93322,93324],{},[1667,93321,1669],{},[898,93323,1782],{"mathvariant":1723},[1667,93325,1680],{},[902,93327,93328],{"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): ",[883,93331,93333],{"className":93332},[886],[888,93334,93335],{"xmlns":890},[892,93336,93337,93355],{},[895,93338,93339,93345,93347,93349,93351,93353],{},[1661,93340,93341,93343],{},[898,93342,2146],{},[1667,93344,1669],{},[1656,93346,3453],{"stretchy":1658},[1667,93348,1669],{},[1656,93350,2856],{"separator":1672},[1667,93352,1669],{},[1656,93354,3462],{"stretchy":1658},[902,93356,93357],{"encoding":904},"A_1[1; 1]",[883,93359,93361],{"className":93360},[886],[888,93362,93363],{"xmlns":890},[892,93364,93365,93383],{},[895,93366,93367,93373,93375,93377,93379,93381],{},[1661,93368,93369,93371],{},[898,93370,2146],{},[1667,93372,1680],{},[1656,93374,3453],{"stretchy":1658},[1667,93376,1669],{},[1656,93378,2856],{"separator":1672},[1667,93380,2877],{},[1656,93382,3462],{"stretchy":1658},[902,93384,93385],{"encoding":904},"A_2[1; 8]",[883,93387,93389],{"className":93388},[886],[888,93390,93391],{"xmlns":890},[892,93392,93393,93411],{},[895,93394,93395,93401,93403,93405,93407,93409],{},[1661,93396,93397,93399],{},[898,93398,2146],{},[1667,93400,2617],{},[1656,93402,3453],{"stretchy":1658},[1667,93404,1669],{},[1656,93406,2856],{"separator":1672},[1667,93408,2707],{},[1656,93410,3462],{"stretchy":1658},[902,93412,93413],{"encoding":904},"A_3[1; 27]",[883,93415,93417],{"className":93416},[886],[888,93418,93419],{"xmlns":890},[892,93420,93421,93440],{},[895,93422,93423,93429,93431,93433,93435,93438],{},[1661,93424,93425,93427],{},[898,93426,2146],{},[1667,93428,2673],{},[1656,93430,3453],{"stretchy":1658},[1667,93432,1680],{},[1656,93434,2856],{"separator":1672},[1667,93436,93437],{},"0,353",[1656,93439,3462],{"stretchy":1658},[902,93441,93442],{"encoding":904},"A_4[2; 0{,}353]",[883,93444,93446],{"className":93445},[886],[888,93447,93448],{"xmlns":890},[892,93449,93450,93469],{},[895,93451,93452,93458,93460,93462,93464,93467],{},[1661,93453,93454,93456],{},[898,93455,2146],{},[1667,93457,5193],{},[1656,93459,3453],{"stretchy":1658},[1667,93461,1680],{},[1656,93463,2856],{"separator":1672},[1667,93465,93466],{},"2,828",[1656,93468,3462],{"stretchy":1658},[902,93470,93471],{"encoding":904},"A_5[2; 2{,}828]",[883,93473,93475],{"className":93474},[886],[888,93476,93477],{"xmlns":890},[892,93478,93479,93498],{},[895,93480,93481,93487,93489,93491,93493,93496],{},[1661,93482,93483,93485],{},[898,93484,2146],{},[1667,93486,9112],{},[1656,93488,3453],{"stretchy":1658},[1667,93490,1680],{},[1656,93492,2856],{"separator":1672},[1667,93494,93495],{},"9,545",[1656,93497,3462],{"stretchy":1658},[902,93499,93500],{"encoding":904},"A_6[2; 9{,}545]",[883,93502,93504],{"className":93503},[886],[888,93505,93506],{"xmlns":890},[892,93507,93508,93527],{},[895,93509,93510,93516,93518,93520,93522,93525],{},[1661,93511,93512,93514],{},[898,93513,2146],{},[1667,93515,6240],{},[1656,93517,3453],{"stretchy":1658},[1667,93519,8845],{},[1656,93521,2856],{"separator":1672},[1667,93523,93524],{},"0,544",[1656,93526,3462],{"stretchy":1658},[902,93528,93529],{"encoding":904},"A_7[1{,}5; 0{,}544]",[883,93531,93533],{"className":93532},[886],[888,93534,93535],{"xmlns":890},[892,93536,93537,93556],{},[895,93538,93539,93545,93547,93549,93551,93554],{},[1661,93540,93541,93543],{},[898,93542,2146],{},[1667,93544,2877],{},[1656,93546,3453],{"stretchy":1658},[1667,93548,8845],{},[1656,93550,2856],{"separator":1672},[1667,93552,93553],{},"14,696",[1656,93555,3462],{"stretchy":1658},[902,93557,93558],{"encoding":904},"A_8[1{,}5; 14{,}696]",[883,93560,93562],{"className":93561},[886],[888,93563,93564],{"xmlns":890},[892,93565,93566,93584],{},[895,93567,93568,93574,93576,93578,93580,93582],{},[1661,93569,93570,93572],{},[898,93571,2146],{},[1667,93573,2698],{},[1656,93575,3453],{"stretchy":1658},[1667,93577,1680],{},[1656,93579,2856],{"separator":1672},[1667,93581,5193],{},[1656,93583,3462],{"stretchy":1658},[902,93585,93586],{"encoding":904},"A_9[2; 5]",[724,93588,93589,93592],{},[38,93590,93591],{},"5.14"," Dokažte, že izokvanty Cobb-Douglasovy produkční funkce jsou klesající a konvexní.",[724,93594,93595,93598,93599,93629,93630,93643,93644,93657,93658,77981,93677,93696,93697,1863],{},[38,93596,93597],{},"5.15"," Produkce firmy je dána vztahem ",[883,93600,93602],{"className":93601},[886],[888,93603,93604],{"xmlns":890},[892,93605,93606,93626],{},[895,93607,93608,93610,93612,93614,93620],{},[898,93609,1665],{},[1656,93611,1713],{},[1667,93613,1680],{},[2062,93615,93616,93618],{},[898,93617,18539],{},[1667,93619,13779],{},[2062,93621,93622,93624],{},[898,93623,18544],{},[1667,93625,32506],{},[902,93627,93628],{"encoding":904},"Q = 2 L^{0{,}5} K^{0{,}25}",". (a) Vypočtěte produkci, mezní produkt práce a mezní produkt kapitálu, zaměstnává-li firma ",[883,93631,93633],{"className":93632},[886],[888,93634,93635],{"xmlns":890},[892,93636,93637,93641],{},[895,93638,93639],{},[1667,93640,5267],{},[902,93642,5267],{"encoding":904}," pracovníků a disponuje-li ",[883,93645,93647],{"className":93646},[886],[888,93648,93649],{"xmlns":890},[892,93650,93651,93655],{},[895,93652,93653],{},[1667,93654,73101],{},[902,93656,73101],{"encoding":904}," jednotkami kapitálu. (b) Určete mezní míru technické substituce ",[883,93659,93661],{"className":93660},[886],[888,93662,93663],{"xmlns":890},[892,93664,93665,93675],{},[895,93666,93667,93669,93671,93673],{},[898,93668,1703],{},[898,93670,1763],{},[898,93672,11577],{},[898,93674,1769],{},[902,93676,19340],{"encoding":904},[883,93678,93680],{"className":93679},[886],[888,93681,93682],{"xmlns":890},[892,93683,93684,93694],{},[895,93685,93686,93688,93690,93692],{},[898,93687,1703],{},[898,93689,1763],{},[898,93691,11577],{},[898,93693,1769],{},[902,93695,19340],{"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 ",[883,93698,93700],{"className":93699},[886],[888,93701,93702],{"xmlns":890},[892,93703,93704,93709],{},[895,93705,93706],{},[1667,93707,93708],{},"95",[902,93710,93708],{"encoding":904},[724,93712,93713,92114,93716,79655,93748,93767,93768,93781,93782,93795,93796,93809],{},[38,93714,93715],{},"5.16",[883,93717,93719],{"className":93718},[886],[888,93720,93721],{"xmlns":890},[892,93722,93723,93745],{},[895,93724,93725,93727,93729,93735,93737,93739],{},[898,93726,1665],{},[1656,93728,1713],{},[2062,93730,93731,93733],{},[898,93732,18544],{},[1667,93734,1680],{},[1656,93736,3633],{},[1667,93738,1680],{},[2062,93740,93741,93743],{},[898,93742,18539],{},[1667,93744,1680],{},[902,93746,93747],{"encoding":904},"Q = K^{2} + 2 L^{2}",[883,93749,93751],{"className":93750},[886],[888,93752,93753],{"xmlns":890},[892,93754,93755,93765],{},[895,93756,93757,93759,93761,93763],{},[898,93758,1703],{},[898,93760,1763],{},[898,93762,11577],{},[898,93764,1769],{},[902,93766,19340],{"encoding":904},". (b) Odhadněte změnu práce potřebné k udržení produkce, která je realizována ",[883,93769,93771],{"className":93770},[886],[888,93772,93773],{"xmlns":890},[892,93774,93775,93779],{},[895,93776,93777],{},[1667,93778,9267],{},[902,93780,9267],{"encoding":904}," pracovníky a ",[883,93783,93785],{"className":93784},[886],[888,93786,93787],{"xmlns":890},[892,93788,93789,93793],{},[895,93790,93791],{},[1667,93792,86273],{},[902,93794,86273],{"encoding":904}," jednotkami kapitálu, jestliže se kapitál sníží na ",[883,93797,93799],{"className":93798},[886],[888,93800,93801],{"xmlns":890},[892,93802,93803,93807],{},[895,93804,93805],{},[1667,93806,9280],{},[902,93808,9280],{"encoding":904}," jednotek.",[724,93811,93812,93815,93816,19135,93846,1863],{},[38,93813,93814],{},"5.17"," Odvoďte, že pro Cobb-Douglasovu produkční funkci ",[883,93817,93819],{"className":93818},[886],[888,93820,93821],{"xmlns":890},[892,93822,93823,93843],{},[895,93824,93825,93827,93829,93831,93837],{},[898,93826,1665],{},[1656,93828,1713],{},[898,93830,2146],{},[2062,93832,93833,93835],{},[898,93834,18539],{},[898,93836,207],{},[2062,93838,93839,93841],{},[898,93840,18544],{},[898,93842,3403],{},[902,93844,93845],{"encoding":904},"Q = A L^{a} K^{b}",[883,93847,93849],{"className":93848},[886],[888,93850,93851],{"xmlns":890},[892,93852,93853,93883],{},[895,93854,93855,93857,93859,93861,93863,93865,93873,93875],{},[898,93856,1703],{},[898,93858,1763],{},[898,93860,11577],{},[898,93862,1769],{},[1656,93864,1713],{},[4138,93866,93867],{"scriptlevel":4032,"displaystyle":1658},[3294,93868,93869,93871],{},[898,93870,207],{},[898,93872,3403],{},[1656,93874,2751],{},[4138,93876,93877],{"scriptlevel":4032,"displaystyle":1658},[3294,93878,93879,93881],{},[898,93880,18544],{},[898,93882,18539],{},[902,93884,93885],{"encoding":904},"MRTS = \\tfrac{a}{b}\\cdot \\tfrac{K}{L}",[115,93887,10198],{"id":10197},[120,93889,93890,93923,93950,93959,94009,94040,94093,94116,94171,94244,94322,94365,94397,94430,94471,94543,94604,94670,94687,94760,94826,94878,94934,94968,95011],{},[123,93891,93892,93895,93896,45578,93909,93922],{},[38,93893,93894],{},"Faktory (vstupy) produkce:"," práce ",[883,93897,93899],{"className":93898},[886],[888,93900,93901],{"xmlns":890},[892,93902,93903,93907],{},[895,93904,93905],{},[898,93906,18539],{},[902,93908,18539],{"encoding":904},[883,93910,93912],{"className":93911},[886],[888,93913,93914],{"xmlns":890},[892,93915,93916,93920],{},[895,93917,93918],{},[898,93919,18544],{},[902,93921,18544],{"encoding":904},", půda.",[123,93924,93925,2533,93927,1863],{},[38,93926,49131],{},[883,93928,93930],{"className":93929},[886],[888,93931,93932],{"xmlns":890},[892,93933,93934,93948],{},[895,93935,93936,93938,93940,93942,93944,93946],{},[898,93937,1665],{},[1656,93939,1713],{},[898,93941,1665],{},[1656,93943,1659],{"stretchy":1658},[898,93945,18539],{},[1656,93947,1683],{"stretchy":1658},[902,93949,83206],{"encoding":904},[123,93951,93952,3247,93954,20863,93957,1863],{},[38,93953,859],{},[614,93955,93956],{},"production function",[38,93958,83704],{},[123,93960,93961,1643,93963,1863],{},[38,93962,83750],{},[883,93964,93966],{"className":93965},[886],[888,93967,93968],{"xmlns":890},[892,93969,93970,94006],{},[895,93971,93972,93974,93980,93982,93984,93986,93988,93990,93992,93994,94000,94002,94004],{},[898,93973,1703],{},[1661,93975,93976,93978],{},[898,93977,8194],{},[898,93979,18539],{},[1656,93981,1713],{},[898,93983,3768],{},[898,93985,1665],{},[898,93987,1782],{"mathvariant":1723},[898,93989,3768],{},[898,93991,18539],{},[1656,93993,1713],{},[2062,93995,93996,93998],{},[898,93997,1665],{},[1656,93999,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,94001,1659],{"stretchy":1658},[898,94003,18539],{},[1656,94005,1683],{"stretchy":1658},[902,94007,94008],{"encoding":904},"MP_L = dQ\u002FdL = Q'(L)",[123,94010,94011,1643,94013,1863],{},[38,94012,84684],{},[883,94014,94016],{"className":94015},[886],[888,94017,94018],{"xmlns":890},[892,94019,94020,94038],{},[895,94021,94022,94024,94030,94032,94034,94036],{},[898,94023,2146],{},[1661,94025,94026,94028],{},[898,94027,8194],{},[898,94029,18539],{},[1656,94031,1713],{},[898,94033,1665],{},[898,94035,1782],{"mathvariant":1723},[898,94037,18539],{},[902,94039,83274],{"encoding":904},[123,94041,94042,94044,94045,19135,94062,1863],{},[38,94043,84171],{}," — od určitého ",[883,94046,94048],{"className":94047},[886],[888,94049,94050],{"xmlns":890},[892,94051,94052,94060],{},[895,94053,94054],{},[1661,94055,94056,94058],{},[898,94057,18539],{},[1667,94059,4032],{},[902,94061,84214],{"encoding":904},[883,94063,94065],{"className":94064},[886],[888,94066,94067],{"xmlns":890},[892,94068,94069,94091],{},[895,94070,94071,94081,94083,94085,94087,94089],{},[2062,94072,94073,94075],{},[898,94074,1665],{},[895,94076,94077,94079],{},[1656,94078,1725],{"mathvariant":1723},[1656,94080,1725],{"mathvariant":1723},[1656,94082,1659],{"stretchy":1658},[898,94084,18539],{},[1656,94086,1683],{"stretchy":1658},[1656,94088,4373],{},[1667,94090,4032],{},[902,94092,84360],{"encoding":904},[123,94094,94095,1643,94098,94115],{},[38,94096,94097],{},"Inflexní bod",[883,94099,94101],{"className":94100},[886],[888,94102,94103],{"xmlns":890},[892,94104,94105,94113],{},[895,94106,94107],{},[1661,94108,94109,94111],{},[898,94110,18539],{},[1667,94112,4032],{},[902,94114,84214],{"encoding":904}," — přechod z konvexity do konkavity.",[123,94117,94118,1643,94121,2533,94138,1863],{},[38,94119,94120],{},"Bod maxima produkce",[883,94122,94124],{"className":94123},[886],[888,94125,94126],{"xmlns":890},[892,94127,94128,94136],{},[895,94129,94130],{},[1661,94131,94132,94134],{},[898,94133,18539],{},[1667,94135,1669],{},[902,94137,21945],{"encoding":904},[883,94139,94141],{"className":94140},[886],[888,94142,94143],{"xmlns":890},[892,94144,94145,94169],{},[895,94146,94147,94149,94155,94157,94163,94165,94167],{},[898,94148,1703],{},[1661,94150,94151,94153],{},[898,94152,8194],{},[898,94154,18539],{},[1656,94156,1659],{"stretchy":1658},[1661,94158,94159,94161],{},[898,94160,18539],{},[1667,94162,1669],{},[1656,94164,1683],{"stretchy":1658},[1656,94166,1713],{},[1667,94168,4032],{},[902,94170,84433],{"encoding":904},[123,94172,94173,94195,94196,19135,94215,1863],{},[38,94174,94175,94176],{},"Princip maximalizace ",[883,94177,94179],{"className":94178},[886],[888,94180,94181],{"xmlns":890},[892,94182,94183,94193],{},[895,94184,94185,94187],{},[898,94186,2146],{},[1661,94188,94189,94191],{},[898,94190,8194],{},[898,94192,18539],{},[902,94194,83295],{"encoding":904}," — v bodě maxima ",[883,94197,94199],{"className":94198},[886],[888,94200,94201],{"xmlns":890},[892,94202,94203,94213],{},[895,94204,94205,94207],{},[898,94206,2146],{},[1661,94208,94209,94211],{},[898,94210,8194],{},[898,94212,18539],{},[902,94214,83295],{"encoding":904},[883,94216,94218],{"className":94217},[886],[888,94219,94220],{"xmlns":890},[892,94221,94222,94242],{},[895,94223,94224,94226,94232,94234,94236],{},[898,94225,1703],{},[1661,94227,94228,94230],{},[898,94229,8194],{},[898,94231,18539],{},[1656,94233,1713],{},[898,94235,2146],{},[1661,94237,94238,94240],{},[898,94239,8194],{},[898,94241,18539],{},[902,94243,83325],{"encoding":904},[123,94245,94246,1643,94249,1343,94288,1343,94305,1863],{},[38,94247,94248],{},"Polynomiální produkční funkce",[883,94250,94252],{"className":94251},[886],[888,94253,94254],{"xmlns":890},[892,94255,94256,94286],{},[895,94257,94258,94260,94262,94264,94266,94268,94270,94276,94278,94280],{},[898,94259,1665],{},[1656,94261,1659],{"stretchy":1658},[898,94263,18539],{},[1656,94265,1683],{"stretchy":1658},[1656,94267,1713],{},[898,94269,207],{},[2062,94271,94272,94274],{},[898,94273,18539],{},[1667,94275,2617],{},[1656,94277,3633],{},[898,94279,3403],{},[2062,94281,94282,94284],{},[898,94283,18539],{},[1667,94285,1680],{},[902,94287,84551],{"encoding":904},[883,94289,94291],{"className":94290},[886],[888,94292,94293],{"xmlns":890},[892,94294,94295,94303],{},[895,94296,94297,94299,94301],{},[898,94298,207],{},[1656,94300,4373],{},[1667,94302,4032],{},[902,94304,51762],{"encoding":904},[883,94306,94308],{"className":94307},[886],[888,94309,94310],{"xmlns":890},[892,94311,94312,94320],{},[895,94313,94314,94316,94318],{},[898,94315,3403],{},[1656,94317,2850],{},[1667,94319,4032],{},[902,94321,27536],{"encoding":904},[123,94323,94324,1643,94327,1863],{},[38,94325,94326],{},"Diferenciál produkce",[883,94328,94330],{"className":94329},[886],[888,94331,94332],{"xmlns":890},[892,94333,94334,94362],{},[895,94335,94336,94338,94340,94342,94344,94346,94348,94350,94356,94358,94360],{},[898,94337,3750],{"mathvariant":1723},[898,94339,1665],{},[1656,94341,3815],{},[898,94343,3768],{},[898,94345,1665],{},[1656,94347,1713],{},[898,94349,1703],{},[1661,94351,94352,94354],{},[898,94353,8194],{},[898,94355,18539],{},[2461,94357,7828],{},[898,94359,3768],{},[898,94361,18539],{},[902,94363,94364],{"encoding":904},"\\Delta Q \\approx dQ = MP_L\\,dL",[123,94366,94367,2533,94369,1863],{},[38,94368,92624],{},[883,94370,94372],{"className":94371},[886],[888,94373,94374],{"xmlns":890},[892,94375,94376,94394],{},[895,94377,94378,94380,94382,94384,94386,94388,94390,94392],{},[898,94379,1665],{},[1656,94381,1713],{},[898,94383,1665],{},[1656,94385,1659],{"stretchy":1658},[898,94387,18539],{},[1656,94389,1673],{"separator":1672},[898,94391,18544],{},[1656,94393,1683],{"stretchy":1658},[902,94395,94396],{"encoding":904},"Q = Q(L, K)",[123,94398,94399,2533,94401,1863],{},[38,94400,86721],{},[883,94402,94404],{"className":94403},[886],[888,94405,94406],{"xmlns":890},[892,94407,94408,94428],{},[895,94409,94410,94412,94414,94416,94422],{},[898,94411,1665],{},[1656,94413,1713],{},[898,94415,2146],{},[2062,94417,94418,94420],{},[898,94419,18539],{},[898,94421,207],{},[2062,94423,94424,94426],{},[898,94425,18544],{},[898,94427,3403],{},[902,94429,83391],{"encoding":904},[123,94431,94432,2533,94435,94470],{},[38,94433,94434],{},"Ryzí Cobb-Douglas",[883,94436,94438],{"className":94437},[886],[888,94439,94440],{"xmlns":890},[892,94441,94442,94468],{},[895,94443,94444,94446,94448,94450,94456],{},[898,94445,1665],{},[1656,94447,1713],{},[898,94449,2146],{},[2062,94451,94452,94454],{},[898,94453,18539],{},[898,94455,207],{},[2062,94457,94458,94460],{},[898,94459,18544],{},[895,94461,94462,94464,94466],{},[1667,94463,1669],{},[1656,94465,3964],{},[898,94467,207],{},[902,94469,87548],{"encoding":904}," (konstantní výnosy).",[123,94472,94473,2533,94475,1863],{},[38,94474,88264],{},[883,94476,94478],{"className":94477},[886],[888,94479,94480],{"xmlns":890},[892,94481,94482,94540],{},[895,94483,94484,94486,94488,94490,94492,94494,94496,94498,94500,94502,94512,94514,94516,94526],{},[898,94485,1665],{},[1656,94487,1713],{},[898,94489,2146],{},[1656,94491,3453],{"stretchy":1658},[1656,94493,1659],{"stretchy":1658},[1667,94495,1669],{},[1656,94497,3964],{},[898,94499,207],{},[1656,94501,1683],{"stretchy":1658},[2062,94503,94504,94506],{},[898,94505,18539],{},[895,94507,94508,94510],{},[1656,94509,3964],{},[898,94511,3403],{},[1656,94513,3633],{},[898,94515,207],{},[2062,94517,94518,94520],{},[898,94519,18544],{},[895,94521,94522,94524],{},[1656,94523,3964],{},[898,94525,3403],{},[2062,94527,94528,94530],{},[1656,94529,3462],{"stretchy":1658},[895,94531,94532,94534,94536,94538],{},[1656,94533,3964],{},[1667,94535,1669],{},[898,94537,1782],{"mathvariant":1723},[898,94539,3403],{},[902,94541,94542],{"encoding":904},"Q = A[(1-a)L^{-b} + aK^{-b}]^{-1\u002Fb}",[123,94544,94545,3247,94548,20863,94570,3247,94573,94603],{},[38,94546,94547],{},"Lineární",[883,94549,94551],{"className":94550},[886],[888,94552,94553],{"xmlns":890},[892,94554,94555,94567],{},[895,94556,94557,94559,94561,94563,94565],{},[898,94558,207],{},[898,94560,18539],{},[1656,94562,3633],{},[898,94564,3403],{},[898,94566,18544],{},[902,94568,94569],{"encoding":904},"aL + bK",[38,94571,94572],{},"Leontiefova",[883,94574,94576],{"className":94575},[886],[888,94577,94578],{"xmlns":890},[892,94579,94580,94600],{},[895,94581,94582,94584,94586,94588,94590,94592,94594,94596,94598],{},[898,94583,88492],{},[1656,94585,2093],{},[1656,94587,1659],{"stretchy":1658},[898,94589,207],{},[898,94591,18539],{},[1656,94593,1673],{"separator":1672},[898,94595,3403],{},[898,94597,18544],{},[1656,94599,1683],{"stretchy":1658},[902,94601,94602],{"encoding":904},"\\min(aL, bK)",") produkční funkce.",[123,94605,94606,2533,94622,1863],{},[38,94607,94608,94609],{},"Homogenita stupně ",[883,94610,94612],{"className":94611},[886],[888,94613,94614],{"xmlns":890},[892,94615,94616,94620],{},[895,94617,94618],{},[898,94619,2292],{},[902,94621,2292],{"encoding":904},[883,94623,94625],{"className":94624},[886],[888,94626,94627],{"xmlns":890},[892,94628,94629,94667],{},[895,94630,94631,94633,94635,94637,94639,94641,94643,94645,94647,94649,94655,94657,94659,94661,94663,94665],{},[898,94632,1665],{},[1656,94634,1659],{"stretchy":1658},[898,94636,20776],{},[898,94638,18539],{},[1656,94640,1673],{"separator":1672},[898,94642,20776],{},[898,94644,18544],{},[1656,94646,1683],{"stretchy":1658},[1656,94648,1713],{},[2062,94650,94651,94653],{},[898,94652,20776],{},[898,94654,2292],{},[898,94656,1665],{},[1656,94658,1659],{"stretchy":1658},[898,94660,18539],{},[1656,94662,1673],{"separator":1672},[898,94664,18544],{},[1656,94666,1683],{"stretchy":1658},[902,94668,94669],{"encoding":904},"Q(rL, rK) = r^n Q(L, K)",[123,94671,94672,87646],{},[38,94673,87579,94674],{},[883,94675,94677],{"className":94676},[886],[888,94678,94679],{"xmlns":890},[892,94680,94681,94685],{},[895,94682,94683],{},[898,94684,2146],{},[902,94686,2146],{"encoding":904},[123,94688,94689,94691,94692,94714,94715,94737,94738,12702],{},[38,94690,87080],{}," — konstantní (",[883,94693,94695],{"className":94694},[886],[888,94696,94697],{"xmlns":890},[892,94698,94699,94711],{},[895,94700,94701,94703,94705,94707,94709],{},[898,94702,207],{},[1656,94704,3633],{},[898,94706,3403],{},[1656,94708,1713],{},[1667,94710,1669],{},[902,94712,94713],{"encoding":904},"a+b=1","), rostoucí (",[883,94716,94718],{"className":94717},[886],[888,94719,94720],{"xmlns":890},[892,94721,94722,94734],{},[895,94723,94724,94726,94728,94730,94732],{},[898,94725,207],{},[1656,94727,3633],{},[898,94729,3403],{},[1656,94731,2850],{},[1667,94733,1669],{},[902,94735,94736],{"encoding":904},"a+b>1","), klesající (",[883,94739,94741],{"className":94740},[886],[888,94742,94743],{"xmlns":890},[892,94744,94745,94757],{},[895,94746,94747,94749,94751,94753,94755],{},[898,94748,207],{},[1656,94750,3633],{},[898,94752,3403],{},[1656,94754,4373],{},[1667,94756,1669],{},[902,94758,94759],{"encoding":904},"a+b\u003C1",[123,94761,94762,1643,94764,1343,94794,1643,94796,1863],{},[38,94763,83750],{},[883,94765,94767],{"className":94766},[886],[888,94768,94769],{"xmlns":890},[892,94770,94771,94791],{},[895,94772,94773,94775,94781,94783],{},[898,94774,1703],{},[1661,94776,94777,94779],{},[898,94778,8194],{},[898,94780,18539],{},[1656,94782,1713],{},[1715,94784,94785,94787,94789],{},[898,94786,1665],{},[898,94788,18539],{},[1656,94790,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[902,94792,94793],{"encoding":904},"MP_L = Q'_L",[38,94795,86653],{},[883,94797,94799],{"className":94798},[886],[888,94800,94801],{"xmlns":890},[892,94802,94803,94823],{},[895,94804,94805,94807,94813,94815],{},[898,94806,1703],{},[1661,94808,94809,94811],{},[898,94810,8194],{},[898,94812,18544],{},[1656,94814,1713],{},[1715,94816,94817,94819,94821],{},[898,94818,1665],{},[898,94820,18544],{},[1656,94822,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[902,94824,94825],{"encoding":904},"MP_K = Q'_K",[123,94827,94828,1643,94830,1863],{},[38,94829,3735],{},[883,94831,94833],{"className":94832},[886],[888,94834,94835],{"xmlns":890},[892,94836,94837,94875],{},[895,94838,94839,94841,94843,94845,94847,94853,94855,94857,94859,94861,94863,94869,94871,94873],{},[898,94840,3768],{},[898,94842,1665],{},[1656,94844,1713],{},[898,94846,1703],{},[1661,94848,94849,94851],{},[898,94850,8194],{},[898,94852,18539],{},[2461,94854,7828],{},[898,94856,3768],{},[898,94858,18539],{},[1656,94860,3633],{},[898,94862,1703],{},[1661,94864,94865,94867],{},[898,94866,8194],{},[898,94868,18544],{},[2461,94870,7828],{},[898,94872,3768],{},[898,94874,18544],{},[902,94876,94877],{"encoding":904},"dQ = MP_L\\,dL + MP_K\\,dK",[123,94879,94880,2533,94882,1863],{},[38,94881,89211],{},[883,94883,94885],{"className":94884},[886],[888,94886,94887],{"xmlns":890},[892,94888,94889,94931],{},[895,94890,94891,94893,94901,94903,94905,94913,94915,94917,94919,94921,94923,94925,94927,94929],{},[898,94892,18539],{},[1715,94894,94895,94897,94899],{},[898,94896,1665],{},[898,94898,18539],{},[1656,94900,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,94902,3633],{},[898,94904,18544],{},[1715,94906,94907,94909,94911],{},[898,94908,1665],{},[898,94910,18544],{},[1656,94912,1725],{"mathvariant":1723,"lspace":1724,"rspace":1724},[1656,94914,1713],{},[898,94916,2292],{},[2461,94918,7828],{},[898,94920,1665],{},[1656,94922,1659],{"stretchy":1658},[898,94924,18539],{},[1656,94926,1673],{"separator":1672},[898,94928,18544],{},[1656,94930,1683],{"stretchy":1658},[902,94932,94933],{"encoding":904},"L Q'_L + K Q'_K = n\\,Q(L,K)",[123,94935,94936,94939,94940,1863],{},[38,94937,94938],{},"Izokvanta"," — křivka ",[883,94941,94943],{"className":94942},[886],[888,94944,94945],{"xmlns":890},[892,94946,94947,94965],{},[895,94948,94949,94951,94953,94955,94957,94959,94961,94963],{},[898,94950,1665],{},[1656,94952,1659],{"stretchy":1658},[898,94954,18539],{},[1656,94956,1673],{"separator":1672},[898,94958,18544],{},[1656,94960,1683],{"stretchy":1658},[1656,94962,1713],{},[898,94964,89452],{},[902,94966,94967],{"encoding":904},"Q(L, K) = q",[123,94969,94970,1643,94972,1863],{},[38,94971,89641],{},[883,94973,94975],{"className":94974},[886],[888,94976,94977],{"xmlns":890},[892,94978,94979,95009],{},[895,94980,94981,94983,94985,94987,94989,94991,94993,94999,95001,95003],{},[898,94982,1703],{},[898,94984,1763],{},[898,94986,11577],{},[898,94988,1769],{},[1656,94990,1713],{},[898,94992,1703],{},[1661,94994,94995,94997],{},[898,94996,8194],{},[898,94998,18539],{},[898,95000,1782],{"mathvariant":1723},[898,95002,1703],{},[1661,95004,95005,95007],{},[898,95006,8194],{},[898,95008,18544],{},[902,95010,83466],{"encoding":904},[123,95012,95013,1643,95016,1863],{},[38,95014,95015],{},"Substituční vztah",[883,95017,95019],{"className":95018},[886],[888,95020,95021],{"xmlns":890},[892,95022,95023,95047],{},[895,95024,95025,95027,95029,95031,95033,95035,95037,95039,95041,95043,95045],{},[898,95026,3750],{"mathvariant":1723},[898,95028,18544],{},[1656,95030,3815],{},[1656,95032,3964],{},[898,95034,1703],{},[898,95036,1763],{},[898,95038,11577],{},[898,95040,1769],{},[2461,95042,7828],{},[898,95044,3768],{},[898,95046,18539],{},[902,95048,95049],{"encoding":904},"\\Delta K \\approx -MRTS\\,dL",[115,95051,10640],{"id":10639},[120,95053,95054,95150,95157,95164],{},[123,95055,95056,1643,95058,10693,95061,1343,95064,95067,95068,95071,95072,95091,95092,10722,95111,95114,95115,95134,95135,12702],{},[38,95057,59395],{},[207,95059,784],{"className":95060,"dataFsResolvedFilePath":782,"href":783},[210],[207,95062,10692],{"className":95063,"dataFsResolvedFilePath":764,"href":765},[210],[207,95065,793],{"className":95066,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace produkce s rozpočtovým omezením), ",[207,95069,880],{"className":95070,"dataFsResolvedFilePath":878,"href":879},[210]," (paralela: izokvanty ↔ indiferenční křivky, ",[883,95073,95075],{"className":95074},[886],[888,95076,95077],{"xmlns":890},[892,95078,95079,95089],{},[895,95080,95081,95083,95085,95087],{},[898,95082,1703],{},[898,95084,1763],{},[898,95086,11577],{},[898,95088,1769],{},[902,95090,19340],{"encoding":904}," ↔ ",[883,95093,95095],{"className":95094},[886],[888,95096,95097],{"xmlns":890},[892,95098,95099,95109],{},[895,95100,95101,95103,95105,95107],{},[898,95102,1703],{},[898,95104,1763],{},[898,95106,1766],{},[898,95108,1769],{},[902,95110,7362],{"encoding":904},[207,95112,12608],{"className":95113,"dataFsResolvedFilePath":827,"href":828},[210]," (analogie principu max ",[883,95116,95118],{"className":95117},[886],[888,95119,95120],{"xmlns":890},[892,95121,95122,95132],{},[895,95123,95124,95126],{},[898,95125,2146],{},[1661,95127,95128,95130],{},[898,95129,8194],{},[898,95131,18539],{},[902,95133,83295],{"encoding":904}," ↔ min ",[883,95136,95138],{"className":95137},[886],[888,95139,95140],{"xmlns":890},[892,95141,95142,95148],{},[895,95143,95144,95146],{},[898,95145,2146],{},[898,95147,1766],{},[902,95149,64229],{"encoding":904},[123,95151,95152,1643,95154,1863],{},[38,95153,12584],{},[207,95155,12613],{"className":95156,"dataFsResolvedFilePath":848,"href":849},[210],[123,95158,95159,1643,95161,1863],{},[38,95160,24939],{},[207,95162,1094],{"className":95163,"dataFsResolvedFilePath":838,"href":839},[210],[123,95165,95166,1643,95168,1863],{},[38,95167,10742],{},[207,95169,1869],{"className":95170,"dataFsResolvedFilePath":10746,"href":10747},[210],{"title":641,"searchDepth":642,"depth":642,"links":95172},[95173,95174,95175,95179,95181,95186,95187,95194,95195,95197,95198,95199,95201,95206,95207,95208,95212,95213],{"id":83489,"depth":642,"text":83490},{"id":83622,"depth":642,"text":83623},{"id":83725,"depth":642,"text":95176,"children":95177},"Mezní produkt práce (MPLMP_L)",[95178],{"id":84170,"depth":649,"text":84171},{"id":84659,"depth":642,"text":95180},"Průměrný produkt práce (APLAP_L)",{"id":84777,"depth":642,"text":84778,"children":95182},[95183,95184,95185],{"id":85014,"depth":649,"text":74166},{"id":85325,"depth":649,"text":85326},{"id":86045,"depth":649,"text":86046},{"id":86617,"depth":642,"text":86618},{"id":86720,"depth":642,"text":86721,"children":95188},[95189,95190,95192,95193],{"id":87079,"depth":649,"text":87080},{"id":87578,"depth":649,"text":95191},"Parametr efektivity AA",{"id":87649,"depth":649,"text":87650},{"id":45861,"depth":649,"text":87989},{"id":88176,"depth":642,"text":88177},{"id":88515,"depth":642,"text":95196},"Mezní produkty MPLMP_L, MPKMP_K a totální diferenciál",{"id":89205,"depth":642,"text":89206},{"id":83551,"depth":642,"text":18522},{"id":89616,"depth":642,"text":95200},"Mezní míra technické substituce 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pojmy a princip modelování v ",[207,103616,25106],{"className":103617,"dataFsResolvedFilePath":10746,"href":10747},[210],". Slouží jako vstupní bod pro celý kurz — bez těchto pojmů nedávají další kapitoly smysl.",[724,103620,103621],{},[5956,103622],{"alt":103623,"className":103624,"src":103625},"imek-model-promenne",[210,5960],"\u002Fwiki-assets\u002Fimek-model-promenne.jpeg",[115,103627,103629],{"id":103628},"co-je-matematická-ekonomie","Co je matematická ekonomie",[724,103631,103632,103635,103636,103639],{},[38,103633,103634],{},"Vědní disciplína",", která ekonomické vztahy vyjadřuje ",[38,103637,103638],{},"exaktními (matematickými) prostředky"," a provádí jejich analýzu. Cílem není jen popis, ale i predikce a optimalizace.",[115,103641,10198],{"id":10197},[120,103643,103644,103650,103656,103662,103671],{},[123,103645,103646,103649],{},[38,103647,103648],{},"Model"," — zjednodušený obraz reálné situace nebo jevu. Vždy jde o redukci skutečnosti, ne její kopii.",[123,103651,103652,103655],{},[38,103653,103654],{},"Endogenní proměnné"," — zahrnuté do modelu, mohou se měnit (vysvětlované).",[123,103657,103658,103661],{},[38,103659,103660],{},"Exogenní proměnné"," — nejsou v modelu zahrnuté (potenciálně by mohly), berou se jako dané.",[123,103663,103664,2533,103667,103670],{},[38,103665,103666],{},"Ceteris paribus",[614,103668,103669],{},"za jinak stejných podmínek",". Sledujeme změnu jedné proměnné, ostatní fixní.",[123,103672,103673,103675],{},[38,103674,59307],{}," — odezva endogenních proměnných na změnu některé exogenní.",[115,103677,103679],{"id":103678},"ilustrace-funkce-poptávky","Ilustrace — funkce poptávky",[724,103681,103682,103722],{},[883,103683,103685],{"className":103684},[886],[888,103686,103687],{"xmlns":890},[892,103688,103689,103719],{},[895,103690,103691,103693,103695,103697,103699,103701,103703,103705,103707,103709,103711,103713,103715,103717],{},[898,103692,1665],{},[1656,103694,1713],{},[898,103696,6787],{},[1656,103698,1659],{"stretchy":1658},[898,103700,8194],{},[1656,103702,1673],{"separator":1672},[898,103704,8184],{},[1656,103706,1673],{"separator":1672},[898,103708,27017],{},[1656,103710,1673],{"separator":1672},[898,103712,900],{},[1656,103714,1673],{"separator":1672},[1656,103716,2337],{},[1656,103718,1683],{"stretchy":1658},[902,103720,103721],{"encoding":904},"Q = D(P, Y, N, U, \\ldots)"," — plná (vícefaktorová) funkce poptávky.",[724,103724,103725],{},"Zjednodušení:",[120,103727,103728,103756],{},[123,103729,103730,1643,103733],{},[38,103731,103732],{},"Jednofaktorový model:",[883,103734,103736],{"className":103735},[886],[888,103737,103738],{"xmlns":890},[892,103739,103740,103754],{},[895,103741,103742,103744,103746,103748,103750,103752],{},[898,103743,1665],{},[1656,103745,1713],{},[898,103747,6787],{},[1656,103749,1659],{"stretchy":1658},[898,103751,8194],{},[1656,103753,1683],{"stretchy":1658},[902,103755,12971],{"encoding":904},[123,103757,103758,1643,103761],{},[38,103759,103760],{},"Inverzní zápis:",[883,103762,103764],{"className":103763},[886],[888,103765,103766],{"xmlns":890},[892,103767,103768,103782],{},[895,103769,103770,103772,103774,103776,103778,103780],{},[898,103771,8194],{},[1656,103773,1713],{},[898,103775,6787],{},[1656,103777,1659],{"stretchy":1658},[898,103779,1665],{},[1656,103781,1683],{"stretchy":1658},[902,103783,13412],{"encoding":904},[115,103785,103787],{"id":103786},"principy-řešení-ekonomických-úloh","Principy řešení ekonomických úloh",[152,103789,103790,103799],{},[123,103791,103792,103795,103796,12702],{},[38,103793,103794],{},"Princip rovnováhy"," — hledáme stav, kdy se protichůdné síly vyrovnají (např. tržní rovnováha, viz ",[207,103797,24966],{"className":103798,"dataFsResolvedFilePath":800,"href":801},[210],[123,103800,103801,103804,103805,103808,103809,103812,103813,103817],{},[38,103802,103803],{},"Princip optimalizace"," — hledáme extrém účelové funkce, případně vázaný omezujícími podmínkami (viz ",[207,103806,1145],{"className":103807,"dataFsResolvedFilePath":764,"href":765},[210]," pro 1D, ",[207,103810,24979],{"className":103811,"dataFsResolvedFilePath":782,"href":783},[210]," pro 2D, ",[207,103814,103816],{"className":103815,"dataFsResolvedFilePath":791,"href":792},[210],"lagrangeova-metoda"," pro vázané extrémy).",[115,103819,103821],{"id":103820},"konvence-z-přednášek","Konvence z přednášek",[120,103823,103824,103831,103837],{},[123,103825,103826,103827,103830],{},"Symbol ",[103828,103829,3815],"code",{}," pro přibližné rovnosti (typicky linearizace přes diferenciál).",[123,103832,103833,103834,1863],{},"Numerické výsledky ",[38,103835,103836],{},"na 3 desetinná místa",[123,103838,12678,103839,103842],{},[614,103840,103841],{},"jednotková změna"," má standardní význam (změna o 1).",[115,103844,10640],{"id":10639},[120,103846,103847,103852,103860],{},[123,103848,103849,103851],{},[38,103850,12584],{}," —",[123,103853,103854,1643,103856],{},[38,103855,12592],{},[207,103857,103859],{"className":103858,"dataFsResolvedFilePath":764,"href":765},[210],"Derivace a diferenciál",[123,103861,103862,1643,103864,1343,103868],{},[38,103863,12600],{},[207,103865,103867],{"className":103866,"dataFsResolvedFilePath":745,"href":746},[210],"Souhrn KS 1. blok",[207,103869,103871],{"className":103870,"dataFsResolvedFilePath":10746,"href":10747},[210],"kurz ImeK",{"title":641,"searchDepth":642,"depth":642,"links":103873},[103874,103875,103876,103877,103878,103879],{"id":103628,"depth":642,"text":103629},{"id":10197,"depth":642,"text":10198},{"id":103678,"depth":642,"text":103679},{"id":103786,"depth":642,"text":103787},{"id":103820,"depth":642,"text":103821},{"id":10639,"depth":642,"text":10640},"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":103880},[1135],"topics\u002Fzaklady-matematicke-ekonomie",[1128,103887,103888,103889,103890,103891],"model","endogenni","exogenni","ceteris-paribus","komparativni-statika","UZ1xD3l_gK41y8KlCBmpjprMOjIWmHZR8WZt-takTSI",{"id":103894,"title":103895,"body":103896,"course":1128,"courses":659,"created":10774,"description":641,"extension":661,"meta":108168,"navigation":664,"path":108169,"seo":108170,"sources":108171,"stem":108172,"tags":108173,"type":10786,"updated":677,"__hash__":108177},"topics\u002Ftopics\u002Fzdaneni-trhu.md","Zdanění trhu — dopady daně na rovnováhu",{"type":9,"value":103897,"toc":108151},[103898,103901,103995,103999,104021,104035,104087,104089,104093,104156,104199,104218,104381,104480,104483,104550,104554,104683,104722,104752,104864,104909,104975,105028,105104,105160,105162,105166,105230,105274,105294,105455,105458,105542,105639,105642,105708,105712,105761,105787,105892,105956,105961,106057,106104,106106,106109,106131,106173,106180,106213,106215,106286,106340,106449,106453,106542,106618,106882,106920,106922,106926,106929,106936,107247,107250,107308,107488,107517,107519,107523,107529,107667,107676,107678,107680,108105,108107,108109],[12,103899,103895],{"id":103900},"zdanění-trhu-dopady-daně-na-rovnováhu",[1981,103902,103903],{},[724,103904,103905,51305,103907,103920,103921,103924,103925,103927,103928,103931,103932,103953,103954,103977,103978,103981,103982,1863],{},[883,103906,3472],{},[883,103908,103910],{"className":103909},[886],[888,103911,103912],{"xmlns":890},[892,103913,103914,103918],{},[895,103915,103916],{},[898,103917,11577],{},[902,103919,11577],{"encoding":904}," uložená na každou prodanou jednotku zboží posouvá jednu z křivek — ",[38,103922,103923],{},"nabídku"," (je-li daň uložena výrobci) nebo ",[38,103926,1950],{}," (je-li uložena spotřebiteli). Výsledné ",[38,103929,103930],{},"daňové břemeno"," se dělí mezi obě strany trhu na ",[883,103933,103935],{"className":103934},[886],[888,103936,103937],{"xmlns":890},[892,103938,103939,103951],{},[895,103940,103941],{},[1661,103942,103943,103945],{},[898,103944,11577],{},[895,103946,103947,103949],{},[898,103948,51354],{},[898,103950,724],{},[902,103952,51359],{"encoding":904}," (spotřebitel) a ",[883,103955,103957],{"className":103956},[886],[888,103958,103959],{"xmlns":890},[892,103960,103961,103975],{},[895,103962,103963],{},[1661,103964,103965,103967],{},[898,103966,11577],{},[895,103968,103969,103971,103973],{},[898,103970,51377],{},[898,103972,10839],{},[898,103974,20776],{},[902,103976,51384],{"encoding":904}," (výrobce). Klíčovým zjištěním je ",[38,103979,103980],{},"ekvivalence obou přístupů",": rovnovážné množství i čistá cena pro výrobce jsou v obou režimech totožné; liší se pouze nominální cena na trhu o ",[883,103983,103985],{"className":103984},[886],[888,103986,103987],{"xmlns":890},[892,103988,103989,103993],{},[895,103990,103991],{},[898,103992,11577],{},[902,103994,11577],{"encoding":904},[115,103996,103998],{"id":103997},"dvě-formy-zdanění","Dvě formy zdanění",[724,104000,104001,104002,104020],{},"Uvažujme jednotkovou daň ",[883,104003,104005],{"className":104004},[886],[888,104006,104007],{"xmlns":890},[892,104008,104009,104017],{},[895,104010,104011,104013,104015],{},[898,104012,11577],{},[1656,104014,2850],{},[1667,104016,4032],{},[902,104018,104019],{"encoding":904},"T > 0"," (Kč na kus), kterou stát ukládá na každou prodanou jednotku zboží. Daň může být uložena buď:",[120,104022,104023,104029],{},[123,104024,104025,104028],{},[38,104026,104027],{},"(a) výrobci"," — výrobce ji musí odvést státu z každé prodané jednotky,",[123,104030,104031,104034],{},[38,104032,104033],{},"(b) spotřebiteli"," — spotřebitel ji platí navíc k ceně, kterou si účtuje prodejce.",[724,104036,104037,104038,104051,104052,104055,104056,1863],{},"V obou případech dochází k posunu jedné z křivek o ",[883,104039,104041],{"className":104040},[886],[888,104042,104043],{"xmlns":890},[892,104044,104045,104049],{},[895,104046,104047],{},[898,104048,11577],{},[902,104050,11577],{"encoding":904}," svisle (buď nabídky nahoru, nebo poptávky dolů) a k rozdělení ",[38,104053,104054],{},"daňového břemene"," mezi spotřebitele a výrobce. Výchozí rovnovážný bod bez daně označujeme ",[883,104057,104059],{"className":104058},[886],[888,104060,104061],{"xmlns":890},[892,104062,104063,104085],{},[895,104064,104065,104067,104069,104075,104077,104083],{},[898,104066,1842],{},[1656,104068,3453],{"stretchy":1658},[2062,104070,104071,104073],{},[898,104072,1665],{},[898,104074,1842],{},[1656,104076,1673],{"separator":1672},[2062,104078,104079,104081],{},[898,104080,8194],{},[898,104082,1842],{},[1656,104084,3462],{"stretchy":1658},[902,104086,50047],{"encoding":904},[45652,104088],{},[115,104090,104092],{"id":104091},"daň-uložená-výrobci","Daň uložená výrobci",[724,104094,104095,104096,104109,104110,104127,104128,104155],{},"Je-li daň ",[883,104097,104099],{"className":104098},[886],[888,104100,104101],{"xmlns":890},[892,104102,104103,104107],{},[895,104104,104105],{},[898,104106,11577],{},[902,104108,11577],{"encoding":904}," uložena výrobci, pak z podmínky, že výrobce za každou prodanou jednotku obdrží ",[883,104111,104113],{"className":104112},[886],[888,104114,104115],{"xmlns":890},[892,104116,104117,104125],{},[895,104118,104119,104121,104123],{},[898,104120,8194],{},[1656,104122,3964],{},[898,104124,11577],{},[902,104126,49802],{"encoding":904}," (hrubá cena mínus odvod), plyne z rovnice ",[883,104129,104131],{"className":104130},[886],[888,104132,104133],{"xmlns":890},[892,104134,104135,104153],{},[895,104136,104137,104139,104141,104143,104145,104147,104149,104151],{},[898,104138,8194],{},[1656,104140,3964],{},[898,104142,11577],{},[1656,104144,1713],{},[898,104146,1769],{},[1656,104148,1659],{"stretchy":1658},[898,104150,1665],{},[1656,104152,1683],{"stretchy":1658},[902,104154,49831],{"encoding":904}," nová funkce nabídky:",[883,104157,104159],{"className":104158},[886],[888,104160,104161],{"xmlns":890,"display":2408},[892,104162,104163,104197],{},[895,104164,104165,104167,104169,104175,104177,104179,104181,104183,104185,104187,104189,104191,104193,104195],{},[898,104166,8194],{},[1656,104168,1713],{},[1661,104170,104171,104173],{},[898,104172,1769],{},[1667,104174,1669],{},[1656,104176,1659],{"stretchy":1658},[898,104178,1665],{},[1656,104180,1683],{"stretchy":1658},[1656,104182,1713],{},[898,104184,1769],{},[1656,104186,1659],{"stretchy":1658},[898,104188,1665],{},[1656,104190,1683],{"stretchy":1658},[1656,104192,3633],{},[898,104194,11577],{},[898,104196,1863],{"mathvariant":1723},[902,104198,49876],{"encoding":904},[724,104200,104201,104202,1643,104215,104217],{},"Nabídka se tedy posouvá o ",[883,104203,104205],{"className":104204},[886],[888,104206,104207],{"xmlns":890},[892,104208,104209,104213],{},[895,104210,104211],{},[898,104212,11577],{},[902,104214,11577],{"encoding":904},[38,104216,49909],{}," (ekvivalentně doleva). Poptávka se nemění.",[724,104219,104220,104221,104261,104262,1896,104290,104318,104319,104338,104339,104363,104364,12702],{},"Nový rovnovážný bod ",[883,104222,104224],{"className":104223},[886],[888,104225,104226],{"xmlns":890},[892,104227,104228,104258],{},[895,104229,104230,104236,104238,104246,104248,104256],{},[1661,104231,104232,104234],{},[898,104233,1842],{},[1667,104235,1669],{},[1656,104237,3453],{"stretchy":1658},[1715,104239,104240,104242,104244],{},[898,104241,1665],{},[1667,104243,1669],{},[898,104245,1842],{},[1656,104247,1673],{"separator":1672},[1715,104249,104250,104252,104254],{},[898,104251,8194],{},[1667,104253,1669],{},[898,104255,1842],{},[1656,104257,3462],{"stretchy":1658},[902,104259,104260],{"encoding":904},"E_1[Q_1^E, P_1^E]"," splňuje ",[883,104263,104265],{"className":104264},[886],[888,104266,104267],{"xmlns":890},[892,104268,104269,104287],{},[895,104270,104271,104279,104281],{},[1715,104272,104273,104275,104277],{},[898,104274,1665],{},[1667,104276,1669],{},[898,104278,1842],{},[1656,104280,4373],{},[2062,104282,104283,104285],{},[898,104284,1665],{},[898,104286,1842],{},[902,104288,104289],{"encoding":904},"Q_1^E \u003C Q^E",[883,104291,104293],{"className":104292},[886],[888,104294,104295],{"xmlns":890},[892,104296,104297,104315],{},[895,104298,104299,104307,104309],{},[1715,104300,104301,104303,104305],{},[898,104302,8194],{},[1667,104304,1669],{},[898,104306,1842],{},[1656,104308,2850],{},[2062,104310,104311,104313],{},[898,104312,8194],{},[898,104314,1842],{},[902,104316,104317],{"encoding":904},"P_1^E > P^E",". Spotřebitel platí ",[883,104320,104322],{"className":104321},[886],[888,104323,104324],{"xmlns":890},[892,104325,104326,104336],{},[895,104327,104328],{},[1715,104329,104330,104332,104334],{},[898,104331,8194],{},[1667,104333,1669],{},[898,104335,1842],{},[902,104337,56532],{"encoding":904},", výrobci ale zůstává pouze čistá cena ",[883,104340,104342],{"className":104341},[886],[888,104343,104344],{"xmlns":890},[892,104345,104346,104360],{},[895,104347,104348,104356,104358],{},[1715,104349,104350,104352,104354],{},[898,104351,8194],{},[1667,104353,1669],{},[898,104355,1842],{},[1656,104357,3964],{},[898,104359,11577],{},[902,104361,104362],{"encoding":904},"P_1^E - T"," (ta je nižší než původní rovnovážná ",[883,104365,104367],{"className":104366},[886],[888,104368,104369],{"xmlns":890},[892,104370,104371,104379],{},[895,104372,104373],{},[2062,104374,104375,104377],{},[898,104376,8194],{},[898,104378,1842],{},[902,104380,50146],{"encoding":904},[724,104382,104383],{},[614,104384,104385,104386,104416,104417,104430,104431,14434,104448,104461,104462,1863],{},"Obrázek 2.17 (resp. 2.18): Posun ",[883,104387,104389],{"className":104388},[886],[888,104390,104391],{"xmlns":890},[892,104392,104393,104413],{},[895,104394,104395,104397,104399,104405,104407,104409,104411],{},[898,104396,1769],{},[1656,104398,11915],{},[1661,104400,104401,104403],{},[898,104402,1769],{},[1667,104404,1669],{},[1656,104406,1713],{},[898,104408,1769],{},[1656,104410,3633],{},[898,104412,11577],{},[902,104414,104415],{"encoding":904},"S \\to S_1 = S + T","; svislá vzdálenost mezi křivkami je přesně ",[883,104418,104420],{"className":104419},[886],[888,104421,104422],{"xmlns":890},[892,104423,104424,104428],{},[895,104425,104426],{},[898,104427,11577],{},[902,104429,11577],{"encoding":904},". Průsečík ",[883,104432,104434],{"className":104433},[886],[888,104435,104436],{"xmlns":890},[892,104437,104438,104446],{},[895,104439,104440],{},[1661,104441,104442,104444],{},[898,104443,1769],{},[1667,104445,1669],{},[902,104447,49677],{"encoding":904},[883,104449,104451],{"className":104450},[886],[888,104452,104453],{"xmlns":890},[892,104454,104455,104459],{},[895,104456,104457],{},[898,104458,6787],{},[902,104460,6787],{"encoding":904}," je nový rovnovážný bod ",[883,104463,104465],{"className":104464},[886],[888,104466,104467],{"xmlns":890},[892,104468,104469,104477],{},[895,104470,104471],{},[1661,104472,104473,104475],{},[898,104474,1842],{},[1667,104476,1669],{},[902,104478,104479],{"encoding":904},"E_1",[198,104481,53980],{"id":104482},"příklad-29",[724,104484,104485,50335,104487,50370,104511,104531,104532,104549],{},[38,104486,46615],{},[883,104488,104490],{"className":104489},[886],[888,104491,104492],{"xmlns":890},[892,104493,104494,104508],{},[895,104495,104496,104498,104500,104502,104504,104506],{},[898,104497,8194],{},[1656,104499,1713],{},[1667,104501,9140],{},[1656,104503,3964],{},[1667,104505,1680],{},[898,104507,1665],{},[902,104509,104510],{"encoding":904},"P = 12 - 2Q",[883,104512,104514],{"className":104513},[886],[888,104515,104516],{"xmlns":890},[892,104517,104518,104528],{},[895,104519,104520,104522,104524,104526],{},[898,104521,8194],{},[1656,104523,1713],{},[1667,104525,2673],{},[898,104527,1665],{},[902,104529,104530],{"encoding":904},"P = 4Q",". Na výrobce je uložena jednotková daň ",[883,104533,104535],{"className":104534},[886],[888,104536,104537],{"xmlns":890},[892,104538,104539,104547],{},[895,104540,104541,104543,104545],{},[898,104542,11577],{},[1656,104544,1713],{},[1667,104546,9112],{},[902,104548,49948],{"encoding":904}," Kč.",[724,104551,104552],{},[38,104553,46647],{},[724,104555,104556,104559,104560,14337,104586,2836,104606,1343,104628,104658,104659,1863],{},[614,104557,104558],{},"Bez daně."," Z rovnosti ",[883,104561,104563],{"className":104562},[886],[888,104564,104565],{"xmlns":890},[892,104566,104567,104583],{},[895,104568,104569,104571,104573,104575,104577,104579,104581],{},[1667,104570,9140],{},[1656,104572,3964],{},[1667,104574,1680],{},[898,104576,1665],{},[1656,104578,1713],{},[1667,104580,2673],{},[898,104582,1665],{},[902,104584,104585],{"encoding":904},"12 - 2Q = 4Q",[883,104587,104589],{"className":104588},[886],[888,104590,104591],{"xmlns":890},[892,104592,104593,104603],{},[895,104594,104595,104597,104599,104601],{},[1667,104596,9112],{},[898,104598,1665],{},[1656,104600,1713],{},[1667,104602,9140],{},[902,104604,104605],{"encoding":904},"6Q = 12",[883,104607,104609],{"className":104608},[886],[888,104610,104611],{"xmlns":890},[892,104612,104613,104625],{},[895,104614,104615,104621,104623],{},[2062,104616,104617,104619],{},[898,104618,1665],{},[898,104620,1842],{},[1656,104622,1713],{},[1667,104624,1680],{},[902,104626,104627],{"encoding":904},"Q^E = 2",[883,104629,104631],{"className":104630},[886],[888,104632,104633],{"xmlns":890},[892,104634,104635,104655],{},[895,104636,104637,104643,104645,104647,104649,104651,104653],{},[2062,104638,104639,104641],{},[898,104640,8194],{},[898,104642,1842],{},[1656,104644,1713],{},[1667,104646,2673],{},[1656,104648,2751],{},[1667,104650,1680],{},[1656,104652,1713],{},[1667,104654,2877],{},[902,104656,104657],{"encoding":904},"P^E = 4 \\cdot 2 = 8",". Rovnovážný bod ",[883,104660,104662],{"className":104661},[886],[888,104663,104664],{"xmlns":890},[892,104665,104666,104680],{},[895,104667,104668,104670,104672,104674,104676,104678],{},[898,104669,1842],{},[1656,104671,3453],{"stretchy":1658},[1667,104673,1680],{},[1656,104675,1673],{"separator":1672},[1667,104677,2877],{},[1656,104679,3462],{"stretchy":1658},[902,104681,104682],{"encoding":904},"E[2, 8]",[724,104684,104685,104688,104689,104721],{},[614,104686,104687],{},"S daní uloženou výrobci."," Nová nabídka je ",[883,104690,104692],{"className":104691},[886],[888,104693,104694],{"xmlns":890},[892,104695,104696,104718],{},[895,104697,104698,104704,104706,104708,104710,104712,104714,104716],{},[1661,104699,104700,104702],{},[898,104701,1769],{},[1667,104703,1669],{},[1656,104705,2114],{},[898,104707,8194],{},[1656,104709,1713],{},[1667,104711,2673],{},[898,104713,1665],{},[1656,104715,3633],{},[1667,104717,9112],{},[902,104719,104720],{"encoding":904},"S_1: P = 4Q + 6",". Z rovnice",[883,104723,104725],{"className":104724},[886],[888,104726,104727],{"xmlns":890,"display":2408},[892,104728,104729,104749],{},[895,104730,104731,104733,104735,104737,104739,104741,104743,104745,104747],{},[1667,104732,9140],{},[1656,104734,3964],{},[1667,104736,1680],{},[898,104738,1665],{},[1656,104740,1713],{},[1667,104742,2673],{},[898,104744,1665],{},[1656,104746,3633],{},[1667,104748,9112],{},[902,104750,104751],{"encoding":904},"12 - 2Q = 4Q + 6",[724,104753,104754,104755,2836,104775,1343,104799,104835,104836,1863],{},"plyne ",[883,104756,104758],{"className":104757},[886],[888,104759,104760],{"xmlns":890},[892,104761,104762,104772],{},[895,104763,104764,104766,104768,104770],{},[1667,104765,9112],{},[898,104767,1665],{},[1656,104769,1713],{},[1667,104771,9112],{},[902,104773,104774],{"encoding":904},"6Q = 6",[883,104776,104778],{"className":104777},[886],[888,104779,104780],{"xmlns":890},[892,104781,104782,104796],{},[895,104783,104784,104792,104794],{},[1715,104785,104786,104788,104790],{},[898,104787,1665],{},[1667,104789,1669],{},[898,104791,1842],{},[1656,104793,1713],{},[1667,104795,1669],{},[902,104797,104798],{"encoding":904},"Q_1^E = 1",[883,104800,104802],{"className":104801},[886],[888,104803,104804],{"xmlns":890},[892,104805,104806,104832],{},[895,104807,104808,104816,104818,104820,104822,104824,104826,104828,104830],{},[1715,104809,104810,104812,104814],{},[898,104811,8194],{},[1667,104813,1669],{},[898,104815,1842],{},[1656,104817,1713],{},[1667,104819,2673],{},[1656,104821,2751],{},[1667,104823,1669],{},[1656,104825,3633],{},[1667,104827,9112],{},[1656,104829,1713],{},[1667,104831,8580],{},[902,104833,104834],{"encoding":904},"P_1^E = 4 \\cdot 1 + 6 = 10",". Nový rovnovážný bod ",[883,104837,104839],{"className":104838},[886],[888,104840,104841],{"xmlns":890},[892,104842,104843,104861],{},[895,104844,104845,104851,104853,104855,104857,104859],{},[1661,104846,104847,104849],{},[898,104848,1842],{},[1667,104850,1669],{},[1656,104852,3453],{"stretchy":1658},[1667,104854,1669],{},[1656,104856,1673],{"separator":1672},[1667,104858,8580],{},[1656,104860,3462],{"stretchy":1658},[902,104862,104863],{"encoding":904},"E_1[1, 10]",[724,104865,104866,104869,104870,104894,104895,104908],{},[614,104867,104868],{},"Rozklad daňového břemene."," Spotřebitel platí ",[883,104871,104873],{"className":104872},[886],[888,104874,104875],{"xmlns":890},[892,104876,104877,104891],{},[895,104878,104879,104887,104889],{},[1715,104880,104881,104883,104885],{},[898,104882,8194],{},[1667,104884,1669],{},[898,104886,1842],{},[1656,104888,1713],{},[1667,104890,8580],{},[902,104892,104893],{"encoding":904},"P_1^E = 10"," Kč namísto původních ",[883,104896,104898],{"className":104897},[886],[888,104899,104900],{"xmlns":890},[892,104901,104902,104906],{},[895,104903,104904],{},[1667,104905,2877],{},[902,104907,2877],{"encoding":904},", navýšení je",[883,104910,104912],{"className":104911},[886],[888,104913,104914],{"xmlns":890,"display":2408},[892,104915,104916,104972],{},[895,104917,104918,104928,104930,104938,104940,104946,104948,104950,104952,104954,104956,104958,104960,104970],{},[1661,104919,104920,104922],{},[898,104921,11577],{},[895,104923,104924,104926],{},[898,104925,51354],{},[898,104927,724],{},[1656,104929,1713],{},[1715,104931,104932,104934,104936],{},[898,104933,8194],{},[1667,104935,1669],{},[898,104937,1842],{},[1656,104939,3964],{},[2062,104941,104942,104944],{},[898,104943,8194],{},[898,104945,1842],{},[1656,104947,1713],{},[1667,104949,8580],{},[1656,104951,3964],{},[1667,104953,2877],{},[1656,104955,1713],{},[1667,104957,1680],{},[2461,104959,11112],{},[895,104961,104962,104964],{},[2461,104963,18544],{},[2033,104965,104966,104968],{"accent":1672},[2461,104967,1745],{},[1656,104969,33774],{},[898,104971,1863],{"mathvariant":1723},[902,104973,104974],{"encoding":904},"T_{sp} = P_1^E - P^E = 10 - 8 = 2\\ \\text{Kč}.",[724,104976,104977,104978,104894,105014,105027],{},"Výrobci zůstává čistá cena ",[883,104979,104981],{"className":104980},[886],[888,104982,104983],{"xmlns":890},[892,104984,104985,105011],{},[895,104986,104987,104995,104997,104999,105001,105003,105005,105007,105009],{},[1715,104988,104989,104991,104993],{},[898,104990,8194],{},[1667,104992,1669],{},[898,104994,1842],{},[1656,104996,3964],{},[898,104998,11577],{},[1656,105000,1713],{},[1667,105002,8580],{},[1656,105004,3964],{},[1667,105006,9112],{},[1656,105008,1713],{},[1667,105010,2673],{},[902,105012,105013],{"encoding":904},"P_1^E - T = 10 - 6 = 4",[883,105015,105017],{"className":105016},[886],[888,105018,105019],{"xmlns":890},[892,105020,105021,105025],{},[895,105022,105023],{},[1667,105024,2877],{},[902,105026,2877],{"encoding":904},", pokles je",[883,105029,105031],{"className":105030},[886],[888,105032,105033],{"xmlns":890,"display":2408},[892,105034,105035,105101],{},[895,105036,105037,105049,105051,105057,105059,105061,105069,105071,105073,105075,105077,105079,105081,105083,105085,105087,105089,105099],{},[1661,105038,105039,105041],{},[898,105040,11577],{},[895,105042,105043,105045,105047],{},[898,105044,51377],{},[898,105046,10839],{},[898,105048,20776],{},[1656,105050,1713],{},[2062,105052,105053,105055],{},[898,105054,8194],{},[898,105056,1842],{},[1656,105058,3964],{},[1656,105060,1659],{"stretchy":1658},[1715,105062,105063,105065,105067],{},[898,105064,8194],{},[1667,105066,1669],{},[898,105068,1842],{},[1656,105070,3964],{},[898,105072,11577],{},[1656,105074,1683],{"stretchy":1658},[1656,105076,1713],{},[1667,105078,2877],{},[1656,105080,3964],{},[1667,105082,2673],{},[1656,105084,1713],{},[1667,105086,2673],{},[2461,105088,11112],{},[895,105090,105091,105093],{},[2461,105092,18544],{},[2033,105094,105095,105097],{"accent":1672},[2461,105096,1745],{},[1656,105098,33774],{},[898,105100,1863],{"mathvariant":1723},[902,105102,105103],{"encoding":904},"T_{vyr} = P^E - (P_1^E - T) = 8 - 4 = 4\\ \\text{Kč}.",[724,105105,105106,105107,105159],{},"Kontrola: ",[883,105108,105110],{"className":105109},[886],[888,105111,105112],{"xmlns":890},[892,105113,105114,105156],{},[895,105115,105116,105126,105128,105140,105142,105144,105146,105148,105150,105152,105154],{},[1661,105117,105118,105120],{},[898,105119,11577],{},[895,105121,105122,105124],{},[898,105123,51354],{},[898,105125,724],{},[1656,105127,3633],{},[1661,105129,105130,105132],{},[898,105131,11577],{},[895,105133,105134,105136,105138],{},[898,105135,51377],{},[898,105137,10839],{},[898,105139,20776],{},[1656,105141,1713],{},[1667,105143,1680],{},[1656,105145,3633],{},[1667,105147,2673],{},[1656,105149,1713],{},[1667,105151,9112],{},[1656,105153,1713],{},[898,105155,11577],{},[902,105157,105158],{"encoding":904},"T_{sp} + T_{vyr} = 2 + 4 = 6 = T",". Spotřebitel nese třetinu daně, výrobce dvě třetiny.",[45652,105161],{},[115,105163,105165],{"id":105164},"daň-uložená-spotřebiteli","Daň uložená spotřebiteli",[724,105167,104095,105168,105181,105182,105200,105201,105229],{},[883,105169,105171],{"className":105170},[886],[888,105172,105173],{"xmlns":890},[892,105174,105175,105179],{},[895,105176,105177],{},[898,105178,11577],{},[902,105180,11577],{"encoding":904}," uložena spotřebiteli, pak spotřebitel platí celkem ",[883,105183,105185],{"className":105184},[886],[888,105186,105187],{"xmlns":890},[892,105188,105189,105197],{},[895,105190,105191,105193,105195],{},[898,105192,8194],{},[1656,105194,3633],{},[898,105196,11577],{},[902,105198,105199],{"encoding":904},"P + T"," (cena prodejce plus daň). Z podmínky ",[883,105202,105204],{"className":105203},[886],[888,105205,105206],{"xmlns":890},[892,105207,105208,105226],{},[895,105209,105210,105212,105214,105216,105218,105220,105222,105224],{},[898,105211,8194],{},[1656,105213,3633],{},[898,105215,11577],{},[1656,105217,1713],{},[898,105219,6787],{},[1656,105221,1659],{"stretchy":1658},[898,105223,1665],{},[1656,105225,1683],{"stretchy":1658},[902,105227,105228],{"encoding":904},"P + T = D(Q)"," plyne nová funkce poptávky:",[883,105231,105233],{"className":105232},[886],[888,105234,105235],{"xmlns":890,"display":2408},[892,105236,105237,105271],{},[895,105238,105239,105241,105243,105249,105251,105253,105255,105257,105259,105261,105263,105265,105267,105269],{},[898,105240,8194],{},[1656,105242,1713],{},[1661,105244,105245,105247],{},[898,105246,6787],{},[1667,105248,1680],{},[1656,105250,1659],{"stretchy":1658},[898,105252,1665],{},[1656,105254,1683],{"stretchy":1658},[1656,105256,1713],{},[898,105258,6787],{},[1656,105260,1659],{"stretchy":1658},[898,105262,1665],{},[1656,105264,1683],{"stretchy":1658},[1656,105266,3964],{},[898,105268,11577],{},[898,105270,1863],{"mathvariant":1723},[902,105272,105273],{"encoding":904},"P = D_2(Q) = D(Q) - T.",[724,105275,105276,105277,1643,105290,105293],{},"Poptávka se tedy posouvá o ",[883,105278,105280],{"className":105279},[886],[888,105281,105282],{"xmlns":890},[892,105283,105284,105288],{},[895,105285,105286],{},[898,105287,11577],{},[902,105289,11577],{"encoding":904},[38,105291,105292],{},"svisle dolů",". Nabídka se nemění.",[724,105295,104220,105296,104261,105336,1896,105364,105392,105393,105412,105413,105437,105438,12702],{},[883,105297,105299],{"className":105298},[886],[888,105300,105301],{"xmlns":890},[892,105302,105303,105333],{},[895,105304,105305,105311,105313,105321,105323,105331],{},[1661,105306,105307,105309],{},[898,105308,1842],{},[1667,105310,1680],{},[1656,105312,3453],{"stretchy":1658},[1715,105314,105315,105317,105319],{},[898,105316,1665],{},[1667,105318,1680],{},[898,105320,1842],{},[1656,105322,1673],{"separator":1672},[1715,105324,105325,105327,105329],{},[898,105326,8194],{},[1667,105328,1680],{},[898,105330,1842],{},[1656,105332,3462],{"stretchy":1658},[902,105334,105335],{"encoding":904},"E_2[Q_2^E, P_2^E]",[883,105337,105339],{"className":105338},[886],[888,105340,105341],{"xmlns":890},[892,105342,105343,105361],{},[895,105344,105345,105353,105355],{},[1715,105346,105347,105349,105351],{},[898,105348,1665],{},[1667,105350,1680],{},[898,105352,1842],{},[1656,105354,4373],{},[2062,105356,105357,105359],{},[898,105358,1665],{},[898,105360,1842],{},[902,105362,105363],{"encoding":904},"Q_2^E \u003C Q^E",[883,105365,105367],{"className":105366},[886],[888,105368,105369],{"xmlns":890},[892,105370,105371,105389],{},[895,105372,105373,105381,105383],{},[1715,105374,105375,105377,105379],{},[898,105376,8194],{},[1667,105378,1680],{},[898,105380,1842],{},[1656,105382,4373],{},[2062,105384,105385,105387],{},[898,105386,8194],{},[898,105388,1842],{},[902,105390,105391],{"encoding":904},"P_2^E \u003C P^E",". Výrobce obdrží ",[883,105394,105396],{"className":105395},[886],[888,105397,105398],{"xmlns":890},[892,105399,105400,105410],{},[895,105401,105402],{},[1715,105403,105404,105406,105408],{},[898,105405,8194],{},[1667,105407,1680],{},[898,105409,1842],{},[902,105411,56593],{"encoding":904},", spotřebitel platí celkem ",[883,105414,105416],{"className":105415},[886],[888,105417,105418],{"xmlns":890},[892,105419,105420,105434],{},[895,105421,105422,105430,105432],{},[1715,105423,105424,105426,105428],{},[898,105425,8194],{},[1667,105427,1680],{},[898,105429,1842],{},[1656,105431,3633],{},[898,105433,11577],{},[902,105435,105436],{"encoding":904},"P_2^E + T"," (tato částka je vyšší než původní ",[883,105439,105441],{"className":105440},[886],[888,105442,105443],{"xmlns":890},[892,105444,105445,105453],{},[895,105446,105447],{},[2062,105448,105449,105451],{},[898,105450,8194],{},[898,105452,1842],{},[902,105454,50146],{"encoding":904},[724,105456,105457],{},"Daňové břemeno:",[883,105459,105461],{"className":105460},[886],[888,105462,105463],{"xmlns":890,"display":2408},[892,105464,105465,105539],{},[895,105466,105467,105477,105479,105481,105489,105491,105493,105495,105497,105503,105505,105507,105519,105521,105527,105529,105537],{},[1661,105468,105469,105471],{},[898,105470,11577],{},[895,105472,105473,105475],{},[898,105474,51354],{},[898,105476,724],{},[1656,105478,1713],{},[1656,105480,1659],{"stretchy":1658},[1715,105482,105483,105485,105487],{},[898,105484,8194],{},[1667,105486,1680],{},[898,105488,1842],{},[1656,105490,3633],{},[898,105492,11577],{},[1656,105494,1683],{"stretchy":1658},[1656,105496,3964],{},[2062,105498,105499,105501],{},[898,105500,8194],{},[898,105502,1842],{},[1656,105504,1673],{"separator":1672},[3316,105506],{"width":14644},[1661,105508,105509,105511],{},[898,105510,11577],{},[895,105512,105513,105515,105517],{},[898,105514,51377],{},[898,105516,10839],{},[898,105518,20776],{},[1656,105520,1713],{},[2062,105522,105523,105525],{},[898,105524,8194],{},[898,105526,1842],{},[1656,105528,3964],{},[1715,105530,105531,105533,105535],{},[898,105532,8194],{},[1667,105534,1680],{},[898,105536,1842],{},[898,105538,1863],{"mathvariant":1723},[902,105540,105541],{"encoding":904},"T_{sp} = (P_2^E + T) - P^E, \\qquad T_{vyr} = P^E - P_2^E.",[724,105543,105544],{},[614,105545,105546,105547,105577,105578,104430,105591,14434,105608,104461,105621,1863],{},"Obrázek 2.19: Posun ",[883,105548,105550],{"className":105549},[886],[888,105551,105552],{"xmlns":890},[892,105553,105554,105574],{},[895,105555,105556,105558,105560,105566,105568,105570,105572],{},[898,105557,6787],{},[1656,105559,11915],{},[1661,105561,105562,105564],{},[898,105563,6787],{},[1667,105565,1680],{},[1656,105567,1713],{},[898,105569,6787],{},[1656,105571,3964],{},[898,105573,11577],{},[902,105575,105576],{"encoding":904},"D \\to D_2 = D - T","; svislá vzdálenost mezi poptávkovými křivkami je ",[883,105579,105581],{"className":105580},[886],[888,105582,105583],{"xmlns":890},[892,105584,105585,105589],{},[895,105586,105587],{},[898,105588,11577],{},[902,105590,11577],{"encoding":904},[883,105592,105594],{"className":105593},[886],[888,105595,105596],{"xmlns":890},[892,105597,105598,105606],{},[895,105599,105600],{},[1661,105601,105602,105604],{},[898,105603,6787],{},[1667,105605,1680],{},[902,105607,47009],{"encoding":904},[883,105609,105611],{"className":105610},[886],[888,105612,105613],{"xmlns":890},[892,105614,105615,105619],{},[895,105616,105617],{},[898,105618,1769],{},[902,105620,1769],{"encoding":904},[883,105622,105624],{"className":105623},[886],[888,105625,105626],{"xmlns":890},[892,105627,105628,105636],{},[895,105629,105630],{},[1661,105631,105632,105634],{},[898,105633,1842],{},[1667,105635,1680],{},[902,105637,105638],{"encoding":904},"E_2",[198,105640,54060],{"id":105641},"příklad-210",[724,105643,105644,105646,105647,50370,105670,105689,105690,105707],{},[38,105645,46615],{}," Pokračuje z Příkladu 2.9 — stejný trh, poptávka ",[883,105648,105650],{"className":105649},[886],[888,105651,105652],{"xmlns":890},[892,105653,105654,105668],{},[895,105655,105656,105658,105660,105662,105664,105666],{},[898,105657,8194],{},[1656,105659,1713],{},[1667,105661,9140],{},[1656,105663,3964],{},[1667,105665,1680],{},[898,105667,1665],{},[902,105669,104510],{"encoding":904},[883,105671,105673],{"className":105672},[886],[888,105674,105675],{"xmlns":890},[892,105676,105677,105687],{},[895,105678,105679,105681,105683,105685],{},[898,105680,8194],{},[1656,105682,1713],{},[1667,105684,2673],{},[898,105686,1665],{},[902,105688,104530],{"encoding":904},". Daň ",[883,105691,105693],{"className":105692},[886],[888,105694,105695],{"xmlns":890},[892,105696,105697,105705],{},[895,105698,105699,105701,105703],{},[898,105700,11577],{},[1656,105702,1713],{},[1667,105704,9112],{},[902,105706,49948],{"encoding":904}," Kč je tentokrát uložena na spotřebitele.",[724,105709,105710],{},[38,105711,46647],{},[724,105713,105714,105715,104721],{},"Nová poptávka je ",[883,105716,105718],{"className":105717},[886],[888,105719,105720],{"xmlns":890},[892,105721,105722,105758],{},[895,105723,105724,105730,105732,105734,105736,105738,105740,105742,105744,105746,105748,105750,105752,105754,105756],{},[1661,105725,105726,105728],{},[898,105727,6787],{},[1667,105729,1680],{},[1656,105731,2114],{},[898,105733,8194],{},[1656,105735,1713],{},[1667,105737,9140],{},[1656,105739,3964],{},[1667,105741,1680],{},[898,105743,1665],{},[1656,105745,3964],{},[1667,105747,9112],{},[1656,105749,1713],{},[1667,105751,9112],{},[1656,105753,3964],{},[1667,105755,1680],{},[898,105757,1665],{},[902,105759,105760],{"encoding":904},"D_2: P = 12 - 2Q - 6 = 6 - 2Q",[883,105762,105764],{"className":105763},[886],[888,105765,105766],{"xmlns":890,"display":2408},[892,105767,105768,105784],{},[895,105769,105770,105772,105774,105776,105778,105780,105782],{},[1667,105771,9112],{},[1656,105773,3964],{},[1667,105775,1680],{},[898,105777,1665],{},[1656,105779,1713],{},[1667,105781,2673],{},[898,105783,1665],{},[902,105785,105786],{"encoding":904},"6 - 2Q = 4Q",[724,105788,104754,105789,2836,105808,1343,105832,104835,105864,1863],{},[883,105790,105792],{"className":105791},[886],[888,105793,105794],{"xmlns":890},[892,105795,105796,105806],{},[895,105797,105798,105800,105802,105804],{},[1667,105799,9112],{},[898,105801,1665],{},[1656,105803,1713],{},[1667,105805,9112],{},[902,105807,104774],{"encoding":904},[883,105809,105811],{"className":105810},[886],[888,105812,105813],{"xmlns":890},[892,105814,105815,105829],{},[895,105816,105817,105825,105827],{},[1715,105818,105819,105821,105823],{},[898,105820,1665],{},[1667,105822,1680],{},[898,105824,1842],{},[1656,105826,1713],{},[1667,105828,1669],{},[902,105830,105831],{"encoding":904},"Q_2^E = 1",[883,105833,105835],{"className":105834},[886],[888,105836,105837],{"xmlns":890},[892,105838,105839,105861],{},[895,105840,105841,105849,105851,105853,105855,105857,105859],{},[1715,105842,105843,105845,105847],{},[898,105844,8194],{},[1667,105846,1680],{},[898,105848,1842],{},[1656,105850,1713],{},[1667,105852,2673],{},[1656,105854,2751],{},[1667,105856,1669],{},[1656,105858,1713],{},[1667,105860,2673],{},[902,105862,105863],{"encoding":904},"P_2^E = 4 \\cdot 1 = 4",[883,105865,105867],{"className":105866},[886],[888,105868,105869],{"xmlns":890},[892,105870,105871,105889],{},[895,105872,105873,105879,105881,105883,105885,105887],{},[1661,105874,105875,105877],{},[898,105876,1842],{},[1667,105878,1680],{},[1656,105880,3453],{"stretchy":1658},[1667,105882,1669],{},[1656,105884,1673],{"separator":1672},[1667,105886,2673],{},[1656,105888,3462],{"stretchy":1658},[902,105890,105891],{"encoding":904},"E_2[1, 4]",[724,105893,105894,105895,105931,105932,104549],{},"Spotřebitel platí celkem ",[883,105896,105898],{"className":105897},[886],[888,105899,105900],{"xmlns":890},[892,105901,105902,105928],{},[895,105903,105904,105912,105914,105916,105918,105920,105922,105924,105926],{},[1715,105905,105906,105908,105910],{},[898,105907,8194],{},[1667,105909,1680],{},[898,105911,1842],{},[1656,105913,3633],{},[898,105915,11577],{},[1656,105917,1713],{},[1667,105919,2673],{},[1656,105921,3633],{},[1667,105923,9112],{},[1656,105925,1713],{},[1667,105927,8580],{},[902,105929,105930],{"encoding":904},"P_2^E + T = 4 + 6 = 10"," Kč; výrobce obdrží ",[883,105933,105935],{"className":105934},[886],[888,105936,105937],{"xmlns":890},[892,105938,105939,105953],{},[895,105940,105941,105949,105951],{},[1715,105942,105943,105945,105947],{},[898,105944,8194],{},[1667,105946,1680],{},[898,105948,1842],{},[1656,105950,1713],{},[1667,105952,2673],{},[902,105954,105955],{"encoding":904},"P_2^E = 4",[724,105957,105958],{},[614,105959,105960],{},"Rozklad daňového břemene:",[883,105962,105964],{"className":105963},[886],[888,105965,105966],{"xmlns":890,"display":2408},[892,105967,105968,106054],{},[895,105969,105970,105980,105982,105984,105986,105988,105990,105992,105994,105996,105998,106000,106002,106012,106014,106016,106028,106030,106032,106034,106036,106038,106040,106042,106052],{},[1661,105971,105972,105974],{},[898,105973,11577],{},[895,105975,105976,105978],{},[898,105977,51354],{},[898,105979,724],{},[1656,105981,1713],{},[1656,105983,1659],{"stretchy":1658},[1667,105985,2673],{},[1656,105987,3633],{},[1667,105989,9112],{},[1656,105991,1683],{"stretchy":1658},[1656,105993,3964],{},[1667,105995,2877],{},[1656,105997,1713],{},[1667,105999,1680],{},[2461,106001,11112],{},[895,106003,106004,106006],{},[2461,106005,18544],{},[2033,106007,106008,106010],{"accent":1672},[2461,106009,1745],{},[1656,106011,33774],{},[1656,106013,1673],{"separator":1672},[3316,106015],{"width":14644},[1661,106017,106018,106020],{},[898,106019,11577],{},[895,106021,106022,106024,106026],{},[898,106023,51377],{},[898,106025,10839],{},[898,106027,20776],{},[1656,106029,1713],{},[1667,106031,2877],{},[1656,106033,3964],{},[1667,106035,2673],{},[1656,106037,1713],{},[1667,106039,2673],{},[2461,106041,11112],{},[895,106043,106044,106046],{},[2461,106045,18544],{},[2033,106047,106048,106050],{"accent":1672},[2461,106049,1745],{},[1656,106051,33774],{},[898,106053,1863],{"mathvariant":1723},[902,106055,106056],{"encoding":904},"T_{sp} = (4 + 6) - 8 = 2\\ \\text{Kč}, \\qquad T_{vyr} = 8 - 4 = 4\\ \\text{Kč}.",[724,106058,106059,106060,1863],{},"Opět ",[883,106061,106063],{"className":106062},[886],[888,106064,106065],{"xmlns":890},[892,106066,106067,106101],{},[895,106068,106069,106079,106081,106093,106095,106097,106099],{},[1661,106070,106071,106073],{},[898,106072,11577],{},[895,106074,106075,106077],{},[898,106076,51354],{},[898,106078,724],{},[1656,106080,3633],{},[1661,106082,106083,106085],{},[898,106084,11577],{},[895,106086,106087,106089,106091],{},[898,106088,51377],{},[898,106090,10839],{},[898,106092,20776],{},[1656,106094,1713],{},[1667,106096,9112],{},[1656,106098,1713],{},[898,106100,11577],{},[902,106102,106103],{"encoding":904},"T_{sp} + T_{vyr} = 6 = T",[45652,106105],{},[115,106107,51335],{"id":106108},"daňové-břemeno",[724,106110,106111,3247,106113,106116,106117,106130],{},[38,106112,51335],{},[614,106114,106115],{},"tax burden",") je rozdělení zaplacené daně ",[883,106118,106120],{"className":106119},[886],[888,106121,106122],{"xmlns":890},[892,106123,106124,106128],{},[895,106125,106126],{},[898,106127,11577],{},[902,106129,11577],{"encoding":904}," mezi spotřebitele a výrobce:",[883,106132,106134],{"className":106133},[886],[888,106135,106136],{"xmlns":890,"display":2408},[892,106137,106138,106170],{},[895,106139,106140,106142,106144,106154,106156,106168],{},[898,106141,11577],{},[1656,106143,1713],{},[1661,106145,106146,106148],{},[898,106147,11577],{},[895,106149,106150,106152],{},[898,106151,51354],{},[898,106153,724],{},[1656,106155,3633],{},[1661,106157,106158,106160],{},[898,106159,11577],{},[895,106161,106162,106164,106166],{},[898,106163,51377],{},[898,106165,10839],{},[898,106167,20776],{},[898,106169,1863],{"mathvariant":1723},[902,106171,106172],{"encoding":904},"T = T_{sp} + T_{vyr}.",[724,106174,106175],{},[5956,106176],{"alt":106177,"className":106178,"src":106179},"imek-dan-rozklad-bremene-sklony",[210,5960],"\u002Fwiki-assets\u002Fimek-dan-rozklad-bremene-sklony.jpeg",[1981,106181,106182],{},[724,106183,106184,106186,106187,1896,106200,1863],{},[883,106185,3472],{}," 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 ",[883,106188,106190],{"className":106189},[886],[888,106191,106192],{"xmlns":890},[892,106193,106194,106198],{},[895,106195,106196],{},[898,106197,6787],{},[902,106199,6787],{"encoding":904},[883,106201,106203],{"className":106202},[886],[888,106204,106205],{"xmlns":890},[892,106206,106207,106211],{},[895,106208,106209],{},[898,106210,1769],{},[902,106212,1769],{"encoding":904},[198,106214,11258],{"id":11257},[724,106216,106217,106218,106239,106240,106253,106254,106271,106272,106285],{},"V grafu ",[883,106219,106221],{"className":106220},[886],[888,106222,106223],{"xmlns":890},[892,106224,106225,106237],{},[895,106226,106227,106229,106231,106233,106235],{},[1656,106228,1659],{"stretchy":1658},[898,106230,1665],{},[1656,106232,1673],{"separator":1672},[898,106234,8194],{},[1656,106236,1683],{"stretchy":1658},[902,106238,46373],{"encoding":904}," je svislá vzdálenost mezi původní a posunutou křivkou právě ",[883,106241,106243],{"className":106242},[886],[888,106244,106245],{"xmlns":890},[892,106246,106247,106251],{},[895,106248,106249],{},[898,106250,11577],{},[902,106252,11577],{"encoding":904},". Vedeme-li v novém rovnovážném bodě vodorovnou přímku na úrovni původní rovnovážné ceny ",[883,106255,106257],{"className":106256},[886],[888,106258,106259],{"xmlns":890},[892,106260,106261,106269],{},[895,106262,106263],{},[2062,106264,106265,106267],{},[898,106266,8194],{},[898,106268,1842],{},[902,106270,50146],{"encoding":904},", rozdělí se úsečka ",[883,106273,106275],{"className":106274},[886],[888,106276,106277],{"xmlns":890},[892,106278,106279,106283],{},[895,106280,106281],{},[898,106282,11577],{},[902,106284,11577],{"encoding":904}," na dvě části:",[120,106287,106288,106313],{},[123,106289,106290,106291,106312],{},"horní část odpovídá ",[883,106292,106294],{"className":106293},[886],[888,106295,106296],{"xmlns":890},[892,106297,106298,106310],{},[895,106299,106300],{},[1661,106301,106302,106304],{},[898,106303,11577],{},[895,106305,106306,106308],{},[898,106307,51354],{},[898,106309,724],{},[902,106311,51359],{"encoding":904}," (o kolik vzrostla cena placená spotřebitelem),",[123,106314,106315,106316,106339],{},"dolní část odpovídá ",[883,106317,106319],{"className":106318},[886],[888,106320,106321],{"xmlns":890},[892,106322,106323,106337],{},[895,106324,106325],{},[1661,106326,106327,106329],{},[898,106328,11577],{},[895,106330,106331,106333,106335],{},[898,106332,51377],{},[898,106334,10839],{},[898,106336,20776],{},[902,106338,51384],{"encoding":904}," (o kolik klesla cena přijímaná výrobcem).",[724,106341,106342],{},[614,106343,106344,106345,3619,106358,106379,106380,106403,106404,1896,106425,106448],{},"Obrázky 2.20 a 2.21: Ilustrace rozkladu svislé vzdálenosti ",[883,106346,106348],{"className":106347},[886],[888,106349,106350],{"xmlns":890},[892,106351,106352,106356],{},[895,106353,106354],{},[898,106355,11577],{},[902,106357,11577],{"encoding":904},[883,106359,106361],{"className":106360},[886],[888,106362,106363],{"xmlns":890},[892,106364,106365,106377],{},[895,106366,106367],{},[1661,106368,106369,106371],{},[898,106370,11577],{},[895,106372,106373,106375],{},[898,106374,51354],{},[898,106376,724],{},[902,106378,51359],{"encoding":904}," (nahoře) a ",[883,106381,106383],{"className":106382},[886],[888,106384,106385],{"xmlns":890},[892,106386,106387,106401],{},[895,106388,106389],{},[1661,106390,106391,106393],{},[898,106392,11577],{},[895,106394,106395,106397,106399],{},[898,106396,51377],{},[898,106398,10839],{},[898,106400,20776],{},[902,106402,51384],{"encoding":904}," (dole). Obrázek 2.21 porovnává obě varianty — daň výrobci vs. daň spotřebiteli — a ukazuje, že velikost ",[883,106405,106407],{"className":106406},[886],[888,106408,106409],{"xmlns":890},[892,106410,106411,106423],{},[895,106412,106413],{},[1661,106414,106415,106417],{},[898,106416,11577],{},[895,106418,106419,106421],{},[898,106420,51354],{},[898,106422,724],{},[902,106424,51359],{"encoding":904},[883,106426,106428],{"className":106427},[886],[888,106429,106430],{"xmlns":890},[892,106431,106432,106446],{},[895,106433,106434],{},[1661,106435,106436,106438],{},[898,106437,11577],{},[895,106439,106440,106442,106444],{},[898,106441,51377],{},[898,106443,10839],{},[898,106445,20776],{},[902,106447,51384],{"encoding":904}," je v obou případech stejná.",[198,106450,106452],{"id":106451},"sklony-křivek-a-rozklad","Sklony křivek a rozklad",[724,106454,106455,106456,106459,106460,3247,106483,106500,106501,3247,106524,106541],{},"Platí obecně: ",[38,106457,106458],{},"čím strmější křivka (menší elasticita), tím větší část daně nese daná strana trhu."," Pro lineární poptávku ",[883,106461,106463],{"className":106462},[886],[888,106464,106465],{"xmlns":890},[892,106466,106467,106481],{},[895,106468,106469,106471,106473,106475,106477,106479],{},[898,106470,8194],{},[1656,106472,1713],{},[898,106474,207],{},[898,106476,1665],{},[1656,106478,3633],{},[898,106480,3403],{},[902,106482,45742],{"encoding":904},[883,106484,106486],{"className":106485},[886],[888,106487,106488],{"xmlns":890},[892,106489,106490,106498],{},[895,106491,106492,106494,106496],{},[898,106493,207],{},[1656,106495,4373],{},[1667,106497,4032],{},[902,106499,51762],{"encoding":904},") a lineární nabídku ",[883,106502,106504],{"className":106503},[886],[888,106505,106506],{"xmlns":890},[892,106507,106508,106522],{},[895,106509,106510,106512,106514,106516,106518,106520],{},[898,106511,8194],{},[1656,106513,1713],{},[898,106515,1745],{},[898,106517,1665],{},[1656,106519,3633],{},[898,106521,3768],{},[902,106523,48922],{"encoding":904},[883,106525,106527],{"className":106526},[886],[888,106528,106529],{"xmlns":890},[892,106530,106531,106539],{},[895,106532,106533,106535,106537],{},[898,106534,1745],{},[1656,106536,2850],{},[1667,106538,4032],{},[902,106540,48940],{"encoding":904},") lze rozklad odvodit pomocí multiplikátorů a platí",[883,106543,106545],{"className":106544},[886],[888,106546,106547],{"xmlns":890,"display":2408},[892,106548,106549,106615],{},[895,106550,106551,106575,106577,106587,106589,106613],{},[3294,106552,106553,106563],{},[1661,106554,106555,106557],{},[898,106556,11577],{},[895,106558,106559,106561],{},[898,106560,51354],{},[898,106562,724],{},[1661,106564,106565,106567],{},[898,106566,11577],{},[895,106568,106569,106571,106573],{},[898,106570,51377],{},[898,106572,10839],{},[898,106574,20776],{},[1656,106576,1713],{},[3294,106578,106579,106581],{},[898,106580,1745],{},[895,106582,106583,106585],{},[1656,106584,3964],{},[898,106586,207],{},[1656,106588,1713],{},[3294,106590,106591,106603],{},[895,106592,106593,106596,106599,106601],{},[898,106594,106595],{"mathvariant":1723},"∣",[2461,106597,106598],{},"sklon ",[898,106600,1769],{},[898,106602,106595],{"mathvariant":1723},[895,106604,106605,106607,106609,106611],{},[898,106606,106595],{"mathvariant":1723},[2461,106608,106598],{},[898,106610,6787],{},[898,106612,106595],{"mathvariant":1723},[898,106614,1863],{"mathvariant":1723},[902,106616,106617],{"encoding":904},"\\frac{T_{sp}}{T_{vyr}} = \\frac{c}{-a} = \\frac{|\\text{sklon } S|}{|\\text{sklon } D|}.",[1981,106619,106620,106625],{},[724,106621,106622,106624],{},[883,106623,10188],{}," Postup výpočtu rozkladu",[152,106626,106627,106662,106715,106794],{},[123,106628,106629,106630,106661],{},"Spočti rovnovážný bod ",[883,106631,106633],{"className":106632},[886],[888,106634,106635],{"xmlns":890},[892,106636,106637,106659],{},[895,106638,106639,106641,106643,106649,106651,106657],{},[898,106640,1842],{},[1656,106642,3453],{"stretchy":1658},[2062,106644,106645,106647],{},[898,106646,1665],{},[898,106648,1842],{},[1656,106650,1673],{"separator":1672},[2062,106652,106653,106655],{},[898,106654,8194],{},[898,106656,1842],{},[1656,106658,3462],{"stretchy":1658},[902,106660,50047],{"encoding":904}," bez daně.",[123,106663,106664,106665,1348,106690,12702],{},"Urči posunutou křivku (",[883,106666,106668],{"className":106667},[886],[888,106669,106670],{"xmlns":890},[892,106671,106672,106688],{},[895,106673,106674,106680,106682,106684,106686],{},[1661,106675,106676,106678],{},[898,106677,1769],{},[1667,106679,1669],{},[1656,106681,1713],{},[898,106683,1769],{},[1656,106685,3633],{},[898,106687,11577],{},[902,106689,51431],{"encoding":904},[883,106691,106693],{"className":106692},[886],[888,106694,106695],{"xmlns":890},[892,106696,106697,106713],{},[895,106698,106699,106705,106707,106709,106711],{},[1661,106700,106701,106703],{},[898,106702,6787],{},[1667,106704,1680],{},[1656,106706,1713],{},[898,106708,6787],{},[1656,106710,3964],{},[898,106712,11577],{},[902,106714,51462],{"encoding":904},[123,106716,106717,106718,12694,106737,20863,106756,12694,106775,12702],{},"Vyřeš novou rovnovážnou rovnici — získáš ",[883,106719,106721],{"className":106720},[886],[888,106722,106723],{"xmlns":890},[892,106724,106725,106735],{},[895,106726,106727],{},[1715,106728,106729,106731,106733],{},[898,106730,1665],{},[1667,106732,1669],{},[898,106734,1842],{},[902,106736,56511],{"encoding":904},[883,106738,106740],{"className":106739},[886],[888,106741,106742],{"xmlns":890},[892,106743,106744,106754],{},[895,106745,106746],{},[1715,106747,106748,106750,106752],{},[898,106749,1665],{},[1667,106751,1680],{},[898,106753,1842],{},[902,106755,56573],{"encoding":904},[883,106757,106759],{"className":106758},[886],[888,106760,106761],{"xmlns":890},[892,106762,106763,106773],{},[895,106764,106765],{},[1715,106766,106767,106769,106771],{},[898,106768,8194],{},[1667,106770,1669],{},[898,106772,1842],{},[902,106774,56532],{"encoding":904},[883,106776,106778],{"className":106777},[886],[888,106779,106780],{"xmlns":890},[892,106781,106782,106792],{},[895,106783,106784],{},[1715,106785,106786,106788,106790],{},[898,106787,8194],{},[1667,106789,1680],{},[898,106791,1842],{},[902,106793,56593],{"encoding":904},[123,106795,106796,106797,1896,106818,106841,106842,1863],{},"Dopočítej ",[883,106798,106800],{"className":106799},[886],[888,106801,106802],{"xmlns":890},[892,106803,106804,106816],{},[895,106805,106806],{},[1661,106807,106808,106810],{},[898,106809,11577],{},[895,106811,106812,106814],{},[898,106813,51354],{},[898,106815,724],{},[902,106817,51359],{"encoding":904},[883,106819,106821],{"className":106820},[886],[888,106822,106823],{"xmlns":890},[892,106824,106825,106839],{},[895,106826,106827],{},[1661,106828,106829,106831],{},[898,106830,11577],{},[895,106832,106833,106835,106837],{},[898,106834,51377],{},[898,106836,10839],{},[898,106838,20776],{},[902,106840,51384],{"encoding":904}," z definice, vždy ověř ",[883,106843,106845],{"className":106844},[886],[888,106846,106847],{"xmlns":890},[892,106848,106849,106879],{},[895,106850,106851,106861,106863,106875,106877],{},[1661,106852,106853,106855],{},[898,106854,11577],{},[895,106856,106857,106859],{},[898,106858,51354],{},[898,106860,724],{},[1656,106862,3633],{},[1661,106864,106865,106867],{},[898,106866,11577],{},[895,106868,106869,106871,106873],{},[898,106870,51377],{},[898,106872,10839],{},[898,106874,20776],{},[1656,106876,1713],{},[898,106878,11577],{},[902,106880,106881],{"encoding":904},"T_{sp} + T_{vyr} = T",[1981,106883,106884],{},[724,106885,106886,106888,106889,106892,106893,1896,106906,106919],{},[883,106887,1987],{}," Pozor — zákonný vs. ekonomický nositel daně\nI když zákon ukládá daň formálně pouze jedné straně (výrobci nebo spotřebiteli), ",[38,106890,106891],{},"ekonomicky ji vždy nesou obě strany",". Skutečné rozdělení určují sklony ",[883,106894,106896],{"className":106895},[886],[888,106897,106898],{"xmlns":890},[892,106899,106900,106904],{},[895,106901,106902],{},[898,106903,6787],{},[902,106905,6787],{"encoding":904},[883,106907,106909],{"className":106908},[886],[888,106910,106911],{"xmlns":890},[892,106912,106913,106917],{},[895,106914,106915],{},[898,106916,1769],{},[902,106918,1769],{"encoding":904},", nikoli paragrafové znění zákona. Kupující a prodávající tak fakticky platí daň bez ohledu na to, na koho je uvalena.",[45652,106921],{},[115,106923,106925],{"id":106924},"ekvivalence-obou-přístupů","Ekvivalence obou přístupů",[724,106927,106928],{},"Porovnáním Příkladu 2.9 (daň výrobci) a Příkladu 2.10 (daň spotřebiteli) zjistíme:",[724,106930,106931],{},[5956,106932],{"alt":106933,"className":106934,"src":106935},"imek-dan-ekvivalence-vyrobce-spotrebitel",[210,5960],"\u002Fwiki-assets\u002Fimek-dan-ekvivalence-vyrobce-spotrebitel.jpeg",[16,106937,106938,106950],{},[19,106939,106940],{},[22,106941,106942,106944,106947],{},[25,106943,62965],{},[25,106945,106946],{},"(a) daň výrobci",[25,106948,106949],{},"(b) daň spotřebiteli",[30,106951,106952,107007,107074,107134],{},[22,106953,106954,106957,106982],{},[35,106955,106956],{},"Rovnovážné množství",[35,106958,106959],{},[883,106960,106962],{"className":106961},[886],[888,106963,106964],{"xmlns":890},[892,106965,106966,106980],{},[895,106967,106968,106976,106978],{},[1715,106969,106970,106972,106974],{},[898,106971,1665],{},[1667,106973,1669],{},[898,106975,1842],{},[1656,106977,1713],{},[1667,106979,1669],{},[902,106981,104798],{"encoding":904},[35,106983,106984],{},[883,106985,106987],{"className":106986},[886],[888,106988,106989],{"xmlns":890},[892,106990,106991,107005],{},[895,106992,106993,107001,107003],{},[1715,106994,106995,106997,106999],{},[898,106996,1665],{},[1667,106998,1680],{},[898,107000,1842],{},[1656,107002,1713],{},[1667,107004,1669],{},[902,107006,105831],{"encoding":904},[22,107008,107009,107012,107037],{},[35,107010,107011],{},"Cena placená spotřebitelem",[35,107013,107014],{},[883,107015,107017],{"className":107016},[886],[888,107018,107019],{"xmlns":890},[892,107020,107021,107035],{},[895,107022,107023,107031,107033],{},[1715,107024,107025,107027,107029],{},[898,107026,8194],{},[1667,107028,1669],{},[898,107030,1842],{},[1656,107032,1713],{},[1667,107034,8580],{},[902,107036,104893],{"encoding":904},[35,107038,107039],{},[883,107040,107042],{"className":107041},[886],[888,107043,107044],{"xmlns":890},[892,107045,107046,107072],{},[895,107047,107048,107056,107058,107060,107062,107064,107066,107068,107070],{},[1715,107049,107050,107052,107054],{},[898,107051,8194],{},[1667,107053,1680],{},[898,107055,1842],{},[1656,107057,3633],{},[898,107059,11577],{},[1656,107061,1713],{},[1667,107063,2673],{},[1656,107065,3633],{},[1667,107067,9112],{},[1656,107069,1713],{},[1667,107071,8580],{},[902,107073,105930],{"encoding":904},[22,107075,107076,107079,107109],{},[35,107077,107078],{},"Cena přijímaná výrobcem",[35,107080,107081],{},[883,107082,107084],{"className":107083},[886],[888,107085,107086],{"xmlns":890},[892,107087,107088,107106],{},[895,107089,107090,107098,107100,107102,107104],{},[1715,107091,107092,107094,107096],{},[898,107093,8194],{},[1667,107095,1669],{},[898,107097,1842],{},[1656,107099,3964],{},[898,107101,11577],{},[1656,107103,1713],{},[1667,107105,2673],{},[902,107107,107108],{"encoding":904},"P_1^E - T = 4",[35,107110,107111],{},[883,107112,107114],{"className":107113},[886],[888,107115,107116],{"xmlns":890},[892,107117,107118,107132],{},[895,107119,107120,107128,107130],{},[1715,107121,107122,107124,107126],{},[898,107123,8194],{},[1667,107125,1680],{},[898,107127,1842],{},[1656,107129,1713],{},[1667,107131,2673],{},[902,107133,105955],{"encoding":904},[22,107135,107136,107139,107193],{},[35,107137,107138],{},"Rozklad břemene",[35,107140,107141,1343,107166],{},[883,107142,107144],{"className":107143},[886],[888,107145,107146],{"xmlns":890},[892,107147,107148,107164],{},[895,107149,107150,107160,107162],{},[1661,107151,107152,107154],{},[898,107153,11577],{},[895,107155,107156,107158],{},[898,107157,51354],{},[898,107159,724],{},[1656,107161,1713],{},[1667,107163,1680],{},[902,107165,51653],{"encoding":904},[883,107167,107169],{"className":107168},[886],[888,107170,107171],{"xmlns":890},[892,107172,107173,107191],{},[895,107174,107175,107187,107189],{},[1661,107176,107177,107179],{},[898,107178,11577],{},[895,107180,107181,107183,107185],{},[898,107182,51377],{},[898,107184,10839],{},[898,107186,20776],{},[1656,107188,1713],{},[1667,107190,2673],{},[902,107192,51682],{"encoding":904},[35,107194,107195,1343,107220],{},[883,107196,107198],{"className":107197},[886],[888,107199,107200],{"xmlns":890},[892,107201,107202,107218],{},[895,107203,107204,107214,107216],{},[1661,107205,107206,107208],{},[898,107207,11577],{},[895,107209,107210,107212],{},[898,107211,51354],{},[898,107213,724],{},[1656,107215,1713],{},[1667,107217,1680],{},[902,107219,51653],{"encoding":904},[883,107221,107223],{"className":107222},[886],[888,107224,107225],{"xmlns":890},[892,107226,107227,107245],{},[895,107228,107229,107241,107243],{},[1661,107230,107231,107233],{},[898,107232,11577],{},[895,107234,107235,107237,107239],{},[898,107236,51377],{},[898,107238,10839],{},[898,107240,20776],{},[1656,107242,1713],{},[1667,107244,2673],{},[902,107246,51682],{"encoding":904},[724,107248,107249],{},"Výsledek je v obou režimech reálně totožný — liší se pouze to, kterou cenu nazveme \"tržní\":",[883,107251,107253],{"className":107252},[886],[888,107254,107255],{"xmlns":890,"display":2408},[892,107256,107257,107305],{},[895,107258,107259,107267,107269,107277,107279,107281,107289,107291,107293,107295,107303],{},[1715,107260,107261,107263,107265],{},[898,107262,1665],{},[1667,107264,1669],{},[898,107266,1842],{},[1656,107268,1713],{},[1715,107270,107271,107273,107275],{},[898,107272,1665],{},[1667,107274,1680],{},[898,107276,1842],{},[1656,107278,1673],{"separator":1672},[3316,107280],{"width":14644},[1715,107282,107283,107285,107287],{},[898,107284,8194],{},[1667,107286,1669],{},[898,107288,1842],{},[1656,107290,3964],{},[898,107292,11577],{},[1656,107294,1713],{},[1715,107296,107297,107299,107301],{},[898,107298,8194],{},[1667,107300,1680],{},[898,107302,1842],{},[898,107304,1863],{"mathvariant":1723},[902,107306,107307],{"encoding":904},"Q_1^E = Q_2^E, \\qquad P_1^E - T = P_2^E.",[1981,107309,107310,107329,107483],{},[724,107311,107312,107314,107315,107328],{},[883,107313,10188],{}," Věta o ekvivalenci zdanění\nNezávisle na tom, zda je jednotková daň ",[883,107316,107318],{"className":107317},[886],[888,107319,107320],{"xmlns":890},[892,107321,107322,107326],{},[895,107323,107324],{},[898,107325,11577],{},[902,107327,11577],{"encoding":904}," uložena výrobci, nebo spotřebiteli, se po jejím uložení rovnají:",[120,107330,107331,107363,107399,107436],{},[123,107332,107333,107334,1673],{},"rovnovážná množství obou režimů, ",[883,107335,107337],{"className":107336},[886],[888,107338,107339],{"xmlns":890},[892,107340,107341,107361],{},[895,107342,107343,107351,107353],{},[1715,107344,107345,107347,107349],{},[898,107346,1665],{},[1667,107348,1669],{},[898,107350,1842],{},[1656,107352,1713],{},[1715,107354,107355,107357,107359],{},[898,107356,1665],{},[1667,107358,1680],{},[898,107360,1842],{},[902,107362,51585],{"encoding":904},[123,107364,107365,107366,1673],{},"čistá cena přijímaná výrobcem, ",[883,107367,107369],{"className":107368},[886],[888,107370,107371],{"xmlns":890},[892,107372,107373,107397],{},[895,107374,107375,107383,107385,107387,107389],{},[1715,107376,107377,107379,107381],{},[898,107378,8194],{},[1667,107380,1669],{},[898,107382,1842],{},[1656,107384,3964],{},[898,107386,11577],{},[1656,107388,1713],{},[1715,107390,107391,107393,107395],{},[898,107392,8194],{},[1667,107394,1680],{},[898,107396,1842],{},[902,107398,51619],{"encoding":904},[123,107400,107401,107402,1673],{},"celková cena placená spotřebitelem, ",[883,107403,107405],{"className":107404},[886],[888,107406,107407],{"xmlns":890},[892,107408,107409,107433],{},[895,107410,107411,107419,107421,107429,107431],{},[1715,107412,107413,107415,107417],{},[898,107414,8194],{},[1667,107416,1669],{},[898,107418,1842],{},[1656,107420,1713],{},[1715,107422,107423,107425,107427],{},[898,107424,8194],{},[1667,107426,1680],{},[898,107428,1842],{},[1656,107430,3633],{},[898,107432,11577],{},[902,107434,107435],{"encoding":904},"P_1^E = P_2^E + T",[123,107437,107438,107439,1896,107460,1863],{},"rozklad daňového břemene ",[883,107440,107442],{"className":107441},[886],[888,107443,107444],{"xmlns":890},[892,107445,107446,107458],{},[895,107447,107448],{},[1661,107449,107450,107452],{},[898,107451,11577],{},[895,107453,107454,107456],{},[898,107455,51354],{},[898,107457,724],{},[902,107459,51359],{"encoding":904},[883,107461,107463],{"className":107462},[886],[888,107464,107465],{"xmlns":890},[892,107466,107467,107481],{},[895,107468,107469],{},[1661,107470,107471,107473],{},[898,107472,11577],{},[895,107474,107475,107477,107479],{},[898,107476,51377],{},[898,107478,10839],{},[898,107480,20776],{},[902,107482,51384],{"encoding":904},[724,107484,107485,107486,1863],{},"Z hlediska reálných dopadů na trh (objem transakcí, reálné platby stran) jsou tedy obě formy zdanění ",[38,107487,43885],{},[724,107489,107490,107491,1896,107504,12702],{},"Ekvivalence má zásadní politickou implikaci: otázka, \"kdo má platit daň\", je z hlediska trhu formální — skutečné rozdělení určuje struktura trhu (sklony ",[883,107492,107494],{"className":107493},[886],[888,107495,107496],{"xmlns":890},[892,107497,107498,107502],{},[895,107499,107500],{},[898,107501,6787],{},[902,107503,6787],{"encoding":904},[883,107505,107507],{"className":107506},[886],[888,107508,107509],{"xmlns":890},[892,107510,107511,107515],{},[895,107512,107513],{},[898,107514,1769],{},[902,107516,1769],{"encoding":904},[45652,107518],{},[115,107520,107522],{"id":107521},"úlohy","Úlohy",[724,107524,107525,107526,5642],{},"Z kapitoly 2 se zdanění týkají zejména následující úlohy (zadání v hub-page ",[207,107527,24966],{"className":107528,"dataFsResolvedFilePath":800,"href":801},[210],[120,107530,107531,107561,107592],{},[123,107532,107533,107536,107537,107560],{},[38,107534,107535],{},"Úloha 2.4"," — Poptávka ",[883,107538,107540],{"className":107539},[886],[888,107541,107542],{"xmlns":890},[892,107543,107544,107558],{},[895,107545,107546,107548,107550,107552,107554,107556],{},[898,107547,8194],{},[1656,107549,1713],{},[1667,107551,9140],{},[1656,107553,3964],{},[1667,107555,1680],{},[898,107557,1665],{},[902,107559,104510],{"encoding":904},"; najděte novou poptávku po uložení daně 6 Kč na kupujícího.",[123,107562,107563,107566,107567,107591],{},[38,107564,107565],{},"Úloha 2.9"," — Nabídka ",[883,107568,107570],{"className":107569},[886],[888,107571,107572],{"xmlns":890},[892,107573,107574,107588],{},[895,107575,107576,107578,107580,107582,107584,107586],{},[898,107577,8194],{},[1656,107579,1713],{},[1667,107581,13779],{},[898,107583,1665],{},[1656,107585,3633],{},[1667,107587,44930],{},[902,107589,107590],{"encoding":904},"P = 0{,}5Q + 15","; najděte novou nabídku po uložení daně 5 Kč na výrobce.",[123,107593,107594,107597,107598,1896,107624,107648,107649,107666],{},[38,107595,107596],{},"Úloha 2.13"," — Komplexní úloha se zadáním ",[883,107599,107601],{"className":107600},[886],[888,107602,107603],{"xmlns":890},[892,107604,107605,107621],{},[895,107606,107607,107609,107611,107613,107615,107617,107619],{},[898,107608,8194],{},[1656,107610,1713],{},[1656,107612,3964],{},[1667,107614,2673],{},[898,107616,1665],{},[1656,107618,3633],{},[1667,107620,9280],{},[902,107622,107623],{"encoding":904},"P = -4Q + 80",[883,107625,107627],{"className":107626},[886],[888,107628,107629],{"xmlns":890},[892,107630,107631,107645],{},[895,107632,107633,107635,107637,107639,107641,107643],{},[898,107634,8194],{},[1656,107636,1713],{},[1667,107638,2617],{},[898,107640,1665],{},[1656,107642,3633],{},[1667,107644,8580],{},[902,107646,107647],{"encoding":904},"P = 3Q + 10",": rovnováha, daň ",[883,107650,107652],{"className":107651},[886],[888,107653,107654],{"xmlns":890},[892,107655,107656,107664],{},[895,107657,107658,107660,107662],{},[898,107659,11577],{},[1656,107661,1713],{},[1667,107663,6240],{},[902,107665,56490],{"encoding":904}," Kč uložená postupně výrobci i spotřebiteli, rozklad daňového břemene a analýza ekvivalence.",[724,107668,107669,107670,107672,107673,107675],{},"Související úvodní příklady posunu křivek při zdanění: ",[38,107671,53905],{}," (posun poptávky při zdanění kupujícího) a ",[38,107674,53939],{}," (posun nabídky při zdanění výrobce).",[45652,107677],{},[115,107679,10198],{"id":10197},[120,107681,107682,107701,107759,107816,107899,107945,107988,108033,108099],{},[123,107683,107684,1643,107687,107700],{},[38,107685,107686],{},"Jednotková daň",[883,107688,107690],{"className":107689},[886],[888,107691,107692],{"xmlns":890},[892,107693,107694,107698],{},[895,107695,107696],{},[898,107697,11577],{},[902,107699,11577],{"encoding":904}," — fixní částka na každou prodanou jednotku zboží",[123,107702,107703,107705,107706,107744,107745,107758],{},[38,107704,104092],{}," — posun nabídky ",[883,107707,107709],{"className":107708},[886],[888,107710,107711],{"xmlns":890},[892,107712,107713,107741],{},[895,107714,107715,107721,107723,107725,107727,107729,107731,107733,107735,107737,107739],{},[1661,107716,107717,107719],{},[898,107718,1769],{},[1667,107720,1669],{},[1656,107722,1659],{"stretchy":1658},[898,107724,1665],{},[1656,107726,1683],{"stretchy":1658},[1656,107728,1713],{},[898,107730,1769],{},[1656,107732,1659],{"stretchy":1658},[898,107734,1665],{},[1656,107736,1683],{"stretchy":1658},[1656,107738,3633],{},[898,107740,11577],{},[902,107742,107743],{"encoding":904},"S_1(Q) = S(Q) + T"," (o ",[883,107746,107748],{"className":107747},[886],[888,107749,107750],{"xmlns":890},[892,107751,107752,107756],{},[895,107753,107754],{},[898,107755,11577],{},[902,107757,11577],{"encoding":904}," svisle nahoru)",[123,107760,107761,107763,107764,107744,107802,107815],{},[38,107762,105165],{}," — posun poptávky ",[883,107765,107767],{"className":107766},[886],[888,107768,107769],{"xmlns":890},[892,107770,107771,107799],{},[895,107772,107773,107779,107781,107783,107785,107787,107789,107791,107793,107795,107797],{},[1661,107774,107775,107777],{},[898,107776,6787],{},[1667,107778,1680],{},[1656,107780,1659],{"stretchy":1658},[898,107782,1665],{},[1656,107784,1683],{"stretchy":1658},[1656,107786,1713],{},[898,107788,6787],{},[1656,107790,1659],{"stretchy":1658},[898,107792,1665],{},[1656,107794,1683],{"stretchy":1658},[1656,107796,3964],{},[898,107798,11577],{},[902,107800,107801],{"encoding":904},"D_2(Q) = D(Q) - T",[883,107803,107805],{"className":107804},[886],[888,107806,107807],{"xmlns":890},[892,107808,107809,107813],{},[895,107810,107811],{},[898,107812,11577],{},[902,107814,11577],{"encoding":904}," svisle dolů)",[123,107817,107818,2533,107821,3228,107860],{},[38,107819,107820],{},"Rovnovážný bod s daní",[883,107822,107824],{"className":107823},[886],[888,107825,107826],{"xmlns":890},[892,107827,107828,107858],{},[895,107829,107830,107836,107838,107846,107848,107856],{},[1661,107831,107832,107834],{},[898,107833,1842],{},[1667,107835,1669],{},[1656,107837,3453],{"stretchy":1658},[1715,107839,107840,107842,107844],{},[898,107841,1665],{},[1667,107843,1669],{},[898,107845,1842],{},[1656,107847,1673],{"separator":1672},[1715,107849,107850,107852,107854],{},[898,107851,8194],{},[1667,107853,1669],{},[898,107855,1842],{},[1656,107857,3462],{"stretchy":1658},[902,107859,104260],{"encoding":904},[883,107861,107863],{"className":107862},[886],[888,107864,107865],{"xmlns":890},[892,107866,107867,107897],{},[895,107868,107869,107875,107877,107885,107887,107895],{},[1661,107870,107871,107873],{},[898,107872,1842],{},[1667,107874,1680],{},[1656,107876,3453],{"stretchy":1658},[1715,107878,107879,107881,107883],{},[898,107880,1665],{},[1667,107882,1680],{},[898,107884,1842],{},[1656,107886,1673],{"separator":1672},[1715,107888,107889,107891,107893],{},[898,107890,8194],{},[1667,107892,1680],{},[898,107894,1842],{},[1656,107896,3462],{"stretchy":1658},[902,107898,105335],{"encoding":904},[123,107900,107901,3247,107903,107905,107906],{},[38,107902,51335],{},[614,107904,106115],{},") — rozklad ",[883,107907,107909],{"className":107908},[886],[888,107910,107911],{"xmlns":890},[892,107912,107913,107943],{},[895,107914,107915,107917,107919,107929,107931],{},[898,107916,11577],{},[1656,107918,1713],{},[1661,107920,107921,107923],{},[898,107922,11577],{},[895,107924,107925,107927],{},[898,107926,51354],{},[898,107928,724],{},[1656,107930,3633],{},[1661,107932,107933,107935],{},[898,107934,11577],{},[895,107936,107937,107939,107941],{},[898,107938,51377],{},[898,107940,10839],{},[898,107942,20776],{},[902,107944,51521],{"encoding":904},[123,107946,107947,107970,107971,1683],{},[38,107948,107949],{},[883,107950,107952],{"className":107951},[886],[888,107953,107954],{"xmlns":890},[892,107955,107956,107968],{},[895,107957,107958],{},[1661,107959,107960,107962],{},[898,107961,11577],{},[895,107963,107964,107966],{},[898,107965,51354],{},[898,107967,724],{},[902,107969,51359],{"encoding":904}," — část daně nesená spotřebitelem (navýšení ceny nad ",[883,107972,107974],{"className":107973},[886],[888,107975,107976],{"xmlns":890},[892,107977,107978,107986],{},[895,107979,107980],{},[2062,107981,107982,107984],{},[898,107983,8194],{},[898,107985,1842],{},[902,107987,50146],{"encoding":904},[123,107989,107990,108015,108016,1683],{},[38,107991,107992],{},[883,107993,107995],{"className":107994},[886],[888,107996,107997],{"xmlns":890},[892,107998,107999,108013],{},[895,108000,108001],{},[1661,108002,108003,108005],{},[898,108004,11577],{},[895,108006,108007,108009,108011],{},[898,108008,51377],{},[898,108010,10839],{},[898,108012,20776],{},[902,108014,51384],{"encoding":904}," — část daně nesená výrobcem (pokles čisté přijímané ceny pod ",[883,108017,108019],{"className":108018},[886],[888,108020,108021],{"xmlns":890},[892,108022,108023,108031],{},[895,108024,108025],{},[2062,108026,108027,108029],{},[898,108028,8194],{},[898,108030,1842],{},[902,108032,50146],{"encoding":904},[123,108034,108035,2533,108037,1343,108066],{},[38,108036,59146],{},[883,108038,108040],{"className":108039},[886],[888,108041,108042],{"xmlns":890},[892,108043,108044,108064],{},[895,108045,108046,108054,108056],{},[1715,108047,108048,108050,108052],{},[898,108049,1665],{},[1667,108051,1669],{},[898,108053,1842],{},[1656,108055,1713],{},[1715,108057,108058,108060,108062],{},[898,108059,1665],{},[1667,108061,1680],{},[898,108063,1842],{},[902,108065,51585],{"encoding":904},[883,108067,108069],{"className":108068},[886],[888,108070,108071],{"xmlns":890},[892,108072,108073,108097],{},[895,108074,108075,108083,108085,108087,108089],{},[1715,108076,108077,108079,108081],{},[898,108078,8194],{},[1667,108080,1669],{},[898,108082,1842],{},[1656,108084,3964],{},[898,108086,11577],{},[1656,108088,1713],{},[1715,108090,108091,108093,108095],{},[898,108092,8194],{},[1667,108094,1680],{},[898,108096,1842],{},[902,108098,51619],{"encoding":904},[123,108100,108101,108104],{},[38,108102,108103],{},"Zákonný vs. ekonomický nositel daně"," — rozdíl mezi formálním ustanovením zákona a skutečným rozdělením břemene",[45652,108106],{},[115,108108,10640],{"id":10639},[120,108110,108111,108119,108137,108144],{},[123,108112,108113,1643,108116],{},[38,108114,108115],{},"Kontext (hub):",[207,108117,802],{"className":108118,"dataFsResolvedFilePath":800,"href":801},[210],[123,108120,108121,1643,108123,108126,108127,10722,108129,108132,108133,108136],{},[38,108122,59395],{},[207,108124,820],{"className":108125,"dataFsResolvedFilePath":818,"href":819},[210]," (daň vyvolává ztrátu blahobytu — ",[614,108128,63703],{},[207,108130,10692],{"className":108131,"dataFsResolvedFilePath":764,"href":765},[210]," (sklony křivek, rovnovážný bod jako řešení soustavy), ",[207,108134,12613],{"className":108135,"dataFsResolvedFilePath":848,"href":849},[210]," (kvantifikace, jak se daňové břemeno dělí podle citlivosti stran trhu)",[123,108138,108139,1643,108141],{},[38,108140,59430],{},[207,108142,59434],{"className":108143,"dataFsResolvedFilePath":745,"href":746},[210],[123,108145,108146,1643,108148],{},[38,108147,10742],{},[207,108149,1869],{"className":108150,"dataFsResolvedFilePath":10746,"href":10747},[210],{"title":641,"searchDepth":642,"depth":642,"links":108152},[108153,108154,108157,108160,108164,108165,108166,108167],{"id":103997,"depth":642,"text":103998},{"id":104091,"depth":642,"text":104092,"children":108155},[108156],{"id":104482,"depth":649,"text":53980},{"id":105164,"depth":642,"text":105165,"children":108158},[108159],{"id":105641,"depth":649,"text":54060},{"id":106108,"depth":642,"text":51335,"children":108161},[108162,108163],{"id":11257,"depth":649,"text":11258},{"id":106451,"depth":649,"text":106452},{"id":106924,"depth":642,"text":106925},{"id":107521,"depth":642,"text":107522},{"id":10197,"depth":642,"text":10198},{"id":10639,"depth":642,"text":10640},{},"\u002Ftopics\u002Fzdaneni-trhu",{"title":103895,"description":641},[1138,1135],"topics\u002Fzdaneni-trhu",[1128,59495,108174,108175,108176,24966],"dane","danove-bremeno","posun-krivek","cFuKqHgzIrqvY-l4jNdqjFEM7_ixjw33HOL0So8cPn0",[108179,108181,108183,108187,108190,108194,108198,108200],{"slug":24979,"path":783,"title":18319,"snippet":108180},"… nice** funkce. V ekonomii: - **Indiferenční křivky** užitečnosti $U(Q_1, Q_2) = c$ — viz \u003C\u003Cuzitecnost>>. - **Izokvanty** produkce $Q(L, K) = c$ — viz produkce. ## Parciální derivace Pro $ …",{"slug":1128,"path":10747,"title":681,"snippet":108182},"… okvanty, MRTS, Eulerova věta ### Blok 3 — Užitečnost a národní důchod - \u003C\u003Cuzitecnost>> — pojem, mezní užitečnost, Cobb-Douglasova $U$, indiferenční křivky, MRCS - [[optimalizac …",{"slug":108184,"path":746,"title":108185,"snippet":108186},"imek-blok-01","KS 1. blok — Kalkul a mikroekonomie","… Produkce (Blok 2) — využívá parciální derivace. - \u003C\u003Cuzitecnost>> (Blok 3) — využívá Lagrange a 2D kalkul …",{"slug":24943,"path":869,"title":108188,"snippet":108189},"KS 3. blok — Užitečnost a národní důchod","… ele) a makroekonomií (modely národní ekonomiky). ## Témata bloku — doporučené pořadí 1. \u003C\u003Cuzitecnost>> — pojetí kardinalistické vs. ordinalistické, model užitečnosti, mezní užitečnost ($MU$), …",{"slug":108191,"path":1109,"title":108192,"snippet":108193},"imek-kniha","Kniha — *Úvod do matematické ekonomie pro ekonomy*","… omezení i duální minimalizace výdajů). **Příklady 6.1–6.8**, **Úlohy 6.1–6.13**. Topic: \u003C\u003Cuzitecnost>>. ### Kapitola 7 — Národní důchod *(str. 133–144)* Zjednodušený makroekonomický model, G …",{"slug":108195,"path":959,"title":108196,"snippet":108197},"imek-vzorce-prehled","ImeK — kompletní přehled vzorců se zdroji a intuicí","… dí 1 jednotka práce, aby produkce zůstala stejná\". Je to sklon izokvanty. Přesná analogie \u003C\u003Cuzitecnost>> z teorie užitečnosti. ### Eulerova věta pro homogenní funkce $$L \\cdot MP_L + K \\cdot M …",{"slug":103816,"path":792,"title":25007,"snippet":108199},"… gradienty jsou rovnoběžné]] - **Maximalizaci užitečnosti** při rozpočtovém omezení (viz \u003C\u003Cuzitecnost>>) - **Minimalizaci výdajů** při dané úrovni užitečnosti (duální úloha) - Optimalizaci prod …",{"slug":1874,"path":912,"title":8672,"snippet":108201},"… e před optimalizací — tvar funkce $U$, indiferenční křivky a $\\text{MRCS}$ — je shrnuta v \u003C\u003Cuzitecnost>>. > [!warning] Pozor — dvě úlohy, totéž řešení > **Primární úloha** (max $U$ při pevném r …",[108203,108204,108207,108208,108209],{"slug":24979,"title":18319,"path":783,"sharedTags":642},{"slug":108205,"title":108206,"path":839,"sharedTags":642},"imek-blok-02","KS 2. blok — Elasticita a produkce",{"slug":24943,"title":108188,"path":869,"sharedTags":642},{"slug":1874,"title":8672,"path":912,"sharedTags":642},{"slug":18557,"title":83126,"path":858,"sharedTags":642},1777154973629]